A translation of Landau's Grundlagen in AUTOMATH · authors thesis (Eindhoven, 1977): On verifying Landau's "Grundlagen der Analysis" in the AUTOMATH System. LAYOUT tROK fiLE AUTOE/LANDAU/H4A

A translation of Landau's "Grundlagen in AUTOMATH"

Benthem Jutting, van, L.S.

Published: 01/01/1976

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Citation for published version (APA):Benthem Jutting, van, L. S. (1976). A translation of Landau's "Grundlagen in AUTOMATH". Eindhoven:Technische Hogeschool Eindhoven.

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EINDHOVEN UNIVERSITY OF TECHNOLOGY

Department of Mathernaties

A translation of Landau's *) "Grundlagen" in AUTOMATH

L.S. Jutting

Contents: chapter 4a

October 1976

: .. !OT~-!r- .... l\

8 110531'

*) . . . I<'or an introduetion to and a discuesion of the present work, see the

authors thesis (Eindhoven, 1977): On verifying Landau's "Grundlagen der

Analysis" in the AUTOMATH System.

LAYOUT tROK fiLE AUTOE/LANDAU/H4A OCTOSER 11, 1978

lJ (P:CUTJ[Q:CUTltR:CUfl 3PL1J :: TR31SCCUT,PUP,.PU41l.R)hPt(PL(Q,.!thP h

R 3 3PUZ

S ; •PLZJ

R a 3PI.23

P a AZISAI'A

; DIF u1 :cur l t az:cun or

a [A:OIF l STH sro

AZ a STHIS rssn STDIS ISSfl

A a 1A u DrtS ISDf

AZ a [Bl:CUTJtaz:cUTJ lZtSSKSD

S"'SOISU

A a r:u: cunlRz:cun 1SDISS!1SD

SHSOISlSD

SKZISS!CSD

SHS!HSSHZ

PtCPL(R,.QJ,p),pl(R•PlCO•Pl), COHPL< p,. PL<Cl• R J), I SPllCPL C:J,R ),.PL(R, Q) •P•COMPl.Hl•RH•ASSPlHI\•Cl•i>)) : ISCPU:t •PL<O•RlhPUR•PU:l•Pl))

:: TR3IS<CUT •Pl(PL( P;Q),.f'L( R•S)),. PlCP,.Pl(OrPL(R,SJJ),pt(P,PL<S•PLCR,Q)) hPUPUP .. ShPU R• Q) lo ASSPtl<P,Q,.Pl.<R,.S)l,.ISPlZlPl(Q,.pL{R,.SJ l•PL<S•PL(R,Q)),p,JPL13(Q,R,S)), ASSPlZCP•S,.PUR,. QJ J} : IS<PlC2 l<P• OhPL<R•SJhPU PUP•S>-PLCR" OH l

:= TRliSCCUT,PL(P,.PL(Q,.R)),.pL(PL(P,.Q),ft), PL(PLCQ,p)~R>•PLfQ~PLCP•R>J~

ASSPU(P,QrR },. ISPLH PLCP" QhPl(Q,.P)•R• COHP((p,Q)J,ASSPLlCOrP•RJJ : ISCPLC~•PL(Q,.R)),PLCO•PLCP,.RJ)J

:• TR3IStCUT,PLCPL<P,QJ,PLCR,.SJJr PtCPrPl<O•PLCR•SJ)),.pt(p,pt(R•PL(Q,S)J hPLCPL(P, RhPL( Q,.SJ h ASSPLlCP,Q,PLCRrSJ>•ISPLZtPt{Q,.Pl<R•S) ),pt(R,PL<OrS)),p,.JPL12(Q,R,.S>)• ASSPLZ<P•RrPL< 0• SJ U .: ISCPU" UP, QJ,Pl(R,SU ,pl( PL(P,R),.pL(Q;oS}) J

:• TR3IS<CUT~>PL<PL(P,Q),RJrPl.<P•PL(Q,RJJ~> Pl(P,PL(R,.Q)J,PLCPL(P,RJ•OJ• ASSPLUP,Q,.R), ISPL2CPLC OrRhPL(R,Q hP• COHPLCQ,. RU.ASSPLZCP,R,Q)) : lS(PL(~l(p, Qt,.RhPUPUP .. R hOU

:= TRISCCUT•TSCP•PLClRP•lRPJ), PLCTSIP,lRPh TS(P,lRP) hPUPrPh DISTTP2CP;lRP,lRPJriSPL12<TSCP#lRP),p, TS(PrlRPJ,.p,sATZ151(P)rSATZ151CPJJ) t IS<TS(?,PLClRP•lRPJl•Pl<PrP))

:: PAIRlTYPE<CUTJ : •TYPE'

:•

:=

== := ;: := ::: == := := :a

PAIR1CCUT,A1•A2)

F"'RS TH CUT •Al SECONOUCUT,U FIRSTliSlfCUT,.Al,AZJ fiRST1IS2<CUT•Al•A2) SECON01ISl<CUT,.Al•A2J SECDND1IS2tCUT,A1rA2J SIMCAl STOCA) PAIRUSUCUT, Al PAIR1IS2<CU!,AJ

: Dif

: CUT : CUT : IS<STMI: DfUt.AUhAU : IS<At.STKCDFCA1,.A2))) : ISCSTI)( Of<At.A2) >•AZ)

ISCA2 .. S TD\OFCAl,.AZ>)) CUT CUT

: Is-r·o rr .. or<!Ar21\),oA1 : IS•E•(lt If'~>hDF< u,zu>

:: ISPL12CA1•ST~(OfCAl•A2JJ,.at, STO( Of(B 1• 62) h ISSTIIU1,A2),. ISSTDCS1•82ll : ISCPLCAI,BZJ .. PLCSTH(DF<Al,A2JJ,.STOCOFCE1,.82JJ)l

:: SYMl5tCUT .. ?LCAl•B21•PLCSTMCOFfA1•A2)), 5TOCDFCB1•82J)J,12ISSMSDl ISCPLCST~(OFCA1,AZ)J,STOC0f(Bl,BZJ)),pl(Alr82Jl

:: ISPL1CP.l .. STM!CFCRl~R2)),zA, I SS TM( Rl•R2l J : IS(?LH 1,2A >..PL< STIHOFCR1" R2) h2AH

:= SYMISCCUTrPl<Rlr2AJrPL<STHCOf<Rl,RZ)), 2Al•lSOISSHSOJ s IS <PLU TM(DflRl•RZ) h2U ,:o URI ,.2A,))

:•' ISPLZCRZrSTD<DfCR1 .. R2Jlr!A, ISSTOUl rRZ> ~ ISU'l <1 1,,. R2 hPU u, STO(DF'{ R1 .. R2))))

:= SYHIS<Cur.~LC1ArRl)~

....

- 4.1 -

HlH65

-101&5

AZ a [R:CUTl(I:IS<Al,RJl JSSM == uncur .. otr .. n :cunorn .. AZ hAt..R.u

R a ti:lSCAZ .. RJl ISSD := ISfCCUTrDif.tT:CUTJOF<Al.TJ .. At .. R .. Il

BZ; ti:IS<Al,.Bl>ltJ:IS<AZ .. BtJl ISSHSD := TRISCOIF .. Of<Al .. A2J .. DF<B1 .. A2Jr0f(81•82J

•ISSK(Al•A2,.Bl•I>,.ISS0(81rA2,.S2•JJ) A a ta:orrl

18 :: STM<BJ ZB := STOCS) E~ :: ISCPL(lA,ZB>•PUlB•ZA))

BZ a ti:ISCPl<Al,BZ>•Pl<Bl•AZJJl EOII:! ::: TR3ISCCUT .. Pl<STHCDf<A1 .. A2>h

STD<Df(Blr82J)),.pLCAt .. B2>•Pl<B1 .. AZJ, PLCSTK(0f(91 .. 82)J,SlDCDf(A1•A2J)),. S"SDIS12CAt .. A2 .. B1 .. B2),.I, 12ISSMSD<Bl,.BZ,.At .. A2J>

RZ a [I:tSCPL(lA•RZ),PlCRl .. ZA>JJ EOI1 := ISPCOir .. rx:DiflEQ(X,.Qf(Rl,R2)),.

Of<lAr2A),.A,.EG11Z<lA•2A,R1,.RZ•I>•Df!S) RZ a ci:IsCPL<Rt .. ZA>.PLCtA .. R2)>J

(012 := ISPCDlf•(X:DlflEQ(Df(Rl,.RZJ,.X)• 0f(1A .. 2AJ .. A.EOI12CR1~Rz,.tA.2A .. IJ,OflSJ

82 a tE:Et(DfCAl•A2l•DfCB1•BZlll EOE.lZ ·- TR3ISCCUT,.PLU1~8Z),.PLCSTKCDFU1,.AZJ ),.

STD<DfCSl•B2l)JrPL(STMCDF'<61~82)),. STOf DfUt~A2)) J,. Pl(Bl•AZh 12ISSHSOCA1rAZ•Bl,SZJ•E• SHSDIS12(81rBZ,.AlrAZ)J

A ; SATZ0163 :: REfiSCCUlrPLC1ArZAJl REFEQ t= SATZD163

e 3 tt:ts•E•corr.A.a>l REFE:l ·- ISPCDif~tX:OiflEQCA.X).A,a.REfEOrlJ REFE~Z :: ISPCOif,.tX:DiflEQCX•A)rArBrREFEQ,.J)

BZ a ti:ISCAlrBlll[J:ISCAZ.aZJl EOSKSO :: REF'EQ1(0f(At .. AZJ~Df(81r82J•ISSKSD!t,.JJ

)

R ; tt:ts<Al•R)l EOSM :: REF'EOHDFtA1,.A2J.DF'U.A2hiSSMUH

R a ti:IS(A2,.Rll EQSO := REFEQUOFUt.AZhOFUl..RhiSSOU))

8 a tE:EQU,.BJl SATZ~16' := SYMISCCUTrPLC1A•ZBJ,.FLC1BrZAJrEJ SYHE:l :: SATZ0164

8 ; [C:Dlfl 1C := STI!(C) ZC := STDCC) [E:(Q(A,.BJl[f:EQ(BrCll

T1 := ISPL12<PL<1A .. 29JrPlC10r2A),pLr1B•ZC)r

: CUT CUT

: 'PRQ.JU

I ISCPUA 1r82 hPLUt.AzJ J : Eou..u · : EQU,.AJ

: EIHA.B) : EQ<B•U

: EQCDF'CA l ... Az ),OFCR,A2H

: EO<DfUl•A2hDfUlrRU

: EQ(B,AJ : EG<B•AJ

: CUT CUT

PU1C,.28),.[,.f') : IS(Pl( 10 LUA.28)•Pl< 1Sr 2C)) ,pL(PL(19•2AJ.PlctC .. 21U)) T2 := TP.4IS<CUTrPLCPL~1ArZC)rPLC18•28J),.

PL[PL(1Ar2SJ,Pt(18,.ZC1JrPLCPL<1Br~AJ. PLC1Cr28))rPL(Pl(1Cr29JrPLC18•2AlJr PLCPL(1Cr2A),.PL(18•ZS)Jr 4Pl?ft( lA .. zC,lB ... ZB) • Th COMPL<PtH8•2A) r PLHC• ZB) h4Pl24UC,. 2BilerZA l) : ISCPL<' l<1A.2CJ •Pl< 18,. ZBU ,.pl(PLUCrZA hPL us,ze)))

s

- 4.2 -

s

.. rz•.tot65•J TREQ :: SATZD165

C a [(:E~CC .. A)J[f:EQCC•B>l TREOl :a TR[Q(A,.C•B•STMEO<C•A•E),.f)

C a [E:EQ(A,.ClJ[F:EQCB,.C)l TREQZ := TREQCA,.c,.a,.E .. SYHEO<B•C,.f))

C a tO:OIFllEl:[Q(A,BJl(EZ:EQCB•CJlCEl:[OCC•D>J TR3EQ :: TREO(A•B~D•E1,.TREO(B,.C,.O,.EZ•E3))

0 a ([:OIFl[El:E~CA•B)J[EZ:EQ(S,.C>JCE3:EO!C,Q)J(E4:EO<D•E>J TR4EQ := TR3EQCA .. B.C•E•E1.EZ,.TREQtc,.o,[,[3,.E4))

A a POSO :: HORE<1A .. 2A) ZERO := ISUA• ZAl NEGD :: LESSClA•ZA>

AZ a [H:MDRECA1•AZ>l POSOt :: JSMDRE12<Al•STK(QfCAl•A2))•AZ•

AZ a [J:IS<Al•AZll ZERO I

AZ a [LtLESSCAI•AZJJ !fEGDJ

A a AXRDE AXRDO AXRO

STOCDF(A1•A2)),.ISSTM(A1 .. A2l" ISSTD( AhAZhM)

:: TRU S( CUT,. STfo!(Df( Al• AZ))"' Al•A2• STOCOF<Al .. AZJJ.STMIS<Al•A2),.J,. ISSTDUt.A2l J

: = ISLE S's 12<A 1• ST M< OHA hA 2 J J,. AZ" STD<OF<Al;A2)J;ISSTK<A1•AZJ• ISSJIH AhAZhU

:= SATZ1238(1A;2A) := SATZ123AC1A,.ZA) :: OREC3I<ZERO(AJ~POSDCAJ;NEG0(AJ•AIRDO•

: EOChBJ

: EQ(A,.[) 1 PROP 1

a 1 PROP 1

: 'PROP'

: ZERIH OF' Uh AZ))

t NEGO<Df" Ut. AZU t ECJCZEtOCAJ•POSDCAJ,NEGD<AJJ : OR3UDOUhPOSOUhNEGOU))

AXROEJ t ORECl<Z EROC AhPOSDUh NEG!)( A)) tP:''ROP•J(Pl:(T:PQSDCAJ1P1CP2:tT:ZERDCAJJP1tP3:ETtNEGOCAJJPJ RAPPO t= OR3APPCZEROCA1rPOSDCAJ•NEGDCAJ•P•

AXROO,.PZ•Pl"' P3) : p A a [P:P:tSOC U 1

PNllUO == EC3EZ1<ZERO<AJ,POSD<A>,.NEGOCAJ .. AXRDE• PJ : NOT( ZEt OU>)

PNOTNO := EClEZlCZERDCAl,.POSDCA),.NEGOCA)"AXRDE• PJ : NOTUC OCU J

1 a U:ZEROUJl ONOTPO == EC3E12CZERO(AJ,.POSD(AJ•NEGD<AJ,AXROE•

l) NOHPOS OU)J !)Mono := EC3EllCZERO<AJrPOSDCA>•NEGDCAJ•AXRDE•

ZJ : NOT( NES OU)) A a (II:NEGDCUl

NNOTPO := EC3E3ZCZERO<AJ.POSD<AJrNEGOCAJ•AXROE• !U NOT< POS OU))

NNDT)D := EC3E31CZERO(A),.P0$0(AJ•NEGD(AJ,AXRDE; fH : NDHZERDCAJJ

B a [EtE:IU•BU[PtPOSOU)J

tiVl~ S

Tl

•IVll

EQPOSD E a (l:Z[ROU)l

HIVlD

:a ISKORE12(PL( 1A•Z8J,PU 18• ZA hPL<ZA•ZB> ,.pl( 2B•Z.U ,.[.,. COMPl( ZA• 281 • SATZ135U1A•2A,.zB,.P)} : MOR((P';. ue,.zu,.puze,.zA))

: POSD<BJ

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-rvn l a EI1ZE!t0 E ;a (N:NEG!HAll

Na n

t= TR3ISCCUT•Pl(1Sr2A>•PL(1A•2S>• Pl<2A;. ZB),. Pt.C213r ZA),. SY11EO u .. s.n,. ISPL1ClA•2A•ZS•Z>rCOMPl<ZA•28>)

:• ISLESS1Z<PLC1Ar2Bl•PL<lB•2A>•PL<ZA•ZBJ •PL<ZB.ZA ),(,.COMPL<ZA, 28 l.

: ZER0(8J

SATZ 1l5C<1A• ZA,. za,. NJ) : LESS<P:. UBr ZAhPUZB,ZAU

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••IVlD

N a EONEGO :: SATZ136CC1Br2Br2A•T3•.IV10•) : NEGOCBt 8 a tz:.ZERCCAJ ltT:ZEROCUl

Z~ROEO := TRISCCUTrPLClA.ZB>•Pl<ZArlBJrPLClB•ZAJ •ISPL1Z!1Ar2A•2Br1B•Z• SYMIS!CUT,.1B,zB,.Y>>•COHPL<2A,.18)) : EO(A,.BJ

1 [R:ClJTl PDOFRP t= Of(PUR,.tRPhlRPJ t DIF' ~DOF~P :z DFClRP•PLCR•lRP)J : DIF ts:CUTJ[I:ISCR•S>l ISRPEPD := REFEOlCPDOFRPCRJ,.PDOfRP(S),

ISF'CCUT•Oif• tx:CUTlPOOFRPUhRrSrt U : [QCPDDF RP(R ~rPOOFRPUJ J ISRPEND := REfE01CNOOFRPCRJrHD0fRP<S>•

ISFCCUTrDif•tXtCUTlNDOFRPCXJ•R•S•l)) : EOCIOOtRPCRJ•NDOFRP(SJJ S a [[:EQCPOCfRPCRJ,PDOfRPCS)))

t a u := SATZ136BCPLCRr1RPJ,PL<S•1RPl•1RPr EOE12CPL<R•lRP>•1RP•PL<S•lRPJ,.lRP•ElJ : ISCPL<t•lRPl•PLCS•lRP)J

E a ISRPIPO t• SATZU6B<R•S•lRPrT4"' .. IV10•J S a tE:E~(NOOFRPCR),N00FRPCSJJ1

E a n

E a JSRPINO

P. a POSDlRP

NEGOIRP

A 11 [!":!'OSD<A> l lfPOF'i»D

:= SATZ136E<Pl<S.1RP),Pt<R•lRP>•1RP• EOE12(1RP•rlCR•lRPl,lRP.PL<S•1RP>•ElJ ; IS<PLCSrlRP)•PL(R,.lRPlJ

:: SYMISCCUT•S•R•SATl136BCS•R•1RP• rs•. IV10")) t IS<R,S2

:: PGSDICPL(R,.lRPJ,.lRP .. ISHO~ElCPLC1RP .. RJ• PlCR,l~Pl•lRP,COHPlClRP .. R), SATZ1l3<1RP,RJ)) POSD(P)OfRPCRJ)

:: NEGOIC1RP,PL(R,.1RPJ,ISLESSZ<PLC1RP,.Rl• PL(R,1RPJ•1~P•COHPLC1RP•R>• SATZ133AC1RP,.R)J) : NEGOCN~UFRP<RJJ

: CUT

s

s

s

$

- 4.4 -

•nu

UIVID

-nu

P ; rs :• TR4IS<CUT•Pl(lA•lRP),PL<PL(RPOFPO,ZA>• lRP)•PlCRPOfPOrPl(ZA•lRP>)• PltRPQFPO.PL<lRP.ZAJ)• PL<PU RPOFPO rl!lPhZA ),. ISPLl(lA,.PltRPOfPD•ZA)rlRP. SATZ14~ftlA,.zA,P)), ASSPLlCRPOFPO,.zA,tRP),.ISPLZCPl<ZA•lRP) •Pl<!R?•ZAJrRPOFPO,COMPLC2ArlRP)),. ASSPLZCRPOFPO•lRP,. ZA)) : ISCPl<l A .. lRPJ,.PUPt.<RPOFPJ •lRP),zAn

P a EOPD!tPl EOPD~PZ

A 2 [NH~E:GDU) l RPOntD

N a T7

:• EQll(A,PlCRPOfPDrlRPJ•lRP•T6•.IVlD•) :• SYMEOU,PDOfRPCRPOfPDU.P) hEQPDRP1)

:: TR3IStCUT•Pl<1A~PLCRPOFMD•lRP)),. PLCPl!lA.RPOfNO),lRP),pL(ZA•lRP), PltlRP•2A)•ASSPLZC1A•RPOfND•lRP)• ISPL HPU U, RPOf NOh ZA.o1RP,. SATZ140C<ZA•1A•SATZ1ZZ<!ArZA•N))), COMPUZA,lRPH

N 2 t;KO~Pl :: EQilCA.tRP.PLlRPOFND•lRPJ .. TT-.JYlD•) EO~D~PZ :• SYKECCA*KDOfRPCRPDfNO<A~N)J,EONDRPl)

a [H:Oifl[PtPOSD(H)l[K:OifJ[Q:PQSDtKll[E:EQCH•K)]

E a ra :a TR3EQ(PDOfRP(RP0fPO<HrPJJ•H•K• PODFRP(RPOFPDtKrOJJ•EOPDRP2CH.Pl•E• EOPORPl(I(,QJ J

E ; EQPOERP :: ISRPIPDCRPOFPDCH•P)•RPOFPO(I(,.Q), TB•. IVto•J

Q 1 [I:ISCRPOFPDCH,PJ•RPDFPDlK,Q)JJ

z a n

I a EQPOIRP ta fR3EQtH.P08FRPCRPOFPOCHrPJJ, PDDFRPtRPOFPDCK•Q)JrK~EOPDRPlCHrPJ• T9•.tV10•,[QPORPZ<K*Q))

H a tN:HEGOCHJJ[KtDIFltO:NEGDCr.ll[E:EQCH•KJl

E a HO :• TR3EOCNDOFRPCRPOFNDCH,NlJ•HrKr NOOFRP<RPDfNOCK•U>J•EONORPZCH•N),[, EONORPUK .. O) l

: EQ(A,.p)QfRP<RPOfPOCbP))) : EQCPODr RP<RPOFPOU, P) hU

: CUT

: EOCA,fGOFRPUPOFifOU,.NUJ EQCHDDF RPtRPOfNIHA• NUrU

: EOCPDOFRPCRPOFPD<H•f')),PDDFRPCRPOFPOCK•Q))J

: EQOhiO

s

s

s

s

s

s

s

s - 4.5-

ui VlO

•IVU

+•IVtD

•IvtD

+•IYU

•I VlO

E OI EQNDERP :: ISRPINDCRPOF'NOCH#N)~RPDF'NOCK•Ol~ no·. rvto•,

0 a II:ISCRPDf'ND(H#NhRPOPUHK.GHl

I a Tll

I 2 EOHDIRP

<I [R:CJT l

R a UZ

R OI ISRPP!)l

ISRPPOZ

R a T13

R a ISRP't401

ISRPNDZ

AZ 3 tR:CJT l LE!U4A01

LEMMAOZ

A a tR:CUTl LEK11AD3

LEKHAD• A a ASSD

(N:NEGDU) l ABS NO

A a [NtNOTCNEGDCA))l ASSN~D

AZ a (l:LESS<Al~AZ>l ABSOEOL

:= TR3E :l<H• H~OFRPCRPOF'NOCH•N))~ NDOF'P.P<R?::ln.iOCK, Q) hK~EC:!'tORPlCH.Nh Tlt'".IVtD••EONDRPZCK•O))

:: EQPDRPtCPDOF'RPCRJ,pCSO!RPCR))

:= ISRPIPD(R,RPOFPOCPOOFRP(R),POSDIRPCRJ)

: EOUbiO

: EOCPDW RP<R hPOOF'RP€RPOFPD CPDOFRP!RhPCSDI RP< RU))

•TlZ•.IVlO•) : ISCR•R'OfPOCPOOF'RP(R)~POSDIRP(R))) := SYKISCCUT.R.RPOtPO(PDDF'RP<RJ•

POSDIRPUU h ISRPP01> : IS<RPW POCPOOF'RPCRlPPOSDUP<R1 ),R)

:a EQWDRPl(NOOF'RP<R>•NEGDIRP<RJl

:• ISRPINOCR•RPOF'NOCNDlfRPCRl•NEGDIRPCR)) .T13•.IY1!l'"J : IS<R•R"OFHOCNDOFRPCRhNEG3IRP<R)JJ

:: SYMIS<CUT•R•RPOFNO<NDOFRP<R>• NEGD IRP<R) h ISRPt!OU IS<RPO=- NOCNDOFRP<RhNEGDH P( R>) ,.ft)

:: EQI12C41.AZ,.PLCAl•RJrPL<A2•RJ, fRISCCUT-Pl(Al.PtCAZ .. RJ), Pl(Al•Pl(R,.A2J),PL{Pl(Al•R>•A2)• ISPLZ(PLCAZ.Rl,.PlCR,AZlrAlrCOMPL<AZ,RJ ),.,SSPLZCAl .. R .. AZ)Jl

:: SYMEQCOf(Al•AZ>•OFCPt<Al•RJ•PLCAZ•RlJ• LEKIUI)l)

:a TREOCA,OfC1A,2A> .. DFCPL<lA•R>•PL<2A•R>J •REFEQ1(Ar0f(1A•2Al•ISOF>~ lEMHA01ClA•2A•R>>

:= SYMEOCA,QF(PlClA•R>,PLCZA•PJJrlEMHADl> ·- ITECNEGD(AJ,.OlF•OF<ZA•lA),A)

•- REFEQl(ABSD<A>•OFCZA•lAl•ITET<NEGD<A>• Olf" .or (ZA~ 1A hA• fD)

:= REFEOl<ASSO(A),A,.ITEF'CNEGO(A),.OIF,. OFC2A•1A>•A•t0)

:: TREQ(ABSOC0f(Al•A2>l•OF<STD<Df<Al•AZJl .STK(OfCAl•A2l))•0F(AZ·A1),. ABS NO( 0!"'( Alo Al), ~EGO!< U• A2•U ), EOSMSOCSTO<OFCAl,A2>)•STM(GF<Al,A2>)•

EQCA,or (PU lA•R> rPL<2A,R))) : EQ(0F('l(lA•R>•Pl(2A•R>>•'l : Dlf"

: EO<ASSiHAhU

s

s

s

s

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- 4.6-

•IV2)

+20166

•ZD166

AZ 2 [H:MDREISCAt~AZJl ABSOEQM := A9SN!'fO<OF(A1,.AZhT1U"l•IMP"'CNEGOCDf

CN:N(GOUJ! Tl

TZ

E a [N:NOT(NEGOCA)Jl f3

EOABSD

A a tP:PlJSOCU l SATZDHI6A

A ; U:!'iEGDU)]

Tl

CA1,.AZJJ~LESSCA1~AZJ~SATZ1ZlCCAl,.A2rMl ,[T:NEG0(0FCA1,.A2J)] iSLESSIZCSTH<DFCAl,.AZllrAlr STOCOFCAl,.A2J:,.AZ,.sTMI$CA1,.AZ),. ST!HS(Al,.AZlrT>n : EOUBSiHDf"CAhAZJJ,.Of'Ub,Z))

:: TR3ISCCUT•PLCZA,.1BJ,.PLC18•2Alr Pl(1A,.29J,.PLCZB•1AJ,.COMPL<ZA,.1BJ• SY~~~(A,.8,.(J,.COMPLC1A,.28J) : 1S(PLCZA•1B)•PL(28,1AJJ

:~ TR3EQCABSDCA>,.OFCZA,.1AJ,.OF<Za,1BJ,. ABSUtSJ,.ABSNOCA•N>• EQI1Z<ZA,.1A,.ze,.1S,T1),.SYMEOCA8SO<B),. OfCZB•lB t..ABSHO<BrEONEGOU,.B,.E•N J) )) : EOU8Sl Uh ABSO• E•SYMEQCABSDCBJ,.e,.ASSN!'f0(8,.TH3"l•IMP" CNEGDtBJ,.NEGOCA},.N,.tT:NEGDCSJJ EONEG!HB•A•S YMEQ<A,.a ,.[ h TJ )))) : EOUBS!HA),. ABSO( 8))

:= THl•.L. IKP•(NEGDC A) •EQUBSOU J..ABSDCB U ,.(f:NEGDCAllT2".IY2D"CT),. [J:NOT<NEGOCA))JT3•.IV20•CT>J : UUBS> (U,.ABSOCBU

:a EOPDSO(A,.ABSOCA),.SYMEQCABSDCA),.A,. ABSN~D(A,.PNOTND(A,.p))),.pJ : POSDU8SOUJJ

t= PDSDI<zA,.lA .. SATZ1ZZC1A,.zA,.N)l : POSD<Of CU .. lAl)

SATZD166B :: EOPOSO<Df(2A•1AJ,.A9SOCA),.SYMEOCABSO(A) .,Qf( z.a,tAJ,.ABSNOU,. N )J,. u•.zo166•) : POSOC A3 SOU))

B ; [P:P350(A)][Q:POSD<Bll[E:EOCABSüCA),.ABSOCSlJ1 SATZD1&6C := TiUE O<A,ABSD (A hASSD (8 J,.a,

SYKEQCASSO(A),.ArASSNNO(A,PNOTNOCA~P})) ,.[,.A13SNND( a,. PNDTNO (B,.Ql)) EOCA• 8)

8 a [N :NEGOU) HO:NEGOCBlHE:EQ<ABSDU ), ABSO!B ))]

E a T2

E a SA TZ01660

:: TR3EO(OfC2A•1Al•A8SO(A)•ABSDCBJ•. OFC2S ... lB ), SY KEQ<ABSO(A hOFC2A•lA h A8SNO<A•N>J•E•ABSN0(8•0))

:.= TRli S<CUT,.Pl UA, 28 h PU2B• 1A), PLC2A•lB>•Pl<1So2A),.COHPL<1A,.2B),. SY~IS(CUT•PLC2A•l8J•PL(28,1A>, · · [Q[1t{2A,.1A,2S,1B~T2"·2~1G&~)), CO!'!Ptc U•l él D

s

s

$

s

s

s - 4.7-

-SATZ3l&&E :• RAPPD(A,POSO(ABSOCA)J~CT:POSCCA)J

SATZD1&6AO.• f),TH~·L.IMP"'CZEROCA h POSO(ABSOCA)),N),[T:MEGD!A)J SATZOl&ólHA• T))

A a [ZIZE:RDUH SATZO!S&F' :: EOZEROt A.ASSIH AhSYHEQUBSD<AhAr

RZ ;

~z a

82 ;

a ;

B 2

82 a

RZ a

R2 ;

sz a

8 2

ABSNNO~A,OX~TNOCA,Z)~l.Zl -~QREl := MO!ECPL<lA•2Bl•PLClB•2AJ) tM:~~RE<PL<Al·BZ>,PL(81·A2J)l MD~EOllZ :: ISHDRElZCPLCAl•SZJ,PlCSTM(DF'CAl•AZJJ,

ST0(0f<Bl•B2>J),PLCB1,AZJ, PLCSTMC0f(B1•B2>)•ST0(0f{Al•A2J))• 12ISS~SOtA1r~2•Bl•BZlr 1ZISS~50C8l,B2•Al•A2),Ml

[M:KJRE(P~ClA,RZ>•PLCRl•ZA)l) MORE,I1 :a ISHGRElZCPLClA,RZ),Pl<lA,STD<OFCRl.RZJ

J>•PL(Rl•2A),pL(STKCDFCRl•R2ll•ZA>• SKZ!SSHSO<A•Rl·RZ>•lSDISSHSD<ArRl•RZ), H)

[K:MJRE(PLCR1,2Al•PlC1A•R2))J ~O~EDIZ := ISMO~Ell<Pl<PlrZ~i~PlCSTH{Cf<Rt;RZJ),

2AJ,Ptt1A•RZJrPLC1ArSrD<Df<rtlrP.ZJJ), lSOISS~SOCA.R1,R2J~sHZISSHSDCA,RlrR2)• lH

[M:K~RE0(0f(Al,A2),0f'<B1,82l)] MDREOElZ :: ISMIJRElZ(PUST!UDF'Ut.AZJ),

tESSlJ Ut: M:JREDU ,u l lEMKA05 (l:lESSDU ,.g) l

STD<OF<B1rS2JJ)rPl<A1•82Jr PL{STMCDfCBlrB21JrSf0(0f(Al•A2J)Jr PltB1rAZlrSMSDIS1Z(A1.A2rBlr82J~ SMSDIS12CBlr32,AlrAZJ•K)

:= lESS<Pl{1Ar28lrPL<1BrZAl)

lEM~AOS :: SATZ1Z2(PL<1A .. ZBhPLUB,ZAhl) [L:LESSCPttA1•82)•'LCB1rAZ>Jl LESSDI12 := LEMMA05(0f(81,82)r0f<AlrA2lr

MOREDI1ZlB1rBZ•A1rAZrSATZ12Z<Pl<A1•B2J •PL<Bl .. AZhl)))

[t:LESSC PUU, RZJ. PLC Rt .. ZA)) l LESSOit :a LEMHA05COflRlrR2>•A•

KOREOIZCA•RlrRZrSATZ1ZZCPL<1ArRZJr PURlo>ZAhUJJ

El:lESSCPLtR1•2AJrPlC1A,R2))} LESSJIZ :: lEMMA05(ArDFCRlrR2>•

KOREall(~•PlrRZ,SATZ1ZZ<?LCRlr2AJr Pl( lA• R2 hl)))

[L:LESSDCDF'CA1•A2);0F'(81•82Jll LESSDE12 := SAH121<PL<Bl•AZ J.Pl<AlrB2h

MOREDE12tB1r92rllrAZr~EHMA06COF(AlrA2) ,.OF<81•8ZhL ll >

SATZ0167 1: SATZ123CPLC1A,28l•Plt18•2A)l SATZa167A := SAIZ1Z3AlPL<lA~2B)rPLC1Br2AJ) SATZD1S78 :: SATZ1236CPl<1'•2BJrPL<1BrZAJ1 10 :: STH(()) ZO ·- STlH O> ((:E~<ArB>ltf:EQ(C,Q)}[HIHOREO(ArC)l

: POSO Uil SOU U

ZERIH A:l SD CA )) •PROP'

MOREO() F' U1,.A2) ,.Qf'( 81• BZ))

ftDRECP'- CA1r82hPLCSbA2)) : 'PROP•

LESSOC3 rA J

: MORED(9 rU

LESSOO F'CAlrAZ J •OF (Sb 82))

: LESSlP-<AlrBZJ,PLCB1,A2)) OREC H:: Q(A, B hMOREDUr !U •LESSD<A•B>) OR3CEwC A .. S>, KOREt:lU.BJ •LES SOCA.>!!)) EClCEQCArSlrMOREDCA,B>rlESSOCArB)} CUT

: cur - 4.8-

•IVZ>

PLCPLC1B•2A);PLClC•20)),pl(PLClA•29)• PLCtO.ZCl>•Pl<PLClA•ZCJ•Pl(lD•ZB>J; PLCPLC1D•2B>•Pl(1A•2CJ). ~PL24C16•20•1C•ZA>•ISPL12<PL(1B•2A)• Pl< lA• 28 >- i'LUC .. 20 h PLUD.ZC >·• SYMEC<A•B•E),f};~PLZ4C1A•2B•lD•2C>• COMPl{ PL UA, ze h PU 10• 2B N l ISCPlPLUS .. ZOhPl< lC• ZU) .PL<PL< 10.28 hPUU~zc> U

T5 := ISMCRE2CPL(PL{l5•23),.Pl(1C•2A)), PLCPLt1D,29),.PlC1A,zC~J.PLCPLC1B•2~>• PlClA•2C)J,.T4•SATZ1350{PLC1A•2C), PLUC. ZA h PI.C lB .. 20 h MJ) : MORE CP:.. CPL( 1 a,zOhPl<t A,z::)) •PUPL< 10• ~Bh FLUA• 2C)))

f ·a tl:LESSOCA•C>J EOlESS012

:: SATZ 13óA(Pl< 1B•20h PL< 10~29 hPl

:= LEMHAD5f0•B~EO~ORED12CC*D•A•B•f•E*

c a LEMMA06(~•C•Ll))

tE:EQ<A•B>JCK:MDREOCA.CJJ EOMOREDl := EQMGREDlZ<A•B•C•C•E•REFEQCC>•MJ

a a

tHH!ORED<C•A>J EQHOREDZ tL:LESSDU~C)J EOLESSD1 [L:LESSD<C•U J EQLESSD2 HOREQ LESSEO r!UMGREO<A •B)) SA TZDlr.&A

B a tt:LESSEQ<A•BJl

:: EOLESS012<C•C•A•B .. REFEQ(C)•E•LJ := DR(MOREO<ArBl•EO(A,.Sl) := OR<LESSD<A•BJ•EQ(A,B)J

:: TH9'"t.OR~CMOREO<A,Sl,.[Q(A,Bl• lESSDtB•A>•EOCB .. A>•M•(T:MOREDCA•B)l LEMMAOS<A•B,.T),.[f:EQtArBJlSYMEQ<A•B•TJ )

SATZD1688 :: TH9•t.OR'"ClESSD<A•B>•EO<A~B)• MORED<S•A},(Q(B,.A),.L,.[T:LESSO{A,.B>l LEMMAO&<A•B•T),.(T:EQCA•B>lSYHEQCA•B•Tl )

C a tE:E~<A•SJl[H:MOREQ<A•CJJ EOMOUQl :: Ttt9•L. OR•< KOREOU,.c hEQCA•C J.

E ; [M:M3REQCC .. A)J EOKOREQ2

E 3 (L:tESSEQ(A,CJl EOLESSEIU

E a CL: LESSEO< c, All EOLESSEOZ

HORED<B•C>rEO<B•C)•H•CT:MORED{A•C>l EOHJREDltArB•C•E•f),[J:EQCA,C)l TREQ1(B,.C•A•E•f))

:z TH9~L.OR•<HORED(C,A),(Q(C;AJ, MOREDCC;B)~EQCC•S>,M,[T:HORED(C,AJl EQMORED2CA,e,c.E,TJ,(T:EQ(C,AJJTREO<C• A•B•T.oEJ>

:= SATZD168A( c,. B~EOMOREQ2tA•B•C•E• SATZ01688(A•C•LJ>~

== SATZ0168ACB•C•EOKOREQl(A,B•C•E• SATZD1688(C;A,.LJi)

I) a ((:E~<A•e)J[~:(Q(C•D>lCM:MOREQ(A,C>l EQHOREQ12 ::: EOMORE01<A~B•D•E•E;KORE02<c~o.A,f,M}J

f' a t:t:LESSEOCA•C>l EOLESSE012 := EOLESSEQ1(A,.s.o,E,EQLESSE~2<C•O•A•f•Ll

)

B .. CMH!JRE::><A•B) l • HORE:lll ::: ORitCHOREDCA~B>rE~<A~B),Hl

: ~ORED<3 ,.o)

: LESSD<B~O)

: MOREO<B,.CJ

: LESSD

fo!OREQ(C •Bl

: LESSEOC: c,.B)

MOREQ(3 ,.QJ

: LESSE~C s,.O)

M:JREQ<A •lH

$

- 4.9-

.. .._ • .,_~.."..,itl,nPU#J

LESSEOll :z ORil(LESSD!A•Bl•EO(ArB)rll LESSEOC AriU B :1 CE:E:HAr.Bl l

MORE~ I~ :a ORl2CKOREDCArBlr(Q(ArB)r() : KOREOc:A •BJ lESS~OIZ := ORI2CLESSD<Ar8)rEO(A,SlrEJ LESSEQ( A,.B)

B ; (lof:MJREQ<A,BJ J SATZ:>167C :: TH7•L.EC3"CEQ<AtBJ,KOR".OlA,8)r

tESSC<- .. eJ,SATZ0167S,.COHOR{KOREDCA,.B),. EQU.r8Jrl1D NOHLES SD<ArB))

8.41 tL:LESSEO< A,.B) l SATZi>1&7D := TH?•t.EC3w((Q(A,BJrKûREO<Ar8)r

lESSD<A•BlrSATZ0167B•Ll NOT<HOlEOU .. B)) B 4l (N:~~TCHDREO<A .. BJ>l

SATZJ167E :: TH2•L.DR3~CEQ(A,B)rMOREO{ArB),. lESS0(Ar3,oSATZ0167ArN) LES$(:)[ A,B)

8 :1 [N:NDTCLESSOCAr8))] SATZD167F' :-= CCKORCEO<l•B>•HOREO(Ar~),

TH3•t.CR!•((0(Ar9),H0REOCA•8)r lESSOC~·S1rSATZ0167ArN)J. HORt OU ,9)

s a [M:Kt'IRED<Ar8)] SATZiH&TG :: T~l·t.IMP•ttESSEQ(A,BJr~OTCMOREOCAr9))

.~ELI<~DREDCA,3JrM),(T:LESSEQCArB>l SATZ01&7:l<T)) : NOf(tES SEOC A .. B>)

a a ruu:ssou .. a n SATZ!H67H := TH3•t.IMP"(HOREO<Ar8J•NOT<LESSD<A•8))r

iiELl tlESSO (I,, B )rlh tT :MOREQC A,. 8) l SATZD1ó7C( T)) : NOT<MO~EOCArBU

8 4l [N:NQT(HOREOCArBlJl SATZiH67J :: OR3E3(EQ<Ar8 h MOREOU .. BhLESSD<A,B h

SATZ01&7ArTHS"L.oR•tHOREO(lrBJrEOCArB> rN)rTM4"l~OR"CMOREOCA•B>rEO(A,B>rN)) : LESSOCA •B)

8 ; tN:NDTCLESSEQCArBJ)l SATZ0167K == OR3EtCEQCA .. B>rMOREDCAr8J•LESSO(ArB)r

SAfZ01&7A•TH4~L.OR"<LESSO(A,.BJrEOCArB1 ,N},TH5•t.OR"CLESSOCArBJrEOCAr8)rN)) MOREDCA ,8)

a a tz:ZEROl[P:POSD<A>l SATZ!)169A ::' ISMOP.E12(Pl(1A•l9l,Pl<1A,2S)#PLC2Ar18)

rPL( tB.ZA ),. I SPLZ <lB .. ZBr lA• l),. COMPL<ZA,18)rSATZ135A(1A•ZArlBrPJ1 : MOREDCA r8)

z a [H: MJREDU •8> l SATZD1699 : .. SATZ136DC1Ar2A,ZBriSKORE12(Pl<1A,ZB>•

PU2Br1AhPU 18" ZA> r PU ZB •ZA h CO~PLC1A,.ZB>,.ISPL1C1B•2Br2A,.z),.M)) : POSIH At

z tl (H: NEGO (A) 1 SATZJ169C ::: ISlESS12<PlClA,lB>•Pl<1A•29JrPlCZA,.18)

rPLC1B.2A),.ISPL2Cl9•2S•IA•Z>r CO~PL<2Ar18),.SAiZ1l5CC1A•ZAr1B•NJ! : LESSOU ,.a)

z a tL:.LESSD<A,BJl SATZD1690 == SATZ136f(1A•2A•2B•ISLESS1Z<PLC1A,ZB>•

PU zs,. 1A h Pl <1 s,. ZA h PL ( 28 ,.zA J.. CQKPL<1A•2Bi•ISPt1<1B•ZB•ZA•Z),lJ) NEGlH A>

•Z017) s

z a [P:P!JSDU> l Tl := HOREQil<ABSDCA)r8rSATZD169A{ABSDCAJrBr

ZrSATZ0166A(A,.P>JJ : MOREOUBSO<AhU - 4.10 ° z ; (Y: ZERO U) l

TZ := MGREQIZ<,SSO<AJ,.B•fREQ(AaSD<A>,.A•B' ASSNNO(A,ONOTNO<ArY)),.zEROi:O(A,.a"y,.z}) , HOREQU BSDC A hBJ

Z a (N:NEGDUJl

+20171

•ZJ171

•2D173

•20173

:: MOREOI1CA9SO(AJr8rSATZD169ACABSO(A)r8r ZrSATZ016&8CArH)J)

Z a SATl,170 :~ RAPPDCArKOREOCABSOCAJrBJr[T:POSDCA)l rr•. ZD170•<T h CT: ZERO<A) lT2 ... 20170 .. ( T > ,.{f:NEGO<A )JT3 ... 20170 .. (T J >

C a (L:LESSOCAr8Jl[K:LESSD<3•C>l

u :: SAfZ137ACPLC1Ar28J,.PL<1B .. ZAJoPL(1Br2C}

HOREQ(ABSO<AJrB)

.. Pt< lC•ZBhl• 10 LESS(P'. <PLC u,ze> .. Pl< 18•2!:) h PUPL( 18• ~A), FU lC•ZBJ)) TZ := ISLE SS 12\PU PU u .. ZB hPL C1!h2C)) •

PtCPl(tA .. ZCJ .. PlClB•ZeJ>rPLCPL<lB•ZA>" PL(lt•2BJ),.PL<PlC1Cr2AJ,pL(18r2BJ), ~Pl2~ClAr2B•lB,.2Clr TRIS<CUTrPL<PLC1B.2A)rPLC1Cr28l), PlCPtC1Br2BJ,.PLC1Cr2AJ)rPL<Pl(1Cr2AJr PLUBo.ZB) J. 4Pl24U!J, 2Ar1C rZB J, CD!1Pt.< PLC 1B• 213 l, f'l UC • ZA J) h Tl) : LESS< P. CPL< u,zc hPl< 18r23) h PL( PU lC• 2A J. FLUS• 28>})

'"SA TZ 0171 :: SATZ136CCPU u .. zchPL<lC•ZAJrPUlB,.zB> .rz·.zot71">

TRLESSD :: SATZD1Tl c a tH:HlREO(A,B)JtN:HORED<B•C)l

TlUfO=IE'l :: LEMKAOS<C•ArTRLESSO(C,.s,A,. lEMMA05(B-C,NJ-LEH~A05<A•B•KI))

c a [L:LESSEQCArB)ltK:tESSOCB•C>J

c a

c a

c a

c a

SATZiJ172A :: ORAPP<LESSO(A.B),[Q(A,BJ,.LESSD(A,Cirl• tT:tESSD<A•BJlTRLESSDCT•K),.(fiEQCA•B>l EOLESSOl(B"A,C.SYHEOCA,B.T),K)J

tt:tESSO<A•B>l[K:LESSEOCa*C>J SATZ0172B := ORAPPCLESSO(B"cJ.EQCB•C),.LESSOCA"CirK,

tT:LESSDCS•C)JTRLESSO(L,.T>.tT:EQ<B•C>J EQLESSDZ<B•CrA,J"L))

tM:~OREQ(A•B}l[N:MOREO(B•C>l S.UZD172C :: lEHMAQ6CCrA,SATZD1728(C"B•A,

LEH~A05(8•C•N>rSATZD168A(A•B,H))J (K:KOREDCArBJltN:HOREQ(S.CJl SA TZ0172D :: LEHMAD6<C•A•SATZD172A<C•B•A•

SATZ0168A<B•C•N)•L~HHA05<A•B•MJJ) CL:LESSEQ{A,BJltK:LESSEO<B•C>l

tJ:te:ssou.a u Tl

K ; tE:E:I<A•B> l TZ

SATZJ173 :: ORAPPCLESSO(ApB),[Q(A,.S)•LESSEQ(A,C),. l•[TtLESSOCA•S>lT1•.2D173•<rJ"

LESSOU .c} : LESSOU ,c)

: KOftEOU rC)

: LESSOU "c)

: LESSOU •C>

KDREDU •C>

: MOREDU •Cl

: LESSEOf A•C>

LESSEQ[ A•C>

rr:Eo<A .. SJ nz·.zot73"'(f> > u:sstor t. .. c, TRLESSEO :: SATZ0173 : LESSEQ{ A .. Cl

C a [M:HJREQ{A#BJJ(N:HOREOCB .. CJl TRKO~EO := SATZD168B(C,.A.TRLESSEO<C•B•A•

SATZD168A(B,c .. nl,.SATZ0168ACA•B•HJl) MOREO<A .. Cl

s

s

s

s

- 4.11-

•IYZ)

•IVZD

A a RATD :: [T!NOHLEROUIJJJRAIRPtiH"Uff'!JtAB:>IHA1• SATZ0166E(A.TJ))

tRRAfD := NOURATi)(A)} 8 I [(:(Q(A.,BJl[R:RATO<AJl

R a [N:NJTCZERDJl TS :: TH3•l.IHP•(ZERD(A).,ZERO•N•

'PRDP• 'PROP'

[f: Z ERO<A> JE QZE~O( A•B•E• T J) NOH ZE~ OCU J T7 := EQPOERPCA9S0(AJ,SATZ0166ECA•T5),

ASSOCS )r SATZ'Ol66E(B, NJ.. EtUBSOCA .. B•EJ J : IS<FtPW PO U BSO{ AhSATZ016S EU .. T6J hRPOfPOC ABSDC Bh SATZDli 6E(B,N)))

T8 == ISPCCUr.cT:CUTJRAiRP(TJ.R?OfPD<ABSO(A) •SATZD166EtA,T&Jl•RPOfPO(ABSDCBJ• SATZ0166ECB.NJJ.<T6>R,T7J : RATRPC~PDFPOCA8SD(8).,SATZD166E<B•I)J)

R ; EQRATD := [T:NUT<ZERO<BJJlT8".IVZD•(TJ : RATDC SJ E 3 CI:I~tRATOCAJJ

E:liR'tlTO := TH3•L.IMP•(P.ATOCBJ•RATO(AJ•I• tT:P.ATD<BJJEQRATOC9 .. A•SYH(QCA•B•E),TJ) : IRRATOt 9)

A 3 tZ:ZE!HH U l RATl>I~ := THZ•L.R.I!tP•tNOHZERO<An,.

tT:NQT(ZEROCAJllRATRP<RPOfPDCABSD(A),. SATZ0166E(A,.T)}),.WELI<ZEROUhZ)) 'J RATDUJ

a [R:Cafl[t:IRJATRP(R)l[XO:~ATJ

XO ; [S:RATRPCPL( R .. RPOF'RT( XO))) ][ YO: RAT H J: IS<PLC R• RP!VRTCXO> J,.RPOF RHYOJ}] T9 :: TRISCCUT.PLCRPOFRTtXO>rR)r

PL(RrRPOfRT(XOJ),.RPOFRTCYO)., COHPl<RP~FRTtXO>•R),.J)

T10 := ISHORE1CPL<RPOFRTCXO),.R).,RPOFRTCY0)• RPOF'RTtXOJ,.f9,SATl133(RPOFRTCXOJ.RJ>

T11 := SATZ15~0CYO.xO,T10J J12 := SATZ155BCYO•XO•i11l

T13 :: SATZ140G( RPOfU( YOh RPOFRHXOJ..R,

lS<PLU POFRT< XO J,.RJ ,.RPOF'Rf (YO n

MORE<R" OFRTCYO> ,.RPOFRTCXOJ) : MORE•Rf •no • XO) : tS<RPOFRT(MN•RT•CYO,.XO•Tll))•MNCRPOfRT(YO),.RPOFRTCXOJ•

SATZ15~ A(YO,.XO .. T11J))

SATZ 154HYO,. xo, T 11 ), T9 > IS{q ,M'f CRPOFRT< YOJ,.RPOFRH X Oh SATZ15~A<YO,. )0,. T11 l l) TU

Tl5

XO a REMAqKl

R ; R? RN T17 f18

:= TRIS2<CUT,.RrRPOFRTCMN•RT•cyo,.xo,T11))• HNCRPDFRT<YO),R?Of'RT<XO), SATZ l5.fA<YO, XO. T11)),. Tl3,. Tt2 > IS<R•R" Of'RH H~·Rt•oo, XO, T 11))}

:: SOMEICRAf,[X:RATliS<R•RPOFRT(X)),. 1Uf"RT.,<YO,.XO .. T1U•T14) RATRPC't)

:: SDMEAPPCRAT,[X:RATJISCPLCR.RPOFRTCXG>> ,RPOFRT(XJ),.S.CON,[X:RATJ[T:IS<PLCR,. RPOfRT<XO>>•~POfRTCXlll<T15(X,.T>>I) : CON

:: [T:RATRPCPL<R.,RPOFRT<XOJ))J Tló .. • IV2D•<TJ

:: POOF'RPCR) : N.OOF'RP<Rl = POSO lRP< Rl

pr.;(')T O!H qp,. Tl 'I')

IRRATR~CPl<R•RPOfRTCXOJ))

OIF' Dif

: POSIHR" > NOH ZE~ OO~P))

s

s

.s - 4.12-

T19 (N:NOTtZEROCRPJJl T20

R ; TZl

tN:NJTtZEROCRN))]

:= NNOTOO<RNrNEGDIRPCR))

:: TRJSZCCUT•R• RPQrPO(ABSOCRPh SATZOlS6E(RP,NJ)rRPOFPO(RP•T17), tSRP?Cl<R>•EOPOERP(A8SOCRP>• SATZD16&E<RP~NJ,RPrTl7• ASSNN:)(Rf>•PNOJNO(RP• T17l J ))

:: TR!~{16SOCRNJrOFCSTOCRNJrSTMCRN))rRPr ASS~OCRN~~EGOIRPCR))•EOSMSO(STOCRN), ST~(R;)~PLCRrlRP)rlRP~

'STJIS<lRPrPLCRrlRP>l• STKISClRPrPltRrlRP)))}

NOTC ZE:te(RN))

ISUrR~~' Of PO< ABSO(RP hSATlD 166EtRPrN.J H

EO<ABS) <RNhRP>

TZ2 :: TRISZCCUT,RrRPOFPOtABSDtRN), SATZ0166ECRNrHJ)rRPOFPDlRP,T17)r ISRPPOlCR)rEOPDERPCABSO<RN), SAIZ01SIECRNr"),RP•T17rT21)J

R; [S:CUTl[I:IS(RrS)JtRR:RATR?CRll T23 :: IS~fCCfr{X:CUTlRATRPfXlrR~S•RR•I) RATRPCi J

RATRPU) I ; [RS:~ATRPCSJl

rz~ := ISP1<CUT.tX:CUTJRAfRPCX)•S•R•RS•l>

R ; CRR:RATRP<R>l REHU!(z,\

REMARK U REttnK3A

REMARK3B R ; [l:IRRATRP<R>l

REMUK4A

REMARKCtS REMUK5A

RE11A~K5B A ; ftiATD

UUNATO<A> l

:: (T:NOT<ZEROCPDOFRPCRll)] TZJ•.Ivzo•(RPDFPO<ABSOCPDOFRP(RJ)• SATZD16SE(P00fRP(RJrTJ),fZO·.zvzo•(tJ• RR} : RATO< PIJ OfRPCRU

:= f17•. IV2D• : POSO(P)DfRP(R)) : = [T HUlT< ZE ROCNCOf' RP (RH> 1

T23•.rvzo•CRPOFPOCABSOCNDGrRP(R)J• SATZD166E<NDDfRP(RJ.TJJ,T2Z•.IV2D•CT), RR> : RATOCN)OFRP(R))

:= NEGOIR!>CR) NEG!)(N)GfRP(R))

:: TH3•L.IMP•(RATD<PDOFRP<Rl)rRATRP(RJII• (T:RATOCPDOfRP(R)ll Tz~·.tvzo•(R?OfPOCABSO(PDCfRPCRJJ,

SATZ0166EtPOOfRP<R>•T18•.IVZO•))• rzo•.zvzo•tT18•.tvzo•)p<f18*.IV20•>TJ): IRRATMPOOFRP(RJ)

:: nr•.nzo• : f'OS!HPlOfRP<RH := T~3"L.IMP"(RATO<NDOF'RP<R>>·RATRP(R),l•

tT:RAfO<NOOFRP(~))J TZ~·.Ivzo•CRPOFPD<ABSDCNDOfRP{R)),. SATZ Dl SSE<NO OfRPC R>, T19,.. I.'/20 .. )) • TZZ ... !VZIJ•(f19 ... IVZO•J,.<T19 ... IVZO•>T )) : IRRAT()( NDOF'RP(R))

·- NE(<IHRP<R> ; Nf:GOOOOf'RP(R)) :: ANDCPOSO(Ab[TIPOSO(AJlNAfRP{RPOFPOCAr

J))) t?R~P•

HATPlSO := ANDEltPOSOCAl•[l:PQSOCA>l NATRP( RPC.F'PD (A,. T )). N)

NATDERP :: ANDEZ•t.R•(POSOCA)r(T:POSDCA>l

B ; CE:E~(ArBlltN:NATDCA)l

N•ftp• ; TZ5 (P:PCISO( 8) l TZ6

NATRP(RPCfPO(A~T)),Nl

POSO( AJ

P0$0(5)

s

-4.13.

-IV2)

N a (QHAT;)

a [X:NAT.l li'OOF!\IT

RPOFPOCA•NATPOSO(A,N,J.RPOFPO(BrP>• NAH>ERP<A•l'U,.T25)

:= ANOICPGSD(BJr[T:POSOCBJl NATRP( RPOF' PO (a,. T) ),. T ZS". I Vto•, tT:POS0(8JlT2ï•.zvzo•(~))

:= PDOFRPCRPOFNT(X))

X a U8 := POSDIRP<RPOF'NTUH (P:POSOCPJOFNTCX))J T29 := !SRPPDURPOFNTUH T30 :: EQPDERPCPDOFNHXlrT25oPDOFNHXJ,.Pr

Hl REFE Q{ PO Of NT C X) J )

·- TRISCCUT•RPOFNT{X),RPOFPO{POOFNTCX),. fl8),. RPOFPOC P!lOF NH X hPJ • T29• Tl:J l

;: ISPCCUT,.rT:CUTlNAT~PCTlrRPOFNT(X),. RPOFPOCPOOFNH lU ,p) •liATRPIUJo> T3U

: NATRPUPOFPD(S,.P))

NATOCBJ.

: OIF'

: POSO(PIJOFNTOCU

IS CR POF NHX hRPOFPOCPOOFNT <U" T28))

IS<RPIF POfPDOFMT< Xl • T2 8) .~POF PO C PO Of' NT<XJ,. P) J

lS(RPO~NT(X)•RPOFPD<POOFNT(X),.p))

t NATRP<~POrPDCPDOFNT<X),P))

s

•IV2) S

X a NATOI := Al\IDICPOSD(POOFNHUhi:i:POSO!PDOrNT<U' )JNATRP<RPOFPD<PDOFNT(X),.f)),. J2B•.IV2Q•,.[T:POSDCPOOfNTCX))J T32'".IV20'"HH : NATOCP)OFNHX))

A a INTO :: ORCZEROCAJ,HATDCASS!HAJ)) t •PR!JP 1

Ba tE:Ea<A•Bllti:INTO<A>l

I•RP• a tZ:lERDCAJl T33 ·- EQZEROU,.BrE•Z> : ZERIHB)

t•RP• a CN:NATO<ASSOCA))]

HIV20

T34 :2 EQNATDCABSDCA>,.ABSOCBJ,.EQABSOCA,.B•E>• NJ : NATO<A3 50(8))

I a EOINTD

A a {N:NAT!>CUl

T35

·- TH9Rl.OR'"CZERDCA>•NAT~<ABSD!A)), ZERO!Bl,NATD(ABSD>•I•tT:ZERO(A)l T33'".IV2C'"(f),[t:NATOCABSO(A))J J34•. IV20"tT))

:= SYKEO<ASSO(A),.A,I\IJSNHOtA,.PNCTNO (A,l\IATPOSD<A~N})))

•- EONATDCArABSD<AJrT34Arl\l)

N a 'iATUn := ORIZCZEROUlrNATOUSS!HU >. ns-.IV20 .. ) A a (P1POSD<A>lti:INTO(A)]

: INTOCS)

EQ CA" A8 SOCA) J NATO( A3 SOCA))

INfO( .U

s

$

$

- 4.14-

z•RP'" ; T3S := OREZfZEROCA>rNATOtABSO(A))rlr PNOTOO<A•P)) NATDUS SO(,A U

-IYU s

t OI 100SINTNATD := EQNATDCABSO(A)rA,ASSN~O(A,PNCTNOCArP)} ,rJr.•. Ivzo•J : NATO U)

A ; [Z:ZEROU>l INTOIO :a QRil<ZERO(AJrNATOCABSD(A)),zJ INTO<AJ

R ; OI:NHRP<R)}

H·IVZl s

N•RP" ; TlT ·- POSOIRP<R> : PDSD(Pl OF"RP(ft)) CP:PDSOCPOOfRP(RJJl T38 :a TRISCCUirRrRPOFPD<PDOfRP(R),f37)r

RPOfPO(POOfRPCRJrPlriSP.PPDl<R>• EC~OEP.PC?DOfRPCR>•T37rPODfRPCR),p,

REFEQCPDOFRPCRllJJ ISCRrR,OFPOCPDOFRP!R>,PJ) T39 == ISPCCUT,(T:ClTJNATRPCTJrRr

RPOfPOCP00FRP!R),p},~.T38) NATRPCRPDFPOfPOOfRPCRJrP)a

-IVZJ s

N ; REPWf't6A := A,.OI (POS!)( PO OF RP<R>) • ( T:POSDC PDCfRPC R) ) lNA TRP<Rf'Of PO<PDDFR?(Rh T > ),. T37•.rvzo•,[J:POSDt~OOFRPCP.lJl

TJ9•.xvzo·n H : NATDCP,OFRPCR)) REMAU6 := NATINTD<POOFRP<R>rREMARK6A) : INTI)(P) OfRP<R))

uiVZD s

N•RP• ; HO ·- ABSDEOL<1RP.Pl<R•lRP), ISLESSZ<PL<1RP•Rl•PL<R•1RP>•1RP• COHPL<1RP.R),SATZ133A(1RP,R))) : EO<ABS) (NOOrRP( In h PODf"RP( RJ)

T41 == EQNATO<POOFRP(Rl•ASSD<~OOFRP(R)J, SYMEQCABSOCNOOFRP(R>i•PDOFRPCR),T~O>• REKARKGAl NATO< AB SD<NOOFRP(R) U

-IV2) s N a RE: HA~lC7 == DRIZCZERO<NOOFRPCR}),

NATOCABSDCNOOfR?CRJ)),T41•.IV20"') INTD( Nl !JfRP (RH A ; CI:INTDU> l

•20174 s

[N:N~T<ZEROCA))l

Tl :a OREZ<ZEROCA),NATOCABSOCA>>•I•N> : NATDC A3 SD<A) > T2 := ANOE:2CPOS0tAlSOCA}),(T:POSDIABSDCA)Jl

NATRP<RPCFPOCASSO(A),f}),T1l : (T:POSlCABSOCAJllNATRPCRPDFPDCABSO(A),TJl Tl := LEKHAIIISCRPOFPDCASSO(A),

SATZD166ECArNJ)•<SATZ01G&E<A•N)>lZ) RATRP(tPOrPO<ABSO(AJrSATZ0166ECA .. Nll)

•20174 s

SATZJ1T4 := tT:NOTCZERO\AlJlTl~.zo174"(i) RAT:> U) 8 ; PO == 0f(Pl<lAr1B>~PLC21•29JJ !HF - 4.15-

82 ~ P012 ·- ISSKSDCPL(STHtDFCA!.AZlJ*ST"CDF<Bl•BZJ )}rPl(Sl0(0f(Al•A2}},Sf0(0f(Bl•B2)~),

PL<A1.Bll•PlCAZ•B2), ISPL12(SfM(0F(Al•A2))rAlrSTM(0f(8l•BZJ ) •91• ST I-: I SCA 1• AZ hST lU SC 8 1•62) h

+IV 3!)

•IV3l

•IV 3D

ISPllZ{SI~(UFtAl;AZ>l•AZ•Sf~(DrtBl~BZJ

),gz,STJ!SC~1•AZ>•STOIStSJ•B2>>J .: ts-t•<)If•PDtOF(Al•AZJ•Df(Bl•BZlJ•OfCPL(Al•Bll• Pl. U 2 ,3 2)))

R2 a POl := ISS~SO<PL!lA•5TM(Or<Rl•RZ>l), PL(2AoS!O<OFtRl•R2Jll•PL(lA•Rl>• PLC2A·R2>•ISPLICSTKCOFCR1~R2Jl•R1•1A, STMISCRl•«2>)•lSPL2(SfD(OflRl•R21J•R2• 2A•STOIS<Rl•R2J)) : IS~E•()lf•POCA•Df<R1•R2J>•Of(PLClA•Rl>•Pl(2A•R2lJl

PD2 := ISSMSD~~l<STMtCfCRl,R2)),1A}, PLCSTDCDF[ql,R2JJ,2Al.PL<R1•1AJ• PI.<R2•2Al•ISPL1CSi~CDF<R1•R2)J,R1•1Ar STMIS{~l•R2>~•ISPL1(Sf0{0f(Rl•R2)),R2• 2A,STOIS<Rl,R2>>J : IS•t•<J IF ,p D< Of< Rh RZJ •Ah Dr< Pl< R 1.o Uh Fl< F2•2-'>) ~

az a ?il(Ol2A :a REFEQ1(Fnt0f(A1•A2l•OF(31•BZ>J• Of<PL{A1~31),pt<A2•82))rPD12) : EQCPOU f<Al .. AZhDfUt. 82 H ,.Of( PU Al .. BI l•Pl U2 .. 82l} >

POE01ZB == REF"E QZ(P!HDf U hAZ >•IJFC81 .. BZ) h OFCPLCA1~3ll•PL(A2•82)J•PD12) : E~<OFt•t<Al•B1>,PL<AZ•BZJ),pQ(0f(A1,A2J,Df<B1•B2JJJ

R2 a POE UA ·- REFEQ1(P0(l,OF\Rl,R2J> .. OF<Pl!1A,R1>• Pl( ZA, R2 n •POl> EO<POCA.OfCRl,.a2>J .. OFCPL<1A~RtJ .. PL<2A.RZJ)l

PDEQ18 :: REF'EQ2 {P!HA, OH Rl• R2 > >•Cf<PU lA• Rl ).o

PL<ZA•RZH•Pvll EQ(I)f(:t l( 1A •Rl hPL< ZA• RZJ> •PO( A•Df< R l•liZ)} J PDE:I~A == REFE01CP0(0Ft~1.R2),A),OfCPltR1.1AJ•

PURZ .. UH.POZ> EQCPOClF(Rl•R21rAJ,OfCPL<~1.1A),pL(R2,2AJ)J

PDEQZB := REfEgzCPOCDF<Rl•R2J•AJ•OfCPl(R1r1A)• PL<RZ.ZAH.P02) [Q(~fC7 l(Rl.lAJ,Pl<RZ,2AJJ,P0(0fCR1,R2J•AJJ

a a SATZlH75 :: EOS~SO(PL(l~.tBJ•PLCZA,zBJ,PL<lB•lA), PLC23•2Al•COMPlClA•lBJ,COMPL<ZA;26)) EQCPD<A;8JrPOCB~A>J

COKPl := SATZD175 EQCPOC~ rBh PD<B;A)) c ; tE:E:l<A•B))

T1 := TR3IS<CUT•Pl(PlClA•1C)~PlCZB•ZCJ), PLCPl(1A•2Ö)•PLC1C•2CJJ~PLCPl(l9•2A); PL(tC.ZCl1•PlCPL<lS•lC)~PLC2A•ZCJ)•

4PL23C1A•1C•2B•2C>•ISPL1(PL<1A•ZBJ• Pt<1B•ZA>•Plt1C•ZC>•E>• 4PLZ3<1B•ZA•lC•ZCJ> ISCPLC•lC1A•lCJ•PL<2SrZC>>•PlCPLC18•1CJ•PL<2A•ZC>)J

EQP01 :• EOI1ZCPL<1A•lCJ,PL(ZA•ZC>•PLC1B•lC)~ PLCZa"zo,n•.IV30,.) : EQCPO(A,.C)"pQ(S,C))

EQPOZ :: TR3EQCPO<C•A>•PD(A•C> .. POC8;C),pi)(C;8)• CGHPOCC, A hE QPO l•CilMPO ( e, C} J EQ(P OC!: "Ah PO< C • B))

0 ; CE:E~CA"B)l[F;EQ<C•D>l EQPDlZ t: TREQCP0<A•C>•POC9•C>•POCB .. OJ ..

8 ; rz:ZEROCAJ J

Z a TZ

Z ; P!>Ol

EQPDlCA•B•C•EJ.EQP~ZfC•D•B•Fl> : EQt~O(,,C>•PD<BrOJ>

:• TR4ISCCUT-PL<PLC!A~1B>•ZBJ~ PU u,. PU 18• ZB>) .pt( ZA ,PLCZ\3.18) h PLCPL<ZA•ZBl•lBJ•PL{lSrPL<ZArZBJ>• ASSPllllArlB.2B>riSPL12t1Ar2A~ PlClB•2SlrFl(28•1B)•Z•CDMPL(lS•281), ASSPLZ{ 21.• ZB ,1 8 ),COY.?L {PL <2A • ZB>, 16)}

s

I

- 4.16-

s

B a [l:ZERDCBJJ P002 :: TREO<PO<ArB!rPO<BrAlrA•COMPOCA.Blr

PO:>U9rArZH EQ(PO U.rB hU B :1 (PtP3S3<AJ][Q:PGSOCBJl

PPD :: POSDI<PLClA, 1BJrPL<ZA .. 2BJ,. SATZ131(1Ar2Ar1B•2BrP,.QJJ POSD<Pl<ArBll

B a [H:MEGDCA>ltO:NEGD<BJl tlPD :: NEtiD !(PLU Ar l.BJ • PL<ZA• ZB h

SATZ131A(l~r2Ar1BrZS,Nr0J) NEGD<PJ UrB H A a 'I)!) ::: CfCZArlA) Olf'

AZ :1 KlOE:lA == EOSMS0{ST0(0f(AlrA2l)rSTM<OF(AlrAZJJ,. AZ•A lr STO 1 S{At,A 2>~ S TMIS <At,.AZ)) EQCMODC OfCA1rAZ))rDfUZrA1 JJ

HOOE:IB :: SYHEQCHOD<Df'<A1•A2JJ,.Qf(A2rAl>•MODEQA) EQ(i)f U 2r Al ) r HOD ( DfU1rA2l)) s a CE:EQ<A,.S>l

H•IV3:l s

E a T3 := TR3ISCCUTrPL<2ArlBJrPL<1Br2AJr PLC1Ar2BlrPL<2BrlAJ•CDMPLC2ArlBlr SYMEQCArSrEJrCOHPL<lArZS)J I SCPL <2 ArlB h•PU 28, lA) l

•Iv.n s

E a EQMI)O ::: EOI12(2A .. lAr28,1BrT3••IV30•) EQtMOOC AhMOD< BJ) A :3 [?:POSDU> J

SATlll16A :: ~EGOIC2Ar1A.SATZ121<1Ar2A,PJ) : Nt:G!H H' D (A)) A ; [Z:Z!::RIJ(A))

SATZD1768 == ZEROI(2Ar1ArSYMIS(CUT,lA.ZA.ZJ) t ZERD< Hl 0( U J A ; tNH~EG!H.Ul

SATZ!ll16C ; .. PDSDICZArlArSATZlZZ<lArZArNJ> PDSO< H3 D< AJ 1 A ; {I'H NEGOCM00(A))}

SUZJ116D ·- SATZ122(2ArlAriSLESS1Z<STMCMODCAJ)r2Ar ST0CKOOCAl)rlA,STHISC2A•1AJr STOIS(2ArlAJrN)) : POSO< A)

A a tZ:ZERDCMOOCA))J SATZJlTiiE := SYMI S<CUT, 2A, lA• TR3I S<CUT,. 2Ar

STMCOfC2Ar1A)JrSTDC0f(2ArlA)),.1Ar ISSTHC2Ar1AJrZrSTDISC2Ar1A))) : ZERO U)

A ; tP:PlSOCH30(A))} SATZ:J176r := SATZ 12H2A .. 1Ar IS MORE 12<STHCMODCA JhZA"

STO(MOOCA>>•lArST~IS<ZArlAl• STOIS<2Ar1AJrP)) : NEGO( At

A a CZ:lERIHU 1 HOOO ::: ZEROEQ(H00(A)rA•SATZ0116B(ArZ),ZJ EGOlOOt AhA)

•3l>117 s

A a n :: TRISCOIFrMOD(MODCA)JrOFClA•ZA>rAr ISSHSO<STD<MOCCA)),SfH(HODCA>Jr1Ar2A• STOl S( 2Ar1A},. ST!'! IS< ZA' lA) hOFI SU) 1 IS"'E•O If .. H OOOIOD< Uh U

-30171 s

A ; SATZ)171 -== REFEQl(H00CK00(A)),ArT1".30117"J : EQ(HOOt MOO<AUrA~ SATZ0117A := SY~EOCM00(~00CA>J•A•SATZ0177' EIHA• H:J 001000)))

a a tE:E:ICAr'!30CSJ>l SATZJ117S == TREQO!OfHA h MOOOIOO<El )JrBr - 4.17-

EQMODC A• MQO( B) ,E), SA TZD 1 TH 8 lJ · EQ(K00( AhB) SATZ3171C ·- SYHEO<HOOCAJ~C•SATZ0117SJ ECHB•H)û(A))

s a [E:EH lfOD< A>.rB JJ SATZD1710 == SA1ZD177C<B•A•SYH(Q(MOOCA>rB•EJ) : EiHAr HO OCSJ} SATZi>17TE . - SY~!î o'.: ~" :~c·~ !B ''sAr zn 1770, [;)('fOOI: Bh A)

+30178 s

" ., tP:PlSDU> l Tl := TR3E QU!! SI> 011)0<4}); KOiH 1'.00 <Al hA;

ABSD(A>eASSNO{M00(A),SATZ017&Ä(A;PJ); SATZ0177<AlrSYMEQ(A85D<A>•A• ABSNNaCA.PNàTNOCA;P)))} : EQ(ABSl<HOD<A>>•ABSU(A))

A ~ tZ:ZEROU) 1 T2 := TRJEC<ASSO<MO~<AJJ;HOD(A)rA•ABSO(A),.

AaSN~D{HQ){A)rONOTNO<MO~{A},

SATZD1763CA•Z>l)r~000(A,z>,. SYH~Q(ABSOCAJ,A,A3SNNO(A,ONOTNO(A,zJ)) ) : EQUBS) <MOO( Al), ABSO( A))

A ; [N:HEGOU>l T3 == TREQ(ABSOCKOO(A>>•MOO<A>•ABSDCAJ,

ASSNNOC~O~(A),PNCT~J(~OOCA),

SATZ0176C(A;N))l•SYMEOCASSOCA)•HODCA>• ASSNO<A, N))) EQCABSl(MOD<A));ABSCCAJJ

-3a178 s

A a SATZ0178 := RAPPDCA;EQCABSOCMOD(A));ABSD(AJ>• [T:POSO<A>lT1•.30178•(T),(l:ZERO(A)l rz•.30ir8•tT>•tT:NEGOtAJlT3•.30176•(TJ ) : EQ(ABSJ<MOO(A)J,ABSD(A)l

SATZD178A == SYMEO<ABSO(MOOCA)J;ASSD<Al,SATl0178) EQ<ABSIJ (A), ASSDO!OOUJ))

+30179 s

Tl :: POEQ lBU,zA,lU : EO<Or<" l< 1A ,zA) ,pl( 2A.o lA)) •PO< A;JUll)( U)) TZ :: ZEROI<PL<1A.ZAJ,PLCZA.1AJ.oCOHPL(1A .. 2A)

) : ZE~OC D=' CPL( 1A•2A hPl<2A.ol\)))

-3!)179 s

SATZD179 := EVZER0(0f(PLC1A,ZAJ.oPl(2A,.1A)), PO(A,MOOCAJ);Tl•.J0179•.oT2•.3C179•) ZE:RIHPJ u .. KOO<A)JJ

SATZD179A ·- EQZEROCPO(A,.KOO{AJJ,pO(KOD(AJ•A>• CCMPOCA-H00(A}),.SATZD179) : ZERDCPJ(HOO<AJ•AJ)

s a SATZ\ll8D := TREQCMOO(PO(A.oBJ),OFCPL<ZA.oZBl.o Pt<1A .. 18)J.oPDtHOO!Al.oM00(8}); MOCEQA(Pl<lA.olS>•PLCZA,zB>>• ?OE012B<ZA.olA,zB,1BJJ : EQCHOOCPO<A•B)l,POC~OO<AJ.oHOO(Bll)

SHZ!>l!J:lA ::: SYMEQ(MOOCPO(ArSJ),pQ(MOOCA>•HOD<SJ), SHZ018!> J EO<PD(~OOtAJ,KODCS)J.MCDCPO(A~BJ))

MD := POC A; 1":00(8)) : OIF' BZ a MDEQlZA := TRtO<MOt0f(Alr~ZJ~DfCB1•32)l,

POCDF<Al•AZ),QF(SZ•BlJ)•OFCFLCAl,BZ)• Pl<A z,. B 1J hE QPOZ OSOO <Of <91 .. 82) ), OFCBZ~B1J,OFCA1•1ZJ,.HODEQA<81•B2l)• POEQlZA< Al•A z.,g:f,B U) : EO<MO(,f(Al .. A2J,Of<B1•8Z)),.OFCPlCAlr82),.p((AZ•Bl>JJ

MOE OI ZB ::: SYMEQCMD(0f(Al,,ZJ,.~FCS1,62)),. D~CPL<Al.o&ZJrPtCAZo3l)),.MOE01ZAl ; EQ{Qf(~L<Al .. S2J .. PLCA2oBlJJ,MDCDftAl•AZJ,Of<B1•92JJ)

RZ a MOEQU :: TREQ(M0(A,QFC~l•P.Z)),p~cA~OFCR2•R1lJ• DH PU lA,. RZ), f'U ZA r iU) h - 4.18 EQP02(H00CO~CRl•R2)),QF{RZ•RlJoA~

MODECA(RhR~ }),PDF.:Q!AC~•fl-Z•Rl }) EQCM0{~,DFCRl,R2>J•DF<Pl(lA•R2>•PLC2'•Rl1J) MOEQla :: SYHE QCMO (A,.QF< R! •R2) )• Jf' <PL <1 A rRZ),.

PLI2A•Rl))•MOEOJA) EOCOF<'" l< lA •R2h PU2A, lU)) ;KOC JI,Df'CR!.R2> n HOE'lZA :: POEOlZACR!.RZ,zA,lA) : EQ<MDrlFCRl·R2),.~),QFCPL(~1•2AlrPlCR2•14)Jl

"!DEO ZB ·- POE!l129( ru •RZ• 2A •lA) : Et:{IJft=''l<Rt .. UhPLCR2o1.lH .HOCI)f(IU,R2hAl 1

c ; CE:EHArB) J EQKOl :: EO~Ol(ArSrMOOCCJ~El : EQCKDC,,C>•HO<B-ClJ EQMOZ :: E~POZCHOO(A),.HOOCBJ,c,.EQKOO<ArB,EJJ EIHMOC: ,Ah11DfCrE))

0 ; (E:E~CA•BJJtF:EQ(C•D>l EQMOU == TREO<HO(ArC),H0(8,C},M0CS,O),

EQMOl(A•B•C•EJ.EOMD2<C,D-B~F)J : EQ(ItO(,•Cl~HDUhO)) 9 a SATZi>lS1 := TR3EQ(MOO!H0(A,BJJ,PO(MQO(A),

~OOCHOOCB>>>•PO(M00(A),9)•MD(8,A)r SATZ0180(A,MOO<Bl}•EQPJZCK00(M00(8)), 9.~00(A)r5Ail0177{8));CaMP0(M00(~),9)) EQCMODC~OCAr8)),~0(B•A>>

SATZ:l13U := S YKE -Q( !40()( MO (S,A) ), MO C.A ,a) • SATZ0181CB•A)) EO<MD<~•B>•MOD(HO<B,A>>>

•30182 s

Tl := TREQCMO(A,Bl•DFCPl(1A•2B),PLC2A•1B)); ;)>CPL<14,2B)•PL{l3•2AlJ• POEQ1A<A•lBrlBlrEQS0(PLC1Ar2S)r PLC2A•1Bl•PLC1Br2AJ,COMPLI2A~1B)J) EQ(~0(Ar8l•Of(PL<1A•2B)rPL<1BrZAJ}}

rz :::. SYH~Q(KOCA,BJ,Of<PL(!A,2BJrPL<19r2A}), TU : EO<OFt,L<1A•2Bl•PLC18•2A)J,~OCArBlJ

r:s :: STHI S{ PL <tA, 28 h PLu a, 2A l) IS{STHC Of(Pl< 1A•2ln ,pL( lS• 2AJ J J ,pL( H, a)) Tlt := STDISCPL<1A•2BJ•PL(19•2All IS<STOt0f(Pl<1A•2El•PLC1BrZAJ)),pl(1B,2Al)

•3'182 s

(P:PDSDCKO(ArB)ll

H3D182 s

P a rs :·= EQPOSO<HO<A•BlrOFCPL<lA•ZBlrPL<1B•2AJ) ,.rt.P> P::ISDC OrtPl( 1A•2B hPlU a,z, U)

•30182 s

P ;a SATZ3182A := ISHDRE12<STH(Of<PL<lA•2BlrPL{18rZA)))• PlC1A.28)rSTOCOF<PLClA•2B)rPL<1B•ZA))) rPL(1Br2A>•T3".30182••t4•.3D182•• T5ft.30132"J HOREOU •B>

B a tZ:ZERDCHD(ArBJJl

H3018Z s

z a r& := EQZEROCHDCA,BJ,OfCPl<lA,zB>•PL<lBrZA}) .n.n lf:RO(Or CPL( lA•ZBJ•PUl BrZA )))

-30182 s

Z iJ SATZ:>lSZB ·- TR3ISCCUT,PLC1A,ZB>rSTMCDF<PLC1Ar2B), PLC16•2A))),STOCDFCPLC1A.ZSJ,PL(19,2A> ))~PL<lB•ZA>•ISSTHCPl<1Ar2B>•Pl(15•2A> ),TS".30162",T4".30182*) EO <A, Bl

B iJ [N:NEGO<HD(ArB))]

H3!)182 s

N iJ T7 ::: EONE~D{HD<A•B),Or(?l(tA .. 28>,Pl<lB•ZAJJ - 4.19 ,Tt,NJ NEGDCOF<PL< UrZBHPUlB,z' )))

•3i>l52 s

N ~ SA'I'Z!llS2C ::: ISlESS1Z:SiKCCf<Pl(1A.ZB),PLtlSr2A)})•

•3C1!!Z

•3&1!!

+30133

•30133

8 ; tM:MORED<A~B)l

H ~ TS

1t ; SATZJUZO

6; tE:E~CA.oBll

E ;~ T9

E a SATD18ZE

B ; tt:LESSDCA.oB)l

L ; HO

l a SA TZ:>le ZF

a ; u

B ; tM:HOREOCA.oB>l SATZJ183A

8 ; tE:E:ItA•B>l STAZ183B

B ; CLtLESSDCA.oB)J SATZ0163C

TT•. 31Jl62'")

:= EOPOSO<OF<PLttA.ZBl.oPL<lB.oZA)).oMO<A.oB) ,rz-.3otaz•.ra•.3otsz•>

: = EOZ(ROCOH PU lA• ZB),. Ft( 18 ,.ZA) );MD (A,. B) .. rz·. 3~taz· .. T9 ... 3:Haz· >

:= EONEGD<DfCPLt1ArZB).oPLC1B,2A)).oHO<A#B>

: POS!lOt> <A..B))

ZER:JOD u~a))

,.rz•.Jotaz· .. no-.3:.naz·l : NEGD<MJ u~s"

:= TRiSCCUT .. Pl<lA,.2à>.oPlC2B.o1A}, Pl<STMCM00{8)l•Si0(M00(A))).o COMPL{lA,.ZS>•l2ISSHSO<ZB.olB.oZA.olA))

:= TU!hA>

:= ISLESS12tPLC1B.oZA>•PL<STHCMOO<A>>~ STOCMOO{B)J),Pl<1A~2B>~PL<STMCHOOCB)), STOCMODCA))lrT2~.30183•rT1".3018l".o

: IS(PL<1 A.o2B hPLC STMCM00(8) hSTOO!OD< Al))) IS(PLtlB.o2A).oPL(STMCMOOCAJ),STO(M00(8)))}

lE!iHAOSCA,B.o H) > : LESSDnOOU ),.MQO(Bl)

:= EOMOO<ArBrEl : EOCMQO[ AlrMCDCBll

·- ISMOREltCPLClBrZAJrPL<STMCMOOlAJJ.o STOtHODtB)ll•PLClAr2B)rPLCSTHCH00(8)), STO<MOO(AJJJ,i2".30183"rT1~.30183", lEHHAD&!ArBrLll MOREO<~OD(A)rMODCBll

B a Ct:LESSD<KOD(Al.oMOOCBlll SAT!l183D :: E~HO~En12CK0C(M00(A)}rArMODCM0~(3)).o8.o

SATZD177(Al~SATZal77(9lr

St\TZ !H33CO~ODO h·!o!OiH e > ,l H : IU!aED U .. a' B a [E:E~<HOD<AlrMODCBJJl

SATZ3l83E := TR3EC(~.oMOCC~00(.\)),MOOCKOOCB>lrBr SATZ01r7AtAlr~~~~J(M00(A),~00!SlrElr SATZD177<3H

s

s

s

s

s

. s

- 4. 20-

B a {H:HGREDCMOO<A>-HOD>J SATZ0183F .~ EQLESSD12CKODCHOO<A>>•A•XOO<HOD>•B*

A a Tl

T2

T3

A a SATZD1S4

C a ASSPOl

ASSP02

3P023

0 :il ~P023

B :il POMO

M:>PO

0 41 SATZJ1!35

SATZD177CAJ*SATZD177C9>• SATZ0183ACHOO<A)oMOO<B),H))

:= TR3EQCAoOf<PL<lA•PL<lP.P.!RP>>• PLC2A.PL(1RPolRPJ)),Q~(?LCPL<1A*1RP), lRP~oPLClRPoPLCZA•lRP))l,MOCPDOfRP{lA)

.POOFRPC2A>>•LEHMA03CA.PLC1RPolRPllr EQSKSOCPl(lAoPLC!RPolRP>>• PLC2AoPL<lRP*lRPlloPLCPLC1AolRPlolRPl* PL<lRPoPl(2A•lR?l)oASSPl2(1AolRP•lRPlo 3PL12C2A.lRP.lRP>l•HOEQ12B<PL<lAolRP>* 1RP•PL(2AolRPlolP.P>>

:= AH03IC?CSO(P90FRPC1A>>•POSOCPOOFRPC2A) )o(Q(AoM~(POOFRP<lA),PQOfRPC2A}l)•

POSDI~P<lAJoPOSJIRPC2AloT1>

:= SOME!<DIFoCX:OIFlAND3<?0SOCPDOfRPC1All oPOSC{X)o~O(A~MO<PDOFR?ClA>oX))),

PDOFRPCZA>•TZ>

·- SOMEI<OIFo[X:DiflSOME•t•<Oif,[Y:Oifl AND3<POSOCX1oPOSD<Y>oEQ(Ao~O(XoY1)))*

LESSOU -B>

EO< Ao 14) CPDO FRPC 1 A>* PDOFRP< 2A)))

AN03(PJSD<POOFRP(lA))*POSD<POOFRPC2A))o (Q(A* M:l CPDO fRP( lA>- POOFRP< ZA))))

SO~E·L•<Dif-CX:OIFlAND3<PJSOCPOOFRP<1Al),PCSDCX>• EQ<A,KJ CPDOnPC lA),X))))

POOFRPC1A),T3w.30184w) : SO"E•t•<DIFo[X:OIFJSOME•t•<DIF,[Y:OIFJAN03CPOSD<XJ,

·- TR3EC<POCPO{A,Bl,CloDF<PL<PL<1A,lB>• 1C>,PL<PL<ZA,zB>•2Cl>• OF<PL<lA•PL(lB,lCl),PL<2A,PL<2Bo2C>>>• POCAoPD<B•C))oPOEQZACCoPL<lAolB>• PU ZA, ZB J J.E QSKSD< PUPU lA .1 B J.lC), Pl<PLC2A,2B>-2C>oPL(1~•PLClB•lC))o PL<2AoPL<2B,2C)),ASSPC1ClA,lBolCl• ASSPL1<2A•28•2C>J,PDEQ18(A•PL<lB•lC)•

POSDC Y) ,(Q( A,I!O(X,y ))) >>

PU Zfl, 2C > >) EIHPO(:t OCA* BloC> ,PO CAo PD<B•C>)) •- SYHEQCPO(POCA•9l•C>oPDCA*PD<B•C)),

ASSPOl) EQ<PD(A,POCBoCJ),pQ(PO<A•B>•C>) :: TR3EQ<PD<PC<A-BloC},PDCAoPOC9.C)),

PDCA,POCC,B>>•PDCPO<A-CJ,B), ASS?Dl(A,B,CJ,EQPOZCPDCBoC)oPO(C,B>•~• COH?D<BoC>l•ASSPD2<A•C•B>l (Q(PO(:tQ(A•BloCJ,PDCPD<A•C>•Bl)

:: TR3E !H PO <PO o, B loPO (C, 0) ), PDCPDCPOCA•B>•C>•D>oPDCPD<PD<AoCl*9)o O>•PD<PO(A,c>-PO(B,OJ)oASSP02(POCA,B>• c,Q),EQPD!<PDCPD<A•B>-Cl•POCPO<A•C>•B> oOo3P023JoASSP01<POCA.C)o6~0)) : (Q(PO<'O<A,BJ,PO(C,O)),PDCPO(A,C),pQ(B,Ol))

:= TREQCPOCMOCA•B>•S>•PDt~oPO<HOD-B>>• A.ASSPOl<A•MOO•B>•P002CArPO<M00{8)• BJ.SATZ0179ACB))) EQCPOO! O(A, BJoB>.A>

:: TREQ(MOCPOCAoB)oSlrPO<A•PD(BoHOOCB))), A.ASSPOl(A,SoHOOCB>), PD02CA•POCBoHOOCBl>•SATZ017fC8l)) EOC~0('0<A•Bl•9>•~>

:= TREQ<POCMO<A•B>•HDCCoDllrPOCPO(A,C), PDCMODCB>•HCOCD>>>·M~CPD<AoCJoPDCB•D>> ,4P023<A,HOOCB>oCoMOOC0}}, EQP02CPO<~OJC6>•KODC~l},M00(PO(Br0)),

PO<.~.c >• 5A il0180t.C3• :J) I i E~<PO(II O<A, SloHO<C .. O»rHOC PO<A .. CloPOCB•Dl l l

s

s

- 4.21.

-30138

-30188

H31)1!J8

-30188

U·3:J188

-30188

H31)166

•3ilU6

ç ; SATZJ18ó := ASSPOl !3 ; SATZIH87 A :: TP[Q(?0(8PMJ(A.S)JPP~[M0(A•B)r8);A•

COMPO(B,~O<A,Sl!.POKO)

tX:DIFl[E:EOCPD<B•XJ•A>l SATZ3167C t= TREQ<HD<A•B>•M~(PJ<X•BJ•B)•X•

SATZJ1570 X; CE:E~<~D<X.~),A>l

SATZ0167E.

SATZ0187F

c a u

T2

H ; T3

E~H01(A,?OCX.Sl•3•TREQ1<~•POCX,Bl• PO(B•X>•E•CCM?~C9.X))),~OPO<X•SlJ

:: SYMEQ(!iOU.Sl•X,SHZOleTCl

:e SAT10187CtTREQ(?~<S•Y.>•PO(X•B)rA• COM?C<a.XhE >)

:= SYMEC<MD!A,g>,X•S4TZ0187EJ

:: TR3E~(HO<P~(A,Cl•PJ(B•C)),pQ(P0(ArC)r POCM00(S),M00(C)]),P0(H0{A,Bl•HD(C,Cl} •HO<A•S>•EQPC2C~O~<POtB•C>>•PD<MODC8l• H00( C > h PO U .• c ), SA HO l6lHB, C >), 4P023<A•C•MOD(B)•~GDIC)),pQQ2CH0(A,B)• KD(C"C)•SATZ0179(Cll}

::: SY~EQ( ~OCPD< A. .. CJ .P:HS•C) J,MoU.B h Tl)

·- EQPOSO(HO(PO<A•CJ,PDCB•C>JrKD<A•B)#Tl* SATZ016ZDCPOtA.CJ,PDCB,CJ.Kl)

H ; SATZ3159A := SATZD132A(A,a.T3~.30188") Ca [E:EQ<PO(A.C),PO<BrC>>l

Eau :: EOZEROCHOCPDCA•C>•PD<B•C)),MO(A•BJ•Tl•

EQCP 0<3, HOC A• Bl > •AJ

t EQC'4DU~BhXJ EQOC,'4) CA .. I'! U

EQ(MOc.\,.BhlO EO<X•H) (A,.B>l

EO<MCP DU, Ct.PD<B• CH .HO( A,S)) EOt~OtA.B>•HDCPOC~•C>•P0<9•C>>>

f'DSD013 U.oB))

SATZ0162(( PIHA.c ), POCB,c ),EJ J : ZERDUG (A,B))

E Cl S'TZ0188B := SATZD182B<4•B•T4·.3~188•J C Cl tt:LESSDCPO(A,CJ,POCB.C>Jl

L a rs

l Cl SATZll86C C Cl tH:M~REOCA•B~J

H a T&

:= EQNÈGD<MDCPO(A,CJ,PD(B,C>>•H0(4•B),Tl• SATZ0162ffPOtA.C);PD<S,C)•L))

:= S.\Tl018.2CU~a.rs•.30l~8"l

:: (!;}!"OSDC HO<A• SJ .~O<~O CA.•C l ~PDCI.hC) h TZ ~ SATZ01820(A~8,~)1

rou~e,

LESSOCA rB}

s

s

s

s

s

s

s

- 4.22-s

s

+*3Jl88

-30158

~ 2 SATZJU80 C ; CE:E::I<ArBll

SATZI)168E C a {l:LESSOCArBJl

!10REOC" OtA~ ChPOCB;C))

·- EONEGOtHOCA,9),~0(PO<A~c>~POCB,C))~T2; SATZ 0182H 4, s,u) : NEG:l01) (POCA ... ChPOt s .. c)))

L ~ SUZ::l1!3!!F' :: SATZD18ZCCPO(A,.ChPOt!3...ChT7•.3D188") : LESSOC~OU,.ChPOCS,.C)) C a CM:HJ~ED<~D(C,.A>•POtC•B>ll

SATZD138G := SATZD168aCEQ~OREÖ12CPO(C;A),.pQtA ... C>• PDtC .. SJrPD<B•C),COMPO!C ... AJ;COMPO(CrB),. MH HOREDU,. B l

Ca CE:E~(PO(C,AJ,PD(C,.B))J SA TZOl38 H := SA TZ0166SCTR 3E lH PO (A,C >,PO {C,. A),.

POCCo3),P~ca .. CJ•CDKPO(A•CJ,[, tOio!P:Hc .. ~nl EQU.d3J

[LtLESSDCPO<C•A>,PO(C;3))~

SATZD168J := SATZ0188CCE~LESS012<POCC ... AJ,POCA;C)" PDCC.3JoPD<S•C);COMPOCC;A) ... C0MPD(C,Bl,. l)) lESSD(A.OB)

C ; [H:MJ~EO(A,Sll

SATZiJ13SK

C a n::E:HA .. B)]

:= EQKOREDlZ<PD u ... c hPO (C,.A ),PDCB .. C .h POCC•B>~ÇJMPO<A•C>,COMP0!8 ... C), SATZ0188000 J

SATZ~1,6l := EOPOZCA .. s,C,[) C ; (L:LESSOCA.B)l

SATZ0188K := EOLESS012CPOCA.C>•PD(C;A),p0(8,C), PDCC.B),CO~PO(A,CJ.CDMPO• SATlD1S8Hll >

D ól tE:EIHA .. BJHM:MOREOCC,O)} SATZD188N ;: E~NORE02CPOCA•D>,p~(B,O),p0(A,.CJ,

EQPO U A .. a~ o~ E) rSAT l0188K cc,o, A, !4)}

SATZD1880 :: EOHOREOlZ<PD<A ... CJ ... PD<C~A>•PO<B,.O)..,

E ; rt:ttssocc .. o>J

PDCO .. B)rCOMPOCA .. cJ .. COKPO(B,O)• SATlD188H)

SATZ0198P := EOLESSOZ<P~(A,Q)..,pO(S..,Q),PO{A,cJ .. (QPOl(A•3•0,[),SATZD188MCC .. O•A•L>)

SATZD188Q := EQLESS012tPO<A.CJ .. PD<C ... A) .. P0(8o01 .. PD(O,Bl .. tO~PO{A,C);CQHPOCB,O>• SATZOl88PJ

D ; [M:MOREO<A•B)][N:HOREO<C•O>l SATZD189 := TRHOREOCPO(A,CJ,POCBoCJ,PO(B,OJ,

SATZD133DCA•B•C•~>•SAiZD188KCC,o ... a.N>J D ~ tl:lESSO(A,BJltK:LESSO<C•O>l

SATZD189A := lEt~MA05<POCB•O>•POU,CJr SATZOle9CBoArO,C,LEHKAOG<A•B•L>• lEM"'AOó( C• Q,.Jo)}

D 3 (~:"J~EO(AoB)J[N:MOREO<C•O)J SA T Z!ll 9:) A : = ORfl PPOW~EOCA, B >, E:IH AtiB h HOREO(PO(A, C J

•POC3.~J>•~•iT:HORED{A•BllSATZ0169!T, Nl.CT:EO<A·S>JSATlD188N(T,NJ)

D a [K:KORED(A,B>ltN:HOREO<C•D>J SATZD19'B := EÇ~êRE~!ZtPO(C,AlrP0<4rCl~PD(O,B)•

P0~3.Ql,~JvPn{CrA)oCOMP~(0•8t,

: MOREDC" Q(C, AhPO(C,BH

LESSOP DCC .. AhPD(C., B))

LESSOP O<C, A),P0(0,8))

HORtOP OU,ChPDCB;O))

MOREOP OU, ChPO(a,ou

s

s

- 4.23-

SATZ0190AtC~D,A~B•N,H)J 0 ~ CL:LESSEQtA.B>JCK:LESSD(C,O>l

SATZ0190C :: LEMMA?S<PO(B,.DloPOCA~C>• SATZ0190A(B.A•D•C•SATZD1688tA,B.L>• LEMMA~5(C,Q,X)))

D a tL:LESSDCA.BlltX:LESSEQ(C,OJJ SATZ01900 := LEMHAD5CPDCB•DJ•PDCAoClo

SATZDl908<B•A•D•C•LEH~A06tA•B•L>• SAiZDi5881C•D•K>J)

0 a (M:KOREQCA.BlltN:HO~EO<C.OlJ

CE:[~(l•B)J{f:EQ<C•O>l

Tl :: HORE Qt 2< PlHA,. C h PO (8 ,.o >-EQP012{A•B•C•O•E•f))

E a CO:HORED(C,.Oll rz == HOREQI1<POCA•C>•PO<B•D>•SATZ0190A(~•O>

)

E a Tl ::: ORAPP<MOREO(CoO),[Q{C.OloMOREQCPOCA•C> ,pQtS.Q}},NoCT:MORSC<CoO)JTZ<T>• tT:[Q{C,Q)JTl{J})

N ~ CD: HJRED CA •B l l T4 := KOREQI1tPO(ArClrP0(8;0),SATZ0190SCO,N>

'

s

;

MORE OP 1H A• C ),p()( Br 0))

-30191 s

SATZ0191 ·- ORAPPCMOREOCA.S>•EO(A;8);MOREQ(PO<~•C) .PDCB.O>>•~•[T:MORED<A.Bl1 T4w.3019t•cr>.rT:EQ(A•BllTJ•.3D191•(Jl > : KOREQP D<Ar Cl.PDCBrD»

0 a [L:LESSEOCA;BlltK:tESSEQCC•OlJ SATZ)l91A :: SATZ0168A(P0(B•Ol,POCA.Cl~

SATZ0191(8,ArO,C;SATZDl&88<A•B•l)• SATZ0168!HC• 0.10)) LESSEO[ PD<A.CJ.PO(B,Ol l

Ba TO :: OfCPLCTS<lA•lBl.TSC2A,2B)),

AZ a [R:CiJT J Tl

TZ

[S:CUTl T5

fó

T7

PLCTS(lA,2BhT5(2A,l8))) OIF

·- ISTS1CSTHCOr<Al•A2>)•Al•R•STKISCAlrAZl ) IS<TS(S TKCOFUt.A2l h R ),. TS <At,. R))

·- ISTS2(SJM(0f(Al,A2)),A1•R•ST~IS(Al•A21 ) : IS<TS<~rSTH(Of<A1rA2))),fS(RrAllJ

;: ISfSl<ST0(0FCAl•A2J),A2•R•STOISCA1.A2) ). t IS<TSti TOCDF<Al.AZ) h~.J,TS UZ•R»

:= ISTS2<STO<DFCA1•A2lJ;A2.R,STD1SCAltA2) l IStTSit•STO<OFCAl.A2))),JS(R.A2l)

·- ISPL12<TSCSTMCOFCAl•A2!},R);TSCA1rRl• TS(STOC0f(Al~A2)),$J,TS<A2rS)r11CRJr

T 3( S)) I SCPL<T St STIH Of'( U, AZ l) r R> • TSC STO< OF (A 1• AZ)), sn,.

:: ISPL12<T SC R• ST fo4( Of< A l.A2 J J J. TS<R.Al) • Tscs.sr~cor1Al•A2>>>·Tscs.AZ>PT2(RJ• J4( s})

:: ISPL12~ T $( STO( OH Al• A2)) • Rh TS U2•fD, TSCSTMCDF(Al~AZJJ,S>.TSIAl•SJ,T3CR:• TH$})

Pl<TSH l•RhTSCA2rSJ)}

ISCFL<fSCR.STMCOFCAtrA2l)lrTS(S,STOCOFCAl.A2))J), Pl n Sn , Al) • TS ( S ,Az)))

- 4.24-

·-rOEQlB :: REFEQ2(TCtA~OF<R1rR2)),0f<PL<TS{1A.R1> rTS(ZA.R2l>•PL(TS{lA•R2}•TS<2A•RlJ)), rou E'.HOF"P LCTSt U..Rl hTS< 2A .. ~zn,PU TS< 1Arfi2J.TS(2A.R1)) h

TO<A .. OF"(Rl.RZ>ll TOEQ2A == P.ErEQ1(TO<Or<Rl,.F.2i .. A),.Of<PL<TS<RlrlAJ

• Ts< RZ• 2A > h Pl( TS( Rl. 2Al ~ TS(I~2.1A l J), T02> EO<TO()f(Rl•R2J•Al,OF"<PL(TS(R1•1AJrTS<R2r2Allr

PlUSH t .. ZA hTS( RZ.l.\) n) TOEQZS :: REFER2CiD<OFCR1•RZJ,A)rOF<PL<TS<Rl•lA>

,.TS<R2,.2A>l•PLCTS\R1,~A),TS<R2r1AJ)},

T:>z l : EQ(~f{'l(TSCR1•1A>•TS(R2•2A)),pt(TS<R1•2A),TS(R2•1A))), TO<DfU l•R2 >~AH

i-401?4 s

B ~ T1 := ISPL1ZtTStlA•lBJ,fSClB•1AlrTSC2A•2B>• TS<2B•2A),COKTS(1Ar19lrCOMiS(2Ar2BJ> ISCPL<fStlA•lS),TS<ZA•ZB>>•PttTStlB•lAlrTStzB,ZA)))

TZ :: TRISCCCTrPLCTS(1,*2B>•TS(2Ao18)), PLtTSCZA•lSJoTS(lA•ZSJ)rPLCTSilB•ZA>• TS<ZB.1A)),~û~?L<TS<1Ar2B>.TSCZAolB> >• IS?L12C~S~2Aol3J,TSC18o2~l,TS(1Ar2B)•

TSC23rlAloCO~TS<2Ar1B>rCOMTS(1Ar23J)l ISC~LCTSflA,zB>•TSC2Ao19)JoPL(TSC1Br2AlrTSC2Br1A)))

•itOU4 ' 8 ~ SATZD194 ·- EOSMSO<PLCTSC1Ar1BlrTS(2Ar28)),

PlCTSC1ArZ8)rTSC2Ar18)},pl(TS<1Bo1A}r TSCZB.ZA)),Pl<TSClB.ZA),TS<ZBrlA}), rt•.4Dl94•,rz·.4C194•> : EQ(TO(A ,8),. TD<B•AH

CO!Hi) := SATZ0194 : (QH DCA ,ah TO<B• A)) c a [(:(;)(A,B) l

••I 'o/t,J s

E ; u:c:JT J Tll == TR3ISCCUTrPLCTSClA•R> .. TS(ZBrR)},

TSCPLClA,ZB>oRloTSCPlC10•2Al•R>• PLCTS<1B,Rl,ïS(2A.R>>•DISTPT1C1Ar29•R) oiSTS1<PLC1Ar2B!•PLC1Br2AlrRr()r DISTTPlClB,zA.R)) : IS<Pl(fS(lA•R>•TS<ZB .. R)),Pl<TS<1B,.R),TS<2A•R)))

E a T12 := TR3ISCCUT.PL(PlCTSClA.1ClrTSC2A•2C)), PLCTS< la,.zc Ir iS( 2B.1C n).. PLCPl(TS(lA•lCl•TS<ZB•lC)J, Pl<TSC1B•2CJ,TSCZA,.2Cl>>• PLCPLCTSCl8•1Cl,TS(2A•lC>>• PL!TS(1A·2C>,.TSC2B·2C)))• PLtPLCTSCl8•lCJ,fS(2B•2C)), PLCTSC1AoZC>,.TS<2A.lCJ)), 4PLZ4C iS( U•lCh TS<2A•ZC>rTS<lB•2C ),. TS(2S·l~JJriSPltZ<PL<TS<lA,lCl~ TSC2B•1C)loPL!TS<lS•lt'•'SC2A•lCJ),. PLtTSCtS.ZCJ,TS<2A,2C)},PLCTS<1A,2C>, TSC2B•2CJJiTllC1CJ, Tl1<3•A•C• SYHC: QC A,a, E J. 2C t}, 4PL24{TSClB•lCJ•TSC2A•lCJ,TS(1A,2C)r TSC2B, 2C H > ISCPL<?L<TSClA .. lCJ,TSC2A•ZC)l,PL<TS<lB•2C),TS<2B•1C))),

- 4.26-PLCPL(TS<ts.tc>.rstze,zc>J.PL<Ts<lA~zc,.rs<zA,tc}>>,

-IV4) s

E 3 E~TOl := EQI12(Pt<TS(lA,lC>•TSC?.A•2C}), Pl<TS(1~*2Cl.TS<ZA.tr.>J,PLCfS~18.!C},

D 2

9 ;

+40192

-r.019Z

B :il

8 ~

8 lCr:EQ(C,Q)l EHD1Z :=

[Z:ZEROa>l

Tl ::::

SATZ!l19ZA :=

tz:ZEROCB>l SATZ01926 == [Z:ZEROCA>J TD01 ::: rz :ZERIH 8) 1 TDOZ ·-SATZDUTA :=

SATZD1978 :=

SATZD197C . -SATZ01970 ·-SATZD197E ·-SATZ0197f . -SATZ0198 ::

TS!2B•2C)>•PlCTSC!8,2C>,TSC29~1C)), T12 ... I V40"') T R 3E tH TO ( t:,. A h T 0 (A • C h T 0 ( B, C >. TD ( C "B h CO~TO(C,A),EQT01,Cj~T0(8,C))

TREQ<TO(A;C),f0C2•C>,TO!B•O>r EOi01<A•B•CrE),EQTQ2(C,O,B.r>>

TRIS!CUT.PL<TS(lA•1B>•TS(2A•2Bll• PLCTS<2A,1SlrTS<1~·2B>>•PL<TSflA•2B>• TSC2~•1B>>•ISPL12\TStlA•18),JS<2A•lB>• TSC2A.2B>,TS<1A•23>.!STS1(1A,zA,19,z>, ISTSltzA,lA•2B,sTviS<CUT.1A,2A•l>>>• COMPLCTS<2A.1BlrTS<lA.26>>>

ZEROICPL<TS<1A•lB)rTSClA•ZB>>• PL(TS{lA,28>•TS<2~.18)),T1ft.40192")

EQZE RO<TiH s, A>. TOH., B ),COtHO< BoA h SATZ0192A<B•A•Z>>

SATZD192HZJ

SATZ0192B<Z> TR3EaC~DCM00(AJ,BloOF<PLCTS(2Aol8),

TSC1Ao28)loPl<TS<ZA•ZBl•TS<lA•lBJ)), Dr<PLCTS<1Ao2B>,TS(2Aol8)), Pl(TS(lA•lBl.TS{2Ao2B>>l•M00(TOCAoB})o TOEQ2ACB.ZA.1A>•E~SKSO(PL(TS{2Ao1B>• TSClA•2S>>~?L<TS(2~·23)oTS(1A•1B>>• PL<TS!lA.2B>.TS{2ArlBlloPlCTS<lA•lB), TSCZA•2BlloCOMPL<<S<2A•lB>•TS(lA•2B>>• COMPLCTS<2A.28),TS<1A•18))), HOOEOB<PL(TS{lAolS>•TS<ZA·ZB>>• Pl( TS< lA, 28), TS< 2A•lS)))) TR3EO<TO~A.M00(8)},f0(~00(B)•A'~

MOD<TO(u.A)J,~OD<TD<A.e>>•

CCHTOCAr~00(8)>•S~TZD197A(B•A>• EQMOO<TD<S,Al,TO<A~B>•COHTO<B,A)}) TREQ2<TO(M00CA)r6lrTO<A•M00(8)), MOOCTO(A,Bll,SATZD197~.SATZ0197B) SYMEQlTO(K00(Alr6JrTDCA•M00(8}), SA TZ0197C l SYME Q(TO O!O!H A>, B },. MOO·<To CA, B)), SHZ0197 Al SY~EQtTD(A,MOO(B>l.HCO<TO<A,BJ),

SATZ01979) T REQ CTO< !'IOOH h MOiHB) l, TO (A,MOOO!OD )),T0\ArB>•SATZD197C<A~M00(8)), EQT02(M00(MOOC8Jl•9•A•SATZD177{8))J

SATZ!l1964 := S':'l-lE QOOOWO CA },!IO!HS) ),TO<A,B ), SATZD198)

tP:POSOC~>JtQ:?OSOCS>l

s

$

ZERtHT!HA•B))

ZERlH T) tA•B U

ZERO( Tl (A,B))

- 4.27-

s

•H'4)

++40192

ru

rs:c!Jr J T14

Tl5

:: TRIS(CUT•PLCTS(R,~~ClB•ZBoQ)),TSCR,2B) )rTSCR•PL(~~(l8•2S•Q),2B>l•TS(Rr1B>• OISTPTZCR.~N(!B•29,Q),Z6Jo ISTS2!Plt~NC1B,ze,~>•28J•lB•R• SATZ140E(l9,2BoQ)))

•- !RtS<CUT•PLCTS<R,MN~18o2B•O>>~ Pl(TS(Ro2B)o5)}•Pl{Pl(TS<Rr~NC1Br2BrQ) ),TS{R,ZS}),SloPLCTS<R.18)rSlo ASSPL2(T5{R,MN<l3o2S,Q)),TSCR,2SloS}• ISPLlCPL<Ts:q,M~<lB•2BrQJJ,TSCRo28)), TSCRo19hS .. Tl3!)

:: TR1SCCUT•PLCTSCR.~N(l8•28oQ)), PU T S { R, 2 8 ), S ) i, Pl {T S ( R • 18 l • S ) , PL(S,TS<P.•l8)},T14rCOMPL(TS(RolS>•S)>

Q :" TH> ·- S~TZ133HCPlCTS(lAo28>•TSC2A•28))o PLCTs:zA,2BloTSClAo23)), TSClA•M~{lSo2B~Q}},TS(êAoMN(lB•2B,QJ),

COHPL(TSC1Ar2!J,TSC2A•2Bt>, SATZ1'5AtlA•2A•'N{lB,zS,QJ,p))

Tl/ :: IS~ORE12<PLCTS(lA,~NC1Bo2S,Q)), FLCTStlA•23l•TS<ZAo28J>J•Fl<TS<1A,lSJ, TSC2A.2BJJ,PLCTSCZA,HN<lB•2B,Q)), PLCTS(2A•2B},fS{lA•2BllJoPlCTS<lA•2B>• TS(2A,l6)),f14<1A~Ts<2A•28}),

Tl5(2A.TS(1A,28))ofló)

0:3 PTOP:. := POSOHPL<TSC1A,.1SJ,TS(2A,.28)), PLCTS(1A•2B>•TSC2Ar1BJJ,T17•.JV40•)

8 ; (P:POSD(A)J(N:NEGOl

N ; T18 ·- EOPOSO(TO<A.M00(8}),.M00CTOCA,.8JJ, SATZ0197B<A•BJoPTOPP<A•MOOtBJ,.p, SATZ0176C<B.NJ))

" ; a ;

8 a

B ;

0 ;

p ;

p 3

NTOPN := SATZ0176F<TD<A•9>•T18ft.IV40•J (N:NEGD(A))[~:POS~(BJl NTON~ :: EQNEGO<TD<B•~J.Ta<A•B>•CCHTD<B•A>•

NTOPNCB,.A,P. N)) {~:NEGO<All[D:NEGDJ , PTONN :: EQPOSDCTOOfOOCA>~140iHBllrTOCA .. Bh

SATZ0198(A~B>•PTOPPCMOOCA>~MOOCB)• ~~TZ0176C{A,Nl.SATZ017&Ct8.0)))

{N:NOT<ZEROCA>>l[O:NOT<ZER0(8))J

(P:PDSDCAll[Q:POSCCSll T2 t~ rNOTOO<TD~A.a),PTOPP<A~s,p,.Q))

PI OI EG 0 ( B >l n Tlt

·- N~OTO~(TDCArB),.NTJ?N<A~a,F,M>>

•- RAPPO(B,NOTCZE?.O<TG(~•B))),[J:POS0(3)1 T2(JJ,TH2•L.IMP•CZER0(81P NOTIZEROCTD(A,6l'J•0)r[T:NEGDJT3(T) l

ISCPLH SCR,. MNC1B .. 2S.QJ hTS(R,.ZBHrTStR•lB> J

MORE<P~CTSC1A•HN(1SrZB,Q))•Pl(TSC1A•ZB>•TSCZA#~S)))• PUTS<Z A.MNClB•ZB•Q H• PLU S<ZAr28hTS< Ur2E )) > >

POSO<Tl u. .. a))

POSOOO OCTO( A,B) I)

NEGD(TJ CAo8))

NEGOt Tl (A,.B))

PIJS!lCTl <A .. B))

NOHZE~O<TOCA,B))l

$

. $

- 4.28-

-4ctn

0; tM:NEGOCA)J[P:PDSO<S>l TS :: NN~TOO(TO(A,SlrNTONPCArS•M•Pll : NOTCZE~D<TO(A,Bll)

!1 ~ tl:NEGOCB) l f& :: PNOTOOCT~<ArBlrPTONN{Ar8rMrl>) NOT(ZE~O{TO(A,B)))

K ~ T7 ·- RAPPOCSrNOT(ZER0(T~<A~6))),~T:POSD<8)l TS<TlrTH2•L.I~P~<ZERO(B),

NOTCZEROCTO<Ar9J)),Q).{J:NEGD<BJlTGCTJ l NOT(Z~O<TD<A•S)))

0 ~ SATZ:>1920

Z 4 tN:NJTCZERO(A))] T8

Z :1 SATZ0192C

:: RAPPO{A,~OTCZEROCTDCA•Bll)r(T:PQSOCAl~ T4·.4~192•(TlrTH2•L.IM?•(ZEROCA}• HCTtZERO{TQ(ArB))J,N),[T:NEGDCAJl T7 ... 4!)1g2•(T)}

:= ET<ZEROrTHJ•L.IKP•<NOi<ZERO<BJ)r NOT(ZERO<TD<A.SlllrHELICZE~OCTO<A•Bllr ZlrtT:NOT<ZEPQ(S))JSATZ01920(Nrf))l

B ~ CP:POSO(A)J[Q:POSO<B)l Tl :: TRE02(ABSD<TD!A•B>l~TD(ASSO<A>~ABSO<BJ

),TO{ArBl~ABSNND<TOCA.B),

PNOTNO{TOtA.Sl,PTOPP(A•B•PrQ)))~

EQT~!2{A8SO<A>.A,ASSDCB>•B• ASSNNO(A•PSOTNO<A•P)),

ZER!H Bl

OR<ZERl <Ah ZERO( B> l

ABSNNO<B•PNCTNO! s, 0))) > EO <ABS:) U 0( A,B) h T O<ABSOU hA BSO( Bl) J p ~ {N:NtGOCSJl

T2

T3

B OI tz: ZERO <A) l fit

g OI tz:ZER!HB> l

:= TREQ(A8SO(TD(A;8}),H00(T0(A,B)J, TDCArHODl~ABSND<TO<A~Bl• HTOPNC A.S .. p, ro ), SA TZIH97F u,s)) EQ<ABSJ HO< Ar 8)) .r TQ(A., M00( 8)) l

:= TREQ2(ABSO<TO<A•B>>,TD(ABSO(AJ,ABSD );f0(Ar~00(B)JrT2oEOT31ZCABSOCA)•A•

ABSD(!)oKODCBJ,ABSNND{A•PNOIND<A•Pllr ABSN0(8,N)J) t EO<ABS~<TOCA•B)),TO<ABSD(A),ABSOCBJ))

:= ZEROE~<ABSO(T0(A,8)),T0CASSO<A>• ASS0(8))pSATZDló6f(TO<A•B>·TD01(A,B,Zl ),TQ01CABSOtA},ABSD(B>•SATZ0166f(A•Z>> > EQCABS~CTO(A,S)J,TO<ABSOCA)rABSOCB)))

T5 := ZEROEQ<ABSO<TD<A.B)),ïD<ABSD(Alr A8SDCBJJ~SATZ0166FCTOCA•BI•TD02CA•B•Zl >•T002(ABSOCA),ABSOCBJ.SATZ0166f(BrZ)) )

B ~ [~:NEGO(AJJCP:POSOCB)l T6 :: TR~EQCABSO{TD<~•BlJrABSO<TDCS•Al)r

Pf :1 {Q:NEGOCB>l f7

TO(hBSu(Blr~BSD<A>>•TDCABSO(A),ASSO<Bl

J,[QA8S~{;D(ArBlrTO(B•AJ~COHTOtA•B)),

f3(BrA,P•NlrCGMTO<ABSOCBi•ABSOCA)))

:: TREQ(T0(A8SO{A~PA8SO<BJJ•T0{~00(A), ~OD<P,),TD!~.~l~EQTD12tABSD(4).M0~CA>•

(Q(ABS!HTD( A. SJ hTtHABSDCA ),ABSO(f3) > J

s

s

$

s

- 4.29

Aö~U\UI#MUUl~lrAö~NU\A•~J#Aö~NU\U#UJJ#

SATZD1980.B)' EO<TOCA BSO{ Ah ABS lH 8)) r TOC A,.S)) T8 ;:: TREQ2(ABSO<TOtA•8)),;0c4BSOCAl•ABS0(8)

),TOCA.B)rABSNNa<T~<ArB)r PNOTNDCTD<ArB>•PTCN~CA~B•N•OlJJrf7} EQ(ABSJ <TOC A•!D hT!HABSOU >•ABSO(B)) J

8 ; (P:P:JSOCA) 1 T9 :: RAPPIH a. EiH A !3SO< TD( A .a) J • TOCABSDU h

ASSO<BJJ},[T:POSOJT1(P.ïJ, [T:ZEROlTS<T>.[T:NEGO<BllT3CP•T>> EOCABSJ(T~(ArBJJrTO(ABSOC'>•ABSOCB>J>

B ; [N:NEGOCAJ l TlO == RAPP0{8?EQ!ABS~<TO<A•3llrTO(ABSOCA)r

ABSO\BJJ),(T:?OSOC~)JTGCN.T>•

CT:ZEROCBl~T5CT>•tT:NEGO<BllT8CN•T)) EOCA8SJCTDCAr8))rTOCABS0(4JrABSDCBJ))

•40193 s

B a SA TZ0193 := RAPPO(;,EOCABSDtTO(A,B}l,TOCABSO(A>, ABSO\B))),(T:POSDtAJJT9*.40193"(Tl• {T;ZERO~A>JT4·.4~193*CT),(T:~EGD!A)J T10 ... 4t!193 .. t T)) f.:Q<ABS:l <TD< A .. S)) • TO CAB SOU hABSlH B>l)

SATZ'H03A ::: SYHEQ(,3SDCTO<A•B>)rTO<ABSO(A),ABSO<Bl >•Sjl. ïZJ! 9H [Q{TOC,BSO(A)rABSO<B)l,ABSQ(TO(A,BlJl

;; lOF' ·- POOF RP( 1 RP l OIF"

+40195

A ~ Tl ·- TRIS<CUTrPL(PL<TS<lA•PL<lRP•lRP)); TSC2A•1RPll•2AJ,Pl(TSC1ArPL<lRP•1RP)J, PLCTS[2A.1RP)r2A>l,?LCPLC1ArlAJ, PtC2Ar2AllrASSPL1<TSC1Ar?L(lRP•lRP}lr TSC2Ar1RPJr2AlriSPL12CTSC1ArPl(lRP• 1RP}},PL(1A,1AJ,Pt(TS(2A,1RPJ,2A)r PL(2A•2A)rA2ISAPA!1Al•ISPLl(TSC2A•lRPl ,zA, 2A, SH Z151<ZH)) > IS<PlC,lCTS<1A.PtC1RPr1RPJ),TS(2ArlRPJ),2Al,

PLCPL<l A• lA) ,pl.( 2A• 2AJ)) TZ ·- TRIS!CUTPPL(lArPLCTSClA-lRPlo

TSC2A,?l(lRPr1RP>>>>• PltPL<lA•TSC1A·l~?)),TS{2A,PltlRPolRP) }J,PL<PL<1A~lA)oPLl2Ar2A>>•

ASSPL2<1AoTS<1A•lP.PlrTS<2Ao?L{1RP•lRPl )1•ISPL12(PL{1Ao!SClA•lRP>>•PL<1A•lA>• TSC2A,Pl(1RPo1RPJ),Pl[2A•2A>• ISPl2<TS<lA•lRP),lA•lA.SATZ151ClA)), A2ISA?A<2A))) IS<PLClA•Pl<TStlA•l~P>•TSCZA•PLClRP•lRP)))lo

PU?L (1 A,lA J • PU: 2A, ZAl)) T3 :: TRIS2<CUT•PltPLCTS~lA•PLC1Rr•lRP>>•

TSt2A•lRP> h 2.\ hPl( lA.?LCTS< 1A•1R?lr TSC2A• ?U 1 RP•lRP Jl) hPLCPU 1A•1A ), Plt2A• 2A) >• T l• T2) tSCPLC,ttTS<1A•PL<1RPolRPJtrTSC2A.iRP))o2AJ,

Pl<lA•2 LtTSCIA•JRPJ,TSC2A•PLC1RPolRP1)JJ)

•41)195 s

A 2 SATZ:Jl 95 :: TREO<TO<Ar1DF1o0f(PL<TSC1A•PLC1P.P•lRP) ),fS<ZA,1RP)),pl{TSC1A.1RPl• TSC2ArPt(1RP.1R?l})).A, TDEQ1ACA.PLC1RP.lRPJrlR?lr EQI2(A~?l!TSC1A•Pl(1R?•l~?)),

- 4.30-

TS<2A.lR?J>.Pl<TSClA.lR?}, TSC~ArPlflRP.lR?lllrT3~.4D195~l) EO<TD<A ~tOF J~,u

SAT7.0195A :: SVME Q( TO<ArlDF' hA• S.~ TZ'J1'l5 l E<HA, ii> <A,l Df'>) SATZJ1953 ·- TRrj{TDf1ryf,~!,T3<A•10flrt•

-------,------------ -- ---CO~T0(10r•A>-SATZ0195)

-40196

HftQ19&

•40196

SATZ0195C := SYHEQHOt10r•A>•A,SATZ0195Sl B ~ [P:PJSOCÄ)J[Q:PQSOl

SATZ0196A :: SYfCEOCTO<ABSO(AJoA3SOCBl),.TO(A,BJ• EQT012CA6SOCAJ,A.A95DC3J•B• ABSNNDCA•PNOTNDfA•P>J• ABSNNO<B•PNOTNO<B•Q)J))

8 ~ [N:NEGD(AJltO:NEGOl SATZD196B := T~EQ2<TOCA,BJ•TD<ABSJCA1•ABSOCBJ1•

TDCMODCA),M00(8)),5ATZ)198ACA.BJ• EOTD1Z(~8SQ<Al•HOD,A};ABSOCB>•MOOCB>• ABSND<A•NJ.ABSNDCB~QJJJ

8 • (P:POSDCA)J[N:NEGOCB)J SATZ0196C ·- TREQ1<TD<A,BJ•MOOCTOCA3SOCA1•A9SDCB)J)

,TO<ABSO(Al.KOO<ABSD<Sl)l• EOT012(ABSDCAJ•A•H00(ABSD>•8• ABSNND<A•?NOTNO(A,PJ), sarzotn ec AB soc 8 > .s. /4!3S~m<s, N> > J, SATZ01978(A8S0{A),ABS0(9)))

8 ~ [N:NEGDCAJltP:POSOCB)J SATZJ1960 := TR3EQ<TO<A.SlrTO<B.Al.~00{TOCABS0(8),

8 ~ P1P2 P1N2 NlP2 NlNZ

ABSOCA>J>,~OOCTOCABSDCAJ,4BS0(B)}),

CQ~TO{A.B),S~TZ0196C<B,A.P.N>•

EOMOOCTO<ASSOCB>•ABS~(A)J,TD<ABSDCA>• ABSO<BJ)rCOHTD<ABSO·ABSO<AJ)))

·- ANOCPOSO{AJ.POSO> := A~O(PQSD<AJ,NEGO(Bl) ·- ANO<NEGO(A),POSOC81) ·- ANOCNEGOCA}.NEGOCBJ)

B ~ [N:NOT<ZERO(A))J(O:NOTCZERO(B>> lEE:EQCTO(A•BJ,TO<ABSD<AJ•ABSOCBJ))J

0 ~ n := PTDPP!ABSDCAl,ABSO(BJ.SATZD166E(A,Nl• SATZ D166E< a, !J) l

E ~ T2 :: PNOTNO(TOCA,Bl.EQ?OSDtTO{ABSO<A>• ABS0(8)),TOCA~B>•SYHE~CTD<A•BJ, TO{ABSO<A>,A8S0(8)),[),TlJ)

[P:Pr.JSOUl l T3 :: TH3•t.IMP•<NEGD.NEGJ<TDCA;B)l•T2.

CT:NEGOCB>lNTOPN(A•B•P•f;.) Tlt ·- OR3E2<ZE~0(8J.POSOCBJ.NEGOCBl,AXR00(B)

,T3,Q) r; := AN0I{P0SO<A)rPOSD<S>•P•T4> T& := ORil<P1PZrN1NZ,T5l

E ~ UHNEGDC A)) Tl ·- THJ•t.IMP-<POSDCB>•~EGD<TD<A•Bl>•TZ•

(T:POS0(6)JNTCNP(A,5,H,i)) re :: OR3E3tZERGtB>•POSD<Sl•NEGOCS),AXR00(B)

,. O. T 7)

T9 ·- ANDlCNEGOCAJ.NEGOfBl•~•TS) T10 ·- ORI2<P1PZ.N1N2,T9>

EQ<TO<l or .. A J..,'O EQ<A, TO Cl or,. A))

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• : EQCTOU •Bh HOD<TDCABSO(A},ABSOCBHJ)

EQ<TD(A,8),H00(TDCABSOCAl·ABSOCBJl)J

'PROP' : 1 f'ROfH

1 PRDP 1

'PRO P•

POS!H T) <ASSO( A) .ABSO<B)))

NOH N E:O OHO (A, B))}

NOHNE:i 0(8))

: POSD( Bl PlPZ OR{PlP? .-NtNZ>

NOHPOS0(8))

NEGC(B) Nlit2 OR<P 1P2 ,tf1N2 l

s

s

s

- 4. 31 -

H4j)19!)

E :J SHZD196E :: ftAPPD(A,9~{P1P2~.4019S•,NtM2•.4Dl96"J, tT:POSOC\)lT6•.4Jl96"Cf), THZ"L~I~P*(ZERC\Al. ORCP1P2".4019&·,~1~2".•Dl96•J,N), tT:NEGDCAJlT10".4D196~!T))

0 a [E:EQ<TO(A,BJ,M00(T0(A8SO{A)rA6SDCB')})J O!HANOC POSOO>,PûSDCBJ hAND( NEGOC u,. I>EGO<B) > >

o a ru E 41 T12

·- SATZDl~GACTD(ASSDCAJ,ABSOCBJJ.Tl> : ~EGOCH)Q(TOCASSD<AJ,.ABSOCa)J))

·- NNOTPD<TO<A~9>•E~N~~O!MOCCTOCASSO(A},. ABS0(9}}J,f0(A,a>,STMEQ(TDCA.SJ• M00{i~CASSO(A),A3SOC:)l),E),f11)J NOT(POSOCTOCA,B)})

(P:PQSOC f,> l Tll

f14

Tl5 H6

E ; [Mtf.IEG!HA> l T17

T18

f19 T20

E OI SATZD196F

·- TH3•L.IM?"<PGS0(8J,POSD<TOCA,S)),.Tl2• CT:POSDCSl~PTOPP(A,a.p,f))

:= OR3E3CZERO(B>~PDSOCBlP~EGD(BJ~AXR00(8) ,!J.T!l>

:= A~~!{POSOtAl~ME~a(~>•PrT14) := OR!l(P1~2•N1P2•T15)

·- TH3•L.IM?"(NEGOta>.POSDCiOCArBJ>•Tl2• CT:NEGûCBllPTONNCArB•~•T)l

·- OR3EZCZERG(Bl.POSC(SJ•N~GO(B),AXR00(8} .. nT .. !!>

:: A!ûiC~EGO{A).PCSDC6l•~•T18l := OR!2tP1NZ.~lP2,T19t

·- ~APP0(A,0R(P1N2•.4Q196•,NtP2•.4Dl96•J, tT:PUSO(AlJT16~.40196•(T),

THZ•L.IMP•CZE?.O<A}r 0RlPl~ZR.4019&•rNlPz•.4D196~),N),

[T:NEGOCAlli20ft.40196•tT)/

2 CP:CUTl[Q:CUTltR:CUTJ[S:CUTJ[T:CUTl[U:CUTl Tl ·- TRISCCUT .. TStPL{TS(P,Rl·TS{Q,SJ),T),.

rz

T3

Pl<TS<TS<P•Rl,T>•TSCTS<O•S),f))• Pl<TSCP,TS(R,T)l,TS(Q,TS(S,!))}• OISTiPliTSCP~Rl~TSCQ•S),f), I5Pl12CTSCTStP.R),Tj.rscp,TS(R,iJ), TSU 5( g, Sh T }, iS( Q, TS{S, T )), ASSTSHP~~, T hASSTSlC.hS. TU)

:= TRIS<CUToPlfTS(Q,TS(S#Tll.TS(Q~TS<R.U> )l,Pl(iS{Q.TS<R~U}),jS(Q,TS(S,T))},

TS(Q,?L<TS<R.U>,rStS.T))}, COMPLCfS(Q,TSCSoT)l,TS!Q,TSlR•Ul)}, DISTPT2CO.TS(R,U),TS(S,.T~J)

:: TR3ISCCUT,PL<TS<PLfTSC?.R>•TS<O•SJ),T) ,TSfPLCTS<P.S>.TS(Q,R)l?U}), PL<PL<TS(P.TS<R•~)J,TS(C,TSCS,T))), PL<TS(P,TSCS,U)),TSlC.TS{R,Q)))), PLCPL(TS(P,fS(R$TilrTStP•TS(S.U}l), PlCTS(Q.iS(SrTl),TSCO~TSfR.U)))),

PUtst p,purs< "~ n, rscs. u,>,. TS(Q,PLCTS(R,Ul,TSCS,TJJJJ. !SPL!Z{TSCPLETSCP•Rl.TS{O,S)),fl•

:

NOTCPOi OCSJ >

NÈG;)( 6} PlN2 iJR<PHI~ •NlPZ>

NOHNE:.JD<BJ>

POSO( 8) NlPZ OR<r>lNZ ,H1P2)

OR UNOC POSO (Ah NEGDC B> ),. ANOC NEGDCA),. POSD C BH)

IS(TS( 2 lCTS(P,.RJ,TS(QrS)J.TJ,PLCTS!P,TS<R•T>l• TS<O• TS CS•T))) >

IS(Pl(f S(Q.., TS(S,. TU, fS ( Q,. T SCR. U)) J.. TS< c.:, Pl <T$CR, Uh rscs.n>n

$

J

- 4.32-

-40199

C OI SATZJ199

J\SSTD1 ASSTDZ

PleTS( f', TS<R• T) ), TSC Q, TS<S• T J) );o TSCPL(TSCP,SJ,TS(Q,RJJ,UJ, PLCTS(P,TS(S,UJl,iS(Q,fStR•Ul)),Tlr TlCP,Q•S•R•U•f)),4PL23!TStP.TS(?.rT)), TSCQ,fS(S,T)J,TS<P~TSCS.U>>• TSCQ,TS<R•U>J>•ISPll~!PlCTS<P•TS<R•l)J ,rsrP,TSCSrUJ)J,TSCP,PL<TSCR,T), TS<S.UJll•PLrTS(Q,TS<S•T>I• TS(Q,TS(~.UJ)J,TS(Q,PLCTS(R,U>,TS(S;oT) )J,OISTPT2(PrTS(R,TJ,TS(SrUJJ,T2J)

·- TR3EO<TOCTD(A,eJ,C), Of{PlCTSCPl(TS(l4•1Bl•TSC2A•2B>>•1C), TSO'!..( T3 UA• ZB hTS< ZA,lB) >•2C J h Pl!7S!P~CïS!lA•lB~.TS!2A•28Jl,2Cl• TSCPl<TS(l4,2S),TS<2A,lB)J,lCJJ), 0f(PLCT5(1A•PLCTSC18,1Cl.TS<ZB,2C))), TS(ZA,?LCTS(l8~Zc>,TS!2S,lC)')), PL<TS( lA•f'L< rsue.zc >. rs<zs.tc D ,. TSC2ArPL<TS<1S,1C),TS<2S;o2C))}))• TDCA,T~tB•CJl•TOEQ2~CC•PL<TS~lA~lB>• TSC2~·26)J,PL!TS<lA.2B>.TSC2A,lBJ)), [QSHSJ(PL<TS<P~(TS(lA•lS>.TSC2A.29)), 1C h TS{Pl( TS< l.A• 28 }, TSC 2A .. 1B}} ,ze)), PLCTS(?ttTS(lA•18),TS<2A•2B>>•2CJ• TSCPlCTS<lA.28),T$(2A,18)),lC)), PL<TSC1A•PlCTS(18,1C),TS(2B.2CJJ), TS(2A•Pl(TS(lB•2C>•TS!2B•lC)))), PLCTSClA•PlCTS<lB.ZC>.TS<2B.lC))), TS{lA•PLCTS( lB•lC);ofS(28•2C)J)), T3•.4Dl99•(tA.2A,lS.2SolC•2C>o T3*.4~199.(lA•2A•lB•2B,2C•lCJ),

TD~OlS(A,?l<TSC1S.1C>•TS(28,2CJ), Pl(TSC18,2CJ~TS<2S•1CJJ)}

:= SATZIH99 ·- S'r>!E:lCTO<TOCArSlrClrTJ(.~. fO(B,cH~

SATZ019:'}

; [P:CUTJ[Q:CUTlCR:CUTl[S:CUTl[T:CUTJtU:CUTl Tl ·- TRIS<CUToPLCTSCP.Pl<R•T>>•TS<Q.PlfS,U)

SATZD201

) hPU PleT SC Pr R),. TSC p, f) hl'U TS( Q, Sh TSCQ,UJ>l•PL{Pl<TS(P,R)riS(Q,S)),. Pl\TS{P,T),TS{Q,U))), IS~llZCTS<P•PLCR,Tll•PLCTSCP,.R), TS{PrT)}•TS(QrPl(SrUJJ~Pl(TS{Q,SJ•

TS(~,U)),DISTiP2<P•R•TliOISTTP2{Q,S,UJ l•~PlZJ<TS{P,RJ,TStP,TlrTSCO~S)•

rsc~.;nn

:: TR3EOCTO{APP0(3-C)),. Df"!PU TS<lA• PU 1B•1C )), T S(2A,.pl( 2B•2C) ))•?LCTS<1A.PlCZBr?.C))rTS<2A•PL(lBr1Cl 1)l,J~{P~<PLCfS{l~~1G1.TSC2A•?.6!l•

IS(~LCTS<PlCTStPrR),TSCOrS)),Tl.TSCPLCTS<P•Sl•TS<O•~)), U) hPU TS(P rPLC T S<R•T h i SC Sr U)) hTS< c,. fl< H< R,. Uh TS(S,TJ J)JJ

EQ CTD (T lH A, B hC), TO U• Tl)(3 .. c)))

EQ<TOCT DCA .. BhCJ "TOU. TOCB ,.en J

IS(PLCTSCP~Pl(R,:JJ,TS(Q,PlCS.U))J,.PlCPl(T5CP•A), TS{Q,S) >•Pl(TS(P;ol),TS{Q,~))})

s

s - 4. 33 .

H40203

OISHP!l2 !H SPTDl

OISPTD2

SATZ0232

DISTTI101

OISTTHD2 DIST'4"l'Dl

DISHTD2

SATZOZOO ( lU MD RED !A •B))

Tl

[P:P('ISDCC)J

P a rz

P ; SATZJ203A M :11 [Z:ZERO<C>l

SATZ02HB

PltTS<lAr1C)rTS(~A•2C)))•

P!..( Pl< TS \lA• 2B)" T 5{ 2A .. l3)),. ?LCTS(lA•2Cl•TSC2A•lCJ1l)rPO{TOCA•8>• rocA.CJl•TOEQlAC~rPL<lS .. lC>•PLC2er2C)~ •E~SMSC{PL<ïS(lA•PL<~3•lC>>• fSC2AoPL<2E .. 2C))JrPL<TS!tA.PLC2Br2C))r TSC2A•PL(16o\CJ>>.PLCPL<rS<lAr1B)r TS(2~•2Bl)•PL(f5{1ArlCJ~TSC2Ar2CJ)Jr PLCPlCTSC1Ar28JrTSC2AolBJ), PLCTSCiA•2C)tfS(2Ar1C))}, TlR.4020t"ClAr2A,1~•2B•lCo2C), T1*.40201•(1hr2A•2B•13•2C•lCJ), PD~Ql23CPL{T5(1A,19)oTS{2Ao2S));

PLCiSC1Ar2B>rTSC2ArlBJlrPl<TSClA•1Clo TSC2A·2C)J,FL<TS<lA~2C)~TS(ZA,1C)))) : [Q{f0(A~P0(B,CJ),p0(TO<A,3),T0(A,CJJJ

::: T?.J::Q{ ï:>< PO{ A • B), C) • TO( Co ?DU.o B)), PD<TOtCrA)rTDCCo8}),pO<TD(A,CJrT0(8oC) >•CJY.TCCPD{Ao8),~),$ATZD201{CoAo8)o

E~?012CTG(CoA)oTD(A,C)oTG{C,S>,T0(8,CJ

, C0'-:7!) (.Cn\ h COMTO(C, a))> EQ<fOP ou, 8 hC hPDUD<A~>C J.. TO< BrCJ) l := SATZD20l EQCTOCAoPOCBrC)J,PD<TO(A,3)•TOCA,CJl) := SY~E:CTD<PDCA•B> .. CloPOCTOIAoCJ,TOCB•C)

J,.OISTo?lH > EO<POU OCAr ChT0{8,CH•T0{ PO< ArBJrC) J ;: SY~E~{T0(A.P0(8,C)),pQ(TO<A•BJ,TOCA,C)

>r ::>I STTP02} EQ(PO(T O<A• Bh TDCA• CJ h TOt A•PDC B•CJl) := TR~0(7Q{AoM)(S,CJJ .. PO<TO(A,.BJ,

TO\A.~GJ(C,}),~DCTDCAoBJoTD<A•C))p

DISTTP02(A,e,HOOCCJJ,E0?02CTO{A,M00(C) >•~OO<TO(A;C)JoTO(ArB),SATZ0197BtA•C>> ) : EIHTOUoMDC a .. en ,.I!Q<TO<A,!J J..TD<A,C>) J

:= TREQ{TOCKO(A,B>•ClrPOCTO(ArC>• TO<~ODrC));HOCTO<ArC)rTO<B.C>J,

OiSTTP01tA•XOO•C>•E~P02CTOCM00(S>• C>.~OOCT0(8rCl)oTOCA,CJrSATZ0197ACB•C) J} EQ(TQ(!1 DCA• 3>rC hKtHTD u,.c h TlH B•CH)

:= SATZ0202 : EQ(f0(A,.KO(S,C)),.t!0(TOCA,.3)rTD<A.C))) •- SY~E~CTO<MOCA .. BlrC>•MDCTD<A•C),TQ(B,.CJ

),O:::STHiOl) EQ<MOH OCA,.ChTOts.cu,.TOC MD< A•B>rC)) •- SY~E~<TO(AoMOCS#C)),HO{TQCA,.B>rTOCArCl

>•DISTiM02) EQC,O<TO(A•B>•TD<A•C>>•TDCArHO<B•Cl)) := SAiZOZG2 : EQHO<ArM!lCBoC)),.I!DOO(A,.3),JO<A,.C)})

:= SATZD162D<A•B~H>

:= EOPOSOCTOCMO(A,.B),.CJ,MO<TD<A•C>• T~CS.C},.OISTTMDlCA,.a,c>,?TO??CHO<A•B) ,c,Tlo?l>

:: ZEROEQCTOCA.C)rTOCB~C>rTD02tA~C·Z),. ron<:.c.zn

POSDOO <A•B) J

POSiH IQ CT 0{ ArC) "TOt B• C)) >

s

- 4.34-

+•IVftO

H ê tN:NEGlHCl l

N ; T3

N ; SHZ02l3C p OI SATZD2330

z a SATZ02HE

N ~ SATZin33F'

:: EQNEGDCTO(KO<A•Bl;CJ,HO<TO<A•C>• T0(8,C)),OISTTK0l{l•B•C>•NTDPN(K0(A,BJ ,c,Tl,.PU) : NEGIHHJ UDC A•ChTO<B•CHl

== SATZ01B2CCTOCA,.c>,TO<B·C>•T3•.4DZ03•J LESSO<T O(A,. ChTOCB,.CH := EQ~ORE012CTO<A•C>•TO<C•A>•TOCB•C>•

TO<C,.3>,COMTO{A,c:,.COHT9CB,.C), SAiZJ203.0 : MORE OU O(C• A),. TO<C• BH

::: ZER3EQCTO<C•Al•TO<C•BJ.T001CC•A•l)• TODl (C ,a, l}) to<roc: .. u,.rocc .. s>J

== E~LESS012CTO(A•Cl•TOCC,.Al•f0(8,.C),. TOCC.S),COHTOCA,C),.COHTO{a,.c), SAT.Zn03C) LESSO <T DCC" Ah TD<C• BH

c a (L:LESSOCA,.B)l[P:POSDCC>l SATZD2BG :: lEM~A05(T0(B•C1•TO(A,C>•

SATZD203A{S•A•C•lEHHAOG<A•B•l),P)) LESSOU OC A• ChTOCB,CU L :11 [Z:ZERtHC>l

SATZ1>233H ·- ZEROEQCTOCA.C),10tB,c>,TOOZ<A•C•Z>• rooz (e.c. z u EO<TD<A•C)•TD<B•C>l

L a OI:N~Gl}(C) J SATZD233J ·- lEHMAD&CTO<B•Cl•TO<A•C>•

SATZD203CCS;ArCrlEMMAO&<A•B•Ll•Nl) : MOREDU OU, ChTO(S,CU p :11 SATZJ203K ==- lEHMA05(T0(CrB>•TOfC,Al•

SATZOZOJO<B•A•CrLEHHAD&<A•B•L>•P)} lESSOU D(C,. AJ.TD<C•BH z öl SATZOZHL ·- ZEROEQ(TO<C•Al•TO<C•BJ•T001(C,.A•Z>•

TOOHc,a,zH ronoc:: .Ah rocc.au N :11 SATZOZ\1311 ·- LEMHA06{T0(C,9},TO<C•Alr

SATZD2C3f(B,.A•C•L~~HA06CA,S•L>•NJJ MORED<T OCC,. AJ.TO{C,.B))

a [p :CJT ]( Q: CUT l T19 ·- TRIS(CUT.JS(G,PlCP•lRP)lrPLCTSCQ.P)•

TS(Q,1RPJJ,PL<TS(Q,p),Q), OISTTP2(Q•P•lRP)•!SPlZCTS(Q,1RP),Q, TS{Q,p),SATZ151tQJl) ISCTS(öl,Pl(P,1RPl>•PL<TS(2,P),Q))

[R:C:JTl TZO ·- TRISCCUT•Pl(JS(Q,.Pl(P•lRP)J,fS(R•lRP))

rPl<PL(TS(Q,p),Q),R),pL(TSCQ,p), Pl(Q,R)),ISPllZCTSCQ•?~(p,lRP>>• Pl<TS(Q,pJ,Q),TS{R,l~P),n,Tl9•

SATZ151(R)),ASSPL1(TSCQ,p),Q,R)) IS(PLCfS(Q,PL<P•lRP)),TS<~•lRP>>•PLfTS(Q,p),pl(Q,R))'

TZl :: TR3IS(CUT,PlCTS(R,tRP),TS(Q,Pl<P.lRP)) ),PL<TS(Q,PLCP•lRPl},TSCR•lRP)l• Pt<TSCQ,p),PL(Q,R)),PlCTS(Q,pJ,ptCR,Q) ),COMPlCTS<R•lRPJ•TS<O•PLIP•lRPJJ), TZO.ISPLZtPL<Q,R),pL(R,Q>,TSCQ,p), COMPl(Q,R)l) : IS(Pl H SCR .. 1 RP), TS( Q,.PL(P• lR?)) h PU TSC ~),p ), PL. <ft, Q >))

A :l (P:PQSOCU l A~P' := RPOfPO(A,p) CUT ARPI := OV<1RP.ARP> CUT AI ·- PDOF'RP(ARPI> DIF' TZZ ·- TRlEQCTO(A,AI>,Of'CPLCTSClA,PlCARPI•

1RP)),JS(ZA•1RP>lrPltTSC1A•1RP), TSCZA,PlCARPI.lRP}))), 0f{PLETSC11,~RPIJ.PLCIA•2AJ)•

s

$

s

- 4.35..;.

•I VIt]

TZ3

T24

T25

T26

TZ7

A ; [N:NEGDCAJ l

PLCTSCZArA~PI>•PLC1A~2A))),

onrsc H..•A?i'Il.TS<ZArA:'\?i J h TOEQ1A(ArPLCAR?I#l~?>•1R?), EQS~S~<PlC!SC1A,?l{ARPI~l~PJ)

TSC2A•lRFll•PlCT5<1A•l~?>~ TSC2ArPL<ARP!?1RPl)),PlCTS(lA.ARPI), PlC1A•2A))rPlCTSC2ArARPil•Pl(lA•2A)Jr T20CAR?I,1Ar2A>•!2l(A~PI,zA,1AJJ• LE~~AOZ<fS(lArARPI>•rSCZA•ARPI>• PU lA • ZAl)) EQ<T D<A • A I>, Of'(TSU ArA RPU "TSC 2A., A RPI>)>

·- TR3IS~CUT,TSC1A•ARPI)•TSCPLC2A•ARP>• ARPl),?L{TSCZA.AR?IlrTSCARP,ARPt)), Pl(TSt2A•A~PI>•1RP),

lSTS!ClA,~lC2A,ARPJ.ARPir SATZl~ODC1Ar2A•P>J• 3ISTTP1CZ~.ARP,ARPI),

!SPLZCTSCA~P.ARP!>•l~P.TSC2A,ARPil• SA TZ 15 3C Cl !<'P • ARP))) : I Sn S (1 Ar ARP U *Pt<T SC2Ar AlP n .. tRP))

:: T~3IS<C~T.PL<TS<l~•ARPI>•1RP),. Pl(Fl(TSCZÁ.A~PI),lqp),lRP>•

Pl(TS'Z~•ARPI>•PLClRP•l~Pl), PL(PL!lRPrlR?),TS<ZA,ARPl)}, ISPllCTSClA•ARPI>•PlCTSC2ArA~Pt>•1RP), 1RPrTl3J,ASSPllCTSC2A .. ARPI)•lRP,.lRPJ,. CD~Pl(TSC2A•ARPI>•PL<iRP•lRPl1J : IS<~LCTSCtA .. ARPil•lRP>•PLtPLClRP•lRP),.TSCZArARPI)))

:: EQI12tTS<1ArAR?IJrTS{ZA.ARPIJ,. PLC1RP•lRPlrlRP,T2~) EO<DiCTSC1A•ARPI>•TSC2A.A~PIJl,1DrJ

:: TREQ<rD<A,AI>.OrCTS(tA.ARPI>• TSC2A,ARPI>>•l0Frf22,T25l : EO<TO(A,AIJ,tOF'>

·- SOHEICDIF'~[X:Oir1EQCTDCA,X)•10r),.AI• T2&> : SOME'"L•COIF',.[X:DIF'lEOCTOHrlOr10Fll

TZ8 ::: SATZOlT&C<Ar N) : POSD<K:J OCU) [H:oirltE:tQCTOCM00{A},H),10fJJ TZ9 : = TREQ C TDO.• HO OCH>), TO ( KOD CA hH) .tOF'"

SATl0197D< A,. H>rEJ EQ<TOCA .. HOD CH)) rlDf) T30 ·- SOMEICOIF,(X:OIFlE~CTOCArXJrlOrJ•

MO~CHJ.T29J : SDME•t•<Dif,[X:OIFlEOCTDCA,X),.10f)) N ; T31 ::: SOMEAPP!Oif,.(X:OtfJEOCTO(H00(AJ•X),

A ; [N:NOT(ZEROCAJJJ

10f),.T27(M0ûCAl,.TZS1r SOHE•t•CDIFrCX:CIFlE~CTD<A.XJ,.lOf)), CX:Oifl[T:~~<TD(HO~<AJ,X)•lOfJJT30(X, TJ J : SOME .. L• <Oif" Ut 0 IFHOUOU rXh ton J

lEMKA07 :: P.APPD<A•SCME~t•<Oif,.(X:OirJEQ(TOCA .. X)• 1DfJ)~(T:POS~!A)lTZ7•.IV4C"CTJ,

TH2"L.IMP•(ZEROCA>•SOME•L•CO!f•(X:Oifl EQCT0(ArXJ,10t)),.N),.[T:NEGO<Ail T3t•.IY4D•tf>> : SOKE•L•(OJr,[X:DiflEQ(TDC-·XJ .. tOrJJ

B ; tN:NDTCZEROCBJJl[H:OirltK:Difl[E:EQCTO(S,HJ .. AJltF:EOITO(S,KJ,A) )

T1 rz

T3

:~ TREOZ<TO<B·HJ~TO(B,K),A,E~F> :~ EOZERD(H0(f0(6,Hlrr0(8,Xl),.

TOCB.KD(H,.J)},QISTHT02(!,H~K)~

SATZ0182E(T0<3•H'•f0(e•Kl•T1Jl :: OREZ(ZERO<OJ,ZERûCMO~H~~l1,

SATZD19ZC(9r~O·~·K)~iZI~Nl

-4.36-

•IVSJ

-IVSJ

H•I \'5)

SATZnOtts

N ; tK:OIFI(E:EQCTDCBrHl•lDFll T~ := TRJEQCTOHJ.TO(H,AlJ,TD<TOCB .. HhAJ.

TDC1DF .. A>•A•~SST~2(8rH,AJp EOT0l(T~(B,HJ,1GF,ArE),SATZD195BCA)) EQCT0<3,TO~H.AJJ,A)

T5 •- SOKEI{DIF•[X:O!FlEQ<TD<B•X>•AJ,TO<H•A) ,Hl : SOME•t•<DIF',(lODlFlUCTO(BrX),A))

:: SO~EAPP<DIF,[X:DIFlEOfTD<B•Ä),10F)., lEMMA07(3•N'•SO~E~L~CO!f,[X:OtFJ EO(TOCB,XJ,A)),[X:OIF1tT:EQCTOCB•Xl• 1DF>:rs·.4ozo4·cx.r>>

a tR:C~Tl(S:CUTl(M:MORE<R.Sll

Tl

MORERPEPD

:: ISMORE12(Pl<R,PLC1RP,1RP}), PlCPL<R,lR?lrlR~J.PL<SrPL(lP.P,lRP)),

PLCPl(S,1RPJ,l~PJ,ASSPL2<Rr1RPr1RPJ,

ASSPl2(Sr1RP,lRPJ•SATZ134CR•S .. PU 1 R? •1 RP >. K) >

n·.t..-so .. , S a CM:MlREOCPDOFRP(R),pOGFRP($))]

" a rz := MOREOE!ZCPL(R,1RP)w!RP,PL(S,1RPJ .. !RP,

: MORE(P~(PL<R~1RPJ~1RPJ,PLCPLCS.1RP>•lRP}J

HOREDt~OOFRPlR>•PDOFRPCS))

10 : HORECPL (PL( R•!RPhlRP),pl( Pl<S•!RP), lRP})

H ill MDRE~PIPD

s a [L:LESStR .. SJ l LE:SSRPEPD

:= SAfZ136A<R,S,PLC1RP•lRP), ISMOR~!ZCPLCPL<R•lRP)•lRP), PLCR,PlCIRP,!~PJJ,pt{PL(S,lRPJ~lRP),

PltS.PL<lRP~lRPJlr4SSPLl<R•lRP•lRP), ASSPLl(S,!RPrlS?).,r2".IV50"JJ

::: LEHMAOSCPOOFRP!SlrPDOFRP<R>• ~OrtERPEPD<S•P.•SATZ122<R•S•L)l)

s a (L:LESSDCPOOFRPCR>,PODFRP(SJ>J LESS~PIPO ·- SATZ121(S•R•~ORERPIPD<S•R•

lEM~A06(POO• RP<R), POL'FRP(S hl J))

a I ::: lRP 2 ·- PLU •!)

R a RPI := Pl<!'t• IJ s a Sf't :: PUS•l>

RPS := FU~·S> ~s ::: TS!R#S>

MORE<R• S>

LESSDC~DOFRPCR>~POOFRP<S))

LESS<R, S>

CUT CUT CUT CUT

~ CUT Ct!T

s

s

s

s

s

s

s

- 4. 37-

T3 == TR!S(CUTrPL<PL<RPl,SP!l•I>• FLCPLCRPS>Zl•l)•PLCPL<RPS•I>•Z>• ISPL1C?l<RPl.SPll.PL\RPSr2l•l• 4PLZH R• h Sr IJ~· 3PL2HRPS•2• I}> ts<PL (" L<RP1,.SP 1 h I h PU Pl <RPS• U • 2 l J

u ::: TR~Q<POCPOOrRPCR),POOiRPtSll• OFCPLCRP1•5P1l,z),pQQfRP(RPS)• POEQlZA<RPl.I.SPl.I>,EQilZ<PLCRPlrSP1) ,z,Pl\RPS6I>•IrT3Jl : EQCPO(POOFRP(R)•PDOFRP<S>>•PDOFRPCRPS)J

-IV5) s

S a LEMMAOS :!:: T4 ... IVSC" : EQ(P0(~00FRP(RJ.POOFRPCSJ),P00FRP<PL<R•SJ))

ttrlV5!)

s 41 TS ·- TRIS(CUT,TS<RrSP!JrPl<RS•TStR•I>>• PlCRS•R>.OISTTPZ{R,S.!>•ISPLZ(fS<R•I ), R•RS•SATZ15l(P.))) tSUS(~ •SP1 hPURS•RD

TS ·- TR4IS<CUT.TS<RP1rSP1J.PLCTSCR.SP1), TSCirSPl>>•Pl(PL!RSrR>•SPl>• PL(Pl<PLCRS.P.)rS),!J,PL(PLCRS~RPS>•I>•

O!STTPl(R,IrSPllriSPLlZCTS<R•SPl>•· Pl<RS~R}rTSCI,SPl),SPl.T5r SAT~151S(SPl)),AS~PLZ(PLCRS•R>rSri)r ISPll(?l(Pl(RSrRlrS),PlCRS,RPSlr!• ASSPll<RSrRrS))) JS(TS(~Pl•SPllrPl(PllRS•R~Sl•I>>

T7 . - !R3ISCCUirPLCTSCRP1rSP1lrTS(I,Illr PL!Pl(Pl<RSrRPSlrll•l>•PL(Pl<RS•RPSl• ZJ,PlCRSrPl<RPS,Z)),ISPL1ZCTS(RPlrSP1) rPLCPlCRSrRFSlr!lrTS(I•I)ri•T6r SATZ151<IlJ,ASSPLlCPLCRS~RPSJ,!r!)~ ASSPllCRS•R?SrZ)l ISCPLU SCRP I.> SPI h TS<I,. I}) ,pL( RS,.PLC RPS,ZJ))

T8 ·- TRIS(CUT•PL<TSCRPlril•TS<I•SPl)), Pl(RPlrSPlJ,PLCRPSr2lriSPL1ZCTStRPl.IJ •RPl,TS{l•SPll•SPlrSATZ151CRPl)• SATZ1516CSP1)),4P~Z3<P.•!•S•I)) ISCPLCTSCRPl,JJ,TS(lrSPl)),PL<RPS,ZJJ

T9 ·- TRISCCUTrPL<PL<~S,I>~Pt(TSCRPl•l>r TSCI,SPl))),PLCPL<RS,!J,PL<RPSr2)), PL(PLCRS,Pl(RPS•Z>l•I>• ISPL2<PLCTSCRPlrilrTSCI•SP1>>• PLCRPS•2}•PL<RS•I>•T8>• 3PLZ3<RS·I,PL<RPS,Zll) ISCPLC? LCRS • I >.Pl<TSCRPl• I 1. T SC I • SP 1)) h

PLCPLC~S•Pl(RPS•2)),1l)

T10 := TRISZCCUT,PLCPLCTS<R?l,SPtJ.TSCt.t>>• I),PL<PLCRS,I),pl(TS(RPl•IloTS(I,SPl )) >•PL<?LCRS~PL(RPS.Z>>•I>• ISPLl(PLCTSCRPlrSPl>•TS<I•!)), PLCRS.PLCRPSrZ>>•I•T7J,f9} IS<PlC~LCTSCRPl•SPll•TS(l•Illoil•PLCPL<P.S~I>•

PUTS U Pl•I >•TS< I,SP1J))) T11 t= TREQCTO(POOFRP<R),POOfRPCS)),

0F(PltTSCRP1.SP1),TS<I,I:), PL(TS(RPl•IlrTSCI•SPlJJ)rPDOFRP(RS)r TOE012ACRP1•I~SP1•!>~ EQ!12( ?lCTSC RP 1• SPlJ, TS<t ~! }), PL<TS<RPl.!t.TSCI,SPl)J~Pl{RSri>~I• n:n > : EOCTOC~OOFRP<R>•POOFRP(S)),pOQFRPCP.SJJ

- 4.38-•IVSJ $

s O) : •PRJP'

; CSO=SET(C~TlltTO:SETCCUT>lCPO:ALL<tX:CUTJOR<IN(XoSO>,INCXoTOJJ) l[PlA:~ONEMPTYCCUTrSOJltP18:NQNE~PTY<CUT.TOl ltP2:ALL<tX:CUTltT:IN(X,SOJlALLCtY:CUT1[U:I~CY,TOllLESS<XoYlJ)}

TO ~ [R:CIJTl PROP1 :: ALLCCX:CUTltT:LESS<X•RlliNCX.SO)l P~OPZ := ALLC:X:CUTJtT:~ORECXr!lliN(X.TOl> PROP3 := AS!H?~C?!,.PROPZ>

P2 ~ tRl:CUfltR2:CUTltPRl:PROP3~Rl)J[PR2:rROPJCR2)] Tl := ANOE2(PROP1CRlJ•PROP2CRll•PR1J T2 == ANDElCPRDPlCR2J.PRCP2<R2),.pR2) [L:LESSCRlrR2llCXO:RATl RX := RPO!='lH<XO) ttl:~ESSCRlrRXlltL2:LESSCRXrR2ll Tl :: <tZ><îH>T2 T4 ·- <SATZ122(R1rRX•Lll><RX>Tl T5 ·- <REfiSCCUT•RXJ>EC3E31<ISCRX•RXlo

HORECRXrRX>.LESSCRX,RK), SATZ123BCRX.~Xi•<T4><RX><T3><RX>PZ>

t ~ T& := SATZl59APPCRl•RZ:L•CGN,(X:RATl [T:LESSCR1.~?0FRi(X))J

tU:LESS<RPCF~TCX>•R2JlTSCXoT,U)) PRZ ~ T7 :: [T:LESS<RlrRZlJT6CT>

TS :: tT:KORECR1.RZ>JTG<R2rR1,PR2oPR1, SATZl21(RlrRZ•T>>

T9 :: OR3EHISCR1oRZ>.KDRE<Rt..RZ>r LESSCRlrR2l,SATZ123A<R1,RZ),T8of7)

- PZ a T10 :: (X:CUTJ[Y:CUTHT :PROP.HX> )[U:PROP3(Y Jl

cxo:un SCH~ITTPROP :: SOKECCY:CUTlANO<lN(Y,SOJ.LRTCYrXOJ))

PZ ~ SCHNITTSET := SETOt(RAT•(X:~ATlSCH~ITTPROPCXJJ [R:C~Tlti:INCR,SOJJtXO:R~TlttX:LRT<R~XOJl Tll ·- ANDHIN(R,SOJ•lRHR•XOhi .. LXl TlZ := SOMEJ<CUTrfY:CUTlANO(IN<Y•SO),

LRTCY.~Oll•R•Tll) Til := ESTIICRAT•CX:RATlSCHNITTPROP(X),XO,

Tl2J R a CI:IN(Rrf0)l[XO:RATlCUX:URT<R•XOJJ[S:CUTltJ:IN<S•S011

Tl4 :: SATZlZZ<S~R,.<R><J><S>PZ> T15 := SATZ158B(R,.xO .. UXl Tl& := HOREISil(RPOfRHXOhS•

SATZ127C(RPCFRTCXO>,.R•S•Tl5,T14)) T17 ·- SATZ158!J(S;X:i•T16>

S :1 T16 ::: WELitEC<!fHS .. SOJ,L!HCS.XO)), tT:IN<S•SOllT17(T))

UX :1 Tl9. := TH5•t.SOI1E•<cUJ,.tY:CUTlANOUN<Y .. SOh LRT(Y,X0l),.(Y:CUTJT18CYll

TZO :: TH3•L.IHP"<IN"RT"(XO•SCHNITTSETJ .. SCHNITTPR0P{XO),Tl1• [T:IH"RT"CXO,SCHNIJTSETJ.lESTIECRAT~ (I:RATlSCHNITT?ROP(X}.XO~T))

PZ ~ CXOHUT H I :u•Rr•n:o.scHNI TTSETl H YO: RA TJ [ULE SS"RT .. CYO" XG ll I a T21 := ESTIE{RATrOORATlSCH)tiTTPROP(X),.XOoi) L a tR:CUTl[A:A~OliN(R,.SOJ,LRTCR,XOl)l

TZZ := I.NOEHIN<R•SO>•LRHR•XOl•A) T23 :: ANOEZf:INCR.SOhLRTtR,.XO).A) f24 ·- SATZlZOCR•XO• T23•YG•U T25 := A ttDI< IN( R• SO J,lflf Oh YO l • T zz,. T24) T26 ·- SO~!ICCUT,.(Y:CUT1A~OCI~<Y•S0lr

'PR!JP I 1 PROP'

: 'PRilP'

PROPZU 1J : PROPUR 2>

: CUT

IN<RX oS Ol INtRXrTO>

CON

CON : NOTClEiS(R1•RZl)

: NOHHDlECR1,RZ))

: AHONE<C UT .tx :CUT 1PRGP3CXH

'PROP I

SEJ(RAT l

AND( INt R•SO l •LRT<Rr XO))

: SC~ ITT PROPCXO)

: IN'"RT"'t XlhSCHNITTSETJ

: HORE<Rr SJ : HOREISCRPOrRTCXO),.R)

HOREIS[RPOrRTCXOlrSl URHS,.I( 0)

NGT(SC~NITTPROP(XO>>

NOT< IN• RT .. < XO,.SCHNITTSET))

SCHIIITT PROPOOl

INOrS) l : lrtTCR,.I( 0) : lRHR•YQ).

ANC( Hi[ R .. SO hlRTCR,TOl)

s

-4.39.;.

L 2 Tl7 := SOHEAPP<CUr, [Y:CUT lANJ<INCY,.SO}, lRT<Y·XOll•T2l•SCHNiiTPR3PCYCJ,[Y:CUTl (R:ANOCINCY.SQJ,LRTlY.X~)JlT26(Y,R))

TZ8 ·- ESTil<RAT•tX:RATJSCH~ITTPRDP(X),yQ, 127>

I ; CR:CJTltA:ANO<INfR,SOJ,LRT(R,XOJ)l T29 :~ ANOElC~N(R,SOl~LRT(R,XOl,At

T30 := A~CEZClN(f::,SO>.l~H?.,XO>./d [YO: UT HL Y:tRH R• YO> Jt t:u::ssp RT~c XC, YOl J T31 := ANDI(I~~f·SO>•LRTtR.YO),fZ9•LY) T32 := SOME!!t;IJT,(Y:CUTJAND(HIO,SOh

LRH y, YO) >•R• T31) T33 ·- ESTII<RAT,(X:RATJSCHNITTPP.OPCXJ,YO,

T34 r35

T36

A ; T37

I a T38

Tl?J :r. sArze3cxc.ro.Ll := ANDICI~·RT•ryo,SCH,ITTSETJ,

MOPE•RT•<YO,X0>~133•T34) := SOHtiCR~T,(Y:RATlAHD<IN•RT•

{Y,SCH~!;Ts~T),!10RE•RT"CY•X0}),Y0•Tl5;

·- CUTAP?3(R.xO,T30,SOME·~T-([Y:RATl AND!l~~~t·(T•SCHNITTSET}•

KORE~RT"<Y~XO))},(Y:RATl(T:LP.TCR~Y)l

(U:LESS"~T·cxo,YJlTJ6{Y,T•U)J

:= SOMEAPP<CUT•tY:CUTJAN~CIN<Y•SOJ• LRT<Y•XOJJ•T21•SOMEwRT•f[Y:R-Tl AHD<IN•RT•cy~scHNITTSET>r MORE•Rf•(Y.XOlJJ,[Y:CUTJ[J:ANO(!N(Y• SO J, UH< Y • XO )} lT 3 7 n • T> >

PZ a tR:CJTl[t:INCR.SOlltXO:RATl[LX:LRTCR.XO)l[S:CUTltJ:IN<S•TO> lCYO:RATlCUY:URT(S,YOJl T39 := CUT2CSCHNITTSET,.XO.H3CR,!.XO.tXhYQ,.

T20<S•J,.YO.UY>,.[X:RATJ(T:IN"RT~(X• SCHNITT5ET)J(Y:RATJ{U:LESS"RTwcy,X)l T28(X,.T~Y•U>.CX:RATJtT:tN•RT•<X• SCHNITTSET)ll38(X•T)l

J 2 T40 := CUTAPP18CS,CUTPR0P{SC~NITTSETJ,[X:RATJ CT:URT<S•XJJT39(X•TJ)

LX a Hl :: NONEHPTYAPPCCUT.TOrP18 .. CUTPROP\SCHNITTSETl,(Y~CUTlCT:IN<Y•TO) ]Tt,Q(Y, T))

I a T42 :::: CUTAP!>lACR .. CUTPRONSCHN!TTSEThtx:RATl (T:LRT<R•X)lT41(X,f)l

P2 :1 i43 := NONE KPT'I'AP!"CCUi, so,p lA• CUTPRDPCSCHNITTSETJ,(Y:CUTltT:IN(Y,SQ) JH2(Y,.T))

SNT := CUT~FCSCHNITTSET,T43> CR:C:JT l(t: lESS<R• SNT )] UO: RAT HUX: URH R, XOlHLX~LRHSNT .. xo Jl TH :: !NICSC!i~!TTSET,.T43,l(0•!..Xl T~S :: ESTIE(RAf,[X:RAT1SCHNiTTPROPCX)•XO•

T44) tS:CUTlCA:AN~<IN<S•SOl•LRTCS~X~lJl rt.& := AN!.'IE H INC s.so hLRTCS.r:n,. A) TH :: 1\NOElU~CS•SO),LI~HS•XOh~J PoS := ANOHURT<R,XOhLRHS,.lCOhUX,TifT) T49 := SOMEI<RAT.tX:RATIANDCURTCR,Xl•LRT(S,X)

hX0l'H8J TSO ::: EC31:23(ISCS,•R>~l10Rf:.:(S,;n,:..r.::s<S,R),.

SATl1253<S•Rl•SAïZ1Z2CR·S•T49))

SCHlUTf PROP<YO)

: IN-RT--E YO.SCHNITTSEU

INC~•Sl> LRH:'t•( 0)

ANDCINC R•SO ),LRT<R•YO> l

SCH:U Tr PROP CYO)

IN•RT•(yQ,SC~NITTSET> : MORE'"IU .. (YO, XO)

SGHE•Rf•((Y:RATlANDfiN•RT"(Y•SCHNITTSET)•HCRt-af•(Y,XO> ))

: SOHE•Rf•([Y:RATlAND<IN•RT•cy,scHNITTSET)•HCRE•Rr•tY .. XO> ) )

: SOME'"RT •en :RAT JAND<IN•RT"CY,.SCHNITTSETl•KCRE•Rf•(y,xo> ))

: CUTPRO' <SCHNITTSET)

: CUTPRQ»(SCHNITTSET>

CUTPRO,CSCHNI!TSET)

CUTPRO,<SCHNITTSET>

: CUTPRO, CSCH~JTTSEJ) CUT

: IN•H•( XO .. SCHNITTSEH

SCtl~ITf PROPCXO)

IIHS,Sl > t.!nt s •IC o > ANO(URF<R•XOJ,.LRT(S,.XO))

lESS(R• S)

~ICTllEi!HS•R>)

- 4.40-

----------------~51 :: TH3"l.IM?.{I~CR~TO>•L~SS(S•R)•T50•<R>

•5P2)5

•IYAJ

•!VA)

<H&><S>"'ZJ NOHI!'.'{R,.TO)) T5Z :: :JRE1<I~<R~SOh!'l<RrTO>•<R>PO•T5l) IN<R•S))

LX 2 T53 :a SO~EAPPCCUTr[Y::uTlANO(!NIYrSOJ,. lRT(Y,X0}),f45•I~(RrSO),[Y:CUTl [T: A N!H I tlCY~ SO hl RH y, XO)} JTSZ(Y rT)) INCR ,sl l

l ~ T54 ·- LESSA~PCP•SNT•L•:~[RrSOlo[X!RATJ [f:URTCR.X)J[U:L?TCSNT,X>lT53<XrTrU)) IN(R,.S)l

R 2 CH:HJRE(R•SNT>l(XO:RATJtLXtlR;(?,oXOl!(~X:URTCSNT.XOl HI:tNCR,SOJl

u x

"' PZ

R s

s

~

2

~

T55 := /.tmH!N(R,.SOJ,LRHR.XOJ,IoLU ANDtiN(R,SOhlRHR,XOJJ T56 :: SOKLICCUTr[Y:CUTlANO<IN<YrSO),

T57

T56 T59

T&O Tól

T&Z

T&3

snz•z:>s

SCHNITT

SATZPZ05A

SATZPU5B

lRTCYoXO)),a,T551 SCHN!TfPROPCXOl •- EST!iCRAi,(X:~ATlSCHNITTPP.O?CXJ•XO,.

T%> : tN•:H'"( XO,SCHNITTSET> ·- IN::<SC!·H-I!T-:'SETrT43.XC,.i57) LRHSNr ,.Xo> := TH3~L.I~?·ct~CR,SOJ,LRTCSNT,XO},.UX,

n:!'HR.SOÜT53CnJ NOHUtR .. SOll ::: ORE:ZCHI(i',SOhiN<R,TOJ,<R>PO,T59) : IN(R,l)) ·- HOREAPPCR•SNT•M•I~<R~TO),(X:RATl

tT:LRT{RrJllC~:URT{SqJ,X)JT60<X•T•UlJ IN<R,T) i ·- A~JI(~RD~lCS,Tl.PR~P2<SNJJ,:X:CUTJ

rr:lESS(X•S~TJli54(X,T),[X:CUTl {T:MO~EO::,s:~T>JH>HX,T)) : PROi'3GNTJ

·- S0~E!<CUT•CX:CUTJPROPl{X)rSNT,Tó2J SOHE(C(:CUTJPROP3(XJ)

:: ONEICCUT,CX:CUTlPROP3w.spzos•<X), rlo~.spzos•.t63•.spzós•>

:= IND<CUT,(X:CUTJPROP3".5P205"CX>• SATZP205J

:: ANOEl<PRCPl•.sPZ05•<SCHNITTJ, PROPz•.SP205•csCH~ITTJr ONEAXCCUT•CX:CUTlPROP3•.SP205"(X), SATZPZ05))

::. A N!)E Z(PROP 1". 5?205"( SCHI'fi TT),. PR3PZ•.5PZ05•csc~NITfl,

ONEAXCCUT,[X:CUTlPROP3•.spzos~tX),

SATZPZ05Jl

: ONEC[X:CUTlAND(ALL<CY:CUTJtT:LESS<Y,.XJliN<YrSOJ),. ALL({Y:CUTJCT:MORE<Y•X>liN(Y,.TOll))

CUT

a (R:CUTltS:CUTl

a I a Rl a Sl

RPS a 2 a Tl

f2

Tl u

T5

::: lRP := PUR,. I> := PUS•D ::: PU R• S) ::: Pl<i•Il :: PDEQ12ACR1•I,.Sl•I} :: TRiSCCUT•PlCRl•S1>•PLCRPS•Z),.

PLCPl(RPS.IJ,tJ~4Pl23'R•I•S•I>• ASSPL2CRPS•I•lJJ

:: ISPt.l< 0 URb Sll• PUPURPS• I i.. I h I,. TZ) := TRlS{CUT .. PLCPl(Rl,Sl)•I>,.

PLO'L< PU RPS • I h Il,! h f'LtPU !'tPS•! hZ h T3rASSPllCFlfRPS,I),I.t>>

:: EQ!l2<?UR1, 51 h 2•PUP.f'S• IJ,.!, H J

CUT CUT CUT

: CUT : CUT : EO<PO(~OOfRP<RJrPDOfRP(S)),.Qf(Pl(Rl•SlJ•ZlJ

: IS<PLU 1.s1 hPl(Pl<RPS•U• I» ISCPL<~L<R!•Sl>•I>•PL(PL<PL(RPS•I>•I>•Il>

lSCrLt~L<R1•SIJ,IJ,.pL(PLCRPS1IJ,.zl, EO<DF<,L<Rl•S1J,zJ,.pDOFRPCRPS))

s

s

- 4.41-

•IVAO

HIVAO

S a RS T&

T7

TB

T9

HO

TU

TlZ

TU

Of<Pt<PL ?.,lqp),~l<Srl~Pl>•PlClRP,lRPl · >•PDOrRP PL<R•S>I•Tt•.Iv~o~.ts•.IVAO"J t EOCPO<»OOFRP<R>rPOOFRPCS)>•PDOFRP(PL(R•S))~

:: TS<R•S> CUT := TOE:Q tZAOUo I, St.!) : EO CT OP OOf'RP CR) ,POOFRP < S)) oDF< Pl. <TH Rî • Sl h TSCI, I) h

:: TR!S(CUTrTS<Rl~S)rPLtRS.TSCloSl)r PLCP.SoSlrD!STTPlCR•I•S>~ISPLZ<TS<I•Slr

PlCTSC~l•I>,TSCI•Sl>>>>

SrRSrSA!Z!5iS<S> )) ISCTS<l l•S>•PL<RS•S)) :: TR3IS!~UT •. TSCR1.S1loPL<TSCR1rSJ,

TSC !H,.!) h?U PU '!Sr S h Rl >, PUPUR.S•I h RPSJ.~ISTT?2!RloSr!JoiSPL12<TSCRlrS), Pl(RS,s,~TS<Rlrl>•Rl•T7rSATZ151Cal)), 4Pl24C~S· s.~,!)} ISCTSc:t bSl hPLCPLCRS• U•~PS))

:: TRIS(CUToPLCTS<Rl,Sl>,TStloi)), Pl(PL<PL{RS•l)oRPS)ol>•PlCPL<RS•I>• PlCRPS~IlJt1~PL12CTS(RlrS1Jr PLCPL{RS,IlrRPS>rTS<I•Il~I·T~. SATZ151(IJlrASSPtl<Pl!RSr!l.RPS,!)) IS<PL<TS!Rl•Sl),TS<I,I)l,Pl(PLCRS,IJ,Pl<RPS,!J))

:= TRISCCUToPL(?l\TSC~ltSl};iSCI•I>l•!>• PLCPL<PL<Rs~t),PlCRPSr!lJ•l>• PLCPL\RS•!),PL(PL<RPS•!~•!>>• !SPll(PL<TS(Rl~SlloTS({,IJl; Pl(PL(RSoi>•PltRPStilJol•T9lo ASSPllCPL<RS.IJ,PL<RPS.IJ•IlJ : IS<PL<~L<TS<Rt.SlloTSCI,IJJ,I);Pl(PLCRS•lltPL<Pl<RPS,IJ

•- TR3IS!CUToPL{Pt(RPS,Ilrl),pL(RPS,z), PL(RloSll•PL<TS<Rl•IltTSCI•Sl)), ASSPL1CRPSoiril•4~l23(R•S•I•Il• ISPL12<R1•TS<Rl,I>•Sl·TSCr,s1J,

• I)))

SATZ151A(RlloSATZ151CC5lJ)J ISCPLC~LtRPSoil•I>•Pl<TSC~l•IJ,TSCI•SlJlJ :: TRIS{CUToPL<PLCTS<Rl•Sl)oTS<I•!))•I)r

PlCPLCRS.!J,PL<PL<RPSr!),!)), Pl(PLCRSriJ•Pl(fS(Rlrl),TSti?StJJ)r TlO;ISPlZCPLCPLCRPS.Il.I>•Pl(TSCRl•I>r TSCirSt>>•PL(RS•l>•T11>> : IS<PLC~LCTSCRl•SlJ•TSCiril>•I>•Pl(Pl(RS•IlrPLCTSCRlril•

TSCI ,.sl ) H) :: EQI12CPLCTSCRlrS1J,TSCir!llr

PU TSC Rt.!),. TS<l .. SU hP!.CRS, I);! .nz) EQCDf'P LUS CRl,sU, TSC J,. U ),pl( TS<R bH• T SUr SU)); PDOFRPC RS n

S a LEMI1AIVADZ :: TREQUIHPI>O!"RPCR},PCCFRPCSJh OftPl(TS<PLCR,lRPlrPLCSrlRPl},. TSC1 RP•lRP > h PL< TS( ?L( R• 1 RPI. 1 qp), TS<1RP,PL<SrlRP)))),P00fRPCTS(RrS>J• T6w.IVAo•,Jt3".IVA0")

CH:MOREOCPDOFRP(RlrPOOFRP<S~>l

" a ru T15

:: MQP.EDE12CRlri•Sl•I•~' :: SATZ15SACRt,s1~I·T~4J

M a LEHHAIVA03 :: SATZ136A<R~S•1RF~Tt5~.IVAO•) ~ tc:oirlCA:OIFltB:OIFJtN:~QTCNEGO(A)Il(O:NOTCNEGO!Bl)

: !OCTO<~DOFRPCR>rPOOFRPCSll•PDOFRPCTSCRrSl)J

MORE<P:.. <Rl• I hPUShi>) : HORE<R1,S1J

: ~ORE(R.- SJ

s

- 4.42-

lEE:EQtlOtA•AJ,.~JJif:EQ{lOt~•S),C)J

•3161 s

Tl := TRE~Z<TO(ArAJ•TOCB•B>•C•E•F) EQHD<\ "AhTD<B,.BJ) TZ == TREQCPDCM~<TOCA,AloTOCA,BJJ,TOlB•Al)•

PO{vJ(T~(A,AJ,TO<A•3)J,TCCA•S))• TOCA.A),[QP~Z<TO<B.A>.TO<A•B>• HJJCT ')(~ .• Ah T 0( A• 8)) • CO?HD (8, A)), PDMO<TOCA,A),.TO<A.9J)) EO<PD<'I onou.u,. rou. BH· roe a .. u" rou .. A,,

T3 := TR4EQCT~tPDCA•S>•MJ(A•8)), PO(TOtA.Kv(A,BJ>,TOCB.KD(A,SJ))• PDCMO(!DCA,Al•T~<A•alJ,HOCTO<B•A>• TOC6.6))J.~~(P0(K0(f0(A,.A),TO<A•B>l•

TDCB.A})•TO(B•B>>•KC(TQ(A,AJ.TOCB•BJl• DIST7?al<A•B•~DCA,9)),

E2P01Z<TD<A•MD(A•9>J,HlCTO<A.A>• TOCA.SJJ,.TO{B.MOCA.SJ),.HOCTO(B,AJ• TDCB•S>>•OISTT~OZ<ArA,Blr DISTTH02CS,A,BJJ,ASSPDZCMO(T0CA•Al, TO<~•a>>•T~CSrA>.~OO<TO<B•BJ>l• EQM~1{?0{~J(T~tArÄ),i~(A,8)),TOCS,Al)•

TOCA.~J,Tv<S•B>•TZ>l EOCT !')(" lH A• 8 J..MD<A• 8) h HOt TOC A.- A J. TOC B• B)) l H := EOlEROCMOCTJ(A,A),TOCBrS)l,TD<PDCA,Blr

MOCAr9})rSYHEQCT~CPDCA•B),HO<A•B)J,

KDCT~CA,A),TOCSrB)),Tj},

SATZ~18ZECTDCArAlrTD<S•Bl•Tlll : ZERO( Tl CPOC A• 8) • MDC A. 9 )} ) T5 :: SATZ0192C<PDCArB),K0(A,8)rT4J : OR<ZERl CPD! A.BJ hZEROO!DU ,.B))) rz:ZEROUJ l T& := EOIEROCTOCA,A},f0(8,B>rTl,T001(A,A•ZJ) : ZER1J< nes .. a,, T7 := THt•L.I~P*CZEP.O•ZEROCB)•

REFI~PCZEROC8lJrSATZ019ZCCBrBrT6)) ZERO< 8) TB == ZERGE~<A•9•ZrT7) EO <A• 8)

r a [P: NOH ZER OU) H T9 -- OR3EZ<ZEROCAJ•POSDCAJ,NEGOCA),AXRDO(A)

,N,P} POS!H A, TlO == TH3•L.IHP•<ZERO(B),ZEROCAJ,p,

[T:ZERO<BJJT7<8•A•O•N•r•EPTJ) NOH Z~ OCBJ J TU ·- T9CB•~•O•N•f•E•T10J POSO< BJ T12 :s PNOTOOCPOCA,a),ppQ(A,S,T9,T11)) : NOH ZE!t OCPO( A.BJ J J TU := OREZCZERO(PO<A•B>>•ZEROCHDCA.B>>•TS•

T12} : ZERO 013 u, B }) T14 == SATZJ1828(A•B•T13> EOU•!U

-0161 s

SATZDUlB == THt•L.IMP•czEROCA> .. EO(A,BJ,(T:ZERO(AJl ra•.C!&l•(Tl•(i:~OTCZEROCA>JJ n4•.:n61•n >l : EO<A"BJ

C OI [N:NJTCNEGD(CJ)l

u!)1!)1 $

N ; CZ:ZEROCCJl TlS := ZERCEOfTD<C•CJ•C•iOOl<C•t•Z>•Zl EO(TO(i:,.CJ,.C) Tl& == ANJit~OTCNEG0(C)),~Q(T~(C,CJ.CJ•N•T15J : AND! NOi (NEG 0( CU • EO<TO CC•C J"C > J - 4.43-TlT == SOMEICDIF.tX:OIFJANDtNOT(NEGOCXJJ,

E~tTD(~,.xJ,.Cl),C,T16) : SG~E·t-~O!F•[~:Q!FJANOCNOT(NEGDCXJ)•EO<TDCX•X>•C>>> N OI CO:NQTCZEROCCJ)]

T18 ::: OR3E2tZEROCCl•POSDCCJ.NEGO<C>•AXROOCC) ,N.Ol POSOCC)

CRP :: RPOf!"OCC•T18) ClJT

•0161

•INTD

+-INTO

+*I NTil

;)l'lr-

s T19

TZO

TU

N 41 SATZ!>161A

; [A:Oifl[I:INTOCA>l

rz: ZEP.O<A> l

: = PDOF RI' CS F!P) Oir ~· TRJE?CTOCS•S>rPDGFRPCTSCSRP•SRP))•

POCFRPCCRP>.CrlEH~ll~~OZtSRP,SRPJ, IS~PEPCITS<~RP•SRP>~CRPiTHSORllC~RP)J, EQ?û~i'ZtC.Tl'l)) EQ<TDtS.ShCJ

:: AN~IC~DTCNEG~CSJl•E9CTD<S•SlrC)• P~<OP;~ ( S •? !iS:! I RP (S1P n • U 9 l ANOt NOf UI EG l)( S)) ,(Qt'TD <S•S hC))

:: SO~[!(OIF•\X:J!F~AN~(NOJ(NEGO(X)), EQ{; D 0:• :0 •C) )., s .. TZO > SOHE •t• (0 If • (X: 0 If'l AN!H NOT ( NEGO( X l hEQCTOO:• X) ~>C)))

:: THl•L.I~P~<ZEP.CtCl.SCMEnt•<orr.cx:Oifl ANDCNOTtNEG~CXJJrEQCTO<X•X>•ClJ)• [J:ZEROCC)~i17•.~1&1•(J),

[T:NQT<ZEROCC))~TZt•.Ot61•(J)) t SOME~L•(Olf•(X:DIFlANOCNCT(NEGD(X)J,EQ(TO(),XJ•C>>J

Tl :~ ORilCZERO<ABS~CA)JrNATOtASSO~ABSDCAJJJ •SAT lOl&&fC Ar Z)) : I NT i)( AS SOU))

I ; tN:NATOCABSO(A))l TZ ·- NAH NiOCABSOUh N> INT:> <AB SD<A > >

INTUSO :: ORAPP<ZERO(A).NATO(ABSDCA)), INTOCABSD<A>>•IrtT:ZERO<AlJ Tl•.INTO•CTJ.CTtNATD<ABSO(A)JJ f2•. INTO•( T>)

:a EQNATDCABSOCAJ,ABSO(MOO<AJJ, SATZ017SAUhNJ

I a INTH3D := TH9•t.OR"ClEROCAlrNATOCABSOCA)), ZEROC~OO<AJJr~~TOCA8SOCM00{A))),I• tT:ZERO<~>lSATZ017GBCArT), CT:NATOtAS50(A)llT4".!NTC"(f))

A a tB:OiflCI:INTDCAJl[J:INTO<BJl

J a tz:ZEROU)!

: INTDUBSOCA ))

NATOCAB SD<KOD<A)) J

: UH:> 013 OU) J

T5 t: ST~EO<POU,BJ•B•PDOlU.;B•Z)) EO<B•P·l<A•G)} T& := EQlNTll<B•PIHArSl,TS ... .!J INTD<PlUrB))

J a tz:ZEROl TT :a SYKE Q( PI)( A rB ÎrAr POO<:<A,.s, ZJ J EIHA ,p, u~a)) T8 ::: EQINTD<ArPO<A,.BJ•J7,I> : INTOCP)(A.BH

A a [1: INTI)( AJ ]( P: POSO<A)] . f9 ::: ANOEZ(PCS~(A)~[T:POSOU.H

NATRPCRPC~PJtA,T>>•PDS!UrNAfD<A•P'I,J NATRPC.POFPO(A~P>l J ; [PP:POSD!PO(A~Blll

APB1 ::: RPOFP!HPD<A•BhP!>) : CUT CP:POSDCAJ l Al :: RP~fPO(A,?l CUT

s

$

s

s

$

s

(QtPOS:>(S)) lH = RPOF PO (!h 0) CUT TlO = NA?PL(Al,T?<A•l•P>.Blri9(8rJr0J) NATRPt~l<AlrBllJ

Tl1 = EOPD1ZlArPOOrR?(Al)rS•POOFRP<91)• EQPO?.PlCArPlrE~?ûR?l(g,S)) : EQCPD(ArSJrPD<PbCFRPCA1J,,OQFRPC81JJ)

T1Z ·- TREQ<PO(ArBJrPD(PD~F~PC~llrPOOFRP(BlJ) ,?QOFRP(Pl(Alr31))rfllr LEHMAIVADICAlr81Jl : EO<PDCArBJ.PDOFRP(PlCAlrBll))

T13 ·- TP.!S(CUT.AP8!rRPOfPO<PlOFRPCPL(AlrB1)J ,pasOI~P(PL(AlrBllJlrPLCAlrBl)r EQ?OER?CPD~Ar9J7PPrPOOFRPCPL<Al•BlJ), POSOIRPCPL<Al.B1J)7T1Z>r iSRf'!"JZ( Pl< A l• !H))) : lSUPBl rPU Alr91 U

rt4 :: ISPH:Uh t 1': C:Jil NATRP{ T hPUAhBl h AP3l,TlCrTUl NATRPCA PSU

T15 :a ANDif?OSOCP~(ArB)J,[T:PDSO<PD<Ar9J)J NATRPCAP91(T)J,pp,(J:PDSDtPnfA.rS)Jl Tl4(J,P,Q)} NATOCPl u,s))

T1& :• NATINTDfPOCA.rS)rT15J : INTiHPl U .oB)) P a Uf:NEG!)(SJ J

TLT := S.HZ0!7~C(B• N) POSO<Hl O(BJ J BZ ::: RPOfPC(H?J(3J,T17l : CU i Tl8 . - EQPDZCB.r~ODCM00(8)J.oA•SATlD177At9)) ECICPDCA rBl.rMOU.MODUJ)) T19 ·- EOPOSO<P:lU• B hMO( A.o ~00( B> h TJB,.PP) POSIH M) U .. HOD.oT19) : MOREO{A,K00(8)) Tzt := EO~QREDl~[A.rPOCfRP<AlJ•MOOtS>•

PDGfRP<BZJ.rEOPORP1(A.rP>.oEOPDRPl<MOD(9i •T17hTZO> : MOREDt»DOfRP<A1J.oPDOfRP(82l)

rzz := LEMHAIVA03(At.92.oTZll : MORE ( Al ,. BZ> T23 ·- NATMN(Al.oT9(Ari.rP>•B2.rT9(HODCB).r

INTMOO€BtJ)rT17>•T22) NATRP(I4 NUl rBZ.o TZZJ) 1'24 := EOPD1Z(H00(8l.rPDOf~P(B2J.rPOCA.r8l•

PDOFRPtAP61J.rEQPORPl(~OO<BJ•T17).o EOPDRPl(PQ{A,SJ .. PP)> EOCPDC~OOCBl.oPDCA .. 8J),pQ(P00FRP(BZJ,poCFRP(AP81JlJ

T25 ::: TR4EQ(A,~O(POCA~a>~s>,PD(MOD<Bl, P0(A,B)l.rPOCPOO•RP!B2J~POOFRPCAPB1)), PDOfRPCPL<BZ,APSlJJ,SYMEO!HD<POCA•Blr BlrA.KOPD<A,BJ),COMPCCPO<A•BlrMODCB>J• TZ4•LEMMAIVAD1CBZ,APetJJ : EQCA .. P)OfRPCPLCBZ,APB1J)J

T26 == TRISZ<CUT.PL<BZrAPBll•Al.o RPOfPOCPUOfRPCPLCBZ,APBl)), POSDIRPCPL(82rAPB1J)J, ISRPP01CPL(82rAPelJ), EQPDERPCArP.POOFRPCPlCBZ,APBl)}, POSOIP.P<PL{B2•APB1lJ,TZ5J) !StPLCS z,.APBlJ rA 1)

127 :a SATZ14~CA1,82,AP81.ïZZ.Tl&> : IS!APBlrMNCAl.oBZ•TZZlJ TZ8 '"' ISPl(CUTr[T:CUTlNATRP<TJ.MN(Al.oBZ,TZZJ

.oAPS1rTZ3.oTZT) : NATRPCAPBlJ T29 :a ANDICP3SDCPJ(A,B)JrCT:PDSD(PDCArBlll

NATRPClPS1CTJJ,pp,(J:PQSOCPDCArBl)l rzao.r>.NJJ : NATDCPl CAr8))

f30 := NATINTOCPO(A.r8)•l29) INTOCP) u~a )) p a T31 :: RAPPOtS.INTD(P0(A,8J),[f:?OSD(8)]

T16CTl~tT:ZEROlT6(T),[T:NEGOC6)l T30(J)) INTOCPiJ u,.a U

PP a tH:N5:GDU)l - 4. 45-T31A := TH3'"l• J)fP"CNEGOC Bl~> NEGDCP!).(h8) h

PNOTNOCPDCA.BJ,PPJ.tT:NEGDEB)lNPOCA•B~ NH>) ·: NOHNEl 0{8))

J3Z ·- TH3•L.lMP"<ZER0(8).oNEGO(P0(A•B)), PN~TNO<PO(ArB),pp),[J:ZCRO!B'l

CO~EGOCA•PO{A,B>•SV~f.Q(OO(A•B)•A•

•IN Tl

HINT!)

POOZ<A•B~T)l,N:J

T3l ::: OR3EZCZEROC9lrP~SOCB)rNEG0{8J,AY.RDO<B) .. TH~-· i'3ZJ

T34 : .. EQPIJSOCPDU,. g hPOCS• AJ,.COKPO:ArS hPP l T35 :: r 3:>< a. A• J" h TH• n:s .. ~u TJS := EQ!~TJ(P0(8.A),POCA.S).C0MPDC8 .. A).TJ5)

pp ~ T37 :: RAP?O{A.INT~(PO<A•B)};(T:?QSD{AJ] T31<TJotT:Z~ROCA)lf6(T)rtT:NECD{AJl T3ó{ T>)

J ; t3P:ZEROCPO(Ao8))J T38 :: I~TOI~<PO(Ar9);0P)

J a CNP:NEGO(POCA.B)JJ Tl9 :: SATZa176C(PDCA;9)•NP> T40 := ECPOSOtHOD(POCAr8)),pQ(H00tA),.H0D{8))r

SATZ01eOtA,g),i39) TH :: -T37CM00(A)rKODtB>•lNTM3D{Aoll•

ilf:MO'HB•J'' HO> HZ ·- EQINTD<POC~~D(A),~00(8)),MODCPOCA•B)),

SATZ0130A{A,g),T41J T43 == INTMGDC~C~C 0 0{Ar9l},f4ZJ Tftlt := ~QI~TOtMC~t~CD<POCA•B>>J•FD<A•B>•

SAiZ~177(?0'J•B>>rT43l

J a IHTP) := RlPPO(PD<A•B'•INTDCPO<A•B)l• (T:POSDCPDCAr9))lT37•.INTO•(T)r tT:ZEROCPDCAr9l>lTl8".INrD•(f), [T:NEGOCPDCArSJ>lT44•.INTO•(TJJ

INT MD ·- INTPD(ArMOOC9J•I•INTKOOCSrJ))

J ~ [H:NOTtZEROCTO(ArB>J>J T45 := TH3•t.IMP•czEROtAJ.!EP.OCTO(Ar8)),Nr

CT:ZERO<A>lTOOlCA,S,T>> T46 :: TH.J•L.IMP"CZERCCBJrZEROCTOCArBllrN•

(T:ZER0(8)JTC02<A•B•T>> U7 :: SATZD166E<A• T45l A3 := RPGfPOCABSOUhT47> H8 := SATZ0166EC IJ,. T46) 83 :: RPOFP~<ABSO!BlrT48) H9 :: NATTS<A3•T9C MIS!HAh tNTASSIHAriJ.T47 h

B3,T9(A8SDCS>riNTA9SOCB•J),T48)) TSO := SATZD166E(T~<A .. s> .. N> [P:POSD(ABSDCTDCA .. B)))] ATB3 :: RPOF'POCABSOCTOCA.B)),.p) T5l ·- EOT012<ABSOCAJrPOOFRP(A3)rABS0(8),

PDOrRP(BJ),.~QPORPl(ASSDCA>•T~7)r EQPDRP1CA85~(8),T48J)

TS2 :: TR3EQ< ABS.O(T!i( A,S)}, TO<ABSD<A>,ABSD ),TO<POOFRP(AJ}o?OOrRP!83)J, PDOfRP(iSCA:SrBJJlrSATZD193C~•B>•T51• LEMMAIVADZCAl,Bll)

T53 :: TRIS2CCUf,ATB3 .. TS{Al•B~Jr RPOFP0<?00fRP!TSCA3,SJ)),. P050IRP(TS(A3,~3)l)•

EQPOERpCABSJ<TC{A,B)J,p, POOFRP<TS,AJ,g3)},pOSOIRP(TS<A3•83)), T52),.ISRPPOl<TSCA3 .. 83)))

154 :a ISPl(CUT,.[T:CUTlNATRP(f),.T5(A3r83),. ATB3r149, I '53 >

NOH ZEt 0(8))

POS!)( BJ t POSO( Pi) <BrA J l : I NTH PJ CB rA)) : INTIH PJ (A,. B))

INTDtPl <A•S))

INTi)(P) (A oB))

POSO< H) OCPO< ArS)))

: POSOCP)(H00(A),MOOCBJ)l

I INTDCP3CKODCAJoKOCC8)))

: INTDC H:J OCPD (Ar 8))) : INTD01) !)(K()~(P0Ur8 ))) )

: INTDCP~UrBll

: IfiTD( PI) u .. a)) : INTDCM) (A,.B))

NOH ZER 0( A) J

: NOHZElO<BJJ : POSOUBSD(A))

CUT POSDUB SD.ABSO< B)) • TDC POOrRP( A3 h PDtf RF<B~J) l

NIITr:IPU Ti!.H

s

s

- 4. 46-

•INTl

•IVR1

•tVRl

Na ns

J a INTTl

a EO ~EH; S Y'!E;

TREQ

:= ANDitPOSO<ABSDCTDCAr8)))# tT:POSDCABSDCTD(A,BJJ)JNATRP<ATB3<T)), T50rtTIPOSOCAB50(TJIA•B)))JT54(f)J N.\Toua sonou.su>

INTOCT9 u .. s J J

:= tX:I>If"HY:OIFlEQ"P.f'"(X,YJ tx:OtrJ tY:O!Fl'PROP' :: [X:OIFlREfEQ"RP"(X) : tX:DIFJ<X><X>EQ :: [X:DIFltY~D!Fl[T:<Y><X>EOlSYMEQ"RP•tx ..

: U:OifJ n:OIFHT:<V><X>EOl<X><Y>EO

$

s

•- tX:DirJ[y:CIFltZ:DIFlCT:<Y><X>EOl (U:<Z><Y>EOlTREQ"RP"<X•Y•Z•T~U) : tx:OIFJ (Y:O IFH Z:OIFJ[ H<Y'><X>EOJ[U:<Z><Y>Eill<ZHX>EQ

a

a

R a

A a R a A a R a

R a

R a

[A:OIFJ[StSET<~IF>l Uf.f :: ESTI CO If" ,A,S) REAL :: ECT"EQ"COIFrE9rREfEOrSYHEQ,TREOJ tR :REAL HS :REAll IS IHS tP:tx:~EAll'PRQP•l SOHE ALL DHE tSO: SETC RE AL) l

:: IS•E•CREALoR•S> :: NOTCIS(R,S))

:: SOHE•L•<REALrP) :: ALL•t•(REAL•P> := ONE•E•CREAL•P>

I!i1 •- ESTHREAL•R•SO> REALOF := ECTELT~EQ"(OIF,[Q,REFEOrSYMEQ,TREQ,A) CLASS :: ECEcT-(Q"(DIFrEO•R~FEO•SYMEOrTREO•R> INNC~ASS :: THS•(Q.4"(DlfrEO~REFEOrSYHEOoTREQoA) tA:OIFJtB:DifltE:Eo•RP•(~,BJltAIR:INN<ArClASS(R))l EOIN~ :: TH8•EQ.4•(DifoEOoRErEOrSYHEOoTREO•R•A•

AIR.s.o [P:•,~OP 1 lCP1:tX:Oifl[XI:IN~CXrCLASS<R))JPJ REALAPPl :: THJ•EQ.4•COif,EQ,REfEOoSYH(OoTREO•RoPo

PU

: 'PR!JP' 'TYPE'

'P=tJP' : 'PR:lP'

·: •PRDP• 'PROP' 'PROP'

: 'PROP' REAL SET{ Oir J

: INN(A,:lASS(REALQF(AJ))

: INNtB .: LASSCR))

p ($ :REAL ](P: t PROP' l[P1:[X:DifltY:DIFltXI:INN<XoCLASStRJJltYI:INN<YoClASSCSlJJPJ

tA:OifllAIR:INN(AoCLASSCR>Jl Tl :: REALAPPl(SoPr[Y:Dtfl<AIR><Y><A>PlJ : p

:: REALAPPl<R•P•tX:OIFlCXI:INNCXoClASSCRJ JlT1•.IVRt•<XoXl}) : P

S ~ [T:REALltP:'PROP' l tP1: U:Oif l (Y:Oif l [l:!>IF ltXI:I,NtX•ClASS(R)JltYI:INNCYrCLASSCSJJltZI:INN(ZoClASSCTJJ]PJ

Pl ; CA:DifltAIR:INN<AoCLASS(R)tl TZ := REALAPPZ(SrTrPoCY:OtfltZ:OifJ<A!R><Z>

. I

s

- 4.47-

·IVR1

T a tu:R~ALJ[P:'PROP' ) [Pl: (X:OIF }

[ y: !)I f 1 cz:orr l cv:ntr J

:: RE~LAPPl,RoP,[X:O!Fl[Xt:INN<X.CLASSCRl )liZ•.IVRl·(~•Y.I>> : P

rxt:!N,(X•CLASS<Rll ltYI:iNN(T,CLASSCSl)l[ZI:INN(Z~CLASSCTJJJ[VI:I~NCV,CLASS<UJJlPl

uiV?.l

•IYRl

Pl ~

P1 a

s :)

Bl!S a

SliS a

aus a

a

tA:O!flCAIR:INNCA~ClASSC~JJl T3 :: REALAPP3(S,J#U•P•[Y:OIFJCZ:OIFlCV:Oifl

<AIR><V><Z><T><A>P1)

REALAPP' :: REAtAPPlCRrP,tX:OitlCXI:INN(X,CLASS(R) >li3".IYRt•<x~XIJJ : P

tA1:Jifl[91:0IflCA1IR:INN<Al,CtASS(R))Jt91IS:IN~(Bl,CLASSCS)) J[[:[Q•Rp•(A1o81JJ ISIN := TH3*Eo.s•<OIF,(Q,REFEQ,SYMEQ~TREO~R•S•

AlrAliR•B1r31!S.•Ël ISCihSJ ri:iS(R,S)J ISEX :: IHS•Ea.s•<DifrEOrREFEOrSYM[Q,TREO•R•S•

u.AtiR~!n.aus.o : Eo•RP"t AhBU CN:MJf([Q•Rp•(Al,B11ll NISIN :: THl*l.I~P·<ISCRrS},[Q•RP•tAlrBl)oHr

CT:ISIR,S)JISEXO)) : NIS(R,.SJ [N:NISCihS)) ~ISEX :: THJ•t.IMP•([Q•Rp•(Al•Bll•ISCRrSJrN•

CT :E Q•RP,.( Al, a U li SII\C TiJ NOH [Q• R?•( HrSlJ l CALP~A:'TYPE'l[F:tX:OiflALPHAJ fiXF :: FIXfU•Ea·c~If,[Q,~EFEQ.SY~EQ,TREQ•

ALPHA•F) 'PROP' [Ff:F'IXF(AtPHArf)J(RO:REALl INOREAL :: INOEQ•Eo•<oir~EQrREfEQrSYHEQ•TREO•

ALPHA.~~rr.RO> ALPH~ {AtOifl[AIR:IHNtAoClASS<f.O>lJ ISINDREAL := TH2"EC.10"<0lFrEO.REF'EQ.SY~(Q,TREQ•

ALPHA•F,ff,RO•A•A!~l ALPHA a [G:[~:OIFl[T:OIFlAlPHAl

FIXF'Z := F!XFUZNEQ.(Dlf,[Q,REFEQ•SYM[Q,TREQ, AI.PHA.G)

CFFZ:FIXFZCAL~HA.G>lt~O:~EALJêSO:REAll INOREALZ :: INDE92~(Q•(OIF~EQ,REfEO.SYMEQ,TRE;,

ALPHA•G.rFz,RO,SQ) tA:OIFlCB:OIFltAIR:INN(A,ClASSCROl)J[BIS:I~NCB,CLASSCSDJ)J ISINDREALZ :: THt•Eo.tt•(O!FoEQ•REFE~•ST"[Q,TREQ•

ALPHA•~•~FZ·R~.S0,4.~!~.s~BIS) ~ 0 ;-, f:E.\lQf"<Ortl~P,1t:f>iJ

: 'PROP•

ALFHA

: IS"E~!~t~HA,<3><A>G,iNORE,t2;

R:AL

s

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- 4.48 ..

•IVR1

•IVR1

•IVR1

•IVR1

HlV~l

•IVRl

R ; UO:IrifJÜOIR: INN( ltO~ClASSCRJJ Hz: ZEROCAO>l OIH := ISHHR~IhAOrOF'<lRP.lRPhAOIRr

AOIR a ri:IS<R•O>l OEX

R il P!lS AOIP. i1 [P:POSO(AOll

==

::

==

IN~CLASS(OfClRP•lqp)), ZEROEOCA0o0r(1RP.1RP>•Z• ZEROI(lRF'•IRP,REflSCCUT.lRPJ)))

EOZERO<Df<lRPolRP),AO• ISEXHhR•Of'( lRP.tR!>l,.AO• I NNC LA SS {Of' ( lRP. lRP J lo AOIR, SYM!S(RE~L·R•O•I>>• TRISCCUT.STM(OfClRP,lRPJ),lRP, STOCOF'ClRP,lRP)),.STMIS(lRP•lRPl• I SST:( lRP, 1RP) ))

ANO<INN<AO•CLASSCRllrPOSD<AOJJ

SOHE·~·cO!f'•[X:OiflPROPP•.IYRl"(XJJ

;· ZER!)( A))

: 'PROP'

'PROP'

P a H :: ANOI<INSCAO,CLASSCR)J;POSD<AO);AOIR,.Pl : PROPPCAOl

P a P!JSU

AOIR ; [P:PQS(Rll

:: SOMEICOif•[X:OIFlPROPP•.IYRl•(X)•AO• Tli".IVR1•)

Pa tA:DIFl[Ql:PROPPCAll T5 :: ANOEHINN(ArClASS<RJJ,POSO<Al.Oll T6 :: ANDE2(1NN(A,ClASS(RJl•POSD<Al•Oll T7 :: EOPOSOCA.AO.ISEX<R•R•ArAOrT5rAOIR•

P ; POSEX

REFIStREALrR)lrT6)

:: SOMEAP?<CIFr[X:OIF'lPROPP•.rvRl•(XlrPr POSO<AO>,[X:OIFl(T:PRnPP•.IVRl"(X)l

POSCRJ

: INNCA.CLASS(R)) POSD( U

: POSO< A3)

rr•.tVRl•(X,.T)) : POSDCAOJ

AO :1 PROPil

R ; NEG 'PROP' AOIR ; [N:NEGD(A0)]

N ; ra :: ANDHINNUO;CUSSCR>);NEGDUOhAOIR;IU PROPHUO>

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111 i NEGil'i :o:: SCKEttOIY•[~:OiflPRUPNw.IVRl•t~),AO# re ... I'lfn•• NEG(R)

AOIR a HHNEGCR>l

+•IV:U s

N a [A:Olfl(PL:PRDPN(A)] T9 == ANDEl(fNNCA•CLASS(R}),NEGOCA),PLJ INN( h!!LASS<R >) no :-• ANOE2CIUNCA,ClASSCRJJ~NEGDCA>•PL) NEGO< A> T11 :• EO~EGJ(A,AO,!SEXCR•R•A,AO;T9•AOIR,

REFIS,REAL,Rl>,TlOl NEGiH AJ >

•IVR1

H ; NEGEr =· SOMEAPP<OIF•tX:~IflPROPN•.IVRt•CXJ•N• NEG!HA O>r [x:~ IF'l tT :PROP~., .1'/R t•C 10 l ru•.tv!H·cx,.rn NEGO( Al>

u IYl!l s

AOIR ; [P:f':JSOUOJl TlZ :: CRliZCISCR,Q),POSCR>•NEGCR)•POSIN> : ORlCISlR•O>•POSCR>•NEG<R>)

AOIR ; tz:ZEROUO Jl T13 := OR3Il<ISCR•OJ,POSfRl•NEGCR>•OtNCZ)J OR3( IS( R•O>•POSCRhNEGCR))

AOIR ; tN: NEG I)( AO)] ru == OR3Il<IS<R•Ol.PDS<R>•NEGCRJ,.NEGINCN)) OR3( ISC R,.OhPOS(RhNEG<R))

AOIR ; T15 :: RAPPO(AOr0~3CIS(Rr0lrPOSCRl,.NEG(R)),. (T:POSilUOll T12< Th( T: ZEROUOlJTU<T ),. [T:NEGOCA0)jf14(J)) OR3.POS( Rh NEG CR))

•IYRl s

R i AXRLO := RE~LAPP1CRP0R3CISCRr0)rPOS(R),.NEGCR)), tX:OIFJCXI!!K~(XrClASSCR)Jl Tl5~.IVP.l•<XrXI>1 OR3C IS( R, 0),. POS CR),. NEGtR))

UIVRl ' AOIR a cz:uu.o> J

T16 := THJ•L.I"P•(POS(R),.POSO(AQ), O~OTPDCAOrOEXCll)r{T:POSCRJlPOSEXCT)J : NOHPOS CRU

AOIR i tP:PDS(R)] T17 :• TH3•t.I~P·(~EGCR>rNEGOCAO>•

PNllTNDCAOrPOSEXtP)),(T:NEG<R>lNEGEXCT) ) : NOT( NE:O CR))

AOIR a tN:NEG(R)] f18 ·- THJ•t.IMP•tiS!R,.O>•ZERO<AO)r

NNOTOO(AO•~GEXCN)J,[T:IS<PrOJlOEX(T)) NllH ISC R,O)) AOIR a T19 := TH6~l.EC3~CISCRrOJ.POSCRlrNEGCRl•

[T:ISCP.rOllT16(T)r{T:POS(RllT17CT>• (f:NEG(R)lT18(T)) ~ EC3<ISt R,O)rPOS<RhNEGCRH

-IVRl s

R a AXRLE := !tE AL APPl(R,EC3U S CRrO h POS CR h NEG<R 1 >.. [XIOIFl(XI:I~NtXrClASS(RJ>J Tt9•.tVR1-tX,X!)) ECJ( !S\ RrO>•POSCR>•NEGCRJ> - 4.50-

AXRL := OREC3tCIS(R,OJ.PGSIRt.NEG(R>.AX~LOr .. AX~lE: : OP.EC HlS (Rr 0 J ,poSCR hNEGC~))

[p: 'PROP'l tPt:tt:POSCR>lPJ tPt:tT :I SCR .. O ))PHP3: CT :NEGCR) lP l RAPP == OR3APP(iS(Rr~)rPOS(R),N~G(F.l•P,AXRl0r pz,rt.P.J> p

•IVRl

•IVRl

R ;a

R ;)

R a

s il

I • ;)

s' a

tP:P!JSCR)] !»NOTN ·- ECJE23ClS<R•O),P0S(Rl•NEG(R)•AXRLE•PJ ·-PNOT) :: EC3( 2H I SCR• 0 hi'DSCR h NEG (Rh AXRI.,E,.P) [i: IS<~t•O> J ONOT:> := ECIE12(IS(R•Ol,POSCR>•NEG<R>.AXRLE•I) )SCT~ ·- ECJE 13C I Sf R~ 0) ,.PQS(R h NEG <R), AXRLE,.J} tN:NEIHfUl ~NOT~ == EC3E 32( ISCR,. 0) •POS< R ),. NEG< R)" AXRl.E •N l ~men := ECJE3l(IS<R.O>.?OS<R>•NEGCR),.AXRLE,.N) [I:IS(R•S)l[P:POSCRJl !SPDS := ISP(R~AL•CX:REAtlPDS<X>•R•S•P•I> (N :!'~EGC R)} IS NEG ·- ISPCREAt .. ~x:REALlNEG<X>•R•S•N•I> ·-rRo:cun f'OFR?' := REALOF<POOFP.PCRO>> ~JFfP :a REALOHNDOFRPC RO)) lSO::UTlti:IS"RP•CRO.SO)J ISRPEr> :: ISF'C CUT" REAL• tx: CU Tl PCFRPUh RO• SO .. I J ISRP!:N :s ISF(CUf,REALr[X:CUTlNOFRP<XlrROrSO•I> [I:IS<POFRPCRO>rPOFRP<SOJJJ

:: ISEXtPOFRP(ROJrPOfRPCSQJ,.POOFRPCRO)r POGFRP(SOl.INNC!.ASSCPODFRPCRO>>• INNCtASS<POOfP.PCSO>>•IJ

l 2 ISRPI? := ISRPIPOCRO .. sO,T20•.tVR1•) SO a n:ISCifDFRPCROhNOF'RP(SO))l

:= ISEX<NOfRPCROJ,.NCFRPCSQ),NOOFRPCRO>• NOOFRP<SOJ.IN~CLASSCNOOFRPCRO)J, INNCLASS(NOOFRP(SQ))r!)

I ; ISRPIN :: tSRPINOCRO.SOrTZ1•.tVR1"> RO ; POSI :: POSINCPOfRPCROJ.PDOF'RP(ROh

INNCLASS(POOfR?CROJJrPOSDIRP<ROJJ NEGI := NEGUOiOfRPCROJ.NOOFRP<ROJ..

INNCLASSC~DOFRPCR0)),NEGOtRPCR0)) S a [RO:CUTl(SO:CUTlti:IS(R,POfRP(ROl>J(J:JS(SrPOfRP(SO>J

HK:IStR•S))

K a T2Z := ISRP1PCRO,SO•TR3ISCREAL,.POfRP<ROl"R~'S' POfRP(SO h S'tXISC REALrR,.?OFRP<RO h I ),.I(,.

NOTeNG (RH NIS<R.))

NOHPOS CRU NQTOfEa {R))

NOH POS CR)) NI SC R rJ )

POS(S)

NEGC S)

REAL : REA!.

: ISCPOFlP(ROlrPOFRPCSO)l ISC"ORPCRO hNOF'RPCSOJ 1

: EQ•RP•c PDOFRPt:ROhPDOFRPCSOJ)

: EQ""RP•t NDOFRPCRO > rNDOFRPCSO))

: IS""RP""t RO .. SOJ

: POSt POF RP<RO))

NEGC NOF' RP<R 0))

Jn : IS""RP""t Ro.so> R <a TZ3

AOIR a CP1:~GS(R)l TZ4 PR 1'25

T2G

:: tX:CUTl[Y:CUTJ[TilS(R,POfRPCX))J (U: IS< R .. PIJFRPt Yl J lTZZC R" Rr x,. y, T ,u,. REFISCREAL•Rl> : AfoiO~E<::UTr[X:CUTliSCRrPOf'RPCUH

•- POSEXCPU PliSOO.) ~ :: RPOfPD!IO,T!4l . : CUT := ISINfR•POfRPCPR),AO•POOFRP<PR>rAOIR•

INNCLASSCPOOfRP<PR)),[QPORPl(AO,T24JJ : ISCR,PlFRP<PR)) :: SG~EI<CUT,(X:CUTJIS(RrPOfRP<X>l•PR,

TZ5 J S01<4E,.R"' •([X ~CUT liSCR.POFRP U)))

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·IVR1

utYRl

·IVRl

•IYR1

hlVRl

R a [PtPJSCRll

rza

P a RPOfP

t= REALAPPl<SOME 8 RP•C[X:CUTliSCR,POfRPCX) )),[X:OlfltT:INN{X,CLASSCR>>lT26(X,T, P)l SOME .. R:t•((X :cuT J ISCRrPOfR:t {X)))

:: ONEI<CUTr(~:CUTliS(RrPOFP.P(X)),T23r T27J : ONt•RP'"UX:CUTliS<R•POf"RP(X)))

i28*.IVR!•) : CUT ISPRPl :: ONEAX(CUT,[1:CUTJIS(R,POFRP(X)),

T28'". I VR1 .. l ISC~,. Pl fRP( RPDfP(R, P))) tSPR=>2 :" · SY"'! S: RU. Lr R • POfRP ( PP3F'P< R• P)) • I SPRP1} I S(POn PC RPOfP( R,p > hR)

3 tR1::tEAll[ P: POS< RUHS 1 :lltAl H \:: PQS( 51}) EI ::::SC!HrSl) 1 ISPE~P :• rzz•.:v~1r<RlrSl•RfOfP(Rl•P>~

R?Of P< Sl• 0 h ISPRP1< R l•P) • ISPRP1< Sl,Q h 1) : IS"RP•t RPOfP(ftl•P>•RPOfPCS l•OU

0 a CI: IS,.RP•( RPDfP<RlrPh RPOf?(S!,QH l ISPIRP :• TR3IS<REALrRl•PGfRPCRPOfP(RlrP))•

a tRo:cuTJ

POFRPCR?OfP(S1,QlJ,S1.!SPRP1<R1,P), ISRPEP( RPOfP( Rl• PhRPOF'P (St- Oh I Jr ISPRPZ<St .. OJ l : IS<R l•S U

ISRP~l :• Tzz•.IVR1•CPOFRPCROl•POFRP<RO>•ROr RPOFP(POfRPCRO>,POSICROJJ, REFIS{REAL•P~FP.P<RO;),JSPRPlCPOFRPCROJ ,POSICRO>J,REfiS(R~Al,POFR?<RC>JJ : IS·~p·~RO .. RPOFP<POFRPCROJ,PDSICROJJ)

ISRP~Z :: SYMISCCUf,RO•RPOF?<POfRP(R0l•POSICR0)) •IS~PPH : IS"'RP"t RPOfP<POFRP<ROl•POSI(ROUiROJ

Sa [RO:CUfltSO:CUTlti:ISCR•NOFRPCROJ)J[J:ISCS.NDFRPCSOJ) HK:ISU,S)]

K a TZ9

R a T30

AOIR a tNllNEG(RJl T31 Nit T3Z

T33

R ; CN:NEGOOJ

:: ISRPINCRO,sO.TR3ISCREAl·NOFRP(R0JrR•S• f!OFRP( SO h SY MIS< REAL• R• NOFRf'C RO hl h 1(, J)) : IS'"RP"'[ RO,.SO>

:: (X: CUT H Y :CU Tl tT: IS(R,.. Ntlf"RPCJOH tU:ISCR.H~FRPCYJJ1TZ9CR.Rri•Y•T•U• R~FISCREAL•Rl) AKONE<:UT,[X:CUTliSCR•NDf~P(X)))

:: NEGEXOill : NEGi.HAJ l ;: R?CPIOCAOrT3U CUT := ISIN(R,NCFRP<NR),ACoNOOFRP<NRJ,AOlR•

INNCUSSCNOOFRPC N!U J rt: QNDRP1C AO" T31)) I SCR,. H:l FRP<NR)) :: SOHEI<CUf,[X:CUTliSCR.NOFRP<X)),NR,

T32 J SOMS: .. R~ •([X :cUT liS< R• NOFR=> CU) l

s

s

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s

J1rtXJOIF1ET:INNtXrt~A55(HJJJl55tXrlr

N)) SOME•Rs .. ([X :tUT HSU• HOFRiJ <X)))

T35 :" ONE I <CUT • [ X:CUTl IS<RoNOfRP~X >),. T 30r T34) : ONE•Rp•((X:CUTltS(R•NOFRPCXlJ)

N ; RPOFN := tNOCCUT,[X:CUT1ISCR•N3fRP(X)),. TZS".IVRl"l CUT

ISNRP1 := ONEAXCCUTotX:CUTJIS<R,NOFRP<X)),. T35" • IVRl*) : ISCR• NJ fRPC !'POfN(R,.fU))

tSN~'"2 :: SYI>I!S{REALrR,.NOfRP<RPOfN<R,tO hiSNRP 1) ISCNOF~ P<RPC!'"N(R,N) lrR > ; [lU: ~EALH N:N(GIRl )l(St:REAU:~t: NEG{ 51 JH I :IS<Rt..Sl >1

ISNE~P :: T29•.IVP.l~<Rl .. Sl•RPOfN(R1,NJ,. RP~FN<Sl•H),!SNRPl(Rl•Nl•ISN~PlCSl•M)o I> : IS"'RP•[ RPOFMCR1 .. tU .. RPDFN(Sl,.M})

K a [I:zs•RP•CRPQfN(Rl•N),.~POF~CS!•M>Jl ISNIRP := iR3ISCREALoP.1.NOfP.P<RPOFN<RloNl)•

; [RO:CUTl

NJ!'"R?CRPOfN{Sl•H)),Sl•ISNRPl{Rl•N), ISRP[N{RPOFN<Rl,NJ,RPOFNCS1,.MJ,.tJ-ISSRP2(Sl,H)) : IS(iU•51l

ISR~Nl :• fZ9•.iVRt•<NDFRPCROJ,NOFRPCROJ,R0• RPOFNCNOFRPCROJ,.NEGICR0)),. REFIS<RE~L•~OFRP<~O)J,IS~RPttNOFRPtROl .. HE:GHROllrREFIS<REAL,~OfRP<RO))l : IS~P"'[ ROrRPOf'IHNOfRPCRO)~ NEGUR0)))

ISRPN2 := SY"IStCUi .. RO,.RPOFNtNOFRPCROl•~EGI(ROJi "ISRP~U : Js•RP""t RPOFlUNOF'RP(ROh NEG HROU• RU

R a SATZ1S3 :: REfiS!RtAl .. Rl : IS(R,.RI 5 :1 [I :ISCR•Sl l

SATZ1&4 := SYI4ISCREAL•R•S,.I) : ISCS,Rt T a ti:tS<R•S)l[J:IS<S•TJl

SATZl&5 := TRISUtEAL .. R.s .. r,I..J) IS(R,.f) a ABSD't := [X:OIFlREALOFCABSO<XJ> tX:DIFl REAl

[A:DIF'l[B:OIF'l[E:Eo•RP•<A•Bll fl ·- ISIN<REALOFCABSDCAJ),.REALOF<ABS0(8)),

ABSOCAJ,ABS0(8)•!NNClASS(A850(A)), INNCllSS(ABSDCBJJ .. EQABSO(A,.B•E)) : ISC<A>ABSOR•ABSORJ

•IVRZ S

•!YR2

+2Rl55

tABS:>R

R ~ ABS

AOIR ~ T2

AOIR a AICA

S a ~.I:ISCR .. S) l IS ABS

:= [X:Oitl[Y:OirltT:<Y><X>EQlTl•.IVRZ•<x, y,.n

·- INDREAL<REAL,ABSDR,fABSOR,RJ

t= ISP( REAL• I ~:REAL liNNUBSDUO hCLASS( lC) ),REALûf(ABSOCAO)),ABS(Rlr

fiXte RE: AL,ABSDR) RE At.

IS<REAi. Of<ABSDCAO)).ABSCR} J

INNClASSUBSOC AO)), T2" .IVRZ" J : INN( AB. DUO hCt ASSC ABS <RH>

IS<ABSC RhA!!S(S))

s

$

- 4.53-

AOIR ~ [P:POS(R)) Tl == SATZ016óA(AO,POS(X{P)) POSDUBSDU.OJ) TZ := POSINCA8SCR2,AaSOfAOl,A!CA~T1) POSC Aai CRH

·ZRlóó s

R ~ CP:PJS(R)] SAfZló&A := REAlAPPltPQS(ABSC~JJ,[X:OIFltTtiNNCX,

CLASS(R})]Jz•.zRló&•(x,y,p)) : POS< ABS <R))

H2ft153

AOIR a ('t:NE:GCR)l T3 := SÄTZ0166BCAO,NEGEXCNJ) POSiH Aa SD<A.O)) Tlt == POSIN{ASSCR),ABSOCAO),AICA,f3) POSCABS <R) J

·2R1SS s

R .. HlHIEGCRJ~ .. SATZ1&S9 :: REALAPPlCPOS<ABS~R}),(X:OIFl(T:tNN(X,

ClASSCR))Jt4•.zR1&6•(x,T,NlJ POS( ABS tRH

n2R1U $

SliS ; [P:PDSCR>ltQ:POS<S>lti:IS<ABSCR>,.ABS<S>)J T5 := SATZ0166Ct'l•3l•PCSEX<R•A1,A1IR•P),

POSE X< s, 61. a liS,. tiDr i SEX< ABS< R hABSCS h. ABSOCA1J,A9SD<Bl>•A!CA<R•Al•A1IR>• AICA<s,st.BliSJ .. I)J : EO-RP-I At.BU

T6 := IStNCT5) ; IS(R,S>

•ZR106 s

s ~ (P:PJS(~)l[Q:?OSCS)J[1:IS(ABS{R)PA8SCS)Jl

SATZl&SC ::: REALAPPZ<ISCRrS),[X:OIFl[Y:OIFl tT:INNCX;CLASSCR)Jl(U:INNCY.CLASSCS))] r&·.zRt&&•cx.v~r .. u,p,o,I>J . ISCR•SJ .

H2R16S s

B1IS a [N:NEGCRlltO:HEGCS>lCI:ISCABSCRl.ASS(Slll TT :=: SATZ01660(Al•Sl•NEGEX<R•Al•A1IR•N),

NEGEX(S,S1,SliS.O>riSEX(A8S(R)rABSCSJ. A8SOCA1}rA3SD<6ll•~ICA<R•AlrAliRl• AICA(S;BlrBllS)olJ) : [Q•RP"[ At.Bl>

T8 ·- ISIN<T7> ISCRrS)

•2Rló& s

s a ;;N:NEGCR )J [0 HolEGCS > J[ I: IS< ABS( R),ABSC Sl J 1 SATZ1&60 == REALAPPZtlS(R,SJr[X:OIFltY:OfFl

[T:JN~CX.ClA~S<RJJJ(U:INM<Y .. CLASSCSJll ra•. 2R 1&6 .. { x. Y ~ T .. u. rc .. :J. I, J : ISCR • S)

R a tN:NtS<R.O)l SATZlóóE :: RAPPCR~PUSCABS(R)l,rT:PQS(R)l

SATZlfióACi>~THZ«L.~~~"(ISCR.O>• -4.54-PCS{A9SCR)),NJ,tT:NEGCRI~SATZ166S(T)) POS( A Bi (R))

HZRH.ó s

AOIR ; U:ISCR•OJl T9 ::: SATZ0166f(AQ,OEX<Ill : ZER:H A9 SOfJ\0)}

... ., V.A,~0~'ni,~O~V~AVI'ft~~ft·i71 • 4~'1\0~It "''"~I

•2R1S6 s

R a U :IS(It,(l) l SATZ16óF := REALAPPlCISCABS(R>·O>•(X:atFltT:INNCX,

CLASS(R)JJTlOw.zRt&G"<X•T•I>> tsUBS[ RhO > s • ICORE :: SOME•L"<DIF,CX:DiFJSOME"L•<oir.cY:Oifl

AN03CINNtX•Cl4SSCR)),iNNCY•CLASS(S)J~ MOREQ<X, Y> )) > 'PROP'

+*IVRZ s

!U >•INNCB1,CLASS(5)) ;MORE!.HAloBl)) 'PROP'

•IVRZ s

aus :: CM: MGREDU 1to 81 )l

HIV:t2 s

" . T3 ·- AN03tCINN(A1,CLASS<RlJ,.INN<B1,CLASSCS) );MORED<Al•Bl>•A1IR•S1IS•Ml : PROPMU 1•81)

H :: SOMEI<OIFrtX:OIFJPROPMCAl,X>.at ... Tl> SOME"t•COif,(X:DIFJPROPMCAl•X))

•IVRZ s

M 2 MORE IN := SDHEitDif,(X:DIFlSDHE•t•<OIF,[Y:OIF] PRDPM•.tVRz•cx,.Y>J,.A1,.T4•.IVR2•) : MORECR• SJ

sus :1 CM:MORE(R, S>l

+•IVRZ s

M ; [A: DIF H SA :SiJME'"t•( Dit" rx: DiflPROP~( A;.X)) l te: Oifl t P2:PROPH (A,. B) l T5 == AN03E1CINN(A;CLASS<R)),INNC8•CLASS<S)l

, MOR EO (A, 8); P2) : INNC A,.: LASS ( R)) Ti := AND3EZCINN(A,ClASSCRll•INNCB•ClASS{S))

.MOREiHA•B h PZ) INNCS,!:LASSCS)) T7 :: AN03E3<INN(A,CLASSCR>>•INN(B,CLASS<Sl>

, 11JJRED <A,. B); PZ) HOREOCA,B) f8 -== EQMORE01ZCA .. Al•B•Bl•

ISEX<R•R•A.Al,.TS,.AliR,REfiS<REAL,.R)),. ISEX<S•S•B•Bl,.TG.BliS;REflS(REAL•S>>• f7) : MORE OU 1•81)

SA ; T9 ::. SOKEAPPCDtF,[X:OlFlPROPMCA.X),.SA• MOREO<Al,Bl),[X:OIFJ[T:PROPMCA•Xll rsu .. r}) MORE OU 1,. 81)

•IVR2

M ; KOREEX :• SOMEAPPCOIF•tX:OiflSOME•t•<Dif•[Y:DIFl PROPH•.IVRZ•cx,Y>J~M•MOREO<Al•Bl), [X:DIFJ[T:SOMEftL•cO!r•[Y:O!fJ PROPH•.tVR2"<X.YJ>JT~•.tVP.2"(X,T)) HOREO<A l•Bl J

S a LESS == SOME•t•cDif,t~:~IfJSOM(•l•<oif•tY:Difl - 4.55-AN03(iNN(X,CLASSCR)J,.INNCY,.CLASS(S)J~

LESSO<X, n)} J 'PROP'

HIVRZ s

•IYR2

•IVRZ

HIVRZ

•IVRZ

HIVR2

·IVRZ

.. LESSOUl•Bl)) 'PROP'

SliS a tl:LESSOCA1•B1Jl

:= AN03I{INN(Al•CLASS(R))•INN(Sl,CLASSCS) L a HO

Tll l .u;ss:>c l.l.oi:lll, A liP.• B liS.ol} PROPl<A 1 .. B! J

:= SOHEl{DIF.oCX:OitlPRO~L<A1rXl .. Bl•T10l : SOHE"L•<Oif,[X:OIF'lPROPt(,l,XJ)

l ; LESSIN :• SCMEI<Oif,.[X:OIFlSOME•t•(DtF.tY:OIFJ PROPL•.IVR2•{X,Y)),Al,Tll••IVRZ*) l.ESS<R• S>

!. a t.\: DIF H SA tSOME•l.•< 0 IF, [x: 0 IF'I PROPt.CA .. X)} 1 [IJ :o I F' H P2 :PROPL <A•ID ]

TlZ

Tll

Tl4

f15

SA tl T16

:= ANQ3E1<IN~<ArClAS~(R)),JNNC8,CLASS(SJ) .oLESSDU• S )". PZl

:z AN03EZCINNCA .. ClASSCRl),INN(B,CLASSCS)) •LI:SSO( A • Bh PZ)

:= A N!J3E3UNNU ... ClASS(R) hiNN<B•CLASSCS}) .. tESSUU•B h PZ)

:• EOLESSD12lA,A1,B,B1• ISEX(R,P..oA,Al.oT12•AliR,REflSCREAL"R)J,. ISEXCs .. s .. a,s1,Tl3,a1IS,REFISCREAL•S>>• Tl4)

:: SOMEAPPCOIF,(X:OifJPROPl<A~X>,SA• lESSD(Al•Bll,(X:DlfltT:PROPL(A~X>l Tl5<X;T))

l t1 lESSEX := SOMEAPP<Dif• C<:DiflSOHE'"L.,<DIF'•tY:OIF'J PROPL~.IVR2•(X,Yllrl•L~SSO<Alr8l); tX:Difl(T:SOME•t"COif,[Y:DifJ PROPt•.tVR2•tX,Y)llT16•.tVRZ•<x,Tl)

T a ti:tS<R•S>ltM:KORECR;T)J ISMO~El :: ISP<REAl;(X:REAllKORE{X,Tl.R,S.K•lJ

l Q (M:MJRE(T;Rl1 ISMOREZ := ISP<REAl,[X:REALJHORECTrX),R;S;M;I)

I a Ct:LESS<R•Tll ISlESS1 := ISP(REAl,[X:REALll~SSCXrTl,RrS•L~lJ

I tl [L:LESS(TrRJl lSlESS2 := ISPCREALrtX:REAllLESS(T,XJrRrSrL•IJ

U a [I:IS<R•S>JtJ:IS{T,U)l[M:HO~E<R•TlJ ISMO~E12 :• ISMORE,2<T;U• s,J, ISHO?.H<R,s .. T..I,M> J

Ja [L:LESSCR•T>J ISLESS12 :: ISLES$2CTrU;$;J,ISLESSl(R;SrT;I;L))

SliS a tH:KORE(P.,Sll T17 TU

:= LE~MA05(Al•Sl,MOREEK(M)) :: lESSIH<S•R•81.A1rBliS•AllR•T17J

: INNCA,:LASStR)J

INNC a .. !:LASS<S»

LESSOCA •B>

: LESSOCAt..Bl>

: LESSD<Ah81J

'lESSOUt..Bll

HORE( s, T)

: MORE CT,. S)

: u:sscs. TJ

: u:ss<r,. SJ

: HORE(S,.IJ)

lES$CS, U>

LESSO CB lt> A1 ) : Lrsscs .. Rl

'

s

s

I

s - 4.56 ...

s ·~ CIUM:lREU,. Sl l LEMMA! ~= REALAPP2<LESSCS~~),[X:DIFJCY:OIFl

(TIINN(X,.CLASS(ft))J[U:INNCY,.CLASS($))] rta•.rrRz·cx,r,r~u .. H>J : u:ss<S ... Rl

uiVR! s

81!5 a tt:LESSCR.o SJ l T19 :: L(KMAD6CA1•81,.LESSEXCLl) MOREDU l•Al l TZO := MOREINCS,R,9l•Al•BllS,.A1IRrT19J MORE< s .. R>

•IYR2 s

s a tL:LEssu .. s, 1 L(HKA2 ·- REAtAPPZ<MORECS•Rlr(X:Oifl[Y:DIFl

tT:IN~CX•CLASSCRJlJ[U:tNNCYrCLASSfS))J rzo·.IvRz·cx .. r .. r .. u .. tJ> MORE<S• R)

•2P.1&7 s

BliS a Tl :: SATZ0167UA1 .. SU OR3((Q•Rp•(Al.oB1J,.HOREOCAl•B1J,lESSO<A1 .. BllJ CE:EQ•RP•CAl.oBl)J ~~ :: OR3Il<tSCR .. SJ .. MORECR .. s> .. LESSCR .. S),

ISIN<E}) OR3( I St R•Sl" I'!ORE<R• Sh lESS <R•S J J SliS a tM:~OREDCA1rB1l1

T3 :: ORJIZ< IS( R•S h HORE<RrSJ •LESSCR .. s h MOREINUUJ : OR3t IS( R .. ShMOREU.ShLESStRrSU

BUS a tL:LESSD1Al,81Jl T4 :• OR3I3CIStR .. SJrMDRECRrSJ,LESSCR,.Sl•

LESSIN<Ll} : OR3CISCR,SJ•KORE(R,S>•LESS<R•SJ) BliS a T5 == OR3APP<EQ•R?•(Al,Bl>•HORED<Al•Bll•

tESSOCAl•81J,.OR3<ISCR,.Sl,M9RECR;S)r LESSCR•S>>•Tl,[T;EQ"RP•(Al .. 61JJT2C~),. CT:MO~EOCA1,Sl)lT3CTJ,(T:LESSO<Al•Bl>l f4(J)} : OR3( IS( R,.S) .. KORE<R,.S),. LESS<R .. S))

TG == SATZD1G7S<Al.B1> EC3CEQ•RP•tA1,.81)•MOREO<AlrB1),.LESSD<Al .. B1l) u:rsu .. su TT :a THl•t.IMP•CHORE<R,sJ,HOREDCAl,.Sl)•

EC3E1ZCEQ"RF•(Al•B1>•HOREDCA1•Bl), LESSOCA1rBl>rT6 .. ISEX<IJl,.{T:MORECR .. S)J MOREEX(T)) NOH HOHCRr SU

SliS a t!UMORE<R• S) J TS ·- TH3•t.!HP"CLESS<R•Sl•LESSOCA1,91),

EC3E23CEQ"RP~<Al .. B1J .. HOREOCA1,31Jr LESSDCA1•Bl>•T5•MOREEXCM)), tT:LESSCR .. SlllESSEX<T)) NOHLES S(R,. SJ)

BUS a [ULESS(R,.Sl l T9 :: THJ•t.I~P·CISCRrS),.[Q~RP•CAl .. Bl>•

EC3Ell<EO., Rf'""Ul, !31 h HOREO !A lP 31 ).0

LESSOCA1•8l),T6~LESSEX<LtJ,[f:lS(R,S>l ISEX<T J) : NOT< IS( R,SJ}

BliS ; TlO := TH&•t.tcl~<ISCR,Sl.MORE<R•Sl•LESS<R,.S) .. TH1•L.EC"CIS<~,s),M0RECR~S), tr: I 5 CR, S )]! 7 CT),, TH 1"l.EC•<KORE CR,S h tESSCR,sJ,[T1HCRE<~•S>IT8[l}),

- 4.57-i'Hl"L. EC .. <LE SS <R,S ), IS< R, S ),. CTil(SS<R•S>JT9CJ))) ECl( ISl R•Sl •KORUR•Sh LESS CR•S))

T11 ::. OREÇ 31< IS< R• S >rHORE CR,. S >,LES sa,. S ), T 5, T10) : OREC3<!S<R•S)•MORECR•SJ~LESS<R,Sl)

•Z!H67

S a SATZ167 := REALAPP2COREC3<IS<R•S),HOR~!R,.S>• LESSC!rSJ).{X:Difl[Y:DIFJ(T:INNCX,. CLASSCR)ll[U:INN<Y~CtASSCSlll Ttl•~2Rl&7•(x,Y,T,UJJ

SATZ167A

SATZ167B

MO~EIS U: SS IS Ut: Kil RE: I SC R,. S) i SATZ168A

:= OREC3El<IS<n•S),.MORE<R•S>rLESS<R•S>• SATZl€.7>

:= U~EC3E2CISCR,S)•MORE<R•S>,LESSCR.S),. SA!ZlHl

:: CRC~:~EtR,sl~ISCR~$)) := CRCLESSCR,SlFISIRoS))

:= T~9·t.DR"CMOREC~•S>•lSCR,.S),.lESSCS~R),. IS<S .. ~),K,[i:~OR[(R,.SJJLEMMA!(T)o {T:ISCR•S>lSYMIStR~AL,R•S•T>>

ORÈC 3Cl S(R,. S} • MORECR,.S ),L:: SSC R,. S))

OR3C ISC R, S),. HORE<R,. SJ# LESS <R• SU

: EC3( IS( R•ShHORE<R• S>. LESS<RtiSl} 'PitJP' 'i>RJP'

: LESS IS( s,RJ S a [t:tESSISCR,S)]

SATZ168B :: T~9·t.OR•(LESSCR•S)•ISCR•Sl·MORE<S•R),. IStS .. ~lrlrtT:LESSCR,SllLEM~A2tT~ .. CT: !SC ilr Sl!SY!HSfREAl•R•S•TH MOREISt S.oR)

T a [I:ISlR.oSlltM:MOREIS<RrT~l tSKOREIS1 := ISP<REALr[X:REAllMDREIS(XrTJ,.RrSrM•I) MOREISCS .. T>

I a (H:HORE!S<TrR)] ISMOREIS2 := ISP!REAL•tX:REALlMDREIS<TrXJ.oR•SrMriJ : MOREIStTrSJ

I a tl:LESSISCR,TJJ ISLESSISl :: ISP< REAl•[lC: REALlLE:SS!S<XrThRrS"l"I) LESSISt s,.TJ

I a {t:LESSIS<TrRJl ISLESSISZ := ISP(R(Al,.[X:REAlllESSIS<TrXhR.rS•L,.I) . : LESSISt TrSJ

U a [I:IS(R,SJJ[J:IS<T.U>JtM:HOREIS<R•T>l

J a

s a

s a

s a

SliS a

SliS a

atiS a

31IS :2

s a

lSKO~EISlZ ·- ISHOREIS2tTrUrSrJriSMOREIS1<R•SrTrirH)

[L!LESS ISC R" f) l ISLESSISlZ

Uf:KJRE< Rr S)] KORElS U [l:LESS( R,. 5) l LESSIS U U:ISCR,.SJJ HOREISIZ LESSIS IZ tH:M3REOCAlr8l)l MOREIS IN

[M:M:JREIS(Ib$)1 MOREIS EX

lL:LESSEOC&l,BlJl LESSIS IN

tl:LESSIS(R,Sll LESSISEX

[11: MORE IS< R~ S > l SATZ167C

) MOREISt S.UJ

:= ISLESSIS2(TrU,S•J•ISLESSlS1<R,.SrT•I•l> J : LESSISCS,UJ

:= O!UULESSCRr ShiS<R• SJ .. U : LESSISt R•S>

:: CRIZ(MORECR .. sJ,IS<R .. Sh IJ : KOREISt R•S> :: !JRI2ClESS{R,.Sl..IS<RoShi) LESSISt R,.S)

:= ORAPPCHOR~OCAlrBl)•EO"RP"<Al,Bl), MOREISCR,.SJ.M .. ~T:MOREDCA1~61ll MOREISI1CMORE!NCT>> .. tT:EQ•RP•tAlr81)J HO~E: 1SI2C I SI NCT))) HOaE I St R~S>

:= OR,P?CM~RECR,.s>.IS{R,.S),.HOREOCAlrB1),. H•[T:HQRE(RrS>l~CREOI!CA!•al•HGRECX(T) } ,[t :IS< Rr S l HIORt:QI 2 (.U •Bl. ISEXO i H MORE OU 1, 81)

:= ORAPPCLESS~CAl,.81)rEO~RP•tA1,8l)r LESSIS<R•SJrl,(T:LESS~<A!•Sl>J LESSISI1{LESSINCTJ),.[T:EQ"RP"CA1 .. B1)1 LESSISI2CISr:-t(T))) LESSIS(R,SJ

·- ORAPPC~ESSCR.Sl•ISCR•S>,LESS~QCA!•Bl>• t,tT:lESSC~rSllLESSEIIl<Al,Bl• LESSEX{f)),[T:IS(R.S)llESSEQIEtAl,.BI,. I SEXHUl

:: TH7"L.EC3-CIS(R,SlrMORE<R•SI~LESS(R,S) ,sATZ167B,CU~0R(~OR~(R~S),IS<R•S)oH))

LESSEQt ,u,.au

- 4.5E

------------

+2R169

•2R159

H2R169

H2!US9

s a [L:I.ESSI SC R• S )l SATZ1670

s ; tN:NOTCMORECR•SJJJ SATZ1HE

s a [N:NOTCLESSCR•S>Jl s ; tN:NaTCLESSC~•Sl)J

SATZ1STF'

S ; CH:HJRE<R•SJl SATZ1&7G

:: TH9•L.EC3"CIS<R•Sl•MORECR•SJ•LESS<R•S) ,. SU Z 1&7Eh U

== THZ•L.ORl•(tS<R~sJ~~ORE<R•SJ,.LESSCR,.Sl .. sATZ167A•N)

:= COM0!\1: IS< R• S J• ~0 RE< fl,. S h THJ•L.O~J•CIS<R•S>~~GRE<R•SJ•LESSt~•Sl rSATZ167.t,.N1l

:: THJ•L.IMP~<LESSISCR,S),.NOT<MORE<R•SJ),. nELI(MCRE(R,Sl .. M},[f:LESS!S<R•S}l

; NOH KO~ ECR~ SU

: LESSISt R.oSl

: MOREISt R,. S l

SA TZ 1S7!HT>) : NOTHES SIS< R .. SU S ; tL:LESS(R,.Sll

SATZ1STH :: THJ•t.IKP•CMOREISCR.s> .. NOiCLESSCR•Sl>• WELI<LESS(RrSl•L>•tT:r.o~ElSCR,SJl SATZlST':nn t NOTCMO:tEISCR,S))

S ; [N:~JTtHDREISCR .. Slll SATZ1S7J :: QqJE3CISCRrS),MDRE(RrSJrLESS(R,S)r

SAiZ1ó7A•THS~L.OR~(KORE(RPStriSCR~S>r NJ,.TH4•L.OR~CHORtCR,SJ,ISCR,Sl,Nll

S a [N:NJT<LESSIS(R,.S))J SATZ1ó7K := OR3EZCIS<R.SJ.MûRECR•SJ~LESSCR.sJ,

R a tP:POUR>l

SATZ1?7ArTH4"l.OR-{LESS<R•Sl•ISCRrSl• NJ,THS•L.OR"ClESS<R•Sl•lS(R,SJrNJ)

U :OIF" ltS: t)ff'l [A IR :I NNU .. Cl.ASS<R J) ltBIO: ï:NN<B• CLASS( 0) J1 Tl :: SATZ0169ACArB•OEX(0;BoBIO,

REFISCREAL .. O)J,PGSEX(APAIR•PlJ T2 ;a MCREIN(RrO,ArB,AIR•BIOrT1J

SATZl69A :a REALAPPZ<R•O•MDRECR•O>•[X:DtFl[Y:DIFl [T:INNCXrCLASS<RllltU:INN!Y,ClASSCOJll rz•.ZR16,w<x,y,r,ul>

M a [A:OIFltB:DIFltAIR:INN(A•CLASSCRJ)ltBIO:INN<a•ClASS<O>>l Tl := SATZ01&9B(A,SrOEX<Op~,BIO,.

REFIS<REAL•O>l•MOREEX<R•O•A•B•AIR•BIO•

LESS(R,. SJ

MORECR,. SJ

: MOREDCA rB) M!JRE<R, 01

M)) POSOCAJ H i:: POS1N(R•.o\•AIR .. T3J : POSCR>

M l SATZ1698 :a REALAPPZtR.O.?OS<Rl,tX:DIFltY:DIFJ [T:tNNCX•CLASS(R))l(U:INNCY .. ClASS<OJ)l T~*.2P.l69~<x.Y,T:,U))

N a tA:Dtfl(B:DIFltAIR:INNCA.ClASS(RJJlCBIO:INNCB,ClASS(O)Jl T5 :: SAT10169t(A~B•O~X(O,s,s!Or

REF"t ${ '?~lil•O )}, NE:GE lC (A ,A Tl?.::''

POSCR)

s

s

s

s

- 4. 5~-s

•2RlS9

+2P.11)

•ZR170

N a SATZ159C :s REALAPPZ<~•O•LESS(R•O>•(XIOlFltY~DlFl CT: I NNU,.CLASS<R} )l r t;: INNU.ClASS(O))) rs·.zR169 .. o:.r .. r .. u, > LESs<R. o>

L; CA:OIFlt8:DIFlCAIR:tNNCA•CtASSfRJlltBIO:!NNCB•CLASSC0))l T7 :s SATZ01690CA.B,OEX<O•B•BIO•

REFI SC ilEAL .. O) l .LESSEX< R •0 ,,,. a .. AIR•BIO. LH

T8 :: NEGINCRrA•AIR.T7)

L a SATZ169D :: REAlAPP2CR.O .. NEG<Rl,.[X:OIFJ[Y:D&fl tT:IN~<X•CLASS(R})J[U:INNtT .. CtASSC~))] rs·.zR169•(x,.y,r,u>)

R a [A:DIFl(B:OIF1tAIR:INNCA.ClASS(RlllCBIO:INNCB•ClASSC0))] Tl := SATZD170(A,.S .. OEXCO•B•BIGrREFISCREAL,.Of

NEGOU) !'4EGC R)

: NtGtR)

)) : MOREQCA BSO( A hB) T2 := MOREISIN<ASSCR),OrABSOCA),.B,.

AICACR•A•AIRhBIO•Tl> : HOREISt ABSCRhOJ

R a SATZ170 := REALAPPZCR.O,.MOREIS<ABSCRl,OJ,[X:OIFl [Y:OIFJ[TtiNN(X~CLASS(Rlll[U:INN<Y•

ClASSCIJ)llT2 ... ZR170'"(X,.Y"T,.Ul) : MOREIS[ ABS<R>.OJ SATZ17~A ·- TH3•t.IMP•tNEG(ABStR>>•LESSCASSCRJ,.Q),.

SATZ1S7C(~BSCRJ,.OrSATZ170J,. [T:NEGtABSCRlllSATZ169CCA8S(Rl~Tll NOTCNE.CABSCR)))

T ; [L:LESSCR .. Sll[K:LESSCS.TJI

s

s

s

s

+2R!71 S

[A:OIFl[B:Oifl{C:OIFJ[AIR:INNCA,.CLASS(Rl)l[BIS:INN(S,CLASSCSl) lCCIT:INN{C,.CLASS(Tlll Tl •- SATZ0171CA;S,.C•LESSEXCR.SrA,.B•AIR•BIS,.

L>rLESSEXCS,r,s .. c,BIS•CIT,~>J LESSOtA .. C) TZ := LESSIN(R,.T,A,.C,AIRrCIT,.Tl> : LESS(R.T>

SATl171 := RE-LAPP3(R,.s,T,.LESS<R;T),(~:OIFJ [Y~OIFJ[ZZOifl[W:INN(X,.CLASSCRl)] [U: I NN<Y,ClASSCS)) J r \' :HltHZ.ClAS S< T> )J TZ".2Rl7l~tx.v .. z,w,u,v'>

TRLESS ·- SATZlTl T a (~:HDRE<R•S>l[N:MORE(SrTJJ

TRKCR[ :: LEHHA2fTrRrTRLESS<T .. S,RrLE"MA1CSrT,N,, LE11HA1(R,s~M )) )

T a [A2tDIFlf92:DIFl[~Z:OtFJ[AZIR1INNCAZ•CLAS3CRJl J[92IS:IN~(SZ,.ClASSCS):J[CZIT:IHMCCZ,ClASSCTJ~l

ltSS(Rr Tl U::SS(R• T)

s

- 4.60-

•ZR17Z

•ZR17Z

t>ZR17J

tt:~ESSIS<R~Sll[K~LESSCS.Tll Tl :: SATZ017ZA<AZ~az,cz,

LESS ISEXEAZ~ BZ•A 2I Rr 82ISrL )r LESSEx<s~r.sz~cz,szrs.czxr.K>>

TZ :: LESSIN<R•T•AZ•C2•AZIR.C2If•Tl>

T a tt:LESSISCR,SJJ(K:LESS<S•T>J SATZ172A := REALAPPltLESSCR•Tl•(X:DtfJ(Y:OIFl

[Z:DIFltU:INNtX•CLASSCR>ll[V:INNCY, CLASSCS))J(W:INNCZ•CLASSCT)J) rz·.z~172"<x.v,z,u,v.w.t.Kll

C2IT a [L:ttSS(R;S)l[KtlESSISCS;T)l Tl := SATZD1728CA2,B2•CZ,.

LESSEXCAz,.gz,AZIR•BZIS•L), LESS!SEX<S•T•32•CZ•BZIS•C2IT•KJ)

T~ := LESSINCR•i,A2,cZ,AZIR,c2IT,T3J

T a CL:LESS(R,S>ltK:tESSISCS .. TJJ SATZl7ZB := REAUPPlCLESS( R• Th [X: !Hf'][ Y :OIFl

[l:DIFJtU:INN<X•CLASStRJ)l(V:INNtY• CLASSCS)Jl[W:INN!ZrCLASSCT))] T4w.zR17Z-cx.y,z.u,v.w.t.K>J

T a tK:MOREIS(R,.SJJ(N:MORE<S•T>J SATZ17ZC := LEMHA2CTrRrS~TZ112BCTrSrRr

lEHHAt(SrTrNJrSAiZ166A(M))) T a (M:HORE(RrSll(N:MOREIS<S•T>l

SATZl72D := lEMMAZCTrR•SATl172A(TrSrR• SATZ168ACSrTrNJolEHMAl(H)J)

C2IT a [L:LESSISCRrS)J[K:LESSIS<SrTJl Tl :: SATZD17lCA2rB2rC2•LESSISEX<A2r82•AZIRr

BZISrLJrLESSISEXCSrTr82rC2rBZISrCZITr I())

TZ := LESSISIN<R.TrA2rCZrA2IR.CZITrT1)

: LESSOU z,.cz) LESS(R,. f)

: LESSCR• n

: LEssonz.czJ : LESS CR,. Tl

: lESS<R• n

: HORECR, T)

: HORE<R• f)

LESSEO( A2,C2J LESS ISC R• T P

s

s

s

s

•2R173 S

T a (L:LESSIS(R,SJJ[K:LESSISCS•TJJ SAT.Z17 3 := REALA?J>3CLESSIS<R,. Th(X:OIFHY :DIFJ

[Z:DIFl[U:INNCXrCLASS(R))J[V:INN(Yr CLASSCSJllCW:INNCZrCLASS(TJ)J rz•. ZR 173 .. {)(,. Y ,z,u., V .w,.L •10 l lESSISt R1 TJ

TRLESSIS := SATZV3 LESSISt R,T) T a (M:HJREISCR,S}l(N:KGREISCS,T>l

TR~D~EIS ·- SATZ1QS8(T,R,TRLESSISCT.SoR• SATZlf>!lA<S•T .. NhSATZlGSAOOH ; HOREISt ft, Tl

R a =!A!Rt := SOME .. L"<Otr, (l(:OIFJANDCIHiHX .. ClA.SS<R)) .RAïDCXl)) . : 'P'R!JP'

s

:- 4.61-

•IVR!

R1 ·~ T21

R1 ~ ltATR:..U

AOIR ; (RR:~ATRLCR>J

:e ANQitiNN(AO~CLASS<Rl>~R~TO(AO>•AOIR• lUJ

. . := SOHE ICOtf • CX :D If JArm C I N~H x, CU, SS (R)) •

RATOO()J,AO,T2l•.IVR2'"l.

RR ; tA:OtfltB:ANDCINN<A•CLASS!R)),RATD!A))] T22 := ANOElCIN~(A•CLASSCRll•RATD{A~•BJ T23 :: ANDE2CI~~(A,CLASS(R)J,RATDCAJ,BJ i24 •- EORATD(A,~O.ISEX(R•R~A•AO•T22•AOIR•

REFIS<REAL.RlJ,T23l

ANOC t~ CAO,CLASS(R) );RATOC AOU

RATIH.U)

INNC A•~LASSCRH RATD<At

RATO( AJ J

s

•IVR2 S

HIVRZ

•IVR2

RR ; RATR~EX := SOMEAPPCDIF,[X:OiflANDtiNN(X,CLASS(R)) ,RATO(XJ),RR.RATDCAO),(X:OIFl tT:ANDtiHNCX•CLASSCRJJ•RATD<I))J T24".!VR2'"{X;T)) RATO(A))

R ; IRRATRL := NCHRATRURl> : 'PROP' ; tRO:CUilCRR:RATRPCRO>l

REH-~KZ ta RATRLIN(POfRPCRa),pOOFRP<RO>• INNCLASS<POOFRPCR0))rREMARKZACRO•RR)J : RAT~t(•OFRP<RO))

ltEHHKJ :a RATRLIN( NOfRPUO hNOOfRP (RO h

RO ; tiR:IR?.ATR?(ROJl REMH~4

R ~ NATRl

AOIR a CN:NAT~CA3ll

N 2 T25

AOIR a [N:NATRL(R)l

INNCLASS<NOOfRP<ROJ>~REMARKJA(RO•RRl) : RATRL(~OFRPCROJ)

:a TH3wl.IKP"(RATRLCPnrRP<R0)), RATO<POOfP.PCR0}),R~MARK4ACRO•lR)r (T:RAiRLCPGFRPCROlll~ATRLEXCPOFRPCRO>• POOt RPCR'} h BINCLASSC POOfRP (RO J h T t > : lRRATR:.. <POFRPC ROU

:= TH3ftl.IMP•<RATRLCNOfRPCROl>• RATOCNOOfRP<ROlJ,REMARK5A{R0•IR}• {i:RATRLCNOrRP<ROJ)JqATRLEXCNOFRP<ROJ, NOOfRP(RO>•HiNCLASS<NO!lfRP<RO>>•T)) : IRRAT!t.. (NOFRP<ROJ)

:= SOME•t•COIF, U:OiflANIHINti<X.CLASSfR }) .NATD<X))) 'PROP'

ANDC IN'I CAO, ClASS<R>l,HATDC AO))

:: SOHEifOif~(X:DiflANDCINNCX.ClASS(R)), NATOU>hAO•T2S .... IVRZ*) : NATRLn)

N ; [A:Oif'][S:.\1\0C INNU•CLASS< R})rNATD!A)) l T26 ;: ANi:JEHINNCA .. CLASS<R)h~ATOCA),.B) T27 :s ANOE2<INN<A•CLASS(R)),~AT0(~).B) T28 := EQNATO(A,AO,!SEXCR.R,.A,.AO,.T26 .. aOIR•

REFISCREAL~Rl>•T27J

1 INN<A,!:t.ASS(R)) NA TD (;,)

NATO( AJ)

s

s

s

- 4.62-

N ; riA T!ti.U == SOHEAPP< D If,. [X: :JtflA ND ( Il'fNtX rCLA SSCR)) rNATD(X));NrNATOCAO>,.[X:OIFJ [T:ANO<INN<X,.CLASS<RJ),.NATDCXl)J rzs•. rvRz•o:, T)) i NATD< Al )

u nu $

AOIR ; ttUNATRI.<R)) TZ9 :: NATPOSO(AO.NATRLEX(N)) POS!)C Al ) f30 :: POSIN(;Z9) POSCID

·IVR! s

R a tN:NATRL<R Jl liATPlS := REALAPPl<POSC~),.{X:OifltT:INN(Xr

ClASSCR>JlT30•.IVRZ~cx.Tr~)) : POS(Rl a UHIAT l

RLOF'IT := RE~lOfCPOOFNH lO) : REAL liATR;.I :: NATRLINCRLD>NT<XJrPOOfNT(XJr

!NNCLASS<FOOFNT<Xl)rNATDI<X)) NATRL<lLOFNTCXJ) (Y:NATJti:Is•N~(XrYJl ISNTERL := ISf(NAT,REAL,.(U:NATlRLOFNT(U)rXrY,.IJ IS OU. Of NT< X l.r RL CFIITC Yl )

y ; [l:ISCRLOFNTCXl;RLOFNT(Y))J ISNTIP.L :: ISNTIRP<X"Y"ISRPIP<RPOFNT<XJ,.RPOFNT(YJ

rl)} : IS•N•U,YJ

+*IVR2 s

a T31 := [X:NAT HY :NA TlrT :ISCRLOF'NHX h RtOFHTCY))JISNTIRL!XrY.TJ INJECTI VE(N AT rREAlr tx: NATl RlOfNT( X))

AOIR a tN:NATRL(R)] T3Z :: NATPOSQ(AO~NATRLEX!N)) : POSDC AJ ) AP :: RPOFPO<AO• T321 : CUT T33 := NATDERP<AG~NATRlEXCNJ) : NATRPU P) X3 ·- ~TOFRPCAP• T3 :n : NAT TH :: ISRPEPD<APrRPOfNTtXOJ~tSRPNT1(APrT33)) : EQ~P"'C PDOfRPUPhPDOfNHXO}) T.J5 := TREQ•RP•tAOrPDOFRP<AP)rPOOF'NT<XOlr

EQPDRP1<A0rT3ZlrT34l : EO"'RP""[ AOrPDOFNTUOJJ T36 == ISINCRrRLOFNTCXOlrAOrPOOFNTCXOJ,.AOIRr

INNCl4SS(P00f~T<XOllrT3Sl IS<RrR. OFNT <X01) T37 :: SOMEICNATrtX:NATJIS(Rr~LOFNTCX)JrXOr

Tló) I IHAGE("J AT rR EAl, [ X:N A Tl RL OF' NT< X hRJ

•IVRZ s

R a (N:NATRL(Rll ~ATI~AGE := REAlAPPl(IMAGE(NAT•REAlrtX:NITl

RlOF'NTCIOr iDr ( lOOIF'J CT: IN.NCXrCLASS(R)) lT37•. IVRZ•( x .. r,. fU J : IMAGE(-. AT rR EAL" CX:tiATJ RL Of' NT<Xl ,.R)

R a [J:IKAGE(NAT,REAl,tX:NATlRLOFNT<XJ•RJJ

+*IVR2 S

•IVR2

IWRW 2 [X:NAfl(J:ISCR.RlOF'NT(X))] T38 :: ISPl<REAl,[U:RtALlNATRI.CUl•RLOFNT(X),

I a IMAGENAT

R.,NA TRLI<XhJ)

::: SOHEAPP( NAT, tiJ: NAT HSCi'!rRLOFNHUU,I • NATP.tCR),.[U:~ATl[V:ISCR,RlOFNT<U)lJ

NATRlCl)

s - 4.63-

•IVRZ

HI\'R2

•IVR2

urnz

•IVR2

R a [N:NATRLCR)l NTOFRL :: SOFH!Ui ,REAL• [X:NAT lRLOFN!'a)~

TJt•.IvRz•,R•NAfiMIGEtR,N)) a tRl:REAllCN:NATRL<R11JCSl:REAL][H:~ATRl<S1)1[I:IS<R1,Slll

ISRLENT :: ISINV<NAT•REAL•CXHIHlRLilFNHX)r Tll".IVR2••Rl•N•TIHA&E<R1,NlrSl• NATI:R~E<$1, ~>.I-)

H 2 rt:ts•N•(NTOFRLCR1rN),NTDFRLCS1•M)J] ISRLINT := ISI'~':EO!A.T .• REAL.~X:N~TJqLOFtH(X),.

R a [N:NATRL(R11 ISRLNT 1

ISRL'tT2

a [X:NAT 1

TH

x a ISNUL1

Tll".IVR2"•Rl•NATIHAGEfRl•~>•S1• NATlHAGE<Sl,M)rll

:= ISTSl"E"<NATrREAL,rX:~ATlRLOFNTCX), T3t•.IVR2·•~•NATIHAGE<R•Nll

:: SY~IS(REALrRrRLOFNT{UTOFRL<RrN)),. ISRLNTll

:: SOfTCNATrREALrCU:NATlRLOFNT(U>rT31r RLOF'~H X h I~AGEI<N~ T" REAL• CU: NAT l RLOF'NTCUh X))

:a ISINVCNATrRE~lr(U:NATlRLOF'NT(U> ... T31r RLOfNTCXl,IHAGEI<NAT,REALr[U:NATJ RLOFNTCUJrXJrRLOfNTCX), NATIHAGE(RLOFNT<X),NATRLI<XJ), REFISCREAL•RLOFNTCX)ll

·- TRISCNAT,X,XN•.IYRZ",NTOF'RLCRLOFNTCX), NATRLI<X>>,.ISSTltNATrREAL~[U:NATl

NAT

IS .. N•(-. TOFRL<Rlr Nh NTQfRU Sh M))

: ISCRt.S U

NAT

: IS""H .. (l( fbNTllf'Rl(RLOfNT<XJ,. NATRLI<X> >)

RLOF'NHUh TH ... IVRz•, u, T39•. IVRZ•) : IS .. N'•(l( rNTOfRLCRLOfNTC X)r!U TRLI<Xl)) ISNTRL2 := SYHI~CNATrX,NTOFRLCRLOfNTCX),NATRLICXJ

), ISNTRLU IS .. N•n TOfRURLOfNHXJ ,NAT RL IC X> hX> R a INTRL := SOME•t•(Dlfr[X:OifJANO(INN<X•CLASS<R>>

.INTDCX))J 'PROP' AOIR a [I :INTOCA3 )]

I a TttO

I a

UIR a

INTRLIN

U :INTRUR)]

:= SOMt HDIF' • tx :0 IF'lAf:O U NNtx,CLASS(R J> • !NTO<X}),.AO,T~O·.IVR2•>

I ; tA:Difl[B:ANDCINN(A~CLASSCR>JriNTO(Al>l T~l :: ANOElti~N<A•ClASS(Rl)•INTO(~)~B} flt2 := ANOE 2< HiNU, ClASS(R) h ISTD {Ah S> T43 := tOINTQ(ArAO•ISEX<R•R#A•AO.T4l•AOIRr

REFI 5{ RE AL• R)). !lt2 >

I Cl INTILEX :: SOMEAPPCOtF~Cr:OIFJAND(IN~<X·CLASS{R)}

ANOC IN'f <AOrCLASS(R)), INTOC AO))

I NUL(~)

: INNC A.:ussoru INTOC.O

: INTO(Al >

s

s

$

$

s

-4.64·

$

·I~TOCX)),I•I~TO<AOJ.tX:Difl CT:~ND(INNCXrCLASSCRJJriNTOCXJ>l 1'43'". IVRZ,.<.X .. rn INTOC Al>

+•lV'f2 $

AOIR " [N:NAULCR )J TU . . := NATINTO(AO,NATRLEX(N)) : INTOCA:J ) HS.· == INTRLINCTH) INTRL(~)

•IVRZ I R a [NHfATRL<R )1

~Ar !HUL := REALAPPlCINTRL(R},(X:Oirl[T:INN(X, CLÜSC lH) l T45 ... IVRZ,.<XrT ,N)) INTRlU l

••IV~Z s

AOIR a CP:POS(Rllti:INTRL<Rll Tr.& :·= PDSI~TNATDCAO,PDSEX<PJ,INTRLEX<Il) NATO( Al) 147 := NATRUNCT4&l : NATRLO)

•IVRZ s

R ; tP:POSU>J [l:INTRL<Rll POSINTHATRL == REALAPPl(NATRL(R),(X:OIFJ[T:INNCX•

CLASSCR>JlT47•.IVRz•cx,r,p,JJJ NATRLU)

UIVRZ $

A OIR a tiZ:ISCR .. O)] rr.a ·- INTDIOUO .. OE X<I2H INTOC A)) ·-149 ::: INTRLINU46l INTRLU l

-n~z s

R a UliS<R,.OJ l INTRUO :: REALAPPl(INTRL(R)r[X:aifl[T:INNCXr

CLASStRJJJT49 ... IVRZ•cx,T.I>> : INTRLU) RO a [N:NATRPCRO)J

REHAU6 := INTRLIN( POrRPC RO>,. PO OFRPC RO h INNCLA SS CPDOFRPCRO) J,.REHARK6•RP .. (RO,.N > ) ': I NTRL CP OF"RP ( RO > )

REHARK7 := INIRLI NC NOf"f! PC RO ),. NDOFRP( RO )r INNCLASS!NOOFRPCROJ>.REMARKT•RP*CROrN) ) ~ JNTRL(H OF"RP<RO)}

t>ZR114 $

A OIR :1 [I:INTRUR)J Tl := SATZD174CAO.INTRLEXtil) RATO( A))

rz :: .RATP.li'4CTU RAfRLH)

•2RH4 $

R ~ CI:INTRlCR)l SATZ174 :: REALAPP1(RATRL<R>,tX:CifJ[T:INNCX•

CL~SSIR)llT2•.zR174w(X,T,JJ) RATRLC:t > - 4~65-~ I'L:JSDR ·- (X:Difl[T:OIF"JREALDFCP~<X•YJ) tX:Difl [Y:DIFlREAl

+IV!U $

[A:OtFl(B:Difl[C:OIFJ(DIQ!FJ[E:EQ•RP•CA,.9JltF:[Q•RP•<c.DJ1

---~----- .----;;;; 1~1~,n~R~Ur,rV\ft#~ll~n~A~~r~~U\D,UI#,

PD<A•C>•PDIB•Dl•I,NClASS<POCA,Cll• !NNCLASSCPD(B,O>l•EiPOlZCArB•C•D•E•F)J : IS<<C.><. A>Pli.'SOR .. <C>PLUSOR>

•IVR3 s Fl'lUSOR := tX:Oifl[Y:OIFltZ:OIFltV:OI~ltT:<Y><X>

EQlCU:<V><Z>EOlft•.Iw~J•tK.v.z.v.r.uJ : FIXFZHEAL,.PLUSDR> s a ,L :a INDREAL2CREAL•PLUSJR,FPLUSDR•R•Sl REAL

u nu s

SliS ;, rz == ISlNOREAL2CREAL,PLUSOR,.FPLUSDR•R•S•A1• Bl1>A liR• BUS> ISCREA.. OFCPD< At.BU hl'l<R• Sl)

·I.'IIU s

SliS 2 P!CP == ISP<REAL,(X:REALliNNCP~CAl,Bl>• CLASS(X>>•REAtOf(PO<Al•BlJl,Pl(R,S>, INNCLASS<PDCA1,811)rTZ•.tYR3•J : INN<PD[Al•Bl>•CLASSCPLCR•S>>>

T a [I:IsCR.S)] ISPLl := ISf(REAL•REAL.(X:F.[ALlPL(X,T>•R•S•I> : ISCPL n, T ),. PLCS• Tl> ISPLZ :: ISF(REAL,REAl,[X:REALlPLCT,Xl•R•S•I> ISCPLH .. RlrPL<T.Stl

u a ti:ISCR.SJltJ:ISCT .. U)l IS?LlZ :: TRISCREAL,?L<R,f)pPl(S,TJ.PLCS.U),

ISPL1(ll•ISPL2CTrU•S•J)) Is<nn .r >•PL<s .. un

•3R175 s

!JUS a Tl := SATZ0175<A1.o Bl) :: EQ•RP•t PO <A 1• Bl) .PDCBl .. AU > TZ := JSIN<Pl(R•S>•PL<S•R>•P3<A1•81l•

PD<BJ,Al),P[CP.PICP{S,R .. 81•Al,.B1IS, A1IR>,T1> : ISCPL(~•S),PL(S,Rl)

.•3!U75 s

s a SATZ175 == REALAPP2tiSCPL<R•S>,Pl(S,.R)J,[X:OIFl [Y:OIFJCT:IMNCX•CLASS<RJlJCU:INN<Y• ClASSCSlJlTZ•.JR175•(x,y,r,U)) : IS<Ptn •SlrPt<S .. R)}

CDMP:. :: SATZ175 : ISCPL<l JOS >•PLCS .. R})

HIVR3 s

9US a U:ISCR .. OJl T3 == PDOl(Al•Bl•OEX<R•Al•AliR•I>l : EO~P"'t PO (A 1•81 hBl) n == ISINCPL<R•SJ,S,PD<AI,Bl>•Sl,PICP.oBliSr

T3) IS<PU~•S),Sl

-IVR3 s

s 41 U:ISCR,.OJJ !"LOl == REALAPPZCIS(Pl(R,Sl•S~,.(X:OIFJtY:DIFl tT:INN(X,CLASS<Rl>J(U:INMCY,CtASS<S)>l

ï4-.IvRlwcx.r.r.u.Il} lS(Pl,.U,.ShS) s 2 n :zscs.u 1

PL02 ·- TRIS<REAL.PL{~,sl,Pl{S,.RJ.R,COMPL, PLOHs,.~~I>J : I SCPU~ "S h R >

HIVU -4.66

BUS 2 [P:POSfR)J[Q:POSCS)J T5 ::: PP0(A1•8l•POSEXCR•Al*A1IR•P>•

POSE)((S,Bl•SliS,q)) POSOCPJ U1, Sl H

•IVR3

S ~ tP:PDS(ftJl(Q:POSCS)l POSPL :: REAtAPPZC?OS<Pl(R;S})r[X:CifltY:Oifl

[T:INNCX .. CLASSrR>>JCU:INNCY,CLASS<SJJ1

POS( PU R .. SJ)

TG'!'. IV.fU•(x,y,r"u,p,..Q)) POSCPU R•S>)

s

••IVRl . S

BliS a t~:NEGCR>ltO:NtGtS)l TT := NPO<Al•Bl.PNEGEX<R•A1•A1IR•N),

NE (iEl~ s, 61•8 liS~ 0)) NEGD< P!J <Al .. 81}) TS := NEGIN<PL<R•Sl#?0(;\l•BU.rPICP•T7J NEGCPU RrSJ l

•IVR3 S

S a tN:NEG(RJl(O:NEGtS>l NEGPL := REALAPP2CNEGCPl(R,S1J,(X:DIFl[Y:DIF1

tT:INNCX.rCLASSCR>Jl(U:INN(Y,CtASS(S))] TB". I'IR3 .. ( x, Y r.T, u, N, Ol) NEG( PU R• S))

:il ~:>OR := U:O!FlREALOF< M~O<X> > rx:DIF'J REAL

a (A:DtFJ(B:OifltE:Eo•ftp•(A,Sll TSA := ISIN<REALOF<MOD(A)),REAL0f(M00(8)),

MODCA),MOOCBl•l~NCLASSCMOOCA))• !NNCLASSUiO!HBH •EOKO!H A~ B•E)) : lSC<A>'t ODR" HODR)

•IVR3 s

a f'!tOD~ :z (X:OIFJ(Y:DtrJ[T:<Y><X>EQl T5A".IVR3~<X•Y•T> : fiXF'C R! AbHODR)

R a HO := INOREALCREAL .. HOORrFMOORrRJ REAL

+-IU3 s

AOIR a TU :: ISINDREALCREAL•KODR•FHOORrR"AO.AOIR) : IS<REAi.. Of'(MOOUO > h MO( RH

•IYR! s

AOIR ; MICM) == ISP<REAlrtXiREAlli~N(MODCAO>,CLASSCX)) •REALOtC~DOCAO>J•~OCRl• INNCLASSCMD~CAO>>.TGA•.IVR3") : INNCMO~tAO),CLASSCHO<RlJ)

s a U:ISU•S>l ISKO ::: ISFCREAL•REAtr[X:REAllKO(XJrRrS•I> ISHIO!R >..KO ($))

HIYR3 s

AOIR a [N:NEGtRJl T7A == ABSNO<AO,.NEGEX<N>J : EQ•R.P .. ! ABSO CAO)" MOOUO)) T8A ·- ISJN(A8SCR>•KOCR>•ABSO(A0lrKOOCAO>•

AICA .. !1ICMO• TH> : ISCABS( RhKO(R))

•IVR3 s

R a (N:.N[GCRJJ ABSN == REALAPPl<IS(ASSCR),~OtRJ)•[X:OIFJ

(T:INNCXrCLASS<R>)JT6A•.IVR3•CXrf•N)) : ISCABSC R)rMO<RH

- 4.67-

HIVB s

AOIR :1 CNN:NOICNEGCR>ll T9 ,:: ABSNNDCAO,THJ•L.IMP"<NEGOCAO),NEGCR),

NN• ( t: NEGO CA 0) 1 NEG IN CT))> : EO•RPW( ABSO(AO),AO) HO := ISIN(A8SCR>•RrABSOCAOl,AO•AICA~~ÓIR'

T9) ISUBSl RJ,,R 1

•IVR3 s

R a [NN:'IOHNEG<R>>l ABSNN ::= RE~LAPPl(IS<ABSCR),RJ,[X:Oifl(T:INNCX.

CLASS(RJllT10•.IVR3•(X,T .. N~)) IS CABS( RhR) R a [P;POS(R})

ABS!" ·- ABSNN(RrP~OTN(P.rPJJ ISCABSC Rl~>R> R ; ti:ISCR,O)]

ABSO == TR!SCREAL•ABS(R)•R•O, ASSNN<R,CNOTNCRriJ),I} I SC ABS[ Rl~>O l

•3P.17& s

AOIR :1 (P:P:JS(R)l T1 := SATZ0176ACAQ,POS~X{Pll : NEGOt KJ OUO)) rz == NEGIKCHD(RJ.HOOCAOJ,HICHO,fl) NEG( MOt R))

•3R17& s

R a CP:PIJS(R)] SATZ176A := REAtAPPlCNEGCKO(R)l,tX:DIFl(T:INNCX•

CLASSCR>>1T2•.3Rl75w(X,T,p)) : NEGtffQ[ RU

H3Rl7S s

AOIR ; n:zsu .. oJ l T3 == SATZD17GBCAO,OEXCI)) ZEROOO D<AO U H := OINCKOCR>,HODCAOl .. MICMO,T3J : ISOtOn ),0)

•3R11& s

R a U:IS<R,.Ol l SATZ176B :: REALAPPlCIS<MOCRlrO>•[X~DitlCT:INN(X,.

CLASSCRlllT4".3R17&•cx,T,I)) ISOIO(R hOJ

h31!176 $

AOIR il tn:H!!GCRll T5 :: SATZD176C(AO,NEGEXtN>> POSD ( !Q OUO)) T& := POSINtK0(R)rHOOCAOl .. MICHO,T5) POSCMOCR1)

•3R176 s

R a UC:NEGCR)] SATZ176C := REALAPPltPOStMCCR)),[K:Oifl[T:INNCXr

CtASSfRJ)lT&•.3Rl76•Cx,r,NJ} POSUOt lU)

+tt3R17S s

AOIP. il [N:NEGCMOCR))l - 4.68-TT == SATZ0175!H AO rNEGl:':X ( MOC r:t) • MOO ( AO),

MICKO,N)) : POSDUY > ra ::: POSI NCT7J POS(RJ

•3R176

R a [N:NtGCHOCR))} SATZl7&0 :a RE~lAPPH POS C Rl • rx: Dlf" J( T: INN(lC,.

CLASS(Rl>Jta•.JR17&•cx~r~N)J POSU >

H3R17So $

AOIR a [I: ISOiOCR J.. 0) 1 T9 := SATZ0176E<AO•OEX<HO(RJ,MOO<AO)~HICMO•

IU ZERO< Al J T10 := OHI( T9l I SCR, O>

-3R17; $

R ; I:I :ISC"OCR h!Hl SATZ17&E =· REALAP~l<IS<R,()),[X:OIFlCT:tNN<X• CLASSC!D llT10".3R176•0CrT ri) l IS<R.oOt

U3R17ó $

AOIR a [p :POS (HO< Rl) 1 Tll := SATZOl76tCAOrPOSEX<MO<R1~"00(AOJ,.

HICt!OrP)) : NEGOC A)) ra ·- NEGUHT11l : NEGCRJ

"'3R176 s

R a [P:P!JSOtOCRU l SATZ17&f ·- REAlAPPltNEG<R>•tX:OtFJCT:tNN(Xr

Cl4SS( Rl)} T12,. .3R176,.U:,. T ,.p J) . NEG< R > . •3R1T7 s

AOIR "' T1 := ISIN<MO<MO(R)),.ft,.MOO{HODCAO)),.AO• • MICMOCMO<Rl,.MOOiAO>,HICHO),AOIR• SATZ0177CAO» ISCMOCII OCR) ),R}

•3P.177 s

R a SATZ177 := REAlAPPl<ISCHOCMO(RJ>rR>~cx:OIF! (T: IP~.,(X rCtA SS< RH Hl'" .3Rt77•(X,. J)) t I S<MO C"' OCR J hR>

SATUT7A == SYHIS<REAlrMOtHOCRJ>,RrSATZ177J : I Sn" Hl CMO<R)) J s ; U:IS(R,HOCSHl

SATZ117B := TRISfREAL,.HO(R)rMOCHOCSl),.S• ISXO(R,.~O(S)rl),SATZ177(Sll IS<NOH hSl

SATZ177C := SYMISCREAl .. HO(RlrSrSATZl778) 'ISCS .. IO(R)) s a U: ISOt!HR ),.$) l

SATZ177D :: SATZ177CCSrF,.SrHISCREAL,MO(RJ•S"IJ) : IS<R" M) CS)) SATZ177E ::: SYMIS{REALrR,HOtSlrSATZ1770) ISCKOCS hR>

•3P.178 s

AOIR a Tl := !SIN<ASSCHOCR>l,.AB$(Rl,ABS0(MODCA0l)r ABSD<A~),.AICA<MOCR>rMOO<AO>~MICHO),. AICArSATZ0178(A0ll : IS CAB St MOCR l hABSCR))

•H178 s - 4.69 "-

R a SATZ178 := REALAPP1CISCABS<MO(RJ).A95(R)J,.[X:OIF1 rT: I NN(X rClASSCR)) JT 1". S!U 78" ( !{r f)) ISU.BSl ~O(R lhASSCRl>

SATZ171U :: SYHISfREAt•ABS<HCC~JJ.ABSCR),SATZ178) IS Cl\ SS[ R) • A BSC t!i} Cf:l })

•3R119 s

AOIR a n ·- OINCPlCRrMOtR>JrPO<AO~M00(A0J)r PICPCR.XOCR)rAOrM00(A0JrAOIR•MlCM0)r SATZû119<A1)) : ISCPLU ,.HOC R})rOl

•3R179 s

SATZ179 ::: REALAPPi<IS<PLCRrMO{Rl)•O>•EX:Difl (T: I?:~u.c LA SSCR)) H 1•. 3R179"{ Xr T)) : IS<PLC~ rHOCRlhOl

SATZ119A := TRIS{~EAL• 0LC~O(Rl•RlrPl(RrMOCRJlrOr

CO~Pl(~0CRlrRlrSATZ179) : IS<PLC~OCRlrR)r0)

+5R18:l s

BUS ;J Tl :a ISIN(MOCPl<R~SllrPL(MOCR>,HOCS))r MODCPO<Al•Bl>J•PD<MODCAllrMOOCBlllr MICH,{PL(RrSlrPDCAlr81JrPICPlr PICP(~OCRlr~OCSlrM00<41lr~OO<Bl>• KICMO(RrA1rA1IR>,MICMGCS,.Slr91IS))r SAiZOl31CAlr8lJ> ISCMOC,lCRrSllrPLCHO(RlrHl{S)))

-3RU3 s

S a SATZ18~ == REALAPPZ<IS<KOCPL<RrSJ>rPlCHOCR>~MOCS) )),[X:OifltY:3!fltT:IHN(X~CLASS(R)JJ

[U: UINCY,.CLASSCS )} JT 1•.3R180,.( Xr Yr T" U) ) : ISCMOC,lCRrS)l•PlCMOCRlrMOCSJ))

SATZ18!)A := SYMIS<P.EAL,KOCPLCRrSJJrPLCKOCRlrHOCS)) ,.sATZ180) : ISCPLC~OfR),.MOCSJJ,~O(PlCt,Sl))

!!H ::: PLCR~HO(Sl) : RE Al B1IS a HICMN := PICPCR.KOCSJ,AlrMODCB1l•A1IRr

KICHO(SrBl•BliSll INN\KO[ Al,Bl>rCLASSCHNCRrSU) T a U:ISUr$)]

ISHNl :: ISPllCRrS~~OCTlrll : ISCHNt~rTlrH~(SrT>>

IS!1N2 := ISPLZCMO<RlrHOCS},T"ISMO<RrSt~lJ) : ISCHMCf ,RJ.M?é(T.•SH u a Ct:IiC~•Sll(J:tSCTrUll

ISHN12 == ISPL12CR•SrMCCTlrHOCU)rlriSMOCTrUrJJ) ISUtNn "r ,, MNcs .. uu s a SATZ181 :: TR3lSCREAl,'-OCHHtRrSllrPLCHOCRl"

HOCHO,SillrPLCMOCRlrSJ,~NCSrR), SATZ130(Rr~O!S11riSPLZ<~OCK0(S))rSr MOtRlrSATZ!77CSll•CDHFL(H0CRJ•S>l ISCMOC~N(RrSI>•HNCS .. R})

SATZ181A := SYHIStREALrHO(MN(S,RJJ,MN<RrS), SATZ13U:S,i'D l ISO!Nt~ rSh MO<HNCSrR)))

•3R18Z

SliS :a [P:POS(HNCR,S)Jl Tl := SATZ0132A<AlrBl•POSEXCHN(RrS)r

HDCA1r81)•HlCMN•P)) MORE OU 1•81 1 rz == MORE IH<T H KORECR• Sl

•3!U82 $

CP:POSC MNC R.r S> >J SATZ182A := REAlAPPZ<MORE(R,Slr~X:OiflCY:Oitl

(T:!NN(X,CLASS<Rl~J[U:INN(YrCLASS<S>Jl - 4. 70-T2".3R182•(X•1•TrU.PJ} MORE CR• S>

h3R18Z s

iUl:i 11 {l:l5{"NIH•5JrQJJ Tl := SATZ018ZBCAlrB1rOEXCHNCRrSlrMOCAlr81 )r

HIC'IN• Il l : EQ•;u••t A1,.BU H == ISHHT3l lS<R.oS)

~3Rl6Z s

s a ti~ISCHN(RrSlrO>l SATZ1828 := REALAPPZCJS<RrS)r(X:DIFlCY:OIFJ

CT:IN~CXrClASSCR))][U:INN<YrCLASSCS))J

T4-.3~1BZ"CXrTrT•Uri1) : IS(IhSl

H3Rl:S2 s

B1IS a [N:NEGtMN(RrSl)J T5 := SATZ0132C(Alr31r~EGEXCMNCRrSJr

HD<AlrBllrMICMNrNJ) LESSOU l.oBl) T6 == LESS!IHTS> : LESHR• Sl

~3R1SZ s

s a tN:NEGUIHC R,.S) )J

SATZUZC :: RE4LAPPZCLESSCRrS)r[X:OIFltY:DIFl tT:IN~CXrCLASS(R))J[U:INN(YrClASSCSJJl T6•.3R182"CXrYrTrUrNJJ : LESS<Rr $)

H3Rl8Z s

sus a tM:M\IRECRr Sll T7 ·- SATZD162,tA1rBlrMOREEXCMJl : POS!)( 10 Cu,. Bl U T8 ·- POSIN(MN(RrSlrMDCAlrB1JrKICHNrT7J : POSUtN[ Rr S))

•3R18Z

s a Ot:H:JRE<R .. SJ l SATZ18l0 == RE,lAP?2<POSCHN(R,S)l~[X:O!Fl[Y:Difl

(T: UHHX,ClASS<R)) HU: IN!HY.CLASS< SJ )l re•.3Rtsz•cx.Y,r.u .. KJ> POSOfNtR,.SJJ

*-3R182 s

sus ::1 CI: ISCR• SJ l T9 := SATZC18ZE<Al.B1.ISEX<IJJ ZERlH Kl Ut,. BU) TlO =· 0 IN< MN{ lbSh 1!0 CA 1r Sl ), MI CI'!N• T9) : ISOtNH •Sl-OJ

•3R13Z $

s a U:tS<R.oS)l SATZ162E := REALAPPZ(ISCMN(R,S)rD)r(X:Oifl[Y:OIFl

tT:INN<X•CLASSCR>Jl[U:IN~CYrCLASS(Sl>J rto·.3~taz~<x .. v .. r .. u .. IJJ ISOINU rShOJ

+tr3R1 SZ s

BUS a ct:ussu .. s> 1 TU := SATZD182F(Al•Bl.olESSEX<LJ) NEGIH MJ C Al• 81)) - 4. 71-TlZ ·- NEGIN(KNCR•Sl•MD<Al•Bl),MICMN .. TllJ : NEGOt~:t R. SJ )

•3R182 $

s a CL:LESS<R .. S)] SATZ182F == RE~LAPP2CNEG(MN!R.oS)).o(X:Oifl[Y:Oif1

Ll:l~N\X•~LA~~'HJJJlU:1NN\T•~L~~3\~JJJ

rtz•.JRtaz~<x.r.r.u.t)J NEG(!i:NrR,.S))

+3~183

SliS ; UH HORt CH,. SJ l Tl := SATZ0183ACA1•Bl,KOREEI(M)) LESSDC~OOCA1),.M00<81J) TZ ::: LESStNCMO(R)•MOCSJ.~O~CA1>•MOOtetJ,.

HfCHOrs,;.i.,A1IfO,MICI10(S,B1•BliS ),Tl) LESSO!) CRJ, MOCSJ>

•3R183

s a [H:MORE<R• SJ J SATZ133A :: q[ALAPPZ<LESStHO{R>•~'<S>>•C~:Oifl

[T:OIF:tT:INNCX,CLASSCR)))[U:INNCY, CLASS{SJJ1TZ~.3Rl83~c~,y,r,u,HJ) : LESSCM)(Rl,.MOCS))

s a CI:ISCR•Sl) SATZ183B := ISMlHR•S•IJ ISOIOC:t );M0(S))

+*3R1JJ3

•3P.183

SliS a [L:LESS(R,. S>l n :: SArZel83CCA1rBl•LESSEX<L>J MOREOCiODCAl);MODtBl)) rr. ::: HQRE~NCKO{R),HO<Sl,H0v(Al>•HOD<81),

MICMO<R,Al,AliRl•MICHO<S•Blr81ISJ,T3J KORE04J (R), KOCS))

s a [t:lESSCR• Sl J SATZ183C := REAlAPP2tMORECH0(Rl,~O(Sllr[X:OIF1

(Y:DifltT:INN<XrClASS(RlJl[U:INNCY, CLASS<SlllT4~.3R153"<X•Y•T•Url)J : MQR[(M3 {Rh MO(S))

S ; tl :LESS< M3CR h M:H S Hl SATZla3D ·- ISM3RE1Z(MOCKOCRll,~rM0(H0(S)),S,

SATZ1??<Rl•SATZ177(S},SAT1183CCH0(R)r XO<s> .. UJ : KORECR. SJ

S 3 ti:IS<MO(Rl.HD(SJll SATZ183E := TR3IS(REAL•R•MO<HOCRllrMOCMOCS)),.Sr

S a [M:KDRE010(Rhi'!(HSHl

SATZ177A(R),.!SM0(HOCR)rMOCSlrllr SHZ177( Sl J

SATZ183F := ISLESS12CKOCMOCRJJrRrH0(H0(S)},.S• SATZ177CRi,SATZ17T(S},SATZl83A<HO(R),

IS(fh SJ

KO<Sl•HlJ : LESSCRrS)

T s R

AOIR

ia PROPt a PRO?Z a PROP3 i [A:OIF1(B:Olf]

PROPlD

:= AN03(P3SCSJrPOSCTlriS<RrHN(S~Tl)) := SDME([X:REALJPROPlCX)) ·- SOHE((X:REALjPROPl<X)'

:: A ~03 ( POSO <Ah POSIHS hEO"F.P .. U(h MQU,. B > )}

PROPZD :: SOKE"L«(QJF,[X:DIFlPROPlDCXJ) (PZ:PROP2D(A)l[B:OifJtP1:PROPlQ(A,SJJ fl := AN03Elt?OSO<Al,POSO(Bl•

TZ EQ•Rp•(AO•MD(A,.BJJ•Pl)

:= ~S03E2(PCSO<A)...POS!)(6.J? tQ•Rp•(A0rHO(A,BJ~,P1}

:= AND3E3(POSOCA),P~Sr<e:, EQ~~P~CAO•~D~ArO)J,fll

: = 1\f.:iiUlf'< A}

: 'PR:3P 1

'PROP' 'PROP•

tpp,!Jp. 'PROP'

POSi)( Si

:: EO .. I1?'"t AO.MJCA,.BJ> PC: . .\l

s

s

$

s

- 4. 72-

-----~II"T"""!!"'"tn:l""""-------"l:iaa RtÁ;LOfCB J Pi :ti #tB

•3RU5

•3Rl85

+31:!186

r4 T5 T6

T7

T8 PZ :1 T9

rtO AOIR :1 TU

::: INNCLASS!A) : = I NNC !..A SS 0~ ) :: tSfN(ft,HNCRA~RB>,AO~MD(A•BlrAOI~•

HICK~{RAr~3.Ar8rT4~T5)rT3~ :: AN03 H PC$( 't~ J.POS{ R8 ), IS C Rr MN (RA •R9 > ),

POS!NCRArArT4rTl>rPOSlN<RBr8rT5rT2)r Tó>

:: SOKEICREALr[X:REALlPROP1CRArXJrRB~T7J :: SO~EAPPCD[F,[X:DiflPRO?lO<I~X>~PZr

PROP2(RAJr[X:Difl[i:PROP1D<ArX>lT8CXr f))

:a SCHE !C REAL• [X :REAl.lPROP2 CX hR ArT 9) :: SO"EI~P<DiFr[X:OIFlPROP2~CX)r

SATZ0184<AO}rPROP3r[X:Oifl(T:PROPZO<XJ lTlO(X,.f)}

:: REALAPP1<PROP3~.3R184"r[X:OIFl {~:IHNCX•CLASSCRJJlT11w.3R184•(XrTl)

U ; fA3:Difl[B3:0IflCC3:0IFlC03:DIFJ[A3IR:INNCAlrCLASS(Rl) H93IS: IN~HUrClASS<S)} ltC3 IT: INN( C3rCLASSCTl) l(03IUliNNC03,CtASSCU>Jl

T1 i2

U ; SATZ185

C2IT :1 T1 TZ

T :1 SATZ16&

== SATZ 01&50 3r S3 .. C ],.{)3)

:= ISIN<Pl(MN(R,S)•MNCT.UJ),MN(Pl<R•T>• Pl<SrU)J,PDtMOCA3 .. B3l,.HDCC3,03JJr MOCPDCA3•C3J,POt83•0l)J,piCPCKN<R•S>• M'N(T, Uh KlHA 3, 83 ).r HO<C 3rD 3 )p

MIC~~(R,.SrA3rB3•A3IR .. S3ISJ, KICKNrr,u,c3 .. D3rC3IT,03IU>>• MICHN<PL(R,T>•PL<S•U>•POCA3.C3>• POC83,0]J,PICPCRrTrA3,C3.A3IR.C3IT), PICP<S•U•S3•03r93IS•03IU>l•Tll

== REALAPP4<ISCPlCHN(R•S>,HNCT,U>>• HN(PlCR,TJrPL<S•U))},[X:Difl[Y:OIFl {Z:OifJ[V:DIFJ[XI:INN(XrCLASS<R>>l (Yl:IN~CY•CLASS<S)JJ[ZI:INN<z,ctASS<TJ ))[Vt:INNCVrCLASS{UJ)Jf2«.!Rl85"(XrYr ZrVrXIrYirzi,VIJ>

:= SATZ0186<A2,B2rCZ1 := ISIN(~LCPLCRrS>rTJ•PL(RrPL(SrT)),.

POCPOCAZrBZlrC2)•PO(AZrPD<B2rC2>>• PICP(Pl(R,SlrTrPOCAZ,.B2l.C2r PICPCR•S•AZ,.BZrAZIR•BZTSl•CZ!T), PI:P(R,PL(S,T)vA2r?O<B2rCZ),AZIRr PI~P(s,r.az,.cz,azzs,czttl),TlJ

:: REALA?P3<IStPLCPl(RoSlrT),pL(R,Pt(Srf) JJr[X:OIFlCY:OIFJ[Z:O!FlEU:~~N(Ir

REA I. INNC A,.C tASSCRU > INN< B•ClASSCRIH)

PROP1UA .. R8> : PROPZHA)

: PROi"ZU Al PROI"3

PROP3

: SOKEC(C :REAlJSOMECtY:REALlAND3CPOS<XJrPCSCYJ, ISC:trMII tX•Y )})J)

: EC:""RP"t POtHOC Ah 83) •HD<C3. 03) J.MO(POU3,C3hP0(83•03)})

ISCPL(~N<R•S),MN<T•U>J•MNCPL<R•Tl,Pl<S•UJ)J

: IS<PL(,H(R•S>,HN(T,U))rMHCPLCR•TlrPL(S,U>>J

s

s

s

$

- 4. 73...;

s

•3R187

•3R188

•3R138

ASSPU ASSPLZ

S ; PLH~

HNPL

SATZ167A

~L~~~'~I·IJLV~·RN'l'~L~~~\~IJJL"i'R~\L,

CLASS(J)>JJZ•.3Rl16•(XoYoZ~u,v,w>~ := SATZ::.~s := SY.l'I S< REAL• PU PUR• S h T hPL<RrPL CSo TH

rSATll8ól :: TRIS<~EALrPL<HN(RrSlrSloPLCRrPLtHOCSJ•

S>1rR.ASSPLlfRrMO(SlrSJo PL02(RrPL(MOCS>•Sl•SATZ179ACSJJ)

:= JRIS<R~Al,MNCPL(R,S)rSl• PLCR.PLCSrMO<S>ll•R•ASSPLlCRoS,HOCS>>• PLOZ<?.,PL(S,~O(S)lrSATZ179<Sl)J

:= TRIS<REAlrPL(S,MNCRrS))oPL(MN(RrSlrSJ• ~.c:~PL(So~NCR.Sl>•PLMNl

SATZ167B := SO~EI<P.EhlotX:~EAlliS<PL!SoXJ,p), ~NCRrSlrSAlZ187AJ

[X:REALltiiiSCPLCSrXlrRll SATZ187C := TRIS<~EALoHNtRrSJrKNCPLCX.SlrSlrXo

SA TZ1810 X ; ti:ISCPLtX,.S),R)J

SATZ187E

SATZ187F

IS"Nl(R,PL<XoSlrSoTRISl<REALoR,PlCXoS) oPLCS.Xl•I•COMPL(SrXll}rMNPL(XoS))

:= SYMISCREAL.MNCRoSloX•SATZ167C)

:= SATZ!37CtTRIS<REAlrPLCS.X),PLCX.S)oRo CCMPUS~:O•I H

:= SYMISCREAL,MN(RoS)•X•SATZ167EJ

S ~ [K:REALltY:REALlti:tS(Pl(S•XJrRJJ[J:ISCPL<S•Y,,RJJ Tl := TRIS1CREAL•X•YrMNCR.SJ.SATZ187C(X,Il•

SATZ187CH•J)) S ~ TZ := (X:REAlltY:REAlltT:ISCPL<S•X).RJl

S ; SATZ187

[U:IS(PL(S,YJ•RllTl<X•YrT•U>

:= OMri<REAl•[X:REAlliS<PL(S,.X),R)• rz•.JR1&7••SATZ187BJ

CZIT a tM:MORE(PLCR.TJrPLCS.T))l Tl := SATZD188A(A2o82rC2,MOREEX<PL(R,TJ•

Pl(S,TJ.PO(AZ•CZ),P0(BZ•C2)r PICP(R,T.AZ.C2oAZIR.CZIT>• PICP<s.r.sz.cz.azrs.czrr>.M>>

Tl :• HOREIIHRoS.Az.az,AZIR.B2IS .. T1J

T a tM:MORE(PL(R,.TlrPL(S,.TJJJ SATZ188A ·- REALAPPJOHJRE<R,.SJ.(X::JIF][Y:OIFl

tz:DifJ[U:INNCXrCLASS<Rll](V:INN<Y• CLASS<Slll[W:INN<ZrCLASS<Tl1l TZ".3?.lae•<x.v.z.u~v.w~M>>

+<>3R188

C?.IT a ti:ISCPL<R.T>rPL<S#Tl>l Tl -- SATZD188B(A2.82oC2riSEKCPL<R.T>r

PL~S#i>rPBC~2 .. t2>•P0(82•C2Jr PICP(R,ToA2rC2,~2IR,C2IT>.

PICPCSrTrB2rC2o92iS•CliT>•I>>

: ISCPLC~l(R,S),.Tl,Pl<RoPLCS,T))) ISCPLC~L<R•S>•T>rPL(RrPL(irT)))·

IS (f'l <loPl.C 5~> T) > •Pl. (PURrS) ,.·y))

ISO'IN(i'UR• SJ,S hR)

: IS(MNU •S >• U IS<X"M" <R .. S)}

ISHINn •ShXJ ISU.M.'4 (R,.S ))

: ISCXrY)

: AHONECREAlr[X:REAl]ISCPLCSrX)rR))

: ONE( [X: REAlliS(PLCS.X) .. RH

MOREDCA Zr82) HORECR .. SJ

: HORE<R. 5)

s

s

s

' -4.74-

•3RU8

CZIT a [ltLESSCPlCR,.T>rPLCSrT))]

•3R188

TS ·- SATZ01138::02rB2•CZrU:SSë:XCPl(R,.Tlr PlCSrTJrPOCA2 .. C2l,.PDCB2,.C2lr PICP(R,.TrA2•CZrAZIR~C2tTJr PtCP<s .. r .. sz,cz.azts.cztrl.LJJ

T6 := lESSINtR•SrA2rB2•A2IR•B2ISrT5J

T a (L:LESSCPlCRrTlrPL{SrTlJl

H31U88.

czn a

•3R188

T ~

T ~

+*3R188

CZIT a

-3~158

T a

SATZ188C ·- REAlAPP3tlESS<RrS)r[X:DtrltY:CIFl

tH: HO~EtR• S) l T7

T8

(H: MOR[(R,. 5) l SATZ1880

u:rsu.s1 1 SATZ188E

tL:LESS<R• Sl 1 u

uo

[L:LESSCR•Sl l SATZ18SF

:=

:=

:=

:=

:=

:::

rz:Oifl(U:INNCXrClASS(R))J(VtiNNCY, ClASStSJ>ltW:INN(lrCtASS!TJJl T6•.3R188"tx.y,.z,u,v,.w,L>J

SATZ0188DCAZ.82rC2r HOREEX<R•SrA2r62•A2IRrB2ISrH)) HOREIN<Pl(RrTlrPl<SrT>,POCAZrCZ>• PO(B2rC2)rPICPtR.T,A2•C2,.A2lR•C2IT>r PIC?(s,.r,az,.cz,.eziS•CZITJ•T7>

REAlAPP3<HORE<Pl(R,.T> .. PL(S,.T)),.[X:Oifl (Y:OIFltZ:DIFJ(U:INN<X .. ClASS(Rlll [V:INNCY,.CtASS<S>Jl(W:INN<Z .. CLASS(T)>l re•.3Rlaa•cx,.y,.z,u.v.w .. H>>

ISPLH R,. s, T, I)

SATZ0188F<AZ.BZ,.CZ,. lESSEX€ R, s,.Az .. az.AZI R.BlJS,l)) lESS IN<PLtR•l),.pl( S• ThPD<AZ.CZJ,. P0(82,.C2>•?lCPCR,.T,A2rC2,A2IRrC2ITJ. PICP<S•T•B2•C2•B21S•C2If),f9)

:: RE~lAPP3(lESS<PlCR,.J),.Pl<S .. TJ),.[X:OIFJ tY:OtFltZ:DifltO:INN<X,ClASS(RJ>l tv:INN(Y,CLASS(S))}[W:INNClrClASSCTJJl rto•.3Riaa•tx .. v.z .. u,v .. w .. L>J

LESSOCA 2rB2l : LESS<R• S>

: lESSCR,. Sl

: HORED(;- OCAZ rC2hP0( az,. C2)J

: MORECP:.. (~,T J•PL<S .. TH

: MORECP:. (R,.T ),.pt<S,.T>l

IS<~lt~ .. T),Pl(S,.f))

LESSOP O<A2,.C2) ,.poe sz,. CZ))

: LESSCP:.. tR" T ),.pl( S• T))

: u:ss<P:. (R .. T hPl(S•T))

s

s

s

s

s

s

s - 4. 75-

+3R191

T ia U'I:M\JRElPI.U~R)rPl{T.Sl)]

SATZ1a8G := SATZ1aBA<tSMORE12<PL<T~R>•PL(R,Tl• PL(T,S),pL~S,fl,CC~PL(f.!),CG"PLCT,S)• Jo!))

T a CI:IS<PL(T,R>•PLCTrSlll SATZ138H := SATZ!8!9(TR3!StRE'L•rl~~.T),Pl(TrRlr

PLCT,s>~PLCS,r:,cOMPLCR.T>~I•. CCHPL.))

T a (L:L~SSCPL<T.R>•PlfTrS))J SATZ188J :: SAfl168C(I,LESS12<PLCTrRlrPLCR,TJr

T a tH:H?RECR•Sll SATZ1881(

T a U:ISCR.S> l

?LCT.SJ.PLCSrT>rCCMPL<T,R>,COMPL(T,S)r l)}

:: ISMGR~12t?L(RrTlrPL(T,RlrPL(S,T}r PlfT,SlrCC~P~tR.ï>.COH?L(SrT),

SATZ188DOOJ

SATZ188L := ISPL2CRrSrT•Il T a tL:LE:SSCRrSll

SATZ188~ := ISLESS12<Pl(RrT)rPL(TrRlrPL<S•T>• PLlTrS),COMPLCRrT),COMPLCS,T), SATZ168rtl))

U a ti:IS<R~S>lCK:KORE<TrUll SATZ188N :a ISMORE2CPl(R~U)rPL<S•U>rPlfR•T>,

SATZ1880

I a [L:LESSCT.Ull

ISPl.lC R, Sr IJ,! hSATZ168K CT ,.u,.R.MJ) := ISMORElZ<PLCRrTloPL!T,Rl~PLCSrUJ•

PltU.S),CO~PlCR,T>.CCM?LCSrUlr

S.\TZ188t0

SATZ188P :: ISLESS2(PLCihUhPL(S,UhPUR,T), ISPL1CRrS,.UoiJrSATZ188~(T,u~R•l)J

SATZ188Q :: IStESS12<PL<R•T>•PL{T,R>•PLCS,U)• PL(U;S),COMPl{R,TJrCOHPL(S,U>• SATZ188Pl

U a [M:MORECRrSll[N:MORE(T,UlJ SATZ189 := TRHDRECPL<R•TJ,PLCS,TJ,.PLCS~U>•.

SATZ186D(M),SATZ168K(T,U,S,N)) U a tL:LESS(R,SJl[K:LESS(TrUJl

SATZ189A :: lEHMAl(Pl<S,UJrPl(RoT>~ SATZ189(S•R•U•T•lE~MA2(RoS•LJo LEMMAZ<T ,u •K)))

U a [H:MOREIS(R,Sll(N:MORECToU)J SATZ190A :: ORAPP(MORE<P.•S>~IS<RrSJ.KO~E<Pl(R,TJr

?LCSrU}),~.CV:~GRE'R•S>JSATZ189CVrNlo {V:IS(RrSllS~TZlSeNCV~N))

U I [K:MORECR,S)J[N:MOREISCT,U>J SATZ190B :: ISHORE12CPl(T•R>,PL(P.oT>•Pl(UrS)•

PLCSrUlrCOHPl(T,RJ,COKPl<UrS>• SATZ190ACTrUrR•S•N,M)~

U ~ [l:LESSIS<RrSlltK:LESSIT.U>l SATZ190C := lE"MAl(PL(SoU)rPltR~Tir

SATl190A(S;R.c,7~S~TZ!&SSCLJ, lE'!MA2CT .. u~ro >,

U ; CL:LESSCRrS)l[K:LESSIS<T.UJl SATZ190D :: LEM~AliP~(S•UlrPl(R,TJ,

SATZ19QB(StR,U,hlEHlo!A2Cll. SATZ168SCT•U•KlJl

D31U a [H:H3REIS<R~S>l(N:HOP.EISCTrU)} fl := SA!ZQ1nt(A3•Bl•~l·~3·

HORE ( R• S)

: ISCRrS)

LESHR" SJ

HORECP't.. CT•R J.Pt.UrS))

IS<PL<T rRhPL(T ,.5))

LESSCP;.. c'r .. RhPltT•S»

HORECPLCR,TJ,PL(S,U))

: MOR((P;,. CT •R hPL(U,S U

: lESSCPi.CRrThPUSrUH

: lESSCP. U.oR >•PLCUrSU

~ORECP:.<RoT),fl(S,UJ)

: LESSCP:. CR•T hPL<SrUH

MORE C P'~o. CR~ T ),pl.( s,u))

: t!ORE(P'. <R•Tl•Pl.CS•U))

LESSCP:.. CR•T )•PL<SrU))

LESUP:. (R,. T lrPU s .. u)) - 4. 76-

~

+IVR~

-IYR\

+U192

rz MOREISEXCR.S.A3.B3.A31R,83IS•"'' MORE ISEXCT •tl•Cl,C!,C 3IT ·~3IU,NJ>

:= MORE IS HHPL<R• TJ,Pt.<5• :.H.P!l! Al•Clh P:>CB J,.Q3),. PI CPCR, T ,.A3,. C l•A 3lR.C3JT h PICP(S,u .. al .. Dl•BliS•~liUl•Tl>

U a tM:HlREISCR.S)][N:MOREISCT,U>J SATZ191 := REALA~P4CMOREISCPLCR•TJ•Pl<S•Ull•

[X:DIFltY:DtfJ[Z:~:Fl(V:OIFJCXI:INNCX• CLASS!RlJltYI:IN~CY,ClASSCSJJl tzt:INNCZ•CLASSCT>Jl[VI:INNCV•CLASSCUJ JlT2•.JR19l•cx,.y,z,v,xi,.!I,zi .. VI•M,.NlJ : MOREIStPLCR,TJ,PlCS,.UJ>

U a [L:LESSIS<R•S)l[K:LESSISCT,Ull SATZl91A :: SATl1!;8A<PL<S.UhPL(R,.T),

SATZ19l(S•R•U•T•SATZ1S89(L)• SATZl&e!HT.<U,I() l l : LESS IS[ PUR, ThPUS.Ul)

; TIMESilR ·- (X:OIFJrY:O!FlREALCFCTIHX•Y)) [X:Dtn t:Y:Oif'JREAl

[A:DIFl[B:OIFltC:D[fl[O:OIFJ[E:Eo•RPwcA,BJl(f:EO*RP*(C,D>l Tl :: ISIN<REALCf<TO(A,C))•REALOF<TD<B~D>>•

TDCA~C),TOCS.~1.INNCLASS<TOCA,CJ), IHNCLASSCT0(9,DJ),[QTD1Z<A•9•C•D•E•F))

:= tX:DIFltY:OIFltZ:DIFltY:DIFJ[T:<Y><X>

ISC<C>< A> TI KESOR,<D>TIIfESDR>

F"TI!tESDR

s a rs EQltU:<V><Z>EOHl ... I VRft•( X• y" z, V• T ,u) : flXF'ZUEAL• TIMESDR)

t= INDREAL2CREAL,TIHESDR .. FTIMESOR.R•SJ t REAL

BUS a TZ := ISINOREAlZCREAL•TIMESDR•FTIMESDR•R•S• Al.B l.AliR,BliSJ : IS<REAL OfCTDCA1,81J ),TS(R, SU

BUS a TICT

T a U :tsU .. S)]

·- ISPCREAL•(XtREALJI~NCTO(A1•81)• CLASS<lO ), RE AtOF<TDC Al,el) )~ TS<R•S), INNCLASSCTDCA1•6l)>,Tz•.IVRft•)

ISTS1 := ISFCREAL•REAt,[XtREAllTS<X•Tl•R,.S•I> ISTSZ :~ ISF(REAL,REAl•(X:REALlTSCT,X>•R•S•IJ

U a tl:IS<R•S)J[J:ISCT .. Ull ISTS1Z := TRIS<REAt.TS(R,Tl,TS(S,T),TSCS .. UJ•

81IS a [I:IS(R•OJJ Tl TZ

sa n:tsu .. o)J SATZ19ZA

ISTSl•JSTSZ(T,u,s,Jl)

:= SATZD19ZA(Al•Bl•OEXCR•Al•AliR•IJJ :: OINCTSCR~SJ-TDCAl•Bl>•TICi.Tl)

:: REALAPPZUSC !S<R·SJ~O),U:OifltYtOirJ CT:INN(X•ClASSCa))][U:IU~<t•ClASSCSJJl

: INN<Tilt At.Bl >.CLASSCTSCR•S l.))

IS USU" Th TSCS• T >) : IS<TS(f .u, TSU .su

: ZERIJCTHAt..BUJ IS<TSC!t .. SJ.OJ

T2•.4R192•o•,y.,y,.u,.t )) : IS<TS<lrS),O)

s

s

s

s

'

I

s - 4. 77-

HfoR19Z s

SliS a Ct:IHSrO)J T3 . :;: SATZ01929tA1rB1,QEX<S•9lrB1fSoill : ZEROCTl CAl• SU> T4 :: 0 IN( TS { R,. S ), JO tAl, '31 h i 1 CT,. r3 J lSUS<l .. ShO)

•4RUZ s ~,

s a tx:Iscs .. oJl SHll9ZB := REALAPPZCISCTSCRrSt,OJ,[X:OIFJ[Y:OIFl

CT:INN(XrCLASSCR>lJ[U:INNCYrCLASS(S))] T4·.4~192"Cx,r,.r.u.I>l I S<T SU ,s ),. 0 J

H4R19Z s

BUS a [I:IStTSCRrSJ,Q)l T5 := SATZD192C(AlrBloOEX(TSCRrS)rTO<A1rS1 ),

TICTriH ORClERl <AlhZEROCBl U T6 :: TH9•t.oR~CZEROCA1>rZERn!Sl)oiS<R.O)o

ISCS .. Olr!S,(T;ZE?.OCAl>lOINCR•~t•Ali~• T>rCT:ZEROCBl>JOI~<Srölo81ISrT)) OR(ISC~,.Ol• ISCS,.Q))

•t.Rl9Z s

s a tl:tstTSCRrSJrO)J SATZl92C :s REALAPP2COR<ISCRrOJ,ISCSr0)),(X:OIFl

tY:3IFltT:IN~(X,CLASS<RJ>JtU:INN<Y• CLASSCSJJ!T6w.4R192"tX,rrTrUri>> : OR<IS<~~OblSCSr0))

s a tN:NISCRrOJlEO:NISCSrO>l SATZUZO :: TH3•L.IHP"(IS<TSCR,SJ,Olr0RCISCR•OJ~

ISCSrOtJrTH3"l.OR•(JS(R,OJ,IS(S•OJ.Nr ) 0)r{T:ISCTS(RrS)rO>JSATZ192CCT>> : NI S(TSt RoSJ rOJ

s a u:Isur .. o>l TSOl :: SAH192AUl uusn .. st.o>

_ .. s ~ U:ISCS,O)l TSOZ ·- SATZ1921:l : ISCTSnrShOJ

., HtR193 s ;

SliS ~ Tl t= SA TZD l<J3U 1• 91 > : EQ-RP"'[ A8SOUO>~TSCABSCR> .. ABSCS>>•

ABSO<TD<Al•BlJ)riOtABSOCAlJrABSD(Bl)}r AICA(TSCR .. S> .. TO<AlrBll.TICTJ, ,. TICT\A6S(RirAaS<S>•A9Sa<A1lrABSD<91),. AICACRrA1~A1IR),AiCA<Sr91rBllSJ1rT1> IS<AB~TSCR .. S))~TSCASSCRJrABSCS)))

•4R193 s

S a SATZ193 :: REALAPP2CIStAéS<TSCR,.Sl)rTSCABS<Rl• ASS(S))),(X:Oif-ltY:Otf){T:INN<X; CLASSCR>)ltU:lN~f!~CtASSCS>)J Tz•. 4R19 3"<X" Y,.T,.U)) : IS<ABSt TS<R .s > J P TSC ABS CR), ABS< SJ))

'• SATZ193A == SYMISCREAL•ABSCTS<R,SlJ.TSCABS(RJ• J

ABS< S> h SATZ195> : ISH SU B.SCR). A8SC 5) JrABS<T S<R ,.5)) >

•4P.194 s - 4. 78-

Blts ll Tl :: SAT'Z0194 (Al; lH l : EQ .. RP"'[ iO{Al;Bl lrTOCBt .. AlJ) rz ·- ISINCTSCR.S),.TSCSrR>rTDC~lrB1Jr

T0(81•AllrT1CT,TICTtS•R•8l•AlrBIISr A1HD• TU : !S<TS(~•Sl•TS(S,Rll

•ltRl"

+4R195

•4R195

SATl194 ;:: REALAPPZ<ISCTSCRrSlrTSCSrRllr[X:Oifl CY:DtFJ[T:INNtXrCLASSCRJJJtU:INN(Y• CLASS<~>llT2•.4R194"CX.~.T.U)) t ISCTSC~rSlrTSCS.R))

CO MTS :: SHZ194 ISCTSI~•S>rTS{SrR1) a 1RL == ~E~LOF' C lOf J : REAL

POSt := POSINCIRlr10f•INNCLASSC10F)r POSOIRP<lRP)) : POS( 1R'. l

NATR~l := NATRLHl> NHaL<l RU INTRL1 := NATINTRlClRL•NATRLlJ INTRL<l RL)

AOIR ; Tl := Sr.TZ0195UO> : EQ'"RP""C TD<AOr10HrAU TZ :: ISIN<TS<R•lRLlYRrTOCAO•lOFlrAOr

TICTC~r1RL.A0.1DF,AOIR~INNCLASS(l0F))• JI.O!RrTU Isnsn .. tRL hR>

R 1 SATZ195 =· REALAPPl<ISCTS(RrlRL>•R>.CX:OIFl tT:IMNCX•CLASSCRl>lTZ•.4R195"(~•T>> : ISCTSH •lRL lrR>

SATZ195A :: Snii SC REAL• T S< R• IRL >.Rr SA TZ195) !S<R,.TS CRrlRUl SATZl95B :: TRIS<~EAL•TS(lRL•RlrTSCR,lRL>•P.•

CC"T S{ lRL~;:! h SAT Z195 l ISCTS<l Rt. .. R hR) SA1'Z195C == SYMIS<REAlrTSC1RL•Rl•R•SATZ1958J : IS(R,.fi <lRL.R))

s a tP:?DSCR>l(Q:POSCSll SATZ196A := SYKIS<REAL.TSCASS<R>•ABS(S)J,TS<R•S>•

ISTS12CABSCRJ,R.ABS<S>•S•ABSPCR,P), ASSPCS,Q}}) IS(TSC~•Sl•TS<ABS<Rl•ABS(S)))

BliS ~ (N:NEGCRJltO:NEG(S)J Tl := SATZD196BU1rBl•NEGEXCR,AlrA1IR,Nh

NEGEX<S.B1•B1IS ... OJJ : EO"'RP"'t TDU1..81J,TDUBSOUU,.ABS0(8UU f2 := ISIM<TS<R•ShTSOBSCR),.ABS(S}),.

TD<Al.BlJ,TOCABSDCA1>•ABSOCB1JJ,TICT, TICT(43S(R)•ABSCSJ,.ABSaCAl>•ABSOCB1>• AICA(R,A1.Al!R),AICA(S,S1,S115)),f1) : ISCTS<~•S>.TS(ABS<RJ,ABSCS))J

s

$

s

•4R196 S

S ~ tN:NEG(R)l[O:NEG<SJl SATZ196B :: REAlAPPZCISCTSCR•Sl•TSCABSCRJ,.ABS<S)))

BliS a [P:POS(Rll[N:~EG(Sll

,[X:Oifl[Y:DIFltT:INN<X•CLASSCRJll [U:INNCYrCLASS<SJ>lf2«.4Rl9&"<X•Y,r,u, N,.O))

TlA :: SATZD196CCAlr81rPOSEX<R,.AlrA1IR•P>• NEGEXtSrB1rB1IS•N>>

TZA :• ISINCTSCRoS)rKO<TSCABS(RJ,.ABS<S)1)r TOCAlr6ll•MGDCiJ(AaSOCAl)•ABSDC81)))~

TICT,KICMO<TS<A~SCRJrASSCS'J• TO<ABSOIA1J•ABSDC8l)),JICT~ASSCR)• ABS(SJ,.ABSO(Al)rABSO(Sl)r A!CA(RoAl•Al!P.)•A!C~CSrB1,61ISJJ~,T1Al

IS<TSC~.s>,.TSCABSCRJ.ABS<S>>J

s

ISCTSH ,.5 ),. KO<TSU8S(R >.A3 S(S)}))

-4.79

•4R19&

S ~ [P:P~StR>l(N:NEGtS>l SATZ196C :: REALAPP2<ISCTS<R,S),~O<iS{A8SCR),

S ~ [N:N~GtR>lCP:~CSCS>l

ASS<SJ))),(X:OI>lrY:~•rJtT:INN<X•

CLASSJl[U:INN<Y•CLA55(5)J) T2A•.4Rl9~·<x.v.r,u,p,N>>

SATZ19~0. := ";"R3IS~R:::Al•TS<R•S>.TS<S.Rh

AOIR ~ [N:NDT<IS<R.O>Jl T3

HQCTSrA3S{S),AêS(R)ll•MOCTS<ABS<R>• A6S{S))J,:O~iS(R,Sl,SATZ19?C<S,R,r.NJ,

ISMO<TS<ASSC~l.ABSCRJ>~TS<ABSCR),

ABS<S>>•C~~iS{A3S<SJ,ABS<R>>>>

(T:ZERGCAOl~OI~<T'l SliS ~ (N:NOT<ISCR,O>JJ[O:NOTC&S<S,O>>

lri:IS<TS<R•S>,TS<~SSCR>·A3S(Si)J! T~ ·- SAïZ019óE(A1,81,T3<R,A1,AliR,N),

T3CS.BJ,SliS•O>•ISEX<TS<R•S),TSCASS<R> ,A3S<S>J.TOCA1,Bl>•TOCASSO<A1>• ABSOC3!)J,TICT,T!CT\ABS{RJ•ABSCSJ, A9SD<Al>•A9S0\61J,AICACR,A1,Al!Rl• AICA<S•Bl,61IS)),Il)

tA:AND(POSD(Al),POSDCBlJJJ T5 := ANDI<POSCR ), POS< SJ.

POSIN<R•Al,AliR,ANDEl(POSO(Al), FOSO<Sl),A)J,POSIN<S,Sl.BliS, ANOE2CPOS~CA!J,PCSDCB1),A))}

I ~ [A:ANOCNEGDCAl>•NEGO(Bl>~l T6 :: ANJIOitGCRhi~EGCS>.

NEGI~CR•Al•AliR•ANOEl<NEGO<Al>• NEGO!Bl),A}),NEGIN(S,Sl,SliS, ANDE2CNEGOCAl>•NEGOCS1>•A)))

I a TT :: TH9wl.GR•{ANDCPOSO<Al)•PDSO<B1)), ANOCNEGDCAl>•NEGOC61)),ANOCPOSCR>• POS< S> ),A~iH ~IEGCR>.NEGCS) >•T4• [T:A~~CPOSOC,lJ,POSOCBllllTSCT),

[T:ANO<NEGOCAli.NEGUCB1JlJT6(T)l

S ~ tN:NDTtiS(R,O))][Q:NOTCISCS,Ol) l(I:IS<TS<R.s>,TSCABSCR),ABSCS>>Jl SATZ196E ·- REAlAP?ZCOP.CANOCPDSCRJ,POSCS)),

AND<NEG<R>,NEGCSJ)),[X:Oifl[Y:OIFl (T:INN(X,ClASS(Rl)J[U:INNCY•CLASS<S>>l rr•.4R19&•cx.v.r.u.N.o,I>>

+*4P.196

0 a [I: IS<TS<R,S >• HO(fSCABS<RhASSCS ))))] T3 :: SATZD19&F<Al,SlrT3fR.Al,AliR,N>-

T3( S• 81• 31 !S• O>. I SS X< TS{ R• Sh MO<TS<A3SCP)rASSCS>>~.TO<A1,81)• MODCTO!ABS0(~1J,A8S0<6!))),flC1,

~tCMOCTSCA6SIR),A3SCS)'•TD(A8SOCAl>• A8S~CS1)loT:CT(A0S(R),45S<S>•AnS0(~~ >•

s

!S<TSU ,5 h HOCT S<ABS<R h A3 SC SJ J) J

I se-;- Sn ,s ), HOCT S<ABS< Rh A3 S< S > >))

s

NOT< ZE~ 0 C :.0))

CR <A NIK POSOUlJ .PCSO(BU ), ANOt NEGOU 1J ,NEGCCBl IJ J

ANDCPOS <RhPOS(S)l

OR (A 'fiX POS< R >.POS CS )J. ANO( NEG< R>, NEG CS>))

s

OR CA NO[ POS( R hPOS<S )h ANOC NEG< RJ, NEG<S J))

s

~ 4.80-

ABSO<Bll•AICA<R•Al•AliRl• AICA(SoBloBliS)lJol})

CA: .\NO{ POSD( Al Jr NEGD( Bl > > l U :: ANDICPûSCRhNEG(Slo

POS[NCR•AloAliR•~MDEl<POSD<A!)• NEG0(~1>.AJJ.N~SIN<S~3l•SliS. ANOE2CPOSO<A1JoNEGOIB1l•A})l

I ~ (A:AND<NEGOCAlJoPOSD<Bt,>J HO ::::: AND!O!EGHDrPOS<S>r

NEGIN<R.Al,AliRoANDEI<NEGO<Allo PUSD(êl>•A>>oPOSIN(SoBl•EliS• A NJEZ~ >:EGD U 1 hPOSD tiH Jo A)))

I a Til :: iH9·~.CR•CAN3CPOSDCA1JoNEGDCSll)• ANJC~[5~[,1JoPOSDCB1tl.ANDCPOS<RJ•

NEGCSJl~A~~<NEGtR>•POS(S)),f8• {f;A~~(PQSCCAlloNEG0<91JJlT9(Tlo

tT:Art~(NEGO(Al)oPOSOCSlJ>JTlO<T>J

Q a ti:IStTS<R.oSl.oMOtTS<ABSlq),ASSCS))))J SATZ195f := REAtAP?2COR(ANDCPOS<R>.oNEG<S>>•

AN3fNEG<Rl.oPOS<SlJJ.o[X:Oifl[Y:Oifl [TtiNN<X.oCLASSCRl)][U:INN(Y.oCLASSCS))J

; tiRUNDC POSDCA U• t.EGDt:BU J. AND( NE GOU U.o PCSO<IH)))

: ANOC POS <Rh NEG( S))

AND< NEli CR h POS( S))

TU•. 4R191)""( X.o Y.o T .. U.o N,. D • I)) : OR (ANI)[ POS< R >. NEG<S )),. ANDC NEG<RJ .POSCS))) S a tP:PaSCTSCR•SJ)l

Tll

T14

P a SATZ195G

S a [N:NEGCTS<R•Sl)l

tt~· a ns

TU

nr

~ a SAll196H

:= TH3•L.IMP~(IS(R.oOJ.IS<TS(R.oSloOJo PNOTOCTS<R.oSl.oP>.oCT:ISCRoOllTS01(R•S• T)) NISCR .. l)

:= THJ•t.IHP•<IS<SrOJ.oiSCTSCR.oSl.oOJ.o PNOTOtTS<R.oSl.o?J.otT:IS<S.oOJJTSOZ<R.oS.o T)} :H!SCS.oQJ

:: TRIS1CREAL.oTS<R.oSJ,TS<ABSCRJ.oABSCSJJ.o ABSCTSCR•S>1.oA8SP!TS(R.oSJ.oP1.o SATZH3(RoSl J : IS<TSCR .oSJ,.TSUBS<R loABSCS )))

:• SATZ19SECT12".4R196".oT13•.4R196"" T14'".41U96•) CR CANOt POS CR l#POS<S )),. ANOC HEG< R J. NEG<S U)

:: TH3•L.IMP•CIS<?.oOJ.oiS<TS<R•SJ.o0),. NNOTO<TS<R•S>~N)•tT:IS(R,QllTSOl(R•S• T)) : NIS(R,3)

: .. TH3•L.lHP"CIS<S.o0),IS(TS(R•SJr0), NNOTOtTSCR,S),NJ,.[T:IS<S.o0)JTS021R•S• i)} NIS($,.3)

':= SAT!177C<TS(A8S(R).oABSCSJJ,TS<R.oSl.o TRIS<REAt.TSCABS(RJ.ABS<SJ),. ABSCTS<R•Sl>•KOCTS<R·S>J.oSATZ193A(R,S> .AgSNCTS(Rr5lrNJ)~ ISCTS<R .s >• KOOSCABSCR h A3 SCS))) J

== SATZ196~(T15".4Rl96•rT16".'R196•r nr•.4R196'"J : GR{ANIX POS{RhNEG(S)J,AND{ NEG<R>.PCS(SJ))

s

s

s

s

- 4.111-s

HolU!iTT s

31IS ;r Tl =· S~TZD197A(A1,81) EO .. RP"'[ T0040DU1 h8 1)" HOOC TDC .u,au)) n :a ISIN(TS<~OCRl~SJ,MOCTS{R-S>>•

TOCMOJ!Al>•BlJ,MOOCiQ,~l,SlJ), r:CT<MD(RJ~S,HO~(Al>•Sl,

MICMD!5rAl•A!!~),BliS),MICMOCTS(R•Sl• TOtAl,Bl)•TlCT},T!> : IS<TS<KO<R>,SJ,MQCTSCR,Sl>>

•4R197 s

S :Z SATZ197A := RE t.L APPZ( Z SC 15040{ R} •S h HO CTS< R• S) J) •

IXtD!~lCY:Cifl(T:INNCX.CLASS<Rlll [U;I~~CY~CLASS<S>JlT2•.4R197"'(X,Y•T•U> ) : ISCTSCMOCR),S),MO(TS<R•S>ll

SATZ197S := iR3IStREAl.TS<R•M0(S)J,TSCK0(Sl•~>• ~~(TS'S•R>>•KO(TS<R•S>>•tOMTSCR,MOtSlJ oS4TZ19iACS;R),ISMOCTSCS,R),TS<R•S>, C:n<TS{S~RJ J) ISCTS<~•MO(Sll•MOC!S(RoSJl)

SATZ197C := TR!SZ<REAL.TS<~O(RlrS),TS<RrMOCSJ), ~O~TSCRrS)J,SATZ1?7ArSATZ197Bl lSCTSCMO<R>•S>•iSCRrMOCSlll

SATZ197D := SYMISC~EALriSCMOCRlrSloTSCRrHOCS>>• SAT'Zl97Cl ISCTSt~rMOCS1lrTSCMO<R>rSll

SATZ197E := SYMISCREAlrTS<MOCR>oS)rHOCTSCRoS)lr SATZ197U IS(ItOU SCRr $)), TSUtOCR );SJ)

54TZ197F == SYMISCREAl~TSCRrMOCSl>•MOCTS<R•S>Jr SATZ197B> : IS<MO(fS(R,SU".TSCRrKOCS}))

SATZ198 == TRIS<REAlrTS(MOCR>•HO(S)), TSCR,MOtHOCSll)rTSCRrS)o SATZ197CCRr~OCS)J,JSTS2<KO(MOCS))oSrR• SATZ17i"CS))) IS<TSCM OCRJ • MOCS l); TSC R•SJ )

SATZ19!1A == SYMIS<REAlrTSCMOtRJ,MOCSJ>rTS<R,Slr SATZ198l : IS<TS<R•SlrTSCMO<R>,MOCS>>>

uiYH s

!HlS ~ (P:PDSCR>ltQ:POS<S>l u :z PTDPPfAlr8loPOSEX(RrA1rA1IRrPJo

PCSEXCSrBlrBliSrQ)) : POSO( fl) (At. 81) J ftt := POSINtTSCR~SirTOCA1~8l)~fiCT•T3l : POSCTSt R,S) J

•IV!H s

s ; tPtPOSCRJl[Q:POS<SJl 11>3ST5PP ·- REAtAPP2tPOS(TS<R•Sl),[X:DIFl[Y:OIFl

[T:IHM<XrClASS<P.)l1[U:tNNtY,ClASS<SlJJ r~o·.IVR4•(x,,,,,u,p,QJJ POS( TS( R;S) J

uinc. s

!'" a [N:N[!i(S)] T5 ;: NTOPN<Al,Sl.POSEX<R,AlrAliRrP),

NEGEXt S• Bl•81!S• N' > NEG!)( T:> Utr aU J i6 :: NEGIN<TS<R.SlrTD(llrBl>•TICT,T5! : NEGCTS[ R•Sl >

•IV~~ s -4.82-

5 a CP:PJS(RlltN:NEGCSJl NEGTSPN := REALAPPZ<NEGCTS<R•S>>•[X:OlflCY:OIFl

[T:IN~(X;CLASS<R>>ltU:INN(Y,CLASSCSJ>l T6•.IVR4·~y,y,J,U•P~N)) ; HEJ;HSt R,.S))

s a tN:NEG(~lltP:POSCS)l

+~1'!199

-r.r:199

+UZH

•t.R2H

NEGTSNP :: ISUEGCTSCSrRl•TS(RrSJrCOMTSCSrRJ• NEGTSPN(SrRrPrN>> : NEGCTStRrSJJ

S a [M:NEG<R>l[O:NEGtSJJ POSTSNN := ISP0S(~S<HO<RJ,MO<Sl.JrTSCR.SlrSATZ198r

R a [NtNIS(R,OJJ POSSQ

R a NNEGSQ

CZIT a Tl T2

T :1 SATZ199

ASSTSl ASSTSZ

czn a Tl TZ

SATZ~Dl

OISHPl

DISHPZ. OISTPT1

POST SPP< !'!?( R i, V.O t S>• SA TZ 176C t R" N h SATZ176CCSr!lli)

:u RAPP(R,POSCTS(RrR)),[TtPOS(RJl POST S?P< R• R• Tr Th THZ .. L. I MP'"< IS< R•O h POS( TS( R• R) h N h [T: NEG CR) lPOSTSNN<Rr R,

POSHSt R .. SJ J

f,.TJ J POS<TSt R .. R)) :: THt•L.IHP•tiS(R,OloNDTCREG<TStR.R)))r

CT: IS ( !h 0} JO NOTN<T S< R, Rh SATZl924(RoRrl)),[T:NISCR,OJl PNOHHTS(!bR ),POSSQ(P,,.f))) : HOUNE&<TS<RrRUJ

:: SATZD199CAZ•~Z,C2) :: ISi~CTSCTSCRrSlrTJ,TS{R,TS{S,Tl>•

T~CTOCAZrBZJrC2J,TOCAZoTD<3Z•CZ))r

TICT<TS(R.S>•T•i0{A2r8Zl,C2• TICT<R•S•A4•8ZrAZIRrB2ISl•CZtTJr TICT(R,TS(S,T),A2~TO<SZ.CZJrAZ!R•

TICTCSrT•B2rCZ•92ISrCZIT)J•T1J

:a REAlAPP3<IStTSCTSCR.SJ.TJ.TS(R,TStS.T) ))r[X:Oifl[Y10IFJ[Z:OIFJ(U:INN(X• CLASSCRJ)l(V:INN(Y,.CLASSCS))J[W:INNCZ. CtASS<ï>JJTZ".4R199•(XrY•Z•U•V•W>>

== SA TZ 199 := SY~ISCREAl•TSCTSCR.sJ,J),TS{R•TS(SrTJ)

,sHZ199l

:= SATZ0201(AZ•92rCZJ :: ISIHCTS<RrPLCS.TJJrPllTSCR•Sl•TSlR•TJJ

.TO<AZ,.P0(8Z.CZ)J•?D(T0t~2.B2>• TOCA2•C2)lrTICTCR•Pl(SrTJ.A2•PO(B2•C2) rAZIR,PICPlS,T,S2,CZr82IS,CZIT)), PICP<TSCR•SlrTSCR.T>rTDCA2rSZJ• TO(A2rCZlrTICT(R,s.AZrBZrAZIR,BZISJr TICTCR•T•AZrCZ•AZIRrCZITl)rfl)

== REALAPP3C ISC TS( R•Pl< Sr Tl), PL( TS( R, S>, TSCR,Tl))r[X:OIFl[Y:OIFJCZ:OIFl (U: HI~<X.rCLA SS<R)) H V: INNCYrClASS<S)) J (W;INN(ZrCLASSCT>JJTz•.4RZOl•<X•Y•l•U• y, 11) )

::: TR3IS(REAL.TSCPL<R•S>•T>~TSCT•PLCR.SJJ rPLCTStT.R)rTSCTrS)lrPL<TS(R,T), TS[Srf)JrCOMTSCPLtR.S)rTl• SATZ2~1(T~R,S>oiSPL12<TSCT.RJrTS<RrTï~ TS(TrSJ•TSCSrTlrCOHTS(irRl•COHTS(TrS>• )

== SATZZOl := SY~tS<P.EAlrTS<Pl(R,S)rT)rPL<TS(R,T>.

: ISc:TS<f SCR•ShT >.TS<R• TSU •T>)) IS<TSH S(R,. S ), T lr TStR, TS(S "f) J)

: ISCTStR .. TS(S,TJJ,TStTSCR .. Sl•T>J

EQ•RP""C: TD<Az,pouz,cz> hPHTD<Az,.azJ,TDCA2,C2)) J

IS<TSCRrPLtSrTJJ,PLITS(RrSJrTSCR•TJ))

: ISU S(R •PL( s, T lhPl<TS(RrS hTS<R •. n J)

JSCTSC~L(R,SJrTJrPl(TStR,TJ,TS(S,TJ)J IS(TSt~~Pl<SrT)lrPl~TStR•SJ,TS(R•T)J)

s

s

s

s

- 4.83-

TS(SrTJJrOISTTPll DISPTZ :: SYMISCREAL .. TS:RoPL(S,fJJ•PltTS(R•Slr

'!'SCR.v T) ),.i)IS TTP2) SATZZGZ :: TRIS{~EAL;TSCRr~NtS•'!'>J•FlCTSCR•5>•

fStR.MC{T)J).~~CT3(R•S:.TS{RoTl>• DISTTP2CR•S•MOCT>l•lSPL2(TS(RrKO(f))~ HOCTStR,T,)rïS(R,SJ .. SATZ197BCR,.f)))

DlSHMl =· TRISt~EALrfS(MN(R,s> .. TJoPLCTStR•T>• fS<MO<SJrT,JrH~<TStP.oT>rTS(S,TJ},. ~ISTTPl(RrMOCSJ.TJ.ISPLZCTSCHO<SJ,f),.

M J (T St S • T> >r TS < R,. i >,. SA T Z 1 9 7 A CS • T > ) ) OlSTTHZ :: SUZZ02 OISTl1T1 :: SPU SC RE Al" TS< KN(I!,S ),. T hKNHSU.o Th

TSCS .. Tl> .. OJSTT~l) DISTMT Z := S'rHI S\ REAL,. i SOh MIH s, T) ),.MN<TS<R•S ),.

TS(R,.J)),.OISTTHZJ SA TZZOO := SArZZ02

CZIT; CH:HJRECa,SJltP:PCSCTll

M ;

H4RZOJ

11 :il

•lt!l2H

H a

p a

I OI

N ~

Tl :: SATZDZ03~CA2•BZ•C2• HOqEEXtR .. s .. Az,.az,.AtiR .. B2tS .. H), POSEXCT.C2•C2IT,Pl)

TZ :: MORE IN(TS(R, ThTSCS• T),.To<Az,.cz>,. TO(B2•CZ>,TICTtR•f,AZ•CZ•~ZlP.,.CZITJ.o rtcrcs .. r.sz .. cz.szis .. cztr> .. Tl>

[H: MORE CR• S> lt P: POS<T 1 l SATZZ03A := REALAPP3CHORE(TS<R•T>•TSCSof)),.[X:Ditl

tY:Oifl[Z:OifJ[U:INN(X.ClASSCRJ)l tV:tSN(Y,.ClASS(S)ll[W:ISNtz,.ctASSCTJll rz•.4R2D3•cx.v .. z,u.1.w~M .. P>J

ruucr..o> 1 SATZZ03B := TRISZCREAL~TSCR,.TJ,TS(S,TJ,.o,.

TS02(R,.T~IJ,TS02(S•T•I>l

[N:NEGU)] n := SATZOZOlC<Az,az,cz,

MOREEXtR•S•AZ•BZ•A!IR•BZISrH), I~EGE XCT ,cz, C 2IT,. N) >

H == LESS INCTSC R• T>, T SC s .. Th TiH AZ• CZ),. TiHB z,c 2)., TIC HR • T ,A z, cz,,,ziR,.C2IT }, TICT{S•T•BZ,cz,.aziS•C2ET>,T3>

tHU4EG(T U SATZ20 JC := REALAP?3ClESS~TStRrT>,TS<S .. TJ),{X:OIFl

CY:OIFJ[Z:OifJCU:!N,lX•CLASStR)ll tV:INN(Y,CLASS{SllJ(~:INN(Z,.CLASS<T>ll r••.4R2o5•(x.v,z.u,v.~.~-~,,

SATZ20l!l := ISMORE12CTS<R•T),TSCT,RJ,TSCS,T), TS(f,S),~OHTS<R•T1•CG~TS(S?f), SATZZOJA J

SATZ20JE :.: TRIS2<REAL•TSCT,RJrTSCT#SJ•O~ rsou:-.R .. ! i• rsour.s,r n

SATZ20Jr ·- ISLESS1Z(TSCR.Tl,fS<TrR:.rstsgT)•

: IStPLH S(ft,. Th TSt S•T)) ,.rst PLt R• SJ. TJ J

lS<'PLH SCP., S ),. T S<R• T)),. T SC RoPLt s,. T>))

lS{fS(R,.HNCS,.TJJ,.HN(TS(R,.SJrTS(R,TJJJ

lS(fS(MNtR .. SJ,T),.MNCTS<R.TJ,.TS(S,TJ)) IStTSt~•HHCS .. iJ),MNCTS<RrSJ•TS(R,.f)))

: lS(HNtTSCR .. T)rTS(S,f)),.TSCHN(R.oSJ .. TJJ

IS04N(f S<R• S h TS(R,. T)) .. TSt RrHN( s,. T))) ISCTSC~rHNtS•il);HN(fStR•S),.TSCR .. TJ))

s

MORED<T DU2 ,.cz),. TDC BZ.o CZ))

$

MORECTS <R• T ) , TSt S• T))

: ISCTSt,,.f)•TSCS .. T>>

$

LESSOCTDCA2,C2l•TCCBZ.C2))

lESSUS CR .. T },.fS(S,T))

$

: lESS<TS CR•T J,rscs .. r )) - 4.84-

HOREOS CT,.R),.TSCT,SU

; !~HSU .. RhTS(T,.SH

TStT•SlrCOMTS<RrT)•COMTStS.T>• SATZ203C J LESSUS n rR ),fS(T ,s))

T ; tt:LESS<R•S>ltP:POStT)f SATZZ03G := LE!oii'M HTS< s,. T hT Slrh T ),.

SATZ203AlS•R•TrlEM~A2<R~S•l),p)) LtSSC T5 <R• Th TS<S• T)) l ~ c::tsn.on

SATZi?03H ·- TRIS2(REAL•TSlR•fJ,.TS!S•T>•O• TS02lR,T,Il•TSC2<S•T•il)

L a t!HNE5<f Jl SA TZ2JJJ := tEMMA2<TS(S,T),TS<R,T).

SATZZOlCtS•R•f•LE~~AZtR•S•l>•N>> p ; SATZZ!HK := LEMMA1CTStT.SJ,rS<!,Rlr

SATZE33DCS•R•T•LE!~AZCR•S•L>•P)J I il SATZ~Hl := TRISZ<REAt.rscr.P.:.rscr.s>.o.

_TSOlCT•R•Il•TSOltT•S•Il) N ; SATZZ03!4 := tEKMA2CTS(T,S),TS<T•R>•

SATZ203fCS•R•I•LEMMA2CRrSrl)rN))

AOIR a (NltNISCR•O>J Tl :a TH3•t.IMP•tZEP.O<AO)•IS(Rr0)•N1•

CT:ZEROCAO>lCIGCT>> 03IU a [Nl:NlStS•O>l[I:ISCTSCS,J),Rl1{J:ISCTSCS.UlrRll

TZ :: SATZ0204BCA3rS3,T1CSrB3,.8JIS•Hl)rC3, 03~ISEX<TStS,TJ,~,TDC3lrC3),A3r TlCiCSrTrBl•C3,B3IS•C3ITJ,A3IR,I>• ISEXtfS(S•U>•R•TO<Bl•Dl)•Al• TICTCS,UrS3,03r83IS•OliUJ,A3IR,J))

T3 := ISINtf•UrC3•03rC3ITr03IUrTZ>

NOH ZER O<AO J)

: EQ-RP'"t C3r03J : I S<T • U)

Sa [N:NIS(S,Q)J[X:REAll[Y:REAtJ(I:ISCTSfS.X),R)l[J:IS(TS(S,Y),Rll SATZ204B :: REALAPP4CX•Y•IStX•Y>r[Z:OifJ[U:Difl

BllS a CNl:NIS(S,Oll

tV:OifJ(W:OIFltZI:IHN(ZrCLASSCR>>l [UI: INN(U•CLASSCSJ)][1I:INN<V•CLASSCX> )J[WI:INN(W,CL~SS(Y))1T3•.4R204•(X,Y, z,.u, Y ,lhZI •U ! .. VI ,WZ,l'b I, J >J IS (X,. Yl

T4 := SATZ0204A(AlrBl•T1CS•Bl•BliS•NlJ) SOHE•L•tDif•(X:DiflEQ•Rp•(fOCBl•X>•Alll tA:OtfJ[E:Eo•Rp•(TO<Bl•A>•Al)l AR :: REAton AJ : REAL T5 := IS!NUSCS,.AR ),R,T0(81,.AhA1•

TICTCS,.AR•Bl•A•81IS,!NNCLASS<A),,.A1IR• E> ISCTSCS •ARhR)

T& := SOMEI(REAL•(X:~EAlliSC!S(S,.Xl.R),AR• TS> : SGME((IC :REAlliS<TS(S,X),.R) J

Nl i1 T7 := SOMEAPPCDIF,[X:DIFl(Q•Rp•(TOtBl,X),Al) ,14, SOME([X: REALUS( TStS•O•RHr (X:OlF1tT:(Q•Rp•cTDIBl.XJrAlllT6(X,.T)) SOKEC[( :REAlliS(TS<S,X),R)J

s

s

•4R2J4 S

N ~· SA TZZOU

SA TZZ04

:= REAlAPP2(SOMEC(Xt~EALl!S<TSCS-X)rR))p {X:OIFl[Y:DifJ{T:INNtX~CLASS(RlJl [U:INN(Y,CLASSCS>JlT7•.4RZ04•(XrY•T•U• N})

:= OR[[(REAL,[X:REALJISCTS(S~X'•~). SOME((( :REAUIS(TSCSrX hR>)

- 4;.85-

[X:REALJLT~KL~LJ1ili~ll~~5•~J•~JJ

(U:IS{TSCS.YJ.R)l5ATZ2348(~,y,r,u),

SIITZ20U J or~Et ex: RE!\L lt'itTS<SrXhRH ov :a IND(REALr[X:REALliS<TSrS,XloR)r

SATl20'•) RE Al,. SATZZ~4C := ONEAX[REALrtX:aEALJIStTS(S,X),ft),

SATZ204l IS<TSC$ •OVCR .. s,NJhRl SHZl!OitO := S YMI S< ~EAL.• T S (5, OV (R,. S • Of)) ,R •SAT Z201t C) ; lStR,TStS,OVtR,S,.N>>> SATZ204E :a TRIS<~EAL•TS<OVIR•SrN),SI•

TSCS.OYCR,S,NJJ.R,COHTS(OVER.S,.H>rS)• SAH204C> IS (TSO V<R• S•N> •ShR)

SA T ZZ!HF' := S'i'HI St RE~L.• TS< CV <R• s,.N hS hP..SATZ204 El IS<It• TS (QV( R.s, N>.S H s a [X:REALJtN;KIS(So011CI:ISCTS(SoXJoRJJ

SATZ2HG ::: SATZ<049{N.X,OV{R,SrN).I,SATZZ04C(N)) ISU.OI (R,SoNU s ~ (N:HIStS .. Oll(P:PQS(~)J(Q:PQS<SJl

U/t~l!'t. $

H 2 !tOS := oveR. s .. 1n REAL ? a T8 :::: ISPOS(RtTSCS.ROSJ .. SATZZ040(Nl?Pl PCSCTSt S•ROSU Q ~ T9 ·- THl"L·A~J*(N(G(S}rNEG<ROSJ,PNOTN(S,.Ql) NOT<ANJtNEG<S>*NEGCROS)J)

TlO ·- OREltl~DCPOS<Sl•POS<RDSJ),.-NOCNEGlSl• NEGtRCSJJ .. SATZl96G(S,.ROS,J8),.T9) ANOCPOS (S),.POSCRilS))

•4RZ)4 s

Q a POSO,PP := ANOEZ~POSCSJ,PDS<OVCR~S,Nll• T10 ... 4R204 .. l : POS<Ovt R•SrNH

l" ; tiUNEGCS)]

+*4R234 $

H ~ TU := TH1wl.AN&•CPOSCSJ .. PDS(R0Sl.NNOTP(S,.M>l NOTtAN3CPOSCS);PQS(R05))) UZ ·- OREZCAN~(POSCS>•POS<ROS>l~ANOCNEG(Sl•

NEGtR0S)),SATZ196GCS·ROS,T61•Tlll ANOtNE:O CS h NEG(RIJSJ J

•4RZ)t. s

" a NEGOtPN ::: ANDEZCNEG(Sl;NEGCOVCR•S•Nll• TlZ ... 4R204 .. } : NEG( OVt R,.S, NU

N a tH:NEGCR>ltP:POS!S1l

H4RZ'4 s

" a f13 := IS~EGCR,TSCS,ROS),SATZZ04DCN>,HJ : NEGCTS( S .. ROS)} p a T14 == THl•t.AND•(NEGCS),POSCROS),PNOTNCS•Pll NOTCANlCNEGCS>•POSCROS))J

f15 := ORElCANO!PCSCS)~~E~<RCSJ)•AND<NEGCS), POS(~GSll•SATZl9GHCS•ROS,Tl3J,Tl4) AND<POi(S)•NEGCROS))

•4R2:14 s

p ~ NEGOVNP ::: ANDEZCPOSCSJ,.NEGCCV<R,.SrN)),. ns•.4R204 .. l : NEG<OV[ R,s, N))

K ~ tl: NE:GCS)]

u6RZ:>It s

L a T16 := THl•t.A~o·cPOS(S),NEG<ROSJ.NNDTP(S,LJ) NOTO.NJ CPOSCShNEGCRO;Dl) - 4.86-T17 :: OREZCANOCPOSIS},NEGCROS>J,ANDCNEGCS)~

PCS(R0SJJ,SATZ196H(S,ROS•Tl3)·T16> ANDCNE~<SJ,POSCROSlJ

•t.R2l4 s

L i POSOiNN :• ANDEZOlEG(SJ .. POS<OVtR,s .. NJ),. Tl7'".4~204•) : POSCOVCR~>S~>N»

a tRO :CUT ][SO: CUT]( lU MO?.F.:,.RP,.( ?.lh SO):: MtJRBPEP ;:: t~CaE HHf'Of"RP< ROl ,.ptJfï'lil'( SO hP!)Of'RP(RO h

P00f~PCS01r!NNCL4SS<POOfRPCR0)),. INNC~ASSIPD3fRPCS0)),. MORERPEPJCRO~SO,MJJ HORE<Plf'RPCROJ•POFRP(SOJJ

SO; tM:MORE<PDFRP<ROJ,.POFRPCSOJJl ~O~E~PIP · := MCRERPIPD{?O~so .. MOREEX<POfRPCROJ,

SOa tt:LESS•Rp•(RO .. SOll

PO~R?CSOJ.PJDFRP<RQ),.PDDf~PCSOJ,

lNNCLASSCPDDfRP(RQ)),. IN!I!Ct.A S.S C ?iHlfRP( SC) h 1-1>.} HORE"R!IO .. <RO ,.so)

lESS~PEP := LEMMA~CPCfqpcs~l.POfRP<RO),. HCqERPEP< SO• P.O .. SATZlZZ< RO, SO•L))) : LESS<Pl fRPC ROhPOfRP(SO))

S3 a tL:l.ESS(POfRPCROJ,.pOfRP<SOl'l LESS~PIP :: SATl121(SO•RDrMORERPIPCSO•ROr

. LEMKI.20"Ct"R?<RO),P0fRPCSOJ,L)}) : LESS•R!IO .. (ROrSOJ S ~ CP:PDS<R>lCQ:POS<S)l(H:MOR~CP. .. Sl] 0 iJ Of: MORE( Rr S) l

•IYR5 S

•IVR5

•IVR5

+5R2l5

·sn:1s

Tl := ISMORE12(R,POFRP(RPOFP(R,P>>•S• POfRP<RPGfP(S,Q)),JSPRPlfR,PJ, ISPRPHS,.Q>• MJ

MDRE~ERP :a MOREP.PIPCRPOFP(R,PJ,RPOFP(S,.QJ,. Tl ... IVRS•>

0 ; [M:KORE•RP•CRPOFPCR,.p),.RPOFP<S•Q))J

" a rz

M a KOREf'IRP

Q a tl:LESS(R,Sll

:= ISMORE12CPOfRP<RPOFP(R,.P)),R, POfRP(RPOFP(S,QJ),S•ISPRPZ(R•Pl• ISPRP2<S,.QJ,TZ•.IVR5")

LESSPERP :: SATZ121(RPOfPtS•O>•RPOfP<R•PJ, HOREPERP(S,R,Q,p,.LEMMA2(R,s.L)))

Q a (t:tESS,.RP•tRPOFP<R•P),RPûfPCS•Q))J LESS?IRP := LEHHAl(S,R,MOREPIRP(S,R,Q,p,

SATZl2Z<RPOFP(Rr?),RPOrP(S•OJrlJ)) R a 501 := SETOFlREAL,CX:REALllESSISCX,.RJ)

SOZ :: SETOF'tREAL,[ X:REAUMGRE<XrRJ)

S a tN:NQTtiNCS,.S01Jll Tl := TH3• L. IMP"{ LESSISt s, RJ..lH ( s,. SO 1) ,:~,

[T;LESSIS<S,R1lESTI1CREAL,(X:REALl LESSIS<X .. R>rS•Ï)}

TZ := ESTII<REALr[X:~EALJHORECX,RJ,S, SATZl67K<S•RrT11j

: MORE<PJfRP<RPOFP<RrP)),pOfRP(RPOFP{SrQJ))

: MllR[ .. R!IO •tRPOFPt:RrP),.RPOFP( S,.Q))

: MORE(PlfRPCRPOFP<R,.pJ)rPOrRP<RPGFP(S,Q)))

: MORE<Rr S>

: tESS<R• SJ SC:T<REHJ SEHREUJ

s

s

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s

s

- 4.87-

•5R2l5

• '5?.Z~ 5

HSR235

vaoo

R OI T3

?. a V301A

R ;a T4

T5

R a VBOlB

:: t~:REilltT:~QT{INC~,SOll)l i2'"•5~205"'UrTJ

:a ESTI HREAL,( X:.REAL llESSISUrR ).R .. lESSISIZCR.R,REFISCREALoR}ll

:• lSMOREZtPl<R,O>rR .. PLCRolRL>• PlOZ(R•O .. R(fiS<REAL•O>l• SATZ1S8K<lRL .. OoRoSATZlS9AC1RL .. POS11)J

:: ESTII!REAL,(X:REA~lMORE<XrRloPLCR,lRL> ,U)

·- NONEMPTYI(REAloSOZoPLCRolRLlr T5"'. 5R205")

S a ti~INCS .. SOl)l[T:REALltJ:tNCToSOZ>l T& := SATZ172ACSrRoT,ESTIECREAlo[X:REAll

R a vaoz

s a (l:LESS (5, R> l V BOlA

s a CM: MûRE<S• Rl l VS033

R a Sll 512

S a [NtNJTCINtS,S11)1l

LESSISCX .. R>•S•Il•LEMMAlCT•R• ES TIE< REALo [ X:REAL JHORE<X,.R h T oJHl

:= [X:REALltT:INCX•SOl)l[Y:REALJ(U:IN<Y• S02)JT6".5R205 .. { x,T" y., U J

·- ESTII<REAl•(X:REAlllESSISCX•Rl•S• LESSISil(S.,R,L>>

:= ESTIItREALr[X:REAll~ORE(X,RJ.S,M) := SETOftP.EALr{X:RE~LJLESS(~,RJl := SET OF' (REALo (X :REAUM!JRE IS U .. R))

T7 := TH3wl.IMP•<LE5S\SrR),IN!S1S1tl,N, tT:LESSCS•R>l~Sflt<RE~L,tX:REALl LESSCX.RJrSrT>> ·

TS :: ESTII<REAL,[J:RCALl~OREIS'X•R)•S•

R a VBlO

R ; T9

SATZ167F(SrR•77l)

:= {X:RE~LJrT:NOTII~<X•Slll)J T3 ... 5Rl05 .. <XrH

: All( [URE AL lOR( IHtX .. $01 ),I NU.SOZ H)

: NONEMPrY<REALoS02J

: LESSCS .. TJ

: ALLC tx: REAL HT: UICX,SOl) l- LU tY: REAL 11: U :I lH y, 502)] l.ESS(X• Y)))

: IN<S•S3 2) SEHREAU SEHREAU

: NCHLES S(S,RJJ.

s

s

s

s

s

- 4.88-

$

•5RZ)5

H5RZl5

•5R2l5

H5RZQ5

"'5RZlS

uiYR5

•IVR5

no

R ; V811A

R ; TU

R a vsus

rLU~\~pU~~~r 1~~n~AL~UII#

SATZ188K(~'ClP.L>rO~R•SATllG9C<MCC1RL)• SA TZ!7&.\ :lR~,PCSU ))) Lf:SS(!tf <R .. tRl)..R}

:: ESlfi<REAL•[X:REALlLESSCX•R)•MN<~•lRLl , T9) : INCKNU •lRL ),.Sll)

:: NONEHPTYI<REAL.,Sll,MN<R•lRl), TlO•. 5R20S">

:• ESTII(R~AL,.[X:REALJMORI!IStX•RJ•R• MORE!SIZ<R•R•REFISCREAL•Rl))

N!JtfEMPT Y (RE At, S 11)

S a CI:I~tS.S11lltT:REALJ[J:IN<T•S12)l T12 :: SATZ17ZB<S•R*T•ESTIECREAL•(X:REALJ

R a V812

s a tt:L~SS<S•RJl VB13A

s ; [!i: HJRE(S,. lUl· vsua

a ZRL PllS2 HALf POSHALF

R a u

lESS{X,.R)•S•!>•SATZ168A<T,R, ESTIE<REAL•(X:REALlHDREIS<X•RJ•T•J)))

:= tX:REALl(T:INCX.SllJlCY:REALJ(U:IN<Y• S1Z>lTtZ•.SRZ05"<X•T•Y•UJ

:: ESTIICREAL,(X:REALlMOREIS<X.R>,.S• HOREISil(S,R•H>J .

:: PL(lRl•lRll := POSPl<lRl•lRlrPDSl.POSl) := 0V(lRL•2RLrPNCTO<ZRl•POS2J) .- POSOVPPClRt,ZRL.PNOTOC2RlrPOS2J,POS1•

POSZ J

:: TRISCREAL,Pl{R,.RJ,?LCTS<lRL·R>• TSClRl•R>JrTS<ZRl•Rl• JSPL12(R,TSC~RL,R>•R•TS<1RL,R),

SATZ19SC<RJ,.SATZ195C<RJJ, DISTPTl<lF~.lRL•Rl)

:= TR4IS<REAL•TS(HAlFrPl(R•R>)• TSCHALF,TS(2RL.R)l,TSCTSCHALF,ZRL),.RJ, T Sn RL .. R hR• !STS2( PLOf, R), TSO! RL "R>• flALf,.ï3J,ASS!S2CHALf.ZRL•R>• ISTS1CTSCH4Lf•2RLlrlRLrR, SkTZ2~4E(lRL,ZRL,PNOTC<2RL,POS2))),

SAfZ195SCR))

LESStS• n

: ALLC[X:REAlltT:IN(X,.S11)lALlCtY:REAL1(U:INCY•S1Zll lESS <x,. Y J i>

IN<S,.SlU

IN<S•Sl2J REAL

: POS( ZR'-) REAL

POSCHAi.. n

s

s

s

s

s

s

- 4. 89-

s

•IVR5

•IYR>

L a TS

l a lEM!1A3

L a r:,

l a LEK~A4

tP:P::sun

:a SATZZ03K(PL(R,RJ,?L<R~s>.HALF'• SATZ188MCR•S•?.,LJ~POS~Atr-;

:a ISLESS1CiSCHALf,PL(R,RJi~P.• TS(~ALF•PL<R•S)J,T4•.:vR~·.rs·~IVRS•)

:: s•TZZJ~XC,L<R•Sl,PLCS.S>•HALF, s~rztB&f<R·~~S•L)•POSHILFJ

:= ISLESSZ<TS<HALF.Pl(S,S>>•S• TSCHAlF•PLCRoS)J•T••.tvRS•CS>•

LE'41f.\5 : .. SATZl61B(S,.TRMORECS,R,-O,LEl4!>1A2CR,S•L h

: LESS(Ti (HALF'•PL(Ib•S Jh TS(I!ALF •PLCS•SH)

SATZ1ó9ACR.PJ)) POSCS) a tS1:SET(REAL>ltSZ:SET<RE~L}

l(PO:ALL<tX:REALlORtiN<X•Sl>•INCX•S2l))J[PlA:NQNEMPTYCREAL•SlJ J[Pla:NOV!EMPTY<REAL•SZJ l CPZtALLC[X:REALJ[T:I~CX.SlJJALL<tY:REALl[U:INCY,SZJlLESS(X,YJ)) ]

SZ a tiU REAL l PROPl := AllC[X:REALlCT:LESS<X•R>liN(X•SlJ) PRCP2 :: ALL<CX:REAllCT:KORECX,RlJINCXrS2)) PR!J!"l ::: A'i::J(PROPl.,?ROP2>

P2 a tX:REALltY:REALltPX:PRCP3CX)][PY:PROP3CY)][L:LESS<X.Y)l KXY := TSCHALfrPl{X,Y)) T13 ;: LEMMA2(X,.MXY .. lEMMA3U,.Y,LJ) T14 ::: LEIH!A4<X•Yrl) T15 :: <Tl4HMXY>AN:>EHPROPHYhPROP2(Y),PY) f16 :: <T1l><KXY>ANvE2CPROPl(X),pROP2(X}~?X) TlT ;: <T1G ><>;XP<T 15><MXY>P2 T18 ·- <REF'iS(REALrM~Y1>EC3E31<IS<MXYrHXY)r

HORE(MXYrMXYl .. LESSCKXYrMY.Yi• SATZ167BtHXYr~XY>•T17)

PY; T19 :: tT:LESS<XrY>lT!B<T> TZO :: [T:M()~E<X•Y>JTHU:Y,XrPYrPX•

lEM ... \1 C X• Y,. T)) T21 :: ORJ<:H ISCX• YJ, HORE \X• Y hLESS<X• Y>•

SlTZli7A<XrYbT20•Tl9J PZ ; T2Z := EX:REI'.LHY:REALHT: PROP3(U]

[U:PRCP3CY)JT21CX,T•T•U> [tASEt:SGHE([Y.~REALlANDCPOS(XJriNCX•Sl))JJ[RtREAL l(A:AND<POStR>•IN<R•S1))J TZ3 := A:':J(H?CS(Rl~Ii·lU~ .. Sl ;.;n T24 := A~~E2t?OSO!hHHR,S!hA)

. SCl :::; 5ETOrt\:l!T•[iPCi.HJIN(PCF~PO:hSl>J SCZ := SETCfCCUT~rx:C~fli1tPC~RPCX>.SZJ) tRO:CUTlti:INCPOFRPCR~1.S1Jl T25 :: ESTtHCUf,(X;.CUTlPHPtJfRP<Xl•SlhP.O~>I>

RO ; [I:IN~RP•CRO.SC1Jl TZG :" (Sr!~<CUT.oO::C!JTl!NC!'!JF'!!"('O•SU .. ROd>

: 'PROP' : 'PROP'

'PRJP'

REAL : KORE<MiCY,lO : t.ESS(H( y,.Y)

IN<KXY.o 51) : INOlXY• SZ>

LESSO!X Y .. lfX'rJ

CON NOH U:S SU .. Y))

flOTO!OiH (X. Y))

: Isu .. n

AMO~E(~ EAL• U:REIIl.lPROP3U H

PCStR) IN{",.Sll

: srrccur, :>(TC Clif )

!~HPOF'~i'(R~hSl)

s

s

s

-4.90-

~0 ~ ti:I~lPDfRP(ROJ•SZJl T~T := ESTlHCUi,. [X:CUT JIN(f>Of'RP(X),SZ) ,.RQ, I) : IN•RP"[ RO ... SCZJ

RG ; Ct:IN"RP*(RO•SCZJl T26 := ESTIE<CUT•~X:CiJT :!N{f>ilF"RP<XhSZ> .. RO, t} : IN<P'Of'RP(RO J.SU

RO ~ T29 :: iH9"t.o~w<IN<?CëR?CROJrSl). INCPOf'R?(RO>•SZ>•l~"RP"<ROrSCl),. lN"RP•CRO,SC2),<POfRP(~0J>PO, er: I~C!'GfRPC ROhSlJ lTZS< Th (f:! ti{ r>QF'RP< RC h S2 J JT2·7<T 1 J OR <IN"~ P•<RO .. SCl J..IN .. RP•<RO .. SCZ»

A ;: ~>Rl :: RPOfPO:. '!'Z3> CUT T30 := ISPtRZS.!..,!X:R:':AlJI!HX .. S1hR .. PCf'RPtPR1l

,rz4,1S?~Pl<R•T23)l : IN(P0f~P<PR1J•S1) T31 := NONE:HPTYr(CUhSClrPP.hT25{?Rl,T30H N014EI4PTHCUT.sCU rs:R~ALlCI:IN<S•S2Jl 1'32 TH •st T34

:= <S><TZ4><R>P2 :: lEHMA5CRrS•T32.T23J := RPOFP':S•i331 := ISP< REAt.t x:~t:ALJIN( X•S2hS.POf'RP<PS1)

rlriSPRPl(S,T33l} T35 := NC1<t:r~?TYHC:.iT•S:z,pshTZHPSt.T34))

A ; T36 :"' NOIH:: ;'lf'TY:.Pi"( !\E:ALrS2o PlB• NC~EMPTY<C~T.SC2Jr[X:REALl[T:INCX•S2>l T 35< Xr Tl l

RO a CI:I~·RP•(RO-SCl)l[Sa:CUTlCJ:I~~RP•(SO•SC2ll f3T ·- <T26CSO,Jl><POFRP(S0}><T26CR0.t}>

<PCF'R?t?.Ol>PZ T38 := lE55~PlP(<::!hSO,T37l

A ; STC :: SCiîNITTCSClrSC2o[X:CUTlTZ9UJ..f31.,T36• (X:CUTlCT:IN~RP•(X,SC1Jl[Y:CUTl [U:IN~P.P•CYrSC2>JT36(X,frT•U))

T39 :: SATZP205ACSCl•SC2rCX:CUTlT29(XJrT31r T36rtX:CUTltT:!N"RP•cx,SCl>lCY:CU!] (U:IN"RP"<YrSC2JJT33(X,TrYrUll

T40 := SATZP205eCSC lrSCZr (X :CUT lT29C X),.T31, T3&,.[X:C~Tl[T:IN"RP•<XrSC1)J(Y:CUTl [U:IN~RP-CY•SC2>JT38<XrTrYrU)}

STP := POFRP<STCl Hl := POSI<STC> [S: REAL ][l :tESS( Sr STP J l[ P: POS( SJ l PSZ :: RPOF'PCS.P) T4? : = lt:SS R? IPt Psz,. STC" I SU: SS 1< s .. POFRP tPS2) •

STP,.!SFRPl(SrPl•LlJ Hl ::: <T4Z><PSZ>T39 U 4 := ISPC RE~L• t l(: REAL l IN< x, S 1 l" POf"RP( PS2)"

s,rz&CPS2•T43),ISPRPZ<S~PJ) l a [~:NJT(P0S(S))J(I:IN(S,.S2ll

H5 := <S><T24><R>P2 T46 ·- <LEI"IofA'5CR•S•T45rT2H>N

N a TH := OREHINCS,.Sl l .. HHS,S2h<S>PO,. [T:JNCS,$2)JT46<TJ)

L a T48 :: THl"t. IK?"'CPOS<SJ.INCS,Sl),.(T:POS<SJ l T44CTJ.[T:~OTCP0S(S))JT47CTJ)

s a t H: MORE ( s,. ST P) l '1'49 ·- lEHMA5!STP•S•lEMMAlCSrSTP,M),f41l ?Sl :: RPCfP(S,.T49l TSO == MORERPIPC?S3.STC,.IS~OREl(S.POFRPCPS3), STP.I5?RPl<SrT49>•M>l T51 :-: <T5Q><PS3>T40 T5Z ·- ISPCREAL,.(X:REALJINCXrS2irPûFRPCPS3),.

s .. TZ8CPSJ,.T51J,.ISPRP2<S•T49)) A a rs:s :.: ANniCPRG?1<ST?),PROP2{SiPJ.tX:REALl

tr n ::s so: .. ~r P) 1rt.E· n. r ~.ct:~<:: .\u

lESSCR• SJ POSC S l

: CUT

HHPOnP<PSl>,S2) NONEM?rY(CUT•SCZ)

: NONEKPfYCCUT,SC2)

LESS ( PJ FRP( RO) ,p(lfRP<SOJ 1 : tESS•R, •<RO .. SOl

CUT

t ALL"RP• ([X: CUT HT :HORE"'RP• (X,STCl JIN•RP .. <X•SCZJ) RE.At.

t POSCST10 J

CUT

: l~SS'"R" •tP$2.-STCJ IN .. RP•[ Psz,. SClJ

:

I!HS .. Sl)

LESS(R,. SJ CON

IN<S• St )

IN(S,.Sl)

PlJSCSl CUT

MORE,.R" •tPS3•STCJ iN"RP"C PS3• SCZ>

- 4. 91-

[f: MORE< x, ST? l JT52( x. T)) PROl"! U TP) T54 :: sa~EICREAl.[X:REALlPROP3(Xl·!TP,T53) SGHE([~:REALlPRQP3CX>>

CASEl <! f55 :: SO)'.EAi'P( REA:,.,. (X: 1\EAL:#A"'lHPUSa>. IN<X.St)!.CASElrSGMEC(XIREALlPPOP3CI)) ,(X:REALl[T:~NCCP~S(XJoi~CX,SlJll T54tX.TJ) SOKE([(:REALlPR~P3(X))

PZ ; [CASEZ:SDHECti~~EAllANOCNEG(X)•lNCX,S2llll SPI := SETOF(REAt•CY.:REA!.lH1C!1~(XhS1l) : SEHRE,Ll SPZ := SETOF<?.EAl. ( lO~G:AllHHMO CX >•S2)) SEHREAU CR:R~ALlti:INCMOCRl•Sill TSG :: ESTI H REAL~( X:R'::Al.ll~HMOCOoSl hit.. I) IN(=t,S' 1J

R ; [I:INCR,SPlJl f57 := ESt'IE<REAL,[:{:REALliNO!lHlO"Sl>"R"Il IN<KO(~hSll

R ; tl:INC~~(RlrS2)l 'f58 :: ESTI H~EAL"i x:REALJ INCK0ClO•S2hR•I) INOhS' 2)

R a ri:IN(R•SP2Jl T59 := ESriE<REAl•O::P.Ef.lJINO!G<X> .. SZl"R'O IN<HOCl hSZJ

R 3 T50 := COMOR<tN<R .. SPll .. !N(R.SP2),

U: INC f(, S2 Jl T51

TS2 CAS5:2 a Tó3

R a ti:UI<R•Sl)]

TH9«:...c~~(!NC~O(R},Sll·I~<~OCRJ,S2>• INCR.SP!l•IN(R .. SP2>•<~Q[Rl>PO• tT:IN<HO~?.J.Sl)lTSG<Tl .. ti:lN("OCR)r$2) lT580)))

:: TSS\MO<~lriSPCQ,EAL,(X:REALliNlX.SZ),R, MOCMO(R))•I,SATZ177A(R)ll

:= NONttl?TYHREAl•SP2.M~(RhT61l := NDNEKPTYAPP(RE~L,S2,Pl9•

NONEMPTY<REAt.SP2),[X:REAtlCT:IN(X,S2J lT62(X., T)}

T64 := T560!0CR>riSP!REAt,.[lC:~EAllHHX,SU•R• HO<MO<R>>•I .. S~TZ177A(R)})

T65 := NONE~PTTICREAL .. SP1,MOCR),f64J CASE2 ; Tó6 := NONEMPTYAPP{REAt,Sl•PlA"

NONE KPTHi\EAl.., SP u. C X:REAtHT :ItHX,S 1 J 1T65<X,T))

R a [I:IHtR .. SP2lltS:REALJCJ:lN(S,.SP1)l T6T := <f59(R,!l><HOCR)>~T57CS~J)><HO(SI>PZ T&8 :: LEMXA1CS•R•SATZ183DCS.R,T67))

R a CA:ANDtNEG(R)•IN(R,SZ)JJ 1&9 ::: SATZ176C<R•ANDEHNS:!HRhlNCR•SZhAH T70 := ISP<REAlr[X:RE4Ll!NCX,S2>•R·K0(K0<R>l•

ANOE2CNEG(R>•IN<~•S2}rA)rSATZ177A(RJ) T71 :: ANOI<POS(MO<R)),IN(KOCRlrSP2>.T69•

T5SC t-!0(R>,..f7G}) T72 := S011E H REA!.,[ X:REAUANIHPOSU h

INCXrSP2}),~0{RJ,T71>

CASEZ ; TTl :: SOMEAPPtREAl•!X:F.EALlA~OlEG<Xh IN<X.S2))rCASE2,SOHEt(X:?.EAL1 ANO< ?OS{ X l • I !H.X• SPll) >. (X: RE AU tT:ANDlNEG<X>riNCXrSZlllT72CXrT)>

T74 := T55(SP2,SPl•[X:REALJT&OIX>•T63,T66• {lCtREALl[T:!NCX,SP2Jl[Y:REALJ[U:INCYr SP!>Jr&s,x.r.r~u>.r7J3

(R:REAt1tP:PROP3(SP2rS?l.RJltS:REALJfL:LCSSCSr~O(R))] T75 ::: lSHORE2CM0(MO<Rll•R•HOCSJrSATZl77~P.),

SATZ183C{S,HO(P.),L)} 176 •- <T75><~D(St>~NDE2CPROPl<SPZrSPl•R>•

PROPZ<SPZrSPl•RlrPI T77 :: ISP<RE;t!..•lX:REALJltHX,.Slht:OtHOCSlhS•

rS7(M0{S)rT76J•SATZ177(S>>

OR<INC~rSP2J,INCRrSP1))

: IN<HO<=! hSP2> NCNEHPiYCREAlrSP2)

: NONEHPTY<REALrSP2J

: INUIOU hSPU NONEMPT YCREAL,SP1J

NONEMPf YCREAL,SPU

: lESSCMJ CS)•KOCRJJ LESSCRr S)

POSCHO[ R))

: tNOtOn 0(R) J,sz)

. A :.JO( POS (HOC R Jl ..t NOIO( R >. S? 2)) . . : SOHE((( :REALJAN~<POSCXJ,JN(X,SP2J))

SOHEltX:REALJANO(POSCXJ,I~(XrSP2)))

SOHEIC~:REAllPR~PJtSPZ•SPlrXll

MOttE O!J ( S h 10

; INOlO<S hSPU

IN(S,Sl) ., (

- 4.92-

T78 :: ISLESS2<HOCMO<R>>~R·MO(S),SATZ177<R>~ SATZ183A(S .. MO(R),.M)} LESS<M3 (SJ..R>

!79 :: <T7S><Jo!IHSJ>ANOE!<PROP.HSP2;oS.?1,.R),. PROPZfSPz,. SP 1, P.h?) INOtOU hSPZJ

T80 :: ISP<REAt.,()I::Rë:At.liN<X,S!D .. MIHKO<SJhS" T59(MOCShT79hSATZ17HS)) IlHS .. S! >

P a T81 := ANOI<!'ROP10HH!HhPRQP2Cl-!0(Rlh tX:REALJtT:LESS(X,KO~Rlllf77(X,T),. (X:REALJ[T:MC~ECX.MO(R)llf80(~,f)) PROP3C~O<R)l

T82 := SOMt::iCREAL .. tX:RE.I.LlPRiJ?H)(~~)'!0(R),T61J S014E<t< :REALlPRGPJ<XU CASE2 ~ T63 :: SCMEArP<REAL,[X:RZAllPR~PJ(SP2,SP1,XJ,

r74,S~4E((I:REALlPROPJ(I)J,{X:IEALJ

tT:PRJPl(SP2•SP1,X)lT82{Xrf>l SOKE((~:REAllPROPJ<X>> PZ a CNOTCASEt: NOH S!lME HX: Rt:ALJAN\HPOS tx >r Hl< x, $1 J > > >

R il

J C MOfCASE2 :MOHSOH(( [X: REA Ll -\NIH NEG<Xl • IIH X• SZ) J)) 1 [ R: RE AL Ht:LESSU .. O}] T8~ := TH4•L.SCNE•<REALo[X:REALlANOCNEGtXJ,.

T85 · == T86 == tHUIJRE(R,.O) l i87 =· T88 :=

T89 :=

I N<X, SZ>) • NO TCASEz, R) NOH ANl CNEG( R), IN<R .. SZ))) TH3•L.ANv•<NEG(F.lriNCRoS~>.T84• SATZ1690(R,UJ NOHINt!hSZ)) CR!:lC!N<R .. Sl hlN(R,SZl,<R>PO,T65l : lN(R,Sl)

NCTC A Hl (POSCRh IN<R .. S1)))

NOT( INt R .. S1 > J : HHR•SZ >

NOTCASE2 a f90 :::

TH~·L.SD~E·(REAt,[X:REALJANOCPDS(X),.

INC~•Sl>>•NOTCASEl•R> TH3•t.AND•(POSCRJoiN{R,.Sl),.T87, SATZ1698(R,M)) ORE2<I~(R,.Sl),IN(RoSZ)•<R>POoT88)

ANOI<PROPl(Q),.PROPZ(OJ,[X:REAtl [T:LESSCXoOllT86{XoTJ,.(X:REALl tT:MURECX.OJJT69(Xri))

T91 :a NOTC,SEt 4 T9Z :=

SOI'EH REAL" t X :REALlPROP3( XJ ,.o,. T90) THl•t.IKP~CSOHEC[XtREAllAND(NEGCX),.

lNCXoS2l>},SO~E([X:REALlPROP3CX>>~

•5R2J5

P2 2 T93

T94

P2 ; SATZ205

DEOEKINO

[T:SUMECtK:REAllAND<NEG<X)~IN<X~S2)))]

T83{T),[T:NOT(SOMECCX:REALlAHO(NEGCX>• INCX,S2ll)lJT91tT))

·- iHt•t..IMP•<SOHEt(X:REAtJANO<POS<X),. INtX,SlJJ),SOMEC[X:REALlPROP3(X)), CT:SOMEC(X:RE~LJAND<POSCXJ•IN<X•SlJJ)l T55{!),{J:NOTCSOHEC(X:REALlA~O(P0S(X),.

IN(X,Sl)l)JJT92{T)l := nNEI<REAL,(X:REAllPROP3CXJ,TZ2,T93)

:= T94•.5R205,.

:: SATZ205

SCHNITT := INOCREAL,[X:~EAtlPROP3•.5RZOS•cxJ,. SATZ205J

(R:REAlltL:LESS(ft,.SCHNITTJl SATZ205A :: <L><R:JoANDElCPROP1".5RZ05•(SCKNITTh

R a [M:HORECR,SCHNITT>l

PROPz•.SP.ZOS•<sCHNITT), ONEAXtREALoCX:REftLJFROP3".5R205"(X), SAfZ2Q5) J

SATZZD58 :: <~><R>ANDE2CPRGPt•.sazos•tSCHNITTJ•

d rRo:curJcso:c~rJ

PROP2". 5R205 "( 5CHNI TT h ONEAXt REAl•( X:REAUPROPl'" .5Rl05• tX ), SATZZOS> l

PROP3<l) SOKE<tK:REAllPROP3(X))

SDME<t~ tREAllPROP3CX)J

SOKE<tX:REAllPROP3CX)) : CNEC[X:REAllPROP3(X))

: ONEt[X:REALJANO(All([Y:REALl[TtLESSCY,XJl!~(Y,.S1J>• ALL( (Y: REAL JtT: HOREn, X> li N<Y ,.szu)) GNE([X:REAllANOCALL([Y:RE,LJ(TILESS(Y,.X>l!~(Y,.Sl)),

ALLCtY:REALlCT:MDRE<Y,XJliNCY,S2))))

REAL

s

-4.93-

-IVA

•IYA

•IVA

DR os Tl

LEMMA IV Al

SO a TZ

SO a LEMKAIVAZ

:= P!>OFR?tRO> :: PDOi"RP(S!H := tE~MAIVAD1<P.OrSOl

:= ISINt?LCPOFRPCR0)PPGFRP(S0J)~ PÖ~RPtPL*RP~(~Q,30J),PD(PDOFRPC~O>, PL>Cfï\P( SO) ),. POOi'" P.P { PL .. R? .. <RO • SO) ), P!:PtFC,RP<Rvl,?OFRP(SO),pQQFRPCRO), ?O~fRP!SQ),lKNCLASS(PDOFRP!RO)),

INXCLASS~PDUFRP(SDll},

IN~CLASSiPaOFRPCPt"RP•<RO .. SOJ)), Tl"• I'lA'")

:= lEKKAIVAOZ<RO .. SO)

:= ISIN{TS{POFRPCROJ,pQfRP(SO)), POFR?,TS"RP•<P.O·SO)J,TOCPèOFRP<RO), POOFRP!SO>>,PDDF~P(JS•RP"<RO,SOJ}, TICTCPOFRP<ROJ,POfRPCSO),pQOFRPtRO> .. POOFRP{SQ),INSCLASSCPOOF~P(~Q)),

INNCLASS{PDOFRPCSQ))), IM~CLASS(P~UFRP<TS•Rp•(RQ,SOJ)),

TZ". Iit A• > [H:KORECPOFaP(ftQ),POFRP<SOJ)l

" a Tl :: MOREEXCPOFRP(ROlrPOFRP<SOJ,DR•DS• INNCLASS<OR>•INNCtASS(OSJ•M)

M Q LE"MAIVA3 := LEMMAIVA03(RO.SOrT3•.tvA•) SO a [M:HORE•RP•<RO .. SOJJ

M ; [L:LESSCPOFRPCRO>,POFRPCSOlll T4 := SATZ!Zl<SOPRO•LEM~AIVA3<SOrRO•

LEHMA2( PCF RP ( RO) ,POfRP{ SO) ~l}) J M a TS ·- EC3EZ3CIS•RP"(RQ,S0l;MORE~RP•<RO .. SO>•

lESS"Rr•{P.0tSOl~SATZ1233<RG.SCJ,Hl T6 :: THJ•t.IMP•(LESSCPOtRP(RGJ,POfRPISOJ),

LESS•RP•CRO•SOJ•T5•[T:LESSCPOFRPCROJ .. PO•RP(50J>JT4<Tll

T7 := EC3E2H I S"RP•t !":th SOl.. MORE .. RP"( RG • s;n, LESS-RP"(R0PSQ),SATZ1~3B<R~,SC),M)

T8 := TI-'J'"L.IH?"(ISU'UFR?tRO>•?OFRP{SOD•

M ; lEHMA!VA4

1S•R?~<RO,SOJ,T7 .. tTtiS!PU~R?\P.O), PûfRP<SOJlliS~PIPtRO,SO•T>)

: Dtf' Oif'

: EQ-RP•( I'D{OR .. DS hPDOFRPU'L •RP,.<RO • SO)))

: ISCPL (• Of'RP <ROJ..PCFRP( SO)) •POf'RP( PL'"RP.,CRO •SO)) l

: MOREDO R•DS 1

MORE"R' •cRO,. SO)

.lESS•R• '"(RO .. SOl

: NOH LES S'"RP"<RO,SOJ l

NOH LES S (POfRP<RO ),. POf' RP<SO) J l

: NIS .. RP•<RO,SOJ

: NI SC PO=' l\P (Î~ 0 J .,pQf'RP (50 )}

s

s

s

s

s

- 4. 94-

$

HO~ECPDFRP{R0lrPOFRP(S0)), LESStPOf~?CROJ,POFRP<SOllr SATZ 1&7 A( P!Jf'Ri'( R:>> • POf RI'( SO >), r&·.rvA•,rs•.tvA·> : MORECP3fRP<ROJ,P0FRPCSOlJ

; [l(: !fAT ltY: NAT l t:H MORE< ?.LOF }lf(X )r Rl:.Ofi\T (Y l) J

H·IV4 s

"' 3 T9 := LE~MAIVA3CRPOfNTCXlrRPOFNT(Yl~H) : MORE~R»•(RPOFMTCXJrRPOFNTCY)) TlO := S~TZ!S4C<RTOfN(X,,RTOFNCYlrT9J MORE"RT •(RTOFNCXhRTOfN<n J TU := llG?.E E• RT" ( RT OF 'l{ X), P. TOF N (Y hf R ()(, 1 h

fRCYrll•I~CLASS"RT"(fR(X•l)}, I~ClASS"Rf"(fR(Y,l)),TlOl : MOREF<FR<Xr lhFRCY .. l))

•!VA s

M ; LEHifUVA5 :: SATZlllA(X,Y,.Ttt•.zvA•J : MORE•H• (XrY) y a tM:MORE"N"(X,Y)J

*'•I'IA s

" 2 TlZ == SATZUlD<X•Y•M> KOREf(F' RU•l hfR(Y,. lH T13 :a MORt: I" Rr•c RT OF' N< X >o RTOFN<Y hFRC X •l),.

fRCY,l>•I~CLASS"RT•CFRCXrl)J, IHCLAss~RT•CfR<Y,l>l~TlZ) HORE•Rt•<RTOFNCXJ~RTOFN(YJJ

T14 :: SATZ154ACRTOFtH X h RTOFN( Y h T 13) HORE: .. R» •(RPOFNH XhRPOfNH YU

•IU s

H a lEHHAIVA6 :: LEKMAIVA4CRPOFNT(X),RPOFNT(Y), T14•. IVA•> : MORE ( R'- OFHT< X) • RL Of NT< Y) >

a CRtREAll

•INT s

AOIR a U:INTRL(R)] n == INTABSD<AO.INTRLEXCR,AO.AOIR,I)J INTOC AJ SOCAOH TZ == I~TRLIH(ABS<R>•ABSOCAOJ•AICA,Tl) INTRLU BSCR))

•IP.:T s

ti: INTRUR)] INTABS := REALAPP1(R.INTRL<ABS(Rl),[X:DIF1

(T:INN(X•CLASSCRJ)lT2w.INT•<R•XrTriJ) : INTRLHBSCRU

ui~r s

I a T3 :: INTMOO(AO,INTRLEXCRrAO,AOIR~IJJ : INTDCM)OCAOH T4 i= IXTRLIN<HO<Rl,HDO<AOl•MICMO•TlJ : INTRU!fO(R)}

•INT

I a tNTM) :: ~E~LAPPl<R•INTRL(MOCRJ),(X:OIFl IT:INN(X,CLASS<RlllT4w.INT•<R•X•T•I>l !NTRL (14 0 CR H

••INi s

BliS ~ ti:INTRLCRJJ[J:INTRLCSll - 4.95-T5 == INTPO<A!•Bl•INTRLEX<R•Al•AllR•I>•

IN!~lEJCS.Bl•BliS,J)J : !NTO(P) Ul• BUJ T6 :: iKTRLIN(PLCR•S),pQ(A1#8l),p!cP,T5) INTRLPUR,.Sll

H·I"'T

•INT

+IVR24

I ; tS:REALltJ:INTRL(S)l W'!'P!..

Ilif)tN

J ; T7

T8

J :1 IlHTS

R ; trHNATRUR Jl

i1 TZ

::: REALAPPZ ( Rr Sr INT RLCPL< !!• S l h (X :o Ifl CYtDIFl[T:I~NCX,CL,~StRJJJta:INNCTr CLASS(SJl!T6".lNT"<R•3•XrYrTrUrlrJ)J . : IHTRL($L(RrSJ)

:: INTPL<Rr!rloi~<S>riNf!'IOCSrJll : INTRL(tffHR .. SJJ

:a INTTOCA!·31rlNT~LEX<RrAl,~!!Rr4lr INTRLEXCS,SlrBliSrJJ)

:: INTRLIN<fSCRrS)rTOCA1rB1JrTitTrT7J

:a REALaPPZ<R .. SriHTRL<TS!RrSJ),[X:OIFl [Y:Oi~l[!t!NN(XrCLASS<R>JlCU:INNCYr

CLASSCS>>lTa•.INT~<RrS•XrYrTrUrirJ))

:: SATZZ4A< NTOfRLCRrNJ J := TH3•t.!KP"<MO~EC1RLrP.lr

MQq[•N•(lr~T~FRL(R,~>lr

SATZlODtl•NfOFRLCRrNJrTl>• tT:MGRE<1RlrRllLEMMAIVA5(1,NTCrRt<R•N> riSMGREZ<R•RLDrNTCNTOfRL(R,Nl)•lRLr

INTtl<T3 Ulr Bl)) INTRUf S<R• SJ)

: INTUU S<R•Sl)

ISRUHHR.oNhTJ)) : NOT(MO~EURL,.RU

s

$

s

·IVRZ~ S

SATZ~Z~ := SATZ1S7E<1RL•R ... TZ ... IVRZft'") LESSISt 1Rl.rR) R ~ C!:I~TRL<R>ltS:REALlCJ:INTP.L<SllCL:LESSCR.oS)J

+IVRZ5 S

•IVRZS

Tl TZ T3 H T3

SATZRZ5

a [X:NATl(Y:NATl

T1

TZ

:= SATZ16ZOCSrRrLEMMAZCRrSrL)) := INTMNCS.oJ.oR•!> := POSlNTNATRL!MN(S;P.),!t,TZJ :: SATZ~Z4C~~(SrR1rT3J :: TH!l"t.DR .. <LESSClRL.oMiHSrR)),

ISC1Rt•H~($,Rl)•LESStPL{1RL•R).o PLCMN<S,.3)rRJ),ISCPL(!RL ... R1rPLCMN(S,R> ,.RJJ,T4,(T:tESS(lRL•KHCS•Rlll SATZlSSf(lRt,MN(S,R),R,TJ, tT~IS<lRL•M~{S.Rl>JISPLl<lRL.oHNtS•R>• R,T>)

:: ISLESSIS1Z(PLt1RlrRJ•?L{R,lRL),. PL01N\ s, fU • f: l"' s. C:2."?U 1 Rt.• R) • PLMfH Sr R) •T5*.IVR25*:

:= LEHHAIVA 1C RPOf'NH Xl• R?Gf'NH Y H

:= ISRPEPCRPOFHTCPL•N~<X•Yl)• PL"R?•<RPOFN!(~)~R~UFNT<Y~>•

POSCMN(SrRJ> INTRL<!t fH S• R))

: NATRLC'fN(S,.RH LESSISt1RL•HNCS•R>>

IS(PLCRLOFNT(XJrRLOfNTCYJ)•POFRP{Pt•RP•<RPC<N!<XJ• RPOfNU '() H >

s

- 4.96-

•IVR155

SATZil155A

SATZU55S

' a T3

SATZ155E<XrY»

:= TRI SZ< REAL~RLDFNTCPL *N*(X,.'[)),. PL<RtOFNTfXJ~RLGrNTtY)J• POFR ?{ P!.. *P.P .. { RPOfNT< X l r.RPOF'NHYJ)) r rz•.ZVR155"rTl*.IVRl5S~)

:= STMISt~EALrRtD~NTtPL*N•(XrYJ)r PLCR~QFNT(X}r~LOFNT<Yl)r5ATZR155AJ

:: LEMMAlVA2<RPQrNTCXl,RPOFNT(Y)J

:= ISRPEP<R?CFN<CTS"N•(XrY))r TS"RP•CRPOFNrtX>rRPOFUT<Yl)r SATZl55f"C X rY))

IS<RlOrNTtPt•N•(XrYJJrPOFRPtPL~RP•(RPOf'NT())rRPOf'NT(Y)) ))

IS(iU.IP" NHPL•N .. ( Xr Y )), PLC'tLOF'NHXlr RLOF'NTC Y)))

• t IS<TSH LOFNTC X)" RlOFNT <Y)),. POF'RP( TS .. RP.,CRPUf'NTCICh

RPOTNTI Yl)))

IS CR LOF" NT<T s•N.,.( X• Y)),. POF'R P<TS" RP•( RPOf'NT ( lf > r RPOF'NT CY) J ))

s

$

•IYR155 S

Y a SATZ~155C := TRIS2(~EAlrRLOFNT<TS*N•(XrY)),. TSCRlOFNT<Xl .. ~lOFNT(Y)), POrRP<TS"RP*CP.POFNTCXl~R?GFNT{Y))), !4 ... IVR15s•,. T3"• IVR155 .. } ISCRlot NTns•N•( x. Uh TSUlOF'NTCXJ,. RLOF'NT< Y)) J

SATZ~155D := SYMIS<REAL,.RLCFNTCTS•N•cx~Y>J• TSCRlOFNTCXJ,.RlOFNT<Y>>•SATZ?.155CJ : IS(fS(~LOFNT(X)~RLOFNTtYJJ•RLOf'NT<TS•N•(XrY)JJ

a [TtRU!. JtR :REALl [StREAU[A:ANO( NOH NEG CR> h IS<TS<R,.fU.,. T>) ltS:AND<NDTCNEG(S)l~!SCTS<SrS),.T)JJ

+7R1S1 S

[CO:DIFJtCIT:I~~CCO•CLASS(Tlll[AO:OIFlEAIR:IN~(AO,CLASSCR)) J(BO:OIFJtBIS:INN<BO•ClASS(Sl>l Tl :: TH3•L.IM?•tNEGOCAOJ,NEGtRJ,.

ANDE1<NCTCNEGCRl>•ISCTS(R,RJ,.J),A)• CU:NEGiHAO>l!'4::GINOhAOrAIRrU)) : I',IQT(N~D<AOiJ

TZ := THl .. L. I!'l?·tr~EGOC B\»hNEG<Sl• AN~E!<NOT<NEG(SJ)~ISCTSCS,.S},.T),B)r

(U: fl EGO< 60 )J tJEGJH{ s,. B(), BIs,. U)) NOTC NE:i D ( 80 J> T3 :: ISEX(TS(R,RJ,.T,TD,AO,AOlrCO,

TICT(~,P.rAO,AO .. A4R,.AIR)rCITr A NCE ZC NOT <NEG( RJ h IS O'SCP.,R ),. T), A)) : EO""RP"( TOCAO, AO) ,co J

r~ := tsc:xcrs<s·sl.r.rotso.ao>.co. ïtCi(s,.s .. ao .. so,sis .. ais> .. ciT. IH:OE2(NOT<~ë:G(S))riS<TS(S,.ShT>r8)) : C:Q .. RP•CTDCSOrBOJ,CO)

T5 :: ISfN{RrStAOrSO,AIRr6lS, SATZD1&18(CO .. AC•SO•Tl .. T2,TJrT4J). IStR~S>

•7Rl61 S

SATZ1U51B

H7RlS1

:: RE 'lA?P3 ( r, R • S• IS< R'S >• rx :OIFHY:D If l CZ:OifJ[U:!NN(X,ClASS(TJ)J(V1INNCY, CLASS(RJJl(N:t~NEZ,CtASSCSJJl

T5•.7Rl&l•cx,.u.v.v,.z,~1> IStR,.S) - 4.97,..;

•7R1&1

H7R161

•7!US1

CU: NE~D~ CO) l NEGI N(T .co.c :T ,u)} : NOiCNEä DCCO)) C Ai): !Hf' HA: A ~0 (~OH NEGC ( 1\0 > hEO"itP .. <T:HA o~ A~ h CO>) l AR ·- REn Of( Aûi REAL T7 :: TH3•L.IMP"CNEG<ARlrN~G~<AOJ•

ANOE1(~0TCNEGO(A0)),~~·RP•tTDCAO,A01~ CO),A)r{U;NEG(ARllNEGEXC,RrAC, INÎ't.:USS(AOhiJ>) : NOT<NEii eARl>

T8 :: ISH!t'7:,CA.R.AP.hT,.TtHAO .. AOhCO,. TICT<~~~A~•AO~Ao.:NNCLASSCAO}*

IN~CLASSCA3J>•C!TrANQE2CNOTC~EGDCA0)), E<i"'RP,.<TD< AC •A'l) •CO bAl) : I SU SC\ R•AR ).-Tl

:: ASOltNOT!NEG<AR}}•!StlS[ARrAR),Tl•T7, T9

T10

en :~ ru

Tal .\NO( NOT UI EG <AR>) • IS(TS <AR• AU• T)) :: SOMEI<REAlrtU:REALlA~DCNOT(~[G(U}l•

IS<TSt<;,:J>,T>hA1hT9) : SOMECU :REALJAND<NCTCNEGCJ H•ISUSCU,.UhT)))

N ~ SATZU61A

SATU161

SI}RT

N a 112

N :1 THSCHfTlA

THSQltflB

:: SO~E~PP(JiF•[X:OIFlASO(N0TtNEG3CX)J,. EO"RP•(j~{X,X1rCOll,SATZD161A<CO~T6)• SDMECru:q[AllA~JC~GTtNEG>• ISCTSC,;, Jh T n ,, tX:OIF'J [V:AIO!NDT(UEGDCXJ),[~~RP•tTDCX~X>•COJ )l uocx, 'i))

:= REALAPP1(T,SOHECtU:R[AllAND<NOTtNEG(U) )•ISCTS(U,U),f))),[X:DlFJCV:iNNCX• CLASSCTl)JTll•.7RlS1 8 (X,V))

:: ONEI <R[At, tu :REAUANtH NOH NEG( IJ)),. IStiSCU•IJ),i)l,[U:REAll(V:REAtl [A:AN~!NOT(NEGCUJlriStTS(U,U},T))l tB:ANOCNOT(~EGCV>>•ISETS(V,Vl•i))J SATZR1&18(1J,.v,Ar8),SATZR161A1

·- I~O<REALr(U:REAllAMO{NOTCNEG(~)), IS<TS(U,.U),TllrSATZRl&l>

: = ON:;: A X( RE AL• ( IJ:.RE AllAUlHNOHNEG<U) )p

rscrscu,u> .. T>> .. sATZR1&1>

:: ANJEl<NOT<NEGCSORT)l~IS<TS<SORT•SORTJ~ n. TlZ" .. 7R1G l"l

:: A~JE2<NDT(NEGCSQRTllriS<TS(SQRTrSORT>• 1'),T12'".7Rl6l .. l

(X:R(4~l[O:NOTCNEG<X>>ltl:IS<TSCI•Xl,Til THSQRfZ :: SATZR1&1S(X,SQRT,ANOI<WOT(HEG(I)Jr

ISCTSC~•X),TJ•O•I>•T1Z".7R16lw)

0 a tt:IS<T•TS<X,.XJJl THSORT3 := SYKISCREAL•X•SORTCT.N>,

REAL

NOHNE:HSO!H!l

IS<T S<S ORT, SORT ), Tl

THS~RT2{ SYMl S<REAL.-r, rscx, X) • I))) IS(SQRT (T • N), X)

~ [R:REALl!S:REALJ[N:NOfCNEGCR})][V:~~~(VE~<~lJl(!:IS!R•S>l ISSQRT :: THSQRT2CZ.DrSQ~T{R~NJ~:HSQRJ1A~R,I~

TRlSC~EAL•TSCS~?T(~,N~·S~RT<R,N}l•R•S• THS(fRTl!HR·Nl,.lll : ISCSQRf tR.NhSQRTC$,.0))

R; (N:N~T<NEGCRJ)J[~:IStR.O}J SQR:T) := THSQRT3( Rr N. O, O~OT N( (), ?.Eri St ~:::AL ,o.)),

TRISZ<REAL,R~TS(O.D,,o,I, TSO!( OrO • IU.:F IS C RE At, 0) n > IS<SQRr (R;IO •lH

$

s

s

-4.98-

Tl

*SORT

SQRnOTO

:: TH!•L.IHP*CISCSQ~T(R,NJ,O)plS(~,O),Q, CT:IS(SQRTCR,Nl,O>lTRISl<REAl•R,O• TS(SQRT<R•Sl.SQRT<R•N)),THS~~ilBCRr~J• TSOl!!CRT<R•~>,SwRT(R,N),f))l

:: OR3E2<:SCSQRTfRrNJ.OirP~SISQ~TCRrNl)• NE~tS~RTCR,N>J,AX~~J(SQRT(R,~J),

THSGatlA<R••>•Tl•.SQRT•J

,··:·':~/"

POS<SOlf(i~,fO)

s

s

- 4.99-

EINDHOVEN UNIVERSITY OF TECHNOLOGY

Department of Mathernaties

A translation of Landau's *) nGrundlagen'' in AUTOMATH

L.S. Jutting

Contents: chapter 5

October 1976

*} ' For an introduetion to and a discussion of the present work, see the

authors thesis (Eindhoven, 1977) : On verifying Landau' s "Grundlagen der

Analysis" in the AUTOMATH System.

, I

L A N D A U

C H A P T E R 5

H'O

-vo ·

+•110

-vo

L~TU~I tROM FILE: AUTQE/LANOAUIH5 CCTQSER 1!• 1778

n

N 4 TZ

N 'a lEKMAT

R ó! ("tr~!SCR.9U lt~MAd .

LE~M.49

R ~ :I:ISCR•M3C~>Jl

I ~ CP>PJSO:OCR)}) T3

. ~ CN:NEGUII)( Rl) l À

Tft

I J-T),. TS(R,fSCGVCS,T,NJ.T)l,.TSCRoS), COHTSCT .. tS~R .. OVCS,.T .. N)))r ~SSTSl<R-OV<S•i,N},T), ISiS2(TSt?Vts,T,N),T),S,R,. SATZ2C4ECS,TrNll>

:= SATZ204GCTSC R .. SJ- T,. TS<R .. OVCSr T ,N) ),.N, Tl ... VO .. l : IS U Sn •OV( s .. T •Nl1• OV( TS(!t •Sl ,r ,.N))

:: TRISCREAL,TS(T,Pt<OVCR,TrN),QV(S,;,.Nl) >•PL<TSCJ,.QVCR,.TrN)),.JS(T,.OV<S•l•NJl),. PL<R.S>,OISTTPZ(T,.OV(R.T .. NlrOVCS,.T.NJ) •ISPL12<TS<T•OY<R•T,.Nll•R• TSCT ,.ov< S• Tó• NJ h s,. SATZZ04C(R,.T ,N),. SATZZO,ccs,T .. Nlll : ISCTS(T,.Pl<OV<R•T,.H),.QV(S•T•N)J),.pl(R,.SJJ

:= SATZZ04GCPl(R,SJ,.T .. PL(OV<RrTrN),. ovcs~r .. N>l•N .. rz•.vow>

:= SATZi04BCR"R"l\l"OV(R• R• Ni "lltl• SATZ204C[R,.Rr~J,SATZ195(R}J ISCOVCR,.R.Nl.tRLJ

:= ORE2<IS<R.O)o!SCOVC~.R.NJrO),. SATZ19ZC(R,CV<O•P.•Nl•SATZ204C(0•R•N>J• H) : ISc:JV(),R,t:hOJ

·- <ISNEG<R·~O<R:~I•SATZ175~<R•P>J> PNQTt;( M:J< R j, P 1

:= <ISP0S{R.~OCR),IoSAT71760{R,N)l> . HNGiP( MO!!Dr iO

:= SATZ17S[(RrGR3E1(!SCMOCRl,~J,?CS\~3{~i >•NEG{HO(RlJ,AX~LO<MO\~)~•tT:PCS(M,(R~ JlT3w.vo•(t),[T:KEGCM0(R)JJT4•.vo•cTJJ }

:: SATZ!67f(T5(R,~)·~oTH3•t.I~P·<LESSlT3CRrR),.G~·~EG<TS(RrR)

),.NNEGSQ(RloCT:tESStTS<R.~)·O~; s .\'n: 1; ?O os! r.. Ri, r n 1

:: ~A~F<~•!S(TS(R,R),TS(A~S(R),AAS(R)JJ~

CON

co~

$

s

s

- 5.1 -

-----------

+SHIF"T

•SHIH

u SHirt

•SHIF'T

+~<SHIFT

tT:POS(Rl J SA TZ 196A( R• R" T, Th (T: iS(R,.O) lTaiS2CREit~TSCR,RJ.TS[A6S(R>,ABSCR>>, O,TS01<R,R,T),TS01<ASSCR},A6S(R), ~BSO(R,TJ)J,[J:NEG(RJJSATZ1968tR•R~T,

rn a (X:REAll[IX:tNTRLCXll[Y:~EALJCIY:!NTRLCYJJClY:L(SSIS<Y,Xll

Tl

TZ

T3

fft T5

Tó

SHIFfl tN:t TOCSHIFTU l

N a Hl T7 N2 T8

:: SATl190ACX,X,1Rt,o, HOREISIZCX,X,REFISCREAL•X)), SATll69A<lRL,NAT?CS(lRL,NATRl1J>)

:= ISMORE2\Pl{XrO>,X•PL(X,lqllr PL02(X,O,REFIS(ft[ll•0)),T1>

·- SATZ172DCPl(X,1RlJ,.x,y,.rz, ·-SATZ1683CY .. X,LYJ)

:: SATZ!82D<PL(X,.1RLJ,.Y,J3) ·- INT:4N( PUX •1RLJ, lNTPlC X• IX•lRL• INTRll >

,Y,IY) := POSI~TNATRLC~~(Pl{X,1RLJ,y),T4,T5J

::: NT Of !lUKNC PL<X, 1Rl J,. Y>.. T6•. SHtF'T•J

::o INr.-w•csHif'TL, N) := lTOPCSHIFTL•N) :: RLDFNT<Nl) := NATINTRL(N2.oNATRLICN1J)

N a SHIF'fR := MNtPLCNZ•.SHifJ•,.YJ,lRU INTS'HFTR := !NTKNtPLCNZ'".SHIFJ•,u,

INTPL< NZ•. SHIFT'".o T8'".SHIFT•,. y,JY'),.1Rl, INTRll J

(M:lJOCSHIFTLlllt:ISCSHIFTRCNl.SHIFTRCKJJl

N a T6A :: TRISCREAL.HNCPlCSHIFTRCNJ,lRL),.y), HIUPLC NZ .. Y). Y' Jr Nz,. I SMNH PlO!NtPL CNZr U .. 1Rl J.olRL),pl.( N2~Y h Y•PLMt«Pt.CNZ,.n,.

IS<TSU rRh TSUSStR h.IIBSc:t )))

KORE(Pi. (X,UL),PLCX,O) J

: MORE(Pl u,uu,u

HOR[(P~ (X,.lRLJ,YJ : POSO!N( PL CX •lRt h Yl)

INTRL(MN(PlCX,lRLJ,.Y)J : NATRUif N(PL <Xr1RL ).o YH

NAT

: NAT : LESSIS• N•U!t.SHIF'TL >

REAL : INTRt.nz>

: REAL.

: lNTilllSHIFTRJ

1RL)),KNPLCN2 .. YJ) : ISCHNC~lCSHIFTRCNl•lRL),y),NZ>

I a T9A

T10A

nu

I ·:1 ISESHIFTR

:: ISHN1CPLCSHifTRtNJ.o1RL),.pl(SHIF1R(HJ,. 1RLl,Y,ISPL1tSHifTRCNJ,SHlfTRCH),1RL• I>> : ISCMNC~tCSHifTRCN>•lRL),Y>•MNCPlCSHifTR(K>•lRL)rY>J

:: TR3tS<RÉAL~NZCN),KN(PL<SHIFTR<N>t1RL)r Y>,Hn<PL<S~lfTRCK),1~Ll7Yl,W2(M},

SYKIS<REAltK~<Pl<SHIFTR<N>,lRtJ,YlrMz,

T8Al.T9A.T8A00) IS<'fZ<'t hN2<K)) :: I S~H I RL< Nl<N h Hl 0!),. TlOA > IS .. ~ ,.('f HN),. NHM))

s

s

s

$

s

s - 5.2 ...,.

s

u SHifT

•SHIFT

HSHlf'T

------·--·~ ... ~-.~tt&J t '''Al .I T9 no Tl1 T1Z

Tll

T14

T15

Na Hi

H a SHIF"TRLS .

N " (M:HaRE<T•SHIFTR)J T17 T18

T19 rzo

~ :IJ TZ1

:: SATZ1860(SHIFT~rX•1Rt,V} :: IS~OREltPtC~HlfTR,l~llr~CMZ•Yl•

?U X• !RL hrt MN{ PlC !iZ.. Y> •l RL hT9) :: SATZ1B8D<PLCN2.Y),PlCX•1RL)•MOtY)•f10) := IS!40REH ~N (f'l< N2, YJ, 'o, l'f2,?1NU'LC XrlRl J

.. n. ~1'{-?U ~z,n. T!U := ISKORE12012• RlOF NH tHOf"RUN2rNAT Rli

(S1)l)o~~(~L(X,l~L:•Y),

RLDF~T!~TD~~l{~~[PL(X•!~l)rYI•TiJ>• ISRL~Tl(~Z.~A~RL!(Nl,J,

ISRLNil~M~C?L(X,lRL1,Tl•T6J,T1ZJ

.- tEMMAIV•S<UTOFRL<NZ,NATRLI(NlJ>, SHifTL•T13J

:= ISHGRE1•N•<NTOFRL<N2•NATRLICN1J),N1• SHIFTLriSNTRL2<Nl)oT14}

·- THJ•t.IMP-(MORECSHIFTR.X), MORE·~·<Nl,SHIFTLI• SATZIOa<~loSKIFTL,TT),

tT:MOaE<S~I~TR,X1lT15(i))

:= :=

:= :: ::

SATZ1880CT.SHIFTR,1RL•MJ IS~ORE12CPl(Y•1RL),pl(1RL•T),

PU SHIFTR, 1RU•PL< NZ•·'fhCIJMPU Y" lRU • PLKNCPlCNZrYJ,lRL),T17l SATZ168A(1Rl•NZ,Y•T18> lEMH~IVA5(1,Nl,T11l

TH]•t.I~P·<~DRECY,SHIFTR>•

MORE"'N,.( hN1 h SA TZ10iH hN1 .. SATZZ4A<N1) ),[T:MORE<T•SHIFTR>lTZO<~JJ

N ; LSSHIFTR := SATZ167[(Yt~SHifTR,T21•.sHIFT•) LY a tU:REALl[AtAH03(INTRLCU),LESSISCY,UJrLESSIS<U•XlJl

A :a

A a

A ;

TZZ

T23

T24

[L:lESS(U,. X> l TZ5

U:ISCU,JO l TZ&

TZ7

:: AN03E1CINTRLCU>,LESSISCY,U), LESSIS (U,x; hA)

:= AND3EZCINTRLCUl•LESSIS(Y,UJ, LESSIS(UoXhA}

:= AN03Elti~TRLCU>•LESSIS<Y•Ul• LESSIS<U.X J .. AJ

:: SATZ188HPLCU.1Rlt.PLCX.1RU.~O"'R .. U ), SATZ188f(U,X•lRL-L)}

·- ISM~l(Pl{UrlRL>•PLCXrl~lJrYr IS?llCUrXrlRlril>

·- TH9~t.oR•(tESS(UrXl•ISCUrX), LESSOHH ?ltUrlRLhYlr MNO'UlCr 1RL h Y> h IS(MN(PLCUrlRLlrYJ,HN(PLCX~lRLJ,.Y)), T24r[T:LESSCU•X>lT25CT>•(T:ISCUrX)l T2S0))

KORE( P:. <NZ. Y hPU X:,.lRl)) HOREON CPtt N2rY lrYhHfHPU XrlRLJ .. Y))

KORE(R~OFNTCNTOfRL<NZrNAT~LI<Nl))J•RLOFNTCSHIFTll)

MORE"W' CNl, SHIFTLJ

NOT(MO~E(SHIFTRrX)).

LESSISCSHIFTR•X>

MORECPL URL ,.Y),PUNz,. Y)) : HORE:C1RL,N2)

HORE•N• u,.Nl J

LESSISC Y .. SHIFTR>

: INTRUJ)

lESSISf Y .. Ul

: LESSISC u-x>

l.ESS I St MNCPL<U• 1 RU, n .,ltNC PLU,.tRlh Y>)

s

s

s

- 5.3 -

•SHif'T

•SHIF'T

!JL TZS

TZ9

T30

A a SHIFrl1

A a Hl nz

TH

A :1 SHIF'fi~Vl

SHIF'TINYZ

LY a (ALPHA:•TYPE'l SEQ

[S:SEOl PROOFSIRRELEYANT

AL PHA a tf:SEO l SHIHf

LY a tS:SEQ(REALll INSEQ

INJSEQ

:::. SHIF"Tt.CIJ,HZ .. Y .. IY.T23> NAT :: lS~ESSIS12C~N<PLCU•lRLJ~YJ,RLOf~TCULJ,

MNtPlCX,.lRlJ,Y).,9LDFNTCSHIFTL),. IS~LNTl(~~(PlfUrlRtJ,Y), r&cu .. rzz .. r .. IY•T23J> .. ISRLNTH !HU PU X•l"llh\'h Hoh T27> : LESS IS[ RLOFNTCUL >•RlOFNHS HIFTtl>

:: Tlt3'"L. It!P .. <MO~E .. I·i .. CUL• SHIFTL h MG~EtRLOFNTtUL)•RLOFNT<SH!FTLl>• SATZló7D(P.LCF~T<Ull•RLryfN!CSHIFTL>r T2S),rT:~JR2•N .. {UL•S~I~TLll LE!1!4A HASC üL. SHI!'TL,. n} NOH KOR E"N,.CUL .. SH!fTl))

:: SATZ10EU.Il•SHiqL,.T29> U:SSIS"'N .. (UbSHifTL)

: 1TO(SHI HU

•- !SINQ!JTN(SfUFTt..UL, TlO > ts·~ .. <:JI..,.Nl<SIHF'Tll)) :: TRIS<~EllrP~(PLCUol~LJ,Y),RLOFNT<UL)•

N2CSH!FTLl)•ISRL~T1<H~CPL(U,.lRL>•Y>• rscu~rzz,r.IY.TZ3>>· !SN~ERLCUL•Nl<SHrfTL1>oT31>> ISC~NC~l(UolRLl•Y>•N2tSHIFTL1>>

:: TRIS(~EAlr~NCPLCHN(PL!UolRL>•Y),y)., lRLloMNCPL(U,lRL>•lRlJoUo ISHN1CPL<KNCPl(U,1RlJ•Y>•YloPL(U,1RL>i 1RloPLMNCPL(Ur1Rll•Y>J.MNPl<U,1RtJ) : ISC,NC~LCMNCPL<U•lRLJ•Ylrf)•lRL),UJ

·- TRISl<REAloUoSHIFTRCSHIFTllJ, MNIPLCMNlPL(UrlRlJoY>•Y>•lRLJ• T33•.SHiff•,ISHN1<PLtMN(Pl<U.1Rl)•YJ, YJ,PlCNZ•.SHIFT•(SHlfTLl)•Y>•lRL• ISPLlCHNCPLCUolRLJoY), f<z•. s:-nn-c SHIHlll, y, nz•. SIHFf•) H ISCU• Si If"TR(SHIFTLl })

:= SYMISCREAL,UoSHifTRCSHifTLl)o SHIFTINVll : ISCSHIFTRCSHIFTL1)•U)

:= tT:RE4ll(U:INTRLCTJJtV:LESSISCY.T)l U:LESSI S<T,. X>JALPHA •TY?E •

:= (T:REAll[IT:INTRLCT>JCLT:LESSIS(Y,.TJl CTL:LESSISCT .. XJJ(U:REALJ[IU:INTRL<U)l [LU:tESSIS(Y,.U>ltUl:lESSISCU.X)l [V:IStf,U>liS•E•<AlPH~ .. <Tl><lT><IT><T> s.<UL><LU><IU>S) 'PR~P'

:: (T:lTO<SHIFTL)J<SHIFTRLS(T}> <lSSHIFTR<TJ><INTSHIFTR<J)><SHIFTRCTJ> F . : [T:lTO( SHIF'TUlAlPHA

:= tT:REAll[U:INTRL(TlJCV:LESSISCY,.Tll [W:tESSIStT.XllAND3CINTRLC<W><V><T> SJ.LESSIS<Yr<W><V><T>SJ,LESSIS<<W> <V><T>S•X)) . : · •FR:JP'

:= [T:REAlH IT: INTRl<T J HL T :LESSIS<Y• T> l CTL:lESSIS(T,.XJltU:REAllCIU:INTRL(U)l CLU:LESSIS(Y~UJltUl:LESSIS<LT><IT>~T>So<Ul><LU><IU> S) l rs .. P.•{ r, Ul 'PR!Jf"'

s

. s

..... 5.4 -

tU:REALltV:REALltA:ANC3(I~TaL(Vl•lESSIS(YrVJ~tESSIS<V~X))J

••S'ii='T s

A ~ PROPl := iS(U,<TZ.<V•A)><T23(V~A)><T22(V*A)><Y> S> 'PROP'

•SHFT s

V ~ ItiPRDP := ~Na(AND3CINTRLCV>*l[SSIS{Y,Vlr LESSIS(V,Xi),{T:AND3{!NTR~(V);

LESSIS(Y,vl,LESSISCV,X>JJ PRQP!•.SHifT~tr>> : 'PROP'

u :a IMSEQ ·- SO~E<:T:REAll!MPROP{U,T)) • PROP' s " SU•VSEO := tT:REILl{O:I•TRL{TlJ[V:LESSIS<YrTil •

t w:u:.ssi sn. 10 H MSEo<T > 'PR:JP' PE ?.:~ :: A~~ti~JSEO•SUEJSEOJ 'PROP' t:INS:! NSEQ <S)]

HS!tH"T s

INS a (N:tfOCSHif"Tlll >.!$ :: <SHifTRlS(N}><tSSHIFTRCNl>

<I~TS~IFTR(N)><SHifTRCNl>S REAL TH := <SHIFTRLSCNJ><LSSHIFTR(NJ~

<INTSHIFTR<NJ><SHIFTRCNJ>INS AN03CINTRL<NS>•LESSIS(Y,NS),LESSIS(NS.X))

•SHirT s

INS ~ SHirTSEQ ·- tT:tTO(SHIFTtJlSHIFTll<NS•.SHlfT•(f), T34•.SHifT•(T)) [T:tTOfSHIFTL)JlTOISHifTl)

· [JS:INJSEQ(S) l

HSHii"T s

JS ~ .[N:lf0(SHIFTLJ1[M:1TOCSHIFTL) l [I: IS•E•( lTO( SHifTL~•<N~SHif"TSEO• <11>SHIF"TSEQ) l T35 := ISOUTNrCSHifTl.oULCNS<NJ,T34CNJ),

TllCNSCH)rTJ4(N).JrUL<NS(I1)•134(~))•

T30CNS{H},T34{Ml)rl) IS•N•()Il(NSCN>. T 34( N)) .oUU NS( M), T 34C liJ)) T36 :: ISRLI~TCKN(PLCNSCN>•lRll•J),T6CNS(N)r

TZZC~S<N>rT34(N)),y,IY,T23CNSCN),

T3t.OU l J. !Hl( PLO~ SOU •!RU .o Yl• T6( NSCH >• T22<NSCI1J-T34(")J.oY.oiYrT23CNSf~), T34(foi))).T35) IS(HN<?LCNS(N).olRLJ.oY).oi1NtPL(NSCKl•1RLl•Y})

rl7 ·- SUZ 138iHNS( N>.NSOI h 1Rl• SATZ1383fPL(NS(NJrlql)rPLINS(I1)rlRL), I10,.R,.( Y), T 3&)) ; ISUSnl >.NS<MH

. T38 :: <T37><SHIFTRLS<M)><LSSijlFTRCM)> <UT SH.If"TRCM )><SHIF'TROO><SHifTRlS<N )> <LSSHIFTRC N) >< INTSHifTP.CNJ><SHifTROI }> JS : ISCSHIFTRCN),SHIFTR(M)J

T39 == SArZt689CNZ(N)rN2(MJ~Yr SATZ1388(PL<NZ(N)rY>•PL<N2(K),Y}, MO u RL h TJa J , xscnc~ lrNZOIJ'

HO ·- IS~TIRL<Nl!N)rNl<Mt,T39) IS"~~(Nl(N)rNl(M))

T41 :: ISIUNE(SKlFTLrNrH•T40> !S•E~11Tn<SMIFTLl•N#K1 - s.s ·~ •SHI;:'T :

JS ;: INJSHif"TS::Q :::: (T:lTC<SHifTL>ltU:1TO!SH:fTLJl f'U• r~'l"frnr"f .,.nre-u-rr-T• '_ JT'-..~U'fC"'f'~'f!'t\_,u.,..

HSHtF"T

•SHirT

SHIFTSEQ>JT41•.sHIFI"(J,U,J) INS ~ [PRI:PROiJF'SIRRELEHNH RE:.Al•S)} [SS: SURJSE?( SLi

SS a (N:tTO<SHifTL>l T~2 :: <SHIFTRLS(NJ><LSSHIFTR(N)>

<I~TSHIFT~(Nl><SH!FT~CNJ>SS

(J:REALJ[P:IHPROPCSHIFTRCNJ,U>1 TH

Ul1 flt5

T4G f47

TU T49

N ; J50

·- A~DE!CING3CINTRL(U),LESSISCYrU)r LESS!S(U,X)J,tT:AND3CI~TRLCU)•

LESSIS(Y.U>•LESSIS(UoX)lJ PROP1CSHIFTRCNJ,U,T1.Pl

·- ANiiEz•t. R•c A N03( I NTRLC \1)" LES SI SC y, Uh LESS!S(UoXJJ,[T:AS03(I~TRLCU),

tESS!SCY.Ut.tESSISCU•Xi>l -PROP1tSHIFTR<NJ,u,r;,pJ

:: SHlFTl1{U,T43) :: <SHIFTINVlCUrT43)><SHIFTRLS(UtlJ>

<tSSHIFTRCULl)><INTS~!FTP.<ULl}> <SHIFTRCUL1l><T24CU,~43>><T23(U,T43J> <T22CU,T43)>PRI

:= SHIFTIN~1<~S(UL1>rT34<Ull)) ·- TR3IStREAL.SHIFTRCN),cT24(1.J,T43>>

<T23{U,T43J><T22<UrT43l>S.NSCULi), SHlffR<<Ull>SHifTSEQ)rT44rT45rT4G)

:= ISESHifTR(N,<ULl>SHIFTSEQ,T47J ·- SOME!<lTOCSHIFTL),(T:lTO<SHIFTL)l

IS•E•ClTOCSHIFTtl.H,cT>SHifTSEQJrUllr T4Sl

:= SOMEAPPCREALrtT:REALJIMPROPCSHIFTR(N), T>rT42•IMAGEC1TOCSHifTL>•lTO(SHIFTLJ• SHIFTSECrNJ,[T:REAll (U:IHPROPCSHifTR(N)•T>lT49(T,UJ)

INJECTt 'IE U TO(SHIFTlh lTO< SHIHL hSHiflSEQ)

IMSEQ(S HIFT!HN> >

AND3CI~TRLCU>rLESSIS<Y,UJ•lESSIS(U,X))

: ISCSHIFTRCN h<T24(U,.T4 3}.>< T23CU, T43)><T22( li• T~3J>S J 1 TOC SHI FTL)

: ISC<TZ4CU,T43)><T23tUrT43J><T22CU,T43J>S,NSCUL1ll IS(NSC!Jll h SHirTR(<ULl >SHI rTSEID)

: IStSHIFTRCNJrSHifTR<<ULl>SHIFTSEQJ) IS•E•U TOCSHIF"TU .. N,<ULl>S HIFTSEQJ

IMAGEU TOCSHIFTLh1 TQC SHifTLJ •SHIFTSEO•NJ

SS a SURJSHifTSEO PRI a [PS:PER~CSJJ

BIJS!UHSE Q

::: [J: 1 TOCSHIFTL) lT50,.. SlilfT"'(TJ SURJECT lVEC 1T0( SHifTLJ .. no <SHIFTU .. SHIFTSECJ

::: ANDICINJECTIVEClTOCSHifTLJ,lTOCSHifTL> .. sHIFTSEQJ,SURJECTIVE(lfO{SHtfTLJr lTOCSHifTLJ .. SHIFTSEQ), INJSH!FTS(Q( ANOEl< Il'\JSEOCShSURJSEQC S> ,psJJ,SURJSHIF'TSEO<A~DE2<!NJSEQCS>• SURJSEQCSJ,?S)J) : 8IJECTIYEt1TO<SHIFTL>•1TOCSHifTL)•SHIFTSEQJ

; COMPLEX :" PAIR lTYPEC RE AL> tX := COMPLEX (X:COHPLEXltY:COMPLEXl IS :: IS'"E .. <Cx,x,y J IHS :: NOT( IS{X,y))

a [P:CT:COHPLEXl 'PROP'l SOHE .-All ·-ONE ::

SOMt•v•ccx,pJ All'"L .. fCXoPl ONE .. E•<cX,P>

; U:REALHB:REAU PLI := PAIRl<REAL~A•B>

:= flqSTlCREAL•X> :: SECONJl(?.EALPX)

x a RE Ilf

' ..

: •PROP' : 'PR!Jiu

'PR!lP • • PROP' 'PROP'

COHi"LEX REAL RE Al.

s

s

s

-5.6-

ISRE ·- f'IP.SHISlCROl,A,.Sl lMIS ·- SECO.N01ISHREH ... A,8) ISIM := SECOND1!S2(REAL•A,B)

X ~ PLIIS ::. PAIRliSlCREAl,XJ ISPLI := PAIR1IS2CREAL,X)

Y a U:IS(X,YJl tSCE~E := !SFCCX,REAL,[TrCXlRECT>•X,.Y•I) ISCEIM := ISFCCX.REAL,[T:CXJI~CT)•X•T•I)

B ~ (C:~EAll(I:IS"R'"CArS>l ISP.E:Xl :: ISF'<REA~,cx,rT:REALl?litT,ç),A,B,I> ISRECXZ :; ISFt?.EALrCX•tT:REALJPL!{C,J);A,B,IJ

C 2 tO:REAlJCI:IS'"R'"(A,.Bll(J:ISPR'"CCrO>l IS~ECX12 :: TRISCCirPLtCA,C)IPliCBo:loPLtCBoO)r

ISRECX1CA.BrCriJ,ISRECX2!CrOrBrJJ) X 3 SATZ20& :: REF'ISCCXrX) Y :l a:Isn.nJ

SATZ?Q7 :2 SYKIS(CXrX•Y•Il Y a tl:COHPLEXlti:ISCXrYll[J:IS(YrZll

SATZ208 •- TRISccx .. x,y,z,IrJl 3 )C ·- PLHOrOJ

lC :: PlH 1i~lr0) Y ~ PL ·- PLICPL"R•(RECX)rREtYJ)rPL•R•tiM(X)r

I"'' y >' ) 3 a PLIS12A :: IS~ECK12CPL"R"<RECPLI<~•3l)r

RECPll(CrO)))r?L"R•tArC)r P!. ,.R .. C IKC Pli UrB )),. I I'!( PLHC•O)) h Pt•Rft<SrDJriSPL12CRE<Pt!tArB)),Ar RECPtlCCoD)JrCrREIS<A•SJrREIS<CrDJ)r ISPl12(1HCPLICArB)),SoiMCPLI(CrDJJrD•

: IS""R '"CA ,RE< Pt.H A.B))) : IS'!"~'"H !H1'l H ~~uh B>

IS•R*(3,.IK(PLI(A•Bl)) IS (Pl It P.E CX ), IM <X> h Xl

: iSCX,Pi.HRE<X> • IHCX )})

: ts•R•(R E(XhRECY)J : IS"R"(IMCXl,IK<YJl

IS(?I.It A,ChPLHB,C)) : ISCPLU c,AJ,.PLI<C .. BH

ISCPLU A•CJ;PLI COMPLEIC

: COHPLEIC

COHPLEIC

l~IS U ,g h IIUSCC, 0 J l) : ISCP[{i"LI U • Bh PLU CrD UrPL U PL •R•U rC h PL •R•ta,. D))) PLIS128 :: SYMIS(CXrPltPLICAr3J,PLICCrDJlr

X ; [R:REALltS:REAll PUS lA

PLIS1B

i'LISZA

!"l.ISZB

Z ~ U: ISCX,.Y)l

Pll(PL"R"(ArClrPt•RP(BrDJlrPLIS12Al : IS(PliCPt•R•(ArCJrPL•R•tBoOJJrP[(PLICArB)rfli(CrOlJJ

:: ISRECX12CPL•P.•<RE(?LICR~S)lrRE<Xl)r Pt•R•<R~RECXJJ;PL•R•CIMtPLI<RrSJl~

IM(X)J,pt•R•(S,IH<X>>~.

ISPll<~E(Pti<R•Sl>•R•~ECX>•REJS(R,SJJ~ ISPllCIH<Pll{R,S)JrS.!MCXJ.IMISCRrS))} : IStPLCPLICR~s>.X),PLICPL·~·(RrRECX}),pt•R•<S•IHCX))))

:: SYMIS<CX,PLCPliCR•S>•Xl• PLICPt•R•CR,RECX>>•PL•R•CSr!MtX)l)• PliSlA > ISCI"LU Pl -R•(R,REU )), Pt•t •cs,Ut(X) > ),.pl( PLI CRrSJ .x U·

:: IS~ECX12CPl*P."<RE(X),RECPli<R,S))),. Pt•R•(RE(X)~RJ,p[•R•tiKCX>•IHCPLI(RrS)

)),.pt•R•(IMCX>•S>,!S~-ZtP.(\Pli(R,S)),

R,R[(XJ•REISCR,Sl),ISPLZ(<~tPLICRrSl); S·IM<Xl;IMIS(R,SJll IS<PLtXrPLI(R,S>JrPliCPl"~·(RECX>,R),pL"R"CIKCX),SJl)

:: SYK!SCCX.PLCXrPLICR~S>l• PLICPL•R•IRECXlrRJ~Pt•R•<IM<XJrS)J, PliSZAJ : tS<~LICPt•R•<RE<XJrRJ,PL·~·ciH(XJ,SJ),pl(X•PLI(RrS)l)

ISPL1 := tSr<cx,.cx~rr:CXlPL<T,zhX•Y•IJ : IS<PLCK•ZlrPLCY,zn ISPLZ :: ISF<cx,cX,[T:CXlPltZ,.TJ,X•Y•I> : IS(PLfZrXlrPL(Z,YJ)

Z; [U:CJMPLEXlCI:[S(XrY)J(J:IS<ZrUll IS?i.l2 := TRIS<CXrPUX,l),.pl(v,zhPLO,U},.

ISPll(X,.Y•Z•l),.ISPl2<l•~·Y•J)) IS<Pl(~,z>tPL(1•U)) Y ~ SATZZ09 := ISRECXlZ<PL"R'"<RECX)rRE<YJ),

Pl"R•<RECY)~RECXJJ.Pt•R•ct~(XJ,IH(Y~J; PL "R,.C !HCY h IMCX lh CO~!>L( RE C !Or RE( U ), CO MPU IMCX ), UH Y))) : lS(f>l llt "Y h PL(Y,. X))

COMPL := SATZ209 ISCPl(l(,.YJ,f'lO'rXlJ X; SATZ~13 :: TR3ISCCX .. PL<X .. OCl,P!..HP!.'-Ii .. CREUhO>•

"' -- .,. -y ~

- 5. 7-

PLIS2A<X•O•O>,ISRECX12<PL~R·CRE(X),O),. RE< X hPL•R"< HHX> • 0) • !MC X h Pl02Hl.E (X h O,.REFIS<REAL.OJ),Pl02<IM(XJ,.O• REF'IS(REAL•O H hPLII SClO) : IStPL <X •OChXJ

SATZ21U := SYKIStCX.PUX.OC>..X,SATZ210l : ISU,.Pt.<X.OC)) SATZZ13B :: TRIS<CX•PL(OC•Xl•Pl(X•OC>•X•

Cûii?UOC.U,SATZ210) : IS(Pl<3C•XhX) SATZ210C •- SYMISC:CX•Pl<OC.XhX•SATZ2106) ISCX .. PLCOC .. XH

Z a SATZZ11 :: TR3ISCCX•PLCPLCX .. Yl•ZJ• PLI<Pt•a•<PL~R"<P.E(Xl.P.EtYJJ,RECZ)J,

Pl"R•(PL"R .. < I!o!<Xl•!H<Y>>•IIHZ>J), PLICPL"R"CRE<XJ~PLRR"CRE(YJ,RE(Z))),. PL"R•(!MtX>•PL"R"(IMCJJ,IH(Z)))), PLCX.?LtY.Z>l•PLISlA<Z•PL"F."CRE<X), RECY)J,Pl"~e<IMCX>·I~CYl)),. ISRECX12<PL .. R"(Pl~R·(~ECXJ.RE<Y>l• REClJ>,PL"R"tP.E<XJ,Pt•R•tRECY)•RE(ZJ)) rPl"R•<Pt•R"(IHCXJ~IH{Y)J•I"<Zl), Pt•R•(IMCXJ~Pt•R•(IM<Y>•!M(ZJ>>• ASSPLlCRECX),RECY),RECZJ),ASSPll<IM{X) •lH{YJ,IMCZl)J,PLISZB<X•PL•R•<RECY>• R!::(Z} ),pt•R•<IH<Y>•IM( Z> )) ) ISCF'L(!tl(X,Y),.Z),PL<X,PLU' ,l) ))

ASSP!.l :: SATZ2ll : IS<PU?'LU•YhZ>•Pl<X~PLU"l))) ASSPL2 :: SYMIS<CX•PLCPLC){,YJ,z),PLCX,Pl(Y,Zll•

ASSPL1) : IS<PL<l•PL<Y•lll•Pl<PL<X•YJ•ZJ) Y ~ [~tCOMPLEXlti:IS(PL(Y,U>.XJl

•2212 s

Tl :=

T2 ::.

Tl ::. Tft ·-

-2212

SATZ21ZA :•

Y a SATZZ1ZB :=

SATlZlZC ::

SATU12 :=

TRI S< RE Al• PL •ft•( R[( Y >..RE UJ > h REtPL(Y,.U)J,RE(XJ,.ISRECPt•R•<RECY), RECU>>•Pt•R•<!M(Y),!HCU))), ISCERECPl{Y,U),.){,J)) TRISCREAlrPt•R•CtMCYJ•t~<UJ),

IM<Pl(Y,UlJ,IKCXl.ISIMCPL•a•cRECYl• RECU>l•Pt•R•ttKCYJ,IHCUlJJ, ISCEIMCPLCY.U),X,I)) SATZ187DCRE(XJ,RECYJ,RECUJ.T1l SATZlS7DtiM(Xl•lK{Y),IKCUJ,TZJ

TRIS<CX•U~PLI<RE(UJ•IMCU)), PLICMNCRECX).RE(Y)),~N(IKCX),!H(Y)J)•

ISPli(UlriSRECX12CRECUlrMNCRECXJrRECYJ ),IMCUJrMN<IMCX),IHCYJ),T3•.zztz•, r~o•.2:nz·u TR3ISCCXrPlCYrPliCKN<RECX),RECYJJr MNCIMCX),JM(YJ)Jl•PLICPL~R"(RECY)• MNCRECX>.RECYJJ)rPL•R•CIMCYJ.HN(IM<XJ~

IM(YJll)rPll(RECXJriKCXll•X• PLIS2AtYrMNCRECX>•RECY)>·~~(I~CX>• IK{Y))),ISRECXl2{Pl"R~(R~<YlrMNCRE<X),.

RECT)llrRECX),PL"R•<IH<Y1rMN(IM(XJ• IKCYJ>l•IM<X>•SATZ187ACRE<X>•RE(Y))• SATZ167ACIH< X),. I K.CY l) >.PLI IS< X>) SO~EICCX.tT:CXJISCPLCY•f),.Xlr PLICMNCRECX),RE(YJJ,~NCIKCXJ,.IM(Y)}), SATZ21ZB> ONEHCx.n:cxHSCPU y, T hXh (T :CXl [U:CXl[V:ISCPl(Y,TlrXlJ[W:IS<PLCYrU),. lOHRIS2(CX.o T • u .. PLIC 1'1~{ REUhRE< Y) h

: IS"R•PLWft•<IHO),li!(UUriMU)) : IS"R"U E ~MN(P.E<X hRE<Y) J J : IS•R•U M<UhMNUMUhlMU) U

. s

- 5.8-

•2213

•ZU3

MN

D ; MUS12A

"fN!SlZB

X ; (R:~EA~l(S:REAL1

!f?fiSU

!UHSlB

MNISZA

!fNISZB

z ; U :ISC x, YJ l ISttNl ISKNZ

MNC I MU > ~ J;t( n )) ,.54 TZ212A(T" V) •

SArZZ12HIJ•W H rSA.TZ21ZCJ ONEC (T: COMPLEXliSCPL(Y,.T),. XJ) ·- PL!t~~·R·<~ECXlrP.ECY)J,.MN•R"{lH(X},

IMCYJ)) : COMPlEX ·- tSRECX12C~R·R·CRECPLI(Ar8)),.

REtPLI!C .. ~J)),~N~a·{ArClr HN"R"(IHCPLICA.Bllrl!CPLICC,.O))),. KN•R•(B•~l,!S~IlZCREtPLICA .. BJ),A,. RECPL!(C.DJ),.C.REIStA .. Sl.REIS!C,DJ>, ISM~lZ~I~(Pli(A,.8)J,.Br!H{Pli(C,û)l,O,

!HISCArBJ.IP!SfC,~)J) ISlMNC~li<A•Bl•PLI<C .. D)),PLJ(PN•R"(A,CJ•HN•R•Ce,.oJ)) :• SYHISCCX•HNtPLICA•S>,PLICC.OJ),.

PliC HN•R,.CA,. C h MN•R• <B, 0) h MNIS12A J : ISCPLH MN .. R •u, ChHN*R'"(B,. OJJ •HHC Pl IC A, Bh FLI<C •D >)}

:= ISRECX12C~N"R~CRE<PLI(R,S)},.RE(X)),. MU"R•(R~RECXll•MN•R•(JHCPLICR•S>l• IHCX}),HN"R"(S,IM{X)),. ISMNlCRECPLICR•S>J•R•RE<XJ•REIS<R•Sll• IS !'IN H IMCPt.I CR. S )),. So I H(Xl,. I~IS(RrS))) : ISCMN<"lHR ,.s h X hPll( IOI .. 't •( R,. RE <X> J ,.!H.•R• C So tlt(X))) J

:: SYMISCCXoH~CPLICRoSl•X>• Pli<HN*R•CR.~E<Xl),MN"R"'CSoi~CXll),.

~NIS!\) ISCPLICMN•R•tR•RECX>>•~N·~·(SoiK(X))),MN(PLI<R•S),.X)) := ISRECX!2CMX•R•<RECX)oRECPLI<RoSJJ),.

H~wR•<RECX>•RloMN"'R"(IMCXl•I~CPLI<R•S> )l,.KN•R•(IK(XJ.SloiSX~2CREtPLICR .. SJ), RoRE<Il•REIS(R.Sil•liH~2CIMCPLICR,Sl)• s.tMCXl•!~ISCR,.SJJ) ISCKN<X,Pli<R•S>J•PLICMN·~·CRElX),R),Kh•R•CIMCX),.S))J

:: SYKISCCX•IoHi(X,PLUR,SHo PLICKN"R'"CRECXJ.R),.KN•R•<IM(XJ,.S)),. MNISZAJ : ISCPLU MN,.R""(!l[(X J.R)~ HN•=t•t HU X) oSH• HNCX•PLI<R•SHJ

:: ISrCCX .. CX•[T:CXlMN(foZJ•X•Y•Il : ISC!fNU: •ZhMN<YoZH := lSrCCX .. CX,.[T:CXlKN(Z,.TJoX•Y•l) : ISCMN(Z,Xl,.MNCZ,YJ)

z • [U:CJH~LEXlti:ISCX•Y)J{J:(S(ZoU)J ISMN12 := TRISCCX,.MNCX,z>,~NCY,z),MN{Y,Ul• ISMNlCX•Y~I•Il,.ISMNZCZ•U•Y•J)J : IS<MNCX•ZJ,.HN(Y,Ul)

y ; [U:COMPLEXlti:ISCPLCY.~JoX>l SATZZIZD := SATZ?l2UU .. U : ISCO .. M't CX•Y)) SATZZlZE := SYMIS(CX,U,M~CX.YJ,SATZZ120) IS<KN(I(,Y),UJ

u ; ti:ISCPltU.YJ•XJJ SATZZ12f := SATZ21ZDlTRISCCX.Pl<Y•UJ.Pl<U,YJoX•

COMPU Y" Ul • I)} : IS<U.M!t<X .. YH SATZZlZG := SYMIS(CX.U,MN<X,.Y)oSATZZ12f) : IS(IINU .YhUJ

y ; SATZ212!f ::: SATZ21Z9 !S(Pl(YoHNCXrY)JrX) [I:ISC~NCX.YJ,.OCJJ

n := TR3IS<REAL•KN~R"<RE(X),RECY)l,. RE(KNCX.Y>>•RE<OC>•O•ISRECKN•R•<RE<X>• RECYJ h MN"R•( IMC X),. I 1'1( n Ur ISCERE(MNCioYJ.OCrJ>•REISCO,.O)J . ts•R"'('fN'"R'"(R[(XJ..RE«Ylhl J .

TZ := TRl!SIREALrHN•R•tiMCXJriM(Yl>• IH(MN<X.Y)),IH<OCJrOriSIMCHN"R'"(RE(X),. REUHrlo!fi .. P.•( lM(XhiH<Y) )), IS:EI~CMNCXrYJ,OCrtJ,IHIS<OrOlJ IS .. R ,.(!11 N•R"( IH( X), I I!<Y )),3)

n := SATZ18ZB<RE{XlrRE(YlrT1) IS"R"'c:t E<X> •RE( Y J J H := SA TZ I 8 ZB (1 M( X h I ~fY h T 2) : IS•R .. Cl M('() • IP~C Y))

SATZZUA :: TR3ISCcx~x~PlifRE<X>•IMCX)JrPLI<RE(Y)•

s

' -5.9 -

IKCYJ>~YPI5PliCX>~!SRECX12<RE(XJrRECY) ~!HCXlriHCY)~T3".2213"~T4•.zzt3">•

PlliSfY>) rsu .. n Y a CI:IS<XrY>l

H2213 s

I a TS ::: SATZ192ECRE<XlrRE<Y>.ISCERE(X,Y,Ill I s~•OtN•R•<REU ),.RECY )),) ) T& ::. SATZ13ZE<IH<X>riHtYJPISCEIMCXrY•IlJ ts•R•(HN"R"CIH(XJriMCY>J,J)

-2213 s I a SATZZ138 == ISRECX12(HN•P.•<RECX>rRE<rlJr0•

MN•R•(I~CX>.IX(Y)),Q,TS•.2213 .. , T5".221J .. ) ISOHHl( ,Y),OCJ

x ~ lol;) ·- MNcoc.u COM!»LEX SATZ214 == ISRECX12CKN•R•<RE<OC),.RECXJ),.

HJ·~~(qE{X)J,MN"R•CIMCOC>•!MCX)),.

HO"R•<IMCXll~PLCl<P.E<OCJrHO•R•<RECXJ)r REISCO•C>>•PLOlCIHCOC>•HO"R"ClH(X)),. IH!S(O~O))) ISCKOCl( l•PLI<MO•R•<RE(X)J,.MO•R•<IMCXJ)))

SATZZ14A == SY~IS<CX?MO(XJ,PLI<HO"R"CRE<XJ), M~·R"Cl~{X)Jl,SATZ214) ISC?LU MO•R•CRECX)),KO"R•t IH{X})),,.OOC))

s a MOISA ·- TRISCCX•HO<Pll(ArBlJ• FLICHO"R•tRE<PLICArBJ>>• MO•R•CIHCPLICA.BJJ)),pliCKO•R•CA>• MO•ft•(Bl1rSATZZ14(Pl!<A•B>>• ISRECX12(~0"R"CRECPll(A,8)J),M0"R"<A>i HO"R•CIH<PliCArBJ>l•MO•R•CB),. ISHQ(q[(PLI<A•B>>•ArREISCArB>>• ISHOC!H\PL!(A•B>>•B•I~ISCArBJ))J IS(MO<~LI(A,.BJ>•PLI<KO"R•tA>•HO"R"(BJJ)

HOI Sa := SYMISCCX,.HO(PLI<ArBJ>rPLI<MO"R•(A),. MO"R•<BJ>rMOISA) : ISCPLU MO•R•CAJ.HO,.R•( 8)),. MO< PLICA,. 8)))

T a u:zscx.n 1 ISKO ·- xsrccx.cx.rr:cxlMO<T>.x.v.r> IS (140 U l rl10 CY))

x a SATZ215 ·- TR4ISCCXrHOCHO<XJ),KO<PLI<KO"R•<RE<X>> rMO"R"<IMCXJ))),PLI<KO•R"CMO"R"CRECXlJ JrMO•R•<MO•R•(IH(XJJ))rPLI<RECXlriM(XJ J,X,ISMOCHOCXJ,PLifMO"R"CR[(X)), HO"R•CIHCXJ)lrSATZ214J, MOISACMO"R"CRE<Xl)rHO"R"<IHCX)l)• ISRECX12C~O"R"CHO"R"CRE<X>>>•RE<X>• KO"R"(HO"R"CIH(XJJ>•IH<X>• SATZ177CRECXJJrSATZ1T7CIM<XJ)), PLII SC X>> IS(Iol0()f0<X)),XJ

SATZZ15A == SYKISCCXrHOCMOCXllrXrSATZ215J IS <X• HJ (HO( X>> J Y a U:IsU.MO(YJJl

SATZ215B ·- TRISCCXrHO(XJrHO(HO(YJJrYriSHO(X,.MO(YJ , I>. SA TZ215< Y)} IS<HO(J( >•Yl

SATZ215C == SYKISCCXrMOCXJrYrSATZ215BJ : IS<Y,.HJ (X)) y a [l: ISOfO CX),. YJ l

SATZ215J = SATZ215CCYrXrSYHISCCX,MO<X>rYrl)) IS<XrH) (Y))

SATZZ15E = SYHISCCXrX~~OCYJrSATZ2150) : ISCMOCY hXJ 1C a SATZ21ó = TR3ISCCXrPl<X,MO<XJ),

PLCX.PLIC~O"R"<RE<X>>·MO"R"<IHCXJJ)), P~I<Pl"R"CRECX)rKO"R•<RE<XJ)), PL•R•(IH<X>•M3"R"CI~CX)))),0Cr

ISPL2<MOCK>•?LICMO~R"CRE(X)J, - 5.10 MO"R"<!M(X)ll•X•S~TZ214(X)), PLIS2A(X,MO•R•(RE<X>>rM0"R"<IHCX))), ISREClClZ<Pl" R"( REC X h HO" R"< RE U) l hl>,. PL"R"! IIHX ), I'!~"R .. (lH(X)) ),0, SAH 179{ RE <X)) •SATZ 1 T9('HH U J)) IS<Pl<XrMO(X)),OC)

•221&

ANDERS := SATZ2:12H(0CJO 'lO : ISCPL(I( JO HOC X )),.OCJ

•2:21&

SATZZ16A :: TRISCCX .. PL<KOCX>"Xl .. PltX.~OtX)),.OC" CDHPLOIO(JO,. XhSATZ21ó) : IS<Pl(~OCX)"X>•OCJ

y ; SATZZ17 := TR41SCCX.~9(PL<X,.YJJ. PL!(MO"R•(pL•R"CRECXl,RECY)llr KO"R•C?L-R"CIMCXJ.IM(Y)}l)" Pll(Pt"R•tMo·~·CRECX)l .. ~O"Rft(~E<Y))),. PL~R·(~O"R"{!MCXJ).KC"R•CIM(Yi))J,

PLCPLI<Mo•R•{RE<XJ),~O·~·cx~<Xl))JO

PLICP.O*R•CREtY)),MO•R•<I~CY))Jl•

PLOI!H X h MC{ Y) h MO I SA< PL,.R'"< RE a),. RECYlJ,.PL"P.•(IKCX>•I~CY)J),.

ISRECX12CMO•R•(pl•R•CR[~~>•RE<Yl)),. PL ,.R"'CM:l•R•< RE C X> h KO"R"'< RE O'J l h ~O·R•(pt•R•ti~(X),iM(Yll)•

PL"R•CMO"R"(!~<Xtl.YO•R•(J~(Y)J),.

SAfZ180t~E(X)rRE(Y))•S4TZlS0(1M(XJ~ IMCY)))rPLIS129CMO•R•tR~CXJJr

MG*RftCIHCXJJ~MO•R•<RECYlJ•MO•R•(IHCY))

)"ISPL12C~LI<MO•R•CRECX>>·MO"R•tiMCX)) JJOMOUJ.. PLU MO•~t•c REn'l h MO•R•UM<Y> ))' ,HO(f)rSATZ214A(XJrSATZZ14A(Y))) t ISOCO<"LUJO YJJrPL.<MO(l( )•MHYJ))

SATZ2U'A :: SYHISCCXrMOCPL{XrYllrPLC~OCXJ,HO(Y)), SATU17J : ISCPL<~O<XJrMOCY))•P.OCPl((rY)))

SATZ2U ·- TRISCCX"KNCX"YJ,PlCXrPLICKO•R•tRECYJ)r MO•R"CIMCYJ))),pL(XrHOtYll• Pl!SZBCXrMO•R•CRECYJ)"MO•R•(JM(YJJ)r ISPL2(PLI(H0"R"tRE(Y))"MO•R"CIH(Y))),. MO(YJrXrSATZ214ACYJJ) : lSCMNC(JOYJrPL(XrHOCYlJ)

SATZZ18A == SYHIS(CXrHN(XrYJrPLCXrH0(Yl)rSATZ218) IS<~LCX•KOCY))rHN(XrY))

+2219 $

Tl == TR3ISCCXrHOCHNCX"Yl)rHOCPLCXrMOCY))), PLCHOCX)rMOCHOCYl)),pl(HOCX),y),. ISKO<MNCX•Yl"PLCXJOMO<YJl.SATZ218),. SATZ21T<X•MOCY>>•ISPLZtMO(H0tT)J,Yr HOCX>.SATZ215CY))) ISCKOC~N(XrYJ)"PlCHOCX),.Y))

•2219 s

SATZZ19 := TR3ISCCXrHOCHNCXrY)JrPL<HOCXJrYl• PL(Y,.HO(X)J,.MNCYrXJrT1•.zzt9"• COMPLCMOCX>,.YJrSATl21SAfYrXJJ : IS(H0('1 N<X• YUrHtHYrX))

SATZZ19A == SYMIS!CX-HO<HI(Y,XlJ.KN{XrYJ, SATZZ19(YrX)) iS<KN (X in,. MOfMNCY• X)))

TS == PLICHN"R"<TS"R"(RE(XJrP.ECYJ), TS"R"(IM(XJriMtYl)),pt•R•CTS*R"tRE<X>• IMCYJJ"TS•R•(IMCX)rRE(Y)))) : COHPlElC

!tETS :: HNffR*<TS•R•<RE<X>,.RECY>J~rs•R"(lH<XJr HI(Y))) RUL

-5.11-IHTS ·- Pt•R•CTS"R"CRECX>•I~(YJ)rTS"R"CIKCX>" RECY J}) REAL

+V3 b

-··-

D ; n == ISKNt2•R•tTS"R"tRE<PLICAr8)), RE<PLI<C~D)l)•TS*R•tA.CJr

TS•R•t IMCPLI< A"B)) •: H( PLI<Cr Dl))" TS•R•tSrD)riSTS12CRECPLlCA,.BJ1•Ar RECPLICC•O H •CrREISC A• 8 >" REIS(CriH )" ISTS12CIMCPllCA•Bll•B•IMCPlltC .. OJ),O,. IHIS(A.BJiiMISCtrOJ}l : IS-R'"U ETSC PliC ArBIPPLH C• 0)) rMfl•R.,.( TS•R•U,.Ch

rs-a•n ... ouJ rz := ISPllZ~R"CTS'"R•tRECPliCArBlJr

IM(PLI<C .. O)lJrTS•R•<ArDJr TS"R•(IMCPLI<A•Bl)rRE(PLI<C•O)))r TS•R•CBrCJ.ISTS12(RECPLICA .. S1)rA• IMCPliCC•Dli•D•RE!SCA•B>•IMIStC .. O)Jr ISTS12CIMCPL!CArBl)rBrRE<?LICC.O)},.C; IHISCA•B>•REISCC.D))) : IS-R•ttMTSCPLICArBlrPLI<C•Dl),.PL•ft•trs•R•(ArO)•

rs-a ·u .. c n' •V3

0 a TSIS12A := ISRECX12<RETS(PLI<A•B>•PLI<CrDJ), MN•R•<TS"R"(ArCl.TS•R•ta .. OJ), IHTS<PLI(A,S>•PliCCrDl)r PL•R•tTS•R•(A,OJ,TS•R•cs,cJ>,T1•.v3•r rz•.v3•1 : IS<TSt~LI<A•B>•Pli(C•DllrPLICHN•R-(TS•i•(A•C)r

TS•R•(3r0}),pL•R•tTS•R•tA.OJrTS•R•(BrC)J)) TSISIZB :z SYMISCCX•TSCPLI(ArB>•PLI<C•O>>•

PLU HN•R•c rs•a•tA.c,.. rs•a•cs .. ol,.. PL•R•trs•R•<A•D> .. TS•ft•(BrC!)J,TSISIZA) : IS(PLU MN•R'"HS•R•c A•C J..TS •R•<B•Dlhf'L •rcts•a-<A•Dh

TS-a•n ,c )J hTSCPUU, BhPLJ<C•OJU X a [R:REALJ(S:REALl

••V3 s

s a n == lSMNt2•R•(tS•ft•(RE<PLI<R•S>l•RECX)), rs•a•tR•RECX)J,TS•R•(IMtPLICR•SJJr IHCX>>•TS•R•cs,IK{X)), ISTSlCRECPLICR.S)),RrRE(XJ,REISCR•S>>• ISTSl<IHCPLltR.S)J,.S,IMCXJ,IMISCR,SJJ) : IS-a•<11ETSC PLin .. s J • XJ .. HN•R•<TS•ft•(ft,.RECXJ )".

TS-R•(i,.IMU)HJ n := ISPL1Z•R•<TS•R"<RECPLI(R,SJJ,IKCXJ),.

TS"R•(ft,IHCXJJrTS"R•<IMCPLI<R•S>J• REU)l,.TS•R•(S,RECX) ), tSTS1<RECPli<R•S>>•R,tMCX>~REISCRrSJJ, ISTSlCIM(PLI(R,Sl),S,REtXJriKISCR .. S)JJ : IS~•ttMTSCPLI<R~SJ•XJrPl•R•CTS•R•(R,IMtiJJ•

rs•!t•tä JOREtJOJU

-u $

S a TSIS1A == ISRECX1ZtRETSCPll(ft,SJ.XJr I'CN•ft•(TS•ftw( R•. R[(X)) ,rs•R•( 5,. IK( X))) JO IMTStPLI(ft,S),X},Pl"R•CTS•R•tR .. IMCXJJ• TS"R•cs.RECX)J),f3".V3•,r~·.v3•) : IStTSt~LICR•S>•X»•PLICMN•~•ttS•R•CR#RECXJ),.

TS•!t•U ;IMC 10) hPL "R'"C TS•R •u, I lH Uh TS•R•<S.RE'U))))) TSIS1B ,. SYMISCCX•TSCPLICR•S>•X>•

PLICKNwR•CTS"R"(R,RE(X)),TS•R•(S,IMCXJ )),PL•R•trs•R•tR•IM<XlJrTS•R"<S•RECXJJ )J.TSISlU : ISC~LICMN•R•tTS•R•(R,RECX)J,rS•R•(SriM<XJ)),.

-5.12 Pl -R•u S"R•tR• IIHU )• TS•R• (S, REUJ) )), TSCPli<fbS1 •X)) H·Y3 s

s a rs := ISMN12~R•trs•R•CRECXJ.RE(PLI<R•SI))• TS•R•CRE<XJ,RJ,TS"R"CI8CXJ.IKCPLICR,S)

rs

S il TSIS2A

TSISZB

z a u:tsn .. nl

))~Ts~R•<t~C~>.s>~ISTSZ<RECPll(R,.SJ)~ R•RECX)rREIS!~ .. Sl)~tSTSZ!IHCPLI<R,.S>J, S.>HH X h IKIS (R,S Hl : IS"'R•U ETSC XrPLI<R,S)) ,MN"R•CTS .. R,.(RECXhR h TS•R•(IM( x>

:.. ISPllZ•R .. C TS .. R .. ( RE CX ),. IfHPLI CR rS >) l, JS•R•CRElXJ,.Sl.tS·R~(tHIXJ,.REtPLI<R•S> }),JS•R•CIMCXlrRJriSTS2CIHCPLilRoS)J, SrREUh !KIS(R.S1hiSTS2{RECPLUR""Sl l. R~IHCY.J~r.EIS{R,S)))

·- ISR[CX12CRETS<XoPLI<R•S>>• MN"R .. <TS·~·(RE!Xl;R)•TS•R•(IM(X),.SJ},. lMTS(X,PllCR.S>lrPL•R•CTS•R•<REtXJ.S),.

.. sn >

IS"R•CI MTS(X,PLHR .. SU ,pL .. R•<TS'"R'"(RE( X Jr S h TS .. R'"< IM< :0 ~RJ)) .

TS•R•< !M<X ), R> h T5•. V3"• !ó'". Vl .. ) ·: IS(TS(I( ,.pu (R,.S J hPLH MN""~·ns•R .. CRECX hRl •TS•ff"CIMCX >•

:= SY"ISCCXrTSCXrPLI<RrS)}, P~I(HN~R•(iS~R~!RECXlrRJrTS~R~(IMCX), SJ)rPl~R•tTS*R~!RECX)rSJ,.TS•R•CIK{X),

SJl.Pl"R•(tS•R•tRECXJ.Sl,rS•R•Ctr.txJ,.R))))

R))),TSIS2Al : ISC?LICMN*R•crs•R•<RECX),~).TS•R•(JM(X)rSll• Pt•R•tfS"R•<RE<X>•S>;TS•R•<tH(XJ,R}J),TSCX•PLI<R•S>>J

xsrs1 == tsrccx.cx.cr:cxlrscr,z>.x.r .. t> : rsuscx .. n. rsn .. zu ISlTSCZ .. x hTS( z, YJ J ISTSl := zsrccx.cx.cr:cxlTSCZ.TJ.x,y,I>

Z 3 [U:ClKPLEXJtt:tS(X,.Y)l(J:ISCZ,UJJ ISTSl2 := TRISCCX,TStX.ZlrTSCYrZlrTSCY.UJr

Y :::a n

ISTSl<XrY•l•IlriSTSZ<z,.u,y,J))

:= ISKN12"R .. <TS .. R .. ( ~E(Xh REC Ylh TS*R•CRE(YJ .. RE(XJJrTS"R•ttK(X)r!KCYJ>• TS•R•<IM<YlriK(X)J,COMTS<~E<XJrRECY)),

COMTSUIHX h II'O'))) : IS .. R•n ETSCX .. YhRETS<Y •XU TZ

Y il 5ATZ!23

CO MTS X :il ti:IS(XrOCJl

LEMKAl

LEKMA2

X a HOOZ

I a U:M11A3

:= TRIS(R,Al•IMTSCX .. Y)rPL•R•(TS"R"(IMCX),. RECY>>,TS"R•(RECXlri~<YJJJ,.IHTSCY•X>• COHPL•R-<TS•R•CRECXJrlMCYJJ, rs•R•ctH<XJ,RECYJ)), ISPLlZ•R•tTS•R•<tKCXl•RECY)J, TS•R•CRECYl•t~(X)J.TS•R•<RECXJ,.IMCY)),.

TS•R•CIMCYl.RE(XJl.COMTS{IMCX),RECYJ), CDHTSCRECXl•IMCYl)J)

:: ISRECXlZCRETSCX.YJ,RETSCYrXlriHTSCX~Y) ,. I KT SC v.x>r r t• • .Jzzo•. rz· .3zzo· J

:: SATZZZO

:: TRIS<REAlrRE ex h RE COC hO• ISCERECX .. OC,I>rREIS{O•OJ)

:: TRISCREALrlKCX)riHCOCJrO, ISCEI~CX .. OC,.IlriMISCO,,JJ

:a PL•P.•CTS•R•CRECXJrRECXlJ,JS•R•(tMCXJ, IM<:O J J

:: TRJS(REAL•~D02,Pt•R•(Cr0)•0• lSPL12•R•CTS"R*(RECXJrRE(X)),C,. TS•R•CIHCXlriM<X>>•O•TSOlCRE(X),RE<X>• LE~HA1l,TS01CIMCX> .. tM(XJ.LEHKA2JJ~

: ts•R•CIHTS<X•YJ•IHTSCYrXlJ

ISHSU ,Y),JS(T.,X)) ISCTSCtrYJrTSCY,XJl

: IS•R•n EU hOl

. ts"'R•U IHXJ..O) . : REAL

PL,l<O•O#~EfiSCREAL~O))J : IS"f:t•('400~CXhOJ

s

s

s

- 5.13

x a (N:tUSU#OC) l

••V3 ' x a RE2 ::: TS•R•<RE<XJ,RECXl) : REAL

IHZ ::: Ts~~·<I~<Xl•!M(X)) REAL N a ti:IS•R•<RE<X>•Oll

TT ·- TH3•L•IKP"C4S.R"CIMCX>•O>•IS<Xr0CJ•N• tT:IS"~•{J~CX),Q)JTRISCCXrX•PLI<RECXl• IM(X)J,OCr:SPtiCXl•!SRECX12tRECXlrO• PHo.o.r..nl> NIS•R-t IH<X !PO)

T6 :: IS?DS(I~Z.M002rSY~tSCREALr~002oiM2• Plvl(RE2oi~2.TS01CF.E(XloRE<X>rl)llo

#

POSSQtiM{Xl•TTtl POS< MOl 2) N 2 [Q:NIS"R•CRECXJ.OJlCI:Is•R•CIHCXlr0)1

i9 ::: lSPOS(REZr~CDZrSYHIS{REALrMOD2rREZr PlOZ<RE2riM2riSG1<IHCXJ,!M{XJ,I))), POSSi;;{ RE <X~. Ol l : PDSC HOl Zl

0 a (P:NIS•R•CIHCXloOlJ TlO ·- POSPltRE2oiH2oPOSSQ(~((X>•O>•

POSSQC IIHXh P» : POS( KOJ 2> 0 ~ TH ·- 7Hl"L.IHP~(1Sft~·<IM<Xl•O>•POSCMGD2J~

[T: IS"R•CI M{ X hO }JT9(T h [T:NIS"R•(JM(Xlo0JJT10(T)J POSCKO) 2)

-Y3 s

N a LEMHU ·- TH1~L.IMP•<IS•R•<RECXJ~OJ•POS<MOD2l• CT:Is•R•tRE<XJ.O)JT8•.v3•(f), [T;NIS•ft~(RECX)~OJlT11•.v3•tTlJ : POSCHOl ZUl)

x a LEMMA5 == THt•t.IHP•<IS<XrOCJ~NOT<NEG<MOD2llo [T:IS<XoGCJJONOTN(MOD2•LEMMA3(f)); tT:NIS<Xr0CJJPHOTN(HODZoLEMHA4(T))) : NOH NG CHDOZ•O• rs•R•( IIHX h HI<Y> hO• TSOHRE<Xh RE(Y Jo TlJ,TSOl<IMCil.!HCYJ,TZJJ~ SATZ187CCO.OrOrPLOZCO•O•REfiSCREAL•O>l )) : IS"'R•(!t ETSC x,. YJ,. 0)

"' :: TRIS<REAL•IMTSCXrYloPL"R•<O•O>•O• ISPltZ•a•tTs•R•<RE(X),.IM<YJlrC• TS•R"Cllt{XJ.RE(Y)),O,TS01CP.ECX)o!K(Y), T1JrTSOl<IKCX>.~E<YJ,T2J), PlJZ(O.OoREfiS<REAL•Oll> IS"R•<IHTSCXrYloOJ

•3221 s

SATZZ2U == ISRECX12CRETS(X,YlrOoiHTS(XrYJrOr T3•.322t•rT4•.32Zt•J : IS<TSU ,y ), OCJ

y a U;IS<YrOC)J SATZ2Z18 := TRIS<CXrfS(XrYJ,TS<YrXJrOC•COMTS<XrY)r

SATZZZlACY.Xri)) I SU SU ,.Y),OC) • 5.14 -'( .oc>l

h32Zl

I 2 CN:Ntsn.ocn T5 :: LE1'4MA4(Y riU POSC MOl ten) T6 :: rR4SlC~E~L~RETStX,YlaOaREtTStXaYJJa

REIS ( RET Stxa Y),. I!IT S< !Ca Y)), LE~KAlCTStXaYJ,I)l : lS•R .. H ETSC X•YhOJ

H :: TPISlCREAlri~TSCXrT)~Orl~CTSCX,.Yl)a I M! S ( RET SC X, Y 1 , I !IT S { j: • Y ) l • lEMMA2<TSCX.Y>ri iJ : IS""R•U HTSO:a U a0)

T8 == TRIS!REALrPL·~·crs•R•CRETS<XaY)rRECY)) aTS~RM{!~TS(XrYl,!M(Y)))~Pl~R•(O,O)r0•

ISPl12~R~crs•R"(RETStXaYJ,RE(Y))a0r >S"R"<IHTS{X,Y)r!~~Yl)r0•

TS01(RETS(X,Y),.RE~Yl•T6>r TS01{!HTSCXrYlriYCYl~T7JJ• PL02{0,0,REFIS(RëAL,~))) : IS•ft•p L•R•ns•R•<RETS u,.r hRE( Y> h TS•R"<I!'TS(Xr Y ),.

l!HYl)) ,o) y :1 IIlR :: TS•R•crs•R•Ct~CX),!~CY))aRECYJJ REAL

IliR ·- TS"R•CIM<XJ,TS•Rw{!KCYl•Rf(Y))) REAL IRli ·- fs•R•(TS•R"C!M<Xl,Rf(Y)),IM<YJ) : REAL Il~I ·- TS"R"t!~<XJ,TS"R~CRECY),JKCY>>J REAL R!UR ·- TS•R•<TS•Rw(RE(X)r~E(Y)},q((YJ) REAL ~1!B :: TS•R•CRE(X),TSr~~c?.ECY),RE<YlJl REAL RUR :: TS'"~ .. < Ts•R•( R;::(X h I HUl hRE'O J l : REAi. !Hl~ ·- TS~R"(R((XlrTS"R~CIH(YJrRE<YJJl : RE Al RUI == TS"Rn(TS"R"(Rf(XJ,IMCY)J,lM<Y)l REAL •uii ·- TS•R•(Rf(Xl•TS~R"(I~CYJriM(Y)JJ : RE At.

" :1 T9 ·- TRIS<REAL.!IlR,I1IRri1RlrASSTS1<IMCXlr' IMCY)rRECYJJ•ISTSZ"R"CTS"R"CIHCYJ• RE(Y)),.TS"R"CRECY)rl"CYJJ,IMCXJr COMTS"R"ClM<Y>rRE(YJJ)l : IS""R"U IlR• URI J

T10 := TRISCREAL~rs~~"(RETS<XrY)rRE(YJ), KN"R"<RR1Rri!lRJr~~·R"(RlRR•!1RII• OISTTHlCTS"R•tRECXJ,RECY)),TS"R•CIHCIJ •I~CY)l•RE(Y)JriS~NlZ"R"<RR1R•RlRR~ IllRrilRI,ASSTS1<R!<X),RE(Y),RE(Y)), f9)) : ts-a•n S"R"<RETSCX• n. RECY') h MN,.R"'( R1RR,I1RI))

TU := TR3IS(REALrïS"R"CIMTSCXrY).IMCY)), PL*R«<Rill•IRl!l•Pl"R•CRlii•IlRIJ• PL•R•<I1RI•~l1l>•DISTTP1(TS"R"<RE<X)r 'I"(Y)J,TS"R"CIK<XlrRE(Y)JriKtYJJ, ISPtlZ•R•CRI1I,R1II.IR1l•IlRI• ASSTSlCRECXlriM{Y)~IH(Y)),ASSTSl{!H(X)

"RECY h I M( Y> l lrC OMPL "R"{ R 1 It r I1P.I H : ts-a•cr S"R""( Il1T SC x, YJ, IMH J J,. Pl. •ft•( I lR X. Rl I I l) T12 == TR4ISCREAL•Pl"R*(TS"R•<RETS<X•Yl•RECY)

lrTS"~"<IHTSCXrYl.IM(Y)J)r

Pl'R"(MN"R"<RlRR•IlRilr PL .. R"C IlRI,!H ID ),. Pl "R"(PL .. R .. OIH'"R'" tR1RR• IlRIJ, IUU.Rl II>• Pt•R•<RlRR,Rl!IJrTS•q•(RECXl.MDDZ<YJ),. ISPllZ .. R•( TS":?~( ~::: T Sex, Y h RE< Y )),. MN .. R"( Rl RR, IlRI >. TS .. 'l,.( lHT St Xr Y hiMC Y)

JrPL"R"<ttRI•Rlii>rTlO•Tll>• ASSPL2"R"UIN•R .. C RlRR.Il RI hi1RI.Rltl ), iSPLt•R•(pt•R•<HN"R"CRlRR•IlRI)•IlRI>• RlRR.Rlii,PlMNCRlRR,IlRI)}, DISTPTZ<RECX>,TS•R•CRECYl•RECY)), TS"R•t UHY h t!'H Y)))) : IS"R"T" l"R'"CTS•R"CRETSUa J' hRECY> h TS"R•<Inscx. Y J, -5.15-

I~CY)))rTS•R•fREtXl,HOD2Cf)))

Tll =~ TRIS1CREAL.ts•R•CRE<X>,KD02(J)),O, PL*R•trs•R•(RETS<XrYJ.RE<YJJ, TS"R•t Il1TS ex, Y )~ IIHY l: h T12• 18) : IS~·trs•R"CRECX>•KOD2<YJ)•01

TH ::: OREl<IS•R•<RE<XJ,~),JS·~·<HOD?.(YJ,OJ,

SATZ !12C CREC Xl. KOOZC Yh T13 h PNOTOC~002(YJ~JSJ) : ts•R•n ECXJ 100l,

T15 == TRIS H REAlr TS .. R"G!H :o~ IIHY> hO,.· TS•R•<?.E<X>•RE(Y)), SA TZ·18 ZB <i S"R"{ ?:;:oo,. R!:! Yl ), TS"R"(lMIXJ·IMCY)),fil~tSOlCRE(X)r RE(Y ), Tl4)) : IS .. R•CT S"R"C IM< X h II'CY lh l J

T16 :: TRISlCREAL,TS"R"<IMlX),RE(Y)),Or IKTS<X.Ylr?LO!<TS"R~{P.ECX),IMfY))• TS"R"(!M<X>,RECY)),TSOl(RE(X),IKCY)r T14JhT7) IS"R"'U S"R .. UHU hREH )),.) )

[J:IS"R"CRECY>,.Oll T17 == TT"C.VJ•(y,.N,Ji NIS"R"( I!HY ),.Q)

T18 ·- OREl<I5"R"(lM(X),.O),IS~R"C!H(YJ,0),.

SATZl92CCI~<X>ri~CY),T15),T17) : JS•R .. UIHXhO) N ; [0:NIS"R"CRECY)r0Jl

T19 :: OREltiS"R"CIMCXl.OJ,IS"R"CRECYJ,O)r SATl19ZCCI~<XlrRE<Y>,T16)~0) : IS•R•<t HUJrO)

N ; TZO := THl"l.I~P"(ISwRftCRECY}~OJ~!s•R•<IKCX)r OJrtT:ts~R•(RECYJ.OJlTlStT>, [T:NIS•R~(REtYJ~Cl1!19(f)J IS .. R•CI PHXJrOJ

TZl :: TRISCCX•X•PLI(F.E(X),!H!XllrOC•ISPLICX) .ISRECX1ZCREfXJrO,IH(X)r0rT14,TZOlJ : tsn .. o:,

•3221 s

I • snzzuc := THZ"L.OR"<ISCXrDCJriSCY•OCJr [T:NISCYrOC>lTlt•.JZZl•CTJJ : ORCIS((,OCJriSCY,.Ot)J

y a [N:NISCXrOCJl[O:NISCY;OC>l SATZZ2ll == TH3"L.IMP•tiSCTSCX,Ylr0ClrOR<ISCXr0CJr

ISCYr0C)JrTH3~L.OR-ciSCXrOC>rlSCYrOCJ; NrD>~tT:ISCTSCX,Y>•OC;lSATZZZlCCTll : NISCTSI XrYhOCJ

+32ZZ s

x ; Tl := TRISCREAL.~N"R"CTS•R•tRECXJrlRl>r TS•R•CtKCX>~OJJ,HN•R•CRE(XJrOJ,RECXJr lSMN12,.R"( TS"R'"C RE <X >• lRL hRE < Kh TS•R•CIMCXl•OlrOrSATZ195CRECX)), TSOZCIKCXJrO•REFIS<REALrOJ)),. P~OZCRECXJrMO•R"(O)r SATZ17ó9(Q,REfiS<REAL,O)J)) : IS"R•(.IC N•R• ns•R•(R E<X hUL J. TS•R•( U'C X hO)), RE (l())

rz ::: TRIS<REAlrPl"ft•(fS•R~<RE{Il•OJ• TS"R*(lMCXl,lP.l)J,Pl"R•(O,!H(XJ),JM<XJ •ISPllZ•R"<TS"R"(R~(X),Q},O•

TS"R•<IHCXJ,1Rl>•IHCX>,TS02<RE<X>•Or REFIS<REAL•OJ)rSATZ195<IMCXl)), PLOlCO~IM(XJ,qEFIS<REAL•Oll) : IS*R•(»L•R•crs•ft•CRE<XJ,O),fS"R•CIH<X>•lRLJ),.IM<X>>

•3Z2Z s

x a SATZZ22 == TR3I S(CX,. TS< X.lc h Pl.ICHN•R,.<TS•R•(RE CXhlRLh TS"'R .. < H!CX>..DU,. PL"R•<TS"R"CRECKJ,OJ,TS•R"'<IHCX),lRL)) >•PLI<RE<X>riH<X>l•X~TSISZA<X•lRL•Olr ISRECX12<~N"R"<TS•R"(REC1),1Rtl, TS•R•CIH(Xlr0)},RE<X>• Pt•R•<TS"R"(RE<X>rO),TS"R•CIMlX),lRLll -5.16-, Il't<Xh T1".3222'"" tz• .. 3222" h PLU SU>) Is U SC( rlChXJ

SATZ222A :• SYHISfCX,. TS( l•lChX~> SATZ222l : IS <X• TS CXrlCH SATZZ!ZB := TRIS<CX.TSClC•XlriSIX•lCl-Xr

CDMTSC1C,X).SATZ222l ISCTS<l CrXhX)

-32Z3

SATZ22ZC

Tl

T2

SATZ2Z3

SATZ223A SATZ223B

SATZZ23C

Y ; RXRY IXIY UIY IXRY n

:= TRIS( REAlid'IN'"R•CTs•R'"( ~EC )( >• MO*R"URL l J~rs•R•(IMtlJ~M?•R•(Ql)}, MS'"R•CMO'"R•<RE(X)J,aJ,MQ"R•cRECXll, ISMN12"R"( TS ,.R•( RE Cl( hM? .. R"< IRL > h HO•R"CRE{~)lrTS"R~{I~(X),MO"R•(Q))~O, TRISCREAL.TS~R"CRECX),~~·R•<lPL)>~ MO~R•crs-R~{RE<X)•1Rll),M0'"R~CRECX)),

SI\ TZ 1 9 7 S ( R ~ < X h l RL h ISHOPR~trs•Ra<R~(Xl•!RLJ•RE(X;,

SAiZ115(R[{~~)I),TS02CI~CXloMO"R"(0Jr

SATZ17&BCO•REFIS<REAL,OJJ)}, PL02CHO"R'"(RECX)J,M0"R'"'O>•

: rsn .. rs nc,.xn

SA TZ 1766 C 0, REF IS <RE At, 0)) IJ : IS-~t•n N'"R" <TS•R .. CR E<X h Ml *R'"{ 1 RL}), TS"R'"( Ilo!(X),

:: TRISCREAt~?t•R•crs•R•(R[CX>,HO'"R'"(0)J, TS"~"(IM(X>•~'·Rft<lRlJ)), PL~R"COrKO•R"(IMCX))),MO~R"(I~<X))~

IS?l12~~~\;S•R~(R~tX>•~?·R•<O)J,Or

TS"R~CJM(X)rMD"R"ClRLJ),HO•R•CIH(X))r

TSDZCR((X>•~O"R"(Q),

SATZ1768CO.R~FIS(REAL,OJJ), TR!SCRE~t.rs•R"C!M<X~.MO-R"C1RtJ), MO•R•<rs·~·CIMCX),lRt)J,MO"R•fiMCX)J,

SATZ197BCIM(X),1Rll• ISHO•R~crs•R•<IKCXlrlRLl•IMCX),

SATZ195CIHCXJJJ)JrPl01(0•MO•R"CIMCXJ)r

KO-P.•(,))J,MO"R•CRECX)))

REF"I S( REAL,.O J l > : JS"R•Pt•R•CTs•R•(R[(X hM3"R•(O)), TS'"R•UHUJ,

;: TR,ISCCX.TSCX,HOCICJJ, TSCX•?LI<HO"R•(tRL>•~O·R•CO)))r

PLI<MN'"R"CTS•R•(RECXJrKO"R"(lRL)), TS"R•CI~tXJ,MO"R"COJ)},

Pl"R•CTS"R"(RE<XJrHO•R•(O)), TS"R"CIMCX).~0"R"(1RLJ)))~

PLICHO"R"CRE<X)J,"O"R•CIHCXl));KOCX)~ ISTSZC HOUCJ, Pt:( ~O·R•(lRlh ~O"R .. (O) h KrMO ISH lRl• 0 J Jr TSI SZ.U Xr HC"R .. ( 1 RL)., MO"R"(OJ>•ISRECX!Z<MN"P"CTs•R•tRE(Y.); HO•R•C!RlllrTS"R"<IH<XJ,MO"R"COJJ), HO"R•CREC~l)rPt•R~CTS"R"<~ECXl• KO"R"(0))~TS"~"<IP.CXJ~M~"R"<1Rl)));

KO"R•Cl~<Xllrf1".3ZZ3•,rz".3223"l•

MO"R•(l RL)) hMO'"R'"( IH( XlH

SATZ214A(Xll . ISCfS(t,MO(lC))rHOCXJ) :: SYMISCCXrTSCX~M0<1ClhM~HXJ .. SA'l'ZZ23J ISCKO(( hTS<X.KOUCJ)) :: TRIS (C Xr TS 010( lC), X h TSO:,MO< lC) .),

MO{Xl•COMTSCHDC1C)rX1rS4TZ223) ISCTSC~O(lClrX>rMO(X)) := SYMISCCXrTSt MOUCh X hKOUhSATZ2238) : ISCIIOC'( hTS< HO( lChX))

:: TS"R•(RE<X>•R~<YJJ := TS"R•tiMCX>.IMCYJ) := TS*R•(R({Xlr:H<YlJ := TS"R-CIH(X>•RE(Y)J ·- TR4 IS( RE. AL ~MN,.R'"( TS"R .. ( MO"R"f RE( Uh

RECY}l,TS•~•(HO"R•(IM(X)),IMCY))),

REAL RE Al REA:.: REAI.

s

s

-5.17-

f2

-322ft

Y - SATZZZU:

SATZ2Z48

SATZZ24C

SATZ2ZitD

SATZZ24E

SATZ224F

KN"R-t~o-R"tRXRT1~~~ft~r{lXITJ1o

PL"R•(MO"R"(~XRY),!XIYJ,

~N·R"tiXIYoRX~YJ,~O"R~<~~·R•(RIRY~

IXIYJ).IS~Nl2"R"(iS"R•tMO"R•CRECt)Jr RECY!JrKO•R•!RXRYirTS•ft•(MQ•R"t!MCX)lr IHtYl)r~O·R•tiXIY>~SATZ197AC~ECXJr RE<YllrSAiZ197ACI~{X)~IH<Y>)lr ISl"tZ•R• UIO'"R .. C MO"R" < IXI ~ J), I XIY • MO"R"CRXRYl,SATZ177{IX!Yl)r CC~Pt"R·C~O"R"(RXRYlo!XIYJa SA iZ 181A U XI Y • RXP.'!' l) : I s•R•f'l N•R .. <TS"R "( I!O"R •<RE 00) • RECY) h T S"R"( MO"R"( !HC X)

:: TRISCRrALoPl~R•crs·~·(MO"R"<RECX>>• IM<Y)) • TS"'?.'"( MO•P. .. ,IXRY)r HO"R•CPL"R"CRXIY,IXRY>lr ISPL 12•R'"( TS'"R .. (HO"R .. t RE< X)), IlH U), MO .. R"<RXI~i•TS"R~CMO"R"(!MCXl)•RECY))~ "0"R~(IXRYJ.S~TZ197ACRE<Kl.IM{Y)J~ SATZ197ACIH{Xl,~~(Yl>>•

),; VHYl ) bMO"R•OUi"R•c RXRI' • IX IY>))

SATZ180A<RXIY,IXRYll t IS·~·c~L-R"CTS•R•tMO"R•(R~CXJJ~I,<YJJ,TS•R•<MO"R"CIM(Xl >•P.ECYl >>•MOwR"<PL•R"CRXIYriXRY)))

:= TR4lS(CX,TSCMOCXJrYl.· TS<PLICKO"R"CRE(XJl,MO"R"CIMCXJ)lrY>~ PLICHH•R"<TS"R"<MO"R"(RE(XllrRE(YJ), Ts•R"CHO"R"CIM(X}J,IM<Y>>J~ PL"R•(TS"R~(HO"R"<RECX>>•IM(T)),

TS•R"CMO~R"C I~CXJJ,RE(Yll>l• PliCMO"R"(~H"R"(TS"~"(RE<X>·RE(T))• TS"R"CIH<X>•!M(Y1lJ>• UO"R"CPL"R"CTS"R"CRE<X>~IK<Y>>• TS"R"<IHtXl•RECYlJlll•MO<TS<X•Y)), I STS H MO <X)~ PLI< KO•R"< RE< X)), MOPR"CIH<X>>>•Y•SATZZ14<XJJ, TSISlA<Y,HO"R•<RECXJlrHO•R"CIMfX)J), ISRECX12CKN•R"CTS•R•CHO•R•CRE(X)Jr RE{YJ>~rs•R•<MO•R•<IKCX>>•IMCY))), HO•Rw(MN"R"CTS"R•CRECXJrRECYJlr TS"R•<IK{X)riMCY)J)), Fl~R•CTS"R"C~O"R~(RECX)l~IH(Y)l• TSPft«(HQ•RwfiM(XJJ.RE{Y))), MO*R"CPt•R~CTS"R"CRECXl~IMCYllr TS•R•<IMCXlrRECY>>>lrT1".l2Z4", T2".3224•)•KOISBCMN•R•CTS•R"<RE(X)• RECYl)rTS"R•(t~(Xl•lHCYJ)>• PL•R•crs·~·CRE(X),IM<Y>l7TS"R"tiHCXJ• RE<Y)) l J J IS<TSC'40(XJ,YJ,MO<TSOC,.YU J

:: TR3IS< CX "'TSC X• KOCYH• TSOIOCYJ,. X>r MO<TS<Y, X> h 140CI'SCX, Y> hCOMTSOC• KO<Y) J •SATZ224ACY•X>•IS~OtTS(YrXJ•TS<X~Y>r COHTS(Y,X))) t ISCfSCKrltOCUhKOCTSU.YH)

:: TRI52CCXrTSCMOCX>•YlrTS(X.MOCYll• HOCTSCXrY1)rSAT7.2Z4AoSATZZZ46) : IS<TS{~Q(X)rYJrTS(X,~O(Y)))

·- SYMIS(CX•TS(~0(K),Y)riS(X.HOCYJ)r SATZ2Z4C) ISUSU rM0(Y)hTSC!10CXJrn)

:= SYHISCCX~TSCMOCX)rYJrHOCTSCX.Y))r S4TZ2'24U : IS<MOH SUr Y )), TSUO<X J. n)

::: SYHISCCX•TSCXrMOCY)JrMO<TStX•YJJr SATZ2249) t !S("tCH S<XrYl),TSClt .. MOCYU)

s

- 5.18-

•322&

SATZZZ5

SATZZZ5A

Z :il RR!1 IIR iUI I 1H RRI III RIR IRR Tl

Tl

:: JRIS{CX•TSCM~CXl•HOtYl>•TS{X,MOtMO(YJJ J,TSCX~Il•SATZ224C(X,M0(Y}l• ISTS2<MOU!O<Y1 h Y,'f.., SA rZZ15<Y>n : lS<iS(ltOCXJ~MOC'OJ..TSC l(,Y))

:s SY~IS(CXrTS(~0(X),~0(YJ),JSCX,Y1• SATZ225> IS(TSU ,YJ,TSCMOCU.Hl)(Y)J >

:: TS•R•(TS•R•(~~CX>.RECY)),RECZ)) :: TS•R•trs•R"l!~(XlriM<YllrRE<Z>J := rs~R•(~S"R~<HEtX!,fM(YJJ,IMCZl> :: Ts•~r<TS"~~(!~CX)~?.ECYJ),!M(l)l := TS•R*CTS·~·C?.~<Xl,~E(Yl>,IM<Z)) :: TS"R•{TSftR•(IM(XJ,!MCY>>•I~<Z>> := TS•R•CTS~R"(RE(X),IHCY)J,RECZ)) :: TS"R•CTS'"R"( Ill{::O•RE:<Y)).oRa:::<ZH :: TR3IS(F.EAL,MN•R•<TS'"R"<P.~TS<X•Y),RE<ZJ

!•TS'"?.~CIMTS(X,~>•I~CZ),l,

H~·~-(M~·~~{R~R~IIR>~P~~~"<RII,[Rll),

?L•?.•(RRP.•Pl~R·c~~~R~!IIP.l,

MJ~R"<PL*R•tR!I.!P.IlJ)),

XN·~·<RRR,Pl"q"(IIR•PL•R•CRilriRIJ)),

ISMN12"R"{TS•R~CnETSCX~Y>rRE(Z)),

~~-R"CRRR•IIRlrTS"R•(tMTSCX,YJ,JM(l)J• Pl~R"{RII,!R!>.O!STTM!(TS"R~CRECX), RECY)), T S .. R. ( P!{ Xh UlO')) • R~ ( Z> i, O!STTPlCTS•R•(RE(X),lHCY)),TS•R•(IMCXr ·~ECY))riH<ll)),ASSPL1•R•(R~R•

MO"R"<IIRJ,MO•R•(Pt•R•(RII·IRJJ)J, ISPLZ•R•cpt•R•(MO•R•ttlR>• H~•R•(pl•R•CRII.IFI)l},

xo•R,.< PL *R•( IIR• PL •R•C RII •lP. I)) hRRR"

: REAL REA~ P.F.:AL ROL REAL REAL REAL REAL

SATZ!30ACIIR~PL•R~<RII·IRI>>JJ : IS-R·C~N·R•CTS•R•<RETSCX,rJ.RECZ)J,TS•R•Ct,TSCX,YJ,

:: TR3ISCREAL,PL•R•<TS•R•CRETSC%,Y>riHCZJ ),Ts•g•(IMTS<XrYlrRECZ)Jl, PL•R•CMN•R•tRRiriiil•PlftR'"<RIRriRRlJ• PL"R•( Pt .. R"C RIRr IRIU, MN,.R'"_(R!U,I Il )) • MN"R"<PL"R"(Pl"R"CRIRriRRJrRRilriii>r ISPLlZ'"R'"<TS•R•CRETS<X,YJ.IM<Zl), MN'"R"CRRiriii>rTS•R•<I~TS(X•Y>rRr<Z>l• PL•R"CRIRriRRl.OISTTKlCTS'"R"<RECX), RECYJJrTS•R•(JM(XJ•IMCYJJ,I~CZ>l• DISTTPl<TS"R"{RE<XJ,IH<Y>>•TS•R•CIM<X) rRE<Y>lrRE(ll)},C~~Pt•R•<MN•R•(RRI• III),pL•R•<RIR,IRR)), ASSPLZ~R•(PL"R•(RlR•lRR),RRI• MO .. R"C II I)})

:= TRIS(CX.TSCTSCX•Yl•Z>• PLICMN*R•<ïS"R•CREiSCX.YlrRECZll~ Ts•R•tiHTSIX,YJ.!MCZl)), Pt•ft•(TS"R"CRETSCX.Y),IHCl)), rs•R*CIHTS(X,Yl•RE(l)}}), PLICMN•R"CRRR.PL·~·<ttR.PL·~~cqii•IRIJ )),KN~R-CPL~R•(rt•Rw<RIR•IF.F.J,RRIJ•

I!I)),TSIS1ACZrP.ETSCX,YlPIMTS(X,Y))r ISRECX12{MMRR~<Ts•R•<RETS{X,Il•RECZJl• Ts•R•(IMTSCXrY)r!M{l))), xrrR"( RRR• PL *R .. < HR .. Pl*lt .. C RH• IRI)) J • PL•R-CTS*R•tR[TS(X,r>,Ia(ZJ), rs·~·{IHTSIX,YloREtZlJ),

IMCZJl)rHN•R•CRRR,Pt"R"(IIRrPL•R•CRII·IRl)J))

Is•tf•(" t•R•ns•R .. <RETS n.r h lf4C ZJ h TS"R•ct !'TS<X.o Y >• Rt<Z>»•KN"R•<PL"R'"(Pl"R•tRIR•IRRlrRRIJrJIIll

- 5.19-

TlO

T11

:= !SMN12•R•CPL•R"<PL•R•CRIR~IRR>~RRI>, Pt•R"CPt•R"'RIRlriRRlJrRRil>,IIIriiil' T8rT4CIH<XlriM<Y>riH<Zll)

·- TRisccx .. rsnscx.n .. zh PLI<H~·R"<RRRrPL"R•ctiRrPL•R•<RIIriRil )),MN"R•<PL"R"CPL•R"CRIRriRR>•RRilr III>l•PLI(MN"R"<RRRl• Pt·~·<IIR1.PL•R•<RII1,!Rlllll• MNwR"CPl"R•(Pl"R"CRIRlriRRllrRRil)r

· IIIlll.T3riSRECX12CKN"R"<RRR. PL•R"<IIRiPL"R•CRII•IRIJ>>• MN"R"(RRRl.Pl"R•(IIRlrPL"R•(RIIiriRill ))~MN"R•CPL"R"CPL•R•CRIR•IRRJ,RR!lr IIIlrMN"R"CPt•R"<Pt•RwCRIRlriRR1), RRrl>riiil>rT9.T10))

IS•R•CHN•R•CPL•R•CPl"R"<RIRriRRlrRRilriiiJ, MN"R"<'L"R"<Pt•a•<RIRlriR~llrRRillriiill)

- 5.20-

•32ZS

UZ

T13

Z a SATZZZ5 ASSTSl ASSTS2

c a n

o a rz

T3

z a r4

;: TRISCCXrTSCXrTSCYrZ''•TS(iS(Y,zJ,X)r Pl!CHN"R"CRRR1.PL"R"(I!Rl, PL"R"CRli1•IRI1))), !Ul"R*( PL .. R" r Pl. "R"< RI Rb• IRRl ), RRI 1 h I1Iill.COMTS(X,TSCY~Z)),f3(YrZ•X>>

·- TRisz~cx.rscrscx.y,,z,,rscx.rscr.z>>• PL!<~~"R"CP.R~1.?L~P.*C!IR!•

PL"R"tRIIl•IRil>l>• MN"R"(?lnR~<PL•R"CRIR1,IRRl),RRil)r

IIIl »rTll.oT 12)

·- ru•. 32Z&· := SATZ22& ·- SYHISCCXrTS<TS(X,YJ,.ZJrTS(X,.!SCYrl)),

ASSTSU

:: TR3IS!REAl•PL*R•(pt•R•\A,.BlrCJr rt•R•CArPt•R•CB•ClJ,pt•R•CArPt•R"(CrB) JrPt•a•<PL•R•tArClrBlrASSPLl•R•tArB,.cr riSPt2•R*CPL"R"tBrC),.pL•R*(C•BJrA•

PL•R•CIIR1~PL"R•<RIIlriRI1)))~ . MN•R '"P L "~"<PL"R .. CR IRl • IR:t 1 hRRU hliil)))

: ISCTS<X.iSCYrZlJrPLICMN"R"CRRR1r PLWJ'!"U IRhPL•R,.CRIIl• I~It ))). KN"R•<2 L"R"<PL"R"CRIP.l,IR~l),RRil>•III1JJ)

: ISnsn SU,. Y hZhTSfXr TSCf •Zl >)

unsu sex, Y >.n. rsu. rsn ,n" : ISHsn su .. n,z".rsn, rsH .. n > >

: IStTSCXrTSCYrZllrTSCTStXrfJrZll

CDHPt•R .. CSrC >hA SSPt2•R•.u,.c,.s U : !S-R•(" t•R•<Pt•R•(ArBJ rC)., PL•R•<rt.•R•( ArChB)) :: TR3IS<REAl•PL"R•(pt•R•tAr8JrPt•R•tC•D>

),.pt~R"(Pl~R"CPt~R•(A,B),C),,),

Pt•R•(ptwR•CPl"~"{A,CJ.Slrûlr

Pt•R•CPL•R"(A,ClrPL"~·ca,.O)),

ASSPtZ•R•tPt•R*CArBlrCr)),. ISPll .. R" CPL'"R"CPL"R•O, 3 hC )r PL•R•<rt~R·(ArC)r8lrOrTllr

ASSPtl~R"(PL•R"CArC>•BrOJJ

·- TRIS<REAL .. MN"R•( Pt•ft•u,s hPL •R•tc.O J) •Pl"R"CPt•R"CArBJ•PL•R•(MO•R•(C), HO"R•(OJJ)rPL•R"{MN~R"<A~CJ,HN"R"(S,OJ

)riSPtz•a•<MO*R"<Pl"R"{~,OJ),

PL•R•<HO"R"<C),KO•R"CO)J,Pt•R•<A•B>• SATZ180Ctr0)),f2(ArSrKO•R•<CJ.~O"R"(0)

~ IS•R•C 2 t•R•CPL•R"(ArBJrPL•R•<CrOJJrPL•R•CPL"R•CArCl• PL•R•CBrDlJ)

) ) : IS,.ft•(lt N•R"CPL •R•CA ... BJ rPL•R•tCrO)),. Pt•R•(Mt.•R•CArC h

:: TRIS<REALrMN"R"<TS"R"<RE<XJ, Pl•R•( RE(Y ), RE<Z>H • TS"R•(!~HXh PL•R•(IMCY>riH<Z>J)), H~·R•CPL"R"(TS"P."(RE(X>~P.E<YJ), TS"R"<RE<X>rRE(Z)}J,PL"R"<TS"R"CIMCX), I MC Y) h TS"R"( I M(lCJ, IIU ZJ lU • . PL•R"< RETS\X• Y h RE l'S (X, Z}),

HN"R•(S rD )) )

s

s

ISHtnZ•R .. {TS"R"C REC Uo ?L .. R"<RECYJ, RE(Z)>),~L"R•CTS"R"CF.ECX)•RE(Y)),

TS"R"<RE<K>•RE(Z))),TS"R"(f~(Xlr PL•R .. CI.IHYh IMCl)JhPL"R"<TS"'R"<I!HXJ,. -5.21-I lH Y J hTS .. R .. U ~l( X),. Il1( Zl > J.. OlSTTPZCRE(Ä)•RECYJrRECZ>J• DISTTPZCIH<X>•lM(~),IHIZll},. T3CTS"R"CP.ECXJ~RE<YJlrT5~RnfRE{X)• RECZJJ.TS~9•(IM!XJ,IK<YJ>,fS"R*(!~(X)r

T5

T6

•3227

· SATZZ27 OISTTP1

DISTTPZ DISPT1

OISPU

SAiZ22!1

DISTFHl

I"CZ))))

:: TRISOH:AL• Pt,.R•c rs•R''TREC X h Pl,.R"( I!HY h Jl'ltZ))), TS'"R•(IMOO, PL"R"C REtrh REU ll > >• PL "R"( Pt. "R"<TS,.f!""( RE (X J, I !H n h TS"R .. ( RE( X h !'HZ n l• PL .. R"< TS"R'"( UHX h REO' > }, rs•R"( !I'H XlrRE( l))) h PL"R.<l~TSC~•YlriMTSCXrZ>>• IS?l!Z•RPCTS"R"CRE<XJ,PL•R"<!H(Y), :~(z~;),pL•R .. CTSP~"{R:CXlr[~(Y)), TS•R•(RECXl~IM<Z>JJ,TS"R"CIH<Xlr Pt•R"~'E(Yl•RE(Z)Jl•PL"R"<TS•R•t!~(X),

REtY)),iS"R"fi~<XlrRE(Zll)r OISTT?2(F.E{X),IM(Y),IMCZJ), 0 IS TTP2,TS•R•<I~CX),RE(Y)),TS•R•(JM{X)r

IS"~ •(lt N•R• US'"R"CRE<X J..PL •ft•( RE<Yh REfZJJ ), TS .. R"'( IM< X) ;PL•R-t UHY h IM< Z>> JhPL'"R'"<RETS(Xp YhRETSCX, Z)))

REtZ>>>J : IS"~•(?L•R•(TS•R"CRE<X>oP~·R"CIM(Yl•I~CZ>>l•iS•R•CIMCX> ,.PL'"R•( RE<Y hREt Z> J )),.PL "~"(HIT SC x, Y h IMTSCX .. Z>h

:: TR3IS!CX~TS<X•Pl<Y•Z>>• PLI<HN"?.~<TS"R•<RECXJ.PL•R•CRECY}, P.ECZ)))oTS•F.ftC!M(X),PL•R"CI~CY>,.IMCZ>>

J)rPL"R"CTS"RutRE<XJoPL"R"<IM<YloiH<Z) JJ,fS•R•<I~tXJ,~l"R•(RE(Y}.?.ECZl)))),.

Pl!<PL"R"tRETS<XoYlrPETSCX,ZJ), PL•R•CIHTSCX,YJr!MTStXoZJJJ,pt(TSCX.Y) ,. TS( Xo Z> h TSISZA UoPt•R"(REl Y hRE{l) >o Pl"P.•<IM(YJ,.JH(Zlt)o ISRECX1ZCKN"R"(TS"R"(RE<XlrPL•R•(RECYJ oRE(Z))JrTS"R"(IM<X>•Pl"R•CIH<YJoiM(ZJ )lJoPl"R~CRETS(X,Y>•RETS{XolJlo

Pl3 R"(TS'"R"(RECXJoPL"R•CIM!YlriKCZJ))o TS•R•<IM<XJ,Pl"R"lRE<Yl.~E<Z>J!)o PL~R"<IKTSCXoYloiMTS(X,Z)J,T4oT5Jo

PliSlZBCRETSIXoYJ,.IHTSCX,YJ,RETSCX,ZJr tHTS<X•ZJJ) : IS{fSCX•PLCY•ZJJ,pl(TSCX•fJ,TS(X•Z>>>

::

==

== ·-:=

::

: ..

T6 ... 3227• TR3ISCCXoTS<PLIXoY>•ZJ,TSfZ,Pl(X,Y>>r PUT SC z, Xh TSC Zon h PL< TS( X.. Z h TSCYr Z> l•COMTS<PLCXrY>•Z>•SATZ227(ZrXoYJr ISPL tznscz,. u .. rsc !(,. Zh rsu .. n.rsn.u .c~HTSCZ .. X>•COMTS<ZoYJ>> SATZ227 SY~IS(CX•TS<Pl<X•Y>•Z)•PLCTS(X,.z)r TS(Y,Z)loDISTTP1J SY'IiS( ClC, TSC X• PLCYr Z) h PUTSCXoY h TS<X•Z)JrDISTTP2> TR4ISCCioJS(X,K~(Y,.z>>,.TSCXoPL<Y•HOCZ> )J,PltTSCX•YJ,TS<X•HOCl))J•PL(TS<X~Y>• HOCTSCX,Z>>>•M~(JS(X,.Y>oTS(XrZ)), ISTS2(H~{y,.z),pL(Y.M0(Z)loX•

SATZZ18CY,ZJJ,.OISiTP2(X,.Y.MOtZ)J, ISPL2( TS CX • HOC Z>), MO( TS< X• Zl h TS(Xo Y )o

S4TZ2248(X~ZJJrSATZZ10ACTS(X,.Y), rscx.z » 1 TR3ISCCX.TSCMN(X,YJ,ZJrTSCZrHK(X,Y)), MNCTS(l•X>•TSCZ•Y>l .. ~N<TS(X•Z>•iS(Y,z) )*CO~T5óMN<XrY)~Z>rSAiZZZ8CZoXrYJr

ISCTS<PL(XoYl•Z)•PLCTS(Xrl);TSCYrZ))) : IS<TSCXoPL<Y,Z)lrPLtiS<X,.r),TStX;Z)))

IS<PLU SCXo Yh TS<X• Z)) r TSl X•PUY ,z.)))

'

-:-- 5.22-

t3229

•3229

+•3229

IS~~lZ(TSCZoXJ~TS(X•Zl•TS<Z•Y)•TSCY•ZJ , CO~TS( z, X h CO.'IT scz,. Y))) : ISU'SCH NU• n,z hKNt'TS (X ,z h TSU ,.ZJ))

~ISTTHZ :• SATZ2Z8 ISCTS((,MNCY,Z)J,."NfTS(X,fJ,TSCXoZ))) ~IST1Tl ;: SY~IS(CXoTSC"~CX•Y>•Z)~HN(fS(X,z),

rsrr .. z u.nsn 111, tsot:HT su. z hT sn .. zu, rsc HtH x .• y l•U 1 01ST~T2 ·- SY~!S!CX,TSCX•MNIY•Z>)•HNCTSCX,YJ,

TS(X,Zll•DISTTM2> ISC~N<TS(X•YJ,TS(I,zJ),fSCX·M~(y,z))) Y ~ tM:WIS(Y,OC>ltU1:COHPLEXJ(U2:CO~PlEXl[I:ISCTSCY,Ul>•X>

J[J:!S(fS(Y,UZJ,Xll

Tl TZ

T3

SATZZZ98

N OI n J

rv :REAL J DO

N :1 f5

T7

re

:: TRIS2CCX,.TS(Y,UlJ,TS(Y,Q2J.x,I,J} :: TRISCCX•TS<Y·H~CU1,U2))•MNCTSCYoU!J•

TSCY .. U2)),0C,aiSTTM2(Y,U\rU2>• SATZ2l391TSCYrUl1•TSCY.U2J~T1>J

·- 0~~2{!S{Y~9CJ,!S{MNCU1,U2J•0C), SATZ221~~Y.MN(U1,U2i•T2J,~l

: Isnsn .uu .. rsn,uz))

::: PNOTOOIOOZ<YhLEMMA4(Y,Nl> : NIS•R-c H002(Y},Q) := TS(Pli<CVCREU),KOOZCYhTit >~

KO•R•UlVUH( n ... HOOZ( n,. Tit) Ho U : COMPLEX

:: DVCV,KODZ!YJ.H) : REAL ·- TR3IS<REAL•MO~R•(fS•R•(tHCY),

M0•~*(00(l"(Y))})),

MO•R•tMO•R•(TS-R"(IMCYJ,OOCIHtT))))), TS•R"CiM<Vl,OOCIKCY)))~00{TS•R•<IMCYJo IM(r)l)o!SMO-R•crs•R•(JM{Y), MO•Rft(OO<IH{Y))))oMO"R"!TS•R"(IHCY>• DDCIMCYJ>JJ,SATZ197BCIMCYJ,QO(JM(YJ))) .S-TZ177CTS"R"(IMCYJ,OO<IKCYl)J), LEMMA&( I'lt Y),. IKC YJ, HC!>2( Y>• H)) : IS"'!f"'('tO•R•<Ts•R•( IH(Y hM) "'R .. CDDtiHCYJ)) >) •

:= TR3IS<REAL,HN"R•(TS"R"(RECYJ.DOCRE(Yll >•TS·~·<IMCYJ,MO•R•(OOCIHCYJ)))J~

Pt•R"(09(TS"R•<RE<Yl•RE(Yl)), OOCTS"R•(IH<Y1riK<Y)))),00fH002(YJ), 1RL• ISPUZ"R"( TS"R*( RE< Yl .. !HHRE 0 l U • OO<iS"R"<~E<Yl,RECYJ)), MO"R"<TS"R~<IMCY),KO"R•(OO(!KtYll)J),

00(TS•R•(IHCYJriM<Y))),.L[HKA6CRECY),. RCCYJ .. ~lOZCYlrT4>•T5>• LEHHA7CT S .. R" CRE<Y h RE<Y > h TS .. R .. ( IH:Y )o

ODCTS•R •t IIHU,IMCY ))) )

IHU) hMOOZ< Th T4hlEKHA8CM002n hT4 )) : IS·~·<~ N•R• CTS•R•(REU ).,DO UEU))), TS,.R•( I 11( Y h HO-rt"CO 0( I lH Y)))) h 1Rll

:= TR;S(REAL,TS"R•(REtll•MO•R"CDDClM(Y))) >•iS"R"tHO"R"CREiY)},.QO(IHCYl)), OOnS .. P."CMO"R"CRE{ Y> ), I:.I(YJ)),. SATZ1970(RECYlrD0(f~(Y})), LEHMAGOIO" R'" (RE( Y)} • IK!Y J •HOOZH h T4)) : IS"~":(f S'"R"'( RE<Y h .. O .. R'"< DJ (!HOl))),.

:: TRlS(REAL•PL•R•(TS"R"(~E(Y), NO•R•(OO<IM(Y)J)J,TS•R•<IMCY),OOCRECYJ J)),PL~P.~(00(TS•n•tHO•R•tREtY)J,IM<YJl ),~CCTS"R•CIV.(Yl,RE(Y)))),.

O:>H s•:t "<HO"R .. < RE<\" J h IMU))))

s

s

-5.23-

•3229

T9

110

T11

TtZ

N a SATZ!29A

SUZ229

:JV SATZZ29C SATZ2Z9D SA TZZ29(

OOCPL"R•crs•~•tHO•R•CRECYJJ,IMCY)J~ TS"R•<IM(Yl,RE(~)))),

ISPll2 .. R .. ( TS "R•( ?.E ( ~ hMO"R"(!}O (I lH Yl)) J-Dn(TS•R•(HO~R"(R~CY)JriHCYlJ), TS•R"'C I lH 'l' h OO<RE<'O )),QOOS .. R"UIHY ), RE<Y>llrT7.LE~~A~f!~{YloRECY);HQ02(Y)~ T4JlrLEH~A7CTS"R"(HD•R•(RECYtlPIHCYJlr TS,.R•( I HO' h RE( Y>), HOD2C Y), f4))

:: TR3IS<~EAL.PtMR"{TS"R•(H~"R"<RE<Y>J• IH(Y)J,TS"R•(t~(YlrRE(Y))),

PL "R"'( HO'R"( TS"R"( RE t1 hHH Y))) • TS~R"{[HCY>rRECYJJ)rN~·R•CTS"R"CI~(Y)r RECYJJoTS•R•CRE(Y)•I~CY))),O,

ISPLl"R•CTS"R"<HD•R•(R[(Y)l,IMCY)), MO•R•trs•R•tR~iYl•I~(Y))),JS•R•CIMCTJ~

RECTJJ•SATZ197ACRE(YJ,1MCYJl), CO~Pl"R•(M~·R•CJS•R"(R~(y),I~<YJ));

rs•R•CIMCYl•RECYll)r SAiZld2E<TS~R~<IM(YJrRE<Yl>~ Ts•?."CRE(Y)r!~{Y))~COMTS"R"(IHCY),

: IS"'R•(~t ,.R~trs•R•(Rf(Y hM) ,.R .. COO( ItH U))) rlS .. R•t I lH Yh DOCRE(Y)J)),QO(Pl"R"<TS"R•<MO"R"CRE<Yl)riK(Y))p Ts~-CI IHYhRECY ))) ))

RE<YJ))) : IS-R•<'L"R•crs•R•<HO•R•<R~(Y)J,I~(Y)),TS•R•CIHCY)rRECYJ

:= TR3IS<RE~lrPL•R•(fS•R•CRE(Y)P H3•R•(00(l~(YJ)l)rTS~R·CIM<YlrDD<RECY>

l)),O~(PL•R•CTS"R•CMO•R"<RECYJJ,IHCY); .rs•R•<IKCYl•RElYJ))J,DnCOl•O•T8~ ISFCREALrREAt.tT:REALlDO<TJr PL"R•crs·R~(MO•R•(RE<Yl>•IHfY)J~

TS•R•CIMCY),q[(Y)))r0rT9),

lhOJ

lEM~A9(H002CYl.T4l) Is·~·(~L•R•(fS•R•(RECY)rH3•R•(DDCIH(YJ)J),tS•R•(IMCY),

:: TRIS(C~,TSCYrPLI<DD<RECYJ), HO•R-(00(IMCYJ)l)}, PLICHN•R•<TS"R"CRECYJ•ODCRE<YJ)Jp rs•R•(IM<YJ.HO"R"<DD<IH<YJJJ))~ PL•R•(TS•R"<RECY>•HO~R•CDOCIHCYJ))), TS"R•(IK(Y),OO<R((Y))J)J,lC, TSIS2ACYrDDCRECY)),M0"R"COOC1HtYlJJl• ISRECXlZCKN"R"CTS"R"CRECYJ,DD<RECYJ)J, TS"R"<IM<Yl•MO"R"<DD<IHCYJ))J)rlRl• Pl"R"<TS"R"CRECYJ,HO~R"CDO<IM<Y>JJJ,

DOCRE<Y)))) •0>

TS"R .. C liHY J. OO<RHYJ)) hO • TEir TlO J) : ISUSCY •Pli (OO(RE<Y )), MO"'l•(DDCIMCU)) )), 1C) :: TR3ISCCX,TSCY,U>rTS<TSCY,PLI<DOCRE(YJJ

•MO*R•COD(I~CYJ))))•X>•TS<lC•Xl•X• ASSTS2(Y,Pli<DDCRECY}),MO"R"<OD<IH(Y)) >>•X>•ISTSlCTSCYrPLICOOCRECY)J; HO"R•COOCIHCYJJ))J,lC•X•Tlll• SATZ222BU))

:: SO~EI<CX,[T:CXliS<TSCYrTt.x>,u~.3ZZ9•• T12 ... 3229'")

:= oN:: u ex, n :cxnsn sn ... n .. u .. n :c Xl (U: CX HV: I St TSCY, Th lO H !i :I SHS<Y•U> • X)lSATZ229S(T,UrV•W>,SATZ229A)

:: I~O(CI,.[T:CXliSITSCYrf),XJ•SATZZ29) := ON!: A x< ex .. r r:cxnsnsn. r ,,.X),SAT Z229, := SYHISccx,.rscr,ovcx,y.N}),x.sATZ229Cl :• TRISCCX.TSCOV(IoYrHJoYl.IS(f,QV{~,y.~)

ON Et n: cxnsnscv,r J.X n COMPLElC

: IS<TS(f,.OV(X,.Y .. N)J,X) tsu, Ti npovu.r.tu n

s

- 5.24-

Jr~r~U~I~\UVlA~IrN1r~1r~AiL~CY~J ,~\1~\JY\ArT•NJrllrAJ

SATZZ29F := SY'!lS':CX .. TSC:JV(XrY•NhYhX ... SIITZZZ90 : ISO:rli(OV<XrY,NhYU Y a [U:COMPLEXJ[N:NIStY.~CJl:r::~<~SClrUlrXJJ

SATZZ296 -- SATZZ~95~:: .. u .. ovcx,y~•n,IrSATZt29COHJ IS(IJcrOV<X.rYrNll SATlZ29H := SYHIS<CXrUr0VCXrYrN)rSATZ229G) IS<CVCXrY~NJrU)

N ~ rt:Iscrsca.Y>•X>l SATZ229J := SATZ221G<TRISCCXrTStYrUlrTS<UrYlrXr

CO~-iTS<YrU>.-I )) IS(Ur!.W (X,.y,N)) SATZ!29K ·- SYM!S!CXrU~DV<XrT,N)oSATZ229JJ I lSCDV(t,YrNJ,U)

Z ~ [IIISCXrYJJ(N:NtS(ZrOC>J ISOVl :: ISFCC~.cx.~T:CX10VCTrZrN),XrYr!) : ISfOV<CrZrNlrOV<YrlrN}l

I a cn:NISCX•~CJJ[O:NIS(Y•OC)] lSOVZ :: SAfZZ29H<Z•X,QVClrY.OJrN•

TRIS<CX•T3tXrCV<Z•Y•DlJrTStYr0V(Z,Y•GJ ),.z, ISTSH l(, ':',. OVl: z~ Y ~ 0 >.I l• SATZ229CCl•Yr0})) ISC31CZ .. XwN)rOVCZrY•0))

Z a {U:C~M?LEXlti:ISCXrY)](J:IS<?rUiltN:NIS(Z,OC)lrO:N!SCU,OCll ISOV12 := TRrsccx.ovcx .. z .. N: .. ovtr.z,N,,ovcr.u~o>•

Y a SATZZl~ SATZ231 SATZ2H

z ;a Tl

Z a SATZZ3l

SATZZllt

SATZZJitA

SATZ23ft8

SATZ!HC

SATZ235

ISOilCI•l•Zrl,NlrlSDY21ZrU,.Y,J,N,UJ} · := THISCCX.PL(M~(XrJ),y),pLCY.~~fXrYl>rX,

COH?l(~N(X,YlrYl•S~Tl212H(X,Y))

:= SATZ212E<PL(XrY>•Y•X•COMPLtYrXl) := SATZ212ECX,MNCXrY)rYrS~TZZ30)

:= TR3IS<CXrPlCPL(Y,z),KNCK~CXrY)•l))• PLCKNCMN(X,YJ,z),PltY,.Z)); PU MN( ~:OH X ,y), l) ,pl( z, Y) h P!..(PLO~NOI!H Xr Y)r Z ), Z lr '! h Cû~Pl<~L(YoZlr~~<HN(X,Y?,z>>•

IS?L2<PL(YrZ>•PLCZ~Y)rMS(KNtX~YJ~ZJr

tSf~~C·NCX;Y),Y>•X) IS<~NC~lCX•Y>•TlrXl

: IS<ICN(( ,MN(l(,.YJ),Y)

CO~Pl<Y•l)JrASS?Ll(HN<~N(XrYJ .. ZJrZrY)) : ISC~l('l(YrZJ•KN(ftN(XrYJrlll•PLCPl(HN(MN(XrY)rZJrlJrYJ} :: TRJIS(CirPLCPL<Y~z>,MNCMNCX,YJrZJ)r

PLCPLCMN<~HCXrY},ZJrZlrYJrPLC~NCXrYJr YJ,XrTlriSPLl(PL{MNC~N(XrYl•ZlrZlr MNCXrYl~Y,SATZZJOCMNtXrYlrZJJr SATZZlOCX,YJJ : IS<PLPL(T,.l),MNoCHH(X,.YJ,.ZJhU

:= SATZZlZOCX•PlCYrZJrMNCHNCXrYJrZ)r rz•.42ll"J : ISCMNC~NCX,YJ,.zJ,MNCXrPL(Y,l)))

:= SATZ212GtPL(X,YJrZrPl(X,MN(YrZJ)r TRIStCXrPL(PLCXrHN(Y.~JJ,zJ, PLCXrPLCMNtY•ZlrZJlr?l(X•Y>• ASSPLltXrK~(y,zJ,z>,[SPLZCPL(HNCYrZJr Z>, 'f • X, SA iZZ 300 • Zl J) J I SCMN(,LCX• Y hZ hPL (Xr MNU rl)) J

:: SYMISCCX.HN(PLCKrY>•ZJrPl(XrMN(f,Z)), SATZ2~4i : IS(Pl(KrMN(Y,.z)),MNCPL{X~Y>•l))

:a TR31SCCX.HN<PLCX~Yl.ZJrHNCPLCY.XlrZJ• PLCYrHN(X,.Z>>•Pl(MN(~,z),YJ. ISM~l H'l.U•Y hPLC·Y ,x Jr z,.cn~PL()r~ '() )r SATZZ34CY;X•ZlrCOM?L<YrMN[X•Z>1> ISCKNC2 LlK.Y>•Z>•PLCKN(X,z),Y))

:: S!KISICX•HNCPL(X,Yi•Z>rPLCMNCX .. Zl•Y>r SA TZ 23'•8) I SCPlOl N<Xr Z ». YJ rH~HPL OC•Y), Z} J

:= SAfZ212FCX~HN(J,z),PLCMNCXrY),.z), TRJ! SC CX,PU PL( M1H x,. Y), Zl•!HHY•l H• PllKKCXrYl•Pl(Z,KU[Y,ZJ)),PLlMN(X,Y),. y),K,ASSPLl(M~{XrYlrZ•MNCTrZJJ, ISPL2( P!..lZ•M~;(Y, ZJ h Y, Mt;( Xr Y h SArZ2l2HO'•Z) l•SATZ23CIO .. rn) ISC?lt'l rHXr YJrZ : .. 1-!NCXr H"lCY' rZ)))

s

s

- 5. 25-

+ ,.237

+lt239

-4238

SATZ235B

SATZZ35C

SATZ236

SATZ2l6.A

Cl.I:COHPLEICl

T1

rz

SATZ237

T1

f2

:• ~T"l~\C~~~L\"N{X•TI~41•"~\X#"R\fPL1I# SATZ2351 : lS<MN({,HNCY,Z)),PLCMNCXrYlrZ)J

;: TRISCCX•MN(XrMN{Y;Z)),pl(KNCX•YlrZ>• HN<PL<X,z),Yl~SATZ235A,SATZ234CCXrZ•Y) ) ; ISCliN<X•IfN(l';l)hHNC:PL(X;ZhY))

:: TRIS<C x, !1NU.MN!Y,. l) ), H~ICPL< X,l) r Ur HN(PL<Z•X)rYJ~SATZ2353•IS~Nl{PLCX•Z>r PltZrXI•Y•COMPLCX~Z))) ISCMN((,MNCY,Z)),MNCPL(Z,X),Y)l

:: SATZ2!2Gt~l(X•Zl•PL<Y•Z>•~~{X•Y>• TRISCCXrPL(KNCX.Y).PLCYrZ)), PLIPLCMN{X•Yl•Y>•Zl•PL<X•Z>• ASSPLZ!HNCX.Y),Y,zl,ISPL!CPl(~NC~.Y),

Y>•X•Z•SATZZJ~<X•!l)ll : ISCMN<'L(X,ZJrPL(YrZllrHNCX•Y>) ;: TRIS(CX,XNCPL<z,x>,Pl<Z•Yl>•HN!PLCX,Zl

•PL<Y•ZJ>•M~<X•Y>riS~N1Zt?L(Z•Xlr PLCX,zl,PLCZ,YlrPL<Y,Z>rCOKPL(Z,X>~ CO'iPU z, n h SUZZ3ó) . IS<MN P LCZ• XhPl<Z• Y>h MN( x .. n)

:: TR3tS<tXrPLCMNCZrUl•PLCUrY)), PLC PL( ~tlCZrU h Ul.Yh PLC z,. Y>rPlCY ,.l),. ASSPLZCHNCZ•Ul .. UrY>rlSPLl<PLC~NtZ•ü>r O>·Z~Y.SATZZ30CZrU)),CCMPLCZrYJJ TR3!SCCXrPLCPl(HNCXrYJ•M~CZrUllr PL{Y,UlJrPL(PLCHNCXrY),M,(Z,U>>• PtCUrY>l•PL(MN(X,Yl•Pl(H~(ZrUlrPl(U;Y) )),PL{MN{X,.YJ.PLCYrZJ)riSPLZC?LCYrU), Pl(U,Y1•Pl(MN(XrYJ,MN(Z,.U>J•CC~Pl(YrUJ J,,SSPLl(~R(XrYJ,KNCZrUlrPlfUrY)),.

ISPl2CPL(~~CZ•U>rPL<U•Y>>•PLCT•Z)r MNU, Yh Tl))

:: TR3IS<CXrPLCPLCHN(XrYJrMNCZrU)), PLCY.U)),Pl(HN{X,Y)rPLCYrZllr PLCPLCKNCXrYJrY>•Z>•Pl(XrZl•TZ, ASSPLZCM~(X,y),T,Z>#ISPllCPL<MNCX,Y),

Y1•X•Z•SATZZ30tX•Y>Jl

:: SATZ212HPtt X,.ZhPLtY.UhPLCMNtX,YJ• HNCZrUJ)rt3•.4zJT•)

:= TRISCCXrPL<PLCX,.UlrZlrPLCXrPLCUrZJlr PlCX•PLCZ•U>>•ASSPl1CXrU•ZJr ISPLZ<PL(U,Z);PLCZrUJrX,.COKPLCU,ZJl) : ISCPl(~L(X,UJ,Z>rPLCXrPL(ZrU)))

:: TRJISCCX,PLCMN(PLCXrU),PlCYrZJJ, MN(Z;U)J•MNC?l<PLCXrUJ,.Zl;PLCPL(Y,ZJr UJ ), H'-HPL(X• PLC Zl' UJ) rPLC Y rPUZrU) J h KH{X,YJ,S,TZ!JT(PlCX,U),pLCT,z>.z,u), ISH!U2C PUP!..( XrU), Z>r PU x,.?t cz,.ul h PLC?lCY,zJ,U)rPL<YrPltZrUJlrT1r ASSPL1<Y•Z•Ull;SATZZ36<X•Y•PLCZ,U>JJ : ISCPLt~NCPL<X•Ul•PlJYrZ))•MN(ZrUJJ,MNCXrYJJ

SATZZ39 :: SATZ212GCHNCXrYlrMN(Z,UJ,~NCPltXrUJr PLCYr~)),f2•.4Z36•)

CI:tSCHNCX,Y),HNCZrU))]

s

s

s

s - 5.26-

U4Z39

::: TRISH CX .. ~N( PL(X,'Jh PLCY,. zu,.o.c,. MNC~NCX,.YJ,M,tZ,U)l,$ATZ23~ ..

. SATZZllBOINC X• Y> .. ~N( z,.U), I) J

SATZZ39A := SATZ213~C?lCX.U>,~t<Y,z>,Tl•.~z39") U ; ti:IS(PL(X,.UJ,rLCY,.z>>l

I 01 rz ::: TRIS<CX,MNCKM(X,y),HNCZ•U)J,MN(Pt<X•Ul ,PLCY,Z)),.OC .. SATZZJ3,SATZ2138CPl(X,U), PlCYrZ>•I>l : IS(K~(~N(X,r>,MN(Z•U>),OC>

s

•4239 s

I ; SATZ239S := SATZ213A(MN(X,.YJ,~N(Z,uJ,T2•.4239•) IS(KNCC,YJ,HN(Z,U)J T a [N:NiS(Y,OCJl

s~rzz•3 := TRIS<cx.rstovcx,v.N>.Y>•TSir.ov<x .. v,NJ J,X,COMTS(C,(X,y,s),y),SATZ229C(X•Y,N> ) : IS<TS(]V(X,.Y,NJ,YJ,XJ

SATZZH :: SATZ229H<TSO:,n,y,.x,Pt.COI4TS(T,.X)) : lSC!JVHSCX,Y),y,.N),X) Y ~ CN:NIS(X,~C))[Q:NISCY,OCJJ

LEKKAS ·- THl•t.IMP•(JS(OVCXrY,Q),OCJ,ISCX,OC)• N,[T:ISCUV(X,Y,.QJ,OCJlTRISlCCX,x.oc, TS(Y,OVCX,YrCJJ,SATZ229C(X,.Yr0), SAT Z221B<Y, i.'!\' (X, y, C h Tl)) : NIS<OYt x,. Y, 0 J,OC)

SATZZ42 :: SATZ229H(X,GV<X•!,Q),y,LEHMAG• SATZ240C0)) ISC!JYU ,ovc x,Y,OJ.LEMMA6h U

Z ~ [N:NISCY.OCJl(DtNISCZ,OCll

+52ft! s

-5243

T1

rz

SATZ~H

Z ; [N:NISCZ•OCJl SATZZH

:: TR3IS<:X,TSCTSCYrZJ,OV<OV(X,Y,.NJ,z-oJ) .TSCOV(OY(X,Y•Nl•Z•O>•TSCY•Z>J• TSCOVCOV(X,.Y,~J,.z,o>.TSCZ,Y)l,

TSCTS{OV(OVCX•Y•N>•Z,Q),.z),yJ, CO~TS(TS(Y,zJ,GV<OV(X,Y.NJ,z,QJ),.

ISTS2CTS<Y•Z>•TSCZ~YJ,.OVCOVCX•Y•NlrZ• 0),C0MTS(Y,.Zllr~SSTS2COV<CV(X,.Y,NJ,.z, ohz,yu

== TR!Isccx.rscrscr .. z>.ovcovcx,y,.N>•Z•D>J ,. TSt TS(QVUiV (x,. y, ~; h z,o),. Z), Y h rscovcx.v.~> .. r> .. x.Tl• ISTSl(TS<OV(OVCX,T,")•Z•O>•Z>, QV(X,~.~J*Y•SA7~240CGV<X~Y·N>•Z•OJ>• SA TZ Z40<X, y, lH >

:= SATZ2Z9G<x~rs<r,zJ,ovcovcx.v .. NJ,z.oJ, SATZ2Zl0CY,z,N,O>.rzw.5Z43•>

:• SATZ229KCTSCXoY),Z,TSCX,QV(Y,Z,NJ>~H, TRIS<CX.TSCTSCXoOVCY~z,.N>>•Z>• TSCX.TS(OV(Y,Z,N>,Z)J,TSCX,y), ASSTSICZoOV(YoZrN),z), ISTSZCTSCOV(Y,z,~J.z>,y,x,

IS<TS(rSCY•l)•OV<OV(X,.J,NJ,.z,OJ),fSCTSCDVCCV(X,Y•NJ•Z• OJ,zJ,.Y))

ISCtJv<J V CX, Y, NJ. z,o b OVC X• TS<Y • Zh SA TZ2210 <Y, z,N, 0 >) >

$

- 5.27-

z a t52U

SAT2:240H.Z.o rO)))

SATZ~44A ::: SYMIStCX,QV(TS(X•Yl•Z#NJ, TS(l(, OV(Y, z, N) ), SA TZ244)

SA!Z~44 B ::: TR3I S{ CX• DVCTS<X" YJ, z, N>" OVtTS<Y .oX >.. z, N)•fSCY,QV(X~Z•N)J;iSCOV{X;Z•N),Y);

!SOV 1C TS<X•Y h Tstv .. X h z,tOMTS( X• YJ,N) • SATZ244( Y,. x, z, NhCOM!S(Y,. OVC X. ZrN)))

SATZ~lt\C ::: SY~iSCCX,CV(TS<i•Y>•Z•NJ•lStOY(X•Z•N)• Y>,SATZ2443J -

[N:~IS(Y,QC)](Q:NISCt .. OC>J SATZ~45 :: SATZ229JC~•OVCY•Z•Ol•TS<OVCX,Y,N),z),

LEMXAG(Y,z,N,O>.oTR3IS<CX,TSCTS<0V(X,y, NJ,z),QVCY•ZrOJ),TS<OVCX•Y•N), rscz.orcr.z .. o>>>·Tscov<x.r.N> .. Y>.x. ASSTSl(QV(X•Y•N>•Z•OVCY•Z•O>>• ISTSZCTS(Z,OVCY~Z,DI>•Y•OVCI.Y,~)r S4fZ229C(Y•Z,QJ);SATZZ40CX•Y.oN)J)

SATZZ45A := SY~IS<CXrTS{QV(K,Y.NJrZlr OVCX~OV(YrZ•Ol•LE~MA&tY•Z•N•O}), SATZZ45)

SATZZ45B := TRlSCCX.OVCX•OV(Y•Z•D)•LEMHA&<T•Z•N•O> ) , T SC OV (x. Y, N), Z h 01.· CTS {X • Z ), '!' ,N) • SATZ245A•SATZ244C(X,z,y,N))

SATZl45C :: TRISCCXrOVCXrOVCYrZr0Jrl~MM,6<Y,ZrNr0) >.~vcrscx.Z>·Y•N>.or<TSCZ•X>•Y•Nl• SATZZ45SrlSOVlCTS<XrZlrTSCZrXJrYr COHT SU,.l).oN))

SATZZ4& :• SATZ229K<TSCX,z),TSCYrZ)r0Y(X;YrN), SATZ221DCY•Z•NrOlrTRIS(CXrTSCOVCX.oYrN) rTS<Y,ZJ)rTSCTSCOVCXrYrN),y),z), TSCXrZ>•ASST52(0VCX•Y•N>rYrZ>• ISTSl<TSCOVCXrYrN>.YbX•Z• SATZZ40CX•YrN))))

SATZZ4&A := TRtsrcx,ovrrscz,x>.rscz,r>. SATZ22lO<Z•Y•O•N>>•OVCTSCXrZl•TSCYrZ>• SATZ221DCYrZrNr0}),0VCX,YrNJr ISOVlZCTSCZrXlrTSCX,z>,rscz,y),TSCYrZ> rCOMTSCZrX~COMTS<ZrYJ, SATZ221DCZ•Y•O•Nl;SATZZZ10CYrZrNr01lr SATZZ46)

[O:C~MPLEXJ(N:NISCYrOCll[O:NISCUrOC>J

Tl

TZ

T3

== TR3Isccx.rscovcz.u,o>.rscu .. v)J, TSCTSCOV<Z•UrOJrUlrY}rTSCZ·Y>•TSCYrZl• ASSTS2COVlZ• U.oO)rU,.Y ),. ISTS1CTSCOVCZrU.oOJ,C),z,y, SATZ240< z, u, Ó) hC!JIUSC z, Y)'

::: TRliSCCX .. TS(TSCOVCX•Y•N),OVCZiUrOJlr T.S<Y .oU) h T SC TS(OV(X, y, N h OV( z,u.o J ), TSCUrY)lrTSCOVCX•f•NlrTSCOVCZrU•OJ• TSCUr YHl. iSCOVC x .. y, Nh TS n, ZJ ), ISTS2(TS<YrU),JS(U,y),TSCOV<X•Y•N>• OVCZrUrOJ),COHTSCYrU)J, ASSTSl(OVCX•Y•N>.OV(Z,UrO>•TSCUrYJ)• 1STS2<TSC0V(Z,U.Q),TSCU.YJJ,TS<Y•Z>• OV(X,Y,NhTlU

:: TR3IS<CK,JS(TSCOVCXrY;N),QVCZ•U•O>l• TS(Y,UJJrTSCOV(X,Y,NJ,TS(Y,z))r TS(TSIOVCX·Y~N),YloZ)•TSfX.7)•T2~

: ISCDV(f SU.r YhZ;Nl.TSCX,.OI n~z,.rn) J

ISCOVU SU.o Y),.~ ,.tn, TSC CVU rZ•Nh '())

IS<TSClV(X,.ZrN)rYlrCV<TSCKrJ),.z,N)J

: lS(TSCTSCOV(X,Y.oNJ,.OV(Z,UrOJJrTSCYfUJJ•TSCCVCXrYrN)r TSCY•l) U

s

- s. 28-

-5241

SATZZ47

ASSTS2(01(X•Yr~)~Y·Zl~ IST$l(TS(0V(ï,Y,NJ~Y}rX•l•

SAIZZ40(XrY•!lJ)

:: TRIS<CXrTSCTSCX•U>•Z),TS(X,TS(U,ZJ)• TS(X,;$(Z,U>l•ASSTSlCX~u,z>•

IST~ZCTSCU•Z>•TS{Z,Ul•X•COMTSCU•Z)J) :: TR3IS<CXrTSCOVCTSCX.U).TS(Y,z),

SATZ221DCY•Z•~·DlJ•OV<Z•U•P>>• OV<TSCTSCX.UJ,z>,TSCTS<YrZ>,U>• SATZ221DCTS(YrZ>rU•SATZ2210CYrZrN•O), P));OVCTS<X•TSCZ,U>l•iSCY.TS(Z.Ul)• SATZ221J<Y•TS<ZrUl•~•SATZ221~(l~U•~•P> )),OV<X•YrNJrSATZ247CTSCX,Ul.TS(Y;Z), z,j,SATZ2210(Y,z,N,OJ,p), ISGVlZCTStTS<XrUl•ZlrTS<X-TS(Z,UJl• TSCTSCYrZJoUlrTS<YrTS(ZrU)JrTlr ASSTS!CYoZoUJrSATZ221DCTS(YrZJ,U• SATZ221DfYoZrNoD),p), SATZ2ZlOCYrTSCZoUlrNrSATZ221D<ZrUrO,p) ))rSATZ24&(XrYrTS<ZrUloNr

.: IS(TSU S<OV<X•Y•NhCVC lrU• OlhTS(Y•UH•TSO•Zl J

: IS<TSClVCX,Y,NJ,CVC!,u~OJJ,OVCTSCX,Zl .. ~SCY,U>• SATZ221 OCY•U•N•ODJ

S.UZZZ HH z,u,. Q,p l J) : I SUS U Y<TS (X,IJ h TS(Y, ZJ,SATZ2210U, Zr ~. C J ), OV( z, U•P) ),. OV(X, Yr N))

s

s

~sz4s s

SATZZ48

X a [N:NISCX.OC)l

:= SATZ229KCOV<XrYoNJ,OV(Z,UrPJr OVCTSCXrU)oTS(YoZJrSATZZZlO(YoZrH,Q))r lEMMA6(z,u,o,pJ,TZ•.5248•J

SATZ249 :: SATZZ29M(OC•Xr0C•N•

: IS<OV<lJVU, YrNJ "QV( z,u ,pJ. LEMMA6UrU,Q,pJ hOV<T $.(X, UJ • TS(YrZl•SAIZ221D<Y•Z•N•DJJ)

SATZZ219CXrOCrREFIS(CX,OC))) : IS<DV<3C .. X .. N),OCJ SATZZ53 :: SATZ229H(XrXr1CrNoSATZ222CX)) : ISCOVC~,X.NJ,lCJ

Y a {N:NIS(YrGCJJ(I:IS(X,Yll SATZ251A :: TRISCCXrOV(XrYrNJrOV<XrXr

THZ•€.NOTIS•ccx,y,ac~x.NriJ)r1Cr ISOV2< Yr x, x, SYKI SfC x,x, y, I >.N, THl•E.NOTIS•(CXrY•OCrXrN•I>>• SATZ250<X.TH2"E.NOTIS•tcX.Y .. OC,XrNrl)l J IS<DVU: -r,.N h1C)

N a ti:ISCOV(XrYrNJrlCJl SATZ251B ·- TR3IS<CX•XrTSCYr0V(X,Y.NJJrTS<YrlC>•Y•

SATZ2290(X,Y .. NJ,IST52(0VCX.YrN),lCrYr IlrSATZ222tYJ) : ISCX•Y)

U a [N:NIS(Y•OCJl[O:NIS<UrCC>ltt:IS<DV<X,.Y,NJrDV(ZrU,O>Jl

[J:ISC z,oc >l n := TR3IS<CX,OVCXrYrNJ.OVCZrU•O>•

OVCOC•UrO}rOC•I•ISOVitZ,OC•U•~•Ol•

s - 5. 29-

•525Z

+*5252

•5252

T2

T3

I ~. {~:~XSfZ•OCJl rr.

T5

SATZZ49CUr 0' > : IS<OVU rY•NhOC> :: TR:S{ClC•X•fS(Y,OVtX~Y,.NlhOCr

SAiZ2Z9D<X•Y~•>•SATZ221BfY~OVfX,Y•NJ• Tl)) IS<X ... O::)

:= TRIS2CCX.TSCXr~lrTSCT•Zl•OC• SATZ22~A(X,u~i2),SArZ22lB<Y•Z•J)) : ISCTS((,UJoTS<Y.Z)l

;: TR!S~<:X.CVtTS{XrU),TSCY.l)r SATl22lD(Y•Z•~·P);,1C•DV(OV<X•Y•N>• ovcz.~.aJ.LE~M~&<z.u.P.ol>· SAiZ2ft5(X•Y• lriJ• N.P~Oh SA iZ251H OVC x, y, Nl. CV( z,u,o ), LE~~~stz.u,p,o).l}l

:: SATl2513<TStX .. U>~TS!YrZ).o SAiZ2210CYrZ•N•PloT4) : ISCJS(l(rUhTS!Y•Z>J

SATZ252A :: THl•t.IHP~CISCZrOC),JS<TSCX,UJ,TS<Y,Z) >•CT:rscz.oc,lr3~.szsz"<T>. (T:NISCZ,OC>JT5".525ZwCTJ>

o ~ tt:zscrscx.u> .. ts<T .. Z>>J

I a (J:ISCZrOCJJ TS :: TRIS<CXrTSCXoUJrTS(Y,.zJ,OCri"

SATZ221B<YrZrJJ) T7 := DREl<ISCXrOCJriS<U•OCJ•

SATZ221CCX.U.TGJr0) re == TRIS2<CX .. OVCXrY,.NJrOV<Z•UrOJrOC•

TRISCCX,OV(X,YrNJ,QVCOC•Y•NJrOC• !SOfl{XrOC~YrT7rNJrSATZ249CYrN)), TRisccx .. ovcz,u .. o>.ovcoc .. u.o> .. oc .. ISOY 1( z, OC, ür JrO),. SA TZ24 9 (IJ,.O}) l

I ; [P:NISUrOCJ l T9 == TRISCCXrGV{OV(X,YoN),QV(Z,U·O),

tE~MAG(z,.u,p.o>> .. ov<rscx.u> .. rscv .. z>, SATZ2210{Y,.z,.N,?JlrlCr SATZ246<X•Y•ZrUrNrPrOJr SATZ251A(TS{X,UJrTS<YrZJ, SATZZ210{YrZrNrP)riJJ

no == SATZ2518(0V(X,.y,~),OVCZ,U,.Q),

lEMMA&CZrU•P.oOJ•f9)

I a SATZ252B :: Tal•L.IHP•CISCZrOClrlS<OYCXrY•N),. ovcz .. u .. o>J•tT:Is<z .. oc>lT6·.szsz•cr),. tT:NIS(Z.oOCllT10".5252"CT>J

z ; OUNISCY rOCJ l SATU5l ;-;: . SA T,Z2Z9\HPt.n. lh Y • ?L<OV {X, Y ,.N h

OV(Z,YrNII~N•TRISfCX~Tscr,PL(OVCXrY,N) ,.nY<ZrYrN)))rPL<TS(Y,.OV(X,.Y,NJ)• !S(Y,.QV(ZrT•~JllrPLCX~ZJr UISTTPZ<Y•OV(XrYrNlruV!Z•YrN}), ISPL12(TS<Yr0V(X~Y,.NJ),X,

TS(YoOVCZrYrN)JrZrSATZZZ9C(XrYrN)r SATZZ21C(lofrNJ)Jl

z ~ [l'UNIS(l,.,C> l SYKIS<CX .. Pt(OV(X~Z,.NJ,.OVCY,z,Nl),. OIST:JP. == DVCPL<X•Y>•Z·~> .. SATZ253CXrZ•Y•NlJ

iHSTPO :: SATZZ53CI,.z,.y,.~)

ISCTSU ,Uh TS(Y,.l))

I S<T SU ,.uh OC)

IS<X,OC)

: IS<DVC~l(X•Y>•Z•N>•PLtOVCX•Z•NJ,.OV<Y•l•NJll IS(I"l(!) VCXr z,. lH • CVC y,.z. HH rOV( Pl( x,. Y J,. Z •N l l

s

s

- 5.30-

t-6258

U ; (N:NIS(Y,OC>JtO:NISCUrOC>l S~TZ~S~ :.= TRISl<CX•PL{CV<X•Y•N)oOV<Z•U•C>>•

Z ~ [N:N!S{Y,OC)J SATZZ55

Z ; [N:NISCZ.~CJl

0VCPL{fSCX,UJ,TSfY,zl>•7SCY.UJ, SATZ2210(Y•U•N•O>>•PL(OV<TSCX•U>• TSCY,U},SATZ221Q(Y,u.~,G!)o0VCTS{Y,Z), TSCY.~lr5ATZ221D<Y•U·~•DJJ)~ ISPL1ZCC1(TS(X•UloTS!Y.Ul, SATZZZ!DCY~u~~·:l:~:vc~,y~~)r OVCT~:YoZl·iS(Y,~),~!iZ221CCY,UoN,0)),

OV~Z,UrGl~S,TZ245(X~Yr~r~•G>, SATZ246A<Z•U,Y,Q,~)),$A~Z253(TS(X,U},

T Si: Y • U h T S ( Y • Z J. SA T Z 2 2 1J ( Y • iJ • N oO )} )

·- SATZ229GC~N(X~z),y,~~CCV{Y,Y.NS, OV(ZrY•Nl)oNoTRiS<CXoTS(Y,MNCCVCX,YoN) ,ovtz.r.~~>>·~~<Ts<r.crcx.v.n,,,

rscr.av<z,y,~)>>·x~cx.z>,

0 I ST TM 2 { Y, OH X • Y. ~ > • 0 !," ( Z, Y • N ) ) , iSMH12<TS<Y•OVtX.YoN)),X, TSCY,CV(z,y,~)),Z,SATZ229C(X,Y,N),

SATZ229~cz,y,\)))J

OISTJ~ ·- SYMISCCXoHNCOVCXrZrNJoOVCYrZ•N>>• üVO!'H Xr YlPZ.NJ. SATZ255CX.o Zr YrN)}

OIST~O ·- SATZ25SCXrZrYrNl U a [N:~IStY.~C)l[O:NISCUrOC>l

SATZZ5& ·- TRISlCCX.HNCOV<X•Y•K>.OVCZ.U.O>>•

x ~ B ..

y ;

x ;

.CDNJ CDNJISA

CONJISB

u:rscx.nl ISCONJ SATZ257

U:IsU,OCJJ SATZ258A

X a [I:ISCCO~J(X>rOC>l

Tl

OVCH~CTSCX•U~.!SCY•Z>>•TSCYoUJ, SATZ2210{Y,U.N.O>>·H~!OVCTSCX.U>•

TSCYoUJ.SATZ221DCY•U•N•0)},QVCTS<Y•Z>• TS{Y,U>,SATZ221JCY,UrS,Jl>l• ISM~12{0VCTS<X•U>•TSCY.U>• SATZ221C{Y,u,~.0>>•0V[X.Y,N),

CVCTS<Y,z},fSCYoUl•SATZ22l~<Y.oU•N•O>>• CVCZ.~.Ol.SATZ2~5(X,Y,UrN•O>,

SATZ246ACZ•U,Y,OrNllrSATZ255CTSCXoUl• TS<YrUJ,TS(Y,z>,SATZ221DCY,u,N,OJ))

:: PliCRECiJ,HO"R•CIK<X>>J :: ISRECXlZ<RECPliCArBl>rAr

~O•R•CIM<PLI[A,SJ)JrHOPR•(BlrRElSCArB)

,JSHO"R"CIHCPLI<Ar3J>rB•IMISCAr8~)) := SYMISCCX oCONJC Pl IC A• 3 l >•PLICA.MO"R•( B)

hCONJ !SA>

:= ISF<cx.cx,rr:cxJcONJCT>.x.r,I> := TR3IS<CX.CONJCCGNJCXJ),PliCRECXJr

HO•R•<nO"R"!IHCXJ))),PLICRE<X>•I~CX)), X•CONJIS,(RE{X)oHJ"R•C!~{X))),

ISREC JC2C :IO'"R,.OI:> .. R•

·- TR3IS<CX~CGNJ{X}rCGNJCOCJ, PLI< o, HO'"R"( 0 > lr IJC, I SCGSJ ({,Oe, I>. CONJISACOrOlriSRECY2C~'·R-<O>~O•O• SATZ17SB(O,REFIS<REAL.O))JJ

IS<PL<JVCX,YrN>oOV<Z•U•OJJ•OV<PLCTS<X•UJ•TSCY•Z>>• TS<Y,UJ rSATZZ21CCY,u,N,Q)))

ISClVC~NCX.YJ.z,N>,~NCOV(~,z,NJ,OV(Y,zrNJ))

IS(HN{] HX• ZrNl oOVCY,z,NJ) ,QVO!N<X•Y >.ZoN> l

IS<HNCJV(X,Y.NJ,QV(Z,UrO)J,OV(~NCTSCX,U>rT~CY,lll• TSCY,uJ,SATZZZlOCYrU•N•O)l) COMPlEX

IS<CONJ U J. CONJ< YJ)

ISCCONJ CCONJCXl>oX>

IS<CONJ<XJ.OC> -5.31-

s

IS~Et~ECXlrMO~Rft(lfoi(Xi>>r

LEM~Al<CONJ<X>r!)) ts-R•U EOD,O> TZ := SATZ 17 Gt: (Hl{ X) r i RI$( REAL; MO•R•UIH lC) );

IHtCONJCX))~OriSIHCRECXl.MQ*R"(IM(X)J) -LEMMA2CCO~J(Xlrl))) ts .. R•u MU> ,o,

•6258 s

SHz:!558 ·- TRIStCXrX•~liCRE(X>•l~(X)),QCriSPLI(X)

•lSRECX12(RECX>rO•l~(Xl•O•Tl".~Z58•, rz·.&zss .. >> IS<X rOC J

Hó258 $

I <il AHOERS :: TRIS1CCX•X~oc.cONJCCONJ(Xl)•SATZ257r SATZ258A<CONJ(II•I)) ISCX .. oe>

·&253 s

x ; (N:NISUr3CJ J SUZl59C :: TH3•t.IMP•(ISCCONJCX>•OCJ,IStX.OC>•N•

{T:ISCCCNJCXJrOCJJSITZ2588CTJJ NISCCOJ JCXhOCJ x a ti:IS{CONJ(~).X)l

•&259 s

Tl == TRISCREAl•HOwR•ciMCX>>•I~(CONJ(XJJr IM(XJriSIH<RE(X)rMO•R•<IMCXJ)), ISCEIH(CONJCXJrXri)J IS,.R•(!fO .. R•UMUJh lM( X)J

-&Z59 s

SATZZS'A ::: LE"MA10(IHCX>.SYHIS<REAL,HO~R•(IM(Xl)• IM(X)•f1•.&259R)) : JS•F(•(I MUhOJ

X OI [I:Is•R•<JH(XJrOJJ SAJZZS98 :: TRIS€CX~CONJ(XJ~PLICRECX1riK(XJ>•X•

tSRECXZ(MD"R•tiMCXJJ,IMfXJ,RE(XJ, TRISZCREAL~HO"R"tiM!X)J,IHCX>•O• SATZl769ClK(X),I)riJ),PliiSCX)) IS<CONJ (X), U

x ; (l:IS<XrCOHJ(X)Jl SATZZó9C := SATZ259ACX,SYMIS<CX~X•COHJCXJ,IJ) : IS-R•U MCU,Ol

x :a [!:Is•R•(IH<X>•Oll SA TZZó90 ·- SYHIS<CX.COMJ(XJrX•SATZ259B(Ill : ISOC .cil NJU))

y a SATZZ&O ·- TRJISCCXrCONJCPLCXrY)l,PLI<PL•R•CRE(X} .RE(YJ),KO•R•CPL•R•CIHCXJ.IHCYJ))), Pli<PL"R•tRECXl·~ECYl>• Pt•R•(MO•R•CIH<XJJ.HOwR•CIMtYJJ)), PLCCONJCX>•CGNJ(Yll• CONJISAfPL"R•CRECX>.RECY)J,PL•R•tiM(X) • H!C Y J) > • ISRECX.ZCMO'"R'*(Pl,.R'"( I 11( XJ• IK<Yl)),Pl"R,.CMOwR•CIMCIJ1.MO•R•CIM(Y1 )J,PL"R•(RECX),RECY>>~SATZ160(JH<X>• IMCY))l,PLIS1ZB<RE(X),~3·R•<IK(X)),

REO h HO•R•( HH Y.)) >) IS<CONJCPL(X,Y))rPL<CDNJCX>.CONJ(Y))) SATZZ60A == SYMIS(CX,CONJCPLCX•YlJ,PLCCONJCX)•

CONJCYJ),SATZZ&O> : IS<PLCC: ONJ( X hCONJ< "!)) rCON JC PL< X• n >)

•6Z61 s - 5~32.

u := TRISCREAL•KO•R•<iMTSCXr!)), PL~~·(Mo-R•(TS•R•tRECX>,I~(Y))); nO•R•(TS•R•(tMCX},?,EtYJlJ), Pt,.R"(TS•R•(R[CX)•HO"R•:tHCY))),

-62.61

SATZZól :=

SATZZ61A :a

•5262

rt := T2 :=

•626l

SATZ2ó2 ::

SATZZ62A ::

[N:NISU.OC)]

•626J

n := TZ r= n := T4 ::

T5 ::

-6263

SATZZU ·-

r~-~-t~o-K-~iM~'-11r~~\T111~

SATZl60(TS"?."(RE~~}~lM!Y)).TS•R•(IM(X) •RECYl)}~ISPL1Z~~~cr.o-Re<TS•R•(R[(X);

IHCY))J,TS•R~IRECXJrMO•~·<IMCYJ)1~ MD•R•<Ts-~-ci~CXl;RE(Y)J),

ts•R·C~~·R•{!M(X}l•RECYJ)~ SA Tl !97f{!\t{ Xl ri !l{ Y} J, SAT Z197ECIMOO., REtYJll1 -

TRJIS<CX·CC~J(TSCXrYl}.,PLI<RETS<X•Y>• MO•R•c:~iSCXrYl)lrPLI<~q·~·crs•R•<RE

CXl·R~t!'l•tS•R~<xOwR•<JM(X)),

MD"R~<l~<YJ>>l~?L•R•<TS~R-<RECXl• HO~R·~r~<YJ));ÏS"R•(KQ•R~<l~{X)J.,P.ECY)

)ll•TStCONJCXl.CD~JCYl>•

CONJ!SlC~ETSCX;Y),IMTS<X.Y});

ISRECXl2<PETSCXrY>·M~·R•crs•R•<RECX)• RE{Y}>·TS~?."<~o·R•(I~tX))r~O·R"CIM<Y)l

)).~Q~~·{I~TSCX;Y)l•Pl"R"<TS"R~(RE<X>• MO•R•CIMCY))}rTS"R"C~O"R•(!~(X));R((Y)

))rtSM~Z~R•crs~R·CIM<XJ.IM<YJ)r

TS"R·<~O~?.•( IH{Xl)rHC"R"<!M(Y))), TS"R"IREtXb~ECY))rSATZ196ACIMCXJr IHCYll}rft•.6Z6t•)rlSIS12B<RECXJr KO•R•(tHCX>J~RE~YlrMO•R•CIHtY)))) SY,ISCCXrCONJ(TSCXrY));TSCCCNJ(XJr CONJCY)),S~TZ261)

SYMISCCXrPl(H~!XrY),y),X.,SATlZ30<X•YJl TRISCCX,.C!HóJ <X ),.CO!-lJ (Pl<H'I(X, Y h Y)),

PlCCONJCKN(X,.Y)J,CONJ{Y)}r ISCDNJ(XrPL(~~(X,YlrYlrTl)r

SATZ260(MN(X,Yl,YJ)

SATZ21Zf<COMJCX),C0NJ(YJ,.CONJ(MN(X,Y)) ,SYHISCCX•CONJ(Xl•PlCCO~JtHN(X;YJ), C0NJ(Y)J,T2•.&26Z~))

SYMISCCX•C~NJCMN<X.Yl);H~CCONJ(X),

C ONJ Ct ) l" SA T ZZ &2 l

SATZ 229F U, Y,. tO ISCONJCX•TSCOY<X•Y•Nl•Yf,Tl) SATZ2&1(0VCX,Y,N),y) TRlSCCX•CONJCXJ.CONJCTS<OVCX•Y•NlrYJJ, TSCCG~JCOVCX,Y~N)),CONJ(Y1JrTZ ... T5J SATZ 258CU •Nl

SATZZ29JlCONJ( XhCONJ( Y h CONJtOV(~,.y,N)),f5•.&zsJ•,

SYHIS<CX,CnNJ(X),TS(CC~J(QV(X.,Y~N)t~

:

:

:

:

:

:

: :

IS•R·<~O-R"(l~TS<X•Y))•PL"R~crs•R8CRE(XJ.KO•R•CIMCYJ)); TS"R•CMO"R"CIM<Xl);R[(Y))))

ISCCONJ CTS< x.n hTSCCONJ(lC ),.CONJ<Y)) J

ISCTS<CONJ(XJ,CO~J(Y)),.CO~J(TSCXrY)lJ

ISCXrPi. OIN<XrYhYJ)

ISCCONJ(Xl.PL(CONJ<'-NCXrY)),CONJ(Y)J)

ISCCGNJCMNCX,Y)),MNCCONJ(X),CO~JCY))J

IS<HNCCONJ(X);CONJ<YJJ,CONJ(MN(X,Y)J)

ISCXrTICOVCXrY,NJ.YJJ ISCCONJ (X Jr CDrU<TS< OVC X• y, Nh Y))) IS(CONJCTSCOV(X;Y,NJrY)),TS(CONJCDVCX.YrN)J,CONJCY)J)

!S<CONJ Uh TS( Ct!NJ( OYC X• y, NJ l .cONJ( Y))) ~US(CO'fJ(Y>,OCl

$

s

s

s

s .;... 5.33-

•7265

x ; y ;

x ';I

x ;

x a

SATZZ&3A

HOO tx:rscx.n 1 IS HO:> (NHIISCXoOCJ l SATZ2&4A

n:tso:.oc u SATZZSB SATZZ34C SATZZS40

Tl

TZ

T3

T5

T6

TT

CO~J(Y))~T4*.626l*l) :: SYMISCCX~COUJ(OVCX,Yr~ll.OV(CCNJ()(),

CONJCY>rSATZ258C(YrNllrSATZZi3) ·- SORT<HOD2tX),LEHMA5(X))

:: ISF<CXoREALorT~CXJ"ODCTJoXrYoi)

:= SORT~OTO'.~OOZCX)olEM~A5(X), PNOTD:M002CXlrLEMMA4CXrN>>>

:: SQRTQ!M002<XloLEMMh5(X)rLE~~A3CX•I>> ::: THSa?.TlAC~002<X>.LEHMA5CX)) :: SATZ1&7f-(M0J{X)•O•Tn3•L.I~P~CtESS<HOO

(X),O),NEGCMOOCX)IrSATZ2&4Co tT:LESS{K00{Xl•O>lSATZ1S90<M00(XJ,T}))

:: SYMISCREAt~rs•R•(M03CXJ~H00(X)J,.

: IS<(} V«: ONJC X hCONJ( Yh SATZ Z58C(Y • NU •CONJ( CV C X• Y • N >) J RE At.

IS .. ~'"(>! OD{X hHOD<n >

': POS\ HO) CX))

IS,.ft•("f OO<X hO> NOH Nn OHJO ( Xl) >

: MORE I St 1400{ X h 0)

KOD2(XJrTHSQRT1B(H002tX)~LEKKA5(X))J : IS•R·t~DOZCXJrTS•R•(MOOCX)•HOOCXJ)) :: TRtSC~EAlrPtwR~CTS"R•{RE(X),R((X)),O),

Ts•o,u{REtY.l,Rf.(X)),fS•R"CA35(R((X)lr ABS<RE<X))};?l02CTS•R•(R(tXl.RE(X)),Q, REflS(REAloO)J,LEM~AlZ•R•<RECX>l> : IS•R"(~L•R•trs•R•tRECXJ•R~CXJl•O>•TS•R-tABSCRECXJ),

:c SATZ191CTS•R~CRECXlrRE(X1>rTS•R•tRECXJ .REC X>), TS•R•C IHCX>• IH<X) hO, . MOREISIZCTS•R•CRE<X>rRECX)),. TS•R•[RECXJ,RECXl>• REfiS(REAL•TS"R•CRECXJrRECX)))J•

ABS< REC XJ)) J

LEMMA tt•R., UH( X>> J : MORE ISC MOOZC X),Pl"R•<T s•R•CRE<XJ.REC X) ),Q J)

:• ISMOREIS12<KODZ<X>rTS•R"CHGOCX>•MDOCXJ ),pl•R•(TS~R•CRECX),.RE{Xl>r')~ Ts•R•CABSCRE<XJ>•ABSCRECXllJrT1rT2rT3l : MOREISt TS"R"(HOO(Xl•MOOCX)),fS"R•CABSCfiECXl)•ABSCRECXJJ

)) := TR{S<REAL.PL•ft•(OrTSwR•ct~CXJ,IMIXJ)),

TS•R•<IMCXl•IMCX)J,TS•R•(ABSCIMCX>J• ABSCIM(XlJJ,?LOlC07TS~?."CIP.{XJriM(X)),. REfiS(REALo0J)•LEHKA1Z•R•tiM(X)))

:= SATZl91CTS*~•(RECXlrRECX))r0• TS•R•CIH<XJ.IHCX>>•TS•R•CIM(XJ.IM(X)Jp LEHHA11 .. R"CRE(XJJrMOREISI2CTS•R•CtM(X) ,.IMCXJJrTSftR•(JH(X),JM(X}), REtiSCREAL•TS•R•<I~CX),IMCXJ}))l

:= ISMOREIS12(HGDZ<XlrTS•R•(K0ûCX),.HOOCXJ ),?L•R•(Q,TS•R•(IP.(X),IM<XJJJ~

TS•R•<ABS<IH<XJ>~ASS(lM(X})J~Tl•T5•T6)

ts-a·c~L·R•co.rs•R•<tHCXJriH(X))),.TS•R•tABSCIM<XIJ• ABS( UK U U J

: MORE IS( TS'"R'"CHODCXhMOOUJ h TS•R•UBSC Ut <X) h ABSUMCX)) ) )

a tR IREAL lts :R[ALHH: 140REIS( TS"'R .. ( Rr RJ • T S"R,. (Sr S) JH N :!fOREl S CR ;0} l U.:LESS<R .. Sl l T8 T9 tO UtiJRE( R,. 0) l T10

L ~ EI~Is•R•CRrOJl 111

:: LEHMA2•R·c~~S•l) := SATZló98(SrSATZ17ZO<S•R~O,f8•NJJ

:: TRMORE<Ts•R•(S•S>~Ts•R•cR~S>• TS*R"(RrRlrSATZZO!ACSrRrS•T8rT9Jr SATZ203D(SrRrR•f3tSATZ1&9B(R,olJJ

:: ISMORE2COrTS•RP(RrRJ•TS•R•cs,SJr SYHIS!R(AlrTS"R"CRrR)rOrTSOl(P.rRriJJr sATZ1&9A<rs•n•cs,s>~

MORE (Sr R> : POSCS)

POSSO<S•PN~TOC5rTtrl)J : HOR!CTi·~~cs.sJ.TS•R•(R,RJ)

- 5.34-

-7265

HZ66

-7266

N ~· Tll

SATZ255A

-:-- - -c-r::-t:nf"!•\l'"R"'{ T!S' -R-( S• SJ • T:i•R- ( R• Rh OR,PPr~~~E(R.O>.is-P.•tR.O>• M~~~<TS~R~<S•Sl•TS~P.~(p,p,)),N,

{T:~CRt(RoC)JTlOtTl.rT:IS•p•(R,Q))

HHT>>> ::: SATZl5if{R.S,[TtlESS~R.S>J<Tl2CTl>

S'TZ157C<TS•R•CR•!l•TS"R"<S•S),Ml>

:: T13".7265"{H0G(X},ABSrRECX)}, i4"'.726S•.sATZZ64D{X))

:: TtJ•.72ó5"'CMC~CXi;A8S\IH<X>l• K3RE I Sf MOOC X hABS<RE<X)))

a [R:RtALJCS:REAL l[I:ISCTSC~LICP.,Q},pli<R.OJ>.TSCPlltS.Q).PLICS.O)JJ l[N:NJTCNEG<R>)l[O:NOT(NEGCS):J

; H :R~AL l Tl

T2

T3

f&

T7

SATZ2ó6

x ; Tl

:: ?l,Z(TS·~·cT.Tl•~o·p•(fS•R•(Q,Oll• 5ATZ176SCTS"R"<D,OJ, TSOlCO•O•REf!SCREAL•O)J)) ; IS*R·t~N•R•<fS•R•<T•f),fS•R~(O,Q)),fS•R•(f,fl)

:= TRIS(R~Al•PL•R•crs•R•tT,Ol.TS•R•co.TJ) , rs• R"'( '!" rO h {), PlOZC TS"Il'" { T ,.(i),

fS•R'tO.TloTSOl<OrT•RE•IS<REAlrOJ)Jr TS'nCT rO• REF IS<REAL• 0 >J l : IS~ •(»l•R•ns•R•<T ,Q) rTS•R•<O.r TU ... O)

:: TRISCCXoTSCPLICTrO>•~li(T,O)J, PLI{M~·R•<rs•R•(T,TJoTS•R•co,OJ},

PL"R8 {TS"R•(ToO>rTS·~~{0rf)l)r

PLI<TS"R"CTrThOlrTSISlZACTrOrTrOlo ISRECX12CMN•R•crs•R"CTrT>•fS•R*COr0)), rs·~·CTrT).PL•R•crs•R•(TrO>•TS•R•(Q,f)

l rO• Tl• TZ)) IS (TSPLUT •OhPLH T •0 U •l"LH TS'"R"'< T • T hOJ) := TR3ISCCX.Pti(JS•R•<RrRJ.OJrTSCPLICR.O)

•PLitRrOllrTSCPLICSrOlrPLICS.Ol)r PLH TS"R"<S• Sh3 lrSYMISfCXr TSCPLHR• 0) •PLICRrO)JrPll<TS•R"CRrRJrOJrTJCR)lri• T3CS}) ISCPLU TS•R.,(R,.RJ..OhPLIUS•R,.(S,SJ...O)J

:: TR3ISCREAl•TS'"R"CRrRl• RE<PLICTS•R•(RrRlr0)), RECPLI(TS"R"tSrSlrOllrTS"R"<S~S>• ISRE<TS~R"<Rr?JrOJ. ISCERE<PLI{iS"P."tR•RlrOJ• ?LICTS•a•cs,SJ.OJ.T4),~EIS<TS"R"(S,S>• o>> : IS~-u s•R•<R•RJ .. rs•R•cs.s >>

:= ANOICNCTCNEGtR)),IS"R"(fS"P.•(R,.R>~ TS•R•c S• S) }, H• T5 l AND( NOT OI EG CR))" JS•R•( TS•l•(R,.R h TS•R" (Sr S )).)

:: ANOI<NOT(NEG(S)JriS .. R"<TS"R"(SrSlr Ts•R"CSrSl)rOrREflSCREAL•fS•R•ts,Sl)) ANO(NCf(NtG(S))rlS"R•(JS•~•cs~S),JS•R•(S,.SlJ)

:: SATZR1613<TS~R"<S•S>•R•S•T&•.7266•• rr•.rz&&">

:= TRISCCXrTSCPll(KOJ(X)r?),.PLI<MOOtX>•Ol ),.PLI<TS~R•<KaOCX).~OD<Xl)•Ol, Pl H :-!:JOZU h 0) • T 3wc • 7ZiiG,. C M30J X} Jr

s

s

s - 5.35-

•7267

TZ

T3

X a SATZZ&7

SATZZ61A

z a n

[U:CJMPLEICl T2

Y a T3

ISRECXl(TSwR•\MUU(~1,~UU~X11•~UUZtXJ~

O.THSQRT18{HC02(XlrLE~~ASCX)J)) IS<TS(~LI<HODCXlrOJ~PLICMOO<X>•Ol)rPLI<~C02<Xlr0)) :: lSPL2~R"C"O~R"(fS•R"CIMCXJrMO"R•CIHtX)

))),TS"R•<t~CXlrlM{X)l~Ts"R"<PE{X), P.E<X>JrTRIS<~Ehl•~O·P.·crs•R•{IMCX>r XD•R•(!M{~)J)l~Ts~q·{MO•R•(IMCXJl~ MO•R•([Mtt)))oTS·~·~~rCXJ,IMCXJ>• S~fl197E(I~CXJ,MO•R•(!~(IJ)), sATZ19eC!HCx>.rM<X>>>> : xswR·<~N8R•crs•R•<RE<X>·R~<XJ>•TS-R"<IM<x>~Ho~R"<IHCX)>

:= TR!S!REALrPt•R"<Ts•p·~~ECX>• HO•R"C!M!Xl)l.TS~R•:I~!I)~RECX~)), Pl"R·t~O•R•tTS"R•CnECX>•IHCX)1)•

rs~R~t~E(t>~!~(~))!,Or

ISPLl2•R•trs•R•CRECXl•MD"R•CIM<XI>J• MO~R•cTS•R•{R[<Xl.IM<Xll)oTS«R•CIHCX),

RE(X)),fS«R•CP.ECX>•T~<X>>• SATZl9Te<RE(~l.I~CX))rCOMTS~R·<IHCX),

> hMOOZ <X))

RE(Xl>>•SATZlT9A<TSwR"CRE<K>•lMCX)))) : IS~~-(~L•R•CTS•R•(RECXJrHl~R•CIHCX)JJrTS"R•(t~CX>•RECX) ) },3)

:: TRISCCX;TS<X•CC~JCX>J• Pll(MN~R•(TS·~·(RE<X>•q[{X)),

TS•R•tiHCXl•MO"R~CIM<X>>>>• PL•R•CTS•R•CRE(X),HO•R•<IM(X))), TS•R•<IHCXJoRECXJ))J.PLICMOOZ<XJoOJo TSIS2A<X•RECXJ.~O·R~cr~<XllJr

ISRECXl2CHH"R"CTS"R"<RE<X>.RECX))o TS"R"CIHCX)rMO"R•CtKCXJ)))rMOD2CXJ~

PL•R•CTS"R"CRE<XlrMO•R•<IH(X)))~

TS"R"CIM(Xl•RE!X))),Q,;2,T3lJ

:= TRIS2CCX•TSCPLICHGDCXi•O>•PLICK00(Xl• OJJ,TSCXrCONJCX)J,PLICM002CXJ,O), Tl•.7267·~T4•.72&7•)

:= SYMISCCX.TSCPliLMOOCX),Q),pliCHOO(X)r 0)>,TSCX,CGNJCX)),SATZ2G7)

:: TR3ISCCX•TSCXrTS<Y~ZJ)~TS(TSCX•Yl~Zl• rsu se y, Xh z ». rsn~ rsoc. n >. ASSTS2<X•Y•Zl~!STSlCTSC~.YlrTSCY•XJ•Z•

IS<TSCXrCONJ(X)JrPLICKOD2CXJ•OJJ

CCHTS<XrY> ), ASSTSl< y,x. n) : IS<TSU ,rsn,zu,TS<Y• TSU ~ZJ))

:= TR3Isccx~rscrscx.rl.TS<Z•U>>• rscx.rscv.rsrz,u>l),TS<x.rscz,rscv~uJ)

>•TSCTSCX•Z>•TSCY•Ullr ASSTS1CXrY•TS<Z•U>J•ISTS2CTS<Y~rscz,u> ,,rscz.rscr.u>>·X·Tl<v~z.u>>• ASST S2(X,z, TSO• U>)) ISCTSU SU~ Y> • TS<Zr U)) .rsc TSU•U, TSCY ,U) J J

:: TR3ISCCX~TS<PLifHO~CTSfX,YJJ,OJ• PLlfMOOCTS(XrY)>•OlJ,TSCTSCX.Y), CONJCTS(X,YllJrTSCTS(X.Y>~TS(CONJCX>• CCSJ(Yl)J,TSCTS(X,CO~JfX>>~

TS(Y,CONJ<Y>>>•SATZ267{TS(X•Y}), ISTS2(CONJ(TStXrY)),TS{CCNJ(XJ,CONJ(Y) ) , TSU • Y h SA TZ2S l< ~~ '0 ), TZ<X• Y•CONJ( )0

. rCONJCY))) : ISCTSI~LI("DDCTS<XrY)lrO),fli("QOCTS<X~YJ)r0)), TSUS ü •Cll'iJtxJ),. TSCY, CONH Y))))

s

s

- 5.36-

•72&8

~ tR:R~A~l[S:REAtl

TS

TS

T7

Y :1 T8

~Ll\~00(TSCX,Yl)r0)),TSCTSC~.CDNJ(XJ),

TStYrCO~J(Y})),TS<TSCPLlt~ODCX>rO>•

PLIC~OJCXJ,O>l.TS(~llt"CD<Y>.O>• PLifMODCYJ.OlJ>•TSCTSCPL!CMOO<XJ•O>• PLICV~~(~}.0)J.TSCFLIC"DO(X)r0)•

PLICMJDCTlo0)lloT3~ISTSlZ<TSCXrCONJ(XJ ) • r S( ?U OI 0;) [X ) •IJ) • PU O!!JO (X h 0 ) h TSCToCDUJ{T)t.lSCP~ICMQD(Yl•Ol, PLr!MJD{Y)r0)lr5ATZ2ó7A(~),SATZZS7A(Y)

J•i2<PLICY.COCXl•Ol•Pl!CMGOtXJ,OJ• PLICMQJ(Y),Q)flPL!(MGJ<Y>•Cl))

== P~ozcrs~R~tR.S),MO~R·crs•R"<O·O>>• SAiZ176B<TS"R"(0,0)r TSC1(0rO~REFIS<REAL,Q;\))

:= TRIS(R~AlrPL"RP(fS•R•(R,OJ,TS"R•(O,SJl .rs·~·<~.o,,o.PL02<Ts•R•cR.o,,

TS .. R"'{Or Sh TS01((h SrRUISCREAL•OH), TSC2(~•C•P.~r!SCP.EALr0)))

:: JqiS(C!.rTS<PliCR•~l·Pt!(SrO)lr PLI<~~·R•CTS•R•<R·S~•TS"R•(c,Ollr PL"R•(fS"R"CR.O)rTS•R"<O•S>>>• PLIC!S•R"CRrSlrO>rTSISlZA<R•O•S•O>• ISRECr.t2(M~"R"CTS"R"CRrS}rTS"R"<Or0)), TS"R•<R•S>rPl"R"(TS"R"CRrOlrTS•R•(OrSl'

IS<TS<$titMOOCTSCX.Yll•O>·Pli<~OOCTS(X,YJ)•0)), fS(TS(»LI(MOO(Xl•Ol•PLI{HüOtYlrOl>•TS(PliC~OOCXl•Ol• PLIOIO) (Y),.O))J)

hOr T5,. TU) : ISCTS<»UCR rOJ..PlHS..OlhPLUTS•R•<R•Sl•OJJ := TRIS!CX•TSCPLICMOJCTSCXrY))rO)r

PLIC~~JCTSCXrY)),Q}),TS(TSCPL!CMOOCX); OJ.Pti(MOOCYJ,O)lrTSCPLIC"OOCX>•O), PLICMOOCYJ•OJJJ,TSCPLICTS•R~<MODCXl•

MO~<Yi>•O>.PliCTSftP•CMOO(XJrMCO<YJ);Ol lrT4,ISTS12!TSCPLIC~00{XJrO>. PLit~00(Y)r0))rPt!tfS•R•(MCQ(XlrH00(Y)

),OJ.T~:PLitHCO<X>•Ol.PLitMOOCY),O}),

PltCTS•R·<~OO(XJ~MQO(Y)JrO),f7(H00(X)•

MOQtY)J,T7(M00tX)rM00(Y)J)) ISCTSC»LI<HODCTS(X,Y)),OJoPLl(MOOCTS<X.YJJ•Ol)~ TSCPLitTS•R•CHODCXJ.MOO(Y)),OJ.PLI<TS•R•(MCOCXJ,HOO(YJ) .. on,

{N:NEGCTS•R•(MOOCX);MOOCY)JJJ T9 :: OR~PPCAHD<POSCMOOCX>>•NEGCKODCY)}}•

Y a SATZZ68

SAHZ68A

[N:NtSCYrOC>l

AND<NEG(MOOCX)J,PCSCMGJ(Y})J,CONr SATZ195H(MOD<XJ,MO~(y),S),

[T:AND<POS(HDDCXJ>••EG(MCQ<Yl)Jl <ANOEZCPOS(MODtXll•NEG<MOD<Y)JoTJ> SATZ264CCY),(T:ANO<NEGCHOQ<X>>• POSC "!OQCY >)) l<ANDE1 ( ló[(j{ MOOOO Jr PDS<~OO(Y));TJ>SATZ254C(X))

:: SATZZS6tHOOlTS<X•Y>l•TS•R•(HQO(Xl• ~GO<rJl,f8•.726&•,sATZ264C<TS(X,YJ), tT:NEG{TS•R•(M00(X);~QO(Y)))1

Ct)N

T9•. 7263"{ V} : IS•R•(ltODUS(X,Y)),.TS"a•otOOCXhfo!CO( Y) J > :: SYHIS<REAL~M~OCTS<X•Y>>•TS"R•(MOD<X);

MO()('f} hSHZ266) . : IS"'l"<f S"'R .. OIOQ(X),. 1'00 CY)) .MOOCTS( X.Y>})

s

- 5.37

s

•727)

+7271

Tl T2

SATZZó9

X :a TZ

I a Tl

SATZZ70

y ; ti:ISCPL(X•Y>,OC>l Tl rz

Y a tN:NtS(PL(X;Y)rOC>l T3

ft.

T5

:= PNOiOCMOOCYlrSATZZ64A<Y•N)) :: T iHS lUEALr TS':'R .. (l'IOO COVC x,. Y,N >) rHOOC Yl

} , HO 0 ( X) ")t OlH T St Cl H X, Y • N J • Y ) h SATZ2&6<0VCX.Y.N},y), ISMODCTStOVCX•Y•N>•Yl•X•SATZ240(X;Y•Nl J) '

:: SATZ204G(K~D<X>•MODtY),RODCDV<X•Y•N>>• Tl•T~ISCREAL.TS•R•CMOD(Y)~ MD~(S~~X•Y••Jl!.TS•R•CKOOCOVCX•Y•N})• ~CDCY)),HOOCX),CO~TSffR"<~OOCY),

M00{0V(X•Y•N))),T2))

:: T3 ... 7ZG9"

:= THl"l.I~P·(NEGCR)rMOREIS<ABS(R),R)r tT:NE~(R)lMOREISilCASSCR>•R• TRMOP.E<A3SC?.>•O•R•StT7.169AtABS<R>• SATZ1566{~.Tll•LEMMA2-R•CR•O• SATZ169CCR.Tl))l,[T:NaTCNEG{R))] MO~EISIZ<AöS<R>•R•ABSNN(R•l)))

:: TRKOREISCHOO<X>•ABS<RE(X)J;RECX). SATZ26SACX1.T!CRECXJ)J

:= TR3I SUEAL,Pl .. R,.CRE OOrREU )}, RE(?LCX.YJlrREC1C)rlRL• ISRECPL,.R•<RE(X),RE(Y)J,Pl•R•(JM(X)r IM(Yl>>•ISCERECPt(X•Y>•lC•I)~ REISClRL,Ol) .

t= ISHOREISZ<PL"R•tRECXJ,RECY)),lRl• Pt•R•tMOO<XJ,MODtYJJ,f3•.rzro•, SATl191CMDOCX1,R((XJ,HO,CY),R[(Y), rz·.rzro·~rz·.rz708 tY>JJ

:= SATZZ64ö<Pl(XrYlriJ ::: ISHOREISZlPl~R•(O,O),HOO<PLCXrY));

Pt•R•CMOOCXlrMOJCY)), TRIS Z< REAL .. Pt '*R .. (0, 0 h ~00 <PL <X, Y J hO, PlOlCO,O•REFt~\REAL•OJJ,Tll• SATZ191<MOOIXJr0oMODCY>•O•SATZZ640(X)• SA TZZó40 (Y U)

== PNOTOCK00(Pl(XrY)J,SATZ2&4A(PL(XrYJ•N> )

== TRIS<CX•PLCOV(X,PLCX,YJrN), OYCY,.?LCX,YJ,H)),QVCPL(X,Y>rPl(X,Y),N) •1CrSATZ25lCX•PLCX•Y>•Y•~), SATZ250C?LCX,y),n)J

== SATZ270CO~CX,PltX,Y>rNJ~OVCY,PLCXrY), N>rT4>

NI s•R-c HOO<Y Jr 0)

: Is·~·t"OD<CVCX,YrN)J,OV"R•t~ODtX},K00(Y)#P~OTOtH00(Yl• SATZ2ó~ A<YrN))))

. .

MORE IS( ABSC R lrR)

HOREISt MOOUhREUJ)

NIS"R"t MODCPUX,Y)),Q)

MORE IS[ Pt .,R .. (KO:>C!JV(X, Pl<'< ,Y) ,.N) hHODCOVU •PlUrYlrN >))

•lRU

s

s

s

I

- 5.3.8-

rt rY i&

PRL '"~R rr

T8

T9 T10

y a Tll

-rzn Y a SATZZT1

SATZZ71A

x; n

TZ

= OV•R•(MQO(X},.MQO(PL(XrYl>.T3)

" OV"R~(~CO(Y},MO:tPL(XrY)),T]} = ISHOF.E IS H ?t.,.R•( !o!OOfOY t !:r ?U x,. Y J..~ J 1.> HOO( 0\' (Y • PU Xr Yl # Nl J lt Pt ,.R,.(FX#f Yh 1Rf..,ISPLl2,.~"CMGO<CV<XrPL(X,YlrN))~FX, M[j::J( 0\'(Y,?L( Xr Y) .~;)),;y,

SATZ2&9EX,PL(XoY>rM),SATZ269CYrPL<X~Y) ,NJ>rT5J

::: TS•R•CPt,.R•tFXrfYlrMOOCPL(X,Y))) :: rs~R~{l~L.~OQC?L<XrY))l := ORAP?C~O?.E!Pl"R*(fX,FY}•lRl)•

xs-R~<Pl"~·<rx,rv>.lRL>•

~DRE!SCP~l•P~~l.T&r [T:HCRE(Pl~R~[FX,fYJ•l~L'J MOREIS!lt?RL~PRR,S~TZZOlACPL"R•iFX,fY) r1RL,MGC<PLtX.Y)),T,.SATZ2S~A(Pl(X,.Y), Nl)l,[T:IS~R•tPl,.R"(FX,~YJ.lRl)J

MOREIS!ZtPRLr?RRriSTSl"R•(pt.•R~trX,fYl ,lRL,KOCCPlf~rY)),J)))

-== TRISCREAL•PRL•PL•R•<rs•R•(fX~~ODCPL CXrY))),TS•P.•CfY.~OOC?l(X•Y)))),

Pl~Ro-~nJtXl~~COCY>>• CISTTPl•R•(FX.FYrHOO(PL<X•Y))}, ISPllZ•R•trs~Rft(FX~~GOtPL{X;Y)))r

MaDCX>rTS•R"{fYr~OOCPl{XrY)l)•MOOCY)r

SATZ204~(HGJ<XJ~M3~<PL(X,YJJ,.T3)r SATZ204ElKOû(Y),M30(Pl(X,Y>J~T3l))

:= SATZ195S(MODCPt(X,YllJ := ISMOREISlZCPRL,Pt•R•CHCDCXlrHOO<YJ)r

PRR.~OO<?LtX•Y>),TS•T9•f7) := THl~L.!MP•tiSCPlCX.YJ,OCl.

HOREISCPL•P.•(~QO(XJ,MOOCY>l•

MOiH PUXr Y ))), U :I S<PltX, u,. OC JlTZ<T h [T:NISCPL<X•Yl•OCJ1T10CT>>

:: SATl168A(Pt•P.•tM00(XJ•KOOCYJJ, M03(Pl(X,YJJrT11•.7Z71•J

:= Ttt·.rzrt•

:: TRISCREAL•REtMOfXJJ,REfPLI<K~·R•<RE(XJ ),~O"R"CIMCXJJ)J,MO•R"<RE<X>Jr ISCERECMOCXl•PLI<KO•R'"<RECX}), HO•R•ttMCXl)J,SATZZ1~<X>l•

Ri:At..

MORE I St PL ,.R.,Cf'XrfYJ ~ lRL) REAL REA1.

MORE I Sl PRL• PRR)

: IS•R•t~RL.Pt•R•tKODCXJrK03CY))) : IS .. R .. <~RR•MflDCPL<X•Y>JJ

: LESSIStMOD<PL(X,YJ>•PL"R•(MQO(XJ,MOO(Yll) : MOREIS[PL•R•(HOD<X>•MOO(YJJ,MODCPL«X~Y)))

REISCKO"R'"CRE(X)JrHO"R'"<I~CXJ))) : IS-R·<~E(KO<XJJ,KQ•R•(RECXJJJ := TRIS<REAL,Js•R•<RECHO(XJJ,RECMO(XJ)),

TS"R"'C 1-lO .. P.•t RE<XHrMO .. R'"CR[<X J )), TS•R"(RECXJ,RtCX))~!STSlZ'"R•<RECMOCXJ) ,MO"R"CREOO )~ RECMOU)) rMO".fP'( RE {X)), Tl• Tl lr SA TZ! 95( RE< X> • REC U)) : IS .. R .. (f S'"R•tRE( KOC X)), RE(ItOCX))) • TS .. f!•( RE< X Jo RE( U) J

t= TRI S<FE:ALr I lH KG( X J ), PH i'L ICHO .. R"<RE< XJ ),MO'"R"(I~CXJJ)),HO'"R•(I~<X>J,

ISCEIMCMOCXJrPLICHO•R•(RECX))~ M0 8 R•<IH<KJllrSATZZ14fX)), IKISHiO•R'"(R::<lO lrl10 .. R•U!ICX)))) : IS"R'"CI K{M!HXlJ •'0'"R"'t IMU ))}

:: TRIS<REAl,TS•P.•{J~(MOtXl>•IM<r.O<X))J, TS"R'"( MO,.R•( UHlOhMO .. R .. (IM(U > h TS~R•(IK<X>riMC~)),ISTSlZ·R~<IH(MO(X)) ,M3•R•(J~!XlJrlHCM0(X)),Ml•R•(tH(X)),

$

s

".. 5.39-

•7272

H273

x a

Y a

f5

SIITZZ7Z

SATZZ12!A

SUH Tl

rz

Tl• r3 hSII TZ198C 1 ~( :o,. I 1400 H : IS""ft•U s•R•(IM( HOU )h IMOIOCX>)),. TS"R .. C IMtx h IH( U)) := IS~l12•R•crswR"(FE<H0(X)),.?EtMOtX))),.

rs~R~tRE(K),.RECX)l,.TS~P."C[MCMOtXl)•

HiO!OCO) h TS"R'"UI'I( XhUUX) h T2, T4) : IS"R•(M OOt< ~000 hMil02U))

:: ISSORT(H002(H0CXilrHOD2tXl• lEKMA5CHQ(XJJolE~NA5<X>•T5•.7272*)

:: SYH!SCREAL•HOC\~0(XJ),M0D(Xl,SATZ272)

:: Pt•R•(MOO{Y),.~QOCMN(X.YJ)) . := !SlESSISl(KOQ<PLtY.HN\X,.Y))),.HQO(X),.

SUK•ISMOO(~l(Y•MN(X;Y)),.l(,.

SATZ212n(X,.Y)l,SATZZ71(Y,H~(X,Y)))

:= TH9•t.o?.•CtESSCMC~CX>•SUM), IS"R'~~r.~•x},SU~>,LES5\~N·R .. CMOOCX)o HO~[YJJ.HN•R•csUMrKDD(Yl)),. !S~R*(KN~R~<~CO(X).~QD(Y))•

MN*R*(SC~·MCDCYi)),Tl,(T:LESS<~CD<X>• SUK>lSATZ13eFCMOOC~J~SuM.MO•RwCMOOCY)) rTl,[T:IS"R"tMOOtXlrSUM))

: IS~R"(MOOtMOCX))rHOD<X>J IS"R•(~QO(X),.HOOCMO(X}})

: REAL

LESSIStMOOCX>,SUMl

ISHN l .. R .. O!O:J <X h SUlh MO'J <Y h Tl) LESSISt MN•R•( MOOU)" M00(YJ ),.~N•R•<SUI'r Jlll0(Y)) J T3 :: TRIS<REALr~N"'R .. (SU~h~O)(Y)),

M~·R•(pt•R·{~ODCM~{X,.Y)),.MDOCY));

MOOCYllrMOOtMN(XrYllr !SMN1"R*(SUM,PL"R•(MQJ(MN<XrY)JrK00(Y) ),KOOCY),CGM?L•R*CMOOCY},.HOD(HN<XoY))J ) ,. MNPl< HOO ( MN( X• Y)), HOi) ( Y))) : I S~•(M ff•R•( SUM• MOD(Y) )..MIJD( MN(Xo YJ))

T~ ·- SATZlS83CMN"R"CKCDtX),.MCO(Y)), MODCMN(X,Y)),!SLESSIS2CKN•~·csuK,.

KO'JCY)),HOO(~N(XrYJJ,.HN•R•(KOD(X)r HOGCY>),TJ•TZJJ • : MORE!StHOO(MNCX,.YlhMN•R•tMCDCXhMODCY)})

T5 := ISHOREIS12CMDOCHNCY,XJ)rMOOCHKCX,Y)), MN•R•(MOO(Y)rMDOCXJJr "O•R•{KN•R•t~OOCXlrMODCYlJ)r TRISlCREAlrMOOCHN(Y,.Xl)•MODCHNCXoY)), HOD<~Q(MN(X,Y)))rlSMOO[HOCMNCX,.Y)),

MN(Y,XJrSATl219CXrYllrSATZZ7ZfMN(XrY)} JrSATZ181A(~OO<YJ,HO~tX)),T~<Y,Xl) MOREISfMODCMN(X,Y)),MO•R•CMH•R•CMDOCX),MCDCY))J)

a tR:REAL ltS :REALl tM:MOREIStRrSl H N: KOREIS<R•i'!O"R"(S))J R ~ T& ·- TH9"L.OR•CNEG<R>rNOT<UEG<RlJ,

IS"R"CASSCRlrMO"R•(R)JriS"R"(A9S(R),R) rTHó•t.OR"CNEG(R)),(T:NEGCRlJABSNCRrT) ,{T:NOT(NEG<R>llABSNNCRof)) : OR<IS-1•(A8S(Rl,.MOwR•CR)),.tS•R•(A8S(R)rR))

N a T7 :: ORAP?(!S•R"(ABS<S>rMO•R .. CSJlr IS•R•(A3SCSlrSlr~OREIS<R•ABS(S)),f6($) ~cr:ts•R•<A3S(S>~Ka•R•csrrJ

ISKGREIS2CHO•R•(S),A8SCS),R• SYMISCREAL•ABS(S),MO"R•(S)#f),N)• [T:Is•a•CABS<sr~SlliSKOREIS2(S,ABSCS),. R,sy MISCR~AlrABSCS), s,. ThMU : KORE IS( R,.ABS(S))

'

·727S s

Y ; SATZZ73

-:::

.- T7~.7273•(~00(M~(X,f)J,xN•R•(~ODCX), HOO(Y>>•T~".7273•;TS•.7273•)

- 5.40-

•RP

•RT

+azn

f"ROP1 lT~CT>lB!JECT!VE(lTDCX>•lTDCYJif)J 'PS~P•

X a PROPZ :: ALLC{Y:NATJIMPCLESS<XrTJ.NOT<PkDPlCYJ) )) 'P?.JP'

a tY:NATl[L:LESStl.Yll[f:tT:lTO(lJllTO<YJl 1Y :: lOJT!'O : 1TO<Yl YY := XGUHY: lillt Y)

{IttS•E•CtTOCYl•1Y•YYJ1 T1 ·- ISOUP::;:o,.l,SATZZ4A<YJ,.y,.LESSISI3<Yh

IJ : tsu.n f a TZ ·- EC3E31!IS<1•Yl .. ~ORE<l•Y>•LESS<i•Y>•

SATZ103Cl•Y>•U NISU.Y) T3 := TH3"L.IMP*!Is•r•ctTOCY>•1Y•YYJ.IStl•Y>

,rz, [T:ts,.E•U TOCYl•lY•YYllTHTl) : NOH IS•t•U TD<Y>•lY,YY))

r a

[U:trQU)J rr. := ISf<1iOC1>•lTOCY),.f•U•10,

THt•N.SI~GLET•tU>> tl:IS•E•<tTO<Y>,<lO>f.lYJl[U:lTO(lJ1 T5 t= TH2wE.NOTis•ctTOCY),tY.YY,f,.T3•

I a n TRlS<lTO(Y)•f•<lO>F•lY•t••I>>

:= THS•L.SOME•(tTO(l),[U:lT0(1Jl IS~E*(lTO(YJ,.yy,f},[U:!TO<lll

SYMNO!IS{lTC!Y),F~YY,fS<UJ})

T7 :: THt•t.ALL~C1TO{YlotU:1TO(YJJ I~~SEClTOCl>rlTOCYlrr,U),YY,T6)

tN:N~TttS•E•CtTO<Y>•<lO>f•lY))J[U:lTOtlll T8 := TH2•E.NOTIS"I1TOCY),clD>F•lY•F•N•

N ; T9

no

F' a ru

fit( U)) :: TH5"l.SOME"C1TOC1),[U:1T0<1Jl

IS•E•<tTOtY>•lYrf),[U:1T0(1Jl SYMNOTIStlTO(YJ,F,1Y.i6(U)J)

:= THl•t.AtL•CtTOtY),[U:lTOCY>J IHtGEC1T0<1l,1T0(Y},f,U),tY,T9>

:= THl-L.I~P•(ISwE"<lTO(Y),<lO>f•lY), NOTCSURJECTIVE<lTO(l)•lTQ(Y),f)), CT:IS"E"tlTC<Y)o<lO>f,1YllT7(T),

: Is"'E•U TO<Y hf•<lO>F>

: NOTCIMAGE(lTO(ll•lTO<Yl•f•TYJJ

NOH SIJR. JECT IVEC HOU h lTOCYhF>)

NOH IHA GEU TOCl h1TO<Y ),f,. lYJ J

: NOT< SUR JECTIVEU TO< 1),- 1TOC YJ,f'))

T1Z NDTCSU~ JECT IVH lTOC 1),. lTOC Yl.f")J [T:NQTCIS•[•(ti0(YJ~<10>f•1Y)llT10(T)) :

•- TH2"L.ANO•tiNJECTIVE<1T0(1l•lTOCY>•f), SURJECTIVEt1T0<1>•1TC<Y>•r)ol11J : NOT<BIJECTIVEUTOUhlTOUhFJJ

L. a rn ·- THS•t.S~ME•t[T:lTO(lJllTCCY), [F:(T:1TOtlll1TOCYllBIJECTIVEClT0(1), 1TOCYl*f)o[fztT:lTO(lllli0(Y)lf12(fJ)

a T14 :: [YHIAlHT:lESS(l,Y)}T13(Y,T) X a [P:PROP2(X)JtY:NATl[L:LESSC<X>SUC•Y>l X a XS :: <X>S!JC l a XXS ·- XCU'!"OS)

YYl :: XCJT(Y) Tl5 : = T RLESS<l•<X> SUC• !# SATZZ4C C X)•l) YMl ·- KNCY.!,ilS) Tl6 ·- ISLESSll{<X:JoSUC•PtU•!h Y•PUYH1•1 h

SAT7.4((Xl.THlC•N.MN~<Y•l,.TlSl,.L)

T17 :: SAï(20CCX•YHl•l•Tl~l

: NOT<PRlPl(l•YJ) : PROPZU >

.: NAT 1TOC <X• SUC) lTQ(Y)

: LESSCbYJ NAT

: lES5(P~CX,l)•PL(YM1,.1J) u: ss n. Yl'! u

s

$

-5.41-

~--------------,T~1~8.----- :: ISLESSZCPL(YHl•l>•Y•YMl•

. u ~

THtO•N.MH"(Y,t,T15l•SATZ18A{YMl,l)J [f'":[ r: lfOC XS) l1TO(Y) J( B:B! J:::CTIV(( lTO( XS) d !'CO' hf'll T19 ::: ANOEH!NJECTIVEUT!JOSl•lTO<Thf)•

SU~J::TIVE<ITG<XSJ.~TOtY)rF),8l TZO := r.:~::H:::.'(!NJECTI'fEOTO<XS>•lT::J(Y),fh

SORJEC n VE ÜTOCXS !.-l'fO<Y hf h B 1-CI:Is•E'"U TOUh<XXS>f,YYl lH:.JH TOO:>l :.~ 1 · :"' I 111111 r x, u l T21 :: SAfZl6A<Ul•X•XS•lTn?cX,vl•SATZ18t(X)) TZZ :: EC3ElHIS<Ut ... XSlrMOfiE!Ul•XSh

T23 J2 TZ4

LESS(U!rXS>rSATZ103CU1·XSJ,T21) ::o U:SSISr!,Ul•XS·i:!!> :• OUTN(XS.Ul.TZJJ :: TH3"L.IHP•(IS~E'"ClTG{XS>•U2,XXSl•

ISCUl,XS)•TZZ,(T:lS"E•(tTO(XSl•U2rXXSJ liSOUTNE<XS•Ul.T2l•XSrLESSISil<XS>•TJ>

[J:IS•E•(tTO(y),<U2>f.YY1Jl T25 :: TRI52( 1TO<Yl•<U2>F•<XXS>f•YYl•J• IJ TZS : = I sn: { lTO\ XShlTO <Y hf" Tl ?•UZ" XXS .o T25 J T27 :: TH3•L.!M?•(!SPE•<tTC~Y)r<U2>F.oYY1)r

111 [J:ISUl.Y )l T2&

rs•E•<1T0{XS).oUZ•XXSl .. TZ~• [T:ts•Eft<lT0(Y).o<U~>F.oYY1JlT2ó(T})

:: INNCT•<UZ>n

:: TRIS<1TOCil•<U2>f~OUTNCY.olll• 1T~P(Y.o<U2>F)J.oYYl.oiSOUTIN~(Y.o<U2>f).o ISOUTNI<Y•Wl•lTOP(Y,<UZ>f),.y, lESSISIHYhJ))

u a T29 := TH3•t.I~P·tiSIWl•Yl.oiS•t•<tTOCY).o<U2> f,YYtJ .. T27.o[T:IS<IIl,YllT28(TlJ

I ; u il

I ;

T30

T3l

T32

:: GRE1CLESSCW1•YJ,JSCWl,YJ.olTOPCY.o<U2>f) ,rz9,

:: ISLESSISZCY.oPlCYMl.tl,Pl<Wl .. tJ.o T!il c•N.!-!N .. (Y; 1• US J • SATZ258( y, iU "T 33) J

:: TH?•t.oR~CtESS(PlCWl .. l),?ltYHt .. l)),.

lS(PLCWl•lJ.oPL<YMl.ol}),.LESS(Wl.oYMll.o IS<W1~YM1J~T31 .. tT:LESSCPlC~1•1>• PltYM1•1>JlSATZ20CCW1•YHl .. t•T>, [T:IS<PLCII1•1> .. PL(YMl.ol}JlSATZi09(111• YMh t..T> J

HZ :: O:JtN<nu .. wt, HZ> F'1 := CT:lTO<XJlll2H> [V:lfO(X)l[J:ts•E•(tTO(YHl)•f1,<V>f1>1 T33 ::: ISOUTi'IEfYMl,WlCUl.T32CUl,.WUYJ .. T32(Yh

T31t Tl5 Tló

1'37 [V:lTOUMl)] .Vl ne T39

J) :: ISINNECY,.<U2CUJ>f,.<UZCV>>F,.T33) ::: <T34><U2CVJ><U2CUJ>T19 :: ISOUTNECXS .. Ul(U),T23CU> .. U1CVJ,T23CVJ•

T35) := ISINNE<x,u,.y,.f36)

·- INN<YMbVJ :: SATZ164CV1,.Y~t .. Y,1TOPCYH1,.V),.T18) :: ~C3E31CIS<Vl•Y)•MORECVl,YJ,.LESS(Vl,Y),

SATZ10B(Vl•Y),f38} HO :: lESSISIHV1•Y•TJ8) vz == ourNn .. vt.. HO> WJ := <VZ>tNVF'ClTOCXSl .. lTOtYlrf•S> f41 := TliiNiiF2(HOCXSh1T0("(),f,B.o\'2J [J:ts•t•ctTO(XS> .. WJ,XXSll uz := rsruroo:s>,lfO\Yhr.~tJ.xxs .. J>

LESS CY'f lr Y)

HIJECTI VEC1TOUS),1T0(Yh::- >

: SURJECT IVE<1TOUShlTOtU,.n

NAT USSCU1 •XS)

NIStUt .. XSJ lESSISl UhXSJ li CC lCS)

NOH IS'" E .. U TOCXS J,uz,.XXS))

: IS"E•(l TO CY h <U2>F,. <XX S>f") : IS•E"(lTO(XSJ,.U2•XXSJ

NDTtis• E .. C1TOC Y) .. <U2>F ,yyt)) : NAT

: IS-t•u TDU h<U2>F.oYYl J

: NI SOU .. Y)

lE ss Clfl ,. Y)

: LESS IS{ Nl,YMU : lTOCYtn l

[f :1 T!Jt U 11 TOUMl>

IS(Ifl<J hWHVH : IS•[~(1TOCYl,<UZCU>>F,<U2CVl>f)

ts•E•(tf0(XS),U2(U),U2(V))

ISC.IlCJ > .. uuvn : IS•[• U TO<X ),.U, V)

NAT LESSCVl ,u NIS(VloY) lESSISt VhY) HOO"> lTO( XS>

; Is•p•a TO<Y ),.yz,.<N3>f)

: IS•[•(l TOCY h<Wl>f',. <XXS>n

':'"' s. 42-

TH := TR3IS<lTOtY),V2•<ft3>r•<XXS>r•YYl•T41, Tl.2, I>

TU :: ISOUT~E(Y,Vl•T4),Y.LESSISI3CY),T43) V :1 ns :: TMJ•L.IMP•(IS·E-ClTOCXS),NJ,XXSl,

ISCVl•T),T]9,[T:zs•E•t1fOCXS),~3•XXSll f44( Tl}

!14 ::. z;mr:cs,;r;n tJ:IS(WiuXS>J H6 := TRISC1TDtXS),WJ,QUTN(XS•W4•1TOPCXS•W3>

) , ·o: '>• ;sGiHI NN( X s, w 3 h ISDUT1IC~S.~4•1TC=~XS•NJJ,XS• U.: SS IS B CXS lt J l)

V ; TH := TH]•L.ts~~czsCH4,XSJ,IS•[•ttTCCXS),W3• XXS1,!45,[!:IS(ft4•XSI1T•s<~ll

Tft8 := OR~lClESS<W4,KS>,ISC~4,XSl71TO?(tS,W3) ,f47)

TU := SATZ26UX .• W4,T46) 115 := ouna x.~ ... T49l TSO :: IS!~OUT~(XrM4,T49) T51 :: T~!S1:TO(ZS),W3,QUTM<XS•~4.1TOPCXS,W3)

l•J2{H5Jo!SD~TINNCXS,WJJ, IS~~ï1!ttS,W4.1TG?CXS,~3>,Ul<W5), T230i5>•T50))

T52 := ISFClT9<XS>•lTOtY),F,WJ,U2<WS).T51J T53 == TRISflTO<Y>•V2,<W3>F•<U2<W5}>F,T41•

rst > T54 :: TR!SCNAT,Vl•I,~(y,yz),Wl(WSJ,

I5I~GUTNCY•Vl,T40)•ISINNICY,V2•<UZCN5l >F,.T5J))

T55 ;: TRIS{lTC<T~1l•V•OUTN(YHl•Vl• I TCP C nu, V)),. WZC lol5 h ISO!JT Il'tN( Ylfl•V h ISQUT~I(YM1,V1•1TOPCYH1•Vl•Wl(W5)• T32C W5 h T54))

T56 ·- SO~EIClTCCX}o(T:lTOCX>liS"E•<tTOCYMl ), '/,<T>fl}oiiS,T55)

I a T57 := INJI(INJECTIVE<1TDti)•1TOCYK1l,FlJ• SURJEC7IVE!l!OCXl•lTO<YH1l•Fll• [U:tTO<X>JtV:lTOCXll[T:IS•("(lTOCYHl ), rl•<V>Fl)JT37<Û•r•T1•CU:1TO(YK111 TSS<!J))

T58 :: SO~EI(rTHTOCXU1TOOHlh{G:[T:1TGCX>l 1\0(YMlJlBIJECTIVE(lTOCX),lTO(YKl)•û)• rt. T57>

T59 ·- <T56><T17><H!l>P 8 a [N:N~TCIS"E•ttTO(Y)~<XXS>f,vYl)JJ

1'!0 :: <YYl>IN'IF'Cll'OCXShlTO<Yhf•B> TSO :: THI!'IYFZ<lTO<XS),1f0<YhF.S,YY1> FZ := CH,NGE><tTQl XS), lfl"l( n,.r,.M.O,XXSl Til :: CHANGEr2C1Tij(XS)•lTO<YJor•KO,XXSoXXS•

REFISilTQ[XSJoXXS)J T6Z :: TRIS2C1TOCYl•<XXS>F~oYT1•<MO>foT61•

T60l T63 := TH5•[.WISSEL•(tf0(~SJ,.1TOCYJ•f•MO,XXS,.

Bl Tó4 :a T59(F2oi63rT6Zl

a a T65 :: THt•L.IMP•CIS•E•CtTOCYJ,.cXXS>F•IYll• ca::, [T 1 i s•t:"< !TO CY), <XXS>F oYYU H59\T) ,[TrNGiCIS•E•ClTOtYJ•<XXS>F,YTll)J TG4!Tll

L a T65A := TH5'"l.SOICE,.([T:1TIJUSlHTOCYh tr:rTrl!GtXSlllTO<ïllBIJECTIYE<1TOCXS) o!TOCY>•f),[f:[T:lTO(XSlltTCtvl;

IS .. I:"ct TO<Y J.vz,yyt l :JS(Vl,.fl

NOTC ts• [•(1 TO<XS ),.W 3,X XS)) NAT .

: IS•[•(l TO<XSJ,WJ,XXS)

~II SOI4• XS)

: LESS ( 114 •XS> l.ESS IS[ 114 ,x l

: !TO<lO : ISCifluJ Hil5 )J

: IS .. E•f•<U2CW5J>fJ

IS•(•(t TOCYJ.YZ•<UZCW5)>F)

IS<Vl.f UWSU

: IS•E•(tTOCYHl),V,<WS>Fl)

: IKAGEU TO<X )~1TOCYHU•Fl•V)

~ PRC!' UY Hl ) : CON

1 TO( XS) IS'"E•n TOCY ),.yyt,<HO>f)

: rr :noc xs)] 1too,

: BIJ::CTI Yf:(l TOUS>•t TO< TJ•f'Z> : CON

CGtl

- 5.43-

+8275

-ezr:;

U8Z75

P a TG6 x a Tó7

[L:LESSCX .. Y)) SATZH4

[T:BIJECTIYE<1TO<XSJr1TO<YJ,~)lT65<F• T))

:• (Y:,ATl[T:lESSCXS~YJlT65A<Y•T) := INrlUCTt0N([T:I'~ATlPROPZUJ,T14.n:N.\Tl.·

(U:P?.OPZ(f)~TSó(TrU)~Y.J

:= <L><Y>T&7•.&274"

[F:(T:1TOCXJ11TO(Y)l SATZ!74A ;: T~4·L.SO~E*CtT:1T~tXJl1TO<YJ,

[ :;: t:T: 1 H!CX) l1 TO(Y l l8IJECTIVEU TO<Xh

NOTCPRJPl(XS~Y)) PRC!'ZC~Sl

NOT<SO•t•t•([T:1TO(XJ!1TOCYJ•[F:tTI1TOCXJl1TO<YJl BIJECTIVEllTO<XJ;lTOCYJ,f))J

lT::CYl,GhSAHZrt•rf) : NOH8IJECTIVEC1TO<Xh1 TO('( hFU

3 tX:NAT l(lJ:lTOtx)] INN := IN~""N•cx,.ul

1 [Q:[T:CXltU:CXlCXltX:NATJ[f:[T:lTOCX>lCXJ X ; [N:lfOCX>ltO:NOTCIS*E•(tTD<XlrN,XOUTCXJ)Jl

n

TZ

I.EMifAZ75 ; ~ (G:tT:lTOUJ)CXl

RECPROP

:= THJ•L.IMP•(IS•N•CtNNCX•NJ,.Xl• IS•t•(!TU(XJ•N,XOUTCXJJ,Q, {f: l S"N"( I NNt x,. ~D r lO lTRISU TOCXhNr OUTNCX.IH,CX.NJ.tTOPCI,N)),XOUT<X),. ISCUTIN~<X.Nl•ISOUTNI<X•INN(X,Nl• 1TOP<~•N>•X•LESSISI3{XJrTl)}

:: OREl<lESs•N•CINNCX.N>•X)r IS•N~liNNCXtNl•Xl•lTOPfX,NJ,.fl}

t= ANO<ISC<lOUT(X)>G,<lOUTCXJ>FJ• (T:lTQ(X)l{U:NOT(IS•[•ttTO<X>•T• XOUH XJ > J liS< <OUTNC x, >SUC,. LE~MA275(T•Ull>G~<<OUTN<X•<INN{X,TJ> SUC.LE~~A275{T,Ull>F><<T>G>Ol1

X 2 10 :: lOtiTUJ XIJ :: XOJHX·l [U:NATlti.:LESSIS•N•(SJC•Xl! Tll ::: SATZ163(U,.SUC .. X.SATZ18C(UhU T1Z :: lESSISI1•N•(U,X•Tl1) JX := CUTN(X,u,TtZJ Tl3 :: EC3~3l<Is•N•<U•X>•HORE•N•<UrX),

tEss~n·cu.XJrSATZIOB(U•XJ,TliJ T14 •- TH3•t.IMP~czs•r-t1TOtXJ.UX,.X0)~

IS"~·<U•Xl•T13,(T:IS"~"C110(X),UX•XO>l Is:JT~~tX~UrT12~X,LESSISI31~),.T))

: NAT

: NOT< IS•N"UNN(X,N}.,X))

LESS IS• N"'( < INN< x, N) >SU Cr X>

: 1 P~DP 1

: lTOU) 1T0( X)

: lESS•N"(U.oXJ LESS zs• N•cu .oU HOO'

:-:xs•N"r u~x,

s

s

$

$

- 5.44-.

T16 ISt~OUTn~x.u.TtZJl

:= ISOUT~I(X,SUCrl•<INN(XrUX)>SUCr LEH~AZ75~UX•Tl4).T15)

X 2 tM:1TOCXJlCO:NOTCIS*t•<1TGtXJ .. ~•XCJJl

· : IS'"E•U TO.CX hOCTN<X•SU: ,u .. oUTHtx•< INN<X, UU>SUC. lEMMA zr 5(UX, T14)) l

NS :: OU.TNCX·<I!iN(X .. N)>SUC•LEM"AZ75UbC)) : liOOO F a [G:('f:lTOUHCXJ .

PP.OPl. := IS<<10>{;,<10>F} : 'PR!JP' PROPZ :: tT:lTOCY.)~(U:NOi(IS•E"<lTOCXJ,T;XOlll

IS(<NS(T•U~>Gr<<NSCT .. UJ>F><<T>G>Q) 'PROP' [PG:UCPRJPC G) l T3 :: ANDE 1{ P'Wi' l• PPCPZ,PG) PRO? 1 tN:lTCCXJJtO:NOTCIS•E•CtTOCX;,~ .. XGlJl T~ := <O><N>A~DEZCPRCPl•PROPZ•PGJ tS<<NSrN,QJ>G,<<NSCN,GJ>F><<N>G>Q)

PG a {U:NATltL:lESSIS•N•<SUC .. Xll T17 :: !SF'( trC( u,ex .. !hOUTNU,.SUC .. L}•

NStUX( U,Lh T lfoCI•l l) "Tl6(U,.l) J ISC<OUT NU, SUC"l )>G•<NS CUX(U,l).o T 14CU .. L Jl>Gl TU :: TRIS(CX,<O~T~(X~SUC~l)>G.o

<MSiUX<~•L>rTl4!U•llJ>Gr<<~SCUX(U•l>• T14CUrLJJ>F><<UKCU.Ll>G>Q,Tl7o T ft( PG, Uxt:i•U" Tl4( U•U) l : IS<<OUT NU• SUC•l )>G.o<<~ SCUX<U•U,. T14CU,. U )>f><<UX{ u,

l )>G>Q) G a t~:[TtlTDCXllCXl[U:NATl[L:LESSIS•N•cu,x>:

PROP3 ·- ISC<OUTN<XoUrl)>G,<OUTN<X,U,.LJ>H) 'PROP' U a P~OP~ :: ASDILESSIS·~·<~•Xlr[T:L[SSIS•N~(UrXll

PRG?~(T)J 'PRJP' !'ROI"5 := OR\PRGPforMC!tE•N''(U,X)) 1 PR:JP•

H a tPG:~ECPROPCGJltPH:RECPROPCHJltL:LESSIS•N•(l,X)l T5 :: ISOUJNICX,l.ol•l•SATZZ4ACX)r

REf'ISUATrl U : JS•t•(l TOU hOUTN<Xrl•lJ•l OJ T6 := ISF( lTOCXhCX .. GrOUTNCX•l.rlJ,lQ,.T5) : ISC<OUTNCXrl•lJ>G•<lO>GJ TT := TRISCCX .. <OUHHX.ol•Ll>Gr<lO>G,.<lO>f•f&,.

T3CPln > ISC<OUf NCX,lPLJ>Gr<lO>fJ T8 :: TRIS2CCXr<!:!!JT'I{X"l•Ll>S,<OUT:'HXrhL)>

Ho <l O>F" T7,. T7(HoG,. PH,p;;,L) l PRC? 3C1 •L) 1"'4 a T9 := ANOHLESSIS"S"<1•Xl..[T:LESSIS•N"C1PXJJ

PROP3Ct,T},.SATZZ4ACX), U:LESSts·~·U.UlT8(T)) : PROP4<l l

Tl!) :a DRil<PR::JP4U J..MO!H:·~~·(l,XJ,T9J : P!f0P5U J [U:NATJ[P:PROP5(U)l[L:tESSIS~N'"CSUC,Xll T17 :: EC3ESZ<Is•N•<u.x>,MQRE·~·c~,.Xlr

LESS•n•cu,t),.SATZlOBCU•Xl•TllCU,LJ) NOTtMD~E·N•(U.oXJ> TZO :: tlRE1CPROPHUhM'ORE'"N"fU,X),p,f19) : PROi>ltÜ) !21 :: <Tl2(Url)>~NDEZCLESSIS•N•(g,.l(),

[J:LESSIS"N•(U,X)J?~OP3(UoT),T20) PR0?3(U,T1Z<U,LJJ TZZ :: ISFCCXrCX,(T:CXl<<KS<UXCU.tl.T14CUol))

TZ3

T24

Tt5

>F><T>Q,<UXCUrlJ>G,<UX(UoLl>HrT21) IS<<<NSCUXtU•LJ,.T14CU.oLJJ~F><<UX(U,LJ>G>O•<<NS<UX(U,l1•

:: SYMISCCX,<CUTN!X•SUC•L)>H, «NSCIX(U#U • Tt4(U, L) l>r>«UXCU,U>H>

T lft( U,;. ) ) >f >«UXW.o l)> H>QJ

g,. T180tr Pli.U .. U> : IS<<<M.i WX( U•L h T14<U•ll )>f><<UU Url.J>H>Q, <OUTN( l(,

:: TR31S{CX,<OUTNCX,SUCrll>G• <<NSCUX(UrlJ" Tl4<Url) l>F>«UX<U•l )>3 > Q~c<NSCU~C~,L),il•cu,L>)>F><<UXCU•L)>

H>Q,<DUTNCX~SUC•Ll>H•Tl6CG .. PGrU•LJ• T22, T2:;)

:: ANOI(lESSIS~N•(cU>SUC,X)• [T:LESS! S"'tf•( SUC • JO lPROPH SUC• Tl

SUC.ol ,,. HJ

PROP3(SUC,.L>

,L, t r: LESSIS"N .. ( SUC • X J Hzt, CT)) : PROP 4(SU C) ::: ORI 1(PROP4(<tJ>SUC> ,Mt.J!?E .. N .. (S·UC• U"

- 5.45-

T2'5 l PROP5 (SUCJ P ; tN:NOTCLESSIS•N•(cU>SUC•X>>J

127 ·- S4'l'Z10tc:(<1J>SUC•.X .. N> : HGat•N•.(SUCrlO f ZIJ • - ORI2 ( :> ;>0P4CSlJC h KORE "N•( SUC• n •

T2Tl PROP5(SUC) P ; T29 :• TFl'"t.I!1P'"ClESSIS"N .. (SUC .. Xlr

PRCP5(SUCJ,[T:L~SSIS•N•(cU>SUC•XJl T2.CTl•fT:NDT<LE~SlS"N•CcU~SUCrXl)] rzann : PROPSCSUC)

U ~ 130 :: ISDUCTIONt(V:~~TlPROPSCYJ.TlOrtV:~ATl

P't ~ [NHTO(XJl T31 :=

T32 := Tll == TH :=

135 :::

136 ::

?!i il J'37 := r ; PROPi :=

x ; PROPT :=

[T:?::(C?5{1i>HZ90,.T),U) : PROPS<J)

ISf(lTO(X),CX•G•N•G~;~<XriNNCX,NJ, l!JP(X.NJl,ISGUTlNS{Y.,Nl) SATZlODCINNIX•Nl~X,lTOP<X,N)) OREl<PRDP~CINNC~.N}J,MORE·N~(J~N(X,Nlr XJ,T30(lqN(X,Nl)rT32) <lTDPtX,N>>~NDtZ<LESSis•N•CINNCX,NJ,XJ ,[f:LESSIS~NP(!NN(I#N),X)lPRCP3ti~~(X,

n>.rJ.T33J SYY.ISCCX,<~>H#<OUT~<X•INNCXrN)• 1TOP<X~N)J>H,T31(H,G.PH,PG.NJJ

TR3IS(CX,<~>G•<OU7N<X•INN<X .. N), lTOP{X,N)l>G•<OUTN!X•!NU<XrN)r 1TOP<X,NlJ>Hr<N>H,T31•T34rT35) fiSi(lTJ(X)rCXrG•H,{T:1TOCX>lT36CT>> Sl!\0:;: .. t. "tE T: 1 TOOOlC x., [ G: (T :1 JO U )lCX l . RECPROP(GJl ALL•t.•C(T:lTO<XJJCXr[F:[T:tTO<X)JCXJ PR!JPS(f))

ISC<N>~r<OUTNCX•iNN(X,NJ,lTOPCX .. NJJ>G) NOT<MO~E·N•CINNCX~N)rXJ)

: IS(<N>i r<N>H) IS"'t,. ([ T: 1T 0 CX JlCX• G• H)

'PROP'

: 'PROP' 0 ; tf":tT:1T0(1JlCXl

l38 := P.CfiS<CX•<lOCl)>f') PROP1Urf"f"J tN:lTD(l) J [0: NOTH S"E"H TOU ,, N,. XOU) J }~ f39 :::: <THl"N.SINGLET•c N)>O : CON T40 :: CO'iEtiS<<NS{ l,.NrG)>f"•«NS(bJ!I,Q)>f'>

<<N>f>OhT39 J lSHNSt l .. N.OJ>f,«NSU,.NJiiU>F>«N>f'>QJ F a f41 ·- ANOI<PROP1(l,Frf)rPROPZ(1,frf"),Tl8r

[T:1TOC1Jl[U:NOT<IS~E•t1TOC1),T,X0t1JJ JlT40<T .. Ull : RECPRO?(l,.f,f)

T~2 := SOMEI<CT:lT0<1)JCXrt~:[T:tTOC1JlCXl RECPROP(t.frGlrfrTfoll : PR0?"6U •F>

0 ; T43 :: tf':rT:lTOClllCXH4Z<FJ PR<l?7U J X a (P:PROPTCXJl

XS := <X>SiiC NAT [f":[J:lTOCXSJlCXJ Fl :s LEFTCCXrXS•X•LESSISil•N•(X•XS•

SATl18C(X) ),F') : [T:t TO( UJCX T~4 :: ONElC(T:1TOtXJ1CX,[G:tT:1TOCXJJCXJ

RECPRQP(XrFl•Glr(G:(T:lTOCXJJCXl tH~[T:lTOCX)JCXlCU:RECPROP<J,.fl,GJl

[V:RECPRCPCXrfl•H)lJ3Ttf1•G•H•U•Vl, <fl>Pl : ONE·E~ tT:tT0(1JlCX,[G:[T:1TOCXJlCXlRECFROFCX,flrG)J

Gl :: INOCtT:tTOCX>JCX•[G:tr:HOUJlCXl RECPROPtxrFlrGJ•H4) [T:1TOC XJlCX

T45 :: ON~AX({T:lTOCX>lCXr(G:(T:lTDCXJlCXl SECPR::t?U•fl .. G), THJ RECPRO? ()(;fl,Gl)

tN:lTOCXSJl us (Q;NOT(NXSJl H6 N1 B

= SATZZ6A<X~INNCXS~NJrTZ(XS•N•O)l : ûUTN(X,I~N(XSrN},T~;)

::: <Nl>::;l

'PROP'

LESS I s• N•U NtnlCS•N )r XJ lTOC X) ex

- 5.46-

f a ~ ;

D ;

r ;

nr :=

TU :-= 4 =-= c ::

CI :l'ollCS l H9 :=

TSO ::

GZ := T51 ·-

T52 :: T53 := T54 :=

T55 ::

T56 ::

nr == T58 ::: T59 ·-

ISOUTNIIX.I~~(XS,H),T46COI•INNCXS,N), T 46( 01 h !t(f'"I st:lAT, IN'H )($, N) n ISF'f li::JCO .. CX,GI..~H C),.N1(01 hT4 1l <<KO{:S)~F~<<lCtXl>Gl>Q

ITERL.R·t~xs.:x .. rr:~xsJA .. CT1NOtc•xs>J 9(T} .. ~T!NXSl[~t~XSlREF!$(CX•A>• (T:NGTI~XS~J[U:~GlfNtS)lT45(T,U))

!TET•L.!•(NXSoCX.!T:~XS'A•tT:NOTCNXS>l 8(T),[T:~XS:r~~~XSl~EfiS<CX•~),

[T:~CT(~~SJJi~:,o~;~XS)lT48(T,UJ,!l

ITEF•L.R·:~xs,cz,[T:NXSJA,[T:NOTI~ZS>l BCTJ,[T:NXS![~:HXSJq[flSCCI•A),

(J:NQ!(IXS)J[U:NOT(~ISllTh6{f~UJ•0) {T:lTOO::S)JC(fl TH3"L.I~P·CIS•E•(lTOCXSl•lD(XS),XQCXSJ >•IS"N~(l,XSJ.SYMNOTIS(NATrXSrlr<X> AXl),(T:!S"E~ClTO<XSl•lCCXSlrXOCXSJ)l ISOUTNECXS•l•S•TZZ4ACXSirXS· LESS!$!3(XSl•i>l T51H 1GOtS),751) ISINOUTN!XS•l•SATZ24AtXS)J ISOUTNICX•l•SAJZ2.A(X),INN(XSrlOCXSJJr T45{1~(~S)r!51lrT53)

I5fC1iOtXl•CX•GlrlCCXl•Nl<10lXS>•T51J• T5t.} TRISZtCX•C<lOCXS)),<lOCXJ>GlrB<lOCXSlr T51 )rT5ZrT55) TRIS<CXrC(lO<~SJ)r<l0(Xl>Gl,<10(X)>flr T5&rT3{XtflrG1rTt.5)) lSINOUTN(Xrl•SATZZ4ACXl) ISOUTNICXSrlrSATZ24A(XSJriNN(Xr10(X))r r~~tssts·~·c:s~rx.lCtXlJ.x.xs. 1TQPCX•4C(X>>•LtSSISI1•N•<XrXS•-SATZlSC<lO )), TS!l >

IS'"E•U TO<X hN1CilhN1Hll H IS<B<OhB<Olll ex

ex

IS(C • SJ n :trot: xs n ex

NOTCIS•t•<lTOCXSJriOCXS>r~O<XSJJl IS<C ( 1l US) hB< 10CXS1r T5U) Is•N•n • I~NUS,. HHXS)))

IS-t•<tTO<XJ,10(XJrN1{10(XSJrT51J)

ISC<10[X}>G1rBC10CXS),.T51J)

: IS(C(I] <XSJ h<lO(U>GU

: ISCCCll USJ h<lOU>>F'U : IS"~•<t .. INN(XrlO<X)))

lS•[•ttTOCXSJrlO<XS>rLEFTlTCCXSrXr LESS ISll"N• (X;XS•SATZ18CU.) h lOCX n J

l'óO ::: ISH lTO<XShCX,f rlOUSh L(fTlTCCXS•X•LESSISil·N~(XrXSr

SATZ18COOlr13UJJrT59J : IS<<lot XSJ>fr<lOUJ>Fl J T61 ·- TRlSZCCX,CtlOCXS>J•<lO<XSJ>fr<lOCX)>

flrT5t.i6:>> PROP1US.FrG2J a ; [I:ts•E•(lTOCXSJ,HS<XSrN•O>rXG<XSl)1

T62 := ISOUTNECXS•<I!öNOCSrNJ>SUC,. tE"IMA275<XS• 'i• 0> • XSrlE SSI SI H XS J.I > : IS""'' •(< INN( XS .. N) >SUCrXS)

HIJ := <TóZ><lC><IM!'HlCS .. fU>AX4 : IS•N•UNN<X.SrNJ,.XJ T&4 :: ISOUTNitX .. INNC:S .. HJ•T46•X•L(SSISIJ(X}r

T6H IS"'t•u TG<X hNlrXOU}) T65 •- ISH liO<XhCXrG!.XQCXJrNlrSYHISC 1f!)(X)

rHhXOO:hió4)) : ISC<XQ[ X>>Gl•IH T&& := TRISZCCXr<XD<X>>Gt .. c~B·i65rT50> : IS(<XO[ lC)>Gl,.C> T&7 := ISF<CX•CX .. tT;CXl<<XQ(XSl>f><T>O~<XCCX>

>G! .. C• T&6l ISU,. « XO<XS J>F><C>Q) 168 :: ISF"< 1TOCXSlrCX,.f,XOCXShNSCXS•N•Oh

SYMI S J ISC<XO[ XS l>F' r <NSO:SrNr Ol>F' ) T69 :: ISFCCX .. CX .. <C>Qr<XQ(XSl>F•<NSCXS~N•Ol>

r,r&aJ ISC<<XltXS)>f><C>Or<<NSCXSrNrCJ>f><C>Q) T70 := TR~ISCC~r~(~SCXSr~,Cl)r~•<<XO(XSJ>F>

<C>Ih <<NS{ XS• :1.0 )>-f> :<C>O• T490lS CXS, t4, 0 hl h TG.7,. TS 9) ISCC( NS US. N,.O)) ~«NS( XSrN,. Q)>n<C>Q)

0 i [Jl:~OTCIS*E•C!TOCXSJ,NS[IS•N•Dl•XC(XS>)J H I: IS •[•( 1T 0( lCh NI.XOClD))

-5.47-

T71 :: ISUUTNEtX~INNCXS-N>-T4&,X,lESSISI31XJ• n : Is~~·ctNN(lCS•Nl•XJ

TTZ =~ A X2< !'HKXS, N h IC,. T71 l : IS ""i .. (< INN~ XS,.NJ>SUCrXSJ T13 == ISaUT~!CXS•<INNCXS~~l>SUC•

LEHHAZl5~Xs,N,O),XS•LESS:SI3CXSJrTT2> lS.,.E•(l TO<XS hNS<XS,.N,.OhiC OUSJJ 01 a T74 ·- TH3*L.IMP•(tS•E•(lTOCX>•Nl,XO<X>l•

IS"E•< lf0( XS h !-.SUS; lt• 0 h lCO{ XS l) ,.{Jl,. (Ttts•E•tlTOCX> .. ~l.XOCX>lJI73(~)) NDT<IS•E•<li0{X),.N1,X~{XJJ)

T75 :: ISIND~!~(Xri~~CISr,!,T46J IS .. N•n NNCXSrN),. INNOC• NlH T76 . - AX2<I~~(XS .. ~JPI~~(~i~1),.J75) : I S"''C •t< INN< XS,III) >SU c, SUC J T11 := ISrND~T~!XS,~!1"~{XS,,l>SUC~

LEXMA275~XS .. N,O)J : I S""i • CN) >SUC, I NN(( S• NSC X S ,N,.Q) J) T78 :: TRI51C~~r .. tN~!ISrR~CXSr~r0J),

<INU('•Nl)>SUCr<IN,<XSr~J>SUCrT77,.T76> : I S"'N•U NN<X SrNSC XS• Nr 0)) r< INfH X •lH) >SUC) 179 := ISOUTNI<X,INNCXS.NS<XSrNrO)),

T46C~SCXS•N•OlrOl>•<INNCXrN1>>SUC,. lE~NA275(XrNlrT7~).T78> : ts•E .. U TOU),. Nl( NS< XS• N, OJ,. Cl h t.$( Nt.. T7U J

T80 == I Sf( 1 TOCO • C X• Gt rN!C NSC XS .. Nr 0 hOU • NSOH,.T?C.hT79J r IS{9CNi{XSrNr0) .. 01)r<NS(NlrT74)>GlJ

181 :: ISI~D~T~CXr<I~N(XrNll>SUC .. lEMXA275(X•NlrT74l) : IS•ll•(c INN( htU) >SUC .. I NNU •NS<N.l• T74}))

raz == IRISC~AT,<!YNCXSrN)>SUCr<i~NCX .. Nl)> SUCr!SM(XrNSCNl,.T74J),T76•T6ll : ISftN•C<INNCXSrNl>SUCriNN(X,.NSCNl,.T74JJ)

TU :: ISOUTNitXSr<INNCXS.Nl>SUCr LEMKA275(XSrNrCJ,INNCXrNSCN1rT74J), TRLESSIS"N•<INNCX~NSC~l .. T74)lrX,.XS• 1TOPIX•NS<NlrT74)), LESSIStl•N•cx,xs,sATZ18C<X>JJ,T8ZJ : ts•t•<lTO<XS)rNSCXS.NrO),LEFTlTOCXSrXr

LESSIStt•N•cx,xs .. SATZ18C<XJJrNSCN1,.T74J)) fat. := ISF<1TO<XSlrCX.frHStXS.N .. OJ•

LEFTlTOCXS•X,.LESSISI1•N•(XrXS,. SATZ18CCXl1rNSCN1.i74)J,.T83) : IS<<NS[ XS .. N .. Ol>F' ,.cNS< Nlr T7 U>F' U

f85 := ISftCX~>CX•Q,<NS<XS•NrOJ>F'r <NSCN1.T74J>F1.T84) : ISC<<Ni(XSrN,.OJ>f>O•<<~S<Nt .. T74)>f1><8>CJ

T86 := !SflCX .. CX•[T:CXJ<<NSCXSrN•O>>F><T>Q,.c,. B;T50l IS(<<Ni<XS•N•Ol>F><C>Or<<NS<XS,.N .. O)>F>Q)

T87 == TR3IS<CX .. C<NS<XSrN,OlJ,B<NS<XS.N,.OJr Ollr<NS(Nl•T74l>Gl•<<NSCN1•T74)>f1><8> o .. 150( nsocs .. te. Oh 01 ,,. no .. T4(Fl•Gl .. T45,.N1rT74JJ : IS(C(fü US,. N,.QJ )•«NSC Nt..T 74J>F'l>Cl

T88 ;e TRI 5 (C x, <<NS (XS, N,. 0 l>F'> <C>Q, <<NS(XS•N•G)>f>Or<<NSCN1,T74)>f1> o .. ra&. ras J : ISC<<NS<XS,.N,.OJ>f><C>O,<<NS(Nl,T14J>F1>CJ

189 == TRIS2(CX,C(NSCXSrN•OlJr<<NSCXSr~rOJ>f> <C>Cr<<NSCNlrT7~)>tl>QrT87rT68) : IS(C(NiCXS•N•O>J•<<NSCXS•~•Ol>F><C>QJ

!) :J T90 := THl•L.IHP•t:s~E·ctTOCXS),NS<XS,NrO),. XO<XSJJ,IS<CtNSCXS .. ~·~>>,<<NS<XS•N•O>> F><C>QJ,tT:Is~t·<lTOtXS>,NSCJS,.N,.Q),

XOCXS>lJTTOCTJ,[T:NQT{IS•E"<lTOCXSJ• NS(XS,NrOJrXC(XSl)lJT89CTJJ : ISCCCNStXS,N,.Q)),.<<NSCXS .. ~,OJ>F><C>Q}

F' a T91 := [T:1TOtXSJltU:NOTCNXS(Tl)lT90(f,.U) PROPZC( s,.F,.GZ> Ut := ~NDI<PROP1CXS,frG2>•PROPZCXS,f,G2>•

Tbl•T91J RECPR03 CXS,f,GZJ TH := SOHEIC[T:lTO<XSJlCX.,(G:tT:tTO<XS>lCXJ

RECPROPCXSrF,G~•G2rT9Z) PROP6{'< s,.n p a T94 := tr:tT:lTC<XS>lCXl793Cfl PROPTCIC SJ -5.48-x • T95 := INDUCTI~~([Y!NAilPROP1CY),T43,.(Y:NATJ

[f:PROP7CY>lT94(Y,rJ,z) PRCP7U:) t.r:crn roe X>lcXJ T96 :: <F'>T95 : PROP'6 U .,r) T!IT ·- ONEX<tT:lfOCXJlCX.(G:tT:liO{X)JCXl

RECPRJP(X,.r,.Gl,{G:{T:1TOCXJJCXJ

lM~~~~~lU\AJ~~AJLU~~C~r~U-\A•r-U6J

[ V:RECPR~P{X,f .. H HT3T(F" .. c,.;;,.u,. V h T96) : ONE•E•t tT :tTO( 10 lCX,. [G HT: lTO<XJ lCX) RECPROftX•r ,G))

-szr; s

H8Z75

F a SATZ275 RECF

S4TZ275A

tN:tTOC:Ol

·- nr-.szrs .. u·., :: !NOCtT:lTOCXllCX,.[G:[T:1TO<X)lCXl

RECPR~?C x.r ,GlJoSA TZZ75 l :: ONEAX<[TilTQ(XlJCX,.[G:tT:lTO(XJlCXl

RECPROP<X,f,.Gl.SATZZ75)

RE.C :: <N>RECf r a SATZZ759 ·- T3•.szrs•cx.F" .. RECf,.SATZ27SA> N :t [Q:~OTtiS•t:•(tTO(X),.N,.XO~TCX!Jll

SIJCX :: NS ... 821'5"(N,Ol SATZZ75C :: T4".8275•cx,.F,.RECF .. SATZZ75A,.N,.Oi

F 3 !G:rr:1TO(X)JCXlCR:RECPRO?CX,F,.Gll SATZZ75D. :: T37".6275"U,.r,G,.RECf,.R•SATZZ75A) OC:lTOCX>l SATZ275E :: FISEC1TOCX>•CX .. G•RECF .. SATZ2150•NI

x a n =~AT 1

Y' :t (L:LESSIS"N•n,.XJHF:n:UO<X>lCIO rL := LEF"Hcx,.x .. r .. t .. n Rf :: RECf{X,.f) Rfl :: i.EFHCx,.x,.y,.L,.Rf) T98 := ISINOUTN(Y.lrSATZZ4A(YJJ f99 := ISOUTNHX•l•SATZ24AUhiNNCY,10UT(Y') ),.

TRLESSIS•tt•( ISN( y" lOtiHY> ),.y,.x,. 1TOPCY .. t0UTCYJ)rl)•T98)

TlOO :: IS?C lTO(XJ.[ T:lTG!XJJJS<<T,.RF,.<T?'F),. IOUTCX)•l~FT!Tacx,y,l•IDUT<Y>J,. T3(X,.FrRfrSA!Z275A(X,f)J,T99)

[N:trOCY)l[O:NOTCis•E•(tTO(Y)•~•XOUTCTlJ)l TlOOA ;: THl•L. IHP•cts•t-~•U!UHY.NhYJ ..

IS•E"ClTCCY>•N•XOUTCYJJ•O• {f:Is•N•<INN(Y,NJ,Y')lTRIS(lTOCY),.N,. OUTNCT•IN~<Y•NJ•lTOPCY•N>J,XOUT<Y), ISOUTINHtY.NJ.ISOUTNICY,INN(Y,N), 1T3PCY•N>•Y•lESSISI3CYJ,Tll>

T1009 :: ORElCLESS"N'"UNNCY,N),YJ,. IS"N•(INN(Y,.N),y),.lTOPtY.NJ,TIOOAJ

f101 :: SATZl&BCINN(Y,.N),.y,.x,TlDOS.L) TlOZ := ECJE31CIS"N .. Uti~<Y .. NJ•Xl.

MORE"N"CI~N(Y,~l.X)•lESS"N~CI~N(YrN),

XJ•SATZlOSC!NNCT•NJ,.X)illOlJ T103 := THJ•t.IK?•(!S"E"(HOCIC),

lEFTlTO(XrY',l•I),XOUTCXlJ~ IS•N•t I~NCY, ~n .. :O,.flOZ. ET :tS•E•( lTO( U .. LEf Tl TîHX• 'r •L•tj), XOUTO:)) li SOUTNE (X, INH(Y,N),TRLESSIS•n•t[N~<YrNJ .. y,x, lTOPCY .. N)rL),.X,LESSISIJ(X),.f))

!104 :: T4U,Fr~f' .. SATZ27SACX,F},. LEfTlTOtX,Y,l•NJ,f103)

T105 :: ISINOUTNCX•i~N(Y,N}r TRlESSIS•N•<tNNCY•N),y,x.tTOPtY .. N)rl))

T106 ::: AXZ( INNO,. NJ,. INN<X..LEfTl TO<X .. Y ,.t, Pi)),. T105)

T107 ;: ISINOUTN(Y.<IN~(Y.Nl>SUC,.

ONE•E•([T:lTOCX)lCX•tG:tT:lTOCXJlCXlRECPRGFCX.F,.GlJ

n:trCK xncx

ex : IS<RECt lOiJT(X)),. <lOUTC XJ>f")

: lTOU) : ISCREC( SUClC CN,.O) h«SUCXC!'f •O)>f><RECCN )>Q)

n :t TCK Y) lCX : tT:1TOt lOJCX : tT:lTD(Y))CX : IS_,.•U •lNHCY .. tOUTCY»)

LESS•N•CtNNtY•Nl•Y> lESS•N- <INNCY,. NJ ,X}

: IS<<NS[X•lEFTlTOCX•Y•l•NJ,T103)>Rf, <<NS<X•lEfT 1 TOC IC•'f•bN hTlOH>F>«N>RrL>Q)

IS"N•l T108 == TRISl!HATr<INNCXrlEFTlTOÇX•Y•l•NJ)>

SUC,:N~(Y.~S<Y.N,OJtr<INNCY.N)>SUC•

TlOG .. T107> T109 == ISOU1NICX,<INNCXrlEFT1TOCXjY,lrN)J>

SUCrLEMMAZ75tlrLEFT1TOtX.Y~LrNJrTI33>• INN(Y,NSCYrN•O>JrTRLESSIS•N•ti~N(YrNS (YrN,Q)JrYrX•lTC~(~rNSCYrN•OJJrL)r T106) : I s•E•n TOCX Jr NSC X,.LEF'T 1Tt'Jt XrY .L,.IU,T 10 3),.

LEFTlTJtX .. Yrl•NS(YrNrOJ)) 7110 :: IS?<lTC<XJ,[T:ITQCX)J!S(<T>RFr<<T>F>

<<N>RFL>QJ.NSCX.LEFTlTDCXrY•LrNJ,T103J rlEFTl TD(X,Y • L•NS{ y,. Nr O> J • HO~ .. T109)

r a 1111 := [Jt 1 TOn' HU :!>OHI s•t:•c 1 TO<Y hT" XO~TCYJJJJTllOtTrUJ : PROPZtY rflrRfll

U12 ·:= A NOUPROPHY .. rt. RFLl..PROP2CY•fl•RFU • Tl OOr TH U

Y a (l:LESSIS•N•cY,XJJtf:[T:lTO<XlJCXl SATZZ75F t= SATZ275VCYrFt•.a275•<L•F>•

xs X1 Tl rz T3 rx n f'U lil GlX G H

T5

T6 T7

T6 T9

U:lTOU>l TlO

TU

T12

Rrt ... azrs•ct,.r>. ruz•. szrs•ct.r> J

:: <X>SUC := PL •N•( x .. u := lESSI5Il•N•(XrX1.SATZ18AtX,1J) ·- lESSISit•N~(XrXSrSATZ18CtXlJ := LESSISIZ•N•<XS .. XlrSATZ4E<XJJ :: LErltCXrXl•X•Tl,.f) :: lEfHC X; XbXSr TJ;F) := rt•c.827s•<x .. r9s•c.szrs•cx>,r1J == Gz~c.szrs•cx .. T9s~c.azrs•cx>.rtJ := Gl•C.6275•<XrT95•C.627S•(Xlrf1J :: lEFT<CXrX1rXSrT3rRECF<X1rf)J == T49•c.ozrs•cx.r9s·c.szrs•cxJ.rt.

XOJTCXSJrREFISClTO(XSJrXOUT<XS))J ·- SATZZ75D<XSrf1rGl•T9Z•C.6275•

<XrT9s•c.a27S•<xJ.F1J> := SATZ275f'(X1rXSrTlrFJ := TRIS2CCT:1TD<XSJlCX•G•G1rRECf'(X$,F'1Jr

Ht•TS) := FISE< 1TOUShCX•G,.Glr T7r XDUH XSJ) :: TRIS<CX,<KOUTtXS>>G,.<XOUTtXSJ>Glr

<<XOUT(XSJ>Fl><<XOUT(X)>GlX>OrT8r14)

:: ISINOUTNCXS•INNCX•N>, TRLESSIS"N•< INNC x .. ro, x~ xs .. UOPU.N>.

: IS•[•(( T:HOUJ JCXrlEFHCV: ,.x, Y •lrRECfCXrFJ h RE CF'< y, LEFT t cx.x,y •l•f J J J

: NAT : NAT : lESS IS• ?f•tx" XU : lESSIS•N•(X•XSJ : LESSts•N•<xs .. X1)

tT:l TO( U lCX n:UOtXSJlCX (T :lTOl U lCX.

: n:nacxsucx : U :lTO[ XllCX : n :noc xs u ex

: IS(<XOJTCXSJ>Gl .. <<XOUTCXS)>f'l><<XOUTCX)>GlX>Q)

: ts•E•C[T:lTOCXS)JCX .. Gt .. REtfCXS,.F1J) : Is,.E•([ T:tTO<XS) lCXrGr RECFCXSrflt J

IS•[•([T:lTO<XSJlCXrG,Gl> IS(<XOJTCXS>>Gr<XOUTCXSJ>ä1)

; IS<<XOJHXS J:>Gr«XOUT< XS l>Fl>«XOUTC Xl >GlX>Q)

T2)) Is-,• u NN(XrNh INN<XS•LEF'f 1TOCXs,.x, rz,. fi) U :: ISOUTNICXl~I!'fHtX,Nh

TRlESSIS•N~CiNN(X,NJ,XrXl•lTOPCXrN), Tl>•INN(XS•LiFT1TO<XS .. I•T2•N)),. TRLESSIS"N•CIN~tXS•LEfTlTO<XS•X•TZ•N)} .. xs.xt .. 1TOPCXSrLEFT1TCCXS,.X,.T2rN)),.T3> ,.no > : IS"E .. U TO<Xt hLEFTl TOC Xl"K .. Tl•:O•

:: !S~(1TDCX1J•CX•frLEfi1TO(Xl•X•Tl,.KJ• LE~T~TO~Xl•XS~T3~LEFT1T0{lS•~,.T~.~J)•

LEFT1 n cu.xs.;tlJtlEfTl rou s.x.n;,rn> t

$

s

-5.50-

-azrs

+8277

·B277

+va

r a

x :il

;

Q ..

TU

TH

Tl'S

T16

T17

T18 T19

TZO

T21

T22

SATUT6

[f :t:.Ul JO( n lCitl SHPR

Tlll : IS(<N>FX~<N>FlX) := FISitlTDCX>•CX•fX•FlX•CT:lTO(X)JJl2(T}

> IS'"E"<C r:trou> Jcx .. rx. n;o := ISrttT:lTQCXJlCX .. tT:lTtHXHCX•

ï:u:c r: UGCO lCXlRECf'<X .. Ul#FX~f1X•Tl3) : IS•E: .. {[ T :HO<XJ JCX•RECFU• F'lO rRECf(X,flX>) ;: SATZZ750(~,r1XrG1X,

rr.s•t. 8275 "( )(,. T9s•c. 8Z75"UhfU) : IS""f:•([ T :1 TO( U lCX• GU .. aECFCX rflX U :: TRIS2<!TtlTO(Xl!CX,.GlX .. RECf(X,fll•

RECrtX ~Fllt: h Tl 5,. TH> : IS"E'"<t T: 1T Q(XJ lCX• GlX •RE:nx,.fX)) ::: FI3~(~TD(X),.CX,G1X .. ~ECF(X,fX)rTl6,.

X~;T,Xl) : ISC<X3JTCXl>GlX,<XOUTCX)>~ECf(X,.fXJ) := iS!'IC\JTNU'S•XS•lESSISl3(XSll : IS"''<"' U: S•i:NIICXS .. XOUHXSiH ::: T?.!SC~'-T,Xl,XS .. INN(XS•XOUTCXS)),

SATZ4A(X),.Tl8l IS~~((l•INNCXS•XOUT<XS))l

·- ISC1T"I<Xl•Xl,LESSISI3CX1Jr IN~(ISriOUT<XSJl,fRLESSIS•N•ti~H

CXS,XDUJ<XS))rXS•Xl•lTOPCXSrXOUJ[XSJ>r T 3)~ Tl9' : IS•[• U iO<X 1 hXOUH Xl hL Er TlTO< X1 r X Sr T :hXOtiTUS JJ)

:= ISP1C1TGCX1Jr[T:1TCCX1JliSC<T>RECF(Xlr f),<<T>f><<XOUi(X}>GlX>Q), LEFT1TOCXlrXS~T3rXOUTCXS)lrXOUTCX1), T9,TZ0) . ISC<XOJTCXl)>RECF<X1,f),<<XOUT<X1J>f><<XtUTCXJ>GlX>Q)

:: ISFCCX,cX.tT:CXJ<<XOUTCXlJ>f><T>Qr <XO~TCX)>GtX.<XOUTCXJ>RECf<XrfX)rT17J : ISC<<XJUTCXl)>f><<XOUTCX)>G1X>O•<<XOliTCXl)>f><<XOUT(X)>

RE Cf ( )(, FX J>Q)

:a TRISCCX•<XOUT<PL"N•<X•l))> RECF<PL*N•(X,llrflr<<XOUTCPL"N•tXrlJ)> f><<XOUTCX)>GtX•.szrn•>Q,

:=

«l[IJIJHPt•ti• ( X .. l ))>f><<lCOUH Xl>R(Cf( x. rx•.e276~J>o.rzt·.a276*•TZZ•.az76•)

REC( X• f, XOUT (X))

: ISC<XOJT<PL•N•tx.tJ)>RECFtPL•N•<X•l>•fl• «XOUTl Pl'"N*<X"l) )>D«XOJ HU>RECf( x,

:

lEf'T ( CX rPL"N•CX,. 1 >, X•lESSI S Il"'N'"( x,. Pl•t.•( x,u, SAiZ 1s' u .. t > s.r, >>o >

ex [X:NATl[F:[U:tTOCX>lCXl SUlt := SMPR[tr:cxlru:cxJPt<T·U> .. x.rJ : ClC PROO ::: SM?~([T:CXltU:CXlTS(t,uJ,Xrf) : ex tF:tU:lTOCl>lCXl

Tl :: ISDUTNI<l•l•SATZ24A(1),1,.lESSISil(1J, REFISCNAT .. t)) : IS•t•<t TOU J. lOUTCl lPXOUT(l))

SATZ277 :: IS~(lTOCl>•lT:lTCC1JliS<RECCt,.r,r>,<T> n .. 1 OU'!'< 1 >rXOUH lh SATZ2759( t .. Fh n·.azrr .. > : ISCSI!PlU,fJr<XOUT<l>>f)

0 a [X:NATl[F:[U:lTO<PL•N•(X•lJJlCXJ SATZ275 :• SATZZ76<X~FJ ISfSKP~ (pt•N•()C"l),. rl• <<XOUHPl•PJ•<X;ol) )>fHSHPR(X ..

lEFTCC< .. Pl"NM(X,.l),.)(;olESSISil•N•(X,Pt•h•(X,l), SATZ18~ <X•l )hf"))>Q)

s

s

s

':'" 5.5.1 ....

s

ro :::: tE=-r <c x" x. '• n,.r, U:1T0( Y)]CX rz := F!SE(1f0(YJ,CXrtEFT<CX•XrYrTl,.

RECftX,F) hRECf<Y,.FO >• S~TZ275Ftx.Y,Tt,.f);XOUT(Y)) IS<<LEF' Tl TP< x,.y, Th lCOUT<Y) )>RECFU,n,. SMPR<Y.rO))

T3 ·- TFISl!~AT,INN(Y,XOUTCY)J,XrY• ISISD~TN(Y,.Y.LESSISI3CY)),l) : IS '"N .. <I NNCY,. X OUT< U),. X)

fit := !SOUTN!tX•INN(YtXOUTIYJJ• TRLESSIS .. N"( INN( y,. XOUHYJ ),. y,. x,. 1TOPtYrXCUTIYJr.Tll•X•LESSISI3(X),!3) : ts-r•<tTO(X),LEFTlTO(X•Y•Tl,.XOUTCYJ),.XQUT<XJJ

TS : .. IS~I!~J(Xl•CX~RECf(X,.Flr

LErTlTO(XrY•T!•XOUTIY)lrXOUfCX)rT4l : IS<<LE~T!TOCX•Y,T1•XOUT<YJ )>RECF(X,.f},SMPR<X•f))

·va s

ISSIPR := TP.lSl(CX•SMP~(Y,fO•.vs .. ),SMPR(X,.F),. <LEfTlTOIX•Y•Tlw.vs•,.xoUTlY>l>RECf(X• rJ.rz~.vs•,rs•.va~> : ISCSMP:C <Y rl.EFH CX,.Xr Yr LESS ISI2•tt•n,. x, I),.f U•SitPR<X•F))

~ tz:COHP~EXJtX:NATJ

+!279 s

u :: RLOnH'ClO REAL PROPl =· ISCSU~CXr[T:lTOCX)JZJrTS<Z•PliCXP.r3llJ 'PROP'

z ~ Tl := SATZ277CCT:CXJ[U:CXJPLCT,.UJr(T:tTOClJl Zl IS<SUHt lrCT:lT:JUJlZhZJ

T2 :: TRIS<CXr SUl1( 1• CT: tTOO)] Z>r z,. TSC Z•lC ), ThS4i'Z222A<Z>) : PROPlU)

x ;) [P:PROPlUU Tl := SATZ278([T:CXlCU:CXJPL(TrU>•X•

(T:tTO<Pl~N•cx.lJJJZJ ISCSUMt PL•N•u,.u,.tT:lTOCPL•N•<X,U) lZh PLUUH[ XrtT :tTOCXJJZhZ))

H == tSPLlZ<SUH(Xr[T:tTOCXJJZ)• TSCZ,PliCXR.OJ>,.z,.TS<Z•lC),p,. SATZ222A<ZH ISCPLCSUHCXr{T:lTOCXllZl•Z1rPLCTS<Z•PliCXR•Oll•TS(Z,.1CJ

) )

T5 == OISTPT2CZrPliCXRrOlr1Cl IS(PL<rS<Z•PllCXRrOl)•TSCZrlC)JrTSCZrPl<PLICXRrO>•lC>JJ n := PL1S12ACXR.0,.1RLr0) IS(PlC~li<XRrOlrlCJrPLI!Pl"R•<XR,.lRlJ,.Pl"R~co,.O>JJ

T1 :: IS~ECX12<PL"R•(XRr1RLl• RLOfNTCPL•N•CXrl)),pt•R•(Q,O),.Q,. SATZR1558{X,.lJ•PLOl·R~CO•O• REfi S< RE:ALrO))) : IS(Pl Il PL .. R"CXR,.lRL hPL"R" (0,.0> J. PL I<RLCFNH PL'"N"CX .. n J

.. on f8 := TRIS<CX.PLCPLI(XR,.OJ,.lCI•

PLICPL"R"CXR•lRL)•Pl~R"CO•O>>• PLICRLOFNTC?L•N•(X,lJJr0)rT6 .. T7) IStPLP liCXR,.OJ..lC),. PlU RL Of' NT< Pl"N"<X,.l) hO))

T9 := ISTS2CPL<PLI(XR•0)~1C),. Pl.H RlOf •;ï CPL•N• {X,.l U• 0 ),. z, T8J : ISCTSCZ.PL(PLICXR,.OJ.lCJJ•TSCZ•PLI<RlOfHT<fl"N"<X•l>J•

Q}})

T10 := TR4ISCCX.SUH(PL"N"(X,l)• (T:lïO<PL•N"CX.l>JlZI• PltSUH<X,.(T:tTOCX)llJ•ZJ• PL(TS<Z,PliCY.R.OJ)rTSCZ•lC))o TSCZ•PLCPLI(XR,QJ,lCJ),. TS(Z,PLI<RLOfNT<Pl"N"(X,1JJrOJJrT3.T4,. T5•T9) PROPl(~t·N•(X•l))

Tll ·- ISP(NATr[T:NATJPROP1CfJ,.Pl~N"(X,ll•<X>

S~C.T10•SATZ4ACX)) PROPH<X>SUCJ - 5.52-

:-8279 S.

SATZZ79 := INOUCTIONCtT:NATlPRDP1".6279"{Tlr rz·.8279"r[U:NAfl[T:PROP1".82l9"CU)J

+828)

-828)

0 ~ [F:(ft1TOt2llCX1

Tl f1 rz f3 H r;

T6

TT

T8

:: LESSIStl•N"(1•2•SATZ18ACI•l)) := LE~rccx,.z,.t.rt,.rJ :: SATZ27S(Q;lrFt := SAE2T7(C,f"l) :: IS!XCUT~(l,l•LESSISI3tl)) := !SJUT~Ii2ol,.SATZ2•AC2loiNN!l;XOUTC1>>•

TRlESS!S~~·ciNN<l•XOUTC1>>•1•2;

1TO?Cl>X'1UH l))•fl>•T4) •- IS~Cliv(2l•CX,frl0Uif2>•

LEfTiTOC2•l•Tl,IGUT(l)),T5) ·: = TP.IS2( ex, S~PR{ 1,. t1 h <10UH2 )>f,.

<XG~T(l)>fl•T3,.Tó> := lSF(CX•CX•[T:CXl<<XOUTt2)>f><T>Qr

SMPRt1rFl)•<lOUT(2J>frT7)

SATZ~83 := TP.IS<CX•SMPR(Zrf),<<XOUTCZ)>f><SKPR(l• Fl,.. 6Z8Q• PO, <<XOUT C Z i>f> «ltiU"t < 2 >>F > o.rz•.szao•.rs•.ezso·>

0 a ASSOC. :: CX:CXHY:CKJ U:CXl:i:SC<Z><<Y><X>Q>Q,. <<Z".<Y>Q><X>\:}

~ ASSOCPl t= tX:CXl(Y:C.XltZ:CX1ASSPL1CX.Y,.ZJ ASSOCTS := tX:CXltY:CXltZ:CXlASSTSl<X•Y•Z>

Q a (A,ASSOCltZ:CX1tU,CXJ(V,CXJ ASS~l :: <V><Z>A ASSO~ : = SYKI S<CX.<V><<Z>O>O• <<V>O><Z>O,.

ASSGl) 0 a (A:ASSOCCO>ltX:MATltY:NATltF:tT:lTOCPL•N•CXrYJllCXJ

y ::1 Tl := lESSISft•N•(X,.Pl•N•cx,.y),SATZ18ACX•Y)) :: lEFTCCX,Pt•N•CXrY),X,Tlrfl r a n

rz PROPt

·- RIGHTCCX•X•Y•fl := ISCSMPRCPL•N•CX;T)rfJ;<SHPRCTrfZ)>

<SMPR<X•Fl )>Q) Y a PROP2 :: Att•L•crT:lTO(Pl•N•cx,y))lCX•

[U:[TtlTO<PL•N•CX;Y))JCXlPROPl(U)J [FO:tT:lTO(Pt•N•(X•l>JlCXl x ~ T2 :: SATZ278(1bX•f0)

T3 n TS Tó

T7

:: SATZ277(QoFZ<l•f0)) :: ISINOUTN{l,l,lESSISI3(1)) := ISPtz•N•(lriNN<l•XOUTCl)),X,T4> :: ISOUTNI(Pl"N~cx,.l>•Pl'"N•<X,l),.

LESSISil(Pt"N"<X•ll>• Pt•n•cX,INN(lrXOUTtlJJ), SATZ190CinNC1oXGUT<l>>•l•X• 1TOP{l,XOUTt1))J,T5)

:: ISr<lTOCPL•N•<X;lJJ,CX~ro, XO~TCPt•NR(X;l)J,RIGHT1TOCX•l•XOUTCl))

• &.'o/6,~Yn• AJ''-1 •4-I.Y,.f'#~&.IJ' t~'-t.fl'r'-l.'l"li.Uf ,,.,1\I'I"VIII

: LESSIS•N•<lr2l CT :1 T OC 1 ) JC X I SOMP~ <Z•F h«XOUHZJ>F>c SMPR< l•FU>Q) ISCS MP" (t.f Uo <X CUTF 1J IS 'N" U •I N:H t,XOUH 1J)}

ISC<10JTC2J>Fr<XOUT(l)>f1)

: ISCSMP~ Cl.>Flh<UiUT<ZJ>Fl

s

: ISC<<XJUTC2}>f><SMPR(l,.fl)>Q,<<XOUTC2l>F><<10UTC2)>f>Q) s

:

:

: :

:

::.

IS(SHP~<2•f>•<<XOUTC2l>F><<10UTCZJ>F>Q)

•PR!JP' ASSilC<t x: CX )[Y: CXJPUX ,'()) Assocct x:cxuv:curscx .. n>

ISC<Y>< <Z>O>O•«Y>Q><Z>O>

IS<<<Y• Q><Z>Q,.<V><<Z>O>Q)

LESSIS• N•U;PL "N•u"n) n :nat u Je x CT:l TO< Y) lCX

I PR:JP.

'PROP•

IS<SMPl<Pt•N•cX,l>,fOJ•<<XOUTCPL•N•<X•l)J>FO><SMPRCX, F1 C1 ,. f) , ) >0 ) IS<SMPl {hf2(1"f0»•<XOUH l)>f2(1,f0))

: I s•N•u, IN~H 1, X OUT< 1)) > : Is·~·l~t·N•cx,.l)•PL•N•(X•INN(l.oXOUTCl)J)J

: IS .. E.,U TOCPl'"N•(X.ol JhXOUTCPlwN•CX,l)h RIGtiTlf O<X.ol•XOUTCl JU

s

,.T&) ISC<XDJ TtPt•N .. U•l> J>f'O,<IC OUT( l)>f'Z( l•fOH T8 := TP.IS2< CXr <XOUHPL"N'" CX,.li )>fO,.

SMPIH hf2( l;f0}) ;<KOUT( 1 )>F2< hf'Ol.t> T r .. Tl> : IS<<XOJTCPL'"NwCX;l)J>fQ,SHPR<l•F2<1•f~}))

T9 ·- IS~CCXrCX•<SMPR(X,.fl(l,.fO>J>Q,.

- 5.53-

1'10

x a n1 Y <l YPl

Xf"Y x :on XYPl T12

<XOUTCPL·~·cx,l))>fO•SMPR(lrfZ(lrfO)lr TSl

:: TRIS(C:(rSl4PR<Pt•N•fr~ll•f0>• <<XGUT(PL•N•CXrl)J>FO><SMPRC~rfl(lrfO) }>Qr<S"PRtl•FZ(l•FOJ)><SMPR<X•Fl<l•fO) )>Q, TZ,T?l

:: tu:rr:lTt(PL•N•(X,lllJCXJTlO(U) : = Pt"" tl'• ~ Y • 1 ) :: ?t•N"()(,'{} •- PV'N .. {XrY?l) ·- P!.. .. N"(X?'f,l) := LESSISI2"N~CXYPl,XPYl•ASSPl1wN•(X•Y•1>

}

[P:P~OPZ(Y)J(f:[T:lTO<XPYlJJCXl 113 := ISINOUTNCXYPl,XTP1,LESSISI3<XYPlJ) TH ·- T?.ISCN.\T,~"Yl•XYPl•INNCXYPl•XCUHXYPU

T15

T16

fR T17

T18

Tl9 f'RR J21) TU

TZ3 n T24

TZS TZ6 T27

! .~SS:">LZ .. ~i"( '-<• y, U• T 1l l •- ISO~T~IlXPYl,XPYl.LESSISI3<XPY1J,

INN(XY?l•XOUTCXYPl)), TRLESSIS .. )j•( I!v!H ln'f>l, XCUT<XYP1 )},XYP 1• XPY1,l:C?~XYP1•XOUT(XY?l)),Tl2}•Tl4l

:a ISftlTO{XPYli•CX•RECF(XPYl•FJ• XC~TCX?Yll•LEfTlTOCXPYlrXYPl•TlZ• XOJTCXY?lJ J. Tl5)

:= l.EFHC x, XPT1r XYP 1,. T12rf J := SATl275f(XPYl•XTP1•TlZ•fl

·- FISE<1TO(XYP1J•CX•LEfT(CX,XPYl•XYP1• T1Z•RECf{XPYl•f)J,RECf(XYPl•fR>•Tl7• Xtl":JHXY?U)

·- lESSlS11"N•(XPY,XYPl~SATl18ACXPY,1JJ :: LEfT(CXrXYPl•XPY~Tl9•f'RJ ;: SATl278CXPY.FRJ :: ISFCCX.cx.ru:CXJ<<XOUTCXYP1J>fR>Q•

SMPRCXPYrfRRJ,<SKPR(Y,FZ(FRRJJ> <SMPRCX•fl(FRRlJ>O•<FRR>Pl "

:: ASSOlCA.SHPRtX~ftCFRR)J,SMPRCY•f'Z(fRR) J•<XOUTtXYP1l>fR)

:: LESSISI1•N•cy,ypt,SATZ18A(Y,1J) :: LEff(CX•YPl•YrT23~f2(YPl•f)) := SATZZi5(Y,f2iY?t,.f))

:= ISINOUTN!YP1,TPl•lESSISI3<YP1)) :a 1SPLZ'"N•CYf't.INIHYP1•XOUT<YP1 )J..JC,TZ5J :: TRISlC~AToiNNCXYPl•XOUTCXYP!ll•

~l'"N•<XriNN(Y?1,XOUTCYP1)))rXPY1,T14•

ISC<<XJ~TCPt•N•<X•lJ)>FO><SHP~CX•fl(l•fO)J>O• <S~P RU ,rzc t .. FO) )>< SMPRU• f 1( l• FO ))>Ql

: PRQP1(1,f0) PROP2U) NAT

: NAT NAT NAT

: IS8(•(tTO(XPYll•XOUTCXPY1J•LEFT1TO<XPYl•XYPlrT12, XOUH Xf Pl)))

lS(SMP~(XPY1rflr<XOUTCXYPll>LEFTCCX,XPY1•XlP1rT12•

RECF U'" Ylrf)) > : U :1 TOC XYPl) JCX : Is-r•ctT11TOCXYP1)lCX•LEf'TCCX•XPYl•XYPlrT12•

RECfU'" Yl,.f JhRECfUYPI.Fif))

: lS(<XOJTCXYPl)>LEfTCCXrXPtl,XYPl,T12rRECf<)PYlrf)), SI'!PR<Xr Pt..fR))

: LESS IS" N•CXPY~XYPU : CT:1TOCXPY>lCX

ISCSHP~CXYPl,fRJr<<XOUT(XfPlJ>FR><SMPRCXPY.FRR)>Q)

: ISC<<XlUTCXYP1l>FR><SMPRClPY,.fRRl>Or<<XOUT(XYPIJ>FR> <<SMP~Y.f2(fRRJ)><SMPR(X,FlCFRR)J>Q>OJ

: ISC<<XJUT<XYP1J>fR><<SHPR<Y•f2(fRRJJ><~MPRCX•F1CFRRJl> O>O~<<<XOUTCXYPlJ>fR><SHP~(Y,fZtfRRJ)>,><S~PR(X,fl<FRRJ )>Q)

: LESS IS" N"<Y ,.YPU : n : 1T 0( n 1c x

ISCSHPRCYPl•FZ<YPl•Fl)r<cXOUT(YPJJ>fZ<YPl,f)><SMPR<Y• f'{}>Q) I S":<~•(f Pl• I NNCYP 1•XOUT<YP1)))

: ts•N•((PY1rPl"N•<x,INNtYPlrXOUT(YP1))))

T26l : IS"~•(INN(XYPl•XOUTCXYPll)•PL•N•(X,INNCYPl•XOUTtYPl))))

TZS

TZ9

:= ISOUTNI<XPYl~IU~CXYPl,XOUT(XYPl)), TRLESS!S8 N•( INNCXYPlrXO~T(XYPlJl,XYPt, XPY!•lTOPCXYPlrXOUTCXYPl)},TlZ>* PL•N•(X,INN(Y 0 lrXOUT<YPl)))r SATZ190(INNCYPl•XOUT<YPl)},YP1rX• H()PtYPhXOU TUPl)) ), T27) : IS•E•(l TO(X P'l'l hlEFTlTOUPYl•XYPlr 112• XCUHXYP1 )),

R!GH TU EH x, YPlr XOUT tYPl)) >

-5.54-

LEFTITDCXPY1,XYP1,T12•XDUTCXYP1))• ~IGH!lTO{X,YPl,XOUT~YP1)J,T26) : ISC<XDJT(XYP1)>fR,<XOUT<Y~l)>f2C!Pl.fJ)

HO ==- !SF<CX.~X,<SMP~<Y~f2(fRR))~q, <XCUTt~YP1)>fR,<XOUT<YPl)>f2CYP1,F)•

T29J : IS<<<XJ UHXYPl) >fR><SKPR<Y.•fZCFRR) >>e• «XOt;T( YPU> FZCYPt. f)><SHPR<Y•FZ<F'RRH >0)

rN: u on u N3 ::: HlN<Y,N> : ~AT ~YPl :: lEFTlTO(YPl•Y•T23oN) 1TOC!P1 > TH := !SINSJTN(WDt,~O.TRLESS!S•N•(~O•Y•YPl•

1T:J?(ï.'!hT23)} IS~N•(NO,INN(YP1•NYP1))

nz ·- ISgLz·~·(10•INN(YP1•NYP1>•X•T31) : IS "~·p l "N• ( X;NO) •Pl .. N"C X• iNNC YP1•NYP1))) NXPY := RIGff~li~CX.Y.Il) 1T0()(Pf) ~lX'tPl :: LErrt-ccx~Pl.XPY•T19oNXPY) lTOCXT"l) TH == ISINC~TNCXYPl•INNCXPY,NXPY>•

TRLESSrs·~~tiNNCXPY,~XPYJ,KPY.XYPl,

1TeP{XPY•NXPY)•Tl9)) : IS•N•CtNN<XPY,NXPY>•INN(XrPl•NXYPl)) T34 := !SINO~Tri~X?Y.PL•N•cx.~~),

SA!Zl9e(N~~y,t,1TC?(Y.Nl)) : IS•N•( 2 t•N•<x,NOJ,INN<XPY,NXPYll T35 :: TRIS ('lAT ,pt~ N'"C(, NO> • IN':( XPY,NXPO•

~~~(XY?lrNXYF1),T34rT53) : IS•N•(~t•N•(X,NOJ•lNN(XYP1•NXYP1lJ

T3& :: TRISlC~ATiPL·~·tx.INNCYPl,NYPl>>• ~~~{~~P1r~XY?1J•PL«H'"(XrNOl•T32•T!5) IS·~·p t•N•cx, INN<YP!P 1\iYPl) h INtH XYP lP NXYP 1))

T31 == [SOUTNI<X?Y1iPL•N•(X,INN<YP1.NYP1>>• SAfZl~O(l~~lTPl•NYPll•YPl•l• lTOP(v?l,NYPll)rl~~(XYPl,NXYPl>•

TR~(SSIS•H•(tNNtXYPl,NXYPll,XYPl,XPYl•"

1TOPCXYP1•NXYP1J•i1ZJ,T36) : IS•t•ttTOtXPYl)•RIGHT1TO(X,TPl•NYP1)• LEfT lTl CXPY 1• XYP t. HZ• NXYl' l) l

na := ISFC1TO<XPY1J,cX,f* c: RIGHT1f0(X,YP1PNYP1), lEFT1TCCXPYt.XYPl•TlZ•NXYP!)•f37J : ISt<N>=" Y•<N>fZCFR!U >

f :1 139 := fiSI{lTOCY),CX,FY,FZ<fRRl.tU:tTOCYJl T38( U)) : IS .. [•([ U!lTO(YJ lCX" FY,. fZ(f RRU

J40 :: ISF<tU:lTO(YJJCXrCX,(T:[U:lTO(Y)lCXl SMPR(Y,TJ,fY,f2(fRR)rTJ9) : ISUMP~ n.rn,SMPR(YpfZCfRRU>

T41 := ISFCcx,cx.tT:CXJ<<XOUTCYP1J>f2(YP1•f)> <T>Q~SX?a(Y,f2(fRR)J,S~?RCY,fY),

SYHIS<CX.SHPR(Y,.fYJ,.SHPR(Y,fZCFRR))., T40)) . IS<<<XJ UHYPU>FZCYPlr f)>< SMPR<Y •fZ<FRR) )>,, «XOUH YP 1) .

>fZ<YPl,f)><SMPR(Y,fY)>Q) HU := TRISCCX•<<XOUT(XTPl>>FR><SKPR<Y•

f2CfRRlJ>Q,<<XOUTCYP1J>f2(YPl .. f)> <SMPRCY,fZ(fRRl>>O,<<XOUT(YPll>fZ(YPl• f)><SMPR{Y•fY)>Qpf30,T41J ISC<<XJUTCXYP1)>fR><SMPR(f,f2<fRR))>Q,<<XOUTCYP1J>

fZCYPl• fi><SHPR(Y,fY)>Q) nz := TRISZtCX,<<XOUTCXYP!)>fR><SKPRCY,

fZtFR~)J>O•SHPRC!Pl,FZ!YPl,fJ), C<XOUTCT?l)>FZCYPt.Fl><SHPR(Y,fYJ>Q, T41A,T24J ISC<<XlUTCXYPlJ>FR><SKPRCY•fZCFRRJ)>Q~

SMPIH Y" 1.-FZ<YPl,f)) l T43 ·- ISF(CX,CX•<SMPRCX,Fl<FRRJ)>Q,

<<IOUT!XYP1J>FR><SKPRCYrf2tfRRJJ>Q, SMPR(YP1,f2(YP1,f)J,T42J ISt<<<(OUTCXYPll>FR><SKPRCY•f2CfRR)l>O><SMFR(X,FlCFRRJJ

>Q,<SH"R(YPl,f2(YPl,FJJ><SKPR(X,F1CFRRJl>Q) [lntrocxu 'fO := INlfU,.I!) NAT -5.55-MXPY := lEFTlTO(XPY.X .. Tl,Hl : 1TOUPf J "XYPl := LEFT1TO<XYP1,XPY,Tl9,HXPYJ : 1TDCXY~ IJ TH ·- !SINGaTNCXYPl•INN<~PY~HXPYJ,

TRLESSIS~N"CINN<XPYrMXPYJ,X?Y,XYPl• 1T~?{XP~•MXPYJ,Tl9)) : IS·~~CINN(XPY,MXPYJ,INN(Xrrt.~XYPl)J

•8281

•826Z

TH

H6

:z [SlNCUTNtXPY,~OrTRLESSIS"N"CMOrXrXPYr 1TOP {X • ~ h Tl) l I s•N .. <'f 0• INH( XPY r MXPY>)

;~ TRIS(~~T.~~·IN~t~PY~HXPTlr !NlH XYPloMXYPt h T 45• T44) : IS"!C•('I 0• IHNCXYPbKXY!i' 1)}

:= ISDUTN:<XPYl.~O,TRLESSIS•N•CHOrXrXPYlr lTJPCXrXJrTlCYPl))riN~CXYPlr~XYPl)r TRLESS Is .. n<•( Hl~l( X'!Pb KX'fPl h XY?bXPYlr l TG?( XYP 1r KXYP1h TlZ )., T 4f>) IS•t:•<t TO<XPY1 hlEFTlT OUPYlrXr T1CYPlhMJr

lEFT1TJ(XPYlrXYPlrT12•MXY~1>>

:: IS~(lTD(XPYl)oCXrFr lEfilTJlX•YlrXril<TPlJ,~), LEtT l i::i<XPYl, XYPh T12r HXYP 1) • Hn . : IS (<H>?" 1( Xo YPl>•f' h<M>F l CX• Y rf'RRJ)

F :a Tft9 :: FISitlTG<X>rCX.r1CXrYPlof)of'l(XrYoFRRl

TSO

f51

f52

TSl

rC:H lTCCX>H4lHUH : IS*E•([ IJ:lTOlCXrCXr(T:tU:1TOCXllCXl

SH;>P. 1.:1( • T),. i' H 'r?lrf hf HfRR h T4 9} t IS<S MP:t <Xrf HYP1,.F') ),.S MPR{ Xrf 1< FRR}J) := IS~<cx.cx,.tT:CXl<SMPRCYPl,fZ<YPlrf')}>

<T>QrS!'PP.(lCtf"HFR:\l ),S~:f'R(X,fHYPhF )) , SY!!! SCC Xr Sl'IPR tXrfH ':?1 rf' J h SK?iH X,f HF'RR> h TSO)> IS<<SH" R<YP t .. rzc YPt .. n )><S MPRCX rfl(f'liR))>Q r

<SM~RClP1rf2(YPl,f))><SHPq(X,fl(YP1,.f))>QJ

:• TR4l5[CX•S~PRCXPY1rf)r<XOUTCXYP1J> LEFTCCX,XPYlrXYP1rf12rRECf'CXPYl,f)),. SM?RCXYPlrf?.),<<XCUT<XYPlJ>fR> <SMPRtXP~,FRRl>Q,<<X~UTtXYPl>>FR>

<<S~P~<Y•FZ(FRR>l><S~PRCXrf'l(FRR)J>Q> OrT16oi18rT20rT21> : ISCSMPlCXPY1rfJr<<XOUTCXYP1l>FR><<SMPRCYrf2CFRR))>

:• TR4ISCCXrS~PRCXPY1,f),.<<XOUTCXYP1J>FR> <<SMP~<Yrf2tfRR)J><SKPR{X,fl(f'RRJJ>Q> Q,.<<<XOUTCXYP1J>FR><SMPR<Yrf'2(fRRl)>Q> <SXPR<Xrf'l!fRRl)>Q•<SMPRCT?l•fZCYPlrfJ }><S~?RCX.fl(fRR}}>O# <SKPR<YPlrfZCYPl,f'Jl><SMPRCX•F1CYP1rf')

<SMPRU ,.fl( fRRJ J >Q>QJ ,

)>Cr T5Zr rzz, T43r T51) PROPlU Pl.F) P a T51t

T55 := [U:lT:lTO<XPY1JlCXlT53(U) : PftOPZCTPl> :: ISPCNAT,CT:NATJPRDPZCTJ,YPlr<Y>SUC•

T54rSATZ4UY)} : PROPZC<Y>SUC) y lil T56 :: INOUCTIONC(itNATlPRDPZCT>•Tll,[Z:NATl

Q a a

0 a

A a

x a

c a

CT:PROPZU>H55CZ,TJ,Y) : PROPZ<Y)

SATZZIU

CDMMUT t= tXtCXJCY:CXliSC<Y><X>Oo<X><Y>Q) CO!OIJTPL ;: lXtCXHY:CXlCOMPUX,YJ COMKUTTS .:= [XtCXJ(YtCXlCOHTSCX•Y) [CtC3MMUTl[ZtCXl[U:CXl COMQ t• <Z>C tCtCDMMUT(OJJ(X:NATJ[F:tT:1TOCXJlCXJ[G:tT:1TOCXJlCXJ

PROPl := IStSMPR(Xr!TtlTOCXil<<T>G><<T>F>O)• <SMPRCXrGJ><SMPR(X,f)>Q)

PROPZ t= ALL•t•crT:lTOCXJlCX•{U:[T:lfOCX}lCXl All*L"CtT:lTO(X)]CX•[V:[T:lTOCX)lCKl PROPl< IJ, V) H

CF'O:(T :1 TOCI) l CX JCGO H T :t TO< lllCXl Tl := SAT2'277C(f:lTOO>J«T>GI}>«T>F"0>0)

: ISCSHP~CPL•N•(X,.YJrf)•<SMPRCYrRIGHTCCX,x .. Y,f))><SMPRCXr LEfT(C(•PL•N•(X,YJ•XrLESSlSil-N•tX•Pl"~"CXrY), SATZ16A U; Y J hF) )>0 J

t 'PR1JP 9

COH!tUH [X:CXHY:CXJPLC x,n J : tOKMUT( [X:CXHY:CXlTSCX,n)

: ISC<Z>Or<Z>Q)

'PROP'

: 'PROP'

: IS<SMP~t1.[T:1TQ(!Jl~<T>G~><<T>fO>QJr<<XUUT{l)>GO>

s

s

- 5.56...:

T2 := IS!"'< C .t:rC Xr <S K?P< 1 ~ro l>Q,. SHP~( t,.GO) • <XD~T(l}>GDrSATZ277CCQ))

f3 := I SF"< CXrCX. rT :c:o «lCOUH 1 )>GO><T>Q,. SMPq(1r~~Jr<JOUT<1J>FOrSATZ277Cf0))

fit := TRIS<CXr <SKPR< l•GO )><SHP!Ht.>FO J.>O• «I:OUH 1 Hot;O ><SW"i::t 1 rf"O J > Q, <<XOUT (1 )> GO><<XCUTtl)>Fv>~•T2rT3l

T5 :: TRiS2tCX·S~?RC1•(T:1TO(lll<<T>GO><<T> FO>Q),<SKP~t!.äO}><S~PR<l,FOJ>Or

<<XDUT<lJ>GO><<X:UT<1J>FO>QrTt .. T4) c a T5 -- CU:[T:tTO<t>lCXltV;[t:tTQ(l>JCXJTS(U,.

VJ X a XP1 :: Pl•N~CX,.l)

[P:PROP2(lJJ[F:[T:1TOCIPIJ!CXi[5~tT:lTC(XPlJlCXl

C a [U:CXJ[V:CXl[~:CXl[Z:CXl

G a

T7 :: ASSQ2(Ar<\">Q,.W,.ZJ TB :~ CC~Q(Cr<V><~>Q•W>

T9 := ASSQZCA,.ii•:i··n T10 :: TP.IS<CX,.<W><<V>Q>Or<<V>O><W>Q,.

TU

UZ rn T14

T15

TU srx slix K SHX f17 ns

T19

TZO

ru

TZZ

TZ3

T2~

T25

<V><<~>Q>~•T8rT9> := ISF<tx .. cx.rr:cxJ<Z><T>Or<W><<V>Q>Or

<V><<~>Q>Q•TlOJ :: ASSQl{Ar<M>Q,v,.z> -- COHQ(C,.W,.U> :: ISFtCX•CXr(T:CXJ<<Z><V>O><T>Or<W>O•

<W:.<IJ>Q,Tl!) := TR4ISfCXr<<Z><W>Q><<Y>O>O•<Z><<K>

<<V>Q>Q>Qr<Z><<<><<W>O>O>Q,.<<Z> <V>Q><<Ä>Q>Or<<Z><ï>Q><<ft>O>Q, T?,.T1t.T12 .. Tl4l

:: LESSISil"N•CX•XPlrSATZ16A(Xr1JJ := SMPRtXrlEFTCtX.XP1.XrT16rf)) :: SKPRCXrlEFT<CXrXPlrXrTl6•G)) :: CT:lTCCXPlJ]<<T>G><<T>F>O t=,SHPR<XrlEFT<tX.XP1rXrT16•H)) ·- SATZ278tx.HJ :: <lEFT{CXrXP1,.XrT16•G>><LEFTCCX,.XP1•X•

T16rF>>P := Isrccx.cx.cr:cxl<<<XOUT<XPtJ>G>

<<XOUT<XPl>>F>O><T>QrSHX•<SGX><SFX>Q,. Tl8)

:: Tl5(SFXrSGXr<XOUTCXP1l>Fr<XOUTCXP1J>GJ

:: SYKI S< Cl(, SM?RUP l..F' J • « XOUH XP 1 > >F> <SFX>OrSATZ27S<X.F)J

:z ISfCCX,CXrtT:CXl<<<XOUT(XPl)>G><SGX>O> <T>Q•<<XOUT<XPlJ>F><SFX>O•SMPR<XPl•t>• TZU

:: SYMIS<t~•SMPRCXPl,G>•<<XOUTCXPlJ>G> <SGX>Q,.SAiZ278CX.~))

·- ISF<CXrCX•<S~PRCXPl•Fl>Qr<<XOUT<XP1J> G><SGX>Q,.SKPRCXP1.GJ,T23J

:= TR3IS!CX•SMPRCXP1•Hl•<<<XOUTCXP1J>G> <<XOUT!XPlJ>F>Q><SH~>Qr<<<XilUT(XPl,>G> <<XOUT(~Pll>F>Q~<<SGX><SFX>Q>O~

<<XütJH lJ>FO>QJ

: ISt<SH»R(1,GO>><SMPR(lrfOJ>Q,<<XOUTC1)>GO><SMPR(l,F0)> Q)

ISC<<XlUTC1J>GO><SMPRC1,.Fli>Q,.<<XOUT(1)>GO><<XOUT<lJ> . FO>O)

: IS(<S~~R{lrGOJ><SMPRCl•FOJ>Q,<<XOUTClJ>GO><<XOUT(l)>FO> Q,

: PRO?lU,rO,GO)

PROPZU J NAT

: !SC< <Z> <lf>Q>.<<Y> O>O,.<Z> <<W><<V>Q> Q>O l ISt<W><<V>Q>Q•<<V>O><W>Q) 1 SC <<V> Q ><K>Q, <V>« U><ll >Q>Q}

ISC<W>< <V>O>Qr<V>«U><ll >Q>OJ

.: IS ( < Z>< <H>< <V>Q>O>Q ,<Z> <<V><<ti><W>Q>Q>Q J IS<<Z><<V><<W>Q>Q>O•<<Z><V>O><<W>O>OJ

: ISC<II>Q,.<II>OJ

: IS<<<Z><V>O><<W>Q>Q,c<Z><V>Q><<W>Q>QJ

: IS(<<Z> <W>Q ><<V>O>O•<<Z ><V>O><<II> Q> Q J : L.ESSts• N•(X,XP1J : ex

ex : CT:1TO[XP1JJCX

ex IS<SMP~<XPl,.HJ,.<<<XOUT(XPl>>G><<XDUTCXPlJ>f>Q><SHX>Q)

: ISCSHX• <SGX><SFX>Q)

I SC <<<X OUTC XP1 > >G>< <XOUT U Pl J>f>O><SHX>Q,. < «XOUT <XP U> G><<XOJTCXP1)>f>Q><<SGX><SFX>Q>Q} IS<<<<( OUT< XPU >G>< <XOUH ~ Pl>>f>Q><<SGX><SFX>O>Q, «<XOUf <XPl )>G><SGX>Q><«XOUHXPlJ>f><SfX>C:>OJ

I S(<<lCl UT <XP1 l>F ><SFX>IbSM PRUPl •f))

IS(<< <X CUH XPl l >G><SGX >0>< «XllUTCXP 1 )>F><SFX>Q:~>Q,. <<<XOUF (XPll>G><SGX>~><SHPR(XPl,fJ>Q)

ISC<<XlUTtXP1)>G><SGX>Q,SMPRCXP1,.GJ)

ISC<<<(OUTCXPll>G><SGX>Q><SMPRCXPl•f)>Q,.<S~PR(XPl•G)> <SKPRU Pl,.F )>0)

- 5.57-

•8282

HS283

f26

<<<XOUTCXPlJ>û><SGX>Q><<<XOUT<XPlJ>F> <SFX>O>~~Tl7#r19•iZ0)

:: TR3IS<CX•SHPRCXP1•HJ•<<<XCUT(XP1J>G> <SGX>Q><<<XCUT(XPl)>F><SfX>Q>O~ <<<X3UT(XP1l>G><SGX>O><SMPR(XPl•fl>O• <SHPRCXP1.G)><SM?RCXPl.f)>Q,TZ5;t22•

I S<SMPl UPl,Hl • <«XOUHXPl )>G><SGX>Q>«<XOHCXPU >F'> <SF'X>O> CU

T2fd : PROPl<XPl•F'•G> P tt T27 :: (U:[T;lTO<XP1lJCXlCV:tT:1T~(XP1)JCXl

T2ó(U,n PROPZC(.Pl) TZ3 := ISP(NAJ•[T:~AilPROPZC!),XPl•<X>SUC•

T27•SATZ4ACX)) - PROP2C<X>SUC) x a f29 :: I~OUCTIONC[T:NATJP~OP2Cf),f6,[Y:NATl

tT:PROPZtY>lTZSCY•T>•X> : PROP2(()

SATZZSZ := <G><f>TZ9•.azaz•

X ; [S:(T:lTOCX)JlTOCXllCe:BIJECTIVEClTO<XhlTOCX>•S) lCF:[T:lTO(X)JCXl

s a

x a

[t; tr:UOCX) JCXJ G PROPl PRDPZ

:: tT:lTOCXll<<T>S>F' := IS(SMPRCX.G),S~PR<X•fl) :: ALL•L•CtT:lTOCX>llTOCXJ,(U:tT:tTO<XJl

lTDCXllALL•t•C[T:ITOCXJlCX• tV:tT:lTOCXlJCXliMPCSI~ECTIVEC1TO(X)• 1T O< :C h U h PR OP H U, V ) ) > )

Ca [S:CT:1TOC1Jl1TOC1)l[f:tf:1TC\1)lCXJ Tl := TP.IS2ClT3<l>•<XOUTCll>S•XOUTC1>~1D"N••

THl•N.SINGlET•(<XOUTCll>S>• THl-N.SINGlEt•cxOUT(l))}

·- SATZ277CGC1•S•fl)

ISCSHP~(X,(T:lTO(X)J<<T>G><<T>F>Q),cS"FR(XrG)><SHPR<X• rJ>Q)

: [f:1TQ[ X)]CX : 'PRiJP•

'PROPt

T2 T3 T4

: IS•E•<tTOC1l•<XOUTC1J>S•X~UT<1JJ IS<SKP~ u .. GH•S• f)) •<XOUT( U>G.U.oS•F)) ISC<XOJTCIJ>C<l•S•f>•<XOUfCll>fl :: ISF<ITO<l>•CX,f,<XOUTC1)>S,XOUTC1l•l1) :

·- SYHISCCX•SMPR<l•f),<XûUTClJ>f•

f5 SATZ2TT<F') l

:: TRJIS(CX•S"PR{l•G<l•S•f>J•<XOUT(l)> G(1•S•f),<XOUT(ll>f,SHPR(1,f),T2.T3• Tft)

:= [U:[T:lTO(l)llT3(1ll[Y:[T:lTOCl)JCXl tw:aiJECTIVEC1TOC1J,ITO<IJ,UJJT5(U•Vl

X a XP1 :: PL .. N"'(X,l) T7 ·- lESSISI1 .. N"<X.XP1,SATZ18A(X,l)) [PtPROPZU: lHS :( T: HO< XPl) l1 TCOC Pl} Hf:{ T: lTO( XPl l l CX HB:BI~ECT IVEU TOUPl>• HOC XPl h Sll TS :: ANDEl(INJECTIVEClTOCXPll•lTOCXPlt•S),

SURJECTIVEClTOCXPl),lTOCXPlJ,S>•B) . (CASE1:tswE•CtTO<XPllr<XOUT<KP1l>SrXOUf(XPl})](U:tTO(X)l Ul ·- LEFT1TO<XP1•X•f7,U) N1 := INNCXPl,<Ul>S) CI:ts•,•(Nl•XPlj] T9

TlO

:= TRJISC1TO<XP11r<UI>S• OUHHXP!.Nlrl TOP<XPl,<'Jl>SH.XOUHXP U r<XCUTCXPlJ>SriSQUïiNNCXPl•<Ul>Sl• iSOUTNICIPlrNl.lTOP(XPlr<Ul>S>•XPlr LESSISil!XPl>•I)rSYKIS(lfû{XPlJ• <XOUT<XP1J>S,XOUTCIP1)•CASE1J)

·- ISFE~1TOCX?ll•lTO(XPll•S•T8rUJr XC'.iHXPlh ï91

PROP 1<1 ,s,f)

PROP2C1 ) : NAT

LESS ts• N•<X • XPU

r JNJECTIVE<lTO<XP!),ITD<KPl)•S)

1TOUP1 > NAT

s

s

- 5.58-

Tll

ru

T13

:: ISOUTNE<XPlriNNCXoU!, TRlESSIS•n•c!NNCXrU).X,XPltlTOPCX,U), T7JPX?l•lESSISt3(XP1)pfl0) : IS·~·<INNCX,UJrXPll

:a S~TZliA(INNCXrUt,X.XP1.1TOPCX,U), SATZ tU<x •U 1

·- <Tll~EClE31CIS•N"CIN~CX.UJ,Xpl)~ MaR~·~·CtNN{X.U),XP!:.LESS·~·CINNtX,U> •XPl}rS~;ztOS(!NN(XoU).~Pl>•T12) tOK

u :1 T14 :: CR~lCLESS·~-(~l·ZPl),!S*"•(~l,KPl)• liJP<XPl•<Ul>S)rtT:IS"Q·{~l•XPlll

CASE:l :1 u :1

u a

u ;

Tl.HTn T15 :: SATZ25()(,NlrT14> W1 :: OUTNCI.Nl,T15) S:)l := CT:tTOCX)J:ilCT) (V:lfO(X)l[I:Is•E•ClTO(X)r~l(U)oWl(V))J

lESs·~· ('<1• XPl J LE SS IS .. N" C'll, X>

: HO( X> CT:l TOt Xl l1 TO<X J

Tl& := IS1JUT~E('J(, ~lC.Ih TlS<UhNHVh TiSCYlo. I) : rt7 :: <iSIN:E<XP1•<til(U)>S•<t:HV>>SrT1&>>

rt8 U2 NZ [I:ts•N•(NZ•XPl>l T19

rzo

TU

TZZ

TZ3

TZ4

TZ5 wz TZ& T27

TZ8

T29

TJO

UI

·- THLEFTl(Y.P~•X,f7;U,V;T17}

·- <Ul>INVF<lTO<XPl);lTO(X?lJrS•Bl := INNCXP1,tJ2)

:= TRIS<lTO<X?l),UZrOUTNCXP1.M2; 1TOP<XPl,UZ>>•XOUT<XPl>• ISGUTIRN[XPI,UZl,ISOUTqi(XP1,~2,

1TDPCXPl•U2lrXPl•LESS1SI3{XP1),It> ·- TR3IS!1TO\X?l);Ul•<U2>S,<XOUT(~P1)>S,

XOJT<XPl>,THINVtZ(lfG(XP!J,lTOCXPll•S• a.Ull,ISFC1TO<XP1J,1TOlXP1JrS•U2• IOUT(XPll•Tl9J,CASElJ

:: ISOUTNE!X?l•INNCX•U), T?.LESSIS•NP( I~N{X,U>,X,XPl,lTGP(X,.U>, T7>•X?l•LESSISI3<XPl>,T20)

:: SATZ16A(iNN(X,UlrXtX?1,1TOPCX,U)! SAiZl!iAO: .. l) l

:: <T2l>EC3Ell<Is•N•<INN(X,Ul,XPl)r MORE•N•CINN{Y.,UJ,XPllrLESS"N•(JNN(X,UJ .XPl)•SATZlOB<tNN(X,U),XP1lrT22)

·- OREltlESS•N•CN2rXP1J,IS·~·(N2rXPl>• lTCPCXPl•U2),{f:IS•N•(N2•XP1)lT23(T))

:: SATZ2&CI,N2rT24J :: OUTN(XoN2,T25J :: ISINOUTNCXrM2,T25) :: TRISC1TJCXP1>,uz,oUTNCXP1rN2r

lTCP(XPlrU2>>•UlCW2lriSOUTIN~(XPlrU2)• ISOUTKitXP1rN2,1TOP<XP1•U2lriNNCXrW2),. TRLESStS•N•<INN<X•W2)•X•XPI•lTOP(X•W2> rT7hT2óJ)

·- TRISC1TOCXPll•Ul•<U2>S•<GltW2J>S• ~ THINïf2(1TO(X?1),1TO<XPll•S•8•UlJr

lSF<tTOC~PI>•1TO<XPllrSrU2•UlCH2),TZT) )

:: TRIS<UAT,1N~(X,Ul•INNCXP1•U1>•N1<WZl• !SINOUTNCXPl,tNN<X•U>, TRLESSISw~•( IS~(X,U)oX•XPlolTCP<X•U>• T7>)~ISINN!CXP1.Ul,<Ul!w2l>SrT28JJ

·- TR!SClTO(XJ•U•OUTN(X,IN~<X•UJ, 1TCP{X,UJ),WlCWZl·ISOUf!NH(XrU), ISOUTNilXriNNlXrUJ•lTOP<X•U>•Nl(W2l• Tl5( 112 h TZ9) l

:: SO~E1CtT~tXJ,~i:lTOCilJiS•E•<lTOlXl•U• 1r;.cr u,iöz, no,

:;:s .. E•ct ïO<XPUrUHU ),\J HVJ) iS~E•<lTOtX),U,VJ

HOC XP1) NAT

: Iswr•n TO<XP1hU2•XOUHXPl )) .

CON

LESS'"N• (N2rXP1J lEssrs• N .. tNz,u lT!J(X} IS •H•(~ Z• IN N<X•II Zl)

IS•E•U TOCXPlhUh<UlCifZJ,.S)

rs·~ •n NNCX ,u,, N1U2n - 5.59-

CASE! a

u ;

CASE! ;

T32 ::: ANJlflKJ~CTIVE(lTC{X),lTQ(X),SOlJ• SU~JEC~iVEC!iû(X)•lTGCX),S0!), [T:lT~(KJ][~:lTO(X)J~V:Is•E•ClTOtXJ• <f>SOl.SOlllTlS{T,U.V),[TtlTOtXJl TJl(T)}

r01 := LEFT<CX.XPt,X.T7,f) TH == <TlZ><FOl><SOl>P Gl := LEFTCCX,XPl,~ri7,GCXPl•S,f)) ~2 ;·: GO:, SC!.FOU Tl lA ::: IS0~TI~~txr1r<Ul>SJ T34 := IS:~OUT~<X,Nl,Tl5> B5 == lS~UTNiCXPl•~l•lTOP<XPl,<Ul>SJ•

UI:H X• !41) • TR LESSIS •t\"( I NN ()(, W 1 h x .. XPl• 1TC?{X,~l>,T7!.T3~)

T36 == TP.!S<lTOtXPl>•<Ul>S• OUTN(X?l.Nl.lTO?<~?l,<Ul>S))•

lE>T1TC:XPl•X•ii•nlJri33A•Tl5) T37 ::: ISF(lTG(~Pl>rCX .. r,cUl>S,

LEfT1T~(XPl•X•T7,Wl>•T3&) f38 ::: FISI(lTCtXlrCX•Gl•G2•CT:1TOCX)JT37(Tll T39 :: ISFC~i:lTC(X>l~X.CX.tv:tT:lTDtXJlCXJ

SMPRCX,VlrGlrG2rT38) TltO := TRISCCXrSK?R(X,.Gll>SM?RCXrGZl•

SMPR(XrFO!J.T39rT3lJ TH := lSF(lT~(XPl)rCXrFo<XOUTCXPlJ>S•

XOUT(XPl>rCASEll T42 := SATZ278(X ... G( XPhSrF) J

Ul == ISFCCX,CX•<SHPR(X.Gll>O.<XOUT(XPlJ> GCXP1rS•F>•<XOUTCXPl)>FrT41J

Til4 := ISFCCX•CX•CT:CXl<<XOUTCXPl)>f><T>O• SMPROC .. G 1 hSKPiH XrFOl). T40)

T45 ::: SY~IS<CX.SMPRCXPl•Flr<<XOUT<XP1J>f>

BIJECfi VEU TO<X) •lTO(X hSl 1) tT:lTOC KJJCX PROPHiOb•fOU rT:lTI}[XllCX n :nor x nc x

: :s~~·ct TC(XP1Jr<U1>Sr0UTNCXP1•Nlr1TOPCXP1r<Ul>Sl>> Is-~"<~lriNNCX,Wll)

: Is•E•CtTOCXPllrOUTNCXPlrNlrlTOPCXPlr<Ut>Sll• LEH1Tl CXPl•XrT 7•H1))

: ISC:ilrGZJ : IS .. E•([ T:1TOCX»lCXrGhG2>

: ISCSltPt (X,Gl hSMPR(X,f01))

: ISC<XDJTCXPIJ>GCXPl,Srf),<XOUTCXPll>f) : IS<SMP,CXP1PG(XP1*S•f)),<<XOUT(XP1J>G{XP1rSrfl><SMPRtX,

GU>O)

: ISC<<XlUTtXP1>>GtXPl•S•f>><SMPRCXrG1J>O•<<XOUTCXP1J>F> <SMPR(( .GU>iH

ISC<<X1UT<XP1J>f><SMPRCX,j1J>O•<<XOUTCXP1>>f><SltPR(X• fOlJ>O)

<SHPR(X,r01J>O,SATZ278CX,f)) : ISC<<XJUTCXPl)>f><S~PR<XrrOlJ>Q,SKPRCXFl•fJ) T46 ::: TR4ISCCX,S~P~CX?l,G<XPl•S•f)),

<<XDUi!XP1J>GCXP1,Srf)><SMPR<X,G1)>Q, <<XOUT(XPl)>f><SMPRCX•Gl)>Q• <<XOUT<XP1l>F><SKPR(X,.f01J>Q, SMPRCXPl,f),f42,T43rT~4,T45) : PROPlC~PlrS,f)

B a lP X := Pl'"N .. ( lr XJ : NAT (CASEZ:ts•E .. (1TDCXP1J,<lOUTCXPll>S•lOUTCXP1J)l[U:tTOtXJl J3 := RICHT1TQ(l,X.U) HO< lP( J

CASEZ a T4T :: LESSISIZ~N"<lPXrXPl•COMPL~N"<lrXJJ LESSIS•N•ttPX.XPlJ 532 ::: lEFT(1TO(XP1),XPl•lPXrT47•Sl (T:1TOt1PXJJ1TO(XP1J

U a N3 :: INN( X?h<U3>5;)2) NAT U: IS"H•(NJ, U l Tttt8 := TR3IS< 1TO<XP1J,<U3>S02,

OUTN(XP1•N3•1TC?CXP1,<U3>S02)), 1DUT(XP1J•<10üi{XP1l>S• lSOUTINN<XPl•<U3>SOZ>; lSOUT,I<XPl .. ~l#lTO?<X?t,<Ul>SOZJ,lr SATl24ACXP1>•Il~sr~ISt1TO<XP1), <lOUT{XPl)>SrlnUTtXPl),CASEZJJ : IS-t•CtTOtXPlJ,<U3>SOZ,<llUT(XP1)>SJ

T49 := IStE(lTO<XPl)•lTC!XPll•S•T8• LEFT1TO<XPlr1PXrT47,U31r10UT<XPl),T48J : ts•E"CtTO(XPt),LEfTITOCXPl•lPX•T47•U3),1CUT<XPl)l

TSO :: ISOUTNECXPlriNNC1PX•Ul)• TRLESSIS•N•(INN(1PX•Ull•1PX,XP1• lTOPC lPX,l,! 3h T47 J ,.1, SJ\ TZZH C X?l l..T49) :: I s•tt•U HNUPX,U 3l .-1)

TSl

- 5.60-

u ;

CASE2 il u il

CASEZ a

u a

T52

T5l

T54

NMl T5H

f55

~~~L~7~'\li'1'~~U~~A#~,,JUr'~~U#~# • 4~ ~ ,-~ n 'A·~~~'~rUI#P,YR\4i·ArU~II

:: ISMCREl•,•(PL·~·tlol~N(X~~)), IN';( 1PX.!J3l• 1.' T5! • :;' TZ l 'H l• I NN<XrU))} IHiRE .. N• <INN UPX,Ul) •V

:: <T50>E:3E21<IS•N•ci~Nt1PXrU3J,lJMO~i .. N"( ~~··;cn·x .. u.n.l.h LE~~·~·(INNClPXrUllrl)r SATZlOE't I~l~l( lf'X,tJ!b 1 J.T52) CON

:: D~ElC~C~E·N·(~3.1J.;s•N•tN3•l),-SA!Z2:4~·a>.CT:rs·~; .. {:;::;,l1~T53<TlJ MORE"N•(tl:htJ

·•- M~~~~c~z.t.TS~J ~~T

·- ISL!$S1Sl~~~(~J~?L~NHf~MlrlJrXPi, TH1C~~.~N·\~3tlrT54l•1TO?CXPl•<ül>SOZ> ) tESSIS•N•cPL"'N"<NHl .. U,.XPl)

:: TH9"l.OR"<lESS·~·t?L"N"CNK1•1>•XP1lr IS•N•!?L•~·t~Mlol)oXPl)oLESS·~·CNMlrX)

CT:LESS•N•(PL•N•(NMlrl)oXPlJJ SATZZOCt~~l~X•l•T>• ~T:IS•N•[pt•~·tNM1~1>rXP1Jl

SATZ!DBC~Hl•X•l•TJJ 113 := OUTtHX,lt~l.T55J

I..ESS I s•N•(N Hl •X) 1TÜ{ X)

Sl3 :: (T:1TO(Xi)W3{f) : [T:l TO[ X} l1 TOCX l {Y:lrC{X)J(I:Is•E•CtTOCK),WJ(U),W3(VJJl T56 :: ISOUiNEtX .. NMH U),T55U:>..NM1<VlrT55(V ),.

I) T57 :: TR3I 5( NAT • N3 CJ >. PL '"N"{ NMH:J hl h

PL"N•(MHlCV),lJrNJCVJ,THlC•N.MN"(Nl(UY rlrT54CU)J,ISPL1•N•tNH1(U),NH1CVJ .. l, T5&J,fH1G•N.~N•(N3CV),1rT54(V)J)

158 t= ISINN:. O:?h<U.HU J>SOZ, <UJ(V J>SOZ.,T57) : IS• .. •n 3(UJ•N3(V}J

IS•E•ClTO<XP1J,.<Ul(U)>S02o<UitYJ>S02) T59 ·- ISFEClTûCXPl>•lTOCXPl},S,Ta,

T60 fSl 504

U4

t" n:ts•N•cN4 .. 1Jl T62

T63

T&4

'!';)5

T66

:= ;: ::

::

--·-

LEFTlTOCX 0 lolPX,T~7,U3(U}),.

lEfî1TC<XPlr1PX,T47•U3<V>l,T58J

THlEFT1CXP1 .. lPX,T47rU3<U)oU3CVJ,T59J THP.IGHT1(1•Xru,v,T&O> lEfTClïU{XPl>.XPlrlPXrT4!• INVf(lTC(XPllrlTO(XPll~S•81) <U3>S04 INN<X?!oU4)

TRISClTQ{XP11rU4,QUTNCXPl•N4r 1TOPCXPl,U4)),.10Uf(XP1l• ISOUTIN~tXP1rU4lriSOUTNI<XPlrN4r

: ts•E•(l TO<XPll•LEFT1TOtXP1 .. 1PX•T47rU3(Ul1• lEFTlTJ<XP1,1PXrT47,U3(V))) IS-t•n TOUPX>rUl<UlrU3CY))

: Is•r .. u rou >.u.v >

: tT:lTOC 1PXlllTOCXP1J nco:Pt,

: NAT

lTQP(XP1rU4Jrl,SATZ2~A(X?llrll) : IS•[•(t TO<XP1),U4r10UT<XP1J)

== TR3!S<1iG<XP1;•LEfTlTOCXfl•lPX,T47rU3> r<U4>Sr<10UT(XP1)>5,10UTCKP1), TH!NVf2(1JD<XPIJrlTDCXPl)oSrSr LEFT 1T OUPlr li'X, T4 7 .. U3 J J . .XSf U TO CXPl >.. 1TO(XPli•S•U4.10UT<XPlJoT62)rCASE2l . : IS•E"ClTOCXP1lrlEFT1TOCXPlr1PX,T47•UlJ~lQUl(XP1)J

== ISOIJT .. t:C~Plr !NP.j( 1PX .. U3h TRLESStS•N .. ( UH!< l?X• U:SJ •lP X• XPl• lT!lPC 1PX,U )), r;.n,l, St.T Z24A<XP1 ),T63) : IS"~"CI N~U PX,.IJ3},1)

:= TRIS(XAi~?L·~·cl,INNCX.U)l,INNilPX,UJ) •l•ISI~DUTN(lPX•PL~n~cloiN~<X•UJ>• SATZ190tiNN(X,Ul,X.loli~?CX.U))J,.TG~> : Is·~·t't•N"(l,.INNCX,U)),ll

:: <T65>E~JE2l<IS•N•(pL•N•t!ol~N(X,U>>•l> ,MDRE•U"lPL•N•(t,INN(XoU)JolJ, lESS•N•CPL"N"<l•INNCXor)l•l)o SATZlOBCPL•N•ct,INNCXoU}},!J,. SATZ18(1•INN(X,U))) CON

U; H7 := ORE1C~OR~~n•tN471l,IS·~·cU4,ll~

-5.61-

. '1~.2 ·-T58 ·-T;9 . -

lf4 ·-T70 . -!Tl ·-

T72 ·-

T73 :=

T74 . -

T75 ·-T76 ·-

T7T ·-CASE2 a T78 ==

roz := F03 ·-T79 ·-G3 ::: Gft ·-G5 ·-

0 41 T80 . -

SATZZ4CN4)o[T:IS"N"CN4olJJTGGCT)) ~N"N"CN4olrTG7l ISLESSISl"N"(X4,PL"N"CN~2.lloXPlo THtC•N.HN•(N4rloT67lolTO?(XPloU4)) TH9"L.OR"<LESS"~"<Fl"N"CNHZ•l>•X?ll• IS"N"(PL"N"{NMZolloXPllolESS"N•<NH2,XJ , IS .. ~l"OIMZ•X >• T68o CT:LESS .. N"CFL "N" CNM2,JJ,XPllJSAft2DC<NMZ.XoloTJ, [T:rs-~·tPl"~"[~~Z•ll•XFlll

SATZ209{N~2.X•l•T>J CUil;{ )(,N1>2• T69) iSINO~ïNCX•NM2oT69l TR3IStNAT.N4oPL"~·<loNM2)r

PL"N":loiN~CX.W4Jl,INNClPXoU3<W4J),.

THlA"N.HN•(N~rloTó7),

ISPL2~N·{~H2r!NG(Xo~4loloT701o

ISI~OUT~(lPXoPL"N"(l,IN~CXrW4)),

SATZ19C<!~N(X.~4loX,lrlTOPCX.~4))))

TRIS<lTO<XPlloU4,QUTNCXPl,N4r lTOPCXPloU4)l,LEFT1TOCXPlr!PÄoT47, UlCW4)J,ISOUTINNCXPlrU4}o ISOUTNI{X?lrN4,1TOPCXPloU4)~ INN(1PXrU3(W4})oTRLESSI5eN"CI~NC1PX~

U30i 4 J l, lP Xr XPlo HOP C lP l(, U3C 114}), T 47 >. T71)) TRIS<lTOCXP1JrlEfT1TOCXPlrlPXoT47•U3}, <U4>Sr<U3CW4J>S02rTHINVF2ClTOCXPllo lTOtXPl>•S•B,LEfTlTOCXPlrlPXrT47rU3J), ISFC1TUCXP1J,1TOCXPl),S,U4, LEFT1TGCXPlr!PXoT4ToU3CW4)),T72)) TRH St NAT • Pt-w•c l• I ~!I( X• U J >• INNC1PXrU3loiK~CXPl• ~EFT1TO<XPlrlPX,T47rU3JJ,N3<W4J,

ISINOUTNClPXoPL"~·<t•INNCXoUl>• SATZ190CI~N(X,U>oXrlrlTOPCXoUJ)J,

ISINOUTNtXPlriNNClPXrUJJ,. TRLESSIS•N"CINNC!PX,U3)r1PXrXPlr 1TOPCl?X,U3JoT47)), ISINNICXPl•LEfT1TOCXPl,lPXoT47oU3J, <U3C lflo}>S02• Tï 3> J TH1E~N.HN•CN3CW4),1,INNCX,UJ,T54CW4},

T74 J TRISClTOCXJ,UrOUTNCXriNN<X•U>• 1TOP(XoUlloW3{W4)r!SOUTINNCXoU), ISOUTNICXriNN{X,J>rlTOPCXrUloNMl(W4lo T55C 11.4 >• TTSl > SOMEI<lTQCXl•[T:lTO<X>JIS"E"<lTO<Xl,Ur W 3 {T ) >, W 4, T7 ó J ANOICINJECTIVEClTO<XJ,lTOCX>·S03), SURJECTIVEClTOCXJ,lTO(X),S03), tT:1TO<XJJ[U:1TD<X>J[V:IS•E•<lTO(X)o <T>S03oS03>JT61(T,u,v>,[T:1TO(X)J T77( T))

LEfTCCXoXPlo1PXrT47oF} RIGHT<CXrl•XrfOZ> <T73><f03><S03>P LEFT(CXrXPlr1PXoT47rG(XPl•S,f)) RIGHTCCXrl~XrGJ)

GCX,S03of03) TR3lSCNAToN3rPl"N"CloNHl)o PL"N"(lriNN<XrX])), IN~ClPXrRIGHT1fC(1,XoH3)),

HORE•N• 044, 1) NAT

lESSIS .. N,.CNH2oXJ lT oe x> ts•N .. C'i H2olNNCXoW4))

BIJECTIVE{lTO(X)olTOCXlrS)3) CT : 1T 0( lPO JCX [T :1 TGC Xl !CX PROP 1C5 0 3rf03) tT H TûC lPX> JCX n:troc xncx (T:lTO. X>lCX

-5.62-

TH!A•N.M~•[NJrlrTS•>• I5PL2·~·(NMl•!KN(XrHJ)rlr

ISINOUTN<XrN~!.T55l>• ISIN.CU TN{ lPX .. Pt• N•t; 1• I NIH X• W3 )h SATZ190(INN(XrW3lrXrlrlTOPIK.W3)))} IS•N,.OJ3. INN<lPX•RIGHT lJO( l•X• w:H))

T81 :: TRIS(lTntXPl>•<V3>S02r O~TN(IP1.Nl.1TOP(XPlr<U3>S02)),

LEFT1TrlXP1 .. 1PXoT47•RtGHT1TCC1•X•~3)), !SGU7~~~CXPl.<U3>502lo

!SDU~~I(XPl•~l·llDPCXPl•<U3>S02)• l~>;'~{lPX,.;UGHTlïQ(!,l::,j.j3)),

TRLESSIS•N•( !NN<lPXoRIGHT1TO<l•X•W3))r lPX, XP1.1 TOP(l?X,.RlGHTlTO(l, X,il] ))• T'47hTa0}) : IS•[•(t TO<Xpllr<U3>S02rlE~TlTOCXP1•lPX•T47•

RIGHT1f0(1,X.W3J)) f82 ·- ISf(1TO<XPllrCX•Fr<U3>S02r

lEFTlTCCXPl•lPX•T47•RIGHTlTO<l•X•W3lJ~ reu IS\:O :,,cU>G5>

CAS EZ .. T83 == fiSIC1TO<X>rCXrû4•G5•CT:1TO(XJJi82(ll) IS .. f.: .. C( T: 1T C<X> lCX• G4• .GS) T85 == ISrCti:1TO{X)JCXrCXr(U:(T:1TOCX)lCX1

SMPR(X,UJ.G4rGS~T83l ISCSMP't tX,G4)•SHPR< X•G5D T8& ·- TRIS<CX,S~?~(X,G4lrS~?R<XrG5)r

SMPR(Y..F03),T35rT79} :SCSHP'l <XrG4>rSHPRCX,f03H rar := LESSISil"Nn(lolPX•SATZ18AClrX)) LESS IS• N•( l•lPX l G& :: lEFT<C XrlPXrlr TS7,G3 > n:uor l>JCX fD4 :: L~fTCCX,lPX•l•T87,F02> ETHTOC l>JCX T87A :: !SINOUTN(lrl•LESSIS!J(l)) : IS•N'•n •INNCl•XOUH U>> 10 ::: LEFflf0(1PX .. lrT87,XOUTC1l) . lTOUP( > . T87B :: ISI~OUTNClPXriNN<l•XOUf(l)),

T?.LESSis-N~CINN{lrXOUTC1J)rl•lPXr

1TCP<l•Xry~TCl)}rT87)) : ts•N•CINN(l•XOUTClllriN~ClPX•lD>l

T86 := TRIS(NAT~lriKN<1~XOdT(1)),INN(1PX,.1DJ• T67A,T873) t S "l11'" C1 .. I NN U PX,. 1 0 J l

1E := lEfT1TO!XP1.olPX•T47~10> lTO<XPl > T88A := ISOUTNICXP1•l•SATZ24A(XP1)rlNNC1PXrl0)

•lRLESSIS•N•<INNClPiolD>•(PX•IPl• 1T0P(lPI.olOlrT47),T88J IS•E•CtTOCXPlJ,.lOUT<XPlJ,.lEJ

T888 := ISf(lTGCXPl>•lTQ{XPl>~S•lE•lOUTtXPl>• SYMIS(1TO<XP1),10UT(XP1JrlErT88Al) : IS•E'"ClTOCXPlJ.o<lE>Sr<lGUT(XPl)~S)

T89 :: TR3IS<1TOfXP1>•<1E>S•<lOUT(XP1)>S• lnUT{XPll~lE•T88B•CASEZoT88A) IS•E•U TO<XP1h<1E>S•1El

T89A :: TRliStCX.oSMPR(lrG6J,.<XOUT<11>G6, <XOUT(lJ>F04,SMPR(1,f04),$ATZZ77CG6lr ISF(lTC<XPl).oCX,f,<lE>SrlErT89>• SYMIS(C~;SMPRC1•f04l•<XOUT(1}>f04, SHZ27HF04) )) IS<SKP'l (l,Gf>},SMPR( t.F04))

T90 == S~TZ25HhX•G3l ISCSMPl(lPX .. G3)~<SMPRCXr~\)><SMPR(lrG6)>Q) T91 := ISFCCX.CXr<SMPR(l,G6l>QrSMPRCX.G4)•

SHPR(Xrf03l•T8ó) ISC<SM,RCX .. G4J><SMPRC1rGS)>Q,<SHPR(XrF03)><SMPRt1rG6)> Q)

T9~ == tsrccx.cx.rr:cxl<SMPR<x .. ro3l><T>Q• SMPRCl•G6)rSMPR<lrF04JrT89AJ : I S<<S M» ROC;. F03> ><SMPR( 1rG:2 J >Or<SHPIH Xrf 0 3) >< SHP!H 1 rfO 4)

>Q) T93 := SY~IS(CXrSMPR!1PXrt02)r<S~PR(XrF03)>

<SMPR,1.F04>>0rSATZ281Cl?Y.,F02)) ISf<SM,RCXrf03)><SMPRC1,F)4)>Q,SMPR(lPX,F02)) T94 :: TR41S<CXrSMPR<lPX,G3)r<SHPR(XrG4)>

<SHPR(l,S6)>Q,<SMPR<X·f03)><SXPR(l•G6) - 5.63.., >Qr<S~?P.CXrf03)><S~PR<lrrv4)>Q~ S~?R<1PX•f02lrT90rT91•T92rT93J : 1SCSMP~(1PXrG3)rSMPRC1PX•~02J)

T95 := ISS14PRC X?l~ F • 1 PX,.CGMPL .. N .. (l, X n IS<SHP:t UPX rf02 hSMPRC XPb FJ) f96 :=- SYMISCCX.SMPR{lPX.GlJ.

SM?RCXPlrG(XPI•S,F)Jo

ISSK~R(X?lrG<XPt,s,r>•lPXr COMPL;,.N"(l.X > > l IS<SMPl (XPl.G()(Pl•SrF> ),SMPRC 1PX.G3))

T97 ::: TRHStCX•SMPRClcPlrG(XPlrS•f'>ir SHPR<lPXrG3JrSHPR<lPX•f02>rSKPR(XP1rF) rT9&rT94,.T95l : PROP1UP1"S"rJ.

B ~ tNOT1:NOT<Is•t•t1TOtXP1l,<XOUT<XP1l>S•XOUT(XPllll j { N0i2 :NCHIS•E•n TOCXPl h<l OUHXP ll>SrlOUHX?l l))] AO := <1\JUTCXPll>S HCCXP1 > 8!) :::: <l::!:JHX?1P·n;vFClTC~::Ptl .. 1iOC~PlhS•B) 1HHX?l l T98 :: TH!NYf2(lTCCXP1)rlTO(XP1JrS~B·

lOJI<XP!l) ts•E"<l TOCXP1J,lGUTCXPl)r<BO>S) T9!1 :: NOTZ NOT<Is•r.•uTO!XPlhA0•10UT<XP1))) TlOO := SYKNOTIS<l!OIXPll•<lOUT(XPl>>S,<BO>S•

TH3•E.HCTJS•(1TGCX?lJr<IOUT<XPl)>S• 1 CUT\ XPllr <SG>S• ~HJTZ• f98)) : NOH IS" t•U TO<XP 1 h <60 >S,.< lOUTUPU >SH

T101 :: THJ~l.IMP*tiS"E•<tTO(XPl>~90.10UTCXP1J ),!s~E•<lïCCXPl>~<BO>Sr<lOUT!XPl>>S)~

!lQQ,(T:IS"~·<tTO<KPlJrBOrl~UT(XPl))J

ISrC1T3{XPllrlTOCXP1>•SrBO•lOUT<XPll• T>> NOTtis•t:•<tTOCXPllrBOrlOUTCXPllJ)

Sl ·- CHANGEr<lTO<XPl>•lTO<XPll•SrlOUT<XPll• 80> tT:1TO[XP!)l1TO<XPll

(~:lTO<XPl)](l:Is•E•<tTO(XP1>rU•10UTC~P1))] T102 ·- CHANGEf1<1TOCXP1>•1TO<XPl>•S•10UT<XPll

.eo.u, ll IS-E•ct TO<XP1 hSlr<BO>S) T103 := TRIS2!1TOCXPllrS1rlOUT(XP1lr<BO>Sr

T102rT98) IS-t•ttTO(XPl)rSlrlOUTCXPl)) U a (I:Is•t•ttTO<XPlJrUrBOll

n:u := CH~NGEf"2(1T0UP1 h1TO<XP1 hSrlOUTC XPl) ,ao.u,n IS•E•ct TO<XPlhSt.AO)

U; [N:~OT<IS•t•<tTOCXPllrUrlUUTCXPl>>l Jt!l: ~OH IS .. t:•< lT 0( XPl hU,.B 0)) l T105 :: Ct11HIGEf3U TOUPl>• 1TO<XP1 hS, 10UTCXP1 >

,ao,u.N.OJ : Is-t•(t TO<XPlJ,SlrS) >tDTZ a Tl06 :: THG•E.iiiSSEl .. (lTO<XPll,.lfO<XPU ... S,

10UHXP1 lr BO•B > BIJECTI VEU TO<XP1Jr1T!HXP1 hSU UlPH.UNOT( IS•E•U TO<XPU.I.Or X DUT< XPU J l1 SZ :: WISSEt(lTO<X?l}rlOUTtXPl>•AOl : [T:1TOtXPllllTOtXPlJ T107 :: TH3"E.WISSEL•f1TO<XP1),10UTCXP1J,.A0) : BIJECTIVE<lTOCXPlJ,.lTO(XPl)rS2J [U:lfD(XPl)l[I:IS"E•CtTOCXPll,.U•lOUT(XPl)JJ TlOB := lSWISSEL1<1TOCXPlJ,.lOUTCXPl>rAO~Slr

T103<U,IlJ : IS•E•<1 TOCXPl>•<Sl>SZ,.\OJ T109 := TRI SZ! lTO<XP 1 >•S,.«U>Sl>S2•AO •

ISfClTOCXPll.lTCCXPlJ,.s,u,lOUTCXPlJ,.IJ ,T103> : ts•t•ctTOCXPl>•Sr<S1>S2>

U ~ CI:IS•t•<lTO~XPl),.U,.BO>J TllO :• ISNISSEL2(1TDCXPll•lGUTCXP1),.AO,.Slr

T104(U,.IJ> : IS-E•<tTOCXP1J•<S1>52•10UTCXP1lJ TUl •- TRIS2<1TO<XP1),Sr<Sl>S2r

10JTCXP1J,TRIS2<1Tn<XP1J,.S,. 10Uf(XP1),.<80>S•lSF{lTO<XP1JrlTOCXP1Jr S•iJ,. so, I h T9 81 • TllOJ : JS-E:•U TOCXPl h S,« U>Sl >SZ J

U~ [~:NOTtiS•E•tlTO<XP1),Ur1GUTCXP1)))

l(O:~OTCIS"Eft<lTOtX?lJ,U•30)J l(I:Is•t•(!TO<XPl)•S1,10UT(XP1>>1 TllZ :: ISfE<lTOCXPlJ,lTO<XPll•Sl•

T6(Sl~F,.T10&JrU•lOUTCXPll•

fRIS2<1TOfXP1JrSl•<lOUTCXP1l>S1r 10UTCXPl>,.I•T103ClOUTtXP1), REri SU TOCXP 1> ,1 OUHXPU)))) . I S .. t:•ct TO<XPl hUrlOUT( XPU J

0 ~ T113 ·- TH3 .. l. IMP .. fiS'"E'"UTO<XP1 hSl. 10UT(XPllJ•IS~(•(1TOtXP1>·U,lOUTCXP1 ))

- 5.64-

,N,(T:Is~E•<1TOCX?l)•S1•10CTCXP1))J T112nn Nt'H IS• E"Cl TOCXPlhSl•l OUTCXPll)J

ti:Is"E"ClTOCXPll•Sl•.\Oll T11tt := ISfE<lTCCXPl),lTOCXPU,Sl•

T8t Sl• F", TlO&>•li• 30• TRIS2! lfO(XPl h Sl•<90>5loAO,I,Tl04C80.REfiSC1TOCXPl ), fl())) n . _ . : IS"E"<l TOCXPl>•O•BO)

0 a T115 := TH!"L.I~P~<IS~E"ClTCCXPll,Sl,AOl,

Tl1&

T117

N ~ T116

u ., T119

rs~E~<:TC{X?lJ,u~~o>~c,

[T:rs•E•tlT:~XP~J.<~>Sl••OlJT114(T>> := IS~ISSEL3C1TCC~?i~·lDUTCXPl>,AO,Sl,

ïll3•T115} ·- SYHIStlTCCXPl>.<Sl>SZoS,

TRISC1TCCXPllr<Sl>~2,SloS• Tll&,T105CU·~·C;J)

·- THl•L.IHP"tiSRE"tlTUCXPlJ,UoB~>• ts•E"ClTCCXPlJ.~U>S•<Sl>S2l•

[T:!SnEft<lTCC~ 0 l}oJoC0>1Tll~CT>•

CT:NQTCIS"E"C1TCCXP1l•U•BCJ>JT11T(f)) := TH1~L.IMP"CIS"E"ClTûCXPl>•U•lOUTCXP1 ))

•IS"E"<lTJCXPl>.So<S1>S2)r [f;IS"E•(lT~(~P1JrU,lCUTCKPl>>lT109CT} ,[T:~OTCiS•E•ClTCCX?ll,U,lOUT<XPll))]

IS"E"C1TCCXPl>•So<Sl>S2>

IS"E•U TO<XPUoS•<Sl>S2>

ïlloCT>> IS•E•(t TOCXP1JoSr<Sl>S2) AlPHA :1 T12~ := FISIC!TCCXP1},1TDCXP1lrSr[T:1TOCXP1)J

<<T>Sl>S2r[T:lTJ<X?!liT!19(J)J IS"E"((T:lTOCXPl>llTO<XPllrS•(T:lTO<XP1Jl<<T>Sl>S2l NDTZ a T1Z1

T1Z1A

:= T103~1avTCXPl>•rtEFISC1TO<XP1Jo lOUT< X?l) J > IS•E•U TOUPl h <lOUHXPl )> St.lDUH XPU)

:= EC3EZ1<IS•N•<XFl•l>•MORE•N•<XPloll• lESS•N"<XPlollrSATZlOS<XPlrl), IS~OREl•N•<tPXoXPl•l•COMPL•N•ct.X>•

T1ZZ SATZ18Cl,Xlll NIS•N•[XPl,ll

·- TH3~L.lMP-{lSwE"tlTG<XPlJ•XOUTCXPll• lOUTCXPll>riS"N"CXPlol),Tl21A• [T:IS"E"<lTO<XPllrXOUT<XPllrlOUTCXPl )) JISOUTNECXFlrXPlrlESSISI3CXPllrl• SATZzt, .\( XPl>, Tl) NOH I s• E•U TOCXP 1 h XOUHX, 1>•10UTCXP U})

AlPHA a T1Z3 f1Z4

•- SYMNOTIS<lTOCXPlJ,AOrXOUTCX?l),AlPHA) NOTCIS•E•ttTOCXPll•XOUTCXPlJoAOJ) ·- ISWISSEL3C1TQCXPllrlOUTCXPll,AOr

NGTZ a

XOUTCXPl)oT1Z2•TlZ3J : IS•E•ctTOCXPl)r<XOUTCXPll>SZ•XOUTCXPll> T1Z5

TlZ&

:: ISFCCT:lTOCXPl>llTO<XPlJ.CXr CU:[T:lTDCXPlJllTCCXPlJlSHPRCXPlo GCXPloU;f)),Sr[T:lTO<XPlll<<T>Sl>SZo 1120)

T12T ·- T4&<sz,F,T107rT124> TlZ6 := TR3IS<CXrS~PR<XPl.GCXPloSof)),

SMPR<XPl,GCXPl,Sl•GCXPlrSZoFJ)), SHPRCXPlrG<XP1.S2.fl)o5HPR<XPl,r>• T1T3 rT126• TlZ7l

[I3:Is•E•ClTDCXP1JrAOrXOUT~XPl))

lCBErA:NOTCIS•Ew(lTOCXPlJrBO•XOUTCXPl>>>J S3 :: WISSELC!TO<XP1J,1GUTCX?l>,SO) T129 :: TH3"E.WISSEL"<1TOCXPl>rlOUTCXP1lrBO> (U:lTD<XPl>JCI:IS"E•<tTOCXPlJrU•lD~TCXPll}]

Tl30 :: T104tS3.ISHISSELlClTOCXPlir lO~iCXPi)•30rUrill

T131 .- TRISZClTOtXPl),<U~S.<S3>SloAO"

ISf(lTQ{Y.Pl),lTOCY.rl>•S•U•lCUT<XPl>riJ ,Tl JO)

IS<SHPl(XPloGCXPl•S•f)),S"PRCXPloGCXPloSlrGCXPl•SZ•F)J) )

ISCS~P~ (XPlrGCXPl•SloGCXPloSZ•f))J,S~PRCXPl•G<XPlrSZ•fl ) )

ISCSHP~CXPlrGCXPlrS2•fJloSHPR<XP1•f))

PROP HX Pl•S•fl

CT : 1T oe x P u 11 r o < x P 1 > 6IJECTIVEC1TOCXP1JrlTO<XPl)oS3J

IS"'E'"<l TO<XPl )rS,«U>S3 >Sl)

- 5.65-

U; CI:ts•t•<1TO!XPl>•U•80)J T13~ ·- Tl03<S3•!SniSSEt~ClTOCXP1)•

l~UT<XPlJ.BO,Url)) fl33 ·- TRIS2<1TO<XP1),S•<S3>5l•<BO>S•

ISf(lTO(XPl>,lTOCXPl>•S•U•BO•Ilr TR!SClTUCXPl>•<S3>S1•10UT(XPl>•<BO> s.n:;z.r?a>>

U ê tH:N~T<IS•E•ttTOtXPll•U•lCU7(XP1Jll lCO:NDT<IS•E•ClTC(X?1>·0·30))J Tl34 :• IS~ISSEL3(lf0(XP1>,10UT<XP1l•BO•U•N•O> Tl35 ·- !S~{lTO{XP1>•1TOC~Pl}~Sl•<O>S3•u~T134l Tll& ·- T105tv.N.OJ T139 ·- S!~!S{lT0(XPll•<S3>Sl•S•

TRIS<lTO<XPl),<S3>Sl•Sl,S• T 135• T UG> l

N ê T140 := THl~L.IMP•CIS•[•(tTO<XPl),U,SOlr

u a T141

BETA a T14Z

T143 U44

T145

Tl46

IS"E•ctTOCXPlJ,S•<S3>S1Jr tT:Is~Eft<lTOCXPl)•U•30JlT133<T>•

CT=NGT(IS•E•CtTO{XPl>~U~BOJ)JT139(f)) .- THl•L.iHP•CIS•[•tlTG(XPl)•U,lOUTCXPil)

,Is•E•<lTO<XP1)~S,<S3>Sl>•

[T:ts•[•(lTDCXP1J~U•lOUTIXP1JllT131<f) rtT:NJT<Is•E~{lTOCX?l),U,lDUTCXPl)})l

THOCT}) := FISI<1TO<XP1>•1TO<XP1>~SrCT:lTOfXP1Jl

<<T>Sl>Sl•CT~lTOCXP1JJT141(TJJ SY~~OTIStlTO<XP1)•60rXOUT<XPl)r9ETA>

·- ISWISSEL3C1TO(XP1J~10UTCXP1l,BO• Xû~TCXP1>•Tl22•Tl43)

:= ISf(ET:1TOCXP1JllTOCXPl),CX• [~:[T:tTOCXPll11TOCXPl>JSMPRCXPlr GCXPlrU,f)},S,[T:lTO(XP1)l<<T>S3>Sl• Tl42)

T147 ·- T97tSl•f,T10&.Tl21J Tl48 ·- TR3ISCCXrSHPRCXP1,GCXPlrSrf)),

SHPRCXP1rGCXPl•S3rGCXPl~Sl•f)J), SHPRCXPl.GCXPlrSlrf)),SMPR<XPlrf), Tl45rT146rT1471

I3 a [GAMMA:ISwE•(lTO<XP!J,BO,XOUT(XPl)JJti:IswN•(X,lll T149 ·- ISPLl•N•<l•X•l•SYMIS!NATrX•l•IlJ T150 .- lESSISIZ•N•cz.xPt.Tl49) t35 ·- lEFTCCX.XPt,z,Tl50rF> S'5 ·- LEFTt1TOCXPll•XP1•2•T150rS) G7 ·- lEFT<CX,XPlr2rT150.GCXPlrS•f)) Tl51 -- iSS~PR<XPl•f•2•T149} 1152 ·- ISSMPR<XPlrGlXPl•S•f),~,T14~J 1153 := SATZ280Cf05) T154 ·- SATZ280tG7) 1155 ·- TRIS1CNATrlNNC2oXOUT(2)),XP1r2r

IS!NOUTN(2rZrlESSISI3(~)),f149J

T15& ·- ISCUTNI<XF'lo INN\Z~XOUHZH, TRLESSIS~N-( INNC2rXOUT(~)),z,XP1• 1TOPCZrXOUT(2)),T150J.XPlr lESSISI5C~Pl>oT135>

T157 :: ISFClTOC~Pl>•lTOCXPl>•S• lEFT1TOCXPl•2•Tl50rXOUf(2))•XOUTCXPlJ• Tl5&)

T158 :: SYMIStNAï#l.ZMNCZr10UH2)), !SINûUTN(2~l•SATZ24A<Z>:J

IS"E•n TO<XPl>rS3rU) IS•E•U TOO<Pl h<S3>~1,SU IS•E"Cl TOC!(PlJ.Sl;Sl

: ts•E•([T:1TOCXP11l1TO(XP1l•S•[T:1TO<XP1ll<<T>S3>S1) : NOT( IS• E•ct TOUPU• XOUTU" 1 hBOH

: ISCSHPlCXPl,GClPl•S,f)),S.PR<XP1,G(XP1rS3,G<XP1•51•f))) )

IS<S~Pl<XPl•GCXP1~S3;G(XP1,Sl•f))J•SMP~CXPl•GCXPl•Sl•f)

) ' : IS<SMPl <XPl•G<XPt.S1rfHrSMPR<XPb•f))

: IS .. N .. <2 •XPl) LESS!S•N•(ZrXPll n:t rm zncx

: [T:lTOC2>JlTOU:P1l n:tTOCZJJCX ISCSH~l(2•F05)rSKPRCXPl•F1) IS<SMPl <2,.G7 hSHPR<XPl,GU Ph Srr> l J IS<SHPl(2,.F05l~<<XOUTCZl>~05><<10UTC2J>f05>Q)

: ISCSHPl(2,G7)•<<XOUT(~J>G7><<10UT(2)>G7>01

- 5.66-

fl59

Tl&O

T16l

T164

T1&5

Tl&G

T167

f168

Tl69

T170

T171

T172

TRIVIAL GAHHA a [N:NIS,.N'"(Xrl)J

T173

XMl Sft

T174

T175

T17ó T177

·- IS!JUT'H{XPbHHl!Z.•lCIJHZJh TRLESS:S"N"CI~~[2o!DUT{2J>•!•XP1~ ITOPtZ.lOUTC2Jl•T150l,l•SAfZ24ACXP1.)~ T15c3)

:: TR3IS<lTOCXPl>~LEFT1TOCJP1•2•T150~ lG~T<2J),lGUTtXP1),<30>Sr<XOUT(X?l)>S,

T159•T93,ISF~lTO(XPl)rlTD<XP1JrS•SO• XOUTCX?l),GA~~AJ>

·- T?.IS2<!T~<XP1},<X~~TC2)>$0S, LEFT1TCrXPlrZ•T15GolC~T(2)),<XOUT<XPl) >S,TlST,Tl&Q)

:: ISF<lTO(XPl}rlTOCX?ll•S• LEI'"f lTO< XPl,. z, T1 SO, lCUT( 2> ), lOUT<X?l h Tl59)

:: TRIS(lTO<X?l },<iOUI(2J>S05~<10UT<XPl)> S•XOUT~XP1l•Tl63,IJJ

·- TR!S2<1TO(XP11,<10UTCZJ>S05, LEFT1TG{X?l,z,TlSO,XGUf{2)J,XOUTCXP1), T1&luTl5Sl

·- IS~<lTO<XP1l•CXrf,<XOUTC2J>S05r LEH lTQ( X?lrZ, !150, lJUHZ UrT161)

:: ISF(lTJ<XPl>-CX•f•<lD~T(Zl>SOS• LEFT1TOCXP1,2rT150.XCUT(2)1,Tl&5l

:: ISF<Ch,cx,<<10UTC2)>G7>Qr<XOUT(Z>>G7r <lOUT<ZJ>fOS,TlSGl

·- COMQ(Co<lOUTCZl>G7•<10UT<Z>>FG5)

:= ISf(CX,CX•<<10UTCZ)>FOS>Q,<lOUTC2)>G7• <XOUT(2)>f05rT167l

:: TR4ISCCX~SHPRCXPlrGCXP1rSrF))r SMPRI2rG7>.<<XOUTCZl>G7><<10UT(Zl>G7> Q,<<1GUT<Z>>f05><<10UT<2l>G7>Q, <<10UT<Z>>G7><<1C~T<2l>f05>Q,

SYHIS<CXrSM?R<Z,CTJ, SMPR(XPlrG{XPl•Srf)},T152>•T154,T168• T169)

:= TR4IS<CX•SMPRCXPlrGCXP1rSrf)), <<10UTCZl>G7><<iOUTCll>F05>Q,<<XOUTC2J >f05><<10UTC2!>F05>0•S~PR<2•f051• SH?R{XPlrFlrT17lrTl70, SYHISCCX•S~PR{2,f0Sl•~<XOUT<2>>f05>

·-·-:: ::

== ·-

:::-

·-

<<1QUT(21>f05>~,i153),T151)

T172

ORE1<KORE~N•(Xrll,IS"N•(X,1J~SATZ24(XJ ,N) MN"N•cx, h T173) CHANGEF<lTOCXP1JrlTOCXPl~rS•lOUT(XP1 )r XOUHXPl >) TH&•E.WISSEL•CtTC(XPlJrlTDCXPl>•S• 10UT!XP1J,XOUTCX?1),9) CHANGtf2fiTOLXPl)rlTOCXP1lrS•lOUt(XP1) ,XOUT(XPlJ,XGUT!XPll•REFIS<lTO<XPl)• XOUTCXPU)J SYMISC1TO<X?1lrAO,XOUi(X?1l•I3l TR!S2<1TD<XPl>;<XGUT{XP!)>S4,XOUTtXPlJ •<lOUT(XPl)>SrT175•Tl76J

I S'"E• Cl TO<XPlhlEFT1TO<XPlrZrT150,. 10UH2J l •IOUH XPl >)

IS•E•<!TOCXP1lrlEFT!TOCXPt,z,Tt50r10UT<2J),<XOUT<XP1J> Sl

IS•[•(tTOCXPl)~<XOUT(2J>S)5rLEFT1TG<XP1,.2•Tl50•10UT<Z>> )

!S•t•u HHX Pl)" < 10UT<2 J>S) 5•lEfT1 T:H XP lr2r HSO• XOUT<2)} )

IS<<XOJT<2J>G7~<10UT(2J>F)5)

IS(<10JTC2)>G7~<XCUT(2)>~J5)

ISC<<XlUTC2J>G7><<10UT(2l>G7>Q,<<10UT(2J>F05><<10UT(Zl> G7>Q l

: 15{<<1JUT<2>>f05><<10UTCZ>>GT>Qr<<10UT(2J>G7><<10UT<Zl> ros>o,

: !S(<<l!UT<Z1>G7><<10UT(ZJ>f05>0r<<XOUT<Zl>FOS><<10UTC2J >f05>0)

PROPlUPlrSrfJ PROPlU Pl•S •fl

: MORE•fi•(Xpl) NAT

CT:1T0{XP1)J1TO<XP1J

SIJECTI VEU TO(XPl>•lTOCXPl )~54)

IS•E,.U TOCX PU • <XOUHX PU> S4r <1 OUT< XPl )>S) IS"E .. <lTOlXPl>•XOUTCXPl>P<lOUT<XPl>>SJ

- 5.67-

T178 --:: lESSISil·~·<X•XPl•SATZ16ACX~lJ) L E :SS l s- N- Ot • XP 1 J

Ga ·- LEFT \C x. :t? 1, X• Tl re, G fXPl• S• F)) tT:lTOC X>lCX H79 ·:= SATZ278(X,G(XP1.s,rJJ IS{SMP~tXPl.GCXPl•S•F>>•<<~OUT(~PlJ>GCXPl•5•F>~<SKPRCX,

GS>>Ol T180 ·-· THla·~.HN•(Xrl•T173J Is·~'"(l' L"N'"( l,XtclhlO '!'181 :: LESSIS!2'"N•CPL•N•(l•XMI>•X•T160J LESS ts• N•<Pl "N•(hXHl>•X> G9 . - LE~T<CX•X•PL•,•(loXMl),f16l.G8) : (T :1 Tot FL"N .. ( l .. XMl> JlCX Tl82 :: srv:~(CX~S~P~(~L~~~(l•X~l)~Gtl~

S~?R!X,GOJ.ISS~PR(X,Ga.PL•N•t1.XKl>• Tl30)} IS<SMP~ CX.G8),SKPR(Fl"ti'"Cl•XI11hG9))

Gl() . - RIGH!!CX•!•X~l~G9) tr:l TO{ XHU lCX T183 := LESSISil•G•ct.Pl'"H'"(l•XMll•

SATZ13.H l• '{H!) i : LESSIS•N•<t.PL•N•(t,XKlJl :;u :: LEFTC:l~?L·~·(l•X~ll•l,T183•G9l (T:lTO(l)lCX Tl84 :: SA!l2.:H<A• h >;Ml.G9l IS<SMP~ {Pt '"N"<l .. X Hl h G9h< SKPRC Xl'h G 10 )>< Sf'PIH 1• Gll )> 0) T185 := SATZ27HG:U IS($HP't U .. Gllh<XOUT(l >>Glll Tl8ó :: IS!~CJT~Il•l•LESSISIJ(1)) IS'"N"U riNN(l,XOUH 1)))

u == LEfTlTO(PL"N•ct.XKl)rl,T18J,XDUTC1J> : lT 0( PL• r-i"Ur XMU l f187 :: IS t:-:GLiT?lC PL"' ~ .. ( 1• IOH h UI!H 1• X!:! UT U)) r

TRLESStS•N•<I~N(l,XDUT(lJ),l• PL"~"{l•~~ll•lTO?(lrXOUT(l)),T183)J : IS .. N"CI ~iN U, XOUT(l) ), I NN(?t•Nw( 1• XH 1), 1U)

13 . - LErTli~[~r?t•N•(l,XM1),Tle:.1Al liOOO T188 . - ISINOUTMf,,:~N<PL~~4 (l•X~ll•l~),

TRLESStS•N•<!NNCPL•N•(t,XHlJ,lAl• PL•N•ct.X~l>•X•lTOPCPl"N•(t,XMl>•lA), Tl81)) : IS"N•U NN(Pl"N•( t..X 'll ".U), tNMU .. tBJ J

T189 :: TRJISCNAT•l•INN(l,XOUTCt>>• lUN!Pt•N•(l,XM1)•1A>riNN(X,18),Tl86• THI7 • r188) : I s""N•n .. INN< x.ts > >

te ::: LEFT!i0{XPl.X,Tl78.18J : 1T0( XPl ) T190 ·- ISOUT~!CXPl•l•SATZZ4ACXP1J,INNCX~1Bl•

TRLESSIS•N•CINNCX .. lB),X,XPl•lTOP<X•lB> .. T178), Tl89) : IS•[•(l TO<XP1J,JOUTCXP1J,lCJ

T191 ·- ISrClTO(XPl>•CX•GCXPl•S•t>•lOUTCXPll• 1C,T11?) !S(<10J HXP 1 J>G( XPt .. s, n,c XDUH 1 )>Gl U

Tl9Z ·- TRISZCCX,SMPR!l•Glll•<lOUTCXPll>GCXPl• s,F},<XOUT<l>>G11•T185,T191l IS<SKPt<l.G11),<10UT<XP1J>GCXP1,S•f))

T19l . - SYHIS<lTO(XPll•<XOUTCXPll>S4• <10UTCXP1>>S•Tl75) : rs•E•<t TO<XP1)•<10UT(XP1l>S•<XOUTCXP1)>S4)

T19ft :: ISfClTO<XP1J,cx,r,ctOUTCXP1J>S, <X~UT\XP1)>S~•T193) ISC<lOJT<XPll>GCXPl•S•FJ,.<XOUT<XPl)>GCXP1,S4•t)}

f195 ::: TRIS<CX,SMPR(l,GllJ,<lOUTCXPlJ>GCXPl• S•F),.<XOUTCXP1l>GCXPl•S4•F1,T192,T194) ISCSHP~<1•Gll)•<XOUT(XP1l>GCXP1,S4•f))

T19& ·- ISFCCX.GX,rT:CXl<SHPR<XMl•GlOJ><T>Q, SM?R<l.G11J,.<XOUT(XP1J>G(Xfl,S4,f},. ï195) ISt<SM>R(XKl•GlOJ><SMPR<l•Gll)>Q,<SHPR<XHl•GlO)>

<<XJUTlXP1J>G(XP1,S4,.f)>Q) rt 97 :: TR3IS<CX•SKPRCX•G8J,SHPR<PL~N-<1•XH1),

G9J,<SMPR<XM1,G10l><SHPRC1.Glll>Q, <SMPRCXKl•GlOJ><<XDUT(XPl>>GCXP1,S4•f> >Q,Tla2,T184.Tl9ól : IS<SMP~(X,G8J,<SMPR<XM1,GlG)><<XOUT<XPll>G<XPl•S4,f)>Q)

l'l98 :: ISr<CX•CX•CT:CXl<<XOUTCXPll>GtXPl•S•f) ><T>Q,S~?R(X,Gêl•<SMP~(XMl,G10J> <<XOUT<XPl>>GCXPi•S4,Fl>Q,!l97J IS(<<X,UT<XP1)>GCXP1,S,f)><SHPRCX,G8)>G•<<)0UT(XP1>>

G<XP l>•S •f )> «SHPRUKl• GlOJ >«XOUTC XP U >G( X F l• 54 • F) > Q> Q > T199 ·- -'SSQ 1{ A, <XOtl TUP l>>G <XP l• S4,F),

SHPRCXMl,G10l•<XDUTCXPlJ>GCXP1•S•f)) IS<<<XJUT(XP1l>GCXPl•S•fl><<SHPRCXKl•GlOJ><<XOUT<XP1)> G<XP 1 ~> 4,f) >Q>Ih <«XOUHXP 1 J>G( ltPb s,.r J><S~PR<XIH • G10 )> - 5.68-Q>«XOJ HXP l )>G( XPl ,54 ,.f)> QJ

TZOO :: COMQ(C,<XOUT<XP1J>GCXPI•S••FJ, <<XûUT(XPll>GCXP1,s~f}><S~PR<XMl,G10)> Q) : IS ( « <t; OUH l<Pl> >GCXPt. s.n ><SMPR~ XM t .G 10 l >C:><<XOUT CXP 1 l

GlZ = tErrccx.xPt-x.rtra,GcXPt~s• .. r>l G13 :: !.UT<C x, lt. PL .. t·l"'( 1• X!1ll • T16h~ 12 J G14 = RIGHTCCX•l•XMI•Gl3J G15 :: lEff{CX.~L·~·<t.XHl>•l•

LEss:sa "~:·c 1. ~>L "N .. { h XMl,. SA T Z 1 :L~ { 1 ,. ~~ 1 > l". G l 3 l'

rz:n . - SArZ273<X.G(XPl,S4,f))

TZOZ := SYMIS<c~.s~?~(?L~N"(1.~~i),G13>• SM~~!X.G!2lriSSKPRCX•G12•Pl"Nw(l•X~l}~

nao >l T203 :: SA~Z281C~•lrX~l•Gl3>

TZ04 ·- SHZ277CG15J T205 := ISFCl!OCXP1},CX•G<XP1•54•F>•10UTCXP1J•

te. r 190l TZ06 :: TRI !>2( CX •SMP RC h Gl5 J • <lC:JHXP 1 J>GUPl •

S~.FJ,<XD~Ttli>G15rT204,1205l T207 ::: CH~NGEFl(lTGC.Pl)•1TOCXP1J,S•lOUTCXP1J

rXOJi{X?l>•lO~T<XPl>•RS~:S{lTO(XPl>• lCJT!Y.?l l >)

T208 :: ISFClTD<XPll•CXrf,<lDUTCXPl)>S4• <XCUTCXP1>>S,T207)

Tj?09 ·- TP.ISCCX~SMP~Cl•G15l;<lOUT<XP1l>G<XP1~ S4~f ), <X OU i( XPl)>li(XPlJIS,.f ),. TZ06 .. iZG8)"

TZlO :: ISfCCX,CX,(T:CXl<SMPRCXMlrG14)><T>Q, SMPR<l•G15l•<XOUTCXP1>>G(XPl•S,f), T209 >

T211 == TR3ISCCX,SMPR(XrG1ZJ,SMPR(PlwN"(l,XM1J ;G13l,.<S~PR<X~l.Gl4)><SM?R(l,.Gl5J>Q,

<SMPR<X~l•Gl41><<XOUTCXPll>G<XP1•S•f>> o .. rzoz,rzoJ.TZlO>

tU:lfQCXMl>l UA :: RIGHT!T::J(l,Xfo!'lrU> US •- LEF'T1TO<X•Pl"ri"<l•XMU,.T181•UAJ UC ·- lEfT1TO{X?1rX•Tl78rUB) ti:Is•E•(tJO(XPl)rUC.XOUTCXPll)l TZ12 ·- IS::JUTf~E<XPl• INNCXrUBh

TRLESSIS•N•CJNN(X,UB>,X•XPl,lTOPCX,USl rT178>•XPl•LESSISI3CXP1l•I>

fZll := SATZ16A<IN~<XrUBhX•Xf'1•1TCP{X,.UB>• SHZ13A!Xrl})

TZH := <T212>EC3E31<IS"N•CINNCX.Uel.XP1 ), MORE•N"(INRIX•UBJrXP1>• lESS•N•<INNCX.USJ,XPl>• SATZ10B<INNCX.UBl,XPl),T213J

U ~ 1215 := CT:IS"E•(lTO(XPl)•UC•XOUT(XPl)}J T214(T)

ti:IS"E•ttTOCXPll•UC•lOUTCXPllll T21ó ·- ISCUTNEC<Ph INi'H x,ua ),

T217

TRLESSIS~N"( INN(X,UB>rX,XPl•lTGP<X•UB) , Tl76 h 1.o SAT Z24A UPl ), I)

:= ISINGUTNCX,IN~(PL•N•Cl•X~ll~UAJr TRLt SSIS"1: .. < INN( Pl"N .. { 1• X~l ), UA), PL •N"( 1• XMU .. X• 11'JPt Pt ·~·{ :, XMl > •UA) •

~titXPl•~~·~ J>Q•<<XUUi{XPlJ>ti{~Pl•~~•tJ><<<~UUI~XPlJ>

GCXPl.S,FJ><Sl'!PR(X~l .. Gli)}>Q>Q) . [ T: 1 TOf X) JC X n :1 TOC Pl"N"'( l.X .. lJ JJCX rT :1 TOt XKU JCX . .

(T:!TO( 11 JCX ISCSMP~CXP1,G<XP1,S4,f)),<<XOUTtXP1)>G(XPl•S4,fJ> <SMPRC(,G12)>Q)

ISCSHP~{X,G1Zl•S~PRCPL"N•Ct,XM1l,G13J)

IS <S MP~ tPL" N"(l, X!H ), G 13) • <SHPR<XMl,Cl t, )>< SMPRCl• G 15) > Q} IS(SMP~ C1.G15),cXOUTCll>G15>

ISC<10J HXP 1 >>G< X?1 ~s4 ~r h <XOUT (1 J>G 15)

: ISCSHP~<l~G15>~<1ûUTCXP1l>GCXPl•S4•f))

; IS•E•(l TOUP1 h <10UT<XPU> S4,<XOUH X!'U>S)

IS CS MPl U•G 15J, <XOU HXPU> G<XP l•S•f l)

t IS<<SM~RCXH1 .. G14)><S"PRC1,G15J>Q,<SMPR<X~l•Gl4)> <<XOUTCXPl)>G(XPl,S;f)>Q>

: lTOCPL•H•(t,XMlJ) 1T:JCX>

; lTO( XPl)

CON

KOT(IS•E•<tTOCXP1J,uC,XGUf(XP1lll

Tl81)} . : IS·~·<tNNCPl .. ~"(l,xt'H,.UA),INN(X,.UB>) TZ16 :: ISINOUTNCPL"N"(l,XMl>,

PL~N"CljlNN<X~l.U)},S,TZ190CINNCI~l.Ul ;XM! •l•l Ttlr< >::'l• U))) IS"'N•P l .. N'"C !Jo t Nt~(lOil• UJ ). INl'H Pl•tl .. { h X Hl) •UA))

- 5.69-

•8283

tS28.4

SOT2 ~ TZ36

NOil a TZ39

............ , .... .., -. """'"""'""~ .... ~,., .... ."~..., .... , ........ >•PRCPltXPl•S•flr[T:IS•[P(lTDCXPl>•&Cr XOUT(XP1JilT236CTJ, [J:NOTCJS•[•(lJO[XPl>•BO•XOUTCXPl)JJl Tl48{T))

:: THlpL.:~p•(IS~E*(lTOCX~l)•AO.~OUTCXPl) Jr?RD?~CXPl•S•flr(T:Iswr•<1TO<X?1lrAO; XDUTCX?1JJJT237{TJ, tT:~CTE~S~Ew{lTO<XPlJ•AO•XOUT{XPlJ))] Tl2Z<Tl>

:= THl"L.ZH?*(!SP(•!tTO<XPl>•<lQUT<X?l)> SrlOVT(X?lJl.PRJPl(XPl•S•f), [J:!s~E"(liû{X?!Jr<lCUï<X?l>>S•

lOUiCXPll)JT97(FJ,~T:NOT~IS•E•(1TO

<XPll•<lGUT<Y.?ll>S•lDJT!XP1J}lJi238CT>

PROPH( Pl.Srr>

> : PROPl((PlrS•f> B a T240 := TH!•t.!MP•(IS•[•(l!O(IPl),<XOUTiXPlJ>

S•XOUT<X?l)),Prt0Pl(XP1.S•r>, (T:Is•E•t1iC(XPll,<XCUTCX?l)>S~

XOJHXPl) > H 45( ih ( T: N:JH IS .. E'"Cl TO CXPlJ,<XOUT(XPlJ>S,KCUT{XPl))JJT239CT> l PRCP lU PloS,.FJ

P a TZU ·- [U:[T:1T~{X?llllT0(XPl>JCV:[T:1TO<XP1> lCXl[W:BIJECTIVECl!~[XPll,lTO<XPl>•U>J T240 ru,v,IO : PROP2(( PU

TZ42 := IS~{NAT,.[T:NATJPRCP2CT>•XP1•<X>SUC" T241.SATZ4ACX)) PR0?2(<X>SUC)

X a TZ43 := INOUCTION<CT:NATJPROPZCTJ,f6,{TtNATl (U:PROP2HJlT24Z<T•UhiO : PROP2U)

SATZZ53 :: <F><S>TZ43 ... 8283• a tX:REALltiX:INTRl(XJJ[Y:REAll[IY:INTRL<Y)J[LY:LESSIS(Y,Xll

S~IFTL := SHIFTL"R~<x .. tx,y,Jy,LYJ t~:HtHSHIF'TU l S~IFTR :: SHifTR'"R•<x.rx,.Y,IY,LY,.Nl INTS~IfTR ·- I~TS~IFTR•Rw<x .. IX•Y•IY .. LY .. Nl SHIFTRLS ·- SHIFTRts·~-(X,.IX,.y,zy,LY,.N)

LSS~IFT~ ·- lSSHiffR•R•(X•IX•Y•IY•LY•N> [H:1TO{SHifTLlJtt:IS•R•<SHifTRCNJ,.SHIFTRCHl>l ISESHifTR := ISEShlfTR•R•tX.IX•Y,.IY,LY~N•K,.!)

tY a ru:REAlliA:AN03(INTRL<ul.LEssrscr,.ulPLEssxscu.x>>J S~IFfLl :: SHIFTtl•R•cx,Ix,.y,IY•LY•UrA> SHiffiNYl := SHlfTlNVlwR•<Xrl~•YriY,L),.U,A1 SHlfTISY2 :: SHIFTINV2·R~<x.IXrY,IYrlYrUrAl

LY ~ tF:SEO<X•Ix,.y,zy,LYrCX>1 SHifTf := SHIFTF{X,IXrYriYrLY.CXrf) (Q:tr:CXJ[U:CXJCXl SHPRI :: SMPR(Q,SHIFTlrSHIFTfl

F ; EPI:,ROOFSIRRELEVANTfXriX•Y•IY•LYrCX.FJJ[Q:[T:CXJtU:CXlCX l tA:AS S OC< Q) HU: RE Al H IU: I NT RUU) J (l :LESSI Str riJ> H K :L[SS CU • U ltV:REALlttV:INTRL(V)J(LV:LESS!S<Y•VJlCKV:LESSIS<V~Ull

Tl

K 3 LF'T ·- [T:RtAlJ(VtiNTRt(T)J[LT:t~SSISCYrT)l (KT:lESSIS<TrU)l<Tl".B284•cT,.VrLT•KT)>

: NAT

REAL INTRUiHtfTR)

: LESSISt SHIFTR,.XJ lESS ISC Y, SH IfTR)

: lTOC SHIfT U : IS•R•(J;SHiflRCSHitTL111 : IS"R*<S HIFIRCSHIHLlJ..U)

[J:lTOt SHIFTt11CX

ex

LESS ISC V,. U

.s

s

-5.71-s

H82!14

-828!t

<LT><w><l>~

IV ; [LV:LESSISCPL•R•(UrlRL>•V)j(~V:LESSISCVrX}J

f'L MN

x a Pl KV ·- ~~,..R·cx,v>

·- Pl~?.•('(,lRli

·- SATZ110C(UrUrOr1RL• LESSISI2CUrUrREriSCRE'L•U>>• lEM~Al·~·{lRL•O•SATZ169ACl~L•

NATP~S!IRL.NATRLl)J))

:: ISLE551[PLCUrOJrUrPl{UJ• Pl02~~~(Ur0rREF!S\REAL.0)),T2>

·- lESSIS!l(Y.VrSATZ172BCYrPltUlrY• SATZl72A<YrU•Pl<Ulrlrf3lrLV))

·- [T:~EALlCV:INTRL<T>J [LT:LESS!StPL"R"C~•lFL>•T>J [Ki:LESSIS~T.X>J<KT><T4•.aza4•(T,VrLTr

KT>><V><T>F

·- INTPLCUriUrlRlriNTRll> := SATZR2Scu.ru.x.rx.K> :: TR3ISCREAL•Pl<H~CP1(U),y),MN(Pl(X)•

PlCU)}},Pl(MNCPlCX>•PlCU)J,~N(PlrYJ

),MNCPL<~~(Pl{X),PlCU>>•PlCU}},y),

M~CPl{X),y),COMPL•R"CMMCPlCU),y),

MNCPl{XJ,Pl>>•ASSPLZ"R"CHNCPl(X), PlCUJl.Pl(Ul.MO"R~{y)),

ISM~l~R·tPL<H~CPlCXloPlJ.PlCU>>~

PlCXJ.ToPlMNCPl<X>•PlCU)))J == ·-·-·-

·-·-·-·-·-:=

SHIFTL<K~IXrY~IYrLY> SHIFTLCU.IU~Y~IYrL> SH!Fïl<X.IX,Pl{UlrTS,T&> TR4ISCREAlrRLOFNTCPL~N·<SUYrSXU)Jr

PlCRLOFNTCSUYJ,RLQfNT<SXU>>• PLCXN(PltU>•Y>rHNCPl(X)oPlCU))), f!!;(PHXl.YloRLDFNT<SXY>o SATZP.l55ACSUYrSXU>• ISPltZ•R•CRLOFNTCSUYJ~~NCP1rYJ•

RLGFNTCSXUloMNlPl<X>•Pl>• ISRLNT2CKH<Pl(U),YJ, T&•R.SHiff«(Ur!UoYoiY•L>>• ISRLNT 2< M1H? 1: X}, PH Ul > • r&·R.sHrrr·cx~rx.Pl.rs.T&>>>•T7• ISRLNTlCHN<PlCX},y), TG•R.SHIFT•cx.IX•Y•IY•LY))) ISNTIRLCPL~N·CSUY~SXUJrSXY.T8)

LESSiSI2"N"CPL·~·tSUY~SXUl.SXYrT9) lEFTCCXoSXYrPL"N"<SUYrSXU>.TlO .. SHIFTFCXriX•Y•IY.LY~F>J ISS~Prt(Q,SXY•SHIFTFCX•IXoYoiY•LYrf>• Fl "N .. { SUY• SXU J, T 9) RIGHT{CXoSUYrSXCofl) LESSISI1 1 ~·csUYoPL•N•<SUYrS(U),

: l I :tH. A. Jl 'I: l NI KI. { f J JL 1.. I : l.:. :i :i l :3\ T • I J J ll\ I :Lt.;:;, i;,\ I • U J J!; 1.

REAL R~AL REAL

lESS<P. <u~o J.Pl>

LESS ISC y,y)

(T:!tEA:... ](V: INTRUT> ][L T:L:: SSIS<PL•R•(UrlRL ),T)J

!KT :lES SIS<T • U lCX

INTRL<" lC!Jl) LESS IS( Pl(U hU

IS"~·c~L(MN<Pl<UJoYlrMNCP1CX>•Pl(U)))r~NCP1CXl~Yl}

NAT NAT NAT

IS"R•(~lOFNT<PL•N"(SUYoSXJJ),RLOFNT<SXY)) IS•'f .. P l"~'"( SUY, SXU >. SXY J LESS I s• N"CP l"N" {SUY rSX U>.S XY>

IS(SMP~(Q,PL•N•tSUYrSXUJrFl)rS~PRI<X.IX,YriY,lY~f,Q))

[T:lTOCSXU>lCX

s

s

s

- 5. 72-

SATZ13ACSUY.SXU>> LESSIS•N•(SUYrPt•N•(SUY.SXU)) F'L :: LEfrccx.PL·N·csur.sxu>.sur.rtr.rl> [T:lT:]( SUY> lCX Tl ZA ·- SATZ23ltO•A•S~Y.SXUrf1) IS C:> ~P~ (Q ,p L •N•( SUY rSXUh;:- lJ • <St'PR( Q • S XU• F'fD>< SKPR{ Q,

SIJY• F"U >0) Oi:lTO<SXU ll T13 == !S !N::JUT~'H PL • N• ( SUY,. SXUl •

PL~~·CSUY.[NN(S~U.N))•

S~TZ19DCIN,CSX~.~1.SXU•SUYrlTOP(SIU•,) )} IS·~•<>t•~·<SUY.INN<SXU.NJ>•INN(Pt•N•<SUY,SXU),

R!G"!Tlf O<SUY•SXIJ•N))} 114 :: IS!,DUTNf5XY.INNtPL•••(SUYrSXU),

P.IGH'1TO<SUY;SxJ,~>>• TRlCSSIS~M•CINNC?L"N"(SUY.SXUl•

RIG~TlTG<SUYrSX~rU)J,~L·N•csur,sXU),

SXt,lTCPC?t·~·tSUY.SXUJ• RIGHTlTOCS~r.sxu.Nl>•TlO)J : ts•H•(INNtPt·~·csUY•SXUJ•qiGHTlTO(SUY,SXUrhJ),

INNtSXYrLEFT1TO<SXY,PL•N«(SUY•SIU)•T10r RIGHTH J<SUYrSXU,Nl »>

Nl :: LEfilTOCSXYrfl"Nw{SUY.SXUlrTlOr RIGHTliO<SUY>SXU.~}l 1TOC SXY l

H5 :::: TRISCNAT•Pt·~·csuT,!N~(SXUrNllr ~~~tPL•H•(SU!rSX~i.~IGHT1'0(SUYrSXU,N)

l•[NN(SXY•Nll•Tll•Tl4) IS"N•C»L"N•(SUYriNNCSXU•N>>•INNCSXY•Nl)) Tló == ISNTEP.L{rL•N•(SUYriNN(SXU,N)),

I ~Nt SXY • Nl >• TlS> Isw~·(~LOFNTCPt•N•(SUT.INN<SXU.N)J),RlêFNTCINNCSXY.Nl>> )

T17 := SATZR15SSCSUY·I~K(SXU•N>> : IS•R•<,tCRLOFNT(SUY>•RlOFNTCINN<SXU•N>>>• RLOFNTCPL-N•CSUY,IN~(SXU,N))))

T18 := ISPLl•R•(HN(PlCU>•Y>rRLOFNTCSUYJ, RLOfNT<INNCSXU,NJ),ISRLMTl<MNCPl(U)rY) .r&·R.SHirT•<U•IU•Y•!Y•L)}) IS~•(,L(KNCPl•YlrRLOf~T(INNCSXUrN)))rPL<RLOFNTCSUY>

, P.LOFNT UNN CSXU, N J)))

T19 := TRl!StREAL•PL(H~<Pl(UJrY), RLOFNTtiNS<SXU.NJ)),PLCRLGFNTCSUYlr RL~FNTCIN~CSXU,NJJ),

RLJFNTtPl~N•(SUYriNNCSXUrNJJ)r

RLOFNTCINN<SXY•Nl>>•Tla•Tl7•T16l : IS·~·(,l(KNCPltUJ•Yl•RLOFNTCINN<SXU•Nl)J, RU:lFNT[ INNCSXYrN1Hl

rzo == ISPLt•R•(PLCMNCPl(U),y), RlOFNT!INN<SXU.N))),RLOFNTCINN(SXYrNlJ hhT19) ts·~•t>t(Pl(~NCPl(UJ•YJ•RLOFNTtiNN(SXUrN)))•Ylr

PL<RLOFNT(INNtSXY,NlJJrYJ) TU ·- TR3IS<REAl•PltPLCHNCP1{U},y),

RLOFNHINN<SXUrll}) h Y>. PltPL<RLOFNTt[NNCS~U.~)J,MNCPl(UJrYJ), YJ.PlCRLOfNTliNN(SXUrNJJ,PL(HNtPlCUJr YJrYJJrPLCRLOFNTCIN~(SXU.NJJ.PlCU)J, ISPLl•R•(PLCMN(PllUJ,YJ, RLOFNT<IN~CSXUrNJ>l• PlCRLCFNTCINNCSXU,NJ>•MN(Pl<UlrYJlrY• COMPL•Rw(HGCP1CUJ,y),RLJFNT<INN<SX~,N)

J)),ASSPLl"R•\Rl~FNT<INNCSXU,N>>• MNCPlCU),y},y).ISPL2·~·tPltMN(Pl•Y)

,y),PltU),RLDFNT<lNN<S~U.N))•

PUmtP1.Y>D IS•R•<:.UPU M~H P HU J. Y hRL OF NT< INNC SXU.NJ) l• Yh PL<RLO!'"NT<IN!'HSXU.NH.Pl(} )))

TZZ := TRISlCREAL•PL(RLOFNT<IN~CSXY•N!)),y), Pl<RlOFNT(INN<SXU.~)),PlCUJ), - 5. 73-PLtPL<HH(PlCU),y},RL3f~T<IKN(SXUrNJ)), YhTZG.TZlJ . IS"~·<~L(RLOFNT(INNCSXY.Nl)JrYJrPL<RLQFNTC!NN(SXUrN)J,

PlWlH T23 :: ISMNl"R"CPLCRLOFNTCINNtSXY.Nl)),Y).

TZ4 TZ5 T2ó TZT T26 T2? T30

T31

!( a T32

K :1

T33

T34

(lH 1 TfJ( S:JY)] Tl5

T36

HZ

UT

T38 T39

HO

Hl T42 T43 H4 Tft'5 !46 TH T48

TH

TSO

:: INTSHIFTRCX.IX,Y,IYrlYrNll :: lSSHIFT!~~·IX•Y,IYrLT.Nl) := SH!fT~LSlX.IX~~·IY·L~•~lJ :: I~TS~IfTRC~,;~,~~tJl•rSPTG.N) :: tSSH!~TR(X,rX.?l{Ul,ïS,75•~> :: SHIFT?~5{X~IX.Pl(~lrTS,T6~NJ :: T4(SHlFTRCX•IX•?l<Ul.T5•Tó•N>rT27•T28•

T29) := <T23><T29><T30><T27><SHIFTRCXriX,Pl!V>

,rs.T&,N~><T25><T25><T24><SHifTR(X,IX•

: lSwRw(SHlFTR(XriXrYrlYrLT,NlJrSHlfTRlXrlXrfl(UJ•i5rT6r N)) I'iHL(S HIFTRC x, I x, Y, IY •lY• NU) LESSISt Y.SHIFTR<X•IX•Y•IY•LY•Nl)) LESSISt SHIFTR<X•lXrYriY•L1" •NlJ~XJ VI HL G H>:H R o;, IX, P HU), T5, TG, tO > LESSISCPtrJ>•S~IFTP.<X•IX•,l(~),fS•TórN)) lESSIS!SHifT?.(X,IX,PlCUlrTSrTórN),X)

Y,IY.LY•Hll>?I ISC<N>FR,<N>SHIFTF<X~IX,PlCUJ,T5rT6,RGT)J

:= FtS~ClTG(SX~l.CX•FR•S,!FTfCXrtX,Pl(U), TS.T&.~~Tl •• T:lTO<SXU}jT3l(TJ) IS•E-CCT:lTOCSXUJJCX,fRrSHIFTF<XriX,Fl(U)rTS~T6rRGT)J

:: IS~C[T:lTJCSXUJlCX.cX,(V:CT:1TOCSXU)l CXlS~?~(~•SXU•VJ,FR•SHifTf!XriX~PlCUJr TS.T6,?.5Tl.TJ2l : ISCSMP~(Q,SXUrfP.JrS~PRICX,IX.Pl(UJrT5,T6,RGT,~JJ

:= ISr(CX.CX•<SH?R(Q,SUY•fl)>O• S~PR(Q,SXU,F~lrSMPRI<XriX,Pl<UJ,TS,T6r

:= ISINOUTNCPL•N•CSUY.SXUlriNNCSUYrNJr TRLESSIS•N•<IN~(SUTrNl.$UY• PL~N•tSUY•SXUJ.lTOPCSUY,N>oT12J)

:= ISINOUTNCSXYriNNCPL•N•<SUYoSXUJr tEFTlTOC?l•N~CSUY•SXUl•SUY·T12•N>>• TRLESSIS•N~CINNCPL•N•csur,SXU>o LEfTlTOCPL"N•<SUY~SXUl.SUYrTl2•N))r PL•N•(SUYrSXU>rSXYrlTCPCPL"N•<SUYrSXU) •LEfTlTO<PL•N•(SUYrSXUJrSUY~T12rNl)• 110))

:: LEfTlTC<SXYrPL"N"{SUY•SXUJrTlOr LEfT1TO<PL•N•<SUY•SXUJrSUY~Tt2•Nl)

:s TRIS<NATriNNtSUY.~lriNN<?L•N•tSUYrSXU) •LEFTlTOCPl"N•lSUYrSXU>,SUYrT12rNllr INN< SXYr NZ }, T35r T36)

:: !SNTERL<IS~CSUY•Nlri~N<SXYrNZJrT37> := ISfll.R"tRLO'~TCINN(SUYrNllr

P.LQfNr<INN{SXY•N2J)rYrT38J

:= ISMNt·~·(PL(RtGFNT<IN~(SUYrNJJrYJ~ PlCRLOfNT<INN(SXYrNZl)rYlrlRLrT39)

:: !~TSHifTRCUriUrYriY•l•Nl :: lSSHIFTR(U,IUrY;IY•L•Nl := SHifTRLS<UriUrYriY•l•KJ ·- Tl(SHlfTRCUrlU•Y•IYrl•N)rT41rT42rT43) := INTSHIFTRCXrlXrY,IYrlYrN2J ·- LSSHIFTR(XriX•Y•lY•LY~N2) ·- SHIFTRLSCXriX.Y,IYrlY;N2> :: <T40><T47><T4S><T45><SHIFTR(X,IXrYriYr

LY•N2)><T44><T42><T41><SHIFTR<UriUrY; !T,L,N>>PI

:: SY~IS,CKr<N>SHifTffUrlU•r•IY•l•Lff), <~>FL,.T48)

·- FISI<lrG<SUYJ~CX,FLr SHIFif{UriU•YriY•L,tfT),[f:tTOCSUY)J f49( T))

ISC<SM~R(Q,SXU,FR)><SMPR<l•SUY,Fl)>Q,cS~PRI<X•IX~Pl(U), rs.r& .~ GT .o >><Sl'?Rc o.sur.i"U>o>

IS"'N •<I NN<S UY, Nh IN M Pl .. N• C SUY, SXUJ. lEFT1TJ(Pl"N•<SUYrSXUJrSUf•T12•N)J)

IS-N•<INNtPL•N•CSUYrSXUlrlEfT1TOCPl•~·<SUYrSXUJrSUYr Tl2;N)J,INN<SXYrlEFT1TO<SKY•PL•N•tsUY,SXU)•TlOo lEfT 1Tl (pt•N•( SUY ,sXUl .SU'I', TlZ • N))))

: !Hl( SX'I'}

: IS•N•<INNCSUY,NJriN~<SXYrN2))

IS•R•(~LOfNT<INNCSUY•NllrRLOfNTCINNCSXY•N2J)J

: IS•R•(SL(RLOFNTCIN~CSUY,N} lrY),PltRLCFNTCI~NCSXYoN2JJ, \'})

: IS"R•cs HIFTRCU, tu,y, IY •LoN J,SHIFTRC x.u.y,. JY,.\.Y, NZ)) INTRLC$HifTR{U,!UrYoiYjt•1))

: tESSISCYrSHifTR<UrlUoY,JY,L,NJ) LESS I SC SHif TR( U, IU • y, IY ,L, tl>. 0) LESSISC SH!fiiHU•lU•Y•IY•L• NhXJ liH~l(S HJFTIH Xo IX• Y • IY rlY• NU) LESSISt Y • SH IH!H x, rx, Y • IV. LY• NZH LESSIS{ SHifTRCX.IX.T,IY•LYrNZJ•X)

IS"'E,. ([ T: l Hl< SUY) lC x, fl• SKI fT F( U • IU,. 'f.• lY ol•lfH)

- 5. 74-

•628i

-8285

T52

T53

K .; suzzsr.

•= 1~r,tl•4lU\~VliJ~AP~AP~,.,, •• ,U,~Ull~

C.XJS '!PR( 'h S!.l y, VhfL• SHIFTF~v.::.Jd'riY•l•lfT1rT5Q) .

:= ISF<CXoCX,[TICXl<S~PRI<XoiXrP1(UloT5• TirRGT,Q)><T>QrS~PR(U,SUT,FLJ• S~PRI(UriUrYr!Y•L•LfToGlrTSll

:= TRliSCCXrS~?~{g,pL•N•CSUTrSXU)of'l)• <S~PR~Q,SXUrFRl><SNPR(Q,SUToF~l>Q,

<S"PR[(XriKo?llUJoJS,T&•RGTrQ)> <SKPRCQ.SUYrFLJ>Do<SMPRllKriXoPl(U)r TS.T6rRGir~,,<S~PRICUriU•Y•!TrL•lfTrQ) >~• T 12A, !3~-, TSZJ

I~TPLC~.IUrl~~.INTqlllr

SAfZR25<U•IC•X•rX•K>·?.~T,Ql><SMPRI<U• I U, \'" ! Y, L, LF T, Q ) > Q, S~?RCQ•?L"N•tSUY"•82S4•,sxu•.ez64"lr

rt•.aze4•>•Tll~.eza4*•T53•.sza4•>

Q ~ [V:REALltiV:INTRt(V)l[W:REALlCIW:INTRL<W> }(LV:LESSISCPL"R•(y,y),W)J[KW:LE~SISCWrPL"R"(I,V))]

x a [Y:REALl ?L == Pt·R-cx.n MN := MN•R•( Xr Y>

x ; ?1 :: PL,.R"<XrlRU KW a Tl :: TH9«L.~R*<lESS(PL<Y.VlrWlr

IS"R"(PLCY•V),Wl•LESSCM~{PLCY•V>•V>r HNCWrV)JriS"a•CMNCPL(Y,V),y),~N(W,V)),

tW.tT:LESS<PL<YrVlrW))SATZlö8F(Pt<Y•V> ,w,HO•R•(V)rTt,[T:IS"R~<PL<Y.V),W)l.

ISMNl*R•<PL<Y•V),W,V,J>> TZ ·- ISlESSISlCMN<?LCYrV),V).YrM~(W,v),

MNPU Y • V l r Tl J Tl == TH9"L. OR.,.( LE SS <li ~ PU '1" V> h

iS"R•(~oFLCX,Vll•LESSCMN(~•Vlo HN{Pl(X,VJrVllriS~R"(MN(W,Vlr HNtPLCXrVlrV})rKW.CT:tESS(WoPLCXrVJJ] SATZ18à~(W,?l{XrV)rMO•R•(y),fJr [T:IS•R•(WrPL<X~VJJliSM~!-R"(W,PlCX•V)

.. v.T>J T4 ::: ISlESSISZ(HN{Pl{XrV>rY)oXrM~(KrVlr

HNPU Xr V h T3)

IV asrr :: [ T: REAL1 [ W :i NTP.L CT}.] ttT:lESSIS<?L•8•(y,v),T)J[KT:tESSIS(T, Pl"R"(X,V)lJ<T4".82BS•(T,~.LTrKT)>

crz•.B26S•<T,W,LTrKTI><INTMNCT,W,VriV) ><MN"R,.(TrVl>f

ISC<SM,RI(XoiirP1CU)rT5•TSrRGTr0)><S~PR[Q,SUYrFL)>Qr <S'I?!! IC Xr IX ,.pl(U hT Sr T 5r·IU T, QJ><SM?R t< Lr IU • y, IY •l•Lf'T, Q)>Q) .

IS(SMP~(Q,Pl*~w(SUYrSXUJ,~l)r<S~PRl(X,IXrPl(UJrT5rT6r RGT, Q }l> <SMPRI<!Jr IU, Y,Y YrLolrT r Q) >Q}

ISCSMPli<X•lX•YriYrLYoF"Q),<SMPRI(XriXoFL•"•cu,lRLl• INTPL(J,IU"lRLriNTRllJ,SATZR25<U,ru,x,IXrKlrRGT,QJ> <SMPRU U•IU•Y•.IY•L•trT,Q)>Q)

REAL P.EAL REAL

LESSIS( MN!PltY•VhVJrHNCW~ Y))

LESS ISC Y rK!HihV) J

LESS ISl MNOir Vh KN<Pl(X rV h V))

LESS IS[ .KNOf rV J.X J

n :1EAI. H lU INT RU Tl lelT: LESSISt PL "'R .. ('h V>, T)] [KT ;L E'i S IS<T .. ?L •R .. U,.V)) 1: X

s

s

s

- s. 75-

tv ~· r;

T5

T7

ra

so SV

T9

T10 n

Tll

[N:lfQ(SVJl T1Z

Nl f13 Tl4

STO STV

T15

:: TR!StREAL,MO•R•(PL{Y,V)),HO•R•(pl(V,Y) lrFL C ~~""l" {V .)d10 ,.R,.( "'')),. . . ISM0·2~CPL(Y,VJ,PLCV,YJ,.CO~PL•R•CY~V)) #SATZ130tv•Y I)

:• TRJiSt~EAL·H~tPL<lRL,PL(X,.VJJ,.VF• PLC1~l•~hi?L<X•V>•Vll.PLC1RL .. X>•P1CX>• ISSPLl•q•clRL.Pl{X,VJ,~D·R·<V)),

iS~Lz•RP(~~{PLCX•VJ.Vl•X•lRL•"NPLCX•V> ),.CC~~L"R"{IRL,.Xll

·- TR3ISC~E~L·M~(Pl(PL{X•VJ),pl{Y,VJJ,. ?ltPLC!Rl~PLCX.YJ),PL(HD•R•[V),

~D·R•CY~IJ•MN{MNC 0 L{IRL•PLCX.Vl)•~),.y) ,KNCP1,X>•Y),!SPL12-R~CP1(Pl<X.V))•

PLC!~L•'l(X•VJl.MO~R.(Pl(Y•V>J• PLO!O•rt" (V,,. MO,.R .. { ':' > h C OMPL "fl"(PU X•.V) •lRll.TS),~SSPl2"R•tPL(lqL,PL(X,V>>• MD•R•[v>.RO~R·<Y>J• !S~Nl•p•(~NtPLClRL•PL<X•V>J•VJ•Pltll• Y,. TS n

:: TH9"L.c~·CLESS(Y,.Xl•IS•~~{y,x),. LESSCPL(Y,V),PL(X,V)),IS•R"tPL(Y,VJ, Pl<X•Yl)•LY•tT:LESS<Y•X>JS4TZ186f(Y•X• V.TJ,[T:Is•R•(y,XlJISPLl"R"(Y,X,V,T))

:: SHifTL<X•IX•Y•IY•LY) :: SHIFTLCPL<X•VJ,INT?LCX,IX,.V,IV),.

PltY•Y>•INTPlCY•lY•V•IV>•f8) := ISRLE~TC~~(Pl<PL<X.VJJ.Pl<Y,VJ),

T&•R.SHifT•CPL<X•Vl.INTPLCX•IX•V•IY>• Pl(Y,.1),INTPLCY,IT,V.IV),T8>.MN(P1(X}~ YJ.T6·R.s~rrr•cx.rx .. v .. IY•LY>•T7)

:= lESSISt2~N·tsv,sO,r9J :: lErT<CX•SO•SV .. TlO•SH!fTFCX•IX•Y•lY•LY•

f))

:= ISSKPR(C,SO•SHIFTF<X•lX•Y•IY•LY,fl•SV, f9)

·- IS!NOUTN<SO•INN<SV.NJ• TRLESSIS"N•<INNCSV,NJ.SV,sO,!TOP(SV,.N> ,. TlO l)

:: LEFT!TOtSO~sv~TlO.NJ :: IS~TERLCIUNCSV•N>•INN<SO.Ntl .. T12J :: TRISIREAl•HN<PLCRLOFNT<iNNCSV~N)J,

PL(T,VJJ,VJ,.pl{RLDFNT<INN<SV,N)J, IHH Plt T, VhV) J,PU RLOFNH INNtSOr Nl}) ~ Y)oASSPtt•R•<RLOFNT<INN'S~rNJJrPLCY~V> ~Ho•R8 {VJJriSPL12•R•t?.LOFNT<INNCSVrNl) ,RLClfNH HHH SOr~H J h H.NtPL <'r, V J ,y h Y • TB .. :.~N?L<Y•Vl})

~= SHIFTRCX•IX•Y,.IYrlYrNlJ :: SHIFTRCPLCXiVJ,INTPLCXrlXrVriVJ,.

PLCYr~J.INTPL(Y,IY•V•IVlrT6rN) :: TR4IStREALrHNCSTV.VJo

PLCPLCRLOFNTCINNCSV•N)J,PLCY•V}), PLCHv•R~{l~l),~OwR•<VI));

Pl(PL<RLDfNT<INNCSV•N>>•PLCY•Vl)r Pl<MO•R•tV)rHO~R•<lRlJJ),

MN(~NCPLCRLOFNTCINNCSV•N>>•PL(YrV)>•V> ,1Rtl·STO,ASSPL1•R•trt!RLJFNT(INN

ts•;p•(lfNCPU lRLrPLCXrV )),.1 >..PHXJ)

LESSlStPLCYrYJrPl(X,.Vl) NAT

NAT

: IS•N•CiY,SOJ u:ssxs• N'"ts v~so J

[T:lTOC SV>JC1C

: IS'"N•ttNNCSV,N),.INN(SO,.lEFTlTOtSO,.SVrTlO,Nll) 1TOCSOJ

: IS·~·(~LOFNTCINN<SV.N)l~RLOFNTCINNCS0,~1J))

IS"'R•t-1 N{PlCRLOrNT< INNCSV• N) hPL<Y • V)), Y) • Fl !RLOF NTC I NN( SO ,.Nl) h YJ) REAL

: REAL

s

- 5. 76-

+8286

-6263

Tl& T17 T16 Tl9

T20

T21

T22 T23 T24 T25

IV ; T2&

TZT

IV a lE1'111A285 SATZ285

\~Y;Nilt~L,TrY:Ir~v-~-ll~~1;Mv-K-tV11~

ISPLZ~R•(Pl{uc~~~<lRl)•~O~R~!Vil•

PL(KQ"R•(Y).~O~~·tlRlll•

PL,~LQFNT([~~:sv.~J),Plt!oV)), C C'-'?t~R .. f" ::-R~ t1 1l }, r-o~R•{V))), ISSPLZ·~-~~Lt~L~F~T~:~,{SV.~)),PLCY•V>

lo~O·?·t~)rHQ-R•(lRL)),

IS~~~"P"(H\CPL!2L2r~T<I~•<sV.~)), PLt~·VJ2,VJrPLCPLD~NT<I~NCSOrMl))~Ylr

·- I~TsH;Fr~tX,IX~Y,IY,LY,~l) := SKIFT~LSCX•IX,Y,IY,LY,N1l •- lS~~!:rTR(X,IX~Y,IY,LY·~!l

·- !~I~ri~FTR[PL~X.YJ#I~TPL~X,IX~V,IVJ. FLlYrV)ri~TPLCYrlT•~•IVJr~3•NJ

:: SHIFTP.LStPl[X,1lriSTPLtX.IXrVriVlr PLCYrV)rl~iPL(Y,IY•VrlVJ.T8rN)

:= tSSHIFJ?.(?L{X,V},I~TPLCXriX.VrlVJr PLCY;V)r!1TPL<Y•IYrV•IVlrT3•Nl

.- INT~N[STYrTl9rV,[V)

·- T2{ST1,TtYrT21•T20l := T4C5TV.T!9,721?T20) ·- <Tl5><Tlr><Tl6><T15><STO><TZ~><T23>

<T22><~N<STVrV}>PI

:= fiSIC1TCCSVJ,cX,SHIFTf<PlCX•V>• INTPlCXriX,V,IV)rPL<Y,VJ, lNT?L{Y,IY•V•IVJrTS,SfT),fl;[f:lTO<SV> JT25{T))

:= ISFC(T:1TO<SV>JCX,cX,{W:(T:lTO<SV>lCXl SHPR{Q•SV•W>•SHifTFCPLCXrV}, INTPLCX,IX•V,IVJ•Pl{Y,V), INT?LCYoiY,VriVJ,T8,SFTJ,Fl,T26)

-- rs·.azss• :: TRISCCX.SKPRI<PL·~~(X•V>•

INTPL<X,IX•V•IV>;PL•R•(Y,VJ, INTPL<YoiY•VriV>•L~~MA28S.SFT,Q), S~?Rco.sv~.azss•,fl•.sz3sa>• SM?R!CX•It.•Y•IY•LY•f•Q),T27".8285"• Tll".~265•)

LY ; [S:SEQCXrlX•~•IY•LY•REAl)J[INS:INSEO<X•IX•Y•IY•LY•S1 J(f:S(Q{XoiX.Y.IY,tY,CXl1[U:R~All[IU:;~TRL<U)J(lU:LESSISCYiUl ltUL:LESSiS(U.XJ1

I s•R•(!f N<STY•V> • STO > I~TRUS TO) LESSISt STO•X> lESSISt Y •ST 01

: INTRUiTVJ

lESSIS! STV•PUX.V))

lESSIS[PL(Y,VJ,STV) INTRU"f N( Si V ,y)) lESSIS[ Y•WHSTtr\')) lESSISt H!HSH,.Vh•X>

IS<<N>S HIF'T Fl Pl( x.v >.I t\TPL ex. IX• V •IV h l'lCY ,y h INTPl<friY•V•IV>,T6.SFTJ,<N>Fl)

IS•E•C[T:lTO(SVJlCXrSHIFTF{Pl(X,VJri~TFLCXriX.VrlV)r FL(Y,V>•INTPLCY•IY•V•IVl•T6rSFTJrf1J

: lS(SMP~I<PL<X,vJ,INTPL(X,IX.V,IVJ.PL<Y,V),

INTPL<Y•lY•Y•IVJ•Ta•SFTrQ),S~PR(Q,SVrFl))

IS CS !1Pl I<Pl .. R'"< X,V), INTPLC XrlX• y, IV h Pl"R,. ( y, V h INTPL<T•IY•V•IV1•lEMMA285•SfT,Ql, SHPRI<( .u.r.n.tr.r.o ,,

US :: <UL><LU>~!U>S REAL

Tl

INSE:!El

INSEQEZ

:= <UL><lU><IU>I~S

:: TZZ"R.SHIFT~(X,IXrY•lYrlY.US. Tl ... 6285 .. )

:= T23"R.SHtrr•cx,rx,Y,IY.LY.us, n·.s<?!lc.->

INTRUJ S>

s

s

$ - s. 77-

H82!1!)

-8286

INSEOE3 :: TZ4"R.SHiff•(X.IX•T•IY•LY•US• Tl".aze6"l

USF :"' <I~SE~E3><'I':SEQEZ><ItlSEOEl><US>f f a PERMSEQ := (T:REALHU:INTRL('flHV:LESSIS<Y .. TJl

( \l: LESSISfi • :o 1U Sf{ t • t;, v, 10 Q :i1 U:ASSOC(Q J]{C:COI'!!oi:JT< Q) H s: SE Hl• IX,YriY•lY•RE:Al >

JCI~S:INSEO<X•!l•T•IY•LT•S> JCPRI:PRDOFSlRRELEVANT!X,IX,Y,IY,LY,REAl•Sl l(PS:PERHC~•lX•Y•IY•LI•S)J

PS 41 ss fZ

tN: HOC SHI fTL) l NS

T3

H

T5

f&

T7 T8 T9 T10

PS a T11

HZ

:• SHIFTSEQ(X,I~,Y,IY.LY,S.INSJ := SAfZ2S5\~•A•C•SHIFTL,SS•

BIJSHIFrS~Q(X,IX.Y.IY.tY,s,INS,PRI,PS)

.. sHiftnn>

:= US(S,tNS•f•SHIFTR(Nl,!NTSHIFTR(N), LSSHifTRt~>.SHIFTRLSCNll

:• SHIFTINY1C~S.T34•R.SHIFT"{X,IX,Y,IY• L r.s. u:s. ·nJ

:• I~SE~El(SriNSrFrSHIFTR{~)riHTSHIFTR(NJ •lSS~!FTRtN>rSHIFTRLS<N>>

:: INSEQEZ<S,!NS,frSHIFTRCN)riNTSHlfTR(N) •LSSHifTRCK>•SHIFTRLS(NJl

:• I~SEQE3<SriNs,r,SH!fTRCM),INTSHlFTR<N) •LSSH!FTRCNJ#SHIFTRLSCN)J

:= l~TSHIFTRC<N>SS> :: LSSHIFTRC<~>SSJ :• SHIFTRLSC<N>SSJ ·- <T3><T9><T8><T7><SHIFTRC<N>SS)><T6>

<T5><T4><NS>PI :: fiS!ClTO<SHIFTLJ,CX•

Sij!FTFCPERHSEQ<S•INS,F>l• [T:lTCCS~IF~L)J<<T>SS>SHIFTF(f),

tT:lTOCSHIFTL>JT10<TJJ

:: ISF<(T:lTOCSHIFTLJlCX,CX• tu:rT:lTO<SHIFTLllCXlSMPR(Q,SHIFTl,U), S~IFTF<PER~SEQCS,INS.FJJ, tT:lTDCSHIFTL>J<<T>SS>SHIFTFCf),Tll)

PS a SATZ286 := T:HStCX,SHPRHPERHSEQ{S,HIS,FhOh S~PR(Q,SHIFTL•tT:lTO(SHIFTLJl<<T> ss~.azssw>SHIFTF{f)),S~PRI<F,QJ,

TlZ-.5286",T2u.8286") ; tX:NATltF:[t:lTOtXJlCX!

HOOF :: ET:lTOCXJJPliO!QOC<T>FJ.Ol

(R:REALl PROPt PROP2 PROPJ

f :il PRO?r. X • f>R!JP5

~ rr:tr:tTOClllCXJ

:: l~SSIStHOD(SUMCX,f)},Rl :: IS<StPHX,HOJHFl hPLHRrOJ> := l~DCPRGP1.?ROP2l :: SC,E•R•ttr:REAL1PROP3CTJ> ·- :~:tr:!TQ(XJJCX;PRCP~(U}

LESSIS! us,.x l ex

: n:~EA:.. HU: INTRUT> lCV:LE:S SIS<Y•T UOI:LESSISCTJOX) ;ex

U :1 TOt SHIFT U l1 TCC SHIF'Tll

: IStSHPt <ChSHifTl;o CT HTO<Si IrTL> l«T>SS>SHHTFtf'l ),. SHPRI(f'",Q))

REAL

INTRU'4 S>

: LESSISt NS~'X) INTRLCSHifTRC<N>SS)) lESSISCY;oSHifTR(<N>SS)l LESS I SC SHIF'TR( <N>SS ),.X)

IS"E•ctTtlTOCSHIFTlllCX•S;IFTFtPERHSEQ(S•I~S,f)), [T :t TOC SHifTU l«T>SS>SHI>Tf<Fl)

ISCSKP~ I<PERHSEQCS, INS,.FJ, Ol• SHPRCQ• SHifTL,[T:lTO<SHIFTLll<<T>SS>SHIFTf(f)))

IS<SHP~ HPE RHSEQ(S• INS,.rJ• 0 hSHPRI<F ,Q) l

: CT:lTO(X)lCX

'PROP' 'PRlP' 'PRJP' 'PROP' 'PRO?•

s

s

- s. 78-

Tl rz T.l

:= SATZ277([!':c:ocu:CXJFUT~U>rfl !S~SUMC hFJr<XOUTCl )>F> :: IS~00(SU~<1•fl~<XCUT(1)>f•fl) : IS"?.·C~On(SUH(lrr))rMûaC<XOUT(l)>f))

·- U: SS I>I2H'O:; <SUIHlrf) ),"40D~<XCUT C1 )>.f) ,r;n : PROPUlrfrM!:IOC<XOUT<H>f)J

n T5

·- SATZ277((!':CXH:J:CX1PUT,UhMOOFU,.f )) PR0?2<1;FrM00(<XCUHl>>F)l ·- ANDIC~~~PlC!rfr~OD(<XDUf(lJ>f)),

PRDP2Cl•f•~:~C<XDUT(ll>F)l~Tl•f4) PRD?3Cl•f•"COC<XOUTC1l>F>> .- SO~E!{~EALr[I:REAllP~JPJ(l,F.Tlr

HOQt<XOUT{l;>>}•T5) a T7 .- [U:[P:1TDlll1CXlT6CUJ

X a [,:P~OP5(XJJ[f:[T:lTDtPL•N•()(,:JJJCXl T8 := u:ss!::;!l"'';"''X•PL"N•<x.!>.SATZ13A<Xr1J> LF :: LEFTCCX•PL•N"((rllrX.TBrFJ t?.:REA~ltPR:PP.C?3<LF.R}l T9 .- ANOE~{PRC~l<LF .. ~),?~Q?2(LfrRlrPR> Tl~ ·- Ä~;::>EZ{f'R::?H LFr?.);?R:::P2,Lf.:H,.?R) i11 :: SATZZ/8( tT :::; ~HU :c:O?L<T .~ J.X,q T12 :: ISMaCtP~CSGYCXrlfJ,<XDUT(PL-N~cx,l>l>

" TU

Tllt

ns

LHf

T15

T17

Tle T19

TZO

T21

T2Z

FJrSUMCPL·~·cX,l),r),

SYMIS\CX,SL~C?L~N•tx.tJ.F), PU SU~<X .. L1'), <X:! UH PL "N'" ( X .. l) }>F' ),. TU> )

:• MOD<<XOUTCPL•N•<X~llJ>F) := ISlESSISlt~C~CPL<SU~<X·LF>,

<X~UT(?L"N~CX•ll}>r))r

KOO<SU~CFL~~·cx.l>•f}},

PL~R•CHOJ(SUM(Xrlf)),.~),T12•

SATZ271CSU~{X,LF),<XOUT(PL"N•<X,.1J)>r> )

:= TH9•t.OR•<LESS(HODCSUH(X,lf)),.R), Is•R•(MODCS~~(XrLFJ>•R>•

lESS<Pl"R"!MOD(SUH<X.lf)),M)r

:=

::

:=

:::

:: :::

:=

Pl"R·t~ .. ~llriS~R•(PL~R"(MODCSUM(X,.Lf)) rHh Ft .. f! .. t'~riO '• T9• tT:LESS(HQ~(S~M{Xrlf)},R)]

SATZ183FCM~~CS~N(XrlFJ)rR•HrT), (T:Is•P."{MCQ(SUM<X•lf)),R)l ISPtl•R .. <HC~<SUM(X,lf)),RrH,J)) !RLESSIS(HOJCSUHCPL•u•cxrl)rf)), Pl*R~<~GOCSUM<Xrlf}),H),PL•R•(R,M)~

ru, Tl4> Lt~TCCXrFL·~·c:,lJrX,TOr KOOft?t·~·(X,lJ,fil

SATZ278<!ï:CXl{U:C~lPL(TrU>rXr HOOF(PL•N'CXrllrf))

lSPLl<SUX(XrlHFJrPLI(R,Q),Pll(M,O), T10) PLIS12A(R,O,MrOJ ISRECX2tPt•R•[Q,Q),OrPt•ft•(R.MJ• Pl~1-R"(0rOrREfiS<REAL•0))} TR4IStCXrSUM(~t'N"CXrlJo HODF(PL•N~CXrl>rf)),pl(SUM(X,lHf)r

Plt< !o!,OJ ), ?UrU (R, 0 ), PLI OlrO) h PLHPl"R .. CR•~l.Pl"P.,.COrO).), PlltPL~R·<~.~lrO>.Tl&.T1i~T16ri19)

:= ANDICPRDPlCPL·~-cX,lJ~FrPt•R•CRrM)), PRDP2(PL•N•(X,lJ,;,pt•R*(R,M}J,T15r T20>

::: SOMEitREAL,[T:REALlPROP3CPL•N•<x~1>~F~ T>,Pt~q•tR,~l~TZ1)

PR0"4U rf J P?.(i"'5U >

tESSlS .. N"OC ,pL•N"(X,.l} l narct u1cx

PRDi>l C .. FrR> PR0?2(_f"rR> IS<SU~PL·~·(X,1),.F),pl[SJKCX,.LFJ,.<XCU1CPL•N•cx .. t>J>FJ>

IS"R*C~OO<PL<SV~CX .. tf)r<XOUTCPL"~*(X,.lll>f)), HODCSU1<PL•n•cx,1J,flll REAL

[T:lTOC lOlCX

IS<SUMt Pt•N•CXrl>rHCOFCPl*N"CXrl)rfJJ,.FL<SlKCX,.lHFJ, PL!Oir:l J))

ISCPl(iUH<X•LHf),.plJ(H,OJ),pl(PLI<R•O>•PLICK•OJJ) tS<PLC,LilRrOJ,PLICP,.Ql)rPLICPL"R•CRrH>•FL•R•(OrO)))

-5.79-

-8267

+!1288

f i IZl :: ::>UX!:.Itt"'P~ !'lt. AL#[ T: R!:.ALH'I<UI'.HI.t "III'"Lt > p,pRDP4CPL•N·<~ .. l)"F)o[T:REALJ (U:PR1Pl(Lf•TllT22CT.U))

P 3 T25 . f26

•- (U:(T:1TnCPt~n·(X,lJiJCXlT23<UJ ·- !S?<~AT,[T:UATJPRQPS(f),PL•N•Cx.lJ•<X>

suc.rzs .. 3ATZ4A<Xll

x

SATZZ87

!>RO?l

3 ?ROP~ ll t f :r r: 1T oIN~UCTION({T:N~TJPRC?S•.szar•(T>• rr·.äzar· .. rr:~ATlru:pqops•.azs7•CT>l TZG".szar•cr .. u>.x>

::: IStPLitMCOCPRCO(~•f}),Q), P~ODCX,MC~F{<JJ)

::: fU:tT:lTOCXJJCX]PROPlCUJ

·- SATZ2l7C[T:CXltU:CXliS(f,U),f) ·- ISMCO(?RC~(l,ë>,<XO~T(l)>f,Tll

:= JsqEC~l<~OOCPRC~<l•tJJ,HOOC<XCUT!l)>F) •lh T2 J

:= SATZ277CET:CXl[U:CXJTS(T,U),HOOFC1"f))

== TRIS2{CX .. PLICHQOCPRCD{lrt)l~Ol• PRCDClr~ûDF(l,f)),?LICHOO(<XOUTtll>f)"

O>rTJ,i4l êJ TS := [lJ:[f:1T!HllJCXli5CUl

X a tP:P~OP2(XlJ[F:tT:1TOCPL•N•CXrll)~CXl T7 := LESSISI1"N"CXrPL·~"(X"llrSATZ16A(XrlJ) LF .- lEFTCCXrPL"N"CXrll•XrT7,fl T8 := SATZ278([T:CXJ(U:CXlTSCTrUlrXrf)

M := HOCC<XOUTCFt•N•(Xrlll>Fl T9 := ISMODCPROaCPL•N•cx.ll•f),TSCPROOCXrlfl

•<XOUTCPt•N•cX,l))>f),f8)

flO == SATZ266CPRODCX•lf),<XOUTCPL"N"<X•1l)> n

Tll := TRISCREALrMQDCPROJCPL"N•tXrllrF))r KOOCTSCPROOCX.LFJ,<XOUTCPL"N"C~,llJ>f) )rTSnR"CMOOCPROacx .. LF)l•MlrT9 .. T10)

T1Z :: ISRECXlCMODCPRODCPl"N•tx,t>•f))r TS"R"CHOOCPROD(XrLFllrHlrOrTll>

LHt == LEFTCCXrPL•N•(XrllrXrT7, HOOf(PL•N•cx.l>•f))

T13 . - SATZ278<CT:CXJ[U:CXlTS<T~u>~x~ MOOF<Pl"Nw(X.l)rf))

T14 := SY~ISCCXrPLI(MOOCPROO(Xrlf)J,O), PROD(X,LMFJ•<LF>P)

Tl5 := 1STS1CPR0DtX .. LKFJr?LICMODCPROOCXrlF))r 0)rPLl(HrO),Tl4J

Tló ·- TSIS12A(M00tP~3J(X,Lfl>rOrH•Ol

T17 := TRIS<REAL,MN~R"CTS~R"CHOO<PR~O<X•Lf)), H),TS~,•{Q.Ql;,~N~R·<rs•R"<KOC\PPOO

PR0~4(,L"N•cx"1>•f>

PRC?5P L .. lli"(X~U J

PROPSC<X>SUC)

SO'!E: "R• ([ T: REAL JAN!HLESS IS 0!00( SUH(X,f > 1 • T ), IS<SU!o'\ x, MO DHFl hPLH T, OJ >))

'PR:JP• 'PR:JP'

: ISC"ROl u,r h<XOUTC U>r> : Is·~·OH!OCPRODCl•Fl J,fo~Q!)(c XOUHU>F})

IS<PLIC HOO( PRODC hf J Jo OJr'"LH MOO(<XOUT< 1)>0•0)) ; IS<?ROJ(l,HODF<lrF)l,PLI<MOOt<XOUT(ll>FlrOlJ

PROPlU ,f> PRO?ZU)

: LESSIS•N•cx,.pt•N•tx,.U> : CT:tTOCXJlCX : IS<PROJ<PL"N•<X•l),f)rTSC?ROO(X~LFl•<XOUTCFL"N~(X•lll>

f))

REAL

: ts•R·C~OOCPRODtPt•N•cx,lJ•f)),MODCTSCPROO(X,LFJ, <XO:JTP L "N" ()(,.1) }>f H)

IS•R•(~OOCTSCPROO(X,Lfl•<XOUTtPL"N•cx,1l)>f)),.

T s·~·('l OD(PRODC x,Lf)), HU

IS<PLitHGOCPROOCPL"N•CXrllrf)),Q)" PLU rs• R•HIOOCPROOC X•Lfl lr Mh 0))

er :trot xncx

IS<?ROJ(PL•N-CX•l>,MODFCPl"N•cx,t>•f))rTSCFROa(X,LMf), PLIOhl)) l .

ISCTSC'ROOCX•LHf),pLICHr0)},TStPLI<MOO(PROCCX .. Lf)),0), P!.Hl'I~J ))) . ISCT3<,LICMDO(PROOC1rlf)),OlrPLIC~~0)), PLH ~,_ .. R,.<T S .. R .. < HOD (PROO<K rLf > l rM h TS,.R .. CO •0 n, PL•!f•H s·'"R" C HOD( PRODCX rln J ,Q h T·S,.R•(O, 14 J J H

s

- 5.80

•6Z8!

+8289

T18

T19

T20

\A"'-l14r.~I!IIVIi,l..l '"' \.C'VU'-rHVLI'\.1'\FI...- #17TI#

,:SM\Z"R"<Ts•R•(Q,QJ~~•

TSw~~cM~OCPRDOIX.LFJJ,Ml•

TSDl·~~ct.O•REF:SCREAL•Ol)~~ ?l02~R~<TS"R~{~O~<PRGOCX,tf}),M),

~!"R~COJ.SATZ176BCO•~EFISCREAL•0)))}

·- TRIStRZZL,PL~R•<TS"R•CHITDtPROOCX~L~)), OJ•IS~RR(O,H}),fL•R•fO.~>~O•

ISDL12-R~<rs~n·<~D:(PRDD<X.LF>>·OJ·O· TS•R•tc.~>•D•TS02"~"CMOD:PRDJCX•LF>J• Q,REr:s~REAL~a;:~TS~l·R~<o,M,

REFt~C~E~L•O>)l•PLOl"R•(O•O• R~:--1 S{ ~EAL~G) l l

·- iS~Et112{~N"R•[JS"~"(HDD!PRODCI•Lf}), H>,TS"?.•{O,Q)J,TS~R~<~OO<?RCó(X,lF)),

Ml~Pt·~~crs•R•CMCDtPRJD<X•lfJ),Q),

TS"R"{!),. i'll >• 0• Tl7, T 18)

:: TR4!S[CX.P~ODCPL•N•(X,llr ~~~F(PLfts•<X•l>•fll?TS<PRQQ(X•LHF)• ?llC~.0)),TS<PLI(~00(?ROQCXrLF)),O),

?L!<~•O>l•PLI<MN"~~<rs~R•(MOO!PROO (X,LFJ),~loT$ 8~"(0,0)},

Pl~R•<TS•R•<MCOCPRG)CX•LF>lrO>• rs•R•(Q,HJ)),pLI<TS•R•CMOO<PRCO<Xrlf)t

IS•R•C~N·R•(fS•P.•C~OCCPRC~(X,tf)),HJ,TS"R"CO•O>>• T S"R .. ("' !Jt)(PROOC Y., lF) >• M})

: IS<PLIC HN•R•ns•R.,( MOOtPROOCX.lf> ),11,), Ts .. R•(O,Q'> ), Pt•R•~rs•R•(MOv<PROO<X•LfJ),Q),fS•R•(Q,H))),

PLIC TS'" R-.<MOiH PR CO <X• tn h Hh 0 >}

,x>, Oh T 13• 115• T16 .. T19J IS<PR!ll <Pt •r.:•cx,u, MOOf(PL •N•<X,llof H" Ptlt TS" R"O!OO<PP.lJD( x .. tn h MhOl)

TZ1 :: TRIS2CCI•PlllM00(PROO(PL•N•(X,1J,f)}, Ol•PRJ~(PL"N•CX•llrMOOF<Pt•N•{X,.ll•f))

,PLI<TS•R•(MODCPRODCXrlF)l,K),.O),T12• T20l

P a TZ1A TZZ

:= tU:tT:lïOCPL~~"(X,1JJlCXJT21(U) := lSP(~If,(T:NATlPRDP2(T),pl"N"CX.t11•<X>

S:JC, TZ!J., SAT Z4AC X) l

x a a

r a

SATU88

PROPl PROP~ PROPl PROP'< tr: n :1 roe 1J lCXl Tl [P:PROPH1•F> J TZ T3

·- <F>INDUCTION((T:NATJPROPZ•.azss•(f)• Tó".S288•,[T:NATJ[U:PROP2".8268"(TJl rzz·.azaa•cr.u>.x>

:: ISCPRODCX.tFl.tOCJ :: SO~E"l"ClTO(X).o(T:lTU<X>JISC<T>F.oOCl) := IFF<PROPl.tPROPZ> :: (U:[T:lTOtXllCXlPROP3CUl

:: TRISlCCX.t<XOUT(l)>r,oc,pRQO(l,f),fl•P> .- SO~EICtTDfl),[T:lTDCllliSt<T>F,OC>•

XGJT<lhTZ' [P:PROPZ(l.oF)JtU:lTQ{llJ(!:ISCf•OC>J T~ ·- THt•N.SI~GLET• T5 •- TR5~S<CXoPRQD(l,f),<XDUT(l}>f,F.oOC.t

Tl.ISF(~TCCl>.oCX•t•XG~T(l},U,

SYM!SC1TO{l)PUrXOUT(lJ•T4JJ,.Il P ~ Tó ·- SD~EAPPClTO(t),[f:lTOCl)JISC<l>f,OC>•

p,p.QPlCl•f),[i:tTGCliJ[U:IS<<T>frOC)l

PROP H"' L •N•( X.ol hF > PROPZPL"N"U.",l))

PR0?2(< X>SU Cl

'PROP' 'PR:JP' 'PROP• 'PROP'

IS<PROJ (l,f' lr<XOUT< ll>F>

ISC<XOJ HU>f,.OC>

PRO?ZCl ,.F)

: PROPlCl•fl

s

-5.81·

T5CT•U>> f a T7 ·- IFf!(PROP1(1,F),PRCP2(1rf),

tT:PP,OPl\l,f)jT3!T)r[T:P~QP2(1•F>l TM T)}

; T8 ·- (U:[T:lTC(UJCXJT7CUl X a [P:P~OP4CXJlCF:tT:lTD(Fl~~-(X,tlJJCXl

T9 .- lES3<::l!l•ï;'"(XrPL~I'"(X•lJ•SATZ184CX•ll> LF := lEfH•:X.Pl"N"<X,l'•X•T9oF') TlO := SATZZ78(tT:CXltU:CXJTS<ï.U1oXof)

[Q:pqQpt(PL-N•<x~l>.F>J

Tl1 ·- TRISlCCX.TSlPROD<Xol.f>o

?~notP~~~·cx,:>,f>~r:o~Q>

T12 .- SAïZ22lC(?R00(X,lF)r<XGUT~PL•Nwcx,t>)> r.nu ·

ri:IS(PROa{X,.LFl•OC>l T13 :: TH3•t..Iff•(PROP1(X,LFl.PROPZCX,Lf},

<tf>P.n tN:tTO(XJJCJ:ISC<N>LF',OCll Tl4 ·- SCc'!:HlTCO't•N•cx,l>l•

tT:lTD<?L~N~(X,!})JiS(<T>F,O:Jr

LEFTlTOCPL•N•<X•ll•I•T9,NJoJJ I a T15 := SO~EAPP<lTOtX),(T:lTJ<X>liSC<T>LFoOCl•

T13,PROPZtPL"N•(X,lloF>.rT:lTO<XJl [U:IS<<T>Lf,OC)lT14(T,Ul>

0 a CI:IS(<XOUT(~t•N•(X•l)}>FoOC)J l16 :"' S!l'IE re 1T 0( PL .. N .. ( )(,1 )),

{T:lTO(PL"N•(Xol))liSC<T>frOCJ, XOUTCPL•N•CX,IJJ,Il

Q ;; T17 •- OR~PP( IS(PRCOU•LI:·),OCl, lS(<XOUTCPL•N•()(,l}J>F',OC)r PR3P2tPL*N•cx,l>•F)rTlZ• tT:IS<P~OJ<XrlF>~OC>JT15CT>, [T:I5(<XGUTtPt.•~•(XrllJ>r~oc>1Tl&lT)l

ra [O:PROPZ(PL•N•<X~l),F)J(N:lTOCPL•N"(K,l>>lt!:IS(<N>r,OCJ J[J:Is•E•ClTOCPL•N•(X•ll),N,1.0UTCPl"N"<X•l>>>l T18 := TRISlCC~,<XCUT(PL·~·cx,t>>>f,QC,<N>Fr

ISF<lTOtPl*N•(X,llJ.CX,f,N. XOUTCPt•N•ct.tJ),Jl•I>

TZO :: SATZ221B<PRCOCX,Lflr<X3UTCPL'"N"(X,lll> r.na>

I a [M:NOTtiS•E•tlTDtPL*~•(X,l>l•~,XOUTCPl"N"(X,l>>>>J Nl :: INNCPt•N"[Xrll•N> [J: IS .. N'"UJh PL,.N•cx,u > l JZ1 :: lSDUTNICPL"N"(XrlJrNlrlTOP<PL•N•CXrllr

rzz

tn rPt. .. ,., .. (X •1) •LE SSI 5 13< PL •N• {X, 1 )).J)

:= TRIStlTO(Pl"N•(X,lJ>~N~OUTN(Pt•N•(X#lJ ~NlYlTDP(PL"N•(X,tJ,N)),

XOJHPL "N"(X, 1)) .. I SOUîU~CPL •N"CX•l l"

PRCPlH rf)

PR0?3U ,.r) PRCP4<1 >

LESSIS•N•(XrPL'"N•<X•l>> (f: 1T 0[ X) lC X IS(PaCJ(PL·~·(X•l>•f>,TS<PROOCX,LF),<XCUT(FL .. N"(X,lJ)> f))

OR<ISP RQD( Xrt.r>.OC >. IS<<X DUHPl•Ji .. ( Xol })>f,OC))

?R0?2U: .tn

: NAT

: IS,.E•U TO(PL .. N.•<X•l )), OUT!f(Pl'"N•(x., 1h Nl• lTOP.tP.!. •N"{ X.l h !U hXDUT<PL .. N .. ( x, 1 J))

llhTZV zs-e:•n TO<Pt•N•CX,l)h l'bXOUTCPL"N'"<X•U» K a TU

T25 NZ TZ6

:= TH3'"t.IHP"<IS"N"<Nl,PL"N•(Xr1JJ, IS'"E"'( lT Ct PV•N•( X• 1) h H• XOUT(Plw~~(X,1J)J,H,

(T:IS"N"(Nl•PL•N*CX•l>JJTZZ~TJJ NIS"N"!Nl•Pt•N•(X•l>J • - OR;: 1 CLES S'":'i" CN1, Pl"~;-o:,l > >r

IS·~-{Ul,PL·~·(X,lJ>•iTOPCPL•N•(X•l>•

NloT23l = SaTZZG(X,Ul~T24J = OUTN<X,~a,T25J : = ISINO!JfN(X,t:t.T25 IS•N .. Cil,.II'\

-5.82-

•8289

.•8289

+Y9

rzs

T29

T.30 f31

T32

T34

I ; !35

T36

o a n1

r a ns

p ; T.39 HO

SATZZ89

U>.IHN(I~,z>~TRLESSIS·~·CI~N(X,N2J•X• Pl .. N .. n:~ l h 1 TCP< Xr NZ h T9 h TZ&) : IS-t•u TO.CPL .. N ... { X• 1 1 h OUT'l CPL .. N .. <X• 1), t.l"

·-

. -

. -:=

==

,Nl~li~P!?L~~P(X,l)r-~)),

lEFTlTCCPL~~·crolJ~X.79rN2J, !SCUTIN\[P~R~·cx.1)•Nl,T27)

IS~tlTCt?L~~:~(X71lJ.cx~r,N.

lEFT!i~(PL•N-iX•l}oKoT9.N2),T26)

T~I5l(CY,<~2>LF,OC.<~>~•i29•I>

SD~E!ClTDCI,,[J:l~DttlltSC<T>Lf,OC),

1T OP ( P. •N•< x •. U, tU hLE FT 1T Q( Pt. •N•(X, U" X • TS• N2 J)

: IS!<"!>"" ,<!IIZ>LF> : IS<<~ Z. Lf • 0 C >

<Lf>Pri3D : PROPl<(•lfJ ::: SAr122l~t?R00(X,lf),<XOUTCPL•N•(X,1)J>

f•T32) 1 IS(TSt~RoO<X•Lf),<XOUT<PL .. N•(X,l>>>FJ,OCJ :: ~Ht .. t. !1'? .. (1 s•t:•(l TO<PL .. N .. {)(,l)) ,N,

XGJTtPt•N•(X,ll)l•IS(TSCPROvCX•Lr), <XO~T{?l~~~cx.tl>>r),CCl•

rr:ts•E~<lTCCPL"~·cx.:>>•N• XG~T(PL~,•(Xrll)}JT2Q(T),

tT:NGT<!S•E•ctTO<Pl"N•<Xrl))rN• Ä0UT(?L•n•tXrl))))JT34lTl) : IStTSC?ROOCX .. tfJ,<XCUT<Pt•N•cx,l))>FlrOCl

:= TRISCCXrPRJ~CPL.N"(J,l>•FJ, T SC PRO!H x, u· h <XOUH Pl.. "N" ( Xrl) J>F hOc, T!OrT35) : PRO?lC~t·N"(Xrl),f)

:= SOKEAPDC1T9CPL"N•(J,1)), tT:lTC(PL•N•(X,1Jlli${<T>f,OC>rG• PROPllPt•N•(X•lJrFJ,tT:lTOCPL•N•(X,lJ) liU:IS<<T>F,QC)lT36<TrU)) : PROP1C'L'"N•<X,ll,f)

:: IFFI<PRGPltPl•N•(XtlJ,r}, PROP2CPlw~•(X,llrF),

CT:PRC?ltPL•N•cx,l),fJJT17<TJr rt:?<;G?2(PL,.N"C(,.l),FJJT37{T)) 1 PR0!'3PL'"N"{X,1J,FJ

·- [iJ: t: i: 1 Bt?L ,.s•c x, 1) > ~ :::0 H8C U) PROPliP l"N•tX•l>) :: ISP<N~T,tT:NATlPROP4<T),pt•N•<X.1Jr<X>

SUC,THrSHZ4ACX>J : PROP'H<X>SUCl

:: <F>INDCCTION((f:RATlPROPft•.8269•(f}, TS•.azs7•7[T:NATl(U:?RCP4·.e~s9-<T>1 TftO•.azs9•(TrUl,X1 : IFftlS[PROO<Xrfl•OC)rSOME-L•(tTOCX>rCT:lTOCXJllS(<T>Fr

oe»> [1: ISC PRODU,f hOC J l SATZZ89A t= TH3•t.IFF•(p~QP1•.8289*,PROP2".82S9",

SATZ289,I) SOKE•L•(tTOCXJ,[T:lTO(X)llSC<T>F,OCJJ ~ :1 tN:lfO(X}J[I:IS(<N>f,OC)l

:: SO~E H lTG<Xh [J: ~TO<lO]JS(<T>F ,.oc>,N • U : PROP2

I a .SATZZ89B :: TH4 .. L. Iff•<PROP1·.szS9,.,PROP2•.szes•,. SATZ 269r T41'". 826 9") IS<PROl (X,f hOC)

a tX:COMPLEXltKIREAllCMI:INTRL(MJl[O:OHCNISCXrOCJrPOS<K>>l

s

s - 5.83-

[P:POSCH>l .Tl Hl ?iH

= POSI~TNATRL<M•P•Ml) = NTOFRL(!'f,.Tl) = PRQDCHl;[T:lTOCMl>JXi

X~ [Y:CJHPLEXJ[M:REALJ[N:REAt:~I:IS<X.Y>J[J:IS•R•(M,NJ

JtMil:INTRL(H)J[Nil:INTRL(~JJ[GX:OR(NISCX•OC>•POS{Hll

J[ OY: iJR( NI SC':', OC>• POS< Nl >J

OY a [HP:~OSCKll[NP:POS(Nll HO •- Ml{X.H.Hll•OX•HPl N~ ·- HlCY.~.TUl.OY,\IIP) TZ ·- IS~L~NTC~·Tl<X•M•~Il•OX•MP>•N•

T3 Tlt

T5

Tó

TT

P a tP1:?0SCHJJ ra

P a [N:NIS(X.OCJl T9

T10

!J a [N:NEGCK)]

·- LESS:s:z·N·c~O.NO•T2> ·- ISS~P~~(7:CXl(U:CX1TStT.Ul.NOo

[T:lTJCNOllY~~O,T2)

:= FISI<lTO<HOJ.CX.tT:lTO<HO>lXo LEFTCCX.~O.HO,T3•[T:lTO{N0llYJ• [T:l T:JC!Hilll >

:= ISf([T:lTOCKOl1CX.CX•[U:[T:1TOCMO>lCXl PRUO<~O.Ul.tT:lTOCMOJJX,

LEFTCCXoHOoHO.T3.tT:lTOCNOJ1Yl•T5>

:: TRISCCX.PWl(X•M•MlloOX•MP>• PRCOC~O.lEFTCCXoNOoMO.T3,[T:lTO<NOJJY)

>•P~lCYoNrNll•OYoNPJoTG.T4J

:: T7CX~X•K•M•REFISCCX•X>•REFIStREAL•K>• HI.JH,Q,Q,p, Pl >

•- THS-L.SOKE•<tTO(Ml),[T:lTOCMl)liSC<T~

[U:lTJCHl>JX,OCJ,[T:lTOCMl>lN) := TK3-L.IMP"<IS(PW1r0C),SOME"l"(1TO<Hl >•

(T:1TaC~lljiSC<T>tU:lTD<M1>1XoOCJ),T9,

tT:IS<PWl.OCJlSATZZ89A\Ml•(U:1TO<Kl>l x.rJl

MI ; Tll := INTABSCMrHIJ N 3 T12 ·- SATZ1~5B(H,n>

T13 :: ORI2<~ISCX.OCJ,POS<ABS<H)JrT12J T14 :: OREl<~IS(XrOC>•PCS<X>rO~NNOTP<H•N>> T15 ·- T10<~2S<KJrTlloTl3•T1ZrT14) PWZ ·- OVC1C.PW1tABSCM>,T1l•Tl3,TlZ>•T15J

DY a [NK:~EG(H)][NN:NEGCN)l PWK ·- PlU(X,ABSOilrT11(X,HrHilh

T13( X • M• 1'11 1• OXr NH), T 12( X • M•KI 1 •!JXoNH)) PIIN :: PWHYrABSOU,TlHY,N,Nil>•

T13CY•~•NI1rOYrNNJ,T12(T.NrNil•OY•NN)) T16 := T7CASSCHJ,,BSCN)rlriSASSCM.N,J},

~ll(X•~•Hll>•Tll(Y•N•N[llr T13(X,. HoHllr OX.NM), T lHY,N,~Il ,QY,NN), T12<X•KrHilrOXrNM>rTlZCYrNoNll•OYrNN)J

T17 := ISOV2CPWMrPM~.1CrTl6• T15CX•~•Hll•OX.~M>.T15CY>N•Nil•DY•NN))

NATRU" l NAT ex

NAT NAT

: IS•Nwc .. O,NOJ LESS I s• N•CH Or NO)

ISC?RDJ CMO, LEFH cx,~;Q,MO,T 3,[T: lT!lCNOJlY> ), PWl(Yr~rNilrOY•NP)}

IS •E•C[ T: 1T 0010 J lCX • tT : lT!H MOl l X• LEFTCC( •t~O.MOrT3,[T:lTOCN) JlY)J

: IS(PIIlt Xrfb Hil•OX•HPJ. PROiHHO• LEFHCl: ,NO, HO,T 3, tT: 1T OC Nl JJY)))

: ISCPlfl[ PJ.PWHPl)}

NOT<S01E•L•<tTOCH1lr(T:1T3CH1lliS<<T>[U:1TCCM1J1X•OCJJ)

NI SC PWl ,oe>

INTRLU BSCH J l POSUB5 00) ORHIISC XoOC ),POS<ABSCKl) > NIS< Xrl C> NIS<PWl uasoo.ru~r13.T1ZhOCJ ex

ex

ex

IS(f'lfK• PWN)

s

s

-5.84-

UV9

N a rNU:'iEGOO J Tl6

0 ; PW3

N 2 TI9

0 ·~ tin:~Qf(NEG<!U>l T20

NM a T21 i22 T23

TZ4

OY a (NNt'fOHNEGOO)] T25 i2ó T27 T28

OYil TZ9

o a Pil

P a HO

0 a [N:NJT(PCS(M)ll T31

0 a CI:IS•R•(~*OJl HZ

0 a UHtiEGODJ T33

·= =

:=

T17t x~ x,~- t.t .. REFI S<!:: x,.x h REF"l S< REAL .. M h MI,.~ I .. ·s,. C, ~~. N 1 J ITE"'t.~·<~EGCMJ,CXoCTtNEGCM>1PW2(T1,. [T:~c·t~!Gt~J)JlC•tT:~EG(~)ltU:NEGCMll TlBCTo~),[J;~CT~~E~CM)ll[U:~OTCNEGCM))

ISCPWZt NhPWZUt1))

J"!Er::s::::::.Ic~> ex ::

. -

:: ::;: :=

·-

::::

== :: ·-:?=

ITET•L.•·<~E~{Ml•C~,(T:NEGCMlJPII2(T), [T:KDTCSEGC~JJ:l:,:r:~EG<Mll[U:NEG!Hll T 1\3{ ï • :)J , [ T: ':C':t ~::;::.; t )! l >HU: UQH NEG 0! ) ) JF.:::r !5\:x~ 1c J, ~~>

I!Ef"'L. "'"{ NEGOOrCX,. (T: NEG<M )JPWZ{i)" (J:~:Tt\E::~)J]l~•[T:~EG(Xl][U:N[G(M)]

T18(T,U),[T:~JTlNEGCH)J][U:IQT(NEGCM))

JREFiSCC~rlCl.~N)

1Sn!REAlr[i:~EALJUEGCT)~~·~~NHrJ) t l1~ x~~, 'H! 1,. UX··~~;.{) StMIS!CXoP~3(Y.~rNI1•0Y), ? '4 2 ·: ~·,. '·i, 71 I 1" :; r .. ; z:. > , !1Ç(Y~~r~I1"QY,T21l) T~3IS!cx,?·nO:rl'•>.:!l•C)(), PO:Z( x,~,~: h ox, '·P~} .. Pii2( Y r N .. NI 1•0Y • TZ1) ,.p.J(Y,S.~IlrOYJ.T22•T17<T21),.TZ3)

ISPC?.EAlrtT:?.EALlSOT<NEGIT>>rHrNrNNrJ) r z:>< "X~~. ~i h ox.mn TZOC YJ.IirlH !,. OY r 125) TRIS2<CX,P~l<Xr~•~Ilr0Xlr

P~3<Y•NrNll•OY> .. 1C•TZ6rT27J TH1wL.I~P~(NEGCMlriS(PW3CX.HrHl1r0X)r PW3(YrNrNilr0Y)),[i:NEG(HllT24(T}r CT:NOTCNEG(MJJJTZI<TJJ

·- ITE"L.R•CPOSCMlrCXrtT:POS(MJ) PWln.19R(Tlr[T:kOTC?OSCHJ>lPW3•.v9•, [T:PQS(Mil[v:PQSCM>lTS•.Y9"<TrU>• [T:NOTCPOS<H)JJ[U:NOT<POSCHJ)] REFIS<CXrPW3•.v9•1J

·- ITET•L.R•!POSC~J .. c~,.(T:POS(M)lPWl<T),. CT:NOTCPOS(~)JJPW3r(T:PQS{H)ltU:POS(M) lf8(J,.ut,.(T:~OTCPCSIHJ)J[U:NOTCPOS<H))

IS(PW3• 1Cl NEGCN)

: I SCPW 3[ x~M• Mil.oOU, PII2CXrM,. HU,. OX,NM))

: NOTOIE:i(H)) : IS<PII3( x,.H,Mil.oOX>rlC)

ISCPW3[ y,.tbNil•OYJrlCl

: ex

lREFISCCX•Pij]),.pJ lSCPW,~Hl(P))

::: iTEF"L .R•( POSC M) ,:; '<• rT !POS CM JlPWH T>,. [T:h0i(OQS(M))JPW3.IT:POS(M)l[U:P0S(H) lTS(f,Ul.[T:~GT<POS(M))]{U:NOTCPOS(Mll

JREFIS(CX,.PWH,.N> : ISCPW,.:tW3)

:: TRIS<CX.PW.PWJ,1C~T3l<O~OTP<M,IJ)• T20CO~lCi'Hl'l• IJ)) IS<Plhl Cl

:: TRISCCX,.P~.?II3•PH2C"l•T3l(NNOT?(M•N)l, T19CNI I

$

s

- 5.85-

s

(J .; (P:P[JS(IUJ POSUP

(N:NISCXrOC.J l LEH'iAPMl

0 • CI :Is•R,.C!hO > J OEXP

0 a [N:~EG< !Ol · LO!l1APWZ

LE:M'1APW3

N :1 T34

T35

••V9

MP a Tl& f37 T38

T39

DY a [NP:NOTCPOSCMJ>J T40 T41 Ttt2

TU

:=

:::

~=

== ==

TJo•.v9 .. CP>

TK2"E• N!lT I S .. CCXr PlU,.. V9" 

T 14,. .1!9 .. 011 T13 ... '(9•(N)

ISCPK(KrMrM4;0J,PRODtNTOr~L(KrPOSINT~ATRL(~,p.HI1lr CT :1 TOt NTOFRLCHrPOS INUAT~ U M, p, MI))> l Xl)

NISCXrl Cl OR<~IStXrOC>•POS<ASSCM)))

·- T33CASSCMJrTlljJ13(HlrT12CN}) IS(PVC(rA8S(H)rT1l•T13(N)),pW1CXrABSCMlrTllrT13{N)r

:: ISOVZCPW(XrA9SCM)rTllrT13(NJJr PHl<XrABS(M)rTllrT13{~)rT1ZCNll•lC• T34,LEK"APW1CA8S(H)rT11rT13CN)rT12lN),.

H200))

T14(N))rT15{N}) : ISCOVClCrP~(XrABSCMJ,T11rT13(N)}rLEM~APW1(JSS(M}•Tllr T 13{ N>. Tl2C NhTl40l))),PWZ(N))

:= T~IS2CCX,PMCXrM .. MI .. OJr OYtlC,PW(X,ASS(M),INTABSCM .. Kil, tEMMAPW3)•LEHHAPW1(X,ASSCM), INTABSCM•Hil•lE~MAPWl•SATZ1668(H,N)" LEHMAPWZ)),PW2•.v9•(N),T33•.v9•(N)r 135*. Y9·" ( N)) ISCPNCC•K•KI .. OJ•OVClC•PWCK•ABSCM),INTAES(M,MIJ,

lEMMAPf3JrlEKM4PW1(X,ABSCM),INTABSCM,MI> .. LEMMAPN3, SATZ16iB(M"NJrLEMHAPW2lll

:= ISP{ REA Lr[ T: REALlP.OSCT hH•NrMP,J J : POS OU :: T30CX•I1• MI b OX,KPJ : ISCPWU: ,.pt,.lf I1rQXJ,PMU x,. M• Mih OX, MP)> ::= SYHISCCX,PWCY .. N,Nil•DYJr

PW1(f,N,NI1,.QY,T36l, T3îH y,. ~b NI h OY r T36)) : ISCPW U 'hN• NI l"oy ,r 36),.plf(Y•N•Nil•OY H

== TR3I SCCX .. Pil( x, K .. Mil• QX),. PWl<X•M,Mil~Ox~HP>rPW1(Y~N,.Nil•OY•T3ó) ,pW(YrNrNil,OYJ,T37,T7<T36lrT38> : IS<PW((,K,Mil"QX)rPW(Y,N,NI1rOYJ>

:= ISP<REAL~[T:REALJNOT<PDS<TJ)rHrNrNPrJ) : NOTCPOS(NJ) :a T .$1( X• H• Mll• OX•NPl ISCPMU rHr!HlrOX hPW3( XrM~ Milr OX))

=· SYHIS(CXrPW(YrNrN!lrOYJ, PW3( Y, N"t\I lr OYJ, T3H Yr Nr NilrOY rHOH : IS<PW 3[ Y,N" NU, DY hPIH Y,N, NilrOO)

== TR3ISCCXrPWiXrM•HI1rOX>~ Pli3( x, Mr MI lr OX h PWH y, NrNUrOYJ" PWU, NrtHlrO'O • T 41• TZ9r T!fV IS(PWU r)!.M IlrOX ),pwn, Nr!l IlrO.YJ l

s

s

•V9 S

DY; ISPK1Z :: THt•L.IMP•(POSCHlriS<PWCX,.MrHI1rOXJr PWCYrNrNI1rOYJ),[T:POSCHllT39".V9•(f)r [T:NOT<POS<~))]T43~.v1w(f))

H ; ti:ISCI•Y>JtHIJlNTRLCHJJ(OX:OR(NISCXrOC)•PJSC~,, lCOY:ORCNISCYrOClrPOSCM))J

·ISPW1 := ISPIU2CXrY,.M•Kri•REFiS<REAl•IOrlfhMI • ox .. on

X a [H:REALJ[~:REAlJCI:IS"R"(M•N>l[HI:rNTRtCHllC~I:INTRl(N)

- 5.86.;..

•929)

-929)

•9293

JlUn>UK\~L~\~•UÇJ,~L~\MJJJlUN<L~\Nl~\~•U~I•FU~\NJIJ

ISPVZ ·- IS?~ll(XrXr~·~·REfiS<CX,XlrirMJ~NI,.OMr

[P':PDSOOl Tl

; [l:ISClCrOCll TZ

a 1NOTl

N a ti:xs·~~(~.o'l T4

N a tNMUIEGOO l ?0 T5

T7

ra

H : Is•R•(lRL,Q)

·- THl~L.I~?~EISClCrO:}.IS~R•CtRlrOlr PNOT0(lRL,~QSllr(T:IS<1CrOC>l TZ ... 9290"1: n >

:: THZ•E.NOTts•ccx.lc.oc,pwcx.M.HI•D>• lNOTO.OEXPU))

NIS< IC• oe)

·- PW(X,ASS<MJ.INTABSC~.MilrLEMKA~W3CNM>> : CX ·- LEMKIPMlCXrABSE~J.I!TABSCMrMIJr

LEH~APW3(N,)•SATZl&&B(MrNM>• LEMl'IAPWZ<N~>) : NIS<PO,.OCJ

:= TRIS(CXrTSCPWCXrM•MirOlrPO>r TSCUV! lCr?O,. T5hPO)r lC• IST51(PH{X•M•»I•Ol·OVC1C•PO,T5J,pQ, NEGE JC!>( NIO h SA TZ2Z?E: <lC ,.pQ,.T5)) IS<TSP lH X .. M,.Ml,.Qh POl .te)

== THZ·E.~CTIS~!cx .. tc .. oc.rscrwcx.M .. MI·O>• PO), 1N'JTt\,. i6)

:: TH3"t.IMP•(I5(P~{X,M.MI,QJ,OC)r IS<TS(?~(X,K,MI•D>•?OJ,OC>•T7• tT:!Sf?K(X,M.HI,OlrCCJlSATZZ21AtPMCX, M .. Kt ,.Q)..f'O• T) J

:= RA PP ( H, :tiS (p \f( x .. Mr MI ,o hOC), tT :POS Of) J T1~.9290•<TJ,(T:Is~R•(H•O>J

T4~.9290-\T).,[T:NEGCMJl18".9290•(f))

:= ORI2<NIS(X,OC>•P0S(1Rl),P051)

J= NTOFRLClRL .. POSINTNATRL((RLrPOSl; INTRLl)}

:= POSE~P(X,.1RlriNTRl1•LEMMA291.POS1J :: TRIS{NAT•l•l'HOfRUlRL•NATRllh

NTOrRL< lRL.~>OSHITNA nt< lRL,.POSh !NTRL1J),JSNTRL1(1)• ISRLENTClRL.NAtRtl.IRL• POSinT~ATRLClRL•P~Sl•INTRLl)• REF1SIREAL~1RLJ}J

:: LESSIS:Z~N-t1~1A~f2) := lSSHPR((T:CXJ(U!CXlTSCT.U>•lA,

[T:lTO<lAJlX•l,T2)

NISC PW[ )(, H,. HI,O) rOC) ORCNIS( x,oc ),POSURL))

NAT IS<P~{(,1RL,INTRLlrLEMHA291),pROD<1A,[T:lTC<lAlJX))

: IS .. N•U ,In I.ES::i IS" N"'ct,lAl

: IS(;!>ROJ U .. LEfH CX .. 1A•l rT 3, CT: lTOC lAJ lJO h PP.O!)( 1' ,.[T: 1T3( lA)]X))

s

s

s

. s

- 5.87-

•929?

+tr929Z

x ~

x 41

N a

TS

T6

SATZZ91

:= SATZ277(tT:CX)[U:CXlTSCT,uJ, lEFTCCXrlA~l#TJ,[T:tTD<lAJJX))

::: TtUSHCX,PROOOA,. t r:! .,.0( lA) lX h X • PRCOCt.LEFTCCX•l&~l,T!,(T:lTOClAllX>J, T4.TS)

:: TRIS(CX,?WCX,lRL,INTRL1,LEMMA2?1l• PRDDC1A~.929l~,[TI1T0(1A"•929l•JJXJ•X• T1".9Z91 .. ,TG ... 9291•)

CY:CXltM:R[ALJCMI:INTRL<~l J[Q:O~CA~D<NISCX,OC>•NIS{Y.QC)J,POSC~lll

tA:ANOCNISCX•~Cl,NISCY,OClll T1 :: AtDtHN!S(X,QC),NISCY,QC),.A) T2 ·- AN~E2tNIS<X,OCl,N!S<Y•~ClrAl T3 :: SAJZ2210(X,y,.Jl,T2J

LEMHA292A

LEI1!fA2?28

LEKMAZ9ZC

UUNAT] NR T4 n

PO Tó

NO

TT

T8 T9

no

T11

Nl Tl2

: = THT .. t... OR•UNlH NI 5( x,. OCh NIS< Y•OC) h POSCHl,NIS(X,OCJ,.O•CT:ANOCNIS<X,OCJ, ~IS(Y,QC}Jjr1~.929ZwCTl)

:: TH7•t.OR•CANOCNISCY.,.OC)r~ISCYrOCJ)r POS( !U,. NIS('(, OC J,. Q, Cï! AlfiHNI SU•OC ),. NIS<Y,OCJ1JT2".9292•<T)}

:= TH7•t...aR•(ANOCNISCX,.OC),NISCY,.OCl), POSCM),N!SCTSCX,YlrOCJrO• (T:ANOCNISCX,.OCJrN!SCY,.OC)Jl n•.n9z•<r>>

:= RLOfNTUU :: NArt NT.RL<NRr NATRLI (N)) ·- ORIZCNISC~rOCJ,POSCNRlr

NATPOSCNRrNATRLICNJ)) ·- P'!ICX,.IlRrT1uT5J := TRISCCXrPOClJ,.PWCXr1RlriNTRllr

l.EMHA291CX)J,X,.IS?WlCXrXr1RL, REFISCCX.IJ,INTRllrT5ClJ,lEKMA29l(XJlr SATZ27HXl >

·- NTOfRt.C llRr POSINT NA TRL( NRr NATPOS (NP,, NATRli<N JhT4))

·- TRIStNATrNrNTCFRLCNRrNATRL!(N)),NOr IS~TRLl(N)riSRLENTtWR.NATRLI(NJ,NR• POSINTNAT~L!IR~~ATPOS<NR•NATRLICNJ), T4l,REFtSCREAL,NRJ>l

. := LESSiStz•N•<N•ADrT7l := PCSEXPCX,.NR,T4.TS,NATPOS<NRrNATRLl(N))

) :: ISSMPR{[T:CXJtU:CXJTS(f,UJ.~Or

tT:lT0(N0)JX.NPT7l

:= TRIS2CCX,POoPRnOCNoCT:1TOCN>JX)r PRDO(NO,[T:tTO(NOJJXJ,f9•Tl0)

::: PL•:-I"<N•l> ;: lESSISI1•N•(N,Nl~SATZI8A(N.!)J

ISC?R::J) U .. u:nt CX .. U•l•T3• [T: 1TOCl.U JX> hX)

I S<PROJ <lA• (T :1 TG U AJ l XhlC l

NISCX .. ) CJ : NISC Y .. ) CJ : NISCTSl x,n .. OCJ

: QR(NISC XrOC hPOSCMl)

: REÁL : INTRLU R)

OR<'HS( x .. oc hPOS<NRH ex

: IS(F'0<1 ),X}

NAT

Is-N•n ,NOl U::SSIS•N•(N,.NO>

IS<POr~ROO<NO,[T:lTOCNO)l{))

IS<PROJCN,LEfJ{CX,NO,WrT8otT:1TOCN0)JXlJr PiWD<,.l ,.[T: 110( NO)JX))

IS<PO ," ROOC "" n: 1TO(N) lX)) NAT LCSS IS .. ~"(N,Nl)

s

s

$

s

-5.88-

T13 . -

T14 :: Tl:i ·-

TlS == y ~ (N:"lo\T l

?'lGP1 ·-y ; T! 7 :=

Tl3 :=

N • [P: P~Of'l( N)] T19 ==

rzo ·-

TZ1 ·-

TZ2 :=

T23 ==

T24 :=

T25 ·-N ~ T2G ·-0 - PR:JP2 ·-

[!':P'JSOOl T28 ·-MJ ·-T29 ... T30 := T31 ·-

SATZZ?B<CT:CXJ(U:CXlTSCT~u>~N,

CT: 1 Hl C:'il > JXJ

ISTS1CPOoPRO~CNo[T:lTO<,>JXJ,X,Tlll TRIS2fCX,?~00{Nl,[T:!r~CNl>lY.>~

T S< PC • :0 • r SC PnGJ ( N• CT: 1 TQ ( N lJ :o' X h T13rT14) TR!SCCX•POC~1lrPRC9CNlo[T:lTGCN1llXlo IStPOoX>oT1l(Nll,lt5J

IS<PG<TS<X.~J.~>rT~CPOCXoNJoPO(T,NJ))

ISfSl2(?Jrx.1'·X·PO~Y·l>•r,rscx>.TGCY> )

TRIS2(:X,?OCTS{XoYlrl>•TSCPO<~•l>• POCY•l>>•TS{XoYloTS<TS(XrYlloT17)

ISTSl(DQ(TS<XoYloN),TSC?O(X,N),pQ(Y,N) loTS<XoT)o?l

TR3ISCCXoTS<TS<POCX.~>~POCToN)l~XJo TSCPOCKrN)•TS{P~[ToN)ri)),TSCPGCXoMlo TS(X, POC 't, :o) ), TSCTSCPO{':(,!; >• X),

POCY~N)J,ASSTSlCPOCX,~J.POCYo~lrX>• ISTS2tTSCP0CYoNloX)oTSCXoPOCY,N),, POCXo~lrCC~iSCPOCYoNlrX>>• A SST S 2 CP IJ C :<. ~~ l, X • P \H '!', ~ ) ) ) TR3IS<CX.TSCTSEPOCX•~>.PO<Y•N>>• TS{;(, y)), T S< TSCTSCPOCX,'lloPO<Y,N )),.IC>~ Y>oTS<TStTSCPOCX•Nl•X>•POCY.NJ)rYl" TS(T $( POO::.N J. X), T SC PO< Y, ~~),. Y>), ASSTSZ<TSEPO(X,NloPO<Y•N>>•X•Y>• ISTSlCTSCTS<PO<XrN),POCY,NlloX), TSCTS!POCX•NlrXl.PO(YrNlloY,TZOJ• ASSTSl<TS<PO(X,NJ.XlrPOC~oNlrY))

TR3ISCCX,POCiS()(,y},N1CN>>• TSCPO\TS(X,Yl.NloTSCXrY)Jo TS<TSCPO(XrNlrPOCY.N)l,TS<X•Y>>• TSlTS{PO<X•NloXl•TS<PO<Y,NJ,Y)), T1SCTSCXoYl•Nl.Tl9~TZll ISTS12CPOCX,N1CN)),TS<PO{Xo~J.X),

POtY.Nl{N)J,TS<PO<Y~N>oYloTlG<X,NJ•

TlG<Y~ ~n >

TRISZ< CX.PO< TS( X• Y>, N1 00 h T SCP()()(, Pil<N l hPO<Y, :HOl>> h TS{TSCPO(XoN)oX),TSCPOCY~NloY)),f22• TZ3> ISP<NATo[T:NATJPROPltT>•NlCN),<N>SUCo T24• SA TZ4HN )} INOUCTiGNC~T:NATJP~OP1CTl,T18•[T:NATl (U:PRC?1{TlJTZ5<T•Ul•N> IS{PW(TS<X•Yl,KoMI•LEMMA292Clr TSCPWCX~M.~I·LEMHAZ92Alo

PH<rrM,Miol~MMAZ92B>>>

POS!NfNATRLCHoPoMil NTOFRLO!,i28l IS':UHH!",728l ISRLt.IT20t.>T23> ISPH2CTSCXoY)oHrNRCHO>•T29~Mio T4,TSCX,fJ,HO>oLE~~A212C.T5CTSCXoY>•

I SCPRO) OH• (T: 1 TO<NlJ J X> oT SCPRC!H N•LEf TC CX •Nlo N• TlZ• CT :1 T 0( N l> l X> h X > ) ISCTS<~OoX)oTSCPROO<N•(T:lTO(NflXloXl>

IS<?ROJ CN1r LT :1 T CC NUl)(), T S( POoXJ >

ISCf'O(': lloTSCPO< NJo X))

'PR:l?'

PROP 1 <1 )

• ISCTS<~O<TSCXoY>•NloTS<XrYll.TS<TSCPO(X,N>,POtTrN>>• TS\X.rYJ))

I SUS Cf S(PO <x, N hPO <Y, NJ h TS<Xo Y )) .. T S< TS< PO< x, N h XJ, TS<POCY •NhYJJ)

ISCTSC'OCX•Nl(NJ),pQ(YoNl(N)J),TS<TS<PO<X•N>•Xlo TS<POCY ,NJoYlH

PROPl('l 1CN>)

PROP H< N>SUCl

PRO? 1

'PROP'

riATRL<'I > NAT

· rs"~ .. <'I.NRO!Q)) : lS•R•(t ROIO ),H)

- s. 89-

•9292

+929:1

TSZ

TSl

TH

f55

T56

T57

rsa

D a SATZ292

. ; UURE:ALl LEI'lMAZH [Hl: INT RL( KJ l

Tl

Hf TZ T3

T5

: ,-::;: NEGEXP( TS( X• '() • }!•MI •lE ~MA 292C • N>

::-c: ZSOVI2Clt•TS(lC•1Cl•PWtTS<X•Y>•A8SCK)r T :Sór Tt. H, iS< PIH X,AI':ISU!.) • T :SG .. f41J • ?iH 'r, .1,350! h T 3&• 1'42) > • S AT Z22211( 1 C) • 147, TSO, TSH

:;"'t: TRIS(CX,PH(TS<X,Y>·~•MI,LE~MAZ92Cl• DVt1C,fW{TSCXrT>r~6S(M),T3~,T43},T50), OVtTSClC•lClrTS{?~CX•ABSCHl.T36.T4lJ• PW(YrASS<H>•T36.T42}J,T5ll•TSZ,T53)

=~ ISTSl Z<!'lH '(, H,.lH ,.u:~MA292A h 0V(1CrPW[I?ABS(MJ,T35oT41J~T48), PiH Y,; M·MI• U: :-;)1429213} rOVC lC•PII( y, ABSOO r13&rT42JrT49),NEGEXP(X,H,HI, LEHMA29ZA;N)oNEGEXP<Y•M,MI,LEMMA29ZS• !i))

:;r: SATZZ47<1=,p~(X,.ABSCH),T3&,T41),.1C• P~<Y•ABS<MltT36•T4Z>•T48rT49J

:s TRISCCX .. TS{PW{XrK,KI•lEMMA292AJ, PW[ Y, K, MI, lE !-!'~AZ 923 J h TSC01(lC•P~(X,A35(H),f36,T41JrT48l• OV!1C,P~(y,.ASS(HJ,T36,T42)•T49)),

OVtTSC1C~tCJrTStPW<X•ABSIMJrT3&rT41lr PW(Y,ASSCHJ,T3órT42)JrT51JrT55rT56)

:• TRIS2!CXrPWCTS<XrYlrHrHI,lEKMA29ZC>r TSCPI<X•~rMl•LEM~A292AJ• FiiCY, !h 14!. LE MMAZ 929 l ), iJHTS< lC ,tch TSCP~<X•ABSCMlrT3&rT4ll"P~CYrASSCH)r

f3&,. T42) h T51 J,T54rT57}

:• RAPPCMrPROP2•.9292•,tr:~OS(M)] T33~.92~2*<Tlr[T:ts•R"{M,O)l

IS(PWCFS<X•Y>•~•MI•lEKIA292C>•OVC1C•PWCTS<X•Y>•A8SCMl# T3!;:,T43 ),TSOH

ISUlVH c,P\1 <TSO:• n,. :.as on rT35r T4 n .. TSO hOVC TS( lCdC h TSCPW(~,A8S(M),T3ó,T41J,P4(Y,ASS(M),T36,T42>),r51l>

: !SCPH{fS(X,Y> .. ~.~IrlEMHA292CJ,OVtTS(lC.tC>• TSt?W(~,ABSCMl.T36•T4l),p~(y,A3SCMl,T36rT42J>,TSll)

IS<TSl,V(XrMrHI•LEKMA292AJrPW<Y•~•MI•LEMKA292B1J• T~(~VC1CrPI<XrABSCMl,.Tl&,.T41J,.T46Jo0V(1C•P~CY,.ABS<Mb

T3ó.T42hT49Jll

IS{TSClV<lC•PW(X,ABS<M>•T3&rT41JrT48),QV(lC•PWCYrABSCK) .. T36rT~2),.T49>JrCVtTS(lC,lCJrTS<PW(X,AES(HJ,T36,T41>• Pli(Y,. A~ SOU" T3&,. 142) h TSU l

ISCTSC~WCXrH,HI .. LEHrA292A)rPWCYrMrMI,LEHHA292BJ)• QV<TSC1C•lC),TS(PMCX .. ASS<~JrT36.T41JrPWCYrABS(HlrT36, T42) hT 51))

: PROPZ

T35•.9292~(T)r(T:S(6{MJlT58".929Z"<TJ) ISCPWCTS!X•Y>rM•MI .. LEKMAZ9ZClrTSCPW<X•MrMirLEMHA292Al• PII<Y • Hr 111 •LEKMAZ92B))) .

:t• 0RI1CNISUC.OCJ .. POS0th1NO.TOJ ; ORCSIS[ lC .. OChPDSCMH

:• ORI1CAND(NISC1C•0C},NISC1C,QC)),p0S(M) ,ANOlC~IS(lC•OC>•NISClC•OCl•lNOTO• 1NIHO> l

:• PW(lC•M•MI•LEMMA293) :• SATZ222<110 1• ISP~l(lC.TSC1C•1ClrM•SATZZZ2AC1C),M!•

lEMMlZ93•LEM~AZ92C<lC•lC•H•HI•T1)) :s SATZZ92( lC•lCrl':,!fl;T 1)

:• ISTS!Z(Pk!lC•H•Hi•LEMMA292A(lC•lC•M• HI•Tl}),IM.PWClc .. H.HI.

OR<ANO[ NIS( lC .. OChNIS< u:.3CU .. POSOO J ex

: ISCfS(lM;1C),1M)

ISUM•'" 'li<TS ( lC•lChH•MI•LE: MMA29.2CUC,1CrM• I' I • Tl J n IS<PK<TS<lC.1C),!'.MI•LEHH,Z92CC1C•lC .. H,MI,T1J); JS(PW(lC•M•MirLEHMA292ACl:•lC•M•H!•TllJ• PK<l C ,.!'I,Hl,l.EMMA29ZIH1 CrlC .H.IlhTl))))

s

$

-5.91.-

•9291

TS.

f7

lEKMA29ZB<lC.lC•M•MI.Jl)J,lM• IS~HlClC•lC·~·REFISCCX•lCl•Kl• UHMii292A< lC, !C, !h rl! • Tlh lEXMA29 3), ISPMl(lC•lC•~•REFISCCX•lCJ~?I• LEMKAZ92BllC•lC.H,HI.TlJ,LEMSA293J)

·- TR4IStCX,TS(1H•lCJ.lM•PWCTS(lC•lCJ,H• MI.LE~~A?.92C(1C.lCrM,MI•fll1• TStPH~lC•M•"Ir~EMMA292A{lC•:C,M•Ml~Tl) JrPW[lC•~•MJ•LEM~A2923ClC•lC•H•Ml•TlJ) ) , iS.~ 1 K.- ! H } .- T 2,. T 3 P 7 4, T 5 )

:: TR!S(CX•TSCl~•H~(l~•lC)J,M~CTSClM•lM), TS<l~.:cJJ.~C.DISfTH2<1~·l~•lC>• SAïZ21JiHTS\ illo!U·T5(1":•1Ch SYKISiCX.TS!lMo1C),TS<lMrlM),T6)))

:: OREZ<:S{lM•0C)•ISCMNC1M•lCJ•OCJ• SATZ221C<1M~K~ClH,lC),J7),

SATZ290(1C•M•MI•LEMMA293•1NOTOJJ

SATZ!93 :: SATZ213AC1M~.9293•,~c.re•.9293"J X ~ [M:REALlCM:REALl(MI:INTRL(M)][NI:I~TRLCN)

l(O:aRCNIS(X,OC>•ANO<POSCMJrPOS{N)l>J

U :AN!)[ POS< K).o POSC N))) T1 I= AND[lCPOSCK)•POSCNJ,A> T2 := ANOE 2( POSC tl h PDSCN hAl T3 := POSPL<M•llh•T1•T2>

LEM!'I'A294A :: THB•t.OR~(NISCX~Ocl,ANJCPOSCMJ,.POS(N)) •POS(M),Q,.(T:ANDCP~SCHJ,pQS(NJll

ISH S<" SI ClC, ?!•Hl• i.E t'ICA 29Za. HC. IC, lf .. lH, TU h P WU C.lf •MI• lE"':iA292 B<l C•l:::, lof. MI~ T 1) J h TSC lh• U!J J

IS<TS <1 M•lC hTS (lM, HOl

: P0$('4} POSCNJ

: POS(PL"R .. CM.tU)

Tl".9294'"<T>> : OR(HIS(X,.OChPOS(M)) lEMMA294B

LEKHA294C

0 ; PROPl

A a Ml Nl Tlt

1'1

rs

:: THS•t.G?•<NIS<X•OCl•ANOCPOS<M>•POS(NlJ .PGSCN>?O.CT:ANDIPOS<M>,POS<NlJl TZ ... 9Z94•CJ)) : OROUS( x .. oc hPOSUU)

:= THS•t.OR•<NIS(X,QC),A~D(POSCM>•POS(Nl) •POS{~L~R•<M•N>>•O~IT•ANO(POSC~>• POSOi> )JT 3•. 9294 .. 0 J l OROUSC X,.QC hPOSCPl.,R'"(H,N )))

:: ISCTSCPW(XrH,KI•LEHHA294A), PH(X,N,NI•LEM~A2948}J,?~(XrPL"R•CHrHJ,

INTPL(~•MI•N,Nl)rLEM~A294Cl) := NTDFRL(M,POSINTNlTRLC~-Tl,HlJJ := NTOFRLCN.POSINT~AJRL(N,TZ.NIJJ :: ISTS12(P~(X,M.KI,L~M~A294AJ•

PR00{M1,[T:tTO(H1JlXJ, PlH x,. !h ~U • LE Ml"A294a h PRODCNl•tT:lTCCNlJJX)• POSEXPCX,HrM!,LEM~4294ArTll• PCSEXPCX•I•NI•LEMNI294S,T2J}

:= NTO~RlC,L•R•<H•Nl•POSINTNATRlCPL•R* (K,N),T3,I~TPL(M,HI,N.NIJ))

:: POSE~P(X,PL"R•c~.NJ•I~i?l(~,MI•N•NI).o lEM~A294C• T3)

: 'PROP' : NAT

NAT

ISCTSC~WCXrH•HI•LEHMA294AJ,pW(X•NrNI•LEMMA294BJl• TS<PROJ OH.CT:lTCCHlllXlrPRIJDCNt.(T: 1HCN1 JlX)))

: NAT

s

s

- 5. 92-

ió

T7

T8 T9

TlO

Tll

TlZ

T13

T14

·- TRISC~EA ~PL"R"t~•~>~Pt•R"<RLCFNTCMl>~ R~~FNT<N '>~RLOFNTCPL~N•(Xl~Nl>>• ISPL12"R CH•RLOf!'<HMl>•N~RLOfNHNl)~ IS~L~!l{l~~~OSINTNATRlt~.Tl.M!))~

IS~~~T1<M-~C5INT~,ATR~(N•T2•X!)lJ• ~A7ZR155tJ(;Jl,.~l.J i

:= TRIS21~AT#PLRX~C~l.~l1~P1# NT~~~l!RLOFN![PL·~~C~l#Nl))~

:~:T?~!Y.:~z,N,NI)'~~LCr~TCPl"~~(~l,Sl))

,N~T~LI(PL"N~(t1l,Nlll•T6})

:= LESS!SI2•N•[pL·~~C~l,~llrPl~T7J :~ !SS~?R((T:CXl~U:CX1TS(T,u:,?1,

[T:IT~{Pl>JX~Pl"N•t~l~Nll#T7)

:= TR!S2CCX,PlHX.oPL~?.•(p.o,'i)# IP:TPL(~,MI,N•N!J,LE~'!A294C},

P~C~\?L"N•(Ml~Nlï.rT:lTCCPL"N"CMl.oNl )) 1Xl,PRJJ(Pl.o(T:lTO<?lllXl,T5~T9l

:: LESSIS!l"~·CMl~Pt"N•(Hl~Nll• SATZ13M Ml.•Nl >)

·- SATZ281C[T:CXJ[U:CXJTS(T,U>,ASS0CTS• Hl,Nl#(i:lTO(PL"~~cMl.oNllJlXJ

:= TRISCCX.PW(X,PL"R•(H,n>, II\TPU M~ MI•N• NIJ .. LE!'l~A294C J. PR~O<fL•N~{Ml#Nllo[T:lTDCPL•,•(Ml,Nll)

lKl•TS<PRCJ!~l,[T:!TCCHl)JX),

PR30C~l.o[T:1TOCNllJX)loTlOoTl2)

•- TP.IS2CCX,TS<PW(XoMoMI•LEMMA294A)• PW(X,N,NI.LEMMA294B)J,PW<X•PLnR"CM.N), INTPLCM.HI•N•Nil•LEM~A294CJo TSCPROO!Hlo[T:lTCCMl}JX), PR~JC~lo[T:lTOtNlllX)},f4•Tl31

0 ~ CNA:NQT(ANDCPOS<Ml.POSCN>l>J Tl5 ·- ORElCNISCX.OC),A~J(PCSCM),pQS(Nll•O•

NA> Tl& ·- THtS•L.oR•cPOSCHl•POS<NloNAl

0 ; AM :: ABS{Hl AN ·- ABSOH AP := A95(PL•R•(HoN)) T17 ·- IN!ABSCM,MI) T18 •- INiA35(N,Nil T19 •- INTA9SCPL"R•(M,N>.INTPL<M,"I•N•Nl)l

NA a [NH:NEGCM)J[NN:NEGCNll TZO := AND!CPDS<AHloPOSCAN),

T21

TZZ TZ3 T24 125

SATZlóó(CM•NNOTO(M,~Mi),

SAT:l&&ECNoNNOTO<N.~~))) ·- CRt2{~!SCX,OCJoA~:<Pn5<AH},POSCA~)),

Té:Cl ·- LEKMAPW3CX•~•HloLE~~A294AoNM) = lEMMAP~3CXoNoNI•LE~~A2949•NNJ = l~M~A294ACX,AM,A~•il7,TlS•T21) = LEK~A2?~eCX•AM.AN•Tl7.T13rT2ll

PROD<PloCT:1TOCP1JlX>>

Is·~·<'L"N"CMloNlJ.oPll LESS I s• N• {Pl"S"" C Hl• Nl) ,pl)

ISCPROJ CPL" ~·on .Nl hLEfTC CX.Pl,PL "N"( Ml•N 1 h T8, [T:lTOCPl>lXJl•PRDO<Pl•CT:lTOCPlJlXJJ

ISCPWC{#Pl"R"<M•N>•INTPL<~·~I•N•NI>•LEM~A254Cl• PROOCP."N"CHl,Nll•[T:lTOC?L"N"(~l•NlJllXJJ

ISCPROl CPL"N•on •Nl >• ( T:tT O<Pl"N"O! t.Nl)} lX J. TS CPROJ t!'ll# LEFH CX• Pl." ti•0!1,N1 J. M 1, T 11• [T:1TOCPL"N"CMl.~l)JJXJ),~RGDCN1.RIGHTCCX,~l.oN1, n :1 !Q[ PL "N"< Hl• NlJ )]X)))}

ISCPW(t,Pl"R"{H,Nl.INTPlC~.MI,N,Nil.olE'-MAZS4Cl•

TSCPROJCMl,[T:lTO<HlJJXJ,PROOCNl•[T:lTOCNlJJXJJJ

PROP 1

N ISC X ,3 C) OR<NOTlPOSCHJ),NOT<POSCNJJ) REAL RE:-.L REAL HIT~ UA Hl I:HRL<' Nl Ii'HRUA P)

OR(~ I SC X ~oe b !.NOC POS< A HhP OS<AN))) CRCNISCXrOC>.PCSCAKJJ ORHHSl X•OC hPOSUN)) ORC~IIS[ XoOC ),POS <AIO) ORC'HS[ X•OC >•?OSCAr-DJ

- 5.93-

UV\1~,~~\A•A~~Ila•iC,1•!~~~~,

OV\TS<lC.1ClrTS(?~(X~~~.Tl7,T22l•

pw~x.An~rta.rz3>>.~3:l. CV(lC·P~~X.Af,T19.ï3aJ,T35), PN(XoPL·~·cM-HJ,[NTPL[M•KI,N•NIJ•

lEM~AZ94C)~T3SrT3a,T3?,T40) : PRO~l ~A~ [~~:~os<~>lCNN:NEGCN)J

Tt.Z ·- .LEI'I"!.\PliHX,.N,)IJ,U:~~A2943,tPO : ORr'HSl r.,OC),.POS<UJ> T43 :• LEMMAPWl[X,AN,Tl8•T42•SATZl&&BCN•NNJr

LE~MA?~2(X,~.NI•LEMK~294B•NNll : N!S(PNCI•A~•Tl8•T42l•OCJ

H5

H6

UT

[CASEA:KG~ECM,AN)l

T48 Tt.9 T50 TH

T52 T53

T54

T55

T56 T57

T58 T59

TóO

T61 T&Z

•- lSTS2(P~CXrN~NI,tEM~A2P43J• 0~(1C,P~tX.AN,T1B,T42),T43),

PWCX•~·~I~LtM~A2944l• ~i: GE)(?( l(,. N, N:l:• LE!nt. 2 943,. NtO l

:= SATZ244A(PW(X,K,.Ml.LEM~A294AJ,1C• Pif( x. 1\N, T 16, T4 2>.· i4 3 >

:: ISOVltTS(PW(X,M,M!,LEMMI\2941\),lC), P~CX•~•~I,~E~~A294~l~P~<X~AN.T18•T%2)• SAïl2Z2CPW<X•~~KI,LE~~A294A>J.T43)

:= TR3IS<CX,TSCPW{X,K,~I.LEMMA29~A)• Pft( X, Nr NX.LE M"t.291't3)),. TS<PW<X•~•Ml•LEMMA2941>• 0VC1C,PW!X,ANrT18,T42),T43))r OVCTSCPWCX•M,MI•LEM~A294Al•lCl• Pf!C X,.A Hr T 16 .. T42J. T lt3 h OY<P~(X•M•Ml•LEMMA294Al• P~<X.ANrT18,T42),T43),f44,T45 .. T46)

·- SATZ1620CH•AN•CASEA) ·- SATZ166E(~,NNOTO(N,N~)) ·- ANDICPOS(A«>•POSCM~"R•CH•AN)),J49•T48) ·- ORI2<NIS<~•OC>,ANOCPCSCANJr

POSCxN•R•<H•AN))},f5Cl ·- INTMN(H,MI,AN,f18> := LEMKAZ94A(X,ANrKN"R~tM,AN),Tl6,T52•

T51> •- tEMHA294SCXrAN,HN"R"CM,AN>•Tl8,T52,

TSl> :: LEM~A294CCXrAN.MN~R"(HrANl•Tl8•T5Zr

T51) := INIPL<A~.Tl8~KN•R•CH•A~J,T52J ·- T14{ x:, Afo .. MN"R .. CM.AID, TtS,. TSZ,. T5ll• T5i) l

:= SATZ187A(MrAN) := ISP~2CX,PL•R~<AN,MNwR•(K,ANl>~H,T58•

T5GrHirT55rlEMMA294AJ

•- ~RIS(CX,TSCPH<XrANrTl8rT5J), PW{X,~N·Re(HrANl;T52•T54))~

PlH Xr PL .. R"'\.Hir KN,.R• ( KrAN)}, T56, T55 ), PWCX•~•Hl•LEM~A294A)•T57•T59)

·- ISP~lCX•X,AN•REFISCCXrXIrTli~T5J•T42) :: !SPl<CXP{!:CXlN!SCT,OC)~

PH(XrANr718rT42)•P~CXr~N,T16rT53Jr143• TóU

:= ISOVlZ<TS(PW(X,~NrT18rT53)• P~(X,"N~Rw(M,ANJ,TSZ.T54)),

IS<TS( 2 W(X,M,~I.tEM~A294AJ,PWCX,~rNirLE~MA2948)},

TSC?W{(rH•MirlEMMAZ94A),Q#(lC,PW(XrAN,T18r1421•T43l))

: IStrSC,W<X~M,KirlEM~A294Al,OV(lC•PW(XrAN.T18rT42>•T43)J ,QVCTStPWCXrH,~I•LEMHAZ94')•1Cl•PWCXrAN;Tl8rT4ZJ~T43))

IS<aV<rSCPW{X,M•~I,lEHMA214AlrlCJrP~CX,AN,T18•T42l•T43) rOV{PW[ ~.MrHI•LE~PA2941\),~WCX,AN•T18rT42lrT43J)

: IStTSC 2 W(X,M,MI,tEM~A294A),pwcx,~,NI,lE~HA294Bl>• O'HPW (I( ,H,M I •LEHMAZ94A > ,pif (X,. AN,. T 18, T42 >, T lt3))

PO SOU, .. R .. CM, AN) > PCS( A Nt ANOtPDi<AN)rPOS{HN•R•(H,A~)))

CRCNISCX,OC),ANO<?OS(AN),POS<MN•R•c",A~)))) INTRLCIII N'"R .. O!rAN)l

ORCNIS[ x.oc hPOStAN U

OiHN IS[ X,OC >rPOS O~N'"R .. CM,~ N > >)

OR<~IStX.OC!.POStPL•R•CAN,MNwR•(M,ANJ)))

I~TRLC~t·R•CAN,~N·R•cM,ANJ))

JS(TSC~W(X,ANoTl8rT5J),pW(XrHN•R•(H,AN)rT521T54)J, Pil CX, PL. •R•( AN,I'!N"R" 0~. ANU, T5&,. T55))

: IS""ït.,Pl"R•(AibKN'"R~cH,.AN) hHJ

; ISCPWClrPt•R•<AN•~N"R"(M,tNJl,T56,.T55)~

PIHX,M, MI,LEMMA29U))

: IS<TSt~W(X,AN•Tl8•T53),pW(X,KN•R•(H•ANl•T52•T54J), PWCI,.K,HI~LEM~A294A))

: IS!?W((rA~,J18•T53lrPW(X•'N•Tl8•T42})

-5.95-

T&4

T65

T&6

T67

T&8

T10

T11

T72

T73

NN ~ [CASEC:LESS(K,ANlJ T74 TTS T7ó

T77 T78 T79

PVC X, "1, Mh LE: 1'!1A294A l, PIH X, Al'h T18,. T'S3 h P~(X,AN .. Tl8,.i42J,.T50,T&l,.Tó2•T45l

•- T~ISZtCX,TS(PI{X,"~M!,.LEMMA294A),. PWtx.n.~I•LE~~~2946JJ,. 0V(T5{P~(IrAN,.TlB,.TSJJ,

PWCX·~~·R·(~rAN)rT52•T54)},. PWCX,A~·TlB,.T53:,r;zJ,.

DV(f~(S,.H,ri•lfMMl2F4A)•

PW[K.~~ .. 718,T,2J,.T43)~f47,.T63l

•- SATZ229H[TSCPWCX,ANrT18,.T53),. P~iX•YN•R•(~,-nJ.TS2,T54}1• PHCX.ANrT18,T53),p~(X,HN•R~CKrANJ,.T52,.

T54J,TS2,?.Sf~SCCX,TSCPW(X,.AN•T18•T53)r PICX,r~·R·(~,.A~>~T52ri54)))}

·- TRISCREAL,.MN·~·!M,.A~J,MN•R•(M,MO"R•<N> >•PL•R•cx.NJ,JS"KZ•R"CA~,.MO•R•(N),~, A35~(~.n~JJ•ISPL2RR•c~~·R"(H0~R·CNJ)• Nr M,. SATZ177C 10))

:: ISPHZ<X·~~ftR•(M,.AN>•PL•R~(M,.N1rT66, T52,.1NTPLCM,.HI.NrNIJ,.T54,LEHMA294C)

:= TR3IS<CX•TS(PW<X•M•Hl,.LEMMA294A)• Pli{X,.N,.!H,.LE:MHJ\2948 > h tlVtTS< PiHX .. A N• 1'18• TSlh PII'(X,.H~"Rw(H,.AN),T52,T54)),

PW( x. At:, f18, T53l,. f62 >• PlH Xr HN•R•{MrA N) ,ï52rT54),pW{X,.Pl"R"CM,.N), I~TPLCM,.MI,.N,.NI>•LEM~A294ClrT64rT65,. T67)

;: ISPW2!XrKrAH.CASE3•M!rT18,.LEMHA294Ar

IS<O VCT S(Pif(X,. AM • Tl 8r T 53 Jr PWC X .. HN"R"( M • ATO • TS2 • T54 J J. PW(X,.A~,Tl8,T53Jrf62l,.OV(?W(X,.~ .. HI,LtM~A29AAl• PlHXo.A'f •Tl6,.T42J,.T43)) .

ISCTSC~H(x,M,MirlEM~A294AJ,.PW{X,.N,NI,.LE~MA294BJ),. 0V(T5(3W(X•AN•Tle,T53),pW(X,.HN"R"(M,.AN),f52,.T54)), PWCX,.A'f•Tl6•T53),T62>>

ISC1VCfSCPW(X,.AN,.T18,.T53J,PW(X,MNwR•<~ .. AHJ,TS~rT54)),. PII'CX,. A 'i, T18, T53), T& 2), PWCX, MN•R .. Oir ANJ "T52r ;'54t)

ISCPW{(,MN•R•(M,.AN},.T52•T54JrPW(X,.PL•R•CM,~Jr

lNTPL(If ,.MZ, N;NI>rlEI'MA294C))

: PROPl

T42} ISCPlHlC •H•M I "lEHHA294A),. Pll UrAfC.. T18,. T4 2)) .- SATZ251A(PW(XrM,MlrlEMHA294AJr

PHUrA N .. ne,. T4Zh Hl, Tó9 J ISCDVP lHXr M. KI..LEMI'A294U ,pvcx,.ANr f18,. T42 h T43),. lC) :: TRliSCREAL•Pt•R•(M,NJrKN~R•(HrMO•R•(N)

JrMN•R•<M,.ANl,.O.ISPLZ•R•(N,MO"R•(KO•R• (N)),H,.SATZ177A(N1lriSHNZ•R•(HO•R•(N},. AN;K,SYHISt?.EALrANrMO•R*(NJ,ASSN(N,.NN) )};5kTZl6ZE<HrANrC~SEB>J ts-a•c•t•R•(K,.NJ,OJ

::: SY:-IISCCX,PlnX,.PL .. R .. (M,fH• lNTPl(M,.MlrN•~IJ,.LEMHA294Cl•lC• OEXP(X,.PL•R•CHr~),INTPLCHrHirH,NIJr LEM~A294C,.T71ll : ISl1C•~M(XrPL•R•<M•NlriNTPL(M,.Ml•N;Nl),.LEMI'A294C))

:: TR3IS(CX,TSCP~(X;~rHI,LEMKA294A),.

·-:: ::

"' :

PiH )(, N, tH, LE Mt<!A2948) h OV<P~{X,X,MI,.LEKHA294AJ~

PW(X,A~•t1S,.T4ZJ•T4]),1C• PWCXoPl~R~(H,.N),.INTPlCMrMI,.N.,NI>• lEHMA294CJrT47.T70,T72) : PROPt

SATZ182DCAN•H•LE~~A2•R•(H,A~.CASECJJ ANll(PQS{M),P0SCMN•R•CAN.M)),pH,T74) O~I2C~!SCX•OCJ•A~DCPDSCM), POSCMN"R"<AN.~))J,T7SJ INTHNCANoT18•M,MtJ lEMMA294ACX,M•M~"R•CA~ .. MJ,.MirT77•T7ó) LEM~Mé!948{ ~' H,. '<'l"f!"( AN • •1 h 14!.• T 77,. T 76 J

POS( HN• R•CAN,.M J) AnOtPU5{MbPOSCMN•R•CANrM>JJ

ORn I SC x,.oc l.. ANCCP(}SC K ),.p() S(HN•R•UN,M)))} INTRLC~N•R•(AN,.HJ)

O?.HHSt X•OC ),PQSO!)) oqcNIS! Xr0C),P0S{M~·R•(AN,MJJ)

- 5.96-

I OU

T81 f61A

T!!Z 1'81

T64

T85 Taf> T87

ra a T89

T90

T91

T92

T93

T94 T9U

T95

T96

T97

T98

T99

noo

\..C.·"l,'11-\G.;T .... ,,,,.n,t·u• n \.n:•''-'"'""''''t'f':tJ~I • Yi''-~11&V' 1\'VVI,rll.lltll'' ._ n \,lfJII'.-1,,. n. '·nn..-n~lll#

:: INT~L(~,HI,MN"R•<•~~~)rT77) INTRL( 2 L"A•<M•MN"R'"(AN•H)J) ::: Tl 4t X:• '<• ,_.~l"'R .. ( AN, 1'1; • MI,.! 7 7, T 76·,. T 75) IS (T S <" W u:" !1,. KI,. T7 6 l.. P W (X. MN .. R.• (A li. !1 h T77,. T 79)),

PliCX•P- .. R'"C H•,~"R"tAN,. X})• T8X.·T80)) : = S4 TZ 137 ;.(A~;,~) IS .. ~ .. c~ L .. R .. C I",M~l"R..,.<ANr r;)) ,A lU ::: ISP~2CXrPL•R•(M,.M~~R·cA~.~)),.AN,T8Z,

~6l•Tl;.rao.T42) : IStP~((,.PL"R•(M,MN•R•(A~•~J),.fe1~T60),pW(X•ANrT18•T42)) •- T~ISCCX.TS{?~(X,K.MI,T78),

r~cr.~~-~~cftN.~J.T77.T7g)).

?li~ X r ::>:_•c:: 1 o~. tiN"' R .. L!. ·;,. :.<) h T81,. TSO h P if( X: • ;. ·1. 71 B,. T 1, 2 ~ • T3 P, T 53)

~= SATZ29~(X•~•"!tT7a~T13J :: ShiZZ?D(I,MN•~w(~~·HJtT17,Tr9~Tl5J := s~TZ22Ia<?~(x,M~Mt~rrs·>~

P~lX•MN•R•tA~rM),J77.T77},T85,.T66J

c: SATZ222C~K(E,Hr"I•T73ll ·- ISP~l(i•X•~•~EFISCCX,x>.~I.T78,

LEM,.~2?t.~l

·- rsrsrc;-:.rst?iHX.H.xi.T7ah1C>. PKtx.u.~I•T78},PK{X,~r~I•lEM~A294A),

ras,T3n := ISDV12(T5(P~<X•~·MI•T78),1Clr

PW(X,M,KI•LEMMA294AJ,TS<P~(X,M,KI•T78) ,p~(X~M~·R•(A~.M),r77,T79)),

PW(X,An.T16,T42l•T90ri84.T87,T43>

·- TRISZCCX,TSCPW(XrM,KI•LEKHA294A>• PW()(,. s, !i I • LE MMA2 9'49 l ), 0V{T5(P~(~,H,MI,T78l•lC>• TSCPWCX•M•MI•T7S),p~cx,."n•R"(AN•M)• T77.T79}J,T87),0V(P~(X,K,MI,LEMHA294AJ

,p~cx.AN•Tl8rT42J,T43JoT47.T91}

:= SATZZ46AClC•PW{X,HM•R•CAN~MJ•T77•T79)• PWCX•~•MI.T78l.T86•i85)

·- SATZ182F("•AN,.CASEC> ::: TRISCREAlrHN"R .. (H.ANJrMN"R"(MrMO"R"C~)

J rPL '"R•( Mr ~U~ I SMNZ"R'"'( A "~• MO•R .. CN ),M, ABSNCN.~N)JriSPt2«R•t~O·R•CKO•R«(N;),

N• J>!, SArZ177C 'D >) := TR3iSCqEJL.~~·R•<AN~K>•

KO•R•CM~·R•(M•AN)>,A3S(~N·R•(H,ANJ)•

AP.SATZ181ACAN,H>·SYHIS<REAL, ABS(~N·~·CMrA~}),MO"R•(~N·R·<~•AN)),

ASS~(MN·R~(M,ANJ,Jg4)), ISABSCH~·R·c~,AUJ,pL•R•(K,.~>•T9~l)J

:= ISPCREAL,[T:REALJNEGtTJ,MN•R•(M,AN>• Pl"R~f~•NI•T94.T94A)

:: lE~~APWlCK.Pt-R•IKv~J,INTPL(~,HI•N•Nl) ,LE::•nt:.294C• T9&'

:: LEHMAPY.!(X.AP,Tl9•f97• S HZ l&&'HI>l~ R•( Mr Nh T95 l,. lEi'!~: A;:: ;;zo: ,p l "k'" O!r ~ h I ~Jf•t 0: • Hl ,N .:.;J)

: IS CT SP wc x, lhMI• T7!1lrPliCX• MN•R•(AN.Mlr T77• 179)),. Plrl( X • A'i , T 18 , T 42) J NIS( P nL X • ~ • !'!I • i7 8), 0 C) t• IS( Pif( 1(,. XN .. R .. Ol\• t!)• T 77 • T i9 l ,oe l

NISCTSCPW<X•~"HI•T78loP~Cl•MN~R·<ANoM),T77•T7')},.0CJ IS<TS(~W(X,M.MI•T78JolC>•PW<X~~•~!oT78l)

ISC0V(fS<PW(X,K,,.I,T78l•l:J.TSCPW(X,~.~I.T76), PW(XoM~•R•lA~ .. H)•T77,.T79)),T67},.CVCPW(X,.K•~I.LEMMA29.A) •PWCXoA N .. Tl8•Tt.2hT43J J

ISCTS<,WCX•K•Hl•LEMMAZ94AJ•PIICXrN•NiolEMMA2948)),. OV<TSC 2 WCX.M,MI~T78lolC>•TS{PW(XrM•KI•T78)• f>W(X •l1'l .. R"'< AN,H >. TTT• T ?9)), T67 > J

IS <tlV H S{PiH x, M, M h TTS ),1::: h T SC Pil (X, l'.rq, T7 8 >• PW(X,.M~·R•<AN•HJ•T77,.f79)),T87J•OVC1C•PW(X,MN•R•<AN.Ml•

rn, T79 ". rs&» NEGC MN• R'"04, AfU)

NEC<PL• R"<lhNU

ORCNISCX,.OCJoPOStAPll

,.LEMH~Z9r.;:,t96)) : NIStPIU X.AP,f19,T97h0C) : = ISPifl<X .IHJ-R•( AN• tO, AP• T95• f77 • T19 •

T79.T97) ISCPW(l,MN•R«(AN.MJ,T77.T79J.P~(X,AP.T19,TS7)) :: ISOVZCP~IX•MN•R•<AN•M)~T77•T79)•

- 5.97-

T101

TlOZ

·- sr~tstcx.?a(X,Pt"R·c~~Nl• INTFU "~• l'llrN• NI) •lEl0'A294C),. CVtlC•~~{XrAPrTl9•T97),TJ8>• ~E~EX?CX.PL•R•(M,M),I~TPLCM.Ml~N,~I)• L:::~r:~Z94C" T96J)

:= rq•tsccx.rscP~cx.M.MI•LE~MAZ94AJ. FiH r. • '~• ~i r •. LE M1-!.t.2 946 >). Ci[TSCP~lX•~•~IrT78l•lCJ• TSCP~tx,M.~:.T781·P~tx,uN•R•(ANoH)~

T77,T7;J:,TS7l,QV(lC•?~(X,~NwR"CAN,~)~

T77.T7~}~i:6~rOV<1Cr?~(~,AP.Tt9.T97),

TJSJ~P~CX•Pt"R•CH.Nl•INTPL(M,MI•N•Nll• LE~MA294ClrT92;T9J,T100~T101J

!tN ; T103 :: ::!R3AP?CIS .. !\"( I1•ANl,MORE:tM•ANh LESS<M.~~}.PSC?l;SATZ1&7A(K,AN>• CT:ts·~-(~.~~)JT73(TJr[T:~ORE<H•ANll T63(T}otT:LES~(H,A~}JT1~2CT)}

~A~ [~M:,EGCH)ltQN:POSCS)l NA ; 1104 :: C~I~CNISCXrD:J.AND<PQS(~l.POS(M)),T15)

Tl04A ·- T~s·t.A~D~<POSCM)rPOS(NJrNA) T105 := LEMMA294HXrN,.MrXIrlll•Tl04) T105 :: LE!o!!'!:c294!l{XrNrM,Nf,J1I,T104) TlOT ·- L'E!'l't.2~!,C(Xr'I,HrNI•iH•Tl04) 1108 := ISTS12(PIHY.r Y.,I1Z,.LEH?!.~Z9Uh

T109

oN a nto

NA :J T111

ON a T112

NA ~ CI:ts•R•(Mr0)] T113

T114 Tl15

T1!6

TUT

PWCXrMrHI•Tl06>•PW<X•N•NlrLEHMA2948)• PWCX.~.~I.T10SlriSPW1<X•X•~• REFISCCX•X>•Hl•LEMMA2941rT106Jr ISPlH<X~ X• ~ .. REFI SCC x,x >.rH,.LEHMA2948• Tl()5)}

:: ISPW2(X,PL•R•(N;H},Pl~R•(H,N)r CCHPt•R•(N•M>•INTPL(N•NirH,Hil• IHTPL(~,HI~H .. NI},.T107•LEHMA294C)

:= TR4ISCCX.TSCPW(X,.MrMirLEMHA294Alr PW(Xr~r~IrlE~KA2946)), TSCP~(X•~·~IrT106)rPW<X•NrN!rT105)lr TSCP~(X,N.~I.Tl05lrPW<XrM,HirT!OG))r PWCXrPL•ft•(~rM)riNTPL(~~NI,Mr~I)•T107) ;PWCXrPL•R•<"•N>,INTPL(~,HirN,NI)• lEMMÄ294C)rT1~8•Tl09rT110rT111J

·- !STS1{PW[XrR•Ml•LEMMA294A)r1Cr Pil< X• N .. lHr Lë: MHA2943 )" OEXPC<• Hr~I,. LEI'IHAZ9U, IJ)

:= SATZ2228(P~(XrNrNirLEM~A2948)} := SY~!SCREAL•?t•R•(MrN)rNrPLOl•R•CH•N•J)

)

·- ISPWZO;,N.,f'L .. R"(l>!,.fH•Tl15riHr I 1<T?U Hr11i: ~ ~ • '>I) .LCMMA294 3 rLEMHA294C)

:• TR3lS(CX,TSCPWCXr~rMirLEHMA294A); PV(X•NrXIr~EM~A294B)lr TSllCrP~cr,N,,[,~EMHA2949)J•

: IS(UYtlt•P~(XrM~·H•tAN•M}rlffri79J•TU~J•

OVUc,.:~~wcx, APrT19rT97l rT93 ))

IS C::JV U C•!'>if <X~AP" Tl ç, T 97>. T98hPWUrPL .. l'\ .. H•ID • INT?tc'l ,u., N, NI h•LE~MA 294;: H

PROl' I

PRC?l

ORt~ISCXrOC>~ANO(POS(N)~PJSCM>>> : NOTtiHll CPOSOU.PCS< I')))

0 IHN IS{ XrOC )•POS (N >)

OR(~ISCX,OCJ~POS<M>> OROU St X•OC hPOS<PL "R'"Ui~"t) >>

: ISCTSC,WCX~H~MI•LEMMA294AJrPWCX~N•NirLEMMA294B>>• TSCPlHIC ~K,M X. Tl06), PH <X~ Nr NI• T105)))

: IS<TSC2 WCXrMrMI,T106J,pW((,N,~I.T105)J,

TSCPWClrN,NlrT105J,p~{XrM•MI•Tl~6J)) : ISCTSC,~cx~N,NJ,.J105>•P~((,M,MI,ï106)),PW()~Pl"R•<N,M},

INTPL(11 r:III• Mr MI h T1 07>)

: IS<?WCC.Pl•R•tN.Kl.INTPL<N,Nirl'rMIJrT107), PW<X•P-"R•<HrN)riNTPL(H,MI .. NrNilrlEM~A294C})

IS<TSC,WCX~M•Ml•LEM'-AZ94AlrPW(XrNrNI~LEMHA29481>• T S<lC ,, lH Xr N, NI .tEMI'AZ 946) J)

IS<TSC1C~PWCX.N;N1rlEMMA294BJ)rPW<Xr~•~I~LEMMAZ94B>>

ISCPW ((,. N,.N I• LEI'II'A294B ), P:f (X, t'L •R'"( Mrff h INTPLC~•MI•N•Mil•LEHKA294Cl> - 5.98-

NA ~ ti:IS•R•(NrO)J T118

Tll9

NA ; {?H:~QS(H)l

T120

Tl21

~A ; [S~:NEG(H)J

Tl22

'fA a Tl23

0 a SATl294

NI a fO:NISCXrOC)l LEK~A295A

LEMHAZ958 LEHM!\.295C

u T2 T3 U' f5 fó

TT

T8 T9

t" n \ "' , .. , ~ a: 1 r ~t ~ n~ c. ':f 'f ::i 1 r t" n" ?.. r t'"L ~· :< ~ \ r;, ff 1 r

INTPL<~·~I•N•~IJ,LE~~AZ94CloT113rT114r Tl1ó J

:: T~•IS~CX.TSCPH(X•M•~IrLEM~A294A)• P~\~,l~,s!,LE~~!A2$4f;) )~

TSCP!(X•r-nz,T10~l·?WCX~N~~IrT105l)~ T5i?~!X~Nr~Irrl~3~,?~tXr~#H!~Tl05)), PHt~-~~·R·C~·~Jri~TaLr~.~IrM•2!),TlJ7) ,p~{y.~~~R~(M~~>~INTFL{·•1,H!rNr~I),

LE~~A2~~C>•!1Q8,:1G9rfll8•Tll11

1: ORE2CaJTI?CS<MJl,~OTCPOS(~Jl•T16•

PRC?l

: tSH SC, lH ltr "'r !>I I" il0'5h PlftlC, Kri4I, T 106 >J, PWO• Pl"R " ( N,l'! h lNT?l(~,NI;~,MllrT107))

PROP 1

t<ELH?OSOOr?M)) NOHPOS (N))

·- RAPPC~•PR~PlrTHz•t.IMP•CPOSCNJ~PR0°1, T120),[T:[S•R"(N~OJ]J119(TJrtT:NEGCX)l T133(~~~T>J : PROPl

:: RJPPC~~P~CP1,[T:P~S(~JJT11Z(~H.TJr [T:Is·~·[N,O>:Tl19tT),[T:~EGCNJl i41C~HI•Tll : PRO?l

:= RAPPC~.PROP1rCT:POS{M)JT121CT)r [f:Is~~~{MrO>lTll7CT)o[T:NEGCMll

Tl22<~>> : PRDP1

:: THt•L.IHP•<ANJ(PQS(MJrPOS(N))r PR0Pt•.9294•,[t:ANO<P~S<H)rPOSCN)Jl Tl~·.9Z94•(T)o[T:~OTtANJCPOS(H)rPOS(N) >>JT123•.9294•(f))

:= ORI1<NIS<XrOClrPOSfM)r0l :: ORI1<NIStX,3Cl•POSCN>r0) ;: ORilCNISCX·OC)rPOS<KN*~•(HrN)),Q)

:= OR!l(NIS<X .. OC>rANO<POSCM~•R*(MoNllr POS( :U l..Ol

·- I~ï~:i!~,MirNoNil •- LE~XA294ACXrHN*R*(M,NlrNrT2rNirTll •- LE~~AZ94B<X•K~·R~<M•~).N,T2,NI,Tll := lE~MAZ94C<XrMN•?.w(H,NJoNrT2rNI,TlJ • - IS TS 12 C PI-i <X~ H~<,.R"! M. N) • TZ rLEl1K A295C),

P~(X,MN•R•(M~~J,TZrT]),

PWCX. ~.~!• LEM!UZ95i? }oP:.IO:,N,.~II ,T4 h ISP~l{XrX•HN·R·C~·NlrREFlSCCXrXloT2r LE~MA295CrT3J,ISPMl(X,X,NoREFIS(CXiX),

NlrLEKHA2958rT4l>

:: PLMNOiriO :: ISPU2CX?PlRR~(MN•R•CH.UJ,N)~HrT8•

INTPL<M••R•(MoN)•J2rN•NI)•M[,TSLEMHA<:95AJ

IS CT SP lf(l(, H,. HirlEHI'A294Al •PIU Xr N, I'IIrlEI!MA29ftB > ), PW{Xo P:.. "R •obM), INTPLC H, MI,.~. NI hlE HJI!A Z94C H

ORC~ISt x~oc >..POSCH)) : ORCN!SCX•OC),pQS(N))

ORCNIStX,OC>oPDS<MH"R"(H,N)J)

ORCNIStX .. OClrANO<POSCHN"R"(M,N>>•POS(N)J) INTRlOtN•R•(HrN)) , ORCNIStX .. OCJrPOSCHN•R•CHr~))) ORCMIStX .. OCJ,.POSCN)J OR<NISCX•OC>•POS(PL•R•CMN•R•CM•NJ,NlJJ

ISCTSC~WCXoHN"R•(H,NJoTZrLEMHA295C)P PW CX P No NI •LEMHAZ 95B )), TS(?Ii( x, t!N"R,.( l'r f\ h rz,. T 3 h PliCX,.Ilr tH .. T4))) l~{TSP W<X" MN"R,.(H, Nh TZrf 3lrPIHX,N .. NI" T4) h PliO:,P:.. "R .. t t'.~"R" Ol,. ~), t,), I NTPL< KN .. R .. (M,N), T2,. N,NI h T5)) IS,.~".(" l"R·(I~N.,R .. Oi,N), !'I>. 10

iS(~W(t,.Pl"R,.(MN"Rw(H,N),N)riNTPll"N"R"CHr~),TZrN,NI>• TSJ.PWt x.H.lH.tEMMA295A>>

s

s

•9295

+9297

no

Tll

SATZZ95

·- TR3IS<CXrTS<PW<Xr~N•Rw(~,~>•T2r LEMHA295C>~PW<X.NrN!rlEX~A2958J), TS(PiiO:rè'N~R-c)',!l;),72rTJ),

PIH X ,l! ~~\!• !4 1 l, ?iH X• f'l .. R .. Ol"' .. "! .. { l'ir!H, N>riNTPL(~~·R·<~·~lrTZ·M,~:>.TSI• PH(I,MrHI•LEMHA293AJ,:SrT7.TJJ

:= SATZ229K(PÄ(I•~•MirLEH~AZ95Alr PM(X?N.~Irl~~MA!953~rP~CX,MN•Rwc~.nJ,

rz~.929S .. ,~E~HA29SCJrT11 ... 9295•r Tl0".?Z95•)

K a [HI:INTRL{M)l[N:NISCXrCCJJ LEMHAZ9S :: CR!l<NISO:•OC}rPOSOih!O

T1 rz T3 T4 T5 T6 TT

T8

T9

no

TU T12 TU

TH

SATZZ9&

CP:NISCXrOCJ l

:= INTRLIO!OrREFIS(REAtrO)) ;: LEMMA295A(XrOrMrTlr~IrN) ;: L[KMA295B(I,O.HrTl.~IrNl :: LEM~A295CCXrO•M•TlrMI,NJ :: SATZ2~0~X .. M,MI.LE~HA29&rNJ := SATZZ90<X•MrHirT3rNJ := SY~lS(CXrPHtX.OrTlrTZirlC•

OEXP<X~O,Ti~rz,RtfiSCREAL,O)ll

·- ISPW1(X•X•M•P.EfiSCCX,XJ,MI•LEMMA296• T3)

:: ISGVlZ(lC•PWtX.O,Tl,TZl, PWCX•~?HirLEH~A29ólrPW(XrKrMirT3)rT7• ra,rs .. rr.l

:= PLOlCO, MO•wo t H).. RE ti 5( REAL,O U :: lEMMAZ96(X,MO•R•(M)•INTHO<K,Mil•N> := ISPW2CK,HN•R•(Q,MJ,MO•R•tH),fll•

INTMN(OrTl•M•MI>•INTMO(M,MI>•T4rTlZl

:: TR3IS{CX,OVClC,PW(XrMrHI,tEMHA296),f5) ,QV(P~CXoO•Tl•T2J•?H(X,H,MirTJ),Tf>>• PWCXrHN~R•(Q,M),INTKN{O,Tl.K,~I)rT4),

PlU X•f'IO•R•ou, lNTMOC Mr Mil• TlZ h T9• Tl Or T13l

Tl := SATZZ90<X•H,MI,LEMHA294A(Oi .. P) 0 ; [A:A~DCPDS!HJ,POS(NJJ]

IS<TS(~W(XrKN"R"(W,N),T2rLEMKA295CJr PW(X•~•Nl•LE~MA295BJJ,p~(X,H,MI•LEMMA295A)) NIS(Pift X,N,tH•LEMMA295S)rJO

ISCOY(~W(X~MrKirLEMrAZ95AJ,pW(XrH,NirLEMMA2959l• SATZ29J(X,N,NI.LEMM~295Br0)J,pW(X,MN•n•(M,~),

INTKN(~rHI•MrNIJrLEHHAZ95C))

OIHN I St X•OC hPOS 00 >

: INTRL()) O!HMIS[ XrOC ),PQS(OJ J OR<'HSt XrOC hPOSOIJ) ORC.ISCXrOC)•POSCMN•R•(O•M)J)

: NISC P:tC XrH~> NirlEI'MAZ9& JrOC) : NIS<Pii[ X,.!t. KI,.T3h0CJ

IS<OV U c,. Pll n, !'!, I"IrlEMMA29 6 J ~ T5 J, CV( f'lf{ x,o, Tlr TZ), PIICXrMr KI .. T 3>rT&Jl IS<Ovc~wcx,O,Tl•TZ).,pW(X.,MrHt~T3),.T6JrFWCX .. MN•R•(Q,H), INTHNCl•T1rMrMl)rT4J) ts•R·<~N·R•(O,HJ,HO•R-(M)J

: DRCNISCX•OCJrPOSCMO•R•(HJJ)

: ISCPWCXrHN"R•(Q,MJ,INTHNC3rTlrHrHIJ,T4),PWCXrMO"R•(Mlr INTHO<MrKIJrTlZJl

: ISCDVC1C .. PW(X,M .. HlrLEMMAZ96)rT5)rPMCX,MO•R•CHJ, tNTMOC~•H!lrTlZJ>

: IS<OV<1CrPW<X~H .. HirlEMHA296J•SATZ290CXrM•KirLr~HA296•N) >~PlHX• MO'"R"'(!f), INTrOe H,HI hLEl'I'A296CMG .. P.•on,. INTI10('4 .. HihtU))

s

s

s

s - 5.100.

•9297

H9297

... T3

LE !!~AZ 9 7 A

LEMMA2$'7B

:: TH7"t.03~CNIS(X~OCl~A~DCPOS(H),pQSCNJl Ii NIS { ?H( x, M•I\I,LE!H1.!\ Z94A( 01 hOC h PO$( S}, !!• [ T: ~!St X• OC) H !. ... 9297"(T h [T:A~'CPOS<~I,PJS(N))JJZ•.9297•CJJ)

:: THB•L.GR·(~[~(X•OC),ANJ<PDSCHttPGS<NlJ r ?OS (iS" R,. ("!.~I) l ,o, C '!': .HiO CPOS ( ~),. PDSt~J)JT3•.9297•tJl)

MI a rn:O~<NISCXrOCJ.POSC~Jllri:!SCX.vCl~

I a H := OR~ZCNIS<X,.OC>•FOSCHl•D•WELI(IS(X,.OCJ,. !))

.. 1 == NTJtRL(M,POSINi~ATRL(M,.T4•~!)J

T5 ·- POSE X? ex, M.tH, c, T4 J T6 := SATZ239E(~l•tT:lTDCM1JlX•XDUTCMlJ,!) T7 ·- TRIS{CXr?~tX.MrH!PD),

PRCGIMl•[f:lT3CM1llXJ.rOC.rT5.rT6)

I 2 Pl., :: TT•.9297• NI ~ tO:OR<~IS(X•OC).rANOCPOSCMJ.rPDS!N>J)l

NI a T8 := INTTS(K,MI,N.rNIJ 0 a PROPl ·- IS<P•<P~CX.rM,MI•lEMMA294A(Q));N.rNI•

tEM~A297AC0)).rPU(X,TS"R"CM.Nl,.T8,

U:~~AZ97BU:l>})

u:rscx,.oc n T9 :: PW3CX.rl1.rMI.rLE!1f!A294Af0}, I> TlO :: PWOCP~(X,H,MI•lEMMA294A(0}),~.rNI•

LEMMA297A(Q),f9) Tll := PWO(X,.TS'"!P'( M.rtO .. T!hLEMMAZ978CIJ),t) TlZ := TRISZtCX,PH(PW(X,~.rMI.rLEMMAZ94AC0)).rN.r

NI.rlEMMA297A(0)J.rPWCX.riS"R•(M,.NJ,.T8.r LEMM~297BC0)l.rOC,TlO.rTllJ

M a [MI:INTRLCM)J[P:NIStX.rOC>l T13 := OR!ltNISCX.rOCJ,POS(Hl.rP) !»!) == PW(X .. M•MI•TlJ) CN:NAT l NR ·- RLOfNTOU T14 ·- NATINTRLC~R.NATRL!(N))

T15 ·- ORI2CN!SCP0•4CJ,POS{NR).r NATPGSCSP.,. NAT RU (~l)))

T16 :: OR:lCNIS<X~OC),PDS<TS~R•(M,NR)),.p) 1"17 := INTTSCM•HI•NR.rï14) PRDPZ :: ISC PlH POl ~R; Tliu T15)- PW ( Xf. TS .. R"( K, NR h

T17.rT16>> p a T18 :: ISPWlCPO.PO,l~l.~EFIS<CX.rPO).INTRll,

USU) ,LEMI'!A29H "0})

T19 == SATZZ9UPOJ rzo := ISPHZ(X;H;TS•R•(H,1RlJ,.SATZ195ACMJ,~I•

T17tl>•Tl!.T16(1J) TZl ;: TRJI SC CX ,plf( P<h 1 !ll• T14 {i) • T1 ~<Uh

0Rt!11 IS{ x,.oc hPOSHS ,.R,.(!i,.~ )) J

: POS( KJ : NAT

ISC?lH( ,.M,.I't X,O hPROC011,. [ T : 1T O< I" U llOJ ZSCP!'WJ ('U,. n:tTO(lHJlXhlCl

: ISCi'W(( ,M,~I I,.Q),.CC>

: 'PROP'

IS(PW(,W(X,H."I,LEM.AZ94AC0)J,.N.NI.LEMP.A297A(QJ).r0Cl : ISCPVCI.rTS•R•(M.rNl.rT8.rLEHMA297BCOJJ .. OtJ

PRO?l

: CRUIIS[ X;OC hPOS( M)) : ex

. • RE:A.L INTUC\1 R)

: OiHNISt PO .. OChPOSURH. : OR(~lSt XoOCJ,POSCTS"R .. CM .. HRJ)) I~HlH s•R•(!hNRU

: 'PROP'

: tSCP~<~0,1RL.rTl4(1),J15C1>>,

PW(f>Q •l RL ..X NTRL!, LE: MI-1A.Z91< PO>) J IS(PWC~0,1Rt.IHTRL1•LEMMA291CPO>),p0)

s

s

s

s

-5.101 -

N a [P2:?~0P2(Nll Nl T22 T23

TZ4 T25 T26 TZ7

PW(PO•lRL•INTRll•lEMMA291(POJJrPOr Pft(XrTS~R·C~rlP.L),T17t1>•Tló(lllrTl8r

T19· ï20)

:: P!..."~~<~·~•ll

:• SArZZ90(XrHrMI.Tl!rP) :: GRil<~ISCPO•OCJ.ANDCPDS<NRl•POSCIRLJ),

T22) ·- LEM~!:)41C?O.~R•lRL~rl'•INTRllPTZ3l :• ~E~~~2J4BCPO.~R•lRL•Tl••INTRLl•T23> := L~~~429~:<~C,~~,lRLrT14•I~TRLlrT23) ;: IS?NZ<POrMR(~lJ•PL•R•(~~•lRLJ•

sarz~!55~<N·!>.Tl4<~l>• I~TPLC\R,Tl'•iRl•I~TnLllrTl,(NllrT26l

:= TR!S2CCXrPW<POrNR<NlJrT14CNl)r•tS<NlJ) .TS(PJ(P0r~R•Tl4rTZ4>• P~[pQ,1Rlo!NfRLlrT2Sll•

PlH PO• ' .. "R .. ( ';\:!,l f~L): INTFLPiq, T14•' ,-x_.l '; T :'_:) • T2G lr T27, T27Al

PROi"ZCl J

NAT rH se Po. oe >

ORHIISC PO .. OC),.ANDtPOS( NRh POSURL>H ORCNIStPO.OC),.POSCNRJ) ORCHSt PO .. OChPOSC1RU > ::n {~I St PihOC ).,?OS ( Pl"'R"trn "1RLJ))

ISC~W( 3 0 .. NR<~l),.T14(NllrT15CN1JJ,.pW(PO .. PL~"•txR .. 1RL>• HHPU~ Rr T14.o1RL,. HITRLU • T 26)) !SCfS(3 W(PO,.NR,T14rTZ4>,.P~(P0rlRLriNTRLl,T25)l.o PIHPO ,.:o L ""R" c:•R•lRl h INT?U UR, T14, 1Rl ... U, TRll b T2.&) >

: ISCPW('0•NR(N1J,.T14<N1JrT15(N1)J_,.fS(PW(P0r~R .. T14•T24J,. PM(~O,lRL .. INTRLlrTZSJJ)

r~'~v~~~~~~t9tn~~ 1~;'~'

TSCPMCXrT!•R·c~. R1rTl7.T30)r PHCX.~rMI,T31J>o ~(X,FL•R~(TS"R~(",NR)

.~>r INTfltTS"!1"( ,'1Rif.T!.T,I!rMI),f!2>• Pi.;()(, r:;~~ .. ( l'oti!'C ! } ) , i17( Nl hT16(11:1) h T23~ i.l3r T J&, 7 3C.:f PR0?2<'11 J

:= !S?C N.Ho{T::>~AT1?R':":~'>2( f) r:H .. <:-:>SUC,.T39• SAïZ4HN)} . : PR0?2(<N>SUCJ

N; T41 ·- I~~JCT::~ttT:~ATl?~DP2<Tl•T21rET:NATJ tU:FRJ~2{T>JT4~CT·~J.S) PR'J?2 C'l )

0 ~ r~:,ISCX•OCJJ(Q:POS<N>J rr.z 'i)

H3 u:.

c a Pl 0 a nu

rr.s

fitS

TH TB

T%9

P ~ tt:rs·R·c"·01l TSO T51 T52 TH

P : UrNC:GU)] A~ T54 T55 Pl n; 156 Ti5A r;r T58 T59

r:;o T&l l~Z T5l T54 ns T&6

Tó7

:= POSlNT~Ai~l{~,;~_N:> := NiC!"R!.t'i•HZ) := I SR i.. ~H i { N • r:. 2 ) :_:: ISRLNTZ! 'üHZ)

== PW(XoM.~I .. LE~M~294AtQ)) :: ISPWZ{X,~.M.REFI~CREALrH)rHI~Kir LEMHA2?4,(0)rT13C~I•Pl)

:= ISPK12CP!,P~t~I.PJ.~rRLOFNTCN0lrT44Ar 1' 43" ;-~!, T 14( ~I,?, ~.C} ~ LE MMA297t. COl' Tl5<H!.?rN0} l

:= T4HMI,.P,NQ)

::: ISTSZ•R•<RLGfNT<S'l•N .. M,T44> . - ISPI2CX,TS•R~(M,~~D~NTt~0)),.TS•R•(M,NJ

ri47rT17CKl•P•NJ);T3;Tl&\M!•P•NO), t.EHitA297BHll)

:= TR3tSCCXrPW<?l•N•~I•lEMHA297ACO)J• PWlPOC ~Ir Ph RL Of NH NO),. Tl4(Hl ,p • '10 ),. T15CMI•P•N0))rPWCX,TS•R~(K,RLOFNTtHQ))

,.T17CKlrP,.NO),.TlE{~I•P,NO>l• PiU X• TS"'R .. O!, Nh Ta, lE M~A297!H 0-) J. T45" T4&,T48'

tHTRLC~ l ~AT

Is•R•(~rRLDFNT<NOl)

ts .. a• n LCfN !(NO J.NJ ex

IS<?W <" t. Nr N I.lEfoti'IA297 A(!)) ),plf( PO <I'' I, P )r RLtfNH NO >r T14CMbP•~Ol•Tl5<~l,P• NO})) IS<PWC?O<MI,p),RlOFNTt~O>•T14<MI,.P•NO>•Tl5t~IrPrNO>>• PW(X,TS•R«(M,RlOfNT<NO)l,TlTC"I"P,.NO),.T16(~I,P,N0)))

: 1S"R•crs•R•<M•RLOFNT(N0)),TS,.R•(MrN))

: ISCPW{[,.JS•R•CH,RlOFNT(N0Jl~Tl7(MirPrNOJ,.T16(MirP-NOJJr Pil <X • T5 •R .. ( Mr:OH r T6;L(HMA2HBt 0)))

PROPt

:: OEXP(PlrNrNI,.tf.:HKA297A(0Jri> : ISCPii("' 1rN,.MI .. lEHKA297A(0) h1CJ :: TSOZ•R•t~•N#Il : IS•R-(fS•R•(MrNlrO) :: OEXPCXrTS•R•(MrNJrT8rlEMHA297BCO)rT51) : ISCPW(X,.TS"R•(HrN>rTS,.LEM~A2978(Q)),.1Cl

::: TRIS2(CXrPWCPlrNr~I.LEMMA297A(Q)),. P~CXrTS*P.•!M·~1rTo•LEMMA297B(C)JrlC• T5:lri52)

•- ABS(N) ·- INTASStU,.NI) :: ORI1CNIS<X,OClrASJ!POSCK)rPOSfANJlrPl

. :: P!(AN•~IrT54·T55} :: SATZlGGE{N•N~OTOCNoQ)J :: lEMMA294A(ANr~I.T54oT55) := LEHMA297ACANrM!~T54oT55l := LEMH4297BCAN,~!.i5'•T55l := Tft9CANr ril,. T341T55,;>, TS&l

:= SATZ177ClANrN~A6SH(N,.Ql) ·- I~TNO<ANrT54> r: SA!Z290CXrH.~I.T~6A,PJ := LE~M.276CP1T55·A~•i54,TS21 :: SATZ290tPlT55•AS·T~4~i63,T62J :: LEHMA296CPlT5S,MO•R•C4N>,f61-T62) ~= SATZZ96CP1T55•AN•:S,,.T62l

PRO?l

REAL INT!lLU ~) ORCN ISC x,..oc),. ANO( POS CM ),pi) S(A N))) ex POS( ANJ . URC~ISCXrOCJ,.POSC~J) OiHN I St Pl 15 5• OC) • POSU N> > OR<NISCX,OClrPOS(TS•R•(K,lN))l

: ISfPW(~lT55,AN .. T54,T5T),pi(X,TS•R•(MrAA),T!CIN;MirT54), T~8) > IS·~ .. U ,.MO•R•tANJl INTRL(~O·R•(AN))

: SIS< Ptr SS,OCJ Or<~IStPlT5S,OC>,POS(A~)l

~! S( f' llt PH5 S• Al;, T54#T6 31 ,) C) ORC~IStPli55.0CJrPOS{HO•R•<ANJ))

I SCO~U CJiPW(Pl T55• A !'I• T 54•1 &lJ,. T6HrPiflP1 T5'5•MO•R•( AN h T&l· r&;.;))

- 5.103

T56

T&9

TTO

T11 TTZ

T73

T74 T75

T76

177

T78

TT9

TSO

T81

p ; T82

0 :1 SATZ297

+10298

Tl

~~~0~,~~~\UJ~iJ9h~

·- ISP~l2CPl•P1T55r~rHO•R•<AN)rT67rT60r ~I.T6l•LE~HA297ACClrTS5l

== T~IS2[CXtPWCPlrN•~I•LE"~I297A(0)lr OVC1Cr?V.CP1T5SrANrT54rT63)rTG4), ~W(PlT55,KQ"R·t~Nl•T61rT65),~68rT66)

:: TniSt~~~L·~O~Rrcrs~Rw(~rAN)), Ts·~•{Y,MO"R•{ANJ),TS·R~C~.N)r

SATZ1?7FCHrA~J.IST52w?~{H0"~•(AN)rN,M,

SYM[$[~EAl•~•jQ•~·~ANJtT501))

. - !~:~c~rs·~~,~.~~J.78(AN.MirT541>

·- LE~~l27itX•TS·r·c~.A~J,TBCAMoMI~T5~),

Pl ·- SATZZ90CX•TS•R•CM•AN)rT6CAN,HI•T54)r

TTZ,P) :: LEMMA296CX.MDPR"(TS•R•(M,ANt)~T71rP} ::: SATZ2~E(XoTS"R"(~rAN>•T8<AN•Mf,.T54)rPl

:= ISP~2!X.~O·R·crs•P. .. tM.AN>>·TS•RGCM .. NJr T70oT7!,T6•T14rLEM~A2P73{0Jl

:= IS~~1{P1T55•PlT55rAN•REriStCXrPlT55Jo TSt., TG 3r T5 7)

:: ISPHlCX~x,Ts•R•CMoAN)•REFISCCXoX)• T5tA~~~Iri54JrTS8.T72J

:.: TR3IS<CX•PWCPlT55~AN•T54oTS3Jr PW{P1TSS.ANrTS4,T57)rPI(X,TS•R*CKrANJ, T8CANr~t.T54J.T58l•PWCX•TS•R•(MrAN)r TStAN.MI.T54J.TT2>rT77rTS9,T78)

:: ISOV2CPHfP1T55rAN,T54rT63)• PHCX.TS•R•tMrA~JrT3(AN,NI•T54J,T72)• lC• T79• T6ltr T73l

:= TR4IStCX,PW<Pl•N•NirlEMMA297A(Q))r 0Y(1C.PW<PlT55rANrT54•T63J.T64), 0ï(1C•P~(XrTS"R~CHrANl•T8{ANrMl•T54)o T7Z},T73>oPWtX.MO*R•<TSftR•tM•A~))rT71• T74,•P~CX•TS•R•(Hr~)rio•LEHHA297B(Q))• T69 .. rso. rrs. TTS >

:= RAPP{Nr?ROPloCT:PQSCN>lT49CT>~ [T:ts•Rw<N.O)JT53Cf),{f;NEGCNJJT81CT))

:• TH1~t~IMP•CIS<X,OC)rPRcrPt•.tZ97•~ [T:IS(X,OCllT12•.9297"CT),(T:NIS<Xr0C) usz-. n9r•n))

:: TRIS<CXrPL<Pli(RrOlrPLICSrOJ>• PLICPt•R•<RrSl~PL•R•co,Q))r

PLI<Pt•R•CRrS),Q),PLIS12A(Rr0rSr01, ISRECXZCPL•R•<OrO>rOrPt•P.•fRrS)r PL01CO.OrREFISCREALr0)J}.)

. 4...J''-'r &.r- &. I ..JJ I

: IS(PW!'l•NrNirLEMMA297ACOl1rPW<PlT5SrMO•R•<AN)rJ6lrT65) )

tS(PW('l,NrNirLEHMA297A(QlJrOVClC•PWCP1T55rANrT54rT63), !64)}

: ts•a•(~O~R•(TS•R•(MrAN))rTS*R•(MrN)J

INTRLC~~·R•<TS•R"(M,ANl))

OR<-. I St X rOC ),POS CTS•R,. < !(,, N)))

N4 SC PWC x, TS •R•( H• ~:'4 h T 8( A .. ,.!f! ,.T54h T72h0CJ OR<~I~X.OClrPOS<MO•R•crs•R•<"•ANll)l IS (J 'Hl CrPlH X:, T 5 .,R .. OI• UH• TiH AN •I' I, TSU, TTêJ, ö73) • PiiCXrMJ '"R"t Ts .. R•(M,AN) )of71,f74))

ISC~W({oMO*R•crs•R•(MoAN))oTT1rT741rPWCXoTS•R•CHrN1•i8o

LEMMA2'J 78{0 l) J

ISCPWC~1T55oAN,.T54rT63),p•(PlT55rA~.T54rT57l)

: IS<?W{(,TS•R•CKrANlrT8(ANrMirT54JrT56)rPWC)rTS•R"CMrAN) ,T6(AN,MirT54JrT72)J

ISCPW(,1T55.ANrT54oT63)rPICXrTS•R•(M,A~),Je(ANrKirT54), T721)

IS(0YC1CrPHCP1T55rANrT54rT63),T64)• 0V(1Cr•W<XrTS•R•(H,ANl,T8CAN.MlrT54)rT72),173))

PRO?l

; PROP1

: ISCPW(,V(I•K•MirlEMKA294AC0))•~•NI•LEM~A297ACOJJ, PWCX,JS•R•<MrN)riNTTS{M,"I•N•NI)rLEM~AZ97BCOJJ)

ISH't(:t LICR.O h PLit s .. o »• PLH f'L"R•C RrS lrO) l

s

- 5.104 -

•1\,IC:llö

SATZZ9$A :: SYHISCCXrPl(PL!(R,Q>•PLICSrO))r ..

Pl!(Pl"R~fR~S)rO)•flN-10298•) ; IS<PLRPL•R•{RrSJ•OJrPL(FL!CR•O)•PLI(SrO)J) SATZZS'Sa :: T1".102?<>" IS<'Lt~LI(a,OJ.PliCS,OlJrPLICPt•R•<RrSJ,C>J

.... 10298 s

s a rz := TRISCCXrMN(PL!CRrOlrPLI<SrOJJ, PLI!M~·R•cR.s>-~~-R·ca.a>>• Pl!lN~•R"C?rSJ.o,,~~!SlZACCrO•S•O>• I5REC!2€MN•R~co,o>~O.MN~R•(R.S),

PLJ2:0rH?"R•COJrSATZ!7&aCOrREFIStREAL• (i)}})i IS<~NtaliCRrOJrPLI<SrOJlr~LI(M~•R•(R,SlrOJl

-1:>298 s

s a SATZZ9!'1C := sv~ISCCY.r"N<rLI<R•Ol•PLICSrOl>• PL:<"!•R•cR.SJ,OJrT2•.t0298•) I SC!t!.It MN•R•<Rr S >. 0 h MN<PL H Rr 0 h Pl I<S,.O)) l

SA.TZZ980 :: T2 ... 1C293" ISC~N<'LICRrOJrPL!CSrOJJ,.'LIC~N"R~(RrS1r0)J

H10Z98

s a T3 == PL02(TS"R•tR~Sl;HO~R•(JS•R•(O,.Oll• S~TZlTGBCTS•n~co.oJ,

TSOlCOoO•P.EFISfP.SAL•O>))) : IS--t•CM N•R'"C TS•R•(RrSJ, T s• R•((),O J h T S"R'" ( R,. SJ J tï't := TR!SCREAloPl~R"tTS"R"(RoOJ,TS•R•to.SJl

.rs-?.•CR,Olr0oPL02CTS•R•(R,Q), TS"R•COoS),TS01t0oS•R~fiS{REAL•0))Jr TS02{R,OoREFIS(REALo0)J) : Istr.:t•P L •R•CTS•R .. {R,OJ ,.ys•R•COo S) hO J

T5 ·- TRIS<CX~TS(PLICR.Ol;PLI<S•O>l• PLICMU•R•tTS"R*(R•S>•TS"R"(OoOJJr PL•R'"<TS·R~CRoO)rTS"R .. {OoS)}), PLifTS'"Rw(?,,S}.~)rTSISl2A(R•O•Sr0)•

ISRECXlZCHN"R•crs•R~CR.S>•iS•R•(Q,Q)),

TS"R"'Ob S> .Ft. '"R'"(TS'"R .. ( R•O},. TS•R-tOo SJ ),l),.f3,flt)) lS(TSC~LI(R,Q),.PliCSo0J),.PLitTS•R•(R,Slo0)1

-13298 s

s a SATZ298E :: SYMIStCXoTS(?LICR•O),PLI(SoO)), PLitTSwR'"CRrSJ~OlrTS~.l0298•J ISt?L H TS .. R .. CRrS > rO h T S<P~ HR rO hf'li(S,.OJ) l

SATZZ98F :: T5" .10298* IS<Ts<sLI<RrOlrPlt<S,.OJ),pltCTS*R•CRrSJrOJl [N:NIS"R•< s .. o) l

utOZ98 $

N a tt:tS<Pli(SrO)rOCJl T& := TR3IS<REAlrSrRECPLI{Sr0))rRECOCJr0r

IS?.ECS,.OlriSCERECPLI<S.lJ,OC .. t),. REIS<OoO)) ; lS"ït•c; •0)

•10298

N a LEHMA298 :: TH3"L.IMP~(lSCPLI<S .. OJrOC1riS•R•cs,OJ, N .. rT:IS<PLt<SrO>rOCJJTG".10Z98•(TJJ NISCPU (S,.O )rOCJ

Hl3Z98 s - 5.105 -

N a rr := TRIS(CXrTS(PLI<SrOJ,.PltCOV•R•cR,~,.N), OJloPLl<Ts•R•cs,dv•R•<R•S,NJJ,Q}, PLICR#OJrT5lStDV•R•[RrS,Nll,. !S~ECX1<TS•R•cs.ov~R•{RrS,~J),Rr0•

-10296

-10298

N .;;~ SATZt9SG

SATZZ98H

R a ra

R ~ SATZZ98J

SATZZ931t

R ~ T9

AR tP:P!JS CR J1 TlO

R ~ ti:ts•R•<R~O)l ru

R a tN:tfEGtRl1 HZ

R a T13

T14

T15

:: SATZ229GCPLI<R~o>~PL!<S.OJ~ PLI<o~·R•tR•S•~l,O)rLEM~A298r T:"". !0 296-) .

:= SATZ227~ffLICR.ClrPLICSr0)r PLI<Cv·~wcR.S.~J.OlrLEHMI298, T7•.t~293~)

t= T~ISCCXr~'(?L:tRrOllrPLI(MO•R•(R), MO•P.8 {0))rFli{M0~R~<R>rOJ,HOISACR,OJr

IS~ECXZ(P.~·R•CO>rOrKO"R•{R), SATZ1753(0rP.EFISCR~ALr0})})

:= SYMISCCX~~OCPLI<R.OJJrPLICKO•R•<RlrOlr T8,..1029B•)

:= rs•.Hl298 ..

:: TRIS(REALr~002CPliCRr0J), TS•R•<RE(Pll(R,OllrRE<PLI<R•Olll• rs•R•(R,RJ,?L02(TS•RwCRE<PLI<R~OlJ,

RECFLI<R~Oll>•TS"R•<tMCPll(R•O)J~ IMCPLl(RrO)ll~TSOlCIH{PLitR.O)),

I~tPLI<R•O)l~I~!S!R•Olllr 1STS12"~·<R~<PLI!R~Ol1·R•RE<PLICR~0)J,

IS<!'LI( KO,.R•onrOlrKOCPLU R,O))) IS<MOC~LICRrOJJrPLICHO•R•CRJrOll

R·RE IS:: R, 0 h RE IS(R, 0 Hl : ! S-R•<'f 002( PLI< RrO H• T s•R'" CR• RJ) ·- ABSCRJ REAL

:: TRISZCREAL,TS"Rw{R,RJ,fS~R•(ARrAR),O, TSOl<R•R•I>•TSOl<ARrAR.ABSO{R,[))) : tS•R•trs•R•(R~RJ,TS*R•CARrARJJ

·- SATZ1966(R•R•N,NJ : IS*R•crs•R•(RrR>•TS•R•(ARrARJ) ·- RAPPCRriS*R•<r~·R•(R,R)•TS*R•CARrAR))r

(TtPOSCR)Jf10CTJ,[J:Is~R•(R,O)JT11{T),

{f:NEG{~>JT12(J)) : IS"R•CTS*R•(RrRl•TS•R•<AR•ARll :: TRIS(REAL.~~Q2CPLICRr0)),TS'"R*(RrR>•

TS"R•( AR• AR) • T9• Tlll t IS "R• ('f 002( PlU Rr OJ >• T s•R• UR • AR) l :: THl•t.IMP•tiS*R*(R,OJ,NOT(NEG<AR)),

[f~IS"R"(Rr0lJOIO!NCARrA8S0tRrTJ>r CT:Nrs•R•CRrDJJPNOTN<ARrSATZ16&ECRrTl> ) NOTCNEHAR))

R ~ SATZZ98L :z THSQRTl<MDD2tPLI(RrO>lrlEMHA5CPLI<R•0) >~ABSCR)rT15".1029a~,T14•.10!98~J

SATZ298M :: SYMIStRE~L~MJOCPLI(R•O>>•ABSCR>r SATZ298L.)

COFR. := PL!<R•Ol S 3 Ct:IS(COFRtCR>rCOFRLCS))]

ISRLIC ·- TR3ISCREALrR•PECCOrRLCR>>•R~CCOFRLCSJ> ~s.ISRE!R.O!o!SCERECC~F~LC~).COFRL(SJ•

IS .. R.,.(I! OO<Pl.I< R,O) hABS<RJ)

Is·~·u 9S(R hMOO<.PliCRr0))) COMPlElC

$

s

- 5.106 -

+'110

•VlO

.. VlO

S 3 [t:IS"R"(R•S)J ISRi..EC

; n:cxJ RE: A:.C

R 41 RE:ALI X 41 ERX::tEA:..CCXlJ

RLOfC

·- tTrRSALJ(U:P.EALJtV:IS(COrP.L(T}, CD~RL(~))JISRLlt:~~U.VJ

·- !~~GEC~~~L~cx.:T:?.E:ALJCjfRLCi)•X) ·- I~A~e:I(~e;AL.CX,[7:fiEALlCOfRL(T),R)

tY:CXltRY:REALC(Y)Jti:ISftR•t~L~fC{X,SX>•RLOrC(Y,RY))]

RY OI

R 41

RX a

41

ISCI~l ·- ISI~VE~REAL•CX~tT:REA~JCDFRL(f),

n :rsu.n J ISCERL :"'

ISRLC1 ::

ISRLCZ ::

ISCR;.l :=

lSCR:.z ::

OI: NA Tl COFN := (MHUT )[I: IS,.N,.( N.t !0 J IS~E: :=

· Tl".vtoff.x.:::x,v,Rr .. I!

IS!~VtRE4L.cX,[T:REALlCOfRL<Tl, Tl".VlQ~,x.Rx,y,RY•I>

ISSTlCREAL.cX,[T:REAllCOfRL<T>~ r:. ... vlo~,.f:, ISST2CREAL~CX,CT:REALJCDFRLCT), Tl".VlO,.,fil ISfSl•Eftt?.EALrCX•tT:REALlCOFRL<T>• rt•.vlo•,.x,.Rxl ISTSZ•E-CREAL,CX,[T:REALJCOFRL(f)r n·. VlO",. x .. R u CC~Rt<RLOFNT(N))

!SRlECCRLOFNT(~),RLOFNT(M),

!S<CDR ltR J ,.COf~L(Sl)

INJECTIVE<REAL,cX,{T:REAllCOFRl(TJJ

'PRJP' RE AL. Ct: tlfRU R))

REAL

rsu.n

: IS•R·~~ .. RLOFCCCOFRLCRJ,RE,liCRl)l

: IS '"R" n LOFC t COFRl CR),. REAli t R)),. R >

: IS<XrCJFRlCRLOFCCXrRXJ)J

: JS(COR l<RlOfC( X .. RX) ),. X)

: COMPLEX

ISNTERLOhM• IH : iSCCOn CNhCOrN(H)) M ; ti:ISCCOFN(N),.COFN(H})J

ISNIC :: ISNTIRL(N,MriSRLICCRLOFNT<N>rRLOfNT<MJ rl)) IS•N•CN,Hl

41 TZ ;: CT:NATl[U:NATl[V:ISCCOFN(Tl,COFNCU)}] ISNIC(T,.U,.Vl : INJECTIVECNAT,.CX.tCT:NATlCOFN(f))

X 41 UTC ::: H!AGEt NAT .. CXrrT: !\.HlC'Jt:"N(ThU : •PR!JP' N 41 ~Art ·- IMAGEUNAT:.CXrET:NHlCOf'I'HT).,N) : NATC(CJFNOO> X a tNX:~ATC<X>l

NOFC := SCFTCNAJ,CXrtT:NATJCGFN(T)rT2•.vtO•rXr NI) : NAT

tY:CXl ENY: NATC(Y)](l:Isn, YJ1 ISCEN :: ISINY(~ATrCXr[T:NATlCOfN<T>.Tz•.vlo•,

x."ix,y,:n,IJ : IS .. N•t'40fC(XrNXhNOf'C(Y,NY')) NY 41 ti:Is•N•CNDFCCXrNX)rNCFC'Y•NY))J

ISCI'4 • · ISI~lVEOlAhCXrCTH!ATJCOfN(T),TZ".V10~,

N ; ISNC1

ISNCZ

x.~x.·f.~IY .. o Isu~n := iSSTlCNATrCXr[T:NATlCOFNCTl,TZ•.vtQ•,

N> : 1S~N·(~rNOFCCCOFNCNl•NATl(N))J :: ISSi2CNAr,cXrtT:NATjCOFN(T>.ïZ•.V!QA,

N)

s

s

s

- 5.107 -

H·Yl)

•Y10

+•Vl)

•VlO

N'( a ISC!IIl := IST5l.~"<NAT•CX,[T:NATlCOfN<T>• rz•.vlo~.x.Nn

HT a

NX a NY a

NY a 'IT a

NX • T?. ... '.fl')•,.x,NY.l

:= Citcx.cr:cxl~ATC(f}l

C1F~T :~ IN•[•t:x.rt:CXJ~~TCCT),.Nf) NATTI := l~PCCX,[T;CXlNAfC(f),~J) t~T:'l.\TTH I:IS'"E'"(NATf,t;f,tirlJ ISNTEC :: ISII':HfX,[T:CXWATC(Thln.rn,I> [I:tS(C~FNTCNT);CC~N!CMf})j

IS~TIC := IS:~ECCXo[T:CX!NA7CCTJ,NT,MT,.IJ sr:rc CI:Iscx.nl ISCE'i :: ISDUTI(CI•[T:CXJNATC<T>•X•NX•Y•NY•I> n: IS'"E•<NATT .. tnon:< x. Nu, raorc n, rn, > l ISCI~T ·- ISOUT~(CX.CT:CXîNATC(T}•X•~X•Y•NY•I> !S~TCl •- ISCUTINCCX,(T:CXl~~TCCT>,NTJ IS,TCZ := 5T~IS:~ATfrNT,\f~fCCCC~NT<NT),

ISCNTl ISC'HZ NTOP-1 ti:IS .. N•C!'(,~)l

WATTICNT1>•ISNT:lJ :: ISINOUT(CY.,ri:CXJ~ATC~T),X,NX) ·- SYVISCCX•I•CDFNTCNTDfC<X•NXJJriSCNTlJ := NTOfC(COfN{~),NATI(N))

ISNENT :: ISCE~T<COF~(~J.NATI{N),COfN(M),.NATICM) •ISNEC!Nrl",!)}

U:IS,.E•tNATT,. HTOFNOih NTOF~HM>) l ISNI~T := ISNICCNrK•ISCINTCCOfN(N)rNATICN),.

COFNCMJ,NAT!<~lrl))

NOFNT •• NOFCCCOFNTtNTJrNATTI<NT)J [!:Is•t•CNATT.NT .. KT>l ISNTER :: ISCEKtCOFNTC~TlrNATT!CNT)rCOFNT(MT)r

NATTI<MT).ISHTEC<~T.~T.!))

ti:Is·~·(~QF~T(NJ),N0FNTC~Tl11 ISNTIN ·- ISNi!C(NT,MT,IS:!NCCOF~T-NT),~ATT!(NJ)

rCOfNT\~TlrNATTICMTJ,ll)

N ~ T3 ·- ISCNTlCCOFN(N),NATI<N>J

N ~ ISNNfl

ISNNTZ

NT .::1 Ttt

NT :l ISHnll

ISNTNZ 3 H

:= TRISCNAT•N•~GFCCC~FN{N),NATICN)),. HOfN!CNTOrN<NJJ,!SNCl<SJ,ISCEN(COFNCNl •NATICN)rCCFNTCNTDFN<NJ), NATTICNTQFN(N)).iJ•.vlO~))

·- SYI'.I St ~Ah l'b NCFNTOHOF N\ N > J. ISNNTl)

:= ISCNlCCDF~T<NTl.NATTt(NT))

:= TRISCNATT,NT,NiOFCtC~FNT<NT>•NATTICNT) ),NTOFNCNOFNT{S7ll•IS~TC1(NTI, ISCE~T[COfNT{NTJ,~ATTICNT),. CCFN{IOfNTCNTllrNATitNOFNT(Nf}), T4•.vtO""H

t= ~YHISCNATTtNT.NTDFNCNOFNT<NT))riSNTNl) ::: NT:JnH U

IS<X.CJFN<NOFC(X,NXJ))

IS<COF't OIOF'CCX,NXlJ..X) • TY? E'

ex NATC( Cl FNT<NT))

: IS!CCfliTOIThCOFhHI'T)l

IS ""E .. <'I A iT, NT, M T ) NATT

IS<X• n : I s•E• (lf ATT, NT .NT OFC<CO FNTC NT 1 ,NA TT H t.T)))

: tS•E•(~ATT•~TOFC(CCFNTCNTJ,NATTitNT>>•~T) ISOC ,cl FNH NHlFCU:, hXl))

: IS(COF'JHNTOfC(X•NUhXl NATT

: IS .. E•n ATT • NTOF"NU-IhNTOfNt lUl

: IS-N•cH,.M) : NAT

: IS<COFl (NJ,COF::TOITOfN(N))}

: IS•N "<'I ,NOfNH NT OFNCNJ)) : IS,.N•C'lOfNTUHOFï'HNlh NJ

: IS<CDF''H<NT hCOffHNOFNHNT )))

ts•E•n ATT • NT liNT OFNC NOfNTC NT>)) IS•E•('UTT • NTOfNOHlFNT<NTJ J,.NTJ NA '!'T

s

s

- 5.108 -

+10299

-1:1299

uUZ99

•10299

•10330

~~ a ci:Is•r•c•arr,cNT>SUCTrlTJl Tl :: ISNINTC<NOF~T<~Tl>SUCrlriJ : ts·~·C<NOF'NHNTJ>!iUC .. l)

'H .a SATZZ99A ·- THJ•L.I~~~(tS•[•(NAJTr<NT>SUCT~lT)r

IS·~P(c~:f1T{,Tl>SUC·llr<~OFN!tNT)>

AX3.tT:IS~E·C~hT!,.c~T>SUCT.1T)J

: NQTt IS• E•CNATTr <NT>S:.JCT•lT)) ; AXJT :: [J:~aT:JSATZ299A(T) tT :t,~ATT ~NOT< Is .. E•<N HT, <T> SUCT •lT))

~~ a ti:zs~E•CNATTr<NT>S~CT,<HT>SUCT)l

:: l:S~I NT<<NOF"NTC NTl >SUCr< NOfNHMThSUC,. !) : IS•N•C<NOr'HO:TJ>SUCr<NûnHMTJ>SUCl

T3 ·- <T2><NOFNTOHJ><NOFNHNT)>AX4 : IS~·('COfNT<rlH,.NOfNTO!T))

I iil SATZZ99B a AX4T

:: ISNTHHNT,.MT.T3 ... 10299•) : IS•E·P~AïT,.l\IT,.MT)

·- tT:NATTJtU:N4TTlCV:IS"E•(NATT.<T>SUCT"

C2 a

cz a N a

cz a

C2 a

a

tS:SETOIATTJ l

SUCT > j SATZ299S(T • :;, V J n :te .Hf HU: NATT HV: IS•E .. UATT ,.cT>SUCTr SCCTl l IS•E•n ATT,. T,.U)

CilNtllT :: ESTHNATT,.lf,.S) : 'PROP• CON02T := All"l"<NATT,.[T:NATTJIMP<ESTICNATT,T .. SJ

•EST H llATT ,.c T>SIJCT,. S))) : 'PR!JP • ·tct:CDN01TltCZ:COND2Tl

[N:NAT l PRDP1 := ESTICNATf,.NTOfN(N),.S) : 'PP.OP• H ·- Cl : PROJ»lU J (P:PROPUN)] T5 ·- < NTOFN( Nl>CZ ESTI'N~TT,.NrOFN(<NOFNTCNTJfN(N))>SUCJ,.Sl

TS ·- ISP{"Af,.[T:NATlE$TI{NATf,.NTOfN(<T>SUC) ~sJ,.NOFNTCNTDfN(N)J,.N,.T5r!S~NT2(Nll : PRO?lC<N>SUCJ

CNT:NATT l TT := INOUCTIONC[T:NATlPROPl(TJ~T4,.[T:NATJ

lU:PROPl(TllT6lTrU)•NOFNT<NT)) PROP 1 n OFNT (NT))

SATU99C ·- {T: NATTJ ISP< NATT r [UHJATT lEST I <"'A TT rU,. SJ~NTOFN!NOrNT(i)J,.T,.T7~.10299"(f),

ISNT NZCT ~) : [T:NATT JESTICNATf,T,.S) AXST ·- (T:SETCNATTl1(UtC0~01TCT)l[Y:COND2T<TJ

JSAT Z299C( T • ll• Yl : r:T:SETC NATT) HU: CONOlT<Ul tV:CONOZH T> HW: IIATTl ESTHN4 n,.w,.TJ

IC := PLIC 0.1RU CCM;>LEt

Tl :: TSIS12AC0~1Rl•0•1RL) . : lSHSU c, tC hPLHMN""R•ns•R•(O,.QJ .. TS•R•URLdRU '" Pt.,R•cr s•R'" CO .. lRlh TS'"R'"(liU ... O))) 1

T2 :: TR!S(REAL,MU•R•cts•R•to.o> .. TS*P.~ClRL•1fll)),HO~P."(TS .. R~(1RLr1RL)},.

s

s

$

$

s

.,.. 5.109

M0"P.•(tRL),FL01CTSw1"<0~0), ~O"R"fTS•R"(lRl•lRLll>

TSOl~O,O.~EF!S(RE~l.~))), iS~1·~rt~s•RwtlRL•l~Ll•lRL•

SATZl?5-Cl~L~>> ts•it•<!t ~·R•CTS .. R"'< Q,OJ, T s• R .. { I RL, tRL)), MO .. R• ( 1 RL>} T3 :: TRISt?.E~L~Pl•R•trs•R"tO.lRL>•

Ts•R•<!R~•01J•7S•A•Ct~L•O>•D• PLv1CTS~~w{Q,1PLi,TS~~~tlRL~OJ,

TSOl(O,:~L.REf!S(REAloOl}),

TS02!1Rl,~~REF!5{REAL?0))l ts•Rw(~L·R•CTS•R~<c.tRLJ,TS•RP(lRL,OJ),Q)

H :: IS~ECX!2~~:~•pw(TS'RP{O•Ol~ TS"RP(1~L.1ît~)},HJ~P.K(1RL>·

PL~~·~rs~R~<Crlatl~TS"R~t1~~*0))#0*tz,

TH IS<PLU HN*R•(TS•R•CO.OJ,ts•R•ftRL.tRLll• PL•R•<rs•R•(O,lRL),TS•R•(tRL,OJl},C3rRLCMO•R•(tRLJ))

r; :a SATZ296JURLJ : ISCCOnUMO,.R"(lRLJ hMOU::))

-1!) 3)3 s

SATZZ300 :: TR3ISCCX,TSCIC,ICJ, Pll ( X1l"~"< TS•fi•{ 0• 0 l, ts•R .. <1 RL• 1 !11.)) • Pl"R"(TS~R"(O,lRL>,rs•Rft(lRL,O))),

CO~RLCMO•R•(lRl)),K0C1C>•Tl'".10300'"• T4•.10300•,T5".10300•) ISCTSU c, IC)., MOC lCl J

[R:R~ALltS:REAll

•10331 s

T1 := TSIS 1ZAC s,. o, o, 1Rl J IS<TSC:OFRL(SJ•ICJ•PLI(MN•R•trs•R•<S•OJ,TS•R•<0•1Rl)), PL ,.R .. CT S'"R• C S.1Rll, TS• R•(3, OJ) > J

TZ == TRIS<REAL•MN•R•<TS'"P.,.CS•O>• TS,.P."<O.lRLJ),MO•R•(TS•R•CO,tRL)),O, PLOl<TS"R"(S,.Ql,wO"R"CTS"R•co,lRLll• TS02{S,O,P.EfiSC~EAL,OJ}),

SATZ17~~(TS~R~<O•IRL>•

TSOlCO,!RL,P.EflS(REAL,~J})) : ts•R•(~N·R•<tS•R•CS,O),JS•R•<O.tRlJ),Q)

T3 :: TRIS(REAL•PL"R,.(TS"P."CS•lP.Ll• TS"R"(Q,Q)),TS~R·<S,lRL>,s,

PL02{TS"R"CS•1fil),TS'"R•co,oJ, TS01CO,Q,RE~IS<REAL•0))J,SATZ195CSJJ : tS•R•<~L·R•(TS•R•<SrlRL),JS•R•{O,O>)•S>

H :: ISR~CX12<MN~~·(Ts•Rft(S,01•TS~R"(0,1RLJ )?Q,pL•R•(fS~R·<S•lRl>•iS•R•to.OJJ,s,

T2,J3) . IS<PL IC HN•R "<TS •R•( s, 0 hTS"~"( o, lRL) >• . PL"~•(TS"R•<S•lRLJ,TS"R•(),Q))),pLI(O,SJ)

T5 := TRIS(CY.,TSCCOFRLCSJ•IC>• PLI(M~·R•<TS~R•cs~D),TS.R"(O,lRL)),

Pl"R"<TS"R"(S,IRL>•TS"R"(O,OJ)), PLI<~hShTh H) ISCTS(C OFRL<Sh IChPLHO•S))

T5 ·- ISPL2( TS<C Of' RUSh IC hPL I (Q,S ), CGFRL(RJ.T5) IS(PL<:OfRLCRJ,TSCCDFRL(SJ,Iè>J•PlCCCFRL(R),ptl(O,S>>>

f7 ·- PLISlZA<R•O•O•Sl ISCPL<COFRL{RJ•PLICO•S>>•~ll<PL"R"CR•O>•PLrR•to•SJ)J

T8 ·- ISRECX1Z<PL•R•tR,Q),R,Pl"R•tO,SJ.S, PL02<R•O•Rf.FlS(RE~L•O>>• PLOl(Q.S,REflS<REAL,Q}l) ISCPLICPL"R"CR.OJ.Pt"R"<O•S>>•PLICR,SlJ

•103)1 s

SATZ30lA :: TR3ISCCI,PLC~OFRLCRJrTS<CDFRL<Sl•lC)l• 5.110 -PLtCOFRLCRJ,PLI<O.S>>#PLI<?L·R~(R.O},

Pt•R•<O•SJ>•PLJCR•S>•T&•.lO!Ot•• T7".10~01•7tn".l0301"J : ISftE"C:X,PL(COFRt<RJ,TSCCaFRL(S),ICJ),PtiC~.S))

SATZJ018 :: SY~i~(~r,Pt~COFRL(1J~fSC~CFPl(3l•lC)),

A translation of Landau's Grundlagen in AUTOMATH · authors thesis (Eindhoven, 1977): On verifying Landau's "Grundlagen der Analysis" in the AUTOMATH System. LAYOUT tROK fiLE AUTOE/LANDAU/H4A

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