A translation of Landau's "Grundlagen in AUTOMATH"

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A translation of Landau's "Grundlagen in AUTOMATH"

Citation for published version (APA):

Benthem Jutting, van, L. S. (1976). A translation of Landau's "Grundlagen in AUTOMATH". Technische Hogeschool Eindhoven.

Document status and date: Published: 01/01/1976

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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.

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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)

-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

(5)

.. 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_PROP1 a 1_PROP1 : 'PROP'

: ZERIH OF' Uh AZ))

t NEGO<Df" U t . 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 : _NOTUCOCU 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

s

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Z ~ T2

-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

$

s

•IYl) I

-nu

uiYtD ••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

$

4.4

(7)

-•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

-

(8)

4.5-u i 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

$ -

(9)

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

_-

(10)

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

(11)

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<

u ..

zc)

.rs•.Ivzo'">

:= LEMHAD5f0•B~EO~ORED12CC*D•A•B•f•E*

c

a

tE:EQ<A•B>JCK:MDREOCA.CJJ LEMMA06(~•C•Ll)) 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<B •CJ : LESSD<C ,.9) : •PROP • •PROP• LESSEOt B•AJ : MORE Q(9 ,. U : MOREQ(9

,.c

>

fo!OREQ(C •Bl : LESSEOC: c,.B) MOREQ(3 ,.QJ : LESSE~C s,.O) M:JREQ<A •lH $ -

(12)

4.9-.. 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

(13)

+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

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

(14)

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

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(15)

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.

(16)

-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!JP1

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

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(17)

4.14-z•RP'" ; T3S := OREZfZEROCA>rNATOtABSO(A))rlr

PNOTOO<A•P)) NATDUS SO(,A U

-IYU s

t OI 10_0SINTNATD := 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

(18)

+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

-

(19)

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)

(20)

+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

(21)

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)})•

(22)

•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 - 4.

(23)

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

(24)

-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

-

4.22-s

s

(25)

+*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<B ...

C>•

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

(26)

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))) -

(27)

(28)

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},

(29)

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)) -