A Proof of Weak Termination of the Simply-Typed {$\lambda\sigma$}-Calculus
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(76) N <>DN < GF<>VEFM>ILJ [ Oba ; EFMa [ [ IhcVRVM>NI OPDVc ESOfy_<> GFGÊ IKRh[ DVcV; < c ; NIKNUObG2YVRXOPSE;I [ ch< [ EFDVJ<>[ VN; <>DVc+EFDVJN ; < [ <>y [ EFN< [ <>GO NEFIL D'; I IbyÝMObGFGXO R+GF< # Xd7?# 14< 0E ObDVc0ILD+GFTE EQNS EFJ N¬ OPDhcfSEFcV<ES IL=<>IK='I a EFMObGFGT<>=0WX< c+cV< cEQ; D0EFN[ SÇGF< N¬ ObDVc S}EFch< E <Lm FVEFN_MObD7W"<HS}EF=0m R+GO N<cm WVT O0S}<>YVR+<)D+M><[ I [ <>y [ EFN<HSN<>a+SI N ; < I [ = " `W` ` m `W` ` a oqm"> < R+GF< S= LO=PV) = O9P8LL)+ >+k Sh>~= gaR4LK>+ U>" ULL>~4 UO=PVO <<>=0WX< c+c+EFDVJX_ EQD~M><6NIKNUObG+N< [ ='EFD+O NEFILDEF='a+GFEF< S2SEF=a+GF<N< [ ='EFD+O NEQIKD ESNIKNUObGFGFT,N< [ =EFDO NEFDVJ'E ObDVcCIL[ D+GFT,; E [ ='EFDL[ R~ S[ N ; < S}< [ [ R+GF<S0ES I [ <>IblK[ < [ k U RÖMObDW"<S}EF=R+GO N< c7WhT = PQU a+GF[R+S<)=W"<c~c+EF DhJ"SI|y_<'M ObD{; EFJK D+I <N < I =< I a+R aXIKS}<SI [ NILNUObGN< ='EFD+O NEFILD I,SURV=R~aÇ ESNIKNUObGFGFT N< ='EFD+O NEQDVJE ObDVc7ILD+GFTE N < ILGFGFIbyEFDVJHSTVSUN<>= B ES_NILNUOPGFGQTN< ='EFD+O NEFDV~J
(77) 9PrU UmL=nsRWt{o 4UmLMnLRLkUmsLMt 9grU Uto m RL9tvLwSh 9 LL = msLMnL_ LMtoqmL= nwLMt k S U SpLwUmo|m~LwS k S U LKy SpL+k UmsLMnLa oqmsL4 SL nK k U@U Um0LwUnoU 9 mLMnL " R = m RWnL LMtuo 9 mLMt RK= nvLMt k U@ULK UmsL4 UnvLMta oU|= msLMnL_ LMt ´X 0 m"_ LMtuo= m0LrU t Iby"EFD| B N ; < [ R~GQ< S=P UHOPDVc{xRÖO [ < 1& 59V 147 685=14;<V 6/2# I [ RF"ObDVc,D+I7ILN ; < [[ R+GF< <O NR [ <SQR+ILDCN ; <0GF< N¬ ; ObDVc S}EFch<K[ 2ObDVN<>='[ O SÇN ; <>I [ <>= [
(78) 2ObD" j 2N ; <);|D [ SNUO N<SN ; ; O NN ; < [ <>y [ EFN[ <SUTVSUN<>= BB ; ILW+NU[ OPEQDV; < c ; [ IL=d B WVTc [ IbaVa+[ EFDVJN ; <S}< c+ESN ; EFW+RVNEFIL[ D R+GF< SObDVc <)a+; GObM>EFDV;J'<[ OPM ; R+GF<yEF[ N SUIK=<HSRLW+N< q = mR nILD,N < EFJ N ObDVc7S}EQcV<WVT7Ny_I R~GQ< S ILDV< yEFN mdR n <>a+GOPM><c7WV T mVN <ILN < yEFN mpR n <>a+GObM)<c7WV T n+VES_NILNUOPGFGQT0N< [ ='EFD+O NEQDVJE ObDVc'IKD+GFTE B ES < [ <ES BB
(79) Utuo m Uto|tvLwS 9 mLMnL LMto|mL= nwLMt SLrU mQoqm~LwS SL+k UmLMnLa o|mL4 SpLnL Um~LwUnoU|9 mLMnL UmLk UnwLMt oU= mLMnK_ LMt 0 mX@ LMto9 m~LwUt BB E SÇN ; <>D7a [ IblL< c'NIKNUObGFGFTN< [ ='EFD+O NEFDhJWVTR+S}EFDVJNy6I0a"ILGFTVD+IL=E O GVEFDVN< [ a [ <>NUO NEFILD~ S OPDV c KI [ cV< [ <cGQ<)hEFM>IP . |. @. |. @. |. . |. g. }.
(80) J [ Oba ; EQM ObGFGFThLOPSEFD _Lj Vy_<GQ<)NW
(81) }. m LMn 0m n Um m. 1. m. . m. m9n g m. m. m m ~m m m S}EFDVJN ; < ObM)N6N ; O N =m" I [ <>lK< [ T7N< [ = m+ObDVc = m" m XOfYVR+EFM 'MOPGQM)R+GO NEQIKD'S ; IbySN ; O N I [ <)lL< [ T [ R+GF< ; ; ; IKo GQGFIbyfSÇW+RVN ; NO N N,<GE ObS6SUNNIKIKNUObDVGF< GFT EN <<K[ Q=2´EQXD+O >N EFDV JX bObDVc b>Vy EQGF<EFD7N <MObS}<I " b>°N D OPM>NbE SGFIV[ MObGFGFTM>IKD h R+<)DhN ; hOPSÇO DLRVN ; j_<>DV[ c+EF0N<SNÇS ;; IbyS[Py ; <)[ N ; < [; OP[ SN ; <SURKW+SUTVSN<>=zI EFJLR [ < m I [a EFJLR [ <g~ SUIEFN_ESM>IKDhlK< JK<>DVN ~W+RVNy_<HS ObGFG2D+ILN_W"<HEFDVN< <SN<cCEFD'N ESa IbaX< NT < <L -'
(82) # L
(83) 1302
(84) 83
(85) 2
(86) 8.
(87)
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(89) &
(90) ` `W`8
(91) &
(92) c
(93) &
(94) c !" I VlLO [ EO W+GF< S¦I N ; <EQDVc+EFMO N< c0NTha"< S ; <M>ILD+S_Iba"< [ O NI [
(95) &
(96) VES2\}R+SUNO0=<)NUO GQEFDVJLR~ESUNEMyOPTI I [ =EFDhJfGQE SUNS VEFNESObSSURV=< c NIW"< [ EQJ ; NUObSUSIVM>EO NEQlK<LÖ x <c+I0D+ILNOPSUSURV=<N ; < ='ObaV# a+EFDV[ J[ NIW"<EQD \}<>M>NEFlL<EFD OPDV[ T'S}<>D+S}<L [ $ m [N< ='S R N
(97) &
(98) 'Ob` D~`WSU`8GO
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(100) NEFILD7
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(103) &O0
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(106) I
(107) &
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(109) &
(110) '` ` `:
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(112)
(113) 2
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(118)
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(120) 2
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(122)
(123) A [ ` `W` c U
(124) 2
(125) 8` W` `8
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(127) &
(128)
(129) A3 c ( ` `W`
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(137) + y ; < [ <pm
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(139) 2(
(140) + A BmrLMn U-+ AG Bmz ¬" Bn U-+ U BO=P U-+ A + . BmdR n U,+ AG Bmz ¬,+
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(142) ' Bn U-+ S U
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(151)
(152) 2
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(154) &
(155)
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(159) {` ` `{
(160) &
(161)
(162) 2
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(164) &
(165) 8` `W`8
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(167)
(168) 2
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(173)
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(178) °
(179)
(180) Cu ! + o + 5
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(182) Bmz U
(183) 2
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(186)
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(189) 2
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(195) &
(196) r`W` `r
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(198)
(199) &
(200) ] ; A Bn ; U
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(203) &
(204)
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(209) &
(210)
(211) &
(212) ) A Bt ¬ p
(213) &
(214) a` `W`
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(216)
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(219) &
(220) `W` `
(221) &
(222)
(223) &
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(225) &
(226) a` `W`
(227) &
(228) @[ u
(229) &
(230) [ 0 [ `W` ` 0 [ 0 [ U <>WN
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(233) _` ` `{
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(236) 2
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(240) 2
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(244) 2 A 2B 0 [ ` `W` 0 [ U <>_D
(245) Bmz U
(246) &
(247) 8`W` `8
(248) &
(249)
(250) &
(251) A n} U
(252) &
(253) 8`W` `8
(254) 2
(255)
(256) 2
(257) A n} U= [
(258) &
(259) '` `W`8
(260) &
(261) [
(262) &
(263) [ 0 [ `W` ` 0 [ 0 [ WVT'EFDVcVRVM>NEFILD ; TVa"ILN ; < S}ESObJVObEFDX A n} U= [
(264) &
(265) '` `W`8
(266) &
(267) [
(268) &
(269) [ ) B 0 [@ `W` ` 0 [ 0 [ " 0 [ `W` ` B 0 [@ `W` ` 0 [ 0 [ i 0 [ WVT, U A n} U= [
(270) &
(271) '` `W`8
(272) &
(273) [
(274) &
(275) [ ) B 0 [ `W` ` B ) 0 [ x 0 [@ ` `W` 0 [ 0 [ A n} U B
(276) &
(277) '`W` `8
(278) &
(279) B
(280) &
(281) B 0 [ ` `W` 0 [ 0 [ WVTEFDhcVRVM>NEFILD ; Tha"ILN ; <S}ESOPJhOPEQD" A mz U= [
(282) &
(283) '` `W`8
(284) &
(285) [
(286) &
(287) [ 0 [ `W` ` 0 [ 0 [ WVT| m mA nwLMtVN ; <)D,N ; <O [ JLRV=<>DVN_ES6EFcV<>DVNEFMObGVy ; EFGF<HOPGFG2ILN ; < [ MOPS< SHO [ <N [ EFlVEObG& ` ; [ ; ; [U[ ; ; ; [ [N< = <>M ObGFGÇ N 0O cVN<>D+KO IL3N; < S<'59#- y5EF{N ; ESN ; Ob< DV;T,ILNGF<< =[ <>a+yGObEQM>N < c,O'WVc~T ESUNv EFDVVJLEFR+='E SEFGO <[ cGFTIhE M) M>R ES<>EFD+NS}M><>< G 2O0y M>IKDVEQM N<>Vy6N2<0EFMD7OPyGQG°; N EFM < ;
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(289) °
(290)
(291) Cu !mn 5
(292) '# < m n r! ; Vr < 3; <'59#- 5 !vm n 5
(293) '# <}m n ! ;V < 3;<'5=#-5 tb¤2 ¤ >w ; <MObS}<I 3E SN [ EFlhEOPGVW"<>MO)R+S}<0ILR [ ch< XD+EFNEFILD7I ESM>IK='a"ILS}EFNEQIKD+ObG ; O NES I [ OPDhTM>ILDVN<>VN ¦ N ; < [ x <ESO [ RVD+M>N;EFIKDOPG [ SRhM ; N ; O N [ I [ <>lL[ < [ T m@ m @AG ; ¬" Bm8
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(295) Ö0 m U- + A0 ^dR Bmz ¬9 ^d
(296) 2
(297) + o 0 ^dR Bn U= ^
(298) 2
(299) '+ S}EQD~M>p< m# nLr A Ö~ n} U- + >v VEFD+M)< +0ES ; ; ; [ ; [ [ [ ; [ ; [ [ ;N s< U|GF<E N_MOPIbS}aX<< S[ O y NI <>[ D O [ C<E<>SYVRXN Ob<'GFGFTObaV<a+OPGFSUEFTVMO NEFILDSUTV=0WXIKG2I N < R"aXObE Iba"< O NI y O N<>lK< N <'O JLRV=<>DVNa"ILS}EFNEQIKDX>"I x ; <>D 7ESÇN ; < Iba"< [ O NI [ Vy_< ; O lL<Ny_IMOPS}<S NO [ JLRV=<>DVNÇa"ILS}EFNEFILD m Ly_<=R~SUN_S ; Iby N ; O vN m!Nn0<>DVNUObEFGFS m t Fn tU j6RVNN ; ESE S6N [ EFlVEObGKSEFD+M) < Bm_Bt U- + a A mz Ux Bt - + U o Bn Ux Bt U, +WVT'ObSSURV='a~NEQIKDXM A nBt U, +) NO [ JLRV=<>DVNaXIKSEFNEFILD y6<=0R+SUNS ; IbyzN ; O N m$ n7<>DVNUObEFGFS tB m8% tsBn U j_RhQN tsBm8B U- + r AZ Bt Ux Bmz , + o Bt Ux Bn} ¬, +S}EFD+M>< mn'OPDhcWVT 2<)='='O M A BtBn B U- + > ; <M ObS}<I L0E S6<>DVNE [ <)GQT7ObD+ObGFIKJLILR~S # W+S}< [ lK<HN ; O N6N ; <EFDhN< [ a [ <>NUO NEFILDESÇD~ILNÇSN [ EFM>N GFT0='IKD+ILNIKD+EFML EQDN ; O N m!Nnc+IV< SÇD+IKNÇEF='a+GF T m &}n'hVIKD+GFT }m ( }n 8
(300) M>ILD~SEFcV< [ N ; <M>IKDVN<>V%N AwSL+ RWt I [ SIL=v< tf ; ESGF<Obc~SNIN ; < IKGFGQIbyEFDVJcV< XD+EFNEFIL_D
(301) |. < "< . <. . . < . <. < . . . <. )< . < . . |. <. < . <. . <. <1. <1. )< . <1. <. < . <1. <. < . . . <. <. <. <. =< . < . < . < . 7<. < . < . . . . < . . |. < . <. <. < . <. < . <. 6. < . . . . 1 <1. <1. . <. @< . )< . . <. . <. )< . . <. . @< . . <. <. . )< . <. 1 < . 6. < . )< . )< . 1 <1. <. . < . @<. . <1. <1. . <1. . . . <. <. |. . |. |. |. . . |. . . |. . |. . .
(302) ´s¤ 3; <5=#- 5 N1 p3 /4/&# fSO <1 ! < ; <8/ 1 !vm# nK14X.~/21k# %}m n ! ; Vs#WY #WV 59#WV Xs vmu < n ;x!s5
(303) # Xd#d5 ".'# 683
(304) 5
(305) ' 5}m < }n V"#p5 ".z 7 /&# x ; ; ; [ [ ; [ [ [ I [ <=dS WVObT GFG2[ S}<<>cV<RVM>EFDNEFILVD~<>SM>NRhEFILDVDcV< [ N SO O N<N M>IL< DVN< <>VO NS < <>D+IKR+J SO <M>ILDVN<>VNSNI'ObGFG2NTVa"<c,"~N< ='SNIW"< < chRVM>< cCNID+I ='ObG °
(306)
(307) C
(308) u ; Vr# 3
(309) KV 6/2# o Q#- 3#i.T5d 14< 168Vx# ; VV6 /&# tb¤2 ¤ >w x <IL=EFN6ObGFG2NTVaX<EFD I [ ='O NEFILDfRhD~GQ< SUSSN [ EFM>N GFTDh<)M><SSO [ TV ` R~GQ<0
(310) U- + A x Ö0 m U- + U>" Bn U- + U A 0 ^rR Bmz ¬9 ^
(311) &
(312) /+ U)x Bn U- + U o" Bm8 U= ^s
(313) &
(314) /+ & Bn U- + 0 ^ A Bm8 Ux Bn} ¬, +
(315) &
(316) /+ WVT <>; ='='Og+Vy ; [ EQGFd< U, + A mz Ux BnMR O=P} ¬, +a A[ mz Ux Bn U, +
(317) &
(318) / + > ;~[ ` R~GQ<H<M x Ob S} <
(319) dSI ¬, +R~M GQ< A S" BBmO=P n} > "Ux = BLtO=PV ¬, +ObDV cA = O9 BP8mzLL ¬_" BO n U<x BILtWV UlV- EF+ ILUR+ Sa
(320) AZ U Bm8- + U " A nLM t U- U+ - { + UAw A Bm8 U B, m+BnEFLMD,tObGF G"U- N + ><>OP<0DVMc|ObS}S}< EFS=' EFGO [ GQT I [ [ R~GQ<9 LL> ` R~GQ<0 m
(321) M U- + AG m Ux BmR n ¬, + AG m Ux Bmz ¬, +
(322) &
(323) : Bn} ¬, + AG Bmz ¬, + A U- + > ` R~GQ<04 SV
(324) M U- + AG S Ux BmR n ¬, + AG S Ux Bmz ¬, +
(325) &
(326) : Bn} ¬, + AG Bn U, + A U, +) ` R~GQ< " R
(327) U- + A BmdRWn U" t U- + U A Bm8 U" t U- + U
(328) &
(329) Bn Ux Bt ¬, + A Bm_BtB U, +
(330) &
(331) BnMLMt U- + q A F= mBt @ RL9 nvLMt9 U- + AG U- + > ` R~GQ<,´X
(332) U, + A Ö0 m8 U" t U- + Ur A ~ ^ R0 Bm8 U= ^K
(333) &
(334) t U- + U>y ; EQGF< U- + A 0 ^ R' Bm_ U t2 U9 ^
(335) &
(336) + A ~ ^ R Bm8 U" Ut U9 ^p
(337) &
(338) /+ U A0 ^ R Bm8 U= ^s
(339) &
(340) : Bt ¬, +> ` R~GQ<0= "
(341) S}EF='EFGO [ O [ JLRV=<>DVNObS I [[ R+GF<x RÖ> ` R~GQ<9 gdU
(342) r U v
(343) &
(344) /+M A r
(345) 2
(346) t U- + >+y ; EQGF< U
(347) &
(348) '+ A m U v
(349) &
(350) + v
(351) &
(352) 0 BtvLMS U v
(353) &
(354) + A r
(355) 2
(356) 0 BtvLS U v
(357) &
(358) + A
(359) &
(360) Bt Ux S U
(361) &
(362) /+ Ua A
(363) &
(364) ' Bt U, +) ` R~GQ<= g0RÖ
(365) r U
(366) &
(367) + M A m U
(368) 2
(369) '+
(370) &
(371) @ S ¬
(372) &
(373) +M A
(374) &
(375) +A U v
(376) &
(377) + ObDVc
(378) &
(379) +0E SN ; <0='IKSUNJL<>DV< [ ObG I [ = I O [ JLRV` =<>DVN_NI WV T'NTVm a+EFDVJXVSI V m R~GQ<9 gpR LL
(380) Az Bmz RV4 SpLmX z RSh LMmWVT7MOPS<x U% O9PvLvm WVT'MOPS}< 9 g~RÖ% m A 7WVTMObS}<'9 O=P8LL> # W+S}< [ lK<N ; O Ny6< ; O lL<R+S}<c 2<)='='O0g,N ; < aXO [ N}EF='a+GFEFM>EFN´GQT0N ;+[ IKR+J ; ILRVN GQGN ; <ILN ; < [[ R+GF< S O [ <0cV<ObGNHyEFN ; S}EF='`EFGO [ GF@T
(381) m m mm m m ` R~R~GQGQ<0< m UUK LL
(382)
(383) A A U m Umz m LMn} RK= mm0FLv m SV9RK6= m0 WhLwTCShU= gsLMUn U% WVT|9 A gU WVT| m F >m Bn RKU= m0LrSV@ LMnL9 WVT|" RÖU% m Bn _A WVT m U)` m ` R~R~GQGQ<0<044 SSUU LL
(384)
(385) Aw SAwSLwL~U4 UmwmvLSnLL+ vRKSd= m0L+LwU Shm UR = m0 WVLvT|SV=Ug0 LaUnLU WVT,m0Lv= gsS8AUU vWVSdT|L+k USh Um )Bn @ R U9 m~L Sh' LnLWVT,x RÖU 9 m~LrSV' Lan WVTC` 4 Sh% msL4 SL nKa A WVT,9 LLm U) R~m GQ<04 U@U m
(386) AwUm~LwUn RL= m0LwShx Lwm Un7WVT|9 gU% 3 m U n} m Rb= m0LrSh" LwUnKWVT|" RÖU m Rb= ; m0LvSVx LwUnL WVT7 UU R)= mML_4 SvLrUnKUWVT 9 LL R>= mML_9 n LwShWVT74 S U R)U= mML nKx LMSVWVT7= LKÇR+S}< c'EFD0N <IbaVa"ILS}EFN< c+E [ <)` M>NEFILDX% wU= m LMnK A ' WhTC= gsU_R+S}<cEQDN ; <IbaVa"ILS}EFN<c+E [ <>M>NEFIKDX> ; R~GQ<k U@U LL
(387) AwUmvL4 UnLt 3k Um~LwUnL0 Lat WVT 9 LL°R+S}<c7EFDN <IbaVa"ILS}EFN<c+E [ <)M>NEFILDX wU 9 mvLanK~ LtA WVTC` 4 U@UU) R~GQ<,k UGRÖ
(388) AwU mL09 n m R t m R"= m0LSh L= nRtWVT 9 gKUU m BnR t R"U9 m~LSh L= n R t' WhT x RÖ nRbU9 m~L Sh@ L= nsRWtUWVT, U% nRK= mLk SL+= nsRWtUU WVT|= LKU% nrRL9 mLMta A WhTC4 SVU> ` R~GQ<04 UO9Ph
(389) AwUO9P m Rb9 O=P8LrSV WhTC= gsUU m R S, WVT|= O9P8LL O=PdA WVT|9 g0R > N ILGFGFIbyWS
(390) h¤"tb
(391) u V¤"tb
(392) YW# V dVx# 683 5=1k; <14<5
(393) #p5 ".'# " x3 /&3W6/26
(394) '# Vx#s#WY #WV p3; <5=V" 3 5=# xVx# #A. . /. *. *. *. *. |. *. *. *. *. !. !. *. !. !. <. <. <. *. <. <. <. <. <. <. <. <. <. <. <. *. <. A. #<. $*. *. $*. $*. *. $*. *. %*. %*. %*. ; 3?3 68V 68< # V "! #p3;<'5=#-5 1 <'1459# . @. l. /. A.
(395) tb¤2¤ >w DhT0SUN<)a EFDSRhM ; O [ < cVRVM>NEFILDESÇ< EQN ; < [ O ´M>ILDVN [ ObM>NEFIKD h´~m"xn' o }mBnMR?O9P hbN ; <>DV 0mX"n }m nsRWO9P WVT 2<>=='Or OPDhc7N ; < OPM>NN ; O N ,E SSO < ~I [ O~M>IKDhN [ OPM>NEFILD m o +n "y ; < [ <mnWVT <>='='O . ObDV; c ; <>='='Og+ ; < [ < I [ <H< ObM ;'; [ <>y [ EQN<SN<>a'ES°SUN [ EFM>N´GF[ Tch<)M [ <OPS}EQDV J[ EQDN ; <GQ<)hEFM>IKJ [ [ Oba ; EFM_a [ IVcVRVM>NI OPm DVc o y EFM E S6y_<>GFG ILRVDVch< c7S}EQD~M><N <NTVa"<c,MOPGFM>R+GFR+SN< ='EFD+O N<S I ObDVc,,N< ='EFD+O N<SWVT 2<>=='O > # f
(396) # L
(397) $1 0
(398) 8 N [ <)='ObEFD+S_NIa [ IVcVRVM><SUIK=<D+IKDVN [ EFlhEOPGXS}O <M>IKDhN<)hNS
(399) ´s ¤ & # 55
(400) '#SUTVDVNUObM>NEFMOPGFGQT0SO <M>ILDVN<>VN S 7# # a<'# 5
(401) '; #d14<0D +_J
(402) '# Vx# D
(403) &
(404) BA Eb D E D G E D E D B,HIE C D J aE m J J
(405) &
(406) BA J E D RW,uE N R
(407) J E U J E U,L J E J LM, J
(408) &
(409) BANC@JdL_ JE SL J E J LM, j6< I [ <y6<S ; Iby 2<)='='On+Vy_<DV<>< c N ; < IKGQGFIbyEFDVJN<>M ; D+EFMObGGF<>='='O~ <>N WX<cV< XDV< c,WVT v
(410) 2
(411) +aA +L"ObDVc GF<>N W"<HcV<"Dh< c,WVT@
(412) ,+A.+K A L °
(413)
(414) Cu ; Vd#WY # V 3?;<'59#?-5 14< J 5
(415) #WV"#1& 5= 3?>Y V 1k 7/2#c d.@Vx;.z# V 6873; <'59#?-5 N;x! 1k< _ J < <$14<'59# # V 683
(416) 5
(417) ' 5 !; Vr#WY # V p59# V X mK 6:3
(418) 5
(419) ' 5 }m 1& a#/4/ x5 ".'# !; Vv# Y #WV 4+ ;x!r5
(420) '#V1
(421) 5a5 ".z# ! ; V ; Xd# + }m U- + a A x cQ Ux }m x U- + U tb¤2 ¤ >w j6T,SN [ RhM)NR [ OPGÇEFDhcVRVM>NEFILD7IKD ; ESESILWVlVEFILR+SE ; OPSN ; < I [ = c L%"yEFN ; J
(422) Z A3iObDVc +vA + AwS L B yEFN ; B 2N ; <>D I [ <)lL< [ T mCSRhM ; N ; O N m 0ESy6<)GQGNTVaX< c"EFD,aXO [ NEFM>R+GO [ B }m E SHy_<>GFG NTVaX< cSI,WVT|EFDVcVRhM)NEQIKD ; TVa"ILN J ; < S}E S B }m U- + A ! x cQ Ux }m x U- + U I [ SUIK=< iObDVc|SIL=< +L ; <>D }m U- + A S ¬" B m U- + Ua A " B }m U, + Ua A " cQ Ux }m x U, +U> A B Lrtfy ; < [ < B; " ;J N ; <>D [ I [ <>lL[ < [ T m SRhM; ; N[ ; O ; N }m E Sy6<)GQGNTVaX< c2EFD aXO [ NEFM>R+GO [ B }m 'ES y_I <>[ GFGÊSUIKNTV=aX< < c "SUI7:WVi|T,OPEFDhDVccVRhSM)ILN=EQIKD< +TV aXIKN ; < <>SD E S I m <>lK U< - + T d + Aq I BN < m EFUJ x BtN UN- TV+ a" U<L a _ GF <>N´B N}EFDhm J U+ - + W"M < A Bt ¬, "+ cQ)v U x }}m m x U U- , + + >UA B }m U- + a A " cQ Ux }m x U, + >U> °
(423)
(424) Cu$# Y # V d <'5= 3W59143 /k/ s "! #d3?;<'59#?-51 "! # tb¤2 ¤ >w x < ; O lK<NI,S ; IbyzN ; O NE m$ n~N ; <>$ D m n I [ ObDVTCSUTVDVNUObM>NEFMOPGQGFT7SO <'M)ILDVN<>VN ; E SES WV# T|; SN [ [ RhM)NR [ OPGEQDVcVRVM>NEFILDIKD ¦R+S}EFDVJ%< XD+EFNEFILD m ; <'WXOPS<MObS}<Ly ; <>$D ESN ; <<>='a~NT,M>ILDVN<>VN ESM>GF<O [ N < yES} <
(425) ; [ A ; 0bVy ; < < 0& D [ ~N ; <>; D }m " ¬, + A[ 0 ^R 0 }m U[ 9 ^p
(426) &
(427) /+ o ~ [ ^sR 0 n [ ¬9 ^
(428) &
(429) (+ AG }n' ¬, +_WVT EFDV[ chRVM>NEFIKD TVa"[ ILN <S}ES a VEF=' EFG[ O GFTy <)D [ A 0t I A t%0VI A ~ R?t I SUIK=<N< Z = t ObDVcSUIL=%< 0 D I AwU 0I A tu R [ 0 I SUIL=<N< Z = tObDVc7SUIK=%< 0& J ; A ~ t I SIL=< 0'( D OPDh; c SIL; =< SNUObM ZtC[ N <>q D ; }m U- + A 0[ }m ¬" Bt U- + U o }n' Ux Bt U, + A }n' U- + WVT|EFDVcVRVM>NEFILD TVaXIKN < SE S VEF='EFGO GÊT7y <>&D NA Lt I SIL=< EFD$_ J ObDVc SUIK=< SNUObM tf ; [ A [_ Çy < < [CE SHOb DCN< [ = lLO [ EO W+GF<ObDVc ; _ J N ; ; <>ND }m x U- + v A [ ` `W` y ; < [ <
(430) &
(431) `W` ; `@
(432) &
(433)
(434) &
(435) A }m ¬, + o n U, +WVT,EFDVchRVM>NEFIKD Tha"ILN <S}ES <>N' W` `W` WX< }n U- +
(436) N E S =<OPD+SN ; O N *2 o 2 I [ <)lL< [ T OU m 3 O 3 $ m ObDVcN ; O N *2 o 2 I [ SUIK=\< O I [ ` ` ` o [ `W` ` A n U, +) N [ <)='ObEF[D+SN[ IcV<; OPGXyEFN ; N ; <; M[ ObS}< S6y ; <>!D 'ESEFD J VObDVcy ; <>D 7ESI N ; < I [ = ; m [ XI [ UtL yEF[ N ; J ^_ILD+S}EFcV< SUN0N <MOPS}<y < < ÝESSUIK=<M>ILDVN<>VN EQD) j6T 2<)='='O l+ N < <'ESOSUNUOP?M ClLO EO W+GF< cO a[ [ Ib; aX< [ SURKWXM>IK; DVN[ <>V(N 0EFD [ J OPDhc,OPD ; EFDV;N<>JK< [ i0SURVM ; N ; O N J I [ <>lK< [ T m I N ; < [ EFJ ; N_NTVaX<L I [ <>lL< [ T + I ; N ; [ < EFJ NNTVa"<L2N < <ESO'N< = +SURVM N O N }m ¬, + w A x cQ Ux 0 }m U- + U> <>rN cW"p< c * y < < -. |. <. . <. . "<. <. <. <. . <. <. @. @. . @. /. <. |. |. <. <. <. <. |. @. <. @. @. |. |. =<. < . < . <. <. =<. <. <. <. < < . +<. < )< . "<. < < . /< < . n. <. + "!. ?. ? ! ?.
(437) WVT'NTVa+EFDVJ , 2<>NOPGQSI
(438) &
(439) :` ` `:
(440) &
(441)
(442) &
(443) W"< m U,+)+ObDVc
(444) 2
(445) 8` `W`8
(446) &
(447)
(448) &
(449) W"<\ n U,+) ; <)D_
(450) m U- + A cQ _`W` ` >
(451) 2
(452) `W` `8
(453) 2
(454) ~ c _` ` ` >
(455) &
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