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APONML@ w~w~N %w~w~@&get_L1F@@@T@ 3z}!+ 8z}!+a >zzwv t s r q p o n @ o}!}!(* u}!}!(*@3get_SimplifyEqLemmaF@@@@ NPٓ NP٠ NNPSؠנǠƠ㠐 Ġ à       ᠐@ ؒ @1get_SimplifyLemmaF@@@@ { { ('3BA        1@?>=<@ {{J {{@&get_L4F@@@D@ #& (&Q .xwgf d c b a ` _ ^ @ _#% e#%@-get_CondLemmaF@@@@ sCEӓ xCEӠ ~CCEHȠǠӠ⠐᠐        Ѡࠐߠޠݠ@ Ғ @)get_FldEqF@@@@ mx mx #21        !0/.-,@ mmtwI mmtw@.get_FldCarrierF@@@4@ @Z   !s@k(+L )@@ .ʓ 3ʠ 9(Ring_tac+setoid_ring#Coq@@0relation_carrierV I@*get_RingFVF@@@x@ We \e b頕ƠŠ        Ġà @ eel eel eelne@"FV6h eeov eew~ ee  ee  ee  ee  ee  ee  ee@@'get_FFVF@@@@ 6z 6z BA10M\[.-,+*)(KZYXWV@)66=y.66=y466=@@I}<66AHC66IPJ66QSQ66TVwX66W[{_66\`f66aem66fjt66ko{66pt66uy@@,get_RingMetaF@@@@YY堐䠐ԠӠѠРϠΠ̠͠ˠ@XX'@)mkPolexpr1p()(*1,29F:<J=?"@D& EI*JN.OS,TX@@(get_MetaF@@@N@-qs@2qs@[8qqsvqpnmlkjih@i?n?t@.,k|ĐȐ!"&Ɛ'+ʐ,0ΐ15Ґ6:֐;?@@+get_Hyp_tacF@@@@[.]p[.]p[[]`,+7FE5DCBA@@ @%mkPol쓠*"KW)q0u7 > EkLoSsZ wa!%uh&*@@v"lH@t..Boy..Bo..BKF@)mkHyp_tac ..LMӐ..NQ@..ak..ak..af..gh..ik@I..mo@@*get_FEevalF@@@@ @(@RȠ@@ B(@@@@@ՠޠ\ ⠠a栠 렠 Đ#𠠐 ɐ+ ΐ3 Ӑ; ؐCyKS [ &powphid l@@@@u !@@@@~"#@#@@yޛݛ 5 4 3 2 1 0˛<5@ 7))0vF@))9?))@A))BD))EG t))HK x))LO |))PS ))TW ))X[ ))\_())`a))be))fj))kq ))ru@))8u@ AA 1field anomaly: bad correctness lemma (get_FEeval)@@/fold_field_condF@@@ p@ A*fold_concl2   D@ B=&&01MC&&01@@@#andЖw@@W77=E!x`77=?!yi77CE@@@ @"fx|IIUWII[gVII[e/IIfg@@ @"fyIIoqIIuqIIuAII@@IIMj@IIGII3II@@@@@@ @%Logic$Init#Coq@@%Falsee@@@@ L@Ð@#notШ@$  r.֐5Ԑ<@?@@FВVL@@ @"ftU䓠Z/`򠓠f0@(Get_goal*{@@@@@!u @@@+simpl_PCondF@@@ @ @ ̐%%+.%%2?%%2;r %%<?@@ @%lemmaCCINCCRcCCR_@HC7 ِCC`c@@@A@@)ggty@@@@@@$lockgg(lock_defgg@@@@@@@AA@gg@@@@@@ gg @0clear_#_4C69D547<,@6@@@  ߠ@5protect_fv_#_2BA1BA21bXɠ7bZ*field_cond@!'y@0G s/@ 5;@0exact_#_4C69D568점(R@$Truey@A@J@@1simpl_PCond_BEURKF@@@ y@ @ [&&,/`&&3@f&&3<E m&&=@@@ @ӐuDDJOzDDSdDDS`Ҡ DDad@@@A@@hhqv@@@@@@ϐhhΐhh@@@@@@@A͠@hh@@@@@@ hh̠ɠ@@@@ ۠Ƞ*field_cond@򓠐򠐠Ġ 6@.Field_norm_genF@@@? %"rl@ @$mkFV ;;AE;;IW;;IS j@/*3 C ;;TW@@ @%mkFFV)[[af.[[ju4[[jq @T4; _<[[ru@@ @$mkFEEyyJyyPyy @0! O4 {Xyy@@ @#fv0af͠l3@+FV_hypo_tac;{iu|ɓɠf @$@@ @)lemma_tac$kont@ @ ! @ 6p @@ @#lpe??GJ??Nc??NY!'@ &  ??Z]??^`z??ac@@ @$vlpeggos$hyps@@@@ ;@@AA@ @#prh@,proofHyp_tac#@@ @$vlmp, %hyps'@@ @'vlmp_eq9    ''hyps_eq@@ @)mk_monpolF > > F OK > > S cQ > > S ] @*get_MonPol!HZ > > ^ c@@` g g k e g g k k g g k | 2@1compute_assertion3=ޠ<t g g } P{ g g  C g g   g g  @ g g  @@ @#lem    є*f_rw_lemma@@@@A@       !  !!ѐ  !! Ґ  ! !Đ  !!  !!  !!@   !@ A@ ,type error when building the rewriting lemma@!!!!!!!!P!!!!e!!!!@ !!!! v@@@#@@@=Field_norm_gen:cleanup failed@@ @(main_tac "X"X"^"f!H@ ,"X"X"l"@:protect_fv_#_in_#_2BA1BA22B7bZ%fieldE @?"X"X""D"X"X""<J"X"X"")Q"X"X""@@W"""#\"""#b"""" )@6ReflexiveRewriteTacticvDCk""""᠒.r""""栒ܐy""""𠒑a""""'"""""""#@############"@')Xʐ####@2Field_simplify_genF@@@ؠF@#A#A#C#T#A#A#C#T#A#A#C#M#@ D.8#A#A#N#Q@@#V#V#X##V#V#X##V#V#X#f#6@Tސ#V#V#g#h @0ring_subst_niter!@@@!#V#V#z#}#V#V#~# #V#V##@ # ### # ### # ####n@ Fl_G$ # ###@@.Field_simplifyF@@@2 # ###ᓠ7 # ###᠐= # ####@(ꩠ@@@A`@*R # ###@@@@@@@"_7(#@9field_simplify_#_7A2D332Bs߿@@.field_simplifye##$$!?LFIg@i@ @!Gu$%$%$+$,z$%$%$0$8@@ $<$<$>$mu@?field_lookup_#_[_#_]_#_2BA1BA25%[=$<$<$L$d$<$<$L$d$<$<$L$U#@2EK$<$<$V$d#@{;@@?LFI@?LFI$<$<$i$k@M$<$<$l$m@@@@"_8($@?field_simplify_[_#_]_#_7A2D33286H@@.field_simplify![$$$$?LFIl!]$$$$Ǡ?LFI@|@ @$$$$ғ$$$$ޠ@@ $$$%~| $$$% $$$% $$$${$$$% z@@y+$$% %@@28$$%%@̐@$$%%@@@@"_9($@>field_simplify_#_in_#_7A2D3329&Q@@.field_simplifyQ%%%9%H?LFIS"in_%%%N%T<>@bA@ @n%W%W%]%^s%W%W%b%j @@ @~%n%n%t%u_%n%n%%@@ @!g%%%%$goal@@@@0%%%%@@@A@ %%%%@1revert_#_4C69D54C<@@@ %%%%97%%%%䓠%%%%䠐%%%%6%%%%䠐5@@4@3%%%%@%%%%@@@ %%%%@0intro_#_4C69D577LE @@@| %%&&@@@ %%&& @@@@#_10(%q@ $field_simplify_[_#_]_#_in_#_7A2D332E:;@@.field_simplify![."&0"&0&7&F?LFI Š!]<"&0"&0&K&Z?LFI>"inJ"&0"&0&`&f(@ M,@ @Y#&i#&i&o&p^#&i#&i&t&|@@ @si$&$&&&Jr$&$&&&@@ @z%&%&&&$goal@@@@&&&&&&@@@A@ '&'&&&̠ꠐ蠠x@@@ (&(&&' (&(&&&(&(&&&(&(&&&(&(&&&@@ \(&(&&&@@"Ԑ(&(&&&@(&(&''@@@ )')''' @@@h*'*'''@@@ *'*''' z@@@@,Field_SchemeF@@@)Simpl_tacTu< @ @d >) >) )&))%>) >) )-):+>) >) )-)6 U2>) >) )7):@@ @.:?)>?)>)D)H??)>?)>)L)ZE?)>?)>)L)V-oL?)>?)>)W)Z@@ @,T@)^@)^)d)iY@)^@)^)m)x_@)^@)^)m)t+f@)^@)^)u)x@@ @*nA)|A)|))sA)|A)|))yA)|A)|)))A)|A)|))@@ @'Main_eqB)B)))Ƞ@ @C)C)))C)C)))֠C)C)))7C)C)))ϠC)C)))Ӡ GC)C)))@@ @ǐD)D)))䓠D)D)))󠑠D)D))) D)D)))𠒑D)D)))@@ @E)E))*E)E)**ĐE)E)** !E)E)* * E)E)**@@ @9F*F***F*F**#*8 F*F**#*.87F*F**/*2"F*F**3*5 "F*F**6*8@@ @*G*<G*<*D*G/G*<G*<*K*Z5G*<G*<*K*W ː<G*<G*<*X*Z@@ @QDH*^H*^*f*j(list_hyp@@ @#fe1QI*I***VI*I***\I*I***cI*I***qjI*I***@@ @#fe2sJ*J***xJ*J***:~J*J***J*J***J*J***@@@@ϐK*K***@@AA@ @&nlemmaL*L***┠+field_lemma@@@@A@M*M*+ + M*M*++M*M*++ԐM*M*++M*M*++#M*M*+$+'pM*M*+(++ېM*M*+,+/@M*M*++/@ A@ #field anomaly:failed to build lemma@O+fS++j,$O+fS++j,$O+fO+f+j+x@.ProveLemmaHypsh O+fO+f+y+&ilemma@@A@@  Q+Q+++@@@@ A@ 'field anomaly: failed in applying lemma@+S+S+,,1S+S+,,7S+S+,,"<S+S+,,"BS+S+,,lIS+S+,,"@@@ NT,&T,&,*,6 T Q@@@ [U,8U,8,<,F a@0subst_#_4C69D5350<v@@@@kV,JV,J,L,bpV,JV,J,L,bvV,JV,J,L,V=@*OnEquation0ZcÐV,JV,J,W,ZV,JV,J,[,b@%FIELDF@@@ #@ @%Simpl\,\,,,敡@@@@\,\,,-\,\,,-)Notations$Init#Coq@@+reflexivity/&k@ A@:not a valid field equation@@ @ &]-*]-*-0-5]-*]-*-9-C]-*]-*-9-? ]-*]-*-@-C@@^-G^-G-I-Z^-G^-G-I-Z^-G^-G-I-S%^-G^-G-T-W@@_-\_-\-^-_-\_-\-^-_-\_-\-^-j)Z@, u_-\_-\-k-p$@@@ |_-\_-\--H%_-\_-\-- ,_-\_-\--@ 2`-`---   @>`-`---@@Ca-a---Ha-a---Na-a---2xUa-a---)@@#_11()@.field_7A2D332F@@%field@@ @md-d---퓠rd-d--- @@ ze-e--."e-e-. .e-e-. .e-e-. .e-e-..)@@@@󠠠7e-e-.!."@@@@#_12(*@4field_[_#_]_7A2D332C20@@%field![g.%g.%.N.]?LFIV!]@[@ @]h.eh.e.k.lh.eh.e.p.x p@@ i.|i.|.~.\Zi.|i.|..i.|i.|..i.|i.|..Yi.|i.|..d@@W i.|i.|..@@^i.|i.|..@@@@+FIELD_SIMPLF@@@E @ @+n/Vn/V/\/a 1n/Vn/V/f/x $ !%field@@ @ ?o/}o/}//Do/}o/}//Jo/}o/}//*@,rH0uRo/}o/}//@@Yp/p///^p/p///dp/p///kp/p///?@@tq/q///yq/q///q/q///wq/q///Р@@@ q/q///𠒑q/q///1q/q///@r/r//0 r/r//0 r/r//0ܐr/r/00 @@#_13(+@:field_simplify_eq_7A2D332D&:b@@1field_simplify_eq@@ @]u0Du0D0J0Ku0Du0D0O0W p@@ v0[v0[0]0\Zv0[v0[0k0v0[v0[0k0v0[v0[0k0tYv0[v0[0u0+N@ha8@@X@W v0[v0[00@@@@#_14(+f@ field_simplify_eq_[_#_]_7A2D3322~@@1field_simplify_eq![ #x0x000͠?LFI!]@@ @ 5y0y000ܓ :y0y000蠐 @@  Bz0z001 Lz0z001 Qz0z001 Wz0z001 ]z0z011d@@ mz0z011@@  zz0z011@@@@1Field_simplify_eqF@@@Š@ @Ӑ 1l1l1r1u 1l1l1y1 1l1l1y1yĐ 1l1l11@@ @  1111 1111 1111 ސ 1111@@ @  1111 1111Ġ 1111  1111@@ @  1111ғ 1111⠐ 1111  1111@@ @ U 1111񓠐 1111!1111,T@Rˠ-! 1111@@ @#hyp!222 2 #hyp@@ !222!2*%#@!'2,42.4!,2,42.4!22,2,2.2;@-OnEquationHyp+!;2,2,2<2?0!B2,2,2@2C  {@ @!Y!R2W2W2a2c!W2W2W2g2~!]2W2W2g2r 񠒑 X!d2W2W2s2w!k2W2W2x2{!r2W2W2|2~@@ @!!z2222!2222 ]!2222 Ð!2222!!2222@@ @!!2222!2222 ~!2222 ې!2222!!2222@@ @ !2222͓!2222栐!2222 򠒑!2222ࠒ!ܐ!2222㠒k!2222@@ @ ֐!2222!2223 !2223 ՠ!2233 @@ @!3333"3333) Ő" 3333#!G"333$3&""333'3)@@ @"3-3-373:"$3-3-3>3H "*3-3-3>3B!_"13-3-3C3E"?"83-3-3F3H@@ @ M"@3L3L3V3Z$vlpe@@"I3n43t4"N3n43t4"T3n3n3t3S"a3n3n33"h3n3n33"v"o3n3n33 "v3n3n33-"}3n3n33"3n3n33 }"3n3n33@"3n3n33@@ B"3333ޑ"3333@@@@@"3333@@@@"3333@@@@"3333@"3333@@@@@@"3334"EQ"3344"3334"3334@@,##@$ @#tmp"4 4 44!#tmp@@@@A@#44444K4N/# 44444Q4S@@A@@#4V4V4m4s@@@@ #4V4V4w4ꠐ蠠#+4V4V4}4@@#14V4V44#64V4V44#<4V4V44.@%t|g#D4V4V44@@ #K4444Ġ  %field g@ #Z4444Р  t@@@@ #g4444mj`@@@@@@.FIELD_SIMPL_EQF@@@ y@#5#5#5%56#5#5#5%56#5#5#5%5/ Ơ#5#5#5053i@@#58585:5l#58585:5l#58585:5K.@.>c @@@ې#58585f5iN#58585j5l@#5n5n5p5#5n5n5p5#5n5n5p5{ #5n5n5|5@@#_15(/1@?field_simplify_eq_in_#_7A2D3323/l@@1field_simplify_eq"in#5555  @ @ @$#5555̑ ܐ$5555@@@@ $5555@@@ $5556  $"5556$'5556$-5556 $35566/@5,@@ @ $S$I5566@@@ $P666%6,@$\666+6,@@ $c6-6-6168if F@@@ $p6-6-696@ x v P@@@#_16(/@ %field_simplify_eq_[_#_]_in_#_7A2D3320)&@@1field_simplify_eq![$6b6b6|6?LFI !]"in$6b6b66 ; x@1 {@ @$$6666 $6666@@@@ $6666@@@ $6666 C A$6666𓠐$6666𠐠$6666 @$6666𠐠@@ >$6666@@ E%$6666@@@ %6677 Ϡ͠@%6677 @@ %7 7 7 7 @@@ %$7 7 77 , *@@@.gen_with_fieldF@@@| @ @(MetaExpr%=888 8h@B@ @;%M8"8"8*8+%R8"8"8/8A%X8"8"8/8=0@R8ଅ%`8"8"8>8A@@ @@%h8E8E8M8R%m8E8E8V8a%s8E8E8V8]?%z8E8E8^8a@@ @>%8e8e8m8q%8e8e8v8%8e8e8v8~=%8e8e88@@ @#csr%8888 B%8888%8888@@)Datatypes$Init#Coq@@$list]@B@%8888A!AA@@ !r%8888@@@@%8888@%8888@/@B&(%8888Ē!%8888Ġ AA8anomaly: ill-formed list@@@ @& &999 9 & 9999&&9999{&9999lA@&&9999#&-999$9%@&09999%@@@ @$expr&99*9*9296&>9*9*9:9E&D9*9*9:9>&K9*9*9?9B&Y&R9*9*9C9E@@&W9I9I9M9Z&\9I9I9M9Z&b9I9I9M9N&i9I9I9O9R&w&p9I9I9S9U?&w9I9I9V9Z@@ &|9^9^9`9  &9^9^9n9&9^9^9n9&9^9^9n9w \&9^9^9x9@ @ 򠠠\@"eq @@&9^9^99@@@@ "n&9^9^99"u&9^9^99@@@@/prove_field_eqnF@@@#ope&ޠ@ @#res&: : ::&: : ::"&: : ::&: : ::"@@ @%expr'&:&:&:,:1*input_expr@@@@ Ґ' :K:K:\:`@@AA@ @$res'':c:c:i:m&result@@@@ G'%::::@@AA@ @'/::::'4::::':::::dd'A::::@@ @'I::::&蠠'V::::֠)Datatypes$Init#Coq@@#nat@A@'j::::ؠ'x'q::::۠W@'{::::䠠_AA@@ @'::::䠠'::::ꠠ'::::V@'::::񠠐@'::::AA@@ @'::::@  @A@':::; A!AA@@ @@@@'::;;@':::;@':::;@@ @"ty'; ; ;;D'; ; ;;$@@ @#lhs';(;(;.;1 B';(;(;;;= ';(;(;;;=@@@@@@@( ;C;C;N;O@@j@(;C;C;Q;We@@5(#;C;C;Q;U@@@@(,;C;C;V;W@@@@@(4;C;C;[;\(7;C;C;Q;\(:;C;C;G;\@@x@@Y(I;C;C;`;ca(O;C;C;`;c@@ @#rhs(X;o;o;u;x B(_;o;o;;(e;o;o;;@@@@@@@(t;;;;@@@(;;;;@@@@@@(;;;;@@@@(;;;;@@@@@@(;;;;@@@(;;;;@@a(;;;;@@@@(;;;;@@@@@(;;;;(;;;;(;;;;(;;;;(;;;;@@@/@@@7@"$$(;;;;(;;;;@@ @$lhs'(;;;;є#lhs@@ @&lhs_eq);;;;&lhs_eq@@ @$rhs')<<< <#rhs@@ @&rhs_eq)"<<<%<+&rhs_eq@@)->>><*g>>>><*m>>>>5@Cc.*u>>>&>9*z>>>&>9*>>>&>55@&1*>>>6>9@&>*>>>;><@(prove_rwF@@@ɠ>@*>>>>*>>>>*>>>>5@X*>>>>[*>>>>@ @*>>>>)Heq_maple@@ *>>>>Ҡ֠@@@A@*>>>>@@@@@@ *>>>>렠@@@@1reduce_field_exprF@@@+W"$+ @ @%evfun+ ?O?O?U?Z+?O?O?^?l+?O?O?^?h6h@[-VƠ"A+?O?O?i?l@@ @H+&?p?p?v?y++?p?p?}?_+1?p?p?}?+8?p?p??@@ @&+@????0simpl_field_exprD+N????+\+U????~+\????@+_????@@+d????ɓ+i????ɠǐ+o????Ǡ'%+v????@+return_termF@@@#@@@@+@@@:@AߠAA@@ >+@@@B@C@+@@@:@C@@@(get_termF@@@ B@@@@@ @+@i@i@p@v@@d+@i@i@p@r@@@@+@i@i@u@v@@@@@+@i@i@z@{+@i@i@p@{@@0@"""+@i@i@@+@i@i@@@0reduce_field_opeF@@@%'@+AAAA֓,AAAA֠,AAAA, AAAAӓ,AAAAӠ,AAAA7j@&#~-N, AAAAǠ,&AAAAӠ7{@.)@@',1AAAA@-ring_of_fieldF@@@,/@ B,@ B  B BB,;,I B  B BB@@@+@3almost_field_theory@@,\ B# B#B'B: A!RA@@ @@@@,m B# B#B;B<@@@@,v B# B#B=B>@@@@, B# B#B?B@@@@@, B# B#BABB@@@@, B# B#BCBD@@@@, B# B#BEBF@@@@, B# B#BGBH@@@@, B# B#BIBJ@@@@, B# B#BKBL@, B# B#B'BL@f@("""""""""", B# B#BPB`,b,_@%AF_ARi*@, B# B#BXB] AxA@@ B"rOA@@C"rIA@@#D$raddA@@"+E$rmulA@@*3F$rsubA@@2;G$roppA@@:CH$rdivA@@BKI$rinvA@@JSJ#reqA@@R--* B# B#B^B_@-- B# B#BXB_@@@,@,field_theory2@@-@ Ba BaBeBq AA@@ @@@@-P Ba BaBrBs@@@@-Y Ba BaBtBu@@@@-b Ba BaBvBw@@@@-k Ba BaBxBy@@@@-t Ba BaBzB{@@@@-} Ba BaB|B}@@@@- Ba BaB~B@@@@- Ba BaBB@@@@- Ba BaBB@- Ba BaBeB@e@(##########- Ba BaBB-E-B@#F_RP@- Ba BaBB A[A@@ BA@@CA@@!DA@@(EA@@&/FA@@-6GA@@4=HA@@;DIA@@BKJA@@I-. 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