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BF F   ʑ F F   @@@"x'@AƐ@@@G G   ݠ@@@G G   栠@@!xG G   ᠠ*G G   @@@@@G G   G G   G G   @7*@@1#A4@ @OI I   #res@@ @=%J #J # / 0&res_eq@@/K FK F N f4K FK F N f:K FK F N _Z@R3=ޠZBK FK F ` aIK FK F b ddPK FK F e f@ @&lemma'YL hL h t z?LFIgL hL h  nL hL h  uL hL h  @xL hL h  @@M M   M M   NM M   9M M   @ N N   ;8@@@=ProveLemmaHyp: cleanup failed@ O O   L@0subst_#_4C69D5350<@@@@@ A@ -ProveLemmaHyp: lemma not of the expected form@@.ProveLemmaHypsF@@@@ BT cT c k x T cT c s x@@@@AƐ@@@U ~U ~  @@@U ~U ~  @@U ~U ~  ;U ~U ~  @@@@@ U ~U ~  U ~U ~  U ~U ~  @6;@@B4AE@ @`*W W   #res@@ @N6X X   ޔ&res_eq@@@Y Y   EY Y   KY Y   jRY Y   YY Y   t`Y Y   @ @hZ Z  " (uZ Z  4 9|Z Z  : <Z Z  = >@Z Z  4 >@@[ C[ C K e[ C[ C K e[ C[ C K Y@H[ C[ C Z `k[ C[ C a e@ \ g\ g p wQN@@@>ProveLemmaHyps: cleanup failed@ ] ]   @@@@^ ^   ӓ^ ^   Ӡ^ ^   ͠.^ ^   @@.ApplyLemmaThenF@@@:$expr@ @#lemi i   ֐Ri i   砠i i   @i i   @@j n Ǔj n Ǡ!j j  A@we'0)j j $lem'@ @#Heq9kk"#thm@@@@A@Il5l5ADPl5l5FJ@UmMmMQZmMmMQ`mMmMQ^@7+AS0hmMmM_bomMmMit@xmMmMqt@@@mMmMmMmMQmMmM\mMmM@@ nn>;m@@@>ApplyLemmaThen: cleanup failed@@5ApplyLemmaThenAndContF@@@à#tac(CONT_tac@&B(u&B(u&&(6@ 7+&&7<&&=A@BB^hBB^h8BB^aBBbh@BBjtBBjtLBBjra@@@6ReflexiveRewriteTacticF@@@&FV_tac'SYN_tac)LEMMA_tac(MAIN_tac"fv%terms@ @ */ 5+ListTactics%Lists#Coq@@.list_fold_leftܠ0E+L/S@@ @&RW_tac\ҕ@ @%fconsj$term@ @z mr@@ @$main!!+/@ B55CLɐ55KL@@@$RR]a@@@@RRbcRRdh@RR]h@>@@KRRux|RRy}RR~@RRu@@@@@A@-@@ࠐ%E@~q֠x-͠C4Ҡ;נB@@G7L7R@4lazy_list_fold_right=M0[@@@Dh27@@m;;=Pr;;=P]x;;=F^;;GI+;;JP@+FV_hypo_tacF@@@$mkFV"lH@ @ӐΠ@V@@ @-FV_hypo_l_tacF@ BO@@+InitialRing+setoid_ring#Coq@@$hypo?@A@S"pe  @@@@ @@@@@ @@=@A(CC!&,<3@@@ @-FV_hypo_r_tac<$$*7@ BG==GHҐM==GH@@@[==OUɐe==WZ@@@@n==[\v==]`@y==W`@@@@==bc@==Nc@@A==gn==gn==gk==ln@@@ @vv|~vvvv@/list_fold_right oD vv)Datatypes$Init#Coq@@$list]@A@vvvv@vv@Xvv@@ԓԠDː Π Ѡ} @)mkHyp_tacF@@@!C%Reify@ @%mkHyp .#res@ B <  ǐ B  @@x@ P#) Z+."r1 c/2"r2 l36@ o+6@@@@ x89@ {"9@@A렛(! @#pe1 ==FI ==MUx ==MRB ==SU@@ @#pe2 YYbe YYiq YYinT YYoq@@ uuzkB@ uu A!AA@@ e@$prodt@A@ uuAA@@ B!BA@@q uu] uu@ ؐ uu@ uu@ AA !hypothesis is not a ring equality@@@   $  *o 1접m@ >򠠐b@ I,Ring_polynom+setoid_ring#Coq@@%PExprk@@ _F f@ i @ sZ z@ }@7@ @  @,proofHyp_tacF@@@@ @)get_proof %%+4 &@ B ::DE / ::DE@@@ KKRX@@@@ KKYZ!p KK[]@ KKQ]@@A  KKab KKab@@ A"bh nnxz!l@ B   @@9@ AA7A@@ @ @H@A B Ǡ @$Truey@A@ 0@@@m@ >uAkA@@  Ґ M@ WAA@@ @ a@ d@@B  @A  yɓ ~ɠ Ǡ  @@@@ ԠРAA@@  - נ"tl @ @@B ⛐ E @Ր ꓠ :  ^ @@ @!r     D @@ , @#andЖw@A@ #'A A@@ B!BA@@0 "()H )*+@ ,#+@@@ 188:? 688:?S <88:< C88=?@*get_MonPolF@@@ @ B R[[cp  [[[kp@@@@@.mk_monpol_list@ mvv A!CA@@ "cO ~vv"cI vv$cadd vv$cmul vv$csub vv$copp vv$cdiv vv$ceqb vv@@@@ vv@ vv@e( VOHA:3,%   @ ⠠AA@@  堠 蠠} { 򠠐y w !u (s /@ 2@ AA 6ring/field anomaly: bad correctness lemma (get_MonPol)@@"FVF@@@#Cst&CstPow"rO"rI#add\#sub#opp#pow f@@ A#TFV g vP@ @ / v B } C   @@@@+NotConstantX@   @ B )*  )*@@m 008:@q@@ 00HJ 00HJ@@ KKSU@@@ KKce KKce@@ ffor"t1 ffsv"t2ffwz@ffoz@@@ffffff%%ff,ff1ffѐ7ffG>ff$Eff@@@@[Sd[cc@f@swp@@uٓz٠ŠȠؓؠ3Ҡՠ@@@@_栠ƐꠠŐ@@wٛ@@|       @@@@ (!$@"$@ΐ3@@/2;42;Ԑ:25JA68 'H9;@@@V<<EHg^<<IL!ng<<MO@j<<EO@{ BwTTbj|TTbj:TTbh#TTij@@@@ppz@@@pppppp u@)AddFvTailIpp pp@@@ΓΠiȠߐˠ @@@@H ߐ@@@@      @@((*-((*-ِ ((*+ |@@@)..2:...2:ΐ4..25B;..67 !B..8:@)mkPolexprF@@@.   $radd$rmul$rsub$ropp$rpown H@ A#mkPo    ~@ @5|     B        I        @@@@    @  B    풑    @@o    @s@@!!!!& j~A@!!! !#!!!$!%@!!!!%@@@!'!'!1!3@@@!8!8!K!Z B@!8!8!T!W!8!8!X!Y@ !8!8!S!Y@@@![![!f!j(![![!k!n''![![!o!r@*![![!f!r@נ;4@@ @"e1=!!!!B!!!!ڐH!!!!XO!!!!@@ @"e2X!!!!]!!!! c!!!!jj!!!!@@o!!!!ݐ*E@~!!!!Ԡe!!!!֠P!!!!٠<!!!!@!!!!@@@I!!!!!!!!񠠐!!!!@!!!!@aț@@ @" " """ " "!"'f" " "!"$" " "%"'@@ @"+"+"9";"+"+"?"E"+"+"?"B"+"+"C"E@@"+"+"I"`G@ "+"+"R"W"+"+"X"Yې"+"+"Z"\ǐ"+"+"]"_@!"+"+"Q"_@@@ѐ/"a"a"l"p@7"a"a"q"t??"a"a"u"x@B"a"a"l"x@頛SL@@ @T""""Y""""_""""of""""@@ @n""""s""""Ƞ y""""Š""""@@""""㐠,@F@""""ڠ {""""ܠf""""ߠR""""@""""@@@Y""""󠠐ː""""@""""@i@@ @#########)r#####&###'#)@@###-#AH@###6#; ###<#=͐ ###>#@@ ###5#@@@@ #B #B#M#Q+" #B #B#R#UĐ* #B #B#V#X@- #B #B#M#X@Π> B: #] #]#m#u? #] #]#m#uE #] #]#m#sL #] #]#t#u@@@@W #{ #{##@@@ @e # ###j # ###̠p # ### ;@'Find_at4坠y # ###ɠ _ # ###@@ # ###, @D@ # ###۠ { # ###ݠِ # ###@ # ###@@@!c # ###@@@ @ # #$$ # #$$ \ # #$$ ڐ # #$ $ @@ # #$$&} I@ # #$$ ̐ # #$$  # #$!$#I # #$$$%@ # #$$%@@@@ @ A $D$D$[$\$D$D$`$l$D$D$`$g#$D$D$h$i#$D$D$j$l@@($D$D$p$Ϡ@5$D$D$x${ <$D$D$|$} zC$D$D$~$@F$D$D$x$@@@@R$$$$@@@\$$$$ C@k$$$$ Rr$$$$Ȑy$$$$@|$$$$@@@$$$$Ǔ$$$$ǠE$$$$Ġ@@@$$$$ѓ$$$$Ѡ2$$$$Ϡ$$$$@(PackRingF@@@!F#sth#ext%morph$arth'cst_tac'pow_tac&lemma1&lemma2#pre$post@ @#RNG%I%I%O%R B%V%V%`%n %V%V%h%n@@@@ @ "s @%%%%9%%%%"r0 %%%% %%%%ː%%%%!,$%%%%֐,%%%%ې4%%%% <%%%%#phiE%%%%$CpowN%%%%&powphiW%%%%Ơ_%%%%ˠ@@@@h%%%%͠@@@@q%%%%@t%%%%@8u 3!21 lJC<8$proj@% &%&\% &%&\%%%%%%%&%%&& %%& &%%&& & &&!&"4 & &&#&&̐ & &&'&) | & &&*&, & &&-&0! & &&1&4 & &&5&8 & &&9&<  & &&=&> & &&?&C & &&D&J & &&K&NS & &&O&UW$ & &&V&\@ AA ,field anomaly: bad correctness lemma (parse)@@@0#&#&&&5#&#&&&;#&#&&&iB#&#&&&@+get_CarrierF@@@u@P&&('A&'OU&&('A&'O[&&&&&&ѠҠe  #"~ " ! \1* &@('A('A'M'NĐ('A('A'M'N@&get_EqF@@@@+'e-''g'ꓠ+'e-''g'ꠑΐ+'e+'e'g'j점렐䠐㠐 \ o"ʠ n m }v r@-'-'''钑>-'-'''@'get_PreF@@@ @0(2(v((0(2(v((0(0(((870/:j  #   ɠ  RQ@ 2(v2(v((V&2(v2(v((@(get_PostF@@@Y@45(7)()$95(7)()$f?5(5(((|{I  #b  @ @l7)7)))#r7)7)))#@-get_NormLemmaF@@@@:)A<))C)ɓ:)A<))C)ɠ:)A:)A)C)FРϠȠǠҠ@ S# R QaZ Vꠐ@<)<)))Ȓ<)<)))@1get_SimplifyLemmaF@@@@?)A*_)*r?)A*_)*r?)?)))N᠐ #  ؠ 65@A*_A*_*k*q= A*_A*_*k*q@*get_RingFVF@@@=@D*F+*+:D*F+*+:J#D*D***hg`_j-ؠ 렐$F ꠐ 預$ @PF+F++ +9UF+F++ +9[F+F++ +${@ !6hcF+F+++jF+F+++fqF+F++ +"xF+F++#+% .F+F++&+)$F+F++*+- 7F+F++.+1 ;F+F++2+5 ?F+F++6+9@@,get_RingMetaF@@@@I+VK++X, I+VK++X, ېI+VI+V+X+[+i |$נ { z @K+K++, K+K++, K+K+++% @1pԐK+K+++⠒7K+K+++ꠒ;K+K+++򠒑 K+K+++K+K+++ ƐK+K+++%&K+K++, ϐ%K+K+,, Ӑ,K+K+,, א3K+K+, , @@.get_RingHypTacF@@@f@AN,+Q,,--/FN,+Q,,--/sLN,+N,+,-,0àV %o  M" @ @%mkPol}P,P,,,P,P,,,預P,P,,,oP,P,,,ҐP,P,,,Ǡ֐P,P,,,ϠP,P,,,ҠIP,P,,,ՠ aP,P,,,٠%P,P,,,ݠ jP,P,,,᠒ nP,P,,,堒 rP,P,,,@@@@Q,Q,--.Q,Q,--.Q,Q,-- &@ ̐Q,Q,- - WQ,Q,- -@Q,Q,- -*Q,Q,- -* Q,Q,- -%Q,Q,-&-'Q,Q,-(-*@Q,Q,-,-.@@&;2 Q@@@@#_19&J@&F!AA@@@@@@@@#_202M접A#_21'`o@@@@$RingF@@@p@ @RX-X---WX-X---]X-X---&}@ eX-X---@@jY-n0-0oY-n0-0uY-Y---&@h0Zc}Y-Y---ZS@ @Z-Z---ݓZ-Z---Z-Z---&@"z`ǐZ-Z---@@ @,[-[--.[-[-..[-[-..&@!6[-[-..@@ @\.\.. .%\.\..).;\.\..).7&@X@\.\..8.;@@ @].?].?.G.I].?].?.M.r].?].?.M.X' @b;{_].?].?.Y.]].?].?.d.n].?].?.d.n].?].?.d.j1 ].?].?.k.n@z].?].?.p.r@@ @^.v^.v.~.^.v^.v..$^.v^.v..+^.v^.v..2^.v^.v..@@ @:_._...?_._...E_._...L_._...2S_._...@@Y`.`...^`.`...d`.`.../@(check_fv-gLm`.`...@ @ua.a...̓za.a...ܠa.a...ՠ[a.a...٠ma.a...@@ @b.b...든b.b...%b.b...sb.b...b.b...@@ @#lpec.c.// c.c.//c.c.//c.c.//:c.c.//@@ @$vlped/d//%/)(hyp_list@@ @#vfve/Ae/A/I/L'fv_list@@@@Bf/cf/c/u/x@@AA@@@g/{g/{//@@AA@@A@@dh/h///: h/h///N'h/h///.h/h///5h/h///@8h/h///@@@@ A@ typing error while applying ring@ @#prhIj/j///Nj/j//0 Tj/j//0(t@Ő\j/j/00 @@ aj/j/00@0exact_#_4C69D568점((pj/j/00@@ (can not automatically prove hypothesis :@ 6 maybe a left member of a hypothesis is not a monomial@@@@@ n0n000Ԡ&$&@n0n000Π.AA@@ @$boolZ'@A@n0n000@n0n000@@ A@9not a valid ring equation@@@-Ring_norm_genF@@@w砐 -"rl@ @:q1&q1&1,10q1&q1&141Bq1&q1&141>?q1&q1&1?1B@@ @jr1Fr1F1L1Qr1Fr1F1U1er1Fr1F1U1a>r1Fr1F1b1e@@ @Ӑs1is1i1o1ts1is1i1x1 s1is1i1x1=9s1is1i11@@ @)mk_monpolt1t111 t1t111&t1t111)F@!Hy.t1t111@@ @6u1u111;u1u111栐Au1u111XHu1u111ѠOu1u111ⓠTu1u111⠐Zu1u111au1u111@ѐhu1u111@@ @)lemma_tacqv1v111X?@ @ɐw2w22 2w2w222^w2w222qw2w222w2w222@@ @Ȑx2#x2#2+2/(list_hyp@@ @$vlmpy2Gy2G2O2S-list_hyp_norm@@ @'vlmp_eqz2pz2p2x20list_hyp_norm_eq@@ @{2{222{2{222{2{222~B{2{222@@@@ /|2|222@@AA@}2}223 }2}223 }2}222E}2}222Y}2}222}2}223A}2}233 @}2}223 @@ @=%~3~333*ring_lemma@@@@A@P831313>3?B31313C3HpI31313I3M/P31313N3PW31313Q3T^31313U3Ye31313Z3a@h31313C3a@ A@ )type error when build the rewriting lemma@ r3333@@@33333333N33333333@ 3333ʠ;8@@@=Ring_norm_gen: cleanup failed@ 3334@@@@@ @*simpl_ring4 4 44@ 4 4 4!477bZ$ringE @4 4 494<4 4 494<4 4 494:4 4 4;4<@@4A4A4C44A4A4C44A4A4C4Y+@vDo4A4A4Z4^4A4A4_4d4A4A4e4n\4A4A4o4y4A4A4z4|^$4A4A4}4@(Ring_genF@@@ Wn@ @94444>4444D4444+d@k sL4444@@R4444ѓW4444Ѡ]4444+}@'2 e4444Π@@n4444s4444y4444+@;6 4444ݠِ4444䠠j@4444@4444@ 4444@#_22(+@-ring_2BA1BA26 y@@$ring@@ @5#5#5)5*5#5#5.56+@*{@@ 5:5:5<5` X=5:5:5I5Z5:5:5I5Z5:5:5I5Q+@ 1A@@ ֐ 6z6z66@ 6z6z66@@@@B@ 6666@@@ 6666 6666 6666  6666N@@ @8 6666 B@@@@@ @!6666蠠 @@*!6666⠠"RL!%6666@@@@@!-6666!06666@@!@ ^I a!?6666!!E6666 AA )ring_simplify anomaly: bad goal after pre@@@ @!T7?7?7E7H#Heq@@@@-!e7[7[7d7g@ !j7[7[7h7s =@@@@!y7u7u7w7!~7u7u7w7!7u7u7w7-@c E!7u7u77 !7u7u77!7u7u77@!7u7u77@!7u7u77@!7u7u77!7u7u77@!7777!7777!7777-@ 9 !7777,@@-Ring_simplifyF@@@!7778!7778!7777. @1 @@@AA@ !7777@@@@@@@#_24(.&@8ring_simplify_#_2BA1BA28Ih@@-ring_simplify"88808??LFIT@V@ @!#"!8C8C8I8J"&8C8C8N8Vl@@ ".8Z8Z8\8"àk"88Z8Z8i8"=8Z8Z8i8"C8Z8Z8i8qj"I8Z8Z8r8.l@w@6@@i@h"_8Z8Z88@!i"g8Z8Z88@@@@#_25(.@>ring_simplify_[_#_]_#_2BA1BA29"Q?@@-ring_simplify!["{8888͠?LFI점!]"8888᠒?LFI@@ @!"8888쓠"8888@@ "8889,#;"889 9!"889 9!"889 9⠓"8899!x@@ࠠ:"889$9&@@砠"889(9*@!"889+9,@@@@#_26(/ @=ring_simplify_#_in_#_2BA1BA2A W@@-ring_simplify"9/9/9O9^?LFI9"in#9/9/9d9j<!$@H!'@ @"#9m9m9s9t#9m9m9x9_@@ @#+#$9999!E#-9999@@ @!g#69999$goal@@@@"J#H9999@@@A@@@!o#W9999@@@ #\999:#񠐠#f9999#k9999#q9999#w9999.@@@Ɛ#99::@##99::@@@ @"H'#::::ᔠ!H@@ #::::!>!<@ #::;;!Y@7move_#_after_#_4C69D548:!#+<%@<!@@ #;;;;!m!j!@@@ #;;;;+!z@1rename_#_4C69D54D /H!@@@@#;-;-;6;7@@@ #;-;-;8;?!!@@@@#_27(0 @ #ring_simplify_[_#_]_#_in_#_2BA1BA2BU@@-ring_simplify![$;B;B;e;t?LFI!]$;B;B;x;?LFI_"in$+;B;B;;&"I@n"M@ @#<$:;;;;$?;;;;@@ @$Q$J;;;;"k$S;;;;@@ @&$[;;;;̔$goal@@@@4#o$m;;;;@@@A@@@"$|;;;;@@@ $;;<=E""#@@@ $=<=<=F=V(&m#!@@@@ܐ%=X=X=a=b@@@ %=X=X=c=j""@@@@@@x2]%762f@An Eℕ@i0( I! @52bZ|v?%4}HìLû.