"`܄q-SetoidTactics'Classes#Coq@4$Init'Classes#Coq@/RelationClasses'Classes#Coq@)Notations$Init#Coq@%Logic$Init#Coq@*Logic_Type$Init#Coq@)Datatypes$Init#Coq@&Specif$Init#Coq@%Peano$Init#Coq@"Wf$Init#Coq@'Tactics$Init#Coq@%Tauto$Init#Coq@'Prelude$Init#Coq@4Relation_Definitions)Relations#Coq@X)Notations$Init#Coq@0&v!D]hwnv %Logic$Init#Coq@0\͉!Ig)Datatypes$Init#Coq@0.i bYN Z*Logic_Type$Init#Coq@0 1jc6&Specif$Init#Coq@0;RWMi\N'Decimal$Init#Coq@0C涳N*ua#Nat$Init#Coq@0eʤģPSR蠠%Peano$Init#Coq@0 jha|ؠ"Wf$Init#Coq@0q+W,J+'Tactics$Init#Coq@0/9m+ a%Tauto$Init#Coq@0̂"&/r'Prelude$Init#Coq@0JqTttֱ&Basics'Program#Coq@0!bs߯? :VU$Init'Classes#Coq@0](p{yOh.'Tactics'Program#Coq@03u%+Equivalence'Classes#Coq@07;ꮹ8+dzܜKʄF^65Р-SetoidTactics'Classes#Coq@A/DefaultRelation,<!R4Relation_Definitions)Relations@@(relation'JjA!A1٠B,+@@@   A5Build_DefaultRelation'%CB@@@AB@ @@@B@> @@A@@@@BA@BB><.,@@1@,@A@A@.A8ӠA@@A@AA@@A@0default_relation @A1ՠF?@@ZX!HJ@k @;:@S@ji^@| @LgtP (+k()'@@1@+@A@A@-Al@/A8ӠA4Relation_Definitions)Relations#Coq@@AB@@F3equivalence_default @1I@@C/RelationClasses@+Equivalence~@LA@@4Relation_Definitions)Relations#Coq@@(relation'JjAi/RelationClasses'Classes#Coq@@+Equivalence~@ũe@CB (+k()G'@@1@L@A@A@NA݋X_A/RelationClasses'Classes0@VA@XAl@ABC@@@@@ ӳ2@ ӳ2[)Datatypes$Init#Coq@@A@A Գq@ Գq\ @A@1@1@1@ABCD@@A@@AB!C@@@X&Basics'Program#Coq@0!bs߯? :VU*CMorphisms'Classes#Coq@0qیZBeϠ0CRelationClasses'Classes#Coq@0TL;0RUfw1/.-@0.i bYN Z'Decimal$Init#Coq@0C涳N*ua+Equivalence'Classes#Coq@07;ꮹ$Init'Classes#Coq@0](p{yOh.%Logic$Init#Coq@0\͉!Ig*Logic_Type$Init#Coq@0 1jc6)Morphisms'Classes#Coq@0Imӽ%\$PD.Morphisms_Prop'Classes#Coq@0% :B'.>u%#Nat$Init#Coq@0eʤģPSR蠠)Notations$Init#Coq@0&v!D]hwnv %Peano$Init#Coq@0 jha|ؠ'Prelude$Init#Coq@0JqTttֱ@0Gz rA6ՠ  @0]4Ѐd{n^&Specif$Init#Coq@0;RWMi\N'Tactics$Init#Coq@0/9m+ a'Tactics'Program#Coq@03#_103=@@@@@@ 2 Q@@@@#_18l@ n@VBC@Ao@A@@@@@@#_192M접CB@@#_20'`o@#Cm@@@@@#_216E@@AA@AAI@AA@@@@@2 Q@@J@#_22@%ú @BC@AÐ@A@@@@#_232M접@#_24'`o@ C@@@@%@#_253C@@AA@AA@@@@#_2646@D@@#_27X@3typeclass_instances@D@'META472'META4732@@@@jp2)@>Coq.Classes.SetoidTactics#<>#1@-setoidreplaceF@@@̠!t@ @#Heq "./theories/Classes/SetoidTactics.vqbqbhk#Heq@@ r~r~r~r~r~r~)Notations$Init#Coq@@#cut#u'r~r~@@@@@@@ ;r~r~@0intro_#_4C69D577LE H@ Ir~r~Š@;setoid_rewrite_#_#_4C69D5C80A= A_^r~r~@@@ cr~r~Ѡ(@0clear_#_4C69D547<r@@@tr~r~Ւzr~r~@/setoidreplaceinF@@@["H'@ @uu#Heq@@vvvvvvvv@@@@@@@ vv>G@ vvJb@ setoid_rewrite_#_#_in_#_4C69D5C91 = AvvY\@@<`@@ vven@@@vvqrvvqr@1setoidreplaceinatF@@@ߠ$occs@ @yy#Heq@@!zzÓ&zzà,zz3zz@@@ @@@@ Fzz O@ Pzz @ %setoid_rewrite_#_#_in_#_at_#_4C69D5F46蠐= Afezz @@<@Бeuzz  @ zzz  @@@zz  zz  @/setoidreplaceatF@@@o@ @} D} D J M#Heq@@~ `~ ` d j~ `~ ` d j~ `~ ` d g~ `~ ` h i@@@@@@@ ~ `~ `  @ ~ `~ `  @ setoid_rewrite_#_#_at_#_4C69D5F6(Р= A~ `~ `  @@Б~ `~ `  @ ~ `~ `   @@@~ `~ `  ~ `~ `  @#_28(Z@ setoid_replace_#_with_#_31A5F54C)@@.setoid_replace&@ @   ?LFI!x$with4@ @   ?LFI!y@@AA A   /FA A   /LA A   @`\_(@[A A   $ AA@@ BA@@CHA@@JwA A  % &C~A A  ' (@A A   (@A A  * /s@%idtac$PsF@@@#_29(@ %setoid_replace_#_with_#_at_#_31A5F54F r@@.setoid_replaceC 2C 2 S \?LFIw$withC 2C 2 d m?LFIv"atD nD n u ?_!o@@E E   E E   E E   @B树@E E   AA@@ B A@@CA@@ΐE E   ǐE E   @E E   @ E E   @VE E   @@#_30(Z@ %setoid_replace_#_with_#_in_#_31A5F54E@@.setoid_replace&G G   蠕?LFI$with3G G   ?LFI"in@H H   <"id@@NI I   =SI I   =YI I   @x @gI I   /AA@@ BA@@#CTA@@VI I  0 1OI I  2 3@I I   3@MI I  5 7I I  8 =@@@#_31(@ *setoid_replace_#_with_#_in_#_at_#_31A5F549t@@.setoid_replaceK @K @ a j?LFI$withK @K @ r {?LFI"inL |L |  "atM M   ?_@"@N N   ݓN N   ݠN N   .@?'@N N   ͠A$A@@ B=A@@CA@@N N   ϠN N   @"N N   @)N N   ՠ/N N   ۠@z9N N   @@#_32(~@ %setoid_replace_#_with_#_by_#_31A5F548{?@@.setoid_replaceJP P   ?LFI$$withWP P   ?LFI#"bydQ Q  # -=Cr@@3v@qR 1R 1 3 `vR 1R 1 3 `|R 1R 1 3 @0/@R 1R 1 B R7AA@@ >BA@@ECvA@@xR 1R 1 S TqR 1R 1 U V@R 1R 1 B V@R 1R 1 ^ _ÐR 1R 1 ^ _@@#_33(@ *setoid_replace_#_with_#_at_#_by_#_31A5F54Bxw@@.setoid_replaceT cT c  ?LFI$withT cT c  ?LFI"atU U   ?_0"byV V   ʠ=C@ѠĠA@W W   W W   W W   =@W W   񠠐ɠACA@@ РB\A@@נCA@@ 7W W   󠠐>W W   @AW W   @HW W   UNW W   UW W   @@#_34(@ *setoid_replace_#_with_#_in_#_by_#_31A5F54A)0@@.setoid_replacefY Y  % .?LFI@$withsY Y  6 ??LFI?"inZ @Z @ G N@?"by[ O[ O V `=C@h[P@\ d\ d f \ d\ d f \ d\ d f uLX@\ d\ d w `AA@@ gBA@@nCA@@\ d\ d  \ d\ d  @\ d\ d w @\ d\ d  \ d\ d  \ d\ d  @@#_35( 1@ /setoid_replace_#_with_#_in_#_at_#_by_#_31A5F545=YP@@.setoid_replace^ ^   Š?LFIנ$with ^ ^   ֠?LFI֠"in_ _   堕א֠"at#` `   ?_l"by1aa=C?@ ~E@@bbMEbbMKbb(]@Xbb*:A A@@  B A@@C EA@@Gtbb;<@{bb=>@~bb*>@>bb@BbbIJbbIJڐbbLM@@#_36( @ 1setoid_replace_#_with_#_using_relation_#_31A5F544$"e@@.setoid_replacedPdPqz?LFI$withdPdP?LFI%using(relationee?LFI#rel@@ffϓffϠffffĠǐffƠff@ff@ffϠ}@@@#_37( L@ 6setoid_replace_#_with_#_using_relation_#_at_#_31A5F547@@.setoid_replacehh?LFI$with%hh ?LFI%using(relation5ii#.?LFIn"atBj/j/6H?_@@QkLkLNoVkLkLNo\kLkLN]ikLkL_bCpkLkLcd<wkLkLef@zkLkL_f@kLkLhm@ːkLkLno@@#_38( @ 6setoid_replace_#_with_#_using_relation_#_by_#_31A5F546ɦ @@.setoid_replacemrmr?LFIu$withmrmr?LFIt%using(relationnnΠ?LFI"byooࠦ=C@@ppppppppŐpppp@pp@pp pp@@#_39( N@ ;setoid_replace_#_with_#_using_relation_#_at_#_by_#_31A5F541 s@@.setoid_replacer r *3?LFI$with'r r ;D?LFI%using(relation7sEsEZe?LFIp"atDtftfm?_"byRuu=C`@.!f@avvfvvlvvyvvSvvLvv@vv@vvvvߐvv@@#_40( @ 6setoid_replace_#_with_#_using_relation_#_in_#_31A5F540 @@.setoid_replacexx蠕?LFI$withxx?LFI%using(relationyy?LFI"inzz")@@{-{-/Q{-{-/Q{-{-/>0{-{-@Cؐ {-{-DEѐ {-{-FG@ {-{-@G@ϐ {-{-IK {-{-LQ@@@#_41( d@ ;setoid_replace_#_with_#_using_relation_#_in_#_at_#_31A5F543=@@.setoid_replace 0}T}Tu~?LFI $with =}T}T?LFI %using(relation M~~?LFI"in Z"at f٠?_@C6,@ v {  h a @ @_  %@ @@#_42( @ ;setoid_replace_#_with_#_using_relation_#_in_#_by_#_31A5F542 @@.setoid_replace )2?LFI$with :C?LFI%using(relation DDYd?LFI"in eels"by tt{=C @٠̠:  @   V $ + 2@ 5@ < C P I@@#_43( @ @setoid_replace_#_with_#_using_relation_#_in_#_at_#_by_#_31A5F55D=(@@.setoid_replace Zݠ?LFI4$with g?LFI3%using(relation w?LFI"in DC"at &8?_٠"by 99@J=C @zm۠c @ NNPy NNPy NNPaˠ NNcf NNgh NNij@ NNcj@ NNln NNuv  NNuv3 NNxy@@5red_subst_eq_morphismF@@@%concl@ B **27  **27@@ @*respectful%WO?@ ==CW@@@@ @@@@%Logic$Init#Coq@@"eq @@ ===DLc E==MO@ H==CO"R' Q==TW@9@@@+@@@@@@@ r==ag@  w==jo <@.subst_4C69D532χ@ ==r ==r ==r@B ==@@@@ @@@@  h @@ggt@_@@@@f @ Ɠ Ơ V @@@/destruct_properF@@@ B@@@ Y@&ProperL@   (   B    "!m   #%@   %@%FZ@Š@@@.reverse_arrowsF@@@ @ B =PPXY  CPPXY@@;@ Q__ey6@@4@@ 2@ c__fn k__oq@ n__eq& v__vy@(@e%%O@8 __} __}'Tactics'Program#Coq@@+revert_last ؎@ __ __ __@}&Yޠd __@@@@ @@@@   @@C  `@ Փ ՠ W @@@;default_add_morphism_tacticF@@@@@&Basics'Program#Coq@@$flip$@@@@@@Ȑ 2#)@ 8,,3B =,,3B@U0g7@ B@@@:@ PXXdm5@@3@@  3 `XXdf - hXXkm@@@@ qXXop@@@@ zXXqr@ }XXcr@l,, Z N00 XXx XXx XXx@@ XX@@@@   XX  XX@@@ XX XX XX @&Yޠ@ XX@@@@   XX  XX@@@@3add_morphism_tacticF@@@ 򓠐 򠐠A@=a@#_46,0+@   @-program_simpl=NA@@@S_`nOU$K󄕦@x