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U\DҠàkb LEנiXok@@b@@X(eq_trans @]@6Equivalence_TransitiveWV@UgZ@T〚^@S*r΀@p@*Transitive++-i@hgm@g【RET;LW@-W\=D7'_XB;,֠XGĠ@@@@*eq_sym_iff @VF7ߠ֠~waZKݠ̠wf@b@!x@g!y@g%Logic$Init@#iffС)@〠BA@〠@@@@AA@@A@'neq_sym @'Ơg`=%@A!n@g!m @g@I@#notШ@D @〠KC@@@@@D(eq_stepl @ߠϠh_IBԠ~fU@BA@@gF@Eg!zM@Lg@S@M〠6@Z@T〠Da@[〠D@@@Aۓό^)Morphismsu@@AB@@(succ_inj @) QJ4-ȠJ9@5C"n1@g"n2@g@@〠@m݀Ω@s݀ө@Y@@@AviAK@AAۀߠKN@R@@ABC@@۠+succ_inj_wd @vfW?8٠zk@DM@gK@g@〠@݀J@݀I@"@@@G@A8ӠA4Relation_Definitions)Relations@AB@@"/succ_inj_wd_neg @F=ޠ' Ƞ\D3ޠ@E@g$@#gc-@'〠3@݀8@݀.?@9m@@@@@d1central_induction @' Ƞib u @ F!A@d@cgA$A_wd@&ProperL@v@ug @*respectful%WO?@g@?@g@n@@gѠE@j݀@gF@@@@@ɠ'add_0_r @dTE-&ΠǠohYڠ@@A&NZBase%NZMul&NatInt'Numbers#Coq@@A@%NZMul&NatInt'Numbers#Coq@)NZMulProp@A@@@@"NZ@A@%NZAdd&NatInt'Numbers#Coq@)NZAddProp/@@@A@@@A&NZBase%NZAdd&NatInt'Numbers#Coq@A@A@@@"NZ+@@,R@2@!t,RJ@@A@A,Y@@"eq,Y^@@A@,@@ @#add,@d@@A@AB,w@@#mul,wd@@A@,@@#one,T@@A@A,@@#sub,d@@A@,@@#two,T@@A@A,@"@$pred,d@@A@,@'@$succ,r@@A@,筷@,@$zero,筷T@@A@ABCDE@A@E@CC@BgH@B〠N@A{S@s@@@@@v@ABC@@AA@@A@*add_succ_r @ A:۠|$v@A@~g}@g@〠@@b݀署@g݀@ΐ@@M@@J-add_succ_comm @`PA)"ʠàkdU֠ܠˠ@Bƚ@gĚ@g@〠@@݀<@@݀A@@@@(add_comm @0'ϠȠpi F.C6(#@C  @ g @g@〠@K"@H@@@@̠'add_1_l @Ҡàkb LEנiX~qc^M?@JDHH@GgM@G〠S@FX@8 ]@*݀@@ @@'add_1_r @ E>ߠ(!z@E@g@〠@@s @e݀@@E@@B)add_assoc @XH9ؠy! c\MߠΠ٠Ԡà@F@g@g!p@g@〠@@ @@@@@@,add_cancel_l @/&ΠǠoh E-B5'"@G  @ g  @ gN @ gU @ 〠 #@P )@O .@ (ې@@@@ؠ,add_cancel_r @ޠϠwnXQud}ojYK@VHT T@ SgR Y@ Xg ^@ ]g e@ _〠 k@^N q@d v@ p#@@#@@ ,add_shuffle0 @ 6 & ^WA:+ՠҠŠ@I @ g @ gޚ @ g @ 〠 @ @d㩚 @ @W@@o@@l,add_shuffle1 @  r c  KDw! @J蚠 @ g暠 @ g* @ g!q @ g @ 〠 @ @ @> @ @ @@@@@ʠ,add_shuffle2 @  Р  i `  JCՠgV|oa\K=@HKF F@ EgD K@ Jg P@ Og^ U@ Tg Z@ T〠 `@S f@Y\ k@^ p@c v@i |@o)@@)@@&,add_shuffle3 @ < ,  Š  d ] G@1۠àؠˠ@L @ g @ g䚠 @ g @ 〠 @ @멚 @𩚠 @]@@u@@r'sub_1_r @  x i     Q J}'$ @M @ g @ 〠 @/& @  @xh]@@@@'mul_0_r @ à   L C     - &ΠǠbJ9_RD@]@& &@ %g +@ %〠 1@À^ 6@s :@s@@@@AA@@A@*mul_succ_r @   ޠ  } %  Ơ  g `  s~@A` `@ _g^ e@ dg j@ d〠 p@VÀ v@C݀Щ {@n @gÀ@@.@@G(mul_comm @ A 1 " ʠ  i b     L E 6ȠݠР@B @ g @ g @ 〠 @À⩚ @Àߐ@@f@@/mul_add_distr_r @ y i Z     B ;  ܠ  } n  @Cܚ @ gښ @ g @ g @ 〠 @À @# @ @À @À5@@@@͠/mul_add_distr_l @ Ǡ   P G     1 * Ҡ ˠ  f N =cVH@aD* *@ )g( /@ .gl 4@ 3g 9@ 3〠 ?@ %À" E@ 8s J@ = P@ 6À U@ ;À@@@@)mul_assoc @      = 6 ޠ נ  x      @Ex x@ wgv }@ |g @ g @ 〠 @ sÀp @ yÀ @ ~À @ ÀKʐ@@K@@d'mul_1_l @ ^ N ?  ޠ   '  Ƞ  i b S   Ԡ@F @ g @ 〠 @ À @  @@~@@'mul_1_r @   r     Z S      0  - @+G @ g @ 〠 @ À, @  0@@@@ʠ,mul_shuffle0 @ Ġ   M D     . ' Ϡ Ƞ  c K :`SE@^H' '@ &g% ,@ +gi 1@ 0g 6@ 0〠 <@ "À B@ (Àn G@ -À M@ 3Àz@@@@,mul_shuffle1 @      5 . ֠ Ϡ w p      @Ip p@ ogn u@ tg z@ yg @ ~g @ ~〠 @ pÀ @ vÀ @ {Àé @ À @ ÀF @ À:@@R@@k,mul_shuffle2 @ e U F     . ' Ϡ Ƞ p i Z   ۠@JȚ @ gƚ @ g  @ g @ g @ 〠 @ À @ Àީ @ À  @ À @ À @ À@@@@à,mul_shuffle3 @    F =  ޠ   '  Ƞ   \ D 3YL>@WK  @g %@$gb*@)g/@)〠5@ À ;@ !À i@@ &À nF@ ,Àې@@@@ %le_wd @     . ' Ϡ Ƞ p i      |@@A&NZBase'NZOrder&NatInt'Numbers#Coq@ & $@A@'NZOrder&NatInt'Numbers#Coq@+NZOrderProp 5 3@A@@@@"NZ * )@A@@@@g@@g,@g@@g7@〩)@gA@ 皠@ \@@Z@@AA@@A@*lt_le_incl @p`Q     9 2 ڠ Ӡ { t e   j]O@hA Ӛ@g њ@g@@"ltk @ \ @@@@@7'le_refl @-$ ̠ Š m f      C + @B @g @ \ 9 9@@ .@@`.lt_succ_diag_r @͠VM     7 0 ؠ Ѡ   l T CǠ@C 00@/g5@Wk b;@ ݀ @@@@@.le_succ_diag_r @ܠ{# Ġ  e ^      q@D ^^@]gc@ `\ i@ 6݀ Ð@@@@@/neq_succ_diag_l @) QJ     4 -  Ƞ  #@!E @g @〠@ f݀  Ő@@ @@젠/neq_succ_diag_r @YI:٠z" à  d ] N   ϠSF8@QF @g @〠 𩚠@ ݀ #@@@@@/nlt_succ_diag_l @yj RK     ~ (  vh@G 욠@g ␩@k@ ݀ S %@@@@@L/nle_succ_diag_l @B9ڠ{# Ġ   X @ /@H @g #@ \)@ ݀  U@@@@@|)le_succ_l @٠ʠri SL   ޠ  p _֠@I LL@Kg JQ@Pg X@ U\^@ +݀  c@k @@ @@+le_gt_cases @#KD.'    @J @g @g @"or @@ \ Ʃ@k Ð@@ J@@-lt_trichotomy @]M>ݠ~&ǠhaR   ӠWJ<@UK @g @g:@k A@ @k @@@@@+(lt_asymm @y!aZ7w@L @g @g@@(k 4  @/k @@ a@@`(lt_trans @͠VM70ؠѠ lTCǠ@M 00@/g .5@4gr:@9g@@@bk @F@hk 󩚠K@mk  .@@ @@(le_trans @ 4-ՠΠvo@N oo@ng mt@sgy@xg@@|\ ,@@\ 2@\?@@ 7@@ݠ+lt_strorder @J:+Ӡʠrk UN?ѠD7)@BO@+StrictOrder.[@@g@k@@ @@ +le_preorder @xhYA:۠|mreW@pP@(PreOrder@@g@\@@@@9/le_partialorder @/&ΠǠoh E-@Q@,PartialOrder5͛К@g@ 〚@ *r΀@\:@b.:@@@ s@A @B@CAhC5@ABC@@y)lt_compat @4@%lt_wdqK@ ̰@<@;g@A@@g ݩ G@Fg@L@Kg 蚠P@J〩 V@Ug 򚠐Z@T ^@k@@@%lt_wd']ɠ HA+$ @@@@@Р(lt_total @@) *@ @g @g @k ʩ@ ѩ@k ΐJ3@ aǠeUF.'ϠȠpiZ۠_RD@@@@@'le_lteq @@+lt_eq_cases;@ ֚@g Ԛ@g@\W@ k@@+lt_eq_cases&y3*Ҡˠsl I1 @@@@@Z0Private_OrderTac+A'IsTotal3 A @#@*r΀@6@+Equivalence~@/@.g3@-【@(eq_equiv7LߠРxoYRveܠ@@@@@ @t@p@_@^gc@k@,Q^F?)" @@@@@ΠU @@]) RR@ @@g@@g 0 @g@@g ;@〩 -@g E@뚠@kSjZK3,Ԡ͠un_ dWI@@@@@J @@R(v@ٚ@gך@gS@kZ@@kI3*Ҡˠsl I1 @@@@@ZE @/@MS@@g@g]%@"\S,@NkZ1@+_Cڠˠsj TMߠq`נ@@@@@@@@@ʐ@#TacnGAm @81٠Ҡzs @@D!P)OrdersTac*Structures#Coq@rk@@@A@@C!O@@&@ @!t&J@@A@A&a@@"eq&a^@@A@&@ @"le&ڠh@@A@AB&@@"lt&h@@A@&̌@@#one&̌T@@A@A&̔I@@#two&̔IT@@A@&H@@$pred&Hd@@A@&؝[@"@$succ&؝[r@@A@&C@'@$zero&CT@@A@ABCDE@A@G,MakeOrderTacBo?@A@@@BONR@@@A@@AEUH@@@N@!tJ@@A@A$:@@"eq$:^@@A@$@ @"le$h@@A@$@@"lt$ h@@A@ABC@A@+*OrderFacts.#@A@@s@3@g@@@@@AA@@A@ @;2ڠӠ{tQ9(]VP5@Ac@g @\@@A@@0)lt_irrefl @Рi`JCՠgVڠ͠Р~c@BI@Hg?P@rkD@@q@@`d @70ؠѠyr @Cx@wg}@|g@@}@k@@@@*le_antisym @H8)ѠȠpi SL=ϠB5'8(@9D@g@g@@\@@\@ @@@@נ @vgOH{% sevf1*$ @wE7@g5@g@됩@*򐩚@@@@@@*interp_ord @!o)OrdersTac0@#ordȠ@ @@@@@@@@@@@D@%@$g@*@)gV/@)〚3@Uk7@4\@*(@=@<g@B@Agސ +k= R'6'6'6''+k+7T'+7T'6'ࠒA̠ܠ۠@@"lt\ @@"eq8L@lР@TȠ@@QPO@@A@B@A@xA܀, TM70!ˠ&  נРʠ@@@@@%trans @O?0ؠϠwpZSD֠ŠI<.?/@@F"o'@g@g{@g@@6=!:@@6=! @6=!@)trans_ord-0uGDRɐ@@;@@ @=@g;@g@g!@r SМA76@W@gU@gΚ@g@@̶@%@ҩ*@$ߐ L+k() LL7#'S@$tޠϠwnXQud۠͠ޠΠq@@@@@a @_@^gd@cgi@hgd"@ SМbCV@y@xg~@}g8@g@@\6@@\<@\I L+k() NN7#'jtTD5ݠԠ|u_XI۠ʠ N A 3D4@@@@@Ǡ @ @g @g@g@B SМB@'@g%@g@g@@ k@@ k@ k L+k() MM7#'АtC:۠|$ŠYA0   e^X=@@@@@-+le_lt_trans @t,@+gr1@0g뚠6@5gX1@ Sg kj@C@BgH@GgM@Lg@S@P\@Y@ {k^@ k L+k() MN7#'4tF?)"   ɠ @@@@@+lt_le_trans @ؚ@g֚@gO@gS@  S1@@g횠@gf@g@@ kd@@\j@ kw L+k() NM7#'trc KDw!  | o arb-& @@@@@%eq_lt @<@g:@g@g @q S/32@S @ gQ@gʚ@g@@ȶ@!@ CkΩ&@ Hkې L+k() ML7#'t֠ǠofPI۠m\  Ӡ Š֠Ơi@@@@@Y%lt_eq @X@Wg]@\gb@ag]@ ScL@o@ngt@sg.y@xg@@ k,@@2@ k? L+k() LM7#'`tJ:+Ӡʠrk UN?Ѡ D 7 ):*@@@@@%eq_le @@g@g{@g@9 S]@@g@g@g@@@@\@\ L+k() NL7#'Đt7.֠ϠwpM5$   YRL1@@@@@!%le_eq @h @gf%@$gߚ*@)gL%@ S+_^@7@6g}<@;gA@@g@G@D\@M@GR@O\  L+k() LN7#'(t:3۠Ԡ|u   @@@@@&eq_neq @5%]V@9*Ԡ / " %٠Ӡ@&G暠@g䚠@g]@g@@[@@c@ r@@@@@͠&neq_eq @}m^F?r w j \m](!@nH.@g,@g@g@琩@@@@ @@@@@*not_neq_eq @ŠNE/(РɠdL;   picH@Iv.@-gt3@2g@*,=@7kB@<@@@@R)not_ge_lt @*#ˠĠle x   @Jk@jgp@og@gx@u\}@ k*@@@@)not_gt_le @=-Ơe^HA2ܠĠ 7 * -۠@.K@g욠@g@@ k٩@\e@@@@@Ƞ)le_neq_lt @xhYA:۠|m r e WhX#@iL)@g'@g@@\@㐩@@ k@@@@@ @@@@'|@@@@@'~@<_neq @F=ޠ' Ƞ\D3   @ R  @g%@$g@+@ MkY!2@,ߐ@@@@@ &le_neq @Ӡ{r\Uyh  ߠ @ SUU@TgSZ@Yga@ k@#andЖw@n@k\du@o@@@@@ Ƞ*eq_le_incl @5%]V@9*Ԡ/"@-T@g@g@@ѩ@\U@@@@@ (lt_stepl @hXI1*Ҡˠsl]ޠbUG@`U@g@g@g@@ k@@@k@@@@@9(lt_stepr @/&ΠǠoh E-@VQ @gO@ gȚ@g@@;kƶ@@̩$@Fk ِ@@@@@w(le_stepl @ԠŠmd NG٠kZޠѠ@WG@FgL@KgQ@Pg@W@T\@]@Wb@_\@@@@@(le_stepr @"JC-&@X͚@g˚@gD@g@@\B@@H@\ U@@@@@ @_O@ߠ(!ɠ jcTՠYL>@WYš@g@g@g@@\@@k@k @@@@@0\ @}%Ġe^;#{@Z@g@gA @g@@1k@@\©@<k ϐ@@@@@m+le_antisymm @ڠʠcZD=ޠϠyaPԠǠ@[==@<g;B@Ag@H@E\v@N@K\1S@MI@@@@@)le_succ_r @;4ܠՠ}v @ \vv@ugt{@zg@\@U݀ @\@〠©@g݀@@@@@)lt_succ_l @ZJ;ڠ{#Ġe^OРTG9@R]@g@g@@k@݀.@k@@@@@&,le_le_succ_r @t\U2 r@^@g@g@@\/@\驚 @݀l@@@@@_,lt_lt_succ_r @̠UL6/נРkSBƠ@_//@.g-4@3g@:@\kh?@ak"E@݀@@@@@,succ_lt_mono @-&ΠǠoh {@`hh@ggfm@lgt@ky@k@L݀ߩ@Q݀ސ@@@@@נ,succ_le_mono @D4%͠Ġle OH9ˠ>1#@ߠРzbQՠȠ@d >@`k C@#  G@ˀ@@@@<_0_2 @ /(Рɠqj }@e j@k o@7s s@Iˀ@@@@Ơ&le_0_2 @ 3 # [T>7(Ҡ- @+f @\ @cs @uˀ@@@@@<_1_l @ _ O @ߠ(!ɠ jcTՠYL>@Wgš @ g @ g@ @k @s@ @k @k @ Đ@@@5@3@@ABC@@8+lt_ge_cases @    . %͠ƠngD,@h!@!g! @! g!@6kB!@\?@@@@@l+le_ge_cases @ ٠ ɠ  b Y C<ݠΠx`OӠƠ@i<!<@!;g:!A@!@g!H@E\v!M@J\s@@@@@+lt_gt_cases @!      5 .֠Ϡwp@jp!p@!ogn!u@!tgm!~@!x󠩚!@k!@k@@@@@ݠ,eq_decidable @!J!:!+ Ӡ ʠ r k  UN?ѠD7)@Bk!@!g!@!g)Decidable!@)decidable r!@!@@@@@&eq_dne @!!r!c! !   K Dw! |oa@zl嚠!@!g㚠!@!g)␩䐩!@!#!@!(@@@@@M&le_ngt @!!!!C!:  ۠  | $ ŠYA0@m"@"g""@"!ga")@&\W"0@RkV@@@@@&nlt_ge @!!!Ѡ!y!p!!   Z Swfݠ@nS"S@"RgQ"X@"WgP"a@k"f@c\@@@@@,lt_decidable @"&""!!!N!G     1 * Š @o"@"g"@"gܐ"@kÐ@@@@@蠠<_dne @"U"E"6!ޠ!ՠ!}!v!!   ` Y JܠˠOB4@Mp"@"g"@"g"@k"@k@@@@@ &nle_gt @""}"n"" !!!V!O      ,  zl@q𚠐"@"g"@"g4퐩"@\,#@%k)@@@@@V<_nge @"à"""L"C!!!!!-!& Π Ǡ  b J 9@r&#&@#%g$#+@#*gj#2@Tk`(#9@ 6\_@@@@@,le_decidable @"""ڠ""y"!"! !!c!\!     o@s\#\@#[gZ#a@#`g#h@ e\@@@@@&le_dne @#(## """P"I!!!!!3!,! Ǡ  "@ t#@#g#@#gϠ#@ \ɩ#@ \ΐ@@@@@*nlt_succ_r @#`#P#A""""")""!ʠ!à!k!d!U   ֠ZM?@XuÚ#@#g#@#g#@k#@ ݀7#@k @@@@@/5lt_exists_pred_strong @###}#%#"Ġ""e"^"!!!!!;!#!{@v#@#g$@$g$ @$g@$@1k@$@!\U@"ex @$!@$ g!k$(@$'gǠ$/@$)〠թ$5@!݀$:@!7\g@@@@A@@A _@ `AРD.Morphisms_Prop$R@ fA1@D@ABCD@@.lt_exists_pred @$ #####1#*"Ҡ"ˠ"s"l"" !!!!@w!$l@$kgq$q@$pg@$w@kb$}@$|g\$@$g!$@$〠l$@!\݀驚$@!\@@@O@A@@蠠,lt_succ_pred @$U$E$6#ޠ#ՠ#}#v##"""`"Y"J!!ܠ!ˠOB4@Mxm$@$g$@$g@$@k񩚠$@$〠$@!݀$@!xh4 @@@(@A%@t@ @@ABCD@@,&rs_rs' @$$$z$"$###b#[#"""""8" "x@y@$@$g@%@%g% @% g%@%  M ;ɚ%@%g@@ %@%g@%!@"\@>%*@!݀  0%0@%/g@%6@"3\@ =%=@%<g ;%B@%Ag@%H@"E\c u@%O@qk 2K'H)@@@@(rs'_rs'' @%%$$$$;$4#ܠ#ՠ#}#v###""" @ z@%w@%vg@%@%~g %@%g!%@%   C%@%g@ %@%g@%@"\ ȶ@ %@%g %@%g@%@"\ ٶ@%@k I  %@%g  Ú%@%g %@%g@%@"\"@%@k ! . ښ%@%g ؚ%@%g@%@"\9@%@ k 8%@"݀ K@@ E@@D%rbase @%%%%:%1$٠$Ҡ$z$s$$####P#8#'@{@&@&g Ϛ&@&g! & @&g!&%@&$g@&+@#(\@&1@Sk!| @@@@@)A'A_right @%%%Ҡ%z%q%%$$$[$T#####x#gޠ@|@&U@&Tg!&Z@&Yg@!`&`@&_g!f&f@&eg!d&k@&jg@&q@#n\@&w@k!ZN Ҷ!}&}@&|g@&@#\ @@@@@נ6strong_right_induction @&D&4&%%͠%Ġ%l%e% %$$$O$H$9##ˠ#>1#@<} F@&@&g D B @@&@&g L :&@&g R&@&!!!t&@&g@!Ś&@&g@&@#\!@!Қ&@&g!К&@&g@&@#\1@&@k!0!C.!蚠&@&g@&@#\̐@@@!B@A!@#@@ABC@@E/right_induction @&&&&;&2%ڠ%Ӡ%{%t%%$$$$Q$9$(@~ @'@'g   @'@'g  '$@'#g '(@'""f"T!⚠'-@',g@ @"4'4@'3g@':@$7\϶@V'B@$݀"G'G@'Fg@'M@$J\שh!@@@@@0right_induction' @'&&&&&6&/%נ%Р%x%q%%%$$$@!@'r@'qg!! ! @'z@'yg!!'@'g!'@'~""">'@'g@"'@'g@'@$\"@"'@'g@'@$\6@'@$v݀"'@'g! @@#@@7strong_right_induction' @'n'^'O&&&&&7&0%ؠ%Ѡ%y%r%c% $$h[M@f@!p@'@'g!n!l!j@'@'g!v!d'@'g!|'@'#"#"'@'g@"'@'g@'@$\#r@"'@'g@(@$\@#(@(g#( @( g@(@%\ٶ@(@;k"J"{# ( @(g!~@@@@@s&ls_ls' @''Р''i'`''&&&J&C%%%ՠ%%g%Vڠ͠@A!@(D@(Cg!!ީ!ܰ@(L@(Kg!!(R@(Qg!(V@(P###([@(Zg@!Ѷ@#b(b@(ag@(h@kE@!ǐ(p@%=݀"#u(u@(tg@({@%x\##!@#(@(g#(@(g@(@%\#@(@%\#BF(@%h݀"J@@@@(ls'_ls'' @([(K(<''۠''|'$'&Š&&f&_&P%%%ѠUH:@SB"]@(@(g"["Y"W@(@(g"c"Q(@(g"i(@($##(@(g@#ܚ(@(g@(@%\$@#隠(@(g#皠(@(g@(@%\$!"`@(@%\#H)@%݀#aL$)@)g$E$)@) g$ )@)g@)@&\%@)@&\#l#y$%)%@)$g$#)*@))g@)0@&-\<@)6@&3\#)<@& ݀#@@Z@@%lbase @(((ݠ((|($('Š''f'_''&&&&r@C"@)`@)_g"$)e@)dg$k)k@)jg$i)p@)og@)v@&s\ S@)|@&y\$)ǐ)@&O݀#ܐ@@@@@ՠ(A'A_left @)B)2)#(ˠ( (j(c( ('''M'F'7&&ɠ&</!@:D#D@)@)g#B$`)@)g@$)@)g$)@)g$)@)g@)@&\G@)@&\$uQ$"$͚)@)g@)@&\ P@@%@@&5strong_left_induction @)))t))(((\(U''''''2'' r@E#@)@)g###@)@)g##*@*g#* @*%G%5$Ú*@* g@%*@*g@*@'\%@@%!*!@* g%*&@*%g@*,@')\8@*2@'/\$*8@'݀$%=*=@*<g@*C@'@\! !@@@$@&e@@ABC@@.left_induction @*))))).)'(Ϡ(Ƞ(p(i(( ''''|@F$@*j@*ig$$$@*r@*qg$#*x@*wg$*|@*v%%%6*@*g@#@%*@*g@*@k!k@#퐩*@'c݀$%*@*g@*@'\&T@@@@@/left_induction' @*a*Q*B)))))*)#(ˠ(Ġ(l(e(V(''נ[N@@YG$c@*@*g$a$_$]@*@*g$i$W*@*g$o*@*&&%*@*g@%⚠*@*g@*@'\&e@%*@*g@*@k!Ѷ@$S*@'݀%\&+@+g$_@@ @@T6strong_left_induction' @****J*A)))))+)$(̠(Š((`(H(7@H$ö@+%@+$g$$$@+-@+,g$ɩ$+3@+2g$Ϛ+7@+1&u&c%񚠐+<@+;g@&B+B@+Ag@+H@(E\&vŶ@&N+N@+Mg@+T@(Q\"1@&[+[@+Zg&Y+`@+_g@+f@(c\&$Ķ@+m@(j\&T+s@(@݀%&x+x@+wg$֐@@ @@ˠ/order_induction @+8+(+***`*Y*))))C)<)-(נ((2%@0I%:@+@+g%8%6%4@+@+g%@%.+@+g%F+@+&&ڶ&h+@+g@%)@&+@+g@+@(\"U@ܐ+@(݀@&Κ+@+g@+@kY@𐩚+@(݀&<&ᚠ+@+g&<@@@&5@&3@AB@@70order_induction' @++++-+$*̠*Š*m*f**))))C)+)@J%@,@,g%%%@,@,g%%,@,g%,@,'X'F&Ԛ,@,g@%@'&,&@,%g@,,@))\"@ H,4@)݀ @':,:@,9g@,@@)=\Ŷ@𐩚,H@)xh'M,M@,Lgl@@k@@1order_induction_0 @, +++++5+.*֠*Ϡ*w*p***)))@K&@,q@,pg& & & @,y@,xg&&,@,~g&,@,}''@',@)Rs@',@,g@,@)\,@)cs'Ƕ@%,@)p݀y@',@,g@,@k'ܚ,@)|s@&,@)݀'E',@,g&@@@@@2order_induction'_0 @,,q,b, ,+++J+C*****v* *){n`@yL&@,@,g&&&}@,@,g&&w,@,g&,@,(5(#@(&,@)s@(-@-g@- @*\-@)s(;@&n-@)݀@(-@-g@-#@* \(P-(@)s@D-0@*xh(5-5@-4g&@@@@@<_ind @,,,֠,~,u,,+++_+X+****|*k@M&@-Y@-Xg&&&@-a@-`g&&-g@-fg'-k@-e(((p-p@-og@(T-x@*E݀'Ҷ@(w-~@-}g@-@k$@c-@*Y݀b(-@-g@-@k#!J@@@@@ꠠ&le_ind @-W-G-8,,נ,,x, ,+++b+[+L**ޠ*͠QD6@ON'Y@-@-g'W'U'S@-@-g'_'M-@-g'e-@-) ((Қ-@-g@'H@(Қ-@-g@-@*\$t@-@*݀(嚠-@-g@-@*\#|@@@@@E&Rlt_wd @----;-2,ڠ,Ӡ,{,t,,++++Q+9+(@O(ʚ.@.g'@.@.g@.!@. g''.'@.&g@.,@.+g'Ț.0@.*〩'.6@.5g'Қ.:@.4)x)?.?@.>g)=.D@.Cg㠩.K@+H\(.P@rk)~@@&@@&Rgt_wd @..----8-1,٠,Ҡ,z,s,,,+++ @ P)(.s@.rg( @.z@.yg@.@.~g(( .@.g@.@.g(&.@.〩(.@.g(0.@.)ַ).@.g).@.gA.@k)ϩ.@+\)@@'[@@ %lt_wf @.n.^.O-----7-0,ؠ,Ѡ,y,r,c, ++ h [ M@ fQ).@.g"Wf*@,well_founded8E.@.g)䚠.@.g)⚠.@.g.@+\).@ k*#@@@+A𱍠G @+A7iA)@AB@@ P%gt_wf @....F.=--ޠ---'- ,Ƞ,,,\,D,3   @ R)՚/ @/gO/&@/%g*+/+@/*g*)/0@//gϠ/7@ Yk*]/<@,9\*@@G@@ -add_lt_mono_l @...ݠ..|.$.-Š--f-_--,,,,r@,n@*\/\@/[g*Z/a@/`g&/f@/eg*/m@ k*/r@ k/x@,k&U/}@,p*@@(*@@AA@@A@-add_lt_mono_r @/@/0/!.ɠ..h.a. .---K-D-5,ߠ,Ǡ,@,A*/@/g*/@/g&⚠/@/g*頩/@ k*^/@ k/@,&Q/@,*@@(n@@D+add_lt_mono @//q/b/ /...J.C-----v- -,@,B*ᚠ/@/g*ߚ/@/g'#/@/g%/@/g@/@!k%@/@!k*0@!#k0@,)e*0 @-@@@@@-add_le_mono_l @/͠///V/M.....7.0-ؠ-Ѡ- -l-T-C@-?C+-0-@0,g++02@01g'o07@06g+v0>@-;\*멚0C@-@\0I@-<'&0N@-A+t@@(@@Ѡ-add_le_mono_r @0/////6//.נ.Р.x.q...---@-D+n0n@0mg+l0s@0rg'0x@0wg+0@-|\+,0@-\0@-}'0@-+@@)<@@+add_le_mono @0O0?00/ؠ/Ϡ/w/p//...Z.S.D--֠-@-E+0@0g+0@0g'񚠐0@0g&ǚ0@0g@0@-\&@0@-\+w0@-\0@-Ω0@-@@@@@].add_lt_le_mono @000{0#0/ //c/\/.....9.!.@. 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