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U\D{VOܠiXok@@b@@X(eq_trans @{@6Equivalence_TransitiveWt@sbx@rj|@q @@*Transitive++-@b@jpcTYLu@-W\[DUE6٠РslG@1֠XGĠ@@@@*eq_sym_iff @tdU.'ʠàf_Pݠ̠wf@b@!x@b!y@b%Logic$Init@#iffС)@jBA@j@@@@AA@@A@'neq_sym @@7ڠӠvo =%@A!n @b!m'@&b@I@#notШ4@.jD ;@5jKC@@@@@D(eq_stepl @ޠxSL٠~fU@B_@^bd@cb!zk@jb@q@kjCB@z@tjD@{jD@@@Aۓό^)Morphisms@@AB@@(succ_inj @J:+ΠŠha<5&ˠM<@8C"n1@b"n2@b@@j@pѩ@v֩@j\@@@AviAK@AAۀߠKN@R@@ABC@@ޠ+succ_inj_wd @xQJs@DM@bK@b@j @J@I@j%@@@G@A8ӠA4Relation_Definitions)Relations)@AB@@%/succ_inj_wd_neg @ޠΠbY4-Рɠ_G6@E"@@?b E@DbfN@HjT@Y@1`@Zjp@@@@@g1central_induction @ >7ڠӠvo x#@F!A@@bA$A_wd@&ProperL@@b @*respectful%WO?@b@jB@b@q@@bԠE@m@bF@@@@@̠'add_0_r @uf ?8۠Ԡwpaݠ@@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@,@$zero,筷T@@A@ABCDE@A@E@Fd@cbi@cjo@Dǀ~t@ʾ>@@@@@y@ABC@@AA@@A@*add_succ_r @:*XQ,%v@A@b@b@j@ǀ@e署@j@ǀѐ@@M@@J-add_succ_comm @qb;4נРsl]٠ܠˠ@Bɚ@bǚ@b@j@ǀ@< @ǀ@A@@@@(add_comm @ȠLCߠ{I1 C6(#@C.@-b3@2b8@2j>@ǀNC@ǀK@@@@̠'add_1_l @~!YRߠl[~qc^M?@JDKi@hbn@hjt@Iǀy@;D~@-@@ @@'add_1_r @>. \U0)z@E@b@j@ǀ@vD@h@@E@@B)add_assoc @yiZ3,ϠȠkdUѠ٠Ԡà@F@b@b!p@b@j@ǀ@ǀ  @ǀ @ǀ@@@@,add_cancel_l @ǠKBޠzH0B5'"@G -@ ,b  2@ 1bN 7@ 6bX >@ 8j D@ǀS  J@ǀR O@ Ijސ@@@@ؠ,add_cancel_r @ -&ɠ e^xg}ojYK@VHW u@ tbU z@ yb @ ~b @ j @aǀQ @gǀ @ j&@@#@@ ,add_shuffle0 @ W G 8۠Ҡun IB3ؠҠŠ@I @ b @ bޚ @ b @ j @ǀ @ǀg橚 @ǀ @ǀW@@o@@l,add_shuffle1 @    ' ]V$ @J뚠 @ b隠 @ b* @ b!q @ b @ j %@ǀ +@ǀ𩚠 1@ǀA 6@ ǀ <@ǀ© A@ǀ@@@@ʠ,add_shuffle2 @     |  WPݠjY|oa\K=@HKI g@ fbG l@ kb q@ pb^ v@ ub {@ uj @Vǀ @\ǀ\ @aǀ @fǀ @lǀ @rǀ,@@)@@&,add_shuffle3 @ ] M >  ؠ { t  OH9ޠƠؠˠ@L @ b @ b䚠 @ b @ j @ǀ @ǀ @ǀ󩚠 @ǀ]@@u@@r'sub_1_r @    - $ Ǡ  c \*$ @M񚠐 @ b @ j @ j) @D $@ã]@@@@'mul_0_r @  Ԡ Š h _     : 3֠ϠeM<_RD@]@) G@ Fb L@ Fj R@a W@ʾ> [@ʾ>@@@@AA@@A@*mul_succ_r @      < 5 ؠ Ѡ t m  v~@Ac @ ba @ b @ j @Y @FЩ @qǀ @j@@.@@G(mul_comm @ b R C  ݠ  y     T M >ˠݠР@B @ b @ b @ j @婚 @@@f@@/mul_add_distr_r @   {     T M     v  @Cߚ @ bݚ @ b @ b @ j @ @ǀ& @ǀ #@ (@8@@@@͠/mul_add_distr_l @  ؠ ɠ l c     > 7 ڠ Ӡ Ġ i Q @cVH@aD- K@ Jb+ P@ Obl U@ Tb Z@ Tj `@ (% f@ ;ǀv k@ @ǀ q@ 9 v@ >@@@@)mul_assoc @ 6 &    T M     ( !    @E{ @ by @ b @ b @ j @ vs @ |ĩ @  @ N͐@@K@@d'mul_1_l @  o `     9 2 ՠ Π q j [   נ@FĚ @ b @ j @  @ D@@~@@'mul_1_r @    6 - Р ɠ l e      3  - @+G @ b @ j @ / %@ D3@@@@ʠ,mul_shuffle0 @  ՠ Ơ i `     ; 4 נ Р  f N =`SE@^H* H@ Gb( M@ Lbi R@ Qb W@ Qj ]@ % c@ +q h@ 0 n@ 6}@@@@,mul_shuffle1 @ .     L E    }      @Is @ bq @ b @ b @ b @ j @ s @ y @ ~Ʃ @  @ G @ :@@R@@k,mul_shuffle2 @  v g     @ 9 ܠ ՠ x q b   ޠ@J˚ @ bɚ @ b  @ b @ b @ j@  @ ީ@  @ @ @ @@@@à,mul_shuffle3 @ ޠ Π  b Y     4 - Р ɠ  _ G 6YL>@WK #A@@b !F@EbbK@JbP@JjV@  \@ $ la@ ) qg@ /ې@@@@ %le_wd @'   E >  ڠ } v      @@A&NZBase'NZOrder&NatInt'Numbers#Coq@ ) '@A@'NZOrder&NatInt'Numbers#Coq@+NZOrderProp 8 6@A@@@@"NZ - ,@A@@@@b@@b,@b@@b7@j)@bA@j ꚠ@ j@@Z@@AA@@A@*lt_le_incl @r    K D    | m   j]O@hA ֚@b Ԛ@b@@"ltj @ j @@@@@7'le_refl @ŠI@  ܠ  x      F . @B (@'b-@ j < <@@ 1@@`.lt_succ_diag_r @ޠϠri    D =  ٠ ʠ o W FǠ@C 3Q@PbV@Wj e\@  @@@@@.le_succ_diag_r @ :3 ֠ Ϡ r k      t@D a@~b@ cj @ 9 Ð@@@@@/neq_succ_diag_l @J:+ΠŠha    < 5 & ˠ  #@!E @b @j@ i  Ȑ@@ @@젠/neq_succ_diag_r @zj[4- Р ɠ l e V   ҠSF8@QF @b @j 󩚠@  #@@@@@/nlt_succ_diag_l @.%Ƞd]     +  vh@G  @ b 吩@j@  S (@@@@@L/nle_succ_diag_l @ڠʠ^U0) ̠ Š  [ C 2@H =@<b D@ #jJ@   X@@@@@|)le_succ_l @ (!Ġ`Y     s b֠@I Om@lb Mr@qb y@ Xj@ .  @j @@ @@+le_gt_cases @D4%Ƞb[6/  Š  @J @b @b @"or @@ j ɩ@j Ɛ@@ J@@-lt_trichotomy @~n_81Ԡ͠piZ   ֠WJ<@UK Ú@b @b:@j A@j @j @@@@@+(lt_asymm @=4נРsl:"w@L @b !@ b@'@(j 7 .@/j @@ a@@`(lt_trans @ޠϠri D=٠ʠoWFǠ@M 3Q@Pb 1V@Ubr[@Zb@a@bj @g@hj l@mj  1@@ @@(le_trans @-KD| @N r@b p@b@b@@j /@@j 5@j?@@ 7@@ݠ+lt_strorder @k[L%]VGԠàD7)@BO@+StrictOrder.[@@b@j@@ @@ +le_preorder @zSLureW@pP @(PreOrder@@b@j@@ @@9/le_partialorder @ǠKBޠzH0@Q7@,PartialOrder5͛К0@/b4@.j8@- <@j[@b#u@@@ s@A @E@FAhCV@ABC@@y)lt_compat @U@%lt_wd؆@ ̰@]@\b@b@ab ݩ h@gb@m@lb 蚠q@kj w@vb 򚠐{@uj @j@@@%lt_wd']ɠA1"Š_X3,  @@@@@Р(lt_total @@We@ @b @b @j ͩ@j ԩ@j ѐJ3@ aǠvg @9ܠՠxqbޠ_RD@@@@@'le_lteq @@+lt_eq_casesk!=@ ٚ@b ך@b@jW @ j@ j@+lt_eq_cases&yˠOF~!L4#@@@@@Z0Private_OrderTacLA'IsTotalT A1 @D@9 @W@+Equivalence~@P@ObT@Nj@(eq_equiv7L.'ʠàf_yhܠ@@@@@ @@@@b@j@,Q^?/ à]V1* @@@@@ΠU @@]O@ @@b@@b 0 @b@@b ;@j -@b E@j@jS{lE>ڠ}vg dWI@@@@@J @@R#@ܚ@bښ@bS@jZ @j@jIˠOF~!L4#@@@@@ZE @P@MC"@:@9b?@>b`F@%jVM@Nj]R@LjbC )"ŠaZtcנ@@@@@@@@@"A@#TacGA @1!OH#  @@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@6 @ b@ j@@@@AA@@A@ @ӠàWN)"ŠT<+]VP5@Af<@;bA@ j@@D@@0)lt_irrefl @|WPݠjYڠ͠Р~c@Bj@ibBq@rjD@@t@@`g @0 NG"  @CÚ@b@b@@j@jn@@@@*le_antisym @iYJ#[TEҠB5'8(@9D@b@b@@j@@j@j @@@@נ @+"ŠaZ(sevf1*$ @wE:@b8@b@@j-$@j@@@@@*interp_ord @!o)OrdersTac3@#ordȠ@ @@@@@@@@@@@D@F@Eb@K@JbYP@JjT@UjX@7j@*(@^@]b@c@bbސ +k= R'6'6'6''+k+7T'+7T'6'ࠒA̠ܠ۠@@"lt\ @@"eq8L@lР@TȠ@@QPO@@A@B@A@xA܀M=.ѠȠkd?8)Π&  נРʠ@@@@@%trans @p`Q*#Ơb[L٠ȠI<.?/@@F"o'@b@b~@b@ @܀:@@܀ @܀@)trans_ord-0uGDR̐@@;@@ @@@b>@b @bB@r5A~МA:9@Z0@/bX5@4bњ:@9b@@@:j϶@F@@jթK@Ejߐ L+k() LL7#'S@$t-&ɠ e^xg۠͠ޠΠq@@@@@a @@b@b!@bd"@5A~МbCY@Ě@bš@b;@b@@j9@@j?@jI L+k() NN7#'jtueV/(ˠĠg`Qޠ͠ N A 3D4@@@@@Ǡ @@b@b@b@B5A~МB  @*@b(@b @ b@@ j@@ j@ j L+k() MM7#'Аt۠ˠ_V1*͠Ơ\D3   e^X=@@@@@-+le_lt_trans @wM@LbuR@QbW@Vby1@5A~g#nm@d@cbi@hbn@mb@t@Sj@z@ {j @ j L+k() MN7#'4t?/ à]V1*   ɠ @@@@@+lt_le_trans @ۚ@bٚ@bR@bS@ 5A~1@򚠐@b𚠐@bi@b@@ jg@@jm@ jw L+k() NM7#'t']V$  | o arb-& @@@@@%eq_lt @?@b=@b@bA@q5A~/65@V,@+bT1@0b͚6@5b@<@6j˶@B@ CjѩG@ Hjې L+k() ML7#'t%]Vp_  Ӡ Š֠Ơi@@@@@Y%lt_eq @y@xb~@}b@b]@5A~cO@@b@b1@b@@ j/@@j5@ j? L+k() LM7#'`tk[L%]VGԠà D 7 ):*@@@@@%eq_le @@b@b~@b @95A~]@@b@b@b@@j@ @j@j L+k() NL7#'ĐtϠSJ%P8'   YRL1@@@@@!%le_eq @kA@@biF@Eb⚠K@Jbm%@5A~+ba@X@Wb]@\bb@ab@h@Gj@n@hjs@Rj  L+k() LN7#'(t3#QJ%   @@@@@&eq_neq @VF7ڠѠtm HA2נ / " %٠Ӡ@&G隠@b皠@b`@b@@j^@@jf@j r@@@@@͠&neq_eq @"XQz w j \m](!@nH1@b/ @ b@b@ꐩ@j@@j&@ j @@@@@*not_neq_eq @֠Ǡja<5ؠѠ gO>   picH@IyO@NbwT@Sb@-/^@Xjnc@]j@@@@R)not_ge_lt @#A:ݠ֠yr{   @J@b@b@j@xj@ j-@@@@)not_gt_le @^N?٠|uPI:ߠǠ 7 * -۠@.K񚠐@b@b@@ jܩ@jh@@@@@Ƞ)le_neq_lt @zSLu r e WhX#@iL,@b*@b@ @j@搩@j@ j@@@@@ @@@@)@@@@@)@<_neq @ޠΠbY4-Рɠ_G6   @ R#A@@b!F@Eb@L@ Mj\$S@Mj@@@@@ &le_neq @1*͠Ơib|k  ߠ @ SXv@ubV{@zb@ j@#andЖw@@njg@j@@@@@ Ƞ*eq_le_incl @VF7ڠѠtm HA2נ/"@-T@b@b@@jԩ@jX@@@@@ (lt_stepl @yj C<ߠؠ{te bUG@`U@b@b@b@@ j@@j@j@@@@@9(lt_stepr @ǠKBޠzH0@VT*@)bR/@.b˚4@3b@:@;jɶ@@@:jϩE@Fj ِ@@@@@w(le_stepl @#[Tn]ޠѠ@Wh@gbm@lb r@qb@x@Wj@~@xj@bj@@@@@(le_stepr @C3$ǠaZ5.Ġ@XК@bΚ@bG@b@@jE@@jK@j U@@@@@ @pa:3֠Ϡrk\ؠYL>@WYŚ@bÚ@b@b@@j@@j@j @@@@@0\ @A8۠Ԡwp >&{@Z @b%@$bA*@)b@0@1j@6@jũ;@<j ϐ@@@@@m+le_antisymm @ܠvQJנ|dSԠǠ@[@^@]b>c@bb@i@Hjy@o@Nj4t@njI@@@@@)le_succ_r @4$RK& @ \y@bw@b@j@X @j@jũ@j@@@@@)lt_succ_l @{k\5.ѠʠmfWӠTG9@R]@b@b@@j@.@j@@@@@&,le_le_succ_r @8/Ҡˠng 5 r@^@b@b@"@j2'@j쩚-@l@@@@@_,lt_lt_succ_r @ݠΠqh C<ߠؠɠnVEƠ@_2P@Ob0U@Tb@[@\jk`@aj%f@@@@@@,succ_lt_mono @&D=٠|u~@`k@bi@b@j@j@Oߩ@Tސ@@@@@נ,succ_le_mono @eUF|WPAΠ>1#@ @D@@C@@B&le_0_1 @РTK& Q9(@c 3@j 8@ʾ> <@D@@@@@n<_1_2 @ݠwRKؠ}eTՠȠ@d _@`j d@&D h@ @@@@<_0_2 @ (  F?۠~w@e @j @:ʾ> @L@@@@Ơ&le_0_2 @ T D 5ؠϠrkF?0ՠ- @+f @j @fʾ> @x@@@@@<_1_l @  p a :3֠Ϡrk\ؠYL>@WgŚ @ bÚ @ b@ @j @ʾ>@ @j @j!@Dǐ@@@5@3@@ABC@@8+lt_ge_cases @ Ơ   J AݠyG/@h !)@!(b !.@!-b!5@6jE!:@jB@@@@@l+le_ge_cases @   ۠ ~ u  PI֠{cRӠƠ@i?!]@!\b=!b@!ab!i@Hjy!n@Mjv@@@@@+lt_gt_cases @!.!!   L E}  @js!@!bq!@!bp!@!j󠩚!@j!@j@@@@@ݠ,eq_decidable @!k![!L     % ]VGԠàD7)@Bk!@!b!@!b)Decidable!@)decidable r!@!j@@@@@&eq_dne @!!!!'!   ] V$ |oa@zl蚠"@"b暠" @" b,吩琩"@"j&"@"j+@@@@@M&le_ngt @!۠!ˠ!!_!V     1 *͠Ơ\D3@m ">@"=b"C@"Bbd"J@)jZ""Q@RjY@@@@@&nlt_ge @""!!!!/!( ˠ Ġ g ` ziݠ@nV"t@"sbT"y@"xbS"@j"@fj@@@@@,lt_decidable @"G"7"(!ˠ! !e!^!    9 2 #Ƞ @o"@"b"@"bܐ"@jƐ@@@@@蠠<_dne @"v"f"W!!!!!0!) ̠ Š h a RߠΠOB4@Mp"@"b"@"b"@j"@j@@@@@ &nle_gt @""""2")!̠!Š!h!a!     /  zl@q󚠐#@#b񚠐#@#b7𐩚#@j/#$@%j,@@@@@V<_nge @""Ԡ"Š"h"_"!!!!:!3 ֠ Ϡ  e M <@r)#G@#Fb'#L@#Kbm#S@Tjc+#Z@ 9jb@@@@@,le_decidable @## """"8"1!Ԡ!͠!p!i! !    r@s_#}@#|b]#@#b#@ hj@@@@@&le_dne @#I#9#*"͠"Ġ"g"`"!!!!;!4!% ʠ  "@ t#@#b#@#bҠ#@ j̩#@ jѐ@@@@@*nlt_succ_r @##q#b#"""";"4!נ!Р!s!l!]!  ٠ZM?@Xuƚ#@#bĚ#@#b Ð#@j#@ 7#@j @@@@@/5lt_exists_pred_strong @####A#8"۠"Ԡ"w"p"" !!!!>!&!{@v$ @$b$%@$$b$*@$)b@$0@1j@$6@!jX@"ex @$B@$Ab!k$I@$HbǠ$P@$Jj֩$V@!$[@!:jj@@@@A@@A b@ cAРD.Morphisms_Prop$s@ iA1@D@ABCD@@.lt_exists_pred @$*$$ ###H#A""ݠ""y"""!!!@w$$@$bt$@$b@$@jb$@$b\$@$b!$@$jo$@!_驚$@!j@@@O@A@@蠠,lt_succ_pred @$v$f$W#####0#)"̠"Š"h"a"R!!ߠ!ΠOB4@Mxp$@$b$@$b@$@j$@$j$@!$@!ã4 @@@(@A%@t@ @@ABCD@@,&rs_rs' @$$$$>$5#ؠ#Ѡ#t#m## """";"#"x@y@%@%b@%&@%%b%,@%+b%0@%*j P >̚%5@%4b@@ %<@%;b@%B@"!j@>%K@!  3%Q@%Pb@%W@"6j@ @%^@%]b >%c@%bb@%i@"Hjc x@%p@qj 5K'H)@@@@(rs'_rs'' @%4%$%$$$R$K#####&##""" @ z@%@%b@%@%b %@%b!%@%j   F%@%b@ %@%b@%@"j ˶@ %@%b %@%b@%@"j ܶ@%@j I  %@%b  ƚ%@%b Ě%@%b@%@"j"@%@j ! . ݚ%@%b ۚ&@%b@&@"j9@& @ j 8&@" K@@ E@@D%rbase @%Ҡ% %%V%M$$$$$($!#Ġ###S#;#*@{@&6@&5b Қ&;@&:b!#&A@&@b!!&F@&Eb@&L@#+j@&R@Sj!| @@@@@)A'A_right @&&%%%%0%)$̠$Š$h$a$####{#jޠ@|@&v@&ub!&{@&zb@!c&@&b!i&@&b!g&@&b@&@#qj@&@j!]N Ҷ!&@&b@&@#j @@@@@נ6strong_right_induction @&e&U&F%%%%|%%$$$W$P$A##Π#>1#@<} F@&@&b D B @@&@&b L :&@&b R&@&j!!!w&@&b@!Ț&@&b@&@#j!@!՚&@&b!Ӛ&@&b@&@#j1@'@j!0!C.!뚠' @'b@'@#j̐@@@!B@A!@#@@ABC@@E/right_induction @&Ӡ&à&&W&N%%%%%)%"$Š$$$T$<$+@~ @'7@'6b   @'?@'>b  'E@'Db 'I@'Cj"i"W!嚠'N@'Mb@ @"7'U@'Tb@'[@$:j϶@V'c@$"J'h@'gb@'n@$Mjשh!@@@@@0right_induction' @'/''&&&M&F%%%%~%!%% $$$@!@'@'b!! ! @'@'b!!'@'b!'@'j"""A'@'b@"'@'b@'@$j"@"'@'b@'@$j6@'@$y"'@'b! @@#@@7strong_right_induction' @'''p'' &&&I&B%%ޠ%%z%k%$$h[M@f@!p@'@'b!n!l!j@'@'b!v!d(@(b!|(@'j#%#"( @( b@"򚠐(@(b@(@$j#r@"(@(b@("@%j@# ()@((b# (.@(-b@(4@%jٶ@(:@;j"J"{##(A@(@b!~@@@@@s&ls_ls' @(''''|''&&&W&P%%%ݠ%%j%Yڠ͠@A!@(e@(db!!ީ!ܰ@(m@(lb!!(s@(rb!(w@(qj###(|@({b@!Ѷ@#e(@(b@(@jE@!ǐ(@%@"#x(@(b@(@%{j##"@#(@(b#(@(b@(@%j#@(@%j#EF(@%k"J@@@@(ls'_ls'' @(|(l(](''''6'/&Ҡ&ˠ&n&g&X%%%ԠUH:@SB"]@(@(b"["Y"W@(@(b"c"Q(@(b"i(@(j$$#(@(b@#ߚ(@(b@)@%j$ @#욠) @) b#ꚠ)@)b@)@%j$$"`@)@%j#H)"@%#aL$ )'@)&b$H$)/@).b$)4@)3b@):@&j%@)@@&j#l#y$()F@)Eb$&)K@)Jb@)Q@&0j<@)W@&6j#)]@& #@@Z@@%lbase @)) ((((;(4'נ'Р's'l''&&&&u@C"@)@)b"$)@)b$n)@)b$l)@)b@)@&vj S@)@&|j$,ǐ)@&R#ܐ@@@@@ՠ(A'A_left @)c)S)D((ޠ((z(('''U'N'?&&̠&</!@:D#D@)@)b#B$c)@)b@$)@)b$)@)b$)@)b@)@&jG@)@&j$xQ$"$К)@)b@)@&j P@@%@@&5strong_left_induction @))))8)/(Ҡ(ˠ(n(g( (''''5'' r@E#@*@*b###@* @*b##*&@*%b#**@*$j%J%8$ƚ*/@*.b@%*5@*4b@*;@'j%C@%$*B@*Ab%"*G@*Fb@*M@',j8@*S@'2j$*Y@'$%@*^@*]b@*d@'Cj! !@@@$@&h@@ABC@@.left_induction @*'**)))E)>((ڠ(}(v((('''@F$@*@*b$$$@*@*b$#*@*b$*@*j%%%9*@*b@#@%*@*b@*@j!k@#퐩*@'f$%*@*b@*@'j&T@@@@@/left_induction' @**r*c*))))<)5(ؠ(Ѡ(t(m(^(''ڠ[N@@YG$c@*@*b$a$_$]@*@*b$i$W*@*b$o*@*j&&%*@*b@%嚠+@+b@+ @'j&e@%񚠐+@+b@+@j!Ѷ@$S+@'%\&+"@+!b$_@@ @@T6strong_left_induction' @**Ҡ*à*f*]*))))8)1(Ԡ(͠((c(K(:@H$ö@+F@+Eb$$$@+N@+Mb$ɩ$+T@+Sb$Ϛ+X@+Rj&x&f%+]@+\b@&E+c@+bb@+i@(Hj&yŶ@&Q+o@+nb@+u@(Tj"1@&^+|@+{b&\+@+b@+@(fj&$Ķ@+@(mj&T+@(C%&{+@+b$֐@@ @@ˠ/order_induction @+Y+I+:*ݠ*Ԡ*w*p** )))K)D)5(ڠ( (2%@0I%:@+@+b%8%6%4@+@+b%@%.+@+b%F+@+j&&ݶ&k+@+b@%)@&+@+b@+@(j"U@ܐ+@(@&њ+@+b@+@jY@𐩚+@(&<&䚠,@,b&<@@@&5@&3@AB@@70order_induction' @+Š+++I+@**ܠ**x**))))F).)@J%@,)@,(b%%%@,1@,0b%%,7@,6b%,;@,5j'['I&ך,@@,?b@%@'),G@,Fb@,M@),j"@ H,U@) @'=,[@,Zb@,a@)@jŶ@𐩚,i@)ã'P,n@,mbl@@k@@1order_induction_0 @,.,,+++L+E****}* ** )))@K&@,@,b& & & @,@,b&&,@,b&,@,j''@',@)Uʾ>@',@,b@,@)j,@)fʾ>'ʶ@%,@)sy@',@,b@,@j'ߚ,@)ʾ>@&,@)'E'Ě,@,b&@@@@@2order_induction'_0 @,,,,&,+++\+U*****~*#* ){n`@yL&@-@-b&&&}@-@- b&&w-@-b&-@-j(8(&@()-@)ʾ>@(-%@-$b@-+@* j-0@)ʾ>(>@&n-8@)@( ->@-=b@-D@*#j(S-I@)ʾ>@D-Q@*ã(8-V@-Ub&@@@@@<_ind @--,,,,4,-+Р+ɠ+l+e++****n@M&@-z@-yb&&&@-@-b&&-@-b'-@-j(((s-@-b@(W-@*H'Ҷ@(z-@-b@-@j$@c-@*\b(-@-b@-@j#!J@@@@@ꠠ&le_ind @-x-h-Y,,,,,2,++Π+Ǡ+j+c+T***РQD6@ON'Y@-@-b'W'U'S@-@-b'_'M-@-b'e-@-j)((՚-@-b@'H@(՚-@-b@.@*j$t@.@*(蚠. @. b@.@*j#|@@@@@E&Rlt_wd @-Ӡ-à--W-N,,,,,),"+Š+++T+<++@O(͚.6@.5b'@.=@.<b@.B@.Ab''.H@.Gb@.M@.Lb'Ț.Q@.Kj'.W@.Vb'Қ.[@.Uj){)B.`@._b)@.e@.db㠩.l@+Kj(.q@rj)@@&@@&Rgt_wd @.1.!.---O-H,,,,,#,, +++ @ P)+.@.b( @.@.b@.@.b(( .@.b@.@.b(&.@.j(.@.b(0.@.j)ٷ).@.b).@.bA.@j)ҩ.@+j)@@'[@@ %lt_wf @...p.. ---I-B,,ޠ,,z,k,++ h [ M@ fQ).@.b"Wf*@,well_founded8E/@.b)皠/@/b)嚠/ @/ b/@+j)/@ j*&@@@+A𱍠G @+A7iA)@AB@@ P%gt_wf @.ޠ.Π..b.Y-----4--,Р,ɠ,,_,G,6   @ R)ؚ/A@/@bO/G@/Fb*./L@/Kb*,/Q@/PbϠ/X@ Yj*`/]@,<j*"@@G@@ -add_lt_mono_l @// 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888K8D7777|7m7@7jL4њ9@9b4Ϛ9@9b@4͐9@9j5 :@6ʾ>5":@:j:@644ҩ:@: j5#:@6D@@2@@1mul_le_mono_pos_l @9ؠ9Ƞ99\9S88888.8'7ʠ7à77Y@7M5:6@:5b5:;@::b1W:@@:?b@:F@+Gj:K@6ʾ>5Y5l:R@71j0':W@76j:]@7%+:b@7*5'@@4@@̠1mul_le_mono_pos_r @:"::999@998ܠ8ՠ8x8q88 77@7N5b:@:b5`:@:b1:@:b@:@+j:@7?ʾ>55:@7{j0q:@7j:@7o5-:@7t5;@@38@@1mul_le_mono_neg_l @:l:\:M99999&98 88^8W8H7@8EO5:@:b5:@:b1뚠:@:b@:@+j5隠:@7ʾ>6:@7j0:@7j:@75:@7Đ@@@@`1mul_le_mono_neg_r @::::::19Ԡ9͠9p9i9 988887@8P5;@;b5;@;b25;@;b@;$@,%j63;)@7ʾ>6J;0@8j1;5@8j;;@85ʩ;@@85Ɛ@@3@@2mul_lt_mono_nonneg @;::::{::999V9O888ܠ8@8Q6@;^@;]b6>;c@;bb2;h@;gb1U;m@;lb@;s@8Rj;x@8"ʾ>5@;~@,j46@;@8dj;@84ʾ>6@;@,j;@,j;@8c)4ة;@8i$4@@@@@ 2mul_le_mono_nonneg @;b;R;C::ݠ::y::999T9M9>8@9;R6;@;b6;@;b2ᚠ;@;b1;@;b@;@8j;@8ʾ>6_@;@8jb@;@8j;@8ʾ>6p@;@8js;@8j;@8a<@8`@@64@@k+mul_pos_pos @;;;;E;<:ߠ:ؠ:{:t::9999B@9S7<@<b6<$@<#b@<*@-+j7>@<5@-6j<:@8ʾ>7I@<}@-~j7<@9,ʾ><@-j<@96ʾ><@9Y2f@@@@+mul_pos_neg @7ζ@<@-j7՚<@9tʾ><@-j<@92<@9ʾ>@@7 @@C+mul_neg_pos @<<@= @.j=@9ʾ>8!=@.j=@92򚠐=!@9ʾ>@@@@1mul_nonneg_nonneg 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