"` t t0$NAdd(Abstract'Natural'Numbers#Coq@)Decidable%Logic#Coq@$Bool#Coq@2Relation_Operators)Relations#Coq@4Operators_Properties)Relations#Coq@)Relations#Coq@*Equalities*Structures#Coq@&Orders*Structures#Coq@4Relation_Definitions)Relations#Coq@-SetoidTactics'Classes#Coq@&Setoid'Setoids#Coq@$Init'Classes#Coq@/RelationClasses'Classes#Coq@)Morphisms'Classes#Coq@.Morphisms_Prop'Classes#Coq@*NumPrelude'Numbers#Coq@-GenericMinMax*Structures#Coq@(NZAxioms&NatInt'Numbers#Coq@(NZParity&NatInt'Numbers#Coq@%NZPow&NatInt'Numbers#Coq@&NZSqrt&NatInt'Numbers#Coq@%NZLog&NatInt'Numbers#Coq@%NZDiv&NatInt'Numbers#Coq@%NZGcd&NatInt'Numbers#Coq@)Notations$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$Init#Coq@&NZBits&NatInt'Numbers#Coq@'NAxioms(Abstract'Natural'Numbers#Coq@%NBase(Abstract'Natural'Numbers#Coq@)Notations$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$Init#Coq@0JqTttֱ)Decidable%Logic#Coq@0ND걸풬/Oߠ$Bool#Coq@0j 2cZ`FW&Basics'Program#Coq@0!bs߯? :VU$Init'Classes#Coq@0](p{yOh.'Tactics'Program#Coq@03u%+Equivalence'Classes#Coq@07;ꮹ-SetoidTactics'Classes#Coq@0S_`nOU$&Setoid'Setoids#Coq@0D9AsWE!>*Equalities*Structures#Coq@0όe얟)H.Ƞ2Relation_Operators)Relations#Coq@0%s鯰s4Operators_Properties)Relations#Coq@0U3y#h&)Relations#Coq@0r砠*NZMulOrder&NatInt'Numbers#Coq@0}\^ !"k}@R(NZParity&NatInt'Numbers#Coq@0H>ca'^^%NZPow&NatInt'Numbers#Coq@0)6*9 B:vȻ&NZSqrt&NatInt'Numbers#Coq@0` .%m%NZLog&NatInt'Numbers#Coq@0ꔉ .uV%NZDiv&NatInt'Numbers#Coq@0$ |J?d (w%NZGcd&NatInt'Numbers#Coq@0KgT7|&NZBits&NatInt'Numbers#Coq@0MlIpKt'NAxioms(Abstract'Natural'Numbers#Coq@0Zخb1Z3uuѠ,NZProperties&NatInt'Numbers#Coq@01D%E`|3x0 Y?V vIu?I B]o*BYԄLI Р$NAdd(Abstract'Natural'Numbers#Coq@ A(NAddPropA@!N@!t @J %'A*Equalities*Structures#Coq@@@@@ %'@ @A@A@@@AA@@A@"eq @^@)@%5 i@.@*5 iA@@@@@(eq_equiv @@/RelationClasses'Classes1@+Equivalence~@J@F5 iN@/5'倐@@@FA݋X_A/RelationClasses'Classes#Coq@@A@@A$zero @Tf@!t5 i@@@@@AA@@A@$succ @r@y@5 i}@5 i@@@@@$pred @d@@&5 i@*5 i@@@@@)'succ_wd @@)Morphisms'Classes#Coq@@&ProperL@@F5 i@J5 i@*respectful%WO?@U5 i@Y5 i@"eq5'倚@5'倚@]A߀@@@AviA4'Classes#Coq@@A@@n'pred_wd @@E@@5 i@5 i9@5 i@5 i@45'倚@85'倚@}Aj@@@A3@A@@)pred_succ @@!n@5 i@S5'倠@Aj"@A߀A@@@@@,bi_induction @@!A@5@5 iA@@?@5 i E@5 iI@5'倚%Logic$Init@#iffС)0@B[@B|@Ra@5 iDCl@A߀Jbq@ 5 iEQ@@@kA@A@@#one @T@5 i@@@@@#two @T@+5 i@@@@@*(one_succ @@@5'倠@@@15  @AA߀@$zeroB|@@@@@O(two_succ @@@5'倠@A5̀@_A߀@Y5 @@@@@l"lt @h@@!t5 i@@5 iA@@@@@AA@@A@"le @h@@5 i@@5 i@@@@@%lt_wd @@q@@5 i@@5 if@5 i@!@5 i욠%@b5'倩u+@5 i/@l5'暠3@"lt5(m@@@,Ah@A@@Ϡ+lt_eq_cases @@5D@5 i!mK@5 iR@`5(^0 @"or @`@-5(me@5'@@@@@)lt_irrefl @@ds@ 5 i+@#notШ@L5(m]]@@@@@)lt_succ_r @@@(5 iJ@-5 iK@g5(mF@1A߀~@5(^S@@@@@>#add @d@@N5 i@@S5 i@W5 i@@@@@V#sub @d@@f5 i@@k5 i@o5 i@D@@m#mul @d@@}5 i@@5 i@5 i@[@@&add_wd @@[@@5 i@@5 i@5 iT @5 i@@5 i@5 i@T5'倩g@5 i!@5 i%@b5'倚)@f5'倚-@5@@@%Aa@A@@Ƞ&sub_wd @@@?@5 i@D@5 iH@5 iN@5 i@S@5 iW@5 i[@5'倩a@5 ie@5 ii@5'倚m@5'倚q@51@@@iA@A@@ &mul_wd @@㰶@@5 i@@"5 i@&5 i@,5 i@@15 i@55 i@5'倩@?5 i@C5 i@5'倚@5'倚@5ŀ@@@A@A@@P'add_0_l @@@_5 i@5'倠@&5@xB|@@@@@n*add_succ_l @@Ԛ@}5 i@5 i@*5'倠@I5@A߀ש@A߀@[5@@@@@'sub_0_r @@@5 i@U5'倠@\51#@B|@@@@@*sub_succ_r @@"1@5 i횠6@5 i;@x5'倠A@51G@A߀%L@AjR@51@@@@@렠'mul_0_l @@Q`@5 ie@5'倠k@5ŀp@B|Mt@B|@@@@@ *mul_succ_l @@s@5 i>@!5 i@5'倠@5ŀ@)A߀u@5@5ŀQ@@@@@<#max @d@@!t5 i@@5 i@ 5 i@@@@@AA@@A@%max_l @@!x@5 i!y@$5 i@@"le5(^AB@"eq5'倠@D5UC@@@@@2%max_r @@/@J5 i-@O5 i@@+5(^)* @(5'倠@k5U'4@@@@@W#min @d@"@p5 i@'@u5 i+@y5 i@@@@@o%min_l @@l9@5 ij>@5 i@D@h5(^=I@d5'倠O@75cb@@@@@%min_r @@]@5 ib@5 i@h@5(^m@5'倠s@[5@@@@@&pred_0 @@@"eq5'倠@Aj@0B|@4B|@@@@@AA@@A@@'NAxioms(Abstract'Natural'Numbers#Coq@/NAxiomsMiniSig'@@@@5 i@@5 iJ@@A@A5'@@5'^@@A@5(^@@5(^h@@A@AB5(m@@5(mh@@A@5@@5d@@A@A5U@@5Ud@@A@5@@5d@@A@ABC5@@5Šd@@A@5 @@S5 T@@A@A51@@51d@@A@5@@M5͠T@@A@AAj@@VAjd@@A@A@@mAߠr@@A@B|@@B|T@@A@ABCDE@'eq_refl @/RelationClasses'Classes#Coq@@5Equivalence_Reflexive@$zero ɠT@@A@ABCDE@A@&NZBase&NatInt'Numbers#Coq@*NZBasePropbl@@@A@@@@"NZ&NZBase&NatInt'Numbers#Coq@t@@’H@|@!t’HJ@@A@A™@@"eq™Ġ^@@A@š=@ @"leš=h@@A@ABšL@@"ltšLh@@A@"m@@#add"md@@A@A34@@#max34d@@A@3@@#min3 d@@A@ABC4@!@#mul4d@@A@6@'@#one6T@@A@A=@+@#sub=d@@A@>@1@#two>T@@A@AI@5@$predId@@A@G@:@$succGr@@A@@?@$zeroT@@A@ABCDE@A@@M@]@@@d@!tРJ@@A@A L@@"eq L^@@A@r@ @#onerT@@A@AB4@@#two4T@@A@b@@$predbѠd@@A@F@@$succFr@@A@]l@@$zero]lT@@A@ABCD@A@@L4.+*@A@4*BackportEq@@@A@@@@ %'A*Equalities*Structures A݋X_A@A@@AA@@A@&eq_sym @"@5Equivalence_Symmetric. U@,@)SymmetricFgq@5 i@5'倐zTpL@$. U\rD)lVEߠ\X@@O@@E(eq_trans @d@6Equivalence_TransitiveW]D4-@n@*Transitive++-C@^5 iG@]5'倐ɐTL@$W\Dk[TE2!ˠ@@@@*eq_sym_iff @piZàG6@2@!x@5 i!y@5 i%Logic$Init@#iffС)@5'倠BA@5'倠@@@@AA@@A@'neq_sym @ڠt@pA!n@5 i!m@5 i@?@#notШ@5': @5'倠AC@@@@:(eq_stepl @ޠϠ8"@Bu@5 is@5 i!z@5 i@@5'倠,m@ @"5'倠Du@)5'倠:@@@?Aۓό^)MorphismsK@E@AB@@z(succ_inj @5%xbQ@C"n15@P5 i"n2<@W5 i@B@X5'倠H@A߀N@%A߀T@j5'O@@@AviAA@AAۀߠKD@H@@ABC@@+succ_inj_wd @xhaR?.@*DCv@5 iA{@5 i@5'倠@_A߀@@dA߀?@5'@@@=@A8ӠA4Relation_Definitions)Relations@AB@@/succ_inj_wd_neg @Ѡ|k@gE@5 i@5 i1@5'倠@A߀@A߀~@5';@@@@@21central_induction @ݠ֠Ǡ0 @F!A@@ 5 iA$A_wd@&ProperL@@5 i @*respectful%WO? @&5 i@%5'u@/5 i@<ȶ@`@75 iEҩ'@A߀ٶp,@G5 iF@@@@@'add_0_r @H81"ud@@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@,@$zero,筷T@@A@ABCDE@A@E@@5 i@5'倠@55@B|9@@@~@@@ABC@@AA@@A@*add_succ_r @ܠ͠6 zl@wA9@5 i7@5 i@5'倠@5m @A߀@A߀@5~@@C@@@-add_succ_comm @0  s]L۠͠Ƞ@Bv2@M5 it7@R5 i<@R5'倠B@?5H@A߀M@J5S@*A߀@@@@}(add_comm @m]VG% @Co@5 it@5 iy@5'倠@|5穚@5@@@@'add_1_l @xˠVI;6%@"D䚠@5 i@5'倠@5@5 @A߀g@@@@ߠ'add_1_r @ϠzlgVH@SE@5 i@5'倠@5C@5 @A߀@@@@)add_assoc @ڠC-y@FF@5 iD@"5 i!p@)5 i@)5'倠@5@@5$@!5*@'5%@@W@@T,add_cancel_l @D4-q`ܠˠ@GF@a5 iK@f5 iDP@k5 iɠW@m5'倠]@Z5c@`5éh@~5'c@@@@,add_cancel_r @rk\Š:- @HȚ@5 iƚ@5 i@5 i@5'倠@5@5 @5'@@@@Р,add_shuffle0 @ܠxk]XG9@DI@5 i@5 i@5 i@5'倠@5@5C@5@5MO@@@@,add_shuffle1 @ܠE/{@JH@5 iF @$5 i@)5 i!q@05 i@05'倠 @5&@#5M,@)51@.57@45+<@95@@i@@f,add_shuffle2 @VF?0rݠ@KX@s5 i]@x5 iVb@}5 iTg@5 il@5'倠r@o5x@u5R}@z5婚@5@5|署@5@@@@,add_shuffle3 @ՠĠ`SE@/!@,L@5 i욠@5 i@5 i@5'倠@5橚@5-@52@55@@@@'sub_1_r @ڠӠĠ-qc@nM0@5 i@5'倠@51^@5 @Aj@@.@@+'mul_0_r @ ^H7ӠƠ@@^@55 i@55'倠%@5ŀ*@B|.@B|@@[@@AA@@A@*mul_succ_r @K;4%xg@AJ@e5 iO@j5 iT@j5'倠Z@J5ŀ©`@7A߀e@b5k@[5ŀҐ@@@@=(mul_comm @un_Ƞ=0"@;BȚ@5 iƚ@5 i@5'倠@5ŀ@5ŀ@@@@k/mul_add_distr_r @Ϡk^P@iC@5 i@5 i@5 i@5'倠@5ŀ@53@5@5ŀ=@5ŀE@@ @@/mul_add_distr_l @Ѡ:$@D:@ 5 i8@ 5 i @ 5 i @ 5'倠 @5ŀ2 @5y @5 @ 5ŀ !@5ŀ@@N@@)mul_assoc @ ; + $ ~hW@E~ :@ U5 i| ?@ Z5 i8 D@ _5 i I@ _5'倠 O@?5ŀv U@E5ŀ Z@J5ŀ `@P5ŀ[Ɛ@@@@2'mul_1_l @ z j c T2%@0F y@ 5 i ~@ 5'倠 @t5ŀ @s5 @@@@['mul_1_r @    }Р[N@@YG暠 @ 5 i @ 5'倠 @5ŀ @5 @@@@,mul_shuffle0 @ ̠    wi@H @ 5 i  @ 5 iɚ @ 5 i @ 5'倠 @5ŀ @5ŀL @5ŀ @5ŀVX@@@@à,mul_shuffle1 @     N 8 'à@IN @ %5 iL @ *5 i @ /5 i @ 45 i @ 45'倠 $@ 5ŀ *@ 5ŀ /@ 5ŀ 4@ $5ŀ :@ *5ŀ. ?@ /5ŀ@@l@@,mul_shuffle2 @ Y I B 3   u@J X@ s5 i ]@ x5 iV b@ }5 iT g@ 5 i l@ 5'倠 r@ b5ŀ x@ h5ŀR }@ m5ŀ婚 @ r5ŀ @ x5ŀ @ }5ŀ@@@@_,mul_shuffle3 @      Ԡ à_RD@]Kꚠ @ 5 i蚠 @ 5 i @ 5 i @ 5'倠 @ 5ŀ⩚ @ 5ŀ) @ 5ŀ. @ 5ŀ1@@@@%le_wd @  ֠ Ϡ  )  @@A&NZBase'NZOrder&NatInt'Numbers#Coq@  @A@'NZOrder&NatInt'Numbers#Coq@+NZOrderProp  @A@@@@"NZ  @A@@ @ @ "5 i@ @ '5 i  @ -5 i@ @ 25 i) @ 15'倩 !@ <5 i3 %@ ;5' )@ 05(^@@V@@AA@@A@*lt_le_incl @ F 6 /   s b`SE@^A E@ `5 i J@ e5 i@ P@"lt5(m V@ ]5(^Q@@@@@-'le_refl @ p ` Y J   }o@B o@ 5 i t@ {5(^ې@@ @@L.lt_succ_diag_r @   x i Ҡ  @CҚ @ 5 i @C5(m @ pA߀K@@@@@p.le_succ_diag_r @       Ϡ͠@D @ 5 i @ 5(^  @ A߀o@@@@@/neq_succ_diag_l @ נ Ǡ     @E  @ 5 i  @ 5'倠 @ A߀ I@@@@/neq_succ_diag_r @    נ @ *  @F @ @ 5 i 6 @ 5'倠 j @ A߀@@@@@ࠠ/nlt_succ_diag_l @ #    f P ?=0"@;G f "@ =5 i \ )@5(m /@ A߀ @@@@@/nle_succ_diag_l @ I 9 2 #  v ecVH@aH  H@ c5 i  O@ V5(^ U@ ,A߀  @@@@@,)le_succ_l @ o _ X I   |n@I  n@ 5 i  s@ 5 i 젩 z@ 5(^ @ WA߀ 8 橚 @55(m @@ 1@@\+le_gt_cases @    y  ̠ @J ⚠ @ 5 i  @ 5 i @"or @ @ 5(^  @e5(m @@@@-lt_trichotomy @ Ϡ      ܠ@K  @ 5 i  @ 5 i0 @5(m B7 @ 5' I @5(m F@@@@@(lt_asymm @    ڠ C -  @L C @ 5 i A @ 5 i@ @5(m r D @5(m 8@@ @@蠠(lt_trans @ +    n X GE8*@CM n *@ E5 i l /@ J5 i( 4@ O5 i@ :@5(m 5@ @@5(m ; E@5(m ' l@@ @@(le_trans @ ` P I :   |zm_@xN  _@ z5 i  d@ 5 i] i@ 5 i@ o@ v5(^ j@ u@ |5(^ p z@ 5(^5@@@@Q+lt_strorder @   } n נ  @O @+StrictOrder.[@ @ 5 i @N5(m@@ @@u+le_preorder @       ԠҠŠ@P @(PreOrder@ @ 5 i @ 5(^@@ @@/le_partialorder @ ܠ ̠ Š    @Q @,PartialOrder5͛К @ 5 i @ 5'倚 @ Ѐ @ 5(^@N" @@@ @A @ @ AhC+@ABC@@Ϡ)lt_compat @*@%lt_wd @ @@-5 i@@25 i ) @85 i@"@=5 i 4&@<5'倩 &,@G5 i >0@F5' 4@5(m@=YXWV@@%lt_wd']ɠP@9*  } lj]O@@@@@ (lt_total @ yD@3v䀠jZSD@ c@~5 i h@5 iŠo@5(m ש̠v@5' ީ{@+5(m ېG@aǠ{l ՠ  @@@@@b'le_lteq @@+lt_eq_cases*Ȁ@ 皠@5 i 嚠@5 i !@ 5(^  @f5(m @5' #@+lt_eq_cases&yѠ  ޠ@@@@@0Private_OrderTacA'IsTotal A @۠@@+Equivalence~@@ 5 i@ 5'倐@(eq_equiv7L O9(& @@@@@ܠ @@;{" @@75 i @5(m@,Q^5%xbQOB4@@@@@6 @@>e K;4%@ L@F@a5 i@K@f5 i ] KQ@l5 i@V@q5 i hZ@p5'倩 Z`@{5 i rd@z5' ܚh@5(m4{kdUz@@@@@K+ @*@3/C0zk@ Κ@5 i ̚@5 i젩@F5(m 󠩚@5' @R5(m 'ѠϠ @@@@@# @d@+Yˠ@ @5 i @5 i B@5(^ 8-@5(m ?@5' D!ߠؠɠ2  @@@@@@@@@@#Tac%A2 @ N8'% @@D!P)OrdersTac*Structures#Coq@3F?@@@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,MakeOrderTacBe?@A@@@BONR@@@A@@AEUH@@@N@!tJ@@A@A$:@@"eq$:^@@A@$@ @"le$h@@A@$@@"lt$ h@@A@ABC@A@+*OrderFacts.#@A@@s@@5 i@5'@@@@AA@@A@4 @}РSLF+@A*@5 i@5(^9@@@@&)lt_irrefl @Ǡ ԠƠwpjO@BN@5 i@5(m_@@@@L @ܠՠƠ/Ѡt@Cs@ 5 iq@5 i@@5'd@5'(@@,@@z*le_antisym @ ^H75(ˠĠ@D @;5 i%@@5 i@+@25(^@1@85(^X6@L5' @@a@@ @O?8)|ki\ND4@EE֚T@o5 iԚY@t5 i@a@w5'ɩh@~5'@@@@@ᠠ*interp_ord @!o)OrdersTac@#ordȠ@ @@@@@@@@@@@D@@ @<t1@t"z@" @@5 i@@5 i +k= R'6'6'6''+k+7T'+7T'6'ࠒA@@"lt\ @N@"eq8L@PlР@LȠ@@IHG@@A@B@A@xA܀Ӡ̠&ؠȠk@@@@@[%trans @֠?) @F"o'@ 5 i @%5 i@*5 i@;H(@8 >@DQ1@8 KX8@8@)trans_ord-0uGV@@@@  @bcCd/vV@^ МAoYIB3@ԚR@m5 iҚW@r5 i_\@w5 i@b@x5']@h@~5'cm@5'( L+k() LL7#'@$t{teΠp;4.@@@@@D @ZМ$C@&@5 i$@5 i@5 i@@5(^@@5(^@5(^z L+k() NN7#'Rt٠ɠ ؠΠ|a@@@@@Qǐ @h b  МrBPO@t@ 5 ir@5 i@5 i@@5(m@@5(m @5(mȐ L+k() MM7#'t'jTCA4& נРʠ@@@@@+le_lt_trans @YZ:[O[E5.@>@Y5 iC@^5 iKH@c5 i@N@U5(^I@T@5(mOY@ 5(m L+k() MN7#'tsc\MrhX#@@@@@렠+lt_le_trans @Czk@ @5 i @5 i@5 i@@J5(m@@5(^@U5(m` L+k() NM7#'8t۠٠̠ohbG@@@@@7%eq_lt @OI43ݠ͠Ơ@X@5 iV@5 i㚠@5 i@@5'@@5(m穚@5(m L+k() ML7#'t N8' %  @@@@@%lt_eq @=>?3?)@"@=5 i'@B5 i/,@G5 i@2@5(m-@8@N5'3=@5(m L+k() LM7#'АtWG@1s q d VL<@@@@@Ϡ%eq_le @j'ˠue^O@𚠐n@5 is@5 i{x@5 i@~@5'y@@5(^@5(^D L+k() NL7#'t}Р   SLF+@@@@@%le_eq @3շ-ַשsk@<@5 i:@5 iǚ@5 i@@5(^Ŷ@@5'˩@5(^ L+k() LN7#'htߠؠɠ2    Ԡw@@@@@g&eq_neq @K5$ "  @G @(5 i@-5 i@25 i@@35'@X%@;5' _,@B5'@@@@@&neq_eq @F6/ sb ` S E;+@@5 i<@5 i@@5(^)@ ~5(mɐ@@@@G)not_gt_le @ؠѠ +   ݠ͠p@Ko@5 im@ 5 i@-@ 5(mZ@5(^@@@@@x)le_neq_lt @ \F5 3 & ɠ @L@95 i#@>5 i@)@05(^@d1@G5',6@ 5(m@@@@@@@@@2@@@@@4@<_neq @TD=.p n a S@ lRS@n5 iX@s5 i@^@ 5(mƩe@{5'`@@@@@ <&le_neq @ohY    ~@ Sš~@5 i@5 i@ :5(m򩛠@#andЖw@@5(^ѐ@5'@@@@@ u*eq_le_incl @Ԡ Ҡ Š @ T@5 i@5 i@@5'*@5(^@@@@@ (lt_stepl @Ѡʠ$   @ Ub@5 i`@5 i횠@5 i@@ 5(m@@ 5'꩚@ 5(m@@@@@ Ҡ(lt_stepr @XB1 / " @ -V@/5 i@45 i!@95 i@$@ 5(m@*@@5'%/@ 5(m @@@@@ (le_stepl @I92#ve c V H@ aWʚH@c5 iȚM@h5 iUR@m5 i@X@_5(^S@^@t5'Rc@j5(^P@@@@@ :(le_stepr @}mfW   |@ X|@5 i@5 i@5 i@@5(^@@5'@5(^ R@@@@@ nq @ݠ̠ ʠ  @ Y󚠐@5 i񚠐@5 i@5 i@@5(^@@ u5(m@ z5(m @@@@@ X @Ӡ̠&   @ Z&@5 i$@5 i@5 i@@ 5(m@@5(^󩚠@ 5(m @@@@@ Ԡ+le_antisymm @ZD3 1 $ @ /[Z@15 iX@65 i@!@(5(^@'@.5(^N,@B5'@@@@@ )le_succ_r @F6/ sb ` S E@ ^\E@`5 iJ@e5 iàQ@X5(^W@.A߀  ^@e5(^Ʃc@y5'倠˩i@@A߀@@@@@ @)lt_succ_l @sl]Ơ   @ ]ƚ@5 iĚ@5 i@@ =5(m@jA߀K@ H5(m@@@@@ o,le_le_succ_r @ߠΠ ̠  @ ^@5 i󚠐@5 i@@5(^$@5(^詚@A߀@@@@@ ,lt_lt_succ_r @Ѡʠ$   @ _$@5 i"@5 i@@ 5(mS@ 5(m@A߀@@@@@ ͠,succ_lt_mono @S=,*@(`S@*5 iQ@/5 i@ 5(m @ 5(m&@A߀ީ+@A߀ݐ@@@@@,succ_le_mono @E5.ra_RD@]aD@_5 iI@d5 i P@W5(^U@\5(^[@2A߀`@7A߀@@@@@7<_0_1 @zjcTy@by@)5(m~@PB|@l5 @@.@@Y&le_0_1 @vߠɠ@c@5(^@rB|@5 @@@@@{<_1_2 @ڠؠˠ@d@m5(m@5 @5̀@@r@@<_0_2 @Рɠ# @e@5(m@B|@5̀@@@@&le_0_2 @ܠE/@f@5(^@B| @5̀@@@@@ᠠ<_1_l @$ gQ@>1#@5 ie(@C5 i@.@5(m3@B|@9@5(m4>@5(mC@-5 i@@@@@p@ABC@@+lt_ge_cases @`PI:|zm_@xh_@z5 id@5 i k@5(mөp@w5(^А@@@@@G+le_ge_cases @zsd͠@i͚@5 i˚@5 i 렩@5(^@5(^@@@@@q+lt_gt_cases @РΠ@j@5 i@5 i1@5')@x5(m0@}5(m-@@@@@,eq_decidable @נР*@k*@5 i(@5 i)Decidablef @)decidable r@5'c@@@@@Ҡ&eq_dne @XB1/"@-lX@/5 iV@45 iUW$@:5')@?5'@@@@@&le_ngt @C3,p_]PB@[mB@]5 iG@b5 iN@U5(^U@5(m@@@@@,&nlt_ge @o_XI|n@nn@5 is@5 i젩|@,5(m䩚@5(^@@@@@X,lt_decidable @uޠȠ@oޚ@5 iܚ@5 i@V5(m@@@@@}<_dne @ܠڠ͠@p@5 i@5 i=@5(m7@5(m<@@@@@&nle_gt @ޠנȠ1 @q1@5 i/@ 5 ik.@5(^c@5(m`@@@@@נ<_nge @ ]G64'@2r]@45 i[@95 i%@5(m_,@35(^@@@@@,le_decidable @F6/ sb`SE@^sE@`5 iJ@e5 i_Q@X5(^@@@@@(&le_dne @k[TExj@tj@5 io@5 i蠩z@5(^⩚@5(^@@@@@V*nlt_succ_r @sܠƠ@uܚ@5 iښ@5 iِ@V5(m @A߀d@a5(m@@@@@5lt_exists_pred_strong @ˠؠ@v͚@5 i@5 i@5 i@@5(m?@@5(^Z@"ex @@5 i!k@5 ii@5'倠@A߀@ 5(^l@@@@A@@A4@5AРD.Morphisms_PropA@;A1@D@ABCD@@렠.lt_exists_pred @.q[JH;-@Fw0-@H5 iv2@M5 i@8@5(mX>@Y5 iRC@^5 iJ@`5'倠qP@'A߀U@\5(^͐@@@E@A@@-,lt_succ_pred @p`YJ}o@xro@5 it@5 i@z@*5(m⩚@5'倠@\A߀@gAjC@@@7@A4@y@@@ABCD@@g&rs_rs' @נƠĠ@y@@5 i@@5 iĩ@5 iʚ@5'4"Ě@5 i@@ @5 i@@5(^3@ @A߀!@5 i@@5(^[@.@5 i,@ 5 i@@5(^ \@@5(m#K'H)@@u@@נ(rs'_rs'' @ ]G64'@2z.@@55 i,*(@"@=5 i4"(@C5 i:,@B5'41@L5 i@{7@R5 i@=@D5(^@D@_5 iI@d5 i@O@V5(^1@V@5(m}I,^@y5 iנf@5 ik@5 i@q@x5(^"@w@'5(m!)}@5 i@5 i@@5(^9@@>5(m8@kA߀F@@@@@k%rbase @۠ʠȠ@{¶@@5 i@5 i@5 i@5 i@@5(^)@@z5(mr|@@@@@)A'A_right @Ԡ͠'@|@@5 i욠@5 i@3@ 5 i9@5 i7@5 i@@5(^x@@5(m- 0P @'5 i@@5(^wː@@@@@ꠠ6strong_right_induction @-pZIG:,@E}A@-@H5 i?=;@5@P5 iG5;@V5 iM?@U5'GD@_5 i@J@e5 i@P@W5(^@W@r5 i\@w5 i@b@i5(^@h@5(m m@5 i@s@z5(^@@@@A`@@l@ABC@@N/right_induction @zkԠ@~@@5 i@@5 i@5 i@5' @5 i@@󚠐@5 i@@5(^@ @A߀@5 i@@5(^@ @@@@@0right_induction' @Ӡ̠&@@@5 i@@ 5 i@ 5 i@ 5'm[@ 5 i@D @ 5 i@ @ 5(^f@P @ '5 i@ @5(^w@D 吩 @A߀Cc @ :5 i@@J@@7strong_right_induction' @ 9 ) " |fUSF8@Q@M@ 9@ T5 iKIG@ A@ \5 iSA G@ b5 iY K@ a5'S P@ k5 i@ V@ q5 i@ \@c5(^J@ b@ }5 i@ h@o5(^Ͷ@ o@ 5 i t@ 5 i@ z@5(^u@ @05(mJ:|˚ @ 5 i[@@@@@^&ls_ls' @    {Π@A@ @ 5 i@ @ 5 i @ 5 i @ 5'+ @ 5 i@@ @ 5 i@ @u5(mh@ @A߀Ƕ @ 5 i@ @5(^?̶@$ @ 5 i" @!5 i@ @5(^R@ @5(^ @A߀@@@@Ϡ(ls'_ls'' @!!   U ? .,@*B&@!@!-5 i$" @!@!55 i,! @!;5 i2!$@!:5',!)@!D5 i@s!/@!J5 i@!5@ <5(^@!<@!W5 i~!A@!\5 i@!G@ N5(^)@!N@ U5(^I!T@ +A߀ !Y@!t5 iҠ!a@!|5 i!f@!5 i@!l@ s5(^%@!r@ y5(^m$!x@!5 i!}@!5 i@!@ 5(^<@!@ 5(^3!@ fA߀A@@L@@f%lbase @!!!!  ֠ Šà@C@!@!5 i!@!5 i!@!5 i!@!5 i@!@ 5(^b@!@ 5(^m!@ A߀}@@@@@(A'A_left @!!ՠ!Π!!(!!@D@!@"5 i횠!@"5 i@4!@" 5 i:!@"5 i8!@"5 i@"@!5(^)@"@!5(^P" @"'5 i@"@!5(^@@ =@@頠5strong_left_induction @","""!o!Y!HF9+@DE@@",@"G5 i><:@"4@"O5 iF4":@"U5 iL">@"T5'F"C@"^5 i@"I@"d5 i@"O@!V5(^@"V@"q5 i"[@"v5 i@"a@!h5(^@"g@!n5(^b"m@!DA߀%"r@"5 i@"x@!5(^@@@#@ @p@ABC@@R.left_induction @"""~"o!ؠ! !@F@"@"5 i@"@"5 i"@"5 i"@"5'  "@"5 i@@"@"5 i@"@i5(m\@"@!A߀y "@"5 i@"@!5(^@@@@@/left_induction' @""֠"Ϡ"")""@G@"@#5 i@"@# 5 i"@#5 i"@#5' p ^ "@#5 i@ G#@#5 i@# @"5(^ q@ S#@#*5 i@#@5(m@ꐩ#@!A߀ f#"@#=5 i@@@@6strong_left_induction' @#<#,#%#""i"XVI;@THP@#<@#W5 iNLJ@#D@#_5 iVD#J@#e5 i\#N@#d5'   V#S@#n5 i@ #Y@#t5 i@#_@"f5(^ M@ #e@#5 i@#k@"r5(^@ #r@#5 i #w@#5 i@#}@"5(^ Q@#@"5(^ #@"aA߀ B Ӛ#@#5 ic@@ L@@f/order_induction @####""֠"Šà@I@#@#5 i@#@#5 ié#@#5 iɚ#@#5'!3!! Ú#@#5 i@@! #@#5 i@#@"5(^2@#@"A߀@!#@#5 i@#@5(m @#@"A߀ !2#@$ 5 i @@@ @ @AB@@Ƞ0order_induction' @$ ####N#8#'% @#J @$ @$&5 i   @$@$.5 i % $@$45 i +$@$35'!!!%$"@$=5 i@ @!m$)@$D5 i@$/@#65(^@a$7@#A߀`@!$=@$X5 i@$C@#J5(^k@|F$K@#'Ajt!$P@$k5 ib@@a@@'1order_induction_0 @$j$Z$S$D###wi@K ~@$j@$5 i | z x@$r@$5 i  r$x@$5 i $|@$5'!!@!吚$@#UB|@!͚$@$5 i@$@#5(^$@#fB|!@ i$@#sA߀Ŷ@!暠$@$5 i@$@X5(m"$@#B|@ $@#A߀!m!$@$5 i @@@@@2order_induction'_0 @$Ԡ$Ġ$$$$#@L @$@$5 i   ⰶ@$@$5 i  $@$5 i $@$5'"^"L@"O$@#B|@"7$@%5 i@$@$5(^$@#B|"d@ Ӑ%@#A߀/@"P% @%'5 i@%@$5(^"y%@#B|@Iꐩ%@#AjH"h%$@%?5 i @@@@@<_ind @%>%.%'%$$k$ZXK=@VM!R@%>@%Y5 i!P!N!L@%F@%a5 i!X!F%L@%g5 i!^%P@%f5'"""%U@%p5 i@"}%]@$4A߀"@"%c@%~5 i@%i@5(mζ@<%q@$HA߀"%v@%5 i@%|@,5(m@@@@@S&le_ind @%%%%p$٠$à$@N!@%@%5 i!!!@%@%5 i!!%@%5 i!%@%5'# #"񚠐%@%5 i@!@"񚠐%@%5 i@%@$5(^@%@$A߀#%@%5 i@%@$5(^E@@@@@&Rlt_wd @%%נ%Р%%*%%@O"隠%@&5 i!@%@&5 i@%@& 5 i"!%@&5 i@%@&5 i"&@&5'倩"&@&"5 i"& @&!5'##T&@&+5 i#R&@&05 i&@%#5(^#&!@5(m#@@!N@@&Rgt_wd @&;&+&$&%~%h%WUH:@SP#=&:@&U5 i"G@&A@&\5 i@&F@&a5 i"X"F&L@&g5 i@&Q@&l5 i"c&U@&k5'倩"U&[@&v5 i"m&_@&u5'#׷#&d@&5 i#&i@&5 iߠ&p@ 5(m#Щ&u@%|5(^#@@!@@L%lt_wf @&&&x&i%Ҡ%%@Q#&@&5 i"Wf$@,well_founded8E&@&5 i#嚠&@&5 i#㚠&@&5 i&@%5(^#&@b5(m$@@@$A𱍠G @$A7iA)@AB@@%gt_wf @&Ԡ&Ġ&&&&%@R#֚&@&5 iE&@&5 i$"&@&5 i$ &@&5 iY&@5(m$J&@%5(^$@@=@@Ơ-add_lt_mono_l @' &&&&L&6&%@&!@$I'@' 5 i$G' @'%5 i!'@'*5 i$'@5(m$'@5(m'!@&5 ĩ'&@&#5$@@"S@@AA@@A@-add_lt_mono_r @'C'3','&&p&_@&[A$'?@'Z5 i$'D@'_5 i!='I@'d5 i$ 'P@5(m$K'U@5(m'[@&X5 '`@&]5$Ȑ@@"@@:+add_lt_mono @'z'j'c'T&&&@&B$'v@'5 i$'{@'5 i!t'@'5 i r'@'5 i@'@;5(m e@'@A5(m$'@F5(m'@&5#p$'@&5]@@@@@|-add_le_mono_l @''''&&&@&C$'@'5 i$'@'5 i!'@'5 i%;'@&5(^$ĩ'@&5(^'@&5!w'@&5%9@@#@@-add_le_mono_r @'''ܠ'͠'6' '@' D%3'@( 5 i%1'@(5 i!횠'@(5 i%r(@'5(^$(@' 5(^( @'5!p(@' 5%x@@#=@@ꠠ+add_le_mono @(*((('m'W'F@'BE%j(&@(A5 i%h(+@(F5 i"$(0@(K5 i!"(5@(P5 i@(;@'B5(^!@(A@'H5(^%<(F@'M5(^(L@'I5(Q@'N5 @@@@@+.add_lt_le_mono @(k([(T(E'''@'F%(g@(5 i%(l@(5 i"e(q@(5 i!c(v@(5 i@(|@,5(m!V@(@'5(^%}(@75(m(@'5񩚠(@'5M@@@@@l.add_le_lt_mono @((((''٠'@'G%욠(@(5 i%ꚠ(@(5 i"(@(5 i!(@(5 i@(@'5(^!@(@s5(m%(@x5(m(@'52(@'5@@@@@+add_pos_pos @((ݠ(֠(Ǡ(0(( @(H&-(@)5 i&+(@) 5 i@(@5(m(@'B|&`@(@5(m)@'B|&k) @5(m)@'B|)@(5!@@@@.add_pos_nonneg @)-)))(p(Z(I@(EI&m))@)D5 i&k).@)I5 i@)4@5(m)9@( B|&@)?@(F5(^)D@(B|&)I@5(m)N@( B|)S@(P5"-@@@@-.add_nonneg_pos @)m)])V)G(((@(J&)i@)5 i&)n@)5 i@)t@({5(^)y@(KB|&@)@/5(m)@(VB|&멚)@95(m)@(`B|)@(5"m@@P@@m1add_nonneg_nonneg @))))((ڠ(@(K&횠)@)5 i&뚠)@)5 i@)@(5(^)@(B|' @)@(5(^)@(B|'+)@(5(^)@(B|)@(5"@@@@,lt_add_pos_l @))ݠ)֠)Ǡ)0)) @)L'-)@*5 i'+)@* 5 i@)@5(m)@(B|'`)@5(m'f*@)5&@@@&@(0@AB@@ࠠ,lt_add_pos_r @* ** ))c)M)<@)8M'`*@*75 i'^*!@*<5 i@*'@5(m*,@(B|'*1@5(m'*7@)45'^@@&@@,le_lt_add_lt @*Q*A*:*+))~)m@)iN'*M@*h5 i'*R@*m5 i$K*W@*r5 i#I*\@*w5 i@*b@)i5(^#<@*h@5(m*n@)k5'[*s@)p5'&U*y@)5(m#S@@@@@S,lt_le_add_lt @***|*m)֠))@)O'Ӛ*@*5 i'њ*@*5 i$*@*5 i#*@*5 i@*@T5(m#~@*@)5(^*@)5'*@)5B*@j5(m#@@@@@,le_le_add_le @*Ԡ*Ġ****)@)P(*@*5 i(*@*5 i$Κ*@*5 i#̚*@*5 i@*@)5(^#@*@)5(^*@)5'ީ*@)5*@*5(^#Ր@@@@@ՠ,add_lt_cases @++***X*B*1@*-Q(U+@+,5 i(S+@+15 i%+@+65 i$ + @+;5 i@+&@5(m+,@*)5$+1@*.5(+8@5(m󩚠+=@5(m(1@@@@@,add_le_cases @+W+G+@+1***s@*oR(+S@+n5 i(+X@+s5 i%Q+]@+x5 i$O+b@+}5 i@+h@*o5(^+n@*k5$H+s@*p5(۩Р+z@*5(^5+@*5(^(s@@@@@Y-add_neg_cases @++++s*ܠ*Ơ*@*S(ٚ+@+5 i(ך+@+5 i@+@ P5(m+@*5)+@*|B|+@ a5(m(ؚ+@*B|+@ k5(m)#+@*B|@@(l@@-add_pos_cases @+ڠ+ʠ+à+++*@*T)+@+5 i)+@+5 i@+@ 5(m+@*B|+@*5)SH+@ 5(m+@*B|)+@ 5(m,@*B|)h@@@@۠0add_nonpos_cases @,, ,++^+H+7@+3U)[,@,25 i)Y,@,75 i@,"@+)5(^,(@+%5),,@*B|,3@+:5(^)Z,8@+ B|,=@+D5(^),B@+B|@@(@@0add_nonneg_cases @,\,L,E,6+++x@+tV),X@,s5 i),]@,x5 i@,c@+j5(^,h@+:B|,m@+j5)թʠ,t@+{5(^,y@+KB|),~@+5(^,@+UB|)@@@@@]-le_exists_sub @,,,,w++ʠ+@+W)ݚ,@,5 i)ۚ,@,5 i@,@+5(^* Ġ,@,5 i&,@,5 i%,@,5'倠)ݩ,@+5 䩚,@+5(^,@+B|*,@@@)r@A)@*@A*AA@@);@ABCD@@+mul_lt_pred @,,٠,Ҡ,à,,@,@&ך,@,5 i%՚,@-5 i*1,@-5 i*/,@- 5 i@,@-5'倠,@+A߀)*%*x-@!5(m- @+5ŀǩ-@,5ŀ(*y-@!5(m-@,5-#@,5ŀ%*-(@,%5-.@,5ŀ*"*T@@([@@AA@@A@1mul_lt_mono_pos_l @-K-;-4-%,@-#A'9-E@-`5 i*-J@-e5 i*-O@-j5 i@-U@"5(m-Z@,,B|**Ӡ-a@"5(m*\-f@"5(m-l@,\5ŀ&F-q@,a5ŀ*e@@@*@A*@*_@+@k@ABCD@@H1mul_lt_mono_pos_r @---y-j,@-hB'~-@-5 i*Ӛ-@-5 i*њ-@-5 i@-@"J5(m-@,qB|*ũ+-@"V5(m*-@"[5(m-@,5ŀ*-@,5ŀ+*@@(@@1mul_lt_mono_neg_l @-Ѡ----@-C'-@-5 i+-@-5 i+-@-5 i@-@"5(m+-@,B|+Y-@"5(m*⩚-@"5(m-@,5ŀ*橚-@,5ŀ&ѐ@@@@ɠ1mul_lt_mono_neg_r @..---T@-D'. @.&5 i+T.@.+5 i+R.@.05 i@.@"5(m+B. @,B|+.'@"5(m+".,@"5(m.2@-"5ŀ|.7@-'5ŀ+$@@)d@@ 4mul_le_mono_nonneg_l @.Q.A.:.+-@.)E+.K@.f5 i+.P@.k5 i(I.U@.p5 i@.[@-b5(^.`@-2B|+ƶ@.f@-m5(^'@.k@-r5(^.q@-a5ŀ+*S.w@-g5ŀ+d@@+#@@I4mul_le_mono_nonpos_l @...z.k-@.iF+Ϛ.@.5 i+͚.@.5 i(.@.5 i@.@-5(^,.@-rB|@.@-5(^'.@-5(^.@-5ŀ+.@-5ŀE@@+b@@4mul_le_mono_nonneg_r @.Р....@.G,.@.5 i, .@.5 i(Ț.@.5 i@.@-5(^.@-B|,E@.@-5(^'.@-5(^.@-5ŀ!.@-5ŀ'ϐ@@+@@Ǡ4mul_le_mono_nonpos_r @/....R@.H,M/ @/$5 i,K/@/)5 i)/@/.5 i@/@. 5(^,/@-B|@/$@.+5(^'/)@.05(^//@.5ŀ( /4@.$5ŀ!@@+@@,mul_cancel_l @/N/>/7/(.@/&I,/H@/c5 i,/M@/h5 i)F/R@/m5 i@,/Z@/p5'倠,/_@.1B|,ؠ/f@/|5'倠/l@.\5ŀ/q@.a5ŀ,/v@/5'(P@@@,!@-@+@ABC@@K,mul_cancel_r @///|/m.@/kJ,њ/@/5 i,Ϛ/@/5 i)/@/5 i@,Ґ/@/5'倠-/@.vB|-/@/5'倠/@.5ŀ,/@.5ŀ,/@/5'(@@*@@(mul_id_l @/ՠ/Š///@/K-/@/5 i-/@/5 i@-/@/5'倠-C/@.B|-Z/@/5'倠/@.5ŀ,-U/@0 5'倠-/@.5 @@,@@ʠ(mul_id_r @00///U@/L-P0 @0'5 i-N0@0,5 i@-L0@0/5'倠-0@.B|-0%@0;5'倠0+@/5ŀ-&-Q00@0F5'倠-05@/5 @@+b@@1mul_le_mono_pos_l @0O0?080)/@0'M-0I@0d5 i-0N@0i5 i*G0S@0n5 i@0Y@% 5(m0^@/0B|-ĩ-נ0e@/l5(^)?0j@/q5(^0p@/`5ŀ0u@/e5ŀ-@@-!@@G1mul_le_mono_pos_r @000x0i/@0gN-͚0@05 i-˚0@05 i*0@05 i@0@%I5(m0@/pB|..0@/5(^)0@/5(^0@/5ŀ-0@/5ŀ-@@+@@1mul_le_mono_neg_l @0Ϡ0000@0O. 0@05 i. 0@05 i*ǚ0@05 i@0@%5(m.@0@/B|.W0@/5(^)0@/5(^0@/5ŀ.0@/5ŀ?@@@@Ǡ1mul_le_mono_neg_r @10000R@0P.M1 @1$5 i.K1@1)5 i+1@1.5 i@1@%5(m.1@/B|.1%@0,5(^)1*@015(^10@0 5ŀ.+15@0%5ŀ.)@@,b@@2mul_lt_mono_nonneg @1O1?181)0@1'Q.1I@1d5 i.1N@1i5 i+G1S@1n5 i*E1X@1s5 i@1^@0e5(^1c@05B|.V@1i@&5(m-K.]@1p@0w5(^1u@0GB|.h@1{@&+5(m1@&05(m1@0v5ŀ-Z1@0|5ŀ^-n@@@@@_2mul_le_mono_nonneg @11110@1R.嚠1@15 i.㚠1@15 i+1@15 i*1@15 i@1@05(^1@0B|.@1@05(^X@1@05(^1@0B|.@1@05(^i1@05(^1@05ŀW1@05ŀV@@.@@+mul_pos_pos @1111֠1?@1S/:1@25 i/81@25 i@2@&5(m2@0B|/m@2 @&5(m2@0B|/x2@&5(m2@0B|2 @15ŀ*@@@@+mul_neg_neg @2:2*2#21}@2T/x24@2O5 i/v29@2T5 i@2?@&5(m/2D@1B|@2J@&5(m/2O@1!B|2T@'5(m2Y@1+B|2^@1N5ŀ+8@@@@0+mul_pos_neg @2x2h2a2R1@2PU/2r@25 i/2w@25 i@2}@'-5(m2@1TB|/@2@'85(m/𚠐2@1_B|2@'B5(m2@15ŀ+r2@1nB|@@/H@@n+mul_neg_pos @22221@2V/2@25 i/򚠐2@25 i@2@'k5(m0#2@1B|@2@'v5(m2@1B|022@'5(m2@15ŀ+2@1B|@@@@1mul_nonneg_nonneg @222ݠ2Π27@2W022@3 5 i002@35 i@2@25(^2@1B|0e@3@2 5(^3 @1B|0p3@25(^3@1B|3@25ŀ+@@@@ꠠ0mul_pos_cancel_l @323"33 2u@3 X0p3,@3G5 i0n31@3L5 i@37@'5(m3<@2B|003C@'5(m3H@2B|3M@2=5ŀ0H3R@(5(m3W@2)B|0@@ S@@)0mul_pos_cancel_r @3q3a3Z3K2@3IY03k@35 i03p@35 i@3v@(&5(m3{@2MB|003@(25(m3@2YB|3@2|5ŀ03@(A5(m3@2hB|0@@ @@h3mul_nonneg_cancel_l @33332@3Z03@35 i0욠3@35 i@3@(e5(m3@2B|1!133@25(^3@2B|3@25ŀ0Ʃ3@25(^3@2B|1<@@ @@3mul_nonneg_cancel_r @33ߠ3ؠ3ɠ32@3[1-3@45 i1+3@4 5 i@3@(5(m3@2B|1_1r4@35(^4@2B|4 @25ŀ14@35(^4@2B|1:@@ @@栠,lt_1_mul_pos @4.4443q@4\1l4(@4C5 i1j4-@4H5 i@43@(5(m48@3"5 1@4>@(5(m4C@3B|14H@(5(m4M@375 4R@3B5ŀ-,@@@@$(eq_mul_0 @4l4\4U4F3@4D]14f@45 i14k@45 i1䠩4r@45'倠4x@3h5ŀ14|@3NB|'٠4@45'倠1뚠4@3ZB|4@45'倠14@3dB|@@/@@d)neq_mul_0 @44443@4^1ꚠ4@45 i1蚠4@45 i2$#1鐩4@45'倠24@3B|14@45'倠2)4@3B|24@45'倠4@35ŀ2<4@3B|@@0@@+eq_square_0 @444۠4̠45@4_204@55 i2e4@5 5'倠4@35ŀ)4@3B|5@55'倠2i5@3B|@@@@@٠*eq_mul_0_l @5!55 44d@4`2_5@565 i2]5 @5;5 i@5&@5<5'倠5,@45ŀ250@4B|@2k58@5N5'倠25=@4B|5B@5X5'倠265G@4B|@@@@@*eq_mul_0_r @5a5Q5J5;4@59a25[@5v5 i25`@5{5 i@5f@5|5'倠5l@4\5ŀ2Ԛ5p@4BB|@25x@55'倠25}@4OB|5@55'倠25@4YB|@@@@@Y(mul_eq_0 @'>@>Ĉ5555@2⚠5@55 i25@55 i35@55'倠5@45ŀ35@4B|)5@55'倠3#5@4B|5@55'倠3,5@4B|5555@5@~^\55ՠ5Π55(@@@@@*mul_eq_0_l @'@0*5555@345@6 5 i325@65 i@5@65'倠6@45ŀ3i6@4B|@3@6 @6#5'倠3u6@4B|6@6-5'倠3 6@4B|R@24pe616!66 5t@@@@@*mul_eq_0_r @'@0*6C636,6@36<@6W5 i3~6A@6\5 i@6G@6]5'倠6M@5=5ŀ36Q@5#B|@36Y@6o5'倠36^@50B|6c@6y5'倠36h@5:B|@!24pk6}6m6f6W5@@@@@ C(lt_0_mul @66{6t6e5@6cb3ɚ6@65 i3ǚ6@65 i46@+A5(m6@5hB|6@55ŀ4) 6@+T5(m6@5{B|46@+^5(m6@5B|4 )6@+j5(m4!6@5B|6@+t5(m4,6@5B|@@3u@@ 5square_lt_mono_nonneg @66Ӡ6̠66&@6c4!6@65 i46@65 i@6@55(^6@5B|4T@6@+5(m36@+5(m6@55ŀ33򩚠7@55ŀ4+4+@@@@@ נ5square_le_mono_nonneg @77766b@6d4]7@745 i4[7@795 i@7$@6+5(^7)@5B|4@7/@665(^4*74@6;5(^7:@6*5ŀ<7?@6/5ŀ;@@@@@ 6square_lt_simpl_nonneg @7Y7I7B736@71e47S@7n5 i47X@7s5 i@7^@6e5(^7c@65B|4ɶ@7i@,5(m7o@6_5ŀk7t@6d5ŀ44ܩ7z@,*5(m0T@@@@@ L6square_le_simpl_nonneg @777}7n6@7lf4Қ7@75 i4К7@75 i@7@65(^7@6pB|5@7@65(^7@65ŀ7@65ŀ;7@65(^0@@@@@ ,mul_2_mono_l @7Π7777@7g5 7@75 i5 7@75 i@7@,5(m5;7@,5(m7@657@65 7@65ŀ7@65̀57@65ŀ7@65̀5^@@3$@@ ɠ*add_le_mul @88777T@7h!a8 @8(5 i!b8@8/5 i@8@,5(m8@7 5 5@8%@,5(m8*@75 58/@765(^85@72518:@7*5ŀ1@@4@@ -square_nonneg @8T8D8=8.7@8,iC8N@8i5 i8S@7Z5(^8X@7*B|8]@7M5ŀ,@@@@ /5crossmul_le_addsquare @8w8g8`8Q7@8Ojf8q@85 id8v@85 i@8|@75(^8@7SB|5@8@75(^8@7^B|5󩚠8@75(^8@758@75ŀ58@75ŀ1|8@758@75ŀ8@75ŀ@@'@@ -add_square_le @8̠8888@8k8@85 i8@85 i@8@75(^8@7B|6=@8@75(^8@7B|6H8@75(^8@758@75ŀ8@75ŀ󩚠8@75ŀ9@751ܩ9@851@@5@@ ٠-square_add_le @9!99 88d@8l9@965 i9 @9;5 i@9&@8-5(^9+@7B|6@91@885(^96@8B|69;@8B5(^9A@815ŀ9G@8D52!9L@8I52&9Q@8A5ŀ9V@865̀9[@8X59a@8Q5ŀc9f@8V5ŀb@@6@@ 84quadmul_le_squareadd @99p9i9Z8@9Xmo9z@95 im9@95 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