"` ń |$NGcd(Abstract'Natural'Numbers#Coq@()Notations$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$Init#Coq@)Notations$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"&/rk0JqTttֱ$Bool#Coq@0j 2cZ`FW&Basics'Program#Coq@0!bs߯? :VU$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`|3x%NBase(Abstract'Natural'Numbers#Coq@0 Y?V vI$NAdd(Abstract'Natural'Numbers#Coq@05;ZW:㥜un$&NOrder(Abstract'Natural'Numbers#Coq@0]@7U#oY)NAddOrder(Abstract'Natural'Numbers#Coq@02'8zn7Hfɠ)NMulOrder(Abstract'Natural'Numbers#Coq@04> Aat/ j $NSub(Abstract'Natural'Numbers#Coq@0:DfJs)Z 'znnР$NGcd(Abstract'Natural'Numbers#Coq@ A(NGcdProp@@!A@!t @J %'A*Equalities*Structures#Coq@@@@@ %'@ @A@A@@@AA@@A@"eq @^@)@% ]@.@* ]A@@@@@(eq_equiv @@/RelationClasses'Classes1@+Equivalence~@J@F ]N@/ e;@@@FA݋X_A/RelationClasses'Classes#Coq@@A@@A$zero @Tf@!t ]@@@@@AA@@A@$succ @r@y@ ]}@ ]@@@@@$pred @d@@& ]@* ]@@@@@)'succ_wd @@)Morphisms'Classes#Coq@@&ProperL@@F ]@J ]@*respectful%WO?@U ]@Y ]@"eq e;@ e;@] 5@@@AviA4'Classes#Coq@@A@@n'pred_wd @@E@@ ]@ ]9@ ]@ ]@4 e;@8 e;@} @@@A3@A@@)pred_succ @@!n@ ]@S e;@ "@ 5A@@@@@,bi_induction @@!A@5@ ]A@@?@ ] E@ ]I@ e;%Logic$Init@#iffС)0@B[@ [@Ra@ ]DCl@ 5Jbq@  ]EQ@@@kA@A@@#one @T@ ]@@@@@#two @T@+ ]@@@@@*(one_succ @@@ e;@@@#one a @B 5@$zero [@@@@@P(two_succ @@@ e;@B #@` 5@Z a@@@@@m"lt @h@@!t ]@@ ]A@@@@@AA@@A@"le @h@@ ]@@ ]@@@@@%lt_wd @@r@@ ]@@ ]g@ ]@"@ ]횠&@c e;v,@ ]0@m e;皠4@"lt eÀ@@@-Ai@A@@Р+lt_eq_cases @@6E@ ]!mL@ ]S@` e1 @"or @a@- eÀf@ e;@@@@@)lt_irrefl @@et@ ],@#notШ@L eÀ^^@@@@@)lt_succ_r @@@) ]J@. ]L@g eÀG@2 5@ eS@@@@@?#add @d@@O ]@@T ]@X ]@@@@@W#sub @d@@g ]@@l ]@p ]@E@@n#mul @d@@~ ]@@ ]@ ]@\@@&add_wd @@\@@ ]@@ ]@ ]U @ ]@@ ]@ ]@U e;h@ ]"@ ]&@c e;*@g e;.@ 䀐@@@&Ab@A@@ɠ&sub_wd @@@@@ ]@E@ ]I@ ]O@ ]@T@ ]X@ ]\@ e;b@ ]f@ ]j@ e;n@ e;r@ @@@jA@A@@ &mul_wd @@䰶@@ ]@@# ]@' ]@- ]@@2 ]@6 ]@ e;@@ ]@D ]@ e;@ e;@ @@@A@A@@Q'add_0_l @@@` ]@ e;@& 䀠@y [@@@@@o*add_succ_l @@՚@~ ]@ ]@+ e;@I 䀠@ 5ة@ 5@[ @@@@@'sub_0_r @@@ ]@V e;@\ $@ [@@@@@*sub_succ_r @@#2@ ]횠7@ ]<@y e;B@ H@ 5&M@ S@ @@@@@젠'mul_0_l @@Ra@ ]f@ e;l@ q@ [Nu@ [@@@@@*mul_succ_l @@t@ ]>@" ]@ e;@ @* 5v@ 䀠@ Q@@@@@=#max @d@@!t ]@@ ]@  ]@@@@@AA@@A@%max_l @@!x@ ]!y@$ ]@@"le eAB@"eq e;@D C@@@@@2%max_r @@/@J ]-@O ]@@+ e)*@( e;@k '4@@@@@W#min @d@#@p ]@(@u ],@y ]@@@@@o%min_l @@l:@ ]j?@ ]@E@h e=J@d e;P@7 9cb@@@@@%min_r @@^@ ]c@ ]@i@ en@ e;t@[ 9@@@@@&pred_0 @@@"eq e;@ @1 [@5 [@@@@@AA@@A@'compare @d@@!t ]@@ ])Datatypes$Init#Coq@@*comparison;f@@@@@@AA@@A@,compare_spec @@!x@& ]!y@- ](@+CompareSpec!Q]@@"eq e;BA@"lt eÀ @ eÀ @YT@@@@@<#eqb @d@@!t ]@@ ])Datatypes$Init#Coq@@$boolZ'@@@@@@AA@@A@#ltb @d@'@ ]@,@ ]@$boolZ'@@@@@@{#leb @d@A@ ]@F@ ]@@@@@&eqb_eq @@!xV@T ]!y]@[ ]%LogicU@#iffС) @"eq @gt@| }BApA@ e; @@@@@j<b_lt @@Ś@ ]Ú@ ]%Logic@#iffС) @ @w@ ɜ}A@ eÀѐ@@@@@&leb_le @@@ ]@ ]1)@ x$@"le e@@@@@$even @d@@!t ])Datatypes$Init#Coq@@$boolZ'@@@@@@AA@@A@#odd @d@@  ]@@@@@$Even @!n@!A(NZParity&NatInt'Numbers/@:7퀩%Logic:@"ex @!m@"eq7iB$@#mul7I*@#two7QA@'NAxioms(Abstract'Natural'Numbers#Coq@+NAxiomsSig'O@@@A@@@@@?>=k@'NAxioms(Abstract'Natural'Numbers#Coq@@@U@@Ud@@A@A6@@l6J@@A@B6 h@@T6 h^@@A@6 @@6 h@@A@AC6 @!@6 h@@A@6@'@6d@@A@A6@*@6d@@A@6@.@P6d@@A@6@2@n6 d@@A@ABC6@5@6ؠd@@A@6f@9@y6fd@@A@ADE6H@<@6Hd@@A@6@A@ 6T@@A@A6@D@6d@@A@6P@I@6PT@@A@A6b@L@#6bd@@A@6÷b@P@:6÷br@@A@6]@T@P6]T@@A@ABCDF@A@(NZParity&NatInt'Numbers#Coq@c@@@A@@@!t ]A t+k+ 77%'77!7%'Р`HPl̐d1@@@ %'A*Equalities*Structures#Coq@A1@D%Logic$Init#Coq@@A@@#Odd @֠ѩ@#add7ך@#one7Ϡa@@S ]R +k+ 77%'6 77!7!7%'tPX l(d%D"d@@@VAN@A@@H)even_spec @@5E@d ])@#iffС)1@$ @qX@ xAa@[ DU @@@@@r(odd_spec @@_o@ ]*%x@  }@ Ԃ%@@@@@#pow @d@@!t ]@@ ]@  ]@@@@@AA@@A@&pow_wd @@)Morphisms'Classes#Coq@@&ProperL@@) ]@@. ]@2 ]@*respectful%WO?@= ]@@B ]@F ]@"eq e;@Q ]@U ]@ e;@ e;@k @@@ %'A*Equalities*Structures#Coq@AviAT'Classes#Coq@@A@@h'pow_0_r @@!a @ ] @= e; @ A @$zero [ $@#one a@@@@@*pow_succ_r @@' 3@ ]!b :@ ]@ @@"le e F@' [, K@u e; Q@ C X@$succ 5B `@#mul  g@ @@@@@Ҡ)pow_neg_r @@j v@ ]C {@ ]@ @"lt eÀi @h [ @ e; @ + @w [@@@@@$sqrt @d@ @!t ] @ ]@@@@@AA@@A@)sqrt_spec @@!a @ ]@ @"le e @$zero [A%Logic$Init#Coq@@#andЖw@ @ e @#mul  @Q B @X  @"lt eÀ  @  @$succ 5 @q   @  5 @| +@@@@@m(sqrt_neg @@j %@ ]@ +@3 eÀb 0@g [ 5@"eq e; <@ P @@w [@@@@@$log2 @d@ O@!t ] T@ ]@@@@@AA@@A@)log2_spec @@!a g@ ]@ m@"lt eÀ s@$zero [A%Logic$Init#Coq@@#andЖw@ @"le e @#pow  @#two # @W OMB @6 eÀ @  @ # @$succ 5 @u OM@@@@@f+log2_nonpos @@c @y ]@ @E e[ @` [ @"eq e; @ OMC @p [@@@@@#gcd @d@ @!t ]@ @ ] @  ]@@@@@AA@@A@÷ @!n @ ]!m @% ]%Logic$Init#Coq@@"ex @ *@8 ]!p 1@? ] 6@"eq e;B >@#mul AC@9 H@!t ]9 O@!t ]A +k() + 77%' 7!7%'A!A%NZGcd&NatInt'NumbersD@t0Ret@50Rl@20S_\Z|7@@G[@&@6H@6@-@6Ϡd@@A@A6@6@1@6d@@A@AB6@6P@6A@7@6Ad@@A@6z@;@O6zd@@A@ABC6b@6ò@@@6òd@@A@A6÷bBDEF@A@%NZGcd&NatInt'Numbers#Coq@&NZGcd'P@A@@@B!B47 @@ OY@@ OYd@@A@A@A@ )NZGcdSpec @@@A@@@AbGJ@@3Gk@R@|3GkJ@@A@A3G!@@"eq3G!^@@A@3G"`@ @"le3G"`h@@A@AB3G"o@ @"lt3G"oh@@A@3G@@#add3Gd@@A@A3GW@@#max3GWd@@A@3G@@#min3Gd@@A@ABC3G@ @3GǠd@@A@3G @%@#one3G T@@A@A3G3@)@#sub3G3d@@A@3G@/@#two3GϠT@@A@A3S{l@3@$pred3S{ld@@A@3S@8@$succ3Sr@@A@3Tv@=@$zero3TvT@@A@ABCDE@A@@@ %'A*Equalities*Structures#Coq@A1@D%Logic$Init#Coq@@A@@,gcd_divide_l @@ (@6 ] -@; ] 2@./X䀠 8@P G@@@@@=,gcd_divide_r @@9 G@U ]7 L@Z ] Q@M/X䀠 W@o G@@@@@[,gcd_greatest @@W e@s ]U j@x ]@ o@} ]@ u@q/X6@ {@w/X䀠D; @}/X䀠A @ GED@@@@@*gcd_nonneg @@ @ ] @ ] @"le e @ [ @ Gu@@@@@#div @d@ @!t ]@ @ ] @  ]@@@@@AA@@A@&modulo @d@ @ ]@ @! ] @% ]@@@@@&div_wd @@)Morphisms'Classes#Coq@@&ProperL@ @A ]@ @F ] @J ]@*respectful%WO? @U ]@ @Z ] @^ ] @"eq e; %@i ] )@m ] -@ e; 1@ e; 5@ 򐀐@@@ %'A*Equalities*Structures#Coq@AviAT'Classes#Coq@@A@@&mod_wd @@e@ V@ ]@ [@ ] _@ ]Y e@ ]@ j@ ] n@ ] r@T e;l x@ ] |@ ] @b e; @f e; @1퀐@@@SAK@A@@Ġ'div_mod @@!a @ ]!b @ ]@%Logic$Init@#notШ @ e;A @$zero [ @ e;C @#add 䀠 @#mul B @# 򐀠 @ 1@@@@@-mod_bound_pos @@Q @- ]O @2 ]@ @"le e @A [+@@"lt eÀ@M [7e@#andЖw@@ e@_ [@O1퀠D_$@$ eÀ*@\1 j@@@@@d'testbit @d@9@!t ]@?@ ])Datatypes$Init#Coq@@$boolZ'@@@@@@AA@@A@&shiftl @d@^@% ]@c@* ]g@. ]@@@@@&shiftr @d@v@= ]@{@B ]@F ]@@@@@3$land @d@@U ]@@Z ]@^ ]@@@J#lor @d@@l ]@@q ]@u ]@/@@a%ldiff @d@@ ]@@ ]@ ]@F@@x$lxor @d@@ ]@@ ]@ ]@]@@$div2 @d@@ ]@ ]@@@@@*testbit_wd @@)Morphisms'Classes@&ProperL@@ ]@ @ ]Ω@*respectful%WO?@ ]@@ ]ޚ!@"eq e;(@ ]隠,@  e;%Logic@ @:@ 5+垀@@@ %'A*Equalities*Structures#Coq@AviAL'Classes#Coq@@A@@-testbit_odd_0 @@!a[@" ]/b@35+垀h@#add 䀠o@#mul u@#two #A{@#one a@$zero [CA@@@@@8.testbit_even_0 @@9@Y ]fU@j5+垀@0 @/ #.@( [jB@@@@@_0testbit_odd_succ @@`@ ]!n@ ]@@"le e@L [V@5+垀@q 䀠@p @o #C@n a@$succ 5B@5+垀@@@@@1testbit_even_succ @@@ ]L @ ]@@J e@ [ة@5+垀"@ '@ #C,@> 5=1@5+垀;@@@@@堠-testbit_neg_r @@暠?@ ]D@  ]@J@"lt eÀ֚P@ [$W@(5+垀a@@@@@ +shiftr_spec @@ e@, ]j@1 ]!mq@8 ]@w@ e|@ [P?@T5+垀@1ݸsD@a5+垀@. 䀠@@@@@K0shiftl_spec_high @@L@l ]욠@q ]@@v ]@@ e@: [D@@ eʩ@5+垀@y1ݸmEE멚@5+垀@#sub R@@@@@/shiftl_spec_low @@@ ]1@ ]@ ]@@ eÀ ϰ@5+垀@1ݸm`@@@@@)land_spec @@@ ]!b@ ]d"@ ]婚)@5+垀/@ @1@#two>T@@A@AI@5@$predId@@A@G@:@$succGr@@A@@?@$zeroT@@A@ABCDE@A@@M_qp}@]@@@d@!tРJ@@A@A L@@"eq L^@@A@r@ @#onerT@@A@AB4@@#two4T@@A@b@@$predbѠd@@A@F@@$succFr@@A@]l@@$zero]lT@@A@ABCD@A@@L.+*@A@4*BackportEq@@@A@@@@ %'A*Equalities*StructuresA݋X_A@A@@AA@@A@&eq_sym @@5Equivalence_Symmetric. U@ ]@ e;@0&@@)SymmetricFgq@ ]@ e;TL@-. U\DѠ ja KD֠hWok@@b@@X(eq_trans @\@6Equivalence_TransitiveWU@T ]Y@S e;]@R0&@o@*Transitive++-h@g ]l@f e;QDT:LV@-W\7ߠؠyj@DM@ ]K@ ]@ e;@ 5J@ 5I@ e;"@@@G@A8ӠA4Relation_Definitions)Relations@AB@@"/succ_inj_wd_neg @E<ݠ~&Ǡ[C2ޠ@E@ ]#@" ]c,@& e;2@ 57@ 5.>@8 e;m@@@@@d1central_induction @ߠ~&Ǡha t @ F!A@c@b ]A$A_wd@&ProperL@u@t ] @*respectful%WO?@ ]@~ e;?@ ]@n@@ ]ѠE@j 5@ ]F@@@@@ɠ'add_0_r @cSD,%͠ƠngX٠@@A&NZBase%NZMul&NatInt'Numbers#Coq@@A@%NZMul&NatInt'Numbers#Coq@)NZMulProp@A@@@@"NZ@A@%NZAdd&NatInt'Numbers#Coq@)NZAddProp/@@@A@@@A&NZBase%NZAdd&NatInt'Numbers#Coq@A@A@@@"NZ+@@,R@2@!t,RJ@@A@A,Y@@"eq,Y^@@A@,@@ @#add,@d@@A@AB,w@@#mul,wd@@A@,@@#one,T@@A@A,@@#sub,d@@A@,@@#two,T@@A@A,@"@$pred,d@@A@,@'@$succ,r@@A@,筷@,@$zero,筷T@@A@ABCDE@A@E@CB@A ]G@A e;M@@ 䀠{R@ [@@@@@v@ABC@@AA@@A@*add_succ_r @@9ڠ{# v@A~@} ]}@ ]@ e;@ 䀠@b 5署@g 5@ ΐ@@M@@J-add_succ_comm @_O@ߠ(!ɠ jcTՠܠˠ@Bƚ@ ]Ě@ ]@ e;@ 䀠@ 5<@ 䀠@ 5A@@@@(add_comm @/&ΠǠoh E-C6(#@C  @  ] @ ]@ e;@ K!@ H@@@@̠'add_1_l @Ѡ ja KD֠hW~qc^M?@JDHG@F ]L@F e;R@E 䀠W@ a\@* 5@@ @@'add_1_r @ D=ޠ' z@E@ ]@ e;@ 䀠@ a@e 5@@E@@B)add_assoc @WG8נx b[Lޠ͠٠Ԡà@F@ ]@ ]!p@ ]@ e;@ 䀠@  @ 䀠@ @@@@,add_cancel_l @.%͠ƠngD,B5'"@G  @  ]  @  ]N @  ]U @  e; "@ 䀠P (@ O -@ ' e;ې@@@@ؠ,add_cancel_r @ݠΠvmWPtc}ojYK@VHT S@ R ]R X@ W ] ]@ \ ] d@ ^ e; j@] 䀠N p@c  u@ o e;#@@#@@ ,add_shuffle0 @ 5 % ]V@9*ԠҠŠ@I @  ] @  ]ޚ @  ] @  e; @ 䀠 @ d㩚 @ 䀠 @ W@@o@@l,add_shuffle1 @  q b  JCv @J蚠 @  ]暠 @  ]* @  ]!q @  ] @  e; @ 䀠 @ 䀠 @ > @ 䀠 @   @ @@@@ʠ,add_shuffle2 @ ߠ Ϡ  h _  IBԠ~fU|oa\K=@HKF E@ D ]D J@ I ] O@ N ]^ T@ S ] Y@ S e; _@R 䀠 e@X \ j@]  o@b 䀠 u@h 䀠 {@n )@@)@@&,add_shuffle3 @ ; +  Ġ  c \ F?0ڠ ؠˠ@L @  ] @  ]䚠 @  ] @  e; @ 䀠 @ 멚 @ 䀠𩚠 @ ]@@u@@r'sub_1_r @  w h     P I|&$ @M @  ] @  e; @ & @( a @ ]@@@@'mul_0_r @     K B     , %͠ƠaI8_RD@]@& %@ $ ] *@ $ e; 0@ ^ 5@ [ 9@ [@@@@AA@@A@*mul_succ_r @   ݠ  | $  Š  f _  r~@A` _@ ^ ]^ d@ c ] i@ c e; o@U  u@C 5Щ z@m 䀠 @f @@.@@G(mul_comm @ @ 0 ! ɠ  h a     K D 5ߠǠݠР@B @  ] @  ] @  e; @ ⩚ @ ߐ@@f@@/mul_add_distr_r @ x h Y     A :  ۠  | m @Cܚ @  ]ښ @  ] @  ] @  e; @  @ # @ 䀠 @  @ 5@@@@͠/mul_add_distr_l @ Ơ   O F     0 ) Ѡ ʠ  e M <cVH@aD* )@ ( ]( .@ - ]l 3@ 2 ] 8@ 2 e; >@ $ " D@ 7 s I@ < 䀠 O@ 5  T@ : @@@@)mul_assoc @      < 5 ݠ ֠ ~ w      @Ex w@ v ]v |@ { ] @  ] @  e; @ r p @ x  @ }  @  Kʐ@@K@@d'mul_1_l @ ] M >  ݠ  ~ &  Ǡ  h a R   Ӡ@F @  ] @  e; @   @ a@@~@@'mul_1_r @   q     Y R      /  - @+G @  ] @  e; @  , @. a0@@@@ʠ,mul_shuffle0 @ à   L C     - & Π Ǡ  b J 9`SE@^H' &@ % ]% +@ * ]i 0@ / ] 5@ / e; ;@ !  A@ ' n F@ ,  L@ 2 z@@@@,mul_shuffle1 @      4 - ՠ Π v o      @Ip o@ n ]n t@ s ] y@ x ] ~@ } ] @ } e; @ o  @ u  @ z é @   @  F @  :@@R@@k,mul_shuffle2 @ d T E     - & Π Ǡ o h Y   ڠ@JȚ @  ]ƚ @  ]  @  ] @  ] @  e; @   @  ީ @    @   @   @  @@@@à,mul_shuffle3 @    E <  ݠ  ~ &  Ǡ   [ C 2YL>@WK @ ] $@# ]b)@( ].@( e;4@   :@   i?@ %  nE@ + ې@@@@ %le_wd @     - & Π Ǡ o h      {@@A&NZBase'NZOrder&NatInt'Numbers#Coq@ & $@A@'NZOrder&NatInt'Numbers#Coq@+NZOrderProp 5 3@A@@@@"NZ * )@A@@@@ ]@@ ],@ ]@@ ]7@ e;)@ ]A@ e; 皠@  e@@Z@@AA@@A@*lt_le_incl @o_P     8 1 ٠ Ҡ z s d   j]O@hA Ӛ@ ] њ@ ]@@"lt eÀ @  e @@@@@7'le_refl @,# ˠ Ġ l e      B * @B @ ] @  e 9 9@@ .@@`.lt_succ_diag_r @̠UL     6 / נ Р  k S BǠ@C 0/@. ]4@W eÀ b:@  5 @@@@@.le_succ_diag_r @۠z" à  d ]      p@D ^]@\ ]b@ _ e h@ 6 5 Ð@@@@@/neq_succ_diag_l @( PI     3 ,  Ǡ  #@!E @ ] @ e;@ f 5  Ő@@ @@젠/neq_succ_diag_r @XH9ؠy!    c \ M  ߠ ΠSF8@QF @ ] @ e; 𩚠@  5 #@@@@@/nlt_succ_diag_l @xiQJ     } '  vh@G 욠@ ] ␩@ eÀ@  5 S %@@@@@L/nle_succ_diag_l @A8٠z" à   W ? .@H @ ] "@  e(@  5  U@@@@@|)le_succ_l @ؠɠqh RK   ݠ  o ^֠@I LK@J ] JP@O ] W@ T e]@ + 5  b@ eÀ @@ @@+le_gt_cases @"JC-&   @J @ ] @ ] @"or @@  e Ʃ@ eÀ Ð@@ J@@-lt_trichotomy @\L=ܠ}%Ơg`Q   ҠWJ<@UK @ ] @ ]:@ eÀ A@ e; @ eÀ @@@@@+(lt_asymm @x `Y6 w@L @ ] @ ]@@( eÀ 4  @/ eÀ @@ a@@`(lt_trans @̠UL6/נРkSBǠ@M 0/@. ] .4@3 ]r9@8 ]@?@b eÀ @E@h eÀ 󩚠J@m eÀ  .@@ @@(le_trans @ 3,Ԡ͠un@N on@m ] ms@r ]x@w ]@~@{ e ,@@ e 2@ e?@@ 7@@ݠ+lt_strorder @I9*Ҡɠqj TM>РD7)@BO@+StrictOrder.[@@ ]@ eÀ@@ @@ +le_preorder @wgX@9ڠ{lreW@pP@(PreOrder@@ ]@ e@@@@9/le_partialorder @.%͠ƠngD,@Q@,PartialOrder5͛К@  ]@  e;@ 0&@ e9@b5G @@@ s@A @B@CAhC4@ABC@@y)lt_compat @3@%lt_wd ӣ@ ̰@;@: ]@@@? ] ݩ F@E ]@K@J ] 蚠O@I e; U@T ] 򚠐Y@S e; ]@ eÀ@@@%lt_wd']ɠG@*# @@@@@Р(lt_total @@0jR@ @ ] @ ] @ eÀ ʩ@ e; ѩ@ eÀ ΐJ3@ aǠdTE-&ΠǠohYڠ_RD@@@@@'le_lteq @@+lt_eq_casesZ@ ֚@ ] Ԛ@ ]@ eW@  eÀ@ e;@+lt_eq_cases&y2)Ѡʠrk H0@@@@@Z0Private_OrderTac*A'IsTotal2 A @"@0&@5@+Equivalence~@.@- ]2@, e;@(eq_equiv7LޠϠwnXQudܠ@@@@@ @s@@^@] ]b@ eÀ@,Q^ E>ߠ(! @@@@@ΠU @@]/@ @@ ]@@ ] 0 @ ]@@ ] ;@ e; -@ ] E@ e;뚠@ eÀSiYJ2+Ӡ̠tm^ߠdWI@@@@@J @@R/f΀@ٚ@ ]ך@ ]S@ eÀZ@ e;@ eÀI2)Ѡʠrk H0@@@@@ZE @.@M?@@ ]@ ]]$@! eS+@N eÀZ0@* e;_C٠ʠri SLޠp_נ@@@@@@@@@ѐ@#TacmGAl @70ؠѠyr @@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@ ]@ e;@@@@AA@@A@ @:1٠ҠzsP8']VP5@Ac@ ]@ e@@A@@0)lt_irrefl @ߠϠh_IBԠ~fUڠ͠Р~c@BH@G ]?O@r eÀD@@q@@`d @6/נРxq @Cw@v ]|@{ ]@@| e;@ e;k@@@@*le_antisym @G7(РǠoh RK<ΠB5'8(@9D@ ]@ ]@@ e@@ e@ e; @@@@נ @ufNGz$ sevf1*$ @wE7@ ]5@ ]@됩@ e;*򐩚@ e;@@@@@*interp_ord @!o)OrdersTac0@#ordȠ@ @@@@@@@@@@@D@$@# ]@)@( ]V.@( e;2@U eÀ6@3 e@*(@<@; ]@A@@ ]ސ +k= R'6'6'6''+k+7T'+7T'6'ࠒA̠ܠ۠@@"lt\ @@"eq8L@lР@TȠ@@QPO@@A@B@A@xA܀+ SL6/ ʠ&  נРʠ@@@@@%trans @N>/נΠvoYRCՠĠI<.?/@@F"o'@ ]@ ]{@ ]@@"L;y:@@"L;y @"L;y@)trans_ord-0uGDRɐ@@;@@ @=@ ];@ ]@ ] @rМA76@W@  ]U@ ]Κ@ ]@@ e;̶@$@ e;ҩ)@# e;ߐ L+k() LL7#'S@$tݠΠvmWPtc۠͠ޠΠq@@@@@a @^@] ]c@b ]h@g ]d"@МbCV@x@w ]}@| ]8@ ]@@ e6@@ e<@ eI L+k() NN7#'jtSC4ܠӠ{t^WHڠɠ N A 3D4@@@@@Ǡ @ @ ] @ ]@ ]@BМB@'@ ]%@ ]@ ]@@  eÀ@@  eÀ@  eÀ L+k() MM7#'АtB9ڠ{#ĠX@/   e^X=@@@@@-+le_lt_trans @t+@* ]r0@/ ]뚠5@4 ]W1@g kj@B@A ]G@F ]L@K ]@R@O e@X@ { eÀ]@  eÀ L+k() MN7#'4t E>ߠ(!   ɠ @@@@@+lt_le_trans @ؚ@ ]֚@ ]O@ ]S@ 1@@ ]횠@ ]f@ ]@@  eÀd@@ ej@  eÀw L+k() NM7#'tqb JCv  | o arb-& @@@@@%eq_lt @<@ ]:@ ]@ ]@q/32@S @  ]Q@ ]ʚ@ ]@@ e;ȶ@ @ C eÀΩ%@ H eÀې L+k() ML7#'tՠƠne OHڠl[  Ӡ Š֠Ơi@@@@@Y%lt_eq @W@V ]\@[ ]a@` ]]@cL@n@m ]s@r ].x@w ]@~@  eÀ,@@~ e;2@  eÀ? L+k() LM7#'`tI9*Ҡɠqj TM>Р D 7 ):*@@@@@%eq_le @@ ]@ ]{@ ]@9]@@ ]@ ]@ ]@@ e;@@ e@ e L+k() NL7#'Đt6-ՠΠvoL4#   YRL1@@@@@!%le_eq @h@ ]f$@# ]ߚ)@( ]K%@+_^@6@5 ]};@: ]@@? ]@F@C e@L@F e;Q@N e  L+k() LN7#'(t92ڠӠ{t   @@@@@&eq_neq @4$\U?8)Ӡ / " %٠Ӡ@&G暠@ ]䚠@ ]]@ ]@@ e;[@@ e;c@ e; r@@@@@͠&neq_eq @|l]E>ߠq w j \m](!@nH.@ ],@ ]@ ]@琩@ e;@@ e;@ e; @@@@@*not_neq_eq @ĠMD.'ϠȠcK:   picH@Iv-@, ]t2@1 ]@*,<@6 e;kA@; e;@@@@R)not_ge_lt @)"ʠàkd w   @Jj@i ]o@n ]@gw@t e|@  eÀ*@@@@)not_gt_le @<,Šd]G@1۠à 7 * -۠@.K@ ]욠@ ]@@  eÀ٩@ ee@@@@@Ƞ)le_neq_lt @wgX@9ڠ{l r e WhX#@iL)@ ]'@ ]@@ e@㐩@ e;@  eÀ@@@@@ @@@@'@@@@@'@<_neq @E<ݠ~&Ǡ[C2   @ R @ ]$@# ]@*@ M eÀY!1@+ e;ߐ@@@@@ &le_neq @Ҡzq[Txg  ߠ @ SUT@S ]SY@X ]`@  eÀ@#andЖw@m@j edt@n e;@@@@@ Ƞ*eq_le_incl @4$\U?8)Ӡ/"@-T@ ]@ ]@@ e;ѩ@ eU@@@@@ (lt_stepl @gWH0)Ѡʠrk\ݠbUG@`U@ ]@ ]@ ]@@  eÀ@@ e;@ eÀ@@@@@9(lt_stepr @.%͠ƠngD,@VQ@ ]O @  ]Ț@ ]@@; eÀƶ@@ e;̩#@F eÀ ِ@@@@@w(le_stepl @ӠĠlc MFؠjYޠѠ@WF@E ]K@J ]P@O ]@V@S e@\@V e;a@^ e@@@@@(le_stepr @!IB,%@X͚@ ]˚@ ]D@ ]@@ eB@@ e;H@ e U@@@@@ @^N?ޠ' ȠibSԠYL>@WYš@ ]@ ]@ ]@@ e@@ eÀ@ eÀ @@@@@0\ @|$àd]:"{@Z@ ]@ ]A@ ]@@1 eÀ@@ e©@< eÀ ϐ@@@@@m+le_antisymm @٠ɠbYC<ݠΠx`OԠǠ@[=<@; ];A@@ ]@G@D ev@M@J e1R@L e;I@@@@@)le_succ_r @:3۠Ԡ|u @ \vu@t ]tz@y ]@~ e@U 5 @ e@ e;©@g 5@@@@@)lt_succ_l @YI:٠z"àd]NϠTG9@R]@ ]@ ]@@ eÀ@ 5.@ eÀ@@@@@&,le_le_succ_r @s[T1r@^@ ]@ ]@@ e/@ e驚 @ 5l@@@@@_,lt_lt_succ_r @ˠTK5.֠ϠjRAƠ@_/.@- ]-3@2 ]@9@\ eÀh>@a eÀ"D@ 5@@@@@,succ_lt_mono @,%͠Ơngz@`hg@f ]fl@k ]s@ eÀx@ eÀ~@L 5ߩ@Q 5ސ@@@@@נ,succ_le_mono @C3$̠àkd NG8ʠ>1#@@Wgš @  ] @  ]@ @ eÀ @ [@ @ eÀ @ eÀ @2  aĐ@@@5@3@@ABC@@8+lt_ge_cases @    - $̠ŠmfC+@h!@! ]! @!  ]!@6 eÀB!@ e?@@@@@l+le_ge_cases @ ؠ Ƞ  a X B;ܠ͠w_NӠƠ@i<!;@!: ]:!@@!? ]!G@D ev!L@I es@@@@@+lt_gt_cases @!      4 -ՠΠvo@jp!o@!n ]n!t@!s ]m!}@!w e;󠩚!@ eÀ!@ eÀ@@@@@ݠ,eq_decidable @!I!9!* Ҡ ɠ q j  TM>РD7)@Bk!@! ]!@! ])Decidable!@)decidable r!@! e;@@@@@&eq_dne @!!q!b! !   J Cv |oa@zl嚠!@! ]㚠!@! ])␩䐩!@! e;#!@! e;(@@@@@M&le_ngt @!!!!B!9  ڠ  { # ĠX@/@m"@" ]"!@"  ]a"(@% eW"/@R eÀV@@@@@&nlt_ge @!!ߠ!Р!x!o!!   Y Rveݠ@nS"R@"Q ]Q"W@"V ]P"`@ eÀ"e@b e@@@@@,lt_decidable @"%""!!!M!F     0 ) Ġ @o"@" ]"@" ]ܐ"@ eÀÐ@@@@@蠠<_dne @"T"D"5!ݠ!Ԡ!|!u!!   _ X I۠ʠOB4@Mp"@" ]"@" ]"@ eÀ"@ eÀ@@@@@ &nle_gt @""|"m"" !!!U!N      +  zl@q𚠐"@" ]"@" ]4퐩"@ e,#@% eÀ)@@@@@V<_nge @" """K"B!!!!!,!% ͠ Ơ  a I 8@r&#%@#$ ]$#*@#) ]j#1@T eÀ`(#8@ 5 e_@@@@@,le_decidable @"""٠""x" "!!!b![!     n@s\#[@#Z ]Z#`@#_ ]#g@ d e@@@@@&le_dne @#'##"""O"H!!!!!2!+! Ơ  "@ t#@# ]#@# ]Ϡ#@  eɩ#@  eΐ@@@@@*nlt_succ_r @#_#O#@""ߠ"""("!!ɠ! !j!c!T   ՠZM?@XuÚ#@# ]#@# ]#@ eÀ#@  57#@ eÀ @@@@@/5lt_exists_pred_strong @###|#$#"à""d"]"!!!!!:!"!{@v#@# ]$@$ ]$@$ ]@$@1 eÀ@$@! eU@"ex @$ @$ ]!k$'@$& ]Ǡ$.@$( e;թ$4@! 5$9@!6 eg@@@@A@@A _@ `AРD.Morphisms_Prop$Q@ fA1@D@ABCD@@.lt_exists_pred @$#####0#)"Ѡ"ʠ"r"k"" !!!!~@w!$k@$j ]q$p@$o ]@$v@ eÀb$|@${ ]\$@$ ]!$@$ e;l$@!\ 5驚$@! e@@@O@A@@蠠,lt_succ_pred @$T$D$5#ݠ#Ԡ#|#u##"""_"X"I!!۠!ʠOB4@Mxm$@$ ]$@$ ]@$@ eÀ񩚠$@$ e;$@! 5$@! 4 @@@(@A%@t@ @@ABCD@@,&rs_rs' @$$$y$!$###a#Z#"""""7""x@y@$@$ ]@%@% ]% @%  ]%@% e; M ;ɚ%@% ]@@ %@% ]@% @" e@>%)@! 5  0%/@%. ]@%5@"2 e@ =%<@%; ] ;%A@%@ ]@%G@"D ec u@%N@q eÀ 2K'H)@@@@(rs'_rs'' @%%$$$$:$3#۠#Ԡ#|#u###""" @ z@%v@%u ]@%~@%} ] %@% ]!%@% e;   C%@% ]@ %@% ]@%@" e ȶ@ %@% ] %@% ]@%@" e ٶ@%@ eÀ I  %@% ]  Ú%@% ] %@% ]@%@" e"@%@ eÀ ! . ښ%@% ] ؚ%@% ]@%@" e9@%@  eÀ 8%@" 5 K@@ E@@D%rbase @%%%%9%0$ؠ$Ѡ$y$r$$####O#7#&@{@&@& ] Ϛ&@& ]! &@& ]!&$@&# ]@&*@#' e@&0@S eÀ!| @@@@@)A'A_right @%%%Ѡ%y%p%%$$$Z$S#####w#fޠ@|@&T@&S ]!&Y@&X ]@!`&_@&^ ]!f&e@&d ]!d&j@&i ]@&p@#m e@&v@ eÀ!ZN Ҷ!}&|@&{ ]@&@# e @@@@@נ6strong_right_induction @&C&3&$%̠%à%k%d% %$$$N$G$8##ʠ#>1#@<} F@&@& ] D B @@&@& ] L :&@& ] R&@& e;!!!t&@& ]@!Ś&@& ]@&@# e!@!Қ&@& ]!К&@& ]@&@# e1@&@ eÀ!0!C.!蚠&@& ]@&@# e̐@@@!B@A!@#@@ABC@@E/right_induction @&&&&:&1%٠%Ҡ%z%s%%$$$$P$8$'@~ @'@' ]   @'@' ]  '#@'" ] ''@'! e;"f"T!⚠',@'+ ]@ @"4'3@'2 ]@'9@$6 e϶@V'A@$ 5"G'F@'E ]@'L@$I eשh!@@@@@0right_induction' @' &&&&&5&.%֠%Ϡ%w%p%%%$$$@!@'q@'p ]!! ! @'y@'x ]!!'@'~ ]!'@'} e;""">'@' ]@"'@' ]@'@$ e"@"'@' ]@'@$ e6@'@$v 5"'@' ]! @@#@@7strong_right_induction' @'m']'N&&&&&6&/%נ%Р%x%q%b% $$h[M@f@!p@'@' ]!n!l!j@'@' ]!v!d'@' ]!|'@' e;#"#"'@' ]@"'@' ]@'@$ e#r@"'@' ]@(@$ e@#(@( ]#( @(  ]@(@% eٶ@(@; eÀ"J"{# (@( ]!~@@@@@s&ls_ls' @'ߠ'Ϡ''h'_''&&&I&B%%%Ԡ%~%f%Uڠ͠@A!@(C@(B ]!!ީ!ܰ@(K@(J ]!!(Q@(P ]!(U@(O e;###(Z@(Y ]@!Ѷ@#b(a@(` ]@(g@ eÀE@!ǐ(o@%= 5"#u(t@(s ]@(z@%w e##!@#(@( ]#(@( ]@(@% e#@(@% e#BF(@%h 5"J@@@@(ls'_ls'' @(Z(J(;''ڠ''{'#'&Ġ&&e&^&O%%%РUH:@SB"]@(@( ]"["Y"W@(@( ]"c"Q(@( ]"i(@( e;$##(@( ]@#ܚ(@( ]@(@% e$@#隠(@( ]#皠(@( ]@(@% e$!"`@(@% e#H)@% 5#aL$)@) ]$E$) @)  ]$ )@) ]@)@& e%@)@& e#l#y$%)$@)# ]$#))@)( ]@)/@&, e<@)5@&2 e#);@&  5#@@Z@@%lbase @(((ܠ(({(#('Ġ''e'^'&&&&&q@C"@)_@)^ ]"$)d@)c ]$k)j@)i ]$i)o@)n ]@)u@&r e S@){@&x e$)ǐ)@&O 5#ܐ@@@@@ՠ(A'A_left @)A)1)"(ʠ((i(b( ('''L'E'6&&Ƞ&</!@:D#D@)@) ]#B$`)@) ]@$)@) ]$)@) ]$)@) ]@)@& eG@)@& e$uQ$"$͚)@) ]@)@& e P@@%@@&5strong_left_induction @)))s))((([(T''''''1''r@E#@)@) ]###@)@) ]##*@* ]#*@* e;%G%5$Ú* @*  ]@%*@* ]@*@' e%@@%!* @* ]%*%@*$ ]@*+@'( e8@*1@'. e$*7@' 5$%=*<@*; ]@*B@'? 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[-a@29@#\ eÀ2>@/ [-l2C@#f eÀ2H@/ [2M@/@ (D@@l@@Ѡ1add_nonneg_nonneg @2 1111151.0֠0Ϡ0w0p000///@/K-n2m@2l ]-l2r@2q ]@2x@/u e2}@/F [-@2@/ e2@/Q [-2@/ e2@/[ [2@/ (@@@@,lt_add_pos_l @2W2G2811נ11x1 1000b0[0L//ޠ/@/L-2@2 ]-2@2 ]@2@# eÀ2@/ [-2@# eÀ-2@/ -@@@-&@.@AB@@X,lt_add_pos_r @222u22111]1V000000300 @0M-2@2 ]-󚠐2@2 ]@2@$" eÀ3@/ [.23 @$, eÀ.83@0 -@@-d@@,le_lt_add_lt @2Ϡ222X2O111119120ڠ0Ӡ0Ġ0n0V0E@0AN.03/@3. ]..34@33 ]*r39@38 ])H3>@3= ]@3D@0A e);@3J@$m eÀ3P@0C -𩚠3U@0H 䀠.,©3[@$~ eÀ)R@@@@@ߠ,lt_le_add_lt @33 2222C2<11ݠ11~1&11000@0O.|3{@3z ].z3@3 ]*3@3 ])3@3 ]@3@$ eÀ)@3@0 e3@0 .<3@0 L3@$ eÀ)@@@@@*,le_le_add_le @3f3V3G22222/2(1Р1ɠ1q1j1[100@0P.ǚ3@3 ].Ś3@3 ]+ 3@3 ])ߚ3@3 ]@3@0 e)Ҷ@3@0 e3@0 .3@0 3@0 e)@@@@@u,add_lt_cases @3333:312٠2Ҡ2z2s221111P181'@1#Q/4@4 ]/4@4 ]+T4@4 ]**4 @4 ]@4&@%I eÀ4,@1 *#41@1$ /`#48@%[ eÀ"4=@%` eÀ.@@@@@,add_le_cases @333ޠ33}3%32Ơ22g2`221111s@1oR/^4]@4\ ]/\4b@4a ]+4g@4f ]*v4l@4k ]@4r@1o e4x@1k *o4}@1p /#󠩚4@1 e#:4@1 e/0@@@@@ -add_neg_cases @4I494*3Ҡ3ɠ3q3j33 222T2M2>11Р1@1S/4@4 ]/4@4 ]@4@% eÀ4@1 /隠4@1 [$44@% eÀ/4@1 [4@% eÀ/4@1 [@@/)@@X-add_pos_cases @444u44333]3V222222322 @2T/4@4 ]/󚠐4@4 ]@4@&" eÀ5@1 [5 @1 08$5@&3 eÀ5@1 [/5@&= eÀ5@1 [0M@@>@@0add_nonpos_cases @4ߠ4Ϡ44h4_44333I3B222Ԡ2~2f2U@2QU0@5?@5> ]0>5D@5C ]@5J@2G e5P@2C 05T@2 [$ʠ5[@2X e0?5`@2) [5e@2b e05j@23 [@@/@@0add_nonneg_cases @5*55 444R4K3333353.32ɠ22@2V05@5 ]05@5 ]@5@2 e5@2c [5@2 0Ω%5@2 e5@2t [05@2 e5@2~ [0@@@@9-le_exists_sub @5u5e5V44444>473ߠ3ؠ33y3j322@2W0֚5@5 ]0Ԛ5@5 ]@5@2 e1̠5@5 ]-$5@5 ]5@5 e;0֩5@2  ~5@2 e6@2 [1/@@@0W@A0@2'@A2'AA@@0@ABCD@@+mul_lt_pred @5ˠ555T5K4444454.3֠3Ϡ33j@3@-b6)@6( ],86.@6- ]1463@62 ]1268@67 ]@6>@68 e;6D@3 501(16L@'o eÀ6R@38 %6W@3= /16]@' eÀ6c@3V 䀠6i@3O ,`16n@3a 䀠6t@3Z 11W@@/"@@AA@@A@1mul_lt_mono_pos_l @676'6555_5X54444B4;4,3@4)A-Κ6@6 ]16@6 ]16@6 ]@6@' eÀ6@3s [11꠩6@' eÀ1_6@' eÀ6@3 ,6@3 1h@@@1@A1@1b@2@@ABCD@@R1mul_lt_mono_pos_r @66v6g66555O5H44444{4%@4xB.6@6 ]1ꚠ6@6 ]1蚠6@6 ]@6@( eÀ6@3 [1ܩ297@(# eÀ17@(( eÀ7 @3 17@3 2?1@@/@@1mul_lt_mono_neg_l @6Ѡ666Z6Q55555;544ܠ4ՠ4Ơ4p@4C.h7/@7. ]2574@73 ]2379@78 ]@7?@(b eÀ2#7D@4  [27K@(n eÀ17P@(s eÀ7V@4< 17[@4A -R@@@@砠1mul_lt_mono_neg_r @77 6666C6<55ݠ55~5&554@5 D.7y@7x ]27~@7} ]2}7@7 ]@7@( eÀ2m7@4W [2Π7@( eÀ2C7@( eÀ7@4 7@4 2E@@0S@@14mul_le_mono_nonneg_l @7e7U7F66666.6'5Ϡ5Ƞ5p5i5Z5@5WE2Ě7@7 ]2š7@7 ]/7@7 ]@7@4 e7@4 [3@7@4 e-թ7@4 e7@4 21V7@4 2@@2D@@{4mul_le_mono_nonpos_l @777787/6נ6Р6x6q665555N@5F38 @8  ]3 8@8 ]/P8@8 ]@8@5 e3K8"@4 [@8(@5% e.8-@5* e83@5 2ө88@5 O@@2@@Ġ4mul_le_mono_nonneg_r @777٠77x7 7666b6[6555@5G3W8V@8U ]3U8[@8Z ]/8`@8_ ]@8f@5c e8k@54 [3@8q@5n e.h8v@5s e8|@5b '28@5g .x@@2@@ 4mul_le_mono_nonpos_r @8A818"7ʠ77i7b7 7666L6E665@63H38@8 ]38@8 ]/⚠8@8 ]@8@5 e3ݚ8@5} [@8@5 e.8@5 e8@5 .8@5 '@@3@@V,mul_cancel_l @88z8k88 777S7L666666)@6|I3隠8@8 ]3皠8@8 ]0+8@8 ]@3ꐩ8@8 e;4(8@5 [4?9@9 e;9 @5 9@5 39@9 e;/ @@@3j@59@3$@ABC@@,mul_cancel_r @8٠8ɠ88b8Y87777C7<66ݠ6Π6x@6J4897@96 ]469<@9; ]0z9A@9@ ]@499I@9C e;4w9N@6 [49U@9O e;9[@6A 49`@6F 49e@9_ e;/\@@2@@(mul_id_l @9%99888M8F7777707)76@7K49@9 ]49@9 ]@49@9 e;49@6^ [4ՠ9@9 e;9@6 4P4Щ9@9 e;49@J a@@4K@@8(mul_id_r @9l9\9M8888858.7֠7Ϡ7w7p7a7 @7^L4˚9@9 ]4ɚ9@9 ]@4ǐ9@9 e;59@6 [59@9 e;9@6 44̩9@9 e;59@K a@@2@@1mul_le_mono_pos_l @9999<938۠8Ԡ8|8u887777R@7M5:@: ]5:@: ]1T:@: ]@:!@+D eÀ:&@6 [5S5f:-@7* e0$:2@7/ e:8@7 (:=@7# 5!@@4@@ɠ1mul_le_mono_pos_r @999ޠ99}9%98Ơ88g8`8877@7N5\:[@:Z ]5Z:`@:_ ]1:e@:d ]@:k@+ eÀ:p@79 [55:w@7t e0n:|@7y e:@7h 5):@7m 55@@35@@1mul_le_mono_neg_l @:G:7:(9Р9Ǡ9o9h99 888R8K8<7@89O5:@: ]5:@: ]1蚠:@: ]@:@+ eÀ5㚠:@7 [5:@7 e0:@7 e:@7 5:@7 @@@@]1mul_le_mono_neg_r @:::r::999Z9S8888880@8P5𚠐:@: ]5:@: ]22:@: ]@:@," eÀ6-;@7 [6D; @8 e1;@8  e;@7 5ĩ;@8 5@@3@@2mul_lt_mono_nonneg @:۠:ˠ::d:[:9999E9>88ߠ8Р8z@8Q6:;9@;8 ]68;>@;= ]2|;C@;B ]1R;H@;G ]@;N@8K e;S@8 [5@;Y@,| eÀ46@;`@8] e;e@8. [6 @;k@, eÀ;p@, eÀ;v@8\ &4թ;|@8b $4@@@@@ 2mul_le_mono_nonneg @;=;-;:Ơ::e:^:9999H9A928@9/R6;@; ]6;@; ]2ޚ;@; ]1;@; ]@;@8 e;@8~ [6[@;@8 eb@;@8 e;@8 [6l@;@8 es;@8 e;@8 a;@8 `@@61@@h+mul_pos_pos @;;;};%;:Ġ::e:^:99999;@9S6;@; ]6;@; ]@<@-( eÀ< @8 [78@<@-3 eÀ<@8 [7C<@-= eÀ<@8 [<$@9  2@@C@@+mul_neg_neg @;;Ԡ;Š;m;d; ;:::N:G999٠9@9T7C@: [929D> @; e>@: [>@: 8é>@; e>@: [9M@@ M@@3mul_nonneg_cancel_r @=ߠ=Ϡ==h=_==<<>=@>< ]9<>B@>A ]@>H@/k eÀ>M@; [9z9>T@;Q e>Y@;" [>^@;D 9 >c@;` e>h@;1 [9K@@ @@,lt_1_mul_pos @>(>> ===P=I<<<<<3<,<;@<\9>@> ]9>@> ]@>@/ eÀ>@O a9Ķ@>@/ eÀ>@;j [9ϩ>@/ eÀ>@O a>@; 4@@@@<(eq_mul_0 @>p>`>Q=====9=2<ڠ<Ӡ<{@> ]9͚>@> ]:>@> e;>@; :>@; [.Z>@> e;:>@; [>@> e;:#>@; [@@7@@)neq_mul_0 @>>>>C>:==۠==|=$=<Š<<>>>>2>+=Ӡ=̠=t=m==<<@<_:i?h@?g ]:?o@?i e;?u@<[ 0j?y@̠>à>k>d> >===N=G=8<@=5`:?@? ]:?@? ]@?@? e;?@< :ᚠ?@< [@:?@? e;:횠?@< [?@? e;:o?@< [@@@@@ Y*eq_mul_0_r @??}?n?? >>>V>O======,@=a:욠?@? ]:ꚠ?@? ]@?@? e;?@< ;+@@< [@:@@@ e;:욠@ @< [@@@  e;:@@< [@@@@@ (mul_eq_0 @@@@p1d'@;+@*@@) ];)@/@@. ];o@6@@0 e;@<@=" ;k@@@=  [/@G@@A e;;v@L@= [@Q@@K e;;@V@= [====@=@^\@@??????8>>٠>>z>">> =@@@@@ *mul_eq_0_l @@@ av0@;@@@ ];@@@ ]@@@@ e;@@=y ;š@@=` [@;@@@ e;;Κ@@=m [@@@ e;;P@@=w [X@+24pe@i@Y@J?????2?+>Ӡ>̠>t>m>^>@@@@@ M*mul_eq_0_r @@@ av6@;՚@@@ ];Ӛ@@@ ]@@@@ e;@@= <@@= [@;ᐩ@@@ e;;՚@@= [@@@ e;;ߚA@= [@324pk@@@@D@;??ܠ??}?%?>Ơ>>>Z@@@@@ (lt_0_mul @@Ӡ@à@@\@S?????=?6>ޠ>נ>Ƞ>r@>b<2A1@A0 ]<0A6@A5 ]  [AG@>-  [<AZ@2} eÀA_@>( [<$Af@2 eÀ<Ak@>4 [Ap@2 eÀ<Au@>> [@@;@@ 5square_lt_mono_nonneg @A5A%A@@@]@V?????@?9?*>@?'c<A@A ]<A@A ]@A@> eA@>l [<Ѷ@A@2 eÀ <[<[A@> <<@@@@@ G5square_le_mono_nonneg @A{AkA\A@@@@D@=??ޠ???p?@?md<ښA@A ]<ؚA@A ]@A@> eA@> [=@A@> e<A@> eA@> FA@> E@@@@@ 6square_lt_simpl_nonneg @AAAAHA?@@@@@)@"?ʠ?à??^@?e=B@B ]=B"@B! ]@B(@?% eB-@> [=Z@B3@3V eÀB9@? 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