"`Z m&BinNat&NArith#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@'BinNums'Numbers#Coq@4)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@0JqTttֱt0dmk(5Ju<*EqdepFacts%Logic#Coq@0FI$ͼՋ`)Eqdep_dec%Logic#Coq@0u wWIϰ߼&Basics'Program#Coq@0!bs߯? :VU$Init'Classes#Coq@0](p{yOh.'Tactics'Program#Coq@03u%+Equivalence'Classes#Coq@07;ꮹ-SetoidTactics'Classes#Coq@0S_`nOU$&Setoid'Setoids#Coq@0D9AsWE!>$Bool#Coq@0j 2cZ`FW*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 $NSub(Abstract'Natural'Numbers#Coq@0:DfJᠠ'NMaxMin(Abstract'Natural'Numbers#Coq@0]v|Qg̟ʠ'NParity(Abstract'Natural'Numbers#Coq@0̗SKz*!&4h$NPow(Abstract'Natural'Numbers#Coq@0҆mulf%NSqrt(Abstract'Natural'Numbers#Coq@0<ge$NLog(Abstract'Natural'Numbers#Coq@0K99'6''+k6'+@@AAAAtA@l@@@@@&double @!nC=<:k5@ 4@ +k= R'>99'G''+k6'^3AAt@@@@@Ҡ$succ @*k(dca&BinPos&PArith #Pos@=)a)BinPosDef@#Rl@Ak@ +k= R'>7 9'6''+k6'T+@Р1@@pABtA@p@@@@@$pred @lEj@@&pred_N!,:@4s)@w@ +k= R'>7$'G''+k6'^@TРg@@ABt@@@@@D(succ_pos @uݷwנ$q@'BinNums'Numbers#Coq@@!N7@ @(positive*@8TCABt@@@@@y#add @!mҐB C!qi@== R'> 7!9'''''+k6'+k6'@$Р@@DCBAC|@@@@@@#sub @?R="n'JW>B="m'OР@$mask=(@#Q@@@A@@A@@@@@@Dk @(sub_mask@@)Jطig`@5_gc@ +k()=A RV'>=- R='> 7!= R'>9'G'G''''G''+k6'+k6'+k6'Р-@@)('@@AAA@AA̠*@\Р0@@oAD|@0@@@@@#mul @hABgB@=N;@#F@x"@ 0+k()=) R4'>= R'> 7!9'G''G''+k6'+k6'c@$Рi@@AC|@"@@@@@I'compare @z{})Datatypes$Init}@*comparison;f@ڠ렜A뜠B 砜C@+#@, )Qڀ@ț򀶐)Datatypes$Init#Coq@@-;f@ +k()=( RQ'>= R.'> 7%'I''= R'>H'G'''+k6'+k6'+k6' Р@@)('AA|@H@pH@@@@@#eqb @@@ ۶1ܛ_@$boolZ'@ :M 9P?JALJBPN[ F@Q@.=C@/#F<@$NVR\@$boolZ'@ ,kk(*()=( RQ'>= R.'> 7%'H''= R'>H'G'''+k6'+k6'+k6'+7Tk+7T'6'̠TAAX>`&@@@@@#leb @+!y.@@@@@@@@@@@DYC@00@?H{{QQM@<@ +k() 7!= R'G'G'H''+k6'@@@A@B@A@Tx>=US@?H{hF@@@@@:#ltb @k@l@>=<:|@00W@?H{@նLӛu@ +k() 7!= R'H'G'H''+k6'98A@T4ht@@@@@h#min @@lkj @.00@/?H{@ +k() 7!= R'''''+k6'feA@Tah@@@@@#max @ƷJ@-@Z00@[?H{00"@0.. +k() 7!= R'''''+k6'A@Th@@@@@$div2 @ZS"p0R@AA@AA@@@@@@@D [`@)S@ 4+k=- R8'>= R'>9'>9'G''G''+k6'+k6'(}RADt"AABA@@AAt@@@@@$even @Q*EA6SBFB@Y1@ $+k=) R4'>= R'>H'>G'H''G''+k6'+k6'~ADtN,AAtl1@@@@@%#odd @}V@$negbk@> F@?>4܀@2)Datatypes$Init#Coq@@hZ'@ 8+k7 7$'!@X>4ܐX&df@@@@@Z#pow @@ݠ_D@=Rx@#Fu@ě򀛠n@ 4+k()=) R5'>= R'> 7!9'G''6''+k6'+k6'@(Р@@AC|@A@Р)@@@@@&square @4-,*@&@5,xր*@)@ +k= R'>7 9'G''+k6'TV+ABt@@@@@ʠ$log2 @"c \ʷ Y_^\@$size=)R@#R] @2\@ L+k=3 R>'>= R$'>7 9'>7 9'G''G''+k6'+k6'@[ADt+ ABt  @@@@@$ @X1V3@[@\AABtDT1@@@@@%(size_nat @}VX@#nat@A[@%t2T@ O@@#nat@ABt'Tk@@@@@_,pos_div_eucl @@@,pos_div_eucl!a!b"@$prodt@'BinNums'Numbers@@7@ _@ "a'BBB@@@@@!&&D+ȷ!rȐ"r'@C @D.^4'@@@@@@@@A?=@ T@3ECGA驚@^ @_.^4<@ c@3W@+@,'޺__G[aBEDC?>N<:@8@9'޺__ 0@8764@ T@331%@ @.^4.+@? c@@3-?%%3@W@X'޺_<-J00:Q77@€@t@ |,Bk(*()= MR!'> 3!= R'>7 7!= R' 7! 7 :' 7 :'''> 3!= R'>7 7!= Rw' 7! 7 :' 7 :'''=, R'>= R`'>6'>6'6''6'''+k677%'+k677%'+k677%'+k677%'+k677%'+k677%'+k677%'+7Tk+7T'677%'4@~'޺_TLBABAFA@A@<(gD`XD|t<4|t@.^40(@3 ADaAA\%@[3Ԡ hD@@@A@ABAA@@$|@@@@@p(div_eucl @@   uu"na@} @,}@-&`Ȁ @ ?!C l+k()=+ R='>= R'> 7%'L:''6''+k677%'+k677%'РA@@ؠ{@L&`ȐPHEAC|@AX@@@@@#div @US署r@#fst @`u^@a <@dDcB X+k() 7!777&' @|t@wu^@xh$D@@@@@&modulo @!"@#snd))7@u^@ o@wu3<@|tM@u^(@h#D@@@@@"#gcd @STVVZZ V@=DO@#F̀@̛͛w$AC|@d@@@@@X$ggcd @詛)Datatypes$Init@t@젩onB@@@@B   #@1=( }@2#Q^z!g 0"aa"bb'vɩz@34!@J +k()=W R'>=? Rw'> 7!= RP'>= R-'>9 9: 9:'''6 :''6 :''+k677!77%'+k677!77%'+k677!77%'+k677!77%'<ACĠA@A@0tl4 ĠY.AF|@U |<(ԠGAA@@d@@@@@ݠ'sqrtrem @5v7rpkomsBWV@@@@D{v}@3~ @7]%{t!s{%2}'E++bcH..@#@W@88  +k=K Rm'>7 = RL'>= R,'>9 9:'G 9:'G 9:'''6''+k677%'+k677%'+k677%'𠑤A@@L6AExX)ABO|AFt >TC@@@@@7$sqrt @hɠ7Ʃe@=)]H^@#RE@ŀA@TABtq@@@@@e#lor @N@=L@#F̀@͛䐰$%AC|@@@@@@$land @ʷ 3+)6!,@=(@#Q̀@)1-@ ,+k()=( R3'>= R'> 7%'G''G''+k6'+k6' Z/AC|@@@@@@Π%ldiff @@@ . ]  1 ` s0^ڷkiv]a\[l @=U@$'RW@?iqm@ ,Mk(*()=( R3'>= R'> 7%'''G''+k6'+k6'+7Tk+7T'6' -pT8oACX @@@@@ $lxor @f ? @e>@=(_7@#Q\@t ,+k()=( R3'>= R'> 7%'''''+k6'+k6' ` AC|@ M@@@@@ A*shiftl_nat @ r@(nat_rectb@" zڷ#. c@曠!n @@@@A h+k+ + 7&'6'6'KL(t \ @@@@@ |*shiftr_nat @ ;6 XY@>À @<75@0-+LRt ɐ\ @@@@@ &shiftl @> ׷  @+ B 6 @@5XH@K 5 'BinNums'Numbers#Coq@@!N7@ @ +k()= R'> 7!9'G''+k6'  n CAC@*d @@@@@ 堠&shiftr @}  >  @  ~ } = yl x v @$iter=(T @#Q # 0@; hx @<>Àt @' R |+ +k()= R'> 777#'''+k6'd :l  |AE@%t *@@@@@ +testbit_nat @ O  Q v @e   M@nTq F@6n  A@ě〶 ˛)Datatypes$Init#Coq@@#nat@k@ +k= R'>7$'+''H'+k+7T'6'  ABt̠*/T n@@@@@ b'testbit @       󩚠 @>4' @8g$@  ʛ@ +k()= R'> 7%'H''+k6'Р @@    AC@d@@@@@@ &to_nat @/  01 r *l ) ' @" @5L  % @; Zi@  J ABtT @@@@@ Š&of_nat @ @@A@A@@@@D %  ^ ̷   @+of_succ_natq @$ \ @ 2@ @4 (@@AAABt T @@@@@   @ W 0!A;ܠ@@!f@      g @{{   '    *@ m ̀@@A  BC +k()= R'>7# '''+k'  AE@El J@@;@2@A@A@4AUNf V&PArith#Coq@@A@@ I'of_uint @!d'Decimal@$uint):U@ }@7 B v@*`]? ޠ q@'Decimal$Init#Coq@@$uint):U@ ,+k7$'X @@@@@ &of_int @86@#int).J@@AAAA@@@@@D + E@&option >v@ ɩM@$norm)9փ "WUA Q][B @cP@#int).J@ =@# >v@" +k7 = R'>7 9'>G''+k67$'Рk` BAABAAB@>9X @@@@@ ࠠ'to_uint @ 8  y :  sBA z x @fz @9w v @ L v'Decimal$Init#Coq@@):U@ +k= R'>7$'6''+k6'  zABt!TA@l͐ 2@@@@@ &&to_int @ ~ WA @V.  G@ >@ 0+k7 9'X W@@@@@ K"eq @%Logic@ @@!x'BinNums'Numbers#Coq@@!N7@@A867 kD(L@@@@@AA@@A@(eq_equiv @/RelationClasses'Classes @.eq_equivalence()':@/RelationClasses'Classes#Coq@@+Equivalence~@E%Logic$Init@"eq @D=D2L@@@@@B"lt @!xO!yR}k@ x;f@  X @'compare00)BinNatDef @?H{BAB@" t! r T+k()H 7!77&'&x#l@@@@@@"gt @A?=8>C@H G  T+k()I 7!77&'LxIlѐ@@@@@@"le @ge@#notШ-@p ¶o А `+k()I 7!77"7$'uxrl@L@@@@@ՠ"ge @,@ 鶐 ' `+k()H 7!77"7$'xl @CL@@@@@÷ @!p!q 6@"ex @!rA@  @ 3BC@ r r4 +k() + 77%' 7!77&'\/lt'|at@@@HAA1DH%Logic$Init#Coq@@A@@D$Even @!nQFS!mVX@\Ba@(positive*@BC@ } |+k+ 77%'77!77&'Р[Px`dplAB@Hh@@@QAP@A@@#Odd @HFŰ3C@  >@ 3 KI=@V  +k+ 77%'6 77!7!77&'XtdlAB@P#dA@D|@@@A@A@@Π'succ_wd @)Morphisms@0reflexive_properm+@㩚 @*respectful%WO?ꚠ@ \@:reflexive_eq_dom_reflexive=[ @,eq_ReflexiveaN3@$succ ! @?\@)Morphisms'Classes#Coq@@&ProperL@./)Morphisms'Classes#Coq@@6%WO?=>@U \@  ! @ ?\ /6 67 7777  67777 + 7T7k6'8LGLU =xD|`Jhj\pht@@@@@H'pred_wd @zrqf@$pred @?U@Y@}~OFH@  @ ?U瀐D"LL xD|`hpht@@@@@&add_wd @@   @@@©Ƕ@ɛʚћҚl@  G@ 3 ^6 .67 7777  67777 +67T77  677777 +7T77 +7T7k6'6'+7T'6'֠TD @d<0LDhِppxp|;L@@@@@ڠ&sub_wd @ ONL@#sub c@3@뀰@@@܀!"䀚怚@  c@ 3P%T3D @d<0LDh(p;LKp=xp|@@@@@)&mul_wd @[@4@X@Z[,`@bc%6jk-/@  @ 3BnTGLD g@d<0LDhtppxp|@@@@@r%lt_wd @@ @   @#iffС)     @-iff_Reflexive/h9@P \@@@¶@%Logic$Init#Coq@@#iffС)o@y \ [6 + 67777  67777 +67T77  677777 +7T77 +7T7k6'6'+7T'6'$ؠH8 $X0$|@dOdpDL lOhxtx@@@@@㠠&div_wd @XWU@#div l@3@􀰶@@ @"#倩*+퀚@  l@ 3Y.T<D4L '@d<0LDh4pTpFxp|@@@@@2&mod_wd @d@&modulow@)1@C@g@ij;o@qr4Eyz<>@ w@ )1}TD s@d<0LDhppxp|AL@@@@@&pow_wd @󚠡3@#pow /@3@@@@țɚc@  >@ 3̠TڰD @d<0LDhϐppxp|AL@@@@@Р*testbit_wd @@ ݶ@ ޛ @$boolZ'@       @'testbit5z@-T|ŀ@􀰶@@ @"倩* 퀩b@"eq @@65z@7-T|ŀ g6 467 77 777 67 7777 +97T77 !67 77777 +7T77 +7T7k6'6'+7T'6'$6`9LGh, /$`T$X@$Truey@@(@%Falsee@A_RQ @)False_induُXC/;w ]w Ʃo ʩpbdE `@>< 7 t5r-@V5(kt.#C "p0Y@+sumbool_rec=_b5!s  D?C!a )@(eq_ind_r!2#~2 x? R%diseq$&absurd!A@'f_equal= {  !FʐE]R V 6C5&BinPos&PArith .#Pos@ @웠Z뛠^&Specif$Init#Coq@@'sumbool7̂K@@@E @ BA @#notШ-BA +k() + +9 +7#'()=8 R'> 7! +- +m +77"7 77"7# '+9'' +9'99+777$'= R'>'''+k6'L+ 779'9 977&'9977"7 9977"7%'LL +97777%'= R'>6'6''+k6'+k977"7 977"7%'= RS'>+ 9'6''9L +L7777%'= R'>6'6''+k6'+kL77"7 L77"7%'+7T'77"7 77"7%'D@`< {4X0H/X@@AAAA$H4DؠsPՠ䠒mĠGl,`8PDA@PPD\(@@@@@%discr @n Vp h@%sumor$|@p@#sig#* @GH iA jajBTUN_[V A]^ /W Yw$Ag m `@@@7$|@@#sig#* @#@(positive*@B?Bƀ(A@@7@A $+k= R'>G :9'6''+kG 77" + 77!7%'977&'𠑑fԠB@pא̠<ABtࠑr@@@@@J+binary_rect @!P@X2FR@@"f0"f2g@Jשs@&double@'޺_#fS2'v@S!@+succ_double @.^4Ƿ3Ȑ"P'e1Ȑ#f2'h@G H*Ȑ$fS2'@ I& :T@-positive_rect0ڀD<E@[@Ѐ\@YAYXo @CYZRx@DbT퀩EA `+k()=$ R='> L!+++7# '''9$'9$'9$'+k$'5z^AF@@@2F@@A@A@AGɠA'BinNums'Numbers#Coq@@A@@*binary_rec @@@@N o@@" PAONZ@LKJI^@GFEDA ,+k7$'X@@@@@*binary_ind @,@Զ@IAxAжwv@tsrq@Conmli(EX@@@@@D*peano_rect @@P2Y@@!f [@fd`ն\Ȑ"f'`ީpb@ِqnPJk驚D@-lXRW@%@.@#A/:@C&4CDA 0+k()=  R1'>+L!+7# '''9$'9$'+k$'.>"AE@@@2@W@A@A@YAF&BinPos&PArith#Coq@@A@@/peano_rect_base @@y@h@C2`e@@˩AWsDC@fڐtCA@CBA B@@2@(@A@A@*A@,A@AB@@젠/peano_rect_succ @@A@}2 e@@A~}@DA>DCB ABALDCBA@@2 @8@A@A@oHA1GK@A@A@BA@DA@FA@ABCD@@ @)peano_ind @̩@@@ q(ԩAӶҶж@=̶ʩgǐJX@@@@@ f)peano_rec @x&@@ pA@^萐k9X@@@@@ .peano_rec_base @@NB= A%A@~ 4BOCA^@D缙CBA B@@@@@ .peano_rec_succ @@{CjMƩARn?>@ aՐoZ~DA1DCB ABA?DCBA@@@@@ ,bi_induction @@D!A@ Զ@@h  6A@ @@\С)" $"ϛ = @@@@@ #)recursion @22 io @@ꐷ@8 @= @@A@@ _@ %M@ cP D+k+7$''d@@2 i@"@A@A@$A@A@@ T,recursion_wd @@Ec2 q @@#Aeq4Relation_Definitions)Relations#Coq@@(relation'JjAw@B@@?@[@=\pB@@H@ k@FAz@P@ s@N tV@B zBBAAdBAc@-)ɀB@@2 @W@A@A@A@A[AviA@@cAs@AdA@fA@hA8ӠA4Relation_Definitions)Relations#Coq@@ABCD@@ Ѡ+recursion_0 @@F2 es @@A@ @ CBCBAAB@@2 e@ @A@A@"A @$A@AB@@ .recursion_succ @@G2 u @@A!BǶ@ ?@-@CBB@ *@@ @&: (GG ն  ^!"Q " V 䩚,[ @@2 @E@A@A@^A @A_A"@LA@ABMA @OAd@QA0@SA@ABCD@@ b(one_succ @@)HS@X@Bzy;@@ *@C ]kA@@@@@ (two_succ @@QIC{@(B(@B-C :B9C@@@@@ &pred_0 @@|Jn YAA@@@@@ ͠-pos_pred_spec @@K қ'BinNums'Numbers#Coq@@(positive*@@!N7@&BinPos&PArith#Coq@#Pos@&pred_N!,)BinPosDef&PArith#Coq@#Pos@&pred_N4s)A =BA@@@@@ -succ_pos_spec @@L MрQ@VB@jB@k񀐐A A@@@@@ ;-pos_pred_succ @@M ra[!AA@@@@@ U-succ_pos_pred @@N Z ?yABA@@@@@ t)pred_succ @@;O 0 /ש  bAA@@@@@ (pred_sub @@UP J者I񩚠 4A A5B E@@@@@ ,succ_0_discr @@tQ iD[lJ AA@@@@@ ɠ'add_0_l @@R @  !AAA@@@@@ 䠠*add_succ_l @@S { ѩө ԀBA ڀ+BA@@@@@ 'sub_0_r @@T ŀ@ c AAA@@@@@ %*sub_succ_r @@U ȶ ‰ȩB A ׀+BA@@@@@ K'mul_0_l @@V @  EAAIA@@@@@ h*mul_succ_l @@/W $ !Ʃ%ȩ XBA-BAA@@@@@ &eqb_eq @@VX KC HAPGY@ Y4@3BA)Datatypes$Init#Coq@@$boolZ'@AkhBA@@@@@  <b_lt @@Y ~Ҷ {Щ@ qg@3BA3A )BA@@@@@ ꠠ&leb_le @@Z  怠f@ T@3BA[A@ c \BA@@@@@.compare_eq_iff @@[ $ "Հ(@a00@b?H{BA@*comparison;f@A逰BBA@@@@@@.compare_lt_iff @@\ P N<T,BA)B BA@@@@@e.compare_le_iff @@,] !u sa*}UBARC|BA@@@@@/compare_antisym @@U^ J GKvAB@'CompOppBA@@@@@,compare_spec @@@N!S+OrdersFacts*Structures#Coq@x@@ T@@~ T^@2@A@A @@  @A@B l@@ l @A@ Y@@ Y5@A@AC #@@: #l@<3n@A@ T@@g T@A@AD "@@ "t@3m@A@ q@@2 q@A@A @@ @3@A@B @@  @ 3`@A@ @@i  @A@A ~@@W ~@Y3@A@ =@@b =@d3@A@ABC @@+ ˑ W@A@ c@@ c @A@ @@J @L3J@A@AB hx@@ hx@>@A@CDE @@ @>4@A@ @@D Б@F>U@A@A @@ @>:@A@ 3"@@  3"@>m@A@ F)@@ F)@>t@A@ABCF S@@ S@>@A@ @@  @A@A @@ ܑ@?'@A@B !@@ !@?@A@ ! @@ !  @A@ !7@@ !7@@P@A@ABC *@@ *@@A@B@@B%@A@AD.@ @.@MS@A@u^@@ku^@m @A@A}@@}@&`@A@@@=@?'޺_@A@Aw@@wɑ @A@BCEK@ @kK@m)j,I@A@K@%@,K@.)j2_@A@I@+@QI@S*O@A@AO@/@O @*O@A@,@4@e,@g*ow@A@ABCFZ@8@Z@*81@A@`@>@s`@u*9G@A@e@C@eđ@+@A@+{@H@7+{ё$@9,J@A@ABC5z@L@5z @A@ @R@> ͑.@@.@A@ @W@ 3@.^4@A@AB00@[@00~@A@2kF@_@2kF;@{@A@AC5Z@c@5Z?@y/@A@5f}@h@5f}D@4@A@ADEGH@A@@M!Op@A@@L!Fv@A@@K!C |@A@@J!E@@ T@@!t TJ@A@ \@@"eq \^@A@AB @C l   #BD "E F SH@A@+OrdersFacts*Structures#Coq@.BoolOrderFacts@@@A@@76CompareBasedOrderFacts @@@A@@@IB?E@A@@H<E?@@ x@D@'compare xd@@A@A@A@@GCRF@@&d@L@@&dJ@@A@A&@@=&^@@A@&Y@@"le&Yh@@A@&h@ @"lt&hh@@A@ABC@A@hn!xӶ!y֩)Datatypes$Init#Coq@@+CompareSpec!Q]@jABA@  \BA@( \AB@J00)BA@@@@@AA@@A@*compare_eq @zrma@oHG@%Logic$Init#Coq@@"eq @)Datatypes$Init#Coq@@*comparison;f@G@00iBAk@*comparison;f@AͰCB@@@@@K,compare_refl @Ϡ @pbE:t@00AA-A@@@ %'A*Equalities*Structures#Coq@A݋X_A/RelationClasses'Classes#Coq@@A@@.compare_gt_iff @*-(#@/q}@#iffС)z@00րBAmC@ \AB@@@@@.compare_ge_iff @`c^YT</'"@er϶ѩ6@#notШ@100BAB@' \AB@@@@@/compare_ngt_iff @via\P@s7 6 p:멚%@h00GBACM4@] \AB@@@@@-/compare_nlt_iff @ՠؠӠΠɠ@trDqFu1&`@00BABo@ \BA@@@@@h/compare_nle_iff @ ߠנҠ@u怠h]@00BAPC@ \BA@@@@@/compare_nge_iff @GJE@;# @Lv@00BAB@  \AB@@@@@֠)lt_irrefl @~|wrZME@4@w@( \AA@@@@@+lt_eq_cases @|ogbV@x!n!mx%@S \BA@"or @5@^ \BABA@@@@@2)leb_spec0 @mJΠݠܠ@@!t&dv $Bool @+iff_reflect s1@"le&YAL @#leb( ~ /RelationClasses'Classes)@(symmetry0xjA%Logic$Init6@С)@-iff_Symmetric!x@"eq @)Datatypes@$boolZ'@5 A@N6X@&leb_leFB;>94/@$Bool#Coq@@'reflectc@@ \BA@^ TBA +k() 7!7!L7!77"7777 7! 7!7&'(vDi̠bz\ShIpsepn|g@@@@@(leb_spec @v@y3 2 1@(BoolSpecޜ@ @K \BA %@N \AB -@ TyBA@@@@@&)ltb_spec0 @谩@"lt&hߩ@#ltb( Ʃ @<b_ltdܠ@ S U g@ \BA o@& q〠BA(9D 9\,̠h@$boolZ'@ @ TABA@$boolZ'@B!!@6 \BA@@@@@&leb_gt @@|B!A!{=!,@ TxBA7B!7@` \AB@@@@@0'ltb_nlt @ؠ۠֠Ѡ̠@}q!Cp!E,l![@ qπBAfB!j@ \BA@@@@@c<b_ge @  @ ~!v!x݀_!@E qBAB!@ \AB@@@@@(leb_refl @:=83.@;!ȩ!@I TAAA@@@CA;@A@@+leb_antisym @]`[VQ9@^@!ȶ!ʩ!@n T(AB@$negb!@ q_BA@@@@@䠠*ltb_irrefl @h@A%!ڀ" @ q}AAB@@@A@A@@+ltb_antisym @@BH"G"?".@ qABR":@ TBA@@@@@3+eqb_compare @۠ޠ٠ԠϠ@Ct"Fs"H+)Datatypes$Init@$boolZ'@"e@#eqb Y BA4@@@@@@@@@@@D<"y@00BAABB@@@@@|+ltb_compare @$'"@%D""t"@Z qBAq@=<@@@@D;vé"@00ՀBABAB@@@@@+leb_compare @^a\WR:@_E"ɶ"˩"@o T)BA@wv@@@@Du"@000BAAAB@@@@@%min_l @@#_ [ Y@NBAb#@| pKK@@@@@j%min_r @@#1`& v# |@mAB.h@@@@@%max_l @@#NaC @ @ABKr#T@ =@@@@@%max_r @@#mbb _ @BAjZZ@@@@@à)lt_succ_r @@#c Ӷ|"\ BAӀBA@@@@@堠'eq_refl @/RelationClasses'Classes#Coq@@5Equivalence_Reflexive@1@#two>T@@A@AI@5@$predId@@A@G@:@$succGr@@A@@?@$zeroT@@A@ABCDE@A@@Mfxw@]@@@d@!tРJ@@A@A L@@"eq L^@@A@r@ @#onerT@@A@AB4@@#two4T@@A@b@@$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((@@@)SymmetricFgq('TܐL@. U\ސDؠw$aXB;ܠ͠w^Mc_@@V@@L(eq_trans @D@6Equivalence_TransitiveW(e(@=@O@*Transitive++-(p</T%LA@W\'D!ӠmZIB,%@/٠@@@@*eq_sym_iff @D}%͠Ġle OH9ʠcR@N@!x)$@@@<@A8ӠA4Relation_Definitions)Relations@AB@@/succ_inj_wd_neg @j, K3,Ԡ͠un_ ߠx@tE*`*a"琩$*u@ ! }*z@ ! |$('@@@@@$1central_induction @cS@ڠ*!ɠ jc @'@F!A@*A$A_wd@&ProperL@* @*respectful%WO?*4oa*@)@>*uEé*@/ ! ʶJ*F͐@@@@@q'add_0_r @:'ϠwnXQtc@@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@,@$zero,筷T@@A@ABCDE@A@E@+a%+q@ +6@@@p@@@ABC@@AA@@A@*add_succ_r @]M:Ԡ|$àd]:!|n@yA++%򩚠+@1 :Q+@ ! Ҁ+@ ! ׀+@B Kba@@F@@C-add_succ_comm @۠z'd[E>ߠРzaPҠ͠@B_+ն]+֩[&2+@q z+@S ! +@| +@^ ! @@@@(add_comm @ܠ̠fSB;ܠ}%, @C,,&q,%@ n,*@ Ր@@@@'add_1_l @N/נΠvoYRCԠà`SE@/!@,D,HͰ&,X@ 쀠,,^@ ! `@@@@頠'add_1_r @C3 ͠b JCv xsbT@_E,{ &ש,@ 5,4,@ ! @@@@)add_assoc @vfS=4ܠՠ}vS:)Ơ@F8,6,!p, 7',@M V1,@S \,@X a,@^ gB~}@@b@@_,add_cancel_l @C0ؠwaZ}l ؠ@G{,y,C, z'Q-@ t- @  '^{@@@@,add_cancel_r @ 0Ϡ|iXQ;4%ϠB5'"@H-*-+|-, '->@ Ҁ詚-D@ ؀ '@@@@Ѡ,add_shuffle0 @ i +  J2+Ӡ̠tm^ޠ{n`[J<@GI-c-d-e '-u@   -{@  $-@  -@  H0@@@@,add_shuffle1 @  k [ H2)Ѡʠrk H/|@J--+--!q-!-(-@ C L-@ I R--@ O X -@ T ]-@ Z cz-@ ` i@@c@@`,add_shuffle2 @     D 1٠x b[~m ٠@K|-z-D-O-!z(Q.@  . @  M.@  Y.@  .@  ]ũ.!@  N@@@@,add_shuffle3 @ D     } %͠Ġle OH9ʠVI;6%@"L.>.?.@!Ű(.P@  䀠.V@  .[@  .a@  #@@@@젠'sub_1_r @  F 6 # Р  e  MFy# {veW@bM.~"(ک.@  cҀ8.7.@  v@@"@@'mul_0_r @  y i V    @ 7ߠؠy! V=,ɠ@@8."3) .@ < h..@@M@@AA@@A@*mul_succ_r @     1  Ơ n e  OHڠkZ@Af.ܶd.ݩ"b)9.@ k 耠.@ Z !  .@  .@ | G@@@@?(mul_comm @ !  Ӡ  m Z    I B,%3&@1B//")u/)@  $r/.@  )@@@@o/mul_add_distr_r @ Q      2 ڠ Ѡ y r  \UFנƠcVH@aC/H/I/J"ϰ)/Z@  U/`@   /e@  /k@  f-/p@  k@@@@/mul_add_distr_l @  U E 2 ߠ ̠ t     \ U2@D///#)詚/@   /@ -  6멚/@ 2  ;/@ + ک/@ 0 t@@@@@)mul_assoc @ ՠ   t !   ^ U     ? 8٠ʠt[Jڠ@EV/̶T/Ͷ/Ω#S**/@ \ ـM/@ b ߀-/@ g 䀠/@ m @@}@@0'mul_1_l @  Ԡ Ġ  ^ K    : 3 ۠ Ԡ | u   $ @"F0 #*e0@   /Ð@@@@['mul_1_r @ =   ܠ  v  Ơ  e ^     H A 2ܠàOB4@MG04#*0D@   ?/@@@@,mul_shuffle0 @ h *     I     1 * Ҡ ˠ s l ] ݠzm_@xH0_0`0a#*0q@   l0w@   r 0|@   w0@   }D,@@@@à,mul_shuffle1 @  g W D  ޠ  . % ͠ Ơ n g      D + @I&0$000$$*0@ -  0@ 3  0@ 8  0@ =  0@ C  0@ H  ŀ@@X@@ ,mul_shuffle2 @     9 & Π v m     W P     s b@Jn0l060A0$l+C0@ u  򀠩0@ {  ?1@   K1@  !1 @  !򩚠1@  ! ?@@@@S,mul_shuffle3 @ 5   Ԡ  n    ] V     @ 9 * Ԡ  G:,@EK1,1-~1.$+1>@  !91D@  !?1I@  !D1O@  !J@@@@%le_wd @ r 4 $    S     ; 4 ܠ ՠ } v g   砠@@A&NZBase'NZOrder&NatInt'Numbers#Coq@  @A@'NZOrder&NatInt'Numbers#Coq@+NZOrderProp  @A@@@@"NZ  @A@@鰶@1@11@1%1%Q1@ 3 \@@,@@AA@@A@*lt_le_incl @ Ġ  v c    M D     . ' Ϡ Ƞ  c J 9RE7@PAE1C1@1@"lt \1@ f \@@@@@3'le_refl @     @ - ՠ } t     ^ W     z iug@Bu1멚1@  \@@ x@@\.lt_succ_diag_r @ ߠ Ϡ  i V    E >  ߠ   ( !    @C22"@W \̩2(@  ! #N*@@@@@.le_succ_diag_r @K      , Ԡ ˠ s l     V O @  Ѡ ٠̠@D2B2P@  \2V@  ! #|X@@@@@/neq_succ_diag_l @y;+ Š  Z     B ;  ܠ  } n   @E2p%,Ω2@  ! # +@@@@䠠/neq_succ_diag_r @gWD  ޠ  . % ͠ Ơ n g      D + 3&@1F &2 &#, R2@ ! #Ԁ@@@@@/nlt_succ_diag_l @Ѡp   Z Q     ; 4 ܠ ՠ Ơ p W F_RD@]G R2ȩ L2@  \2@E ! $ @@@@@@/nle_succ_diag_l @àM:    ) " ʠ à k d      vt@H 2 |3@ \3@u ! $4  @@@@@p)le_succ_l @1Р}j   Y R     < 5 & Р  @I 3( 3) ꠩39@ \3?@ ! $e G 詚3D@y \@@ C@@+le_gt_cases @g)H     0 ) Ѡ ʠ r k \   ܠ@J 3^ 3_ !@"or @3u@  \3z@ \P@@@@ܠ-lt_trichotomy @_O<֠~& Š  f _      < # +@)K 3 363@ \='#- S R3@ \@@@@@(lt_asymm @Ѡp ZQ     ; 4 ܠ ՠ Ơ p W F_RD@]L R3ȶ P3ɶ@3@  \! S3@ \  N@@ @@B(lt_trans @ŠO<+$ ̠ Š m f      xv@M 3 3L3@4 @@ \8@4@F \>4@K \ W @@ @@y(le_trans @:٠sàb[    E > / ٠  Ƞ@N 41 4243@4B@ \o@4H@ \u4M@ \7@@@@+lt_strorder @p2"Q92 ڠ Ӡ { t e   @O@+StrictOrder.[@4n4{@ \@@ @@ݠ+le_preorder @`P=נ'Ơg`    = $ ,@*P@(PreOrder@44@> \@@ '@@ /le_partialorder @̠~kUL6/ נ Р  k R AZM?@XQ-@,PartialOrder5͛4(N4@&4@o \4@^Tl@@@ @A @ ^@ _AhCD@ABC@@G)lt_compat @4@%lt_wd @ L@4@4 U G4@4 X(w J4 Z(y 5@6 \@y@@%lt_wd']ɠ&ؠŠr_NG1* Š  @@@@@(lt_total @52@x*\@ 5* 5+̠5;@p \ Ӡ(/  詚5D@y \ C@aǠd&E-&ΠǠohY  ٠@@@@@Ġ'le_lteq @5p@+lt_eq_cases 6@ 5i 5j +5z@ \ é5@ \ ʩ(/ - ,@+lt_eq_cases&ydTA۠+"ʠàkd A(0#@@@@@0Private_OrderTac5A'IsTotal5 A @5@ @@+Equivalence~@5)@@(eq_equiv7L/Ġlc MFؠiXqdV@@@@@C @5@>@5皠5@) \@,Q^ԠĠ^K:3۠Ԡ|u@@@@@r+ @6@3p@ u@6@6 ~ p6@6 ) s6 ) ݚ6*@_ \)F'ϠƠngQJ;̠ԠǠ@@@@@  @6Q@(s@ 6I 6J렩6Z@ \ )ذ0  6c@ \ 9A1ˠ`HAt @@@@@ߠ @6@#r@ 6 6 D6@( \ ܩ+6@ \ *0 F EzjWA8٠z"àW>-F9+@@@@@@@@@@#Tac6A, @.àkb LEנhWpcU@@D!P)OrdersTac*Structures#Coq@~hLE@@@A@@C!Ok@@&@r@!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@'@$zero&CT@@A@ABCDE@A@G,MakeOrderTacBs?@A@@@BONR@@@A@@AEUH@@@N@!tJ@@A@A$:@@"eq$:^@@A@$@ @"le$h@@A@$@@"lt$ h@@A@ABC@A@+*OrderFacts.#@A@@s@7Q*ְ1@@@@AA@@A@ @C3 ͠b JCv ZSM2@AD7~7@! \@@ @@0)lt_irrefl @qaN8/נРxqN5$=0"͠{`@Br707@ \Ð@@:@@`- @ޠ}*g^HAӠ}dSl_Q@C7۶7ܶ@+b29+d2;X@@h@@*le_antisym @ ϠYF5.֠Ϡwp+ߠ٠@,D8 8 @8@ \ c@8 @ \A+2sc@@@@ƠŐ @D}%͠Ġle OH9ʠҠŠbR@cE8A8B@ǐ+ʰ2ː+ΰ2@@@@@*interp_ord @!o)OrdersTac@#ordȠ@ @@@@@@@@@@@D@8i@8j +𚠐8x@ \8|@ \@@8u@8v ܐ +k= R'6'6'6''+k+7T'+7T'6'ࠒA@@"lt\ @R@"eq8L@TlР@@Ƞ@@=<;@@A@B@A@xA܀̠~kUL6/נРkRAZM?ڠ}@@@@@t%trans @?,Ԡ|s]Vyhtf̠Š@F"o'88H8@9bJ@7SHv@9kS@7S 9rZ@7S@)trans_ord-0uGV`@@@@ĠH @9!9"u9#93v@^EМA@9/9091@,3@,3,3 L+k() LL7#'@z$ti+J2+Ӡ̠tm^ޠܠwB;5@@@@@V @49n29o9p9@EМ!C.-@B9|@9}9~@9@" \ @9@( \ 9@- \ L+k() NN7#'Vt}mZD;ܠ}%ƠZA0I<.٠ɠl@@@@@cߐ @999©9-@EМsBD@9ζ9϶"9ж@9@ \ @9@ \ 9@ \Ԑ L+k() MM7#'t ϠYF5.֠Ϡwp+ߠ٠@@@@@+le_lt_trans @::g::%h@PES@::r: @:/@ \ \@:5@j \ b::@o \$ L+k() MN7#'t]>ݠ~&ǠhaRҠޠР{k6/)@@@@@+lt_le_trans @):c':d:e:u@E @4:n2:o:p@:@ \ @:@ \ :@ \t L+k() NM7#'Hto_L6-ՠΠvoL3" ; . ˠy^@@@@@U%eq_lt @y:w::: @E4po@:::@.F5:v@:@  \ :@  \ L+k() ML7#'tF3۠z"àd]o  { mӠ̠Ơ@@@@@%lt_eq @;;T;;mU@=E@@; ; _; @;@ Q \I@.5pɩ;$@ Y \ L+k() LM7#'tG (РǠoh RK<͠ ՠ Ƞ eU @@@@@%eq_le @;M;N;O;_@E,  @;X;Y;Z@.5@;l@ \;q@ \[ L+k() NL7#'/tVF3͠u]V3  "  mf`E@@@@@<%le_eq @`;^;;;@E,yWV@k;i;;@;@K \@/36 'c;@S \ L+k() LN7#'|t- ja KD֠gV o b T@@@@@&eq_neq @ʠTA0)Ѡʠrk }   {&ڠԠ@'G<<Y<@/6d@/6i©/6m\@@@@@&neq_eq @?ޠx Ƞg`JC4ޠŠ ͠  ]M @^H<<<=<>@Ð/ư6@/ɰ6ʐ/Ͱ6@@@@@*not_neq_eq @v8( W?8٠zk   OHB'@I9=@1=8ml=@] \@@@@@ *(lt_stepl @7$̠tk UNq` y l ^@ wU==6=@=@ ( \ @1p8G7=@ 0 \j=@@@@@ ^(lt_stepr @ѠkXG@*#   @ V>>j>@>'@ \ \T@18{ԩ>/@ d \ @@@@@ (le_stepl @R3۠Ҡzs]VGؠǠ  Ӡ @ W>I >J>K@>Z@ \@1װ8>b@ \g@@@@@ Ġ(le_stepr @G7$ѠfNGz$    @ XB>|@>}>~@>@" \@2 8:>@* \ @@@@@  @yiV@7ߠؠy! V=, E 8 *@ CY8>6>>@>@T \@>@  \򩚠>@  \ @@@@@ ,i @8%͠ul VOra z m _@ xZm>k>5>@>@ ) \!@>@ \'>@ 4 \ @@@@@ a+le_antisymm @"Ԡn[JC-&   @ [??@?)@ \r@?/@ \ P29r@@@@@ )le_succ_r @T5ݠԠ|u_XIڠɠ  ՠ @ \?K?L ?\@ \?b@ ! 0d ?i@ \29?p@ ! 0r@@@@@ Ҡ)lt_succ_l @UE2ߠ̠t\U2!@]??@?@  \?@ ! 0ƀI?@  \Ґ@@@@@,le_le_succ_r @ȠzgQH2+Ӡ̠gN=VI;@T^I?G?@?@d \?@i \C?@A ! 1@@@@@<,lt_lt_succ_r @I6ޠ}%Ơg`r~p@_~?|?@@@9 \M@ @> \x@@v ! 15@@@@@q,succ_lt_mono @2Ѡ~kZS=6'Ѡ@`@)@*렩@:@o \@?@t \@E@ ! 1kM@J@ ! 1pL@@@@@,succ_le_mono @m/ N6/נРxqb @a@d@e&@u@  \@z@ \@@ ! 1@@ ! 1@@@@@砠<_0_1 @jZG1(Рɠqj G.6)@4b@@ \@q@U@@@@&le_0_1 @Рo YP:3۠ԠŠoVE^QC@\c@@i \@@}@@@@@7<_1_2 @D1٠x b[~myk@d@@1 \@@@@@@_<_0_2 @ ҠlYHA+$@eA$@Y \@@@@@@&le_0_2 @H )ѠȠpi SL=Π֠ɠ@fAL@ \A@А@@@@@<_1_l @p2"Q92ڠӠ{te@gAgAh@Aw@ \A<"@A~@ \A@ \A,@@@@@@ABC@@頠+lt_ge_cases @l\I3*Ҡˠsl I08+@6h+A)ACA@ \A@L \@@@@@+le_ge_cases @ڠy&cZD=ޠϠy`Oh[M@fi[AѶYAҩsA@w \+A@| \@@@@@I+lt_gt_cases @ ̠VC2+Ӡ̠tm}@jBBà5ؠ(Ǡha >%- @+m BBXB@< \"B@ \@@@@@&nlt_ge @Ѡp ZQ;4ܠՠƠpWF_RD@]nRBȶPBɩOB@ \$B@u \@@@@@B,lt_decidable @ŠO<+$̠Šmfxv@oBBÐC @@ \T@@@@@m<_dne @.͠zgVO92#͠@pC%C&砩C:@o \C?@t \@@@@@&nle_gt @b$C+$̠ŠmfWנ@qCYCZCl@ \Cq@ \G@@@@@Ӡ<_nge @VF3͠u]V3 "@ rCCMC@ \C@8 \y@@@@@,le_decidable @ƠxeOF0)ѠʠeL;TG9@RsGCECC@c \@@@@@0&le_dne @=*Ҡzq[Twfrd@}trCpCoqC@ \FD@ \K@@@@@d*nlt_succ_r @ %נĠq^MF0)Ġ@uDDޠD/@d \٩D5@ ! 5[=D:@o \@@@@@5lt_exists_pred_strong @ ]  >ݠ~&ǠhaRҠޠ@vDTDUDV@De@ \'@Dk@  \$@"ex @Dj!kDm렩7>D@ ! 5D@  \.@@@@A@@A@AРD.Morphisms_Prop @ A1@DH@ABCD@@.lt_exists_pred @  x h U ?6ޠנx U<+D7)@BwD8D@D@ \RDLD58>?2D@ 0 ! 5˩D@ c \@@@?@A@@1,lt_succ_pred @     > +Ӡ{r\Uxgse@~x;DtD@D@. \B8u?LE@ g ! 6&E@ r 5@@@@A@F@@{@ABCD@@m&rs_rs' @!.   ͠ z g VO92#͠@y@E&@E*E,8޶E-@}@E0@E?@  \@wI #EH@  ! 6nEA@EP@  \5@EJEK@EZ@  \ <@Ea@ \KkH@@_@@Ǡ(rs'_rs'' @!!J!:!' Ԡ  i  QJ}' @z@Eⰶ@EE9 F8E@E@E@!- \@EE@E@!7 \L@E@ \ʩIcd.Ee2E0E@E@!M \@E@ \AE?E@E@!\ \%@E@ \$E@!: ! 6Ր@@@@5%rbase @!!!!!B!/ נ  v  `Y|kwi@{V@ETAE勺{EyE@F@! \ö@F@< \(\ @@@@@i)A'A_right @"*!!ܠ!ɠ!v!c!    R K5.ɠ@|@F"uF#@F%F'F(@F7@! \@F=@r \^ @F6@FE@! \N@@@@@6strong_right_induction @"i"+""!!!J     2 +Ӡ̠tm^ޠ@}ɶ@FaǶũð@Fe˩Fg9'Fh@Fj@Fy@" \¶@FsFt@F@" \@F@ \޶ F@F@"% \RP@@@@A@@ @ABC@@/right_induction @""y"i"V"!!!@!7 ߠ ؠ  y !  V=,E8*@C~@F@F F::ugF@@CF@F@"] \@ F@"7 ! 7RFȶ@F@"l \ @@@@@:0right_induction' @"""""G"4!ܠ!!{!#! Ġ  e ^ p|n@[@FYWU@F]OF_:~LF@F@G @" \ƶ@G@G@" \ն@ԩ G@" ! 8AӶGS@@@@~7strong_right_induction' @#?#""ޠ""x" !Ƞ!!g!`!!   J C 4ޠŠ͠@@@G7@G;G=:G>@G@@GO@" \% @GH@GW@" \@GQGR@Ga@" \ݶ@Gg@ \J!q,Ga@@@@@̠&ls_ls' @##O#?#,"٠"Ơ"n"" !!!V!O      ,  @A@G簶@GG;K=G@ܶ@G@G@ \@֐G@#  ! 8̀i(G@G@#B \W@2G0G@G@#M \b@G@#T \^G@#, ! 8b@@A@@'(ls'_ls'' @#####4#!"ɠ"q"h"" !!!R!K   ݠ  n ]vi[@tBH@GFDB@GJ<GL;k9G@sG@G@# \ζ@|GzG@H@# \C@H @# \6`H@#v ! 95dHȠH H @H@# \@H!@# \Nx#HH@H*@# \(@H0@# \]H6@# ! 9\8@@@@%lbase @$Y$$ ####:""٠""z"""!à!!d!]!N  ߠ Πڠ@C@HQHRHTHU@Hd@# \_@Hj@# \Hp@# ! 9r@@@@@Ҡ(A'A_left @$$U$E$2#ߠ#̠#t##"""\"U!!!!!!2!!!@D@HH@HHH@H@$5 \@H@$; \i(H@H@$B \h@@ +@@5strong_left_induction @$Р$$$o$$ ##Y#P""""":"3!۠!Ԡ!Š!o!V!E^QC@\E0@H.,*@H2$H4!X!J@!MJh@!'J@J@&A \Jq!V@i吩J@& ! ;ۀm@!8J@J@ \!gJ@J@&- ! ; !HJ@@@@@)2order_induction'_0 @&&&&&6&#%ˠ%s%j%% $$$T$M###ߠ##p#_xk]@vL J@J H F D@J L >J N>m!!@!J@!wJ@J@& \J!@ 5K@&l ! <+@!J@K @& \!JҶ@ϩ񐩚K@& ;ζ!K N@@@@@y<_ind @':&&&٠&&s&%à%%b%[%$$$$E$>$/#٠##Ƞ@M @K2   @K6  K8 >!!!K9@!KJ@& ! LN@' \{LS@ \ @@@#A𱍠G@#A7iA@AB@@%gt_wf @(~(@(0('ʠ''_'&&&&G&@%%%%%s%%$ @ R"LuCLw#Lx#LyL@ \ _L@(# \@@;@@-add_lt_mono_l @((s(c(P'''':'1&٠&Ҡ&z&s&&%%%%P%7%&@%"@#/L#-LL#hL@ \䩚L@ \L@(M =VL@(R =[ @@!U@@AA@@A@-add_lt_mono_r @(((((9(&'Π'v'm''&&&W&P%%%%%s%b@%^A#kL#iL 3L#L@( \ L@- \L@( =M@( =!L@@!@@<+add_lt_mono @)&((ؠ(Š(r(_('''N'G&&&&&1&*&%Š%%@%B#M#M lMwM@M,@a \n@M2@g \ _M7@l \M=@( =р"t#MC@( =׀-@@@@@|-add_le_mono_l @)f)())(((G'''''/'(&Р&ɠ&q&j&[&%%@%C#MZ#M[ M\$Ml@) \ Mq@) \Mw@) >  rM|@) >!R@@" @@-add_le_mono_r @))a)Q)>((ؠ(((('Ǡ''h'a' '&&&&>&%&@&D$M$M M$VM@): \ ҩM@)? \M@); >D rM@)@ >I!@@"C@@+add_le_mono @)ؠ)))w)$)((a(X(''''B';&&ܠ&͠&w&^&M@&IE$VM̶$TMͶ!Mζ )M϶@M@)s \ @M@)y \!M@)~ \M@)z >M@) >ސ@@@@@-.add_lt_le_mono @*)٠)ɠ))c)P((((?(8''٠''z'"'' &&&@&F$N $N !]N  hN@N@R \ _@N#@) \!PN(@] \N.@) >€񩚠N3@) >ǀ@@@@@l.add_le_lt_mono @*V**))))7(ߠ(֠(~(w(('''a'Z'K&&ܠ&@&G$NJ$NK!NL NM@N\@) \ @Nb@ \!Ng@ \Nm@) ?0Nr@) ?\@@@@@+add_pos_pos @**W*G*4))Π)v))(((^(W''''''4'' @'H%N%N@N@ \N^%D@N@ \Ne%KN@ \NkN@*7 ?@ @@ (@@堠.add_pos_nonneg @*Ϡ***n**))X)O(((((9(2'ڠ'Ӡ'Ġ'n'U'D@'@I%MNö%KNĶ@N@ \N%~@N@*o \N%N@ \NN@*q ?z!(@@ b@@.add_nonneg_pos @+ *ˠ***U*B))))1)*(Ҡ(ˠ(s(l(( ''''~@'zJ%N%N@O @* \N%@O@I \N%O@O \NߩO @* ?!b@@ @@Y1add_nonneg_nonneg @+C+****|*$)̠)à)k)d) )(((N(G(8''ɠ'@'K%O7%O8@OG@* \O %@ON@* \O%OT@* \OOZ@* ?!@@ @@,lt_add_pos_l @+}+?+/+*ɠ**^*))))F)?(((((r(('@'L%Oq%Or@O@ \OF&,O@ \&2O@+ @!"@@@%@' @AB@@Ƞ,lt_add_pos_r @++t+d+Q****;*2)ڠ)Ӡ){)t))((((Q(8('@(#M&0O&.O@O@ \O{&aO@ \&gO@+M @V@@%@@,le_lt_add_lt @+++++1+*Ơ*n*e* *)))O)H(((ڠ((k(Z@(VN&cOٶ&aOڶ#+O۶"6Oܶ@O@+ \"-@O@& \O@+ @O@+ @&%=P@7 \"D@@@@@;,lt_le_add_lt @,%++נ+Ġ+q+^+***M*F)))))0)))(Ġ((@(O&P&P#kP"vP@P+@` \"m@P1@+ \P7@+ @ˀ<P<@+ @Ѐ@PA@v \"@@@@@z,le_le_add_le @,d,&,,+++E*****-*&)Π)Ǡ)o)h)Y)((@(P&PX&PY#PZ"P[@Pj@+ \"@Pp@, \Pv@, A {P{@, AP@, \"@@@@@,add_lt_cases @,,e,U,B++ܠ++,+#*ˠ*Ġ*l*e* *))))B)))@)Q'!P'P#P"P@P@ \P@,: AC"񩚠P@,? AH$LP@ \P@ \"@@@@@,add_le_cases @,,,,,/,+Ġ+l+c+ +***M*F)))ؠ))i)X@)TR'aP׶'_Pض$)Pٶ#4Pڶ@P@,~ \P@,z A#1P@, A%=P@, \婚Q@, \#1@@@@@9-add_neg_cases @-#,,ՠ, ,o,\,+++K+D*****.*'*) ))@)S'Q'Q@Q'@\ \Q-@, A%vPŠQ4@i \'PQ:@o \'P@@':@@t-add_pos_cases @-^- -,,,,?++ޠ+++'+ *Ƞ**i*b*S)))@)T'QR'QS@Qb@ \Q'Qh@, A%Qo@ \Q4'ީQu@ \Q:( @@@@0add_nonpos_cases @--[-K-8,,Ҡ,z,",+++b+[+*****8**@* U(Q(Q@Q@-2 \Q@-. B7%Qg;Q@-? \(QoQ@-E \([Qu@@'@@ꠠ0add_nonneg_cases @-Ԡ---s- - ,,],T+++++>+7*ߠ*ؠ*ɠ*s*Z*I@*EV(RQȶ(PQɶ@Q@-m \QQ@-i Br&'vQ@-z \Q(TQ@- \Q(@@h@@%-le_exists_sub @.-Ѡ---[-H,,,,7,0+ؠ+Ѡ+y+r+++***@*W(R(R@R@- \&\ R %]R ELk(R@- B rR$@- \Q(ΐ@@@($@A(d@)@A)AA @ @'@ABCD@@g+mul_lt_pred @.Q..----2,ڠ,Ѡ,y,r,,+++\+U+F*@+C@%RC$RD(RE(RF@ḚLRW@- ! C}((Ʃ)R_@  \Re@- B`ORj@- Be')Rp@  \Rv@. C R|@- Bw$)&R@.  CR@. B$(@@'@@AA@@A@1mul_lt_mono_pos_l @..o._.L----6--,ՠ,Π,v,o,,++++L@+A%R)*R)(R@R@  \Ru))iR@  \%婚R@  \R@.A B%R@.F BÀ$@@@(@A(@)@*I@C@ABCD@@F1mul_lt_mono_pos_r @.....<.)-Ѡ-y-p--,,,Z,S++++@+B&2R)mR)kR@R@!( \R)b)R@!0 \&(S@!5 \S@. C S @. C))M@@'@@1mul_lt_mono_neg_l @//...Π.{.h.---W-P,,,,,:,3,$+@,!C&qS!)S")S#@S2@!g \)R)렩S:@!o \&gS?@!t \SE@. C@%vSJ@. CE%@@@@à1mul_lt_mono_neg_r @/m//// ...N-----6-/,נ,Р,x,q,b, @,_D&S_)S`)Sa@Sp@! \)S5*)Sx@! \&S}@! \S@/ C~xS@/ C@@(@@4mul_le_mono_nonneg_l @//m/]/J....4.+-Ӡ-̠-t-m--,,,,J@,E*'S*%S&S@S@/C \Ss*X@S@/J \%S@/O \S@/> C*/)S@/D Cː@@)@@?4mul_le_mono_nonpos_l @/////5/".ʠ.r.i.. ---S-L,,,ޠ,@,F*eS۶*cSܶ'-Sݶ@S@/ \*S@S@/ \&5S@/ \S@/| CT@/ CC@@*@@|4mul_le_mono_nonneg_r @0&//ؠ/Š/r/_/...N.G-----1-*-,@-G*T*T'jT@T)@/ \S*Ӷ@T0@/ \&rT5@/ \T;@/ D6 %T@@/ D;&@@*?@@4mul_le_mono_nonpos_r @0c0%00///D.....,.%-͠-Ơ-n-g-X-@-UH*TU*TV'TW@Tf@/ \+T+@Tm@0 \&Tr@0 \Tx@/ Ds&T}@/ Dx g@@*|@@,mul_cancel_l @00b0R0?//٠//)/ .Ƞ..i.b. .----?@-I+T+T'T@+HN+KTf+ZH NT@0) DT@0. D ѩH,O*+ @@@*@,1@*u@ABC@@.,mul_cancel_r @0ؠ000w0$0//a/X/....B.;--ܠ-͠-w@-J+TTʶ+RT˶(T̶@+QHTO++T+HXO/T@0a Dހ'T@0f D(HdO;+++X@@)x@@c(mul_id_l @1 0Ϡ000Y0F////5/..֠.Ϡ.w.p...-@-K+T+U@+HO_+Tҩ+ƠHOcU@0 E(D+HOj+T@@+W@@(mul_id_r @1<000۠00u0/Š//d/]/....G.@.1-@..L+U.+U/@+HO+U+HOUF@0 EA(s+H°O+T@@)@@1mul_le_mono_pos_l @1k1-11 000L/////4/-.ՠ.Π.v.o.`. @.]M+U]+U^(U_@Un@# \U3,,'Uv@1  \'U{@1 \U@0 E|vU@1 E!@@+@@1mul_le_mono_pos_r @11k1[1H000020)/Ѡ/ʠ/r/k// ....H@.N,%U,#U(U@U@# \Uq,V,eU@1I \'U@1N \U@1= E'𩚠U@1B E(@@*R@@=1mul_le_mono_neg_l @1111131 0Ƞ0p0g00///Q/J...ܠ.@.O,cUٶ,aUڶ)+U۶@U@$ \,U,U@1 \(4U@1 \U@1{ E"V@1 E@@~@@{1mul_le_mono_neg_r @2%11נ1Ġ1q1^1000M0F/////0/)/.@/P,V,V)iV@V(@$] \,U,ᠩV0@1 \(rV5@1 \V;@1 F6)hV@@1 F;(q@@*@@2mul_lt_mono_nonneg @2c2%22111D00000,0%/͠/Ơ/n/g/X/@/UQ,VU,VV)VW(VX@Vg@1 \V,,@Vn@$ \+,@Vu@2  \V:,@V|@$ \V@$ \V@2 F$+V@2  Fo+ΐ@@@@@2mul_le_mono_nonneg @22s2c2P1111:110٠0Ҡ0z0s00////P@/R--V-+V)V)V@V@2J \Vz,@V@2Q \N@V@2W \V-@V@2^ \[V@2c \V@2R FπMV@2W FԀL@@,@@R+mul_pos_pos @22222H251ݠ11|1$10Š00f0_00//@/S-xV-vV@V@%3 \V-@W@%: \V-W @%@ \VЩW@2 G )S@@@@+mul_neg_neg @34222Ӡ22m2111\1U00000?080)/@0&T-W&-W'@W6@%k \-V@W=@%r \-WWC@%x \WWI@2 GD)@@@@ +mul_pos_neg @3l3.33 222M1111151.0֠0Ϡ0w0p0a0 @0^U-W^-W_@Wn@% \W3.@Wu@% \. W:W{@% \W@2 G|)WE@@-@@+mul_neg_pos @33f3V3C22ݠ22-2$1̠1Š1m1f110000C@0V. W.W@W@% \.QWk@W@% \Wr.XW@% \W@37 G)W}@@5@@21mul_nonneg_nonneg @3ܠ333{3(322e2\21111F1?000Ѡ0{@0W.XWζ.VW϶@W@3s \W.@W@3z \W.W@3 \WW@3o G*3@@m@@j0mul_pos_cancel_l @43֠3Ơ33`3M2222<251ݠ1֠1~1w111 0@1X.X.X@X@&K \W..ϠX@&S \W㩚X$@3 H+QX)@&^ \W.Ԑ@@@@0mul_pos_cancel_r @4M433333.2֠2͠2u2n22111X1Q1B0@1?Y.X?.X@@XO@& \X./XW@& \XX]@3 HX+Xb@& \X'.ѐ@@@@ܠ3mul_nonneg_cancel_l @44H484%3Ҡ33g33222O2H11111{1%@1xZ/Xx/Xy@X@& \XM/3/AX@4% \XUX@4 H+éX@40 \X`/F@@ @@3mul_nonneg_cancel_r @444q4^4 333H3?22222)2"1ʠ1à11^@1[/;X/9X@X@& \X/k/zX@4^ \XX@4M Hʀ+X@4i \X/C@@ H@@N,lt_1_mul_pos @44444D413٠33x3 3222b2[2111@1\/tX/rX@X@'/ \X/@Y@'6 \X/Y@'< \XY @4 I+O@@@@(eq_mul_0 @50444Ϡ4|4i4333X3Q22222;242%1@2"]/Y"/Y#/䠩LSY5@4 I0-~X%͠LS/XLS/X@@-@@)neq_mul_0 @5^5 54444?33ޠ333'3 2Ƞ22i2b2S1@2P^/YP/YQ0Ѡ/ِLܰS0 Y&/ݐLS0Y*/ᐩLSYo@4 Ij-Y3@@-@@蠠+eq_square_0 @55T5D514ޠ4ˠ4s44333[3T2222221@2_0Y0EM S⩚Y@5 I'YZMS0AY\@@@@@*eq_mul_0_l @55}5m5Z5444D4;33ܠ33}3%32Ơ222Z@2`07Y05Y@M4T Y@5= I.Y@0;M>T0nYM@T0Y@@@@@?*eq_mul_0_r @5555555"4ʠ4r4i44 333S3L222ޠ2@2a0eY۶0cYܶ@MbT9Y@5k I.6Y@0iMlTC0`YMnTE0bY@@@@@m(mul_eq_0 @Z@ <@0Y0Y0MTYZ @5 J.VYѩ&MTb0YթMTd0Yא3333@2@ ^\67555֠55p5444_4X43333B3;3,2@@@@@*mul_eq_0_l @Z>@3oN @0Z60Z7@MTZH@5 JC.Z @0ĐMǰT0ZMɰT0Z<@24pe6m6/66 555N4444464/3נ3Р3x3q3b3 @@@@@ߠ*mul_eq_0_r @Zt@3oN@0Zl0Zm@MTʩZ~@5 Jy.ZB@0MT0ZGMT0ZIr@24pk66e6U6B55ܠ55,5#4ˠ4Ġ4l4e4 43333B@@@@@(lt_0_mul @666q6^6 555H5?44444)4"3ʠ3à33^@3b1;Z19Z1sZ@( \ZZ@6F JÀ/'`?Z@) \Z1|Z@)  \Z1MZ@) \1ZZ@) \1Z@@0@@_5square_lt_mono_nonneg @7 6ˠ666U6B555515*4Ҡ4ˠ4s4l44 33@3c1Z1Z@[ @6 \Z1@[@)G \.?[@)L \[@6 K1_1_[#@6 K11@@@@@5square_le_mono_nonneg @7G7 66666(5Р5Ǡ5o5h55 444R4K4<3@49d1[91[:@[I@6 \[1@[P@6 \.}[U@6 \[[@6 KV>[`@6 K[=@@@@@٠6square_lt_simpl_nonneg @77E757"6Ϡ66d6 6555L5E44444x4"@4ue1[u1[v@[@7 \[J2/@[@) \[@7 Ko[@7 K2B2B[@) \-ߐ@@@@@ 6square_le_simpl_nonneg @777r7_7 666I6@55555*5#4ˠ4Ġ44_@4f2<[2:[@[@7W \[2l@[@7^ \[@7M Kʀ[@7R Kπ=[@7n \.@@@@@ R,mul_2_mono_l @77777H756ݠ66|6$65Š55f5_5544@4g2x[2v[@[@*3 \0G\@*8 \\ @7 L[\@7 L [2~\@7 L[2@@0@@ *add_le_mul @89777ؠ77r76 66a6Z65555D5=5.4@5+h!a\-!b\0@\?@*t \[2@\F@*{ \[2񩚠\L@7 \\R@7 L.\W@7 LR.@@2V@@ Р-square_nonneg @8z8<8,87Ơ77[76666C6<55ݠ55~5o5@5liA\l\z@8 \\?\@7 L{*@@@@ 5crossmul_le_addsquare @88e8U8B77ܠ77,7#6ˠ6Ġ6l6e6 65555B@5jj\h\@\@8: \\j3P@\@8A \\q3W\@8G \\@8C ML\@8< Lé\@8A L/\@8S M\\@8L Lɀ\@8Q L΀@@@@ L-add_square_le @88888B8/7נ77v77666`6Y6555@5k\\@\@8 \\3@\@8 \\3]@8 \] @8 M]@8 M ]@8 M󩚠]@8 M]!@8 M/c]&@8 M/h@@3%@@ -square_add_le @9I9 88888*7Ҡ7ɠ7q7j77 666T6M6>5@6;l];]<@]K@8 \]3@]R@8 \]3]X@8 \]^@8 MY]d@8 M/]i@8 M/]n@8 Mi\򩚠]t@8 N]z@8 Mu]]@8 Mz\@@3~@@ 4quadmul_le_squareadd @99d9T9A88۠88+8"7ʠ7à7k7d7 76666A@6mi]g]@]@99 \]i4O@]@9@ \]p4V]@9F \]@95 M]@9; M]@9A M]G]G442]@9G MĀ]@9Z Nc0]@9_ Nh0@@3@@ M*neq_succ_0 @99999C908ؠ88w88777a7Z7@7W@4p]4jQmXD]@9_ ! O3]@@3@@AA@@A@*neq_0_succ @:99Р99j9W8888F8?77777)@7~A4^ 4QXk]ީ^@9 ! OE4!@@@@@'&le_0_l @:B:9999{9#8ˠ8 8j8c8 8777M@7B4^1^?@9 \^4@@2@@H)induction @:c:%::999D88888,8%7͠7Ơ7n@7C3@^S3@3@^W33^Y3Q55 @5^)@4^^@44k3^p@9 ! O4x4^h3@@@4o@A@@z-case_analysis @::W:G:499Π9v99888^8W777@7D3@^3@3簶@^33^3R5K5=@5@^[@5^4ې^@: ! Oƀ45"^3@@0@@%neq_0 @:Ġ::v:c:999M9D88888.8'7@8$E565?^R:Y5i^@@@@@Ƞ'neq_0_r @:::::/:9Ġ9l9c9 9888M8F7@8CF5\^ҩ55XR[Y25^v^ڷ5b^۩R`Y75^@:R ! P4@@@4@A5*@6k@ @`@ABCD@@,zero_or_succ @;:ՠ:Š::_:L9999;948ܠ8ՠ8}8v8@8sG5_+RY`5^ө_5_ RYe5_@: ! P?5@@.@@!)eq_pred_0 @;<:::۠::u:9Š99d9]98888G@8H5_+5젩RY_=@: P5?_+ՠRY5_RY5^@@3@@K)succ_pred @;f;(;;:::G99999/9(8Р8ɠ8q@8I5_U@5ڐRݰY6 _'R߰Y_j@: ! P_p@: PR5x6@@3@@x(pred_inj @;;U;E;2:ߠ:̠:t::999\9U888@8J6 _6 _@6S Y6;_U@6 SY6@_Z@SY꩚_@;  P G_@; P[SY45@@5@@.pair_induction @;Ƞ;;z;g;;::Q:H9999929+8@9(K5 @_555@_5"5_5$SC6~6p@6s_@6:_u@6P_ƶ@5@5_@;? ! P5&_@;F ! Q_@;L ! Q 6g_5@@@@@1two_dim_induction @< ;ˠ;;;U;B::::1:*9Ҡ9ˠ9s9l9@9iL!R@_@_5b$R_wd5`@`@`5i5[`@`5lS5^`5nS66@6__ض@6` 6`@5Y4b5P6` @; ! QF6(@6`@6`5[4n5\`,@; ! QR64_6`$6`%'4x@@@@70double_induction @<<ؠ<<(<;Ǡ;;h;a; @;^E8a8a@8U[8Da_U[a@=- R68a@= R7a@= Ra@=> RG4@@6A@@'lt_wf_0 @Ȑ!H8a8a$;A@a@0 \6$Ea@=l \a8Fa@0 \5 @$Sa@=z \a8a@0  \64a@0% \53a@0+ \6?1a@= \a8lb@08 \50b@䞀8"H0$b@= \a8b@0M \6a$BBB@@@@D@$b(@= \a8b.@0c \5[b3@0h \4u8ܐ$_tmpb<@= \b8bC@0x \48C>@1pointwise_liftings׾9>@%TlistР@BbJAb[@0 \8]8bS$Ѡbc@= \b(9bi@0 \6C>@4relation_equivalencesbgbt@0 \8bl8bm$렩b}@> \bB9(b@0 \6C-SetoidTactics>@0default_relation ж@b@b7&b@3equivalence_defaultú@b@b71b>@ relation_equivalence_equivalence*+rbb@0 \9)b9'b%b@>E \bu9[b@0 \63ж@b@b8Qb+@b@b8Wb&bb@0 \9Jb9Hb%?b@>f \b9|b@1  \7 #Heqsb՚b@1 \9dbڷ9bb۩%Yb@> \b9b@1& \7:8I@2subrelation_properJ7,@b@b8X8X8J8@(relation'Jjb8bb9̐c@5well_founded_morphism=lc8`@c @c 8r8rc&Basics'Program?y@$flip$888 @$impl7o)Datatypes9@$unitUe@A8@6subrelation_respectful>6z @c1@c288Ґc4Ԑc68@0subrelation_reflv @c>@c?8ߐcA:38@9iff_flip_impl_subrelation2VAcS@1 \9cK9cL%ʠc\@> \c!:cb@1 \7: cg@J ʁc,C@ж@cc@cd8ʩcfް@ci@cj8Щ clِcnc{@1 \9cs9ct%򠩚c@? \cI:/c@1 \7өOcc@1 \9@Ucc@1 \ 67 + +7 :6  67777777 +7T7!77 77 7 +7T7L ! 6777777 7 +7T777 77 677 777 7 + +7TT7 k() + +(:'= R '>''+k7%'7 :'() 7! 77!7%'+7T'6'+7T'6'+7T'6'6'+7T'6'T4Relation_Definitions)Relations=@@'Jj(=٠=ؠ=נ= =@&le_0_l\%Logic$Init@#andЖw@"Wf @,well_founded8E䠒"@%lt_wf ÐT)Morphisms'Classes3@2VAT @*respectful%WO?4@J7t@>=@$zero3F6L7@#iffС)۠'ProgramU@$p@"lt3<@@!t3@t4d #@"le3A8XHh`XxpC@v РeBABAB䠒O@>6z(/RelationClassesT@s 9@ 7oPh.Morphisms_Propa@)=lЀ@R@@????3>۠>Ҡ>z>s>@@@/d@A;A I@@: @ABC@@AA@@A@'nlt_0_r @@q@3@#@???R>>>>>:@>@:d\:dl@2 \;d1@@@@@"*nle_succ_0 @@@R@B@/?ܠ?ɠ?q??>>>Y@>A;d{:d@@  \d@? ! U:dU@@@@@F&le_0_r @@@v@f@S@???=?4>ܠ>ՠ>}@>B;)d;`d@@D \;YdtX,_;[dv@@@@@g)lt_0_succ @@ՠ@@@t@!@??^?U>>>@>C;Jdd@3 \dd@@; ! U:֐@@9b@@*neq_0_lt_0 @@@@@@C@0?ؠ??w??>@?D;ld;;hXk_B;dd@3+ \d;@@9@@/eq_0_gt_0_cases @A@ܠ@̠@@f@S????B?;>@?8E;e1X_c;d֩e@3L \d;@@9@@͠(zero_one @A;@@@ڠ@@t@?Ġ??c?\?@?YF;e&1ǠX_;d1ˠX_;dߩe<@3q \d;@@@;<@A;9@;~@A<@ @<f fN@A ! Wt(g@C \:@@&@@9*lt_pred_lt @CCiCYCFBBBB0B'AϠAȠAp@AT>g>g@g@5 \>Mg@C X=g@5 \:ڐ@@@@@b*le_pred_le @CРCCCoCC BBYBPAAA@AU>Eg>Cg@g@C` \>vg@C= X=өg@Ck \;@@@@@,pred_le_mono @CCCCCEC2BڠBByB!BA@BV>ng>lg@g@C \<=g@C \g@Ck X"h@Cp X> @@>@@,pred_lt_mono @D'CC٠CƠCsC`CBBBOBHA@BEW>h>h@>[br>g>٠h(@6] \;Uh-@6b \h3@C Y"멚h8@C Y>@@@>7@@/lt_succ_lt_pred @D[DD CCCC<BB۠BB|B$@ByX>hF>hG?hW@6 \h]@C ! Y>e?hb@6 \? hh@C YJ>j@@@@/le_succ_le_pred @DDMD=D*CנCĠClCC BBBT@BY?hv>hw@h@D \h@C ! Y>?5h@D& \?h@D Yy>@@@@@L/lt_pred_lt_succ @DD|DlDYDCCCCC:BB۠B@BZ?/h?-h@h@6 \h@D' Y>?dh@6 \?/h@D- ! Y>ΐ@@@@@{/le_pred_le_succ @DDDDD5D"CʠCrCiCC B@C[?^hԶ?\hթ?h@Dz \h@DW Ỳ>?h@D \?h@D] ! Z>@@i@@(le_add_r @ED۠DˠDDeDRCCCCA@C@?i?ii@D \?i@D Y=`@@?@@AA@@A@+lt_lt_add_r @E=DDDܠDDvDCƠCCe@CA?i&?i'D5C@D2D@(i@&i@i@7 \is@Xi@7 \iyi@EE ZN<@@@@@.square_lt_mono @EݠEEE|E)EDDf@D@@NiĶ@Liũ@i@8  \>i@8 \i@E^ YۀIi@Ec Y7@@@@@AA@@A@.square_le_mono @F E͠EEEWEDDD@DA@|i@zi@j@E \>Lj@E \j@E Z wj@E Z8@@@@@.-mul_le_mono_l @F6EEEՠEEoED@EB@j@j=oj@j.@E \=[j3@E \j9@E Z4.j>@E Z96_@@@@@Y-mul_le_mono_r @FaF#FFEEEBD@E?C@jH@jI=jJ@jY@E \=j^@E \jd@E Z_<ji@E Zd=@@@@@+mul_lt_mono @FFNF>F+EؠEŠEmE@EjD@js@jt=ju<jv@j@8 \<Ƕ@j@8 \=j@8 \j@F ZYj@F Z6@@@@@+mul_le_mono @FFFpF]F EEEG@EEA/jA-j=j=j@j@FL \<@j@FR \=꩚j@FW \j@FF ZÀj@FK ZȀ6@@@@@蠠)lt_0_mul' @FFFFF<F)EѠEy@EFAaj׶A_jةAj@9 \jj@Fl Z?7-cj@9* \jAj@90 \jA@@@@@(eq_mul_1 @GFFѠFFkFXFE@EGAkAkAȠ^eek@F [?bj-^enAjũ^epAjǐ@@A@@:(mul_eq_1 @k-@, <@Ak%Ak&A砩^ek8@F [3?j-^eAj^eAj搑F4F3F2F1F0@E@I1,GcG%GGFFFDE@@@@@l'sub_0_l @GtG6G&GFF@F@AkY^ްeki@F c[k.Bk.@@?@@AA@@A@(sub_succ @GGRGBG/FܠF@FAAkuAkv^eҩk@F c[ʀk@F ! \Ak@F ! \Ak@G  c[ڀ?ߐ@@@$@@,(sub_diag @GG{GkGXGF@FBB(k_#ek@G# c[9kr@@@<@@D&sub_gt @GѠGGGpGG @GCB@kB>k@k@9 \?BA_Dfk@GD c\>k@@@]@@e-add_sub_assoc @GGGGG>G+@G'DBak׶B_kض?)kٶ@k@G} \?_df;k@Gz \B1k@Gj c\9?"k@Go c\>l@G \>BB@@@@@*sub_succ_l @H#GGՠG GoG\@GXEBlBl @l@G \@a_fkl@G c\cl%@G ! ]KB-Bl*@G ! ]Pl0@G c\t8Q@@@@@Ơ'add_sub @HSHHGGG@GFBl8Bl9_flI@G c\lO@G \@BB@@@@@堠'sub_add @HrH4H$HGG@GGBlWBlX@lg@G \@_fln@G ]lt@G c\8BC@@A@@ ,add_sub_eq_l @HHYHIH6GG@GHCl|Cl}?l~@`f۩l@H ]#@B` f⩚l@H  c\ڀ>C@@@B@@,,add_sub_eq_r @HH{HkHXHG@GIC(lC&l?l@`&fl@H< ]E@C`-gl@H- c\>C&@@B@@N-add_sub_eq_nz @H۠HHHzH'H@HJCJlCHl@l¶@CG`Jg!Cyl@`Mg$l@HM c]?C`Tg+l@Hj ]s?!B@@B@@u-sub_add_distr @IHĠHHHNH;@H7KCqlCol@9l`ngEl@Hn c]=Chl@H ]AHm@Hy c]Hm @H c]N@7C@@A@@,add_sub_swap @I-HHߠH̠HyHf@HbLCmCm@dm@m#@H \@`gvm*@H c]nm0@H ]Ā?rCکm5@H ]ɀm;@H c]?lC@@A@@Ѡ(le_sub_l @I^I IHHH@HMCmCCmDmR@H \mX@H c]AD@@CW@@(sub_0_le @I{I=I-IHǠH@HNCm`CmaD"`gms@H c]Am7mx@I  \A@@B@@*sub_add_le @II]IMI:HH@HOD mDmm@I$ \D:m@I  ^)m@I c]߀ADD@@C@@1/le_sub_le_add_r @IIIpI]I H@HPD-mD+m@mDfm@IJ \m@I0 c]@}Dem@IU \D/m@IQ ^ZB@@,B@@\/le_sub_le_add_l @IIIII5I"@IQDXmζDVm϶A mЩDm@Iu \m@I[ c^*ADm@I \DZm@I| ^B:@@B@@/lt_sub_lt_add_r @JI֠IƠII`IM@IIRDmDmAKm@n @JIIݠIIw@IsSDn#Dn$Aun%@n4@n@J c^݀0@@ @@//lt_add_lt_sub_r @JJ~JnJ[JI@IVE+nE)nAnEdn@< \n@JD _MA{Ecn@< \E-n@J9 c_C @@D@@Z/lt_add_lt_sub_l @JJJJJ3J @JWEVn̶ETnͶBnΩEn@= \n@Jo _xAEn@= \En@Jd c_3;@@b@@&sub_lt @KJԠJĠJJ^JK@JGXEnEn@o@J \Bݶ@o @=B \nEo@=H \o@J c_]A[EZ@@-@@-sub_le_mono_r @K<JJJ۠JJu@JqYEo!Eo"Bso#@o2@J \B_o7@J \o=@J c_AnoB@J c_Bo@@F@@ؠ-sub_le_mono_l @KeK'KKJJ@JZEoJEoKBoL@o[@J \Bo`@J \of@J c_;ok@J c_`@@F@@*mul_pred_r @KKPK@K-JڠJ@J[EosEotbiЩo@K _F/o@J `lEo@K c_Ӏo@K _CF?@@E@@+/mul_sub_distr_r @KKzKjKWKJ@J\F'oF%oBoc$io@K- _o@K* c_BF^o@K/ c_o@K> _Bo@KC _D@@@E@AE@F@AGF@GGA1ՠF G@GKA1I K@ABCD@@g/mul_sub_distr_l @KKKKK@K-@K)]FcoٶFaoڶC+o۩c`j7o@Ki _怠Fo@Kf c`5Co@Kk c`:o@Kz _Bp@K _Cא@@D@@&le_alt @FpFp+pCWpcjcp@K `CF@FpFpEv +k() + 77%' 7!7%'@KoKnKmKlKkKj@@#add# `%Logic$Init@"ex @|@!t# t @"eq# !lL_L!LKKK@@+}@@ᠠ<_alt @FpMFpN+pPCpQcְjpa@K `pg@K ! aFiFG@Fp_Fp`EƐ +k() + 77%' 7 7!7%'РPlF|=t:x]@K##`LL]LML:KK@@+@@(le_equiv @LLlL\LIKK@K^GpGpGQp@*D驚p@L: \D@@+@@;(lt_equiv @LȠLLzLgLL@K_G7pG5pGop@nEp@> \E @@+@@Y)le_alt_wd @LLLLL2L@L`F+@pͶ@pF4F&pж@pF7dVF)pF9dXGp@*@@@@v)lt_alt_wd @MLŠLLLOL<@L8aFH@p@pFQFCp@pFTdsFFpFVduGp@@@@@0le_alt_dichotomy @M LLҠLLlLY@LUbGqGq=q@*E_q@*D@@,@@-add_dichotomy @M>MLLݠLLw@LscGq#Gq$=Š,Ġq(Dyq)dkq9@L àD4G,Πq2Dq3dkqC@L a׀EG@@,u@@٠'max_0_l @MfM(MM@M@GqIdΰkqY@L UqHH@@@@@AA@@A@'max_0_r @MMBM2M@MAGqcdkqs@L UπHq8H@@@@@'min_0_l @MMYMIM6@M2BHqzdk֩q@M  U†qOH4qO@@@@@1'min_0_r @MMpM`MM@MICHqekq@M# UHKqfqf@@@@@H.succ_max_distr @MŠMMwMd@M`DH2qH0qe.lq@M  ! b߀q@MF VFq@MK V q@M1 ! bGҩq@M6 ! bGѐ@@F]@@u.succ_min_distr @MMMM@MEH_qնH]q֩e[l2q@MM ! c q@Mn VDF5q@Ms VIq@M^ ! cGq@Mc ! c"G@@F@@/add_max_distr_l @NMMѠM@MFHrHrETrel`r@M Vpr@M bEr@M bEr$@M bHΩr*@M VEW@@F@@Р/add_max_distr_r @NMNMM@MGHr0Hr1Er2elrB@M VrH@M b܀E rM@M bFrR@M b怠rX@M VEI@@F@@/add_min_distr_l @N{N=N-N@NHHr^Hr_Er`elrp@M VȀrv@N c Eqr{@N cFQr@N  cI*r@N VހE@@G@@,/add_min_distr_r @NNkN[NH@NDIIrIrErfl꩚r@N  Vr@N/ c8Efr@N4 c=F򩚠r@N9 cBr@N6 W EI]@@GB@@Z/mul_max_distr_l @NנNNNv@NrJIDrIBrF rfAmr@NS W(r@NP b̀Eͩr@NU bҀFr@NZ b׀Ir@Ni W>F@@Gp@@/mul_max_distr_r @ONǠNN@NKIrrIprF:rfomFr@N WVs@N~ bE©s@N cGNs @N cs@N WlF=I@@G@@/mul_min_distr_l @O3NNN@NLIsIsFhsfmts(@N Ws.@N c)F)s3@N c.G s8@N c3I⩚s>@N WFk@@G@@䠠/mul_min_distr_r @OaO#OO@NMIsDIsEFsFf˰msV@N Ws\@N cWFsa@N c\Gsf@N casl@N WĀFJ@@G@@/sub_max_distr_l @OOQOAO.@O*NIsrIssFstfmЩs@O  Ws@N cc΀Fs@O ccӀGes@O  cc؀J>s@O WFǐ@@H(@@@/sub_max_distr_r @OOOoO\@OXOJ*sJ(sFsg'ms@O9 Xs@O- ccFzs@O2 cdHs@O7 cds@OO X$FJq@@HV@@n/sub_min_distr_l @OOOO@OPJXsζJVs϶G sЩgUn,s@Ob X8s@O[ cd*Fᩚs@O` cd/Gs@Oe cd4Js@O} XRG#@@H@@/sub_min_distr_r @PO۠OˠO@OQJsJsGNsgnZt@O Xft@O cdXF֩t@O cd]Hbt@O cdbt$@O X|GQJ͐@@H@@ʠ+Private_Tact-A'eq_refl @@@K!M-GenericMinMax*Structures#Coq@tAX@A@@J!O tG@@ T@tQ@!t TJtK@A@A X@B lXXC #XXD "XXE XXF SXtXpH@A@v@^K߀МA14ncQK: @vAvSv@-v=@@0v@C2vQB L+k() LL7#'@$tpjY,& @@@@@Ġ(le_trans @oCМCmpvI@vݶ}v޶v߶@v@Z \}@v@a \v@f \ L+k() NN7#'GtРŠoiNIB<!@@@@@(lt_trans @%@ABМVB(Рʠ@3w w!w"@w1@ \C@w7@ \Iw<@ \B L+k() MM7#'tݠ}b@@@@@H+le_lt_trans @fAf+ @qw^w_w`@wo@ \@wu@$ \wz@) \ L+k() MN7#'ƐtOD2,͠Ƞ@@@@@+lt_le_trans @1C,/i^LF5@w<wNw@w@\ \@w@ \ũw@g \ L+k() NM7#'tpjY,& @@@@@Ġ%eq_lt @oC<jmsF@wڶzw۶wܶ@fwvy@w@ \w@ \ L+k() ML7#'?tȠgaFA:4@@@@@%lt_eq @89:~wנŠ@(xxx@x&@ \8@x x.@ \4 L+k() LM7#'ztϠ|uoT@@@@@:%eq_le @XstuvX@cxPxQxR@ܰxU@xd@ \vxi@ \o L+k() NL7#'t>3! ݠנ@@@@@u%le_eq @ 2XM;5$@x+x=x@x@ \@x-0x@ \ L+k() LN7#'tyn\VE@@@@@&eq_neq @qkZ-' @(GxǶgxȶyxɶ@Sxcf@Xxhk\x{l@@@@@ՠ&neq_eq @RL1,%@MHxxx@zx@}xx@@@@@*not_neq_eq @ؠ͠wqVQJD)@rI$yy@ܐސy(y@@@@)not_ge_lt @ܠ֠ŠwrkeJ@JEy2y3@yD@ \K֩yJ@ \\@@O@@A)not_gt_le @p@KkyXyY@#yj@ \&yo@ \@@@@@f)le_neq_lt @D9'!ݠ @Ly}y~@y@ \@Ny #y@F \&@@@@@@@@@\@(max_spec @odRL;@pE!ny!my%Logic$Init#Coq@@"or @@#andЖw@y@3 \BAOyȩy@p ^2BAAy@O \ABfyߩy@ ^IBAB@@@ %'A*Equalities*StructuresqA݋X_A/RelationClasses'Classes#Coq@@A@@AA@@A@+max_spec_le @٠Πx@Fjz izh]z%@ \BAz!z/@ ^BAAtz<@ \ABz8zF@ ^BAB@@@@@I1Proper_instance_0 @@ G)Morphisms'Classes#Coq@@&ProperL@z`@za@*respectful%WO?zi@zjzl znzp8@#iffС)z@ \@@@AviA)Morphisms'Classes#Coq@@A@@*max_compat @aVD>-@bHB@z@zz8z@zz%z=zz)z+zz@K _ @@@A/@Aۓό^1@A@ABC@@+max_unicity @qkZ-@Iz¶zĶ!pzǶ@!z@E \CBazڐAB&z@Z \BCqzACuzz@ _Xb@@@@@/max_unicity_ext @ҠǠq@J!f{ "x0{ { @l{k{j_{'@ \.{!C3Ao{7@ \>ɩ{1CCB{7{9°{;L{K@ _R@@@@@K(max_mono @!@"KO@{V{V@@{\{\@@*respectful%WO?{g{g{i{kA@@{r{r{v{v{@ \{@ \{ { {{@, _1&35{@8 _0@@@A@A@A@ABC@@&max_id @zo]WF@{L {7{{@X `AAA@@@@@)max_assoc @ztc6@M%{˶*{Ͷ {ϩX{ѩ{@y `;C{@ `BBA{@ `J{@ `PCBA@@@Aw@A AۀߠKx@ AK@A @ABC@@(max_comm @נ̠v@Nh| g| ||@ `yBA|%@ `AB@@@7Au@9A3@AB@@+(le_max_l @ޠ͠@O|5|7|E@ \B|L@ `BA@@@@@N(le_max_r @$@%P|X|Z|h@ \A|o@  `ˀBA@@@@@q)max_l_iff @G<*$@HQ|{|}@#iffС) ||@. `BAB|@  \AB@@@@@)max_r_iff @ujXRA@vR||.8||@Y aBAA|@4 \BA@@@@@ʠ&max_le @}l?@S1|Զ0|ֶ|ض@|@S \A|@ aJCBA|@f \`}@l \@@@@@*max_le_iff @֠ˠu@Tg} f} H}} @ \A}'@ aCBz}3@ \AC};@ \AB@@@@@=*max_lt_iff @  ߠ@ U}G}I}K΀}]@ \A}d@ aCB}p@ \AC}x@ \AB@@@@@z)max_lub_l @ P E 3 - @ QV}}}@}@  \}@ 7 aCBA}@  \ 8@@@@@)max_lub_r @ | q _ Y H @ }W } }}@}@ / \}@ c b%CBA}@ > \ad@@@@@Ҡ'max_lub @     t G@ X9}ܶ8}޶}@}@ [ \CA@}@ d \}@ j \~@  b`j@@@@@+max_lub_iff @ ڠ Ϡ    y@ Yk~j~L~~$@  \~*@  bCBAo~7@  \CA~?@  \BA@@@@@A*max_lub_lt @      @ Z~K~M~O@~^@  \CA@~g@  \~m@  \~s@  bπ @@@@@s.max_lub_lt_iff @ I > , &  @ J[~}~~~@  \~@ 3 bCBAހ~@  \CA~@  \BA@@@@@/max_le_compat_l @  { i c R %@ \~~~@~@ 9 \CB~@ A \~@ u c7 m A~@ { c= s p@@@@@ᠠ/max_le_compat_r @      V@ ]H~붐G~)~@~@ j \CB@ r \ @  ch r @  cn  @@@@@-max_le_compat @  ݠ ˠ Š  @ ^yxZ !q#@2@  \DC@;@  \  ͩA@  \G@  c M@  c ܐ@@@@@M(min_spec @ #     @ $_WYo@  \BA ky@  cрBAB@  \AB @ % c耠BAA@@@A@A@@+min_spec_le @ k ` N H 7 @ l`@ # \BA :@ V dBAB@ : \AB Qʩ@ m d0BAA@@@@@۠*min_compat @     } P@ a@@@ u y {@  dY@@@A@AP@A@ABC@@+min_unicity @ ܠ Ѡ    {@ bmlN@nc+@  \CB 'ACs;@  \BC 7AB °; թI@  d  ؐ@@@@@I/min_unicity_ext @      @ cM gULWW@Z\r@  \  y lC  ~B@  \   |C  A   " @ + d ( @@@@@(min_mono @ l a O I 8 @ md@@Q@K 4 6A@`@Z@ 3 \@ 7 \ \ Ķ dƩ Oȩ@ k e. u j w  y@ w e: t @@@Aa@A2@A@ABC@@蠠&min_id @      ]@ eO {@  eZAAA@@@@@)min_assoc @ ۠ Р    z@ finM #@  e{C*@  eBA2@  e8@  eCBA@@@LA@AMAD@OA@QAK@ABC@@C(min_comm @      @ gMO ذQ_@  eBAg@  eAB@@@yA@{Au@AB@@m(le_min_r @ C 8 &   @ Dhwy@  \@ " e倠BAA@@@@@(le_min_l @ f [ I C 2 @ gi@  \@ E fBAB@@@@@)min_l_iff @  ~ l f U (@ jB Lũ@ h f+BAB@ H \BA@@@@@ޠ)min_r_iff @      S@ kE趐D꩚m w𩚠@  fVBAA@ s \AB@@@@@ &min_le @ ߠ Ԡ     ~@ lpoQ@&@  \,@  fCBA9@  \  ˩?@  \  ѐ@@@@@?*min_le_iff @     @mIKMЀ_@  \e@  fCBAr@  \CAz@  \BA@@@@@|*min_lt_iff @RG5/ @Sn @ \@7 fCBA@ \CA@ \BA@@@@@)min_glb_l @rl[.@o ö ŶǶ@@B \A@r g5CB@Q \ w K@@@@@堠)min_glb_r @Z@p L﶐ K-@@n \A @ gaCB@} \  @@@@@ 'min_glb @ܠʠĠ@q x wY@.@ \AC@7@ \  Ʃ=@ \ ̩C@ g  @@@@@ C+min_glb_iff @@r M OQԀc@ \Aj@ g€CB v@ \AC~@ \AB@@@@@ *min_glb_lt @VK93"@Ws  @@ \AC@@  \85@ \;@G h  P@@@@@ .min_glb_lt_iff @}keT'@t  C@9 \A@n h1CB @L \AC@T \AB@@@@@ /min_le_compat_l @Šd@u V U 7@ @x \CB@ \@ hr @ hx@@@@@ /min_le_compat_r @٠Ӡ @v * , h.@=@ \CBE@ \K@ hݩQ@ h@@@@@ Q-min_le_compat @' @(w [ ] _?a@p@ \DC@y@ \ @ \@ h݀ 멚@  h〠)@@@@@ 2min_max_absorption @aVD>-@bx   @A iB@C iBAB@@@ A 0@ A @ A @ABC@@ 2max_min_absorption @pjY,@y  éLũ@h i+B@t i6BAB@@@ A \@ A -@ A @ABC@@ 㠠-max_min_distr @X@z J I﶐ +z󩚠@ i]C@ i`BA@ ih@ irCB@ izCA@@@ 0A @ 2A p@ 4A .@ABC@@ &-min_max_distr @ߠ٠Ƞ@{ 0 2 n46D@ iCK@ iBAS@ iY@ iCBa@ iCA@@@ sA @ uA @ wA q@ABC@@ i/max_min_modular @?4" @@| s u wy@! i〠C@# i怠B@/ i񀠐CA@2 i@= iCB@E jCA@@@ A ,@ A @ A @ABC@@ /min_max_modular @~lfU(@}   Jé@f j)C@r j4B@t j7CA@ jC@ jECB@ jMCA@@@ A v@ A G@ A @ABC@@ 0max_min_disassoc @ӠȠr@~ d c  E @ \@ jwC&@ jBA.@ j4@ jCBA@@@ GA @ IA @@ KA E@ABC@@ =0max_min_antimono @ߠ@ A@HH@ @NN RRېTݐVA@ @]] aan@ \&Basics'Programs@$flip$qq~@ \wy{@# j倠(*,@* j퀠'@@@ A @A A @ A @ A!s̓P&Basics'Program#Coq@@ A!t Q @ABCD@@ 0min_max_antimono @tb\K@@ @@ d@ ^GIA@ s@ɩ m͚@F \l@L \qٶy۩dݩ@ kC@ kS@@@ A w@A A G@ A @ Ab@ AZ@ABCD@@ ,max_monotone @נ̠@A @  @ @  @ \$@ \A0  y@"eq @(6@ kʩAB@ kI@@@ RA @ TA1DH   @@ [A1FdJ@ABC@@ O,min_monotone @%@#B P@WW@ @]] aan@ \r@ \A~l nNr@ k؀됩@! k䀠@@@ A @ AJ@ AE@ABC@@ 4min_max_antimonotone @h]K@fC @@ J@ D@ \CϚ@# \AQ@Z l,Y.Щ0@k l-cؐ@@@ A Q@A A8@ A0@ A@ A@ABCD@@ ۠4max_min_antimonotone @@D ܶ@@ @驚 횠@f \@l \A ܀@ ljuwy@ lr!@@@+A @A,A@.Ay@0A@2A@ABCD@@$+Private_Dec.A/max_case_strong @L]@\5!P@ Ⱥhii@@&CompatX@@k @]@"Hl@(@=ʩ"Hr@  ҩȐ!c)Datatypes1@-CompSpec2Type2KC+EE@0=J@'comparet<%Q@,compare_spec@)CompSpecTӊ]2Ȑ"c0!(@*comparison;f@Р.@,CompareSpecT, /@CAAAAAA@@@@@@@@D?@c}IH;=M@^JW"EQzSȐ!H%lemma@ MС)z"@"or @+/x@9iff_flip_impl_subrelation2VA&p)*:@'le_lteqS%>BDH"H@@(symmetry0xj@5Equivalence_Symmetric. U@(eq_equiv*uT\T@%max_rSc "LTiSQ2IA,M+"GTu_][wWzSؠt_yDOHGA@%max_l54@@MRm@A@@LW@@ T@a@ TJZ@A@A m@B lmmC #mmD "mmE mmF SmmH@A@8UsualMinMaxDecPropertiesil@A@@3a,b+@d)@yfg@!jy@@z@ \@@@ \琩@" m T+k()7!7!7777= gR'>#97!7!7!7!7!7  #7"  7!7777"7777! # '>#97!7!7!7!7!7  #7"  7!7777"7777! # '>"97!7! 7!7! 7!7  "7"  7!7777"7777! # '' +k()7!$'D?@p#p<Pࠒ@t<D@V=xX@5H,h@S%Hؠ4Ġ&@=#(@$\`+@*= 0Р"@CAABACAAL~@h8th@|E@*u@T@@@Ⱥhi@@A@A@@A ALx@AB@@렠(max_case @@”j"@@!X"X0m"X13@+sـ5KNϠˠ@@)@/@װ /Ҷ@$@ 2@ n +k()+++7# '''$'^3MinMaxDecProperties@G\ࠠ@@G|@@@@@A@Ǡ@@Ǡ@A@AB@A@@Fà@@t<@@'comparet<d@@A@A5@@5@A@=#@@=#^@A@A=@@=@A@=@@=@A@ABC@A@1 H@A@@@j"@x@A@A@zA0@A@@t'max_dec @IHBIu@<VrP&SpecifI@'sumbool7̂K@C]#E_(`/aJ"H0Oi/>Qk1BAAAA@@@@@D!s&`z8b|Q,f?!E 5A sb*[@=trans_co_eq_inv_impl_morphism&ni$Q@6Equivalence_TransitiveWoXYZqj@/eq_proper_proxy)f%j#+VB,2!$klmmo ,}}@+reflexivity(ϓ/x@5Equivalence_Reflexive977!    7777"777  7777"777 9'>977!    7777"777  7777"777 9'' +k7!7!7%' 7! 7!7%'4U@@@1<V/D(젒<`Р@BAABAAQL@W588x8xX|4Р@V=#@00Ptu$$@9*u  lu@@@@@@[@ABC@@V/min_case_strong @+*$+#@-k۠@@!@ @ַ޷ ɩÐ@Ǡ  N  @%min_lɀu@rpn hfd`\ߩ@%min_rπMI9@g`_@<@:@U8P@@@ \I@@@! \CH@Q p5 L+k()7!7!7777= eR'>#97!7!7!7!7!7  "7"  7!7777"7777! # '>#97!7!7!7!7!7  "7"  7!7777"7777! # '>"97!7! 7!7! 7!7  #7"  7!7777"7777! # '' +k()7!$'D4@:pVp@6ϐH@Iɠx<ڰ@ؠL@Yt<DQ@=pXV@58h[@S%@ؠ$c@ =#(0T`.@Ǡ0lXm@l=0Рd@Ca`_BALx@*ux 2@|Ġ@@k@@A@A.@@(min_case @@딑mH@@)ݷ'%#! @4{[fgŠ@/0@2@G45@8G@<@8J@ pÐ@(.>\@@m@8@A@A@:A@A@@]'min_dec @21+2^@Ukv{9:#{ǩɩ+E@>trans_sym_co_inv_impl_morphism'\|L @/Equivalence_PER/;'TW,ީ⩷éD^3`5b !MI9@g`Q@= q9X@D q x+k()7777"7779 7777"7779 ++7#'()= XR'>G   7777"777  7777"777 7777"7779'>G   7777"777  7777"777 7777"7779'' +k7!7!7%' 7! 7!7%'0 D\$ĠϠ`Р8@BANL6@5@T8pTX|@>@=#PXDL0hLPtC@*u |(DlR\\xU@d$u@k@@@d@@AB@@@@@@pMS @@rA@@@j@kϩmѷҷ>Ȑ!e@!y@'f_equal='&)(A/0ٰ2@'eq_rect=߀9}ͷ"X2=<ǩ0==@35@8H@@@K@ \BC@@W@ \鐩a@ qǐ +k()++h7# '()9777 G +17 +17T7   77   + 77# ' $'6''$'ࠒ=_PxH<^iP0,@@rA@@A@A@@=@A@7@AC@AA1E%IB@AF@AA@ABCD@@ @ba[bZ@dr@@K7MF@|7K>=EAc_O@ w@@@AC@UST@f r(j2 +k()+++7# '''$'-Xv@@r@>@A@A@@A@A@@ܠh @@p+`@C涐B詛&Specif$Init#Coq@@m7̂K@ր@ rdBAB〰@ rqBAA4Р̠@@@.A@A@@ ʐ @@t9S@@4@I14@. 5Fq6320,,+*%$̩#Ω/ک54  TTT@JL@O*@@@b@ \CB̶@@n@ \ԩ֩x@  rЀސࠒSJl\H`PPFB2@@t9@h@A@A@k@S@Al@M@oA8@ApA@AZ@AU@ABCD@@ @vuovn@xt@@@a`؀[#TMOQso_@@@@AC@ecd@q s4zB*X@@t@9@A@A@;A@A@@렠 @@,)@RQۀ @ seBAB耰 @ srBAA*ՠѠ@@@3A@A@@%+double_spec @@>d3E|2G;@_s!Au3wBvBw#CA@@@@@0succ_double_spec @@ge\|[d@ s Auހu`wLBw$BaAwWBg@@@@@Ϡ*double_add @@f|Zv BAvhBmA@@@@@/succ_double_add @@g趐橛|[v6BAv<BnA@@@@@#*double_mul @@h|uހBAu䀠BA@@@@@I/succ_double_mul @@iK}vBAvv怐BAA@@@@@t+div2_double @@;j0B}/%8@C hxtqAA@@@@@0div2_succ_double @@WkL}KA􀐐AA@@@@@*double_inj @@qlfxcz@}h}6B;A}vb@@@@@ˠ/succ_double_inj @@mͶ϶@}ѩ.B3A}@@@@@젠.succ_double_lt @@n@@BAFU꩚@@@@@ +compare_0_r @@o}}̀uA} AuB@@@@@,'pow_0_r @@p@}瀰>@b A}'AxBxC@@@@@N*pow_succ_r @@q bU\@vQ}EAA~k-NGwV9Z@@@@@y)pow_neg_r @@@r5@̀A}qA~?Xy/}|A@@@@@+square_spec @@bsWt~Vv_@,u*AwWAA@@@@@)size_log2 @@tt}@@~j~{ A}A~G@{ uu@ F)u@@@@@蠠'size_gt @@u9AyBybB/A@@@@@ 'size_le @@vw yByB©RAA@@@@@4)log2_spec @@w@@~)AA~@#andЖw@wEyByB/yByBS@@@@@+log2_nonpos @@Hx=@wA~wAE25~A@@@@@)even_spec @@hy] {`&i@< vAxAs@{ ;1A@@@@@Ơ(odd_spec @@zE{@5 ~v݀Ax3A@X ^A@@@@@렠1pos_div_eucl_spec @@{~򀶐!bdBBB@@@@@o@,}vBA ǀG@LBDyLx΀BCA@@@@@0-div_eucl_spec @@|@(C&B@?@@@@@?JJZ@Zu^vBAKBʩGDyyCBA@@@@@g(div_mod' @@.}w_zɩ$eByy#A7@F lrBA?@w+BA@@@@@'div_mod @@Z~@@GX AA`y܀y^T:X6\@@@@@Š6pos_div_eucl_remainder @@՛̀ڛ@z AA)y9@#snd署䀠@@@@@&mod_lt @@@붐@@ AAV@@@@@-mod_bound_pos @@A)%,'@yAB@vAϩy0$AP(X00@@@@@O,sqrtrem_sqrt @@B Щ y@#fst   @ +{wрA!@ !x,A@@@@@t,sqrtrem_spec @@;C0B@@@@@&A:<MICzƀzH>>AyAzR|>B|BSB@@@@@)sqrt_spec @@Dxȶ@yAAȐ婚fnyπzyyĩ(ȩzŀɀ@@@@@(sqrt_neg @@E@EAA;A@@@@@(ggcd_gcd @@F#&Ѐ˩ƀϩ1+@R y BA@ #yUBA@@@@@:5ggcd_correct_divisors @@GJMBJI@@@@B#]XXh.BA!g^mhhoBji@@@@B wssA"aax"bb|40^F{+!9cE{4)@@@@@,gcd_divide_l @@ZH߶ݩU@OuBAB@@@@@,gcd_divide_r @@uIBAA@@@@@Ǡ,gcd_greatest @@J!#!c(@8AC@?{ũCɩ@@@@@젠*gcd_nonneg @@K86zAπBA@@@@@.testbit_even_0 @@Lc€{}B}BAA{B@@@@@0-testbit_odd_0 @@M@뀰@(|k{퀠}B}BA}B@A{A@@@@@b3testbit_succ_r_div2 @@)Nrt p@{eYAA(}eb[mn$@@@@@0testbit_odd_succ @@TO鶐K@{AAS|Ӏ|U~AB~B~EC~NB~MCdh@@@@@Ѡ1testbit_even_succ @@P-߶@{ԀAA쩚Ԁ|~B~YB~C⩚ۀ퀠@@@@@ -testbit_neg_r @@Q@]AAπ$  |zB@@@@@+-shiftr_succ_r @@R;ڶĩ耰@OzBAŀBA@@@@@S-shiftl_succ_r @@Sc 쩛@?Iz퀠BFAꀐBA@@@@@{+shiftr_spec @@BT*96@|tAAC_7}ˀ?@@@@@0shiftl_spec_high @@oUufc@|AA@|]uʩi}@@@@@ڠ/shiftl_spec_low @@V趐@0AB݀}OB@@@@@)div2_spec @@WA؀ABC@@@@@"-pos_lxor_spec @@X'U"p'Z9怰;#O@$lxor=(_F@$lxor#Q\CBA}@$xorbȀb@'testbit>4'Y@'testbit8g$CA BA@@@@@c)lxor_spec @@*YsǶ"a'ƶ$v#x`0@ S|MCBA:qCAwBA@@@@@,pos_lor_spec @@\ZȀs̀Y@[)Datatypes$Init#Coq@@$boolZ'@k@#lor=L@#lor#F̀CBA)Datatypes$Init#Coq@@#orbCABA@@@@@砠(lor_spec @@[〠@ "}CBA;􀠐CABA@@@@@-pos_land_spec @@\KO.ۀ0D@$land=(;@$land#Q̀CBAs@$andb=CABA@@@@@S)land_spec @@]c,*egO@R 3"}ECBA4`CAfBA@@@@@.pos_ldiff_spec @@K^bHG@%ldiff=U@%ldiff$'RCBAl^CA@$negbkBA@@@@@à*ldiff_spec @@_\`Zթש@ *}CBAЀCA8ڀBA@@@@@'Even_wd @@@B!Puʠ~?@A@@AuuϠ@@ T@@u TJ@A@ \@@u \^H@A@AB ~H@C l~E~C #~?~;BD "~7~3 ~*~& ~~"@ =@@u =T}@A@ABC ~@ c~@ @@u T_@A@AB hx~@CDE ~~F S}} !}@ ! }@ !7@@u !7T@A@ABC *}}D.}}EK}}FZ}}GH@A@u*NExtraProp}K@A@@'NParity(Abstract'Natural'Numbers#Coq@+NParityPropuu@A@@@A"NP'NParity(Abstract'Natural'Numbers#Coq@\u@A@@@!N]@@ <@f@v! <u@A@A Ѹ@@v Ѹu@A@ 1@@u 1u@A@AB @@@u @u@A@ Za@ @u Zau@A@A _ @@#div _ d@@A@ `@@#eqb `d@@A@ABC b@@#gcd bĠd@@A@ i@@#leb id@@A@A j@"@#lor jàd@@A@ k@'@#ltb kd@@A@AB k(@+@u k(u@A@ k@/@u ku@A@A l@1@u lu@A@ n@4@#odd nd@@A@ABCD n@8@vH nu@A@ pl@>@#pow pld@@A@A u@B@u uu@A@ v@E@vM vu@A@AB@G@$div2d@@A@ 2@M@$even 2d@@A@A@Q@$landàd@@A@@V@$log2ʠd@@A@ABCS@Z@$lxorSd@@A@+=@a@u+=u@A@A{<@c@$sqrt{<d@@A@@h@uu@A@AB%@j@vf%u@A@I@o@%ldiffId@@A@A% j@s@&modulo% jd@@A@%$@x@&shiftl%$d@@A@AB%$@|@&shiftr%$d@@A@%D@@&square%D͠d@@A@).R@@'testbit).Rd@@A@:@@'compare:Ѡd@@A@ABCDEFG@A@(NZParity&NatInt'Numbers#Coq@,NZParityProp@@@A@@@C!C(NZParity&NatInt'Numbers#Coq@@A@@B!B@@ R@@&modulo Rd@@A@A @@&shiftl d@@A@ @ @&shiftr d@@A@AB r@@&square rd@@A@@@'testbitd@@A@A v@@'compare vd@@A@9.@@!t9.J@@A@ABC96]@!@"eq96]^@@A@96@(@"le96֠h@@A@A96@,@"lt96h@@A@9Կ@1@#add9Կd@@A@AB9ò@5@#div9òd@@A@9ş@;@#eqb9şd@@A@A9i@?@#gcd9id@@A@9Κ@D@#leb9Κd@@A@ABCD9h@H@#lor9hd@@A@9Ϸ@P@#ltb9Ϸd@@A@A9@T@#max9͠d@@A@9[@Y@#min9[d@@A@AB9=@]@#mul9=d@@A@9@c@#odd9Ġd@@A@A9Ӄ@g@#one9ӃT@@A@9@l@#pow9d@@A@ABC9٩@p@#sub9٩d@@A@9E@w@#two9ET@@A@A9B@{@$div29Bd@@A@9n@@$even9nנd@@A@AB9 h@@$land9 hd@@A@9 o@@$log29 od@@A@A9-@@$lxor9-d@@A@9@@$pred9d@@A@AB9@@$sqrt9d@@A@9W@@$succ9Wr@@A@9}@@$zero9}T@@A@:@@%ldiff:d@@A@ABCDEFG@A@@A!AǠ@A@@)Morphisms'Classes#Coq@@&ProperL@A)Morphisms'Classes@@*respectful%WO?%%Logic$Init @#iffС)@$Even ;1@@@ %'A*Equalities*Structures#Coq@AviA)Morphisms'Classes#Coq@@AAۓό^ @A݋X_A/RelationClasses'Classes#Coq@@AA.Morphisms_Prop'Classes#Coq@@)A1@D%Logic$Init#Coq@@ABCD@@AA@@A@&Odd_wd @HCSB4}@@Ax@nlpa@#Odd ^@@@WAO@AXAG@ZAE@\A=@^A5@ABCD@@-'even_wd @rm>9(}l^@jB@))Datatypes@$boolZ'@4 @"eq @I@$even @@@A@A8ӠA4Relation_Definitions)Relations#Coq@@AB@@j&odd_wd @{veU@C߀@f=h?4u@#odd ~ŀ@@@A@A,@AB@@+Even_or_Odd @ӠΠyޠ͠@D!x@@"or @@ ;1A@ ^A@@@A@AAۀߠK@A@A@A@ABCD@@ˠ,double_below @ ܠנƠ E@E!nŶ!mȶ@@"le \BA@"lt \@#mul 〠lC@#add @ zB@@@@A8@AAAM@CA2@EA0@ABC@@,double_above @YT% dSE@QFI H@@> \BA&@F \,@= 2@K -J۩8@Q 3B@@@Ay@AA@As@Aq@ABC@@U.Even_Odd_False @faP@@GN@]@ ;1A@e@W ^o%Logic$Init#Coq@@%Falsee@@@@A@AA@A@A@A@ABCD@@,orb_even_odd @֠Ѡ|Р  @H@"eq @)Datatypes$Init#Coq@@$boolZ'@)Datatypes$Init#Coq@@#orb@r A@M ~A@#Z'@A@@@@@ޠ(negb_odd @#٠ɠ.X@IשMI@?@$negb@~ ~BA@ /A@@@@@)negb_even @UP! `OA@MJE 2/@ TA&@ ~uA@@@@@<&even_0 @|MH7'{m@yKE@ z A@@@A@A}@Ak@ABC@@c%odd_0 @to^N@LЀ5l@ ~1B@@@@@%odd_1 @ɠĠoԠà@MV@ ~܀6A@@@A@AA@A@A@ABC@@&even_1 @ޠ'@N@m 뀐_B@@@@@Π&even_2 @ߠڠɠ H@ O;@  [A@@@#A@A$A0@&A@(A@*A@ABCD@@%odd_2 @>9 I8*s@6Pf˩@ ~Q?B@@@@@(Odd_succ @_Z+&jYK@WQO@oС)'@ ^-@$succ ! TA5@~ ;1A@@@Aw@AAo@Am@A[@A@ABCD@@U(odd_succ @faP@@RNĀ)`@ ~f@9 ! Am@$ A@@@@@)even_succ @Ƞà~nӠ @S|W@E À@g ! A@& ~ꀐA@@@@@)Even_succ @ +@T@ ;1@ ! 耐A@ ^A@@@@@ߠ.Even_succ_succ @$ڠʠ/Y@Uةŀ@3 ;1@ ! @ ! A@F ;1A@@@@@-Odd_succ_succ @XS$cRD@PVH @ ^$@ ! J*@ ! PA1@# ^A@@@@@G.even_succ_succ @XSB2x@W|@R@  X@+ ! ~^@1 ! Ae@ A@@@@@{-odd_succ_succ @vfˠ@XtꀰO@ ~Հ@_ ! @e ! A@$ ~耐A@@@@@(even_add @)@Y @s 񀐩@ VBA$Bool#Coq@@#eqbP@  B@ A@@@(A @A)A5@+A@-A@/A@ABCD@@'odd_add @C> N=/x@;Z32oԩ @ ~Z@" BAl@$xorbȀ @ ~oB'@ ~vA@@@@@=(even_mul @}NI8(|n@z[r6q8J@ P@i KBA@^@ Be@ A@@@A@AA@A@A@ABC@@'odd_mul @Ƞà~nӠ @\|~Y@ ~߀@ BA@$andb=@0 ~􀐐B@7 ~A@@@@@ -even_add_even @ӠΠ<@]@@ ;1A;@  @ q穚@ @@@@@,odd_add_even @=8 H7)r@5^-,@@K ;1Aq֩ @ ~\@$ +@ ~h1@@@@@.1even_add_mul_even @sn?:)~m_@k_c'b)!p,@;@ ;1BF@ {L@] DS@l Nk]Y@  @@@@@n0odd_add_mul_even @ziY@`gi@k@z@ ;1B逰N@ ~Ԁ@ ?@ @" ~怐K@@@@@.even_add_mul_2 @ݠ&@a@p @ SB@ JA@ B@@@@@㠠-odd_add_mul_2 @ ( #ޠΠ3"]@ bܶީT@{ ~?@ B@ A@ ~SB@@@@@(odd_pred @ _ Z + &  @ @!n@%Logic$Init#Coq@@#notШ{A者%Logic$Init#Coq@@"eq @)Datatypes$Init#Coq@@$boolZ'@L@ ~R@$pred 5BZ@ @@@ %'A*Equalities*Structures#Coq@A݋X_A/RelationClasses'Classes#Coq@@A@@AA@@A@)even_pred @ ɠ Ġ    o@ |Ajy@iڐAN_T@J Ȁ@G {F@* ~L@@@EA=@A@@5(even_sub @   Ǡ    @ B!m@@"le \AB@ @#sub cC$Bool#Coq@@#eqbP@ @  @@@AviA)Morphisms'Classes#Coq@@AAۀߠK @Aۓό^ @A@A1@DՠԠ@@ABCD@@'odd_sub @ ` [ , '  @ Ce@!@d \AB-@ ~|3@c cwbਗ਼)Datatypes$Init#Coq@@$xorbȀG@ ~vM@ ~@@@@@ᠠ-Private_NZPowWA'pow_0_l @   z@@B!C$NPow(Abstract'Natural'Numbers#Coq@ t(@A@$NPow(Abstract'Natural'Numbers#Coq@(NPowProp 9@A@@@A!B! z?@A@@@!A' y x@A@%NZPow&NatInt'Numbers#Coq@)NZPowProp: N@@@A@@@J!C%NZPow&NatInt'Numbers#Coq@+@A@@I!B,@@qj@5@'compareqjd@@A@Ag@@!tgJ@@A@@ @"eq^@@A@AB\@@"le\h@@A@k@@"ltkh@@A@A@@#addd@@A@8@@#div8d@@A@ABC%@!@#eqb%d@@A@@'@#gcdd@@A@A @+@#leb d@@A@@0@#lord@@A@ABD=@4@#ltb=d@@A@S@=@#maxSd@@A@A@A@#mind@@A@@F@#mulàd@@A@ABJ@J@#oddJd@@A@ @P@#one T@@A@A@T@#powd@@A@/@Y@#sub/d@@A@ABC@]@#twoˠT@@A@+D@c@$div2+Dd@@A@AW]@g@$evenW]d@@A@@l@$landd@@A@ABD@p@$log2d@@A@~@x@$lxor~d@@A@Axh@|@$predxhd@@A@g@@$sqrtgd@@A@AB@@$succݠr@@A@s@@$zerosT@@A@ot@@%ldiffotd@@A@AB*:@@&modulo*:d@@A@CD+ar@@&shiftl+ard@@A@+ar@@&shiftr+ard@@A@+t@@&square+td@@A@.F@@'testbit.Fd@@A@ABCEFG@A@@H!AǠ@A@@!ai@x@"lt \>AΩ@#pow  HBI@@@ %'A*Equalities*Structures#Coq@AviA)Morphisms'Classes#Coq@@AAۓό^ @A݋X_A/RelationClasses'Classes#Coq@@A1@D%Logic$Init#Coq@@ABC@@AA@@A@(pow_0_l' @   נ]N>94"]@ AX@%Logic$Init#Coq@@#notШT+AW.@` _@@@]AU@_AN@aAL@ABC@@:'pow_1_r @ B = upkYK@WB|S@ AA@@@A|@Au@As@ABC@@a'pow_1_l @ i d 5r@~C@-@"le \A7@ Ԁ@@@A@A@A@ABC@@'pow_2_r @   cڠʠŠ@DLѰ\@ Aᩚc@#mul _AA@@@A@A@A@ABC@@(pow_eq_0 @ Ơ   ݠϠ@E{!b~@@` \RA@ 㩚@ 4C]D`@@@A@A@A@ABC@@+pow_nonzero @   ǠM>.)$M@FH5@򀐩<B@@ \FJ!@S r;>@@@@@',pow_eq_0_iff @ / * rb]XF8@DG|䶐i橚IHG@@#iffС)vM@ BAȩ@"or @@ \Aש%@#andЖw@ @ \AuB@@@A@AAۀߠK@A@A@ABC@@)pow_add_r @   Tڠˠ@H=?!cB@Q@$ \B@Y@, \ְ֩a@ Eh@#add ҩo@  ju@ ۩{@ @@@A@A@A@ABC@@Ӡ)pow_mul_l @ ۠ ֠ - -@I(S𩚠@" A@G CBA@P @7 VCA@? ^BA@@@>A6@@A/@BA-@ABC@@)pow_mul_r @# ufVQL:,u@8Jpض]ڶܶ@@ \B@@ \ppG@y @ gj@  @ sv@@@A@Ay@Aw@ABC@@e*pow_nonneg @mh9v@K"$@3@ \B:@  \@@ ݀@@@A@AA@A@A@ABC@@.pow_pos_nonneg @nՠРˠ@LWY@h@ \-B@p@C \5v@ \;|@ @@@A@AAX@A@A@ABC@@֠-pow_lt_mono_l @ޠ٠0! 0@M+V@@. \kA@%Logic$Init#Coq@@#andЖw@@ \#@K \),@Q \@M ln8@S r;>@@@QAI@ARA@TAC@VAA@ABC@@/-pow_le_mono_l @72zje`N@@LN춐q@Q@ \ȐC @ \CB@ \@ ~@ @@@A@AA@A@A@ABC@@x(pow_gt_1 @{LҠà@O57@F@ \BYQ@ \ΩW@ \]@ ڐ@@@A@AA9@A@A@ABC@@-pow_lt_mono_r @֠Ƞ@P tv7x@@ \0C@@b \T @@ \@$ \@  ?FB@' F@@@%A@A&A@(A@*A@,A @ABCD@@-pow_le_mono_r @ ٠_P@;6$_@"QZ¶GĶƶ@@] \C@@ \FZ@ \@g O@m X@@@kAc@AlA@nA]@pA[@ABC@@I+pow_le_mono @QLzhZ@fR !d @n @ \D'@ \DB@0@ \6@  \<@ ـ۩B@ ߀@@@A@A@@+pow_lt_mono @jѠ̠Ǡ@SSUWMY@l@ \1Ds@ \DB@΀@ \E橚@ \@ \@ /1@ 5@@@A @At@A@ABC@@)pow_inj_l @ĠJ;+&!J@ TE2p@@ \C@@ \1@@W \8@M$@V u6>@\ {}D[2G?@@@@@3)pow_inj_r @;6~nidRD@PUu@@ \C@ @ \t@@ \{@g@ y!@ u@@@@@u1pow_lt_mono_l_iff @}xIϠ@V246@E@ \ C@M@  \@T@ \f^@ \d@ \j@ Щp@  ֐@@@@@ 1pow_le_mono_l_iff @ʠŠ Ӡ@WB@@e \WC@@m \_@@) \f @~ \ J@ \@5 T@; Z\#@@@@@1pow_lt_mono_r_iff @iZJE@. i@,Xd̶Qζж@@g \C@@ \d@y \WZ@ \@{ c@ l@@@@@U1pow_le_mono_r_iff @]X)tf@rY@%@ \ΐC@-@ \?7@  \=@ \C@ I@ 怠@@@@@,pow_gt_lin_r @o֠Ѡ̠@ZXZ@i@ \B@q@D \6w@ \ਗ਼}@ @@@A@AAY@A@A@ABC@@נ-pow_add_lower @ߠڠ1" 1@[,W@@z \lC@@ \t@@> \{@ \@Z V@F e&.@L km4@R q@r n8y@@@@VAN@AWA@YAH@[AF@ABC@@4-pow_add_upper @<7ojeSE@Q\v@@ \ɐC@ @ \u@@ \|@ \@ %@ +@ &1@ ΀7@$pred >@ ҀD@ ဠJ@ 瀠@@@A@AA&@A@A@A@ABCD@@@@@  @ @A@B@CD@+pow_succ_r' @ @ @!af!biũy@ B@$succ ! A@#mul B@ -BA@@@@@AA@@A@'pow_0_l @ A 2 " @ @A;@%Logic$Init#Coq@@#notШ4 A7@@ _B@@@@@1'pow_1_r @ @ Ҁ"@jϩT+@] |AA     @ n @&1c>9    q l@@@@@b'pow_1_l @NI    |@ B[@ A@@@@@~'pow_2_r @" @ ;oj;@x,@ ɀA3@ .AAT@%1cV ܠ ͠  @@@@@)pow_add_r @f  ݠ ͠ @ CKM!cPհ`@ Cg@#add BAp@ kv@ CB~@ CA@@@@@)pow_mul_l @ڠՠ ,   @ +D&%@멚@  <@ CBA@& @ 2 QCA@ : YBA@@@@@,)pow_mul_r @ j [ K F@ iEdɶc˶~ͩR)@ [ zC@\ ߀BA@ j @ p CBA@@@@@c(pow_eq_0 @OJ    }@ F@bcA׶@g@  CZpD@@@@@+pow_nonzero @ytE ˠ   @ G*,@BH@  倠- @@@@@,pow_eq_0_iff @n   ՠ @ HSU%Logic$Init#Coq@@#iffС)s@  BA:@#andЖw@ԀՐAIؐBL@@@ %'A*Equalities*Structures#Coq@AviA)Morphisms'Classes#Coq@@Aۓό^ @A݋X_A/RelationClasses'Classes#Coq@@ABC@@-pow_lt_mono_l @͠ S D 4 /@ RIMLg@@A@@"lt \@ \@ X wE@ _ ~Ɛ@@@@@O-pow_le_mono_l @;6  ~ n i@ J춐@@"le \CB@  \@  L@  R@@@@@(pow_gt_1 @ni:    @ K!@0@c \ِB@v>@q \穚D@  ဠ&)@@@@@-pow_lt_mono_r @j   Ѡ @ LOQS@b@ \ C@j@ \Op@ \v@  X|@  a@@@@@ꠠ-pow_le_mono_r @֠Ѡ (   @ 'M"!<@뀐C`@@ \ਗ਼@ \@ , K@ 2 Q@@@@@"+pow_le_mono @ ڠ ` Q A <@ _NZYtö!dƶ@&P'D@@ \¶@@ \ ɩ@ \@ n GF@ v ڐ@@@@@f+pow_lt_mono @  @ 29WR#@E @%Logic$Init#Coq@@#andЖw@(@[ \D/@b \DB@<@o \B@u \$H@{ \N@  뀠]tT@  69s@\Uu   ܠ @@@@@͠)pow_inj_l @    @ Ojln@΀ϐAC@ө@  $iũ@  *r˩ q@@@@@)pow_inj_r @ ; ,  @ :P54O@@ \VC@,@ 5 T@ ; Z:@@@@@-1pow_lt_mono_l_iff @ k \ L G@ jQeʶd̶ζ@.X/A@ \ͩ@! \@ r 2@ x 8@@@@@h1pow_le_mono_l_iff @TO     @ R @ijAީ#@$ \)@* \/@  ̀m5@  Ҁs@@@@@1pow_lt_mono_r_iff @[  Ҡ   @ S@BD@S@ \C^@ \Cd@ \j@  LOp@   R@@@@@ޠ1pow_le_mono_r_iff @ʠŠ   @T{}0@@ \7C2@ \~ש@ \@ # B@ ) H@@@@@,pow_gt_lin_r @ѠWH83@VUQP@@ \pB@ \ @ R q@@@@@B-pow_add_lower @.)qa\@Vz߶yᶐ@CmDA@ \@ @  C @  I@  @ U@@@@@-pow_add_upper @ql=à@W"$&@A<@= \B@  ߀H@ ܀*-N@ IT@  ةZ@$pred =a@ g@  Im@   R@@@@@۠(even_pow @Ǡ  @Xxz@ڀېAO.@"eq @)Datatypes$Init#Coq@@$boolZ'@@$even ۀ@* I꩚@  瀐@@@+A#@-A@/A@ABC@@&'odd_pow @ ޠdUE@@cY^ö]Ŷ@%O&AKG@#odd ~/@d $@  ~;ѐ@@@@@Z.Private_NZSqrtA0sqrt_spec_nonneg @MH@@A!B%NSqrt(Abstract'Natural'Numbers#Coq@@A@@@!A@A@)NSqrtProp @A@@&NZSqrt&NatInt'Numbers#Coq@*NZSqrtProp<@@@A@@@J!C&NZSqrt&NatInt'Numbers#Coq@:@A@@I!B1@@[@:@'compare[d@@A@Ax5K@@!tx5KJ@@A@x<@ @"eqx<Ǡ^@@A@ABx=@@@"lex=@h@@A@x=O@@"ltx=Oh@@A@Axp@@#addxpd@@A@x@@#divxd@@A@ABCx @!@#eqbx d@@A@x@'@#gcdxӠd@@A@Ax@+@#lebxd@@A@x@0@#lorxҠd@@A@ABDx!@4@#ltbx!d@@A@x7@=@#maxx7d@@A@Ax@A@#minxŠd@@A@xק@F@#mulxקd@@A@ABx.@J@#oddx.d@@A@x@P@#onexT@@A@Ax{@T@#powx{d@@A@x@Y@#subxd@@A@ABCx@]@#twoxᯠT@@A@I(@c@$div2I(d@@A@AuA@g@$evenuAd@@A@@l@$landҠd@@A@ABD&@p@$log2&٠d@@A@4b@x@$lxor4bd@@A@AL@|@$predLd@@A@K@@$sqrtKd@@A@AB@@$succr@@A@@@$zeroT@@A@Z X@@%ldiffZ Xd@@A@AB,vXy@@&modulo,vXyd@@A@CD-K@@&shiftl-Kd@@A@-K@@&shiftr-Kd@@A@-^@@&square-^ܠd@@A@0*@@'testbit0*d@@A@ABCEFG@A@@H!AǠ@A@@!b@@"lt \ @#mul AA@  @$succ ! BA#@ ! IA*@"le \B@@@ %'A*Equalities*Structures#Coq@AviA)Morphisms'Classes#Coq@@AAۀߠK @Aۓό^ @A݋X_A/RelationClasses'Classes#Coq@@ABC@@AA@@A@+sqrt_nonneg @y`QLF6(q@4A!abp@F \5v@$sqrt !A@@@LAD@AMA<@OA:@QA8@ABC@@0+sqrt_unique @ڠՠ~yscU@aB-@%Logic$Init#Coq@@#andЖw@@ \@ AAB@ \B@ @ ! A@ ! AO&@d !倐C@@@A@A@@'sqrt_wd @72۠֠Р@C)Morphisms'Classes#Coq@@&ProperL@)Morphisms'Classes@@*respectful%WO?@ !@@@A@AA@A@A@ABC@@ɠ-sqrt_spec_alt @sn?& 7@D'@6@  \A%Logic$Init#Coq@@"ex @>!rA@#andЖw@ΰyY@#add `@T [f@ !ql@ !wAԀw@M \< }@S \@w ~@ !@@@]AU@A^AM@`AK@bAI@dA1@DZYX@@ABCD@@H,sqrt_unique' @{m@yEE!c@@ \A@ \A@ ǀPB@K"D@~ k@ ؀Z1@o !E@@@A@AA@A@A@ABC@@+sqrt_square @HCѠà @F@ @ \АA`@ !@ @@@A@A@AB@@Π0sqrt_pred_square @xsD+<@G,@;@6 \AD@ !OJ@$pred -Q@E L&&W@  9,@@@+A#@A,A@.A@0A@ABC@@,sqrt_le_mono @l]XRB4}@@H mzo@~@T \BA@\ \@ !@ !g@@@eA]@gAV@iAP@ABC@@H.sqrt_lt_cancel @{m@yIE@@ \@G !ȀB@N !πA@ \@@@A@AA@A@A@ABC@@.sqrt_le_square @-(Ѡ̠Ơ@Jᶐ@@ \B@@ \ϩ@#iffС)@ \ @ 33=@ \9@ !$I@@@A@A@A@ABC@@Ϡ.sqrt_lt_square @ytE,=@K-:/@>@ \B@F@ \ LP@K \V@J Q||\@W \b@ !m@@@6A.@A7A&@9A$@;A"@ABC@@&sqrt_0 @Ġwhc]M?@KLҩ@ !KK@@@YAQ@[AF@]AD@ABC@@<&sqrt_1 @oa@mM@2 !QQ@@@{As@}Ah@Af@ABC@@^&sqrt_2 @Ԡ@N?@T !ՀNs@@@A@AA@A@A@ABC@@(sqrt_pos @,'ߠРˠŠ@Oਗ਼@ \@ !A@ \ĐA@@@A@A@A@ABC@@+sqrt_lt_lin @`[,۠$@P@#@ \̐A*@% \0@ !;@@@A@A@A@ABC@@栠+sqrt_le_lin @\C4/) T@QD@S@) \AZ@0 \`@ !k55@@@4A,@A5A$@7A@9A1ՠF-SetoidTactics'Classes#Coq@@CA1I @ABCD@@$.sqrt_mul_below @ΠɠrmgWI@UR!@h \@ @( !B@/ !A@6 !@ BA@@@A@AAx@Av@At@ABC@@l.sqrt_mul_above @  ɠ@Siʶ̶@@ \B@@ \@ \@y !@ %@ @ ! '@ !7 @ ! 3@ !9@@@A@AA@A@A@ABC@@ˠ,sqrt_succ_le @ u p A(9@T)@8@ \A?@ \E@ !PK@0 ! q Q@6 ! wW@ !b,@@@+A#@A,A@.A@0A@ABC@@,sqrt_succ_or @   l]XRB4}@@U m@|@R \AAF@"or @٩@ !@x ! h@~ ! @) !t󩚠@1 !@ ! Ӏ@= !@@@@@c7sqrt_eq_succ_iff_square @! ! ٠@V`@@ \A׀R)@g !耐@ !  @ ! @y !ĩ뷐@ \|S@ ! -- @ @@@A@AA@A@A@A8ӠA4Relation_Definitions)Relations#Coq@@ABCD@@Ϡ+sqrt_add_le @!y!t!E,=@W-:/=@ \C@ !NI@ ݀BAQ@ 倠W@ !bB^@ !iA@@@3A+@A4A#@6A!@8A@ABC@@+add_sqrt_le @!!!te`ZJ<@HXuw@@\ \KB@@d \Sc@j \@A .@* !Щ@0 !̩@6 !@ 6@_ Lސ@@@Ar@A@@j@@@@]@A\@B@@A@B[@CQ@@ADE%@*sqrt_spec' @""!Ѡ @@!aϩ%Logic$Init#Coq@@#andЖw@@"le \@#mul @ !A@ ! AA @"lt \A@  @$succ ! >@ !)A%@ ! K+@ !6A@@@@@AA@@A@+sqrt_unique @;:987@*T@=6"""aH94@wE!bH@z[@o \a@n \AABj@a \Bq@~ lw@` ! A~@g ! Aө@ !CBQ"ݠ"ؠ"|@@@@@f+sqrt_square @"""@A!@6 !@ AAA@@@@@,sqrt_le_mono @@ '؀##"ߠƠ@ö~Ŷ@@ \BA@ \@l !퀐[@r !`*#<#7#@@@@@Š.sqrt_lt_cancel @@ !9RЀ#O#J# @1@@ \@ !!B@ !(A$@ \*#x#s#D +  @@@@@.sqrt_le_square @###S : + &@ 8Bi79%Logic$Init#Coq@@#iffС)U@i \[@h VAABd@x \Ak@ !vB@@@@@@.sqrt_lt_square @#Ơ## y j e@ wCv1x?@ \B@ AA@ \@) !BA@@@@@u&sqrt_0 @r@ #8###ˠ   @2 @G !Ȁ$$ #ݠ Ġ  @@@@@&sqrt_1 @@ #8$$$# נ Ƞ @W.@l !퀐$6$1$  ڠ @@@@@&sqrt_2 @@ #8$I$D$   @|S@ !$[$V$'   @@@@@䠠+sqrt_lt_lin @@ <ۀ$n$i$: !  @P@-@$ \֐A4@+ \:@ !E!$$$Z A 2 -@@@@@+sqrt_le_lin @$$$i P A <@ NDM[@o \a@ !lAA@@@@@7.sqrt_mul_below @4@ .m$$$ t e `@q,s@ \@ @  !B@  !A@ % !@ BA7$$$à   @@@@@.sqrt_mul_above @%%$Ҡ   @ Eq@ \@ V !׀@ ̀BA@ Հ@ ! @ p !񀐐B@ ! @ } !A@@@@@Ƞ,sqrt_succ_le @%N%I%   @ F0 @  \@  !@ ! >A@ ! E%@  !0A@@@@@,sqrt_succ_or @%%{%L 3 $ @ 1Gb0@"or @H@  !SN@7 ! tAU@> ! {[@  !fAٰd@  !oj@S ! Aq@  !|A@@@@@F+sqrt_add_le @C@ :%Р%ˠ%  t o@;@ \@  !@#add 1BA@  9@ 5 !B@ < !A8&&%Ӡ   @@@@@+add_sqrt_le @&&% ɠ  @ Hƶȩ@ \@@ p@ l !퀐B@ s !􀐐A@ z !@ z@` BA@@@@@Ҡ'sqrt_up @ K  ݠ ܠ  @!tР)Datatypes$Init @*comparison;f@@@@@@@@@@@@D!x@'compare%@$zero Ȱ,@ gL 2@ :@ &&&e L = 8@ 2,NZSqrtUpProp < (@A@@@N!D ' C k /@A@@M . - % 4@A@@L $ 2 # "@A@@K q 7 ( '@A@ ee +k77!= R'6'7 7 7$'6''+k6'b@@A@B@AALM`XV`FAt~ԠU&ޠ&٠&   }E@:62@@@@@ H,sqrt_up_eqn0 @&&&   YTNJF@ zY F@@  \A|4 @+b9 @@@@@ o+sqrt_up_eqn @''& ̠  {uqm@ Z mζ@@  \A[2@+b9 @  ! @ | !@  ڀ ͐@@@@@ ,sqrt_up_spec @'R'M'   @ [ @@  \ېA ~!@  \'@  "-@  3@/+b9 9@  ?@;+b9  E@  \ K@ ? FQ@M+b9 &W@S+b9 ,@@@ +A #@A ,A @ .A @ 0A @ABC@@ .sqrt_up_nonneg @''' l ] X  @ A\ n|@ R \A@~+b9A@@@ WA O@A XA G@ ZA E@ \A C@ABC@@ ;*sqrt_up_wd @'''   LGA=9@ m] @ $$@+b9@@@ A w@A A k@ A i@ A1DH @ A1FdJ $@ABCD@@ i.sqrt_up_unique @(('ߠ Ơ  zuokg@ ^ gȶ ʶ@@  \A@ B@  \@  怠@  Ӏ Ʃ@  ـ  @  \ #@    ةW @+b9 ; 1@@@ A @A A @ A @ A@ABC@@ à.sqrt_up_square @(m(h(9  ԠϠɠŠ@ _ "@1@  \A:@6+b9@@ 4 ;   @@@ A @A A @ A @ A @ABC@@ 3sqrt_up_succ_square @(((nUFA @*` W@f@ < \+Ao@k+b9u@ Z ! {@ o v P P@ f !  V@@@ TA L@ VA A@ XA ?@ABC@@ 7)sqrt_up_0 @((ܠ(HC=95@ia𩚠¤@+b9ii@@@ wA o@ yA d@ {A b@ABC@@ Z)sqrt_up_1 @)((Рkf`\X@b<@+b9pp@@@ A @ A @ A @ABC@@ })sqrt_up_2 @)')"(ڠˠƠ{@c_6@+b9nn@@@ A @A A @ A @ A @ABC@@ /le_sqrt_sqrt_up @)L)G)@d @  \@  ! A@+b9A@@@ A @A A @ A @ A @ABC@@ ՠ4le_sqrt_up_succ_sqrt @))z)K2#۠נ@e 4B@ \H@D+b9AO@4 ! uU@  !`A@@@*A"@A+A@-A@/A@ABC@@1sqrt_sqrt_up_spec @)))k\W @@f m@|@R \AA 䀠Ç@] \Í@ Ó@ !hÙ@# !nnß@u \tå@ ë@+b9ñ@+b9@@@A}@AAu@As@Aq@ABC@@i2sqrt_sqrt_up_exact @**)ߠƠzuokg@ggȶ@@ \ÜA ހY0@n !@+b9 淐詛 @ \ÿ wN"@   @@@A@AA@A@A@A y@ABCD@@/sqrt_up_le_mono @*f*a*2 ͠Ƞ @h(@,@ \BA4@  \:@6+b9`@@<+b9@@@A @AA@A@A@ABC@@1sqrt_up_lt_cancel @***nUFA @*iWdY@h@c \n@j+b9Bu@q+b9A|@w \Q@@@PAH@AQA@@SA>@UA<@ABC@@41sqrt_up_lt_square @*ޠ*٠*}E@:62@fj2ēĕ@Ĥ@z \iB@Ĭ@ \q Ķ@ \ļ@  쩚@ \詚@+b9 @@@A@A@A@ABC@@~1sqrt_up_le_square @+(+#*̠۠Ǡ|@k|ݶ߶@@ \ijB@@ \Ļ˩ @ \0@ ,, @ \@+b9B8@@@A@AA@A@A@ABC@@ʠ+sqrt_up_pos @+t+o+@'۠֠Р̠@l) 7;@6 \A@=+b9AH@C \ A@@@A@A @ A@ABC@@.sqrt_up_lt_lin @+++u\MH @1m^@m@h \At@o \z@v+b9OO@@@NAF@AOA>@QA<@SA:@ABC@@2.sqrt_up_le_lin @+ܠ+נ+{C>840@dn0ő@Š@v \eAŧ@} \ŭ@+b9@@@Ay@AAq@Ao@Am@ABC@@e1sqrt_up_mul_above @,, +۠ vqkgc@ocĶƶ@@ \ŚB@@ \Ţ@ \@+b9@ ꀠ@ @+b9+@+b9'@@@A@AA@A@A@ABC@@1sqrt_up_mul_below @,c,^,/ʠŠ@p%@)@$ \B@1@, \7@2 \=@1 8C@ %I@E+b9yO@ 1U@Q+b9{[@W+b9a@U \@@@5A-@A6A%@8A#@:A!@ABC@@/sqrt_up_succ_le @,à,,vgb*%@Kqx@Ƈ@] \LAƎ@d \Ɣ@+b9ƚ@ ! oƠ@ ! ƀƦ@+b9{@@@zAr@A{Aj@}Ah@Af@ABC@@^/sqrt_up_succ_or @--,Ԡojd`\@r\ƽ@@ \ƑA PN%@+b9@ ! @ !  @+b9h?@+b9@ ! Ω@+b9Ԑ@@@@@:sqrt_up_eq_succ_iff_square @-Y-T-% @s@@ \A$v*@&+b90@ ! V6@ ! \<@8+b98E:L@" \ɰtT@H O@@@(A @A)A@+A@-A@/A@ABCD@@.sqrt_up_add_le @---k\W @@t mzo}@S \ǃ@+b9lj@0 BAǑ@8 %Ǘ@+b9BǞ@+b9A@@@sAk@AtAc@vAa@xA_@ABC@@W.add_sqrt_up_le @.--͠hc]YU@uUǶǸ@@ \njB@@ \ǔ@ \@ o@+b9@+b9 @ ! @+b9@ }@ /%@@@A@AA@A@A@ABC@@+log2_nonneg @.a.\.-@@C!D$NLog(Abstract'Natural'Numbers#Coq@.'@A@@B!C.-@A@$NLog(Abstract'Natural'Numbers#Coq@)NLog2Prop.>@A@@@A!B'.3@A@@@!A-.2.1@A@%NZLog&NatInt'Numbers#Coq@*NZLog2Prop?@@@A@@@J!E%NZLog&NatInt'Numbers#Coq@R-Private_NZPow@A@@I!D3@A@@H!C4@@ @=@!t J@@A@A /@@"eq /^@@A@ @ @"le h@@A@AB @@"lt h@@A@ ;@@#add ;ؠd@@A@A @@@#div @d@@A@ Bq@@#eqb Bqd@@A@ABC D;@!@#gcd D;d@@A@ Kl@(@#leb Kld@@A@A L:@,@#lor L:d@@A@ L@1@#ltb Ld@@A@AB L@5@#max Ld@@A@ M-@;@#min M-d@@A@A N@?@#mul Nd@@A@ O@D@#odd Od@@A@ABCD PU@H@#one PUT@@A@ Q@P@#pow Qd@@A@A V{@T@#sub V{d@@A@ X@Y@#two XT@@A@AB @]@$div2 d@@A@ @c@$even 멠d@@A@A :@g@$land :d@@A@ A@l@$log2 Ad@@A@ABC @p@$lxor ʠd@@A@ @w@$pred d@@A@A \@{@$sqrt \d@@A@ a)@@$succ a)r@@A@AB O@@$zero OT@@A@ @@%ldiff d@@A@A@@&modulod@@A@qa@@&shiftlqad@@A@ABqg@@&shiftrqgd@@A@&D@@&square&Dd@@A@3@@'testbit3d@@A@1H@@'compare1Hd@@A@ABCDEFG@A@@G!BР@A@@F!A֠@A@@!a0>@"le \E@$log2 F)gA@@@ %'A*Equalities*Structures#Coq@AviA)Morphisms'Classes#Coq@@AAۀߠK @Aۓό^ @A݋X_A/RelationClasses'Classes#Coq@@ABC@@AA@@A@+log2_unique @/Ƞ/à/gXSC>9([V@(AQɀ!bɃ@ɒ@T \WA@%Logic$Init#Coq@@#andЖw@ɩ@k \ɯ@#pow M4BCɸ@"lt \ɿ@ \C@$succ ! 쀐C@ F)D@@@@@d'log2_wd @0)0$/Ƞys@B)Morphisms'Classes#Coq@@&ProperL@)Morphisms'Classes@@*respectful%WO?@ F))@@@A@AA@A@A@ABC@@-log2_spec_alt @0i0d05ߠڠɠ@C!@0@x \A%Logic$Init#Coq@@"ex @8!r;@#andЖw@ȰğS@#add 耠Z@ ީ`@ F)Àk@- \0 q@ \w@ }@8 F)̐@@@6A.@A7A&@9A$@;A"@=A1@DTSR@@ABCD@@!,log2_unique' @000vqa\WF60yt@FDoʞʠ!cʣ@ʲ@t \wB@ ʾ@ \ʃ@  \@ gN@HE@ h@+ w^ )W.@ F)F@@@A@AA@A@A@ABC@@)log2_pow2 @1E1@1ՠРؠ@E@ @ \ѐAa@ F)6@l ʟkk@@@A@A@AB@@.log2_pred_pow2 @1y1t1E ٠ɠà @F1@@@ \AŕI@ F)jO@$pred 2V@ \@  >@@@A @AA@A@A@ABC@@&log2_1 @111]NI94/QL@GЩ˄@? F)-I@@@A)@@A'@ABC@@&log2_2 @11ߠ1to_ZUD4.wr@DH˪@e F)ˀ.S@@@bAZ@dAO@fAM@ABC@@E(log2_pos @2 21֠{jZT@jI¶@@ \zA@  \˝@ F).@@@A@AA@A@A@ABC@@{)log2_null @2@2;2 ߠРˠӠ@J@#iffС)[@ F)0Aթ@ \A@@@A@AA@A@A@ABC@@,log2_le_mono @2y2t2E ٠ɠà @K13@B@ \BAJ@  \P@  F)qV@ F)w@@@A@A@A@ABC@@.log2_lt_cancel @222UFA1,'ID@L?np@@ \̅@@ F)B̌@G F)A̓@ \@@@LAD@AMA<@OA:@QA8@ABC@@0,log2_le_pow2 @222pkfUE?@UM~̭-̯@̾@ \̃B@ \@  lS@ \%@ F)*@@@A@A@A~@ABC@@v,log2_lt_pow2 @3;363ڠˠƠΠ@Ns@@L \ɐB@W \^@f ̙e@c \!@ F)Bpq@@@A@AA@A@A@ABC@@+log2_lt_lin @33~3O"Ӡ͠@O ;@J@ \AQ@ \W@ F)x@@@@@젠+log2_le_lin @333}PA<,'"D?@P:i@x@: \=A@A \ͅ@@ F)Ր@@@=A5@?A.@AA(@ABC@@ .log2_mul_below @333up`[VE5/xs@EQn͟͝@ͮ@ \sB@Ͷ@ \{ͼ@~ \@o V@ F)逐@ F)@ F)@#mul ր *@@@A@A@A~@ABC@@v.log2_mul_above @4;464ڠˠƠΠ@Rs@@ \ɐB@ @ \\@ \@ F)9@D Pm$@ *@ 0@ F)Qb6@ F)Wߐ@@@A@AA@A@A@ABC@@Ӡ-log2_mul_pow2 @444d7(# +&@S!PR@a@ \&B@i@+ \.Ƚq@, F)w@ r}@ ̩΃@0 ҩΉ@D F)@@@BA:@ACA2@EA0@GA.@ABC@@&+log2_double @444{vfa\K;5~y@KTtΣ@β@ \wA0λ@v F)܀@ E@ ! 퀐@ F)@@@A}@Ar@Ap@ABC@@h)log2_same @5-5(4̠}w@U嶐e@@> \λB@@F \N@|S@ F)(9 @ F).\@[ \F@? ΝK@@@A@AA@A@A@ABC@@,log2_succ_le @5{5v5G ۠ˠŠ @V3A@ \G@ F)hM@ ! sAT@ ! zZ@ F){A@@@A @AA@A@A@ABC@@,log2_succ_or @555\MH83. PK@WFuL@"or @٩ύ@H F)ϓ@ ! AϚ@ ! Ϡ@[ F)Aϩ@d F)ʀϯ@ ! ՀA϶@q F)׀A@@@@@L4log2_eq_succ_is_pow2 @66 5ݠqa[@qXɶ@O&@ F)@ ! A@" !  @ F)A귐jqH@7 ! "K@S φ@@@A@AA@A@A@A@ABCD@@5log2_eq_succ_iff_pow2 @6f6a62ܠנƠ@Y@-@u \A.ïʆ:@ F)[@@{ ! fF@ ! lL@ F)mHJϰʦZ@ ! `@ @@@A@AA @A@ABA@ A@"A1ՠF-SetoidTactics'Classes#Coq@@,A1I @ABCD@@ 0log2_succ_double @6Ҡ6͠6qb]MHC2"e`@2Z[Њ@Й@ \^AТ@] F)ÀШ@U <Ю@ 2Wд@ ! ڀк@u F)ۀ @@@sAk@AtAc@vAa@xA_@zA=@ABCD@@Y+log2_add_le @776~nh@~[ֶVض@%Logic$Init#Coq@@#notШlCBЛ@tKIТ@ \@ F)& @ =Z@ @ F)8I@ F)>l@@@A@AA@A@A@ABC@@+add_log2_lt @77z7K   ߠϠɠ @\79@H@ \ B@P@ \V@ \\@  b@ F)h@# F)n@ i򩚠t@/ F)z@' ɐ@@@3A+@A4A#@6A!@8A@ABC@@'log2_up @W7}@!t <Р)Datatypes$Init@*comparison;f@@@@@@@@@@@@D!x7@ <7@'compare:р7@#one nހW7@$zero%؀7@7@ʀ7@$pred+=p7@%؀8$87@ѐ +k77!= R'6'7 7 7$'6''+k6' K   @dt @\ҦcԠ@/[ِc@ZYX@@A@B@AAL@KKX"@J`'@[`M ,@!8c8^8/    ޠ ٠@@P!F    @A@@O  Ǡ  @A@@N  ̠  @A@@M  Ѡ  @A@@L  ֠  @A@@K  ۠  @A@ ,NZLog2UpProp  @A@@@@@@ՠ,log2_up_eqn0 @888f 9 * %  72.*&"@ ] $S@b@ $ \A ̷k@ !Ӏ0@@@@@ +log2_up_eqn @8Š88 d U P @ ;b]YUQMI@ &^ O~@ҍ@ \6A ⩚Җ@ !Ӏ橚Ҝ@ ! €Ң@ ] F)ÀҨ@Y Ê@@@@@ =,log2_up_spec @988Π    } x@ c_ һ@@  \sA 7@  \@ , x_@ À@_ !Ӏ 7 7@  \ =@ D w@q !Ӏ I@@@ A @A A @ A @ A @ABC@@ .log2_up_nonpos @9[9V9'    ֠ Ѡ@ ` @#@  \Aơx,@ !Ӏ |@@@@@ *log2_up_wd @999R %    # @ a ^@BB TDDɚQ@ !Ӏ@@@ A @A A @ A @ A1DH@ A1FdJ@ABCD@@ .log2_up_nonneg @999 W H C 3 .UPLHD@<@ b Bq@ A \DӅ@ !ӀA@@@@@ .log2_up_unique @99۠9  p k [ V}xtplhd@ Ac jә ӛ@Ӫ@  \oA@ Ӷ@  \Ӽ@  Y@@s Ĥ  @  \ @  kR K"@N !Ӏ  %@@@ A @A A @ A }@ A {@ABC@@ s,log2_up_pow2 @:8:3: נ Ƞ à  ՠР̠ȠĠ@ d @@  \ŐA~U @ !Ӏ@ ` ¬ӓ _ _@@@ A @A A @ A @ A @ABC@@ 1log2_up_succ_pow2 @:q:l:=      @ e *@9@  \AǷΎB@ !ӀH@  ! nN@  뀠 T@  ! z @@@ A @A A @ A @ A @ABC@@ )log2_up_1 @::: U F A 1 ,SNJFB>:@ fɩ}@ !Ӏ&B@@@ 5A @A@@ )log2_up_2 @:٠:Ԡ: x i d T Ovqmiea]@ :g쩚Ԡ@ !Ӏ$I@@@ XA P@ ZA E@ \A C@ABC@@ ;/le_log2_log2_up @;::̠    { v@ ah Թ@  \@  F)A@L !ӀA@@@ A @A A ~@ A |@ A z@ABC@@ r4le_log2_up_succ_log2 @;7;2; ֠ Ǡ    ԠϠˠǠà@ i 𩚠@  \@| !ӀA @ F ! 1@  F)2A@@@ A @A A @ A @ A @ABC@@ 1log2_log2_up_spec @;t;o;@      @ j -@<@  \A G@  \M@  ꀠѩS@  F)t  Y@  \ _@  㩚e@ !Ӏ @@@ A @A A @ !A @ #A @ABC@@ 2log2_log2_up_exact @;Ǡ; ; f W R B =d_[WSOK@ (k QՀ@Տ@  \TA 詚՜@ W F) 쩚բ@ !Ӏ 򩛠 q՞ ՠ% հ@  M4 P@@@ iA a@A jA Y@ lA W@ nA U@ pA 3@ABCD@@ O+log2_up_pos @<<;     @ ul Ͷ@@ $ \ՅA@ + \ը@a !Ӏ 9@@@ A @A A @ A @ A @ABC@@ ,log2_up_null @@o Ds u@ք@  \֊@ !ӀB֑@  !ӀA֘@  \  @@@ QA I@A RA A@ TA ?@ VA =@ABC@@ 5/log2_up_lt_pow2 @<<<Ơup~@[p ֳ 3ֵ@@  \։B ŀ@  \@ & rY % $@ # \ +@Y !Ӏ 0@@@ A @ A @ A @ABC@@ |/log2_up_le_pow2 @=A=<= Ѡ̠ޠ٠ՠѠ͠ɠ@q  z@ @ S \АB @  \ e@ m Ź֠ l"@  \(@ !Ӏ w x@@@ A @A A @ A @ A @ABC@@ Š.log2_up_lt_lin @===V)'"@rC@R@  \AY@  \_@ !Ӏ  @@@A@AA@A@A@ABC@@ .log2_up_le_lin @===`QL<7^YUQMIE@"sKz@׉@K \NAא@R \ז@ !Ӏ  @@@NAF@PA?@RA9@ABC@@11log2_up_mul_above @=== ql~z@Wtׯ/ױ@@ \ׅB@@ \׍@ \@L !Ӏ@  Հ )@  t@^ !Ӏ@d !Ӏ;@@@A@AA@A@A@ABC@@1log2_up_mul_below @>N>I>ޠ٠ɠĠޠڠ֠@u @@` \ݐB@ @h \p&@ \,@  2@ !Ӏd8@ !Ӏ>@y ! dD@ !ӀJ@ p E|@@@A@AA@A@AA@ A@ A@ABCD@@렠0log2_up_mul_pow2 @>>>|O@;+&MHD@<84@v:ik@z@ \?B@؂@D \Gҩ֩؊@ !Ӏؐ@  ȋ©ؖ@ 3婚؜@I 0멚آ@ !ӀԐ@@@[AS@A\AK@^AI@`AG@ABC@@?.log2_up_double @?>>Рz@ewؽ@@ \ؑAJ!@M !Ӏ@  ր_+@ ! @_ !Ӏ7@@@A@A@A@ABC@@,log2_up_same @?G?B?נҠ ߠ۠נӠϠ@x@@Y \֐B@@a \i@̗n"@ !ӀT(@ !Ӏw.@v \a4@ Z /ظf@@@A@AA@A@A@ABC@@Ѡ/log2_up_succ_le @???b5&! 3.*&"@y O]@ \c@ !Ӏi@ ! ʏAp@ ! ʖv@ !ӀA@@@0A(@A1A @3A@5A@ABC@@/log2_up_succ_or @?٠?Ԡ?xidTOvqmiea]@:zcْ 򩚠٦@ !Ӏ٬@ ! ҀAٳ@ ! ـٹ@1 !ӀA7@: !Ӏ@ ! A@G !ӀA@@@@@e7log2_up_eq_succ_is_pow2 @@*@%?ɠǠ @{@i@@l !Ӏ@5 !  A@< ! '@ !ӀA׀͋b_@g ȳٚ@@@A@AA@A@A@A@ABCD@@8log2_up_eq_succ_iff_pow2 @@z@u@F  @|3@B@ \ACİԛO@ !ӀU@ ! {[@ ! ˁa@ !Ӏ0]_Իo@  @@@(A @A)A@+A@-A@/A@ABCD@@3log2_up_succ_double @@Ӡ@Π@rc^NIpkgc_[W@4}]ڌ@ڛ@ \`A𩚠ڤ@  !Ӏڪ@W >ڰ@  ʫ4Yڶ@c J:ڼ@w F)݀ @@@uAm@AvAe@xAc@zAa@ABC@@Y.log2_up_add_le @AA@@~׶Wٶ@ c:Bڒ@ kB@ڙ@ \@ t !Ӏ@ ˖4Q@ ˜@  !Ӏ@@  !Ӏc@@@A@AA@A@A@ABC@@.add_log2_up_lt @AvAqAB     @/1@@@ \B@H@ \ N@ \T@ 耠Z@  !Ӏ`@  !Ӏf@  a꩚l@  !Ӏr@ @@@+A#@A,A@.A@0A@ABC@@-Private_NZDivۄA.div_mod_unique @A۠A֠A@$NDiv(Abstract'Natural'Numbers#Coq@(NDivPropAV@A@@@A"NP$NDiv(Abstract'Natural'Numbers#Coq@Af@A@@@!NAA@A@%NZDiv&NatInt'Numbers#Coq@)NZDivProp#*H@@@A@@@J!C%NZDiv&NatInt'Numbers#Coq@5@A@@I!B,@@%@5@!t%J@@A@A%@@"eq%^@@A@% @ @"le% h@@A@AB%@@"lt%h@@A@&:@@#add&:d@@A@A&#@@#div&#d@@A@&%@@#eqb&%Ӡd@@A@ABC&'@!@#gcd&'d@@A@&.@'@#leb&.Πd@@A@A&/@+@#lor&/d@@A@&/@0@#ltb&/d@@A@ABD&0@4@#max&0d@@A@&0@=@#min&0d@@A@A&1q@A@#mul&1qd@@A@&2@F@#odd&2d@@A@AB&3@J@#one&3T@@A@&5E@P@#pow&5Ed@@A@A&9@T@#sub&9ݠd@@A@&;y@Y@#two&;yT@@A@ABC0@]@$div20d@@A@0 @c@$even0 d@@A@A1m@g@$land1md@@A@1@l@$log21d@@A@ABD1,@p@$lxor1,d@@A@1@w@$pred1d@@A@A2@@{@$sqrt2@d@@A@2D@@$succ2Dr@@A@A2@@$zero2걠T@@A@e"@@%ldiffe"d@@A@A##C@@&modulo##Cd@@A@BCD#@@&shiftl#àd@@A@#@@&shiftr#ɠd@@A@A$ @@&square$ d@@A@'G@@'testbit'Gd@@A@9@@'compare9⪠d@@A@ABCEFG@A@@H!AǠ@A@@!bܐ"q1ܓ"q2ܖ"r1ܙ"r2ܜ@%Logic$Init#Coq@@#andЖw@ܺ@"le \܀B@"lt \BE@!@ \ܕB@ \F@V-@#add v@#mul 䀠GD@ ͅ@ EC%Logic$Init#Coq@@#andЖw@Ѕ\!3Ї^"@@@ %'A*Equalities*Structures#Coq@AviA)Morphisms'Classes#Coq@@AAۀߠK @Aۓό^ @A݋X_A/RelationClasses'Classes#Coq@@ABC@@AA@@A@*div_unique @CCCY|n@zA!aBD!qG!rJ@Y@ \D@e@ \*k@ \@t@ z@ u݂@#div l̾@@@vAa@xA_@AB@@W*mod_unique @CCܠCР  @BTݕݗSݙRݛ@ݪ@ \oD@ݶ@ \{橚ݼ@ \Ҷ@:詚@ Y@ ƀөH㩚@&modulow@@@A@A@AB@@0div_unique_exact @D2D-CWG83!\@C涐Y趐@@? \ݾC@@? \ @V  @"  ч^"@ lM;@@@A@A@AB@@栠(div_same @DpDkD<vq_Q@]D$@3@q \Aѱ؈<@ lwll@@@/A@1A@AB@@(mod_same @DDDf{@E N@]@ \"A۰زf@wR+@@@YAQ@[AF@]AD@ABC@@<)div_small @DƠDD̠۠Ǡ@F9z|@ޏ@ \TBޖ@ \BA쩚ޠ@ lۀe@@@A@A@A~@ABC@@v)mod_small @EDD̠%*@Gs޴'޶@@ \ގB@ \BAO&@wƀ @@@A@A@A@ABC@@'div_0_l @E:E5E_O@;)d@'H@@; \A{R@ lA6ː@@@@@֠'mod_0_l @E`E[E,ufaOA@MI@#@a \Aҡx,@Yw\@@@@@'div_1_r @EEERug@sJ:@I@ \AǰٞR@ l΍@@@EA0@GA.@AB@@&'mod_1_r @EEE|ՠŠ@K#d@s@ \8Aȩ|@wh%A@@@oAg@qA\@sAZ@ABC@@R'div_1_l @EܠEנEݠˠ@LOߐ@ߟ@ \HAߨ@& l〠Qm@@@@@x'mod_1_l @FEEΠ',@Mu߶@@ \nAC@wκww@@@@@'div_mul @F(F#EM=.) R@NܶO޶@@3 \߲B@@3 \ߺ%rI@{ l8@   @@@A@A@@ՠ'mod_mul @F_FZF+te`N@@LO@$@j \B@,@j \\өڀ4@aw :@R 5PBB@@@-A@/A@AB@@&mod_le @FFFdy@P LN@]@ \"B@e@ \*k@ \q@w]y@@@@@A'div_pos @FˠFƠFѠ̠@Q>@@ \UB@@ \]ȩ@ \c@" l߀@@@A@AA@A@A@ABC@@|+div_str_pos @GGFҠ+ 0@Ryຶ-༶@ @  \A@ \AB@ \ࣩ@b l@@@A@A@A@ABC@@-div_small_iff @GDG?GiYJE3%n@1Sk@ @O \ΐB@@O \A@#iffС)ԕl @ l[6(婚&@d \<.@@@A@A@@-mod_small_iff @GG}GNqc@oT68@G@ \ B@O@ \>аۧ[@wGqcqa@ \wi@@@TAL@VAA@XA?@ABC@@7/div_str_pos_iff @GGG֠Ǡ @U4uw@@ \KB@@ \S}@ \]@ lـ@ \@@@@@t&div_lt @GGGʠ#ߠ(@VqᲶ%ᴶ@@ \ሐB@@  \t@ \@U l@@@A@AA@A@A@ABC@@+div_le_mono @H9H4H^N?:(c@&W`﶐!c@@? \ƐA@^ @S \#@Y \)@_ \@ lZ('%@ l`;-@@@A@AA @A@A@ABC@@*mul_div_le @HHHSvh@tX;=@L@ \B@T@ \Z@ \`@x [hf@ lѡ|n|@@@YAQ@[AJ@]AD@ABC@@ ճ%@=  N.;.+@J տT1@ llG:@@@$A@&A@(A@ABC@@0div_mul_cancel_r @KKK]      r@ ~bEGXI@X@ \C@`@ \%h@g@ \,o߻o@ lԪu@ p{@ v@ lԼ@@@tAl@vAa@xA_@ABC@@W0div_mul_cancel_l @KKܠK     Р   @ cT啶 嗶噶@@ \mC@@ \u@@ \|4 @= l@ @ ƀԩ@O l ڐ@@@A@A@A@ABC@@/mul_mod_distr_l @L1L,K V F 7 2   [@ d嶐 X綐@@ > \彐C@@ > \ @@ E \ ل[@<w@ -  + >@ 3  1 $!@ 9  7'@Tw P 0@@@ A @ A @ A @ABC@@/mul_mod_distr_r @LLLS     v h @ te; =N?@N@  \C@V@  \ ^@]@  \" eڰ౩e@wQk@  f  q@  l z w@  r}@wi   @@@ pA h@ rA ]@ tA [@ABC@@ S'mod_mod @LݠLؠL    ޠ ̠  @ f P摶!n收@@  \hB@@  \p ۩(@w՟@wե   @wի  ǐ@@@@@ /mul_mod_idemp_l @MML > .     C@ g Ͷ @϶>Ѷ@@ & \楐C@@ . \ @@ - \ lC@ $w〠@  @ 0w ,    @ 6w@ '   8  %@@@ A @ A @ A @ABC@@ 堠/mul_mod_idemp_r @MoMjM;   u p ^ P @ \h # %'@6@ | \C@>@  \ F@E@  \  M°ᙩM@ zw9S@ k N |Y@ wE b o o_@ wKe@ } `  n {@@@ XA P@ ZA E@ \A C@ABC@@ ;'mul_mod @MŠMM  ڠ ˠ Ơ   @ i 8y {}@@  \QC@@  \Y @@  \` 署@ w֏@  פ   @ w֛@  װ@ w֧  ѩ@ w֭   א@@@ A @ A @AB@@ /add_mod_idemp_l @NNM D 4 %    I@ j Ӷ FնD׶@@ , \竐C@@ 4 \ @@ 3 \ rI@ *w造@ " ؗ @ 6w 2   @ <w@ 4 ة >  +@@@ A @ A @ A @ABC@@ 렠/add_mod_idemp_r @NuNpNA   { v d V @ bk ) +-@<@  \C@D@  \  L@K@  \ SȰ⟩S@ w?Y@ x 퀠 _@ wK h u ue@ wQk@    t @@@ ^A V@ `A K@ bA I@ABC@@ A'add_mod @NˠNƠN   Ѡ ̠   @ l > 聶胶@@  \WC@@  \_ @@  \f @ wו@  C   ũ@ wס@  O@ w׭  ש@ w׳   ݐ@@@ A @ A @AB@@ 'div_div @O%O N J : + &   O@ m ٶ L۶ݶ@@ 2 \豐C@@ 2 \ @@ 9 \ xO@  l> @  lD 2  @  lJ 8@ -   +@@@ A @A A @ A @ A @ABC@@ )mod_mul_r @OwOrOC   } x f X @ dn + ->/@>@  \C@F@  \  N@M@  \ Uʰ㡩U@ wA ~[@ s V d qa@  g@ wS  pm@  h vs@ w_y@  lش   @@@ lA d@ nA Y@ pA W@ABC@@ O*div_mul_le @O٠OԠO   ߠ ڠ Ƞ  @ o L鍶 鏶鑶@@  \eC@@  \m @@  \t @  \@  ٶ ѩ@ ? l  ʩ@ E l@  Ȁ   ֐@@@ A @ A @ A @ABC@@ +mod_divides @P-P(ORB3. W@p ᶐ T@@ 8 \鷐B@@ 8 \ *造{R@ 3w  ˩ @"ex @ݍd @ 0  .A@@@ A @A A @ A @ A @ A1@D ( ' &@@ABCD@@ @@@@@A  BC͎@/mod_upper_bound @PPPS@@!a8!b;@%Logic$Init#Coq@@#notШϰ䦐A[@"lt \b@ wNCB@@@@@AA@@A@&mod_eq @PPP֠@A:q9s@8ԐAHש@ ww)(@#sub cր0@#mul ڔ6@  lڀ=<@@@ %'A*Equalities*Structures#Coq@A݋X_A/RelationClasses'Classes#Coq@@A@@M.div_mod_unique @Q QPנ0 @B껶"q1꾶"q2"r1Ķ"r2Ƕ@@{ \BE@@ \|F@^5@#add ~@X 뀠GD@ ی@f E%Logic$Init#Coq@@#andЖw@ދb 1ލd!@@@@@*div_unique @QlQgQ8r@~C!q!!r$@3@ \AC@޳:>@U ҀD@ ?SUL@  lڇmN@@@@@蠠*mod_unique @QQQrˠ@DVX:Z9\@k@ \AC@rv@  |@ w@ wp@@@@@ 0div_unique_exact @QޠQ٠Q@EW뎶V됶r뒶@WBg@ @ ۦIH(K@1 l@@@@@O(div_same @R RQ٠2"@F뽶@GA뒩J!@S lrr~@@@@@q(mod_same @R/R*QTD5@AG߶@i@A봩lC@$w〠뼐@@@@@)div_small @RQRLRvfW@cH@@ \BAߑh@ lW@@@@@)mod_small @RvRqRB|@I&(@7@ \BA߶捩A@nw-ߐ@@@@@ݠ'div_0_l @RRRg@JK@հ欐A ذ毩c@ l۞((@@@@@'mod_0_l @RRRҠ@K6m@2ΐABѩ@wqJ"J@@@@@!'div_1_r @RߠRڠR@LX쏩멚@ lڀAIA@@@@@='mod_1_r @RRRǠ @ Mt쫩0@wۧAe쁐@@@@@X'div_1_l @SSR;+@(Nƶ@@z \~AS*@\ l{죐@@@@@z'mod_1_l @S8S3S]M>@JO@@ \점AuL@-w쀠쩐@@@@@'div_mul @SZSUS&o`@lP  @рmAp$@ l_*@ %Ȑ@@@@@Ơ'mod_mul @SSSP@Q46@痐A ð皩N@{w:T@ O@@@@@&mod_le @SSSzӠà@R'^&`@%A5v@"le \}@wi@@@@@+div_str_pos @SנSҠS@SP퇶O퉶@%Logic$Init#Coq@@#andЖw@@L \lA@8 \AB@[ \{@: lZY@@@@@X-div_small_iff @TTS;+@(Tƶȶ@R)A흩@#iffС)\3@e l"@ \@@@@@-mod_small_iff @TGTBTl\M@YU@ჰZAΩ1ኰa@Bw@ \@@@@@/div_str_pos_iff @TuTpTA{@V%'@쀐ᱰ舐A_A@ \G@ l݂䩚M@ \@@@@@頠&div_lt @TTTs̠@W WY@h@  \-B@p@ \ v@ \|@ lݷ@@@@@+div_le_mono @T֠TѠT@XON!c@PA`@@, \@@2 \@, l造L@2 lR@@@@@P*mul_div_le @UU Tڠ3#@ Y@J!A@` \@D ׀y@` l@@@@@~/mul_succ_div_gt @U<U7UaQB@NZ춐@xOAé@ \ @r @$succ ! 7@ lR@@@@@)div_exact @UqUlU=w@[!#@耐⭰鄐A[ⴰש?@ :ܩE@ lހ°险M@zw9@@@@@頠2div_lt_upper_bound @UUUs̠@\ WY;[@ 鼐B0@r@ \x@ s~@# \@ l޿"@@@@@ 2div_le_upper_bound @UޠU٠U@]WVr@WBg@@3 \@ ߪML@? \@9 lY@@@@@W2div_le_lower_bound @VVU:*@'^ŶǶɶ@S*B@@j \@N ဠ@v \@p l-@@@@@/div_le_compat_l @VLVGVqaR@^_!p@x@ \ِB@ \BA#@ \)@ ld8Ʃ/@ lj>͐@@@@@ˠ'mod_add @VVVU@`9;=@ǰꞐAʰꡩU@wA[@r ja@ \g@wSv@@@@@'div_add @VVV֠@a:q9su@:֐AJ٩@  lȀ@ '@ 766@ 3@# lBC@@@@@A)div_add_l @VVVˠ$@bx𯶐w𱶐)@x=B@@I l@ e@? Ҁutu@ q쩚@a l@@@@@0div_mul_cancel_r @W=W8W bRC@Oc﶐g@{RBƶ@䃰Zͩ䅰\@ lK@~ @ +"@ l]$1@@@@@0div_mul_cancel_l @W|WwWH@d,.0@亰두B@° İ뛩O@ lU@ PW[@ Vja@ lcp@@@@@/mul_mod_distr_r @WWWР@e4k3mo@4АBD@<#Kک@wz@ Ꮐ2@ ᕀ8@ ᛀ@wD@@@@@B/mul_mod_distr_l @XWW̠%@fy񰶐x񲶐*@y>B@FhH@w࿀@A Ԁw۩@G ڀ}@M @w׀@@@@@'mod_mod @XEX@XjZK@Wg!n@傰YAͩ兰\@=w@Cw@Iw@@@@@/mul_mod_idemp_l @XvXqXB|@h&(3*@崰싐A巰쎩B@ow.H@ CN@{w:]멚T@w@Z@ Ui@@@@@/mul_mod_idemp_r @XXX٠ɠ@i-d,fqh@-ɐA=̩@wl@ ⁀@wx*))@w~@ Ⓚ65@@@@@4'mul_mod @XXX@jk򢶐j򤶐@k0A{3 @w᪀@, ⿀ba@wᶀ@8 ˀ@w€s@ wȀzyy@@@@@x/add_mod_idemp_l @Y6Y1Y[K<@Hk涐趐@tKAwN@/w@ 㜀@;w@Aw@1 㮀)@@@@@/add_mod_idemp_r @YtYoY@z@l$&1(@퀐沰퉐A浰팩@@mw,F@] ڀUL@yw8驚R@w>X@o 쀠g@@@@@'add_mod @YYY~נǠ@m +b *dof@ +ǐA;ʩ~@wj@  " !@wv@ $@w₀ 3@w∀ : 9 9@@@@@ 8'div_div @YYY  @n o󦶐 n󨶐 @ o4 B@ w< ^>@G l@M l  m@S lש@ C ր y@@@@@ w)mod_mul_r @Z5Z0ZZJ;@Go 嶐 綐_@ sJB@ {R ũ}T@5w @ v    @ + 䨀@Gw  ) @   /&@Sw,@ lg . ; ʐ@@@@@ Ƞ*div_mul_le @ZZZR@p 6 8:@ İBP@ \V@  Q 󩚠\@ l㗀 k b@ l㝀h@  c  w @@@@@ +mod_divides @Z ZZנ@q ;r :t@ 9ՐAIܩ@w| . -U @"ex @ @  䝀 @A@@@ A1@D   @@A@@ F)divide_wd @[ZZР@$NGcd(Abstract'Natural'Numbers#Coq@(NGcdPropZ@A@@@A!B$NGcd(Abstract'Natural'Numbers#Coq@ZЏ@A@@@!AZZ@A@@J!C%NZGcd&NatInt'Numbers#Coq@"@@@A@@I!B@@T@#@'compareTd@@A@A ]@@!t ]J@@A@ e;@ @"eq e;^@@A@AB e@@"le eh@@A@ e@@"lt eàh@@A@A @@#add d@@A@ @@#div d@@A@ABC }@!@#eqb }d@@A@ G@'@#gcd Gd@@A@A x@+@#leb xd@@A@ F@0@#lor Fd@@A@ABD @4@#ltb d@@A@ @=@#max d@@A@A 9@A@#min 9d@@A@ @F@#mul d@@A@AB @J@#odd d@@A@ a@P@#one aT@@A@A @T@#pow d@@A@ @Y@#sub d@@A@ABC #@]@#two #T@@A@ q@c@$div2 qd@@A@A @g@$even d@@A@ /xs@=F@)@~ \A@1@KOکꮰ|ܐ@@@LA7@NA%@AB@@+divide_refl @]]]]}niZ@hGES@mOAA@@@nA]@pA[@rAI@ABC@@A,divide_trans @]]]~Ǡ@H>ik!pn@}@OCB@@O@OE֐@@@A@AA@A@A@ABC@@{0divide_reflexive @]@gŀ]]]@/RelationClasses'Classes#Coq@@)ReflexiveW@Oܠ۠@6Ν٠^^ ]ޠ۠$@@@A@A@@1divide_transitive @]@{Ȁ^+^&]@8@*Transitive++-ݚ@O1@.~ܠ^>^9^ :*PK@@@A@A@@ߠ5divide_antisym_nonneg @^S^N^O?0+e`@*In @@m \ݐB@ @u \@'@AOap@.@HOh뫰F@@@KAC@ALA;@NA9@PA'@ABC@@1mul_divide_mono_l @^^^_pk\@jJGIK@Z@tOCBb@|Oh@ cn@ i@@@A@AAx@Av@Ad@ABC@@\1mul_divide_mono_r @^Р^ˠ^̠@KY@@OCB@O@ 蠀!@ 覀'@@@A@AA@A@A@ABC@@3mul_divide_cancel_l @_ _^٠ ֠@L(öXŶ@%Logic$Init#Coq@@#notШY0A&@#iffС)@O@< 퀠n,@B tA@O8G@@@A@A@A@ABC@@ꠠ3mul_divide_cancel_r @_^_Y_*ZJ;6'pk@5My@Q젰wA멚G0@JO6@ 1p<@ 7B@\O|@@@[AS@]AL@_AJ@ABC@@.,divide_add_r @___nzk@yN+VXZ@i@OCB@r@Ox@O쩚~@#add Ȑ@@@A@AA@A@Au@ABC@@m,divide_mul_l @__ܠ_ݠ͠@Oj,@@OCB@O꩚@ 鱀2@@@A@AA@A@A@ABC@@,divide_mul_r @``_*%@P̶3ζcж@@OCA@O!@7 耠6i@@@A@A@ A@ABC@@٠/divide_factor_l @`M`H`I9*%_Z@$Qh@+OB@b BA@@@@@/divide_factor_r @`t`o`@p`QL=@KR(*8@ROB?@ :AB@@@@@'-divide_pos_le @```gxsd@rS$OQ@`@"lt \&A@i@O婚o@ \@@@A@AA@A{@Ay@Ag@ABCD@@_*gcd_unique @`Ӡ`Π`Ϡ@T\@@ \_A@@Oܶ@@O@!q@@OAG@@O9@O @@#gcd #;@@@@@@&gcd_wd @a&a!`"83@U+@ݶ@ީ@f"hh@% #_@@@ A@A A&@ A@A@ABC@@ݠ.gcd_divide_iff @aQaLaM=.)c^@(Vl 2@5OA"@W #ߑCBl.@HOAC6@POAB@@@QA<@A@@ .gcd_unique_alt @aaa`ql]@kWHJL@[@ \ A@Wi@Os@O穚y@Oͩ@ #ʐ@@@@@g(gcd_comm @a۠a֠aנǠ@Xd@ #BA@ #AB@@@@@)gcd_assoc @bbaѠݠΠ@Y PB@ #A6@@A/@BA-@ABC@@.gcd_mul_diag_l @cccQqb]N@\b9;@J@ \BȰS@ #€Y@ T@@@@@?.divide_gcd_iff @ccc|Š@c<gi@x@ \=B@Oש@ #Ԑ@@@A@AA@A@A@A@ABCD@@{*divide_1_r @!nc@!t <c@1divide_1_r_nonneg+ Ac@&le_0_l&J€ddc@@@OAl@Bo <+k7 7%'     @ @,EhA  @+1 ĐXd0d+c ,  @@@@@AA@@A@.divide_antisym @Sc@Q h9h  : * @ 'E)Morphisms'Classes#Coq@@&ProperL@@@A)Morphisms'Classes:@*respectful%WO? @ @ @@ >С)#@7@@@A@AA@A@AA.Morphisms_Prop'Classes#Coq@@A@ABCD@@O,bezout_1_gcd @hhhZ  z k@ wF>O@@O@7BAΰY@ #Ȁ2@@@A@AA@A@A@A@ABCD@@~2gcd_bezout_pos_pos @hhh   @ Gm@|@"lt \BAx@@  \L٩@@#andЖw@@:7oԩ@ #uک@F7{@ #@@@8A0@A9A@;A*@ABA@@AРD@DA%@ABCD@@֠.gcd_bezout_pos @iih @ H,ŶǶ@@Z \B@~7@ #R@@@oAg@ApA@rAa@tA_@vAW@ABCD@@*gcd_bezout @iGiBiC3$@0I^z@"or @@7BA@L #熀BA@7AB'@\ #疀BA@@@A@AAX@A@A@A@ABCD@@N.gcd_mul_mono_l @iiiYyj@vJ=N?AưQ@ #W@| RAC_@ ZABg@ bAn@ #݀CB@@@A@AA@A@A@A@ABCD@@.gcd_mul_mono_r @iԠiϠiР@K; 䩚@ #@ 󙀠CA@ 󡀠BA@ 󩀠@ ##CBA@@@BA:@DA3@FA1@ABC@@ؠ%gauss @jji@L.Ƕɶ~˶@@ OC@ ܀BA@a8@ ! #[@ Oː@@@~Av@AA!@Ap@An@Af@ABCD@@0divide_mul_split @jVjQj"RB3@?Mm @%Logic$Init#Coq@@#notШuC@+@EO1@V , l@"ex @1!q4 8!r;İGP@u KɀZ@tO`@zO@@@A@AA@A@A@A@ABCD@@*mod_divide @jĠjj@@C!D$NLcm(Abstract'Natural'Numbers#Coq@j>@A@@B!CjD@A@$NLcm(Abstract'Natural'Numbers#Coq@(NLcmPropjU@A@@@A!B'j[@A@@@!A-jj@A@.@!a!b@%Logic$Init#Coq@@#notШ<A%Logic$Init#Coq@@#iffС)M$@&modulowŀCB@÷O @@@ %'A*Equalities*Structures#Coq@AviA)Morphisms'Classes#Coq@@AAۓό^ @A݋X_A/RelationClasses'Classes#Coq@@A1@DA@?@@ABC@@AA@@A@4divide_div_mul_exact @kfkak2~y@Ats!c@u~B@4@SO[D=@#div lyD@#mul @lEL@ GsR@ l􍀠 @@@oAg@qA`@sA^@ABC@@O.gcd_div_factor @kkk~ߠڠʠ@BdfLh@ɐA=@@OK@@ORک@#gcd #@X lЀFb@_ l׀Wh@e l݀@ #ct@@@A@AA@A@A8ӠA4Relation_Definitions)Relations#Coq@@ABC@@+gcd_div_gcd @ll kޠN?:*%@NC Ķƶ!gɶ@!S*A@W.@T #Q _6@\ #Y@ l+@ l1@@@A @AAۀߠK @A@A@ABC@@'gcd_mod @lZlUl&rm@Dh g@foAr&@ #ꕀ,@TwSRR2@ #ꡀXY@@@OAG@QA@@SA>@ABC@@/#lcm @@Π̠͠ˠ@@!tL9Հ@#mulL1@"LΦA@#gcdL]lllߠϠ@ikk \+k() 7! 7! 7%'h*H&xlӠlΠl@@@@@&lcm_wd @llߠl  @ E)Morphisms'Classes#Coq@@&ProperL@@)Morphisms'Classesh@*respectful%WO?@6 88@ 9@@@A@A@A@ABC@@*lcm_equiv1 @mml[LG72@[F-Ѷ,Ӷ@+]4@Z #WBAg>@ 퀠@ l3@p #m%$@ l? @ 10@ #76@@@-A@/A@AB@@ *lcm_equiv2 @mnmim:@G| {"@z7@ #릀BAA@ <G@  lnM@ #뼀tssS@ lY@ T_@ #΀@@@|At@~Am@Ak@ABC@@\,gcd_div_swap @mmmנ@Hqsϩ@? ~@L lĀB@ #BAA@U B@c lۀA@ #BA@@@A@AA@A@A@ABC@@,divide_lcm_l @n nmנG83#@GI@O󩚠@ 9l@@@@@ɠ,divide_lcm_r @n,n'mhYTD?@hJ:޶9ਗ਼@ O@ 9@@@A @AA@A@A@ABC@@*divide_div @nUnPn!}mh@Kcb  @clC@"@AOI@)@HOP/@NO5@ lp;@ lv@@@YAQ@AZAI@\AG@^A?@ABC@@:)lcm_least @nnni٠ʠŠ@LOQ7S@b@OCA@k@Oq@Ow@9 92C@@@A@AA@A@AA@A}@A@ABCD@@z(lcm_comm @nݠnؠn @M@c 9BA@k 9AB@@@A@A@A@ABC@@.lcm_divide_iff @o onנG83#@GN!n!m!pĩ @O@ 9CBA@#andЖw@@ OCA@OBA@@@A@A@@*lcm_unique @oSoNo{kf@OH G F @ @"le \ސA@ !@@OG@ (@GOO@!q $@ 3@ROGն@ ;@ZOa A@`Oh I@  9@@@@@@.lcm_unique_alt @ooooߠРˠ@P U W Y@ h@P \ -A@A d v@O @O;! @OR'ک @P 9IZ@@@@@)lcm_assoc @ooo$@$Q   # @p 9C @w 9BA @ 9 @ 9CBA@@@@@'lcm_0_l @p po\MH83@\R ҩW. @ 9 A @@@@@ڠ'lcm_0_r @p=p8p yjeUP@yS2 tK @ 9A  Ő@@@A@A@!A @ABC@@'lcm_1_l @p`p[p,xs@TU n "@ 9 ːAA@@@@@'lcm_1_r @p~pypJ@Us 0 @@ 9A A@@@_AW@aAP@cAN@ABC@@?(lcm_diag @pppnޠϠʠ@V Tٰ d@& 9AAA@@@@@^(lcm_eq_0 @ppp٠@W s uթ @K 9BA P@"or @B [A ^@@@A@AA@A@A@ABC@@/divide_lcm_eq_r @pppǠ7(#@7X  @ @OBA= @ 9@@@A@A@@.divide_lcm_iff @q$qp`QL<7@`Y ֶ ة @ OBAi@ @ 9BAA@@@A @AA@A@A@ABC@@.lcm_mul_mono_l @qYqTq%ql@ZN M L k @ 9 %@  AC -@ (AB 5@ 0A <@ 9CB@@@\AT@A]AH@_AN@aAL@cA@ABCD@@?.lcm_mul_mono_r @qqqnޠϠʠ@[ T V Xݰ h@* 9 n@* iCA v@2 qBA ~@: y @F 9CBA@@@A@AA@A@A@ABC@@-gcd_1_lcm_mul @qqq%@%\  @'B r@/ y򀠩5  @2 #/ i= @ 9署 @ ɀ@@@A@AA@A@A@ABC@@͠*eqb_compat @r0r+q@@E!F%NBits(Abstract'Natural'Numbers#Coq@q@A@@D!Eq@A@@C!Dr@A@@B!Cr@A@%NBits(Abstract'Natural'Numbers#Coq@)NBitsPropr@A@@@A!B3r@A@@@!A9r r @A@@Z!E*Equalities*Structures#Coq@@@qѭ@@!tqѭJ@@A@Aq)@@"eqq)^@@A@q٢@ @"leq٢h@@A@ABqٱ@@"ltqٱh@@A@ra@@#addraҠd@@A@Arf~@@#divrf~d@@A@rhk@@#eqbrhkd@@A@ABCrj5@!@#gcdrj5d@@A@rqf@'@#lebrqfd@@A@Arr4@+@#lorrr4d@@A@rr@0@#ltbrrd@@A@ABDrr@4@#maxrrd@@A@rs'@=@#minrs'd@@A@Art @A@#mulrt d@@A@ru@F@#oddrud@@A@ABrvO@J@#onervOT@@A@rw@P@#powrwݠd@@A@Ar|u@T@#subr|ud@@A@r~@Y@#twor~T@@A@ABC|@]@$div2|加d@@A@}@c@$even}d@@A@A}4@g@$land}4d@@A@};@l@$log2};d@@A@ABD}@p@$lxor}Ġd@@A@~2@w@$pred~2d@@A@A~@{@$sqrt~d@@A@~#@@$succ~#r@@A@A-I@@$zero-IT@@A@S@@%ldiffSd@@A@A&o@@&modulo&o۠d@@A@BCD'E,[@@&shiftl'E,[d@@A@'E,a@@&shiftr'E,ad@@A@A'XL>@@&square'XL>d@@A@*Y@@'testbit*Yd@@A@@&eqb_eqZˀ)ssߠs|@R J $Bool#Coq@@'reflectc@/BA @ YcBA +k() 7!7!L7!77"7777 7! 7!7&'(6pTo̠gDRېh]ǐpq\_|t6t1tؠӠΠ@@@@@'eqb_neq @tKtFt &@C%Logic$Init#Coq@@С)@"eq @&&@ ỲBA)Datatypes$Init#Coq@@$boolZ'@B+@#notШBA@@@@@(eqb_refl @tttgk\WRM=83v@0D QAcc@> Y AA=A@@@CA1@A@@)'eqb_sym @tĠtt{vfa\@YE2z*|l@i Y5BA@q Y=AB@@@sAa@A@@Y)pow_sub_r @tttĠ@@!a!b!c@9 C@@"le \BCF @#pow oE@#sub cD@#div l@ @ &@@@ %'A*Equalities*Structures#Coq@AviA)Morphisms'Classes#Coq@@Aۓό^ @A݋X_A/RelationClasses'Classes#Coq@@ABC@@AA@@A@)pow_div_l @ukufu7;,'" @=Awv!u#@ B@ <@&modulow)cu E@t †K@j lyqQ@p lW@ ]@ @@@pAh@AqA_@sA]@uA8ӠA4Relation_Definitions)Relations#Coq@@ABC@@_#b2n @ƛ)Datatypes$Init@@$boolZ'@ @@@@@@@@A@r@^qѭA @#onervO@$zero-Iuuu @)Datatypes$Init#Coq@@$boolZ'@ +k= R'6'6''+k6'*H(X<H@@A@A@tv"vuޠ٠ԠĠ@@@@@͠*b2n_proper @v5v0vנ@B)Morphisms'Classes#Coq@@&ProperL@)Morphisms'Classes@*respectful%WO?%Logic@"eq @@ }@@@,A$@A-A@/A@1A1DH%Logic$Init#Coq@@ABC@@+exists_div2 @vv~vOSD?:5% @UC7 @@"ex @C"a'FӰ C_@#add 􀠩f@#mul bm@ }א@@@Am@Ak@A1@DR@ABC@@g+testbit_0_r @vϠvʠvql@Dڛ߀P@"eq @)Datatypes$Init#Coq@@$boolZ'@@'testbit5z߀@R E@#mul /*%  @@Fz"K$ 4@ }:@5znBAB@w.H@g lBO@~ 쀠ӐAԐ@@@cA[@AdAR@gAQ@AhAРD.Morphisms_Prop'Classes#Coq@@rA@tA@ABCD@@V,testbit_spec @wwwzup`[@Grt=x!l{D!hK@#andЖw@%Logic$Init#Coq@@#andЖw@@ \lB@"lt \B@ S:C4 D@a TB@ €@n a@` }@/5z DC@* ܀eA@ lC@@@A@AA@A@A~@A@ABCD@@堠,testbit_true @xMxHx @HY*@#iffС)@r5zPBAqA u)@w/@N ljB6@e ӀA@@@@@)-testbit_false @xxx]aRMHC3.@cIEnGDĀ]@5zBAB߰ j@.wVp@ lBw@ A=@@@@@j+testbit_eqb @xҠx͠xto@J@5z΀BA@} YI@lw@ l造B@ R9A:_@@@@@'b2n_inj @yy xܠѠ̠Ǡ @K"a0"b0$@R )@j }B@q }NU !@@@@@ڠ3add_b2n_double_div2 @yBy=y@L2PR V @) lE@ @ }B@f AA@@@1A)@3A!@5A@ABC@@3add_b2n_double_bit0 @yyzyKO@;61!@QMo7I@5z}O@ 〠U@ }B\@ WA"B@@@pAh@rA`@tA^@ABC@@V(b2n_div2 @yyyzup`[@Ǹ Щ@ l@ }AP@@@A@A@A@ABC@@(b2n_bit0 @yyy@Oۛ@ 5z瀠@F }AA@@@A@A@A@ABC@@.testbit_unique @zzyܠנҠ͠@P'϶Ѷ-]׶Xٶ@@: \B@ sD@nEF@ 2@I @  @ }2@[  K@G F"@x5zVG0Q@@@5A-@7A%@9A#@ABC@@&bits_0 @zz~zOSD?:5% @UQ^7I@5z}AB@@@_AW@aAO@cAM@ABC@@E(bit0_odd @zzzy}nid_OJ@Raڀ֩s@5zA9z@#odd ~ʀA@@@A@Az@A@ABC@@t(bit0_eqb @zܠzנz~y@S @5zրAh@ YP@swA4Y@@@A@A@A@ABC@@(bit0_mod @{{ zܠѠ̠Ǡ @TĩI @a }@05zA@ẁAf@@@A@A@A@ABC@@ڠ+testbit_odd @{B{={  @ UNqm @`5z>BA@ ~a@&shiftrO造BA@@@-A%@/A@1A@ABC@@(bit_log2 @{{{v{G K < 7 2 -  @ MV/@AI@5z}O@$log2 F)qA@@@fA^@AgAU@iAS@kA@ABC@@M/bits_above_log2 @{{{  v q l g W R@ Wik@z@ \@1 F)BA署@5zŜB@@@A@AAۀߠK@A@A@ABC@@)div2_bits @{{{ à      @ X"@5z@ lBFA@5zB@ ! A@@@A@A@A@ABC@@ɠ-div_pow2_bits @|1|,{      Ӡ @ Y=嶐綐!m꩛c_@R5z0@! l=C @8 BA@g5zEC@ AB@@@-A%@A.A@0A@2A@ABC@@0double_bits_succ @|||w|H L = 8 3 .  @ NZ0Y2D@5zxJ@ EΐBQ@K ! wAX@5zBA@@@lAd@nAX@AB@@P1mul_pow2_bits_add @|||  y t o j Z U@ [lnp逰婚@5z@ C@ ,B@7 *AB@5zҀCA@@@A@A@AB@@2mul_pow2_bits_high @|||ʠ Π      @ \ @@ \BA84@'5z@  Ҁ@  za@95z @ c-"!@@@A@A@A@ABC@@ᠠ1mul_pow2_bits_low @}I}D}       @ ]U&@@b \AB@r5zP"@k H(@W ŀ`a{B@@@=A5@?A-@AA+@ABC@@#2mod_pow2_bits_high @}}}W [ L G B = - (@ ]^?hAZC@R@ \BAŀ^@5zd@(wPj@ B@@@Aw@Ak@AB@@c1mod_pow2_bits_low @}ˠ}Ơ}     } m h@ _@@ \AB@5zҀ@hwʩ@ G.㩚@5z䀠@@@A@A@A@ABC@@#eqf @!f@8K!g=R ` a~~}  ޠ ٠ Ԡ Ϡ  @@қ,@כ1A |+k() +7T'  77&'^tu`h~E~@~       @@@@@)eqf_equiv @~X~S~$ (      @ *`/RelationClasses'Classes#Coq@@+Equivalence~@@H'@k ]@@@@@ +testbit_eqf @~~{~L P A < 7 2 " @ RaK@7@8ǩB:@; H@ ]L@'testbit5z@@@ ^A V@ `A J@AB@@ B*bits_inj_0 @~~~v z k f a \ L G@ |b ^@aڀ֩s@5zBAB  ?@@@@@ l(bits_inj @~Ԡ~Ϡ~      v q@ c  @@ ]@5zӀB@5zڀ  #  @@@ A @A A @ A @ AX@ A M@ABCD@@ ,bits_inj_iff @ ~ؠ ܠ ͠ Ƞ à   @ d  ©@ ]@05zB@75zA _6BA@@@@@ ؠ(are_bits @@;        @ e:@ O@ @   @@*respectful%WO?   Aր:!@e ] Y'@}5z[ 耠#!k&?(@7@ q \ p > j v B@@@ SA K@A TA B@ VA @@ XA@ ZA@ABCD@@ <,shiftr_spec' @p t e ` [ V F A@ vf XZs\Հѩn@5zt@\ODCBA}@5zC@ %  AB@@@@@ x1shiftl_spec_high' @۠       }@ g @@  \BA  @ 5z瀠@&shiftlI   󩚠@ 5z 橚@  c   @@@@@ /shiftr_div_pow2 @    ܠ נ Ҡ   @ h ,Զ֩ [2@OBA@  l )B@ $ yA@@@@@ 蠠/shiftl_mul_pow2 @PK    @"i \ - b@]IꀠBA@ g  B%@ T €A@@@@@ /shiftl_spec_alt @{LPA<72"@Rj 4 ]6O8  J@ 5z~P@I$CBX@   쀠AB`@ 5zCA@@@ tA l@ vA `@AB@@ X)shiftr_wd @|wrb]@k @w@xx z@{{ }}@rOZ@@@ A @ A @ A @ABC@@ )shiftl_wd @@l @@ @) ++@I@@@ A @ A @ A @ABC@@ -shiftl_shiftl @ ޠӠΠɠĠ@m ƶ ȶʩO&@!I@'ICBA@0IC@   BA@@@ A @ A @ A @ABC@@ ꠠ-shiftr_shiftr @RM" @$n ^ /! f@Oꀠ @OCBA)@OC0@   ĀBA@@@ DA <@ FA 4@ HA 2@ABC@@ */shiftr_shiftl_l @^bSNID4/@do F oHaJ@Y@  \ABذc@KO3i@I=   o@IC u@  c   @@@ A @ A w@ A u@ABC@@ m/shiftr_shiftl_r @ՠРwr@p  @@  \BA򩚠@Ov@I   婚@O ة@  c   @@@ A @ A @ A @ABC@@ *shiftl_1_l @٠ԠϠʠ@q ̩Q(@#IA@   gA@@@ A @ A @ A @ABC@@ ܠ*shiftl_0_r @D?@r P}T@OI܀AΐA@@@ A @ A @ A @ABC@@ *shiftr_0_r @je6:+&! @A?@@@ A @ A |@ A z@ABC@@ r/shiftl_eq_0_iff @ڠՠ|w@v   𩚠@IxBAk#Bn@@@ A @ A @ A @ABC@@ /shiftr_eq_0_iff @ ՠ٠ʠŠ@w  H@OBA @"or @Z1B V@ < \B@ C \@ F)BA@@@ A@ A @A @ABC@@ +shiftr_eq_0 @YT%) @+xe  6@@ p \$@ F)EBAz.@Ofg@@@@@ (div2_div @TXID?:*%@Zy<L@$div2 hxAT@s l Aِ@@@gA_@iAW@kAU@ABC@@M'div2_wd @vqlgWR@z @ll vnn󚠡{@$div2 hx@@@A@A}@A{@ABC@@s(div2_odd @۠֠}x@{A@ A 4@   *@` hx倐A@@ }@ ? ~A@@@A@A@A@ABC@@'lxor_wd @۠֠Ѡ̠@| 倰@Ѷ@ҩ Զ@Z \\@$lxor S@@@A@A@AB@@ڠ'land_wd @B=@} @@@ @$land 3"3@@@A@ A @AB@@&lor_wd @je6:+&! @<~5@!@"",$@%%/''4@#lor "@@@FA>@HA2@AB@@*(ldiff_wd @^bSNID4/@d]@I@JJTL@MMҩWOOԚ\@%ldiff *[@@@nAf@pAZ@AB@@R'lxor_eq @{vql\W@@n+p@ͩ@$lxor SBAI@@@A@A@AB@@|.lxor_nilpotent @ߠ@A@' SŀAAo@@@@@-lxor_eq_0_iff @РԠŠ@Bu C@M S뀠BAM$BA@@@A@A@A@ABC@@̠(lxor_0_l @4/֠@C@mD@w SAA@@@@@젠(lxor_0_r @TO $ @&D`d@ S5AސA@@@@@ )lxor_comm @to@D50+&@FE(*:@ SWBAB@ S_AB@@@@@6*lxor_assoc @jn_ZUP@;@pFRTV۰f@ Sl@ SCBAu@ SC|@ SBA@@@@@p'lor_0_l @ؠӠzu@G詚@#lor "bAA@@@@@'lor_0_r @Šɠ@H2 @! "$AA@@@@@(lor_comm @ڠՠРˠ@I%Ͷ$ϩT+@C "FBA@K "NAB@@@@@۠)lor_assoc @C>@JONMW @o "rC @v "yBA @~ " @ "CBA@@@@@(lor_diag @}xIM>94/@OK 1 A@ "AAA@@@@@6*lor_eq_0_l @jn_ZUP@;@pL R T@ڰ e@ "̀BA , .@@@{As@}Ag@AB@@_,lor_eq_0_iff @Ǡ ~yid@M { }zݩ @ "BA X B _A b@@@A@AA @A@A@ABC@@(land_0_l @ˠϠ@N  8 @$land 3"ꀠ A @@@@@(land_0_r @۠֠Ѡ@O+ өX/ @  3" A  @@@@@֠)land_comm @>9 @PJ I yP!@A 3"*BA! @I 3"2AB@@@@@*land_assoc @hc48)$ @:Qt!s!r! |!0@m 3"VC!7@t 3"]BA!?@| 3"e!E@ 3"kCBA@@@@@:)land_diag @nrc^YTD?@tR!V۰!f@ 3"AAA@@@@@[)ldiff_0_l @àzue`@S!wө!@%ldiff *!MA!N@@@@@{)ldiff_0_r @ޠ@T!󩚠!@  *A!mA@@@@@*ldiff_diag @ϠӠĠ@U!<!@@ *ŀAA!@@@@@0lor_land_distr_l @#ߠڠՠŠ@V/!׶.!ٶ-!۩`7!@O "R!@. 3"CBA!@7 3" "@d "gCA"@l "oBA@@@@@0lor_land_distr_r @d_04% @6Wp"o"n"x",@ "C"3@p 3"YBA";@x 3"a"A@ "CB"I@ "CA@@@@@=0land_lor_distr_l @qufa\WGB@wX"Y"["]"m@ 3""s@ "ڀCBA"|@ "〠"@ 3"CA"@ 3"BA@@@@@~0land_lor_distr_r @@Y"""#"@ 3"ԀC"@ "BA"@! "$"@ 3"造CB"@ 3"񀠐CA@@@@@-ldiff_ldiff_l @'"ޠ٠ɠ@Z3"۶2"ݶ1"ߩd;"@h *퀠"@n *󀠐CBA"@w *C#@i "lBA@@@@@-lor_ldiff_and @a\-1"@3[m#l#s#'@ "#-@ *+BA#5@r 3"[BAB@@@@@**land_ldiff @^bSNID4/@d\#F#HͰ#X@ 3"~#^@ *\BAA#&@@@@@S&setbit @ ⩚@@rr4@ 'E,[ʠŠ|lg@#~## P+k()77! 7%'ld&|@@@@@(clearbit @@  !"@WS?ΠҠà@###8Ql1d|۠֠Ѡ@@@@@ʠ,setbit_spec' @2-Ԡ@]>#涐#mD#@bBA$@d "gB$@6 #A@@@A@A @A@ABC@@.clearbit_spec' @hc48)$ @:^t$E$z$.@#?{BA$6@ *4B$=@l ڀ#A@@@PAH@RA@@TA>@ABC@@6)setbit_wd @jn_ZUP@;@p_i@$U@$V$V`$X@$Y$Yީc$[$[$h@b@@@yAq@{Ai@}Ag@ABC@@_+clearbit_wd @Ǡ ~yid@`@$~@$$$@$$$$  $@#?{@@@A@A@A@ABC@@.pow2_bits_true @@a$$@ 5zꀠ$@ Y$@AAA@@@A@A@A@ABC@@/pow2_bits_false @!ݠؠӠà@b$ն$׶@a8BAYU$@H5z&$@' $|01KB@@@ A@A@A@ABC@@-pow2_bits_eqb @[V'+ @-c6%(%%#@y5zW%)@X ƀ$BA%1@  Y ؀BA@@@@@%*setbit_eqb @Y]NID?/*@_d%Aj%C\%E%W@5z%]@bCBA)Datatypes$Init#Coq@@#orb%t@O Y BA%|@5zCA@@@A@A|@AB@@t*setbit_iff @ܠנ~y@e%%% %@5zހ%@IbCBAAဠ7 BA/+%@5zCAA@@@@@)setbit_eq @'"ޠ٠ɠ@f3%۶%ݩVR%@E5z#%@bBAAKA@@@ A@A@@*setbit_neq @WR#' @)gc& 4& &&@‐ pBA&*@5z^&0@bVhi&6@5zj\o@@@@@(,clearbit_eqb @\`QLGB2-@bh&Dm&F_&H&Z@5z&`@#?{CBA@$andb=&p@5zCA@$negb&@Z Y &BA@@@A@A@AB@@w,clearbit_iff @ߠڠ|@i&&&&@5zဠ&@ #?{CBA A/.*&@5zCAAM!$BA@@@@@Ơ+clearbit_eq @.)Р@j:&ⶐ &䩛]Y&@L5z*&@U#?{BAARB@@@@@,clearbit_neq @\W(,@.kh'9'+'@瀐!uBA'/@5zc'5@#?{[mn';@5zoat@@@@@-+shiftl_lxor @aeVQLG72@gl'I'Kt'MҰ!']@ I 1'c@ S CBA'l@ S 'r@ I FCA'z@ I NBA@@@@@n+shiftr_lxor @֠Ѡxs@m'''!꩚'@O n'@ # S CBA'@ , S ʀ'@O CA'@O BA@@@@@+shiftl_land @ؠӠΠɠ@n#'˶"'Ͷ'ϩT"+'@&I '@" 3" CBA'@+ 3" '@;I ȀCA'@CI ЀBA@@@@@+shiftr_land @XS$( @*od( c(7("l( @O (&@c 3" LCBA(/@l 3" U(5@O CA(=@%O BA@@@@@1*shiftl_lor @eiZUPK;6@kp(M(Ox(Qְ"(a@I 5(g@ " ΀CBA(p@ " ׀(v@I JCA(~@I RBA@@@@@r*shiftr_lor @ڠՠ|w@q((("(@O r(@  " CBA(@  " (@O CA(@O BA@@@@@,shiftl_ldiff @ܠנҠ͠@r'(϶&(Ѷ(өX#/(@*I (@b * 瀠CBA(@k * (@?I ̀CA)@GI ԀBA@@@@@,shiftr_ldiff @\W(,@.sh)g);)#p)$@ O 􀠩)*@ * (CBA)3@ * 1)9@!O CA)A@)O BA@@@@@5$ones @©@$pred~2qufa\WGB@)Y)Y @+k77!7$'`ӐXl}xsc^@@@@@l$lnot @@ }Āũ@K7(>'ޠ@))) H+k()7 7%'!tdʠΠ@@@@@'ones_wd @ ݠҠ͠Ƞà@t܀@))ȩ))OO)@ <@@@A@A@A@ABC@@Π'lnot_wd @61ؠ@u@)@)))@))v))xx*@ E@@@A @A@A@ABC@@*ones_equiv @_Z+/ @1v:*$o*#@ !9!4!/!!@!O-1Z-3@-B@ \-H@ F)iBA ǰ'-R@  3"x-X@ <@@@kAc@AlA@nA\@pAZ@ABC@@R,ldiff_ones_r @!!{!v!q!l!\!W@!-n-p '̩-@  *~B-@> !0@i0B#ǰ*0R@ So0X@ ECA0`@ EBA0h@ SCB@@@@@!\+lnot_lxor_l @Ġ$$$${$v$f$a@$!0x!0z0|$*ة0@  E0@ SCBA0@ S0@! ECAB@@@@@!+lnot_lxor_r @ʠ$Π$$$$$$@$" 0" 00$;+0@F E0@K S造CBA0@T S򀠐C0@\ EBA@@@@@!Р(lxor_lor @83%$$$$$ڠ$@% "D0춐"C0@$t+K0@< 3"%BA0Ʃ$~+U1 @ S&"A"B1@s "v"G"H@@@"!A"@"#A" @AB@@"0log2_bits_unique @mh9%=%.%)%$%%% @%?"y1! J1#@  16@ 5zjBA!A@M16@1E@ \"}!  1O@ 5z"}"!B$ϰ+1Z@  F){""@@@@@"L+log2_shiftr @%%u%p%k%f%V%Q@%"1h 1j$+Ʃ1z@+ F)1@hOPBA1@" c!̀1@? F)BA@@@"A"@A"A@"A"@"A"@ABC@@"+log2_shiftl @% %%%%%%@%"1 1@#{%2, B1}%5, 1@q F)တ1@ I""1@!m "`1@ F)# # @@@"A"@"A"@"A"@ABC@@"ʠ(log2_lor @2-&%%%%%Ԡ%@&#>1涐#=1%m,D1@ F)1@b "eBA2@#max c2 @ F).B2@ F)5A@@@#'A#@#)A#@#+A#@ABC@@# )log2_land @upA&E&6&1&,&'&&@&G#2)#2+29@#s \2?@ F)`2E@ 3"kBA2M@#min 2T@ F)uB2[@  F)|A@@@@@#N)log2_lxor @&&w&r&m&h&X&S@&#2j#2l2z@# \2@1 F)2@ SBA2@ ꀠ2@E F)B2@L F)A@@@@@#(add_bit0 @ &Ơ&&&&&&@&$2$2"%"!2@"5z 򀠩2@"e #XBA2#@$xorbȀ2@")5z!B22@"05z!A2@@@@@#͠)add3_bit0 @50'&&&&&נ&@'$A2鶐$@2붐$?2"f"b2@"U5z!33@" #3 @" #CBA2өHL3@"r5z!PC2⩚3#@"y5z!WB2驚3*@"5z!^A2@@@@@$.add3_bits_div2 @Q'U'F'A'<'7'''"@'W u# t#"c0#&ɰ-3T@$s l"3Z@" #3`@# #􀠩3f@# }C3m@# }$3s@$ }#23y@$ } CB A(CB@@@$A$@A$A@$A$@$A$@ABC@@$.add_carry_div2 @'''''''@'$3$3g$'/.3@$ l"3@#a $T3@#g $ZCB3@$[ }A3S3@#v $i3@#| $o3@% l#C3f3@% l##B3m3@$| } 3@#S5z"1C3é4@#Z5z"8B3ʩ A4@#j5z"HC3ک4@#q5z"OB3@@@%/A%'@A%0A%@%2A%@%4A$@ABC@@%.add_carry_bits @~yJ(N(?(:(5(0( (@(P%42%44$$4<%4>"'ǰ.4R@# $怠4X@# $쀠DC4`@$ }B4g@ S4m@ SDCA"怠'.ȩ4|@% l#$44@ "造4@ 3"DC4@ 3"A4@ "DC$ $4@#5z"׀% 4hB@@@%A%@A%A@%A%@AB%A%@%A#W@A%A$=@%A1ՠF-SetoidTactics'Classes#Coq@@%A1I @%A%[@ABCDE@@%(add_bit1 @((۠(֠(Ѡ(̠((@(&&4ζ&%4Щ$I$E4@$85z#4@$ %|BA4$(4@$N5z#,B44@$U5z#3A45 @$`5z#>B4Щ5@$g5z#EA4א@@@&%A&@A&&A@&(A&@&*A&@&,A$@ABCD@@&-nocarry_equiv @vqB)F)7)2)-)())@)H&5*&5,&5.@(/5?@&^ l$zA4ĩ5F@ "5L@ 3"rCB5T@ 3"zA5[@ "€CB@$π$˩5h@$5z#&5-%B#`(/&56(/ũ5y@ 3"&&5>@@@&A&@A&A@&A&}@&A&{@ABC@@&s0add_nocarry_lxor @۠֠))))))})x@)&5&5@)/5@ 3"ȀBA5i)!/5@%M &@&&婚5@1 Sπ&&@@@&A&@A&A #@&A&@&A&@&A%I@ABCD@@&(ldiff_le @))נ)Ҡ)͠)Ƞ))@)'"5ʶ'!5̶@)R0)5@V *ۀBA55@' \''@@@@@&נ1sub_nocarry_ldiff @?: **)))))@*'K5'J5@){0R6@ *AB5ͩ)0\6@'7 c&T'H'I6@ *'N'O@@@'(A' @'*A'@',A'@ABC@@'1add_lnot_diag_low @vqB*F*7*2*-*(**@*H'6*%S6,@6;@$ \6A@  F)bBA)06K@% &߀'6Q@  E''6W@  <'@@@'iA'a@'kA'Y@'mA'W@ABC@@'O,lnot_sub_low @**x*s*n*i*Y*T@*'6k%6m@6|@$ \6@!3 F)BA*0ة6@  E''ũ6@' c&ր6@ O <''А@@@'A'@'A'@'A'@ABC@@'3add_nocarry_lt_pow2 @Ġ*Ƞ******@*(6(6%6@*61 6@ 3"瀠CB6@6@% \'𩚠6@' %m6T( @6@%) \'6@(  %z6a(6@%5 \6@& '}"(6@( %6s(@@@(A'@A(A!`@(A'@(A'@ABC@@'頠7add_nocarry_mod_lt_pow2 @QL+!++ ++**@+#(]7(\7&07 @*1f7@W 3"@CB6ᩚ7"@%t \7(@& '7.@'w&(T74@(c %р6(m7:@'w&&(r7@@(o %݀6(y7F@(u %〠6(@@@(XA(P@(ZA(D@AB@@(<)gt_lt_iff @@7c`)X4)U4 7b@*+ \@BA&AB@@@@@*%gt_lt @@7a)x4̶)u4ʶ@BA'*l)@@@@@*ՠ%lt_gt @@7b)4嶐)4@')BA<*)ϐ@@@@@*)ge_le_iff @@7c)4)4 ꀠ7@*+ \1BAAB@@@@@+%ge_le @@7d)5)5@BA**@@@@@+'%le_ge @@7e)57)55@*BA<**!@@@@@+@3pos_pred_shiftl_low @@8f*Es*5P)5V@'AB%-]&Equ@&shiftll@&shiftl5X%w*O+A@@@@@+q4pos_pred_shiftl_high @@88g*v1*/5*,5@vBA%7-&t/%*y+/&7%*+;@@@G#"A"q@A@@+,pred_div2_up @@8oh*'BinNums'Numbers@@(positive*@%oکԀ@'div2_up%%@'div2_up "AN怐A@@@@@+@@@rA@Ar@t9@t@ABC2F#@2#<@2"@ABD2 "@2 i!@A2 !/@2 e @2  @AB;-*@CDE@@@AB@@@ABC@@A@B@@A"@TA"@ABC*@@ADE@@A*@@@ABC%@]@l@AB@@ACDF#@u@Ar@l@@ABC@c@|@ABD$(@#f@A#&@#%@ABE"@"@A"@![@A"@B!@CDFG!Z!U!S@!T@A!R@B!@!@ @ABCD @ @A @ @-_@ABCEHZ@+Nplus_reg_l @@8i*7*7+*7@%ူ788@7> )CB CA%7(+*+@@@@@,I*Nmult_Sn_m @@9j+7ඐ+6&6%@6 ) +@8 ! *;BA3ABA@@@@@,t2Nmult_plus_distr_l @@9;k+07c+-7a+}6ة&36֩-AWCB]@!$:@A@@@@(sub_mask@@)@A@ABCD c@R@'testbit cI@!ć@A@7 B@(@'of_uint7 B@*`]?@A@AG@-@)mask_rectG$@+ED@A@F˱@3@)add_carryF˱*@+p@A@AB^Ҷ@k@'to_uint^Ҷb@#m@A@ p@>@0double_pred_mask p5@0-+m@A@AC T@87@A@ @9+S@A@A l@8)@A@ Y@7 k@A@AB #@65@A@ T@4 @A@ACDE "@32@A@ q@2 F@A@A @10@A@ @0/@A@AB @,*@A@ ~@,+@A@AC =@)(@A@ @*)@A@A c@'+)@A@ @&%@A@AB hx@$#@A@ @#"@A@ACD @@A@ @! @A@A 3"@@A@ F)@@A@AB S@@A@ @+@A@AC @@A@ !@@A@A ! @,.@A@ !7@@A@ *@ @A@AB g_@@+pred_double g_@25\@A@CD m@@÷ m@2j@A@S@@&of_intS㫑@4}5@A@AS@@&of_natS@4};@A@BEFGH\R@@(mask_ind\R@4@A@\^@@(mask_rec\^@4@A@A!,@@&pred_N!,@4s)@A@B@@&shiftl@5X@A@@@&shiftr@5X@A@A&@@&square&ّ@5,x@A@BC"@@&to_int"@5L@A@"@@&to_nat"@5L @A@AnTq@@+testbit_natnTq@6n@A@B@Z"~@A@.@ZY@A@AB3~@@'sqrtrem3~@7]%{@A@CD,@&@'bitwise,@/v@A@>4'@@'testbit>4'@8g$@A@A{U@@,sqrtrem_step{U@8R@A@u^@on@A@Afz@ @'to_uintfz@9w@A@Bl@A@'comparel8@3R@A@CDEFs8@F@+of_uint_accs8=@5+@A@}@@A@@~}@A@ABq@"@+of_succ_natq@$@A@w@*@A@ACK@@A@K@@A@AI@}|@A@O@|{@A@AB,@yx@A@Z@xw@A@ACD`@ts@A@e@ts@A@A+{@qp@A@5z@q)@A@A @ml@A@ @lk@A@A#@N@'compare#ݑE@ )Q@A@BCD%t2@S@(size_nat%t2J@ @A@%9@Z@+of_uint_acc%9Q@ ΋@A@A%V@_@+double_mask%VV@ S@A@%%@e@'div2_up%%\@ "@A@ABEF'ş@j@'Ndouble'şa@ @A@(b0@r@*shiftl_nat(b0i@9-@A@A(nՖ@w@*shiftr_nat(nՖn@'@A@(@}@0succ_double_mask(t@@A@*W$@@,compare_cont*W$z@!@A@.0@@.sub_mask_carry.0@΂@A@ABCD.@@!t.@ ;@A@.먩@@#add.먩@ `@A@A.U@@#div.U@ @A@.B@@#eqb.B@ @A@A. @@#gcd. @ @A@.=@@#leb.=@ @A@ABCEGHI. @@#lor. @ @A@.Z@@#ltb.Z@ @A@A.p@@#max.p@ '@A@B.@@#min.@ @A@.@@#mul.@ @A@AC.g@@#odd.g@ @A@.&@ @#one.&@ @A@A.뾴@@#pow.뾴@ k@A@.L@@#sub.L@ @A@.@@#two.@ @A@ABCD.,a@"@$div2.,a@ @A@.Xz@*@$even.Xz!@ ?1@A@A.@/@$iter.ؑ&@ @A@B. @4@$land. +@ @A@. @:@$log2. 1@ @A@ACE.@?@$lxor.6@ R@A@.y@F@$pred.y=@ `<@A@A.Ʉ@K@$sqrt.ɄB@ ;@A@.@R@$succ.I@ @A@.t @X@$zero.t O@ Z@A@AB/@]@.to_little_uint/T@ @A@CDF/@b@%ldiff/Y@ H@A@00@ U!@A@2kF@ T S@A@AB3@q@(tail_add3h@^q@A@C3@v@(tail_mul3m@^@A@5Z@ _ ^@A@5f}@ ] \@A@AB5a@P@'iter_op5aG@ @A@C6w~@@'of_uint6w~@^5@A@:x@[@,Nsucc_double:xR@ ʭ@A@ADE@3@&divmod>*@C@A@>@:@&double>1@NĴ@A@A?;@?@&modulo?;6@"i@A@BEFGHJ@4&Basics'Program#Coq@0!bs߯? :VU=j03@1O,[{ (((@0dmk(5Ju<(=(<(;@0vyػ0= u)BinPosDef&PArith#Coq@0}H d.%,b$Bool#Coq@0j 2cZ`FW*CMorphisms'Classes#Coq@0qیZBeϠ0CRelationClasses'Classes#Coq@0TL;0RUfw1B0.i bYN Z)Decidable%Logic#Coq@0ND걸풬/Oߠ'Decimal$Init#Coq@0C涳N*ua*EqdepFacts%Logic#Coq@0FI$ͼՋ`)Eqdep_dec%Logic#Coq@0u wWIϰ߼*Equalities*Structures#Coq@0όe얟)H.Ƞ+Equivalence'Classes#Coq@07;ꮹÐ0måj$$Init'Classes#Coq@0](p{yOh."Le%Arith#Coq@0d}Omq++ 0\͉!Ig*Logic_Type$Init#Coq@0 1jc6"Lt%Arith#Coq@0KZ-eJkP܏/`0Imӽ%\$PD.Morphisms_Prop'Classes#Coq@0% :B'.>u%$NAdd(Abstract'Natural'Numbers#Coq@05;ZW:㥜un$)NAddOrder(Abstract'Natural'Numbers#Coq@02'8zn7Hfɠ'NAxioms(Abstract'Natural'Numbers#Coq@0Zخb1Z3uuѠ%NBase(Abstract'Natural'Numbers#Coq@0 Y?V vI%NBits(Abstract'Natural'Numbers#Coq@0qteo_hɅ $NDiv(Abstract'Natural'Numbers#Coq@0bz$?[p(5$NGcd(Abstract'Natural'Numbers#Coq@08E-S ;j_Ҡ$NLcm(Abstract'Natural'Numbers#Coq@0 ~xZ9L{:$NLog(Abstract'Natural'Numbers#Coq@0K Aat/ j &NOrder(Abstract'Natural'Numbers#Coq@0]@7U#oY'NParity(Abstract'Natural'Numbers#Coq@0̗SKz*!&4h$NPow(Abstract'Natural'Numbers#Coq@0҆mulf0unt"kwpYC%NSqrt(Abstract'Natural'Numbers#Coq@0<ge$NSub(Abstract'Natural'Numbers#Coq@0:DfJᠠ%NZAdd&NatInt'Numbers#Coq@00h`ZK4*NZAddOrder&NatInt'Numbers#Coq@0e~1>r砠(NZAxioms&NatInt'Numbers#Coq@0] ρ5r&NZBase&NatInt'Numbers#Coq@0^&8yUL&NZBits&NatInt'Numbers#Coq@0MlIpKt%NZDiv&NatInt'Numbers#Coq@0$ |J?d (w%NZGcd&NatInt'Numbers#Coq@0KgT7|%NZLog&NatInt'Numbers#Coq@0ꔉ .uV%NZMul&NatInt'Numbers#Coq@0ctR~6[Ƞ*NZMulOrder&NatInt'Numbers#Coq@0}\^ !"k}@R'NZOrder&NatInt'Numbers#Coq@0 q;Ve7R W,(NZParity&NatInt'Numbers#Coq@0H>ca'^^%NZPow&NatInt'Numbers#Coq@0)6*9 B:vȻ,NZProperties&NatInt'Numbers#Coq@01D%E`|3x&NZSqrt&NatInt'Numbers#Coq@0` .%m#Nat$Init#Coq@0eʤģPSR蠠)Notations$Init#Coq@0&v!D]hwnv *NumPrelude'Numbers#Coq@05WUVŦ]xVXԠ4Operators_Properties)Relations#Coq@0U3y#h&&Orders*Structures#Coq@0$Znl0\͗$g05Mܿ獐ζΖLB)OrdersTac*Structures#Coq@05'4Ԗ+9%%Peano$Init#Coq@0 jha|ؠ(PeanoNat%Arith#Coq@0O~2$k[#lZ$Plus%Arith#Coq@04tmG'Prelude$Init#Coq@0JqTttֱ3:3938@0Gz rA6ՠ(((@0]4Ѐd{n^2Relation_Operators)Relations#Coq@0%s鯰s)Relations#Coq@0-SetoidTactics'Classes#Coq@0S_`nOU$-?0;RWMi\N'Tactics$Init#Coq@0/9m+ a'Tactics'Program#Coq@03@mrHȠ@@r#tӡ)BinNatDef&NArith#Coq@@d@ @|%@A@32 Q@@@@#_101@A@@@@@@@@#_112M접 @#_12'`o@B'N_scope@44@32 Q@@@@#_13@@3+*@#_142M접 @#_15'`o@@@@3Π2 Q@@@@#_160`FE@#_172M접 C#_18'`o@BBD@@)@,@32 Q@@@@#_19 kj@#_202M접 h#_21'`o@Bgi@@N@Q@32 Q@@@@#_22&Y@#_232M접 @#_24'`o@B@@t@w@32 Q@@@@#_25 @#_262M접 &#_27'`o@B@@@@#_28@FF@F@@F@@FA@&_ <= _@F @@&_ <= _!x"<=!y@@@@@A@@# <=@A@@B@@@@@#_29%c?@'N_scope4@@4 @@@&접44@@@@&_ <= _AA@&x <= y#_30@FF@F@@F@@FA@%_ < _@F @@%_ < _]!<\@@@[@A@@" <@A@@B@@@@@#_31%c?@'N_scope4_@@4d@@@15 5@@@@%_ < _BB@%x < y#_32@FF@F@@F@@FA@&_ >= _@F @@&_ >= _">=@@@@A@@# >=@A@@B@@@@@#_33%c?@'N_scope5V@@5X@@@ 5c5b@@@@&_ >= _BtBj@&x >= y#_34@FF@F@@F@@FA@%_ > _@F @@%_ > _!>@@@@A@@" >@A@@B@@@@@#_35%c?@'N_scope5@@5@@@ X55@@@@%_ > _BΠB@%x > y#_36@FF@F@F@@F@@@@FA @+_ <= _ <= _@F @@+_ <= _ <= _q"<=p"<= !z@@@x@A@@# <=@A@@B@@# <=@A@@C@@@@@#_37%c?@'N_scope6$@@6%@@!z@@@46766@6;@@@@@+_ <= _ <= _COCE@+x <= y <= z#_38@FF@F@F@@F@@@FA@*_ <= _ < _@F @@*_ <= _ < _񠐐"<=𠐐!< @@@@A@@# <=@A@@B@@" <@A@@C@@@@@#_39%c?@'N_scope6@@6@@@@@~66@6@@@@@*_ <= _ < _C̠C@*x <= y < z#_40@FF@F@F@@F@@@FA@)_ < _ < _@F @@)_ < _ < _n!<m!< @@@t@A@@" <@A@@B@@" <@A@@C@@@@@#_41%c?@'N_scope7 $@@7!#@@'@@@)7170@075@@@@@)_ < _ < _DID?@)x < y < z#_42@FF@F@F@@F@{@@FA@*_ < _ <= _@F @@*_ < _ <= _렐!<ꠐ"<= z@@@@A@@" <@A@@B@@# <=@A@@C@@@@@#_43%c?@'N_scope7@@7@@y@@@x77@7@@@@@*_ < _ <= _DƠD@*x < y <= z7 2 Q@@@@#_44r>=@#_452M접 ;#_46'`o@B:<@D!B|@#_47@@ȐȠȐ@@@)( _ | _ )@@ @@!(7L!|7Q!)@@@@@@AȠ@A@@"| @BȠ@@@@@#_48%c?@'N_scope7{@@7}@@@頑77@@@@OEQEG@)( p | q )7O2 Q@@@@#_49ɠ@#_502M접 Ơ#_51'`o@A@C@7'2 Q@@@@#_52頠@#_532M접 栠#_54'`o@A@D@72 Q@@@@#_57E@7  @#_582M접 6@7m+#_59'`o@@@@62 Q@@@@#_61E@6 *)@#_622M접  #_63'`o@@@@62 Q@@@@#_65E@67FE@#_662M접 <#_67'`o@@@@6Q2 Q@@@@#_69E@6\ba@#_702M접 X#_71'`o@@@@62 Q@@@@#_73F@6)G~}@#_742M접 t#_75'`o@@@@52 Q@@@@#_77F"@5 @#_782M접 #_79'`o@@@@52 Q@@@@#_81F>@5C@#_822M접 #_83'`o@@@@5i2 Q@@@@#_85FZ@5tYҠ@#_862M접 Ƞ#_87'`o@@@@562 Q@@@@#_89Fv@5Ac@#_902M접 䠠#_91'`o@@@@52 Q@@@@#_93F@53k(  @#_942M접 #_95'`o@@@@42 Q@@@@#_96F@4R@A@@@@&@#_972M접 BAAA#_98'`o@B$&@:3:6@3e2 Q@@@@#_99F@3p @A@@@@N@$_1002M접 AA@A$_101'`o@AL@3H@22 Q@@@@$_102F@2N #p@$_1032M접 EE@A$_104'`o@E.function_scope@v@A@AA:@2}2 Q@@@@$_105G*@2)-nT@$_1062M접 EE@A$_107'`o@E1@46@A@AA:@2~2 Q@@@@$_108GZ@2)-b@$_1092M접 EE@A$_110'`o@Ea@df@A@AA:@22 Q@@@@$_1111@$_1122M접 DD@A$_113'`o@D@@A@A;@2D2 Q@@@@$_114G@2O-^!@A@@@@-@$_1152M접 $_116'`o@C@@A@A@232 Q@@@@$_117G@2>-@@A@@@@V@$_1182M접 $_119'`o@D@ꠐZ@A@AGD@2 2 Q@@@@$_120H @2簔.@$_1212M접 DD@A$_122'`o@D@@A@A;@22 Q@@@@$_1231Y@$_1242M접 DD@A$_125'`o@D>@A@A@A;@22 Q@@@@$_126Hc@2(Cv@A@@@@@$_1272M접 $_128'`o@Cl@o@A@A@22 Q@@@@$_129H@2$EY6@A@@@@@$_1302M접 $_131'`o@D@@A@AG@2 2 Q@@@@$_132H@2G @A@@@@2@$_1332M접 $_134'`o@Eà@@Ǡ7@A:&@A@=,@E;=7@@QS8@D(@;df:<;'=\@u84@DJ@S2@@@@3@@J@8Coq.NArith.BinNat.N#<>#1Fq@22 Q@@@@$_145J@2<@A@@@@ @$_1462M접 $_147'`o@C5@*@@@A@$_148%#C@3@AA@@@@@22 Q@@@@$_149JY@2=l@A@@@@ @$_1502M접 $_151'`o@Gp@@f@@ @@3_@A@;Π=@$_15242G@3@AA@@@@@@@@@22 Q@@A@$_153J@2(0X"@A@@@@ @$_1542M접 $_155'`o@@@@2}2 Q@@A@$_156J@2 K@A@@@@ >@$_1572M접 $_158'`o@@@@2q2 Q@@@@$_159J@2|a@A@@@@ ]@$_1602M접 $_161'`o@@@@2x2 Q@@A@$_162K@26ie@A@@@@ |@$_1632M접 $_164'`o@A.positive_scope@2@2T2 Q@@A@$_165K)@2_@A@@@@ @$_1662M접 $_167'`o@A @I@2S2 Q@@A@$_168KM@2^6pL@A@@@@ @$_1692M접 $_170'`o@A @I@2]2 Q@@A@$_171Kq@2hB(@A@@@@ @$_1722M접 $_173'`o@Am@2@2b2 Q@@@@$_174K@2m'@A@@@@ @$_1752M접 $_176'`o@A @J@2l2 Q@@@@$_177K@2w( }@A@@@@ 1@$_1782M접 $_179'`o@A 0@K@2q2 Q@@@@$_180K@2|"D`@A@@@@ U@$_1812M접 $_182'`o@A T@K9@2y2 Q@@@@$_183L@2)_@A@@@@ y@$_1842M접 $_185'`o@A x@K]@22 Q@@@@$_186L%@2'R@A@@@@ @$_1872M접 $_188'`o@B  @KK@22 Q@@@@$_189LN@2;@A@@@@ @$_1902M접 $_191'`o@A @K@22 Q@@@@$_192Lr@2@A@@@@ @$_1932M접 $_194'`o@B 預 @KРK@22 Q@@@@$_195L@2 u@A@@@@ @$_1962M접 $_197'`o@A @K@22 Q@@@@$_198L@2B@A@@@@ 7@$_1992M접 $_200'`o@B 6 8@LL @22 Q@@A@$_201L@2ڴ@A@@@@ `@$_2022M접 $_203'`o@B _ a@LFLI@22 Q@@A@$_204M@2LD@A@@@@ @$_2052M접 $_206'`o@B  @LoLr@22 Q@@A@$_207M:@2x6@A@@@@ @$_2082M접 $_209'`o@B  @LL@22 Q@@@@$_210Mc@2/@A@@@@ @$_2112M접 $_212'`o@B ڠ @LL@22 Q@@@@$_213M@27@A@@@@ @$_2142M접 $_215'`o@B  @LꠐL@22 Q@@@@$_216M@2q,8@A@@@@ -@$_2172M접 $_218'`o@B , .@MM@22 Q@@@@$_219M@2@A@@@@ V@$_2202M접 $_221'`o@B U W@M<M?@M#tӡ1f@1hN1_@A@1N@@ T@N @1 TJN@A@A \@N@1 \^A@A@ @2>@A@AB l@2=S@A@ Y@23@A@A #@22@A@ T@23m@A@ABC "@22@A@ q@23@A@A @22@A@ @22@A@AB @2>*@A@ ~@22@A@A =@22@A@ @2<@A@ABCD c@2|>~@A@ @2~2}@A@A hx@2|2{@A@ @2{2z@A@AB @2w2v@A@ @2w2v@A@A 3"@2t2s@A@ F)@2r2q@A@ABC S@2p2o@A@ @2j?9@A@A @2i2h@A@ !@2h2g@A@AB ! @2e?@A@ !7@2e2d@A@A *@2c2b@A@B@2a5@A@ABCDE.@2`2_@A@u^@2`2_@A@A}@2^2]@A@@2[2Z@A@ABw@2Y=b@A@K@2Z2Y@A@AK@2W2V@A@I@2T2S@A@ABCO@2R2Q@A@,@2R2Q@A@AZ@2P2O@A@`@2M2L@A@ABe@2J2I@A@+{@2J2I@A@A5z@2H<@A@ @2E2D@A@AB @2B2A@A@00@2B3@A@A2kF@2@2?@A@5Z@2?2>@A@5f}@2=2<@A@ABCDEFG@A2,N@@ T@3-3,@A@A @3+?E@A@ l@3+=@A@AB Y@3)4]@A@ #@3*3)@A@A T@3'4@A@ "@3'3&@A@ABC q@3!45@A@ @3#3"@A@A @3!3 @A@ @3>@A@AB ~@33@A@ =@33@A@A @3=p@A@ c@3?@A@ABCD @33@A@ hx@33@A@A @33@A@ @33@A@AB @33@A@ 3"@33@A@A F)@3 3 @A@ S@3 3 @A@ABC @3?@A@ @33@A@A !@33@A@ ! @3@ @A@AB !7@22@A@ *@22@A@AB@26 @A@.@22@A@ABCDEu^@22@A@}@22@A@A@22@A@w@2=@A@ABK@22@A@K@22@A@AI@22@A@O@22@A@ABC,@22@A@Z@22@A@A`@22@A@e@22@A@AB+{@22@A@5z@2=d@A@A @22@A@ @2ޑ2@A@AB00@2ܑ4Y@A@2kF@2ۑ2@A@5Z@2ڑ2@A@5f}@2ؑ2@A@ABCDEFG@2ΠOB@@ T@3ɑ3@A@A @3Ǒ?@A@ l@3Ǒ>@A@AB Y@3ő4@A@ #@3Ƒ3@A@A T@3Ñ4@A@ "@3Ñ3@A@ABC q@34@A@ @33@A@A @33@A@ @3?b@A@AB ~@33@A@ =@33@A@A @3> @A@ c@3?@A@ABCD @33@A@ hx@33@A@A @33@A@ @33@A@AB @33@A@ 3"@33@A@A F)@33@A@ S@33@A@ABC @3@n@A@ @33@A@A !@33@A@ ! @3@@A@AB !7@33@A@ *@33@A@AB@36@A@.@33@A@ABCDEu^@33@A@}@33@A@A@33@A@w@3>@A@ABK@33@A@K@33@A@AI@33@A@O@33@A@ABC,@33@A@Z@33@A@A`@33@A@e@33@A@AB+{@33~@A@5z@3>@A@A @3|3{@A@ @3z3y@A@AB00@3x4@A@2kF@3w3v@A@5Z@3v3u@A@5f}@3t3s@A@ABCDEFG@3pOޠ@@ T@4e4d@A@A @4c@}@A@ l@4c?'@A@AB Y@4a5@A@ #@4b4a@A@A T@4_5@@A@ "@4_4^@A@ABC q@4Y5m@A@ @4[4Z@A@A @4Y4X@A@ @4V?@A@AB ~@4U4T@A@ =@4T4S@A@A @4R>@A@ c@4P@R@A@ABCD @4N4M@A@ hx@4P4O@A@A @4N4M@A@ @4K4J@A@AB @4I4H@A@ 3"@4H4G@A@A F)@4E4D@A@ S@4D4C@A@ABC @4;A @A@ @4=4<@A@A !@4;4:@A@ ! @49AX@A@AB !7@4746@A@ *@4746@A@AB@447X@A@.@4443@A@ABCDEu^@404/@A@}@4241@A@A@4.4-@A@w@4-?6@A@ABK@4,4+@A@K@4+4*@A@AI@4'4&@A@O@4&4%@A@ABC,@4#4"@A@Z@4$4#@A@A`@4 4@A@e@44@A@AB+{@44@A@5z@4>@A@A @44@A@ @44@A@AB00@45@A@2kF@44@A@5Z@44@A@5f}@44@A@ABCDEFG@5 Pz@@ T@55@A@A @4A@A@ l@4?@A@AB Y@461@A@ #@44@A@A T@45@A@ "@44@A@ABC q@46 @A@ @44@A@A @44@A@ @4@@A@AB ~@44@A@ =@44@A@A @4?D@A@ c@4@@A@ABCD @44@A@ hx@44@A@A @44@A@ @44@A@AB @44@A@ 3"@44@A@A F)@44@A@ S@44@A@ABC @4בA@A@ @4ّ4@A@A !@4ב4@A@ ! @4ՑA@A@AB !7@4ӑ4@A@ *@4ӑ4@A@AB@4Б7@A@.@4Б4@A@ABCDEu^@4̑4@A@}@4Α4@A@A@4ʑ4@A@w@4ɑ?@A@ABK@4ȑ4@A@K@4Ǒ4@A@AI@4Ñ4@A@O@4‘4@A@ABC,@44@A@Z@44@A@A`@44@A@e@44@A@AB+{@44@A@5z@4?8@A@A @44@A@ @44@A@AB00@46-@A@2kF@44@A@5Z@44@A@5f}@44@A@ABCDEFG@ABCD.2 Q@@@@$_222Q!@." >@A@@@@@$_2232M접 $_224'`o@C@@PP6@.%2 Q@@@@$_225QN@.0 D@A@@@@@$_2262M접 $_227'`o@CŠǠ@@PP6@.52 Q@@@@$_228Q{@.@ @A@@@@@$_2292M접 $_230'`o@C@@PڠPݠ6@.C2 Q@@@@$_231Q@.N @A@@@@ @$_2322M접 $_233'`o@C!@@QQ 7 @.S2 Q@@A@$_234Q@.^į@A@@@@M@$_2352M접 $_236'`o@BLN@Q3Q6@Q#tӡ-@-ϠQ5W@A-Q5X@B@-Q@@ T@R@. TJQ@A@A \@R @. \^E@A@ \@R@- \-@A@ \@R@- \-@A@AB @6B@A@CD l@6AQ@A@ Y@67@A@A #@66@A@ T@67k@A@ABE "@66@A@ q@67@A@A @66@A@ @66@A@AB @6B(@A@ ~@66@A@A =@R3@.$ =TQ@A@ @6@@A@ABCF c@6|B~@A@ @R@@.) TQ@A@A hx@6~6}@A@ @6}6|@A@AB @6y6x@A@ @6y6x@A@A 3"@6v6u@A@ F)@6t6s@A@ABC S@6r6q@A@ @6lC;@A@A @6k6j@A@ !@6j6i@A@AB ! @6gC@A@ !7@Rd@.A !7TR*@A@A *@6g6f@A@B@6e9@A@ABCDG.@6d6c@A@u^@6d6c@A@A}@6b6a@A@@6_6^@A@ABw@6]Af@A@K@6^6]@A@AK@6[6Z@A@I@6X6W@A@ABCO@6V6U@A@,@6V6U@A@AZ@6T6S@A@`@6Q6P@A@ABe@6N6M@A@+{@6N6M@A@A5z@6L@@A@ @6I6H@A@AB @6F6E@A@00@6F7@A@A2kF@6D6C@A@5Z@6C6B@A@5f}@6A6@@A@ABCDEFH@.R@ \@ @AB lC "D czxE.GEG@ABR#tӡ-GenericMinMax*Structures#Coq@e@ R6@A@~Rà@@ T@R@{ TJR@A@A @7JCd@A@ l@7JB@A@AB Y@7H8|@A@ #@7I7H@A@A T@7F8'@A@ "@7F7E@A@ABC q@7@8T@A@ @7B7A@A@A @7@7?@A@ @7=B@A@AB ~@7<7;@A@ =@7;7:@A@A @79A@A@ c@77C9@A@ABCD @7574@A@ hx@7776@A@A @7574@A@ @7271@A@AB @707/@A@ 3"@7/7.@A@A F)@7,7+@A@ S@7+7*@A@ABC @7"C@A@ @7$7#@A@A !@7"7!@A@ ! @7 D?@A@AB !7@77@A@ *@77@A@AB@7:?@A@.@77@A@ABCDEu^@77@A@}@77@A@A@77@A@w@7B@A@ABK@77@A@K@77@A@AI@77 @A@O@7 7 @A@ABC,@7 7 @A@Z@7 7 @A@A`@77@A@e@77@A@AB+{@77@A@5z@7A@A@A @66@A@ @66@A@AB00@68x@A@2kF@66@A@5Z@66@A@5f}@66@A@ABCDEFG@(Sa@@ T@77@A@A @7D@A@ l@7B@A@AB Y@79@A@ #@77@A@A T@78@A@ "@77@A@ABC q@7ܑ8@A@ @7ޑ7@A@A @7ܑ7@A@ @7ّC@A@AB ~@7ؑ7@A@ =@7ב7@A@A @7ՑB+@A@ c@7ӑC@A@ABCD @7ё7@A@ hx@7ӑ7@A@A @7ё7@A@ @7Α7@A@AB @7̑7@A@ 3"@7ˑ7@A@A F)@7ȑ7@A@ S@7Ǒ7@A@ABC @7D@A@ @77@A@A !@77@A@ ! @7D@A@AB !7@77@A@ *@77@A@AB@7:@A@.@77@A@ABCDEu^@77@A@}@77@A@A@77@A@w@7B@A@ABK@77@A@K@77@A@AI@77@A@O@77@A@ABC,@77@A@Z@77@A@A`@77@A@e@77@A@AB+{@77@A@5z@7B@A@A @77@A@ @77@A@AB00@79@A@2kF@77@A@5Z@77@A@5f}@77@A@ABCDEFG@ABT#tӡIʙ@T7a@A@ʯT@@ T@T@߽ TJT@A@A @8D@A@ l@8CP@A@AB Y@89@A@ #@88@A@A T@89i@A@ "@88@A@ABC q@89@A@ @88@A@A @88@A@ @8D'@A@AB ~@8~8}@A@ =@8}8|@A@A @8{B@A@ c@8yD{@A@ABCD @8w8v@A@ hx@8y8x@A@A @8w8v@A@ @8t8s@A@AB @8r8q@A@ 3"@8q8p@A@A F)@8n8m@A@ S@8m8l@A@ABC @8dE3@A@ @8f8e@A@A !@8d8c@A@ ! @8bE@A@AB !7@8`8_@A@ *@8`8_@A@AB@8];@A@.@8]8\@A@ABCDEu^@8Y8X@A@}@8[8Z@A@A@8W8V@A@w@8VC_@A@ABK@8U8T@A@K@8T8S@A@AI@8P8O@A@O@8O8N@A@ABC,@8L8K@A@Z@8M8L@A@A`@8I8H@A@e@8G8F@A@AB+{@8D8C@A@5z@8EB@A@A @8A8@@A@ @8?8>@A@AB00@8=9@A@2kF@8<8;@A@5Z@8;8:@A@5f}@8988@A@ABCDEFG@RT@@ T@9*9)@A@A @9(EB@A@ l@9(C@A@AB Y@9&:Z@A@ #@9'9&@A@A T@9$:@A@ "@9$9#@A@ABC q@9:2@A@ @9 9@A@A @99@A@ @9D@A@AB ~@99@A@ =@99@A@A @9Cm@A@ c@9E@A@ABCD @99@A@ hx@99@A@A @99@A@ @99@A@AB @99 @A@ 3"@9 9 @A@A F)@9 9 @A@ S@9 9@A@ABC @9E@A@ @99@A@A !@98@A@ ! @8F@A@AB !7@88@A@ *@88@A@AB@8<@A@.@88@A@ABCDEu^@88@A@}@88@A@A@88@A@w@8C@A@ABK@88@A@K@88@A@AI@88@A@O@88@A@ABC,@88@A@Z@88@A@A`@88@A@e@88@A@AB+{@88@A@5z@8Ca@A@A @8ݑ8@A@ @8ۑ8@A@AB00@8ّ:V@A@2kF@8ؑ8@A@5Z@8ב8@A@5f}@8Ց8@A@ABCDEFG@AB2 Q@@A@$_237UJ@2@A@@@@@$_2382M접 $_239'`o@A@T@2 Q@@A@$_240Un@5*?@A@@@@@$_2412M접 $_242'`o@A@T@2 Q@@A@$_243U@3@A@@@@ @$_2442M접 $_245'`o@B  @T𠐒T@2 Q@@A@$_246U@4ɕ@A@@@@3@$_2472M접 $_248'`o@B24@UU@2 Q@@A@$_249U@ F @A@@@@\@$_2502M접 $_251'`o@B[]@UBUE@2 Q@@A@$_252V @4ɨ.@A@@@@@$_2532M접 $_254'`o@B@UkUn@2 Q@@A@$_255V6@;#f@A@@@@@$_2562M접 $_257'`o@A@U@ 2 Q@@A@$_258VZ@.[>_@A@@@@@$_2592M접 $_260'`o@A@U@2 Q@@A@$_261V~@ ?@A@@@@@$_2622M접 $_263'`o@C@@UݠUࠐC@!2 Q@@A@$_264V@,4ɢ@A@@@@#@$_2652M접 $_266'`o@C"$@@V V C@-2 Q@@A@$_267V@8sl@A@@@@P@$_2682M접 $_269'`o@COQ@@V7V:F@92 Q@@@@$_270W@DM D@A@@@@}@$_2712M접 $_272'`o@A|@Va@>2 Q@@A@$_273W)@I}@A@@@@@$_2742M접 $_275'`o@A@V@@2 Q@@A@$_276WM@KK@A@@@@@$_2772M접 $_278'`o@CĠƠ@@VV<@B2 Q@@A@$_279Wz@M"*@A@@@@@$_2802M접 $_281'`o@C@@V٠VܠG-@M2 Q@@A@$_282W@X@A@@@@@$_2832M접 $_284'`o@A@W@T2 Q@@A@$_285W@_8@A@@@@C@$_2862M접 $_287'`o@BB@@nD@L2 Q@@A@$_288W@W u@A@@@@k@$_2892M접 $_290'`o@Aj@WO@L2 Q@@A@$_291X@W v@A@@@@@$_2922M접 $_293'`o@A@Ws@H2 Q@@A@$_294X;@SY@A@@@@@$_2952M접 $_296'`o@B@@WG@#2 Q@@A@$_297Xc@.6VX@A@@@@@$_2982M접 $_299'`o@Bڠ@@W=@+2 Q@@A@$_300X@6't7@A@@@@@$_3012M접 $_302'`o@A@W@*2 Q@@A@$_303X@5 >@A@@@@'@$_3042M접 $_305'`o@A&@X @)2 Q@@@@$_306X@4:1v@A@@@@K@$_3072M접 $_308'`o@B ϠL@E6L\@ 2 Q@@@@$_309X@ޕ@A@@@@t@$_3102M접 $_311'`o@Bsu@WW@2 Q@@@@$_312Y%@ C@A@@@@@$_3132M접 $_314'`o@B@WX@2 Q@@@@$_315YN@2g@A@@@@@$_3162M접 $_317'`o@CŠǠ@@W⠐F^@2 Q@@@@$_318Y{@0J@A@@@@@$_3192M접 $_320'`o@Cw@@EߠMF@2 Q@@@@$_321Y@X@A@@@@ @$_3222M접 $_323'`o@C!@@X<F@2 Q@@@@$_324Y@ `!@A@@@@M@$_3252M접 $_326'`o@DLN@@@Y5Y8?8I@2 Q@@A@$_327Z@| h@A@@@@~@$_3282M접 $_329'`o@A}@Yb@2 Q@@A@$_330Z*@|@A@@@@@$_3312M접 $_332'`o@A@Y@Ӡ2 Q@@A@$_333ZN@@A@@@@@$_3342M접 $_335'`o@BŠ@@Y?@Ġ2 Q@@A@$_336Zv@U4@A@@@@@$_3372M접 $_338'`o@B@@YӠJ$@̠2 Q@@A@$_339Z@*N@A@@@@@$_3402M접 $_341'`o@B@YY@Π2 Q@@A@$_342Z@!-w@A@@@@?@$_3432M접 $_344'`o@B>@@Z%Z(@Ş2 Q@@A@$_345Z@ũd@A@@@@h@$_3462M접 $_347'`o@Bgi@ZNZQ@Ŭ2 Q@@A@$_348[@ŷd@A@@@@@$_3492M접 $_350'`o@B@ZwZz@ż2 Q@@A@$_351[B@o?@A@@@@@$_3522M접 $_353'`o@E@@@XXZ@͠2 Q@@A@$_354[x@<+ @A@@@@@$_3552M접 $_356'`o@B@Z֠Z@۠2 Q@@A@$_357[@%&@A@@@@@$_3582M접 $_359'`o@A@Z@֠2 Q@@A@$_360[@=W@A@@@@=@$_3612M접 $_362'`o@A<@[!@Ƞ2 Q@@A@$_363[@ J@A@@@@a@$_3642M접 $_365'`o@C`b@@[H[KAK@ʠ2 Q@@A@$_366\@>5@A@@@@@$_3672M접 $_368'`o@C@@[u[xAx@ų2 Q@@A@$_369\C@ž0@6@A@@@@@$_3702M접 $_371'`o@C@@[[A@Ũ2 Q@@A@$_372\p@ų;y@A@@@@@$_3732M접 $_374'`o@C砐@@[Ϡ[ҠL#@ų2 Q@@A@$_375\@ž=\?@A@@@@@$_3762M접 $_377'`o@B@[[@Ŵ2 Q@@A@$_378\@ſ=8]@A@@@@>@$_3792M접 $_380'`o@B=?@\$\'@ŵ2 Q@@A@$_381\@.@A@@@@g@$_3822M접 $_383'`o@Dfhj@@\P\S\VBV@ź2 Q@@A@$_384]!@@A@@@@@$_3852M접 $_386'`o@E@@@\\\BB@ž2 Q@@A@$_387]W@/d4@A@@@@@$_3882M접 $_389'`o@DΠРҠ@@\\\M@ʠ2 Q@@@@$_390]@%X@A@@@@@$_3912M접 $_392'`o@A@\@̠2 Q@@A@$_393]@'@A@@@@%@$_3942M접 $_395'`o@C(@E>EAS@Ź2 Q@@A@$_396]@e@A@@@@S@$_3972M접 $_398'`o@CRTV@];]>T@ŵ2 Q@@A@$_399^ @oqI@A@@@@@$_4002M접 $_401'`o@C@EE@ő2 Q@@A@$_402^7@Ŝ &*@A@@@@@$_4032M접 $_404'`o@C@]]Td@Ŏ2 Q@@A@$_405^e@ř4Mw@A@@@@@$_4062M접 $_407'`o@Cac@EET@Ł2 Q@@A@$_408^@Ōt`*@A@@@@ @$_4092M접 $_410'`o@C  @]󠐒]T@~2 Q@@A@$_411^@ʼnX@A@@@@9@$_4122M접 $_413'`o@C<@FRFUT@m2 Q@@A@$_414^@x62<@A@@@@g@$_4152M접 $_416'`o@Cfhj@^O^RU@_#tӡ*@,_Bu@A@^_@@ T@_"@;# TJ_@A@A \@_&@;! \^R@A@ @CO@A@AB l@CNh@A@ Y@CD@A@A #@CC@A@ T@CD@A@ABC "@CC@A@ q@CD@A@A @CC@A@ @CC@A@AB @CO?@A@ ~@CC@A@A =@_J@;; =T^@A@ @CM@A@ABCD c@CO@A@ @_W@;@ T^@A@A hx@CC@A@ @CC@A@AB @CC@A@ @CC@A@A 3"@CC@A@ F)@CC@A@ABC S@CC@A@ @CPR@A@A @CC@A@ !@CC@A@AB ! @C~P@A@ !7@_{@;X !7T_A@A@A *@C~C}@A@B@C|F@A@ABCDE.@C{Cz@A@u^@C{Cz@A@A}@CyCx@A@@CvCu@A@ABw@CtN}@A@K@CuCt@A@AK@CrCq@A@I@CoCn@A@ABCO@CmCl@A@,@CmCl@A@AZ@CkCj@A@`@ChCg@A@ABe@CeCd@A@+{@CeCd@A@A5z@CcM@A@ @C`C_@A@AB @C]C\@A@00@C]D@A@A2kF@C[CZ@A@5Z@CZCY@A@5f}@CXCW@A@ABCDEFG@ _ @@ T@DIDH@A@A @DGPa@A@ l@DGO @A@AB Y@DEEy@A@ #@DFDE@A@A T@DCE$@A@ "@DCDB@A@ABC q@D=EQ@A@ @D?D>@A@A @D=D<@A@ @D:O@A@AB ~@D9D8@A@ =@D8D7@A@A @D6N@A@ c@D4P6@A@ABCD @D2D1@A@ hx@D4D3@A@A @D2D1@A@ @D/D.@A@AB @D-D,@A@ 3"@D,D+@A@A F)@D)D(@A@ S@D(D'@A@ABC @DP@A@ @D!D @A@A !@DD@A@ ! @DQ<@A@AB !7@DD@A@ *@DD@A@AB@DG<@A@.@DD@A@ABCDEu^@DD@A@}@DD@A@A@DD@A@w@DO@A@ABK@DD@A@K@DD@A@AI@D D @A@O@D D @A@ABC,@DD@A@Z@DD@A@A`@DD@A@e@DD@A@AB+{@CC@A@5z@DN@A@A @CC@A@ @CC@A@AB00@CEu@A@2kF@CC@A@5Z@CC@A@5f}@CC@A@ABCDEFG@AB)2 Q@@A@$_417`i@)@A@@@@@$_4182M접 $_419'`o@Bࠐ@_Ǡ_@)2 Q@@A@$_420`@)" i@A@@@@ @$_4212M접 $_422'`o@C  @@_񠐒_)R@)+2 Q@@A@$_423`@)6 _@A@@@@ 7@$_4242M접 $_425'`o@C 6 8@@``!Pr@)?2 Q@@A@$_426`@)J5;@A@@@@ d@$_4272M접 $_428'`o@B c e@`J`M@)H2 Q@@A@$_429a@)S Fu@A@@@@ @$_4302M접 $_431'`o@C  @@`t`w)@)\2 Q@@A@$_432aB@)g 7k@A@@@@ @$_4332M접 $_434'`o@C  @@``F@)p2 Q@@A@$_435ao@){ !@A@@@@ @$_4362M접 $_437'`o@Dk 蠐 @@I`Ӡ`֠Q'@)q2 Q@@A@$_438a@)|3K@A@@@@!@$_4392M접 $_440'`o@D!!@@I3aaG@)l2 Q@@A@$_441a@)w+è2@A@@@@!K@$_4422M접 $_443'`o@A@)@@$_444YS'N_scope) @a TFrUd@$_445@rrAr@@r@BrA@%_ + _@r @B%_ + _ !+ @@@ @AA@" +@A@@B@@@@@$_446%c?@'N_scopeU@Q@@UBV@@@)`UMUL@@@@%_ + _b^@%x + y$_447@rrAr@@r@BrA@%_ - _@r @Z%_ - _ !- @@@ @AA@" -@A@@B@@@@@$_448%c?@'N_scopeU@@U@@@)@` cR砑UU@@@@%_ - _b@%x - y$_449@hhAh@@h@BhA@%_ * _@h @%_ * _!U!*!T@@@!S@AA@" *@A@@B@@@@@$_450%c?@'N_scopeU@@U @@@)VV@@@@%_ * _c@%x * y$_451@^^@^A@^@A^A@%_ ^ _@^ @A%_ ^ _!!^!@@@!@A@@A@@"^ @BA@@@@$_452%c?@'N_scopeVN_@@VPd@@@*n@^ QV]V\@@@@%_ ^ _cn@%x ^ y$_453@FF@F@@F@@FA@&_ ?= _@F @@V"?=V@@@}@A@@A@@#?= @B@@@@@$_454%c?@'N_scopeV@@V@@@*VV@@@@>c@&x ?= y$_455@"a&_ <= _"Q";@@$_456%c?@'N_scopeV̠@@VΠ@@@*@Vy \V۠V@@@@&_ <= _c@&x <= y$_457@"+%_ < _""@@$_458%c?@'N_scopeV󠠐@@V @@@+@W \WW@@@@%_ < _d@%x < y$_459@!&_ >= _!!@@$_460%c?@'N_scopeW+@@W0@@@+:@V \1W)W(@@@@&_ >= _d:@&x >= y$_461@!%_ > _!!@@$_462%c?@'N_scopeWAR@@WCW@@@+a@W \@WPWO@@@@%_ > _da@%x > y$_463@!+_ <= _ <= _!}!_@@$_464%c?@'N_scopeWh@@Wi@@!D@@@!CWyWx@W}!V@@@@@+_ <= _ <= _d@+x <= y <= z$_465@!A*_ <= _ < _!-!@@$_466%c?@'N_scopeW@@W@@!t@@@!sѠWW@W!@@@@@*_ <= _ < _d@*x <= y < z$_467@ )_ < _ < _  @@$_468%c?@'N_scopeWȠ@@Wɠ@@!@@@!ڠW٠W@᠑Wݠ!@@@@@)_ < _ < _d@)x < y < z$_469@ *_ < _ <= _  v@@$_470%c?@'N_scopeW@@W@@!Ԡ/@@@!Ӡ X X@8X !@@@@@*_ < _ <= _e!@*x < y <= z$_471@FF@F@@F@@FA@&_ =? _@F @@X9"=?X>@@@ 0@A@@# =?@A@@B@@@@@$_472%c?@'N_scopeX[l@@X]q@@@,{@b YK XjXi@@@@@ez@&x =? y$_473@FF@F@@F@@FA@'_ <=? _@F @@X#<=?X@@@ @A@@$ <=?@A@@B@@@@@$_474%c?@'N_scopeX@@X@@@,@b TK XàX@@@@@e@'x <=? y$_475@FF@F@@F@@FA@&_ !|" YC!)@@@!@@AȠ@A@@"| @BȠ@@@@@$_482%c?@'N_scopeYl6@@Yn;@@@.E@YOY{Yz@@@@PgD@)( p | q )&N_rect9D{(@@Z@&N_rect ݐBUC9D{(@@Z@%N_recL %N_ind9D{(@@Z@%N_ind@"N09D{(@@ZA$Npos9D{(@@eB(&Ndiscr9D{(@@.@T @0Ndouble_plus_one9D{(@@.@f K'='Ndouble9D{(@@.@fKo@%Nsucc9D{(@@.@%Npred9D{(@@.@fU X@)Nsucc_pos9D{(@@.@f0BNƐ@'Ppred_N9D{(@@O@%Nplus9D{(@@rw&Nminus9D{(@@ ~%Nmult9D{(@@$Neqb9D{(@@l@(Ncompare9D{(@@'@#Nlt9D{(@@@#Ngt9D{(@@@#Nle9D{(@@@#Nge9D{(@@Ր@$Nmin9D{(@@/@de LY@$Nmax9D{(@@/"@dC Lh@%Ndiv29D{(@@/-@d" hxLP@%Neven9D{(@@/8@c LW@$Nodd9D{(@@/C@c ~L|@$Npow9D{(@@@%Nlog29D{(@@/V@cB F)La@(nat_of_N9D{(@@/a@]`L  (N_of_nat9D{(@@/k@]\KL/(N_eq_dec9D{(@@/u@ViR@%Nrect9D{(@@/@Sr(*Nrect_base9D{(@@/@S-^!2*Nrect_step9D{(@@/@R-@<$Nind9D{(@@/@R簔F$Nrec9D{(@@/@Rx缙P)Nrec_base9D{(@@/@RaCvZ)Nrec_succ9D{(@@/@R>EY6d*Npred_succ9D{(@@/@O'@+Npred_minus9D{(@@/@Oy( }y*Nsucc_pred9D{(@@/@)succ_pred" )@,Ppred_N_spec9D{(@@/@PP6ie.Nsucc_pos_spec9D{(@@/@P@+Ppred_Nsucc9D{(@@/@O6pL)Nplus_0_l9D{(@@0@Os)_)Nplus_0_r9D{(@@0@'add_0_r)_*Nplus_comm9D{(@@0@(add_comm" Ġ+Nplus_assoc9D{(@@0&@)add_assoc<]BϠ*Nplus_succ9D{(@@01@O'R٠'Nsucc_09D{(@@0;@O"D`㠠)Nsucc_inj9D{(@@0E@(succ_inj8@-Nminus_N0_Nle9D{(@@0Q@(sub_0_lev*Nminus_0_r9D{(@@0\@O;-Nminus_succ_r9D{(@@0f@Ow)Nmult_0_l9D{(@@0p@O[ u)Nmult_1_l9D{(@@0z@'mul_1_l #)Nmult_1_r9D{(@@0@'mul_1_r .*Nmult_comm9D{(@@0@(mul_commI[r9+Nmult_assoc9D{(@@0@)mul_assoc&XD2Nmult_plus_distr_r9D{(@@0@/mul_add_distr_rnO'Neqb_eq9D{(@@0@OXڴ@%Nle_09D{(@@0@&le_0_le-Ncompare_refl9D{(@@0@LW7PȢ@.Ncompare_Eq_eq9D{(@@0@L6o1z3Ncompare_eq_correct9D{(@@0@N/*Nlt_irrefl9D{(@@0@J@)Nlt_trans9D{(@@0@(lt_transt-<@(Nle_lteq9D{(@@0@J 6*Nlt_succ_r9D{(@@1@Fzį@)Nle_trans9D{(@@1@(le_trans.d:@*Nle_succ_l9D{(@@1@)le_succ_l;t@-Ncompare_spec9D{(@@1*@N7PԐ@*Ncompare_09D{(@@15@^M Dݠ,Ndouble_div29D{(@@1?@;#f砠5Ndouble_plus_one_div29D{(@@1I@.[>_+Ndouble_inj9D{(@@1S@?ސ@4Ndouble_plus_one_inj9D{(@@1^@4ɢ(Npow_0_r9D{(@@1h@r}@+Npow_succ_r9D{(@@1s@[KӐ@*Nlog2_spec9D{(@@1~@؀Y@,Nlog2_nonpos9D{(@@1@>6VX@*Neven_spec9D{(@@1@)'t7@)Nodd_spec9D{(@@1@ >@*Nlt_not_eq9D{(@@1@<_neqS'Ngt_Nlt9D{(@@1@3/ i]1̠2 Q@@A@$_483j@16e@A@@@@*$@$_4842M접 $_485'`o@DѠӠՠ@@j jjW@1֠2 Q@@A@$_486j@1U$2*U@$_4872M접  $_488'`o@B  @j;j>@1Ӡ2 Q@@A@$_489k @1#MZ*}@$_4902M접  $_491'`o@C * , .@jejhjk@1Ѡ2 Q@@A@$_492k:@1 x|*@$_4932M접  $_494'`o@E W Y [@@@jj1񠐑XHXX@1ՠ2 Q@@A@$_495ko@1*@$_4962M접  $_497'`o@B  @jŠj@1Ԡ2 Q@@@@$_498k@1`䠠+@$_4992M접 EA@A$_500'`o@E $@$$@_A@AA@1ʠ2 Q@@@@$_501k@1<+7@$_5022M접 EA@A$_503'`o@E 㠐$ɠ@$̠$@_IA@AA@@@K11ڤs+@ty4]Ag,KS4@glы}!p 鄕@wObv/.B!P@'BinNums'Numbers#Coq@@!N7@2`&BinNat&NArith @@!aAA!f!n&@CD!(@$succ ! )BinNatDef%.@?\B%Logic$Init>@"eq @A#/Q@O2 eB@@><644XX@@A@A@@@@D<`#E:?;@*peano_rect DGHV HKXX9M{B@(positive*@CKj_C'_^p$cfSTs(gjWu!pZ@(eq_ind_r!2#;(&BinPos&PArith#Pos@{=)a)BinPosDef@#R=@Ol+)F 1/3'f Q)V@>GrECt<'$ ::@/peano_rect_succ K'C(à68@@۷ө@/peano_rect_base-^!␑߷@&-@!A@A$A_wd)Morphisms'Classes@&ProperL @*respectful%WO?'ǐ)@#iffС)"A0"AS6ԩҰ=!HȐ"H0!Etu2"JȐ"H1%&H)Р@#andЖw@BBB@@@@D@@IJ>@ C   W2$_tmp@KAs2 qr@@#Aeq4Relation_Definitions)Relations@(relation'Jjj}Z"a'p"Eatb~@@ͷ"f'@@U"Efr!x"x'"ExW~{@&eq_ind JI@)recursion-)ɀLbg@)peano_ind簔&թ]p+ڷ#IHxFM{@Nn ϩ@OuȩX"ө3?ĩà /֩!٩#C>F+ީH-9C;LRNCv@W@ZZ\C @@@&@¶@(é@@,@@.@1 3@  8u02 es/@@+(# =2 u<@@ȷ91-$a_wd/$f_wdGG":^=a@fMOBQ@q  FTZYY[>]]>|_TS{\#IHn"ǠZ@!]s%&r'@A/~01}Šr2 Ktޠc6eQ < =>X}Hr!I*-C@`@\WU[9ȩQQ;9O@AA@AA@@@@@@@DDBw٩6@&pred_N!,0@4s)@$pred @?U'̰VT trAʷa_}Bթ  @(succ_posB@P~נ.C|@+pred_N_succ Zʰ,Ux3FCӰ5^JK@0succ_pred_double=,@+pred_double g_@25\#R Y@(eq_trans!y[␩w 퐩nz+@'f_equal=@qqQX; {`RC}PE C#X g3i-*uutC3uAw;uq@#sub co@3-k 2"p0Pҩ;#!zA(&F#JJnȩ@#notШojtKB@@@@@D!y@Yɶ@ʛ@%Falsee@Ґ9i!eޠ@f@$Truey@A@)False_induُ$@'CH>~ש0A;@1<°$W Ȱ*  r-</I,%"Ch57:!m=?߰A@#add @3  2,PR9';==C\A1EEε÷ҩi-kʩ@*=x[Y^=C2>+;@R@!HT:hC7E=m3q@_sGug@1JyYxCGCo9{KyE{wADkv@bK@Ngtiqܷ@]@[WYyr{tsXש @aKCȷ@i@#E@C'CvǩE+E%lemmaҩ@@=C9@#FMȩVЩ@=trans_co_eq_inv_impl_morphism&ni$ɚ/RelationClasses@.iff_Transitive*zܩj2@/eq_proper_proxy)f f@&eqb_eq 2as@)@F_-~ݷeߠN ݩ!-"ʷ$  W )ȰC̰x23Ȑ!c @'compare00@?H{-@*comparison;f@@@@@@@@@@@@D #> @6119B<&@ A @%"U@@  M(!*#"iTF@8C417@:]@=@'2`;"=$5D%E?PGvj2k]@'K55@oOO9C-[@X @ YTZU Va@M6Z[CG@S`U]ȷ@I@G c\e^]B@s3Col׷r@Qu;su!m|"}w8i/74C"C_@#ltb q@3,@"lt \2ѷҵx~HŰ@P@@{@\ ِȐ"H2B{eԶ@hh搩ƠlC C!!ȩ@Щ@t@յ׵;5ַ@&#cʷ*:&: :$!CC@ܩ])@ߵTN@ն@ 詷M0 @C5;CCݰ.@#leb T@3%@"le \+OP.R* 36Z2 '1D/@(  Z@[*+]--CC 18dܵ@@9#)@';Ȑ#Heqa;A+a~"d{!fThF3 j7DkimoCb,PW2>8nj4X_ :\g@<`A@b'`f GFyk0l@&eq_sym Xcp,˩CVz%\ %_@#@ )Qڀ+jީ$שi oˠ*@.compare_eq_iff܀7÷ ojڷk1bbesId÷̩vL!tʠ@RC5ِ𩚠@+reflexivity(ϓ/Κ@-iff_Reflexive/h4     ө@'CompOpp֠ ةW CCkη  (Ȱ ]"Cа(|@/compare_antisymOCܰq6W ! E  F @n L N  $ $ ' $m  S +L0Ȑ"n0Xqq@@D@u ^ 3 CC@ a 4@#min  2@3`# @ G k1 l1e:=4@  u1)?) OРf@+CompareSpec!Q]@CAAAAAA@@@@@@@@DQH@ +  e RIƠ U h u@ɐ 3W \ 6 TL q 5 5 o o m@,compare_spec7PԀdaې EiL nli㐩 Mq]\Z@ͩ T  Q ylw [''ni @(C@z f g   ˷ ̵ 5`@ q ^    ^@Q@H y     x xC(=6    9@    * ΀32   .C@)  𩚠 @#max  @3Ҁ ϐ   @#   . ˰  @"     C@Ʃ   Ӑ      젩NIR ܠ   TE @[zĶ@ ʰVP@ а A   >~8 R5 <9CCC t ! \ @{ (  * x@ʩ .       |v@ ! =+ ?i ?   ' CAȩ  & l)0 L Kh Ne @liC$C' ,"C B Q &    M q I. :E@ȩ5  `@8      h   H FL@ +OV   w@M  1 { } X :^e % g (M a CgQ [jq 1 4Y Ʃ  @)j# )   v t߷z@ Y}W D @Ex G \    e Px Rw  m{   [, ^ Ӡ  @Sv S  @ # ʶ@m ̐     5 n     ɶ@l j vȐ!l@1  C Ӡ5 j ]@)lt_succ_r\ jC ޠ@S   Ѡ            @+succ_double  @.^4     '栩      .! |   5 6 ޷  8 ذ : @&double @'޺_       $ H  J  2  3  Q    V      8 \  ^$ש'= ' ' e$ ө , j)  K o5 p  N r  tY+44\ > = ! W {  }b)=3e e E B8j j   K H>p ̷   5 k  / v Q3y Y Y VA  ^ [= } g  J   D l#g o o S   M u,f   x 1k  & $ } 6p  + ) f   ` ©?e    ɩDs   7  ΩIo   ӷ  |  ֩ v ةS 4           ɠ ȷ Q 0  %C  ce ϩ; ѷ Z X       ؠ ׷ ` | ީ;      m    ɠ ɠ \ s p u N  | z   [Р  4 H ۠ ؠ  g KC  " 㠩  퐑  + ӷ  - Ͱ / @$div2 hx @>À  v  :   < ܰ >% % %  C  D   G  I ] ) M  O 4 '  Q  . R  T% , - (@+div2_double;#f ! @ 3 m ; _% ` #  cH  e6L y  j =@0div2_succ_double.[>_ 6  U H  P t: u  S w@/ ? # Y }@(= f E# CI@X@> p K -Q ; O G V%@ y  { m@]  [  w  C y @נ^ g f k  i񵵩 n @)switch_Eq8〠vb xby W{ # g0 , j @-compare_xI_xOH{ ~C c&fsC   s  ͩ  o}  G @@`  N P L @XVC T O M  .   @    Ӑ  w     ?à B   sC 4      r        @#pow  @3  $          D  䠵 C  # Ʒ   C ɰ +! $   ط  2 Ұ 4*E h-   < Ð~ % C  B8I ;    @*pow_succ_r    @G=Rx @H#Fu     ɩ  8  :   e 쐩 A  ~  F |   t T  [       {   ` RC  }s vʐ `    - c @ɩ )  b R p r Q  N  T@c@ 4   { { } X  Z R      v@ @  y     h e з k@@2 K  O   o q i ͩ    @0 W  V  2   f   ` © @&square, @*ow D     / < :  .@+square_spec ^u  w D 6@& /@5,xր    O  %    o  u  ʩ      ې  M ~ ~   e     C  : =x I I   @ =       @$size  @?' ة 吩 @$log2 F) @>t  ߩ U    9ȷ@ ; °$       [  @ d ΰ0%     o ٰ; N =+   { G O* I7   R 5T'B ߐ6Z8\CTOU8F׷  ε @'size_gtkAC b]c NrPt.[[ ;=Dsn[ > D g  ~C<  ﵩ @*lt_le_incl)7ူ;{ @=)R @#Rk   X  E@ :@ @=L 6 @\== b@  K@ @@  c(} d@'size_leͻCwS4jĶ@G eà N @  Π tΠҠ÷ 3J NL@I ܠ Ѱ[Y z' }DZ0\[J@I v gC  nDpӷ~| J Ѡ#PQR!dRC ؠYZ[ݷ  icޠ ӰQ  }T 7 Q 4CC ؠ2-ũvǩ61!E#G@ K7.0"Hn+ շ]R k@ mVB ):<6Z8\4 O3@$even 1@>4܀> F:@$Even ;1DR <@ bX S Y@9;@"ex @A F!ftfG\H I a+ |- m't `@ L.V@0  O[ PX ÷  @ D@ B7 ` Yb [Z ?   ~@ pA 2i2BBB@@@@D@< ~Y, r gb/ {f  ˷@lΩU e@r vCz$ߩf h    T@ ːd <SV  @ֶ@ o  ې, u-! { J     %zx ?|z   )  ) @ ʩ٠C  0  @ ֶ@ -  ' (Ȱ* [,2  Cϰ  ;  @ @   c ] +@ @ #    \ ?*@  η@K LN? 3 P0T  Y0  }\@_DD ! f r e=K  =ҷ*j:)  m@}S.rx2vv,y z" `  pc    ~d  VolVCW! r#  cNc/ea+ |`@#odd ~^@3ɀk sg@#Odd ^q i@>   @fc  ?    h @ tO xv]z }|Z{  @ @a%  } @   Ơ.@m1?=s  ط@ @z e@Ðũ k˩ q2 c  #Ķ@R֐ ˷b`'dbϠ n< ۩h=ⰷlj @ x rǶ@t ~   C֠2  C @ ( Զ@+°    P J @ʰ  @ өqհ &   )h  ; ! U 8#@  ȷ @E FH &- J *NQ/ BƐܐ] 7\5  _@b G@ Tؐob IO* nG.rK(u} y! _ ob    }Wc  zeW@0 E#WD  @)p@, }. syT6CX:'R8'   x@B 1 }C~ w@L !7 8@t; zU>z  {C ( N@,positive_ind?Uз1Р @$prodt@BBB@@@@@@ȩ@,pos_div_eucl}@&`Ȁ    ĩ  `̷S#IHa%\a+B'&@@@@De%3(ߐ    }0>3?t44̐ &    @@@@@@@@A  > ҠPA{ʩ <  "C ᠩ    E( )Aʰ, ̩ 렩 q2  b7qf.) Ԡ(>>#-CC ݐ cF GI Ơ2Oܷ0T tW XZ2\ נ;_( b ce$?LР W@(BoolSpecޜ@BAAAA@@@@@@D  e@ 5B =btoDlFpL I  (*K Vv&Q [{i@(leb_spec.@&a Ya cUUGh &'Gol-prdvVw!z~l^([] @'sub_addzd@ " pk+v--zܩ WsvQkFUm詚 f,ـ4^ 9퐩"Р Ϡpө@)add_assoc<]Buک ʩ@/succ_double_mul4ɨ.ѷ [Q'ة@*double_mulF @/succ_double_add4ɕ8Cqfr3JX; <Ȑ"r'$?50 '/EEީ,3II.hK LN  ˠ7CN@@Fɶ _I̷ bL)a=j k/Qlb] . T\rr ԠY-pxy=7z" |aibgp i M=Ca@rŵZ6 ZJX']O^_CE2H{ qagwlfvnZ\su&q~o,jʷi˩kͩIg a @[ $  t=wYXTP SKG;TE fMmˠ  E@<:8ȩ7Ԡy;30+638X$Z!&" 7++! xz h^4  @*double_add3Ҁ >"Cwlx9P^AB CbEFH tCwD Cyt% .RِrUVXߩ @@ ^䐷fgi(2NRRک3q09w6g>|;bC-C-C.Fl-c[@(div_euclu^Y@ C02lS |\@vɩE=?`_j Cש!IKMn,xDyC0:Z\};.k>=ɷhʩj+Щ3C K@ַuשw*jEJ) N@Ȑe& yypܐ bw÷@à ˩ ʠਗ਼@(mul_commI[r@1pos_div_eucl_spec:1v>CVKg= !#e&'X:Z@h]N12Ұ4uװ9ԩ,@#fst DD 3@#snd/(L MP5C@(qTUW,Y1֠"0@#div l.@37@&modulow5@)1&?@-div_eucl_specޕހ֐]uvrJ@(div_mod'C8h"Hbзo Ewduö ϠUܩ ӠYeA e@  2  ELƩ 砩mzNH@B uW V  XY }`)`E`3z T ѷҷ@@u@ K M@@ @-add_lt_mono_l+,@@ Ҷ]+Z//ީc:Eɶǩ ߩ @ ʠ'Hթ ͠0 @2Q 6WbR ܠ Q`t@.succ_double_ltsl&@(add_diag%Cp0  IyzvCzFF2HH   2C QQCUUKFDZZ G]]   #Caa\Аde) Kf\W(NVll ΠS'CC,rrmIC2xx OOcBN*}N) L|  Q.y51+@%X: Uؠ W<ڠ`lC iCC] jrjqƩ LLvPé!xũd={3 ]F u@ ?rc>RHAF IG (  t#  ][)= ZC.3A4R1C5ũecǩ= C@ư  UCDʰe w  CPְV<  !CY߰%%_  C^**Sط2 .k77 6t@@#2s |HHzz.  ÷ &CCC SS|-@XY7[@ W $D# D>T{ @}VJLFj@© QH4 F[޵H@6pos_div_eucl_remainder0JPC@:ccC@!gqEڷOܩ\Ju.ˠmh@&le_0_l䞀 o@&mod_ltXȀx{Li )ߐm (jշp@ @7 p %r 'j #Ω @1 /&$| !zr@`y{ ΩiC^tΩnЩҩ@'sqrtrem+{@,J@$sqrt !@?Š ȷRP;D@3~=@7]%{ĩZ^H $ܐ!sfԷ+㰩2mNɰs퐷uҰbݰ!유A- ש5"%$%CCް@BBpj#G%IxxSLMQ)9;Ѡ G=']@B 6oap@2PreOrder_Reflexivevvh!:@+le_preorderTl D٩3@(SqrtSpec@^ΩA @CECE@@@@@@@@@@@@@D@i246iGRB `b  cA   HJ3i ݩS<qS}](@dj5o 9>CCvx W'J~K2LOɩy@ ERW.ŷB\?|9<<EɠC ʠ C@J??퐷Ðu@,sqrtrem_specu!ʷ$,L%Š `a꠩QQl WJ<@)sqrt_specU"F$H@ Kr/1 Է zt@ j@ܩW~<> k h fwZ E7@کcFGېOghFj l/nA@$ggcd ?@>U)H@#gcd #F@3n0A%[D-.j C'L+,C/T%>t8]ɩ.(cC@eѩ60k@(ggcd_gcd^Ot  @G=( } @H#Q^z@F=D@G#F̀% ~0շ5i68nЩ BBB@@@@B, !gLO/Q1 ɐ"aaS"bbV 9v64ؐ`JCeEfhJjLD-Bư23#ː"s t 8 R;+|)}թذdfdЩðfj)77oǩ2é ,6b  Cְ8:g&<iܩ(>>oŐ!CBDq1IJ(Lzs?qP~7nTlUYé[֠2B"<`ސcJgh lO֩ n S>ffC&萷u\yz~a#굩g#yrS{' K@'mul_1_rIfCCy7/9;@ DzRFH>oO,9 u*Cg$[]_)C+ҷ2@58::;pr? IuB|۷I   ߷k ROn ͐ U?8Z:@#Ԑ \ ]a6שd%9(k +, -䐷r (y&zөAAX@ķ@̩]L*°$@fiȰ*CloѰհ7-yg֩۰=YĐm ϩLӐՐh~T4;wY >0?d^^됩~jJQnSEC@^sVw@5ggcd_correct_divisors$C4=  j(񐑷uS $pg@÷O    ö@S  GIZKRr vL!  ÷# @ []n_<T.   ʷ˵mo;x~@suRxFv j\ knbQfvjC@&_ $  & @!-wef@Y*Nk  R }zé~6 8@ug9 F ( H@eZ_: 8!Vз@Rh TK ,-Ͱ/H13Ӱ5 c(C@lFg@:9&>? @B@@Ԡ##*N@4@* @C@@ɠ7ӷ}˵$!Ϡ=JC@@Ӡ> Im@ @ܠ ELL97S^@C@@T *`@lh@ceMJ @ ޠ35hض@;a H~eC @ onLNmHfx̩  !yW xp8ש,a.0 @ ʷi˩kmHH@;=&}׶@x ۩U@I K Ơ"HsbU @@ 9m ِG@v i样"Hta˩P $ & .{,_#ة]$33:e)@ð% &qK }@ v,-4=1ٷ3@԰6RQ7ڰ<U1?[K>'$X%^>C_^Ȑ!d@,gcd_greatestx- <{Z@]B@`%琩, lf3s'6z{#YaX(c@8h#Šɠ,sΠT Pxjj@4**6#~^)% = ? (Lfd˷@E@Ho15NЩMvT=T~\EYZ0n|h5m:9>CAvCG @}))Lh!ǐ'B@Q m;@R2jA@:[\^8+5~c!ujL#<zT+1QIөW929=% Q- CͰ/"dCC@Ѷ@ hԩĠ &>?@,D"F7@'testbit5z@-T|ŀA35B?W5YJ;@<B!"Jb?cG BfW X!CCJn_()DXY9%Cg0<1^X,Cn78̷%v?ߩA\aqv6l0J-LgW|l]@S>4'@T8g$CA[]xmK rtRxV#wY␩j$ꀐ   lc wij ozCz˩@J*LԩSCݩeַ_KC0EܠC  xCȠ+ʠ^ Ӡޠİ 1)Ȱ*Է .ΰ0qҰ4)ܰ>3߷G8 k hFXI:A LdDK  ~\##1 %q'#6sb7uLL-XJJ@3testbit_succ_r_div2 J_Cci^Eft=XhNfHbJ4j.awgѩ2e^kV8kZ7RXIVSNLL:K\ISK@HݷI`EffCGhwAj={b@5]w4u?@@Ng3?A=ˠ @Kré2LCA3@@c|ͩ1Đ @`ة0a򩚠@&shiftrO@*Oː ⠵à C {אwuh@)iter_succe C "/琩&d   Ʒ  "@&shiftlI@*O0 0 շ  /ϰ 1 vCذ :ݷ  BJC D"K % ' K M+ 4+/' *C V47۷ƵR $d D̩@$iter=(T@#Qn No r R 21 ܩx 8y| < O# y  X   ^ [  h o b  $    t fC / ooYsW   v ` ' {   f  A[ ^ m ɷ  o       Mg8 wj wmu @'add_0_r)_Ԁ   >     ) é  ũ eנ [  3 ͩ t  8 ҩ    թ uߩ ک u #ͩ zrѩ  ɩ Lթ    R    ީÐ   O @-shiftr_succ_r=\?!!  l ٩ * ݠ   ِ6 @^'R:>BKΠ gF   א ! !!۩թ? !ݠ  6$ Ð4@-eq_Transitive(㠩 <!!   ϩ @>Reflexive_partial_app_morphism 2R,!;m  !=,  )@0reflexive_properm+@!Ew %!Gy   3@:reflexive_eq_dom_reflexive=[!N!P?-_@,eq_ReflexiveaN32 )U!X+!-(g@(symmetry0xj!_ 8n@,eq_Symmetric9^ =5!:!J 5fX!A!D!QȐ"m'O!o!N!r![!s!t!e.V ķ!b!z@!{ !}!b!Z!~!o8` !h;?!,!b!!&w@U!O!O!O|E7  !SI !Xܷ!p!#!~!\! !_y!y!!=W!`!h 3 ! !!!!F`pc!*!! !!߷!!!Rl !O3!p#M!]!<!'!&!!©!b|!vD , r.1ĩS3 7 ֩!@-shiftl_succ_r=8]!o!!!!׷!!ط!٩ !!ܶ!!ݶ!޶@˩!ѩ!!!! `䠩!۩l! Y!!X萩!^!!d! K>!!$!"" ũ;!l"\!"!!!"  ЩF! !ʠڐ'!!ܠ ۩Q! Ʃ!!_"!Ʒ!" !ڠ"" Է!! ^!r  o"*!S!" ".!ΰ蠩"!& '+!ܰ-"#!"@*""A!2"*l W!!! y \"/ !ҩ!"M" "4 "."R"9! !"X"+"?! "9"]"2 "F"I!"gH"D"h"O"="0">("@@-succ_pos_predB( C(4!!&o7!5r+B&g4jTlT V!"H"Y`:"I"\"i"o""K"向!!"p'!"m""!""r""6P!@$lxor=(_!@#Q\ \"@$xorbȀ !"""IH#p'0"" """"Tn#""!'""2"+k""i""é"c}-8"(0"2>""&""""ԩ"tũ>"8@4""ݩ"""5"""/CK!" "٩"I@'Ndouble'ş"C@ """ؠI"""kW_!"aR"iS"#"y"C"mri"hpv"ro"""{f"!$"#"Π~"x #"Ƿ"#!v"##"ðp!#"ɰAͩ!ȩ X!˩"`###7"װ(U!*ڷ,"ݰ.U#&#'#3 !"#0"#+#O"@O,!B "$E"Gn=\#@#L 0#C.#%C"P" ʠ"̠""շ#k##I#m# ^'נ #XҠڠ #\#\#W#{#$#Z#~#p9"@,Nsucc_double:x"@ ʭ#P#mi#oO"Q#TC#.H A#w E#{#u#F##E#{#~#@Z!Dw#p!m9#Ic*#N#ljd #b!_C#Sm4#][#~C#XrK#Y# X# k##i##é#c}-2#K#(0[##.6'#8#W###Ah=#u!ql˩#|#é=##Š#ҩB#֩FC#ک&#7LTZ#;V#u#=#a#_IaG#a!(#e#c###c=##^fA#Z#谷w#p$##$# r}#mu#E#C#Π~Xz#y\$##C#ڠ#n#r#$*#ҷ$$,#̰栩 $$$eC#ְ'z $"$#/C#1# $G#$%$I#:#$4P$6$C$;$5#ĵC#K#Š#q#!##ж$B$f$W  $Pʠ$R#ڷ$p$$N$r$c,ܠ#$]נ$_$?lܠr$\#$\!su$&w$m"b2{{$q$qP$1Q$$}$$ש$wȩ $;-$C$ҩ $˩E[[$V$T{P hC$ݩ$ r$Pb$a$_$$$$. q$өZ$0$$נ(C$: s$̩fx+!^$u$@-pos_lxor_spec'$$$C$̠J `$vѠ$e$󐑷$$$$% b$$$%%%$Ű$@#lor=L$@#F̀"%@#orb$$$"k$$%%<$ܰ-%&%'$%E$%#%G$8"%1%2%? G%.$$C$E $($ŷ%[%%9%]$NĠ8%G2%H%(U6ҷ%D$ӵC% ZР $=%o%%M%q%bؠL%[F%\%<iJ%X$絩$no% q$X%i%HuV=$Bool%@+orb_false_r4C%3"$g%%w%"ͷ% %%z%%>y%s%%Q%%O%%%I%~%%t%%bC%U %-%&f%%d%%%^%%%%%%4wC%j1 %z%%x%%ҩ%ré9%%%ʩ%%HaC%~ϩE %,5%O#%S%Q%%%ةN%ѩ%Ұa%Z%%%%%Y%ܩ%ݠ%~%%h%ns%l&%%&%km%l%%Ϡk%%z%Ӡ g&%%&% |f%e&% d%%% c%%&&&&$&'&&(%з&&*%ʰ 䠩&@ "%@3m%b& %޷&&8%ذ )!& a&C% 1!&*_%%&  9_C% ; !&^%%%&/&S% D )!&0(]&1% Lr M% O&F1x ېzC& V;!&/:c"%׵&@@,pos_lor_specoqIbC& d-I!&PHa%%%&Z&~%%%&_&&# t=%@$land=(%@#Q̀$I&s }@$andb=&&&#ɷ&&&v&&: T&&& M&&K&&&E _"&&ܶ&&&O i, &&&&&_&&&&&[ /?&&&&a 65 #&0&&ǩ&g   &C&i F&@ŷ&&;&&&ө&s ĩP &J&ک&&&ݶ2&&ߩ& ,S& BV&ʠ;&&& ]-%1 D^#B&YC&&& %9 B&C& O&Bjl&e&&&&& z&t&蠵Z4X&T'&&' _Q#&aM#b&ycI&C&!ɠ&&&lFB'&·&'q?&!;'u:%h!7ٷ#x&y6%l!C&C&ǰ!*&uo'-&շ' '/&ϰ! 頩l'k'&!'i'&&!,  !- @,andb_false_rAC&!6&\&&˷&$&&','P&!A W':V';&÷'Y''7'[&!L S'ER'F^C'!T O'KN'F&յTC' !\ %&K&ܷ'r''P't'!e .H'^G'_wC'!m 6F'dE'_&mC'$!u >&ҩD4''2'h'',!} F C'vB'w'W!A's']C'8! R &>' $з' ' '}''A! [R';''T''R'''L! f):'#9''w!'8''"'{!+(-'&f''d'''^! x;''5&''!9%''4'!=!w''u''ϩ'o! L 'F''!ǩJ''E'!˩N'''''&K'''''''!թ '@a 3"'@b>m'`'Ǡ''''! #'i' C'! #'q'n'l C'! #'̩y'v't''( '! Š'#''頵'{"! ĩC'" Ѡ3#'$r''@-pos_land_spec4MwC'Ű" ߠA#s('''( (0r'''((5'հ"& '@%ldiff=U'@$'R%(%"1@$negb'''%~''(+(O'"@ (9Ơ(;'÷(Y((7(['"L &(EҠ (I(D(h("Y "3 @(Rߠ-(N(r((Q(uʶ(S(w("hĩ9(bӶ(\(( "qB 5$'ܶ(e(()"z :(QC(+"| EV(sP(q((t((8" Rc ](]L((K(((((G"i(M"!o( (((V"+?&"~x,vzvt%(*(((a"' "rpjh(C(e" j(;ff@(9y((w((ѩ(q"© d(H e(1 v(r(ީ(((6lc(Ǡ8e"%9(P:^"(C("ש X(Ω]Y(([F[W((((KQ("WJ(ޠOF'B"UC%R(iS?'F"OR(C(" 0(OwŐK) (() (" ƠI(WѐJ((ڠ#IؐI(((#HJ#@+andb_true_r2=ÀC(Ȱ# (v??(((&e(())6(ְ#' =) <)"()@())B(#3  :),9).C(#< 7)3 6)/(C(#E (ʠ4(Ʒ )\)):)^(#O )2)HՠU)JC)#X !21)OޠR)K(ڵC)#a *(Po !)w))U)y)#j 3D0)cm)e)E#r/k)b(iC)'#x A(թ-_(&(()m))1# K\B){V)} ) E))C)y))=# Wh+)B))i#)))n#!) Z))X)))R# l}))))~#.ѷ))*)#3 n))l))Ʃ)f# )=))#B))>)#ĩG)))))ڷ(E)۷)))))ީ)~#ϩ )@ *)@)Zi)Ġ))))# %)f ) C)# %)qtv)q)o C)# '%)ϩ|.ʐ})|)z))*)$ ˠ3%)֐)򠵩)$ 3֩5#C)$ ۠C%)L&))@.pos_ldiff_specX!C)Ұ$# 젩T%*<"**>&*?)#!8##)"g)# # "#m)")#!D")#! #e$)C))#`)#!J")# *=#W)K$J@+CompOpp_iff.ˀ" "ʩ!r)U);!m*#("##/ &C)?*<@"gt \@( *N*r&8*s)6*Q*u&;*v)#@)@ @ ũ(8@"9*R@)gt_lt_iff(鐷@ @@  $*O*g*&Q**r(H*l*&V*)T*o*&Y*)A@@@*~*v*&`* *! *{*&e** #e!#o#f)|&ސ#V&*J#ne##ѩ)*P#t!#^*R#v"^!#$))#ĩ&*X#|f#f&*\#w!.Morphisms_Prop)@0not_iff_morphism Z *  #Ǡ)"p"w#y!))!ة'*q#"}#;#mC)*@"ge \1)?!**޷&*)**&*)@)@"!Y@!$(@"*@)ge_le_iff5;)V@@@!%***&*m**&*)**&+)@ @@**+&+l*w*u*+ )>*+&+@!Y*% ʠ(;*s@ *l@ 5X(*$&+*ŷ*+@*% ڠ(K*%+ ))'S'M#@ @#*ΰ% 蠩(Y*b++%+)))'T'7+"+@#*ް%/ +%%!#'***'n'h$ @^@#Щ*%: (t9*+4$%0+6*c*`* ^'o'R+=+/@#ҩ*%J (I'A%?#׷+=+a(T'(+c*&#T++E+i('0+k@!+ %] &(\*+L+9%S*7#+L+J+%h 1(+%$[)*+\* *(*+g+%a+W)'J+@+&%w @=+O%i*M#à+e++7+m+*T#'+3% (R+]%w+m*\!w(ͷ+ +)'d+@+@% Z _+i%+D% (V+%*B++)*'q+@%+M% g(!"+w%%u+ +)3'z+@.+V% p((T+%%~);'+@6+^% x(;+%%)ӷ(+.*!J'+f% -3*%+'@'nlt_1_rs*4+C+p% (+~$+L*++D x+F(*u++%++G)\'+޶@$"+%ѩ ) Р*'+%Ƿ*$!+'ǵ+T+Y( +](*+ʷ+`+^+% )+8%ֵ  +d+++*$5+++^*+% i(*+%+H*˩$A++ P)?+|+z)',@$Jso+ذ+)',@k%۷+)',@ f%߷)',@$W-b%)u'+*$Z+n%*k& ޠ  %&+ɰ& ()(,*u& 蠩'&!% + +,8+i,,9+ٰ&* '&!0 +,&)t++)Ķ( ,F@$+&9 ((( &ˠ!A &+(#,*W+)Զ(,V@,&H(&ؠ!N)!+(1d+̷)((,c@,(&U('&![)!+(>)(4,o@^,4&a*(3&!g(+(Y+ N R,K@0testbit_odd_succ>5 : S &^, U+@,_,(I,+1@+&@$$*,^@$Ġ,a,'#@,b@,succ_lt_mono k<*@@ ,},u,(_,, W,,(,{,$נ,,t,h 8 6,iC,C&])ΐ,D& H,)+E& ,,)+GC,M&g)ؐ,[%(6,O& C,T&n)ߐ+*,&,,,,*,,*,,ö(,Ķ@$,e&  ,,(,̷+", m,,x,,ҩ,r&é ,,,,,,,,F,%,,,&ͩ,Y)4,K,&ѩ,.,C,&թ*H,, ,ҷ,,[,w(3,C,& ՠ ,,,,*z8(,+$+,,g-!ǐ ᠩ*,+,۷,-,&*2,;+, ,,-*(-@$ϩ,'Ϡ *B,,+ߩ$נ,,,'٠*J++9,©ߠ!,-*(-.@#,ϰ' 頩 *\.-,+$,-,--<+$(,ް'/*i.+,- " (*sB-0--",% ("\%Q)j#@)l,'D *~C+,->"# =*[-E-E-G)(,η,&%(*,,Ӷ*)/-j@#N- '\%*[-7* R 1-Y-;-'g0*f x)N5"E _ W-f)T,,,+)L-@#k-('yB*x"-s-UH p-w-Y-X'N"^ x=-)m- -+)d-@#-@'Z*ː*@--m` --q-p'f"v H-)+4){-@#-W'q*␩ -v *;---'|")+---4+I)-˶@#X-l' )-,%)--~--ض,%)--{'̩+ˠ,j--" Ơ'--,%)-"%*$@* -'+,/-̐-ީ"Ð ݠ+(--瀷)-n,Ʃ%)-P,M. ޷-. -'à-Š--w.(#+-.-(Π# Р- -( Ԡ6 '(-( .,h(۠+L,'  -(㠩!P '(-а(!.꠩+[ ,n9 ,-.; -۰.=  ,--+H -+K,|----.I"++q -+S,n-z* -+---.S"$*+{.9*-..X+!*-ĩ..[*ܩ..]*֩ -+d,-,U--+g,C..d"5q2-&..j";+X,.C+^,-,..y H H+%(j2/j,.U- Cɐ,+)(.tǩ.{-OQ+H+5=ҷ.>.U&#aa>+B.c0.r+D.($$.s.&..i <  5. -v..*.-g@-\@&y&y6@&{5 @&}(Ω.@,succ_le_mono ]O-.@@ ...ζ*.. .9.*..ԩ&f.. k i .@1testbit_even_succ0@6  _.@+double_spec2က. d."à,= .͐.X.V,.Z.X..,.N@'div2_up%%.H@ "..ݰ.g.e+C..,$,"+˷.o.m,4.q.o./,-,..x.vC./,5,,%"䐩,<...ܠ/.+C./,D.,',)",K,C.ư/(,O9$",T$./0#+//4*/5./6.@%proj1O@.ް/@*,+#F%@-./E+)P+!/@,add_cancel_l D </,/P+/Q+/S)Π/(/:+)-/=+/?/-@)B-é/2@(add_comm" /D/h+./i./j/=@/mul_add_distr_ln〰/V/I/6/P/t+:/u./v.9!rA@//|%s@///T/W//))/U@,mul_cancel_r./g/+Q/&(P'8&%a1&k