"` +NProperties(Abstract'Natural'Numbers#Coq@$Bool#Coq@2Relation_Operators)Relations#Coq@4Operators_Properties)Relations#Coq@)Relations#Coq@*Equalities*Structures#Coq@&Orders*Structures#Coq@4Relation_Definitions)Relations#Coq@-SetoidTactics'Classes#Coq@&Setoid'Setoids#Coq@$Init'Classes#Coq@/RelationClasses'Classes#Coq@)Morphisms'Classes#Coq@.Morphisms_Prop'Classes#Coq@*NumPrelude'Numbers#Coq@-GenericMinMax*Structures#Coq@(NZAxioms&NatInt'Numbers#Coq@(NZParity&NatInt'Numbers#Coq@%NZPow&NatInt'Numbers#Coq@&NZSqrt&NatInt'Numbers#Coq@%NZLog&NatInt'Numbers#Coq@%NZDiv&NatInt'Numbers#Coq@%NZGcd&NatInt'Numbers#Coq@)Notations$Init#Coq@%Logic$Init#Coq@*Logic_Type$Init#Coq@)Datatypes$Init#Coq@&Specif$Init#Coq@%Peano$Init#Coq@"Wf$Init#Coq@'Tactics$Init#Coq@%Tauto$Init#Coq@'Prelude$Init#Coq@&NZBits&NatInt'Numbers#Coq@'NAxioms(Abstract'Natural'Numbers#Coq@)Notations$Init#Coq@0&v!D]hwnv %Logic$Init#Coq@0\͉!Ig)Datatypes$Init#Coq@0.i bYN Z*Logic_Type$Init#Coq@0 1jc6&Specif$Init#Coq@0;RWMi\N'Decimal$Init#Coq@0C涳N*ua#Nat$Init#Coq@0eʤģPSR蠠%Peano$Init#Coq@0 jha|ؠ"Wf$Init#Coq@0q+W,J+'Tactics$Init#Coq@0/9m+ a%Tauto$Init#Coq@0̂"&/r'Prelude$Init#Coq@0JqTttֱ$Bool#Coq@0j 2cZ`FW&Basics'Program#Coq@0!bs߯? :VU$Init'Classes#Coq@0](p{yOh.'Tactics'Program#Coq@03u%+Equivalence'Classes#Coq@07;ꮹ-SetoidTactics'Classes#Coq@0S_`nOU$&Setoid'Setoids#Coq@0D9AsWE!>*Equalities*Structures#Coq@0όe얟)H.Ƞ2Relation_Operators)Relations#Coq@0%s鯰s4Operators_Properties)Relations#Coq@0U3y#h&)Relations#Coq@0r砠*NZMulOrder&NatInt'Numbers#Coq@0}\^ !"k}@R(NZParity&NatInt'Numbers#Coq@0H>ca'^^%NZPow&NatInt'Numbers#Coq@0)6*9 B:vȻ&NZSqrt&NatInt'Numbers#Coq@0` .%m%NZLog&NatInt'Numbers#Coq@0ꔉ .uV%NZDiv&NatInt'Numbers#Coq@0$ |J?d (w%NZGcd&NatInt'Numbers#Coq@0KgT7|&NZBits&NatInt'Numbers#Coq@0MlIpKtߐ0Zخb1Z3uuѠ,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$NLog(Abstract'Natural'Numbers#Coq@0K@*@ A@@@@@(eq_equiv @@/RelationClasses'Classes2@+Equivalence~@##@-7@@@CA݋X_A@A@@9$zero @T5@@@@@AA@@A@$succ @r@CC@@@@@$pred @d @@@@@'succ_wd @@)Morphisms?@&ProperL @*respectful%WO?ggDDg@.p1@@@AviA@A@@:'pred_wd @@"8z@6@@@@I)pred_succ @@!nh(A@@@@@\,bi_induction @@!A@H@%Logic$Init@#iffС)@B@W@.D+.4E/@@S@@#one @TȐ@@@@@#two @TҐ@@@@@(one_succ @@@_]{3@@@@@(two_succ @@ɠ@$g@@@@@"lt @h@@@@@AA@@A@"le @h @@@@@ %lt_wd @@ w@#¿@@@@栠+lt_eq_cases @@%!m(+@*°@"or @"  @@@@@)lt_irrefl @@D@#notШ5@@@@@)lt_succ_r @@W2XD2@@@@@'#add @d@g%@@@@@2#sub @d @@@@@<#mul @d@@@@@F&add_wd @@. &Fe(@+J@@!@@W&sub_wd @@?1@/e@@0@@f&mul_wd @@N@ @4]@@?@@u'add_0_l @@,/((@@@@@*add_succ_l @@:¶é>a9cD@@@@@'sub_0_r @@N֩BJ*J@@@@@*sub_succ_r @@\àQoT@@@@@'mul_0_l @@mӠRAH@@@@@à*mul_succ_l @@zᠩ`@cy@@@@@Ԡ#max @d@@@@@AA@@A@%max_l @@!x"!y%@z+@![C@@@@@%max_r @@;<@@@@@@,#min @d@@@@@6%min_l @@3S1T@+3X@\5-,@@@@@I%min_r @@FfDg@BF@@@@@W&pred_0 @@QƐ@@@@@AA@@A@@'NAxioms(Abstract'Natural'Numbers#Coq@.NAxiomsMiniSig@@@@@@J@@A@A7@@"eq7^@@A@°@@°h@@A@AB¿@@"lt¿h@@A@J@@DJd@@A@A[@@[d@@A@\5@@h\5d@@A@ABC]@@9]d@@A@_]@@_]T@@A@Ae@@Ked@@A@g@@gT@@A@A@@wd@@A@p1@@p1r@@A@W@@WT@@A@ABCDE@'eq_refl @@5Equivalence_Reflexive@1@#two>T@@A@AI@5@$predId@@A@G@:@$succGr@@A@@?@$zeroT@@A@ABCDE@A@@M @]@@@d@!tРJ@@A@A L@@"eq L^@@A@r@ @#onerT@@A@AB4@@#two4T@@A@b@@$predbѠd@@A@F@@$succFr@@A@]l@@$zero]lT@@A@ABCD@A@@L/.+*@A@4*BackportEq@@@A@@@ @@AA@@A@&eq_sym @)@5Equivalence_Symmetric. Up@/@)SymmetricFgq*k^TTLp@. U\VDP?OF0)ѠʠeL;Ԡ~QM@@P@@D(eq_trans @j@6Equivalence_TransitiveW@p@*Transitive++-kTL@W\DS@/(Рɠqj |&@@@@*eq_sym_iff @ta PI3,ǠG6@2@ض٩8@@@@AA@@A@'neq_sym @٠Ƞ0ؠϠwpZSDՠĠn]@YAw@ʩYא@@@@+(eq_stepl @àX@9ڠ{l@B'(!z+@ @ wy@@@NAۓό^@@AB@@[(succ_inj @1 0'ϠȠpi F-Ơ@C"n1Y"n2\@;3@@@@A|AۀߠK @2@>@ABC@@+succ_inj_wd @`O"_V@9ڠˠu\K@D/-,P@@@@A8ӠA4Relation_Definitions)Relations@AB@@/succ_inj_wd_neg @{N;*#ˠĠle w!@ E*qZ@@@@@۠1central_induction @s`OH2+ƠF5@1F<Ͷ$A_wd<۶@N@Wߩ>%%U[㩐FV@@@@@ 'add_0_r @ߠΠ6ޠՠ}v`YJ۠ʠ@@A&NZBase%NZMul&NatInt'Numbers#Coq@sq@A@%NZMul&NatInt'Numbers#Coq@)NZMulProp@A@@@@"NZwv@A@%NZAdd&NatInt'Numbers#Coq@)NZAddProp/@@@A@@@A&NZBase%NZAdd&NatInt'Numbers#Coq@A@A@@@"NZ+@@,R@2@!t,RJ@@A@A,Y@@"eq,Y^@@A@,@@ @#add,@d@@A@AB,w@@#mul,wd@@A@,@@#one,T@@A@A,@@#sub,d@@A@,@@#two,T@@A@A,@"@$pred,d@@A@,@'@$succ,r@@A@,筷@,@$zero,筷T@@A@ABCDE@A@E@  `@@@ @T@ `@ABC@@AA@@A@*add_succ_r @tG4ܠ{#Ġe^pug@rA '   +X@@.@@+-add_succ_comm @o\KD.' Π@B O ׶ ة (@@U@@R(add_comm @Ԡà+Ӡʠrk UN?РڠՠĠ@C v   ݠ6zې@@}@@z'add_1_l @S;4ܠՠ}vg@D  &  M  @@@@'add_1_r @$Ӡ{# c\9 E8*%@E  N ,ɠ  u Đ@@@@ʠ)add_assoc @L;KB,%͠ƠaH7m`RM<.@9F  v Q w!p z XNR @@@@,add_cancel_l @{j=*Ҡzq[Twf|k]@hG    /    $ }@@(@@%,add_cancel_r @iVE>ߠ(!Ƞ@H I Ѷ  Ҷ[ ө 2  P I @@T@@Q,add_shuffle0 @Ӡ *Ҡɠqj TM>Ϡ٠Ԡà@I u     ݠ z, U@@~@@{,add_shuffle1 @T<5ݠ֠~wh@J  '  ( )!q ,    y  g  ^@@@@,add_shuffle2 @/ޠ.%͠ƠngD+PC50@K  Y 4 Z [2 \ :0 נ ٠  @@@@ڠ,add_shuffle3 @\K [R<5ݠ֠ǠqXG}pb]L>@IL   a   f  @@@@'sub_1_r @uH5ݠ|$Šf_qvh@sM (   b : %@@/@@,'mul_0_r @p]LE/(àϠ @@ M թ  2  (@@S@@AA@@A@*mul_succ_r @ՠĠ,Ԡˠsl VO@Ѡ@A t    ۠ Z  y  T@@}@@*(mul_comm @S;4ܠՠ}vg@B  #  $    @@@@O/mul_add_distr_r @ ! Рx `Y6 B5'@@C  H # I J ( Ω Ơ x H@@@@x/mul_add_distr_l @ J 9 I@*#ˠĠ_F5k^P@iD  q L r s Q    J*@@@@)mul_assoc @ s b 5 "ʠri SLޠo^y@E   u $  z  p  * @@@@ʠ'mul_1_l @   ^ K:3۠Ԡ|u@F ; é   6@@A@@'mul_1_r @    o ^WA:+ՠԠ@G _  Š D Z@@e@@,mul_shuffle0 @  Ӡ   ;ڠ{#Ġe^OϠ@H      o j c@@@@9,mul_shuffle1 @   ͠  b  JCv ,@*I  2  3 4  5     2  @@@@e,mul_shuffle2 @ 7 &    6 -ՠΠvoL3"XK=@VJ  ^ 9 _ `7 a ?,  @@@@,mul_shuffle3 @ ` O "   _ V@9ڠˠu\Ktf@K   b   g  >@@@@%le_wd @  v I 6 ޠ  } % Ơg`r@@A&NZBase'NZOrder&NatInt'Numbers#Coq@@A@'NZOrder&NatInt'Numbers#Coq@+NZOrderProp*(@A@@@@"NZ@A@@ w   @@J@@AA@@A@*lt_le_incl @ ̠   { # ˠ   j c  MF7ȠE8*@CA k   @   ǐ@@@@@''le_refl @  ߠ   G     / (Рɠqj[۠i\N@gB   ̐@@ @@I.lt_succ_diag_r @   Ԡ  i     Q J}'~p@C 9 #  @@@@@l.le_succ_diag_r @ 5 $    4 + Ӡ ̠ t m  J1 @D \ 2#@@@@@/neq_succ_diag_l @ W F    V M     7 0ؠѠ lSBРà@E ~ :^  @@#@@/neq_succ_diag_r @ | k > + Ӡ { r     \ Uxg@F _l@@@@@נ/nlt_succ_diag_l @   b O    > 7 ߠ ؠ  y !   @G?ǩ  I@@@@@/nle_succ_diag_l @ Ġ   s  à  b [     E > /٠=0"@;Hc  m@@@@@)le_succ_l @  נ   ?  ޠ   '  Ƞ  i b SӠaTF@_I o  M ې@@@@D+le_gt_cases @   Ϡ  d     L E     x " yk@J45 ! @@@@i-lt_trichotomy @ 2 !    1 ( Р ɠ q j      G . @KY4Z*$,%'@@@@@(lt_asymm @ X G    W N     8 1 ٠ Ҡ à m T CѠĠ@LZ@I=m~@@%@@(lt_trans @ ~ m @ - ՠ } t     ^ W     z i@M/@ z@ |@@M@@ݠ(le_trans @   h U    D =  ޠ   '     @NEͶζW϶@۶@ܩ'@@M@@+lt_strorder @ ̠   { # ˠ   j c     M F 7  Ƞ E8*@CO@+StrictOrder.[@@@@@++le_preorder @     K     3 , Ԡ ͠ u n _   ߠm`R@kP@(PreOrder@"@@@@S/le_partialorder @   ޠ ˠ s     [ T      1  z@Q+@,PartialOrder5͛I& rI{@P@@@@A@*@nAhC<@ABC@@)lt_compat @`@Ur0@Q@@@%lt_wd']ɠ ` O "   _ V     @ 9  ڠ ˠ u \ K٠̠@@@@@(lt_total @F@V@;/@]aǠ  y L 9    ( ! ɠ   j c      u@@@@@ࠠ'le_lteq @@@&@F,Q^   Ϡ  d     L E     x "  yk@@@@@cܐ @@7@@,۠2!    1 ( Р ɠ q j      G . @@@@@Ґ @@=@ ѠWF  V M     7 0 ؠ Ѡ   l S BРà@@@@@͐ @<@+A@e̠|k>+ Ӡ { r     \ U     x g@@@@@@@@@@#TacA @fS    B ;  ܠ  } %     @@D!P)OrdersTac*Structures#Coq@+@@@A@@C!O@@&@@!t&J@@A@A&a@@"eq&a^@@A@&@ @"le&ڠh@@A@AB&@@"lt&h@@A@&̌@@#one&̌T@@A@A&̔I@@#two&̔IT@@A@&H@@$pred&Hd@@A@&؝[@"@$succ&؝[r@@A@&C@'@$zero&CT@@A@ABCDE@A@G,MakeOrderTacBq?@A@@@BONR@@@A@@AEUH@@@N@!tJ@@A@A$:@@"eq$:^@@A@$@ @"le$h@@A@$@@"lt$ h@@A@ABC@A@+*OrderFacts.#@A@@s@#C!@@@@AA@@A@Q @@/?6 ޠ נ  x      U < +WPJ/@AMmV@@F@@)3 @fU(e\    F ?   Ѡ { b QߠҠĠ }vpU@BsO@@l@@O ] @{N;*# ˠ Ġ l e      wؠ{@C@ @@@@w*le_antisym @wd SL     6 /  ʠ  .!̠Š@D@@ @@@@  @Ϡ7ߠ֠~w   a Z K  ܠ ˠYL><,@=E  @@@@@ʠ*interp_ord @!o)OrdersTac6@#ordȠ@ @@@@@@@@@@@D, @. +k= R'6'6'6''+k+7T'+7T'6'ࠒA[kji@@"lt\ @@"eq8L@lР@4Ƞ@@10/@@A@B@A@xA܀Q@PG1* Ҡ ˠ  f M <ʠha[@@@@@@8%trans @ve8%͠ul VO     r aԠҠ e@F"o' @ @h@  @)trans_ord-0uG @@ `@@{ H @ɷʷ ˩!@O6hМA&D@նֶ ׶@ @ / L+k() LL7#'@f$tؠǠ/נΠvoYRC  Ԡ àQD64$@@@@@W @  DМCf@ H L+k() NN7#'=tӠhPI|&  }om](!@@@@@ @&F$G H}М0B@.N,O 'P L+k() MM7#'vtJ9 I@*#ˠĠ_F5àaZT9@@@@@1+le_lt_trans @`^ Ys:T@ec ^@ߐ L+k() MN7#'tqD1٠x b[~mޠΠq@@@@@i+lt_le_trans @ r,@ @@ L+k() NM7#'t}jYR<5&Р4'ҠˠŠ@@@@@%eq_lt @ ($Ge@ @ P L+k() ML7#'tJ2+Ӡ̠tm^ޠl_QO? @@@@@ڠ%lt_eq @ )* +`\@. / 0@@  L+k() LM7#'Xt,۠+"ʠàkd A(xC<6@@@@@%eq_le @Bb@c ;dU6@GgEh @i@ > L+k() NL7#'tdS&cZD=ޠϠy`OݠР {tnS@@@@@K%le_eq @zx sn@} x@@ wҐ L+k() LN7#'ɐt_L;4ܠՠ}v @@@@@&eq_neq @ q`YC<-נ;. ٠Ҡ̠@G @ ƶ@ ɩ@@@@@&neq_eq @H0)Ѡʠrk\ܠj]OM=@NH  @.@ -@@@@@ޠ*not_neq_eq @ ޠˠs[T1zxh3,& @yI)I'J@L!@@ @@ )not_ge_lt @G6 F=ޠ' Ƞ\C2^WQ6@JTtRu@2RА@@Q@@4)not_gt_le @ra4!ɠqh RKݠn]ޠРΠ|a@K}@]l@@@@@_)le_neq_lt @_L;4ܠՠ}v  @Lʶ˶@@ک @@@@@@@@@@@@@@@<_neq @̠{#ˠ jc MF7Ƞ E 8 *@ CRk@@@@@@ &&le_neq @ޠF.'ϠȠpiZڠ h [ M@ fSvᩛy@#andЖw@ @@@@@ R*eq_le_incl @ ݠʠrZS0   y@ TBC@  O@@@@@ u(lt_stepl @>-=4ܠՠ}vS:)   @ UEeCf>g@@;S9@@@@@ (lt_stepr @dS&cZD=ޠϠy`O ݠ Р @ V]@@@@@ (le_stepl @sF3۠z"àd]o   @ W@ @@@@@@ ᠠ(le_stepr @lYHA+$ #  @ !X2@@@@@ [ @ɠx Ƞg`JC4ޠŠ B 5 '@ @Yh zk@@@@@ #E @ڠB*#ˠĠleV֠ d W I@ bZ U@@@@@ E+le_antisymm @Рe MFy#   z l@ [56S@@@@@ g)le_succ_r @0ߠ/&ΠǠoh E,   @ \W2X0+3;@@@@@ )lt_succ_l @XGWN81٠ҠàmTC Ѡ Ġ @ ]Z@kڐ@@@@@ ,le_le_succ_r @|k>+Ӡ{r\Uxg   @ ^~@{{w@@@@@ ؠ,lt_lt_succ_r @cP?8٠z"    @ _@ȶɶ@%@@@@@ ,succ_lt_mono @ŠtĠc\F?0ڠ > 1 #@ <`dL@@@@@ !,succ_le_mono @٠A)"ʠàkdUՠ c V H@ aaq@@@@@ F<_0_1 @ѠfNGz$   { m@ bZ@@@@ h&le_0_1 @1 0'ϠȠpi F-   @ c-"@@@@@ <_1_2 @RAQH2+Ӡ̠gN= ˠ  @ db@@@@ <_0_2 @tc6#ˠsj TMߠp_   @ e@@u@@ ͠&le_0_2 @XE4-ՠΠvo   @ f"@@@@@ <_1_l @yfUN81"̠ 0 # @ .gV޶߶@ʠ24@ ;͠@@@z@@@ABC@@ +lt_ge_cases @Ѡ9ؠy! c\Mޠ͠ [ N @@ Yh  ڠ@@@@@ =+le_ge_cases @Ƞ]E>ߠq  r d@ }i-. @@@@@ a+lt_gt_cases @*٠) Ƞib ?&   @ jQ,RS$ @@@@@ ,eq_decidable @P?OF0)ѠʠeL; ɠ  @ kwRx)Decidable@)decidable r@@@@@ &eq_dne @|k>+Ӡ{r\Uxg   @ l~[m@@@@@ נ&le_ngt @bO>7ߠؠy!    @ m?Ƕȩ')@@@@@ &nlt_ge @Ġsàb[E>/٠ = 0 "@ ;ncKʐ@@@@@ !,lt_decidable @٠A)"ʠàkdUՠ c V H@ ao$@@@@@ D<_dne @ Ϡd LEx"   y k@ p45K@@@@@ j&nle_gt @3"2)Ѡʠrk H/   @ qZ5[5 (@@@@@ <_nge @YHXO92ڠӠĠnUD Ҡ Š @ r[K @@@@@ ,le_decidable @}l?,Ԡ|s]Vyh   @ s-H@@@@@ נ&le_dne @bO>7ߠؠy!   @t?Ƕȩ'o@@@@@ *nlt_succ_r @ƠuŠd]G@1۠ ?2$@=ueMܠd-@@@@@%5lt_exists_pred_strong @ݠE-&ΠǠohY٠gZL@ev@A@ 5z@"ex @"!k% pG@@@@A@@A@KAРD.Morphisms_Prop@QA1@D@ABCD@@j.lt_exists_pred @3"2)Ѡʠrk H/@w1Z[@$B^<_F?3թ9@@@/@A@@,lt_succ_pred @_N!^U?8٠ʠt[Jؠˠ@x]@Pf$ߐ@@@#@A.@]@i@\@ABCD@@à&rs_rs' @{N;*#ˠĠle w@y@ڶ@0@@X9@_@=Ŷƶ@ 9@ GK H@@A@@(rs'_rs'' @ȠwǠf_IB3ݠĠA4&@?zTR@k@ʶ@o@Ϡ>k@ yI?6@x_ tw@@@@5%rbase @U=6ޠנxiwj\@u{&()@q@ -@@@@@\)A'A_right @%Ԡ|$àd]:!@|B$M@OQ,R@@ ѩ ƶV@@@@@@6strong_right_induction @RAQH2+Ӡ̠gN=ˠ@}oܶR{@}@Ð@@@@AM@Y@R@ABC@@/right_induction @|k>+Ӡ{r\Uxg@~|@ʶ@ @F @@@@@۠0right_induction' @fSB;ܠ}%@0.Ͷ@G϶@y@@@@@7strong_right_induction' @ˠz"ʠib LE6ǠD7)@B@WU@'@o@?@s@Զ@{JA8@@@@@1&ls_ls' @Q92ڠӠ{tesfX@qAJ#@H@&@|@Fd׶,@v@2 3@  x@Bm k@@R@@h(ls'_ls'' @1 0'ϠȠpi F-@BN1Z@\@7@`;a@8@pi;gfŠ ک ݐ@@@@%lbase @dS&cZD=ޠϠy`OݠР@Cci@f@@@@@@à(A'A_left @{N;*#ˠĠle w@D@.0@@g,4@-f@@@@5strong_left_induction @yfUN81"̠0#@.ECԶA@Z@S(@@@x@@@ABC@@.left_induction @Ϡ7ߠ֠~waZKܠˠYL>@WFl0j @.@ @d@@@@@>/left_induction' @ɠ^F?rse@~G$W0@2@ ܶ@R@@O@@e6strong_left_induction' @.ݠ-$̠ŠmfC*@HK~.W@'@Z@˶@^9_@6~@ne9@@~@@/order_induction @]L \S=6ޠנȠrYH֠ɠ@Iz]@@Ѷ@@u^@ d¶ @@@%@1@AB@@à0order_induction' @{N;*#ˠĠle w@J@ڶ@@1@@D0@@.@@1order_induction_0 @zgVO92#͠1$@/KDնB@4@[@.@*@a@ @@@@@2order_induction'_0 @Ԡ<۠|$Šf_PР^QC@\Lq 5o@a@-@ @:@Y WY3@@@@@F<_ind @ѠfNGz$ {m@M ,_ 8@ @ <@% >@)@@@@@q&le_ind @:)90ؠѠyrO6%@N WĶ c@@@ fA g@@@@@&Rlt_wd @aP#`WA:̠۠v]Lڠ͠@O_  2 u  f  sV@@ @@&Rgt_wd @wJ7ߠ~&Ǡha s@P  Y  *   ~ А@@0@@栠%lt_wf @q^MF0)Ġ( @&Q ֩"Wf 5@,well_founded8E V@@@ A𱍠G@!A7iA@AB@@%gt_wf @Ѡ9ؠy! c\Mޠ͠[N@@YR! 3! Z@@+@@<-add_lt_mono_l @Ǡ\D=ޠp@@ !) !*!+  @@@@AA@@A@-add_lt_mono_r @+ڠ*!ɠ jc @'@A !O *!P!Q  =~@@@@&+add_lt_mono @N=MD.'ϠȠcJ9@5B !r M!s!tK!u@ @ϩ a ©ѐ@@@@@N-add_le_mono_l @ve8%͠ul VOra@]C!! u!$!  t@@@@q-add_le_mono_r @[H70ؠѠyr@D!5! !G!!̩ @@=@@+add_le_mono @~kZS=6'Ѡ@E!X! !j!!@ @ o@@@@@.add_lt_le_mono @Р8נx b[Lݠ@F!}" """@ <@@@@@@ܠ.add_le_lt_mono @Ơ[C<ݠ~o@G!"(!")"*"+@H@@@@@+add_pos_pos @&ՠ}%Ġe^;"@ H!"J!%"K@l@m!7!@@j@@!.add_pos_nonneg @I8 H?)"ʠà^E4@0I!"m!H"n@@!F$@@@@C.add_nonneg_pos @kZ- ja KD֠gV@RJ""!j"@!E@@@@c1add_nonneg_nonneg @zM:)"ʠàkd v@rK"'"!"@A@B!e@@@@,lt_add_pos_l @o\KD.' @L"I"Ѷ!"Ҷ@!"'U@@@"j@"@AB@@,lt_add_pos_r @Ѡ(РǠoh RK<͠@M"m"!"@ !"K!r@@@@̠,le_lt_add_lt @K3,Ԡ͠un_ @N"#!###@8@"!!"t"e U@@@@@,lt_le_add_lt @  ޠˠs[T1@O"#@"#A#B#C@ w@"( y@@@@@,le_le_add_le @ @ / ?6ޠנx U<+@'P"#d"?#e#f=#g@@$@@@@@;,add_lt_cases @ c R % bYC<ݠΠx_N@JQ"#"b##`#@"u]"\"x`@@@@@a,add_le_cases @  x K 8' Ƞib t@pR#%#"#7##@"""@@@@@-add_neg_cases @   q ^ MF0)Ġ@S#K#Ӷ"#Զ@"" #'""à!#+"Š#/#-@@~@@-add_pos_cases @ נ Ơ   .֠͠unXQBӠ@T#s#"#@"#O"4"Ϡ"#S! #@@ @@ՠ0add_nonpos_cases @     T<5ݠ֠~wh@U#$!"$"@"N""M"L@@@@0add_nonneg_cases @!"!  Ѡ y ! aZ7 @ V#$F#!$G@#K##!Jܐ@@ g@@-le_exists_sub @!F!5!   E <ݠ~&Ǡ[B1@-W#$j#E$k@#BR$n$o V$O"C"F@@@$ @AC@$P@A$AAH@F@@ABCD@@O+mul_lt_pred @!w!f!9!& Π v m  WP@@!$p$$$#v$@${$9#"q$########s##%r"~@@)@@AA@@A@1mul_lt_mono_pos_l @!!!m!Z!   I B,%@AU$Ͷ$F$ζ#$϶@ϩ$/*#@@@$j@Au@@$@@ABCD@@+1mul_lt_mono_pos_r @!Ӡ! !!!* Ҡ ɠ q j  TM>@;B}$$n$#$@$WR#䠩#W̩#X$Q$F@@z@@Q1mul_lt_mono_neg_l @!!!!!P     8 1٠Ҡzsd@aC%$%#%@E$}x$ @@N@@t1mul_lt_mono_neg_r @"" !ޠ!ˠ!s!!   [ T1@D%>$%?$%@@h$$-HI@@@@4mul_le_mono_nonneg_l @"?"."!!!>!5 ݠ ֠ ~ w  T@E$%a$<%b%c@@$;# #9$m@@ @@4mul_le_mono_nonpos_l @"c"R"%"!!b!Y!    C <ݠΠx@F$%$`%%@v@$_$@@,@@ݠ4mul_le_mono_nonneg_r @""t"G"4!ܠ!!{!#! Ġ  e ^ @G%%$%1%@ƶ@ǩ$t@@N@@4mul_le_mono_nonpos_r @"""i"V!!!!E!>  ߠ   ( ! @ H%A%ɶ$%ʶS%˶@@$*@@p@@!,mul_cancel_l @"ɠ"""x" !Ƞ!!g!`!!   J C 4@ 1I%c%$%u%@$%$%P%Ѡ$P@@@%@%@n@ABC@@K,mul_cancel_r @"""""J!!!!!2!+ Ӡ ̠ t m ^ @ [J%&$&&@*%w%6@@@@n(mul_id_l @##"ؠ"Š"m"" !!!U!N      +@ ~K%&8%&9@L%&%&$%c@@@@(mul_id_r @#:#)""""9"0!ؠ!Ѡ!y!r!!    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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@@$zero OT@@A@ @@%ldiff d@@A@A@@&modulod@@A@qa@@&shiftlqad@@A@ABqg@@&shiftrqgd@@A@&D@@&square&Dd@@A@3@@'testbit3d@@A@1H@@'compare1Hd@@A@ABCDEFG@A@@G!BР@A@@F!A֠@A@@!a{@!t <{@"le 1{@$zero%؀{@$log2ʀA@@@ %'A*Equalities*Structures#Coq@AviA)Morphisms'Classes#Coq@@AAۀߠK @Aۓό^ @A݋X_A/RelationClasses'Classes#Coq@@ABC@@AA@@A@+log2_unique @n_ZJE@/b]@/AX{@!t ʀĐ@@@@+ @D@ʀ89@@@A@AA@A@A@ABC@@+log2_lt_lin @ܠנҠ@Oꚠh@ <@n@[ @s@%؀Ay@f @@ʀtt@@@@@Ƞ+log2_le_lin @3$ ޠ'"@P@ <@@ 1@%؀A@' 1@!ʀ@@@A@ A@"A @ABC@@.log2_mul_below @l]XHC>-`[@-QV@ <@ <@@ @@Z%؀B@@ @@f%؀婚@q 1@ Za@qʀЩ@wʀ@}ʀ@#mul l @@@Ay@Ar@Al@ABC@@d.log2_mul_above @Ϡzà@R7@a <`=@g <@C@ 1H@%؀B@O@ 1T@%؀HY@ 1_@ʀe@Q l3Yk@ Zaq@ Zaw@ʀE}@ʀq@ nހ@@@A@AA@A@A@ABC@@Ҡ-log2_mul_pow2 @=.)1,@S'@ <Κ@ <@@ @@+%؀B@@8 1@7%؀@ Ѹ@<ʀ@ l@ pl@ vѩ@ Zaש@Xʀ@@@VAN@AWAF@YAD@[AB@ABC@@:+log2_double @|wfVP@fT @7 <@@ @@%؀A@ Ѹ$@ʀ*@ l/@$ v#4@:@ʀ/@@@A@A@A@ABC@@)log2_same @РˠƠ@Uޚ\@ <b@ <@h@U @m@%؀B@t@a @y@%؀m@@T Ѹ@ʀS@ʀ@~ @@ l@ vi@@@A@A A@ A@ A@ABC@@젠,log2_succ_le @WHC3.)KF@VA@ <@? 1@9ʀ@A@@LʀA@@@KAC@ALA;@NA9@PA7@ABC@@/,log2_succ_or @vql[KE@[W@> <Q@"or @@ Ѹ@ʀ@A"@(@ʀA/@ Ѹ5@ʀ;@AB@ʀA@@@@@4log2_eq_succ_is_pow2 @ӠΠɠ@Xᚠ_@ <@e@: Ѹk@ʀq@MAx@T~@ʀAπ@ <@ <@h Ѹ@u@ pl@ v@@@A@AA@A@A@A@ABCD@@5log2_eq_succ_iff_pow2 @ a R M = 8 3 "  UP@ "YK@ <@@ @@I%؀A†@ Ѹ@Sʀ@ߩ@@eʀ멛F@: <(@@ < @ Ѹ@@ pl@ v*@@@A@AAx@Av@ABAs@A@A1ՠF-SetoidTactics'Classes#Coq@@A1I @ABCD@@{0log2_succ_double @  נ Ҡ       ڠ@ ZКN@x <@T@A @Y@%؀A_@4 Ѹe@ʀk@ Zaq@] lv@k vjz@ nހ@[@ʀz@@@A@AA@A@A@Ap@ABCD@@ؠ+log2_add_le @ C 4 /       7 2@ [ -@k <Ԛ@q <@%Logic$Init#Coq@@#notШ@ ѸB@9 nހ@@ Ѹʚ@H nހ@ Z 1@ Tʀ@  Zaߩ@ Za@ fʀũ@ lʀ@@@ jA b@A kA Z@ mA X@ oA V@ABC@@ N+add_log2_lt @       z j d  @ z\ !@ K < J'@ Q <@-@  @2@ 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jvv@@@YAQ@[AF@]AD@ABC@@<'div_0_l @ޠР@H9X@ <@^@ @c@%؀Ai@ Ѹo@ _ t@%؀ܚx@%؀@@@@@s'mod_0_l @K;,'P@Ip@J <@@ @@%؀A@ Ѹ@% j@-%؀@1%؀@@@@@'div_1_r @rc^L>@JJ@ <@@T 1@S%؀A@1 Ѹ@j _ F@q nހJ@@@A@A@AB@@ᠠ'mod_1_r @u@Kޚ@ <@@ 1@%؀A@h Ѹ@3% j}@ nހ@%؀@@@;A3@=A(@?A&@ABC@@'div_1_l @נҠ@L:@ <@@@ @E@ nހAK@ ѸQ@ _ V@ nހZ@%؀@@@@@U'mod_1_l @- 2@MRq@, <@w@ @|@  nހA@ Ѹ@% j@ nހ@  nހ@@@@@'div_mul @dTE@. i@,N@c <j@i <@@< 1@;%؀B@@; @@G%؀-@$ Ѹ@] _ @" l  @@@A@A@@Ԡ'mod_mul @vh@tOњ@ <@ <@@ 1@%؀B@@ @ @%؀u@l Ѹ@7% j@j lhZZ#@%؀@@@AA,@CA*@AB@@"&mod_le @۠֠Ġ@P>@ <D@ <@J@ 1O@%؀B@V@ @[@%؀é`@ 1f@% j@@@@@b'div_pos @:*?@Q_~@9 <@@? <@@ 1@%؀B@@ @@%؀@( 1@'%؀@7 _ @@@A@AA@A@A@ABC@@+div_str_pos @vgbPB@NR@ <@ <@m@U @@a%؀A@m 1AB@h @@t%؀@ _ 3`@@@A@A@A@ABC@@-div_small_iff @Ѡ@S@ <ך@ <@!@ 1&@%؀B@-@ @2@%؀k@#iffС)>@ ѸD@ _ I@%؀N@ @@@@mAT@A@@L-mod_small_iff @$)@TIh@# <*n@) <@t@ 1y@%؀B@@ @@%؀S@ Ѹ@% jީ@ @֐@@@A@A@A@ABC@@/div_str_pos_iff @tdUP>0y@@QA<@SA:@ABC@@2+div_le_mono @ ԠƠ@W/N@  <T@ @QA<@SA:@ABC@@2)div_exact @ ԠƠ@Z/N@  <T@ <@Z@ 1_@%؀B@f@ @k@%؀ө9t@ Ѹz@ l@  _ @ Ѹ@% jȚ@%؀@@@A@A@A@ABC@@2div_lt_upper_bound @ j Z K F 4 &o@ 2[@i <p@o <@m <@@H 1@G%؀C@@G @@S%؀ @@R @@) l'@^ @@v _ K&3@@@@@堠2div_le_upper_bound @      y@ \⚠@ <Ú@ <ᚠ @ <@@ 1@%؀C@@ @$@%؀_@*@ 1g0@| lzl6@ 1<@ _ y@@@@@82div_le_lower_bound @     ڠ ̠ @ ]5T@  < Z@  <4`@  <@f@ 1k@%؀C@r@ @w@%؀@}@  1@ l@  1ө@ _ ̐@@@A@AA@A@A@ABC@@/div_le_compat_l @ k [ L G 5 ' p@ 3^!p@ k <@ q <@ w <@@ J 1@ I%؀C@ e@ M @@ Y%؀ @ d 1  E@ j 1@u _  % $@{ _  + 8@@@ A @A A@ A@ A@ABC@@'mod_add @ ʠ      @ _@  < К@  <@  <@ @  1%@ %؀C@,@  11@ %؀6@  Za <@  l x @C@  @H@ %؀ M@  ѸS@r% jY@  Za _@  l   e@% j  @@@ A |@ A q@ A o@ABC@@ g'div_add @ ? /     D@ ` d@ > < E@ < <5@ B <@@  1@ %؀C@@ ) 1@ (%؀@  Za @  l  @@ 3 @@ ?%؀ @  Ѹ@ U _ @ ! Za 0@  l   @ - Za@ m _  B * @@@ A @ A @ A @ABC@@ ⠠)div_add_l @      v @ a ߚ@  < @  < @  <@@  1@ %؀A@@  1!@ %؀&@ y Za,@ x l v h @3@  @8@ %؀ =@  ѸC@  _ I@  ZaO@  l    U@  Za [@  _   @@@ zA r@ |A g@ ~A e@ABC@@ ]0div_mul_cancel_r @ 5 %     :@ b Zy@ 4 < ;@ : <+@ @ <@@  1@ %؀C@@  @@ %؀ ׶@@  @@ )%؀ ⩚@  Ѹ@ ? _ @  l  @  l  @ Q _  & @@@ A @ A @ A @ABC@@ Ơ0div_mul_cancel_l @    z h Z @ fc Ú@  < @  <@  <@@ | 1@ {%؀C@@ { @@ %؀ @@ @  @@ %؀ K@ o Ѹ@  _ !@ m l k '@ s l q d-@  _   j@@@ LA D@ NA 9@ PA 7@ABC@@ //mul_mod_distr_l @     Ѡ à @ d ,K@  < Q@  <W@  <@]@  1b@ %؀C@i@  @n@ %؀ @t@  @y@ %؀ ~@  Ѹ@ % j@  l  쩚@  l  ͩ@  l ਗ਼@ % j  ِ@@@ A @ A @ A @ABC@@ /mul_mod_distr_r @ v f W R @ 2 {@ >e @ u < |@ { <l@  <@@ T 1@ S%؀C@@ S @@ _%؀ @@ ^ @@ j%؀ #@ G Ѹ@ % j@ E l [ C@ K l < I@ Q l @ *% j m H U@@@ *A "@ ,A @ .A @ABC@@ 'mod_mod @  ՠ Ơ    @ f )@  %؀C@@K 1@J%؀@@I @@U%؀@2 Ѹ@ % j@7 ZaF!.@ % j@C Za@% jX@@% j9FF@@@A@A@AB@@'div_div @ԠĠ@m@ <ښ@ <ʚ$@ <@*@ 1/@%؀C@6@ @;@%؀v@A@ @F@%؀K@ ѸQ@ _ W@ _ ]@ _ c@ l@@@A{@AAs@Aq@Ao@ABC@@g)mod_mul_r @?/  D@nd@> <E@D < 5@J <@@ 1@%؀C@@ @@(%؀@@' @@3%؀쩚@ Ѹ@% j@ l @ Za@% j0 @  l@% j@m _ B*@@@A@A@A@ABC@@⠠*div_mul_le @v@oߚ@ <@ <  @ <@@ 1@%؀C@@ @!@%؀\@'@ 1,@%؀g1@ 17@ l=@ _ zC@ _ I@ l@@@hA`@jAY@lAS@ABC@@K+mod_divides @#ߠ(@pHg@" <)m@( <@s@ 1x@%؀B@@ @@%؀쩚 R@ Ѹ@% jϚ@%؀@"ex @@W < P@] <@  Ѹ쩚@ lA@@@A@AA@A@A@A1@D@@ABCD@@@@@@@A  BCN@/mod_upper_bound @@@!a@!t @<%؀C@H ѸI@h% j:9O@#sub uAV@#mul lG]@ _ NM@@@ %'A*Equalities*Structures#Coq@A݋X_A/RelationClasses'Classes#Coq@@A@@^.div_mod_unique @C3$@0B@!t <"q1@!t <"q2@ <"r1@ <"r2@ <@@ @BE@@ @F@@ Ѹ@#add Za@o lGD@ Za@} lEũ%Logic$Init#Coq@@#andЖw@@ Ѹ$9@ Ѹ)@@@@@ޠ*div_unique @à@C%@s <# @ @ _ k@@@@@-*mod_unique @@DtR@ <rX@ <O^@ <Nd@ <@j@b @AC@s@x Ѹy@ Za@) lpo@ Ѹv@% j@@@@@z0div_unique_exact @_O@@LE@ <@ <@  <@Ā@ ѸB@%؀@@ Ѹ@q l@ Ѹ@` _  @@@@@ (div_same @@F @W <@@ ѸA@%؀@ Ѹ@ _ 򚠐@#one nހ@@@@@(mod_same @۠ˠ@G=@ <@4%@* ѸA+@)%؀0@5 Ѹ6@U% j&&;@9%؀@@@@@))div_small @@HpN@ <nT@ <@Z@R @BAb@g Ѹh@ _ YXm@k%؀@@@@@[)mod_small @@0!@-I@ <@ <@@ @BA@ Ѹ@% j@@@@@'div_0_l @n^O@[JК@ <@ǀ@ ѸA@%؀@ Ѹ@V _ @%؀@%؀@@@@@'mod_0_l @@K@U <@@ ѸA@%؀@ Ѹ@% j@%؀ @%؀@@@@@'div_1_r @ܠ̠@L>@= <!@& Ѹ'@ _ A-@& nހA@@@@@'mod_1_r @@McA@b <F@K ѸL@k% jAR@K nހV@T%؀@@@@@D'div_1_l @) @Ni@ <@o@g @t@m nހAz@ Ѹ@  _ @~ nހt@%؀@@@@@w'mod_1_l @\L=@IO@ <@@ @@ nހA@ Ѹ@% j@ nހ@ nހ@@@@@'div_mul @p@|P񚠐@D <@E <@@ ѸA@%؀@ Ѹ@} _ @ l@@@@@堠'mod_mul @ʠ@Q, @ <*@ <@)@ ѸA @%؀%@* Ѹ+@J% j1@ l"!!6@4%؀@@@@@$&mod_le @ @RkI@j <iO@ <@hY@^ ѸA_@]%؀d@"le 1k@% j\[\@@@@@Z+div_str_pos @?/ @,S@ <@ <@%Logic$Init#Coq@@#andЖw@@ @@%؀A@A 1AB@ @@%؀@D _ @@@@@-div_small_iff @{l@xT횠@ <뚠@A <@ꀐ@ ѸA@%؀ @#iffС)@ Ѹ@ _ 㚠@%؀@ @@@@@@젠-mod_small_iff @Ѡ@U3@2 <1@ <@0!@& ѸA'@%%؀F0@5 Ѹ6@U% j'&'<@4 @-,@@@@@+/div_str_pos_iff @@VrP@q <pV@ <@o`@e ѸAf@d%؀o@g @t@r%؀y@ _ ji@ 1op@@@@@n&div_lt @SC4@@W@ <@ <@@ @@%؀B@@ @@ nހ@ @@H _ @@@@@+div_le_mono @p@|X񚠐@L <@R @@@@@*mul_div_le @ؠȠ@Y:@9 <8@ <@7(@- ѸA.@,%؀3@ 19@ l)?@ _ 0/0@@@@@./mul_succ_div_gt @@ZuS@ <sY@ <@rc@h ѸAi@g%؀n@f @_t@ ldz@$succ@ _ rq@@@@@p)div_exact @UE6@B[@ <@  <@@ ѸA@%؀ʀ@ Ѹ@d l@M _ @ Ѹ@% j@%؀@@@@@2div_lt_upper_bound @@\@a <@Z <ᚠ@e <@ @ ѸB@%؀@@ @@ @ l@  @@ _ ER @@@@@2div_le_upper_bound @ܠ@]N,@ <L2@ <)8@ <@QB@G ѸBH@F%؀@N@ 1T@ lEDZ@ 1`@ _ Q@@@@@O2div_le_lower_bound @4$@!^t@ <z@ <q@ <@@ ѸB@%؀@@2 1@F l֩@> 1@5 _ @@@@@/div_le_compat_l @|l]@i_!p@ <@@ <@F <@D@ @@%؀B@z 1BA@ 1@y _ &ܩ@ _ ,@@@@@ᠠ'mod_add @Ơ@`(@{ <& @ <7@ <@+@! ѸA"@ %؀'@, Ѹ-@L% j3@u Zam9@ l*))?@^% jy/@@@@@.'div_add @@auS@ <sY@ <_@ <@xi@n ѸAo@m%؀t@y Ѹz@ _ @ Za@0 lwvv@ Za@ _ @@@@@)div_add_l @fVG@SbȚ@ <ƚ@ <ך@' <@ˀ@ ѸB@%؀@ Ѹ@Z _ @ Za@ lʩ@! Za@r _ ֐@@@@@Ԡ0div_mul_cancel_r @@c @n < @o <*@u <@ @  ѸB@ %؀@ .@ $ Ѹ $@ "%؀)@ . Ѹ/@ _ 5@ lb &;@ lu ,A@ _ n{@@@@@ 00div_mul_cancel_l @@d wU@ < u[@ <a@ <@ zk@ p ѸBq@ o%؀@ {@  Ѹ k@ ~%؀@  Ѹ@ _ @ ; l @ A l ѩ@* _ א@@@@@ /mul_mod_distr_r @qaR@^e Ӛ@ & < њ@' <⚠@- <@ ր@  ѸB@ %؀@ 怐@  Ѹ ǚ@ %؀@  Ѹ@% j@  l  ީ@  l - 䩚@  l@% j , 9 @@@@@ /mul_mod_distr_l @Ӡà@f 5@  < 3@ <D@ <@ 8)@ . ѸB/@ -%؀@ H9@ > Ѹ )>@ <%؀C@ H ѸI@h% jO@  l @ |U@  l F [@  l La@% j  @@@@@ P'mod_mod @5%@"g u@  S@  ZaY@x% j  _@  l e@% jk@ _    \@@@@@ Z*div_mul_le @ ? / @ ,p @  < @ <@  <@ @  ѸB@ %؀@ < 1@ P l @9 _   @? _ @ b l   @@@@@ +mod_divides @  | m@ yq @  < 욠@ B <@ 뀐@  ѸA@ %؀ @  Ѹ@% j  ᚠ@ %؀ !@"ex @@ w <-@ } < @ Ѹ G@  lA@@@ A1@D @ ? >@@A@@ )divide_wd @@$NGcd(Abstract'Natural'Numbers#Coq@(NGcdProp@A@@@A!B$NGcd(Abstract'Natural'Numbers#Coq@l@A@@@!AM@A@@J!C%NZGcd&NatInt'Numbers#Coq@"@@@A@@I!B@@T@#@'compareTd@@A@A ]@@!t ]J@@A@ e;@ @"eq e;^@@A@AB e@@"le eh@@A@ e@@"lt eàh@@A@A @@#add d@@A@ @@#div d@@A@ABC }@!@#eqb }d@@A@ G@'@#gcd Gd@@A@A x@+@#leb xd@@A@ F@0@#lor Fd@@A@ABD @4@#ltb d@@A@ @=@#max d@@A@A 9@A@#min 9d@@A@ @F@#mul d@@A@AB @J@#odd d@@A@ a@P@#one aT@@A@A @T@#pow d@@A@ @Y@#sub d@@A@ABC #@]@#two #T@@A@ q@c@$div2 qd@@A@A @g@$even d@@A@ @V#a6@#add ZaKb@@@]AU@A^AM@`AK@bA9@ABC@@1,divide_mul_l @Ҡ@O.@ <@3 <@ <@@#aCB @#a@ l@@@A@AA@A@Ay@ABC@@q,divide_mul_r @ݠؠɠ @Pn/@C <㚠5@I <;@y <@A@#aCAI@#aũO@ l'@@@A@A@A@ABC@@/divide_factor_l @:*PK@Qm@ <!s@ <x@#aB@ lBA@@@@@۠/divide_factor_r @fVGB3|w@ARؚ@ <M@ <@2#aB@? lAB@@@@@-divide_pos_le @sn_@mS@ <y@ <@@"lt @@%؀A@@l#aq@ 1`w@@@rAj@AsAQ@uAd@wAb@yAP@ABCD@@H*gcd_unique @Ӡà@TE@D < @J <@ <@@ 1@%%؀A@$@#a@+@#a@!q4@H <@:@#aAG@C@#aI@#aO@( ѸU@#gcd bĀĐ@@@@@&gcd_wd @;+QL@UD@q@: <@v@? <z@C <;@I <@@N <@R <@4 ѸN@\ <@` <@B Ѹ@F Ѹ@N bĀ@@@0A(@A1A@3A"@5A @ABC@@.gcd_divide_iff @pk\@jV@ <v@ <R@ <@e#aA@ bĀCBn@x#aAC@#aAB@@@Al@A@@P.gcd_unique_alt @۠ˠ@WM@L <š@R <@ <@ @ 1%@-%؀A@-@A <6@#aɩĀ@@#aF@#a ©L@% ѸR@ bĀ@@@@@(gcd_comm @7'MH@Xj@3 <p@9 <u@N Ѹ{@& bĀBA@. bĀAB@@@@@ߠ)gcd_assoc @jZKF7{@EYܚ@f <Q@l <-@r <@ Ѹ@_ bĀC@f bĀBA@n bĀ@t bĀCBA@@@@@&.gcd_0_l_nonneg @~Ǡ@Z#@ <@@ 1@%؀A@ Ѹ@ bĀ@%؀א@@@@@Y.gcd_0_r_nonneg @ԠŠ@[V@ <@@ 1"@*%؀A(@ Ѹ.@ bĀ3@;%؀ @@@A@A@A@ABC@@'gcd_1_l @  3.@\P@ <U@. Ѹ[@ bĀ`@ nހAe@ nހ@@@@@'gcd_1_r @ I 9 * % _Z@ $]|@E <@Z Ѹ@2 bĀA@ nހ@ nހ@@@A@A@!A @ABC@@/gcd_diag_nonneg @ { k \ W H@ V^횠@c <@@[ 1@%؀A@ Ѹ@p bĀ@@@@@*gcd_eq_0_l @     w@ _@ <@ <@@ Ѹ@ bĀBA@%؀@ Ѹ@%؀@@@A@Ay@AB@@]*gcd_eq_0_r @  ؠ ɠ Ġ @ `Z@ <Ϛ!@ <@'@ Ѹ-@ bĀBA4@<%؀9@ Ѹ>@F%؀@@@A@A@A@ABC@@(gcd_eq_0 @ (     > 9@ a[@ $ <a@ * <Kj@C Ѹp@ bĀBAw@%؀@Y ѸB@%؀@d ѸA@%؀@@@ A @ A @ !A @ABC@@.gcd_mul_diag_l @ { k \ W H  @ Vb횠@c <b@ <@@a 1@%؀B@ Ѹ@v bĀ^@e ldd@@@@@ +.divide_gcd_iff @      ̠ @ c (@ <@ - <@@ 1@ %؀B倠@ #aܩ @ Ѹ@ bĀ@@@ A @A A}@ A @ A @ A |@ABCD@@ t*divide_1_r @!n,@!t <@1divide_1_r_nonneg+ Aw@&le_0_l&J€@B@ <@H@ #aAN@#one nހT@"eq ѸB[@  nހ <+k7 7%' , + * ) (@ 8@;EhA 9 @:1 ĐX O ? 0@@@@@AA@@A@.divide_antisym @_@] @ ѸD@ bĀJ@ uP@ bĀ@@@9A1@;A*@=A(@ABC@@ࠠ&Bezout @<f@: <ݚk@? <p@D <%Logic$Init@"ex @@U @9Ǔ@ <7Ǚ@> <ǝ@ < \+k() 7! 7! 7%'"h3H/x}xhc@@@@@⠠&lcm_wd @vq@E)Morphisms'Classes#Coq@@&ProperL@@x <@@} <@ <)Morphisms'Classesv@*respectful%WO?@ <@@ <@ <@"eq Ѹ@ <@ <@ Ѹ @ Ѹٮ@.R@@@gA_@iAX@kAV@ABC@@G*lcm_equiv1 @۠@Fњ+@l <Ϛ1@r <@̀;@ ѸA@ bĀBAH@%؀M@ ѸS@3 lY@@ _ _@ bĀĩe@L _ k@K lЩq@ bĀ֐@@@A@A@AB@@*lcm_equiv2 @_PK;6@_G1ȋ@ </ȑ@ <@-ț@# Ѹȡ@" bĀBAȨ@)%؀ȭ@5 Ѹȳ@ lȹ@ _ ȿ@@ bĀ%$$@ _ @ l10@R bĀ76@@@)A!@+A@-A@ABC@@ ,gcd_div_swap @@H@ <@4 <@ Ѹ@ l@ _ B @ bĀBAA@ lB@ _ A"@ bĀBA@@@}Au@A~A@Ao@Am@ABC@@^,divide_lcm_l @@I蚠B@!t <皠I@ <N@#a@.R͐@@@@@,divide_lcm_r @=.)@=Ji@t < o@- <t@#a@.R@@@A@AAs@A@A@ABC@@*divide_div @k\WGB@kK=ɗ@4 <;ɝ@ <ɣ@ <@?ɭ@5 ѸCɳ@4%؀@ɹ@#a@@#a&@ #a@ _ F@ _ L@@@+A#@A,A@.A@0A@ABC@@ )lcm_least @Ġ@L@ <@ <@ <@@\#aCA@ @e#aqp@k#a۵@.R }@@@pAh@AqA@tAc@AuA`@wAX@yA@ABCD@@U(lcm_comm @ @ Mߚ9@D <ݚ?@ <D@ Ѹ@.RBA@.RAB@@@A@A@A@ABC@@.lcm_divide_iff @D50 @DN!nq@| @%؀A@VF@_ <ƀO@#aЩY@#a8ک_@#aSਗ਼e@ Ѹ @ .RJ_ѐ@@@@@)lcm_assoc @UFA1,@UQˁ@ <ˇ@ <ˍ@2 <˒@ Ѹ6@9.RC=@@.RBAE@H.RK@N.RCBA@@@@@⠠'lcm_0_l @vq@RV@k <@S Ѹo@r.R@W%؀A@\%؀@@@@@ 'lcm_0_r @Ġ@S@ <@} Ѹݙ@.RA@%؀@%؀@@@\AT@^AM@`AK@ABC@@<'lcm_1_l @Р@T @ <%@ Ѹ@.R0@* nހAA@@@@@c'lcm_1_r @ @UךG@R <L@ Ѹ@.RAX@R nހA@@@A@A@A@ABC@@(lcm_diag @H94$@HVt@ <y@ Ѹ@ .RAAA@@@@@(lcm_eq_0 @l]XHC@lW(̘@ <'̞@C <̧@/ ѸK@N.RBA̴@5%؀5@"or @@I ѸB@H%؀@T ѸA@S%؀@@@*A"@A+A@-A@/A@ABC@@ /divide_lcm_eq_r @à@X@ <~@ <@@U#aBA@ Ѹާ@.Ronn@@@aAL@A@@=.divide_lcm_iff @Ѡ@Y!@ <'@@ <0@#aBA8@ Ѹ@.RBAA@@@A@AA;@A@A@ABC@@{.lcm_mul_mono_l @3$ @3Z_@j <e@p <횠k@v <p@ Ѹ@.R|@\ lAC̈́@d lAB͌@l lA1@4.RCB@@@A@AA@A@A@A@ABCD@@Ѡ.lcm_mul_mono_r @zue`@[E͵@ <Dͻ@ <C@ <@N Ѹj@m.R@ lCA@ lBA@ l߆@.RCBA@@@DA<@AEA@GA6@IA4@ABC@@%-gcd_1_lcm_mul @ݠΠɠ@\ @ <@ <@@ ѸB@%؀@)@ Ѹ.@%؀7@ Ѹ=@ bĀ1B@< nހG@ Ѹ@.RAS@3 lG@@@A@AAM@A@A@ABC@@*eqb_compat @@@E!F%NBits(Abstract'Natural'Numbers#Coq@@A@@D!E@A@@C!D @A@@B!C& @A@%NBits(Abstract'Natural'Numbers#Coq@)NBitsProp7@A@@@A!B3 @A@@@!A9Υ,@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@AviA)Morphisms'Classes#Coq@@Aۓό^ @A݋X_A/RelationClasses'Classes#Coq@@ABC@@AA@@A@(eqb_spec @!xZN+@w4Բ!y $Bools@+iff_reflect s1@_4.BA@N4kp/RelationClasses@(symmetry0xjAf@#iffС)@-iff_Symmetric!xrA(=@&eqb_eqZˀ)͠@NB@ <KH@ <$Bool#Coq@@'reflectc@[@ ѸBAc@ `BA +k() 7!7!L7!77"7777 7! 7!7&'(?p]x̠pD[hfΐpz\h|( 3@@@@@'eqb_neq @:+&! 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