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YRߠkZ@Af47d48"*4H@ 1P]4N@ }1\wv4S@ 1P&4Y@ 1P]G@@@@?(mul_comm @ K     }  à  ] V1*3&@1B4s4t"԰+;4@ 1P]>r4@ 1P]C@@@@o/mul_add_distr_r @ { ; +    P     ) "ŠaZKנƠcVH@aC444#+l4@ 1P]o4@ 1P& 4@ 1P&4@ 1P]-4@ 1P]@@@@/mul_add_distr_l @  } m Z    5 , Ϡ Ƞ k d  2@D444#G+4@ B1P] 4@ U1P&P멚5@ Z1P&U5@ S1P]€ک5 @ X1P]ǀt@@@@@)mul_assoc @     D 1 Ԡ w n     I BޠϠt[Jڠ@EV5'T5(5)#+𩚠59@ 1P]M5?@ 1P]-5D@ 1P]5J@ 1P]@@}@@0'mul_1_l @ <   ٠  n    N G     "  $ @"F5d#İ,+5t@ 1P].5Ð@@@@['mul_1_r @ g '     < ߠ ֠ y r     M F 7ܠàOB4@MG5#,V5@ 1P]Y5H@@@@,mul_shuffle0 @  R B / נ Ġ g     @ 9 ܠ ՠ x q b ݠzm_@xH555$,5@ 1P]5@ 1P] 5@ "1P]5@ (1P]D,@@@@à,mul_shuffle1 @ Ϡ   l    G >  ڠ } v      D + @I&5$555$Z,6 @ U1P]Ā6@ [1P]ʀ6@ `1P]π6@ e1P]Ԁ6 @ k1P]ڀ6%@ p1P]߀@@X@@ ,mul_shuffle2 @  נ Ǡ  \ I    ) " Š  a Z     s b@Jn6?l6@66AA6B$- 6R@ 1P] 6X@ 1P]?6]@ 1P]K6b@ 1P]6h@ 1P]"򩚠6m@ 1P]'?@@@@S,mul_shuffle3 @ _      4 נ Π q j     E > / Ԡ  G:,@EK66~6$-P6@ 1P]S6@ 1P]Y6@ 1P]^6@ 1P]d@@@@%le_wd @  \ L 9  Π q     J C  ߠ  { l   砠@@A&NZBase'NZOrder&NatInt'Numbers#Coq@  @A@'NZOrder&NatInt'Numbers#Coq@+NZOrderProp  @A@@@@"NZ  @A@@鰶@6@66@6%J6%LQ6@ [1P,@@,@@AA@@A@*lt_le_incl @     3  à f ]     8 1 Ԡ ͠  c J 9RE7@PAE7C7@7&@"lt1P-7,@ 1P,@@@@@3'le_refl @ ޠ Π  c P    0 ) ̠ Š h a     z iug@Bu7F7T@ 1P,@@ x@@\.lt_succ_diag_r @G    y    Y R     - &    @C7o7}@W1P-̩7@ 1\w!*@@@@@.le_succ_diag_r @u5%   J     #    [ T E  Ѡ ٠̠@D77@ 1P,7@ 1\w!ـX@@@@@/neq_succ_diag_l @cS@  ՠ x     Q J     s   @E7˩&-.7@ 1\w" +@@@@䠠/neq_succ_diag_r @Ϡl  G >  ڠ } v      D + 3&@1F &7 &Y. R8 @81\w"1@@@@@/nlt_succ_diag_l @@- Р s j     E >  ڠ ˠ p W F_RD@]G R8# L83@ 1P-89@h1\w"a @@@@@@/nle_succ_diag_l @+۠Ƞp]   = 6 ٠ Ҡ u n      vt@H 8S |8c@1P,8i@1\w"  @@@@@p)le_succ_l @[ 0 Ӡ ʠ m f     A : + Р  @I 8 8 ꠩8@1P,8@1\w"€ G 詚8@y1P-@@ C@@+le_gt_cases @QA.֠àf    ? 8 ۠ Ԡ w p a   ܠ@J 8 8 !@"or @8@21P,8@1P-P@@@@ܠ-lt_trichotomy @Ǡwd ?6 ٠ Ҡ u n      < # +@)K 8 869@1P-='Y/ S R9 @1P-@@@@@(lt_asymm @@-Рsj    E >  ڠ ˠ p W F_RD@]L R9# P9$@93@ 1P-! S9:@1P-  N@@ @@B(lt_trans @-ݠʠr_?8 ۠ Ԡ w p      xv@M 9U 9VL9W@9f@@1P-8@9l@F1P->9q@K1P- W @@ @@y(le_trans @d$9ܠӠvo    J C 4 ٠  Ƞ@N 9 99@9@1P,o@9@1P,u9@ 1P,7@@@@+lt_strorder @ZJ7ߠ̠o HA  ݠ  y j   @O@+StrictOrder.[@9ɚ9@1P-@@ @@ݠ+le_preorder @Ƞxe @7ڠӠvo     = $ ,@*P*@(PreOrder@9:@f1P,@@ '@@ /le_partialorder @;(ˠne@9 ܠ ՠ Ơ k R AZM?@XQW@,PartialOrder5͛:$(:1@P4h:5@1P,:9@^Ҁ@@@ @A @ ^@ _AhCn@ABC@@G)lt_compat @:N@%lt_wd23@ L@:I@:J U G:L@:M X( J:O Z( :\@61P-@y@@%lt_wd']ɠP%Ƞb[6/  Š  @@@@@(lt_total @:@€@ : :̠:@p1P- Ӡ(1V  詚:@y1P- C@aǠN>+Ӡc<5ؠѠtm^  ٠@@@@@Ġ'le_lteq @:@+lt_eq_cases0㜀@ :Ķ :ũ +:@71P, é:@1P- ʩ)31 - ,@+lt_eq_cases&y̠|iD;ޠנzsA(0#@@@@@0Private_OrderTac;A'IsTotal;  A. @;@64h@I@+Equivalence~@;)v@(eq_equiv7L ͠R?|WPݠiXqdV@@@@@C @;I@&6Y@;B;O@)1P-@,Q^<٠nNG" @@@@@r+ @;x@3?@@ u@;r@;s ~ p;u@;v )֩ s;x ) ݚ;@_1P-)p0  Eߠ{VO@̠ԠǠ@@@@@  @;@(?@ ; ;렩;@1P- *2u  ;@1P- 9iYF۠~!WPy @@@@@ߠ @;@#/B@ ;ݶ ;ީ D;@P1P, ܩ+;@1P- *L2 F E'ZQ,%ȠW>-F9+@@@@@@@@@֐@#Tac<AV @ ̠Q>{VOܠhWpcU@@D!P)OrdersTac*Structures#Coq@~hLE@@@A@@C!Ok@@&@r@!t&J@@A@A&a@@"eq&a^@@A@&@ @"le&ڠh@@A@AB&@@"lt&h@@A@&̌@@#one&̌T@@A@A&̔I@@#two&̔IT@@A@&H@@$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@<+ 3s@@@@AA@@A@ @k[Hݠ#YR{ ZSM2@AD<٩<@I1P,@@ @@0)lt_irrefl @٠v QH#N5$=0"͠{`@Br=0=@1P-Ð@@:@@`- @ȠM:ݠwRKؠ}dSl_Q@C=6=7@+3+4X@@h@@*le_antisym @7Ԡ|i IBޠz+ߠ٠@,D=e=f@=u@1P, c@={@1P,A+Ұ49c@@@@ƠŐ @n. CݠyTM>ʠҠŠbR@cE==@ǐ,4gː,4k@@@@@*interp_ord @!o)OrdersTac@#ordȠ@ @@@@@@@@@@@D@=Ķ@= ,&=@1P-=@91P,@@=ж@= ܐ +k= R'6'6'6''+k+7T'+7T'6'ࠒA@@"lt\ @R@"eq8L@TlР@@Ƞ@@=<;@@A@B@A@xA܀;(ˠne@9ܠՠƠkRAZM?ڠ}@@@@@t%trans @ݠ͠bO/(ˠĠg`yhtf̠Š@F"o'>O>PH>Q@>bbJ@7ùHv@>kkS@7ù >rrZ@7ù@)trans_ord-0uGV`@@@@ĠH @>|>}u>~>v@^BМA@>>>@,5T@,5W,5Y L+k() LL7#'@z$tSC0ؠŠh A:ݠ֠yrcޠܠwB;5@@@@@V @4>ɷ2>ʷ>˩>@BМ!C.-@B>׶@>ض>ٶ@>@J1P, @>@P1P, >@U1P, L+k() NN7#'Vt*]T/(ˠĠZA0I<.٠ɠl@@@@@cߐ @????--@BМsBD@?)?*"?+@?:@1P- @?@@1P- ?E@1P-Ԑ L+k() MM7#'t7Ԡ|i IBޠz+ߠ٠@@@@@+le_lt_trans @?n?og?p?h@PBS@?y?zr?{@?@1P, \@?@j1P- b?@o1P-$ L+k() MN7#'tG7$̠\5.ѠʠmfWҠޠР{k6/)@@@@@+lt_le_trans @)?'???@B @4?ɶ2?ʶ?˶@?@1P- @?@B1P, ?@1P-t L+k() NM7#'Htנt OF~!L3" ; . ˠy^@@@@@U%eq_lt @y@w@@@  @B4po@@@@@.|6:v@@-@ 1P- @2@ 1P- L+k() ML7#'t$ԠiV6/Ҡˠng o  { mӠ̠Ơ@@@@@%lt_eq @@[@\T@]@mmU@=B@@@f@g_@h@@w@ Q1P-I@.ϰ76ɩ@@ Y1P- L+k() LM7#'tq1!F|WPA͠ ՠ Ƞ eU @@@@@%eq_le @@@@@@B,  @@@@@/7}@@@)1P,@@.1P,[ L+k() NL7#'/t~n[6-Рɠle3  "  mf`E@@@@@<%le_eq @`@^@@A@B,yWV@kAiAA@A@s1P,@/i7'cA@{1P, L+k() LN7#'|t ˠP=zUN۠gV o b T@@@@@&eq_neq @2ϠwdD=٠|u}   {&ڠԠ@'GA`AaYAb@/ð8*@/Ȱ8/©/̰83\@@@@@&neq_eq @i)>ؠ{tOH9ޠŠ ͠  ]M @^HAAA@Ð/8c@/8fʐ08j@@@@@*not_neq_eq @`P=ҠuNGp   OHB'@I9Aζ7A϶@048.-0680@@@@*)not_ge_lt @ӠpKBޠzH/ 7 * Ǡ{uZ@JlBjB@,B@u1P,B@ 1P-@@;@@a)not_gt_le @ ʠO<ߠyTMڠfU n a S@KB8B9@cBJ@ $1P-ũBO@1P,!@@@@@)le_neq_lt @AޠsSL'    5%@6LBoBp@B@1P,m@0ٰ9@өB@ c1P-p@@@@@@@@@%N@@@@@%P@<_neq @?/ĠT-&ɠ e^O۠ʠ  ֠ @ RBB@B@ 1P-א19w @@@@@  &le_neq @m]Jߠ%[T}"    @ SBնB֩<B@ 1P-ԩD@#andЖw@B@U1P,1L9FE@@@@@ *eq_le_incl @.aX3,ϠȠ^E4 M @ 2@ KT@C>C@1s9mlC#@1P,@@@@@ *(lt_stepl @ՠŠZG' à_Xq` y l ^@ wUC=C>6C?@CN@ (1P- @1: 7CV@ 01P-j=@@@@@ ^(lt_stepr @I {[T/(   @ VCqCrjCs@C@ \1P-T@1ڰ:AԩC@ d1P- @@@@@ (le_stepl @|<,Q*#Ơb[LؠǠ  Ӡ @ WC CC@C@1P,@2 :tC@1P,g@@@@@ Ġ(le_stepr @o_L']V$    @ XBC׶@CضCٶ@C@J1P,@2@::C@R1P, @@@@@  @~&YP+$ǠV=, E 8 *@ CY8D 6D D @D@|1P,@D @ 1P-򩚠D%@ 1P- @@@@@ ,i @֠Ơ[H(!Ġ`Yra z m _@ xZmD>kD?5D@@DO@ )1P-!@DU@1P,'DZ@ 41P- @@@@@ a+le_antisymm @L ~!Ġ^W2+   @ [DtDu@D@1P,r@D@1P, P2;Hr@@@@@ )le_succ_r @~>.àS,%Ƞd]Nڠɠ  ՠ @ \DD D@1P,D@1\w.d D@&1P,3;D@1\w.r@@@@@ Ҡ)lt_succ_l @}mZ5,ϠȠkd2!@]DD@D@ 1P-D@*1\w/#IE@ 1P-Ґ@@@@@,le_le_succ_r @7$Ǡja<5ؠѠ gN=VI;@T^IEGE@E*@1P,E/@1P,CE5@d1\w/]@@@@@<,lt_lt_succ_r @'נĠlY92ՠΠqj r~p@_~EO|EP@E_@91P-MEd@>1P-xEj@1\w/@@@@@q,succ_lt_mono @\ 1Ԡˠng B;,Ѡ@`EE렩E@o1P-E@t1P-E@1\w/ȀME@1\w/̀L@@@@@,succ_le_mono @WG4ܠɠlE>ڠ}vg @aEE&E@21P,E@71P,E@ 1\w0E@1\w0@@@@@砠<_0_1 @ҠoJAݠyG.6)@4bF@1P-EE@@@@&le_0_1 @?,Ϡri D=٠ʠoVE^QC@\cF/@1P,EEؐ@@@@@7<_1_2 @"ҠgT4-Рɠle~myk@dFW@11P-FEې@@@@_<_0_2 @J | \U0)@eF@Y1P-FDF@@@@&le_0_2 @r2"G} XQBΠ֠ɠ@fF@ 1P,FlF+@@@@@<_1_l @ZJ7ߠ̠o HAݠyj@gF¶Fö@F@1P-F"@F@1P-F@1P-F@@@@@@ABC@@頠+lt_ge_cases @ԠqLCߠ{I08+@6h+F)FCG @1P-G@t1P,@@@@@+le_ge_cases @ĠI6٠|sNGԠy`Oh[M@fi[G,YG-sG=@1P,+GB@1P,@@@@@I+lt_gt_cases @4Ѡyf F?۠~w}@jG\G]à5>(Gs@M1P-aGx@R1P-@@@@@,eq_decidable @j*?٠|uPI:ߠƠΠ@kGG)Decidable@)decidable r5>e@@@@@&eq_dne @[K8͠p IBޠzk@lGöGĩ*6*>$#6,>&%@@@@@ޠ&le_ngt @ɠyfA8۠Ԡwp >%- @+m GGXH@d1P,"H @1P-@@@@@&nlt_ge @@-Рsj E>ڠˠpWF_RD@]nRH#PH$OH6@1P-$H;@1P,@@@@@B,lt_decidable @-ݠʠr_?8۠Ԡwp xv@oHUHVÐHf@@1P-T@@@@@m<_dne @X-РǠjc>7(͠@pHH砩H@o1P-H@t1P-@@@@@&nle_gt @L<)Ѡa:3֠Ϡrk\נ@qHHH@)1P,H@1P-G@@@@@Ӡ<_nge @~n[6-Рɠle3 "@ rHHMH@1P-H@`1P,y@@@@@,le_decidable @5"Šh_:3֠ϠeL;TG9@RsGIEII)@1P,@@@@@0&le_dne @ ۠ˠ`M-&ɠ e^wfrd@}trICpIDoqIX@1P,FI]@1P,K@@@@@d*nlt_succ_r @ O $ǠaZ5.Ġ@uIwIxޠI@d1P-٩I@1\w3=I@o1P-@@@@@5lt_exists_pred_strong @  G 7 $̠\5.ѠʠmfWҠޠ@vIII@I@1P-'@I@ (1P,$@"ex @Iŷ!kIȩ렩8*@I@ 1\w4I@ A1P,.@@@@A@@A@AРD.Morphisms_Prop!@ A1@DH@ABCD@@.lt_exists_pred @    } % XO*#ƠU<+D7)@BwJ8J @J@1P-RJLJ58t@2J$@ S1\w4L˩J)@ 1P,@@@?@A@@1,lt_succ_pred @! ܠ ̠  a N.'ʠàf_xgse@~x;JDtJE@JT@.1P-B8AJ[@ 1\w4Ja@ 1\4E@@@@A@F@@{@ABCD@@m&rs_rs' @!X!!    -РǠjc>7(͠@y@J@JJ8޶J@}@J@J@ 1P,@wI #J@ 1\w4ˀJ@J@! 1P,5@JJ@J@!1P, <@J@1P-KkH@@_@@Ǡ(rs'_rs'' @!!r!b!O    * !Ġ`Y' @z@Jⰶ@JJ9AF8J@J@J@!U1P,@JJ@J@!_1P,L@K@1P-ʩIcd.Je2K0K@K@!u1P,@K@1P-AK?K@K"@!1P,%@K(@1P-$K.@!]1\w5VՐ@@@@5%rbase @" !!Р!!e!R    2 +ΠǠjc|kwi@{V@KITAKJ{KLyKM@K\@!1P,ö@Kb@<1P-(\ @@@@@i)A'A_right @"T""!!!!) ̠ à f _ :3$ɠ@|@K}uK~@KKK@K@!1P,@K@r1P-^ @K@K@"1P,N@@@@@6strong_right_induction @""S"C"0!ؠ!Š!h! !   A :ݠ֠yrcޠ@}ɶ@KǶũð@K˩K:"'Kö@KŶ@K@"61P,¶@KζK϶@K@"@1P,@K@1P-޶ Kܶ@K@"M1P,RP@@@@A@@ @ABC@@/right_induction @""""~"&"!!Y!P     + $ǠV=,E8*@C~@L @L L:pugL@@CL@L#@"1P,@ L+@"Z1\w6SRL#@L2@"1P, @@@@@:0right_induction' @#%""ՠ" "j"W!!!!7!0 Ӡ ̠ o h  p|n@[@LNYWU@LR]OLT_:LLU@LW@Lf@"1P,ƶ@L_@Ln@"1P,ն@ԩ Lv@"1\w6ӶLnS@@@@~7strong_right_induction' @#i#)##""">!!ؠ!{!t!!   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@8͠88}8j8777E7<6ߠ6ؠ6{6t665555B@5jjaha@b@8b1P,a3P@b@8i1P,a3Wb @8o1P,b@8k1P&Kfb@8d1P]JӀéb@8i1P]J؀/b#@8{1P&Kvb)@8t1P]Jb.@8y1P]J@@@@ L-add_square_le @9 88Р88e8R777727+6Π6Ǡ6j6c6555@5kbCbD@bS@81P,b3@bZ@81P,b3b`@81P,bf@81P&Kbl@81P]K&bq@81P]K+󩚠bv@81P]K0b|@81P&Kπ/cb@81P&KԀ/h@@3%@@ -square_add_le @9s939#9888H7777~7!7666Y6R6C5@6@lbb@b@91P,bk3@b@91P,br3b@91P,b@91P]Ksb@91P&L/b@91P&L/b@91P]KbMb@9'1P&L"b@9 1P]K]b@9%1P]K\@@3~@@ 4quadmul_le_squareadd @9̠99|9i9888D8;7ޠ7נ7z7s776666A@6mibgb@b@9a1P,b4O@c@9h1P,b4Vc @9n1P,c@9]1P]K̀c@9c1P]KҀc@9i1P]K؀bb442c$@9o1P]Kހc*@91P&L}0c/@91P&L0@@3@@ M(pred_inj @:!99Ѡ99f9S888838,7Ϡ7Ƞ7k7d7@7a@4pcA4ncB@QZ cS@91\M74cX@91\M<3QZ4m4@@3@@AA@@A@+pred_inj_wd @:O:99999$8Ǡ88a8Z777775@7A42co40cp4֠QҰZ9c@91\Mf4/c@91\Mk4.QްZE44א@@3@@/'succ_m1 @:{:;:+:999P88888)8"7Š77a@7BQZac@91\wMҀc@91PMQcYcu@@2@@W*add_pred_l @::c:S:@99ՠ9x99888Q8J7@8G@4c4c©R"Zc@:*1P&M%c@: 1\M45&c@:1\Mc@:;1P&M62ѐ@@3@@AA@@A@*add_pred_r @:ؠ:::u:: 99P9G88888"@8|A5%c5#cRWZd@:_1P&MZ5Wd 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@IHܠH̠HHaHNGG@GICcr4Car5CrE@H1P,A3rJ@H1P,rP@H1P[BrU@H1P[C@@A@@x+opp_pos_neg @IGIHHHHyHG@HJCr_CŠro@;I1P-r4ru@H1P\Crz@;T1P-Cr?@@@@+opp_neg_pos @ImI-II HHHBG@H?KCrC렩r@;o1P-r@H1P\<CBr_r@;z1P-reC@@A@@Ġ1opp_nonneg_nonpos @IISICI0HؠHŠHhH @HeLCrDr@I1P,rr@I1P\bChr@I(1P,Dr@@@@ꠠ1opp_nonpos_nonneg @IIyIiIVHHHH1@HMDrѩD7r@IC1P,r@I(1P\Crr@IN1P,rD;@@B @@'lt_m1_0 @IߠIII|I$IHHW@HNs@;1P-s @IK1P\rrϐ@@@@@.-sub_lt_mono_l @IIIIIBI/HҠHu@HODDsDBsA sD}s'@<1P-@s,@<1P-s2@In1P\5As7@Is1P\:@א@@Bj@@Z-sub_lt_mono_r @J)II٠IƠInI[HH@HPDpsADnsBA8sCDsS@<-1P-A%sX@<21P-s^@I1P\a@ũsc@I1P\fBQ@@B@@+sub_lt_mono @JUJJIIII*H@I'QDsmDsnAdso@osp@s@1P-u;@K1P&^BFu@@>1P-FTuF@K1P^ID4@@ ^@@i/le_add_le_sub_r @L8KKKՠK}KjK J@K [FuPF}uQCGuRFub@K1P,uh@K1P&^BFum@K1P,Fus@K1P^vDa@@ @@/lt_add_lt_sub_l @LeL%LLKKK:J@K7\Fu}Fu~CtuF堩u@>i1P-u@K1P&^BF䩚u@>t1P-F驚u@K1P^1P-u@L+1P^CVG>u@>1P-Gu@LR1P&_MD@@!@@/le_sub_le_add_r @LLLLL1LKKd@K_G3vG1vCvGlv@Lx1P,v@LX1P_CGkv!@L1P,G5v'@L1P&_zE@@!?@@J/lt_sub_lt_add_l 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@O!NNѠNNfNSMM@MkIhx9Ifx:@xI@N1P,xxO@N1PaRG=?xV@N1P,xIjx\@N1P,Ix!@@I@@,zero_pos_neg @OOONNNNN$M@N!l!P@xjHu$P_wdHs@xpH{HmxrH}fIIɶ@I̐xB@Ixw@x@A`1P-xKIթ5,Hox@N1Pb1I=IxHw@@)@@2mul_lt_mono_nonpos @OOCO3O NȠN@N@IxIxFxEx@x@O 1P,Ixp@x@A1P-@x@O1P,Ix}@x@A1P-x@A1P-x@O1P]a⩚x@O1P]a@@@@@AA@@A@2mul_le_mono_nonpos @OĠOOtOaO N@NAJ xڶJx۶FxܶExݶ@x@ON1P,Jx@x@OU1P,*@x@O[1P,J x@y@Ob1P,7y@Og1P,y @OV1P]aŀ#y@O[1P]aʀ.@@@@@A1mul_nonpos_nonpos @PO OOOGO4@O0BJGyJEy@y(@O1P,Jxx@y/@O1P,Jxy5@O1P,xy;@O1P]aF"@@2\@@l1mul_nonneg_nonpos @P-OOݠOʠOrO_@O[CJryCJpyD@yS@O1P,yJ@yZ@O1P,Jyy`@O1P,yf@O1P]b FMy*@@J @@1mul_nonpos_nonneg @PXPPOOO@ODJynJyo@y~@O1P,JyC@y@O1P,yJJթy@O1P,y@O1P]bKFxyU@@2@@ (lt_mul_0 @PPCP3P OȠO@OEJyJyKy@B1P-y@O1P]bjHyt@6̠y@B1P-K y~y@B1P-yK6ڠy@B1P-yKy@B1P-Ky@@Jr@@(le_0_mul @PPPpP]PO@OFKyֶKy׶@y@PH1P,yy@P71P]bHکA)7y@PW1P,yK y@P]1P,yKK7z@Pe1P,Kyȩz @Pk1P,KYyΐ@@@@@;(le_mul_0 @PPPPPAP.@P*GKAzK?z@z"@P1P,z(@Ps1P]bIyAe7Dz1@P1P,yKEz7@P1P,Ky7Rz?@P1P,KSzzE@P1P,z K@@@@@w,nlt_square_0 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@W_WWV@VPQsQtNju@@V1P,IQөnܰwC@V1P{_ڀ@V1P]iL(,@V1P]iQG]@V1P]iVQ쩚@V1P{_M@@O@@6mul_min_distr_nonneg_r @WWTWDW1@W-QQQN@@W1P,~Rowx@W1P{`@W1P]iM@W1P]iN@W1P]i@W&1P{`%MR&@@P @@(6mul_max_distr_nonpos_l @WɠWWyWf@WbRR ݶR ޶N߶@@WP1P,R=oFw@WJ1P`H@WG1P]i(@WL1P]iGǩ@WQ1P]iRV @W[1P{`ZM@@P?@@]6mul_max_distr_nonpos_r @WWWW@WSRAR?O @#@W1P,Rro{w⩚+@W1P`}1@W|1P]iN6@W1P]iO;@W1P]iA@W1P{`N(R@@Pt@@6mul_min_distr_nonpos_l @X3WWW@WTRvGRtHO>I@X@W1P,Rox`@W1P{`f@W1P]j )k@W1P]j%H1p@W1P]j*Rv@W1P`ȀN]@@P@@Ǡ6mul_min_distr_nonpos_r @XhX(XX@XUR|R}Os~@@W1P,RRoxL@W1P{`〠@W1P]jUNq@W1P]jZOr@W1P]j_@W1P`NR@@P@@+Private_TacA'eq_refl @@@K!M-GenericMinMax*Structures#Coq@a@A@@J!O Π@a#aaqanakIaf@3xab@1P%@@!t1P%J@A@AB1Pa`a\CD1PaXaUEFG1Pňa>a:H@A@ +%Ơ@D ! @@1P,#@ @1P,*'D*@@@@'neq_sym @rgTN= ݠ@ E2J3@u78Jy;<NK@@@@@*interp_ord @!o)OrdersTac@#ordȠ@ @@@@@@@@@@@D@D@!t@ A찚 @"eq@@`^@31@{@| +k= R'6'6'6''+k+7T'+7T'6'ࠒAHcba@@"lt\ @4@"eq8L@6lР@UȠ@@RQP@@A@B@A@xA܀ߠ٠ȠzunhM@@@@@3%trans @ݠ}b@F"o'aֶ׶!zڶ@:@7QE@C@7Q I@7Q@)trans_ord-0uGF @@@AviA)Morphisms{@AAۀߠK@Aۓό^ @@ABC@@(eq_trans @,>w@^K߀МA14odQK: @)A*S+@-.=@@01@C23QB L+k() LL7#'@$tpjY,& @@@@@Ġ(le_trans @oCМCmpvI@e}fg@v@Z1P,}@}@a1P,@f1P, L+k() NN7#'GtѠƠoiNIB<!@@@@@(lt_trans @%@ABМVB(Рʠ@3@@1P-C@@1P-I@1P-B L+k() MM7#'tݠ}b@@@@@H+le_lt_trans @fAf,!@q@@1P,@@$1P-@)1P- L+k() MN7#'ƐtPE2,͠Ƞ@@@@@+lt_le_trans @1C,/j_LF5@$<%N&@5@\1P-@;@1P,ũ@@g1P- L+k() NM7#'tpjY,& @@@@@Ġ%eq_lt @oC<jmsF@bzcd@fgvy@v@1P-{@1P- L+k() ML7#'?tɠgaFA:4@@@@@%lt_eq @89:~wؠŠ@(@@1P-8@@1P-4 L+k() LM7#'ztϠ|uoT@@@@@:%eq_le @XstuvX@cضٶڶ@ܰ@@1P,v@1P,o L+k() NL7#'t?4! ݠנ@@@@@u%le_eq @ 2YN;5$@+=@$@1P,@-0,@1P, L+k() LN7#'tzo\VE@@@@@&eq_neq @qkZ-' @(GOgPyQ@STcf@XYhk\]{l@@@@@ՠ&neq_eq @RL1,%@MHtuv@z{@}~@@@@@*not_neq_eq @٠ΠwqVQJD)@rI$@ܐސ(@@@@)not_ge_lt @ܠ֠ŠwrkeJ@JE@@1P,K֩@1P-\@@O@@A)not_gt_le @ p@Kk@#@1P-&@1P,@@@@@f)le_neq_lt @E:'!ݠ @L@@1P,@N #@F1P-&@@@@@@@@@i@(max_spec @peRL;@qE!n,!m/%Logic$Init#Coq@@"or @@#andЖw@T@31P-BAOP^@p1PfBAAk@O1P,ABfgu@1PfǀBAB@@@ %'A*Equalities*StructuresqA݋X_A/RelationClasses'Classes#Coq@@A@@AA@@A@+max_spec_le @ڠϠx@Fjih]@1P,BA@1Pg BAAt@1P,AB@1Pg BAB@@@@@I1Proper_instance_0 @ @!G)Morphisms'Classes#Coq@@&ProperL@@@*respectful%WO?@ 8@#iffС) @1P,@@@AviA)Morphisms'Classes#Coq@@A@@*max_compat @bWD>-@cHB@ @!!8#@$$%&=(()*+,9@K1Pg@@@A/@Aۓό^1@A@ABC@@+max_unicity @qkZ-@IJL!pO@!f@E1P-CBabAB&v@Z1P,BCqrACuv@1Pgրb@@@@@/max_unicity_ext @ӠȠq@J!f"x0@lkj_@1P-.C3Ao@1P,>ɩCCB°éL@1Ph%R@@@@@K(max_mono @"@#KO@޶@@䩚@@*respectful%WO?A@@ @1P,@1P,    @,1Phl1&35&@81Phx0@@@A@A@A@ABC@@&max_id @{p]WF@|L 678F@X1PhAAA@@@@@)max_assoc @ztc6@M%S*U WXYg@y1PhCn@1PhBAv@1PhȀ|@1Ph΀CBA@@@Aw@A AۀߠKx@ AK@A @ABC@@(max_comm @ؠ͠v@Nhg@1PhBA@1PhAB@@@7Au@9A3@AB@@+(le_max_l @ޠ͠@O@1P,B@1Pi&BA@@@@@N(le_max_r @%@&Pඐ⩚@1P,A@ 1PiIBA@@@@@q)max_l_iff @H=*$@IQ@#iffС) @.1PinBAB%@ 1P,AB@@@@@)max_r_iff @vkXRA@wR13.89G@Y1PiBAAP@41P,BA@@@@@ʠ&max_le @}l?@S1\0^`@o@S1P,Av@1PiȀCBA@f1P,`@l1P,@@@@@*max_le_iff @נ̠u@TgfH@1P,A@1PjCBz@1P,AC@1P,AB@@@@@=*max_lt_iff @  ߠ@ U϶Ѷө΀@1P-A@1Pj>CB@1P-AC@1P-AB@@@@@z)max_lub_l @ Q F 3 - @ RV @@ 1P,%@ 71PjwCBA.@ 1P, 8@@@@@)max_lub_r @ } r _ Y H @ ~W 8 :<@K@ /1P,Q@ c1PjCBAZ@ >1P,ad@@@@@Ҡ'max_lub @     t G@ X9d8fh@w@ [1P,CA@@ d1P,@ j1P,@ 1Pjހj@@@@@+max_lub_iff @ ۠ Р    y@ YkjL@ 1P,@ 1PkCBAo@ 1P,CA@ 1P,BA@@@@@A*max_lub_lt @      @ ZӶն׶@@ 1P-CA@@ 1P-@ 1P-@ 1PkM @@@@@s.max_lub_lt_iff @ J ? , &  @ K[ @ 1P-!@ 31PksCBAހ.@ 1P-CA6@ 1P-BA@@@@@/max_le_compat_l @  | i c R %@ \BDF@U@ 91P,CB]@ A1P,c@ u1Pk m Ai@ {1Pk s p@@@@@ᠠ/max_le_compat_r @      V@ ]HsGu)w@@ j1P,CB@ r1P,@ 1Pk怠 r @ 1Pk쀠  @@@@@-max_le_compat @  ޠ ˠ Š  @ ^yxZ!q@@ 1P,DC@@ 1P,  ͩ@ 1P,@ 1Pl! @ 1Pl' ܐ@@@@@M(min_spec @ $     @ %_߶ᩛ@ 1P-BA 󩚠@ 1P{lOBAB@ 1P,AB  @ %1P{lfBAA@@@A@A@@+min_spec_le @ l a N H 7 @ m`')?@ #1P,BA :;I@ V1P{lBABV@ :1P,AB QR`@ m1P{lBAA@@@@@۠*min_compat @     } P@ a@p@qqs@tt uvxx yz {|@ 1P{l׀@@@A@AP@A@ABC@@+min_unicity @ ݠ Ҡ    {@ bmlN@nc@ 1P-CB ACs@ 1P,BC AB ° թ@ 1P{m  ؐ@@@@@I/min_unicity_ext @      @ !cM gݶL߶@ⶐ䩛@ 1P-  y C  ~B @ 1P,   C  A     " @ 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L@@@ )A !@ +A @ -A @ABC@@ /mul_mod_idemp_r @JOJKJ ڠ ˠ      @ h  @*@ 1P,C@2@ 1P, n@9@ 1P- uᑰA@ NH/퀠G@ 1P] M@ NH/   S@ NH/Y@ 1P]   @@@ A x@ A m@ A k@ABC@@ c'mul_mod @JJJq 1 "      @ i `n pr@@ 1P,FC@@ 1P,N Ŷ@@ 1P-U ̩O@ NH/D@ 1P]X   詚@ NH/P@ 1P]d@ NH/\  @ NH/b   @@@ A @ A @AB@@ /add_mod_idemp_l @KJJ̠  } m h c Q C s@ Oj ɶ p˶HͶ@@ V1P,C@@ ^1P, @@ ]1P- 'Cꪩ@ RNH/۟@ L1P&L@ ^NH/۫ \ I < I@ dNH/۱ @ ^1P&^ h H U@@@ 2A *@ 4A @ 6A @ABC@@ /add_mod_idemp_r @KXKTK#  Ԡ Ġ     @ k   "$@3@ 1P,C@;@ 1P, w@B@ 1P- ~⚰J@ NH/P@ 1P&ݣ V@ NH/   \@ NH/b@ 1P&ݵ   @@@ A @ A v@ A t@ABC@@ l'add_mod @KKKz : +      !@ l iw y{@@ 1P,OC@@ 1P,W ζ@@ 1P-^ թX@ NH/M@ 1P&   񩚠@ NH/Y@ 1P&@ NH/e  @ NH/k   @@@ A @ A @AB@@ Ǡ'div_div @L LKՠ   v q l Z L |@ Xm Ҷ yԶֶ@@ _1P,C@@ _1P- )@@ f1P- 0L볩@ 1P@ 1P _ ? L@ 1P e@ Z1P]Ȁ K X@@@ 6A .@A 7A &@ 9A $@ ;A "@ABC@@ )mod_mul_r @L]LYL(  ٠ ɠ Ġ    @ n % 'U)@8@ 1P,C@@@ 1P- |@G@ 1P-  㟰O@ NH/ U@ 1P]  [@ 1P&ޮa@ NH/   g@ 1P]! m@ NH/s@ $1Pn   @@@ A @ A @ A @ABC@@ }*div_mul_le @LLLK<,'" 2@o z /@@ 1P,`C@@ 1P-h ߶@@ $1P,o 橚@ *1P,@ 1P]p @ m1Pݷ  @ s1Pݽ@ 1P]ނ  % @@@ A @ A @ A @ABC@@ Ҡ+mod_divides @MML|weW @cp ݶ ߶@@ h1P,B@@ h1P- Z R칩@ aNH/ݮ L >ǩ =@"ex @0d K@ `1P]΀ ^A@@@ =A 5@A >A -@ @A +@ BA )@ DA1@D X W V@@ABCD@@ (@@@@@A  BC@&mod_eq @MpMlM;ܠ@@!a5!b8@%Logic$Init#Coq@@#notШ䧰A䪰Z@ NH/CBb@#sub1Pf i@#mul1P]$p@ !1Pk@@@ %'A*Equalities*Structures#Coq@A݋X_A/RelationClasses'Classes#Coq@@A@@AA@@A@-mod_bound_abs @M̠MȠMWH83@VA\[@Z^Ag@"lt1P-@1P0@ NH/a[Z@1P<`@@@LAviA)Morphisms'Classes#Coq@@AUAۀߠK @YAۓό^ @]AU@ABC@@M.div_mod_unique @NNM}@Bڶ"q1ݶ"q2ඐ"r1㶐"r2@%Logic$Init#Coq@@"or @%Logic$Init#Coq@@#andЖw@@"le1P,ِB@s1P-BE'@1P-EB/@1P,B@B7?@,1P,䩚E@1P-FHP@1P- V@C1P,@寰_@#add1P&ೀf@1P] G"Dn@1P&t@ 1P].E@#andЖw@հ<:װ> @@@A@A@A @ABC@@*div_unique @NΠNʠNYJ:5@XC^]!q!r@@1P,vA@1P-AC@1P-CA@1P,A@&\@w1P&)@s1P]u4w@1P߀p@@@tA@vAn@AB@@f.div_unique_pos @O/O+N@Da`@ @1P,ѐA@k1P-AC@n@1P&q$@1P]ހɩ|,@1P'@@@@@.div_unique_neg @OsOoO>ߠ@E79;=@HP@1P-CAX@E1P,A@沰詚b@1P&ᵀh@1P]" 'p@!1Pk+@@@@@*mod_unique @OOOB3#@AFG{F}@@1P,]A@1P-AC@1P-CA@1P,Ay@ tC@^1P&@Z1P]}\ihk@*NH/wW@@@[A@]AU@AB@@M.mod_unique_pos @PPO}@GڶܶH޶G@뀠@1P,A@R1P-AC@U@1P&X @1P]ŀc@rNH/࿀@@@@@.mod_unique_neg @PZPVP%֠Ơ@H "$@/7@1P-CA?@,1P,A@癰ϩI@1P&✀O@1P] 称W@NH/@@@@@ՠ,mod_bound_or @PPPi) @(I.b-d@,ɰ0A9z@o1P,G@NH/4.-@1P-@NH/@:99@1P-C@NH/PJI@1P,@NH/\VUu@@@@@.0opp_mod_bound_or @PPP sc^@J@"AހӀ@1P,@1Pむ@FNH/ᓀ@E1P-@1P㔀@XNH/᥀@1P㠀 @a1P-@1P㰀@ 1P㶀@zNH/ǀ!@1P,'@1PȀ-@NH/ـ@@@@@+div_opp_opp @QtQpQ?@K8:@蟰A袰 R@1PMX@L1P^@R1Pd@1P_  @@@A@A@A@ABC@@蠠+mod_opp_opp @QQQ|<-@;LAu@w@?ܰCAL߰F@NH/;@1P6;@1P<@@1PB@NH/SML@@@7A@9A@;A3@ABC@@++div_opp_l_z @QQQp`[@~M@A@#񊩚@2NH/yx+񒩚@1Pր@1P䂀z@1P䈀@1P耠@@@}A1@A&@Ay@ABC@@q,div_opp_l_nz @R:R6RŠ@N@Ȁe̐Aն@Ѐmԩ@|NH/ɀuܩ%@1P +@1P̀ѩ1@1P47@+1P؀=@1P8@@@A@Av@A@ABC@@+mod_opp_l_z @RRRU@ONP@鵰A%@鹰 i@NH/.(q@NH/w@k1P<@@@A@ A@ A@ABC@@,mod_opp_l_nz @RĠRRO@0+@NPTS@RVA_@Z^@NH/SMLlf@NH/[@1PVN[@Y1P侀a@ NH/mZg@@@QA@SA@UAM@ABC@@E+div_opp_r_z @SS R٠zu@QҶԶ@9A@=򤩚@LNH/㙀E򬩚@1P@1P圀@1P墀@1P@@@AK@A@@A@ABC@@,div_opp_r_nz @STSPSߠР@R@‐A@ꀐꇰ7@NH/〠ꏰ?@1P:ةE@91P怐멚K@1PNQ@E1P򀐩W@1PR@@@A@A@A@ABC@@۠+mod_opp_r_z @SSSo/  @.S4h3j@2ϰ6A?@Ӱ:@NH//)(H۰B@NH/7$@1P27V@@@!A@#A@%A@ABC@@,mod_opp_r_nz @SޠSڠSiZJE@hTnm@l pAy@tx@ NH/mgf󀩚@(NH/ub@1Ppu@s1P؀@:NH/䇀t@@@kA@mA@oAg@ABC@@_+mod_sign_nz @T(T$S@U춐@SAö@[© @jNH/䷀Щcʩ@1PC@xNH/ŀ@1POŐ@@@Ac@AX@A@ABC@@(mod_sign @TlThT7ؠ@V02@뗰A랰N@31P~T@NH/Z@N1P`@E1Pܐ@@@A@A@A@ABC@@䠠,mod_sign_mul @TTTx8)@7W=q<s@;ذ?AH@v1P,N@&1P]I@NH/A;::@@@@@(div_same @TܠTؠTgXHC@fXl@hlAuo@i1P峀]]a@@@HA@JA@LAD@ABC@@<(mod_same @UUTРql@Yɶ@.A1@@NH/區@@@qA%@sA@uAm@ABC@@e)div_small @U.U*T@Z@@1P,̐B@f1P-BAhϩ@1Pݐ@@@@@)mod_small @U_U[U*۠ˠ@[#%@08@%1P,B?@1P-BA왰I@NH/@@@@@Ǡ'div_0_l @UUU[ @\ T@칰 A)켰#l@1Pg11@@@A@A@A@ABC@@'mod_0_l @UUUD5% @C]I}@EIARL@NH/AZ:Z@@@%A@'A@)A!@ABC@@'div_1_r @UUޠUm^NI@l^rm@g1P汀A`A@@@HA@JA@LAD@ABC@@<'mod_1_r @VVUРql@_ɩ)@8NH/慀A@@@jA@lA@nAf@ABC@@^'div_1_l @V'V#U@`@@R1P-AS@1PȐ@@@@@'mod_1_l @VJVFVՠƠ@a@@u1P-ƐAvݩ&@NH/Ҁϐ@@@@@'div_mul @VmViV8٠@b13@혰A훰K@1PFQ@1P] @@@A@A@AB@@Ӡ'mod_mul @VVVg'@&c ,` +b@ *ǰ.A7ʰ1z@NH/&@ 1P]: & % %E@@@ A@ A@ A @ABC@@ 0div_unique_exact @V͠VɠVXI94@Wd ] \!q@ ^bBk@fB@ F1P]i U Tn W@h1P粀CP@@@ GA@ IA@ KA C@ABC@@ ;&mod_le @WWVϠpk@e ȶ ʶ@@1P,B@@ 91P- @1P,@LNH/癀 @@@@@ k'div_pos @W4W0V@f  @ @1P,ΐB@@ i1P- @ 1P,ܩ@1P Ð@@@@@ +div_str_pos @WdW`W/Р@g ( *@ 5=@ 1P-AD@ 11P,ABL@ 1P-R@1PM  @@@@@ Р-div_small_iff @WWWd$@#h )] (_@ 'İ+A4 @#iffС)ΰ5~@/1Py $ #C  @ y1P,Q 2@ 1P- 8 7 @ 1P- A B@ 1P, Hg@@@ 2A @ 4A @ 6A .@ABC@@ &-mod_small_iff @WWWzk[V@yi  ~@ }AV!@0NH/} w v w † ׀@ 1P, @ =1P-   瀠@ G1P-  @ 1P, @@@ A 9@ A .@ A @ABC@@ y&div_lt @XBX>X ͠@j  @@ o1P-ܐB@@ w1P- ĩ%@ }1P-+@1P&   Đ@@@@@ +div_le_mono @XrXnX=ޠ@k 6 8!c;@J@ 1P-A@R@ ?1P,  X@ E1P,^@1PY  d@1P_  @@@ A @A A @ A @ A @ABC@@ ꠠ*mul_div_le @XXX~>/@=l Cw By@@ 1P-MA@ |1P,@ ,1P]O :@L1P門 A @ A@@@ ,A @A -A @ /A @ 1A )@ABC@@ !*mul_div_ge @XXXufVQ@tm z y@@ 1P-A@ 1P, l@ c1P]ꆀ q@1P̀ x w@@@ cA @A dA @ fA @ hA `@ABC@@ X/mul_succ_div_gt @Y!YX@n 嶐 @@ N1P-A@ U1P- @ 1P]꽀  @$succ1\w2@1P   @@@ A U@A A M@ A K@ A @ABC@@ /mul_succ_div_lt @Y_Y[Y*۠ˠ@o # %@4@ 1P-A;@ 1P-A@ 1P] 橚G@>1\woM@1PH   @@@ A @A A @ A @ A @ABC@@ Ӡ)div_exact @YYYg'@&p ,` +b@ *ǰ.A7ΰ5 ~@ 1P]8 #@51P * )ܰC@NH/8 2 1Q@@@ A @ A @ A @ABC@@ 2div_lt_upper_bound @Y٠YՠYdUE@@cq i h @@ 1P-uB@@ 1P- Q@ U1P]x d c@ 1P-@{1Pŀ V c p@@@@@ H2div_le_upper_bound @ZZ Yܠ}x@r ն ׶Dٶ@@ @1P-B@@ 1P, @ 1P]밀  @ 1P,@1P   @@@ A G@A A ?@ A =@ A @ABC@@ 2div_le_lower_bound @ZQZMZܠ͠@s  @(@ 1P-B@0@ 1P,6@ 1P]   ϩ<@ )1P, ⩚B@1P=  ې@@@ A @ A @ A @ABC@@ Ơ/div_le_compat_l @ZZZZ @t!pTV X@g@ T1P,,C@ ks@ 1P-8 y@ f1P,  @ l1P,@61P뀀  +@<1P놀  $@@@@@ 'mod_add @ZҠZΠZ]N>9@\u b a`@ bfAoi@NH/^@ Y1P&  Q@ U1P]x d c c@#NH/p ] i@@@ TA @ VA @ XA P@ABC@@ H'div_add @[[ Zܠ}x@v ն ׶ٶ@ >AA@1P쀠@ 1P&J @ 1P]췀   @ 1P&V @1P   @@@ A M@ A B@ A @ABC@@ )div_add_l @[V[R[!Ҡ @w  @ 怐B6@1P1<@ 1P&폀B@ 1P]    詚H@ 1P&훀 ᩚN@1PI  @@@ A @ A @ A @ABC@@ Ҡ0div_mul_cancel_r @[[[f&@%x+_*a)c@+Ȱ/B8@3а7?Ұ9@31P}@1P]B .@%1P]H '4@E1P쏀  -@@@$A @&A @(A @ABC@@0div_mul_cancel_l @[[ݠ[l]MH@kyqpo@quB~@y}e@y1PÀ@e1P]툀t Z@k1P]펀z m@1PՀ f s@@@jA@lA@nAf@ABC@@^/mul_mod_distr_l @\'\#[@z붐@TBĶ@\˩^ũ@mNH/캀@1P]΀ @1P]Ԁ  @1P]ڀƩ&@NH/Ҁ  @@@Aj@A_@A@ABC@@/mul_mod_distr_r @\s\o\>ߠ@{79;@B@ Z@NH/`@1P] f@1P]   l@1P]&r@NH/  @@@A@A@A@ABC@@'mod_mod @\\\J;+&@I|O!n@NRA[U@NH/J@NH/PJII@ NH/VPO@@@@@(/mul_mod_idemp_l @\\\|m]X@{}4@A!@0NH/}@n1P]@<NH/퉀v@BNH/폀@1P]@@@yA-@{A"@}Au@ABC@@m/mul_mod_idemp_r @]6]2]@~y@ƀcʐAөfͩ@uNH/€@1P]ր"@NH/΀ǩ(@NH/Ԁ.@1P]耠Ӑ@@@Ar@Ag@A@ABC@@'mul_mod @]{]w]F@ ? AC@ A[@NH/a@1P]g@NH/m@1P]'s@NH/ y@NH/%@@@ A@ A@AB@@/add_mod_idemp_l @]Ġ]]O@0+@N@TS@TXAa[@NH/P@K1P&@NH/\IUVU@NH/b@]1P&Uba@@@LA@NA@PAH@ABC@@@/add_mod_idemp_r @^ ^]Ԡup@AͶ϶LѶ@6A9@HNH/@1P&B@TNH/@ZNH/@1P&T@@@AE@A:@A@ABC@@'add_mod @^N^J^٠ʠ@B@ހ{A~婚.@NH/ڀ4@1P&٩:@NH/怠@@1P&𓀠F@NH/멚L@NH/@@@A@A@AB@@Π'div_div @^^^b "  @ !C'[&]%_@'İ+B4@v@1P-;ΰ5~@/1Py@51P*@;1P@'1P]J)6@@@!A@A"A@$A@&A@ABC@@)rem_mul_r @^ߠ^۠^ j [ K F@ iDonm@o sB|@@1P-c}@%NH/rR@c1P]er@s1P&%@7NH/dq@u1P]𘀠w@CNH/@1P倠v@@@zA.@|A#@~Av@ABC@@n'mod_div @_7_3_     @ E@ŀbɐAҩe̩@1P@zNH/ǀ@@@@@*div_mul_le @_b_^_-  ޠ Π @ F&(*@9@&1P,C@A@1P-@H@51P, N@;1P,T@1P]Z@ 1PU橚`@1P[f@1P] !@@@@@䠠+Private_DivpA(Quot2Divx A#div @_Z@$quot/___@@@@!A)ZDivTrunc(Abstract'Integer'Numbers#Coq@@9T_ؠ_Ԡ_@@B!C@_-@A@)ZDivTrunc(Abstract'Integer'Numbers#Coq@)ZQuotProp_>@A@@@A!B_D@A@@@4!__@A@@@@@AA@@A@&modulo @_@#rem.#``_@@Ҷ@ӐR@ 9``_E;+&@@@@@"&div_wd @_@'quot_wd>|`2`._@)Morphisms'Classes#Coq@@&ProperL@@  @*respectful%WO? @  h  jj @$quot1\u@(`Y`U`$wgb@@@@@^&mod_wd @`@&rem_wdw`n`j`9@<@ /@ 0 00 2@ 3 33 5 5 B@#rem1P;Q@ ,\5```O@@@@@'div_mod @`2@(quot_rem E```d@!a Z!b ]@%Logic$Initn@#notШʰ1A :Ͱ4C ~@#add1P&Ҁ @#mul1P]@B @v1\ꀠ @Q1P; @<q`Ԡ`Р`@@@@@٠-mod_bound_pos @`@-rem_bound_pos![```@P N @ @"le1P, ~3@ @"lt1P- ;\@#andЖw@ @1P,  @1P;〠D_ @1P- @1P; jX@;%a#a`KA1,@@@@@(@@@@첐@&NZQuot A.div_mod_unique @a=a9ae[KF@%NZDiv&NatInt'Numbers#Coq@)NZDivPropwb'@@@A@@@J!C%NZDiv&NatInt'Numbers#Coq@m@A@@I!B@@ @@#div Πd@A@ ?+@@&modulo ?+de@A@AB@A@@H!A)@@ @@&modulo d@@A@A W-@@&shiftl W-d@@A@ W3@ @&shiftr W3d@@A@A j@@&square jd@@A@^@@'testbit^d@@A@ g@@'compare gd@@A@ABCD9_@@!t9_J@@A@9f@#@"eq9f^@@A@9gt@(@"le9gth@@A@AB9g@,@"lt9gh@@A@9@2@#abs9d@@A@A9@6@ 9鸞d@@A@9P@:@#div9Pd@@A@ABCE9=@>@#eqb9=d@@A@9@E@#gcd9d@@A@A98@I@#leb98d@@A@9@N@#lor9d@@A@AB9U@R@#ltb9Ud@@A@9k@X@#max9kd@@A@A9@\@#min9d@@A@9@a@09۠d@@A@ABCF9b@d@#odd9bd@@A@9!@l@#one9!T@@A@A9R@p@#opp9Rd@@A@9@u@#pow9d@@A@AB9@y@9d@@A@9 I@~@#sgn9 Id@@A@A9 G@@#sub9 Gd@@A@9 @@#two9 T@@A@ABC9s\@@$div29s\d@@A@9u@@$even9ud@@A@A9>@@$land9>d@@A@9Q @@$log29Q d@@A@AB9^@@$lxor9^d@@A@9@@$pred9d@@A@A9T@@9Td@@A@9@@$sqrt9d@@A@A9@@$succ9r@@A@9@@$zero9T@@A@:f5@@%ldiff:f5d@@A@ABCDEFG@A@@!b "q1 "q2 "r1 "r2 @%Logic$Init#Coq@@#andЖw@ 6@"le1P, B >@"lt1P-BE@! L@1P, B S@1P-F@ ]@#add1P& d@#mul1P]GD m@1P& s@1P]-EC%Logic$Init#Coq@@#andЖw@ܰC!3ްE"@@@ %'A*Equalities*Structures#Coq@AviA)Morphisms'Classes#Coq@@AAۀߠK @Aۓό^ @A݋X_A/RelationClasses'Classes#Coq@@ABC@@AA@@A@*div_unique @bbb@A!a  !q Ķ!r Ƕ@ @1P, D@ @1P,  @1P-@A @1P&D @1P]O @{1\\@@@vAa@xA_@AB@@W*mod_unique @cJcFcrhXS @BT   S R @ '@1P, D@ 3@1P, 穚 9@1P-Ӷ@驚 B@1P& H@1P]ԩ䩚 P@z1P;^@@@A@A@AB@@0div_unique_exact @cccfà^K=$@IC cZ e g@ v@@1P, ;C@ ~@@1P- C @װ> @#1P]A!߰F# @ 1\쀠<@@@A@A@AB@@砠(div_same @cڠc֠c|c@D @ @s1P- vA q @61\nn c@@@1A@3A@AB@@(mod_same @ddcР-#Ƞ@E Ͷ@ @1P- A5 @1P; @@@\AT@^AI@`AG@ABC@@?)div_small @d2d.cZP@;Ԡ@F<  @䀠 @1P, ԐB @1P-BApש @1\} @@@A@A@A@ABC@@z)mod_small @dmdid8{v0@Gw 5, 7@ J@1P, B Q@1P-BA [@1P;i@@@A@A@A@ABC@@'div_0_l @dddsРƠkXJ1@VH p@ @A1P- DAذ? @1\倠 M< M@@@@@ܠ'mod_0_l @dϠdˠdݠؠqX@}I @ @h1P- kAf @1P; tc t@@@@@'div_1_r @ddd@J @ @1P, A& @R1\3 @@@MA8@OA6@AB@@.'mod_1_r @e!edI?/*Ѡà@K+ @ @1P, AQ@+1P;  Ɛ@@@xAp@zAe@|Ac@ABC@@['div_1_l @eNeJevl\W@LX@%@1P- ΐA~婚.@1\  @@@@@'mod_1_l @eueqe@~8%@#M=@L@1P- A U@1P;c   @@@@@'div_mul @eeegĠ_L>%@JNd[f@u@?1P,:B@}@?1P-B1հ<@1\†@'1P]E%%@@@A@A@@ᠠ'mod_mul @eԠeРeݠv]@O@@w1P,rB@@w1P-zi t@1P;ˀ@_1P]}]OO@@@:A%@f j`PK@QL  @@1P,B@#@1P-ש)@1P,/@1\@@@A@AA@A@A@ABC@@+div_str_pos @f~fzfIA. @,RF=H@0[@1P- Ab@,1P,ABj@,1P-/p@1\̀$@@@A@A@A@ABC@@ʠ-div_small_iff @fff۠ˠƠm_F@kS|@@`1P,[B@@`1P-cR(@#iffС)d@)1\ G9r@u1P-M?@@@*A@A@@ -mod_small_iff @fffǠ$ @TĶƶ@@1P,B@@1P-?9@1P;u@1P-{@@@fA^@hAS@jAQ@ABC@@I/div_str_pos_iff @g<g8gdZJEޠ@UF@@1P,ڐB@@1P-ѩ'@1P-쩚-@1\3@1P,͐@@@@@&div_lt @gzgvgE=*@(VB9D@S@1P-B@[@1P-a@#1P-g@1\Ā@@@A@AA@A@A@ABC@@à+div_le_mono @gggޠԠĠyfX?@dW~u!c@@T1P-WA@s@h1P,c8@n1P,>0@t1P,@,1\ =<@21\PB@@@.A&@A/A@1A@3A@ABC@@*mul_div_le @hhgР-#Ƞ@XͶ϶@@1P,B@@1P-@1P,@1P]~@t1\U@@@oAg@qA`@sAZ@ABC@@R/mul_succ_div_gt @hEhAhmcSN@YO @@1P,B@&@1P-ک,@1P-Ʃ2@1P]쀠8@$succ1\wa?@1\ː@@@A@AA@A@A@ABC@@)div_exact @hhhYQ>0@A )@ @A '@ABC@@ /mul_mod_distr_r @llkݠ : 0   ՠ    @ e ڶ ܶ\޶@@ 1P,C@@ 1P- @@ 1P- T @ .1P; @ 1P]Ā  @ 1P]ʀ  @ 1P]Ѐ@ F1P;*   @@@ A @ A @ A ~@ABC@@ v'mod_mod @lilel4   w r ,   @ f s1!n4@C@ 1P,B@K@ 1P-  S@ }1P;aY@ 1P;g   婚_@ 1P;m  @@@@@ /mul_mod_idemp_l @lllq Π Ġ   i V H /@ Tg n ep?r@@ K1P,FC@@ S1P,N @@ R1P-U  O@ 1P;@ :1P]X@ 1P; Q > 1 >@ 1P;@ L1P]j ] = J@@@ 'A @ )A @ +A @ABC@@ /mul_mod_idemp_r @lllȠ %       @ h Ŷ Ƕɶ@@ 1P,C@@ 1P, l@@ 1P- s? @ 1P;@ 1P] @ %1P;    @ +1P;@ 1P]   @@@ ~A v@ A k@ A i@ABC@@ a'mul_mod @mTmPm | r b ]    @ i ^  @/@ 1P,C@7@ 1P, ö@>@ 1P- ʩ F@ p1P;TL@ 1P]   橚R@ |1P;`X@ 1P]^@ 1P;l  d@ 1P;r   @@@ A @ A @AB@@ /add_mod_idemp_l @mmmz נ ͠   r _ Q 8@ ]j w nyH{@@ T1P,OC@@ \1P,W @@ [1P-^ % X@ 1P;@ J1P&@ 1P; Z G : G@ 1P;@ \1P&  f F S@@@ 0A (@ 2A @ 4A @ABC@@ /add_mod_idemp_r @nnmѠ.$ ɠ   @ k ζ жҶ@@ 1P,C@@ 1P, u@@ 1P- |H @"1P;@ 1P&Q @.1P;    @41P;@ 1P&c   @@@ A @ A t@ A r@ABC@@ j'add_mod @n]nYn({kf    @ l g% ')@8@ 1P,C@@@ 1P, ̶@G@ 1P-  өO@y1P;]U@ 1P&   署[@1P;ia@ 1P&g@1P;u  m@1P;{   @@@ A @ A @AB@@ Š'div_div @nnn֠Ơ { h Z A@ fm  w@@ ]1P,XC@@ ]1P-` '@@ d1P-g .a@&1\@,1\  ] = J@21\ c@ X1P]v I V@@@ 4A ,@A 5A $@ 7A "@ 9A @ABC@@ )mod_mul_r @o on֠3) Π   @ n Ӷ նU׶@@ 1P,C@@ 1P- z@@ 1P- M@'1P;  @ 1P]   @ 1P&\@91P;  @ 1P]π @E1P;)!@1\~   @@@ A @ A @ A @ABC@@ {*div_mul_le @onojo9|w1 @o x6 -8:@I@ 1P,C@Q@ 1P- ݶ@X@ "1P, 䩚^@ (1P,d@ 1P] j@1\ǀ  p@1\̀v@ 1P]0  # @@@ A @ A @ A @ABC@@ Р+mod_divides @oàooѠ̠seL@qp  @@ f1P,aB@@ f1P-i X g@1P; J <u ;@"ex @0y I@ ^1P]| \A@@@ ;A 3@A A )@ @A '@ BA1@D V U T@@ABCD@@ &@@@@@A  BC@@@@@&rem_eq @p poH>.)@G@!a嶐!b@%Logic$Init#Coq@@#notШWAǩZ @1P;CB@#sub1P @#mul1P]Ԁ @ 1\}@@@ %'A*Equalities*Structures#Coq@A݋X_A/RelationClasses'Classes#Coq@@A@@n+rem_opp_opp @pypupD@AY=X?@W AW@1P;e]@1PSc@1PXi@1P o@-1P;}ed@@@OAviA)Morphisms'Classes#Coq@@YAۓό^ @]AU@ABC@@*quot_opp_l @pƠp pԠ@B@XAa[@1\@1PK@1PQ@1\@@@AG@A?@A@ABC@@*quot_opp_r @qppΠ+! @*CǶɶ@တ.A1@1\>ש@#1Pܩ@)1P@1\P@@@A@A|@A@ABC@@5,quot_opp_opp @q@q<q h^NI@gD @kҐA۩nթ@1\{$@`1Pŀ*@f1Pˀ0@1\&%@@@A@A@A @ABC@@r/quot_rem_unique @q}qyqH@EZA"q1D"q2G"r1J"r2M@%Logic$Init#Coq@@"or @%Logic$Init#Coq@@#andЖw@z@"le1P,@B@"lt1P-BE @ 1P-EB@1P,B]@C8@-1P,l@+1P-FI@61P- @D1P,@ ~@#add1P&@1P]G"D@1P&)@1P]Eө@#andЖw@ =: ? @@@Az@Ar@A@ABC@@++quot_unique @r6r2r^TD?@]F!q!r@@1P,֐D@@1P,#@1P-T@ |y,@e1P&2@1P]쀠Vc( X:@#1\l@@@@@v*rem_unique @rr}rL@GaE`GKIJK@Z@1P,D@f@1P,+[l@1P-a@ Ű,©u@1P&Ȁ{@b1P]5q Ӱ:@A1P;֐@@@@@)quot_same @rʠrƠrؠ@H@ ZAc ]@1\O@@@A7@A/@A@ABC@@蠠(rem_same @rrr@I@π A @1P;݀@@@A`@AX@A@ABC@@*quot_small @ssrD:*%@CJඐ@@{1P,B@z1P-BA V@1\cː@@@@@B)rem_small @sMsIsuk[V@tK-,@&@1P,B-@1P-BA 7@1P;E-,-@@@@@s(quot_0_l @s~szsI@L^B@Z A Z@C1\O@@@:A@A6@ABC@@'rem_0_l @sssrϠŠ@Mk@ а7A@ Ӱ:@A1P;HxH@@@cA@eA @gA_@ABC@@Š(quot_1_r @sРs̠sޠ@N [@1\ANA@@@A7@A/@A@ABC@@蠠'rem_1_r @sss@O ~@1P;ՀAq@@@AY@AQ@A@ABC@@ (quot_1_l @tts=3#@%@= A =@1P;K3C@1PĀ8I@1P;W?>@@@)A@+A@-A%@ABC@@'rem_abs @vvva@\vZu\@t (A1 İ+t@21P;z@1Pp@1Pu@1P@J1P;@@@lA@nA@pAh@ABC@@Π*quot_abs_l @v٠vՠv@]@kAtn@1\@71P>@1P]}@1P@1\,Đ@@@Aa@AA@AZ@A@ABC@@*quot_abs_r @wwvF<,'@E^ⶐ@IAL@1\Y򩚠 @|1P @1P]€ @<1P> @1\q  @@@A@A@A@ABC@@V(quot_abs @waw]w,oj@_A %@ '@?A ?@(1\ E@1Pƀ; K@1P̀@ Q@1PҀ W@@1\ML@@@7A@9A@;A3@ABC@@-rem_bound_abs @wwwo̠ @` h j@ϰ6A ? @1P- @1P @J1P; @ 1P@@@rA#@tA@vAn@ABC@@Ԡ&rem_le @wߠw۠w@a  @ @:1P, yB@ @:1P-  @H1P, @1P;ր@@@@@(quot_pos @xx wڠ7-@6b Ӷ ն@ @j1P, B@ @j1P- ᩚ @x1P,  @1\U)@@@@@4,quot_str_pos @x?x;x g]MH@fc!!@!@1P- ݐA!@1P,AB!'@1P- 쩚!-@1\#"@@@@@i.quot_small_iff @xtxpx?}@dT!8S!:@RA!@#iffС)!Y@B1\ON!!_@1P-!e@1P怐[!k@1P쀐`@@@KA@MA@OAG@ABC@@-rem_small_iff @xxx֠Ơ@e!|!~@JA!SDQ!@X1P;!@1P-!@ 1P'!@&1P-@@@A=@A5@A@ABC@@'quot_lt @xxxĠ!@ f!!@!@L1P-!B@!@T1P-!˩!@Z1P-!@1\ ?@@@@@,quot_le_mono @y)y%xQG72@Pg ! !﶐!c!@"@1P-!ƐA@" @1P,:"@1P,"@1\ r9 "@1\ xL @@@A@AA?@A@ A@ABC@@_+mul_quot_le @yjyfy5xs@h J". I"0@"?@1P,"B@ P <" †"Q@1P,""W@ >1P]  M"]@F1\  S"c@1P,"i@ P1P] # _"o@X1\ ̀ e@@@ OA @ QA@ SA K@ABC@@+mul_quot_ge @yyyڠʠ@i " "@"@1P,B"W@ V "^4"@)1P,ԩ"@ 1P] c "@1\  "@;1P,"@ 1P] u "@1\  "@@@ A R@ A J@ A @ABC@@0mul_succ_quot_gt @zz y٠6,@5j "Ҷ "Զ@"@i1P,"B@"@i1P-" ਗ਼"@o1P-""@ 1P]  "@$succ1\w &#@1\ a5 @@@@@@0mul_pred_quot_lt @zKzGzsiYT@rk +# *#@# @1P,B"@#(@1P-" #.@1P-#4@ 1P]  *#:@$pred1\ #A@*1\ r 7r@@@ "A @A #Ae@ %A @ 'A @ABC@@0mul_pred_quot_gt @zzz[@l p#T o#V@#e@1P,#*B@#m@1P- b#2#s@1P-#y@ `1P] 3 o#@E1\ c#@n1\ † {@@@ fA @A gA@ iA @ kA c@ABC@@ɠ0mul_succ_quot_lt @zԠzРz@m # #@#@ /1P,B#o@#@ /1P- #v#@ 51P-#@ 1P] w #@1\w 뀐#@1\ & @@@ A [@A A@ A T@ A @ABC@@ *quot_exact @{{z@6&!@?n #ܶ #޶@ CA#J ꩚#@ 1P]  署$@1\ ]  X$@1P;   #͐@@@ A @ A @ A @ABC@@J3quot_lt_upper_bound @{U{Q{ }sc^@|o 5$ 4$ $@$,@ 1P,#C@$4@ 1P-# *@$;@ 1P- _$A@ (1P]  r 7$G@ 1P-$M@61\   q ~@@@@@3quot_le_upper_bound @{{{_@p t$X s$Z ^$\@$k@ 1P-$0B@$s@ 1P, $y@ `1P] 3 o n$@ 1P,$@n1\ †   {@@@ fA @A gA@ iA @ kA c@ABC@@ɠ3quot_le_lower_bound @{Ԡ{Р{@q $ 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