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S@@@@@&shiftr @d@}@= S@@B S@F S@@@@@3$land @d@@U S@@Z S@^ S@@@J#lor @d@@l S@@q S@u S@/@@a%ldiff @d@@ S@@ S@ S@F@@x$lxor @d@@ S@@ S@ S@]@@$div2 @d@@ S@ S@@@@@*testbit_wd @@)Morphisms'Classes@&ProperL@@ S@@ SΩ@*respectful%WO?@ S@$@ Sޚ(@"eq Z/@ S隠3@  Z%Logic@ @A@ a@@@ %'A*Equalities*Structures#Coq@AviAL'Classes#Coq@@A@@-testbit_odd_0 @@!ab@" S/i@3ao@#add 㧀v@#mul ހ|@#two 怐A@#one $@$zero CA@@@@@8.testbit_even_0 @@9@Y SfU@ja@0 ހ@/ .@( jB@@@@@_0testbit_odd_succ @@`@ S!n@ S@@"le [w@L V@a@q 㧀@p ހ@o 怐C@n $@$succ B@a@@@@@1testbit_even_succ @@ @ SL@ S@@J [w@ ة#@a)@ ހ.@ C3@> =8@a;@@@@@堠-testbit_neg_r @@暠F@ SK@  S@Q@"lt [֚W@ $^@(aa@@@@@ +shiftr_spec @@ l@, Sq@1 S!mx@8 S@~@ [w@ P?@Ta@}6D@aa@. 㧀@@@@@K0shiftl_spec_high @@L@l S욠@q S@@v S@@ [w@: D@@ [wʩ@a@y}0EE멚@a@#sub JR@@@@@/shiftl_spec_low @@@ S1@ S@ S@@ [ ϰ @a@}0`@@@@@)land_spec @@@ S!b$@ Sd)@ S婚0@a6@ 2 9@$andb=B@ aXƩH@aR̐@@@@@(lor_spec @@W@ S:\@ Sa@! S.h@2an@ q񩚠(@#orbz@Da8@Ia7@@@@@,*ldiff_spec @@-@M Sp@R SҚ@W SdS@ha@ )'n@uaie@$negb@ao@@@@@d)lxor_spec @@e@ S@ S @ S@a@  R_@$xorbȀ@a@a@@@@@)div2_spec @@@ S@ Z@ g_ @}6@ $@@@@@&square @d@ @ S$@ S@@@@@+square_spec @@#2@ S7@t Z=@'B@q ހː@@@@@@ =@@@@ S@Q@M S @A@A Z@S@4 Z @A@ [w@V@l [w @A@AB [@X@ [ @A@ @\@  @A@A @^@  @A@ S@a@ Sd@@A@ABC @@d@ @ @A@ @i@  @A@A ;@k@ ; @A@ @n@ d@@A@AB X@q@ X @A@ n@u@ n @A@A @w@g  @A@ @z@  @A@ABCD e@|@  e (@A@ $@@ $ @A@A U@@ U @A@ @@ 8  -@A@AB @@ d@@A@ L@@ L "@A@A J@@ J !@A@ @@   !@A@ABC g_@@ g_d@@A@ x@@+ x <@A@A 2 @@ 2 d@@A@ E@@  E >@A@AB R@@ Rd@@A@ @@'  2@A@A W@@( Wd@@A@ @@ G  G@A@ABC @@B  7@A@ @@Y  8@A@A )@@ )d@@A@v@@vd@@A@AB}0@@d}0d@@A@}6@@Q}6d@@A@A@@d@@A@a@@ad@@A@1@@1 M@A@ABCDEFG@A!B@'eq_refl @/RelationClasses'Classes#Coq@@5Equivalence_Reflexive@@#max<>d@@A@<@@#min<̠d@@A@ABC<@!@#mul<d@@A@<@(@#one@$zero ɠT@@A@ABCDE@A@&NZBase&NatInt'Numbers#Coq@*NZBasePropbl@@@A@@@@"NZ&NZBase&NatInt'Numbers#Coq@t@@’H@|@!t’HJ@@A@A™@@"eq™Ġ^@@A@š=@ @"leš=h@@A@ABšL@@"ltšLh@@A@"m@@#add"md@@A@A34@@#max34d@@A@3@@#min3 d@@A@ABC4@!@#mul4d@@A@6@'@#one6T@@A@A=@+@#sub=d@@A@>@1@#two>T@@A@AI@5@$predId@@A@G@:@$succGr@@A@@?@$zeroT@@A@ABCDE@A@@M~@]@@@d@!tРJ@@A@A L@@"eq L^@@A@r@ @#onerT@@A@AB4@@#two4T@@A@b@@$predbѠd@@A@F@@$succFr@@A@]l@@$zero]lT@@A@ABCD@A@@L.+*@A@4*BackportEq@@@A@@@@ %'A*Equalities*StructuresA݋X_A@A@@AA@@A@&eq_sym @&@5Equivalence_Symmetric. 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S E@D SfN@H ZT@ Y@ 1`@Z Zp@@@@@g1central_induction @ >7ڠӠvo x#@F!A@@ SA$A_wd@&ProperL@@ S @*respectful%WO?@ S@ ZB@ S@q@@ SԠE@m @ SF@@@@@̠'add_0_r @uf ?8۠Ԡwpaݠ@@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@Fd@c Si@c Zo@D 㧀~t@ @@@@@y@ABC@@AA@@A@*add_succ_r @:*XQ,%v@A@ S@ S@ Z@ 㧀@e 署@j @ 㧀ѐ@@M@@J-add_succ_comm @qb;4נРsl]٠ܠˠ@Bɚ@ Sǚ@ S@ Z@ 㧀@ < @ 㧀@ A@@@@(add_comm @ȠLCߠ{I1 C6(#@C.@- S3@2 S8@2 Z>@ 㧀NC@ 㧀K@@@@̠'add_1_l @~!YRߠl[~qc^M?@JDKi@h Sn@h Zt@I 㧀y@; $~@- @@ @@'add_1_r @>. \U0)z@E@ S@ Z@ 㧀@v $@h @@E@@B)add_assoc @yiZ3,ϠȠkdUѠ٠Ԡà@F@ S@ S!p@ S@ Z@ 㧀@ 㧀  @ 㧀 @ 㧀@@@@,add_cancel_l @ǠKBޠzH0B5'"@G -@ , S  2@ 1 SN 7@ 6 SX >@ 8 Z D@ 㧀S  J@ 㧀R O@ I Zސ@@@@ؠ,add_cancel_r @ -&ɠ e^xg}ojYK@VHW u@ t SU z@ y S @ ~ S @  Z @a 㧀Q @g 㧀 @  Z&@@#@@ ,add_shuffle0 @ W G 8۠Ҡun IB3ؠҠŠ@I @  S @  Sޚ @  S @  Z @ 㧀 @ 㧀g橚 @ 㧀 @ 㧀W@@o@@l,add_shuffle1 @    ' ]V$ @J뚠 @  S隠 @  S* @  S!q @  S @  Z %@ 㧀 +@ 㧀𩚠 1@ 㧀A 6@  㧀 <@ 㧀© A@ 㧀@@@@ʠ,add_shuffle2 @     |  WPݠjY|oa\K=@HKI g@ f SG l@ k S q@ p S^ v@ u S {@ u Z @V 㧀 @\ 㧀\ @a 㧀 @f 㧀 @l 㧀 @r 㧀,@@)@@&,add_shuffle3 @ ] M >  ؠ { t  OH9ޠƠؠˠ@L @  S @  S䚠 @  S @  Z @ 㧀 @ 㧀 @ 㧀󩚠 @ 㧀]@@u@@r'sub_1_r @    - $ Ǡ  c \*$ @M񚠐 @  S @  Z @ J) @ $ $@ ]@@@@'mul_0_r @  Ԡ Š h _     : 3֠ϠeM<_RD@]@) G@ F S L@ F Z R@ ހa W@  [@ @@@@AA@@A@*mul_succ_r @      < 5 ؠ Ѡ t m  v~@Ac @  Sa @  S @  Z @Y ހ @F Щ @q 㧀 @j ހ@@.@@G(mul_comm @ b R C  ݠ  y     T M >ˠݠР@B @  S @  S @  Z @ ހ婚 @ ހ@@f@@/mul_add_distr_r @   {     T M     v  @Cߚ @  Sݚ @  S @  S @  Z @ ހ @ 㧀& @ 㧀 #@ ހ (@ ހ8@@@@͠/mul_add_distr_l @  ؠ ɠ l c     > 7 ڠ Ӡ Ġ i Q @cVH@aD- K@ J S+ P@ O Sl U@ T S Z@ T Z `@ ( ހ% f@ ; 㧀v k@ @ 㧀 q@ 9 ހ v@ > ހ@@@@)mul_assoc @ 6 &    T M     ( !    @E{ @  Sy @  S @  S @  Z @ v ހs @ | ހĩ @  ހ @  ހN͐@@K@@d'mul_1_l @  o `     9 2 ՠ Π q j [   נ@FĚ @  S @  Z @  ހ @  $@@~@@'mul_1_r @    6 - Р ɠ l e      3  - @+G @  S @  Z @  ހ/ %@  $3@@@@ʠ,mul_shuffle0 @  ՠ Ơ i `     ; 4 נ Р  f N =`SE@^H* H@ G S( M@ L Si R@ Q S W@ Q Z ]@ % ހ c@ + ހq h@ 0 ހ n@ 6 ހ}@@@@,mul_shuffle1 @ .     L E    }      @Is @  Sq @  S @  S @  S @  Z @ s ހ @ y ހ @ ~ ހƩ @  ހ @  ހG @  ހ:@@R@@k,mul_shuffle2 @  v g     @ 9 ܠ ՠ x q b   ޠ@J˚ @  Sɚ @  S  @  S @  S @  Z@  ހ @  ހީ@  ހ @  ހ@  ހ@  ހ@@@@à,mul_shuffle3 @ ޠ Π  b Y     4 - Р ɠ  _ G 6YL>@WK #A@@ S !F@E SbK@J SP@J ZV@  ހ \@ $ ހ la@ ) ހ qg@ / ހې@@@@ %le_wd @'   E >  ڠ } v      @@A&NZBase'NZOrder&NatInt'Numbers#Coq@ ) '@A@'NZOrder&NatInt'Numbers#Coq@+NZOrderProp 8 6@A@@@@"NZ - ,@A@@@@ S@@ S,@ S@@ S7@ Z)@ SA@ Z ꚠ@  [w@@Z@@AA@@A@*lt_le_incl @r    K D    | m   j]O@hA ֚@ S Ԛ@ S@@"lt [ @  [w @@@@@7'le_refl @ŠI@  ܠ  x      F . @B (@' S-@  [w < <@@ 1@@`.lt_succ_diag_r @ޠϠri    D =  ٠ ʠ o W FǠ@C 3Q@P SV@W [ e\@   @@@@@.le_succ_diag_r @ :3 ֠ Ϡ r k      t@D a@~ S@ c [w @ 9  Ð@@@@@/neq_succ_diag_l @J:+ΠŠha    < 5 & ˠ  #@!E @ S @ Z@ i   Ȑ@@ @@젠/neq_succ_diag_r @zj[4- Р ɠ l e V   ҠSF8@QF @ S @ Z 󩚠@   #@@@@@/nlt_succ_diag_l @.%Ƞd]     +  vh@G  @  S 吩@ [@   S (@@@@@L/nle_succ_diag_l @ڠʠ^U0) ̠ Š  [ C 2@H =@< S D@ # [wJ@    X@@@@@|)le_succ_l @ (!Ġ`Y     s b֠@I Om@l S Mr@q S y@ X [w@ .   @ [ @@ @@+le_gt_cases @D4%Ƞb[6/  Š  @J @ S @ S @"or @@  [w ɩ@ [ Ɛ@@ J@@-lt_trichotomy @~n_81Ԡ͠piZ   ֠WJ<@UK Ú@ S @ S:@ [ A@ Z @ [ @@@@@+(lt_asymm @=4נРsl:"w@L @ S !@  S@'@( [ 7 .@/ [ @@ a@@`(lt_trans @ޠϠri D=٠ʠoWFǠ@M 3Q@P S 1V@U Sr[@Z S@a@b [ @g@h [ l@m [  1@@ @@(le_trans @-KD| @N r@ S p@ S@ S@@ [w /@@ [w 5@ [w?@@ 7@@ݠ+lt_strorder @k[L%]VGԠàD7)@BO@+StrictOrder.[@@ S@ [@@ @@ +le_preorder @zSLureW@pP @(PreOrder@@ S@ [w@@ @@9/le_partialorder @ǠKBޠzH0@Q7@,PartialOrder5͛К0@/ S4@. Z8@-通<@ [w[@bU@@@ s@A @E@FAhCV@ABC@@y)lt_compat @U@%lt_wd f@ ̰@]@\ S@b@a S ݩ h@g S@m@l S 蚠q@k Z w@v S 򚠐{@u Z @ [@@@%lt_wd']ɠA1"Š_X3,  @@@@@Р(lt_total @@ HE@ @ S @ S @ [ ͩ@ Z ԩ@ [ ѐJ3@ aǠvg @9ܠՠxqbޠ_RD@@@@@'le_lteq @@+lt_eq_cases X@ ٚ@ S ך@ S@ [wW @  [@  Z@+lt_eq_cases&yˠOF~!L4#@@@@@Z0Private_OrderTacLA'IsTotalT A1 @D@9@W@+Equivalence~@P@O ST@N Z@(eq_equiv7L.'ʠàf_yhܠ@@@@@ @@܀@@ S@ [@,Q^?/ à]V1* @@@@@ΠU @@]ڠ}vg dWI@@@@@J @@R@ܚ@ Sښ@ SS@ [Z @ Z@ [IˠOF~!L4#@@@@@ZE @P@M 0@:@9 S?@> S`F@% [wVM@N []R@L ZbC )"ŠaZtcנ@@@@@@@@@"A@#TacGA @1!OH#  @@D!P)OrdersTac*Structures#Coq@rk@@@A@@C!O@@&@ @!t&J@@A@A&a@@"eq&a^@@A@&@ @"le&ڠh@@A@AB&@@"lt&h@@A@&̌@@#one&̌T@@A@A&̔I@@#two&̔IT@@A@&H@@$pred&Hd@@A@&؝[@"@$succ&؝[r@@A@&C@'@$zero&CT@@A@ABCDE@A@G,MakeOrderTacBo?@A@@@BONR@@@A@@AEUH@@@N@!tJ@@A@A$:@@"eq$:^@@A@$@ @"le$h@@A@$@@"lt$ h@@A@ABC@A@+*OrderFacts.#@A@@s@6 @  S@  Z@@@@AA@@A@ @ӠàWN)"ŠT<+]VP5@Af<@; SA@  [w@@D@@0)lt_irrefl @|WPݠjYڠ͠Р~c@Bj@i SBq@r [D@@t@@`g @0 NG"  @CÚ@ S@ S@@ Z@ Zn@@@@*le_antisym @iYJ#[TEҠB5'8(@9D@ S@ S@@ [w@@ [w@ Z @@@@נ @+"ŠaZ(sevf1*$ @wE:@ S8@ S@@ Z-$@ Z@@@@@*interp_ord @!o)OrdersTac3@#ordȠ@ @@@@@@@@@@@D@F@E S@K@J SYP@J ZT@U [X@7 [w@*(@^@] S@c@b Sސ +k= R'6'6'6''+k+7T'+7T'6'ࠒA̠ܠ۠@@"lt\ @@"eq8L@lР@TȠ@@QPO@@A@B@A@xA܀M=.ѠȠkd?8)Π&  נРʠ@@@@@%trans @p`Q*#Ơb[L٠ȠI<.?/@@F"o'@ S@ S~@ S@ @2G:@@2G @2G@)trans_ord-0uGDR̐@@;@@ @@@ S>@ S @ SB@rМA:9@Z0@/ SX5@4 Sњ:@9 S@@@: Z϶@F@@ ZթK@E Zߐ L+k() LL7#'S@$t-&ɠ e^xg۠͠ޠΠq@@@@@a @@ S@ S!@ Sd"@МbCY@Ě@ Sš@ S;@ S@@ [w9@@ [w?@ [wI L+k() NN7#'jtueV/(ˠĠg`Qޠ͠ N A 3D4@@@@@Ǡ @@ S@ S@ S@BМB  @*@ S(@ S @  S@@  [@@  [@  [ L+k() MM7#'Аt۠ˠ_V1*͠Ơ\D3   e^X=@@@@@-+le_lt_trans @wM@L SuR@Q SW@V Sy1@g#nm@d@c Si@h Sn@m S@t@S [w@z@ { [ @  [ L+k() MN7#'4t?/ à]V1*   ɠ @@@@@+lt_le_trans @ۚ@ Sٚ@ SR@ SS@ 1@򚠐@ S𚠐@ Si@ S@@  [g@@ [wm@  [w L+k() NM7#'t']V$  | o arb-& @@@@@%eq_lt @?@ S=@ S@ SA@q/65@V,@+ ST1@0 S͚6@5 S@<@6 Z˶@B@ C [ѩG@ H [ې L+k() ML7#'t%]Vp_  Ӡ Š֠Ơi@@@@@Y%lt_eq @y@x S~@} S@ S]@cO@@ S@ S1@ S@@  [/@@ Z5@  [? L+k() LM7#'`tk[L%]VGԠà D 7 ):*@@@@@%eq_le @@ S@ S~@ S @9]@@ S@ S@ S@@ Z@ @ [w@ [w L+k() NL7#'ĐtϠSJ%P8'   YRL1@@@@@!%le_eq @kA@@ SiF@E S⚠K@J Sm%@+ba@X@W S]@\ Sb@a S@h@G [w@n@h Zs@R [w  L+k() LN7#'(t3#QJ%   @@@@@&eq_neq @VF7ڠѠtm HA2נ / " %٠Ӡ@&G隠@ S皠@ S`@ S@@ Z^@@ Zf@ Z r@@@@@͠&neq_eq @"XQz w j \m](!@nH1@ S/ @  S@ S@ꐩ@ Z@@ Z&@  Z @@@@@*not_neq_eq @֠Ǡja<5ؠѠ gO>   picH@IyO@N SwT@S S@-/^@X Znc@] Z@@@@R)not_ge_lt @#A:ݠ֠yr{   @J@ S@ S@j@x [w@  [-@@@@)not_gt_le @^N?٠|uPI:ߠǠ 7 * -۠@.K񚠐@ S@ S@@  [ܩ@ [wh@@@@@Ƞ)le_neq_lt @zSLu r e WhX#@iL,@ S*@ S@ @ [w@搩@ Z@  [@@@@@ @@@@)@@@@@)@<_neq @ޠΠbY4-Рɠ_G6   @ R#A@@ S!F@E S@L@ M [\$S@M Z@@@@@ &le_neq @1*͠Ơib|k  ߠ @ SXv@u SV{@z S@  [@#andЖw@@n [wg@ Z@@@@@ Ƞ*eq_le_incl @VF7ڠѠtm HA2נ/"@-T@ S@ S@@ Zԩ@ [wX@@@@@ (lt_stepl @yj C<ߠؠ{te bUG@`U@ S@ S@ S@@  [@@ Z@ [@@@@@9(lt_stepr @ǠKBޠzH0@VT*@) SR/@. S˚4@3 S@:@; [ɶ@@@: ZϩE@F [ ِ@@@@@w(le_stepl @#[Tn]ޠѠ@Wh@g Sm@l S r@q S@x@W [w@~@x Z@b [w@@@@@(le_stepr @C3$ǠaZ5.Ġ@XК@ SΚ@ SG@ S@@ [wE@@ ZK@ [w U@@@@@ @pa:3֠Ϡrk\ؠYL>@WYŚ@ SÚ@ S@ S@@ [w@@ [@ [ @@@@@0\ @A8۠Ԡwp >&{@Z @ S%@$ SA*@) S@0@1 [@6@ [wũ;@< [ ϐ@@@@@m+le_antisymm @ܠvQJנ|dSԠǠ@[@^@] S>c@b S@i@H [wy@o@N [w4t@n ZI@@@@@)le_succ_r @4$RK& @ \y@ Sw@ S@ [w@X  @ [w@ Zũ@j @@@@@)lt_succ_l @{k\5.ѠʠmfWӠTG9@R]@ S@ S@@ [@ .@ [@@@@@&,le_le_succ_r @8/Ҡˠng 5 r@^@ S@ S@"@ [w2'@ [w쩚-@ l@@@@@_,lt_lt_succ_r @ݠΠqh C<ߠؠɠnVEƠ@_2P@O S0U@T S@[@\ [k`@a [%f@ @@@@@,succ_lt_mono @&D=٠|u~@`k@ Si@ S@ [@ [@O ߩ@T ސ@@@@@נ,succ_le_mono @eUF|WPAΠ>1#@@WgŚ @  SÚ @  S@ @ [ @ @ @ [ @ [!@ $ǐ@@@5@3@@ABC@@8+lt_ge_cases @ Ơ   J AݠyG/@h !)@!( S !.@!- S!5@6 [E!:@ [wB@@@@@l+le_ge_cases @   ۠ ~ u  PI֠{cRӠƠ@i?!]@!\ S=!b@!a S!i@H [wy!n@M [wv@@@@@+lt_gt_cases @!.!!   L E}  @js!@! Sq!@! Sp!@! Z󠩚!@ [!@ [@@@@@ݠ,eq_decidable @!k![!L     % ]VGԠàD7)@Bk!@! S!@! S)Decidable!@)decidable r!@! 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[w2@. -%2@# [2 @. 2%@. 㧀'@@"@@.add_nonneg_pos @11ՠ1Ơ1i1`10000;04/נ/Р//f/N/=@/9J-'2E@2D S-%2J@2I S@2P@// [w2U@. -d@2[@#\ [2`@/  -o2e@#f [2j@/ 2o@/D 㧀(D@@l@@Ѡ1add_nonneg_nonneg @2/22111M1F0000~0!00 ///@/K-q2@2 S-o2@2 S@2@/y [w2@/I -@2@/ [w2@/T -2@/ [w2@/^ 2@/ 㧀(@@@@,lt_add_pos_l @2y2i2Z1111131,0Ϡ0Ƞ0k0d0U///@/L-2@2 S-2@2 S@2@# [2@/ -2@# [-2@/ 㧀-@@@-&@.@AB@@X,lt_add_pos_r @2222:211Ԡ1͠1p1i1 10000700@0 M-3@3 S-3@3 S@3!@$" [3&@/ .53+@$, [.;31@0 㧀-@@-d@@,le_lt_add_lt @222Ҡ2u2l22111G1@00ܠ0͠0r0Z0I@0EN.33Q@3P S.13V@3U S*r3[@3Z S)H3`@3_ S@3f@0E [w);@3l@$m [3r@0G 㧀-񩚠3w@0L 㧀.,©3}@$~ [)R@@@@@ߠ,lt_le_add_lt @3=3-3222[2T11111/1(1000@0O.3@3 S.}3@3 S*3@3 S)3@3 S@3@$ [)@3@0 [w3@0 㧀.=3@0 㧀L3@$ [)@@@@@*,le_le_add_le @33x3i3 3222B2;1ޠ1נ1z1s1d1 00@0P.ʚ3@3 S.Ț3@3 S+ 3@3 S)ߚ3@3 S@3@0 [w)Ҷ@4@0 [w4 @0 㧀.4@0 㧀4@0 [w)@@@@@u,add_lt_cases @3Ӡ3à33W3N22222)2"1Š111T1<1+@1'Q/43@42 S/48@47 S+T4=@4< S**4B@4A S@4H@%I [4N@1# 㧀*#4S@1( 㧀/c#4Z@%[ ["4_@%` [.@@@@@,add_le_cases @444333=362٠2Ҡ2u2n22 1111w@1sR/a4@4~ S/_4@4 S+4@4 S*v4@4 S@4@1s [w4@1o 㧀*o4@1t 㧀/#󠩚4@1 [w#:4@1 [w/1@@@@@ -add_neg_cases @4k4[4L33333%3222]2V2G11Ԡ1@1S/4@4 S/4@4 S@4@% [4@1 㧀/욠4@1 $44@% [/4@1 4@% [04@1 @@/)@@X-add_pos_cases @4444:413Ԡ3͠3p3i3 32222722@2 T/5@5 S/5@5 S@5!@&" [5&@1 5+@2 㧀0;$52@&3 [57@1 /5<@&= [5A@1 0P@@>@@0add_nonpos_cases @54444|44333W3P222ݠ22j2Y@2UU0C5a@5` S0A5f@5e S@5l@2K [w5r@2G 㧀05v@2  $ʠ5}@2\ [w0B5@2, 5@2f [w05@26 @@/@@0add_nonneg_cases @5L5<5-4Р4Ǡ4j4c43333>373(2͠22@2V05@5 S05@5 S@5@2 [w5@2f 5@2 㧀0ѩ%5@2 [w5@2w 05@2 [w5@2 0@@@@9-le_exists_sub @555x55444Q4J33333s332@2W0ٚ5@5 S0ך5@5 S@6@2 [w1̠6@6 S-$6 @6  S6@6 Z0٩6@2 㧀 ~6@2 [w6$@2 12@@@0W@A0@2*@A2*AA@@0@ABCD@@+mul_lt_pred @55ݠ5Π5q5h5 5444C4<3ߠ3ؠ3ɠ3n@3@-b6K@6J S,86P@6O S176U@6T S156Z@6Y S@6`@6Z Z6f@3 01+16n@'o [6t@3< ހ%6y@3A ހ/16@' [6@3Z 㧀6@3S ހ,`16@3e 㧀6@3^ ހ11Z@@/"@@AA@@A@1mul_lt_mono_pos_l @6Y6I6:5ݠ5Ԡ5w5p55 444K4D453@42A-Κ6@6 S16@6 S16@6 S@6@' [6@3v 116@' [1b6@' [6@3 ހ,6@3 ހ1i@@@1@A1@1b@2@@ABCD@@R1mul_lt_mono_pos_r @6666,6#5Ơ55b5[444444)@4B.7@7 S1횠7 @7  S1뚠7@7 S@7@( [7@3 1ߩ2<7"@(# [17'@(( [7-@3 ހ172@3 ހ11@@/@@1mul_lt_mono_neg_l @666Ԡ6w6n66 555I5B44ޠ4Ϡ4t@4C.h7Q@7P S287V@7U S267[@7Z S@7a@(b [2&7f@4 27m@(n [17r@(s [7x@4@ ހ17}@4E ހ-R@@@@砠1mul_lt_mono_neg_r @7=7-7666[6T55555/5(54@5D.7@7 S27@7 S27@7 S@7@( [2:7@$zero 2Ҡ7@"lt [2H7@ [7@#mul ހ7@ ހ2I@@0V@@44mul_le_mono_nonneg_l @77z7k77666D6=55٠5|5u5f5 @5cE2ʚ7@7 S2Ț7@7 S/ 7@7 S@7@4 [w7@4 3 @8@4 [w-ة8@4 [w8@4 ހ21Y8@4 ހ2@@2G@@~4mul_le_mono_nonpos_l @7Ԡ7Ġ77X7O66666*6#5Ơ555U@5F382@81 S387@86 S/S8<@8; S@8B@5! 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S@:F@+G [:K@6 5Y5l:R@71 [w0':W@76 [w:]@7% ހ+:b@7* ހ5'@@4@@̠1mul_le_mono_pos_r @:"::999@998ܠ8ՠ8x8q88 77@7N5b:@: S5`:@: S1:@: S@:@+ [:@7? 55:@7{ [w0q:@7 [w:@7o ހ5-:@7t ހ5;@@38@@1mul_le_mono_neg_l @:l:\:M99999&98 88^8W8H7@8EO5:@: S5:@: S1뚠:@: S@:@+ [5隠:@7 6:@7 [w0:@7 [w:@7 ހ5:@7 ހĐ@@@@`1mul_le_mono_neg_r @::::::19Ԡ9͠9p9i9 988887@8P5;@; S5;@; S25;@; S@;$@,% [63;)@7 6J;0@8 [w1;5@8 [w;;@8 ހ5ʩ;@@8 ހ5Ɛ@@3@@2mul_lt_mono_nonneg @;::::{::999V9O888ܠ8@8Q6@;^@;] S6>;c@;b S2;h@;g S1U;m@;l S@;s@8R [w;x@8" 5@;~@, [46@;@8d [w;@84 6@;@, [;@, [;@8c ހ)4ة;@8i ހ$4@@@@@ 2mul_le_mono_nonneg @;b;R;C::ݠ::y::999T9M9>8@9;R6;@; S6;@; S2ᚠ;@; S1;@; S@;@8 [w;@8 6_@;@8 [wb@;@8 [w;@8 6p@;@8 [ws;@8 [w;@8 ހa<@8 ހ`@@64@@k+mul_pos_pos @;;;;E;<:ߠ:ؠ:{:t::9999B@9S7<@< S6<$@<# S@<*@-+ [@<5@-6 [<:@8 7I S8=D@=C S@=J@:) [w=O@9 8^@=U@:4 [w=Z@: 8i=_@:> [w=d@: =i@:1 ހ3>@@f@@Ӡ0mul_pos_cancel_l @=)== <<@> S8>@> S@>$@/% [>)@: 989J>0@; [w>5@: >:@; ހ8ɩ>?@; [w>D@: 9S@@ P@@3mul_nonneg_cancel_r @>====="=<<b@>a S9B>g@>f S@>m@/n [>r@; 99>y@;X [w>~@;( >@;K ހ9>@;g [w>@;7 9Q@@ @@,lt_1_mul_pos @>M>=>.=Ѡ=Ƞ=k=d==<<@> S9>@> S@>@/ [>@;} $9ʶ@>@/ [>@;p 9թ>@/ [>@; $>@; ހ4@@@@?(eq_mul_0 @>>>v>>===O=H<<<<@> S9Ӛ>@> S:>@> Z?@; ހ:? @; .]?@?  Z: ?@; ?@? Z:)?@; @@7@@)neq_mul_0 @>ߠ>Ϡ>>c>Z=====5=.<Ѡ<ʠ<<`@<^:?=@?< S:?B@?A S:c" :?M@?G Z:]?R@; :*?Y@?S Z:h?^@< :6?e@?_ Z?k@<3 ހ:{?o@< @@7@@٠+eq_square_0 @?/??>>>M>F====~=!== <@=_:o?@? S:?@? Z?@>>>>">===Z=S=D<@=A`:?@? S:?@? S@?@? Z?@< ހ:皠?@< @:?@? Z:󚠐?@< ?@? Z:s?@< @@@@@ \*eq_mul_0_r @????6?->Р>ɠ>l>e>>====3@=a:򚠐@@@ S:𚠐@@@ S@@@@ Z@!@< ހ;1@%@< @:@-@@' Z:򚠐@2@< @7@@1 Z:@<@< @@@@@ (mul_eq_0 @@e@pY@;1@O@@N S;/@T@@S S;u@[@@U Z@a@=) ހ;q@e@= /@l@@f Z;|@q@= @v@@p Z;@{@=% >>>=@=@^\@<@,@???Z?S>>>>>.>'>=@@@@@ *mul_eq_0_l @@@5k@;@@@ S;@@@ S@@@@ Z@@= ހ;Ț@@=f @;@@@ Z;Ԛ@@=s @@@ Z;T@@=} X@+24pe@@~@o@@ ???H?A>>ݠ>>y>j>@@@@@ P*mul_eq_0_r @A@5k@;ۚ@@@ S;ٚ@@@ S@A@@ ZA @= ހ<A@= @;琩A@A Z;ۚA@= A @A Z;嚠A%@= @324pk@@Р@@d@[?????6?/>Ҡ>ˠ>>a@@@@@ (lt_0_mul @@@@٠@|@s@@???N?G>>>Ԡ>y@>b<8AV@AU S<6A[@AZ S<|Ab@2c [Ag@> Al@>4 ހ<|0$젩Au@2v [Az@>$ <A@2 [A@>. <%A@2 [<A@>: A@2 [<A@>D @@;@@ 5square_lt_mono_nonneg @AZAJA;@ޠ@ՠ@x@q@@ ???L?E?6>@?3c<A@A S<A@A S@A@> [wA@>r <׶@A@2 [<]A@2 [A@> ހ<_<_A@> ހ<<@@@@@ J5square_le_mono_nonneg @AAAA$A@@@Z@S?????|?!@?yd<A@A S<ޚB@B S@B @> [wB@> =@B@> [w<B@> [wB@> ހFB$@> ހE@@@@@ 6square_lt_simpl_nonneg @AAԠAŠAhA_A@@@@:@3?֠?Ϡ??e@?e=$BB@BA S="BG@BF S@BM@?, [wBR@> =`@BX@3Y [B^@?& ހBc@?+ ހ=s=sBi@3j [8>@@@@@ Ӡ6square_le_simpl_nonneg @B)BB AAAGA@@@ܠ@@x@@@?@@f=iB@B S=gB@B S@B@?q [wB@?A =@B@?| [wB@?k ހĩB@?p ހEB@? 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[wi:@1 i?@1{ ހBAsoiO@; [wiT@1 c⩚iY@E [wi^@1 c멛ig@S [wcil@1 iq@] [wciv@1 @@@@@+(le_mul_0 @i6i&@i"Gi@ Si@ S@i@ [wi@1 ހBAi@1 Ҁ΀i@ [wi@2 dAi@ [wdFi@2  怠i@ [wdUi@2 i@ [wi@2% db@@@@@,nlt_square_0 @ii@iH𚠐i@? S8@#notШi@ [i@25 ހAAj@2P @@@@@5square_lt_mono_nonpos @ii@iIj@ Sj@  S@j@  [wBj$@2t @j*@  [ddj0@ [j6@2r ހddj<@2x ހddː@@@@@5square_le_mono_nonpos @ii@iJXjO@W SVjU@] S@j[@G [wBja@2 @jg@S [wddjm@Y [wjs@2 ހdd򩚠jy@2 ހee@@@@@/6square_lt_simpl_nonpos @j:j*@j&Kj@ Sj@ S@j@ [wAj@2 @j@ [j@2 ހe9e9j@2 ހe>e>j@ [eEe5@@@@@l6square_le_simpl_nonpos @jwjg@jcLҚj@! SКj@ S@j@ [wAj@3+ @j@ [wj@3# ހevevj@3) ހe{e{j@ [weer@@@@@,lt_1_mul_neg @jj@jMk@ S k @ S@k@ [Bk@jj Uk@js $@k$@ [ek)@3y k.@  [k3@#one $k9@3u ހeeȐ@@@RAJ@TAB@VA@@ABC@@-lt_mul_m1_neg @kj@jN[kR@Z SYkX@` S@k^@= [kc@0 $B@kj@I [eko@3 kt@S [kz@3 ހef k@j Uk@j $@@@A@AA@A>@A@ABC@@B-lt_mul_m1_pos @kMk=@k9Ok@ Sk@ S@k@ [Bk@k Uk@k  $@k@ [k@4 fOk@ [k@4  ހfLf\k@k$ Uk@k- $@@@A@AA@A@A@ABC@@*lt_1_mul_l @kk@kPk@ Sk@P S@k@ [l@ $B5l @ [l@4O ހffl@kj Ul@ks $Ol'@"eq Zl.@4j ހffl3@4 l8@ [l=@  $lB@4~ ހffА@@@[AS@]A@_AI@ABC@@+lt_m1_mul_r @l k@kQdl[@c Sbla@ S@lg@F [Bln@k Uls@k $l|@[ [l@4 ހggl@k Ul@k $l@o Zl@4 ހg+g*l@4 l@ [l@x $l@4 ހg?g>@@@A@Ah@A@ABC@@l(eq_mul_1 @lwlg@lcRҚl@! SКl@' S@l@ Zl@5 ހBAl@ $l@ Zgzl@ $l@ Zgl@lL Um@lU $@@@A@AA@A@AA@ AРD.Morphisms_Prop'Classes#Coq@@*A8ӠA4Relation_Definitions)Relations#Coq@@ABCD@@Ѡ-lt_mul_diag_l @lܠl@lS7m.@6 S5m4@< S@m:@ [Bm@@5 mI@( [mN@ $g۩mS@2 [mY@5 ހggg@@@rAj@tA@vA`@ABC@@-lt_mul_diag_r @m m@m T{mr@z Symx@ S@m~@] [m@5 BՀm@l [m@_ $hm@v [h&m@5 ހh,h+@@@A@A@AB@@W-le_mul_diag_l @mbmR@mNUm@ Sm@ S@m@ [Bm@6 m@ [wm@ $ham@ [wm@6 ހhnhmhn@@@A@A@A@ABC@@-le_mul_diag_r @mm@mVm@ Sm@ S@n@ [n @6Y B[n@ [wn@ $hn@  [whn#@6_ ހhh@@@A(@AB@@ݠ(lt_mul_r @mm@mWCn:@B SAn@@H S@nF@N S@nL@+ [nQ@6 C@nX@7 [n]@* $h@nc@B [Ah⩚ni@H [ no@6 ހMh@@@A@A'@Av@ABC@@+(mul_eq_1 @n@Y@n@ Sn@ S@n@m Zn@6 ހn@k $n@~ Zi4n@w $n@ Zi>n@n Un@n $nan`n_n^n]@nm@ &!۠n|nl@@@@@|@nnΠ@@|@B!C@&abs_wd @@'ZSgnAbs(Abstract'Integer'Numbers#Coq@+ZSgnAbsProp|@A@@@E"ZP'ZSgnAbs(Abstract'Integer'Numbers#Coq@o|@A@@D!Zoo@A@E)Morphisms'Classes#Coq@@&ProperL@o@!t So@ S)Morphisms'Classes,@@*respectful%WO?o-@ So1@ So5@"eq Zo:@ Zo>@#abs 㐀@@@ %'A*Equalities*Structures#Coq@AviA-'Classes#Coq@@AAۀߠK@Aۓό^ @A݋X_A/RelationClasses'Classes#Coq@@ABC@@AA@@A@'abs_max @s@F!noy@!t So@"eq Zo@#abs 㐀Ao@#max nAo@#opp UA@@@YAQ@[AG@]AE@ABC@@=(abs_neq' @͠@G:o@9 S@o@"le [wo@$zero o@. UAo@L Zo@K 㐀Bo@B U@@@@@w*abs_nonneg @@Hto@s So@9 [wo@8 o@u 㐀A@@@A@AA@A@A@ABC@@*abs_eq_iff @3#@ Ip@ S%Logic$Init#Coq@@#iffС)p+@ Zp1@ 㐀AAp9@ [wp>@ A@@@A@AA@A@A@ABC@@堠+abs_neq_iff @ueU@bJ⚠pZ@ SBpc@ Zpi@ 㐀App@ UApw@ [wAp}@ @@@>A6@A?A/@AA-@CA+@ABC@@#'abs_opp @@K p@ Sp@ Zp@ 㐀p@ UAp@* 㐀A@@@rAj@tA`@vA^@ABC@@V%abs_0 @֠@Lp@K Z@#abs 㐀@@@@@o)abs_0_iff @@Mlp@k S̀p@n Zp@m 㐀Ap@; p@ ZAq@F @@@A@A@A@ABC@@'abs_pos @8(@%Nq@ Sq&@"lt [q,@n q1@ 㐀A%Logic$Init#Coq@@#notШqF@ ZAqL@ @@@ A@AA@A@A@ABC@@-abs_eq_or_opp @rb@oOqg@ SP@"or @qt@ Zqz@ 㐀AAq@ Zq@ 㐀Aq@ UA@@@QAI@SA?@UA=@ABC@@5.abs_or_opp_abs @Š@P2q@!t SDq@5 ZAq@5 㐀Aq@C ZAq@3 Uq@I 㐀A@@@A}@A{@AB@@s.abs_involutive @@Qpq@o Sq@n Zq@m 㐀q@s 㐀Ar@z 㐀A@@@@@(abs_spec @0 @Rr@!t S@#andЖw@r'@o [wr,@n Ar2@ Zr8@ 㐀AA!rD@ [ArJ@ rO@ ZrU@ 㐀Ar\@ UA@@@@@/abs_case_strong @|l@yS!P@rs@!t SAr|@g S@y@r@ SAl?>@@*respectful%WO?r@ SAr@h Z%Logic$Init@#iffС)B@@r@ [wr@ ⩐DC@@r@ [w r@ Er@6 U r@N 㐀 @@@A@A@AB@@w(abs_case @@T{@r@z Sy{r@ S@@r@S Swus@ Sns @ ZlB@U;@Zs@ U_Rs@ 㐀i@@@A@A@@,abs_eq_cases @N>.@;Us3@ S!ms:@ S@s@@ ZsF@ 㐀BsM@ 㐀A耠sX@ Zs^@ Zsd@ U@@@%A@'A@)A@ABC@@ &abs_lt @y@V!as@ S!bs@q Sns@i [s@ 㐀BA%Logic$Init#Coq@@#andЖw@s@ [s@ UABs@ [BA@@@}Au@Ak@Ai@ABC@@a&abs_le @@WXs@] SWs@ SĀs@- [ws@e 㐀BAVs@? [ws@g UABt@M [wBA@@@A@A@A@ABC@@,abs_triangle @<,@)Xt!@ St'@ St,@t [wt2@ 㐀t8@#add 㧀BAtA@  㧀tG@ 㐀BtN@ 㐀A@@@A @AA@A@A@ABC@@0abs_sub_triangle @vf@sY󚠐tk@ S8tq@ Stv@ [wt|@#sub Jt@ 㐀Bt@ 㐀At@  㐀t@ JBA@@@[AS@A\AL@^AJ@`AH@ABC@@@'abs_mul @Р@Z=t@< St@B St@A Zt@@ 㐀t@#mul ހBAt@  ހt@U 㐀Bt@\ 㐀A@@@A@A@A@ABC@@*abs_square @@[t@ Su@ Zu@< ހu@ 㐀Au@ 㐀Au@P ހAA@@@A@A@A@ABC@@à&sgn_wd @SC3@@\.@u;@$ Su?@( S#uE@. SuI@2 SuM@ ZuQ@ ZuU@#sgn L@@@A@AA@A@A@ABC@@(sgn_spec @|l@y]uq@\ S [u~@X [u@ Au@  Zu@#sgn LAu@#one $0u@% Zu@ Au@0 Zu@& LAu@ u@ [Au@  u@P Zu@F LAu@F Uc@@@A@A@A@ABC@@%sgn_0 @@^u@v Z@#sgn Lߐ@@@A@A@@+sgn_pos_iff @, @_v@ Sv@ Zv @ LAv&@ $v+@ [v0@r A@@@A@A@A@ABC@@ՠ,sgn_null_iff @eUE@R`ҚvJ@ S2vS@ ZvY@ LAv_@ vd@ ZAvj@ @@@*A"@,A@.A@ABC@@+sgn_neg_iff @~@a v@  Skv@  Zv@ LAv@ Uv@#one $v@~ [Av@ @@@jAb@lAX@nAV@ABC@@N'sgn_opp @ޠΠ@bKv@J Sv@I Zv@? Lv@> UAv@E Uv@R LA@@@A@AA@A@AA@A1ՠF-SetoidTactics'Classes#Coq@@A1I @ABCD@@*sgn_nonneg @'@cw @ S􀠩w@] [ww@\ w@ LAw&@n [ww+@m A@@@A@AA@A@A@ABC@@Ҡ*sgn_nonpos @bRB@OdϚwG@ S/wP@ [wwV@ LAw\@ wa@ [wAwg@ @@@'A@)A@+A@ABC@@ 'sgn_mul @{@ew@ SMw@  Sw@  Zw@ Lw@ ހBAw@ ހw@ LBw@ LA@@@nAf@pA\@rAZ@ABC@@R'sgn_abs @Ҡ@fOw@N Sw@M Zw@ ހAw@J LAw@Z 㐀A@@@A@A@A@ABC@@'abs_sgn @  @ gw@ Sx@ Zx@: ހx @ 㐀Ax@ LAA@@@A@A@A@ABC@@'sgn_sgn @ J : *@ 7h!xx0@ Sx5@ Zx;@ LxA@ LAxH@ LA@@@ A @A A@ A@ A@ABC@@@ {xZ ]@@0@C!Dc@-Private_NZDivA.div_mod_unique @@)ZDivFloor(Abstract'Integer'Numbers#Coq@(ZDivProp!U@A@@@B!C)ZDivFloor(Abstract'Integer'Numbers#Coq@ f@A@@A!B l@A@@@!AxyB@A@%NZDiv&NatInt'Numbers#Coq@)NZDivProp*1L@@@A@@@J!C%NZDiv&NatInt'Numbers#Coq@+@A@@I!B,@@ĩ@5@&moduloĩd@@A@A)@@&shiftl)d@@A@/@ @&shiftr/d@@A@A @@&square d@@A@)Z@@'testbit)Zd@@A@$@@'compare$d@@A@ABCD={@@!t={J@@A@=@#@"eq=^@@A@=p@(@"le=ph@@A@AB=@,@"lt=h@@A@=1@2@#abs=1d@@A@A=1@6@#add=1d@@A@=6L@;@#div=6Ld@@A@ABCE=89@?@#eqb=89d@@A@=:@F@#gcd=:d@@A@A=A4@J@#leb=A4d@@A@=B@O@#lor=Bd@@A@AB=BQ@S@#ltb=BQd@@A@=Bg@Y@#max=Bgd@@A@A=B@]@#min=Bd@@A@=C@b@#mul=Cנd@@A@ABCF=E^@f@#odd=E^d@@A@=F@n@#one=FT@@A@A=FN@r@#opp=FNd@@A@=G@w@#pow=Gd@@A@AB=I@{@#rem=Id@@A@=KE@@#sgn=KEd@@A@A=LC@@#sub=LCd@@A@=M@@#two=MߠT@@A@ABC=X@@$div2=Xd@@A@=q@@$even=qd@@A@A=@@$land=d@@A@= @@$log2= d@@A@AB=@@$lxor=d@@A@=|@@$pred=|d@@A@A="P@@$quot="Pd@@A@=R{@@$sqrt=R{d@@A@A=V@@$succ=Vr@@A@=@@$zero=T@@A@>w@@%ldiff>wd@@A@ABCDEFG@A@@H!A@A@@!by@!t S"q1y@!t S"q2y@ S"r1y@ S"r2y@ S@%Logic$Init#Coq@@#andЖw@y@"le [wy@$zero By@"lt [BE@&y@ [wy@ By@ [F@y@"eq Zz@#add 㧀z @#mul ހGDz@ 㧀z@ ހEC%Logic$Init#Coq@@#andЖw@z2@4 Z%<z8@: Z*@@@ %'A*Equalities*Structures#Coq@AviA)Morphisms'Classes#Coq@@AAۀߠK @Aۓό^ @A݋X_A/RelationClasses'Classes#Coq@@ABC@@AA@@A@*div_unique @۠֠Ѡ@A!azy@ S㚠z@ S!qz@ S!rz@ S@z@ [wz@ D@ހz@ [wz@ z@ [@z@ Zz@ 㧀z@ ހz@ Zz@#div Sא@@@A@A}@AB@@u*mod_unique @m]MHC1#S@/Brz@M STz@S Sqz@Q Spz@_ S@{@2 [w{@1 D@M{@B [w{@A '{@? [-@{#@% Z-{)@$ 㧀{/@# ހ!{5@7 Z'{;@&modulov/F@@@A@A@AB@@䠠0div_unique_exact @ܠ̠@Cᚠ{Y@ SÚ{_@ S{e@ S@{k@ [w{p@ C@{w@ [{|@ _@{@ Zg{@| ހzl{@ Z{@ Sy@@@[AF@]AD@AB@@<(div_same @4$ @D9{@ S@{@ [{@ A{@ Z{@ Sٚ{@#one $@@@A@A}@AB@@u(mod_same @m]MHC1#S@/Er{@M S@{@ [{@ A{@ Z|@v|@0 @@@A@A@A@ABC@@)div_small @}k]@iF|$@ S|*@ S@o|4@d [w|9@c B|?@b [BA|G@I Z|M@ S1^|R@| @@@A@A@A@ABC@@)mod_small @ӠΠɠ@G|p@ Sښ|v@ S@|@ [w|@ B|@ [BA|@ Z|@^v}}@@@`AX@bAM@dAK@ABC@@C'div_0_l @;+!@H@|@ S@|@ [|@ A|@ Z|@ S|@ 䚠|@ @@@@@{'mod_0_l @scSNI7)Y@5Ix|@S S@|@ [|@% A}@ Z}@v} @6 }@: @@@@@'div_1_r @oa@mJ}(@ S@}.@^ [w}3@] A}9@; Z}?@s SP}D@w $T@@@ A@ A@AB@@렠'mod_1_r @Ӡà@K蚠}`@ S@}f@ [w}k@ A}q@s Z}w@<v}|@ $}@ @@@FA>@HA3@JA1@ABC@@)'div_1_l @!נ@L&}@ S@}@ [}@ $A}@ Z}@ S}@ $ʚ}@ @@@@@a'mod_1_l @YI94/?@M^}@9 S@}@ [}@ $A}@ Z}@v}@% $}@) $@@@@@'div_mul @qlgUGw@SN~@q Sx~@w S@~@J [w~@I B@~&@I [~+@U ;~0@2 Z~6@j S~<@0 ހ.  .@@@A@A@@⠠'mod_mul @ڠʠ@Oߚ~W@ S~]@ S@~c@ [w~h@ B@~o@ [~t@ ~y@{ Z~@Dv~@y ހwii~@ @@@PA;@RA9@AB@@1&mod_le @) ߠ@P.~@  S~@ S@~@ [w~@ B@~@ [~@ ө~@ [w~@v@@@@@r'div_pos @jZJE@. P@,Qo~@J SQ~@P S@~@# [w~@" B@~@" [@.  @9 [w@8 @G S@@@A@AA@A@A@ABC@@+div_str_pos @{m@yR4@ S:@ S@D@g [I@s AO@ [wABW@z [\@ a@ SEr@@@(A @*A@,A@ABC@@ -div_small_iff @ޠ٠Ǡ@S@ Sꚠ@ S@@ [w@ B@@ [@ ~@#iffС)@ Z@ S@ @ [@@@Ag@A@@_-mod_small_iff @WG72- =@T\@7 S>@= S@@ [w@ B@@ [@ T@ Z@v򩚠@) [@@@A@A@A@ABC@@/div_str_pos_iff @~l^@jU%@ S+@ S@1@a [w6@` B@=@` [B@l RK@n [P@z U@ SG9[@ [w?M@@@@@&div_lt @נҠ͠@Vt@ Sޚz@ S@@ [@ B@@ [@ $@ [@ S@@@dA\@AeAT@gAR@iAP@ABC@@H+div_le_mono @@0 &@WE@  S'@& S!c@- S@@ [@ A@@ [w@ ֩@ [wΩ@  [w@* Sک@0 S@@@A@AA@A@A@ABC@@*mul_div_le @{vdV@bX@ S#@ S@)@Y [w.@X B@5@X [:@d J?@o [wE@9 ހ)K@ S=/=@@@A @A@A@ABC@@/mul_succ_div_gt @ݠ͠Ƞà@Y򚠐j@ SԚp@ S@v@ [w{@ B@@ [@ @ [~@ ހv@$succ @ S@@@gA_@AhAW@jAU@lAS@ABC@@K)div_exact @ C 3 #   )@ ZH@# S*@) S@@ [w@ B@@ [@ @@ Zة@ ހЩ@& S֩@ Z@v⚠@- @@@A@A@A@ABC@@2div_lt_upper_bound @     z h Z@ f[!@ S'@ S-@ S@3@c [w8@b C@?@b [D@n '@J@m [/P@D ހB4V@y [\@ SfAN@@@@@2div_le_upper_bound @   ؠ Ӡ Π  @ \u@ Sߚ{@ S@ S@@ [w@ C@@ [@ {@@ [w@ ހ@ [w@ S@@@@@T2div_le_lower_bound @ L < , ' "   2@ ]Q@ , S 3@ 2 SP@ 0 S@@  [w@  C@@  [@  ϶@@ " [w@ ހݩ@ . [w𩚠@8 S @@@A@AA@A@A@ABC@@/div_le_compat_l @     ~ l ^ @ j^!p&@  S,@  S2@  S@8@ h [w=@ g C@ H@ k [M@ w  0R@  [w 6 cX@  [w^@ S C Bd@ S I V@@@ ,A $@A -A @ /A @ 1A @ABC@@ 'mod_add @     ޠ ̠  @ _ @  S @  SȚ@  S@@  [w@  C@@  [w@  @  㧀 @  ހ  Ķ@@  [@   @  Z@v@  㧀 ک@  ހ   ȩ@v  ΐ@@@ A @ A @ A @ABC@@ 'div_add @ ~ n ^ Y T B 4 d@ @` @ ^ S e@ \ S>@ b S@ @ = [w@ < C@@ I [w@ H #@  㧀 )@  ހ  :@0@ S [5@ _  :@ < Z@@ t SF@ A 㧀 PL@ @ ހ 1 > >R@ M 㧀X@  S b J =@@@ A @ !A @ #A @ABC@@ )div_add_l @   ڠ ՠ Р   @ a w@  S ᚠ}@  S@  S@@  [w@  A@@  [w@  @  㧀@  ހ   @@  [@   @  Z@  S@  㧀@  ހ    @  㧀 ة@  S  @@@ A @ A @ A @ABC@@ ~0div_mul_cancel_r @ v f V Q L : , \@ 8b {@ V S ]@ \ S6@ b S@@ 5 [w @ 4 C@@ 4 [@ @  @@ ? [!@ K  &@ ( Z,@ ` S2@ & ހ < $8@ , ހ  *>@ r S H #@@@ A @ A @ A @ABC@@ 蠠0div_mul_cancel_l @  Р      @ c 嚠]@  S ǚc@  Si@  S@o@  [wt@  C@{@  [@   c@@  [@   n@  Z@  S@  ހ  @  ހ  @  S  @@@ oA g@ qA \@ sA Z@ABC@@ R/mul_mod_distr_l @ J : * %    0@ d O@ * S 1@ 0 S @ 6 S@@  [w@  C@@  [@   Ͷ@@  [@   ة@  Z@ v@  ހ   @  ހ  񩚠@  ހ @ v " @@@ A @ A @ A @ABC@@  /mul_mod_distr_r @      ~ p @ |e 7@  S =@  SzC@  S@I@ y [wN@ x C@U@ x [Z@   =@`@  [e@   Hj@ l Zp@ 5vv@ j ހ  h|@ p ހ a n@ v ހ@ Mv  m z@@@ OA G@ QA <@ SA :@ABC@@ 2'mod_mod @*    @ f /@  S!n@  S@@  [w@  B@@  [@   թ@  Z@ v@ v   @ v  @@@@@ /mul_mod_idemp_l @xhXSN<. ^@:g }@ X S _@ ^ ST@ d S@@ 7 [w @ 6 C@@ C [w@ B  @@ A [#@ M  (@ * Z.@ v4@ ( ހ:@ v D ,  ,@@ vF@ : ހ P + 8@@@ A @ A @ A @ABC@@ /mul_mod_idemp_r @ؠȠà @h 횠e@  S Ϛk@  SĚq@  S@w@  [w|@  C@@  [w@   k@@  [@   v@  Z@ cv@  ހ @ ov   @ uv@  ހ   @@@ }A u@ A j@ A h@ABC@@ `'mul_mod @XH83.>@i ]@8 S?@> S4@D S@@ [w@ C@@# [w@"  ۶@@! [@-  橚@  Z@ v@ ހ @ v @ ހ&@ v0,@ v@@@ A @ A @AB@@ Ԡ/add_mod_idemp_l @̠@j њI@ SO@ SU@ S@[@ [w`@ C@g@ [wl@ O@r@ [w@ Z|@~ Z@ Gv@ 㧀@ Svs@ Yv@ 㧀@@@aAY@cAN@eAL@ABC@@D/add_mod_idemp_r @<,"@kA@ S#@" S@( S@@ [w@ C@@ [w@ @@ [@ ʩ@ Z@ v@ 㧀@ v𩚠@ v @ 㧀@@@A@A@A@ABC@@'add_mod @pb@nl)@ S/@ S5@ S@;@k [w@@j C@G@w [wL@v /@R@u [W@ :\@^ Zb@'vh@c 㧀rMZn@3vt@o 㧀z@?vl@Everr@@@GA2@IA0@AB@@('div_div @ ֠@m%@ S@ S@  S@@ [w@ C@@ [@ @@ [@ @ Z@  S@ SΩ@ S쩚@ ހڐ@@@A@AA@A@A@ABC@@)mod_mul_r @|lgbPBr@Nn @l Ss@r S L@x S@@K [w @J C@'@J [,@V @2@U [7@a <@> ZB@vLH@< ހ-:N@I 㧀T@v^9Z@N ހ?`@%vf@ SpKX@@@-A%@/A@1A@ABC@@*div_mul_le @ޠ̠@o @ S@ S Ț@ S@@ [w@ C@@ [@ @@ [w@ @ [w@ ހ@ S@ S@ ހ@@@A@A@A@ABC@@z+mod_divides @rbRMH6(X@4pw@R SY@X S@@+ [w@* B@@* [ @6  o@ Z@v  @J @"ex @,@ S i2@ S7@9 Z=@1 ހ/A@@@A@AA@ A@ A@ A1@D)('@@ABCD@@@@@@@A  BC*@&mod_eq @ޠΠ@@!ah@!t S!bp@ S@%Logic$Init#Coq@@#notШ@"eq ZA@$zero @  Z@\vCB@#sub J @#mul ހ@ S@@@ %'A*Equalities*Structures#Coq@A݋X_A/RelationClasses'Classes#Coq@@A@@AA@@A@-mod_bound_abs @^N>9@LAp@o Sn@ S@m@c ZA@b @"lt [@ 㐀@vhg@ 㐀m@@@YAviA)Morphisms'Classes#Coq@@AbAۀߠK @fAۓό^ @jAb@ABC@@Z.div_mod_unique @@B.@!t S"q16@ S"q2=@ S"r1D@ S"r2K@ S@%Logic$Init#Coq@@"or @%Logic$Init#Coq@@#andЖw@o@"le [wu@ B{@ [BE#@ [EB@  [wB@  @J?@4 [w@ @ [FT@ [  @O [w&@8 @@E Z@#add 㧀@0 ހG*D@ 㧀@> ހEN@#andЖw@@o ZF@u Z"@@@LA@NA@PAH@ABC@@@*div_unique @{v@C@) S@!t S!q"@!t S!r*@ S@߀Ԁ8@ [w=@ AC@Q [AC뀠O@] [CAW@ [wA]@ @c@ Zi@ 㧀o@ ހשu@ Z{@ S@@@Ah@A@AB@@.div_unique_pos @ @ D-@ S+@ S@~ S}@ S@L@A [w@* A@ [AC@@@ Zਗ਼@ 㧀@* ހ98@R Z@ S/@@@@@.div_unique_neg @xhXS@fE@ S@ Sܚ@ Sښ@ S@ @ [CA@ [wA@ @!@ Z='@X 㧀-@ ހV3@ Z\9@m SU@@@@@z*mod_unique @ՠŠ@F皠N@c S嚠T@: S9Z@8 S7`@F S@ n@ [ws@ Ay@ [AC!@ [CA@ [wA@ @@ Z@ 㧀@ ހ @' Z@vv͐@@@A@A@AB@@.mod_unique_pos @QA1,@?Gc@ Sa@ S@ S@ S@@w [w@` A@ [AC@@v Z@1 㧀@` ހ/on @ Zu@ve.@@@@@S.mod_unique_neg @@H'@< S-@ S3@ S9@ S@߀C@Q [CAK@ [wAQ@ @W@ Zs]@ 㧀c@ ހ˩i@ Zҩo@4v@@@@@,mod_bound_or @ @I@ S@ S@@ ZA@ NC@8 [w@! @vv@ [@v&%%c@ [/@v65@d [w@vBA@S @@@@@0opp_mod_bound_or @yiYT@gJ@ S@  S@@~ ZA@} @ [w@ @ U%@v+@9 [1@ U7@v=@ U〠G@U [M@  US@ UY@v_@ [we@% Uk@0vӚp@ @@@@@+div_opp_opp @ @K@b S@ S@@ ZA@ @ Z@ S@k U@q U@ S @@@ A@ A@A@ABC@@+mod_opp_opp @YI94@GLk@ Si@ S@h@^ ZA@] @i Z@v@ Ub@ Ug@ U @vts@@@^A@`A@bAZ@ABC@@R+div_opp_l_z @@M&@ S,@A S@6@ ZA<@ @B@ ZH@ vM@ R@ ZX@ S^@ Uǩd@$ Uj@ SӐ@@@Ad@AY@A@ABC@@,div_opp_l_nz @ @N@ S@ S@@ ZA@ @+@! Z@pv@% @1 Z@ S@ U*@( J@ U@ S<@#one $@@@+A@-A@/A'@ABC@@+mod_opp_l_z @zjZU@hO@ S@ S@@ ZA @~ @@ Z@v~}@ @ Z%@v+@ UT0@ @@@A)@A@A~@ABC@@v,mod_opp_l_nz @Ѡ@P㚠J@ SᚠP@e S@Z@ ZA`@ @j@ Zp@5vؚu@ z@ Z@Ev@F U署@ J@Wv@@@A@A@A@ABC@@٠+div_opp_r_z @4$@"QF@E SD@ S@C@9 ZA@8 @@E Z@v87@I @U Z@ S@ UN@ U@% SZ@@@DA@FA@HA@@ABC@@8,div_opp_r_nz @sn@R @ S@' S@@ ZA"@ @,@ Z2@v7@ <@ ZB@v SkH@ UN@ JT@ UZ@ SÚ_@ $@@@AX@AM@A@ABC@@+mod_opp_r_z @@Sy@ S@ S@@ ZA@ @@ Z@`v@ @! Z@pvԩ@q U@+ @@@A@ A@ A@ABC@@,mod_opp_r_nz @WG72@ETi@h Sg@ S@f@\ ZA@[ @v@l Z@v_^@p @| Z@v/ @ Uu@s J@vA@@@kA@mA@oAg@ABC@@_+mod_sign_nz @@U̚3@ Sʚ9@N S@ɀC@ ZAI@ @ـS@ ZY@v^@ c@ Zi@ Lo@4vةu@& Lސ@@@Ao@Ad@A@ABC@@(mod_sign @@V )@ ( S '@ S@ &@  ZA@   5@ + Z@f L@v $ #@ U@x L /@@@ A@ A@ A @ABC@@ ,mod_sign_mul @iYID@WW {@ z S y@ S@ x@ n ZA@ m @ [w@ w @ a ހ @v v u u@@@@@ N(div_same @@X "@7 S@ ,@  ZA2@  7@  Z=@q S  B@j $@@@ A ;@ A 0@ A @ABC@@ (mod_same @Ӡà@Y \@q S@ 쀐f@  ZAl@  q@  Zw@<v  ߚ|@  @@@ A u@ A j@ A @ABC@@  )div_small @ @ Z /@| S -@ S@ B@ 7 [w@  B@  [BA@ 5 Z@ S ( '@ 9 @@@@@ )mod_small @_O?:@M[ q@ S o@ S@ @ y [w@ b B@  [BA@ w Z@v j i j@@@@@ B'div_0_l @}x@\ @+ S@  @  ZA&@  +@  Z1@e S6@   :@  @@@ A 3@ A (@ A @ABC@@ 'mod_0_l @۠ˠ@] 횠T@i S@ 䀐^@  ZAd@  i@  Zo@4vt@   ۚx@  @@@ A q@ A f@ A @ABC@@ 'div_1_r @ @^ +@ * S@  Z@ SA@ $A@@@ A @ A @ A @ABC@@ ꠠ'mod_1_r @E5% @3_ W@ V S@ ? Z@vA@ $@ H @@@ %A @ 'A @ )A !@ABC@@ 'div_1_l @tdTO@b` @  S@@  [@  $A@ z Z@8 S @1 $ p @  @@@@@ M'mod_1_l @@a !@  S@'@ 5 [,@T $A2@  Z8@v=@e $ A@i $@@@@@ 'div_mul @ܠ̠@b U@ 3 S 욠[@p S@ 뀐e@  ZAk@  p@  Zv@ S|@  ހ    @@@ A i@ A @AB@@ 'mod_mul @ @ c .@ s S ,@ S@ +@ ! ZA@  @ , Z@{v@  ހ % $ $@ 6 @@@ A @ A @ A @ABC@@ 0div_unique_exact @bRB=@Pd t@ S r@ S!q@  S@ x@ n ZB@ m @@ z Z '@ ^ ހ m l @  Z s@D S , 9@@@ cA @ eA @ gA _@ABC@@ W&mod_le @@e Ě+@  S š1@  S@7@  [w<@  B@C@ Q [H@   M@  [wS@v |  |@@@@@ 'div_pos @ߠϠ@f h@ N S n@ T S@t@  [wy@  B@@  [@   쩚@  [w@  @ S  @@@@@ ՠ+div_str_pos @ 0   @ g B@  S @@  S@ U@  [@ 3 A@ U [wAB@  [@ F @  S ? >@@@@@ -div_small_iff @ r b R M@ `h @  S @  S@ @ w ZA@ v  @#iffС) @  Z@G S | {@   ̀ %@  [w*@   /@ = [   Հ9@ G [  ?@  [w D@  @@@ A =@ A 2@ A @ABC@@ -mod_small_iff @  ՠ Š @ i ^@  S d@ y S@ 􀐩n@  ZAt@  s}@  Z@Hv   쩛 8 -@ " [w@   @  [ A@  [ @ < [w@% @@@A @A @A @ABC@@ &div_lt @!Q!A!1!,@!?jc@  Sa@  S@@  [@P B@@  [@ $N@  [@& S [ @@@@@3+div_le_mono @!!~!n!i@!|k@  S @  S!c@  S@@( [@ A@&@  [w O,@  [w2@f S N8@l S a@@@A3@AA+@A)@A@ABC@@*mul_div_le @!ܠ!̠!!@!lU@ S욠[@ A S@a@o [f@ Al@  [wr@ ހکx@ S@@@As@AAk@Ai@A@ABC@@*mul_div_ge @"" !!@" m.@ { S,@  S@@ [A@ @= [w@  ހ@ S! @@@ A@A A@A@A @ABC@@/mul_succ_div_gt @"\"L"<"7@"Jnn@  Sl@  S@@ [@[ A@ [U@L ހZ@$succ @ 3 Shg@@@SA@ATA@VA@XAP@ABC@@H/mul_succ_div_lt @""""~@"o@ S"@ S@(@6 [A.@ 3@A [9@ ހ?@G E@ y S@@@A@@AA8@A6@A@ABC@@)div_exact @""٠"ɠ"@"pb@"w Sh@"} S@r@ ZAx@ w@ Z꩚@ ހ署@  S@ Z@ ^v@ @@@A@A@A@ABC@@䠠2div_lt_upper_bound @#?#/##@#-qQ@ SO@ Sݚ@ S@@ [@D B@@ [@6 ހED@ [@! SQ@@@@@)2div_le_upper_bound @##t#d#_@#rr@ S@ S" @ S@@ [@ B@@ [wD!@{ ހ'@ [w-@!a SIV@@@A(@AA @A@A~@ABC@@v2div_le_lower_bound @#Ѡ###@#s㚠J@0 SᚠP@6 SoV@4 S@\@j [a@ B@h@ [wn@ ހt@ [wݩz@! S@@@At@Am@A@ABC@@/div_le_compat_l @$$ ##@$ t!p@| S@ Sy@ S@@9 [w@" C@T@ [@2 %@S [w+*@Y [w@" S7@" S@@@@@'mod_add @$p$`$P$K@$^u@ S@ S⚠@$  S@@{ ZA@z  @ Z@!v@G 㧀?@v ހ"@!vK@@@uA@wA@yAq@ABC@@i'div_add @$Ġ$$$@$v֚=@ SԚC@! S6I@$^ S@ـS@ ZAY@ ^@ Zd@" Sj@ 㧀p@ ހةv@ 㧀|@" S@@@Av@Ak@A@ABC@@à)div_add_l @%%$$@% w0@u S.@$ S@ S@3@) ZB@( @4 Z@" S@ 㧀@$ ހ323@ 㧀@#  S>?@@@)A@+A@-A%@ABC@@0div_mul_cancel_r @%x%h%X%S@%fx@ S@%  Sꚠ@% S@@ ZB @ @@ Z@ !@ Z'@#[ S-@ ހI3@ ހ\9@#m SUb@@@A3@A(@A@ABC@@0div_mul_cancel_l @%۠%ˠ%%@%y횠T@2 S뚠Z@%o SM`@%u S@j@ ZBp@ @z@ Z⚠@ @ Z@# S@ ހ@ ހ@# SŐ@@@A@A@A@ABC@@㠠/mul_mod_distr_l @&>&.&&@&,zP@ SN@% S@% S@S@I ZB@H @c@Y ZE@W @c Z@#v@M ހ\@S ހb"@Y ހh@#v!.@@@XA@ZA@\AT@ABC@@L/mul_mod_distr_r @&&&&@&{ @ S&@&; S,@&A S@6@ ZB<@ @̀F@ ZK@ P@ ZV@$v\@ ހxũb@ ހ˩h@ ހn@$3vא@@@Ah@A]@A@ABC@@'mod_mod @''&&@&|"@! S!n@& S@ @ ZA@ @! Z@$pv@$vv@$|v @@@@@/mul_mod_idemp_l @'S'C'3'.@'A}e@d Sc@ SI@& S@h@^ ZA@] @i Z@$v@S ހ@$v(ghg@$v @e ހ4ts@@@^A@`A@bAZ@ABC@@R/mul_mod_idemp_r @''''@'~&@ S,@ S2@'G S@€<@ ZAB@ G@ ZM@%vS@ ހ|Y@%v_@%$ve@ ހ͐@@@A_@AT@A@ABC@@'mul_mod @('''@'@^ S@d S@' S@@ ZA@ @ Z@%lv@ ހ@%xv@ ހ@%v'@%v.--@@@A@A@AB@@ /add_mod_idemp_l @(e(U(E(@@(S@w@v Su@ S[@' S@z@p ZA@o @{ Z@%v @< 㧀@%v:yzy@%v@N 㧀F@@@pA@rA @tAl@ABC@@d/add_mod_idemp_r @((((@(Aњ8@ SϚ>@ SD@(Y S@ԀN@ ZAT@ Y@ Z_@&$ve@ 㧀k@&0vөq@&6vw@ 㧀ߐ@@@Aq@Af@A@ABC@@'add_mod @)) ((@)B+@p S)@v S@( S@.@$ ZA@# @/ Z@&~v@ 㧀('@&v@ 㧀@&v9@&v@??@@@*A@,A$@AB@@'div_div @)w)g)W)R@)eC@ S@)  S隠@ S@@ ZB @ @@  [@ ~@ Z"@'V S(@'\ SDQ.@'b SJ4@ ހ]@@@A/@AA'@A%@A@ABC@@})rem_mul_r @)ؠ)Ƞ))@)DꚠQ@ S蚠W@)l SJ]@C S@퀐g@ ZBm@ @s@ [x@ ߩ}@ Z@'Hv@ ހ򩚠@ 㧀@'Zv@ ހĩ@'fv@' S@@@A@A@A@ABC@@'mod_div @*I*9*)*$@*7E[@Z SY@) S@X@N ZA@M @Y Z@( S@'vRQQ@c @@@@@.*div_mul_le @**y*i*d@*wF@ S@ S@ S@@ [w@ C@ @. 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