"`넕- Zﰠ$Mult%Arith#Coq@8$Plus%Arith#Coq@%Minus%Arith#Coq@"Le%Arith#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@"Lt%Arith#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@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$NLog(Abstract'Natural'Numbers#Coq@0K!BdA@@@@@)mult_O_le @@Cכ)Datatypes$Init#Coq@@#nat@֛@x׀ AA%Peano@@"le UxT@BۀAB@@@@@0mult_le_compat_l @@%D>@@%CB+D@@@@@堠0mult_le_compat_r @@IE9b+d(,@ICBO $ǩ$ː@@@@@.mult_le_compat @@lF\NK!q@oDC@v꩛zKFPPE@@@@@52mult_S_lt_compat_l @@G)Datatypes$Init#Coq@@#nat@)Datatypes$Init#Coq@@#nat@@@"lt UxcBA 4@BD BE@@@@@0mult_lt_compat_l @@H>13@1CB@8Ad?ŀtuɀx͐@@@@@0mult_lt_compat_r @@Ii\^@\CB@cAj@@@@@ؠ/mult_S_le_reg_l @@ 7!3&'''+k6'+7Tk+7T'+7T'6'*y<(РB@@AAAEX@@@@@Ġ,mult_acc_aux @@(L   BCA;@BAC@@@@@젠)tail_mult @~Xk@z@JV<gV @+k() L7&'l@@@@@ .mult_tail_mult @@qMa`SRMB?BA}@9ـBA@@@@@-@@@ ӳ2@ ӳ2[)Datatypes$Init#Coq@@A@ Գq@ Գq\ @A@AB@@@"O@(PeanoNat%Arith#Coq@#Nat@&of_int"O#Nat$Init#Coq@@ 6@A@As2@@&shiftls2 @vY@A@Bs8@@&shiftrs8@vY@A@ѓ@!@&squareѓ@y@A@@'@&to_intϑ@@A@AB/@,@)log2_iter/#@wd@A@l@2@)sqrt_iterl)@!$:@A@ACD c@7@'testbit c.@!ć@A@^Ҷ@?@'to_uint^Ҷ6@#m@A@A,@D@'bitwise,;@/v@A@l@J@'comparelA@3R@A@ABs8@O@+of_uint_accs8F@5+@A@.@W@!t.N@ ;@A@A.먩@\@#add.먩S@ `@A@B.U@a@#div.UX@ @A@.B@h@#eqb.B_@ @A@A. @m@#gcd. d@ @A@.=@s@#leb.=j@ @A@ABCDE. @x@#lor. o@ @A@.Z@@#ltb.Zz@ @A@A.p@@#max.p@ '@A@B.@@#min.@ @A@.@@#mul.@ @A@AC.g@@#odd.g@ @A@.&@@#one.&@ @A@A.뾴@@#pow.뾴@ k@A@.L@@#sub.L@ @A@.@@#two.@ @A@ABCD.,a@@$div2.,a@ @A@.Xz@@$even.Xz@ ?1@A@A.@@$iter.ؑ@ @A@B. @@$land. @ @A@. @@$log2. @ @A@ACE.@@$lxor.@ R@A@.y@@$pred.y@ `<@A@A.Ʉ@@$sqrt.Ʉ@ ;@A@.@@$succ.@ @A@.t @@$zero.t @ Z@A@AB/@@.to_little_uint/@ @A@CD/@@%ldiff/@ H@A@3@@(tail_add3@^q@A@A3@@(tail_mul3@^@A@B6w~@ @'of_uint6w~@^5@A@@@&divmod> @C@A@>@@&double>@NĴ@A@A?;@ @&modulo?;@"i@A@BDEFG@ &Basics'Program#Coq@0!bs߯? :VU$Bool#Coq@0j 2cZ`FW*CMorphisms'Classes#Coq@0qیZBeϠ0CRelationClasses'Classes#Coq@0TL;0RUfw1[ZY@0.i bYN Z)Decidable%Logic#Coq@0ND걸풬/Oߠ'Decimal$Init#Coq@0C涳N*ua*Equalities*Structures#Coq@0όe얟)H.Ƞ+Equivalence'Classes#Coq@07;ꮹ-GenericMinMax*Structures#Coq@0måj$$Init'Classes#Coq@0](p{yOh."Le%Arith#Coq@0d}Omq+0\͉!Ig*Logic_Type$Init#Coq@0 1jc6"Lt%Arith#Coq@0KZ-eJkP܏%Minus%Arith#Coq@0LFtR")Morphisms'Classes#Coq@0Imӽ%\$PD.Morphisms_Prop'Classes#Coq@0% :B'.>u%$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@0҆mulf+NProperties(Abstract'Natural'Numbers#Coq@0unt"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#NatȠ@0eʤģPSR蠠)Notations$Init#Coq@0&v!D]hwnv *NumPrelude'Numbers#Coq@05WUVŦ]xVXԠ4Operators_Properties)Relations#Coq@0U3y#h&&Orders*Structures#Coq@0$Znl0\͗+OrdersFacts*Structures#Coq@05Mܿ獐ζΖLB)OrdersTac*Structures#Coq@05'4Ԗ+9%0 jha|ؠ(PeanoNat%Arith#Coq@0O~2$k[#lZ$Plus%Arith#Coq@04tmG'Prelude$Init#Coq@0JqTttֱ/RelationClasses'Classes#Coq@0Gz rA6ՠ4Relation_Definitions)Relations#Coq@0]4Ѐd{n^2Relation_Operators)Relations#Coq@0%s鯰s)Relations#Coq@0-SetoidTactics'Classes#Coq@0S_`nOU$&Specif$Init#Coq@0;RWMi\N'Tactics$Init#Coq@0/9m+ a'Tactics'Program#Coq@03(mult_0_l9D{(@@(PeanoNat%Arith#Coq@#Nat@'mul_0_l2^B(mult_0_r9D{(@@@'mul_0_r2d (mult_1_l9D{(@@ @'mul_1_l2(mult_1_r9D{(@@+@'mul_1_r2""_8X@%arith%Logic$Init@@"eq @@@)Datatypes@#nat@#Nat$Init#Coq@@#mul )Datatypes@@#nat@B @A'META714Z@@@@_!n!@P@D@&@#mul.CBAqq@@L@3Coq.Arith.Mult#<>#1!͡o@@@g@b'META715\@Bb@A@@RQOLIF@D.CA?@3Coq.Arith.Mult#<>#2!͡@)mult_comm9D{(@@@(mul_comm7 [ᠠ"_9X@%arith@@@@'META718'META719 0@@4!m@.؀G@.ހM@3Coq.Arith.Mult#<>#3!͡@1mult_plus_distr_r9D{(@@>@/mul_add_distr_r251mult_plus_distr_l9D{(@@I@/mul_add_distr_l2@2mult_minus_distr_r9D{(@@T@/mul_sub_distr_rLRK2mult_minus_distr_l9D{(@@_@/mul_sub_distr_lLRV#_10X@%arith4@@@,@',@#add `'META722'META723'META724AJi@@-m,*,!p0-*'@%.g-@#add.먩B4@.먩H:@8.z@@>.5 @3Coq.Arith.Mult#<>#4!͡@#_11X@%arith@@@@@#sub 'META728'META729'META730@@̀v@.ۀ@#sub.L@ Y Q@.LF@. e@. c @3Coq.Arith.Mult#<>#5!͡@#_12X@%arith@@@@'META736w'META734'META735)2!0@@4u @ .Ms@r.L  ©@x.L@._ ֩%@#.e  e@3Coq.Arith.Mult#<>#6!͡@*mult_assoc9D{(@@@)mul_assoc  o2 Q@@A@#_13 ~@ z>"@A@@@@@@@@#_142M접#_15'`o@C)nat_scope@   @#_16X@%arith @@@ @  'META740'META741'META742  b@@ ۛ ٶ ͛ ˶ ʛ ͩ ɰ    l d  o  j! @3Coq.Arith.Mult#<>#7!͡@#_17X@%arith%@@@@'META746 'META747'META748+0@@΀u @ .M ĩ@.S y@.Y@._   _@3Coq.Arith.Mult#<>#8!͡@ 2 Q@@A@#_18 m@ w@A@@@@@#_192M접 #_20'`o@C@@ y | i@ 2 Q@@A@#_21 @ 7R .@A@@@@@#_222M접 #_23'`o@C@@   @+mult_succ_l9D{(@@@*mul_succ_l+mult_succ_r9D{(@@$@*mul_succ_r 2 Q@@A@#_24 @ ܲ@A@@@@_@#_252M접 #_26'`o@B]_@  @#_27X@%arith @@@ @ @'META753 @A @'META752 󠛐 W@@ X W K J H G Q j F D  9 q  K@3Coq.Arith.Mult#<>#9!͡@ 52 Q@@A@#_28 Y@ @m,@A@@@@@#_292M접 #_30'`o@D٠۠ݠ@@   m {@#_31X@%arith @A@ ]'META758'META756 h 'META757Q@@  Ͷ  ϶  @  0 (   .   1 9w @4Coq.Arith.Mult#<>#10@ 2 Q@@A@#_32 @ m2@A@@@@R@#_332M접 #_34'`o@DPRT@@   䠐 @ 2 Q@@A@#_35 @ Ë@A@@@@@#_362M접 #_37'`o@F@@@ = @ C F * -@ 2 Q@@A@#_38 =@ G@A@@@@@#_392M접 #_40'`o@D@@ à   @#_41X@%arith A@ @ @B'META764'META765 R @B'META766^@@x      @   Щ 렩 ꠩   * 栩   (n @4Coq.Arith.Mult#<>#11@ 2 Q@@A@#_42 @ w@A@@@@I@#_432M접 #_44'`o@EGIK@@@ ? B E 5 8@ 2 Q@@A@#_45 @ w@A@@@@@#_462M접 #_47'`o@E}@@@ u x { k n@ 2 Q@@A@#_483@ _@A@@@@@#_492M접 #_50'`o@D@@ DG U@ 2 Q@@@@#_51e@ *ɝ@A@@@@@#_522M접 #_53'`o@B堐@ps@ ̠2 Q@@E@#_54 S(@#_552M접 CC@A#_56'`o@C  @ ܠ  @ 2 Q@@A@#_57@ &@A@@@@;@#_582M접 #_59'`o@C9;=@Ơɠ@ 2 Q@@@@#_60 j-g@#_612M접 BA@A#_62'`o@Bdf@ 3 @ 2 Q@@A@#_63 @ @A@@@@@#_642M접 #_65'`o@B@@*tail_simplF@@@@@@A@$Plus%Arith#Coq@@.plus_tail_plus6SOh@7./theories/Arith/Mult.v@@@@@@@@@@P@@@@@@@@AAAAAA@@@@@@햖Qyb0Kn@ظs*<K@}ߞ0mؼiu(K@(́&ahMZ)AB 8!n)Datatypes$Init#Coq@@#nat@!m!p%Logic@&eq_sym X#Nat@#mul C BA (PeanoNat%Arith1@)mul_assoc B@3AȐ!HGE8FР3@#andЖw@BBB@@@@D@@F@"eq @`0@@.D<fAV@"or @rK tJ@ yN!{M@'DR@(eq_mul_0?_@3@@$4.i+f;hdVT@I@GABASP R @ZWY8@a^7@(eq_mul_1?@"@@j6#Ŷ(4ɷ@@A@A@@@@Dҩj]%Peano@"le UxT@ {AΠõAC BZ)ةڵ@(le_add_rN*C     @4mul_le_mono_nonneg_l*`O驚@&le_0_l?@4mul_le_mono_nonneg_r*`O*()*!q-Z"H0^@2mul_le_mono_nonneg9؀ FE(*EC6D4E6GJH;I@u@"lt Uxc* @@ (  ک"6@ҩ8Զ@.-0驚:@1mul_lt_mono_pos_lJGF@@@+Lfwzxky@0%P>VSM@)lt_0_succ5%DywG3Z@Ȑ"H1HdVUfiT@g  @RV@K@KWC$jEl@^J+L-L@MeQxyS4{@1mul_lt_mono_pos_rK@@@J¶@y#5ƷǷʷ˷̷@j@~@1,@-y@  w@1mul_le_mono_pos_l2.dt@@ @qp@#add `ߠ]__ש@.Even_Odd_False-?> @"ex @A)İ )  "-(C@#notШ80..@'nat_indJ86)7'8:E$Mult @(mult_acc!<J:K8M#X%꩚z@(plus_n_O0G؀,CIWGXZe2?54b`#IHn-WeUfS@(eq_ind_r!2#m=@x.먩yKWKywyN;$PlusJ@)tail_plus~ZIH]G 3  Mg9iiS/*Ap !@.plus_tail_plus6SOh5s@(add_commbQ 0lVCWZyy)]I@(eq_trans!y̠HGJM@'f_equal=ҷ!fK$ !% 0  ඐ!sƐ=1 ,70ѩ.)66 82$99; ۠ة۩@)add_assoc7!+Cذ퐑 @&eq_ind J$/)'ϰ);+@,mult_acc_aux&Հ  Cܰ6@)tail_multـ(ae j@