"`C' \&$Znat&ZArith#Coq@`(PeanoNat%Arith#Coq@"Gt%Arith#Coq@$Plus%Arith#Coq@%Minus%Arith#Coq@"Le%Arith#Coq@"Lt%Arith#Coq@$Mult%Arith#Coq@'Between%Arith#Coq@)Peano_dec%Arith#Coq@+Compare_dec%Arith#Coq@)Factorial%Arith#Coq@%EqNat%Arith#Coq@)Notations$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$Init#Coq@&Wf_nat%Arith#Coq@*Arith_base%Arith#Coq@)Notations$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$NLog(Abstract'Natural'Numbers#Coq@0Kj&BinNat&NArith#Coq@!N@&of_natK)BinNatDef&NArith#Coq@!N@&of_nat)j2_A7@&of_natbz.@&of_nat1?G!A@@@@@AA@@A@'N_nat_Z @@Az'BinNums'Numbers#Coq@@!N7@yn,L@&to_nat`C@&to_nat*9GAqA@@@@@5.positive_nat_Z @@B!p'BinNums'Numbers#Coq@@(positive*@3]&BinPos&PArith#Coq@#Pos@&to_nat")BinPosDef&PArith#Coq@#Pos@&to_nat5L A'BinNums'Numbers#Coq@@!Z7@BA@@@@@,positive_N_Z @@ CO'BinNums'Numbers#Coq@@(positive*@署‐2@!N7@BA  6+8@#mul @3BBA@#mul1P]#@ 4B9A@@@@@+inj_sub_max @@XtBAFlaTn@#sub c4@3BAb@#max1PY@#max A@#sub1Pe@ pvB{A@@@@@?'inj_sub @@Y@|ABE3@@@@@l(inj_succ @@Z㛠׀̩@$succ ! @$succ?\A@$succ1\w@$succ րA@@@@@,inj_pred_max @@![߀퀐@$pred @$pred?U瀐AA@$pred1\@$pred j A@@@@@Ϡ(inj_pred @@V\F@ဠAAA6)</5@@@@@'inj_min @@]o=::cXK4@#min +@#min3`BAZ@#min1P{Q@#min "cBhA@@@@@,'inj_max @@^qnnh@#max _@#max3ҀBA,BA@@@@@['inj_div @@_қX\ʀ@#div l@3BAh@#div1P@ yȀB̀A@@@@@'inj_mod @@`6ӛT@@@#notШAeA@&modulow@)1ᩚ@&moduloNH/@1,ր @@@@@Ҡ(inj_quot @@YaIwu=2%sBA@$quot1\&@ }7BÀA@$div21[8@$div2 A@@@@@])inj_quot2 @@d.ƀ,A@%quot22=*@%quot2 рA@@@@@'inj_pow @@ eɀț̀詚ۀ@#pow @3BA@#pow1P1@ ؀񀐐BA@@@@@+inj_testbit @@Af!a4!&C@$boolZ'@@'testbitq @'testbit5)B"A @'testbit5z@'testbit-T|ŀBA@@@@@@@@@@@@#Z2NsA_ @@gq'BinNums'Numbers;@@:7@@AAwl_ EE@@@@@&h @@h+g-@AB@&Ac@2D7rPE @@@@@Wu @@i\^@NCAB@WLAր˩f4j‰<@@@@@Q @@j䩚tASA@@@@@H @@&k@BABA@@@@@'inj_neg @@Fl6;(`CAA@@@@@ܠK @@bmRᶐ@ӀAB@܀AWL瀐M&[2@@@@@K @@nS@ AB@AOM\[)-h@@@@@Hܐ @@oM@=2AAI؀怐U@@@@@p1 @@p曠uy@i^AA倰کuc}@@@@@ѐ @@ &q 0 򀐐AA@@@@@I @@ Gr 7ƶȶ@AB@A < M@*comparison;f@@րڀ^@@@@@> @@ s o:@AB@A6'?M کK@@@@@ +B @@ t 0l2@"AB@+ AhYIqV> B}@@@@@ ]e @@ u ӛbf ɀY[BAlgBlA@@@@@ \ @@ v + 穚|BAaBA@@@@@ V @@ 7w '@AB@A ,!XfȀ̀@@@@@ 砠V @@ mx ]춐(@ހAB@A$ bW򀐩K1W̩ =@@@@@ K @@ y "^$@ AB@AZ  (UgҀ 4 8s@@@@@ SS @@ z XZ@J?AB@SHA ΀é ^]0À j8 n@@@@@ Z @@ {  詚 OA^ A@@@@@ O @@ 2| "    KA A@@@@@ ϠK @@ U} EԶ ֶ@ƀAB@πA  J ? ڀM [ 怐 ꀐ %@@@@@ K @@ ~J h } @AA xRL d G FA K  N@@@@@ /@@@@>@&Zabs2N A*abs_N_spec @@      逐A 8̀A@@@@@ X,abs_N_nonneg @@ @ ^@ N CAA ʀ)   ^ @@@@@ y&id_abs @@ A  . ‰ ש ʀ ,A A@@@@@   @@ B   ^ E 뀐AA@@@@@  x @@ 6C u \ A zA@@@@@ Ǡ o @@ MD  B / u gBA ;BA@@@@@ 栠' @@ lE  a N  CA ZBA@@@@@ 'inj_opp @@ F |  pϩ  @#opp1P S@ {A ÀA@@@@@ ) @@ G .@  AA   hǀ 쀐 p@@@@@ Q @@ H V X@ H =AB@ Q FA  ̀+ €. Ѐ 6 " @@@@@  @@ I  ʛ T ;BAŀ IB NA@@@@@ u @@ :J * @%Logic$Init#Coq@@#andЖw@  AA €AB <   Ԁ    @@@@@ ( @@ }K m@  AA hǩ R 6g  >@@@@@   @@ L $ `&@  AB@  A \ ^  䀐 耐 m  q@@@@@ Q  @@ M V X@ H =AB@ Q FA   \*   2  @@@@@   @@ N  @ z oAB@  xA   \ ɩ  Ld P Ր@@@@@  @@;O+ @  AB@  A 򩛠0 v€ р   @@@@@ 렠 @@qPa ,@ † AB@ 뀠 A (fũ   5Ӏ Щ  A@@@@@!O @@Qz d~ ՀLBAˀ 【B 耐A@@@@@NN @@R- + GBA B A@@@@@w @@S훠Ѐ @ p eAA쀰K 2   > é B Ɛ@@@@@,inj_succ_abs @@.Tq X 1 :A D iA@@@@@Ϡ+inj_add_abs @@VUF( *:  0 bB gA H B A@@@@@+inj_mul_abs @@VxZ C\l˩  , B A D ȀB ̀A@@@@@3@@@@B@%Nat2ZA  @@W)S)Datatypes$Init@@#nat@A 4A@@@@@]  @@Xӛ)Datatypes$Init#Coq@@#nat@ҀY@BA A@@@@@  @@Y @#nat@  |AA@@@@@ @@0Z !ɀAA@@@@@Š @@K[;8:@0တB怐A>M@@@@@堠 @@k\[X&ZSکB AapBA@@@@@   @@]}Kt  )B.A(PeanoNat%Arith#Coq@#Nat@'comparel#Nat$Init#Coq@@ 3RЀBA@@@@@C  @@^)Datatypes$Init#Coq@@#nat@m%Peano@@"le UxT@BAY~BA@@@@@~  @@_)Datatypes$Init#Coq@@#nat@̛<@"lt UxcBA BA@@@@@  @@;`+7;րh@"ge UwBA တB怐A@@@@@ᠠ  @@gaWc$g@"gt UxBA  BA@@@@@ +inj_abs_nat @@b v'A A@@@@@+  @@c)Datatypes$Init#Coq@@#nat@y)Datatypes$Init#Coq@@#nat@6`#Nat$Init#Coq@@#add `BA xB}A@@@@@x  @@dMQ䀰k5@#mul BA BA@@@@@  @@,el@ꛠƀf@#sub BA A ހB【A@@@@@ޠ  @@dfT@ABO֩: р &)@@@@@  p @@g)Datatypes@@#nat@}.(PeanoNat%Arith#Coq@@$pred.y@$pred ` x@@@@@r z @@i蛠hlgc@#min.Y@#min BA }BA@@@@@ x @@*j盠À@#max.p@#max 'BAրBۀA@@@@@@@@@ @%Z2NatWAC @@ekU @ԀAAPשڀ@@@@@A @@lu @ @AB@A<@{i ٩J (  @@@@@.L @@m 3o 5@%AB@.#Ak\3 7| Z @@@@@`( @@nƀLKAA@@@@@w @@o򩛠߀ͩeBA9A@@@@@ ֐ @@p 멚5CA0A@@@@@  @@7q'  @AB@A,"  €@@@@@砠  @@mr] 춐( @ހAB@瀠A$bP耐" 1 ̩=@@@@@ @@s "@AA|\B!e@@@@@F @@t ֶ M@=2AA?7KO@@@@@t @@u ܀ʩbƀAdoA@@@@@ @@v   @AB@Aҩ)Datatypes$Init#Coq@@*comparison;f@ 𩚠9 @@@@@Ԡ @@ZwJ ٶ ۶@ˀAB@ԀA߀ ݀ တ&@@@@@ @@x| G @AB@AC4$ L 穚X@@@@@8@ @@y ۶y?(4BAȀ6B;A@@@@@a5 @@z hˀQUBA_BdA@@@@@@@@@@(Zabs2Nat A,abs_nat_spec @@{  :A'A@@@@@.abs_nat_nonneg @@:|*@AA%)a署@@@@@Ԡ [ @@Z}J^<é퀐|AeA@@@@@U @@w~gdY]AA@@@@@ Ґ @@ptAA@@@@@!ɐ @@ŀBA【A@@@@@? @@ 【CAA@@@@@] @@b@RGAA΀ҩ 퀐B@@@@@ @@ @}rAB@{Aé=cЩVIkMܐ@@@@@ @@B2 5 3&*b怠BAHpBuA@@@@@堠 @@k[궐&@ 1AA耠ABbf10Q9<@@@@@N @@"@%AAʀx\րd@@@@@E͐ @@JL@<1AB@E:A>"܀*@@@@@w @@|~@ncAB@wlAP<6X:ɐ@@@@@ @@/@AB@A橚׀ǀ署1hl@@@@@۠ @@aQඐ@ҀAB@ۀAVZ耠%z1@@@@@ @@R@AB@ANȀ[~Ԁ؀g@@@@@G  @@ 뀐΀׀ABA@@@@@m  @@ Ŷ ǩ׀۩̀BA6)B.A@@@@@  @@$   DȀ0B5A2ZB_A@@@@@@@@@ސ@#neq @!x  _@@ @!y %Logic @#notШ @"eq @A@"  A P+k() 77"7$'1hp+|@@@@@'inj_neq @@%Z#@@V'mBAo@#Zne>o=@ZD]@@@@@>2Zpos_P_of_succ_nat @@)Datatypes$Init#Coq@@#nat@@B @+of_succ_natq@+of_succ_nat$퀐Aတ{A@@@@@v&inj_eq @@'f_equal=`_@]7@&BinIntf@&of_natbzk@1?G!@!x !y @@@ @ BA C (6777"k;L6DG\T@@@@@Π @D@%proj1O@%Peano@ UxT@ 񩚠_@1P,eg@ lo @F+F@s > @ ,  1 2 +k() 7! + 7 7 7!T +7!T7&'7%'7 7 7%'Рh:\LH9h@@@@@)@ @[UZVY@S@"lt UxcQ@1P-P@K HG@\+U^@ ö @ pU  u vDР%h\L+h@@@@@kV @@@"ge Uw@1P,@ @r+@ ζ ̶@ Ǡ   Рh\L%h̐1@@@@@l @ٷکݰ@@"gt Uxթ3@1P,Զ@ϩ ̩@+@; 䶐 @ ݠ٩ ֠ Ԑ ѐȐРhU\L .#h@@@@@*inj_minus2 @@vf |3 @ ABe쩚 P43A@@@@@@@@ ӳ2@ ӳ2[)Datatypes$Init#Coq@@A@ Գq@ Գq\ @A@AB@@@"O@(PeanoNat%Arith#Coq@#Nat@&of_int"O#Nat$Init#Coq@@ 6@A@A\@-~@'quotrem\~@/@A@\@@+pred_double\@/S@@A@As2@"@&shiftls2@vY@A@BCs8@'@&shiftrs8@vY@A@ѓ@-@&squareѓ$@y@A@@3@&to_intϑ*@@A@z@$@&doublez@/!@A@ABCD/@>@)log2_iter/5@wd@A@NH/@1@NH/@A@A\d@4@&of_int\d@1?A @A@bz@:@bz@A@#@>@&shiftl#@1dV@A@#@D@&shiftr#@1d\@A@ABCD/x@&BinPos&PArith#Coq@#Pos@)pred_mask/x)BinPosDef&PArith#Coq@#Pos@ )X@A@6@c@&square6@19@A@AV+L@h@&to_intV+L@2@A@V1b@n@V1b@A@V5=@r@&to_posV5=@2@A@ABCl@@)sqrt_iterl@!$:@A@@@4@(sub_mask@+@)@A@ADEF c@@'testbit c@!ć@A@7 B@B@'of_uint7 B9@*`]?@A@AG@G@)mask_rectG>@+ED@A@F˱@M@)add_carryF˱D@+p@A@AB^Ҷ@@'to_uint^Ҷ@#m@A@gL7@@'sqrtremgL7@40@A@Aq@@q@A@ݎO@@+succ_doubleݎO)@6r@A@A p@h@0double_pred_mask p_@0-+m@A@BCD T@&BinNat&NArith#Coq@!N@!t T)BinNatDef&NArith#Coq@!N@ 2@A@ @@#add @3 @A@A l@@#div l@3@A@ Y@%@#eqb Y@3@A@AB #@*@#gcd #!@3n@A@ T@0@#leb T'@3@A@ACEG "@5@#lor ",@3m@A@ q@?@#ltb q6@3@A@A @D@#max ;@3@A@ @J@#min A@3`@A@AB @O@#mul F@3B@A@ ~@U@#odd ~L@3@A@AC =@Z@#one =Q@3@A@ @b@#pow ˑY@3@A@A c@g@#sub c^@3@A@ @m@#two d@3J@A@AB hx@r@$div2 hxi@>@A@ @x@$even o@>4@A@ACD @}@$ggcd Бt@>U@A@ @@$iter }@>:@A@A 3"@@$land 3"@>m@A@ F)@@$log2 F)@>t@A@AB S@@$lxor S@>@A@ @@$pred @?U@A@AC @@$size ܑ@?'@A@ !@@$sqrt !@?@A@A ! @@$succ ! @?\@A@ !7@@$zero !7@@P@A@ *@@%ldiff *@@A@AB g_@-@+pred_double g_$@25\@A@CD m@2@÷ m)@2j@A@S@9@&of_intS㫑0@4}5@A@AS@>@&of_natS5@4};@A@BEFGH\R@C@(mask_ind\R:@4@A@\^@M@(mask_rec\^D@4@A@A!,@R@&pred_N!,I@4s)@A@B@W@&shiftlN@5X@A@@^@&shiftrU@5X@A@A&@c@&square&ّZ@5,x@A@BC"@h@&to_int"_@5L@A@"@p@&to_nat"g@5L @A@AnTq@u@+testbit_natnTql@6n@A@B@@(succ_posB@@A@I@@I@A@AB.@@'of_uint.@MS@A@3~@@'sqrtrem3~@7]%{@A@ACD,@@'bitwise,@/v@A@>4'@@'testbit>4'@8g$@A@A{U@@,sqrtrem_step{U@8R@A@u^@7@(div_euclu^.@ @A@Afz@@'to_uintfz@9w@A@Bl@ @'comparel@3R@A@CDEFs8@@+of_uint_accs8@5+@A@}@P@,pos_div_eucl}G@&`@A@3x@ @3x@A@A@Z@&doubleQ@'޺_@A@BCq@@+of_succ_natq@$@A@w@e@&modulowɑ\@)1@A@ADK@j@&of_intKa@)j,I@A@K@r@&of_natKi@)j2_@A@AI@w@&shiftlIn@*O@A@O@}@&shiftrOt@*O@A@AB,@@&square,y@*ow@A@Z@@&to_intZ@*81@A@ACE`@@&to_nat`@*9G@A@e@@+testbit_nateđ@+@A@A+{@@'sqrtrem+{ё@,J@A@5z@@'testbit5z@-T|@A@A @@'to_uint ͑@.@A@ @@+succ_double @.^4@A@A#@@'compare#ݑ@ )Q@A@BCD%t2@$@(size_nat%t2@ @A@%9@+@+of_uint_acc%9"@ ΋@A@A%V@0@+double_mask%V'@ S@A@%%@6@'div2_up%%-@ "@A@ABEF'ş@;@'Ndouble'ş2@ @A@(b0@C@*shiftl_nat(b0:@9-@A@A(nՖ@H@*shiftr_nat(nՖ?@'@A@(@N@0succ_double_mask(E@@A@*W$@T@,compare_cont*W$K@!@A@.0@Z@.sub_mask_carry.0Q@΂@A@ABCD.@@!t.@ ;@A@.먩@@#add.먩@ `@A@A.U@@#div.U@ @A@.B@@#eqb.B@ @A@A. @@#gcd. @ @A@.=@@#leb.=@ @A@ABCEGHI. @@#lor. @ @A@.Z@@#ltb.Z@ @A@A.p@@#max.p@ '@A@B.@@#min.@ @A@.@@#mul.@ @A@AC.g@@#odd.g@ @A@.&@ @#one.&@ @A@A.뾴@@#pow.뾴@ k@A@.L@@#sub.L @ @A@.@@#two.@ @A@ABCD.,a@@$div2.,a@ @A@.Xz@'@$even.Xz@ ?1@A@A.@,@$iter.ؑ#@ @A@B. @1@$land. (@ @A@. @7@$log2. .@ @A@ACE.@<@$lxor.3@ R@A@.y@C@$pred.y:@ `<@A@A.Ʉ@H@$sqrt.Ʉ?@ ;@A@.@O@$succ.F@ @A@.t @U@$zero.t L@ Z@A@AB/@Z@.to_little_uint/Q@ @A@CDF/@_@%ldiff/V@ H@A@00@@'compare00@?H{@A@A1P%@Z@!t1P%@  @A@B1P@_@1P@A@1P&@d@1P&@A@A1P@g@,1Pґ,@A@BC1P@j@#eqb1P@ f@A@1P@r@#gcd1P@ 0@A@A1P@w@#geb1P@ T@A@B1P@|@#gtb1Pʑ@ q@A@1Pĺ@@#leb1Pĺ@ a@A@A1Pň@@#lor1Pň@ /@A@BCD1P@@#ltb1Pב @ ~@A@1P@@1P@A@A1P{@@1P{@A@B1P]@@1P]@A@1P@@#odd1P@ @A@A1Pɣ@@#one1Pɣ#@ J@A@BC1P@@1Pԑ@A@1P1@@M1P1M@A@A1P;@@1P;@A@B1P@@#sgn1Pˑ4@ r@A@1P@@1Pɑ@A@A1Pe@@#two1Pe>@  @A@BCDE1[8@@1[8ޑ@A@1[d@@$even1[dJ@ I@A@A1[6@@$ggcd1[6O@ i@A@B1[U@@$iter1[UT@ @A@1\@@$land1\[@ /@A@A1\@@$log21\`@ 6@A@BC1\$@@$lxor1\$e@ @A@1\Y@@b1\YÑm@A@A1\@@u1\w@A@B1\@@M1\֑M@A@1\@@$sqrt1\y@ @A@A1\w@@1\w@A@BC1\k@@/1\k1@A@1]@ @$zero1]@ eD@A@A2:@@2:@A@21@@%ldiff21@ ߵ@A@2=*@@2=*@A@ABC2kF@f@(size_nat2kF]@{@A@3@7@(tail_add3.@^q@A@ADEFGH3@<@(tail_mul33@^@A@5Z@{@*shiftl_nat5Zr@y/@A@5f}@@*shiftr_nat5f}x@4@A@AB5a@@'iter_op5a@ @A@C6w~@V@'of_uint6w~M@^5@A@8j@H@'of_uint8j@'"h@A@9E@N@(div_eucl9Eđ@(*k@A@AB:x@ @,Nsucc_double:x@ ʭ@A@CD@#lor=Lϑ5@#F@A@=M@H@#ltb=M?@#F@A@A=M4@M@#max=M4D@#F1@A@=M@S@#min=M‘J@#F@A@AB=N@X@#mul=NO@#F@A@=Rx@^@#pow=RxU@#Fu@A@AC=W@c@#sub=WZ@#F @A@='%@k@$div2='%b@#Q"@A@A=(@p@$gcdn=(g@#QX@A@=( }@v@$ggcd=( }m@#Q^z@A@AB=(T@{@$iter=(Tr@#Q@A@=(@@$land=(ϑx@#Q@A@ACD=(@@$mask=(}@#Q@A@=(_@@$lxor=(_@#Q\@A@A=) I@@$pred=) I@#R_F@A@=)R@@$size=)R@#R@A@AB=)]H@@$sqrt=)]H@#RE@A@=)a@@$succ=)a@#R@A@A=9R@@.to_little_uint=9Rˑ@#b@A@=@@%ggcdn=͑@$*@A@=U@@%ldiff=U@$'R@A@ABCD>@@&divmod>@C@A@>@!@&double>@NĴ@A@?2@@,pos_div_eucl?2 @-u@A@AB?;@,@&modulo?;#@"i@A@CEFGIJ@*Arith_base%Arith#Coq@0Ĕ}CS&Basics'Program#Coq@0!bs߯? :VU'Between%Arith#Coq@06v*0ur`C0c0BpHޞun^)BinIntDef&ZArith#Coq@0ådR4Tuyݐ0K11ڤs+Π)BinNatDef&NArith#Coq@03@1O,[{    @0dmk(5Ju<&BinPos&PArith#Coq@0vyػ0= u)BinPosDef&PArith#Coq@0}H d.%,b$Bool#Coq@0j 2cZ`FW*CMorphisms'Classes#Coq@0qیZBeϠ0CRelationClasses'Classes#Coq@0TL;0RUfw1+Compare_dec%Arith#Coq@0jXF 8@0.i bYN Z)Decidable%Logic#Coq@0ND걸풬/Oߠ'Decimal$Init#Coq@0C涳N*ua%EqNat%Arith#Coq@0AIgՋXRV *EqdepFacts%Logic#Coq@0FI$ͼՋ`)Eqdep_dec%Logic#Coq@0u wWIϰ߼*Equalities*Structures#Coq@0όe얟)H.Ƞ+Equivalence'Classes#Coq@07;ꮹ)Factorial%Arith#Coq@0@oehJd-GenericMinMax*Structures#Coq@0måj$"Gt%Arith#Coq@0䙛#c:D $Init'Classes#Coq@0](p{yOh."Le%Arith#Coq@0d}Omq+!0\͉!Ig*Logic_Type$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%$Mult%Arith#Coq@0햖Qyb0$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#NatŠ@0eʤģPSR蠠$Nnat&NArith#Coq@0$W;s #%M)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%ߐ0 jha|ؠ0O~2$k[#lZ)Peano_dec%Arith#Coq@0Kݢ*k$Plus%Arith#Coq@04tmG$Pnat&PArith#Coq@0,?pr.gZ'Prelude$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%72 Q@@A@"_8%F@%B+.@A@@@@@@@@"_92M접#_10'`o@A)nat_scope@%R@$2 Q@@A@#_11%m@$lN@A@@@@'@#_122M접 #_13'`o@A'N_scope@$@$נ2 Q@@A@#_14%@$'J2@A@@@@L@#_152M접 #_16'`o@A.positive_scope@$@$2 Q@@A@#_17%@$C1@A@@@@q@#_182M접 #_19'`o@A%@$@$2 Q@@A@#_20%@$' R)@A@@@@@#_212M접 #_22'`o@AI@$@$2 Q@@A@#_23%@$'J2 @A@@@@@#_242M접 #_25'`o@Am@%\@$2 Q@@A@#_26&#@$2@A@@@@@#_272M접 #_28'`o@A'Z_scope@&@$2 Q@@A@#_29&H@$3+@A@@@@@#_302M접 #_31'`o@A%@&5@$2 Q@@A@#_32&l@$d@A@@@@&@#_332M접 #_34'`o@AI@&Y@$2 Q@@A@#_35&@$VD@A@@@@J@#_362M접 #_37'`o@Am@&}@$rHȠ@$2 Q@@A@#_38$@$; -@A@@@@s@#_392M접 #_40'`o@AL@$@$2 Q@@A@#_41$@$; @A@@@@@#_422M접 #_43'`o@Cpr@@$נ$ڠ&@$2 Q@@A@#_44$@$2Q@A@@@@@#_452M접 #_46'`o@B@%%@$2 Q@@A@#_47% @$9@A@@@@@#_482M접 #_49'`o@A@%*@$2 Q@@A@#_50%D@$;@A@@@@@#_512M접 #_52'`o@@@@$2 Q@@A@#_53%c@$2@A@@@@0@#_542M접 #_55'`o@A@&@$2 Q@@A@#_56%@$ Ui@A@@@@T@#_572M접 #_58'`o@B-/@%%@$2 Q@@A@#_59%@$ p}5@A@@@@}@#_602M접 #_61'`o@BVX@$$@$}2 Q@@A@#_62%@$ p}D@A@@@@@#_632M접 #_64'`o@B@$Ơ$@$z2 Q@@A@#_65&@$ p|@A@@@@@#_662M접 #_67'`o@B@$$@$w2 Q@@A@#_68&+@$ p|@A@@@@@#_692M접 #_70'`o@BѠ@%%@$t2 Q@@A@#_71&T@$ 3>@A@@@@!@#_722M접 #_73'`o@AD@(T@$t2 Q@@A@#_74&x@$2@A@@@@E@#_752M접 #_76'`o@B @%e%h@$g2 Q@@A@#_77&@$r2@A@@@@n@#_782M접 #_79'`o@BGI@%%@$Z2 Q@@A@#_80&@$e8S@A@@@@@#_812M접 #_82'`o@Bpr@%%@$A2 Q@@A@#_83&@$L2 @A@@@@@#_842M접 #_85'`o@C@@%᠐%䠐%@$A2 Q@@A@#_86' @$L7|f@A@@@@@#_872M접 #_88'`o@A@& @$72 Q@@A@#_89'D@$B,U@A@@@@@#_902M접 #_91'`o@A@&/@$&2 Q@@A@#_92'h@$17'@A@@@@5@#_932M접 #_94'`o@B@@&T&"@$%2 Q@@A@#_95'@$026@A@@@@]@#_962M접 #_97'`o@B68@&}&@$2 Q@@A@#_98'@$%2@A@@@@@#_992M접 $_100'`o@B_a@&&@$2 Q@@A@$_101'@$2@A@@@@@$_1022M접 $_103'`o@B@))@$2 Q@@A@$_104( @$2@A@@@@@$_1052M접 $_106'`o@C@@)$$$"@#2 Q@@A@$_107(8@#7G@A@@@@@$_1082M접 $_109'`o@Bޠ@)ݠ)@#2 Q@@A@$_110(a@#2@A@@@@.@$_1112M접 $_112'`o@B @** @#2 Q@@A@$_113(@#5@A@@@@W@$_1142M접 $_115'`o@A0@'u@#ޠ2 Q@@A@$_116(@# U@A@@@@{@$_1172M접 $_118'`o@AT@'@#۠2 Q@@A@$_119(@#2@A@@@@@$_1202M접 $_121'`o@Bxz@''@#Π2 Q@@A@$_122(@#9;@A@@@@@$_1232M접 $_124'`o@B@)) @@#rHȠ@)2 Q@@A@$_125#@)% %M@A@@@@@$_1262M접 $_127'`o@B@@#֠(@) 2 Q@@A@$_128#@)+ @A@@@@@$_1292M접 $_130'`o@EAC@@@@$$((+p@)12 Q@@A@$_131$'@)<x"q@A@@@@S@$_1322M접 $_133'`o@Dvx@@@$6$9)*)-@) 2 Q@@A@$_134$X@) @A@@@@@$_1352M접 $_136'`o@@@@) 2 Q@@A@$_137$w@)x-@A@@@@@$_1382M접 $_139'`o@AW@*@#Ƞ2 Q@@A@$_140$@#x)l@A@@@@@$_1412M접 $_142'`o@A{@+@(2 Q@@A@$_143$@(%x@A@@@@@$_1442M접 $_145'`o@D@@@$Π$Ѡ) )@(2 Q@@A@$_146$@( x)8@A@@@@@$_1472M접 $_148'`o@D?A@@@$%)󠐑)@'2 Q@@A@$_149%!@'+@A@@@@M@$_1502M접 $_151'`o@Bp@@%-*@'2 Q@@A@$_152%I@(x1@A@@@@u@$_1532M접 $_154'`o@C@@%W%Z*K@'2 Q@@A@$_155%v@'+O@A@@@@@$_1562M접 $_157'`o@A@%@*2 Q@@A@$_158%@*9@A@@@@@$_1592M접 $_160'`o@D預@@@%%**@)2 Q@@A@$_161%@*TU@A@@@@@$_1622M접 $_163'`o@D@@@%ڠ%ݠ*Π*@)2 Q@@A@$_164%@* Td@A@@@@(@$_1652M접 $_166'`o@DKM@@@& &*+@(!2 Q@@A@$_167&-@(,x(V@A@@@@Y@$_1682M접 $_169'`o@B|~@&:&=@(2 Q@@A@$_170&V@(!x'@A@@@@@$_1712M접 $_172'`o@B@&c&f@(2 Q@@A@$_173&@(x@A@@@@@$_1742M접 $_175'`o@DΠР@@@&&++@( 2 Q@@A@$_176&@(x(@A@@@@@$_1772M접 $_178'`o@D@@@&& +*@'2 Q@@A@$_179&@(+n@A@@@@ @$_1802M접 $_181'`o@D02@@@&𠐒&󠐑+䠐+@'2 Q@@A@$_182'@( x/@A@@@@ >@$_1832M접 $_184'`o@Dac@@@'!'$,,@(2 Q@@A@$_185'C@( +@A@@@@ o@$_1862M접 $_187'`o@A@'N@'2 Q@@A@$_188'g@(9/@A@@@@ @$_1892M접 $_190'`o@A@.@'2 Q@@A@$_191'@'x- @A@@@@ @$_1922M접 $_193'`o@Dڠܠ@@@'',,@'2 Q@@A@$_194'@' w[@A@@@@ @$_1952M접 $_196'`o@C  @@-('͠,@@#rHȠ@#2 Q@@A@$_197#@#VBA@A@@@@ @$_1982M접 $_199'`o@A =@/M@#2 Q@@A@$_200#@#@A@@@@ >@$_2012M접 $_202'`o@B a@@(-@#2 Q@@A@$_203#@# @A@@@@ f@$_2042M접 $_205'`o@A @/@-2 Q@@A@$_206$!@-2r@A@@@@ @$_2072M접 $_208'`o@A c@-@-62 Q@@A@$_209$E@-A3V@A@@@@ @$_2102M접 $_211'`o@@@@-52 Q@@A@$_212$d@-@*Fz@A@@@@ @$_2132M접 $_214'`o@A @/"@'2 Q@@A@$_215$@'*Fv@A@@@@ @$_2162M접 $_217'`o@A @/F@#Р2 Q@@A@$_218$@#*Fy9@A@@@@ @$_2192M접 $_220'`o@A 8@(@+2 Q@@A@$_221$@+@A@@@@ 9@$_2222M접 $_223'`o@B \@@). @,2 Q@@A@$_224$@,*Fd@A@@@@ a@$_2252M접 $_226'`o@D  @@@)D)G.8.;@,2 Q@@A@$_227%)@,*Fv@A@@@@ @$_2282M접 $_229'`o@B  @)s)v@,<2 Q@@A@$_230%R@,G*F.@A@@@@ @$_2312M접 $_232'`o@C ޠ @@))#@+٠2 Q@@A@$_233%@+霛@A@@@@ @$_2342M접 $_235'`o@B @@)Ƞ-@.X2 Q@@A@$_236%@.cޛ@A@@@@ @$_2372M접 $_238'`o@D 3 5@@@)󠐒).砐.@.F2 Q@@A@$_239%@.Q"@A@@@@ A@$_2402M접 $_241'`o@D d f@@@*$*'//@.I2 Q@@A@$_242& @.T"@A@@@@ r@$_2432M접 $_244'`o@D  @@@*U*X/I/L@,k2 Q@@A@$_245&:@,v*Fu@A@@@@ @$_2462M접 $_247'`o@D Ơ Ƞ@@@**/z/}@,h2 Q@@A@$_248&k@,s*FuR@A@@@@ @$_2492M접 $_250'`o@D  @@@**//@+2 Q@@A@$_251&@+o@A@@@@ @$_2522M접 $_253'`o@B ( *@2:2=@+2 Q@@A@$_254&@+*F|@A@@@@ .@$_2552M접 $_256'`o@B Q S@2c2f@+2 Q@@A@$_257&@+*Fz@A@@@@ W@$_2582M접 $_259'`o@C z |@@2+<0-@#2 Q@@A@$_260'@# g@A@@@@ @$_2612M접 $_262'`o@A @+c@#2 Q@@A@$_263'?@#;ے@A@@@@ @$_2642M접 $_265'`o@B ˠ @++@#2 Q@@A@$_266'h@#l9@A@@@@ @$_2672M접 $_268'`o@B  @++@@#rHȠ@02 Q@@A@$_269#@0OU@A@@@@ @$_2702M접 $_271'`o@@@@.r2 Q@@A@$_272#@.}:w@A@@@@@$_2732M접 $_274'`o@A@#@02 Q@@A@$_275#@1{@A@@@@B@$_2762M접 $_277'`o@A@@#@12 Q@@A@$_278#@1rr>@A@@@@f@$_2792M접 $_280'`o@Ad@#@12 Q@@A@$_281$@1s@A@@@@@$_2822M접 $_283'`o@C@@#ڠ#ݠ3@12 Q@@A@$_284$J@1ob@A@@@@@$_2852M접 $_286'`o@B@$$ @1(2 Q@@A@$_287$s@13+@A@@@@@$_2882M접 $_289'`o@Bޠ@$/$2@12 Q@@A@$_290$@1+F@A@@@@ @$_2912M접 $_292'`o@B @##@1 2 Q@@A@$_293$@1+U@A@@@@2@$_2942M접 $_295'`o@B02@##@12 Q@@A@$_296$@1+@A@@@@[@$_2972M접 $_298'`o@BY[@##@12 Q@@A@$_299%@1+@A@@@@@$_3002M접 $_301'`o@B@#⠐#@#`2 Q@@A@$_302%@@#k$@0@A@@@@@$_3032M접 $_304'`o@A@4@12 Q@@A@$_305%d@1 c@A@@@@@$_3062M접 $_307'`o@BϠ@##v@02 Q@@A@$_308%@0v)@A@@@@@$_3092M접 $_310'`o@B@##@02 Q@@A@$_311%@0eǪ@A@@@@#@$_3122M접 $_313'`o@B!#@#Y#\@0͠2 Q@@A@$_314%@0~@A@@@@L@$_3152M접 $_316'`o@CJL@@$栐$預$@02 Q@@A@$_317& @0 t@A@@@@y@$_3182M접 $_319'`o@Aw@#I@02 Q@@A@$_320&0@0:@A@@@@@$_3212M접 $_322'`o@B@@$$@02 Q@@A@$_323&X@0uG@A@@@@@$_3242M접 $_325'`o@Bà@##@02 Q@@A@$_326&@0t@A@@@@@$_3272M접 $_328'`o@B점@##@@"rHȠ@4@2 Q@@A@$_329# @4K@A@@@@@$_3302M접 $_331'`o@B?@@.3@4F2 Q@@A@$_332#4@4Q),@A@@@@D@$_3332M접 $_334'`o@Egi@@@@/(/+446@4W2 Q@@A@$_335#i@4b @A@@@@y@$_3362M접 $_337'`o@D@@@/\/_4P4S@422 Q@@A@$_338#@4= txq@A@@@@@$_3392M접 $_340'`o@@@@412 Q@@A@$_341#@4< q@A@@@@@$_3422M접 $_343'`o@A}@6@.2 Q@@A@$_344#@. @A@@@@@$_3452M접 $_346'`o@A@6B@3@2 Q@@A@$_347$@3K j@A@@@@@$_3482M접 $_349'`o@D46@@@//4蠐4@3;2 Q@@A@$_350$2@3F @A@@@@B@$_3512M접 $_352'`o@Deg@@@0%0(55@2Ǡ2 Q@@A@$_353$c@2>@A@@@@s@$_3542M접 $_355'`o@B@@0S5D@32 Q@@A@$_356$@3' @A@@@@@$_3572M접 $_358'`o@C@@0}05q@22 Q@@A@$_359$@2>þz@A@@@@@$_3602M접 $_361'`o@A@0@542 Q@@A@$_362$@5?/z@A@@@@@$_3632M접 $_364'`o@D@@@0Ϡ0Ҡ5à5@5"2 Q@@A@$_365% @5-/@A@@@@@$_3662M접 $_367'`o@D@B@@@1155@5%2 Q@@A@$_368%>@50/@A@@@@N@$_3692M접 $_370'`o@Dqs@@@11146%6(@3G2 Q@@A@$_371%o@3R @A@@@@@$_3722M접 $_373'`o@B@1`1c@3<2 Q@@A@$_374%@3G 1@A@@@@@$_3752M접 $_376'`o@Bˠ@11@@#rHȠ@#2 Q@@A@$_377#@#@A@@@@@$_3782M접 $_379'`o@A@9 @#2 Q@@A@$_380#6@#C@A@@@@@$_3812M접 $_382'`o@B@@1ڠ6@-i2 Q@@A@$_383#^@-t(d@A@@@@"@$_3842M접 $_385'`o@AE@9U@7j2 Q@@A@$_386#@7uP@A@@@@F@$_3872M접 $_388'`o@AD@)@62 Q@@A@$_389#@6_ @A@@@@j@$_3902M접 $_391'`o@@@@62 Q@@A@$_392#@6 @A@@@@@$_3932M접 $_394'`o@A=@8@12 Q@@A@$_395#@1 o@A@@@@@$_3962M접 $_397'`o@Aa@9@5%2 Q@@A@$_398$ @507j@A@@@@@$_3992M접 $_400'`o@B@@27@6(2 Q@@A@$_401$5@63 @A@@@@@$_4022M접 $_403'`o@D@@@2ܠ2ߠ7Р7@6#2 Q@@A@$_404$f@6. ;@A@@@@*@$_4052M접 $_406'`o@BMO@3 3@5Ԡ2 Q@@A@$_407$@5 @A@@@@S@$_4082M접 $_409'`o@Cvx@@3538-~@5q2 Q@@A@$_410$@5|7@A@@@@@$_4112M접 $_412'`o@B@@3`7d@72 Q@@A@$_413$@7(X@A@@@@@$_4142M접 $_415'`o@Dˠ͠@@@3388@7ޠ2 Q@@A@$_416%@7(kX@A@@@@@$_4172M접 $_418'`o@D@@@3388@72 Q@@A@$_419%F@7(kg@A@@@@ @$_4202M접 $_421'`o@D-/@@@33𠐑8᠐8@62 Q@@A@$_422%w@6 Y@A@@@@;@$_4232M접 $_424'`o@D^`@@@44!99@62 Q@@A@$_425%@6  @A@@@@l@$_4262M접 $_427'`o@D@@@4O4R9C9F@,2 Q@@A@$_428%@,1@A@@@@@$_4292M접 $_430'`o@A@4|@,2 Q@@A@$_431%@,!~U @A@@@@@$_4322M접 $_433'`o@B䠐@44@,2 Q@@A@$_434&&@,@A@@@@@$_4352M접 $_436'`o@B @4ˠ4@@#2 Q@@@@$_437"@A@@@@@$_4382M접 @$_439'`o@B@,y,|@"2 Q@@A@$_440<@"jD@A@@@@:@$_4412M접 $_442'`o@C8:@@,,#@"2 Q@@A@$_443<@"8@ -f@$_4442M접  $_445'`o@Ad@#@"Ԡ2 Q@@@@$_446<@"8FP@$_4472M접 CC@A$_448'`o@C@@,ؠ,۠"@92 Q@@@@$_449<@98F{@$_4502M접 <@%proj1O$_451'`o@C@@,Q,T,C@92 Q@@@@$_452=*@98F@$_4532M접 /$_454'`o@Cߠ@@,@,C,0@92 Q@@@@$_455=T@98F7Ԡ @$_4562M접 Y$_457'`o@C  @@,j,m,.@92 Q@@@@$_458=~@98FF7@$_4592M접 $_460'`o@C35@@,,,,@:9D{(@@=-@:OUB%inj_S9D{(@@ @8:w :9D{(@@@:+*inj_eq_rev9D{(@@@;s*inj_eq_iff9D{(@@=@@;@@%Logic$Init#Coq@@'iff_sym"㡠A!AA@@B!BA@@L@;ob=砑;@@O*inj_le_iff9D{(@@Z@:+FY*inj_lt_iff9D{(@@d@:+Uc*inj_ge_iff9D{(@@n@:+m*inj_gt_iff9D{(@@x@:`+w*inj_le_rev9D{(@@>@@;泑@@Y@%proj2OARA@@ BQA@@B>4;@@*inj_lt_rev9D{(@@>>@@< @@%(AsA@@-BrA@@Y>U< @@*inj_ge_rev9D{(@@>_@@<,@@FIAA@@NBA@@p>v@@8@@ @&eq_sym XAA@@ B$A@@C$A@@$>T@@f-Z_of_nat_of_N9D{(@@o-Z_of_N_of_nat9D{(@@x)Z_of_N_eq9D{(@@R@'f_equal=AKA@@ BJA@@>@-Z_of_N_eq_rev9D{(@@?A=1@=; -Z_of_N_eq_iff9D{(@@?>@@= @@~AsA@@BrA@@!@=2Q?X=#@@.Z_of_N_compare9D{(@@/@<| Uiʠ-Z_of_N_le_iff9D{(@@9@ @@#&AqA@@+BpA@@ܠ@S>@@-Z_of_N_ge_rev9D{(@@@]@@>*@@DGAA@@LBA@@@t>?@@ܠ-Z_of_N_gt_rev9D{(@@@~@@>K@@ehAA@@mBA@@ @>`@@*Z_of_N_pos9D{(@@l@=2*Z_of_N_abs9D{(@@v@< 3>+Z_of_N_le_09D{(@@@>:9+Z_of_N_plus9D{(@@@<2%+Z_of_N_mult9D{(@@@<2/,Z_of_N_minus9D{(@@@2rb/Zabs_N_succ_abs9D{(@@ @1 gl+Zabs_N_succ9D{(@@@<4v/Zabs_N_plus_abs9D{(@@@1;ے+Zabs_N_plus9D{(@@)@=#*Fd/Zabs_N_mult_abs9D{(@@3@1l9+Zabs_N_mult9D{(@@=@=*Fv%۠2 Q@@@@$_461AP@%{@A@@@@ @$_4622M접 $_463'`o@C @@1s1v0@@@&^ 2JV@S `x@I.el0/@IaV>"!ut+H!n)Datatypes$Init#Coq@@#nat@ @@A@A@@@@D%Logic@"eq @'BinNums'Numbers @!Z7@&BinInt&ZArith, @$of_N1\Y)BinIntDef@ >j&BinNat&NArith>!N@&of_natK)BinNatDef @)j2_A&@ bz@1?G!DA= `Aec EiBpN@+7@@@A@A@@@@D} f],B@&to_nat`;@*9G7[870j_A!pr@(positive*@Ȑ!e$Pnat&PArith'Pos2Nat@'is_succ%Z@"ex @&BinPos#Pos@:")BinPosDef@?5L B^BBB@@@@D@%зѩөCoB !mⷐ!H@(eq_ind_r!2#*ٰEȐ"H0[+SuccNat2Pos@#inv=Ƞ=DrP@+of_succ_natqL@$H } <@(eq_trans!y=DF @'f_equal=@  !fݐ>TTנ VXCK]C$ꐩB|MKi0v©V@H"!ecfzigR,*ywujya^1Y2SQ@LJ668W :aZ*+Ce?G>aF.aa@@AA@AA@@@@@@D!zlwe@$to_N1\k_@ Hl@V1be@2 NMF ANZSCd5.L}%,lfR4CT$4$64$Znat@.positive_nat_N'J2 Cd,D,FDC°k.K.^W̰d@%abs_N2:@ @'abs_natI@?n VhfRljQzɐ#LCϐ)n~JC֐0mQCݐ7o"$ ֠iР됑/N2¶@qrarķ;˶@%'z^,#C@/&1h6-Ȑ#Heq;2x_>@&eq_ind J;<۷>AK@$Truey@@֛R@%Falsee@A! [@)False_induُc *C@f]:h@@of[ s*Ơxo?Bz@&eq_sym XwEGGD0'.LC@\3""p0éVX<JJ+8>9^nn8Bp !t4-%g@'i@(hjC@7zQ_@TU@#andЖw@A@Ic @f#N2Z@#inj; аyɩѩѷ    @"le1P,a}/RelationClasses'Classes@+reflexivity(ϓ/ @2PreOrder_Reflexivevv@+le_preorderҀ< !@*comparison;f@@'compare3x@]=유C>B@@@@@D!y@)@0&T4*$Z:0"Ȑ"H15/-ݷ::@@@@@@@@@@@D!cC6@SI;;M?CrASѐ(z  } f\VLB@X00:@Y?H{6 tjd??8q=v Z '.}w!#RޠK&hP+-mAB4ԷS@#iffС)@ \@#notШ{o@-iff_Reflexive/h#R@+inj_compare UiC)$ wx6ɩ5@"lt \1ݰBC,H%#CF@1P-,'#WV@"ge \1RQ#aJU CACd<@1P,J&EAut@"gt \@ph-}f_][C~ V @ 1P,d +"_@#abs1P@ - 15[z^G>3#@#add @3 ⩚<@1P&5@ ̀r[RG&Y$^=neZ'!Š2l%K7q* P()$+{p`@#mul Y@3By@1P]r@ ,8?$'c\=(&`<,*IP%"%m#;'7q':ab]d@#sub c@3X@#max1P@ C@1P@ pm'yٰЩŐeSjکZZCީӐ*n$a%s+h[Cᐩ8w2o,쐩Cy=z7~YǠDCQKELHԷ!x@ #z@  )QڀY@f=W@g#F he&1(Р@$mask=(@#Q@@@A@@A@@@@@@D& 멚@(sub_mask@@)շ#֩E@(mask2cmpW NZQ)D$өƐ;?Ȑ"m0)6+mdY<17'.Z$<ݐD_97C GO JJC}Dp:YA^P2АUҠVLlBi-iaޠbXwCC}r[h(oe@0compare_sub_mask9,M񩚠@'pos_sub<@+ie@,pos_sub_spec=Cɰ 8CT{ |/gΩN iөް"ک|;@'CompOppD@/compare_antisymJI-+?Sʩ%C Z #@71ةE@+compare_sub: o8S\},"F2)lj:0T,Y%÷sC9]5/@ϷOEiA;Ȑ"n0@@D@ \SөY&K@+inj_sub_max8Sof[K@$succ ! D@?\@d@1\w]@ pE>x    @=)a@#RU͐ ZRҐ@N=SC^UJ:@#min 3@3`S@1P{L@ "jط*kwnc5.7cCaР@+CompareSpec!Q]@CAAAAAA@@@@@@@@DA@1YRKTt@,compare_spec7PԀװMN8OnPݩ<iC@ @3Ҁcd_f@#div l@3 @1P@  yau|հ̩dlh.թ|ge٩mi@.div_unique_pos^],א,1ǩې@&modulow@)1 Lq ҩ>@)is_nonneg99>@@&%3@'9@:(1P@&inj_lt p}DM@ @@En5ŶT尩.7@&mod_ltXȀ>^M ַ@0@3W7©[X@ @ C ?4Ġ$_DOFo=4LAhQ\S|#7@'div_mod2g<h@MG@n%5>5詷=869<$'=43Cʐy""}&4bc{;G̀L©DbcKU@'inj_add2Ky@'inj_mul2`WX"Hm_}A@.mod_unique_pos!G8<  #ɩN)dΩٰǐ֩ː!(9*h2/$!!!oli f%+# Ʃ.@ctF^/ ? #  M@$quot1\@ }Dڠ /  C ?l٠ ݠ T [g  )  ] $  % 0 'gRé +It@'inj_div2L. '@/quot_div_nonneg+VD ;h a d M D 9^ <@#rem1P; 6@   s  \ S Hm  Z $ ^ b W@zNH/ P@{1,րL i t k# ; m  n y p @I 9 s@'inj_mod22^ o@.rem_mod_nonneg8H  5 0  7   | l@$div2 hx e@>À a @1[8 ~@  f _  ! + ) )@AA@AA@@@@@@@D 4 2     z < : t   DA  I G  +  QB   ǩ7  ~ y   ٰ I @%quot22=* @ р   ک b l jA n l  :@  s q  7 w u  .  %   1       ꐩ @#pow  @3 @1P1 @ ؀ `  )     ݠ ֠    M     "  ʩ @'pow_0_l<    ѷ H ة 1 ( 3-   /1÷  &%Pos2Z@'inj_pow,:(ŀz!a  b 򩚠 5@,testbit_of_N _ˀ k I K@p  X O D   " xz   {V   ~rȐ!l@ k b W 6  i  j B < y "  t  > t i    x  z J F | q     v   TȐ"H2 W  ;  ?   Ɛ Gΐ    ͩ nHϩ  V   t u é#Z2N@"id %M   ܩ        J K@K İ   ڶ@ ǰ   7@ À          ȶ } ԰ }zH  L   Z    4  c͐  f :  ۷   { t ޶@@ ` -   tvxy E   @@    Q Ű 4 #   X X   ; *# ϩ ɠ à a  M   F 5.  } j ՠ Ϡ m   `     @@ $ ͩ ֠  jߠ    bη Qҩ  ک%   i- X.  ,  p4 _*@ B  ɐ ?  m А D Ґ      G@>@ީ T  ې      G   P @ @  I k    h '    =  e f 8 $2c  w  x   z@/@  0  ް "  @2@  ;  ] ; < X D $ " A  ^ J * ( G  d P! 0 . ? 8 @@9  X 6$,  U Y u a2 / ?   { g8 5 E    m> N L ] V @@W Ͱ v TByJx $ p w  Pw M ] Ʒ ҩ  Vqз T d | @ @   n\|e{   絷 & $  }e     © @_)a=  YsY@ix _y ӵ 0     @    ߐ        C :C@̩ # ̩  zΐ C ! b "   $@ 0 ٩ dҩt  ̷  /@ ;  o    v  A } ˷ {    Ґ   ӷ  @  T  ې   s    S@ _  搩  W     &     $_tmp  i .ZW  l w  D96}0  q,; 3 t  )  >j J  쐩a  Đd%JLY N  9  Nz   cU  * `   C  E # Z$Bl,C  M +ؠ  m_  0 IH Z \W@ ^  Z 8 WCJ ~  = N G @f  f D i  h  p P   Q m  x  W po  ~@  ذ  _ ~q   ص  % m3     p @2 @@x1 ` )    멷       Cݩ,  @'sub_1_r= C   $   $  C "Hn`         ߩ  K  1       R  d   %   L    .}c~ à l J ( i )& g -  .   > 4& &  Q     D : ,@ 9}C  fP ! i G  HE޷ߵ  L-  M  [ QC ~  n    _ U6 4C  zf 7  ]  ^   ` k     ð   j u  ,   A ; ' C  * $   F 2) C  5 '/  Է  C  > 08  ַ "  1 *   H &: h jCZ ,  f RI C  U 3GiO   ' 7 q l   b @ w     yr  v v W  k Z C İ m K         8 d d C ΰ w Ui q >C ԰ }t  L \  z t gC ް  ey  J  l j { t ީ   p & v BuC   z 4 K n ~sC    ǩ9 E x  ·         h h hC     ~      C ĩ  C  Y ^> ]  * ө  f }  ŷ (3 ܩ     C=  Đ \<  Ƶ  CG  ΐ ?  еCN  Ր _    KV  ݐ   Ca  萩   뵵  a@p   é @ =L ˩ =x!  6 b ΰ \  \ 81 а 5 5  @*YJ    N  ܷ5  C S  η é "O; IC=  R ~а ] _ ] TM  r r 2CE # ש CKη )dPCS 1 ̩˷64 E >\ : ʩ Cd B lȷ 5ECðl J ǩƷ =M   éϰx V  а^ Cհ~ \  İ AC۰ b C0۷ { t޶@@ r$ t-B  @@ }/80>6% D<+ȠJ  @@ LUjM<٠ũ[ p ̩ f  Cө,թ eWec*j   -8/ 1=4t|uC:/  NIw Ġ L PG"Xĩ ƩWZ *+< @; -BCj /4 bg] Ő w m g `@9 r l b - (@ /+ @>M @w@698䰷07S?7 6 H K F@ MI'53k *C  W R@ YU3ũwJC@b@ ϩdBR DVO@f@  ǰpN^p  zηZXw ̷ͩa_~ ɩǷhfwpڶ@ܶ@!n~é>> C& ַ  @  @ M   s Ő4   %8'   ˷   а     -  Զ@  2 2א  @ ©@(n‷ nI ʩ4@Щ)ҩa_&(3*,m\  @?c eE      C LC*QH&=b[   W  Q , ]` 01DFCl"}6 diǐ  m _>& !@({$97Fy@p@/ 21ݰ)L80/C >@EA/-+c";O J@QM+;oB;@ƶ@<[98=~NG@f@_gE7 JʷMKNL5OM©é  \ƩѰzX G~ Xɷڰ c1@x !7 $:om   @vT 2|X1@@K N˰@@ M LbE4CH7Ԡ &N=Q4@PT$ 3SWЩ 6RBҩ+@x(NhPlO[&  @>ŐO PN ^<۷>IА کWސȩȐ# ΐ鐩%֐,ݐ{1pr}&H4G3 ޷  / /P-7XR>޷" ZF & ٩aM- 퐑B;@ƶ@<[9}D\xdDECַkIqʰsQŠǩɠUƷb̩װ ^ gѩܰcנ̐kߠ k;=&*@2)+xv&  @ À@-testbit_of_N'/yUN=" ? ְϠ ޷Ԡ ߷٠ũ :@ϩ&ϩX{]̩~aͩe ܷ@6ߩhS1VXAs4  368dBDO=@#opp1P7@ { d` \}[Dj1 r  @(inj_succ+U&Zabs2N@,abs_N_nonnega bs@,le_le_succ_rU ?H CEcSũK)LN,W _q U2VX f2xF7 8:@1add_nonneg_nonneg7.F񐑷WPŰn:ZBaZĩϰxD LQa_Vfd[޷kizsݩ]Ie Akiyp n~u4w9>:[Ƞ͠ Ҡ3R> ɩ9 @ > é&ϩXZ -j bI aکe :Nީ7xk2lV?Ɛs:h wηaJ _sdӠu>F0Private_OrderTac#Tac@)not_gt_le$Ҁx֩(@)lt_irrefl,SX@+le_lt_trans uj:m=CːGHtu q@ j@ݶ@Y@{@(le_0_subL̐@@ _bԩUL* PRp ?U RVX6  ⩚ @(inj_pred+O = j1נ5]s@(lt_trans*? ?C)R*ȷ  ŷ@ @, aT@S@@)lt_succ_rM@@@bv=#c= 2~QD yB@)succ_pred.]ۏ;31   0 [6   ZXkW&E  ` C թ꩚@Sޛ MC{Щv򐑷8W  r UCƩRD"c#a P `٩ 7Mݩ6 i S<Ð  E r ȷ\E   @'inj_minx(VP~Ҡ;@'min_glb3[UlrPQ ~ 吩e{ d + ȩ j s ũ s  ĩ @'inj_maxx'Ȁ~ǩ@,transitivity>4 {@3PreOrder_Transitive4(ۀ*ݩv@(le_max_lwdɷ!qD" ַHJh Z; @(inj_quot+noq @>||٩0H7kqtroC ư@Ͱ#]}C t9Z:@(quot_pos=w[4 fdIe !Oyrܩ ݠ- */}$  4#I 8" <! @ 9 h IMˠ MTIC@ SƩO ^S'YYU[@'inj_opp*Fy9 %@*quot_opp_r$ ^!6@B9 @E<  I@MD G0H  @*C @'opp_pos=dՃ&C`  V h^i _ g- e6l$ *ny" oDBܩv\[X s Hm@*quot_opp_l$ N r/C3  }S >ǐ ` \)GА Q j 2@,quot_opp_opp tU &CXᐩ  @>#?eC ni°k ! @'inj_remx/  O@*rem_nonnegq _C2dbGc Mwpک  +y  E~| 5 dIǠCF  I XL^Q]  @)rem_opp_r.'FC(ѩZ J:0÷&1کc HC/wG-4ȷ5@r u<*x7z ̩8@)rem_opp_l.'@ =CT XfG޵ST_ %[K\g c'P& ǩY@+rem_opp_oppa: ^Cu 'ccst  ))V }۷/1O _ a: <   =ZB-CE e $ө&J{ G&L I}٩dPR  ߩVЩY 1[     Hjjj *rr ' 4N@*abs_N_specVBAVF $@ x- J*@*abs_nonnegLр [@'abs_pow(9ab~wv~#AC(/xکr pohC:CC2QǩPРw[w)ҩ[۠[کZީYXѷ4?q YWϩ Vө UKV. /VT  S$RbcepRư mx!OB u)A  }123F\]V!U c@(ݟ?lClXZ1]ũ@'nat_indJͩѠ-~tҷ#IHn°9@ʰA~ӰɩàJܰթϠV C"ַxm@x߷   I(ҷN- Ʃ۩$Nnat%Nat2N@ Uy\@'Z_N_nat2 ةb@'nat_N_Z+.42S3Qt9h?=(?jA dD/F,d+,7NP%Nat2Z@ rr>^\}]@,Kb@NePG,1@s y{[rqbT"\X~|\\S% ^a 121g\LǷkvlf?Y(PeanoNat%Arith#Nat@ol@r3RЀݩJu|zjX+#oK_ ["Z @Á٩4kc%Peano@ UxT@%lemmaİ*)Morphisms@=trans_co_eq_inv_impl_morphism&ni$/@.iff_Transitive*z#(װ_@/eq_proper_proxy)f +Compare_decf@.nat_compare_le'SK4*ڠ@++(CS4 /+a^M@) UxcY(Jg ? p-F$m>172@.nat_compare_lt'bN*zc/-C{4186W7Su@0 Uw/r g*n$f*_Z@.nat_compare_ge'vRWUC>Y`^_{AB@: Ux $ !~@.nat_compare_gt'v{yCǠH}bdof5D7Ctk:?GCyp?}@LC~uD{AF|qa @@ `ŷXAotV%#tM'a. SO]Q;Z<^ =yq#0@:56ط٩H@B [ũаC?ca˩ְͩ1Neʷl֩ TU^Qy[>^IzݐN`.@O:݀0T346퐩ݐ@F A ԩGA~   pTN " \VWЩhBҩ+"e_`'jd+6- /$8;@8:"Iw.!=/>^\}]ݩOE8@2subrelation_properJ74!A!B@*respectful%WO?@Ʃ  Ț&Basics'Program}@$impl7o.Morphisms_Prop@9iff_iff_iff_impl_morphism8C4!ܩ66ީ@$flip$===@$unitUe@A@6subrelation_respectful>6z K8󩚠@0subrelation_reflv R4 TT @9iff_flip_impl_subrelation2VA@-Emn@6reflexive_proper_proxy5i DLDl@ İTɰ =Yéΰũecͩذ  Ɛ Qou XvِaکHMΩ6KW搩֐@..y@/ `<̷ΩA~&ߩ됩hNHH3éV;R\A3( !l@,inj_pred_max,Uր 62@!?%;&<USB D:h4IKAoNE=F AK12O@\S"`|=cY&\V]h_/ +abmdYIivmq\r}tD<vak@7'NvUi:vwEIQ|l@4.@5 ѷ(d6 a0.A2l9 G"ZQ\FN QG{@z2613@:%89ɩ^@.pW@ 'jԩ߰Nrpکܩѐ@$tٷ{ *d#C`1M*4XB@2s3@:mCg89*F+/-Z !cSɷ=ͩ&hX{ !}ҩ}b+%N2Nat@~#*ک"*S1r2pȷ_ɷ@W;; mǩ @ CNEITkȩXo_Qۀ[Y\S.   _b  23%Z2Nat@no@?@,@),I}~3U:JGTϐNIW()`7 k`fi@#éD %wpsɩJ˩ -P;drfW6 ک:ݩȰ b@/ހ ; ͩS = >ϷзfgufTA@tb(B A    .@)sη5>08=à@c.`@hx)8FA@340Lé1646ϐ:=;&= ةZDԩ-Dũݐ}aHLJ5LNϐ@ +cc  3\:{;y^ߐА}fdOfJjmkVm 2T"tIwu`w [)  idgZq80 J@r1FE:2p3wCNTL& ;<-y#d\7v@ +. o'p(;<skzͷEs SvTGpqRS,}"Ѱ @>trans_sym_co_inv_impl_morphism'\|9@/Equivalence_PER/;@@/iff_equivalenceZ4@:ߩqE /@-/z'CU)0KC`D&2f-a+Ϡ<MCn*I +P3137 :8#:~CFD/F cܩӠOߩ8OЩ̩kR)ƷWU@WYڐ@ 33 4?5hFGiꐩېqoZq!>tIwu`w鐩=)k <;r :y@8R@ 祀N. NM/x0  TM ~Q }U |2+@JmiG,*Fe(]1/HGY[V@]ǩC1DyxϩJ D@&id_abs Ꞁ@'N_nat_ZlN@*Zabs_N_natdp Fɷkթ3񩚠 h@32r׀֩TU] (  t©(A ܷ9 : %% C*Ð/-/ נ1  @ YUwNWA` ^MDŐ {IG2I_[`0OА TR=TՐq   [4^\G^  } $hQhȠ l̠GqoZq! s 5  @*Fdg0` Щ ѐbcep ư mx BC  CàC̠-& ԠS򰵩@(mult_n_O(ހiCՐgз%5,@ %'Cϩ㐩-ڷ3CCة쐩6(߷NL]V˰ ɩ"0CӰHN^)CܰQWg2CZө  %# ө %        ک      Щ;L   '  ' C * / -  /נ 1* @*F.=%M٩Vڐ @ \  A ` F D / F14 I2 L J 5 L͐i :jj: U > U֩@0q XC. \ Z E \   ^ߐI ~ @ 霛-z   m K Ly p! s q \RE  vO y w bXK&[ RP]>R@ T S=@4IP Cp 8  g heؠΐ }sf9FN֐ { Sn MaSL (Zabs2Nat@(XCI   %& %ũ]Kr " nUP.!C L   >?v ̩ M k  ϩ   &~   թ  ש X /   ީ ɰ  5 ul   w а  h<  ?~   װ     q  a@ *Fu}|     ݷ  ޷ t u!  s!! ! ! ! !  !  * #!!! ! ) 2 R ٷ! !! 0 9! 3!$!"! !$  ̠!&   @ *FuRKB K !5!!5  4!:!8!#!:  Ӑ!>[!A!?!*!A ^   b  C!L ܩ!5!L " g!N r!R!P!;!R!( !T Ր Ps T@,inj_succ_abs g!qyq Zz [!d!B !C!e 搩 2(!n!l!W!n!Π\!r[!u!s!^!u   B۠!-ũ)!!!!k! ]!4 !&K!!!t!! a !y!!!|!!C!;!!1@+inj_add_abs;ےe78!! !P!!'ÐA!!!!!^@[!!!!!!5ѐ?>f!ٷ!!!! = !T%<!!V!!!G !ɩ;!!˩!!!}!u!!PK*@@+inj_mul_absl9 01!!ݷ !޷  @#neq'm"H' !&  !!C!@#Zne>o=K!! @k:w!"!! "!}!"!""!!! eש%Minus w@.not_le_minus_0?!<!M"Gt @)gt_not_le nV!W!F!˥ '%71b{qT