"`17t,PermutSetoid'Sorting#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@\)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$Init#Coq@0̂"&/rk0JqTttֱ'BinNums'Numbers#Coq@0dmk(5Ju<*EqdepFacts%Logic#Coq@0FI$ͼՋ`)Eqdep_dec%Logic#Coq@0u wWIϰ߼&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!>$Bool#Coq@0j 2cZ`FW*Equalities*Structures#Coq@0όe얟)H.Ƞ2Relation_Operators)Relations#Coq@0%s鯰s4Operators_Properties)Relations#Coq@0U3y#h&)Relations#Coq@0r砠*NZMulOrder&NatInt'Numbers#Coq@0}\^ !"k}@R(NZParity&NatInt'Numbers#Coq@0H>ca'^^%NZPow&NatInt'Numbers#Coq@0)6*9 B:vȻ&NZSqrt&NatInt'Numbers#Coq@0` .%m%NZLog&NatInt'Numbers#Coq@0ꔉ .uV%NZDiv&NatInt'Numbers#Coq@0$ |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$NLog(Abstract'Natural'Numbers#Coq@0KI'BinList+setoid_ring#Coq@0Au,Ring_polynom+setoid_ring#Coq@0gaKw9`UW+ListTactics%Lists#Coq@0,Jcy{+InitialRing+setoid_ring#Coq@0k/T=cN(Ring_tac+setoid_ring#Coq@0x2]%762f)Ring_base+setoid_ring#Coq@0fbU(2cNe$Ring+setoid_ring#Coq@0Msᬠ)ArithRing+setoid_ring#Coq@0ṔCgt?}%Arith#Coq@0I|кX*o4#Max%Arith#Coq@04=;3$>aU堠#Min%Arith#Coq@0Ce-Fѕ(PreOmega%omega#Coq@0\|چBb~w4%Omega%omega#Coq@0t.J'6\ϨrK&Permut$Sets#Coq@0!?edb>(Multiset$Sets#Coq@0ڛs FѤa+Relations_1$Sets#Coq@0k<⪚(тc1&Sorted'Sorting#Coq@0bb1z٠*SetoidList%Lists#Coq@0k窪ܸqS'ListDec%Lists#Coq@0a&:׃j#Fin'Vectors#Coq@0r'gް؅/׸&FinFun%Logic#Coq@08@OcսtG20+Permutation'Sorting#Coq@00zVybI fZ]Ns)N#xtfР,PermutSetoid'Sorting#Coq@A-list_contents @!AHA@@@#eqA4Relation_Definitions)Relations@(relation'JjA'eqA_dec!xB!yC&Specif$Init'@'sumbool7̂K@%Logic@#notШ Ȑ(emptyBag(Multiset$SetsB@(EmptyBag5𿣀) @(multiset"Y@Ȑ,singletonBag@,SingletonBag.iD;?!aE@@s!l)DatatypesK@$list]@-FA@B@B@@@@@DG?Hv21$"R@&munion'I8}@@42WVG |+k()7 7" ,6'*(= R'>3  7&'''+k7$'+7 Tk7$'ࠒT|?Pqd"ؠ;@@ABAEsh$@@@A3XyA@A alW@AB@@AA@@"s @,Ring_polynom+setoid_ring#Coq@@&PEeval"s @@A@AA@A@1list_contents_app @@@ڶ˶{G!m|I@#meqTy@(Dש@#appʀo@@@E@B@ A s@ABC@@C+permutation @ 52-/ @'%  @>A +k() 7  7 7&'>dxHx@@u@@m+permut_refl @@TADB97*(R@8=w(,33@@@@A@@*permut_sym @@iBYWNL?="l1"l2t@?CJEA@@@@,permut_trans @@CqofdWUѶ!n@2VZ@5Y]7[@@@@.permut_cons_eq @@D~)eqA_equiv/RelationClasses'Classes@+Equivalence~@g~x{?xBml54@_+CH"a'@zgАJ%AB9S@@@@젠+permut_cons @@EW#ڶ@fhL?NfAnC@@ @@*permut_app @@FضͶn:"l'p"m'd@[j¶@[^mɩQ]`SqUː@@@@$4permut_add_inside_eq @@ GpnbVx"l3r"l4o@q@АKaАL}i m @@@^@A!AviA)Morphisms@'AۀߠK@AB*Aۓό^ @/A݋X_A@Ak@)@*Am@ABCD@@k1permut_add_inside @@RHB@75(& YֶEȶC@ϩP)R/6 ƩVhY28@@@@A@P@'@ABC@@9permut_add_cons_inside_eq @@xIhf][۶O϶  ݶ@@-zSW1jɰlnͰp[@@@@v@M@ABC@@6permut_add_cons_inside @@Jtr0l#7"5@N 2r xR 8>z<@@!@@ՠ-permut_middle @@K@ öPLj6NT8:<>@@@@@AB@@.permut_sym_app @@Lƶo(mߩioҩҰk@@w@@*permut_rev @@Mٶζo;Ʃ$List%Lists@#rev$tҐ@@@AUDM @A>@,@ABC@@)/permut_conv_inv @@N䶐!e@YUZ@@I@@A/permut_app_inv1 @@(O  x/@$& @@@@X+if_eqA_then @@?P/-$" Զ!B/H4@@!b%"b'!@ҩ@"eq @%BAAAA@@@@@A!s1N%Q@@;;@@/@+@A@A@-A1DH.@A@@/permut_app_inv2 @@QqofdWUѶ@0ĩ}n@@!@@3permut_remove_hd_eq @@Rzxl., +P@@H.t6N 4@@y@@͠0permut_remove_hd @@S 9M8K*J@e"I!Q#%m'9QY@@@@A@@@ABC@@+if_eqA_else @@TŶi!lKd@@@z@@K@@A@A@Ay@A@@+if_eqA_refl @@U۶][OM#f@@ڶԩӠpȐ@ݷ@@@M#@@A@A@@A@AB@@<&if_eqA @@#Vz㔑Nbg@@@&ProperL@@ĩ @*respectful%WO?@ @ڷ@@@Nb@*@A@A@!@A@.A"@0A@ABC@@|0if_eqA_rewrite_l @@cWSQHFƶ:"a1#a1'"a2,R^k^@@*M(G@^% G <@@R+$SpG%@!@\@@R^@"@A@A@S@%A"@AB@@0if_eqA_rewrite_r @@Xx>691#a2'fVZo@@db@ 2`GZS /wI @R@G@@VZ@@A@A@@AS@AB@@렠0multiplicity_eqA @@Y75)W٩@dW@#nat@lr @,multiplicity5uw}@@@@A@@FA1GK@ABC@@0multiplicity_InA @@ZcaU@#iffС)*SetoidList@#InA q9@䩚%Peano@"lt UxcGA?@@@Ai0A@V@AB@@O2multiplicity_InA_O @@6[&$ =ƶ@4g]=%@@@@h2multiplicity_InA_S @@O\?=42&V߶@K@@"ge UwBB@@;@@3multiplicity_NoDupA @@l]\ZQO϶Cösmh@&NoDupA @ P g@"le UxT@a'@@]@@.permut_InA_InA @@^~|sqe&$@> (bf@i+g-@@@v@@@ABC@@à/permut_cons_InA @@_ B@.#@Z&D@@@@v@@ABC@@ܠ*permut_nil @@`(&Hʶ@qU[JAZz@E@@t@@/permut_length_1 @@aʶA?3oql@Wo#Y%[\@@@@/permut_length_2 @@bضZXL"b1p"b2d@dgBfDhҩ=jGk٩Im@"or @@#andЖw@~ @@@@J-permut_length @@1c!8@`@&length䷀ @@@@Ap@I@ABm@5A o@9A1@D@A_@ABCD@@t8NoDupA_equivlistA_permut @@[dKI@>2br߶@2@5@\@*equivlistA~9@@@@*permut_map @@{ekyi@@>ge׶YWQTQj#eqB@@S'eqB_decc`])eqB_trans@*Transitive++-l!f@@s@l 8}<'<*@WY@#map$MEG@@@p@ADA@FA@ABGA@JA@AKA訠@PA@ASA@UA@WA@ABCDE@@[J @ABa@@ACVQDM@K@A@@AB{A al+@L@Aw@J@AA1FdJ%Logic$Init#Coq@@BCA1GK @A8ӠA4Relation_Definitions)Relations#Coq@@A9@BDEF@@A[@BY@@d@AB@@A@B@CDEB@@A@BAA@v@AA݋X_A 'Classes#Coq@@B@CDE@@A@@A~@{@ABA+@@@ABCDFGH@@"O@(PeanoNat%Arith#Coq@#Nat@&of_int"O#Nat$Init#Coq@@ 6@A@A\@&BinInt&ZArith#Coq@!Z@'quotrem\)BinIntDef&ZArith#Coq@!Z@ /@A@\@@+pred_double\@/S@@A@As2@3@&shiftls2*@vY@A@BCs8@8@&shiftrs8/@vY@A@ѓ@>@&squareѓ5@y@A@@D@&to_intϑ;@@A@z@5@&doublez,@/!@A@ABCD/@O@)log2_iter/F@wd@A@NH/@B@&moduloNH/9@1,@A@A\d@G@&of_int\d>@1?A @A@bz@M@&of_natbzD@1?G!@A@#@S@&shiftl#J@1dV@A@#@Y@&shiftr#P@1d\@A@ABCD/x@&BinPos&PArith#Coq@#Pos@)pred_mask/x)BinPosDef&PArith#Coq@#Pos@ )X@A@6@x@&square6o@19@A@AV+L@}@&to_intV+Lt@2@A@V1b@@&to_natV1bz@2 @A@V5=@@&to_posV5=@2@A@ABCl@@)sqrt_iterl@!$:@A@@@6@(sub_mask@-@)@A@ADEF c@@'testbit c@!ć@A@7 B@D@'of_uint7 B;@*`]?@A@AG@I@)mask_rectG@@+ED@A@F˱@O@)add_carryF˱F@+p@A@AB^Ҷ@@'to_uint^Ҷ@#m@A@gL7@@'sqrtremgL7@40@A@Aq@@'testbitq@5)@A@ݎO@@+succ_doubleݎO@6r@A@A p@l@0double_pred_mask pc@0-+m@A@BCD T@&BinNat&NArith#Coq@!N@!t T)BinNatDef&NArith#Coq@!N@ 2@A@ @@#add @3 @A@A l@@#div l@3@A@ Y@%@#eqb Y@3@A@AB #@*@#gcd #!@3n@A@ T@0@#leb T'@3@A@ACEG "@5@#lor ",@3m@A@ q@?@#ltb q6@3@A@A @D@#max ;@3@A@ @J@#min A@3`@A@AB @O@#mul F@3B@A@ ~@U@#odd ~L@3@A@AC =@Z@#one =Q@3@A@ @b@#pow ˑY@3@A@A c@g@#sub c^@3@A@ @m@#two d@3J@A@AB hx@r@$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@@$zero !7@@P@A@ *@@%ldiff *@@A@AB g_@1@+pred_double g_(@25\@A@CD m@6@÷ m-@2j@A@S@=@&of_intS㫑4@4}5@A@AS@B@&of_natS9@4};@A@BEFGH\R@G@(mask_ind\R>@4@A@\^@Q@(mask_rec\^H@4@A@A!,@V@&pred_N!,M@4s)@A@B@[@&shiftlR@5X@A@@b@&shiftrY@5X@A@A&@g@&square&ّ^@5,x@A@BC"@l@&to_int"c@5L@A@"@t@&to_nat"k@5L @A@AnTq@y@+testbit_natnTqp@6n@A@B@@(succ_posB@@A@I@@'abs_natI@?n@A@AB.@@'of_uint.@MS@A@3~@@'sqrtrem3~@7]%{@A@ACD,@ @'bitwise,@/v@A@>4'@@'testbit>4'@8g$@A@A{U@@,sqrtrem_step{U@8R@A@u^@9@(div_euclu^0@ @A@Afz@@'to_uintfz@9w@A@Bl@'@'comparel@3R@A@CDEFs8@,@+of_uint_accs8#@5+@A@}@R@,pos_div_eucl}I@&`@A@3x@(@'compare3x@]=@A@A@^@&doubleU@'޺_@A@BCq@@+of_succ_natq@$@A@w@i@&modulowɑ`@)1@A@ADK@n@&of_intKe@)j,I@A@K@v@&of_natKm@)j2_@A@AI@{@&shiftlIr@*O@A@O@@&shiftrOx@*O@A@AB,@@&square,}@*ow@A@Z@@&to_intZ@*81@A@ACE`@@&to_nat`@*9G@A@e@@+testbit_nateđ@+@A@A+{@@'sqrtrem+{ё@,J@A@5z@@'testbit5z@-T|@A@A @@'to_uint ͑@.@A@ @@+succ_double @.^4@A@A#@'@'compare#ݑ@ )Q@A@BCD%t2@,@(size_nat%t2#@ @A@%9@3@+of_uint_acc%9*@ ΋@A@A%V@8@+double_mask%V/@ S@A@%%@>@'div2_up%%5@ "@A@ABEF'ş@C@'Ndouble'ş:@ @A@(b0@K@*shiftl_nat(b0B@9-@A@A(nՖ@P@*shiftr_nat(nՖG@'@A@(@V@0succ_double_mask(M@@A@*W$@\@,compare_cont*W$S@!@A@.0@b@.sub_mask_carry.0Y@΂@A@ABCD.@@!t.@ ;@A@.먩@@#add.먩@ `@A@A.U@@#div.U@ @A@.B@@#eqb.B@ @A@A. @@#gcd. @ @A@.=@@#leb.=@ @A@ABCEGHI. @@#lor. @ @A@.Z@ @#ltb.Z@ @A@A.p@@#max.p@ '@A@B.@@#min. @ @A@.@@#mul.@ @A@AC.g@@#odd.g@ @A@.&@&@#one.&@ @A@A.뾴@+@#pow.뾴"@ k@A@.L@1@#sub.L(@ @A@.@7@#two..@ @A@ABCD.,a@<@$div2.,a3@ @A@.Xz@D@$even.Xz;@ ?1@A@A.@I@$iter.ؑ@@ @A@B. @N@$land. E@ @A@. @T@$log2. K@ @A@ACE.@Y@$lxor.P@ R@A@.y@`@$pred.yW@ `<@A@A.Ʉ@e@$sqrt.Ʉ\@ ;@A@.@l@$succ.c@ @A@.t @r@$zero.t i@ Z@A@AB/@w@.to_little_uint/n@ @A@CDF/@|@%ldiff/s@ H@A@00@@'compare00@?H{@A@A1P%@w@!t1P%n@  @A@B1P@|@#abs1Ps@ @A@1P&@@#add1P&z@ @A@A1P@@#div1Pґ@ y@A@BC1P@@#eqb1P@ f@A@1P@@#gcd1P@ 0@A@A1P@@#geb1P@ T@A@B1P@@#gtb1Pʑ@ q@A@1Pĺ@@#leb1Pĺ@ a@A@A1Pň@@#lor1Pň@ /@A@BCD1P@@#ltb1Pב@ ~@A@1P@@#max1P@ @A@A1P{@@#min1P{@ "@A@B1P]@@#mul1P]@ @A@1P@@#odd1P@ @A@A1Pɣ@@#one1Pɣ@ J@A@BC1P@@#opp1Pԑ@ {@A@1P1@@#pow1P1@ @A@A1P;@@#rem1P;@ @A@B1P@@#sgn1Pˑ@ r@A@1P@@#sub1Pɑ@ p@A@A1Pe@@#two1Pe@  @A@BCDE1[8@@$div21[8ޑ@ @A@1[d@@$even1[d@ I@A@A1[6@@$ggcd1[6@ i@A@B1[U@ @$iter1[U@ @A@1\@@$land1\@ /@A@A1\@@$log21\ @ 6@A@BC1\$@@$lxor1\$@ @A@1\Y@$@$of_N1\YÑ@ >j@A@A1\@)@$pred1\ @ j@A@B1\@.@$quot1\֑%@ }@A@1\@5@$sqrt1\,@ @A@A1\w@:@$succ1\w1@ @A@BC1\k@?@$to_N1\k6@ @A@1]@G@$zero1]>@ eD@A@A2:@L@%abs_N2:C@ @A@21@R@%ldiff21I@ ߵ@A@2=*@X@%quot22=*O@ @A@ABC2kF@@(size_nat2kF@{@A@3@x@(tail_add3o@^q@A@ADEFGH3@}@(tail_mul3t@^@A@5Z@@*shiftl_nat5Z@y/@A@5f}@@*shiftr_nat5f}@4@A@AB5a@@'iter_op5a@ @A@C6w~@@'of_uint6w~@^5@A@8j@@'of_uint8j@'"h@A@9E@@(div_eucl9Eđ@(*k@A@AB:x@6@,Nsucc_double:x-@ ʭ@A@CD@[@&divmod>R@C@A@>@b@&double>Y@NĴ@A@?2@S@,pos_div_eucl?2J@-u@A@AB?;@m@&modulo?;d@"i@A@CEFGIJ@\%Arith#Coq@0I|кX*o4)ArithRing+setoid_ring#Coq@0ṔCgt?}*Arith_base%Arith#Coq@0Ĕ}CS&Basics'Program#Coq@0!bs߯? :VU'Between%Arith#Coq@06v*0ur`C0&BinInt&ZArith#Coq@0BpHޞun^)BinIntDef&ZArith#Coq@0ådR4Tuy'BinList+setoid_ring#Coq@0Au&BinNat&NArith#Coq@0K11ڤs+Π)BinNatDef&NArith#Coq@03@1O,[{ 'BinNums'Numbers#Coq@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$ͼՋ`)Eqdep_dec%Logic#Coq@0u wWIϰ߼*Equalities*Structures#Coq@0όe얟)H.Ƞ+Equivalence'Classes#Coq@07;ꮹ)Factorial%Arith#Coq@0@oehJd#Fin'Vectors#Coq@0r'gް؅/׸&FinFun%Logic#Coq@08@OcսtG20-GenericMinMax*Structures#Coq@0måj$"Gt%Arith#Coq@0䙛#c:D $Init'Classes#Coq@0](p{yOh.+InitialRing+setoid_ring#Coq@0k/T=cN"Le%Arith#Coq@0d}Omq+$List%Lists#Coq@0>I'ListDec%Lists#Coq@0a&:׃j+ListTactics%Lists#Coq@0,Jcy{@0\͉!Ig*Logic_Type$Init#Coq@0 1jc6"Lt%Arith#Coq@0KZ-eJkP܏#Max%Arith#Coq@04=;3$>aU堠#Min%Arith#Coq@0Ce-Fѕ%Minus%Arith#Coq@0LFtR")Morphisms'Classes#Coq@0Imӽ%\$PD.Morphisms_Prop'Classes#Coq@0% :B'.>u%$Mult%Arith#Coq@0햖Qyb0(Multiset$Sets#Coq@0ڛs FѤa$NAdd(Abstract'Natural'Numbers#Coq@05;ZW:㥜un$)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#Nat$Init#Coq@0eʤģPSR蠠$Nnat&NArith#Coq@0$W;s #%M)Notations$Init#Coq@0&v!D]hwnv *NumPrelude'Numbers#Coq@05WUVŦ]xVXԠ%Omega%omega#Coq@0t.J'6\ϨrK+OmegaLemmas%omega#Coq@0TJ#Jes4Operators_Properties)Relations#Coq@0U3y#h&&Orders*Structures#Coq@0$Znl0\͗+OrdersFacts*Structures#Coq@05Mܿ獐ζΖLB)OrdersTac*Structures#Coq@05'4Ԗ+9%%Peano$Init#Coq@0 jha|ؠ(PeanoNat%Arith#Coq@0O~2$k[#lZ)Peano_dec%Arith#Coq@0Kݢ*k&Permut$Sets#Coq@0!?edb>+Permutation'Sorting#Coq@00zVybؠ$Plus%Arith#Coq@04tmG$Pnat&PArith#Coq@0,?pr.gZ(PreOmega%omega#Coq@0\|چBb~w4'Prelude$Init#Coq@0JqTttֱ%Quote%quote#Coq@0J@ŹVz-,3%x X W@0Gz rA6ՠ { z y@0]4Ѐd{n^2Relation_Operators)Relations#Coq@0%s鯰s)Relations#Coq@0*SetoidList%Lists#Coq@0k窪ܸqS-SetoidTactics'Classes#Coq@0S_`nOU$&Sorted'Sorting#Coq@0bb1z٠&Specif$Init#Coq@0;RWMi\N'Sumbool$Bool#Coq@0sB ,$11.]m'Tactics$Init#Coq@0/9m+ a'Tactics'Program#Coq@0342 Q@@E@#_31C@?(DAA@@@@@AB@A@@@@@@#_322M접Z@V(DDD@A#_33'`o@c@_(DD*type_scope@.function_scope*list_scope@@WA@2 Q@@A@#_34@8AA@@@@@B@A@@@@@@@@#_352M접@8#_36'`o@@8ED@CBD@@A<?@2 Q@@@@#_37@=wF@ǐB@A@@@@@@@#_382M접@=w@#_39'`o@@=wE@@@ݠA@2 Q@@A@#_40 @=nAA@@@@@ B@A@@@@@@@#_412M접%@=n#_42'`o@/@=nD̠@ˠ@@ A@2 Q@@A@#_43M@9a AA@@@@@KB@AEF@A;@A @A@A@@@@@#_442M접x@9a #_45'`o@@%9a F@@@@vAH@)2 Q@@A@#_46@4 JMAA@@@@@B@AG@A@AI @AҐ@ALH@A@@@@@@#_472M접@f JM#_48'`o@@p JMH@@@@@ܠA~@{2 Q@@A@#_49@'AA@@@@@B@A C@A@G@A@A@ @A@@@@@@@@#_502M접E@'ː#_51'`o@O@'J@@점렐@@@@@@GɠA점@@@@2 Q@@A@#_52@= BAA@@@@@~B@AxF@An@A  @A@A@@@@@@#_532M접@= B#_54'`o@@= BGS@RQS@@@@AMP}@@2 Q@@A@#_55@9GAA@@@@@ݐB@AאH@A͐@A @A@A I@A@A@@@@@@#_562M접@89G#_57'`o@ @B9GI@@@@@AĠ񠐑@K2 Q@@A@#_58U@V9AA@@@@@SB@AMC@A@DL@A@@@@@@@@@@@@#_592M접@9#_60'`o@@9L&@@&@@')+-@@@@A@@,/25@c@s2 Q@@A@#_61@~NAA@@@@@B@AI@A@A@@@@@@@@@@#_622M접@N#_63'`o@@NI@@@@@A@@2 Q@@A@#_64'@<\AA@@@@@%B@AC@A@K@A@@ː@A@@@@@@@@#_652M접T@<\#_66'`o@^@<\K@@@@@@@@XڠA@@@3@2 Q@@A@#_67@ 3AA@@@@@B@AH@A@A@5 @A@@@@@@@#_682M접@+ 3Ր#_69'`o@@5 3Hd@c@ceg@@@A@adg@:2 Q@@A@#_70@E<&AA@@@@@B@A@@@@@@@@@#_712M접@_<&#_72'`o@@i<&F@@@@ A@@g2 Q@@A@#_73>@r?nAA@@@@@cAA@@@@@B@A@@@@ݐG@A@@@@@@#_982M접*@_c#_99'`o@4@icIѠ@Р@@ؠ@@@@@*A@@@@@@f2 Q@@B@$_100]@qAA@@@@@@AUC@A@@@6G@A@@@@@$_1012M접@$_102'`o@@H)@@)@0@@@@A@@@@@2 Q@@J@$_103@-^lAA@@@@@B@AC@A@@F@A@@@@@@@@@@@$_1042M접@-^l$_105'`o@@-^lG@@@@@@۠]A@@@@$_152X@3typeclass_instancesA@@(META1360@(META1364@ (META1361 @#,/A@@褐@(BA3BAG(META1363BA@ @EBA(META1365A@7VBA(META1366@@r-^l@@@@s@@@=Coq.Sorting.PermutSetoid#<>#1b@$_10646@ @&ProperL@@@J2 Q@@B@$_108@UzAA@@@@@B@AC@A@@@@@I@A@@@@@@$_1092M접@}z$_110'`o@@zK {@@ {@@@ @@@@@֠XA@@@@@@@@k2 Q@@B@$_111 @vAA@@@@@ B@AC@A@@@@@搐I@A@@@@@@$_1122M접3@$_113'`o@=@K ڠ@@ ڠ@@@ @@@@@5A@@@@@@@@2 Q@@J@$_114j@چAA@@@@@hB@AbC@A@@@@@@@@@$_1152M접@چ$_116'`o@@چE 1@@ 1 0@@A+@$_153X@A@@(META1374@ @(META1375@@$+(META1377(META1378@.چ@@k.j@=Coq.Sorting.PermutSetoid#<>#2c@$_11746@id@2 Q@@A@$_119@AA@@@@@ B@AC@A@@@@@@@$_1202M접-@;ѐ$_121'`o@7@EF Ԡ@@ Ԡ Ӡ@@@*AϠ@@&2 Q@@A@$_122[@1K AA@@@@@YB@ASC@A@@G@A @A@@@@$_1232M접@YK $_124'`o@@cK G *@@ * )@@@@A&@f@g2 Q@@A@$_125@rKAA@@@@@B@AC@A@@RG@Af@A@@@@$_1262M접@K$_127'`o@@KG @@  @@@@۠]A@@2 Q@@A@$_128@xAA@@@@@ B@AC@A@@@@@@$_1292M접,@x$_130'`o@6@xE Ӡ@@ Ӡ @@(A@ˠ2 Q@@A@$_131X@;AA@@@@@VB@APC@A@GH@A @A @ApI@A@@@@@$_1322M접@ ;ڐ$_133'`o@@;I 2@@ 2 1 3@@@@@A14@b@2 Q@@A@$_134@(:MZAA@@@@@ĐB@AC@A@H@A{@A} @Aސ@A@@@@$_1352M접@Y:MZÐ$_136'`o@ @c:MZH @@   @@@@yA@@l2 Q@@A@$_137 .@w9XAA@@@@@ ,B@A &C@A@ F@AА@A@@@@$_1382M접 U@9X␐$_139'`o@ _@9XF @@  @@@ RԠA$@2 Q@@A@$_140 @=AA@@@@@ B@A }C@A@ tG@A 5@A^ @A@@@@$_1412M접 @=$_142'`o@ @=G X@@ X@@@@@ 0A@@@2 Q@@A@$_143 @=AA@@@@@ ސB@A ؐC@A@ ϐI@A@A  @A@A@A@@@@$_1442M접!@-=$_145'`o@! @7=I @@ @@@@@@@!A@@@@@2 Q@@A@$_146!I@$;HAA@@@@@!GB@A!AC@A@!8G@A@A  @A@@@@$_1472M접!u@P;HӐ$_148'`o@!@Z;HG@@@@@!tA!! I@P2 Q@@A@$_149!@[PRAA@@@@@!B@A!C@A@@!GG@AސH@A@@@@@@@$_1502M접!@PR$_151'`o@!@PRI}@@}|~@@@@@!נ YA!|!@2 Q@@A@$_182"@9VAA@@@@@"C@A㐐F@A"E@A"M@A@H@A@@J@A@ ݐ@A ߐ@A@@@@@$_1832M접"U@9V吐$_184'`o@"_@9VM@@@@@@@@"`A 䠐AAA`""!A@Š2 Q@@A@$_200"@ȳUAA@@@@@"B@A"D@A@@"?G@A ֐@A@@@@@$_2012M접"@ȳU$_202'`o@"@ȳUGr@q@qs@@@"ʠA!N"o"r @2 Q@@A@$_203#@9LAA@@@@@"B@A"D@A@@"G@A!4@A@@@@@$_2042M접#)@'9L$_205'`o@#3@19LGР@Ϡ@ϠѠ@@@#(A!"͠"Р@@22 Q@@A@$_206#^@=5:i^AA@@@@@#\B@A#VD@A@@@@@@@$_2072M접#|@[5:i^$_208'`o@#@e5:i^F#@"@"$@@#zA!##"@,permut_right9D{(@@#@!= BB+permut_tran9D{(@@#@"@ JM @@ uQYc2m4w@Nrz}I @3(4r>hɄ@._/QȪ%ׄ 1!AHA,PermutSetoid'Sorting#Coq@@@#eqA4Relation_Definitions)Relations@(relation'JjA'eqA_dec!xB!yC&Specif$Init(@'sumbool7̂K@%Logic@#notШ Ȑ(emptyBag(Multiset$SetsC@(EmptyBag5𿣀) @(multiset"Y@Ȑ,singletonBag@,SingletonBag.iD;?!aE!l)DatatypesC@$list]@ @(list_indjАF!mGB@#meqTyH@-list_contents(D *@#appʀzY@&munion'!*#,),I'w@"eq @AI@#nat@w@,multiplicity55%7] C>A8CLa+EiCJMEH?JSh9LgAQ8RIT]rx_"l0[!HawW^IY\dSϩN_ bj̩a dlշq@)meq_trans,04J_rul g i z$}|&oq@)meq_right,+Qn@'meq_sym $@*munion_ass1QP+(C@H813H5B:<>S /=;/- ޵׵ȩé'.CİЩ2C䩚@+permutation=w::ZXLJ=; "l1"l2ᩛߩGRT䩚:@&eq_sym Xé`YdiC" @4 bi6 d`}{nlKI=64,'%!n +"H09AC:8#&"@W#,@Z&\ F)eqA_equiv/RelationClasses'Classes@+Equivalence~@be˩ztrgmlhQjUSQOJILTrKNVty"a'HLGbYKnM hQ b  @(meq_left2i @-meq_singleton8C@0 * @('|)#&ܰ+-'*/C@2<@:936  IdG CĶ@ NPRשT V CҶ@\ FD86)'絷ැ"l'з̷"m'ptͰo׷а]P_t7fsucxȰwðy{i~}kmҰC@1list_contents_app8v}ְ|~Rް  \o  ei^C; 9@;+e@>hl@3)yVA˵8><"l36"l4;ʩ/DJMHN%̩;P+ ҩ% \"a0)[O82EN> 8 io@(eq_ind_r!2#"P=N1QP3 ]Q.}0ɩ*QZ8TgrW@&eq_ind JA;j!5Md#owٷkHJDs*QmJ.j0-{2F^4H`Z T8:Nf}<Eb\2|46Dk8Fm3kmgRBd.Df JG?{1|˰~xRtS~TV"XfZh۰^`bpcdr$Ȑ!sn)m-BAAAA@@@@@D7>,#Nat>@#add `TS#ZSHe!eBAӰ+ٰ#%"1D{t)$i" 574."HaM'Tactics@+decide_left:׀%lemmaG )Morphisms @2subrelation_properJ74@U@VA@*respectful%WO? @  c e@#iffС)j@,PER_morphism qq/@/Equivalence_PER/;"xu$z&#|&Basics'Program@$impl7o@$unitUe@AB@6subrelation_respectful>6z >2I@0subrelation_reflv E8! GD 8!Q@4iff_impl_subrelation5PcW@6reflexive_proper_proxy5Sg@5Equivalence_Reflexive:$" (  .Morphisms_Prop-@0not_iff_morphism Z!! ##%.n$,0CppӷZCҩrʷQ]CKΩzCQKk|%G~'Iް'++9`&W;=Qi?8AUm:C?;,~|z@x@wA)yũ{x}Az|ǩ~ϩ 64(&׵Է\MaF۰\^La`-bdRgf(,3gqsuo]ܩwq_>@By>?Ұݩ:EڰB M۰Wbʶ@ͩǰש٩gn(שѰ:b-x@0ݰ7?}:6é .z'@H& )( Nm7kv:@de D"'Om&J(-^*N,1wx+y'V!49ɩ ;;͠omai80g2EJj>6m8KPxD<s>QV砷@S>yV@Y._[?AUhaEG[n1mPp@sàqUWk~5ɩuY[oNVku@+f_equal_nat!-., ՠhflڠuuyC@}iZVRu8C@whd`C@ɰ:IѰԩBQ}^`fhɰ)cn +epѰ+v(-x}C2.75@Ki|P <sEv,mXN5-JѷU·SשQW!jZ%HU?]^0`7 EVj#?[LrK@4permut_add_inside_eq90.3S[dyĐԷkg  aiWCPT_&V Td+VͰZl!԰#x@1permut_add_insideN$$'񐑷@6permut_add_cons_inside 3Հ @+permut_refl=n +) ̷ķbyҰVXZp*e)0(PeanoNat%ArithM@(add_commbC(ѩʰ?;FA=H٩AKBFMCհJQװSLsqecVT31% +`$List%Lists{@#rev$t̵h#) C<&,-(#IHlE zu  swy7Q{  (@)app_nil_r)7C\ (}3usg`^V6R[<Y8߶\2Y Zm;hGKI=EShq$Plus@*plus_reg_l U8#@ĩ%é̩5^jh\dC@c=7fiqưܩ=low̰L#!C@wհz^  5b\3^579:Pmg)+ r@°uoCE3HG ʰ}wQ ySf}?A4 @ذY[!(glQ0nzi/k1m3 @.먩 E~l@3 à  &  Y#'*C@YC-+°\g^iʰ*$o!,&qvC@zC@@ 1wlꐑzx6r9!B/H@@!b"b'˩&_(#y\gѠ3<T@BAAAA@@@@@Ax͠<DF@Q@gg$_tmp&)#NEQР@%Falsee@@@D@z]{f׷njd>8gjraܩ=lowf.KEe fdsP@SM!ک:WQqr\@_Y-y/起;g@@L C@p%j,.C0  2G  r46K@ 9N C@E7C@3 = ; / - !~wvusƷ·daM#Heqkmj 2 +s ^ַҩ}e Diΰ6 A  LS O H <ɩ a°ͩS $  iҩ̰ĩƩ   l۩*ݩװ  o zް֩   o :  ~<=P   '  u., (    + ( N - T Uh   H   FD8@  >  ?j  G*   3 &-@3X@2T +y{ ũ $ n é  7@lj^f_ < > ש9 Ϡ! n  Đ HL@{@w H w .U   L"  V4<-= Z@8 ] _ ·  D    ko5 qΠUРSQ L[ xՠVX {ʰ } ݷ>ϰ ߠ} W Y ة   %@@ " ߩߠ ) "f    η 8] t v ϩ4@@@?AACE GI~tm  KKhMq OOc x  W  ^QY *-  ĩ!   [ + b [b   P  mA  ک(GC;( _t  $%w4     (OR 6 F%!S  <|W| ? ũ ʩ   E  Щ I   % N  P `?o ' ) )@,>@:]pEB?MH c [ @]Z# Ki a` O c U  '@Z@Vy{ ũ s  e  7lj ^fP r > > >K ِ =1 m> Ԡ  s ɐ M@@|< \j W W<*   =6@)add_assoc7!+C?=  t C  e _C EIB  c[ ]p ? _   at C   C      G  D 0@ L@  K Ȱ { u  Q 9    ֶ  Ѱ  ~  T    #C  ¶    `  ] I@ e@  e _ b <  g   i )   k S ɩ   鐑 T R F D   8         ۷  ׷  y  v ~  d y ک / f E  ˰ h < 3 j I B @3permut_remove_hd_eqE ,  q     E I IP  s  K R r p d b U S  M  ۔Kd u@@ a [  Hש g7ש  ʷ;  l@ #@ * d ܩ  ' g      ߷ v ӷ 2 4M#f @@  {Щ  A A < @+reflexivity(ϓ/  %  ' 0 K`  x K Rh  + R R  T @ \@     `   ÷      -Nbg @@+ )   M"x' H$Hxx' L   ැ"y' $Hyy'       à Aѩ   6 ̠ E   ݠ@ @ @ ֠ ɐ  样@ @  ꠷ )   ֐  d .UƩ N ސP e @R l@ 7 "H'Ω r s =K@E  s x B  r@,transitivity>4  G U y@6Equivalence_TransitiveW N \ p O :  @(symmetry0xj U c @5Equivalence_Symmetric. U G \   ] k I    ݀ fWDH=   a9 .0v@p   m  *+  m {& Y n  ǩ-  o }( p   :! q    =L   rC b  w  ߷ : d  9  ,  @ @  D n  C s H S 8  @ @ C@&ProperL@ @   @     \   5 d  a ʷ ; ` S   W@ (@ /       x շ"a1 8#a1' 5"a2 #R^k @@   ʩ   ^  ( F   y \ g  Π + <  T @ q  ޠ  =  ? @ J@ `  |    I@ T@ j "A1      .  w R Z#   2     ˠ@ \@ e Π#A1' B'@   g o ِ  3 Fʰ 5 H M    7 J    ր+F 86  )  v $ 砷+/@)  #  | 㐩  H [ $  '  "3 bX     b `  T z #a2' VZo @@~ |  E ?n ٩ p  /s  ַ   Hi  Ͱ y   Wߩ   @ ·@  F} %"A2      Q       *  m p  r <@ ͷ@  ?#A2'qp F<   m | j  > #5 '  !    O#h HI   z   w V=  x y  )g y w k i  Ʒ ]  :   %     _        ҩ ̰      o * а  f   C * ݩ װ      o ۰  u t  1 "Hl 7         <   D   ]  ʠ  G w  @ .@ * #  O  P    -     8 V i    d I    G E 9 A   Q  h { ) # R) P D( L  + J -    ^  / u       f  / @ b@ ^ Z@0if_eqA_rewrite_r, B     s  : j e C  < 6 F e H    z ; K  C@ v F - x H   J D | s ~   琑   V T  H  A @  ? =         9*SetoidList@#InA q9@ 7   ]@"lt Uxc  i @  B      @#andЖw@A@"   e T  @( V  ^  +CCCCC@@@@@@@@@@D  Z@; T i(3@  /V6/ n    \ 5    z -    3 > Ω w 8    A@B@B@@@@@D    Z@ @ D@$Truey@AhM@)False_induُ  Vqrkj '    2w ; 5 1   5e@ 7 h   m Р @"le UxT@A@B@B@@@@@@D ! @ 3@ S 1  V_ ' Y  < 7 + N  A D@@A@A@@@@D = @VP GMS =! ` p# S  O e u( X T G , \ a X^ M1 b $ 7\u]@ 8 c c  ԐcCm נ l;kjmu޷vk 'ߩ zI x "쵷 -@ & ߰ (    1h8    f @ B <?@    Է we    t H J8 ! R L TַY+ @*  ["@ ٰv%  ݠ 'T f U Ʒ U © 2+ mu   ީ & 15(6  - 8/ { ʩ    G Q  KT@  B yX   V  a  _R `T b c  d   $  Ȑ"H2s)     1 ˶@/,   Р y  7 Jz   o  ( & "   IF & ' K + P" .  թ 4 W j     H F: BYA    :  '  &2. ' K ) M  (  9 S v =@)lt_0_succ5%耐[ *S ; @ѷ x zY}[{m]kig & / F 0@ec p 2 PafOrj /K <Lk T x SIn { = [ C ag  I   頩F  <ސb   _ZQ   F ]@ ^ m P] R   o@9iff_flip_impl_subrelation2VA {[   T)! V ǩ s g@-iff_Symmetric!x ( _C)  N-c-..@/ ĩ  1no n Ϸn ˩  v^2> -9 CI  G ܩ  IN      _   W Y    iA  J  ^f   vB  % ԩ ~  + u Hg   { ߰   "8C< Ƞ lWG2N,  ܠ*2 /. 4 $    @     Ӛ @9iff_iff_iff_impl_morphism8C        󩚠 @$flip$     ٩                 M T#RUf  ȩ~1 \   2@-iff_Reflexive/h `@0multiplicity_InAрhpyd=A/fC@ޠ sDᠷ ȐspM$̐ } Ȑ"n0𐵩"Gt @'gt_le_S3r @"Lt @'lt_le_S0?n LC8C OC g@"gt UxV C PX@Rʰ}Q 64(&wponl  4 Q~y Gnhd$ @"ge Uwi  2 } qa \l/OMA?3֩ѷԩ G@&NoDupA @Eթ@ ߵ;@ީ  @ ; 橜B  A %AC !Р$  2q+ڠ f@:ept5䠩߰i@=IMB@D@D@@@@@@@@DJ @[@Q \WUh  EC7?>F5g) 9kxu ^  T lp  _@)@h[X%÷I8ɷ p6;ŷ\w(bx\ Ttܠ}ɰߩg _ݷw԰r) )b?H_I@~c~ߐ O1 ° l :Pj̷Y u s˰M !dq(  U  ǩq $۠%-. ʷƩ6ͷC ~   286E?+IB5G7T\@Q\"EQ4Ͷ@Қ 9@1Proper_instance_02>   hݰ] (<֩ T@'succ_wdy΀ @0multiplicity_eqAچ :wNz<u>{R..@/eq_proper_proxy)f53,  ;H=ON6@2multiplicity_InA_OK VXdCfJ\J n|bduc$BAWͰFk~G-(^XNc̰sC5czhҰ˶@K>שРŐI~|pxGW鐩ZCv+WB)멷Z=/_3^(>=;U%J =7gA7>,AI *uĠ׷7ZJ W ]@@/1ȩ@+if_eqA_refl qkYnʩ6ӵ©=!P@'BinNums'Numbers`@!Z7@R&BinInt&ZAritho@ 1P&)BinIntDef@ ̀@&of_natbz @1?G!Ʃΰ ,ְpw.$Znat(%Nat2Z@'inj_addc C@6@1P,+ ͷͩ?QBU@(positive*@C<Q;*S@1P-hAD@&ex_ind 5{qrqxY 8pr@#mul1P]m@ 9! %Zvar0&Omega3@'and_ind14ۀЩx?٩W6R: $&Omega0a@)\D0@YKQ@tSm@#opp1P@ {w  I+OmegaLemmas%omega&@/fast_Zplus_comm11ҷӶ@oȠ \@4fast_Zopp_plus_distrpe!@}  g@7fast_Zopp_eq_mult_neg_1=Ҁ,@87 x/@2fast_Zplus_permute|CC@K &Omega2ŠVQXY@֠e"d \@8fast_Zplus_assoc_reverse '#+'c@1fast_Zred_factor0#*q1@ &Omega1ҩ+7?w@,fast_OMEGA13K)FBɩqD@@*comparison;f@C1 ٩  C@XQ@'compare3xL@]=i C@$ 쩚@&OMEGA2.$DbY%vf]z)auxiliaryi@(Zlt_left,ڀc*5k@(Zle_left*x퀰@p7GDxة@'intro_Zz,jc@&inj_lt8Fyzਗ਼@&inj_le8FNCՐV9+,a\6착°:4;jd9D oѷ  x G )Decidable.@+dec_not_notHɀ+Compare_dec @&dec_le*c< &*̩bж@Ѷ~t?ֶ@Eܩ (IHl_left)IHl_right@TVO B Ʃ  ư_\$3jc V ک    ڰ!  t{21"N~ q  * ($.k6E@1P,; [\꠩Y`ARQ e&Omega5 ЩelM  ͩturyZT5/dbV^  %Zvar1&Omega4ЩrթΠHHÐG2|znv "&5㠩Dؐ\@sRlg= FƷH 5X/q ϶@kĠQ Z۷ܶ@xѠӠ('R g'@ܠޠn5 sr.7@ }oJĩEL萩M @ʠ W@Ԡ aB ߠ C'ϠC +auxiliary_2+auxiliary_1 t@,fast_OMEGA12J C5Š+9ɠMI@,fast_OMEGA10H$T6S@Hؠҩڠ^  ߩ@1fast_Zred_factor5(UK&Omega7(`tt5 v r0 h+lRé@&OMEGA7.$I Bw@88lͩ@(Zgt_leftE?s֩Ϡޠ"ĐHM}{owH,U ᠩA4*֐Z@&inj_gt8FF|p@¬_le+g C ,*{ymfedb{^ %S W]!@>Reflexive_partial_app_morphism 2R,xl{U@{XNuNc"4sc@ :Sh+ <gU)@ 4ɩZ\q4  = G`u84Fupz9D R%,u @ Hݩp D.,~X RxzNRYU\ȩ°*cİe϶@ h̰(n7oC@=gk*߷vS>ȷ86 K by@.permut_InA_InA;ڀ$sD~+F ép[K6 IM3@h,4R Sީn:C^ ?=ZJ9 #;  >ⷐ#AbsL<ک; t` o }@ ._@vx lĠ#n8a÷Z u ^ t ty"e0 *ڠ@Է@ ~ x( vѰ 2 w"*F W\}#!/  +) @   WOm[S$5#8 "" qoc\[ZX̶ŰxrIKM xOQS԰XZ Sc##@ʷ@Ʒ6/"ٷթEEܩ h}<٩HA 5  ( +PѩCӶʩ+b[ϩOlp 1)oC6./ _%   #@ - GCC7C@T >u qw sp[ 8"b12 +"b2շ^m9_˩詚9@/permut_cons_InA:MZÀ Aoԩm o? p ~@ /W@w/e1|@"or @< - b?k@nfנ6_K2  ˰8xͰ:   Ӱ,xհ.ph    ڰ%&ܰ' zr   2G  6 ?R[w\@ B_}Y bG K][Oqc tbTְ w]o  &r u  fxh} ?n1"uA,& 2,*B@/permut_length_1=~ O  @ B P Z  J L  b"Ʒ7\ &Pԩ)@@٩(۩)v+>un }'sc9L| 2q*($GZ 86*22q 8@B@>:@0if_eqA_rewrite_lz,  B\JEijl e(Q][OWWz'0!d'bV&^˩Ġ !©<eŠqockkŰDgK)Peano_dec@*dec_eq_nat5뵀qU%͐*Sĩ頩Lސb @@ɷZr [̩u l @@ؠ"˩ Ƿ*1͐ 3@;א<LFLڷK֩ C<1 OVX =[bA?` @#yj/*(n 412$Axf`f e7Jz *o q(&"",GR@NUGIEܩ^\ީPAaLdVG)R-2+k@gn`DtlseV k}+ @^@Zufɩ  %; #pnbj,v Ey wks۠ ΠАT <{E1B·8mk ʶ@@#Zne>o=VַXtiک̠ _zŷ(/ːũ1@';yy,:MGzvЩLE_ ;U|vtX -d]b nSש`   u1&Omega6Щ18E|uc jk祖a% #˷LM۠JQ2ifKd@ <@8䷐%Zvar2dЩbiJgF e@ T@P֩~Щeũa'k,w7i@ k@g@ީ|ߩؠjGΐRh zD젩xe̷$u#ffPзRqbSfɩR_#@߰ؠڠܠ1AoqA/6Ґ5qjqӷo:@GLJ  D rJQPI>©\ @  "e;J% h (@$ + .rI/p 0@, 3 %6 '|{ +bַ~ >@: A 3DWƩ_ F@B I ;L =_ ?/ҩZЩ CS EY Ge X@T [ީ9]  ^@Z aulq d@` g Y{ G   l@h o a cm ey @0fast_Zplus_assoc Da~~ p-)@1fast_Zred_factor3& @  }ҩ  (f @    2 & 4?   !! T <L   ?  +?; H 頩l]Mߐco @ ة   _ _I  ɷKũZ C  طvk4T ۶@ Р Ҡ { & }g a ' @ ܠ 1 o i/ @%  w 7 @-|  < @2 F ذD @:   ?       L@,fast_OMEGA15M$     %   #+      %-ԩ   2_  ũr 0 ɩ j@'OMEGA17 PЩ )  ;~w@(Zne_left0߀署@*Zegal_left;6t 9 *aĠ*{@2@. I :fԠ"DB6>  Y Jv M K?G b S6( ][OW /ũ' 76L@i@eөҩˠQ)Dywks  @'inj_neqjD⩚ @&inj_eq8F6(Ca[  LKcT=Cuw_yCY{}ekCi 7LPt#?93-+$"$ pyz@3|`L -#y;+3>kpB'!y0@JB@E?@ IBKLE:B<MQD>R M XO   ! !r(- (ua ,2c "z07 26>197t *?v ߩC /⩷ΩG?*#J%%%R@PM2ԩݩ5 $ 렩! # O *_\$<>b/h f a > R A!?W: j E$ ɩ~1+Z,b| ԩ5d6lİ  \ư"  ܵ  G@֠+uߩːOe@@~wTV頩[ސbZǷiph շ w L ~v{f@@z,n !ްߠ+$y-з̩92 y;'޷کG/*// ;Tdxfܩ=   ^  ÷4Y|Nҩ@@ &9pi .^  < . V{+p@'@# -H[ɠ;97+33 =X  * c@_ f GbuȠ,jSQEMpZ&TZZXLYTT  Ɛ t eXp  z k<v@ V> @  x.  ݐ  |3 ~)0   ࠩՐY> ucout     @ ĩ  D a K  ˷M   Yb ө Š "  & $  ڶ@ְ  ϠD $b ۰  Ԡ Ő !{ z@ͷ@ɩ 䠩 Ր 8 1 &ݷ    H A  6  ! X0*0/    d   $  3 j c  Xܩ  r y 0  { ;@q  C Aé  E 7 (T   + y20$,?   6Q0 #  \@ Q  + V   h  i f mG    n  Щl s T   O  )^\PX     ީ       k Ω Ǡn   Avthp    i Щ    ܠo& Ґ Vm ~  2 {  G    B  _Щ r]  op@ @!  LKg ɷ d <Щǰ Ω u! sP_! q@ @! Ca S z ;   e 5t  !#!* Ɛ!"wHܩ! u@ з@ !7 @  젩 !C   !D!=vE!3 t   T !!X!Qv!F ʩ1!h!a$!V ک#     75  o7 !u!|D!{!tRe-!i Q"  !!G@ CJ<d< ϩQO Q!!2^!!lG!!k<: .6ݠ!a@ ]dVX!b/ \!J勺qo  q!V!!R~!!!US GO!x!z@ v}o Ðs7  !!@ {% $ !:!@ -!, !!@ 5! 8"  :!@ A @* ð '!@ IdH2 Щ! 5 5 P` !\ !TX VV!@  թ!!B" `JP !ɩ!tK! Ϸ"ζ@ ʰѩà"Š!PǠW rr\ !"ܶ@ ذߩѠJӠ"(|f !נg!6 _ !qF"/"6Ґ"5".x "$!۷ "B@8K!  "N"U"T"MY"B!Ʃ !EF!;=!5.$/, &# $!. 8 !">" 8@ *өF 0!"" 62H:+b"`"|"@3@/J;g""p""EC!7?ZKw"""" US!GOj["0"**^0\!P/X 0"Ʃ (" 8""7@j@f"ԩ "ө"̠'!""Ezx!lt" 8yv""C!"Z"TX"Z=s!\0"D^""\`"bE{!d"C"a"c|!e"Rg"i!kC!m "0#"E####{"·"Ob#é"U"W"Y# i"@"_,"E"b|#& rwu"x"g4c#,v"j7|!""+@>|#6@!"@#3Au#@#9""q!a!""6#A#E""#g"?i##J"!۩ # "G####{#b@}@#"#h!# #s#kҷ#(2!#x3!,"%"#6#@"8R}}Ω#"E"#"###@"?Myy W#"@ /"#"###@"FS"~!#O"!#T Ϡᠩ! !ՠ#=#X!٠#V#A##"!#\"!#d##Ƿ##""#" #""#u"!"o#P#Y#K"r#N"p"@""#H#Y##"o#"#k@&length䷀"#"#"#^#"#W#_#}#ȩ!"J"""#4""#ѩ#A#:# U#Ω#c@*permut_nil9X##k#s#|#թ#j@*permut_sym9a ##r#c####{"#$IHl1"#@"# #"###"#U3"##5"%#"!n#1"")###"{ L "2",##/####"4".## @)InA_split!i4!r"<##$#@"ex @g"h !x$!y "[!l"˰##!\$#!^$$BBB@@@@D@!w"x$!$!!'Ϸ"Щv!sm"#ɩ#!i$)# !k$/$6"#}!!#$<"h2"H3(@B!$?!E#!]##ߩ#ְ!J$ #>!L$M$T# #!!#$Z!B@\#!]"$[###!$#V!$a$l#"#թ! !#$r"t2)6gBBB@@@@D@ɠ!)!$?#:"#$ !1$(#t!3$E$#@#Ѡ #z !!ՠ "$ :$#K"ʩ$ $0# $P$! "$# $.# $A$\#\'##p 4 !N# 6!!$#,  9!$#`$#!!$##!!![#!""!#< I! !$@ K## M$U$s" $'!u /#  1# 3$W$h#S$0#$2$˵!$5!e! ?$t#_$<#$>!n)"$k" $E# K$f M$$#m$J#$L $"=$u@0permut_remove_hd$ Y }!?!A"1$$$}$|@,permut_trans JM  ` !H# b$":# d"."<$ f$5  "6$"`P$s$l#$n"U$rk!ܩ%$$y ~"@!@!#$~#Ͱ$!߷%%%$o!!#!%$$$!$ 䠷@!·@! ,.| !#a%'$!!%##$!%-%$ !%!˷#%!!%2$!!з#!̩˩#$%"#$ǩ $!" %D%=Π"%%2$4!!#!$% " "%T%Mޠ %%B$ƩD!!#! $̷ %g$ɰ $  % "!'"#!  #$ %w">%u%n"%%c$(""$""8"8$":!$"<A1%!$$77$$9%%C!3%Gܩ$D$$% !#$$"%$%&!)$"B"%C!C$j! !$$"$%ѩA@*app_length4UmƩ$]%!"۩<$c%֩"d#%L!Q%"N""R"r#%R!?!:%,!9!;%ǐ "p"`"`!.!F%3%3"b%%ͩ" "e!,C$%:!@!Bީ6$%$ $%ؐ%%%%$G$E%$9%$2$1%$0$.%%#%{% %t%|%޷$j%%w%!@*equivlistA~%%&%%嵵%$&"W":$2$,%%"%\$6$2%,"O]"CR",שg%b#r%"" "U"I9@n%i#y%#{$E%-%&"@"R#{#&%#}#&%$ɰ%|%v#ng%ҩ%x#p%Զ@@"`"%#&,"s"g!^"P}"*"u"iY@"k2#$c&#%4#$e&%%̩$%%#%##$e%&'@"x4"6  "x$"""s""$@/iff_equivalenceZ &B"I""x$%E>"M""|Щw$$~%l%%&K""Y$$&Q&P"%$$&U4,"""/XT>@R@">Z"/J<,""!"Y<-@"-a"\83"@8per_partial_app_morphismp""28C &m))'$$%%&%&p%٠x# $n"@@y#g{#%߰#&5@#l#%#&<%=% &"1@#!%#Ʃ&###$&3%K%%#&9  [& / ٠&#8&#&?#<& #&:##$$&E&@&or_ind"&#K&#a&I#c#$$&L#Q& #g&O#i#$$2&RSU#Z&)#s&"r&Ϡ#d&3#'&b#)##$-%ՠ#j&9#-&h#/##$F%.&Ðߠ#t&C#5&r#7#9#$)%#z&I#;&x#=#?#$C%*""ˠ#&R"&"#F#$*%.&4n&\"h&"j"#R#$nk%x&fU&W"t#Z$$suʩ &p&a"#$j&v&g"#$p@1P,u& & '"#$j"ϩǐ&֩&#$f'+}%Ԑ&s&u""#'>}|q&Omega8oЩ%␩& & #'Elf d 'H & & &   ?"'[ Щ&&İ &   "'` )'&a$)&'g'n &Ѱ '    ''q1@ g&'{z& '    /gCA&$C'(''$& ש'    5'I'K@ @&xөl'R'S@ ٩',\ b/'.'[@ rᩚ@1fast_Zred_factor6)~ ۩ Zn\qo&_%q'M''R' Ω'H    3>'q'y@6n'z'@>v D#|%''%J%!&''שs': 'i   @ Y&!'6-iZ92;#+@'& '署@,fast_OMEGA16N&)J 'f=&? &  'Omega21& \#&(ǩ&°S('1d'ͩh&ʰ3 "'Omega22&԰ <t $%Ϡ_%[zz %ՠ  'Omega23  $%+ %-  'Omega24  ǩ-@'OMEGA20 PЩ젩|%;(C' Щ+% '}(G=@&OMEGA8.$J kW''(O(P 8's(G(R(S@(Zge_lefts&& ݰ' '    c'ư '   i&(i'̰ '  o$(o'Ұ(u$%m@&inj_ge8F7%P(2%]( tn'%&% &g@¬_lt+v%#($8'ѩ 2'8'$ (.$ $1$%&c B( (8$$%R&=$X p(q'nuV(@(LBg%%( |'Omega33Щ'|d(+(ZP$]%t( 'Omega25 #('u(< T(k V n%0( %Zvar3'Omega32Щ'(L ({  f $~( -'Omega28  (3&B((({(<а(6Q'Omega27wV h(B&Q':))(=(@^é(B'Omega26eЩ(6i|ε$CyCljǠ7))_r(?̰t( (   t(G)&N( (  ,%),T(ש(%&gT%(ꐩ%#(ؐ W6(ʐU%'qXP%'t)A.@(imp_simp{ys&@&dec_lt*c<~(ư%)R$)<X%(&(&&&&(^ % % A(ԩ'Щ+ȩȠc%Wȩ(װ\)^z$%&7)t8Ơ(5<) %Zvar4@'Omega42 Щ(@GT) ʷ'Omega34 M)Nܠ(KR3.) ַ%Zvar5V'Omega41 Щ(V]M) ැ'Omega37 fd(&f())G))= -@)@UK)CqmF)EA'Omega360hz}{(w' }'))T(( 'Omega35A y "L($7"))ҩ(w(*r)98)h:XS*()ܩ)?o)nqd0&5) n&xp)&{)`&~ )%),f_(yl)Z%)%&N&'@(6ie]Y_%aYYŷ*ƩT(ðʩ*O!N%Zvar6η'Omega51 CЩ(ΰ`*:!X'Omega43 4o۷*ܩj(ٰ*&e!d%Zvar7䷐'Omega50 YЩ(W*)P!n'Omega45 J)tD')*2*9)#)1'Omega49)'(}*C*J)4")(B 'Omega48ɠ ©)*Z)')*U*\)詷)'(*[*b)*_@U*L!@)*g'@]$!**n.@d#*x!հŷ*v6@l+**!'Omega47u4ݩIG)ɩ*)Ʃ'J)**+)*!)*,9/*/UQ**1%'Omega46L!^a_)'a(**B* ٩*8@(PF(lhA(<'Omega44+ c u)g*w)ry*)},}*0})xÐr Z)~ɐy:'Omega52)**( I*)*('P*T#(-V) )1(-d'Omega53)T=([pA'\CG'zz ө  '|d|+ ̶@.+j"Tu'Šn{ 'Omega54 ̠u $(f (hҠb 'Omega55  HH+.*Щݠ0.(*h+27⠩r(1**o+9+:h}**+>+?(( İ(y&({䐩*ȩ*&(+Nv+Ow.r'>+u'* u^*sc'*}v}'*+_  ++c"+`'˩'.))+ +')֠"0('}5()+ +.(ݠ"(+w+@3multiplicity_NoDupAx))**++:+''ƠF))+:+?)*(+(!'O()+.+H(*(c+(*+))**+K++*C+,)˩+&)*+)+OMC*g)*+++Q+W+y+@@#'++)׷+++++f+**r#eqB@+l@+g('eqB_dec++k++W+)eqB_trans*!@*Transitive++-"'4@+Q+Q+j@**(*h+Ƿ*)C+o)*)A*@*)>**++ϩ*)@++`$q@#map$)B)G+x+ͩ)D)I+z+ӷ*)Q***++ީ)*%<%4*%=*)R++r)O)T+%2)Q)V++$*"+x+)Z*$+%?+)\* +#++)^*"+%C+++*#* *%O@*)`*/*)++*)b++.')Q)d++))S)f++*%N*)W)o*91,*W )G)n*=)s+++,)I)p++( )>)`++, ÷*ĩ ),) ·*é[) $*˰++(,+(,,@ҷ*ө(ȷ,(ɩ *©o(f*߰+©+(,"+(,(,/*))))+)+*g+mc().*i+ͩe()0*k+,8 @:(,7(=*(U*+ש+ΰ(,+6(,E,L+())+:())˩(()+(()+,U#)=@W+(+++',+P',[,f+3()`)+T()+'()*'()+,o1@(+-;++',+g',8,v+J')()%+k')%ҩ'))')*,(.+?<*,,$+y,D,) L,,"+,5,P+PQU+d}(+)),+ E),+kG( (/+I(U'L()ک)N(,f+u((9+**+1),5++,J,h)a,;`)b+کb)d+d,L,],qj+g(+(O , (R)+)o}o)q* +)t,,Q+x)z,q({ַ*5~g,H,A,;^,j`,(I b)1),+,Is)4(w*],,ܠ,А)),㠩֠(_,,ِ+,_),,M,,,h))+))˷-,Z&g,ǩ,,u-))+)-"))ڷ)- ,Щ-+Ӱ,)--[ ,Ʃ- ,-())+))-+,+-1!' k,թ6(*,-,$u$}@$w+,))-;H* <C**)+,")-A ++Ω-:!; #,I*(!1é!,(*,-N$$@$-P 6ߩ,,*-P-IX(-S-?,é))+)*&-]z,})z)+z),,*/-f-_R(-e-U,٩s** ,**<-s,ߩy**,* <,3,,-*g)-@)!,*<*O-u,3s*'v*%,t*!,- :) )-J*J*]--&-S--H*<*:,.*6) "- "f0"ө-- A-;C1-E)@-Q*f**h)Q")3E"F-*@*r*r:):-'"*t7)-)<-)-)33-2-+5--C)k-m,|-/-)L-XN)7,P* -ϩ-0S-_U!)>,W*'+P-C)},)D)h9,Ű*/-9,& )m*/'+ *-h---,)R)vD-+? $)V9+.- --z ;,ٰ-~+2,۰+&+4-w-8)"+Vz-i-b-\4-6*-,-h+O-l%e*֩- --s @*@*,-x,ǰ-z*ٷ.. O -- **,*.--%*.. -㠷@*@*,*,`.&-**.",-*.,*-%***ʷ,***.1-**Ϸ,*˩ʩ,-*+.:.3y.'-**޷,*ڷ ,--ĩ-*. )-++.P.I .=- **,*--*.++*.a.Z .N-ҩ ++,+ )#-ط#.s-հ.*.+-'+/*#) # .+I..y .m- +&+$-+ +B+B * -#+D=,.* --44.-6..C*;.O-L--ѩ.(C--+.-ש..I-+J+.C*KЩ-r)-+-+ީ--++-..1ީ'M@'map_app%3s[+]-.TC-*E+_+aǩ a+c-,.,-C-,,-ݩ,,.M,,.O...~.@@..ַ..Ƿ-6-4?..-,..+Permutation.@3.~@.{..۩ @/Permutation_ind*(I$.y..|,.-..u.}..'.+....#,..((j-IHPermutation--$..'..꩚.@+permut_cons= B-1-+...........%( ..3..-.Z..@.permut_cons_eq'ˀ(.'.<..//(...+C-.+.@. ..-h/ ..,.H#l''.;.OA.IHPermutation1--K.9.N./ -H(.IHPermutation2-,-X-R..ک 1 ,,-Z...//!///!/Aa/3/1/$/"-[.Z,.ڷ.g'@'Forall2:@.../+/2'@+Forall2_ind;?$...WS/5.ѷ/2.ʷ..f- ,.{.`#-ĩ-{-{-u/7/;)IHForall2.,--z//<H(,,-|-.//I../>/>/B/I/i/[/Y/L/J-/-!/!C@.!./ //O/V S.J..//]3.../_/T@ ]/T/./\/g=/// /i/b.6// / /`/d.///"/-@.. n,e,-/3/xN--./z/o-K/..I/ //!d/~ |A.u.͠.(/^...//( .ȩ .//$( //.Z.//&/(.ͩ ../)/!//.H-/(,- (-g- ࠩȰ-!Y!Yq---![/!ΰ-((w--.((éA-~A--./g//f/D/a.(9-.ڶ..~../B// -+-,-/u/---//--8..-.. /#/.--. // -5-.-/{//f/!-7./h// -5-://b/  @ ʠ!w.!x ͠-/- Р .  . /i/`,/  ٠!!(- /---(//|/吷.!/% ͷ@ -!/-"  . 9,.-/. /,/|,/.,//   F.,0,,,0/90/-:/C @  . T,-~0.Ű /2/,/ȩ.,0 0    aI,o 0,q,q,0.Q0. ѷ/^ @l,Ϡ-/.ݰ .\/,~/˩/,/0& * ! ya+ 04 ++,06-06' /v. .t/,/ԩ/),/04- /ǰ+/ҩ//+/0. $G/++, R0I F=} P 0P& R R 0R0G$S/ +,, $V% ,++,,-/0 -/0M0X/%++,-/+/0$]-/ /00a ^U h-`0h> j j 0j/ l.0 Q@ k+b, Y-0uK [ [ w0w/ ].0 v'm(Š'/l),-+0X++ h00 --/r/./0{E/ @֠8-:0g:: w00<./˩ ./ᠩɰө/,-,0t"00&-/..0#IHP#IHA//T0031./)P@1Forall2_app_inv_rҀ9..0r0 K/wL L/wMPPm0- TTq0.4/{A0g0MX00 @ Ƞ]/^ ˠJ/KLLd0-ͩPPh0.C/00r0aT00ݩ ڠYZ)[/а] !40__w00na-/ְc./.V0쐷$l1''0.# ַ@ J/K?q0-Cu0.U/d0001 hiN6/ 1 1 0-/. .T1$l2''j0S  @a0-ũe1.c/ְq0X001 !  pXq0sd1-uu1/0w-0y-.+13#Hl10u11.q/ 0_0İ015 ɷ@1.>//{0ΰ01 G>~0=1S)1U0۰,©0C-.1Y#Hl200'/001.001X©~1j g^0]1sI1u0![0c!-ԩ(-p.Ƞ0o1[11 !0u,-ܩ10é0y1&#0 $ k 1!0-*-@4Permutation_cons_app4l10191*B@+Forall2_app;?z݀$0!1^B$%-=1E..T1/1//1/1110O @[0~1B1J1S1n111N0:] ?@01q1001M11y0001O1`1u10(00011z  /001^11g1U@