"`!܄!*yD)SeqSeries%Reals#Coq@P'Rseries%Reals#Coq@'SeqProp%Reals#Coq@)Rcomplete%Reals#Coq@'PartSum%Reals#Coq@)AltSeries%Reals#Coq@(Binomial%Reals#Coq@&Rsigma%Reals#Coq@%Rprod%Reals#Coq@+Cauchy_prod%Reals#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@(Alembert%Reals#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'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$>aU堠#Min%Arith#Coq@0Ce-Fѕ(PreOmega%omega#Coq@0\|چBb~w4%Omega%omega#Coq@0t.J'6\ϨrK(Zpow_def&ZArith#Coq@0f蓜DX;V*ZArithRing+setoid_ring#Coq@0{#'[{nm!/,Zcomplements&ZArith#Coq@0ʾq %RIneq%Reals#Coq@0JUڻIu)$w&DiscrR%Reals#Coq@0z41pV.%Rbase%Reals#Coq@0Jܡ\ c6{%R_Ifp%Reals#Coq@0c4+ZŠ,Fourier_util'fourier#Coq@0ϳ> 4`*r0'Fourier'fourier#Coq@0wV9TN*Rbasic_fun%Reals#Coq@0hܒiclE>%R_sqr%Reals#Coq@0X%MԹ%M+SplitAbsolu%Reals#Coq@0M)&qYlݹ5*SplitRmult%Reals#Coq@0sD\rt/$Even%Arith#Coq@0YO%q}d߫%$Div2%Arith#Coq@0n*Áht!,)ArithProp%Reals#Coq@0B+L?>*e˃a j*Rfunctions%Reals#Coq@0d¹d‹@'Compare%Arith#Coq@0OM v먣5L:08]$u+?0Lt2|9D }SSԻ0{ڸ4q 0j&2"(>S0d US^0]JrHr#E0䟄WCJҦ<0gȀn_}!W0K*ߞ4q0I͗Huz&KBzRH 3yW95ܠР)SeqSeries%Reals#Coq@A(sum_maj1 @@@"fn@)Datatypes$Init#Coq@@#nat@@,Rdefinitions%Reals#Coq@@!RӀ "An@ !x"l1"l2#!N6@'Rseries%Reals#Coq@@%Un_cvɀ!nJ'PartSum%Reals#Coq@@"SP?v GAEC@&e*Rfunctions%Reals#Coq@@(sum_f_R0YcGAC@2{,Rdefinitions%Reals#Coq@@#Rle=*Rbasic_fun%Reals#Coq@@$Rabs; wI&'H)"*@&Rminus&HFcD? ER  @@@@@AA@@>@,Field_theory+setoid_ring#Coq@@&FEeval>@@A@A"s @,Ring_polynom+setoid_ring#Coq@@&PEeval"s @@A@BA@A@/Rseries_CV_comp @@AǶ@怚ڀ"Bn@‶@%Logic$Init#Coq@@#andЖw@,Rdefinitions$#@@#IZR/r'BinNums'Numbers1@@!Z7@ACCB@&Specif$Init#Coq@@#sig#* @2!l K怠۩ G *_@@@@@&Cesaro @@BS@rf@ym;q@IB@A@#Rlt=z@/r@'SeqProp%Reals#Coq@@(cv_infty?7e)Datatypes$Init@#nat@*Rfunctions'@(sum_f_R0YcM5@$Rdiv̀!k&A@%Rmult׀?>h?g$ji,@@@@@"(Cesaro_1 @@CͶ@쀚䀶@BA€@$Rdiv̀[#Nat$Init#Coq@@$pred `<'Raxioms%Reals#Coq@@#INRr@@@@@m@@@ ӳ2@ ӳ2[)Datatypes$Init#Coq@@A@ Գq@ Գq\ @A@AB@cAnml@A.0TQ+Ring_theory+setoid_ring#Coq@@ABA.U>[J @B@@"O@(PeanoNat%Arith#Coq@#Nat@&of_int"O#Nat$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@(Alembert%Reals#Coq@0I͗Huz&)AltSeries%Reals#Coq@0d US^%Arith#Coq@0I|кX*o4)ArithProp%Reals#Coq@0B+L?>*e˃a j)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(Binomial%Reals#Coq@0]JrHr#E$Bool#Coq@0j 2cZ`FW*CMorphisms'Classes#Coq@0qیZBeϠ0CRelationClasses'Classes#Coq@0TL;0RUfw1+Cauchy_prod%Reals#Coq@0K*ߞ4q'Compare%Arith#Coq@0OM v먣5L:+Compare_dec%Arith#Coq@0jXF 8jih@0.i bYN Z)Decidable%Logic#Coq@0ND걸풬/Oߠ'Decimal$Init#Coq@0C涳N*ua&DiscrR%Reals#Coq@0z41pV.$Div2%Arith#Coq@0n*Áht!,%EqNat%Arith#Coq@0AIgՋXRV *EqdepFacts%Logic#Coq@0FI$ͼՋ`)Eqdep_dec%Logic#Coq@0u wWIϰ߼*Equalities*Structures#Coq@0όe얟)H.Ƞ+Equivalence'Classes#Coq@07;ꮹ$Even%Arith#Coq@0YO%q}d߫%)Factorial%Arith#Coq@0@oehJd%Field+setoid_ring#Coq@0J _ȫ)Field_tac+setoid_ring#Coq@0d vDZl^۹HO0B~uYٮ٠'Fourier'fourier#Coq@0wV9TN,Fourier_util'fourier#Coq@0ϳ> 4`*r0-GenericMinMax*Structures#Coq@0måj$"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+ListTactics%Lists#Coq@0,Jcy{%Logic$Init#Coq@0\͉!Ig*Logic_Type$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$NAdd(Abstract'Natural'Numbers#Coq@05;ZW:㥜un$)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$Znl0\͗+OrdersFacts*Structures#Coq@05Mܿ獐ζΖLB)OrdersTac*Structures#Coq@05'4Ԗ+9%'PartSum%Reals#Coq@0j&2"(>S%Peano$Init#Coq@0 jha|ؠ(PeanoNat%Arith#Coq@0O~2$k[#lZ)Peano_dec%Arith#Coq@0Kݢ*k$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%%RIneq%Reals#Coq@0JUڻIu)$w%R_Ifp%Reals#Coq@0c4+ZŠ%R_sqr%Reals#Coq@0X%MԹ%M'Raxioms%Reals#Coq@0S]jnj][L%Rbase%Reals#Coq@0Jܡ\ c6{*Rbasic_fun%Reals#Coq@0hܒiclE>)Rcomplete%Reals#Coq@0{ڸ4q  0(2{Ze$ќ8)RealField+setoid_ring#Coq@0 >ʾq /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$ 0;RWMi\N+SplitAbsolu%Reals#Coq@0M)&qYlݹ5*SplitRmult%Reals#Coq@0sD\rt/'Sumbool$Bool#Coq@0sB ,$11.]m'Tactics$Init#Coq@0/9m+ a'Tactics'Program#Coq@032 Q@@A@#_19@'@A@@@@@@@@#_202M접#_21'`o@I.function_scope'R_scope)nat_scope@@@AAΠѠԠ堐A@2 Q@@A@#_22 @^@A@@@@L@#_232M접 #_24'`o@DJLN@@AAA @ 2 Q@@A@#_258@ S@A@@@@{@#_262M접 #_27'`o@Fy{x@@@AA>A @ t2 Q@@A@#_28p@ .Ie@A@@@@@#_292M접 #_30'`o@C@@AoF@@@Npc$5|T y„@h,kyT\uIy넕@|ޛ3P 4uz@5wvЍ uSgR"fn@)Datatypes$Init#Coq@@#nat@@,Rdefinitions%Reals @!RӀ "An@!x"l1"l2!N(!H'Rseries@%Un_cvɀ!n8'PartSum+@"SP?v GAEC"H0L*Rfunctions?@(sum_f_R0Yc"H1$ZM@#Rle=*Rbasic_funT@$Rabs; wI+,H.Ȑ"H2&Specifv@#sig#* @Ar!luXP:L#Nat@#add `BYXJYY@&Rminus&HFl:De#eps:@#Rgt=<p@#IZR/r'BinNums'Numbers@!Z7@A%Logic@&ex_ind 5{зѶҶ@%Peano@"ge UwB@#Rlt=@&R_distNeK+@"ex @@(OyqnƐM-n԰ ʷ"N0"H3C%A@I>9Ԡ#Q'M#P@AR0"H4`Ȑ"H5Ȑ(hyp_list>@$list]@AF@$prodt@,Ring_polynom+setoid_ringN@%PExprk@Ȑ'fv_list&BY!klI+k b$P-fk8h%RIneqj@2RField_ring_lemma1!7𚠐(Ring_tac2@0ring_subst_niter!F=F4BE9GD>@(positive*@C G BNA#T%V @$Truey@A@"eq @A@$boolZ'@A@ Ȑ#lmp@.mk_monpol_list(~B7&BinInt&ZArith!@R1P&)BinIntDef&@W ̀@#mul1P] @ @#sub1P@ p@#opp1P@ {%Zbool @(Zeq_bool0߀)@'quotrem\$@/ŀ.Ƞʠ@#Monf@@#Polj@ũ@#Peqj*(@*norm_subst7:d0rTPA;5/'0tVRC=71)gd"%@%Rplus+1<PAXYj @&eq_ind JD"M!rK{&'(PeanoNat%Arith_@&le_0_l?$@"le UxT@sA@"Lt@*le_lt_n_Smݩ$Plus$@)le_plus_lx&̀ @"lt Uxc ` Y"H660Ȑ"H7&Rsigma@+sigma_split'9΀FUpSB*vu۩@%sigma:ۀO  S© 1'@(eq_ind_r!2#ѩE@ AMliܩЩwᩐWXt5 ze]RE%bnf'%Minus@)minus_n_OL]1> V,T:ߠǠ Dˠ "MIY%;&\ܠ+XJ = ꠷91nNCEx6fNj&^Ȑ"H8@&sum_eqcǀ*U*I)!iZǐӠrUYZ@<^ o df1B*yZ9Pl0BY;9&Hط4B#LנgɰI)KNO4%tJװW<[E{lc1 ( uTnB@&INR_eqpĀ,8<0>.'Raxioms@#INRr ˩ԩѩ/ ש٩Kh!ߩ#)'Wà+N.Ƞ 0Է4dР"Ҡ:%,22C@{jc@Q\OM#0hJF71+%0jLH93-']C@(plus_INR eT@%S_INR=sidnes@)minus_INR"ӳxt"Le@&le_n_S84{GKzDPȠHh!WK \]{ɐՠ`1 jࠩؐD--,-d& u\&F.n0 B BB9*D{="J;DE*Sh@8/0Y A@(le_trans:a'%@)le_plus_rx&Ӏ,P@.le_succ_diag_r C#l'0n<ɠ3+&T(_C蠩.B3+CөU֩蠩LD9p@g`!Xطf٩l堩c[v̠|skgéld`^D  @<1,Ǡ8ѩ%@G<7Ҡ!F٠$8(+,-@[PK样5AM^O6b @  9 ;?_֩A'˩ X5}QU RĠ0'v./`4ɩܐ?u␩y8ߩ Qݩ쐩bDbCzΰXҰj԰  *'dаP5t^oWԠ5[@ kݠ&Hwq!lQ'rPv[ũ4''ͩhҩo3=I< tީ{_/שI7M8D\hE>0-+d;ĩՠhƩbʩ^ r O ϠlѠnՠ$~\ܠ+N'样5.i2v4x zp~<k@ByH$wLN,4U1 iXZ̠h842 cfd%M3,H/I7<C<©>l<<}C4Wz9`WðC(^ 4fN 8P5  +bbab۰[@N #yacHV( TuuHulVwJJp(4}`wxTp頩h/7`\0.+_2-fa+f&bCe4]ީ,T<FCDECme"X0xΠ~@'sig_ind5πޠ ˷-3  y|ˠ#l1N#נ2J Πɐ #l2N!k@&eq_sym X*L9'SeqProp/@+UL_sequenceiހзGJ( @Q,RS@vq L}Jj\7](^@|fwʠ0\FZ&\k5XnIo:p@)xޠ˩DRp<IMIG'$"x$z<E(~°^F@H^ Pm KEf:41)!'+uoPJȐ"H9X©fR.: Z^O թAMliܩЩwᩐ_x N[g? -j'̠1uU84OB&EŠ`3頩Ѡ ܩӠ"WƩ,taO>SIȐ#H10%9%$< ӠT7akf~<95@Q oqFH$ [bIaנϐ $R4k&*Ʒn;.e`i+)ҩ-ԩ0o1%m ,uw9cE2]NE  WTgⰩ̠ - / ݐ ߐ թ}з\tTީܷh%: ηt1ͩlwtr`%5,4/9 >>:i>\>EX],Wc^Y(eqdp̠   {sȩA d/&ᠩɠˠ  >2ݩԠX ؠw  !QАȩCj ˩  Cid= mZGC %  F% JW "gS. &, Qà^%з . d  gXݠK ( (  & _7© p K q < r@ +i 5 { V | G }@ 6  w ; E{ w  h  Y @ H  ~ Y f jTfdDA? A  Y bE 532߰  { c e 3    m  htub=WQzN ; #F> 6D < H mg5j F R| |   ԩ(r,v.4!  Y ey   *   Z Ƞ -Y   yd ĩ6 s f   E  Š 3u&㠩 ˠH Ϡ =O3Y %'  &\  ܠ +       蠷 7֩h =r 0 H7 LDȐ#H114 J   à b E[ H. C,  L  ] Q S /  ҩ   hN &' n*6 dz g ) +3. m /  ~) r t 6  u   X I @   Mٰà      Ґ Ԑ ʩ rŷQ ް   iө ~ѷ]   4 x  ÷i   &©   l i g  U%3,4/7<<:A<Q<  C M  ۩ W   L X ݷ    ۩   쩐fN X d        o g      5     e#Ӡ      z  $   ϩ Ơ    J  ʠ  k `  ҠT  C    \  _  fafbC \e * (    C Y T  MlC ީ s 1   w 5    D } ; ڷ <  Y  , D  E  T  @*sum_cv_majQ}   ^D  a E T ؠs  #  õ %C < 4 j 2  m Q `C 5  / /b  . = s  ؠ R *h J 5 ܠ B N 7   7 7   f d"Bn g Z N  @#andЖw@ 2 ۩ J  5  "    k s  M  X X c@+cv_cauchy_2.fC  \ k@+cv_cauchy_1.fB e g r@2Cauchy_crit_seriescZ l   ^       !m @   z@    䠩 ߠ z  " |;  ٠ ˷  ̶  Ͷ ζ@@    S  M    ط g!  ۷  ܶ  ݶ$ ޶@"@    w    {   /  *     Ȑ!s+Compare_dec @,lt_eq_lt_dec*& U  @%sumor$|@ @'sumbool7̂K@  B  h ɩ   jBAAAA@@@@@D*   y U !  {  } ߩ ɠ @ ۠ &   E  @   B  C.BAAAA@@@@@DL8    u A   砩 ^       d  %    B    U 2g   ·  K  v  ;   z    V 2   i <{  ]   = %  t w  5  6  o K r@$Ropp΀A6 2 { / * [2 - ^1 b5 J A  v%   jU!< L  I D uL w,P.> N : g   s92 b  _ ` Z ^ BbD/ z   -+ u  r m  w)' y   #  ɩ } x  0 |  "    2  ة    9?   - & l      Š F6 / [    S  6  |    é E >  j    a ̩ E     ѩ Q K     ש @'sum_Rle ˷"n0 $    a@'and_ind14ۀЩ Ԡ } < 3 W ڠ     ߠ   8  K  7 @*Rabs_right |T⩚ @&Rle_ge @ H 驚 @,cond_pos_sum,?ʀ5 W0Щ      ) - @)Rle_trans" -)  % fzg(# N pI < @   ֩ @)Rabs_Ropp&#۩  M ᩚ @)Rplus_0_l 6ʀ U   @+Rplus_opp_r {Gک  _H @+Rplus_assoc O hW Y< )@/Ropp_plus_distr:A'XXC O J j_ N hOC Y   @%tech2g  |  {w  ~  }!e   "  ƶ    . o 栩    8 렩   w é  4 k   (  Ω   }   /  թ   4    6  ܩ    (@"or @B  D D -  F F A  H @'Rabs_R00Jp Π ~{C   n    rC  - .   з  K   ͠   F M }  ޷  ɠ @ ީ ]  ߠ . , " ֠ M  ꠷ 9   j  c X  w5  .Ȑ  <   됩  + U (א1 L (. *3ߐ2 S 3  53$  _ ;*F b  BO D&" l H N &o# O< ( w Sn UB` 3|0 1+ \i  `i b8h @=8 ig k6X D   KHC treG xZ zX   ZWR V ix  gd e_ r  pmh p  wto  ~ǩ{/ٷ  pЩ- VN  E   a   ȩʩD̩۷ЩKҩOԷ  f S)éȠðZ  v07 c @)Rplus_0_rH€* k @+Rplus_opp_l73Щ ^@*Rplus_commq  թ ש   Cߠڐ(ސC頩`a["HhHq*ts   @,Rle_lt_trans*GӀ=8!   C:@+Cauchy_crit ܀Gm!,CO[YZhNj@ͩ{V|G}@A ?=OԩD2M@(cv_infty?7[$!_]@%tech1g‰0Y{ 4j V8atpw ް^ivi Рd| h _ؠuué@)False_induُ@%Falsee@N@*Rlt_irreflnQC@#notШ*@.cv_infty_cv_R08 k6ߩ@$Rinv85 Ks@1Rmult_lt_0_compat=@VQ@0Rinv_0_lt_compatD @1Rplus_lt_0_compat-P@"R1Ȁ@'Rlt_0_14CC1^@$Rdiv̀% R@J?:4 )14&'(@VKF㠷2%@%Rmult׀ ʩ8^ (2Ϸ"N1>$Ȑ!CᐩG^Co> _BAAAA@@@@@D@iNn`;a,b@  U$ Ycy@'Req_dec3{ `vAw -  mȷ<nm=4X vѷ.wDUYک©@)Rmult_0_l+€ CͩW A SqD :I@+Rabs_pos_lt CҠ@۠֠ސs թҩd ֠ȷɶʶ@h,޷ҷ շֶ׶@uɠm ͠x: ;9۠WuȠZީРQ@&Ropp_0 GU`+۠0Š`$ &ԩ !j@ũ-1)+I*Щϐ!?A@(RRle_abs q/ ސb6fW@.Rmult_lt_reg_l>eЩp-^b\1 K')9P.Y Z8) $f5Ȑ#H12lH-&oqM>!HF&#!wҩ#y%{' H?G68: @̰{Av0CZx0E\ ة*@/Rinv_mult_distr1@'IZR_neq%<YȐ#H13k^÷_@@AA@AA@@@@@@D!zjA@/@C p@*Rabs_no_R0 C ϩ̠,}ԩp   @)Rmult_1_l9|@*Rinv_l_sym9`g~)Ƞ0@+Rmult_assoc&ĩӠlƩ@)Rabs_mult)C/ݩΠ$"fө&@= yRY!1#$%@SHC࠷/"©V*"N26@#max.p@ 'c@,BCD@rgb8NoDuvB$T  _  O`.03[](n< Ԡ!-% uC&۠i"z HCA!rUѩu C.0>H57@ɰx>s0@Wu0BY թjR7?ĩU:?ǩl@(plus_sumM Ωa;ҩdghpiNj;7ve}©$x]ǩZz$gxéȐ(list_hyp|Ȑ+field_lemmad@3RField_field_lemma1(Mka 5t,Field_theory@%FExprs@J EDfGHhb!F& `B@H CѶ$nfe1.@&linear@Ŷ@U 7@%Fnormw$nPL=71+@嶐$nfe2@b $vXTE?93'@gr80}_[LF@:2ߩO@#num:uV@%denum0j"0qm^XRLD @d@%PCondS<Gs""թV&BinNat&NArithV9@&to_nat`)BinNatDef?@*9G(Rpow_defX@#pow#׀ b$ sA  km/  }@#appʀ7@)condition.1G3Hð@&FEeval>@cc<@04L1i .)<C>V 0@ss &LP@Ȑ#resmȐ&res_eqm@(ZoqȐ$res0Ab.d+3f6h#`wyȐ'res_eq0@Ȑ$res1wHC,Ȑ'res_eq1 @ 52!@b@-RField_lemma55vrc^_$locky%&(lock_def#8>Tq=[( 8CYvBɠ a m  ÐE'-C<X)nW I.@/#@$Fapp{F*@&Fcons2w$aC?0*$Щ|=[Ӡ"jݩ@(scal_sumWJ_CG~%"$(X |@+lt_le_trans ŵ˰#Max@(le_max_l2EHCsĠ F" Y' On`.7AǠDX#[ \,Azd@B zD|"k  Щ M r/$v,e(@+Rabs_triang9  `rg:S8pA5 yF_V|MX[ҩrs?@/Rplus_lt_compat":Ȁ<)8)annvηt#},*1,3@(le_max_r2KCr00穜A 7 9C1Cwd/ɠ;5$Ҡ]Щؠڠ " ש蠩Рsm)̠$穚@1Rmult_le_compat_lڀ54#N@(Rsum_abs$+k@*Rmult_comm83(4EKV;&< QBb I%]L*B4dR}FRAc 0#Z6  ֠Ih5FE9mp6u-v*T')+c]Ng)#@2@(Rabs_pos+F.-JӰ/L36ɩ"7CӠ:<g>b@ɰРDFFCYMKdVOI|er-ulb^n砩xݩ ĩ @1Rmult_lt_compat_l` ҩթ<8  $1ƠȠ;͠!&Ԡ >I@/&̩EߠǠ3&T K X ]kAީ:נY@1Rplus_lt_compat_l ]߀ky*lnCQp  4{RE8T@)Rmult_1_r+1? \}RE@*Rinv_r_sym9lU䀠HYKYMMO}}[]Cp|_T.a "eZZg\Cz(`k:5YC?@*double_var?l7o@2Rmult_plus_distr_r~vCe$zT,"ԩ$9ࠩmop=CU@tDCom n |@`@ @c[G,d*W)VM󐑷 u@ZlCŠ pPreg UxРd @!M ȩ@@'Rle_dec3  e  թ lڠ̷Ͷζ@l.g#Hle gڷic*p=緐$Hnlerm@*Rnot_le_lt.J8 : 4@"upʠ ЩJE a@%U֩mX3k,ة@&le_IZR̀\ѵ5<ii0UnU@)Rlt_transCu KCCϠxx |Q@1P,xl4 {5k󩚠\@&of_natbzW@1?G!ΩN@A B@eVYj+H5K&LM@pG$uuSrI%wN~UR?ةv< # '\5,`0)x  tʠv?C*$@+INR_IZR_INZ#]KK@<_INR%耰<R>>Ka@'sum_cte";C +@#IZN=D{ @(archimed ŀ C%{ )SeqSeries@&CesaroS€zxwyuZĩ$W\X|'#!ϷжѶ@Šq۩nEV@ؠ䩚a@$pred `<'j&@(g2ĩq XЩqŠ%&  y͠꠩2Ӡ24~ 5E[ R!e#"4J l  . /1u3 2HB @1Rplus_eq_compat_l'=E jY'y!n\(&$U@ #ө۰U@aNqI0ysk-ݩK0{um/ fc(+jC"kmj:1?o6VxTU6ð~N 񩚠@&S_pred<=ÀV)b+ }X?@)lt_0_succ5% Ʃٰ`Zrް` @ 58t1ː1m"qVC  C2zéxr9Ơrܩo`bީ)թI@&le_S_n8ދKO^Y-c&"uC,[C#a C٠]R.e;