"`Q5&Qcanon&QArith#Coq@D+Ring_theory+setoid_ring#Coq@)Ring_base+setoid_ring#Coq@+InitialRing+setoid_ring#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@+ListTactics%Lists#Coq@(Ring_tac+setoid_ring#Coq@$Ring+setoid_ring#Coq@*ZArithRing+setoid_ring#Coq@|)Notations$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!>'BinNums'Numbers#Coq@0dmk(5Ju<*EqdepFacts%Logic#Coq@0FI$ͼՋ`)Eqdep_dec%Logic#Coq@0u wWIϰ߼*Equalities*Structures#Coq@0όe얟)H.Ƞ2Relation_Operators)Relations#Coq@0%s鯰s4Operators_Properties)Relations#Coq@0U3y#h&)Relations#Coq@0r砠*NZMulOrder&NatInt'Numbers#Coq@0}\^ !"k}@R(NZParity&NatInt'Numbers#Coq@0H>ca'^^%NZPow&NatInt'Numbers#Coq@0)6*9 B:vȻ&NZSqrt&NatInt'Numbers#Coq@0` .%m%NZLog&NatInt'Numbers#Coq@0ꔉ .uV%NZDiv&NatInt'Numbers#Coq@0$ |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$NLog(Abstract'Natural'Numbers#Coq@0KI'BinList+setoid_ring#Coq@0Au$Pnat&PArith#Coq@0,?pr.gZ'ZAxioms(Abstract'Integer'Numbers#Coq@0\}zK=PK%ZBase(Abstract'Integer'Numbers#Coq@0 TL}2_} ؠ$ZAdd(Abstract'Integer'Numbers#Coq@0Y9Vgⲫ򐠠$ZMul(Abstract'Integer'Numbers#Coq@0Mtr\b"H#ZLt(Abstract'Integer'Numbers#Coq@0xK|j2[&=}۠)ZAddOrder(Abstract'Integer'Numbers#Coq@0w:}H#NK}{)ZMulOrder(Abstract'Integer'Numbers#Coq@0Dr~-~ECM'ZMaxMin(Abstract'Integer'Numbers#Coq@0bAX1'ZSgnAbs(Abstract'Integer'Numbers#Coq@02`ou{Z'ZParity(Abstract'Integer'Numbers#Coq@0S)*Dd$ZPow(Abstract'Integer'Numbers#Coq@0AşsאI)ZDivTrunc(Abstract'Integer'Numbers#Coq@0`]f5FԠ)ZDivFloor(Abstract'Integer'Numbers#Coq@0dj_TYQc|$ZGcd(Abstract'Integer'Numbers#Coq@0G0=$ZLcm(Abstract'Integer'Numbers#Coq@0(9g%MmN]%ZBits(Abstract'Integer'Numbers#Coq@0ܹCF5s+ZProperties(Abstract'Integer'Numbers#Coq@0Ve*ʞ_OV)BinIntDef&ZArith#Coq@0ådR4Tuy&BinInt&ZArith#Coq@0BpHޞun^,Ring_polynom+setoid_ring#Coq@0gaKw9`UW+ListTactics%Lists#Coq@0,Jcy{%Zeven&ZArith#Coq@0i?eK#aU堠#Min%Arith#Coq@0Ce-Fѕ(PreOmega%omega#Coq@0\|چBb~w4%Omega%omega#Coq@0t.J'6\ϨrK,Zcomplements&ZArith#Coq@0@,Field_theory+setoid_ring#Coq@@&FEeval>@@A@A"s @,Ring_polynom+setoid_ring#Coq@@&PEeval"s @@A@BA@A@[ @!q`@w(m@@?@@@@@@oJsqfdB@@(m@z&QArith#Coq@@!Q4+@ +k= R '>''+k6''YABpx@@@@@[ @?=6A?C@5&=@98%Logic$Init#Coq@@"eq @ +k= R '>''+k7 7 7 77&'Р|_ABpʐ@?@@-Qred_identity @@@~d@4'BinNums'Numbers#Coq@@!Z7@&BinInt&ZArith#Coq@!Z@#gcd1P)BinIntDef&ZArith@@#gcd 0@$Qnum4OA'BinNums'Numbers#Coq@@!Z7@B+QArith_base&QArith#Coq@@$Qden4A'BinNums'NumbersT@@!Z7@B A@(positive*@C+QArith_base&QArith#Coq@@!Q4+@A&QArith#Coq@@$Qred<m@@@@@0.Qred_identity2 @@A@ˀ- AAՀ{Bp%eB[@@@@@c(Qred_iff @@BH.@#iffС)fYAAک̀ABAB@@*@C@@@@@+Qc_is_canon @@Cx@"q'@@#Qeq4?@5&=B⩛Z@@@@@Ҡ)Qc_decomp @@/D*(.@q'BB*A~ @@@@@/Qred_involutive @@SEۛ򩚠倐逐AA@@@@@$Q2Qc @ZAD@0)@@쀛{ @+k7 7 :'XXh@@@@@=+Q2Qc_eq_iff @@F" ހ߀(@A1.~BABA@@@@@i$Qcle @!xN!yQ@#Qle4?|I@ЀԀA T+k()7 7 7%''td@@@@@@$Qclt @/{-|@#Qlt4?+@78('Mtd@@@@@@)Qccompare @!p@(Qcompare7=΀S@  $)Datatypes$Init#Coq@@*comparison;f@[ @td@@@@@(Qceq_alt @@OG4*,/1)Datatypes2@*comparison;f@@Srf+A@@@@@(Qclt_alt @@wH\zx}@1uBA^@zrfBA)Datatypes$Init#Coq@@*comparison;f@B@@@@@N(Qcgt_alt @@I7"x0"y0 *@4?ABBAFBADC@@@@@(Qcle_alt @@Jn $@01uBA,@#notШ4ҩtBArC@@@@@(Qcge_alt @@K Vg f @W4?|ABBA>o BAB@@@@@)Qc_eq_dec @ӷȐ!s8@'Qeq_dec'΀&Specif0@'sumbool7̂K@I@R4??@#notШ BAAAA@@@@@D( >(Z DEH!H4A @ 1OހVW@B"H0Рw@%Falsee@@@D@@(eq_ind_r!2#8/9QE@(Qeq_refl= 3> C=@&Specif$Init#Coq@@'sumbool7̂K@BA뀐#BA L+k()7 7 7!= R\'> 7"9'> +9''7 7 +77 =R''7 7 7%'+k6' +k77"7 77"7%'4_TĠ@\A@X?xtdGAABAADh^,$$8,@@@@@̠&Qcplus @ca@1.~@%Qplus5p1ye@q2r6 `+k()7 7 7!7$'tdL@@@@@@&Qcmult @޷ߩ/B@%Qmult5o@]a萐+td@JL@@@@@%%Qcopp @Xk@$Qopp4\@ś D+k7 7 7$'dڐXpp@@@@@K'Qcminus @.//@_$5@8{w@; H+k()7 7%'td@@@@@v%Qcinv @ Y@$Qinv4ƀ@׀^Qd*Xp@@@@@%Qcdiv @2~0@t@7r@?@Ptd@@@@@Š+Q_apart_0_1 @@"L.A@7@B۩  A@@@@@ꠠ,Qcplus_assoc @@GM!zЩP@3_CBA CBA@@@@@AA@"s  @<m@A@A@ABA@@A*Qcplus_0_l @@{N@/ۀN@4+@AW6AA@@@@@)*Qcplus_0_r @@Of؀!QA#AwVA@@@@@H+Qcplus_comm @@PBrBAxAB@@@@@f0Qcopp_involutive @@QbO^@h{AA@@@@@,Qcplus_opp_r @@R~1zA!A\A@@@@@,Qcmult_assoc @@S!n!mZ#@CBA CBA@@@@@Ӡ*Qcmult_0_l @@GT.ᩛ˩(A AA* @@@@@*Qcmult_0_r @@nUU 򩚠OAπAH'؀AQ0@@@@@!*Qcmult_1_l @@V|/ЀvA'BinNums'Numbersm@@!Z7@B\ y@@(positive*@CAA@@@@@Z*Qcmult_1_r @@Wl RA/TA:B0CA@@@@@+Qcmult_comm @@X/.2{؀BAހAB@@@@@3Qcmult_plus_distr_r @@YML޶ܩRCЀBAրCB CA@@@@@Π3Qcmult_plus_distr_l @@BZ| { ਜ਼ʩ'CBA6CA%nˀh@+rnPuA[BQCTC@@@@@,Qcmult_inv_l @@ ^R@'XAz𩛠a<ABCC@@@@@ޠ0Qcinv_mult_distr @@ R_7ةf9BA?tByA@@@@@,Qcdiv_mult_l @@ |`@ ]  HQ  @k S   S@@@@@),Qcmult_div_r @@ a@!߀ / ! m@@@@@C)Qcle_refl @@ b⩚̀ ~ ~@@@@@S,Qcle_antisym @@ c@ D @倠 I   ^U @@@@@o*Qcle_trans @@ d @  b@  g? @@@@@+Qclt_not_eq @@ e;:@ ~ ˩    @@@@@,Qclt_le_weak @@ fTS@  䩚7  @@@@@-Qcle_lt_trans @@ 1gk\jZ4@L  @  € @@@@@۠-Qclt_le_trans @@ OhRPz@׀  ζ@o  ө #@@@@@*Qclt_trans @@ mipn&p@ 8 @ = 񩚠 A@@@@@+Qcnot_lt_le @@ j@ @1u0  ]@@@@@3+Qcnot_le_lt @@ kҶж@ 5@1uL6 - y@@@@@O+Qclt_not_le @@ lƶĶ@I @ ؀  F @@@@@h+Qcle_not_lt @@ m@ Y 񀐩U@@@@@-Qcle_lt_or_eq @@ n.-@  q ymp@@@@@&Qc_dec @G E  @%Q_dec5n]vD@%sumor$|@Ơ)) dO BAAAA@@@@@D۩ՠ89_ܠ?xAz 'A  ȩ-BC Ͷ Ω3  @RP@%sumor$|@ +k()7 7 7!= R'>9'> 7"9'' +k77"7 7 7!7 7 7!7!7%'$АDAABAADh L< tdvX,[p !d Up@@@@@@+Qclt_le_dec @   v@*Qlt_le_dec- C  @M@Հ Ð td@@@@@@C/Qcopp_le_compat @@ oⶐ A@Ѐ 4 ԀI@@@@@\.Qcle_minus_iff @@ p Z ((0 @@@@@r.Qclt_minus_iff @@ q鶐 p穚 &ZZ@@@@@0Qcplus_le_compat @@ r 3 $ 2 " (!t '@ Ƕ@   fFi] Ր@@@@@2Qcmult_le_compat_r @@ s Y J X H J@:  @? C9 : @@@@@̠4Qcmult_lt_0_le_reg_r @@ @t z޶ yඐ C@Ȁ @`V fҐ@@@@@젠2Qcmult_lt_compat_r @@ `u  c  a c@耠5 ,@퀠 0A@@@@@@ 'Qcpower @A@   n .@#nat@      @@A@A@@@@D  [s ^ ` a@ (  @#nat@ 8,7k(*()= R'> 3! 7%'67$''+k6'+7Tk+7T'6'ࠑ ;,ࠒ4AA@@<@@AAACX@@@@@h)Qcpower_1 @@ v8 6 @n5B >cAIB?CBCA SxA^BTCWC@@@@@)Qcpower_0 @@ ww@@ - ^ AA fO A   A  @@@@@ݠ+Qcpower_pos @@ Qx 6 x:@ j A@ACB  ŀAAC B @@@@@*Qc_eq_bool @     5B  @@@@@A E = @ / B >@$boolZ'@ $@ \:[ ;@ OA@B@ 盠  蛠  !@$boolZ'@ +k() 7!= R'>G'>H''+k6'6AAP.*h@@@@@b2Qc_eq_bool_correct @@ y  р  Հ@ . @a}h+BA7@A (  g@@@@@$Qcrt @@ z+Ring_theory+setoid_ring#Coq@@+ring_theory؛@   bAAaC qA|BrCuC܀ 0@5%̀V%Logic$Init#Coq@@ r @ @@@@@@ߠ$Qcft @@S{,Field_theory+setoid_ring#Coq@@,field_theory2@( ਗ਼ . @F;o@k?@@@@@3Qcfield_ring_lemma1 @@|!n)Datatypes$Init&@@#nat@!l@$list]@ #lpe @$prodt@KJ#@%PExprk@'BinNums'Numbers#Coq@@!Z7@#pe1#pe2"@$@-interp_PElist36< Wwutrqomk%Logic$Init#Coq@@"eq @o2+InitialRing+setoid_ring2@(gen_phiZA{ K E'BinNums'Numbers@!N7@+Ring_theory+setoid_ring$@(id_phi_Ny @%pow_NH DC@%Logic@"eq @@$boolZ'@Ȑ#lmp{@.mk_monpol_list(xyA}B ݚ&BinInt&ZArith~@#add1P&)BinIntDef@ ̀@#mul1P] @ @#sub1P@ p@#opp1P@ {%Zbool!@(Zeq_bool0߀*@'quotrem\$@/ŀVАŠǠ@#Monf@@#Polj@ĩ@#Peqj*)@*norm_subst7:d0ZWRB<60(GAz 0^[VF@:4,{oA @)"s 8 /-+)F8 20.,@@@@@ 23Qcfield_ring_lemma2 @@} "lH 3@< 6V T RPNLCE     G  7B,!#\V@7,.ga(!xO"pe0'#npen,@аs1f03H*a l[8 n86820fݩB@(Pphi_devRI< u?=?9  <@@)get_signZ#7v>@@@@@ 4Qcfield_field_lemma1 @@ ~!n)Datatypes$Init@@#nat@!l@$list]@#lpe @$prodt@,Ring_polynom$@%PExprk@ #fe1@%FExprs@#fe2 @ @-interp_PElist36<ީ  ` s ) 7  d i^T 9 fDC#lmpJ @$prodt@ A,Ring_polynom+setoid_ring[@#Monf@ @#Polj@@%Logic|@"eq @w-c@.mk_monpol_list(lifeUOIC;EA$nfe1`@&linear@8@# =l@%Fnormw$~nhb\F$nfe2J@5O$ '{uoiG&@=@$boolZ'@@#Peqj*z@*norm_subst7:d0#?yL&Gol@#num:ux f @%denum0e0;W= 1A@@%PCondS< W  QJ '@#appʀ@%PExprk@/@)condition. _٩>@>@ v & pi+ MK@ z * tm/$J@@@@@ 4Qcfield_field_lemma2 @@0&$  !¶@<ũܩ  G gZ    K PE;  MB.#%@f@$@j@@հC8:(9632" ̶"fe+#nfeА@Ր$KC3-'!3ݶ@<>=   <:}8;@n.< k@ HG   DBH(F@.display_linear1+\YDPO  " `'6L@#7 0f-^NHB<4qਗ਼S@:u:0n5fVPJD<y詚[@0B@@@@@ :4Qcfield_field_lemma3 @@@7|zr} @p<Ib`_]  X MO     ɩQ  kji~@N&(K(*FEDB.@_G3<$5 7O6L8@iQ=F$?4Y#den@&rsplit@J@{ O@%splitў9V,pXsrZt@8@(Pphi_devRI<XW q ! kd:TH0f<NCikm@,rsplit_right=r<hg  1 {tJd X0vLRxzѩ@+rsplit_left>@?<xw  A vtF;r:  Ġi˩+@  M RG~O(.@  P UJp@@@@@ ᠠ4Qcfield_field_lemma4 @@UAKI=;޶5>3-/#!$@<   r  ; I  v {pf K xXMO*%Ķ@cXZ50ϩ(YVSRB<60(ն@ک$d \LF@:ݩ߶@$nfVPJD@x`N   J#np1Z@*_0/pjd^VpIݰ%]!#np2m @=r0B}wqiQ8 54@Z@\lk , i &eahf @^nm . k (gc!jh@<aqp 1 n +o$mkR۰)c+e-- l<n~} > { 81`zYS4<q A ~ ;4c}\@@@@@ .Qcfield_lemma5 @@Bݩې~"l1͐H@$lock"le됩ؐSA@ ] w8 n  h>c1   r " l'  $ؐ@$Fapp{Fp@'Fcons00W$wΩA<<"!  >  C8@@@@@ Ϡ*test_field @@CC}>~B@X A !۩ 8%%@@@@@ @@@ ӳ2@ ӳ2[)Datatypes$Init#Coq@@A@ Գq@ Գq\ @A@AB@cAA.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@|%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$Bool#Coq@0j 2cZ`FW*CMorphisms'Classes#Coq@0qیZBeϠ0CRelationClasses'Classes#Coq@0TL;0RUfw1+Compare_dec%Arith#Coq@0jXF 810/@0.i bYN Z)Decidable%Logic#Coq@0ND걸풬/Oߠ'Decimal$Init#Coq@0C涳N*ua%EqNat%Arith#Coq@0AIgՋXRV *EqdepFacts%Logic#Coq@0FI$ͼՋ`)Eqdep_dec%Logic#Coq@0u wWIϰ߼*Equalities*Structures#Coq@0όe얟)H.Ƞ+Equivalence'Classes#Coq@07;ꮹ)Factorial%Arith#Coq@0@oehJd%Field+setoid_ring#Coq@0J _ȫ)Field_tac+setoid_ring#Coq@0d vDZl^۹H0B~uYٮ٠-GenericMinMax*Structures#Coq@0måj$"Gt%Arith#Coq@0䙛#c:D $Init'Classes#Coq@0](p{yOh. 0k/T=cN"Le%Arith#Coq@0d}Omq+$List%Lists#Coq@0>I+ListTactics%Lists#Coq@0,Jcy{l0\͉!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*NArithRing+setoid_ring#Coq@0_ .Ys!Р'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$k[#lZ)Peano_dec%Arith#Coq@0Kݢ*k$Plus%Arith#Coq@04tmG$Pnat&PArith#Coq@0,?pr.gZ(PreOmega%omega#Coq@0\|چBb~w4'Prelude$Init#Coq@0JqTttֱ&QArith#Coq@0H#oޞ6 78n0#-\D7* Q,"f\&Qfield&QArith#Coq@0td;X񦐳#@`*Qreduction&QArith#Coq@0nDk%}Y%Qring&QArith#Coq@0F%pw;}=O5}%Quote%quote#Coq@0J@ŹVz-,3%/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$`0;RWMi\N'Sumbool$Bool#Coq@0sB ,$11.]m'Tactics$Init#Coq@0/9m+ a'Tactics'Program#Coq@03N$@@B@A@@@@z@"_9@A@@@@@@@@A@#_10'`o@@@@@#_11'`o@@AB'Q_scope@@6*@>2 Q@@H@#_12E/H-@#_132M접NAA@A#_14'`o@UA@@@#_15_@@@@W2 Q@@H@#_16@bXV@#_172M접 AA@A#_18'`o@A@@ @#_19L4xAAA@&@#_20YS(Qc_scope"Qc#_21YS(Qc_scope@#_22'`oAA@'Q_scope@@@#_23&Ű@A(Qc_scope2 Q@@A@#_24@,@A@@@@@#_252M접 #_26'`o@B@@_.@r2 Q@@A@#_27@},n<@A@@@@@#_282M접 #_29'`o@B̠@@V@g2 Q@@A@#_30 &@r.%@A@@@@@#_312M접 #_32'`o@A@@F2 Q@@A@#_33 J@Q 1O@A@@@@@#_342M접 #_35'`o@C@@be]@#_36X@$core@A@@(META1351(META1352A@@@@@  f i  @6Coq.QArith.Qcanon#<>#1I@2 Q@@@@#_37 @24@A@@@@@#_382M접 #_39'`o@C@@ɠ̠ @2 Q@@A@#_40 @)@A@@@@@#_412M접 #_42'`o@A@ f@2 Q@@@@#_43Z#@#_442M접 @#_45'`o@A@ @#_46'`oAu@]@@2 Q@@A@#_47!*@K@A@@@@@#_482M접 #_49'`o@B@  @#_50%c?@(Qc_scope@6AAC@@@@@!0!h@# 0 #_51%c?@(Qc_scope@RB@@@@@@!1!@# 1 Š2 Q@@@@#_52_]@#_532M접 @#_54'`o@B蠐@@2 Q@@@@#_553@#_562M접 @#_57'`o@B@Ġ@$Qcgt9D{(@@ѵ@@$Qcge9D{(@@$$͠*/@@#_58@FF@F@@F@@FA@%_ < _@F @@%_ < _!x!<!y@@@@@A@@" <@A@@B@@@@@#_59%c?@(Qc_scopew@@y@@@Ƞ@@@@%_ < _"R@%x < y#_60@FF@F@@F@@FA@&_ <= _@F @@&_ <= _\"<=[@@@Z@A@@# <=@A@@B@@@@@#_61%c?@(Qc_scopeР@@Ҡ@@@ݠ@@@@&_ <= _"@&x <= y#_62@FF@F@@F@@FA@%_ > _@F @@%_ > _!>@@@@A@@" >@A@@B@@@@@#_63%c?@(Qc_scope )@@@ *@@@@@"@%!EJ@ > =@@@@%_ > _# @%x > y#_64@FF@F@@F@@FA@&_ >= _@F @@&_ >= _">=@@@@A@@# >=@A@@B@@@@@#_65%c?@(Qc_scope @@@ @@@@o@  @@@@&_ >= _#m@&x >= y#_66@FF@F@F@@F@@@@FA @+_ <= _ <= _@F @@+_ <= _ <= _}"<=|"<= !z@@@@A@@# <=@A@@B@@# <=@A@@C@@@@@#_67%c?@(Qc_scope!5@@!4@@8@@@#@#andЖw@?!!@F!@@@@@+_ <= _ <= _#@+x <= y <= z#_68@FF@F@F@@F@@@FA@)_ < _ < _@F @@)_ < _ < _!<!< @@@@A@@" <@A@@B@@" <@A@@C@@@@@#_69%c?@(Qc_scope!@@!@@ @@@!!@!@@@@@)_ < _ < _$l@)x < y < z!Y2 Q@@@@#_70 HF@#_712M접 BA@A#_72'`o@BѠ@""@#_73@FF@F@@F@@FA@&_ ?= _@F @@&_ ?= _!x"?=!y@@@@@A@@A@@#?= @B@@@@@#_74%c?@(Qc_scope!$@@$f)@@@!X!ˠ$p@@@@&_ ?= _$@&p ?= q!2 Q@@A@#_75$@!/@A@@@@@#_762M접 #_77'`o@BVX@# #@!2 Q@@A@#_78%@!=@A@@@@@#_792M접 #_80'`o@B@#5#8@!2 Q@@A@#_81%G@! @A@@@@@#_822M접 #_83'`o@B@#^#a@!2 Q@@A@#_84%p@!  @A@@@@E@#_852M접 #_86'`o@BѠ@##@!2 Q@@A@#_87%@!c5@A@@@@n@#_882M접 #_89'`o@B@##@!v2 Q@@@@#_90%@!:[@A@@@@@#_912M접 BAAA#_92'`o@B"$@#ؠ#@  2 Q@@@@#_93'@#_942M접 @#_95'`o@BGI@#$@#_96@rrAr@@r@BrA@%_ + _@r @B%_ + _!+@@@@AA@" +@A@@B@@@@@#_97%c?@(Qc_scope#@@#@@@ ##@@@@%_ + _&b@%x + y!2 Q@@@@#_98F<@#_992M접 @$_100'`o@BƠ@$|$@$_101@hhAh@@h@BhA@%_ * _@h @%_ * _!*@@@@AA@" *@A@@B@@@@@$_102%c?@(Qc_scope$@@$@@@$$@@@@%_ * _&@%x * y!f2 Q@@@@$_103 $@$_1042M접 @$_105'`o@AD@$@$_106@ccA@cAA@#- _@c  @A#- _!-@@@@ @A@@AA@@@@$_107%c?@(Qc_scope$o@@@ Z$w@@@@#- _'C@#- x!2 Q@@@@$_108@$_1092M접 @$_110'`o@B@%]%`@$_111@rrAr@@r@BrA@%_ - _@r @`%_ - _r!-q@@@p@AA@" -@A@@B@@@@@$_112%c?@(Qc_scope$栠@@$蠠@@@$$@@@@%_ - _'@%x - y!2 Q@@@@$_113@$_1142M접 @$_115'`o@A%@%@$_116@ccA@cAA@#/ _@c  @#/ _!/@@@ݠ@ @A@@AA@@@@$_117%c?@(Qc_scope%O`@@@&%W@@@@#/ _(#@#/ x"32 Q@@@@$_118g@$_1192M접 @$_120'`o@B@&=&@@$_121@hhAh@@h@BhA@%_ / _@h @@%_ / _R!/Q@@@P@AA@" /@A@@B@@@@@$_122%c?@(Qc_scope%Ơ@@%Ƞ@@@%%Ӡ%@@@@%_ / _(@%x / y"2 Q@@A@$_123(@"u@A@@@@ }@$_1242M접 $_125'`o@@@@"qcF@@@ B@(S:./theories/QArith/Qcanon.vmmpq@@ mmrt@(K@@@@@@@mmxy@@@@@@(z@@@@@@*mm/mm(@@(p!@@A@@@D@@@@@AAAAAA@@@@@@AA@'@,Qred_correct <@]@@@@@@@"2 Q@@@@$_127)5@"&l@A@@@@ @$_1282M접 $_129'`o@C   @'N'Q'T@"2 Q@@A@$_130)c@"5}@A@@@@ 8@$_1312M접 $_132'`o@A @'x@"2 Q@@A@$_133)@"5}#@A@@@@ \@$_1342M접 $_135'`o@A @'@"2 Q@@@@$_136)@"rB@A@@@@ @$_1372M접 $_138'`o@B  @' '@"2 Q@@A@$_139)@#^T@A@@@@ @$_1402M접 $_141'`o@A 5@'@#2 Q@@@@$_142)@#&1@A@@@@ @$_1432M접 $_144'`o@A Y@( @#2 Q@@@@$_145*@#;Z@A@@@@ @$_1462M접 $_147'`o@C }  @(5(8(;@#2 Q@@A@$_148*J@#-#@A@@@@ @$_1492M접 $_150'`o@A @(_@#2 Q@@@@$_151*n@# -)@A@@@@ C@$_1522M접 $_153'`o@A @(@"2 Q@@A@$_154*@# -@A@@@@ g@$_1552M접 $_156'`o@A @(@"2 Q@@@@$_157*@"-@A@@@@ @$_1582M접 $_159'`o@A @(@"2 Q@@@@$_160*@"++>@A@@@@ @$_1612M접 $_162'`o@B ; =@(񠐒(@"2 Q@@@@$_163+@""g9 @A@@@@ @$_1642M접 $_165'`o@C d f h@)))"@"2 Q@@@@$_166+1@""g9@A@@@@ @$_1672M접 $_168'`o@C   @)J)M)P@"2 Q@@@@$_169+_@"g4@A@@@@ 4@$_1702M접 $_171'`o@C   @@)w)z*@"2 Q@@@@$_172+@"I@A@@@@ a@$_1732M접 $_174'`o@D  @@@))'*@"2 Q@@@@$_175+@";jB@A@@@@ @$_1762M접 $_177'`o@B @@)Ӡ'@"Π2 Q@@@@$_178+@";jB@A@@@@ @$_1792M접 $_180'`o@B F@@)(@"2 Q@@A@$_181, @"9A@A@@@@ @$_1822M접 $_183'`o@B n p@*$*'@"2 Q@@@@$_184,6@"4|@A@@@@ @$_1852M접 $_186'`o@C  @@*N*Q(f@"Ǡ2 Q@@@@$_187,c@";_^@A@@@@ 8@$_1882M접 $_189'`o@C Ġ Ơ@@*{*~(@"ڠ2 Q@@A@$_190,@"(@A@@@@ e@$_1912M접 $_192'`o@A @*@"2 Q@@A@$_193,@"-U@A@@@@ @$_1942M접 $_195'`o@D  @@@*͠*Р((@#2 Q@@A@$_196,@# @A@@@@ @$_1972M접 $_198'`o@E F H J@@@+++)#)&@#2 Q@@A@$_199-@#&aH@A@@@@ @$_2002M접 $_201'`o@C | ~@@+3+6)@#/2 Q@@A@$_202-H@#:.@@A@@@@@$_2032M접 $_204'`o@C  @@+`+c)@#E2 Q@@A@$_205-u@#P@$_2852k@"9š\?@$_2862M접  $_287'`o@IǠ=?@B@@@@@$###Ǡ$###1#@'Qcfield/>00.$8$@%Eqsthl2<$@&Eq_ext W2C-,- "@.gen_phiZ_morph0Z,2J,,-,ʚ2I@-&5%̀-22P$"V@%Eqsthl @&Eq_ext W!@#F_RP,2e,,-5,-/)T,2d@$1u7+Ring_theory+setoid_ring#Coq@@(Rth_ARth'\,2w,,-G,--A)'@@@+InitialRing"2@@1inv_morph_nothing iNQ@@@@@ր@# 2 Q@@@$_2883@#@$_2892M접  $_290'`o@Nm㠐@@@@@@@@@@@#/#"#%##"#1"Ƞ""Π""Ԡ"נ"g@"<2 Q@@=@$_2913j@"F[>@$_2922M접  $_293'`o@JƠ<>@A@@@@@@##w#z#G###`## "@"2 Q@@@$_2943@"@$_2952M접  $_296'`o@P@@@@@@@@@@@@@#Ӡ#Ơ#ɠ####ՠ#l#U#r#[#x" #~%.#@!2 Q@@@$_2974@!@$_2982M접  $_299'`o@Tp栐@@@@@@@@@@@@@@@@@$8$+$.$ $$$:#Ѡ##נ##ݠ"n#㠐##預##%#@!2 Q@@X@$_3004@!3wvY@$_3012M접  $_302'`o@CUW.function_scope@$$A@2Wj,2.&8@@@@@@@@S >!2 Q@@D@$_3034@!, L@A@@@@@$_3042M접 $_305'`o@C/1@@2栐2預0@@@VhzRZo@qNJ @n*eBV\@ < Zo9ux)QP[!q+QArith_base&QArith#Coq@@!Q4+@ @BB@@@@D@%Logic$Init@"eq @'BinNums'Numbers$@!Z7@&BinInt&ZArith0 @#gcd1P)BinIntDef@ 0A@$Qnum4OA'BN@$Qden4  3@(positive*@CF_*Qreduction_@$Qred<mB"!aJ!b!H_TI9~A985 0n@(eq_ind_r!2#i^CG)!zp}rNBN)Datatypes~@#fst | @$prodt@y@$ggcd1[6s@ i݀!@(ggcd_gcdL'!cȐ!pDu1 ""BBB@@@@D Y91}@1BBB@@@@B!xAv!g+D-F "aaƷ"bbɩ@#andЖw@ްӐK@#mul1P]@ CީJ J hBBB@@@@@Yr|@#sndy"r1"r2@&to_posV5=@2HG吷N wmyA@kYՐXVT,!NMFߩ1&HR5NE>=-/E;ؠRIq5o6D9ǰ;(=*??BC@{SHut&WLnx*[t#TLYZ@j_;la3e f@vkҩxmI}rtOD1BBB@@@@D@5_5@&eq_ind J6@k<c<Qu@NMMzʩNAѩUY۠l@'mul_1_l5DsVC@ȰݩT̰M~а٩ذLN3aשt@5ggcd_correct_divisorsR݀=Cp@۠ĐȐo @@"le1P,A޶@UNשL u\J琷I GE>5#}{ͩ*C:32u,ɠ@,'(@{to7,. s0AZQJI&C2@C>˰?é,A@ؐEF}UJwvDYNpzH,]RTةAV3&2XY gwpo$iYȐ"H0n@'f_equal=!e!JOqD&O w2FqT-s~]7?,WB;^lH@F=@@Π0Ǡkz͠OuV[{ש%_b`@@栩IfYȰ̰ŐQ@ذͩ/-$_tmp#"H'٩g@@AA@AA@@@@@@Dzǐ^V!Ӑ['*y"J߰@%Falsee@@@$Truey@@AA#@)False_induُ+ !dԷҩ*%Q3(<TԩL-Y;0 4^.A6dF;?@kBEE3F!A.#CTICvXM(Q-}M/W XyZ 688&BinPos&PArith#Pos@=N)BinPosDef@#FL}%-) U @)mul_reg_r(hxN568&Xc@&eq_sym XA/l1`3@IDLg;Pk@(eq_trans!y00tB@Z!fKb}}C{ecܩC_: dѰƩ0C {yѠٰ{թ;0h@*comparison;f@CC@tln@$Z!~es@*gcd_nonneg#o5C2吩5ݐ64HA5#5&Qcanon:@.Qred_identity2,n<÷- @-Qred_identity,Ѐʐ"q0@"Qc(m@@BB@@@@D`"q'@b@#Qeq4?/@$this5&=)Y# *vt"hqr#q'0+%~-@4Ao9C A,#hq'-( *9@-Qred_complete/fyXWBCGbKcdN7^llac  bZ.GYTp>G?÷6ĩe,oRdE)Eqdep_dec@1eq_proofs_unicity@"p0wH}%P"H2v/ԩ:5=68'ޠ; Ydmk cI.EE)FBHHq;J9tMw/&exyC2z8QUDqB4 Ȑ"H3(b3Fc_epCŰm5H:tc C-u| ws1y հ}(xiް aa-S82r,a*C ywu'C!r~氩9(\QQYLCҷٰ nްmamljCh氩֩DbE4 [CX}ũX!Rͩ)Z"v$tC ܩ 8i1"0C2Ct  !UFBHjq"nJE)WLE[P-Q^!000CVS@%Z_indr[\k`<cetijEGj{pqqʠtu(WyzU~^xrrq_C 7fѩĐ,}kCC%٠sӐu|2ڐB C@Y]?S °KWnv'oɰ$T' hf}asr94۰er߰;CB"p1{$"p2ywuzlhfcŷ~̰rntaYCuWְVPXLECS۰CAE?JCD'I=ް%5371UC6+++  %#̷:!+)-Ӑ)C.~kChK֩  ($tC Qܩ .*zC >3|o8:4:(j6C<]>MBm~ 'TIyJNP{QrP.OBIAT/OC 6cX4]_ N<\Crg ©hyn%-&u͠wS\ΩZ R84*_a)aCV@bJAE,8::2^kq?OB~?ඐ%canon̩m  O M CV}iưߵwBq@+Qc_is_canon 1OހX~a./RelationClasses'Classes@+reflexivity(ϓ/ @5Equivalence_Reflexive%lemma<)Morphismso@=trans_co_eq_inv_impl_morphism&ni$fy@6Equivalence_TransitiveWmʩ @0Qred_comp_Proper1<+ѩ@/eq_proper_proxy)fzؠ3}C\j890r@#iffС)/z@(Qcompare7=΀1A@@>trans_sym_co_inv_impl_morphism'\|@/Equivalence_PER/;@/iff_equivalenceZ?JQ@(symmetry0xj0@-iff_Symmetric!x x@'Qeq_alt')_@}ckY$@ni\drlbtIoC PŰਗ਼@)QccomparerfdK.@'Qlt_alt(Z18@'Qgt_alt( pB@'Qle_alt(2L  @'Qge_alt'ĩé@/Qred_involutive) ϩ ~շ .O䐷 .g* " 3 1TȐ 1 ]CM&CO ""&#ek F - @&Qcplus_     %this0 V&canon0T ]  D %this1 h&canon1f o V ) )+-I%this2 y&canon2w8:<>/' , @%Qplus5p1y + 5 D ;$ 63 :  >F X A E U|5   TLT$ OL% %X@>Reflexive_partial_app_morphism 2R,   Y`@*respectful%WO?  ``5 @*Qplus_compUU 9l@6reflexive_proper_proxy5 l @20 //'<yq vJ zN t A |<.@>    J  6F[D(HF $   @+Qplus_assoc.ˀ  :C}{ %      )Šxx  $         ȩ$ &  f    b  !  ,@)Qplus_0_lIZ CРː+ ^ = $    A=b 砩 쐩 .$ Q Ơ 4   9L 7$ [Π :, _ ><   C5 `@)Qplus_0_rIZ C&א  r! Y#%,  +! uq! z) a+4 4  ~z;,*$ %" @ ) 6. 3  4  O @*Qplus_commURC=8:$ YS [ ]r@%Qcopp{ m l lb `װ ('e] b @$Qopp4\ k  e q$ li p t   G Gx$ {x   @)Qopp_comp&U~  W Wʠ @/Qopp_involutive+8ƀ C9_    H  mGƵ | A$   >    =$   Fg, baZ UJH  7 "C  ڠ #@+Qplus_opp_r/ x CǠ-Đ󐑷!n巐!m  < #@&Qcmult     I E N 5    V R [  B  !" 4 b ^)ҩ+,.   r@%Qmult5o   )  $ ~   #+ = & * `  808$ 30$ , 7' @*Qmult_comp6z  0@0subrelation_reflv  &3(  ( K (@9iff_flip_impl_subrelation2VAK   d  :  쐩 鐩Ǡ C٠Ԑj F -     I Ej $ W  99IQ <w4rpkdOH, c B@ B@ 9  G1$ l  ? $II nK o@*Qmult_comm)  w@  B BAAAA@@@@@D@  O ] ' #:_ ) <0   T +B6  =   G;  7  8 s =#P v @kSx V@/Qcmult_integralg4$ " K ^5@*(T z*  Y x e U ]h\ /]  Y5  ^eq Y a= dwL {@%QcinvrSRig K א t .㰩  r jo^Cs@$Qinv4ƀ ~$ yv}l# lΩpР $ {2 ;,6 5~W4) 6"[[  U@+Qmult_inv_r쀠r  & C C  I ɐ8 ķk c ȩ ީ @,Qcmult_inv_r;jBl @+Qcmult_comm++>q ۷-  ַ/ ީ z~u퐷7 3 < #  yB >c1   ʵ 렩}$U  b Y  $h ߩi@)Qinv_comp!|( ~ %#6u (    #++B-- )/6 . 1,"7, 5%ĩ 7=;R@/Qinv_mult_distr ;C @ ;a =b ]  ^: at# d fm/ h| i k @*Qcmult_1_r-   @,Qcmult_assoc;Z:`C {  |@#  @%QcdivklF   g2U xR,/[ 03_ Z7c  հ 2 @*Qcmult_1_l-6֩ @,Qcmult_inv_l;jB{9Hn   ĠsM@uOC*  0 @^ ͠=}5 @(Qle_refl` C@#Qle4?|  CE ѩ @$Qcle1uߐP ܷ V ݷ Ʒ  ERw4@+Qle_antisym5iOC$ Cc  i @ @"cl  r  ֩2 L@)Qle_trans%Oɀg Cy    @7Z@9x   쩚`@#Qlt4?   8j@*Qlt_not_eq-X $ %   ?$6 V V@@D@ Z Z:C  CC 6  7@ M@$Qclt1u   B  C3@+Qlt_le_weak# 1RC L  M@F R  S T0Z!E@,Qle_lt_trans!F+ZC ^  _ `@Y@*+ѐ h  i' jF7q@,Qlt_le_trans0~oC s  t2 u@@o {  |: }Y(J)@)Qlt_trans_`C   E @'(   j @*Qnot_lt_le\ZMC    @ d   } Ʃ@*Qnot_le_ltZ#`C  % @ w(  . @*Qlt_not_le-рrC1  7 @ &ΐ9 ŷ ? Ʒ驚@*Qle_not_ltRCB ζ H ϶@ߩ 7#J ַ P ׷(@,Qle_lt_or_eq!<7  P}˷@ T  X" ~       bCj  p @ i ِ P "  q4[ \lC[@(Qle_compXc eRK e   Frg? }! n  u e   ,v x]@y`h{  3 r}@.Qopp_le_compatACk  n3  q%C = >@Nn)Ӑ G H @x R}? 9=I^ E  ~ Q IN" B]  ( i,\ T[ V q   ck ! 4 u 4 Z\,j bi%,  d 9 ^ caZ@-Qle_minus_iffW gC E jGC   O(   é I  \ DBKF@*Qlt_compat+xJũ G V i QO AA,  @YW>  ^ q YW=I,  H_>:@-Qlt_minus_iff[q^ C |ݩ   CX ¶ é 9> ʷ D ˷ ̷!t Ϸ׵ ʩ  ǐ XC4<ɩ͐ I  i3  :  * ݩ ՠڐ Q,? A&wA  H 8 C@/Qplus_le_compat ƀ  x ^C2 㐩 5( 搩 8Cx ~:@7 Ӷ@9 F { M:   34X`K,>>v }@ m  NL,~#e   JH8 wS@1Qmult_le_compat_r%q6Cp! s $ vaCB CD@=@u [.w]TO PQ-Av4 = 8 CC @3Qmult_lt_0_le_reg_r*MG}  ˩ _4aZѩbZ \ f^^ `` 8 f@4iff_impl_subrelation5     g  b sS ,tlYu^SQ zj4|zecb`CCI@Uض@ VuHf 4~|{y x >, ~ xv@1Qmult_lt_compat_r%% , GCvC%+p@'@}~nכs@#nat@y@'nat_indJʩ@'Qcpower5B 䵩T C թ  뜠A !#IHn 3  C 2B 77@@A@A@@@@D?@a4D'66 ߩk>N11&S64޷@6 %C@ HH '= '2[~Qa1$E 1 3  3 q xDC@ [%[ := :*HqkKt@^ D` FipZ@'compare3xT@]=RhLIZSP |B@@@@@D@"c@Ef)+ ,(@@@@@@@@@@@D!cwx y@|C  C@2 <÷P[ @*Qcle_trans   [ȰXRRO@۰ke  ĩ  iZ zĐנ ٩ })u"*ېؐ 6 4|w  0 \tqC ^@2Qcmult_le_compat_r ! cC@p ( lrР&Specif1@'sumbool7̂K@BAAAA@@@@@D!s w @K@$boolZ'@!B@@@@@A+@A@BAB@)Qc_eq_dec:[ o$C @O-v+ .@|1M@4/#KnSR{=(>>@@@@@@@@D:Ea{t5bode@'tfM@)get_signZ#7C@,get_signZ_thW@-Field_correct(yxY l m a k "[[@$F2AF5X4b u v j t z]uoic[QKE@92,@0Field_rw_correctk ~  s } f~xrldZTNIB% ;5@9Field_simplify_eq_correct-\n @@] p q e o VF@;_4a @c v w k u \LFAȐ#resȐ&res_eqt@(l~xrA1xȐ$res0ADC}ΰ Ȑ'res_eq0@Ȑ$res1 Ȑ'res_eq1 @ *X~9@@.Qcfield_lemma53w`\ WyXs$lockש $(lock_defv8    4 S/T{ {8    9 X4HÐ;C<    C b> >@@$Fapp{F"@'Fcons00W$&;2Oq/^[CJ^.Z