"`Ąe&action(fingroup(mathcomp@()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$Init#Coq@0̂"&/rk0JqTttֱ$Bool#Coq@0j 2cZ`FW+ssrmatching#Coq@0L1T=>)ssreflect#ssr#Coq@0 zv)ssreflect(mathcomp@0tn|kN0 D/O&ssrfun#ssr#Coq@01 ZP"};o{'ssrbool#ssr#Coq@0X% 'ssrbool)ssreflect(mathcomp@0o: n߂Q,ssrnotations)ssreflect(mathcomp@0hPB &ssrfun)ssreflect(mathcomp@0âNO=(V&eqtype)ssreflect(mathcomp@0Wn"2&=zH0;&ssrnat)ssreflect(mathcomp@0ͧMy}yWߘ#seq)ssreflect(mathcomp@0=~(sV,Aڠ#div)ssreflect(mathcomp@0W~ě o+ N&choice)ssreflect(mathcomp@02*{;"W$^6'fintype)ssreflect(mathcomp@0ǒ3fp$path)ssreflect(mathcomp@0*%)bhcFrY%tuple)ssreflect(mathcomp@0ýޑР&finfun)ssreflect(mathcomp@0ƜNtD砠%bigop)ssreflect(mathcomp@0#z xW :G؂b&finset)ssreflect(mathcomp@0 @$$~,B|XŠ%prime)ssreflect(mathcomp@0.wFbN_(fingroup(mathcomp@0c"65rk(morphism(fingroup(mathcomp@0ď \n.v((binomial)ssreflect(mathcomp@0io  } $perm(fingroup(mathcomp@0R 嫁_]U,automorphism(fingroup(mathcomp@0$D^ V+b`Š(quotient(fingroup(mathcomp@0鰷 x<G@IŶ:A,I & Р&action(fingroup(mathcomp@A)act_morph @"aT@(FinGroup@$typeKu@"rT!$틠A(@@"to!xA"x0 @$sortKM'@$baseIq䀐CB!a4@(arg_sortڀD!b E%Logic$Init#Coq@@"eq @)V@$mulg ;8F2F&(86J@ig[YRPP:A +k() + 7 7 T'+ 7 7 T'!! 7 7"!7&'K@AL!蠑6@@@qA1DH9@A@@AA@@A@)is_action @!D&finset)ssreflect@&set_of514@+arg_finTypeXs#ssrc@%phant)`@A@@v@#andЖw@&ssrfun@.left_injective,F̀'ssrbool%@(prop_in26'fintypeF&Finite@ XD@#memڕ@,predPredType>h``&SetDef@+pred_of_set#*:̀ːǠשG;@)inPhantoma^H@D@ c <+k() + T 7 7  77%' 77  +87 7 7!7 7 7 7 7 7 7 7"7 7 7 7#'() !! 7 7"!7&'8SX$\<HRp<sn|B.̠* !h_|(d0@@@ DOA(:@AFA@@A:dޠR~A*Z@A*ɔ@ A+rz@ABCD@@⠠|,<caޠvt@@@g@(@k&Actionus#act@j@SY@w@!Q`^r.KSb@@@AB@BB@@$7@@@@AAB@BA@CC@@@@%) @!@$7@CBB@@@@@@@H@@@F@Ѷ@>Ķ +k()= R '>'' +k+T'+ 7 7 T''ĠР'DAB|@@@@@a,clone_action @^\=+'' $' +k+&   7 ++!+9T7T'7&'() :'+  7T'7&'+ 7 7 T''0<;ZAC|ŐܠlZD@@@ A*p`@A A*qZc@QA@SA@ABC@@ࠠ'act_dom @pn۷c!2Oa@@@I@zyԶq@@@$7@\Zn쐩gS琩^mY (+k()'@@!2@,@A@A@ D(fingroup(mathcomp@A*sRk)ssreflect#ssr#Coq@@?A@AB@@-/is_total_action @@@!3G뀠,@$andb=;é  /@%eq_op&-@a_MH'ECd.Q. +k() + 7 7 7% ' 7 77 7"7 7 7!7 7 7 7 7 7 7 7" 7 7 7 7"7%'0PP@/h4 JTԠG5t8ࠒ\(\]h@@@@A'@@@'@ABCD@@$afix @86+"өt#md)SubsetDef@&subset 0֩bԩVݩ߷۩i FJ#7#@VTI@Ġ, p+k() + 7%'+a7 7 7!7 7 7!7 7 7 7 7 7 7 7"7 7 7!7 7 7 7 7 7 7 7"7 7 7&' 7 77 7&',; h@y( 젒`<{XĠ4蠒P,\ tLD@@@@%astab @{w[j|@$setI#QSb٠pɩegykzð}oqʰaR@#!&"$Ґ +k() + 7 7 7! 7 7 7&'+17!7!7 7 7 7"7!7 7 7 7"7&' 7 77 7&'0pD֠@P4蠒3۠$ؠlР\ܠ=|P\@@@@`&astabs @][I`\Z.U6Ωi@(preimsetw?@Ta@R ,+k() + 7 7 7! 7 7 7&'&7!7 7 7 7"+67 77!7 7 7 7"7!7 7 7 7"7&' 7 7#',pD"\̠8 lP '@Ԡ;x蠒&,|Pc\@@@-@A@7@@A9=@ABCD@@'acts_on @A?4ݩ202{|@(prop_in16ߩmߩa(%X>lQ8Un0B.yptro'vJ\7j@lj׶_Ŷ+XVX& h+k() +J 7 7 T7 + 7 7 7! 7 7 7 7 7 7 7 7" 7 7 7 7# ' +7 T'7!7 7 7 7" 7 7"7!7 7 7 7" 7 77 7"77&' +7 T'7!7 7 7 7" 7 7"7!7 7 7 7" 7 77 7"77&'4N$D-HT@ࠒJPL4 dHP4<Ԡy 8$`@ ޠLȠp\RTР0@@@@A@J@AB@E@@C@ABCD@@"&atrans @ NqlҰ'@.set_of_finType;JՐ Р  @qxl@ζ=;)l x+k()/7!7 7 7 7"      77 7 7 7! 7 7 7 7 7 7"L7!7& '$L4 \@p'(QX!d@hАР*@@@W@A*'A@@A@@@ABCD@@z(faithful @ wucɷĩа*{穚@ 5C@'finType0h$8 3 V@:group_set_of_baseGroupTypeڼ91B6@i +k()7 7 7 7 7 7! 7 7 7 7 7 7 7 7"   7 7 7 7" 7 7 7! 7 7 7 7 7 7 7 7" 7 7 7& '0X$tL$tLdVl<Xdd#po̠B X0|@@@@Aa@ @l@@ABCD@@⠠'act_inj @@Arpݶe˶\ƩYAYj:I[[@@@*@A@z@AB#A)@&@A @@(A@ABCD@@&actMin @@BxvtaRUNЩ7[j9];_nl[Щ]er@@+@@(actmEfun @@C}@@'is_true#œz֩u@# рb~e@@@xA@A@s@Am@@M@ABCD@@J%actmE @@DضGE3.@+"@@@@A@A'hyx@A@@A@ABCD@@f'setactE @@EcaOJĩ@&䢀@@@ A@A@@@@ABCD@@*mem_setact @@$FmhֶS@gTW8Y3[.q^7 9D;˩8̩2 &@@@0@A@:@@0@ABCD@@+card_setact @@QGA?4+-+@#nat@s'CardDef@$card׼q+e_1@@@@f@@ABC@@ܠ0setact_is_action @@|Hlj׶_ŶV2AWt@@@}Ad@Aq@A@ABu@!A'kmD@A$@@AB@{@A'A1A)E8@@@ABCDE@@*set_action @{Wf|%@5Ky. @ bq +k() 7  7:'xd@@@9@A@@)&orbitE @@I&$ VTvS@@@"@A@@Ak@@g@ABCD@@B&orbitP @@Jж?=+&om#$Bool@'reflectc@@#ex2М@9 ),֩ .թ/Ȑ@@@\@A@@AB@@A@@A1FdJ@ABCD@@)mem_orbit @@ K  }{ idC@cP4M/!)RlY24?6Ʃ3ǩa@@@@Ac@,@A@@+@ABCD@@%afixP @@ LL < : / &׶ %oi C@.U# ~ +bV :@  !F@@@@A@㳠LA@ABV@@A@V@@t@ABCDE@@٠%afixS @@ yM i gԶ \¶ S!Bڠǐ 1@8   _ɐ@ :b >8| $ @ H Uh D> * F N ]@@e@@ %afixU @@ N      53/- UfR > Z b q @$setU#Q_8 v  k]] I e m | @@@@A@@ABV@@R@@ABCD@@ .&afix1P @@ O   + )     렩 }  ֠  l    9@$set1#Q;[@@@@A}@x@@X@ABCD@@ U)astabIdom @@ P   R P > 9ϩ 1Q       @@@@Az@@A@@@ABCD@@ p)astab_dom @@ Q   m k Y T꩚ 3@'sub_mem*Xv怰 0 $ 2   )" (@@@@A@@A@@A*΀ D@ABCD@@ )astab_act @@ 3R # !   | w    b@vc  G` ;d )    @nG ٩  ` 2/    @@@w@A>@@ABH@@A>@0@@ABCD@@ &astabS @@ aS Q O   D ;"S1="S2@ 2 x2 l $ E& L tT b  & ; .?@@<@@ 蠠*astabsIdom @@ T x v   kѶ b̶db 4ĩ  A m@$Wƀ@@@@A@@AB /@@ +@Y@ABCD@@ *astabs_dom @@ U       ©     ! @@@@A J@@AB E@@@u@ABCD@@ #*astabs_act @@ V         u @  װ ˠB {g@@@@At@T@AB@ s@A@ n@@@ABCDE@@ K)astab_sub @@ W  ٶ H F 4 /ũ+ F@@@@A @@AB @@@@ABCD@@ e'astabsC @@ X   b ` N Iߩ A{   ͩ g@$setC#QM   @@@=@A@@AB@ @A@ @@@ABCDE@@ 'astabsI @@ (Y     q l!Tũk < 0     ^ E 9       @@@@A4@ @AB>@ @4@@ABCD@@ -astabs_setact @@ VZ F D   9 020  @ O 2 i۩ ]+    7\a *@@@@AX@[@AB @f@A @\@A@@z@ABCDE@@ ߠ*astab1_set @@ [ o m  ڶ bȶ Yö[Y +^ 0 8 I \ g@ 9 A P N@@@@A-@@AB @@A ,@@A (@@W@ABCDE@@ +astabs_set1 @@ \       }{ Q V ^ m l@@@@A@ I@AB@ D@@s@ABCD@@ !(acts_dom @@ ]       NL\@zKH ԰HF ȠO  ܰ Р d@@@(@A@ q@A@ l@@ABCD@@ H(acts_act @@ ^  ֶ E C 1 ,us@' @4       @@@F@A@@AB @@A @@@ABCD@@ g(astabCin @@ _   d b P K@I    CȰ;ʰ ĩ $E   @@@q@AH@@AB @ @A @@A@@/@ABCDE@@ &astabU @@ 4` $ "   } x ϩ ᰩ      é g@@@2@A4@ @ @4@ABCD@@ 'astabsU @@ Ua E C   8 /1/- + g٩ [$@@@P@A@ @ ]@ @ABCD@@ Ӡ'astabsD @@ sb c a  ζ V MOMK+I  y  + 3 @$setD#QNE H@@%@@ %actsI @@ c     vܶ m׶ p.lP%AactSؐOu u Ʃ)%AactT䐩[  é  z  ? p [e  I  ΐ    h Ȱ  3 T    x  T@@@ ^@ Y@AB@@ 4%actsU @@ d  ¶ 1 /    a_oA?64*) )' ݠ.T u  ˩5! t@@ @@ R%actsD @@ e   O M  ;  6}_]TR6HG GE Lr   ? @@>@@ p-acts_in_orbit @@ f   m k  Y  T  ?R ?@T˰/+ %3+ 3     ˶@_ L  0ީ + & T      @l Y IE  > 9 4  w d T   I D ?  Ӑ@@@@A 6@ @AB @@ @A 6@)@A@@V@ABCDE@@ /subset_faithful @@ [g K I   >  5  9 @ o; c (?@ J@^/<5 ; X  $ 1   ? \ ( 7 @@@@A @ p@ @ABC@@ 栠.reindex_astabs @@ h v t   i ϶ ` ʶ"vT!b͠ k@@#idx g"op%bigop &Monoid@'com_law o@ c w ~@ c a!F a 9@鐩 ְ k z 5 s  ̐   . @ O    h )%BigOp@) g  X1@*index_enumZ5( b!i @'bigbody0D@A  + F@(operatori  ˩M@,com_operator#       t  p2  +$"      ~    @@@'@AuA o@wA @ABxA4SOAj@}A4[do@AA4`wr@A5[v@ABCA7Zty@ @A @ @AB @ A4[c@ A4`ؠx@ A5@ABCDE@@ ,reindex_acts @@1i!   z  u Ҷ ©  N   Ѷ  %@}  ѩ O ] L G  W K     @ ~"  f t  d _     3   B     < H   z  u  a. é  G T4 gNM Z1@@@ @A@@AB@@A@ }@ABC &@ "@A |@n@y@v@ABCDE@@$act1 @@j 8@(group_of!QBz   lC@$gval Q;  [ ө ` bj w f@@@ @A @ T@A N@ @.@ABCD@@+&actKin @@k(+ $q  ٰ  Ԑ  Ϡ *  @&cancelں7    o6q   t ~@$invg |} Ґ@*right_loopI  $ ̐@@@ @A#@ @AB @t@A @ @AB @ @r@ @ABCDE@@p'actKVin @@lmp Yi RE QЩ> 6 649 D@.rev_right_loop9*@@@ @AI@ @AB@ @A @ @A @@0@ABCDE@@)setactVin @@5m%# ~  @w d.H  < aߩ8,. b2  < u" v 1  7 P$#@@@{@A@@ C@AB @ M@ @ @ABCD@@Ġ&actXin @@dnTRĶG >< :%@  ?-x Dl , s X ?' u (@%expgn!iD ><&ssrnat@$iter+| F]  l ߠ  UB_>>@@@@A @ ~@AB'A*m@,@A&@ @@@ABCDE@@%afix1 @@o ~O L\i} Ɛpb  @@@@A @I@AB @D@ @@ABCD@@!&afixD1 @@p! !G&z Nq anvK٩#zw@@@ '@A@R@ @ABC@@E*orbit_refl @@qӶBE .>$" &     HȐ@@@ H@A@ @AB@@ @k@ABCD@@h,contra_orbit @@reh QaGE + I 7@K K@$negb ? Bة# Dǩ Eѩt^ / )@@@ y@A@@ @3@ABCD@@,orbit_in_sym @@8s(& wu@y KJXE>OvN\IBSh@)symmetricX y% z  z y R] T Q " $ .@@@ @A@ M@ABA ]@@A@ O@AB@@A+S٠@@@ABCDE@@֠.orbit_in_trans @@vtfdֶY P϶@>@*transitive(2@@@ @A@ r@AB@@A r@d@AB#@@@@ABCDE@@,orbit_in_eqP @@uz qԶp   ƶ@ڐ Q ĩ w 7P9 : w_<XUo ya>ZWo ذ s  CD@@@ @A@Q@A @L@ @ABCD@@(/orbit_in_transl @@v%( !   !z @   ߰  Ӡ   נ @  ̩  x^v= z    uI w ܩK y  @@@ M@A@x@AB@ @@ @ABCD@@m,orbit_act_in @@ wjm Vf NrZ@ T ˰ >% > Bt@ _ L0 > 6$ >հv Y    _ @@@ @A c@ )@AB@ -@A@7@@ -@ABCDE@@-orbit_actr_in @@Nx><1 (& $A  }@   m3@   h\/   3J t5N)r74f5  z7Tà " ?3 @@8@@ޠ,orbit_inv_in @@~ynl޶a ǶX׶  W   @  8 ^1   K   [C < X GV  X  () fN+GO\@@@ @A @ @AB8@4@A @@A @ @ @ABCDE@@/orbit_lcoset_in @@z   @ >te @5@  g R8PZ Xyq Y?Ws[AY}@@@ @A @@AB @ @Ai@@ABCd@ @A@ F@ F@ @ABCDE@@D/orbit_rcoset_in @@{ҶAD-= q o &@ (   @ -><Cn'"ȩɩ ( T'O/ʩթ֩ 5@@@ b@A 9@@AB @@A@@A@@ @ABCDE@@/orbit_conjsg_in @@%|n~  ׶T gT@A@=ְ\W˩;/ ]C@)conjugate97)t"L &9@@@ @A j@ @AB2@@A=@@3@ P@ABCDE@@'orbit1P @@U}EC8/.x rl3j$^ 's@@@ @A @ V@ABX@@Ad@@ABY@ @ @ x@ABCDE@@ݠ+card_orbit1 @@}~mkݶ`ƶWֶV@+ - '8 1B 5A7+ xL<DsQv@@@@/orbit_partition @@yܶ| :@ ᐩ X)&$-*(1!@ds @)partition*ʀeg i zjr@@!b@!bj@A@A@+9 @+Ql @A@ A+ˠr@AB @ M@Aj@@ABe@@Aq@d@B@ABCDE@@E1orbit_transversal @ӷBE.>rp D@+transversal1 & @SV?O   +k() 7 7!7 7 7 7"      7! 77  77& '$XlL| =䠒# dx @̀@@@@2orbit_transversalP @@'@ pfd Ȑ!P d Xé gy aȐ!X@^fԀ#ض@ { VmLZR@Z 򩛠i@$and4@ @.is_transversal'7?   Cg 7[G k ;_K  = 6/@w1.k Ƞ>ʠ]6 9M_R 3KT 5@ QWP ?D@ Đ-^/,/ZOK ϐz#*[m@@@@A 9A3@ ;A1@AB @ABCD@@'afixYin @@_DOMB9  @ *@ Ʃ :" @%joing!rA*9ϰ E- &. G/ (?@@@@A l@ @A@z@@ABCD@@'afixMin @@E~sٶjͶ!H@ ԐK]@ ِPé vǩE7N KrZ7SARvn= Szb?[X U|dA]@@5@@-sub_astab1_in @@FLJ@`mx Ұ Ơ x<ڰ Π~ x@@@(@Ao@j@@ABC@@F0group_set_astabs @@GԶCF/? &, ^'@@@ @A@@AB@@A@ @@ABCD@@b,astabs_group @_bK[ܩ'@-)@"3 l||@@@@*astab_norm @@)H r i;:H5.?G>L92C@*normaliser۞րy@@v@@,astab_normal @@JI:8-$&$ @&normal12Gi@@ @@ .acts_sub_orbit @@bJRP¶E<?<@ ˩v Bj X,1$&ĩwt;{;@@@@Am@@ABw@@Am@ @ @ABCD@@*acts_orbit @@K~sٶjͶi@ ҐI o YIQ@@@@A @@AB:@7@A@ @AB @@ @h@ABCDE@@0acts_subnorm_fix @@LCA mȩǰ©̩ ΰɩ ө 9t nv#@@@!@A @@AB@l@Af@@AB @F@ @@ABCDE@@E,atrans_orbit @@MӶBE.>$"&@5$Yo%@@@B@A@@^)amove_act @@N[^GW=;!#sGDn׶@D1e6h ZU U@]SЀ.ȩ שVq g4 @ A l@@@A@AA@N@AB@@A@"@A@@4@ABCDE@@+amove_orbit @@9O)'xv\;簩vc[9TuH@'rcosets/;;z88@@@@A@A@ABI@ @AM@@ABCW@@AM@ @@l@ABCDE@@Ѡ&amoveK @@qPa_ѶTKʶJsߩ.N$"Caޠj >: @$repr `!b[C <9SeewM{bJCZn@@@@A@ ;A@AB <@A@A@@ABC<@@A9@@AB6@@@@ABCDE@@0orbit_stabilizer @@Q۶&f Z/kA}+̰ڐ̐Ǡ@@@ @AAF@@AB@K@Al@@ABg@@AH@H@@ABCDE@@F)act_reprK @@RԶCF/?%# T)+éI6é!@'funcomp5π WŜ9@$unitUe@Aǩ~ک쐩2468Ωǐ@@@A@Ae@=@AB@H@Au@@ABC@@A @@AB@@A@@AB @@@+@ABCDEF@@-card_orbit_in @@0S y om S@ްڠ署@&indexg05&!@@@@A@2@AB@@A=@AA@A@@@ABCDE@@2card_orbit_in_stab @@WTGE:10z@ũ@$muln+.q=e̐@@@@@@ABC@@ܠ3acts_sum_card_orbit @@|Uljܶ_ŶVնY@ݩ*, .  ] 4a@$addn+,} h l+(A.12wGP @@@@A@@@AB;@@ @ @ABCD@@/astab_setact_in @@V  zk@g|l~nvvrz@@@@A@@ABF@@Af@@ABa@@@@ABCDE@@?-astab1_act_in @@WͶ< ?( 8@ݩ ԩ@@@@A@o@AB@@@@ABCD@@d0Frobenius_Cauchy @@Xa dM ]CA@e J. C.0 ;'9)>pܩǩ?3Ġf-(#ln@@@ @A~@ @ABV@A @AA @A @ABC.A@2A0@A3A@(@AB@7A @A-@@ABCD7@@A.@A*̈d@AB#@@A@R@AB 1@ /@A +@A8AH @A8A @ABCDEF@@3atrans_dvd_index_in @@aYQO D; >@϶@~Q %L*#div@$dvdn$&@D"Ұ$W7@@@@A@@ABy@@Ao@@@ABCD@@-atrans_dvd_in @@Z u۶l ϶o-@@1Ր-%?ɐ@@ (@@ )atransPin @@[  E@@I@ܰlU_ >|g@@@@A@;@ABX@@AT@@5@5@ABCDE@@2*atransP2in @@\/ 2 +  m@@@qdڷ ( )     r 2 uy ѐ,@@@C@A@@AB@@A@@A@i@i@ABCDE@@f.atrans_acts_in @@]c fO _ E C@t@ΐ@@@_@A@@AB@ @A@@@@ABCDE@@6subgroup_transitivePin @@!^~ j z ` ^6޶P@eR+6-* ;@m > ~ |2  D  8 V@| M  A QQ  E W@ci#  ̩5ީ l  Щt@@@@A@ @ABj@T@AV@@ABC`@@AV@I@A@@v@ABCDE@@۠$actM @@{_ki]öT=;US><20+h t:I l<n>MK_@@@@A}@'@AB!@|@@@ABCD@@$actK @@`x$ u̩ lfRyy@@@H@A@@AB@B@=@@ABCD@@%actKV @@a> @@@@'$actX @@bL!nvv_K [c U@@@*@A@@A L@L@@ABCD@@J%actCJ @@cض2olnpr!@%conjg!d_@@@Q@A@q@ @ABC@@o&actCJV @@dW;Ͷ=>%@ɩB!ک 5ސ@@@o@A#@@@)@ABCD@@)orbit_sym @@.ev l ܶRp^ݰc^aBc 6d gjKl?m @@q@@+orbit_trans @@SfCA5,ض %+u @\g^[I  #@*s! 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