"`w9$poly'algebra(mathcomp@()Notations$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%prime)ssreflect(mathcomp@0.wFbN_&finset)ssreflect(mathcomp@0 @$$~,B|XŠ(binomial)ssreflect(mathcomp@0io  } &ssralg'algebra(mathcomp@0ⴆg {PK7y=Zqo JnڲР$poly'algebra(mathcomp@A*polynomial,<!R&ssralg@%GRing$Ring@$type;Y@@@@HA@>=z@@*Polynomial'polyseq)Datatypes$Init#Coq@@$list]@/@$sort;1GA@@'is_true#œ@$negb&eqtype)ssreflectE@%eq_op&R@&eqType ԷB#seq@$last'OR5 d`@#one'pt7@$zero'}nt@(zmodType!"DC@@@AB@fBB@@m@@@@AAB@BA@AA@@@>?ޠA alt@A4eA?@B @ABC@AA@@A@ @!p@m@ABB@@@@@hGc@|SulVe`Y|@ֶ+) +k()= R '>''+k7 7$'1ZAB|@@@@@J2polynomial_subType @󩜠@'subType:t}@Aܷ!xQP@cϩWAӷ!K^@@#K_SQ"PxQ緐!urku+갩E۰̐  @*vrefl_rect+ [3%I@HFR +k+ 7 7 7! +3 +V 7 7 8'7 7 7 7 7"7 7"7$'()= R'> %''+k$'() :'4Pp7tࠒ.h"@ADH$Ġ1@@@@@۠2polynomial_eqMixin @A(Equality@(mixin_of3@A㷐!yթN<@*seq_eqType *ϩ"F$k[@'val_eqP1SYXv@8{@, `+k7 + 7 7 7" +&:'7 7 7 7 7"7 7"7$'()7! 7!7 7 7&'0$PgX4@D{4xLؠn䠒lh@@@@@A1polynomial_eqType @꩜f@ qD@ADC@ynI@ P+k7 7 7 ;'SxXh@@@@@i6polynomial_choiceMixin @&choice@/sub_choiceMixin45〰 @.seq_choiceType0$@*choiceType6.B&Choice@;@@64 +k7 + 7 7 7&'7 7 7 7 7"7 7"7$'0'PX)D%x ĠРxl@@@@@5polynomial_choiceType @ki@@b=a@AéH@(class_of+茢@A̩@%class V@8N Q@*݀V@! t+k7 7 7 7 : 7 ;'\Xhx$D@@@@@(poly_inj @@@&ssrfun#ssr@)injectiveЀ @@@@@'poly_of @÷@}@%phant)`@@ζ@  8+k()7$'*d@@@A*sRk@A@@A,type_poly_of @굷@(𩚠>@5B@/@@ (+k()'@@@@A\*coefp_head @!h@$unitUe@!i@#nat@l+WA]@@@@@B%!'Zmodule@$\M@#nth'D ;@?=860.( +k()= R#' 7! 7 7 7 7 7#''+k7 7$'ࠒG\.@@AD|*#xl@@@>9!ؠHZA@@AB@@ ,poly_subType @mkxMq9UBqlh2@+ +k+! 7 7 7! +4 +W 7 L7!8'7 7 7 7 7"7 7"7$'()= R'> %''+k$'() :'4wp]t&䠒ThH@ADL;J.ȠW ,(@@@A @@AB@@+poly_eqType @ðBB@ X+kG 7! 7 L 7!;'Ƞ@\Ɛl@@@@/poly_choiceType @Ʃ][@NG0@p""?f@H d+kG 7! 7 7 L 7!;'L\lx@@@@D)lead_coef @B~#Nat@$pred `<@$size'P@Y +k() 7! 7 7!7 7! 7 7 7 7 7#'  dhx"PDt@@@@I@A@ABC@@*lead_coefE @@EA42Ʃ%Logic@"eq @N@\/`U@@@A1DH@A@m@$@ABC@@(poly_nil @WUQ!8A-[W&Theory@)oner_neq0U0@hf 4+k7 L:'X@@@@A@@Ҡ%polyC @}{!cO8@&insubd60/@=4mB-[:@e=|ѐ +k()G : 7 7 +7 7 7#'7 7 7 7 7"7 7"7$'0tpJؠxdD/|^蠒mQzOK@@@1@A1A@-@*@ABC@@)(polyseqC @@BҶW֠~(@g;u&+@$nseq'P8=&ssrnat@+nat_of_bool1B%@@_@@S*size_polyC @@CΩʰ,@@o@@c%coefC @@D ޶۰>A>xР@$boolZ'@@@@@@@@@C$ ݰA@*nat_eqType4XA\@@@㳠LA@A@A1FdJ@A@@@ABCD@@&polyCK @@XEGE@&cancelں7u@S#"̀LA,@@@A1GK#@HA(?z@LA@ABC@@ )polyC_inj @@~Fmk>!@@@*@A@@A@@@ABCD@@ՠ*lead_coefC @@G~PLCL@@T@@䠠%polyP @@H!!q]@#iffС)@%eqfunF`prpLo@@@x@ALA@NA'hyx@ABx@S@A@@AR@A[@@ABCDE@@+size1_polyC @@IS@@#leq+ΩBxV8@@@@A@|@@@ABCD@@<)cons_poly @j;S8Agh@@@@CBΩu!s5"ns۩שɩA@B@B@@@@@C׶אҐͰÐF 2G͠2됩԰$Z"s0!l!F!!$ې&GH°!1ư@WU'? X+k()= Rz'> = R2'>  +'+'$'':::'7%'+k+$7 7 7 7 7"7 7"7 7 T'G7%'+kG7%'4pD401蠐AK|Ġs@@AB@H4РAܠx@@@@렠,polyseq_cons @@Jfcة@V~#GjzcJ@$nilp'P*  U@@@@@@ABC@@.size_cons_poly @@KA*Ġ*@$andb='t'@@@@A3@@@9@ABCD@@8)coef_cons @@Lf7OөoPqoַˠrx@@@@A@@ABX@@A@A@@ABCD@@_$Poly @ @%foldr(݀u۩9ܩ@$ +k7 7 7! 7 L 7! 7 7#'0XthOtDdX@@@ A9.;@A@@%PolyK @@TMCAP~@ |z&Oթ@S:3c@@@@(polyseqK @@sNb`.ϩ t/@@@@Ǡ)size_Poly @@Orp~Q9yx )=~F@@@@X@AB@@ࠠ)coef_Poly @@Pj|zX}^A\c;^@@@Q@A:@@A9@@t@ABCD@@1poly_expanded_def @!n!E@\1T@%mkseq((\@  \+k() 7 7" 7%'lqHx@@@A9Wn@A@@-(poly_key @@Q͐@@@@@7 @ߩ@+locked_with/Ξ6@~p4;@Pƀ@: +k7 + 7T77&'+ +7TT'G7%'7$'ࠒɐXHt @@@@@@j/poly_unlockable @P@*unlockable|3@A  f@ vo@6:^@&unlock:퀰@e@6locked_with_unlockable!8߀KG@42 +k7 7 +7T7" 7 +,7T7" 7 :'+ +7TT'G7%'7$'+ +7TT'G7%'7$' O`젒H|[XX9@t|.jd/@@@GA*w|@A~@HA@@ABC@@,polyseq_poly @@{RjhXnZ@< HL@4"t@?:5 H(MZ f  xv SڰV}@@@aA@A@@ABAN@A?@A@A@@ABCD@@)size_poly @@Sp砩35Y[[@@@@@@ABC@@,size_poly_eq @@T¶Z@NˠGL@@@:@A8@3@5@1@ABCD@@0)coef_poly @@Uٶ4ɶ24!kͩ` i4@@@@A@@AA#@@&@ABCD@@P.lead_coef_poly @@ VTR@Đ;6@ɐĐ{ѩװΠک!@@hX@hXՠMf@A@iY@iYNj@A@AB@@ @AM@@@ @AB>:"I $@@=BA@AA@ A@ABC !A@*'ssrboolA#@AA @*A)@AA&@@@ABCDE@@%coefK @@ `W O M2VDB$E  @@@@,add_poly_def @ b `ΩD穚@$maxn+kBo_] @#add'p=FA>x CJEB E@ ~ |f +k() +# 7! 7 7! 7! 7 7!7! 7&'7!7 7 7 7 7 7!7 7 7 7 77 7&'(@p@bx  [P)\dx+ /\ +lP@@@@ ,add_poly_key @@ X@@@@@ (add_poly @  ذ @9OjA @h9Ex @G +k7 +L 7!T77&'+ L7!T'G7%'Lް|TX@@@@@ 63add_poly_unlockable @  ߩue@v 4@7Z Ű - 3/@   `+k7 7 +#L7!T7" 7 +&L7!T7" 7 :'+ L7!T'G7%'+ L7!T'G7%'ࠒ=d L,DѐTDdX@@@@A@.@@@ABCD@@ n,opp_poly_def @   l    @#opp'p N@ % # x  +k() + 7! 7 7! 7&'7!7 7 7 7 77 7%'$ +|̠ L:X ؠh Ґ ΰ@@"@@ ,opp_poly_key @@ cYG@@@@@ (opp_poly @ \ Z{ @1ɣ= @T1ə 0@C +k7 +L 7!T77&'G7%'~t|XLT@@@@@ ٠3opp_poly_unlockable @  o @n @7/ Vh -c 3/@  ^ +k7 7 +#L7!T7" 7 +L7!T7" 7 :'G7%'G7%'ࠒDtTAdXId@@@@ -coef_add_poly @@ Z   I(#  C Q@@@@ !-coef_opp_poly @@ [  ʶ ^  Ѡ UL 5 @@@@A@{@AB@y@'@@ABCD@@ <)add_polyA @@ \  婚9@+associative(! B @@@@@@ABC@@ Q)add_polyC @@ ]  N@+commutative1/5/@@@@ c)add_poly0 @@ ^  `@'left_id 0@@@@A@@ A)ZA@i@ABCD@@ })add_polyN @@ 9_ ( &z@,left_inverse:AJ@@@@ .poly_zmodMixin @ : 8@  A`@A 0] @fϗ׀  @Vϗـ  @Iϗƀ  @4ϗ @ W U쐐 +k7 7 7 7 7 7 7 7 7!8'$XܐhX#x+H$h  x@@@@@ ܠ-poly_zmodType @  b@ ~$]@A j@ =B@A(͐ @={ g @o)hZ l4@   |+kG 7! 7 7 7 :L 7!;'d\lH|@@@@ 3polynomial_zmodType @  < 6 ) @$ 7 \X2hx D@@@@@ 9&polyC0 @@ `  wԩ w 7@lU| @@ @@ M(polyseq0 @@ a  ð ة  ĵB@@M@@ ]*size_poly0 @@ b  Ӱ  @@\@@ l%coef0 @@ (c    (*   õ 9 B  @@@@A@@A @ I@t@ABCD@@ *lead_coef0 @@ Dd 3 1  Q#@@@@A@@ -size_poly_eq0 @@ Te C A թ# !J  @1Q  0@@@A @ t@+@ABC@@ .size_poly_leq0 @@ of ^ \ *>e7@@@ @=@AB@@ Š/size_poly_leq0P @@ g p n  $Bool N@'reflectc@H G`@@@N@ @Z@ABC@@ ⠠-size_poly_gt0 @@ h    Ymˠ QL@@1@@ (nil_poly @@ i    1k[@@@@@ )poly0Vpos @@ j    @&Specif @'sumbool7̂K@= ,@@Y@@ )polySpred @@ k  Ŷ  Y@ 9 `ېd@@n@@ 1-lead_coef_eq0 @@ l  ڶ / n n m s@@@@A @ Q@A @ L@ I@ABCD@@ H)polyC_eq0 @@ m  v éө @@ d@@ X+size_poly1P @@ n   V @#ex2М@/ א Ґ Ͱ  C   A y Ӱ Q@@@A1A)E@A@ @A^@ @ @ABCD@@ )leq_sizeP @@ Bo 1 /  ö "  !j %@ v       ?    } @@@@A@ @ j@ !@ABCD@@ %coefD @@ ep T R   F D " ! ( #  Z w :   (@@@ @ @ @ABC@@ à%coefN @@ q n l   _ ] ;` Ab  s Y   A\@@@@ ٠%coefB @@ r     v t R Q X S P  0 r2 6 Y! Yv [@@@ P@A>@ :@ @ABC@@ .coefp_additive @      (Additive@#mapC@A < @ g ]c   $  E @D;[A F h  DB@%axiomYɀ T@  ɶ  & Z +k() + L 7":'() 7#'@x@@@ A @ @AB@@ ?&coefMn @@ s   = |D ٶ  ک       v @&natmul8z e   @@@@ ['coefMNn @@t Y `    ԰ ө   ҩ   ٩ @@~@@ s(coef_sum @@/u!Ig p@@!r !P@ 8ؚi ڶ!F@  I  ,^ )    # @*%bigop %BigOp@ gЩ 'h9   շ B @'bigbody0D@A 6w9G( :)% -E  S . ?N/ A 7  iI@@g@L@A@A@PA m@ASA @UA@@ABVA4[c3@[A4`ؠx8@A 8@ #@A #A4[d=@ 'A4`wA@ @ABCDE@@ 頠)polyC_add @@v @*morphism_2voj , M!am!b;1 Hk 5 5/Lo@@@ b@A P@ L@A( @ABC@@)polyC_opp @@w @*morphism_1vn Q r CM F U@@@@&)polyC_sub @@xϩ= d 86oe|> k< Ekeg@@@5@ @AB@@A.polyC_additive @G Ґ@ = A@,7H5@, @+k7 7 :'X *h@@@*@A@@g*polyC_muln @@#yk Z  < $C  '@@=@@|(size_opp @@8z'%z    ,Ʃ+j 0@@ @@-lead_coef_opp @@J{97 ˩  J   @@ h@@(size_add @@[|JH ܶ    RQ@@ /@@)size_addl @@p}_]   ˶@(  1 U j> l@@@ @@̠(size_sum @@~wuYj@@WUTRLJG  NSFЩ dY =D\Z"D ީP  i C b`1  ~ @@j@%@A@A@)A @A*Al@,A-@AB-A)@0A5IuEd@A*@(@A OA5EtIi@ @ @ABCDE@@+lead_coefDl @@ O . )@^   g J@@@ @A m@ j@A jA4WT@ @ @ABCD@@-,mul_poly_def @ַ+ j I D] 萩 @$addn+,}x  ҩ 'fintype&Finite@ X @/ordinal_finType#LE @*index_enumZ5(˩@'ordinala@   @թҜ A@#mul'p.  ک(@*nat_of_ord2ܵ  " @@$subn+&@ +k() +& 7! 7 7! 7! 7 7!7!7 7&' +( 97 7 7 7 97 7 7 7 7#'#97!7!7!7 7 7 7 7 97!7!7 7 7 7 77"L7 7 8'H1Dp@N@ |\ PL4 M*06P O\+ "6{`hpTP@@@*5A@A:dޠRA@ @AB@@ @ M@ABCD@@ՠ,mul_poly_key @@@ u@@@@@ߠ(mul_poly @@*,@*,-^@ѐ | XLT@@@@@3mul_poly_unlockable @з@ E۩@5+1-@ ϐࠒ L,DT>dXFd@@@@Ao@m@AB }@\@AX@@@ @ABCDE@@@-coef_mul_poly @@A> } \ W  ۩     w@ @@@@A@A7u@AB @ @A @@AB{@ A7Zt@A'@ R@ @ABCDE@@g1coef_mul_poly_rev @@#Be   ~  ' 2       @@@@AA5@A@AB@ @A @ @ABC A4SOA@@A@3@ABW@ @ @#A5[@ABCDE@@)mul_polyA @@WCFD_ @@@@AA@)@ABA*Z@*@A@A/@ABCA8AH@A8A@AA8PK@A8R@AB @ 1@A @ @ABCD;@@A@A6@ABm@ @A t@ @ABC J@_AF@A`A@bA@A@eA8OO6@ABCDEF@@ݠ)mul_1poly @@Dz T%Vِ@@@&@A#@@AB K@ ;@A6@@ABC@@A)@@ @A@ABCDE@@)mul_poly1 @@E@(right_id5#@@@@ *mul_polyDl @@F @1left_distributive?OO Nؐ@@@X@A@V@ABo@XA8)*&j@A @ q@ABCl@@AK@I@A`@@ @ABCDE@@0*mul_polyDr @@G٩-@2right_distributivey,$@@"@@A*poly1_neq0 @@HjB@@@@T.poly_ringMixin @@v#kZ@A$}SV@Vթ[@jnک`@vFߩe@j<䩚j@K<驚o@?9@&$&B +k7 7 7 7 7 7 7 7 7!8'$(h!HxX b#hڐ.x;X@@@@@-poly_ringType @USUA멜Z@@A󩚠;@% @s/q65@mkkǐd\lH|@@@@ޠ3polynomial_ringType @4۩1ݩ+@,G`e]-@( x\X9hAD@@@@@&polyC1 @@I|D)L@k%!@@@@(polyseq1 @@JéƠB[<@s@@ @@,*size_poly1 @@KթƩ۠ @@ +@@;%coef1 @@Lԩ|;B[} А@@@@A@W@AB@ @ G@@ABCD@@\*lead_coef1 @@MҰةɠX@@@@k%coefM @@'Ni l=@@@@A@@AB@@@K@ABCD@@&coefMr @@EO42ƶ &$"@@@@,size_mul_leq @@UPDBֶ   LKϩ=u@@@@-mul_lead_coef @@mQ\Z ȩ)O"é#©3Tr@@@:A$@A=@@ABF@@Ay@,@ABC@@AH@@AB@@Aw@@A@ @U@ABCDEF@@ݠ/size_proper_mul @@R @QLG1\ix/o @@@D@A?@@A @x@@ABCD@@4lead_coef_proper_mul @@S>1O@vql ~{x@>b@@@y@Ab@@AB`@@@%@ABCD@@$-size_prod_leq @@TͶ@2@@ gЩǩkm4  i =͠(  rĩ J'CardDef@$card׼@#memڕ(@,predPredType>h`/@@@@AA @@ABA*ɔ @A*ˠ @A@@ABCA5i\@f@A @@ABA@A@A5hX@@ABCDE@@&coefCM @@QU@>20  F̩8*r ; Ӑ@@@@A@Z@AB @@A@@ABC@@A@X@A|@@@ABCDE@@&coefMC @@xVge7ӶYW54;63m_Q':a @@&@@Ԡ)polyC_mul @@W}P3Qr 8@@@A@A/@,@A@@@ABCD@@젠4polyC_multiplicative @@X)RMorphism@iS@@j@@/polyC_rmorphism @@$pack0Z {e@'#Jʀ@R0@A\_q M Ʃ@'phantom2"@   (@%applyX#@ԩ@@,0OF@( +k+1 7 L7 7 7 7 7 7 7 L7 7# ''0.p7DCĠ5l`P@@@@@X)polyC_exp @@Y \Kp@#exp'p#y@@2@@q,size_exp_leq @@-Zo v 䐩[$`#ة[D@$muln+a@@@S@~@ @ABC@@*size_Msign @@O[><ж - /DCǩ5A -֐ @@@s@A@@+@ABC@@5coefp0_multiplicative @@o\^\ǰ(B@@@@@A@ @AB@@A@@@ @ABCDE@@ˠ0coefp0_rmorphism @vt @\@T -@)$|J@[ȀO[sŠɰxW@Z +k+5 G7!L7 7 7 7L 7! 7 LL7"L7 7# ''ItXԠ(p4dH@@@@@ .scale_poly_def @ $ =q@#g +k() + 7! 7 7! 7&'7!7 7 7 7 77&'$Ġ@РPӐ\ܠ lkg@@@@@.scale_poly_key @@]@@@@@J*scale_poly @E@7LQ=J@N7B_@C +k7 + 7 T77&'+ L7!T'G7%'РXHސx1P@@@@@u5scale_poly_unlockable @  $˷@ks@:р 0  62@.,  X+k7 7 +! 7 T7" 7 +% 7 T7" 7 :'+ L7!T'G7%'+ L7!T'G7%'GD$Ԡ>`XPId@#@@ B@@+scale_polyE @@g^VT&©#@6J F%@@@@A@@A@@;@ABCD@@à+scale_polyA @@_nl> W<OQXRgA@@@@@AB@@۠+scale_1poly @@` xWd@@@tA(:@@@ABC@@,scale_polyDr @@aix^ / BFi@@(@@,scale_polyDl @@b>IJL C{Z} @@@@A@@@ABC@@,scale_polyAl @@cĶ+28۩PNt@@Y@@2.poly_lmodMixin @۩'Lmodule@X ~@A ũ8@9n=@s9DEĀB@e+WG@W+Q@   t+k7 7 7 7 7 8'РhXX#x+H@@@@@w-poly_lmodType @" E@%{@AM@>&7@AЩ@` `쌀@86ː Qd\Hl a|@@o@@3polynomial_lmodType @WU5!/#)@$ːѐx\XD8h@@@@͠-poly_lalgType @xvxt(Lalgebra@s.' @AL @8@AT@;?_@+_'@* +kG 7! 7 7 7 7 ;L 7!;'Рt\LXlz|@@@@3polynomial_lalgType @BK 82@B6癀4@/ +k7 7 7 7 7 ; 7 ;'РlXCTHDhx@@@@;)mul_polyC @@d K:R@%scale(_sA@1m3y@@@@@AB@@Y)alg_polyC @@e iԩаq@-lmod_ringType.$<x_@\$ݩ@(ringTypegׯD@@@@AB@m@AB?w=cA@A@A?v`#@?ă 'B?̅)@ABCD@@%coefZ @@Lf;9  -+  AǩYɩT!@@@@.size_scale_leq @@cgRP "ZYq@@7@@,coefp_linear @geWUfb&Linear@N(b   x@F%{ka@M;[A B@=- ҩJ@ O6  ͠ Ѱ   _@2@ Bܼ@E.*-@  t+k()+C 7!L7 7 L 7"7 7!+"L7"L7 7 7  7# ''() 7#'$Z̠+@Gdࠒ;\0|KT@@ @@$1coefp0_lrmorphism @ͩ*LRMorphism@%clone=i0d+@qJ@e1b<аxq %V@x @ \@$1G@:Pyw@%mixin&U̩@(lmodType+"/@;~ 5@`Q?@M@ q=t@HG +k+ c#G7!L 7  7  7 L 7" 7 #G 7!L 7  7  7 L7" 77 7 7 L 7" 7L 7! 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7  7  7! 7  7  77 7 7!7 7 7 7 :' ϰHh4hؠ |@fT'̠$@@!@@02,deriv_linear @00۩EA0$-Ɛ@nM#1A@00N0% +k+7 L7 7!7 7 7!7  7  7 7 :'TF` xdtDY%@@@@@0d&deriv0 @@1 11 ,ڰ-&$%,@@@@@0r&derivD @@1.11"--0r-+,"|@@@@@0&derivN @@1=1,1*"s--̷0-"k@@@@@0&derivB @@1K1:18"--ڷ0-η+,"c@@@@@0*derivXsubC @@1Z1I1G"1-,a@_@@ @@0'derivMn @@1i1X1V).F0,ĩ-%.Bq0"D#k#u/1@@.@@0(derivMNn @@1}1l1j).Z0,ة-9.V0'U#"Z'W#@@.@@0֠&derivZ @@111-1Q0,-N.k+1 1-(@@.@@0蠠*deriv_mulC @@111-1c0,-`.}1>!K,;@@"@@0+derivMXaddC @@1110.8-*1B-s.1(;$51R!_9@@@#@A-k@,Z@AB.U@.@A,T@,@-@ABCD@@1&derivM @@1111.T,3-.-.z(W}!{1!}1rm@@@#@A,v@.@,p@,@ABCD@@12&derivE @11۩   e g i k m o q s u wtbO30.0c-a-°.ߩ1|# ($'$1.0m-k-̰."($1.-Ұ-s"ݩ'%!0K  .N  /ҩ  0  1  2'  3]  4٩  5  6  7 1|@ !̠11@7N21@ !̉21@ !̞2 1@͒21@7u21@ !̓21@! !̈21@C !̊2#1@9 !̔2(1@)"2-1@"?22@2j2h   \+k7 7 7 7 7 7 7 7 7  7  7  7  7 ::::::::::::'0AؠXL젒@>(H:xh)x6XWĠAhN@@@@@1&derivn @22*/1.-@$iter+|/2P2.2t@22+/,V d+k() 7 L7!7#'ɐh/Ȑ@L@@/@@2'derivn0 @@222ƶ2/Z..52@4 !̴2v-22@@/@@21'derivn1 @@222ڶ2//n..I2-2Ր@@0@@2A'derivnS @@2222?/~+F/۩./֩%2s* 22u)@@0@@2U'derivSn @@3322S/+Z/.Ͱ/922@@0)@@2f+coef_derivn @@3"33+j/2e.}00.߰/ީ///ݩ22O,.2%(////,,#A1~(binomial2@1falling_factorial] 2@@%@@2/polyOver_derivn @@3F3533 fEDB@;:-JP2-K+0)3u-)3 2D82-U @@@@20derivn_is_linear @@3a3P3N+0>2'2h22꠶@2@ߩ04| @@@/@A0@>@;@:@ABCD@@2/derivn_additive @3l3j+0Z%'N0S@0K%3'U#! 3'W%#"!2@3s[2>@3~3|+0l%'` +k()O27!L7  7!  7! 7  7! 7  7  77!7 7!7 7 7 7!:' xP°h< P3d䠒',@@%@@2-derivn_linear @33,03R;'Z0@8%[:@33, 03YB'a +k()-7!L7 7!7!7 7!7  7  7 7!:'BphՐѰxDcT$Ƞ'@@0@@3/'derivnC @@333ض/]3,40ɩ/0ĩ3a3..ȷ2.-..b@@1@@3C'derivnD @@333,G0ܩ%[/[/[TT@@1@@3Q*derivn_sub @@4 33,U0%i/i/i3R/j.p0*&3)&3@@1(@@3e(derivnMn @@4!44,i0 w03e0/ް.%J33&$&33&&&P3@@1?@@3|)derivnMNn @@484'4%,1 13|1/.<a33*&*&@@1U@@3'derivnN @@4N4=4;,1+%//3/%d@@1d@@3'derivnZ @@4]4L4J,1:3@@@1s@A0@-@,@ABC@@3(derivnXn @@4o4^4\ 1L,1M0+1H34,m&q_!$C3*I3+@@!@@3ʠ,derivnMXaddC @@44u4s,1c3//30C.3.3+ P$n!`4& /1E+'%&''l $u!g4 4/@@@0E@A/3@1@.@ABC@@3,derivn_poly0 @@44431+,1@4b'\0i._-@@.@@4-lt_size_deriv @@4 4431>@'4t.렩.搩03+I@@(S@@4'nderivn @44-140-,4F$-4l11&հ1@1ˀ@# X+k() +  7! 7 7!7! 7&' 7!7! 7!7!7 7 7 7 77 7&'0&D3נD14T0`$l1$,͐|%448 @@0@@4Y,coef_nderivn @@5 55-]14X0p110Ұ1ѩ111Щ4 44\@W>.%4J@@/;@@4r+nderivn_def @@5. 55-v2 4q002V.'/'.0@@)factorialċ4ѐ@@'@@40polyOver_nderivn @@5G 5654 g FEC A<;/KQ4/L-2*54D84/U @@ @@4(nderivn0 @@5a 5P5N4110F5@@2w@@4(nderivn1 @@5p5_5]411+0̩UW@@2@@4à(nderivnC @@55n5l05>-2]1;2Xe@@'@@4Ӡ)nderivnXn @@55~5| 2l-2m1K2hu ' 94G@@=@@4栠1nderivn_is_linear @@555-2959")sA4V?>@@@@40nderivn_additive @55-2')45J3)R 5L5)TQP4@!?/`I4m@/+ P x̠< Ph]d䠒)ޠ,@@'@@5).nderivn_linear @55ҷ.-2©5|e)*C2@'#5pxDؠhTFȠ*@@3@@5Q(nderivnD @@6 55.U2'i1i1ikbb@@3"@@5_(nderivnB @@66 6.c2'w1w1wy@@30@@5m)nderivnMn @@6)66.q335m310-(+(5Ɛ@@3D@@5*nderivnMNn @@6=6,6*.335310A$,(@@3W@@5(nderivnN @@6P6?6=.3-'11@@3e@@5(nderivnZ @@6^6M6K.3;5@@@@5-nderivnMXaddC @@6l6[6Y.3I51Ƕ152)0pS,)V&R#DX@@@`@A2"@1@AB3 @3@A@1 @0@2G@ABCDE@@5Ϡ-nderivn_poly0 @@66z6x53 .3i@2H0r> @@0@@5ࠠ-nderiv_taylor @@6665356'35ʶ@@5r2[3k5^6-$5Y66;(S3q&&5a&3&(L(c&2050r6n&&000& 6v5x61!061@@@&J@A%h@%@AB&KA$@%@A&K@%[@ABC3\A@@A2w@1f@AB%@&@A(@@(=@ABCD%T@%@A2@62A@AB.3@.2@A6/@66A%@ABC67A'@"@A"@67?64)4) +k() + 7! 7 7! 7&'7!7 7 7 7 7$' 6H@4%Р7P3T\4$ܠ/8l66@@3<@@6)map_polyE @@7}@7j>7k<:64U3:4W6@P BpW ʩ0$67@)'D@6R67#4B@@@3:@A2(@4$@AB4$A7u7&@4*Ak@A.@4@AB3b@7vA @p@/@ABCDE@@6,commr_rmorph @m7k7ig6|7666qN7"7D/@t7r7pn67=I |+k() + 7 T' 7&'Zh7{|@@@@@7,horner_morph @7767W@7 @0!] 7)Ѱ6U167K77I@7Ƕ7ȶ67f@7 )4 l+k()   7 7& 'cDX@@4@@7:)map_poly0 @@77733Sx7l77j+̐@@@4K@A5@c@@ABC@@7O+eq_map_poly @@8 77ȶ!g@7<7<@2g7?677˩2i2)ͩЩ@@@4g@A7A2]@5.@A@@@ABCD@@7n+map_poly_id @@8*"iR8@/6s/7̶7s3@$/6$7@,seq_predType n66B7l70 3/Đ23/7677 +27޷7;842L77777@@@3A2@A3A$%@3A *@AB3@4@A5i@@,@ABCD@@7,coef_map_id0 @@8e (8R&8S$"75=5G5E@4$7/7ݐ7"5"4(585.5:7&7`7-2L7/778 7鐩56*+2K7h2R78@@@4&@A36@3@A5@3@4I@ABCD@@7Ѡ,map_Poly_id0 @@8!P8zN8{LJ27@4K78(5I74O27R8 8 1681787T7a882@@@4I@A37@53@AB@ @A4@5@AB34@4n@ @{@ABCDE@@71map_poly_comp_id0 @@8"w8u88t@8B7o75@4u7s8.27s4y$?7|26@'funcomp5π2273d8<8:8^H228>J728>8b@@@5@A@5@AB3`@7@@@ABCD@@8$1size_map_poly_id0 @@8#8Ͷ8ζ8$5@8888 8845ʩ4ߠ77ޠ8dp78f8d8@@@6@4@8G@ABC@@8F0map_poly_eq0_id0 @@9$888F5ڶ@"43ԩ88N8)m@@@@8[1lead_coef_map_id0 @@9%99Զ8[5@@8ѐ8̐8ǰ3845٩4߰5484@@@4@A3@5@AB6@@3@4@8@ABCD@@81size_map_inj_poly @@9=&9*9+%inj_f688o8#f_08*56&5;88:8w5?3#8>3(9 @@@4@A4@4~@8@8@ABCD@@8,map_inj_poly @@9b'%9O#9P!%#!թ63g+R@@@3@A4@5@6}@3@ABCD@@81lead_coef_map_inj @@9x(;9e99f75;978+4576G5.38512@@@5-@A4@6@4@5O@ABCD@@8נ)map_polyK @@9)V9T9RP@9 8Z@4@8]89Q9.@14C+T8X3u9 @@@Q@AP@O@AB4a@5@A@49@6@47@ABCDE@@8(coef_map @@9*w9u9s+ٰ9126u86665v6u6|6w6t894@8}96$8x6{6@88999]9$8}69;}@@,Z@@9(map_Poly @@9+9ö9Ķ"3956Y9O9M$686@889v2629U\64 9@@@V@AP@67@6@ABC@@9:-map_poly_comp @@9,999,99t6ΐF9@6ԩ5+9u8@6+84%%386ڐ@339z99389399Ő@@@6A@@7#@ABC@@9a4map_poly_is_additive @@:-: : i,K,-99%C9>9*9ܐ@@@,9@A5@4@6@7;@ABCD@@9y1map_poly_additive @:":#,,.7 @,p,p9z@* u3@:/:0,g,. +k() 7" L7 7 7 7":'ʐl%rl9Π`P@@+A@@9)map_polyC @@:c.&:P$:Q"+96 7=99ة59ܩ%7#9::%@@@,@A6@5@A7@7@5@ABCD@@9à0lead_coef_map_eq @@:/B:l@:m>˶97W@:8:3:.2%7@9:496E7D6<ͩ%9B7E:l@@@69@5@9@ABC@@9⠠5map_poly_is_rmorphism @@:0a:_:]%:6:Y!'C'":::!::<:_@@@*0A'j:@A*3@)R@AB)y@*3@A6Z@5I@ABC7D@,$@A, @7@AB5E@4@A6@)4@)3@)s@ABCDEF@@: 2map_poly_rmorphism @::)%A'm'ͩ7@""-:@>sd4$@:Ķ:Ŷ9%'z' +k() 7"  L7 7":'lbl!T@@7@@:9)map_polyZ @@:1::W6i:#::464y9:o!9:q9:o#9"9::#:v""9:x@:v:9:z :@@@6@A5@7@A8@5@6@ABCD@@:]/map_poly_linear @;;{"(:# 8^@'catcomp*PQ 7!65~:c@;874xB":#) :j@::Ʃ&@(additivefx&j"" :,&f-j &` :@;/;0":#C ) +k()+0 T  L  77"L7 L 7"7 L 7" 7 L 7" 7" 7 L 7";7 L 7"7  L77"7"   L  77"L j 7  7!  L7L 7 7 7 7 +7 L7"7 L7"7 L7"7"7 L7";7 T77 L 7" 7 L 7" 7 L 7" 7" 7 L 7";7  7# ''7 L7"7 L7"7 L7"7"7 L7";7$'@ʐ$8d00D̠"ܐ̠3ؠtdp #b\#^Lt@DX,HP "ȐhJԠ8\At&t"o "0T \p8:@@@n@8@AB@@:͠3map_poly_lrmorphism @L;vJ;wH"0:(p驚:@-4"#l(:&"(" ;R:@(ŀ4";""; ":&Ѡ#;  ;b@o;m;k"; (␐ +k()+r    7"L j 7 7!  L7L7 7 7 7 +57 L7"7 L7"7 L7"7"7 L7";7 T7 7 7  7 L 7" 7    7"L j7 7!  L7L7 7 7 7 +7 L7"7 L7"7 L7"7"7 L7";7 T7 7 7  7 L7" 7 j 7  7!  L7L 7 7 7 7 +~7 L7"7 L7"7 L7"7"7 L7";7 T77 7 7 L 7" 77" +P    7"L 7  7 L 7"77"   L  77"L j 7  7!  L7L7 7 7 7 +7 L7"7 L7"7 L7"7"7 L7";7 T7 7  7  7# ''7 L7"7 L7"7 L7"7"7 L7";7$'7 L7"7 L7"7 L7"7"7 L7";7$'7 L7"7 L7"7 L7"7"7 L7";7$''7 L7"7 L7"7 L7"7"7 L7";7$'T"֐ Ԡ"l:䠒"Ƞ8@  $ d  xThH@T4 젒*X     8 x"X"ܐt    , l D##   p L     <    | H $  X (|`4|#hP$) <|h "Ȑ dP# P@"P  Ġ;h,l\<tH(,ࠒ#j`   `    P    \  p 0@,L@@@@@;D)map_polyX @@<2;;b77];v;`!!Ӑ@@!L@@;U*map_polyXn @@<3;;s4[87ΰ8;;#;;;;'(;ǐ@@9.@@;k)monic_map @@<'4<<;k8@;e6.;;䐩i62:;8;@@@7@A6@7a@;@ABC@@;*horner_map @@;!a;;ة#d6@;#c;;@@@7@A9}@6@6@ABC@@;-map_comm_coef @@sRq6;tXؠ%X80=$tHlL@@ @@=j1horner_lrmorphism @>><=][%J0<&=%!=j@T%?==$)^%9 =%4=𩚠=w@%0<%+::%&<:< %"=5)o%= :B >@ >7 >8 ==ֶ%"= J=Iʐ +k()+  ^7L 4 7  L7L7 7 7 7 +7 T7 7  7 L 7" 7 ^7L 47  L7L7 7 7 7 +&7 T7 7  7 L7" 7 4 7  L7L 7 7 7 7 +7 T77 7 L 7" 7      7 + #7L  7 L 7"7      7    L7  7L 4 7  L7L7 7 7 7 +67 T7  7  7# ''7$'7$'7$''7$'D%v p%;%QT;* xt># hL0<%S@%y<&F0.OH%Y$K]L&\(x%P|L̠=,lhd@@@@@=ؠ)deriv_map @@>=W>U>S=;l:Q;n> ̩>>;Q@@@:J@A98@;4@AB:@;@93@:m@ABCD@@=*derivn_map @@>>t>r>p=;6;:o8 ۰>+>p7=t>- ߰=v>t>Q@@@@> +nderivn_map @@>?>>*> ;7;:8ͩ M=>Cԩ @@@@>!0poly_morphX_comm @@>@>ʶ>˶"pf)+>;@:?>o>X>|%:>9%+>;@;>>:>a%+>>$k@@@@A!@<@9@92@ABCD@@>F,poly_initial @@?A>>%#9Y;2>x> >F@64Wt8[@@@9S@A@:@AB9@!@<$@9@ABCD@@>c)comp_poly @?? 9~;>b:z+©>+6>>@??9;>i: +k() 7 7 7 7 7&'X-x:Jx,qlH@@.size_map_polyC @@?EB?4?2>;Ʃ;<$;9!,>8,K>,M0(?;?@@#@@>-map_polyC_eq0 @@?YC?H?F>;ک;:(?3,_>ߐ3h,b3 @@2@@>*root_polyC @@?mD?\?Z>;>_>;):=,>,? 2JА@@@@>Ġ*comp_polyE @@?E?o?m><9:۩;<y>@p*k15""-polyOver_comp @@?F??1p@(prop_in269>9:1o?m!<U9 l?9: 1y @@@/J@A@/H@AB@@A@=@ABC@@A:d@<`@AB1=@1;@A @<@ABC @!@A @e@AB @;@A'@'@'@ABCDEF@@?)+comp_polyCr @@?G??Ҷ?'ѩ@?@#H#*@@@;@A:@=;@AB:e@'@'@'@ABCD@@?|2comp_poly_additive @@'@%?z<2'=@ 3?'"  ?' $"! ?@2|>@@7@5?<ɩ2l') +k()fA7!L7 L 7" 7!  7! 7 L 7" 7! 7 7  7  77!7 L7"7!7 7 7 7 7!:',(:\hӰ8(^lؠ(Z x-|젒| (KHP?@@2@@?0comp_poly_linear @@l@j?<@'^b=S@xcC@@s@q?='@(ei 0+k();7!L7 L7"7!7!7 L 7"7!7 7  7  7 7!:'((sX |((젒Wp-֐̠+h(D@!؀@@=@@?*comp_poly0 @@@K@@?=7#@ABC@@@a*comp_polyX @@APA A @_=<ذ%@@&@ِ@@@@@q0comp_poly_MXaddC @@A-QAA<@@p<;><f@@7 ,ک71.g@,ސ@@@@@0comp_polyXaddC_K @@AERA4A2@=ƶ@Щ=>Ű@ ǰ@7̰3&4$@@@@@3c@A<@;@A>d@;@;@ABCD@@@2size_comp_poly_leq @@A`SAOAM@=;<A;=W@@V@;,24=i:@@@A-@A0@0A1@AB0;@0@A<@> @ABC2@2@A>@=D@A)K@)H@)G@ABCDE@@@Π-map_comp_poly @@AT M&ssralg'algebra(mathcomp@%GRingAz@$type;Y@ \ ],@30OF@BA)ssreflect#ssr#Coq@@%phant)`@A@1@Az;1GBAYA>ǠC>A<->РD>A%Logic$Init#Coq@@"eq @>栐D>AA@  BpWEDS@-1@AmP@B@D@CB@EAB D$ED"@An@`@שb@ِCA5ED3@A@q@s@CB@@@>9!ؠH@A1DHa`_@@ A1GK@BA*sRk)ssreflect#ssr#Coq@@ABC@@A-poly_mul_comm @@BXUBGBEBA'ComRing@B@C@A?b @*<VB!?<@B)CdB(<ϩ?qB ?G B >1B7/A2\BB72^B9B@@@5kBpA?@A2 @2 @AB1#@>4@A="@?@AB3@3@A1@=@<@ABCDE@@Aࠠ0poly_comRingType @BDFA?K@@7@AG+ /IA@`1@ABC@@Bꠠ*horner_exp @@CWCNBEBCf7;@?e%!#. 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""  RMHC>:0+Cw@/|]C@D.' +k7 77777777::::::::'$:dZLEleTXXts\gDe|@@@@@C+horner_eval @D\C^AoAD˩"oD,D @DeCg  A@C L+k() 7 7&'l"x@@A@@C֠,horner_evalE @@DYD:C(C#@NC@44p=(@@@@@E@AB@@C젠9horner_eval_is_lrmorphism @@DZDPC>8,94C^@@@-A'o]TA@A0@1A@^@AB e@ f@A d@?w@ABC>@ @A @@f@AB?T@A @A'@DA@A@?R@ABCDEF@@D4horner_eval_additive @DwCe7ЩDK,ce+DO.A@A d/ k1m5m43D@Cd2C@DC|7  l+k()J+7!7!7 7  7  7 7  7 77!7 7 7 L7 7"7 7!:' $h\TTx,А04ِt̐<ɐȠ, @@7@@DV5horner_eval_rmorphism @ED JAA萶@DFl;@E ¶D 04I +k()&7!7!7 7 7 7 7 7 7 7!:'ࠒpTDIp5 `-@@BG@@D2horner_eval_linear @E/D1֩,(Щ-)onm,6p}hD@MC0~, zy 0{70u  E @EFDH, H+k()+ +7!L7 7 7 7 L 7 7"L 7 7"7 7! `-  7!  7! 7 7  7  7 7 7 77!7 7  7 7  7 7 L 7 7" 7 77!L7 7 7 7 7 7 L 7 7" 7 7# ''4H`@|hHpT@,[l,$-ULܰ45VT,ߐĠ-](|0РD`@@@7@B@D@ABC@@D٠6horner_eval_lrmorphism @E=D+,0%%멚D@/-DM,,Щ0ʠ,1,E\D@p? рDZ,9,,< ,0۠- B   El@E^DL,FF  +k()+ 37!L 7 7  7 7  7 7 L 7 7" 7 7 3  7!L 7 7  7 7  7 7 L7 7" 7 77 7 7 7 7 7 L 7 7" 7 7 7! +U #7!L 7  7 7 L 7 7"77!7!L7 7  7  7 7  7 7# '''8[Xh `@|\<h,Ƞ,,l&$P,Lؠ,ߐ$>P-5tHtE<,Ő̠-(E_h@@B@@E88comp_poly_multiplicative @@E[E@S1M31OtE@@@w@A@@C@@@ABC@@EM3comp_poly_rmorphism @E@h1M Bߐ@Bא-u.kBܐEEU@. iՀD̩EZ@S(1SE. 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