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E蠠W @@@A.0TQ@ A.U>[J@^A.lDa@ABC@AA@@"s @,Ring_polynom+setoid_ring#Coq@@&PEeval"s @@A@AA@A@ @3 ?GNU$"-+86><CJHRPYW`^hf{y!s@ }[@XunhbRVDD@@@@@@@X{uoD}aD{ߩ~xɷ׶@ѰǩĐ@۰ ܠƩ@JHO~TͶY^chomxvֶĶ̶ٶKI0 +k()= R '>''+k     7#'+NAD@@@@@@ @xv}Ƿηɷз׷߷ &$ywo{f]ÐXb?`5^U)@ʶֶ޶¶ͶӶ"߶'%:8DBV +k()= R '>'' +k7#']ࠐAD@@@@@@ՠ_ @·G P %#-+@>HFUShfrp{[b@e"*18!&n-+53<:CAKI^\fdsq_@cmokl +k()= R '>'' +k+T' +T'+M !77"T'  !7$'r08kAD@p@@@@@4 @#!(W-2c7k<rAyHFQO\Zb`gnlvt}{ŷϷ$"&@ְCt y@GEL{QʶV[`eljus~ӶɶֶHFĶ@ȩ֩c x+k()= R '>''  +k+T' +T'+L !77"T'  %'Ґ08VAD@@@@@@hfdb@)SymmetricFgq>=[@@<@@H>micomega_sor_setoid_Transitive @86=lBGxLQV][fd@6Equivalence_TransitiveW}@IGN}S̶X]bgnlwu@*Transitive++-ut@@s@@3micomega_sor_setoid @omty~ŷ÷@+Equivalence~@A1w@@ö˶Ҷٶ׶ө +k()            7  7" 7  7" 7  7";' ѐͰ (]@@@@2rplus_morph_Proper @@W@0жٶ)Morphisms1@&ProperL@q@st @*respectful%WO?y@z{||5@@@AviA@@AB@@+rplus_morph @۷`%,3  31/-0@*proper_prf4>M-+V@LB@!@(w4< CJ" JHFD@Qi@nXpT |+k()            7     7 +T7 + T7#' '+T''*,&TȀ@@@M@A@@63rtimes_morph_Proper @@A&$+Z05f:n?uD|KITR|zxvyqo@@e@@M,rtimes_morph @=;BqGL}QV[b`ki`1@.|@OMTYҶ^chmtr}{  @[ö@bZY |+k()            7     7 +T7 + T7#' '+T'',Ƞ&@@X@@1ropp_morph_Proper @@'B}{Ŷ̶ӶѶͩаҐ@@@@*ropp_morph @ȷԷܷ驚@.^@ڶ)ɶҶO`Mb@  +k()            7     7 + T7#' 'Ӑ䠒 @@@@ޠ0rle_morph_Proper @@xC̶Q$$" !@@@"$w@#iffС)z@@@@)rle_morph @%t19 @GGECA#!@: f10@7 CKR!Y(&1/YWUS@wĶ@3 +k()            7   67 7 +T7 +T7#' 6'+T'6'Р60]̠&FNxL@@@@H0rlt_morph_Proper @@D86=lBGxLQV][fdjhŐ@@w@@_)rlt_morph @OMTYҷ^chmtr}{rܩC@.;@a_fkpuz @m ն "@tlk +k()            7   67 7 +T7 +T7#' 6'+T'6'Р0̠&xL@@q@@3rminus_morph_Proper @@@Eʶֶ޶¶@@@@A PQU@AB@@ ,rminus_morph @5շ޷ @3k/R@¶G m~k@жp8n@שϩΐ |+k()            7     7 +T7 + T7#' '+T'' ,!Ȁ@@@@%cneqb @" L@'@v[w]@$negb@0.Zi D+k() !7$'p@@@@@'$cltb @GEq%@@`@$andb=& @=}sm]@[Y9¶r l+k() 7!7%'Xx@@@@@V*cleb_sound @@FFDKzPɶUZ_dkitr}Ҷȶն%addonG@@@@@y+cneqb_sound @@Gignsx}ȶж  #h3@`9@@@@@*cltb_sound @@;HŶѶٶʶжܶ @<%#86B@=@?PXAeDdcba_^]\B/MKb@I@Il(!:,@@@@A@@ՠ$PolC @󩛠'EnvRingC@#Pol@@HA@ ,+k7$'X@@@A-#B@A@@&PolEnv @#Envl@"V1(@<\A @+@)X@@@A@A@@$(eval_pol @!@I@(@@]KI@PfW@$PphimgW@%#27XV @@F)^y@@w޼ L+k()7# 't@@@>A-Az@c@AB@@_#Op1,<@@%Equal(NonEqual&Strict)NonStrict@@@@@@@@@@@@Rf@@@@@D@@@A@B@C@@@A@@@@@@@(Op1_rect @!P!ob@6Rf@)KE@@!fAB)Cސ#D(&&@@@@@@@@@@@@@@D/-=*@53%#&'(75ᐐ +k()= R''''''+k$'TA@H@@)K@<@A@A@@@נ'Op1_ind @RPNC@T1lA@H@@@@@'Op1_rec @hfd@t%@o: X@@@@@(NFormula @'%^@$prodt@1@0 @+k6 7 7%'Ր`Tl@@@@@,(eval_op1 @!P<@@BG@@fEq@h@oH@L]{va}~Ǡgy@75<kW`¶@_ +k()= !RC' +' +'+'+'' %' !7$'%'%'+k+T'6'ABHlӐ@@@@@i-eval_nformula @YW^gCl{9@#@8ն@ӷ#env=ط䩚R@~.F~wBBB@@@@@I!p"op k@r<+^:9q@<+`H@>= @Ķzжp76Ŷ 5420 +k()  = R/ ' >   7    7#' ' + k6'7ABAL@&Ԡѐ@@@@@ˠ&OpMult @CA"o'DHF '@&option >v@N I ATD.V YCB7  a ;   eC@hf%g! +k()= /RR'6'= R['6'6'G'G''= RJ'9'G'9'9''= R5'6'G'6'6'''+k67$'+k67$'+k67$'+k67$'ࠑoLNA@H0TAC̠AAA@\@@@@@ %OpAdd @UqS :sE GDBBBuG INFyK M>H>@< +k()= /OR'9'= RW'6'G'G'G''= RG'6'G'6'6''= R5'6'G'6'6'''+k67$'+k67$'+k67$'+k67$'ࠑx@A@HjHACABP@$AA@@@@@Z,OpMult_sound @@ I J H O ~ T Ͷ Y  ^  c  h  o m x v۶ܶ"om߶ @       ߶@       @L@)z     #     !  @@@@@+OpAdd_sound @@ %J { y        ö  ʶ  Ѷ    ϶˶  "oa!e"e' B@5@3@ +թ}@10  Q L K J  P.@@@@@%Psatz,<  @ @'PsatzIn+PsatzSquare)PsatzMulC)PsatzMulE(PsatzAdd&PsatzC&PsatzZ  @ @#nat@ S ;  @  @Ķ@  C  @ I  @    @@ 0AABBBA@AABBBA@@ x@2@@ -@ /@ 1@@@@@ 8@AFAABACBDBEBFA@@@@A@AA  @@@@ *Psatz_rect @ ' %{@]@0)P {@@!nQ A  C B \ L#@ hP o)C |   @ 1 @ 7D  w = @A @ o HE   Ʒ!c  SF  ˩ [G@@!Fh l mAAABBBA@AABBBA@@@@@@@@@@@@@@@@@@D~ ( ) uĩ +M 3             H >q #@    znaQG8 x+k()  , t' *(=X!.?PRT'> $'>$'>3 &'>3 3 #'>3 3 #'>$'''+k$'+7 Tk$'P>AF@@)@@A@A@@@ à)Psatz_ind @  ?7 @  B&ĐP\AF@@@@@ ߠ)Psatz_rec @  [S @*Mq b@  cG <+k() 7%' h@@@@@ *map_option @!A)?Q j@@!B)~R s@@x@ ? |A AAA@A@@@@@DJ >  P ?; @$" +k()= R'>$'G''+k7$'ZAA@@AB@@@)?@7@A@)~@0@A@AB@;A ůM @6A@AB@@ I+map_option2 @M)T @@K);U @@ w)zV @@ȶ@ @ OGHPܩ' נ  V ۠"x'   1@v)n# \]] H+k()=' R6'>= R'> % 'G''G''+k7$'+k7$'4rTAC|@@@)@=@A@);@8@A@)z@3@A@ABC@CAS@>AU@9AW@ABC@@ 'Rops_wd @        ̷  Է  ۷      ܩ [@+ring_eq_ext@A  N    ⩚@*SORplus_wd;oө@+SORtimes_wd=٩@)SORopp_wd-+Y0@      5          ն  ޶    % o (    +k()            7 7 7 ;' !-h@@@@ @AB@@ 젠4pexpr_times_nformula @      _   & $ :@ +@ 2 IY`|xcr, ""ef|zT~|6 ,19 A>@$Pmuli   z s a Z T N 8@ ? = E C J  Q O Y W m310Vސ +k()= RR'>= ),/R0 ' G        7:9' G' G' G' ' '+ k7 7$'+k7 7$'РࠐAN|ALkhĠ\@@Q@@ L7nformula_times_nformula @ l j r p w  ~ |   `"f1"f2bٷa^ ː"e1c"o1 \$` ꐷ"e2"o2㩚 E@|0bl r nk  " !        c@           754d 0+k()= Rn'> = RN ' >7!       +77 7!77#' ' ' 7:9'+ k7 7$'+k7 7$'$|*AKx|젒.ڠؠ3̀@@@A вuX @AA@A@ A@@ABCD@@ Ơ6nformula_plus_nformula @      @ N@  !zRBxTPʠI F{yNY ^trSpUӷ nV۠][]@$Padd2   M F ' r I@     !ʶ <*('%  +k()= Re'>= RF'>7!     +77 7!77#' ''  7:9'+k7 7$'+k7 7$'$)䠒QAIt|!`ؠ 𠑑Dr@@m@@ (*eval_Psatz @ H F N L S  Z X b ` v< @ n@ v A@!l @$list]@nG  зC l4rE$List%Lists @#nth$߀Q | ݩJwѩA  ƷT۩@'Psquare:       "re  K@ ـ        R)& T@>  Z@A5 ( ' &   Ω    96 f@X 4 3   > 3 @@@@@@@@A!b ΐ. A   @ ŠʠéL H Ѡ$S N@  ϶  ն $     Ŷ X+k()   , '(*()='AgR'>G9:7 79'>J 7:9'> 3! 77 7 7#'> 3! 3! 77 7 7 7# '> 3! 3!  77 7 7 7# '> 7= R!'I 9:9'G''G9:9''+k7 7$'+k7 7$'+ 7 7 Tk+7 T'7 7$'8PsPؠŐU``AMJ  DxM@@A@AA̠l48lTD4dj|@@@Ajob@AA@A@AA@A@ @ABCD@@ EtJöOTY^ecnl    {yζѶIGFB@@,<;  @C,/?  @   "! 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IAABCABC@@@@@@@@@@Dt ~   rVysX{o swq[~ @(positive*@"p0 m  "p1 s @jhpn #  (+k()= Rs'>= FKRY'>= &R>' 7# ' % ' % ' 7# ''>H' >H' ''+k6'+k6'+k6'ࠒ X  AH|̠CAABBCCAF|  AE 7@@@@@y8check_inconsistent_sound @@Rignsx}öʶҶ ض  ׶ % ն  Q  @o@-?@? ^y  , gn srN-M+ uNܐ@@@@@9check_normalised_formulas @ҷط'ȷ"cmtN$!F3堷 .Ʃ-d%A@:۶(@@% (+k()         7 = R ' >7#' H' ' + k6'-BԠAFp@@@@@0checker_nf_sound @@Sܶa&-4  420.$l+)31:8A?IG\Zd Mqo L  J4Lf@a@b $gpi4t q$Refl@)make_implub3(wv}AQ@%Falsee@@@@CAtؠA@A@@3#Op2,<@  $OpEq%OpNEq$OpLe$OpGe$OpLt$OpGt______@@@@@@@@@@@@@@@@Rg@@@@@@@F@@@A@B@C@D@E@@@A@@@@@@@](Op2_rect @ ض ֛6@6Rg@)u@@ ԩA ک␜B C !D 'E Ȑ-F 00@@@@@@@@@@@@@@@@@@@@D 7 #@ : . ) $    @ Q +k()=R''''''''+k$'\A@P@@)@F@A@A@@@'Op2_ind @ 0 .XM@ 2 1tA@P@@@@@ˠ'Op2_rec @ F Dn l@z-h @ M; 쐐 X@@@@@堠(eval_op2 @ӷT %  a[ c {{&y-ft*}1,e.5*s18-@ j ϶; Ͷ w +k()= &RQ''+''+'+#'+'''() !7$'() %'() %'() %'+k+T'+T'6'zAAP蠒@@@@@*eval_pexpr @    "K'K@>@Eh@@Ʃ Q@&PEevalʀY@+ 0 5^:^SQ@  ö@ e@%PExpr K*@ ᐐ +k()           7# '  p@@@ @ [@A-bC w@ABC@@['Formula,<!T)w@@@@  -Build_Formula$Flhs6 #Fop$Frhs= @@CC@@-2@@@AACBA@AA-+@@)@+@A@A@-A @A@" @:8 p@H2@ ACC@@@@@@ 1ː<p:N8s #2@SQ  +k()= R '>''+k7$'} 9AC|@@@@@ɠP @lj 32, 5$m_#\pZ"@@tr ;:s +k()= R '>''+k6'{AZAC|@@@@@ꠠn @ TSMEC|zB@A +k()= R '>''+k7$'_xAC|@@@@@,eval_formula @   88 $ L0.s@5@@m    ~  0A#lhs  Ʒ#rhs @N<+^@0N0zsm0|uoY@'%49>gCgJ ζS Ͷ{J_]/. , +W +k()= RU'>7 7     7#''+k6'#lAS@$8j@@@xA@A@@f$norm @ٷ@(norm_aux6KR @ö"peE 58 X+k()7#'@@@@@$psub @nķķ @$PsubՀ$@Ŷ{ѶѶ " a"P'wi P+k()7# 'x@@@@$padd @ݷ H5@D!$ H+k() 7#'p@@@@ߠ)normalise @ R '%/-QP KTS s Ʒ ]ʩ hѩ@"$VO=60{ ө$YR@9k l k/ **v@w> \e^Lw)l  ~h    bkdR/}` b j l@3197>ECMKTR[Yca4  +k()= R ' >=W1yR ' G B 7 7 7:' H B 7 7 7:' J A7  7 7:' J B 7 7 7:' I A7  7 7:' I B 7 7 7:' ' ' + k7$'+ k7$'РAQAT@80hD$d,P,  @@@@C@AB@@?&negate @_]ecjqoyw~`_k*# ']-\ )V T ASH CUJDFHL@B +k()= R ' >=V/xR ' H A7  7 7:' G A7  7 7:' I B 7 7 7:' I A7  7 7:' J B 7 7 7:' J A7  7 7:' ' ' + k7$'+ k7$'РAQAT@q0`@`eH( @@9@@v,eval_pol_sub @@TfdkpuzǶ϶ն  Զ"Ҷop,lk a: <;876 g@ 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