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"".Morphisms_Prop@0not_iff_morphism Z,&Basics'Program~@$flip$ @$impl7o)Datatypesz@$unitUe@A=@6subrelation_respectful>6z 55NND@0subrelation_reflv <UU)J@9iff_flip_impl_subrelation2VA#g  kQ/RelationClassesV@(symmetry0xjQj @-iff_Symmetric!x}@|o&Specif$Init#Coq@@'sumbool7̂K@)BA3BA (+k()G 7!= gR'>G 7!= 6Rm'>%  L7 +L77 +L779'>+ + L779''>G 7!7!= *RN'> 7"= R'>' 9'> (  7"  7!L 7!77"7777L 7!77"  7! '6  677777777!77777L  67777777777  67777 +7T7 9'''L7%' 7%'7! =R''+k6' 7!7$' +k7!7 7!7%'+k+L7!77"T'7%'6' +k7!7 7!7%' +k7!7 7!7%'lL(점$A@ܠU̠ĠO`D蠒th<+AABAAT P48 <4P0|,t(ts@Ԡ@D0LD X( AB@Rx԰T* <H|ࠒ4܀@@@@@/Zdivide_Zdiv_eq @@hJX M@@"lt1P-AB@7J ;݀0@#div1P@ yG8@@@@@1Zdivide_Zdiv_eq_2 @@K1|1!c/@2AC@造Wf9-tebx9mj@@@@@"*Zdivide_le @@L'BinNums'Numbers#Coq@@!Z7@@􀠜OAB@|XA@2 @@@@@Y3Zdivide_Zdiv_lt_pos @@M@aB@\*@CB@A@bߩ%Logic$Init#Coq@@#andЖw@ǀA穚Ҁ@@@@@,Zmod_div_mod @@SN붐!mHQ@쀠AC@A#@GE!IM)&Ȑ@@@@@ޠ1Zmod_divide_minus @@Ozm$c@"AB@%qoKZmဠO@#sub1P@ pTf@@@@@ 1Zdivide_mod_minus @@P]T!V@׀2AA^AB@2g@@@@@B'Zis_gcd,<!gߠᠠ@ }|-Zis_gcd_intro@f@Ŷ@@<@mSoUW@@@AB@CC@@2Qb@@@@AAC@@A@CC3@@@@,Zis_gcd_rect @ C !Plm<@@!f@@@@3@@@mQb@CFG@@@@@D@R ,@QOCPtQ10@,@Р9@Ӡ)@m`@ؠ/@-,"'z@Qb@+9 +k()= R'>  & ' '+k'3lAF|@@l@V@A@A@@@렠+Zis_gcd_ind @yg^@}kAe@ rP@ bS@@hU@}XlZ]b;`crr9kAF|@@@@@!+Zis_gcd_rec @@@!n@Ƕȶɶx u@D@G@Զ@L@OQvu H+k() 7#'%p@@@@@Y+Zis_gcd_sym @@Q!d@@CBA @@@@@x)Zis_gcd_0 @@$RAAA@@@@@)Zis_gcd_1 @@9S)(.ABCBC@@@@@,Zis_gcd_refl @@ZTJIOAAA@@@@@-Zis_gcd_minus @@mU]\Ph`@gCBAr;,N@@@@@ᠠ+Zis_gcd_opp @@V}|p~@CBAWHˀn@@@@@-Zis_gcd_0_abs @@WAAgA@@@@@.Zis_gcd_unique @@X1ɛ@ʀDCB@Ҁn@"or @vz#@@@@@U2Zis_gcd_for_euclid @@Y3曠7;뛠?@CqDvACBߐ@@@g+R+InitialRing+setoid_ring#Coq@@ al)Datatypes$Init#Coq@@A@@3Zis_gcd_for_euclid2 @@CZ$u>y)}!r@HADCO@#add1P&@ ̀€$7@@@@@ʠ&Euclid,<Xeig@lj^k,Euclid_introqocp!us!vvx@d{X@#add1P&S@ ̀`P>bWR@KBgH@@EE@@6@@@AAE@@A@BB@@@@ +Euclid_rect @n@R@}zn{@@HFDCȩ|!"ACƩ$@$BEE@@@@@@@Dө1@߶8* +k()= R'> #' '+k$'WAJ|@@zn@>@A@A@@@a*Euclid_ind @ܶTG@   :sAJ|@@@@@{*Euclid_rec @    nZ@|#GD@     ? @+k() 7&'l@@@@@*euclid_rec @@ F[ 6 4 ( 5"v3 8@ @^1P,"u1 A"u2 D"u3 G"v1 J"v2 M@ 9 Pՠ / I 2  "@ C Zߠ 9 )J < ? ׶@ c@( 2*ML HK@@@@@ޠ&euclid @@ \ z x l yϐ@@@@@ꠠ=Zis_gcd_uniqueness_apart_sign @@ ] Ȁ {̀Ѐ"d'Հ@DCB@ Z ] р C e t G  i쀐 |@@@@@ "&Bezout,<F     @  Ķ  ŶO [Z,Bezout_intro  ʶ  ˶U ̶\ ͶZ ζ@  ѩV    @@@@CC@ @):H@@@AAC@@A@CCo 栠  蠠  @@@@ Z*Bezout_ind @     Ͷ  @        @Q:H@C23@@@@@D@  @       @   ض  0@n:H@    𐐠&LAF|@@@@@ .Zis_gcd_bezout @@ K^ ;} 0J@KCBA.@   0@@@@@ à,Zis_gcd_mult @@ o_ _ Tڛr@sDCAz倠 G 5造 K <퀠 O b@@@@@ )rel_prime @    T p ^ B@ ܀  D+k()6 7&'kpA@`@@@@@ !0rel_prime_bezout @@ `  @ @?jBA   5B 4C@@@@@ H0bezout_rel_prime @@ a 䛠& ٛ*@BA VB2  א@@@@@ j%Gauss @@ b H LP@ bC BA@Y  멚 r  @@@@@ .rel_prime_mult @@ Ac 1s &w{@xCB@  $    @@@@@ 4rel_prime_cross_prod @@ kd [ P֛n@DC@ ? R@ @"gt1P, 5 A@  @ A@ & 3  I M者 2@Жw@ 9EKX =E@@@@@ 1Zis_gcd_rel_prime @@ e 򀶐 ٛ@EB ;A@ G  CA@р    _ 2 c  @@@@@ L-rel_prime_sym @@ f N L@'BA-  @@@@@ e-rel_prime_div @@ g!ph f @CCB@ _  ͩN  ѐ@@@@@ +rel_prime_1 @@ 2h^ B*A@@@@@ /not_rel_prime_0 @@ Hi@܀ BAA u A +@@@@@ -rel_prime_mod @@ jjY J@ AA@ 4 G Q - < <@@@@@ ⠠1rel_prime_mod_rev @@ k}  n(@$ AA@ƀ q \ o o΀ Q `@@@@@ 4Zrel_prime_neq_mod_0 @@ l  L@H BA@쀠 ~  怐 U   {  ;A@@@@@ 3%prime,< @  g f+prime_intro ֶ@ @"lt1P-L @  @   @aj  @@BB@ @.nH@@@AAB@@A@AA. @@@@ l*prime_rect @8 攑I@@@8 @  @ 3?C2V K@XnH@4A45@@@@D@    @[ ) $@@Z @  5@ "R   ; M@znH@  +k()= R'> %''+k',TAD|@@@F@A@A@@@ )prime_ind @ Y9 M@ [;ж4@ A@  e@ ER H # 5l1 ; ;.YAD|@@@@@ ꠠ)prime_rec @ dǩH@5 |@ b¶^@ n@ I @ r c S w R d`_ g g <+k() 7%'h@@@@@ .prime_divisors @@ m@y@A  @   􀠩 f  I@Cҩ t  @Bߩ *   . ɩ * @@@@@ `/prime_rel_prime @@ n >@JA H@ ; ^  ܩM  @@@@@ 2rel_prime_le_prime @@1o! ɶ""@oA@  R B 6 ڀw  @@@@@ *prime_mult @@[pJ @AU J @  ̀A/ $6 (M@@@@@ ࠠ+not_prime_0 @@q d @@@@@ +not_prime_1 @@r s@@@@@ 'prime_2 @@s䀐 B @B C@@@@@'prime_3 @@t B @A #C@@@@@7*prime_ge_2 @@uҶ@A  BB@B Đ@@@@@W&prime' @# Р @ Ԡ  ש  @ A +k+7T 77!7%' + 7! 77!7!T'7!7$'ࠑ H d 9||A@t ̀@@@@@*Z_0_1_more @@9v  Ѷ@ N AAaӀ  Alހ " B I 퀠 B R0@@@@@à)prime_alt @@ow^ @#iffС)v@#DeAA@@@@@⠠0square_not_prime @@x~ ̀ 򀠐AA@@@@@/prime_div_prime @@y@怐B@쀐@etGfi@@@@@+Zgcd_is_gcd @@zBAQ@#gcd1P@#gcd 0BA@@@@@=)Zgcd_spec @@{c b  @#sig#* @ )V􀰐CBAuAA@@@@@n,Zdivide_Zgcd @@|  L Pӛ T@fCB@mqܩb@@@@@+Zis_gcd_gcd @@D}4 v) z  ~@cAA@ M)逰@!@@@@@Ǡ.Zgcd_div_swap0 @@s~c X @ ABA@ A\) FɀJYYN aՀVe@@@@@ -Zgcd_div_swap @@ 逶 퀶 " @ U1ACB@ c?Adq7 Z?GK n%@@@@@[(Zgcd_ass @@@웠 rAECBALCQBA@@@@@0Zgcd_1_rel_prime @@5A%.,Ȁ, @#gcd1P@ 0N@@@@@-rel_prime_dec @A?3@ȷޠӐ⠩c ؐ!"H1'  A @;+%[YMZ 2Ȑ"a0^Ȑ"H0@ cQh<#6ةW@L@[rF-"@czNGj$_tmp@ lW'1d9DBAyDl}<85J319753Cl f@|@(! m%@{=Kv$Ca@ 怠BA뀐BA +k()6 7!7!= )R'> 7!= R'> '9'> +9'' +k7%'7!= R'> ' =R''+k67!77&'+k6' +k7!7 7!7%'4T|A@젒y|8pd AGdߐD @FtࠑA@(`ސL@@@@@j6prime_dec_aux_subproof @@B  &BinInt&ZArith#Coq@!Z@"lt1P-㩚&BinInt&ZArith#Coq@!Z@"le1P,'BinNums'Numbers#Coq@@!Z7@A@@@@@7prime_dec_aux_subproof0 @@RC̛'BinNums'Numbers#Coq@@!Z7@#HH1%Logic$InitI@#notШVB e1$HHH2A&BinInt&ZArithI@H@$succ1\w)BinIntDef N@ Nq)gB J@@@@@7prime_dec_aux_subproof1 @@D(\ONDCo[>=<:9v(Dkk@@@@@#-prime_dec_aux @ {Gi]Raȶ@ϷЩ a *ZArith_dec@(Z_lt_dec6=I $Wf_Z@+natlike_recз@  &ӠM@ܠ((6 4 @)False_induُ@'and_ind14ۀ?9&H_left 'H_rightF+OmegaLemmas%omega@8fast_Zplus_assoc_reverse '橜,C </@ R@1fast_Zred_factor0# E8@ ک  @Be&Omega1  ͠'.@7fast_Zopp_eq_mult_neg_1=Ҁ  aT@  ܠ/%{;@/fast_Zplus_comm116=84&Omega0 ,  ?K@,fast_OMEGA13K3FpB``@*comparison;f@CxOpA C@wk@'compare3xf@]=5lA C@ d @&OMEGA2.$D * l .y)auxiliary@(Zlt_left,ڀpV  'u "Hx "IH\zö@ ǷȩYUwkҶ@ M ٷک k {@ @$succ1\w@   %Ҡ oŠ!F, @!( @@@2ԩ6 R  ? 򠷐!Y~-@#[MP +#HH2f X Р+@ p @BAAAA@@@@@D@ z >U pN   # @4iff_impl_subrelation5 + Tk$ 7I@+lt_eq_cases0㜀 %#4 7 L^@)lt_succ_rM5SN8 DyA K*]^X@ )M^wPbĠ  1VVih!N(J>͠ 5Db@שנ||ˠ Il FԠ O{7 6Y pC @.lt_succ_diag_r&p1+/'ڷ/Ƿ@Щ {$HHH1طs㠩 c  n$ k &  @5) `ѩ@t5*CC(/!E9H1"BBB@@@@D@PKK.X%&SSEK 4"!@,dEːO -,@!m o @אe NO.0||!ݩ䐩r% %"H2 "H3 0h iHJ;?ΩTө J\@,lt_lt_succ_r;\ (dRdI@_+ CƷ=ɩ÷F}ǩ{f~| Kw@1P,Zwwsq\l&Omega2 mG -e o` @ wQ 7 9 bة] = 0 2@ _ E} I h N  P E = }Ҷ@ t Z} F$w { a L̵]C̰lU ShC@ p1P, +auxiliary_2 +auxiliary_1@,fast_OMEGA11I  Щ ٠ lԩ۠ ߠ r r r֩@,fast_OMEGA10H$ y y y y @ Ԡ   7@1fast_Zred_factor5(ũ    &Omega3 ĩ  ȩ +C@VC@ X       "@&OMEGA7.$I  ̠"OI  ' l l@(Zge_lefts     &Zorder1@*Znot_lt_ge>π +@ a Ķ @V頩tA AB \:@G @.=0 󀠩w3BA=ABҀ AC +k()77!= 'R'> 7! 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