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U4 70Ӡ̠oh @O@)SymmetricFgq@?@>TL@.. U\DL;+ΠŠha<5&jYpl@@c@@Y(eq_trans @@6Equivalence_TransitiveWq`P)"ŠaZK@@*Transitive++-h@l@TڐL@.W\ܐD$ZS|֠ZIƠ@@@@*eq_sym_iff @C:ݠ֠yrߠΠyh@d@!x@!y@%Logic$Init@#iffС)@BA@@@@@AA@@A@'neq_sym @ %]V='@A!n@.!m@5@I@#notШ@=D @DKC@@B@@D(eq_stepl @J9)̠àf_:3$~hW@B@@mE@r!zL@y@R@zCB@[@Db@D@@@Aۓό^)Morphisms@@AB@@(succ_inj @vOHqˠO>@:C"n1@"n2@@@@rѩ@x֩@\@@@AviAK@AAۀߠKN@R@@ABC@@ޠ+succ_inj_wd @Ӡàf]81Ԡ͠@DM@K@ @@J@I@%@@@G@A8ӠA4Relation_Definitions)Relations@@AB@@%/succ_inj_wd_neg @+ G@ܠx_I8@E"!@N &@Sf/@W5@:@ 1A@ip@@@@@g1central_induction @m\L%]VGz%@F!A@f@A$A_wd@&ProperL@x@ @*respectful%WO?@@B@@q@@ԠE@o@F@@@@@̠'add_0_r @ҠTK& ߠ@@A&NZBase%NZMul&NatInt'Numbers#Coq@@A@%NZMul&NatInt'Numbers#Coq@)NZMulProp@A@@@@"NZ@A@%NZAdd&NatInt'Numbers#Coq@)NZAddProp/@@@A@@@A&NZBase%NZAdd&NatInt'Numbers#Coq@A@A@@@"NZ+@@,R@2@!t,RJ@@A@A,Y@@"eq,Y^@@A@,@@ @#add,@d@@A@AB,w@@#mul,wd@@A@,@@#one,T@@A@A,@@#sub,d@@A@,@@#two,T@@A@A,@"@$pred,d@@A@,@'@$succ,r@@A@,筷@,@$zero,筷T@@A@ABCDE@A@E@FE@rJ@rP@F׋~U@ W@@@@@{@ABC@@AA@@A@*add_succ_r @vf ?8۠Ԡwpav@A@@@@׋@g署@l@׋ѐ@@M@@J-add_succ_comm @ΠPG"۠ܠˠ@Bɚ@ǚ@@@׋@< @׋@A@@@@(add_comm @1*͠ƠibI3"C6(#@C@<@A@A@׋N$@׋K@@@@̠'add_1_l @P?/Ҡɠle@9*n]~qc^M?@JDKJ@wO@wU@K׋Z@=נ#_@/@@ @@'add_1_r @zj C<ߠؠ{tez@E@@@׋@xנ#@j@@E@@B)add_assoc @ƠH?۠~wӠ٠Ԡà@F@@!p@@@׋@׋ @׋@׋@@@@,add_cancel_l @  0)̠ŠhaH2!B5'"@G @ ;  @ @N @ EX @ G %@׋S  +@!׋R 0@ Xސ@@@@ؠ,add_cancel_r @ \ K ;ޠՠxq LE6zi}ojYK@VHW V@ U [@  `@  g@  m@c׋Q s@i׋ x@ &@@#@@ ,add_shuffle0 @    & \U~ؠ ҠŠ@I @  @ ޚ @  @  @׋ @׋g橚 @׋ @׋W@@o@@l,add_shuffle1 @  ߠ Ϡ r i  D=٠ʠ$@J뚠 @ 隠 @ * @ !!q @ ( @ ( @׋ @׋𩚠 @׋A @ ׋ @׋© "@׋@@@@ʠ,add_shuffle2 @ N = - Р Ǡ j c >7(l[|oa\K=@HKI H@ uG M@ z R@ ^ W@  \@  b@X׋ h@^׋\ m@c׋ r@h׋ x@n׋ ~@t׋,@@)@@&,add_shuffle3 @    , # Ơ  b [ޠȠؠˠ@L @  @ 䚠 @  @  @׋ @׋ @׋󩚠 @׋]@@u@@r'sub_1_r @   ՠ x o     J CߠР*$ @M񚠐 @  @  @צI) @נ# @\]@@@@'mul_0_r @ 1     M F    ~ !  eO>_RD@]@) (@ U -@ U 3@ם݀a 8@W <@W@@@@AA@@A@*mul_succ_r @ k Z J     #    [ T Ex~@Ac b@ a g@  l@  r@[ם݀ x@HЩ }@s׋ @lם݀@@.@@G(mul_comm @    1 ( ˠ Ġ g `     ͠ݠР@B @  @  @  @ם݀婚 @ם݀@@f@@/mul_add_distr_r @  ֠ Ơ i `     ; 4 נ Р   @Cߚ @ ݚ @  @  @  @ם݀ @׋& @׋ @ם݀ @ם݀8@@@@͠/mul_add_distr_l @ 5 $    Q J     %   i S BcVH@aD- ,@ Y+ 1@ ^l 6@ c ;@ c A@ *ם݀% G@ =׋v L@ B׋ R@ ;ם݀ W@ @ם݀@@@@)mul_assoc @  r b     ; 4 נ Р s l ]   @E{ z@ y @  @  @  @ xם݀s @ ~ם݀ĩ @ ם݀ @ ם݀N͐@@K@@d'mul_1_l @ ̠   N E    }        ٠@FĚ @  @  @ ם݀ @ נ#@@~@@'mul_1_r @   ޠ  x     S L   ٠ 3  - @+G @ # @ # @ ם݀/ @ נ#3@@@@ʠ,mul_shuffle0 @ 2 !    N G     "   f P ?`SE@^H* )@ V( .@ [i 3@ ` 8@ ` >@ 'ם݀ D@ -ם݀q I@ 2ם݀ O@ 8ם݀}@@@@,mul_shuffle1 @ { j Z     3 , Ϡ Ƞ k d U   @Is r@ q w@  |@  @  @  @ uם݀ @ {ם݀ @ ם݀Ʃ @ ם݀ @ ם݀G @ ם݀:@@R@@k,mul_shuffle2 @ Ӡ    U L     '  à     @J˚ @ ɚ @   @ @ @ @ ם݀ @ ם݀ީ @ ם݀  @ ם݀ @ ם݀ @ ם݀@@@@à,mul_shuffle3 @+    G @  ܠ  x    _ I 8YL>@WK #"@O !'@Tb,@Y1@Y7@ ם݀ =@ &ם݀ lB@ +ם݀ qH@ 1ם݀ې@@@@ %le_wd @tcS     , % Ƞ  d ] N   @@A&NZBase'NZOrder&NatInt'Numbers#Coq@ + )@A@'NZOrder&NatInt'Numbers#Coq@+NZOrderProp : 8@A@@@@"NZ / .@A@@@@@@,@@@7@)@A@ ꚠ@ v@@Z@@AA@@A@*lt_le_incl @ޠ͠`W     2 + Π Ǡ    j]O@hA ֚@ Ԛ@@@"lt @ v @@@@@7'le_refl @.' ʠ à f _    F 0 @B  @6@ v < <@@ 3@@`.lt_succ_diag_r @;*WP     + $  o Y HǠ@C 32@_7@W e=@  @@@@@.le_succ_diag_r @iXH~!   Y R C   v@D a`@e@ ev k@ ; Ð@@@@@/neq_succ_diag_l @vOH     q ˠ  #@!E @ @@ k  Ȑ@@ @@젠/neq_succ_diag_r @ǠI@ܠx      ԠSF8@QF @ @ 󩚠@  #@@@@@/nlt_succ_diag_l @֠yp KD   Ѡ +  vh@G @ 吩@@  S (@@@@@L/nle_succ_diag_l @'C<ߠؠ{t [ E 4@H @K %@ %v+@   X@@@@@|)le_succ_l @WF6٠РslG@1  u d֠@I ON@{ MS@ Z@ Zv`@ 0  e@ @@ @@+le_gt_cases @p IBޠzk Š  @J @ @ @"or @@ v ɩ@ Ɛ@@ J@@-lt_trichotomy @ˠMD|   ؠWJ<@UK Ú@ @:@ A@ @ @@@@@+(lt_asymm @"ZS:$w@L @* @/@@( 7 @/ @@ a@@`(lt_trans @;*WP+$oYHǠ@M 32@_ 17@dr<@i@B@b @H@h M@m  1@@ @@(le_trans @ziY2+ΠǠjcT@N rq@ pv@{@@@v /@@v 5@v?@@ 7@@ݠ+lt_strorder @:1Ԡ͠pi ֠ŠD7)@BO@+StrictOrder.[@@@@@ @@ +le_preorder @ՠŠh_:3֠ϠreW@pP!@(PreOrder@@@v@@ @@9/le_partialorder @0)̠ŠhaH2!@QN@,PartialOrder5͛К@>@=@<%耚@vr@b.w@@@ s@A @G@HAhCm@ABC@@y)lt_compat @l@%lt_wdYH8۠Ҡun IB3@ ڰ@L@y@Q@~  W@@\@ `@ f@ j@ n@@    @@%lt_wd']ɠ{TMvР( @@@@@ޠ(lt_total @@3v䀠B9ܠՠxq @ @ @)@ 0@ 󩚠@ 𐑠[R@,aǠѠtkF?̠۠&~qc@@@@@4'le_lteq @'@+lt_eq_cases*Ȁ0)̠Šha@@2 @7J@v@@8G@EL@+lt_eq_cases&yE4$ǠaZ5.ycRѠĠ@@@@@0Private_OrderTacA'IsTotal Am @up_O(!Ġ`YJ@@+Equivalence~@h@l@@(eq_equiv7Ls LE}nȠ @@@@@֠ @@;{6-Рɠle@@@@,Q^ѠSJ%ޠ]PB@@@@@ @4@e Рsj E>ڠ@ r@@@@  q@@@! @  @+ @*A@&+ G@ܠx_I8@@@@@m @@/C0K:*͠Ġg`;4%@=<@i;A@nH@hwO@w~T@t{yhX1*͠ƠibS@@@@@ @@YxQJs@@@Ϡ@vũ @̩@ѐǠI@ܠxԠSF8@@@@@ @@@@͐@#TacA @ܠ̠of A:ݠ֠Ǡ! yl^@@D!P)OrdersTac*Structures#Coq@q@@@A@@C!Ot@@&@{@!t&J@@A@A&a@@"eq&a^@@A@&@ @"le&ڠh@@A@AB&@@"lt&h@@A@&̌@@#one&̌T@@A@A&̔I@@#two&̔IT@@A@&H@@$pred&Hd@@A@&؝[@"@$succ&؝[r@@A@&C@'@$zero&CT@@A@ABCDE@A@G,MakeOrderTacBo?@A@@@BONR@@@A@@AEUH@@@N@!tJ@@A@A$:@@"eq$:^@@A@$@ @"le$h@@A@$@@"lt$ h@@A@ABC@A@+*OrderFacts.#@A@@s@\@a@S@@@@AA@@A@~ @~nG@ܠxià]VP5@A՚@@v@@@@0)lt_irrefl @?6٠Ҡun ۠ʠI<.Р~c@B@@@@@@`ؐ @۠ˠne@9ܠՠƠ  xk]@C2@0@@@#@!ݐ@@@@*le_antisym @%A:ݠ֠yrYC28(@9Dk"@Oi'@T@-@-v\@3@3v8@` ,@@\@@נ[ @cRBܠxSL=pԠvf1*$ @wE`@e@@]m@dt@X@@@@@*interp_ord @!o)OrdersTac@#ordȠ@ @@@@@@@@@@@D@@ @@ 5Ȱ@ @ @ ʠ@,*@@@@O +k= R'6'6'6''+k+7T'+7T'6'ࠒAΠޠݠ@@"lt\ @@"eq8L@lР@VȠ@@SRQ@@A@B@A@xA܀ ' à_X?)|٠Ҡ̠@@@@@%trans @. JCߠ{bL;A1@BF"o'x/@\v4@a9@f@@)ܛހ%p@@)ܛހ @)ܛހ@)trans_ord-0uG=@@@@ @ a4@h МAVtMF~o@Ϛ@͚@F@@@D@@J@T L+k() LL7#'Y@$tѠSJ%ޠ ] P BԠw@@@@@gz @  nМVCڠ}tOH@5@3@@#@@v@@v@v L+k() NN7#'ft3"OH# gQ@   F6@@@@@ɠ @n{opМBih]L<ߠ֠yrMF7@N@{S@X@@^@ ~ @d@ i@  L+k() MM7#'ȐttMF~oɠ !  c\V;@@@@@++le_lt_trans @ѷҷSө3c~Ƞ?6٠Ҡun @@@n@@@vl@@ r@ | L+k() MN7#'(tԠwn IBޠϠ)  t fà@@@@@+lt_le_trans @D1>23%)( 92ՠΠqj @W@;U@@Κ@E@@ >̶@$@$vҩ)@ Iܐ L+k() NM7#'tUD4נΠqj E>/sb  Ԡ ƠhX#@@@@@렠%eq_lt @#>}l\5.ѠʠmfW@n@s@.x@@~@,@@ 2@ < L+k() ML7#'t7.Ѡʠmf Ӡ  A 4 &Ƞ|v[@@@@@K%lt_eq @sSKݠ̠_V1*͠Ơ@@@@@@ @@ @  L+k() LM7#'Ht1*͠ƠibI3"   (ܠ֠@@@@@%eq_le @dQ^RSEIH=,YR-&@w.@[u3@`8@e@>@f@D@Dv򩚠I@Iv L+k() NL7#'tudT-&ɠ e^O   xC<6@@@@@ %le_eq @3 ^|UNw@ך@՚@N@@@vL@@R@v \ L+k() LN7#'tՠĠWN)"Š  a T Fؠ{@@@@@k&eq_neq @נzq LEҠ,  w i Ơ@ G>@"<@'@,@@-@ @5@< ǐ@@@@@&neq_eq @@/ \U0)t^M ̠  SC@TH=@jB@oG@t@?O@w@U@}L\@ @@@@@*not_neq_eq @wg @9ܠՠxqb   VOI.@IΚ@̚@@@é@G@@@@8)not_ge_lt @ŠG>ڠ}vҠ Q D 6ؠȠk@J @ @@@v@ @@@@s)not_gt_le @ߠyTMڠ4    qΠǠ@KF@*D@/@ @ *1@v@@@@@)le_neq_lt @;*WP+$oYH Ǡ  N> @OL8@e=@j@C@Cvr@;K@sP@ pD@@@@@@@@@e@@@@@g@<_neq @o_81Ԡ͠piZ   @ Rxw@v|@@@ y@7@@@@@ ڠ&le_neq @7.Ѡʠmf Ӡ A4&@?S@@񠩚@ 穛@#andЖw@@v@@@@@@*eq_le_incl @נzq LEҠ,wi@T𚠐@@!@@")@v@@@@@P(lt_stepl @+ G@ܠx_I8@Uk"@Oi'@T⚠,@Y@2@R@8@`ݩ=@]ې@@@@@(lt_stepr @iXH~!YRCv@V`@e@ j@@p@@v@${@ .@@@@@̠(le_stepl @) à_X۠Š3&@1W皠@嚠@^@@@v\@@Y@vW@@@@@ (le_stepr @ԠĠg^92ՠΠqdV@oX%@ #@@@@v@@@v @@@@@Hk @">7ڠӠvo V@/@Y@F@KY#@P@)@)v׶@/@Oݩ4@T @@@@@H @_N>ؠ{tOH9}lޠ@ZWV@U[@`@@f@@l@lvq@ $@@@@@ +le_antisymm @|UNwѠ)@'[@@@@vζ@@v@@@@@@)le_succ_r @֠ŠXO*#Ơ bUG@`\Κ@̚@@v@7R@v@@I@@@@@B)lt_succ_l @ 92ՠΠqj Q;*@]@A@F@@?%@R*@Jؐ@@@@@{,le_le_succ_r @VE5ؠϠrkF?0tcՠ@^NM@zLR@@X@Xv]@]vAc@3@@@@@,lt_lt_succ_r @~nG@ܠxià@_@@@@@z@l@@@@@,succ_lt_mono @ȠJAݠyՠTG9@R`@@@@@4@3@@@@@,,succ_le_mono @ #[T;%x@a@ + @ 0C @ v9 @v @s @r@@@@@k<_0_1 @ F 5 %Ƞb[6/ zdSҠŠ@b =@] B@ W F@)נ#@@@@&le_0_1 @ r a Q*#Ơb[L@c i@iv n@9W r@Uנ#@@@@@à<_1_2 @   }  VOxҠ*@(d @ @}נ# @wק倐@@@@<_0_2 @ ʠ   L Cߠ{נVI;@Te @ @W @ק倐@@@@&le_0_2 @   ՠ x o  JCߠР*ug@f @v @W @ק倐@@@@@G<_1_l @!"!!   > 7ڠӠvo V@/@g!@!F!@!K@!$@D!)@WW@!/@Oݩ!4@T!9@נ#@@@@@_@ABC@@+lt_ge_cases @!h!W!G    }  XQBu@h`!_@!^!d@!נ!k@!p@pv@@@@@+le_ge_cases @!!!{!!   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R*-/w@/O/}@/*/@/*/@/Ϡ/@ */@,v*w@@G@@ 䠠-add_lt_mono_l @////A/8.۠.Ԡ.w.p.. ---,,ݠ,@,@*/@/*/@/&󚠐/@/*/@ *r/@ /@,׋&/@,׋*@@(@@AA@@A@-add_lt_mono_r @0////|//...W.P---ݠ-7-!-@- A*/@0$*/@0)'70@0.+A0@!(*0 @!-0@- ׋&0@-׋+G@@(@@D+add_lt_mono @0D030#/Ơ//`/Y.....4.-.-x-b-Q@-MB+908@0e+70=@0j'x0B@0o&N0G@0t@0M@!m&A@0S@!s+0X@!x0^@-T׋)+0d@-Z׋@@@@@-add_le_mono_l @000o00 ///H/A..ݠ..y.j-Ġ--@-C+0@0+0@0'Ě0@0+Π0@-v+C0@-v0@-׋'{0@-׋+̐@@)P@@Ѡ-add_le_mono_r @0Ѡ000S0J/////%/....--@-D+ƚ0@0+Ě0@0(0@0,0@-v+0@-v0@-׋'t0@-׋,@@)@@+add_le_mono @110000.0'/ʠ/à/f/_/...F.0.@.E,1@13,1 @18(F1@1='1@1B@1@.v'@1!@.!v+ϩ1&@.&v1,@."׋Ω11@.'׋@@@@@].add_lt_le_mono @1]1L1<0ߠ0֠0y0r00///M/F/7..{.j@.fF,R1Q@1~,P1V@1(1[@1'g1`@1@1f@"'Z@1l@.lv,1q@"1w@.m׋1|@.r׋ /@@@@@.add_le_lt_mono @1111*1!0Ġ00`0Y/////.ܠ.Ơ.@.G,1@1,1@1(ܚ1@1'1@1@1@.v'@1@",e1@"1@.׋d1@.׋ z@@@@@+add_pos_pos @111Ҡ1u1l11000G0@//ܠ/͠/'//@.H,蚠1@2,暠1@2@1@#1@.W-%@1@#2@.W-02@#'2 @.W2@/׋(@@@@=.add_pos_nonneg @2=2,2111Y1R00000-0&0/q/[/J@/FI-221@2^-026@2c@2<@#\2A@/ W-o@2G@/Gv2L@/W-z2Q@#q2V@/!W2[@/Q׋(O@@"@@.add_nonneg_pos @22v2f2 2111?180۠0Ԡ0w0p0a///@/J-|2{@2-z2@2@2@/v2@/VW-@2@#2@/aW-ĩ2@#2@/kW2@/׋(@@l@@Ѡ1add_nonneg_nonneg @2Ѡ222S2J11111%10000//@/K-ƚ2@2-Ě2@2@2@/v2@/W.@2@/v2@/W.2@/v2@/W2@/׋(@@@@,lt_add_pos_l @33 22227201Ӡ1̠1o1h1 100O090(@0$L.3@3<.3@3A@3@$:3@/W.M3$@$D.S3*@0 ׋-ؐ@@@-{@/O@AB@@X,lt_add_pos_r @3X3G372ڠ2Ѡ2t2m22 111H1A1200v0e@0aM.M3L@3y.K3Q@3~@3W@$w3\@0'W.3a@$.3g@0]׋.K@@-@@,le_lt_add_lt @333r33 222K2D1111|1m0Ǡ00@0N.3@3.3@3*ǚ3@3)3@3@3@0v)@3@$3@0׋.F3@0׋.-3@$)@@@@@ߠ,lt_le_add_lt @3ߠ3Π33a3X2222232,1Ϡ1Ƞ1100@0O.Ԛ3@4.Қ3@4+3@4 )隠3@4@3@%)ܶ@3@0v3@0׋.3@0׋L3@%)@@@@@*,le_le_add_le @4*44 333F3?22۠2~2w2221^1H17@13P/4@4K/4#@4P+^4(@4U*44-@4Z@43@13v*'@49@19v4?@15׋.ݩ4D@1:׋4I@1Iv*=@@@@@u,add_lt_cases @4u4d4T33333-3&2ɠ2 2e2^2O111@1~Q/j4i@4/h4n@4+4s@4*4x@4@4~@%4@1z׋*x4@1׋/#4@%#C4@%/:@@@@@,add_le_cases @4444C4:3ݠ3֠3y3r3322211ߠ1@1R/4@4/4@4+4@4*˚4@4@4@1v4@1׋*ĩ4@1׋0$H4@1v#4@1v/@@@@@ -add_neg_cases @5 44444)4"3Š33a3Z2222A2+2@2S05@5.05@53@5 @&,5@2׋0A5@1W$5@&=05"@1W5'@&G0V5,@1W@@/~@@X-add_pos_cases @5X5G574ڠ4Ѡ4t4m44 333H3A3222v2e@2aT0M5L@5y0K5Q@5~@5W@&w5\@2'W5a@2W׋0$Ԡ5h@&5m@28W0P5r@&5w@2BW0@@>@@0add_nonpos_cases @5555%5444[4T33333}2נ22@2U05@505@5@5@2v5@2׋0ך5@2wW%5@2v05@2W5@2v0욠5@2W@@0@@0add_nonneg_cases @55ݠ5͠5p5g5 5444B4;3ޠ3נ3Ƞ3"3 2@2V0㚠5@60ᚠ5@6@5@2v5@2W5@2׋1&%j5@2v6@2W0橚6@3v6 @2W1;@@@@9-le_exists_sub @696(6555U5N44444)4"43m3W3F@3BW1.6-@6Z1,62@6_@68@38v1g̠6>@6k-y6C@6p6J@6r1.6P@3F׋ ~6U@3Uv6Z@3%W1@@@0@A0@2@A2AA@@0k@ABCD@@+mul_lt_pred @66~6n66555G5@44ܠ44x4i3@4g@-6@6,6@616@616@6@6@66@3l1A11ݠ6@'6@3ם݀%]6@3ם݀01ީ6@'6@3׋6@3ם݀,1署6@3׋6@3ם݀1q1@@/w@@AA@@A@1mul_lt_mono_pos_l @666ڠ6}6t66555O5H444ՠ4/@4A.#6@71󚠐6@71񚠐6@7$@6@(7@3W12B7 @()17@(.7@3ם݀-7@4ם݀1@@@1k@A1h@1@3@@@ABCD@@R1mul_lt_mono_pos_r @7J797)6̠6à6f6_65555:535$4~@5"B.r7<@7i2B7A@7n2@7F@7s@7L@(l7Q@4W2427X@(x27]@(}7c@4Lם݀27h@4Qם݀22@@0@@1mul_lt_mono_neg_l @777t77666M6F5555~5o4@5mC.7@727@727@7@7@(2{7@4gW2ܠ7@(2Q7@(7@4ם݀2S7@4ם݀-@@@@砠1mul_lt_mono_neg_r @7ߠ7Π77a7X6666636,5Ϡ5Ƞ55@5D/7@72ך7@82՚7@8@7@)27@$zeroW3'7@"lt27@7@#mulם݀8@ם݀2@@0@@44mul_le_mono_nonneg_l @8,88 777H7A66ݠ66y6665`@6E38@8K38#@8P/^8(@8U@8.@5.v83@4W3`@89@59v.-8>@5>v8D@5-ם݀3(18J@53ם݀2@@2@@~4mul_le_mono_nonpos_l @8v8e8U77777.7'6ʠ6à6f6_6P5@6NF3i8h@83g8m@8/8r@8@8x@5xv38}@5HW@8@5v.w8@5v8@5wם݀3,8@5|ם݀O@@2@@Ǡ4mul_le_mono_nonneg_r @8888A887۠7Ԡ7w7p77 6665@6G38@838@8/񚠐8@8@8@5v8@5W3@8@5v.8@5v8@5ם݀'8@5ם݀.А@@3.@@4mul_le_mono_nonpos_r @988888$8777\7U6666<@6H38@9'38@9,0:9@91@9 @6 v489@5W@9@6v/ 9@6v9 @6 ם݀/9%@6ם݀'ؐ@@3w@@Y,mul_cancel_l @9Q9@908Ӡ8ʠ8m8f8 8777A7:7+6@7)I4D9C@9p4B9H@9u09M@9z@4E9U@9}49Z@6%W49a@99g@6Pם݀9l@6Uם݀4P9q@9/e@@@3@5@3|@ABC@@,mul_cancel_r @9999"9888X8Q77777z6@7xJ49@949@90Қ9@9@49@94Қ9@6tW4頩9@99@6ם݀4[9@6ם݀4i9@9/@@2k@@(mul_id_l @99۠9ˠ9n9e99888@897ܠ7ՠ7Ơ7 @7K4ߚ9@: 4ݚ9@:@4ې9@:59@6W509@:9@6ם݀45+:@:*4暠:@6נ#@@4@@;(mul_id_r @:3:":999O9H88888#88 7g@8 L5&:%@:R5$:*@:W@5":2@:Z5a:7@7W5w:>@:f:D@7-ם݀45':I@:q5x:N@71נ#@@2@@1mul_le_mono_pos_l @:z:i:Y9999929+8Π8Ǡ8j8c8T7@8RM5m:l@:5k:q@:1:v@:@:|@+:@7LW55:@7v0|:@7v:@7|ם݀+:@7ם݀5|@@4@@̠1mul_le_mono_pos_r @:Ġ:::F:=99٠9|9u998887@8N5:@:5:@:1:@:@:@+:@7W56 :@7v0Ʃ:@7v:@7ם݀5:@7ם݀5@@3@@1mul_le_mono_neg_l @;:::::*:#9Ơ99b9[8888B@8O6;@;-5;@;22@; @;7@;@,06>;@7W6U;@8v1;!@8!v;'@8ם݀6 ;,@8ם݀Đ@@@@`1mul_le_mono_neg_r @;X;G;7:ڠ:Ѡ:t:m:: 999H9A928@90P6K;J@;w6I;O@;|2;T@;@;Z@,z6;_@8*W6;f@8fv1Z;k@8kv;q@8Zם݀6;v@8_ם݀6@@4!@@2mul_lt_mono_nonneg @;;;;$;:::Z:S99999|8@9zQ6;@;6;@;2Ԛ;@;1;@;@;@8v;@8yW6R@;@,56Y@;@8v;@8W6d@;@,;@,;@8ם݀)5-;@8ם݀$5A@@@@@ 2mul_le_mono_nonneg @<;;;;}; ;:::X:Q999ޠ98@9R6;@<#6;@<(36<@<-2 <@<2@< @9 v<@8W6@<@9vb@<@9v>====0=)<̠<Š@>39> @>8@>@/1>@:W9C9V>@/=>"@:W>'@;ם݀8թ>,@/L>1@:W9@@ @@e3mul_nonneg_cancel_l @>]>L><=ߠ=֠=y=r==<<O@>|9N>T@>@>Z@/z>_@;*W99>f@;fv>k@;6W>p@;Yם݀9>u@;uv>z@;EW9@@ P@@3mul_nonneg_cancel_r @>>>>(>= ==^=W<<<<<;@<~[9>@>9>@>@>@/>@;sW9թ9蠩>@;v>@;W>@;ם݀9g>@;v>@;W9@@ @@,lt_1_mul_pos @>>ޠ>Π>q>h> >===C=<<ߠ<ؠ<ɠ<#@<\9⚠>@?9>@?@>@0 >@;נ#:@>@0>@;W:*?@0!?@;נ#? @;ם݀4@@@@?(eq_mul_0 @?7?&?>>>S>L====='= =>>>9>2=ՠ=Π=q=j=[<@=Y^:t?s@?:r?x@?:" :s?@?:?@>>>>%>====@=_:Ě?@?;?@??@<ם݀0š?@<W?@@;?@<W@@@@@ *eq_mul_0_l @@ ?????&?> >>^>W====>@=`:?@@):@@@.@@@@/@ @<ם݀;<@@<W@; @@@A;H@@<W@#@@K:Ț@(@<W@@@@@ \*eq_mul_0_r @@T@C@3?֠?͠?p?i? ?>>>D>=>.=@>,a;G@F@@s;E@K@@x@@Q@@y@W@=@ם݀;@[@=&W@;S@c@@;G@h@=3W@m@@;Q@r@==W@@@@@ (mul_eq_0 @-@pĈ@@@@$@???Z?S>>>>>|@;@@@;@@@;ؠ@@@@@=ם݀;Ԛ@@=tW0@@@;ߚ@@=W@@@;蚠@@=W>>>>@>@^\@@۠@ˠ@n@e@@???@?9>ܠ>ՠ>Ơ> @@@@@ *mul_eq_0_l @.K@0*A@@@@@$@???\?U>>>@;@@A&;@@A+@A@A,A @=ם݀<9A@=W@<A@A>@@@@@ l*mul_eq_0_r @.@0*AhAWAG@@@@}@ @???X?Q?B@Sם݀<An@>9W@FWA@APW@]24pkAAAA.A%@Ƞ@@d@]@????>@@@@@ ̠(lt_0_mul @AĠAAAFA=@@٠@|@u@@???>@?b<A@A<A@A<A@2A@>WA@>ם݀<1?%A@2A@>W=A@2A@>W=%,A@3 =A@>WA@3=$A@>W@@W=V@B.@3N<ܩB3@3SB9@?"ם݀<<ީB?@?(ם݀=#=#@@@@@ t5square_le_mono_nonneg @BlB[BKAAAAA$A@@@\@U@F?@@Dd=_B^@B=]Bc@B@Bi@?ivBn@?9W=@Bt@?tv="By@?yvB@?hם݀FB@?mם݀E@@@@@ 6square_lt_simpl_nonneg @BBBB2B)A̠AŠAhAaA@@@@?@@e=B@B=B@B@B@?vB@?}W=߶@B@3B@?ם݀B@?ם݀==򩚠B@38@@@@@ 6square_le_simpl_nonneg @BBBԠBwBnBB AAAIAB@@ޠ@Ϡ@)@@f=蚠B@C=暠B@C@B@?vB@?W>$@B@?vC@?ם݀ĩC@?ם݀EC @@ v9@@@@@ A,mul_2_mono_l @C9C(CBBBUBNAAAAA)A"A@m@Ag>,C+@CX>*C0@C]@C6@4V>eC;@4[CA@@7׋CF@@)נ#CK@@4ם݀CP@@)ק>3CU@@>ם݀CZ@@3ק>@@<@@ *add_le_mul @CCuCeCBBBB>B7AڠAӠAvAoA`@@A^h!aCz@C!bC@C@C@4C@@oנ#>@C@4C@@zנ#>ũC@@vC@@׋9C@@ם݀9@@=@@ ۠-square_nonneg @CӠC CCUCLBBBBB'B AàAAA@AiMC@CC@@vC@@WC@@ם݀4Ɛ@@"@@ 5crossmul_le_addsquare @DCCߠCCyCCBBBTBMAAAڠA4@AjzC@DxC@D$@C@@vD@@W?0@D@AvD @@W?;D@AvD@A׋D@Aם݀>D#@A ם݀:D(@A׋D.@Aם݀D3@Aם݀@@@@ g-add_square_le @D_DND>CCؠC{CtCCBBBOBHB9A@B7kٚDQ@D~ךDV@D@D\@A\vDa@A,W?@Dg@AgvDl@A7W?Dq@AqvDw@Am׋D}@Afם݀DD@Akם݀CD@Apם݀D@A׋:D@A׋:@@>@@ Ơ-square_add_le @DDDD@D7CڠCӠCvCoCC BBBA@Bl8D@D6D@D@D@AvD@AW?@D@AvD@AW?D@AvD@Aם݀D@A׋:ЩD@A׋:թD@Aם݀D@Aק倩D@A׋D@Aם݀D@Aם݀@@?M@@/4quadmul_le_squareadd @E'EEDDDCD<CߠCؠC{CtCCCB[@BmE@EFE@EK@E$@B$vE)@AW@W@E/@B/vE4@AW@bE9@B9vE?@B(ם݀EE@B.ם݀EK@B4ם݀EP@B)ק倚ET@B-ק?@7EY@BBם݀E_@BU׋;SEd@BZ׋;X@@?@@(pred_inj @EEEoEE DDDHDACCݠC@C@!nE@!t!mE@@E@"eqE@$pred\BE@\AE@CB@@@ 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