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U@ ယ#@ ]'@1H@9@)SymmetricFgq2@1 ယ6@0 ]TL @-. U\D{VOܠiXok@@b@@X(eq_trans @{@6Equivalence_TransitiveWt@s ယx@r ]|@q1H@@*Transitive++-@ ယ@ ]pcTYLu@-W\[DUE6٠РslG@1֠XGĠ@@@@*eq_sym_iff @tdU.'ʠàf_Pݠ̠wf@b@!x@ ံ!y@ ဩ%Logic$Init@#iffС)@ ]BA@ ]@@@@AA@@A@'neq_sym @@7ڠӠvo =%@A!n @ ံ!m'@& ံ@I@#notШ4@. ]D ;@5 ]KC@@@@@D(eq_stepl @ޠxSL٠~fU@B_@^ ံd@c ံ!zk@j ံ@q@k ]CB@z@t ]D@{ ]D@@@Aۓό^)Morphisms@@AB@@(succ_inj @J:+ΠŠha<5&ˠM<@8C"n1@ ံ"n2@ ံ@@ ]@p!Wѩ@v!W֩@ ]\@@@AviAK@AAۀߠKN@R@@ABC@@ޠ+succ_inj_wd @xQJs@DM@ ံK@ ဩ@ ] @!WJ@!WI@ ]%@@@G@A8ӠA4Relation_Definitions)Relations)@AB@@%/succ_inj_wd_neg @ޠΠbY4-Рɠ_G6@E"@@? ံ E@D ဩfN@H ]T@!WY@!W1`@Z ]p@@@@@g1central_induction @ >7ڠӠvo x#@F!A@@ နA$A_wd@&ProperL@@  @*respectful%WO?@ @ ]B@ ံ@q@@ ဩԠE@m!W@ ဩF@@@@@̠'add_0_r @uf ?8۠Ԡwpaݠ@@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@,@$zero,筷T@@A@ABCDE@A@E@Fd@c ဩi@c ]o@D n~t@!9}@@@@@y@ABC@@AA@@A@*add_succ_r @:*XQ,%v@A@ ံ@ ဩ@ ]@ n@e!W署@j!W@ nѐ@@M@@J-add_succ_comm @qb;4נРsl]٠ܠˠ@Bɚ@ ံǚ@ ဩ@ ]@ n@!W< @ n@!WA@@@@(add_comm @ȠLCߠ{I1 C6(#@C.@- ံ3@2 ဩ8@2 ]>@ nNC@ nK@@@@̠'add_1_l @~!YRߠl[~qc^M?@JDKi@h ဩn@h ]t@I ny@; ~@-!W@@ @@'add_1_r @>. \U0)z@E@ ဩ@ ]@ n@v @h!W@@E@@B)add_assoc @yiZ3,ϠȠkdUѠ٠Ԡà@F@ ံ@ ံ!p@ ဩ@ ]@ n@ n  @ n @ n@@@@,add_cancel_l @ǠKBޠzH0B5'"@G -@ , ံ  2@ 1 ံN 7@ 6 ဩX >@ 8 ] D@ nS  J@ nR O@ I ]ސ@@@@ؠ,add_cancel_r @ -&ɠ e^xg}ojYK@VHW u@ t ံU z@ y ံ @ ~ ဩ @  ] @a nQ @g n @  ]&@@#@@ ,add_shuffle0 @ W G 8۠Ҡun IB3ؠҠŠ@I @  ံ @  ံޚ @  ဩ @  ] @ n @ ng橚 @ n @ nW@@o@@l,add_shuffle1 @    ' ]V$ @J뚠 @  ံ隠 @  ံ* @  ံ!q @  ဩ @  ] %@ n +@ n𩚠 1@ nA 6@  n <@ n© A@ n@@@@ʠ,add_shuffle2 @     |  WPݠjY|oa\K=@HKI g@ f ံG l@ k ံ q@ p ံ^ v@ u ဩ {@ u ] @V n @\ n\ @a n @f n @l n @r n,@@)@@&,add_shuffle3 @ ] M >  ؠ { t  OH9ޠƠؠˠ@L @  ံ @  ံ䚠 @  ဩ @  ] @ n @ n @ n󩚠 @ n]@@u@@r'sub_1_r @    - $ Ǡ  c \*$ @M񚠐 @  ဩ @  ] @ ) @  $@!>]@@@@'mul_0_r @  Ԡ Š h _     : 3֠ϠeM<_RD@]@) G@ F ဩ L@ F ] R@ =a W@!9} [@!9}@@@@AA@@A@*mul_succ_r @      < 5 ؠ Ѡ t m  v~@Ac @  ံa @  ဩ @  ] @Y = @F!WЩ @q n @j =@@.@@G(mul_comm @ b R C  ݠ  y     T M >ˠݠР@B @  ံ @  ဩ @  ] @ =婚 @ =@@f@@/mul_add_distr_r @   {     T M     v  @Cߚ @  ံݚ @  ံ @  ဩ @  ] @ = @ n& @ n #@ = (@ =8@@@@͠/mul_add_distr_l @  ؠ ɠ l c     > 7 ڠ Ӡ Ġ i Q @cVH@aD- K@ J ံ+ P@ O ံl U@ T ဩ Z@ T ] `@ ( =% f@ ; nv k@ @ n q@ 9 = v@ > =@@@@)mul_assoc @ 6 &    T M     ( !    @E{ @  ံy @  ံ @  ဩ @  ] @ v =s @ | =ĩ @  = @  =N͐@@K@@d'mul_1_l @  o `     9 2 ՠ Π q j [   נ@FĚ @  ဩ @  ] @  = @  @@~@@'mul_1_r @    6 - Р ɠ l e      3  - @+G @  ဩ @  ] @  =/ %@  3@@@@ʠ,mul_shuffle0 @  ՠ Ơ i `     ; 4 נ Р  f N =`SE@^H* H@ G ံ( M@ L ံi R@ Q ဩ W@ Q ] ]@ % = c@ + =q h@ 0 = n@ 6 =}@@@@,mul_shuffle1 @ .     L E    }      @Is @  ံq @  ံ @  ံ @  ဩ @  ] @ s = @ y = @ ~ =Ʃ @  = @  =G @  =:@@R@@k,mul_shuffle2 @  v g     @ 9 ܠ ՠ x q b   ޠ@J˚ @  ံɚ @  ံ  @  ံ @  ဩ @  ]@  = @  =ީ@  = @  =@  =@  =@@@@à,mul_shuffle3 @ ޠ Π  b Y     4 - Р ɠ  _ G 6YL>@WK #A@@ ံ !F@E ံbK@J ဩP@J ]V@  = \@ $ = la@ ) = qg@ / =ې@@@@ %le_wd @'   E >  ڠ } v      @@A&NZBase'NZOrder&NatInt'Numbers#Coq@ ) '@A@'NZOrder&NatInt'Numbers#Coq@+NZOrderProp 8 6@A@@@@"NZ - ,@A@@@@ ံ@@ ,@ ံ@@ 7@ ])@ A@ ] ꚠ@  ր@@Z@@AA@@A@*lt_le_incl @r    K D    | m   j]O@hA ֚@ ံ Ԛ@ ံ@@"lt  @  ր @@@@@7'le_refl @ŠI@  ܠ  x      F . @B (@' ဩ-@  ր < <@@ 1@@`.lt_succ_diag_r @ޠϠri    D =  ٠ ʠ o W FǠ@C 3Q@P ဩV@W 倠 e\@ !W @@@@@.le_succ_diag_r @ :3 ֠ Ϡ r k      t@D a@~ ဩ@ c ր @ 9!W Ð@@@@@/neq_succ_diag_l @J:+ΠŠha    < 5 & ˠ  #@!E @ ဩ @ ]@ i!W  Ȑ@@ @@젠/neq_succ_diag_r @zj[4- Р ɠ l e V   ҠSF8@QF @ ဩ @ ] 󩚠@ !W #@@@@@/nlt_succ_diag_l @.%Ƞd]     +  vh@G  @  ဩ 吩@ 倠@ !W S (@@@@@L/nle_succ_diag_l @ڠʠ^U0) ̠ Š  [ C 2@H =@< ဩ D@ # րJ@ !W  X@@@@@|)le_succ_l @ (!Ġ`Y     s b֠@I Om@l ံ Mr@q ဩ y@ X ր@ .!W  @  @@ @@+le_gt_cases @D4%Ƞb[6/  Š  @J @ ံ @ ဩ @"or @@  ր ɩ@  Ɛ@@ J@@-lt_trichotomy @~n_81Ԡ͠piZ   ֠WJ<@UK Ú@ ံ @ ဩ:@  A@ ] @  @@@@@+(lt_asymm @=4נРsl:"w@L @ ံ !@  ံ@'@(  7 .@/  @@ a@@`(lt_trans @ޠϠri D=٠ʠoWFǠ@M 3Q@P ံ 1V@U ံr[@Z ံ@a@b  @g@h  l@m 倠  1@@ @@(le_trans @-KD| @N r@ ံ p@ ံ@ ံ@@ ր /@@ ր 5@ ր?@@ 7@@ݠ+lt_strorder @k[L%]VGԠàD7)@BO@+StrictOrder.[@@ ယ@ 倐@@ @@ +le_preorder @zSLureW@pP @(PreOrder@@ ယ@ ր@@ @@9/le_partialorder @ǠKBޠzH0@Q7@,PartialOrder5͛К0@/ ယ4@. ]8@-1H<@ ր[@b62@@@ s@A @E@FAhCV@ABC@@y)lt_compat @U@%lt_wd!Sŀ@ ̰@]@\ ံ@b@a  ݩ h@g ံ@m@l  蚠q@k ] w@v  򚠐{@u ] @ 倐@@@%lt_wd']ɠA1"Š_X3,  @@@@@Р(lt_total @@1UҤ@ @ ံ @ ဩ @  ͩ@ ] ԩ@  ѐJ3@ aǠvg @9ܠՠxqbޠ_RD@@@@@'le_lteq @@+lt_eq_cases |@ ٚ@ ံ ך@ ဩ@ րW @  @  ]@+lt_eq_cases&yˠOF~!L4#@@@@@Z0Private_OrderTacLA'IsTotalT A1 @D@91H@W@+Equivalence~@P@O ယT@N ]@(eq_equiv7L.'ʠàf_yhܠ@@@@@ @@Y;@@ ယ@ 倐@,Q^?/ à]V1* @@@@@ΠU @@]0̀@ @@ ံ@@  0 @ ံ@@  ;@ ] -@  E@ ]@ 倐S{lE>ڠ}vg dWI@@@@@J @@R0Q@ܚ@ ံښ@ ဩS@ Z @ ]@ IˠOF~!L4#@@@@@ZE @P@M |a@:@9 ံ?@> ဩ`F@% րVM@N ]R@L ]bC )"ŠaZtcנ@@@@@@@@@F@#TacGA @1!OH#  @@D!P)OrdersTac*Structures#Coq@rk@@@A@@C!O@@&@ @!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@6 @  ဩ@  ]@@@@AA@@A@ @ӠàWN)"ŠT<+]VP5@Af<@; ဩA@  ր@@D@@0)lt_irrefl @|WPݠjYڠ͠Р~c@Bj@i ဩBq@r D@@t@@`g @0 NG"  @CÚ@ ံ@ ံ@@ ]@ ]n@@@@*le_antisym @iYJ#[TEҠB5'8(@9D@ ံ@ ံ@@ ր@@ ր@ ] @@@@נ @+"ŠaZ(sevf1*$ @wE:@ ံ8@ ံ@@ ]-$@ ]@@@@@*interp_ord @!o)OrdersTac3@#ordȠ@ @@@@@@@@@@@D@F@E ံ@K@J YP@J ]T@U 倚X@7 ր@*(@^@] ံ@c@b ސ +k= R'6'6'6''+k+7T'+7T'6'ࠒA̠ܠ۠@@"lt\ @@"eq8L@lР@TȠ@@QPO@@A@B@A@xA܀M=.ѠȠkd?8)Π&  נРʠ@@@@@%trans @p`Q*#Ơb[L٠ȠI<.?/@@F"o'@ ံ@ ံ~@ ံ@ @65ʛ:@@65ʛ @65ʛ@)trans_ord-0uGDR̐@@;@@ @@@ ့>@ ့ @ ဩB@rÌМA:9@Z0@/ ံX5@4 ံњ:@9 ံ@@@: ]϶@F@@ ]թK@E ]ߐ L+k() LL7#'S@$t-&ɠ e^xg۠͠ޠΠq@@@@@a @@ ့@ ့!@ ဩd"@ÌМbCY@Ě@ ံš@ ံ;@ ံ@@ ր9@@ ր?@ րI L+k() NN7#'jtueV/(ˠĠg`Qޠ͠ N A 3D4@@@@@Ǡ @@ ့@ ့@ ဩ@BÌМB  @*@ ံ(@ ံ @  ံ@@  @@  @   L+k() MM7#'Аt۠ˠ_V1*͠Ơ\D3   e^X=@@@@@-+le_lt_trans @wM@L ့uR@Q ့W@V ဩy1@Ìg#nm@d@c ံi@h ံn@m ံ@t@S ր@z@ {  @   L+k() MN7#'4t?/ à]V1*   ɠ @@@@@+lt_le_trans @ۚ@ ့ٚ@ ့R@ ဩS@ Ì1@򚠐@ ံ𚠐@ ံi@ ံ@@  g@@ րm@  w L+k() NM7#'t']V$  | o arb-& @@@@@%eq_lt @?@ ့=@ ့@ ဩA@qÌ/65@V,@+ ံT1@0 ံ͚6@5 ံ@<@6 ]˶@B@ C ѩG@ H ې L+k() ML7#'t%]Vp_  Ӡ Š֠Ơi@@@@@Y%lt_eq @y@x ့~@} ့@ ဩ]@ÌcO@@ ံ@ ံ1@ ံ@@  /@@ ]5@  ? L+k() LM7#'`tk[L%]VGԠà D 7 ):*@@@@@%eq_le @@ ့@ ့~@ ဩ @9Ì]@@ ံ@ ံ@ ံ@@ ]@ @ ր@ ր L+k() NL7#'ĐtϠSJ%P8'   YRL1@@@@@!%le_eq @kA@@ ့iF@E ့⚠K@J ဩm%@Ì+ba@X@W ံ]@\ ံb@a ံ@h@G ր@n@h ]s@R ր  L+k() LN7#'(t3#QJ%   @@@@@&eq_neq @VF7ڠѠtm HA2נ / " %٠Ӡ@&G隠@ ံ皠@ ံ`@ ံ@@ ]^@@ ]f@ ] r@@@@@͠&neq_eq @"XQz w j \m](!@nH1@ ံ/ @  ံ@ ံ@ꐩ@ ]@@ ]&@  ] @@@@@*not_neq_eq @֠Ǡja<5ؠѠ gO>   picH@IyO@N ံwT@S ံ@-/^@X ]nc@] ]@@@@R)not_ge_lt @#A:ݠ֠yr{   @J@ ံ@ ံ@j@x ր@  -@@@@)not_gt_le @^N?٠|uPI:ߠǠ 7 * -۠@.K񚠐@ ံ@ ံ@@  ܩ@ րh@@@@@Ƞ)le_neq_lt @zSLu r e WhX#@iL,@ ံ*@ ံ@ @ ր@搩@ ]@  @@@@@ @@@@M@@@@@M@<_neq @ޠΠbY4-Рɠ_G6   @ R#A@@ ံ!F@E ံ@L@ M \$S@M ]@@@@@ &le_neq @1*͠Ơib|k  ߠ @ SXv@u ံV{@z ဩ@  @#andЖw@@n րg@ ]@@@@@ Ƞ*eq_le_incl @VF7ڠѠtm HA2נ/"@-T@ ံ@ ံ@@ ]ԩ@ րX@@@@@ (lt_stepl @yj C<ߠؠ{te bUG@`U@ ံ@ ံ@ ံ@@  @@ ]@ @@@@@9(lt_stepr @ǠKBޠzH0@VT*@) ံR/@. ံ˚4@3 ံ@:@; ɶ@@@: ]ϩE@F  ِ@@@@@w(le_stepl @#[Tn]ޠѠ@Wh@g ံm@l ံ r@q ံ@x@W ր@~@x ]@b ր@@@@@(le_stepr @C3$ǠaZ5.Ġ@XК@ ံΚ@ ံG@ ံ@@ րE@@ ]K@ ր U@@@@@ @pa:3֠Ϡrk\ؠYL>@WYŚ@ ံÚ@ ံ@ ံ@@ ր@@ @  @@@@@0\ @A8۠Ԡwp >&{@Z @ ံ%@$ ံA*@) ံ@0@1 @6@ րũ;@<  ϐ@@@@@m+le_antisymm @ܠvQJנ|dSԠǠ@[@^@] ံ>c@b ံ@i@H րy@o@N ր4t@n ]I@@@@@)le_succ_r @4$RK& @ \y@ ံw@ ဩ@ ր@X!W @ ր@ ]ũ@j!W@@@@@)lt_succ_l @{k\5.ѠʠmfWӠTG9@R]@ ံ@ ံ@@ 倠@!W.@ @@@@@&,le_le_succ_r @8/Ҡˠng 5 r@^@ ံ@ ံ@"@ ր2'@ ր쩚-@!Wl@@@@@_,lt_lt_succ_r @ݠΠqh C<ߠؠɠnVEƠ@_2P@O ံ0U@T ံ@[@\ k`@a 倠%f@!W@@@@@,succ_lt_mono @&D=٠|u~@`k@ ံi@ ဩ@ @ 倠@O!Wߩ@T!Wސ@@@@@נ,succ_le_mono @eUF|WPAΠ>1#@ڠ}vD,@h!&@!% ံ!+@!* ဩ!2@3 B!7@ ր?@@@@@i+le_ge_cases @   ؠ { r  MFӠx`OРà@i<!Z@!Y ံ:!_@!^ ဩ!f@E րv!k@J րs@@@@@+lt_gt_cases @!+!!    I Bޠz@jp!@! ံn!@! ဩm!@! ]𠩚!@ !@ @@@@@ڠ,eq_decidable @!h!X!I     " ZSDѠA4&@?k!@! ံ!@! ဩ)Decidable!@)decidable r!@! ]@@@@@&eq_dne @!!!!$!   Z S|! yl^@wl嚠"@" ံ㚠"@" ဩ)␩䐩"@"  ]#"@" ](@@@@@J&le_ngt @!ؠ!Ƞ!!\!S     . 'ʠàYA0@m";@": ံ"@@"? ဩa"G@& րW"N@O V@@@@@&nlt_ge @"!!!!!,!% Ƞ  d ] wfڠ@nS"q@"p ံQ"v@"u ဩP"@ "@c ր@@@@@,lt_decidable @"D"4"%!Ƞ!!b![     6 / Š@o"@" ံ"@" ဩܐ"@ Ð@@@@@堠<_dne @"s"c"T!!!!!-!& ɠ   e ^ OܠˠL?1@Jp"@" ံ"@" ဩ"@ "@ @@@@@&nle_gt @""""/"&!ɠ! !e!^!     ,  wi@q𚠐#@#  ံ#@# ဩ4퐩#@ ր,#!@" )@@@@@S<_nge @""Ѡ" "e"\!!!!!7!0 Ӡ ̠  b J 9@r&#D@#C ံ$#I@#H ဩj#P@Q `(#W@ 6 ր_@@@@@,le_decidable @##""""5".!Ѡ!ʠ!m!f! !    o@s\#z@#y ံZ#@#~ ဩ#@ e ր@@@@@&le_dne @#F#6#'"ʠ""d"]"!!!!8!1!" Ǡ  @t#@# ံ#@# ဩϠ#@  րɩ#@  րΐ@@@@@*nlt_succ_r @#~#n#_#""""8"1!Ԡ!͠!p!i!Z   ֠WJ<@UuÚ#@# ံ#@# ဩ#@ 倠#@ !W4#@  @@@@@,5lt_exists_pred_strong @####>#5"ؠ"Ѡ"t"m"" !!!!;!#!x@v$@$ ံ$"@$! ံ$'@$& ံ@$-@. @$3@! րU@"ex @$?@$> ့!k$F@$E ဩĠ$M@$G ]ө$S@!!W$X@!7 րg@@@@A@@A _@ `AРD.Morphisms_Prop$p@ fA1@D@ABCD@@.lt_exists_pred @$'$$###E#>""ڠ"}"v"""!!!@w!$@$ ံq$@$ ံ@$@ b$@$ ့\$@$ ဩ$@$ ]l$@!\!W橚$@! ր@@@O@A@@堠,lt_succ_pred @$s$c$T#####-#&"ɠ" "e"^"O!!ܠ!ˠL?1@Jxm$@$ ံ$@$ ံ@$@ 񩚠$@$ ]$@!!W$@!!>1 @@@%@A"@q@ @@ABCD@@)&rs_rs' @$$$$;$2#ՠ#Π#q#j# #""""8" "u@y@%@% @%#@%" %)@%( %-@%' ] M ;ɚ%2@%1 ံ@@ %9@%8 ံ@%?@" ր@};%H@!!W  0%N@%M ံ@%T@"3 ր@ =%[@%Z ံ ;%`@%_ ံ@%f@"E ր` u@%m@n  2K'H)@@@@(rs'_rs'' @%1%!%$$$O$H######## """ @z@%@%  @%@% %@% %@% ]   C%@% ံ@ %@% ံ@%@" ր ȶ@ %@% ံ %@% ံ@%@" ր ٶ@%@  I  %@% ဩ  Ú%@% ံ %@% ံ@%@" ր"@%@  ! + ښ%@% ံ ؚ%@% ံ@&@" ր9@& @   8&@"!W H@@ B@@A%rbase @%Ϡ%%%S%J$$$$$%$####P#8#'@{@&3@&2  Ϛ&8@&7 ဩ! &>@&= ံ!&C@&B ံ@&I@#( ր@&O@P !| @@@@@)A'A_right @&%%%%%-%&$ɠ$ $e$^$####x#g۠@|@&s@&r !&x@&w ံ@!`&~@&} ဩ!f&@& ံ!d&@& ံ@&@#n ր@&@ !ZN ϶!}&@& ံ@&@# ր @@@@@Ԡ6strong_right_induction @&b&R&C%%ݠ%%y%%$$$T$M$>##ˠ#;. @9} C@&@&  A ? =@&@&  I 7&@&  O&@& ]!!!t&@& ံ@!Ś&@& ံ@&@# ր!@!Қ&@& ံ!К&@& ံ@&@# ր1@'@ !0!@.!蚠'@' ံ@' @# ր̐@@@!?@A!@#@@ABC@@B/right_induction @&Р&&&T&K%%%%%&%$ $$$Q$9$(@~ @'4@'3    @'<@';   'B@'A  'F@'@ ]"f"T!⚠'K@'J ံ@ @"4'R@'Q ံ@'X@$7 ր̶@S'`@$!W"G'e@'d ံ@'k@$J րԩe!@@@@@0right_induction' @','' &&&J&C%%ߠ%%{%%%$$$@! @'@' ! ! !@'@' !!'@' !'@' ]""">'@' ံ@"'@' ံ@'@$ ր"@"'@' ံ@'@$ ր3@'@$v!W"'@' ! @@#@@7strong_right_induction' @''|'m''&&&F&?%%۠%~%w%h% $$eXJ@c@!m@'@' !k!i!g@'@' !s!a'@' !y(@' ]#"#"(@( ံ@"( @(  ံ@(@$ ր#r@"(@( ံ@(@$ ր@#(&@(% ံ#(+@(* ံ@(1@% րٶ@(7@8 "J"x# (>@(= !{@@@@@p&ls_ls' @'''ߠ''y''&&&T&M%%%ڠ%%g%Vנʠ@A!߶@(b@(a !ݶ!۩!ٰ@(j@(i !!(p@(o !뚠(t@(n ]###(y@(x ံ@!ζ@#b(@( ံ@(@ B@!Đ(@%=!W"#u(@( ံ@(@%x ր##@#(@( ံ#(@( ံ@(@% ր#@(@% ր#BF(@%h!W"J@@@@렠(ls'_ls'' @(y(i(Z'''''3',&Ϡ&Ƞ&k&d&U%%%ѠRE7@PB"Z@(@( "X"V"T@(@( "`"N(@( "f(@( ]$##(@( ံ@#ܚ(@( ံ@)@% ր$@#隠)@) ံ#皠) @)  ံ@)@% ր$!"]@)@% ր#H)@%!W#^L$)$@)# ဩ$E$),@)+ ံ$ )1@)0 ံ@)7@& ր%@)=@& ր#l#v$%)C@)B ံ$#)H@)G ံ@)N@&- ր<@)T@&3 ր#)Z@& !W#@@Z@@%lbase @)) ((((8(1'Ԡ'͠'p'i' '&&&&r@C"@)~@)} "$)@) ဩ$k)@) ံ$i)@) ံ@)@&s ր P@)@&y ր$)ǐ)@&O!W#ِ@@@@@Ҡ(A'A_left @)`)P)A((۠(~(w(('''R'K'<&&ɠ&9,@7D#A@)@) #?$`)@) ံ@$)@) ဩ$)@) ံ$)@) ံ@)@& րG@)@& ր$uQ$$͚)@) ံ@)@& ր P@@%@@#5strong_left_induction @))))5),(Ϡ(Ƞ(k(d((''''2'' }o@E#@*@* ###@*@* ##*#@*" #*'@*! ]%G%5$Ú*,@*+ ံ@%*2@*1 ံ@*8@' ր%@@%!*?@*> ံ%*D@*C ံ@*J@') ր8@*P@'/ ր$*V@'!W$%=*[@*Z ံ@*a@'@ ր!!@@@$@&e@@ABC@@.left_induction @*$**)))B);(ޠ(נ(z(s((('''|@F$@*@* $$#@*@* $ #*@* $*@* ]%%%6*@* ံ@#@%*@* ံ@*@ !h@#ꐩ*@'c!W$%*@* ံ@*@' ր&T@@@@@/left_induction' @**o*`*))))9)2(ՠ(Π(q(j([(''נXK=@VG$`@*@* $^$\$Z@*@* $f$T*@* $l*@* ]&&%*@* ံ@%⚠+@* ံ@+@' ր&e@%+ @+  ံ@+@ !ζ@$P+@'!W%Y&+@+ $\@@ @@Q6strong_left_induction' @*ߠ*Ϡ**c*Z)))))5).(Ѡ(ʠ((`(H(7@H$@+C@+B $$$@+K@+J $Ʃ$+Q@+P $̚+U@+O ]&u&c%񚠐+Z@+Y ံ@&B+`@+_ ံ@+f@(E ր&vŶ@&N+l@+k ံ@+r@(Q ր".@&[+y@+x ံ&Y+~@+} ံ@+@(c ր&$@+@(j ր&T+@(@!W%&x+@+ $Ӑ@@ @@Ƞ/order_induction @+V+F+7*ڠ*Ѡ*t*m** )))H)A)2(נ((/"@-I%7@+@+ %5%3%1@+@+ %=%++@+ %C+@+ ]&&ڶ&h+@+ ံ@%&@&+@+ ံ@+@( ր"R@ِ+@(!W@&Κ+@+ ံ@+@ Y@퐩+@(!W&9&ᚠ+@+ ဩ&9@@@&2@&0@AB@@40order_induction' @+ +++F+=**٠*|*u**))))C)+)@J%@,&@,% %%%@,.@,- %%,4@,3 %,8@,2 ]'X'F&Ԛ,=@,< ံ@%@'&,D@,C ံ@,J@)) ր"@ E,R@)!W @':,X@,W ံ@,^@)= րŶ@𐩚,f@)!>'M,k@,j l@@k@@1order_induction_0 @,+,, +++I+B**ޠ**z***)))@K& @,@, & &&@,@, &&,@, &,@, ]''@',@)R!9}@',@, ံ@,@) ր,@)c!9}'Ƕ@%,@)p!Wy@',@, ံ@,@ 倠'ܚ,@)|!9}@&,@)!W'E',@, &@@@@@2order_induction'_0 @,,,,#,+++Y+R*****{* *)xk]@vL&@-@- &~&|&z@- @-  &&t-@- &-@- ](5(#@(&-@)!9}@(-"@-! ံ@-(@* ր--@)!9}(;@&k-5@)!W@(-;@-: ံ@-A@*  ր(P-F@)!9}@A-N@*!>(5-S@-R &@@@@@<_ind @--,,,,1,*+͠+Ơ+i+b+****|*kߠ@M&@-w@-v &&&@-@-~ &&-@- '-@- ](((p-@- ံ@(T-@*E!W'϶@(w-@- ံ@-@ $@c-@*Y!Wb(-@- ံ@-@ #J@@@@@砠&le_ind @-u-e-V,,,,,/,(+ˠ+Ġ+g+`+Q**ޠ*͠NA3@LN'V@-@- 'T'R'P@-@- '\'J-@- 'b-@- ]) ((Қ-@- ံ@'E@(Қ-@- ံ@-@* ր$q@.@*!W(嚠. @.  ံ@.@* ր#y@@@@@B&Rlt_wd @-Р---T-K,,,,,&,+ +++Q+9+(@O(ʚ.3@.2 ဩ'@.:@.9 ံ@.?@.> ''.E@.D ံ@.J@.I 'Ś.N@.H ]'.T@.S 'Ϛ.X@.R ])x)?.]@.\ ့)=.b@.a ဩࠩ.i@+H ր(.n@o )~@@&@@&Rgt_wd @....---L-E,,,,}, ,, +++ @ P)(.@. ဩ(@.@. ံ@.@. ((.@. ံ@.@. (#.@. ](.@. (-.@. ])ַ).@. ့).@. ဩ>.@ )ϩ.@+ ր)@@'X@@%lt_wf @..|.m..---F-?,,۠,~,w,h, ++ e X J@ cQ).@. ဩ"Wf*@,well_founded8E.@. ့)䚠/@/ ့)⚠/@/ ဩ/@+ ր)/@  *#@@@+A𱍠G @+A7iA)@AB@@ M%gt_wf @.۠.ˠ.._.V-----1-*,͠,Ơ,,\,D,3   @ R)՚/>@/= ဩO/D@/C ့*+/I@/H ့*)/N@/M ဩ̠/U@ V *]/Z@,9 ր*@@G@@ -add_lt_mono_l @// ....8.1-Ԡ-͠-p-i- -,,,,r@,n@*\/z@/y ံ*Z/@/~ ံ&/@/ ဩ*/@  */@  倠/@,k n&R/@,p n*@@('@@AA@@A@-add_lt_mono_r @/^/N/?..٠.|.u..---P-I-:,ߠ,Ǡ,@,A*/@/ ံ*/@/ ံ&ߚ/@/ ဩ*頩/@  *^/@  倠/@, n&N/@, n*@@(k@@D+add_lt_mono @////#/...Y.R-----{- -,@,B*ᚠ/@/ ံ*ߚ0@0 ံ' 0 @0 ံ%0@0  ံ@0@! %@0@! *0@!  倠0%@, n)b*0+@- n@@@@@-add_le_mono_l @//۠/̠/o/f/ /...A.:-ݠ-֠-Ǡ-l-T-C@-?C+-0K@0J ံ++0P@0O ံ'l0U@0T ဩ+v0\@-; ր*멚0a@-@ ր0g@-< n'#0l@-A n+t@@(@@Ѡ-add_le_mono_r @0,00 ///J/C..ߠ..{...---@-D+n0@0 ံ+l0@0 ံ'0@0 ဩ+0@-| ր+,0@- ր0@-} n'0@- n+@@)9@@+add_le_mono @0m0]0N/////'/ .à.._.X.I--֠-@-E+0@0 ံ+0@0 ံ'0@0 ံ&Ě0@0 ံ@0@- ր&@0@- ր+w0@- ր0@- nΩ0@- n@@@@@].add_lt_le_mono @0000<03/֠/Ϡ/r/k//....9.!.@. 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'@13@. ր+©18@"9 倠1>@. n1C@. nא@@@@@.add_le_lt_mono @10000~0!0///Y/R...ߠ..l.[@.WG,E1c@1b ံ,C1h@1g ံ(1m@1l ံ'Z1r@1q ံ@1x@.W ր'M@1~@" , 1@" 倠1@.^ nd1@.c n "@@@@@+add_pos_pos @1N1>1/0Ҡ0ɠ0l0e00///@/9/*.Ϡ..@.H,1@1 ံ,1@1 ံ@1@" 倠1@.h!9},Ͷ@1@" 倠1@.s!9},ة1@" 倠1@.}!9}1@. n'@@@@=.add_pos_nonneg @111y11000R0K/////t//.@.I,ښ1@1 ံ,ؚ1@1 ံ@2@# 倠2@.!9}-@2@. ր2@.!9}-"2@# 倠2@.!9}2"@. n'@@"@@.add_nonneg_pos @11Ҡ1à1f1]10000801/Ԡ/͠//c/K/:@/6J-$2B@2A ံ-"2G@2F ံ@2M@/, ր2R@.!9}-a@2X@#Y 倠2]@/!9}-l2b@#c 倠2g@/!9}2l@/A n(A@@l@@Ѡ1add_nonneg_nonneg @2,22 111J1C00ߠ00{000///@/K-n2@2 ံ-l2@2 ံ@2@/v ր2@/F!9}-@2@/ ր2@/Q!9}-2@/ ր2@/[!9}2@/ n(@@@@,lt_add_pos_l @2v2f2W1111101)0̠0Š0h0a0R//ߠ/@/L-2@2 ံ-2@2 ံ@2@# 倠2@/!9}-2@# 倠-2@/ n-@@@-#@.@AB@@X,lt_add_pos_r @222272.1Ѡ1ʠ1m1f1 10000400 @0M-3@3 ံ-󚠐3@3 ံ@3@$ 倠3#@/!9}.23(@$) 倠.83.@0 n-@@-a@@,le_lt_add_lt @22ޠ2Ϡ2r2i2 2111D1=00٠0ʠ0o0W0F@0BN.03N@3M ံ..3S@3R ံ*o3X@3W ံ)E3]@3\ ံ@3c@0B ր)8@3i@$j 倠3o@0D n-3t@0I n.,3z@${ )O@@@@@ߠ,lt_le_add_lt @3:3*3222X2Q11111,1%1000@0O.|3@3 ံ.z3@3 ံ*3@3 ံ)3@3 ံ@3@$ )@3@0 ր3@0 n.:3@0 nL3@$ )@@@@@*,le_le_add_le @33u3f3 3222?281۠1Ԡ1w1p1a100@0P.ǚ3@3 ံ.Ś3@3 ံ+3@3 ံ)ܚ3@3 ံ@3@0 ր)϶@4@0 ր4@0 n.4 @0 n4@0 ր)@@@@@u,add_lt_cases @3Р333T3K22222&21 111Q191(@1$Q/40@4/ ံ/45@44 ံ+Q4:@49 ံ*'4?@4> ံ@4E@%F 倠4K@1  n* 4P@1% n/`#4W@%X "멚4\@%] .@@@@@,add_le_cases @44 3333:332֠2Ϡ2r2k221111t@1pR/^4|@4{ ံ/\4@4 ံ+4@4 ံ*s4@4 ံ@4@1p ր4@1l n*l4@1q n/#𠩚4@1 ր#74@1 ր/.@@@@@ -add_neg_cases @4h4X4I33333"3222Z2S2D11Ѡ1@1S/4@4 ံ/4@4 ံ@4@% 倠4@1 n/隠4@1!9}$14@% 倠/4@1!9}4@% 倠/4@1!9}@@/&@@X-add_pos_cases @444474.3Ѡ3ʠ3m3f3 32222422 @2T/5@5 ံ/󚠐5@5 ံ@5@& 倠5#@1!9}5(@1 n08$|5/@&0 倠54@1!9}/59@&: 倠5>@1!9}0M@@>@@0add_nonpos_cases @444ߠ44y44333T3M222ڠ22g2V@2RU0@5^@5] ံ0>5c@5b ံ@5i@2H ր5o@2D n05s@2!9}$Ǡ5z@2Y ր0?5@2)!9}5@2c ր05@23!9}@@/@@0add_nonneg_cases @5I595*4͠4Ġ4g4`43333;343%2ʠ22@2V05@5 ံ05@5 ံ@5@2 ր5@2c!9}5@2 n0Ω%5@2 ր5@2t!9}05@2 ր5@2~!9}0@@@@9-le_exists_sub @555u55444N4G33333p322@2W0֚5@5 ံ0Ԛ5@5 ံ@5@2 ր1̠6@6 ့-!6 @6  ဩ6@6  ]0֩6@2 n ~6@2 ր6!@2!9}1/@@@0T@A0@2'@A2'AA@@0@ABCD@@+mul_lt_pred @55ڠ5ˠ5n5e55444@493ܠ3ՠ3Ơ3k@3@-_6H@6G ံ,56M@6L ံ146R@6Q ံ126W@6V ံ@6]@6W ]6c@3!W01(16k@'l 倠6q@39 =%6v@3> =/16|@'} 倠6@3W n6@3P =,]16@3b n6@3[ =11W@@/@@AA@@A@1mul_lt_mono_pos_l @6V6F675ڠ5Ѡ5t5m55 444H4A423@4/A-˚6@6 ံ16@6 ံ16@6 ံ@6@' 倠6@3s!9}11꠩6@' 1_6@' 倠6@3 =,6@3 =1f@@@1@A1@1_@2@@ABCD@@R1mul_lt_mono_pos_r @6666)6 5à55_5X444444&@4~B.7@7 ံ1ꚠ7@7 ံ1蚠7 @7  ံ@7@( 倠7@3!9}1ܩ297@(  17$@(% 倠7*@3 =17/@3 =11@@/@@1mul_lt_mono_neg_l @666Ѡ6t6k66555F5?44۠4̠4q@4C.e7N@7M ံ257S@7R ံ237X@7W ံ@7^@(_ 倠2#7c@4 !9}27j@(k 17o@(p 倠7u@4= =17z@4B =-O@@@@砠1mul_lt_mono_neg_r @7:7*7666X6Q55555,5%54@5D.7@7 ံ27@7 ံ2}7@7 ံ@7@( 倠277@$zero!9}2Ϡ7@"lt 2E7@ 倠7@#mul =7@ =2F@@0S@@44mul_le_mono_nonneg_l @77w7h7 7666A6:5ݠ5֠5y5r5c5@5`E2ǚ7@7 ံ2Ś7@7 ံ/7@7 ံ@7@4 ր7@4!9}3@8@4 ր-թ8@4 ր8 @4 =21V8@4 =2@@2D@@~4mul_le_mono_nonpos_l @7Ѡ777U7L66666'6 5à555R@5F38/@8. ံ384@83 ံ/P89@88 ံ@8?@5 ր3N8D@4!9}@8J@5) ր.8O@5. ր8U@5 =2ԩ8Z@5" =O@@2@@Ǡ4mul_le_mono_nonneg_r @88 77778716Ԡ6͠6p6i6 655@5G3Z8x@8w ံ3X8}@8| ံ/8@8 ံ@8@5g ր8@57!9}3@8@5r ր.h8@5w ր8@5f ='28@5k =.x@@2@@4mul_le_mono_nonpos_r @8c8S8D77ޠ77z77666U6N6?5@6!9}88=@. 倠=@:J!9}=@:m =84=@. 倠=@:Y!9}8@@ @@0mul_pos_cancel_r @=o=_=P<<<<<)<";Š;;a;Z;K:@;HY8=@= ံ8=@= ံ@=@. 倠=@:!9}88=@. 倠=@:!9}=@: =8}=@. 倠=@:!9}8@@ @@e3mul_nonneg_cancel_l @====<=3<֠<Ϡ@> ံ8>@> ံ@>!@/" 倠>&@:!9}959G>-@;  ր>2@:!9}>7@: =8Ʃ><@; ր>A@:!9}9P@@ P@@3mul_nonneg_cancel_r @>====|==<<_@>^ ံ9?>d@>c ံ@>j@/k 倠>o@;!9}9}9>v@;U ր>{@;%!9}>@;H =9>@;d ր>@;4!9}9N@@ @@,lt_1_mul_pos @>J>:>+=Π=Š=h=a=<<<<<<5<&;@<#\9>@> ံ9>@> ံ@>@/ 倠>@;z 9Ƕ@>@/ 倠>@;m!9}9ҩ>@/ 倠>@; >@; =4@@@@?(eq_mul_0 @>>>s>> ===L=E<<<<}@> ံ9К>@> ဩ:>@> ]?@; =:?@;!9}.Z? @? ]:?@;!9}?@? ]:&?@;!9}@@7@@)neq_mul_0 @>ܠ>̠>>`>W=====2=+<Π<Ǡ<<]@<^:?:@?9 ံ:??@?> ဩ:`":?J@?D ]:Z?O@;!9}:'?V@?P ]:e?[@<!9}:3?b@?\ ]?h@<0 =:x?l@<!9}@@7@@٠+eq_square_0 @?,?? >>>J>C==ߠ=={===<@=_:l?@? ဩ:?@? ]?@<_ =0j?@>>>|>>===W=P=A<@=>`:?@? ံ:?@? ံ@?@? ]?@< =:䚠?@<!9}@:?@? ]:𚠐?@<!9}?@? ]:p?@<!9}@@@@@ \*eq_mul_0_r @????3?*>͠>Ơ>i>b>=====0@=a:@ @@  ံ:횠@@@ ံ@@@@ ]@@< =;.@"@<!9}@:@*@@$ ]:@/@<!9}@4@@. ]:@9@<!9}@@@@@ (mul_eq_0 @@b@p2I@;.@L@@K ံ;,@Q@@P ဩ;r@X@@R ]@^@=& =;n@b@= !9}/@i@@c ];y@n@=!9}@s@@m ];@x@="!9}====@=@^\@9@)@???W?P>>>>>+>$>=@@@@@ *mul_eq_0_l @@@ LR@;@@@ ံ;@@@ ံ@@@@ ]@@=} =;Ś@@=c!9}@;@@@ ];њ@@=p!9}@@@ ];Q@@=z!9}X@+24pe@@{@l@@???E?>>>ڠ>}>v>g> @@@@@ P*mul_eq_0_r @A @ LX@;ؚ@@@ ံ;֚@@@ ံ@A@@ ]A@= =<A @=!9}@;䐩A@A  ];ؚA@=!9}A@A ];⚠A"@=!9}@324pk@ݠ@͠@@a@X?????3?,>Ϡ>Ƞ>>^@@@@@ (lt_0_mul @@@@֠@y@p@@ ???K?D>>>Ѡ>v@>b<5AS@AR ံ<3AX@AW ဩ!9}Ai@>1 =!!9}<A|@2} 倠A@>+!9}<$A@2 倠<A@>7!9}A@2 倠<A@>A!9}@@;@@ 5square_lt_mono_nonneg @AWAGA8@۠@Ҡ@u@n@@ ???I?B?3>@?0c<A@A ံ<A@A ံ@A@> րA@>o!9}<Զ@A@2  =<\<\A@> =<<@@@@@ J5square_le_mono_nonneg @AAA~A!A@@@W@P?????y?@?vd<ݚA@A ံ<ۚB@A ံ@B@> րB @>!9}=@B@> ր<B@> րB@> =FB!@> =E@@@@@ 6square_lt_simpl_nonneg @AAѠA AeA\@@@@@7@0?Ӡ?̠??b@?e=!B?@B> ံ=BD@BC ံ@BJ@?) րBO@>!9}=]@BU@3V 倠B[@?# =B`@?( ==p=pBf@3g 8;@@@@@ Ӡ6square_le_simpl_nonneg @B&BBAAADA=@@٠@|@u@@@?@?f=fB@B ံ=dB@B ံ@B@?n րB@?>!9}=@B@?y րB@?h =ĩB@?m =EB@? ր8@@@@@ ,mul_2_mono_l @BjBZBKAAAAA$A@@@\@U@F?@@Cg=B@B ံ=B@B ံ@B@3 =㩚B@3 倠B@? nB@? 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AB[@/ րBA@@@A|@Aq@Ao@ABC@@g(lt_sub_0 @[[[[@@[F՚\@ ံӚ\@ ဩ\@ 倠\%@y BA\,@!9}\1@ 倠BA@@@A@A@A@ABC@@(le_sub_0 @[[[۠[~@[G\N@ ံ\T@ ဩŀ\]@ ր\c@ BA\j@!9}\o@ րBA@@@A@A@A@ABC@@㠠+opp_lt_mono @\8\(\[@\HQ\@P ံO\@V ဩ\@"lt 倠DA\@ 倠\@[  \@[ W@@@>A6@@A+@BA)@ABC@@!+opp_le_mono @\v\f\W[@\TI\@ ံ\@ ဩA\@ ր=\@ ր\@[ ;\@[ :@@@wAo@yAd@{Ab@ABC@@Z+opp_pos_neg @\\\\3@\JȚ]@{ ဩt] @ 倠]@!9}]@[ A]@ 倠A]#@!9}@@@A@A@AB@@+opp_neg_pos @\\נ\Ƞ\k@\K];@ ဩ]D@ 倠]J@\3 A]P@!9}]U@  倠]Z@ !9}A@@@A@A@A@ABC@@̠1opp_nonneg_nonpos @]!]]\@\L:]u@ ဩ怠]~@ ր]@2!9}]@\q A]@ րA]@D!9}@@@#A@%A @AB@@1opp_nonpos_nonneg @]Y]I]:\@]7Mr]@% ဩ]@ ր]@\ A]@q!9}]@ ր]@{!9}A@@@[AS@]AH@_AF@ABC@@>'lt_m1_0 @]]]t]@]qN]@ 倠]@]= ]@]F ]@&H!9}@@@@@`-sub_lt_mono_l @]]]]9@]OΚ^ @ ံ̚^@ ံ!p^@ ဩ^@ 倠CB^'@ 倠^-@ AB^5@ AC@@@A@A@A@ABC@@-sub_lt_mono_r @]]]ߠ]@]P^R@ ံ^X@ ံI^^@ ဩπ^g@ 倠CB^o@% 倠^u@ CA^}@ BA@@@A@A@A@ABC@@+sub_lt_mono @^F^6^']@^$Q_^@^ ံ]^@d ံ^@j ံ!q^@q ံ@^@i 倠DC@^@r 倠dQ^@x 倠^@ F_^@# Ee@@@@@<-sub_le_mono_l @^^^r^@^oR^@ ံ^@ ံܚ^@i ဩb^@6 րCB_@> ր_@\ AB_@d AC@@@A@A@A@ABC@@-sub_le_mono_r @^٠^ɠ^^]@^S򚠐_-@ ံ𚠐_3@ ံ$_9@ ဩ_B@~ րCB_J@ ր_P@ CA_X@ BA@@@A@A@A@ABC@@̠+sub_le_mono @_!__^@^T:_u@9 ံ8_{@? ံl_@E ံۚ_@K ံ@_@ րDC@_@ ր>+_@ ր_@ 8_@ =@@@@@.sub_lt_le_mono @_i_Y_J^@_GU_@ ံ_@ ံ_@ ံ#_@ ံ@_@ 倠DC@_@ րs_@ 倠_@> "_@D !@@@@@\.sub_le_lt_mono @____5@_Vʚ`@ ံȚ` @ ံ`@ ံk`@ ံ@`@Y րDC@`&@ 倠`,@ 倠`2@ jȩ`8@ i͐@@@@@,le_lt_sub_lt @___ڠ_}@_W`M@ ံ`S@ ံD`Y@ ံ`_@ ံ@`e@ րDC@`n@$ 倠`t@  `z@ "`@6 倠@@@A@AA@A@A@ABC@@,lt_le_sub_lt @`I`9`*_@`'Xb`@a ံ``@g ံ`@! ံ`@' ံ@`@k 倠DC@`@ ր`@ Y`@ r``@ 倠fe@@@`AX@AaAP@cAN@eAL@ABC@@D,le_le_sub_lt @```z`@`wY`@ ံ`@ ံ䚠`@q ံS`@w ံ@a@A րDC@a@J րa@h Ea@n a @\ ր@@@A@AA@A@A@ABC@@/lt_add_lt_sub_r @``٠`ʠ`m@`Za=@ ံaC@ ံ4aI@ ဩaR@ 倠aX@ nCABaa@ 倠Cah@ BA@@@A@A@AB@@ڠ/le_add_le_sub_r @a/aa`@a [Ha@ ံFa@M ံza@ ဩa@ րa@5 nCABa@ րCa@ BA@@@?A7@AA(@AB@@ /lt_add_lt_sub_l @auaeaV`@aS\a@A ံa@ ံa@M ဩFa@ 倠a@{ nCABa@ 倠Aa@H BC@@@A}@An@AB@@f/le_add_le_sub_l @aaaa?@a]Ԛb@ ံҚb@ ံb@ ဩb$@` րb*@ nCABb3@o րAb:@ BC@@@A@A@AB@@/lt_sub_lt_add_r @baaa@a^bU@ ံb[@ ံLba@ ဩҀbj@  倠bp@ CABby@/ 倠Cb@ nBA@@@A @A@AB@@/le_sub_le_add_r @bGb7b(a@b%_`b@ ံ^b@e ံb@ ဩb@ րb@  CABb@ րCb@] nBA@@@WAO@YA@@AB@@8/lt_sub_lt_add_l @bb}bnb@bk`b@Y ံb@_ ံؚb@ ဩ^b@ 倠b@P CBAc@ 倠Cc @ nBA@@@A@A@A@ABC@@/le_sub_le_add_l @bՠbŠbbY@bac)@ ံ욠c/@ ံ c5@ ဩc>@z րcD@ CBAcM@ րCcT@ nBA@@@A@A@A@ABC@@Ƞ-lt_sub_lt_add @cc bb@bb 6cq@ ံ 4cw@ ံhc}@ ံךc@ ဩ􀠩c@ B 倠c@ DCc@ BAc@ X 倠c@ ? nDAc@ G nCB@@@ AA 9@ CA .@ EA ,@ABC@@ $-le_sub_le_add @cycicZb@cWc c@E ံ c@K ံĚc@Q ံ3c@W ဩPc@ $ րc@B DCc@J BAc@ : րd@  nDAd @  nCB@@@ A @ A @ A @ABC@@ *lt_sub_pos @cՠcŠccY@cd d)@ ံ 욠d/@  ဩd8@  倠d=@ !9}AdC@  倠dI@ BAB@@@ A @ A @ A @ABC@@ -le_sub_nonneg @ddcc@ce ,dg@ ံ *dm@ 1 ဩހdv@  րd{@ *!9}Ad@  րd@ BAB@@@ A @ A @ A @ABC@@ ,sub_lt_cases @dQdAd2c@d/f jd@  ံ hd@ # ံd@ ) ံ d@ / ံ@d@ s 倠d@  DCd@  BA @@"or @d@  倠  qd@  倠  v@@@@@ M,sub_le_cases @dddd&@dg d@ n ံ d@ t ံ횠e@ z ံ\e@  ံ@e@ J րe@ h DCe@ p BAQe(@ d րY e.@ j ր  Ð@@@@@ -sub_neg_cases @ddߠdРds@dh eC@  ံ eI@  ံ@eO@  倠eU@  BAe\@ !9}ee@  倠 ej@ !9}eo@ % 倠et@ #!9} @@@ A @ A @ A @ABC@@ 堠-sub_pos_cases @e:e*ed@ei Se@  ံ Qe@  ံ@e@ P 倠e@ N!9}e@  BAـe@ f 倠e@ d!9} Ie@ p 倠 be@ n!9}@@@ NA F@A OA >@ QA <@ SA :@ABC@@ 20sub_nonpos_cases @eewehe @eej e@ S ံ e@ Y ံ@e@ # րe@ A BAe@ !9}&e@ 9 ր f@ !9}f@ C րf @ !9} @@@ A @ A @ A @ABC@@ }0sub_nonneg_cases @eҠe eeV@ek 뚠f&@  ံ 隠f,@  ံ@f2@ n րf7@ !9}f<@  BAqfH@  րfM@ !9} ᩚfR@  ր fW@ !9}@@@ A @A A @ A @ A @ABC@@ ʠ,zero_pos_neg @fffe@el!P@fu@ 9 နA$P_wd)Morphisms'Classesf @@&ProperL@f@ P @*respectful%WO?f@ [ "f@"eq ]%Logic$Init!@#iffС) @ Of@ \!9}@ yf@ x ံ@f@  倠f@ n!9} "%@#andЖw@ f@e  !f@  ဩ ,@@@ %'A c*Structures[AviAa@ AۀߠKe@AB@@ M2mul_lt_mono_nonpos @ff@f@!nf@!t ံ!mf@ ံ!pg@ ံ!qg @ ံ@g@"le րCg@/k!9}@g@"lt 倠Ea@g'@ րag,@/!9}@g2@ 倠ag8@ 倠g>@/} =G gE@/ =HF@@@@@AA@@A@2mul_le_mono_nonpos @g f@fAig]@h ံggc@n ံfgi@t ံego@z ံ@gu@d րCg{@/!9}@g@p րbb@g@w րbg@/!9}@g@ րtbg@ րg@/ =ag@/ =`_@@@@@^1mul_nonpos_nonpos @gfgV@gRBĚg@ ံšg@ ံ@g@ րBg@0!9}@g@ րb^g@0(!9}g@ րg@02!9}g@0# =bcbs@@@ %'A*Equalities*Structures#Coq@AviA)Morphisms'Classes#Coq@@AۀߠK @A݋X_A/RelationClasses'Classes#Coq@@ABC@@1mul_nonneg_nonpos @gŠg@gC#h@" ံ!h@( ံ@h#@ րh(@0{!9}B@h/@ րbh4@0!9}h9@( րh?@0~ =bbΚhD@0!9}@@@`AX@AaAO@cAۓό^[@gAQ@ABC@@1mul_nonpos_nonneg @hg@gDlh`@k ံjhf@q ံ@hl@[ րBhr@0!9}@hx@g րh}@0!9}c h@q րh@0 =cch@0!9}@@@A@A@A@ABC@@K(lt_mul_0 @hShC@h?Eh@!t ံh@ ဩ%Logic$Init#Coq@@#iffС)h@ 倠h@1 =BAh@1!9}!@"or @)@#andЖw@h@ 倠Bh@1:!9}h@ 倠h@1D!9}Ah@ 倠i@1S!9}Bi@ 倠Ai @1_!9}@@@(A @A)A@+A@-A@ABC@@̠(le_0_mul @hԠh@hF2i&@ ံ0i,@ ံ@i2@! րi7@1!9}i<@1{ =BAsoiL@; րiQ@1!9}cߩiV@E րi[@1!9}c詛id@S րc󚠐ii@1!9}in@] րcis@1!9}@@@@@+(le_mul_0 @i3i#@iGi@ ံi@ ံ@i@ րi@1 =BAi@1!9}Ҁ΀i@ րi@2!9}d>i@ րdCi@2 !9}怠i@ րdRi@2!9}i@ րi@2%!9}d_@@@@@,nlt_square_0 @ii@i~H𚠐i@? ဩ8@#notШi@ 倠i@25 =AAi@2P!9}@@@@@5square_lt_mono_nonpos @ii@iIj@ ံj@  ံ@j@  րBj!@2t!9}@j'@  倠ddj-@ 倠j3@2r =ddj9@2x =ddȐ@@@@@5square_le_mono_nonpos @ii@iJXjL@W ံVjR@] ံ@jX@G րBj^@2!9}@jd@S րdd󩚠jj@Y րjp@2 =dd署jv@2 =ee@@@@@/6square_lt_simpl_nonpos @j7j'@j#Kj@ ံj@ ံ@j@ րAj@2!9}@j@ 倠j@2 =e6e6j@2 =e;e;j@ 倠eBe2@@@@@l6square_le_simpl_nonpos @jtjd@j`LҚj@! ံКj@ ံ@j@ րAj@3+!9}@j@ րj@3# =esesj@3) =exexj@ րeeo@@@@@,lt_1_mul_neg @jj@jMk@ ံ k @ ံ@k@ 倠Bk@jg k@jp @k!@ 倠ek&@3y!9}k+@  倠k0@#one k6@3u =eeŐ@@@RAJ@TAB@VA@@ABC@@-lt_mul_m1_neg @jj@jN[kO@Z ံYkU@` ံ@k[@= 倠k`@0 B@kg@I 倠ekl@3!9}kq@S 倠kw@3 =efk}@j k@j @@@A@AA@A>@A@ABC@@B-lt_mul_m1_pos @kJk:@k6Ok@ ံk@ ံ@k@ 倠Bk@k k@k  @k@ 倠k@4!9}fLk@ 倠k@4  =fIfYk@k! k@k* @@@A@AA@A@A@ABC@@*lt_1_mul_l @kk@kPk@ ံk@P ံ@k@ 倠l@ B5l @ 倠l@4O =ffl@kg l@kp Ol$@"eq ]l+@4j =ffl0@4!9}l5@ 倠l:@  l?@4~ =ff͐@@@[AS@]A@_AI@ABC@@+lt_m1_mul_r @lk@kQdlX@c ံbl^@ ံ@ld@F 倠Blk@k lp@k ly@[ 倠l@4 =gg l@k l@k l@o ]l@4 =g(g'l@4!9}l@ 倠l@x l@4 =g<g;@@@A@Ah@A@ABC@@l(eq_mul_1 @ltld@l`RҚl@! ံКl@' ံ@l@ ]l@5 =BAl@ l@ ]gwl@ l@ ]gl@lI l@lR @@@A@AA@A@AA@ AРD.Morphisms_Prop'Classes#Coq@@*A8ӠA4Relation_Definitions)Relations#Coq@@ABCD@@Ѡ-lt_mul_diag_l @l٠l@lS7m+@6 ံ5m1@< ံ@m7@ 倠Bm=@5!9}mF@( 倠mK@ gةmP@2 倠mV@5 =ggg@@@rAj@tA@vA`@ABC@@-lt_mul_diag_r @mm @m T{mo@z ံymu@ ံ@m{@] 倠m@5!9}BՀm@l 倠m@_ hm@v 倠h#m@5 =h)h(@@@A@A@AB@@W-le_mul_diag_l @m_mO@mKUm@ ံm@ ံ@m@ 倠Bm@6!9}m@ րm@ h^m@ րm@6 =hkhjhk@@@A@A@A@ABC@@-le_mul_diag_r @mm@mVm@ ံm@ ံ@n@ 倠n@6Y!9}B[n@ րn@ hn@  րhn @6_ =hh@@@A(@AB@@ݠ(lt_mul_r @mm@mWCn7@B ံAn=@H ံ@nC@N ံ@nI@+ 倠nN@6!9}C@nU@7 倠nZ@* h@n`@B 倠Ahߩnf@H 倠 nl@6 =Mh@@@A@A'@Av@ABC@@+(mul_eq_1 @n@2J@n@ ံn@ ံ@n@m ]n@6 =n@k n@~ ]i1n@w n@ ]i;n@n n@n  n^n]n\n[nZ@nj@ &!۠nyni@@@@@|@n~nˠ@@b@E!Ca@&abs_wd @@'ZSgnAbs(Abstract'Integer'Numbers#Coq@+ZSgnAbsProp@A@@@E"ZP'ZSgnAbs(Abstract'Integer'Numbers#Coq@o@A@@D!Zoo@A@E)Morphisms'Classes#Coq@@&ProperL@o@!t ယo@ ဩ)Morphisms'Classes,@@*respectful%WO?o*@ ယo.@ ယo2@"eq ]o7@ ]o;@#abs m@@@ %'A*Equalities*Structures#Coq@AviA-'Classes#Coq@@AAۀߠK@Aۓό^ @A݋X_A/RelationClasses'Classes#Coq@@ABC@@AA@@A@'abs_max @s@F!nov@!t ဩo|@"eq ]o@#abs mAo@#max ~̀Ao@#opp A@@@YAQ@[AG@]AE@ABC@@=(abs_neq' @͠@G:o@9 ံ@o@"le րo@$zero!9}o@. Ao@L ]o@K mBo@B @@@@@w*abs_nonneg @@Hto@s ဩo@9 րo@8!9}o@u mA@@@A@AA@A@A@ABC@@*abs_eq_iff @3#@ Ip@ ဩ%Logic$Init#Coq@@#iffС)p(@ ]p.@ mAAp6@ րp;@!9}A@@@A@AA@A@A@ABC@@堠+abs_neq_iff @ueU@bJ⚠pW@ ဩBp`@ ]pf@ mApm@ Apt@ րApz@!9}@@@>A6@A?A/@AA-@CA+@ABC@@#'abs_opp @@K p@ ဩp@ ]p@ mp@ Ap@* mA@@@rAj@tA`@vA^@ABC@@V%abs_0 @֠@Lp@K ]p@J mp@!9}p@!9}@@@@@w)abs_0_iff @@Mtp@s ဩԀp@v ]p@u mAp@C!9}q@ ]Aq @N!9}@@@A@A@A@ABC@@'abs_pos @@0 @-Nq"@ ဩ q+@"lt 倠q1@v!9}q6@ mA%Logic$Init#Coq@@#notШqK@ ]AqQ@!9}@@@A @AA@A@A@ABC@@-abs_eq_or_opp @zj@wOql@ ဩX@"or @qy@ ]q@ mAAq@  ]q@  mAq@ A@@@YAQ@[AG@]AE@ABC@@=.abs_or_opp_abs @͠@P:q@!t ဩDq@= ]Aq@= mAq@K ]Aq@; q@Q mA@@@A@A@AB@@{.abs_involutive @ @Qxq@w ဩq@v ]q@u mq@{ mAr@ mA@@@@@(abs_spec @8(@%Rr@!t ဩ @#andЖw@r,@w րr1@v!9}Ar7@ ]r=@ mAA!rI@ 倠ArO@!9}rT@ ]rZ@ mAra@ A@@@@@/abs_case_strong @t@S!P@rx@!t နA r@g ံ@@r@ နAtGF@@*respectful%WO?r@ နAr@p ]%Logic$Init@#iffС)B@@r@ րr@!9}꩐DC@@r@ ր r@!9}Er@>  r@V m @@@A@A@AB@@(abs_case @@T{@r@z yr@ ံ@@s@S wus @ ns@ ]lB@UC@Zs@ _Rs"@ mi@@@A@A@@Ơ,abs_eq_cases @VF6@CUÚs8@ ံ!ms?@ ံ@sE@ ]sK@ mBsR@ mA耠s]@ ]sc@ ]si@ @@@-A%@/A@1A@ABC@@&abs_lt @@V!as@ ံ!bs@q ဩvs@i 倠s@ mBA%Logic$Init#Coq@@#andЖw@s@ 倠s@$ ABs@ 倠BA@@@A}@As@Aq@ABC@@i&abs_le @@WXs@e ံWs@ ဩ̀s@5 րs@m mBAVs@G րt@o ABt @U րBA@@@A@A@A@ABC@@,abs_triangle @D4$@1Xt&@ ံt,@ ဩt1@| րt7@ mt=@#add nBAtF@  ntL@ mBtS@ mA@@@A@AA @A@A@ABC@@0abs_sub_triangle @~n@{Ytp@ ံ8tv@ ဩt{@ րt@#sub t@ mBt@  mAt@ mt@ BA@@@cA[@AdAT@fAR@hAP@ABC@@H'abs_mul @ؠȠ@ZEt@D ံt@J ဩt@I ]t@H mt@#mul =BAt@  =t@] mBt@d mA@@@A@A@A@ABC@@*abs_square @ @ [u@ ဩu@ ]u @< =u@ mAu@ mAu!@P =AA@@@A@A@A@ABC@@ˠ&sgn_wd @[K;@H\6@u@@, ယuD@0 ဩ+uJ@6 ယuN@: ယuR@  ]uV@$ ]uZ@#sgn @@@A@A A@"A@$A @ABC@@(sgn_spec @t@]uv@\ ဩ [u@X 倠u@!9}Au@ ]u@#sgn Au@#one 0u@- ]u@!9}Au@8 ]u@& Au@!9}u@ 倠Au@!9}u@X ]u@F Au@N u@K @@@A@A@A@ABC@@%sgn_0 @ @ ^u@ ]v@p v @N!9}v @R!9}@@@A@A@@+sgn_pos_iff @@0 @-_v"@ ဩ v+@ ]v1@ Av7@ v<@ 倠vA@!9}A@@@A@A@ A@ABC@@頠,sgn_null_iff @yiY@f`暠v[@ ဩFvd@ ]vj@ Avp@!9}vu@ ]Av{@!9}@@@>A6@@A,@BA*@ABC@@"+sgn_neg_iff @@av@ ဩv@! ]v@ Av@ v@#one v@ 倠Av@!9}@@@~Av@Al@Aj@ABC@@b'sgn_opp @@b_v@^ ဩv@] ]v@K v@R Av@Y v@^ A@@@A@AA@A@AA@A1ՠF-SetoidTactics'Classes#Coq@@A1I @ABCD@@*sgn_nonneg @;+@(cw@ ဩw&@q րw+@p!9}w0@ Aw7@ րw<@!9}A@@@A@AA@A@A@ABC@@栠*sgn_nonpos @vfV@cd㚠wX@ ဩCwa@ րwg@ Awm@!9}wr@ րAwx@!9}@@@;A3@=A)@?A'@ABC@@'sgn_mul @@ew@ ံYw@! ဩw@  ]w@ w@ =BAw@ =w@" Bw@) A@@@Az@Ap@An@ABC@@f'sgn_abs @@fcw@b ဩw@a ]w@ =Aw@V Aw@n mA@@@A@A@A@ABC@@'abs_sgn @ *  @ gx @ ဩx@ ]x@F =x@ mAx$@ AA@@@A@A@A@ABC@@Π'sgn_sgn @ ^ N >@ Kh!xxA@ ဩxF@ ]xL@ xR@ AxY@ A@@@ A @A A @ "A @ $A @ABC@@ @ xk q@@@F!D@A @@@x{@= ံ@x@B ယx@F တ@<@@:7 @6@x@P ံ@x@U ယx@Y တ@4@@M @@x@e ံ@x@j ယx@n ဩx@t ံ@x@y ယx@} ယx@ ]x@ ယx@ ယx@ ]x@ ]e@#ϸ@~@@k @jΰ@x@ ံ@x@ ယx@ ဩx@ ံ@x@ ယx@ ယx@ ]y@ ယy@ ယy @ ]y@ ]@4^@i@@ɠe @dcy@ ံay"@ ံ@_y*@ ]Uy/@T!9}y4@ ]Sy:@R ny@@Q =P@#ϸO@4^T@N@@L @KyU@ ံyZ@ ံ@y`@J րye@!9}t@yk@I 倠yp@!9}Hyw@a րy|@!9}@14^By@d 倠@<4^M@@@@B  @  y@X ံy@] ံ@y@ ]y@!9}y@ րy@!9}I@4^񩚠y@ 倠T@4^y@ m@@@@VyϠ@@@@#ϸ@d@#ϸZ@A@4^@g@4^Y@A@AB@-Private_NZDivEA.div_mod_unique @@)NZDivProp@A@@@J!C%NZDiv&NatInt'Numbers@ @A@@I!B 0@A@@H!Azz@A@@Jz @!t ံ"q1z@!t ံ"q2z@ ံ"r1z#@ ံ"r2z*@ ံ@%Logic$Init#Coq@@ Жw@z>@( րzC@h!9}BzI@"lt 倠BE@#zW@A րz\@!9}kza@ 倠qF@zi@"eq ]zp@ nzv@ =G8z}@ nz@ = E%Logic$Init#Coq@@#andЖw@z@0 ]#8z@6 ]`@@@JAB@AKAۀߠKC@OAۓό^G@SA݋X_A/RelationClasses'Classes#Coq@@ABC@@l*div_unique @ؠӠǠ@A z@ ံ z@ ံ!qz@ ံ!rz@ ံ@z@ րz@ !9}D@z@ րz@!9}z@ 倠 @{@ ]{ @! n{@  =.{@ ]@#ϸ@@@Av@At@AB@@ؠ*mod_unique @D?3-@=By{4@( ံx{:@. ံl{@@, ံk{F@: ံ@{L@6 ր{Q@v!9}D@({\@F ր{a@!9}p{f@ 倠v'@{m@ ] {s@ n{y@ =:{@ ]@@54^$@@@/A@1A@AB@@B0div_unique_exact @@C㚠{@ ံ⚠{@ ံ֚{@ ံ@{@ ր{@!9}C@{@s 倠{@!9}߶@{@^ ]D{@ =쩚{@j ]@#ϸxV@@@A4@A2@AB@@(div_same @@D7{@ ံ@{@ 倠{@"!9}A|@ ] @#ϸ|@#one @@@Ai@Ag@AB@@ˠ(mod_same @72& @0El|'@ ံ@|-@ 倠|2@W!9}A|8@ ]?@4^NN|C@h!9}@@@A@A@A@ABC@@)div_small @mh\V@fF|]@Q ံ|c@W ံ@9|m@W ր|r@!9}B|x@/ 倠BA|@ ]@S#ϸ|@!9}@@@4A,@6A@8A@ABC@@I)mod_small @@Gꚠ|@ ံ隠|@ ံ@|@ ր|@!9}B|@w 倠BA|@_ ]@~4^@@@xAp@zA+@|A)@ABC@@'div_0_l @@H.|@ ံ@|@ 倠|@!9}A|@ ]@#ϸ}@*!9}} @.!9}@@@@@'mod_0_l @-(@&Ib}@ ံ@}#@ 倠}(@M!9}A}.@ ]5@4^}9@^!9}H}=@b!9}@@@@@'div_1_r @a\PJ@ZJ}Q@E ံ@}W@A ր}\@!9}A}b@ ]i@5#ϸx}m@_ |@@@A@A@AB@@)'mod_1_r @~@Kʚ}@y ံ@}@u ր}@!9}A}@- ]@L4^}@ }@!9}@@@NAF@PA@RA@ABC@@c'div_1_l @Ϡʠ@L}@ ံ@}@| 倠}@ A}@g ]@#ϸ}@ ꚠ}@!9}@@@@@'mod_1_l @@M8}@ ံ@}@ 倠}@ A~@ ] @4^~@ ~@ @@@@@ˠ'div_mul @72& @0Nl~'@ ံk~-@! ံ@~3@ ր~8@]!9}B@~?@ 倠~D@i!9}S~I@ ]P@#ϸ~U@f =tt@@@A@A@@'mod_mul @|wke@uO~l@` ံ~r@f ံ@~x@b ր~}@!9}B@~@; 倠~@!9}~@% ]@D4^~@ =[~@!9}@@@HA@JA@AB@@[&mod_le @Ǡ @P~@ ံ~@ ံ@~@ ր~@!9}B@~@ 倠~@!9}㩚~@ ր@4^@@@@@'div_pos @@Q9~@ ံ8~@ ံ@@ ր@*!9}B@ @ 倠@6!9} @ ր@@!9}!@#ϸ?@@@A@AA@A@A}@ABC@@ᠠ+div_str_pos @MH<6@FR=@1 ံC@7 ံ@M@ 倠R@w!9}AX@B րAB`@ 倠e@!9}k@7#ϸz@@@A @A@A@ABC@@)-div_small_iff @~@Sʚ@y ံɚ@ ံ@@{ ր@!9}B@@T 倠@!9}@#iffС)@E ]@#ϸuӚ@!9}@u 倠ݐ@@@hA@A@@y-mod_small_iff @Ԡ@T@ ံ@ ံ@@ ր@ !9}B@@ 倠@!9}P@ ]@4^ ©@ 倠&@@@A@Ad@Ab@ABC@@Ơ/div_str_pos_iff @2-!@+Ug"@ ံf(@ ံ@.@ ր3@X!9}B@:@ 倠?@d!9}NH@ 倠M@r!9}S@#ϸqX@B րw@@@@@&div_lt @}xlf@vVm@a ံs@g ံ@y@0 倠~@!9}B@@< 倠@| @F 倠@b#ϸVV@@@@A8@AAA@CA@EA@ABC@@V+div_le_mono @ @W@ ံ@ ံ!c@ ံ@@| 倠@!9}A@@ ր@!9}@ ր@ ր@#ϸh @#ϸ@@@A@AAR@AP@AN@ABC@@*mul_div_le @ @XS@ ံR@ ံ@@ ր@D!9}B@&@ 倠+@P!9}:0@ ր6@G =U=@ #ϸ[@@@A@A@A@ABC@@/mul_succ_div_gt @gbVP@`YW@K ံ]@Q ံ@c@M րh@!9}B@o@& 倠t@!9}y@0 倠:@ =@$succ!W@Y#ϸM@@@7A/@A8A@:A@@ ံ@@ ր@B!9}C@$@ 倠)@N!9}G@/@ 倠5@F =T;@ 倠B@#ϸ@@@@@2div_le_upper_bound @faUO@_\V@J ံ\@P ံb@N ံ@h@R րm@!9}C@t@+ 倠y@!9}@@i ր@ =F@u ր@^#ϸ0R@@@@@J2div_le_lower_bound @@]뚠@ ံꚠ@ ံޚ@ ံ@@ ր@!9}C@@{ 倠@!9}@@ ր@ =R@ ր@#ϸ^@@@A@AAB@A@@A>@ABC@@/div_le_compat_l @  @ ^!p@ ံ1@ ံ0 @ ံ@@ ր@;!9}C@퀠!@ 倠&@K!9}D+@ րJ;1@ ր 8@#ϸV >@ #ϸ@@@A@AA@A@A@ABC@@'mod_add @ j e Y S@ c_Z@ N ံ`@ L ံf@ R ံ@l@V րq@!9}C@x@b ր}@!9}@ nC@ =@@ F 倠@!9}@ 0 ] @O4^@ n D@ = (ll @a4^ Pr@@@[AS@]A @_A @ABC@@p'div_add @ ܠ נ ˠ @ `@  ံ@  ံ@  ံ@@ ր@!9}C@@ ր@!9}@  n@  = @@  倠@+!9}$ @  ] @#ϸ@/ n @. = ީ#@; n *@#ϸ  @@@A@A @A @ABC@@蠠)div_add_l @ T O C =@ MaD@ 0 ံJ@ 6 ံP@ D ံ@V@@ ր[@!9}A@b@L րg@!9}l@ nr@ =3@y@ 0 倠~@!9}>@  ] @V#ϸ@ n@ = 4 V @ n : @n#ϸb @@@KAC@MA @OA @ABC@@`0div_mul_cancel_r @ ̠ Ǡ  @ b@  ံ@  ံ @  ံ@@ ր@!9}C@@  倠@!9}@@  倠@!9}@  ] @#ϸ@  = @ = ~© @#ϸ  @@@A@A d@A b@ABC@@Ơ0div_mul_cancel_l @ 2 - ! @ +cg"@  ံf(@  ံp.@ " ံ@4@ ր9@^!9}C@@@  倠E@j!9}c@K@  倠P@u!9}nU@  ] \@(#ϸa@r =" g@x =( 䩚 n@:#ϸ  @@@A@A @A @ABC@@,/mul_mod_distr_l @    @ d͚@ | ံ̚@  ံ֚@  ံ@@ ր@!9}C@@ ] 倠@!9}ɶ@@ h 倠@!9}ԩ@ R ] @q4^@ = f@ = J@ = @4^ x V@@@A{@A 6@A 4@ABC@@/mul_mod_distr_r @    @ e9@  ံ8@  ံB@  ံ@@ ր @0!9}C@@  倠@<!9}5@@  倠"@G!9}@'@  ] .@4^3@D = 9@J = ?@P = F@4^  @@@A@A @A @ABC@@'mod_mod @ p k _ Y@ if`@ T ံ!ng@ [ ံ@m@W րr@!9}B@y@ 0 倠~@!9}@  ] @94^ @?4^P @E4^V@@@@@N/mul_mod_idemp_l @    @ g@  ံ@  ံP@  ံ@@ ր@!9}C@@ ր@!9}@@  倠@!9}@ t ] @4^@ = @4^  l @4^@  =  x@@@A@A X@A V@ABC@@/mul_mod_idemp_r @ & !  @ h[@  ံZ@  ံ"@  ံ@(@ ր-@R!9}C@4@ ր9@^!9}W@?@  倠D@i!9}bI@  ] P@4^U@f =  \@ 4^  b@4^g@x =  (@@@A @A @A @ABC@@&'mul_mod @    {@ iǚ@ v ံƚ@ | ံ(@  ံ@@~ ր@!9}C@@ ր@!9}ö@@ b 倠@!9}Ω@ L ] @k4^@ = ` > @w4^@ = @4^ r @4^ V@@@A 4@A 2@AB@@/add_mod_idemp_l @   @ j7@  ံ6@  ံ@  ံ@@ ր @.!9}C@@ ր@:!9}3@@  倠 @E!9}>%@  ],@4^1@I n8@4^  >@4^C@[ n  @@@A@A @A @ABC@@/add_mod_idemp_r @ni]W@gk^@R ံd@X ံj@^ ံ@p@Z րu@!9}C@|@f ր@!9}@@> 倠@!9}@( ]@G4^@ n<@S4^ dd@Y4^@ nN,p@@@YAQ@[A @]A @ABC@@n'add_mod @ڠՠɠ@l@ ံ@ ံp@ ံ@@ ր@!9}C@@ ր@!9} @@ 倠@!9}@ ]@4^ @! nʩ@4^@- n@4^ܩ"@4^@@@A|@Az@AB@@ޠ'div_div @JE93@Cm:@. ံ~@@4 ံF@: ံ@L@6 րQ@v!9}C@X@ 倠]@!9}{@c@ 倠h@!9}m@ ]t@@#ϸz@F#ϸ:@L#ϸ@ =F@@@0A(@A1A@3A@5A@ABC@@F)mod_mul_r @@n皠@ ံ暠@ ံ𚠐@ ံ@@ ր@!9}C@@w 倠@!9}@@ 倠@!9}@l ]@4^z@ =^@ n@4^j@ =p@4^@#ϸ|@@@A@A\@AZ@ABC@@*div_mul_le @*%@#o_@ ံ^ @ ံ h&@ ံ@,@ ր1@V!9}C@8@ 倠=@b!9}[@C@- րH@m!9}fM@7 րS@d =Z@&#ϸ֩`@,#ϸe@v =&@@@A@A@A@ABC@@$+mod_divides @y@pŚ@t ံĚ@z ံ@@v ր@!9}B@@O 倠@!9} @= ]@\4^m˚@!9},@"ex @@ ့ @ ဩ@_ ]E@ =@@@yAq@AzA/@|A-@~A+@A1@DRQP@@ABCD@@@@@@@A  BC{@&mod_eq @@@ge[L@%Logic$Init#Coq@@#notШ@"eq ]A @\!9}@  ]@4^ON@#sub V$@#mul =\,@#ϸcb@@@şA݋X_A/RelationClasses'Classes#Coq@@A@@].div_mod_unique @@AF@!t ံ"q1"q2 "r1"r2@%Logic$Init#Coq@@Жw@o@ րhBx@"lt 倠B@ mE@'éǩF@@#add nGD  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