"`Ȅ. Qﰠ)NMulOrder(Abstract'Natural'Numbers#Coq@)Decidable%Logic#Coq@$Bool#Coq@2Relation_Operators)Relations#Coq@4Operators_Properties)Relations#Coq@)Relations#Coq@*Equalities*Structures#Coq@&Orders*Structures#Coq@4Relation_Definitions)Relations#Coq@-SetoidTactics'Classes#Coq@&Setoid'Setoids#Coq@$Init'Classes#Coq@/RelationClasses'Classes#Coq@)Morphisms'Classes#Coq@.Morphisms_Prop'Classes#Coq@*NumPrelude'Numbers#Coq@-GenericMinMax*Structures#Coq@(NZAxioms&NatInt'Numbers#Coq@(NZParity&NatInt'Numbers#Coq@%NZPow&NatInt'Numbers#Coq@&NZSqrt&NatInt'Numbers#Coq@%NZLog&NatInt'Numbers#Coq@%NZDiv&NatInt'Numbers#Coq@%NZGcd&NatInt'Numbers#Coq@)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@&NZBits&NatInt'Numbers#Coq@'NAxioms(Abstract'Natural'Numbers#Coq@%NBase(Abstract'Natural'Numbers#Coq@$NAdd(Abstract'Natural'Numbers#Coq@&NOrder(Abstract'Natural'Numbers#Coq@)NAddOrder(Abstract'Natural'Numbers#Coq@)Notations$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"&/r'Prelude$Init#Coq@0JqTttֱ)Decidable%Logic#Coq@0ND걸풬/Oߠ$Bool#Coq@0j 2cZ`FW&Basics'Program#Coq@0!bs߯? :VU$Init'Classes#Coq@0](p{yOh.'Tactics'Program#Coq@03u%+Equivalence'Classes#Coq@07;ꮹ-SetoidTactics'Classes#Coq@0S_`nOU$&Setoid'Setoids#Coq@0D9AsWE!>*Equalities*Structures#Coq@0όe얟)H.Ƞ2Relation_Operators)Relations#Coq@0%s鯰s4Operators_Properties)Relations#Coq@0U3y#h&)Relations#Coq@0r砠*NZMulOrder&NatInt'Numbers#Coq@0}\^ !"k}@R(NZParity&NatInt'Numbers#Coq@0H>ca'^^%NZPow&NatInt'Numbers#Coq@0)6*9 B:vȻ&NZSqrt&NatInt'Numbers#Coq@0` .%m%NZLog&NatInt'Numbers#Coq@0ꔉ .uV%NZDiv&NatInt'Numbers#Coq@0$ |J?d (w%NZGcd&NatInt'Numbers#Coq@0KgT7|&NZBits&NatInt'Numbers#Coq@0MlIpKt'NAxioms(Abstract'Natural'Numbers#Coq@0Zخb1Z3uuѠ,NZProperties&NatInt'Numbers#Coq@01D%E`|3x%NBase(Abstract'Natural'Numbers#Coq@0 Y?V vI$NAdd(Abstract'Natural'Numbers#Coq@05;ZW:㥜un$&NOrder(Abstract'Natural'Numbers#Coq@0]@7U#oY02'8zn7Hf` @ gOljS-1wZj]4/Р)NMulOrder(Abstract'Natural'Numbers#Coq@ A-NMulOrderPropA@!N@!t @J %'A*Equalities*Structures#Coq@@@@@ %'@ @A@A@@@AA@@A@"eq @^@)@% ]N@.@* ]NA@@@@@(eq_equiv @@/RelationClasses'Classes1@+Equivalence~@J@F ]NN@/ dʀ@@@FA݋X_A/RelationClasses'Classes#Coq@@A@@A$zero @Tf@!t ]N@@@@@AA@@A@$succ @r@y@ ]N}@ ]N@@@@@$pred @d@@& ]N@* ]N@@@@@)'succ_wd @@)Morphisms'Classes#Coq@@&ProperL@@F ]N@J ]N@*respectful%WO?@U ]N@Y ]N@"eq dʀ@ dʀ@]Ā@@@AviA4'Classes#Coq@@A@@n'pred_wd @@E@@ ]N@ ]N9@ ]N@ ]N@4 dʀ@8 dʀ@}O@@@A3@A@@)pred_succ @@!n@ ]N@S dʀ@O"@ĀA@@@@@,bi_induction @@!A@5@ ]NA@@?@ ]N E@ ]NI@ dʀ%Logic$Init@#iffС)0@B[@ꀶ@Ra@ ]NDCl@ĀJbq@  ]NEQ@@@kA@A@@#one @T@ ]N@@@@@#two @T@+ ]N@@@@@*(one_succ @@@ dʀ@* @:Ā@Qꀐ@@@@@G(two_succ @@@ dʀ@9 @WĀ@Q @@@@@d"lt @h@@!t ]N@@ ]NA@@@@@AA@@A@"le @h@@ ]N@@ ]N@@@@@%lt_wd @@i@ @ ]N@@ ]N٩^@ ]N@@ ]N䚠@Z dʀm#@ ]N'@d dʀޚ+@"lt eR@@@$A`@A@@Ǡ+lt_eq_cases @@-<@ ]N!mC@ ]NJ@` eC(@"or @X@- eR]@ dʀ@@@@@)lt_irrefl @@\k@ ]N#@#notШw@L eRUU@@@@@)lt_succ_r @@w@  ]NJ@% ]NC@g eR>@)Āv@ eCS@@@@@6#add @d@@F ]N@@K ]N@O ]N@@@@@N#sub @d@@^ ]N@@c ]N@g ]N@<@@e#mul @d@@u ]N@@z ]N@~ ]N@S@@|&add_wd @@S@@ ]N@@ ]N@ ]NL@ ]N@@ ]N @ ]N@L dʀ_@ ]N@ ]N@Z dʀ!@^ dʀ%@ s@@@AY@A@@&sub_wd @@@7@ ]N@<@ ]N@@ ]NF@ ]N@K@ ]NO@ ]NS@ dʀY@ ]N]@ ]Na@ dʀe@ dʀi@ @@@aA@A@@&mul_wd @@۰@{@ ]N@@ ]N@ ]N@$ ]N@@) ]N@- ]N@ dʀ@7 ]N@; ]N@ dʀ@ dʀ@ @@@A@A@@H'add_0_l @@@W ]N@ dʀ@& s@p@@@@@f*add_succ_l @@̚@u ]N@z ]N@" dʀ@I s@Āϩ@Ā@[ s@@@@@'sub_0_r @@ @ ]N@M dʀ@\ @@@@@@*sub_succ_r @@)@ ]N횠.@ ]N3@p dʀ9@ 婚?@ĀD@OJ@ @@@@@㠠'mul_0_l @@IX@ ]N]@ dʀc@ h@ El@ꀐ@@@@@*mul_succ_l @@kz@ ]N>@ ]N@ dʀ@ @!Ām@ s@ Qx@@@@@4#max @d@@!t ]N@@ ]N@  ]N@@@@@AA@@A@%max_l @@!x@ ]N!y@$ ]N@@"le eCAB@"eq dʀ@D :C@@@@@2%max_r @@/@J ]N-@O ]N@@+ eC)*@( dʀ @k :'4@@@@@W#min @d@@p ]N@@u ]N#@y ]N@@@@@o%min_l @@l1@ ]Nj6@ ]N@<@h eC=A@d dʀG@7 Ȁcb@@@@@%min_r @@U@ ]NZ@ ]N@`@ eCe@ dʀk@[ Ȁ@@@@@&pred_0 @@y@"eq dʀ@O@(ꀚ@,ꀐ@@@@@AA@@A@@'NAxioms(Abstract'Natural'Numbers#Coq@/NAxiomsMiniSig'@@@@ ]N@@ ]NJ@@A@A d@@ dʠ^@@A@ eC@@ eCh@@A@AB eR@@ eRh@@A@ s@@ sd@@A@A :@@ :d@@A@ @@ Ƞd@@A@ABC @@ d@@A@ @@K T@@A@A @@ d@@A@ @@E T@@A@AO@@NOd@@A@@@eĠr@@A@@@{T@@A@ABCDE@'eq_refl @/RelationClasses'Classes#Coq@@5Equivalence_Reflexive@$zero ɠT@@A@ABCDE@A@&NZBase&NatInt'Numbers#Coq@*NZBasePropbl@@@A@@@@"NZ&NZBase&NatInt'Numbers#Coq@t@@’H@|@!t’HJ@@A@A™@@"eq™Ġ^@@A@š=@ @"leš=h@@A@ABšL@@"ltšLh@@A@"m@@#add"md@@A@A34@@#max34d@@A@3@@#min3 d@@A@ABC4@!@#mul4d@@A@6@'@#one6T@@A@A=@+@#sub=d@@A@>@1@#two>T@@A@AI@5@$predId@@A@G@:@$succGr@@A@@?@$zeroT@@A@ABCDE@A@@M  @]@@@d@!tРJ@@A@A L@@"eq L^@@A@r@ @#onerT@@A@AB4@@#two4T@@A@b@@$predbѠd@@A@F@@$succFr@@A@]l@@$zero]lT@@A@ABCD@A@@L:.+*@A@4*BackportEq@@@A@@@@ %'A*Equalities*Structures5A݋X_A;@A@@AA@@A@&eq_sym @K@5Equivalence_Symmetric. UD+]V@[@)SymmetricFgq0@K ]N4@J dʀT|L@*. U\~DXHA+$xbQhd@@[@@Q(eq_trans @@6Equivalence_TransitiveWyib LE6@@*Transitive++-~@ ]N@ dʀԐTʐL@*W\̐D70ؠѠyrcƠJ9@@@@*eq_sym_iff @RK~ˠeT@P@!x@ ]N!y@ ]N%Logic$Init@#iffС)@ dʀBA@ dʀ@@@@AA@@A@'neq_sym @70ؠѠ %@A!n @& ]N!m@- ]N@E@#notШ@5 dʀ@ &@< dʀGC@@*@@@(eq_stepl @B2+Ӡ̠tmbL;@BF@a ]NK@f ]N!zR@m ]N@X@n dʀ2y@_@u dʀDf@| dʀ@@@@iAۓό^)Morphisms@o@AB@@(succ_inj @xq[TE,@C"n1@ ]N"n2@ ]N@@ dʀ@OĀ©@UĀǩ@ dʀU@@@AviAG@AAۀߠKJ@N@@ABC@@Ϡ+succ_inj_wd @Ѡb[۠ʠud@`DI@ ]NG@ ]N @ dʀ@ĀF@ĀE@ dʀ@@@C@A8ӠA4Relation_Definitions)Relations)@AB@@/succ_inj_wd_neg @F?Ѡ4 @E@3 ]N @8 ]NO &@< dʀ,@Ā1@Ā8@N dʀY@@@@@P1central_induction @RB;ܠ}%r\K@F!A@Y@t ]NA$A_wd@&ProperL@k@ ]N @*respectful%WO?v@ ]Nz@ dʀ/@ ]N@Zڶ@~@ ]NE@@Ā@ ]NF@@@@@'add_0_r @D=ޠpӠ@@A&NZBase%NZMul&NatInt'Numbers#Coq@VT@A@%NZMul&NatInt'Numbers#Coq@)NZMulPropec@A@@@@"NZZY@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@,@$zero,筷T@@A@ABCDE@A@E@+4@O ]N9@O dʀ?@ s_D@c@@@@@H@ABC@@AA@@A@*add_succ_r @dTM70!n]r@}Acl@ ]Naq@ ]Nv@ dʀ|@P s@0Ā۩@5Ā@a s@@I@@F-add_succ_comm @81٠ҠzsdǠ٠Ԡà@B@ ]N@ ]N@ dʀ@ s@sĀ$䩚@ s멚@~Ā)@@@@(add_comm @ڠӠ{t 7*@C隠@  ]N皠@ ]N@ dʀ@ s#@ s @@@@'add_1_l @! SLޠA+naSN=/@:D )@D ]N.@D dʀ4@ s9@ X>@Ā@@@@'add_1_r @XHA+$xbQtf@qEW`@{ ]Ne@{ dʀk@? sp@1 u@#Āΐ@@1@@.)add_assoc @x b[LܠϠ@F@ ]N@ ]N!p@ ]N@ dʀ@ s@ sթ@ s@ sgސ@@{@@x,add_cancel_l @٠ɠ jc Ҡ& @Gؚ@ ]N֚@ ]NJ@ ]N@ dʀ@ sҩ@ s@ dʀ@@@@,add_cancel_r @ OHڠ='j]OJ9+@6H%@@ ]N*@E ]N/@J ]Na6@L dʀ<@ s\B@ scG@] dʀ@@@@,add_shuffle0 @aQJ4-kZ}o@zI`i@ ]N^n@ ]NҚs@ ]Nx@ dʀ~@R s@X s,@] s@c sS@@K@@H,add_shuffle1 @:3۠Ԡ|ufɠ۠֠Š@J@ ]N@ ]N@ ]N!q@ ]N@ dʀ@ s@ st@ s@ s@ s@ s@@@@,add_shuffle2 @ 5.֠Ϡ# PC50@K @ & ]N @ + ]Nt @ 0 ]NZ @ 5 ]N @ 5 dʀ %@ s +@ sX 0@ sQ 5@  s ;@ s[ A@ s@@@@,add_shuffle3 @ [ K D.'{eTwi@tLZ c@ ~ ]NX h@  ]N̚ m@  ]N r@  dʀ x@L sR ~@R s @W s @] sM@@E@@B'sub_1_r @    4 -ՠΠvo`àՠР@M @  ]N @  dʀ @s ֚ @|  @sO@@|@@y'mul_0_r @ ڠ ʠ à k d  Ӡ' @%@֚ @  ]N @  dʀ @   @ꀚ @ꀐ@@@@AA@@A@*mul_succ_r @      B ;ܠ͠0 ]PB@[A  @ 0 ]N  @ 5 ]N @ 5 dʀ %@ F +@Ā 0@ s 6@ WV@@@@C(mul_comm @ P @ 9  ڠ  { #  pZI@BL U@ p ]NJ Z@ u ]N _@ u dʀ e@,  j@1 @@&@@w/mul_add_distr_r @  t m     W P A}ѠĠ@C @  ]N~ @  ]N򚠐 @  ]N @  dʀ @e  @x sLé @} s @v s @{ Ր@@p@@/mul_add_distr_l @ Π   _ X     ؠǠ@Dʚ @  ]NȚ @  ]N< @  ]N @  dʀ @ © @ s @ s @  @ @@@@ )mul_assoc @      J C   ՠ 8 " eXJ@cE @ 8 ]N "@ = ]N '@ B ]N ,@ B dʀ 2@   8@ Y =@   C@  b@@@@P'mul_1_l @ ] M F     0 )  } g V@FY b@ } ]N g@ } dʀ m@ 4  r@ 3 @@.@@'mul_1_r @  | u     _ X I   ٠̠@G @  ]N @  dʀ @ c  @ b @@]@@,mul_shuffle0 @    L E     x ۠ Š @H @  ]N @  ]N) @  ]N @  dʀ @   @   @   @  @@@@,mul_shuffle1 @      2 + Ӡ ̠    M@2@KI @  ]N @ % ]Nn @ * ]NT @ / ]N @ / dʀ @   %@  R *@  K /@   5@  ֩ :@  @@@@G,mul_shuffle2 @ T D =  ޠ   '   t ^ M@JP Y@ t ]NN ^@ y ]Nš c@ ~ ]N h@  ]N m@  dʀ s@ :  y@ @  ~@ E  @ J  @ P N @ U 6@@J@@,mul_shuffle3 @    9 2 ڠ Ӡ { t e Ƞ  @K @  ]N @  ]N @  ]N @  dʀ @   @  驚 @   @  @@@@ࠠ%le_wd @  ݠ ֠ ~ w        栠@@A&NZBase'NZOrder&NatInt'Numbers#Coq@  @A@'NZOrder&NatInt'Numbers#Coq@+NZOrderProp  @A@@@@"NZ  @A@@@ @ / ]N@ @ 4 ]N @ : ]N@ $@ ? ]N˚ (@ > dʀ .@ I ]N՚ 2@ H dʀ c 6@  eC@@@@AA@@A@*lt_le_incl @ S C <  ݠ  ~ &   s ] LfYK@dA O X@ s ]N M ]@ x ]N@ c@"lt eR  i@ G eC @@@@@3'le_refl @  s l     V O @   |{@B  @  ]N @ k eC  @@ @@X.lt_succ_diag_r @    9 2 ڠ Ӡ { t e Ƞ  @C  @  ]N @O eR ҩ @ fĀ @@@@@.le_succ_diag_r @ Ҡ    c \       ܠ ˠؠ@D Κ @  ]N @  eC  @ Ā ;@@@@@/neq_succ_diag_l @      . ' Ϡ Ƞ    @ E @ ]N @ dʀ@ Ā g -@@ a@@ؠ/neq_succ_diag_r @(   Z S    H 2 !;. @9F $-@H ]N 4@J dʀ T:@ Ā @@@@@/nlt_succ_diag_l @TD=  ޠ   '   t ^ MgZL@eG PY@t ]N F`@ eRf@ Ā  @@@@@0/nle_succ_diag_l @pi    S L =   yx@H |@ ]N r@ j eC@ @Ā  @@@@@\)le_succ_l @=6 ޠ נ  x i ̠  @I @ ]N @ ]N 蠩@  eC@ qĀ " ⩚@e eR @@ @@+le_gt_cases @Ҡˠsl       ۠@J ޚ@ ]N ܚ@ ]N @"or @@  eC @ eR @@@@Ƞ-lt_trichotomy @JC   ՠ 8 " +@)K @8 ]N "@= ]N6)@ eR J=0@F dʀ Q5@ eR N@@@@@(lt_asymm @O?8٠z"  o Y HbUG@`L KT@o ]N IY@t ]N@_@ eR  Lf@ eR @@@ @@0(lt_trans @pi SL=   yx@M |@ ]N z@ ]N@ ]N@@2 eR =@@8 eR C@= eR  z@@ @@k(le_trans @LEx ۠ Š Π@N @ ]N @ ]N)@ ]N@@  eC x@@  eC ~@  eC;@@ @@+lt_strorder @ޠ' Ƞ  @O,@+StrictOrder.[@@ ]N@ eR@@ @@Ϡ+le_preorder @QJܠ?)2%@0PV@(PreOrder@+@F ]N/@  eC@@ 1@@/le_partialorder @I92ڠӠ{tiSB\OA@ZQ@,PartialOrder5͛КT@o ]NX@n dʀ\@m%`@> eC@Z|@@@ @A @ h@ iAhC@ABC@@5)lt_compat @@%lt_wdzs]VG@ &@@ ]N@@ ]N 7 %@ ]N@@ ]N B@ dʀ 4@ ]N L@ dʀ ښ@J eR@ŠĠà@@%lt_wd']ɠɠZSӠ ܠϠ@@@@@(lt_total @@3v䀠٠Ҡzs@ ߚ@ ]N ݚ@ ]N@ eR @ dʀ @ eR S@aǠIBԠ7!*@@@@@ࠠ'le_lteq @H@+lt_eq_cases*Ȁ5%Ơg`@ +4@O ]N )9@T ]N k@@ eC aTG@ eR hL@b dʀ m@+lt_eq_cases&ybRK5.l[uhZ@@@@@+0Private_OrderTacA'IsTotal A @yr\UF@@+Equivalence~@@ ]N@ dʀ@(eq_equiv7L:3۠Ԡ|ufɠ@@@@@r͐ @@;{ŠVO@ʠ@ ]N@f eR@,Q^ޠΠǠoh נ@@@@@r @@ze ,%͠Ơ@ @@ ]N@@ ]N  @! ]N@ @& ]N @% dʀ @0 ]N @/ dʀJ@ eRp0 b[P:)C6(@@@@@g @f@o/C0L<5ݠ֠~w @BK@f ]N@P@k ]NdW@ eRxk^@t dʀc@ eR|cvf_IB3o|n@@@@@?_ @@gY{#Ġe^O@@ ]N@ ]NȠ@{ eC@A eRũ@ dʀʐ]MFyܠƠϠ @@@@@@@@@@#TacaA @ޠΠǠoh נ֠@@D!P)OrdersTac*Structures#Coq@@@@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@'@$zero&CT@@A@ABCDE@A@G,MakeOrderTacBk?@A@@@BONR@@@A@@AEUH@@@N@!tJ@@A@A$:@@"eq$:^@@A@$@ @"le$h@@A@$@@"lt$ h@@A@ABC@A@+*OrderFacts.#@A@@s@[@v ]N`@v dʀӐ@@b@@AA@@A@ @|le OH9utYRL1@Aš@ ]N@j eC@@@@,)lt_irrefl @70ؠѠyrcƠȠ|v[@B욠@ ]N@U eR+@@@@X @Ѡb[۠ʠנɠ@C@ ]N@ ]N@@ dʀ@ dʀƐ@@@@*le_antisym @81٠Ҡà& (ܠ֠@)DL@, ]NJ@1 ]N@@ eC=@"@ eC'@= dʀ T@@)@@Ǡ< @@0)Ѡʠrk `J9SF8bR@cEK@f ]NP@k ]N@>X@n dʀyE_@u dʀ9@@@@@*interp_ord @!o)OrdersTacm@#ordȠ@ @@@@@@@@@@@D@@ ]N@@ ]N-@ dʀ@, eR@q eC@*(@@ ]N@@ ]NE +k= R'6'6'6''+k+7T'+7T'6'ࠒAȠǠ@@"lt\ @t@"eq8L@vlР@TȠ@@QPO@@A@B@A@xA܀Ҡˠsl ۠ڠ@@@@@%trans @3,Ԡ͠! #ޠנѠ@$F"o'K@+ ]NI@0 ]Nʚ@5 ]N@>`@4= 퀰C@Gi@4=  Np@4= 퀰@)trans_ord-0uG@@@@۠ @m~nox@d МA-tsdTM70!@c@~ ]Nh@ ]Nm@ ]N@s@ dʀ@y@ dʀ!~@ dʀސ L+k() LL7#'7@$t-&ΠǠohYyrlQ@@@@@A @ӷԷaթfМDCѠ SL@@ ]N@ ]N{@ ]N@@ eCy@@ eC@ eC< L+k() NN7#'^tߠ(!ɠ  Ӡ̠Ơ@@@@@ @D->./МB,+ NG@V@6 ]NT @; ]N՚%@@ ]N@+@ eRӶ@1@ eR٩6@ eR L+k() MM7#'tP@9ڠ{# pZI c V Hrb-& @@@@@+le_lt_trans @[=td]G@1@s@ ]Nx@ ]N-}@ ]N@@a eC+@@ & eR1@ + eR L+k() MN7#'t92ڠӠ{teȠ   ʠ~x]@@@@@M+lt_le_trans @ns ̠۠]V@@ ]N@ ]N@ ]N@@ x eR@@ eC@  eRF L+k() NM7#'ht2+Ӡ̠     "ݠ֠Р@@@@@%eq_lt @O8I9: 43$ VO@^#@> ]N\(@C ]Nݚ-@H ]N@3@I dʀ۶@9@  eRᩚ>@  eR L+k() ML7#'tXHA+$xbQ k ^ Pzj5.( @@@@@%lt_eq @#cE|le OH9@{@ ]N@ ]N5@ ]N@@ ( eR3@@ dʀ9@ 3 eR L+k() LM7#'tA:۠|mР à  Ҡ e@@@@@U%eq_le @v{sԠĠe^@@ ]N @ ]N@ ]N@@ dʀ@@ eC@ eCN L+k() NL7#'pt:3۠ԠŠ(   *ޠؠ@@@@@%le_eq @W@QABm<;,^W@f+@F ]Nd0@K ]N嚠5@P ]N@;@ eC@A@W dʀ驚F@$ eC L+k() LN7#'Ȑt`PI3,jY s f Xr=60@@@@@&eq_neq @oh RK<x   w\UO4@GŚ@ ]NÚ@ ]ND@ ]N@@ dʀB@@ dʀJ@ dʀ @@@@@I&neq_eq @àTM͠ ֠ ɠ ՠx@H @ ]N@ ]N@ ]N@Ɛ@ dʀ@@ dʀӐ@ dʀ M@@@@@*not_neq_eq @92ڠӠĠ'   )ݠנ@*IM@- ]NK@2 ]N@!@7 dʀB&@< dʀΐ@@y@@Ơ)not_ge_lt @@0)Ѡʠrk `J9 S F 8bR@cJK@f ]NP@k ]N@>X@6 eCq]@  eR@@_@@)not_gt_le @wg`JC4p  } oTMG,@K@ ]N@ ]N@u@ , eR@r eC<@@@@@4)le_neq_lt @?8٠zkΠ   Р~c@L@ ]N򚠐@ ]N@@ eC@@ dʀt@ n eR@@@@@q@@@@͐@@@@@ϐ@<_neq @ߠؠy!    @ R뚠@ ]N隠@ ]N@@  eR 쐩@ dʀ@@@@@ Р&le_neq @  RKݠ@* 3 & @ 1S%@@ ]N*@E ]N\1@  eRRd@#andЖw@>@ eC_+E@[ dʀf@@@@@ *eq_le_incl @_OH2+iX r e W@ pT[d@ ]NYi@ ]N@o@ dʀt@R eC@@@@@ >(lt_stepl @~waZK   @ UΚ@ ]N̚@ ]NM@ ]N@@ @ eRK@@ dʀJ@ K eRH@@@@@ x(lt_stepr @ȠYRҠ ۠ Π @ V@ ]N@ ]N@ ]N@@ z eR@@ dʀ@  eR H@@@@@ (le_stepl @4-ՠΠ"  @WB@" ]N@ @' ]N@, ]N@@ eC@@3 dʀ"@ eC@@@@@ 젠(le_stepr @<,%͠Ơng\F5OB4@MX|A@\ ]NzF@a ]NK@f ]N@Q@/ eC@W@m dʀ\@: eC @@@@@& @ue^HA2n{m@Yqz@ ]No@ ]N㚠@ ]N@@h eC2@@- eR8@2 eR @@@@@_ @?8٠zkΠ@Z@ ]N@ ]N@ ]N@@` eRk@@ eCq@k eR .@@@@@+le_antisymm @ؠѠyr@[䚠@ ]N⚠@  ]N@@ eC@@ eCة@ dʀ0@@@@@͠)le_succ_r @ OHڠ='0#@.\"@= ]N'@B ]NY.@  eCO4@Ā H;@ eC\@@V dʀaF@Ā@@@@@)lt_succ_l @`PI3,jYsfX@q]\e@ ]NZj@ ]N@p@  eRv@$Ā{@ eR#@@@@@E,le_le_succ_r @~&ǠhaR@^@ ]N@ ]N@@ eCƩ@ eC@^Ā@@@@@z,lt_lt_succ_r @ʠ[TԠàݠР@_ƚ@ ]NĚ@ ]N@@w eR@| eR@ĀD@@@@@,succ_lt_mono @1*Ҡˠ @`@ ]N @$ ]N;@ eR1@ eR@Āz @Āy@@@@@ꠠ,succ_le_mono @:*#ˠĠle ZD3M@2@Ka6?@Z ]N4D@_ ]NvK@) eClP@. eCV@Ā[@ Ā@@@@@%<_0_1 @ue^HA2n{m@bz@ eR@(ꀚ@D @@@@M&le_0_1 @.'ϠȠpiZ@c@ eC@Pꀚ@l @@@@@u<_1_2 @ŠVOϠؠˠ@d@g eR@ @ @@&@@<_0_2 @ݠ֠~w @e@ eR@ꀚ@ @@@@Š&le_0_2 @G@Ҡ5( @&f@ eC@ꀚ#@ @@@@@<_1_l @=-&ΠǠoh ]G6PC5@Ng9B@] ]N7G@b ]N@M@ eRR@r@X@ eR]@ eRb@# ;@@@@@f@ABC@@/+lt_ge_cases @oh RK<xw@h{@ ]Ny@ ]N@- eR@s eC@@@@@_+le_ge_cases @@9ڠ{lϠ @i@ ]N@ ]N͠@ eCᩚ@ eCސ@@@@@+lt_gt_cases @ߠϠȠpi ؠ@jۚ@ ]Nٚ@ ]Nؐ@ dʀ@ eR@ eR@@@@@Ƞ,eq_decidable @JCՠ8"+@)k@8 ]N"@= ]N)DecidableVW@)decidable r2@H dʀS@@@@@&eq_dne @L<5ݠ֠~w lVE_RD@]lHQ@l ]NFV@q ]NEGa@w dʀf@| dʀ@@@@@0&le_ngt @pi SL=yx@m|@ ]Nz@ ]N@o eC~@5 eR@@@@@b&nlt_ge @C<ݠ~oҠŠ@n@ ]N@ ]N@b eR橚@ eC@@@@@,lt_decidable @Ԡ͠unݠ@o@  ]Nޚ@  ]N̐@ eR@@@@@<_dne @ A:̠۠/"@ p  @ / ]N  @ 4 ]NK  $@ eRE )@ eRJ@@@@@&nle_gt @ C 3 ,Ԡ͠uncM<VI;@Tq? H@ c ]N= M@ h ]N< V@4 eCw [@ eRt@@@@@%<_nge @ u e ^ HA2n{m@rq z@  ]No @  ]N @# eRs @k eC@@@@@W,le_decidable @    8 1٠ҠzsdǠ@s @  ]N @  ]N @ eCِ@@@@@&le_dne @ Ҡ    c \ ܠˠؠ@tΚ @  ]N̚ @  ]Nː͐ @ eC @ eC @@@@@*nlt_succ_r @!     8 1٠Ҡà& @u! @!& ]N!@!+ ]NB!@ eR9!@Ā~!$@ eRE@@@@@5lt_exists_pred_strong @!>!.!' Ϡ Ƞ p i  ^H7QD6@Ov󚠐!C@!^ ]N?!H@!c ]N=!M@!h ]N@!S@ eR@!Y@7 eC3@"ex @!e@! ]N!k!l@! ]N;!s@! dʀ!y@'Āҩ!~@\ eC@@@@A@@A@AРD.Morphisms_Prop!@A1@D@ABCD@@W.lt_exists_pred @!!!!8!1 ٠ Ҡ z s dǠ@w\!@! ]N!@! ]N@!@T eRة^!@! ]NX!@! ]N!@! dʀ!@}Ā(!@ eC@@@K@A@@,lt_succ_pred @!!ߠ!ؠ!!y!!!     @x!@" ]N𚠐!@" ]N@!@ eR "@" dʀ" @Ā"@Oo0@@@c@A`@@@@ABCD@@ߠ&rs_rs' @"/""!!!a!Z!   O 9 (B5'@@y޶@"5@"P ]Nܶکذ@"=@"X ]N"C@"^ ]Nꚠ"G@"] dʀxf"L@"g ]N@Ͷ@J"S@"n ]N@"Y@ 7 eC@ ""b@ Ā<_"h@" ]N@"n@ L eC3@l"u@" ]Nj"z@" ]N@"@ ^ eC G@"@$ eRaK'詐H)@@{@@U(rs'_rs'' @""""6"/!נ!Р!x!q!b Š  @zT@"@" ]NRPN@"@" ]NZH"@" ]N`"@" dʀܶr"@" ]N@"@" ]N@"@  eC@̚"@" ]Nʚ"@" ]N@"@  eCW@"@ eRIHR暠"@#  ]N!"@# ]N욠"@# ]N@#@  eC"@#@ eR!a#@#) ]N#@#. ]N@#@  eC9@#@ eR8#%@ Ā~@@x@@%rbase @#?#/#("Р"ɠ"q"j"" !!_!I!8RE7@P{@#E@#` ]N#J@#e ]NG#P@#k ]NE#U@#p ]N@#[@!9 eC@#a@ eR;x@@@@@+)A'A_right @#{#k#d# #"""N"G"8!!!ts@|*@#@# ]N(6#@# ]N@#@# ]N#@# ]N#@# ]N@#@!{ eCb@#@@ eR}jB#@# ]N@#@! eCs&@@@@@z6strong_right_induction @#ʠ###[#T"""""!!Ԡ!àݠР@}y@#@# ]Nwus@#@# ]Nm#@# ]N#@# dʀ  #@$ ]N@䚠#@$ ]N@#@! eC @񚠐#@$ ]N#@$ ]N@$@! eC%@$ @ eR$j" $@$+ ]N@$@! eC@@@i@A@!@@ABC@@䠠/right_induction @$4$$$#Š##f#_##""T">"-G:,@E~@$:@$U ]Nߩݰ@$B@$] ]N$H@$c ]N$L@$b dʀ } k $Q@$l ]N@Ҷ@ O$X@$s ]N@$^@"< eC"@&$f@"Ā b$k@$ ]N@$q@"O eC68ѐ@@@@@<0right_induction' @$$|$u$$###_#X#I"""@;@$@$ ]N975@$@$ ]NA/$@$ ]NG$@$ dʀ  ö Y$@$ ]N@ $@$ ]N@$@" eC @ $@$ ]N@$@" eC@h$@"wĀg Ś$@$ ]N7@@!@@7strong_right_induction' @$$ؠ$Ѡ$y$r$$####""@@@$@%  ]N@$@% ]N$@% ]N%@% dʀ!1! %@%  ]N@!% @%& ]N@%@" eC!*b@!%@%2 ]N@%@" eC@!%$@%? ]N!%)@%D ]N@%/@#  eC@%5@ eR!J !3%<@%W ]N@@@@@&ls_ls' @%V%F%?$$$$$)$"$#v#`#Oi\N@gA @%\@%w ]N  @%d@% ]N %j@% ]N %n@% dʀ!!!#%s@% ]N@@!q%z@% ]N@%@ eR@ꐩ%@#6Ā !%@% ]N@%@#q eC!!4@!%@% ]N!%@% ]N@%@# eC!m@%@# eC!U&%@#aĀ!*@@Q@@}(ls'_ls'' @%͠%%%^%W$$$$$##נ#ƠӠ@B |@%@% ]N z x v@%@% ]N  p%@% ]N %@% dʀ""!%@& ]N@!皠%@&  ]N@%@# eC"@!%@& ]N!򚠐&@& ]N@&@# eC"( @&@# eC!(&@#Ā!t,"&@&5 ]N"L"&"@&= ]N"&'@&B ]N@&-@$  eC%@&3@$ eC!L!"0&9@&T ]N".&>@&Y ]N@&D@$" eC<@&J@$( eC!c&P@#Ā!@@@@%lbase @&j&Z&S%%%%%=%6%'$$t$c}pb@{C!@&p@& ]N!"%&u@& ]N"r&{@& ]N"p&@& ]N@&@$d eC@&@$j eC"4&@$@Ā!@@@@@\(A'A_left @&&&&=&6%ޠ%נ%%x%i$̠$$@D![@&@& ]N!Y"g&@& ]N@"&@& ]N"&@& ]N"&@& ]N@&@$ eC;@&@$ eC"|1"-"К&@& ]N@&@$ eC0@@#@@5strong_left_induction @&&&&&&+&$%̠%Š%%%$ @ E!@&@' ]N!!!@'@'" ]N!!' @'( ]N!'@'' dʀ#B#0"ƚ'@'1 ]N@#'@'7 ]N@'"@% eC#;@# ')@'D ]N#'.@'I ]N@'4@% eC,@':@% eC"S'@@$Ā"W#<'E@'` ]N@'K@%) eCS@@@"@$N@@ABC@@.left_induction @'h'X'Q&&&&&;&4&%%%r%a{n`@yF"@'n@' ]N"""@'v@' ]N"" '|@' ]N"#'@' dʀ###5'@' ]N@"@#'@' ]N@'@/ eR@!'@%HĀ"#'@' ]N@'@% eC4@@@@@o/left_induction' @''''P'I&&&&&|%ߠ%ɠ%ҠŠ@G"n@'@' ]N"l"j"h@'@' ]N"t"b'@' ]N"z'@' dʀ$##'@' ]N@#ٚ'@' ]N@'@% eC$ 9@#嚠'@(  ]N@'@ eR@"^'@%Ā#[Y#(@( ]N"j@@ @@ˠ6strong_left_induction' @(( ('''M'F&&&ؠ&;&%&.!@,H"ʶ@(!@(< ]N"ȶ"Ʃ"İ@()@(D ]N"Щ"(/@(J ]N"֚(3@(I dʀ$d$R#蚠(8@(S ]N@$5(>@(Y ]N@(D@&" eC$e@$A(J@(e ]N@(P@&. eC X@$N(W@(r ]N$L(\@(w ]N@(b@&@ eC$"˶@(i@&G eC$4(o@&Ā#̶$k(t@( ]N"ݐ@@ @@>/order_induction @((~(w(('''a'Z'K&&&@I#=@(@( ]N#;#9#7@(@( ]N#C#1(@( ]N#I(@( dʀ$$Ŷ$[(@( ]N@#,@$(@( ]N@(@& eC |@_(@&nĀ^@$(@( ]N@(@i eR9@(@&Ā$3K$К(@( ]N$3@@@$,@$*@AB@@0order_induction' @(((ߠ(((((!'ɠ' '''& @J#@(@) ]N###@)@) ]N##) @)% ]N#)@)$ dʀ%?%-$Ú)@). ]N@#@%)@)5 ]N@) @& eC @ǩ萩)(@&Āƶ@%%).@)I ]N@)4@' eC@ĩ)<@&Oڶ%8)A@)\ ]Nh@@g@@ 1order_induction_0 @)[)K)D(((((.('('{'e'TnaS@lK$ @)a@)| ]N$$$@)i@) ]N$#)o@) ]N$)s@) dʀ%%@%)z@'#ꀶ@%w)@) ]N@)@'d eC)@'4%@ݩ#)@'AĀ1@%)@) ]N@)@< eR%)@'Mꀶ@$)@'ZĀ%  %)@) ]N$@@@@@{2order_induction'_0 @)ˠ)))\)U(((((''ՠ'ĠޠѠ@L$z@)@) ]N$x$v$t@)@) ]N$$n)@) ]N$)@) dʀ&&@&)@'ꀶ@%皠)@*  ]N@)@' eC)@'&@M$e*@'Ā@&* @*$ ]N@*@' eC&/*@'ꀶ@ܐ*@'O&*!@*< ]N$@@@@@렠<_ind @*;*+*$)̠)Š)m)f))(([(E(4NA3@LM$@*A@*\ ]N$$$䰶@*I@*d ]N$$*O@*j ]N$*S@*i dʀ&&r&O*X@*s ]N@&3*`@(Ā%@&V*f@* ]N@*l@  eR"0@4*t@("Ā&i*y@* ]N@*@ eR!D@@@@@I&le_ind @******#)ˠ)Ġ)l)e)V(((@N%H@*@* ]N%F%D%B@*@* ]N%N%<*@* ]N%T*@* dʀ&&ж&*@* ]N@%7@&*@* ]N@*@( eC"@j*@(yĀi&*@* ]N@*@( eC!e@@@@@&Rlt_wd @***٠**z*"*)à)))((@O&*@+ ]N%@*@+ ]N@+@+ ]N%%+@+" ]N@+ @+' ]N%+@+& dʀ%+@+1 ]N%+@+0 dʀ'K'+@+: ]N'+$@+? ]N󠩚++@)  eC&ө+0@ eR'Q@@$@@&Rgt_wd @+J+:+3*۠*Ԡ*|*u***)j)T)C]PB@[P&+O@+j ]N%@+V@+q ]N@+[@+v ]N&%+a@+| ]N@+f@+ ]N& +j@+ dʀ%+p@+ ]N&+t@+ dʀ''p+y@+ ]N'n+~@+ ]NM+@" eR'+@)h eC'd@@%F@@T%lt_wf @++++5+.*֠*Ϡ*w*p*a)Ġ))@Q'Y+@+ ]N"Wf'@,well_founded8E+@+ ]N'+@+ ]N'+@+ ]N+@) eC'p+@j eR'@@@(A𱍠G J@(A7iA)@AB@@%gt_wf @++ߠ+ؠ++y+!+* ***))@R'+@, ]NK+@, ]N'+@, ]N',@, ]NӠ, @ eR($,@) eC'@@C@@ڠ-add_lt_mono_l @,*,,+++\+U****J*4*#@*@(#,,@,G ]N(!,1@,L ]N$,6@,Q ]N(h,=@ eR'婚,B@ eR,H@* s$P,M@*! s(f@@& @@AA@@A@-add_lt_mono_r @,j,Z,S+++++=+6+'**t*c@*_A(c,l@, ]N(a,q@, ]N$՚,v@, ]N(,}@ eR(%,@ eR,@*\ s$L,@*a s(@@&I@@@+add_lt_mono @,,,,8,1+٠+Ҡ+z+s+d*Ǡ**@*B(,@, ]N(,@, ]N%,@, ]N#,@, ]N@,@[ eR#@,@a eR(l,@f eR,@* s'8(p,@* s5@@@@@-add_le_mono_l @,,ߠ,ؠ,,y,!,+ +++**@*C(蚠,@-  ]N(暠,@- ]N%Z,@- ]N)--@* eC(-@* eC- @* s%-@* s)+@@&@@Š-add_le_mono_r @-,--,,,^,W++++L+6+%@+!D)%-.@-I ]N)#-3@-N ]N%-8@-S ]N)j-?@+ eC(穚-D@+" eC-J@+ s%-O@+# s)p@@' @@+add_le_mono @-i-Y-R,,,,,<,5,&++s+b@+^E)b-k@- ]N)`-p@- ]N%Ԛ-u@- ]N$-z@- ]N@-@+^ eC$@-@+d eC).-@+i eC-@+e s©-@+j s@@@@@I.add_lt_le_mono @----A-:,,۠,,|,m+Р++@+F)-@- ]N)-@- ]N&-@- ]N%-@- ]N@-@ d eR$@-@+ eC)u-@ o eR-@+ s -@+ s=@@@@@.add_le_lt_mono @------)-",ʠ,à,,,+@+G)𚠐-@. ]N)-@. ]N&b.@. ]N%H.@.# ]N@.@+ eC%;@.@  eR).@  eR.@+ sP.$@+ s@@@@@נ+add_pos_pos @.>...'-Ϡ-Ƞ-p-i-- ,,^,H,7@,3H*7.@@.[ ]N*5.E@.` ]N@.K@  eR.P@+*p@.V@  eR.[@,*{.`@  eR.e@,ꀩ.j@,> s%@@@@.add_pos_nonneg @..t.m..---W-P-A,,,}@,yI*}.@. ]N*{.@. ]N@.@!. eR.@,?*@.@,z eC.@,J*.@!C eR.@,Tꀩ.@, s%ݐ@@N@@c.add_nonneg_pos @.ʠ...[.T-----,,Ԡ,@,J*Ú.@. ]N*.@. ]N@.@, eC.@,*@.@! eR.@,+.@! eR.@,ꀩ.@, s&#@@@@1add_nonneg_nonneg @//....B.;--ܠ-͠-0-- @-K+ /@/- ]N+/@/2 ]N@/@, eC/"@,+B@/(@- eC/-@,+M/2@- eC/7@,ꀩ/<@- s&i@@@@,lt_add_pos_l @/V/F/?.....).".-v-`-O@-KL+O/X@/s ]N+M/]@/x ]N@/c@" eR/h@-+/m@"  eR+/s@-G s+@@@*@,v@AB@@(,lt_add_pos_r @///x/ /...b.[.L---@-M+/@/ ]N+/@/ ]N@/@"9 eR/@-J+/@"C eR+ǩ/@- s+@@*@@_,le_lt_add_lt @/Ơ///W/P.....--Р-@-N+/@/ ]N+/@/ ]N(1/@/ ]N'/@/ ]N@/@- eC' @/@" eR/@- s+/@- s,*e/@" eR'!@@@@@,lt_le_add_lt @0/////@/9..ڠ.ˠ....@.O,0@0+ ]N,0@00 ]N(y0@05 ]N'_0@0: ]N@0%@" eR'R@0+@.  eC01@. s+˩06@.  sH0;@" eR'h@@@@@,le_le_add_le @0U0E0>//ߠ///(/!/.u._.N@.JP,N0W@0r ]N,L0\@0w ]N(0a@0| ]N'0f@0 ]N@0l@.J eC'@0r@.P eC0x@.L s,0}@.Q s0@.` eC'@@@@@5,add_lt_cases @0000-0&/Π/Ǡ/o/h/Y...@.Q,0@0 ]N,0@0 ]N)0@0 ]N'횠0@0 ]N@0@#P eR0@. s'橚0@. s,ߩ!Ҡ0@#b eR!%0@#g eR,k@@@@@},add_le_cases @00Ԡ0͠0u0n00////..@.R,ݚ0@1 ]N,ۚ0@1 ]N)O0@1  ]N(50@1 ]N@0@. eC1@. s(.1@. s-'"1 @. eC!m1@. eC,@@@@@Š-add_neg_cases @1,11000^0W////L/6/%@/!S-%1.@1I ]N-#13@1N ]N@19@# eR1?@/ s-`1C@.ꀩ"W1J@# eR-$1O@.ꀩ1T@# eR-u1Y@/ꀐ@@,@@ -add_pos_cases @1s1c1\10000F0?00//}/l@/hT-l1u@1 ]N-j1z@1 ]N@1@$ eR1@/.ꀩ1@/^ s-"1@$. eR1@/?-o1@$8 eR1@/I-@@>@@S0add_nonpos_cases @1111K1D00000w/ڠ/Ġ/@/U-1@1 ]N-1@1 ]N@1@/ eC1@/ s-1@/zꀩ"堩1@/ eC-1@/ꀩ1@/ eC.1@/ꀐ@@-:@@0add_nonneg_cases @21111131,0Ԡ0͠00!0 /@/V-2@2 ]N-2@2# ]N@2@/ eC2@/ꀩ2@/ s.9#,2@/ eC2$@/-2)@0 eC2.@/.N@@@@ᠠ-le_exists_sub @2H28211٠1Ҡ1z1s1110h0R0A@0=W.A2J@2e ]N.?2O@2j ]N@2U@03 eC.v2[@2v ]N*2`@2{ ]N/2g@2} dʀ.A2m@0A s ک2r@0P eC2w@0 .@@@-@A.@/|@A/|AA@@-@ABCD@@3+mul_lt_pred @2222+2$1̠1Š1m1f1W0@1U@*2@2 ]N)ߚ2@2 ]N.2@2 ]N.2@2 ]N@2@2 dʀ2@0cĀ.V..蠩2@%Z eR2@0 ##2@0 -?.驚2@%k eR2@0 s2@0 *.2@0 s2@0 ..@@,@@AA@@A@1mul_lt_mono_pos_l @32222242-1ՠ1Π11"@1A+a3@3 ]N.3@3" ]N.3 @3' ]N@3@% eR3@0./I3@% eR.Ʃ3#@% eR3)@0 *V3.@0 .ϐ@@@.@A.~@.@03@@ABCD@@N1mul_lt_mono_pos_r @3M3=362ޠ2נ22x2 22 1m@2B+3M@3h ]N/I3R@3m ]N/G3W@3r ]N@3]@% eR3b@1 /;/3i@& eR/3n@&  eR3t@1; /3y@1@ //@@-6@@1mul_lt_mono_neg_l @333}3%32Ơ22g2`2Q1@2OC+󚠐3@3 ]N/3@3 ]N/3@3 ]N@3@&A eR/~3@1Rꀩ/۠3@&M eR/X3@&R eR3@1 /\3@1 *@@@@۠1mul_lt_mono_neg_r @3ڠ3ʠ3à3k3d3 32221@2D,93@3 ]N/֚3@3 ]N/Ԛ3@3 ]N@3@& eR/Ě3@1ꀩ0!3@& eR/3@& eR4@1 4@1 /@@-@@!4mul_le_mono_nonneg_l @4 44 333R3K222ݠ2@@2E04 @4; ]N04%@4@ ]N,4*@4E ]N@40@2 eC45@10T@4;@2 eC+h4@@2 eC4F@2  0 .4L@2 /@@/@@g4mul_le_mono_nonpos_l @4f4V4O333339323#2@3!F0]4f@4 ]N0[4k@4 ]N,Ϛ4p@4 ]N@4v@2T eC04{@2$ꀶ@4@2_ eC+4@2d eC4@2S 0&4@2X K@@/@@4mul_le_mono_nonneg_r @4444<453ݠ3֠3~3w3h2@3fG04@4 ]N04@4 ]N-4@4 ]N@4@2 eC4@2i0߶@4@2 eC+󩚠4@2 eC4@2 %14@2 ,@@0)@@4mul_le_mono_nonpos_r @444٠44z4"43à333@3H0皠4@5  ]N0嚠4@5 ]N-Y4@5 ]N@5@2 eC1 5@2ꀶ@5 @2 eC,85@2 eC5@2 ,C5@2 %{@@0n@@6,mul_cancel_l @555%54Ơ44g4`4433U@3I1,55@5P ]N1*5:@5U ]N-5?@5Z ]N@1-5G@5] dʀ1g5L@2ꀩ1~5S@5i dʀ5Y@3  ਗ਼5^@3% 185c@5y dʀ,@@@0@2f@0s@ABC@@,mul_cancel_r @55p5i55 444S4L4=3@4;J1w5@5 ]N1u5@5 ]N-隠5@5 ]N@1x5@5 dʀ15@3@ꀩ1ɠ5@5 dʀ5@3k 1E5@3p 1Q5@5 dʀ,ې@@/j@@ɠ(mul_id_l @5Ƞ555Y5R444443@4K15@5 ]N15@5 ]N@15@5 dʀ15@3ꀩ2 5@5 dʀ5@3 125@6 dʀ1ƚ5@3 @@1@@ (mul_id_r @6 55555=564ޠ4נ4Ƞ4+@4L26 @6& ]N26@6+ ]N@16@6. dʀ296@3ꀩ2O6$@6: dʀ6*@3 126/@6E dʀ2P64@3 @@/@@O1mul_le_mono_pos_l @6N6>675ߠ5ؠ55y5!55 4n@5 M2E6N@6i ]N2C6S@6n ]N.6X@6s ]N@6^@( eR6c@4 226j@4H eC-6o@4M eC6u@4< 6z@4A 2T@@1@@1mul_le_mono_pos_r @666}6%65Ơ55g5`5Q4@5ON26@6 ]N26@6 ]N.6@6 ]N@6@)A eR6@4R2ȩ2۠6@4 eC-ݩ6@4 eC6@4 2\6@4 2h@@0|@@۠1mul_le_mono_neg_l @6ڠ6ʠ6à6k6d6 65554@5O2њ6@6 ]N2Ϛ6@6 ]N/C6@6 ]N@6@) eR3 6@4ꀩ3!6@4 eC.#6@4 eC7@4 2۩7@4 @@@@!1mul_le_mono_neg_r @7 77 666R6K555ݠ5@@5P37 @7; ]N37%@7@ ]N/7*@7E ]N@70@) eR3P75@4ꀩ3g7<@5 eC.i7A@5 eC7G@5 2署7L@5 2@@1@@g2mul_lt_mono_nonneg @7f7V7O666669626#5@6!Q3]7f@7 ]N3[7k@7 ]N/Ϛ7p@7 ]N.7u@7 ]N@7{@5Y eC7@5)3 @7@*# eR13'@7@5k eC7@5;32@7@*5 eR7@*: eR7@5j 2 7@5p "p2 @@@@@Š2mul_le_mono_nonneg @7Ġ777U7N666665@6R37@7 ]N37@7 ]N0-7@7 ]N/7@7 ]N@7@5 eC7@53~@7@5 eC^@7@5 eC7@53@7@5 eCo7@5 eC8@5 ]8@5 \@@3X@@ +mul_pos_pos @888777Q7J666ܠ6?@6S48@8: ]N48$@8? ]N@8*@* eR8/@54O@85@* eR8:@54Z8?@* eR8D@5ꀩ8I@6 /v@@@@d+mul_neg_neg @8c8S8L7777767/7 6@7T4Z8c@8~ ]N4X8h@8 ]N@8n@+  eR48s@6ꀶ@8y@+ eR48~@6'ꀩ8@+  eR8@61ꀩ8@6T /@@+@@+mul_pos_neg @88888817٠7Ҡ7z7s7d6@7bU48@8 ]N48@8 ]N@8@+O eR8@6`4׶@8@+Z eR4ޚ8@6kꀩ8@+d eR8@6 /8@6zꀐ@@4$@@젠+mul_neg_pos @88۠8Ԡ8|8u887777 @7V4⚠8@9 ]N48@9  ]N@8@+ eR58@6ꀶ@9@+ eR9@65&9 @+ eR9@6 0>9@6ꀐ@@@@01mul_nonneg_nonneg @9/99888a8Z8777O@7W5&9/@9J ]N5$94@9O ]N@9:@7 eC9?@65_@9E@7# eC9J@65j9O@7- eC9T@6ꀩ9Y@7  0@@@@t0mul_pos_cancel_l @9s9c9\98888F8?807@8.X5j9s@9 ]N5h9x@9 ]N@9~@, eR9@7,559@,' eR9@78ꀩ9@7[ 5<9@,6 eR9@7G5@@ +@@0mul_pos_cancel_r @9999I9B88888u7@8sY59@9 ]N59@9 ]N@9@,` eR9@7q559@,l eR9@7}ꀩ9@7 59@,{ eR9@75@@ p@@3mul_nonneg_cancel_l @999999/9(8Р8ɠ88@8Z59@: ]N5򚠐:@: ]N@:@, eR: @76-6?:@7 eC:@7ꀩ:@7 5Ʃ:#@8 eC:(@76H@@ @@C3mul_nonneg_cancel_r @:B:2:+9Ӡ9̠9t9m9988b@8[69:B@:] ]N67:G@:b ]N@:M@, eR:R@76q6:Y@87 eC:^@8ꀩ:c@8* 6 :h@8F eC:m@86F@@ @@,lt_1_mul_pos @::w:p::999Z9S9D8@9B\6~:@: ]N6|:@: ]N@:@-/ eR:@8X 6@:@-: eR:@8K6©:@-D eR:@8m :@8x 1ސ@@O@@̠(eq_mul_0 @:ˠ:::\:U999998@9]6š:@: ]N6:@: ]N7:@: dʀ:@8 6:@8ꀩ+:@: dʀ7 :@8ꀩ:@; dʀ7:@8ꀐ@@4@@)neq_mul_0 @;;::::C:<99ݠ9Π91@9^7;@;, ]N7;@;1 ]N7H 砩7;!@;7 dʀ7B;&@8ꀩ7;-@;C dʀ7M;2@8ꀩ7;9@;O dʀ;?@9 7`;C@8ꀐ@@4@@^+eq_square_0 @;];M;F:::::0:):9}@:_7T;]@;x ]N7;d@;z dʀ;j@91 -ݚ;n@9ꀩ;s@; dʀ7;x@9!ꀐ@@@@@*eq_mul_0_l @;;;{;#;:Ġ::e:^:O9@:M`7;@; ]N7;@; ]N@;@; dʀ;@9j 7Ě;@9Pꀶ@7;@; dʀ7К;@9]ꀩ;@; dʀ7Z;@9gꀐ@@@@@٠*eq_mul_0_r @;ؠ;Ƞ;;i;b; ;:::9@:a7Ϛ;@; ]N7͚;@; ]N@;@; dʀ;@9 8 ;@9ꀶ@7ې;@<  dʀ7Ϛ;@9ꀩ;@< dʀ7ٚ<@9ꀐ@@@@@ (mul_eq_0 @+<@\Ĉ<"<< ;;;T;M:::@8@ =====>=7<ߠ<ؠ<ɠ<,@ @>' ]N:>@>, ]N@>@; eC>@;:;@>"@0 eR>(@; w>-@; :N:N>3@0 eR5`@@@@@ N6square_le_simpl_nonneg @>M>=>6=ޠ=נ==x= == M@>h ]N:B>R@>m ]N@>X@<6 eC>]@<:|@>c@i@<0 >n@<5 A>s@>}>v>>===`=Y=J<@=Hg:>@> ]N:>@> ]N@>@15 eR:>@1: eR>@@@@@<~ >@֠>Ơ>>g>`>>===<@=h!a>@> ]N!b>@> ]N@>@1 eR>@< ; @>@1 eR>@< ;>@< eC?@< s6-?@< 62@@:X@@ -square_nonneg @???>>>Q>J===ܠ=?@=iI?@?: ]N?$@= eC?)@<ꀩ?.@< 1@@ @@ I5crossmul_le_addsquare @?H?8?1>٠>Ҡ>z>s>>>=h@>jr?H@?c ]Np?M@?h ]N@?S@=1 eC?X@=;x@?^@=< eC?c@= ;?h@=F eC?n@=B s?t@=; ;?y@=@ 6?~@=R s?@=K ٩?@=P ؐ@@y@@ 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