K&NM@&lemmasBA@&PrologB@'ProgramB@%TautoB@#InvB@(EqualityB@&ProPreB@0Logic_TypeSyntaxB@*Logic_TypeB@'PreludeB@"WfB@%PeanoB@,SpecifSyntaxB@&SpecifB@+LogicSyntaxB@%LogicB@/DatatypesSyntaxB@)DatatypesB@$CoreB@"IOB@S@'Zgt_neqB'Zlt_neqB +Zopp_lt_gt_@B )Zle_minusB,Zmult_ab0a0b@B,mult_pq1_p1qAB,mult_ppq_p0qAB/simpl_eq_mult_lB!/simpl_le_mult_lB%/simpl_lt_mult_lB)'le_diff@B-.lt_multpred_ppB1*n0n1_or_gtB5-lt_n_nm_m_gt_AB9*lt_lt_multB=*le_le_multBA*lt_witnessBE*le_witnessBI*witness_leBM*sqr_ascendBQ'lt_n_nmBU'le_n_nnBY'le_n_mnB]'le_n_nmBa(sqrboundBe)le_mult_rBi)lt_mult_lBm,lt_plus_plusBq)le_mult_lBu)predminusAB@@z!_@B&ZArith@&ZArithBA AB%EqNat@%EqNatBA(CONSTANT@@@@C)Datatypes@#nat@@!n @C D%Logic@"eq@@D%Peano@$pred@AD%Minus@%minus@ D1@B4@AD%@A;C@@HD"Lt@*lt_le_weak@Q#PQD @(le_or_lt@YXBxsBzpTAA@@@@@z@@@@C@@@!nDУ@'nat_ind@C B!mDv@@@BD~@@D*@BAC.D@A5@AC83AC)#IHnACA-D"Le@&le_n_S@CD@@'D3 .D𣓰)auxiliary@(eq_ind_r@^D 4Ca\DJD9DУ%@-le_plus_trans@"ADPC#D/@(plus_sym@K$KBygAA@@@@@5@@@@C@@@!nC !mD𣓰@@?@D@y@BD @BAC$D @@@C D@n@DD$Mult@(mult_sym@"#BA@B)DУ@@00D(2BKDУe@@@EED @@@AMD@Dv@G@GuDuaBBBD{v]@BW@DcDjepAA@@@@@V@@@@C@@@!nDУ@'nat_ind@C BDN@"gt@AD @B#@A@D`@@BDh@@CD"D~@)False_ind@D#D%%DG@@12CO!mCA#IHmCDED>0@%D𣓰@&or_ind@D@KCD@"eq@@qT DKDV DGC@D{@Q@DD@@D\ Do D𣓰@@DDiCDuEDD𣓰'@&@D$'CDDУI@-lt_plus_trans@3 3D5 5DQD69&DW@(@@-8D@N@GGCaRD=CΥɣDDDD@@@BDDD @A dʣD@+le_lt_or_eq@D@&le_S_n@ڠBAA@@@@@\@@@@C@@@!xC !yCDX@"ex@@C!qDe@d@@#Dc@[@CABD࣓y@&ex_ind@8C9!DDl'gD𣓰 o@ A@DnDRmC!nD`ssD x@@%{D@@ED@&le_O_n@D @ @DpBBBD @@@D}CDxrDlAA@@@@@ ' װ@@@@C m@ l@@!bDУ x@'nat_ind@C!nB!aB!cB!!dBD @ @@CD@BD B@DD @ q@EDFCC,CE)CG&CD#L@A C! "@D𣓰 @&eq_ind@]C^LD9D*A&D-8DA@A -D@)le_n_O_eq@5@CtoACb#IHbAC}fCcC`CD]XD@BL6D=/)D @ @6Ch^A]CnZBDWDDRDCO@DNDHKJTDB~D )@ !@DdgPgCtBDqd@Dc]]DUZC~BD{$Dp& CD{{ODMD @@3} DEDwD T@ @yCCDCDEDDmD B@>_n_S@HD J@'gt_Sn_O@B̥DzBΥIJBDDAA@@@@@  @@@@C ?@ >@@!n @C D @ @@D @ @@A @ADD &D)@B D @j@ D#@AD 9D)D$=D D)@AD%CE@A?CKFD?C[VAUCaRBDODILK@DCD>D9DR6DDWCD_YY5D3DSDNDIbDRddD l@p@klCBCDxDr+tPD𣓰@7@DeD~.D @@5BAA@@@@@Z @@@@C @ @@!bDУ @'nat_ind@C!nB!aB!cBD @ @@BC@BD@@@3 D @ @D@D>?@ACB+E@CI7BK/BD,'@BD%S*+ACU9CD6 HCD1_!7 N@D𣓰 @ @i@CjXD?m3DB@ArI4CsaCuYCDVD|@BV@%CDTD [\%Dh@)False_ind@QD -@ @ZlCAC"IHCCCD|D+lMCD|D1DyEPD ND9DFCBDiDCGfDCDDLnDDD @~@ Df BץAA@@@@@Dܰ@@@@Cr@q@@!aDУ}@'nat_ind@C!nB!bB!cBD@@D@g@CBD A@DC8!C:CD?@AD @)False_ind@D @ @ CTOACB"IHC]FC_CCD@D;Dh@BD;DC:,D𣓰7@&or_ind@D6@"le@@OND]PQKC V@DDeYDQ@@@%` C eA`C D  @ @2CBD~DyD>HsD~EhDGFCDDDN KtDrD DnD B@\@YCFCDУ$Core@#LET@DXDDm'DlPC GDD4rDУ b@)le_not_lt@3D3>D l@ k@DУ@@GD z@ q@ȠBAA@@@@@T谠@@@@C~@}@@!aDУ@'nat_ind@C!nB!bB!cBD@ @)@AC@BD@@@D@@DDB@DCD-CF*CD'""+CD D*'D,5@D,@)False_ind@D @ J@>'CgbACU"IHCpYCrVCDSNDy@B?1CDODJD EYDOG2D𣓰\@&or_ind@NDnfUPCQsAACDADl`DУ .@)lt_not_le@DoD0GmDt(DУ@@v/ sD D@ ;@}$BAA@@@@@"@@@@CH@G@@!aC !bC!cCD@@@ACCD@@@*D@?@DDB@DУ .@*le_antisym@"D࣓@n@E*D𣓰 +@ *@OD% 3CR!nD@@@AD4F0D @AD<!7 D(#L96D"lCmD BrmBtjBvgBd@BW@DX}L_AA@@@@@=@@@@C@@@!p @C!nB!qBDC@B@@ BDB@@A@DT@O@@D3C5@AD9D<@B C?+CD(CD"{D@AD4OD7@AT CUPACYECDB]D$?D>9D9@BDNiD0874D࣓@(@ R9DY@ @FD𣓰@u@CrDi\DcDMDPDD@@Dq+`+CD}pDfCDDxDQ9D@Y@@DBrD@@I~DKBAA@@@@@z@@@@C@@@!p @C!nB!qBD@@@ D@@BAD,@B/@A@D!@@@D ;CD#>C?+CD(C>DУ@@:@%False@@D!C Q@DH@)False_ind@D/"*;D𣓰R@$@j=@D:DQqD DE7C31DD@BD]}N;1C,&@CDdDD@%timesA@RC=!yeedODУ@@ @@@Dm3DD=ywC :@D1@)False_ind@DDDOE>D𣓰@@@DYD<Q6Cť@АA5C@W@@@C@>@AC_CDD@C`DSND|DD CUIDGDADDˣD@D;C974f*1(ӲCCDCBD Dߥ@DܣDD2زCԥңD$ͲCȥC=أDDC{DyDD )DHs2CڥCDD"HCDDD   B;4$mA@@@@@c㰠@@@@C,fast_integer@!Z@@!aC !bCD*zarith_aux@#Zle@ABDУ@0Zsimpl_le_plus_l@ (@AD@&Zminus@CD𣓰G@F@:D<@%Zplus@DD@$Zopp@/CK!zD>D!,D#;D"WDD@)C\DLED,a:CbDRD+MDD𣓰8@ @oTCp%D`Y YD9ZNDd@)Zplus_n_O@b$D@/Zplus_inverse_r@jDKlMDv@-Zplus_assoc_l@tM]DU_OD@)Zplus_sym@gWBBB@D{xAA@@@@@@@@@C@!Z@@!xD࣓@%Z_ind@C!zBD@#Zlt@A"@A@D@#Zgt@D@$Zopp@BCDDУ.@-@@@@D#D++C @D@)False_ind@8D𣓰@@@(relation@@@AC @АAT@@@66@A@B_C0@'@@&CDqD@BpoWDUPDnDhD dxCWMDKDxDrDCDLGH@CCKA?<jj941C.)CDD@C~D9@"eq@@AbBåQA@@@@@쐠d@@@@C@!Z@@!xC !yCD@@BAvCDn@m@@$C@D @@/ C0!zBD%D@N@@CD/(D@)False_ind@D@'Zlt_n_n@::;BTNBVKBH@D@#not@DAA@@@@@`Ӱ@@@@C9@o@@!xC !yCD@*@BACD@@@#C@D +@*@. C/!zBD%D@@@CD/(D@)False_ind@D(@n@D/@&Zgt_lt@""A"ABBZUB\RBO@D@u@JAA@@@@@@