0.00/0.13	% Problem    : theBenchmark.p : TPTP v0.0.0. Released v0.0.0.
0.13/0.14	% Command    : do_cvc5 %s %d
0.13/0.35	% Computer : n003.cluster.edu
0.13/0.35	% Model    : x86_64 x86_64
0.13/0.35	% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
0.13/0.35	% Memory   : 8042.1875MB
0.13/0.35	% OS       : Linux 3.10.0-693.el7.x86_64
0.13/0.35	% CPULimit   : 960
0.13/0.35	% WCLimit    : 120
0.13/0.35	% DateTime   : Tue Aug  9 04:31:06 EDT 2022
0.13/0.35	% CPUTime    : 
0.86/1.02	%----Proving TH0
10.18/10.37	------- cvc5-thf casc j11 : /export/starexec/sandbox2/benchmark/theBenchmark.p at /export/starexec/sandbox2/benchmark/theBenchmark.p...
10.18/10.37	--- Run --ho-elim --full-saturate-quant at 10...
10.18/10.37	% SZS status Theorem for theBenchmark
10.18/10.37	% SZS output start Proof for theBenchmark
10.18/10.37	(let ((_let_1 (@ ord_less_rat zero_zero_rat))) (let ((_let_2 (= neg_nu3811975205180677377ec_int (lambda ((X2 int)) (@ (@ minus_minus_int (@ (@ plus_plus_int X2) X2)) one_one_int))))) (let ((_let_3 (= fI_QUERY (lambda ((P2 assn) (Q2 assn) (F3 assn)) (@ (@ entails P2) (@ (@ times_times_assn Q2) F3)))))) (let ((_let_4 (@ (@ product_Pair_int_int zero_zero_int) one_one_int))) (let ((_let_5 (= semiri1314217659103216013at_int (lambda ((N2 nat)) (@ abs_Integ (@ (@ product_Pair_nat_nat N2) zero_zero_nat)))))) (let ((_let_6 (= fI_RESULT (lambda ((M7 list_P8527749157015355191n_assn) (UP assn) (UQ assn) (F3 assn)) (let ((_let_1 (@ foldr_assn_assn times_times_assn))) (=> (forall ((X2 produc6575502325842934193n_assn)) (=> (@ (@ member7957490590177025114n_assn X2) (@ set_Pr1139785259514867910n_assn M7)) (@ (@ produc7274209992780475162assn_o entails) X2))) (@ (@ entails (@ (@ times_times_assn (@ (@ _let_1 (@ (@ map_Pr8991440229025900053n_assn produc9167289414957590229n_assn) M7)) one_one_assn)) UP)) (@ (@ times_times_assn (@ (@ times_times_assn (@ (@ _let_1 (@ (@ map_Pr8991440229025900053n_assn produc2051961928117032727n_assn) M7)) one_one_assn)) UQ)) F3)))))))) (let ((_let_7 (@ ord_less_int one_one_int))) (let ((_let_8 (= biject3388518990857851981at_nat (lambda ((R3 set_Pr4329608150637261639at_nat)) (and (forall ((X2 set_Pr1261947904930325089at_nat) (Y5 set_Pr1261947904930325089at_nat) (Z5 set_Pr1261947904930325089at_nat)) (=> (and (@ (@ member8757157785044589968at_nat (@ (@ produc2922128104949294807at_nat X2) Z5)) R3) (@ (@ member8757157785044589968at_nat (@ (@ produc2922128104949294807at_nat Y5) Z5)) R3)) (= X2 Y5))) (forall ((X2 set_Pr1261947904930325089at_nat) (Y5 set_Pr1261947904930325089at_nat) (Z5 set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ produc2922128104949294807at_nat X2))) (=> (and (@ (@ member8757157785044589968at_nat (@ _let_1 Y5)) R3) (@ (@ member8757157785044589968at_nat (@ _let_1 Z5)) R3)) (= Y5 Z5))))))))) (let ((_let_9 (@ ord_le6747313008572928689nteger zero_z3403309356797280102nteger))) (let ((_let_10 (= ord_min_filter_nat (lambda ((A3 filter_nat) (B3 filter_nat)) (@ (@ (@ if_filter_nat (@ (@ ord_le2510731241096832064er_nat A3) B3)) A3) B3))))) (let ((_let_11 (= (@ field_o bot_bo7073875226086086771od_o_o) bot_bot_set_o))) (let ((_let_12 (@ ord_le6747313008572928689nteger one_one_Code_integer))) (let ((_let_13 (@ (@ product_Pair_nat_nat one_one_nat) zero_zero_nat))) (let ((_let_14 (= one_one_int (@ abs_Integ _let_13)))) (let ((_let_15 (= pairwise_int (lambda ((R3 (-> int int Bool)) (S2 set_int)) (forall ((X2 int)) (=> (@ (@ member_int X2) S2) (forall ((Y5 int)) (=> (@ (@ member_int Y5) (@ (@ minus_minus_set_int S2) (@ (@ insert_int2 X2) bot_bot_set_int))) (@ (@ R3 X2) Y5))))))))) (let ((_let_16 (= is_pure_assn (lambda ((A3 assn)) (exists ((P2 Bool)) (= A3 (@ pure_assn P2))))))) (let ((_let_17 (@ (@ bNF_re7400052026677387805at_int pcr_int) pcr_int))) (let ((_let_18 (@ (@ bNF_re7408651293131936558nt_int pcr_int) _let_17))) (let ((_let_19 (= finite_finite_nat (lambda ((N8 set_nat)) (exists ((M nat)) (forall ((X2 nat)) (=> (@ (@ member_nat X2) N8) (@ (@ ord_less_nat X2) M)))))))) (let ((_let_20 (@ size_size_list_c xs))) (let ((_let_21 (= biject1468766312547416318et_nat (lambda ((R3 set_Pr8536935166611901872et_nat)) (and (forall ((X2 (-> produc3658429121746597890et_nat Bool)) (Y5 (-> produc3658429121746597890et_nat Bool)) (Z5 produc3925858234332021118et_nat)) (=> (and (@ (@ member6124377750444531601et_nat (@ (@ produc2245416461498447860et_nat X2) Z5)) R3) (@ (@ member6124377750444531601et_nat (@ (@ produc2245416461498447860et_nat Y5) Z5)) R3)) (= X2 Y5))) (forall ((X2 (-> produc3658429121746597890et_nat Bool)) (Y5 produc3925858234332021118et_nat) (Z5 produc3925858234332021118et_nat)) (let ((_let_1 (@ produc2245416461498447860et_nat X2))) (=> (and (@ (@ member6124377750444531601et_nat (@ _let_1 Z5)) R3) (@ (@ member6124377750444531601et_nat (@ _let_1 Y5)) R3)) (= Y5 Z5))))))))) (let ((_let_22 (= pairwi6357175311820755948at_nat (lambda ((R3 (-> product_prod_nat_nat product_prod_nat_nat Bool)) (S2 set_Pr1261947904930325089at_nat)) (forall ((X2 product_prod_nat_nat)) (=> (@ (@ member8440522571783428010at_nat X2) S2) (forall ((Y5 product_prod_nat_nat)) (=> (@ (@ member8440522571783428010at_nat Y5) (@ (@ minus_1356011639430497352at_nat S2) (@ (@ insert8211810215607154385at_nat X2) bot_bo2099793752762293965at_nat))) (@ (@ R3 X2) Y5))))))))) (let ((_let_23 (@ (@ product_Pair_int_int one_one_int) one_one_int))) (let ((_let_24 (= set_or6656581121297822940st_int (lambda ((I4 int) (J2 int)) (@ set_int2 (@ (@ upto (@ (@ plus_plus_int I4) one_one_int)) J2)))))) (let ((_let_25 (= cofinite_nat at_top_nat))) (let ((_let_26 (@ ord_less_int zero_zero_int))) (let ((_let_27 (= pairwi3222497012029234898at_nat (lambda ((R3 (-> produc3843707927480180839at_nat produc3843707927480180839at_nat Bool)) (S2 set_Pr4329608150637261639at_nat)) (forall ((X2 produc3843707927480180839at_nat)) (=> (@ (@ member8757157785044589968at_nat X2) S2) (forall ((Y5 produc3843707927480180839at_nat)) (=> (@ (@ member8757157785044589968at_nat Y5) (@ (@ minus_3314409938677909166at_nat S2) (@ (@ insert9069300056098147895at_nat X2) bot_bo228742789529271731at_nat))) (@ (@ R3 X2) Y5))))))))) (let ((_let_28 (= fi (lambda ((M list_P8527749157015355191n_assn) (P7 assn) (Q8 assn) (Up assn) (Uq assn) (F6 assn)) (let ((_let_1 (@ foldr_assn_assn times_times_assn))) (=> (forall ((X2 produc6575502325842934193n_assn)) (=> (@ (@ member7957490590177025114n_assn X2) (@ set_Pr1139785259514867910n_assn M)) (@ (@ produc7274209992780475162assn_o entails) X2))) (@ (@ entails (@ (@ times_times_assn (@ (@ times_times_assn (@ (@ _let_1 (@ (@ map_Pr8991440229025900053n_assn produc9167289414957590229n_assn) M)) one_one_assn)) P7)) Up)) (@ (@ times_times_assn (@ (@ times_times_assn (@ (@ times_times_assn (@ (@ _let_1 (@ (@ map_Pr8991440229025900053n_assn produc2051961928117032727n_assn) M)) one_one_assn)) Q8)) Uq)) F6)))))))) (let ((_let_29 (= times_times_assn (lambda ((P2 assn) (Q2 assn)) (@ abs_assn (@ (@ times_assn_raw (@ rep_assn P2)) (@ rep_assn Q2))))))) (let ((_let_30 (= set_or4665077453230672383an_nat (lambda ((I4 nat) (J2 nat)) (@ set_nat2 (@ (@ upt I4) J2)))))) (let ((_let_31 (= uminus_uminus_assn (lambda ((P2 assn)) (@ abs_assn (lambda ((H3 produc3658429121746597890et_nat)) (and (not (@ (@ rep_assn P2) H3)) (@ in_range H3)))))))) (let ((_let_32 (@ (@ map_fu3667384564859982768at_int rep_Integ) abs_Integ))) (let ((_let_33 (= uminus_uminus_int (@ _let_32 (@ produc2626176000494625587at_nat (lambda ((X2 nat) (Y5 nat)) (@ (@ product_Pair_nat_nat Y5) X2))))))) (let ((_let_34 (= set_or5832277885323065728an_int (lambda ((I4 int) (J2 int)) (@ set_int2 (@ (@ upto (@ (@ plus_plus_int I4) one_one_int)) (@ (@ minus_minus_int J2) one_one_int))))))) (let ((_let_35 (= biject576505603616484041nt_int (lambda ((R3 set_Pr1872883991513573699nt_int)) (and (forall ((X2 (-> int option6357759511663192854e_term)) (Y5 (-> int option6357759511663192854e_term)) (Z5 product_prod_int_int)) (=> (and (@ (@ member7034335876925520548nt_int (@ (@ produc4305682042979456191nt_int X2) Z5)) R3) (@ (@ member7034335876925520548nt_int (@ (@ produc4305682042979456191nt_int Y5) Z5)) R3)) (= X2 Y5))) (forall ((X2 (-> int option6357759511663192854e_term)) (Y5 product_prod_int_int) (Z5 product_prod_int_int)) (let ((_let_1 (@ produc4305682042979456191nt_int X2))) (=> (and (@ (@ member7034335876925520548nt_int (@ _let_1 Z5)) R3) (@ (@ member7034335876925520548nt_int (@ _let_1 Y5)) R3)) (= Y5 Z5))))))))) (let ((_let_36 (= distinct_nat (lambda ((Xs3 list_nat)) (forall ((I4 nat)) (=> (@ (@ ord_less_nat I4) (@ size_size_list_nat Xs3)) (forall ((J2 nat)) (let ((_let_1 (@ nth_nat Xs3))) (=> (@ (@ ord_less_nat J2) (@ size_size_list_nat Xs3)) (=> (not (= I4 J2)) (not (= (@ _let_1 I4) (@ _let_1 J2))))))))))))) (let ((_let_37 (@ (@ bNF_re8279943556446156061nt_rat pcr_rat) pcr_rat))) (let ((_let_38 (@ (@ bNF_re7627151682743391978at_rat pcr_rat) _let_37))) (let ((_let_39 (@ (@ bNF_re2241393799969408733at_nat intrel) intrel))) (let ((_let_40 (@ (@ bNF_re3099431351363272937at_nat intrel) _let_39))) (let ((_let_41 (= hoare_new_addrs (lambda ((H3 heap_e7401611519738050253t_unit) (As7 set_nat) (H6 heap_e7401611519738050253t_unit)) (@ (@ sup_sup_set_nat As7) (@ collect_nat (lambda ((A3 nat)) (and (@ (@ ord_less_nat A3) (@ lim_Product_unit H6)) (@ (@ ord_less_eq_nat (@ lim_Product_unit H3)) A3))))))))) (let ((_let_42 (= ord_less_nat (lambda ((B3 nat) (A3 nat)) (and (= A3 (@ (@ sup_sup_nat A3) B3)) (not (= A3 B3))))))) (let ((_let_43 (forall ((P assn)) (@ (@ entails bot_bot_assn) P)))) (let ((_let_44 (= entails (lambda ((P2 assn) (Q2 assn)) (forall ((H3 produc3658429121746597890et_nat)) (=> (@ (@ rep_assn P2) H3) (@ (@ rep_assn Q2) H3))))))) (let ((_let_45 (= all_interval_int (lambda ((P2 (-> int Bool)) (I4 int) (J2 int)) (forall ((X2 int)) (=> (@ (@ member_int X2) (@ (@ set_or1266510415728281911st_int I4) J2)) (@ P2 X2))))))) (let ((_let_46 (= ord_less_int (@ (@ (@ map_fu434086159418415080_int_o rep_Integ) (@ (@ map_fu4826362097070443709at_o_o rep_Integ) id_o)) (@ produc8739625826339149834_nat_o (lambda ((X2 nat) (Y5 nat) (__flatten_var_0 product_prod_nat_nat)) (@ (@ produc6081775807080527818_nat_o (lambda ((U4 nat) (V4 nat)) (@ (@ ord_less_nat (@ (@ plus_plus_nat X2) V4)) (@ (@ plus_plus_nat U4) Y5)))) __flatten_var_0))))))) (let ((_let_47 (= set_or5834768355832116004an_nat (lambda ((N2 nat) (M nat)) (@ set_nat2 (@ (@ upt (@ suc N2)) M)))))) (let ((_let_48 (= unique5026877609467782581ep_nat (lambda ((L4 num) (__flatten_var_0 product_prod_nat_nat)) (@ (@ produc2626176000494625587at_nat (lambda ((Q8 nat) (R4 nat)) (let ((_let_1 (@ (@ times_times_nat (@ numeral_numeral_nat (@ bit0 one))) Q8))) (let ((_let_2 (@ numeral_numeral_nat L4))) (@ (@ (@ if_Pro6206227464963214023at_nat (@ (@ ord_less_eq_nat _let_2) R4)) (@ (@ product_Pair_nat_nat (@ (@ plus_plus_nat _let_1) one_one_nat)) (@ (@ minus_minus_nat R4) _let_2))) (@ (@ product_Pair_nat_nat _let_1) R4)))))) __flatten_var_0))))) (let ((_let_49 (= is_empty_o (lambda ((A5 set_o)) (= A5 bot_bot_set_o))))) (let ((_let_50 (= bijective_nat_nat (lambda ((R3 set_Pr1261947904930325089at_nat)) (and (forall ((X2 nat) (Y5 nat) (Z5 nat)) (let ((_let_1 (@ product_Pair_nat_nat X2))) (=> (and (@ (@ member8440522571783428010at_nat (@ _let_1 Z5)) R3) (@ (@ member8440522571783428010at_nat (@ _let_1 Y5)) R3)) (= Y5 Z5)))) (forall ((X2 nat) (Y5 nat) (Z5 nat)) (=> (and (@ (@ member8440522571783428010at_nat (@ (@ product_Pair_nat_nat Y5) Z5)) R3) (@ (@ member8440522571783428010at_nat (@ (@ product_Pair_nat_nat X2) Z5)) R3)) (= X2 Y5)))))))) (let ((_let_51 (= is_emp1662574758705540307at_nat (lambda ((A5 set_Pr1261947904930325089at_nat)) (= A5 bot_bo2099793752762293965at_nat))))) (let ((_let_52 (= ord_le3102999989581377725nteger (lambda ((B3 code_integer) (A3 code_integer)) (or (@ (@ ord_le6747313008572928689nteger B3) A3) (= A3 B3)))))) (let ((_let_53 (= is_singleton_o (lambda ((A5 set_o)) (= A5 (@ (@ insert_o2 (@ the_elem_o A5)) bot_bot_set_o)))))) (let ((_let_54 (= ord_le2604355607129572851at_nat (lambda ((B3 set_Pr4329608150637261639at_nat) (A3 set_Pr4329608150637261639at_nat)) (and (not (= A3 B3)) (= A3 (@ (@ sup_su5525570899277871387at_nat A3) B3))))))) (let ((_let_55 (= is_empty_int (lambda ((A5 set_int)) (= A5 bot_bot_set_int))))) (let ((_let_56 (= remove_int (lambda ((X2 int) (A5 set_int)) (@ (@ minus_minus_set_int A5) (@ (@ insert_int2 X2) bot_bot_set_int)))))) (let ((_let_57 (@ collec3392354462482085612at_nat (@ produc6081775807080527818_nat_o ord_less_nat)))) (let ((_let_58 (= bNF_Ca8459412986667044542atLess _let_57))) (let ((_let_59 (= code_divmod_integer (lambda ((K4 code_integer) (L4 code_integer)) (let ((_let_1 (@ (@ code_divmod_abs K4) L4))) (let ((_let_2 (@ produc1086072967326762835nteger zero_z3403309356797280102nteger))) (@ (@ (@ if_Pro6119634080678213985nteger (= K4 zero_z3403309356797280102nteger)) (@ _let_2 zero_z3403309356797280102nteger)) (@ (@ (@ if_Pro6119634080678213985nteger (= L4 zero_z3403309356797280102nteger)) (@ _let_2 K4)) (@ (@ (@ (@ comp_C1593894019821074884nteger (@ (@ comp_C8797469213163452608nteger produc6499014454317279255nteger) times_3573771949741848930nteger)) sgn_sgn_Code_integer) L4) (@ (@ (@ if_Pro6119634080678213985nteger (= (@ sgn_sgn_Code_integer K4) (@ sgn_sgn_Code_integer L4))) _let_1) (@ (@ produc6916734918728496179nteger (lambda ((R4 code_integer) (S6 code_integer)) (let ((_let_1 (@ uminus1351360451143612070nteger R4))) (@ (@ (@ if_Pro6119634080678213985nteger (= S6 zero_z3403309356797280102nteger)) (@ (@ produc1086072967326762835nteger _let_1) zero_z3403309356797280102nteger)) (@ (@ produc1086072967326762835nteger (@ (@ minus_8373710615458151222nteger _let_1) one_one_Code_integer)) (@ (@ minus_8373710615458151222nteger (@ abs_abs_Code_integer L4)) S6)))))) _let_1))))))))))) (let ((_let_60 (= sup_sup_assn (lambda ((P2 assn) (Q2 assn)) (@ abs_assn (lambda ((H3 produc3658429121746597890et_nat)) (or (@ (@ rep_assn Q2) H3) (@ (@ rep_assn P2) H3)))))))) (let ((_let_61 (= set_or1266510415728281911st_int (lambda ((I4 int) (J2 int)) (@ set_int2 (@ (@ upto I4) J2)))))) (let ((_let_62 (= upto (lambda ((I4 int) (J2 int)) (@ (@ (@ upto_aux I4) J2) nil_int))))) (let ((_let_63 (= unique4921790084139445826nteger (lambda ((L4 num) (__flatten_var_0 produc8923325533196201883nteger)) (@ (@ produc6916734918728496179nteger (lambda ((Q8 code_integer) (R4 code_integer)) (let ((_let_1 (@ (@ times_3573771949741848930nteger (@ numera6620942414471956472nteger (@ bit0 one))) Q8))) (let ((_let_2 (@ numera6620942414471956472nteger L4))) (@ (@ (@ if_Pro6119634080678213985nteger (@ (@ ord_le3102999989581377725nteger _let_2) R4)) (@ (@ produc1086072967326762835nteger (@ (@ plus_p5714425477246183910nteger _let_1) one_one_Code_integer)) (@ (@ minus_8373710615458151222nteger R4) _let_2))) (@ (@ produc1086072967326762835nteger _let_1) R4)))))) __flatten_var_0))))) (let ((_let_64 (= insert8021100735160035049_nat_o (lambda ((X2 (-> produc3658429121746597890et_nat Bool)) (Xs3 list_P7985473006766602707_nat_o)) (@ (@ (@ if_lis2904118647880296857_nat_o (@ (@ member6576561426505652726_nat_o X2) (@ set_Pr400311997697478754_nat_o Xs3))) Xs3) (@ (@ cons_P6219271836124797827_nat_o X2) Xs3)))))) (let ((_let_65 (= inf_inf_assn (lambda ((P2 assn) (Q2 assn)) (@ abs_assn (lambda ((H3 produc3658429121746597890et_nat)) (and (@ (@ rep_assn P2) H3) (@ (@ rep_assn Q2) H3)))))))) (let ((_let_66 (@ ord_less_nat one_one_nat))) (let ((_let_67 (= top_top_assn (@ abs_assn in_range)))) (let ((_let_68 (= ord_le5570908160329646204atural (lambda ((X2 code_natural) (Xa4 code_natural)) (@ (@ ord_less_nat (@ code_nat_of_natural X2)) (@ code_nat_of_natural Xa4)))))) (let ((_let_69 (= sorted_wrt_int (lambda ((P2 (-> int int Bool)) (Xs3 list_int)) (forall ((I4 nat) (J2 nat)) (let ((_let_1 (@ nth_int Xs3))) (=> (@ (@ ord_less_nat I4) J2) (=> (@ (@ ord_less_nat J2) (@ size_size_list_int Xs3)) (@ (@ P2 (@ _let_1 I4)) (@ _let_1 J2)))))))))) (let ((_let_70 (= is_singleton_int (lambda ((A5 set_int)) (exists ((X2 int)) (= A5 (@ (@ insert_int2 X2) bot_bot_set_int))))))) (let ((_let_71 (= sorted_wrt_c (lambda ((P2 (-> c c Bool)) (Xs3 list_c)) (forall ((I4 nat) (J2 nat)) (let ((_let_1 (@ nth_c Xs3))) (=> (@ (@ ord_less_nat I4) J2) (=> (@ (@ ord_less_nat J2) (@ size_size_list_c Xs3)) (@ (@ P2 (@ _let_1 I4)) (@ _let_1 J2)))))))))) (let ((_let_72 (= bot_bo6829958733157050602_nat_o (lambda ((X2 produc3843707927480180839at_nat)) (@ (@ member8757157785044589968at_nat X2) bot_bo228742789529271731at_nat))))) (let ((_let_73 (= set_ord_lessThan_nat (lambda ((N2 nat)) (@ set_nat2 (@ (@ upt zero_zero_nat) N2)))))) (let ((_let_74 (@ finite3254316476582989077op_nat top_top_set_nat))) (let ((_let_75 (= ord_le6747313008572928689nteger (lambda ((A3 code_integer) (B3 code_integer)) (and (= A3 (@ (@ ord_min_Code_integer A3) B3)) (not (= A3 B3))))))) (let ((_let_76 (= ord_less_eq_set_int (lambda ((A5 set_int) (B7 set_int)) (forall ((X2 int)) (let ((_let_1 (@ member_int X2))) (=> (@ _let_1 A5) (@ _let_1 B7)))))))) (let ((_let_77 (@ (@ bNF_re7145576690424134365nt_int ratrel) ratrel))) (let ((_let_78 (= ord_min_int (lambda ((A3 int) (B3 int)) (@ (@ (@ if_int (@ (@ ord_less_eq_int A3) B3)) A3) B3))))) (let ((_let_79 (= (@ field_2862844103579723188at_nat bot_bo7193250159860175667at_nat) bot_bo228742789529271731at_nat))) (let ((_let_80 (= ord_less_eq_assn (lambda ((B3 assn) (A3 assn)) (= (@ (@ inf_inf_assn A3) B3) B3))))) (let ((_let_81 (= insert4149901806602606979at_nat (lambda ((X2 produc3843707927480180839at_nat) (Xs3 list_P5464809261938338413at_nat)) (@ (@ (@ if_lis7508161100780771379at_nat (@ (@ member8757157785044589968at_nat X2) (@ set_Pr3765526544606949372at_nat Xs3))) Xs3) (@ (@ cons_P3940603068885512221at_nat X2) Xs3)))))) (let ((_let_82 (@ ord_less_nat zero_zero_nat))) (let ((_let_83 (= bot_bo482883023278783056_nat_o (lambda ((X2 product_prod_nat_nat)) (@ (@ member8440522571783428010at_nat X2) bot_bo2099793752762293965at_nat))))) (let ((_let_84 (= split_seed (lambda ((S6 produc7822875418678951345atural)) (@ (@ produc8282080750456430313atural (lambda ((V4 code_natural) (W4 code_natural)) (@ (@ produc8282080750456430313atural (lambda ((V5 code_natural) (W5 code_natural)) (let ((_let_1 (@ bit1 (@ bit1 (@ bit1 (@ bit1 (@ bit1 (@ bit1 (@ bit1 (@ bit1 (@ bit1 (@ bit1 (@ bit1 (@ bit1 (@ bit1 (@ bit1 (@ bit1 (@ bit1 (@ bit1 (@ bit1 (@ bit1 (@ bit1 (@ bit1 (@ bit1 one)))))))))))))))))))))))) (@ (@ produc4480994950612372183atural (@ (@ produc3574140220909816553atural (@ (@ inc_shift (@ numera5444537566228673987atural (@ bit0 (@ bit1 (@ bit0 (@ bit1 (@ bit0 (@ bit1 (@ bit0 (@ bit1 _let_1)))))))))) V4)) W5)) (@ (@ produc3574140220909816553atural V5) (@ (@ inc_shift (@ numera5444537566228673987atural (@ bit0 (@ bit1 (@ bit1 (@ bit0 (@ bit0 (@ bit0 (@ bit0 (@ bit0 _let_1)))))))))) W4)))))) (@ produc6591912806276919810atural (@ next S6))))) S6))))) (let ((_let_85 (= divmod_nat (lambda ((M nat) (N2 nat)) (@ (@ product_Pair_nat_nat (@ (@ divide_divide_nat M) N2)) (@ (@ modulo_modulo_nat M) N2)))))) (let ((_let_86 (= code_bit_cut_integer (lambda ((K4 code_integer)) (let ((_let_1 (@ numera6620942414471956472nteger (@ bit0 one)))) (@ (@ produc6677183202524767010eger_o (@ (@ divide6298287555418463151nteger K4) _let_1)) (not (@ (@ dvd_dvd_Code_integer _let_1) K4)))))))) (let ((_let_87 (= list_ex_c (lambda ((P2 (-> c Bool)) (Xs3 list_c)) (exists ((N2 nat)) (and (@ (@ ord_less_nat N2) (@ size_size_list_c Xs3)) (@ P2 (@ (@ nth_c Xs3) N2)))))))) (let ((_let_88 (@ (@ map_fu4960017516451851995nt_int rep_Integ) _let_32))) (let ((_let_89 (= minus_minus_int (@ _let_88 (@ produc27273713700761075at_nat (lambda ((X2 nat) (Y5 nat) (__flatten_var_0 product_prod_nat_nat)) (@ (@ produc2626176000494625587at_nat (lambda ((U4 nat) (V4 nat)) (@ (@ product_Pair_nat_nat (@ (@ plus_plus_nat X2) V4)) (@ (@ plus_plus_nat Y5) U4)))) __flatten_var_0))))))) (let ((_let_90 (= fract (lambda ((Xa4 int) (X2 int)) (@ abs_Rat (@ (@ (@ if_Pro3027730157355071871nt_int (= X2 zero_zero_int)) (@ (@ product_Pair_int_int zero_zero_int) one_one_int)) (@ (@ product_Pair_int_int Xa4) X2))))))) (let ((_let_91 (@ (@ insert9069300056098147895at_nat (@ (@ produc2922128104949294807at_nat bot_bo2099793752762293965at_nat) bot_bo2099793752762293965at_nat)) bot_bo228742789529271731at_nat))) (let ((_let_92 (= fun_min_weak (@ (@ sup_su5525570899277871387at_nat (@ min_ex6901939911449802026at_nat fun_pair_leq)) _let_91)))) (let ((_let_93 (= wand_assn (lambda ((P2 assn) (Q2 assn)) (@ abs_assn (@ (@ wand_raw (@ rep_assn P2)) (@ rep_assn Q2))))))) (let ((_let_94 (= (@ field_int bot_bo1796632182523588997nt_int) bot_bot_set_int))) (let ((_let_95 (@ (@ map_fu5673905371560938248nt_rat rep_Rat) abs_Rat))) (let ((_let_96 (= inverse_inverse_rat (@ _let_95 (lambda ((X2 product_prod_int_int)) (let ((_let_1 (@ product_fst_int_int X2))) (@ (@ (@ if_Pro3027730157355071871nt_int (= _let_1 zero_zero_int)) (@ (@ product_Pair_int_int zero_zero_int) one_one_int)) (@ (@ product_Pair_int_int (@ product_snd_int_int X2)) _let_1)))))))) (let ((_let_97 (= ord_less_set_nat (lambda ((B3 set_nat) (A3 set_nat)) (and (not (= A3 B3)) (@ (@ ord_less_eq_set_nat B3) A3)))))) (let ((_let_98 (= range (lambda ((K4 code_natural) (__flatten_var_0 produc7822875418678951345atural)) (@ (@ (@ produc5538323210962509403atural (@ (@ (@ iterat8892046348760725948atural (@ (@ log (@ numera5444537566228673987atural (@ bit1 (@ bit0 (@ bit0 (@ bit1 (@ bit0 (@ bit1 (@ bit0 (@ bit1 (@ bit1 (@ bit1 (@ bit1 (@ bit1 (@ bit1 (@ bit1 (@ bit1 (@ bit1 (@ bit1 (@ bit1 (@ bit1 (@ bit1 (@ bit1 (@ bit1 (@ bit1 (@ bit1 (@ bit1 (@ bit1 (@ bit1 (@ bit1 (@ bit1 (@ bit1 one)))))))))))))))))))))))))))))))) K4)) (lambda ((L4 code_natural) (__flatten_var_0 produc7822875418678951345atural)) (@ (@ (@ produc5538323210962509403atural next) (lambda ((V4 code_natural) (__flatten_var_0 produc7822875418678951345atural)) (@ (@ produc6639722614265839536atural (@ (@ plus_p4538020629002901425atural V4) (@ (@ times_2397367101498566445atural L4) (@ numera5444537566228673987atural (@ bit1 (@ bit0 (@ bit0 (@ bit1 (@ bit0 (@ bit1 (@ bit0 (@ bit1 (@ bit1 (@ bit1 (@ bit1 (@ bit1 (@ bit1 (@ bit1 (@ bit1 (@ bit1 (@ bit1 (@ bit1 (@ bit1 (@ bit1 (@ bit1 (@ bit1 (@ bit1 (@ bit1 (@ bit1 (@ bit1 (@ bit1 (@ bit1 (@ bit1 (@ bit1 one)))))))))))))))))))))))))))))))))) __flatten_var_0))) __flatten_var_0))) one_one_Code_natural)) (lambda ((V4 code_natural) (__flatten_var_0 produc7822875418678951345atural)) (@ (@ produc6639722614265839536atural (@ (@ modulo8411746178871703098atural V4) K4)) __flatten_var_0))) __flatten_var_0))))) (let ((_let_99 (= pairwise_o (lambda ((R3 (-> Bool Bool Bool)) (S2 set_o)) (forall ((X2 Bool)) (=> (@ (@ member_o X2) S2) (forall ((Y5 Bool)) (=> (@ (@ member_o Y5) (@ (@ minus_minus_set_o S2) (@ (@ insert_o2 X2) bot_bot_set_o))) (@ (@ R3 X2) Y5))))))))) (let ((_let_100 (= set_or6659071591806873216st_nat (lambda ((N2 nat) (M nat)) (@ set_nat2 (@ (@ upt (@ suc N2)) (@ suc M))))))) (let ((_let_101 (@ entails p))) (let ((_let_102 (= ord_le1268244103169919719at_nat (lambda ((A5 set_Pr4329608150637261639at_nat) (B7 set_Pr4329608150637261639at_nat)) (forall ((X2 produc3843707927480180839at_nat)) (let ((_let_1 (@ member8757157785044589968at_nat X2))) (=> (@ _let_1 A5) (@ _let_1 B7)))))))) (let ((_let_103 (= one_one_assn (@ abs_assn one_assn_raw)))) (let ((_let_104 (@ gcd_Lcm_nat bot_bot_set_nat))) (let ((_let_105 (= _let_104 one_one_nat))) (let ((_let_106 (= is_sin2937591304547752795at_nat (lambda ((A5 set_Pr4329608150637261639at_nat)) (= A5 (@ (@ insert9069300056098147895at_nat (@ the_el221668144340439132at_nat A5)) bot_bo228742789529271731at_nat)))))) (let ((_let_107 (= plus_plus_int (@ _let_88 (@ produc27273713700761075at_nat (lambda ((X2 nat) (Y5 nat) (__flatten_var_0 product_prod_nat_nat)) (@ (@ produc2626176000494625587at_nat (lambda ((U4 nat) (V4 nat)) (@ (@ product_Pair_nat_nat (@ (@ plus_plus_nat X2) U4)) (@ (@ plus_plus_nat Y5) V4)))) __flatten_var_0))))))) (let ((_let_108 (= unique5055182867167087721od_nat (lambda ((M num) (N2 num)) (let ((_let_1 (@ numeral_numeral_nat N2))) (let ((_let_2 (@ numeral_numeral_nat M))) (@ (@ product_Pair_nat_nat (@ (@ divide_divide_nat _let_2) _let_1)) (@ (@ modulo_modulo_nat _let_2) _let_1)))))))) (let ((_let_109 (@ (@ product_Pair_nat_nat zero_zero_nat) zero_zero_nat))) (let ((_let_110 (= unique3479559517661332726nteger (lambda ((M num) (N2 num)) (let ((_let_1 (@ numera6620942414471956472nteger N2))) (let ((_let_2 (@ numera6620942414471956472nteger M))) (@ (@ produc1086072967326762835nteger (@ (@ divide6298287555418463151nteger _let_2) _let_1)) (@ (@ modulo364778990260209775nteger _let_2) _let_1)))))))) (let ((_let_111 (= list_ex_int (lambda ((P2 (-> int Bool)) (Xs3 list_int)) (exists ((N2 nat)) (and (@ P2 (@ (@ nth_int Xs3) N2)) (@ (@ ord_less_nat N2) (@ size_size_list_int Xs3)))))))) (let ((_let_112 (= bot_bot_o_o (lambda ((X2 Bool)) (@ (@ member_o X2) bot_bot_set_o))))) (let ((_let_113 (= eucl_rel_int (lambda ((A12 int) (A23 int) (A32 product_prod_int_int)) (or (exists ((K4 int)) (and (= A23 zero_zero_int) (= A32 (@ (@ product_Pair_int_int zero_zero_int) K4)) (= A12 K4))) (exists ((R4 int) (L4 int) (K4 int) (Q8 int)) (and (= A12 K4) (= A23 L4) (@ (@ ord_less_int (@ abs_abs_int R4)) (@ abs_abs_int L4)) (= K4 (@ (@ plus_plus_int (@ (@ times_times_int Q8) L4)) R4)) (= (@ sgn_sgn_int R4) (@ sgn_sgn_int L4)) (= A32 (@ (@ product_Pair_int_int Q8) R4)))) (exists ((L4 int) (K4 int) (Q8 int)) (and (= A12 K4) (= A23 L4) (= A32 (@ (@ product_Pair_int_int Q8) zero_zero_int)) (= K4 (@ (@ times_times_int Q8) L4)) (not (= L4 zero_zero_int))))))))) (let ((_let_114 (= ord_less_assn (lambda ((B3 assn) (A3 assn)) (and (not (= A3 B3)) (= A3 (@ (@ sup_sup_assn A3) B3))))))) (let ((_let_115 (= ord_le2510731241096832064er_nat (lambda ((X2 filter_nat) (Y5 filter_nat)) (= (@ (@ sup_sup_filter_nat X2) Y5) Y5))))) (let ((_let_116 (= fun_max_weak (@ (@ sup_su5525570899277871387at_nat (@ max_ex8135407076693332796at_nat fun_pair_leq)) _let_91)))) (let ((_let_117 (= ord_less_eq_num (lambda ((A3 num) (B3 num)) (or (= A3 B3) (@ (@ ord_less_num A3) B3)))))) (let ((_let_118 (= remove6466555014256735590at_nat (lambda ((X2 product_prod_nat_nat) (A5 set_Pr1261947904930325089at_nat)) (@ (@ minus_1356011639430497352at_nat A5) (@ (@ insert8211810215607154385at_nat X2) bot_bo2099793752762293965at_nat)))))) (let ((_let_119 (= pure_assn (lambda ((B3 Bool)) (@ abs_assn (@ pure_a825153325127701367it_nat B3)))))) (let ((_let_120 (= ord_le3146513528884898305at_nat (lambda ((A5 set_Pr1261947904930325089at_nat) (B7 set_Pr1261947904930325089at_nat)) (forall ((X2 product_prod_nat_nat)) (let ((_let_1 (@ member8440522571783428010at_nat X2))) (=> (@ _let_1 A5) (@ _let_1 B7)))))))) (let ((_let_121 (= insert_int (lambda ((X2 int) (Xs3 list_int)) (@ (@ (@ if_list_int (@ (@ member_int X2) (@ set_int2 Xs3))) Xs3) (@ (@ cons_int X2) Xs3)))))) (let ((_let_122 (= distinct_int (lambda ((Xs3 list_int)) (forall ((I4 nat)) (=> (@ (@ ord_less_nat I4) (@ size_size_list_int Xs3)) (forall ((J2 nat)) (let ((_let_1 (@ nth_int Xs3))) (=> (@ (@ ord_less_nat J2) (@ size_size_list_int Xs3)) (=> (not (= I4 J2)) (not (= (@ _let_1 I4) (@ _let_1 J2))))))))))))) (let ((_let_123 (= (@ complete_Sup_Sup_nat bot_bot_set_nat) zero_zero_nat))) (let ((_let_124 (= ord_less_eq_nat (lambda ((A3 nat) (B3 nat)) (= A3 (@ (@ ord_min_nat A3) B3)))))) (let ((_let_125 (= set_or1269000886237332187st_nat (lambda ((N2 nat) (M nat)) (@ set_nat2 (@ (@ upt N2) (@ suc M))))))) (let ((_let_126 (= unique5052692396658037445od_int (lambda ((M num) (N2 num)) (let ((_let_1 (@ numeral_numeral_int N2))) (let ((_let_2 (@ numeral_numeral_int M))) (@ (@ product_Pair_int_int (@ (@ divide_divide_int _let_2) _let_1)) (@ (@ modulo_modulo_int _let_2) _let_1)))))))) (let ((_let_127 (= ord_le2965882846123202637_nat_o (lambda ((A5 set_Pr4532377907799695533_nat_o) (B7 set_Pr4532377907799695533_nat_o)) (forall ((T2 (-> produc3658429121746597890et_nat Bool))) (let ((_let_1 (@ member6576561426505652726_nat_o T2))) (=> (@ _let_1 A5) (@ _let_1 B7)))))))) (let ((_let_128 (= biject9051520373387432658nteger (lambda ((R3 set_Pr1281608226676607948nteger)) (and (forall ((X2 (-> produc6241069584506657477e_term option6357759511663192854e_term)) (Y5 produc8923325533196201883nteger) (Z5 produc8923325533196201883nteger)) (let ((_let_1 (@ produc8603105652947943368nteger X2))) (=> (and (@ (@ member4164122664394876845nteger (@ _let_1 Z5)) R3) (@ (@ member4164122664394876845nteger (@ _let_1 Y5)) R3)) (= Y5 Z5)))) (forall ((X2 (-> produc6241069584506657477e_term option6357759511663192854e_term)) (Y5 (-> produc6241069584506657477e_term option6357759511663192854e_term)) (Z5 produc8923325533196201883nteger)) (=> (and (@ (@ member4164122664394876845nteger (@ (@ produc8603105652947943368nteger X2) Z5)) R3) (@ (@ member4164122664394876845nteger (@ (@ produc8603105652947943368nteger Y5) Z5)) R3)) (= X2 Y5)))))))) (let ((_let_129 (= sln one_one_assn))) (let ((_let_130 (= neg_nu3179335615603231917ec_rat (lambda ((X2 rat)) (@ (@ minus_minus_rat (@ (@ plus_plus_rat X2) X2)) one_one_rat))))) (let ((_let_131 (= set_ord_atMost_nat (lambda ((N2 nat)) (@ set_nat2 (@ (@ upt zero_zero_nat) (@ suc N2))))))) (let ((_let_132 (= biject2615096655818420098et_nat (lambda ((R3 set_Pr3286484037609594932et_nat)) (and (forall ((X2 (-> produc3658429121746597890et_nat Bool)) (Y5 produc3658429121746597890et_nat) (Z5 produc3658429121746597890et_nat)) (let ((_let_1 (@ produc5001842942810119800et_nat X2))) (=> (and (@ (@ member1996754912294343701et_nat (@ _let_1 Z5)) R3) (@ (@ member1996754912294343701et_nat (@ _let_1 Y5)) R3)) (= Y5 Z5)))) (forall ((X2 (-> produc3658429121746597890et_nat Bool)) (Y5 (-> produc3658429121746597890et_nat Bool)) (Z5 produc3658429121746597890et_nat)) (=> (and (@ (@ member1996754912294343701et_nat (@ (@ produc5001842942810119800et_nat Y5) Z5)) R3) (@ (@ member1996754912294343701et_nat (@ (@ produc5001842942810119800et_nat X2) Z5)) R3)) (= X2 Y5)))))))) (let ((_let_133 (not (@ _let_101 q)))) (let ((_let_134 (= remove_nat (lambda ((X2 nat) (A5 set_nat)) (@ (@ minus_minus_set_nat A5) (@ (@ insert_nat2 X2) bot_bot_set_nat)))))) (let ((_let_135 (= distinct_c (lambda ((Xs3 list_c)) (forall ((I4 nat)) (=> (@ (@ ord_less_nat I4) (@ size_size_list_c Xs3)) (forall ((J2 nat)) (let ((_let_1 (@ nth_c Xs3))) (=> (@ (@ ord_less_nat J2) (@ size_size_list_c Xs3)) (=> (not (= I4 J2)) (not (= (@ _let_1 I4) (@ _let_1 J2))))))))))))) (let ((_let_136 (= insert8944034826898310173at_nat (lambda ((X2 product_prod_nat_nat) (Xs3 list_P6011104703257516679at_nat)) (@ (@ (@ if_lis9186351972506106189at_nat (@ (@ member8440522571783428010at_nat X2) (@ set_Pr5648618587558075414at_nat Xs3))) Xs3) (@ (@ cons_P6512896166579812791at_nat X2) Xs3)))))) (let ((_let_137 (= ord_less_num (lambda ((M num) (N2 num)) (@ (@ ord_less_nat (@ nat_of_num M)) (@ nat_of_num N2)))))) (let ((_let_138 (= bot_bot_int_o (lambda ((X2 int)) (@ (@ member_int X2) bot_bot_set_int))))) (let ((_let_139 (= sorted_wrt_nat (lambda ((P2 (-> nat nat Bool)) (Xs3 list_nat)) (forall ((I4 nat) (J2 nat)) (let ((_let_1 (@ nth_nat Xs3))) (=> (@ (@ ord_less_nat I4) J2) (=> (@ (@ ord_less_nat J2) (@ size_size_list_nat Xs3)) (@ (@ P2 (@ _let_1 I4)) (@ _let_1 J2)))))))))) (let ((_let_140 (= (@ field_nat bot_bo2099793752762293965at_nat) bot_bot_set_nat))) (let ((_let_141 (= remove_o (lambda ((X2 Bool) (A5 set_o)) (@ (@ minus_minus_set_o A5) (@ (@ insert_o2 X2) bot_bot_set_o)))))) (let ((_let_142 (@ ord_less_rat one_one_rat))) (let ((_let_143 (= bot_bot_nat_o (lambda ((X2 nat)) (@ (@ member_nat X2) bot_bot_set_nat))))) (let ((_let_144 (= (@ field_4706345496283612622at_nat bot_bo5327735625951526323at_nat) bot_bo2099793752762293965at_nat))) (let ((_let_145 (= is_emp7572232645145209145at_nat (lambda ((A5 set_Pr4329608150637261639at_nat)) (= A5 bot_bo228742789529271731at_nat))))) (let ((_let_146 (= biject383251550997737151nt_int (lambda ((R3 set_Pr9222295170931077689nt_int)) (and (forall ((X2 (-> produc8551481072490612790e_term option6357759511663192854e_term)) (Y5 product_prod_int_int) (Z5 product_prod_int_int)) (let ((_let_1 (@ produc5700946648718959541nt_int X2))) (=> (and (@ (@ member7618704894036264090nt_int (@ _let_1 Z5)) R3) (@ (@ member7618704894036264090nt_int (@ _let_1 Y5)) R3)) (= Y5 Z5)))) (forall ((X2 (-> produc8551481072490612790e_term option6357759511663192854e_term)) (Y5 (-> produc8551481072490612790e_term option6357759511663192854e_term)) (Z5 product_prod_int_int)) (=> (and (@ (@ member7618704894036264090nt_int (@ (@ produc5700946648718959541nt_int X2) Z5)) R3) (@ (@ member7618704894036264090nt_int (@ (@ produc5700946648718959541nt_int Y5) Z5)) R3)) (= X2 Y5)))))))) (let ((_let_147 (= entailst (lambda ((A5 assn) (B7 assn)) (@ (@ entails A5) (@ (@ times_times_assn B7) top_top_assn)))))) (let ((_let_148 (= set_or4662586982721622107an_int (lambda ((I4 int) (J2 int)) (@ set_int2 (@ (@ upto I4) (@ (@ minus_minus_int J2) one_one_int))))))) (let ((_let_149 (= all_interval_nat (lambda ((P2 (-> nat Bool)) (I4 nat) (J2 nat)) (forall ((X2 nat)) (=> (@ (@ member_nat X2) (@ (@ set_or4665077453230672383an_nat I4) J2)) (@ P2 X2))))))) (let ((_let_150 (= proper (lambda ((P2 (-> produc3658429121746597890et_nat Bool))) (forall ((H3 heap_e7401611519738050253t_unit) (H6 heap_e7401611519738050253t_unit) (As7 set_nat)) (let ((_let_1 (@ (@ produc7507926704131184380et_nat H3) As7))) (let ((_let_2 (@ P2 _let_1))) (let ((_let_3 (@ (@ produc7507926704131184380et_nat H6) As7))) (and (=> (and (@ in_range _let_3) (@ (@ (@ relH As7) H3) H6) _let_2) (@ P2 _let_3)) (=> _let_2 (@ in_range _let_1))))))))))) (let ((_let_151 (= total_7212417256332265445at_nat (lambda ((A5 set_se7855581050983116737at_nat) (R4 set_Pr4329608150637261639at_nat)) (forall ((X2 set_Pr1261947904930325089at_nat)) (=> (@ (@ member2643936169264416010at_nat X2) A5) (forall ((Y5 set_Pr1261947904930325089at_nat)) (=> (@ (@ member2643936169264416010at_nat Y5) A5) (=> (not (= X2 Y5)) (or (@ (@ member8757157785044589968at_nat (@ (@ produc2922128104949294807at_nat Y5) X2)) R4) (@ (@ member8757157785044589968at_nat (@ (@ produc2922128104949294807at_nat X2) Y5)) R4))))))))))) (let ((_let_152 (= uminus_uminus_rat (@ _let_95 (lambda ((X2 product_prod_int_int)) (@ (@ product_Pair_int_int (@ uminus_uminus_int (@ product_fst_int_int X2))) (@ product_snd_int_int X2))))))) (let ((_let_153 (= ord_less_filter_nat (lambda ((A3 filter_nat) (B3 filter_nat)) (and (@ (@ ord_le2510731241096832064er_nat A3) B3) (not (= A3 B3))))))) (let ((_let_154 (@ (@ minus_minus_int one_one_int) one_one_int))) (let ((_let_155 (= _let_154 zero_zero_int))) (let ((_let_156 (= (@ pure_assn false) bot_bot_assn))) (let ((_let_157 (= ord_less_eq_int (lambda ((B3 int) (A3 int)) (= A3 (@ (@ sup_sup_int A3) B3)))))) (let ((_let_158 (= insert_nat (lambda ((X2 nat) (Xs3 list_nat)) (@ (@ (@ if_list_nat (@ (@ member_nat X2) (@ set_nat2 Xs3))) Xs3) (@ (@ cons_nat X2) Xs3)))))) (let ((_let_159 (= (@ frct _let_23) one_one_rat))) (let ((_let_160 (@ (@ bNF_re5228765855967844073nt_int ratrel) _let_77))) (let ((_let_161 (= inf_inf_nat ord_min_nat))) (let ((_let_162 (= bot_bo7824918357723582233_nat_o (@ collec939566748876313656_nat_o bot_bo7963750851167320836at_o_o)))) (let ((_let_163 (= total_on_nat (lambda ((A5 set_nat) (R4 set_Pr1261947904930325089at_nat)) (forall ((X2 nat)) (=> (@ (@ member_nat X2) A5) (forall ((Y5 nat)) (=> (@ (@ member_nat Y5) A5) (=> (not (= X2 Y5)) (or (@ (@ member8440522571783428010at_nat (@ (@ product_Pair_nat_nat X2) Y5)) R4) (@ (@ member8440522571783428010at_nat (@ (@ product_Pair_nat_nat Y5) X2)) R4))))))))))) (let ((_let_164 (= list_ex_d (lambda ((P2 (-> d Bool)) (Xs3 list_d)) (exists ((N2 nat)) (and (@ P2 (@ (@ nth_d Xs3) N2)) (@ (@ ord_less_nat N2) (@ size_size_list_d Xs3)))))))) (let ((_let_165 (= heap_Time_wait (lambda ((N2 nat)) (@ heap_T6183433275982383450t_unit (lambda ((H3 heap_e7401611519738050253t_unit)) (@ some_P1914260805536162275it_nat (@ (@ produc7133225469290080770it_nat product_Unity) (@ (@ produc584006145561248582it_nat H3) N2))))))))) (let ((_let_166 (= neg_nu7757733837767384882nteger (lambda ((X2 code_integer)) (@ (@ minus_8373710615458151222nteger (@ (@ plus_p5714425477246183910nteger X2) X2)) one_one_Code_integer))))) (let ((_let_167 (= insert3246601298802261197n_assn (lambda ((X2 produc6575502325842934193n_assn) (Xs3 list_P8527749157015355191n_assn)) (@ (@ (@ if_lis7173127979115136509n_assn (@ (@ member7957490590177025114n_assn X2) (@ set_Pr1139785259514867910n_assn Xs3))) Xs3) (@ (@ cons_P2971678138204555879n_assn X2) Xs3)))))) (let ((_let_168 (= ord_le7866589430770878221at_nat (lambda ((A3 set_Pr1261947904930325089at_nat) (B3 set_Pr1261947904930325089at_nat)) (and (= A3 (@ (@ inf_in2572325071724192079at_nat A3) B3)) (not (= A3 B3))))))) (let ((_let_169 (= is_sin2850979758926227957at_nat (lambda ((A5 set_Pr1261947904930325089at_nat)) (= A5 (@ (@ insert8211810215607154385at_nat (@ the_el2281957884133575798at_nat A5)) bot_bo2099793752762293965at_nat)))))) (let ((_let_170 (= ord_min_set_nat (lambda ((A3 set_nat) (B3 set_nat)) (@ (@ (@ if_set_nat (@ (@ ord_less_eq_set_nat A3) B3)) A3) B3))))) (let ((_let_171 (@ (@ minus_minus_rat one_one_rat) one_one_rat))) (let ((_let_172 (= _let_171 zero_zero_rat))) (let ((_let_173 (= is_empty_nat (lambda ((A5 set_nat)) (= A5 bot_bot_set_nat))))) (let ((_let_174 (= unique5024387138958732305ep_int (lambda ((L4 num) (__flatten_var_0 product_prod_int_int)) (@ (@ produc4245557441103728435nt_int (lambda ((Q8 int) (R4 int)) (let ((_let_1 (@ (@ times_times_int (@ numeral_numeral_int (@ bit0 one))) Q8))) (let ((_let_2 (@ numeral_numeral_int L4))) (@ (@ (@ if_Pro3027730157355071871nt_int (@ (@ ord_less_eq_int _let_2) R4)) (@ (@ product_Pair_int_int (@ (@ plus_plus_int _let_1) one_one_int)) (@ (@ minus_minus_int R4) _let_2))) (@ (@ product_Pair_int_int _let_1) R4)))))) __flatten_var_0))))) (let ((_let_175 (= is_singleton_nat (lambda ((A5 set_nat)) (= A5 (@ (@ insert_nat2 (@ the_elem_nat A5)) bot_bot_set_nat)))))) (let ((_let_176 (@ (@ map_fu4333342158222067775at_rat rep_Rat) _let_95))) (let ((_let_177 (= times_times_rat (@ _let_176 (lambda ((X2 product_prod_int_int) (Y5 product_prod_int_int)) (@ (@ product_Pair_int_int (@ (@ times_times_int (@ product_fst_int_int X2)) (@ product_fst_int_int Y5))) (@ (@ times_times_int (@ product_snd_int_int X2)) (@ product_snd_int_int Y5)))))))) (let ((_let_178 (= ord_less_eq_set_nat (lambda ((A5 set_nat) (B7 set_nat)) (forall ((X2 nat)) (let ((_let_1 (@ member_nat X2))) (=> (@ _let_1 A5) (@ _let_1 B7)))))))) (let ((_let_179 (= remove5300788332298244428at_nat (lambda ((X2 produc3843707927480180839at_nat) (A5 set_Pr4329608150637261639at_nat)) (@ (@ minus_3314409938677909166at_nat A5) (@ (@ insert9069300056098147895at_nat X2) bot_bo228742789529271731at_nat)))))) (let ((_let_180 (= ord_min_assn (lambda ((A3 assn) (B3 assn)) (@ (@ (@ if_assn (@ (@ ord_less_eq_assn A3) B3)) A3) B3))))) (let ((_let_181 (= normalize (lambda ((P7 product_prod_int_int)) (let ((_let_1 (@ product_snd_int_int P7))) (let ((_let_2 (@ product_fst_int_int P7))) (let ((_let_3 (@ (@ gcd_gcd_int _let_2) _let_1))) (let ((_let_4 (@ uminus_uminus_int _let_3))) (let ((_let_5 (@ divide_divide_int _let_1))) (let ((_let_6 (@ divide_divide_int _let_2))) (@ (@ (@ if_Pro3027730157355071871nt_int (@ (@ ord_less_int zero_zero_int) _let_1)) (@ (@ product_Pair_int_int (@ _let_6 _let_3)) (@ _let_5 _let_3))) (@ (@ (@ if_Pro3027730157355071871nt_int (= _let_1 zero_zero_int)) (@ (@ product_Pair_int_int zero_zero_int) one_one_int)) (@ (@ product_Pair_int_int (@ _let_6 _let_4)) (@ _let_5 _let_4)))))))))))))) (let ((_let_182 (= sorted_wrt_d (lambda ((P2 (-> d d Bool)) (Xs3 list_d)) (forall ((I4 nat) (J2 nat)) (let ((_let_1 (@ nth_d Xs3))) (=> (@ (@ ord_less_nat I4) J2) (=> (@ (@ ord_less_nat J2) (@ size_size_list_d Xs3)) (@ (@ P2 (@ _let_1 I4)) (@ _let_1 J2)))))))))) (let ((_let_183 (= list_ex_nat (lambda ((P2 (-> nat Bool)) (Xs3 list_nat)) (exists ((N2 nat)) (and (@ P2 (@ (@ nth_nat Xs3) N2)) (@ (@ ord_less_nat N2) (@ size_size_list_nat Xs3)))))))) (let ((_let_184 (= pairwise_nat (lambda ((R3 (-> nat nat Bool)) (S2 set_nat)) (forall ((X2 nat)) (=> (@ (@ member_nat X2) S2) (forall ((Y5 nat)) (=> (@ (@ member_nat Y5) (@ (@ minus_minus_set_nat S2) (@ (@ insert_nat2 X2) bot_bot_set_nat))) (@ (@ R3 X2) Y5))))))))) (let ((_let_185 (= (@ (@ minus_8373710615458151222nteger one_one_Code_integer) one_one_Code_integer) zero_z3403309356797280102nteger))) (let ((_let_186 (@ field_3145993188331922222at_nat bot_bo228742789529271731at_nat))) (let ((_let_187 (= _let_186 bot_bo3083307316010499117at_nat))) (let ((_let_188 (= times_times_int (@ _let_88 (@ produc27273713700761075at_nat (lambda ((X2 nat) (Y5 nat) (__flatten_var_0 product_prod_nat_nat)) (@ (@ produc2626176000494625587at_nat (lambda ((U4 nat) (V4 nat)) (let ((_let_1 (@ times_times_nat Y5))) (let ((_let_2 (@ times_times_nat X2))) (@ (@ product_Pair_nat_nat (@ (@ plus_plus_nat (@ _let_2 U4)) (@ _let_1 V4))) (@ (@ plus_plus_nat (@ _let_2 V4)) (@ _let_1 U4))))))) __flatten_var_0))))))) (let ((_let_189 (= code_divmod_abs (lambda ((K4 code_integer) (L4 code_integer)) (let ((_let_1 (@ abs_abs_Code_integer L4))) (let ((_let_2 (@ abs_abs_Code_integer K4))) (@ (@ produc1086072967326762835nteger (@ (@ divide6298287555418463151nteger _let_2) _let_1)) (@ (@ modulo364778990260209775nteger _let_2) _let_1)))))))) (let ((_let_190 (= plus_plus_rat (@ _let_176 (lambda ((X2 product_prod_int_int) (Y5 product_prod_int_int)) (let ((_let_1 (@ product_snd_int_int Y5))) (let ((_let_2 (@ product_snd_int_int X2))) (@ (@ product_Pair_int_int (@ (@ plus_plus_int (@ (@ times_times_int (@ product_fst_int_int X2)) _let_1)) (@ (@ times_times_int (@ product_fst_int_int Y5)) _let_2))) (@ (@ times_times_int _let_2) _let_1))))))))) (let ((_let_191 (= distinct_d (lambda ((Xs3 list_d)) (forall ((I4 nat)) (=> (@ (@ ord_less_nat I4) (@ size_size_list_d Xs3)) (forall ((J2 nat)) (let ((_let_1 (@ nth_d Xs3))) (=> (@ (@ ord_less_nat J2) (@ size_size_list_d Xs3)) (=> (not (= I4 J2)) (not (= (@ _let_1 I4) (@ _let_1 J2))))))))))))) (let ((_let_192 (= minus_minus_assn (lambda ((A3 assn) (B3 assn)) (@ (@ inf_inf_assn A3) (@ uminus_uminus_assn B3)))))) (let ((_let_193 (= top_top_set_o (@ (@ insert_o2 false) (@ (@ insert_o2 true) bot_bot_set_o))))) (let ((_let_194 (@ _let_101 bot_bot_assn))) (let ((_let_195 (ho_1894 k_1897 p))) (let ((_let_196 (ho_1895 _let_195 skv_6101))) (let ((_let_197 (ho_1895 (ho_1894 k_1897 (ho_1941 k_1940 (ho_2624 k_2623 BOOLEAN_TERM_VARIABLE_680062))) skv_6101))) (let ((_let_198 (not _let_196))) (let ((_let_199 (or _let_198 _let_197))) (let ((_let_200 (ho_1895 (ho_1894 k_1897 q) skv_6101))) (let ((_let_201 (or _let_198 _let_200))) (let ((_let_202 (forall ((BOUND_VARIABLE_267024 produc3658429121746597890et_nat)) (or (not (ho_1895 (ho_1894 k_1897 p) BOUND_VARIABLE_267024)) (ho_1895 (ho_1894 k_1897 q) BOUND_VARIABLE_267024))))) (let ((_let_203 (not _let_201))) (let ((_let_204 (not _let_202))) (let ((_let_205 (ASSUME :args (_let_131)))) (let ((_let_206 (ASSUME :args (_let_117)))) (let ((_let_207 (EQ_RESOLVE (ASSUME :args (_let_135)) (MACRO_SR_EQ_INTRO :args (_let_135 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_208 (EQ_RESOLVE (ASSUME :args (_let_120)) (MACRO_SR_EQ_INTRO :args (_let_120 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_209 (ASSUME :args (_let_129)))) (let ((_let_210 (ASSUME :args (_let_46)))) (let ((_let_211 (ASSUME :args (_let_5)))) (let ((_let_212 (EQ_RESOLVE (ASSUME :args (_let_127)) (MACRO_SR_EQ_INTRO :args (_let_127 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_213 (ASSUME :args (_let_116)))) (let ((_let_214 (EQ_RESOLVE (ASSUME :args (_let_132)) (MACRO_SR_EQ_INTRO :args (_let_132 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_215 (EQ_RESOLVE (ASSUME :args (_let_54)) (MACRO_SR_EQ_INTRO :args (_let_54 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_216 (EQ_RESOLVE (ASSUME :args (_let_115)) (MACRO_SR_EQ_INTRO :args (_let_115 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_217 (ASSUME :args (_let_124)))) (let ((_let_218 (EQ_RESOLVE (ASSUME :args (_let_97)) (MACRO_SR_EQ_INTRO :args (_let_97 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_219 (EQ_RESOLVE (ASSUME :args (_let_122)) (MACRO_SR_EQ_INTRO :args (_let_122 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_220 (ASSUME :args (_let_110)))) (let ((_let_221 (EQ_RESOLVE (ASSUME :args (_let_90)) (MACRO_SR_EQ_INTRO :args (_let_90 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_222 (ASSUME :args (_let_157)))) (let ((_let_223 (ASSUME :args (_let_147)))) (let ((_let_224 (ASSUME :args (_let_138)))) (let ((_let_225 (EQ_RESOLVE (ASSUME :args (_let_114)) (MACRO_SR_EQ_INTRO :args (_let_114 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_226 (ASSUME :args (_let_170)))) (let ((_let_227 (EQ_RESOLVE (ASSUME :args (_let_42)) (MACRO_SR_EQ_INTRO :args (_let_42 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_228 (EQ_RESOLVE (ASSUME :args (_let_76)) (MACRO_SR_EQ_INTRO :args (_let_76 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_229 (EQ_RESOLVE (ASSUME :args (_let_145)) (MACRO_SR_EQ_INTRO :args (_let_145 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_230 (ASSUME :args (_let_75)))) (let ((_let_231 (EQ_RESOLVE (ASSUME :args (_let_178)) (MACRO_SR_EQ_INTRO :args (_let_178 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_232 (EQ_RESOLVE (ASSUME :args (_let_150)) (MACRO_SR_EQ_INTRO :args (_let_150 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_233 (EQ_RESOLVE (ASSUME :args (_let_80)) (MACRO_SR_EQ_INTRO :args (_let_80 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_234 (ASSUME :args (_let_107)))) (let ((_let_235 (ASSUME :args (_let_100)))) (let ((_let_236 (SYMM (ASSUME :args (_let_123))))) (let ((_let_237 (ASSUME :args (_let_98)))) (let ((_let_238 (EQ_RESOLVE (ASSUME :args (_let_137)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_237 _let_236 _let_235 _let_234 _let_233 _let_232 _let_231 _let_230 _let_229 _let_228 _let_227 _let_226 _let_225 _let_224 _let_223 _let_222 _let_221 _let_220 _let_219 _let_218 _let_217 _let_216 _let_215 _let_214 _let_213 _let_212 _let_211 _let_210 _let_209 _let_208 _let_207 _let_206 _let_205) :args (_let_137 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_239 (ASSUME :args (_let_168)))) (let ((_let_240 (EQ_RESOLVE (ASSUME :args (_let_128)) (MACRO_SR_EQ_INTRO :args (_let_128 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_241 (SYMM (ASSUME :args (_let_94))))) (let ((_let_242 (ASSUME :args (_let_103)))) (let ((_let_243 (EQ_RESOLVE (ASSUME :args (_let_45)) (MACRO_SR_EQ_INTRO :args (_let_45 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_244 (EQ_RESOLVE (EQ_RESOLVE (ASSUME :args (_let_52)) (MACRO_SR_EQ_INTRO :args (_let_52 SB_DEFAULT SBA_FIXPOINT))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_243 _let_242 _let_241 _let_240 _let_239 _let_238 _let_237 _let_236 _let_235 _let_234 _let_233 _let_232 _let_231 _let_230 _let_229 _let_228 _let_227 _let_226 _let_225 _let_224 _let_223 _let_222 _let_221 _let_220 _let_219 _let_218 _let_217 _let_216 _let_215 _let_214 _let_213 _let_212 _let_211 _let_210 _let_209 _let_208 _let_207 _let_206 _let_205) :args ((= ord_le3102999989581377725nteger (lambda ((B3 code_integer) (A3 code_integer)) (or (@ (@ ord_le6747313008572928689nteger B3) A3) (= B3 A3)))) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_245 (SYMM (ASSUME :args (_let_140))))) (let ((_let_246 (EQ_RESOLVE (ASSUME :args (_let_102)) (MACRO_SR_EQ_INTRO :args (_let_102 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_247 (ASSUME :args (_let_86)))) (let ((_let_248 (EQ_RESOLVE (ASSUME :args (_let_146)) (MACRO_SR_EQ_INTRO :args (_let_146 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_249 (ASSUME :args (_let_83)))) (let ((_let_250 (ASSUME :args (_let_81)))) (let ((_let_251 (EQ_RESOLVE (SYMM (ASSUME :args (_let_105))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_250 _let_249 _let_248 _let_247 _let_246 _let_245 _let_244 _let_243 _let_242 _let_241 _let_240 _let_239 _let_238 _let_237 _let_236 _let_235 _let_234 _let_233 _let_232 _let_231 _let_230 _let_229 _let_228 _let_227 _let_226 _let_225 _let_224 _let_223 _let_222 _let_221 _let_220 _let_219 _let_218 _let_217 _let_216 _let_215 _let_214 _let_213 _let_212 _let_211 _let_210 _let_209 _let_208 _let_207 _let_206 _let_205) :args ((= one_one_nat _let_104) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_252 (EQ_RESOLVE (ASSUME :args (_let_151)) (MACRO_SR_EQ_INTRO :args (_let_151 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_253 (EQ_RESOLVE (ASSUME :args (_let_153)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_252 _let_251 _let_250 _let_249 _let_248 _let_247 _let_246 _let_245 _let_244 _let_243 _let_242 _let_241 _let_240 _let_239 _let_238 _let_237 _let_236 _let_235 _let_234 _let_233 _let_232 _let_231 _let_230 _let_229 _let_228 _let_227 _let_226 _let_225 _let_224 _let_223 _let_222 _let_221 _let_220 _let_219 _let_218 _let_217 _let_216 _let_215 _let_214 _let_213 _let_212 _let_211 _let_210 _let_209 _let_208 _let_207 _let_206 _let_205) :args (_let_153 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_254 (SYMM (ASSUME :args (_let_156))))) (let ((_let_255 (ASSUME :args (_let_92)))) (let ((_let_256 (ASSUME :args (_let_158)))) (let ((_let_257 (ASSUME :args (_let_89)))) (let ((_let_258 (SYMM (ASSUME :args (_let_159))))) (let ((_let_259 (ASSUME :args (_let_161)))) (let ((_let_260 (EQ_RESOLVE (ASSUME :args (_let_48)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_259 _let_258 _let_257 _let_256 _let_255 _let_254 _let_253 _let_252 _let_251 _let_250 _let_249 _let_248 _let_247 _let_246 _let_245 _let_244 _let_243 _let_242 _let_241 _let_240 _let_239 _let_238 _let_237 _let_236 _let_235 _let_234 _let_233 _let_232 _let_231 _let_230 _let_229 _let_228 _let_227 _let_226 _let_225 _let_224 _let_223 _let_222 _let_221 _let_220 _let_219 _let_218 _let_217 _let_216 _let_215 _let_214 _let_213 _let_212 _let_211 _let_210 _let_209 _let_208 _let_207 _let_206 _let_205) :args (_let_48 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_261 (ASSUME :args (_let_165)))) (let ((_let_262 (ASSUME :args (_let_166)))) (let ((_let_263 (EQ_RESOLVE (ASSUME :args (_let_96)) (MACRO_SR_EQ_INTRO :args (_let_96 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_264 (ASSUME :args (_let_93)))) (let ((_let_265 (ASSUME :args (_let_169)))) (let ((_let_266 (ASSUME :args (_let_152)))) (let ((_let_267 (EQ_RESOLVE (EQ_RESOLVE (ASSUME :args (_let_55)) (MACRO_SR_EQ_INTRO :args (_let_55 SB_DEFAULT SBA_FIXPOINT))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_266 _let_265 _let_264 _let_263 _let_262 _let_261 _let_260 _let_259 _let_258 _let_257 _let_256 _let_255 _let_254 _let_253 _let_252 _let_251 _let_250 _let_249 _let_248 _let_247 _let_246 _let_245 _let_244 _let_243 _let_242 _let_241 _let_240 _let_239 _let_238 _let_237 _let_236 _let_235 _let_234 _let_233 _let_232 _let_231 _let_230 _let_229 _let_228 _let_227 _let_226 _let_225 _let_224 _let_223 _let_222 _let_221 _let_220 _let_219 _let_218 _let_217 _let_216 _let_215 _let_214 _let_213 _let_212 _let_211 _let_210 _let_209 _let_208 _let_207 _let_206 _let_205) :args ((= is_empty_int (lambda ((A5 set_int)) (= bot_bot_set_int A5))) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_268 (ASSUME :args (_let_126)))) (let ((_let_269 (EQ_RESOLVE (SYMM (ASSUME :args (_let_172))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_268 _let_267 _let_266 _let_265 _let_264 _let_263 _let_262 _let_261 _let_260 _let_259 _let_258 _let_257 _let_256 _let_255 _let_254 _let_253 _let_252 _let_251 _let_250 _let_249 _let_248 _let_247 _let_246 _let_245 _let_244 _let_243 _let_242 _let_241 _let_240 _let_239 _let_238 _let_237 _let_236 _let_235 _let_234 _let_233 _let_232 _let_231 _let_230 _let_229 _let_228 _let_227 _let_226 _let_225 _let_224 _let_223 _let_222 _let_221 _let_220 _let_219 _let_218 _let_217 _let_216 _let_215 _let_214 _let_213 _let_212 _let_211 _let_210 _let_209 _let_208 _let_207 _let_206 _let_205) :args ((= zero_zero_rat _let_171) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_270 (EQ_RESOLVE (EQ_RESOLVE (ASSUME :args (_let_173)) (MACRO_SR_EQ_INTRO :args (_let_173 SB_DEFAULT SBA_FIXPOINT))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_269 _let_268 _let_267 _let_266 _let_265 _let_264 _let_263 _let_262 _let_261 _let_260 _let_259 _let_258 _let_257 _let_256 _let_255 _let_254 _let_253 _let_252 _let_251 _let_250 _let_249 _let_248 _let_247 _let_246 _let_245 _let_244 _let_243 _let_242 _let_241 _let_240 _let_239 _let_238 _let_237 _let_236 _let_235 _let_234 _let_233 _let_232 _let_231 _let_230 _let_229 _let_228 _let_227 _let_226 _let_225 _let_224 _let_223 _let_222 _let_221 _let_220 _let_219 _let_218 _let_217 _let_216 _let_215 _let_214 _let_213 _let_212 _let_211 _let_210 _let_209 _let_208 _let_207 _let_206 _let_205) :args ((= is_empty_nat (lambda ((A5 set_nat)) (= bot_bot_set_nat A5))) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_271 (ASSUME :args (_let_112)))) (let ((_let_272 (EQ_RESOLVE (ASSUME :args (_let_34)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_271 _let_270 _let_269 _let_268 _let_267 _let_266 _let_265 _let_264 _let_263 _let_262 _let_261 _let_260 _let_259 _let_258 _let_257 _let_256 _let_255 _let_254 _let_253 _let_252 _let_251 _let_250 _let_249 _let_248 _let_247 _let_246 _let_245 _let_244 _let_243 _let_242 _let_241 _let_240 _let_239 _let_238 _let_237 _let_236 _let_235 _let_234 _let_233 _let_232 _let_231 _let_230 _let_229 _let_228 _let_227 _let_226 _let_225 _let_224 _let_223 _let_222 _let_221 _let_220 _let_219 _let_218 _let_217 _let_216 _let_215 _let_214 _let_213 _let_212 _let_211 _let_210 _let_209 _let_208 _let_207 _let_206 _let_205) :args (_let_34 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_273 (EQ_RESOLVE (ASSUME :args (_let_175)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_272 _let_271 _let_270 _let_269 _let_268 _let_267 _let_266 _let_265 _let_264 _let_263 _let_262 _let_261 _let_260 _let_259 _let_258 _let_257 _let_256 _let_255 _let_254 _let_253 _let_252 _let_251 _let_250 _let_249 _let_248 _let_247 _let_246 _let_245 _let_244 _let_243 _let_242 _let_241 _let_240 _let_239 _let_238 _let_237 _let_236 _let_235 _let_234 _let_233 _let_232 _let_231 _let_230 _let_229 _let_228 _let_227 _let_226 _let_225 _let_224 _let_223 _let_222 _let_221 _let_220 _let_219 _let_218 _let_217 _let_216 _let_215 _let_214 _let_213 _let_212 _let_211 _let_210 _let_209 _let_208 _let_207 _let_206 _let_205) :args (_let_175 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_274 (ASSUME :args (_let_167)))) (let ((_let_275 (ASSUME :args (_let_177)))) (let ((_let_276 (ASSUME :args (_let_64)))) (let ((_let_277 (ASSUME :args (_let_85)))) (let ((_let_278 (EQ_RESOLVE (ASSUME :args (_let_163)) (MACRO_SR_EQ_INTRO :args (_let_163 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_279 (ASSUME :args (_let_179)))) (let ((_let_280 (EQ_RESOLVE (ASSUME :args (_let_180)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_279 _let_278 _let_277 _let_276 _let_275 _let_274 _let_273 _let_272 _let_271 _let_270 _let_269 _let_268 _let_267 _let_266 _let_265 _let_264 _let_263 _let_262 _let_261 _let_260 _let_259 _let_258 _let_257 _let_256 _let_255 _let_254 _let_253 _let_252 _let_251 _let_250 _let_249 _let_248 _let_247 _let_246 _let_245 _let_244 _let_243 _let_242 _let_241 _let_240 _let_239 _let_238 _let_237 _let_236 _let_235 _let_234 _let_233 _let_232 _let_231 _let_230 _let_229 _let_228 _let_227 _let_226 _let_225 _let_224 _let_223 _let_222 _let_221 _let_220 _let_219 _let_218 _let_217 _let_216 _let_215 _let_214 _let_213 _let_212 _let_211 _let_210 _let_209 _let_208 _let_207 _let_206 _let_205) :args (_let_180 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_281 (EQ_RESOLVE (EQ_RESOLVE (ASSUME :args (_let_181)) (MACRO_SR_EQ_INTRO :args (_let_181 SB_DEFAULT SBA_FIXPOINT))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_280 _let_279 _let_278 _let_277 _let_276 _let_275 _let_274 _let_273 _let_272 _let_271 _let_270 _let_269 _let_268 _let_267 _let_266 _let_265 _let_264 _let_263 _let_262 _let_261 _let_260 _let_259 _let_258 _let_257 _let_256 _let_255 _let_254 _let_253 _let_252 _let_251 _let_250 _let_249 _let_248 _let_247 _let_246 _let_245 _let_244 _let_243 _let_242 _let_241 _let_240 _let_239 _let_238 _let_237 _let_236 _let_235 _let_234 _let_233 _let_232 _let_231 _let_230 _let_229 _let_228 _let_227 _let_226 _let_225 _let_224 _let_223 _let_222 _let_221 _let_220 _let_219 _let_218 _let_217 _let_216 _let_215 _let_214 _let_213 _let_212 _let_211 _let_210 _let_209 _let_208 _let_207 _let_206 _let_205) :args ((= normalize (lambda ((P7 product_prod_int_int)) (let ((_let_1 (@ product_snd_int_int P7))) (let ((_let_2 (@ product_fst_int_int P7))) (let ((_let_3 (@ (@ gcd_gcd_int _let_2) _let_1))) (let ((_let_4 (@ uminus_uminus_int _let_3))) (let ((_let_5 (@ divide_divide_int _let_1))) (let ((_let_6 (@ divide_divide_int _let_2))) (@ (@ (@ if_Pro3027730157355071871nt_int (@ (@ ord_less_int zero_zero_int) _let_1)) (@ (@ product_Pair_int_int (@ _let_6 _let_3)) (@ _let_5 _let_3))) (@ (@ (@ if_Pro3027730157355071871nt_int (= zero_zero_int _let_1)) (@ (@ product_Pair_int_int zero_zero_int) one_one_int)) (@ (@ product_Pair_int_int (@ _let_6 _let_4)) (@ _let_5 _let_4)))))))))))) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_282 (SYMM (ASSUME :args (_let_79))))) (let ((_let_283 (ASSUME :args (_let_84)))) (let ((_let_284 (EQ_RESOLVE (EQ_RESOLVE (ASSUME :args (_let_71)) (MACRO_SR_EQ_INTRO :args (_let_71 SB_DEFAULT SBA_FIXPOINT))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_283 _let_282 _let_281 _let_280 _let_279 _let_278 _let_277 _let_276 _let_275 _let_274 _let_273 _let_272 _let_271 _let_270 _let_269 _let_268 _let_267 _let_266 _let_265 _let_264 _let_263 _let_262 _let_261 _let_260 _let_259 _let_258 _let_257 _let_256 _let_255 _let_254 _let_253 _let_252 _let_251 _let_250 _let_249 _let_248 _let_247 _let_246 _let_245 _let_244 _let_243 _let_242 _let_241 _let_240 _let_239 _let_238 _let_237 _let_236 _let_235 _let_234 _let_233 _let_232 _let_231 _let_230 _let_229 _let_228 _let_227 _let_226 _let_225 _let_224 _let_223 _let_222 _let_221 _let_220 _let_219 _let_218 _let_217 _let_216 _let_215 _let_214 _let_213 _let_212 _let_211 _let_210 _let_209 _let_208 _let_207 _let_206 _let_205) :args ((= sorted_wrt_c (lambda ((P2 (-> c c Bool)) (Xs3 list_c)) (forall ((I4 nat) (J2 nat)) (let ((_let_1 (@ nth_c Xs3))) (or (not (@ (@ ord_less_nat I4) J2)) (not (@ (@ ord_less_nat J2) (@ size_size_list_c Xs3))) (@ (@ P2 (@ _let_1 I4)) (@ _let_1 J2))))))) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_285 (EQ_RESOLVE (EQ_RESOLVE (ASSUME :args (_let_70)) (MACRO_SR_EQ_INTRO :args (_let_70 SB_DEFAULT SBA_FIXPOINT))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_284 _let_283 _let_282 _let_281 _let_280 _let_279 _let_278 _let_277 _let_276 _let_275 _let_274 _let_273 _let_272 _let_271 _let_270 _let_269 _let_268 _let_267 _let_266 _let_265 _let_264 _let_263 _let_262 _let_261 _let_260 _let_259 _let_258 _let_257 _let_256 _let_255 _let_254 _let_253 _let_252 _let_251 _let_250 _let_249 _let_248 _let_247 _let_246 _let_245 _let_244 _let_243 _let_242 _let_241 _let_240 _let_239 _let_238 _let_237 _let_236 _let_235 _let_234 _let_233 _let_232 _let_231 _let_230 _let_229 _let_228 _let_227 _let_226 _let_225 _let_224 _let_223 _let_222 _let_221 _let_220 _let_219 _let_218 _let_217 _let_216 _let_215 _let_214 _let_213 _let_212 _let_211 _let_210 _let_209 _let_208 _let_207 _let_206 _let_205) :args ((= is_singleton_int (lambda ((A5 set_int)) (not (forall ((X2 int)) (not (= A5 (@ (@ insert_int2 X2) bot_bot_set_int))))))) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_286 (EQ_RESOLVE (EQ_RESOLVE (ASSUME :args (_let_69)) (MACRO_SR_EQ_INTRO :args (_let_69 SB_DEFAULT SBA_FIXPOINT))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_285 _let_284 _let_283 _let_282 _let_281 _let_280 _let_279 _let_278 _let_277 _let_276 _let_275 _let_274 _let_273 _let_272 _let_271 _let_270 _let_269 _let_268 _let_267 _let_266 _let_265 _let_264 _let_263 _let_262 _let_261 _let_260 _let_259 _let_258 _let_257 _let_256 _let_255 _let_254 _let_253 _let_252 _let_251 _let_250 _let_249 _let_248 _let_247 _let_246 _let_245 _let_244 _let_243 _let_242 _let_241 _let_240 _let_239 _let_238 _let_237 _let_236 _let_235 _let_234 _let_233 _let_232 _let_231 _let_230 _let_229 _let_228 _let_227 _let_226 _let_225 _let_224 _let_223 _let_222 _let_221 _let_220 _let_219 _let_218 _let_217 _let_216 _let_215 _let_214 _let_213 _let_212 _let_211 _let_210 _let_209 _let_208 _let_207 _let_206 _let_205) :args ((= sorted_wrt_int (lambda ((P2 (-> int int Bool)) (Xs3 list_int)) (forall ((I4 nat) (J2 nat)) (let ((_let_1 (@ nth_int Xs3))) (or (not (@ (@ ord_less_nat I4) J2)) (not (@ (@ ord_less_nat J2) (@ size_size_list_int Xs3))) (@ (@ P2 (@ _let_1 I4)) (@ _let_1 J2))))))) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_287 (EQ_RESOLVE (ASSUME :args (_let_134)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_286 _let_285 _let_284 _let_283 _let_282 _let_281 _let_280 _let_279 _let_278 _let_277 _let_276 _let_275 _let_274 _let_273 _let_272 _let_271 _let_270 _let_269 _let_268 _let_267 _let_266 _let_265 _let_264 _let_263 _let_262 _let_261 _let_260 _let_259 _let_258 _let_257 _let_256 _let_255 _let_254 _let_253 _let_252 _let_251 _let_250 _let_249 _let_248 _let_247 _let_246 _let_245 _let_244 _let_243 _let_242 _let_241 _let_240 _let_239 _let_238 _let_237 _let_236 _let_235 _let_234 _let_233 _let_232 _let_231 _let_230 _let_229 _let_228 _let_227 _let_226 _let_225 _let_224 _let_223 _let_222 _let_221 _let_220 _let_219 _let_218 _let_217 _let_216 _let_215 _let_214 _let_213 _let_212 _let_211 _let_210 _let_209 _let_208 _let_207 _let_206 _let_205) :args (_let_134 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_288 (ASSUME :args (_let_67)))) (let ((_let_289 (ASSUME :args (_let_136)))) (let ((_let_290 (SYMM (ASSUME :args (_let_144))))) (let ((_let_291 (ASSUME :args (_let_65)))) (let ((_let_292 (EQ_RESOLVE (EQ_RESOLVE (ASSUME :args (_let_113)) (MACRO_SR_EQ_INTRO :args (_let_113 SB_DEFAULT SBA_FIXPOINT))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_291 _let_290 _let_289 _let_288 _let_287 _let_286 _let_285 _let_284 _let_283 _let_282 _let_281 _let_280 _let_279 _let_278 _let_277 _let_276 _let_275 _let_274 _let_273 _let_272 _let_271 _let_270 _let_269 _let_268 _let_267 _let_266 _let_265 _let_264 _let_263 _let_262 _let_261 _let_260 _let_259 _let_258 _let_257 _let_256 _let_255 _let_254 _let_253 _let_252 _let_251 _let_250 _let_249 _let_248 _let_247 _let_246 _let_245 _let_244 _let_243 _let_242 _let_241 _let_240 _let_239 _let_238 _let_237 _let_236 _let_235 _let_234 _let_233 _let_232 _let_231 _let_230 _let_229 _let_228 _let_227 _let_226 _let_225 _let_224 _let_223 _let_222 _let_221 _let_220 _let_219 _let_218 _let_217 _let_216 _let_215 _let_214 _let_213 _let_212 _let_211 _let_210 _let_209 _let_208 _let_207 _let_206 _let_205) :args ((= eucl_rel_int (lambda ((A12 int) (A23 int) (A32 product_prod_int_int)) (let ((_let_1 (= zero_zero_int A23))) (or (not (or (not _let_1) (not (= A32 (@ (@ product_Pair_int_int zero_zero_int) A12))))) (not (forall ((R4 int) (Q8 int)) (or (not (@ (@ ord_less_int (@ abs_abs_int R4)) (@ abs_abs_int A23))) (not (= A12 (@ (@ plus_plus_int (@ (@ times_times_int Q8) A23)) R4))) (not (= (@ sgn_sgn_int R4) (@ sgn_sgn_int A23))) (not (= A32 (@ (@ product_Pair_int_int Q8) R4)))))) (not (or _let_1 (forall ((Q8 int)) (or (not (= A32 (@ (@ product_Pair_int_int Q8) zero_zero_int))) (not (= A12 (@ (@ times_times_int Q8) A23))))))))))) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_293 (ASSUME :args (_let_162)))) (let ((_let_294 (EQ_RESOLVE (ASSUME :args (_let_63)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_293 _let_292 _let_291 _let_290 _let_289 _let_288 _let_287 _let_286 _let_285 _let_284 _let_283 _let_282 _let_281 _let_280 _let_279 _let_278 _let_277 _let_276 _let_275 _let_274 _let_273 _let_272 _let_271 _let_270 _let_269 _let_268 _let_267 _let_266 _let_265 _let_264 _let_263 _let_262 _let_261 _let_260 _let_259 _let_258 _let_257 _let_256 _let_255 _let_254 _let_253 _let_252 _let_251 _let_250 _let_249 _let_248 _let_247 _let_246 _let_245 _let_244 _let_243 _let_242 _let_241 _let_240 _let_239 _let_238 _let_237 _let_236 _let_235 _let_234 _let_233 _let_232 _let_231 _let_230 _let_229 _let_228 _let_227 _let_226 _let_225 _let_224 _let_223 _let_222 _let_221 _let_220 _let_219 _let_218 _let_217 _let_216 _let_215 _let_214 _let_213 _let_212 _let_211 _let_210 _let_209 _let_208 _let_207 _let_206 _let_205) :args (_let_63 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_295 (ASSUME :args (_let_62)))) (let ((_let_296 (EQ_RESOLVE (ASSUME :args (_let_61)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_295 _let_294 _let_293 _let_292 _let_291 _let_290 _let_289 _let_288 _let_287 _let_286 _let_285 _let_284 _let_283 _let_282 _let_281 _let_280 _let_279 _let_278 _let_277 _let_276 _let_275 _let_274 _let_273 _let_272 _let_271 _let_270 _let_269 _let_268 _let_267 _let_266 _let_265 _let_264 _let_263 _let_262 _let_261 _let_260 _let_259 _let_258 _let_257 _let_256 _let_255 _let_254 _let_253 _let_252 _let_251 _let_250 _let_249 _let_248 _let_247 _let_246 _let_245 _let_244 _let_243 _let_242 _let_241 _let_240 _let_239 _let_238 _let_237 _let_236 _let_235 _let_234 _let_233 _let_232 _let_231 _let_230 _let_229 _let_228 _let_227 _let_226 _let_225 _let_224 _let_223 _let_222 _let_221 _let_220 _let_219 _let_218 _let_217 _let_216 _let_215 _let_214 _let_213 _let_212 _let_211 _let_210 _let_209 _let_208 _let_207 _let_206 _let_205) :args (_let_61 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_297 (ASSUME :args (_let_141)))) (let ((_let_298 (ASSUME :args (_let_60)))) (let ((_let_299 (EQ_RESOLVE (ASSUME :args (_let_59)) (MACRO_SR_EQ_INTRO :args (_let_59 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_300 (ASSUME :args (_let_121)))) (let ((_let_301 (EQ_RESOLVE (ASSUME :args (_let_56)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_300 _let_299 _let_298 _let_297 _let_296 _let_295 _let_294 _let_293 _let_292 _let_291 _let_290 _let_289 _let_288 _let_287 _let_286 _let_285 _let_284 _let_283 _let_282 _let_281 _let_280 _let_279 _let_278 _let_277 _let_276 _let_275 _let_274 _let_273 _let_272 _let_271 _let_270 _let_269 _let_268 _let_267 _let_266 _let_265 _let_264 _let_263 _let_262 _let_261 _let_260 _let_259 _let_258 _let_257 _let_256 _let_255 _let_254 _let_253 _let_252 _let_251 _let_250 _let_249 _let_248 _let_247 _let_246 _let_245 _let_244 _let_243 _let_242 _let_241 _let_240 _let_239 _let_238 _let_237 _let_236 _let_235 _let_234 _let_233 _let_232 _let_231 _let_230 _let_229 _let_228 _let_227 _let_226 _let_225 _let_224 _let_223 _let_222 _let_221 _let_220 _let_219 _let_218 _let_217 _let_216 _let_215 _let_214 _let_213 _let_212 _let_211 _let_210 _let_209 _let_208 _let_207 _let_206 _let_205) :args (_let_56 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_302 (EQ_RESOLVE (EQ_RESOLVE (ASSUME :args (_let_51)) (MACRO_SR_EQ_INTRO :args (_let_51 SB_DEFAULT SBA_FIXPOINT))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_301 _let_300 _let_299 _let_298 _let_297 _let_296 _let_295 _let_294 _let_293 _let_292 _let_291 _let_290 _let_289 _let_288 _let_287 _let_286 _let_285 _let_284 _let_283 _let_282 _let_281 _let_280 _let_279 _let_278 _let_277 _let_276 _let_275 _let_274 _let_273 _let_272 _let_271 _let_270 _let_269 _let_268 _let_267 _let_266 _let_265 _let_264 _let_263 _let_262 _let_261 _let_260 _let_259 _let_258 _let_257 _let_256 _let_255 _let_254 _let_253 _let_252 _let_251 _let_250 _let_249 _let_248 _let_247 _let_246 _let_245 _let_244 _let_243 _let_242 _let_241 _let_240 _let_239 _let_238 _let_237 _let_236 _let_235 _let_234 _let_233 _let_232 _let_231 _let_230 _let_229 _let_228 _let_227 _let_226 _let_225 _let_224 _let_223 _let_222 _let_221 _let_220 _let_219 _let_218 _let_217 _let_216 _let_215 _let_214 _let_213 _let_212 _let_211 _let_210 _let_209 _let_208 _let_207 _let_206 _let_205) :args ((= is_emp1662574758705540307at_nat (lambda ((A5 set_Pr1261947904930325089at_nat)) (= bot_bo2099793752762293965at_nat A5))) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_303 (EQ_RESOLVE (ASSUME :args (_let_58)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_302 _let_301 _let_300 _let_299 _let_298 _let_297 _let_296 _let_295 _let_294 _let_293 _let_292 _let_291 _let_290 _let_289 _let_288 _let_287 _let_286 _let_285 _let_284 _let_283 _let_282 _let_281 _let_280 _let_279 _let_278 _let_277 _let_276 _let_275 _let_274 _let_273 _let_272 _let_271 _let_270 _let_269 _let_268 _let_267 _let_266 _let_265 _let_264 _let_263 _let_262 _let_261 _let_260 _let_259 _let_258 _let_257 _let_256 _let_255 _let_254 _let_253 _let_252 _let_251 _let_250 _let_249 _let_248 _let_247 _let_246 _let_245 _let_244 _let_243 _let_242 _let_241 _let_240 _let_239 _let_238 _let_237 _let_236 _let_235 _let_234 _let_233 _let_232 _let_231 _let_230 _let_229 _let_228 _let_227 _let_226 _let_225 _let_224 _let_223 _let_222 _let_221 _let_220 _let_219 _let_218 _let_217 _let_216 _let_215 _let_214 _let_213 _let_212 _let_211 _let_210 _let_209 _let_208 _let_207 _let_206 _let_205) :args (_let_58 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_304 (EQ_RESOLVE (EQ_RESOLVE (ASSUME :args (_let_27)) (MACRO_SR_EQ_INTRO :args (_let_27 SB_DEFAULT SBA_FIXPOINT))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_303 _let_302 _let_301 _let_300 _let_299 _let_298 _let_297 _let_296 _let_295 _let_294 _let_293 _let_292 _let_291 _let_290 _let_289 _let_288 _let_287 _let_286 _let_285 _let_284 _let_283 _let_282 _let_281 _let_280 _let_279 _let_278 _let_277 _let_276 _let_275 _let_274 _let_273 _let_272 _let_271 _let_270 _let_269 _let_268 _let_267 _let_266 _let_265 _let_264 _let_263 _let_262 _let_261 _let_260 _let_259 _let_258 _let_257 _let_256 _let_255 _let_254 _let_253 _let_252 _let_251 _let_250 _let_249 _let_248 _let_247 _let_246 _let_245 _let_244 _let_243 _let_242 _let_241 _let_240 _let_239 _let_238 _let_237 _let_236 _let_235 _let_234 _let_233 _let_232 _let_231 _let_230 _let_229 _let_228 _let_227 _let_226 _let_225 _let_224 _let_223 _let_222 _let_221 _let_220 _let_219 _let_218 _let_217 _let_216 _let_215 _let_214 _let_213 _let_212 _let_211 _let_210 _let_209 _let_208 _let_207 _let_206 _let_205) :args ((= pairwi3222497012029234898at_nat (lambda ((R3 (-> produc3843707927480180839at_nat produc3843707927480180839at_nat Bool)) (S2 set_Pr4329608150637261639at_nat)) (forall ((X2 produc3843707927480180839at_nat) (BOUND_VARIABLE_115858 produc3843707927480180839at_nat)) (or (not (@ (@ member8757157785044589968at_nat X2) S2)) (not (@ (@ member8757157785044589968at_nat BOUND_VARIABLE_115858) (@ (@ minus_3314409938677909166at_nat S2) (@ (@ insert9069300056098147895at_nat X2) bot_bo228742789529271731at_nat)))) (@ (@ R3 X2) BOUND_VARIABLE_115858))))) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_305 (EQ_RESOLVE (ASSUME :args (_let_148)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_304 _let_303 _let_302 _let_301 _let_300 _let_299 _let_298 _let_297 _let_296 _let_295 _let_294 _let_293 _let_292 _let_291 _let_290 _let_289 _let_288 _let_287 _let_286 _let_285 _let_284 _let_283 _let_282 _let_281 _let_280 _let_279 _let_278 _let_277 _let_276 _let_275 _let_274 _let_273 _let_272 _let_271 _let_270 _let_269 _let_268 _let_267 _let_266 _let_265 _let_264 _let_263 _let_262 _let_261 _let_260 _let_259 _let_258 _let_257 _let_256 _let_255 _let_254 _let_253 _let_252 _let_251 _let_250 _let_249 _let_248 _let_247 _let_246 _let_245 _let_244 _let_243 _let_242 _let_241 _let_240 _let_239 _let_238 _let_237 _let_236 _let_235 _let_234 _let_233 _let_232 _let_231 _let_230 _let_229 _let_228 _let_227 _let_226 _let_225 _let_224 _let_223 _let_222 _let_221 _let_220 _let_219 _let_218 _let_217 _let_216 _let_215 _let_214 _let_213 _let_212 _let_211 _let_210 _let_209 _let_208 _let_207 _let_206 _let_205) :args (_let_148 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_306 (EQ_RESOLVE (ASSUME :args (_let_49)) (MACRO_SR_EQ_INTRO :args (_let_49 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_307 (ASSUME :args (_let_53)))) (let ((_let_308 (EQ_RESOLVE (EQ_RESOLVE (ASSUME :args (_let_139)) (MACRO_SR_EQ_INTRO :args (_let_139 SB_DEFAULT SBA_FIXPOINT))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_307 _let_306 _let_305 _let_304 _let_303 _let_302 _let_301 _let_300 _let_299 _let_298 _let_297 _let_296 _let_295 _let_294 _let_293 _let_292 _let_291 _let_290 _let_289 _let_288 _let_287 _let_286 _let_285 _let_284 _let_283 _let_282 _let_281 _let_280 _let_279 _let_278 _let_277 _let_276 _let_275 _let_274 _let_273 _let_272 _let_271 _let_270 _let_269 _let_268 _let_267 _let_266 _let_265 _let_264 _let_263 _let_262 _let_261 _let_260 _let_259 _let_258 _let_257 _let_256 _let_255 _let_254 _let_253 _let_252 _let_251 _let_250 _let_249 _let_248 _let_247 _let_246 _let_245 _let_244 _let_243 _let_242 _let_241 _let_240 _let_239 _let_238 _let_237 _let_236 _let_235 _let_234 _let_233 _let_232 _let_231 _let_230 _let_229 _let_228 _let_227 _let_226 _let_225 _let_224 _let_223 _let_222 _let_221 _let_220 _let_219 _let_218 _let_217 _let_216 _let_215 _let_214 _let_213 _let_212 _let_211 _let_210 _let_209 _let_208 _let_207 _let_206 _let_205) :args ((= sorted_wrt_nat (lambda ((P2 (-> nat nat Bool)) (Xs3 list_nat)) (forall ((I4 nat) (J2 nat)) (let ((_let_1 (@ nth_nat Xs3))) (or (not (@ (@ ord_less_nat I4) J2)) (not (@ (@ ord_less_nat J2) (@ size_size_list_nat Xs3))) (@ (@ P2 (@ _let_1 I4)) (@ _let_1 J2))))))) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_309 (EQ_RESOLVE (ASSUME :args (_let_174)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_308 _let_307 _let_306 _let_305 _let_304 _let_303 _let_302 _let_301 _let_300 _let_299 _let_298 _let_297 _let_296 _let_295 _let_294 _let_293 _let_292 _let_291 _let_290 _let_289 _let_288 _let_287 _let_286 _let_285 _let_284 _let_283 _let_282 _let_281 _let_280 _let_279 _let_278 _let_277 _let_276 _let_275 _let_274 _let_273 _let_272 _let_271 _let_270 _let_269 _let_268 _let_267 _let_266 _let_265 _let_264 _let_263 _let_262 _let_261 _let_260 _let_259 _let_258 _let_257 _let_256 _let_255 _let_254 _let_253 _let_252 _let_251 _let_250 _let_249 _let_248 _let_247 _let_246 _let_245 _let_244 _let_243 _let_242 _let_241 _let_240 _let_239 _let_238 _let_237 _let_236 _let_235 _let_234 _let_233 _let_232 _let_231 _let_230 _let_229 _let_228 _let_227 _let_226 _let_225 _let_224 _let_223 _let_222 _let_221 _let_220 _let_219 _let_218 _let_217 _let_216 _let_215 _let_214 _let_213 _let_212 _let_211 _let_210 _let_209 _let_208 _let_207 _let_206 _let_205) :args (_let_174 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_310 (EQ_RESOLVE (ASSUME :args (_let_44)) (MACRO_SR_EQ_INTRO :args (_let_44 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_311 (EQ_RESOLVE (ASSUME :args (_let_50)) (MACRO_SR_EQ_INTRO :args (_let_50 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_312 (ASSUME :args (_let_125)))) (let ((_let_313 (EQ_RESOLVE (EQ_RESOLVE (ASSUME :args (_let_36)) (MACRO_SR_EQ_INTRO :args (_let_36 SB_DEFAULT SBA_FIXPOINT))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_312 _let_311 _let_310 _let_309 _let_308 _let_307 _let_306 _let_305 _let_304 _let_303 _let_302 _let_301 _let_300 _let_299 _let_298 _let_297 _let_296 _let_295 _let_294 _let_293 _let_292 _let_291 _let_290 _let_289 _let_288 _let_287 _let_286 _let_285 _let_284 _let_283 _let_282 _let_281 _let_280 _let_279 _let_278 _let_277 _let_276 _let_275 _let_274 _let_273 _let_272 _let_271 _let_270 _let_269 _let_268 _let_267 _let_266 _let_265 _let_264 _let_263 _let_262 _let_261 _let_260 _let_259 _let_258 _let_257 _let_256 _let_255 _let_254 _let_253 _let_252 _let_251 _let_250 _let_249 _let_248 _let_247 _let_246 _let_245 _let_244 _let_243 _let_242 _let_241 _let_240 _let_239 _let_238 _let_237 _let_236 _let_235 _let_234 _let_233 _let_232 _let_231 _let_230 _let_229 _let_228 _let_227 _let_226 _let_225 _let_224 _let_223 _let_222 _let_221 _let_220 _let_219 _let_218 _let_217 _let_216 _let_215 _let_214 _let_213 _let_212 _let_211 _let_210 _let_209 _let_208 _let_207 _let_206 _let_205) :args ((= distinct_nat (lambda ((Xs3 list_nat)) (forall ((I4 nat) (BOUND_VARIABLE_118578 nat)) (let ((_let_1 (@ nth_nat Xs3))) (let ((_let_2 (@ size_size_list_nat Xs3))) (or (not (@ (@ ord_less_nat I4) _let_2)) (not (@ (@ ord_less_nat BOUND_VARIABLE_118578) _let_2)) (= I4 BOUND_VARIABLE_118578) (not (= (@ _let_1 I4) (@ _let_1 BOUND_VARIABLE_118578))))))))) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_314 (EQ_RESOLVE (SYMM (ASSUME :args (_let_155))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_313 _let_312 _let_311 _let_310 _let_309 _let_308 _let_307 _let_306 _let_305 _let_304 _let_303 _let_302 _let_301 _let_300 _let_299 _let_298 _let_297 _let_296 _let_295 _let_294 _let_293 _let_292 _let_291 _let_290 _let_289 _let_288 _let_287 _let_286 _let_285 _let_284 _let_283 _let_282 _let_281 _let_280 _let_279 _let_278 _let_277 _let_276 _let_275 _let_274 _let_273 _let_272 _let_271 _let_270 _let_269 _let_268 _let_267 _let_266 _let_265 _let_264 _let_263 _let_262 _let_261 _let_260 _let_259 _let_258 _let_257 _let_256 _let_255 _let_254 _let_253 _let_252 _let_251 _let_250 _let_249 _let_248 _let_247 _let_246 _let_245 _let_244 _let_243 _let_242 _let_241 _let_240 _let_239 _let_238 _let_237 _let_236 _let_235 _let_234 _let_233 _let_232 _let_231 _let_230 _let_229 _let_228 _let_227 _let_226 _let_225 _let_224 _let_223 _let_222 _let_221 _let_220 _let_219 _let_218 _let_217 _let_216 _let_215 _let_214 _let_213 _let_212 _let_211 _let_210 _let_209 _let_208 _let_207 _let_206 _let_205) :args ((= zero_zero_int _let_154) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_315 (EQ_RESOLVE (ASSUME :args (_let_35)) (MACRO_SR_EQ_INTRO :args (_let_35 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_316 (EQ_RESOLVE (EQ_RESOLVE (ASSUME :args (_let_164)) (MACRO_SR_EQ_INTRO :args (_let_164 SB_DEFAULT SBA_FIXPOINT))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_315 _let_314 _let_313 _let_312 _let_311 _let_310 _let_309 _let_308 _let_307 _let_306 _let_305 _let_304 _let_303 _let_302 _let_301 _let_300 _let_299 _let_298 _let_297 _let_296 _let_295 _let_294 _let_293 _let_292 _let_291 _let_290 _let_289 _let_288 _let_287 _let_286 _let_285 _let_284 _let_283 _let_282 _let_281 _let_280 _let_279 _let_278 _let_277 _let_276 _let_275 _let_274 _let_273 _let_272 _let_271 _let_270 _let_269 _let_268 _let_267 _let_266 _let_265 _let_264 _let_263 _let_262 _let_261 _let_260 _let_259 _let_258 _let_257 _let_256 _let_255 _let_254 _let_253 _let_252 _let_251 _let_250 _let_249 _let_248 _let_247 _let_246 _let_245 _let_244 _let_243 _let_242 _let_241 _let_240 _let_239 _let_238 _let_237 _let_236 _let_235 _let_234 _let_233 _let_232 _let_231 _let_230 _let_229 _let_228 _let_227 _let_226 _let_225 _let_224 _let_223 _let_222 _let_221 _let_220 _let_219 _let_218 _let_217 _let_216 _let_215 _let_214 _let_213 _let_212 _let_211 _let_210 _let_209 _let_208 _let_207 _let_206 _let_205) :args ((= list_ex_d (lambda ((P2 (-> d Bool)) (Xs3 list_d)) (not (forall ((N2 nat)) (or (not (@ P2 (@ (@ nth_d Xs3) N2))) (not (@ (@ ord_less_nat N2) (@ size_size_list_d Xs3)))))))) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_317 (EQ_RESOLVE (ASSUME :args (_let_68)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_316 _let_315 _let_314 _let_313 _let_312 _let_311 _let_310 _let_309 _let_308 _let_307 _let_306 _let_305 _let_304 _let_303 _let_302 _let_301 _let_300 _let_299 _let_298 _let_297 _let_296 _let_295 _let_294 _let_293 _let_292 _let_291 _let_290 _let_289 _let_288 _let_287 _let_286 _let_285 _let_284 _let_283 _let_282 _let_281 _let_280 _let_279 _let_278 _let_277 _let_276 _let_275 _let_274 _let_273 _let_272 _let_271 _let_270 _let_269 _let_268 _let_267 _let_266 _let_265 _let_264 _let_263 _let_262 _let_261 _let_260 _let_259 _let_258 _let_257 _let_256 _let_255 _let_254 _let_253 _let_252 _let_251 _let_250 _let_249 _let_248 _let_247 _let_246 _let_245 _let_244 _let_243 _let_242 _let_241 _let_240 _let_239 _let_238 _let_237 _let_236 _let_235 _let_234 _let_233 _let_232 _let_231 _let_230 _let_229 _let_228 _let_227 _let_226 _let_225 _let_224 _let_223 _let_222 _let_221 _let_220 _let_219 _let_218 _let_217 _let_216 _let_215 _let_214 _let_213 _let_212 _let_211 _let_210 _let_209 _let_208 _let_207 _let_206 _let_205) :args (_let_68 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_318 (ASSUME :args (_let_31)))) (let ((_let_319 (ASSUME :args (_let_108)))) (let ((_let_320 (ASSUME :args (_let_30)))) (let ((_let_321 (EQ_RESOLVE (EQ_RESOLVE (ASSUME :args (_let_28)) (MACRO_SR_EQ_INTRO :args (_let_28 SB_DEFAULT SBA_FIXPOINT))) (TRUST_SUBS_MAP (AND_INTRO _let_320 _let_319 _let_318 _let_317 _let_316 _let_315 _let_314 _let_313 _let_312 _let_311 _let_310 _let_309 _let_308 _let_307 _let_306 _let_305 _let_304 _let_303 _let_302 _let_301 _let_300 _let_299 _let_298 _let_297 _let_296 _let_295 _let_294 _let_293 _let_292 _let_291 _let_290 _let_289 _let_288 _let_287 _let_286 _let_285 _let_284 _let_283 _let_282 _let_281 _let_280 _let_279 _let_278 _let_277 _let_276 _let_275 _let_274 _let_273 _let_272 _let_271 _let_270 _let_269 _let_268 _let_267 _let_266 _let_265 _let_264 _let_263 _let_262 _let_261 _let_260 _let_259 _let_258 _let_257 _let_256 _let_255 _let_254 _let_253 _let_252 _let_251 _let_250 _let_249 _let_248 _let_247 _let_246 _let_245 _let_244 _let_243 _let_242 _let_241 _let_240 _let_239 _let_238 _let_237 _let_236 _let_235 _let_234 _let_233 _let_232 _let_231 _let_230 _let_229 _let_228 _let_227 _let_226 _let_225 _let_224 _let_223 _let_222 _let_221 _let_220 _let_219 _let_218 _let_217 _let_216 _let_215 _let_214 _let_213 _let_212 _let_211 _let_210 _let_209 _let_208 _let_207 _let_206 _let_205) :args ((= (= fi (lambda ((M list_P8527749157015355191n_assn) (P7 assn) (Q8 assn) (Up assn) (Uq assn) (F6 assn)) (let ((_let_1 (@ foldr_assn_assn times_times_assn))) (=> (forall ((X2 produc6575502325842934193n_assn)) (or (not (@ (@ member7957490590177025114n_assn X2) (@ set_Pr1139785259514867910n_assn M))) (@ (@ produc7274209992780475162assn_o entails) X2))) (@ (@ entails (@ (@ times_times_assn (@ (@ times_times_assn (@ (@ _let_1 (@ (@ map_Pr8991440229025900053n_assn produc9167289414957590229n_assn) M)) one_one_assn)) P7)) Up)) (@ (@ times_times_assn (@ (@ times_times_assn (@ (@ times_times_assn (@ (@ _let_1 (@ (@ map_Pr8991440229025900053n_assn produc2051961928117032727n_assn) M)) one_one_assn)) Q8)) Uq)) F6)))))) (= fi (lambda ((M list_P8527749157015355191n_assn) (P7 assn) (Q8 assn) (Up assn) (Uq assn) (F6 assn)) (=> (forall ((X2 produc6575502325842934193n_assn)) (or (not (@ (@ member7957490590177025114n_assn X2) (@ set_Pr1139785259514867910n_assn M))) (@ (@ produc7274209992780475162assn_o (lambda ((P2 assn) (Q2 assn)) (forall ((H3 produc3658429121746597890et_nat)) (or (not (@ (@ rep_assn P2) H3)) (@ (@ rep_assn Q2) H3))))) X2))) (forall ((BOUND_VARIABLE_214770 produc3658429121746597890et_nat)) (let ((_let_1 (@ abs_assn one_assn_raw))) (let ((_let_2 (@ foldr_assn_assn times_times_assn))) (or (not (@ (@ rep_assn (@ (@ times_times_assn (@ (@ times_times_assn (@ (@ _let_2 (@ (@ map_Pr8991440229025900053n_assn produc9167289414957590229n_assn) M)) _let_1)) P7)) Up)) BOUND_VARIABLE_214770)) (@ (@ rep_assn (@ (@ times_times_assn (@ (@ times_times_assn (@ (@ times_times_assn (@ (@ _let_2 (@ (@ map_Pr8991440229025900053n_assn produc2051961928117032727n_assn) M)) _let_1)) Q8)) Uq)) F6)) BOUND_VARIABLE_214770)))))))))))))) (let ((_let_322 (SYMM (ASSUME :args (_let_25))))) (let ((_let_323 (EQ_RESOLVE (ASSUME :args (_let_130)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_322 _let_321 _let_320 _let_319 _let_318 _let_317 _let_316 _let_315 _let_314 _let_313 _let_312 _let_311 _let_310 _let_309 _let_308 _let_307 _let_306 _let_305 _let_304 _let_303 _let_302 _let_301 _let_300 _let_299 _let_298 _let_297 _let_296 _let_295 _let_294 _let_293 _let_292 _let_291 _let_290 _let_289 _let_288 _let_287 _let_286 _let_285 _let_284 _let_283 _let_282 _let_281 _let_280 _let_279 _let_278 _let_277 _let_276 _let_275 _let_274 _let_273 _let_272 _let_271 _let_270 _let_269 _let_268 _let_267 _let_266 _let_265 _let_264 _let_263 _let_262 _let_261 _let_260 _let_259 _let_258 _let_257 _let_256 _let_255 _let_254 _let_253 _let_252 _let_251 _let_250 _let_249 _let_248 _let_247 _let_246 _let_245 _let_244 _let_243 _let_242 _let_241 _let_240 _let_239 _let_238 _let_237 _let_236 _let_235 _let_234 _let_233 _let_232 _let_231 _let_230 _let_229 _let_228 _let_227 _let_226 _let_225 _let_224 _let_223 _let_222 _let_221 _let_220 _let_219 _let_218 _let_217 _let_216 _let_215 _let_214 _let_213 _let_212 _let_211 _let_210 _let_209 _let_208 _let_207 _let_206 _let_205) :args (_let_130 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_324 (EQ_RESOLVE (ASSUME :args (_let_24)) (TRUST_SUBS_MAP (AND_INTRO _let_323 _let_322 _let_321 _let_320 _let_319 _let_318 _let_317 _let_316 _let_315 _let_314 _let_313 _let_312 _let_311 _let_310 _let_309 _let_308 _let_307 _let_306 _let_305 _let_304 _let_303 _let_302 _let_301 _let_300 _let_299 _let_298 _let_297 _let_296 _let_295 _let_294 _let_293 _let_292 _let_291 _let_290 _let_289 _let_288 _let_287 _let_286 _let_285 _let_284 _let_283 _let_282 _let_281 _let_280 _let_279 _let_278 _let_277 _let_276 _let_275 _let_274 _let_273 _let_272 _let_271 _let_270 _let_269 _let_268 _let_267 _let_266 _let_265 _let_264 _let_263 _let_262 _let_261 _let_260 _let_259 _let_258 _let_257 _let_256 _let_255 _let_254 _let_253 _let_252 _let_251 _let_250 _let_249 _let_248 _let_247 _let_246 _let_245 _let_244 _let_243 _let_242 _let_241 _let_240 _let_239 _let_238 _let_237 _let_236 _let_235 _let_234 _let_233 _let_232 _let_231 _let_230 _let_229 _let_228 _let_227 _let_226 _let_225 _let_224 _let_223 _let_222 _let_221 _let_220 _let_219 _let_218 _let_217 _let_216 _let_215 _let_214 _let_213 _let_212 _let_211 _let_210 _let_209 _let_208 _let_207 _let_206 _let_205) :args ((= _let_24 (= set_or6656581121297822940st_int (lambda ((I4 int) (J2 int)) (@ set_int2 (@ (@ (@ upto_aux (@ (@ (@ (@ (@ map_fu4960017516451851995nt_int rep_Integ) (@ (@ map_fu3667384564859982768at_int rep_Integ) abs_Integ)) (@ produc27273713700761075at_nat (lambda ((BOUND_VARIABLE_219745 nat) (BOUND_VARIABLE_219746 nat) (BOUND_VARIABLE_219747 product_prod_nat_nat)) (@ (@ produc2626176000494625587at_nat (lambda ((BOUND_VARIABLE_219748 nat) (BOUND_VARIABLE_219749 nat)) (@ (@ product_Pair_nat_nat (@ (@ plus_plus_nat BOUND_VARIABLE_219745) BOUND_VARIABLE_219748)) (@ (@ plus_plus_nat BOUND_VARIABLE_219746) BOUND_VARIABLE_219749)))) BOUND_VARIABLE_219747)))) I4) one_one_int)) J2) nil_int)))))))))) (let ((_let_325 (EQ_RESOLVE (EQ_RESOLVE (ASSUME :args (_let_111)) (MACRO_SR_EQ_INTRO :args (_let_111 SB_DEFAULT SBA_FIXPOINT))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_324 _let_323 _let_322 _let_321 _let_320 _let_319 _let_318 _let_317 _let_316 _let_315 _let_314 _let_313 _let_312 _let_311 _let_310 _let_309 _let_308 _let_307 _let_306 _let_305 _let_304 _let_303 _let_302 _let_301 _let_300 _let_299 _let_298 _let_297 _let_296 _let_295 _let_294 _let_293 _let_292 _let_291 _let_290 _let_289 _let_288 _let_287 _let_286 _let_285 _let_284 _let_283 _let_282 _let_281 _let_280 _let_279 _let_278 _let_277 _let_276 _let_275 _let_274 _let_273 _let_272 _let_271 _let_270 _let_269 _let_268 _let_267 _let_266 _let_265 _let_264 _let_263 _let_262 _let_261 _let_260 _let_259 _let_258 _let_257 _let_256 _let_255 _let_254 _let_253 _let_252 _let_251 _let_250 _let_249 _let_248 _let_247 _let_246 _let_245 _let_244 _let_243 _let_242 _let_241 _let_240 _let_239 _let_238 _let_237 _let_236 _let_235 _let_234 _let_233 _let_232 _let_231 _let_230 _let_229 _let_228 _let_227 _let_226 _let_225 _let_224 _let_223 _let_222 _let_221 _let_220 _let_219 _let_218 _let_217 _let_216 _let_215 _let_214 _let_213 _let_212 _let_211 _let_210 _let_209 _let_208 _let_207 _let_206 _let_205) :args ((= list_ex_int (lambda ((P2 (-> int Bool)) (Xs3 list_int)) (not (forall ((N2 nat)) (or (not (@ P2 (@ (@ nth_int Xs3) N2))) (not (@ (@ ord_less_nat N2) (@ size_size_list_int Xs3)))))))) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_326 (EQ_RESOLVE (EQ_RESOLVE (ASSUME :args (_let_22)) (MACRO_SR_EQ_INTRO :args (_let_22 SB_DEFAULT SBA_FIXPOINT))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_325 _let_324 _let_323 _let_322 _let_321 _let_320 _let_319 _let_318 _let_317 _let_316 _let_315 _let_314 _let_313 _let_312 _let_311 _let_310 _let_309 _let_308 _let_307 _let_306 _let_305 _let_304 _let_303 _let_302 _let_301 _let_300 _let_299 _let_298 _let_297 _let_296 _let_295 _let_294 _let_293 _let_292 _let_291 _let_290 _let_289 _let_288 _let_287 _let_286 _let_285 _let_284 _let_283 _let_282 _let_281 _let_280 _let_279 _let_278 _let_277 _let_276 _let_275 _let_274 _let_273 _let_272 _let_271 _let_270 _let_269 _let_268 _let_267 _let_266 _let_265 _let_264 _let_263 _let_262 _let_261 _let_260 _let_259 _let_258 _let_257 _let_256 _let_255 _let_254 _let_253 _let_252 _let_251 _let_250 _let_249 _let_248 _let_247 _let_246 _let_245 _let_244 _let_243 _let_242 _let_241 _let_240 _let_239 _let_238 _let_237 _let_236 _let_235 _let_234 _let_233 _let_232 _let_231 _let_230 _let_229 _let_228 _let_227 _let_226 _let_225 _let_224 _let_223 _let_222 _let_221 _let_220 _let_219 _let_218 _let_217 _let_216 _let_215 _let_214 _let_213 _let_212 _let_211 _let_210 _let_209 _let_208 _let_207 _let_206 _let_205) :args ((= pairwi6357175311820755948at_nat (lambda ((R3 (-> product_prod_nat_nat product_prod_nat_nat Bool)) (S2 set_Pr1261947904930325089at_nat)) (forall ((X2 product_prod_nat_nat) (BOUND_VARIABLE_121687 product_prod_nat_nat)) (or (not (@ (@ member8440522571783428010at_nat X2) S2)) (not (@ (@ member8440522571783428010at_nat BOUND_VARIABLE_121687) (@ (@ minus_1356011639430497352at_nat S2) (@ (@ insert8211810215607154385at_nat X2) bot_bo2099793752762293965at_nat)))) (@ (@ R3 X2) BOUND_VARIABLE_121687))))) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_327 (EQ_RESOLVE (ASSUME :args (_let_21)) (MACRO_SR_EQ_INTRO :args (_let_21 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_328 (EQ_RESOLVE (ASSUME :args (_let_118)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_327 _let_326 _let_325 _let_324 _let_323 _let_322 _let_321 _let_320 _let_319 _let_318 _let_317 _let_316 _let_315 _let_314 _let_313 _let_312 _let_311 _let_310 _let_309 _let_308 _let_307 _let_306 _let_305 _let_304 _let_303 _let_302 _let_301 _let_300 _let_299 _let_298 _let_297 _let_296 _let_295 _let_294 _let_293 _let_292 _let_291 _let_290 _let_289 _let_288 _let_287 _let_286 _let_285 _let_284 _let_283 _let_282 _let_281 _let_280 _let_279 _let_278 _let_277 _let_276 _let_275 _let_274 _let_273 _let_272 _let_271 _let_270 _let_269 _let_268 _let_267 _let_266 _let_265 _let_264 _let_263 _let_262 _let_261 _let_260 _let_259 _let_258 _let_257 _let_256 _let_255 _let_254 _let_253 _let_252 _let_251 _let_250 _let_249 _let_248 _let_247 _let_246 _let_245 _let_244 _let_243 _let_242 _let_241 _let_240 _let_239 _let_238 _let_237 _let_236 _let_235 _let_234 _let_233 _let_232 _let_231 _let_230 _let_229 _let_228 _let_227 _let_226 _let_225 _let_224 _let_223 _let_222 _let_221 _let_220 _let_219 _let_218 _let_217 _let_216 _let_215 _let_214 _let_213 _let_212 _let_211 _let_210 _let_209 _let_208 _let_207 _let_206 _let_205) :args (_let_118 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_329 (EQ_RESOLVE (EQ_RESOLVE (ASSUME :args (_let_19)) (MACRO_SR_EQ_INTRO :args (_let_19 SB_DEFAULT SBA_FIXPOINT))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_328 _let_327 _let_326 _let_325 _let_324 _let_323 _let_322 _let_321 _let_320 _let_319 _let_318 _let_317 _let_316 _let_315 _let_314 _let_313 _let_312 _let_311 _let_310 _let_309 _let_308 _let_307 _let_306 _let_305 _let_304 _let_303 _let_302 _let_301 _let_300 _let_299 _let_298 _let_297 _let_296 _let_295 _let_294 _let_293 _let_292 _let_291 _let_290 _let_289 _let_288 _let_287 _let_286 _let_285 _let_284 _let_283 _let_282 _let_281 _let_280 _let_279 _let_278 _let_277 _let_276 _let_275 _let_274 _let_273 _let_272 _let_271 _let_270 _let_269 _let_268 _let_267 _let_266 _let_265 _let_264 _let_263 _let_262 _let_261 _let_260 _let_259 _let_258 _let_257 _let_256 _let_255 _let_254 _let_253 _let_252 _let_251 _let_250 _let_249 _let_248 _let_247 _let_246 _let_245 _let_244 _let_243 _let_242 _let_241 _let_240 _let_239 _let_238 _let_237 _let_236 _let_235 _let_234 _let_233 _let_232 _let_231 _let_230 _let_229 _let_228 _let_227 _let_226 _let_225 _let_224 _let_223 _let_222 _let_221 _let_220 _let_219 _let_218 _let_217 _let_216 _let_215 _let_214 _let_213 _let_212 _let_211 _let_210 _let_209 _let_208 _let_207 _let_206 _let_205) :args ((= finite_finite_nat (lambda ((N8 set_nat)) (not (forall ((M nat)) (not (forall ((X2 nat)) (or (not (@ (@ member_nat X2) N8)) (@ (@ ord_less_nat X2) M)))))))) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_330 (EQ_RESOLVE (ASSUME :args (_let_16)) (MACRO_SR_EQ_INTRO :args (_let_16 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_331 (EQ_RESOLVE (EQ_RESOLVE (ASSUME :args (_let_15)) (MACRO_SR_EQ_INTRO :args (_let_15 SB_DEFAULT SBA_FIXPOINT))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_330 _let_329 _let_328 _let_327 _let_326 _let_325 _let_324 _let_323 _let_322 _let_321 _let_320 _let_319 _let_318 _let_317 _let_316 _let_315 _let_314 _let_313 _let_312 _let_311 _let_310 _let_309 _let_308 _let_307 _let_306 _let_305 _let_304 _let_303 _let_302 _let_301 _let_300 _let_299 _let_298 _let_297 _let_296 _let_295 _let_294 _let_293 _let_292 _let_291 _let_290 _let_289 _let_288 _let_287 _let_286 _let_285 _let_284 _let_283 _let_282 _let_281 _let_280 _let_279 _let_278 _let_277 _let_276 _let_275 _let_274 _let_273 _let_272 _let_271 _let_270 _let_269 _let_268 _let_267 _let_266 _let_265 _let_264 _let_263 _let_262 _let_261 _let_260 _let_259 _let_258 _let_257 _let_256 _let_255 _let_254 _let_253 _let_252 _let_251 _let_250 _let_249 _let_248 _let_247 _let_246 _let_245 _let_244 _let_243 _let_242 _let_241 _let_240 _let_239 _let_238 _let_237 _let_236 _let_235 _let_234 _let_233 _let_232 _let_231 _let_230 _let_229 _let_228 _let_227 _let_226 _let_225 _let_224 _let_223 _let_222 _let_221 _let_220 _let_219 _let_218 _let_217 _let_216 _let_215 _let_214 _let_213 _let_212 _let_211 _let_210 _let_209 _let_208 _let_207 _let_206 _let_205) :args ((= pairwise_int (lambda ((R3 (-> int int Bool)) (S2 set_int)) (forall ((X2 int) (BOUND_VARIABLE_124493 int)) (or (not (@ (@ member_int X2) S2)) (not (@ (@ member_int BOUND_VARIABLE_124493) (@ (@ minus_minus_set_int S2) (@ (@ insert_int2 X2) bot_bot_set_int)))) (@ (@ R3 X2) BOUND_VARIABLE_124493))))) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_332 (EQ_RESOLVE (ASSUME :args (_let_14)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_331 _let_330 _let_329 _let_328 _let_327 _let_326 _let_325 _let_324 _let_323 _let_322 _let_321 _let_320 _let_319 _let_318 _let_317 _let_316 _let_315 _let_314 _let_313 _let_312 _let_311 _let_310 _let_309 _let_308 _let_307 _let_306 _let_305 _let_304 _let_303 _let_302 _let_301 _let_300 _let_299 _let_298 _let_297 _let_296 _let_295 _let_294 _let_293 _let_292 _let_291 _let_290 _let_289 _let_288 _let_287 _let_286 _let_285 _let_284 _let_283 _let_282 _let_281 _let_280 _let_279 _let_278 _let_277 _let_276 _let_275 _let_274 _let_273 _let_272 _let_271 _let_270 _let_269 _let_268 _let_267 _let_266 _let_265 _let_264 _let_263 _let_262 _let_261 _let_260 _let_259 _let_258 _let_257 _let_256 _let_255 _let_254 _let_253 _let_252 _let_251 _let_250 _let_249 _let_248 _let_247 _let_246 _let_245 _let_244 _let_243 _let_242 _let_241 _let_240 _let_239 _let_238 _let_237 _let_236 _let_235 _let_234 _let_233 _let_232 _let_231 _let_230 _let_229 _let_228 _let_227 _let_226 _let_225 _let_224 _let_223 _let_222 _let_221 _let_220 _let_219 _let_218 _let_217 _let_216 _let_215 _let_214 _let_213 _let_212 _let_211 _let_210 _let_209 _let_208 _let_207 _let_206 _let_205) :args (_let_14 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_333 (SYMM (ASSUME :args (_let_11))))) (let ((_let_334 (EQ_RESOLVE (ASSUME :args (_let_78)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_333 _let_332 _let_331 _let_330 _let_329 _let_328 _let_327 _let_326 _let_325 _let_324 _let_323 _let_322 _let_321 _let_320 _let_319 _let_318 _let_317 _let_316 _let_315 _let_314 _let_313 _let_312 _let_311 _let_310 _let_309 _let_308 _let_307 _let_306 _let_305 _let_304 _let_303 _let_302 _let_301 _let_300 _let_299 _let_298 _let_297 _let_296 _let_295 _let_294 _let_293 _let_292 _let_291 _let_290 _let_289 _let_288 _let_287 _let_286 _let_285 _let_284 _let_283 _let_282 _let_281 _let_280 _let_279 _let_278 _let_277 _let_276 _let_275 _let_274 _let_273 _let_272 _let_271 _let_270 _let_269 _let_268 _let_267 _let_266 _let_265 _let_264 _let_263 _let_262 _let_261 _let_260 _let_259 _let_258 _let_257 _let_256 _let_255 _let_254 _let_253 _let_252 _let_251 _let_250 _let_249 _let_248 _let_247 _let_246 _let_245 _let_244 _let_243 _let_242 _let_241 _let_240 _let_239 _let_238 _let_237 _let_236 _let_235 _let_234 _let_233 _let_232 _let_231 _let_230 _let_229 _let_228 _let_227 _let_226 _let_225 _let_224 _let_223 _let_222 _let_221 _let_220 _let_219 _let_218 _let_217 _let_216 _let_215 _let_214 _let_213 _let_212 _let_211 _let_210 _let_209 _let_208 _let_207 _let_206 _let_205) :args (_let_78 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_335 (EQ_RESOLVE (ASSUME :args (_let_10)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_334 _let_333 _let_332 _let_331 _let_330 _let_329 _let_328 _let_327 _let_326 _let_325 _let_324 _let_323 _let_322 _let_321 _let_320 _let_319 _let_318 _let_317 _let_316 _let_315 _let_314 _let_313 _let_312 _let_311 _let_310 _let_309 _let_308 _let_307 _let_306 _let_305 _let_304 _let_303 _let_302 _let_301 _let_300 _let_299 _let_298 _let_297 _let_296 _let_295 _let_294 _let_293 _let_292 _let_291 _let_290 _let_289 _let_288 _let_287 _let_286 _let_285 _let_284 _let_283 _let_282 _let_281 _let_280 _let_279 _let_278 _let_277 _let_276 _let_275 _let_274 _let_273 _let_272 _let_271 _let_270 _let_269 _let_268 _let_267 _let_266 _let_265 _let_264 _let_263 _let_262 _let_261 _let_260 _let_259 _let_258 _let_257 _let_256 _let_255 _let_254 _let_253 _let_252 _let_251 _let_250 _let_249 _let_248 _let_247 _let_246 _let_245 _let_244 _let_243 _let_242 _let_241 _let_240 _let_239 _let_238 _let_237 _let_236 _let_235 _let_234 _let_233 _let_232 _let_231 _let_230 _let_229 _let_228 _let_227 _let_226 _let_225 _let_224 _let_223 _let_222 _let_221 _let_220 _let_219 _let_218 _let_217 _let_216 _let_215 _let_214 _let_213 _let_212 _let_211 _let_210 _let_209 _let_208 _let_207 _let_206 _let_205) :args (_let_10 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_336 (EQ_RESOLVE (ASSUME :args (_let_8)) (MACRO_SR_EQ_INTRO :args (_let_8 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_337 (EQ_RESOLVE (EQ_RESOLVE (ASSUME :args (_let_6)) (MACRO_SR_EQ_INTRO :args (_let_6 SB_DEFAULT SBA_FIXPOINT))) (TRUST_SUBS_MAP (AND_INTRO _let_336 _let_335 _let_334 _let_333 _let_332 _let_331 _let_330 _let_329 _let_328 _let_327 _let_326 _let_325 _let_324 _let_323 _let_322 _let_321 _let_320 _let_319 _let_318 _let_317 _let_316 _let_315 _let_314 _let_313 _let_312 _let_311 _let_310 _let_309 _let_308 _let_307 _let_306 _let_305 _let_304 _let_303 _let_302 _let_301 _let_300 _let_299 _let_298 _let_297 _let_296 _let_295 _let_294 _let_293 _let_292 _let_291 _let_290 _let_289 _let_288 _let_287 _let_286 _let_285 _let_284 _let_283 _let_282 _let_281 _let_280 _let_279 _let_278 _let_277 _let_276 _let_275 _let_274 _let_273 _let_272 _let_271 _let_270 _let_269 _let_268 _let_267 _let_266 _let_265 _let_264 _let_263 _let_262 _let_261 _let_260 _let_259 _let_258 _let_257 _let_256 _let_255 _let_254 _let_253 _let_252 _let_251 _let_250 _let_249 _let_248 _let_247 _let_246 _let_245 _let_244 _let_243 _let_242 _let_241 _let_240 _let_239 _let_238 _let_237 _let_236 _let_235 _let_234 _let_233 _let_232 _let_231 _let_230 _let_229 _let_228 _let_227 _let_226 _let_225 _let_224 _let_223 _let_222 _let_221 _let_220 _let_219 _let_218 _let_217 _let_216 _let_215 _let_214 _let_213 _let_212 _let_211 _let_210 _let_209 _let_208 _let_207 _let_206 _let_205) :args ((= (= fI_RESULT (lambda ((M7 list_P8527749157015355191n_assn) (UP assn) (UQ assn) (F3 assn)) (let ((_let_1 (@ foldr_assn_assn times_times_assn))) (=> (forall ((X2 produc6575502325842934193n_assn)) (or (not (@ (@ member7957490590177025114n_assn X2) (@ set_Pr1139785259514867910n_assn M7))) (@ (@ produc7274209992780475162assn_o entails) X2))) (@ (@ entails (@ (@ times_times_assn (@ (@ _let_1 (@ (@ map_Pr8991440229025900053n_assn produc9167289414957590229n_assn) M7)) one_one_assn)) UP)) (@ (@ times_times_assn (@ (@ times_times_assn (@ (@ _let_1 (@ (@ map_Pr8991440229025900053n_assn produc2051961928117032727n_assn) M7)) one_one_assn)) UQ)) F3)))))) (= fI_RESULT (lambda ((M7 list_P8527749157015355191n_assn) (UP assn) (UQ assn) (F3 assn)) (=> (forall ((X2 produc6575502325842934193n_assn)) (or (not (@ (@ member7957490590177025114n_assn X2) (@ set_Pr1139785259514867910n_assn M7))) (@ (@ produc7274209992780475162assn_o (lambda ((P2 assn) (Q2 assn)) (forall ((H3 produc3658429121746597890et_nat)) (or (not (@ (@ rep_assn P2) H3)) (@ (@ rep_assn Q2) H3))))) X2))) (forall ((BOUND_VARIABLE_237640 produc3658429121746597890et_nat)) (let ((_let_1 (@ abs_assn one_assn_raw))) (let ((_let_2 (@ foldr_assn_assn times_times_assn))) (or (not (@ (@ rep_assn (@ (@ times_times_assn (@ (@ _let_2 (@ (@ map_Pr8991440229025900053n_assn produc9167289414957590229n_assn) M7)) _let_1)) UP)) BOUND_VARIABLE_237640)) (@ (@ rep_assn (@ (@ times_times_assn (@ (@ times_times_assn (@ (@ _let_2 (@ (@ map_Pr8991440229025900053n_assn produc2051961928117032727n_assn) M7)) _let_1)) UQ)) F3)) BOUND_VARIABLE_237640)))))))))))))) (let ((_let_338 (ASSUME :args (_let_47)))) (let ((_let_339 (EQ_RESOLVE (EQ_RESOLVE (ASSUME :args (_let_99)) (MACRO_SR_EQ_INTRO :args (_let_99 SB_DEFAULT SBA_FIXPOINT))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_338 _let_337 _let_336 _let_335 _let_334 _let_333 _let_332 _let_331 _let_330 _let_329 _let_328 _let_327 _let_326 _let_325 _let_324 _let_323 _let_322 _let_321 _let_320 _let_319 _let_318 _let_317 _let_316 _let_315 _let_314 _let_313 _let_312 _let_311 _let_310 _let_309 _let_308 _let_307 _let_306 _let_305 _let_304 _let_303 _let_302 _let_301 _let_300 _let_299 _let_298 _let_297 _let_296 _let_295 _let_294 _let_293 _let_292 _let_291 _let_290 _let_289 _let_288 _let_287 _let_286 _let_285 _let_284 _let_283 _let_282 _let_281 _let_280 _let_279 _let_278 _let_277 _let_276 _let_275 _let_274 _let_273 _let_272 _let_271 _let_270 _let_269 _let_268 _let_267 _let_266 _let_265 _let_264 _let_263 _let_262 _let_261 _let_260 _let_259 _let_258 _let_257 _let_256 _let_255 _let_254 _let_253 _let_252 _let_251 _let_250 _let_249 _let_248 _let_247 _let_246 _let_245 _let_244 _let_243 _let_242 _let_241 _let_240 _let_239 _let_238 _let_237 _let_236 _let_235 _let_234 _let_233 _let_232 _let_231 _let_230 _let_229 _let_228 _let_227 _let_226 _let_225 _let_224 _let_223 _let_222 _let_221 _let_220 _let_219 _let_218 _let_217 _let_216 _let_215 _let_214 _let_213 _let_212 _let_211 _let_210 _let_209 _let_208 _let_207 _let_206 _let_205) :args ((= pairwise_o (lambda ((R3 (-> Bool Bool Bool)) (S2 set_o)) (forall ((X2 Bool) (BOUND_VARIABLE_126625 Bool)) (or (not (@ (@ member_o X2) S2)) (not (@ (@ member_o BOUND_VARIABLE_126625) (@ (@ minus_minus_set_o S2) (@ (@ insert_o2 X2) bot_bot_set_o)))) (@ (@ R3 X2) BOUND_VARIABLE_126625))))) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_340 (EQ_RESOLVE (EQ_RESOLVE (ASSUME :args (_let_87)) (MACRO_SR_EQ_INTRO :args (_let_87 SB_DEFAULT SBA_FIXPOINT))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_339 _let_338 _let_337 _let_336 _let_335 _let_334 _let_333 _let_332 _let_331 _let_330 _let_329 _let_328 _let_327 _let_326 _let_325 _let_324 _let_323 _let_322 _let_321 _let_320 _let_319 _let_318 _let_317 _let_316 _let_315 _let_314 _let_313 _let_312 _let_311 _let_310 _let_309 _let_308 _let_307 _let_306 _let_305 _let_304 _let_303 _let_302 _let_301 _let_300 _let_299 _let_298 _let_297 _let_296 _let_295 _let_294 _let_293 _let_292 _let_291 _let_290 _let_289 _let_288 _let_287 _let_286 _let_285 _let_284 _let_283 _let_282 _let_281 _let_280 _let_279 _let_278 _let_277 _let_276 _let_275 _let_274 _let_273 _let_272 _let_271 _let_270 _let_269 _let_268 _let_267 _let_266 _let_265 _let_264 _let_263 _let_262 _let_261 _let_260 _let_259 _let_258 _let_257 _let_256 _let_255 _let_254 _let_253 _let_252 _let_251 _let_250 _let_249 _let_248 _let_247 _let_246 _let_245 _let_244 _let_243 _let_242 _let_241 _let_240 _let_239 _let_238 _let_237 _let_236 _let_235 _let_234 _let_233 _let_232 _let_231 _let_230 _let_229 _let_228 _let_227 _let_226 _let_225 _let_224 _let_223 _let_222 _let_221 _let_220 _let_219 _let_218 _let_217 _let_216 _let_215 _let_214 _let_213 _let_212 _let_211 _let_210 _let_209 _let_208 _let_207 _let_206 _let_205) :args ((= list_ex_c (lambda ((P2 (-> c Bool)) (Xs3 list_c)) (not (forall ((N2 nat)) (or (not (@ (@ ord_less_nat N2) (@ size_size_list_c Xs3))) (not (@ P2 (@ (@ nth_c Xs3) N2)))))))) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_341 (EQ_RESOLVE (EQ_RESOLVE (ASSUME :args (_let_182)) (MACRO_SR_EQ_INTRO :args (_let_182 SB_DEFAULT SBA_FIXPOINT))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_340 _let_339 _let_338 _let_337 _let_336 _let_335 _let_334 _let_333 _let_332 _let_331 _let_330 _let_329 _let_328 _let_327 _let_326 _let_325 _let_324 _let_323 _let_322 _let_321 _let_320 _let_319 _let_318 _let_317 _let_316 _let_315 _let_314 _let_313 _let_312 _let_311 _let_310 _let_309 _let_308 _let_307 _let_306 _let_305 _let_304 _let_303 _let_302 _let_301 _let_300 _let_299 _let_298 _let_297 _let_296 _let_295 _let_294 _let_293 _let_292 _let_291 _let_290 _let_289 _let_288 _let_287 _let_286 _let_285 _let_284 _let_283 _let_282 _let_281 _let_280 _let_279 _let_278 _let_277 _let_276 _let_275 _let_274 _let_273 _let_272 _let_271 _let_270 _let_269 _let_268 _let_267 _let_266 _let_265 _let_264 _let_263 _let_262 _let_261 _let_260 _let_259 _let_258 _let_257 _let_256 _let_255 _let_254 _let_253 _let_252 _let_251 _let_250 _let_249 _let_248 _let_247 _let_246 _let_245 _let_244 _let_243 _let_242 _let_241 _let_240 _let_239 _let_238 _let_237 _let_236 _let_235 _let_234 _let_233 _let_232 _let_231 _let_230 _let_229 _let_228 _let_227 _let_226 _let_225 _let_224 _let_223 _let_222 _let_221 _let_220 _let_219 _let_218 _let_217 _let_216 _let_215 _let_214 _let_213 _let_212 _let_211 _let_210 _let_209 _let_208 _let_207 _let_206 _let_205) :args ((= sorted_wrt_d (lambda ((P2 (-> d d Bool)) (Xs3 list_d)) (forall ((I4 nat) (J2 nat)) (let ((_let_1 (@ nth_d Xs3))) (or (not (@ (@ ord_less_nat I4) J2)) (not (@ (@ ord_less_nat J2) (@ size_size_list_d Xs3))) (@ (@ P2 (@ _let_1 I4)) (@ _let_1 J2))))))) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_342 (EQ_RESOLVE (ASSUME :args (_let_143)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_341 _let_340 _let_339 _let_338 _let_337 _let_336 _let_335 _let_334 _let_333 _let_332 _let_331 _let_330 _let_329 _let_328 _let_327 _let_326 _let_325 _let_324 _let_323 _let_322 _let_321 _let_320 _let_319 _let_318 _let_317 _let_316 _let_315 _let_314 _let_313 _let_312 _let_311 _let_310 _let_309 _let_308 _let_307 _let_306 _let_305 _let_304 _let_303 _let_302 _let_301 _let_300 _let_299 _let_298 _let_297 _let_296 _let_295 _let_294 _let_293 _let_292 _let_291 _let_290 _let_289 _let_288 _let_287 _let_286 _let_285 _let_284 _let_283 _let_282 _let_281 _let_280 _let_279 _let_278 _let_277 _let_276 _let_275 _let_274 _let_273 _let_272 _let_271 _let_270 _let_269 _let_268 _let_267 _let_266 _let_265 _let_264 _let_263 _let_262 _let_261 _let_260 _let_259 _let_258 _let_257 _let_256 _let_255 _let_254 _let_253 _let_252 _let_251 _let_250 _let_249 _let_248 _let_247 _let_246 _let_245 _let_244 _let_243 _let_242 _let_241 _let_240 _let_239 _let_238 _let_237 _let_236 _let_235 _let_234 _let_233 _let_232 _let_231 _let_230 _let_229 _let_228 _let_227 _let_226 _let_225 _let_224 _let_223 _let_222 _let_221 _let_220 _let_219 _let_218 _let_217 _let_216 _let_215 _let_214 _let_213 _let_212 _let_211 _let_210 _let_209 _let_208 _let_207 _let_206 _let_205) :args (_let_143 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_343 (EQ_RESOLVE (ASSUME :args (_let_2)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_342 _let_341 _let_340 _let_339 _let_338 _let_337 _let_336 _let_335 _let_334 _let_333 _let_332 _let_331 _let_330 _let_329 _let_328 _let_327 _let_326 _let_325 _let_324 _let_323 _let_322 _let_321 _let_320 _let_319 _let_318 _let_317 _let_316 _let_315 _let_314 _let_313 _let_312 _let_311 _let_310 _let_309 _let_308 _let_307 _let_306 _let_305 _let_304 _let_303 _let_302 _let_301 _let_300 _let_299 _let_298 _let_297 _let_296 _let_295 _let_294 _let_293 _let_292 _let_291 _let_290 _let_289 _let_288 _let_287 _let_286 _let_285 _let_284 _let_283 _let_282 _let_281 _let_280 _let_279 _let_278 _let_277 _let_276 _let_275 _let_274 _let_273 _let_272 _let_271 _let_270 _let_269 _let_268 _let_267 _let_266 _let_265 _let_264 _let_263 _let_262 _let_261 _let_260 _let_259 _let_258 _let_257 _let_256 _let_255 _let_254 _let_253 _let_252 _let_251 _let_250 _let_249 _let_248 _let_247 _let_246 _let_245 _let_244 _let_243 _let_242 _let_241 _let_240 _let_239 _let_238 _let_237 _let_236 _let_235 _let_234 _let_233 _let_232 _let_231 _let_230 _let_229 _let_228 _let_227 _let_226 _let_225 _let_224 _let_223 _let_222 _let_221 _let_220 _let_219 _let_218 _let_217 _let_216 _let_215 _let_214 _let_213 _let_212 _let_211 _let_210 _let_209 _let_208 _let_207 _let_206 _let_205) :args (_let_2 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_344 (EQ_RESOLVE (ASSUME :args (_let_73)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_343 _let_342 _let_341 _let_340 _let_339 _let_338 _let_337 _let_336 _let_335 _let_334 _let_333 _let_332 _let_331 _let_330 _let_329 _let_328 _let_327 _let_326 _let_325 _let_324 _let_323 _let_322 _let_321 _let_320 _let_319 _let_318 _let_317 _let_316 _let_315 _let_314 _let_313 _let_312 _let_311 _let_310 _let_309 _let_308 _let_307 _let_306 _let_305 _let_304 _let_303 _let_302 _let_301 _let_300 _let_299 _let_298 _let_297 _let_296 _let_295 _let_294 _let_293 _let_292 _let_291 _let_290 _let_289 _let_288 _let_287 _let_286 _let_285 _let_284 _let_283 _let_282 _let_281 _let_280 _let_279 _let_278 _let_277 _let_276 _let_275 _let_274 _let_273 _let_272 _let_271 _let_270 _let_269 _let_268 _let_267 _let_266 _let_265 _let_264 _let_263 _let_262 _let_261 _let_260 _let_259 _let_258 _let_257 _let_256 _let_255 _let_254 _let_253 _let_252 _let_251 _let_250 _let_249 _let_248 _let_247 _let_246 _let_245 _let_244 _let_243 _let_242 _let_241 _let_240 _let_239 _let_238 _let_237 _let_236 _let_235 _let_234 _let_233 _let_232 _let_231 _let_230 _let_229 _let_228 _let_227 _let_226 _let_225 _let_224 _let_223 _let_222 _let_221 _let_220 _let_219 _let_218 _let_217 _let_216 _let_215 _let_214 _let_213 _let_212 _let_211 _let_210 _let_209 _let_208 _let_207 _let_206 _let_205) :args (_let_73 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_345 (EQ_RESOLVE (EQ_RESOLVE (ASSUME :args (_let_183)) (MACRO_SR_EQ_INTRO :args (_let_183 SB_DEFAULT SBA_FIXPOINT))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_344 _let_343 _let_342 _let_341 _let_340 _let_339 _let_338 _let_337 _let_336 _let_335 _let_334 _let_333 _let_332 _let_331 _let_330 _let_329 _let_328 _let_327 _let_326 _let_325 _let_324 _let_323 _let_322 _let_321 _let_320 _let_319 _let_318 _let_317 _let_316 _let_315 _let_314 _let_313 _let_312 _let_311 _let_310 _let_309 _let_308 _let_307 _let_306 _let_305 _let_304 _let_303 _let_302 _let_301 _let_300 _let_299 _let_298 _let_297 _let_296 _let_295 _let_294 _let_293 _let_292 _let_291 _let_290 _let_289 _let_288 _let_287 _let_286 _let_285 _let_284 _let_283 _let_282 _let_281 _let_280 _let_279 _let_278 _let_277 _let_276 _let_275 _let_274 _let_273 _let_272 _let_271 _let_270 _let_269 _let_268 _let_267 _let_266 _let_265 _let_264 _let_263 _let_262 _let_261 _let_260 _let_259 _let_258 _let_257 _let_256 _let_255 _let_254 _let_253 _let_252 _let_251 _let_250 _let_249 _let_248 _let_247 _let_246 _let_245 _let_244 _let_243 _let_242 _let_241 _let_240 _let_239 _let_238 _let_237 _let_236 _let_235 _let_234 _let_233 _let_232 _let_231 _let_230 _let_229 _let_228 _let_227 _let_226 _let_225 _let_224 _let_223 _let_222 _let_221 _let_220 _let_219 _let_218 _let_217 _let_216 _let_215 _let_214 _let_213 _let_212 _let_211 _let_210 _let_209 _let_208 _let_207 _let_206 _let_205) :args ((= list_ex_nat (lambda ((P2 (-> nat Bool)) (Xs3 list_nat)) (not (forall ((N2 nat)) (or (not (@ P2 (@ (@ nth_nat Xs3) N2))) (not (@ (@ ord_less_nat N2) (@ size_size_list_nat Xs3)))))))) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_346 (EQ_RESOLVE (EQ_RESOLVE (ASSUME :args (_let_149)) (MACRO_SR_EQ_INTRO :args (_let_149 SB_DEFAULT SBA_FIXPOINT))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_345 _let_344 _let_343 _let_342 _let_341 _let_340 _let_339 _let_338 _let_337 _let_336 _let_335 _let_334 _let_333 _let_332 _let_331 _let_330 _let_329 _let_328 _let_327 _let_326 _let_325 _let_324 _let_323 _let_322 _let_321 _let_320 _let_319 _let_318 _let_317 _let_316 _let_315 _let_314 _let_313 _let_312 _let_311 _let_310 _let_309 _let_308 _let_307 _let_306 _let_305 _let_304 _let_303 _let_302 _let_301 _let_300 _let_299 _let_298 _let_297 _let_296 _let_295 _let_294 _let_293 _let_292 _let_291 _let_290 _let_289 _let_288 _let_287 _let_286 _let_285 _let_284 _let_283 _let_282 _let_281 _let_280 _let_279 _let_278 _let_277 _let_276 _let_275 _let_274 _let_273 _let_272 _let_271 _let_270 _let_269 _let_268 _let_267 _let_266 _let_265 _let_264 _let_263 _let_262 _let_261 _let_260 _let_259 _let_258 _let_257 _let_256 _let_255 _let_254 _let_253 _let_252 _let_251 _let_250 _let_249 _let_248 _let_247 _let_246 _let_245 _let_244 _let_243 _let_242 _let_241 _let_240 _let_239 _let_238 _let_237 _let_236 _let_235 _let_234 _let_233 _let_232 _let_231 _let_230 _let_229 _let_228 _let_227 _let_226 _let_225 _let_224 _let_223 _let_222 _let_221 _let_220 _let_219 _let_218 _let_217 _let_216 _let_215 _let_214 _let_213 _let_212 _let_211 _let_210 _let_209 _let_208 _let_207 _let_206 _let_205) :args ((= all_interval_nat (lambda ((P2 (-> nat Bool)) (I4 nat) (J2 nat)) (forall ((X2 nat)) (or (not (@ (@ member_nat X2) (@ (@ set_or4665077453230672383an_nat I4) J2))) (@ P2 X2))))) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_347 (ASSUME :args (_let_33)))) (let ((_let_348 (EQ_RESOLVE (EQ_RESOLVE (ASSUME :args (_let_184)) (MACRO_SR_EQ_INTRO :args (_let_184 SB_DEFAULT SBA_FIXPOINT))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_347 _let_346 _let_345 _let_344 _let_343 _let_342 _let_341 _let_340 _let_339 _let_338 _let_337 _let_336 _let_335 _let_334 _let_333 _let_332 _let_331 _let_330 _let_329 _let_328 _let_327 _let_326 _let_325 _let_324 _let_323 _let_322 _let_321 _let_320 _let_319 _let_318 _let_317 _let_316 _let_315 _let_314 _let_313 _let_312 _let_311 _let_310 _let_309 _let_308 _let_307 _let_306 _let_305 _let_304 _let_303 _let_302 _let_301 _let_300 _let_299 _let_298 _let_297 _let_296 _let_295 _let_294 _let_293 _let_292 _let_291 _let_290 _let_289 _let_288 _let_287 _let_286 _let_285 _let_284 _let_283 _let_282 _let_281 _let_280 _let_279 _let_278 _let_277 _let_276 _let_275 _let_274 _let_273 _let_272 _let_271 _let_270 _let_269 _let_268 _let_267 _let_266 _let_265 _let_264 _let_263 _let_262 _let_261 _let_260 _let_259 _let_258 _let_257 _let_256 _let_255 _let_254 _let_253 _let_252 _let_251 _let_250 _let_249 _let_248 _let_247 _let_246 _let_245 _let_244 _let_243 _let_242 _let_241 _let_240 _let_239 _let_238 _let_237 _let_236 _let_235 _let_234 _let_233 _let_232 _let_231 _let_230 _let_229 _let_228 _let_227 _let_226 _let_225 _let_224 _let_223 _let_222 _let_221 _let_220 _let_219 _let_218 _let_217 _let_216 _let_215 _let_214 _let_213 _let_212 _let_211 _let_210 _let_209 _let_208 _let_207 _let_206 _let_205) :args ((= pairwise_nat (lambda ((R3 (-> nat nat Bool)) (S2 set_nat)) (forall ((X2 nat) (BOUND_VARIABLE_128922 nat)) (or (not (@ (@ member_nat X2) S2)) (not (@ (@ member_nat BOUND_VARIABLE_128922) (@ (@ minus_minus_set_nat S2) (@ (@ insert_nat2 X2) bot_bot_set_nat)))) (@ (@ R3 X2) BOUND_VARIABLE_128922))))) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_349 (SYMM (ASSUME :args (_let_185))))) (let ((_let_350 (ASSUME :args (_let_119)))) (let ((_let_351 (EQ_RESOLVE (SYMM (ASSUME :args (_let_187))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_350 _let_349 _let_348 _let_347 _let_346 _let_345 _let_344 _let_343 _let_342 _let_341 _let_340 _let_339 _let_338 _let_337 _let_336 _let_335 _let_334 _let_333 _let_332 _let_331 _let_330 _let_329 _let_328 _let_327 _let_326 _let_325 _let_324 _let_323 _let_322 _let_321 _let_320 _let_319 _let_318 _let_317 _let_316 _let_315 _let_314 _let_313 _let_312 _let_311 _let_310 _let_309 _let_308 _let_307 _let_306 _let_305 _let_304 _let_303 _let_302 _let_301 _let_300 _let_299 _let_298 _let_297 _let_296 _let_295 _let_294 _let_293 _let_292 _let_291 _let_290 _let_289 _let_288 _let_287 _let_286 _let_285 _let_284 _let_283 _let_282 _let_281 _let_280 _let_279 _let_278 _let_277 _let_276 _let_275 _let_274 _let_273 _let_272 _let_271 _let_270 _let_269 _let_268 _let_267 _let_266 _let_265 _let_264 _let_263 _let_262 _let_261 _let_260 _let_259 _let_258 _let_257 _let_256 _let_255 _let_254 _let_253 _let_252 _let_251 _let_250 _let_249 _let_248 _let_247 _let_246 _let_245 _let_244 _let_243 _let_242 _let_241 _let_240 _let_239 _let_238 _let_237 _let_236 _let_235 _let_234 _let_233 _let_232 _let_231 _let_230 _let_229 _let_228 _let_227 _let_226 _let_225 _let_224 _let_223 _let_222 _let_221 _let_220 _let_219 _let_218 _let_217 _let_216 _let_215 _let_214 _let_213 _let_212 _let_211 _let_210 _let_209 _let_208 _let_207 _let_206 _let_205) :args ((= bot_bo3083307316010499117at_nat _let_186) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_352 (ASSUME :args (_let_29)))) (let ((_let_353 (ASSUME :args (_let_188)))) (let ((_let_354 (EQ_RESOLVE (ASSUME :args (_let_3)) (TRUST_SUBS_MAP (AND_INTRO _let_353 _let_352 _let_351 _let_350 _let_349 _let_348 _let_347 _let_346 _let_345 _let_344 _let_343 _let_342 _let_341 _let_340 _let_339 _let_338 _let_337 _let_336 _let_335 _let_334 _let_333 _let_332 _let_331 _let_330 _let_329 _let_328 _let_327 _let_326 _let_325 _let_324 _let_323 _let_322 _let_321 _let_320 _let_319 _let_318 _let_317 _let_316 _let_315 _let_314 _let_313 _let_312 _let_311 _let_310 _let_309 _let_308 _let_307 _let_306 _let_305 _let_304 _let_303 _let_302 _let_301 _let_300 _let_299 _let_298 _let_297 _let_296 _let_295 _let_294 _let_293 _let_292 _let_291 _let_290 _let_289 _let_288 _let_287 _let_286 _let_285 _let_284 _let_283 _let_282 _let_281 _let_280 _let_279 _let_278 _let_277 _let_276 _let_275 _let_274 _let_273 _let_272 _let_271 _let_270 _let_269 _let_268 _let_267 _let_266 _let_265 _let_264 _let_263 _let_262 _let_261 _let_260 _let_259 _let_258 _let_257 _let_256 _let_255 _let_254 _let_253 _let_252 _let_251 _let_250 _let_249 _let_248 _let_247 _let_246 _let_245 _let_244 _let_243 _let_242 _let_241 _let_240 _let_239 _let_238 _let_237 _let_236 _let_235 _let_234 _let_233 _let_232 _let_231 _let_230 _let_229 _let_228 _let_227 _let_226 _let_225 _let_224 _let_223 _let_222 _let_221 _let_220 _let_219 _let_218 _let_217 _let_216 _let_215 _let_214 _let_213 _let_212 _let_211 _let_210 _let_209 _let_208 _let_207 _let_206 _let_205) :args ((= _let_3 (= fI_QUERY (lambda ((P2 assn) (Q2 assn) (F3 assn)) (forall ((BOUND_VARIABLE_260817 produc3658429121746597890et_nat)) (or (not (@ (@ rep_assn P2) BOUND_VARIABLE_260817)) (@ (@ rep_assn (@ abs_assn (@ (@ times_assn_raw (@ rep_assn Q2)) (@ rep_assn F3)))) BOUND_VARIABLE_260817))))))))))) (let ((_let_355 (ASSUME :args (_let_189)))) (let ((_let_356 (EQ_RESOLVE (ASSUME :args (_let_106)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_355 _let_354 _let_353 _let_352 _let_351 _let_350 _let_349 _let_348 _let_347 _let_346 _let_345 _let_344 _let_343 _let_342 _let_341 _let_340 _let_339 _let_338 _let_337 _let_336 _let_335 _let_334 _let_333 _let_332 _let_331 _let_330 _let_329 _let_328 _let_327 _let_326 _let_325 _let_324 _let_323 _let_322 _let_321 _let_320 _let_319 _let_318 _let_317 _let_316 _let_315 _let_314 _let_313 _let_312 _let_311 _let_310 _let_309 _let_308 _let_307 _let_306 _let_305 _let_304 _let_303 _let_302 _let_301 _let_300 _let_299 _let_298 _let_297 _let_296 _let_295 _let_294 _let_293 _let_292 _let_291 _let_290 _let_289 _let_288 _let_287 _let_286 _let_285 _let_284 _let_283 _let_282 _let_281 _let_280 _let_279 _let_278 _let_277 _let_276 _let_275 _let_274 _let_273 _let_272 _let_271 _let_270 _let_269 _let_268 _let_267 _let_266 _let_265 _let_264 _let_263 _let_262 _let_261 _let_260 _let_259 _let_258 _let_257 _let_256 _let_255 _let_254 _let_253 _let_252 _let_251 _let_250 _let_249 _let_248 _let_247 _let_246 _let_245 _let_244 _let_243 _let_242 _let_241 _let_240 _let_239 _let_238 _let_237 _let_236 _let_235 _let_234 _let_233 _let_232 _let_231 _let_230 _let_229 _let_228 _let_227 _let_226 _let_225 _let_224 _let_223 _let_222 _let_221 _let_220 _let_219 _let_218 _let_217 _let_216 _let_215 _let_214 _let_213 _let_212 _let_211 _let_210 _let_209 _let_208 _let_207 _let_206 _let_205) :args (_let_106 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_357 (EQ_RESOLVE (ASSUME :args (_let_190)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_356 _let_355 _let_354 _let_353 _let_352 _let_351 _let_350 _let_349 _let_348 _let_347 _let_346 _let_345 _let_344 _let_343 _let_342 _let_341 _let_340 _let_339 _let_338 _let_337 _let_336 _let_335 _let_334 _let_333 _let_332 _let_331 _let_330 _let_329 _let_328 _let_327 _let_326 _let_325 _let_324 _let_323 _let_322 _let_321 _let_320 _let_319 _let_318 _let_317 _let_316 _let_315 _let_314 _let_313 _let_312 _let_311 _let_310 _let_309 _let_308 _let_307 _let_306 _let_305 _let_304 _let_303 _let_302 _let_301 _let_300 _let_299 _let_298 _let_297 _let_296 _let_295 _let_294 _let_293 _let_292 _let_291 _let_290 _let_289 _let_288 _let_287 _let_286 _let_285 _let_284 _let_283 _let_282 _let_281 _let_280 _let_279 _let_278 _let_277 _let_276 _let_275 _let_274 _let_273 _let_272 _let_271 _let_270 _let_269 _let_268 _let_267 _let_266 _let_265 _let_264 _let_263 _let_262 _let_261 _let_260 _let_259 _let_258 _let_257 _let_256 _let_255 _let_254 _let_253 _let_252 _let_251 _let_250 _let_249 _let_248 _let_247 _let_246 _let_245 _let_244 _let_243 _let_242 _let_241 _let_240 _let_239 _let_238 _let_237 _let_236 _let_235 _let_234 _let_233 _let_232 _let_231 _let_230 _let_229 _let_228 _let_227 _let_226 _let_225 _let_224 _let_223 _let_222 _let_221 _let_220 _let_219 _let_218 _let_217 _let_216 _let_215 _let_214 _let_213 _let_212 _let_211 _let_210 _let_209 _let_208 _let_207 _let_206 _let_205) :args (_let_190 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_358 (EQ_RESOLVE (EQ_RESOLVE (ASSUME :args (_let_191)) (MACRO_SR_EQ_INTRO :args (_let_191 SB_DEFAULT SBA_FIXPOINT))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_357 _let_356 _let_355 _let_354 _let_353 _let_352 _let_351 _let_350 _let_349 _let_348 _let_347 _let_346 _let_345 _let_344 _let_343 _let_342 _let_341 _let_340 _let_339 _let_338 _let_337 _let_336 _let_335 _let_334 _let_333 _let_332 _let_331 _let_330 _let_329 _let_328 _let_327 _let_326 _let_325 _let_324 _let_323 _let_322 _let_321 _let_320 _let_319 _let_318 _let_317 _let_316 _let_315 _let_314 _let_313 _let_312 _let_311 _let_310 _let_309 _let_308 _let_307 _let_306 _let_305 _let_304 _let_303 _let_302 _let_301 _let_300 _let_299 _let_298 _let_297 _let_296 _let_295 _let_294 _let_293 _let_292 _let_291 _let_290 _let_289 _let_288 _let_287 _let_286 _let_285 _let_284 _let_283 _let_282 _let_281 _let_280 _let_279 _let_278 _let_277 _let_276 _let_275 _let_274 _let_273 _let_272 _let_271 _let_270 _let_269 _let_268 _let_267 _let_266 _let_265 _let_264 _let_263 _let_262 _let_261 _let_260 _let_259 _let_258 _let_257 _let_256 _let_255 _let_254 _let_253 _let_252 _let_251 _let_250 _let_249 _let_248 _let_247 _let_246 _let_245 _let_244 _let_243 _let_242 _let_241 _let_240 _let_239 _let_238 _let_237 _let_236 _let_235 _let_234 _let_233 _let_232 _let_231 _let_230 _let_229 _let_228 _let_227 _let_226 _let_225 _let_224 _let_223 _let_222 _let_221 _let_220 _let_219 _let_218 _let_217 _let_216 _let_215 _let_214 _let_213 _let_212 _let_211 _let_210 _let_209 _let_208 _let_207 _let_206 _let_205) :args ((= distinct_d (lambda ((Xs3 list_d)) (forall ((I4 nat) (BOUND_VARIABLE_132148 nat)) (let ((_let_1 (@ nth_d Xs3))) (let ((_let_2 (@ size_size_list_d Xs3))) (or (not (@ (@ ord_less_nat I4) _let_2)) (not (@ (@ ord_less_nat BOUND_VARIABLE_132148) _let_2)) (= I4 BOUND_VARIABLE_132148) (not (= (@ _let_1 I4) (@ _let_1 BOUND_VARIABLE_132148))))))))) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_359 (EQ_RESOLVE (ASSUME :args (_let_192)) (TRUST_SUBS_MAP (AND_INTRO _let_358 _let_357 _let_356 _let_355 _let_354 _let_353 _let_352 _let_351 _let_350 _let_349 _let_348 _let_347 _let_346 _let_345 _let_344 _let_343 _let_342 _let_341 _let_340 _let_339 _let_338 _let_337 _let_336 _let_335 _let_334 _let_333 _let_332 _let_331 _let_330 _let_329 _let_328 _let_327 _let_326 _let_325 _let_324 _let_323 _let_322 _let_321 _let_320 _let_319 _let_318 _let_317 _let_316 _let_315 _let_314 _let_313 _let_312 _let_311 _let_310 _let_309 _let_308 _let_307 _let_306 _let_305 _let_304 _let_303 _let_302 _let_301 _let_300 _let_299 _let_298 _let_297 _let_296 _let_295 _let_294 _let_293 _let_292 _let_291 _let_290 _let_289 _let_288 _let_287 _let_286 _let_285 _let_284 _let_283 _let_282 _let_281 _let_280 _let_279 _let_278 _let_277 _let_276 _let_275 _let_274 _let_273 _let_272 _let_271 _let_270 _let_269 _let_268 _let_267 _let_266 _let_265 _let_264 _let_263 _let_262 _let_261 _let_260 _let_259 _let_258 _let_257 _let_256 _let_255 _let_254 _let_253 _let_252 _let_251 _let_250 _let_249 _let_248 _let_247 _let_246 _let_245 _let_244 _let_243 _let_242 _let_241 _let_240 _let_239 _let_238 _let_237 _let_236 _let_235 _let_234 _let_233 _let_232 _let_231 _let_230 _let_229 _let_228 _let_227 _let_226 _let_225 _let_224 _let_223 _let_222 _let_221 _let_220 _let_219 _let_218 _let_217 _let_216 _let_215 _let_214 _let_213 _let_212 _let_211 _let_210 _let_209 _let_208 _let_207 _let_206 _let_205) :args ((= _let_192 (= minus_minus_assn (lambda ((A3 assn) (B3 assn)) (@ abs_assn (lambda ((BOUND_VARIABLE_265692 produc3658429121746597890et_nat)) (and (@ (@ rep_assn A3) BOUND_VARIABLE_265692) (@ (@ rep_assn (@ abs_assn (lambda ((BOUND_VARIABLE_265682 produc3658429121746597890et_nat)) (and (not (@ (@ rep_assn B3) BOUND_VARIABLE_265682)) (@ in_range BOUND_VARIABLE_265682))))) BOUND_VARIABLE_265692)))))))))))) (let ((_let_360 (EQ_RESOLVE (ASSUME :args (_let_41)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_359 _let_358 _let_357 _let_356 _let_355 _let_354 _let_353 _let_352 _let_351 _let_350 _let_349 _let_348 _let_347 _let_346 _let_345 _let_344 _let_343 _let_342 _let_341 _let_340 _let_339 _let_338 _let_337 _let_336 _let_335 _let_334 _let_333 _let_332 _let_331 _let_330 _let_329 _let_328 _let_327 _let_326 _let_325 _let_324 _let_323 _let_322 _let_321 _let_320 _let_319 _let_318 _let_317 _let_316 _let_315 _let_314 _let_313 _let_312 _let_311 _let_310 _let_309 _let_308 _let_307 _let_306 _let_305 _let_304 _let_303 _let_302 _let_301 _let_300 _let_299 _let_298 _let_297 _let_296 _let_295 _let_294 _let_293 _let_292 _let_291 _let_290 _let_289 _let_288 _let_287 _let_286 _let_285 _let_284 _let_283 _let_282 _let_281 _let_280 _let_279 _let_278 _let_277 _let_276 _let_275 _let_274 _let_273 _let_272 _let_271 _let_270 _let_269 _let_268 _let_267 _let_266 _let_265 _let_264 _let_263 _let_262 _let_261 _let_260 _let_259 _let_258 _let_257 _let_256 _let_255 _let_254 _let_253 _let_252 _let_251 _let_250 _let_249 _let_248 _let_247 _let_246 _let_245 _let_244 _let_243 _let_242 _let_241 _let_240 _let_239 _let_238 _let_237 _let_236 _let_235 _let_234 _let_233 _let_232 _let_231 _let_230 _let_229 _let_228 _let_227 _let_226 _let_225 _let_224 _let_223 _let_222 _let_221 _let_220 _let_219 _let_218 _let_217 _let_216 _let_215 _let_214 _let_213 _let_212 _let_211 _let_210 _let_209 _let_208 _let_207 _let_206 _let_205) :args (_let_41 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_361 (EQ_RESOLVE (ASSUME :args (_let_193)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_360 _let_359 _let_358 _let_357 _let_356 _let_355 _let_354 _let_353 _let_352 _let_351 _let_350 _let_349 _let_348 _let_347 _let_346 _let_345 _let_344 _let_343 _let_342 _let_341 _let_340 _let_339 _let_338 _let_337 _let_336 _let_335 _let_334 _let_333 _let_332 _let_331 _let_330 _let_329 _let_328 _let_327 _let_326 _let_325 _let_324 _let_323 _let_322 _let_321 _let_320 _let_319 _let_318 _let_317 _let_316 _let_315 _let_314 _let_313 _let_312 _let_311 _let_310 _let_309 _let_308 _let_307 _let_306 _let_305 _let_304 _let_303 _let_302 _let_301 _let_300 _let_299 _let_298 _let_297 _let_296 _let_295 _let_294 _let_293 _let_292 _let_291 _let_290 _let_289 _let_288 _let_287 _let_286 _let_285 _let_284 _let_283 _let_282 _let_281 _let_280 _let_279 _let_278 _let_277 _let_276 _let_275 _let_274 _let_273 _let_272 _let_271 _let_270 _let_269 _let_268 _let_267 _let_266 _let_265 _let_264 _let_263 _let_262 _let_261 _let_260 _let_259 _let_258 _let_257 _let_256 _let_255 _let_254 _let_253 _let_252 _let_251 _let_250 _let_249 _let_248 _let_247 _let_246 _let_245 _let_244 _let_243 _let_242 _let_241 _let_240 _let_239 _let_238 _let_237 _let_236 _let_235 _let_234 _let_233 _let_232 _let_231 _let_230 _let_229 _let_228 _let_227 _let_226 _let_225 _let_224 _let_223 _let_222 _let_221 _let_220 _let_219 _let_218 _let_217 _let_216 _let_215 _let_214 _let_213 _let_212 _let_211 _let_210 _let_209 _let_208 _let_207 _let_206 _let_205) :args (_let_193 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_362 (AND_INTRO (EQ_RESOLVE (ASSUME :args (_let_72)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_361 _let_360 _let_359 _let_358 _let_357 _let_356 _let_355 _let_354 _let_353 _let_352 _let_351 _let_350 _let_349 _let_348 _let_347 _let_346 _let_345 _let_344 _let_343 _let_342 _let_341 _let_340 _let_339 _let_338 _let_337 _let_336 _let_335 _let_334 _let_333 _let_332 _let_331 _let_330 _let_329 _let_328 _let_327 _let_326 _let_325 _let_324 _let_323 _let_322 _let_321 _let_320 _let_319 _let_318 _let_317 _let_316 _let_315 _let_314 _let_313 _let_312 _let_311 _let_310 _let_309 _let_308 _let_307 _let_306 _let_305 _let_304 _let_303 _let_302 _let_301 _let_300 _let_299 _let_298 _let_297 _let_296 _let_295 _let_294 _let_293 _let_292 _let_291 _let_290 _let_289 _let_288 _let_287 _let_286 _let_285 _let_284 _let_283 _let_282 _let_281 _let_280 _let_279 _let_278 _let_277 _let_276 _let_275 _let_274 _let_273 _let_272 _let_271 _let_270 _let_269 _let_268 _let_267 _let_266 _let_265 _let_264 _let_263 _let_262 _let_261 _let_260 _let_259 _let_258 _let_257 _let_256 _let_255 _let_254 _let_253 _let_252 _let_251 _let_250 _let_249 _let_248 _let_247 _let_246 _let_245 _let_244 _let_243 _let_242 _let_241 _let_240 _let_239 _let_238 _let_237 _let_236 _let_235 _let_234 _let_233 _let_232 _let_231 _let_230 _let_229 _let_228 _let_227 _let_226 _let_225 _let_224 _let_223 _let_222 _let_221 _let_220 _let_219 _let_218 _let_217 _let_216 _let_215 _let_214 _let_213 _let_212 _let_211 _let_210 _let_209 _let_208 _let_207 _let_206 _let_205) :args (_let_72 SB_DEFAULT SBA_FIXPOINT))) _let_361 _let_360 _let_359 _let_358 _let_357 _let_356 _let_355 _let_354 _let_353 _let_352 _let_351 _let_350 _let_349 _let_348 _let_347 _let_346 _let_345 _let_344 _let_343 _let_342 _let_341 _let_340 _let_339 _let_338 _let_337 _let_336 _let_335 _let_334 _let_333 _let_332 _let_331 _let_330 _let_329 _let_328 _let_327 _let_326 _let_325 _let_324 _let_323 _let_322 _let_321 _let_320 _let_319 _let_318 _let_317 _let_316 _let_315 _let_314 _let_313 _let_312 _let_311 _let_310 _let_309 _let_308 _let_307 _let_306 _let_305 _let_304 _let_303 _let_302 _let_301 _let_300 _let_299 _let_298 _let_297 _let_296 _let_295 _let_294 _let_293 _let_292 _let_291 _let_290 _let_289 _let_288 _let_287 _let_286 _let_285 _let_284 _let_283 _let_282 _let_281 _let_280 _let_279 _let_278 _let_277 _let_276 _let_275 _let_274 _let_273 _let_272 _let_271 _let_270 _let_269 _let_268 _let_267 _let_266 _let_265 _let_264 _let_263 _let_262 _let_261 _let_260 _let_259 _let_258 _let_257 _let_256 _let_255 _let_254 _let_253 _let_252 _let_251 _let_250 _let_249 _let_248 _let_247 _let_246 _let_245 _let_244 _let_243 _let_242 _let_241 _let_240 _let_239 _let_238 _let_237 _let_236 _let_235 _let_234 _let_233 _let_232 _let_231 _let_230 _let_229 _let_228 _let_227 _let_226 _let_225 _let_224 _let_223 _let_222 _let_221 _let_220 _let_219 _let_218 _let_217 _let_216 _let_215 _let_214 _let_213 _let_212 _let_211 _let_210 _let_209 _let_208 _let_207 _let_206 _let_205))) (let ((_let_363 (EQ_RESOLVE (ASSUME :args (_let_133)) (TRANS (MACRO_SR_EQ_INTRO _let_362 :args (_let_133 SB_DEFAULT SBA_FIXPOINT)) (PREPROCESS :args ((= (not (forall ((BOUND_VARIABLE_267024 produc3658429121746597890et_nat)) (or (not (@ (@ rep_assn p) BOUND_VARIABLE_267024)) (@ (@ rep_assn q) BOUND_VARIABLE_267024)))) _let_204))))))) (let ((_let_364 (OR))) (let ((_let_365 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE _let_363) :args (_let_204))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_204) _let_202))) (REFL :args (_let_203)) :args _let_364)) _let_363 :args (_let_203 true _let_202)))) (let ((_let_366 (forall ((BOUND_VARIABLE_266833 produc3658429121746597890et_nat)) (or (not (ho_1895 (ho_1894 k_1897 p) BOUND_VARIABLE_266833)) (ho_1895 (ho_1894 k_1897 (ho_1941 k_1940 (ho_2624 k_2623 false))) BOUND_VARIABLE_266833))))) (let ((_let_367 (EQ_RESOLVE (ASSUME :args (_let_194)) (TRANS (MACRO_SR_EQ_INTRO _let_362 :args (_let_194 SB_DEFAULT SBA_FIXPOINT)) (PREPROCESS :args ((= (forall ((BOUND_VARIABLE_266833 produc3658429121746597890et_nat)) (or (not (@ (@ rep_assn p) BOUND_VARIABLE_266833)) (@ (@ rep_assn (@ abs_assn (@ pure_a825153325127701367it_nat false))) BOUND_VARIABLE_266833))) _let_366))))))) (let ((_let_368 (IMPLIES))) (let ((_let_369 (CONG (CONG (REFL :args (k_1897)) (CONG (REFL :args (k_1940)) (CONG (REFL :args (k_2623)) (MACRO_SR_PRED_INTRO :args ((= false BOOLEAN_TERM_VARIABLE_680062))) :args (APPLY_UF ho_2624)) :args (APPLY_UF ho_1941)) :args (APPLY_UF ho_1894)) (REFL :args (skv_6101)) :args (APPLY_UF ho_1895)))) (let ((_let_370 (_let_366))) (let ((_let_371 (not _let_197))) (let ((_let_372 (or _let_371 _let_200))) (let ((_let_373 (forall ((P assn) (BOUND_VARIABLE_366027 produc3658429121746597890et_nat)) (or (not (ho_1895 (ho_1894 k_1897 (ho_1941 k_1940 (ho_2624 k_2623 false))) BOUND_VARIABLE_366027)) (ho_1895 (ho_1894 k_1897 P) BOUND_VARIABLE_366027))))) (let ((_let_374 (EQ_RESOLVE (ASSUME :args (_let_43)) (TRANS (MACRO_SR_EQ_INTRO _let_362 :args (_let_43 SB_DEFAULT SBA_FIXPOINT)) (PREPROCESS :args ((= (forall ((P assn) (BOUND_VARIABLE_366027 produc3658429121746597890et_nat)) (or (not (@ (@ rep_assn (@ abs_assn (@ pure_a825153325127701367it_nat false))) BOUND_VARIABLE_366027)) (@ (@ rep_assn P) BOUND_VARIABLE_366027))) _let_373))))))) (let ((_let_375 (_let_373))) (SCOPE (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_199)) :args ((or _let_198 _let_197 (not _let_199)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_372)) :args ((or _let_200 _let_371 (not _let_372)))) (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_201 1)) _let_365 :args ((not _let_200) true _let_201)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (EQ_RESOLVE (SCOPE (INSTANTIATE _let_374 :args (q skv_6101 QUANTIFIERS_INST_E_MATCHING ((not (= (ho_1895 (ho_1894 k_1897 P) BOUND_VARIABLE_366027) true))))) :args _let_375) (CONG (REFL :args _let_375) (CONG (CONG _let_369 :args (NOT)) (REFL :args (_let_200)) :args _let_364) :args _let_368))) _let_374 :args (_let_372 false _let_373)) :args (_let_371 true _let_200 false _let_372)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (EQ_RESOLVE (SCOPE (INSTANTIATE _let_367 :args (skv_6101 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (ho_1895 _let_195 BOUND_VARIABLE_266833) false))))) :args _let_370) (CONG (REFL :args _let_370) (CONG (REFL :args (_let_198)) _let_369 :args _let_364) :args _let_368))) _let_367 :args (_let_199 false _let_366)) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_201 0)) (CONG (REFL :args (_let_201)) (MACRO_SR_PRED_INTRO :args ((= (not _let_198) _let_196))) :args _let_364)) :args ((or _let_196 _let_201))) _let_365 :args (_let_196 true _let_201)) :args (false true _let_197 false _let_199 false _let_196)) :args ((forall ((Ofs nat) (A2 nat) (B2 nat)) (= (@ (@ map_nat_nat (lambda ((I4 nat)) (@ (@ plus_plus_nat I4) Ofs))) (@ (@ upt A2) B2)) (@ (@ upt (@ (@ plus_plus_nat A2) Ofs)) (@ (@ plus_plus_nat B2) Ofs)))) (= is_sin2937591304547752795at_nat (lambda ((A5 set_Pr4329608150637261639at_nat)) (exists ((X2 produc3843707927480180839at_nat)) (= A5 (@ (@ insert9069300056098147895at_nat X2) bot_bo228742789529271731at_nat))))) (forall ((Xs list_d)) (= (@ (@ ord_less_nat zero_zero_nat) (@ size_size_list_d Xs)) (not (= Xs nil_d)))) (= (@ rotate1_int nil_int) nil_int) (forall ((T code_integer)) (exists ((Z4 code_integer)) (forall ((X7 code_integer)) (=> (@ (@ ord_le6747313008572928689nteger Z4) X7) (not (= X7 T)))))) _let_194 (forall ((X assn) (Y assn) (Z assn)) (let ((_let_1 (@ sup_sup_assn X))) (= (@ (@ sup_sup_assn (@ _let_1 Y)) Z) (@ _let_1 (@ (@ sup_sup_assn Y) Z))))) (forall ((X assn) (Y assn)) (= (@ (@ sup_sup_assn X) (@ (@ inf_inf_assn X) Y)) X)) (forall ((A2 rat) (B2 rat)) (let ((_let_1 (@ ord_less_eq_rat zero_zero_rat))) (=> (or (and (@ (@ ord_less_eq_rat A2) zero_zero_rat) (@ (@ ord_less_eq_rat B2) zero_zero_rat)) (and (@ _let_1 B2) (@ _let_1 A2))) (@ _let_1 (@ (@ times_times_rat A2) B2))))) (= ord_less_nat (lambda ((N2 nat) (__flatten_var_0 nat)) (@ (@ ord_less_eq_nat (@ suc N2)) __flatten_var_0))) (forall ((A2 product_prod_nat_nat) (B set_Pr1261947904930325089at_nat)) (@ (@ member8440522571783428010at_nat A2) (@ (@ insert8211810215607154385at_nat A2) B))) (forall ((I3 set_nat) (I7 set_nat) (Xs list_d) (Xs4 list_d) (Xsi list_nat) (Xsi2 list_nat) (A (-> d nat assn)) (A6 (-> d nat assn))) (=> (= I3 I7) (=> (= (@ size_size_list_d Xs) (@ size_size_list_d Xs4)) (=> (= (@ size_size_list_nat Xsi) (@ size_size_list_nat Xsi2)) (=> (forall ((I5 nat)) (let ((_let_1 (@ (@ nth_d Xs4) I5))) (let ((_let_2 (@ (@ nth_d Xs) I5))) (let ((_let_3 (@ (@ nth_nat Xsi2) I5))) (let ((_let_4 (@ (@ nth_nat Xsi) I5))) (let ((_let_5 (@ size_size_list_d Xs))) (=> (@ (@ member_nat I5) I3) (=> (@ (@ ord_less_nat I5) _let_5) (=> (= _let_5 (@ size_size_list_nat Xsi)) (and (= _let_4 _let_3) (= (@ (@ A _let_2) _let_4) (@ (@ A6 _let_1) _let_3)) (= _let_2 _let_1))))))))))) (= (@ (@ (@ (@ vEBT_L7820616366081188145_d_nat I3) A) Xs) Xsi) (@ (@ (@ (@ vEBT_L7820616366081188145_d_nat I7) A6) Xs4) Xsi2))))))) _let_193 (forall ((B2 product_prod_nat_nat) (A2 product_prod_nat_nat)) (= (@ (@ member8440522571783428010at_nat B2) (@ (@ insert8211810215607154385at_nat A2) bot_bo2099793752762293965at_nat)) (= B2 A2))) (forall ((X produc3843707927480180839at_nat) (Xs list_P5464809261938338413at_nat) (Y produc3843707927480180839at_nat)) (let ((_let_1 (@ member8757157785044589968at_nat X))) (=> (not (@ _let_1 (@ set_Pr3765526544606949372at_nat Xs))) (not (@ _let_1 (@ set_Pr3765526544606949372at_nat (@ (@ remove8895909992688781315at_nat Y) Xs))))))) (forall ((A2 code_integer) (B2 code_integer) (N nat)) (= (@ (@ power_8256067586552552935nteger (@ (@ times_3573771949741848930nteger A2) B2)) N) (@ (@ times_3573771949741848930nteger (@ (@ power_8256067586552552935nteger A2) N)) (@ (@ power_8256067586552552935nteger B2) N)))) (forall ((N nat) (F4 (-> nat int)) (K3 int)) (=> (forall ((I5 nat)) (=> (@ (@ ord_less_nat I5) N) (@ (@ ord_less_eq_int (@ abs_abs_int (@ (@ minus_minus_int (@ F4 (@ suc I5))) (@ F4 I5)))) one_one_int))) (=> (@ (@ ord_less_eq_int (@ F4 zero_zero_nat)) K3) (=> (@ (@ ord_less_eq_int K3) (@ F4 N)) (exists ((I5 nat)) (and (= (@ F4 I5) K3) (@ (@ ord_less_eq_nat I5) N))))))) (forall ((X (-> produc3658429121746597890et_nat Bool)) (A set_Pr4532377907799695533_nat_o) (X4 set_Pr4532377907799695533_nat_o)) (=> (@ (@ member6576561426505652726_nat_o X) A) (=> (@ (@ ord_le2965882846123202637_nat_o X4) A) (@ (@ ord_le2965882846123202637_nat_o (@ (@ insert5175938949040314269_nat_o X) X4)) A)))) (forall ((A2 (-> int option6357759511663192854e_term)) (B2 product_prod_int_int) (A7 (-> int option6357759511663192854e_term)) (B6 product_prod_int_int)) (=> (= (@ (@ produc4305682042979456191nt_int A2) B2) (@ (@ produc4305682042979456191nt_int A7) B6)) (not (=> (= A2 A7) (not (= B2 B6)))))) (forall ((A set_nat) (C2 set_nat) (B set_nat)) (let ((_let_1 (@ minus_minus_set_nat (@ (@ inf_inf_set_nat A) C2)))) (= (@ _let_1 (@ (@ inf_inf_set_nat B) C2)) (@ _let_1 B)))) (forall ((N nat)) (=> (@ (@ ord_less_nat N) (@ numeral_numeral_nat (@ bit0 one))) (or (= N zero_zero_nat) (= N (@ suc zero_zero_nat))))) (@ proper in_range) (forall ((L12 list_c) (L23 list_c)) (=> (= (@ size_size_list_c L12) (@ size_size_list_c L23)) (= (@ (@ (@ zipf_c684006316856269033od_c_c product_Pair_c_c) L12) L23) (@ (@ zip_c_c L12) L23)))) (forall ((Xs list_nat)) (=> (@ (@ sorted_wrt_nat ord_less_nat) Xs) (@ (@ sorted_wrt_nat ord_less_eq_nat) Xs))) (forall ((X set_nat) (Y set_nat) (Z set_nat)) (let ((_let_1 (@ inf_inf_set_nat X))) (let ((_let_2 (@ inf_inf_set_nat Y))) (= (@ _let_1 (@ _let_2 Z)) (@ _let_2 (@ _let_1 Z)))))) (forall ((X (-> produc6241069584506657477e_term option6357759511663192854e_term)) (Y produc8923325533196201883nteger) (Xs list_P1316552470764441098e_term) (Ys list_P5578671422887162913nteger)) (=> (@ (@ member4164122664394876845nteger (@ (@ produc8603105652947943368nteger X) Y)) (@ set_Pr2135590979564877377nteger (@ (@ zip_Pr8292346330294042792nteger Xs) Ys))) (@ (@ member4242434998011752849e_term X) (@ set_Pr8342322266483756581e_term Xs)))) _let_192 (forall ((I nat) (K3 nat)) (=> (@ (@ ord_less_nat (@ suc I)) K3) (not (forall ((J3 nat)) (=> (@ (@ ord_less_nat I) J3) (not (= K3 (@ suc J3)))))))) (forall ((From nat) (To nat) (Xs list_d) (I nat)) (=> (@ (@ ord_less_nat From) To) (=> (@ (@ ord_less_eq_nat To) (@ size_size_list_d Xs)) (=> (@ (@ ord_less_nat I) (@ (@ minus_minus_nat To) From)) (= (@ (@ nth_d (@ (@ (@ slice_d From) To) Xs)) I) (@ (@ nth_d Xs) (@ (@ plus_plus_nat From) I))))))) (forall ((A2 nat) (C nat) (B2 nat)) (=> (@ (@ ord_less_eq_nat A2) C) (@ (@ ord_less_eq_nat (@ (@ ord_min_nat A2) B2)) C))) (forall ((P assn) (Q assn) (H2 produc3658429121746597890et_nat)) (= (@ (@ rep_assn (@ (@ inf_inf_assn P) Q)) H2) (and (@ (@ rep_assn P) H2) (@ (@ rep_assn Q) H2)))) (forall ((P (-> int Bool)) (P3 (-> int Bool)) (Q (-> int Bool)) (Q3 (-> int Bool))) (=> (exists ((Z3 int)) (forall ((X3 int)) (=> (@ (@ ord_less_int Z3) X3) (= (@ P X3) (@ P3 X3))))) (=> (exists ((Z3 int)) (forall ((X3 int)) (=> (@ (@ ord_less_int Z3) X3) (= (@ Q X3) (@ Q3 X3))))) (exists ((Z4 int)) (forall ((X7 int)) (=> (@ (@ ord_less_int Z4) X7) (= (and (@ Q X7) (@ P X7)) (and (@ Q3 X7) (@ P3 X7))))))))) (forall ((P (-> produc3843707927480180839at_nat Bool))) (= (= (@ collec6321179662152712658at_nat P) bot_bo228742789529271731at_nat) (forall ((X2 produc3843707927480180839at_nat)) (not (@ P X2))))) (forall ((A2 rat)) (= (@ (@ ord_less_eq_rat (@ (@ plus_plus_rat A2) A2)) zero_zero_rat) (@ (@ ord_less_eq_rat A2) zero_zero_rat))) (forall ((A2 code_integer) (M2 nat) (N nat)) (let ((_let_1 (@ power_8256067586552552935nteger A2))) (= (@ _let_1 (@ (@ plus_plus_nat M2) N)) (@ (@ times_3573771949741848930nteger (@ _let_1 M2)) (@ _let_1 N))))) (forall ((A2 int) (B2 int) (C int)) (let ((_let_1 (@ times_times_int A2))) (= (@ _let_1 (@ (@ plus_plus_int B2) C)) (@ (@ plus_plus_int (@ _let_1 B2)) (@ _let_1 C))))) (forall ((C int) (B2 int) (A2 int)) (let ((_let_1 (@ ord_less_eq_int B2))) (=> (@ (@ ord_less_eq_int zero_zero_int) C) (=> (@ _let_1 A2) (@ _let_1 (@ (@ plus_plus_int A2) C)))))) (forall ((X nat)) (= (= one_one_nat X) (= X one_one_nat))) (forall ((Xs list_nat) (Ys list_P8527749157015355191n_assn) (Xy produc1407301962063123414n_assn) (Xys list_P7711101519850957926n_assn)) (=> (= (@ (@ zip_na5338819973521719528n_assn Xs) Ys) (@ (@ cons_P7068465851076118432n_assn Xy) Xys)) (not (forall ((X3 nat) (Xs5 list_nat)) (=> (= Xs (@ (@ cons_nat X3) Xs5)) (forall ((Y2 produc6575502325842934193n_assn) (Ys4 list_P8527749157015355191n_assn)) (=> (= Ys (@ (@ cons_P2971678138204555879n_assn Y2) Ys4)) (=> (= Xy (@ (@ produc1553784393020010504n_assn X3) Y2)) (not (= Xys (@ (@ zip_na5338819973521719528n_assn Xs5) Ys4))))))))))) (forall ((B2 set_nat) (A2 set_nat)) (=> (@ (@ ord_less_set_nat B2) A2) (= (@ (@ sup_sup_set_nat A2) B2) A2))) (forall ((Y (-> produc3658429121746597890et_nat Bool)) (X222 list_P7985473006766602707_nat_o) (X21 (-> produc3658429121746597890et_nat Bool))) (let ((_let_1 (@ member6576561426505652726_nat_o Y))) (=> (@ _let_1 (@ set_Pr400311997697478754_nat_o X222)) (@ _let_1 (@ set_Pr400311997697478754_nat_o (@ (@ cons_P6219271836124797827_nat_o X21) X222)))))) (forall ((A2 int) (E int) (C int) (B2 int) (D2 int)) (= (@ (@ ord_less_eq_int (@ (@ plus_plus_int (@ (@ times_times_int A2) E)) C)) (@ (@ plus_plus_int (@ (@ times_times_int B2) E)) D2)) (@ (@ ord_less_eq_int (@ (@ plus_plus_int (@ (@ times_times_int (@ (@ minus_minus_int A2) B2)) E)) C)) D2))) (forall ((X filter_nat) (Y filter_nat)) (=> (@ (@ ord_le2510731241096832064er_nat X) Y) (or (@ (@ ord_less_filter_nat X) Y) (= X Y)))) (forall ((A set_Pr5949110396991348497n_assn) (Ys list_P8527749157015355191n_assn)) (= (@ (@ ord_le171416862856029873n_assn A) (@ coset_703488708621576356n_assn Ys)) (forall ((X2 produc6575502325842934193n_assn)) (let ((_let_1 (@ member7957490590177025114n_assn X2))) (=> (@ _let_1 (@ set_Pr1139785259514867910n_assn Ys)) (not (@ _let_1 A))))))) _let_191 (forall ((X int) (Y int)) (= (not (@ (@ ord_less_int X) Y)) (or (@ (@ ord_less_int Y) X) (= X Y)))) (forall ((A2 int) (B2 int) (C int)) (let ((_let_1 (@ times_times_int C))) (=> (@ (@ ord_less_int A2) B2) (=> (@ (@ ord_less_int zero_zero_int) C) (@ (@ ord_less_int (@ _let_1 A2)) (@ _let_1 B2)))))) (forall ((A2 int) (B2 int) (C int)) (let ((_let_1 (@ ord_less_int A2))) (=> (@ _let_1 (@ (@ inf_inf_int B2) C)) (not (=> (@ _let_1 B2) (not (@ _let_1 C))))))) (forall ((P assn)) (let ((_let_1 (@ times_times_assn top_top_assn))) (let ((_let_2 (@ _let_1 P))) (= (@ _let_1 _let_2) _let_2)))) (forall ((B2 set_nat) (A2 set_nat)) (=> (@ (@ ord_less_set_nat B2) A2) (@ (@ ord_less_eq_set_nat B2) A2))) (forall ((A2 set_int)) (=> (@ (@ ord_less_eq_set_int A2) bot_bot_set_int) (= A2 bot_bot_set_int))) (forall ((A2 code_integer) (B2 code_integer) (F4 (-> code_integer code_integer)) (C code_integer)) (=> (@ (@ ord_le6747313008572928689nteger A2) B2) (=> (@ (@ ord_le3102999989581377725nteger (@ F4 B2)) C) (=> (forall ((X3 code_integer) (Y2 code_integer)) (=> (@ (@ ord_le6747313008572928689nteger X3) Y2) (@ (@ ord_le6747313008572928689nteger (@ F4 X3)) (@ F4 Y2)))) (@ (@ ord_le6747313008572928689nteger (@ F4 A2)) C))))) (forall ((B2 Bool) (Q assn)) (= (@ (@ entails (@ pure_assn B2)) Q) (=> B2 (@ (@ entails one_one_assn) Q)))) (forall ((A2 rat) (B2 rat)) (=> (@ (@ ord_less_rat A2) B2) (@ (@ ord_less_rat (@ (@ plus_plus_rat A2) one_one_rat)) (@ (@ plus_plus_rat B2) one_one_rat)))) (forall ((X int) (Xs list_int) (Y int) (Ys list_int) (R2 set_Pr958786334691620121nt_int)) (let ((_let_1 (@ lex_int R2))) (= (@ (@ member6698963635872716290st_int (@ (@ produc364263696895485585st_int (@ (@ cons_int X) Xs)) (@ (@ cons_int Y) Ys))) _let_1) (or (and (= (@ size_size_list_int Xs) (@ size_size_list_int Ys)) (@ (@ member5262025264175285858nt_int (@ (@ product_Pair_int_int X) Y)) R2)) (and (= X Y) (@ (@ member6698963635872716290st_int (@ (@ produc364263696895485585st_int Xs) Ys)) _let_1)))))) _let_190 (forall ((M2 filter_nat) (N filter_nat)) (let ((_let_1 (@ (@ ord_min_filter_nat M2) N))) (= (@ (@ ord_le2510731241096832064er_nat M2) _let_1) (= _let_1 M2)))) (forall ((A2 nat)) (= (@ (@ times_times_nat one_one_nat) A2) A2)) (forall ((X1 (-> produc8551481072490612790e_term option6357759511663192854e_term)) (X22 product_prod_int_int) (Y1 (-> produc8551481072490612790e_term option6357759511663192854e_term)) (Y22 product_prod_int_int)) (= (= (@ (@ produc5700946648718959541nt_int X1) X22) (@ (@ produc5700946648718959541nt_int Y1) Y22)) (and (= X22 Y22) (= X1 Y1)))) (forall ((Z int) (X int) (Y int)) (=> (@ (@ ord_less_int zero_zero_int) Z) (= (@ (@ ord_less_int (@ (@ times_times_int X) Z)) (@ (@ times_times_int Y) Z)) (@ (@ ord_less_int X) Y)))) (forall ((A2 code_integer) (N nat)) (let ((_let_1 (@ power_8256067586552552935nteger A2))) (= (@ _let_1 (@ suc N)) (@ (@ times_3573771949741848930nteger A2) (@ _let_1 N))))) (forall ((A2 rat)) (= (@ (@ times_times_rat A2) one_one_rat) A2)) (forall ((A2 Bool) (A set_o)) (not (= (@ (@ insert_o2 A2) A) bot_bot_set_o))) (@ (@ _let_40 (@ produc27273713700761075at_nat (lambda ((X2 nat) (Y5 nat) (__flatten_var_0 product_prod_nat_nat)) (@ (@ produc2626176000494625587at_nat (lambda ((U4 nat) (V4 nat)) (let ((_let_1 (@ times_times_nat Y5))) (let ((_let_2 (@ times_times_nat X2))) (@ (@ product_Pair_nat_nat (@ (@ plus_plus_nat (@ _let_2 U4)) (@ _let_1 V4))) (@ (@ plus_plus_nat (@ _let_2 V4)) (@ _let_1 U4))))))) __flatten_var_0)))) (@ produc27273713700761075at_nat (lambda ((X2 nat) (Y5 nat) (__flatten_var_0 product_prod_nat_nat)) (@ (@ produc2626176000494625587at_nat (lambda ((U4 nat) (V4 nat)) (let ((_let_1 (@ times_times_nat Y5))) (let ((_let_2 (@ times_times_nat X2))) (@ (@ product_Pair_nat_nat (@ (@ plus_plus_nat (@ _let_2 U4)) (@ _let_1 V4))) (@ (@ plus_plus_nat (@ _let_2 V4)) (@ _let_1 U4))))))) __flatten_var_0)))) (= complete_Sup_Sup_nat (lambda ((X8 set_nat)) (@ (@ (@ if_nat (= X8 bot_bot_set_nat)) zero_zero_nat) (@ lattic8265883725875713057ax_nat X8)))) (forall ((Xs list_P8527749157015355191n_assn) (B set_Pr5949110396991348497n_assn)) (= (@ (@ ord_le171416862856029873n_assn (@ set_Pr1139785259514867910n_assn Xs)) B) (forall ((X2 produc6575502325842934193n_assn)) (let ((_let_1 (@ member7957490590177025114n_assn X2))) (=> (@ _let_1 (@ set_Pr1139785259514867910n_assn Xs)) (@ _let_1 B)))))) (= ord_less_eq_int (lambda ((B3 int) (A3 int)) (or (@ (@ ord_less_int B3) A3) (= A3 B3)))) (forall ((A2 nat) (B2 nat) (C nat)) (let ((_let_1 (@ plus_plus_nat A2))) (= (= (@ _let_1 B2) (@ _let_1 C)) (= B2 C)))) (not (@ _let_26 zero_zero_int)) (forall ((A2 rat) (B2 rat) (C rat)) (= (@ (@ times_times_rat (@ (@ plus_plus_rat A2) B2)) C) (@ (@ plus_plus_rat (@ (@ times_times_rat A2) C)) (@ (@ times_times_rat B2) C)))) (forall ((Xs list_P8527749157015355191n_assn) (Y nat) (Ys list_nat) (R2 set_Pr4672072672689440998sn_nat)) (=> (@ (@ member7785779426634843229st_nat (@ (@ produc6174113896479379136st_nat Xs) (@ (@ cons_nat Y) Ys))) (@ listre8031510547128344656sn_nat R2)) (not (forall ((X3 produc6575502325842934193n_assn) (Xs2 list_P8527749157015355191n_assn)) (=> (= Xs (@ (@ cons_P2971678138204555879n_assn X3) Xs2)) (=> (@ (@ member746799484843334599sn_nat (@ (@ produc6456381919915743786sn_nat X3) Y)) R2) (not (@ (@ member7785779426634843229st_nat (@ (@ produc6174113896479379136st_nat Xs2) Ys)) (@ listre8031510547128344656sn_nat R2))))))))) (forall ((K3 nat) (P (-> nat int Bool))) (= (forall ((I4 nat)) (=> (@ (@ ord_less_nat I4) K3) (exists ((X8 int)) (@ (@ P I4) X8)))) (exists ((Xs3 list_int)) (and (forall ((I4 nat)) (=> (@ (@ ord_less_nat I4) K3) (@ (@ P I4) (@ (@ nth_int Xs3) I4)))) (= (@ size_size_list_int Xs3) K3))))) (forall ((A set_Pr4532377907799695533_nat_o) (X (-> produc3658429121746597890et_nat Bool)) (B set_Pr4532377907799695533_nat_o)) (let ((_let_1 (@ ord_le2965882846123202637_nat_o A))) (let ((_let_2 (@ (@ member6576561426505652726_nat_o X) A))) (let ((_let_3 (@ insert5175938949040314269_nat_o X))) (= (@ _let_1 (@ _let_3 B)) (and (=> _let_2 (@ (@ ord_le2965882846123202637_nat_o (@ (@ minus_1801376950450012436_nat_o A) (@ _let_3 bot_bo7824918357723582233_nat_o))) B)) (=> (not _let_2) (@ _let_1 B)))))))) (forall ((A2 product_prod_nat_nat) (A set_Pr1261947904930325089at_nat) (B2 product_prod_nat_nat)) (let ((_let_1 (@ (@ insert8211810215607154385at_nat B2) bot_bo2099793752762293965at_nat))) (= (= (@ (@ insert8211810215607154385at_nat A2) A) _let_1) (and (= A2 B2) (@ (@ ord_le3146513528884898305at_nat A) _let_1))))) (@ (@ member_nat i2) i) (forall ((X21 nat) (X222 list_nat)) (= (@ size_size_list_nat (@ (@ cons_nat X21) X222)) (@ (@ plus_plus_nat (@ size_size_list_nat X222)) (@ suc zero_zero_nat)))) (forall ((A2 rat) (B2 rat) (C rat) (D2 rat)) (=> (@ (@ ord_less_rat A2) B2) (=> (@ (@ ord_less_rat C) D2) (=> (@ (@ ord_less_rat zero_zero_rat) B2) (=> (@ (@ ord_less_eq_rat zero_zero_rat) C) (@ (@ ord_less_rat (@ (@ times_times_rat A2) C)) (@ (@ times_times_rat B2) D2))))))) (forall ((P (-> produc2732055786443039994et_nat Bool)) (P6 produc2732055786443039994et_nat)) (=> (forall ((A4 (-> produc3658429121746597890et_nat Bool)) (B4 produc3925858234332021118et_nat)) (@ P (@ (@ produc2245416461498447860et_nat A4) B4))) (@ P P6))) (forall ((A set_Pr4329608150637261639at_nat) (B set_Pr4329608150637261639at_nat)) (= (@ (@ sup_su5525570899277871387at_nat (@ (@ minus_3314409938677909166at_nat A) B)) (@ (@ inf_in7913087082777306421at_nat A) B)) A)) (forall ((B2 rat) (A2 rat)) (= (= (@ (@ plus_plus_rat B2) A2) A2) (= B2 zero_zero_rat))) (forall ((A2 nat)) (= (@ (@ ord_less_eq_nat A2) bot_bot_nat) (= A2 bot_bot_nat))) (forall ((F4 (-> produc2732055786443039994et_nat Bool)) (A2 (-> produc3658429121746597890et_nat Bool)) (B2 produc3925858234332021118et_nat)) (=> (@ (@ (@ produc5101573711933517782_nat_o F4) A2) B2) (@ F4 (@ (@ produc2245416461498447860et_nat A2) B2)))) (forall ((T3 set_Pr1261947904930325089at_nat) (S set_Pr1261947904930325089at_nat)) (= (@ (@ sup_su6327502436637775413at_nat T3) (@ (@ inf_in2572325071724192079at_nat S) T3)) T3)) (= ord_le2510731241096832064er_nat (lambda ((X2 filter_nat) (Y5 filter_nat)) (= (@ (@ inf_inf_filter_nat X2) Y5) X2))) (forall ((X set_nat) (Y set_nat) (Z set_nat)) (let ((_let_1 (@ sup_sup_set_nat X))) (= (@ _let_1 (@ (@ inf_inf_set_nat Y) Z)) (@ (@ inf_inf_set_nat (@ _let_1 Y)) (@ _let_1 Z))))) _let_189 (forall ((A2 num) (B2 num)) (= (@ (@ ord_less_num (@ (@ ord_min_num A2) B2)) B2) (@ (@ ord_less_num A2) B2))) (forall ((N nat)) (= (@ (@ set_or4665077453230672383an_nat (@ suc zero_zero_nat)) N) (@ (@ minus_minus_set_nat (@ set_ord_lessThan_nat N)) (@ (@ insert_nat2 zero_zero_nat) bot_bot_set_nat)))) (forall ((C assn) (A2 assn) (B2 assn)) (let ((_let_1 (@ ord_less_eq_assn C))) (=> (@ _let_1 A2) (@ _let_1 (@ (@ sup_sup_assn A2) B2))))) (= ord_less_eq_int (lambda ((X2 int) (Y5 int)) (= (@ (@ sup_sup_int X2) Y5) Y5))) (forall ((P (-> nat Bool)) (Q (-> nat Bool))) (=> (forall ((X3 nat)) (=> (@ P X3) (@ Q X3))) (@ (@ ord_less_eq_set_nat (@ collect_nat P)) (@ collect_nat Q)))) (forall ((C int) (A2 int) (B2 int)) (let ((_let_1 (@ times_times_int C))) (=> (@ (@ ord_less_int zero_zero_int) C) (= (@ (@ ord_less_int (@ _let_1 A2)) (@ _let_1 B2)) (@ (@ ord_less_int A2) B2))))) (forall ((X code_integer) (Y code_integer)) (=> (not (@ (@ ord_le6747313008572928689nteger X) Y)) (= (@ (@ ord_le3102999989581377725nteger X) Y) (= X Y)))) (forall ((X produc3843707927480180839at_nat) (A set_Pr4329608150637261639at_nat)) (=> (@ (@ member8757157785044589968at_nat X) A) (not (forall ((B5 set_Pr4329608150637261639at_nat)) (=> (= A (@ (@ insert9069300056098147895at_nat X) B5)) (@ (@ member8757157785044589968at_nat X) B5)))))) (forall ((F4 (-> nat int int))) (= (@ (@ (@ zipf_nat_int_int F4) nil_nat) nil_int) nil_int)) (forall ((A2 set_Pr1261947904930325089at_nat) (B2 set_Pr1261947904930325089at_nat) (R2 set_Pr4329608150637261639at_nat) (C set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ transi2703068831062848130at_nat R2))) (let ((_let_2 (@ produc2922128104949294807at_nat A2))) (=> (@ (@ member8757157785044589968at_nat (@ _let_2 B2)) R2) (=> (@ (@ member8757157785044589968at_nat (@ (@ produc2922128104949294807at_nat B2) C)) _let_1) (@ (@ member8757157785044589968at_nat (@ _let_2 C)) _let_1)))))) (forall ((C produc3843707927480180839at_nat) (A set_Pr4329608150637261639at_nat) (B set_Pr4329608150637261639at_nat)) (let ((_let_1 (@ member8757157785044589968at_nat C))) (= (@ _let_1 (@ (@ sup_su5525570899277871387at_nat A) B)) (or (@ _let_1 B) (@ _let_1 A))))) (forall ((A2 int) (C2 set_int) (B set_int)) (=> (not (@ (@ member_int A2) C2)) (= (@ (@ inf_inf_set_int (@ (@ insert_int2 A2) B)) C2) (@ (@ inf_inf_set_int B) C2)))) (forall ((X nat) (Xs list_nat) (Y nat)) (= (@ (@ (@ list_update_nat (@ (@ cons_nat X) Xs)) zero_zero_nat) Y) (@ (@ cons_nat Y) Xs))) (forall ((B2 set_nat) (A2 set_nat) (C set_nat)) (let ((_let_1 (@ inf_inf_set_nat B2))) (let ((_let_2 (@ inf_inf_set_nat A2))) (= (@ _let_1 (@ _let_2 C)) (@ _let_2 (@ _let_1 C)))))) (forall ((X assn) (Y assn)) (=> (@ (@ ord_less_eq_assn X) Y) (= (@ (@ sup_sup_assn X) Y) Y))) (forall ((C int) (A2 int) (B2 int)) (let ((_let_1 (@ times_times_int C))) (= (= (@ _let_1 A2) (@ _let_1 B2)) (or (= C zero_zero_int) (= A2 B2))))) (@ (@ (@ (@ bNF_re4202695980764964119_nat_o intrel) (@ (@ bNF_re3666534408544137501at_o_o intrel) (lambda ((Y4 Bool) (Z2 Bool)) (= Y4 Z2)))) (@ produc8739625826339149834_nat_o (lambda ((X2 nat) (Y5 nat) (__flatten_var_0 product_prod_nat_nat)) (@ (@ produc6081775807080527818_nat_o (lambda ((U4 nat) (V4 nat)) (@ (@ ord_less_nat (@ (@ plus_plus_nat X2) V4)) (@ (@ plus_plus_nat U4) Y5)))) __flatten_var_0)))) (@ produc8739625826339149834_nat_o (lambda ((X2 nat) (Y5 nat) (__flatten_var_0 product_prod_nat_nat)) (@ (@ produc6081775807080527818_nat_o (lambda ((U4 nat) (V4 nat)) (@ (@ ord_less_nat (@ (@ plus_plus_nat X2) V4)) (@ (@ plus_plus_nat U4) Y5)))) __flatten_var_0)))) (forall ((A2 int) (B2 int) (C int)) (= (@ (@ times_times_int (@ (@ plus_plus_int A2) B2)) C) (@ (@ plus_plus_int (@ (@ times_times_int A2) C)) (@ (@ times_times_int B2) C)))) (forall ((B2 nat) (A2 nat)) (=> (@ (@ member_nat B2) (@ (@ insert_nat2 A2) bot_bot_set_nat)) (= B2 A2))) (forall ((A set_nat) (X nat) (B set_nat)) (let ((_let_1 (@ insert_nat2 X))) (let ((_let_2 (@ (@ member_nat X) A))) (let ((_let_3 (@ ord_less_eq_set_nat A))) (= (@ _let_3 (@ _let_1 B)) (and (=> (not _let_2) (@ _let_3 B)) (=> _let_2 (@ (@ ord_less_eq_set_nat (@ (@ minus_minus_set_nat A) (@ _let_1 bot_bot_set_nat))) B)))))))) (forall ((A2 nat)) (= (@ (@ plus_plus_nat zero_zero_nat) A2) A2)) (forall ((X rat) (Y rat)) (@ (@ ord_less_eq_rat zero_zero_rat) (@ (@ plus_plus_rat (@ (@ times_times_rat X) X)) (@ (@ times_times_rat Y) Y)))) (forall ((B2 nat) (A2 nat)) (=> (@ (@ ord_less_nat B2) A2) (= (@ (@ ord_min_nat A2) B2) B2))) (forall ((X code_integer) (Y code_integer) (Z code_integer)) (let ((_let_1 (@ ord_le6747313008572928689nteger X))) (=> (@ _let_1 Y) (=> (@ (@ ord_le6747313008572928689nteger Y) Z) (@ _let_1 Z))))) (forall ((X produc7773217078559923341nt_int)) (not (forall ((F5 (-> int option6357759511663192854e_term)) (A4 int) (B4 int)) (not (= X (@ (@ produc4305682042979456191nt_int F5) (@ (@ product_Pair_int_int A4) B4))))))) (forall ((R2 set_Product_prod_o_o) (S3 set_Product_prod_o_o)) (= (@ field_o (@ (@ sup_su5769328420594410459od_o_o R2) S3)) (@ (@ sup_sup_set_o (@ field_o R2)) (@ field_o S3)))) (forall ((C filter_nat) (A2 filter_nat) (B2 filter_nat)) (let ((_let_1 (@ ord_le2510731241096832064er_nat C))) (=> (@ _let_1 A2) (@ _let_1 (@ (@ sup_sup_filter_nat A2) B2))))) (forall ((I nat) (L list_P6011104703257516679at_nat) (X product_prod_nat_nat) (Y product_prod_nat_nat)) (let ((_let_1 (@ member8440522571783428010at_nat X))) (=> (@ (@ ord_less_nat I) (@ size_s5460976970255530739at_nat L)) (= (@ _let_1 (@ set_Pr5648618587558075414at_nat (@ (@ (@ list_u6180841689913720943at_nat L) I) Y))) (or (and (forall ((Y5 product_prod_nat_nat)) (@ (@ member8440522571783428010at_nat X) (@ set_Pr5648618587558075414at_nat (@ (@ (@ list_u6180841689913720943at_nat L) I) Y5)))) (@ _let_1 (@ set_Pr5648618587558075414at_nat L))) (= X Y)))))) (forall ((A set_int) (B set_int)) (=> (= (@ (@ inf_inf_set_int A) B) bot_bot_set_int) (= (@ (@ minus_minus_set_int A) B) A))) (forall ((A set_Pr4532377907799695533_nat_o) (X (-> produc3658429121746597890et_nat Bool)) (B set_Pr4532377907799695533_nat_o)) (let ((_let_1 (@ member6576561426505652726_nat_o X))) (let ((_let_2 (@ _let_1 A))) (let ((_let_3 (@ insert5175938949040314269_nat_o X))) (let ((_let_4 (@ _let_1 B))) (let ((_let_5 (@ ord_le2453136405763929_nat_o A))) (= (@ _let_5 (@ _let_3 B)) (and (=> _let_4 (@ _let_5 B)) (=> (not _let_4) (and (=> _let_2 (@ (@ ord_le2453136405763929_nat_o (@ (@ minus_1801376950450012436_nat_o A) (@ _let_3 bot_bo7824918357723582233_nat_o))) B)) (=> (not _let_2) (@ (@ ord_le2965882846123202637_nat_o A) B)))))))))))) (forall ((A2 assn) (B2 assn) (F4 (-> assn nat)) (C nat)) (=> (@ (@ ord_less_assn A2) B2) (=> (@ (@ ord_less_nat (@ F4 B2)) C) (=> (forall ((X3 assn) (Y2 assn)) (=> (@ (@ ord_less_assn X3) Y2) (@ (@ ord_less_nat (@ F4 X3)) (@ F4 Y2)))) (@ (@ ord_less_nat (@ F4 A2)) C))))) (forall ((C nat) (B2 nat) (A2 nat)) (let ((_let_1 (@ ord_less_eq_nat B2))) (=> (@ (@ ord_less_eq_nat zero_zero_nat) C) (=> (@ _let_1 A2) (@ _let_1 (@ (@ plus_plus_nat A2) C)))))) (forall ((A2 code_integer) (B2 code_integer) (C code_integer)) (let ((_let_1 (@ times_3573771949741848930nteger A2))) (= (@ _let_1 (@ (@ minus_8373710615458151222nteger B2) C)) (@ (@ minus_8373710615458151222nteger (@ _let_1 B2)) (@ _let_1 C))))) (forall ((B2 set_nat) (A2 set_nat)) (=> (@ (@ ord_less_eq_set_nat B2) A2) (= A2 (@ (@ sup_sup_set_nat A2) B2)))) (forall ((X int) (Y int)) (=> (@ (@ ord_less_int (@ (@ plus_plus_int X) Y)) zero_zero_int) (or (@ (@ ord_less_int Y) zero_zero_int) (@ (@ ord_less_int X) zero_zero_int)))) (forall ((B2 filter_nat) (A2 filter_nat) (C filter_nat)) (let ((_let_1 (@ ord_le2510731241096832064er_nat C))) (=> (@ (@ ord_le2510731241096832064er_nat B2) A2) (=> (@ _let_1 B2) (@ _let_1 A2))))) (forall ((A2 rat) (B2 rat)) (=> (@ (@ ord_less_rat A2) zero_zero_rat) (=> (@ (@ ord_less_eq_rat B2) zero_zero_rat) (@ (@ ord_less_rat (@ (@ plus_plus_rat A2) B2)) zero_zero_rat)))) (forall ((A2 code_integer) (B2 code_integer)) (= (@ (@ ord_le3102999989581377725nteger zero_z3403309356797280102nteger) (@ (@ minus_8373710615458151222nteger A2) B2)) (@ (@ ord_le3102999989581377725nteger B2) A2))) (forall ((D int) (T int) (A set_int)) (=> (@ (@ ord_less_int zero_zero_int) D) (=> (@ (@ member_int T) A) (forall ((X7 int)) (=> (forall ((Xa3 int)) (=> (@ (@ member_int Xa3) (@ (@ set_or1266510415728281911st_int one_one_int) D)) (forall ((Xb3 int)) (=> (@ (@ member_int Xb3) A) (not (= X7 (@ (@ minus_minus_int Xb3) Xa3))))))) (=> (@ (@ ord_less_int X7) T) (@ (@ ord_less_int (@ (@ plus_plus_int X7) D)) T))))))) _let_188 (forall ((A2 nat)) (= (@ (@ times_times_nat A2) one_one_nat) A2)) (forall ((A set_Pr4329608150637261639at_nat) (A2 produc3843707927480180839at_nat) (B set_Pr4329608150637261639at_nat)) (let ((_let_1 (@ insert9069300056098147895at_nat A2))) (let ((_let_2 (@ minus_3314409938677909166at_nat A))) (= (@ _let_2 (@ _let_1 B)) (@ (@ minus_3314409938677909166at_nat (@ _let_2 B)) (@ _let_1 bot_bo228742789529271731at_nat)))))) (forall ((Xs list_s1210847774152347623at_nat) (Ys list_s1210847774152347623at_nat) (R2 set_Pr4329608150637261639at_nat)) (= (@ (@ member4080735728053443344at_nat (@ (@ produc7536900900485677911at_nat Xs) Ys)) (@ listre8180072825634266816at_nat R2)) (exists ((Y5 set_Pr1261947904930325089at_nat) (N2 nat)) (and (= Ys (@ (@ (@ list_u8444657558853818831at_nat Xs) N2) Y5)) (@ (@ ord_less_nat N2) (@ size_s8736152011456118867at_nat Xs)) (@ (@ member8757157785044589968at_nat (@ (@ produc2922128104949294807at_nat (@ (@ nth_se5679702624988424552at_nat Xs) N2)) Y5)) R2))))) (forall ((X set_Pr1261947904930325089at_nat)) (= (@ (@ inf_in2572325071724192079at_nat bot_bo2099793752762293965at_nat) X) bot_bo2099793752762293965at_nat)) (= times_times_rat (lambda ((A3 rat) (B3 rat)) (@ (@ times_times_rat B3) A3))) (forall ((X int) (A2 int) (Y int) (U int) (V2 int)) (let ((_let_1 (@ ord_less_eq_int zero_zero_int))) (=> (@ (@ ord_less_int X) A2) (=> (@ (@ ord_less_int Y) A2) (=> (@ _let_1 U) (=> (@ _let_1 V2) (=> (= (@ (@ plus_plus_int U) V2) one_one_int) (@ (@ ord_less_int (@ (@ plus_plus_int (@ (@ times_times_int U) X)) (@ (@ times_times_int V2) Y))) A2)))))))) (forall ((C nat) (A set_nat) (B set_nat)) (let ((_let_1 (@ member_nat C))) (=> (@ _let_1 (@ (@ sup_sup_set_nat A) B)) (=> (not (@ _let_1 A)) (@ _let_1 B))))) (forall ((X assn)) (= (@ (@ sup_sup_assn bot_bot_assn) X) X)) (forall ((X set_Pr1261947904930325089at_nat)) (= (@ (@ inf_in2572325071724192079at_nat X) X) X)) (forall ((A set_nat)) (=> (forall ((A4 nat) (B4 nat)) (=> (@ (@ member_nat A4) A) (=> (@ (@ member_nat B4) A) (@ (@ member_nat (@ (@ gcd_gcd_nat A4) B4)) A)))) (=> (not (= A bot_bot_set_nat)) (@ (@ member_nat (@ gcd_Gcd_nat A)) A)))) (forall ((P (-> product_prod_nat_nat Bool)) (Q (-> product_prod_nat_nat Bool))) (=> (forall ((X3 product_prod_nat_nat)) (= (@ P X3) (@ Q X3))) (= (@ collec3392354462482085612at_nat P) (@ collec3392354462482085612at_nat Q)))) (forall ((A2 set_Pr1261947904930325089at_nat) (B2 set_Pr1261947904930325089at_nat) (C set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ ord_le3146513528884898305at_nat A2))) (=> (@ _let_1 (@ (@ inf_in2572325071724192079at_nat B2) C)) (not (=> (@ _let_1 B2) (not (@ _let_1 C))))))) (forall ((X nat)) (= (@ (@ removeAll_nat X) nil_nat) nil_nat)) (forall ((X set_nat) (Y set_nat) (Z set_nat)) (let ((_let_1 (@ inf_inf_set_nat X))) (let ((_let_2 (@ inf_inf_set_nat Y))) (= (@ _let_1 (@ _let_2 Z)) (@ _let_2 (@ _let_1 Z)))))) (forall ((A2 product_prod_nat_nat) (A set_Pr1261947904930325089at_nat) (B set_Pr1261947904930325089at_nat)) (= (= bot_bo2099793752762293965at_nat (@ (@ inf_in2572325071724192079at_nat (@ (@ insert8211810215607154385at_nat A2) A)) B)) (and (= bot_bo2099793752762293965at_nat (@ (@ inf_in2572325071724192079at_nat A) B)) (not (@ (@ member8440522571783428010at_nat A2) B))))) (forall ((A2 filter_nat)) (@ (@ ord_le2510731241096832064er_nat A2) A2)) (forall ((A set_Pr1261947904930325089at_nat) (B set_Pr1261947904930325089at_nat) (C2 set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ sup_su6327502436637775413at_nat A))) (= (@ _let_1 (@ (@ inf_in2572325071724192079at_nat B) C2)) (@ (@ inf_in2572325071724192079at_nat (@ _let_1 B)) (@ _let_1 C2))))) (forall ((A set_Pr1261947904930325089at_nat) (B set_Pr1261947904930325089at_nat)) (= (= (@ (@ minus_1356011639430497352at_nat A) B) bot_bo2099793752762293965at_nat) (@ (@ ord_le3146513528884898305at_nat A) B))) (forall ((A2 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((_let_1 (@ inf_in2572325071724192079at_nat C2))) (= (@ _let_1 (@ (@ minus_1356011639430497352at_nat A) B)) (@ (@ minus_1356011639430497352at_nat (@ _let_1 A)) (@ _let_1 B))))) (forall ((F4 (-> int int nat)) (A2 int) (As2 list_int) (B2 int) (Bs list_int)) (let ((_let_1 (@ zipf_int_int_nat F4))) (= (@ (@ _let_1 (@ (@ cons_int A2) As2)) (@ (@ cons_int B2) Bs)) (@ (@ cons_nat (@ (@ F4 A2) B2)) (@ (@ _let_1 As2) Bs))))) (= ord_less_eq_nat (lambda ((M nat) (N2 nat)) (or (= M N2) (@ (@ ord_less_nat M) N2)))) (forall ((I nat) (J nat) (K3 nat)) (= (@ (@ ord_less_nat I) (@ (@ minus_minus_nat J) K3)) (@ (@ ord_less_nat (@ (@ plus_plus_nat I) K3)) J))) (forall ((X int) (A set_int) (B set_int)) (let ((_let_1 (@ ord_less_eq_set_int A))) (=> (not (@ (@ member_int X) A)) (= (@ _let_1 (@ (@ insert_int2 X) B)) (@ _let_1 B))))) (forall ((B2 nat) (A2 nat) (A set_nat)) (let ((_let_1 (@ (@ insert_nat2 B2) bot_bot_set_nat))) (= (= _let_1 (@ (@ insert_nat2 A2) A)) (and (@ (@ ord_less_eq_set_nat A) _let_1) (= 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(let ((_let_1 (@ ord_less_set_nat A))) (=> (@ _let_1 B) (=> (@ (@ ord_less_eq_set_nat B) C2) (@ _let_1 C2))))) (forall ((X set_o)) (= (@ (@ inf_inf_set_o bot_bot_set_o) X) bot_bot_set_o)) (forall ((X21 Bool) (X222 list_o)) (= (@ set_o2 (@ (@ cons_o X21) X222)) (@ (@ insert_o2 X21) (@ set_o2 X222)))) (forall ((A2 produc3843707927480180839at_nat) (A set_Pr4329608150637261639at_nat)) (=> (@ (@ member8757157785044589968at_nat A2) A) (= (@ (@ insert9069300056098147895at_nat A2) A) A))) (forall ((B2 int) (A2 int) (C int)) (let ((_let_1 (@ minus_minus_int C))) (=> (@ (@ ord_less_eq_int B2) A2) (@ (@ ord_less_eq_int (@ _let_1 A2)) (@ _let_1 B2))))) (forall ((A2 (-> produc8551481072490612790e_term option6357759511663192854e_term)) (B2 product_prod_int_int) (S set_Pr9222295170931077689nt_int) (P (-> (-> produc8551481072490612790e_term option6357759511663192854e_term) product_prod_int_int Bool))) (let ((_let_1 (@ (@ member7618704894036264090nt_int (@ (@ produc5700946648718959541nt_int A2) B2)) S))) (=> _let_1 (=> (=> _let_1 (@ (@ P A2) B2)) (exists ((A4 (-> produc8551481072490612790e_term option6357759511663192854e_term)) (B4 product_prod_int_int)) (and (@ (@ P A4) B4) (@ (@ member7618704894036264090nt_int (@ (@ produc5700946648718959541nt_int A4) B4)) S))))))) (forall ((B2 int) (C int) (A2 int)) (=> (@ (@ ord_less_eq_int B2) C) (@ (@ ord_less_eq_int (@ (@ inf_inf_int A2) B2)) C))) (forall ((X produc6271795597528267376eger_o) (Y produc6271795597528267376eger_o)) (= (@ (@ (@ if_Pro5737122678794959658eger_o false) X) Y) Y)) (forall ((P (-> num Bool)) (P3 (-> num Bool)) (Q (-> num Bool)) (Q3 (-> num Bool))) (=> (exists ((Z3 num)) (forall ((X3 num)) (=> (@ (@ ord_less_num X3) Z3) (= (@ P X3) (@ P3 X3))))) (=> (exists ((Z3 num)) (forall ((X3 num)) (=> (@ (@ ord_less_num X3) Z3) (= (@ Q X3) (@ Q3 X3))))) (exists ((Z4 num)) (forall ((X7 num)) (=> (@ (@ ord_less_num X7) Z4) (= (and (@ Q X7) (@ P X7)) (and (@ P3 X7) (@ Q3 X7))))))))) (forall ((A2 nat) (B2 nat) (R2 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(=> (@ P X3) (@ P (@ (@ minus_minus_int X3) D))))) (=> (forall ((X3 int)) (=> (forall ((Xa2 int)) (=> (@ (@ member_int Xa2) (@ (@ set_or1266510415728281911st_int one_one_int) D)) (forall ((Xb2 int)) (=> (@ (@ member_int Xb2) B) (not (= X3 (@ (@ plus_plus_int Xb2) Xa2))))))) (=> (@ Q X3) (@ Q (@ (@ minus_minus_int X3) D))))) (forall ((X7 int)) (let ((_let_1 (@ (@ minus_minus_int X7) D))) (=> (forall ((Xa3 int)) (=> (@ (@ member_int Xa3) (@ (@ set_or1266510415728281911st_int one_one_int) D)) (forall ((Xb3 int)) (=> (@ (@ member_int Xb3) B) (not (= X7 (@ (@ plus_plus_int Xb3) Xa3))))))) (=> (or (@ Q X7) (@ P X7)) (or (@ Q _let_1) (@ P _let_1))))))))) (forall ((A2 nat) (F4 (-> int nat)) (B2 int) (C int)) (let ((_let_1 (@ ord_less_eq_nat A2))) (=> (@ _let_1 (@ F4 B2)) (=> (@ (@ ord_less_eq_int B2) C) (=> (forall ((X3 int) (Y2 int)) (=> (@ (@ ord_less_eq_int X3) Y2) (@ (@ ord_less_eq_nat (@ F4 X3)) (@ F4 Y2)))) (@ _let_1 (@ F4 C))))))) (forall ((Xs list_Code_integer) (Ys list_Code_integer)) (let ((_let_1 (@ sorted710888440204495920nteger ord_le6747313008572928689nteger))) (=> (@ _let_1 Xs) (=> (@ _let_1 Ys) (=> (= (@ set_Code_integer2 Ys) (@ set_Code_integer2 Xs)) (= Ys Xs)))))) (forall ((A2 int) (B2 int)) (=> (@ (@ ord_less_eq_int A2) B2) (=> (not (= A2 B2)) (@ (@ ord_less_int A2) B2)))) (forall ((N nat) (Xs list_int)) (let ((_let_1 (@ size_size_list_int Xs))) (=> (@ (@ ord_less_nat N) _let_1) (= (@ (@ nth_int (@ rev_int Xs)) N) (@ (@ nth_int Xs) (@ (@ minus_minus_nat _let_1) (@ suc N))))))) (forall ((M2 nat) (Xs list_d) (N nat)) (=> (@ (@ ord_less_nat M2) (@ size_size_list_d Xs)) (= (@ (@ nth_Pr2476257094299001567_nat_d (@ (@ enumerate_d N) Xs)) M2) (@ (@ product_Pair_nat_d (@ (@ plus_plus_nat N) M2)) (@ (@ nth_d Xs) M2))))) (forall ((I nat) (Xs list_int) (X int)) (=> (@ (@ ord_less_nat I) (@ size_size_list_int Xs)) (= (@ (@ nth_int (@ (@ (@ list_update_int Xs) I) X)) I) X))) (forall ((F4 (-> assn assn assn)) (X assn) (Y assn)) (=> (forall ((X3 assn) (Y2 assn)) (@ (@ 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(B3 int)) (@ (@ plus_plus_int B3) A3))) (forall ((I Bool) (J Bool) (R set_Product_prod_o_o)) (=> (@ (@ member7466972457876170832od_o_o (@ (@ product_Pair_o_o I) J)) R) (@ (@ member_o I) (@ field_o R)))) (forall ((A set_nat)) (= (@ (@ inf_inf_set_nat A) bot_bot_set_nat) bot_bot_set_nat)) (forall ((A set_Pr4329608150637261639at_nat) (B set_Pr4329608150637261639at_nat) (P (-> produc3843707927480180839at_nat Bool))) (= (forall ((X2 produc3843707927480180839at_nat)) (=> (@ (@ member8757157785044589968at_nat X2) (@ (@ sup_su5525570899277871387at_nat A) B)) (@ P X2))) (and (forall ((X2 produc3843707927480180839at_nat)) (=> (@ (@ member8757157785044589968at_nat X2) A) (@ P X2))) (forall ((X2 produc3843707927480180839at_nat)) (=> (@ (@ member8757157785044589968at_nat X2) B) (@ P X2)))))) (forall ((I nat) (Xs list_d) (J nat)) (let ((_let_1 (@ nth_d Xs))) (let ((_let_2 (@ size_size_list_d Xs))) (=> (@ (@ ord_less_nat I) _let_2) (=> (@ (@ ord_less_nat J) _let_2) (= (@ distinct_d (@ (@ (@ 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(not (=> _let_2 (=> (exists ((V3 int) (Va list_int)) (= Xb (@ (@ cons_int V3) Va))) _let_1))))))))))) (forall ((N nat) (X int) (Xs list_int)) (let ((_let_1 (@ (@ nth_int (@ (@ cons_int X) Xs)) N))) (let ((_let_2 (= N zero_zero_nat))) (and (=> _let_2 (= _let_1 X)) (=> (not _let_2) (= _let_1 (@ (@ nth_int Xs) (@ (@ minus_minus_nat N) one_one_nat)))))))) (forall ((Xs list_int) (Y produc6575502325842934193n_assn) (Ys list_P8527749157015355191n_assn) (R2 set_Pr3255386646789011632n_assn)) (=> (@ (@ member490958779117458567n_assn (@ (@ produc4510294837168919970n_assn Xs) (@ (@ cons_P2971678138204555879n_assn Y) Ys))) (@ listre4888949683985722578n_assn R2)) (not (forall ((X3 int) (Xs2 list_int)) (=> (= Xs (@ (@ cons_int X3) Xs2)) (=> (@ (@ member241480614033477777n_assn (@ (@ produc3313821056773121708n_assn X3) Y)) R2) (not (@ (@ member490958779117458567n_assn (@ (@ produc4510294837168919970n_assn Xs2) Ys)) (@ listre4888949683985722578n_assn R2))))))))) (forall ((A set_int)) (= (@ (@ 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S))))))) (forall ((X nat) (Y nat) (Z nat)) (=> (@ (@ ord_less_eq_nat X) Y) (=> (@ (@ ord_less_nat Y) Z) (@ (@ ord_less_nat X) Z)))) (= (@ rev_Pr4855572775806611735n_assn nil_Pr5671120429643327159n_assn) nil_Pr5671120429643327159n_assn) (forall ((A2 nat) (C nat) (B2 nat)) (let ((_let_1 (@ minus_minus_nat A2))) (= (@ (@ minus_minus_nat (@ _let_1 C)) B2) (@ (@ minus_minus_nat (@ _let_1 B2)) C)))) (forall ((D int) (A set_int) (P (-> int Bool)) (Q (-> int Bool))) (=> (forall ((X3 int)) (=> (forall ((Xa2 int)) (=> (@ (@ member_int Xa2) (@ (@ set_or1266510415728281911st_int one_one_int) D)) (forall ((Xb2 int)) (=> (@ (@ member_int Xb2) A) (not (= X3 (@ (@ minus_minus_int Xb2) Xa2))))))) (=> (@ P X3) (@ P (@ (@ plus_plus_int X3) D))))) (=> (forall ((X3 int)) (=> (forall ((Xa2 int)) (=> (@ (@ member_int Xa2) (@ (@ set_or1266510415728281911st_int one_one_int) D)) (forall ((Xb2 int)) (=> (@ (@ member_int Xb2) A) (not (= X3 (@ (@ minus_minus_int Xb2) Xa2))))))) (=> (@ Q X3) (@ Q (@ (@ 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(=> (@ (@ ord_le3146513528884898305at_nat B) A) (= (@ (@ inf_in2572325071724192079at_nat A) B) B))) (forall ((A2 rat)) (= (@ (@ ord_less_rat (@ (@ plus_plus_rat A2) A2)) zero_zero_rat) (@ (@ ord_less_rat A2) zero_zero_rat))) (forall ((X int) (Xs list_int) (I nat) (Y int)) (let ((_let_1 (@ cons_int X))) (= (@ (@ (@ list_update_int (@ _let_1 Xs)) (@ suc I)) Y) (@ _let_1 (@ (@ (@ list_update_int Xs) I) Y))))) (forall ((N nat) (P (-> nat Bool))) (= (exists ((M nat)) (and (@ P M) (@ (@ ord_less_nat M) N))) (exists ((X2 nat)) (and (@ P X2) (@ (@ member_nat X2) (@ (@ set_or4665077453230672383an_nat zero_zero_nat) N)))))) (forall ((P (-> list_int list_P8527749157015355191n_assn Bool)) (Xs list_int) (Ys list_P8527749157015355191n_assn)) (=> (@ (@ P nil_int) nil_Pr5671120429643327159n_assn) (=> (forall ((X3 int) (Xs2 list_int)) (@ (@ P (@ (@ cons_int X3) Xs2)) nil_Pr5671120429643327159n_assn)) (=> (forall ((Y2 produc6575502325842934193n_assn) (Ys5 list_P8527749157015355191n_assn)) (@ (@ P 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(@ member8757157785044589968at_nat Y) S) (=> (not (= X Y)) (@ (@ R X) Y)))))) (forall ((L list_nat)) (let ((_let_1 (@ merges1656613366846331073ps_nat L))) (and (@ distinct_nat _let_1) (= (@ set_nat2 _let_1) (@ set_nat2 L)) (@ (@ sorted_wrt_nat ord_less_eq_nat) _let_1)))) (forall ((C code_integer) (A2 code_integer)) (= (@ (@ ord_le6747313008572928689nteger (@ (@ times_3573771949741848930nteger C) A2)) C) (and (=> (@ (@ ord_le3102999989581377725nteger zero_z3403309356797280102nteger) C) (@ (@ ord_le6747313008572928689nteger A2) one_one_Code_integer)) (=> (@ (@ ord_le3102999989581377725nteger C) zero_z3403309356797280102nteger) (@ (@ ord_le6747313008572928689nteger one_one_Code_integer) A2))))) (= ord_less_int (lambda ((A3 int) (B3 int)) (and (@ (@ ord_less_eq_int A3) B3) (not (@ (@ ord_less_eq_int B3) A3))))) (forall ((A2 rat) (B2 rat) (C rat)) (= (= (@ (@ minus_minus_rat A2) B2) C) (= A2 (@ (@ plus_plus_rat C) B2)))) (forall ((L list_d) (Li list_d) (A (-> d d assn))) (=> (not (= (@ 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D2) (@ (@ ord_less_nat (@ (@ plus_plus_nat A2) C)) (@ (@ plus_plus_nat B2) D2))))) _let_179 (forall ((I nat) (Xs list_int)) (= (@ (@ (@ slice_int I) I) Xs) nil_int)) (forall ((X int) (Y int)) (=> (not (= X Y)) (=> (not (@ (@ ord_less_int X) Y)) (@ (@ ord_less_int Y) X)))) (forall ((X int) (Y int)) (@ (@ ord_less_eq_int X) (@ (@ sup_sup_int X) Y))) (forall ((A2 multis2468970476368604999at_nat) (B2 multis2468970476368604999at_nat)) (= (= (@ (@ plus_p7104986032573967614at_nat A2) B2) A2) (= B2 zero_z1048942125864253310at_nat))) (forall ((A2 set_nat)) (= (not (= A2 bot_bot_set_nat)) (@ (@ ord_less_set_nat bot_bot_set_nat) A2))) (forall ((A2 int) (B2 int)) (@ (@ ord_less_eq_int A2) (@ (@ sup_sup_int A2) B2))) (forall ((X produc3843707927480180839at_nat) (Y produc3843707927480180839at_nat) (A set_Pr4329608150637261639at_nat)) (let ((_let_1 (@ insert9069300056098147895at_nat X))) (let ((_let_2 (@ insert9069300056098147895at_nat Y))) (= (@ _let_1 (@ _let_2 A)) (@ _let_2 (@ _let_1 A)))))) (forall ((A2 nat) (B2 nat) (C nat)) (let ((_let_1 (@ times_times_nat C))) (=> (@ (@ ord_less_nat A2) B2) (=> (@ (@ ord_less_nat zero_zero_nat) C) (@ (@ ord_less_nat (@ _let_1 A2)) (@ _let_1 B2)))))) (forall ((C produc3843707927480180839at_nat) (B set_Pr4329608150637261639at_nat) (A set_Pr4329608150637261639at_nat)) (let ((_let_1 (@ member8757157785044589968at_nat C))) (=> (@ _let_1 B) (@ _let_1 (@ (@ sup_su5525570899277871387at_nat A) B))))) (forall ((B2 num) (A2 num) (C num)) (=> (@ (@ ord_less_num B2) A2) (=> (@ (@ ord_less_eq_num C) B2) (@ (@ ord_less_num C) A2)))) (forall ((A2 assn) (B2 assn) (C assn)) (let ((_let_1 (@ times_times_assn A2))) (= (@ (@ times_times_assn (@ _let_1 B2)) C) (@ _let_1 (@ (@ times_times_assn B2) C))))) (forall ((A2 nat) (B2 nat) (S3 nat) (T nat)) (=> (@ (@ ord_less_nat A2) B2) (@ (@ member8206827879206165904at_nat (@ (@ produc6161850002892822231at_nat (@ (@ product_Pair_nat_nat A2) S3)) (@ (@ product_Pair_nat_nat B2) T))) fun_pair_less))) (forall ((A2 rat) 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ord_less_eq_int) L) (@ distinct_int L)))) _let_178 (forall ((A2 int) (B2 int)) (=> (not (= A2 zero_zero_int)) (=> (not (= B2 zero_zero_int)) (not (= (@ (@ times_times_int A2) B2) zero_zero_int))))) (forall ((L12 list_nat) (L23 list_nat)) (let ((_let_1 (@ (@ merge_nat L12) L23))) (let ((_let_2 (@ sorted_wrt_nat ord_less_eq_nat))) (=> (and (@ _let_2 L12) (@ distinct_nat L12)) (=> (and (@ _let_2 L23) (@ distinct_nat L23)) (and (@ distinct_nat _let_1) (@ _let_2 _let_1) (= (@ set_nat2 _let_1) (@ (@ sup_sup_set_nat (@ set_nat2 L12)) (@ set_nat2 L23))))))))) (forall ((B2 set_Pr1261947904930325089at_nat) (A2 set_Pr1261947904930325089at_nat)) (=> (@ (@ ord_le3146513528884898305at_nat B2) A2) (= (@ (@ inf_in2572325071724192079at_nat A2) B2) B2))) (forall ((P assn)) (@ (@ entails P) top_top_assn)) (forall ((T int)) (exists ((Z4 int)) (forall ((X7 int)) (=> (@ (@ ord_less_int X7) Z4) (not (@ (@ ord_less_eq_int T) X7)))))) (forall ((A assn) (B assn) (C2 assn)) (let ((_let_1 (@ entailst A))) (=> (@ 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(forall ((X_1 list_P8527749157015355191n_assn)) (@ (@ P nil_int) X_1)) (=> (forall ((X3 int) (Xs2 list_int) (Y2 produc6575502325842934193n_assn) (Ys5 list_P8527749157015355191n_assn)) (let ((_let_1 (@ (@ cons_P2971678138204555879n_assn Y2) Ys5))) (=> (@ (@ R X3) Y2) (=> (@ (@ P Xs2) _let_1) (@ (@ P (@ (@ cons_int X3) Xs2)) _let_1))))) (=> (forall ((X3 int) (Xs2 list_int) (Y2 produc6575502325842934193n_assn) (Ys5 list_P8527749157015355191n_assn)) (let ((_let_1 (@ P (@ (@ cons_int X3) Xs2)))) (=> (not (@ (@ R X3) Y2)) (=> (@ _let_1 Ys5) (@ _let_1 (@ (@ cons_P2971678138204555879n_assn Y2) Ys5)))))) (@ (@ P Xs) Ys)))))) (@ _let_1 (@ (@ plus_plus_rat one_one_rat) one_one_rat)) (= sup_sup_set_nat (lambda ((A3 set_nat) (B3 set_nat)) (@ (@ sup_sup_set_nat B3) A3))) (forall ((C nat) (A2 nat) (B2 nat)) (let ((_let_1 (@ ord_less_eq_nat C))) (=> (@ _let_1 A2) (@ _let_1 (@ (@ sup_sup_nat A2) B2))))) (= ord_less_eq_int (lambda ((B3 int) (A3 int)) (= (@ (@ sup_sup_int A3) B3) A3))) (forall ((X (-> 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list_P8527749157015355191n_assn) (Y assn)) (let ((_let_1 (not (= Y bot_bot_assn)))) (let ((_let_2 (= Xa nil_int))) (let ((_let_3 (= Xb nil_Pr5671120429643327159n_assn))) (=> (= (@ (@ (@ vEBT_L1620274777744359680n_assn X) Xa) Xb) Y) (=> (=> _let_2 (=> _let_3 (not (= Y one_one_assn)))) (=> (forall ((A4 int) (As list_int)) (=> (= Xa (@ (@ cons_int A4) As)) (forall ((C4 produc6575502325842934193n_assn) (Cs2 list_P8527749157015355191n_assn)) (=> (= Xb (@ (@ cons_P2971678138204555879n_assn C4) Cs2)) (not (= Y (@ (@ times_times_assn (@ (@ X A4) C4)) (@ (@ (@ vEBT_L1620274777744359680n_assn X) As) Cs2)))))))) (=> (=> (exists ((V3 int) (Va list_int)) (= Xa (@ (@ cons_int V3) Va))) (=> _let_3 _let_1)) (not (=> _let_2 (=> (exists ((V3 produc6575502325842934193n_assn) (Va list_P8527749157015355191n_assn)) (= Xb (@ (@ cons_P2971678138204555879n_assn V3) Va))) _let_1))))))))))) (forall ((N nat) (M2 nat)) (=> (@ (@ ord_less_nat zero_zero_nat) N) (= (@ (@ gcd_gcd_nat M2) N) (@ lattic8265883725875713057ax_nat (@ collect_nat (lambda ((D5 nat)) (let ((_let_1 (@ dvd_dvd_nat D5))) (and (@ _let_1 M2) (@ _let_1 N))))))))) (forall ((N nat) (P (-> nat Bool))) (= (forall ((M nat)) (=> (@ (@ ord_less_eq_nat M) N) (@ P M))) (forall ((X2 nat)) (=> (@ (@ member_nat X2) (@ (@ set_or1269000886237332187st_nat zero_zero_nat) N)) (@ P X2))))) (forall ((Y set_nat) (X set_nat)) (=> (@ (@ ord_less_eq_set_nat Y) X) (not (@ (@ ord_less_set_nat X) Y)))) (forall ((A assn) (B assn) (C2 assn)) (= (@ (@ times_times_assn (@ (@ sup_sup_assn A) B)) C2) (@ (@ sup_sup_assn (@ (@ times_times_assn A) C2)) (@ (@ times_times_assn B) C2)))) (forall ((A2 set_Pr4329608150637261639at_nat)) (not (@ (@ ord_le2604355607129572851at_nat A2) bot_bo228742789529271731at_nat))) (forall ((A2 assn) (B2 assn)) (= (= bot_bot_assn (@ (@ sup_sup_assn A2) B2)) (and (= B2 bot_bot_assn) (= A2 bot_bot_assn)))) (forall ((X produc7773217078559923341nt_int)) (not (forall ((F5 (-> int option6357759511663192854e_term)) (D3 int) (I5 int)) (not (= X (@ (@ produc4305682042979456191nt_int F5) (@ (@ product_Pair_int_int D3) I5))))))) (forall ((Xs list_P8527749157015355191n_assn) (Ys list_int)) (= (= (@ (@ zip_Pr1015554993053626726sn_int Xs) Ys) nil_Pr7991254345159696774sn_int) (or (= Ys nil_int) (= Xs nil_Pr5671120429643327159n_assn)))) (forall ((A2 assn) (F4 (-> int assn)) (B2 int) (C int)) (=> (= A2 (@ F4 B2)) (=> (@ (@ ord_less_eq_int B2) C) (=> (forall ((X3 int) (Y2 int)) (=> (@ (@ ord_less_eq_int X3) Y2) (@ (@ ord_less_eq_assn (@ F4 X3)) (@ F4 Y2)))) (@ (@ ord_less_eq_assn A2) (@ F4 C)))))) (forall ((Xs list_int)) (= (@ set_int2 (@ rotate1_int Xs)) (@ set_int2 Xs))) (forall ((B2 num) (A2 num)) (=> (@ (@ ord_less_num B2) A2) (= (@ (@ ord_min_num A2) B2) B2))) (forall ((Xs list_P8527749157015355191n_assn)) (= (= (@ set_Pr1139785259514867910n_assn Xs) bot_bo1176836662018730877n_assn) (= Xs nil_Pr5671120429643327159n_assn))) (forall ((C2 set_Pr1261947904930325089at_nat) (A set_Pr1261947904930325089at_nat) (B set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ ord_le3146513528884898305at_nat C2))) (= (@ _let_1 (@ (@ inf_in2572325071724192079at_nat A) B)) (and (@ _let_1 B) (@ _let_1 A))))) (forall ((X nat) (Y produc6575502325842934193n_assn) (R2 set_Pr247834672394327052n_assn) (Xs list_nat) (Ys list_P8527749157015355191n_assn)) (let ((_let_1 (@ listre3128913020232611374n_assn R2))) (=> (@ (@ member7704815987135142381n_assn (@ (@ produc1553784393020010504n_assn X) Y)) R2) (=> (@ (@ member3687432546746012131n_assn (@ (@ produc7706768604797473534n_assn Xs) Ys)) _let_1) (@ (@ member3687432546746012131n_assn (@ (@ produc7706768604797473534n_assn (@ (@ cons_nat X) Xs)) (@ (@ cons_P2971678138204555879n_assn Y) Ys))) _let_1))))) (forall ((A2 Bool) (B set_o) (B2 Bool)) (let ((_let_1 (@ member_o A2))) (=> (@ _let_1 B) (@ _let_1 (@ (@ insert_o2 B2) B))))) (forall ((C rat) (A2 rat) (B2 rat)) (let ((_let_1 (@ plus_plus_rat C))) (=> (@ (@ ord_less_eq_rat (@ _let_1 A2)) (@ _let_1 B2)) (@ (@ ord_less_eq_rat A2) B2)))) (forall ((A2 nat) (B2 nat)) (@ (@ ord_less_eq_nat A2) (@ (@ sup_sup_nat A2) B2))) (forall ((N nat) (Xs list_nat)) (let ((_let_1 (@ butlast_nat Xs))) (=> (@ (@ ord_less_nat N) (@ size_size_list_nat _let_1)) (= (@ (@ nth_nat _let_1) N) (@ (@ nth_nat Xs) N))))) (forall ((A set_o) (A2 Bool) (B set_o)) (let ((_let_1 (@ sup_sup_set_o A))) (let ((_let_2 (@ insert_o2 A2))) (= (@ _let_1 (@ _let_2 B)) (@ _let_2 (@ _let_1 B)))))) (forall ((F4 (-> nat nat)) (M2 nat) (K3 nat)) (=> (forall ((M6 nat) (N5 nat)) (=> (@ (@ ord_less_nat M6) N5) (@ (@ ord_less_nat (@ F4 M6)) (@ F4 N5)))) (@ (@ ord_less_eq_nat (@ (@ plus_plus_nat (@ F4 M2)) K3)) (@ F4 (@ (@ plus_plus_nat M2) K3))))) (forall ((Xs list_P5464809261938338413at_nat) (N nat) (X produc3843707927480180839at_nat)) (=> (@ distin5355857245021852384at_nat Xs) (=> (@ (@ ord_less_nat N) (@ size_s1588839187904960729at_nat Xs)) (= (@ set_Pr3765526544606949372at_nat (@ (@ (@ list_u4696772448584712917at_nat Xs) N) X)) (@ (@ insert9069300056098147895at_nat X) (@ (@ minus_3314409938677909166at_nat (@ set_Pr3765526544606949372at_nat Xs)) (@ (@ insert9069300056098147895at_nat (@ (@ nth_Pr1239524528086697198at_nat Xs) N)) bot_bo228742789529271731at_nat))))))) (forall ((Xs list_d) (X d)) (=> (@ distinct_d Xs) (=> (@ (@ member_d X) (@ set_d2 Xs)) (exists ((X3 nat)) (and (= (@ (@ nth_d Xs) X3) X) (forall ((Y3 nat)) (=> (and (@ (@ ord_less_nat Y3) (@ size_size_list_d Xs)) (= (@ (@ nth_d Xs) Y3) X)) (= Y3 X3))) (@ (@ ord_less_nat X3) (@ size_size_list_d Xs))))))) (forall ((X product_prod_nat_nat) (Y product_prod_nat_nat) (A set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ insert8211810215607154385at_nat X))) (let ((_let_2 (@ insert8211810215607154385at_nat Y))) (= (@ _let_1 (@ _let_2 A)) (@ _let_2 (@ _let_1 A)))))) (forall ((C set_Pr4329608150637261639at_nat) (B2 set_Pr4329608150637261639at_nat) (A2 set_Pr4329608150637261639at_nat)) (let ((_let_1 (@ ord_le2604355607129572851at_nat C))) (=> (@ _let_1 B2) (@ _let_1 (@ (@ sup_su5525570899277871387at_nat A2) B2))))) (forall ((Xs list_P8527749157015355191n_assn) (Y produc6575502325842934193n_assn) (Ys list_P8527749157015355191n_assn) (R2 set_Pr8116311503512020807n_assn)) (=> (@ (@ member3994142547374651152n_assn (@ (@ produc3014731801419794263n_assn Xs) (@ (@ cons_P2971678138204555879n_assn Y) Ys))) (@ listre4270255209692100112n_assn R2)) (=> (forall ((X3 produc6575502325842934193n_assn)) (=> (= Xs (@ (@ cons_P2971678138204555879n_assn X3) Ys)) (not (@ (@ member4743710847862083984n_assn (@ (@ produc6128706242671166167n_assn X3) Y)) R2)))) (not (forall ((Zs2 list_P8527749157015355191n_assn)) (=> (= Xs (@ (@ cons_P2971678138204555879n_assn Y) Zs2)) (not (@ (@ member3994142547374651152n_assn (@ (@ produc3014731801419794263n_assn Zs2) Ys)) (@ listre4270255209692100112n_assn R2))))))))) (forall ((L list_c) (Li list_c) (A (-> c c assn))) (=> (not (= (@ size_size_list_c L) (@ size_size_list_c Li))) (= (@ (@ (@ vEBT_L7968352277243653187sn_c_c A) L) Li) bot_bot_assn))) (@ (@ pcr_rat _let_4) zero_zero_rat) (forall ((X nat) (Y nat)) (=> (@ (@ ord_less_eq_nat X) Y) (or (@ (@ ord_less_nat X) Y) (= X Y)))) (forall ((P (-> product_prod_nat_nat Bool)) (Q (-> product_prod_nat_nat Bool))) (=> (forall ((X3 product_prod_nat_nat)) (=> (@ P X3) (@ Q X3))) (@ (@ ord_le3146513528884898305at_nat (@ collec3392354462482085612at_nat P)) (@ collec3392354462482085612at_nat Q)))) (forall ((Xs list_d) (Ys list_d)) (=> (= (@ size_size_list_d Xs) (@ size_size_list_d Ys)) (=> (forall ((I5 nat)) (=> (@ (@ ord_less_nat I5) (@ size_size_list_d Xs)) (= (@ (@ nth_d Xs) I5) (@ (@ nth_d Ys) I5)))) (= Xs Ys)))) (forall ((S set_Pr4329608150637261639at_nat) (T3 set_Pr4329608150637261639at_nat)) (= (@ (@ sup_su5525570899277871387at_nat (@ (@ inf_in7913087082777306421at_nat S) T3)) S) S)) (@ (@ (@ filterlim_nat_nat suc) at_top_nat) at_top_nat) (forall ((X produc6575502325842934193n_assn) (Xs list_P8527749157015355191n_assn)) (let ((_let_1 (@ (@ cons_P2971678138204555879n_assn X) nil_Pr5671120429643327159n_assn))) (= (= _let_1 (@ rev_Pr4855572775806611735n_assn Xs)) (= _let_1 Xs)))) (forall ((A2 nat) (A set_nat)) (=> (@ (@ member_nat A2) A) (exists ((B5 set_nat)) (and (not (@ (@ member_nat A2) B5)) (= A (@ (@ insert_nat2 A2) B5)))))) (forall ((A2 assn)) (= (@ (@ sup_sup_assn A2) bot_bot_assn) A2)) (forall ((A assn)) (@ (@ entailst A) one_one_assn)) (forall ((K3 nat) (M2 nat) (N nat)) (let ((_let_1 (@ times_times_nat K3))) (=> (@ (@ ord_less_nat zero_zero_nat) K3) (= (@ (@ ord_less_eq_nat (@ _let_1 M2)) (@ _let_1 N)) (@ (@ ord_less_eq_nat M2) N))))) (forall ((X int) (B set_int) (A set_int)) (let ((_let_1 (@ (@ minus_minus_set_int A) B))) (let ((_let_2 (@ insert_int2 X))) (let ((_let_3 (@ (@ minus_minus_set_int (@ _let_2 A)) B))) (let ((_let_4 (@ (@ member_int X) B))) (and (=> (not _let_4) (= _let_3 (@ _let_2 _let_1))) (=> _let_4 (= _let_3 _let_1)))))))) (forall ((I product_prod_nat_nat) (J product_prod_nat_nat) (R set_Pr8693737435421807431at_nat)) (=> (@ (@ member8206827879206165904at_nat (@ (@ produc6161850002892822231at_nat I) J)) R) (@ (@ member8440522571783428010at_nat I) (@ field_4706345496283612622at_nat R)))) (forall ((C produc3843707927480180839at_nat) (A set_Pr4329608150637261639at_nat) (B set_Pr4329608150637261639at_nat)) (let ((_let_1 (@ member8757157785044589968at_nat C))) (=> (@ _let_1 (@ (@ inf_in7913087082777306421at_nat A) B)) (not (=> (@ _let_1 A) (not (@ _let_1 B))))))) (forall ((Xs list_nat) (A2 nat)) (let ((_let_1 (@ sorted_wrt_nat ord_less_eq_nat))) (=> (@ _let_1 Xs) (@ _let_1 (@ (@ remove1_nat A2) Xs))))) (forall ((Xs list_P7985473006766602707_nat_o) (P (-> (-> produc3658429121746597890et_nat Bool) (-> produc3658429121746597890et_nat Bool) Bool)) (Q (-> (-> produc3658429121746597890et_nat Bool) (-> produc3658429121746597890et_nat Bool) Bool))) (=> (forall ((X3 (-> produc3658429121746597890et_nat Bool)) (Y2 (-> produc3658429121746597890et_nat Bool))) (let ((_let_1 (@ set_Pr400311997697478754_nat_o Xs))) (=> (@ (@ member6576561426505652726_nat_o X3) _let_1) (=> (@ (@ member6576561426505652726_nat_o Y2) _let_1) (=> (@ (@ P X3) Y2) (@ (@ Q X3) Y2)))))) (=> (@ (@ sorted9199660237762088378_nat_o P) Xs) (@ (@ sorted9199660237762088378_nat_o Q) Xs)))) (forall ((I nat) (J nat) (R set_Pr1261947904930325089at_nat)) (=> (@ (@ member8440522571783428010at_nat (@ (@ product_Pair_nat_nat I) J)) R) (@ (@ member_nat J) (@ field_nat R)))) (forall ((Xs list_int) (N nat)) (= (= (@ size_size_list_int Xs) (@ suc N)) (exists ((Y5 int) (Ys3 list_int)) (and (= (@ size_size_list_int Ys3) N) (= Xs (@ (@ cons_int Y5) Ys3)))))) (forall ((K3 nat)) (let ((_let_1 (@ suc K3))) (= (@ linord2614967742042102400et_nat (@ set_ord_atMost_nat _let_1)) (@ (@ append_nat (@ linord2614967742042102400et_nat (@ set_ord_atMost_nat K3))) (@ (@ cons_nat _let_1) nil_nat))))) (forall ((Xs list_nat) (X nat)) (let ((_let_1 (@ (@ cons_nat X) nil_nat))) (= (= (@ rev_nat Xs) _let_1) (= Xs _let_1)))) (forall ((A2 int) (B2 int) (C int)) (let ((_let_1 (@ ord_less_eq_int A2))) (=> (@ _let_1 (@ (@ ord_min_int B2) C)) (not (=> (@ _let_1 B2) (not (@ _let_1 C))))))) (forall ((K3 num)) (= (@ quotient_of (@ uminus_uminus_rat (@ numeral_numeral_rat K3))) (@ (@ product_Pair_int_int (@ uminus_uminus_int (@ numeral_numeral_int K3))) one_one_int))) _let_177 (forall ((A set_Pr4329608150637261639at_nat) (B set_Pr4329608150637261639at_nat)) (=> (= (@ (@ inf_in7913087082777306421at_nat A) B) bot_bo228742789529271731at_nat) (= (@ (@ minus_3314409938677909166at_nat A) B) A))) (forall ((B2 nat) (A2 nat)) (=> (@ (@ ord_less_nat B2) A2) (= (@ (@ sup_sup_nat A2) B2) A2))) (forall ((X set_Pr4329608150637261639at_nat) (Y set_Pr4329608150637261639at_nat)) (= (@ (@ sup_su5525570899277871387at_nat X) (@ (@ inf_in7913087082777306421at_nat X) Y)) X)) (forall ((X int) (Y int)) (@ (@ ord_less_eq_int X) (@ (@ sup_sup_int X) Y))) (forall ((X produc3843707927480180839at_nat) (Xs list_P5464809261938338413at_nat)) (=> (not (@ (@ member8757157785044589968at_nat X) (@ set_Pr3765526544606949372at_nat Xs))) (= (@ (@ count_1483299019173949923at_nat Xs) X) zero_zero_nat))) (forall ((X code_integer) (Y code_integer)) (let ((_let_1 (@ ord_le3102999989581377725nteger zero_z3403309356797280102nteger))) (=> (@ _let_1 X) (=> (@ _let_1 Y) (=> (@ (@ ord_le3102999989581377725nteger Y) one_one_Code_integer) (@ (@ ord_le3102999989581377725nteger (@ (@ times_3573771949741848930nteger X) Y)) X)))))) (forall ((C rat) (A2 rat) (B2 rat)) (let ((_let_1 (@ plus_plus_rat C))) (= (@ (@ ord_less_eq_rat (@ _let_1 A2)) (@ _let_1 B2)) (@ (@ ord_less_eq_rat A2) B2)))) (forall ((A2 (-> produc6241069584506657477e_term option6357759511663192854e_term)) (B2 produc8923325533196201883nteger) (S set_Pr1281608226676607948nteger) (P (-> (-> produc6241069584506657477e_term option6357759511663192854e_term) produc8923325533196201883nteger Bool))) (let ((_let_1 (@ (@ member4164122664394876845nteger (@ (@ produc8603105652947943368nteger A2) B2)) S))) (=> _let_1 (=> (=> _let_1 (@ (@ P A2) B2)) (exists ((A4 (-> produc6241069584506657477e_term option6357759511663192854e_term)) (B4 produc8923325533196201883nteger)) (and (@ (@ P A4) B4) (@ (@ member4164122664394876845nteger (@ (@ produc8603105652947943368nteger A4) B4)) S))))))) (forall ((B6 num) (A7 num)) (= (not (@ (@ ord_less_eq_num B6) A7)) (@ (@ ord_less_num A7) B6))) (forall ((N nat)) (= (@ (@ ord_less_nat zero_zero_nat) N) (exists ((M nat)) (= N (@ suc M))))) (forall ((Xs list_c)) (= (@ size_size_list_c (@ rev_c Xs)) (@ size_size_list_c Xs))) (forall ((A2 multis2468970476368604999at_nat)) (= (@ (@ plus_p7104986032573967614at_nat zero_z1048942125864253310at_nat) A2) A2)) (forall ((N nat)) (= (= (@ set_ord_lessThan_nat N) bot_bot_set_nat) (= N zero_zero_nat))) (forall ((R2 set_Pr8693737435421807431at_nat)) (@ (@ total_3592101749530773125at_nat bot_bo2099793752762293965at_nat) R2)) (forall ((Xs list_int) (P (-> int Bool))) (= (forall ((X2 int)) (=> (@ (@ member_int X2) (@ 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int)) (=> (@ (@ ord_less_int A2) B2) (not (@ (@ ord_less_int B2) A2)))) (forall ((X d) (Xs list_d) (N nat)) (=> (not (@ (@ member_d X) (@ set_d2 Xs))) (=> (@ (@ ord_less_eq_nat N) (@ size_size_list_d Xs)) (= (= (@ (@ nth_d (@ (@ cons_d X) Xs)) N) X) (= N zero_zero_nat))))) (= ord_less_nat (lambda ((A3 nat) (B3 nat)) (and (= A3 (@ (@ ord_min_nat A3) B3)) (not (= A3 B3))))) (forall ((A2 code_integer) (B2 code_integer) (C code_integer) (D2 code_integer)) (=> (@ (@ ord_le6747313008572928689nteger A2) B2) (=> (@ (@ ord_le3102999989581377725nteger C) D2) (@ (@ ord_le6747313008572928689nteger (@ (@ plus_p5714425477246183910nteger A2) C)) (@ (@ plus_p5714425477246183910nteger B2) D2))))) (forall ((X nat) (Xs list_nat)) (not (@ null_nat (@ (@ cons_nat X) Xs)))) (forall ((Q6 code_integer) (R2 code_integer)) (= (@ unique5706413561485394159nteger (@ (@ produc1086072967326762835nteger Q6) R2)) (= R2 zero_z3403309356797280102nteger))) (forall ((X assn) (Y assn) (Z assn)) (let ((_let_1 (@ inf_inf_assn X))) (= (@ (@ inf_inf_assn (@ _let_1 Y)) Z) (@ _let_1 (@ (@ inf_inf_assn Y) Z))))) (forall ((I nat) (J nat) (K3 nat) (L nat)) (=> (and (@ (@ ord_less_nat K3) L) (@ (@ ord_less_eq_nat I) J)) (@ (@ ord_less_nat (@ (@ plus_plus_nat I) K3)) (@ (@ plus_plus_nat J) L)))) (forall ((B2 set_Pr1261947904930325089at_nat) (C set_Pr1261947904930325089at_nat) (A2 set_Pr1261947904930325089at_nat)) (=> (@ (@ ord_le3146513528884898305at_nat B2) C) (@ (@ ord_le3146513528884898305at_nat (@ (@ inf_in2572325071724192079at_nat A2) B2)) C))) (forall ((Xs list_c) (Ys list_c) (R2 set_Product_prod_c_c) (N nat)) (=> (@ (@ member7012247553653173456list_c (@ (@ produc5515445818230282391list_c Xs) Ys)) (@ (@ lexn_c R2) N)) (and (= (@ size_size_list_c Xs) N) (= (@ size_size_list_c Ys) N)))) (forall ((A2 num) (B2 num)) (=> (@ (@ ord_less_eq_num A2) B2) (=> (not (= A2 B2)) (@ (@ ord_less_num A2) B2)))) (forall ((A2 rat) (B2 rat)) (=> (= (@ (@ times_times_rat A2) B2) zero_zero_rat) (or (= A2 zero_zero_rat) (= B2 zero_zero_rat)))) (forall ((X produc3843707927480180839at_nat)) (@ (@ total_1513685709984341995at_nat (@ (@ insert9069300056098147895at_nat X) bot_bo228742789529271731at_nat)) (@ (@ insert398606708087465655at_nat (@ (@ produc2335810615602371415at_nat X) X)) bot_bo7193250159860175667at_nat))) (forall ((A2 code_integer) (B2 code_integer)) (let ((_let_1 (@ ord_le6747313008572928689nteger zero_z3403309356797280102nteger))) (=> (@ _let_1 A2) (=> (@ _let_1 B2) (@ _let_1 (@ (@ times_3573771949741848930nteger A2) B2)))))) (= ord_less_nat (lambda ((B3 nat) (A3 nat)) (and (not (= A3 B3)) (@ (@ ord_less_eq_nat B3) A3)))) (forall ((X (-> produc3658429121746597890et_nat Bool)) (Xs list_P7985473006766602707_nat_o)) (= (@ distin299582740263731014_nat_o (@ (@ cons_P6219271836124797827_nat_o X) Xs)) (and (@ distin299582740263731014_nat_o Xs) (not (@ (@ member6576561426505652726_nat_o X) (@ set_Pr400311997697478754_nat_o Xs)))))) (forall ((P assn) (Q assn) (H2 heap_e7401611519738050253t_unit)) (let ((_let_1 (@ (@ produc7507926704131184380et_nat H2) bot_bot_set_nat))) (= (@ (@ rep_assn (@ (@ inf_inf_assn P) Q)) _let_1) (and (@ (@ rep_assn P) _let_1) (@ (@ rep_assn Q) _let_1))))) (forall ((H2 heap_e7401611519738050253t_unit) (As2 set_nat)) (= (@ one_assn_raw (@ (@ produc7507926704131184380et_nat H2) As2)) (= As2 bot_bot_set_nat))) (forall ((X (-> produc8551481072490612790e_term option6357759511663192854e_term)) (Y product_prod_int_int) (Xs list_P1743416141875011707e_term) (Ys list_P5707943133018811711nt_int)) (=> (@ (@ member7618704894036264090nt_int (@ (@ produc5700946648718959541nt_int X) Y)) (@ set_Pr4943052134776177454nt_int (@ (@ zip_Pr4168994715204986005nt_int Xs) Ys))) (@ (@ member3222579708246209666e_term X) (@ set_Pr16608062948090134e_term Xs)))) (forall ((A2 int) (B2 int) (C int)) (let ((_let_1 (@ ord_less_eq_int A2))) (= (@ _let_1 (@ (@ inf_inf_int B2) C)) (and (@ _let_1 C) (@ _let_1 B2))))) (forall ((X num) (Y num)) (=> (@ (@ ord_less_num X) Y) (not (= X Y)))) (forall ((X nat) (Y nat)) (=> (@ (@ ord_less_eq_nat X) Y) (=> (@ (@ ord_less_eq_nat Y) X) (= X Y)))) (forall ((A set_Pr1261947904930325089at_nat) (R2 set_Pr8693737435421807431at_nat)) (=> (forall ((X3 product_prod_nat_nat) (Y2 product_prod_nat_nat)) (=> (@ (@ member8440522571783428010at_nat X3) A) (=> (@ (@ member8440522571783428010at_nat Y2) A) (=> (not (= X3 Y2)) (or (@ (@ member8206827879206165904at_nat (@ (@ produc6161850002892822231at_nat X3) Y2)) R2) (@ (@ member8206827879206165904at_nat (@ (@ produc6161850002892822231at_nat Y2) X3)) R2)))))) (@ (@ total_3592101749530773125at_nat A) R2))) (forall ((X nat) (Y nat)) (= (= (@ (@ plus_plus_nat X) Y) zero_zero_nat) (and (= X zero_zero_nat) (= Y zero_zero_nat)))) (forall ((A2 assn) (C assn) (B2 assn) (D2 assn)) (=> (@ (@ ord_less_eq_assn A2) C) (=> (@ (@ ord_less_eq_assn B2) D2) (@ (@ ord_less_eq_assn (@ (@ sup_sup_assn A2) B2)) (@ (@ sup_sup_assn C) D2))))) (forall ((I nat) (J nat)) (=> (@ (@ ord_less_nat I) J) (= (@ (@ upt I) J) (@ (@ cons_nat I) (@ (@ upt (@ suc I)) J))))) (forall ((M5 list_P8527749157015355191n_assn)) (@ (@ (@ (@ fI_RESULT M5) one_one_assn) one_one_assn) one_one_assn)) (forall ((R2 set_Pr1261947904930325089at_nat) (X nat) (Y nat)) (=> (forall ((X3 nat)) (not (@ (@ member8440522571783428010at_nat (@ (@ product_Pair_nat_nat X3) X3)) (@ transi6264000038957366511cl_nat R2)))) (=> (@ (@ member8440522571783428010at_nat (@ (@ product_Pair_nat_nat X) Y)) R2) (not (= X Y))))) (forall ((Y set_nat) (X set_nat)) (=> (@ (@ ord_less_eq_set_nat Y) X) (= (@ (@ sup_sup_set_nat X) Y) X))) (= (lambda ((Y4 int) (Z2 int)) (= Y4 Z2)) (lambda ((A3 int) (B3 int)) (and (@ (@ ord_less_eq_int A3) B3) (@ (@ ord_less_eq_int B3) A3)))) (forall ((A2 rat)) (let ((_let_1 (@ ord_less_rat zero_zero_rat))) (= (@ _let_1 (@ (@ plus_plus_rat A2) A2)) (@ _let_1 A2)))) (forall ((T int)) (exists ((Z4 int)) (forall ((X7 int)) (=> (@ (@ ord_less_int X7) Z4) (not (@ (@ ord_less_int T) X7)))))) (forall ((N nat) (P (-> nat Bool))) (=> (@ (@ 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(@ (@ zip_int_int Xs) Ys))) (not (=> (@ (@ member_int X) (@ set_int2 Xs)) (not (@ (@ member_int Y) (@ set_int2 Ys))))))) (forall ((A multis2468970476368604999at_nat) (B multis2468970476368604999at_nat) (Z6 multis2468970476368604999at_nat)) (let ((_let_1 (@ plus_p7104986032573967614at_nat Z6))) (=> (@ (@ member8757157785044589968at_nat (@ (@ produc2922128104949294807at_nat (@ set_ms8126754132646256062at_nat A)) (@ set_ms8126754132646256062at_nat B))) fun_max_strict) (@ (@ member6689249552917799696at_nat (@ (@ produc4348348721325984599at_nat (@ _let_1 A)) (@ _let_1 B))) ms_strict)))) (forall ((K3 int) (L int) (Q6 int) (R2 int)) (let ((_let_1 (@ (@ ord_less_int zero_zero_int) L))) (let ((_let_2 (@ ord_less_int L))) (let ((_let_3 (@ _let_2 zero_zero_int))) (= (@ (@ (@ eucl_rel_int K3) L) (@ (@ product_Pair_int_int Q6) R2)) (and (=> (not _let_1) (and (=> (not _let_3) (= Q6 zero_zero_int)) (=> _let_3 (and (@ (@ ord_less_eq_int R2) zero_zero_int) (@ _let_2 R2))))) (=> _let_1 (and (@ (@ ord_less_int R2) L) (@ (@ ord_less_eq_int zero_zero_int) R2))) (= K3 (@ (@ plus_plus_int (@ (@ times_times_int L) Q6)) R2)))))))) (forall ((X int) (Y int) (A set_int)) (let ((_let_1 (@ (@ insert_int2 Y) bot_bot_set_int))) (let ((_let_2 (@ insert_int2 X))) (=> (not (= X Y)) (= (@ (@ minus_minus_set_int (@ _let_2 A)) _let_1) (@ _let_2 (@ (@ minus_minus_set_int A) _let_1))))))) (forall ((B set_Pr1261947904930325089at_nat)) (= (@ (@ inf_in2572325071724192079at_nat bot_bo2099793752762293965at_nat) B) bot_bo2099793752762293965at_nat)) (forall ((X int) (Zs list_int)) (let ((_let_1 (@ foldl_int_int times_times_int))) (= (@ (@ times_times_int X) (@ (@ _let_1 one_one_int) Zs)) (@ (@ _let_1 X) Zs)))) (forall ((A2 int) (E int) (C int) (B2 int) (D2 int)) (= (= (@ (@ plus_plus_int (@ (@ times_times_int A2) E)) C) (@ (@ plus_plus_int (@ (@ times_times_int B2) E)) D2)) (= C (@ (@ plus_plus_int (@ (@ times_times_int (@ (@ minus_minus_int B2) A2)) E)) D2)))) (forall ((X num) (Y num)) (=> (@ (@ ord_less_num X) Y) (@ (@ ord_less_eq_num X) Y))) (forall ((X (-> produc3658429121746597890et_nat Bool)) (X4 set_Pr4532377907799695533_nat_o)) (=> (not (@ (@ member6576561426505652726_nat_o X) X4)) (= (@ (@ minus_1801376950450012436_nat_o X4) (@ (@ insert5175938949040314269_nat_o X) bot_bo7824918357723582233_nat_o)) X4))) (forall ((X assn)) (@ (@ ord_less_eq_assn X) X)) (forall ((A2 (-> int option6357759511663192854e_term)) (B2 product_prod_int_int) (A7 (-> int option6357759511663192854e_term)) (B6 product_prod_int_int)) (= (= (@ (@ produc4305682042979456191nt_int A2) B2) (@ (@ produc4305682042979456191nt_int A7) B6)) (and (= B2 B6) (= A2 A7)))) (forall ((C int) (A2 int) (B2 int)) (let ((_let_1 (@ times_times_int C))) (= (@ (@ ord_less_int (@ _let_1 A2)) (@ _let_1 B2)) (and (=> (@ (@ ord_less_eq_int C) zero_zero_int) (@ (@ ord_less_int B2) A2)) (=> (@ (@ ord_less_eq_int zero_zero_int) C) (@ (@ ord_less_int A2) B2)))))) (forall ((A2 code_integer) (F4 (-> assn code_integer)) (B2 assn) (C 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(or (@ (@ member6009668390874684176at_nat (@ (@ produc2335810615602371415at_nat X3) Y2)) R2) (@ (@ member6009668390874684176at_nat (@ (@ produc2335810615602371415at_nat Y2) X3)) R2)))))) (@ (@ total_1513685709984341995at_nat A) R2))) (forall ((A2 nat) (B2 nat)) (let ((_let_1 (@ ord_less_eq_nat zero_zero_nat))) (=> (or (and (@ (@ ord_less_eq_nat A2) zero_zero_nat) (@ _let_1 B2)) (and (@ (@ ord_less_eq_nat B2) zero_zero_nat) (@ _let_1 A2))) (@ (@ ord_less_eq_nat (@ (@ times_times_nat A2) B2)) zero_zero_nat)))) (forall ((A2 code_integer) (B2 code_integer) (F4 (-> code_integer int)) (C int)) (=> (@ (@ ord_le6747313008572928689nteger A2) B2) (=> (= (@ F4 B2) C) (=> (forall ((X3 code_integer) (Y2 code_integer)) (=> (@ (@ ord_le6747313008572928689nteger X3) Y2) (@ (@ ord_less_int (@ F4 X3)) (@ F4 Y2)))) (@ (@ ord_less_int (@ F4 A2)) C))))) (forall ((A2 int) (B2 int) (C int)) (= (@ (@ plus_plus_int (@ (@ minus_minus_int A2) B2)) C) (@ (@ minus_minus_int (@ (@ plus_plus_int A2) C)) B2))) (= (@ 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(@ member8757157785044589968at_nat (@ (@ produc2922128104949294807at_nat A1) A22)) (@ transi2703068831062848130at_nat R2)) (or (exists ((A3 set_Pr1261947904930325089at_nat) (B3 set_Pr1261947904930325089at_nat)) (and (= A1 A3) (@ (@ member8757157785044589968at_nat (@ (@ produc2922128104949294807at_nat A3) B3)) R2) (= A22 B3))) (exists ((A3 set_Pr1261947904930325089at_nat) (B3 set_Pr1261947904930325089at_nat) (C5 set_Pr1261947904930325089at_nat)) (and (= A1 A3) (@ (@ member8757157785044589968at_nat (@ (@ produc2922128104949294807at_nat B3) C5)) R2) (@ (@ member8757157785044589968at_nat (@ (@ produc2922128104949294807at_nat A3) B3)) (@ transi2703068831062848130at_nat R2)) (= A22 C5)))))) (forall ((A2 nat) (C nat) (B2 nat)) (=> (@ (@ ord_less_eq_nat (@ (@ plus_plus_nat A2) C)) (@ (@ plus_plus_nat B2) C)) (@ (@ ord_less_eq_nat A2) B2))) (forall ((A2 rat) (B2 rat)) (let ((_let_1 (@ ord_less_eq_rat zero_zero_rat))) (=> (@ _let_1 A2) (=> (@ _let_1 B2) (@ _let_1 (@ (@ plus_plus_rat A2) B2)))))) (forall ((M2 int) (N int)) (= (= (@ (@ ord_min_int M2) N) N) (@ (@ ord_less_eq_int N) M2))) (forall ((A2 code_integer)) (= (@ (@ times_3573771949741848930nteger A2) one_one_Code_integer) A2)) (forall ((X assn)) (= (@ (@ inf_inf_assn X) top_top_assn) X)) (forall ((R2 set_Pr4329608150637261639at_nat) (S3 set_Pr4329608150637261639at_nat)) (=> (forall ((X3 set_Pr1261947904930325089at_nat) (Y2 set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ member8757157785044589968at_nat (@ (@ produc2922128104949294807at_nat X3) Y2)))) (=> (@ _let_1 R2) (@ _let_1 S3)))) (@ (@ ord_le1268244103169919719at_nat R2) S3))) (forall ((N nat)) (not (@ (@ ord_less_nat N) N))) (forall ((A2 code_integer) (B2 code_integer)) (let ((_let_1 (@ ord_le6747313008572928689nteger zero_z3403309356797280102nteger))) (= (@ (@ ord_le6747313008572928689nteger (@ (@ times_3573771949741848930nteger A2) B2)) zero_z3403309356797280102nteger) (or (and (@ (@ ord_le6747313008572928689nteger B2) zero_z3403309356797280102nteger) (@ _let_1 A2)) (and (@ (@ ord_le6747313008572928689nteger A2) zero_z3403309356797280102nteger) (@ _let_1 B2)))))) (forall ((A2 nat) (B2 nat)) (= (@ (@ minus_minus_nat (@ (@ plus_plus_nat A2) B2)) A2) B2)) (forall ((B set_nat) (A2 nat) (A set_nat)) (let ((_let_1 (@ inf_inf_set_nat B))) (= (= (@ _let_1 (@ (@ insert_nat2 A2) A)) bot_bot_set_nat) (and (= (@ _let_1 A) bot_bot_set_nat) (not (@ (@ member_nat A2) B)))))) (forall ((A set_Pr4329608150637261639at_nat)) (= (@ (@ ord_le1268244103169919719at_nat A) bot_bo228742789529271731at_nat) (= A bot_bo228742789529271731at_nat))) (forall ((Xs list_int)) (= (= bot_bot_set_int (@ set_int2 Xs)) (= Xs nil_int))) (= ord_less_nat (lambda ((M nat) (N2 nat)) (and (@ (@ ord_less_eq_nat M) N2) (not (= M N2))))) (forall ((B2 set_nat) (A2 set_nat) (C set_nat)) (let ((_let_1 (@ sup_sup_set_nat B2))) (let ((_let_2 (@ sup_sup_set_nat A2))) (= (@ _let_1 (@ _let_2 C)) (@ _let_2 (@ _let_1 C)))))) (forall ((I nat) (I3 set_nat) (Xs list_c) (A (-> c d assn)) (Xsi list_d)) (=> (@ (@ member_nat I) I3) (=> (@ (@ ord_less_nat I) (@ size_size_list_c Xs)) (= (@ (@ (@ (@ vEBT_L824818263033719201sn_c_d I3) A) Xs) Xsi) (@ (@ times_times_assn (@ (@ A (@ (@ nth_c Xs) I)) (@ (@ nth_d Xsi) I))) (@ (@ (@ (@ vEBT_L824818263033719201sn_c_d (@ (@ minus_minus_set_nat I3) (@ (@ insert_nat2 I) bot_bot_set_nat))) A) Xs) Xsi)))))) (forall ((T int)) (exists ((Z4 int)) (forall ((X7 int)) (=> (@ (@ ord_less_int Z4) X7) (not (= X7 T)))))) (forall ((A2 nat) (B2 nat) (C nat)) (=> (@ (@ ord_less_eq_nat A2) B2) (= (@ (@ plus_plus_nat (@ (@ minus_minus_nat B2) A2)) C) (@ (@ minus_minus_nat (@ (@ plus_plus_nat B2) C)) A2)))) (forall ((A set_nat) (B set_nat)) (=> (= A B) (not (=> (@ (@ ord_less_eq_set_nat A) B) (not (@ (@ ord_less_eq_set_nat B) A)))))) (forall ((X produc3843707927480180839at_nat) (Y produc3843707927480180839at_nat) (A set_Pr4329608150637261639at_nat)) (let ((_let_1 (@ member8757157785044589968at_nat X))) (= (@ _let_1 (@ (@ remove5300788332298244428at_nat Y) A)) (and (@ _let_1 A) (not (= X Y)))))) (forall ((X d) (Xs list_d) (I nat) (Y d)) (let ((_let_1 (@ cons_d X))) (= (@ (@ (@ list_update_d (@ _let_1 Xs)) (@ suc I)) Y) (@ _let_1 (@ (@ (@ list_update_d Xs) I) Y))))) (forall ((Xs list_int) (Ys list_int) (R2 set_Pr958786334691620121nt_int) (X int)) (let ((_let_1 (@ listrel1_int R2))) (let ((_let_2 (@ cons_int X))) (=> (@ (@ member6698963635872716290st_int (@ (@ produc364263696895485585st_int Xs) Ys)) _let_1) (@ (@ member6698963635872716290st_int (@ (@ produc364263696895485585st_int (@ _let_2 Xs)) (@ _let_2 Ys))) _let_1))))) (forall ((X set_Pr4329608150637261639at_nat) (Y set_Pr4329608150637261639at_nat) (Z set_Pr4329608150637261639at_nat)) (= (@ (@ ord_le1268244103169919719at_nat (@ (@ sup_su5525570899277871387at_nat X) Y)) Z) (and (@ (@ ord_le1268244103169919719at_nat Y) Z) (@ (@ ord_le1268244103169919719at_nat X) Z)))) (forall ((A2 int) (B2 int)) (let ((_let_1 (@ ord_less_eq_int zero_zero_int))) (=> (or (and (@ (@ ord_less_eq_int B2) zero_zero_int) (@ (@ ord_less_eq_int A2) zero_zero_int)) (and (@ _let_1 A2) (@ _let_1 B2))) (@ _let_1 (@ (@ times_times_int A2) B2))))) (forall ((B2 int) (A2 int)) (=> (@ (@ ord_less_eq_int B2) A2) (= (@ (@ plus_plus_int (@ (@ minus_minus_int A2) B2)) B2) A2))) (forall ((X assn) (Y assn) (Z assn)) (let ((_let_1 (@ ord_less_eq_assn X))) (= (@ _let_1 (@ (@ inf_inf_assn Y) Z)) (and (@ _let_1 Z) (@ _let_1 Y))))) (forall ((X set_Pr4329608150637261639at_nat)) (= (@ (@ inf_in7913087082777306421at_nat bot_bo228742789529271731at_nat) X) bot_bo228742789529271731at_nat)) (forall ((X product_prod_nat_nat) (Y product_prod_nat_nat)) (=> (@ (@ member8206827879206165904at_nat (@ (@ produc6161850002892822231at_nat X) Y)) fun_pair_leq) (@ (@ pw_leq (@ (@ add_ms2612439473150266591at_nat X) zero_z1048942125864253310at_nat)) (@ (@ add_ms2612439473150266591at_nat Y) zero_z1048942125864253310at_nat)))) (forall ((X (-> produc3658429121746597890et_nat Bool)) (Xs list_P7985473006766602707_nat_o)) (= (@ (@ member6576561426505652726_nat_o X) (@ set_Pr400311997697478754_nat_o Xs)) (exists ((I4 nat)) (and (= (@ (@ nth_Pr6840583978799713108_nat_o Xs) I4) X) (@ (@ ord_less_nat I4) (@ size_s8908918004648414271_nat_o Xs)))))) (forall ((I rat) (J rat) (K3 rat) (L rat)) (=> (and (@ (@ ord_less_rat I) J) (@ (@ ord_less_rat K3) L)) (@ (@ ord_less_rat (@ (@ plus_plus_rat I) K3)) (@ (@ plus_plus_rat J) L)))) (forall ((A2 rat) (B2 rat)) (= (@ (@ ord_less_rat (@ (@ plus_plus_rat A2) B2)) B2) (@ (@ ord_less_rat A2) zero_zero_rat))) (forall ((Xs list_nat) (Ys list_nat) (R2 set_Pr1261947904930325089at_nat)) (= (@ (@ member7340969449405702474st_nat (@ (@ produc2694037385005941721st_nat Xs) Ys)) (@ listrel1_nat R2)) (exists ((Y5 nat) (N2 nat)) (and (@ (@ ord_less_nat N2) (@ size_size_list_nat Xs)) (= Ys (@ (@ (@ list_update_nat Xs) N2) Y5)) (@ (@ member8440522571783428010at_nat (@ (@ product_Pair_nat_nat (@ (@ nth_nat Xs) N2)) Y5)) R2))))) (= ord_less_eq_nat (lambda ((A3 nat) (B3 nat)) (= (@ (@ inf_inf_nat A3) B3) A3))) (forall ((X produc3843707927480180839at_nat) (A set_Pr4329608150637261639at_nat) (X4 set_Pr4329608150637261639at_nat)) (=> (@ (@ member8757157785044589968at_nat X) A) (=> (@ (@ ord_le1268244103169919719at_nat X4) A) (@ (@ ord_le1268244103169919719at_nat (@ (@ insert9069300056098147895at_nat X) X4)) A)))) (forall ((S set_nat)) (= (not (@ finite_finite_nat S)) (forall ((M nat)) (exists ((N2 nat)) (and (@ (@ ord_less_nat M) N2) (@ (@ member_nat N2) S)))))) (forall ((A set_int)) (=> (not (= A bot_bot_set_int)) (=> (forall ((X3 int) (Y2 int)) (=> (@ (@ member_int X3) A) (=> (@ (@ member_int Y2) A) (= X3 Y2)))) (@ is_singleton_int A)))) (forall ((A2 int) (B2 int) (C int)) (let ((_let_1 (@ ord_less_int A2))) (=> (@ _let_1 B2) (=> (@ (@ ord_less_eq_int B2) C) (@ _let_1 C))))) (forall ((P (-> int Bool))) (= (= bot_bot_set_int (@ collect_int P)) (forall ((X2 int)) (not (@ P X2))))) (= entailst (lambda ((P2 assn) (Q2 assn)) (@ (@ entails (@ (@ times_times_assn P2) top_top_assn)) (@ (@ times_times_assn Q2) top_top_assn)))) (forall ((L list_P338744602095350958od_c_d)) (not (forall ((L1 list_c) (L22 list_d)) (let ((_let_1 (@ size_size_list_d L22))) (=> (= L (@ (@ zip_c_d L1) L22)) (=> (= (@ size_size_list_c L1) _let_1) (not (= (@ size_s2827482749765095194od_c_d L) _let_1)))))))) _let_174 (forall ((B set_int)) (= (@ (@ inf_inf_set_int bot_bot_set_int) B) bot_bot_set_int)) (forall ((A2 nat) (B2 nat) (C nat)) (let ((_let_1 (@ plus_plus_nat C))) (=> (@ (@ ord_less_nat A2) B2) (@ (@ ord_less_nat (@ _let_1 A2)) (@ _let_1 B2))))) _let_173 (forall ((A2 num) (B2 num) (C num)) (=> (@ (@ ord_less_eq_num A2) B2) (=> (@ (@ ord_less_num B2) C) (@ (@ ord_less_num A2) C)))) (forall ((F4 (-> int nat produc6575502325842934193n_assn))) (= (@ (@ (@ zipf_i5995984495708165493n_assn F4) nil_int) nil_nat) nil_Pr5671120429643327159n_assn)) (forall ((I nat) (Xs list_d) (Ys list_nat)) (let ((_let_1 (@ ord_less_nat I))) (=> (@ _let_1 (@ size_size_list_d Xs)) (=> (@ _let_1 (@ size_size_list_nat Ys)) (= (@ (@ nth_Pr2944426604534821689_d_nat (@ (@ zip_d_nat Xs) Ys)) I) (@ (@ product_Pair_d_nat (@ (@ nth_d Xs) I)) (@ (@ nth_nat Ys) I))))))) (forall ((A2 set_int) (B2 set_int)) (=> (forall ((X3 int)) (let ((_let_1 (@ member_int X3))) (=> (@ _let_1 A2) (not (@ _let_1 B2))))) (= (@ (@ inf_inf_set_int A2) B2) bot_bot_set_int))) (forall ((P (-> produc2732055786443039994et_nat Bool)) (X produc2732055786443039994et_nat)) (=> (forall ((A4 (-> produc3658429121746597890et_nat Bool)) (B4 (-> produc3658429121746597890et_nat Bool)) (C4 produc3658429121746597890et_nat)) (@ P (@ (@ produc2245416461498447860et_nat A4) (@ (@ produc5001842942810119800et_nat B4) C4)))) (@ P X))) (= ord_less_assn (lambda ((X2 assn) (Y5 assn)) (and (not (@ (@ ord_less_eq_assn Y5) X2)) (@ (@ ord_less_eq_assn X2) Y5)))) (forall ((N nat)) (@ (@ ord_less_nat N) (@ (@ power_power_nat (@ numeral_numeral_nat (@ bit0 one))) N))) (forall ((S set_Pr4532377907799695533_nat_o) (P (-> (-> produc3658429121746597890et_nat Bool) Bool))) (= (@ (@ ord_le2965882846123202637_nat_o S) (@ collec939566748876313656_nat_o P)) (forall ((X2 (-> produc3658429121746597890et_nat Bool))) (=> (@ (@ member6576561426505652726_nat_o X2) S) (@ P X2))))) (forall ((A2 rat) (B2 rat)) (=> (@ (@ ord_less_eq_rat A2) zero_zero_rat) (=> (@ (@ ord_less_eq_rat zero_zero_rat) B2) (@ (@ ord_less_eq_rat (@ (@ times_times_rat A2) B2)) zero_zero_rat)))) (forall ((A set_nat) (A2 nat) (B set_nat)) (let ((_let_1 (@ sup_sup_set_nat A))) (let ((_let_2 (@ insert_nat2 A2))) (= (@ _let_1 (@ _let_2 B)) (@ _let_2 (@ _let_1 B)))))) (forall ((A2 int) (B2 int)) (= (@ (@ ord_less_int A2) (@ (@ plus_plus_int B2) A2)) (@ (@ ord_less_int zero_zero_int) B2))) (forall ((X rat) (Y rat)) (let ((_let_1 (@ ord_less_eq_rat zero_zero_rat))) (=> (@ _let_1 X) (=> (@ _let_1 Y) (=> (@ (@ ord_less_eq_rat Y) one_one_rat) (@ (@ ord_less_eq_rat (@ (@ times_times_rat Y) X)) X)))))) (forall ((Xs list_d) (Ys list_int) (X d)) (=> (= (@ size_size_list_d Xs) (@ size_size_list_int Ys)) (=> (@ (@ member_d X) (@ set_d2 Xs)) (not (forall ((Y2 int)) (not (@ (@ member5252670555746405491_d_int (@ (@ product_Pair_d_int X) Y2)) (@ set_Pr453465341863021319_d_int (@ (@ zip_d_int Xs) Ys))))))))) (forall ((B2 rat) (A2 rat)) (=> (@ (@ ord_less_eq_rat B2) A2) (= (@ (@ plus_plus_rat (@ (@ minus_minus_rat A2) B2)) B2) A2))) (forall ((P6 produc2732055786443039994et_nat)) (exists ((X3 (-> produc3658429121746597890et_nat Bool)) (Y2 produc3925858234332021118et_nat)) (= P6 (@ (@ produc2245416461498447860et_nat X3) Y2)))) (forall ((C int) (A2 int)) (= (@ (@ ord_less_int (@ (@ times_times_int C) A2)) C) (and (=> (@ (@ ord_less_eq_int C) zero_zero_int) (@ (@ ord_less_int one_one_int) A2)) (=> (@ (@ ord_less_eq_int zero_zero_int) C) (@ (@ ord_less_int A2) one_one_int))))) (forall ((A2 nat)) (= (@ (@ times_times_nat A2) zero_zero_nat) zero_zero_nat)) (forall ((X Bool) (Xa produc3658429121746597890et_nat) (Y Bool)) (=> (= (@ (@ pure_a825153325127701367it_nat X) Xa) Y) (not (forall ((H heap_e7401611519738050253t_unit) (As set_nat)) (=> (= Xa (@ (@ produc7507926704131184380et_nat H) As)) (= Y (not (and (= As bot_bot_set_nat) X)))))))) (forall ((A2 rat) (B2 rat)) (=> (@ (@ ord_less_rat zero_zero_rat) A2) (=> (@ (@ ord_less_rat B2) zero_zero_rat) (@ (@ ord_less_rat (@ (@ times_times_rat B2) A2)) zero_zero_rat)))) (forall ((X set_Pr1261947904930325089at_nat) (Y set_Pr1261947904930325089at_nat) (R2 set_Pr4329608150637261639at_nat) (P (-> set_Pr1261947904930325089at_nat set_Pr1261947904930325089at_nat Bool))) (=> (@ (@ member8757157785044589968at_nat (@ (@ produc2922128104949294807at_nat X) Y)) (@ transi2703068831062848130at_nat R2)) (=> (forall ((X3 set_Pr1261947904930325089at_nat) (Y2 set_Pr1261947904930325089at_nat)) (=> (@ (@ member8757157785044589968at_nat (@ (@ produc2922128104949294807at_nat X3) Y2)) R2) (@ (@ P X3) Y2))) (=> (forall ((X3 set_Pr1261947904930325089at_nat) (Y2 set_Pr1261947904930325089at_nat) (Z4 set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ P X3))) (let ((_let_2 (@ transi2703068831062848130at_nat R2))) (=> (@ (@ member8757157785044589968at_nat (@ (@ produc2922128104949294807at_nat X3) Y2)) _let_2) (=> (@ _let_1 Y2) (=> (@ (@ member8757157785044589968at_nat (@ (@ produc2922128104949294807at_nat Y2) Z4)) _let_2) (=> (@ (@ P Y2) Z4) (@ _let_1 Z4)))))))) (@ (@ P X) Y))))) (forall ((C produc3843707927480180839at_nat) (A set_Pr4329608150637261639at_nat) (B set_Pr4329608150637261639at_nat)) (let ((_let_1 (@ member8757157785044589968at_nat C))) (=> (@ _let_1 A) (=> (@ _let_1 B) (@ _let_1 (@ (@ inf_in7913087082777306421at_nat A) B)))))) (forall ((Xs list_P8527749157015355191n_assn) (Ys list_nat) (Xy produc3672657496626091440sn_nat) (Xys list_P2911967483291296064sn_nat)) (=> (= (@ (@ zip_Pr1018045463562677002sn_nat Xs) Ys) (@ (@ cons_P110449348784310650sn_nat Xy) Xys)) (not (forall ((X3 produc6575502325842934193n_assn) (Xs5 list_P8527749157015355191n_assn)) (=> (= Xs (@ (@ cons_P2971678138204555879n_assn X3) Xs5)) (forall ((Y2 nat) (Ys4 list_nat)) (=> (= Ys (@ (@ cons_nat Y2) Ys4)) (=> (= Xy (@ (@ produc6456381919915743786sn_nat X3) Y2)) (not (= Xys (@ (@ zip_Pr1018045463562677002sn_nat Xs5) Ys4))))))))))) (forall ((A2 assn) (B2 assn)) (=> (@ (@ ord_less_eq_assn A2) B2) (= A2 (@ (@ inf_inf_assn A2) B2)))) (forall ((Y set_Pr4329608150637261639at_nat) (Z set_Pr4329608150637261639at_nat) (X set_Pr4329608150637261639at_nat)) (= (@ (@ inf_in7913087082777306421at_nat (@ (@ sup_su5525570899277871387at_nat Y) Z)) X) (@ (@ sup_su5525570899277871387at_nat (@ (@ inf_in7913087082777306421at_nat Y) X)) (@ (@ inf_in7913087082777306421at_nat Z) X)))) _let_172 (forall ((X nat) (Y nat) (Z nat)) (= (@ (@ plus_plus_nat (@ (@ ord_min_nat X) Y)) Z) (@ (@ ord_min_nat (@ (@ plus_plus_nat X) Z)) (@ (@ plus_plus_nat Y) Z)))) (= ord_le6747313008572928689nteger (lambda ((A3 code_integer) (B3 code_integer)) (and (@ (@ ord_le3102999989581377725nteger A3) B3) (not (= A3 B3))))) (forall ((C rat) (A2 rat) (B2 rat)) (let ((_let_1 (@ times_times_rat C))) (= (@ (@ ord_less_eq_rat (@ _let_1 A2)) (@ _let_1 B2)) (and (=> (@ (@ ord_less_rat C) zero_zero_rat) (@ (@ ord_less_eq_rat B2) A2)) (=> (@ (@ ord_less_rat zero_zero_rat) C) (@ (@ ord_less_eq_rat A2) B2)))))) (forall ((X nat) (Y nat)) (=> (@ (@ ord_less_nat X) Y) (not (= Y X)))) (forall ((K3 nat) (M2 nat) (N nat)) (let ((_let_1 (@ times_times_nat K3))) (=> (@ (@ ord_less_nat zero_zero_nat) K3) (= (@ (@ dvd_dvd_nat (@ _let_1 M2)) (@ _let_1 N)) (@ (@ dvd_dvd_nat M2) N))))) (forall ((X product_prod_nat_nat) (Xs list_P6011104703257516679at_nat)) (=> (not (@ (@ member8440522571783428010at_nat X) (@ set_Pr5648618587558075414at_nat Xs))) (= (@ (@ count_4203492906077236349at_nat Xs) X) zero_zero_nat))) (forall ((A2 produc3843707927480180839at_nat) (A set_Pr4329608150637261639at_nat)) (=> (@ (@ member8757157785044589968at_nat A2) A) (exists ((B5 set_Pr4329608150637261639at_nat)) (and (not (@ (@ member8757157785044589968at_nat A2) B5)) (= A (@ (@ insert9069300056098147895at_nat A2) B5)))))) (forall ((X produc6575502325842934193n_assn) (Xs list_P8527749157015355191n_assn)) (=> (not (@ (@ member7957490590177025114n_assn X) (@ set_Pr1139785259514867910n_assn Xs))) (= (@ (@ count_2530312006313534765n_assn Xs) X) zero_zero_nat))) (forall ((A set_Pr1261947904930325089at_nat) (X product_prod_nat_nat) (B set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ ord_le3146513528884898305at_nat A))) (let ((_let_2 (@ (@ member8440522571783428010at_nat X) A))) (let ((_let_3 (@ insert8211810215607154385at_nat X))) (= (@ _let_1 (@ _let_3 B)) (and (=> _let_2 (@ (@ ord_le3146513528884898305at_nat (@ (@ minus_1356011639430497352at_nat A) (@ _let_3 bot_bo2099793752762293965at_nat))) B)) (=> (not _let_2) (@ _let_1 B)))))))) (forall ((C nat) (A set_nat) (B set_nat)) (let ((_let_1 (@ member_nat C))) (=> (@ _let_1 (@ (@ inf_inf_set_nat A) B)) (not (=> (@ _let_1 A) (not (@ _let_1 B))))))) (forall ((A set_Pr1261947904930325089at_nat) (B set_Pr1261947904930325089at_nat)) (= (@ (@ ord_le7866589430770878221at_nat (@ (@ minus_1356011639430497352at_nat A) B)) A) (not (= (@ (@ inf_in2572325071724192079at_nat A) B) bot_bo2099793752762293965at_nat)))) (forall ((X code_integer)) (= (@ (@ minus_8373710615458151222nteger (@ (@ times_3573771949741848930nteger X) X)) one_one_Code_integer) (@ (@ times_3573771949741848930nteger (@ (@ plus_p5714425477246183910nteger X) one_one_Code_integer)) (@ (@ minus_8373710615458151222nteger X) one_one_Code_integer)))) (forall ((P (-> list_nat list_int Bool)) (Xs list_nat) (Ys list_int)) (=> (@ (@ P nil_nat) nil_int) (=> (forall ((X3 nat) (Xs2 list_nat)) (@ (@ P (@ (@ cons_nat X3) Xs2)) nil_int)) (=> (forall ((Y2 int) (Ys5 list_int)) (@ (@ P nil_nat) (@ (@ cons_int Y2) Ys5))) (=> (forall ((X3 nat) (Xs2 list_nat) (Y2 int) (Ys5 list_int)) (=> (@ (@ P Xs2) Ys5) (@ (@ P (@ (@ cons_nat X3) Xs2)) (@ (@ cons_int Y2) Ys5)))) (@ (@ P Xs) Ys)))))) (forall ((Xs list_c) (N nat) (X c)) (=> (@ distinct_c Xs) (=> (@ (@ ord_less_nat N) (@ size_size_list_c Xs)) (= (@ set_c2 (@ (@ (@ list_update_c Xs) N) X)) (@ (@ insert_c X) (@ (@ minus_minus_set_c (@ set_c2 Xs)) (@ (@ insert_c (@ (@ nth_c Xs) N)) bot_bot_set_c))))))) (forall ((B2 code_integer) (A2 code_integer)) (let ((_let_1 (@ ord_le6747313008572928689nteger zero_z3403309356797280102nteger))) (=> (@ _let_1 (@ (@ times_3573771949741848930nteger B2) A2)) (=> (@ _let_1 A2) (@ _let_1 B2))))) (forall ((List list_P8527749157015355191n_assn) (X21 produc6575502325842934193n_assn) (X222 list_P8527749157015355191n_assn)) (=> (= List (@ (@ cons_P2971678138204555879n_assn X21) X222)) (not (= List nil_Pr5671120429643327159n_assn)))) (forall ((Xs list_d) (I nat) (X d)) (@ (@ ord_less_eq_set_d (@ set_d2 (@ (@ (@ list_update_d Xs) I) X))) (@ (@ insert_d X) (@ set_d2 Xs)))) (= insert_int2 (lambda ((A3 int) (__flatten_var_0 set_int)) (@ (@ sup_sup_set_int (@ (@ insert_int2 A3) bot_bot_set_int)) __flatten_var_0))) (forall ((A2 nat) (B2 nat) (R set_Pr1261947904930325089at_nat) (C nat)) (let ((_let_1 (@ product_Pair_nat_nat A2))) (=> (@ (@ member8440522571783428010at_nat (@ _let_1 B2)) R) (=> (@ (@ member8440522571783428010at_nat (@ (@ product_Pair_nat_nat B2) C)) R) (@ (@ member8440522571783428010at_nat (@ _let_1 C)) (@ transi6264000038957366511cl_nat R)))))) (forall ((B2 int) (M2 nat) (N nat)) (let ((_let_1 (@ power_power_int B2))) (=> (@ (@ ord_less_int zero_zero_int) B2) (=> (@ (@ ord_less_int B2) one_one_int) (= (@ (@ ord_less_eq_int (@ _let_1 M2)) (@ _let_1 N)) (@ (@ ord_less_eq_nat N) M2)))))) (forall ((X set_nat) (Y set_nat)) (= (= bot_bot_set_nat (@ (@ sup_sup_set_nat X) Y)) (and (= X bot_bot_set_nat) (= Y bot_bot_set_nat)))) (= ord_less_nat (lambda ((X2 nat) (Y5 nat)) (and (not (@ (@ ord_less_eq_nat Y5) X2)) (@ (@ ord_less_eq_nat X2) Y5)))) (forall ((B2 int) (A2 int) (C int)) (let ((_let_1 (@ times_times_int B2))) (let ((_let_2 (@ times_times_int A2))) (= (@ _let_1 (@ _let_2 C)) (@ _let_2 (@ _let_1 C)))))) (forall ((A2 int) (B2 int) (C int)) (let ((_let_1 (@ ord_less_int B2))) (=> (@ (@ ord_less_eq_int zero_zero_int) A2) (=> (@ _let_1 C) (@ _let_1 (@ (@ plus_plus_int A2) C)))))) (forall ((A2 rat) (B2 rat) (C rat)) (let ((_let_1 (@ times_times_rat A2))) (= (@ _let_1 (@ (@ minus_minus_rat B2) C)) (@ (@ minus_minus_rat (@ _let_1 B2)) (@ _let_1 C))))) (forall ((A set_int) (B set_int) (X int) (C2 set_int)) (let ((_let_1 (@ minus_minus_set_int B))) (let ((_let_2 (@ ord_less_eq_set_int A))) (= (@ _let_2 (@ _let_1 (@ (@ insert_int2 X) C2))) (and (@ _let_2 (@ _let_1 C2)) (not (@ (@ member_int X) A))))))) (forall ((I code_integer) (J code_integer) (K3 code_integer) (L code_integer)) (=> (and (@ (@ ord_le6747313008572928689nteger K3) L) (@ (@ ord_le6747313008572928689nteger I) J)) (@ (@ ord_le6747313008572928689nteger (@ (@ plus_p5714425477246183910nteger I) K3)) (@ (@ plus_p5714425477246183910nteger J) L)))) (forall ((X nat) (Y nat)) (@ (@ ord_less_eq_nat X) (@ (@ sup_sup_nat X) Y))) (forall ((Xs list_d)) (= (= (@ size_size_list_d Xs) zero_zero_nat) (= Xs nil_d))) (forall ((X nat) (A2 nat) (B2 nat)) (let ((_let_1 (@ ord_less_eq_nat X))) (=> (@ _let_1 A2) (=> (@ _let_1 B2) (@ _let_1 (@ (@ inf_inf_nat A2) B2)))))) (forall ((X nat) (Y product_prod_nat_nat) (Xs list_nat) (Ys list_P6011104703257516679at_nat)) (=> (@ (@ member2223272150424702269at_nat (@ (@ produc487386426758144856at_nat X) Y)) (@ set_Pr6710958862608470481at_nat (@ (@ zip_na1006125974040638520at_nat Xs) Ys))) (not (=> (@ (@ member_nat X) (@ set_nat2 Xs)) (not (@ (@ member8440522571783428010at_nat Y) (@ set_Pr5648618587558075414at_nat Ys))))))) (forall ((Xs list_d) (Ys list_nat) (X d)) (=> (= (@ size_size_list_d Xs) (@ size_size_list_nat Ys)) (=> (@ (@ member_d X) (@ set_d2 Xs)) (not (forall ((Y2 nat)) (not (@ (@ member207149538400826391_d_nat (@ (@ product_Pair_d_nat X) Y2)) (@ set_Pr4631316361372218027_d_nat (@ (@ zip_d_nat Xs) Ys))))))))) (forall ((P (-> product_prod_nat_nat Bool)) (Q (-> product_prod_nat_nat Bool))) (= (@ (@ ord_le3146513528884898305at_nat (@ collec3392354462482085612at_nat P)) (@ collec3392354462482085612at_nat Q)) (forall ((X2 product_prod_nat_nat)) (=> (@ P X2) (@ Q X2))))) (forall ((A set_Pr4329608150637261639at_nat) (B set_Pr4329608150637261639at_nat) (X produc3843707927480180839at_nat) (C2 set_Pr4329608150637261639at_nat)) (let ((_let_1 (@ minus_3314409938677909166at_nat B))) (let ((_let_2 (@ ord_le1268244103169919719at_nat A))) (= (@ _let_2 (@ _let_1 (@ (@ insert9069300056098147895at_nat X) C2))) (and (not (@ (@ member8757157785044589968at_nat X) A)) (@ _let_2 (@ _let_1 C2))))))) (forall ((X code_integer) (Y code_integer)) (@ (@ ord_le3102999989581377725nteger zero_z3403309356797280102nteger) (@ (@ plus_p5714425477246183910nteger (@ (@ times_3573771949741848930nteger X) X)) (@ (@ times_3573771949741848930nteger Y) Y)))) (forall ((X assn) (Y assn) (Z assn)) (let ((_let_1 (@ sup_sup_assn X))) (=> (forall ((X3 assn) (Y2 assn) (Z4 assn)) (let ((_let_1 (@ inf_inf_assn X3))) (= (@ _let_1 (@ (@ sup_sup_assn Y2) Z4)) (@ (@ sup_sup_assn (@ _let_1 Y2)) (@ _let_1 Z4))))) (= (@ _let_1 (@ (@ inf_inf_assn Y) Z)) (@ (@ inf_inf_assn (@ _let_1 Y)) (@ _let_1 Z)))))) (forall ((P (-> Bool Bool Bool)) (A Bool)) (@ (@ pairwise_o P) (@ (@ insert_o2 A) bot_bot_set_o))) (forall ((P (-> product_prod_nat_nat Bool))) (= (= bot_bo2099793752762293965at_nat (@ collec3392354462482085612at_nat P)) (forall ((X2 product_prod_nat_nat)) (not (@ P X2))))) (forall ((A2 code_integer) (B2 code_integer)) (let ((_let_1 (@ ord_le3102999989581377725nteger zero_z3403309356797280102nteger))) (=> (or (and (@ (@ ord_le3102999989581377725nteger B2) zero_z3403309356797280102nteger) (@ _let_1 A2)) (and (@ (@ ord_le3102999989581377725nteger A2) zero_z3403309356797280102nteger) (@ _let_1 B2))) (@ (@ ord_le3102999989581377725nteger (@ (@ times_3573771949741848930nteger A2) B2)) zero_z3403309356797280102nteger)))) (forall ((Xs list_int) (A2 int)) (let ((_let_1 (@ sorted_wrt_int ord_less_eq_int))) (=> (@ _let_1 Xs) (@ _let_1 (@ (@ remove1_int A2) Xs))))) (forall ((P (-> produc3658429121746597890et_nat Bool)) (Q (-> produc3658429121746597890et_nat Bool)) (H2 heap_e7401611519738050253t_unit) (As2 set_nat)) (= (@ (@ (@ times_assn_raw P) Q) (@ (@ produc7507926704131184380et_nat H2) As2)) (exists ((As1 set_nat) (As22 set_nat)) (let ((_let_1 (@ produc7507926704131184380et_nat H2))) (and (@ P (@ _let_1 As1)) (@ Q (@ _let_1 As22)) (= (@ (@ inf_inf_set_nat As1) As22) bot_bot_set_nat) (= As2 (@ (@ sup_sup_set_nat As1) As22))))))) (forall ((P (-> nat nat Bool)) (A nat)) (@ (@ pairwise_nat P) (@ (@ insert_nat2 A) bot_bot_set_nat))) (forall ((M2 nat) (N nat)) (let ((_let_1 (@ minus_minus_nat N))) (=> (@ (@ ord_less_eq_nat M2) N) (=> (@ (@ ord_less_eq_nat one_one_nat) M2) (= (@ suc (@ _let_1 M2)) (@ _let_1 (@ (@ minus_minus_nat M2) one_one_nat))))))) (forall ((A2 list_c) (B2 list_d) (A7 list_c) (B6 list_d)) (=> (= (@ size_size_list_c A2) (@ size_size_list_d B2)) (=> (= (@ size_size_list_c A7) (@ size_size_list_d B6)) (= (= (@ (@ zip_c_d A2) B2) (@ (@ zip_c_d A7) B6)) (and (= A2 A7) (= B2 B6)))))) (forall ((X Bool) (Xa produc3658429121746597890et_nat)) (=> (not (@ (@ pure_a825153325127701367it_nat X) Xa)) (not (forall ((H heap_e7401611519738050253t_unit) (As set_nat)) (=> (= Xa (@ (@ produc7507926704131184380et_nat H) As)) (and (= As bot_bot_set_nat) X)))))) (= (lambda ((Y4 assn) (Z2 assn)) (= Y4 Z2)) (lambda ((A3 assn) (B3 assn)) (and (@ (@ ord_less_eq_assn A3) B3) (@ (@ ord_less_eq_assn B3) A3)))) (forall ((Xs list_nat) (Ys list_int) (Zs list_c) (Ws list_nat) (P (-> list_nat list_int list_c list_nat Bool))) (let ((_let_1 (@ size_size_list_c Zs))) (let ((_let_2 (@ size_size_list_int Ys))) (=> (= (@ size_size_list_nat Xs) _let_2) (=> (= _let_2 _let_1) (=> (= _let_1 (@ size_size_list_nat Ws)) (=> (@ (@ (@ (@ P nil_nat) nil_int) nil_c) nil_nat) (=> (forall ((X3 nat) (Xs2 list_nat) (Y2 int) (Ys5 list_int) (Z4 c) (Zs2 list_c) (W3 nat) (Ws2 list_nat)) (let ((_let_1 (@ size_size_list_c Zs2))) (let ((_let_2 (@ size_size_list_int Ys5))) (=> (= (@ size_size_list_nat Xs2) _let_2) (=> (= _let_2 _let_1) (=> (= _let_1 (@ size_size_list_nat Ws2)) (=> (@ (@ (@ (@ P Xs2) Ys5) Zs2) Ws2) (@ (@ (@ (@ P (@ (@ cons_nat X3) Xs2)) (@ (@ cons_int Y2) Ys5)) (@ (@ cons_c Z4) Zs2)) (@ (@ cons_nat W3) Ws2))))))))) (@ (@ (@ (@ P Xs) Ys) Zs) Ws))))))))) (forall ((R2 (-> int int Bool)) (X int) (S3 set_int)) (let ((_let_1 (@ pairwise_int R2))) (= (@ _let_1 (@ (@ insert_int2 X) S3)) (and (@ _let_1 S3) (forall ((Y5 int)) (=> (and (@ (@ member_int Y5) S3) (not (= Y5 X))) (and (@ (@ R2 Y5) X) (@ (@ R2 X) Y5)))))))) (forall ((A set_nat) (B set_nat) (P (-> nat Bool))) (= (forall ((X2 nat)) (=> (@ (@ member_nat X2) (@ (@ sup_sup_set_nat A) B)) (@ P X2))) (and (forall ((X2 nat)) (=> (@ (@ member_nat X2) B) (@ P X2))) (forall ((X2 nat)) (=> (@ (@ member_nat X2) A) (@ P X2)))))) (forall ((A2 nat) (B2 nat)) (let ((_let_1 (@ ord_min_nat A2))) (let ((_let_2 (@ _let_1 B2))) (= (@ _let_1 _let_2) _let_2)))) (not (= zero_zero_nat one_one_nat)) (forall ((A2 multis2468970476368604999at_nat)) (= (@ (@ plus_p7104986032573967614at_nat A2) zero_z1048942125864253310at_nat) A2)) (forall ((X21 produc6575502325842934193n_assn) (X222 list_P8527749157015355191n_assn)) (= (@ set_Pr1139785259514867910n_assn (@ (@ cons_P2971678138204555879n_assn X21) X222)) (@ (@ insert5290817439147925377n_assn X21) (@ set_Pr1139785259514867910n_assn X222)))) (forall ((C rat) (A2 rat)) (=> (@ (@ ord_less_eq_rat C) one_one_rat) (=> (@ (@ ord_less_eq_rat zero_zero_rat) A2) (@ (@ ord_less_eq_rat (@ (@ times_times_rat A2) C)) A2)))) (forall ((N nat)) (@ (@ order_2888998067076097458on_nat (@ collect_nat (lambda ((X2 nat)) (@ (@ ord_less_nat X2) N)))) (@ collec3392354462482085612at_nat (@ produc6081775807080527818_nat_o (lambda ((X2 nat) (Y5 nat)) (and (@ (@ ord_less_nat X2) N) (@ (@ ord_less_eq_nat X2) Y5) (@ (@ ord_less_nat Y5) N))))))) (= ord_le1268244103169919719at_nat (lambda ((B3 set_Pr4329608150637261639at_nat) (A3 set_Pr4329608150637261639at_nat)) (= A3 (@ (@ sup_su5525570899277871387at_nat A3) B3)))) (forall ((A2 nat) (B2 nat)) (=> (not (= (@ (@ times_times_nat A2) B2) zero_zero_nat)) (and (not (= B2 zero_zero_nat)) (not (= A2 zero_zero_nat))))) (forall ((I nat) (L list_nat) (X nat)) (=> (@ (@ ord_less_nat I) (@ size_size_list_nat L)) (= (@ (@ insert_nat2 (@ (@ nth_nat L) I)) (@ set_nat2 (@ (@ (@ list_update_nat L) I) X))) (@ (@ insert_nat2 X) (@ set_nat2 L))))) (forall ((R2 (-> produc3658429121746597890et_nat Bool)) (S3 produc3925858234332021118et_nat) (R set_Pr8536935166611901872et_nat) (S5 produc3925858234332021118et_nat)) (let ((_let_1 (@ produc2245416461498447860et_nat R2))) (=> (@ (@ member6124377750444531601et_nat (@ _let_1 S3)) R) (=> (= S5 S3) (@ (@ member6124377750444531601et_nat (@ _let_1 S5)) R))))) (forall ((Xs list_nat) (A2 nat) (I nat)) (=> (@ distinct_nat Xs) (=> (not (@ (@ member_nat A2) (@ (@ minus_minus_set_nat (@ set_nat2 Xs)) (@ (@ insert_nat2 (@ (@ nth_nat Xs) I)) bot_bot_set_nat)))) (@ distinct_nat (@ (@ (@ list_update_nat Xs) I) A2))))) (= code_divmod_integer (lambda ((K4 code_integer) (L4 code_integer)) (let ((_let_1 (@ (@ code_divmod_abs K4) L4))) (let ((_let_2 (@ produc1086072967326762835nteger zero_z3403309356797280102nteger))) (let ((_let_3 (@ ord_le6747313008572928689nteger zero_z3403309356797280102nteger))) (@ (@ (@ if_Pro6119634080678213985nteger (= K4 zero_z3403309356797280102nteger)) (@ _let_2 zero_z3403309356797280102nteger)) (@ (@ (@ if_Pro6119634080678213985nteger (@ _let_3 L4)) (@ (@ (@ if_Pro6119634080678213985nteger (@ _let_3 K4)) _let_1) (@ (@ produc6916734918728496179nteger (lambda ((R4 code_integer) (S6 code_integer)) (let ((_let_1 (@ uminus1351360451143612070nteger R4))) (@ (@ (@ if_Pro6119634080678213985nteger (= S6 zero_z3403309356797280102nteger)) (@ (@ produc1086072967326762835nteger _let_1) zero_z3403309356797280102nteger)) (@ (@ produc1086072967326762835nteger (@ (@ minus_8373710615458151222nteger _let_1) one_one_Code_integer)) (@ (@ minus_8373710615458151222nteger L4) S6)))))) _let_1))) (@ (@ (@ if_Pro6119634080678213985nteger (= L4 zero_z3403309356797280102nteger)) (@ _let_2 K4)) (@ (@ produc6499014454317279255nteger uminus1351360451143612070nteger) (@ (@ (@ if_Pro6119634080678213985nteger (@ (@ ord_le6747313008572928689nteger K4) zero_z3403309356797280102nteger)) _let_1) (@ (@ produc6916734918728496179nteger (lambda ((R4 code_integer) (S6 code_integer)) (let ((_let_1 (@ uminus1351360451143612070nteger R4))) (@ (@ (@ if_Pro6119634080678213985nteger (= S6 zero_z3403309356797280102nteger)) (@ (@ produc1086072967326762835nteger _let_1) zero_z3403309356797280102nteger)) (@ (@ produc1086072967326762835nteger (@ (@ minus_8373710615458151222nteger _let_1) one_one_Code_integer)) (@ (@ minus_8373710615458151222nteger (@ uminus1351360451143612070nteger L4)) S6)))))) _let_1))))))))))) (forall ((X int) (Xs list_int)) (= (@ set_int2 (@ (@ removeAll_int X) Xs)) (@ (@ minus_minus_set_int (@ set_int2 Xs)) (@ (@ insert_int2 X) bot_bot_set_int)))) (forall ((X int) (A2 int) (B2 int)) (let ((_let_1 (@ ord_less_eq_int X))) (=> (@ _let_1 A2) (=> (@ _let_1 B2) (@ _let_1 (@ (@ inf_inf_int A2) B2)))))) (forall ((Y set_Pr4329608150637261639at_nat) (X set_Pr4329608150637261639at_nat)) (@ (@ ord_le1268244103169919719at_nat Y) (@ (@ sup_su5525570899277871387at_nat X) Y))) (= ord_less_eq_int (lambda ((A3 int) (B3 int)) (= A3 (@ (@ inf_inf_int A3) B3)))) (forall ((A2 set_nat) (C set_nat) (B2 set_nat) (D2 set_nat)) (=> (@ (@ ord_less_eq_set_nat A2) C) (=> (@ (@ ord_less_eq_set_nat B2) D2) (@ (@ ord_less_eq_set_nat (@ (@ sup_sup_set_nat A2) B2)) (@ (@ sup_sup_set_nat C) D2))))) (forall ((A2 int) (B2 int)) (let ((_let_1 (@ ord_less_eq_int zero_zero_int))) (=> (@ _let_1 A2) (=> (@ _let_1 B2) (@ _let_1 (@ (@ plus_plus_int A2) B2)))))) (forall ((A set_Pr4532377907799695533_nat_o) (B set_Pr4532377907799695533_nat_o) (C (-> produc3658429121746597890et_nat Bool))) (let ((_let_1 (@ member6576561426505652726_nat_o C))) (=> (@ (@ ord_le2453136405763929_nat_o A) B) (=> (@ _let_1 A) (@ _let_1 B))))) (forall ((Y set_nat) (X set_nat)) (@ (@ ord_less_eq_set_nat Y) (@ (@ sup_sup_set_nat X) Y))) (forall ((A2 assn) (B2 assn) (C assn)) (let ((_let_1 (@ ord_less_assn A2))) (=> (@ _let_1 B2) (=> (@ (@ ord_less_assn B2) C) (@ _let_1 C))))) (forall ((X nat)) (not (@ (@ ord_less_nat X) X))) (forall ((K3 int)) (=> (@ (@ ord_less_int zero_zero_int) K3) (not (forall ((N5 nat)) (=> (= K3 (@ semiri1314217659103216013at_int N5)) (not (@ (@ ord_less_nat zero_zero_nat) N5))))))) (forall ((C multis2468970476368604999at_nat) (A2 multis2468970476368604999at_nat) (B2 multis2468970476368604999at_nat)) (let ((_let_1 (@ plus_p7104986032573967614at_nat C))) (= (@ (@ minus_4286766774447292334at_nat (@ _let_1 A2)) (@ _let_1 B2)) (@ (@ minus_4286766774447292334at_nat A2) B2)))) (forall ((K3 nat) (M2 nat) (N nat)) (let ((_let_1 (@ plus_plus_nat K3))) (= (@ (@ ord_less_nat (@ _let_1 M2)) (@ _let_1 N)) (@ (@ ord_less_nat M2) N)))) (forall ((K3 nat) (M2 nat) (N nat)) (let ((_let_1 (@ times_times_nat K3))) (= (@ (@ ord_less_nat (@ _let_1 M2)) (@ _let_1 N)) (and (@ (@ ord_less_nat M2) N) (@ (@ ord_less_nat zero_zero_nat) K3))))) (forall ((Xs list_c) (Ys list_nat) (Zs list_c) (P (-> list_c list_nat list_c Bool))) (let ((_let_1 (@ size_size_list_nat Ys))) (=> (= (@ size_size_list_c Xs) _let_1) (=> (= _let_1 (@ size_size_list_c Zs)) (=> (@ (@ (@ P nil_c) nil_nat) nil_c) (=> (forall ((X3 c) (Xs2 list_c) (Y2 nat) (Ys5 list_nat) (Z4 c) (Zs2 list_c)) (let ((_let_1 (@ size_size_list_nat Ys5))) (=> (= (@ size_size_list_c Xs2) _let_1) (=> (= _let_1 (@ size_size_list_c Zs2)) (=> (@ (@ (@ P Xs2) Ys5) Zs2) (@ (@ (@ P (@ (@ cons_c X3) Xs2)) (@ (@ cons_nat Y2) Ys5)) (@ (@ cons_c Z4) Zs2))))))) (@ (@ (@ P Xs) Ys) Zs))))))) (forall ((S set_Pr1261947904930325089at_nat) (T3 set_Pr1261947904930325089at_nat)) (= (@ (@ inf_in2572325071724192079at_nat (@ (@ 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(forall ((A set_int) (B set_int) (C int)) (let ((_let_1 (@ member_int C))) (=> (@ (@ ord_less_eq_set_int A) B) (=> (@ _let_1 A) (@ _let_1 B))))) (forall ((Xs list_P8527749157015355191n_assn) (K3 nat) (X produc6575502325842934193n_assn)) (= (= (@ (@ (@ list_u4534839942911652127n_assn Xs) K3) X) nil_Pr5671120429643327159n_assn) (= Xs nil_Pr5671120429643327159n_assn))) (forall ((A2 set_int)) (not (@ (@ ord_less_set_int A2) bot_bot_set_int))) (forall ((D int) (B set_int) (T int)) (=> (@ (@ ord_less_int zero_zero_int) D) (forall ((X7 int)) (=> (forall ((Xa3 int)) (=> (@ (@ member_int Xa3) (@ (@ set_or1266510415728281911st_int one_one_int) D)) (forall ((Xb3 int)) (=> (@ (@ member_int Xb3) B) (not (= X7 (@ (@ plus_plus_int Xb3) Xa3))))))) (=> (@ (@ ord_less_eq_int X7) T) (@ (@ ord_less_eq_int (@ (@ minus_minus_int X7) D)) T)))))) (forall ((A2 code_integer) (C code_integer) (B2 code_integer)) (= (= (@ (@ times_3573771949741848930nteger A2) C) (@ (@ times_3573771949741848930nteger B2) C)) (or (= C zero_z3403309356797280102nteger) (= A2 B2)))) (forall ((C rat) (A2 rat) (B2 rat)) (let ((_let_1 (@ times_times_rat C))) (= (@ (@ ord_less_rat (@ _let_1 A2)) (@ _let_1 B2)) (or (and (@ (@ ord_less_rat C) zero_zero_rat) (@ (@ ord_less_rat B2) A2)) (and (@ (@ ord_less_rat zero_zero_rat) C) (@ (@ ord_less_rat A2) B2)))))) (forall ((Xa nat) (X nat)) (= (@ (@ ord_le5570908160329646204atural (@ code_natural_of_nat Xa)) (@ code_natural_of_nat X)) (@ (@ ord_less_nat Xa) X))) (forall ((X set_Pr4329608150637261639at_nat) (Y set_Pr4329608150637261639at_nat) (Z set_Pr4329608150637261639at_nat)) (let ((_let_1 (@ sup_su5525570899277871387at_nat X))) (let ((_let_2 (@ sup_su5525570899277871387at_nat Y))) (= (@ _let_1 (@ _let_2 Z)) (@ _let_2 (@ _let_1 Z)))))) (= ord_less_eq_set_nat (lambda ((B3 set_nat) (A3 set_nat)) (= (@ (@ sup_sup_set_nat A3) B3) A3))) (forall ((X produc6575502325842934193n_assn) (Xs list_P8527749157015355191n_assn)) (@ (@ ord_le171416862856029873n_assn (@ 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Xsi)) F)) Q) (@ _let_1 Q))))))) (forall ((B2 code_integer) (A2 code_integer)) (=> (@ (@ ord_le6747313008572928689nteger B2) A2) (not (= A2 B2)))) (forall ((T3 set_Pr4329608150637261639at_nat) (S set_Pr4329608150637261639at_nat)) (= (@ (@ sup_su5525570899277871387at_nat T3) (@ (@ inf_in7913087082777306421at_nat S) T3)) T3)) (= (@ set_ord_lessThan_nat zero_zero_nat) bot_bot_set_nat) (forall ((Xs list_int)) (=> (@ (@ ord_less_eq_nat (@ size_size_list_int Xs)) one_one_nat) (= (@ rotate1_int Xs) Xs))) (forall ((F4 (-> int nat nat))) (= (@ (@ (@ zipf_int_nat_nat F4) nil_int) nil_nat) nil_nat)) (forall ((A set_o) (A2 Bool) (B set_o)) (let ((_let_1 (@ insert_o2 A2))) (let ((_let_2 (@ minus_minus_set_o A))) (= (@ _let_2 (@ _let_1 B)) (@ (@ minus_minus_set_o (@ _let_2 B)) (@ _let_1 bot_bot_set_o)))))) (@ (@ ord_less_eq_nat zero_zero_nat) one_one_nat) (forall ((N nat) (M2 nat)) (= (@ (@ map_nat_nat (lambda ((I4 nat)) (@ (@ plus_plus_nat I4) N))) (@ (@ upt zero_zero_nat) M2)) (@ (@ upt N) (@ (@ plus_plus_nat M2) N)))) (forall ((C2 set_Pr4329608150637261639at_nat) (D set_Pr4329608150637261639at_nat) (A2 produc3843707927480180839at_nat)) (let ((_let_1 (@ insert9069300056098147895at_nat A2))) (=> (@ (@ ord_le1268244103169919719at_nat C2) D) (@ (@ ord_le1268244103169919719at_nat (@ _let_1 C2)) (@ _let_1 D))))) (@ distinct_nat nil_nat) (forall ((X assn) (Y assn) (Z assn)) (= (@ (@ ord_less_eq_assn (@ (@ sup_sup_assn X) Y)) Z) (and (@ (@ ord_less_eq_assn Y) Z) (@ (@ ord_less_eq_assn X) Z)))) (forall ((X assn) (Y assn) (Z assn)) (=> (@ (@ ord_less_eq_assn X) Y) (=> (@ (@ ord_less_assn Y) Z) (@ (@ ord_less_assn X) Z)))) (forall ((X produc3843707927480180839at_nat) (Xs list_P5464809261938338413at_nat)) (=> (not (@ (@ member8757157785044589968at_nat X) (@ set_Pr3765526544606949372at_nat Xs))) (= (@ (@ remove8895909992688781315at_nat X) Xs) Xs))) _let_169 (forall ((A set_nat) (B set_nat) (C2 set_nat)) (let ((_let_1 (@ minus_minus_set_nat A))) (= (@ _let_1 (@ (@ sup_sup_set_nat B) C2)) (@ (@ inf_inf_set_nat (@ _let_1 B)) (@ _let_1 C2))))) (forall ((X produc6575502325842934193n_assn) (Y nat) (R2 set_Pr4672072672689440998sn_nat) (Xs list_P8527749157015355191n_assn) (Ys list_nat)) (let ((_let_1 (@ listre8031510547128344656sn_nat R2))) (=> (@ (@ member746799484843334599sn_nat (@ (@ produc6456381919915743786sn_nat X) Y)) R2) (=> (@ (@ member7785779426634843229st_nat (@ (@ produc6174113896479379136st_nat Xs) Ys)) _let_1) (@ (@ member7785779426634843229st_nat (@ (@ produc6174113896479379136st_nat (@ (@ cons_P2971678138204555879n_assn X) Xs)) (@ (@ cons_nat Y) Ys))) _let_1))))) (forall ((Y set_nat) (Z set_nat) (X set_nat)) (= (@ (@ sup_sup_set_nat (@ (@ inf_inf_set_nat Y) Z)) X) (@ (@ inf_inf_set_nat (@ (@ sup_sup_set_nat Y) X)) (@ (@ sup_sup_set_nat Z) X)))) (forall ((A2 int) (B2 int) (C int) (D2 int)) (=> (= (@ (@ minus_minus_int A2) B2) (@ (@ minus_minus_int C) D2)) (= (@ (@ ord_less_int A2) B2) (@ (@ ord_less_int C) D2)))) (forall ((X nat) (Zs list_nat)) (let ((_let_1 (@ foldl_nat_nat times_times_nat))) (= (@ (@ times_times_nat X) (@ (@ _let_1 one_one_nat) Zs)) (@ (@ _let_1 X) Zs)))) (forall ((F4 (-> nat assn)) (N nat) (N6 nat)) (=> (forall ((N5 nat)) (@ (@ ord_less_assn (@ F4 N5)) (@ F4 (@ suc N5)))) (=> (@ (@ ord_less_nat N) N6) (@ (@ ord_less_assn (@ F4 N)) (@ F4 N6))))) (forall ((K3 nat)) (= (@ set_ord_atLeast_nat (@ suc K3)) (@ (@ minus_minus_set_nat (@ set_ord_atLeast_nat K3)) (@ (@ insert_nat2 K3) bot_bot_set_nat)))) _let_168 (forall ((A set_Pr1261947904930325089at_nat) (B set_Pr1261947904930325089at_nat) (C2 set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ inf_in2572325071724192079at_nat A))) (= (@ (@ minus_1356011639430497352at_nat (@ _let_1 B)) C2) (@ _let_1 (@ (@ minus_1356011639430497352at_nat B) C2))))) (forall ((B2 assn) (A2 assn)) (=> (@ (@ ord_less_assn B2) A2) (not (= A2 B2)))) (forall ((X nat) (Xs list_nat)) (= (@ set_nat2 (@ (@ insert_nat X) Xs)) (@ (@ insert_nat2 X) (@ set_nat2 Xs)))) (forall ((X nat) (B2 nat) (A2 nat)) (let ((_let_1 (@ ord_less_eq_nat X))) (=> (@ _let_1 B2) (@ _let_1 (@ (@ sup_sup_nat A2) B2))))) (@ fun_re2478310338295953701at_nat (@ (@ produc9060074326276436823at_nat fun_min_strict) fun_min_weak)) (forall ((A2 (-> produc3658429121746597890et_nat Bool)) (A set_Pr4532377907799695533_nat_o) (B set_Pr4532377907799695533_nat_o)) (= (= bot_bo7824918357723582233_nat_o (@ (@ inf_in1906310914598751387_nat_o (@ (@ insert5175938949040314269_nat_o A2) A)) B)) (and (= bot_bo7824918357723582233_nat_o (@ (@ inf_in1906310914598751387_nat_o A) B)) (not (@ (@ member6576561426505652726_nat_o A2) B))))) (forall ((A2 set_nat) (A7 set_nat) (B2 set_nat) (B6 set_nat)) (=> (@ (@ ord_less_eq_set_nat A2) A7) (=> (@ (@ ord_less_eq_set_nat B2) B6) (=> (= (@ (@ inf_inf_set_nat A7) B6) bot_bot_set_nat) (= (@ (@ inf_inf_set_nat A2) B2) bot_bot_set_nat))))) (forall ((X int) (Y int) (Xs list_int) (N nat)) (=> (not (= X Y)) (= (= (@ (@ nth_int (@ (@ cons_int X) Xs)) N) Y) (and (@ (@ ord_less_nat zero_zero_nat) N) (= (@ (@ nth_int Xs) (@ (@ minus_minus_nat N) one_one_nat)) Y))))) (forall ((A2 int) (B2 int) (C int)) (let ((_let_1 (@ times_times_int C))) (=> (@ (@ ord_less_eq_int A2) B2) (=> (@ (@ ord_less_eq_int zero_zero_int) C) (@ (@ ord_less_eq_int (@ _let_1 A2)) (@ _let_1 B2)))))) (= ord_less_nat (lambda ((A3 nat) (B3 nat)) (@ (@ ord_less_int (@ semiri1314217659103216013at_int A3)) (@ semiri1314217659103216013at_int B3)))) (forall ((Xs list_P6011104703257516679at_nat) (I nat) (X product_prod_nat_nat)) (@ (@ ord_le3146513528884898305at_nat (@ set_Pr5648618587558075414at_nat (@ (@ (@ list_u6180841689913720943at_nat Xs) I) X))) (@ (@ insert8211810215607154385at_nat X) (@ set_Pr5648618587558075414at_nat Xs)))) (forall ((X filter_nat) (Y filter_nat) (Z filter_nat)) (let ((_let_1 (@ ord_less_filter_nat X))) (=> (@ _let_1 Y) (=> (@ (@ ord_le2510731241096832064er_nat Y) Z) (@ _let_1 Z))))) (forall ((P (-> (-> produc3658429121746597890et_nat Bool) Bool)) (Q (-> (-> produc3658429121746597890et_nat Bool) Bool))) (= (@ (@ ord_le2965882846123202637_nat_o (@ collec939566748876313656_nat_o P)) (@ collec939566748876313656_nat_o Q)) (forall ((X2 (-> produc3658429121746597890et_nat Bool))) (=> (@ P X2) (@ Q X2))))) (not (= _let_20 (@ size_size_list_d xsi))) (= ord_less_nat (lambda ((A3 nat) (B3 nat)) (@ (@ ord_less_int (@ semiri1314217659103216013at_int A3)) (@ semiri1314217659103216013at_int B3)))) (forall ((A set_o) (B set_o)) (= (= (@ (@ minus_minus_set_o A) B) A) (= (@ (@ inf_inf_set_o A) B) bot_bot_set_o))) (forall ((A2 int) (A set_int) (B2 int) (B set_int)) (let ((_let_1 (= A2 B2))) (=> (not (@ (@ member_int A2) A)) (=> (not (@ (@ member_int B2) B)) (= (= (@ (@ insert_int2 A2) A) (@ (@ insert_int2 B2) B)) (and (=> (not _let_1) (exists ((C3 set_int)) (and (not (@ (@ member_int B2) C3)) (= B (@ (@ insert_int2 A2) C3)) (not (@ (@ member_int A2) C3)) (= A (@ (@ insert_int2 B2) C3))))) (=> _let_1 (= A B)))))))) (forall ((A2 code_integer) (B2 code_integer)) (=> (@ (@ ord_le6747313008572928689nteger zero_z3403309356797280102nteger) A2) (=> (@ (@ ord_le6747313008572928689nteger B2) zero_z3403309356797280102nteger) (@ (@ ord_le6747313008572928689nteger (@ (@ times_3573771949741848930nteger B2) A2)) zero_z3403309356797280102nteger)))) (forall ((F4 (-> produc7773217078559923341nt_int Bool)) (A2 (-> int option6357759511663192854e_term)) (B2 product_prod_int_int)) (=> (@ (@ (@ produc9098658269643458507_int_o F4) A2) B2) (@ F4 (@ (@ produc4305682042979456191nt_int A2) B2)))) (forall ((A set_o) (B set_o)) (= (not (= (@ (@ minus_minus_set_o A) B) A)) (not (= (@ (@ inf_inf_set_o A) B) bot_bot_set_o)))) (forall ((A set_Pr4329608150637261639at_nat) (B set_Pr4329608150637261639at_nat)) (@ (@ ord_le1268244103169919719at_nat A) (@ (@ sup_su5525570899277871387at_nat A) B))) (forall ((K3 nat) (M2 nat) (N nat)) (let ((_let_1 (@ ord_less_eq_nat K3))) (=> (@ _let_1 M2) (=> (@ _let_1 N) (= (@ (@ ord_less_nat (@ (@ minus_minus_nat M2) K3)) (@ (@ minus_minus_nat N) K3)) (@ (@ ord_less_nat M2) N)))))) (@ (@ ord_less_eq_rat zero_zero_rat) one_one_rat) (forall ((C set_Pr4329608150637261639at_nat) (A2 set_Pr4329608150637261639at_nat) (D2 set_Pr4329608150637261639at_nat) (B2 set_Pr4329608150637261639at_nat)) (=> (@ (@ ord_le1268244103169919719at_nat C) A2) (=> (@ (@ ord_le1268244103169919719at_nat D2) B2) (@ (@ ord_le1268244103169919719at_nat (@ (@ sup_su5525570899277871387at_nat C) D2)) (@ (@ sup_su5525570899277871387at_nat A2) B2))))) (forall ((A2 code_integer) (B2 code_integer)) (= (= (@ (@ times_3573771949741848930nteger A2) B2) zero_z3403309356797280102nteger) (or (= B2 zero_z3403309356797280102nteger) (= A2 zero_z3403309356797280102nteger)))) (forall ((T code_integer)) (exists ((Z4 code_integer)) (forall ((X7 code_integer)) (=> (@ (@ ord_le6747313008572928689nteger Z4) X7) (not (@ (@ ord_le6747313008572928689nteger X7) T)))))) (forall ((A2 int) (B2 int) (C int)) (= (@ (@ times_times_int (@ (@ minus_minus_int A2) B2)) C) (@ (@ minus_minus_int (@ (@ times_times_int A2) C)) (@ (@ times_times_int B2) C)))) (forall ((A2 rat) (B2 rat)) (= (@ (@ ord_less_eq_rat A2) (@ (@ plus_plus_rat A2) B2)) (@ (@ ord_less_eq_rat zero_zero_rat) B2))) (forall ((Xa product_prod_nat_nat) (X product_prod_nat_nat)) (= (@ (@ plus_plus_int (@ abs_Integ Xa)) (@ abs_Integ X)) (@ abs_Integ (@ (@ (@ produc27273713700761075at_nat (lambda ((X2 nat) (Y5 nat) (__flatten_var_0 product_prod_nat_nat)) (@ (@ produc2626176000494625587at_nat (lambda ((U4 nat) (V4 nat)) (@ (@ product_Pair_nat_nat (@ (@ plus_plus_nat X2) U4)) (@ (@ plus_plus_nat Y5) V4)))) __flatten_var_0))) Xa) X)))) (forall ((A set_Pr4329608150637261639at_nat) (B set_Pr4329608150637261639at_nat)) (= (= (@ (@ inf_in7913087082777306421at_nat A) B) bot_bo228742789529271731at_nat) (forall ((X2 produc3843707927480180839at_nat)) (=> (@ (@ member8757157785044589968at_nat X2) A) (forall ((Y5 produc3843707927480180839at_nat)) (=> (@ (@ member8757157785044589968at_nat Y5) B) (not (= X2 Y5)))))))) (forall ((L list_Code_integer)) (= (@ (@ sorted710888440204495920nteger ord_le6747313008572928689nteger) L) (and (@ distin1543349897113766820nteger L) (@ (@ sorted710888440204495920nteger ord_le3102999989581377725nteger) L)))) (forall ((X c) (Xs list_c)) (@ (@ ord_less_eq_nat (@ size_size_list_c (@ (@ removeAll_c X) Xs))) (@ size_size_list_c Xs))) (forall ((A2 rat) (B2 rat) (C rat) (D2 rat)) (=> (@ (@ ord_less_eq_rat A2) B2) (=> (@ (@ ord_less_rat C) D2) (@ (@ ord_less_rat (@ (@ plus_plus_rat A2) C)) (@ (@ plus_plus_rat B2) D2))))) (forall ((A2 list_d) (B2 list_nat) (A7 list_d) (B6 list_nat)) (=> (= (@ size_size_list_d A2) (@ size_size_list_nat B2)) (=> (= (@ size_size_list_d A7) (@ size_size_list_nat B6)) (= (= (@ (@ zip_d_nat A2) B2) (@ (@ zip_d_nat A7) B6)) (and (= B2 B6) (= A2 A7)))))) (forall ((P (-> nat Bool)) (N nat) (P6 nat) (M2 nat)) (=> (@ P N) (=> (@ (@ ord_less_nat N) P6) (=> (@ (@ ord_less_nat M2) P6) (=> (forall ((N5 nat)) (=> (@ (@ ord_less_nat N5) P6) (=> (@ P N5) (@ P (@ (@ modulo_modulo_nat (@ suc N5)) P6))))) (@ P M2)))))) (forall ((Xs list_P8527749157015355191n_assn) (Ys list_int)) (= (= nil_Pr7991254345159696774sn_int (@ (@ zip_Pr1015554993053626726sn_int Xs) Ys)) (or (= Ys nil_int) (= Xs nil_Pr5671120429643327159n_assn)))) (forall ((A2 nat) (B2 nat) (C nat)) (let ((_let_1 (@ ord_less_eq_nat A2))) (=> (@ _let_1 B2) (=> (@ (@ ord_less_eq_nat B2) C) (@ _let_1 C))))) (forall ((C nat) (B2 nat) (A2 nat)) (let ((_let_1 (@ ord_less_eq_nat C))) (=> (@ _let_1 B2) (@ _let_1 (@ (@ sup_sup_nat A2) B2))))) (forall ((Xs list_P8527749157015355191n_assn)) (= (= (@ rotate328796349445179396n_assn Xs) nil_Pr5671120429643327159n_assn) (= Xs nil_Pr5671120429643327159n_assn))) (forall ((A2 code_integer) (B2 code_integer) (F4 (-> code_integer code_integer)) (C code_integer)) (=> (@ (@ ord_le6747313008572928689nteger A2) B2) (=> (@ (@ ord_le6747313008572928689nteger (@ F4 B2)) C) (=> (forall ((X3 code_integer) (Y2 code_integer)) (=> (@ (@ ord_le6747313008572928689nteger X3) Y2) (@ (@ 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image_4470545334726330049nteger (lambda ((X2 code_integer)) (@ (@ plus_p5714425477246183910nteger X2) L))) (@ (@ set_or8404916559141939852nteger zero_z3403309356797280102nteger) (@ (@ minus_8373710615458151222nteger U) L))) (@ (@ set_or8404916559141939852nteger L) U))) (forall ((A2 int) (B2 int)) (@ (@ ord_less_eq_int (@ (@ ord_min_int A2) B2)) A2)) (= plus_p7104986032573967614at_nat (lambda ((A3 multis2468970476368604999at_nat) (B3 multis2468970476368604999at_nat)) (@ (@ plus_p7104986032573967614at_nat B3) A3))) (forall ((P (-> nat int assn)) (L3 list_int)) (= (@ (@ (@ vEBT_L8298612041380073281at_int P) nil_nat) L3) (@ pure_assn (= L3 nil_int)))) (= (@ butlast_int nil_int) nil_int) (forall ((A2 nat) (B2 nat)) (=> (@ (@ ord_less_nat A2) B2) (@ (@ ord_less_eq_nat A2) B2))) _let_167 (forall ((N nat)) (=> (not (@ (@ dvd_dvd_nat (@ numeral_numeral_nat (@ bit0 one))) N)) (@ (@ ord_less_nat zero_zero_nat) N))) (forall ((X nat) (Y nat) (A set_nat)) (let ((_let_1 (@ member_nat X))) (= (@ _let_1 (@ (@ remove_nat Y) A)) (and (not (= X Y)) (@ _let_1 A))))) (forall ((X set_Pr4329608150637261639at_nat) (Y set_Pr4329608150637261639at_nat)) (@ (@ ord_le1268244103169919719at_nat X) (@ (@ sup_su5525570899277871387at_nat X) Y))) (forall ((X filter_nat) (Y filter_nat)) (@ (@ ord_le2510731241096832064er_nat (@ (@ inf_inf_filter_nat X) Y)) Y)) (forall ((Q6 int) (P6 int)) (let ((_let_1 (@ (@ product_Pair_int_int P6) Q6))) (=> (@ (@ ord_less_int zero_zero_int) Q6) (=> (@ (@ algebr932160517623751201me_int P6) Q6) (= (@ normalize _let_1) _let_1))))) (forall ((B2 nat) (A2 nat)) (= (= (@ (@ plus_plus_nat B2) A2) A2) (= B2 zero_zero_nat))) (forall ((A2 int) (B2 int) (C int)) (let ((_let_1 (@ minus_minus_int A2))) (= (@ (@ minus_minus_int (@ _let_1 B2)) C) (@ _let_1 (@ (@ plus_plus_int B2) C))))) (forall ((A set_o)) (=> (not (= A bot_bot_set_o)) (=> (forall ((X3 Bool) (Y2 Bool)) (=> (@ (@ member_o X3) A) (=> (@ (@ member_o Y2) A) (= X3 Y2)))) (@ is_singleton_o A)))) (forall ((A2 nat) (B2 nat) (C nat)) (let ((_let_1 (@ ord_less_nat A2))) (=> (@ _let_1 B2) (=> (@ (@ ord_less_eq_nat B2) C) (@ _let_1 C))))) (forall ((A2 int) (B2 int) (C int) (D2 int)) (=> (@ (@ ord_less_int A2) B2) (=> (@ (@ ord_less_eq_int C) D2) (=> (@ (@ ord_less_eq_int zero_zero_int) A2) (=> (@ (@ ord_less_int zero_zero_int) C) (@ (@ ord_less_int (@ (@ times_times_int A2) C)) (@ (@ times_times_int B2) D2))))))) (forall ((Y nat) (X nat)) (=> (@ (@ ord_less_eq_nat Y) X) (= (@ (@ ord_less_eq_nat X) Y) (= X Y)))) (forall ((P assn) (A (-> nat int assn)) (Xs list_nat) (I nat) (Xsi list_int) (I3 set_nat) (F assn) (Q assn)) (let ((_let_1 (@ entails P))) (=> (@ _let_1 (@ (@ times_times_assn (@ (@ times_times_assn (@ (@ A (@ (@ nth_nat Xs) I)) (@ (@ nth_int Xsi) I))) (@ (@ (@ (@ vEBT_L7889578638112847646at_int (@ (@ minus_minus_set_nat I3) (@ (@ insert_nat2 I) bot_bot_set_nat))) A) Xs) Xsi))) F)) (=> (@ (@ ord_less_nat I) (@ size_size_list_nat Xs)) (=> (@ (@ member_nat I) I3) (=> (@ (@ entails (@ (@ times_times_assn (@ (@ (@ (@ vEBT_L7889578638112847646at_int I3) A) Xs) Xsi)) F)) Q) (@ _let_1 Q))))))) (= sup_su5525570899277871387at_nat (lambda ((X2 set_Pr4329608150637261639at_nat) (Y5 set_Pr4329608150637261639at_nat)) (@ (@ sup_su5525570899277871387at_nat Y5) X2))) (forall ((X set_o)) (= (@ (@ ord_min_set_o bot_bot_set_o) X) bot_bot_set_o)) _let_166 (forall ((M2 nat) (N nat)) (@ (@ sorted_wrt_nat ord_less_eq_nat) (@ (@ upt M2) N))) (forall ((X code_integer) (Y code_integer) (N nat)) (let ((_let_1 (@ (@ power_8256067586552552935nteger X) N))) (let ((_let_2 (@ times_3573771949741848930nteger Y))) (=> (= (@ (@ times_3573771949741848930nteger X) Y) (@ _let_2 X)) (= (@ (@ times_3573771949741848930nteger _let_1) Y) (@ _let_2 _let_1)))))) (forall ((I nat) (L list_d) (X d) (Y d)) (let ((_let_1 (@ member_d X))) (=> (@ (@ ord_less_nat I) (@ size_size_list_d L)) (= (@ _let_1 (@ set_d2 (@ (@ (@ list_update_d L) I) Y))) (or (= X Y) (and (forall ((Y5 d)) (@ (@ member_d X) (@ set_d2 (@ (@ (@ list_update_d L) I) Y5)))) (@ _let_1 (@ set_d2 L)))))))) (forall ((X list_P5464809261938338413at_nat) (Y list_P5464809261938338413at_nat)) (= (@ (@ (@ if_lis7508161100780771379at_nat true) X) Y) X)) (forall ((A set_Pr1261947904930325089at_nat) (A2 product_prod_nat_nat) (B set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ insert8211810215607154385at_nat A2))) (let ((_let_2 (@ minus_1356011639430497352at_nat A))) (= (@ _let_2 (@ _let_1 B)) (@ (@ minus_1356011639430497352at_nat (@ _let_2 (@ _let_1 bot_bo2099793752762293965at_nat))) B))))) (forall ((A2 int) (B2 int)) (= (@ frct (@ (@ product_Pair_int_int (@ uminus_uminus_int A2)) B2)) (@ uminus_uminus_rat (@ frct (@ (@ product_Pair_int_int A2) B2))))) (forall ((X nat)) (= (@ the_elem_nat (@ (@ insert_nat2 X) bot_bot_set_nat)) X)) (forall ((I int) (J int)) (@ (@ sorted_wrt_int ord_less_int) (@ (@ upto I) J))) (forall ((X product_prod_nat_nat) (A set_Pr1261947904930325089at_nat) (B set_Pr1261947904930325089at_nat)) (= (@ (@ ord_le3146513528884898305at_nat (@ (@ insert8211810215607154385at_nat X) A)) B) (and (@ (@ ord_le3146513528884898305at_nat A) B) (@ (@ member8440522571783428010at_nat X) B)))) (forall ((M2 nat) (N nat)) (= (@ (@ ord_less_eq_nat (@ suc M2)) N) (@ (@ ord_less_nat M2) N))) (forall ((B2 num) (A2 num)) (=> (@ (@ ord_less_num B2) A2) (@ (@ ord_less_eq_num B2) A2))) (forall ((L list_int)) (= (@ (@ ord_less_eq_nat (@ suc zero_zero_nat)) (@ size_size_list_int L)) (not (= L nil_int)))) (forall ((L list_c) (Li list_nat) (A (-> c nat assn))) (=> (not (= (@ size_size_list_c L) (@ size_size_list_nat Li))) (= (@ (@ (@ vEBT_L4839309063161974733_c_nat A) L) Li) bot_bot_assn))) (forall ((Q6 nat) (M2 nat) (N nat)) (=> (@ (@ ord_less_nat zero_zero_nat) Q6) (= (@ (@ ord_less_nat (@ (@ divide_divide_nat M2) Q6)) N) (@ (@ ord_less_nat M2) (@ (@ times_times_nat N) Q6))))) (forall ((A nat) (B nat) (N nat)) (=> (@ (@ ord_less_nat A) B) (=> (@ (@ ord_less_nat zero_zero_nat) N) (@ (@ ord_less_eq_nat (@ (@ 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Xs3) I4)))) (= (@ size_size_list_d Xs3) K3))))) (forall ((B set_Pr4329608150637261639at_nat) (A set_Pr4329608150637261639at_nat)) (= (@ (@ sup_su5525570899277871387at_nat (@ (@ minus_3314409938677909166at_nat B) A)) A) (@ (@ sup_su5525570899277871387at_nat B) A))) (forall ((X int) (Y int) (Z int)) (let ((_let_1 (@ ord_less_int X))) (=> (@ _let_1 Y) (=> (@ (@ ord_less_eq_int Y) Z) (@ _let_1 Z))))) (forall ((Y produc6575502325842934193n_assn) (X produc6575502325842934193n_assn) (Xs list_P8527749157015355191n_assn)) (let ((_let_1 (@ member7957490590177025114n_assn Y))) (=> (@ _let_1 (@ set_Pr1139785259514867910n_assn (@ (@ cons_P2971678138204555879n_assn X) Xs))) (or (= Y X) (@ _let_1 (@ set_Pr1139785259514867910n_assn Xs)))))) (forall ((X nat) (Y nat)) (or (@ (@ ord_less_eq_nat X) Y) (@ (@ ord_less_eq_nat Y) X))) _let_165 (forall ((Xs list_P7985473006766602707_nat_o) (P (-> (-> produc3658429121746597890et_nat Bool) Bool)) (X (-> produc3658429121746597890et_nat Bool))) (=> (forall ((I5 nat)) (=> (@ (@ ord_less_nat I5) (@ size_s8908918004648414271_nat_o Xs)) (@ P (@ (@ nth_Pr6840583978799713108_nat_o Xs) I5)))) (=> (@ (@ member6576561426505652726_nat_o X) (@ set_Pr400311997697478754_nat_o Xs)) (@ P X)))) (forall ((Ns list_nat) (I nat)) (=> (@ (@ sorted_wrt_nat ord_less_nat) Ns) (=> (@ (@ ord_less_nat I) (@ size_size_list_nat Ns)) (@ (@ ord_less_eq_nat I) (@ (@ nth_nat Ns) I))))) (forall ((A2 nat) (B2 nat)) (=> (@ (@ ord_less_eq_nat A2) B2) (= (@ (@ ord_min_nat A2) B2) A2))) (forall ((K3 nat) (N nat)) (=> (@ (@ ord_less_nat zero_zero_nat) K3) (= (@ (@ times_times_nat K3) (@ (@ binomial N) K3)) (@ (@ times_times_nat N) (@ (@ binomial (@ (@ minus_minus_nat N) one_one_nat)) (@ (@ minus_minus_nat K3) one_one_nat)))))) (forall ((A2 assn) (B2 assn) (C assn)) (let ((_let_1 (@ ord_less_assn A2))) (=> (@ _let_1 B2) (=> (= B2 C) (@ _let_1 C))))) (forall ((X produc6575502325842934193n_assn) (Xs list_P8527749157015355191n_assn) (Y produc6575502325842934193n_assn) (Ys list_P8527749157015355191n_assn)) (= (@ (@ zip_Pr8806919808394484215n_assn (@ (@ cons_P2971678138204555879n_assn X) Xs)) (@ (@ cons_P2971678138204555879n_assn Y) Ys)) (@ (@ cons_P9150528168557782045n_assn (@ (@ produc6128706242671166167n_assn X) Y)) (@ (@ zip_Pr8806919808394484215n_assn Xs) Ys)))) (forall ((P (-> nat Bool)) (X nat) (Xs list_nat)) (let ((_let_1 (@ list_ex_nat P))) (= (@ _let_1 (@ (@ cons_nat X) Xs)) (or (@ _let_1 Xs) (@ P X))))) (forall ((A2 nat) (A set_nat) (B set_nat)) (let ((_let_1 (@ inf_inf_set_nat A))) (let ((_let_2 (@ insert_nat2 A2))) (=> (@ (@ member_nat A2) A) (= (@ _let_1 (@ _let_2 B)) (@ _let_2 (@ _let_1 B))))))) (forall ((C int) (A set_int) (B set_int)) (let ((_let_1 (@ member_int C))) (=> (@ _let_1 (@ (@ minus_minus_set_int A) B)) (not (@ _let_1 B))))) (forall ((N nat)) (= (not (= N zero_zero_nat)) (@ (@ ord_less_nat zero_zero_nat) N))) (forall ((A2 set_Pr4329608150637261639at_nat) (B2 set_Pr4329608150637261639at_nat)) (=> (forall ((X3 produc3843707927480180839at_nat)) (let ((_let_1 (@ member8757157785044589968at_nat X3))) (=> (@ _let_1 A2) (not (@ _let_1 B2))))) (= (@ (@ inf_in7913087082777306421at_nat A2) B2) bot_bo228742789529271731at_nat))) (forall ((A2 nat) (B2 nat)) (= (not (@ (@ ord_less_nat A2) B2)) (or (= A2 B2) (not (@ (@ ord_less_eq_nat A2) B2))))) _let_164 (forall ((Xs list_P8527749157015355191n_assn) (X produc6575502325842934193n_assn)) (=> (@ distin4809818325527169450n_assn Xs) (= (@ set_Pr1139785259514867910n_assn (@ (@ remove1670527618125605709n_assn X) Xs)) (@ (@ minus_2301194108115264760n_assn (@ set_Pr1139785259514867910n_assn Xs)) (@ (@ insert5290817439147925377n_assn X) bot_bo1176836662018730877n_assn))))) (forall ((P (-> list_int list_int Bool)) (Xs list_int) (Ys list_int)) (=> (@ (@ P nil_int) nil_int) (=> (forall ((X3 int) (Xs2 list_int)) (@ (@ P (@ (@ cons_int X3) Xs2)) nil_int)) (=> (forall ((Y2 int) (Ys5 list_int)) (@ (@ P nil_int) (@ (@ cons_int Y2) Ys5))) (=> (forall ((X3 int) (Xs2 list_int) (Y2 int) (Ys5 list_int)) (=> (@ (@ P Xs2) Ys5) (@ (@ P (@ (@ cons_int X3) Xs2)) (@ (@ cons_int Y2) Ys5)))) (@ (@ P Xs) Ys)))))) (forall ((X set_Pr1261947904930325089at_nat) (Y set_Pr1261947904930325089at_nat) (Z set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ sup_su6327502436637775413at_nat X))) (=> (forall ((X3 set_Pr1261947904930325089at_nat) (Y2 set_Pr1261947904930325089at_nat) (Z4 set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ inf_in2572325071724192079at_nat X3))) (= (@ _let_1 (@ (@ sup_su6327502436637775413at_nat Y2) Z4)) (@ (@ sup_su6327502436637775413at_nat (@ _let_1 Y2)) (@ _let_1 Z4))))) (= (@ _let_1 (@ (@ inf_in2572325071724192079at_nat Y) Z)) (@ (@ inf_in2572325071724192079at_nat (@ _let_1 Y)) (@ _let_1 Z)))))) (forall ((Q6 int) (R2 int)) (= (@ unique6319869463603278526ux_int (@ (@ product_Pair_int_int Q6) R2)) (= R2 zero_zero_int))) (forall ((C2 set_nat) (A set_nat) (B set_nat)) (let ((_let_1 (@ ord_less_eq_set_nat C2))) (=> (@ _let_1 A) (=> (@ _let_1 B) (@ _let_1 (@ (@ inf_inf_set_nat A) B)))))) (forall ((P (-> nat Bool)) (P3 (-> nat Bool)) (Q (-> nat Bool)) (Q3 (-> nat Bool))) (=> (exists ((Z3 nat)) (forall ((X3 nat)) (=> (@ (@ ord_less_nat X3) Z3) (= (@ P X3) (@ P3 X3))))) (=> (exists ((Z3 nat)) (forall ((X3 nat)) (=> (@ (@ ord_less_nat X3) Z3) (= (@ Q X3) (@ Q3 X3))))) (exists ((Z4 nat)) (forall ((X7 nat)) (=> (@ (@ ord_less_nat X7) Z4) (= (or (@ P X7) (@ Q X7)) (or (@ P3 X7) (@ Q3 X7))))))))) (forall ((A2 int)) (= (@ (@ minus_minus_int A2) zero_zero_int) A2)) (forall ((Xs list_P5464809261938338413at_nat) (A set_Pr4329608150637261639at_nat) (X produc3843707927480180839at_nat) (I nat)) (=> (@ (@ ord_le1268244103169919719at_nat (@ set_Pr3765526544606949372at_nat Xs)) A) (=> (@ (@ member8757157785044589968at_nat X) A) (@ (@ ord_le1268244103169919719at_nat (@ set_Pr3765526544606949372at_nat (@ (@ (@ list_u4696772448584712917at_nat Xs) I) X))) A)))) (= ord_le1268244103169919719at_nat (lambda ((B3 set_Pr4329608150637261639at_nat) (A3 set_Pr4329608150637261639at_nat)) (= (@ (@ sup_su5525570899277871387at_nat A3) B3) A3))) (forall ((B2 rat) (A2 rat) (C rat)) (let ((_let_1 (@ minus_minus_rat C))) (=> (@ (@ ord_less_eq_rat B2) A2) (@ (@ ord_less_eq_rat (@ _let_1 A2)) (@ _let_1 B2))))) (forall ((K3 nat) (Xs list_nat) (X nat)) (let ((_let_1 (@ butlast_nat Xs))) (let ((_let_2 (@ butlast_nat (@ (@ (@ list_update_nat Xs) K3) X)))) (let ((_let_3 (= K3 (@ (@ minus_minus_nat (@ size_size_list_nat Xs)) one_one_nat)))) (and (=> (not _let_3) (= _let_2 (@ (@ (@ list_update_nat _let_1) K3) X))) (=> _let_3 (= _let_2 _let_1))))))) (forall ((X assn) (Y assn)) (@ (@ ord_less_eq_assn (@ (@ inf_inf_assn X) Y)) X)) (forall ((X4 set_Pr1261947904930325089at_nat) (A2 product_prod_nat_nat)) (let ((_let_1 (@ (@ insert8211810215607154385at_nat A2) bot_bo2099793752762293965at_nat))) (= (@ (@ ord_le3146513528884898305at_nat X4) _let_1) (or (= X4 bot_bo2099793752762293965at_nat) (= X4 _let_1))))) (forall ((X int) (Xs list_int)) (= (@ (@ 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B4) (@ (@ P Aa) Ba)))))) (@ (@ P Bx) By))))) (forall ((B2 num) (A2 num)) (=> (@ (@ ord_less_num B2) A2) (not (= A2 B2)))) (forall ((X set_nat) (Y set_nat) (Z set_nat)) (let ((_let_1 (@ sup_sup_set_nat X))) (let ((_let_2 (@ sup_sup_set_nat Y))) (= (@ _let_1 (@ _let_2 Z)) (@ _let_2 (@ _let_1 Z)))))) (forall ((X nat) (Y nat)) (=> (@ (@ ord_less_nat X) Y) (@ (@ ord_less_eq_nat X) Y))) (forall ((A assn) (B assn) (C2 assn)) (=> (@ (@ entails A) B) (@ (@ entails (@ (@ times_times_assn A) C2)) (@ (@ times_times_assn B) C2)))) (forall ((A2 nat) (B2 nat)) (=> (@ (@ ord_less_nat zero_zero_nat) A2) (=> (@ (@ ord_less_nat B2) zero_zero_nat) (@ (@ ord_less_nat (@ (@ times_times_nat B2) A2)) zero_zero_nat)))) (forall ((C (-> produc3658429121746597890et_nat Bool)) (A set_Pr4532377907799695533_nat_o) (B set_Pr4532377907799695533_nat_o)) (let ((_let_1 (@ member6576561426505652726_nat_o C))) (=> (@ _let_1 A) (=> (not (@ _let_1 B)) (@ _let_1 (@ (@ minus_1801376950450012436_nat_o A) B)))))) (forall ((A2 code_integer) (B2 code_integer)) (let ((_let_1 (@ ord_le3102999989581377725nteger zero_z3403309356797280102nteger))) (=> (or (and (@ (@ ord_le3102999989581377725nteger B2) zero_z3403309356797280102nteger) (@ (@ ord_le3102999989581377725nteger A2) zero_z3403309356797280102nteger)) (and (@ _let_1 B2) (@ _let_1 A2))) (@ _let_1 (@ (@ times_3573771949741848930nteger A2) B2))))) (forall ((I nat) (J nat) (P (-> nat nat Bool))) (=> (@ (@ ord_less_nat I) J) (=> (forall ((I5 nat)) (@ (@ P I5) (@ suc I5))) (=> (forall ((I5 nat) (J3 nat) (K nat)) (let ((_let_1 (@ P I5))) (=> (@ (@ ord_less_nat I5) J3) (=> (@ (@ ord_less_nat J3) K) (=> (@ _let_1 J3) (=> (@ (@ P J3) K) (@ _let_1 K))))))) (@ (@ P I) J))))) (forall ((N nat) (P (-> nat Bool))) (= (exists ((I4 nat)) (and (@ P I4) (@ (@ ord_less_nat I4) (@ suc N)))) (or (@ P zero_zero_nat) (exists ((I4 nat)) (and (@ (@ ord_less_nat I4) N) (@ P (@ suc I4))))))) (forall ((A set_nat) (Ys list_nat)) (= (@ (@ ord_less_eq_set_nat A) (@ coset_nat Ys)) (forall ((X2 nat)) (let ((_let_1 (@ member_nat X2))) (=> (@ _let_1 (@ set_nat2 Ys)) (not (@ _let_1 A))))))) (forall ((X int) (Y int)) (= (not (= X Y)) (or (@ (@ ord_less_int X) Y) (@ (@ ord_less_int Y) X)))) (forall ((P assn) (Q assn) (R assn)) (=> (@ (@ entails (@ (@ sup_sup_assn P) Q)) R) (@ (@ entails Q) R))) (forall ((Xs list_d) (Ys list_d) (R2 set_Product_prod_d_d)) (=> (@ (@ member1810801192463332112list_d (@ (@ produc242965421297323863list_d Xs) Ys)) (@ listrel1_d R2)) (= (@ size_size_list_d Xs) (@ size_size_list_d Ys)))) (forall ((I int) (J int)) (@ distinct_int (@ (@ upto I) J))) (forall ((A2 produc3843707927480180839at_nat) (B2 produc3843707927480180839at_nat) (Xs list_P5464809261938338413at_nat)) (= (@ (@ member6009668390874684176at_nat (@ (@ produc2335810615602371415at_nat A2) B2)) (@ set_Pr4552580085251402108at_nat (@ (@ zip_Pr2522280425463452279at_nat Xs) Xs))) (and (= A2 B2) (@ (@ member8757157785044589968at_nat A2) (@ set_Pr3765526544606949372at_nat Xs))))) (forall ((A2 assn) (B2 assn) (F4 (-> assn num)) (C num)) (=> (@ (@ ord_less_eq_assn A2) B2) (=> (@ (@ ord_less_num (@ F4 B2)) C) (=> (forall ((X3 assn) (Y2 assn)) (=> (@ (@ ord_less_eq_assn X3) Y2) (@ (@ ord_less_eq_num (@ F4 X3)) (@ F4 Y2)))) (@ (@ ord_less_num (@ F4 A2)) C))))) (forall ((A2 Bool) (B2 Bool) (A set_o)) (let ((_let_1 (@ member_o A2))) (=> (@ _let_1 (@ (@ insert_o2 B2) A)) (=> (= A2 (not B2)) (@ _let_1 A))))) (forall ((A2 rat) (B2 rat)) (=> (@ (@ ord_less_rat A2) zero_zero_rat) (=> (@ (@ ord_less_rat B2) zero_zero_rat) (@ (@ ord_less_rat (@ (@ plus_plus_rat A2) B2)) zero_zero_rat)))) (forall ((A2 rat) (B2 rat)) (let ((_let_1 (@ ord_less_rat zero_zero_rat))) (=> (@ _let_1 A2) (=> (@ _let_1 B2) (@ _let_1 (@ (@ plus_plus_rat A2) B2)))))) (forall ((C rat) (A2 rat) (B2 rat)) (let ((_let_1 (@ times_times_rat C))) (= (@ (@ ord_less_rat (@ _let_1 A2)) (@ _let_1 B2)) (and (=> (@ (@ ord_less_eq_rat zero_zero_rat) C) (@ (@ ord_less_rat A2) B2)) (=> (@ (@ ord_less_eq_rat C) zero_zero_rat) (@ (@ ord_less_rat B2) A2)))))) (forall ((A2 Bool) (B2 Bool)) (= (@ (@ inf_inf_assn (@ pure_assn A2)) (@ pure_assn B2)) (@ pure_assn (and B2 A2)))) (forall ((A2 code_integer) (B2 code_integer)) (let ((_let_1 (@ ord_le3102999989581377725nteger zero_z3403309356797280102nteger))) (= (@ (@ ord_le3102999989581377725nteger (@ (@ times_3573771949741848930nteger A2) B2)) zero_z3403309356797280102nteger) (or (and (@ (@ ord_le3102999989581377725nteger B2) zero_z3403309356797280102nteger) (@ _let_1 A2)) (and (@ _let_1 B2) (@ (@ ord_le3102999989581377725nteger A2) zero_z3403309356797280102nteger)))))) (forall ((X nat)) (exists ((X_1 nat)) (@ (@ ord_less_nat X) X_1))) _let_163 (forall ((A2 set_Pr1261947904930325089at_nat) (B2 set_Pr1261947904930325089at_nat)) (= (= bot_bo2099793752762293965at_nat (@ (@ sup_su6327502436637775413at_nat A2) B2)) (and (= B2 bot_bo2099793752762293965at_nat) (= A2 bot_bo2099793752762293965at_nat)))) (forall ((Xs list_nat)) (= (= nil_nat (@ rev_nat Xs)) (= Xs nil_nat))) (@ (@ _let_39 (@ produc2626176000494625587at_nat (lambda ((X2 nat) (Y5 nat)) (@ (@ product_Pair_nat_nat Y5) X2)))) (@ produc2626176000494625587at_nat (lambda ((X2 nat) (Y5 nat)) (@ (@ product_Pair_nat_nat Y5) X2)))) (forall ((A2 nat) (B2 nat) (C nat)) (let ((_let_1 (@ times_times_nat C))) (=> (@ (@ ord_less_eq_nat A2) B2) (=> (@ (@ ord_less_eq_nat zero_zero_nat) C) (@ (@ ord_less_eq_nat (@ _let_1 A2)) (@ _let_1 B2)))))) (forall ((X nat) (Y nat)) (=> (@ (@ ord_less_nat X) Y) (not (@ (@ ord_less_nat Y) X)))) (forall ((A2 int) (B2 int) (Q6 int) (R2 int) (Q7 int) (R5 int)) (let ((_let_1 (@ (@ eucl_rel_int A2) B2))) (=> (@ _let_1 (@ (@ product_Pair_int_int Q6) R2)) (=> (@ _let_1 (@ (@ product_Pair_int_int Q7) R5)) (= R2 R5))))) (forall ((A set_nat) (B set_nat) (X nat)) (let ((_let_1 (@ (@ insert_nat2 X) bot_bot_set_nat))) (let ((_let_2 (= A _let_1))) (let ((_let_3 (= B _let_1))) (= (= (@ (@ sup_sup_set_nat A) B) _let_1) (or (and _let_3 (= A bot_bot_set_nat)) (and _let_3 _let_2) (and (= B bot_bot_set_nat) _let_2))))))) (forall ((X assn) (Zs list_assn)) (let ((_let_1 (@ foldl_assn_assn times_times_assn))) (= (@ (@ times_times_assn X) (@ (@ _let_1 one_one_assn) Zs)) (@ (@ _let_1 X) Zs)))) (forall ((A assn)) (@ (@ entailst A) A)) (= ord_le2965882846123202637_nat_o (lambda ((A5 set_Pr4532377907799695533_nat_o) (B7 set_Pr4532377907799695533_nat_o)) (forall ((X2 (-> produc3658429121746597890et_nat Bool))) (let ((_let_1 (@ member6576561426505652726_nat_o X2))) (=> (@ _let_1 A5) (@ _let_1 B7)))))) (forall ((M2 nat) (N nat)) (= (@ (@ ord_less_nat M2) (@ suc N)) (@ (@ ord_less_eq_nat M2) N))) _let_162 (= (@ rev_nat nil_nat) nil_nat) (forall ((A2 code_integer) (F4 (-> num code_integer)) (B2 num) (C num)) (=> (@ (@ ord_le3102999989581377725nteger A2) (@ F4 B2)) (=> (@ (@ ord_less_num B2) C) (=> (forall ((X3 num) (Y2 num)) (=> (@ (@ ord_less_num X3) Y2) (@ (@ ord_le6747313008572928689nteger (@ F4 X3)) (@ F4 Y2)))) (@ (@ ord_le6747313008572928689nteger A2) (@ F4 C)))))) (@ (@ _let_40 (@ produc27273713700761075at_nat (lambda ((X2 nat) (Y5 nat) (__flatten_var_0 product_prod_nat_nat)) (@ (@ produc2626176000494625587at_nat (lambda ((U4 nat) (V4 nat)) (@ (@ product_Pair_nat_nat (@ (@ plus_plus_nat X2) U4)) (@ (@ plus_plus_nat Y5) V4)))) __flatten_var_0)))) (@ produc27273713700761075at_nat (lambda ((X2 nat) (Y5 nat) (__flatten_var_0 product_prod_nat_nat)) (@ (@ produc2626176000494625587at_nat (lambda ((U4 nat) (V4 nat)) (@ (@ product_Pair_nat_nat (@ (@ plus_plus_nat X2) U4)) (@ (@ plus_plus_nat Y5) V4)))) __flatten_var_0)))) (forall ((Xs list_nat) (Ys list_nat) (Xy product_prod_nat_nat) (Xys list_P6011104703257516679at_nat)) (=> (= (@ (@ zip_nat_nat Xs) Ys) (@ (@ cons_P6512896166579812791at_nat Xy) Xys)) (not (forall ((X3 nat) (Xs5 list_nat)) (=> (= Xs (@ (@ cons_nat X3) Xs5)) (forall ((Y2 nat) (Ys4 list_nat)) (=> (= Ys (@ (@ cons_nat Y2) Ys4)) (=> (= Xy (@ (@ product_Pair_nat_nat X3) Y2)) (not (= Xys (@ (@ zip_nat_nat Xs5) Ys4))))))))))) (forall ((P (-> list_P8527749157015355191n_assn Bool)) (Xs list_P8527749157015355191n_assn)) (=> (@ P nil_Pr5671120429643327159n_assn) (=> (forall ((X3 produc6575502325842934193n_assn)) (@ P (@ (@ cons_P2971678138204555879n_assn X3) nil_Pr5671120429643327159n_assn))) (=> (forall ((X12 produc6575502325842934193n_assn) (X23 produc6575502325842934193n_assn) (Xs2 list_P8527749157015355191n_assn)) (=> (@ P Xs2) (@ P (@ (@ cons_P2971678138204555879n_assn X12) (@ (@ cons_P2971678138204555879n_assn X23) Xs2))))) (@ P Xs))))) (forall ((P (-> produc6575502325842934193n_assn produc6575502325842934193n_assn assn)) (L list_P8527749157015355191n_assn)) (= (@ (@ (@ vEBT_L3108143461992071043n_assn P) L) nil_Pr5671120429643327159n_assn) (@ pure_assn (= L nil_Pr5671120429643327159n_assn)))) _let_161 (forall ((P (-> list_int Bool)) (Xs list_int)) (=> (forall ((Xs2 list_int)) (=> (forall ((Ys2 list_int)) (=> (@ (@ ord_less_nat (@ size_size_list_int Ys2)) (@ size_size_list_int Xs2)) (@ P Ys2))) (@ P Xs2))) (@ P Xs))) (forall ((L12 list_int) (L23 list_int)) (let ((_let_1 (@ (@ merge_int L12) L23))) (let ((_let_2 (@ sorted_wrt_int ord_less_eq_int))) (=> (and (@ distinct_int L12) (@ _let_2 L12)) (=> (and (@ distinct_int L23) (@ _let_2 L23)) (and (@ distinct_int _let_1) (@ _let_2 _let_1) (= (@ set_int2 _let_1) (@ (@ sup_sup_set_int (@ set_int2 L12)) (@ set_int2 L23))))))))) (forall ((I nat) (J nat)) (not (@ (@ ord_less_nat (@ (@ plus_plus_nat I) J)) I))) (= bot_bo228742789529271731at_nat (@ collec6321179662152712658at_nat bot_bo6829958733157050602_nat_o)) (forall ((M2 assn) (N assn)) (let ((_let_1 (@ (@ ord_min_assn M2) N))) (= (@ (@ ord_less_eq_assn M2) _let_1) (= _let_1 M2)))) (forall ((Xs list_P7985473006766602707_nat_o) (I nat) (X (-> produc3658429121746597890et_nat Bool)) (Ys list_P9062070895058802706et_nat) (Y produc3658429121746597890et_nat)) (= (@ (@ zip_Pr7134870689397686104et_nat (@ (@ (@ list_u6943956310655620667_nat_o Xs) I) X)) (@ (@ (@ list_u9060326803697358356et_nat Ys) I) Y)) (@ (@ (@ list_u1866171116859985808et_nat (@ (@ zip_Pr7134870689397686104et_nat Xs) Ys)) I) (@ (@ produc5001842942810119800et_nat X) Y)))) (forall ((C produc3843707927480180839at_nat) (A set_Pr4329608150637261639at_nat) (B set_Pr4329608150637261639at_nat)) (let ((_let_1 (@ member8757157785044589968at_nat C))) (= (@ _let_1 (@ (@ minus_3314409938677909166at_nat A) B)) (and (not (@ _let_1 B)) (@ _let_1 A))))) (forall ((L list_num) (I nat) (J nat)) (let ((_let_1 (@ ord_less_nat I))) (let ((_let_2 (@ nth_num L))) (let ((_let_3 (@ size_size_list_num L))) (=> (@ distinct_num L) (=> (@ (@ sorted_wrt_num ord_less_eq_num) L) (=> (@ _let_1 _let_3) (=> (@ (@ ord_less_nat J) _let_3) (= (@ (@ ord_less_num (@ _let_2 I)) (@ _let_2 J)) (@ _let_1 J)))))))))) (forall ((Xs list_P5464809261938338413at_nat) (B set_Pr4329608150637261639at_nat)) (= (@ (@ ord_le1268244103169919719at_nat (@ set_Pr3765526544606949372at_nat Xs)) B) (forall ((X2 produc3843707927480180839at_nat)) (let ((_let_1 (@ member8757157785044589968at_nat X2))) (=> (@ _let_1 (@ set_Pr3765526544606949372at_nat Xs)) (@ _let_1 B)))))) (forall ((X filter_nat) (Y filter_nat) (Z filter_nat)) (let ((_let_1 (@ ord_le2510731241096832064er_nat X))) (=> (@ _let_1 Y) (=> (@ (@ ord_le2510731241096832064er_nat Y) Z) (@ _let_1 Z))))) (forall ((Xs list_d) (I nat) (X d) (Y d)) (let ((_let_1 (@ (@ list_update_d Xs) I))) (= (@ (@ (@ list_update_d (@ _let_1 X)) I) Y) (@ _let_1 Y)))) (forall ((A2 nat) (C2 set_nat) (B set_nat)) (let ((_let_1 (@ (@ inf_inf_set_nat B) C2))) (let ((_let_2 (@ insert_nat2 A2))) (let ((_let_3 (@ (@ inf_inf_set_nat (@ _let_2 B)) C2))) (let ((_let_4 (@ (@ member_nat A2) C2))) (and (=> (not _let_4) (= _let_3 _let_1)) (=> _let_4 (= _let_3 (@ _let_2 _let_1))))))))) (forall ((I nat) (Xs list_c) (X c)) (=> (@ (@ ord_less_nat I) (@ size_size_list_c Xs)) (= (@ (@ nth_c (@ (@ (@ list_update_c Xs) I) X)) I) X))) (forall ((A2 nat) (B2 nat) (F4 (-> nat code_integer)) (C code_integer)) (=> (@ (@ ord_less_nat A2) B2) (=> (@ (@ ord_le3102999989581377725nteger (@ F4 B2)) C) (=> (forall ((X3 nat) (Y2 nat)) (=> (@ (@ ord_less_nat X3) Y2) (@ (@ ord_le6747313008572928689nteger (@ F4 X3)) (@ F4 Y2)))) (@ (@ ord_le6747313008572928689nteger (@ F4 A2)) C))))) (forall ((A2 int) (A set_int) (B2 int)) (let ((_let_1 (@ (@ insert_int2 B2) bot_bot_set_int))) (= (= (@ (@ insert_int2 A2) A) _let_1) (and (@ (@ ord_less_eq_set_int A) _let_1) (= A2 B2))))) (= ord_less_eq_nat (lambda ((A3 nat) (B3 nat)) (= (@ (@ sup_sup_nat A3) B3) B3))) (forall ((X rat) (Y rat)) (=> (@ (@ ord_less_eq_rat X) zero_zero_rat) (=> (@ (@ ord_less_eq_rat Y) zero_zero_rat) (= (= (@ (@ plus_plus_rat X) Y) zero_zero_rat) (and (= X zero_zero_rat) (= Y zero_zero_rat)))))) (forall ((X Bool) (A set_o)) (let ((_let_1 (@ insert_o2 X))) (=> (not (@ (@ member_o X) A)) (= (@ (@ minus_minus_set_o (@ _let_1 A)) (@ _let_1 bot_bot_set_o)) A)))) (forall ((A2 nat)) (= (@ (@ plus_plus_nat A2) zero_zero_nat) A2)) (forall ((A2 assn)) (not (@ (@ ord_less_assn A2) A2))) (forall ((X nat) (Y nat) (Xs list_nat) (Ys list_nat)) (=> (@ (@ member8440522571783428010at_nat (@ (@ product_Pair_nat_nat X) Y)) (@ set_Pr5648618587558075414at_nat (@ (@ zip_nat_nat Xs) Ys))) (not (=> (@ (@ member_nat X) (@ set_nat2 Xs)) (not (@ (@ member_nat Y) (@ set_nat2 Ys))))))) (forall ((A2 rat) (C rat) (B2 rat)) (=> (@ (@ ord_less_eq_rat (@ (@ times_times_rat A2) C)) (@ (@ times_times_rat B2) C)) (=> (@ (@ ord_less_rat zero_zero_rat) C) (@ (@ ord_less_eq_rat A2) B2)))) (@ fun_re7357418987779152907at_nat (@ (@ produc5245064249948416855at_nat ms_strict) ms_weak)) (forall ((M2 nat) (N nat)) (=> (@ (@ ord_less_nat M2) N) (not (= N zero_zero_nat)))) (forall ((L list_P8926467638345140077od_d_d)) (not (forall ((L1 list_d) (L22 list_d)) (let ((_let_1 (@ size_size_list_d L22))) (=> (= L (@ (@ zip_d_d L1) L22)) (=> (= (@ size_size_list_d L1) _let_1) (not (= (@ size_s2191833749160108505od_d_d L) _let_1)))))))) (forall ((A2 nat)) (not (@ (@ ord_less_nat A2) A2))) (forall ((A2 code_integer) (B2 code_integer) (F4 (-> code_integer int)) (C int)) (=> (@ (@ ord_le6747313008572928689nteger A2) B2) (=> (@ (@ ord_less_int (@ F4 B2)) C) (=> (forall ((X3 code_integer) (Y2 code_integer)) (=> (@ (@ ord_le6747313008572928689nteger X3) Y2) (@ (@ ord_less_int (@ F4 X3)) (@ F4 Y2)))) (@ (@ ord_less_int (@ F4 A2)) C))))) (forall ((Y nat) (X nat)) (@ (@ ord_less_eq_nat Y) (@ (@ sup_sup_nat X) Y))) (forall ((S set_nat) (T3 set_nat)) (= (@ (@ inf_inf_set_nat (@ (@ sup_sup_set_nat S) T3)) T3) T3)) (forall ((C nat) (A2 nat) (B2 nat)) (let ((_let_1 (@ plus_plus_nat C))) (= (@ (@ minus_minus_nat (@ _let_1 A2)) (@ _let_1 B2)) (@ (@ minus_minus_nat A2) B2)))) (forall ((X (-> int option6357759511663192854e_term)) (Y product_prod_int_int) (Xs list_i8448526496819171953e_term) (Ys list_P5707943133018811711nt_int)) (=> (@ (@ member7034335876925520548nt_int (@ (@ produc4305682042979456191nt_int X) Y)) (@ set_Pr1633835384712236856nt_int (@ (@ zip_in8766932505889695135nt_int Xs) Ys))) (@ (@ member8845023287901829240e_term X) (@ set_in5217446777445088012e_term Xs)))) (forall ((Xs list_d) (Ys list_d)) (= (@ size_s2191833749160108505od_d_d (@ (@ zip_d_d Xs) Ys)) (@ (@ ord_min_nat (@ size_size_list_d Xs)) (@ size_size_list_d Ys)))) (forall ((Xs list_d) (Ys list_c) (R2 set_Product_prod_d_c)) (= (@ (@ member1739767152416986127list_c (@ (@ produc242965416994095062list_c Xs) Ys)) (@ listrel_d_c R2)) (and (= (@ size_size_list_d Xs) (@ size_size_list_c Ys)) (forall ((N2 nat)) (=> (@ (@ ord_less_nat N2) (@ size_size_list_d Xs)) (@ (@ member2287536777068640527od_d_c (@ (@ product_Pair_d_c (@ (@ nth_d Xs) N2)) (@ (@ nth_c Ys) N2))) R2)))))) (forall ((B2 num) (A2 num)) (=> (@ (@ ord_less_num B2) A2) (= (@ (@ ord_min_num A2) B2) B2))) (forall ((P assn) (A (-> d int assn)) (Xs list_d) (I nat) (Xsi list_int) (I3 set_nat) (F assn) (Q assn)) (let ((_let_1 (@ entails P))) (=> (@ _let_1 (@ (@ times_times_assn (@ (@ times_times_assn (@ (@ A (@ (@ nth_d Xs) I)) (@ (@ nth_int Xsi) I))) (@ (@ (@ (@ vEBT_L7818125895572137869_d_int (@ (@ minus_minus_set_nat I3) (@ (@ insert_nat2 I) bot_bot_set_nat))) A) Xs) Xsi))) F)) (=> (@ (@ ord_less_nat I) (@ size_size_list_d Xs)) (=> (@ (@ member_nat I) I3) (=> (@ (@ entails (@ (@ times_times_assn (@ (@ (@ (@ vEBT_L7818125895572137869_d_int I3) A) Xs) Xsi)) F)) Q) (@ _let_1 Q))))))) (forall ((I set_int) (Ww list_set_int)) (let ((_let_1 (@ foldl_6819690284573351271et_int sup_sup_set_int))) (= (@ (@ _let_1 I) Ww) (@ (@ sup_sup_set_int I) (@ (@ _let_1 bot_bot_set_int) Ww))))) (forall ((Ys list_int) (R2 set_Pr958786334691620121nt_int)) (not (@ (@ member6698963635872716290st_int (@ (@ produc364263696895485585st_int nil_int) Ys)) (@ lex_int R2)))) (forall ((X21 produc6575502325842934193n_assn) (X222 list_P8527749157015355191n_assn) (Y21 produc6575502325842934193n_assn) (Y222 list_P8527749157015355191n_assn)) (= (= (@ (@ cons_P2971678138204555879n_assn X21) X222) (@ (@ cons_P2971678138204555879n_assn Y21) Y222)) (and (= X21 Y21) (= X222 Y222)))) (forall ((U2 set_Pr4329608150637261639at_nat) (V set_Pr4329608150637261639at_nat) (X produc3843707927480180839at_nat)) (let ((_let_1 (@ member8757157785044589968at_nat X))) (=> (@ (@ ord_le1268244103169919719at_nat U2) V) (=> (@ _let_1 (@ transi2703068831062848130at_nat U2)) (@ _let_1 (@ transi2703068831062848130at_nat V)))))) (forall ((B2 nat) (A2 nat) (C nat)) (let ((_let_1 (@ ord_less_nat C))) (=> (@ (@ ord_less_eq_nat B2) A2) (=> (@ _let_1 B2) (@ _let_1 A2))))) (forall ((A2 rat) (B2 rat)) (=> (@ (@ ord_less_rat zero_zero_rat) A2) (=> (@ (@ ord_less_rat B2) zero_zero_rat) (@ (@ ord_less_rat (@ (@ times_times_rat A2) B2)) zero_zero_rat)))) (forall ((B2 nat) (A2 nat)) (=> (@ (@ ord_less_nat B2) A2) (not (= A2 B2)))) (forall ((X set_nat) (B2 set_nat) (A2 set_nat)) (let ((_let_1 (@ ord_less_eq_set_nat X))) (=> (@ _let_1 B2) (@ _let_1 (@ (@ sup_sup_set_nat A2) B2))))) (forall ((X produc6575502325842934193n_assn) (Xs list_P8527749157015355191n_assn) (I nat) (Y produc6575502325842934193n_assn)) (let ((_let_1 (@ cons_P2971678138204555879n_assn X))) (= (@ (@ (@ list_u4534839942911652127n_assn (@ _let_1 Xs)) (@ suc I)) Y) (@ _let_1 (@ (@ (@ list_u4534839942911652127n_assn Xs) I) Y))))) (forall ((C product_prod_nat_nat) (A set_Pr1261947904930325089at_nat) (B set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ member8440522571783428010at_nat C))) (=> (@ _let_1 (@ (@ inf_in2572325071724192079at_nat A) B)) (@ _let_1 A)))) (forall ((A set_Pr4329608150637261639at_nat) (C2 set_Pr4329608150637261639at_nat) (B set_Pr4329608150637261639at_nat)) (=> (@ (@ ord_le1268244103169919719at_nat A) C2) (=> (@ (@ ord_le1268244103169919719at_nat B) C2) (@ (@ ord_le1268244103169919719at_nat (@ (@ sup_su5525570899277871387at_nat A) B)) C2)))) (forall ((X assn)) (= (@ (@ inf_inf_assn bot_bot_assn) X) bot_bot_assn)) (forall ((I rat) (J rat) (K3 rat) (L rat)) (=> (and (= K3 L) (@ (@ ord_less_eq_rat I) J)) (@ (@ ord_less_eq_rat (@ (@ plus_plus_rat I) K3)) (@ (@ plus_plus_rat J) L)))) (forall ((X code_integer) (A2 code_integer) (Y code_integer) (U code_integer) (V2 code_integer)) (let ((_let_1 (@ ord_le3102999989581377725nteger zero_z3403309356797280102nteger))) (=> (@ (@ ord_le3102999989581377725nteger X) A2) (=> (@ (@ ord_le3102999989581377725nteger Y) A2) (=> (@ _let_1 U) (=> (@ _let_1 V2) (=> (= (@ (@ plus_p5714425477246183910nteger U) V2) one_one_Code_integer) (@ (@ ord_le3102999989581377725nteger (@ (@ plus_p5714425477246183910nteger (@ (@ times_3573771949741848930nteger U) X)) (@ (@ times_3573771949741848930nteger V2) Y))) A2)))))))) (= ord_less_eq_rat (lambda ((A3 rat) (B3 rat)) (@ (@ ord_less_eq_rat (@ (@ minus_minus_rat A3) B3)) zero_zero_rat))) (forall ((I nat) (J nat)) (let ((_let_1 (@ suc I))) (=> (@ (@ ord_less_nat _let_1) J) (= (@ linord2614967742042102400et_nat (@ (@ set_or5834768355832116004an_nat I) J)) (@ (@ cons_nat _let_1) (@ linord2614967742042102400et_nat (@ (@ set_or5834768355832116004an_nat _let_1) J))))))) (forall ((Xs list_nat) (Ys list_nat)) (let ((_let_1 (@ sorted_wrt_nat ord_less_nat))) (=> (@ _let_1 Xs) (=> (@ _let_1 Ys) (=> (= (@ set_nat2 Ys) (@ set_nat2 Xs)) (= Ys Xs)))))) (forall ((R set_Pr1261947904930325089at_nat)) (@ (@ ord_le3146513528884898305at_nat R) (@ transi6264000038957366511cl_nat R))) (forall ((X int) (Xs list_int)) (=> (@ (@ member_int X) (@ set_int2 Xs)) (@ (@ ord_less_nat (@ size_size_list_int (@ (@ removeAll_int X) Xs))) (@ size_size_list_int Xs)))) (forall ((Xs list_int) (I nat) (X int)) (=> (@ (@ ord_less_eq_nat (@ size_size_list_int Xs)) I) (= (@ (@ (@ list_update_int Xs) I) X) Xs))) (forall ((A2 nat) (C nat) (B2 nat) (D2 nat)) (=> (@ (@ ord_less_eq_nat A2) C) (=> (@ (@ ord_less_eq_nat B2) D2) (@ (@ ord_less_eq_nat (@ (@ ord_min_nat A2) B2)) (@ (@ ord_min_nat C) D2))))) (forall ((A2 Bool) (C2 set_o) (B set_o)) (let ((_let_1 (@ (@ inf_inf_set_o B) C2))) (let ((_let_2 (@ insert_o2 A2))) (let ((_let_3 (@ (@ inf_inf_set_o (@ _let_2 B)) C2))) (let ((_let_4 (@ (@ member_o A2) C2))) (and (=> _let_4 (= _let_3 (@ _let_2 _let_1))) (=> (not _let_4) (= _let_3 _let_1)))))))) (forall ((Xs list_nat) (Ys list_int)) (= (= (@ (@ zip_nat_int Xs) Ys) nil_Pr1301135604781543011at_int) (or (= Ys nil_int) (= Xs nil_nat)))) (forall ((I nat) (Xs list_d) (X d)) (=> (@ (@ ord_less_nat I) (@ size_size_list_d Xs)) (= (= (@ (@ (@ list_update_d Xs) I) X) Xs) (= (@ (@ nth_d Xs) I) X)))) (forall ((A set_int) (B set_int)) (=> (@ (@ ord_less_eq_set_int A) B) (= (@ (@ minus_minus_set_int A) B) bot_bot_set_int))) (forall ((X int) (Xs list_int) (Y int) (Ys list_int) (R2 set_Pr958786334691620121nt_int)) (let ((_let_1 (@ listrel1_int R2))) (= (@ (@ member6698963635872716290st_int (@ (@ produc364263696895485585st_int (@ (@ cons_int X) Xs)) (@ (@ cons_int Y) Ys))) _let_1) (or (and (@ (@ member5262025264175285858nt_int (@ (@ product_Pair_int_int X) Y)) R2) (= Xs Ys)) (and (= X Y) (@ (@ member6698963635872716290st_int (@ (@ produc364263696895485585st_int Xs) Ys)) _let_1)))))) (forall ((C produc3843707927480180839at_nat) (A set_Pr4329608150637261639at_nat) (B set_Pr4329608150637261639at_nat)) (let ((_let_1 (@ member8757157785044589968at_nat C))) (=> (@ _let_1 (@ (@ sup_su5525570899277871387at_nat A) B)) (=> (not (@ _let_1 A)) (@ _let_1 B))))) (forall ((Xs list_nat) (P (-> nat Bool))) (= (forall ((X2 nat)) (=> (@ (@ member_nat X2) (@ set_nat2 Xs)) (@ P X2))) (forall ((I4 nat)) (=> (@ (@ ord_less_nat I4) (@ size_size_list_nat Xs)) (@ P (@ (@ nth_nat Xs) I4)))))) (forall ((Y int) (X int) (Xs list_int)) (let ((_let_1 (@ member_int Y))) (=> (@ _let_1 (@ set_int2 (@ (@ cons_int X) Xs))) (or (@ _let_1 (@ set_int2 Xs)) (= Y X))))) (forall ((X c) (Xs list_c)) (= (@ size_size_list_c (@ (@ cons_c X) Xs)) (@ suc (@ size_size_list_c Xs)))) (forall ((N nat)) (= (@ (@ order_underS_nat bNF_Ca8665028551170535155natLeq) N) (@ collect_nat (lambda ((X2 nat)) (@ (@ ord_less_nat X2) N))))) (forall ((Xs list_P6011104703257516679at_nat) (Ys list_P6011104703257516679at_nat) (F4 (-> product_prod_nat_nat Bool)) (G (-> product_prod_nat_nat Bool))) (=> (= Xs Ys) (=> (forall ((X3 product_prod_nat_nat)) (=> (@ (@ member8440522571783428010at_nat X3) (@ set_Pr5648618587558075414at_nat Ys)) (= (@ F4 X3) (@ G X3)))) (= (@ (@ list_e7689525607045846085at_nat F4) Xs) (@ (@ list_e7689525607045846085at_nat G) Ys))))) (forall ((A2 rat) (B2 rat) (N nat)) (let ((_let_1 (@ ord_less_eq_rat zero_zero_rat))) (=> (@ _let_1 A2) (=> (@ _let_1 B2) (=> (@ (@ ord_less_nat zero_zero_nat) N) (= (@ (@ ord_less_eq_rat (@ (@ power_power_rat A2) N)) (@ (@ power_power_rat B2) N)) (@ (@ ord_less_eq_rat A2) B2))))))) (forall ((A2 set_nat) (B2 set_nat)) (=> (= A2 (@ (@ inf_inf_set_nat A2) B2)) (@ (@ ord_less_eq_set_nat A2) B2))) (forall ((A2 nat) (B2 nat)) (=> (@ (@ ord_less_nat A2) B2) (not (forall ((C4 nat)) (=> (= B2 (@ (@ plus_plus_nat A2) C4)) (= C4 zero_zero_nat)))))) (forall ((I nat) (I3 set_nat) (Xs list_int) (A (-> int int assn)) (Xsi list_int)) (=> (not (@ (@ member_nat I) I3)) (=> (@ (@ ord_less_nat I) (@ size_size_list_int Xs)) (= (@ (@ (@ (@ vEBT_L8888932350013902202nt_int (@ (@ insert_nat2 I) I3)) A) Xs) Xsi) (@ (@ times_times_assn (@ (@ A (@ (@ nth_int Xs) I)) (@ (@ nth_int Xsi) I))) (@ (@ (@ (@ vEBT_L8888932350013902202nt_int I3) A) Xs) Xsi)))))) (forall ((B2 set_Pr4329608150637261639at_nat) (A2 set_Pr4329608150637261639at_nat) (C set_Pr4329608150637261639at_nat)) (let ((_let_1 (@ sup_su5525570899277871387at_nat B2))) (let ((_let_2 (@ sup_su5525570899277871387at_nat A2))) (= (@ _let_1 (@ _let_2 C)) (@ _let_2 (@ _let_1 C)))))) (forall ((K3 num)) (let ((_let_1 (@ numeral_numeral_nat K3))) (= (@ set_ord_atMost_nat _let_1) (@ (@ insert_nat2 _let_1) (@ set_ord_atMost_nat (@ pred_numeral K3)))))) (@ (@ _let_160 (lambda ((X2 product_prod_int_int) (Y5 product_prod_int_int)) (let ((_let_1 (@ product_snd_int_int Y5))) (let ((_let_2 (@ product_snd_int_int X2))) (@ (@ product_Pair_int_int (@ (@ plus_plus_int (@ (@ times_times_int (@ product_fst_int_int X2)) _let_1)) (@ (@ times_times_int (@ product_fst_int_int Y5)) _let_2))) (@ (@ times_times_int _let_2) _let_1)))))) (lambda ((X2 product_prod_int_int) (Y5 product_prod_int_int)) (let ((_let_1 (@ product_snd_int_int Y5))) (let ((_let_2 (@ product_snd_int_int X2))) (@ (@ product_Pair_int_int (@ (@ plus_plus_int (@ (@ times_times_int (@ product_fst_int_int X2)) _let_1)) (@ (@ times_times_int (@ product_fst_int_int Y5)) _let_2))) (@ (@ times_times_int _let_2) _let_1)))))) (forall ((B2 assn) (A2 assn) (C assn)) (let ((_let_1 (@ ord_less_assn C))) (=> (@ (@ ord_less_assn B2) A2) (=> (@ _let_1 B2) (@ _let_1 A2))))) (= ord_less_set_nat (lambda ((B3 set_nat) (A3 set_nat)) (and (not (@ (@ ord_less_eq_set_nat A3) B3)) (@ (@ ord_less_eq_set_nat B3) A3)))) (forall ((C nat) (A set_nat) (B set_nat)) (let ((_let_1 (@ member_nat C))) (=> (@ _let_1 A) (@ _let_1 (@ (@ sup_sup_set_nat A) B))))) (forall ((A2 nat) (B2 nat)) (=> (not (@ (@ ord_less_nat A2) B2)) (= (@ (@ plus_plus_nat B2) (@ (@ minus_minus_nat A2) B2)) A2))) (forall ((A2 int) (B2 int) (C int)) (=> (= A2 B2) (=> (@ (@ ord_less_int B2) C) (@ (@ ord_less_int A2) C)))) (forall ((F4 (-> int int produc6575502325842934193n_assn)) (A2 int) (As2 list_int) (B2 int) (Bs list_int)) (let ((_let_1 (@ zipf_i7756021159461276697n_assn F4))) (= (@ (@ _let_1 (@ (@ cons_int A2) As2)) (@ (@ cons_int B2) Bs)) (@ (@ cons_P2971678138204555879n_assn (@ (@ F4 A2) B2)) (@ (@ _let_1 As2) Bs))))) (forall ((N nat) (M2 nat)) (=> (@ (@ ord_less_nat zero_zero_nat) N) (=> (@ (@ ord_less_nat (@ suc zero_zero_nat)) M2) (@ (@ ord_less_nat N) (@ (@ times_times_nat N) M2))))) (forall ((Y set_nat) (X set_nat)) (=> (@ (@ ord_less_eq_set_nat Y) X) (= (@ (@ ord_less_eq_set_nat X) Y) (= X Y)))) (forall ((A2 nat) (B2 nat)) (=> (not (= A2 B2)) (=> (@ (@ ord_less_eq_nat A2) B2) (@ (@ ord_less_nat A2) B2)))) (forall ((X nat) (Ys list_nat)) (let ((_let_1 (@ sorted_wrt_nat ord_less_eq_nat))) (= (@ _let_1 (@ (@ cons_nat X) Ys)) (and (forall ((X2 nat)) (=> (@ (@ member_nat X2) (@ set_nat2 Ys)) (@ (@ ord_less_eq_nat X) X2))) (@ _let_1 Ys))))) _let_159 (forall ((Z int)) (= (@ (@ ord_less_nat (@ suc zero_zero_nat)) (@ nat2 Z)) (@ (@ ord_less_int one_one_int) Z))) (forall ((X int) (Ys list_int)) (let ((_let_1 (@ sorted_wrt_int ord_less_int))) (= (@ _let_1 (@ (@ cons_int X) Ys)) (and (forall ((X2 int)) (=> (@ (@ member_int X2) (@ set_int2 Ys)) (@ (@ ord_less_int X) X2))) (@ _let_1 Ys))))) (forall ((X rat) (Y rat)) (=> (forall ((Z4 rat)) (=> (@ (@ ord_less_rat zero_zero_rat) Z4) (=> (@ (@ ord_less_rat Z4) one_one_rat) (@ (@ ord_less_eq_rat (@ (@ times_times_rat Z4) X)) Y)))) (@ (@ ord_less_eq_rat X) Y))) (forall ((P (-> nat nat assn)) (A2 nat) (As2 list_nat) (C nat) (Cs list_nat)) (let ((_let_1 (@ vEBT_L8301102511889123557at_nat P))) (= (@ (@ _let_1 (@ (@ cons_nat A2) As2)) (@ (@ cons_nat C) Cs)) (@ (@ times_times_assn (@ (@ P A2) C)) (@ (@ _let_1 As2) Cs))))) (forall ((A set_int) (B set_int)) (= (not (= (@ (@ minus_minus_set_int A) B) A)) (not (= (@ (@ inf_inf_set_int A) B) 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C)))) (forall ((X filter_nat) (Y filter_nat) (Z filter_nat)) (=> (@ (@ ord_le2510731241096832064er_nat X) Y) (=> (@ (@ ord_less_filter_nat Y) Z) (@ (@ ord_less_filter_nat X) Z)))) (forall ((F4 (-> int int int))) (= (@ (@ (@ zipf_int_int_int F4) nil_int) nil_int) nil_int)) (forall ((X Bool) (B set_o) (A set_o)) (=> (@ (@ member_o X) B) (= (@ (@ minus_minus_set_o (@ (@ insert_o2 X) A)) B) (@ (@ minus_minus_set_o A) B)))) (forall ((Xs list_nat)) (= (= (@ set_nat2 Xs) bot_bot_set_nat) (= Xs nil_nat))) (forall ((K3 nat) (P (-> nat c Bool))) (= (forall ((I4 nat)) (=> (@ (@ ord_less_nat I4) K3) (exists ((X8 c)) (@ (@ P I4) X8)))) (exists ((Xs3 list_c)) (and (= (@ size_size_list_c Xs3) K3) (forall ((I4 nat)) (=> (@ (@ ord_less_nat I4) K3) (@ (@ P I4) (@ (@ nth_c Xs3) I4)))))))) (= ord_less_int (lambda ((A3 int) (B3 int)) (and (not (= A3 B3)) (= A3 (@ (@ inf_inf_int A3) B3))))) (forall ((A set_Pr4329608150637261639at_nat) (B set_Pr4329608150637261639at_nat)) (= (@ (@ 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X)))) (forall ((Xs list_c) (Ys list_c)) (=> (= (@ size_size_list_c Xs) (@ size_size_list_c Ys)) (= (@ (@ zip_c_c (@ rev_c Xs)) (@ rev_c Ys)) (@ rev_Product_prod_c_c (@ (@ zip_c_c Xs) Ys))))) (forall ((X21 c) (X222 list_c)) (= (@ size_size_list_c (@ (@ cons_c X21) X222)) (@ (@ plus_plus_nat (@ size_size_list_c X222)) (@ suc zero_zero_nat)))) (forall ((X int) (Y int)) (=> (= X Y) (@ (@ ord_less_eq_int X) Y))) (forall ((T num)) (exists ((Z4 num)) (forall ((X7 num)) (=> (@ (@ ord_less_num Z4) X7) (@ (@ ord_less_num T) X7))))) (forall ((A2 nat) (B2 nat)) (=> (@ (@ ord_less_eq_nat zero_zero_nat) A2) (=> (@ (@ ord_less_eq_nat B2) zero_zero_nat) (@ (@ ord_less_eq_nat (@ (@ times_times_nat B2) A2)) zero_zero_nat)))) (forall ((Xs list_P5464809261938338413at_nat) (I nat) (X produc3843707927480180839at_nat)) (@ (@ ord_le1268244103169919719at_nat (@ set_Pr3765526544606949372at_nat (@ (@ (@ list_u4696772448584712917at_nat Xs) I) X))) (@ (@ insert9069300056098147895at_nat X) (@ set_Pr3765526544606949372at_nat Xs)))) (forall ((P (-> produc7773217078559923341nt_int Bool)) (X produc7773217078559923341nt_int)) (=> (forall ((A4 (-> int option6357759511663192854e_term)) (B4 int) (C4 int)) (@ P (@ (@ produc4305682042979456191nt_int A4) (@ (@ product_Pair_int_int B4) C4)))) (@ P X))) (forall ((Xs list_c) (Ys list_c) (R2 set_Product_prod_c_c)) (=> (@ (@ member7012247553653173456list_c (@ (@ produc5515445818230282391list_c Xs) Ys)) (@ listrel_c_c R2)) (= (@ size_size_list_c Xs) (@ size_size_list_c Ys)))) (forall ((Begin nat) (End nat)) (= (@ (@ (@ slice_nat Begin) End) nil_nat) nil_nat)) (= ord_le2510731241096832064er_nat (lambda ((X2 filter_nat) (Y5 filter_nat)) (or (= X2 Y5) (@ (@ ord_less_filter_nat X2) Y5)))) (forall ((Xs list_P5464809261938338413at_nat)) (= (= (@ set_Pr3765526544606949372at_nat Xs) bot_bo228742789529271731at_nat) (= Xs nil_Pr8341282898164651117at_nat))) (forall ((Y product_prod_nat_nat) (YS set_Pr1261947904930325089at_nat) (X product_prod_nat_nat) (XS set_Pr1261947904930325089at_nat)) (=> (@ (@ member8440522571783428010at_nat Y) YS) (=> (@ (@ member8206827879206165904at_nat (@ (@ produc6161850002892822231at_nat X) Y)) fun_pair_leq) (=> (@ (@ member8757157785044589968at_nat (@ (@ produc2922128104949294807at_nat XS) YS)) fun_max_weak) (@ (@ member8757157785044589968at_nat (@ (@ produc2922128104949294807at_nat (@ (@ insert8211810215607154385at_nat X) XS)) YS)) fun_max_weak))))) (forall ((X set_Pr4329608150637261639at_nat) (Y set_Pr4329608150637261639at_nat) (Z set_Pr4329608150637261639at_nat)) (let ((_let_1 (@ inf_in7913087082777306421at_nat X))) (@ (@ ord_le1268244103169919719at_nat (@ (@ sup_su5525570899277871387at_nat (@ _let_1 Y)) (@ _let_1 Z))) (@ _let_1 (@ (@ sup_su5525570899277871387at_nat Y) Z))))) (forall ((Xs list_nat) (Xs4 list_nat) (Xsi list_int) (Xsi2 list_int) (A (-> nat int assn)) (A6 (-> nat int assn))) (=> (= Xs Xs4) (=> (= Xsi Xsi2) (=> (forall ((X3 nat) (Xi int)) (=> (@ (@ member_nat X3) (@ set_nat2 Xs4)) (=> (@ (@ member_int Xi) (@ set_int2 Xsi2)) (= (@ (@ A X3) Xi) (@ (@ A6 X3) Xi))))) (= (@ (@ (@ vEBT_L8298612041380073281at_int A) Xs) Xsi) (@ (@ (@ vEBT_L8298612041380073281at_int A6) Xs4) Xsi2)))))) (= ord_le6747313008572928689nteger (lambda ((B3 code_integer) (A3 code_integer)) (and (@ (@ ord_le3102999989581377725nteger B3) A3) (not (= A3 B3))))) (forall ((Z int)) (not (forall ((X3 nat) (Y2 nat)) (not (= Z (@ abs_Integ (@ (@ product_Pair_nat_nat X3) Y2))))))) (forall ((X set_Pr1261947904930325089at_nat)) (@ (@ total_7212417256332265445at_nat (@ (@ insert9200635055090092081at_nat X) bot_bo3083307316010499117at_nat)) (@ (@ insert9069300056098147895at_nat (@ (@ produc2922128104949294807at_nat X) X)) bot_bo228742789529271731at_nat))) (forall ((A2 nat) (B2 nat) (Xs list_nat)) (= (@ (@ member8440522571783428010at_nat (@ (@ product_Pair_nat_nat A2) B2)) (@ set_Pr5648618587558075414at_nat (@ (@ zip_nat_nat Xs) Xs))) (and (@ (@ member_nat A2) (@ set_nat2 Xs)) (= A2 B2)))) (forall ((N nat)) (= (@ field_nat (@ collec3392354462482085612at_nat (@ produc6081775807080527818_nat_o (lambda ((X2 nat) (Y5 nat)) (and (@ (@ ord_less_nat X2) N) (@ (@ ord_less_nat Y5) N) (@ (@ ord_less_eq_nat X2) Y5)))))) (@ collect_nat (lambda ((X2 nat)) (@ (@ ord_less_nat X2) N))))) (forall ((A2 produc6575502325842934193n_assn) (B2 produc6575502325842934193n_assn) (Xs list_P8527749157015355191n_assn)) (let ((_let_1 (@ member7957490590177025114n_assn A2))) (=> (not (= A2 B2)) (= (@ _let_1 (@ set_Pr1139785259514867910n_assn (@ (@ remove1670527618125605709n_assn B2) Xs))) (@ _let_1 (@ set_Pr1139785259514867910n_assn Xs)))))) (forall ((Xs list_d) (P (-> d d Bool))) (=> (@ (@ ord_less_eq_nat (@ size_size_list_d Xs)) one_one_nat) (@ (@ sorted_wrt_d P) Xs))) (forall ((X Bool) (A set_o)) (let ((_let_1 (@ insert_o2 X))) (let ((_let_2 (@ _let_1 A))) (= (@ _let_1 _let_2) _let_2)))) (forall ((I3 set_nat) (I7 set_nat) (Xs list_nat) (Xs4 list_nat) (Xsi list_nat) (Xsi2 list_nat) (A (-> nat nat assn)) (A6 (-> nat nat 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set_Pr4532377907799695533_nat_o)) (let ((_let_1 (@ member6576561426505652726_nat_o C))) (=> (@ _let_1 A) (@ _let_1 (@ (@ sup_su5209123915105501825_nat_o A) B))))) (forall ((A2 Bool) (A set_o) (B2 Bool)) (let ((_let_1 (@ (@ insert_o2 B2) bot_bot_set_o))) (= (= (@ (@ insert_o2 A2) A) _let_1) (and (= A2 B2) (@ (@ ord_less_eq_set_o A) _let_1))))) (forall ((X assn) (A2 assn) (B2 assn)) (let ((_let_1 (@ ord_less_eq_assn X))) (=> (@ _let_1 (@ (@ inf_inf_assn A2) B2)) (not (=> (@ _let_1 A2) (not (@ _let_1 B2))))))) (forall ((F4 (-> nat num)) (N nat) (N6 nat)) (=> (forall ((N5 nat)) (@ (@ ord_less_num (@ F4 N5)) (@ F4 (@ suc N5)))) (=> (@ (@ ord_less_nat N) N6) (@ (@ ord_less_num (@ F4 N)) (@ F4 N6))))) (forall ((A2 int) (B2 int)) (= (@ (@ ord_less_int (@ (@ ord_min_int A2) B2)) B2) (@ (@ ord_less_int A2) B2))) (= ord_less_nat (lambda ((A3 nat) (B3 nat)) (and (not (= A3 B3)) (= A3 (@ (@ inf_inf_nat A3) B3))))) (forall ((D2 int) (D int) (A set_int) (T int)) (=> (@ (@ dvd_dvd_int D2) D) (forall ((X7 int)) (let ((_let_1 (@ plus_plus_int X7))) (let ((_let_2 (@ dvd_dvd_int D2))) (=> (forall ((Xa3 int)) (=> (@ (@ member_int Xa3) (@ (@ set_or1266510415728281911st_int one_one_int) D)) (forall ((Xb3 int)) (=> (@ (@ member_int Xb3) A) (not (= X7 (@ (@ minus_minus_int Xb3) Xa3))))))) (=> (@ _let_2 (@ _let_1 T)) (@ _let_2 (@ (@ plus_plus_int (@ _let_1 D)) T))))))))) (forall ((A2 rat)) (= (@ (@ times_times_rat one_one_rat) A2) A2)) (forall ((Xs list_c) (Ys list_nat) (X c)) (=> (= (@ size_size_list_c Xs) (@ size_size_list_nat Ys)) (=> (@ (@ member_c X) (@ set_c2 Xs)) (not (forall ((Y2 nat)) (not (@ (@ member8195077246299207702_c_nat (@ (@ product_Pair_c_nat X) Y2)) (@ set_Pr3395872032415823530_c_nat (@ (@ zip_c_nat Xs) Ys))))))))) (forall ((A2 int) (B2 int) (F4 (-> int int)) (C int)) (=> (@ (@ ord_less_eq_int A2) B2) (=> (@ (@ ord_less_eq_int (@ F4 B2)) C) (=> (forall ((X3 int) (Y2 int)) (=> (@ (@ ord_less_eq_int X3) Y2) (@ (@ ord_less_eq_int (@ F4 X3)) (@ F4 Y2)))) (@ (@ ord_less_eq_int (@ F4 A2)) C))))) (forall ((A2 code_integer) (B2 code_integer)) (=> (@ (@ ord_le3102999989581377725nteger zero_z3403309356797280102nteger) A2) (=> (@ (@ ord_le3102999989581377725nteger B2) zero_z3403309356797280102nteger) (@ (@ ord_le3102999989581377725nteger (@ (@ times_3573771949741848930nteger A2) B2)) zero_z3403309356797280102nteger)))) (forall ((A2 int) (B2 int) (F4 (-> int assn)) (C assn)) (=> (@ (@ ord_less_eq_int A2) B2) (=> (@ (@ ord_less_eq_assn (@ F4 B2)) C) (=> (forall ((X3 int) (Y2 int)) (=> (@ (@ ord_less_eq_int X3) Y2) (@ (@ ord_less_eq_assn (@ F4 X3)) (@ F4 Y2)))) (@ (@ ord_less_eq_assn (@ F4 A2)) C))))) (forall ((M5 list_P8527749157015355191n_assn) (P assn)) (@ (@ (@ (@ fI_RESULT M5) P) one_one_assn) top_top_assn)) (forall ((X nat) (Y nat)) (=> (not (= X Y)) (=> (not (@ (@ ord_less_nat X) Y)) (@ (@ ord_less_nat Y) X)))) (forall ((S set_Pr4532377907799695533_nat_o) (R (-> (-> produc3658429121746597890et_nat Bool) (-> produc3658429121746597890et_nat Bool) Bool))) (=> (forall ((X3 (-> produc3658429121746597890et_nat Bool)) (Y2 (-> produc3658429121746597890et_nat Bool))) (=> (@ (@ member6576561426505652726_nat_o X3) S) (=> (@ (@ member6576561426505652726_nat_o Y2) S) (=> (not (= X3 Y2)) (@ (@ R X3) Y2))))) (@ (@ pairwi2432143822833250616_nat_o R) S))) (forall ((I nat) (J nat) (K3 nat) (L nat)) (=> (and (@ (@ ord_less_nat I) J) (@ (@ ord_less_nat K3) L)) (@ (@ ord_less_nat (@ (@ plus_plus_nat I) K3)) (@ (@ plus_plus_nat J) L)))) (forall ((A set_Pr4532377907799695533_nat_o) (B2 (-> produc3658429121746597890et_nat Bool)) (B set_Pr4532377907799695533_nat_o)) (let ((_let_1 (@ inf_in1906310914598751387_nat_o A))) (= (= bot_bo7824918357723582233_nat_o (@ _let_1 (@ (@ insert5175938949040314269_nat_o B2) B))) (and (not (@ (@ member6576561426505652726_nat_o B2) A)) (= bot_bo7824918357723582233_nat_o (@ _let_1 B)))))) (forall ((N nat)) (let ((_let_1 (@ bit0 one))) (let ((_let_2 (@ numeral_numeral_nat _let_1))) (=> (= (@ (@ modulo_modulo_nat N) (@ 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_let_1 Xs) (=> (@ _let_1 Ys) (=> (= (@ set_int2 Ys) (@ set_int2 Xs)) (= Ys Xs)))))) (forall ((N nat)) (=> (@ (@ ord_less_nat zero_zero_nat) N) (= (@ suc (@ (@ minus_minus_nat N) (@ suc zero_zero_nat))) N))) (forall ((Xs list_assn) (Ys list_assn)) (= (= (@ (@ zip_assn_assn Xs) Ys) nil_Pr5671120429643327159n_assn) (or (= Xs nil_assn) (= Ys nil_assn)))) (forall ((A2 code_integer) (B2 code_integer) (C code_integer) (D2 code_integer)) (=> (@ (@ ord_le6747313008572928689nteger A2) B2) (=> (@ (@ ord_le6747313008572928689nteger C) D2) (@ (@ ord_le6747313008572928689nteger (@ (@ plus_p5714425477246183910nteger A2) C)) (@ (@ plus_p5714425477246183910nteger B2) D2))))) (forall ((Y nat) (Ys list_nat) (Xs list_P8527749157015355191n_assn) (R2 set_Pr247834672394327052n_assn)) (=> (@ (@ member3687432546746012131n_assn (@ (@ produc7706768604797473534n_assn (@ (@ cons_nat Y) Ys)) Xs)) (@ listre3128913020232611374n_assn R2)) (not (forall ((Y2 produc6575502325842934193n_assn) (Ys5 list_P8527749157015355191n_assn)) (=> (= Xs (@ (@ cons_P2971678138204555879n_assn Y2) Ys5)) (=> (@ (@ member7704815987135142381n_assn (@ (@ produc1553784393020010504n_assn Y) Y2)) R2) (not (@ (@ member3687432546746012131n_assn (@ (@ produc7706768604797473534n_assn Ys) Ys5)) (@ listre3128913020232611374n_assn R2))))))))) (forall ((X set_int)) (= (@ (@ sup_sup_set_int X) bot_bot_set_int) X)) (forall ((C rat) (B2 rat)) (= (@ (@ ord_less_eq_rat C) (@ (@ times_times_rat B2) C)) (and (=> (@ (@ ord_less_rat zero_zero_rat) C) (@ (@ ord_less_eq_rat one_one_rat) B2)) (=> (@ (@ ord_less_rat C) zero_zero_rat) (@ (@ ord_less_eq_rat B2) one_one_rat))))) (forall ((N nat) (Xs list_P8527749157015355191n_assn)) (= (@ (@ ord_less_eq_nat (@ suc N)) (@ size_s6829681357464350627n_assn Xs)) (exists ((X2 produc6575502325842934193n_assn) (Ys3 list_P8527749157015355191n_assn)) (and (= Xs (@ (@ cons_P2971678138204555879n_assn X2) Ys3)) (@ (@ ord_less_eq_nat N) (@ size_s6829681357464350627n_assn Ys3)))))) (forall ((A set_Pr4532377907799695533_nat_o)) (=> (forall ((Y2 (-> produc3658429121746597890et_nat Bool))) (not (@ (@ member6576561426505652726_nat_o Y2) A))) (= A bot_bo7824918357723582233_nat_o))) (forall ((H2 produc3658429121746597890et_nat)) (= (@ (@ rep_assn top_top_assn) H2) (@ in_range H2))) (forall ((X set_int)) (= (@ (@ inf_inf_set_int bot_bot_set_int) X) bot_bot_set_int)) (forall ((C (-> produc3658429121746597890et_nat Bool)) (A set_Pr4532377907799695533_nat_o) (B set_Pr4532377907799695533_nat_o)) (let ((_let_1 (@ member6576561426505652726_nat_o C))) (=> (@ _let_1 (@ (@ inf_in1906310914598751387_nat_o A) B)) (not (=> (@ _let_1 A) (not (@ _let_1 B))))))) (forall ((A2 nat) (B2 nat) (C nat)) (let ((_let_1 (@ plus_plus_nat C))) (=> (@ (@ ord_less_eq_nat A2) B2) (= (@ (@ minus_minus_nat (@ _let_1 B2)) A2) (@ _let_1 (@ (@ minus_minus_nat B2) A2)))))) (forall ((Y nat) (X nat)) (let ((_let_1 (@ (@ bezw Y) (@ (@ modulo_modulo_nat X) Y)))) (let ((_let_2 (@ product_snd_int_int _let_1))) (=> (@ (@ ord_less_nat zero_zero_nat) Y) (= (@ (@ bezw X) Y) (@ (@ product_Pair_int_int _let_2) (@ (@ minus_minus_int (@ product_fst_int_int _let_1)) (@ (@ times_times_int _let_2) (@ semiri1314217659103216013at_int (@ (@ divide_divide_nat X) Y)))))))))) (forall ((A2 code_integer) (B2 code_integer)) (=> (@ (@ ord_le6747313008572928689nteger A2) zero_z3403309356797280102nteger) (=> (@ (@ ord_le3102999989581377725nteger B2) zero_z3403309356797280102nteger) (@ (@ ord_le6747313008572928689nteger (@ (@ plus_p5714425477246183910nteger A2) B2)) zero_z3403309356797280102nteger)))) (forall ((F4 (-> produc1908205239877642774nteger Bool)) (A2 (-> produc6241069584506657477e_term option6357759511663192854e_term)) (B2 produc8923325533196201883nteger)) (=> (@ (@ (@ produc1217013493180205570eger_o F4) A2) B2) (@ F4 (@ (@ produc8603105652947943368nteger A2) B2)))) (forall ((A2 nat) (A7 nat) (B2 nat) (B6 nat) (N7 nat)) (=> (@ (@ ord_less_eq_nat A2) A7) (=> (@ (@ ord_less_eq_nat B2) B6) (@ (@ ord_less_eq_nat (@ (@ plus_plus_nat (@ (@ times_times_nat A2) N7)) B2)) (@ (@ plus_plus_nat (@ (@ times_times_nat A7) N7)) B6))))) (forall ((A2 rat) (B2 rat)) (= (@ (@ ord_less_rat A2) (@ (@ plus_plus_rat A2) B2)) (@ (@ ord_less_rat zero_zero_rat) B2))) (forall ((A2 nat) (C nat) (B2 nat)) (= (@ (@ ord_less_nat (@ (@ plus_plus_nat A2) C)) (@ (@ plus_plus_nat B2) C)) (@ (@ ord_less_nat A2) B2))) (forall ((A2 filter_nat)) (@ (@ ord_le2510731241096832064er_nat bot_bot_filter_nat) A2)) (forall ((A2 int)) (= (@ (@ plus_plus_int zero_zero_int) A2) A2)) (forall ((C int) (A set_int) (B set_int)) (let ((_let_1 (@ member_int C))) (=> (@ _let_1 (@ (@ inf_inf_set_int A) B)) (@ _let_1 B)))) (forall ((A2 nat) (B2 nat)) (=> (@ (@ ord_less_nat A2) B2) (not (@ (@ ord_less_nat B2) A2)))) (forall ((A2 rat) (B2 rat)) (=> (@ (@ ord_less_eq_rat zero_zero_rat) A2) (=> (@ (@ ord_less_eq_rat B2) zero_zero_rat) (@ (@ ord_less_eq_rat (@ (@ times_times_rat A2) B2)) zero_zero_rat)))) (forall ((A2 rat) (B2 rat)) (= (= (@ (@ plus_plus_rat A2) B2) A2) (= B2 zero_zero_rat))) (forall ((Y product_prod_nat_nat) (X product_prod_nat_nat) (Xs list_P6011104703257516679at_nat)) (let ((_let_1 (@ member8440522571783428010at_nat Y))) (=> (@ _let_1 (@ set_Pr5648618587558075414at_nat (@ (@ cons_P6512896166579812791at_nat X) Xs))) (or (= Y X) (@ _let_1 (@ set_Pr5648618587558075414at_nat Xs)))))) (forall ((A2 rat) (B2 rat) (C rat)) (let ((_let_1 (@ plus_plus_rat C))) (=> (@ (@ ord_less_eq_rat A2) B2) (@ (@ ord_less_eq_rat (@ _let_1 A2)) (@ _let_1 B2))))) (@ null_nat nil_nat) (forall ((M2 nat) (N nat)) (let ((_let_1 (@ suc M2))) (=> (@ (@ ord_less_nat M2) N) (=> (not (= _let_1 N)) (@ (@ ord_less_nat _let_1) N))))) (forall ((A2 rat) (B2 rat)) (let ((_let_1 (@ ord_less_rat zero_zero_rat))) (=> (@ (@ ord_less_eq_rat zero_zero_rat) A2) (=> (@ _let_1 B2) (@ _let_1 (@ (@ plus_plus_rat A2) B2)))))) (forall ((B2 product_prod_nat_nat) (A2 product_prod_nat_nat) (A set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ (@ insert8211810215607154385at_nat B2) bot_bo2099793752762293965at_nat))) (= (= _let_1 (@ (@ insert8211810215607154385at_nat A2) A)) (and (= A2 B2) (@ (@ ord_le3146513528884898305at_nat A) _let_1))))) (forall ((B2 multis2468970476368604999at_nat) (A2 multis2468970476368604999at_nat) (C multis2468970476368604999at_nat)) (=> (= (@ (@ plus_p7104986032573967614at_nat B2) A2) (@ (@ plus_p7104986032573967614at_nat C) A2)) (= B2 C))) (forall ((C2 set_Pr4329608150637261639at_nat) (A set_Pr4329608150637261639at_nat) (B set_Pr4329608150637261639at_nat)) (=> (@ (@ ord_le1268244103169919719at_nat C2) (@ (@ sup_su5525570899277871387at_nat A) B)) (not (forall ((A8 set_Pr4329608150637261639at_nat)) (=> (@ (@ ord_le1268244103169919719at_nat A8) A) (forall ((B8 set_Pr4329608150637261639at_nat)) (=> (@ (@ ord_le1268244103169919719at_nat B8) B) (not (= C2 (@ (@ sup_su5525570899277871387at_nat A8) B8)))))))))) (forall ((A2 assn) (F4 (-> code_integer assn)) (B2 code_integer) (C code_integer)) (=> (= A2 (@ F4 B2)) (=> (@ (@ ord_le6747313008572928689nteger B2) C) (=> (forall ((X3 code_integer) (Y2 code_integer)) (=> (@ (@ ord_le6747313008572928689nteger X3) Y2) (@ (@ ord_less_assn (@ F4 X3)) (@ F4 Y2)))) (@ (@ ord_less_assn A2) (@ F4 C)))))) (forall ((P assn) (Q assn)) (=> (forall ((H produc3658429121746597890et_nat)) (=> (@ (@ rep_assn P) H) (@ (@ rep_assn Q) H))) (@ (@ entails P) Q))) (forall ((A assn) (B assn) (C2 assn)) (=> (@ (@ entailst (@ (@ sup_sup_assn A) B)) C2) (@ (@ entailst B) C2))) (forall ((X set_nat) (B2 set_nat) (A2 set_nat)) (let ((_let_1 (@ ord_less_set_nat X))) (=> (@ _let_1 B2) (@ _let_1 (@ (@ sup_sup_set_nat A2) B2))))) (forall ((A set_o)) (not (@ (@ ord_less_set_o A) bot_bot_set_o))) (forall ((Xs list_d) (Ys list_nat)) (= (@ size_s8550281435913984804_d_nat (@ (@ product_d_nat Xs) Ys)) (@ (@ times_times_nat (@ size_size_list_d Xs)) (@ size_size_list_nat Ys)))) (forall ((A2 code_integer)) (@ (@ ord_le3102999989581377725nteger zero_z3403309356797280102nteger) (@ (@ times_3573771949741848930nteger A2) A2))) (forall ((I3 set_nat) (I7 set_nat) (A (-> nat nat assn)) (A6 (-> nat nat assn)) (Xs list_nat) (Xs4 list_nat) (Xsi list_nat) (Xsi2 list_nat)) (=> (= I3 I7) (=> (= A A6) (=> (= (@ size_size_list_nat Xs) (@ size_size_list_nat Xs4)) (=> (= (@ size_size_list_nat Xsi) (@ size_size_list_nat Xsi2)) (=> (forall ((I5 nat)) (let ((_let_1 (@ size_size_list_nat Xs))) (=> (@ (@ member_nat I5) I3) (=> (@ (@ ord_less_nat I5) _let_1) (=> (= _let_1 (@ size_size_list_nat Xsi)) (and (= (@ (@ nth_nat Xs) I5) (@ (@ nth_nat Xs4) I5)) (= (@ (@ nth_nat Xsi) I5) (@ (@ nth_nat Xsi2) I5)))))))) (= (@ (@ (@ (@ vEBT_L7892069108621897922at_nat I3) A) Xs) Xsi) (@ (@ (@ (@ vEBT_L7892069108621897922at_nat I7) A6) Xs4) Xsi2)))))))) (forall ((A2 filter_nat) (B2 filter_nat)) (@ (@ ord_le2510731241096832064er_nat (@ (@ inf_inf_filter_nat A2) B2)) B2)) (forall ((M2 int) (Ms list_int) (N int) (Ns list_int) (R2 set_Pr958786334691620121nt_int)) (let ((_let_1 (@ lenlex_int R2))) (let ((_let_2 (@ size_size_list_int Ns))) (let ((_let_3 (@ size_size_list_int Ms))) (= (@ (@ member6698963635872716290st_int (@ (@ produc364263696895485585st_int (@ (@ cons_int M2) Ms)) (@ (@ cons_int N) Ns))) _let_1) (or (@ (@ ord_less_nat _let_3) _let_2) (and (= _let_3 _let_2) (@ (@ member5262025264175285858nt_int (@ (@ product_Pair_int_int M2) N)) R2)) (and (@ (@ member6698963635872716290st_int (@ (@ produc364263696895485585st_int Ms) Ns)) _let_1) (= M2 N)))))))) (forall ((A2 filter_nat) (B2 filter_nat)) (@ (@ ord_le2510731241096832064er_nat A2) (@ (@ sup_sup_filter_nat A2) B2))) (forall ((A2 int) (B2 int)) (=> (not (= (@ (@ times_times_int A2) B2) zero_zero_int)) (and (not (= B2 zero_zero_int)) (not (= A2 zero_zero_int))))) (forall ((K3 nat) (Xs list_c) (Y c)) (let ((_let_1 (@ size_size_list_c Xs))) (=> (@ (@ ord_less_nat K3) _let_1) (= (@ rev_c (@ (@ (@ list_update_c Xs) K3) Y)) (@ (@ (@ list_update_c (@ rev_c Xs)) (@ (@ minus_minus_nat (@ (@ minus_minus_nat _let_1) K3)) one_one_nat)) Y))))) (forall ((A2 int) (B2 int) (F4 (-> int nat)) (C nat)) (=> (@ (@ ord_less_eq_int A2) B2) (=> (@ (@ ord_less_eq_nat (@ F4 B2)) C) (=> (forall ((X3 int) (Y2 int)) (=> (@ (@ ord_less_eq_int X3) Y2) (@ (@ ord_less_eq_nat (@ F4 X3)) (@ F4 Y2)))) (@ (@ ord_less_eq_nat (@ F4 A2)) C))))) (forall ((A set_Pr1261947904930325089at_nat) (X product_prod_nat_nat)) (let ((_let_1 (@ (@ insert8211810215607154385at_nat X) bot_bo2099793752762293965at_nat))) (=> (@ (@ ord_le3146513528884898305at_nat A) _let_1) (or (= A _let_1) (= A bot_bo2099793752762293965at_nat))))) (forall ((X rat) (Y rat)) (= (@ (@ ord_less_eq_rat (@ (@ plus_plus_rat (@ (@ times_times_rat X) X)) (@ (@ times_times_rat Y) Y))) zero_zero_rat) (and (= X zero_zero_rat) (= Y zero_zero_rat)))) (forall ((A2 produc6575502325842934193n_assn) (B2 produc6575502325842934193n_assn) (Xs list_P8527749157015355191n_assn)) (let ((_let_1 (@ (@ cons_P2971678138204555879n_assn B2) Xs))) (let ((_let_2 (@ cons_P2971678138204555879n_assn A2))) (= (@ distin4809818325527169450n_assn (@ _let_2 _let_1)) (and (not (= A2 B2)) (@ distin4809818325527169450n_assn (@ _let_2 Xs)) (@ distin4809818325527169450n_assn _let_1)))))) _let_155 (forall ((B2 int) (A2 int)) (= (@ (@ ord_less_int (@ (@ plus_plus_int B2) A2)) B2) (@ (@ ord_less_int A2) zero_zero_int))) (forall ((C int) (A set_int) (B set_int)) (let ((_let_1 (@ member_int C))) (=> (@ _let_1 A) (@ _let_1 (@ (@ sup_sup_set_int A) B))))) (forall ((A2 nat) (A set_nat)) (=> (@ (@ member_nat A2) A) (= (@ (@ insert_nat2 A2) A) A))) (forall ((A2 int) (B2 int)) (=> (@ (@ ord_less_eq_int A2) zero_zero_int) (=> (@ (@ ord_less_eq_int B2) zero_zero_int) (@ (@ ord_less_eq_int (@ (@ plus_plus_int A2) B2)) zero_zero_int)))) (= ord_less_set_nat (lambda ((A5 set_nat) (B7 set_nat)) (and (@ (@ ord_less_eq_set_nat A5) B7) (not (@ (@ ord_less_eq_set_nat B7) A5))))) (forall ((A2 code_integer) (B2 code_integer)) (=> (@ (@ ord_le6747313008572928689nteger zero_z3403309356797280102nteger) A2) (=> (@ (@ ord_le6747313008572928689nteger B2) zero_z3403309356797280102nteger) (@ (@ ord_le6747313008572928689nteger (@ (@ times_3573771949741848930nteger A2) B2)) zero_z3403309356797280102nteger)))) (forall ((A2 num) (F4 (-> assn num)) (B2 assn) (C assn)) (=> (= A2 (@ F4 B2)) (=> (@ (@ ord_less_assn B2) C) (=> (forall ((X3 assn) (Y2 assn)) (=> (@ (@ ord_less_assn X3) Y2) (@ (@ ord_less_num (@ F4 X3)) (@ F4 Y2)))) (@ (@ ord_less_num A2) (@ F4 C)))))) (forall ((A set_nat) (B set_nat)) (= (= (@ (@ inf_inf_set_nat A) B) bot_bot_set_nat) (forall ((X2 nat)) (let ((_let_1 (@ member_nat X2))) (=> (@ _let_1 A) (not (@ _let_1 B))))))) (forall ((A2 int) (C int) (B2 int)) (= (= (@ (@ times_times_int A2) C) (@ (@ times_times_int B2) C)) (or (= C zero_zero_int) (= A2 B2)))) (forall ((N nat)) (=> (@ (@ ord_less_nat zero_zero_nat) N) (exists ((M6 nat)) (= N (@ suc M6))))) _let_153 (= inf_inf_set_nat (lambda ((X2 set_nat) (Y5 set_nat)) (@ (@ inf_inf_set_nat Y5) X2))) (forall ((X code_integer) (A2 code_integer) (Y code_integer) (U code_integer) (V2 code_integer)) (let ((_let_1 (@ ord_le3102999989581377725nteger zero_z3403309356797280102nteger))) (=> (@ (@ ord_le6747313008572928689nteger X) A2) (=> (@ (@ ord_le6747313008572928689nteger Y) A2) (=> (@ _let_1 U) (=> (@ _let_1 V2) (=> (= (@ (@ plus_p5714425477246183910nteger U) V2) one_one_Code_integer) (@ (@ ord_le6747313008572928689nteger (@ (@ plus_p5714425477246183910nteger (@ (@ times_3573771949741848930nteger U) X)) (@ (@ times_3573771949741848930nteger V2) Y))) A2)))))))) (forall ((M2 nat) (N nat)) (=> (@ (@ ord_less_eq_nat (@ suc M2)) N) (@ (@ ord_less_nat M2) N))) (forall ((A2 int)) (= (@ frct (@ (@ product_Pair_int_int zero_zero_int) A2)) zero_zero_rat)) (forall ((A set_int)) (= (@ (@ inf_inf_set_int A) bot_bot_set_int) bot_bot_set_int)) (forall ((P (-> list_nat Bool)) (Xs list_nat)) (=> (@ P nil_nat) (=> (forall ((X3 nat)) (@ P (@ (@ cons_nat X3) nil_nat))) (=> (forall ((X12 nat) (X23 nat) (Xs2 list_nat)) (=> (@ P Xs2) (@ P (@ (@ cons_nat X12) (@ (@ cons_nat X23) Xs2))))) (@ P Xs))))) (forall ((A2 nat) (B2 nat)) (=> (@ (@ ord_less_nat A2) B2) (= (@ (@ inf_inf_nat A2) B2) A2))) (forall ((A2 filter_nat) (B2 filter_nat)) (=> (@ (@ ord_le2510731241096832064er_nat A2) B2) (= (@ (@ inf_inf_filter_nat A2) B2) A2))) _let_152 (= ord_less_int (lambda ((X2 int) (Y5 int)) (and (not (= X2 Y5)) (@ (@ ord_less_eq_int X2) Y5)))) (forall ((Y assn) (X assn)) (@ (@ ord_less_eq_assn Y) (@ (@ sup_sup_assn X) Y))) (forall ((A2 assn) (B2 assn) (C assn)) (let ((_let_1 (@ sup_sup_assn A2))) (= (@ (@ sup_sup_assn (@ _let_1 B2)) C) (@ _let_1 (@ (@ sup_sup_assn B2) C))))) (forall ((P assn) (Q assn) (R assn)) (=> (@ (@ entails (@ (@ sup_sup_assn P) Q)) R) (@ (@ entails P) R))) (= ord_le2510731241096832064er_nat (lambda ((A3 filter_nat) (B3 filter_nat)) (= (@ (@ inf_inf_filter_nat A3) B3) A3))) (forall ((Xs list_int)) (= (@ size_size_list_int (@ butlast_int Xs)) (@ (@ minus_minus_nat (@ size_size_list_int Xs)) one_one_nat))) (forall ((K5 set_nat)) (=> (not (= K5 bot_bot_set_nat)) (@ (@ member_nat (@ complete_Inf_Inf_nat K5)) K5))) (@ _let_9 one_one_Code_integer) (forall ((X filter_nat) (Y filter_nat) (Z filter_nat)) (let ((_let_1 (@ ord_le2510731241096832064er_nat X))) (= (@ _let_1 (@ (@ inf_inf_filter_nat Y) Z)) (and (@ _let_1 Y) (@ _let_1 Z))))) (@ (@ (@ (@ bNF_re717283939379294677_int_o pcr_int) (@ (@ bNF_re6644619430987730960nt_o_o pcr_int) (lambda ((Y4 Bool) (Z2 Bool)) (= Y4 Z2)))) (@ produc8739625826339149834_nat_o (lambda ((X2 nat) (Y5 nat) (__flatten_var_0 product_prod_nat_nat)) (@ (@ produc6081775807080527818_nat_o (lambda ((U4 nat) (V4 nat)) (@ (@ ord_less_nat (@ (@ plus_plus_nat X2) V4)) (@ (@ plus_plus_nat U4) Y5)))) __flatten_var_0)))) ord_less_int) (forall ((X nat) (Y nat) (Z nat)) (= (@ (@ ord_less_eq_nat (@ (@ ord_min_nat X) Y)) Z) (or (@ (@ ord_less_eq_nat Y) Z) (@ (@ ord_less_eq_nat X) Z)))) (forall ((A2 nat) (X nat) (B2 nat)) (=> (@ (@ ord_less_eq_nat A2) X) (@ (@ ord_less_eq_nat (@ (@ inf_inf_nat A2) B2)) X))) (forall ((R2 nat) (S3 nat) (R set_Pr1261947904930325089at_nat) (S5 nat)) (let ((_let_1 (@ product_Pair_nat_nat R2))) (=> (@ (@ member8440522571783428010at_nat (@ _let_1 S3)) R) (=> (= S5 S3) (@ (@ member8440522571783428010at_nat (@ _let_1 S5)) R))))) (forall ((M2 int) (N int)) (let ((_let_1 (@ (@ ord_min_int M2) N))) (= (not (@ (@ ord_less_int _let_1) N)) (= _let_1 N)))) (forall ((A set_int) (B2 int) (B set_int)) (let ((_let_1 (@ inf_inf_set_int A))) (= (= bot_bot_set_int (@ _let_1 (@ (@ insert_int2 B2) B))) (and (not (@ (@ member_int B2) A)) (= bot_bot_set_int (@ _let_1 B)))))) (forall ((C produc3843707927480180839at_nat) (A set_Pr4329608150637261639at_nat) (B set_Pr4329608150637261639at_nat)) (let ((_let_1 (@ member8757157785044589968at_nat C))) (=> (@ _let_1 A) (=> (not (@ _let_1 B)) (@ _let_1 (@ (@ minus_3314409938677909166at_nat A) B)))))) (forall ((Xs list_nat) (Ys list_int) (Xy product_prod_nat_int) (Xys list_P3521021558325789923at_int)) (=> (= (@ (@ zip_nat_int Xs) Ys) (@ (@ cons_P2335045147070616083at_int Xy) Xys)) (not (forall ((X3 nat) (Xs5 list_nat)) (=> (= Xs (@ (@ cons_nat X3) Xs5)) (forall ((Y2 int) (Ys4 list_int)) (=> (= Ys (@ (@ cons_int Y2) Ys4)) (=> (= Xy (@ (@ product_Pair_nat_int X3) Y2)) (not (= Xys (@ (@ zip_nat_int Xs5) Ys4))))))))))) (forall ((X21 int) (X222 list_int)) (= (@ size_size_list_int (@ (@ cons_int X21) X222)) (@ (@ plus_plus_nat (@ size_size_list_int X222)) (@ suc zero_zero_nat)))) (forall ((X21 nat) (X222 list_nat)) (not (= nil_nat (@ (@ cons_nat X21) X222)))) (forall ((A set_nat) (B set_nat) (C nat)) (let ((_let_1 (@ member_nat C))) (=> (@ (@ ord_less_set_nat A) B) (=> (@ _let_1 A) (@ _let_1 B))))) (forall ((B set_nat) (C2 set_nat) (A set_nat)) (= (@ (@ sup_sup_set_nat (@ (@ inf_inf_set_nat B) C2)) A) (@ (@ inf_inf_set_nat (@ (@ sup_sup_set_nat B) A)) (@ (@ sup_sup_set_nat C2) A)))) (forall ((A2 code_integer) (B2 code_integer) (F4 (-> code_integer num)) (C num)) (=> (@ (@ ord_le6747313008572928689nteger A2) B2) (=> (@ (@ ord_less_eq_num (@ F4 B2)) C) (=> (forall ((X3 code_integer) (Y2 code_integer)) (=> (@ (@ ord_le6747313008572928689nteger X3) Y2) (@ (@ ord_less_num (@ F4 X3)) (@ F4 Y2)))) (@ (@ ord_less_num (@ F4 A2)) C))))) (forall ((A2 nat) (B2 nat)) (let ((_let_1 (@ (@ ord_min_nat A2) B2))) (= (@ (@ ord_min_nat _let_1) B2) _let_1))) (forall ((A2 int)) (= (@ (@ ord_less_eq_int (@ (@ plus_plus_int A2) A2)) zero_zero_int) (@ (@ ord_less_eq_int A2) zero_zero_int))) (forall ((A2 set_o)) (not (@ (@ ord_less_set_o A2) bot_bot_set_o))) (forall ((X set_int)) (= (@ (@ ord_min_set_int bot_bot_set_int) X) bot_bot_set_int)) (forall ((A2 int) (B2 int) (C int)) (let ((_let_1 (@ ord_less_eq_int A2))) (=> (@ _let_1 B2) (=> (@ _let_1 C) (@ _let_1 (@ (@ ord_min_int B2) C)))))) (forall ((A2 code_integer) (C code_integer)) (= (@ (@ ord_le6747313008572928689nteger (@ (@ times_3573771949741848930nteger A2) C)) C) (and (=> (@ (@ ord_le3102999989581377725nteger C) zero_z3403309356797280102nteger) (@ (@ ord_le6747313008572928689nteger one_one_Code_integer) A2)) (=> (@ (@ ord_le3102999989581377725nteger zero_z3403309356797280102nteger) C) (@ (@ ord_le6747313008572928689nteger A2) one_one_Code_integer))))) (forall ((X int) (Y int) (Z int)) (= (@ (@ ord_less_eq_int (@ (@ ord_min_int X) Y)) Z) (or (@ (@ ord_less_eq_int X) Z) (@ (@ ord_less_eq_int Y) Z)))) (forall ((A2 int) (B2 int)) (=> (@ (@ ord_less_int A2) B2) (not (@ (@ ord_less_int B2) A2)))) (forall ((A2 produc3843707927480180839at_nat) (A set_Pr4329608150637261639at_nat) (B set_Pr4329608150637261639at_nat)) (let ((_let_1 (@ insert9069300056098147895at_nat A2))) (= (@ (@ inf_in7913087082777306421at_nat (@ _let_1 A)) (@ _let_1 B)) (@ _let_1 (@ (@ inf_in7913087082777306421at_nat A) B))))) (forall ((A set_Pr4329608150637261639at_nat) (B set_Pr4329608150637261639at_nat) (C2 set_Pr4329608150637261639at_nat)) (let ((_let_1 (@ minus_3314409938677909166at_nat A))) (= (@ _let_1 (@ (@ sup_su5525570899277871387at_nat B) C2)) (@ (@ inf_in7913087082777306421at_nat (@ _let_1 B)) (@ _let_1 C2))))) (forall ((I produc3843707927480180839at_nat) (J produc3843707927480180839at_nat) (R set_Pr5564308138774400199at_nat)) (=> (@ (@ member6009668390874684176at_nat (@ (@ produc2335810615602371415at_nat I) J)) R) (@ (@ member8757157785044589968at_nat J) (@ field_2862844103579723188at_nat R)))) (forall ((A2 int) (B2 int) (P6 int) (Q6 int)) (=> (= (@ normalize (@ (@ product_Pair_int_int A2) B2)) (@ (@ product_Pair_int_int P6) Q6)) (= (@ (@ fract P6) Q6) (@ (@ fract A2) B2)))) (forall ((K3 num)) (= (@ frct (@ (@ product_Pair_int_int (@ numeral_numeral_int K3)) one_one_int)) (@ numeral_numeral_rat K3))) (forall ((X int) (Y int)) (@ (@ ord_less_eq_int (@ (@ inf_inf_int X) Y)) X)) (forall ((A2 assn) (F4 (-> assn assn)) (B2 assn) (C assn)) (let ((_let_1 (@ ord_less_assn A2))) (=> (@ _let_1 (@ F4 B2)) (=> (@ (@ ord_less_assn B2) C) (=> (forall ((X3 assn) (Y2 assn)) (=> (@ (@ ord_less_assn X3) Y2) (@ (@ ord_less_assn (@ F4 X3)) (@ F4 Y2)))) (@ _let_1 (@ F4 C))))))) (forall ((N nat)) (not (@ (@ ord_less_nat N) N))) (forall ((X int) (Xs list_int) (Y int)) (= (@ (@ (@ list_update_int (@ (@ cons_int X) Xs)) zero_zero_nat) Y) (@ (@ cons_int Y) Xs))) (forall ((A2 int) (B2 int)) (=> (@ (@ ord_less_eq_int A2) B2) (= A2 (@ (@ ord_min_int A2) B2)))) _let_151 (forall ((Xs list_nat) (A set_nat) (X nat) (I nat)) (=> (@ (@ ord_less_eq_set_nat (@ set_nat2 Xs)) A) (=> (@ (@ member_nat X) A) (@ (@ ord_less_eq_set_nat (@ set_nat2 (@ (@ (@ list_update_nat Xs) I) X))) A)))) (forall ((A2 rat)) (= (@ (@ plus_plus_rat A2) zero_zero_rat) A2)) (forall ((A2 int) (B2 int) (C int)) (let ((_let_1 (@ times_times_int C))) (=> (@ (@ ord_less_eq_int A2) B2) (=> (@ (@ ord_less_eq_int zero_zero_int) C) (@ (@ ord_less_eq_int (@ _let_1 A2)) (@ _let_1 B2)))))) (forall ((N nat) (Xs list_P7985473006766602707_nat_o)) (=> (@ (@ ord_less_nat N) (@ size_s8908918004648414271_nat_o Xs)) (@ (@ member6576561426505652726_nat_o (@ (@ nth_Pr6840583978799713108_nat_o Xs) N)) (@ set_Pr400311997697478754_nat_o Xs)))) (forall ((P (-> nat produc6575502325842934193n_assn assn)) (L3 list_P8527749157015355191n_assn)) (= (@ (@ (@ vEBT_L9083610150846024284n_assn P) nil_nat) L3) (@ pure_assn (= L3 nil_Pr5671120429643327159n_assn)))) (forall ((Xs list_c)) (= (= (@ size_size_list_c Xs) zero_zero_nat) (= Xs nil_c))) (forall ((A2 int) (C int) (B2 int)) (= (@ (@ ord_less_int A2) (@ (@ minus_minus_int C) B2)) (@ (@ ord_less_int (@ (@ plus_plus_int A2) B2)) C))) (forall ((A set_Pr4532377907799695533_nat_o) (B set_Pr4532377907799695533_nat_o)) (= (= (@ (@ inf_in1906310914598751387_nat_o A) B) bot_bo7824918357723582233_nat_o) (forall ((X2 (-> produc3658429121746597890et_nat Bool))) (let ((_let_1 (@ member6576561426505652726_nat_o X2))) (=> (@ _let_1 A) (not (@ _let_1 B))))))) (forall ((A2 nat) (B2 nat)) (= (@ (@ ord_less_nat (@ (@ plus_plus_nat A2) B2)) B2) (@ (@ ord_less_nat A2) zero_zero_nat))) (forall ((I nat) (J nat) (L list_int) (X int)) (let ((_let_1 (@ nth_int L))) (=> (@ (@ ord_less_eq_nat zero_zero_nat) I) (=> (@ (@ ord_less_nat I) J) (=> (@ (@ ord_less_nat J) (@ size_size_list_int L)) (=> (@ (@ sorted_wrt_int ord_less_eq_int) L) (=> (@ (@ ord_less_eq_int (@ _let_1 I)) X) (=> (@ (@ ord_less_int X) (@ _let_1 J)) (not (forall ((K nat)) (let ((_let_1 (@ nth_int L))) (=> (@ (@ ord_less_eq_nat I) K) (=> (@ (@ ord_less_nat K) J) (=> (@ (@ ord_less_eq_int (@ _let_1 K)) X) (not (@ (@ ord_less_int X) (@ _let_1 (@ (@ plus_plus_nat K) one_one_nat)))))))))))))))))) (forall ((B2 int) (A2 int) (C int)) (=> (@ (@ ord_less_int B2) A2) (=> (@ (@ ord_less_int C) zero_zero_int) (@ (@ ord_less_int (@ (@ times_times_int A2) C)) (@ (@ times_times_int B2) C))))) (forall ((A set_nat) (B set_nat)) (=> (= A B) (@ (@ ord_less_eq_set_nat A) B))) (forall ((A2 int)) (@ (@ member_int A2) (@ (@ insert_int2 A2) bot_bot_set_int))) (= ord_less_set_nat (lambda ((X2 set_nat) (Y5 set_nat)) (and (not (@ (@ ord_less_eq_set_nat Y5) X2)) (@ (@ ord_less_eq_set_nat X2) Y5)))) (forall ((X assn) (Y assn)) (@ (@ ord_less_eq_assn (@ (@ inf_inf_assn X) Y)) X)) (forall ((M2 nat) (N nat)) (let ((_let_1 (@ ord_less_nat one_one_nat))) (=> (@ _let_1 M2) (=> (@ _let_1 N) (@ _let_1 (@ (@ times_times_nat M2) N)))))) (forall ((A2 int) (B2 int)) (let ((_let_1 (@ ord_less_eq_int zero_zero_int))) (=> (or (and (@ (@ ord_less_eq_int B2) zero_zero_int) (@ _let_1 A2)) (and (@ _let_1 B2) (@ (@ ord_less_eq_int A2) zero_zero_int))) (@ (@ ord_less_eq_int (@ (@ times_times_int A2) B2)) zero_zero_int)))) (forall ((A2 rat) (N nat)) (let ((_let_1 (@ power_power_rat A2))) (= (@ _let_1 (@ suc N)) (@ (@ times_times_rat (@ _let_1 N)) A2)))) (forall ((T3 set_nat) (S set_nat)) (= (@ (@ inf_inf_set_nat T3) (@ (@ sup_sup_set_nat S) T3)) T3)) (forall ((A assn) (C2 assn) (B assn)) (let ((_let_1 (@ entailst A))) (=> (@ _let_1 C2) (@ _let_1 (@ (@ sup_sup_assn B) C2))))) (forall ((I nat) (V2 nat)) (= (@ (@ (@ list_update_nat nil_nat) I) V2) nil_nat)) (forall ((Y produc1908205239877642774nteger)) (not (forall ((A4 (-> produc6241069584506657477e_term option6357759511663192854e_term)) (B4 produc8923325533196201883nteger)) (not (= Y (@ (@ produc8603105652947943368nteger A4) B4)))))) (forall ((A set_int) (B set_int)) (= (@ (@ ord_less_set_int (@ (@ minus_minus_set_int A) B)) A) (not (= (@ (@ inf_inf_set_int A) B) bot_bot_set_int)))) (forall ((S set_nat) (T3 set_nat)) (= (@ (@ sup_sup_set_nat (@ (@ inf_inf_set_nat S) T3)) S) S)) (forall ((A2 int) (B2 int) (C int)) (let ((_let_1 (@ times_times_int C))) (=> (@ (@ ord_less_int A2) B2) (=> (@ (@ ord_less_int zero_zero_int) C) (@ (@ ord_less_int (@ _let_1 A2)) (@ _let_1 B2)))))) (forall ((A set_int)) (= (@ (@ sup_sup_set_int A) bot_bot_set_int) A)) (forall ((X nat) (A set_nat) (B set_nat)) (let ((_let_1 (@ minus_minus_set_nat A))) (=> (not (@ (@ member_nat X) A)) (= (@ _let_1 (@ (@ insert_nat2 X) B)) (@ _let_1 B))))) (forall ((Xs list_nat)) (= (@ (@ sorted_wrt_nat ord_less_eq_nat) (@ rev_nat Xs)) (forall ((I4 nat)) (let ((_let_1 (@ nth_nat Xs))) (let ((_let_2 (@ suc I4))) (=> (@ (@ ord_less_nat _let_2) (@ size_size_list_nat Xs)) (@ (@ ord_less_eq_nat (@ _let_1 _let_2)) (@ _let_1 I4)))))))) (forall ((X (-> produc3658429121746597890et_nat Bool)) (Xs list_P7985473006766602707_nat_o)) (=> (@ (@ member6576561426505652726_nat_o X) (@ set_Pr400311997697478754_nat_o Xs)) (@ (@ ord_less_nat (@ size_s8908918004648414271_nat_o (@ (@ remove7604696131425036249_nat_o X) Xs))) (@ size_s8908918004648414271_nat_o Xs)))) (forall ((X set_Pr1261947904930325089at_nat) (Y set_Pr1261947904930325089at_nat) (R2 set_Pr4329608150637261639at_nat) (Xs list_s1210847774152347623at_nat)) (=> (@ (@ member8757157785044589968at_nat (@ (@ produc2922128104949294807at_nat X) Y)) R2) (@ (@ member4080735728053443344at_nat (@ (@ produc7536900900485677911at_nat (@ (@ cons_s6881495754146722583at_nat X) Xs)) (@ (@ cons_s6881495754146722583at_nat Y) Xs))) (@ listre8180072825634266816at_nat R2)))) (= ord_less_eq_nat (lambda ((A3 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(@ upt M2) N))) (= (@ (@ linord738340561235409698at_nat (lambda ((X2 nat)) X2)) _let_1) _let_1))) (forall ((Xs list_d) (Ys list_c) (R2 set_Product_prod_d_c)) (=> (@ (@ member1739767152416986127list_c (@ (@ produc242965416994095062list_c Xs) Ys)) (@ listrel_d_c R2)) (= (@ size_size_list_d Xs) (@ size_size_list_c Ys)))) (forall ((A set_nat) (B set_nat) (C2 set_nat)) (let ((_let_1 (@ minus_minus_set_nat A))) (= (@ (@ minus_minus_set_nat (@ _let_1 B)) C2) (@ _let_1 (@ (@ sup_sup_set_nat B) C2))))) (forall ((A2 produc3843707927480180839at_nat) (A set_Pr4329608150637261639at_nat) (B set_Pr4329608150637261639at_nat)) (= (= bot_bo228742789529271731at_nat (@ (@ inf_in7913087082777306421at_nat (@ (@ insert9069300056098147895at_nat A2) A)) B)) (and (not (@ (@ member8757157785044589968at_nat A2) B)) (= bot_bo228742789529271731at_nat (@ (@ inf_in7913087082777306421at_nat A) B))))) (forall ((A2 assn) (B2 assn) (F4 (-> assn filter_nat)) (C filter_nat)) (=> (@ (@ ord_less_eq_assn A2) B2) (=> (= (@ F4 B2) C) (=> (forall ((X3 assn) (Y2 assn)) (=> (@ (@ ord_less_eq_assn X3) Y2) (@ (@ ord_le2510731241096832064er_nat (@ F4 X3)) (@ F4 Y2)))) (@ (@ ord_le2510731241096832064er_nat (@ F4 A2)) C))))) (forall ((M2 nat) (N nat)) (let ((_let_1 (@ ord_less_nat M2))) (=> (@ _let_1 N) (@ _let_1 (@ suc N))))) (forall ((M2 nat) (N nat)) (let ((_let_1 (@ (@ ord_min_nat M2) N))) (= (@ (@ ord_less_eq_nat M2) _let_1) (= _let_1 M2)))) (= ord_le6747313008572928689nteger (lambda ((A3 code_integer) (__flatten_var_0 code_integer)) (@ (@ ord_le3102999989581377725nteger (@ (@ plus_p5714425477246183910nteger A3) one_one_Code_integer)) __flatten_var_0))) (forall ((X set_nat) (Y set_nat)) (@ (@ ord_less_eq_set_nat (@ (@ inf_inf_set_nat X) Y)) Y)) (forall ((X assn) (Y assn)) (= (@ (@ inf_inf_assn X) (@ (@ sup_sup_assn X) Y)) X)) (forall ((M2 nat) (N nat)) (=> (@ (@ ord_less_nat (@ suc M2)) (@ suc N)) (@ (@ ord_less_nat M2) N))) (forall ((Y filter_nat) (X filter_nat)) (=> (@ (@ ord_le2510731241096832064er_nat Y) X) (= (@ (@ sup_sup_filter_nat X) Y) X))) (forall ((X product_prod_nat_nat) (S set_Pr1261947904930325089at_nat)) (=> (@ (@ member8440522571783428010at_nat X) S) (not (= S bot_bo2099793752762293965at_nat)))) (forall ((I3 set_nat) (I7 set_nat) (A (-> c c assn)) (A6 (-> c c assn)) (Xs list_c) (Xs4 list_c) (Xsi list_c) (Xsi2 list_c)) (=> (= I3 I7) (=> (= A A6) (=> (= (@ size_size_list_c Xs) (@ size_size_list_c Xs4)) (=> (= (@ size_size_list_c Xsi) (@ size_size_list_c Xsi2)) (=> (forall ((I5 nat)) (let ((_let_1 (@ size_size_list_c Xs))) (=> (@ (@ member_nat I5) I3) (=> (@ (@ ord_less_nat I5) _let_1) (=> (= _let_1 (@ size_size_list_c Xsi)) (and (= (@ (@ nth_c Xsi) I5) (@ (@ nth_c Xsi2) I5)) (= (@ (@ nth_c Xs) I5) (@ (@ nth_c Xs4) I5)))))))) (= (@ (@ (@ (@ vEBT_L824818263033719200sn_c_c I3) A) Xs) Xsi) (@ (@ (@ (@ vEBT_L824818263033719200sn_c_c I7) A6) Xs4) Xsi2)))))))) (forall ((A2 nat) (B2 nat)) (let ((_let_1 (@ ord_less_nat zero_zero_nat))) (=> (@ _let_1 A2) (=> (@ _let_1 B2) (@ _let_1 (@ (@ 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(@ member7340969449405702474st_nat (@ (@ produc2694037385005941721st_nat (@ (@ cons_nat X) Xs)) (@ (@ cons_nat Y) Ys))) _let_1) (or (and (= (@ size_size_list_nat Xs) (@ size_size_list_nat Ys)) (@ (@ member8440522571783428010at_nat (@ (@ product_Pair_nat_nat X) Y)) R2)) (and (@ (@ member7340969449405702474st_nat (@ (@ produc2694037385005941721st_nat Xs) Ys)) _let_1) (= X Y)))))) (forall ((P assn) (Q assn)) (=> (@ (@ entails (@ (@ times_times_assn P) top_top_assn)) (@ (@ times_times_assn Q) top_top_assn)) (@ (@ entailst P) Q))) (forall ((A2 Bool) (A set_o) (B set_o)) (= (= (@ (@ inf_inf_set_o (@ (@ insert_o2 A2) A)) B) bot_bot_set_o) (and (not (@ (@ member_o A2) B)) (= (@ (@ inf_inf_set_o A) B) bot_bot_set_o)))) (forall ((Y produc3843707927480180839at_nat) (X222 list_P5464809261938338413at_nat) (X21 produc3843707927480180839at_nat)) (let ((_let_1 (@ member8757157785044589968at_nat Y))) (=> (@ _let_1 (@ set_Pr3765526544606949372at_nat X222)) (@ _let_1 (@ set_Pr3765526544606949372at_nat (@ (@ cons_P3940603068885512221at_nat X21) X222)))))) (forall ((A2 set_nat) (B2 set_nat)) (=> (@ (@ ord_less_set_nat A2) B2) (@ (@ ord_less_eq_set_nat A2) B2))) (forall ((A set_Pr4329608150637261639at_nat)) (= (@ (@ minus_3314409938677909166at_nat bot_bo228742789529271731at_nat) A) bot_bo228742789529271731at_nat)) (= ord_less_set_nat (lambda ((A5 set_nat) (B7 set_nat)) (and (@ (@ ord_less_eq_set_nat A5) B7) (not (= A5 B7))))) (forall ((T nat)) (exists ((Z4 nat)) (forall ((X7 nat)) (=> (@ (@ ord_less_nat Z4) X7) (not (@ (@ ord_less_eq_nat X7) T)))))) (forall ((A2 nat) (C nat) (B2 nat) (D2 nat)) (=> (@ (@ ord_less_eq_nat A2) C) (=> (@ (@ ord_less_eq_nat B2) D2) (@ (@ ord_less_eq_nat (@ (@ inf_inf_nat A2) B2)) (@ (@ inf_inf_nat C) D2))))) (forall ((A assn) (B assn) (H2 produc3658429121746597890et_nat)) (= (@ (@ rep_assn (@ (@ times_times_assn A) B)) H2) (exists ((Hr heap_e7401611519738050253t_unit) (As1 set_nat) (As22 set_nat)) (let ((_let_1 (@ produc7507926704131184380et_nat Hr))) (and (= H2 (@ _let_1 (@ (@ sup_sup_set_nat As1) As22))) (= (@ (@ inf_inf_set_nat As1) As22) bot_bot_set_nat) (@ (@ rep_assn A) (@ _let_1 As1)) (@ (@ rep_assn B) (@ _let_1 As22))))))) (forall ((X int) (Y int) (Z int)) (let ((_let_1 (@ sup_sup_int X))) (@ (@ ord_less_eq_int (@ _let_1 (@ (@ inf_inf_int Y) Z))) (@ (@ inf_inf_int (@ _let_1 Y)) (@ _let_1 Z))))) (forall ((P (-> list_c Bool)) (Xs list_c)) (=> (forall ((Xs2 list_c)) (=> (forall ((Ys2 list_c)) (=> (@ (@ ord_less_nat (@ size_size_list_c Ys2)) (@ size_size_list_c Xs2)) (@ P Ys2))) (@ P Xs2))) (@ P Xs))) (forall ((N nat) (J nat) (I nat)) (=> (@ (@ ord_less_nat N) (@ (@ minus_minus_nat J) I)) (= (@ (@ nth_nat (@ linord2614967742042102400et_nat (@ (@ set_or6659071591806873216st_nat I) J))) N) (@ suc (@ (@ plus_plus_nat I) N))))) (forall ((Xs list_P8527749157015355191n_assn)) (= (not (= Xs nil_Pr5671120429643327159n_assn)) (exists ((Y5 produc6575502325842934193n_assn) (Ys3 list_P8527749157015355191n_assn)) (= Xs (@ (@ cons_P2971678138204555879n_assn Y5) Ys3))))) (forall ((A2 nat) (B2 nat)) (let ((_let_1 (@ ord_less_nat zero_zero_nat))) (=> (@ _let_1 A2) (=> (@ _let_1 B2) (@ _let_1 (@ (@ plus_plus_nat A2) B2)))))) (forall ((Ys list_P8527749157015355191n_assn) (Xs list_P8527749157015355191n_assn)) (=> (@ distin4809818325527169450n_assn Ys) (=> (= (@ set_Pr1139785259514867910n_assn Ys) (@ set_Pr1139785259514867910n_assn Xs)) (@ (@ ord_less_eq_nat (@ size_s6829681357464350627n_assn Ys)) (@ size_s6829681357464350627n_assn Xs))))) (forall ((C nat) (A set_nat) (B set_nat)) (let ((_let_1 (@ member_nat C))) (=> (@ _let_1 (@ (@ inf_inf_set_nat A) B)) (@ _let_1 A)))) (forall ((X int) (Y int)) (=> (@ (@ ord_less_eq_int X) zero_zero_int) (=> (@ (@ ord_less_eq_int Y) zero_zero_int) (= (= (@ (@ plus_plus_int X) Y) zero_zero_int) (and (= X zero_zero_int) (= Y zero_zero_int)))))) (forall ((M2 nat) (N nat)) (=> (@ (@ ord_less_nat M2) N) (not (= N zero_zero_nat)))) (forall ((L list_int)) (let ((_let_1 (@ merges1654122896337280797ps_int L))) (and (@ distinct_int _let_1) (@ (@ sorted_wrt_int ord_less_eq_int) _let_1) (= (@ set_int2 _let_1) (@ set_int2 L))))) (forall ((X set_Pr1261947904930325089at_nat)) (= (@ (@ inf_in2572325071724192079at_nat X) bot_bo2099793752762293965at_nat) bot_bo2099793752762293965at_nat)) (forall ((X product_prod_nat_nat) (Xs list_P6011104703257516679at_nat)) (=> (@ (@ member8440522571783428010at_nat X) (@ set_Pr5648618587558075414at_nat Xs)) (= (@ (@ insert8944034826898310173at_nat X) Xs) Xs))) (forall ((N nat)) (@ (@ ord_less_nat (@ bit_se2002935070580805687sk_nat N)) (@ (@ power_power_nat (@ numeral_numeral_nat (@ bit0 one))) N))) (forall ((X assn)) (not (forall ((Y2 (-> produc3658429121746597890et_nat Bool))) (=> (= X (@ abs_assn Y2)) (not (@ (@ member6576561426505652726_nat_o Y2) (@ collec939566748876313656_nat_o proper))))))) (forall ((A2 nat) (B2 nat) (F4 (-> nat nat)) (C nat)) (=> (@ (@ ord_less_eq_nat A2) B2) (=> (@ (@ ord_less_nat (@ F4 B2)) C) (=> (forall ((X3 nat) (Y2 nat)) (=> (@ (@ ord_less_eq_nat X3) Y2) (@ (@ ord_less_eq_nat (@ F4 X3)) (@ F4 Y2)))) (@ (@ ord_less_nat (@ F4 A2)) C))))) _let_150 (forall ((Xs list_nat)) (=> (@ (@ ord_less_eq_nat (@ size_size_list_nat Xs)) one_one_nat) (@ (@ sorted_wrt_nat ord_less_eq_nat) Xs))) (forall ((A2 code_integer)) (= (@ (@ times_3573771949741848930nteger A2) one_one_Code_integer) A2)) (forall ((C (-> produc3658429121746597890et_nat Bool)) (A set_Pr4532377907799695533_nat_o) (B set_Pr4532377907799695533_nat_o)) (let ((_let_1 (@ member6576561426505652726_nat_o C))) (=> (@ _let_1 (@ (@ sup_su5209123915105501825_nat_o A) B)) (=> (not (@ _let_1 A)) (@ _let_1 B))))) (forall ((B2 num) (C num) (A2 num)) (=> (@ (@ ord_less_num B2) C) (@ (@ ord_less_num (@ (@ ord_min_num A2) B2)) C))) (forall ((A2 code_integer) (N nat)) (let ((_let_1 (@ (@ power_8256067586552552935nteger A2) N))) (= (@ (@ times_3573771949741848930nteger _let_1) A2) (@ (@ times_3573771949741848930nteger A2) _let_1)))) (forall ((A2 multis2468970476368604999at_nat) (B2 multis2468970476368604999at_nat)) (= (@ (@ minus_4286766774447292334at_nat (@ (@ plus_p7104986032573967614at_nat A2) B2)) B2) A2)) (forall ((B2 int) (A2 int)) (= (@ (@ member_int B2) (@ (@ insert_int2 A2) bot_bot_set_int)) (= B2 A2))) (forall ((B2 set_Pr4329608150637261639at_nat) (C set_Pr4329608150637261639at_nat) (A2 set_Pr4329608150637261639at_nat)) (=> (@ (@ ord_le1268244103169919719at_nat (@ (@ sup_su5525570899277871387at_nat B2) C)) A2) (not (=> (@ (@ ord_le1268244103169919719at_nat B2) A2) (not (@ (@ ord_le1268244103169919719at_nat C) A2)))))) (forall ((B2 rat) (A2 rat)) (= (@ (@ ord_less_rat (@ (@ plus_plus_rat B2) A2)) B2) (@ (@ ord_less_rat A2) zero_zero_rat))) (forall ((C nat) (A set_nat) (B set_nat)) (let ((_let_1 (@ member_nat C))) (=> (@ _let_1 A) (=> (not (@ _let_1 B)) (@ _let_1 (@ (@ minus_minus_set_nat A) B)))))) (forall ((X assn) (Y assn)) (let ((_let_1 (@ sup_sup_assn X))) (let ((_let_2 (@ _let_1 Y))) (= (@ _let_1 _let_2) _let_2)))) (forall ((A2 nat) (B2 nat) (C nat)) (=> (@ (@ ord_less_eq_nat A2) B2) (@ (@ ord_less_eq_nat (@ (@ plus_plus_nat A2) C)) (@ (@ plus_plus_nat B2) C)))) (forall ((A2 assn) (B2 assn) (C assn)) (let ((_let_1 (@ ord_less_eq_assn A2))) (=> (@ _let_1 B2) (=> (@ (@ ord_less_eq_assn B2) C) (@ _let_1 C))))) (forall ((B2 Bool)) (@ proper (@ pure_a825153325127701367it_nat B2))) (forall ((P (-> Bool Bool))) (= (= bot_bot_set_o (@ collect_o P)) (forall ((X2 Bool)) (not (@ P X2))))) (forall ((T3 set_Pr4329608150637261639at_nat) (S set_Pr4329608150637261639at_nat)) (= (@ (@ inf_in7913087082777306421at_nat T3) (@ (@ sup_su5525570899277871387at_nat S) T3)) T3)) (forall ((C rat) (A2 rat)) (= (@ (@ ord_less_rat (@ (@ times_times_rat C) A2)) C) (and (=> (@ (@ ord_less_eq_rat C) zero_zero_rat) (@ (@ ord_less_rat one_one_rat) A2)) (=> (@ (@ ord_less_eq_rat zero_zero_rat) C) (@ (@ ord_less_rat A2) one_one_rat))))) (forall ((A2 nat) (B2 nat)) (= (= A2 (@ (@ plus_plus_nat A2) B2)) (= B2 zero_zero_nat))) _let_149 (forall ((A2 nat) (A set_nat)) (not (= (@ (@ insert_nat2 A2) A) bot_bot_set_nat))) (forall ((A2 assn) (B2 assn) (F4 (-> assn code_integer)) (C code_integer)) (=> (@ (@ ord_less_assn A2) B2) (=> (@ (@ ord_le3102999989581377725nteger (@ F4 B2)) C) (=> (forall ((X3 assn) (Y2 assn)) (=> (@ (@ ord_less_assn X3) Y2) (@ (@ ord_le6747313008572928689nteger (@ F4 X3)) (@ F4 Y2)))) (@ (@ ord_le6747313008572928689nteger (@ F4 A2)) C))))) (forall ((A set_Pr4329608150637261639at_nat) (B set_Pr4329608150637261639at_nat) (C2 set_Pr4329608150637261639at_nat)) (= (@ (@ ord_le1268244103169919719at_nat (@ (@ minus_3314409938677909166at_nat A) B)) C2) (@ (@ ord_le1268244103169919719at_nat A) (@ (@ sup_su5525570899277871387at_nat B) C2)))) (forall ((X int) (Y int)) (=> (@ (@ ord_less_int X) Y) (not (= Y X)))) (forall ((P assn) (A (-> nat nat assn)) (Xs list_nat) (I nat) (Xsi list_nat) (I3 set_nat) (F assn) (Q assn)) (let ((_let_1 (@ entails P))) (=> (@ _let_1 (@ (@ times_times_assn (@ (@ times_times_assn (@ (@ A (@ (@ nth_nat Xs) I)) (@ (@ nth_nat Xsi) I))) (@ (@ (@ (@ vEBT_L7892069108621897922at_nat (@ (@ minus_minus_set_nat I3) (@ (@ insert_nat2 I) bot_bot_set_nat))) A) Xs) Xsi))) F)) (=> (@ (@ ord_less_nat I) (@ size_size_list_nat Xs)) (=> (@ (@ member_nat I) I3) (=> (@ (@ entails (@ (@ times_times_assn (@ (@ (@ (@ vEBT_L7892069108621897922at_nat I3) A) Xs) Xsi)) F)) Q) (@ _let_1 Q))))))) (forall ((L list_nat) (P (-> nat Bool))) (= (forall ((X2 nat)) (=> (@ (@ member_nat X2) (@ set_nat2 L)) (@ P X2))) (forall ((I4 nat)) (=> (@ (@ ord_less_nat I4) (@ size_size_list_nat L)) (@ P (@ (@ nth_nat L) I4)))))) (forall ((A set_Pr4532377907799695533_nat_o)) (= (forall ((X2 (-> produc3658429121746597890et_nat Bool))) (not (@ (@ member6576561426505652726_nat_o X2) A))) (= A bot_bo7824918357723582233_nat_o))) (forall ((Y produc7773217078559923341nt_int)) (not (forall ((A4 (-> int option6357759511663192854e_term)) (B4 product_prod_int_int)) (not (= Y (@ (@ produc4305682042979456191nt_int A4) B4)))))) (= bot_bot_set_o (@ collect_o bot_bot_o_o)) (forall ((I nat) (J nat) (M2 nat)) (let ((_let_1 (@ ord_less_nat I))) (=> (@ _let_1 J) (@ _let_1 (@ (@ plus_plus_nat J) M2))))) (forall ((L list_num) (I nat) (J nat)) (let ((_let_1 (@ nth_num L))) (=> (@ (@ sorted_wrt_num ord_less_eq_num) L) (=> (@ distinct_num L) (=> (@ (@ ord_less_nat I) J) (=> (@ (@ ord_less_nat J) (@ size_size_list_num L)) (@ (@ ord_less_num (@ _let_1 I)) (@ _let_1 J)))))))) (forall ((A set_Pr4329608150637261639at_nat) (C2 set_Pr4329608150637261639at_nat) (B set_Pr4329608150637261639at_nat) (D set_Pr4329608150637261639at_nat)) (=> (@ (@ ord_le1268244103169919719at_nat A) C2) (=> (@ (@ ord_le1268244103169919719at_nat B) D) (@ (@ ord_le1268244103169919719at_nat (@ (@ sup_su5525570899277871387at_nat A) B)) (@ (@ sup_su5525570899277871387at_nat C2) D))))) (forall ((A2 num) (B2 num)) (=> (@ (@ ord_less_num A2) B2) (= (@ (@ ord_min_num A2) B2) A2))) (forall ((X assn) (Y assn)) (@ (@ ord_less_eq_assn (@ (@ inf_inf_assn X) Y)) Y)) (forall ((F4 (-> nat nat nat)) (X nat) (Y nat)) (=> (forall ((X3 nat) (Y2 nat)) (@ (@ ord_less_eq_nat X3) (@ (@ F4 X3) Y2))) (=> (forall ((X3 nat) (Y2 nat)) (@ (@ ord_less_eq_nat Y2) (@ (@ F4 X3) Y2))) (=> (forall ((X3 nat) (Y2 nat) (Z4 nat)) (=> (@ (@ ord_less_eq_nat Y2) X3) (=> (@ (@ ord_less_eq_nat Z4) X3) (@ (@ ord_less_eq_nat (@ (@ F4 Y2) Z4)) X3)))) (= (@ (@ sup_sup_nat X) Y) (@ (@ F4 X) Y)))))) (forall ((A2 nat) (B2 nat)) (= (@ (@ ord_less_nat A2) (@ (@ plus_plus_nat A2) B2)) (@ (@ ord_less_nat zero_zero_nat) B2))) (forall ((A2 nat) (B2 nat) (C nat)) (let ((_let_1 (@ ord_less_eq_nat A2))) (=> (@ _let_1 B2) (=> (@ _let_1 C) (@ _let_1 (@ (@ ord_min_nat B2) C)))))) (forall ((Xs list_P6011104703257516679at_nat) (P (-> product_prod_nat_nat product_prod_nat_nat Bool)) (Q (-> product_prod_nat_nat product_prod_nat_nat Bool))) (=> (forall ((X3 product_prod_nat_nat) (Y2 product_prod_nat_nat)) (let ((_let_1 (@ set_Pr5648618587558075414at_nat Xs))) (=> (@ (@ member8440522571783428010at_nat X3) _let_1) (=> (@ (@ member8440522571783428010at_nat Y2) _let_1) (=> (@ (@ P X3) Y2) (@ (@ Q X3) Y2)))))) (=> (@ (@ sorted5214655850825725294at_nat P) Xs) (@ (@ sorted5214655850825725294at_nat Q) Xs)))) (forall ((X int) (Y int)) (= (not (@ (@ ord_less_int X) Y)) (@ (@ ord_less_eq_int Y) X))) (forall ((A2 int)) (= (@ (@ times_times_int A2) zero_zero_int) zero_zero_int)) (forall ((A2 assn)) (= (@ (@ times_times_assn A2) one_one_assn) A2)) (forall ((L list_int) (I nat) (J nat)) (let ((_let_1 (@ nth_int L))) (=> (@ (@ sorted_wrt_int ord_less_eq_int) L) (=> (@ distinct_int L) (=> (@ (@ ord_less_nat I) J) (=> (@ (@ ord_less_nat J) (@ size_size_list_int L)) (@ (@ ord_less_int (@ _let_1 I)) (@ _let_1 J)))))))) (forall ((A2 int) (F4 (-> nat int)) (B2 nat) (C nat)) (let ((_let_1 (@ ord_less_eq_int A2))) (=> (@ _let_1 (@ F4 B2)) (=> (@ (@ ord_less_eq_nat B2) C) (=> (forall ((X3 nat) (Y2 nat)) (=> (@ (@ ord_less_eq_nat X3) Y2) (@ (@ ord_less_eq_int (@ F4 X3)) (@ F4 Y2)))) (@ _let_1 (@ F4 C))))))) (forall ((A2 (-> produc3658429121746597890et_nat Bool)) (B2 (-> produc3658429121746597890et_nat Bool)) (A set_Pr4532377907799695533_nat_o)) (let ((_let_1 (@ member6576561426505652726_nat_o A2))) (= (@ _let_1 (@ (@ insert5175938949040314269_nat_o B2) A)) (or (@ _let_1 A) (= A2 B2))))) (not (@ (@ eventually_nat (lambda ((N2 nat)) false)) at_top_nat)) (forall ((A2 Bool) (B set_o) (C2 set_o)) (let ((_let_1 (@ insert_o2 A2))) (= (@ (@ sup_sup_set_o (@ _let_1 B)) C2) (@ _let_1 (@ (@ sup_sup_set_o B) C2))))) (forall ((A2 set_Pr1261947904930325089at_nat)) (= (@ (@ sup_su6327502436637775413at_nat A2) bot_bo2099793752762293965at_nat) A2)) (forall ((X assn) (B2 assn) (A2 assn)) (let ((_let_1 (@ ord_less_assn X))) (=> (@ _let_1 B2) (@ _let_1 (@ (@ sup_sup_assn A2) B2))))) (forall ((I nat) (J nat) (P (-> nat Bool))) (=> (@ (@ ord_less_eq_nat I) J) (=> (@ P I) (=> (forall ((N5 nat)) (=> (@ (@ ord_less_eq_nat I) N5) (=> (@ (@ ord_less_nat N5) J) (=> (@ P N5) (@ P (@ suc N5)))))) (@ P J))))) (= ord_less_int (lambda ((X2 int) (Y5 int)) (and (not (@ (@ ord_less_eq_int Y5) X2)) (@ (@ ord_less_eq_int X2) Y5)))) (forall ((B2 assn) (A2 assn) (C assn)) (let ((_let_1 (@ ord_less_assn C))) (=> (@ (@ ord_less_eq_assn B2) A2) (=> (@ _let_1 B2) (@ _let_1 A2))))) (= zero_zero_int (@ abs_Integ _let_109)) (forall ((A2 code_integer) (B2 code_integer)) (=> (@ (@ ord_le3102999989581377725nteger A2) zero_z3403309356797280102nteger) (=> (@ (@ ord_le3102999989581377725nteger zero_z3403309356797280102nteger) B2) (@ (@ ord_le3102999989581377725nteger (@ (@ times_3573771949741848930nteger A2) B2)) zero_z3403309356797280102nteger)))) (forall ((M2 nat) (Ms list_nat) (N nat) (Ns list_nat) (R2 set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ size_size_list_nat Ns))) (let ((_let_2 (@ size_size_list_nat Ms))) (let ((_let_3 (@ lenlex_nat R2))) (= (@ (@ member7340969449405702474st_nat (@ (@ produc2694037385005941721st_nat (@ (@ cons_nat M2) Ms)) (@ (@ cons_nat N) Ns))) _let_3) (or (@ (@ ord_less_nat _let_2) _let_1) (and (= M2 N) (@ (@ member7340969449405702474st_nat (@ (@ produc2694037385005941721st_nat Ms) Ns)) _let_3)) (and (@ (@ member8440522571783428010at_nat (@ (@ product_Pair_nat_nat M2) N)) R2) (= _let_2 _let_1)))))))) (forall ((N nat) (M2 nat)) (=> (@ (@ ord_less_nat zero_zero_nat) N) (@ (@ ord_less_eq_nat (@ (@ modulo_modulo_nat M2) N)) N))) (= ord_le6747313008572928689nteger (lambda ((B3 code_integer) (A3 code_integer)) (and (@ (@ ord_le3102999989581377725nteger B3) A3) (not (@ (@ ord_le3102999989581377725nteger A3) B3))))) (= sup_sup_assn (lambda ((X2 assn) (Y5 assn)) (@ (@ sup_sup_assn Y5) X2))) (forall ((A2 int) (B2 int) (Q6 int) (R2 int)) (let ((_let_1 (@ if_int (= R2 zero_zero_int)))) (let ((_let_2 (@ uminus_uminus_int Q6))) (=> (@ (@ (@ eucl_rel_int A2) B2) (@ (@ product_Pair_int_int Q6) R2)) (=> (not (= B2 zero_zero_int)) (@ (@ (@ eucl_rel_int (@ uminus_uminus_int A2)) B2) (@ (@ product_Pair_int_int (@ (@ _let_1 _let_2) (@ (@ minus_minus_int _let_2) one_one_int))) (@ (@ _let_1 zero_zero_int) (@ (@ minus_minus_int B2) R2))))))))) (forall ((X int)) (= (@ (@ minus_minus_int (@ (@ times_times_int X) X)) one_one_int) (@ (@ times_times_int (@ (@ plus_plus_int X) one_one_int)) (@ (@ minus_minus_int X) one_one_int)))) (forall ((A2 int) (B2 int) (F4 (-> int num)) (C num)) (=> (@ (@ ord_less_int A2) B2) (=> (@ (@ ord_less_eq_num (@ F4 B2)) C) (=> (forall ((X3 int) (Y2 int)) (=> (@ (@ ord_less_int X3) Y2) (@ (@ ord_less_num (@ F4 X3)) (@ F4 Y2)))) (@ (@ ord_less_num (@ F4 A2)) C))))) (forall ((C nat) (A2 nat) (B2 nat)) (=> (not (= C zero_zero_nat)) (= (= (@ (@ times_times_nat A2) C) (@ (@ times_times_nat B2) C)) (= A2 B2)))) (forall ((I nat) (Xs list_nat) (J nat) (X nat)) (let ((_let_1 (@ (@ nth_nat (@ (@ (@ list_update_nat Xs) I) X)) J))) (let ((_let_2 (= I J))) (=> (@ (@ ord_less_nat I) (@ size_size_list_nat Xs)) (and (=> _let_2 (= _let_1 X)) (=> (not _let_2) (= _let_1 (@ (@ nth_nat Xs) J)))))))) (forall ((X set_nat) (Y set_nat) (Z set_nat)) (let ((_let_1 (@ sup_sup_set_nat X))) (let ((_let_2 (@ sup_sup_set_nat Y))) (= (@ _let_1 (@ _let_2 Z)) (@ _let_2 (@ _let_1 Z)))))) (forall ((C int) (A2 int) (B2 int)) (let ((_let_1 (@ times_times_int C))) (=> (@ (@ ord_less_int C) zero_zero_int) (= (@ (@ ord_less_int (@ _let_1 A2)) (@ _let_1 B2)) (@ (@ ord_less_int B2) A2))))) (forall ((Y int) (X int)) (=> (not (@ (@ ord_less_int Y) X)) (= (not (@ (@ ord_less_int X) Y)) (= X Y)))) (forall ((A2 filter_nat) (B2 filter_nat)) (=> (= A2 (@ (@ sup_sup_filter_nat A2) B2)) (@ (@ ord_le2510731241096832064er_nat B2) A2))) (forall ((A2 code_integer) (B2 code_integer)) (=> (@ (@ ord_le6747313008572928689nteger A2) zero_z3403309356797280102nteger) (=> (@ (@ ord_le6747313008572928689nteger zero_z3403309356797280102nteger) B2) (@ (@ ord_le6747313008572928689nteger (@ (@ times_3573771949741848930nteger A2) B2)) zero_z3403309356797280102nteger)))) (forall ((Xs list_P8527749157015355191n_assn)) (= (= (@ rev_Pr4855572775806611735n_assn Xs) nil_Pr5671120429643327159n_assn) (= Xs nil_Pr5671120429643327159n_assn))) (forall ((B2 set_nat) (A2 set_nat)) (=> (@ (@ ord_less_eq_set_nat B2) A2) (=> (@ (@ ord_less_eq_set_nat A2) B2) (= A2 B2)))) (forall ((Xs list_int) (P (-> int Bool)) (X int)) (=> (forall ((I5 nat)) (=> (@ (@ ord_less_nat I5) (@ size_size_list_int Xs)) (@ P (@ (@ nth_int Xs) I5)))) (=> (@ (@ member_int X) (@ set_int2 Xs)) (@ P X)))) (forall ((X code_integer) (Y code_integer)) (=> (@ (@ ord_le6747313008572928689nteger X) Y) (not (@ (@ ord_le6747313008572928689nteger Y) X)))) (forall ((A2 assn)) (= (@ (@ inf_inf_assn A2) A2) A2)) (forall ((Xs list_int)) (= (= (@ size_size_list_int Xs) zero_zero_nat) (= Xs nil_int))) (forall ((L23 list_nat)) (= (@ (@ merge_nat nil_nat) L23) L23)) (forall ((C int) (A set_int) (B set_int)) (let ((_let_1 (@ member_int C))) (=> (@ _let_1 A) (=> (@ _let_1 B) (@ _let_1 (@ (@ inf_inf_set_int A) B)))))) (forall ((X set_Pr4329608150637261639at_nat)) (= (@ (@ inf_in7913087082777306421at_nat bot_bo228742789529271731at_nat) X) bot_bo228742789529271731at_nat)) _let_148 _let_147 (forall ((C nat) (P (-> nat Bool))) (=> (forall ((X3 nat)) (=> (@ (@ ord_less_eq_nat C) X3) (@ P X3))) (@ (@ eventually_nat P) at_top_nat))) (forall ((P (-> nat nat Bool))) (@ (@ sorted_wrt_nat P) nil_nat)) (forall ((I nat) (L list_d) (X d) (Y d)) (=> (@ (@ ord_less_nat I) (@ size_size_list_d L)) (= (@ (@ member_d X) (@ set_d2 (@ (@ (@ list_update_d L) I) Y))) (or (forall ((Y5 d)) (@ (@ member_d X) (@ set_d2 (@ (@ (@ list_update_d L) I) Y5)))) (= X Y))))) (forall ((X assn) (Y assn) (Z assn)) (let ((_let_1 (@ ord_less_assn X))) (=> (@ _let_1 Y) (=> (@ (@ ord_less_assn Y) Z) (@ _let_1 Z))))) (forall ((A2 int)) (= (@ quotient_of (@ of_int A2)) (@ (@ product_Pair_int_int A2) one_one_int))) (forall ((B2 assn) (A2 assn)) (=> (@ (@ ord_less_assn B2) A2) (= (@ (@ ord_min_assn A2) B2) B2))) (forall ((A2 int) (B set_int) (B2 int)) (let ((_let_1 (@ member_int A2))) (=> (@ _let_1 B) (@ _let_1 (@ (@ insert_int2 B2) B))))) (forall ((P assn) (A (-> c d assn)) (Xs list_c) (I nat) (Xsi list_d) (I3 set_nat) (F assn) (Q assn)) (let ((_let_1 (@ entails P))) (=> (@ _let_1 (@ (@ times_times_assn (@ (@ times_times_assn (@ (@ A (@ (@ nth_c Xs) I)) (@ (@ nth_d Xsi) I))) (@ (@ (@ (@ vEBT_L824818263033719201sn_c_d (@ (@ minus_minus_set_nat I3) (@ (@ insert_nat2 I) bot_bot_set_nat))) A) Xs) Xsi))) F)) (=> (@ (@ ord_less_nat I) (@ size_size_list_c Xs)) (=> (@ (@ member_nat I) I3) (=> (@ (@ entails (@ (@ times_times_assn (@ (@ (@ (@ vEBT_L824818263033719201sn_c_d I3) A) Xs) Xsi)) F)) Q) (@ _let_1 Q))))))) (forall ((A2 int) (B2 int)) (=> (@ (@ ord_less_eq_int A2) one_one_int) (=> (@ (@ ord_less_eq_int zero_zero_int) B2) (=> (@ (@ ord_less_eq_int B2) one_one_int) (@ (@ ord_less_eq_int (@ (@ times_times_int A2) B2)) one_one_int))))) (forall ((A2 rat) (E rat) (C rat) (B2 rat) (D2 rat)) (= (@ (@ ord_less_rat (@ (@ plus_plus_rat (@ (@ times_times_rat A2) E)) C)) (@ (@ 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ord_less_num) Xs) (@ (@ sorted_wrt_num ord_less_eq_num) Xs))) (forall ((X produc3843707927480180839at_nat) (A set_Pr4329608150637261639at_nat) (B set_Pr4329608150637261639at_nat)) (let ((_let_1 (@ (@ insert9069300056098147895at_nat X) bot_bo228742789529271731at_nat))) (let ((_let_2 (= B _let_1))) (let ((_let_3 (= A _let_1))) (= (= _let_1 (@ (@ sup_su5525570899277871387at_nat A) B)) (or (and _let_3 (= B bot_bo228742789529271731at_nat)) (and _let_2 _let_3) (and _let_2 (= A bot_bo228742789529271731at_nat)))))))) (forall ((X nat) (Xs list_nat)) (=> (@ (@ member_nat X) (@ set_nat2 Xs)) (@ (@ ord_less_nat zero_zero_nat) (@ size_size_list_nat Xs)))) (forall ((B2 assn) (A2 assn)) (=> (@ (@ ord_less_eq_assn B2) A2) (= (@ (@ inf_inf_assn A2) B2) B2))) (forall ((B set_int) (A2 int) (A set_int)) (let ((_let_1 (@ inf_inf_set_int B))) (= (= (@ _let_1 (@ (@ insert_int2 A2) A)) bot_bot_set_int) (and (not (@ (@ member_int A2) B)) (= (@ _let_1 A) bot_bot_set_int))))) (forall ((A2 int)) (= (@ (@ 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set_Pr1261947904930325089at_nat) (B set_Pr1261947904930325089at_nat)) (=> (@ (@ ord_le3146513528884898305at_nat A) B) (= (@ (@ inf_in2572325071724192079at_nat A) B) A))) (forall ((M2 nat) (N nat)) (let ((_let_1 (@ ord_less_nat zero_zero_nat))) (= (@ _let_1 (@ (@ plus_plus_nat M2) N)) (or (@ _let_1 N) (@ _let_1 M2))))) (forall ((A set_nat) (B set_nat) (C2 set_nat)) (= (@ (@ ord_less_eq_set_nat (@ (@ sup_sup_set_nat A) B)) C2) (and (@ (@ ord_less_eq_set_nat B) C2) (@ (@ ord_less_eq_set_nat A) C2)))) (forall ((Xs list_P5464809261938338413at_nat) (X produc3843707927480180839at_nat)) (=> (@ distin5355857245021852384at_nat Xs) (= (@ set_Pr3765526544606949372at_nat (@ (@ remove8895909992688781315at_nat X) Xs)) (@ (@ minus_3314409938677909166at_nat (@ set_Pr3765526544606949372at_nat Xs)) (@ (@ insert9069300056098147895at_nat X) bot_bo228742789529271731at_nat))))) (forall ((X assn) (Y assn) (Z assn)) (let ((_let_1 (@ inf_inf_assn X))) (@ (@ ord_less_eq_assn (@ (@ sup_sup_assn (@ _let_1 Y)) (@ _let_1 Z))) (@ _let_1 (@ (@ sup_sup_assn Y) Z))))) (forall ((N nat) (Xs list_c)) (= (@ (@ ord_less_eq_nat (@ suc N)) (@ size_size_list_c Xs)) (exists ((X2 c) (Ys3 list_c)) (and (@ (@ ord_less_eq_nat N) (@ size_size_list_c Ys3)) (= Xs (@ (@ cons_c X2) Ys3)))))) (forall ((A2 int) (B2 int) (C int) (D2 int)) (=> (@ (@ ord_less_int A2) B2) (=> (@ (@ ord_less_eq_int C) D2) (@ (@ ord_less_int (@ (@ plus_plus_int A2) C)) (@ (@ plus_plus_int B2) D2))))) (forall ((X int) (Y int)) (= (= (@ (@ plus_plus_int (@ (@ times_times_int X) X)) (@ (@ times_times_int Y) Y)) zero_zero_int) (and (= X zero_zero_int) (= Y zero_zero_int)))) (forall ((A2 rat) (E rat) (C rat) (B2 rat) (D2 rat)) (= (@ (@ ord_less_rat (@ (@ plus_plus_rat (@ (@ times_times_rat A2) E)) C)) (@ (@ plus_plus_rat (@ (@ times_times_rat B2) E)) D2)) (@ (@ ord_less_rat (@ (@ plus_plus_rat (@ (@ times_times_rat (@ (@ minus_minus_rat A2) B2)) E)) C)) D2))) (forall ((X int) (Xs list_int)) (=> (not (@ (@ member_int X) (@ set_int2 Xs))) (= (@ (@ insert_int X) Xs) (@ (@ cons_int X) Xs)))) (forall ((Xs list_P8527749157015355191n_assn) (X produc6575502325842934193n_assn)) (let ((_let_1 (@ (@ cons_P2971678138204555879n_assn X) nil_Pr5671120429643327159n_assn))) (= (= (@ rev_Pr4855572775806611735n_assn Xs) _let_1) (= Xs _let_1)))) (forall ((M2 nat) (N nat)) (= (@ (@ map_nat_nat (lambda ((N2 nat)) (@ (@ minus_minus_nat N2) (@ suc zero_zero_nat)))) (@ (@ upt (@ suc M2)) (@ suc N))) (@ (@ upt M2) N))) (forall ((X (-> produc3658429121746597890et_nat Bool)) (Xa (-> produc3658429121746597890et_nat Bool)) (Xb produc3658429121746597890et_nat)) (=> (not (@ (@ (@ times_assn_raw X) Xa) Xb)) (=> (@ (@ accp_P1862375125659990705et_nat times_assn_raw_rel) (@ (@ produc2245416461498447860et_nat X) (@ (@ produc5001842942810119800et_nat Xa) Xb))) (not (forall ((H heap_e7401611519738050253t_unit) (As set_nat)) (let ((_let_1 (@ (@ produc7507926704131184380et_nat H) As))) (=> (= Xb _let_1) (=> (@ (@ accp_P1862375125659990705et_nat times_assn_raw_rel) (@ (@ produc2245416461498447860et_nat X) (@ (@ produc5001842942810119800et_nat Xa) _let_1))) (exists ((As13 set_nat) (As24 set_nat)) (let ((_let_1 (@ produc7507926704131184380et_nat H))) (and (@ Xa (@ _let_1 As24)) (@ X (@ _let_1 As13)) (= (@ (@ inf_inf_set_nat As13) As24) bot_bot_set_nat) (= As (@ (@ sup_sup_set_nat As13) As24))))))))))))) (forall ((N nat)) (let ((_let_1 (@ set_or1269000886237332187st_nat zero_zero_nat))) (let ((_let_2 (@ suc N))) (= (@ _let_1 _let_2) (@ (@ insert_nat2 _let_2) (@ _let_1 N)))))) (@ proper one_assn_raw) (forall ((L code_integer) (U code_integer)) (= (@ (@ set_or189985376899183464nteger (@ (@ plus_p5714425477246183910nteger L) one_one_Code_integer)) U) (@ (@ set_or2715278749043346189nteger L) U))) _let_145 (forall ((X int) (X6 int) (P Bool) (P3 Bool)) (let ((_let_1 (@ ord_less_eq_int zero_zero_int))) (let ((_let_2 (@ _let_1 X6))) (=> (= X X6) (=> (=> _let_2 (= P P3)) (= (and P (@ _let_1 X)) (and P3 _let_2))))))) (forall ((A2 int)) (= (= zero_zero_int (@ (@ 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semiri1314217659103216013at_int K3)))) (=> (@ (@ ord_less_int I) J) (=> (@ (@ ord_less_nat zero_zero_nat) K3) (@ (@ ord_less_int (@ _let_1 I)) (@ _let_1 J)))))) (forall ((A2 assn) (C assn) (B2 assn) (D2 assn)) (=> (@ (@ ord_less_eq_assn A2) C) (=> (@ (@ ord_less_eq_assn B2) D2) (@ (@ ord_less_eq_assn (@ (@ inf_inf_assn A2) B2)) (@ (@ inf_inf_assn C) D2))))) _let_144 (= (@ quotient_of one_one_rat) _let_23) (forall ((A set_Pr4329608150637261639at_nat) (B set_Pr4329608150637261639at_nat)) (= (= (@ (@ sup_su5525570899277871387at_nat A) B) bot_bo228742789529271731at_nat) (and (= B bot_bo228742789529271731at_nat) (= A bot_bo228742789529271731at_nat)))) (forall ((T int)) (exists ((Z4 int)) (forall ((X7 int)) (=> (@ (@ ord_less_int X7) Z4) (@ (@ ord_less_eq_int X7) T))))) (forall ((S set_nat) (R (-> nat nat Bool))) (=> (forall ((X3 nat) (Y2 nat)) (=> (@ (@ member_nat X3) S) (=> (@ (@ member_nat Y2) S) (=> (not (= X3 Y2)) (@ (@ R X3) Y2))))) (@ (@ pairwise_nat R) S))) (forall ((I nat) (J nat) (R set_Pr1261947904930325089at_nat)) (=> (@ (@ member8440522571783428010at_nat (@ (@ product_Pair_nat_nat I) J)) R) (@ (@ member_nat I) (@ field_nat R)))) (forall ((A set_Pr1261947904930325089at_nat) (B set_Pr1261947904930325089at_nat) (C2 set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ inf_in2572325071724192079at_nat A))) (= (@ (@ inf_in2572325071724192079at_nat (@ _let_1 B)) C2) (@ _let_1 (@ (@ inf_in2572325071724192079at_nat B) C2))))) (= ord_less_eq_int (lambda ((A3 int) (B3 int)) (= A3 (@ (@ ord_min_int A3) B3)))) (forall ((A2 set_nat) (B2 set_nat) (C set_nat) (D2 set_nat)) (=> (= A2 B2) (=> (@ (@ ord_less_eq_set_nat B2) C) (=> (= C D2) (@ (@ ord_less_eq_set_nat A2) D2))))) (forall ((A2 assn) (F4 (-> nat assn)) (B2 nat) (C nat)) (let ((_let_1 (@ ord_less_assn A2))) (=> (@ _let_1 (@ F4 B2)) (=> (@ (@ ord_less_eq_nat B2) C) (=> (forall ((X3 nat) (Y2 nat)) (=> (@ (@ ord_less_eq_nat X3) Y2) (@ (@ ord_less_eq_assn (@ F4 X3)) (@ F4 Y2)))) (@ _let_1 (@ F4 C))))))) (forall ((A set_int)) (@ (@ ord_less_eq_set_int bot_bot_set_int) A)) (forall ((Xs list_P8527749157015355191n_assn)) (= (@ set_Pr1139785259514867910n_assn (@ rev_Pr4855572775806611735n_assn Xs)) (@ set_Pr1139785259514867910n_assn Xs))) (forall ((Xs list_int)) (= (@ distinct_int (@ rotate1_int Xs)) (@ distinct_int Xs))) (forall ((A2 assn) (F4 (-> code_integer assn)) (B2 code_integer) (C code_integer)) (let ((_let_1 (@ ord_less_assn A2))) (=> (@ _let_1 (@ F4 B2)) (=> (@ (@ ord_le6747313008572928689nteger B2) C) (=> (forall ((X3 code_integer) (Y2 code_integer)) (=> (@ (@ ord_le6747313008572928689nteger X3) Y2) (@ (@ ord_less_assn (@ F4 X3)) (@ F4 Y2)))) (@ _let_1 (@ F4 C))))))) (forall ((A2 rat)) (= (@ (@ minus_minus_rat A2) zero_zero_rat) A2)) (forall ((I nat) (J nat)) (let ((_let_1 (@ upt zero_zero_nat))) (=> (@ (@ ord_less_nat I) J) (= (@ (@ append_nat (@ _let_1 I)) (@ (@ upt I) J)) (@ _let_1 J))))) (forall ((Ax (-> produc3658429121746597890et_nat Bool)) (Ay produc3925858234332021118et_nat) (Bx (-> produc3658429121746597890et_nat Bool)) (By produc3925858234332021118et_nat) (R2 set_Pr3444600963470892981et_nat) (P (-> (-> produc3658429121746597890et_nat Bool) produc3925858234332021118et_nat Bool))) (=> (@ (@ member6341495586645257982et_nat (@ (@ produc1940133919992309389et_nat (@ (@ produc2245416461498447860et_nat Ax) Ay)) (@ (@ produc2245416461498447860et_nat Bx) By))) (@ transi5221092739591632921et_nat R2)) (=> (forall ((A4 (-> produc3658429121746597890et_nat Bool)) (B4 produc3925858234332021118et_nat)) (=> (@ (@ member6341495586645257982et_nat (@ (@ produc1940133919992309389et_nat (@ (@ produc2245416461498447860et_nat Ax) Ay)) (@ (@ produc2245416461498447860et_nat A4) B4))) R2) (@ (@ P A4) B4))) (=> (forall ((A4 (-> produc3658429121746597890et_nat Bool)) (B4 produc3925858234332021118et_nat) (Aa (-> produc3658429121746597890et_nat Bool)) (Ba produc3925858234332021118et_nat)) (let ((_let_1 (@ (@ produc2245416461498447860et_nat A4) B4))) (=> (@ (@ member6341495586645257982et_nat (@ (@ produc1940133919992309389et_nat (@ (@ produc2245416461498447860et_nat Ax) Ay)) _let_1)) (@ transi5221092739591632921et_nat R2)) (=> (@ (@ member6341495586645257982et_nat (@ (@ produc1940133919992309389et_nat _let_1) (@ (@ produc2245416461498447860et_nat Aa) Ba))) R2) (=> (@ (@ P A4) B4) (@ (@ P Aa) Ba)))))) (@ (@ P Bx) By))))) (forall ((X produc6575502325842934193n_assn) (Xs list_P8527749157015355191n_assn) (Y produc6575502325842934193n_assn) (Ys list_P8527749157015355191n_assn) (R2 set_Pr8116311503512020807n_assn)) (let ((_let_1 (@ lex_Pr7559194461235888923n_assn R2))) (= (@ (@ member3994142547374651152n_assn (@ (@ produc3014731801419794263n_assn (@ (@ cons_P2971678138204555879n_assn X) Xs)) (@ (@ cons_P2971678138204555879n_assn Y) Ys))) _let_1) (or (and (= X Y) (@ (@ member3994142547374651152n_assn (@ (@ produc3014731801419794263n_assn Xs) Ys)) _let_1)) (and (@ (@ member4743710847862083984n_assn (@ (@ produc6128706242671166167n_assn X) Y)) R2) (= (@ size_s6829681357464350627n_assn 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(forall ((C code_integer) (A2 code_integer) (B2 code_integer)) (let ((_let_1 (@ times_3573771949741848930nteger C))) (=> (@ (@ ord_le6747313008572928689nteger zero_z3403309356797280102nteger) C) (= (@ (@ ord_le6747313008572928689nteger (@ _let_1 A2)) (@ _let_1 B2)) (@ (@ ord_le6747313008572928689nteger A2) B2))))) (forall ((X produc3843707927480180839at_nat) (Xs list_P5464809261938338413at_nat)) (=> (not (@ (@ member8757157785044589968at_nat X) (@ set_Pr3765526544606949372at_nat Xs))) (= (@ (@ remove4908499291543849587at_nat X) Xs) Xs))) (forall ((Xs list_d)) (= (@ size_size_list_d (@ rotate1_d Xs)) (@ size_size_list_d Xs))) (forall ((M5 set_nat)) (=> (@ finite_finite_nat M5) (=> (not (= M5 bot_bot_set_nat)) (=> (not (@ (@ member_nat zero_zero_nat) M5)) (= (@ gcd_Gcd_nat M5) (@ lattic8265883725875713057ax_nat (@ comple7806235888213564991et_nat (@ (@ image_nat_set_nat (lambda ((M nat)) (@ collect_nat (lambda ((D5 nat)) (@ (@ dvd_dvd_nat D5) M))))) M5)))))))) (forall ((M2 nat) (N nat)) 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(let ((_let_1 (@ member8757157785044589968at_nat (@ (@ produc2922128104949294807at_nat A2) B2)))) (=> (@ _let_1 (@ transi2703068831062848130at_nat R2)) (=> (not (@ _let_1 R2)) (not (forall ((C4 set_Pr1261947904930325089at_nat)) (=> (@ (@ member8757157785044589968at_nat (@ (@ produc2922128104949294807at_nat A2) C4)) (@ transi2703068831062848130at_nat R2)) (not (@ (@ member8757157785044589968at_nat (@ (@ produc2922128104949294807at_nat C4) B2)) R2))))))))) (forall ((X nat) (Xs list_nat)) (= (@ (@ insert_nat2 X) (@ coset_nat Xs)) (@ coset_nat (@ (@ removeAll_nat X) Xs)))) (forall ((X Bool) (Xs list_o)) (= (@ set_o2 (@ (@ removeAll_o X) Xs)) (@ (@ minus_minus_set_o (@ set_o2 Xs)) (@ (@ insert_o2 X) bot_bot_set_o)))) (forall ((A set_nat) (B set_nat)) (@ (@ ord_less_eq_set_nat (@ (@ minus_minus_set_nat A) B)) A)) (forall ((B2 code_integer) (A2 code_integer) (C code_integer)) (let ((_let_1 (@ minus_8373710615458151222nteger C))) (=> (@ (@ ord_le6747313008572928689nteger B2) A2) (@ (@ 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I))))))) (forall ((X assn) (Y assn) (Z assn)) (let ((_let_1 (@ sup_sup_assn X))) (= (@ _let_1 (@ (@ inf_inf_assn Y) Z)) (@ (@ inf_inf_assn (@ _let_1 Y)) (@ _let_1 Z))))) (forall ((A set_nat) (B set_nat)) (=> (@ (@ ord_less_eq_set_nat A) B) (= (@ (@ inf_inf_set_nat A) B) A))) (forall ((A assn) (B assn) (C2 assn)) (let ((_let_1 (@ entails A))) (=> (@ _let_1 B) (=> (@ _let_1 C2) (@ _let_1 (@ (@ inf_inf_assn B) C2)))))) (forall ((A2 set_Pr1261947904930325089at_nat)) (= (not (= A2 bot_bo2099793752762293965at_nat)) (@ (@ ord_le7866589430770878221at_nat bot_bo2099793752762293965at_nat) A2))) (forall ((I nat) (Xs list_d) (J nat) (X d)) (let ((_let_1 (@ (@ nth_d (@ (@ (@ list_update_d Xs) I) X)) J))) (let ((_let_2 (= I J))) (=> (@ (@ ord_less_nat I) (@ size_size_list_d Xs)) (and (=> (not _let_2) (= _let_1 (@ (@ nth_d Xs) J))) (=> _let_2 (= _let_1 X))))))) (forall ((A2 product_prod_nat_nat) (B2 product_prod_nat_nat) (Xs list_P6011104703257516679at_nat)) (= (@ (@ member8206827879206165904at_nat (@ (@ produc6161850002892822231at_nat A2) B2)) (@ set_Pr5518436109238095868at_nat (@ (@ zip_Pr4664179122662387191at_nat Xs) Xs))) (and (= A2 B2) (@ (@ member8440522571783428010at_nat A2) (@ set_Pr5648618587558075414at_nat Xs))))) (forall ((M2 nat) (N nat) (L nat)) (let ((_let_1 (@ minus_minus_nat L))) (let ((_let_2 (@ ord_less_nat M2))) (=> (@ _let_2 N) (=> (@ _let_2 L) (@ (@ ord_less_nat (@ _let_1 N)) (@ _let_1 M2))))))) (forall ((A set_Pr1261947904930325089at_nat) (B set_Pr1261947904930325089at_nat) (C product_prod_nat_nat)) (let ((_let_1 (@ member8440522571783428010at_nat C))) (=> (@ (@ ord_le7866589430770878221at_nat A) B) (=> (@ _let_1 A) (@ _let_1 B))))) (forall ((A set_o)) (= (@ (@ minus_minus_set_o bot_bot_set_o) A) bot_bot_set_o)) (forall ((X produc6575502325842934193n_assn) (Xs list_P8527749157015355191n_assn)) (let ((_let_1 (@ member7957490590177025114n_assn X))) (=> (@ _let_1 (@ set_Pr1139785259514867910n_assn (@ butlas3012047794866324995n_assn Xs))) (@ _let_1 (@ set_Pr1139785259514867910n_assn Xs))))) (forall ((D2 int) (D int) (B set_int) (T int)) (=> (@ (@ dvd_dvd_int D2) D) (forall ((X7 int)) (let ((_let_1 (@ dvd_dvd_int D2))) (=> (forall ((Xa3 int)) (=> (@ (@ member_int Xa3) (@ (@ set_or1266510415728281911st_int one_one_int) D)) (forall ((Xb3 int)) (=> (@ (@ member_int Xb3) B) (not (= X7 (@ (@ plus_plus_int Xb3) Xa3))))))) (=> (not (@ _let_1 (@ (@ plus_plus_int X7) T))) (not (@ _let_1 (@ (@ plus_plus_int (@ (@ minus_minus_int X7) D)) T))))))))) (forall ((B2 int) (X nat) (Y nat)) (let ((_let_1 (@ power_power_int B2))) (=> (@ (@ ord_less_int one_one_int) B2) (= (@ (@ ord_less_eq_int (@ _let_1 X)) (@ _let_1 Y)) (@ (@ ord_less_eq_nat X) Y))))) (forall ((A2 int) (B2 int) (Q6 int) (R2 int) (Q7 int) (R5 int)) (let ((_let_1 (@ (@ eucl_rel_int A2) B2))) (=> (@ _let_1 (@ (@ product_Pair_int_int Q6) R2)) (=> (@ _let_1 (@ (@ product_Pair_int_int Q7) R5)) (= Q6 Q7))))) (forall ((Xs list_nat) (N nat)) (= (= (@ size_size_list_nat Xs) (@ suc N)) (exists ((Y5 nat) (Ys3 list_nat)) (and (= Xs (@ (@ cons_nat Y5) Ys3)) (= (@ size_size_list_nat Ys3) N))))) (forall ((A2 produc3843707927480180839at_nat) (B set_Pr4329608150637261639at_nat) (B2 produc3843707927480180839at_nat)) (let ((_let_1 (@ member8757157785044589968at_nat A2))) (=> (=> (not (@ _let_1 B)) (= A2 B2)) (@ _let_1 (@ (@ insert9069300056098147895at_nat B2) B))))) (forall ((A2 int)) (= (@ (@ times_times_int one_one_int) A2) A2)) (forall ((Xs list_int)) (= (@ gcd_Lcm_int (@ set_int2 Xs)) (@ (@ (@ fold_int_int gcd_lcm_int) Xs) one_one_int))) (forall ((P (-> Bool Bool Bool))) (@ (@ pairwise_o P) bot_bot_set_o)) (forall ((X list_list_int)) (=> (not (= X nil_list_int)) (=> (forall ((Xss list_list_int)) (not (= X (@ (@ cons_list_int nil_int) Xss)))) (not (forall ((X3 int) (Xs2 list_int) (Xss list_list_int)) (not (= X (@ (@ cons_list_int (@ (@ cons_int X3) Xs2)) Xss)))))))) (forall ((Y set_nat) (X set_nat)) (=> (@ (@ ord_less_eq_set_nat Y) X) (= (@ (@ inf_inf_set_nat X) Y) Y))) (forall ((X set_Pr4329608150637261639at_nat)) (= (@ (@ ord_mi6693596345299712430at_nat X) bot_bo228742789529271731at_nat) bot_bo228742789529271731at_nat)) (forall ((Xs list_int) (Ys list_int)) (= (= (@ (@ zip_int_int Xs) Ys) nil_Pr2300489316682597567nt_int) (or (= Xs nil_int) (= Ys nil_int)))) (forall ((X c) (Xs list_c) (Y c)) (= (@ (@ (@ list_update_c (@ (@ cons_c X) Xs)) zero_zero_nat) Y) (@ (@ cons_c Y) Xs))) _let_140 (= ord_less_eq_nat (lambda ((A3 nat) (B3 nat)) (or (= A3 B3) (@ (@ ord_less_nat A3) B3)))) (forall ((C product_prod_nat_nat) (A set_Pr1261947904930325089at_nat) (B set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ member8440522571783428010at_nat C))) (= (@ _let_1 (@ (@ sup_su6327502436637775413at_nat A) B)) (or (@ _let_1 A) (@ _let_1 B))))) (= ord_le3102999989581377725nteger (lambda ((X2 code_integer) (Y5 code_integer)) (or (= X2 Y5) (@ (@ ord_le6747313008572928689nteger X2) Y5)))) (forall ((A2 code_integer) (E code_integer) (C code_integer) (B2 code_integer) (D2 code_integer)) (= (= (@ (@ plus_p5714425477246183910nteger (@ (@ times_3573771949741848930nteger A2) E)) C) (@ (@ plus_p5714425477246183910nteger (@ (@ times_3573771949741848930nteger B2) E)) D2)) (= C (@ (@ plus_p5714425477246183910nteger (@ (@ times_3573771949741848930nteger (@ (@ minus_8373710615458151222nteger B2) A2)) E)) D2)))) (forall ((M2 nat) (N nat)) (=> (@ (@ ord_less_nat M2) (@ (@ power_power_nat (@ numeral_numeral_nat (@ bit0 one))) N)) (= (@ (@ bit_se2925701944663578781it_nat N) M2) M2))) (forall ((X int) (Y int)) (=> (@ (@ ord_less_eq_int X) Y) (= (@ (@ ord_min_int X) Y) X))) (forall ((A2 (-> int option6357759511663192854e_term)) (B2 product_prod_int_int) (S set_Pr1872883991513573699nt_int) (P (-> (-> int option6357759511663192854e_term) product_prod_int_int Bool))) (let ((_let_1 (@ (@ member7034335876925520548nt_int (@ (@ produc4305682042979456191nt_int A2) B2)) S))) (=> _let_1 (=> (=> _let_1 (@ (@ P A2) B2)) (exists ((A4 (-> int option6357759511663192854e_term)) (B4 product_prod_int_int)) (and (@ (@ member7034335876925520548nt_int (@ (@ produc4305682042979456191nt_int A4) B4)) S) (@ (@ P A4) B4))))))) (forall ((Y nat) (X nat)) (=> (@ (@ ord_less_eq_nat Y) X) (= (@ (@ sup_sup_nat X) Y) X))) (forall ((Xs list_P8527749157015355191n_assn) (Ys list_P8527749157015355191n_assn) (X produc6575502325842934193n_assn)) (=> (@ (@ ord_less_eq_nat (@ size_s6829681357464350627n_assn Xs)) (@ size_s6829681357464350627n_assn Ys)) (not (= Xs (@ (@ cons_P2971678138204555879n_assn X) Ys))))) (forall ((B2 nat) (A2 nat) (C nat)) (=> (@ (@ ord_less_eq_nat B2) A2) (=> (@ (@ ord_less_eq_nat C) A2) (@ (@ ord_less_eq_nat (@ (@ sup_sup_nat B2) C)) A2)))) (forall ((A2 rat) (B2 rat) (C rat)) (= (@ (@ ord_less_rat (@ (@ minus_minus_rat A2) B2)) C) (@ (@ ord_less_rat A2) (@ (@ plus_plus_rat C) B2)))) (= ord_le6747313008572928689nteger (lambda ((A3 code_integer) (B3 code_integer)) (and (@ (@ ord_le3102999989581377725nteger A3) B3) (not (@ (@ ord_le3102999989581377725nteger B3) A3))))) (= ord_less_eq_assn (lambda ((A3 assn) (B3 assn)) (= (@ (@ sup_sup_assn A3) B3) B3))) (forall ((Y list_int)) (=> (not (= Y nil_int)) (not (forall ((X212 int) (X223 list_int)) (not (= Y (@ (@ cons_int X212) X223))))))) (= pw_leq (lambda ((A12 multis2468970476368604999at_nat) (A23 multis2468970476368604999at_nat)) (or (exists ((X2 product_prod_nat_nat) (Y5 product_prod_nat_nat) (X8 multis2468970476368604999at_nat) (Y7 multis2468970476368604999at_nat)) (and (= A12 (@ (@ plus_p7104986032573967614at_nat (@ (@ add_ms2612439473150266591at_nat X2) zero_z1048942125864253310at_nat)) X8)) (= A23 (@ (@ plus_p7104986032573967614at_nat (@ (@ add_ms2612439473150266591at_nat Y5) zero_z1048942125864253310at_nat)) Y7)) (@ (@ member8206827879206165904at_nat (@ (@ produc6161850002892822231at_nat X2) Y5)) fun_pair_leq) (@ (@ pw_leq X8) Y7))) (and (= A12 zero_z1048942125864253310at_nat) (= A23 zero_z1048942125864253310at_nat))))) (forall ((C rat) (B2 rat)) (= (= C (@ (@ times_times_rat C) B2)) (or (= C zero_zero_rat) (= B2 one_one_rat)))) (forall ((X produc6575502325842934193n_assn)) (= (@ (@ insert3246601298802261197n_assn X) nil_Pr5671120429643327159n_assn) (@ (@ cons_P2971678138204555879n_assn X) nil_Pr5671120429643327159n_assn))) (forall ((A2 code_integer) (B2 code_integer)) (=> (not (= A2 zero_z3403309356797280102nteger)) (=> (not (= B2 zero_z3403309356797280102nteger)) (not (= (@ (@ times_3573771949741848930nteger A2) B2) zero_z3403309356797280102nteger))))) (forall ((N nat) (Xs list_nat)) (let ((_let_1 (@ size_size_list_nat Xs))) (=> (@ (@ ord_less_nat N) _let_1) (= (@ (@ nth_nat (@ rev_nat Xs)) N) (@ (@ nth_nat Xs) (@ (@ minus_minus_nat _let_1) (@ suc N))))))) _let_139 (forall ((B assn) (C2 assn) (A assn)) (=> (@ (@ entails B) C2) (@ (@ entails (@ (@ inf_inf_assn A) B)) C2))) (forall ((X list_int) (Y list_int)) (=> (not (= (@ size_size_list_int X) (@ size_size_list_int Y))) (not (= X Y)))) (= ord_less_eq_set_nat (lambda ((A3 set_nat) (B3 set_nat)) (= A3 (@ (@ inf_inf_set_nat A3) B3)))) (forall ((From nat) (To nat) (Xs list_nat)) (=> (@ (@ ord_less_eq_nat From) To) (=> (@ (@ ord_less_eq_nat To) (@ size_size_list_nat Xs)) (= (@ size_size_list_nat (@ (@ (@ slice_nat From) To) Xs)) (@ (@ minus_minus_nat To) From))))) (forall ((R2 int) (A2 int) (B2 int) (C int) (D2 int)) (let ((_let_1 (@ times_times_int R2))) (=> (not (= R2 zero_zero_int)) (=> (and (= A2 B2) (not (= C D2))) (not (= (@ (@ plus_plus_int A2) (@ _let_1 C)) (@ (@ plus_plus_int B2) (@ _let_1 D2)))))))) (forall ((Xa product_prod_nat_nat) (X product_prod_nat_nat)) (= (@ (@ ord_less_int (@ abs_Integ Xa)) (@ abs_Integ X)) (@ (@ (@ produc8739625826339149834_nat_o (lambda ((X2 nat) (Y5 nat) (__flatten_var_0 product_prod_nat_nat)) (@ (@ produc6081775807080527818_nat_o (lambda ((U4 nat) (V4 nat)) (@ (@ ord_less_nat (@ (@ plus_plus_nat X2) V4)) (@ (@ plus_plus_nat U4) Y5)))) __flatten_var_0))) Xa) X))) (forall ((C int) (A2 int)) (=> (@ (@ ord_less_eq_int C) one_one_int) (=> (@ (@ ord_less_eq_int zero_zero_int) A2) (@ (@ ord_less_eq_int (@ (@ times_times_int A2) C)) A2)))) (forall ((I3 set_nat) (I7 set_nat) (A (-> c nat assn)) (A6 (-> c nat assn)) (Xs list_c) (Xs4 list_c) (Xsi list_nat) (Xsi2 list_nat)) (=> (= I3 I7) (=> (= A A6) (=> (= (@ size_size_list_c Xs) (@ size_size_list_c Xs4)) (=> (= (@ size_size_list_nat Xsi) (@ size_size_list_nat Xsi2)) (=> (forall ((I5 nat)) (let ((_let_1 (@ size_size_list_c Xs))) (=> (@ (@ member_nat I5) I3) (=> (@ (@ ord_less_nat I5) _let_1) (=> (= _let_1 (@ size_size_list_nat Xsi)) (and (= (@ (@ nth_c Xs) I5) (@ (@ nth_c Xs4) I5)) (= (@ (@ nth_nat Xsi) I5) (@ (@ nth_nat Xsi2) I5)))))))) (= (@ (@ (@ (@ vEBT_L6585172037124793648_c_nat I3) A) Xs) Xsi) (@ (@ (@ (@ vEBT_L6585172037124793648_c_nat I7) A6) Xs4) Xsi2)))))))) (forall ((B2 Bool) (H2 heap_e7401611519738050253t_unit) (As2 set_nat)) (= (@ (@ pure_a825153325127701367it_nat B2) (@ (@ produc7507926704131184380et_nat H2) As2)) (and (= As2 bot_bot_set_nat) B2))) (forall ((A2 code_integer) (B2 code_integer)) (let ((_let_1 (@ ord_le6747313008572928689nteger zero_z3403309356797280102nteger))) (= (@ _let_1 (@ (@ times_3573771949741848930nteger A2) B2)) (or (and (@ _let_1 B2) (@ _let_1 A2)) (and (@ (@ ord_le6747313008572928689nteger A2) zero_z3403309356797280102nteger) (@ (@ ord_le6747313008572928689nteger B2) zero_z3403309356797280102nteger)))))) (forall ((A2 product_prod_nat_nat) (C2 set_Pr1261947904930325089at_nat) (B set_Pr1261947904930325089at_nat)) (=> (not (@ (@ member8440522571783428010at_nat A2) C2)) (= (@ (@ inf_in2572325071724192079at_nat (@ (@ insert8211810215607154385at_nat A2) B)) C2) (@ (@ inf_in2572325071724192079at_nat B) C2)))) (forall ((A set_Pr4532377907799695533_nat_o) (A2 (-> produc3658429121746597890et_nat Bool))) (=> (= A bot_bo7824918357723582233_nat_o) (not (@ (@ member6576561426505652726_nat_o A2) A)))) (forall ((L list_c) (I nat) (X c)) (= (@ (@ (@ list_update_c (@ butlast_c L)) I) X) (@ butlast_c (@ (@ (@ list_update_c L) I) X)))) (forall ((Xs list_d) (Ys list_nat) (R2 set_Pr3276347184212964150_d_nat)) (=> (@ (@ member6851837201453759021st_nat (@ (@ produc6793648210820618640st_nat Xs) Ys)) (@ listrel_d_nat R2)) (= (@ size_size_list_d Xs) (@ size_size_list_nat Ys)))) (forall ((A set_Pr4329608150637261639at_nat) (X produc3843707927480180839at_nat) (B set_Pr4329608150637261639at_nat)) (let ((_let_1 (@ insert9069300056098147895at_nat X))) (let ((_let_2 (@ (@ member8757157785044589968at_nat X) A))) (let ((_let_3 (@ ord_le1268244103169919719at_nat A))) (= (@ _let_3 (@ _let_1 B)) (and (=> (not _let_2) (@ _let_3 B)) (=> _let_2 (@ (@ ord_le1268244103169919719at_nat (@ (@ minus_3314409938677909166at_nat A) (@ _let_1 bot_bo228742789529271731at_nat))) B)))))))) (forall ((Xs list_int)) (=> (@ (@ sorted_wrt_int ord_less_int) Xs) (@ (@ sorted_wrt_int ord_less_eq_int) Xs))) (forall ((P (-> list_nat list_int Bool)) (R (-> nat int Bool)) (Xs list_nat) (Ys list_int)) (=> (forall ((Xs2 list_nat)) (@ (@ P Xs2) nil_int)) (=> (forall ((X_1 list_int)) (@ (@ P nil_nat) X_1)) (=> (forall ((X3 nat) (Xs2 list_nat) (Y2 int) (Ys5 list_int)) (let ((_let_1 (@ (@ cons_int Y2) Ys5))) (=> (@ (@ R X3) Y2) (=> (@ (@ P Xs2) _let_1) (@ (@ P (@ (@ cons_nat X3) Xs2)) _let_1))))) (=> (forall ((X3 nat) (Xs2 list_nat) (Y2 int) (Ys5 list_int)) (let ((_let_1 (@ P (@ (@ cons_nat X3) Xs2)))) (=> (not (@ (@ R X3) Y2)) (=> (@ _let_1 Ys5) (@ _let_1 (@ (@ cons_int Y2) Ys5)))))) (@ (@ P Xs) Ys)))))) (forall ((X set_nat) (A2 set_nat) (B2 set_nat)) (let ((_let_1 (@ ord_less_eq_set_nat X))) (=> (@ _let_1 A2) (=> (@ _let_1 B2) (@ _let_1 (@ (@ inf_inf_set_nat A2) B2)))))) (forall ((A2 set_Pr1261947904930325089at_nat) (B2 set_Pr1261947904930325089at_nat) (R2 set_Pr4329608150637261639at_nat)) (let ((_let_1 (@ member8757157785044589968at_nat (@ (@ produc2922128104949294807at_nat A2) B2)))) (=> (@ _let_1 R2) (@ _let_1 (@ transi2703068831062848130at_nat R2))))) (forall ((A2 int) (B2 int) (A set_int)) (let ((_let_1 (@ member_int A2))) (=> (@ _let_1 (@ (@ insert_int2 B2) A)) (=> (not (= A2 B2)) (@ _let_1 A))))) (forall ((Y (-> produc3658429121746597890et_nat Bool))) (=> (@ (@ member6576561426505652726_nat_o Y) (@ collec939566748876313656_nat_o proper)) (= (@ rep_assn (@ abs_assn Y)) Y))) (forall ((X int) (Y int) (Xs list_int)) (let ((_let_1 (@ removeAll_int X))) (let ((_let_2 (@ _let_1 Xs))) (let ((_let_3 (@ cons_int Y))) (let ((_let_4 (@ _let_1 (@ _let_3 Xs)))) (let ((_let_5 (= X Y))) (and (=> _let_5 (= _let_4 _let_2)) (=> (not _let_5) (= _let_4 (@ _let_3 _let_2)))))))))) (forall ((Xs list_P8527749157015355191n_assn) (X produc6575502325842934193n_assn)) (=> (@ distin4809818325527169450n_assn Xs) (=> (@ (@ member7957490590177025114n_assn X) (@ set_Pr1139785259514867910n_assn Xs)) (exists ((X3 nat)) (and (forall ((Y3 nat)) (=> (and (= (@ (@ nth_Pr1769885009046257848n_assn Xs) Y3) X) (@ (@ ord_less_nat Y3) (@ size_s6829681357464350627n_assn Xs))) (= Y3 X3))) (= (@ (@ nth_Pr1769885009046257848n_assn Xs) X3) X) (@ (@ ord_less_nat X3) (@ size_s6829681357464350627n_assn Xs))))))) (@ (@ (@ (@ bNF_re3461391660133120880nt_rat (lambda ((Y4 int) (Z2 int)) (= Y4 Z2))) (@ (@ bNF_re2214769303045360666nt_rat (lambda ((Y4 int) (Z2 int)) (= Y4 Z2))) pcr_rat)) (lambda ((A3 int) (B3 int)) (@ (@ (@ if_Pro3027730157355071871nt_int (= B3 zero_zero_int)) (@ (@ product_Pair_int_int zero_zero_int) one_one_int)) (@ (@ product_Pair_int_int A3) B3)))) fract) (forall ((I nat) (J nat) (K3 nat)) (=> (@ (@ ord_less_nat I) J) (@ (@ ord_less_nat (@ (@ plus_plus_nat I) K3)) (@ (@ plus_plus_nat J) K3)))) (= ord_less_eq_set_nat (lambda ((A5 set_nat) (B7 set_nat)) (= (@ (@ sup_sup_set_nat A5) B7) B7))) _let_138 (forall ((Xs list_d) (Ys list_int)) (=> (= (@ size_size_list_d Xs) (@ size_size_list_int Ys)) (= (@ (@ zip_d_int (@ rev_d Xs)) (@ rev_int Ys)) (@ rev_Pr856933547942721782_d_int (@ (@ zip_d_int Xs) Ys))))) (forall ((Xs list_d) (N nat) (X d)) (=> (@ distinct_d Xs) (=> (@ (@ ord_less_nat N) (@ size_size_list_d Xs)) (= (@ set_d2 (@ (@ (@ list_update_d Xs) N) X)) (@ (@ insert_d X) (@ (@ minus_minus_set_d (@ set_d2 Xs)) (@ (@ insert_d (@ (@ nth_d Xs) N)) bot_bot_set_d))))))) (forall ((A2 assn) (B2 assn)) (=> (= A2 (@ (@ sup_sup_assn A2) B2)) (@ (@ ord_less_eq_assn B2) A2))) (forall ((T nat)) (exists ((Z4 nat)) (forall ((X7 nat)) (=> (@ (@ ord_less_nat X7) Z4) (not (= X7 T)))))) (forall ((As2 set_nat) (H12 heap_e7401611519738050253t_unit) (H23 heap_e7401611519738050253t_unit) (H32 heap_e7401611519738050253t_unit)) (let ((_let_1 (@ relH As2))) (let ((_let_2 (@ _let_1 H12))) (=> (@ _let_2 H23) (=> (@ (@ _let_1 H23) H32) (@ _let_2 H32)))))) (forall ((M5 set_nat) (I nat)) (=> (@ (@ member_nat zero_zero_nat) M5) (not (= (@ finite_card_nat (@ collect_nat (lambda ((K4 nat)) (and (@ (@ ord_less_nat K4) (@ suc I)) (@ (@ member_nat K4) M5))))) zero_zero_nat)))) (forall ((X c) (Xs list_c)) (=> (@ (@ member_c X) (@ set_c2 Xs)) (@ (@ ord_less_nat (@ size_size_list_c (@ (@ removeAll_c X) Xs))) (@ size_size_list_c Xs)))) (forall ((Y produc3925858234332021118et_nat)) (not (forall ((A4 (-> produc3658429121746597890et_nat Bool)) (B4 heap_e7401611519738050253t_unit) (C4 set_nat)) (not (= Y (@ (@ produc5001842942810119800et_nat A4) (@ (@ produc7507926704131184380et_nat B4) C4))))))) (= ord_less_assn (lambda ((B3 assn) (A3 assn)) (and (@ (@ ord_less_eq_assn B3) A3) (not (@ (@ ord_less_eq_assn A3) B3))))) (forall ((X produc6575502325842934193n_assn) (Y produc6575502325842934193n_assn) (Xs list_P8527749157015355191n_assn) (N nat)) (=> (not (= X Y)) (= (= (@ (@ nth_Pr1769885009046257848n_assn (@ (@ cons_P2971678138204555879n_assn X) Xs)) N) Y) (and (@ (@ ord_less_nat zero_zero_nat) N) (= (@ (@ nth_Pr1769885009046257848n_assn Xs) (@ (@ minus_minus_nat N) one_one_nat)) Y))))) (forall ((Xs list_assn)) (= (@ (@ zip_assn_assn Xs) nil_assn) nil_Pr5671120429643327159n_assn)) (forall ((X d) (Xs list_d)) (@ (@ ord_less_eq_nat (@ size_size_list_d (@ (@ removeAll_d X) Xs))) (@ size_size_list_d Xs))) (forall ((X (-> produc3658429121746597890et_nat Bool)) (Xs list_P7985473006766602707_nat_o)) (=> (@ (@ member6576561426505652726_nat_o X) (@ set_Pr400311997697478754_nat_o Xs)) (@ (@ ord_less_nat zero_zero_nat) (@ size_s8908918004648414271_nat_o Xs)))) (forall ((P (-> code_integer Bool)) (P3 (-> code_integer Bool)) (Q (-> code_integer Bool)) (Q3 (-> code_integer Bool))) (=> (exists ((Z3 code_integer)) (forall ((X3 code_integer)) (=> (@ (@ ord_le6747313008572928689nteger Z3) X3) (= (@ P X3) (@ P3 X3))))) (=> (exists ((Z3 code_integer)) (forall ((X3 code_integer)) (=> (@ (@ ord_le6747313008572928689nteger Z3) X3) (= (@ Q X3) (@ Q3 X3))))) (exists ((Z4 code_integer)) (forall ((X7 code_integer)) (=> (@ (@ ord_le6747313008572928689nteger Z4) X7) (= (or (@ Q X7) (@ P X7)) (or (@ Q3 X7) (@ P3 X7))))))))) (forall ((A2 product_prod_nat_nat) (A set_Pr1261947904930325089at_nat)) (=> (@ (@ member8440522571783428010at_nat A2) A) (exists ((B5 set_Pr1261947904930325089at_nat)) (and (not (@ (@ 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ord_less_eq_rat A2) B2) (=> (@ (@ ord_less_eq_rat C) D2) (=> (@ _let_1 B2) (=> (@ _let_1 C) (@ (@ ord_less_eq_rat (@ (@ times_times_rat A2) C)) (@ (@ times_times_rat B2) D2)))))))) (forall ((N nat) (Xs list_int)) (let ((_let_1 (@ butlast_int Xs))) (=> (@ (@ ord_less_nat N) (@ size_size_list_int _let_1)) (= (@ (@ nth_int _let_1) N) (@ (@ nth_int Xs) N))))) (forall ((Xs list_c) (Ys list_c)) (= (@ size_s2756448709718749209od_c_c (@ (@ product_c_c Xs) Ys)) (@ (@ times_times_nat (@ size_size_list_c Xs)) (@ size_size_list_c Ys)))) (forall ((A2 int) (B2 int) (C int) (D2 int)) (let ((_let_1 (@ ord_less_eq_int zero_zero_int))) (=> (@ (@ ord_less_eq_int A2) B2) (=> (@ (@ ord_less_eq_int C) D2) (=> (@ _let_1 A2) (=> (@ _let_1 C) (@ (@ ord_less_eq_int (@ (@ times_times_int A2) C)) (@ (@ times_times_int B2) D2)))))))) (forall ((A2 rat) (B2 rat)) (let ((_let_1 (@ ord_less_eq_rat zero_zero_rat))) (= (@ (@ ord_less_eq_rat (@ (@ times_times_rat A2) B2)) zero_zero_rat) (or (and (@ _let_1 A2) (@ (@ ord_less_eq_rat B2) zero_zero_rat)) (and (@ _let_1 B2) (@ (@ ord_less_eq_rat A2) zero_zero_rat)))))) (forall ((Xs list_P8527749157015355191n_assn) (Ys list_nat)) (= (= nil_Pr2945733327814117674sn_nat (@ (@ zip_Pr1018045463562677002sn_nat Xs) Ys)) (or (= Xs nil_Pr5671120429643327159n_assn) (= Ys nil_nat)))) (@ wf_nat _let_57) (forall ((X21 nat) (X222 list_nat)) (@ (@ member_nat X21) (@ set_nat2 (@ (@ cons_nat X21) X222)))) (forall ((A2 assn) (B2 assn)) (let ((_let_1 (@ sup_sup_assn A2))) (let ((_let_2 (@ _let_1 B2))) (= (@ _let_1 _let_2) _let_2)))) (forall ((X int) (Y int)) (=> (@ (@ ord_less_int X) Y) (not (@ (@ ord_less_int Y) X)))) (forall ((T nat)) (exists ((Z4 nat)) (forall ((X7 nat)) (let ((_let_1 (@ ord_less_nat X7))) (=> (@ _let_1 Z4) (@ _let_1 T)))))) (forall ((C2 set_nat) (A set_nat) (B set_nat)) (let ((_let_1 (@ ord_less_eq_set_nat C2))) (= (@ _let_1 (@ (@ inf_inf_set_nat A) B)) (and (@ _let_1 A) (@ _let_1 B))))) (forall ((B2 code_integer) (A2 code_integer) (C code_integer)) (let ((_let_1 (@ ord_le6747313008572928689nteger C))) (=> (@ (@ ord_le6747313008572928689nteger B2) A2) (=> (@ _let_1 B2) (@ _let_1 A2))))) (forall ((I nat) (I3 set_nat) (Xs list_nat) (A (-> nat int assn)) (Xsi list_int)) (=> (not (@ (@ member_nat I) I3)) (=> (@ (@ ord_less_nat I) (@ size_size_list_nat Xs)) (= (@ (@ (@ (@ vEBT_L7889578638112847646at_int (@ (@ insert_nat2 I) I3)) A) Xs) Xsi) (@ (@ times_times_assn (@ (@ A (@ (@ nth_nat Xs) I)) (@ (@ nth_int Xsi) I))) (@ (@ (@ (@ vEBT_L7889578638112847646at_int I3) A) Xs) Xsi)))))) (forall ((T num)) (exists ((Z4 num)) (forall ((X7 num)) (=> (@ (@ ord_less_num X7) Z4) (not (@ (@ ord_less_eq_num T) X7)))))) (forall ((A nat) (B nat) (N nat)) (=> (@ (@ ord_less_nat A) B) (=> (@ (@ ord_less_nat zero_zero_nat) N) (=> (= (@ (@ modulo_modulo_nat A) N) zero_zero_nat) (=> (= (@ (@ modulo_modulo_nat B) N) zero_zero_nat) (@ (@ ord_less_nat (@ (@ divide_divide_nat A) N)) (@ (@ divide_divide_nat B) N))))))) (forall ((A2 set_nat) (B2 set_nat)) (=> (@ (@ ord_less_set_nat A2) B2) (= (@ (@ sup_sup_set_nat A2) B2) B2))) (= (lambda ((Y4 set_nat) (Z2 set_nat)) (= Y4 Z2)) (lambda ((A3 set_nat) (B3 set_nat)) (and (@ (@ ord_less_eq_set_nat B3) A3) (@ (@ ord_less_eq_set_nat A3) B3)))) (forall ((C int) (B set_int) (A set_int)) (let ((_let_1 (@ member_int C))) (=> (=> (not (@ _let_1 B)) (@ _let_1 A)) (@ _let_1 (@ (@ sup_sup_set_int A) B))))) (forall ((A2 int) (B2 int) (X int)) (=> (@ (@ ord_less_eq_int (@ (@ sup_sup_int A2) B2)) X) (not (=> (@ (@ ord_less_eq_int A2) X) (not (@ (@ ord_less_eq_int B2) X)))))) (forall ((A2 multis2468970476368604999at_nat) (B2 multis2468970476368604999at_nat) (C multis2468970476368604999at_nat)) (let ((_let_1 (@ plus_p7104986032573967614at_nat A2))) (= (= (@ _let_1 B2) (@ _let_1 C)) (= B2 C)))) (forall ((X product_prod_nat_nat) (A set_Pr1261947904930325089at_nat) (B set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ minus_1356011639430497352at_nat A))) (=> (not (@ (@ member8440522571783428010at_nat X) A)) (= (@ _let_1 (@ (@ insert8211810215607154385at_nat X) B)) (@ _let_1 B))))) (forall ((A2 int) (B2 int) (C int) (D2 int)) (=> (= A2 B2) (=> (@ (@ ord_less_eq_int B2) C) (=> (= C D2) (@ (@ ord_less_eq_int A2) D2))))) (forall ((N nat) (Xs list_int)) (= (@ (@ ord_less_eq_nat (@ suc N)) (@ size_size_list_int Xs)) (exists ((X2 int) (Ys3 list_int)) (and (@ (@ ord_less_eq_nat N) (@ size_size_list_int Ys3)) (= Xs (@ (@ cons_int X2) Ys3)))))) (forall ((X code_integer) (Y code_integer)) (=> (@ (@ ord_le6747313008572928689nteger X) Y) (not (= X Y)))) (forall ((A2 int) (B2 int) (C int)) (let ((_let_1 (@ ord_less_eq_int A2))) (=> (@ _let_1 B2) (=> (@ (@ ord_less_eq_int B2) C) (@ _let_1 C))))) (forall ((Xs list_d) (Ys list_nat)) (= (@ size_s8550281435913984804_d_nat (@ (@ zip_d_nat Xs) Ys)) (@ (@ ord_min_nat (@ size_size_list_d Xs)) (@ size_size_list_nat Ys)))) (forall ((I nat) (L list_P6011104703257516679at_nat) (X product_prod_nat_nat) (Y product_prod_nat_nat)) (=> (@ (@ ord_less_nat I) (@ size_s5460976970255530739at_nat L)) (= (@ (@ member8440522571783428010at_nat X) (@ set_Pr5648618587558075414at_nat (@ (@ (@ list_u6180841689913720943at_nat L) I) Y))) (or (forall ((Y5 product_prod_nat_nat)) (@ (@ member8440522571783428010at_nat X) (@ set_Pr5648618587558075414at_nat (@ (@ (@ list_u6180841689913720943at_nat L) I) Y5)))) (= X Y))))) (forall ((X int) (Y int)) (=> (not (= X Y)) (=> (not (@ (@ ord_less_int X) Y)) (@ (@ ord_less_int Y) X)))) (forall ((T code_integer)) (exists ((Z4 code_integer)) (forall ((X7 code_integer)) (let ((_let_1 (@ ord_le6747313008572928689nteger X7))) (=> (@ _let_1 Z4) (@ _let_1 T)))))) (= ord_less_nat (@ transi2163837189807498211lp_nat (lambda ((M nat) (N2 nat)) (= N2 (@ suc M))))) (forall ((B2 int) (A2 int)) (=> (@ (@ ord_less_eq_int B2) A2) (= (@ (@ sup_sup_int A2) B2) A2))) (forall ((N nat) (K3 nat)) (let ((_let_1 (@ binomial (@ (@ minus_minus_nat N) one_one_nat)))) (let ((_let_2 (@ ord_less_nat zero_zero_nat))) (=> (@ _let_2 N) (=> (@ _let_2 K3) (= (@ (@ binomial N) K3) (@ (@ plus_plus_nat (@ _let_1 (@ (@ minus_minus_nat K3) one_one_nat))) (@ _let_1 K3)))))))) (forall ((A2 int) (B2 int)) (=> (@ (@ ord_less_eq_int A2) B2) (= (@ (@ sup_sup_int A2) B2) B2))) (forall ((I nat) (I3 set_nat) (Xs list_d) (A (-> d int assn)) (Xsi list_int)) (=> (@ (@ member_nat I) I3) (=> (@ (@ ord_less_nat I) (@ size_size_list_d Xs)) (= (@ (@ (@ (@ vEBT_L7818125895572137869_d_int I3) A) Xs) Xsi) (@ (@ times_times_assn (@ (@ A (@ (@ nth_d Xs) I)) (@ (@ nth_int Xsi) I))) (@ (@ (@ (@ vEBT_L7818125895572137869_d_int (@ (@ minus_minus_set_nat I3) (@ (@ insert_nat2 I) bot_bot_set_nat))) A) Xs) Xsi)))))) (forall ((A2 int) (B2 int) (C int)) (let ((_let_1 (@ ord_less_eq_int A2))) (= (@ _let_1 (@ (@ ord_min_int B2) C)) (and (@ _let_1 B2) (@ _let_1 C))))) (forall ((A set_o) (B set_o)) (=> (= (@ (@ inf_inf_set_o A) B) bot_bot_set_o) (= (@ (@ minus_minus_set_o A) B) A))) _let_137 (forall ((A2 list_c) (B2 list_int) (A7 list_c) (B6 list_int)) (=> (= (@ size_size_list_c A2) (@ size_size_list_int B2)) (=> (= (@ size_size_list_c A7) (@ size_size_list_int B6)) (=> (= (@ (@ zip_c_int A2) B2) (@ (@ zip_c_int A7) B6)) (and (= B2 B6) (= A2 A7)))))) (forall ((A2 nat) (B2 nat)) (= (@ (@ ord_less_eq_nat (@ (@ plus_plus_nat A2) B2)) B2) (@ (@ ord_less_eq_nat A2) zero_zero_nat))) (forall ((Y nat) (X nat)) (=> (@ (@ ord_less_eq_nat Y) X) (= (@ (@ ord_min_nat X) Y) Y))) (forall ((A2 int) (B2 int) (C int) (D2 int)) (=> (= (@ (@ minus_minus_int A2) B2) (@ (@ minus_minus_int C) D2)) (= (= A2 B2) (= C D2)))) (forall ((A2 rat) (C rat) (B2 rat)) (= (@ (@ minus_minus_rat (@ (@ plus_plus_rat A2) C)) (@ (@ plus_plus_rat B2) C)) (@ (@ minus_minus_rat A2) B2))) (forall ((P assn) (Q assn)) (=> (@ (@ entails P) Q) (@ (@ entailst P) Q))) (forall ((A2 int) (B2 int)) (=> (= A2 (@ (@ inf_inf_int A2) B2)) (@ (@ ord_less_eq_int A2) B2))) (forall ((P (-> nat int assn)) (A2 nat) (As2 list_nat) (C int) (Cs list_int)) (let ((_let_1 (@ vEBT_L8298612041380073281at_int P))) (= (@ (@ _let_1 (@ (@ cons_nat A2) As2)) (@ (@ cons_int C) Cs)) (@ (@ times_times_assn (@ (@ P A2) C)) (@ (@ _let_1 As2) Cs))))) (forall ((X assn)) (= (@ abs_assn (@ rep_assn X)) X)) (forall ((I nat) (J nat) (K3 nat)) (let ((_let_1 (@ upt I))) (=> (and (@ (@ ord_less_eq_nat I) J) (@ (@ ord_less_eq_nat J) K3)) (= (@ (@ append_nat (@ _let_1 J)) (@ (@ upt J) K3)) (@ _let_1 K3))))) (forall ((X product_prod_nat_nat)) (@ (@ total_3592101749530773125at_nat (@ (@ insert8211810215607154385at_nat X) bot_bo2099793752762293965at_nat)) (@ (@ insert5050368324300391991at_nat (@ (@ produc6161850002892822231at_nat X) X)) bot_bo5327735625951526323at_nat))) (= divmod_nat (lambda ((M nat) (N2 nat)) (@ (@ (@ if_Pro6206227464963214023at_nat (or (= N2 zero_zero_nat) (@ (@ ord_less_nat M) N2))) (@ (@ product_Pair_nat_nat zero_zero_nat) M)) (@ (@ produc2626176000494625587at_nat (lambda ((Q8 nat) (__flatten_var_0 nat)) (@ (@ product_Pair_nat_nat (@ suc Q8)) __flatten_var_0))) (@ (@ divmod_nat (@ (@ minus_minus_nat M) N2)) N2))))) (forall ((A set_Pr1261947904930325089at_nat) (B set_Pr1261947904930325089at_nat)) (= (= (@ (@ inf_in2572325071724192079at_nat A) B) bot_bo2099793752762293965at_nat) (forall ((X2 product_prod_nat_nat)) (=> (@ (@ member8440522571783428010at_nat X2) A) (forall ((Y5 product_prod_nat_nat)) (=> (@ (@ member8440522571783428010at_nat Y5) B) (not (= X2 Y5)))))))) (forall ((C nat) (A set_nat) (B set_nat)) (let ((_let_1 (@ member_nat C))) (=> (@ _let_1 (@ (@ minus_minus_set_nat A) B)) (not (=> (@ _let_1 A) (@ _let_1 B)))))) _let_136 (forall ((P (-> int produc6575502325842934193n_assn assn)) (L list_int)) (= (@ (@ (@ vEBT_L1620274777744359680n_assn P) L) nil_Pr5671120429643327159n_assn) (@ pure_assn (= L nil_int)))) (forall ((I3 set_nat) (I7 set_nat) (Xs list_d) (Xs4 list_d) (Xsi list_c) (Xsi2 list_c) (A (-> d c assn)) (A6 (-> d c assn))) (=> (= I3 I7) (=> (= (@ size_size_list_d Xs) (@ size_size_list_d Xs4)) (=> (= (@ size_size_list_c Xsi) (@ size_size_list_c Xsi2)) (=> (forall ((I5 nat)) (let ((_let_1 (@ (@ nth_d Xs4) I5))) (let ((_let_2 (@ (@ nth_d Xs) I5))) (let ((_let_3 (@ (@ nth_c Xsi2) I5))) (let ((_let_4 (@ (@ nth_c Xsi) I5))) (let ((_let_5 (@ size_size_list_d Xs))) (=> (@ (@ member_nat I5) I3) (=> (@ (@ ord_less_nat I5) _let_5) (=> (= _let_5 (@ size_size_list_c Xsi)) (and (= (@ (@ A _let_2) _let_4) (@ (@ A6 _let_1) _let_3)) (= _let_4 _let_3) (= _let_2 _let_1))))))))))) (= (@ (@ (@ (@ vEBT_L7260734717915818975sn_d_c I3) A) Xs) Xsi) (@ (@ (@ (@ vEBT_L7260734717915818975sn_d_c I7) A6) Xs4) Xsi2))))))) (forall ((A2 rat) (B2 rat) (C rat)) (=> (@ (@ ord_less_rat A2) B2) (=> (@ (@ ord_less_rat zero_zero_rat) C) (@ (@ ord_less_rat (@ (@ times_times_rat A2) C)) (@ (@ times_times_rat B2) C))))) (forall ((A2 code_integer) (B2 code_integer) (C code_integer) (D2 code_integer)) (let ((_let_1 (@ ord_le3102999989581377725nteger zero_z3403309356797280102nteger))) (=> (@ (@ ord_le6747313008572928689nteger A2) B2) (=> (@ (@ ord_le6747313008572928689nteger C) D2) (=> (@ _let_1 A2) (=> (@ _let_1 C) (@ (@ ord_le6747313008572928689nteger (@ (@ times_3573771949741848930nteger A2) C)) (@ (@ times_3573771949741848930nteger B2) D2)))))))) (forall ((A2 code_integer) (C code_integer) (B2 code_integer)) (=> (@ (@ ord_le6747313008572928689nteger (@ (@ plus_p5714425477246183910nteger A2) C)) (@ (@ plus_p5714425477246183910nteger B2) C)) (@ (@ ord_le6747313008572928689nteger A2) B2))) (forall ((X product_prod_nat_nat) (Y product_prod_nat_nat)) (= (@ (@ (@ if_Pro6206227464963214023at_nat false) X) Y) Y)) (forall ((S set_Pr1261947904930325089at_nat) (P (-> product_prod_nat_nat Bool))) (= (@ (@ ord_le3146513528884898305at_nat S) (@ collec3392354462482085612at_nat P)) (forall ((X2 product_prod_nat_nat)) (=> (@ (@ member8440522571783428010at_nat X2) S) (@ P X2))))) (forall ((B2 rat) (A2 rat) (C rat)) (=> (@ (@ ord_less_eq_rat B2) A2) (=> (@ (@ ord_less_eq_rat C) zero_zero_rat) (@ (@ ord_less_eq_rat (@ (@ times_times_rat A2) C)) (@ (@ times_times_rat B2) C))))) (forall ((P assn) (B2 Bool) (Q assn)) (= (@ (@ entails (@ (@ times_times_assn P) (@ pure_assn B2))) Q) (=> B2 (@ (@ entails P) Q)))) (forall ((Xs list_d) (Ys list_c)) (= (@ size_s2120799709113762520od_d_c (@ (@ product_d_c Xs) Ys)) (@ (@ times_times_nat (@ size_size_list_d Xs)) (@ size_size_list_c Ys)))) (= ord_less_set_nat (lambda ((A3 set_nat) (B3 set_nat)) (and (@ (@ ord_less_eq_set_nat A3) B3) (not (@ (@ ord_less_eq_set_nat B3) A3))))) (forall ((A2 int) (B2 int)) (= (@ (@ ord_less_eq_int A2) (@ (@ plus_plus_int B2) A2)) (@ (@ ord_less_eq_int zero_zero_int) B2))) (forall ((K3 num) (L num)) (= (@ frct (@ (@ product_Pair_int_int (@ numeral_numeral_int K3)) (@ numeral_numeral_int L))) (@ (@ divide_divide_rat (@ numeral_numeral_rat K3)) (@ numeral_numeral_rat L)))) (forall ((X product_prod_nat_nat) (Xs list_P6011104703257516679at_nat)) (=> (@ (@ member8440522571783428010at_nat X) (@ set_Pr5648618587558075414at_nat Xs)) (@ (@ ord_less_nat zero_zero_nat) (@ size_s5460976970255530739at_nat Xs)))) (forall ((A2 code_integer) (E code_integer) (B2 code_integer) (C code_integer)) (= (@ (@ plus_p5714425477246183910nteger (@ (@ times_3573771949741848930nteger A2) E)) (@ (@ plus_p5714425477246183910nteger (@ (@ times_3573771949741848930nteger B2) E)) C)) (@ (@ plus_p5714425477246183910nteger (@ (@ times_3573771949741848930nteger (@ (@ plus_p5714425477246183910nteger A2) B2)) E)) C))) (forall ((X int) (Xs list_int)) (= (@ (@ nth_int (@ (@ cons_int X) Xs)) zero_zero_nat) X)) (= inf_in2572325071724192079at_nat (lambda ((X2 set_Pr1261947904930325089at_nat) (Y5 set_Pr1261947904930325089at_nat)) (@ (@ inf_in2572325071724192079at_nat Y5) X2))) (forall ((A2 rat) (B2 rat) (C rat)) (let ((_let_1 (@ minus_minus_rat A2))) (= (@ (@ minus_minus_rat (@ _let_1 B2)) C) (@ _let_1 (@ (@ plus_plus_rat B2) C))))) (forall ((X (-> produc3658429121746597890et_nat Bool)) (Xs list_P7985473006766602707_nat_o)) (=> (@ (@ member6576561426505652726_nat_o X) (@ 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set_Pr8116311503512020807n_assn)) (let ((_let_1 (@ listre4270255209692100112n_assn R2))) (= (@ (@ member3994142547374651152n_assn (@ (@ produc3014731801419794263n_assn (@ (@ cons_P2971678138204555879n_assn X) Xs)) (@ (@ cons_P2971678138204555879n_assn Y) Ys))) _let_1) (or (and (@ (@ member3994142547374651152n_assn (@ (@ produc3014731801419794263n_assn Xs) Ys)) _let_1) (= X Y)) (and (= Xs Ys) (@ (@ member4743710847862083984n_assn (@ (@ produc6128706242671166167n_assn X) Y)) R2)))))) (forall ((A2 rat) (B2 rat)) (let ((_let_1 (@ ord_less_eq_rat zero_zero_rat))) (=> (or (and (@ (@ ord_less_eq_rat A2) zero_zero_rat) (@ _let_1 B2)) (and (@ _let_1 A2) (@ (@ ord_less_eq_rat B2) zero_zero_rat))) (@ (@ ord_less_eq_rat (@ (@ times_times_rat A2) B2)) zero_zero_rat)))) (forall ((X int) (Y int)) (not (@ (@ ord_less_int (@ (@ plus_plus_int (@ (@ times_times_int X) X)) (@ (@ times_times_int Y) Y))) zero_zero_int))) (= is_sin2850979758926227957at_nat (lambda ((A5 set_Pr1261947904930325089at_nat)) (exists ((X2 product_prod_nat_nat)) (= A5 (@ (@ insert8211810215607154385at_nat X2) bot_bo2099793752762293965at_nat))))) (forall ((A2 set_Pr1261947904930325089at_nat)) (not (@ (@ ord_le7866589430770878221at_nat A2) bot_bo2099793752762293965at_nat))) (forall ((A2 produc3843707927480180839at_nat) (A set_Pr4329608150637261639at_nat) (B set_Pr4329608150637261639at_nat)) (let ((_let_1 (@ inf_in7913087082777306421at_nat A))) (let ((_let_2 (@ _let_1 B))) (let ((_let_3 (@ insert9069300056098147895at_nat A2))) (let ((_let_4 (@ _let_1 (@ _let_3 B)))) (let ((_let_5 (@ (@ member8757157785044589968at_nat A2) A))) (and (=> _let_5 (= _let_4 (@ _let_3 _let_2))) (=> (not _let_5) (= _let_4 _let_2))))))))) (forall ((R2 product_prod_int_int) (P6 int) (Q6 int)) (=> (= (@ normalize R2) (@ (@ product_Pair_int_int P6) Q6)) (@ (@ algebr932160517623751201me_int P6) Q6))) (forall ((P (-> produc6575502325842934193n_assn nat assn)) (L3 list_nat)) (= (@ (@ (@ vEBT_L4762835640886981758sn_nat P) nil_Pr5671120429643327159n_assn) L3) (@ pure_assn (= L3 nil_nat)))) (forall ((A2 assn)) (= (@ (@ sup_sup_assn A2) A2) A2)) (forall ((B set_nat) (C2 set_nat) (A set_nat)) (= (@ (@ inf_inf_set_nat (@ (@ sup_sup_set_nat B) C2)) A) (@ (@ sup_sup_set_nat (@ (@ inf_inf_set_nat B) A)) (@ (@ inf_inf_set_nat C2) A)))) (forall ((X nat) (Ys list_nat)) (let ((_let_1 (@ sorted_wrt_nat ord_less_nat))) (= (@ _let_1 (@ (@ cons_nat X) Ys)) (and (@ _let_1 Ys) (forall ((X2 nat)) (=> (@ (@ member_nat X2) (@ set_nat2 Ys)) (@ (@ ord_less_nat X) X2))))))) (forall ((Xs list_c) (Ys list_d) (Zs list_nat) (P (-> list_c list_d list_nat Bool))) (let ((_let_1 (@ size_size_list_d Ys))) (=> (= (@ size_size_list_c Xs) _let_1) (=> (= _let_1 (@ size_size_list_nat Zs)) (=> (@ (@ (@ P nil_c) nil_d) nil_nat) (=> (forall ((X3 c) (Xs2 list_c) (Y2 d) (Ys5 list_d) (Z4 nat) (Zs2 list_nat)) (let ((_let_1 (@ size_size_list_d Ys5))) (=> (= (@ size_size_list_c Xs2) _let_1) (=> (= _let_1 (@ size_size_list_nat Zs2)) (=> (@ (@ (@ P Xs2) Ys5) Zs2) (@ (@ (@ P (@ (@ cons_c X3) Xs2)) (@ (@ cons_d Y2) Ys5)) (@ (@ cons_nat Z4) Zs2))))))) (@ (@ (@ P Xs) Ys) Zs))))))) (forall ((X product_prod_nat_nat) (Y nat) (Xs list_P6011104703257516679at_nat) (Ys list_nat)) (=> (@ (@ member3348759134392003351at_nat (@ (@ produc6350711070570205562at_nat X) Y)) (@ set_Pr7836445846575771563at_nat (@ (@ zip_Pr6869450617852699226at_nat Xs) Ys))) (not (=> (@ (@ member8440522571783428010at_nat X) (@ set_Pr5648618587558075414at_nat Xs)) (not (@ (@ member_nat Y) (@ set_nat2 Ys))))))) (forall ((A2 set_o)) (= (@ (@ ord_less_eq_set_o A2) bot_bot_set_o) (= A2 bot_bot_set_o))) (forall ((T int)) (exists ((Z4 int)) (forall ((X7 int)) (=> (@ (@ ord_less_int Z4) X7) (not (@ (@ ord_less_eq_int X7) T)))))) (forall ((Q6 int) (P6 int)) (=> (@ (@ ord_less_int Q6) zero_zero_int) (= (@ normalize (@ (@ product_Pair_int_int P6) Q6)) (@ normalize (@ (@ product_Pair_int_int (@ uminus_uminus_int P6)) (@ uminus_uminus_int Q6)))))) (forall ((A2 (-> produc3658429121746597890et_nat Bool)) (A set_Pr4532377907799695533_nat_o)) (=> (@ (@ member6576561426505652726_nat_o A2) A) (exists ((B5 set_Pr4532377907799695533_nat_o)) (and (= A (@ (@ insert5175938949040314269_nat_o A2) B5)) (not (@ (@ member6576561426505652726_nat_o A2) B5)))))) (forall ((C rat) (A2 rat) (B2 rat)) (let ((_let_1 (@ times_times_rat C))) (=> (@ (@ ord_less_rat C) zero_zero_rat) (= (@ (@ ord_less_eq_rat (@ _let_1 A2)) (@ _let_1 B2)) (@ (@ ord_less_eq_rat B2) A2))))) (forall ((I nat) (L list_P5464809261938338413at_nat) (X produc3843707927480180839at_nat)) (=> (@ (@ ord_less_nat I) (@ size_s1588839187904960729at_nat L)) (= (@ (@ insert9069300056098147895at_nat (@ (@ nth_Pr1239524528086697198at_nat L) I)) (@ set_Pr3765526544606949372at_nat (@ (@ (@ list_u4696772448584712917at_nat L) I) X))) (@ (@ insert9069300056098147895at_nat X) (@ set_Pr3765526544606949372at_nat L))))) (forall ((N nat) (M5 set_nat)) (= (@ gcd_Lcm_nat (@ (@ insert_nat2 N) M5)) (@ (@ gcd_lcm_nat N) (@ gcd_Lcm_nat M5)))) (forall ((P (-> produc6575502325842934193n_assn nat assn)) (L list_P8527749157015355191n_assn)) (= (@ (@ (@ vEBT_L4762835640886981758sn_nat P) L) nil_nat) (@ pure_assn (= L nil_Pr5671120429643327159n_assn)))) (forall ((A2 int) (B2 int) (C int)) (let ((_let_1 (@ plus_plus_int A2))) (= (@ _let_1 (@ (@ minus_minus_int B2) C)) (@ (@ minus_minus_int (@ _let_1 B2)) C)))) (forall ((C assn) (A2 assn) (B2 assn)) (let ((_let_1 (@ ord_less_assn C))) (=> (@ _let_1 A2) (@ _let_1 (@ (@ sup_sup_assn A2) B2))))) (forall ((A set_Pr1261947904930325089at_nat) (A2 product_prod_nat_nat) (B set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ sup_su6327502436637775413at_nat A))) (let ((_let_2 (@ insert8211810215607154385at_nat A2))) (= (@ _let_1 (@ _let_2 B)) (@ _let_2 (@ _let_1 B)))))) (forall ((Xs list_nat) (Ys list_int)) (= (= nil_Pr1301135604781543011at_int (@ (@ zip_nat_int Xs) Ys)) (or (= Xs nil_nat) (= Ys nil_int)))) (forall ((A2 nat)) (@ (@ member_nat A2) (@ (@ insert_nat2 A2) bot_bot_set_nat))) (forall ((A assn) (B assn)) (@ (@ entails A) (@ (@ sup_sup_assn A) B))) (forall ((C int) (A2 int) (B2 int)) (let ((_let_1 (@ times_times_int C))) (=> (@ (@ ord_less_eq_int (@ _let_1 A2)) (@ _let_1 B2)) (=> (@ (@ ord_less_int zero_zero_int) C) (@ (@ ord_less_eq_int A2) B2))))) (forall ((X assn) (Y assn) (Z assn)) (let ((_let_1 (@ inf_inf_assn X))) (= (@ (@ inf_inf_assn (@ _let_1 Y)) Z) (@ _let_1 (@ (@ inf_inf_assn Y) Z))))) (= (lambda ((Y4 assn) (Z2 assn)) (= Y4 Z2)) (lambda ((A3 assn) (B3 assn)) (and (@ (@ ord_less_eq_assn B3) A3) (@ (@ ord_less_eq_assn A3) B3)))) (forall ((X4 multis2468970476368604999at_nat) (Y6 multis2468970476368604999at_nat)) (=> (@ (@ pw_leq X4) Y6) (exists ((A9 multis2468970476368604999at_nat) (B5 multis2468970476368604999at_nat) (Z8 multis2468970476368604999at_nat)) (and (= Y6 (@ (@ plus_p7104986032573967614at_nat B5) Z8)) (or (and (= B5 zero_z1048942125864253310at_nat) (= A9 zero_z1048942125864253310at_nat)) (@ (@ member8757157785044589968at_nat (@ (@ produc2922128104949294807at_nat (@ set_ms8126754132646256062at_nat A9)) (@ set_ms8126754132646256062at_nat B5))) fun_max_strict)) (= X4 (@ (@ plus_p7104986032573967614at_nat A9) Z8)))))) (forall ((A2 num) (B2 num) (C num)) (let ((_let_1 (@ ord_less_num A2))) (=> (@ _let_1 B2) (=> (@ (@ ord_less_eq_num B2) C) (@ _let_1 C))))) (forall ((A2 rat) (E rat) (B2 rat) (C rat)) (= (@ (@ plus_plus_rat (@ (@ times_times_rat A2) E)) (@ (@ plus_plus_rat (@ (@ times_times_rat B2) E)) C)) (@ (@ plus_plus_rat (@ (@ times_times_rat (@ (@ plus_plus_rat A2) B2)) E)) C))) (forall ((X int) (A2 int) (B2 int)) (let ((_let_1 (@ ord_less_int X))) (=> (@ _let_1 A2) (@ _let_1 (@ (@ sup_sup_int A2) B2))))) (forall ((C (-> produc3658429121746597890et_nat Bool)) (A set_Pr4532377907799695533_nat_o) (B set_Pr4532377907799695533_nat_o)) (let ((_let_1 (@ member6576561426505652726_nat_o C))) (=> (@ _let_1 (@ (@ minus_1801376950450012436_nat_o A) B)) (@ _let_1 A)))) (forall ((A2 int)) (not (@ (@ ord_less_int A2) A2))) (forall ((I int) (J int) (K3 int) (L int)) (=> (and (@ (@ ord_less_int I) J) (@ (@ ord_less_eq_int K3) L)) (@ (@ ord_less_int (@ (@ plus_plus_int I) K3)) (@ (@ plus_plus_int J) L)))) (forall ((A2 Bool) (A set_o) (B set_o)) (= (= bot_bot_set_o (@ (@ inf_inf_set_o (@ (@ insert_o2 A2) A)) B)) (and (not (@ (@ member_o A2) B)) (= bot_bot_set_o (@ (@ inf_inf_set_o A) B))))) (forall ((F4 (-> nat int nat))) (= (@ (@ (@ zipf_nat_int_nat F4) nil_nat) nil_int) nil_nat)) (forall ((P (-> nat Bool)) (Q (-> nat Bool))) (=> (@ P zero_zero_nat) (=> (forall ((I5 nat)) (=> (@ P I5) (exists ((J4 nat)) (and (@ Q J4) (@ P J4) (@ (@ ord_less_nat I5) J4))))) (@ (@ frequently_nat Q) cofinite_nat)))) (forall ((A2 assn) (F4 (-> assn assn)) (B2 assn) (C assn)) (=> (= A2 (@ F4 B2)) (=> (@ (@ ord_less_eq_assn B2) C) (=> (forall ((X3 assn) (Y2 assn)) (=> (@ (@ ord_less_eq_assn X3) Y2) (@ (@ ord_less_eq_assn (@ F4 X3)) (@ F4 Y2)))) (@ (@ ord_less_eq_assn A2) (@ F4 C)))))) (forall ((A2 int) (E int) (C int) (B2 int) (D2 int)) (= (= (@ (@ plus_plus_int (@ (@ times_times_int A2) E)) C) (@ (@ plus_plus_int (@ (@ times_times_int B2) E)) D2)) (= (@ (@ plus_plus_int (@ (@ times_times_int (@ (@ minus_minus_int A2) B2)) E)) C) D2))) (forall ((X filter_nat) (Y filter_nat)) (@ (@ ord_le2510731241096832064er_nat (@ (@ inf_inf_filter_nat X) Y)) X)) (forall ((B2 set_nat) (A2 set_nat)) (=> (@ (@ ord_less_set_nat B2) A2) (= (@ (@ inf_inf_set_nat A2) B2) B2))) (forall ((X produc3843707927480180839at_nat) (Xs list_P5464809261938338413at_nat)) (= (@ set_Pr3765526544606949372at_nat (@ (@ insert4149901806602606979at_nat X) Xs)) (@ (@ insert9069300056098147895at_nat X) (@ set_Pr3765526544606949372at_nat Xs)))) (forall ((X set_Pr1261947904930325089at_nat) (A2 set_Pr1261947904930325089at_nat) (B2 set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ ord_le3146513528884898305at_nat X))) (=> (@ _let_1 A2) (=> (@ _let_1 B2) (@ _let_1 (@ (@ inf_in2572325071724192079at_nat A2) B2)))))) (forall ((I nat) (J nat)) (=> (@ (@ ord_less_nat I) J) (= (@ last_nat (@ (@ upt I) J)) (@ (@ minus_minus_nat J) one_one_nat)))) (forall ((X1 num) (X22 num) (L12 list_num) (L23 list_num)) (let ((_let_1 (@ cons_num X22))) (let ((_let_2 (@ _let_1 L23))) (let ((_let_3 (@ merge_num L12))) (let ((_let_4 (@ cons_num X1))) (let ((_let_5 (@ merge_num (@ _let_4 L12)))) (let ((_let_6 (@ _let_5 _let_2))) (let ((_let_7 (@ (@ ord_less_num X1) X22))) (let ((_let_8 (= X1 X22))) (and (=> (not _let_7) (and (=> (not _let_8) (= _let_6 (@ _let_1 (@ _let_5 L23)))) (=> _let_8 (= _let_6 (@ _let_4 (@ _let_3 L23)))))) (=> _let_7 (= _let_6 (@ _let_4 (@ _let_3 _let_2)))))))))))))) (forall ((X int) (Y int) (Z int)) (let ((_let_1 (@ inf_inf_int X))) (@ (@ ord_less_eq_int (@ (@ sup_sup_int (@ _let_1 Y)) (@ _let_1 Z))) (@ _let_1 (@ (@ sup_sup_int Y) Z))))) (= ord_less_num (lambda ((B3 num) (A3 num)) (and (not (@ (@ ord_less_eq_num A3) B3)) (@ (@ ord_less_eq_num B3) A3)))) (forall ((X nat) (Y nat)) (=> (@ (@ ord_less_eq_nat X) Y) (= (@ (@ inf_inf_nat X) Y) X))) (forall ((X product_prod_int_int) (Y product_prod_int_int)) (= (@ (@ (@ if_Pro3027730157355071871nt_int true) X) Y) X)) (forall ((P6 rat)) (= (@ quotient_of (@ inverse_inverse_rat P6)) (@ (@ produc4245557441103728435nt_int (lambda ((A3 int) (B3 int)) (@ (@ (@ if_Pro3027730157355071871nt_int (= A3 zero_zero_int)) (@ (@ product_Pair_int_int zero_zero_int) one_one_int)) (@ (@ product_Pair_int_int (@ (@ times_times_int (@ sgn_sgn_int A3)) B3)) (@ abs_abs_int A3))))) (@ quotient_of P6)))) (forall ((A2 (-> produc3658429121746597890et_nat Bool))) (@ (@ member6576561426505652726_nat_o A2) (@ (@ insert5175938949040314269_nat_o A2) bot_bo7824918357723582233_nat_o))) (forall ((A2 nat) (B2 nat) (F4 (-> nat nat)) (C nat)) (=> (@ (@ ord_less_eq_nat A2) B2) (=> (@ (@ ord_less_eq_nat (@ F4 B2)) C) (=> (forall ((X3 nat) (Y2 nat)) (=> (@ (@ ord_less_eq_nat X3) Y2) (@ (@ ord_less_eq_nat (@ F4 X3)) (@ F4 Y2)))) (@ (@ ord_less_eq_nat (@ F4 A2)) C))))) (forall ((T num)) (exists ((Z4 num)) (forall ((X7 num)) (=> (@ (@ ord_less_num X7) Z4) (@ (@ ord_less_eq_num X7) T))))) (forall ((Xs list_c) (Ys list_d)) (= (@ size_s2827482749765095194od_c_d (@ (@ product_c_d Xs) Ys)) (@ (@ times_times_nat (@ size_size_list_c Xs)) (@ size_size_list_d Ys)))) (forall ((A set_nat) (B set_nat) (C2 set_nat)) (= (@ (@ inf_inf_set_nat (@ (@ minus_minus_set_nat A) B)) C2) (@ (@ minus_minus_set_nat (@ (@ inf_inf_set_nat A) C2)) (@ (@ inf_inf_set_nat B) C2)))) (forall ((X rat) (Y rat)) (=> (@ (@ ord_less_rat (@ (@ plus_plus_rat X) Y)) zero_zero_rat) (or (@ (@ ord_less_rat Y) zero_zero_rat) (@ (@ ord_less_rat X) zero_zero_rat)))) (forall ((X nat)) (= (@ (@ ord_min_nat X) bot_bot_nat) bot_bot_nat)) (forall ((C2 multis2468970476368604999at_nat) (B multis2468970476368604999at_nat) (A multis2468970476368604999at_nat)) (let ((_let_1 (@ plus_p7104986032573967614at_nat A))) (=> (= (@ (@ minus_4286766774447292334at_nat C2) B) zero_z1048942125864253310at_nat) (= (@ (@ 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(@ cons_int Y) Ys))) _let_1))))) (forall ((D int) (T int) (B set_int)) (=> (@ (@ ord_less_int zero_zero_int) D) (=> (@ (@ member_int (@ (@ minus_minus_int T) one_one_int)) B) (forall ((X7 int)) (=> (forall ((Xa3 int)) (=> (@ (@ member_int Xa3) (@ (@ set_or1266510415728281911st_int one_one_int) D)) (forall ((Xb3 int)) (=> (@ (@ member_int Xb3) B) (not (= X7 (@ (@ plus_plus_int Xb3) Xa3))))))) (=> (= X7 T) (= (@ (@ minus_minus_int X7) D) T))))))) (= ord_less_eq_set_nat (lambda ((A3 set_nat) (B3 set_nat)) (= (@ (@ inf_inf_set_nat A3) B3) A3))) (forall ((X nat) (Xs list_nat) (Ys list_nat) (R2 set_Pr1261947904930325089at_nat)) (=> (@ (@ member7340969449405702474st_nat (@ (@ produc2694037385005941721st_nat (@ (@ cons_nat X) Xs)) Ys)) (@ listrel1_nat R2)) (=> (forall ((Y2 nat)) (=> (= Ys (@ (@ cons_nat Y2) Xs)) (not (@ (@ member8440522571783428010at_nat (@ (@ product_Pair_nat_nat X) Y2)) R2)))) (not (forall ((Zs2 list_nat)) (=> (= Ys (@ (@ cons_nat X) Zs2)) (not (@ (@ member7340969449405702474st_nat (@ (@ produc2694037385005941721st_nat Xs) Zs2)) (@ listrel1_nat R2))))))))) (forall ((Xs list_o)) (= (= bot_bot_set_o (@ set_o2 Xs)) (= Xs nil_o))) (forall ((C rat) (B2 rat) (A2 rat)) (=> (= (@ (@ plus_plus_rat C) B2) A2) (= C (@ (@ minus_minus_rat A2) B2)))) (forall ((A2 int) (B2 int)) (= (@ (@ ord_less_int (@ (@ ord_min_int A2) B2)) A2) (@ (@ ord_less_int B2) A2))) (forall ((A set_Pr1261947904930325089at_nat) (B set_Pr1261947904930325089at_nat)) (= (= (@ (@ inf_in2572325071724192079at_nat A) B) bot_bo2099793752762293965at_nat) (forall ((X2 product_prod_nat_nat)) (let ((_let_1 (@ member8440522571783428010at_nat X2))) (=> (@ _let_1 A) (not (@ _let_1 B))))))) (forall ((R2 (-> Bool Bool Bool)) (X Bool) (S3 set_o)) (let ((_let_1 (@ pairwise_o R2))) (= (@ _let_1 (@ (@ insert_o2 X) S3)) (and (@ _let_1 S3) (forall ((Y5 Bool)) (=> (and (@ (@ member_o Y5) S3) (not (= Y5 X))) (and (@ (@ R2 Y5) X) (@ (@ R2 X) Y5)))))))) (forall ((N nat)) (= (@ (@ 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bot_bo7824918357723582233_nat_o)) (= B2 A2))) (forall ((I nat) (J nat)) (let ((_let_1 (@ upt I))) (let ((_let_2 (@ _let_1 (@ suc J)))) (let ((_let_3 (@ (@ ord_less_eq_nat I) J))) (and (=> _let_3 (= _let_2 (@ (@ append_nat (@ _let_1 J)) (@ (@ cons_nat J) nil_nat)))) (=> (not _let_3) (= _let_2 nil_nat))))))) (forall ((A2 int) (B2 int)) (let ((_let_1 (@ ord_less_int zero_zero_int))) (=> (@ _let_1 A2) (=> (@ _let_1 B2) (@ _let_1 (@ (@ times_times_int A2) B2)))))) (forall ((A2 num) (B2 num)) (=> (@ (@ ord_less_num A2) B2) (@ (@ ord_less_eq_num A2) B2))) (forall ((X product_prod_nat_nat) (A set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ insert8211810215607154385at_nat X))) (let ((_let_2 (@ _let_1 A))) (= (@ _let_1 _let_2) _let_2)))) (forall ((P (-> nat nat Bool)) (Xs list_nat) (I nat) (J nat)) (let ((_let_1 (@ nth_nat Xs))) (=> (@ (@ sorted_wrt_nat P) Xs) (=> (@ (@ ord_less_nat I) J) (=> (@ (@ ord_less_nat J) (@ size_size_list_nat Xs)) (@ (@ P (@ _let_1 I)) (@ _let_1 J))))))) (forall ((Y 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B)) (= A B))))))) (forall ((A2 int) (B2 int) (Xs list_int)) (= (@ (@ member5262025264175285858nt_int (@ (@ product_Pair_int_int A2) B2)) (@ set_Pr2470121279949933262nt_int (@ (@ zip_int_int Xs) Xs))) (and (= A2 B2) (@ (@ member_int A2) (@ set_int2 Xs))))) (forall ((P (-> product_prod_nat_nat Bool))) (= (@ (@ eventu1038000079068216329at_nat P) (@ (@ prod_filter_nat_nat at_top_nat) at_top_nat)) (exists ((N8 nat)) (forall ((M nat)) (=> (@ (@ ord_less_eq_nat N8) M) (forall ((N2 nat)) (=> (@ (@ ord_less_eq_nat N8) N2) (@ P (@ (@ product_Pair_nat_nat N2) M))))))))) (forall ((I nat) (I3 set_nat) (Xs list_c) (A (-> c int assn)) (Xsi list_int)) (=> (@ (@ member_nat I) I3) (=> (@ (@ ord_less_nat I) (@ size_size_list_c Xs)) (= (@ (@ (@ (@ vEBT_L6582681566615743372_c_int I3) A) Xs) Xsi) (@ (@ times_times_assn (@ (@ A (@ (@ nth_c Xs) I)) (@ (@ nth_int Xsi) I))) (@ (@ (@ (@ vEBT_L6582681566615743372_c_int (@ (@ minus_minus_set_nat I3) (@ (@ insert_nat2 I) bot_bot_set_nat))) A) Xs) Xsi)))))) (forall ((B2 nat) (A2 nat) (C nat)) (let ((_let_1 (@ ord_less_nat C))) (=> (@ (@ ord_less_nat B2) A2) (=> (@ _let_1 B2) (@ _let_1 A2))))) (forall ((B2 set_Pr4329608150637261639at_nat) (C set_Pr4329608150637261639at_nat) (A2 set_Pr4329608150637261639at_nat)) (=> (@ (@ ord_le2604355607129572851at_nat (@ (@ sup_su5525570899277871387at_nat B2) C)) A2) (not (=> (@ (@ ord_le2604355607129572851at_nat B2) A2) (not (@ (@ ord_le2604355607129572851at_nat C) A2)))))) (= ord_less_eq_assn (lambda ((X2 assn) (Y5 assn)) (= (@ (@ sup_sup_assn X2) Y5) Y5))) (forall ((Xs list_int)) (= (@ (@ sorted_wrt_int ord_less_eq_int) Xs) (forall ((I4 nat) (J2 nat)) (let ((_let_1 (@ nth_int Xs))) (=> (@ (@ ord_less_eq_nat I4) J2) (=> (@ (@ ord_less_nat J2) (@ size_size_list_int Xs)) (@ (@ ord_less_eq_int (@ _let_1 I4)) (@ _let_1 J2)))))))) (forall ((X int) (Y int)) (=> (@ (@ ord_less_int X) Y) (@ (@ ord_less_eq_int X) Y))) (forall ((Xs list_P7985473006766602707_nat_o) (X (-> produc3658429121746597890et_nat Bool))) (=> (@ 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(forall ((A2 assn)) (= (@ (@ times_times_assn A2) one_one_assn) A2)) (forall ((A set_o)) (= (@ (@ inf_inf_set_o A) bot_bot_set_o) bot_bot_set_o)) (forall ((A2 nat) (B2 nat) (C nat)) (let ((_let_1 (@ ord_less_nat B2))) (=> (@ (@ ord_less_eq_nat zero_zero_nat) A2) (=> (@ _let_1 C) (@ _let_1 (@ (@ plus_plus_nat A2) C)))))) (forall ((P assn)) (= (@ (@ times_times_assn sln) P) P)) _let_134 (forall ((X set_nat)) (= (@ (@ sup_sup_set_nat X) bot_bot_set_nat) X)) (forall ((C code_integer) (A2 code_integer) (B2 code_integer)) (let ((_let_1 (@ times_3573771949741848930nteger C))) (= (@ (@ ord_le3102999989581377725nteger (@ _let_1 A2)) (@ _let_1 B2)) (and (=> (@ (@ ord_le6747313008572928689nteger zero_z3403309356797280102nteger) C) (@ (@ ord_le3102999989581377725nteger A2) B2)) (=> (@ (@ ord_le6747313008572928689nteger C) zero_z3403309356797280102nteger) (@ (@ ord_le3102999989581377725nteger B2) A2)))))) (forall ((I nat) (L list_c) (X c) (Y c)) (=> (@ (@ ord_less_nat I) (@ size_size_list_c L)) (= 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(and (@ (@ member_int X) _let_6) (@ (@ member_int Xa) _let_6)))) (=> (= (@ (@ bit_se725231765392027082nd_int X) Xa) Y) (=> _let_1 (not (=> (and (=> (not _let_7) (= Y (@ (@ plus_plus_int (@ zero_n2684676970156552555ol_int (and _let_4 _let_5))) (@ (@ times_times_int _let_2) (@ (@ bit_se725231765392027082nd_int (@ (@ divide_divide_int X) _let_2)) (@ (@ divide_divide_int Xa) _let_2)))))) (=> _let_7 (= Y (@ uminus_uminus_int (@ zero_n2684676970156552555ol_int (and _let_5 _let_4)))))) (not _let_1))))))))))))) (forall ((X filter_nat) (Y filter_nat)) (@ (@ ord_le2510731241096832064er_nat (@ (@ inf_inf_filter_nat X) Y)) X)) (forall ((A2 rat)) (= (@ (@ times_times_rat one_one_rat) A2) A2)) _let_133 (forall ((X nat) (Y nat)) (not (@ (@ member8440522571783428010at_nat (@ (@ product_Pair_nat_nat X) Y)) (@ measures_nat nil_nat_nat)))) (forall ((B2 code_integer) (A2 code_integer)) (= (@ (@ ord_le6747313008572928689nteger (@ (@ plus_p5714425477246183910nteger B2) A2)) B2) (@ (@ 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((P assn) (Q assn) (R assn)) (let ((_let_1 (@ entails P))) (=> (@ _let_1 Q) (=> (@ (@ entails Q) R) (@ _let_1 R))))) (forall ((A set_nat) (B set_nat)) (= (= (@ (@ inf_inf_set_nat A) B) bot_bot_set_nat) (forall ((X2 nat)) (=> (@ (@ member_nat X2) A) (forall ((Y5 nat)) (=> (@ (@ member_nat Y5) B) (not (= X2 Y5)))))))) (forall ((X int)) (@ is_singleton_int (@ (@ insert_int2 X) bot_bot_set_int))) (forall ((A2 product_prod_nat_nat) (A set_Pr1261947904930325089at_nat) (B set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ inf_in2572325071724192079at_nat A))) (=> (not (@ (@ member8440522571783428010at_nat A2) A)) (= (@ _let_1 (@ (@ insert8211810215607154385at_nat A2) B)) (@ _let_1 B))))) (forall ((P (-> produc3658429121746597890et_nat Bool)) (H2 heap_e7401611519738050253t_unit) (As2 set_nat)) (let ((_let_1 (@ (@ produc7507926704131184380et_nat H2) As2))) (=> (@ proper P) (=> (@ P _let_1) (@ in_range _let_1))))) (forall ((A2 rat) (C rat) (B2 rat)) (=> (@ (@ ord_less_rat (@ (@ plus_plus_rat A2) C)) (@ (@ plus_plus_rat B2) C)) (@ (@ ord_less_rat A2) B2))) (forall ((Y produc6575502325842934193n_assn) (Ys list_P8527749157015355191n_assn) (Xs list_P8527749157015355191n_assn) (R2 set_Pr8116311503512020807n_assn)) (=> (@ (@ member3994142547374651152n_assn (@ (@ produc3014731801419794263n_assn (@ (@ cons_P2971678138204555879n_assn Y) Ys)) Xs)) (@ listre5253995379918703921n_assn R2)) (not (forall ((Y2 produc6575502325842934193n_assn) (Ys5 list_P8527749157015355191n_assn)) (=> (= Xs (@ (@ cons_P2971678138204555879n_assn Y2) Ys5)) (=> (@ (@ member4743710847862083984n_assn (@ (@ produc6128706242671166167n_assn Y) Y2)) R2) (not (@ (@ member3994142547374651152n_assn (@ (@ produc3014731801419794263n_assn Ys) Ys5)) (@ listre5253995379918703921n_assn R2))))))))) (forall ((X produc6575502325842934193n_assn) (Xs list_P8527749157015355191n_assn) (Y int) (Ys list_int)) (= (@ (@ zip_Pr1015554993053626726sn_int (@ (@ cons_P2971678138204555879n_assn X) Xs)) (@ (@ cons_int Y) Ys)) (@ (@ 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((B3 int) (D5 int)) (@ normalize (@ (@ product_Pair_int_int (@ (@ times_times_int A3) B3)) (@ (@ times_times_int C5) D5))))) (@ quotient_of Q6)))) (@ quotient_of P6)))) (forall ((Xs list_nat) (Ys list_d) (R2 set_Pr4406443968975187932_nat_d)) (=> (@ (@ member6145252513411111219list_d (@ (@ produc7723716022961710414list_d Xs) Ys)) (@ listrel_nat_d R2)) (= (@ size_size_list_nat Xs) (@ size_size_list_d Ys)))) (forall ((P assn) (B2 Bool) (H2 produc3658429121746597890et_nat)) (= (@ (@ rep_assn (@ (@ times_times_assn P) (@ pure_assn B2))) H2) (and (@ (@ rep_assn P) H2) B2))) (forall ((A2 nat) (B2 nat) (C nat)) (let ((_let_1 (@ ord_less_eq_nat A2))) (=> (@ _let_1 B2) (=> (@ _let_1 C) (@ _let_1 (@ (@ inf_inf_nat B2) C)))))) (forall ((X produc3843707927480180839at_nat) (Xs list_P5464809261938338413at_nat)) (let ((_let_1 (@ size_s1588839187904960729at_nat Xs))) (let ((_let_2 (@ size_s1588839187904960729at_nat (@ (@ remove8895909992688781315at_nat X) Xs)))) (let ((_let_3 (@ (@ member8757157785044589968at_nat X) (@ set_Pr3765526544606949372at_nat Xs)))) (and (=> (not _let_3) (= _let_2 _let_1)) (=> _let_3 (= _let_2 (@ (@ minus_minus_nat _let_1) one_one_nat)))))))) (forall ((F4 (-> filter_nat filter_nat filter_nat)) (X filter_nat) (Y filter_nat)) (=> (forall ((X3 filter_nat) (Y2 filter_nat)) (@ (@ ord_le2510731241096832064er_nat (@ (@ F4 X3) Y2)) X3)) (=> (forall ((X3 filter_nat) (Y2 filter_nat)) (@ (@ ord_le2510731241096832064er_nat (@ (@ F4 X3) Y2)) Y2)) (=> (forall ((X3 filter_nat) (Y2 filter_nat) (Z4 filter_nat)) (let ((_let_1 (@ ord_le2510731241096832064er_nat X3))) (=> (@ _let_1 Y2) (=> (@ _let_1 Z4) (@ _let_1 (@ (@ F4 Y2) Z4)))))) (= (@ (@ inf_inf_filter_nat X) Y) (@ (@ F4 X) Y)))))) (@ (@ _let_38 (lambda ((X2 product_prod_int_int) (Y5 product_prod_int_int)) (@ (@ product_Pair_int_int (@ (@ times_times_int (@ product_fst_int_int X2)) (@ product_fst_int_int Y5))) (@ (@ times_times_int (@ product_snd_int_int X2)) (@ product_snd_int_int Y5))))) 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_let_2 (=> _let_3 (not (= Y one_one_assn)))) (=> (forall ((A4 produc6575502325842934193n_assn) (As list_P8527749157015355191n_assn)) (=> (= Xa (@ (@ cons_P2971678138204555879n_assn A4) As)) (forall ((C4 produc6575502325842934193n_assn) (Cs2 list_P8527749157015355191n_assn)) (=> (= Xb (@ (@ cons_P2971678138204555879n_assn C4) Cs2)) (not (= Y (@ (@ times_times_assn (@ (@ X A4) C4)) (@ (@ (@ vEBT_L3108143461992071043n_assn X) As) Cs2)))))))) (=> (=> (exists ((V3 produc6575502325842934193n_assn) (Va list_P8527749157015355191n_assn)) (= Xa (@ (@ cons_P2971678138204555879n_assn V3) Va))) (=> _let_3 _let_1)) (not (=> _let_2 (=> (exists ((V3 produc6575502325842934193n_assn) (Va list_P8527749157015355191n_assn)) (= Xb (@ (@ cons_P2971678138204555879n_assn V3) Va))) _let_1))))))))))) (forall ((A2 int) (C int) (B2 int) (D2 int)) (=> (@ (@ ord_less_eq_int A2) C) (=> (@ (@ ord_less_eq_int B2) D2) (@ (@ ord_less_eq_int (@ (@ ord_min_int A2) B2)) (@ (@ ord_min_int C) D2))))) (forall ((B6 int) (A7 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B3) A3))) (forall ((Xs list_P8527749157015355191n_assn) (Ys list_nat)) (= (= (@ (@ zip_Pr1018045463562677002sn_nat Xs) Ys) nil_Pr2945733327814117674sn_nat) (or (= Ys nil_nat) (= Xs nil_Pr5671120429643327159n_assn)))) (forall ((A2 int) (B2 int)) (= (not (@ (@ ord_less_eq_int A2) B2)) (and (@ (@ ord_less_eq_int B2) A2) (not (= B2 A2))))) _let_130 (forall ((A set_int) (B set_int)) (= (= (@ (@ inf_inf_set_int A) B) bot_bot_set_int) (forall ((X2 int)) (=> (@ (@ member_int X2) A) (forall ((Y5 int)) (=> (@ (@ member_int Y5) B) (not (= X2 Y5)))))))) (forall ((A2 nat) (B2 nat) (C nat)) (let ((_let_1 (@ plus_plus_nat C))) (=> (@ (@ ord_less_eq_nat A2) B2) (= (@ _let_1 (@ (@ minus_minus_nat B2) A2)) (@ (@ minus_minus_nat (@ _let_1 B2)) A2))))) (forall ((X nat) (Xs list_nat)) (= (@ distinct_nat (@ (@ cons_nat X) Xs)) (and (not (@ (@ member_nat X) (@ set_nat2 Xs))) (@ distinct_nat Xs)))) (forall ((A2 Bool) (A set_o) (B set_o)) (let ((_let_1 (@ inf_inf_set_o A))) (=> (not (@ (@ member_o A2) A)) (= (@ _let_1 (@ (@ insert_o2 A2) B)) (@ _let_1 B))))) (forall ((I nat) (J nat) (L list_nat) (X nat)) (let ((_let_1 (@ nth_nat L))) (=> (@ (@ ord_less_eq_nat zero_zero_nat) I) (=> (@ (@ ord_less_nat I) J) (=> (@ (@ ord_less_nat J) (@ size_size_list_nat L)) (=> (@ (@ sorted_wrt_nat ord_less_eq_nat) L) (=> (@ (@ ord_less_eq_nat (@ _let_1 I)) X) (=> (@ (@ ord_less_nat X) (@ _let_1 J)) (not (forall ((K nat)) (let ((_let_1 (@ nth_nat L))) (=> (@ (@ ord_less_eq_nat I) K) (=> (@ (@ ord_less_nat K) J) (=> (@ (@ ord_less_eq_nat (@ _let_1 K)) X) (not (@ (@ ord_less_nat X) (@ _let_1 (@ (@ plus_plus_nat K) one_one_nat)))))))))))))))))) (forall ((F4 (-> produc7773217078559923341nt_int Bool)) (A2 (-> int option6357759511663192854e_term)) (B2 product_prod_int_int)) (=> (@ (@ (@ produc9098658269643458507_int_o F4) A2) B2) (@ F4 (@ (@ produc4305682042979456191nt_int A2) B2)))) (forall ((X list_int)) (=> (forall ((X3 int) (Xs2 list_int)) (not (= X (@ (@ cons_int X3) Xs2)))) (= X nil_int))) (forall ((A2 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distin5355857245021852384at_nat Xs) (not (@ (@ member8757157785044589968at_nat X) (@ set_Pr3765526544606949372at_nat Xs)))))) (forall ((A2 nat) (B2 nat) (C nat)) (let ((_let_1 (@ ord_less_eq_nat A2))) (= (@ _let_1 (@ (@ inf_inf_nat B2) C)) (and (@ _let_1 B2) (@ _let_1 C))))) (forall ((I nat) (L list_P8527749157015355191n_assn) (X produc6575502325842934193n_assn)) (=> (@ (@ ord_less_nat I) (@ size_s6829681357464350627n_assn L)) (= (@ (@ insert5290817439147925377n_assn (@ (@ nth_Pr1769885009046257848n_assn L) I)) (@ set_Pr1139785259514867910n_assn (@ (@ (@ list_u4534839942911652127n_assn L) I) X))) (@ (@ insert5290817439147925377n_assn X) (@ set_Pr1139785259514867910n_assn L))))) (forall ((B2 num) (A2 num) (C num)) (let ((_let_1 (@ ord_less_num C))) (=> (@ (@ ord_less_num B2) A2) (=> (@ _let_1 B2) (@ _let_1 A2))))) (forall ((C int) (B2 int)) (= (= C (@ (@ times_times_int B2) C)) (or (= C zero_zero_int) (= B2 one_one_int)))) (forall ((A2 set_o)) (= (not (= A2 bot_bot_set_o)) (@ (@ ord_less_set_o bot_bot_set_o) A2))) (forall ((A2 rat) (C rat)) (= (@ (@ ord_less_eq_rat (@ (@ times_times_rat A2) C)) C) (and (=> (@ (@ ord_less_rat zero_zero_rat) C) (@ (@ ord_less_eq_rat A2) one_one_rat)) (=> (@ (@ ord_less_rat C) zero_zero_rat) (@ (@ ord_less_eq_rat one_one_rat) A2))))) (forall ((P (-> produc3658429121746597890et_nat Bool)) (Pr assn)) (=> (forall ((H produc3658429121746597890et_nat)) (= (@ P H) (@ (@ rep_assn Pr) H))) (= (@ abs_assn P) Pr))) (forall ((A2 list_nat) (B2 list_c) (A7 list_nat) (B6 list_c)) (=> (= (@ size_size_list_nat A2) (@ size_size_list_c B2)) (=> (= (@ size_size_list_nat A7) (@ size_size_list_c B6)) (=> (= (@ (@ zip_nat_c A2) B2) (@ (@ zip_nat_c A7) B6)) (and (= A2 A7) (= B2 B6)))))) (forall ((X set_nat) (Y set_nat) (Z set_nat)) (let ((_let_1 (@ inf_inf_set_nat X))) (= (@ (@ inf_inf_set_nat (@ _let_1 Y)) Z) (@ _let_1 (@ (@ inf_inf_set_nat Y) Z))))) (not (@ _let_12 one_one_Code_integer)) (forall ((X set_nat)) (= (@ (@ inf_inf_set_nat X) bot_bot_set_nat) bot_bot_set_nat)) (forall ((C code_integer) (A2 code_integer)) (= (= (@ (@ times_3573771949741848930nteger C) A2) C) (or (= A2 one_one_Code_integer) (= C zero_z3403309356797280102nteger)))) (= ord_less_eq_nat (lambda ((X2 nat) (Y5 nat)) (= (@ (@ sup_sup_nat X2) Y5) Y5))) (forall ((Xs list_int) (P (-> int int Bool)) (Q (-> int int Bool))) (=> (forall ((X3 int) (Y2 int)) (let ((_let_1 (@ set_int2 Xs))) (=> (@ (@ member_int X3) _let_1) (=> (@ (@ member_int Y2) _let_1) (=> (@ (@ P X3) Y2) (@ (@ Q X3) Y2)))))) (=> (@ (@ sorted_wrt_int P) Xs) (@ (@ sorted_wrt_int Q) Xs)))) (forall ((X int) (Y int) (Xs list_int)) (let ((_let_1 (@ cons_int Y))) (let ((_let_2 (@ remove1_int X))) (let ((_let_3 (@ _let_2 (@ _let_1 Xs)))) (let ((_let_4 (= X Y))) (and (=> (not _let_4) (= _let_3 (@ _let_1 (@ _let_2 Xs)))) (=> _let_4 (= _let_3 Xs)))))))) (forall ((C nat) (A2 nat) (B2 nat)) (let ((_let_1 (@ times_times_nat C))) (= (= (@ _let_1 A2) (@ _let_1 B2)) (or (= A2 B2) (= C zero_zero_nat))))) (forall ((A set_int) (B set_int)) (= (= (@ (@ inf_inf_set_int A) B) bot_bot_set_int) (forall ((X2 int)) (let ((_let_1 (@ member_int X2))) (=> (@ _let_1 A) (not (@ _let_1 B))))))) (forall ((X (-> produc3658429121746597890et_nat Bool)) (Y produc3658429121746597890et_nat) (Xs list_P7985473006766602707_nat_o) (Ys list_P9062070895058802706et_nat)) (=> (@ (@ member1996754912294343701et_nat (@ (@ produc5001842942810119800et_nat X) Y)) (@ set_Pr364071364088684201et_nat (@ (@ zip_Pr7134870689397686104et_nat Xs) Ys))) (@ (@ member6576561426505652726_nat_o X) (@ set_Pr400311997697478754_nat_o Xs)))) (forall ((A set_Pr1261947904930325089at_nat)) (= (forall ((X2 product_prod_nat_nat)) (not (@ (@ member8440522571783428010at_nat X2) A))) (= A bot_bo2099793752762293965at_nat))) (forall ((A2 nat) (B2 nat)) (=> (@ (@ ord_less_eq_nat A2) B2) (= A2 (@ (@ ord_min_nat A2) B2)))) (forall ((Xs list_d) (Ys list_int) (P (-> list_d list_int Bool))) (=> (= (@ size_size_list_d Xs) (@ size_size_list_int Ys)) (=> (@ (@ P nil_d) nil_int) (=> (forall ((X3 d) (Xs2 list_d) (Y2 int) (Ys5 list_int)) (=> (= (@ size_size_list_d Xs2) (@ size_size_list_int Ys5)) (=> (@ (@ P Xs2) Ys5) (@ (@ P (@ (@ cons_d X3) Xs2)) (@ (@ cons_int Y2) Ys5))))) (@ (@ P Xs) Ys))))) (@ (@ member8757157785044589968at_nat (@ (@ produc2922128104949294807at_nat (@ bNF_Ca3793111618940312692of_nat (@ field_nat bNF_Ca8665028551170535155natLeq))) bNF_Ca8665028551170535155natLeq)) bNF_We5258908940166488438at_nat) (forall ((A2 set_Pr4329608150637261639at_nat)) (@ (@ ord_le1268244103169919719at_nat bot_bo228742789529271731at_nat) A2)) (forall ((A2 code_integer) (B2 code_integer) (F4 (-> code_integer num)) (C num)) (=> (@ (@ ord_le6747313008572928689nteger A2) B2) (=> (@ (@ ord_less_num (@ F4 B2)) C) (=> (forall ((X3 code_integer) (Y2 code_integer)) (=> (@ (@ ord_le6747313008572928689nteger X3) Y2) (@ (@ ord_less_num (@ F4 X3)) (@ F4 Y2)))) (@ (@ ord_less_num (@ F4 A2)) C))))) (= times_times_assn (lambda ((P2 assn) (Q2 assn)) (@ (@ 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Y Z) (= W X)))))) (forall ((A set_o) (B set_o)) (=> (@ (@ ord_less_eq_set_o A) B) (= (@ (@ minus_minus_set_o A) B) bot_bot_set_o))) (forall ((A2 int) (B2 int) (C int) (D2 int)) (=> (@ (@ ord_less_eq_int A2) B2) (=> (@ (@ ord_less_eq_int C) D2) (@ (@ ord_less_eq_int (@ (@ plus_plus_int A2) C)) (@ (@ plus_plus_int B2) D2))))) (forall ((X filter_nat) (Y filter_nat)) (=> (@ (@ ord_le2510731241096832064er_nat X) Y) (=> (@ (@ ord_le2510731241096832064er_nat Y) X) (= X Y)))) (forall ((T nat)) (exists ((Z4 nat)) (forall ((X7 nat)) (=> (@ (@ ord_less_nat Z4) X7) (@ (@ ord_less_eq_nat T) X7))))) (forall ((P assn) (A (-> c int assn)) (Xs list_c) (I nat) (Xsi list_int) (I3 set_nat) (F assn) (Q assn)) (let ((_let_1 (@ entails P))) (=> (@ _let_1 (@ (@ times_times_assn (@ (@ times_times_assn (@ (@ A (@ (@ nth_c Xs) I)) (@ (@ nth_int Xsi) I))) (@ (@ (@ (@ vEBT_L6582681566615743372_c_int (@ (@ minus_minus_set_nat I3) (@ (@ insert_nat2 I) bot_bot_set_nat))) A) Xs) Xsi))) F)) (=> (@ (@ ord_less_nat I) (@ 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(@ ord_less_nat I) (@ size_size_list_c L)) (= (@ (@ insert_c (@ (@ nth_c L) I)) (@ set_c2 (@ (@ (@ list_update_c L) I) X))) (@ (@ insert_c X) (@ set_c2 L))))) (forall ((A assn) (B assn)) (= (@ (@ entailst (@ (@ times_times_assn A) top_top_assn)) B) (@ (@ entailst A) B))) (= divide_divide_nat (lambda ((M nat) (N2 nat)) (@ (@ (@ if_nat (or (= N2 zero_zero_nat) (@ (@ ord_less_nat M) N2))) zero_zero_nat) (@ suc (@ (@ divide_divide_nat (@ (@ minus_minus_nat M) N2)) N2))))) (forall ((A2 int) (A set_int) (B set_int)) (let ((_let_1 (@ inf_inf_set_int A))) (=> (not (@ (@ member_int A2) A)) (= (@ _let_1 (@ (@ insert_int2 A2) B)) (@ _let_1 B))))) (forall ((Y filter_nat) (X filter_nat)) (@ (@ ord_le2510731241096832064er_nat Y) (@ (@ sup_sup_filter_nat X) Y))) (forall ((N nat)) (@ (@ ord_less_nat zero_zero_nat) (@ suc N))) (forall ((A2 rat) (B2 rat) (D2 rat) (C rat)) (=> (@ (@ ord_less_eq_rat A2) B2) (=> (@ (@ ord_less_eq_rat D2) C) (@ (@ ord_less_eq_rat (@ (@ minus_minus_rat A2) C)) (@ (@ 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(forall ((X (-> produc3658429121746597890et_nat Bool)) (Xa (-> produc3658429121746597890et_nat Bool)) (Xb produc3658429121746597890et_nat) (Y Bool)) (=> (= (@ (@ (@ times_assn_raw X) Xa) Xb) Y) (=> (@ (@ accp_P1862375125659990705et_nat times_assn_raw_rel) (@ (@ produc2245416461498447860et_nat X) (@ (@ produc5001842942810119800et_nat Xa) Xb))) (not (forall ((H heap_e7401611519738050253t_unit) (As set_nat)) (let ((_let_1 (@ (@ produc7507926704131184380et_nat H) As))) (=> (= Xb _let_1) (=> (= Y (exists ((As1 set_nat) (As22 set_nat)) (let ((_let_1 (@ produc7507926704131184380et_nat H))) (and (= (@ (@ inf_inf_set_nat As1) As22) bot_bot_set_nat) (@ Xa (@ _let_1 As22)) (@ X (@ _let_1 As1)) (= As (@ (@ sup_sup_set_nat As1) As22)))))) (not (@ (@ accp_P1862375125659990705et_nat times_assn_raw_rel) (@ (@ produc2245416461498447860et_nat X) (@ (@ produc5001842942810119800et_nat Xa) _let_1)))))))))))) (forall ((B2 int) (A2 int) (C int)) (=> (= (@ (@ plus_plus_int B2) A2) (@ (@ plus_plus_int C) A2)) (= B2 C))) (forall ((X nat)) (@ (@ ord_less_eq_nat zero_zero_nat) X)) (@ (@ (@ filter3212408913953519116et_nat set_ord_lessThan_nat) _let_74) at_top_nat) (forall ((A2 code_integer) (B2 code_integer) (C code_integer)) (let ((_let_1 (@ times_3573771949741848930nteger A2))) (= (@ _let_1 (@ (@ minus_8373710615458151222nteger B2) C)) (@ (@ minus_8373710615458151222nteger (@ _let_1 B2)) (@ _let_1 C))))) (forall ((As2 set_nat) (H2 heap_e7401611519738050253t_unit) (H4 heap_e7401611519738050253t_unit) (P assn)) (let ((_let_1 (@ rep_assn P))) (=> (@ (@ (@ relH As2) H2) H4) (= (@ _let_1 (@ (@ produc7507926704131184380et_nat H2) As2)) (@ _let_1 (@ (@ produc7507926704131184380et_nat H4) As2)))))) (forall ((X produc2732055786443039994et_nat)) (not (forall ((P5 (-> produc3658429121746597890et_nat Bool)) (Q4 (-> produc3658429121746597890et_nat Bool)) (H heap_e7401611519738050253t_unit) (As set_nat)) (not (= X (@ (@ produc2245416461498447860et_nat P5) (@ (@ produc5001842942810119800et_nat Q4) (@ (@ produc7507926704131184380et_nat H) As)))))))) (forall ((A2 multis2468970476368604999at_nat) (B2 multis2468970476368604999at_nat)) (= (= A2 (@ (@ plus_p7104986032573967614at_nat B2) A2)) (= B2 zero_z1048942125864253310at_nat))) (forall ((N nat) (Xs list_int)) (=> (@ (@ ord_less_nat N) (@ size_size_list_int Xs)) (@ (@ member_int (@ (@ nth_int Xs) N)) (@ set_int2 Xs)))) (forall ((A2 int) (B2 int) (C int)) (=> (@ (@ ord_less_eq_int A2) B2) (@ (@ ord_less_eq_int (@ (@ plus_plus_int A2) C)) (@ (@ plus_plus_int B2) C)))) (forall ((A2 nat)) (not (@ (@ ord_less_nat A2) A2))) (forall ((C rat) (A2 rat) (B2 rat)) (let ((_let_1 (@ plus_plus_rat C))) (= (@ (@ minus_minus_rat (@ _let_1 A2)) (@ _let_1 B2)) (@ (@ minus_minus_rat A2) B2)))) (forall ((A2 nat) (A set_nat) (B set_nat)) (= (= bot_bot_set_nat (@ (@ inf_inf_set_nat (@ (@ insert_nat2 A2) A)) B)) (and (not (@ (@ member_nat A2) B)) (= bot_bot_set_nat (@ (@ inf_inf_set_nat A) B))))) (forall ((M2 nat) (N nat)) (= (@ (@ member8440522571783428010at_nat (@ (@ product_Pair_nat_nat M2) N)) (@ transi2905341329935302413cl_nat pred_nat)) (@ (@ ord_less_eq_nat M2) N))) (forall ((A2 int) (N nat)) (= (= (@ (@ power_power_int A2) N) zero_zero_int) (and (= A2 zero_zero_int) (@ (@ ord_less_nat zero_zero_nat) N)))) (forall ((A set_nat) (B set_nat)) (=> (@ (@ ord_less_set_nat A) B) (exists ((B4 nat)) (@ (@ member_nat B4) (@ (@ minus_minus_set_nat B) A))))) (forall ((S set_Pr1261947904930325089at_nat) (R (-> product_prod_nat_nat product_prod_nat_nat Bool))) (=> (forall ((X3 product_prod_nat_nat) (Y2 product_prod_nat_nat)) (=> (@ (@ member8440522571783428010at_nat X3) S) (=> (@ (@ member8440522571783428010at_nat Y2) S) (=> (not (= X3 Y2)) (@ (@ R X3) Y2))))) (@ (@ pairwi6357175311820755948at_nat R) S))) (forall ((N nat)) (=> (@ (@ ord_less_nat zero_zero_nat) N) (= (@ suc (@ (@ minus_minus_nat N) one_one_nat)) N))) (= ord_less_assn (lambda ((X2 assn) (Y5 assn)) (and (not (= X2 Y5)) (@ (@ ord_less_eq_assn X2) Y5)))) (forall ((X nat) (Y nat) (R2 set_Pr1261947904930325089at_nat) (P (-> nat nat Bool))) (=> (@ (@ member8440522571783428010at_nat (@ (@ product_Pair_nat_nat X) Y)) (@ transi6264000038957366511cl_nat R2)) (=> (forall ((X3 nat) (Y2 nat)) (=> (@ (@ member8440522571783428010at_nat (@ (@ product_Pair_nat_nat X3) Y2)) R2) (@ (@ P X3) Y2))) (=> (forall ((X3 nat) (Y2 nat) (Z4 nat)) (let ((_let_1 (@ P X3))) (let ((_let_2 (@ transi6264000038957366511cl_nat R2))) (=> (@ (@ member8440522571783428010at_nat (@ (@ product_Pair_nat_nat X3) Y2)) _let_2) (=> (@ _let_1 Y2) (=> (@ (@ member8440522571783428010at_nat (@ (@ product_Pair_nat_nat Y2) Z4)) _let_2) (=> (@ (@ P Y2) Z4) (@ _let_1 Z4)))))))) (@ (@ P X) Y))))) (forall ((X set_nat) (Y set_nat)) (= (@ (@ (@ if_set_nat false) X) Y) Y)) (forall ((X produc2285326912895808259nt_int)) (not (forall ((F5 (-> produc8551481072490612790e_term option6357759511663192854e_term)) (D3 int) (I5 int)) (not (= X (@ (@ produc5700946648718959541nt_int F5) (@ (@ product_Pair_int_int D3) I5))))))) (forall ((L code_integer) (U code_integer)) (= (@ (@ set_or8404916559141939852nteger L) (@ (@ plus_p5714425477246183910nteger U) one_one_Code_integer)) (@ (@ set_or189985376899183464nteger L) U))) (forall ((B2 filter_nat) (A2 filter_nat) (C filter_nat)) (let ((_let_1 (@ ord_less_filter_nat C))) (=> (@ (@ ord_le2510731241096832064er_nat B2) A2) (=> (@ _let_1 B2) (@ _let_1 A2))))) (forall ((M2 int) (N int)) (@ (@ sorted_wrt_int ord_less_eq_int) (@ (@ upto M2) N))) (forall ((X set_int)) (= (@ (@ ord_min_set_int X) bot_bot_set_int) bot_bot_set_int)) (forall ((A set_int) (A2 int) (B set_int)) (let ((_let_1 (@ insert_int2 A2))) (let ((_let_2 (@ minus_minus_set_int A))) (= (@ _let_2 (@ _let_1 B)) (@ (@ minus_minus_set_int (@ _let_2 (@ _let_1 bot_bot_set_int))) B))))) (= upto (lambda ((I4 int) (J2 int)) (@ (@ (@ if_list_int (@ (@ ord_less_eq_int I4) J2)) (@ (@ cons_int I4) (@ (@ upto (@ (@ plus_plus_int I4) one_one_int)) J2))) nil_int))) (forall ((A2 set_nat) (B2 set_nat)) (@ (@ ord_less_eq_set_nat (@ (@ inf_inf_set_nat A2) B2)) A2)) (forall ((X set_Pr4329608150637261639at_nat) (Y set_Pr4329608150637261639at_nat)) (= (= (@ (@ sup_su5525570899277871387at_nat X) Y) bot_bo228742789529271731at_nat) (and (= Y bot_bo228742789529271731at_nat) (= X bot_bo228742789529271731at_nat)))) (forall ((A1 multis2468970476368604999at_nat) (A22 multis2468970476368604999at_nat)) (=> (@ (@ pw_leq A1) A22) (=> (=> (= A1 zero_z1048942125864253310at_nat) (not (= A22 zero_z1048942125864253310at_nat))) (not (forall ((X3 product_prod_nat_nat) (Y2 product_prod_nat_nat) (X9 multis2468970476368604999at_nat)) (=> (= A1 (@ (@ plus_p7104986032573967614at_nat (@ (@ add_ms2612439473150266591at_nat X3) zero_z1048942125864253310at_nat)) X9)) (forall ((Y8 multis2468970476368604999at_nat)) (=> (= A22 (@ (@ plus_p7104986032573967614at_nat (@ (@ add_ms2612439473150266591at_nat Y2) zero_z1048942125864253310at_nat)) Y8)) (=> (@ (@ member8206827879206165904at_nat (@ (@ produc6161850002892822231at_nat X3) Y2)) fun_pair_leq) (not (@ (@ pw_leq X9) Y8))))))))))) (forall ((A2 (-> produc3658429121746597890et_nat Bool)) (C2 set_Pr4532377907799695533_nat_o) (B set_Pr4532377907799695533_nat_o)) (let ((_let_1 (@ insert5175938949040314269_nat_o A2))) (=> (@ (@ member6576561426505652726_nat_o A2) C2) (= (@ (@ inf_in1906310914598751387_nat_o (@ _let_1 B)) C2) (@ _let_1 (@ (@ inf_in1906310914598751387_nat_o B) C2)))))) (forall ((A2 code_integer) (B2 code_integer) (C code_integer)) (=> (@ (@ ord_le3102999989581377725nteger A2) B2) (=> (@ (@ ord_le3102999989581377725nteger zero_z3403309356797280102nteger) C) (@ (@ ord_le3102999989581377725nteger (@ (@ times_3573771949741848930nteger A2) C)) (@ (@ times_3573771949741848930nteger B2) C))))) (forall ((B2 (-> produc3658429121746597890et_nat Bool)) (A2 (-> produc3658429121746597890et_nat Bool))) (=> (@ (@ member6576561426505652726_nat_o B2) (@ (@ insert5175938949040314269_nat_o A2) bot_bo7824918357723582233_nat_o)) (= B2 A2))) (forall ((A2 int) (B2 int) (C int)) (let ((_let_1 (@ plus_plus_int A2))) (= (= (@ _let_1 B2) (@ _let_1 C)) (= B2 C)))) (forall ((Xs list_nat) (I nat) (J nat)) (let ((_let_1 (@ nth_nat Xs))) (=> (@ (@ sorted_wrt_nat ord_less_eq_nat) (@ rev_nat Xs)) (=> (@ (@ ord_less_eq_nat I) J) (=> (@ (@ ord_less_nat J) (@ size_size_list_nat Xs)) (@ (@ ord_less_eq_nat (@ _let_1 J)) (@ _let_1 I))))))) (@ (@ intrel _let_109) _let_109) (forall ((I nat) (K3 nat) (N nat)) (=> (@ (@ ord_less_eq_nat (@ (@ plus_plus_nat I) K3)) N) (@ (@ ord_less_eq_nat I) (@ (@ minus_minus_nat N) K3)))) (forall ((A2 product_prod_nat_nat) (C2 set_Pr1261947904930325089at_nat) (B set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ (@ inf_in2572325071724192079at_nat B) C2))) (let ((_let_2 (@ insert8211810215607154385at_nat A2))) (let ((_let_3 (@ (@ inf_in2572325071724192079at_nat (@ _let_2 B)) C2))) (let ((_let_4 (@ (@ member8440522571783428010at_nat A2) C2))) (and (=> _let_4 (= _let_3 (@ _let_2 _let_1))) (=> (not _let_4) (= _let_3 _let_1)))))))) (forall ((A2 product_prod_nat_nat) (B set_Pr1261947904930325089at_nat) (B2 product_prod_nat_nat)) (let ((_let_1 (@ member8440522571783428010at_nat A2))) (=> (=> (not (@ _let_1 B)) (= A2 B2)) (@ _let_1 (@ (@ insert8211810215607154385at_nat B2) B))))) (forall ((X nat) (Y nat) (Xs list_nat) (Ys list_nat)) (=> (@ (@ member8440522571783428010at_nat (@ (@ product_Pair_nat_nat X) Y)) (@ set_Pr5648618587558075414at_nat (@ (@ zip_nat_nat Xs) Ys))) (@ (@ member_nat Y) (@ set_nat2 Ys)))) (forall ((A set_nat) (B set_nat)) (=> (@ (@ ord_less_eq_set_nat A) B) (= (@ (@ sup_sup_set_nat A) B) B))) (forall ((Xs list_nat)) (= (@ gcd_Gcd_nat (@ set_nat2 Xs)) (@ (@ (@ fold_nat_nat gcd_gcd_nat) Xs) zero_zero_nat))) (forall ((C nat) (Y nat) (X nat)) (let ((_let_1 (@ (@ set_or4665077453230672383an_nat X) Y))) (let ((_let_2 (@ (@ ord_less_nat C) Y))) (let ((_let_3 (@ (@ ord_less_nat X) Y))) (and (=> (not _let_2) (and (=> _let_3 (= (@ (@ image_nat_nat (lambda ((I4 nat)) (@ (@ minus_minus_nat I4) C))) _let_1) (@ (@ insert_nat2 zero_zero_nat) bot_bot_set_nat))) (=> (not _let_3) (= (@ (@ image_nat_nat (lambda ((I4 nat)) (@ (@ minus_minus_nat I4) C))) _let_1) bot_bot_set_nat)))) (=> _let_2 (= (@ (@ image_nat_nat (lambda ((I4 nat)) (@ (@ minus_minus_nat I4) C))) _let_1) (@ (@ set_or4665077453230672383an_nat (@ (@ minus_minus_nat X) C)) (@ (@ minus_minus_nat Y) C))))))))) (= inf_in2572325071724192079at_nat (lambda ((X2 set_Pr1261947904930325089at_nat) (Y5 set_Pr1261947904930325089at_nat)) (@ (@ inf_in2572325071724192079at_nat Y5) X2))) (forall ((N nat) (Xs list_nat) (P (-> nat Bool))) (=> (@ (@ ord_less_nat N) (@ size_size_list_nat Xs)) (=> (forall ((X3 nat)) (=> (@ (@ member_nat X3) (@ set_nat2 Xs)) (@ P X3))) (@ P (@ (@ nth_nat Xs) N))))) (forall ((Y produc3925858234332021118et_nat)) (not (forall ((A4 (-> produc3658429121746597890et_nat Bool)) (B4 produc3658429121746597890et_nat)) (not (= Y (@ (@ produc5001842942810119800et_nat A4) B4)))))) (forall ((A2 code_integer)) (let ((_let_1 (@ ord_le6747313008572928689nteger zero_z3403309356797280102nteger))) (= (@ _let_1 (@ (@ plus_p5714425477246183910nteger A2) A2)) (@ _let_1 A2)))) (forall ((A2 rat) (N nat)) (let ((_let_1 (@ ord_less_rat zero_zero_rat))) (=> (@ _let_1 A2) (@ _let_1 (@ (@ power_power_rat A2) N))))) (forall ((B2 nat) (A2 nat)) (=> (@ (@ ord_less_eq_nat B2) A2) (= (@ (@ sup_sup_nat A2) B2) A2))) (forall ((X nat) (Y nat) (A set_nat)) (let ((_let_1 (@ insert_nat2 X))) (let ((_let_2 (@ insert_nat2 Y))) (= (@ _let_1 (@ _let_2 A)) (@ _let_2 (@ _let_1 A)))))) (forall ((P (-> (-> produc3658429121746597890et_nat Bool) Bool))) (= (= bot_bo7824918357723582233_nat_o (@ collec939566748876313656_nat_o P)) (forall ((X2 (-> produc3658429121746597890et_nat Bool))) (not (@ P X2))))) (forall ((N nat)) (exists ((Xs2 list_c)) (= (@ size_size_list_c Xs2) N))) (forall ((A set_o) (B set_o) (X Bool) (C2 set_o)) (let ((_let_1 (@ minus_minus_set_o B))) (let ((_let_2 (@ ord_less_eq_set_o A))) (= (@ _let_2 (@ _let_1 (@ (@ insert_o2 X) C2))) (and (not (@ (@ member_o X) A)) (@ _let_2 (@ _let_1 C2))))))) (forall ((A2 nat) (B2 nat) (C nat) (D2 nat)) (let ((_let_1 (@ ord_less_eq_nat zero_zero_nat))) (=> (@ (@ ord_less_eq_nat A2) B2) (=> (@ (@ ord_less_eq_nat C) D2) (=> (@ _let_1 A2) (=> (@ _let_1 C) (@ (@ ord_less_eq_nat (@ (@ times_times_nat A2) C)) (@ (@ times_times_nat B2) D2)))))))) (forall ((A2 num) (B2 num) (C num)) (=> (= A2 B2) (=> (@ (@ ord_less_num B2) C) (@ (@ ord_less_num A2) C)))) (forall ((Xs list_int) (Ys list_int)) (= (@ set_int2 (@ (@ union_int Xs) Ys)) (@ (@ sup_sup_set_int (@ set_int2 Xs)) (@ set_int2 Ys)))) (forall ((Xs list_int) (Ys list_int)) (= (= nil_Pr2300489316682597567nt_int (@ (@ zip_int_int Xs) Ys)) (or (= Ys nil_int) (= Xs nil_int)))) (forall ((A set_nat) (A2 nat) (B set_nat)) (let ((_let_1 (@ insert_nat2 A2))) (let ((_let_2 (@ minus_minus_set_nat A))) (= (@ _let_2 (@ _let_1 B)) (@ (@ minus_minus_set_nat (@ _let_2 B)) (@ _let_1 bot_bot_set_nat)))))) (forall ((A2 code_integer) (C code_integer) (B2 code_integer)) (=> (@ (@ ord_le6747313008572928689nteger A2) C) (@ (@ ord_le6747313008572928689nteger (@ (@ ord_min_Code_integer A2) B2)) C))) (forall ((A2 nat) (B2 nat) (C nat)) (let ((_let_1 (@ ord_min_nat A2))) (= (@ (@ ord_min_nat (@ _let_1 B2)) C) (@ _let_1 (@ (@ ord_min_nat B2) C))))) (@ is_pure_assn one_one_assn) (forall ((X num) (Ys list_num)) (let ((_let_1 (@ sorted_wrt_num ord_less_num))) (= (@ _let_1 (@ (@ cons_num X) Ys)) (and (@ _let_1 Ys) (forall ((X2 num)) (=> (@ (@ member_num X2) (@ set_num2 Ys)) (@ (@ ord_less_num X) X2))))))) (= (@ rev_int nil_int) nil_int) (forall ((A2 int) (B2 int) (D2 int) (C int)) (=> (@ (@ ord_less_int A2) B2) (=> (@ (@ ord_less_int D2) C) (@ (@ ord_less_int (@ (@ minus_minus_int A2) C)) (@ (@ minus_minus_int B2) D2))))) (forall ((A2 nat) (B2 nat)) (=> (@ (@ ord_less_eq_nat A2) B2) (= (@ (@ sup_sup_nat A2) B2) B2))) (forall ((C code_integer) (A2 code_integer) (B2 code_integer)) (let ((_let_1 (@ times_3573771949741848930nteger C))) (=> (not (= C zero_z3403309356797280102nteger)) (= (= (@ _let_1 A2) (@ _let_1 B2)) (= A2 B2))))) (forall ((A set_int) (X int) (B set_int)) (let ((_let_1 (@ ord_less_set_int A))) (let ((_let_2 (@ member_int X))) (let ((_let_3 (@ _let_2 B))) (let ((_let_4 (@ _let_2 A))) (let ((_let_5 (@ insert_int2 X))) (= (@ _let_1 (@ _let_5 B)) (and (=> (not _let_3) (and (=> _let_4 (@ (@ ord_less_set_int (@ (@ minus_minus_set_int A) (@ _let_5 bot_bot_set_int))) B)) (=> (not _let_4) (@ (@ ord_less_eq_set_int A) B)))) (=> _let_3 (@ _let_1 B)))))))))) (forall ((A2 rat) (B2 rat) (C rat) (D2 rat)) (=> (@ (@ ord_less_rat A2) B2) (=> (@ (@ ord_less_rat C) D2) (@ (@ ord_less_rat (@ (@ plus_plus_rat A2) C)) (@ (@ plus_plus_rat B2) D2))))) (forall ((Xs list_nat) (Ys list_nat) (F4 (-> nat Bool)) (G (-> nat Bool))) (=> (= Xs Ys) (=> (forall ((X3 nat)) (=> (@ (@ member_nat X3) (@ set_nat2 Ys)) (= (@ F4 X3) (@ G X3)))) (= (@ (@ list_ex_nat F4) Xs) (@ (@ list_ex_nat G) Ys))))) (forall ((Z code_integer) (X code_integer) (Y code_integer)) (=> (@ (@ ord_le6747313008572928689nteger zero_z3403309356797280102nteger) Z) (= (@ (@ ord_le3102999989581377725nteger (@ (@ times_3573771949741848930nteger X) Z)) (@ (@ times_3573771949741848930nteger Y) Z)) (@ (@ ord_le3102999989581377725nteger X) Y)))) (forall ((A2 code_integer) (B2 code_integer) (C code_integer) (D2 code_integer)) (let ((_let_1 (@ ord_le3102999989581377725nteger zero_z3403309356797280102nteger))) (=> (@ (@ ord_le3102999989581377725nteger A2) B2) (=> (@ (@ ord_le3102999989581377725nteger C) D2) (=> (@ _let_1 B2) (=> (@ _let_1 C) (@ (@ ord_le3102999989581377725nteger (@ (@ times_3573771949741848930nteger A2) C)) (@ (@ times_3573771949741848930nteger B2) D2)))))))) (forall ((A2 set_int)) (= (@ (@ sup_sup_set_int bot_bot_set_int) A2) A2)) (forall ((A2 set_int)) (= (not (= A2 bot_bot_set_int)) (@ (@ ord_less_set_int bot_bot_set_int) A2))) (forall ((A2 rat)) (= (@ (@ times_times_rat A2) one_one_rat) A2)) (forall ((I3 set_nat) (I7 set_nat) (Xs list_c) (Xs4 list_c) (Xsi list_nat) (Xsi2 list_nat) (A (-> c nat assn)) (A6 (-> c nat assn))) (=> (= I3 I7) (=> (= (@ size_size_list_c Xs) (@ size_size_list_c Xs4)) (=> (= (@ size_size_list_nat Xsi) (@ size_size_list_nat Xsi2)) (=> (forall ((I5 nat)) (let ((_let_1 (@ (@ nth_nat Xsi2) I5))) (let ((_let_2 (@ (@ nth_c Xs4) I5))) (let ((_let_3 (@ (@ nth_nat Xsi) I5))) (let ((_let_4 (@ (@ nth_c Xs) I5))) (let ((_let_5 (@ size_size_list_c Xs))) (=> (@ (@ member_nat I5) I3) (=> (@ (@ ord_less_nat I5) _let_5) (=> (= _let_5 (@ size_size_list_nat Xsi)) (and (= _let_4 _let_2) (= _let_3 _let_1) (= (@ (@ A _let_4) _let_3) (@ (@ A6 _let_2) _let_1)))))))))))) (= (@ (@ (@ (@ vEBT_L6585172037124793648_c_nat I3) A) Xs) Xsi) (@ (@ (@ (@ vEBT_L6585172037124793648_c_nat I7) A6) Xs4) Xsi2))))))) (forall ((N nat)) (= (@ (@ inf_in2572325071724192079at_nat bNF_Ca8665028551170535155natLeq) (@ (@ produc457027306803732586at_nat (@ (@ order_underS_nat bNF_Ca8665028551170535155natLeq) N)) (lambda ((Uu2 nat)) (@ (@ order_underS_nat bNF_Ca8665028551170535155natLeq) N)))) (@ collec3392354462482085612at_nat (@ produc6081775807080527818_nat_o (lambda ((X2 nat) (Y5 nat)) (and (@ (@ ord_less_nat X2) N) (@ (@ ord_less_nat Y5) N) (@ (@ ord_less_eq_nat X2) Y5))))))) (forall ((A2 set_Pr1261947904930325089at_nat) (B2 set_Pr1261947904930325089at_nat) (C set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ ord_le3146513528884898305at_nat A2))) (= (@ _let_1 (@ (@ inf_in2572325071724192079at_nat B2) C)) (and (@ _let_1 B2) (@ _let_1 C))))) (forall ((X4 set_nat) (A2 nat)) (let ((_let_1 (@ (@ insert_nat2 A2) bot_bot_set_nat))) (= (@ (@ ord_less_eq_set_nat X4) _let_1) (or (= X4 bot_bot_set_nat) (= X4 _let_1))))) (forall ((C rat) (B2 rat)) (= (@ (@ ord_less_rat C) (@ (@ times_times_rat B2) C)) (and (=> (@ (@ ord_less_eq_rat C) zero_zero_rat) (@ (@ ord_less_rat B2) one_one_rat)) (=> (@ (@ ord_less_eq_rat zero_zero_rat) C) (@ (@ ord_less_rat one_one_rat) B2))))) (forall ((A2 nat) (B2 nat) (F4 (-> nat assn)) (C assn)) (=> (@ (@ ord_less_eq_nat A2) B2) (=> (= (@ F4 B2) C) (=> (forall ((X3 nat) (Y2 nat)) (=> (@ (@ ord_less_eq_nat X3) Y2) (@ (@ ord_less_eq_assn (@ F4 X3)) (@ F4 Y2)))) (@ (@ ord_less_eq_assn (@ F4 A2)) C))))) (forall ((C (-> produc3658429121746597890et_nat Bool)) (A set_Pr4532377907799695533_nat_o) (B set_Pr4532377907799695533_nat_o)) (let ((_let_1 (@ member6576561426505652726_nat_o C))) (= (@ _let_1 (@ (@ inf_in1906310914598751387_nat_o A) B)) (and (@ _let_1 B) (@ _let_1 A))))) _let_128 (forall ((Xs list_P5464809261938338413at_nat) (X produc3843707927480180839at_nat)) (=> (@ distin5355857245021852384at_nat Xs) (=> (@ (@ member8757157785044589968at_nat X) (@ set_Pr3765526544606949372at_nat Xs)) (exists ((X3 nat)) (and (@ (@ ord_less_nat X3) (@ size_s1588839187904960729at_nat Xs)) (forall ((Y3 nat)) (=> (and (= (@ (@ nth_Pr1239524528086697198at_nat Xs) Y3) X) (@ (@ ord_less_nat Y3) (@ size_s1588839187904960729at_nat Xs))) (= Y3 X3))) (= (@ (@ nth_Pr1239524528086697198at_nat Xs) X3) X)))))) _let_127 (forall ((R2 set_Pr958786334691620121nt_int)) (@ (@ total_on_int bot_bot_set_int) R2)) (forall ((A2 num) (F4 (-> code_integer num)) (B2 code_integer) (C code_integer)) (=> (= A2 (@ F4 B2)) (=> (@ (@ ord_le6747313008572928689nteger B2) C) (=> (forall ((X3 code_integer) (Y2 code_integer)) (=> (@ (@ ord_le6747313008572928689nteger X3) Y2) (@ (@ ord_less_num (@ F4 X3)) (@ F4 Y2)))) (@ (@ ord_less_num A2) (@ F4 C)))))) (forall ((T code_integer)) (exists ((Z4 code_integer)) (forall ((X7 code_integer)) (=> (@ (@ ord_le6747313008572928689nteger X7) Z4) (not (= X7 T)))))) (forall ((N nat)) (let ((_let_1 (@ ord_less_nat zero_zero_nat))) (=> (@ _let_1 N) (@ _let_1 (@ (@ divide_divide_nat (@ suc N)) (@ numeral_numeral_nat (@ bit0 one))))))) (forall ((X int) (Y int)) (or (@ (@ ord_less_eq_int Y) X) (@ (@ ord_less_eq_int X) Y))) (forall ((A2 nat) (B2 nat) (C nat) (D2 nat)) (=> (@ (@ ord_less_nat A2) B2) (=> (@ (@ ord_less_nat C) D2) (@ (@ ord_less_nat (@ (@ plus_plus_nat A2) C)) (@ (@ plus_plus_nat B2) D2))))) (forall ((Y set_nat) (X set_nat)) (@ (@ ord_less_eq_set_nat Y) (@ (@ sup_sup_set_nat X) Y))) (forall ((N nat) (P (-> nat Bool))) (= (forall ((I4 nat)) (=> (@ (@ ord_less_nat I4) (@ suc N)) (@ P I4))) (and (forall ((I4 nat)) (=> (@ (@ ord_less_nat I4) N) (@ P (@ suc I4)))) (@ P zero_zero_nat)))) (forall ((A2 set_Pr1261947904930325089at_nat) (A7 set_Pr1261947904930325089at_nat) (B2 set_Pr1261947904930325089at_nat) (B6 set_Pr1261947904930325089at_nat)) (=> (@ (@ ord_le3146513528884898305at_nat A2) A7) (=> (@ (@ ord_le3146513528884898305at_nat B2) B6) (=> (= (@ (@ inf_in2572325071724192079at_nat A7) B6) bot_bo2099793752762293965at_nat) (= (@ (@ inf_in2572325071724192079at_nat A2) B2) bot_bo2099793752762293965at_nat))))) (forall ((A2 nat) (B2 nat) (C nat)) (let ((_let_1 (@ ord_less_nat A2))) (=> (@ _let_1 B2) (=> (= B2 C) (@ _let_1 C))))) (forall ((X nat) (Xs list_nat)) (not (= (@ (@ cons_nat X) Xs) Xs))) (forall ((C code_integer) (A2 code_integer) (B2 code_integer)) (let ((_let_1 (@ times_3573771949741848930nteger C))) (= (= (@ _let_1 A2) (@ _let_1 B2)) (or (= A2 B2) (= C zero_z3403309356797280102nteger))))) (forall ((I nat) (J nat) (K3 nat) (L nat)) (=> (and (@ (@ ord_less_eq_nat K3) L) (= I J)) (@ (@ ord_less_eq_nat (@ (@ plus_plus_nat I) K3)) (@ (@ plus_plus_nat J) L)))) (forall ((P (-> nat Bool))) (= (= bot_bot_set_nat (@ collect_nat P)) (forall ((X2 nat)) (not (@ P X2))))) (forall ((P (-> (-> produc3658429121746597890et_nat Bool) Bool)) (Q (-> (-> produc3658429121746597890et_nat Bool) Bool))) (=> (forall ((X3 (-> produc3658429121746597890et_nat Bool))) (= (@ P X3) (@ Q X3))) (= (@ collec939566748876313656_nat_o P) (@ collec939566748876313656_nat_o Q)))) (forall ((A2 set_Pr4532377907799695533_nat_o) (B2 set_Pr4532377907799695533_nat_o)) (=> (forall ((X3 (-> produc3658429121746597890et_nat Bool))) (let ((_let_1 (@ member6576561426505652726_nat_o X3))) (=> (@ _let_1 A2) (not (@ 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ord_le6747313008572928689nteger A2) (@ F4 C)))))) (forall ((B set_Pr4329608150637261639at_nat)) (= (@ (@ sup_su5525570899277871387at_nat bot_bo228742789529271731at_nat) B) B)) (forall ((B2 assn) (C assn) (A2 assn)) (=> (@ (@ ord_less_assn B2) C) (@ (@ ord_less_assn (@ (@ inf_inf_assn A2) B2)) C))) (forall ((A2 num) (F4 (-> num num)) (B2 num) (C num)) (=> (@ (@ ord_less_eq_num A2) (@ F4 B2)) (=> (@ (@ ord_less_num B2) C) (=> (forall ((X3 num) (Y2 num)) (=> (@ (@ ord_less_num X3) Y2) (@ (@ ord_less_num (@ F4 X3)) (@ F4 Y2)))) (@ (@ ord_less_num A2) (@ F4 C)))))) (forall ((Z code_integer) (X code_integer) (Y code_integer)) (let ((_let_1 (@ times_3573771949741848930nteger Z))) (=> (@ (@ ord_le6747313008572928689nteger zero_z3403309356797280102nteger) Z) (= (@ (@ ord_le3102999989581377725nteger (@ _let_1 X)) (@ _let_1 Y)) (@ (@ ord_le3102999989581377725nteger X) Y))))) (forall ((P (-> nat Bool)) (N nat)) (=> (@ P zero_zero_nat) (=> (forall ((N5 nat)) (=> (@ P N5) (=> (@ (@ ord_less_nat zero_zero_nat) N5) (@ P (@ (@ times_times_nat (@ numeral_numeral_nat (@ bit0 one))) N5))))) (=> (forall ((N5 nat)) (=> (@ P N5) (@ P (@ suc (@ (@ times_times_nat (@ numeral_numeral_nat (@ bit0 one))) N5))))) (@ P N))))) (forall ((Xs list_int) (X int)) (=> (@ distinct_int Xs) (=> (@ (@ member_int X) (@ set_int2 Xs)) (exists ((X3 nat)) (and (@ (@ ord_less_nat X3) (@ size_size_list_int Xs)) (= (@ (@ nth_int Xs) X3) X) (forall ((Y3 nat)) (=> (and (= (@ (@ nth_int Xs) Y3) X) (@ (@ ord_less_nat Y3) (@ size_size_list_int Xs))) (= Y3 X3)))))))) (forall ((A2 int) (B2 int)) (=> (@ (@ ord_less_int A2) B2) (= (@ (@ ord_min_int A2) B2) A2))) (forall ((A2 int) (B2 int)) (let ((_let_1 (@ ord_less_eq_int zero_zero_int))) (= (@ (@ ord_less_eq_int (@ (@ times_times_int A2) B2)) zero_zero_int) (or (and (@ (@ ord_less_eq_int A2) zero_zero_int) (@ _let_1 B2)) (and (@ (@ ord_less_eq_int B2) zero_zero_int) (@ _let_1 A2)))))) (forall ((C2 set_int) (D set_int) (A2 int)) (let ((_let_1 (@ insert_int2 A2))) (=> (@ (@ ord_less_eq_set_int C2) D) (@ (@ ord_less_eq_set_int (@ _let_1 C2)) (@ _let_1 D))))) (= ord_less_assn (lambda ((B3 assn) (A3 assn)) (and (@ (@ ord_less_eq_assn B3) A3) (not (= A3 B3))))) (forall ((M2 int) (N int)) (let ((_let_1 (@ (@ ord_min_int M2) N))) (= (not (@ (@ ord_less_int _let_1) M2)) (= _let_1 M2)))) (forall ((Xs list_P7985473006766602707_nat_o) (I nat) (X (-> produc3658429121746597890et_nat Bool)) (Ys list_P2321686559999237006et_nat) (Y produc3925858234332021118et_nat)) (= (@ (@ zip_Pr8136144321567152340et_nat (@ (@ (@ list_u6943956310655620667_nat_o Xs) I) X)) (@ (@ (@ list_u1866171116859985808et_nat Ys) I) Y)) (@ (@ (@ list_u1913845194572276492et_nat (@ (@ zip_Pr8136144321567152340et_nat Xs) Ys)) I) (@ (@ produc2245416461498447860et_nat X) Y)))) (forall ((A2 int)) (not (@ (@ ord_less_int (@ (@ times_times_int A2) A2)) zero_zero_int))) (forall ((B2 set_nat) (X set_nat) (A2 set_nat)) (=> (@ (@ ord_less_eq_set_nat B2) X) (@ (@ ord_less_eq_set_nat (@ (@ inf_inf_set_nat A2) B2)) X))) _let_126 (forall ((I3 set_nat) (I7 set_nat) (A (-> nat c assn)) (A6 (-> nat c assn)) (Xs list_nat) (Xs4 list_nat) (Xsi list_c) (Xsi2 list_c)) (=> (= I3 I7) (=> (= A A6) (=> (= (@ size_size_list_nat Xs) (@ size_size_list_nat Xs4)) (=> (= (@ size_size_list_c Xsi) (@ size_size_list_c Xsi2)) (=> (forall ((I5 nat)) (let ((_let_1 (@ size_size_list_nat Xs))) (=> (@ (@ member_nat I5) I3) (=> (@ (@ ord_less_nat I5) _let_1) (=> (= _let_1 (@ size_size_list_c Xsi)) (and (= (@ (@ nth_nat Xs) I5) (@ (@ nth_nat Xs4) I5)) (= (@ (@ nth_c Xsi) I5) (@ (@ nth_c Xsi2) I5)))))))) (= (@ (@ (@ (@ vEBT_L8146214880390291086_nat_c I3) A) Xs) Xsi) (@ (@ (@ (@ vEBT_L8146214880390291086_nat_c I7) A6) Xs4) Xsi2)))))))) (forall ((A2 int) (B2 int) (C int) (D2 int)) (= (= (@ (@ insert_int2 A2) (@ (@ insert_int2 B2) bot_bot_set_int)) (@ (@ insert_int2 C) (@ (@ insert_int2 D2) bot_bot_set_int))) (or (and (= A2 D2) (= B2 C)) (and (= B2 D2) (= A2 C))))) (forall ((X assn) (Y assn) (Z assn)) (let ((_let_1 (@ sup_sup_assn X))) (let ((_let_2 (@ sup_sup_assn Y))) (= (@ _let_1 (@ _let_2 Z)) (@ _let_2 (@ _let_1 Z)))))) (not (= zero_z3403309356797280102nteger one_one_Code_integer)) (forall ((A set_Pr4329608150637261639at_nat) (B set_Pr4329608150637261639at_nat) (C2 set_Pr4329608150637261639at_nat)) (= (@ (@ ord_le1268244103169919719at_nat (@ (@ sup_su5525570899277871387at_nat A) B)) C2) (and (@ (@ ord_le1268244103169919719at_nat B) C2) (@ (@ ord_le1268244103169919719at_nat A) C2)))) (forall ((A set_int) (B set_int)) (=> (forall ((X3 int)) (let ((_let_1 (@ member_int X3))) (=> (@ _let_1 A) (not (@ _let_1 B))))) (= (@ (@ inf_inf_set_int A) B) bot_bot_set_int))) (forall ((A2 assn) (B2 assn) (F4 (-> assn nat)) (C nat)) (=> (@ (@ ord_less_assn A2) B2) (=> (= (@ F4 B2) C) (=> (forall ((X3 assn) (Y2 assn)) (=> (@ (@ ord_less_assn X3) Y2) (@ (@ ord_less_nat (@ F4 X3)) (@ F4 Y2)))) (@ (@ ord_less_nat (@ F4 A2)) C))))) (forall ((A2 nat) (B2 nat)) (let ((_let_1 (@ ord_less_eq_nat zero_zero_nat))) (=> (@ _let_1 A2) (=> (@ _let_1 B2) (@ _let_1 (@ (@ times_times_nat A2) B2)))))) (forall ((Y num) (X num)) (=> (not (@ (@ ord_less_num Y) X)) (= (not (@ (@ ord_less_num X) Y)) (= X Y)))) (forall ((A2 code_integer) (C code_integer) (B2 code_integer)) (= (@ (@ ord_le6747313008572928689nteger (@ (@ plus_p5714425477246183910nteger A2) C)) (@ (@ plus_p5714425477246183910nteger B2) C)) (@ (@ ord_le6747313008572928689nteger A2) B2))) (forall ((Xs list_nat) (Ys list_c) (X nat)) (=> (= (@ size_size_list_nat Xs) (@ size_size_list_c Ys)) (=> (@ (@ member_nat X) (@ set_nat2 Xs)) (not (forall ((Y2 c)) (not (@ (@ member8962352060716553276_nat_c (@ (@ product_Pair_nat_c X) Y2)) (@ set_Pr4163146846833169104_nat_c (@ (@ zip_nat_c Xs) Ys))))))))) (forall ((Y num) (X num)) (=> (not (@ (@ ord_less_eq_num Y) X)) (@ (@ ord_less_num X) Y))) (forall ((A set_nat) (B set_nat)) (let ((_let_1 (@ minus_minus_set_nat A))) (= (@ _let_1 (@ _let_1 B)) (@ (@ inf_inf_set_nat A) B)))) (forall ((X product_prod_nat_nat) (Xs list_P6011104703257516679at_nat) (N nat)) (=> (not (@ (@ member8440522571783428010at_nat X) (@ set_Pr5648618587558075414at_nat Xs))) (=> (@ (@ ord_less_eq_nat N) (@ size_s5460976970255530739at_nat Xs)) (= (= (@ (@ nth_Pr7617993195940197384at_nat (@ (@ cons_P6512896166579812791at_nat X) Xs)) N) X) (= N zero_zero_nat))))) (forall ((X set_nat) (A2 set_nat) (B2 set_nat)) (let ((_let_1 (@ ord_less_eq_set_nat X))) (=> (@ _let_1 (@ (@ inf_inf_set_nat A2) B2)) (not (=> (@ _let_1 A2) (not (@ _let_1 B2))))))) (forall ((P (-> nat Bool))) (not (@ (@ list_ex_nat P) nil_nat))) (forall ((I set_o) (Ww list_set_o)) (let ((_let_1 (@ foldl_set_o_set_o sup_sup_set_o))) (= (@ (@ _let_1 I) Ww) (@ (@ sup_sup_set_o I) (@ (@ _let_1 bot_bot_set_o) Ww))))) (= inf_inf_set_nat (lambda ((A5 set_nat) (B7 set_nat)) (@ (@ inf_inf_set_nat B7) A5))) _let_125 (forall ((K3 nat) (Xs list_c) (X c)) (let ((_let_1 (@ butlast_c Xs))) (let ((_let_2 (@ butlast_c (@ (@ (@ list_update_c Xs) K3) X)))) (let ((_let_3 (= K3 (@ (@ minus_minus_nat (@ size_size_list_c Xs)) one_one_nat)))) (and (=> (not _let_3) (= _let_2 (@ (@ (@ list_update_c _let_1) K3) X))) (=> _let_3 (= _let_2 _let_1))))))) (forall ((A2 rat) (B2 rat)) (let ((_let_1 (@ ord_less_eq_rat zero_zero_rat))) (= (@ _let_1 (@ (@ times_times_rat A2) B2)) (or (and (@ _let_1 A2) (@ _let_1 B2)) (and (@ (@ ord_less_eq_rat B2) zero_zero_rat) (@ (@ ord_less_eq_rat A2) zero_zero_rat)))))) (forall ((A2 set_Pr4329608150637261639at_nat) (B2 set_Pr4329608150637261639at_nat)) (= (= bot_bo228742789529271731at_nat (@ (@ sup_su5525570899277871387at_nat A2) B2)) (and (= B2 bot_bo228742789529271731at_nat) (= A2 bot_bo228742789529271731at_nat)))) (forall ((C rat) (A2 rat) (B2 rat)) (let ((_let_1 (@ times_times_rat C))) (=> (@ (@ ord_less_rat C) zero_zero_rat) (= (@ (@ ord_less_rat (@ _let_1 A2)) (@ _let_1 B2)) (@ (@ ord_less_rat B2) A2))))) (forall ((B2 nat) (C nat) (A2 nat)) (= (@ (@ ord_less_eq_nat (@ (@ sup_sup_nat B2) C)) A2) (and (@ (@ ord_less_eq_nat C) A2) (@ (@ 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B2))) (=> (@ (@ ord_le6747313008572928689nteger one_one_Code_integer) B2) (= (@ (@ ord_le6747313008572928689nteger (@ _let_1 X)) (@ _let_1 Y)) (@ (@ ord_less_nat X) Y))))) (forall ((A2 int) (F4 (-> assn int)) (B2 assn) (C assn)) (let ((_let_1 (@ ord_less_int A2))) (=> (@ _let_1 (@ F4 B2)) (=> (@ (@ ord_less_eq_assn B2) C) (=> (forall ((X3 assn) (Y2 assn)) (=> (@ (@ ord_less_eq_assn X3) Y2) (@ (@ ord_less_eq_int (@ F4 X3)) (@ F4 Y2)))) (@ _let_1 (@ F4 C))))))) (forall ((X assn)) (= (@ (@ sup_sup_assn X) bot_bot_assn) X)) (forall ((X assn) (Y assn)) (=> (@ (@ ord_less_assn X) Y) (@ (@ ord_less_eq_assn X) Y))) (forall ((P (-> nat Bool)) (M2 nat) (N nat)) (= (@ P (@ (@ divide_divide_nat M2) N)) (or (and (= N zero_zero_nat) (@ P zero_zero_nat)) (exists ((Q8 nat)) (let ((_let_1 (@ times_times_nat N))) (and (@ (@ ord_less_nat M2) (@ _let_1 (@ suc Q8))) (@ P Q8) (@ (@ ord_less_eq_nat (@ _let_1 Q8)) M2))))))) (forall ((B2 int) (C int) (A2 int)) (= (@ (@ times_times_int (@ (@ minus_minus_int B2) C)) A2) (@ (@ minus_minus_int (@ (@ times_times_int B2) A2)) (@ (@ times_times_int C) A2)))) (forall ((A2 set_nat) (B2 set_nat)) (= (= (@ (@ sup_sup_set_nat A2) B2) bot_bot_set_nat) (and (= A2 bot_bot_set_nat) (= B2 bot_bot_set_nat)))) (forall ((A2 int) (B2 int) (C int)) (= (= (@ (@ minus_minus_int A2) B2) C) (= A2 (@ (@ plus_plus_int C) B2)))) (forall ((X produc6575502325842934193n_assn) (Y produc6575502325842934193n_assn) (R2 set_Pr8116311503512020807n_assn) (Xs list_P8527749157015355191n_assn)) (=> (@ (@ member4743710847862083984n_assn (@ (@ produc6128706242671166167n_assn X) Y)) R2) (@ (@ member3994142547374651152n_assn (@ (@ produc3014731801419794263n_assn (@ (@ cons_P2971678138204555879n_assn X) Xs)) (@ (@ cons_P2971678138204555879n_assn Y) Xs))) (@ listre4270255209692100112n_assn R2)))) (forall ((C produc3843707927480180839at_nat) (A set_Pr4329608150637261639at_nat) (B set_Pr4329608150637261639at_nat)) (let ((_let_1 (@ member8757157785044589968at_nat C))) (=> (@ _let_1 (@ (@ minus_3314409938677909166at_nat A) B)) (@ _let_1 A)))) (forall ((X produc6575502325842934193n_assn) (Xs list_P8527749157015355191n_assn)) (= (@ (@ member7957490590177025114n_assn X) (@ set_Pr1139785259514867910n_assn Xs)) (exists ((I4 nat)) (and (@ (@ ord_less_nat I4) (@ size_s6829681357464350627n_assn Xs)) (= (@ (@ nth_Pr1769885009046257848n_assn Xs) I4) X))))) (forall ((A set_Pr1261947904930325089at_nat)) (=> (not (= A bot_bo2099793752762293965at_nat)) (=> (forall ((X3 product_prod_nat_nat) (Y2 product_prod_nat_nat)) (=> (@ (@ member8440522571783428010at_nat X3) A) (=> (@ (@ member8440522571783428010at_nat Y2) A) (= X3 Y2)))) (@ is_sin2850979758926227957at_nat A)))) (forall ((A2 int) (A set_int) (B set_int)) (= (= bot_bot_set_int (@ (@ inf_inf_set_int (@ (@ insert_int2 A2) A)) B)) (and (= bot_bot_set_int (@ (@ inf_inf_set_int A) B)) (not (@ (@ member_int A2) B))))) (= modulo_modulo_nat (lambda ((M nat) (N2 nat)) (@ (@ (@ if_nat (@ (@ ord_less_nat M) N2)) M) (@ (@ modulo_modulo_nat (@ (@ minus_minus_nat M) N2)) N2)))) (forall ((Y assn) (X assn)) (=> (@ (@ ord_less_eq_assn Y) X) (= (@ (@ inf_inf_assn X) Y) Y))) (forall ((N nat) (X nat) (Xs list_nat)) (let ((_let_1 (@ (@ nth_nat (@ (@ cons_nat X) Xs)) N))) (let ((_let_2 (= N zero_zero_nat))) (and (=> (not _let_2) (= _let_1 (@ (@ nth_nat Xs) (@ (@ minus_minus_nat N) one_one_nat)))) (=> _let_2 (= _let_1 X)))))) (= ord_less_assn (lambda ((A3 assn) (B3 assn)) (and (not (= A3 B3)) (= A3 (@ (@ inf_inf_assn A3) B3))))) (forall ((A2 int)) (not (@ (@ ord_less_int A2) A2))) (forall ((A2 code_integer) (B2 code_integer) (F4 (-> code_integer assn)) (C assn)) (=> (@ (@ ord_le6747313008572928689nteger A2) B2) (=> (@ (@ ord_less_assn (@ F4 B2)) C) (=> (forall ((X3 code_integer) (Y2 code_integer)) (=> (@ (@ ord_le6747313008572928689nteger X3) Y2) (@ (@ ord_less_assn (@ F4 X3)) (@ F4 Y2)))) (@ (@ ord_less_assn (@ F4 A2)) C))))) (forall ((X Bool) (Xs list_o)) (= (@ (@ insert_o2 X) (@ coset_o Xs)) (@ coset_o (@ (@ removeAll_o X) Xs)))) (forall ((X nat) (Y nat)) (= (not (@ (@ ord_less_nat X) Y)) (or (@ (@ ord_less_nat Y) X) (= X Y)))) (forall ((Y nat) (Ys list_nat) (Xs list_int) (R2 set_Pr7995236796853374141at_int)) (=> (@ (@ member4850886304473975718st_int (@ (@ produc7739558402351520821st_int (@ (@ cons_nat Y) Ys)) Xs)) (@ listrel_nat_int R2)) (not (forall ((Y2 int) (Ys5 list_int)) (=> (= Xs (@ (@ cons_int Y2) Ys5)) (=> (@ (@ member4262671552274231302at_int (@ (@ product_Pair_nat_int Y) Y2)) R2) (not (@ (@ member4850886304473975718st_int (@ (@ produc7739558402351520821st_int Ys) Ys5)) (@ listrel_nat_int R2))))))))) (forall ((M2 nat) (N nat)) (=> (@ (@ ord_less_nat zero_zero_nat) M2) (=> (@ (@ ord_less_nat M2) N) (not (@ (@ dvd_dvd_nat N) M2))))) (forall ((A2 int)) (= (@ (@ minus_minus_int A2) A2) zero_zero_int)) (forall ((M2 num) (N num)) (let ((_let_1 (@ uminus_uminus_int (@ numeral_numeral_int N)))) (let ((_let_2 (@ uminus_uminus_int (@ numeral_numeral_int M2)))) (let ((_let_3 (@ (@ upto _let_2) _let_1))) (let ((_let_4 (@ (@ ord_less_eq_int _let_2) _let_1))) (and (=> _let_4 (= _let_3 (@ (@ cons_int _let_2) (@ (@ upto (@ (@ plus_plus_int _let_2) one_one_int)) _let_1)))) (=> (not _let_4) (= _let_3 nil_int)))))))) (forall ((Xs list_P8527749157015355191n_assn) (I nat) (X produc6575502325842934193n_assn)) (@ (@ ord_le171416862856029873n_assn (@ set_Pr1139785259514867910n_assn (@ (@ (@ list_u4534839942911652127n_assn Xs) I) X))) (@ (@ insert5290817439147925377n_assn X) (@ set_Pr1139785259514867910n_assn Xs)))) (forall ((A2 product_prod_nat_nat) (A set_Pr1261947904930325089at_nat)) (=> (@ (@ member8440522571783428010at_nat A2) A) (= (@ (@ insert8211810215607154385at_nat A2) A) A))) (forall ((A set_Pr4532377907799695533_nat_o) (B set_Pr4532377907799695533_nat_o)) (=> (forall ((X3 (-> produc3658429121746597890et_nat Bool))) (let ((_let_1 (@ member6576561426505652726_nat_o X3))) (=> (@ _let_1 A) (not (@ _let_1 B))))) (= (@ (@ inf_in1906310914598751387_nat_o A) B) bot_bo7824918357723582233_nat_o))) (forall ((Xs list_nat)) (= (@ size_size_list_nat (@ rotate1_nat Xs)) (@ size_size_list_nat Xs))) (forall ((I3 set_nat) (I7 set_nat) (A (-> nat d assn)) (A6 (-> nat d assn)) (Xs list_nat) (Xs4 list_nat) (Xsi list_d) (Xsi2 list_d)) (=> (= I3 I7) (=> (= A A6) (=> (= (@ size_size_list_nat Xs) (@ size_size_list_nat Xs4)) (=> (= (@ size_size_list_d Xsi) (@ size_size_list_d Xsi2)) (=> (forall ((I5 nat)) (let ((_let_1 (@ size_size_list_nat Xs))) (=> (@ (@ member_nat I5) I3) (=> (@ (@ ord_less_nat I5) _let_1) (=> (= _let_1 (@ size_size_list_d Xsi)) (and (= (@ (@ nth_nat Xs) I5) (@ (@ nth_nat Xs4) I5)) (= (@ (@ nth_d Xsi) I5) (@ (@ nth_d Xsi2) I5)))))))) (= (@ (@ (@ (@ vEBT_L8146214880390291087_nat_d I3) A) Xs) Xsi) (@ (@ (@ (@ vEBT_L8146214880390291087_nat_d I7) A6) Xs4) Xsi2)))))))) (forall ((A2 assn)) (= (@ (@ times_times_assn A2) one_one_assn) A2)) (forall ((S set_o)) (=> (not (= S bot_bot_set_o)) (not (forall ((X3 Bool)) (not (@ (@ member_o X3) S)))))) (forall ((A2 Bool) (B set_o) (B2 Bool)) (let ((_let_1 (@ member_o A2))) (=> (=> (not (@ _let_1 B)) (= A2 B2)) (@ _let_1 (@ (@ insert_o2 B2) B))))) (forall ((X set_nat) (Y set_nat)) (=> (@ (@ ord_less_eq_set_nat X) Y) (=> (@ (@ ord_less_eq_set_nat Y) X) (= X Y)))) (forall ((X nat) (Y nat)) (= (not (@ (@ ord_less_nat X) Y)) (@ (@ ord_less_eq_nat Y) X))) (forall ((C produc3843707927480180839at_nat) (A set_Pr4329608150637261639at_nat) (B set_Pr4329608150637261639at_nat)) (let ((_let_1 (@ member8757157785044589968at_nat C))) (=> (@ _let_1 (@ (@ minus_3314409938677909166at_nat A) B)) (not (@ _let_1 B))))) (forall ((X nat) (Xs list_nat) (I nat) (Y nat)) (let ((_let_1 (@ cons_nat X))) (= (@ (@ (@ list_update_nat (@ _let_1 Xs)) (@ suc I)) Y) (@ _let_1 (@ (@ (@ list_update_nat Xs) I) Y))))) (forall ((X produc3843707927480180839at_nat) (S set_Pr4329608150637261639at_nat)) (=> (@ (@ member8757157785044589968at_nat X) S) (not (= S bot_bo228742789529271731at_nat)))) (forall ((A2 int) (B2 int)) (= (@ (@ plus_plus_int (@ (@ 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Xs2))))) (@ P Xs))))) (forall ((Xs list_nat) (X nat)) (@ (@ ord_less_eq_set_nat (@ set_nat2 Xs)) (@ set_nat2 (@ (@ cons_nat X) Xs)))) (forall ((X produc3658429121746597890et_nat)) (=> (@ in_range X) (not (forall ((H heap_e7401611519738050253t_unit) (As set_nat)) (=> (= X (@ (@ produc7507926704131184380et_nat H) As)) (not (forall ((X7 nat)) (=> (@ (@ member_nat X7) As) (@ (@ ord_less_nat X7) (@ lim_Product_unit H)))))))))) (forall ((X code_integer) (Y code_integer)) (let ((_let_1 (@ ord_le3102999989581377725nteger zero_z3403309356797280102nteger))) (=> (@ _let_1 X) (=> (@ _let_1 Y) (=> (@ (@ ord_le3102999989581377725nteger Y) one_one_Code_integer) (@ (@ ord_le3102999989581377725nteger (@ (@ times_3573771949741848930nteger Y) X)) X)))))) (forall ((N nat) (M2 nat)) (=> (@ (@ ord_less_nat zero_zero_nat) N) (= (@ (@ divide_divide_nat (@ (@ times_times_nat M2) N)) N) M2))) (forall ((X assn) (Y assn) (Z assn)) (let ((_let_1 (@ inf_inf_assn X))) (let ((_let_2 (@ inf_inf_assn Y))) (= (@ _let_1 (@ _let_2 Z)) (@ _let_2 (@ _let_1 Z)))))) (forall ((X assn)) (= (@ (@ sup_sup_assn X) top_top_assn) top_top_assn)) (forall ((N nat)) (let ((_let_1 (@ set_or4665077453230672383an_nat zero_zero_nat))) (= (@ _let_1 (@ suc N)) (@ (@ insert_nat2 zero_zero_nat) (@ (@ image_nat_nat suc) (@ _let_1 N)))))) (forall ((B2 code_integer) (A2 code_integer)) (= (@ (@ ord_le3102999989581377725nteger (@ (@ plus_p5714425477246183910nteger B2) A2)) B2) (@ (@ ord_le3102999989581377725nteger A2) zero_z3403309356797280102nteger))) (forall ((N nat) (K3 nat)) (=> (@ (@ ord_less_nat (@ suc zero_zero_nat)) N) (@ (@ ord_less_nat K3) (@ (@ power_power_nat N) K3)))) (forall ((A2 set_int)) (@ (@ ord_less_eq_set_int bot_bot_set_int) A2)) (forall ((X nat) (Xs list_nat) (Y nat) (Ys list_nat)) (= (@ (@ zip_nat_nat (@ (@ cons_nat X) Xs)) (@ (@ cons_nat Y) Ys)) (@ (@ cons_P6512896166579812791at_nat (@ (@ product_Pair_nat_nat X) Y)) (@ (@ zip_nat_nat Xs) Ys)))) (forall ((Xs list_int) (Ys list_P8527749157015355191n_assn)) (= (= nil_Pr2440414457004260852n_assn (@ (@ zip_in7098856637274830732n_assn Xs) Ys)) (or (= Ys nil_Pr5671120429643327159n_assn) (= Xs nil_int)))) (forall ((I3 set_nat) (I7 set_nat) (A (-> d int assn)) (A6 (-> d int assn)) (Xs list_d) (Xs4 list_d) (Xsi list_int) (Xsi2 list_int)) (=> (= I3 I7) (=> (= A A6) (=> (= (@ size_size_list_d Xs) (@ size_size_list_d Xs4)) (=> (= (@ size_size_list_int Xsi) (@ size_size_list_int Xsi2)) (=> (forall ((I5 nat)) (let ((_let_1 (@ size_size_list_d Xs))) (=> (@ (@ member_nat I5) I3) (=> (@ (@ ord_less_nat I5) _let_1) (=> (= _let_1 (@ size_size_list_int Xsi)) (and (= (@ (@ nth_d Xs) I5) (@ (@ nth_d Xs4) I5)) (= (@ (@ nth_int Xsi) I5) (@ (@ nth_int Xsi2) I5)))))))) (= (@ (@ (@ (@ vEBT_L7818125895572137869_d_int I3) A) Xs) Xsi) (@ (@ (@ (@ vEBT_L7818125895572137869_d_int I7) A6) Xs4) Xsi2)))))))) (forall ((C assn) (B2 assn) (A2 assn)) (let ((_let_1 (@ ord_less_assn C))) (=> (@ _let_1 B2) (@ _let_1 (@ (@ sup_sup_assn A2) B2))))) _let_124 (forall ((A set_Pr4329608150637261639at_nat) (B set_Pr4329608150637261639at_nat) (P (-> produc3843707927480180839at_nat Bool))) (= (exists ((X2 produc3843707927480180839at_nat)) (and (@ P X2) (@ (@ member8757157785044589968at_nat X2) (@ (@ sup_su5525570899277871387at_nat A) B)))) (or (exists ((X2 produc3843707927480180839at_nat)) (and (@ P X2) (@ (@ member8757157785044589968at_nat X2) B))) (exists ((X2 produc3843707927480180839at_nat)) (and (@ (@ member8757157785044589968at_nat X2) A) (@ P X2)))))) (forall ((R2 (-> product_prod_nat_nat product_prod_nat_nat Bool)) (X product_prod_nat_nat) (S3 set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ pairwi6357175311820755948at_nat R2))) (= (@ _let_1 (@ (@ insert8211810215607154385at_nat X) S3)) (and (@ _let_1 S3) (forall ((Y5 product_prod_nat_nat)) (=> (and (@ (@ member8440522571783428010at_nat Y5) S3) (not (= Y5 X))) (and (@ (@ R2 X) Y5) (@ (@ R2 Y5) X)))))))) (forall ((B assn) (A assn)) (@ (@ entailst B) (@ (@ sup_sup_assn A) B))) (forall ((A2 assn) (B2 assn) (C assn)) (let ((_let_1 (@ ord_less_assn A2))) (=> (@ _let_1 (@ (@ inf_inf_assn B2) C)) (not (=> (@ _let_1 B2) (not (@ _let_1 C))))))) (forall ((A2 code_integer) (E code_integer) (C code_integer) (B2 code_integer) (D2 code_integer)) (= (@ (@ ord_le6747313008572928689nteger (@ (@ plus_p5714425477246183910nteger (@ (@ times_3573771949741848930nteger A2) E)) C)) (@ (@ plus_p5714425477246183910nteger (@ (@ times_3573771949741848930nteger B2) E)) D2)) (@ (@ ord_le6747313008572928689nteger C) (@ (@ plus_p5714425477246183910nteger (@ (@ times_3573771949741848930nteger (@ (@ minus_8373710615458151222nteger B2) A2)) E)) D2)))) (forall ((P (-> num Bool)) (P3 (-> num Bool)) (Q (-> num Bool)) (Q3 (-> num Bool))) (=> (exists ((Z3 num)) (forall ((X3 num)) (=> (@ (@ ord_less_num Z3) X3) (= (@ P X3) (@ P3 X3))))) (=> (exists ((Z3 num)) (forall ((X3 num)) (=> (@ (@ ord_less_num Z3) X3) (= (@ Q X3) (@ Q3 X3))))) (exists ((Z4 num)) (forall ((X7 num)) (=> (@ (@ ord_less_num Z4) X7) (= (and (@ Q X7) (@ P X7)) (and (@ P3 X7) (@ Q3 X7))))))))) (forall ((B2 set_nat) (A2 set_nat)) (=> (@ (@ ord_less_eq_set_nat B2) A2) (= (@ (@ sup_sup_set_nat A2) B2) A2))) (forall ((B2 int) (A2 int) (C int)) (let ((_let_1 (@ minus_minus_int C))) (=> (@ (@ ord_less_int B2) A2) (@ (@ ord_less_int (@ _let_1 A2)) (@ _let_1 B2))))) _let_123 (forall ((X assn) (Y assn)) (=> (@ (@ ord_less_eq_assn X) Y) (= (@ (@ ord_min_assn X) Y) X))) (forall ((B2 set_nat) (C set_nat) (A2 set_nat)) (= (@ (@ ord_less_eq_set_nat (@ (@ sup_sup_set_nat B2) C)) A2) (and (@ (@ ord_less_eq_set_nat B2) A2) (@ (@ ord_less_eq_set_nat C) A2)))) (forall ((A1 nat) (A22 nat) (R2 set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ member8440522571783428010at_nat (@ (@ product_Pair_nat_nat A1) A22)))) (=> (@ _let_1 (@ transi6264000038957366511cl_nat R2)) (=> (not (@ _let_1 R2)) (not (forall ((B4 nat)) (=> (@ (@ member8440522571783428010at_nat (@ (@ product_Pair_nat_nat A1) B4)) (@ transi6264000038957366511cl_nat R2)) (not (@ (@ member8440522571783428010at_nat (@ (@ product_Pair_nat_nat B4) A22)) R2))))))))) (forall ((P (-> code_integer code_integer Bool)) (A2 code_integer) (B2 code_integer)) (=> (forall ((A4 code_integer) (B4 code_integer)) (=> (@ (@ ord_le6747313008572928689nteger A4) B4) (@ (@ P A4) B4))) (=> (forall ((A4 code_integer)) (@ (@ P A4) A4)) (=> (forall ((A4 code_integer) (B4 code_integer)) (=> (@ (@ P B4) A4) (@ (@ P A4) B4))) (@ (@ P A2) B2))))) (= ord_le3102999989581377725nteger (lambda ((A3 code_integer) (B3 code_integer)) (@ (@ ord_le3102999989581377725nteger (@ (@ minus_8373710615458151222nteger A3) B3)) zero_z3403309356797280102nteger))) (forall ((F4 (-> int nat int)) (A2 int) (As2 list_int) (B2 nat) (Bs list_nat)) (let ((_let_1 (@ zipf_int_nat_int F4))) (= (@ (@ _let_1 (@ (@ cons_int A2) As2)) (@ (@ cons_nat B2) Bs)) (@ (@ cons_int (@ (@ F4 A2) B2)) (@ (@ _let_1 As2) Bs))))) _let_122 (forall ((A set_Pr4329608150637261639at_nat) (B set_Pr4329608150637261639at_nat)) (=> (@ (@ ord_le1268244103169919719at_nat A) B) (= (@ (@ minus_3314409938677909166at_nat A) B) bot_bo228742789529271731at_nat))) (forall ((A set_nat) (B set_nat) (C nat)) (let ((_let_1 (@ member_nat C))) (=> (@ (@ ord_less_eq_set_nat A) B) (=> (@ _let_1 A) (@ _let_1 B))))) (forall ((X produc3843707927480180839at_nat) (B set_Pr4329608150637261639at_nat) (A set_Pr4329608150637261639at_nat)) (=> (@ (@ member8757157785044589968at_nat X) B) (= (@ (@ minus_3314409938677909166at_nat (@ (@ insert9069300056098147895at_nat X) A)) B) (@ (@ minus_3314409938677909166at_nat A) B)))) (forall ((Xs list_P8527749157015355191n_assn) (Ys list_P8527749157015355191n_assn) (F4 (-> produc6575502325842934193n_assn Bool)) (G (-> produc6575502325842934193n_assn Bool))) (=> (= Xs Ys) (=> (forall ((X3 produc6575502325842934193n_assn)) (=> (@ (@ member7957490590177025114n_assn X3) (@ set_Pr1139785259514867910n_assn Ys)) (= (@ F4 X3) (@ G X3)))) (= (@ (@ list_e1087220904399170805n_assn F4) Xs) (@ (@ list_e1087220904399170805n_assn G) Ys))))) (forall ((L int) (K3 int) (Q6 int)) (=> (not (= L zero_zero_int)) (=> (= K3 (@ (@ times_times_int Q6) L)) (@ (@ (@ eucl_rel_int K3) L) (@ (@ product_Pair_int_int Q6) zero_zero_int))))) (forall ((X num) (Y num)) (=> (not (= X Y)) (=> (not (@ (@ ord_less_num X) Y)) (@ (@ ord_less_num Y) X)))) (forall ((S set_Pr1261947904930325089at_nat) (T3 set_Pr1261947904930325089at_nat)) (= (@ (@ sup_su6327502436637775413at_nat (@ (@ inf_in2572325071724192079at_nat S) T3)) T3) T3)) (forall ((A set_o) (X Bool)) (let ((_let_1 (@ (@ insert_o2 X) bot_bot_set_o))) (=> (@ (@ ord_less_eq_set_o A) _let_1) (or (= A _let_1) (= A bot_bot_set_o))))) (forall ((A set_nat) (B set_nat) (C2 set_nat)) (let ((_let_1 (@ sup_sup_set_nat A))) (= (@ (@ sup_sup_set_nat (@ _let_1 B)) C2) (@ _let_1 (@ (@ sup_sup_set_nat B) C2))))) (forall ((S set_Pr4329608150637261639at_nat) (R (-> produc3843707927480180839at_nat produc3843707927480180839at_nat Bool))) (=> (forall ((X3 produc3843707927480180839at_nat) (Y2 produc3843707927480180839at_nat)) (=> (@ (@ member8757157785044589968at_nat X3) S) (=> (@ (@ member8757157785044589968at_nat Y2) S) (=> (not (= X3 Y2)) (@ (@ R X3) Y2))))) (@ (@ pairwi3222497012029234898at_nat R) S))) (forall ((C rat) (B2 rat)) (= (@ (@ ord_less_rat C) (@ (@ times_times_rat C) B2)) (and (=> (@ (@ ord_less_eq_rat C) zero_zero_rat) (@ (@ ord_less_rat B2) one_one_rat)) (=> (@ (@ ord_less_eq_rat zero_zero_rat) C) (@ (@ ord_less_rat one_one_rat) B2))))) (forall ((X code_integer) (Y code_integer)) (=> (not (= X Y)) (=> (not (@ (@ ord_le6747313008572928689nteger X) Y)) (@ (@ ord_le6747313008572928689nteger Y) X)))) (forall ((B2 rat) (A2 rat) (C rat)) (= (= (@ (@ plus_plus_rat B2) A2) (@ (@ plus_plus_rat C) A2)) (= B2 C))) (forall ((X int) (Y nat) (Xs list_int) (Ys list_nat)) (=> (@ (@ member216504246829706758nt_nat (@ (@ product_Pair_int_nat X) Y)) (@ set_Pr6647972299459129970nt_nat (@ (@ zip_int_nat Xs) Ys))) (not (=> (@ (@ member_int X) 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Y) (=> _let_1 (not (=> (and (=> (not _let_2) (= Y (@ (@ gcd_gcd_nat Xa) (@ (@ modulo_modulo_nat X) Xa)))) (=> _let_2 (= Y X))) (not _let_1)))))))) (forall ((I nat) (Xs list_c) (J nat)) (let ((_let_1 (@ nth_c Xs))) (let ((_let_2 (@ size_size_list_c Xs))) (=> (@ (@ ord_less_nat I) _let_2) (=> (@ (@ ord_less_nat J) _let_2) (= (@ set_c2 (@ (@ (@ list_update_c (@ (@ (@ list_update_c Xs) I) (@ _let_1 J))) J) (@ _let_1 I))) (@ set_c2 Xs))))))) _let_120 (= ord_less_filter_nat (lambda ((X2 filter_nat) (Y5 filter_nat)) (and (@ (@ ord_le2510731241096832064er_nat X2) Y5) (not (= X2 Y5))))) (forall ((I nat) (J nat) (K3 nat) (L nat)) (=> (and (@ (@ ord_less_eq_nat K3) L) (@ (@ ord_less_eq_nat I) J)) (@ (@ ord_less_eq_nat (@ (@ plus_plus_nat I) K3)) (@ (@ plus_plus_nat J) L)))) (forall ((A set_Pr4329608150637261639at_nat)) (=> (forall ((X3 produc3843707927480180839at_nat)) (not (@ (@ member8757157785044589968at_nat X3) A))) (@ (@ ord_le1268244103169919719at_nat A) bot_bo228742789529271731at_nat))) (forall ((Xs list_int) (I nat) (J nat)) (let ((_let_1 (@ nth_int Xs))) (=> (@ (@ sorted_wrt_int ord_less_eq_int) Xs) (=> (@ (@ ord_less_eq_nat I) J) (=> (@ (@ ord_less_nat J) (@ size_size_list_int Xs)) (@ (@ ord_less_eq_int (@ _let_1 I)) (@ _let_1 J))))))) (forall ((L list_c) (Li list_d) (A (-> c d assn))) (=> (not (= (@ size_size_list_c L) (@ size_size_list_d Li))) (= (@ (@ (@ vEBT_L7968352277243653188sn_c_d A) L) Li) bot_bot_assn))) (forall ((Xs list_P8527749157015355191n_assn) (Ys list_P8527749157015355191n_assn) (R2 set_Pr8116311503512020807n_assn) (X produc6575502325842934193n_assn)) (let ((_let_1 (@ listre4270255209692100112n_assn R2))) (let ((_let_2 (@ cons_P2971678138204555879n_assn X))) (=> (@ (@ member3994142547374651152n_assn (@ (@ produc3014731801419794263n_assn Xs) Ys)) _let_1) (@ (@ member3994142547374651152n_assn (@ (@ produc3014731801419794263n_assn (@ _let_2 Xs)) (@ _let_2 Ys))) _let_1))))) (forall ((B set_Pr1261947904930325089at_nat) (C2 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_let_1 Z4))))) (= (@ _let_1 (@ (@ sup_su5525570899277871387at_nat Y) Z)) (@ (@ sup_su5525570899277871387at_nat (@ _let_1 Y)) (@ _let_1 Z)))))) (forall ((Ys list_P8527749157015355191n_assn) (R2 set_Pr8116311503512020807n_assn)) (not (@ (@ member3994142547374651152n_assn (@ (@ produc3014731801419794263n_assn nil_Pr5671120429643327159n_assn) Ys)) (@ lex_Pr7559194461235888923n_assn R2)))) (forall ((X nat) (X4 set_nat)) (=> (not (@ (@ member_nat X) X4)) (= (@ (@ minus_minus_set_nat X4) (@ (@ insert_nat2 X) bot_bot_set_nat)) X4))) (forall ((X assn) (Y assn) (Z assn)) (let ((_let_1 (@ inf_inf_assn X))) (let ((_let_2 (@ inf_inf_assn Y))) (= (@ _let_1 (@ _let_2 Z)) (@ _let_2 (@ _let_1 Z)))))) (forall ((Xs list_int) (Ys list_int)) (= (@ distinct_int (@ (@ union_int Xs) Ys)) (@ distinct_int Ys))) (forall ((X num) (Y num)) (=> (@ (@ ord_less_num X) Y) (not (@ (@ ord_less_num Y) X)))) (forall ((N nat)) (let ((_let_1 (@ power_power_nat (@ numeral_numeral_nat (@ bit0 one))))) (= (@ (@ minus_minus_nat 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(forall ((P (-> produc6575502325842934193n_assn nat assn)) (A2 produc6575502325842934193n_assn) (As2 list_P8527749157015355191n_assn) (C nat) (Cs list_nat)) (let ((_let_1 (@ vEBT_L4762835640886981758sn_nat P))) (= (@ (@ _let_1 (@ (@ cons_P2971678138204555879n_assn A2) As2)) (@ (@ cons_nat C) Cs)) (@ (@ times_times_assn (@ (@ P A2) C)) (@ (@ _let_1 As2) Cs))))) (forall ((A2 nat)) (@ (@ ord_less_eq_nat A2) A2)) (forall ((A2 assn) (X assn) (B2 assn)) (=> (@ (@ ord_less_eq_assn A2) X) (@ (@ ord_less_eq_assn (@ (@ inf_inf_assn A2) B2)) X))) (forall ((X nat) (Xs list_nat)) (@ (@ ord_less_eq_nat (@ size_size_list_nat (@ (@ removeAll_nat X) Xs))) (@ size_size_list_nat Xs))) (forall ((X21 int) (X222 list_int)) (= (@ set_int2 (@ (@ cons_int X21) X222)) (@ (@ insert_int2 X21) (@ set_int2 X222)))) (forall ((I rat) (J rat) (K3 rat) (L rat)) (=> (and (= K3 L) (@ (@ ord_less_rat I) J)) (@ (@ ord_less_rat (@ (@ plus_plus_rat I) K3)) (@ (@ plus_plus_rat J) L)))) (forall ((P (-> rat Bool)) (D rat) (Q 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member8757157785044589968at_nat (@ (@ produc2922128104949294807at_nat A2) B2)) (@ set_Pr3765526544606949372at_nat (@ (@ zip_se5600341670672612855at_nat Xs) Xs))) (and (@ (@ member2643936169264416010at_nat A2) (@ set_se5049602875457034614at_nat Xs)) (= A2 B2)))) (forall ((A set_nat)) (= (@ (@ inf_inf_set_nat A) A) A)) (forall ((Begin nat) (End nat)) (= (@ (@ (@ slice_7964966981652229398n_assn Begin) End) nil_Pr5671120429643327159n_assn) nil_Pr5671120429643327159n_assn)) _let_118 (forall ((X product_prod_nat_nat) (Xs list_P6011104703257516679at_nat)) (=> (not (@ (@ member8440522571783428010at_nat X) (@ set_Pr5648618587558075414at_nat Xs))) (= (@ (@ remove5766854097993331357at_nat X) Xs) Xs))) (forall ((A set_nat) (B set_nat)) (=> (@ (@ ord_less_eq_set_nat A) B) (= (@ (@ sup_sup_set_nat A) (@ (@ minus_minus_set_nat B) A)) B))) (forall ((A2 code_integer) (F4 (-> num code_integer)) (B2 num) (C num)) (let ((_let_1 (@ ord_le6747313008572928689nteger A2))) (=> (@ _let_1 (@ F4 B2)) (=> (@ (@ 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((X3 nat) (Y2 nat)) (=> (@ (@ member_nat X3) A) (=> (@ (@ member_nat Y2) A) (=> (not (= X3 Y2)) (or (@ (@ member8440522571783428010at_nat (@ (@ product_Pair_nat_nat Y2) X3)) R2) (@ (@ member8440522571783428010at_nat (@ (@ product_Pair_nat_nat X3) Y2)) R2)))))) (@ (@ total_on_nat A) R2))) (forall ((A2 nat) (B2 nat)) (let ((_let_1 (@ suc A2))) (=> (@ (@ ord_less_nat A2) B2) (= (@ (@ ord_min_nat _let_1) B2) _let_1)))) (forall ((A2 set_Pr1261947904930325089at_nat)) (=> (@ (@ ord_le3146513528884898305at_nat A2) bot_bo2099793752762293965at_nat) (= A2 bot_bo2099793752762293965at_nat))) (forall ((R2 set_Pr4329608150637261639at_nat) (X set_Pr1261947904930325089at_nat) (Y set_Pr1261947904930325089at_nat)) (=> (forall ((X3 set_Pr1261947904930325089at_nat)) (not (@ (@ member8757157785044589968at_nat (@ (@ produc2922128104949294807at_nat X3) X3)) (@ transi2703068831062848130at_nat R2)))) (=> (@ (@ member8757157785044589968at_nat (@ (@ produc2922128104949294807at_nat X) Y)) R2) (not (= X Y))))) (forall ((F4 (-> int int nat))) (= (@ (@ (@ zipf_int_int_nat F4) nil_int) nil_int) nil_nat)) (forall ((A2 set_nat) (B2 set_nat)) (=> (forall ((X3 nat)) (let ((_let_1 (@ member_nat X3))) (=> (@ _let_1 A2) (not (@ _let_1 B2))))) (= (@ (@ inf_inf_set_nat A2) B2) bot_bot_set_nat))) (forall ((X product_prod_nat_nat) (Xs list_P6011104703257516679at_nat)) (=> (@ (@ member8440522571783428010at_nat X) (@ set_Pr5648618587558075414at_nat Xs)) (@ (@ ord_less_nat (@ size_s5460976970255530739at_nat (@ (@ remove3673390508374433037at_nat X) Xs))) (@ size_s5460976970255530739at_nat Xs)))) (forall ((X (-> produc3658429121746597890et_nat Bool)) (Xs list_P7985473006766602707_nat_o)) (let ((_let_1 (@ member6576561426505652726_nat_o X))) (=> (@ _let_1 (@ set_Pr400311997697478754_nat_o (@ butlas8287983287669047583_nat_o Xs))) (@ _let_1 (@ set_Pr400311997697478754_nat_o Xs))))) (forall ((A2 (-> produc3658429121746597890et_nat Bool)) (B2 produc3925858234332021118et_nat) (A7 (-> produc3658429121746597890et_nat Bool)) (B6 produc3925858234332021118et_nat)) (= (= (@ (@ produc2245416461498447860et_nat A2) B2) (@ (@ produc2245416461498447860et_nat A7) B6)) (and (= B2 B6) (= A2 A7)))) (forall ((X rat) (Y rat)) (= (@ (@ minus_minus_rat (@ (@ times_times_rat X) X)) (@ (@ times_times_rat Y) Y)) (@ (@ times_times_rat (@ (@ plus_plus_rat X) Y)) (@ (@ minus_minus_rat X) Y)))) (forall ((A2 rat) (M2 nat) (N nat)) (let ((_let_1 (@ power_power_rat A2))) (=> (@ (@ ord_less_rat one_one_rat) A2) (= (= (@ _let_1 M2) (@ _let_1 N)) (= M2 N))))) (forall ((B2 assn) (C assn) (A2 assn)) (= (@ (@ ord_less_eq_assn (@ (@ sup_sup_assn B2) C)) A2) (and (@ (@ ord_less_eq_assn C) A2) (@ (@ ord_less_eq_assn B2) A2)))) (forall ((A2 Bool) (A set_o) (B2 Bool) (B set_o)) (=> (not (@ (@ member_o A2) A)) (=> (not (@ (@ member_o B2) B)) (= (= (@ (@ insert_o2 A2) A) (@ (@ insert_o2 B2) B)) (and (=> (= A2 B2) (= A B)) (=> (= A2 (not B2)) (exists ((C3 set_o)) (and (= A (@ (@ insert_o2 B2) C3)) (not (@ (@ member_o B2) C3)) (not (@ (@ 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Q6))))) (forall ((Xs list_c) (Ys list_d)) (=> (= (@ size_size_list_c Xs) (@ size_size_list_d Ys)) (= (@ (@ zip_c_d (@ rev_c Xs)) (@ rev_d Ys)) (@ rev_Product_prod_c_d (@ (@ zip_c_d Xs) Ys))))) (forall ((I int) (J int) (K3 int)) (let ((_let_1 (@ upto I))) (=> (@ (@ ord_less_eq_int I) J) (=> (@ (@ ord_less_eq_int J) K3) (= (@ _let_1 K3) (@ (@ append_int (@ _let_1 (@ (@ minus_minus_int J) one_one_int))) (@ (@ upto J) K3))))))) (forall ((A2 code_integer)) (= (@ (@ ord_le6747313008572928689nteger (@ (@ plus_p5714425477246183910nteger A2) A2)) zero_z3403309356797280102nteger) (@ (@ ord_le6747313008572928689nteger A2) zero_z3403309356797280102nteger))) (forall ((C produc3843707927480180839at_nat) (A set_Pr4329608150637261639at_nat) (B set_Pr4329608150637261639at_nat)) (let ((_let_1 (@ member8757157785044589968at_nat C))) (=> (@ _let_1 (@ (@ inf_in7913087082777306421at_nat A) B)) (@ _let_1 B)))) (forall ((B2 assn) (A2 assn) (C assn)) (let ((_let_1 (@ sup_sup_assn B2))) (let ((_let_2 (@ 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(= Xa nil_nat))) (let ((_let_3 (= Xb nil_int))) (=> (= (@ (@ (@ vEBT_L8298612041380073281at_int X) Xa) Xb) Y) (=> (=> _let_2 (=> _let_3 (not (= Y one_one_assn)))) (=> (forall ((A4 nat) (As list_nat)) (=> (= Xa (@ (@ cons_nat A4) As)) (forall ((C4 int) (Cs2 list_int)) (=> (= Xb (@ (@ cons_int C4) Cs2)) (not (= Y (@ (@ times_times_assn (@ (@ X A4) C4)) (@ (@ (@ vEBT_L8298612041380073281at_int X) As) Cs2)))))))) (=> (=> (exists ((V3 nat) (Va list_nat)) (= Xa (@ (@ cons_nat V3) Va))) (=> _let_3 _let_1)) (not (=> _let_2 (=> (exists ((V3 int) (Va list_int)) (= Xb (@ (@ cons_int V3) Va))) _let_1))))))))))) (forall ((A2 nat) (B2 nat)) (=> (@ (@ ord_less_nat A2) zero_zero_nat) (=> (@ (@ ord_less_nat B2) zero_zero_nat) (@ (@ ord_less_nat (@ (@ plus_plus_nat A2) B2)) zero_zero_nat)))) (forall ((A2 int)) (= (@ (@ minus_minus_int A2) A2) zero_zero_int)) (forall ((A2 code_integer) (F4 (-> int code_integer)) (B2 int) (C int)) (let ((_let_1 (@ ord_le6747313008572928689nteger A2))) (=> (@ _let_1 (@ F4 B2)) (=> (@ (@ ord_less_int B2) C) (=> (forall ((X3 int) (Y2 int)) (=> (@ (@ ord_less_int X3) Y2) (@ (@ ord_le6747313008572928689nteger (@ F4 X3)) (@ F4 Y2)))) (@ _let_1 (@ F4 C))))))) (forall ((X set_Pr4329608150637261639at_nat)) (= (@ (@ inf_in7913087082777306421at_nat X) bot_bo228742789529271731at_nat) bot_bo228742789529271731at_nat)) (forall ((X set_nat) (Y set_nat) (Z set_nat)) (let ((_let_1 (@ ord_less_set_nat X))) (=> (@ _let_1 Y) (=> (@ (@ ord_less_eq_set_nat Y) Z) (@ _let_1 Z))))) (forall ((A2 int)) (= (@ (@ minus_minus_int A2) zero_zero_int) A2)) (forall ((X code_integer) (Y code_integer)) (let ((_let_1 (@ ord_le3102999989581377725nteger zero_z3403309356797280102nteger))) (=> (@ _let_1 X) (=> (@ _let_1 Y) (= (= (@ (@ plus_p5714425477246183910nteger X) Y) zero_z3403309356797280102nteger) (and (= X zero_z3403309356797280102nteger) (= Y zero_z3403309356797280102nteger))))))) (forall ((X set_nat) (Y set_nat) (Z set_nat)) (let ((_let_1 (@ ord_less_eq_set_nat X))) (= (@ _let_1 (@ (@ inf_inf_set_nat Y) Z)) (and (@ _let_1 Y) (@ _let_1 Z))))) (forall ((X (-> produc3658429121746597890et_nat Bool)) (Xs list_P7985473006766602707_nat_o)) (=> (not (@ (@ member6576561426505652726_nat_o X) (@ set_Pr400311997697478754_nat_o Xs))) (= (@ (@ insert8021100735160035049_nat_o X) Xs) (@ (@ cons_P6219271836124797827_nat_o X) Xs)))) (forall ((A2 list_nat) (B2 list_c) (A7 list_nat) (B6 list_c)) (=> (= (@ size_size_list_nat A2) (@ size_size_list_c B2)) (=> (= (@ size_size_list_nat A7) (@ size_size_list_c B6)) (= (= (@ (@ zip_nat_c A2) B2) (@ (@ zip_nat_c A7) B6)) (and (= A2 A7) (= B2 B6)))))) (= upt (lambda ((I4 nat) (J2 nat)) (@ (@ (@ if_list_nat (@ (@ ord_less_nat I4) J2)) (@ (@ cons_nat I4) (@ (@ upt (@ suc I4)) J2))) nil_nat))) (forall ((X set_nat) (Y set_nat)) (= (@ (@ inf_inf_set_nat X) (@ (@ sup_sup_set_nat X) Y)) X)) (forall ((Y nat) (X nat)) (=> (@ (@ ord_less_eq_nat Y) X) (not (@ (@ ord_less_nat X) Y)))) (forall ((A set_Pr1261947904930325089at_nat) (B set_Pr1261947904930325089at_nat) (C2 set_Pr1261947904930325089at_nat)) (= (@ (@ sup_su6327502436637775413at_nat (@ (@ sup_su6327502436637775413at_nat (@ (@ inf_in2572325071724192079at_nat A) B)) (@ (@ inf_in2572325071724192079at_nat B) C2))) (@ (@ inf_in2572325071724192079at_nat C2) A)) (@ (@ inf_in2572325071724192079at_nat (@ (@ inf_in2572325071724192079at_nat (@ (@ sup_su6327502436637775413at_nat A) B)) (@ (@ sup_su6327502436637775413at_nat B) C2))) (@ (@ sup_su6327502436637775413at_nat C2) A)))) (forall ((X set_o)) (= (@ (@ sup_sup_set_o X) bot_bot_set_o) X)) (forall ((X produc3843707927480180839at_nat) (Xs list_P5464809261938338413at_nat) (N nat)) (=> (not (@ (@ member8757157785044589968at_nat X) (@ set_Pr3765526544606949372at_nat Xs))) (=> (@ (@ ord_less_eq_nat N) (@ size_s1588839187904960729at_nat Xs)) (= (= (@ (@ nth_Pr1239524528086697198at_nat (@ (@ cons_P3940603068885512221at_nat X) Xs)) N) X) (= N zero_zero_nat))))) (forall ((A2 int)) (let ((_let_1 (@ ord_less_int zero_zero_int))) (= (@ _let_1 (@ (@ plus_plus_int A2) A2)) (@ _let_1 A2)))) (forall ((Xs list_P8527749157015355191n_assn)) (= (= Xs nil_Pr5671120429643327159n_assn) (@ null_P7596217980778516671n_assn Xs))) _let_116 (forall ((X (-> produc3658429121746597890et_nat Bool)) (Xa (-> produc3658429121746597890et_nat Bool)) (Xb produc3658429121746597890et_nat)) (=> (not (@ (@ (@ wand_raw X) Xa) Xb)) (=> (@ (@ accp_P1862375125659990705et_nat wand_raw_rel) (@ (@ produc2245416461498447860et_nat X) (@ (@ produc5001842942810119800et_nat Xa) Xb))) (not (forall ((H heap_e7401611519738050253t_unit) (As set_nat)) (let ((_let_1 (@ (@ produc7507926704131184380et_nat H) As))) (=> (= Xb _let_1) (=> (@ (@ accp_P1862375125659990705et_nat wand_raw_rel) (@ (@ produc2245416461498447860et_nat X) (@ (@ produc5001842942810119800et_nat Xa) _let_1))) (and (forall ((H5 heap_e7401611519738050253t_unit) (As4 set_nat)) (let ((_let_1 (@ produc7507926704131184380et_nat H5))) (=> (and (= (@ (@ inf_inf_set_nat As) As4) bot_bot_set_nat) (@ (@ (@ relH As) H) H5) (@ in_range (@ _let_1 As)) (@ X (@ _let_1 As4))) (@ Xa (@ _let_1 (@ (@ sup_sup_set_nat As) As4)))))) (@ in_range _let_1)))))))))) (forall ((A2 int) (B2 int)) (let ((_let_1 (@ ord_less_int zero_zero_int))) (=> (@ _let_1 (@ (@ times_times_int A2) B2)) (=> (@ _let_1 A2) (@ _let_1 B2))))) (forall ((S set_nat) (T3 set_nat)) (= (@ (@ sup_sup_set_nat S) (@ (@ inf_inf_set_nat S) T3)) S)) (forall ((D2 int) (P3 (-> int Bool)) (P (-> int Bool))) (=> (@ (@ ord_less_int zero_zero_int) D2) (=> (forall ((X3 int) (K int)) (= (@ P3 X3) (@ P3 (@ (@ minus_minus_int X3) (@ (@ times_times_int K) D2))))) (=> (exists ((Z3 int)) (forall ((X3 int)) (=> (@ (@ ord_less_int Z3) X3) (= (@ P X3) (@ P3 X3))))) (=> (exists ((X_12 int)) (@ P3 X_12)) (exists ((X_1 int)) (@ P X_1))))))) (forall ((A2 code_integer)) (let ((_let_1 (@ ord_le3102999989581377725nteger zero_z3403309356797280102nteger))) (= (@ _let_1 (@ (@ plus_p5714425477246183910nteger A2) A2)) (@ _let_1 A2)))) (forall ((E nat) (A2 list_nat)) (=> (@ (@ member_nat E) (@ set_nat2 A2)) (=> (forall ((Z22 list_nat)) (not (= A2 (@ (@ cons_nat E) Z22)))) (not (forall ((Z1 nat) (Z22 list_nat)) (=> (= A2 (@ (@ cons_nat Z1) Z22)) (not (@ (@ member_nat E) (@ set_nat2 Z22))))))))) (forall ((X code_integer) (Y code_integer) (P Bool)) (=> (@ (@ ord_le6747313008572928689nteger X) Y) (=> (@ (@ ord_le6747313008572928689nteger Y) X) P))) (forall ((Y int) (Ys list_int) (Xs list_nat) (R2 set_Pr3448869479623346877nt_nat)) (=> (@ (@ member9189046780804443046st_nat (@ (@ produc4542114716404682293st_nat (@ (@ cons_int Y) Ys)) Xs)) (@ listrel_int_nat R2)) (not (forall ((Y2 nat) (Ys5 list_nat)) (=> (= Xs (@ (@ cons_nat Y2) Ys5)) (=> (@ (@ member216504246829706758nt_nat (@ (@ product_Pair_int_nat Y) Y2)) R2) (not (@ (@ member9189046780804443046st_nat (@ (@ produc4542114716404682293st_nat Ys) Ys5)) (@ listrel_int_nat R2))))))))) (forall ((X set_Pr1261947904930325089at_nat) (Y set_Pr1261947904930325089at_nat)) (= (= bot_bo2099793752762293965at_nat (@ (@ sup_su6327502436637775413at_nat X) Y)) (and (= Y bot_bo2099793752762293965at_nat) (= X bot_bo2099793752762293965at_nat)))) (forall ((M2 nat) (N nat)) (let ((_let_1 (@ ord_less_nat zero_zero_nat))) (=> (@ _let_1 M2) (=> (@ _let_1 N) (@ _let_1 (@ (@ gcd_lcm_nat M2) N)))))) (forall ((X set_nat) (Y set_nat)) (=> (not (@ (@ ord_less_set_nat X) Y)) (= (@ (@ ord_less_eq_set_nat X) Y) (= X Y)))) (forall ((I nat) (V2 int)) (= (@ (@ (@ list_update_int nil_int) I) V2) nil_int)) (= (@ quotient_of zero_zero_rat) _let_4) (forall ((F4 (-> nat nat)) (N nat) (N6 nat)) (=> (forall ((N5 nat)) (@ (@ ord_less_nat (@ F4 N5)) (@ F4 (@ suc N5)))) (=> (@ (@ ord_less_nat N) N6) (@ (@ ord_less_nat (@ F4 N)) (@ F4 N6))))) _let_115 (forall ((A2 int) (B2 int)) (= (@ (@ ord_less_eq_int zero_zero_int) (@ (@ minus_minus_int A2) B2)) (@ (@ ord_less_eq_int B2) A2))) _let_114 (forall ((F4 (-> nat nat)) (I nat) (J nat)) (=> (forall ((I5 nat) (J3 nat)) (=> (@ (@ ord_less_nat I5) J3) (@ (@ ord_less_nat (@ F4 I5)) (@ F4 J3)))) (=> (@ (@ ord_less_eq_nat I) J) (@ (@ ord_less_eq_nat (@ F4 I)) (@ F4 J))))) (forall ((Xs list_int)) (= (@ (@ sorted_wrt_int ord_less_eq_int) (@ rev_int Xs)) (forall ((I4 nat) (J2 nat)) (let ((_let_1 (@ nth_int Xs))) (=> (@ (@ ord_less_eq_nat I4) J2) (=> (@ (@ ord_less_nat J2) (@ size_size_list_int Xs)) (@ (@ ord_less_eq_int (@ _let_1 J2)) (@ _let_1 I4)))))))) (forall ((B2 set_nat) (A2 set_nat) (C set_nat)) (=> (@ (@ ord_less_set_nat B2) A2) (=> (@ (@ ord_less_eq_set_nat C) B2) (@ (@ ord_less_set_nat C) A2)))) (forall ((P assn) (B2 Bool) (Q assn)) (let ((_let_1 (@ pure_assn B2))) (= (@ (@ inf_inf_assn (@ (@ times_times_assn P) _let_1)) Q) (@ (@ times_times_assn (@ (@ inf_inf_assn P) Q)) _let_1)))) (forall ((X list_int) (Y list_int)) (= (@ (@ (@ if_list_int false) X) Y) Y)) (forall ((A set_Pr1261947904930325089at_nat) (B set_Pr1261947904930325089at_nat) (C2 set_Pr1261947904930325089at_nat)) (= (@ (@ inf_in2572325071724192079at_nat (@ (@ minus_1356011639430497352at_nat A) B)) C2) (@ (@ minus_1356011639430497352at_nat (@ (@ inf_in2572325071724192079at_nat A) C2)) (@ (@ inf_in2572325071724192079at_nat B) C2)))) (forall ((X21 nat) (X222 list_nat)) (= (@ set_nat2 (@ (@ cons_nat X21) X222)) (@ (@ insert_nat2 X21) (@ set_nat2 X222)))) (forall ((X assn) (Y assn)) (@ (@ ord_less_eq_assn (@ (@ inf_inf_assn X) Y)) Y)) (forall ((B2 int) (A2 int)) (@ (@ ord_less_eq_int B2) (@ (@ sup_sup_int A2) B2))) (forall ((A2 int) (B2 int)) (= (@ (@ ord_less_eq_int (@ (@ plus_plus_int A2) B2)) B2) (@ (@ ord_less_eq_int A2) zero_zero_int))) (forall ((X nat) (Xs list_nat)) (=> (not (@ (@ member_nat X) (@ set_nat2 Xs))) (= (@ (@ count_list_nat Xs) X) zero_zero_nat))) (forall ((From nat) (To nat) (Xs list_c)) (=> (@ (@ ord_less_eq_nat From) To) (=> (@ (@ ord_less_eq_nat To) (@ size_size_list_c Xs)) (= (@ size_size_list_c (@ (@ (@ slice_c From) To) Xs)) (@ (@ minus_minus_nat To) From))))) (forall ((I nat) (J nat) (K3 nat) (L nat)) (=> (and (@ (@ ord_less_nat I) J) (@ (@ ord_less_eq_nat K3) L)) (@ (@ ord_less_nat (@ (@ plus_plus_nat I) K3)) (@ (@ plus_plus_nat J) L)))) (forall ((A2 rat)) (= (@ (@ times_times_rat A2) zero_zero_rat) zero_zero_rat)) (forall ((A2 multis2468970476368604999at_nat) (B2 multis2468970476368604999at_nat) (C multis2468970476368604999at_nat)) (let ((_let_1 (@ plus_p7104986032573967614at_nat A2))) (= (@ (@ plus_p7104986032573967614at_nat (@ _let_1 B2)) C) (@ _let_1 (@ (@ plus_p7104986032573967614at_nat B2) C))))) (forall ((X list_nat) (Y nat)) (=> (= (@ nat_list_encode X) Y) (=> (=> (= X nil_nat) (not (= Y zero_zero_nat))) (not (forall ((X3 nat) (Xs2 list_nat)) (=> (= X (@ (@ cons_nat X3) Xs2)) (not (= Y (@ suc (@ nat_prod_encode (@ (@ product_Pair_nat_nat X3) (@ nat_list_encode Xs2)))))))))))) (forall ((Y produc2732055786443039994et_nat)) (not (forall ((A4 (-> produc3658429121746597890et_nat Bool)) (B4 (-> produc3658429121746597890et_nat Bool)) (C4 produc3658429121746597890et_nat)) (not (= Y (@ (@ produc2245416461498447860et_nat A4) (@ (@ produc5001842942810119800et_nat B4) C4))))))) (forall ((X nat) (Xs list_nat)) (let ((_let_1 (@ size_size_list_nat Xs))) (let ((_let_2 (@ size_size_list_nat (@ (@ remove1_nat X) Xs)))) (let ((_let_3 (@ (@ member_nat X) (@ set_nat2 Xs)))) (and (=> (not _let_3) (= _let_2 _let_1)) (=> _let_3 (= _let_2 (@ (@ minus_minus_nat _let_1) one_one_nat)))))))) (= (@ set_ord_atMost_nat zero_zero_nat) (@ (@ insert_nat2 zero_zero_nat) bot_bot_set_nat)) (forall ((N nat) (P (-> nat Bool))) (= (forall ((I4 nat)) (=> (@ (@ ord_less_nat I4) (@ suc N)) (@ P I4))) (and (forall ((I4 nat)) (=> (@ (@ ord_less_nat I4) N) (@ P I4))) (@ P N)))) (forall ((B set_Pr1261947904930325089at_nat) (A2 product_prod_nat_nat)) (@ (@ ord_le3146513528884898305at_nat B) (@ (@ insert8211810215607154385at_nat A2) B))) (forall ((Y code_integer) (X code_integer)) (=> (@ (@ ord_le3102999989581377725nteger Y) X) (not (@ (@ ord_le6747313008572928689nteger X) Y)))) (not (@ _let_66 one_one_nat)) (forall ((X produc3843707927480180839at_nat) (Xs list_P5464809261938338413at_nat)) (= (@ (@ insert9069300056098147895at_nat X) (@ coset_5307619257043544794at_nat Xs)) (@ coset_5307619257043544794at_nat (@ (@ remove4908499291543849587at_nat X) Xs)))) (forall ((A multis2468970476368604999at_nat) (K3 multis2468970476368604999at_nat) (A2 multis2468970476368604999at_nat) (B2 multis2468970476368604999at_nat)) (let ((_let_1 (@ plus_p7104986032573967614at_nat K3))) (=> (= A (@ _let_1 A2)) (= (@ (@ plus_p7104986032573967614at_nat A) B2) (@ _let_1 (@ (@ plus_p7104986032573967614at_nat A2) B2)))))) (forall ((A set_Pr1261947904930325089at_nat) (B set_Pr1261947904930325089at_nat) (B2 product_prod_nat_nat)) (let ((_let_1 (@ ord_le3146513528884898305at_nat A))) (=> (@ _let_1 B) (@ _let_1 (@ (@ insert8211810215607154385at_nat B2) B))))) (forall ((A2 set_Pr1261947904930325089at_nat) (B2 set_Pr1261947904930325089at_nat)) (=> (@ (@ ord_le7866589430770878221at_nat A2) B2) (= (@ (@ inf_in2572325071724192079at_nat A2) B2) A2))) (forall ((A set_nat) (B set_nat)) (= (= (@ (@ minus_minus_set_nat A) B) bot_bot_set_nat) (@ (@ ord_less_eq_set_nat A) B))) (forall ((X assn) (Y assn) (Z assn)) (let ((_let_1 (@ sup_sup_assn X))) (= (@ (@ sup_sup_assn (@ _let_1 Y)) Z) (@ _let_1 (@ (@ sup_sup_assn Y) Z))))) (= inf_inf_assn (lambda ((X2 assn) (Y5 assn)) (@ (@ inf_inf_assn Y5) X2))) (forall ((M2 nat) (N nat)) (= (@ tl_nat (@ (@ upt M2) N)) (@ (@ upt (@ suc M2)) N))) (forall ((X set_int) (Y set_int)) (= (= (@ (@ minus_minus_set_int X) Y) bot_bot_set_int) (@ (@ ord_less_eq_set_int X) Y))) (forall ((A2 num) (B2 num)) (=> (@ (@ ord_less_num A2) B2) (not (@ (@ ord_less_num B2) A2)))) (forall ((L list_Code_integer) (I nat) (J nat)) (let ((_let_1 (@ nth_Code_integer L))) (=> (@ (@ sorted710888440204495920nteger ord_le3102999989581377725nteger) L) (=> (@ distin1543349897113766820nteger L) (=> (@ (@ ord_less_nat I) J) (=> (@ (@ ord_less_nat J) (@ size_s3445333598471063425nteger L)) (@ (@ ord_le6747313008572928689nteger (@ _let_1 I)) (@ _let_1 J)))))))) (forall ((C code_integer) (A2 code_integer) (B2 code_integer)) (let ((_let_1 (@ times_3573771949741848930nteger C))) (=> (@ (@ ord_le6747313008572928689nteger C) zero_z3403309356797280102nteger) (= (@ (@ ord_le3102999989581377725nteger (@ _let_1 A2)) (@ _let_1 B2)) (@ (@ ord_le3102999989581377725nteger B2) A2))))) (forall ((Y produc2285326912895808259nt_int)) (not (forall ((A4 (-> produc8551481072490612790e_term option6357759511663192854e_term)) (B4 int) (C4 int)) (not (= Y (@ (@ produc5700946648718959541nt_int A4) (@ (@ product_Pair_int_int B4) C4))))))) (forall ((P (-> produc3658429121746597890et_nat Bool)) (As2 set_nat) (H2 heap_e7401611519738050253t_unit) (H4 heap_e7401611519738050253t_unit)) (let ((_let_1 (@ (@ produc7507926704131184380et_nat H4) As2))) (=> (@ proper P) (=> (@ (@ (@ relH As2) H2) H4) (=> (@ in_range _let_1) (= (@ P (@ (@ produc7507926704131184380et_nat H2) As2)) (@ P _let_1))))))) (forall ((X int) (Xs list_int) (Y nat) (Ys list_nat)) (= (@ (@ zip_int_nat (@ (@ cons_int X) Xs)) (@ (@ cons_nat Y) Ys)) (@ (@ cons_P7512249878480867347nt_nat (@ (@ product_Pair_int_nat X) Y)) (@ (@ zip_int_nat Xs) Ys)))) (forall ((A2 rat)) (= (= zero_zero_rat (@ (@ plus_plus_rat A2) A2)) (= A2 zero_zero_rat))) (forall ((M2 nat) (N nat)) (= (@ (@ ord_less_nat zero_zero_nat) (@ (@ modulo_modulo_nat M2) N)) (not (@ (@ dvd_dvd_nat N) M2)))) (forall ((B2 num) (A2 num)) (=> (@ (@ ord_less_num B2) A2) (not (@ (@ ord_less_num A2) B2)))) (forall ((Xs list_int) (N nat) (X int)) (=> (@ distinct_int Xs) (=> (@ (@ ord_less_nat N) (@ size_size_list_int Xs)) (= (@ set_int2 (@ (@ (@ list_update_int Xs) N) X)) (@ (@ insert_int2 X) (@ (@ minus_minus_set_int (@ set_int2 Xs)) (@ (@ insert_int2 (@ (@ nth_int Xs) N)) bot_bot_set_int))))))) (forall ((Y int) (Ys list_int) (Xs list_P8527749157015355191n_assn) (R2 set_Pr3255386646789011632n_assn)) (=> (@ (@ member490958779117458567n_assn (@ (@ produc4510294837168919970n_assn (@ (@ cons_int Y) Ys)) Xs)) (@ listre4888949683985722578n_assn R2)) (not (forall ((Y2 produc6575502325842934193n_assn) (Ys5 list_P8527749157015355191n_assn)) (=> (= Xs (@ (@ cons_P2971678138204555879n_assn Y2) Ys5)) (=> (@ (@ member241480614033477777n_assn (@ (@ produc3313821056773121708n_assn Y) Y2)) R2) (not (@ (@ member490958779117458567n_assn (@ (@ produc4510294837168919970n_assn Ys) Ys5)) (@ listre4888949683985722578n_assn R2))))))))) (forall ((X nat) (Xa nat) (Y product_prod_nat_nat)) (let ((_let_1 (@ (@ ord_less_eq_nat Xa) X))) (let ((_let_2 (@ suc X))) (=> (= (@ (@ nat_prod_decode_aux X) Xa) Y) (and (=> (not _let_1) (= Y (@ (@ nat_prod_decode_aux _let_2) (@ (@ minus_minus_nat Xa) _let_2)))) (=> _let_1 (= Y (@ (@ product_Pair_nat_nat Xa) (@ (@ minus_minus_nat X) Xa))))))))) (forall ((Xs list_nat) (Ys list_nat) (R2 set_Pr1261947904930325089at_nat) (X nat)) (let ((_let_1 (@ listrel1_nat R2))) (let ((_let_2 (@ cons_nat X))) (=> (@ (@ member7340969449405702474st_nat (@ (@ produc2694037385005941721st_nat Xs) Ys)) _let_1) (@ (@ member7340969449405702474st_nat (@ (@ produc2694037385005941721st_nat (@ _let_2 Xs)) (@ _let_2 Ys))) _let_1))))) (forall ((A2 int) (M2 nat) (N nat)) (let ((_let_1 (@ power_power_int A2))) (= (@ _let_1 (@ (@ plus_plus_nat M2) N)) (@ (@ times_times_int (@ _let_1 M2)) (@ _let_1 N))))) (forall ((X set_Pr4329608150637261639at_nat)) (= (@ (@ sup_su5525570899277871387at_nat X) bot_bo228742789529271731at_nat) X)) _let_113 (forall ((X num) (Y num)) (= (not (@ (@ ord_less_num X) Y)) (@ (@ ord_less_eq_num Y) X))) (= (@ comple7806235888213564991et_nat (@ (@ image_nat_set_nat set_or1210151606488870762an_nat) top_top_set_nat)) bot_bot_set_nat) (forall ((A set_int)) (=> (forall ((Y2 int)) (not (@ (@ member_int Y2) A))) (= A bot_bot_set_int))) (forall ((A set_nat) (C2 set_nat) (B set_nat) (D set_nat)) (=> (@ (@ ord_less_eq_set_nat A) C2) (=> (@ (@ ord_less_eq_set_nat B) D) (@ (@ ord_less_eq_set_nat (@ (@ inf_inf_set_nat A) B)) (@ (@ inf_inf_set_nat C2) D))))) _let_112 (forall ((X int) (A set_int) (B set_int)) (let ((_let_1 (@ insert_int2 X))) (let ((_let_2 (@ member_int X))) (=> (not (@ _let_2 A)) (=> (not (@ _let_2 B)) (= (= (@ _let_1 A) (@ _let_1 B)) (= A B))))))) (forall ((X nat) (Xs list_nat)) (=> (not (@ (@ member_nat X) (@ set_nat2 Xs))) (= (@ (@ remove1_nat X) Xs) Xs))) (forall ((I nat) (L list_c) (X c) (Y c)) (let ((_let_1 (@ member_c X))) (=> (@ (@ ord_less_nat I) (@ size_size_list_c L)) (= (@ _let_1 (@ set_c2 (@ (@ (@ list_update_c L) I) Y))) (or (and (forall ((Y5 c)) (@ (@ member_c X) (@ set_c2 (@ (@ (@ list_update_c L) I) Y5)))) (@ _let_1 (@ set_c2 L))) (= X Y)))))) (forall ((C product_prod_nat_nat) (A set_Pr1261947904930325089at_nat) (B set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ member8440522571783428010at_nat C))) (= (@ _let_1 (@ (@ minus_1356011639430497352at_nat A) B)) (and (not (@ _let_1 B)) (@ _let_1 A))))) (forall ((B2 Bool) (A2 Bool) (A set_o)) (let ((_let_1 (@ (@ insert_o2 B2) bot_bot_set_o))) (= (= _let_1 (@ (@ insert_o2 A2) A)) (and (@ (@ ord_less_eq_set_o A) _let_1) (= A2 B2))))) (forall ((P (-> nat int assn)) (A2 nat) (As2 list_nat) (C int) (Cs list_int)) (let ((_let_1 (@ vEBT_L8298612041380073281at_int P))) (= (@ (@ _let_1 (@ (@ cons_nat A2) As2)) (@ (@ cons_int C) Cs)) (@ (@ times_times_assn (@ (@ P A2) C)) (@ (@ _let_1 As2) Cs))))) (forall ((I nat) (K3 nat) (N nat) (J nat)) (let ((_let_1 (@ (@ ord_less_eq_nat N) (@ (@ plus_plus_nat J) K3)))) (let ((_let_2 (@ (@ ord_less_eq_nat (@ (@ plus_plus_nat I) K3)) N))) (=> _let_2 (=> _let_1 (=> _let_2 (=> _let_1 (@ (@ ord_less_eq_nat (@ (@ minus_minus_nat N) K3)) J)))))))) (forall ((I nat) (M2 nat)) (@ (@ ord_less_nat I) (@ suc (@ (@ plus_plus_nat I) M2)))) (= ord_less_nat (lambda ((M nat) (N2 nat)) (exists ((K4 nat)) (= N2 (@ suc (@ (@ plus_plus_nat M) K4)))))) (= (@ butlast_nat nil_nat) nil_nat) (forall ((X filter_nat) (Y filter_nat) (Z filter_nat)) (let ((_let_1 (@ sup_sup_filter_nat X))) (@ (@ ord_le2510731241096832064er_nat (@ _let_1 (@ (@ inf_inf_filter_nat Y) Z))) (@ (@ inf_inf_filter_nat (@ _let_1 Y)) (@ _let_1 Z))))) (forall ((X nat)) (= (@ (@ ord_min_nat bot_bot_nat) X) bot_bot_nat)) (forall ((C rat) (A2 rat) (B2 rat)) (let ((_let_1 (@ times_times_rat C))) (=> (@ (@ ord_less_eq_rat (@ _let_1 A2)) (@ _let_1 B2)) (=> (@ (@ ord_less_rat zero_zero_rat) C) (@ (@ ord_less_eq_rat A2) B2))))) (forall ((Xs list_nat) (Ys list_nat) (Zs list_int) (Ws list_c) (P (-> list_nat list_nat list_int list_c Bool))) (let ((_let_1 (@ size_size_list_int Zs))) (let ((_let_2 (@ size_size_list_nat Ys))) (=> (= (@ size_size_list_nat Xs) _let_2) (=> (= _let_2 _let_1) (=> (= _let_1 (@ size_size_list_c Ws)) (=> (@ (@ (@ (@ P nil_nat) nil_nat) nil_int) nil_c) (=> (forall ((X3 nat) (Xs2 list_nat) (Y2 nat) (Ys5 list_nat) (Z4 int) (Zs2 list_int) (W3 c) (Ws2 list_c)) (let ((_let_1 (@ size_size_list_int Zs2))) (let ((_let_2 (@ size_size_list_nat Ys5))) (=> (= (@ size_size_list_nat Xs2) _let_2) (=> (= _let_2 _let_1) (=> (= _let_1 (@ size_size_list_c Ws2)) (=> (@ (@ (@ (@ P Xs2) Ys5) Zs2) Ws2) (@ (@ (@ (@ P (@ (@ cons_nat X3) Xs2)) (@ (@ cons_nat Y2) Ys5)) (@ (@ cons_int Z4) Zs2)) (@ (@ cons_c W3) Ws2))))))))) (@ (@ (@ (@ P Xs) Ys) Zs) Ws))))))))) (forall ((Xs list_c) (P (-> c Bool))) (= (forall ((X2 c)) (=> (@ (@ member_c X2) (@ set_c2 Xs)) (@ P X2))) (forall ((I4 nat)) (=> (@ (@ ord_less_nat I4) (@ size_size_list_c Xs)) (@ P (@ (@ nth_c Xs) I4)))))) (forall ((Y assn) (Z assn) (X assn)) (= (@ (@ inf_inf_assn (@ (@ sup_sup_assn Y) Z)) X) (@ (@ sup_sup_assn (@ (@ inf_inf_assn Y) X)) (@ (@ inf_inf_assn Z) X)))) (@ (@ _let_77 (lambda ((X2 product_prod_int_int)) (let ((_let_1 (@ product_fst_int_int X2))) (@ (@ (@ if_Pro3027730157355071871nt_int (= _let_1 zero_zero_int)) (@ (@ product_Pair_int_int zero_zero_int) one_one_int)) (@ (@ product_Pair_int_int (@ product_snd_int_int X2)) _let_1))))) (lambda ((X2 product_prod_int_int)) (let ((_let_1 (@ product_fst_int_int X2))) (@ (@ (@ 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(@ (@ ord_less_eq_rat one_one_rat) A2)) (=> (@ (@ ord_less_rat zero_zero_rat) C) (@ (@ ord_less_eq_rat A2) one_one_rat))))) (forall ((M5 set_nat)) (=> (@ finite_finite_nat M5) (= (@ gcd_Gcd_nat M5) (@ gcd_Gcd_nat (@ (@ minus_minus_set_nat M5) (@ (@ insert_nat2 zero_zero_nat) bot_bot_set_nat)))))) (forall ((X list_nat)) (=> (not (= X nil_nat)) (=> (forall ((X3 nat)) (not (= X (@ (@ cons_nat X3) nil_nat)))) (not (forall ((X3 nat) (Y2 nat) (Xs2 list_nat)) (not (= X (@ (@ cons_nat X3) (@ (@ cons_nat Y2) Xs2))))))))) (forall ((A2 nat)) (not (@ (@ ord_less_nat A2) zero_zero_nat))) (forall ((A set_int) (X int) (B set_int)) (let ((_let_1 (@ insert_int2 X))) (=> (@ (@ ord_less_eq_set_int (@ (@ minus_minus_set_int A) (@ _let_1 bot_bot_set_int))) B) (@ (@ ord_less_eq_set_int A) (@ _let_1 B))))) (forall ((I3 set_nat) (I7 set_nat) (Xs list_nat) (Xs4 list_nat) (Xsi list_c) (Xsi2 list_c) (A (-> nat c assn)) (A6 (-> nat c assn))) (=> (= I3 I7) (=> (= (@ size_size_list_nat Xs) (@ size_size_list_nat Xs4)) (=> (= (@ size_size_list_c Xsi) (@ size_size_list_c Xsi2)) (=> (forall ((I5 nat)) (let ((_let_1 (@ (@ nth_c Xsi2) I5))) (let ((_let_2 (@ (@ nth_c Xsi) I5))) (let ((_let_3 (@ (@ nth_nat Xs4) I5))) (let ((_let_4 (@ (@ nth_nat Xs) I5))) (let ((_let_5 (@ size_size_list_nat Xs))) (=> (@ (@ member_nat I5) I3) (=> (@ (@ ord_less_nat I5) _let_5) (=> (= _let_5 (@ size_size_list_c Xsi)) (and (= _let_4 _let_3) (= (@ (@ A _let_4) _let_2) (@ (@ A6 _let_3) _let_1)) (= _let_2 _let_1))))))))))) (= (@ (@ (@ (@ vEBT_L8146214880390291086_nat_c I3) A) Xs) Xsi) (@ (@ (@ (@ vEBT_L8146214880390291086_nat_c I7) A6) Xs4) Xsi2))))))) (forall ((A2 list_d) (B2 list_c) (A7 list_d) (B6 list_c)) (=> (= (@ size_size_list_d A2) (@ size_size_list_c B2)) (=> (= (@ size_size_list_d A7) (@ size_size_list_c B6)) (= (= (@ (@ zip_d_c A2) B2) (@ (@ zip_d_c A7) B6)) (and (= B2 B6) (= A2 A7)))))) (forall ((A2 assn) (B2 assn) (C assn)) (=> (@ (@ ord_less_eq_assn A2) B2) (=> (@ (@ ord_less_assn B2) C) (@ (@ ord_less_assn A2) C)))) (forall ((A2 nat) (B set_nat) (B2 nat)) (let ((_let_1 (@ member_nat A2))) (=> (=> (not (@ _let_1 B)) (= A2 B2)) (@ _let_1 (@ (@ insert_nat2 B2) B))))) (forall ((T code_integer)) (exists ((Z4 code_integer)) (forall ((X7 code_integer)) (=> (@ (@ ord_le6747313008572928689nteger Z4) X7) (@ (@ ord_le6747313008572928689nteger T) X7))))) (forall ((X assn) (Y assn) (Xs list_assn) (Ys list_assn)) (=> (@ (@ member7957490590177025114n_assn (@ (@ produc118845697133431529n_assn X) Y)) (@ set_Pr1139785259514867910n_assn (@ (@ zip_assn_assn Xs) Ys))) (@ (@ member_assn X) (@ set_assn2 Xs)))) (forall ((X code_integer) (Y code_integer)) (or (@ (@ ord_le6747313008572928689nteger Y) X) (@ (@ ord_le3102999989581377725nteger X) Y))) (forall ((X set_Pr1261947904930325089at_nat)) (= (@ (@ inf_in2572325071724192079at_nat bot_bo2099793752762293965at_nat) X) bot_bo2099793752762293965at_nat)) (forall ((B2 int) (C int) (A2 int)) (=> (@ (@ ord_less_eq_int B2) C) (@ (@ ord_less_eq_int (@ (@ ord_min_int A2) B2)) C))) (forall ((A2 produc3843707927480180839at_nat) (A set_Pr4329608150637261639at_nat) (B2 produc3843707927480180839at_nat)) (let ((_let_1 (@ (@ insert9069300056098147895at_nat B2) bot_bo228742789529271731at_nat))) (= (= (@ (@ insert9069300056098147895at_nat A2) A) _let_1) (and (= A2 B2) (@ (@ ord_le1268244103169919719at_nat A) _let_1))))) (= ord_le2510731241096832064er_nat (lambda ((A3 filter_nat) (B3 filter_nat)) (= A3 (@ (@ inf_inf_filter_nat A3) B3)))) (forall ((A set_o) (B set_o)) (=> (forall ((X3 Bool)) (let ((_let_1 (@ member_o X3))) (=> (@ _let_1 A) (not (@ _let_1 B))))) (= (@ (@ inf_inf_set_o A) B) bot_bot_set_o))) (forall ((X set_Pr1261947904930325089at_nat) (Xs list_s1210847774152347623at_nat) (Y set_Pr1261947904930325089at_nat) (Ys list_s1210847774152347623at_nat) (R2 set_Pr4329608150637261639at_nat)) (let ((_let_1 (@ lex_se2245640040323279819at_nat R2))) (= (@ (@ member4080735728053443344at_nat (@ (@ produc7536900900485677911at_nat (@ (@ 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(forall ((B2 int) (A2 int) (C int)) (let ((_let_1 (@ times_times_int C))) (=> (@ (@ ord_less_eq_int B2) A2) (=> (@ (@ ord_less_eq_int C) zero_zero_int) (@ (@ ord_less_eq_int (@ _let_1 A2)) (@ _let_1 B2)))))) (forall ((A2 (-> produc6241069584506657477e_term option6357759511663192854e_term)) (B2 produc8923325533196201883nteger) (A7 (-> produc6241069584506657477e_term option6357759511663192854e_term)) (B6 produc8923325533196201883nteger)) (= (= (@ (@ produc8603105652947943368nteger A2) B2) (@ (@ produc8603105652947943368nteger A7) B6)) (and (= B2 B6) (= A2 A7)))) (forall ((X int) (Y int) (Z int)) (let ((_let_1 (@ ord_less_int X))) (=> (@ _let_1 Y) (=> (@ (@ ord_less_int Y) Z) (@ _let_1 Z))))) (forall ((X assn)) (= (@ (@ sup_sup_assn X) X) X)) (forall ((A set_int)) (= (@ (@ minus_minus_set_int A) bot_bot_set_int) A)) (@ (@ pcr_rat _let_23) one_one_rat) (forall ((A2 int) (B2 int)) (= (@ (@ ord_less_int zero_zero_int) (@ (@ minus_minus_int A2) B2)) (@ (@ ord_less_int B2) A2))) (forall ((A2 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set_Pr400311997697478754_nat_o Xs)))))) (forall ((X set_Pr1261947904930325089at_nat) (Y set_Pr1261947904930325089at_nat)) (@ (@ ord_le3146513528884898305at_nat (@ (@ inf_in2572325071724192079at_nat X) Y)) X)) (forall ((B2 num) (A2 num) (C num)) (let ((_let_1 (@ ord_less_num C))) (=> (@ (@ ord_less_eq_num B2) A2) (=> (@ _let_1 B2) (@ _let_1 A2))))) (forall ((I nat) (Xs list_d) (Ys list_d)) (let ((_let_1 (@ ord_less_nat I))) (=> (@ _let_1 (@ size_size_list_d Xs)) (=> (@ _let_1 (@ size_size_list_d Ys)) (= (@ (@ nth_Product_prod_d_d (@ (@ zip_d_d Xs) Ys)) I) (@ (@ product_Pair_d_d (@ (@ nth_d Xs) I)) (@ (@ nth_d Ys) I))))))) (forall ((X set_int) (Y set_int)) (= (= bot_bot_set_int (@ (@ sup_sup_set_int X) Y)) (and (= X bot_bot_set_int) (= Y bot_bot_set_int)))) (forall ((Y nat) (X nat)) (=> (@ (@ ord_less_eq_nat Y) X) (= (@ (@ inf_inf_nat X) Y) Y))) (forall ((A2 set_nat) (B2 set_nat) (X set_nat)) (=> (@ (@ ord_less_eq_set_nat (@ (@ sup_sup_set_nat A2) B2)) X) (not (=> (@ (@ 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(Z set_Pr1261947904930325089at_nat) (X set_Pr1261947904930325089at_nat)) (= (@ (@ sup_su6327502436637775413at_nat (@ (@ inf_in2572325071724192079at_nat Y) Z)) X) (@ (@ inf_in2572325071724192079at_nat (@ (@ sup_su6327502436637775413at_nat Y) X)) (@ (@ sup_su6327502436637775413at_nat Z) X)))) (forall ((X list_int)) (=> (not (= X nil_int)) (=> (forall ((X3 int)) (not (= X (@ (@ cons_int X3) nil_int)))) (not (forall ((X3 int) (Y2 int) (Xs2 list_int)) (not (= X (@ (@ cons_int X3) (@ (@ cons_int Y2) Xs2))))))))) (forall ((I nat) (V2 c)) (= (@ (@ (@ list_update_c nil_c) I) V2) nil_c)) (forall ((A2 assn) (B2 assn)) (let ((_let_1 (@ inf_inf_assn A2))) (let ((_let_2 (@ _let_1 B2))) (= (@ _let_1 _let_2) _let_2)))) (forall ((X (-> produc3658429121746597890et_nat Bool)) (A set_Pr4532377907799695533_nat_o) (B set_Pr4532377907799695533_nat_o)) (let ((_let_1 (@ ord_le2965882846123202637_nat_o A))) (=> (not (@ (@ member6576561426505652726_nat_o X) A)) (= (@ _let_1 (@ (@ insert5175938949040314269_nat_o X) B)) (@ _let_1 B))))) (forall ((Y assn) (X assn)) (=> (@ (@ ord_less_eq_assn Y) X) (not (@ (@ ord_less_assn X) Y)))) (forall ((A2 (-> produc3658429121746597890et_nat Bool)) (B2 produc3658429121746597890et_nat) (A7 (-> produc3658429121746597890et_nat Bool)) (B6 produc3658429121746597890et_nat)) (= (= (@ (@ produc5001842942810119800et_nat A2) B2) (@ (@ produc5001842942810119800et_nat A7) B6)) (and (= A2 A7) (= B2 B6)))) (forall ((X21 produc3843707927480180839at_nat) (X222 list_P5464809261938338413at_nat)) (@ (@ member8757157785044589968at_nat X21) (@ set_Pr3765526544606949372at_nat (@ (@ cons_P3940603068885512221at_nat X21) X222)))) (forall ((C int) (A2 int) (B2 int)) (let ((_let_1 (@ plus_plus_int C))) (=> (@ (@ ord_less_eq_int (@ _let_1 A2)) (@ _let_1 B2)) (@ (@ ord_less_eq_int A2) B2)))) (forall ((A2 assn) (B2 assn) (F4 (-> assn num)) (C num)) (=> (@ (@ ord_less_assn A2) B2) (=> (= (@ F4 B2) C) (=> (forall ((X3 assn) (Y2 assn)) (=> (@ (@ ord_less_assn X3) Y2) (@ (@ ord_less_num (@ 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(A2 int) (B2 int)) (let ((_let_1 (@ plus_plus_int K3))) (=> (= A (@ _let_1 A2)) (= (@ (@ plus_plus_int A) B2) (@ _let_1 (@ (@ plus_plus_int A2) B2)))))) (forall ((Y nat)) (= (@ (@ count_list_nat nil_nat) Y) zero_zero_nat)) (forall ((B2 code_integer) (C code_integer) (A2 code_integer)) (= (@ (@ times_3573771949741848930nteger (@ (@ minus_8373710615458151222nteger B2) C)) A2) (@ (@ minus_8373710615458151222nteger (@ (@ times_3573771949741848930nteger B2) A2)) (@ (@ times_3573771949741848930nteger C) A2)))) (forall ((A set_Pr4329608150637261639at_nat) (B set_Pr4329608150637261639at_nat)) (= (@ (@ ord_le2604355607129572851at_nat (@ (@ minus_3314409938677909166at_nat A) B)) A) (not (= (@ (@ inf_in7913087082777306421at_nat A) B) bot_bo228742789529271731at_nat)))) (forall ((N nat) (P (-> nat Bool))) (= (exists ((I4 nat)) (and (@ (@ ord_less_nat I4) (@ suc N)) (@ P I4))) (or (exists ((I4 nat)) (and (@ P I4) (@ (@ ord_less_nat I4) N))) (@ P N)))) (forall ((X assn) (Y assn)) (=> (@ (@ ord_less_assn X) Y) (not (= X Y)))) (forall ((F4 (-> set_nat set_nat set_nat)) (X set_nat) (Y set_nat)) (=> (forall ((X3 set_nat) (Y2 set_nat)) (@ (@ ord_less_eq_set_nat X3) (@ (@ F4 X3) Y2))) (=> (forall ((X3 set_nat) (Y2 set_nat)) (@ (@ ord_less_eq_set_nat Y2) (@ (@ F4 X3) Y2))) (=> (forall ((X3 set_nat) (Y2 set_nat) (Z4 set_nat)) (=> (@ (@ ord_less_eq_set_nat Y2) X3) (=> (@ (@ ord_less_eq_set_nat Z4) X3) (@ (@ ord_less_eq_set_nat (@ (@ F4 Y2) Z4)) X3)))) (= (@ (@ sup_sup_set_nat X) Y) (@ (@ F4 X) Y)))))) (= set_or1266510415728281911st_int (lambda ((I4 int) (J2 int)) (@ (@ (@ if_set_int (@ (@ ord_less_int J2) I4)) bot_bot_set_int) (@ (@ insert_int2 I4) (@ (@ set_or1266510415728281911st_int (@ (@ plus_plus_int I4) one_one_int)) J2))))) (forall ((Xs list_nat) (Ys list_nat)) (= (@ distinct_nat (@ (@ union_nat Xs) Ys)) (@ distinct_nat Ys))) (forall ((A set_nat) (B set_nat)) (=> (forall ((X3 nat)) (let ((_let_1 (@ member_nat X3))) (=> (@ _let_1 A) (@ _let_1 B)))) (@ (@ ord_less_eq_set_nat A) B))) (forall ((R2 (-> produc8551481072490612790e_term option6357759511663192854e_term)) (S3 product_prod_int_int) (R set_Pr9222295170931077689nt_int) (S5 product_prod_int_int)) (let ((_let_1 (@ produc5700946648718959541nt_int R2))) (=> (@ (@ member7618704894036264090nt_int (@ _let_1 S3)) R) (=> (= S5 S3) (@ (@ member7618704894036264090nt_int (@ _let_1 S5)) R))))) (forall ((B2 assn) (A2 assn)) (=> (@ (@ ord_less_eq_assn B2) A2) (= (@ (@ sup_sup_assn A2) B2) A2))) (forall ((A2 code_integer) (B2 code_integer) (C code_integer)) (=> (@ (@ ord_le3102999989581377725nteger A2) B2) (=> (@ (@ ord_le6747313008572928689nteger B2) C) (@ (@ ord_le6747313008572928689nteger A2) C)))) (forall ((P (-> produc2285326912895808259nt_int Bool)) (X produc2285326912895808259nt_int)) (=> (forall ((A4 (-> produc8551481072490612790e_term option6357759511663192854e_term)) (B4 int) (C4 int)) (@ P (@ (@ produc5700946648718959541nt_int A4) (@ (@ product_Pair_int_int B4) C4)))) (@ P X))) (forall ((X nat) (A set_nat) (X4 set_nat)) (=> (@ (@ member_nat X) A) (=> (@ (@ ord_less_eq_set_nat X4) A) (@ (@ ord_less_eq_set_nat (@ (@ insert_nat2 X) X4)) A)))) _let_105 (forall ((B2 int) (A2 int)) (=> (@ (@ ord_less_eq_int B2) A2) (= A2 (@ (@ sup_sup_int A2) B2)))) (forall ((A2 nat) (B2 nat) (C nat) (D2 nat)) (= (= (@ (@ insert_nat2 A2) (@ (@ insert_nat2 B2) bot_bot_set_nat)) (@ (@ insert_nat2 C) (@ (@ insert_nat2 D2) bot_bot_set_nat))) (or (and (= B2 D2) (= A2 C)) (and (= A2 D2) (= B2 C))))) (forall ((B2 int) (A2 int) (C int)) (=> (@ (@ ord_less_eq_int B2) A2) (=> (@ (@ ord_less_eq_int C) A2) (@ (@ ord_less_eq_int (@ (@ sup_sup_int B2) C)) A2)))) (forall ((A2 nat) (F4 (-> nat nat)) (B2 nat) (C nat)) (=> (= A2 (@ F4 B2)) (=> (@ (@ ord_less_eq_nat B2) C) (=> (forall ((X3 nat) (Y2 nat)) (=> (@ (@ ord_less_eq_nat X3) Y2) (@ (@ ord_less_eq_nat (@ F4 X3)) (@ F4 Y2)))) (@ (@ ord_less_eq_nat A2) (@ F4 C)))))) (forall ((X21 nat) (X222 list_nat) (Y21 nat) (Y222 list_nat)) (= (= (@ (@ cons_nat X21) X222) (@ (@ 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(@ (@ times_times_int B2) C)) (and (=> (@ (@ ord_less_eq_int zero_zero_int) C) (@ (@ ord_less_int one_one_int) B2)) (=> (@ (@ ord_less_eq_int C) zero_zero_int) (@ (@ ord_less_int B2) one_one_int))))) (forall ((I nat) (Xs list_nat) (J nat)) (let ((_let_1 (@ nth_nat Xs))) (let ((_let_2 (@ size_size_list_nat Xs))) (=> (@ (@ ord_less_nat I) _let_2) (=> (@ (@ ord_less_nat J) _let_2) (= (@ distinct_nat (@ (@ (@ list_update_nat (@ (@ (@ list_update_nat Xs) I) (@ _let_1 J))) J) (@ _let_1 I))) (@ distinct_nat Xs))))))) (forall ((C (-> produc3658429121746597890et_nat Bool)) (A set_Pr4532377907799695533_nat_o) (B set_Pr4532377907799695533_nat_o)) (let ((_let_1 (@ member6576561426505652726_nat_o C))) (= (@ _let_1 (@ (@ sup_su5209123915105501825_nat_o A) B)) (or (@ _let_1 B) (@ _let_1 A))))) (forall ((X set_int)) (= (@ (@ inf_inf_set_int X) bot_bot_set_int) bot_bot_set_int)) (forall ((A2 nat) (B2 nat) (C nat)) (=> (@ (@ ord_less_eq_nat A2) B2) (=> (@ (@ ord_less_eq_nat zero_zero_nat) C) (@ (@ 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list_list_nat)) (=> (not (= X nil_list_nat)) (=> (forall ((Xss list_list_nat)) (not (= X (@ (@ cons_list_nat nil_nat) Xss)))) (not (forall ((X3 nat) (Xs2 list_nat) (Xss list_list_nat)) (not (= X (@ (@ cons_list_nat (@ (@ cons_nat X3) Xs2)) Xss)))))))) (forall ((A set_Pr1261947904930325089at_nat) (B set_Pr1261947904930325089at_nat)) (= (@ (@ sup_su6327502436637775413at_nat (@ (@ inf_in2572325071724192079at_nat A) B)) (@ (@ minus_1356011639430497352at_nat A) B)) A)) (forall ((P assn)) (= (@ (@ entails P) bot_bot_assn) (forall ((H3 produc3658429121746597890et_nat)) (not (@ (@ rep_assn P) H3))))) (forall ((C2 assn) (A assn) (B assn)) (let ((_let_1 (@ times_times_assn C2))) (= (@ _let_1 (@ (@ sup_sup_assn A) B)) (@ (@ sup_sup_assn (@ _let_1 A)) (@ _let_1 B))))) (forall ((L list_nat) (Li list_c) (A (-> nat c assn))) (=> (not (= (@ size_size_list_nat L) (@ size_size_list_c Li))) (= (@ (@ (@ vEBT_L6400351906427472171_nat_c A) L) Li) bot_bot_assn))) (forall ((X list_P8527749157015355191n_assn) (Y list_P8527749157015355191n_assn)) (= (@ (@ (@ if_lis7173127979115136509n_assn false) X) Y) Y)) (forall ((A set_int) (B set_int)) (= (= (@ (@ minus_minus_set_int A) B) A) (= (@ (@ inf_inf_set_int A) B) bot_bot_set_int))) (forall ((B2 code_integer) (M2 nat) (N nat)) (let ((_let_1 (@ power_8256067586552552935nteger B2))) (=> (@ (@ ord_le6747313008572928689nteger zero_z3403309356797280102nteger) B2) (=> (@ (@ ord_le6747313008572928689nteger B2) one_one_Code_integer) (= (@ (@ ord_le6747313008572928689nteger (@ _let_1 M2)) (@ _let_1 N)) (@ (@ ord_less_nat N) M2)))))) (forall ((B2 nat) (C nat) (A2 nat)) (=> (@ (@ ord_less_eq_nat (@ (@ sup_sup_nat B2) C)) A2) (not (=> (@ (@ ord_less_eq_nat B2) A2) (not (@ (@ ord_less_eq_nat C) A2)))))) (forall ((P (-> (-> produc3658429121746597890et_nat Bool) Bool)) (Q (-> (-> produc3658429121746597890et_nat Bool) Bool))) (=> (forall ((X3 (-> produc3658429121746597890et_nat Bool))) (=> (@ P X3) (@ Q X3))) (@ (@ ord_le2965882846123202637_nat_o (@ collec939566748876313656_nat_o P)) (@ collec939566748876313656_nat_o Q)))) (forall ((P6 rat) (Q6 rat)) (= (@ quotient_of (@ (@ minus_minus_rat P6) Q6)) (@ (@ produc4245557441103728435nt_int (lambda ((A3 int) (C5 int)) (@ (@ produc4245557441103728435nt_int (lambda ((B3 int) (D5 int)) (@ normalize (@ (@ product_Pair_int_int (@ (@ minus_minus_int (@ (@ times_times_int A3) D5)) (@ (@ times_times_int B3) C5))) (@ (@ times_times_int C5) D5))))) (@ quotient_of Q6)))) (@ quotient_of P6)))) (forall ((Xs list_P8527749157015355191n_assn)) (= (= bot_bo1176836662018730877n_assn (@ set_Pr1139785259514867910n_assn Xs)) (= Xs nil_Pr5671120429643327159n_assn))) (forall ((A2 nat) (B2 nat)) (=> (@ (@ ord_less_nat zero_zero_nat) A2) (=> (@ (@ ord_less_nat B2) zero_zero_nat) (@ (@ ord_less_nat (@ (@ times_times_nat A2) B2)) zero_zero_nat)))) _let_102 (forall ((I nat) (L list_P8527749157015355191n_assn) (X produc6575502325842934193n_assn) (Y produc6575502325842934193n_assn)) (=> (@ (@ ord_less_nat I) (@ size_s6829681357464350627n_assn L)) (= (@ (@ member7957490590177025114n_assn X) (@ set_Pr1139785259514867910n_assn (@ (@ (@ list_u4534839942911652127n_assn L) I) Y))) (or (forall ((Y5 produc6575502325842934193n_assn)) (@ (@ member7957490590177025114n_assn X) (@ set_Pr1139785259514867910n_assn (@ (@ (@ list_u4534839942911652127n_assn L) I) Y5)))) (= X Y))))) (forall ((P assn)) (= (@ (@ times_times_assn bot_bot_assn) P) bot_bot_assn)) (forall ((A2 nat)) (= (@ (@ minus_minus_nat A2) zero_zero_nat) A2)) (forall ((P (-> int Bool))) (= (= (@ collect_int P) bot_bot_set_int) (= P bot_bot_int_o))) (forall ((A2 set_Pr1261947904930325089at_nat) (C set_Pr1261947904930325089at_nat) (B2 set_Pr1261947904930325089at_nat)) (=> (@ (@ ord_le3146513528884898305at_nat A2) C) (@ (@ ord_le3146513528884898305at_nat (@ (@ inf_in2572325071724192079at_nat A2) B2)) C))) (forall ((X Bool) (A set_o)) (=> (@ (@ member_o X) A) (not (forall ((B5 set_o)) (=> (= A (@ (@ insert_o2 X) B5)) (@ (@ member_o X) B5)))))) (forall ((A set_nat) (B set_nat)) (= (@ (@ inf_inf_set_nat A) (@ (@ minus_minus_set_nat B) A)) bot_bot_set_nat)) (forall ((A2 set_nat) (B2 set_nat)) (let ((_let_1 (@ sup_sup_set_nat A2))) (let ((_let_2 (@ _let_1 B2))) (= (@ _let_1 _let_2) _let_2)))) (forall ((Xs list_P8527749157015355191n_assn) (P (-> produc6575502325842934193n_assn Bool)) (X produc6575502325842934193n_assn)) (=> (forall ((I5 nat)) (=> (@ (@ ord_less_nat I5) (@ size_s6829681357464350627n_assn Xs)) (@ P (@ (@ nth_Pr1769885009046257848n_assn Xs) I5)))) (=> (@ (@ member7957490590177025114n_assn X) (@ set_Pr1139785259514867910n_assn Xs)) (@ P X)))) (forall ((A2 int)) (= (@ (@ plus_plus_int A2) zero_zero_int) A2)) (forall ((P (-> int int assn)) (A2 int) (As2 list_int) (C int) (Cs list_int)) (let ((_let_1 (@ vEBT_L74593716426352029nt_int P))) (= (@ (@ _let_1 (@ (@ cons_int A2) As2)) (@ (@ cons_int C) Cs)) (@ (@ times_times_assn (@ (@ P A2) C)) (@ (@ _let_1 As2) Cs))))) (forall ((P (-> nat int assn)) (L list_nat)) (= (@ (@ (@ vEBT_L8298612041380073281at_int P) L) nil_int) (@ pure_assn (= L nil_nat)))) (forall ((X rat) (Zs list_rat)) (let ((_let_1 (@ foldl_rat_rat times_times_rat))) (= (@ (@ times_times_rat X) (@ (@ _let_1 one_one_rat) Zs)) (@ (@ _let_1 X) Zs)))) (forall ((I nat) (J nat)) (let ((_let_1 (@ upt I))) (=> (@ (@ ord_less_eq_nat I) J) (= (@ _let_1 (@ suc J)) (@ (@ append_nat (@ _let_1 J)) (@ (@ cons_nat J) nil_nat)))))) (forall ((Xs list_P8527749157015355191n_assn) (Ys list_P8527749157015355191n_assn)) (= (= (@ (@ zip_Pr8806919808394484215n_assn Xs) Ys) nil_Pr4327835960982145133n_assn) (or (= Xs nil_Pr5671120429643327159n_assn) (= Ys nil_Pr5671120429643327159n_assn)))) (forall ((L12 list_d) (L23 list_d)) (=> (= (@ size_size_list_d L12) (@ size_size_list_d L23)) (= (@ (@ (@ zipf_d1197059025479841897od_d_d product_Pair_d_d) L12) L23) (@ (@ zip_d_d L12) L23)))) (= ord_le2510731241096832064er_nat (lambda ((A3 filter_nat) (B3 filter_nat)) (= (@ (@ sup_sup_filter_nat A3) B3) B3))) (forall ((Bs set_nat) (H2 heap_e7401611519738050253t_unit) (H4 heap_e7401611519738050253t_unit) (As2 set_nat)) (=> (@ (@ (@ relH Bs) H2) H4) (=> (@ (@ ord_less_eq_set_nat As2) Bs) (@ (@ (@ relH As2) H2) H4)))) (forall ((Y assn) (X assn)) (=> (@ (@ ord_less_eq_assn Y) X) (= (@ (@ ord_min_assn X) Y) Y))) (forall ((X int) (Ys list_int)) (let ((_let_1 (@ sorted_wrt_int ord_less_eq_int))) (= (@ _let_1 (@ (@ cons_int X) Ys)) (and (forall ((X2 int)) (=> (@ (@ member_int X2) (@ set_int2 Ys)) (@ (@ ord_less_eq_int X) X2))) (@ _let_1 Ys))))) (forall ((C int) (A2 int) (B2 int)) (let ((_let_1 (@ ord_less_int C))) (=> (@ _let_1 A2) (@ _let_1 (@ (@ sup_sup_int A2) B2))))) (forall ((M2 code_integer) (N code_integer)) (let ((_let_1 (@ (@ ord_min_Code_integer M2) N))) (= (not (@ (@ ord_le6747313008572928689nteger _let_1) N)) (= _let_1 N)))) (forall ((Y produc6575502325842934193n_assn)) (= (@ (@ count_2530312006313534765n_assn nil_Pr5671120429643327159n_assn) Y) zero_zero_nat)) (forall ((A2 rat) (B2 rat) (C rat)) (let ((_let_1 (@ ord_less_rat B2))) (=> (@ (@ ord_less_rat zero_zero_rat) A2) (=> (@ _let_1 C) (@ _let_1 (@ (@ plus_plus_rat A2) C)))))) (forall ((B set_Pr4532377907799695533_nat_o) (A2 (-> produc3658429121746597890et_nat Bool)) (A set_Pr4532377907799695533_nat_o)) (let ((_let_1 (@ inf_in1906310914598751387_nat_o B))) (= (= (@ _let_1 (@ (@ insert5175938949040314269_nat_o A2) A)) bot_bo7824918357723582233_nat_o) (and (not (@ (@ member6576561426505652726_nat_o A2) B)) (= (@ _let_1 A) bot_bo7824918357723582233_nat_o))))) (forall ((N nat)) (= (@ finite_card_nat (@ collect_nat (lambda ((I4 nat)) (@ (@ ord_less_nat I4) N)))) N)) (forall ((C int) (A2 int) (B2 int)) (let ((_let_1 (@ times_times_int C))) (= (@ (@ ord_less_eq_int (@ _let_1 A2)) (@ _let_1 B2)) (and (=> (@ (@ ord_less_int C) zero_zero_int) (@ (@ ord_less_eq_int B2) A2)) (=> (@ (@ ord_less_int zero_zero_int) C) (@ (@ ord_less_eq_int A2) B2)))))) (forall ((X code_integer) (Y code_integer)) (= (@ (@ minus_8373710615458151222nteger (@ (@ 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(forall ((M2 num) (N num)) (let ((_let_1 (@ uminus_uminus_int (@ numeral_numeral_int N)))) (let ((_let_2 (@ numeral_numeral_int M2))) (let ((_let_3 (@ (@ upto _let_2) _let_1))) (let ((_let_4 (@ (@ ord_less_eq_int _let_2) _let_1))) (and (=> _let_4 (= _let_3 (@ (@ cons_int _let_2) (@ (@ upto (@ (@ plus_plus_int _let_2) one_one_int)) _let_1)))) (=> (not _let_4) (= _let_3 nil_int)))))))) (forall ((A2 nat) (A set_nat) (B2 nat) (B set_nat)) (let ((_let_1 (= A2 B2))) (=> (not (@ (@ member_nat A2) A)) (=> (not (@ (@ member_nat B2) B)) (= (= (@ (@ insert_nat2 A2) A) (@ (@ insert_nat2 B2) B)) (and (=> _let_1 (= A B)) (=> (not _let_1) (exists ((C3 set_nat)) (and (= A (@ (@ insert_nat2 B2) C3)) (= B (@ (@ insert_nat2 A2) C3)) (not (@ (@ member_nat A2) C3)) (not (@ (@ member_nat B2) C3))))))))))) (forall ((Xs list_d) (K3 nat) (X d)) (= (= (@ (@ (@ list_update_d Xs) K3) X) nil_d) (= Xs nil_d))) (forall ((X set_nat) (Y set_nat)) (@ (@ ord_less_eq_set_nat (@ (@ inf_inf_set_nat X) Y)) Y)) (forall ((A2 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(=> _let_1 (=> _let_1 (= (= (@ (@ minus_minus_nat B2) A2) C) (= B2 (@ (@ plus_plus_nat C) A2))))))) (forall ((F4 (-> nat nat int)) (A2 nat) (As2 list_nat) (B2 nat) (Bs list_nat)) (let ((_let_1 (@ zipf_nat_nat_int F4))) (= (@ (@ _let_1 (@ (@ cons_nat A2) As2)) (@ (@ cons_nat B2) Bs)) (@ (@ cons_int (@ (@ F4 A2) B2)) (@ (@ _let_1 As2) Bs))))) (forall ((Xs list_P8527749157015355191n_assn) (R2 set_Pr8116311503512020807n_assn)) (not (@ (@ member3994142547374651152n_assn (@ (@ produc3014731801419794263n_assn Xs) nil_Pr5671120429643327159n_assn)) (@ lex_Pr7559194461235888923n_assn R2)))) (forall ((P (-> int produc6575502325842934193n_assn assn)) (A2 int) (As2 list_int) (C produc6575502325842934193n_assn) (Cs list_P8527749157015355191n_assn)) (let ((_let_1 (@ vEBT_L1620274777744359680n_assn P))) (= (@ (@ _let_1 (@ (@ cons_int A2) As2)) (@ (@ cons_P2971678138204555879n_assn C) Cs)) (@ (@ times_times_assn (@ (@ P A2) C)) (@ (@ _let_1 As2) Cs))))) (forall ((X num)) (not (@ (@ ord_less_num X) X))) (forall ((A2 rat) (C rat) (B2 rat)) (= (@ (@ ord_less_eq_rat (@ (@ times_times_rat A2) C)) (@ (@ times_times_rat B2) C)) (and (=> (@ (@ ord_less_rat zero_zero_rat) C) (@ (@ ord_less_eq_rat A2) B2)) (=> (@ (@ ord_less_rat C) zero_zero_rat) (@ (@ ord_less_eq_rat B2) A2))))) (forall ((C int) (A2 int)) (= (@ (@ ord_less_eq_int (@ (@ times_times_int C) A2)) C) (and (=> (@ (@ ord_less_int zero_zero_int) C) (@ (@ ord_less_eq_int A2) one_one_int)) (=> (@ (@ ord_less_int C) zero_zero_int) (@ (@ ord_less_eq_int one_one_int) A2))))) (forall ((M2 nat) (N nat)) (=> (@ (@ ord_less_nat M2) N) (@ (@ ord_less_nat (@ suc M2)) (@ suc N)))) (forall ((A set_Pr4329608150637261639at_nat) (B set_Pr4329608150637261639at_nat)) (=> (@ (@ ord_le1268244103169919719at_nat A) B) (= (@ (@ sup_su5525570899277871387at_nat A) B) B))) (forall ((A set_Pr1261947904930325089at_nat)) (= (@ (@ minus_1356011639430497352at_nat bot_bo2099793752762293965at_nat) A) bot_bo2099793752762293965at_nat)) _let_99 (forall ((N nat)) (not (@ (@ ord_less_nat N) zero_zero_nat))) (forall ((A2 set_nat)) (=> (@ (@ ord_less_eq_set_nat A2) bot_bot_set_nat) (= A2 bot_bot_set_nat))) (forall ((A2 nat)) (@ (@ ord_less_nat A2) (@ (@ plus_plus_nat A2) one_one_nat))) (forall ((A2 num) (F4 (-> code_integer num)) (B2 code_integer) (C code_integer)) (=> (@ (@ ord_less_eq_num A2) (@ F4 B2)) (=> (@ (@ ord_le6747313008572928689nteger B2) C) (=> (forall ((X3 code_integer) (Y2 code_integer)) (=> (@ (@ ord_le6747313008572928689nteger X3) Y2) (@ (@ ord_less_num (@ F4 X3)) (@ F4 Y2)))) (@ (@ ord_less_num A2) (@ F4 C)))))) (forall ((P (-> Bool Bool))) (= (= (@ collect_o P) bot_bot_set_o) (= P bot_bot_o_o))) (forall ((X int) (L list_int) (I nat) (Y int)) (let ((_let_1 (@ member_int X))) (=> (@ _let_1 (@ set_int2 (@ (@ (@ list_update_int L) I) Y))) (=> (=> (@ (@ ord_less_nat I) (@ size_size_list_int L)) (not (= X Y))) (@ _let_1 (@ set_int2 L)))))) (forall ((A set_o) (X Bool) (B set_o)) (let ((_let_1 (@ insert_o2 X))) (=> (@ (@ ord_less_eq_set_o (@ (@ minus_minus_set_o A) (@ _let_1 bot_bot_set_o))) B) (@ (@ ord_less_eq_set_o A) (@ _let_1 B))))) (forall ((B2 nat) (A2 nat) (C nat)) (=> (@ (@ ord_less_nat B2) A2) (=> (@ (@ ord_less_eq_nat C) B2) (@ (@ ord_less_nat C) A2)))) (forall ((Xs list_c)) (= (@ (@ ord_less_nat zero_zero_nat) (@ size_size_list_c Xs)) (not (= Xs nil_c)))) (forall ((X rat) (Y rat)) (= (= (@ (@ plus_plus_rat (@ (@ times_times_rat X) X)) (@ (@ times_times_rat Y) Y)) zero_zero_rat) (and (= X zero_zero_rat) (= Y zero_zero_rat)))) (forall ((X (-> produc3658429121746597890et_nat Bool)) (S set_Pr4532377907799695533_nat_o)) (=> (@ (@ member6576561426505652726_nat_o X) S) (not (= S bot_bo7824918357723582233_nat_o)))) (forall ((A2 nat) (B2 nat) (C nat) (D2 nat)) (let ((_let_1 (@ ord_less_eq_nat zero_zero_nat))) (=> (@ (@ ord_less_nat A2) B2) (=> (@ (@ ord_less_nat C) D2) (=> (@ _let_1 A2) (=> (@ _let_1 C) (@ (@ ord_less_nat (@ (@ times_times_nat A2) C)) (@ (@ times_times_nat B2) D2)))))))) _let_98 (= ord_less_num (lambda ((A3 num) (B3 num)) (and (not (@ (@ ord_less_eq_num B3) A3)) (@ (@ ord_less_eq_num A3) B3)))) (forall ((C int) (A2 int) (B2 int)) (let ((_let_1 (@ times_times_int C))) (=> (@ (@ ord_less_int zero_zero_int) C) (= (@ (@ ord_less_eq_int (@ _let_1 A2)) (@ _let_1 B2)) (@ (@ ord_less_eq_int A2) B2))))) (forall ((B2 int) (A2 int)) (=> (@ (@ ord_less_eq_int B2) A2) (=> (@ (@ ord_less_eq_int A2) B2) (= A2 B2)))) (forall ((A2 nat) (B2 nat)) (= (@ (@ ord_less_eq_nat A2) (@ (@ plus_plus_nat A2) B2)) (@ (@ ord_less_eq_nat zero_zero_nat) B2))) (forall ((A2 product_prod_nat_nat) (C2 set_Pr1261947904930325089at_nat) (B set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ insert8211810215607154385at_nat A2))) (=> (@ (@ member8440522571783428010at_nat A2) C2) (= (@ (@ inf_in2572325071724192079at_nat (@ _let_1 B)) C2) (@ _let_1 (@ (@ inf_in2572325071724192079at_nat B) C2)))))) (forall ((R2 set_Pr1872883991513573699nt_int) (S3 set_Pr1872883991513573699nt_int)) (=> (forall ((X3 (-> int option6357759511663192854e_term)) (Y2 product_prod_int_int)) (let ((_let_1 (@ member7034335876925520548nt_int (@ (@ produc4305682042979456191nt_int X3) Y2)))) (=> (@ _let_1 R2) (@ _let_1 S3)))) (@ (@ ord_le135402666524580259nt_int R2) S3))) (forall ((X set_nat) (Y set_nat)) (= (@ (@ (@ if_set_nat true) X) Y) X)) (forall ((B2 produc3843707927480180839at_nat) (A2 produc3843707927480180839at_nat)) (=> (@ (@ member8757157785044589968at_nat B2) (@ (@ insert9069300056098147895at_nat A2) bot_bo228742789529271731at_nat)) (= B2 A2))) (forall ((A2 int) (B2 int)) (=> (not (@ (@ ord_less_int A2) B2)) (= (@ (@ plus_plus_int B2) (@ (@ minus_minus_int A2) B2)) A2))) (= bot_bot_set_int (@ collect_int bot_bot_int_o)) (forall ((A set_nat) (B set_nat)) (=> (@ (@ ord_less_set_nat A) B) (@ (@ ord_less_eq_set_nat A) B))) (forall ((Ns list_P8527749157015355191n_assn) (R2 set_Pr8116311503512020807n_assn)) (= (@ (@ member3994142547374651152n_assn (@ (@ produc3014731801419794263n_assn nil_Pr5671120429643327159n_assn) Ns)) (@ lenlex6671093235567761724n_assn R2)) (not (= Ns nil_Pr5671120429643327159n_assn)))) (forall ((L code_integer) (U code_integer)) (@ finite6017078050557962740nteger (@ (@ set_or4266950643985792945nteger L) U))) (forall ((B2 nat) (C nat) (A2 nat)) (=> (@ (@ ord_less_nat B2) C) (@ (@ ord_less_nat (@ (@ inf_inf_nat A2) B2)) C))) (forall ((P assn) (Q assn) (F assn)) (let ((_let_1 (@ times_times_assn sln))) (=> (@ (@ (@ (@ (@ (@ fi nil_Pr5671120429643327159n_assn) (@ _let_1 P)) (@ _let_1 Q)) sln) sln) F) (@ (@ (@ fI_QUERY P) Q) F)))) (forall ((X produc3843707927480180839at_nat) (A set_Pr4329608150637261639at_nat) (B set_Pr4329608150637261639at_nat)) (let ((_let_1 (@ minus_3314409938677909166at_nat A))) (=> (not (@ (@ member8757157785044589968at_nat X) A)) (= (@ _let_1 (@ (@ insert9069300056098147895at_nat X) B)) (@ _let_1 B))))) (forall ((A set_Pr1261947904930325089at_nat) (X product_prod_nat_nat) (B set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ ord_le7866589430770878221at_nat A))) (let ((_let_2 (@ member8440522571783428010at_nat X))) (let ((_let_3 (@ _let_2 B))) (let ((_let_4 (@ insert8211810215607154385at_nat X))) (let ((_let_5 (@ _let_2 A))) (= (@ _let_1 (@ _let_4 B)) (and (=> (not _let_3) (and (=> (not _let_5) (@ (@ ord_le3146513528884898305at_nat A) B)) (=> _let_5 (@ (@ ord_le7866589430770878221at_nat (@ (@ minus_1356011639430497352at_nat A) (@ _let_4 bot_bo2099793752762293965at_nat))) B)))) (=> _let_3 (@ _let_1 B)))))))))) (forall ((I rat) (J rat) (K3 rat) (L rat)) (=> (and (@ (@ ord_less_eq_rat K3) L) (@ (@ ord_less_rat I) J)) (@ (@ ord_less_rat (@ (@ plus_plus_rat I) K3)) (@ (@ plus_plus_rat J) L)))) (= inf_in2572325071724192079at_nat (lambda ((A3 set_Pr1261947904930325089at_nat) (B3 set_Pr1261947904930325089at_nat)) (@ (@ inf_in2572325071724192079at_nat B3) A3))) (forall ((A2 code_integer) (B2 code_integer)) (=> (@ (@ ord_le6747313008572928689nteger A2) B2) (@ (@ ord_le6747313008572928689nteger (@ (@ plus_p5714425477246183910nteger A2) one_one_Code_integer)) (@ (@ plus_p5714425477246183910nteger B2) one_one_Code_integer)))) (forall ((N int) (M2 int)) (let ((_let_1 (@ (@ ord_min_int M2) N))) (= (@ (@ ord_less_eq_int N) _let_1) (= _let_1 N)))) (forall ((Xs list_c) (I nat) (X c)) (@ (@ ord_less_eq_set_c (@ set_c2 (@ (@ (@ list_update_c Xs) I) X))) (@ (@ insert_c X) (@ set_c2 Xs)))) (forall ((J nat) (K3 nat) (N nat)) (=> (@ (@ ord_less_nat J) K3) (@ (@ ord_less_nat (@ (@ minus_minus_nat J) N)) K3))) (forall ((A2 int) (F4 (-> int int)) (B2 int) (C int)) (=> (= A2 (@ F4 B2)) (=> (@ (@ ord_less_eq_int B2) C) (=> (forall ((X3 int) (Y2 int)) (=> (@ (@ ord_less_eq_int X3) Y2) (@ (@ ord_less_eq_int (@ F4 X3)) (@ F4 Y2)))) (@ (@ ord_less_eq_int A2) (@ F4 C)))))) (forall ((A2 multis2468970476368604999at_nat) (B2 multis2468970476368604999at_nat)) (= (@ (@ minus_4286766774447292334at_nat A2) (@ (@ plus_p7104986032573967614at_nat A2) B2)) zero_z1048942125864253310at_nat)) (forall ((P (-> nat produc6575502325842934193n_assn assn)) (A2 nat) (As2 list_nat) (C produc6575502325842934193n_assn) (Cs list_P8527749157015355191n_assn)) (let ((_let_1 (@ vEBT_L9083610150846024284n_assn P))) (= (@ (@ _let_1 (@ (@ cons_nat A2) As2)) (@ (@ cons_P2971678138204555879n_assn C) Cs)) (@ (@ times_times_assn (@ (@ P A2) C)) (@ (@ _let_1 As2) Cs))))) (forall ((I nat) (Y produc6575502325842934193n_assn)) (= (@ (@ (@ list_u4534839942911652127n_assn nil_Pr5671120429643327159n_assn) I) Y) nil_Pr5671120429643327159n_assn)) (forall ((Xs list_P8527749157015355191n_assn) (A2 produc6575502325842934193n_assn) (I nat)) (=> (@ distin4809818325527169450n_assn Xs) (=> (not (@ (@ member7957490590177025114n_assn A2) (@ (@ minus_2301194108115264760n_assn (@ set_Pr1139785259514867910n_assn Xs)) (@ (@ insert5290817439147925377n_assn (@ (@ nth_Pr1769885009046257848n_assn Xs) I)) bot_bo1176836662018730877n_assn)))) (@ distin4809818325527169450n_assn (@ (@ (@ list_u4534839942911652127n_assn Xs) I) A2))))) (forall ((A2 int) (E int) (C int) (B2 int) (D2 int)) (= (@ (@ ord_less_int (@ (@ plus_plus_int (@ (@ times_times_int A2) E)) C)) (@ (@ plus_plus_int (@ (@ times_times_int B2) E)) D2)) (@ (@ ord_less_int C) (@ (@ plus_plus_int (@ (@ times_times_int (@ (@ minus_minus_int B2) A2)) E)) D2)))) (forall ((C2 set_nat) (A set_nat) (B set_nat)) (let ((_let_1 (@ inf_inf_set_nat C2))) (= (@ _let_1 (@ (@ minus_minus_set_nat A) B)) (@ (@ minus_minus_set_nat (@ _let_1 A)) (@ _let_1 B))))) (forall ((R2 (-> produc3843707927480180839at_nat produc3843707927480180839at_nat Bool)) (X produc3843707927480180839at_nat) (S3 set_Pr4329608150637261639at_nat)) (let ((_let_1 (@ pairwi3222497012029234898at_nat R2))) (= (@ _let_1 (@ (@ insert9069300056098147895at_nat X) S3)) (and (@ _let_1 S3) (forall ((Y5 produc3843707927480180839at_nat)) (=> (and (@ (@ member8757157785044589968at_nat Y5) S3) (not (= Y5 X))) (and (@ (@ R2 Y5) X) (@ (@ R2 X) Y5)))))))) (= ord_min_nat (lambda ((A3 nat) (B3 nat)) (@ (@ (@ if_nat (@ (@ ord_less_eq_nat A3) B3)) A3) B3))) (forall ((Y product_prod_nat_nat) (X222 list_P6011104703257516679at_nat) (X21 product_prod_nat_nat)) (let ((_let_1 (@ member8440522571783428010at_nat Y))) (=> (@ _let_1 (@ set_Pr5648618587558075414at_nat X222)) (@ _let_1 (@ set_Pr5648618587558075414at_nat (@ (@ cons_P6512896166579812791at_nat X21) X222)))))) (forall ((A2 code_integer)) (= (@ (@ minus_8373710615458151222nteger A2) zero_z3403309356797280102nteger) A2)) (forall ((Xs list_c) (Ys list_c) (Zs list_int) (P (-> list_c list_c list_int Bool))) (let ((_let_1 (@ size_size_list_c Ys))) (=> (= (@ size_size_list_c Xs) _let_1) (=> (= _let_1 (@ size_size_list_int Zs)) (=> (@ (@ (@ P nil_c) nil_c) nil_int) (=> (forall ((X3 c) (Xs2 list_c) (Y2 c) (Ys5 list_c) (Z4 int) (Zs2 list_int)) (let ((_let_1 (@ size_size_list_c Ys5))) (=> (= (@ size_size_list_c Xs2) _let_1) (=> (= _let_1 (@ size_size_list_int Zs2)) (=> (@ (@ (@ P Xs2) Ys5) Zs2) (@ (@ (@ P (@ (@ cons_c X3) Xs2)) (@ (@ cons_c Y2) Ys5)) (@ (@ cons_int Z4) Zs2))))))) (@ (@ (@ P Xs) Ys) Zs))))))) (forall ((A2 assn)) (not (@ (@ ord_less_assn A2) bot_bot_assn))) (forall ((X nat) (Y nat)) (or (@ (@ ord_less_nat X) Y) (= X Y) (@ (@ ord_less_nat Y) X))) (forall ((A set_Pr4329608150637261639at_nat) (B set_Pr4329608150637261639at_nat)) (=> (forall ((X3 produc3843707927480180839at_nat)) (let ((_let_1 (@ member8757157785044589968at_nat X3))) (=> (@ _let_1 A) (not (@ _let_1 B))))) (= (@ (@ inf_in7913087082777306421at_nat A) B) bot_bo228742789529271731at_nat))) _let_97 (forall ((F4 (-> produc2285326912895808259nt_int Bool)) (A2 (-> produc8551481072490612790e_term option6357759511663192854e_term)) (B2 product_prod_int_int)) (=> (@ (@ (@ produc730925184835016917_int_o F4) A2) B2) (@ F4 (@ (@ produc5700946648718959541nt_int A2) B2)))) (forall ((A2 rat)) (@ (@ ord_less_rat A2) (@ (@ plus_plus_rat A2) one_one_rat))) (forall ((A2 nat) (B2 nat) (S3 nat) (T nat)) (=> (@ (@ ord_less_eq_nat A2) B2) (=> (@ (@ ord_less_nat S3) T) (@ (@ member8206827879206165904at_nat (@ (@ produc6161850002892822231at_nat (@ (@ product_Pair_nat_nat A2) S3)) (@ (@ product_Pair_nat_nat B2) T))) fun_pair_less)))) (forall ((R2 set_Pr1261947904930325089at_nat) (S3 set_Pr1261947904930325089at_nat) (R set_Pr4329608150637261639at_nat) (S5 set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ produc2922128104949294807at_nat R2))) (=> (@ (@ member8757157785044589968at_nat (@ _let_1 S3)) R) (=> (= S5 S3) (@ (@ member8757157785044589968at_nat (@ _let_1 S5)) R))))) (forall ((X set_Pr1261947904930325089at_nat) (Y set_Pr1261947904930325089at_nat) (Z set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ ord_le3146513528884898305at_nat X))) (= (@ _let_1 (@ (@ inf_in2572325071724192079at_nat Y) Z)) (and (@ _let_1 Y) (@ _let_1 Z))))) (forall ((X set_o)) (= (@ (@ sup_sup_set_o X) bot_bot_set_o) X)) (forall ((X set_nat) (Y set_nat)) (= (@ (@ sup_sup_set_nat X) (@ (@ inf_inf_set_nat X) Y)) X)) (not (= zero_zero_int one_one_int)) (forall ((A2 int) (B2 int)) (=> (@ (@ ord_less_int A2) B2) (= (@ (@ sup_sup_int A2) B2) B2))) (forall ((Xs list_int) (Ys list_int)) (=> (= (@ size_size_list_int Xs) (@ size_size_list_int Ys)) (=> (forall ((I5 nat)) (=> (@ (@ ord_less_nat I5) (@ size_size_list_int Xs)) (= (@ (@ nth_int Xs) I5) (@ (@ nth_int Ys) I5)))) (= Xs Ys)))) (forall ((Y set_Pr1261947904930325089at_nat) (X set_Pr1261947904930325089at_nat)) (=> (@ (@ ord_le3146513528884898305at_nat Y) X) (= (@ (@ inf_in2572325071724192079at_nat X) Y) Y))) (forall ((X assn) (Y assn)) (let ((_let_1 (@ sup_sup_assn X))) (let ((_let_2 (@ _let_1 Y))) (= (@ _let_1 _let_2) _let_2)))) (= sup_sup_assn (lambda ((X2 assn) (Y5 assn)) (@ (@ sup_sup_assn Y5) X2))) (forall ((I nat) (Xs list_c) (Ys list_nat)) (let ((_let_1 (@ ord_less_nat I))) (=> (@ _let_1 (@ size_size_list_c Xs)) (=> (@ _let_1 (@ size_size_list_nat Ys)) (= (@ (@ nth_Pr1708982275578427192_c_nat (@ (@ zip_c_nat Xs) Ys)) I) (@ (@ product_Pair_c_nat (@ (@ nth_c Xs) I)) (@ (@ nth_nat Ys) I))))))) (forall ((A set_Pr1261947904930325089at_nat) (A2 product_prod_nat_nat)) (=> (= A bot_bo2099793752762293965at_nat) (not (@ (@ member8440522571783428010at_nat A2) A)))) (forall ((A set_Pr1261947904930325089at_nat) (B set_Pr1261947904930325089at_nat)) (=> (@ (@ ord_le7866589430770878221at_nat A) B) (exists ((B4 product_prod_nat_nat)) (@ (@ member8440522571783428010at_nat B4) (@ (@ minus_1356011639430497352at_nat B) A))))) (forall ((X num) (Y num)) (or (@ (@ ord_less_num Y) X) (= X Y) (@ (@ ord_less_num X) Y))) (forall ((X produc8763457246119570046nteger)) (not (forall ((F5 (-> code_integer option6357759511663192854e_term)) (D3 code_integer) (I5 code_integer)) (not (= X (@ (@ produc6137756002093451184nteger F5) (@ (@ produc1086072967326762835nteger D3) I5))))))) (forall ((A set_int) (X int)) (let ((_let_1 (@ (@ insert_int2 X) bot_bot_set_int))) (=> (@ (@ ord_less_eq_set_int A) _let_1) (or (= A bot_bot_set_int) (= A _let_1))))) (forall ((M2 nat) (Z int)) (= (@ (@ ord_less_nat M2) (@ nat2 Z)) (@ (@ ord_less_int (@ semiri1314217659103216013at_int M2)) Z))) (forall ((X num) (Y num) (Z num)) (let ((_let_1 (@ ord_less_num X))) (=> (@ _let_1 Y) (=> (@ (@ ord_less_eq_num Y) Z) (@ _let_1 Z))))) (forall ((M2 nat) (N nat)) (let ((_let_1 (@ dvd_dvd_nat (@ numeral_numeral_nat (@ bit0 one))))) (= (@ _let_1 (@ (@ minus_minus_nat M2) N)) (or (@ _let_1 (@ (@ plus_plus_nat M2) N)) (@ (@ ord_less_nat M2) N))))) (forall ((X set_Pr1261947904930325089at_nat) (Y set_Pr1261947904930325089at_nat) (Z set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ ord_le3146513528884898305at_nat X))) (=> (@ _let_1 Y) (=> (@ _let_1 Z) (@ _let_1 (@ (@ inf_in2572325071724192079at_nat Y) Z)))))) (forall ((X int) (Xa int) (Y list_int)) (let ((_let_1 (@ (@ ord_less_eq_int X) Xa))) (=> (= (@ (@ upto X) Xa) Y) (and (=> _let_1 (= Y (@ (@ cons_int X) (@ (@ upto (@ (@ plus_plus_int X) one_one_int)) Xa)))) (=> (not _let_1) (= Y nil_int)))))) (forall ((Xs list_int) (Xs4 list_int) (Xsi list_nat) (Xsi2 list_nat) (A (-> int nat assn)) (A6 (-> int nat assn))) (=> (= Xs Xs4) (=> (= Xsi Xsi2) (=> (forall ((X3 int) (Xi nat)) (=> (@ (@ member_int X3) (@ set_int2 Xs4)) (=> (@ (@ member_nat Xi) (@ set_nat2 Xsi2)) (= (@ (@ A X3) Xi) (@ (@ A6 X3) Xi))))) (= (@ (@ (@ vEBT_L77084186935402305nt_nat A) Xs) Xsi) (@ (@ (@ vEBT_L77084186935402305nt_nat A6) Xs4) Xsi2)))))) (= ord_less_nat (lambda ((A3 nat) (__flatten_var_0 nat)) (@ (@ ord_less_eq_nat (@ (@ plus_plus_nat A3) one_one_nat)) __flatten_var_0))) (@ (@ ratrel _let_23) _let_23) (forall ((P6 rat) (Q6 rat)) (= (@ quotient_of (@ (@ divide_divide_rat P6) Q6)) (@ (@ produc4245557441103728435nt_int (lambda ((A3 int) (C5 int)) (@ (@ produc4245557441103728435nt_int (lambda ((B3 int) (D5 int)) (@ normalize (@ (@ product_Pair_int_int (@ (@ times_times_int A3) D5)) (@ (@ times_times_int C5) B3))))) (@ quotient_of Q6)))) (@ quotient_of P6)))) (forall ((X1 nat) (X22 nat) (L12 list_nat) (L23 list_nat)) (let ((_let_1 (@ cons_nat X22))) (let ((_let_2 (@ _let_1 L23))) (let ((_let_3 (@ merge_nat L12))) (let ((_let_4 (@ cons_nat X1))) (let ((_let_5 (@ merge_nat (@ _let_4 L12)))) (let ((_let_6 (@ _let_5 _let_2))) (let ((_let_7 (@ (@ ord_less_nat X1) X22))) (let ((_let_8 (= X1 X22))) (and (=> (not _let_7) (and (=> _let_8 (= _let_6 (@ _let_4 (@ _let_3 L23)))) (=> (not _let_8) (= _let_6 (@ _let_1 (@ _let_5 L23)))))) (=> _let_7 (= _let_6 (@ _let_4 (@ _let_3 _let_2)))))))))))))) _let_96 (forall ((N nat) (Xs list_d)) (= (@ (@ ord_less_eq_nat (@ suc N)) (@ size_size_list_d Xs)) (exists ((X2 d) (Ys3 list_d)) (and (@ (@ ord_less_eq_nat N) (@ size_size_list_d Ys3)) (= Xs (@ (@ cons_d X2) Ys3)))))) (forall ((T int)) (exists ((Z4 int)) (forall ((X7 int)) (=> (@ (@ ord_less_int Z4) X7) (@ (@ ord_less_eq_int T) X7))))) (forall ((R2 set_Pr5564308138774400199at_nat) (S3 set_Pr5564308138774400199at_nat)) (= (@ field_2862844103579723188at_nat (@ (@ sup_su6664651903789602459at_nat R2) S3)) (@ (@ sup_su5525570899277871387at_nat (@ field_2862844103579723188at_nat R2)) (@ field_2862844103579723188at_nat S3)))) (forall ((X (-> produc3658429121746597890et_nat Bool)) (Y produc3925858234332021118et_nat) (Xs list_P7985473006766602707_nat_o) (Ys list_P2321686559999237006et_nat)) (=> (@ (@ member6124377750444531601et_nat (@ (@ produc2245416461498447860et_nat X) Y)) (@ set_Pr7458301993993767461et_nat (@ (@ zip_Pr8136144321567152340et_nat Xs) Ys))) (@ (@ member1996754912294343701et_nat Y) (@ set_Pr364071364088684201et_nat Ys)))) (= ord_less_eq_nat (lambda ((B3 nat) (A3 nat)) (or (@ (@ ord_less_nat B3) A3) (= A3 B3)))) (not (= bot_bot_assn one_one_assn)) (forall ((X produc3843707927480180839at_nat) (X4 set_Pr4329608150637261639at_nat)) (=> (not (@ (@ member8757157785044589968at_nat X) X4)) (= (@ (@ minus_3314409938677909166at_nat X4) (@ (@ insert9069300056098147895at_nat X) bot_bo228742789529271731at_nat)) X4))) (forall ((A2 set_o) (A7 set_o) (B2 set_o) (B6 set_o)) (=> (@ (@ ord_less_eq_set_o A2) A7) (=> (@ (@ ord_less_eq_set_o B2) B6) (=> (= (@ (@ inf_inf_set_o A7) B6) bot_bot_set_o) (= (@ (@ inf_inf_set_o A2) B2) bot_bot_set_o))))) (forall ((M2 nat) (N nat)) (let ((_let_1 (@ (@ ord_min_nat M2) N))) (= (not (@ (@ ord_less_nat _let_1) N)) (= _let_1 N)))) (forall ((A2 code_integer) (B2 code_integer)) (let ((_let_1 (@ ord_le6747313008572928689nteger zero_z3403309356797280102nteger))) (=> (@ _let_1 A2) (=> (@ _let_1 B2) (@ _let_1 (@ (@ plus_p5714425477246183910nteger A2) B2)))))) (forall ((X assn) (Y assn) (N nat)) (=> (= (@ (@ times_times_assn X) Y) one_one_assn) (= (@ (@ times_times_assn (@ (@ power_power_assn X) N)) (@ (@ power_power_assn Y) N)) one_one_assn))) (forall ((L list_nat)) (=> (not (= L nil_nat)) (not (forall ((X3 nat) (Xs2 list_nat)) (not (= L (@ (@ cons_nat X3) Xs2))))))) (forall ((P assn)) (= (@ (@ times_times_assn P) sln) P)) (forall ((A2 int) (B2 int)) (=> (@ (@ ord_less_int A2) zero_zero_int) (=> (@ (@ ord_less_int B2) zero_zero_int) (@ (@ ord_less_int zero_zero_int) (@ (@ times_times_int A2) B2))))) (forall ((X assn)) (= (@ (@ inf_inf_assn top_top_assn) X) X)) (forall ((N nat) (M2 nat)) (=> (@ (@ ord_less_nat one_one_nat) N) (=> (@ (@ ord_less_nat zero_zero_nat) M2) (@ (@ ord_less_nat (@ (@ divide_divide_nat M2) N)) M2)))) (forall ((B2 int) (A2 int)) (=> (@ (@ ord_less_eq_int B2) A2) (= (@ (@ inf_inf_int A2) B2) B2))) (forall ((A2 int) (B2 int)) (=> (not (= A2 B2)) (=> (@ (@ ord_less_eq_int A2) B2) (@ (@ ord_less_int A2) B2)))) (forall ((B2 nat) (K3 nat)) (=> (@ (@ ord_less_eq_nat (@ numeral_numeral_nat (@ bit0 one))) B2) (=> (@ (@ ord_less_eq_nat one_one_nat) K3) (exists ((N5 nat)) (let ((_let_1 (@ power_power_nat B2))) (and (@ (@ ord_less_nat K3) (@ _let_1 (@ (@ plus_plus_nat N5) one_one_nat))) (@ (@ ord_less_eq_nat (@ _let_1 N5)) K3))))))) (forall ((I nat) (L list_P7985473006766602707_nat_o) (X (-> produc3658429121746597890et_nat Bool)) (Y (-> produc3658429121746597890et_nat Bool))) (let ((_let_1 (@ member6576561426505652726_nat_o X))) (=> (@ (@ ord_less_nat I) (@ size_s8908918004648414271_nat_o L)) (= (@ _let_1 (@ set_Pr400311997697478754_nat_o (@ (@ (@ list_u6943956310655620667_nat_o L) I) Y))) (or (and (forall ((Y5 (-> produc3658429121746597890et_nat Bool))) (@ (@ member6576561426505652726_nat_o X) (@ set_Pr400311997697478754_nat_o (@ (@ (@ list_u6943956310655620667_nat_o L) I) Y5)))) (@ _let_1 (@ set_Pr400311997697478754_nat_o L))) (= X Y)))))) (forall ((X product_prod_nat_nat) (Xs list_P6011104703257516679at_nat)) (=> (not (@ (@ member8440522571783428010at_nat X) (@ set_Pr5648618587558075414at_nat Xs))) (= (@ (@ insert8944034826898310173at_nat X) Xs) (@ (@ cons_P6512896166579812791at_nat X) Xs)))) (= (@ nat_set_decode zero_zero_nat) bot_bot_set_nat) (forall ((A2 rat) (B2 rat) (C rat) (D2 rat)) (=> (= (@ (@ minus_minus_rat A2) B2) (@ (@ minus_minus_rat C) D2)) (= (= A2 B2) (= C D2)))) (forall ((B set_Pr1261947904930325089at_nat) (A2 product_prod_nat_nat) (A set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ inf_in2572325071724192079at_nat B))) (= (= (@ _let_1 (@ (@ 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(B2 int)) (=> (= A2 (@ (@ sup_sup_int A2) B2)) (@ (@ ord_less_eq_int B2) A2))) (forall ((A2 nat)) (= (@ (@ times_times_nat one_one_nat) A2) A2)) (forall ((X set_Pr1261947904930325089at_nat) (Y set_Pr1261947904930325089at_nat) (Z set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ inf_in2572325071724192079at_nat X))) (= (@ (@ inf_in2572325071724192079at_nat (@ _let_1 Y)) Z) (@ _let_1 (@ (@ inf_in2572325071724192079at_nat Y) Z))))) (@ null_int nil_int) (forall ((X assn) (A2 assn) (B2 assn)) (let ((_let_1 (@ ord_less_assn X))) (=> (@ _let_1 A2) (@ _let_1 (@ (@ sup_sup_assn A2) B2))))) (forall ((A2 int) (B2 int) (C int)) (= (@ (@ times_times_int (@ (@ plus_plus_int A2) B2)) C) (@ (@ plus_plus_int (@ (@ times_times_int A2) C)) (@ (@ times_times_int B2) C)))) (forall ((A2 code_integer) (B2 code_integer)) (let ((_let_1 (@ ord_le6747313008572928689nteger zero_z3403309356797280102nteger))) (=> (@ (@ ord_le3102999989581377725nteger zero_z3403309356797280102nteger) A2) (=> (@ _let_1 B2) (@ _let_1 (@ (@ plus_p5714425477246183910nteger A2) B2)))))) (forall ((X code_integer) (Y code_integer)) (= (not (@ (@ ord_le3102999989581377725nteger X) Y)) (@ (@ ord_le6747313008572928689nteger Y) X))) (forall ((K3 int)) (=> (@ (@ ord_less_int K3) zero_zero_int) (not (forall ((N5 nat)) (=> (= K3 (@ uminus_uminus_int (@ semiri1314217659103216013at_int N5))) (not (@ (@ ord_less_nat zero_zero_nat) N5))))))) (forall ((A2 assn) (N nat)) (let ((_let_1 (@ (@ power_power_assn A2) N))) (= (@ (@ times_times_assn _let_1) A2) (@ (@ times_times_assn A2) _let_1)))) (forall ((A2 code_integer) (B2 code_integer)) (=> (@ (@ ord_le3102999989581377725nteger A2) one_one_Code_integer) (=> (@ (@ ord_le3102999989581377725nteger zero_z3403309356797280102nteger) B2) (=> (@ (@ ord_le3102999989581377725nteger B2) one_one_Code_integer) (@ (@ ord_le3102999989581377725nteger (@ (@ times_3573771949741848930nteger A2) B2)) one_one_Code_integer))))) (forall ((X assn) (Y assn) (Z assn)) (let ((_let_1 (@ ord_less_eq_assn X))) (=> (@ _let_1 Y) (=> (@ _let_1 Z) (@ _let_1 (@ (@ inf_inf_assn Y) Z)))))) (forall ((Xs list_int) (Ys list_int) (F4 (-> int Bool)) (G (-> int Bool))) (=> (= Xs Ys) (=> (forall ((X3 int)) (=> (@ (@ member_int X3) (@ set_int2 Ys)) (= (@ F4 X3) (@ G X3)))) (= (@ (@ list_ex_int F4) Xs) (@ (@ list_ex_int G) Ys))))) (forall ((A2 code_integer) (B2 code_integer)) (=> (@ (@ ord_le6747313008572928689nteger A2) B2) (@ (@ ord_le3102999989581377725nteger A2) B2))) (forall ((P assn) (R assn) (Ps assn) (F assn) (Q assn)) (let ((_let_1 (@ entails Ps))) (=> (@ (@ entails P) R) (=> (@ _let_1 (@ (@ times_times_assn P) F)) (=> (@ (@ entails (@ (@ times_times_assn R) F)) Q) (@ _let_1 Q)))))) (= ord_less_set_nat (lambda ((X2 set_nat) (Y5 set_nat)) (and (@ (@ ord_less_eq_set_nat X2) Y5) (not (= X2 Y5))))) (forall ((A2 int) (B2 int)) (@ (@ ord_less_eq_int (@ (@ inf_inf_int A2) B2)) A2)) (forall ((X nat) (B set_nat) (A set_nat)) (=> (@ (@ member_nat X) B) (= (@ (@ minus_minus_set_nat (@ (@ insert_nat2 X) A)) B) (@ (@ minus_minus_set_nat A) B)))) (@ (@ _let_37 (lambda ((X2 product_prod_int_int)) (@ (@ product_Pair_int_int (@ uminus_uminus_int (@ product_fst_int_int X2))) (@ product_snd_int_int X2)))) uminus_uminus_rat) (forall ((X set_int)) (= (@ (@ inf_inf_set_int bot_bot_set_int) X) bot_bot_set_int)) (forall ((X nat) (Y nat) (A set_nat)) (let ((_let_1 (@ (@ insert_nat2 Y) bot_bot_set_nat))) (let ((_let_2 (@ insert_nat2 X))) (=> (not (= X Y)) (= (@ (@ minus_minus_set_nat (@ _let_2 A)) _let_1) (@ _let_2 (@ (@ minus_minus_set_nat A) _let_1))))))) (forall ((As2 set_nat) (H2 heap_e7401611519738050253t_unit) (H4 heap_e7401611519738050253t_unit)) (=> (@ (@ (@ relH As2) H2) H4) (@ in_range (@ (@ produc7507926704131184380et_nat H4) As2)))) (forall ((X list_d) (Y list_d)) (=> (not (= (@ size_size_list_d X) (@ size_size_list_d Y))) (not (= X Y)))) (forall ((Xs list_nat) (I nat) (J nat)) (let ((_let_1 (@ nth_nat Xs))) (let ((_let_2 (@ size_size_list_nat Xs))) (=> (@ distinct_nat Xs) (=> (@ (@ ord_less_nat I) _let_2) (=> (@ (@ ord_less_nat J) _let_2) (= (= (@ _let_1 I) (@ _let_1 J)) (= I J)))))))) (forall ((Xs list_P8527749157015355191n_assn) (N nat)) (= (= (@ size_s6829681357464350627n_assn Xs) (@ suc N)) (exists ((Y5 produc6575502325842934193n_assn) (Ys3 list_P8527749157015355191n_assn)) (and (= (@ size_s6829681357464350627n_assn Ys3) N) (= Xs (@ (@ cons_P2971678138204555879n_assn Y5) Ys3)))))) (forall ((A2 nat) (B2 nat)) (=> (= A2 (@ (@ inf_inf_nat A2) B2)) (@ (@ ord_less_eq_nat A2) B2))) (forall ((X set_nat) (Y set_nat)) (@ (@ ord_less_eq_set_nat X) (@ (@ sup_sup_set_nat X) Y))) (forall ((C code_integer) (B2 code_integer)) (= (@ (@ ord_le3102999989581377725nteger C) (@ (@ times_3573771949741848930nteger B2) C)) (and (=> (@ (@ ord_le6747313008572928689nteger C) zero_z3403309356797280102nteger) (@ (@ ord_le3102999989581377725nteger B2) one_one_Code_integer)) (=> (@ (@ ord_le6747313008572928689nteger zero_z3403309356797280102nteger) C) (@ (@ ord_le3102999989581377725nteger one_one_Code_integer) B2))))) (forall ((Xs list_o) (N nat) (X Bool)) (=> (@ distinct_o Xs) (=> (@ (@ ord_less_nat N) (@ size_size_list_o Xs)) (= (@ set_o2 (@ (@ (@ list_update_o Xs) N) X)) (@ (@ insert_o2 X) (@ (@ minus_minus_set_o (@ set_o2 Xs)) (@ (@ insert_o2 (@ (@ nth_o Xs) N)) bot_bot_set_o))))))) (forall ((C nat) (A set_nat) (B set_nat)) (let ((_let_1 (@ member_nat C))) (= (@ _let_1 (@ (@ minus_minus_set_nat A) B)) (and (@ _let_1 A) (not (@ _let_1 B)))))) _let_94 (forall ((A2 assn) (B2 assn) (F4 (-> assn assn)) (C assn)) (=> (@ (@ ord_less_assn A2) B2) (=> (= (@ F4 B2) C) (=> (forall ((X3 assn) (Y2 assn)) (=> (@ (@ ord_less_assn X3) Y2) (@ (@ ord_less_assn (@ F4 X3)) (@ F4 Y2)))) (@ (@ ord_less_assn (@ F4 A2)) C))))) (forall ((Xs list_nat) (Ys list_d)) (= (@ size_s457006183821432778_nat_d (@ (@ product_nat_d Xs) Ys)) (@ (@ times_times_nat (@ size_size_list_nat Xs)) (@ size_size_list_d Ys)))) (forall ((L code_integer) (U code_integer)) (@ finite6017078050557962740nteger (@ (@ set_or189985376899183464nteger L) U))) (forall ((Xs list_nat) (Ys list_nat) (X nat)) (=> (@ (@ ord_less_eq_nat (@ size_size_list_nat Xs)) (@ size_size_list_nat Ys)) (not (= Xs (@ (@ cons_nat X) Ys))))) (forall ((K3 nat) (M2 nat)) (=> (@ (@ ord_less_nat zero_zero_nat) K3) (=> (@ (@ ord_less_eq_nat K3) M2) (@ (@ ord_less_nat (@ (@ minus_minus_nat K3) (@ suc zero_zero_nat))) M2)))) (forall ((A2 set_nat)) (= (@ (@ sup_sup_set_nat A2) A2) A2)) (forall ((M2 nat)) (= (@ (@ set_or4665077453230672383an_nat M2) zero_zero_nat) bot_bot_set_nat)) (forall ((B2 nat) (A2 nat)) (=> (@ (@ ord_less_eq_nat B2) A2) (= (@ (@ ord_min_nat A2) B2) B2))) (forall ((X int) (Xs list_int) (Y produc6575502325842934193n_assn) (Ys list_P8527749157015355191n_assn)) (= (@ (@ zip_in7098856637274830732n_assn (@ (@ cons_int X) Xs)) (@ (@ cons_P2971678138204555879n_assn Y) Ys)) (@ (@ cons_P8828502514829229636n_assn (@ (@ produc3313821056773121708n_assn X) Y)) (@ (@ zip_in7098856637274830732n_assn Xs) Ys)))) (forall ((I nat) (J nat) (Xs list_int) (X int)) (=> (not (= I J)) (= (@ (@ nth_int (@ (@ (@ list_update_int Xs) I) X)) J) (@ (@ nth_int Xs) J)))) (forall ((I nat) (I3 set_nat) (Xs list_d) (A (-> d int assn)) (Xsi list_int)) (=> (not (@ (@ member_nat I) I3)) (=> (@ (@ ord_less_nat I) (@ size_size_list_d Xs)) (= (@ (@ (@ (@ vEBT_L7818125895572137869_d_int (@ (@ insert_nat2 I) I3)) A) Xs) Xsi) (@ (@ times_times_assn (@ (@ A (@ (@ nth_d Xs) I)) (@ (@ nth_int Xsi) I))) (@ (@ (@ (@ vEBT_L7818125895572137869_d_int I3) A) Xs) Xsi)))))) (forall ((X d) (Xs list_d) (Y d)) (= (@ (@ (@ list_update_d (@ (@ cons_d X) Xs)) zero_zero_nat) Y) (@ (@ cons_d Y) Xs))) (forall ((A2 (-> produc3658429121746597890et_nat Bool)) (A set_Pr4532377907799695533_nat_o) (B2 (-> produc3658429121746597890et_nat Bool)) (B set_Pr4532377907799695533_nat_o)) (let ((_let_1 (= A2 B2))) (=> (not (@ (@ member6576561426505652726_nat_o A2) A)) (=> (not (@ (@ member6576561426505652726_nat_o B2) B)) (= (= (@ (@ insert5175938949040314269_nat_o A2) A) (@ (@ insert5175938949040314269_nat_o B2) B)) (and (=> (not _let_1) (exists ((C3 set_Pr4532377907799695533_nat_o)) (and (= A (@ (@ insert5175938949040314269_nat_o B2) C3)) (= B (@ (@ insert5175938949040314269_nat_o A2) C3)) (not (@ (@ member6576561426505652726_nat_o A2) C3)) (not (@ (@ member6576561426505652726_nat_o B2) C3))))) (=> _let_1 (= A B)))))))) (forall ((A2 code_integer) (B2 code_integer) (C code_integer)) (=> (@ (@ ord_le6747313008572928689nteger zero_z3403309356797280102nteger) A2) (=> (@ (@ ord_le3102999989581377725nteger B2) C) (@ (@ ord_le6747313008572928689nteger B2) (@ (@ plus_p5714425477246183910nteger A2) C))))) (forall ((A2 set_o)) (=> (@ (@ ord_less_eq_set_o A2) bot_bot_set_o) (= A2 bot_bot_set_o))) (forall ((X1 (-> produc6241069584506657477e_term option6357759511663192854e_term)) (X22 produc8923325533196201883nteger) (Y1 (-> produc6241069584506657477e_term option6357759511663192854e_term)) (Y22 produc8923325533196201883nteger)) (= (= (@ (@ produc8603105652947943368nteger X1) X22) (@ (@ produc8603105652947943368nteger Y1) Y22)) (and (= X22 Y22) (= X1 Y1)))) (forall ((I nat) (Y d)) (= (@ (@ (@ list_update_d nil_d) I) Y) nil_d)) (forall ((X int) (X4 set_int)) (=> (not (@ (@ member_int X) X4)) (= (@ (@ minus_minus_set_int X4) (@ (@ insert_int2 X) bot_bot_set_int)) X4))) (forall ((C rat) (B2 rat)) (= (@ (@ ord_less_eq_rat C) (@ (@ times_times_rat C) B2)) (and (=> (@ (@ ord_less_rat C) zero_zero_rat) (@ (@ ord_less_eq_rat B2) one_one_rat)) (=> (@ (@ ord_less_rat zero_zero_rat) C) (@ (@ ord_less_eq_rat one_one_rat) B2))))) (forall ((A set_int) (Ys list_int)) (= (@ (@ ord_less_eq_set_int A) (@ coset_int Ys)) (forall ((X2 int)) (let ((_let_1 (@ member_int X2))) (=> (@ _let_1 (@ set_int2 Ys)) (not (@ _let_1 A))))))) (forall ((X nat) (Z nat) (R2 set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ member8440522571783428010at_nat (@ (@ product_Pair_nat_nat X) Z)))) (=> (@ _let_1 (@ transi6264000038957366511cl_nat R2)) (=> (not (@ 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(B2 nat) (C nat)) (=> (= A2 B2) (=> (@ (@ ord_less_eq_nat B2) C) (@ (@ ord_less_eq_nat A2) C)))) (forall ((A2 code_integer) (B2 code_integer) (C code_integer)) (let ((_let_1 (@ ord_le3102999989581377725nteger B2))) (=> (@ (@ ord_le3102999989581377725nteger zero_z3403309356797280102nteger) A2) (=> (@ _let_1 C) (@ _let_1 (@ (@ plus_p5714425477246183910nteger A2) C)))))) (forall ((Xs list_P8527749157015355191n_assn) (N nat) (X produc6575502325842934193n_assn)) (=> (@ distin4809818325527169450n_assn Xs) (=> (@ (@ ord_less_nat N) (@ size_s6829681357464350627n_assn Xs)) (= (@ set_Pr1139785259514867910n_assn (@ (@ (@ list_u4534839942911652127n_assn Xs) N) X)) (@ (@ insert5290817439147925377n_assn X) (@ (@ minus_2301194108115264760n_assn (@ set_Pr1139785259514867910n_assn Xs)) (@ (@ insert5290817439147925377n_assn (@ (@ nth_Pr1769885009046257848n_assn Xs) N)) bot_bo1176836662018730877n_assn))))))) (forall ((X set_nat) (Y set_nat)) (let ((_let_1 (@ sup_sup_set_nat X))) (let ((_let_2 (@ _let_1 Y))) (= (@ _let_1 _let_2) _let_2)))) (forall ((X nat) (B2 nat) (A2 nat)) (let ((_let_1 (@ ord_less_nat X))) (=> (@ _let_1 B2) (@ _let_1 (@ (@ sup_sup_nat A2) B2))))) (forall ((X produc3843707927480180839at_nat) (A set_Pr4329608150637261639at_nat) (B set_Pr4329608150637261639at_nat)) (let ((_let_1 (@ ord_le1268244103169919719at_nat A))) (=> (not (@ (@ member8757157785044589968at_nat X) A)) (= (@ _let_1 (@ (@ insert9069300056098147895at_nat X) B)) (@ _let_1 B))))) (forall ((A2 int)) (= (@ (@ ord_less_int (@ (@ plus_plus_int A2) A2)) zero_zero_int) (@ (@ ord_less_int A2) zero_zero_int))) (forall ((N nat) (M2 nat)) (=> (@ (@ ord_less_nat zero_zero_nat) N) (=> (@ (@ ord_less_eq_nat N) M2) (= (@ (@ divide_divide_nat M2) N) (@ suc (@ (@ divide_divide_nat (@ (@ minus_minus_nat M2) N)) N)))))) (forall ((I nat) (I3 set_nat) (Xs list_int) (A (-> int int assn)) (Xsi list_int)) (=> (@ (@ member_nat I) I3) (=> (@ (@ ord_less_nat I) (@ size_size_list_int Xs)) (= (@ (@ (@ (@ vEBT_L8888932350013902202nt_int I3) A) Xs) Xsi) (@ (@ times_times_assn (@ (@ A (@ (@ nth_int Xs) I)) (@ (@ nth_int Xsi) I))) (@ (@ (@ (@ vEBT_L8888932350013902202nt_int (@ (@ minus_minus_set_nat I3) (@ (@ insert_nat2 I) bot_bot_set_nat))) A) Xs) Xsi)))))) (forall ((E produc3843707927480180839at_nat) (A2 list_P5464809261938338413at_nat)) (=> (@ (@ member8757157785044589968at_nat E) (@ set_Pr3765526544606949372at_nat A2)) (=> (forall ((Z22 list_P5464809261938338413at_nat)) (not (= A2 (@ (@ cons_P3940603068885512221at_nat E) Z22)))) (not (forall ((Z1 produc3843707927480180839at_nat) (Z22 list_P5464809261938338413at_nat)) (=> (= A2 (@ (@ cons_P3940603068885512221at_nat Z1) Z22)) (not (@ (@ member8757157785044589968at_nat E) (@ set_Pr3765526544606949372at_nat Z22))))))))) (forall ((C code_integer) (A2 code_integer) (B2 code_integer)) (=> (@ (@ ord_le3102999989581377725nteger C) zero_z3403309356797280102nteger) (=> (@ (@ ord_le3102999989581377725nteger A2) B2) (@ (@ 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_let_1 I))))))) (forall ((A2 code_integer) (B2 code_integer) (C code_integer)) (= (@ (@ ord_le6747313008572928689nteger (@ (@ minus_8373710615458151222nteger A2) B2)) C) (@ (@ ord_le6747313008572928689nteger A2) (@ (@ plus_p5714425477246183910nteger C) B2)))) _let_93 (forall ((N nat)) (= (@ set_ord_lessThan_nat (@ suc N)) (@ (@ insert_nat2 zero_zero_nat) (@ (@ image_nat_nat suc) (@ set_ord_lessThan_nat N))))) (forall ((A set_Pr4532377907799695533_nat_o)) (= (exists ((X2 (-> produc3658429121746597890et_nat Bool))) (@ (@ member6576561426505652726_nat_o X2) A)) (not (= A bot_bo7824918357723582233_nat_o)))) (forall ((X nat) (Y nat) (Z nat)) (let ((_let_1 (@ ord_less_eq_nat X))) (=> (@ _let_1 Y) (=> (@ _let_1 Z) (@ _let_1 (@ (@ inf_inf_nat Y) Z)))))) (forall ((Xs list_nat) (Ys list_c) (P (-> list_nat list_c Bool))) (=> (= (@ size_size_list_nat Xs) (@ size_size_list_c Ys)) (=> (@ (@ P nil_nat) nil_c) (=> (forall ((X3 nat) (Xs2 list_nat) (Y2 c) (Ys5 list_c)) (=> (= (@ size_size_list_nat Xs2) 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(forall ((Xs list_int) (Y int) (Ys list_int) (R2 set_Pr958786334691620121nt_int)) (=> (@ (@ member6698963635872716290st_int (@ (@ produc364263696895485585st_int Xs) (@ (@ cons_int Y) Ys))) (@ listrel_int_int R2)) (not (forall ((X3 int) (Xs2 list_int)) (=> (= Xs (@ (@ cons_int X3) Xs2)) (=> (@ (@ member5262025264175285858nt_int (@ (@ product_Pair_int_int X3) Y)) R2) (not (@ (@ member6698963635872716290st_int (@ (@ produc364263696895485585st_int Xs2) Ys)) (@ listrel_int_int R2))))))))) (forall ((X d) (L list_d) (I nat) (Y d)) (let ((_let_1 (@ member_d X))) (=> (@ _let_1 (@ set_d2 (@ (@ (@ list_update_d L) I) Y))) (=> (=> (@ (@ ord_less_nat I) (@ size_size_list_d L)) (not (= X Y))) (@ _let_1 (@ set_d2 L)))))) _let_89 (= ord_less_eq_assn (lambda ((X2 assn) (Y5 assn)) (or (@ (@ ord_less_assn X2) Y5) (= X2 Y5)))) (forall ((X list_P8527749157015355191n_assn) (Y list_P8527749157015355191n_assn)) (= (@ (@ (@ if_lis7173127979115136509n_assn true) X) Y) X)) (forall ((X set_Pr1261947904930325089at_nat) (Xs list_s1210847774152347623at_nat) (Ys list_s1210847774152347623at_nat) (R2 set_Pr4329608150637261639at_nat)) (=> (@ (@ member4080735728053443344at_nat (@ (@ produc7536900900485677911at_nat (@ (@ cons_s6881495754146722583at_nat X) Xs)) Ys)) (@ listre8180072825634266816at_nat R2)) (=> (forall ((Y2 set_Pr1261947904930325089at_nat)) (=> (= Ys (@ (@ cons_s6881495754146722583at_nat Y2) Xs)) (not (@ (@ member8757157785044589968at_nat (@ (@ produc2922128104949294807at_nat X) Y2)) R2)))) (not (forall ((Zs2 list_s1210847774152347623at_nat)) (=> (= Ys (@ (@ cons_s6881495754146722583at_nat X) Zs2)) (not (@ (@ member4080735728053443344at_nat (@ (@ produc7536900900485677911at_nat Xs) Zs2)) (@ listre8180072825634266816at_nat R2))))))))) (forall ((A0 int) (A1 int) (P (-> int int Bool))) (=> (@ (@ accp_P1096762738010456898nt_int bit_and_int_rel) (@ (@ product_Pair_int_int A0) A1)) (=> (forall ((K int) (L2 int)) (let ((_let_1 (@ numeral_numeral_int (@ bit0 one)))) (let ((_let_2 (@ (@ insert_int2 zero_zero_int) (@ (@ insert_int2 (@ uminus_uminus_int one_one_int)) bot_bot_set_int)))) (=> (@ (@ accp_P1096762738010456898nt_int bit_and_int_rel) (@ (@ product_Pair_int_int K) L2)) (=> (=> (not (and (@ (@ member_int L2) _let_2) (@ (@ member_int K) _let_2))) (@ (@ P (@ (@ divide_divide_int K) _let_1)) (@ (@ divide_divide_int L2) _let_1))) (@ (@ P K) L2)))))) (@ (@ P A0) A1)))) (forall ((I nat) (V2 d)) (= (@ (@ (@ list_update_d nil_d) I) V2) nil_d)) (forall ((X int) (Y int)) (=> (@ (@ ord_less_int X) Y) (not (= X Y)))) (forall ((C int) (A2 int)) (= (= (@ (@ times_times_int C) A2) C) (or (= C zero_zero_int) (= A2 one_one_int)))) (forall ((As2 set_nat) (H2 heap_e7401611519738050253t_unit) (H4 heap_e7401611519738050253t_unit)) (=> (@ (@ (@ relH As2) H2) H4) (@ in_range (@ (@ produc7507926704131184380et_nat H2) As2)))) (forall ((A2 rat) (B2 rat) (N nat)) (= (@ (@ power_power_rat (@ (@ times_times_rat A2) B2)) N) (@ (@ times_times_rat (@ (@ power_power_rat A2) N)) (@ (@ power_power_rat B2) N)))) (forall ((X list_P8527749157015355191n_assn)) (=> (not (= X nil_Pr5671120429643327159n_assn)) (=> (forall ((X3 produc6575502325842934193n_assn)) (not (= X (@ (@ cons_P2971678138204555879n_assn X3) nil_Pr5671120429643327159n_assn)))) (not (forall ((X3 produc6575502325842934193n_assn) (Y2 produc6575502325842934193n_assn) (Xs2 list_P8527749157015355191n_assn)) (not (= X (@ (@ cons_P2971678138204555879n_assn X3) (@ (@ cons_P2971678138204555879n_assn Y2) Xs2))))))))) (forall ((A2 set_nat) (X set_nat) (B2 set_nat)) (=> (@ (@ ord_less_eq_set_nat A2) X) (=> (@ (@ ord_less_eq_set_nat B2) X) (@ (@ ord_less_eq_set_nat (@ (@ sup_sup_set_nat A2) B2)) X)))) (forall ((X produc254973753779126261st_nat)) (=> (forall ((P5 (-> nat nat Bool))) (not (= X (@ (@ produc4727192421694094319st_nat P5) nil_nat)))) (=> (forall ((P5 (-> nat nat Bool)) (X3 nat)) (not (= X (@ (@ produc4727192421694094319st_nat P5) (@ (@ cons_nat X3) nil_nat))))) (not (forall ((P5 (-> nat nat Bool)) (X3 nat) (Y2 nat) (Xs2 list_nat)) (not (= X (@ (@ produc4727192421694094319st_nat P5) (@ (@ cons_nat X3) (@ (@ cons_nat Y2) Xs2)))))))))) (= nat_prod_decode_aux (lambda ((K4 nat) (M nat)) (let ((_let_1 (@ suc K4))) (@ (@ (@ if_Pro6206227464963214023at_nat (@ (@ ord_less_eq_nat M) K4)) (@ (@ product_Pair_nat_nat M) (@ (@ minus_minus_nat K4) M))) (@ (@ nat_prod_decode_aux _let_1) (@ (@ minus_minus_nat M) _let_1)))))) _let_87 (forall ((Xs list_c) (A set_c) (X c) (I nat)) (=> (@ (@ ord_less_eq_set_c (@ set_c2 Xs)) A) (=> (@ (@ member_c X) A) (@ (@ ord_less_eq_set_c (@ set_c2 (@ (@ (@ list_update_c Xs) I) X))) A)))) (forall ((Xs list_int)) (= (@ (@ sorted_wrt_int ord_less_eq_int) Xs) (forall ((I4 nat)) (let ((_let_1 (@ suc I4))) (let ((_let_2 (@ nth_int Xs))) (=> (@ (@ ord_less_nat _let_1) (@ size_size_list_int Xs)) (@ (@ ord_less_eq_int (@ _let_2 I4)) (@ _let_2 _let_1)))))))) (forall ((Ys list_nat) (Xs list_nat)) (=> (@ distinct_nat Ys) (=> (= (@ set_nat2 Ys) (@ set_nat2 Xs)) (@ (@ ord_less_eq_nat (@ size_size_list_nat Ys)) (@ size_size_list_nat Xs))))) (forall ((C product_prod_nat_nat) (A set_Pr1261947904930325089at_nat) (B set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ member8440522571783428010at_nat C))) (=> (@ _let_1 A) (=> (not (@ _let_1 B)) (@ _let_1 (@ (@ minus_1356011639430497352at_nat A) B)))))) (forall ((X num) (Y num)) (or (@ (@ ord_less_num Y) X) (@ (@ ord_less_eq_num X) Y))) (forall ((L list_nat) (I nat) (J nat)) (let ((_let_1 (@ nth_nat L))) (=> (@ (@ sorted_wrt_nat ord_less_eq_nat) L) (=> (@ distinct_nat L) (=> (@ (@ ord_less_nat I) J) (=> (@ (@ ord_less_nat J) (@ size_size_list_nat L)) (@ (@ ord_less_nat (@ _let_1 I)) (@ _let_1 J)))))))) (forall ((X assn)) (= (= one_one_assn X) (= X one_one_assn))) (forall ((X nat) (B set_nat) (A set_nat)) (let ((_let_1 (@ (@ minus_minus_set_nat A) B))) (let ((_let_2 (@ insert_nat2 X))) (let ((_let_3 (@ (@ minus_minus_set_nat (@ _let_2 A)) B))) (let ((_let_4 (@ (@ member_nat X) B))) (and (=> _let_4 (= _let_3 _let_1)) (=> (not _let_4) (= _let_3 (@ _let_2 _let_1))))))))) (forall ((Xs list_nat)) (= (= Xs nil_nat) (@ null_nat Xs))) (forall ((X (-> produc3658429121746597890et_nat Bool)) (Xa (-> produc3658429121746597890et_nat Bool)) (Xb produc3658429121746597890et_nat)) (=> (@ (@ (@ wand_raw X) Xa) Xb) (not (forall ((H heap_e7401611519738050253t_unit) (As set_nat)) (let ((_let_1 (@ (@ produc7507926704131184380et_nat H) As))) (=> (= Xb _let_1) (not (and (@ in_range _let_1) (forall ((H7 heap_e7401611519738050253t_unit) (As6 set_nat)) (let ((_let_1 (@ produc7507926704131184380et_nat H7))) (=> (and (@ in_range (@ _let_1 As)) (@ X (@ _let_1 As6)) (@ (@ (@ relH As) H) H7) (= (@ (@ inf_inf_set_nat As) As6) bot_bot_set_nat)) (@ Xa (@ _let_1 (@ (@ sup_sup_set_nat As) As6)))))))))))))) (forall ((A2 num) (B2 num) (F4 (-> num num)) (C num)) (=> (@ (@ ord_less_num A2) B2) (=> (@ (@ ord_less_eq_num (@ F4 B2)) C) (=> (forall ((X3 num) (Y2 num)) (=> (@ (@ ord_less_num X3) Y2) (@ (@ ord_less_num (@ F4 X3)) (@ F4 Y2)))) (@ (@ ord_less_num (@ F4 A2)) C))))) (forall ((B2 nat) (C nat) (A2 nat)) (=> (@ (@ ord_less_eq_nat B2) C) (@ (@ ord_less_eq_nat (@ (@ inf_inf_nat A2) B2)) C))) (forall ((B set_nat) (A set_nat)) (= (@ (@ sup_sup_set_nat (@ (@ minus_minus_set_nat B) A)) A) (@ (@ sup_sup_set_nat B) A))) _let_86 _let_85 (forall ((B2 filter_nat) (A2 filter_nat) (C filter_nat)) (=> (@ (@ ord_less_filter_nat B2) A2) (=> (@ (@ ord_le2510731241096832064er_nat C) B2) (@ (@ ord_less_filter_nat C) A2)))) (forall ((C set_Pr4329608150637261639at_nat) (A2 set_Pr4329608150637261639at_nat) (B2 set_Pr4329608150637261639at_nat)) (let ((_let_1 (@ ord_le2604355607129572851at_nat C))) (=> (@ _let_1 A2) (@ _let_1 (@ (@ sup_su5525570899277871387at_nat A2) B2))))) (forall ((A set_nat) (C2 set_nat) (B set_nat)) (=> (@ (@ ord_less_eq_set_nat A) C2) (=> (@ (@ ord_less_eq_set_nat B) C2) (@ (@ ord_less_eq_set_nat (@ (@ sup_sup_set_nat A) B)) C2)))) (forall ((C assn) (B2 assn) (A2 assn)) (let ((_let_1 (@ ord_less_eq_assn C))) (=> (@ _let_1 B2) (@ _let_1 (@ (@ sup_sup_assn A2) B2))))) (forall ((Xs list_nat) (Ys list_int)) (=> (@ distinct_nat Xs) (=> (@ distinct_int Ys) (@ distin2745374544067255638at_int (@ (@ product_nat_int Xs) Ys))))) (forall ((X list_P7985473006766602707_nat_o) (Y list_P7985473006766602707_nat_o)) (= (@ (@ (@ if_lis2904118647880296857_nat_o false) X) Y) Y)) (forall ((P assn) (H2 produc3658429121746597890et_nat)) (=> (@ (@ rep_assn (@ (@ times_times_assn P) top_top_assn)) H2) (not (forall ((H5 produc3658429121746597890et_nat)) (not (@ (@ rep_assn P) H5)))))) (forall ((X set_Pr4329608150637261639at_nat) (Y set_Pr4329608150637261639at_nat) (Z set_Pr4329608150637261639at_nat)) (let ((_let_1 (@ sup_su5525570899277871387at_nat X))) (= (@ (@ sup_su5525570899277871387at_nat (@ _let_1 Y)) Z) (@ _let_1 (@ (@ sup_su5525570899277871387at_nat Y) Z))))) (forall ((M2 nat) (N nat)) (=> (@ (@ ord_less_eq_nat M2) N) (@ (@ ord_less_nat M2) (@ suc N)))) (forall ((B set_o)) (= (@ (@ inf_inf_set_o 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Y5)))) (forall ((B6 nat) (A7 nat)) (= (not (@ (@ ord_less_eq_nat B6) A7)) (@ (@ ord_less_nat A7) B6))) (forall ((A set_Pr4329608150637261639at_nat) (B set_Pr4329608150637261639at_nat) (C2 set_Pr4329608150637261639at_nat)) (let ((_let_1 (@ minus_3314409938677909166at_nat A))) (= (@ _let_1 (@ (@ inf_in7913087082777306421at_nat B) C2)) (@ (@ sup_su5525570899277871387at_nat (@ _let_1 B)) (@ _let_1 C2))))) (forall ((X code_integer) (Y code_integer)) (=> (@ (@ ord_le3102999989581377725nteger X) Y) (= (not (@ (@ ord_le6747313008572928689nteger X) Y)) (= X Y)))) (forall ((Xs list_c) (Ys list_int) (Y int)) (=> (= (@ size_size_list_c Xs) (@ size_size_list_int Ys)) (=> (@ (@ member_int Y) (@ set_int2 Ys)) (not (forall ((X3 c)) (not (@ (@ member4017226226790010994_c_int (@ (@ product_Pair_c_int X3) Y)) (@ set_Pr8441393049761402630_c_int (@ (@ zip_c_int Xs) Ys))))))))) (forall ((X int) (Y produc6575502325842934193n_assn) (Xs list_int) (Ys list_P8527749157015355191n_assn)) (=> (@ (@ member241480614033477777n_assn (@ (@ produc3313821056773121708n_assn X) Y)) (@ set_Pr4510407026980144421n_assn (@ (@ zip_in7098856637274830732n_assn Xs) Ys))) (not (=> (@ (@ member_int X) (@ set_int2 Xs)) (not (@ (@ member7957490590177025114n_assn Y) (@ set_Pr1139785259514867910n_assn Ys))))))) (forall ((A set_o) (A2 Bool) (B set_o)) (let ((_let_1 (@ insert_o2 A2))) (let ((_let_2 (@ minus_minus_set_o A))) (= (@ _let_2 (@ _let_1 B)) (@ (@ minus_minus_set_o (@ _let_2 (@ _let_1 bot_bot_set_o))) B))))) (forall ((B2 int) (A2 int) (C int)) (= (= (@ (@ plus_plus_int B2) A2) (@ (@ plus_plus_int C) A2)) (= B2 C))) (forall ((X nat) (Y nat)) (=> (@ (@ ord_less_nat X) Y) (not (@ (@ ord_less_nat Y) X)))) (forall ((Xs list_c) (Ys list_d) (Y d)) (=> (= (@ size_size_list_c Xs) (@ size_size_list_d Ys)) (=> (@ (@ member_d Y) (@ set_d2 Ys)) (not (forall ((X3 c)) (not (@ (@ member5074992363344545361od_c_d (@ (@ product_Pair_c_d X3) Y)) (@ set_Product_prod_c_d2 (@ (@ zip_c_d Xs) Ys))))))))) (forall ((X int) (Y produc6575502325842934193n_assn) (R2 set_Pr3255386646789011632n_assn) (Xs list_int) (Ys list_P8527749157015355191n_assn)) (let ((_let_1 (@ listre4888949683985722578n_assn R2))) (=> (@ (@ member241480614033477777n_assn (@ (@ produc3313821056773121708n_assn X) Y)) R2) (=> (@ (@ member490958779117458567n_assn (@ (@ produc4510294837168919970n_assn Xs) Ys)) _let_1) (@ (@ member490958779117458567n_assn (@ (@ produc4510294837168919970n_assn (@ (@ cons_int X) Xs)) (@ (@ cons_P2971678138204555879n_assn Y) Ys))) _let_1))))) (forall ((B set_nat) (A set_nat)) (=> (@ (@ ord_less_eq_set_nat B) A) (= (@ (@ inf_inf_set_nat A) B) B))) (forall ((A2 nat) (C nat) (B2 nat)) (= (@ (@ ord_less_eq_nat (@ (@ plus_plus_nat A2) C)) (@ (@ plus_plus_nat B2) C)) (@ (@ ord_less_eq_nat A2) B2))) (forall ((A2 (-> produc3658429121746597890et_nat Bool)) (B set_Pr4532377907799695533_nat_o)) (@ (@ member6576561426505652726_nat_o A2) (@ (@ insert5175938949040314269_nat_o A2) B))) (forall ((C int) (A2 int) (B2 int)) (let ((_let_1 (@ plus_plus_int C))) (= (@ (@ minus_minus_int (@ _let_1 A2)) (@ _let_1 B2)) (@ (@ minus_minus_int A2) B2)))) (forall ((L list_P8527749157015355191n_assn)) (= (@ (@ ord_less_eq_nat (@ suc zero_zero_nat)) (@ size_s6829681357464350627n_assn L)) (not (= L nil_Pr5671120429643327159n_assn)))) (forall ((P6 rat)) (= (@ quotient_of (@ uminus_uminus_rat P6)) (@ (@ produc4245557441103728435nt_int (lambda ((A3 int) (__flatten_var_0 int)) (@ (@ product_Pair_int_int (@ uminus_uminus_int A3)) __flatten_var_0))) (@ quotient_of P6)))) (forall ((A set_o) (B2 Bool) (B set_o)) (let ((_let_1 (@ inf_inf_set_o A))) (= (= bot_bot_set_o (@ _let_1 (@ (@ insert_o2 B2) B))) (and (not (@ (@ member_o B2) A)) (= bot_bot_set_o (@ _let_1 B)))))) (forall ((A set_Pr1261947904930325089at_nat) (B set_Pr1261947904930325089at_nat)) (= (@ (@ sup_su6327502436637775413at_nat (@ (@ minus_1356011639430497352at_nat A) B)) (@ (@ inf_in2572325071724192079at_nat A) B)) A)) (forall ((A2 produc3843707927480180839at_nat) (C2 set_Pr4329608150637261639at_nat) (B set_Pr4329608150637261639at_nat)) (let ((_let_1 (@ (@ inf_in7913087082777306421at_nat B) C2))) (let ((_let_2 (@ insert9069300056098147895at_nat A2))) (let ((_let_3 (@ (@ inf_in7913087082777306421at_nat (@ _let_2 B)) C2))) (let ((_let_4 (@ (@ member8757157785044589968at_nat A2) C2))) (and (=> _let_4 (= _let_3 (@ _let_2 _let_1))) (=> (not _let_4) (= _let_3 _let_1)))))))) (forall ((X set_nat) (Y set_nat) (Z set_nat)) (let ((_let_1 (@ inf_inf_set_nat X))) (= (@ (@ inf_inf_set_nat (@ _let_1 Y)) Z) (@ _let_1 (@ (@ inf_inf_set_nat Y) Z))))) (forall ((B2 code_integer) (A2 code_integer)) (=> (@ (@ ord_le6747313008572928689nteger B2) A2) (not (@ (@ ord_le6747313008572928689nteger A2) B2)))) (forall ((P (-> nat nat Bool)) (S set_nat) (T3 set_nat)) (let ((_let_1 (@ pairwise_nat P))) (=> (@ _let_1 S) (=> (@ (@ ord_less_eq_set_nat T3) S) (@ _let_1 T3))))) (forall ((A2 nat)) (= (@ (@ times_times_nat A2) one_one_nat) A2)) (forall ((P (-> nat produc6575502325842934193n_assn assn)) (L list_nat)) (= (@ (@ (@ vEBT_L9083610150846024284n_assn P) L) nil_Pr5671120429643327159n_assn) (@ pure_assn (= L nil_nat)))) (forall ((X produc8923325533196201883nteger) (Y produc8923325533196201883nteger)) (= (@ (@ (@ if_Pro6119634080678213985nteger true) X) Y) X)) (forall ((N nat) (X nat) (Xs list_nat)) (=> (@ (@ ord_less_nat zero_zero_nat) N) (= (@ (@ nth_nat (@ (@ cons_nat X) Xs)) N) (@ (@ nth_nat Xs) (@ (@ minus_minus_nat N) one_one_nat))))) (forall ((A2 int) (B2 int)) (@ (@ ord_less_eq_int (@ (@ inf_inf_int A2) B2)) B2)) (forall ((I (-> produc3658429121746597890et_nat Bool)) (J (-> produc3658429121746597890et_nat Bool)) (R set_Pr2161125870931222855_nat_o)) (=> (@ (@ member8781333585448626064_nat_o (@ (@ produc7368190662567826135_nat_o I) J)) R) (@ (@ member6576561426505652726_nat_o I) (@ field_81821745747897882_nat_o R)))) (forall ((Xs list_d) (I nat) (X d) (Ys list_c) (Y c)) (= (@ (@ zip_d_c (@ (@ (@ list_update_d Xs) I) X)) (@ (@ (@ list_update_c Ys) I) Y)) (@ (@ (@ list_u5828756922544497492od_d_c (@ (@ zip_d_c Xs) Ys)) I) (@ (@ product_Pair_d_c X) Y)))) _let_84 (forall ((A set_nat)) (=> (not (= A bot_bot_set_nat)) (=> (forall ((X3 nat) (Y2 nat)) (=> (@ (@ member_nat X3) A) (=> (@ (@ member_nat Y2) A) (= X3 Y2)))) (@ is_singleton_nat A)))) (forall ((C nat) (A2 nat) (B2 nat)) (let ((_let_1 (@ times_times_nat C))) (=> (@ (@ ord_less_nat (@ _let_1 A2)) (@ _let_1 B2)) (=> (@ (@ ord_less_eq_nat zero_zero_nat) C) (@ (@ ord_less_nat A2) B2))))) (forall ((F assn) (F2 assn) (A assn)) (=> (@ (@ entailst F) F2) (@ (@ entailst (@ (@ times_times_assn F) A)) (@ (@ times_times_assn F2) A)))) (forall ((M2 nat)) (let ((_let_1 (@ (@ modulo_modulo_nat M2) (@ numeral_numeral_nat (@ bit0 one))))) (= (@ (@ ord_less_nat zero_zero_nat) _let_1) (= _let_1 one_one_nat)))) (forall ((A2 int) (B2 int) (C int)) (let ((_let_1 (@ ord_less_eq_int B2))) (=> (@ (@ ord_less_eq_int zero_zero_int) A2) (=> (@ _let_1 C) (@ _let_1 (@ (@ plus_plus_int A2) C)))))) (forall ((Xs list_P7985473006766602707_nat_o) (B set_Pr4532377907799695533_nat_o)) (= (@ (@ ord_le2965882846123202637_nat_o (@ set_Pr400311997697478754_nat_o Xs)) B) (forall ((X2 (-> produc3658429121746597890et_nat Bool))) (let ((_let_1 (@ member6576561426505652726_nat_o X2))) (=> (@ _let_1 (@ set_Pr400311997697478754_nat_o Xs)) (@ _let_1 B)))))) (forall ((B2 filter_nat) (X filter_nat) (A2 filter_nat)) (=> (@ (@ ord_le2510731241096832064er_nat B2) X) (@ (@ ord_le2510731241096832064er_nat (@ (@ inf_inf_filter_nat A2) B2)) X))) (forall ((A set_Pr1261947904930325089at_nat) (B2 product_prod_nat_nat) (B set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ inf_in2572325071724192079at_nat A))) (= (= bot_bo2099793752762293965at_nat (@ _let_1 (@ (@ insert8211810215607154385at_nat B2) B))) (and (not (@ (@ member8440522571783428010at_nat B2) A)) (= bot_bo2099793752762293965at_nat (@ _let_1 B)))))) (forall ((A set_Pr1261947904930325089at_nat) (B set_Pr1261947904930325089at_nat)) (= (= (@ (@ minus_1356011639430497352at_nat A) B) A) (= (@ (@ inf_in2572325071724192079at_nat A) B) bot_bo2099793752762293965at_nat))) (forall ((X product_prod_nat_nat) (Xs list_P6011104703257516679at_nat)) (= (@ set_Pr5648618587558075414at_nat (@ (@ remove3673390508374433037at_nat X) Xs)) (@ (@ minus_1356011639430497352at_nat (@ set_Pr5648618587558075414at_nat Xs)) (@ (@ insert8211810215607154385at_nat X) bot_bo2099793752762293965at_nat)))) (forall ((X set_nat) (Y set_nat) (Z set_nat)) (let ((_let_1 (@ sup_sup_set_nat X))) (= (@ (@ sup_sup_set_nat (@ _let_1 Y)) Z) (@ _let_1 (@ (@ sup_sup_set_nat Y) Z))))) (forall ((As2 set_nat) (As3 set_nat) (H2 heap_e7401611519738050253t_unit) (H4 heap_e7401611519738050253t_unit)) (= (@ (@ (@ relH (@ (@ sup_sup_set_nat As2) As3)) H2) H4) (and (@ (@ (@ relH As2) H2) H4) (@ (@ (@ relH As3) H2) H4)))) (forall ((Xs list_int) (Y int) (Ys list_int) (R2 set_Pr958786334691620121nt_int)) (=> (@ (@ member6698963635872716290st_int (@ (@ produc364263696895485585st_int Xs) (@ (@ cons_int Y) Ys))) (@ listrel1_int R2)) (=> (forall ((X3 int)) (=> (= Xs (@ (@ cons_int X3) Ys)) (not (@ (@ member5262025264175285858nt_int (@ (@ product_Pair_int_int X3) Y)) R2)))) (not (forall ((Zs2 list_int)) (=> (= Xs (@ (@ cons_int Y) Zs2)) (not (@ (@ member6698963635872716290st_int (@ (@ produc364263696895485585st_int Zs2) Ys)) (@ listrel1_int R2))))))))) _let_83 (forall ((Xs list_c) (Ys list_int) (P (-> list_c list_int Bool))) (=> (= (@ size_size_list_c Xs) (@ size_size_list_int Ys)) (=> (@ (@ P nil_c) nil_int) (=> (forall ((X3 c) (Xs2 list_c) (Y2 int) (Ys5 list_int)) (=> (= (@ size_size_list_c Xs2) (@ size_size_list_int Ys5)) (=> (@ (@ P Xs2) Ys5) (@ (@ P (@ (@ cons_c X3) Xs2)) (@ (@ cons_int Y2) Ys5))))) (@ (@ P Xs) Ys))))) (forall ((A set_nat) (B set_nat)) (= (@ (@ inf_inf_set_nat (@ (@ inf_inf_set_nat A) B)) (@ (@ minus_minus_set_nat A) B)) bot_bot_set_nat)) (not (@ _let_82 zero_zero_nat)) (forall ((X product_prod_nat_nat) (Xs list_P6011104703257516679at_nat)) (let ((_let_1 (@ member8440522571783428010at_nat X))) (=> (@ _let_1 (@ set_Pr5648618587558075414at_nat (@ butlas5569151904373679443at_nat Xs))) (@ _let_1 (@ set_Pr5648618587558075414at_nat Xs))))) (forall ((A2 nat) (B2 nat)) (@ (@ ord_less_eq_nat A2) (@ nat_prod_encode (@ (@ product_Pair_nat_nat A2) B2)))) (forall ((X set_Pr4329608150637261639at_nat) (Y set_Pr4329608150637261639at_nat) (Z set_Pr4329608150637261639at_nat)) (let ((_let_1 (@ inf_in7913087082777306421at_nat X))) (= (@ _let_1 (@ (@ sup_su5525570899277871387at_nat Y) Z)) (@ (@ sup_su5525570899277871387at_nat (@ _let_1 Y)) (@ _let_1 Z))))) (forall ((K3 nat) (M2 nat) (N nat)) (let ((_let_1 (@ times_times_nat K3))) (=> (@ (@ ord_less_nat zero_zero_nat) K3) (= (@ (@ ord_less_nat (@ _let_1 M2)) (@ _let_1 N)) (@ (@ ord_less_nat M2) N))))) (forall ((I nat) (J nat) (P (-> nat Bool))) (=> (@ (@ ord_less_eq_nat I) J) (=> (@ P J) (=> (forall ((N5 nat)) (=> (@ (@ ord_less_eq_nat I) N5) (=> (@ (@ ord_less_nat N5) J) (=> (@ P (@ suc N5)) (@ P N5))))) (@ P I))))) (forall ((A set_Pr4329608150637261639at_nat) (B set_Pr4329608150637261639at_nat)) (=> (@ (@ ord_le1268244103169919719at_nat A) B) (= (@ (@ sup_su5525570899277871387at_nat A) (@ (@ minus_3314409938677909166at_nat B) A)) B))) (forall ((P Bool) (H2 heap_e7401611519738050253t_unit)) (let ((_let_1 (@ (@ heap_T875086893843062177t_unit (@ refine_Imp_assert P)) H2))) (and (=> P (= _let_1 (@ some_P1914260805536162275it_nat (@ (@ produc7133225469290080770it_nat product_Unity) (@ (@ produc584006145561248582it_nat H2) zero_zero_nat))))) (=> (not P) (= _let_1 none_P9117596204409417319it_nat))))) (forall ((X nat) (S set_nat)) (=> (@ (@ member_nat X) S) (not (= S bot_bot_set_nat)))) (= (lambda ((Y4 filter_nat) (Z2 filter_nat)) (= Y4 Z2)) (lambda ((X2 filter_nat) (Y5 filter_nat)) (and (@ (@ ord_le2510731241096832064er_nat X2) Y5) (@ (@ ord_le2510731241096832064er_nat Y5) X2)))) (forall ((Xs list_d) (A2 d) (I nat)) (=> (@ distinct_d Xs) (=> (not (@ (@ member_d A2) (@ (@ minus_minus_set_d (@ set_d2 Xs)) (@ (@ insert_d (@ (@ nth_d Xs) I)) bot_bot_set_d)))) (@ distinct_d (@ (@ (@ list_update_d Xs) I) A2))))) (= plus_plus_nat (lambda ((A3 nat) (B3 nat)) (@ (@ plus_plus_nat B3) A3))) (forall ((X int)) (= (= one_one_int X) (= X one_one_int))) (forall ((A2 set_Pr1261947904930325089at_nat) (B2 set_Pr1261947904930325089at_nat) (S set_Pr4329608150637261639at_nat) (P (-> set_Pr1261947904930325089at_nat set_Pr1261947904930325089at_nat Bool))) (let ((_let_1 (@ (@ member8757157785044589968at_nat (@ (@ produc2922128104949294807at_nat A2) B2)) S))) (=> _let_1 (=> (=> _let_1 (@ (@ P A2) B2)) (exists ((A4 set_Pr1261947904930325089at_nat) (B4 set_Pr1261947904930325089at_nat)) (and (@ (@ P A4) B4) (@ (@ member8757157785044589968at_nat (@ (@ produc2922128104949294807at_nat A4) B4)) S))))))) _let_81 (forall ((A2 assn) (B2 assn) (F4 (-> assn nat)) (C nat)) (=> (@ (@ ord_less_eq_assn A2) B2) (=> (= (@ F4 B2) C) (=> (forall ((X3 assn) (Y2 assn)) (=> (@ (@ ord_less_eq_assn X3) Y2) (@ (@ ord_less_eq_nat (@ F4 X3)) (@ F4 Y2)))) (@ (@ ord_less_eq_nat (@ F4 A2)) C))))) (= ord_less_eq_nat (lambda ((B3 nat) (A3 nat)) (= (@ (@ sup_sup_nat A3) B3) A3))) (forall ((A2 assn) (B2 assn)) (=> (@ (@ ord_less_eq_assn A2) B2) (= (@ (@ inf_inf_assn A2) B2) A2))) (@ _let_9 (@ (@ plus_p5714425477246183910nteger one_one_Code_integer) one_one_Code_integer)) (forall ((B assn) (A assn)) (@ (@ entails B) (@ (@ sup_sup_assn A) B))) (forall ((X (-> produc3658429121746597890et_nat Bool)) (A set_Pr4532377907799695533_nat_o)) (=> (@ (@ member6576561426505652726_nat_o X) A) (not (forall ((B5 set_Pr4532377907799695533_nat_o)) (=> (= A (@ (@ insert5175938949040314269_nat_o X) B5)) (@ (@ member6576561426505652726_nat_o X) B5)))))) (forall ((X product_prod_int_int) (Y product_prod_int_int)) (= (@ (@ (@ if_Pro3027730157355071871nt_int false) X) Y) Y)) (forall ((X code_integer) (Y code_integer)) (=> (@ (@ ord_le6747313008572928689nteger X) Y) (@ (@ ord_le3102999989581377725nteger X) Y))) (= sup_sup_set_nat (lambda ((X2 set_nat) (Y5 set_nat)) (@ (@ sup_sup_set_nat Y5) X2))) (forall ((A assn) (B assn) (H2 produc3658429121746597890et_nat)) (=> (@ (@ rep_assn (@ (@ times_times_assn A) B)) H2) (exists ((H1 produc3658429121746597890et_nat) (H22 produc3658429121746597890et_nat)) (and (@ (@ rep_assn B) H22) (@ (@ rep_assn A) H1))))) (forall ((K3 nat) (Xs list_int) (X int)) (let ((_let_1 (@ butlast_int Xs))) (let ((_let_2 (@ butlast_int (@ (@ (@ list_update_int Xs) K3) X)))) (let ((_let_3 (= K3 (@ (@ minus_minus_nat (@ size_size_list_int Xs)) one_one_nat)))) (and (=> _let_3 (= _let_2 _let_1)) (=> (not _let_3) (= _let_2 (@ (@ (@ list_update_int _let_1) K3) X)))))))) (forall ((K3 nat)) (@ finite_finite_nat (@ collect_nat (lambda ((N2 nat)) (@ (@ ord_less_nat N2) K3))))) (forall ((X nat) (Y nat)) (=> (not (@ (@ ord_less_nat X) Y)) (= (@ (@ ord_less_eq_nat X) Y) (= X Y)))) (forall ((A2 int) (N nat)) (let ((_let_1 (@ (@ power_power_int A2) N))) (= (@ (@ times_times_int _let_1) A2) (@ (@ times_times_int A2) _let_1)))) (forall ((A2 nat) (B2 nat)) (=> (@ (@ ord_less_eq_nat A2) B2) (not (forall ((C4 nat)) (not (= B2 (@ (@ plus_plus_nat A2) C4))))))) (forall ((Xs list_int)) (= (= (@ rev_int Xs) nil_int) (= Xs nil_int))) (= inf_inf_set_nat (lambda ((A3 set_nat) (B3 set_nat)) (@ (@ inf_inf_set_nat B3) A3))) (forall ((A2 assn) (B2 assn) (F4 (-> assn assn)) (C assn)) (=> (@ (@ ord_less_assn A2) B2) (=> (@ (@ ord_less_assn (@ F4 B2)) C) (=> (forall ((X3 assn) (Y2 assn)) (=> (@ (@ ord_less_assn X3) Y2) (@ (@ ord_less_assn (@ F4 X3)) (@ F4 Y2)))) (@ (@ ord_less_assn (@ F4 A2)) C))))) (forall ((R set_Pr4329608150637261639at_nat) (X produc3843707927480180839at_nat)) (@ (@ ord_le1268244103169919719at_nat (@ transi2703068831062848130at_nat R)) (@ transi2703068831062848130at_nat (@ (@ insert9069300056098147895at_nat X) R)))) (forall ((A2 code_integer) (B2 code_integer)) (=> (@ (@ ord_le6747313008572928689nteger A2) B2) (= (@ (@ ord_min_Code_integer A2) B2) A2))) (forall ((A set_nat) (B set_nat) (C2 set_nat)) (=> (@ (@ ord_less_eq_set_nat A) B) (=> (@ (@ ord_less_set_nat B) C2) (@ (@ ord_less_set_nat A) C2)))) _let_80 (forall ((P (-> int Bool)) (P3 (-> int Bool)) (Q (-> int Bool)) (Q3 (-> int Bool))) (=> (exists ((Z3 int)) (forall ((X3 int)) (=> (@ (@ ord_less_int Z3) X3) (= (@ P X3) (@ P3 X3))))) (=> (exists ((Z3 int)) (forall ((X3 int)) (=> (@ (@ ord_less_int Z3) X3) (= (@ Q X3) (@ Q3 X3))))) (exists ((Z4 int)) (forall ((X7 int)) (=> (@ (@ ord_less_int Z4) X7) (= (or (@ Q X7) (@ P X7)) (or (@ P3 X7) (@ Q3 X7))))))))) (forall ((X21 produc3843707927480180839at_nat) (X222 list_P5464809261938338413at_nat)) (= (@ set_Pr3765526544606949372at_nat (@ (@ cons_P3940603068885512221at_nat X21) X222)) (@ (@ insert9069300056098147895at_nat X21) (@ set_Pr3765526544606949372at_nat X222)))) (forall ((A2 nat) (B set_nat)) (@ (@ member_nat A2) (@ (@ insert_nat2 A2) B))) (forall ((A2 code_integer) (B2 code_integer)) (=> (@ (@ ord_le6747313008572928689nteger A2) B2) (not (@ (@ ord_le6747313008572928689nteger B2) A2)))) (forall ((A2 set_Pr4329608150637261639at_nat) (B2 set_Pr4329608150637261639at_nat)) (=> (= A2 (@ (@ sup_su5525570899277871387at_nat A2) B2)) (@ (@ ord_le1268244103169919719at_nat B2) A2))) (forall ((B2 code_integer) (A2 code_integer) (C code_integer)) (=> (@ (@ ord_le6747313008572928689nteger B2) A2) (=> (@ (@ ord_le6747313008572928689nteger C) zero_z3403309356797280102nteger) (@ (@ ord_le6747313008572928689nteger (@ (@ times_3573771949741848930nteger A2) C)) (@ (@ times_3573771949741848930nteger B2) C))))) (forall ((X set_o)) (= (@ (@ sup_sup_set_o bot_bot_set_o) X) X)) (forall ((B2 int) (A2 int)) (=> (@ (@ ord_less_int B2) A2) (not (@ (@ ord_less_int A2) B2)))) (forall ((F4 (-> nat int)) (N nat) (N6 nat)) (=> (forall ((N5 nat)) (@ (@ ord_less_int (@ F4 N5)) (@ F4 (@ suc N5)))) (=> (@ (@ ord_less_nat N) N6) (@ (@ ord_less_int (@ F4 N)) (@ F4 N6))))) _let_79 (forall ((X nat) (S set_nat)) (=> (@ (@ member_nat X) S) (@ (@ ord_less_set_nat (@ (@ minus_minus_set_nat S) (@ (@ insert_nat2 X) bot_bot_set_nat))) S))) (forall ((X (-> produc3658429121746597890et_nat Bool)) (S set_Pr4532377907799695533_nat_o)) (=> (@ (@ member6576561426505652726_nat_o X) S) (@ (@ ord_le2453136405763929_nat_o (@ (@ minus_1801376950450012436_nat_o S) (@ (@ insert5175938949040314269_nat_o X) bot_bo7824918357723582233_nat_o))) S))) (forall ((Xs list_int) (Ys list_int) (Xy product_prod_int_int) (Xys list_P5707943133018811711nt_int)) (=> (= (@ (@ zip_int_int Xs) Ys) (@ (@ cons_P3334398858971670639nt_int Xy) Xys)) (not (forall ((X3 int) (Xs5 list_int)) (=> (= Xs (@ (@ cons_int X3) Xs5)) (forall ((Y2 int) (Ys4 list_int)) (=> (= Ys (@ (@ cons_int Y2) Ys4)) (=> (= Xy (@ (@ product_Pair_int_int X3) Y2)) (not (= Xys (@ (@ zip_int_int Xs5) Ys4))))))))))) (forall ((Y int) (X int)) (=> (@ (@ ord_less_eq_int Y) X) (= (@ (@ inf_inf_int X) Y) Y))) _let_78 (forall ((A2 set_o)) (@ (@ ord_less_eq_set_o bot_bot_set_o) A2)) (forall ((A assn) (B assn) (C2 assn)) (=> (@ (@ entails (@ (@ times_times_assn A) B)) C2) (@ (@ entails (@ (@ times_times_assn B) A)) C2))) (forall ((Xs list_d) (I nat) (X d)) (=> (@ (@ ord_less_eq_nat (@ size_size_list_d Xs)) I) (= (@ (@ (@ list_update_d Xs) I) X) Xs))) (= ord_le2510731241096832064er_nat (lambda ((B3 filter_nat) (A3 filter_nat)) (= (@ (@ sup_sup_filter_nat A3) B3) A3))) (forall ((X code_integer) (Ys list_Code_integer)) (let ((_let_1 (@ sorted710888440204495920nteger ord_le6747313008572928689nteger))) (= (@ _let_1 (@ (@ cons_Code_integer X) Ys)) (and (@ _let_1 Ys) (forall ((X2 code_integer)) (=> (@ (@ member_Code_integer X2) (@ set_Code_integer2 Ys)) (@ (@ ord_le6747313008572928689nteger X) X2))))))) (forall ((A2 rat) (B2 rat) (C rat)) (let ((_let_1 (@ times_times_rat A2))) (= (@ _let_1 (@ (@ plus_plus_rat B2) C)) (@ (@ plus_plus_rat (@ _let_1 B2)) (@ _let_1 C))))) (forall ((X nat) (Y nat) (R2 set_Pr1261947904930325089at_nat) (Xs list_nat) (Ys list_nat)) (let ((_let_1 (@ listrel_nat_nat R2))) (=> (@ (@ member8440522571783428010at_nat (@ (@ product_Pair_nat_nat X) Y)) R2) (=> (@ (@ member7340969449405702474st_nat (@ (@ produc2694037385005941721st_nat Xs) Ys)) _let_1) (@ (@ member7340969449405702474st_nat (@ (@ produc2694037385005941721st_nat (@ (@ cons_nat X) Xs)) (@ (@ cons_nat Y) Ys))) _let_1))))) (forall ((A2 assn) (B2 assn) (Xs list_assn)) (= (@ (@ member7957490590177025114n_assn (@ (@ produc118845697133431529n_assn A2) B2)) (@ set_Pr1139785259514867910n_assn (@ (@ zip_assn_assn Xs) Xs))) (and (= A2 B2) (@ (@ member_assn A2) (@ set_assn2 Xs))))) (forall ((Xs list_int) (Ys list_P8527749157015355191n_assn)) (= (= (@ (@ zip_in7098856637274830732n_assn Xs) Ys) nil_Pr2440414457004260852n_assn) (or (= Ys nil_Pr5671120429643327159n_assn) (= Xs nil_int)))) (forall ((Xs list_c) (Ys list_c) (Zs list_c) (P (-> list_c list_c list_c Bool))) (let ((_let_1 (@ size_size_list_c Ys))) (=> (= (@ size_size_list_c Xs) _let_1) (=> (= _let_1 (@ size_size_list_c Zs)) (=> (@ (@ (@ P nil_c) nil_c) nil_c) (=> (forall ((X3 c) (Xs2 list_c) (Y2 c) (Ys5 list_c) (Z4 c) (Zs2 list_c)) (let ((_let_1 (@ size_size_list_c Ys5))) (=> (= (@ size_size_list_c Xs2) _let_1) (=> (= _let_1 (@ size_size_list_c Zs2)) (=> (@ (@ (@ P Xs2) Ys5) Zs2) (@ (@ (@ P (@ (@ cons_c X3) Xs2)) (@ (@ cons_c Y2) Ys5)) (@ (@ cons_c Z4) Zs2))))))) (@ (@ (@ P Xs) Ys) Zs))))))) (forall ((A set_Pr4329608150637261639at_nat) (B set_Pr4329608150637261639at_nat) (X produc3843707927480180839at_nat)) (let ((_let_1 (@ (@ insert9069300056098147895at_nat X) bot_bo228742789529271731at_nat))) (let ((_let_2 (= B _let_1))) (let ((_let_3 (= A _let_1))) (= (= (@ (@ sup_su5525570899277871387at_nat A) B) _let_1) (or (and _let_3 _let_2) (and _let_3 (= B bot_bo228742789529271731at_nat)) (and (= A bot_bo228742789529271731at_nat) _let_2))))))) (forall ((N nat)) (let ((_let_1 (@ set_or4665077453230672383an_nat zero_zero_nat))) (= (@ _let_1 (@ suc N)) (@ (@ insert_nat2 N) (@ _let_1 N))))) (forall ((X rat)) (= (= zero_zero_rat X) (= X zero_zero_rat))) 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(Xsi list_int) (Xsi2 list_int)) (=> (= I3 I7) (=> (= A A6) (=> (= (@ size_size_list_c Xs) (@ size_size_list_c Xs4)) (=> (= (@ size_size_list_int Xsi) (@ size_size_list_int Xsi2)) (=> (forall ((I5 nat)) (let ((_let_1 (@ size_size_list_c Xs))) (=> (@ (@ member_nat I5) I3) (=> (@ (@ ord_less_nat I5) _let_1) (=> (= _let_1 (@ size_size_list_int Xsi)) (and (= (@ (@ nth_int Xsi) I5) (@ (@ nth_int Xsi2) I5)) (= (@ (@ nth_c Xs) I5) (@ (@ nth_c Xs4) I5)))))))) (= (@ (@ (@ (@ vEBT_L6582681566615743372_c_int I3) A) Xs) Xsi) (@ (@ (@ (@ vEBT_L6582681566615743372_c_int I7) A6) Xs4) Xsi2)))))))) (forall ((I nat) (J nat) (U nat) (M2 nat) (N nat)) (=> (@ (@ ord_less_eq_nat I) J) (= (@ (@ ord_less_nat (@ (@ plus_plus_nat (@ (@ times_times_nat I) U)) M2)) (@ (@ plus_plus_nat (@ (@ times_times_nat J) U)) N)) (@ (@ ord_less_nat M2) (@ (@ plus_plus_nat (@ (@ times_times_nat (@ (@ minus_minus_nat J) I)) U)) N))))) (forall ((X nat) (Y nat) (N nat)) (=> (= (@ (@ times_times_nat X) Y) one_one_nat) (= (@ (@ 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(=> (@ _let_1 C) (@ _let_1 (@ (@ plus_plus_nat A2) C)))))) (forall ((Xs list_s1210847774152347623at_nat) (Y set_Pr1261947904930325089at_nat) (Ys list_s1210847774152347623at_nat) (R2 set_Pr4329608150637261639at_nat)) (=> (@ (@ member4080735728053443344at_nat (@ (@ produc7536900900485677911at_nat Xs) (@ (@ cons_s6881495754146722583at_nat Y) Ys))) (@ listre8180072825634266816at_nat R2)) (=> (forall ((X3 set_Pr1261947904930325089at_nat)) (=> (= Xs (@ (@ cons_s6881495754146722583at_nat X3) Ys)) (not (@ (@ member8757157785044589968at_nat (@ (@ produc2922128104949294807at_nat X3) Y)) R2)))) (not (forall ((Zs2 list_s1210847774152347623at_nat)) (=> (= Xs (@ (@ cons_s6881495754146722583at_nat Y) Zs2)) (not (@ (@ member4080735728053443344at_nat (@ (@ produc7536900900485677911at_nat Zs2) Ys)) (@ listre8180072825634266816at_nat R2))))))))) (forall ((B2 Bool) (A2 Bool)) (= (@ (@ member_o B2) (@ (@ insert_o2 A2) bot_bot_set_o)) (= B2 A2))) (forall ((C nat) (A set_nat) (B set_nat)) (let ((_let_1 (@ 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(forall ((Z1 (-> produc3658429121746597890et_nat Bool)) (Z22 list_P7985473006766602707_nat_o)) (=> (= A2 (@ (@ cons_P6219271836124797827_nat_o Z1) Z22)) (not (@ (@ member6576561426505652726_nat_o E) (@ set_Pr400311997697478754_nat_o Z22))))))))) (forall ((Xs list_c) (Ys list_c)) (= (@ size_s2756448709718749209od_c_c (@ (@ zip_c_c Xs) Ys)) (@ (@ ord_min_nat (@ size_size_list_c Xs)) (@ size_size_list_c Ys)))) (forall ((X int) (Y int) (A set_int)) (let ((_let_1 (@ insert_int2 X))) (let ((_let_2 (@ insert_int2 Y))) (= (@ _let_1 (@ _let_2 A)) (@ _let_2 (@ _let_1 A)))))) (forall ((X int) (Xs list_int)) (= (@ distinct_int (@ (@ insert_int X) Xs)) (@ distinct_int Xs))) (forall ((P (-> int Bool)) (I int) (J int)) (= (@ (@ list_ex_int P) (@ (@ upto I) J)) (not (@ (@ (@ all_interval_int (@ (@ comp_o_o_int (lambda ((_lvar_0 Bool)) (not _lvar_0))) P)) I) J)))) _let_72 (forall ((A2 nat) (B2 nat) (C nat)) (let ((_let_1 (@ times_times_nat A2))) (= (@ (@ times_times_nat (@ _let_1 B2)) C) (@ _let_1 (@ (@ times_times_nat B2) C))))) (forall ((X (-> int nat assn)) (Xa list_int) (Xb list_nat) (Y assn)) (let ((_let_1 (not (= Y bot_bot_assn)))) (let ((_let_2 (= Xa nil_int))) (let ((_let_3 (= Xb nil_nat))) (=> (= (@ (@ (@ vEBT_L77084186935402305nt_nat X) Xa) Xb) Y) (=> (=> _let_2 (=> _let_3 (not (= Y one_one_assn)))) (=> (forall ((A4 int) (As list_int)) (=> (= Xa (@ (@ cons_int A4) As)) (forall ((C4 nat) (Cs2 list_nat)) (=> (= Xb (@ (@ cons_nat C4) Cs2)) (not (= Y (@ (@ times_times_assn (@ (@ X A4) C4)) (@ (@ (@ vEBT_L77084186935402305nt_nat X) As) Cs2)))))))) (=> (=> (exists ((V3 int) (Va list_int)) (= Xa (@ (@ cons_int V3) Va))) (=> _let_3 _let_1)) (not (=> _let_2 (=> (exists ((V3 nat) (Va list_nat)) (= Xb (@ (@ cons_nat V3) Va))) _let_1))))))))))) (forall ((C int) (B2 int)) (= (@ (@ ord_less_eq_int C) (@ (@ times_times_int B2) C)) (and (=> (@ (@ ord_less_int C) zero_zero_int) (@ (@ ord_less_eq_int B2) one_one_int)) (=> (@ (@ ord_less_int zero_zero_int) C) (@ (@ ord_less_eq_int one_one_int) B2))))) (forall ((I rat) (K3 rat) (N rat) (J rat)) (let ((_let_1 (@ (@ ord_less_eq_rat N) (@ (@ plus_plus_rat J) K3)))) (let ((_let_2 (@ (@ ord_less_eq_rat (@ (@ plus_plus_rat I) K3)) N))) (=> _let_2 (=> _let_1 (=> _let_2 (=> _let_1 (@ (@ ord_less_eq_rat (@ (@ minus_minus_rat N) K3)) J)))))))) (forall ((N nat) (K3 int)) (let ((_let_1 (@ (@ power_power_int (@ numeral_numeral_int (@ bit0 one))) N))) (=> (@ (@ ord_less_eq_int _let_1) K3) (=> (@ (@ ord_less_nat zero_zero_nat) N) (@ (@ ord_less_eq_int (@ (@ bit_se2923211474154528505it_int N) K3)) (@ (@ minus_minus_int K3) _let_1)))))) (forall ((T int)) (exists ((Z4 int)) (forall ((X7 int)) (=> (@ (@ ord_less_int Z4) X7) (not (@ (@ ord_less_int X7) T)))))) (forall ((A2 filter_nat) (B2 filter_nat) (C filter_nat)) (let ((_let_1 (@ ord_less_filter_nat A2))) (=> (@ _let_1 B2) (=> (@ (@ ord_le2510731241096832064er_nat B2) C) (@ _let_1 C))))) (forall ((Xs list_P5464809261938338413at_nat) (P (-> produc3843707927480180839at_nat produc3843707927480180839at_nat Bool)) (Q (-> produc3843707927480180839at_nat produc3843707927480180839at_nat Bool))) (=> (forall ((X3 produc3843707927480180839at_nat) (Y2 produc3843707927480180839at_nat)) (let ((_let_1 (@ set_Pr3765526544606949372at_nat Xs))) (=> (@ (@ member8757157785044589968at_nat X3) _let_1) (=> (@ (@ member8757157785044589968at_nat Y2) _let_1) (=> (@ (@ P X3) Y2) (@ (@ Q X3) Y2)))))) (=> (@ (@ sorted8831241538929206612at_nat P) Xs) (@ (@ sorted8831241538929206612at_nat Q) Xs)))) (forall ((Xs list_int) (Ys list_int)) (=> (not (= (@ size_size_list_int Xs) (@ size_size_list_int Ys))) (not (= Xs Ys)))) (= (@ rotate328796349445179396n_assn nil_Pr5671120429643327159n_assn) nil_Pr5671120429643327159n_assn) (forall ((D int) (T int) (A set_int)) (=> (@ (@ ord_less_int zero_zero_int) D) (=> (@ (@ member_int (@ (@ plus_plus_int T) one_one_int)) A) (forall ((X7 int)) (=> (forall ((Xa3 int)) (=> (@ (@ member_int Xa3) (@ (@ set_or1266510415728281911st_int one_one_int) D)) (forall ((Xb3 int)) (=> (@ (@ member_int Xb3) A) (not (= X7 (@ (@ minus_minus_int Xb3) Xa3))))))) (=> (@ (@ ord_less_eq_int X7) T) (@ (@ ord_less_eq_int (@ (@ plus_plus_int X7) D)) T))))))) (forall ((X int) (Y int)) (let ((_let_1 (@ ord_less_eq_int zero_zero_int))) (=> (@ _let_1 X) (=> (@ _let_1 Y) (= (= (@ (@ plus_plus_int X) Y) zero_zero_int) (and (= X zero_zero_int) (= Y zero_zero_int))))))) (forall ((X list_P6011104703257516679at_nat) (Y list_P6011104703257516679at_nat)) (= (@ (@ (@ if_lis9186351972506106189at_nat false) X) Y) Y)) (forall ((P assn) (Q assn) (H2 heap_e7401611519738050253t_unit)) (let ((_let_1 (@ (@ produc7507926704131184380et_nat H2) bot_bot_set_nat))) (= (@ (@ rep_assn (@ (@ sup_sup_assn P) Q)) _let_1) (or (@ (@ rep_assn Q) _let_1) (@ (@ rep_assn P) _let_1))))) (forall ((I nat) (J nat) (Xs list_d) (X d)) (=> (not (= I J)) (= (@ (@ nth_d (@ (@ (@ list_update_d Xs) I) X)) J) (@ (@ nth_d Xs) J)))) (forall ((X nat) (Y nat)) (or (@ (@ ord_less_nat Y) X) (@ (@ ord_less_eq_nat X) Y))) (forall ((A assn) (B assn)) (let ((_let_1 (@ entailst A))) (= (@ _let_1 (@ (@ times_times_assn B) top_top_assn)) (@ _let_1 B)))) (forall ((Xs list_P8527749157015355191n_assn) (Y produc6575502325842934193n_assn) (Ys list_P8527749157015355191n_assn) (R2 set_Pr8116311503512020807n_assn)) (=> (@ (@ member3994142547374651152n_assn (@ (@ produc3014731801419794263n_assn Xs) (@ (@ cons_P2971678138204555879n_assn Y) Ys))) (@ listre5253995379918703921n_assn R2)) (not (forall ((X3 produc6575502325842934193n_assn) (Xs2 list_P8527749157015355191n_assn)) (=> (= Xs (@ (@ cons_P2971678138204555879n_assn X3) Xs2)) (=> (@ (@ member4743710847862083984n_assn (@ (@ produc6128706242671166167n_assn X3) Y)) R2) (not (@ (@ member3994142547374651152n_assn (@ (@ produc3014731801419794263n_assn Xs2) Ys)) (@ listre5253995379918703921n_assn R2))))))))) (forall ((I3 set_nat) (I7 set_nat) (Xs list_c) (Xs4 list_c) (Xsi list_c) (Xsi2 list_c) (A (-> c c assn)) (A6 (-> c c assn))) (=> (= I3 I7) (=> (= (@ size_size_list_c Xs) (@ size_size_list_c Xs4)) (=> (= (@ size_size_list_c Xsi) (@ size_size_list_c Xsi2)) (=> (forall ((I5 nat)) (let ((_let_1 (@ (@ nth_c Xs4) I5))) (let ((_let_2 (@ (@ nth_c Xs) I5))) (let ((_let_3 (@ (@ nth_c Xsi2) I5))) (let ((_let_4 (@ (@ nth_c Xsi) I5))) (let ((_let_5 (@ size_size_list_c Xs))) (=> (@ (@ member_nat I5) I3) (=> (@ (@ ord_less_nat I5) _let_5) (=> (= _let_5 (@ size_size_list_c Xsi)) (and (= _let_4 _let_3) (= (@ (@ A _let_2) _let_4) (@ (@ A6 _let_1) _let_3)) (= _let_2 _let_1))))))))))) (= (@ (@ (@ (@ vEBT_L824818263033719200sn_c_c I3) A) Xs) Xsi) (@ (@ (@ (@ vEBT_L824818263033719200sn_c_c I7) A6) Xs4) Xsi2))))))) (forall ((X set_Pr1261947904930325089at_nat) (Y set_Pr1261947904930325089at_nat) (F4 (-> set_Pr1261947904930325089at_nat nat)) (Fs list_s9130966667114977576at_nat)) (let ((_let_1 (@ F4 Y))) (let ((_let_2 (@ F4 X))) (let ((_let_3 (@ member8757157785044589968at_nat (@ (@ produc2922128104949294807at_nat X) Y)))) (= (@ _let_3 (@ measur2694323259624372065at_nat (@ (@ cons_s2538900923071588440at_nat F4) Fs))) (or (and (= _let_2 _let_1) (@ _let_3 (@ measur2694323259624372065at_nat Fs))) (@ (@ ord_less_nat _let_2) _let_1))))))) (forall ((A2 int) (B2 int) (C int)) (=> (= A2 B2) (=> (@ (@ ord_less_eq_int B2) C) (@ (@ ord_less_eq_int A2) C)))) (forall ((A2 set_nat)) (= (@ (@ inf_inf_set_nat A2) A2) A2)) (= ord_le3146513528884898305at_nat (lambda ((A5 set_Pr1261947904930325089at_nat) (B7 set_Pr1261947904930325089at_nat)) (forall ((T2 product_prod_nat_nat)) (let ((_let_1 (@ member8440522571783428010at_nat T2))) (=> (@ _let_1 A5) (@ _let_1 B7)))))) (forall ((A2 rat) (B2 rat) (C rat)) (= (@ (@ ord_less_eq_rat (@ (@ minus_minus_rat A2) B2)) C) (@ (@ ord_less_eq_rat A2) (@ (@ plus_plus_rat C) B2)))) (forall ((T num)) (exists ((Z4 num)) (forall ((X7 num)) (=> (@ (@ ord_less_num X7) Z4) (not (= X7 T)))))) (forall ((B2 code_integer) (C code_integer) (A2 code_integer)) (=> (@ (@ ord_le6747313008572928689nteger B2) C) (@ (@ ord_le6747313008572928689nteger (@ (@ ord_min_Code_integer A2) B2)) C))) (forall ((P (-> list_int list_nat Bool)) (Xs list_int) (Ys list_nat)) (=> (@ (@ P nil_int) nil_nat) (=> (forall ((X3 int) (Xs2 list_int)) (@ (@ P (@ (@ cons_int X3) Xs2)) nil_nat)) (=> (forall ((Y2 nat) (Ys5 list_nat)) (@ (@ P nil_int) (@ (@ cons_nat Y2) Ys5))) (=> (forall ((X3 int) (Xs2 list_int) (Y2 nat) (Ys5 list_nat)) (=> (@ (@ P Xs2) Ys5) (@ (@ P (@ (@ cons_int X3) Xs2)) (@ (@ cons_nat Y2) Ys5)))) (@ (@ P Xs) Ys)))))) (forall ((M2 code_integer) (N code_integer)) (let ((_let_1 (@ ord_le6747313008572928689nteger one_one_Code_integer))) (=> (@ _let_1 M2) (=> (@ _let_1 N) (@ _let_1 (@ (@ times_3573771949741848930nteger M2) N)))))) (forall ((Xs list_c) (Ys list_nat) (Zs list_d) (P (-> list_c list_nat list_d Bool))) (let ((_let_1 (@ size_size_list_nat Ys))) (=> (= (@ size_size_list_c Xs) _let_1) (=> (= _let_1 (@ size_size_list_d Zs)) (=> (@ (@ (@ P nil_c) nil_nat) nil_d) (=> (forall ((X3 c) (Xs2 list_c) (Y2 nat) (Ys5 list_nat) (Z4 d) (Zs2 list_d)) (let ((_let_1 (@ size_size_list_nat Ys5))) (=> (= (@ size_size_list_c Xs2) _let_1) (=> (= _let_1 (@ size_size_list_d Zs2)) (=> (@ (@ (@ P Xs2) Ys5) Zs2) (@ (@ (@ P (@ (@ cons_c X3) Xs2)) (@ (@ cons_nat Y2) Ys5)) (@ (@ cons_d Z4) Zs2))))))) (@ (@ (@ P Xs) Ys) Zs))))))) (forall ((A assn) (B assn)) (@ (@ entailst A) (@ (@ sup_sup_assn A) B))) (forall ((A set_nat) (B set_nat) (P (-> nat Bool))) (= (exists ((X2 nat)) (and (@ (@ member_nat X2) (@ (@ sup_sup_set_nat A) B)) (@ P X2))) (or (exists ((X2 nat)) (and (@ P X2) (@ (@ member_nat X2) B))) (exists ((X2 nat)) (and (@ P X2) (@ (@ member_nat X2) A)))))) (forall ((X int) (Y int)) (=> (not (@ (@ ord_less_int X) Y)) (= (@ (@ ord_less_eq_int X) Y) (= X Y)))) (forall ((N nat)) (= (@ (@ enumerate_nat N) nil_nat) nil_Pr5478986624290739719at_nat)) (not (= top_top_assn one_one_assn)) (forall ((Xs list_int) (A set_int) (X int) (I nat)) (=> (@ (@ ord_less_eq_set_int (@ set_int2 Xs)) A) (=> (@ (@ member_int X) A) (@ (@ ord_less_eq_set_int (@ set_int2 (@ (@ (@ list_update_int Xs) I) X))) A)))) (forall ((A set_Pr4329608150637261639at_nat) (B set_Pr4329608150637261639at_nat) (C2 set_Pr4329608150637261639at_nat)) (let ((_let_1 (@ sup_su5525570899277871387at_nat A))) (= (@ (@ sup_su5525570899277871387at_nat (@ _let_1 B)) C2) (@ _let_1 (@ (@ sup_su5525570899277871387at_nat B) C2))))) (forall ((F4 (-> int int int)) (X int) (Y int)) (=> (forall ((X3 int) (Y2 int)) (@ (@ ord_less_eq_int (@ (@ F4 X3) Y2)) X3)) (=> (forall ((X3 int) (Y2 int)) (@ (@ ord_less_eq_int (@ (@ F4 X3) Y2)) Y2)) (=> (forall ((X3 int) (Y2 int) (Z4 int)) (let ((_let_1 (@ ord_less_eq_int X3))) (=> (@ _let_1 Y2) (=> (@ _let_1 Z4) (@ _let_1 (@ (@ F4 Y2) Z4)))))) (= (@ (@ inf_inf_int X) Y) (@ (@ F4 X) Y)))))) (forall ((A2 rat) (E rat) (C rat) (B2 rat) (D2 rat)) (= (@ (@ ord_less_eq_rat (@ (@ plus_plus_rat (@ (@ times_times_rat A2) E)) C)) (@ (@ plus_plus_rat (@ (@ times_times_rat B2) E)) D2)) (@ (@ ord_less_eq_rat (@ (@ plus_plus_rat (@ (@ times_times_rat (@ (@ minus_minus_rat A2) B2)) E)) C)) D2))) (forall ((A2 set_Pr4329608150637261639at_nat) (B2 set_Pr4329608150637261639at_nat)) (@ (@ ord_le1268244103169919719at_nat A2) (@ (@ sup_su5525570899277871387at_nat A2) B2))) (= ord_less_eq_int (lambda ((B3 int) (A3 int)) (= (@ (@ inf_inf_int A3) B3) B3))) (forall ((Ns list_int) (R2 set_Pr958786334691620121nt_int)) (not (@ (@ member6698963635872716290st_int (@ (@ produc364263696895485585st_int Ns) nil_int)) (@ lenlex_int R2)))) (forall ((Xs list_o) (A2 Bool) (I nat)) (=> (@ distinct_o Xs) (=> (not (@ (@ member_o A2) (@ (@ minus_minus_set_o (@ set_o2 Xs)) (@ (@ insert_o2 (@ (@ nth_o Xs) I)) bot_bot_set_o)))) (@ distinct_o (@ (@ (@ list_update_o Xs) I) A2))))) (forall ((N nat) (P (-> nat Bool)) (M2 nat)) (=> (forall ((K nat)) (=> (@ (@ ord_less_nat N) K) (@ P K))) (=> (forall ((K nat)) (=> (@ (@ ord_less_eq_nat K) N) (=> (forall ((I6 nat)) (=> (@ (@ ord_less_nat K) I6) (@ P I6))) (@ P K)))) (@ P M2)))) (forall ((B2 nat) (C nat) (A2 nat)) (=> (@ (@ ord_less_nat (@ (@ sup_sup_nat B2) C)) A2) (not (=> (@ (@ ord_less_nat B2) A2) (not (@ (@ ord_less_nat C) A2)))))) _let_71 (= insert8211810215607154385at_nat (lambda ((A3 product_prod_nat_nat) (__flatten_var_0 set_Pr1261947904930325089at_nat)) (@ (@ sup_su6327502436637775413at_nat (@ (@ insert8211810215607154385at_nat A3) bot_bo2099793752762293965at_nat)) __flatten_var_0))) (forall ((X filter_nat) (Y filter_nat) (Z filter_nat)) (= (@ (@ ord_le2510731241096832064er_nat (@ (@ sup_sup_filter_nat X) Y)) Z) (and (@ (@ ord_le2510731241096832064er_nat Y) Z) (@ (@ ord_le2510731241096832064er_nat X) Z)))) (forall ((M5 set_nat) (I nat)) (=> (@ (@ member_nat zero_zero_nat) M5) (= (@ suc (@ finite_card_nat (@ collect_nat (lambda ((K4 nat)) (and (@ (@ member_nat (@ suc K4)) M5) (@ (@ ord_less_nat K4) I)))))) (@ finite_card_nat (@ collect_nat (lambda ((K4 nat)) (and (@ (@ ord_less_nat K4) (@ suc I)) (@ (@ member_nat K4) M5)))))))) _let_70 (forall ((X nat) (Y nat) (P Bool)) (=> (@ (@ ord_less_nat X) Y) (=> (@ (@ ord_less_nat Y) X) P))) (forall ((I int) (J int) (K3 int) (L int)) (=> (and (@ (@ ord_less_int K3) L) (= I J)) (@ (@ ord_less_int (@ (@ plus_plus_int I) K3)) (@ (@ plus_plus_int J) L)))) _let_69 (forall ((X (-> produc3658429121746597890et_nat Bool)) (Xs list_P7985473006766602707_nat_o)) (=> (not (@ (@ member6576561426505652726_nat_o X) (@ set_Pr400311997697478754_nat_o Xs))) (= (@ (@ remove4235003712227595625_nat_o X) Xs) Xs))) (forall ((N1 int) (R1 list_int) (N22 int) (R22 list_int)) (=> (= (@ (@ cons_int N1) R1) (@ (@ cons_int N22) R22)) (and (= N1 N22) (= R1 R22)))) (forall ((X nat) (Xs list_nat)) (=> (not (@ (@ member_nat X) (@ set_nat2 Xs))) (= (@ (@ removeAll_nat X) Xs) Xs))) (forall ((X nat) (Y nat) (Z nat)) (= (@ (@ ord_less_eq_nat (@ (@ sup_sup_nat X) Y)) Z) (and (@ (@ ord_less_eq_nat X) Z) (@ (@ ord_less_eq_nat Y) Z)))) (forall ((Xs list_nat) (P (-> nat nat Bool))) (=> (@ (@ ord_less_eq_nat (@ size_size_list_nat Xs)) one_one_nat) (@ (@ sorted_wrt_nat P) Xs))) (forall ((X int) (B2 int) (A2 int)) (let ((_let_1 (@ ord_less_eq_int X))) (=> (@ _let_1 B2) (@ _let_1 (@ (@ sup_sup_int A2) B2))))) (forall ((M2 num) (N num)) (let ((_let_1 (@ numeral_numeral_int N))) (let ((_let_2 (@ uminus_uminus_int (@ numeral_numeral_int M2)))) (let ((_let_3 (@ (@ upto _let_2) _let_1))) (let ((_let_4 (@ (@ ord_less_eq_int _let_2) _let_1))) (and (=> (not _let_4) (= _let_3 nil_int)) (=> _let_4 (= _let_3 (@ (@ cons_int _let_2) (@ (@ upto (@ (@ plus_plus_int _let_2) one_one_int)) _let_1)))))))))) (forall ((C rat) (A2 rat)) (= (= (@ (@ times_times_rat C) A2) C) (or (= C zero_zero_rat) (= A2 one_one_rat)))) (forall ((X int) (Y product_prod_nat_nat) (Xs list_int) (Ys list_P6011104703257516679at_nat)) (=> (@ (@ member5261114234888836065at_nat (@ (@ produc3525228511222278652at_nat X) Y)) (@ set_Pr525428910217828469at_nat (@ (@ zip_in4043968058504772316at_nat Xs) Ys))) (not (=> (@ (@ member_int X) (@ set_int2 Xs)) (not (@ (@ member8440522571783428010at_nat Y) (@ set_Pr5648618587558075414at_nat Ys))))))) (forall ((A2 rat) (B2 rat)) (= (@ (@ ord_less_eq_rat (@ (@ plus_plus_rat A2) B2)) B2) (@ (@ ord_less_eq_rat A2) zero_zero_rat))) (forall ((P (-> list_P8527749157015355191n_assn list_int Bool)) (Xs list_P8527749157015355191n_assn) (Ys list_int)) (=> (@ (@ P nil_Pr5671120429643327159n_assn) nil_int) (=> (forall ((X3 produc6575502325842934193n_assn) (Xs2 list_P8527749157015355191n_assn)) (@ (@ P (@ (@ cons_P2971678138204555879n_assn X3) Xs2)) nil_int)) (=> (forall ((Y2 int) (Ys5 list_int)) (@ (@ P nil_Pr5671120429643327159n_assn) (@ (@ cons_int Y2) Ys5))) (=> (forall ((X3 produc6575502325842934193n_assn) (Xs2 list_P8527749157015355191n_assn) (Y2 int) (Ys5 list_int)) (=> (@ (@ P Xs2) Ys5) (@ (@ P (@ (@ cons_P2971678138204555879n_assn X3) Xs2)) (@ (@ cons_int Y2) Ys5)))) (@ (@ P Xs) Ys)))))) (forall ((I nat) (Xs list_nat) (Ys list_c)) (let ((_let_1 (@ ord_less_nat I))) (=> (@ _let_1 (@ size_size_list_nat Xs)) (=> (@ _let_1 (@ size_size_list_c Ys)) (= (@ (@ nth_Pr2476257089995772766_nat_c (@ (@ zip_nat_c Xs) Ys)) I) (@ (@ product_Pair_nat_c (@ (@ nth_nat Xs) I)) (@ (@ nth_c Ys) I))))))) (forall ((Xs list_int) (X int)) (=> (@ distinct_int Xs) (= (@ (@ remove1_int X) Xs) (@ (@ removeAll_int X) Xs)))) (forall ((X set_nat) (Y set_nat)) (=> (= X Y) (@ (@ ord_less_eq_set_nat X) Y))) (forall ((X code_integer) (Y code_integer) (Z code_integer)) (let ((_let_1 (@ ord_le6747313008572928689nteger X))) (=> (@ _let_1 Y) (=> (@ (@ ord_le3102999989581377725nteger Y) Z) (@ _let_1 Z))))) (forall ((A2 assn) (F4 (-> assn assn)) (B2 assn) (C assn)) (let ((_let_1 (@ ord_less_assn A2))) (=> (@ _let_1 (@ F4 B2)) (=> (@ (@ ord_less_eq_assn B2) C) (=> (forall ((X3 assn) (Y2 assn)) (=> (@ (@ ord_less_eq_assn X3) Y2) (@ (@ ord_less_eq_assn (@ F4 X3)) (@ F4 Y2)))) (@ _let_1 (@ F4 C))))))) (forall ((P (-> int Bool)) (D int) (Q (-> int Bool))) (=> (forall ((X3 int) (K int)) (= (@ P X3) (@ P (@ (@ minus_minus_int X3) (@ (@ 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Bool))) (let ((_let_1 (@ member6576561426505652726_nat_o A2))) (=> (=> (not (@ _let_1 B)) (= A2 B2)) (@ _let_1 (@ (@ insert5175938949040314269_nat_o B2) B))))) (forall ((C nat) (B set_nat) (A set_nat)) (let ((_let_1 (@ member_nat C))) (=> (=> (not (@ _let_1 B)) (@ _let_1 A)) (@ _let_1 (@ (@ sup_sup_set_nat A) B))))) (forall ((Xs list_int) (Ys list_nat) (Xy product_prod_int_nat) (Xys list_P8198026277950538467nt_nat)) (=> (= (@ (@ zip_int_nat Xs) Ys) (@ (@ cons_P7512249878480867347nt_nat Xy) Xys)) (not (forall ((X3 int) (Xs5 list_int)) (=> (= Xs (@ (@ cons_int X3) Xs5)) (forall ((Y2 nat) (Ys4 list_nat)) (=> (= Ys (@ (@ cons_nat Y2) Ys4)) (=> (= Xy (@ (@ product_Pair_int_nat X3) Y2)) (not (= Xys (@ (@ zip_int_nat Xs5) Ys4))))))))))) (forall ((X set_Pr4329608150637261639at_nat) (A2 set_Pr4329608150637261639at_nat) (B2 set_Pr4329608150637261639at_nat)) (let ((_let_1 (@ ord_le1268244103169919719at_nat X))) (=> (@ _let_1 A2) (@ _let_1 (@ (@ sup_su5525570899277871387at_nat A2) B2))))) (forall ((Xs list_int) (X int)) (=> (@ distinct_int Xs) (@ distinct_int (@ (@ removeAll_int X) Xs)))) (forall ((X set_Pr1261947904930325089at_nat) (Y set_Pr1261947904930325089at_nat) (R2 set_Pr4329608150637261639at_nat) (Z set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ transi2703068831062848130at_nat R2))) (let ((_let_2 (@ produc2922128104949294807at_nat X))) (=> (@ (@ member8757157785044589968at_nat (@ _let_2 Y)) _let_1) (=> (@ (@ member8757157785044589968at_nat (@ (@ produc2922128104949294807at_nat Y) Z)) _let_1) (@ (@ member8757157785044589968at_nat (@ _let_2 Z)) _let_1)))))) (forall ((A2 nat) (B2 nat) (C nat)) (let ((_let_1 (@ ord_less_eq_nat A2))) (=> (@ _let_1 (@ (@ ord_min_nat B2) C)) (not (=> (@ _let_1 B2) (not (@ _let_1 C))))))) (forall ((I nat) (M2 nat) (N nat)) (let ((_let_1 (@ (@ plus_plus_nat I) M2))) (let ((_let_2 (@ upt I))) (=> (@ (@ ord_less_eq_nat _let_1) N) (= (@ (@ take_nat M2) (@ _let_2 N)) (@ _let_2 _let_1)))))) (= code_divmod_integer (lambda ((K4 code_integer) (L4 code_integer)) (@ (@ produc1086072967326762835nteger (@ (@ divide6298287555418463151nteger K4) L4)) (@ (@ modulo364778990260209775nteger K4) L4)))) (forall ((A2 nat) (B2 nat) (C nat)) (let ((_let_1 (@ plus_plus_nat A2))) (= (@ (@ plus_plus_nat (@ _let_1 B2)) C) (@ _let_1 (@ (@ plus_plus_nat B2) C))))) (forall ((X1 code_integer) (X22 code_integer) (L12 list_Code_integer) (L23 list_Code_integer)) (let ((_let_1 (@ merge_Code_integer L12))) (let ((_let_2 (@ cons_Code_integer X1))) (let ((_let_3 (@ cons_Code_integer X22))) (let ((_let_4 (@ _let_3 L23))) (let ((_let_5 (@ merge_Code_integer (@ _let_2 L12)))) (let ((_let_6 (@ _let_5 _let_4))) (let ((_let_7 (= X1 X22))) (let ((_let_8 (@ (@ ord_le6747313008572928689nteger X1) X22))) (and (=> _let_8 (= _let_6 (@ _let_2 (@ _let_1 _let_4)))) (=> (not _let_8) (and (=> (not _let_7) (= _let_6 (@ _let_3 (@ _let_5 L23)))) (=> _let_7 (= _let_6 (@ _let_2 (@ _let_1 L23)))))))))))))))) (forall ((B set_Pr1261947904930325089at_nat) (C2 set_Pr1261947904930325089at_nat) (A set_Pr1261947904930325089at_nat)) (= (@ (@ inf_in2572325071724192079at_nat (@ (@ sup_su6327502436637775413at_nat B) C2)) A) (@ (@ sup_su6327502436637775413at_nat (@ (@ inf_in2572325071724192079at_nat B) A)) (@ (@ inf_in2572325071724192079at_nat C2) A)))) (forall ((I nat) (Xs list_P8527749157015355191n_assn)) (= (@ (@ (@ slice_7964966981652229398n_assn I) I) Xs) nil_Pr5671120429643327159n_assn)) (forall ((A2 set_nat)) (@ (@ ord_less_eq_set_nat A2) A2)) (forall ((C code_integer) (A2 code_integer) (B2 code_integer)) (let ((_let_1 (@ plus_p5714425477246183910nteger C))) (= (@ (@ ord_le6747313008572928689nteger (@ _let_1 A2)) (@ _let_1 B2)) (@ (@ ord_le6747313008572928689nteger A2) B2)))) (forall ((A2 rat) (B2 rat) (C rat)) (let ((_let_1 (@ plus_plus_rat A2))) (= (@ _let_1 (@ (@ minus_minus_rat B2) C)) (@ (@ minus_minus_rat (@ _let_1 B2)) C)))) (forall ((B2 rat) (A2 rat) (C rat)) (= (= (@ (@ plus_plus_rat B2) A2) (@ (@ plus_plus_rat C) A2)) (= B2 C))) (forall ((P (-> int Bool)) (Xs list_int)) (let ((_let_1 (@ list_ex_int P))) (= (@ _let_1 (@ rev_int Xs)) (@ _let_1 Xs)))) (forall ((B2 code_integer) (A2 code_integer) (C code_integer)) (=> (@ (@ ord_le3102999989581377725nteger B2) A2) (=> (@ (@ ord_le3102999989581377725nteger C) zero_z3403309356797280102nteger) (@ (@ ord_le3102999989581377725nteger (@ (@ times_3573771949741848930nteger A2) C)) (@ (@ times_3573771949741848930nteger B2) C))))) (forall ((B2 nat) (X nat) (A2 nat)) (=> (@ (@ ord_less_eq_nat B2) X) (@ (@ ord_less_eq_nat (@ (@ inf_inf_nat A2) B2)) X))) (= binomial (lambda ((N2 nat) (K4 nat)) (let ((_let_1 (@ (@ minus_minus_nat N2) K4))) (let ((_let_2 (@ ord_less_nat N2))) (@ (@ (@ if_nat (@ _let_2 K4)) zero_zero_nat) (@ (@ (@ if_nat (@ _let_2 (@ (@ times_times_nat (@ numeral_numeral_nat (@ bit0 one))) K4))) (@ (@ binomial N2) _let_1)) (@ (@ divide_divide_nat (@ (@ (@ (@ set_fo2584398358068434914at_nat times_times_nat) (@ (@ plus_plus_nat _let_1) one_one_nat)) N2) one_one_nat)) (@ semiri1408675320244567234ct_nat K4)))))))) (forall ((B2 filter_nat) (A2 filter_nat)) (@ (@ ord_le2510731241096832064er_nat B2) (@ (@ sup_sup_filter_nat A2) B2))) (forall ((N nat) (X produc6575502325842934193n_assn) (Xs list_P8527749157015355191n_assn)) (= (@ (@ enumer9200277086812776726n_assn N) (@ (@ cons_P2971678138204555879n_assn X) Xs)) (@ (@ cons_P7068465851076118432n_assn (@ (@ produc1553784393020010504n_assn N) X)) (@ (@ enumer9200277086812776726n_assn (@ suc N)) Xs)))) (forall ((X int) (Xs list_int) (Y int) (Ys list_int)) (= (@ (@ zip_int_int (@ (@ cons_int X) Xs)) (@ (@ cons_int Y) Ys)) (@ (@ cons_P3334398858971670639nt_int (@ (@ product_Pair_int_int X) Y)) (@ (@ zip_int_int Xs) Ys)))) (forall ((A2 list_c) (B2 list_c) (A7 list_c) (B6 list_c)) (=> (= (@ size_size_list_c A2) (@ size_size_list_c B2)) (=> (= (@ size_size_list_c A7) (@ size_size_list_c B6)) (=> (= (@ (@ zip_c_c A2) B2) (@ (@ zip_c_c A7) B6)) (and (= B2 B6) (= A2 A7)))))) (forall ((P (-> code_integer Bool)) (D code_integer) (Q (-> code_integer Bool))) (=> (forall ((X3 code_integer) (K code_integer)) (= (@ P X3) (@ P (@ (@ minus_8373710615458151222nteger X3) (@ (@ times_3573771949741848930nteger K) D))))) (=> (forall ((X3 code_integer) (K code_integer)) (= (@ Q X3) (@ Q (@ (@ minus_8373710615458151222nteger X3) (@ (@ times_3573771949741848930nteger K) D))))) (forall ((X7 code_integer) (K2 code_integer)) (let ((_let_1 (@ (@ minus_8373710615458151222nteger X7) (@ (@ times_3573771949741848930nteger K2) D)))) (= (or (@ Q X7) (@ P X7)) (or (@ P _let_1) (@ Q _let_1)))))))) (forall ((X int) (A set_int)) (let ((_let_1 (@ insert_int2 X))) (=> (not (@ (@ member_int X) A)) (= (@ (@ minus_minus_set_int (@ _let_1 A)) (@ _let_1 bot_bot_set_int)) A)))) (forall ((H2 heap_e7401611519738050253t_unit) (As2 set_nat)) (= (@ in_range (@ (@ produc7507926704131184380et_nat H2) As2)) (forall ((X2 nat)) (=> (@ (@ member_nat X2) As2) (@ (@ ord_less_nat X2) (@ lim_Product_unit H2)))))) (forall ((A2 set_nat) (B2 set_nat) (C set_nat)) (let ((_let_1 (@ sup_sup_set_nat A2))) (= (@ (@ sup_sup_set_nat (@ _let_1 B2)) C) (@ _let_1 (@ (@ sup_sup_set_nat B2) C))))) _let_68 (forall ((A set_int)) (=> (forall ((X3 int)) (not (@ (@ member_int X3) A))) (@ (@ ord_less_eq_set_int A) bot_bot_set_int))) (forall ((C product_prod_nat_nat) (B set_Pr1261947904930325089at_nat) (A set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ member8440522571783428010at_nat C))) (=> (=> (not (@ _let_1 B)) (@ _let_1 A)) (@ _let_1 (@ (@ sup_su6327502436637775413at_nat A) B))))) (forall ((A2 nat) (B2 nat) (F4 (-> nat int)) (C int)) (=> (@ (@ ord_less_eq_nat A2) B2) (=> (= (@ F4 B2) C) (=> (forall ((X3 nat) (Y2 nat)) (=> (@ (@ ord_less_eq_nat X3) Y2) (@ (@ ord_less_eq_int (@ F4 X3)) (@ F4 Y2)))) (@ (@ ord_less_eq_int (@ F4 A2)) C))))) (forall ((A2 nat) (B2 nat)) (= (@ (@ ord_less_nat A2) (@ (@ plus_plus_nat B2) A2)) (@ (@ ord_less_nat zero_zero_nat) B2))) (forall ((A2 filter_nat) (B2 filter_nat) (C filter_nat)) (let ((_let_1 (@ ord_le2510731241096832064er_nat A2))) (=> (@ _let_1 B2) (=> (= B2 C) (@ _let_1 C))))) (forall ((I nat) (L list_P5464809261938338413at_nat) (X produc3843707927480180839at_nat) (Y produc3843707927480180839at_nat)) (let ((_let_1 (@ member8757157785044589968at_nat X))) (=> (@ (@ ord_less_nat I) (@ size_s1588839187904960729at_nat L)) (= (@ _let_1 (@ set_Pr3765526544606949372at_nat (@ (@ (@ list_u4696772448584712917at_nat L) I) Y))) (or (= X Y) (and (@ _let_1 (@ set_Pr3765526544606949372at_nat L)) (forall ((Y5 produc3843707927480180839at_nat)) (@ (@ member8757157785044589968at_nat X) (@ set_Pr3765526544606949372at_nat (@ (@ (@ list_u4696772448584712917at_nat L) I) Y5)))))))))) (forall ((A2 rat) (C rat) (B2 rat)) (= (@ (@ ord_less_rat A2) (@ (@ minus_minus_rat C) B2)) (@ (@ ord_less_rat (@ (@ plus_plus_rat A2) B2)) C))) (forall ((A2 rat) (B2 rat) (D2 rat) (C rat)) (=> (@ (@ ord_less_rat A2) B2) (=> (@ (@ ord_less_rat D2) C) (@ (@ ord_less_rat (@ (@ minus_minus_rat A2) C)) (@ (@ minus_minus_rat B2) D2))))) (forall ((Xs list_int)) (= (@ gcd_Gcd_int (@ set_int2 Xs)) (@ (@ (@ fold_int_int gcd_gcd_int) Xs) zero_zero_int))) (forall ((X int) (Y int)) (@ (@ ord_less_eq_int (@ (@ inf_inf_int X) Y)) Y)) (forall ((A2 code_integer)) (= (@ (@ times_3573771949741848930nteger one_one_Code_integer) A2) A2)) (forall ((C2 set_Pr1261947904930325089at_nat) (A set_Pr1261947904930325089at_nat) (B set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ ord_le3146513528884898305at_nat C2))) (=> (@ _let_1 A) (=> (@ _let_1 B) (@ _let_1 (@ (@ inf_in2572325071724192079at_nat A) B)))))) (forall ((X set_Pr1261947904930325089at_nat) (Y set_Pr1261947904930325089at_nat) (Z set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ sup_su6327502436637775413at_nat X))) (= (@ _let_1 (@ (@ inf_in2572325071724192079at_nat Y) Z)) (@ (@ inf_in2572325071724192079at_nat (@ _let_1 Y)) (@ _let_1 Z))))) (forall ((I int) (J int)) (let ((_let_1 (@ upto I))) (=> (@ (@ ord_less_eq_int I) J) (= (@ _let_1 J) (@ (@ append_int (@ _let_1 (@ (@ minus_minus_int J) one_one_int))) (@ (@ cons_int J) nil_int)))))) (forall ((B2 assn) (A2 assn) (C assn)) (=> (@ (@ ord_less_eq_assn B2) A2) (=> (@ (@ ord_less_eq_assn C) A2) (@ (@ ord_less_eq_assn (@ (@ sup_sup_assn B2) C)) A2)))) (= ord_le6747313008572928689nteger (lambda ((X2 code_integer) (Y5 code_integer)) (and (@ (@ ord_le3102999989581377725nteger X2) Y5) (not (@ (@ ord_le3102999989581377725nteger Y5) X2))))) (forall ((A set_int)) (=> (@ is_singleton_int A) (not (forall ((X3 int)) (not (= A (@ (@ insert_int2 X3) bot_bot_set_int))))))) _let_67 (forall ((A2 assn) (B2 assn)) (= (= (@ (@ sup_sup_assn A2) B2) bot_bot_assn) (and (= A2 bot_bot_assn) (= B2 bot_bot_assn)))) (forall ((X set_Pr4329608150637261639at_nat) (B2 set_Pr4329608150637261639at_nat) (A2 set_Pr4329608150637261639at_nat)) (let ((_let_1 (@ ord_le1268244103169919719at_nat X))) (=> (@ _let_1 B2) (@ _let_1 (@ (@ sup_su5525570899277871387at_nat A2) B2))))) (forall ((P (-> code_integer Bool)) (P3 (-> code_integer Bool)) (Q (-> code_integer Bool)) (Q3 (-> code_integer Bool))) (=> (exists ((Z3 code_integer)) (forall ((X3 code_integer)) (=> (@ (@ ord_le6747313008572928689nteger X3) Z3) (= (@ P X3) (@ P3 X3))))) (=> (exists ((Z3 code_integer)) (forall ((X3 code_integer)) (=> (@ (@ ord_le6747313008572928689nteger X3) Z3) (= (@ Q X3) (@ Q3 X3))))) (exists ((Z4 code_integer)) (forall ((X7 code_integer)) (=> (@ (@ ord_le6747313008572928689nteger X7) Z4) (= (or (@ P X7) (@ Q X7)) (or (@ Q3 X7) (@ P3 X7))))))))) (forall ((X product_prod_nat_nat) (X4 set_Pr1261947904930325089at_nat)) (=> (not (@ (@ member8440522571783428010at_nat X) X4)) (= (@ (@ minus_1356011639430497352at_nat X4) (@ (@ insert8211810215607154385at_nat X) bot_bo2099793752762293965at_nat)) X4))) (forall ((Xs list_int) (Ys list_int) (X int)) (=> (@ (@ ord_less_eq_nat (@ size_size_list_int Xs)) (@ size_size_list_int Ys)) (not (= Xs (@ (@ cons_int X) Ys))))) (forall ((B2 assn) (A2 assn)) (=> (@ (@ ord_less_assn B2) A2) (= (@ (@ sup_sup_assn A2) B2) A2))) (forall ((X product_prod_nat_nat) (XS set_Pr1261947904930325089at_nat) (Y product_prod_nat_nat) (YS set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ produc2922128104949294807at_nat XS))) (=> (@ (@ member8440522571783428010at_nat X) XS) (=> (@ (@ member8206827879206165904at_nat (@ (@ produc6161850002892822231at_nat X) Y)) fun_pair_leq) (=> (@ (@ member8757157785044589968at_nat (@ _let_1 YS)) fun_min_weak) (@ (@ member8757157785044589968at_nat (@ _let_1 (@ (@ insert8211810215607154385at_nat Y) YS))) fun_min_weak)))))) (forall ((P (-> produc6575502325842934193n_assn int assn)) (L3 list_int)) (= (@ (@ (@ vEBT_L4760345170377931482sn_int P) nil_Pr5671120429643327159n_assn) L3) (@ pure_assn (= L3 nil_int)))) (forall ((F4 (-> nat code_integer)) (N nat) (M2 nat)) (=> (forall ((N5 nat)) (@ (@ ord_le6747313008572928689nteger (@ F4 N5)) (@ F4 (@ suc N5)))) (= (@ (@ ord_le6747313008572928689nteger (@ F4 N)) (@ F4 M2)) (@ (@ ord_less_nat N) M2)))) (forall ((B2 rat) (A2 rat) (C rat)) (=> (@ (@ ord_less_rat B2) A2) (=> (@ (@ ord_less_rat C) zero_zero_rat) (@ (@ ord_less_rat (@ (@ times_times_rat A2) C)) (@ (@ times_times_rat B2) C))))) (forall ((A set_o) (B set_o)) (= (= (@ (@ inf_inf_set_o A) B) bot_bot_set_o) (forall ((X2 Bool)) (let ((_let_1 (@ member_o X2))) (=> (@ _let_1 A) (not (@ _let_1 B))))))) (forall ((A2 multis2468970476368604999at_nat)) (= (@ (@ plus_p7104986032573967614at_nat A2) zero_z1048942125864253310at_nat) A2)) (forall ((A2 nat) (B2 nat) (F4 (-> nat num)) (C num)) (=> (@ (@ ord_less_eq_nat A2) B2) (=> (@ (@ ord_less_num (@ F4 B2)) C) (=> (forall ((X3 nat) (Y2 nat)) (=> (@ (@ ord_less_eq_nat X3) Y2) (@ (@ ord_less_eq_num (@ F4 X3)) (@ F4 Y2)))) (@ (@ ord_less_num (@ F4 A2)) C))))) (forall ((A2 int) (B2 int) (C int) (D2 int)) (let ((_let_1 (@ ord_less_eq_int zero_zero_int))) (=> (@ (@ ord_less_int A2) B2) (=> (@ (@ ord_less_int C) D2) (=> (@ _let_1 A2) (=> (@ _let_1 C) (@ (@ ord_less_int (@ (@ times_times_int A2) C)) (@ (@ 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nth_se5679702624988424552at_nat Xs))) (=> (forall ((N5 nat)) (let ((_let_1 (@ nth_se5679702624988424552at_nat Xs))) (=> (@ (@ ord_less_nat N5) (@ (@ minus_minus_nat (@ size_s8736152011456118867at_nat Xs)) one_one_nat)) (@ (@ member8757157785044589968at_nat (@ (@ produc2922128104949294807at_nat (@ _let_1 (@ suc N5))) (@ _let_1 N5))) R)))) (=> (@ (@ ord_less_nat N) (@ size_s8736152011456118867at_nat Xs)) (=> (@ (@ ord_less_nat M2) N) (@ (@ member8757157785044589968at_nat (@ (@ produc2922128104949294807at_nat (@ _let_1 N)) (@ _let_1 M2))) (@ transi2703068831062848130at_nat R))))))) (forall ((A2 (-> produc3658429121746597890et_nat Bool)) (P (-> (-> produc3658429121746597890et_nat Bool) Bool))) (= (@ (@ member6576561426505652726_nat_o A2) (@ collec939566748876313656_nat_o P)) (@ P A2))) (forall ((A2 code_integer) (B2 code_integer)) (=> (not (= (@ (@ times_3573771949741848930nteger A2) B2) zero_z3403309356797280102nteger)) (and (not (= B2 zero_z3403309356797280102nteger)) (not (= A2 zero_z3403309356797280102nteger))))) (forall ((I nat) (Xs list_c) (J nat) (X c)) (let ((_let_1 (@ (@ nth_c (@ (@ (@ list_update_c Xs) I) X)) J))) (let ((_let_2 (= I J))) (=> (@ (@ ord_less_nat I) (@ size_size_list_c Xs)) (and (=> _let_2 (= _let_1 X)) (=> (not _let_2) (= _let_1 (@ (@ nth_c Xs) J)))))))) (forall ((X int) (Y int) (Z int)) (= (@ (@ ord_less_eq_int (@ (@ sup_sup_int X) Y)) Z) (and (@ (@ ord_less_eq_int X) Z) (@ (@ ord_less_eq_int Y) Z)))) (forall ((L list_P8527749157015355191n_assn) (P (-> produc6575502325842934193n_assn Bool))) (= (forall ((X2 produc6575502325842934193n_assn)) (=> (@ (@ member7957490590177025114n_assn X2) (@ set_Pr1139785259514867910n_assn L)) (@ P X2))) (forall ((I4 nat)) (=> (@ (@ ord_less_nat I4) (@ size_s6829681357464350627n_assn L)) (@ P (@ (@ nth_Pr1769885009046257848n_assn L) I4)))))) (forall ((R2 nat) (A2 nat) (B2 nat) (C nat) (D2 nat)) (let ((_let_1 (@ times_times_nat R2))) (=> (not (= R2 zero_zero_nat)) (=> (and (= A2 B2) (not (= C D2))) (not (= (@ (@ plus_plus_nat A2) (@ _let_1 C)) (@ (@ plus_plus_nat B2) (@ _let_1 D2)))))))) (forall ((Xs list_c) (Ys list_nat)) (= (@ size_s2954062820725854115_c_nat (@ (@ product_c_nat Xs) Ys)) (@ (@ times_times_nat (@ size_size_list_c Xs)) (@ size_size_list_nat Ys)))) (not (@ _let_66 zero_zero_nat)) (= ord_less_assn (lambda ((A3 assn) (B3 assn)) (and (not (@ (@ ord_less_eq_assn B3) A3)) (@ (@ ord_less_eq_assn A3) B3)))) (forall ((Xs list_c) (Ys list_nat) (Y nat)) (=> (= (@ size_size_list_c Xs) (@ size_size_list_nat Ys)) (=> (@ (@ member_nat Y) (@ set_nat2 Ys)) (not (forall ((X3 c)) (not (@ (@ member8195077246299207702_c_nat (@ (@ product_Pair_c_nat X3) Y)) (@ set_Pr3395872032415823530_c_nat (@ (@ zip_c_nat Xs) Ys))))))))) (forall ((Xs list_d) (Ys list_d) (R2 set_Product_prod_d_d) (N nat)) (=> (@ (@ member1810801192463332112list_d (@ (@ produc242965421297323863list_d Xs) Ys)) (@ (@ lexn_d R2) N)) (and (= (@ size_size_list_d Xs) N) (= (@ size_size_list_d Ys) N)))) (forall ((A2 set_nat) (C set_nat) (B2 set_nat) (D2 set_nat)) (=> (@ (@ ord_less_eq_set_nat A2) C) (=> (@ (@ ord_less_eq_set_nat B2) D2) (@ (@ ord_less_eq_set_nat (@ (@ inf_inf_set_nat A2) B2)) (@ (@ inf_inf_set_nat C) D2))))) (forall ((B int) (K3 int) (B2 int) (A2 int)) (let ((_let_1 (@ plus_plus_int A2))) (let ((_let_2 (@ plus_plus_int K3))) (=> (= B (@ _let_2 B2)) (= (@ _let_1 B) (@ _let_2 (@ _let_1 B2))))))) (forall ((X set_int)) (= (@ (@ inf_inf_set_int X) bot_bot_set_int) bot_bot_set_int)) (forall ((X code_integer) (Y code_integer)) (= (@ (@ ord_le6747313008572928689nteger zero_z3403309356797280102nteger) (@ (@ plus_p5714425477246183910nteger (@ (@ times_3573771949741848930nteger X) X)) (@ (@ times_3573771949741848930nteger Y) Y))) (or (not (= X zero_z3403309356797280102nteger)) (not (= Y zero_z3403309356797280102nteger))))) (forall ((U code_integer)) (@ finite6017078050557962740nteger (@ (@ set_or8404916559141939852nteger zero_z3403309356797280102nteger) U))) (forall ((C rat) (A2 rat) (B2 rat)) (let ((_let_1 (@ times_times_rat C))) (=> (not (= C zero_zero_rat)) (= (= (@ _let_1 A2) (@ _let_1 B2)) (= A2 B2))))) (forall ((P (-> nat Bool)) (N nat)) (=> (@ P zero_zero_nat) (=> (forall ((N5 nat)) (=> (@ (@ ord_less_nat zero_zero_nat) N5) (=> (not (@ P N5)) (exists ((M3 nat)) (and (not (@ P M3)) (@ (@ ord_less_nat M3) N5)))))) (@ P N)))) (forall ((X nat)) (= (@ (@ ord_less_eq_nat one_one_nat) X) (not (= X zero_zero_nat)))) (forall ((Xs list_c) (I nat) (X c)) (=> (@ (@ ord_less_eq_nat (@ size_size_list_c Xs)) I) (= (@ (@ (@ list_update_c Xs) I) X) Xs))) (forall ((A2 code_integer) (F4 (-> code_integer code_integer)) (B2 code_integer) (C code_integer)) (=> (= A2 (@ F4 B2)) (=> (@ (@ ord_le6747313008572928689nteger B2) C) (=> (forall ((X3 code_integer) (Y2 code_integer)) (=> (@ (@ ord_le6747313008572928689nteger X3) Y2) (@ (@ ord_le6747313008572928689nteger (@ F4 X3)) (@ F4 Y2)))) (@ (@ ord_le6747313008572928689nteger A2) (@ F4 C)))))) (forall ((A2 nat) (B2 nat)) (=> (@ (@ ord_less_nat A2) B2) (= (@ (@ ord_min_nat A2) B2) A2))) (forall ((A2 nat) (B2 nat)) (= (@ (@ ord_less_nat (@ (@ ord_min_nat A2) B2)) B2) (@ (@ ord_less_nat A2) B2))) (forall ((A2 set_Pr1261947904930325089at_nat) (B2 set_Pr1261947904930325089at_nat)) (@ (@ ord_le3146513528884898305at_nat (@ (@ inf_in2572325071724192079at_nat A2) B2)) B2)) (forall ((A2 int) (B2 int) (C int)) (let ((_let_1 (@ plus_plus_int C))) (=> (@ (@ ord_less_eq_int A2) B2) (@ (@ ord_less_eq_int (@ _let_1 A2)) (@ _let_1 B2))))) (forall ((N nat) (X produc6575502325842934193n_assn) (Xs list_P8527749157015355191n_assn)) (let ((_let_1 (@ (@ nth_Pr1769885009046257848n_assn (@ (@ cons_P2971678138204555879n_assn X) Xs)) N))) (let ((_let_2 (= N zero_zero_nat))) (and (=> (not _let_2) (= _let_1 (@ (@ nth_Pr1769885009046257848n_assn Xs) (@ (@ minus_minus_nat N) one_one_nat)))) (=> _let_2 (= _let_1 X)))))) (forall ((M2 nat) (N nat)) (=> (not (@ (@ ord_less_nat M2) N)) (= (@ (@ plus_plus_nat N) (@ (@ minus_minus_nat M2) N)) M2))) (forall ((Y nat) (X nat)) (@ (@ ord_less_eq_nat Y) (@ (@ sup_sup_nat X) Y))) (forall ((A set_nat) (B set_nat) (C2 set_nat)) (let ((_let_1 (@ inf_inf_set_nat A))) (let ((_let_2 (@ inf_inf_set_nat B))) (= (@ _let_1 (@ _let_2 C2)) (@ _let_2 (@ _let_1 C2)))))) (forall ((A2 nat) (B2 nat)) (= (not (@ (@ ord_less_eq_nat A2) B2)) (and (@ (@ ord_less_eq_nat B2) A2) (not (= B2 A2))))) (= bot_bot_set_nat (@ collect_nat bot_bot_nat_o)) (forall ((I nat) (L list_nat) (J nat) (X nat)) (=> (not (@ (@ ord_less_nat I) (@ size_size_list_nat L))) (= (@ (@ nth_nat (@ (@ (@ list_update_nat L) J) X)) I) (@ (@ nth_nat L) I)))) (= ord_less_eq_nat (lambda ((A3 nat) (B3 nat)) (exists ((C5 nat)) (= B3 (@ (@ plus_plus_nat A3) C5))))) (forall ((C nat) (A set_nat) (B set_nat)) (let ((_let_1 (@ member_nat C))) (=> (@ _let_1 A) (=> (@ _let_1 B) (@ _let_1 (@ (@ inf_inf_set_nat A) B)))))) (forall ((X assn) (Xs list_assn) (Y assn) (Ys list_assn)) (= (@ (@ zip_assn_assn (@ (@ cons_assn X) Xs)) (@ (@ cons_assn Y) Ys)) (@ (@ 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list_P8527749157015355191n_assn)) (=> (not (= Y nil_Pr5671120429643327159n_assn)) (not (forall ((X212 produc6575502325842934193n_assn) (X223 list_P8527749157015355191n_assn)) (not (= Y (@ (@ cons_P2971678138204555879n_assn X212) X223))))))) (forall ((Y nat) (Ys list_nat) (Xs list_nat) (R2 set_Pr1261947904930325089at_nat)) (=> (@ (@ member7340969449405702474st_nat (@ (@ produc2694037385005941721st_nat (@ (@ cons_nat Y) Ys)) Xs)) (@ listrel_nat_nat R2)) (not (forall ((Y2 nat) (Ys5 list_nat)) (=> (= Xs (@ (@ cons_nat Y2) Ys5)) (=> (@ (@ member8440522571783428010at_nat (@ (@ product_Pair_nat_nat Y) Y2)) R2) (not (@ (@ member7340969449405702474st_nat (@ (@ produc2694037385005941721st_nat Ys) Ys5)) (@ listrel_nat_nat R2))))))))) (forall ((N nat) (Xs list_d)) (=> (@ (@ ord_less_nat N) (@ size_size_list_d Xs)) (@ (@ member_d (@ (@ nth_d Xs) N)) (@ set_d2 Xs)))) (forall ((A2 int) (B2 int)) (=> (@ (@ ord_less_int A2) B2) (not (= A2 B2)))) (forall ((A2 code_integer) (B2 code_integer)) (=> (@ (@ 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C))))) (forall ((A2 nat) (B2 nat) (F4 (-> nat code_integer)) (C code_integer)) (=> (@ (@ ord_less_eq_nat A2) B2) (=> (@ (@ ord_le6747313008572928689nteger (@ F4 B2)) C) (=> (forall ((X3 nat) (Y2 nat)) (=> (@ (@ ord_less_eq_nat X3) Y2) (@ (@ ord_le3102999989581377725nteger (@ F4 X3)) (@ F4 Y2)))) (@ (@ ord_le6747313008572928689nteger (@ F4 A2)) C))))) (forall ((A2 code_integer) (B2 code_integer) (C code_integer) (D2 code_integer)) (=> (@ (@ ord_le6747313008572928689nteger A2) B2) (=> (@ (@ ord_le3102999989581377725nteger C) D2) (=> (@ (@ ord_le3102999989581377725nteger zero_z3403309356797280102nteger) A2) (=> (@ (@ ord_le6747313008572928689nteger zero_z3403309356797280102nteger) C) (@ (@ ord_le6747313008572928689nteger (@ (@ times_3573771949741848930nteger A2) C)) (@ (@ times_3573771949741848930nteger B2) D2))))))) (forall ((Xs list_int)) (= (= nil_int (@ rev_int Xs)) (= Xs nil_int))) (@ (@ (@ (@ bNF_re6830278522597306478at_int (lambda ((Y4 nat) (Z2 nat)) (= Y4 Z2))) pcr_int) (lambda 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(R2 set_Pr4708930517165415495nt_int) (P (-> (-> produc8551481072490612790e_term option6357759511663192854e_term) product_prod_int_int Bool))) (=> (@ (@ member6582457606847315088nt_int (@ (@ produc7601053194514725023nt_int (@ (@ produc5700946648718959541nt_int Ax) Ay)) (@ (@ produc5700946648718959541nt_int Bx) By))) (@ transi7434818091516421410nt_int R2)) (=> (forall ((A4 (-> produc8551481072490612790e_term option6357759511663192854e_term)) (B4 product_prod_int_int)) (=> (@ (@ member6582457606847315088nt_int (@ (@ produc7601053194514725023nt_int (@ (@ produc5700946648718959541nt_int Ax) Ay)) (@ (@ produc5700946648718959541nt_int A4) B4))) R2) (@ (@ P A4) B4))) (=> (forall ((A4 (-> produc8551481072490612790e_term option6357759511663192854e_term)) (B4 product_prod_int_int) (Aa (-> produc8551481072490612790e_term option6357759511663192854e_term)) (Ba product_prod_int_int)) (let ((_let_1 (@ (@ produc5700946648718959541nt_int A4) B4))) (=> (@ (@ member6582457606847315088nt_int (@ (@ 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(forall ((A2 rat) (B2 rat) (C rat)) (=> (@ (@ ord_less_rat A2) B2) (@ (@ ord_less_rat (@ (@ minus_minus_rat A2) C)) (@ (@ minus_minus_rat B2) C)))) (forall ((X set_nat) (Y set_nat)) (= (= (@ (@ minus_minus_set_nat X) Y) bot_bot_set_nat) (@ (@ ord_less_eq_set_nat X) Y))) (forall ((N nat) (Xs list_int) (P (-> int Bool))) (=> (@ (@ ord_less_nat N) (@ size_size_list_int Xs)) (=> (forall ((X3 int)) (=> (@ (@ member_int X3) (@ set_int2 Xs)) (@ P X3))) (@ P (@ (@ nth_int Xs) N))))) (forall ((A2 code_integer) (C code_integer)) (= (@ (@ ord_le3102999989581377725nteger (@ (@ times_3573771949741848930nteger A2) C)) C) (and (=> (@ (@ ord_le6747313008572928689nteger C) zero_z3403309356797280102nteger) (@ (@ ord_le3102999989581377725nteger one_one_Code_integer) A2)) (=> (@ (@ ord_le6747313008572928689nteger zero_z3403309356797280102nteger) C) (@ (@ ord_le3102999989581377725nteger A2) one_one_Code_integer))))) (forall ((C set_nat) (A2 set_nat) (D2 set_nat) (B2 set_nat)) (=> (@ (@ ord_less_eq_set_nat C) A2) (=> (@ (@ ord_less_eq_set_nat D2) B2) (@ (@ ord_less_eq_set_nat (@ (@ sup_sup_set_nat C) D2)) (@ (@ sup_sup_set_nat A2) B2))))) (forall ((Xs list_P8527749157015355191n_assn)) (= (@ set_Pr1139785259514867910n_assn (@ rotate328796349445179396n_assn Xs)) (@ set_Pr1139785259514867910n_assn Xs))) (forall ((K3 nat) (M2 nat) (N nat)) (let ((_let_1 (@ times_times_nat K3))) (=> (@ (@ ord_less_nat zero_zero_nat) K3) (= (@ (@ divide_divide_nat (@ _let_1 M2)) (@ _let_1 N)) (@ (@ divide_divide_nat M2) N))))) (forall ((Xs list_i8448526496819171953e_term) (I nat) (X (-> int option6357759511663192854e_term)) (Ys list_P5707943133018811711nt_int) (Y product_prod_int_int)) (= (@ (@ zip_in8766932505889695135nt_int (@ (@ (@ list_u8946639151299769843e_term Xs) I) X)) (@ (@ (@ list_u3002344382305578791nt_int Ys) I) Y)) (@ (@ (@ list_u4780935413889332127nt_int (@ (@ zip_in8766932505889695135nt_int Xs) Ys)) I) (@ (@ produc4305682042979456191nt_int X) Y)))) (forall ((A2 assn) (N nat)) (let ((_let_1 (@ 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X))) (let ((_let_2 (@ _let_1 Y))) (= (@ _let_1 _let_2) _let_2)))) (forall ((I nat) (J nat) (X nat) (Xs list_nat)) (= (= (@ (@ upt I) J) (@ (@ cons_nat X) Xs)) (and (= I X) (= (@ (@ upt (@ (@ plus_plus_nat I) one_one_nat)) J) Xs) (@ (@ ord_less_nat I) J)))) (forall ((X produc6575502325842934193n_assn) (Xs list_P8527749157015355191n_assn)) (=> (not (@ (@ member7957490590177025114n_assn X) (@ set_Pr1139785259514867910n_assn Xs))) (= (@ (@ remove1763081955827946941n_assn X) Xs) Xs))) (forall ((M2 nat) (K3 int)) (let ((_let_1 (@ power_power_int K3))) (=> (@ (@ ord_less_nat zero_zero_nat) M2) (=> (@ (@ ord_less_int zero_zero_int) K3) (= (@ (@ divide_divide_int (@ _let_1 M2)) K3) (@ _let_1 (@ (@ minus_minus_nat M2) (@ suc zero_zero_nat)))))))) (forall ((X assn) (Y assn)) (let ((_let_1 (@ sup_sup_assn X))) (let ((_let_2 (@ _let_1 Y))) (= (@ _let_1 _let_2) _let_2)))) (forall ((Y int)) (= (@ (@ count_list_int nil_int) Y) zero_zero_nat)) (forall ((P Bool)) (or (= P false) (= P true))) (forall ((A2 multis2468970476368604999at_nat) (B2 multis2468970476368604999at_nat)) (= (@ (@ minus_4286766774447292334at_nat (@ (@ plus_p7104986032573967614at_nat A2) B2)) A2) B2)) (forall ((A2 code_integer) (B2 code_integer) (N nat)) (let ((_let_1 (@ ord_le3102999989581377725nteger zero_z3403309356797280102nteger))) (=> (@ _let_1 A2) (=> (@ _let_1 B2) (=> (@ (@ ord_less_nat zero_zero_nat) N) (= (@ (@ ord_le3102999989581377725nteger (@ (@ power_8256067586552552935nteger A2) N)) (@ (@ power_8256067586552552935nteger B2) N)) (@ (@ ord_le3102999989581377725nteger A2) B2))))))) (forall ((A2 rat) (B2 rat) (C rat)) (let ((_let_1 (@ plus_plus_rat A2))) (=> (= (@ _let_1 B2) (@ _let_1 C)) (= B2 C)))) (forall ((X nat) (Y nat)) (=> (@ (@ ord_less_eq_nat X) Y) (= (@ (@ sup_sup_nat X) Y) Y))) (forall ((X21 int) (X222 list_int)) (@ (@ member_int X21) (@ set_int2 (@ (@ cons_int X21) X222)))) (forall ((X set_Pr4329608150637261639at_nat) (Y set_Pr4329608150637261639at_nat) (Z set_Pr4329608150637261639at_nat)) (let ((_let_1 (@ sup_su5525570899277871387at_nat X))) (=> (forall ((X3 set_Pr4329608150637261639at_nat) (Y2 set_Pr4329608150637261639at_nat) (Z4 set_Pr4329608150637261639at_nat)) (let ((_let_1 (@ inf_in7913087082777306421at_nat X3))) (= (@ _let_1 (@ (@ sup_su5525570899277871387at_nat Y2) Z4)) (@ (@ sup_su5525570899277871387at_nat (@ _let_1 Y2)) (@ _let_1 Z4))))) (= (@ _let_1 (@ (@ inf_in7913087082777306421at_nat Y) Z)) (@ (@ inf_in7913087082777306421at_nat (@ _let_1 Y)) (@ _let_1 Z)))))) (forall ((A2 rat) (C rat)) (= (= (@ (@ times_times_rat A2) C) C) (or (= C zero_zero_rat) (= A2 one_one_rat)))) (forall ((A2 set_int) (B2 set_int)) (= (= bot_bot_set_int (@ (@ sup_sup_set_int A2) B2)) (and (= A2 bot_bot_set_int) (= B2 bot_bot_set_int)))) (forall ((C filter_nat) (A2 filter_nat) (D2 filter_nat) (B2 filter_nat)) (=> (@ (@ ord_le2510731241096832064er_nat C) A2) (=> (@ (@ ord_le2510731241096832064er_nat D2) B2) (@ (@ ord_le2510731241096832064er_nat (@ (@ sup_sup_filter_nat C) D2)) (@ (@ 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Y5)) R2))))) (forall ((X nat) (Y nat) (R2 set_Pr1261947904930325089at_nat) (Z nat)) (let ((_let_1 (@ transi6264000038957366511cl_nat R2))) (let ((_let_2 (@ product_Pair_nat_nat X))) (=> (@ (@ member8440522571783428010at_nat (@ _let_2 Y)) _let_1) (=> (@ (@ member8440522571783428010at_nat (@ (@ product_Pair_nat_nat Y) Z)) _let_1) (@ (@ member8440522571783428010at_nat (@ _let_2 Z)) _let_1)))))) (forall ((A2 assn) (B2 assn)) (@ (@ ord_less_eq_assn (@ (@ inf_inf_assn A2) B2)) A2)) (forall ((B multis2468970476368604999at_nat) (K3 multis2468970476368604999at_nat) (B2 multis2468970476368604999at_nat) (A2 multis2468970476368604999at_nat)) (let ((_let_1 (@ plus_p7104986032573967614at_nat A2))) (let ((_let_2 (@ plus_p7104986032573967614at_nat K3))) (=> (= B (@ _let_2 B2)) (= (@ _let_1 B) (@ _let_2 (@ _let_1 B2))))))) (forall ((X int) (Y int) (Z int)) (let ((_let_1 (@ ord_less_eq_int X))) (let ((_let_2 (@ _let_1 Y))) (let ((_let_3 (@ ord_less_eq_int Z))) (let ((_let_4 (@ _let_3 X))) (let ((_let_5 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nat)) (= (not (@ (@ ord_less_eq_nat X) Y)) (@ (@ ord_less_nat Y) X))) (forall ((X int) (Xs list_int) (N nat)) (= (@ (@ nth_int (@ (@ cons_int X) Xs)) (@ suc N)) (@ (@ nth_int Xs) N))) (forall ((A2 nat) (B2 nat) (S3 nat) (T nat)) (=> (@ (@ ord_less_nat A2) B2) (@ (@ member8206827879206165904at_nat (@ (@ produc6161850002892822231at_nat (@ (@ product_Pair_nat_nat A2) S3)) (@ (@ product_Pair_nat_nat B2) T))) fun_pair_leq))) (forall ((A2 nat)) (= (not (= A2 bot_bot_nat)) (@ (@ ord_less_nat bot_bot_nat) A2))) (forall ((A2 int) (B2 int) (C int)) (= (@ (@ ord_less_int (@ (@ minus_minus_int A2) B2)) C) (@ (@ ord_less_int A2) (@ (@ plus_plus_int C) B2)))) (forall ((A2 set_Pr1261947904930325089at_nat) (B2 set_Pr1261947904930325089at_nat)) (= (= (@ (@ sup_su6327502436637775413at_nat A2) B2) bot_bo2099793752762293965at_nat) (and (= B2 bot_bo2099793752762293965at_nat) (= A2 bot_bo2099793752762293965at_nat)))) (forall ((Xs list_nat)) (= (= (@ size_size_list_nat Xs) zero_zero_nat) (= Xs nil_nat))) (forall ((A2 int) (C2 set_int) (B set_int)) (let ((_let_1 (@ (@ inf_inf_set_int B) C2))) (let ((_let_2 (@ insert_int2 A2))) (let ((_let_3 (@ (@ inf_inf_set_int (@ _let_2 B)) C2))) (let ((_let_4 (@ (@ member_int A2) C2))) (and (=> _let_4 (= _let_3 (@ _let_2 _let_1))) (=> (not _let_4) (= _let_3 _let_1)))))))) (forall ((N nat) (P (-> int nat Bool))) (=> (forall ((I5 nat)) (=> (@ (@ ord_less_nat I5) N) (exists ((Li2 int)) (@ (@ P Li2) I5)))) (not (forall ((L2 list_int)) (=> (= (@ size_size_list_int L2) N) (not (forall ((I6 nat)) (=> (@ (@ ord_less_nat I6) N) (@ (@ P (@ (@ nth_int L2) I6)) I6))))))))) (forall ((A2 assn) (B2 assn)) (=> (@ (@ ord_less_assn A2) B2) (not (@ (@ ord_less_assn B2) A2)))) (forall ((A2 code_integer) (C code_integer) (B2 code_integer)) (=> (@ (@ ord_le3102999989581377725nteger (@ (@ times_3573771949741848930nteger A2) C)) (@ (@ times_3573771949741848930nteger B2) C)) (=> (@ (@ ord_le6747313008572928689nteger zero_z3403309356797280102nteger) C) (@ (@ ord_le3102999989581377725nteger A2) B2)))) (= ord_less_rat (lambda ((A3 rat) (B3 rat)) (@ (@ ord_less_rat (@ (@ minus_minus_rat A3) B3)) zero_zero_rat))) (forall ((X rat) (Y rat) (N nat)) (let ((_let_1 (@ (@ power_power_rat X) N))) (let ((_let_2 (@ times_times_rat Y))) (=> (= (@ (@ times_times_rat X) Y) (@ _let_2 X)) (= (@ (@ times_times_rat _let_1) Y) (@ _let_2 _let_1)))))) (forall ((A2 int) (B2 int) (P (-> int Bool))) (=> (@ (@ ord_less_int A2) B2) (=> (@ P A2) (=> (not (@ P B2)) (exists ((C4 int)) (and (@ (@ ord_less_eq_int A2) C4) (@ (@ ord_less_eq_int C4) B2) (forall ((D4 int)) (=> (forall ((X3 int)) (=> (and (@ (@ ord_less_int X3) D4) (@ (@ ord_less_eq_int A2) X3)) (@ P X3))) (@ (@ ord_less_eq_int D4) C4))) (forall ((X7 int)) (=> (and (@ (@ ord_less_int X7) C4) (@ (@ ord_less_eq_int A2) X7)) (@ P X7))))))))) (forall ((I nat) (J nat) (K3 nat) (L nat)) (=> (and (@ (@ ord_less_nat K3) L) (= I J)) (@ (@ ord_less_nat (@ (@ plus_plus_nat I) K3)) (@ (@ plus_plus_nat J) L)))) (forall ((X int)) (exists ((X_1 int)) (@ (@ ord_less_int X) X_1))) (forall ((P (-> nat Bool)) (K3 nat)) (= (@ (@ eventually_nat (lambda ((N2 nat)) (@ P (@ (@ plus_plus_nat N2) K3)))) at_top_nat) (@ (@ eventually_nat P) at_top_nat))) (forall ((L23 list_int)) (= (@ (@ merge_int nil_int) L23) L23)) (forall ((X set_nat)) (@ (@ ord_less_eq_set_nat X) X)) (not (@ (@ ord_less_eq_nat one_one_nat) zero_zero_nat)) (forall ((A2 code_integer) (B2 code_integer) (C code_integer)) (=> (@ (@ ord_le6747313008572928689nteger A2) B2) (@ (@ ord_le6747313008572928689nteger (@ (@ minus_8373710615458151222nteger A2) C)) (@ (@ minus_8373710615458151222nteger B2) C)))) (forall ((X nat) (Xs list_nat)) (=> (@ (@ member_nat X) (@ set_nat2 Xs)) (@ (@ ord_less_nat (@ size_size_list_nat (@ (@ removeAll_nat X) Xs))) (@ size_size_list_nat Xs)))) (forall ((A2 nat) (B2 nat)) (let ((_let_1 (@ (@ insert8211810215607154385at_nat (@ (@ product_Pair_nat_nat A2) B2)) bot_bo2099793752762293965at_nat))) (= (@ transi6264000038957366511cl_nat _let_1) _let_1))) (forall ((I int) (J int) (R set_Pr958786334691620121nt_int)) (=> (@ (@ member5262025264175285858nt_int (@ (@ product_Pair_int_int I) J)) R) (@ (@ member_int I) (@ field_int R)))) (forall ((A2 rat) (B2 rat) (C rat)) (=> (@ (@ ord_less_eq_rat A2) B2) (@ (@ ord_less_eq_rat (@ (@ plus_plus_rat A2) C)) (@ (@ plus_plus_rat B2) C)))) (= ord_less_int (lambda ((A3 int) (B3 int)) (and (not (= A3 B3)) (@ (@ ord_less_eq_int A3) B3)))) (forall ((A2 multis2468970476368604999at_nat)) (= (@ (@ minus_4286766774447292334at_nat zero_z1048942125864253310at_nat) A2) zero_z1048942125864253310at_nat)) (forall ((X int) (Xs list_int)) (= (@ size_size_list_int (@ (@ cons_int X) Xs)) (@ suc (@ size_size_list_int Xs)))) (forall ((X num) (Y num) (Z num)) (=> (@ (@ ord_less_eq_num X) Y) (=> (@ (@ ord_less_num Y) Z) (@ (@ ord_less_num X) Z)))) (forall ((X int) (Y int) (Z int)) (let ((_let_1 (@ ord_less_eq_int X))) (=> (@ _let_1 Y) (=> (@ (@ ord_less_eq_int Y) Z) (@ _let_1 Z))))) (forall ((M2 nat) (K3 nat) (N nat)) (= (@ (@ ord_less_nat (@ (@ times_times_nat M2) K3)) (@ (@ times_times_nat N) K3)) (and (@ (@ ord_less_nat zero_zero_nat) K3) (@ (@ ord_less_nat M2) N)))) (forall ((B2 set_Pr1261947904930325089at_nat) (A2 set_Pr1261947904930325089at_nat)) (=> (@ (@ ord_le7866589430770878221at_nat B2) A2) (= (@ (@ inf_in2572325071724192079at_nat A2) B2) B2))) (forall ((Xs list_nat) (I nat) (J nat)) (let ((_let_1 (@ nth_nat Xs))) (=> (@ (@ sorted_wrt_nat ord_less_eq_nat) Xs) (=> (@ (@ ord_less_eq_nat I) J) (=> (@ (@ ord_less_nat J) (@ size_size_list_nat Xs)) (@ (@ ord_less_eq_nat (@ _let_1 I)) (@ _let_1 J))))))) (forall ((P (-> int Bool)) (P3 (-> int Bool)) (Q (-> int Bool)) (Q3 (-> int Bool))) (=> (exists ((Z3 int)) (forall ((X3 int)) (=> (@ (@ ord_less_int X3) Z3) (= (@ P X3) (@ P3 X3))))) (=> (exists ((Z3 int)) (forall ((X3 int)) (=> (@ (@ ord_less_int X3) Z3) (= (@ Q X3) (@ Q3 X3))))) (exists ((Z4 int)) (forall ((X7 int)) (=> (@ (@ ord_less_int X7) Z4) (= (or (@ Q X7) (@ P X7)) (or (@ P3 X7) (@ Q3 X7))))))))) (forall ((B2 set_Pr1261947904930325089at_nat) (A2 set_Pr1261947904930325089at_nat) (C set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ inf_in2572325071724192079at_nat B2))) (let ((_let_2 (@ inf_in2572325071724192079at_nat A2))) (= (@ _let_1 (@ _let_2 C)) (@ _let_2 (@ _let_1 C)))))) (forall ((X assn) (Y assn) (Z assn)) (let ((_let_1 (@ sup_sup_assn X))) (let ((_let_2 (@ sup_sup_assn Y))) (= (@ _let_1 (@ _let_2 Z)) (@ _let_2 (@ _let_1 Z)))))) (forall ((A set_Pr1261947904930325089at_nat) (B set_Pr1261947904930325089at_nat) (C2 set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ inf_in2572325071724192079at_nat A))) (= (= (@ (@ sup_su6327502436637775413at_nat (@ _let_1 B)) C2) (@ _let_1 (@ (@ sup_su6327502436637775413at_nat B) C2))) (@ (@ ord_le3146513528884898305at_nat C2) A)))) (forall ((A2 filter_nat) (B2 filter_nat)) (=> (@ (@ ord_less_filter_nat A2) B2) (@ (@ ord_le2510731241096832064er_nat A2) B2))) (forall ((A2 code_integer) (B2 code_integer)) (= (not (@ (@ ord_le6747313008572928689nteger A2) B2)) (or (= A2 B2) (not (@ (@ ord_le3102999989581377725nteger A2) B2))))) (forall ((Y produc2732055786443039994et_nat)) (not (forall ((A4 (-> produc3658429121746597890et_nat Bool)) (B4 (-> produc3658429121746597890et_nat Bool)) (C4 heap_e7401611519738050253t_unit) (D3 set_nat)) (not (= Y (@ (@ produc2245416461498447860et_nat A4) (@ (@ produc5001842942810119800et_nat B4) (@ (@ produc7507926704131184380et_nat C4) D3)))))))) (forall ((X d) (Xs list_d)) (=> (@ (@ member_d X) (@ set_d2 Xs)) (@ (@ ord_less_nat (@ size_size_list_d (@ (@ removeAll_d X) Xs))) (@ size_size_list_d Xs)))) (forall ((X int) (Xs list_int)) (@ (@ ord_less_eq_nat (@ size_size_list_int (@ (@ removeAll_int X) Xs))) (@ size_size_list_int Xs))) (forall ((A set_int)) (= (forall ((X2 int)) (not (@ (@ member_int X2) A))) (= A bot_bot_set_int))) (= sup_sup_assn (lambda ((A3 assn) (B3 assn)) (@ (@ sup_sup_assn B3) A3))) (forall ((X num) (Y num) (P Bool)) (=> (@ (@ ord_less_num X) Y) (=> (@ (@ ord_less_num Y) X) P))) (forall ((N nat)) (= (@ (@ enumerate_int N) nil_int) nil_Pr1301135604781543011at_int)) (forall ((A2 filter_nat) (B2 filter_nat) (C filter_nat)) (=> (@ (@ ord_le2510731241096832064er_nat A2) B2) (=> (@ (@ ord_less_filter_nat B2) C) (@ (@ ord_less_filter_nat A2) C)))) (forall ((C nat) (A2 nat) (B2 nat)) (let ((_let_1 (@ times_times_nat C))) (=> (not (= C zero_zero_nat)) (= (= (@ _let_1 A2) (@ _let_1 B2)) (= A2 B2))))) (forall ((Y set_Pr4329608150637261639at_nat) (X set_Pr4329608150637261639at_nat)) (=> (@ (@ ord_le1268244103169919719at_nat Y) X) (= (@ (@ sup_su5525570899277871387at_nat X) Y) X))) (forall ((X rat)) (= (= one_one_rat X) (= X one_one_rat))) (forall ((C product_prod_nat_nat) (A set_Pr1261947904930325089at_nat) (B set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ member8440522571783428010at_nat C))) (=> (@ _let_1 (@ (@ minus_1356011639430497352at_nat A) B)) (not (@ _let_1 B))))) (forall ((A2 set_Pr4329608150637261639at_nat) (B2 set_Pr4329608150637261639at_nat)) (=> (@ (@ ord_le2604355607129572851at_nat A2) B2) (= (@ (@ sup_su5525570899277871387at_nat A2) B2) B2))) (forall ((X set_nat)) (= (@ (@ ord_min_set_nat X) bot_bot_set_nat) bot_bot_set_nat)) (forall ((X set_Pr1261947904930325089at_nat)) (= (@ (@ ord_mi4194197829855655752at_nat bot_bo2099793752762293965at_nat) X) bot_bo2099793752762293965at_nat)) _let_63 (forall ((A2 (-> produc3658429121746597890et_nat Bool)) (B2 produc3925858234332021118et_nat) (S set_Pr8536935166611901872et_nat) (P (-> (-> produc3658429121746597890et_nat Bool) produc3925858234332021118et_nat Bool))) (let ((_let_1 (@ (@ member6124377750444531601et_nat (@ (@ produc2245416461498447860et_nat A2) B2)) S))) (=> _let_1 (=> (=> _let_1 (@ (@ P A2) B2)) (exists ((A4 (-> produc3658429121746597890et_nat Bool)) (B4 produc3925858234332021118et_nat)) (and (@ (@ member6124377750444531601et_nat (@ (@ produc2245416461498447860et_nat A4) B4)) S) (@ (@ P A4) B4))))))) (forall ((N nat) (M2 nat)) (=> (@ (@ ord_less_nat zero_zero_nat) N) (= (@ (@ minus_minus_nat (@ suc M2)) N) (@ (@ minus_minus_nat M2) (@ (@ minus_minus_nat N) one_one_nat))))) (forall ((X code_integer) (Zs list_Code_integer)) (let ((_let_1 (@ foldl_1542389171486570077nteger times_3573771949741848930nteger))) (= (@ (@ times_3573771949741848930nteger X) (@ (@ _let_1 one_one_Code_integer) Zs)) (@ (@ _let_1 X) Zs)))) (forall ((N nat) (M2 nat)) (let ((_let_1 (@ ord_less_nat zero_zero_nat))) (=> (@ _let_1 N) (=> (@ (@ dvd_dvd_nat M2) N) (@ _let_1 M2))))) (forall ((X4 set_Pr1261947904930325089at_nat)) (@ (@ member8757157785044589968at_nat (@ (@ produc2922128104949294807at_nat X4) bot_bo2099793752762293965at_nat)) fun_min_weak)) (forall ((P (-> nat Bool)) (M2 nat) (N nat)) (let ((_let_1 (= N zero_zero_nat))) (= (@ P (@ (@ modulo_modulo_nat M2) N)) (and (=> (not _let_1) (forall ((I4 nat) (J2 nat)) (=> (@ (@ ord_less_nat J2) N) (=> (= M2 (@ (@ plus_plus_nat (@ (@ times_times_nat N) I4)) J2)) (@ P J2))))) (=> _let_1 (@ P M2)))))) (forall ((X set_Pr4329608150637261639at_nat) (Y set_Pr4329608150637261639at_nat) (Z set_Pr4329608150637261639at_nat)) (let ((_let_1 (@ sup_su5525570899277871387at_nat X))) (= (@ (@ sup_su5525570899277871387at_nat (@ _let_1 Y)) Z) (@ _let_1 (@ (@ sup_su5525570899277871387at_nat Y) Z))))) (forall ((A2 nat) (B2 nat) (F4 (-> nat int)) (C int)) (=> (@ (@ ord_less_eq_nat A2) B2) (=> (@ (@ ord_less_int (@ F4 B2)) C) (=> (forall ((X3 nat) (Y2 nat)) (=> (@ (@ ord_less_eq_nat X3) Y2) (@ (@ ord_less_eq_int (@ F4 X3)) (@ F4 Y2)))) (@ (@ ord_less_int (@ F4 A2)) C))))) (forall ((Begin nat) (End nat) (X int) (Xs list_int)) (let ((_let_1 (@ (@ minus_minus_nat End) one_one_nat))) (let ((_let_2 (@ slice_int Begin))) (let ((_let_3 (@ cons_int X))) (let ((_let_4 (@ (@ _let_2 End) (@ _let_3 Xs)))) (let ((_let_5 (and (= Begin zero_zero_nat) (@ (@ ord_less_nat zero_zero_nat) End)))) (and (=> (not _let_5) (= _let_4 (@ (@ (@ slice_int (@ (@ minus_minus_nat Begin) one_one_nat)) _let_1) Xs))) (=> _let_5 (= _let_4 (@ _let_3 (@ (@ _let_2 _let_1) Xs))))))))))) (forall ((I int) (J int) (K3 int) (L int)) (=> (and (@ (@ ord_less_int I) J) (@ (@ ord_less_int K3) L)) (@ (@ ord_less_int (@ (@ plus_plus_int I) K3)) (@ (@ plus_plus_int J) L)))) (forall ((A set_Pr1261947904930325089at_nat) (B set_Pr1261947904930325089at_nat) (X product_prod_nat_nat)) (let ((_let_1 (@ (@ insert8211810215607154385at_nat X) bot_bo2099793752762293965at_nat))) (let ((_let_2 (= A _let_1))) (let ((_let_3 (= B _let_1))) (= (= (@ (@ sup_su6327502436637775413at_nat A) B) _let_1) (or (and (= A bot_bo2099793752762293965at_nat) _let_3) (and (= B bot_bo2099793752762293965at_nat) _let_2) (and _let_3 _let_2))))))) (= ord_le1268244103169919719at_nat (lambda ((A5 set_Pr4329608150637261639at_nat) (B7 set_Pr4329608150637261639at_nat)) (= (@ (@ sup_su5525570899277871387at_nat A5) B7) B7))) (forall ((A2 int) (B2 int) (C int)) (let ((_let_1 (@ minus_minus_int A2))) (= (@ _let_1 (@ (@ plus_plus_int B2) C)) (@ (@ minus_minus_int (@ _let_1 C)) B2)))) (forall ((M2 nat) (N nat) (K3 nat)) (let ((_let_1 (@ divide_divide_nat K3))) (=> (@ (@ ord_less_nat zero_zero_nat) M2) (=> (@ (@ ord_less_eq_nat M2) N) (@ (@ ord_less_eq_nat (@ _let_1 N)) (@ _let_1 M2)))))) (forall ((X produc3658429121746597890et_nat) (Y Bool)) (=> (= (@ one_assn_raw X) Y) (not (forall ((H heap_e7401611519738050253t_unit) (As set_nat)) (=> (= X (@ (@ produc7507926704131184380et_nat H) As)) (= Y (not (= As bot_bot_set_nat)))))))) (forall ((P (-> int int Bool)) (A int)) (@ (@ pairwise_int P) (@ (@ insert_int2 A) bot_bot_set_int))) (forall ((A2 set_Pr1261947904930325089at_nat) (B2 set_Pr1261947904930325089at_nat) (R2 set_Pr4329608150637261639at_nat) (P (-> set_Pr1261947904930325089at_nat Bool))) (=> (@ (@ member8757157785044589968at_nat (@ (@ produc2922128104949294807at_nat A2) B2)) (@ transi2703068831062848130at_nat R2)) (=> (forall ((Y2 set_Pr1261947904930325089at_nat)) (=> (@ (@ member8757157785044589968at_nat (@ (@ produc2922128104949294807at_nat A2) Y2)) R2) (@ P Y2))) (=> (forall ((Y2 set_Pr1261947904930325089at_nat) (Z4 set_Pr1261947904930325089at_nat)) (=> (@ (@ member8757157785044589968at_nat (@ (@ produc2922128104949294807at_nat A2) Y2)) (@ transi2703068831062848130at_nat R2)) (=> (@ (@ member8757157785044589968at_nat (@ (@ produc2922128104949294807at_nat Y2) Z4)) R2) (=> (@ P Y2) (@ P Z4))))) (@ P B2))))) (forall ((M2 nat) (N nat)) (= (@ (@ map_nat_nat suc) (@ (@ upt M2) N)) (@ (@ upt (@ suc M2)) (@ suc N)))) (forall ((X produc1908205239877642774nteger)) (not (forall ((F5 (-> produc6241069584506657477e_term option6357759511663192854e_term)) (D3 code_integer) (I5 code_integer)) (not (= X (@ (@ produc8603105652947943368nteger F5) (@ (@ produc1086072967326762835nteger D3) I5))))))) (forall ((X nat) (A2 nat) (B2 nat)) (let ((_let_1 (@ ord_less_nat X))) (=> (@ _let_1 A2) (@ _let_1 (@ (@ sup_sup_nat A2) B2))))) (forall ((Xs list_c) (Ys list_c) (X c)) (=> (@ (@ ord_less_eq_nat (@ size_size_list_c Xs)) (@ size_size_list_c Ys)) (not (= Xs (@ (@ cons_c X) Ys))))) (= ord_less_filter_nat (lambda ((A3 filter_nat) (B3 filter_nat)) (and (not (@ (@ ord_le2510731241096832064er_nat B3) A3)) (@ (@ ord_le2510731241096832064er_nat A3) B3)))) (= (lambda ((Y4 int) (Z2 int)) (= Y4 Z2)) (lambda ((A3 int) (B3 int)) (and (@ (@ ord_less_eq_int A3) B3) (@ (@ ord_less_eq_int B3) A3)))) (forall ((A2 assn) (B2 assn) (F4 (-> assn int)) (C int)) (=> (@ (@ ord_less_eq_assn A2) B2) (=> (= (@ F4 B2) C) (=> (forall ((X3 assn) (Y2 assn)) (=> (@ (@ ord_less_eq_assn X3) Y2) (@ (@ ord_less_eq_int (@ F4 X3)) (@ F4 Y2)))) (@ (@ ord_less_eq_int (@ F4 A2)) C))))) (forall ((A2 code_integer) (B2 code_integer) (D2 code_integer) (C code_integer)) (=> (@ (@ ord_le6747313008572928689nteger A2) B2) (=> (@ (@ ord_le6747313008572928689nteger D2) C) (@ (@ ord_le6747313008572928689nteger (@ (@ minus_8373710615458151222nteger A2) C)) (@ (@ minus_8373710615458151222nteger B2) D2))))) (forall ((X nat) (Y nat) (R2 set_Pr1261947904930325089at_nat) (Xs list_nat)) (=> (@ (@ member8440522571783428010at_nat (@ (@ product_Pair_nat_nat X) Y)) R2) (@ (@ member7340969449405702474st_nat (@ (@ produc2694037385005941721st_nat (@ (@ cons_nat X) Xs)) (@ (@ cons_nat Y) Xs))) (@ listrel1_nat R2)))) (= insert9069300056098147895at_nat (lambda ((A3 produc3843707927480180839at_nat) (__flatten_var_0 set_Pr4329608150637261639at_nat)) (@ (@ sup_su5525570899277871387at_nat (@ (@ insert9069300056098147895at_nat A3) bot_bo228742789529271731at_nat)) __flatten_var_0))) (forall ((D int) (T int) (B set_int)) (=> (@ (@ ord_less_int zero_zero_int) D) (=> (@ (@ member_int T) B) (forall ((X7 int)) (=> (forall ((Xa3 int)) (=> (@ (@ member_int Xa3) (@ (@ set_or1266510415728281911st_int one_one_int) D)) (forall ((Xb3 int)) (=> (@ (@ member_int Xb3) B) (not (= X7 (@ (@ plus_plus_int Xb3) Xa3))))))) (=> (not (= X7 T)) (not (= (@ (@ minus_minus_int X7) D) T)))))))) (forall ((L12 list_d) (L23 list_nat)) (=> (= (@ size_size_list_d L12) (@ size_size_list_nat L23)) (= (@ (@ (@ zipf_d7851395264309270293_d_nat product_Pair_d_nat) L12) L23) (@ (@ zip_d_nat L12) L23)))) (forall ((X produc6575502325842934193n_assn) (Xs list_P8527749157015355191n_assn) (Y produc6575502325842934193n_assn)) (= (@ (@ (@ list_u4534839942911652127n_assn (@ (@ cons_P2971678138204555879n_assn X) Xs)) zero_zero_nat) Y) (@ (@ cons_P2971678138204555879n_assn Y) Xs))) (forall ((S set_Pr1261947904930325089at_nat) (S4 set_Pr1261947904930325089at_nat) (A set_Pr1261947904930325089at_nat) (B set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ inf_in2572325071724192079at_nat B))) (let ((_let_2 (@ inf_in2572325071724192079at_nat A))) (=> (@ (@ ord_le3146513528884898305at_nat S) S4) (=> (= (@ _let_2 S4) (@ _let_1 S4)) (= (@ _let_2 S) (@ _let_1 S))))))) (forall ((Xs list_int) (Ys list_int)) (let ((_let_1 (@ sorted_wrt_int ord_less_eq_int))) (=> (@ _let_1 Xs) (=> (@ distinct_int Xs) (=> (@ _let_1 Ys) (=> (@ distinct_int Ys) (=> (= (@ set_int2 Xs) (@ set_int2 Ys)) (= Xs Ys)))))))) (forall ((A set_nat) (C2 set_nat) (D set_nat) (B set_nat)) (=> (@ (@ ord_less_eq_set_nat A) C2) (=> (@ (@ ord_less_eq_set_nat D) B) (@ (@ ord_less_eq_set_nat (@ (@ minus_minus_set_nat A) B)) (@ (@ minus_minus_set_nat C2) D))))) (forall ((B2 nat) (A2 nat)) (=> (@ (@ ord_less_eq_nat B2) A2) (= A2 (@ (@ sup_sup_nat A2) B2)))) (forall ((A set_nat) (B set_nat)) (= (= (@ (@ sup_sup_set_nat A) B) bot_bot_set_nat) (and (= A bot_bot_set_nat) (= B bot_bot_set_nat)))) (= ord_less_eq_assn (lambda ((B3 assn) (A3 assn)) (= A3 (@ (@ sup_sup_assn A3) B3)))) (forall ((A2 code_integer)) (not (@ (@ ord_le6747313008572928689nteger A2) A2))) (forall ((P (-> produc6575502325842934193n_assn produc6575502325842934193n_assn assn)) (A2 produc6575502325842934193n_assn) (As2 list_P8527749157015355191n_assn) (C produc6575502325842934193n_assn) (Cs list_P8527749157015355191n_assn)) (let ((_let_1 (@ vEBT_L3108143461992071043n_assn P))) (= (@ (@ _let_1 (@ (@ cons_P2971678138204555879n_assn A2) As2)) (@ (@ cons_P2971678138204555879n_assn C) Cs)) (@ (@ times_times_assn (@ (@ P A2) C)) (@ (@ _let_1 As2) Cs))))) (forall ((I set_Pr1261947904930325089at_nat) (J set_Pr1261947904930325089at_nat) (R set_Pr4329608150637261639at_nat)) (=> (@ (@ member8757157785044589968at_nat (@ (@ produc2922128104949294807at_nat I) J)) R) (@ (@ member2643936169264416010at_nat J) (@ field_3145993188331922222at_nat R)))) (forall ((C product_prod_nat_nat) (A set_Pr1261947904930325089at_nat) (B set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ member8440522571783428010at_nat C))) (=> (@ _let_1 A) (=> (@ _let_1 B) (@ _let_1 (@ (@ inf_in2572325071724192079at_nat A) B)))))) (forall ((B2 set_Pr4329608150637261639at_nat) (C set_Pr4329608150637261639at_nat) (A2 set_Pr4329608150637261639at_nat)) (= (@ (@ ord_le1268244103169919719at_nat (@ (@ sup_su5525570899277871387at_nat B2) C)) A2) (and (@ (@ ord_le1268244103169919719at_nat B2) A2) (@ (@ ord_le1268244103169919719at_nat C) A2)))) (forall ((A2 int) (A set_int) (B set_int)) (= (= (@ (@ inf_inf_set_int (@ (@ insert_int2 A2) A)) B) bot_bot_set_int) (and (= (@ (@ inf_inf_set_int A) B) bot_bot_set_int) (not (@ (@ member_int A2) B))))) (= (lambda ((P4 (-> nat Bool))) (exists ((X5 nat)) (@ P4 X5))) (lambda ((P2 (-> nat Bool))) (exists ((N2 nat)) (and (@ P2 N2) (forall ((M nat)) (=> (@ (@ ord_less_nat M) N2) (not (@ P2 M)))))))) (forall ((B2 Bool) (A2 Bool)) (=> (@ (@ member_o B2) (@ (@ insert_o2 A2) bot_bot_set_o)) (= B2 A2))) (forall ((A2 nat) (N nat)) (= (= (@ (@ power_power_nat A2) N) zero_zero_nat) (and (= A2 zero_zero_nat) (@ (@ ord_less_nat zero_zero_nat) N)))) (forall ((K3 int)) (not (forall ((N5 nat)) (let ((_let_1 (@ bit_se1146084159140164899it_int K3))) (=> (forall ((M3 nat)) (let ((_let_1 (@ bit_se1146084159140164899it_int K3))) (=> (@ (@ ord_less_eq_nat N5) M3) (= (@ _let_1 M3) (@ _let_1 N5))))) (not (=> (@ (@ ord_less_nat zero_zero_nat) N5) (= (@ _let_1 (@ (@ minus_minus_nat N5) one_one_nat)) (not (@ _let_1 N5)))))))))) (forall ((F4 (-> int int int)) (X int) (Y int)) (=> (forall ((X3 int) (Y2 int)) (@ (@ ord_less_eq_int X3) (@ (@ F4 X3) Y2))) (=> (forall ((X3 int) (Y2 int)) (@ (@ ord_less_eq_int Y2) (@ (@ F4 X3) Y2))) (=> (forall ((X3 int) (Y2 int) (Z4 int)) (=> (@ (@ ord_less_eq_int Y2) X3) (=> (@ (@ ord_less_eq_int Z4) X3) (@ (@ ord_less_eq_int (@ (@ F4 Y2) Z4)) X3)))) (= (@ (@ sup_sup_int X) Y) (@ (@ F4 X) Y)))))) (forall ((M2 num)) (= (@ (@ unique5052692396658037445od_int (@ bitM M2)) (@ bit0 one)) (@ (@ product_Pair_int_int (@ (@ minus_minus_int (@ numeral_numeral_int M2)) one_one_int)) one_one_int))) (forall ((X nat)) (@ is_singleton_nat (@ (@ insert_nat2 X) bot_bot_set_nat))) (forall ((A2 filter_nat) (C filter_nat) (B2 filter_nat) (D2 filter_nat)) (=> (@ (@ ord_le2510731241096832064er_nat A2) C) (=> (@ (@ ord_le2510731241096832064er_nat B2) D2) (@ (@ ord_le2510731241096832064er_nat (@ (@ sup_sup_filter_nat A2) B2)) (@ (@ sup_sup_filter_nat C) D2))))) (forall ((A2 int) (B2 int)) (= (@ (@ ord_less_eq_int A2) (@ (@ plus_plus_int A2) B2)) (@ (@ ord_less_eq_int zero_zero_int) B2))) (forall ((K3 int)) (@ (@ (@ eucl_rel_int K3) zero_zero_int) (@ (@ product_Pair_int_int zero_zero_int) K3))) (forall ((X assn) (Y assn)) (=> (@ (@ ord_less_eq_assn X) Y) (or (@ (@ ord_less_assn X) Y) (= X Y)))) (forall ((X product_prod_nat_nat)) (@ is_sin2850979758926227957at_nat (@ (@ insert8211810215607154385at_nat X) bot_bo2099793752762293965at_nat))) (forall ((X int) (Y int)) (or (@ (@ ord_less_int Y) X) (@ (@ ord_less_eq_int X) Y))) (forall ((W code_integer) (Y code_integer) (X code_integer) (Z code_integer)) (let ((_let_1 (@ times_3573771949741848930nteger X))) (let ((_let_2 (@ times_3573771949741848930nteger W))) (= (= (@ (@ plus_p5714425477246183910nteger (@ _let_2 Y)) (@ _let_1 Z)) (@ (@ plus_p5714425477246183910nteger (@ _let_2 Z)) (@ _let_1 Y))) (or (= W X) (= Y Z)))))) (forall ((A2 int) (B2 int)) (= (= (@ (@ plus_plus_int A2) B2) A2) (= B2 zero_zero_int))) (forall ((X int) (Y int)) (@ (@ ord_less_eq_int (@ (@ inf_inf_int X) Y)) Y)) (forall ((N nat) (M2 nat)) (let ((_let_1 (@ ord_less_nat zero_zero_nat))) (=> (@ _let_1 N) (=> (@ _let_1 M2) (@ (@ ord_less_nat (@ (@ minus_minus_nat M2) N)) M2))))) (forall ((X Bool) (A set_o) (B set_o)) (= (@ (@ ord_less_eq_set_o (@ (@ insert_o2 X) A)) B) (and (@ (@ ord_less_eq_set_o A) B) (@ (@ member_o X) B)))) (forall ((L list_int)) (=> (not (= L nil_int)) (not (forall ((X3 int) (Xs2 list_int)) (not (= L (@ (@ cons_int X3) Xs2))))))) _let_62 (forall ((X code_integer) (Y code_integer)) (=> (not (@ (@ ord_le6747313008572928689nteger X) Y)) (=> (not (= X Y)) (@ (@ ord_le6747313008572928689nteger Y) X)))) (forall ((A2 int) (B2 int)) (=> (@ (@ ord_less_eq_int A2) zero_zero_int) (=> (@ (@ ord_less_int B2) zero_zero_int) (@ (@ ord_less_int (@ (@ plus_plus_int A2) B2)) zero_zero_int)))) (forall ((X int) (B set_int) (A set_int)) (=> (@ (@ member_int X) B) (= (@ (@ minus_minus_set_int (@ (@ insert_int2 X) A)) B) (@ (@ minus_minus_set_int A) B)))) (forall ((A2 int) (B2 int)) (=> (@ (@ ord_less_eq_int zero_zero_int) A2) (=> (@ (@ ord_less_eq_int B2) zero_zero_int) (@ (@ ord_less_eq_int (@ (@ times_times_int A2) B2)) zero_zero_int)))) (forall ((A set_Pr4532377907799695533_nat_o) (R2 set_Pr2161125870931222855_nat_o)) (=> (forall ((X3 (-> produc3658429121746597890et_nat Bool)) (Y2 (-> produc3658429121746597890et_nat Bool))) (=> (@ (@ member6576561426505652726_nat_o X3) A) (=> (@ (@ member6576561426505652726_nat_o Y2) A) (=> (not (= X3 Y2)) (or (@ (@ member8781333585448626064_nat_o (@ (@ produc7368190662567826135_nat_o Y2) X3)) R2) (@ (@ member8781333585448626064_nat_o (@ (@ produc7368190662567826135_nat_o X3) Y2)) R2)))))) (@ (@ total_7429123086324524369_nat_o A) R2))) (forall ((X (-> produc3658429121746597890et_nat Bool)) (Xs list_P7985473006766602707_nat_o) (Y (-> produc3658429121746597890et_nat Bool))) (let ((_let_1 (@ member6576561426505652726_nat_o X))) (=> (not (@ _let_1 (@ set_Pr400311997697478754_nat_o Xs))) (not (@ _let_1 (@ set_Pr400311997697478754_nat_o (@ (@ remove4235003712227595625_nat_o Y) Xs))))))) (forall ((Xs list_P6011104703257516679at_nat) (A set_Pr1261947904930325089at_nat) (X product_prod_nat_nat) (I nat)) (=> (@ (@ ord_le3146513528884898305at_nat (@ set_Pr5648618587558075414at_nat Xs)) A) (=> (@ (@ member8440522571783428010at_nat X) A) (@ (@ ord_le3146513528884898305at_nat (@ set_Pr5648618587558075414at_nat (@ (@ (@ list_u6180841689913720943at_nat Xs) I) X))) A)))) (forall ((X assn) (Y assn)) (=> (@ (@ ord_less_eq_assn X) Y) (= (not (@ (@ ord_less_assn X) Y)) (= X Y)))) (forall ((X produc3843707927480180839at_nat) (B set_Pr4329608150637261639at_nat) (A set_Pr4329608150637261639at_nat)) (let ((_let_1 (@ (@ minus_3314409938677909166at_nat A) B))) (let ((_let_2 (@ insert9069300056098147895at_nat X))) (let ((_let_3 (@ (@ minus_3314409938677909166at_nat (@ _let_2 A)) B))) (let ((_let_4 (@ (@ member8757157785044589968at_nat X) B))) (and (=> _let_4 (= _let_3 _let_1)) (=> (not _let_4) (= _let_3 (@ _let_2 _let_1))))))))) (forall ((A2 int) (F4 (-> assn int)) (B2 assn) (C assn)) (=> (= A2 (@ F4 B2)) (=> (@ (@ ord_less_assn B2) C) (=> (forall ((X3 assn) (Y2 assn)) (=> (@ (@ ord_less_assn X3) Y2) (@ (@ ord_less_int (@ F4 X3)) (@ F4 Y2)))) (@ (@ ord_less_int A2) (@ F4 C)))))) (forall ((A2 nat) (A7 nat) (B2 nat) (N7 nat) (B6 nat)) (=> (@ (@ ord_less_nat A2) A7) (=> (@ (@ ord_less_nat B2) N7) (=> (@ (@ ord_less_nat B6) N7) (@ (@ ord_less_nat (@ (@ plus_plus_nat (@ (@ times_times_nat A2) N7)) B2)) (@ (@ plus_plus_nat (@ (@ times_times_nat A7) N7)) B6)))))) (forall ((A set_Pr4532377907799695533_nat_o) (B set_Pr4532377907799695533_nat_o) (X (-> produc3658429121746597890et_nat Bool))) (let ((_let_1 (@ member6576561426505652726_nat_o X))) (=> (@ (@ ord_le2965882846123202637_nat_o A) B) (=> (@ _let_1 A) (@ _let_1 B))))) (forall ((M2 nat) (K3 num)) (let ((_let_1 (@ pred_numeral K3))) (let ((_let_2 (@ set_or4665077453230672383an_nat M2))) (let ((_let_3 (@ _let_2 (@ numeral_numeral_nat K3)))) (let ((_let_4 (@ (@ ord_less_eq_nat M2) _let_1))) (and (=> (not _let_4) (= _let_3 bot_bot_set_nat)) (=> _let_4 (= _let_3 (@ (@ insert_nat2 _let_1) (@ _let_2 _let_1)))))))))) (= (lambda ((Y4 list_nat) (Z2 list_nat)) (= Y4 Z2)) (lambda ((Xs3 list_nat) (Ys3 list_nat)) (and (forall ((I4 nat)) (=> (@ (@ ord_less_nat I4) (@ size_size_list_nat Xs3)) (= (@ (@ nth_nat Xs3) I4) (@ (@ nth_nat Ys3) I4)))) (= (@ size_size_list_nat Xs3) (@ size_size_list_nat Ys3))))) (= bot_bot_assn (@ abs_assn (lambda ((Uu2 produc3658429121746597890et_nat)) false))) (forall ((A2 rat) (B2 rat) (C rat) (D2 rat)) (let ((_let_1 (@ times_times_rat B2))) (let ((_let_2 (@ times_times_rat A2))) (= (and (not (= C D2)) (not (= A2 B2))) (not (= (@ (@ plus_plus_rat (@ _let_2 C)) (@ _let_1 D2)) (@ (@ plus_plus_rat (@ _let_2 D2)) (@ _let_1 C)))))))) _let_61 (forall ((Ys list_assn)) (= (@ (@ zip_assn_assn nil_assn) Ys) nil_Pr5671120429643327159n_assn)) (forall ((A2 code_integer) (B2 code_integer)) (let ((_let_1 (@ ord_le6747313008572928689nteger zero_z3403309356797280102nteger))) (=> (@ _let_1 A2) (=> (@ (@ ord_le3102999989581377725nteger zero_z3403309356797280102nteger) B2) (@ _let_1 (@ (@ plus_p5714425477246183910nteger A2) B2)))))) (forall ((X set_Pr1261947904930325089at_nat) (Y set_Pr1261947904930325089at_nat)) (= (@ (@ inf_in2572325071724192079at_nat X) (@ (@ sup_su6327502436637775413at_nat X) Y)) X)) (forall ((C (-> produc3658429121746597890et_nat Bool)) (B set_Pr4532377907799695533_nat_o) (A set_Pr4532377907799695533_nat_o)) (let ((_let_1 (@ member6576561426505652726_nat_o C))) (=> (@ _let_1 B) (@ _let_1 (@ (@ sup_su5209123915105501825_nat_o A) B))))) (forall ((Xs list_nat) (Ys list_c) (R2 set_Pr4335409928928841947_nat_c)) (=> (@ (@ member6074218473364765234list_c (@ (@ produc7723716018658481613list_c Xs) Ys)) (@ listrel_nat_c R2)) (= (@ size_size_list_nat Xs) (@ size_size_list_c Ys)))) (forall ((T int)) (exists ((Z4 int)) (forall ((X7 int)) (=> (@ (@ ord_less_int X7) Z4) (not (= X7 T)))))) (forall ((A2 num) (B2 num)) (=> (@ (@ ord_less_num A2) B2) (not (= A2 B2)))) (forall ((P (-> list_int list_P8527749157015355191n_assn Bool)) (W1 list_int) (W2 list_P8527749157015355191n_assn)) (=> (@ (@ P nil_int) nil_Pr5671120429643327159n_assn) (=> (forall ((E2 int) (W12 list_int) (W22 list_P8527749157015355191n_assn)) (=> (@ (@ P W12) W22) (@ (@ P (@ (@ cons_int E2) W12)) W22))) (=> (forall ((E2 produc6575502325842934193n_assn) (W13 list_int) (W23 list_P8527749157015355191n_assn)) (let ((_let_1 (@ P W13))) (=> (@ _let_1 W23) (@ _let_1 (@ (@ cons_P2971678138204555879n_assn E2) W23))))) (@ (@ P W1) W2))))) (forall ((A2 code_integer) (B2 code_integer)) (=> (@ (@ ord_le6747313008572928689nteger A2) zero_z3403309356797280102nteger) (=> (@ (@ ord_le6747313008572928689nteger B2) zero_z3403309356797280102nteger) (@ (@ ord_le6747313008572928689nteger (@ (@ plus_p5714425477246183910nteger A2) B2)) zero_z3403309356797280102nteger)))) (forall ((B2 assn) (A2 assn)) (@ (@ ord_less_eq_assn B2) (@ (@ sup_sup_assn A2) B2))) (= ord_le3102999989581377725nteger (lambda ((A3 code_integer) (B3 code_integer)) (or (@ (@ ord_le6747313008572928689nteger A3) B3) (= A3 B3)))) (forall ((A2 assn) (B2 assn)) (@ (@ ord_less_eq_assn (@ (@ inf_inf_assn A2) B2)) B2)) (forall ((X assn) (Y assn)) (let ((_let_1 (@ inf_inf_assn X))) (let ((_let_2 (@ _let_1 Y))) (= (@ _let_1 _let_2) _let_2)))) (forall ((F4 (-> filter_nat filter_nat filter_nat)) (X filter_nat) (Y filter_nat)) (=> (forall ((X3 filter_nat) (Y2 filter_nat)) (@ (@ ord_le2510731241096832064er_nat X3) (@ (@ F4 X3) Y2))) (=> (forall ((X3 filter_nat) (Y2 filter_nat)) (@ (@ ord_le2510731241096832064er_nat Y2) (@ (@ F4 X3) Y2))) (=> (forall ((X3 filter_nat) (Y2 filter_nat) (Z4 filter_nat)) (=> (@ (@ ord_le2510731241096832064er_nat Y2) X3) (=> (@ (@ ord_le2510731241096832064er_nat Z4) X3) (@ (@ ord_le2510731241096832064er_nat (@ (@ F4 Y2) Z4)) X3)))) (= (@ (@ sup_sup_filter_nat X) Y) (@ (@ F4 X) Y)))))) (forall ((E int) (A2 list_int)) (=> (@ (@ member_int E) (@ set_int2 A2)) (=> (forall ((Z22 list_int)) (not (= A2 (@ (@ cons_int E) Z22)))) (not (forall ((Z1 int) (Z22 list_int)) (=> (= A2 (@ (@ cons_int Z1) Z22)) (not (@ (@ member_int E) (@ set_int2 Z22))))))))) (forall ((B set_int)) (= (@ (@ sup_sup_set_int bot_bot_set_int) B) B)) (forall ((A2 rat) (E rat) (C rat) (B2 rat) (D2 rat)) (= (@ (@ ord_less_eq_rat (@ (@ plus_plus_rat (@ (@ times_times_rat A2) E)) C)) (@ (@ plus_plus_rat (@ (@ times_times_rat B2) E)) D2)) (@ (@ ord_less_eq_rat C) (@ (@ plus_plus_rat (@ (@ times_times_rat (@ (@ minus_minus_rat B2) A2)) E)) D2)))) (forall ((Xs list_d) (Ys list_c) (X d)) (=> (= (@ size_size_list_d Xs) (@ size_size_list_c Ys)) (=> (@ (@ member_d X) (@ set_d2 Xs)) (not (forall ((Y2 c)) (not (@ (@ member2287536777068640527od_d_c (@ (@ product_Pair_d_c X) Y2)) (@ set_Product_prod_d_c2 (@ (@ zip_d_c Xs) Ys))))))))) (forall ((C nat) (A2 nat) (B2 nat)) (let ((_let_1 (@ times_times_nat C))) (=> (@ (@ ord_less_eq_nat (@ _let_1 A2)) (@ 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bit_se725231765392027082nd_int (@ (@ divide_divide_int K3) _let_1)) (@ (@ divide_divide_int L) _let_1)))))))))))))))) (forall ((A2 set_Pr1261947904930325089at_nat) (B2 set_Pr1261947904930325089at_nat) (C set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ inf_in2572325071724192079at_nat A2))) (= (@ (@ inf_in2572325071724192079at_nat (@ _let_1 B2)) C) (@ _let_1 (@ (@ inf_in2572325071724192079at_nat B2) C))))) (forall ((C rat) (A2 rat) (B2 rat)) (let ((_let_1 (@ times_times_rat C))) (=> (@ (@ ord_less_rat zero_zero_rat) C) (= (@ (@ ord_less_rat (@ _let_1 A2)) (@ _let_1 B2)) (@ (@ ord_less_rat A2) B2))))) (forall ((P assn)) (@ (@ entails P) P)) (forall ((X nat) (Y nat) (Xs list_nat)) (let ((_let_1 (@ (@ count_list_nat Xs) Y))) (let ((_let_2 (@ (@ count_list_nat (@ (@ cons_nat X) Xs)) Y))) (let ((_let_3 (= X Y))) (and (=> _let_3 (= _let_2 (@ (@ plus_plus_nat _let_1) one_one_nat))) (=> (not _let_3) (= _let_2 _let_1))))))) (forall ((X num) (Y num) (Z num)) (let ((_let_1 (@ ord_less_num X))) (=> (@ _let_1 Y) (=> (@ (@ ord_less_num Y) Z) (@ _let_1 Z))))) (forall ((P (-> list_d Bool)) (Xs list_d)) (=> (forall ((Xs2 list_d)) (=> (forall ((Ys2 list_d)) (=> (@ (@ ord_less_nat (@ size_size_list_d Ys2)) (@ size_size_list_d Xs2)) (@ P Ys2))) (@ P Xs2))) (@ P Xs))) (forall ((C code_integer) (A2 code_integer)) (= (@ (@ ord_le3102999989581377725nteger (@ (@ times_3573771949741848930nteger C) A2)) C) (and (=> (@ (@ ord_le6747313008572928689nteger zero_z3403309356797280102nteger) C) (@ (@ ord_le3102999989581377725nteger A2) one_one_Code_integer)) (=> (@ (@ ord_le6747313008572928689nteger C) zero_z3403309356797280102nteger) (@ (@ ord_le3102999989581377725nteger one_one_Code_integer) A2))))) (forall ((A2 nat) (B2 nat) (C nat)) (let ((_let_1 (@ plus_plus_nat C))) (=> (@ (@ ord_less_eq_nat A2) B2) (@ (@ ord_less_eq_nat (@ _let_1 A2)) (@ _let_1 B2))))) (forall ((I nat) (L list_P7985473006766602707_nat_o) (X (-> produc3658429121746597890et_nat Bool)) (Y (-> produc3658429121746597890et_nat Bool))) (=> (@ (@ ord_less_nat I) (@ size_s8908918004648414271_nat_o L)) (= (@ (@ member6576561426505652726_nat_o X) (@ set_Pr400311997697478754_nat_o (@ (@ (@ list_u6943956310655620667_nat_o L) I) Y))) (or (= X Y) (forall ((Y5 (-> produc3658429121746597890et_nat Bool))) (@ (@ member6576561426505652726_nat_o X) (@ set_Pr400311997697478754_nat_o (@ (@ (@ list_u6943956310655620667_nat_o L) I) Y5)))))))) (forall ((N nat) (J nat) (I nat)) (=> (@ (@ ord_less_nat N) (@ (@ minus_minus_nat J) (@ suc I))) (= (@ (@ nth_nat (@ linord2614967742042102400et_nat (@ (@ set_or5834768355832116004an_nat I) J))) N) (@ suc (@ (@ plus_plus_nat I) N))))) (forall ((B2 int) (A2 int)) (=> (@ (@ ord_less_int B2) A2) (= (@ (@ ord_min_int A2) B2) B2))) (forall ((X set_nat) (Y set_nat)) (=> (@ (@ ord_less_eq_set_nat X) Y) (= (@ (@ sup_sup_set_nat X) Y) Y))) (forall ((B2 int) (C int) (A2 int)) (=> (@ (@ ord_less_int (@ (@ sup_sup_int B2) C)) A2) (not (=> (@ (@ ord_less_int B2) A2) (not (@ (@ ord_less_int C) A2)))))) (forall ((A2 produc3843707927480180839at_nat) (B set_Pr4329608150637261639at_nat) (B2 produc3843707927480180839at_nat)) (let ((_let_1 (@ member8757157785044589968at_nat A2))) (=> (@ _let_1 B) (@ _let_1 (@ (@ insert9069300056098147895at_nat B2) B))))) (forall ((I int) (J int) (K3 int) (L int)) (=> (and (@ (@ ord_less_eq_int I) J) (= K3 L)) (@ (@ ord_less_eq_int (@ (@ plus_plus_int I) K3)) (@ (@ plus_plus_int J) L)))) (forall ((A2 int) (B2 int) (C int)) (let ((_let_1 (@ times_times_int A2))) (= (@ _let_1 (@ (@ plus_plus_int B2) C)) (@ (@ plus_plus_int (@ _let_1 B2)) (@ _let_1 C))))) (forall ((A set_nat) (B set_nat) (C2 set_nat)) (=> (@ (@ ord_less_eq_set_nat A) B) (=> (@ (@ ord_less_eq_set_nat B) C2) (= (@ (@ minus_minus_set_nat B) (@ (@ minus_minus_set_nat C2) A)) A)))) (forall ((A2 code_integer) (B2 code_integer) (C code_integer)) (let ((_let_1 (@ ord_le6747313008572928689nteger A2))) (=> (@ _let_1 B2) (=> (@ (@ ord_le6747313008572928689nteger B2) C) (@ _let_1 C))))) (forall ((X filter_nat) (Y filter_nat)) (=> (= X Y) (@ (@ ord_le2510731241096832064er_nat X) Y))) (forall ((Xs list_nat) (Xs4 list_nat) (Xsi list_P6011104703257516679at_nat) (Xsi2 list_P6011104703257516679at_nat) (A (-> nat product_prod_nat_nat assn)) (A6 (-> nat product_prod_nat_nat assn))) (=> (= Xs Xs4) (=> (= Xsi Xsi2) (=> (forall ((X3 nat) (Xi product_prod_nat_nat)) (=> (@ (@ member_nat X3) (@ set_nat2 Xs4)) (=> (@ (@ member8440522571783428010at_nat Xi) (@ set_Pr5648618587558075414at_nat Xsi2)) (= (@ (@ A X3) Xi) (@ (@ A6 X3) Xi))))) (= (@ (@ (@ vEBT_L434182512823356844at_nat A) Xs) Xsi) (@ (@ (@ vEBT_L434182512823356844at_nat A6) Xs4) Xsi2)))))) (forall ((X produc3658429121746597890et_nat)) (=> (@ one_assn_raw X) (not (forall ((H heap_e7401611519738050253t_unit) (As set_nat)) (=> (= X (@ (@ produc7507926704131184380et_nat H) As)) (not (= As bot_bot_set_nat))))))) (forall ((A2 nat) (M2 nat) (N nat)) (let ((_let_1 (@ power_power_nat A2))) (=> (@ (@ ord_less_nat one_one_nat) A2) (= (= (@ _let_1 M2) (@ _let_1 N)) (= M2 N))))) (forall ((A set_nat) (B set_nat)) (=> (@ (@ ord_less_eq_set_nat A) B) (=> (not (= A B)) (@ (@ ord_less_set_nat A) B)))) (forall ((M2 num) (N num)) (let ((_let_1 (@ numeral_numeral_nat N))) (let ((_let_2 (@ numeral_numeral_nat M2))) (let ((_let_3 (@ (@ upt _let_2) _let_1))) (let ((_let_4 (@ (@ ord_less_nat _let_2) _let_1))) (and (=> _let_4 (= _let_3 (@ (@ cons_nat _let_2) (@ (@ upt (@ suc _let_2)) _let_1)))) (=> (not _let_4) (= _let_3 nil_nat)))))))) (forall ((A2 int) (B2 int) (F4 (-> int nat)) (C nat)) (=> (@ (@ ord_less_eq_int A2) B2) (=> (= (@ F4 B2) C) (=> (forall ((X3 int) (Y2 int)) (=> (@ (@ ord_less_eq_int X3) Y2) (@ (@ ord_less_eq_nat (@ F4 X3)) (@ F4 Y2)))) (@ (@ ord_less_eq_nat (@ F4 A2)) C))))) (forall ((B2 nat) (A2 nat)) (= (@ (@ ord_less_nat (@ (@ plus_plus_nat B2) A2)) B2) (@ (@ ord_less_nat A2) zero_zero_nat))) (forall ((A2 nat) (B2 nat)) (=> (@ (@ ord_less_nat A2) B2) (@ (@ ord_less_nat (@ (@ plus_plus_nat A2) one_one_nat)) (@ (@ plus_plus_nat B2) one_one_nat)))) (forall ((X product_prod_nat_nat) (Xs list_P6011104703257516679at_nat) (Y product_prod_nat_nat)) (let ((_let_1 (@ member8440522571783428010at_nat X))) (=> (not (@ _let_1 (@ set_Pr5648618587558075414at_nat Xs))) (not (@ _let_1 (@ set_Pr5648618587558075414at_nat (@ (@ remove5766854097993331357at_nat Y) Xs))))))) (forall ((A2 rat) (B2 rat)) (= (@ (@ ord_less_eq_rat zero_zero_rat) (@ (@ minus_minus_rat A2) B2)) (@ (@ ord_less_eq_rat B2) A2))) _let_60 (forall ((X (-> produc3658429121746597890et_nat Bool)) (Xa (-> produc3658429121746597890et_nat Bool)) (Xb produc3658429121746597890et_nat) (Y Bool)) (=> (= (@ (@ (@ wand_raw X) Xa) Xb) Y) (=> (@ (@ accp_P1862375125659990705et_nat wand_raw_rel) (@ (@ produc2245416461498447860et_nat X) (@ (@ produc5001842942810119800et_nat Xa) Xb))) (not (forall ((H heap_e7401611519738050253t_unit) (As set_nat)) (let ((_let_1 (@ (@ produc7507926704131184380et_nat H) As))) (=> (= Xb _let_1) (=> (= Y (and (forall ((H6 heap_e7401611519738050253t_unit) (As5 set_nat)) (let ((_let_1 (@ produc7507926704131184380et_nat H6))) (=> (and (@ (@ (@ relH As) H) H6) (@ in_range (@ _let_1 As)) (@ X (@ _let_1 As5)) (= (@ (@ inf_inf_set_nat As) As5) bot_bot_set_nat)) (@ Xa (@ _let_1 (@ (@ sup_sup_set_nat As) As5)))))) (@ in_range _let_1))) (not (@ (@ accp_P1862375125659990705et_nat wand_raw_rel) (@ (@ produc2245416461498447860et_nat X) (@ (@ produc5001842942810119800et_nat Xa) _let_1)))))))))))) (forall ((N nat)) (=> (not (= N zero_zero_nat)) (@ (@ ord_less_nat zero_zero_nat) N))) (forall ((Xa product_prod_int_int) (X product_prod_int_int)) (=> (@ (@ ratrel Xa) Xa) (=> (@ (@ ratrel X) X) (= (@ (@ times_times_rat (@ abs_Rat Xa)) (@ abs_Rat X)) (@ abs_Rat (@ (@ product_Pair_int_int (@ (@ times_times_int (@ product_fst_int_int Xa)) (@ product_fst_int_int X))) (@ (@ times_times_int (@ product_snd_int_int Xa)) (@ product_snd_int_int X)))))))) (forall ((X1 (-> int option6357759511663192854e_term)) (X22 product_prod_int_int) (Y1 (-> int option6357759511663192854e_term)) (Y22 product_prod_int_int)) (= (= (@ (@ produc4305682042979456191nt_int X1) X22) (@ (@ produc4305682042979456191nt_int Y1) Y22)) (and (= X1 Y1) (= X22 Y22)))) (forall ((A2 rat)) (@ (@ ord_less_eq_rat zero_zero_rat) (@ (@ times_times_rat A2) A2))) _let_59 (forall ((K3 nat) (J nat) (I nat)) (=> (@ (@ ord_less_eq_nat K3) J) (= (@ (@ ord_less_nat (@ (@ minus_minus_nat J) K3)) I) (@ (@ ord_less_nat J) (@ (@ plus_plus_nat I) K3))))) (forall ((X int)) (= (@ the_elem_int (@ (@ insert_int2 X) bot_bot_set_int)) X)) _let_58 (forall ((P (-> nat nat assn)) (A2 nat) (As2 list_nat) (C nat) (Cs list_nat)) (let ((_let_1 (@ vEBT_L8301102511889123557at_nat P))) (= (@ (@ _let_1 (@ (@ cons_nat A2) As2)) (@ (@ cons_nat C) Cs)) (@ (@ times_times_assn (@ (@ P A2) C)) (@ (@ _let_1 As2) Cs))))) (forall ((X set_Pr1261947904930325089at_nat) (Y set_Pr1261947904930325089at_nat) (Z set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ inf_in2572325071724192079at_nat X))) (let ((_let_2 (@ inf_in2572325071724192079at_nat Y))) (= (@ _let_1 (@ _let_2 Z)) (@ _let_2 (@ _let_1 Z)))))) (forall ((X assn)) (= (@ (@ inf_inf_assn X) bot_bot_assn) bot_bot_assn)) (forall ((I nat) (Xs list_d) (X d)) (=> (@ (@ ord_less_nat I) (@ size_size_list_d Xs)) (= (@ (@ nth_d (@ (@ (@ list_update_d Xs) I) X)) I) X))) (forall ((A2 set_o) (B2 set_o)) (= (= (@ (@ sup_sup_set_o A2) B2) bot_bot_set_o) (and (= A2 bot_bot_set_o) (= B2 bot_bot_set_o)))) (forall ((Xs list_nat) (Y nat) (Ys list_nat) (R2 set_Pr1261947904930325089at_nat)) (=> (@ (@ member7340969449405702474st_nat (@ (@ produc2694037385005941721st_nat Xs) (@ (@ cons_nat Y) Ys))) (@ listrel1_nat R2)) (=> (forall ((X3 nat)) (=> (= Xs (@ (@ cons_nat X3) Ys)) (not (@ (@ member8440522571783428010at_nat (@ (@ product_Pair_nat_nat X3) Y)) R2)))) (not (forall ((Zs2 list_nat)) (=> (= Xs (@ (@ cons_nat Y) Zs2)) (not (@ (@ member7340969449405702474st_nat (@ (@ produc2694037385005941721st_nat Zs2) Ys)) (@ listrel1_nat R2))))))))) (forall ((B2 set_nat) (C set_nat) (A2 set_nat)) (=> (@ (@ ord_less_set_nat B2) C) (@ (@ ord_less_set_nat (@ (@ inf_inf_set_nat A2) B2)) C))) (forall ((P (-> produc3925858234332021118et_nat Bool)) (X produc3925858234332021118et_nat)) (=> (forall ((A4 (-> produc3658429121746597890et_nat Bool)) (B4 heap_e7401611519738050253t_unit) (C4 set_nat)) (@ P (@ (@ produc5001842942810119800et_nat A4) (@ (@ produc7507926704131184380et_nat B4) C4)))) (@ P X))) (forall ((A2 nat) (F4 (-> assn nat)) (B2 assn) (C assn)) (let ((_let_1 (@ ord_less_nat A2))) (=> (@ _let_1 (@ F4 B2)) (=> (@ (@ ord_less_eq_assn B2) C) (=> (forall ((X3 assn) (Y2 assn)) (=> (@ (@ ord_less_eq_assn X3) Y2) (@ (@ ord_less_eq_nat (@ F4 X3)) (@ F4 Y2)))) (@ _let_1 (@ F4 C))))))) (forall ((C code_integer) (A2 code_integer) (B2 code_integer)) (let ((_let_1 (@ times_3573771949741848930nteger C))) (= (@ (@ ord_le6747313008572928689nteger (@ _let_1 A2)) (@ _let_1 B2)) (or (and (@ (@ 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B2) (@ (@ produc5700946648718959541nt_int A7) B6)) (not (=> (= A2 A7) (not (= B2 B6)))))) (forall ((A2 set_Pr4329608150637261639at_nat) (B2 set_Pr4329608150637261639at_nat)) (= (= (@ (@ sup_su5525570899277871387at_nat A2) B2) bot_bo228742789529271731at_nat) (and (= B2 bot_bo228742789529271731at_nat) (= A2 bot_bo228742789529271731at_nat)))) (forall ((X nat) (A2 nat) (B2 nat)) (let ((_let_1 (@ ord_less_eq_nat X))) (=> (@ _let_1 A2) (@ _let_1 (@ (@ sup_sup_nat A2) B2))))) (forall ((X int) (Y int)) (= (@ (@ minus_minus_int (@ (@ times_times_int X) X)) (@ (@ times_times_int Y) Y)) (@ (@ times_times_int (@ (@ plus_plus_int X) Y)) (@ (@ minus_minus_int X) Y)))) (forall ((A2 nat) (B2 nat) (C nat)) (=> (@ (@ ord_less_nat A2) B2) (=> (@ (@ ord_less_nat zero_zero_nat) C) (@ (@ ord_less_nat (@ (@ times_times_nat A2) C)) (@ (@ times_times_nat B2) C))))) (= sup_sup_assn (lambda ((X2 assn) (Y5 assn)) (@ (@ sup_sup_assn Y5) X2))) (forall ((A2 code_integer) (B2 code_integer) (C code_integer)) (let ((_let_1 (@ times_3573771949741848930nteger C))) (=> (@ (@ ord_le3102999989581377725nteger A2) B2) (=> (@ (@ ord_le3102999989581377725nteger zero_z3403309356797280102nteger) C) (@ (@ ord_le3102999989581377725nteger (@ _let_1 A2)) (@ _let_1 B2)))))) (forall ((C int) (A set_int) (B set_int)) (let ((_let_1 (@ member_int C))) (=> (@ _let_1 A) (=> (not (@ _let_1 B)) (@ _let_1 (@ (@ minus_minus_set_int A) B)))))) (forall ((A2 nat) (B2 nat)) (@ (@ ord_less_eq_nat (@ (@ inf_inf_nat A2) B2)) A2)) (forall ((A2 list_d) (B2 list_int) (A7 list_d) (B6 list_int)) (=> (= (@ size_size_list_d A2) (@ size_size_list_int B2)) (=> (= (@ size_size_list_d A7) (@ size_size_list_int B6)) (= (= (@ (@ zip_d_int A2) B2) (@ (@ zip_d_int A7) B6)) (and (= B2 B6) (= A2 A7)))))) (forall ((A set_int) (B set_int)) (=> (@ (@ ord_less_set_int A) B) (exists ((B4 int)) (@ (@ member_int B4) (@ (@ minus_minus_set_int B) A))))) (forall ((A2 int) (B2 int) (C int)) (let ((_let_1 (@ plus_plus_int C))) (=> (@ (@ ord_less_int A2) 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(@ _let_1 S))))))) (forall ((A2 nat) (A nat) (B2 nat) (N7 nat)) (=> (@ (@ ord_less_nat A2) A) (=> (@ (@ ord_less_nat B2) N7) (@ (@ ord_less_nat (@ (@ plus_plus_nat (@ (@ times_times_nat A2) N7)) B2)) (@ (@ times_times_nat A) N7))))) (forall ((A2 int)) (@ (@ ord_less_eq_int A2) A2)) (forall ((A2 nat) (C2 set_nat) (B set_nat)) (=> (not (@ (@ member_nat A2) C2)) (= (@ (@ inf_inf_set_nat (@ (@ insert_nat2 A2) B)) C2) (@ (@ inf_inf_set_nat B) C2)))) (forall ((X assn) (Y assn) (A2 assn) (B2 assn)) (=> (@ (@ syntax7398250324933576852n_assn (@ (@ times_times_assn X) Y)) A2) (= (@ (@ times_times_assn A2) B2) (@ (@ times_times_assn B2) A2)))) (forall ((A set_Pr1261947904930325089at_nat) (C2 set_Pr1261947904930325089at_nat) (B set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ minus_1356011639430497352at_nat (@ (@ inf_in2572325071724192079at_nat A) C2)))) (= (@ _let_1 (@ (@ inf_in2572325071724192079at_nat B) C2)) (@ _let_1 B)))) (forall ((Xs list_nat) (Ys list_nat) (Zs list_int) (Ws list_d) (P (-> list_nat list_nat list_int list_d Bool))) (let ((_let_1 (@ size_size_list_int Zs))) (let ((_let_2 (@ size_size_list_nat Ys))) (=> (= (@ size_size_list_nat Xs) _let_2) (=> (= _let_2 _let_1) (=> (= _let_1 (@ size_size_list_d Ws)) (=> (@ (@ (@ (@ P nil_nat) nil_nat) nil_int) nil_d) (=> (forall ((X3 nat) (Xs2 list_nat) (Y2 nat) (Ys5 list_nat) (Z4 int) (Zs2 list_int) (W3 d) (Ws2 list_d)) (let ((_let_1 (@ size_size_list_int Zs2))) (let ((_let_2 (@ size_size_list_nat Ys5))) (=> (= (@ size_size_list_nat Xs2) _let_2) (=> (= _let_2 _let_1) (=> (= _let_1 (@ size_size_list_d Ws2)) (=> (@ (@ (@ (@ P Xs2) Ys5) Zs2) Ws2) (@ (@ (@ (@ P (@ (@ cons_nat X3) Xs2)) (@ (@ cons_nat Y2) Ys5)) (@ (@ cons_int Z4) Zs2)) (@ (@ cons_d W3) Ws2))))))))) (@ (@ (@ (@ P Xs) Ys) Zs) Ws))))))))) (forall ((A2 rat)) (= (@ (@ times_times_rat zero_zero_rat) A2) zero_zero_rat)) _let_53 (forall ((M2 nat) (N nat)) (let ((_let_1 (@ ord_less_nat M2))) (=> (@ _let_1 (@ suc N)) (=> (not (@ _let_1 N)) (= M2 N))))) (forall ((A2 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A2 B2)) (= (@ _let_1 (@ set_Pr5648618587558075414at_nat (@ (@ remove5766854097993331357at_nat B2) Xs))) (@ _let_1 (@ set_Pr5648618587558075414at_nat Xs)))))) (forall ((A2 list_c) (B2 list_nat) (A7 list_c) (B6 list_nat)) (=> (= (@ size_size_list_c A2) (@ size_size_list_nat B2)) (=> (= (@ size_size_list_c A7) (@ size_size_list_nat B6)) (= (= (@ (@ zip_c_nat A2) B2) (@ (@ zip_c_nat A7) B6)) (and (= B2 B6) (= A2 A7)))))) (forall ((X int) (Y int)) (=> (@ (@ ord_less_eq_int X) Y) (= (not (@ (@ ord_less_int X) Y)) (= X Y)))) (forall ((A2 int) (C int) (B2 int)) (= (@ (@ ord_less_eq_int A2) (@ (@ minus_minus_int C) B2)) (@ (@ ord_less_eq_int (@ (@ plus_plus_int A2) B2)) C))) (forall ((A2 nat)) (= (@ (@ plus_plus_nat A2) zero_zero_nat) A2)) (forall ((A2 code_integer) (E code_integer) (C code_integer) (B2 code_integer) (D2 code_integer)) (= (@ (@ ord_le3102999989581377725nteger (@ (@ plus_p5714425477246183910nteger (@ (@ times_3573771949741848930nteger A2) E)) C)) (@ (@ 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size_size_list_nat Zs2)) (=> (@ (@ (@ P Xs2) Ys5) Zs2) (@ (@ (@ P (@ (@ cons_c X3) Xs2)) (@ (@ cons_c Y2) Ys5)) (@ (@ cons_nat Z4) Zs2))))))) (@ (@ (@ P Xs) Ys) Zs))))))) (forall ((I nat) (Y nat)) (= (@ (@ (@ list_update_nat nil_nat) I) Y) nil_nat)) (forall ((C (-> produc3658429121746597890et_nat Bool)) (A set_Pr4532377907799695533_nat_o) (B set_Pr4532377907799695533_nat_o)) (let ((_let_1 (@ member6576561426505652726_nat_o C))) (=> (@ _let_1 (@ (@ inf_in1906310914598751387_nat_o A) B)) (@ _let_1 A)))) (forall ((A2 code_integer) (B2 code_integer) (C code_integer)) (let ((_let_1 (@ ord_le6747313008572928689nteger B2))) (=> (@ (@ ord_le6747313008572928689nteger zero_z3403309356797280102nteger) A2) (=> (@ _let_1 C) (@ _let_1 (@ (@ plus_p5714425477246183910nteger A2) C)))))) (forall ((A2 nat) (B2 nat)) (=> (@ (@ ord_less_eq_nat A2) B2) (= A2 (@ (@ inf_inf_nat A2) B2)))) (= ord_less_eq_assn (lambda ((A3 assn) (B3 assn)) (= (@ (@ inf_inf_assn A3) B3) A3))) (forall ((B2 product_prod_nat_nat) (A2 product_prod_nat_nat)) (=> (@ (@ member8440522571783428010at_nat B2) (@ (@ insert8211810215607154385at_nat A2) bot_bo2099793752762293965at_nat)) (= B2 A2))) (forall ((I nat) (M2 nat)) (@ (@ ord_less_nat I) (@ suc (@ (@ plus_plus_nat M2) I)))) (forall ((Xs list_P8527749157015355191n_assn) (Ys list_int) (Xy produc8718178513971670540sn_int) (Xys list_P421884338359569308sn_int)) (=> (= (@ (@ zip_Pr1015554993053626726sn_int Xs) Ys) (@ (@ cons_P5155970366129889750sn_int Xy) Xys)) (not (forall ((X3 produc6575502325842934193n_assn) (Xs5 list_P8527749157015355191n_assn)) (=> (= Xs (@ (@ cons_P2971678138204555879n_assn X3) Xs5)) (forall ((Y2 int) (Ys4 list_int)) (=> (= Ys (@ (@ cons_int Y2) Ys4)) (=> (= Xy (@ (@ produc6453891449406693510sn_int X3) Y2)) (not (= Xys (@ (@ zip_Pr1015554993053626726sn_int Xs5) Ys4))))))))))) (forall ((X d) (Xs list_d) (Y d) (Ys list_d) (R2 set_Product_prod_d_d)) (let ((_let_1 (@ lex_d R2))) (= (@ (@ member1810801192463332112list_d (@ (@ produc242965421297323863list_d (@ (@ cons_d X) Xs)) (@ (@ cons_d Y) Ys))) _let_1) (or (and (= X Y) (@ (@ member1810801192463332112list_d (@ (@ produc242965421297323863list_d Xs) Ys)) _let_1)) (and (@ (@ member2287536781371869328od_d_d (@ (@ product_Pair_d_d X) Y)) R2) (= (@ size_size_list_d Xs) (@ size_size_list_d Ys))))))) (forall ((A2 nat) (B2 nat) (F4 (-> nat num)) (C num)) (=> (@ (@ ord_less_nat A2) B2) (=> (@ (@ ord_less_eq_num (@ F4 B2)) C) (=> (forall ((X3 nat) (Y2 nat)) (=> (@ (@ ord_less_nat X3) Y2) (@ (@ ord_less_num (@ F4 X3)) (@ F4 Y2)))) (@ (@ ord_less_num (@ F4 A2)) C))))) (forall ((Xs list_P8527749157015355191n_assn)) (= (@ is_emp7749065762491207043n_assn (@ set_Pr1139785259514867910n_assn Xs)) (@ null_P7596217980778516671n_assn Xs))) (forall ((M2 nat) (N nat)) (=> (@ (@ ord_less_eq_nat M2) N) (=> (not (= M2 N)) (@ (@ ord_less_nat M2) N)))) (forall ((X (-> produc8551481072490612790e_term option6357759511663192854e_term)) (Y product_prod_int_int) (Xs list_P1743416141875011707e_term) (Ys list_P5707943133018811711nt_int)) (=> (@ (@ member7618704894036264090nt_int (@ (@ produc5700946648718959541nt_int X) Y)) (@ set_Pr4943052134776177454nt_int (@ (@ zip_Pr4168994715204986005nt_int Xs) Ys))) (@ (@ member5262025264175285858nt_int Y) (@ set_Pr2470121279949933262nt_int Ys)))) (forall ((X num) (Y num)) (=> (@ (@ ord_less_num X) Y) (not (@ (@ ord_less_num Y) X)))) (forall ((A2 int) (B2 int)) (=> (= A2 (@ (@ ord_min_int A2) B2)) (@ (@ ord_less_eq_int A2) B2))) (forall ((M2 nat) (Xs list_c) (N nat)) (=> (@ (@ ord_less_nat M2) (@ size_size_list_c Xs)) (= (@ (@ nth_Pr2476257089995772766_nat_c (@ (@ enumerate_c N) Xs)) M2) (@ (@ product_Pair_nat_c (@ (@ plus_plus_nat N) M2)) (@ (@ nth_c Xs) M2))))) (forall ((Xs list_d) (Ys list_d) (R2 set_Product_prod_d_d)) (=> (@ (@ member1810801192463332112list_d (@ (@ produc242965421297323863list_d Xs) Ys)) (@ listrel_d_d R2)) (= (@ size_size_list_d Xs) (@ size_size_list_d Ys)))) (forall ((A2 rat) (B2 rat)) (let ((_let_1 (@ ord_less_rat zero_zero_rat))) (= (@ (@ ord_less_rat (@ (@ times_times_rat A2) B2)) zero_zero_rat) (or (and (@ (@ ord_less_rat A2) zero_zero_rat) (@ _let_1 B2)) (and (@ _let_1 A2) (@ (@ ord_less_rat B2) zero_zero_rat)))))) (forall ((A2 product_prod_nat_nat) (P (-> product_prod_nat_nat Bool))) (= (@ (@ member8440522571783428010at_nat A2) (@ collec3392354462482085612at_nat P)) (@ P A2))) (forall ((X int) (Y int) (Z int)) (let ((_let_1 (@ ord_less_eq_int X))) (=> (@ _let_1 Y) (=> (@ _let_1 Z) (@ _let_1 (@ (@ inf_inf_int Y) Z)))))) (forall ((I nat) (J nat) (L list_Code_integer) (X code_integer)) (let ((_let_1 (@ nth_Code_integer L))) (=> (@ (@ ord_less_eq_nat zero_zero_nat) I) (=> (@ (@ ord_less_nat I) J) (=> (@ (@ ord_less_nat J) (@ size_s3445333598471063425nteger L)) (=> (@ (@ sorted710888440204495920nteger ord_le3102999989581377725nteger) L) (=> (@ (@ ord_le3102999989581377725nteger (@ _let_1 I)) X) (=> (@ (@ ord_le6747313008572928689nteger X) (@ _let_1 J)) (not (forall ((K nat)) (let ((_let_1 (@ nth_Code_integer L))) (=> (@ (@ ord_less_eq_nat I) K) (=> (@ (@ ord_less_nat K) J) (=> (@ (@ ord_le3102999989581377725nteger (@ _let_1 K)) X) (not (@ (@ ord_le6747313008572928689nteger X) (@ _let_1 (@ (@ plus_plus_nat K) one_one_nat)))))))))))))))))) (forall ((Xs list_nat) (P (-> nat nat Bool)) (Q (-> nat nat Bool))) (=> (forall ((X3 nat) (Y2 nat)) (let ((_let_1 (@ set_nat2 Xs))) (=> (@ (@ member_nat X3) _let_1) (=> (@ (@ member_nat Y2) _let_1) (=> (@ (@ P X3) Y2) (@ (@ Q X3) Y2)))))) (=> (@ (@ sorted_wrt_nat P) Xs) (@ (@ sorted_wrt_nat Q) Xs)))) (forall ((C product_prod_nat_nat) (A set_Pr1261947904930325089at_nat) (B set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ member8440522571783428010at_nat C))) (=> (@ _let_1 (@ (@ inf_in2572325071724192079at_nat A) B)) (@ _let_1 B)))) (forall ((C nat) (B2 nat) (A2 nat)) (=> (= (@ (@ plus_plus_nat C) B2) A2) (= C (@ (@ minus_minus_nat A2) B2)))) (forall ((Xs list_d) (Ys list_c)) (= (@ size_s2120799709113762520od_d_c (@ (@ zip_d_c Xs) Ys)) (@ (@ ord_min_nat (@ size_size_list_d Xs)) (@ size_size_list_c Ys)))) (forall ((X set_o)) (= (@ (@ inf_inf_set_o X) bot_bot_set_o) bot_bot_set_o)) (forall ((I rat) (K3 rat) (N rat)) (=> (@ (@ ord_less_eq_rat (@ (@ plus_plus_rat I) K3)) N) (@ (@ ord_less_eq_rat I) (@ (@ minus_minus_rat N) K3)))) (forall ((A set_Pr1261947904930325089at_nat)) (=> (forall ((Y2 product_prod_nat_nat)) (not (@ (@ member8440522571783428010at_nat Y2) A))) (= A bot_bo2099793752762293965at_nat))) (forall ((C (-> produc3658429121746597890et_nat Bool)) (A set_Pr4532377907799695533_nat_o) (B set_Pr4532377907799695533_nat_o)) (let ((_let_1 (@ member6576561426505652726_nat_o C))) (=> (@ _let_1 (@ (@ minus_1801376950450012436_nat_o A) B)) (not (@ _let_1 B))))) (forall ((A2 rat) (B2 rat)) (= (@ (@ ord_less_eq_rat zero_zero_rat) (@ (@ minus_minus_rat A2) B2)) (@ (@ ord_less_eq_rat B2) A2))) (forall ((A2 set_Pr4329608150637261639at_nat) (B2 set_Pr4329608150637261639at_nat) (C set_Pr4329608150637261639at_nat)) (let ((_let_1 (@ sup_su5525570899277871387at_nat A2))) (= (@ (@ sup_su5525570899277871387at_nat (@ _let_1 B2)) C) (@ _let_1 (@ (@ sup_su5525570899277871387at_nat B2) C))))) (forall ((Xs list_d) (Ys list_d) (Y d)) (=> (= (@ size_size_list_d Xs) (@ size_size_list_d Ys)) (=> (@ (@ member_d Y) (@ set_d2 Ys)) (not (forall ((X3 d)) (not (@ (@ member2287536781371869328od_d_d (@ (@ product_Pair_d_d X3) Y)) (@ set_Product_prod_d_d2 (@ (@ zip_d_d Xs) Ys))))))))) (forall ((X nat) (A set_nat) (B set_nat)) (let ((_let_1 (@ (@ insert_nat2 X) bot_bot_set_nat))) (let ((_let_2 (= A _let_1))) (let ((_let_3 (= B _let_1))) (= (= _let_1 (@ (@ sup_sup_set_nat A) B)) (or (and _let_3 (= A bot_bot_set_nat)) (and _let_3 _let_2) (and _let_2 (= B bot_bot_set_nat)))))))) (forall ((A2 rat) (C rat) (B2 rat)) (= (@ (@ ord_less_eq_rat A2) (@ (@ minus_minus_rat C) B2)) (@ (@ ord_less_eq_rat (@ (@ plus_plus_rat A2) B2)) C))) (forall ((A2 code_integer) (B2 code_integer) (C code_integer)) (let ((_let_1 (@ times_3573771949741848930nteger C))) (=> (@ (@ ord_le6747313008572928689nteger A2) B2) (=> (@ (@ ord_le6747313008572928689nteger zero_z3403309356797280102nteger) C) (@ (@ ord_le6747313008572928689nteger (@ _let_1 A2)) (@ _let_1 B2)))))) (forall ((S set_Pr1261947904930325089at_nat) (T3 set_Pr1261947904930325089at_nat)) (= (@ (@ sup_su6327502436637775413at_nat (@ (@ inf_in2572325071724192079at_nat S) T3)) S) S)) (forall ((X int) (Y int) (N nat)) (=> (= (@ (@ times_times_int X) Y) one_one_int) (= (@ (@ times_times_int (@ (@ power_power_int X) N)) (@ (@ power_power_int Y) N)) one_one_int))) (@ (@ _let_18 (@ produc27273713700761075at_nat (lambda ((X2 nat) (Y5 nat) (__flatten_var_0 product_prod_nat_nat)) (@ (@ produc2626176000494625587at_nat (lambda ((U4 nat) (V4 nat)) (@ (@ product_Pair_nat_nat (@ (@ plus_plus_nat X2) V4)) (@ (@ plus_plus_nat Y5) U4)))) __flatten_var_0)))) minus_minus_int) (forall ((N nat) (Z nat)) (let ((_let_1 (@ nat_set_decode Z))) (=> (not (@ (@ member_nat N) _let_1)) (= (@ nat_set_decode (@ (@ plus_plus_nat (@ (@ power_power_nat (@ numeral_numeral_nat (@ bit0 one))) N)) Z)) (@ (@ insert_nat2 N) _let_1))))) (forall ((M5 set_nat)) (=> (@ finite_finite_nat M5) (=> (not (= M5 bot_bot_set_nat)) (=> (not (@ (@ member_nat zero_zero_nat) M5)) (=> (forall ((M6 nat) (N5 nat)) (=> (@ (@ member_nat M6) M5) (=> (@ (@ member_nat N5) M5) (@ (@ member_nat (@ (@ gcd_lcm_nat M6) N5)) M5)))) (= (@ gcd_Lcm_nat M5) (@ lattic8265883725875713057ax_nat M5))))))) (forall ((B2 assn) (A2 assn)) (=> (@ (@ ord_less_assn B2) A2) (@ (@ ord_less_eq_assn B2) A2))) (forall ((X nat) (Y nat) (Z nat)) (let ((_let_1 (@ ord_less_nat X))) (=> (@ _let_1 Y) (=> (@ (@ ord_less_eq_nat Y) Z) (@ _let_1 Z))))) (forall ((X d) (Xs list_d)) (=> (@ (@ member_d X) (@ set_d2 Xs)) (@ (@ ord_less_nat zero_zero_nat) (@ size_size_list_d Xs)))) (forall ((X produc3843707927480180839at_nat) (Xs list_P5464809261938338413at_nat)) (= (@ set_Pr3765526544606949372at_nat (@ (@ remove4908499291543849587at_nat X) Xs)) (@ (@ minus_3314409938677909166at_nat (@ set_Pr3765526544606949372at_nat Xs)) (@ (@ insert9069300056098147895at_nat X) bot_bo228742789529271731at_nat)))) (forall ((Xs list_nat) (Ys list_nat)) (= (= (@ (@ zip_nat_nat Xs) Ys) nil_Pr5478986624290739719at_nat) (or (= Xs nil_nat) (= Ys nil_nat)))) (forall ((B2 rat) (M2 nat) (N nat)) (let ((_let_1 (@ power_power_rat B2))) (=> (@ (@ ord_less_rat zero_zero_rat) B2) (=> (@ (@ ord_less_rat B2) one_one_rat) (= (@ (@ ord_less_eq_rat (@ _let_1 M2)) (@ _let_1 N)) (@ (@ ord_less_eq_nat N) M2)))))) (forall ((X int) (Y int)) (=> (@ (@ ord_less_eq_int X) Y) (= (@ (@ sup_sup_int X) Y) Y))) (forall ((Y produc6575502325842934193n_assn) (X222 list_P8527749157015355191n_assn) (X21 produc6575502325842934193n_assn)) (let ((_let_1 (@ member7957490590177025114n_assn Y))) (=> (@ _let_1 (@ set_Pr1139785259514867910n_assn X222)) (@ _let_1 (@ set_Pr1139785259514867910n_assn (@ (@ cons_P2971678138204555879n_assn X21) X222)))))) (= times_3573771949741848930nteger (lambda ((A3 code_integer) (B3 code_integer)) (@ (@ times_3573771949741848930nteger B3) A3))) (forall ((A2 int)) (= (@ (@ times_times_int A2) one_one_int) A2)) (forall ((Xs list_int) (A2 int) (I nat)) (=> (@ distinct_int Xs) (=> (not (@ (@ member_int A2) (@ (@ minus_minus_set_int (@ set_int2 Xs)) (@ (@ insert_int2 (@ (@ nth_int Xs) I)) bot_bot_set_int)))) (@ distinct_int (@ (@ (@ list_update_int Xs) I) A2))))) (forall ((B2 nat) (C nat) (A2 nat)) (=> (@ (@ ord_less_nat B2) C) (@ (@ ord_less_nat (@ (@ ord_min_nat A2) B2)) C))) (forall ((X code_integer) (Y code_integer)) (=> (@ (@ ord_le6747313008572928689nteger X) Y) (not (@ (@ ord_le6747313008572928689nteger Y) X)))) (@ (@ entails (@ (@ times_times_assn (@ (@ (@ (@ vEBT_L824818263033719201sn_c_d i) a) (@ (@ (@ list_update_c xs) i2) x)) (@ (@ (@ list_update_d xsi) i2) xi))) f)) q) (forall ((L12 list_c) (L23 list_d)) (=> (= (@ size_size_list_c L12) (@ size_size_list_d L23)) (= (@ (@ (@ zipf_c44566020827681705od_c_d product_Pair_c_d) L12) L23) (@ (@ zip_c_d L12) L23)))) (forall ((Xs list_nat)) (= (@ is_empty_nat (@ set_nat2 Xs)) (@ null_nat Xs))) (forall ((A2 (-> produc3658429121746597890et_nat Bool)) (A set_Pr4532377907799695533_nat_o) (B set_Pr4532377907799695533_nat_o)) (let ((_let_1 (@ inf_in1906310914598751387_nat_o A))) (=> (not (@ (@ member6576561426505652726_nat_o A2) A)) (= (@ _let_1 (@ (@ insert5175938949040314269_nat_o A2) B)) (@ _let_1 B))))) (forall ((A2 rat) (B2 rat) (C rat)) (=> (@ (@ ord_less_eq_rat A2) B2) (@ (@ ord_less_eq_rat (@ (@ minus_minus_rat A2) C)) (@ (@ minus_minus_rat B2) C)))) (forall ((P (-> produc6575502325842934193n_assn nat assn)) (A2 produc6575502325842934193n_assn) (As2 list_P8527749157015355191n_assn) (C nat) (Cs list_nat)) (let ((_let_1 (@ vEBT_L4762835640886981758sn_nat P))) (= (@ (@ _let_1 (@ (@ cons_P2971678138204555879n_assn A2) As2)) (@ (@ cons_nat C) Cs)) (@ (@ times_times_assn (@ (@ P A2) C)) (@ (@ _let_1 As2) Cs))))) (= (@ butlas3012047794866324995n_assn nil_Pr5671120429643327159n_assn) nil_Pr5671120429643327159n_assn) (forall ((P assn) (H2 produc3658429121746597890et_nat)) (= (@ (@ rep_assn (@ uminus_uminus_assn P)) H2) (and (not (@ (@ rep_assn P) H2)) (@ in_range H2)))) (forall ((A2 nat) (B2 nat)) (= (= (@ (@ plus_plus_nat A2) B2) A2) (= B2 zero_zero_nat))) (forall ((P (-> produc2732055786443039994et_nat Bool)) (X produc2732055786443039994et_nat)) (=> (forall ((A4 (-> produc3658429121746597890et_nat Bool)) (B4 (-> produc3658429121746597890et_nat Bool)) (C4 heap_e7401611519738050253t_unit) (D3 set_nat)) (@ P (@ (@ produc2245416461498447860et_nat A4) (@ (@ produc5001842942810119800et_nat B4) (@ (@ produc7507926704131184380et_nat C4) D3))))) (@ P X))) (forall ((Y int) (X int)) (=> (not (@ (@ ord_less_eq_int Y) X)) (@ (@ ord_less_int X) Y))) (forall ((A2 num) (B2 num) (C num)) (let ((_let_1 (@ ord_less_num A2))) (=> (@ _let_1 B2) (=> (@ (@ ord_less_num B2) C) (@ _let_1 C))))) (forall ((I produc3843707927480180839at_nat) (J produc3843707927480180839at_nat) (R set_Pr5564308138774400199at_nat)) (=> (@ (@ member6009668390874684176at_nat (@ (@ produc2335810615602371415at_nat I) J)) R) (@ (@ member8757157785044589968at_nat I) (@ field_2862844103579723188at_nat R)))) (forall ((A2 rat) (B2 rat)) (let ((_let_1 (@ ord_less_rat zero_zero_rat))) (= (@ _let_1 (@ (@ times_times_rat A2) B2)) (or (and (@ _let_1 B2) (@ _let_1 A2)) (and (@ (@ ord_less_rat A2) zero_zero_rat) (@ (@ ord_less_rat B2) zero_zero_rat)))))) (forall ((A2 int) (B2 int) (C int)) (let ((_let_1 (@ times_times_int A2))) (= (@ _let_1 (@ (@ minus_minus_int B2) C)) (@ (@ minus_minus_int (@ _let_1 B2)) (@ _let_1 C))))) (forall ((Ns list_nat) (R2 set_Pr1261947904930325089at_nat)) (not (@ (@ member7340969449405702474st_nat (@ (@ produc2694037385005941721st_nat Ns) nil_nat)) (@ lenlex_nat R2)))) (= sup_su5525570899277871387at_nat (lambda ((A5 set_Pr4329608150637261639at_nat) (B7 set_Pr4329608150637261639at_nat)) (@ (@ sup_su5525570899277871387at_nat B7) A5))) (forall ((X filter_nat) (Y filter_nat)) (=> (@ (@ ord_le2510731241096832064er_nat X) Y) (= (@ (@ sup_sup_filter_nat X) Y) Y))) (forall ((A set_Pr1261947904930325089at_nat)) (@ (@ ord_le3146513528884898305at_nat bot_bo2099793752762293965at_nat) A)) (forall ((Xs list_nat) (Ys list_int) (Zs list_c) (Ws list_d) (P (-> list_nat list_int list_c list_d Bool))) (let ((_let_1 (@ size_size_list_c Zs))) (let ((_let_2 (@ size_size_list_int Ys))) (=> (= (@ size_size_list_nat Xs) _let_2) (=> (= _let_2 _let_1) (=> (= _let_1 (@ size_size_list_d Ws)) (=> (@ (@ (@ (@ P nil_nat) nil_int) nil_c) nil_d) (=> (forall ((X3 nat) (Xs2 list_nat) (Y2 int) (Ys5 list_int) (Z4 c) (Zs2 list_c) (W3 d) (Ws2 list_d)) (let ((_let_1 (@ size_size_list_c Zs2))) (let ((_let_2 (@ size_size_list_int Ys5))) (=> (= (@ size_size_list_nat Xs2) _let_2) (=> (= _let_2 _let_1) (=> (= _let_1 (@ size_size_list_d Ws2)) (=> (@ (@ (@ (@ P Xs2) Ys5) Zs2) Ws2) (@ (@ (@ (@ P (@ (@ cons_nat X3) Xs2)) (@ (@ cons_int Y2) Ys5)) (@ (@ cons_c Z4) Zs2)) (@ (@ cons_d W3) Ws2))))))))) (@ (@ (@ (@ P Xs) Ys) Zs) Ws))))))))) (forall ((A2 code_integer)) (= (@ (@ times_3573771949741848930nteger zero_z3403309356797280102nteger) A2) zero_z3403309356797280102nteger)) (forall ((M2 int) (N int)) (let ((_let_1 (@ (@ ord_min_int M2) N))) (= (@ (@ ord_less_eq_int M2) _let_1) (= _let_1 M2)))) (= ord_less_eq_set_nat (lambda ((B3 set_nat) (A3 set_nat)) (or (= A3 B3) (@ (@ ord_less_set_nat B3) A3)))) (forall ((X set_Pr1261947904930325089at_nat) (Y set_Pr1261947904930325089at_nat)) (= (= (@ (@ sup_su6327502436637775413at_nat X) Y) bot_bo2099793752762293965at_nat) (and (= X bot_bo2099793752762293965at_nat) (= Y bot_bo2099793752762293965at_nat)))) (forall ((X produc3843707927480180839at_nat) (Xs list_P5464809261938338413at_nat)) (=> (not (@ (@ member8757157785044589968at_nat X) (@ set_Pr3765526544606949372at_nat Xs))) (= (@ (@ insert4149901806602606979at_nat X) Xs) (@ (@ cons_P3940603068885512221at_nat X) Xs)))) (forall ((A2 int) (B2 int)) (=> (@ (@ ord_less_int A2) zero_zero_int) (=> (@ (@ ord_less_eq_int B2) zero_zero_int) (@ (@ ord_less_int (@ (@ plus_plus_int A2) B2)) zero_zero_int)))) (= times_times_nat (lambda ((A3 nat) (B3 nat)) (@ (@ times_times_nat B3) A3))) (forall ((P (-> produc3843707927480180839at_nat produc3843707927480180839at_nat Bool)) (A produc3843707927480180839at_nat)) (@ (@ pairwi3222497012029234898at_nat P) (@ (@ insert9069300056098147895at_nat A) bot_bo228742789529271731at_nat))) (forall ((U code_integer)) (=> (@ (@ ord_le3102999989581377725nteger zero_z3403309356797280102nteger) U) (= (@ (@ set_or8404916559141939852nteger zero_z3403309356797280102nteger) U) (@ (@ image_1215581382706833972nteger semiri4939895301339042750nteger) (@ set_ord_lessThan_nat (@ code_nat_of_integer U)))))) (forall ((X (-> produc3658429121746597890et_nat Bool)) (A set_Pr4532377907799695533_nat_o) (B set_Pr4532377907799695533_nat_o)) (let ((_let_1 (@ insert5175938949040314269_nat_o X))) (let ((_let_2 (@ member6576561426505652726_nat_o X))) (=> (not (@ _let_2 A)) (=> (not (@ _let_2 B)) (= (= (@ _let_1 A) (@ _let_1 B)) (= A B))))))) (forall ((Xs list_d) (Ys list_d)) (=> (= (@ size_size_list_d Xs) (@ size_size_list_d Ys)) (= (@ (@ zip_d_d (@ rev_d Xs)) (@ rev_d Ys)) (@ rev_Product_prod_d_d (@ (@ zip_d_d Xs) Ys))))) (forall ((A2 set_nat) (B2 set_nat)) (=> (@ (@ ord_less_eq_set_nat A2) B2) (= A2 (@ (@ inf_inf_set_nat A2) B2)))) (forall ((A set_nat) (X nat)) (let ((_let_1 (@ (@ insert_nat2 X) bot_bot_set_nat))) (=> (@ (@ ord_less_eq_set_nat A) _let_1) (or (= A _let_1) (= A bot_bot_set_nat))))) (forall ((C (-> produc3658429121746597890et_nat Bool))) (not (@ (@ member6576561426505652726_nat_o C) bot_bo7824918357723582233_nat_o))) (forall ((A2 num) (F4 (-> assn num)) (B2 assn) (C assn)) (let ((_let_1 (@ ord_less_num A2))) (=> (@ _let_1 (@ F4 B2)) (=> (@ (@ ord_less_eq_assn B2) C) (=> (forall ((X3 assn) (Y2 assn)) (=> (@ (@ ord_less_eq_assn X3) Y2) (@ (@ ord_less_eq_num (@ F4 X3)) (@ F4 Y2)))) (@ _let_1 (@ F4 C))))))) (forall ((Xs list_P6011104703257516679at_nat) (P (-> product_prod_nat_nat Bool)) (X product_prod_nat_nat)) (=> (forall ((I5 nat)) (=> (@ (@ ord_less_nat I5) (@ size_s5460976970255530739at_nat Xs)) (@ P (@ (@ nth_Pr7617993195940197384at_nat Xs) I5)))) (=> (@ (@ member8440522571783428010at_nat X) (@ set_Pr5648618587558075414at_nat Xs)) (@ P X)))) (forall ((A2 rat) (B2 rat)) (=> (not (= (@ (@ times_times_rat A2) B2) zero_zero_rat)) (and (not (= B2 zero_zero_rat)) (not (= A2 zero_zero_rat))))) _let_50 (forall ((A2 assn)) (= (@ (@ sup_sup_assn bot_bot_assn) A2) A2)) (forall ((A set_nat) (B set_nat)) (=> (= (@ (@ inf_inf_set_nat A) B) bot_bot_set_nat) (= (@ (@ minus_minus_set_nat A) B) A))) (forall ((A2 filter_nat) (B2 filter_nat)) (=> (@ (@ ord_le2510731241096832064er_nat A2) B2) (= (@ (@ sup_sup_filter_nat A2) B2) B2))) (forall ((A2 rat) (B2 rat) (C rat)) (let ((_let_1 (@ ord_less_rat B2))) (=> (@ (@ ord_less_eq_rat zero_zero_rat) A2) (=> (@ _let_1 C) (@ _let_1 (@ (@ plus_plus_rat A2) C)))))) (forall ((X set_Pr1261947904930325089at_nat) (Z set_Pr1261947904930325089at_nat) (R2 set_Pr4329608150637261639at_nat)) (let ((_let_1 (@ member8757157785044589968at_nat (@ (@ produc2922128104949294807at_nat X) Z)))) (=> (@ _let_1 (@ transi2703068831062848130at_nat R2)) (=> (not (@ _let_1 R2)) (not (forall ((Y2 set_Pr1261947904930325089at_nat)) (=> (@ (@ member8757157785044589968at_nat (@ (@ produc2922128104949294807at_nat X) Y2)) R2) (not (@ (@ member8757157785044589968at_nat (@ (@ produc2922128104949294807at_nat Y2) Z)) (@ transi2703068831062848130at_nat R2)))))))))) (forall ((A2 nat) (B2 nat)) (=> (not (= A2 zero_zero_nat)) (=> (not (= B2 zero_zero_nat)) (not (= (@ (@ times_times_nat A2) B2) zero_zero_nat))))) (forall ((Xs list_int) (I nat) (X int)) (= (@ size_size_list_int (@ (@ (@ list_update_int Xs) I) X)) (@ size_size_list_int Xs))) (forall ((X assn)) (= (@ (@ inf_inf_assn bot_bot_assn) X) bot_bot_assn)) (forall ((M2 nat) (N nat)) (= (@ (@ ord_less_nat zero_zero_nat) (@ (@ gcd_gcd_nat M2) N)) (or (not (= N zero_zero_nat)) (not (= M2 zero_zero_nat))))) (forall ((A2 int) (C int) (B2 int)) (=> (@ (@ ord_less_int A2) C) (@ (@ ord_less_int (@ (@ ord_min_int A2) B2)) C))) (forall ((F4 (-> nat nat)) (N nat) (M2 nat)) (=> (forall ((N5 nat)) (@ (@ ord_less_nat (@ F4 N5)) (@ F4 (@ suc N5)))) (= (@ (@ ord_less_nat (@ F4 N)) (@ F4 M2)) (@ (@ ord_less_nat N) M2)))) (forall ((X set_Pr4329608150637261639at_nat)) (= (@ (@ sup_su5525570899277871387at_nat X) bot_bo228742789529271731at_nat) X)) (forall ((N nat) (Xs list_nat) (X nat)) (=> (@ (@ ord_less_nat N) (@ size_size_list_nat Xs)) (@ (@ member_nat X) (@ set_nat2 (@ (@ (@ list_update_nat Xs) N) X))))) (forall ((N nat) (Xs list_nat)) (=> (@ (@ ord_less_nat N) (@ size_size_list_nat Xs)) (@ (@ member_nat (@ (@ nth_nat Xs) N)) (@ set_nat2 Xs)))) (forall ((X nat) (Xs list_nat) (Y produc6575502325842934193n_assn) (Ys list_P8527749157015355191n_assn)) (= (@ (@ zip_na5338819973521719528n_assn (@ (@ cons_nat X) Xs)) (@ (@ cons_P2971678138204555879n_assn Y) Ys)) (@ (@ cons_P7068465851076118432n_assn (@ (@ produc1553784393020010504n_assn X) Y)) (@ (@ zip_na5338819973521719528n_assn Xs) Ys)))) (forall ((A set_nat)) (=> (forall ((Y2 nat)) (not (@ (@ member_nat Y2) A))) (= A bot_bot_set_nat))) (forall ((Xs list_P6011104703257516679at_nat) (N nat) (X product_prod_nat_nat)) (=> (@ distin6923225563576452346at_nat Xs) (=> (@ (@ ord_less_nat N) (@ size_s5460976970255530739at_nat Xs)) (= (@ set_Pr5648618587558075414at_nat (@ (@ (@ list_u6180841689913720943at_nat Xs) N) X)) (@ (@ insert8211810215607154385at_nat X) (@ (@ minus_1356011639430497352at_nat (@ set_Pr5648618587558075414at_nat Xs)) (@ (@ insert8211810215607154385at_nat (@ (@ nth_Pr7617993195940197384at_nat Xs) N)) bot_bo2099793752762293965at_nat))))))) (forall ((X assn)) (= (@ (@ sup_sup_assn X) bot_bot_assn) X)) (forall ((A set_nat)) (= (@ (@ sup_sup_set_nat A) A) A)) (forall ((A2 assn) (B2 assn) (C assn)) (let ((_let_1 (@ ord_less_eq_assn A2))) (=> (@ _let_1 B2) (=> (@ _let_1 C) (@ _let_1 (@ (@ inf_inf_assn B2) C)))))) (forall ((X set_Pr4329608150637261639at_nat) (Y set_Pr4329608150637261639at_nat) (Z set_Pr4329608150637261639at_nat)) (let ((_let_1 (@ sup_su5525570899277871387at_nat X))) (= (@ _let_1 (@ (@ inf_in7913087082777306421at_nat Y) Z)) (@ (@ inf_in7913087082777306421at_nat (@ _let_1 Y)) (@ _let_1 Z))))) (= dvd_dvd_int (lambda ((D5 int) (T2 int)) (@ (@ dvd_dvd_int D5) (@ uminus_uminus_int T2)))) (forall ((Xs list_P6011104703257516679at_nat) (A2 product_prod_nat_nat) (I nat)) (=> (@ distin6923225563576452346at_nat Xs) (=> (not (@ (@ member8440522571783428010at_nat A2) (@ (@ minus_1356011639430497352at_nat (@ set_Pr5648618587558075414at_nat Xs)) (@ (@ insert8211810215607154385at_nat (@ (@ nth_Pr7617993195940197384at_nat Xs) I)) bot_bo2099793752762293965at_nat)))) (@ distin6923225563576452346at_nat (@ (@ (@ list_u6180841689913720943at_nat Xs) I) A2))))) (forall ((A1 int) (A22 int) (A33 product_prod_int_int)) (=> (@ (@ (@ eucl_rel_int A1) A22) A33) (=> (=> (= A22 zero_zero_int) (not (= A33 (@ (@ product_Pair_int_int zero_zero_int) A1)))) (=> (forall ((Q5 int)) (=> (= A33 (@ (@ product_Pair_int_int Q5) zero_zero_int)) (=> (not (= A22 zero_zero_int)) (not (= A1 (@ (@ times_times_int Q5) A22)))))) (not (forall ((R6 int) (Q5 int)) (=> (= A33 (@ (@ product_Pair_int_int Q5) R6)) (=> (= (@ sgn_sgn_int R6) (@ sgn_sgn_int A22)) (=> (@ (@ ord_less_int (@ abs_abs_int R6)) (@ abs_abs_int A22)) (not (= A1 (@ (@ plus_plus_int (@ (@ times_times_int Q5) A22)) R6)))))))))))) (forall ((X code_integer) (Y code_integer)) (= (not (= X Y)) (or (@ (@ ord_le6747313008572928689nteger Y) X) (@ (@ ord_le6747313008572928689nteger X) Y)))) (forall ((A2 int) (B2 int)) (let ((_let_1 (@ product_Pair_int_int A2))) (= (@ frct (@ _let_1 (@ uminus_uminus_int B2))) (@ uminus_uminus_rat (@ frct (@ _let_1 B2)))))) (forall ((A2 code_integer) (B2 code_integer)) (= (@ (@ ord_le3102999989581377725nteger A2) (@ (@ plus_p5714425477246183910nteger B2) A2)) (@ (@ ord_le3102999989581377725nteger zero_z3403309356797280102nteger) B2))) (forall ((X set_Pr1261947904930325089at_nat) (Y set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ (@ inf_in2572325071724192079at_nat X) Y))) (= (@ (@ inf_in2572325071724192079at_nat _let_1) Y) _let_1))) (forall ((X nat) (Y nat) (Z nat)) (let ((_let_1 (@ ord_less_nat X))) (=> (@ _let_1 Y) (=> (@ (@ ord_less_nat Y) Z) (@ _let_1 Z))))) (forall ((B set_Pr4329608150637261639at_nat) (A set_Pr4329608150637261639at_nat)) (=> (@ (@ ord_le1268244103169919719at_nat B) A) (= (@ (@ sup_su5525570899277871387at_nat A) B) A))) (forall ((A set_nat) (B set_nat) (C2 set_nat)) (let ((_let_1 (@ inf_inf_set_nat A))) (= (= (@ (@ sup_sup_set_nat (@ _let_1 B)) C2) (@ _let_1 (@ (@ sup_sup_set_nat B) C2))) (@ (@ ord_less_eq_set_nat C2) A)))) (= (@ (@ times_times_assn top_top_assn) top_top_assn) top_top_assn) (forall ((X produc3843707927480180839at_nat) (Xs list_P5464809261938338413at_nat)) (= (@ (@ member8757157785044589968at_nat X) (@ set_Pr3765526544606949372at_nat Xs)) (exists ((I4 nat)) (and (= (@ (@ nth_Pr1239524528086697198at_nat Xs) I4) X) (@ (@ ord_less_nat I4) (@ size_s1588839187904960729at_nat Xs)))))) (forall ((I nat) (L list_nat) (X nat) (Y nat)) (let ((_let_1 (@ member_nat X))) (=> (@ (@ ord_less_nat I) (@ size_size_list_nat L)) (= (@ _let_1 (@ set_nat2 (@ (@ (@ list_update_nat L) I) Y))) (or (= X Y) (and (@ _let_1 (@ set_nat2 L)) (forall ((Y5 nat)) (@ (@ member_nat X) (@ set_nat2 (@ (@ (@ list_update_nat L) I) Y5)))))))))) (forall ((A2 product_prod_nat_nat) (B2 product_prod_nat_nat) (C product_prod_nat_nat) (D2 product_prod_nat_nat)) (= (= (@ (@ insert8211810215607154385at_nat A2) (@ (@ insert8211810215607154385at_nat B2) bot_bo2099793752762293965at_nat)) (@ (@ insert8211810215607154385at_nat C) (@ (@ insert8211810215607154385at_nat D2) bot_bo2099793752762293965at_nat))) (or (and (= B2 C) (= A2 D2)) (and (= B2 D2) (= A2 C))))) (forall ((Begin nat) (End nat) (X produc6575502325842934193n_assn) (Xs list_P8527749157015355191n_assn)) (let ((_let_1 (@ (@ minus_minus_nat End) one_one_nat))) (let ((_let_2 (@ cons_P2971678138204555879n_assn X))) (let ((_let_3 (@ slice_7964966981652229398n_assn Begin))) (let ((_let_4 (@ (@ _let_3 End) (@ _let_2 Xs)))) (let ((_let_5 (and (@ (@ ord_less_nat zero_zero_nat) End) (= Begin zero_zero_nat)))) (and (=> _let_5 (= _let_4 (@ _let_2 (@ (@ _let_3 _let_1) Xs)))) (=> (not _let_5) (= _let_4 (@ (@ (@ slice_7964966981652229398n_assn (@ (@ minus_minus_nat Begin) one_one_nat)) _let_1) Xs)))))))))) (forall ((X21 produc6575502325842934193n_assn) (X222 list_P8527749157015355191n_assn)) (@ (@ member7957490590177025114n_assn X21) (@ set_Pr1139785259514867910n_assn (@ (@ cons_P2971678138204555879n_assn X21) X222)))) (forall ((X filter_nat) (Y filter_nat)) (= (@ (@ (@ if_filter_nat false) X) Y) Y)) (forall ((P assn) (Q assn) (R assn)) (let ((_let_1 (@ times_times_assn P))) (= (@ (@ times_times_assn (@ _let_1 Q)) R) (@ _let_1 (@ (@ times_times_assn Q) R))))) (forall ((A2 int) (C int) (B2 int) (D2 int)) (=> (@ (@ ord_less_eq_int A2) C) (=> (@ (@ ord_less_eq_int B2) D2) (@ (@ ord_less_eq_int (@ (@ inf_inf_int A2) B2)) (@ (@ inf_inf_int C) D2))))) (forall ((X assn) (Y assn)) (@ (@ ord_less_eq_assn X) (@ (@ sup_sup_assn X) Y))) (forall ((P6 rat) (Q6 rat)) (= (@ quotient_of (@ (@ plus_plus_rat P6) Q6)) (@ (@ produc4245557441103728435nt_int (lambda ((A3 int) (C5 int)) (@ (@ produc4245557441103728435nt_int (lambda ((B3 int) (D5 int)) (@ normalize (@ (@ product_Pair_int_int (@ (@ plus_plus_int (@ (@ times_times_int A3) D5)) (@ (@ times_times_int B3) C5))) (@ (@ times_times_int C5) D5))))) (@ quotient_of Q6)))) (@ quotient_of P6)))) (= ord_le6747313008572928689nteger (lambda ((X2 code_integer) (Y5 code_integer)) (and (not (= X2 Y5)) (@ (@ ord_le3102999989581377725nteger X2) Y5)))) (forall ((A2 nat) (C2 set_nat) (B set_nat)) (let ((_let_1 (@ insert_nat2 A2))) (=> (@ (@ member_nat A2) C2) (= (@ (@ inf_inf_set_nat (@ _let_1 B)) C2) (@ _let_1 (@ (@ inf_inf_set_nat B) C2)))))) (forall ((B2 int) (A2 int)) (= (@ (@ ord_less_eq_int (@ (@ plus_plus_int B2) A2)) B2) (@ (@ ord_less_eq_int A2) zero_zero_int))) (forall ((A2 int) (C int) (B2 int)) (= (@ (@ ord_less_int (@ (@ times_times_int A2) C)) (@ (@ times_times_int B2) C)) (and (=> (@ (@ ord_less_eq_int zero_zero_int) C) (@ (@ ord_less_int A2) B2)) (=> (@ (@ ord_less_eq_int C) zero_zero_int) (@ (@ ord_less_int B2) A2))))) (forall ((X filter_nat) (Y filter_nat)) (@ (@ ord_le2510731241096832064er_nat (@ (@ inf_inf_filter_nat X) Y)) Y)) (forall ((Xs list_nat) (Ys list_P8527749157015355191n_assn)) (= (= nil_Pr680377793251149648n_assn (@ (@ zip_na5338819973521719528n_assn Xs) Ys)) (or (= Xs nil_nat) (= Ys nil_Pr5671120429643327159n_assn)))) (forall ((Y nat) (X nat) (Xs list_nat)) (let ((_let_1 (@ member_nat Y))) (=> (@ _let_1 (@ set_nat2 (@ (@ cons_nat X) Xs))) (or (@ _let_1 (@ set_nat2 Xs)) (= Y X))))) (forall ((M2 nat) (Xs list_int) (N nat)) (=> (@ (@ ord_less_nat M2) (@ size_size_list_int Xs)) (= (@ (@ nth_Pr3440142176431000676at_int (@ (@ enumerate_int N) Xs)) M2) (@ (@ product_Pair_nat_int (@ (@ plus_plus_nat N) M2)) (@ (@ nth_int Xs) M2))))) (forall ((A2 filter_nat) (C filter_nat) (B2 filter_nat) (D2 filter_nat)) (=> (@ (@ ord_le2510731241096832064er_nat A2) C) (=> (@ (@ ord_le2510731241096832064er_nat B2) D2) (@ (@ ord_le2510731241096832064er_nat (@ (@ inf_inf_filter_nat A2) B2)) (@ (@ inf_inf_filter_nat C) D2))))) (forall ((Xs list_d) (Ys list_c) (Y c)) (=> (= (@ size_size_list_d Xs) (@ size_size_list_c Ys)) (=> (@ (@ member_c Y) (@ set_c2 Ys)) (not (forall ((X3 d)) (not (@ (@ member2287536777068640527od_d_c (@ (@ product_Pair_d_c X3) Y)) (@ set_Product_prod_d_c2 (@ (@ zip_d_c Xs) Ys))))))))) (forall ((A set_Pr1261947904930325089at_nat)) (= (@ (@ inf_in2572325071724192079at_nat A) bot_bo2099793752762293965at_nat) bot_bo2099793752762293965at_nat)) (@ (@ (@ (@ semila1623282765462674594er_nat ord_max_nat) zero_zero_nat) (lambda ((X2 nat) (Y5 nat)) (@ (@ ord_less_eq_nat Y5) X2))) (lambda ((X2 nat) (Y5 nat)) (@ (@ ord_less_nat Y5) X2))) (forall ((X produc3658429121746597890et_nat)) (=> (not (@ one_assn_raw X)) (not (forall ((H heap_e7401611519738050253t_unit) (As set_nat)) (=> (= X (@ (@ produc7507926704131184380et_nat H) As)) (= As bot_bot_set_nat)))))) (forall ((A set_nat)) (= (exists ((X2 nat)) (@ (@ member_nat X2) A)) (not (= A bot_bot_set_nat)))) (forall ((A2 nat) (X nat) (B2 nat)) (=> (@ (@ ord_less_nat A2) X) (@ (@ ord_less_nat (@ (@ inf_inf_nat A2) B2)) X))) _let_49 (forall ((U nat) (U3 nat) (P (-> nat Bool))) (let ((_let_1 (@ upt zero_zero_nat))) (let ((_let_2 (@ filter_nat2 P))) (=> (@ (@ ord_less_eq_nat U) U3) (=> (forall ((I5 nat)) (=> (and (@ (@ ord_less_nat I5) U3) (@ (@ ord_less_eq_nat U) I5)) (not (@ P I5)))) (= (@ _let_2 (@ _let_1 U)) (@ _let_2 (@ _let_1 U3)))))))) (forall ((A2 code_integer) (B2 code_integer) (C code_integer) (D2 code_integer)) (let ((_let_1 (@ times_3573771949741848930nteger B2))) (let ((_let_2 (@ times_3573771949741848930nteger A2))) (= (and (not (= C D2)) (not (= A2 B2))) (not (= (@ (@ plus_p5714425477246183910nteger (@ _let_2 C)) (@ _let_1 D2)) (@ (@ plus_p5714425477246183910nteger (@ _let_2 D2)) (@ _let_1 C)))))))) (forall ((A2 int) (B2 int)) (=> (@ (@ ord_less_int zero_zero_int) A2) (=> (@ (@ ord_less_int B2) zero_zero_int) (@ (@ ord_less_int (@ (@ times_times_int B2) A2)) zero_zero_int)))) (forall ((A2 rat)) (= (@ (@ minus_minus_rat A2) zero_zero_rat) A2)) _let_48 (forall ((Ys list_c) (Xs list_c)) (=> (@ distinct_c Ys) (=> (= (@ set_c2 Ys) (@ set_c2 Xs)) (@ (@ ord_less_eq_nat (@ size_size_list_c Ys)) (@ size_size_list_c Xs))))) _let_47 (forall ((A set_int) (B set_int) (C int)) (let ((_let_1 (@ member_int C))) (=> (@ (@ ord_less_set_int A) B) (=> (@ _let_1 A) (@ _let_1 B))))) (forall ((X Bool) (B set_o) (A set_o)) (let ((_let_1 (@ (@ minus_minus_set_o A) B))) (let ((_let_2 (@ insert_o2 X))) (let ((_let_3 (@ (@ minus_minus_set_o (@ _let_2 A)) B))) (let ((_let_4 (@ (@ member_o X) B))) (and (=> _let_4 (= _let_3 _let_1)) (=> (not _let_4) (= _let_3 (@ _let_2 _let_1))))))))) (forall ((A set_o) (B set_o)) (= (@ (@ ord_less_set_o (@ (@ minus_minus_set_o A) B)) A) (not (= (@ (@ inf_inf_set_o A) B) bot_bot_set_o)))) (forall ((X set_int) (Y set_int)) (= (= (@ (@ sup_sup_set_int X) Y) bot_bot_set_int) (and (= Y bot_bot_set_int) (= X bot_bot_set_int)))) (forall ((A set_Pr4532377907799695533_nat_o) (Ys list_P7985473006766602707_nat_o)) (= (@ (@ ord_le2965882846123202637_nat_o A) (@ coset_9017067850271954240_nat_o Ys)) (forall ((X2 (-> produc3658429121746597890et_nat Bool))) (let ((_let_1 (@ member6576561426505652726_nat_o X2))) (=> (@ _let_1 (@ set_Pr400311997697478754_nat_o Ys)) (not (@ _let_1 A))))))) (forall ((A2 nat) (F4 (-> nat nat)) (B2 nat) (C nat)) (let ((_let_1 (@ ord_less_eq_nat A2))) (=> (@ _let_1 (@ F4 B2)) (=> (@ (@ ord_less_eq_nat B2) C) (=> (forall ((X3 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(forall ((A2 num) (B2 num) (F4 (-> num code_integer)) (C code_integer)) (=> (@ (@ ord_less_num A2) B2) (=> (@ (@ ord_le3102999989581377725nteger (@ F4 B2)) C) (=> (forall ((X3 num) (Y2 num)) (=> (@ (@ ord_less_num X3) Y2) (@ (@ ord_le6747313008572928689nteger (@ F4 X3)) (@ F4 Y2)))) (@ (@ ord_le6747313008572928689nteger (@ F4 A2)) C))))) (forall ((M2 d) (Ms list_d) (N d) (Ns list_d) (R2 set_Product_prod_d_d)) (let ((_let_1 (@ lenlex_d R2))) (let ((_let_2 (@ size_size_list_d Ns))) (let ((_let_3 (@ size_size_list_d Ms))) (= (@ (@ member1810801192463332112list_d (@ (@ produc242965421297323863list_d (@ (@ cons_d M2) Ms)) (@ (@ cons_d N) Ns))) _let_1) (or (@ (@ ord_less_nat _let_3) _let_2) (and (= _let_3 _let_2) (@ (@ member2287536781371869328od_d_d (@ (@ product_Pair_d_d M2) N)) R2)) (and (@ (@ member1810801192463332112list_d (@ (@ produc242965421297323863list_d Ms) Ns)) _let_1) (= M2 N)))))))) (forall ((A2 rat) (B2 rat) (C rat)) (let ((_let_1 (@ times_times_rat C))) (=> (@ (@ 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listre8180072825634266816at_nat R2))) (= (@ (@ member4080735728053443344at_nat (@ (@ produc7536900900485677911at_nat (@ (@ cons_s6881495754146722583at_nat X) Xs)) (@ (@ cons_s6881495754146722583at_nat Y) Ys))) _let_1) (or (and (@ (@ member4080735728053443344at_nat (@ (@ produc7536900900485677911at_nat Xs) Ys)) _let_1) (= X Y)) (and (@ (@ member8757157785044589968at_nat (@ (@ produc2922128104949294807at_nat X) Y)) R2) (= Xs Ys)))))) (forall ((Xs list_int) (X int)) (=> (@ distinct_int Xs) (@ distinct_int (@ (@ remove1_int X) Xs)))) (forall ((I nat) (Xs list_c) (Ys list_int)) (let ((_let_1 (@ ord_less_nat I))) (=> (@ _let_1 (@ size_size_list_c Xs)) (=> (@ _let_1 (@ size_size_list_int Ys)) (= (@ (@ nth_Pr6754503292924006292_c_int (@ (@ zip_c_int Xs) Ys)) I) (@ (@ product_Pair_c_int (@ (@ nth_c Xs) I)) (@ (@ nth_int Ys) I))))))) (forall ((A2 int) (C int) (B2 int)) (=> (@ (@ ord_less_eq_int A2) C) (@ (@ ord_less_eq_int (@ (@ inf_inf_int A2) B2)) C))) (forall ((A set_nat) (B set_nat) (C2 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produc6575502325842934193n_assn) (Xs2 list_P8527749157015355191n_assn) (Y2 nat) (Ys5 list_nat)) (let ((_let_1 (@ P (@ (@ cons_P2971678138204555879n_assn X3) Xs2)))) (=> (not (@ (@ R X3) Y2)) (=> (@ _let_1 Ys5) (@ _let_1 (@ (@ cons_nat Y2) Ys5)))))) (@ (@ P Xs) Ys)))))) (= ord_less_assn (lambda ((A3 assn) (B3 assn)) (and (@ (@ ord_less_eq_assn A3) B3) (not (= A3 B3))))) (forall ((X assn) (A2 assn) (B2 assn)) (let ((_let_1 (@ ord_less_eq_assn X))) (=> (@ _let_1 A2) (=> (@ _let_1 B2) (@ _let_1 (@ (@ inf_inf_assn A2) B2)))))) _let_44 _let_43 (forall ((L list_P1934797086108301456_d_nat)) (not (forall ((L1 list_d) (L22 list_nat)) (let ((_let_1 (@ size_size_list_nat L22))) (=> (= L (@ (@ zip_d_nat L1) L22)) (=> (= (@ size_size_list_d L1) _let_1) (not (= (@ size_s8550281435913984804_d_nat L) _let_1)))))))) (forall ((X int) (Xs list_int)) (=> (not (@ (@ member_int X) (@ set_int2 Xs))) (= (@ (@ removeAll_int X) Xs) Xs))) (forall ((X assn) (Y assn)) (let ((_let_1 (@ inf_inf_assn X))) (let ((_let_2 (@ _let_1 Y))) (= (@ _let_1 _let_2) _let_2)))) (forall ((Xs list_c) (Ys list_d) (P (-> list_c list_d Bool))) (=> (= (@ size_size_list_c Xs) (@ size_size_list_d Ys)) (=> (@ (@ P nil_c) nil_d) (=> (forall ((X3 c) (Xs2 list_c) (Y2 d) (Ys5 list_d)) (=> (= (@ size_size_list_c Xs2) (@ size_size_list_d Ys5)) (=> (@ (@ P Xs2) Ys5) (@ (@ P (@ (@ cons_c X3) Xs2)) (@ (@ cons_d Y2) Ys5))))) (@ (@ P Xs) Ys))))) (forall ((X int) (Xs list_int)) (let ((_let_1 (@ size_size_list_int Xs))) (let ((_let_2 (@ size_size_list_int (@ (@ remove1_int X) Xs)))) (let ((_let_3 (@ (@ member_int X) (@ set_int2 Xs)))) (and (=> (not _let_3) (= _let_2 _let_1)) (=> _let_3 (= _let_2 (@ (@ minus_minus_nat _let_1) one_one_nat)))))))) (forall ((L list_d) (P (-> d Bool))) (= (forall ((X2 d)) (=> (@ (@ member_d X2) (@ set_d2 L)) (@ P X2))) (forall ((I4 nat)) (=> (@ (@ ord_less_nat I4) (@ size_size_list_d L)) (@ P (@ (@ nth_d L) I4)))))) (forall ((A2 int) (B set_int) (C2 set_int)) (let ((_let_1 (@ insert_int2 A2))) (= (@ (@ sup_sup_set_int (@ _let_1 B)) C2) (@ _let_1 (@ (@ sup_sup_set_int B) C2))))) (forall ((X c) (L list_c) (I nat) (Y c)) (let ((_let_1 (@ member_c X))) (=> (@ _let_1 (@ set_c2 (@ (@ (@ list_update_c L) I) Y))) (=> (=> (@ (@ ord_less_nat I) (@ size_size_list_c L)) (not (= X Y))) (@ _let_1 (@ set_c2 L)))))) (forall ((H2 produc3658429121746597890et_nat)) (not (@ (@ rep_assn bot_bot_assn) H2))) (= ord_less_eq_set_int (lambda ((A5 set_int) (B7 set_int)) (forall ((T2 int)) (let ((_let_1 (@ member_int T2))) (=> (@ _let_1 A5) (@ _let_1 B7)))))) (forall ((X assn)) (= (@ (@ inf_inf_assn X) bot_bot_assn) bot_bot_assn)) (forall ((I nat) (Xs list_nat)) (= (@ (@ (@ slice_nat I) I) Xs) nil_nat)) _let_42 (forall ((A2 product_prod_nat_nat) (A set_Pr1261947904930325089at_nat) (B set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ insert8211810215607154385at_nat A2))) (= (@ (@ inf_in2572325071724192079at_nat (@ _let_1 A)) (@ _let_1 B)) (@ _let_1 (@ (@ inf_in2572325071724192079at_nat A) B))))) (forall ((A2 int) (X int) (B2 int)) (=> (@ (@ ord_less_int A2) X) (@ (@ ord_less_int (@ (@ inf_inf_int A2) B2)) X))) (forall ((A2 nat) (B2 nat) (N nat)) (let ((_let_1 (@ ord_less_eq_nat zero_zero_nat))) (=> (@ _let_1 A2) (=> (@ _let_1 B2) (=> (@ (@ ord_less_nat zero_zero_nat) N) (= (@ (@ ord_less_eq_nat (@ (@ power_power_nat A2) N)) (@ (@ power_power_nat B2) N)) (@ (@ ord_less_eq_nat A2) B2))))))) (forall ((A2 Bool) (A set_o) (B set_o)) (let ((_let_1 (@ inf_inf_set_o A))) (let ((_let_2 (@ insert_o2 A2))) (=> (@ (@ member_o A2) A) (= (@ _let_1 (@ _let_2 B)) (@ _let_2 (@ _let_1 B))))))) (forall ((Xs list_c) (Ys list_nat)) (=> (= (@ size_size_list_c Xs) (@ size_size_list_nat Ys)) (= (@ (@ zip_c_nat (@ rev_c Xs)) (@ rev_nat Ys)) (@ rev_Pr3799340238495523993_c_nat (@ (@ zip_c_nat Xs) Ys))))) (forall ((P (-> nat Bool)) (Q (-> nat Bool))) (=> (forall ((X3 nat)) (= (@ P X3) (@ Q X3))) (= (@ collect_nat P) (@ collect_nat Q)))) (forall ((A2 code_integer) (F4 (-> nat code_integer)) (B2 nat) (C nat)) (=> (@ (@ ord_le3102999989581377725nteger A2) (@ F4 B2)) (=> (@ (@ ord_less_nat B2) C) (=> (forall ((X3 nat) (Y2 nat)) (=> (@ (@ ord_less_nat X3) Y2) (@ (@ ord_le6747313008572928689nteger (@ F4 X3)) (@ F4 Y2)))) (@ (@ ord_le6747313008572928689nteger A2) (@ F4 C)))))) (forall ((A2 code_integer) (B2 code_integer)) (let ((_let_1 (@ ord_le3102999989581377725nteger zero_z3403309356797280102nteger))) (=> (@ _let_1 A2) (=> (@ _let_1 B2) (@ _let_1 (@ (@ plus_p5714425477246183910nteger A2) B2)))))) (forall ((A2 (-> produc3658429121746597890et_nat Bool)) (B2 produc3658429121746597890et_nat) (S set_Pr3286484037609594932et_nat) (P (-> (-> produc3658429121746597890et_nat Bool) produc3658429121746597890et_nat Bool))) (let ((_let_1 (@ (@ member1996754912294343701et_nat (@ (@ produc5001842942810119800et_nat A2) B2)) S))) (=> _let_1 (=> (=> _let_1 (@ (@ P A2) B2)) (exists ((A4 (-> produc3658429121746597890et_nat Bool)) (B4 produc3658429121746597890et_nat)) (and (@ (@ P A4) B4) (@ (@ member1996754912294343701et_nat (@ (@ produc5001842942810119800et_nat A4) B4)) S))))))) (forall ((A2 rat) (N nat)) (let ((_let_1 (@ (@ power_power_rat A2) N))) (= (@ (@ times_times_rat _let_1) A2) (@ (@ times_times_rat A2) _let_1)))) (forall ((Ns list_int) (R2 set_Pr958786334691620121nt_int)) (= (@ (@ member6698963635872716290st_int (@ (@ produc364263696895485585st_int nil_int) Ns)) (@ lenlex_int R2)) (not (= Ns nil_int)))) (forall ((X code_integer) (Y code_integer)) (=> (@ (@ ord_le6747313008572928689nteger (@ (@ plus_p5714425477246183910nteger X) Y)) zero_z3403309356797280102nteger) (or (@ (@ ord_le6747313008572928689nteger Y) zero_z3403309356797280102nteger) (@ (@ ord_le6747313008572928689nteger X) zero_z3403309356797280102nteger)))) (forall ((I nat) (I3 set_nat) (Xs list_c) (A (-> c d assn)) (Xsi list_d)) (=> (not (@ (@ member_nat I) I3)) (=> (@ (@ ord_less_nat I) (@ size_size_list_c Xs)) (= (@ (@ (@ (@ vEBT_L824818263033719201sn_c_d (@ (@ insert_nat2 I) I3)) A) Xs) Xsi) (@ (@ times_times_assn (@ (@ A (@ (@ nth_c Xs) I)) (@ (@ nth_d Xsi) I))) (@ (@ (@ (@ vEBT_L824818263033719201sn_c_d I3) A) Xs) Xsi)))))) (= ord_less_eq_num (lambda ((X2 num) (Y5 num)) (or (= X2 Y5) (@ (@ ord_less_num X2) Y5)))) (forall ((I nat) (Xs list_int) (J nat)) (let ((_let_1 (@ nth_int Xs))) (let ((_let_2 (@ size_size_list_int Xs))) (=> (@ (@ ord_less_nat I) _let_2) (=> (@ (@ ord_less_nat J) _let_2) (= (@ distinct_int (@ (@ (@ list_update_int (@ (@ (@ list_update_int Xs) I) (@ _let_1 J))) J) (@ _let_1 I))) (@ distinct_int Xs))))))) (forall ((T code_integer)) (exists ((Z4 code_integer)) (forall ((X7 code_integer)) (=> (@ (@ ord_le6747313008572928689nteger X7) Z4) (not (= X7 T)))))) (forall ((A2 produc3843707927480180839at_nat) (B2 produc3843707927480180839at_nat) (R2 set_Pr5564308138774400199at_nat)) (= (@ field_2862844103579723188at_nat (@ (@ insert398606708087465655at_nat (@ (@ produc2335810615602371415at_nat A2) B2)) R2)) (@ (@ sup_su5525570899277871387at_nat (@ (@ 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list_i8448526496819171953e_term) (Ys list_P5707943133018811711nt_int)) (=> (@ (@ member7034335876925520548nt_int (@ (@ produc4305682042979456191nt_int X) Y)) (@ set_Pr1633835384712236856nt_int (@ (@ zip_in8766932505889695135nt_int Xs) Ys))) (@ (@ member5262025264175285858nt_int Y) (@ set_Pr2470121279949933262nt_int Ys)))) (forall ((X list_P6011104703257516679at_nat) (Y list_P6011104703257516679at_nat)) (= (@ (@ (@ if_lis9186351972506106189at_nat true) X) Y) X)) (forall ((A2 nat) (C nat) (B2 nat)) (=> (@ (@ ord_less_nat A2) C) (@ (@ ord_less_nat (@ (@ ord_min_nat A2) B2)) C))) (forall ((A2 set_Pr1261947904930325089at_nat)) (= (@ (@ inf_in2572325071724192079at_nat A2) A2) A2)) (forall ((T num)) (exists ((Z4 num)) (forall ((X7 num)) (=> (@ (@ ord_less_num X7) Z4) (not (= X7 T)))))) (forall ((B2 nat) (A2 nat) (C nat)) (let ((_let_1 (@ plus_plus_nat B2))) (let ((_let_2 (@ plus_plus_nat A2))) (= (@ _let_1 (@ _let_2 C)) (@ _let_2 (@ _let_1 C)))))) (@ fun_re2478310338295953701at_nat (@ (@ produc9060074326276436823at_nat fun_max_strict) fun_max_weak)) (forall ((N nat) (X int) (Xs list_int)) (= (@ (@ enumerate_int N) (@ (@ cons_int X) Xs)) (@ (@ cons_P2335045147070616083at_int (@ (@ product_Pair_nat_int N) X)) (@ (@ enumerate_int (@ suc N)) Xs)))) (forall ((S set_nat) (T3 set_nat)) (= (@ (@ inf_inf_set_nat (@ (@ sup_sup_set_nat S) T3)) S) S)) (forall ((P (-> list_nat list_nat Bool)) (W1 list_nat) (W2 list_nat)) (=> (@ (@ P nil_nat) nil_nat) (=> (forall ((E2 nat) (W12 list_nat) (W22 list_nat)) (=> (@ (@ P W12) W22) (@ (@ P (@ (@ cons_nat E2) W12)) W22))) (=> (forall ((E2 nat) (W13 list_nat) (W23 list_nat)) (let ((_let_1 (@ P W13))) (=> (@ _let_1 W23) (@ _let_1 (@ (@ cons_nat E2) W23))))) (@ (@ P W1) W2))))) (forall ((X nat) (Xs list_nat)) (let ((_let_1 (@ (@ cons_nat X) nil_nat))) (= (= _let_1 (@ rev_nat Xs)) (= _let_1 Xs)))) (forall ((X int) (Y int)) (@ (@ ord_less_eq_int zero_zero_int) (@ (@ plus_plus_int (@ (@ times_times_int X) X)) (@ (@ times_times_int Y) Y)))) (forall ((S set_nat) (T3 set_nat)) (= (@ (@ inf_inf_set_nat S) (@ (@ sup_sup_set_nat S) T3)) S)) (forall ((X int) (A set_int) (B set_int)) (let ((_let_1 (@ (@ insert_int2 X) bot_bot_set_int))) (let ((_let_2 (= A _let_1))) (let ((_let_3 (= B _let_1))) (= (= _let_1 (@ (@ sup_sup_set_int A) B)) (or (and _let_3 (= A bot_bot_set_int)) (and _let_3 _let_2) (and _let_2 (= B bot_bot_set_int)))))))) (forall ((X num) (Y num)) (= (not (@ (@ ord_less_num X) Y)) (or (@ (@ ord_less_num Y) X) (= X Y)))) _let_41 (forall ((A2 nat)) (= (not (= A2 zero_zero_nat)) (@ (@ ord_less_nat zero_zero_nat) A2))) (@ (@ _let_40 (@ produc27273713700761075at_nat (lambda ((X2 nat) (Y5 nat) (__flatten_var_0 product_prod_nat_nat)) (@ (@ produc2626176000494625587at_nat (lambda ((U4 nat) (V4 nat)) (@ (@ product_Pair_nat_nat (@ (@ plus_plus_nat X2) V4)) (@ (@ plus_plus_nat Y5) U4)))) __flatten_var_0)))) (@ produc27273713700761075at_nat (lambda ((X2 nat) (Y5 nat) (__flatten_var_0 product_prod_nat_nat)) (@ (@ produc2626176000494625587at_nat (lambda ((U4 nat) (V4 nat)) (@ (@ product_Pair_nat_nat (@ (@ plus_plus_nat X2) V4)) (@ (@ plus_plus_nat Y5) U4)))) __flatten_var_0)))) (forall ((X produc6575502325842934193n_assn) (Xs list_P8527749157015355191n_assn)) (= (@ set_Pr1139785259514867910n_assn (@ (@ insert3246601298802261197n_assn X) Xs)) (@ (@ insert5290817439147925377n_assn X) (@ set_Pr1139785259514867910n_assn Xs)))) (forall ((P (-> list_int Bool)) (Xs list_int)) (=> (@ P nil_int) (=> (forall ((X3 int)) (@ P (@ (@ cons_int X3) nil_int))) (=> (forall ((X12 int) (X23 int) (Xs2 list_int)) (=> (@ P Xs2) (@ P (@ (@ cons_int X12) (@ (@ cons_int X23) Xs2))))) (@ P Xs))))) (forall ((A2 code_integer) (F4 (-> code_integer code_integer)) (B2 code_integer) (C code_integer)) (let ((_let_1 (@ ord_le6747313008572928689nteger A2))) (=> (@ _let_1 (@ F4 B2)) (=> (@ (@ ord_le6747313008572928689nteger B2) C) (=> (forall ((X3 code_integer) (Y2 code_integer)) (=> (@ (@ ord_le6747313008572928689nteger X3) Y2) (@ (@ ord_le6747313008572928689nteger (@ F4 X3)) (@ F4 Y2)))) (@ _let_1 (@ F4 C))))))) (forall ((I nat) (M2 nat) (N nat)) (let ((_let_1 (@ power_power_nat I))) (=> (@ (@ ord_less_nat zero_zero_nat) I) (=> (@ (@ ord_less_nat (@ _let_1 M2)) (@ _let_1 N)) (@ (@ ord_less_nat M2) N))))) (forall ((A2 nat) (B2 nat) (A set_nat)) (let ((_let_1 (@ member_nat A2))) (=> (@ _let_1 (@ (@ insert_nat2 B2) A)) (=> (not (= A2 B2)) (@ _let_1 A))))) (forall ((X c) (Xs list_c)) (let ((_let_1 (@ size_size_list_c Xs))) (let ((_let_2 (@ size_size_list_c (@ (@ remove1_c X) Xs)))) (let ((_let_3 (@ (@ member_c X) (@ set_c2 Xs)))) (and (=> _let_3 (= _let_2 (@ (@ minus_minus_nat _let_1) one_one_nat))) (=> (not _let_3) (= _let_2 _let_1))))))) (forall ((M2 nat) (N nat)) (=> (@ (@ ord_less_nat M2) N) (exists ((K nat)) (= N (@ suc (@ (@ plus_plus_nat M2) K)))))) (@ distin4809818325527169450n_assn nil_Pr5671120429643327159n_assn) (forall ((A2 filter_nat) (B2 filter_nat)) (= (not (@ (@ ord_less_filter_nat A2) B2)) (or (not (@ (@ ord_le2510731241096832064er_nat A2) B2)) (= A2 B2)))) (forall ((K3 int)) (=> (@ (@ ord_less_int zero_zero_int) K3) (exists ((N5 nat)) (and (= K3 (@ semiri1314217659103216013at_int N5)) (@ (@ ord_less_nat zero_zero_nat) N5))))) (forall ((M2 nat) (N nat)) (= (= (@ (@ ord_min_nat M2) N) M2) (@ (@ ord_less_eq_nat M2) N))) (forall ((A set_int) (B set_int) (X int)) (let ((_let_1 (@ (@ insert_int2 X) bot_bot_set_int))) (let ((_let_2 (= B _let_1))) (let ((_let_3 (= A _let_1))) (= (= (@ (@ sup_sup_set_int A) B) _let_1) (or (and _let_2 (= A bot_bot_set_int)) (and (= B bot_bot_set_int) _let_3) (and _let_3 _let_2))))))) (forall ((N nat) (Xs list_P6011104703257516679at_nat) (X product_prod_nat_nat)) (=> (@ (@ ord_less_nat N) (@ size_s5460976970255530739at_nat Xs)) (@ (@ member8440522571783428010at_nat X) (@ set_Pr5648618587558075414at_nat (@ (@ (@ list_u6180841689913720943at_nat Xs) N) X))))) (forall ((A set_o)) (= (@ (@ minus_minus_set_o A) A) bot_bot_set_o)) (forall ((B2 code_integer) (A2 code_integer) (C code_integer)) (let ((_let_1 (@ ord_le6747313008572928689nteger C))) (=> (@ (@ ord_le3102999989581377725nteger B2) A2) (=> (@ _let_1 B2) (@ _let_1 A2))))) (forall ((K3 nat) (M2 nat) (N nat)) (let ((_let_1 (@ times_times_nat K3))) (=> (@ (@ ord_less_nat zero_zero_nat) K3) (= (= (@ _let_1 M2) (@ _let_1 N)) (= M2 N))))) (= ord_less_nat (lambda ((X2 nat) (Y5 nat)) (and (not (= X2 Y5)) (@ (@ ord_less_eq_nat X2) Y5)))) (forall ((Xs list_P7985473006766602707_nat_o) (A set_Pr4532377907799695533_nat_o) (X (-> produc3658429121746597890et_nat Bool)) (I nat)) (=> (@ (@ ord_le2965882846123202637_nat_o (@ set_Pr400311997697478754_nat_o Xs)) A) (=> (@ (@ member6576561426505652726_nat_o X) A) (@ (@ ord_le2965882846123202637_nat_o (@ set_Pr400311997697478754_nat_o (@ (@ (@ list_u6943956310655620667_nat_o Xs) I) X))) A)))) (= ord_less_eq_set_nat (lambda ((X2 set_nat) (Y5 set_nat)) (= (@ (@ inf_inf_set_nat X2) Y5) X2))) (forall ((N nat) (K3 nat)) (let ((_let_1 (@ binomial (@ (@ 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(let ((_let_1 (@ list_e1087220904399170805n_assn P))) (= (@ _let_1 (@ (@ cons_P2971678138204555879n_assn X) Xs)) (or (@ _let_1 Xs) (@ P X))))) (forall ((A2 rat) (B2 rat) (C rat) (D2 rat)) (=> (@ (@ ord_less_rat A2) B2) (=> (@ (@ ord_less_eq_rat C) D2) (@ (@ ord_less_rat (@ (@ plus_plus_rat A2) C)) (@ (@ plus_plus_rat B2) D2))))) (forall ((A2 nat)) (not (@ (@ ord_less_nat A2) bot_bot_nat))) (forall ((X nat) (Y nat) (Z nat)) (let ((_let_1 (@ ord_less_eq_nat X))) (=> (@ _let_1 Y) (=> (@ (@ ord_less_eq_nat Y) Z) (@ _let_1 Z))))) (forall ((X set_Pr4329608150637261639at_nat) (Y set_Pr4329608150637261639at_nat)) (let ((_let_1 (@ sup_su5525570899277871387at_nat X))) (let ((_let_2 (@ _let_1 Y))) (= (@ _let_1 _let_2) _let_2)))) (forall ((N nat)) (=> (@ (@ ord_less_nat (@ suc zero_zero_nat)) N) (@ (@ ord_less_nat N) (@ bit_se2002935070580805687sk_nat N)))) (forall ((A2 int) (B2 int) (R2 set_Pr958786334691620121nt_int)) (= (@ field_int (@ (@ insert5033312907999012233nt_int (@ (@ product_Pair_int_int A2) B2)) R2)) (@ (@ sup_sup_set_int (@ (@ insert_int2 A2) (@ (@ insert_int2 B2) bot_bot_set_int))) (@ field_int R2)))) (forall ((I nat) (J nat)) (= (@ size_size_list_nat (@ (@ upt I) J)) (@ (@ minus_minus_nat J) I))) (forall ((P (-> int Bool)) (X nat) (Y nat)) (= (@ P (@ semiri1314217659103216013at_int (@ (@ minus_minus_nat X) Y))) (and (=> (@ (@ ord_less_nat X) Y) (@ P zero_zero_int)) (=> (@ (@ ord_less_eq_nat Y) X) (@ P (@ (@ minus_minus_int (@ semiri1314217659103216013at_int X)) (@ semiri1314217659103216013at_int Y))))))) (forall ((A2 int) (B2 int) (C int)) (=> (@ (@ ord_less_int zero_zero_int) A2) (=> (@ (@ ord_less_eq_int B2) C) (@ (@ ord_less_int B2) (@ (@ plus_plus_int A2) C))))) (forall ((A2 int) (C int) (B2 int)) (=> (@ (@ ord_less_int A2) C) (@ (@ ord_less_int (@ (@ inf_inf_int A2) B2)) C))) (forall ((N assn) (M2 assn)) (let ((_let_1 (@ (@ ord_min_assn M2) N))) (= (@ (@ ord_less_eq_assn N) _let_1) (= _let_1 N)))) (forall ((X int) (S set_int)) (=> (@ (@ member_int X) S) (not (= S bot_bot_set_int)))) (forall ((Xs list_nat) (Xs4 list_nat) (Xsi list_P8527749157015355191n_assn) (Xsi2 list_P8527749157015355191n_assn) (A (-> nat produc6575502325842934193n_assn assn)) (A6 (-> nat produc6575502325842934193n_assn assn))) (=> (= Xs Xs4) (=> (= Xsi Xsi2) (=> (forall ((X3 nat) (Xi produc6575502325842934193n_assn)) (=> (@ (@ member_nat X3) (@ set_nat2 Xs4)) (=> (@ (@ member7957490590177025114n_assn Xi) (@ set_Pr1139785259514867910n_assn Xsi2)) (= (@ (@ A X3) Xi) (@ (@ A6 X3) Xi))))) (= (@ (@ (@ vEBT_L9083610150846024284n_assn A) Xs) Xsi) (@ (@ (@ vEBT_L9083610150846024284n_assn A6) Xs4) Xsi2)))))) (forall ((B2 int) (A2 int) (C int)) (let ((_let_1 (@ plus_plus_int B2))) (let ((_let_2 (@ plus_plus_int A2))) (= (@ _let_1 (@ _let_2 C)) (@ _let_2 (@ _let_1 C)))))) (forall ((A2 code_integer) (B2 code_integer) (C code_integer)) (= (@ (@ times_3573771949741848930nteger (@ (@ plus_p5714425477246183910nteger A2) B2)) C) (@ (@ plus_p5714425477246183910nteger (@ (@ times_3573771949741848930nteger A2) C)) (@ (@ times_3573771949741848930nteger B2) C)))) (forall ((X nat)) (@ (@ total_on_nat (@ (@ insert_nat2 X) bot_bot_set_nat)) (@ (@ insert8211810215607154385at_nat (@ (@ product_Pair_nat_nat X) X)) bot_bo2099793752762293965at_nat))) (= ord_le3146513528884898305at_nat (lambda ((X2 set_Pr1261947904930325089at_nat) (Y5 set_Pr1261947904930325089at_nat)) (= (@ (@ inf_in2572325071724192079at_nat X2) Y5) X2))) (forall ((A2 nat) (B2 nat) (C nat)) (=> (@ (@ ord_less_eq_nat A2) B2) (@ (@ ord_less_eq_nat C) (@ (@ minus_minus_nat (@ (@ plus_plus_nat B2) C)) A2)))) (forall ((Xs list_d) (Ys list_d)) (=> (not (= (@ size_size_list_d Xs) (@ size_size_list_d Ys))) (not (= Xs Ys)))) (forall ((A2 filter_nat) (B2 filter_nat) (C filter_nat)) (let ((_let_1 (@ ord_le2510731241096832064er_nat A2))) (=> (@ _let_1 (@ (@ inf_inf_filter_nat B2) C)) (not (=> (@ _let_1 B2) (not (@ _let_1 C))))))) (forall ((A2 nat) (A set_nat) (B set_nat)) (let ((_let_1 (@ inf_inf_set_nat A))) (=> (not (@ (@ member_nat A2) A)) (= (@ _let_1 (@ (@ insert_nat2 A2) B)) (@ _let_1 B))))) (forall ((A2 set_Pr4329608150637261639at_nat)) (= (not (= A2 bot_bo228742789529271731at_nat)) (@ (@ ord_le2604355607129572851at_nat bot_bo228742789529271731at_nat) A2))) (forall ((X4 set_Pr1261947904930325089at_nat)) (=> (@ finite6177210948735845034at_nat X4) (@ (@ member8757157785044589968at_nat (@ (@ produc2922128104949294807at_nat bot_bo2099793752762293965at_nat) X4)) fun_max_weak))) _let_36 (forall ((Xs list_int)) (= (= (@ set_int2 Xs) bot_bot_set_int) (= Xs nil_int))) (forall ((F4 (-> nat nat int))) (= (@ (@ (@ zipf_nat_nat_int F4) nil_nat) nil_nat) nil_int)) (forall ((X nat) (Xs list_nat)) (let ((_let_1 (@ member_nat X))) (=> (@ _let_1 (@ set_nat2 (@ butlast_nat Xs))) (@ _let_1 (@ set_nat2 Xs))))) (forall ((A2 code_integer) (B2 code_integer)) (let ((_let_1 (@ ord_le6747313008572928689nteger zero_z3403309356797280102nteger))) (=> (@ _let_1 (@ (@ times_3573771949741848930nteger A2) B2)) (=> (@ _let_1 A2) (@ _let_1 B2))))) (forall ((Z nat) (X nat) (Y nat)) (let ((_let_1 (@ ord_less_nat Z))) (= (@ _let_1 (@ (@ ord_min_nat X) Y)) (and (@ _let_1 X) (@ _let_1 Y))))) (forall ((X int) (Y int)) (=> (@ (@ ord_less_int X) Y) (not (@ (@ ord_less_int Y) X)))) (forall ((L list_d) (I nat) (X d)) (= (@ (@ (@ list_update_d (@ butlast_d L)) I) X) (@ butlast_d (@ (@ (@ list_update_d L) I) X)))) _let_35 (forall ((S set_Pr1261947904930325089at_nat) (T3 set_Pr1261947904930325089at_nat)) (= (@ (@ inf_in2572325071724192079at_nat (@ (@ sup_su6327502436637775413at_nat S) T3)) S) S)) (forall ((A2 (-> produc3658429121746597890et_nat Bool)) (A set_Pr4532377907799695533_nat_o) (B set_Pr4532377907799695533_nat_o)) (let ((_let_1 (@ inf_in1906310914598751387_nat_o A))) (let ((_let_2 (@ insert5175938949040314269_nat_o A2))) (=> (@ (@ member6576561426505652726_nat_o A2) A) (= (@ _let_1 (@ _let_2 B)) (@ _let_2 (@ _let_1 B))))))) (forall ((P (-> list_int list_int Bool)) (R (-> int int Bool)) (Xs list_int) (Ys list_int)) (=> (forall ((Xs2 list_int)) (@ (@ P Xs2) nil_int)) (=> (forall ((X_1 list_int)) (@ (@ P nil_int) X_1)) (=> (forall ((X3 int) (Xs2 list_int) (Y2 int) (Ys5 list_int)) (let ((_let_1 (@ (@ cons_int Y2) Ys5))) (=> (@ (@ R X3) Y2) (=> (@ (@ P Xs2) _let_1) (@ (@ P (@ (@ cons_int X3) Xs2)) _let_1))))) (=> (forall ((X3 int) (Xs2 list_int) (Y2 int) (Ys5 list_int)) (let ((_let_1 (@ P (@ (@ cons_int X3) Xs2)))) (=> (not (@ (@ R X3) Y2)) (=> (@ _let_1 Ys5) (@ _let_1 (@ (@ cons_int Y2) Ys5)))))) (@ (@ P Xs) Ys)))))) (forall ((P assn)) (= (@ (@ times_times_assn P) bot_bot_assn) bot_bot_assn)) (forall ((Xs list_P8527749157015355191n_assn) (Ys list_P8527749157015355191n_assn)) (= (@ set_Pr1139785259514867910n_assn (@ (@ union_944050417204428971n_assn Xs) Ys)) (@ (@ sup_su1735938885662425829n_assn (@ set_Pr1139785259514867910n_assn Xs)) (@ set_Pr1139785259514867910n_assn Ys)))) (forall ((B set_Pr4329608150637261639at_nat)) (= (@ (@ inf_in7913087082777306421at_nat bot_bo228742789529271731at_nat) B) bot_bo228742789529271731at_nat)) (forall ((X nat) (Y nat)) (=> (not (@ (@ ord_less_nat X) Y)) (@ (@ ord_less_eq_nat Y) X))) (forall ((H2 heap_e7401611519738050253t_unit) (As2 set_nat) (As3 set_nat)) (let ((_let_1 (@ produc7507926704131184380et_nat H2))) (= (@ in_range (@ _let_1 (@ (@ sup_sup_set_nat As2) As3))) (and (@ in_range (@ _let_1 As2)) (@ in_range (@ _let_1 As3)))))) (forall ((A2 rat) (C rat) (B2 rat)) (=> (@ (@ ord_less_eq_rat (@ (@ plus_plus_rat A2) C)) (@ (@ plus_plus_rat B2) C)) (@ (@ ord_less_eq_rat A2) B2))) (forall ((X nat) (Xs list_nat) (N nat)) (= (@ (@ nth_nat (@ (@ cons_nat X) Xs)) (@ suc N)) (@ (@ nth_nat Xs) N))) (forall ((A set_nat)) (not (@ (@ ord_less_set_nat A) bot_bot_set_nat))) (forall ((C int) (A2 int) (B2 int)) (let ((_let_1 (@ times_times_int C))) (=> (@ (@ ord_less_int C) zero_zero_int) (= (@ (@ ord_less_eq_int (@ _let_1 A2)) (@ _let_1 B2)) (@ (@ ord_less_eq_int B2) A2))))) (= ord_less_set_nat (lambda ((A3 set_nat) (B3 set_nat)) (and (not (= A3 B3)) (= A3 (@ (@ inf_inf_set_nat A3) B3))))) (forall ((A2 nat) (F4 (-> assn nat)) (B2 assn) (C assn)) (=> (= A2 (@ F4 B2)) (=> (@ (@ ord_less_eq_assn B2) C) (=> (forall ((X3 assn) (Y2 assn)) (=> (@ (@ ord_less_eq_assn X3) Y2) (@ (@ ord_less_eq_nat (@ F4 X3)) (@ F4 Y2)))) (@ (@ ord_less_eq_nat A2) (@ F4 C)))))) (forall ((N nat) (Xs list_c) (P (-> c Bool))) (=> (@ (@ ord_less_nat N) (@ size_size_list_c Xs)) (=> (forall ((X3 c)) (=> (@ (@ member_c X3) (@ set_c2 Xs)) (@ P X3))) (@ P (@ (@ nth_c Xs) N))))) (forall ((M2 nat) (N nat)) (=> (@ (@ ord_less_eq_nat M2) N) (= (@ (@ ord_less_nat N) (@ suc M2)) (= N M2)))) (forall ((C nat) (A2 nat) (B2 nat)) (let ((_let_1 (@ plus_plus_nat C))) (= (@ (@ ord_less_nat (@ _let_1 A2)) (@ _let_1 B2)) (@ (@ ord_less_nat A2) B2)))) (forall ((P (-> list_nat list_int Bool)) (W1 list_nat) (W2 list_int)) (=> (@ (@ P nil_nat) nil_int) (=> (forall ((E2 nat) (W12 list_nat) (W22 list_int)) (=> (@ (@ P W12) W22) (@ (@ P (@ (@ cons_nat E2) W12)) W22))) (=> (forall ((E2 int) (W13 list_nat) (W23 list_int)) (let ((_let_1 (@ P W13))) (=> (@ _let_1 W23) (@ _let_1 (@ (@ cons_int E2) W23))))) (@ (@ P W1) W2))))) (forall ((X num) (Y num)) (= (not (= X Y)) (or (@ (@ ord_less_num X) Y) (@ (@ ord_less_num Y) X)))) (forall ((Xs list_nat) (Ys list_c)) (= (@ size_s385972143775086793_nat_c (@ (@ product_nat_c Xs) Ys)) (@ (@ times_times_nat (@ size_size_list_nat Xs)) (@ size_size_list_c Ys)))) (forall ((R2 set_Product_prod_o_o) (S3 set_Product_prod_o_o)) (=> (@ (@ ord_le192195778054999463od_o_o R2) S3) (@ (@ ord_less_eq_set_o (@ field_o R2)) (@ field_o S3)))) (forall ((As2 set_nat) (As3 set_nat) (H2 heap_e7401611519738050253t_unit)) (let ((_let_1 (@ produc7507926704131184380et_nat H2))) (=> (@ (@ ord_less_eq_set_nat As2) As3) (=> (@ in_range (@ _let_1 As3)) (@ in_range (@ _let_1 As2)))))) (forall ((A2 produc3843707927480180839at_nat) (B2 produc3843707927480180839at_nat)) (=> (= (@ (@ insert9069300056098147895at_nat A2) bot_bo228742789529271731at_nat) (@ (@ insert9069300056098147895at_nat B2) bot_bo228742789529271731at_nat)) (= A2 B2))) (forall ((B2 code_integer) (A2 code_integer)) (=> (@ (@ ord_le6747313008572928689nteger B2) A2) (@ (@ ord_le3102999989581377725nteger B2) A2))) (forall ((A2 code_integer) (B2 code_integer)) (= (= A2 (@ (@ plus_p5714425477246183910nteger B2) A2)) (= B2 zero_z3403309356797280102nteger))) (forall ((A assn)) (@ (@ entails A) (@ (@ times_times_assn A) top_top_assn))) (forall ((A2 set_nat) (X set_nat) (B2 set_nat)) (=> (@ (@ ord_less_set_nat A2) X) (@ (@ ord_less_set_nat (@ (@ inf_inf_set_nat A2) B2)) X))) (forall ((A2 code_integer) (B2 code_integer)) (= (@ (@ ord_le3102999989581377725nteger zero_z3403309356797280102nteger) (@ (@ minus_8373710615458151222nteger A2) B2)) (@ (@ ord_le3102999989581377725nteger B2) A2))) (forall ((X set_Pr1261947904930325089at_nat) (Y set_Pr1261947904930325089at_nat)) (= (@ (@ sup_su6327502436637775413at_nat X) (@ (@ inf_in2572325071724192079at_nat X) Y)) X)) (forall ((X nat) (A2 nat) (B2 nat)) (let ((_let_1 (@ ord_less_eq_nat X))) (=> (@ _let_1 (@ (@ inf_inf_nat A2) B2)) (not (=> (@ _let_1 A2) (not (@ _let_1 B2))))))) (forall ((A2 (-> produc3658429121746597890et_nat Bool)) (B2 produc3658429121746597890et_nat) (A7 (-> produc3658429121746597890et_nat Bool)) (B6 produc3658429121746597890et_nat)) (=> (= (@ (@ produc5001842942810119800et_nat A2) B2) (@ (@ produc5001842942810119800et_nat A7) B6)) (not (=> (= A2 A7) (not (= B2 B6)))))) (forall ((A set_Pr4329608150637261639at_nat)) (not (@ (@ ord_le2604355607129572851at_nat A) bot_bo228742789529271731at_nat))) (forall ((X int) (A set_int) (B set_int)) (let ((_let_1 (@ minus_minus_set_int A))) (=> (not (@ (@ member_int X) A)) (= (@ _let_1 (@ (@ insert_int2 X) B)) (@ _let_1 B))))) (forall ((A2 assn) (B2 assn) (C assn)) (let ((_let_1 (@ times_times_assn A2))) (= (@ (@ times_times_assn (@ _let_1 B2)) C) (@ _let_1 (@ (@ times_times_assn B2) C))))) (forall ((Xs list_c) (I nat) (X c) (Ys list_d) (Y d)) (= (@ (@ zip_c_d (@ (@ (@ list_update_c Xs) I) X)) (@ (@ (@ list_update_d Ys) I) Y)) (@ (@ (@ list_u8616212508820402326od_c_d (@ (@ zip_c_d Xs) Ys)) I) (@ (@ product_Pair_c_d X) Y)))) (forall ((L list_nat) (I nat) (J nat)) (let ((_let_1 (@ nth_nat L))) (let ((_let_2 (@ size_size_list_nat L))) (=> (@ distinct_nat L) (=> (@ (@ sorted_wrt_nat ord_less_eq_nat) L) (=> (@ (@ ord_less_nat I) _let_2) (=> (@ (@ ord_less_nat J) _let_2) (= (@ (@ ord_less_eq_nat (@ _let_1 I)) (@ _let_1 J)) (@ (@ ord_less_eq_nat I) J))))))))) (forall ((C set_nat) (B2 set_nat) (A2 set_nat)) (let ((_let_1 (@ ord_less_set_nat C))) (=> (@ _let_1 B2) (@ _let_1 (@ (@ sup_sup_set_nat A2) B2))))) (forall ((Y int) (X int)) (@ (@ ord_less_eq_int Y) (@ (@ sup_sup_int X) Y))) (forall ((I rat) (J rat) (K3 rat) (L rat)) (=> (and (@ (@ ord_less_eq_rat K3) L) (= I J)) (@ (@ ord_less_eq_rat (@ (@ plus_plus_rat I) K3)) (@ (@ plus_plus_rat J) L)))) (forall ((F4 (-> produc2285326912895808259nt_int Bool)) (A2 (-> produc8551481072490612790e_term option6357759511663192854e_term)) (B2 product_prod_int_int)) (=> (@ (@ (@ produc730925184835016917_int_o F4) A2) B2) (@ F4 (@ (@ produc5700946648718959541nt_int A2) B2)))) (= (@ nat_set_encode bot_bot_set_nat) zero_zero_nat) _let_34 (forall ((A2 nat) (B2 nat) (R2 set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ member8440522571783428010at_nat (@ (@ product_Pair_nat_nat A2) B2)))) (=> (@ _let_1 (@ transi6264000038957366511cl_nat R2)) (=> (not (@ _let_1 R2)) (not (forall ((C4 nat)) (=> (@ (@ member8440522571783428010at_nat (@ (@ product_Pair_nat_nat A2) C4)) (@ transi6264000038957366511cl_nat R2)) (not (@ (@ member8440522571783428010at_nat (@ (@ product_Pair_nat_nat C4) B2)) R2))))))))) (forall ((I set_Pr1261947904930325089at_nat) (J set_Pr1261947904930325089at_nat) (R set_Pr4329608150637261639at_nat)) (=> (@ (@ member8757157785044589968at_nat (@ (@ produc2922128104949294807at_nat I) J)) R) (@ (@ 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(B2 rat)) (=> (@ (@ ord_less_eq_rat A2) zero_zero_rat) (=> (@ (@ ord_less_eq_rat B2) zero_zero_rat) (@ (@ ord_less_eq_rat zero_zero_rat) (@ (@ times_times_rat A2) B2))))) (forall ((B set_o) (A2 Bool)) (@ (@ ord_less_eq_set_o B) (@ (@ insert_o2 A2) B))) (forall ((N nat) (I nat)) (=> (@ (@ ord_less_nat zero_zero_nat) N) (@ (@ ord_less_nat (@ (@ minus_minus_nat N) (@ suc I))) N))) (forall ((Y nat) (X nat)) (=> (not (@ (@ ord_less_eq_nat Y) X)) (@ (@ ord_less_nat X) Y))) (forall ((A2 int) (A set_int)) (let ((_let_1 (@ insert_int2 A2))) (= (@ _let_1 (@ (@ minus_minus_set_int A) (@ _let_1 bot_bot_set_int))) (@ _let_1 A)))) (= ord_less_int (lambda ((A3 int) (B3 int)) (@ (@ ord_less_int (@ (@ minus_minus_int A3) B3)) zero_zero_int))) (forall ((Y list_nat)) (=> (not (= Y nil_nat)) (not (forall ((X212 nat) (X223 list_nat)) (not (= Y (@ (@ cons_nat X212) X223))))))) (forall ((B2 rat) (A2 rat) (C rat)) (let ((_let_1 (@ times_times_rat C))) (=> (@ (@ ord_less_eq_rat B2) A2) (=> (@ (@ 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(@ (@ list_update_c Xs) I) X)) (@ (@ (@ list_update_c Ys) I) Y)) (@ (@ (@ list_u8616212504517173525od_c_c (@ (@ zip_c_c Xs) Ys)) I) (@ (@ product_Pair_c_c X) Y)))) (forall ((A set_o) (B set_o)) (= (= (@ (@ minus_minus_set_o A) B) bot_bot_set_o) (@ (@ ord_less_eq_set_o A) B))) (forall ((C (-> produc3658429121746597890et_nat Bool)) (A set_Pr4532377907799695533_nat_o) (B set_Pr4532377907799695533_nat_o)) (let ((_let_1 (@ member6576561426505652726_nat_o C))) (=> (@ _let_1 A) (=> (@ _let_1 B) (@ _let_1 (@ (@ inf_in1906310914598751387_nat_o A) B)))))) (forall ((N nat)) (=> (@ (@ ord_less_nat zero_zero_nat) N) (= (@ num_of_nat (@ (@ plus_plus_nat N) N)) (@ bit0 (@ num_of_nat N))))) (= is_singleton_o (lambda ((A5 set_o)) (exists ((X2 Bool)) (= A5 (@ (@ insert_o2 X2) bot_bot_set_o))))) (= (lambda ((Y4 rat) (Z2 rat)) (= Y4 Z2)) (lambda ((A3 rat) (B3 rat)) (= (@ (@ minus_minus_rat A3) B3) zero_zero_rat))) (forall ((A2 produc3843707927480180839at_nat) (A set_Pr4329608150637261639at_nat) (B2 produc3843707927480180839at_nat) (B set_Pr4329608150637261639at_nat)) (let ((_let_1 (= A2 B2))) (=> (not (@ (@ member8757157785044589968at_nat A2) A)) (=> (not (@ (@ member8757157785044589968at_nat B2) B)) (= (= (@ (@ insert9069300056098147895at_nat A2) A) (@ (@ insert9069300056098147895at_nat B2) B)) (and (=> (not _let_1) (exists ((C3 set_Pr4329608150637261639at_nat)) (and (= B (@ (@ insert9069300056098147895at_nat A2) C3)) (not (@ (@ member8757157785044589968at_nat A2) C3)) (not (@ (@ member8757157785044589968at_nat B2) C3)) (= A (@ (@ insert9069300056098147895at_nat B2) C3))))) (=> _let_1 (= A B)))))))) (forall ((N nat)) (not (@ (@ ord_less_nat N) zero_zero_nat))) (forall ((C code_integer) (A2 code_integer) (B2 code_integer)) (let ((_let_1 (@ times_3573771949741848930nteger C))) (=> (@ (@ ord_le6747313008572928689nteger zero_z3403309356797280102nteger) C) (= (@ (@ ord_le3102999989581377725nteger (@ _let_1 A2)) (@ _let_1 B2)) (@ (@ ord_le3102999989581377725nteger A2) B2))))) (forall ((X nat)) (@ (@ ord_less_eq_nat X) X)) (forall ((M2 set_nat) (N set_nat)) (let ((_let_1 (@ (@ ord_min_set_nat M2) N))) (= (@ (@ ord_less_eq_set_nat M2) _let_1) (= _let_1 M2)))) (forall ((X int) (Y int)) (= (@ (@ ord_less_eq_int (@ (@ plus_plus_int (@ (@ times_times_int X) X)) (@ (@ times_times_int Y) Y))) zero_zero_int) (and (= X zero_zero_int) (= Y zero_zero_int)))) (forall ((A2 code_integer) (B2 code_integer) (C code_integer) (D2 code_integer)) (=> (= (@ (@ minus_8373710615458151222nteger A2) B2) (@ (@ minus_8373710615458151222nteger C) D2)) (= (@ (@ ord_le6747313008572928689nteger A2) B2) (@ (@ ord_le6747313008572928689nteger C) D2)))) (forall ((P assn) (A (-> int int assn)) (Xs list_int) (I nat) (Xsi list_int) (I3 set_nat) (F assn) (Q assn)) (let ((_let_1 (@ entails P))) (=> (@ _let_1 (@ (@ times_times_assn (@ (@ times_times_assn (@ (@ A (@ (@ nth_int Xs) I)) (@ (@ nth_int Xsi) I))) (@ (@ (@ (@ vEBT_L8888932350013902202nt_int (@ (@ minus_minus_set_nat I3) (@ (@ insert_nat2 I) bot_bot_set_nat))) A) Xs) Xsi))) F)) (=> (@ (@ ord_less_nat I) (@ size_size_list_int Xs)) (=> (@ (@ member_nat I) I3) (=> (@ (@ entails (@ (@ times_times_assn (@ (@ (@ (@ vEBT_L8888932350013902202nt_int I3) A) Xs) Xsi)) F)) Q) (@ _let_1 Q))))))) (forall ((M2 nat) (N nat)) (=> (@ (@ ord_less_nat zero_zero_nat) M2) (= (@ (@ dvd_dvd_nat (@ (@ times_times_nat M2) N)) M2) (= N one_one_nat)))) (forall ((R (-> (-> produc3658429121746597890et_nat Bool) (-> produc3658429121746597890et_nat Bool) Bool)) (S set_Pr4532377907799695533_nat_o) (X (-> produc3658429121746597890et_nat Bool)) (Y (-> produc3658429121746597890et_nat Bool))) (=> (@ (@ pairwi2432143822833250616_nat_o R) S) (=> (@ (@ member6576561426505652726_nat_o X) S) (=> (@ (@ member6576561426505652726_nat_o Y) S) (=> (not (= X Y)) (@ (@ R X) Y)))))) (forall ((A2 nat) (F4 (-> int nat)) (B2 int) (C int)) (=> (= A2 (@ F4 B2)) (=> (@ (@ ord_less_eq_int B2) C) (=> (forall ((X3 int) (Y2 int)) (=> (@ (@ ord_less_eq_int X3) Y2) (@ (@ ord_less_eq_nat (@ F4 X3)) (@ F4 Y2)))) (@ (@ ord_less_eq_nat A2) (@ F4 C)))))) (forall ((B2 assn) (A2 assn) (C assn)) (let ((_let_1 (@ times_times_assn B2))) (let ((_let_2 (@ times_times_assn A2))) (= (@ _let_1 (@ _let_2 C)) (@ _let_2 (@ _let_1 C)))))) (forall ((I int) (J int) (K3 int) (L int)) (=> (and (@ (@ ord_less_int K3) L) (@ (@ ord_less_eq_int I) J)) (@ (@ ord_less_int (@ (@ plus_plus_int I) K3)) (@ (@ plus_plus_int J) L)))) (forall ((A2 int) (A set_int)) (=> (@ (@ member_int A2) A) (= (@ (@ insert_int2 A2) A) A))) (not (@ (@ ord_le3102999989581377725nteger one_one_Code_integer) zero_z3403309356797280102nteger)) (forall ((A2 rat) (B2 rat) (C rat)) (let ((_let_1 (@ plus_plus_rat A2))) (= (= (@ _let_1 B2) (@ _let_1 C)) (= B2 C)))) (forall ((X nat) (Xs list_nat) (Y int) (Ys list_int)) (= (@ (@ zip_nat_int (@ (@ cons_nat X) Xs)) (@ (@ cons_int Y) Ys)) (@ (@ cons_P2335045147070616083at_int (@ (@ product_Pair_nat_int X) Y)) (@ (@ zip_nat_int Xs) Ys)))) (forall ((C set_nat) (B2 set_nat) (A2 set_nat)) (let ((_let_1 (@ ord_less_eq_set_nat C))) (=> (@ _let_1 B2) (@ _let_1 (@ (@ sup_sup_set_nat A2) B2))))) (forall ((X int) (Y int)) (=> (@ (@ ord_less_int X) Y) (not (@ (@ ord_less_int Y) X)))) (forall ((A set_int) (B set_int) (B2 int)) (let ((_let_1 (@ ord_less_eq_set_int A))) (=> (@ _let_1 B) (@ _let_1 (@ (@ insert_int2 B2) B))))) (forall ((X set_Pr1261947904930325089at_nat)) (= (@ (@ inf_in2572325071724192079at_nat X) bot_bo2099793752762293965at_nat) bot_bo2099793752762293965at_nat)) (forall ((A2 product_prod_nat_nat) (A set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ insert8211810215607154385at_nat A2))) (=> (@ (@ member8440522571783428010at_nat A2) A) (= (@ _let_1 (@ (@ minus_1356011639430497352at_nat A) (@ _let_1 bot_bo2099793752762293965at_nat))) A)))) (forall ((A2 nat) (B2 nat)) (= (@ (@ minus_minus_nat A2) (@ (@ plus_plus_nat A2) B2)) zero_zero_nat)) _let_31 (forall ((N nat) (P (-> d nat Bool))) (=> (forall ((I5 nat)) (=> (@ (@ ord_less_nat I5) N) (exists ((Li2 d)) (@ (@ P Li2) I5)))) (not (forall ((L2 list_d)) (=> (= (@ size_size_list_d L2) N) (not (forall ((I6 nat)) (=> (@ (@ ord_less_nat I6) N) (@ (@ P (@ (@ nth_d L2) I6)) I6))))))))) (forall ((From nat) (To nat) (Xs list_int)) (=> (@ (@ ord_less_eq_nat From) To) (=> (@ (@ ord_less_eq_nat To) (@ size_size_list_int Xs)) (= (@ size_size_list_int (@ (@ (@ slice_int From) To) Xs)) (@ (@ minus_minus_nat To) From))))) (forall ((A2 list_d) (B2 list_nat) (A7 list_d) (B6 list_nat)) (=> (= (@ size_size_list_d A2) (@ size_size_list_nat B2)) (=> (= (@ size_size_list_d A7) (@ size_size_list_nat B6)) (=> (= (@ (@ zip_d_nat A2) B2) (@ (@ zip_d_nat A7) B6)) (and (= A2 A7) (= B2 B6)))))) (forall ((N nat) (Xs list_c)) (= (= (@ suc N) (@ size_size_list_c Xs)) (exists ((Y5 c) (Ys3 list_c)) (and (= (@ size_size_list_c Ys3) N) (= Xs (@ (@ cons_c Y5) Ys3)))))) (forall ((A set_Pr4532377907799695533_nat_o) (B set_Pr4532377907799695533_nat_o)) (=> (forall ((X3 (-> produc3658429121746597890et_nat Bool))) (let ((_let_1 (@ member6576561426505652726_nat_o X3))) (=> (@ _let_1 A) (@ _let_1 B)))) (@ (@ ord_le2965882846123202637_nat_o A) B))) (forall ((C product_prod_nat_nat) (A set_Pr1261947904930325089at_nat) (B set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ member8440522571783428010at_nat C))) (= (@ _let_1 (@ (@ inf_in2572325071724192079at_nat A) B)) (and (@ _let_1 B) (@ _let_1 A))))) (forall ((T nat)) (exists ((Z4 nat)) (forall ((X7 nat)) (=> (@ (@ ord_less_nat X7) Z4) (not (= X7 T)))))) (forall ((X num) (Y num) (Z num)) (= (@ (@ ord_less_num (@ (@ ord_min_num X) Y)) Z) (or (@ (@ ord_less_num Y) Z) (@ (@ ord_less_num X) Z)))) (= ord_less_num (lambda ((A3 num) (B3 num)) (and (= A3 (@ (@ ord_min_num A3) B3)) (not (= A3 B3))))) (forall ((A2 produc3843707927480180839at_nat) (C2 set_Pr4329608150637261639at_nat) (B set_Pr4329608150637261639at_nat)) (=> (not (@ (@ member8757157785044589968at_nat A2) C2)) (= (@ (@ inf_in7913087082777306421at_nat (@ (@ insert9069300056098147895at_nat A2) B)) C2) (@ (@ inf_in7913087082777306421at_nat B) C2)))) (forall ((A2 set_Pr1261947904930325089at_nat)) (@ (@ ord_le3146513528884898305at_nat bot_bo2099793752762293965at_nat) A2)) (= upto_aux (lambda ((I4 int) (J2 int) (__flatten_var_0 list_int)) (@ (@ append_int (@ (@ upto I4) J2)) __flatten_var_0))) (forall ((X set_Pr4329608150637261639at_nat) (Y set_Pr4329608150637261639at_nat) (Z set_Pr4329608150637261639at_nat)) (let ((_let_1 (@ sup_su5525570899277871387at_nat X))) (let ((_let_2 (@ sup_su5525570899277871387at_nat Y))) (= (@ _let_1 (@ _let_2 Z)) (@ _let_2 (@ _let_1 Z)))))) (forall ((M2 nat) (N nat)) (let ((_let_1 (@ upt M2))) (= (@ butlast_nat (@ _let_1 N)) (@ _let_1 (@ (@ minus_minus_nat N) one_one_nat))))) (forall ((K3 nat) (P (-> nat nat Bool))) (= (forall ((I4 nat)) (=> (@ (@ ord_less_nat I4) K3) (exists ((X8 nat)) (@ (@ P I4) X8)))) (exists ((Xs3 list_nat)) (and (forall ((I4 nat)) (=> (@ (@ ord_less_nat I4) K3) (@ (@ P I4) (@ (@ nth_nat Xs3) I4)))) (= (@ size_size_list_nat Xs3) K3))))) _let_30 (forall ((A2 multis2468970476368604999at_nat) (C multis2468970476368604999at_nat) (B2 multis2468970476368604999at_nat)) (= (@ (@ minus_4286766774447292334at_nat (@ (@ plus_p7104986032573967614at_nat A2) C)) (@ (@ plus_p7104986032573967614at_nat B2) C)) (@ (@ minus_4286766774447292334at_nat A2) B2))) (forall ((A set_Pr4329608150637261639at_nat)) (@ (@ ord_le1268244103169919719at_nat bot_bo228742789529271731at_nat) A)) (forall ((A set_Pr4329608150637261639at_nat)) (= (@ (@ minus_3314409938677909166at_nat A) A) bot_bo228742789529271731at_nat)) (forall ((Y produc3843707927480180839at_nat) (X produc3843707927480180839at_nat) (Xs list_P5464809261938338413at_nat)) (let ((_let_1 (@ member8757157785044589968at_nat Y))) (=> (@ _let_1 (@ set_Pr3765526544606949372at_nat (@ (@ cons_P3940603068885512221at_nat X) Xs))) (or (@ _let_1 (@ set_Pr3765526544606949372at_nat Xs)) (= Y X))))) (forall ((C nat) (A2 nat) (B2 nat)) (=> (@ (@ ord_less_eq_nat C) zero_zero_nat) (=> (@ (@ ord_less_eq_nat A2) B2) (@ (@ ord_less_eq_nat (@ (@ plus_plus_nat A2) C)) B2)))) (forall ((A2 code_integer) (B2 code_integer)) (=> (= (@ (@ times_3573771949741848930nteger A2) B2) zero_z3403309356797280102nteger) (or (= A2 zero_z3403309356797280102nteger) (= B2 zero_z3403309356797280102nteger)))) (forall ((N nat) (P (-> nat nat Bool))) (=> (forall ((I5 nat)) (=> (@ (@ ord_less_nat I5) N) (exists ((Li2 nat)) (@ (@ P Li2) I5)))) (not (forall ((L2 list_nat)) (=> (= (@ size_size_list_nat L2) N) (not (forall ((I6 nat)) (=> (@ (@ ord_less_nat I6) N) (@ (@ P (@ (@ nth_nat L2) I6)) I6))))))))) (forall ((A2 rat) (B2 rat) (C rat)) (let ((_let_1 (@ plus_plus_rat A2))) (= (@ (@ plus_plus_rat (@ _let_1 B2)) C) (@ _let_1 (@ (@ plus_plus_rat B2) C))))) (forall ((C int) (A2 int) (B2 int)) (let ((_let_1 (@ times_times_int C))) (= (@ (@ ord_less_int (@ _let_1 A2)) (@ _let_1 B2)) (or (and (@ (@ ord_less_int C) zero_zero_int) (@ (@ ord_less_int B2) A2)) (and (@ (@ ord_less_int zero_zero_int) C) (@ (@ ord_less_int A2) B2)))))) (forall ((A2 nat) (B2 nat)) (= (@ (@ ord_less_eq_nat A2) (@ (@ plus_plus_nat B2) A2)) (@ (@ ord_less_eq_nat zero_zero_nat) B2))) (forall ((A2 code_integer) (C code_integer) (B2 code_integer)) (= (@ (@ ord_le6747313008572928689nteger A2) (@ (@ minus_8373710615458151222nteger C) B2)) (@ (@ ord_le6747313008572928689nteger (@ (@ plus_p5714425477246183910nteger A2) B2)) C))) (forall ((A2 filter_nat) (X filter_nat) (B2 filter_nat)) (=> (@ (@ ord_le2510731241096832064er_nat A2) X) (=> (@ (@ ord_le2510731241096832064er_nat B2) X) (@ (@ ord_le2510731241096832064er_nat (@ (@ sup_sup_filter_nat A2) B2)) X)))) (forall ((X assn) (Y assn)) (= (@ (@ (@ if_assn true) X) Y) X)) (forall ((N nat) (X nat) (Xs list_nat)) (= (@ (@ enumerate_nat N) (@ (@ cons_nat X) Xs)) (@ (@ cons_P6512896166579812791at_nat (@ (@ product_Pair_nat_nat N) X)) (@ (@ enumerate_nat (@ suc N)) Xs)))) _let_29 (forall ((Y filter_nat) (X filter_nat)) (=> (@ (@ ord_le2510731241096832064er_nat Y) X) (= (@ (@ inf_inf_filter_nat X) Y) Y))) (forall ((I nat) (M2 nat) (N nat)) (let ((_let_1 (@ power_power_nat I))) (=> (@ (@ dvd_dvd_nat (@ _let_1 M2)) (@ _let_1 N)) (=> (@ (@ ord_less_nat one_one_nat) I) (@ (@ ord_less_eq_nat M2) N))))) (forall ((N nat)) (= (@ (@ enumer9200277086812776726n_assn N) nil_Pr5671120429643327159n_assn) nil_Pr680377793251149648n_assn)) (forall ((B set_Pr1261947904930325089at_nat)) (= (@ (@ sup_su6327502436637775413at_nat bot_bo2099793752762293965at_nat) B) B)) (forall ((C rat) (B2 rat) (A2 rat)) (let ((_let_1 (@ ord_less_eq_rat B2))) (=> (@ (@ ord_less_eq_rat zero_zero_rat) C) (=> (@ _let_1 A2) (@ _let_1 (@ (@ plus_plus_rat A2) C)))))) (forall ((Xs list_nat) (Ys list_int) (Zs list_c) (Ws list_c) (P (-> list_nat list_int list_c list_c Bool))) (let ((_let_1 (@ size_size_list_c Zs))) (let ((_let_2 (@ size_size_list_int Ys))) (=> (= (@ size_size_list_nat Xs) _let_2) (=> (= _let_2 _let_1) (=> (= _let_1 (@ size_size_list_c Ws)) (=> (@ (@ (@ (@ P nil_nat) nil_int) nil_c) nil_c) (=> (forall ((X3 nat) (Xs2 list_nat) (Y2 int) (Ys5 list_int) (Z4 c) (Zs2 list_c) (W3 c) (Ws2 list_c)) (let ((_let_1 (@ size_size_list_c Zs2))) (let ((_let_2 (@ size_size_list_int Ys5))) (=> (= (@ size_size_list_nat Xs2) _let_2) (=> (= _let_2 _let_1) (=> (= _let_1 (@ size_size_list_c Ws2)) (=> (@ (@ (@ (@ P Xs2) Ys5) Zs2) Ws2) (@ (@ (@ (@ P (@ (@ cons_nat X3) Xs2)) (@ (@ cons_int Y2) Ys5)) (@ (@ cons_c Z4) Zs2)) (@ (@ cons_c W3) Ws2))))))))) (@ (@ (@ (@ P Xs) Ys) Zs) Ws))))))))) (forall ((X int)) (= (= zero_zero_int X) (= X zero_zero_int))) (forall ((A2 set_Pr1261947904930325089at_nat) (B2 set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ (@ insert9069300056098147895at_nat (@ (@ produc2922128104949294807at_nat A2) B2)) bot_bo228742789529271731at_nat))) (= (@ transi2703068831062848130at_nat _let_1) _let_1))) (forall ((A2 set_int) (B2 set_int)) (= (= (@ (@ sup_sup_set_int A2) B2) bot_bot_set_int) (and (= A2 bot_bot_set_int) (= B2 bot_bot_set_int)))) (forall ((X int) (Xs list_int)) (=> (@ (@ member_int X) (@ set_int2 Xs)) (@ (@ ord_less_nat zero_zero_nat) (@ size_size_list_int Xs)))) (forall ((B2 nat) (A2 nat)) (=> (@ (@ ord_less_nat B2) A2) (not (@ (@ ord_less_nat A2) B2)))) (forall ((S set_Pr4329608150637261639at_nat) (T3 set_Pr4329608150637261639at_nat)) (= (@ (@ inf_in7913087082777306421at_nat (@ (@ sup_su5525570899277871387at_nat S) T3)) T3) T3)) (forall ((A2 rat) (B2 rat) (C rat)) (let ((_let_1 (@ plus_plus_rat C))) (=> (@ (@ ord_less_rat A2) B2) (@ (@ ord_less_rat (@ _let_1 A2)) (@ _let_1 B2))))) (forall ((X c) (Xs list_c) (Y c) (Ys list_c) (R2 set_Product_prod_c_c)) (let ((_let_1 (@ lex_c R2))) (= (@ (@ member7012247553653173456list_c (@ (@ produc5515445818230282391list_c (@ (@ cons_c X) Xs)) (@ (@ cons_c Y) Ys))) _let_1) (or (and (@ (@ member5074992359041316560od_c_c (@ (@ product_Pair_c_c X) Y)) R2) (= (@ size_size_list_c Xs) (@ size_size_list_c Ys))) (and (= X Y) (@ (@ member7012247553653173456list_c (@ (@ produc5515445818230282391list_c Xs) Ys)) _let_1)))))) (forall ((Xs list_c) (Ys list_c) (Zs list_d) (P (-> list_c list_c list_d Bool))) (let ((_let_1 (@ size_size_list_c Ys))) (=> (= (@ size_size_list_c Xs) _let_1) (=> (= _let_1 (@ size_size_list_d Zs)) (=> (@ (@ (@ P nil_c) nil_c) nil_d) (=> (forall ((X3 c) (Xs2 list_c) (Y2 c) (Ys5 list_c) (Z4 d) (Zs2 list_d)) (let ((_let_1 (@ size_size_list_c Ys5))) (=> (= (@ size_size_list_c Xs2) _let_1) (=> (= _let_1 (@ size_size_list_d Zs2)) (=> (@ (@ (@ P Xs2) Ys5) Zs2) (@ (@ (@ P (@ (@ cons_c X3) Xs2)) (@ (@ cons_c Y2) Ys5)) (@ (@ cons_d Z4) Zs2))))))) (@ (@ (@ P Xs) Ys) Zs))))))) (forall ((A2 int) (C int)) (= (@ (@ ord_less_eq_int (@ (@ times_times_int A2) C)) C) (and (=> (@ (@ ord_less_int zero_zero_int) C) (@ (@ ord_less_eq_int A2) one_one_int)) (=> (@ (@ ord_less_int C) zero_zero_int) (@ (@ ord_less_eq_int one_one_int) A2))))) (forall ((P (-> nat nat assn)) (L list_nat)) (= (@ (@ (@ vEBT_L8301102511889123557at_nat P) L) nil_nat) (@ pure_assn (= L nil_nat)))) (forall ((X rat)) (= (@ (@ minus_minus_rat (@ (@ times_times_rat X) X)) one_one_rat) (@ (@ times_times_rat (@ (@ plus_plus_rat X) one_one_rat)) (@ (@ minus_minus_rat X) one_one_rat)))) (forall ((P (-> int Bool)) (X int) (Xs list_int)) (let ((_let_1 (@ list_ex_int P))) (= (@ _let_1 (@ (@ cons_int X) Xs)) (or (@ _let_1 Xs) (@ P X))))) (forall ((P (-> produc1908205239877642774nteger Bool)) (X produc1908205239877642774nteger)) (=> (forall ((A4 (-> produc6241069584506657477e_term option6357759511663192854e_term)) (B4 code_integer) (C4 code_integer)) (@ P (@ (@ produc8603105652947943368nteger A4) (@ (@ produc1086072967326762835nteger B4) C4)))) (@ P X))) (forall ((X (-> nat nat assn)) (Xa list_nat) (Xb list_nat) (Y assn)) (let ((_let_1 (not (= Y bot_bot_assn)))) (let ((_let_2 (= Xa nil_nat))) (let ((_let_3 (= Xb nil_nat))) (=> (= (@ (@ (@ vEBT_L8301102511889123557at_nat X) Xa) Xb) Y) (=> (=> _let_2 (=> _let_3 (not (= Y one_one_assn)))) (=> (forall ((A4 nat) (As list_nat)) (=> (= Xa (@ (@ cons_nat A4) As)) (forall ((C4 nat) (Cs2 list_nat)) (=> (= Xb (@ (@ cons_nat C4) Cs2)) (not (= Y (@ (@ times_times_assn (@ (@ X A4) C4)) (@ (@ (@ vEBT_L8301102511889123557at_nat X) As) Cs2)))))))) (=> (=> (exists ((V3 nat) (Va list_nat)) (= Xa (@ (@ cons_nat V3) Va))) (=> _let_3 _let_1)) (not (=> _let_2 (=> (exists ((V3 nat) (Va list_nat)) (= Xb (@ (@ cons_nat V3) Va))) _let_1))))))))))) (forall ((P (-> produc6575502325842934193n_assn produc6575502325842934193n_assn Bool))) (@ (@ sorted3986126766855596574n_assn P) nil_Pr5671120429643327159n_assn)) (forall ((S set_Pr4329608150637261639at_nat) (T3 set_Pr4329608150637261639at_nat)) (= (@ (@ inf_in7913087082777306421at_nat S) (@ (@ sup_su5525570899277871387at_nat S) T3)) S)) (forall ((X set_o) (Y set_o)) (= (= bot_bot_set_o (@ (@ sup_sup_set_o X) Y)) (and (= Y bot_bot_set_o) (= X bot_bot_set_o)))) (forall ((M2 nat)) (=> (@ (@ ord_less_nat zero_zero_nat) M2) (@ finite_finite_nat (@ collect_nat (lambda ((D5 nat)) (@ (@ dvd_dvd_nat D5) M2)))))) _let_28 (forall ((C code_integer) (A2 code_integer) (B2 code_integer)) (let ((_let_1 (@ plus_p5714425477246183910nteger C))) (=> (@ (@ ord_le6747313008572928689nteger (@ _let_1 A2)) (@ _let_1 B2)) (@ (@ ord_le6747313008572928689nteger A2) B2)))) (forall ((Xs list_c) (Ys list_nat) (R2 set_Pr6903500605879609269_c_nat)) (=> (@ (@ member6184937725913850668st_nat (@ (@ produc6126748735280710287st_nat Xs) Ys)) (@ listrel_c_nat R2)) (= (@ size_size_list_c Xs) (@ size_size_list_nat Ys)))) (forall ((A2 code_integer) (B2 code_integer) (C code_integer)) (let ((_let_1 (@ times_3573771949741848930nteger C))) (=> (@ (@ ord_le6747313008572928689nteger A2) B2) (=> (@ (@ ord_le6747313008572928689nteger zero_z3403309356797280102nteger) C) (@ (@ ord_le6747313008572928689nteger (@ _let_1 A2)) (@ _let_1 B2)))))) (forall ((X assn)) (= (@ (@ inf_inf_assn X) X) X)) (forall ((I nat) (Xs list_nat) (X nat)) (=> (@ (@ ord_less_nat I) (@ size_size_list_nat Xs)) (= (= (@ (@ (@ list_update_nat Xs) I) X) Xs) (= (@ (@ nth_nat Xs) I) X)))) (forall ((Xs list_assn) (Ys list_assn)) (= (= nil_Pr5671120429643327159n_assn (@ (@ zip_assn_assn Xs) Ys)) (or (= Xs nil_assn) (= Ys nil_assn)))) (forall ((X num) (Y num)) (=> (not (@ (@ ord_less_num X) Y)) (@ (@ ord_less_eq_num Y) X))) (forall ((X assn) (Y assn) (Z assn)) (let ((_let_1 (@ sup_sup_assn X))) (let ((_let_2 (@ sup_sup_assn Y))) (= (@ _let_1 (@ _let_2 Z)) (@ _let_2 (@ _let_1 Z)))))) (forall ((B2 code_integer) (A2 code_integer)) (=> (@ (@ ord_le6747313008572928689nteger B2) A2) (= (@ (@ ord_min_Code_integer A2) B2) B2))) (forall ((A2 int) (B2 int) (N nat)) (let ((_let_1 (@ ord_less_eq_int zero_zero_int))) (=> (@ _let_1 A2) (=> (@ _let_1 B2) (=> (@ (@ ord_less_nat zero_zero_nat) N) (= (@ (@ ord_less_eq_int (@ (@ power_power_int A2) N)) (@ (@ power_power_int B2) N)) (@ (@ ord_less_eq_int A2) B2))))))) (forall ((P (-> produc3843707927480180839at_nat Bool))) (= (= (@ collec6321179662152712658at_nat P) bot_bo228742789529271731at_nat) (= P bot_bo6829958733157050602_nat_o))) _let_27 (forall ((B2 code_integer) (A2 code_integer) (C code_integer)) (let ((_let_1 (@ times_3573771949741848930nteger C))) (=> (@ (@ ord_le3102999989581377725nteger B2) A2) (=> (@ (@ ord_le3102999989581377725nteger C) zero_z3403309356797280102nteger) (@ (@ ord_le3102999989581377725nteger (@ _let_1 A2)) (@ _let_1 B2)))))) (forall ((Y nat) (X nat)) (=> (not (@ (@ ord_less_nat Y) X)) (= (not (@ (@ ord_less_nat X) Y)) (= X Y)))) (forall ((K3 num) (N nat)) (= (@ (@ ord_less_nat (@ numeral_numeral_nat K3)) (@ suc N)) (@ (@ ord_less_nat (@ pred_numeral K3)) N))) (forall ((A2 nat) (B2 nat) (Xs list_nat)) (let ((_let_1 (@ member_nat A2))) (=> (not (= A2 B2)) (= (@ _let_1 (@ set_nat2 (@ (@ remove1_nat B2) Xs))) (@ _let_1 (@ set_nat2 Xs)))))) (forall ((X d) (Xs list_d)) (= (@ size_size_list_d (@ (@ cons_d X) Xs)) (@ suc (@ size_size_list_d Xs)))) (= insert_o2 (lambda ((A3 Bool) (__flatten_var_0 set_o)) (@ (@ sup_sup_set_o (@ (@ insert_o2 A3) bot_bot_set_o)) __flatten_var_0))) (forall ((P (-> int int Bool))) (@ (@ pairwise_int P) bot_bot_set_int)) (forall ((X list_P7985473006766602707_nat_o) (Y list_P7985473006766602707_nat_o)) (= (@ (@ (@ if_lis2904118647880296857_nat_o true) X) Y) X)) (forall ((A set_nat) (B set_nat)) (= (not (= (@ (@ minus_minus_set_nat A) B) A)) (not (= (@ (@ inf_inf_set_nat A) B) bot_bot_set_nat)))) (forall ((Y int) (X int)) (=> (@ (@ ord_less_eq_int Y) X) (= (@ (@ sup_sup_int X) Y) X))) (forall ((A set_nat) (B set_nat) (C2 set_nat)) (let ((_let_1 (@ inf_inf_set_nat A))) (= (@ _let_1 (@ (@ sup_sup_set_nat B) C2)) (@ (@ sup_sup_set_nat (@ _let_1 B)) (@ _let_1 C2))))) (forall ((Xs list_nat) (B set_nat)) (= (@ (@ ord_less_eq_set_nat (@ set_nat2 Xs)) B) (forall ((X2 nat)) (let ((_let_1 (@ member_nat X2))) (=> (@ _let_1 (@ set_nat2 Xs)) (@ _let_1 B)))))) (forall ((Xs list_c) (Ys list_int) (X c)) (=> (= (@ size_size_list_c Xs) (@ size_size_list_int Ys)) (=> (@ (@ member_c X) (@ set_c2 Xs)) (not (forall ((Y2 int)) (not (@ (@ member4017226226790010994_c_int (@ (@ product_Pair_c_int X) Y2)) (@ set_Pr8441393049761402630_c_int (@ (@ zip_c_int Xs) Ys))))))))) (forall ((R2 (-> (-> produc3658429121746597890et_nat Bool) (-> produc3658429121746597890et_nat Bool) Bool)) (X (-> produc3658429121746597890et_nat Bool)) (S3 set_Pr4532377907799695533_nat_o)) (let ((_let_1 (@ pairwi2432143822833250616_nat_o R2))) (= (@ _let_1 (@ (@ insert5175938949040314269_nat_o X) S3)) (and (@ _let_1 S3) (forall ((Y5 (-> produc3658429121746597890et_nat Bool))) (=> (and (@ (@ member6576561426505652726_nat_o Y5) S3) (not (= Y5 X))) (and (@ (@ R2 X) Y5) (@ (@ R2 Y5) X)))))))) (forall ((X int) (Xs list_int) (Ys list_int) (R2 set_Pr958786334691620121nt_int)) (=> (@ (@ member6698963635872716290st_int (@ (@ produc364263696895485585st_int (@ (@ cons_int X) Xs)) Ys)) (@ listrel1_int R2)) (=> (forall ((Y2 int)) (=> (= Ys (@ (@ cons_int Y2) Xs)) (not (@ (@ member5262025264175285858nt_int (@ (@ product_Pair_int_int X) Y2)) R2)))) (not (forall ((Zs2 list_int)) (=> (= Ys (@ (@ cons_int X) Zs2)) (not (@ (@ member6698963635872716290st_int (@ (@ produc364263696895485585st_int Xs) Zs2)) (@ listrel1_int R2))))))))) (forall ((M2 nat) (N nat)) (let ((_let_1 (@ ord_less_nat M2))) (= (@ _let_1 (@ suc N)) (or (= M2 N) (@ _let_1 N))))) (forall ((A set_Pr1261947904930325089at_nat) (B set_Pr1261947904930325089at_nat)) (= (not (= (@ (@ minus_1356011639430497352at_nat A) B) A)) (not (= (@ (@ inf_in2572325071724192079at_nat A) B) bot_bo2099793752762293965at_nat)))) (= (@ quotient_of (@ uminus_uminus_rat one_one_rat)) (@ (@ product_Pair_int_int (@ uminus_uminus_int one_one_int)) one_one_int)) (forall ((A2 int) (C int)) (= (@ (@ ord_less_int (@ (@ times_times_int A2) C)) C) (and (=> (@ (@ ord_less_eq_int zero_zero_int) C) (@ (@ ord_less_int A2) one_one_int)) (=> (@ (@ ord_less_eq_int C) zero_zero_int) (@ (@ ord_less_int one_one_int) A2))))) (forall ((X nat) (Y nat)) (=> (@ (@ ord_less_nat X) Y) (not (= X Y)))) (@ _let_26 (@ (@ plus_plus_int one_one_int) one_one_int)) (forall ((B2 rat) (A2 rat)) (let ((_let_1 (@ ord_less_rat zero_zero_rat))) (=> (@ _let_1 (@ (@ times_times_rat B2) A2)) (=> (@ _let_1 A2) (@ _let_1 B2))))) (forall ((A set_Pr1261947904930325089at_nat) (B set_Pr1261947904930325089at_nat) (C2 set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ minus_1356011639430497352at_nat A))) (= (@ _let_1 (@ (@ sup_su6327502436637775413at_nat B) C2)) (@ (@ inf_in2572325071724192079at_nat (@ _let_1 B)) (@ _let_1 C2))))) (forall ((A set_nat) (B set_nat) (X nat) (C2 set_nat)) (let ((_let_1 (@ minus_minus_set_nat B))) (let ((_let_2 (@ ord_less_eq_set_nat A))) (= (@ _let_2 (@ _let_1 (@ (@ insert_nat2 X) C2))) (and (@ _let_2 (@ _let_1 C2)) (not (@ (@ member_nat X) A))))))) (forall ((X nat) (Y int) (Xs list_nat) (Ys list_int)) (=> (@ (@ member4262671552274231302at_int (@ (@ product_Pair_nat_int X) Y)) (@ set_Pr1470767568048878706at_int (@ (@ zip_nat_int Xs) Ys))) (not (=> (@ (@ member_nat X) (@ set_nat2 Xs)) (not (@ (@ member_int Y) (@ set_int2 Ys))))))) (forall ((Q6 nat) (R2 nat)) (= (@ unique6322359934112328802ux_nat (@ (@ product_Pair_nat_nat Q6) R2)) (= R2 zero_zero_nat))) (forall ((L list_nat)) (= (@ (@ sorted_wrt_nat ord_less_nat) L) (and (@ distinct_nat L) (@ (@ sorted_wrt_nat ord_less_eq_nat) L)))) (= ord_less_eq_int (lambda ((B3 int) (A3 int)) (= (@ (@ ord_min_int A3) B3) B3))) (forall ((X produc6575502325842934193n_assn) (Xs list_P8527749157015355191n_assn) (N nat)) (=> (not (@ (@ member7957490590177025114n_assn X) (@ set_Pr1139785259514867910n_assn Xs))) (=> (@ (@ ord_less_eq_nat N) (@ size_s6829681357464350627n_assn Xs)) (= (= (@ (@ nth_Pr1769885009046257848n_assn (@ (@ cons_P2971678138204555879n_assn X) Xs)) N) X) (= N zero_zero_nat))))) (forall ((H2 heap_e7401611519738050253t_unit) (As2 set_nat)) (=> (@ in_range (@ (@ produc7507926704131184380et_nat H2) As2)) (@ (@ (@ relH As2) H2) H2))) (forall ((A2 nat) (B2 nat)) (let ((_let_1 (@ ord_less_eq_nat zero_zero_nat))) (=> (@ _let_1 A2) (=> (@ _let_1 B2) (@ _let_1 (@ (@ plus_plus_nat A2) B2)))))) (forall ((A2 nat) (P (-> nat Bool))) (= (@ (@ member_nat A2) (@ collect_nat P)) (@ P A2))) (forall ((D int) (A set_int) (T int)) (=> (@ (@ ord_less_int zero_zero_int) D) (forall ((X7 int)) (let ((_let_1 (@ ord_less_int T))) (=> (forall ((Xa3 int)) (=> (@ (@ member_int Xa3) (@ (@ set_or1266510415728281911st_int one_one_int) D)) (forall ((Xb3 int)) (=> (@ (@ member_int Xb3) A) (not (= X7 (@ (@ minus_minus_int Xb3) Xa3))))))) (=> (@ _let_1 X7) (@ _let_1 (@ (@ plus_plus_int X7) D)))))))) (= code_bit_cut_integer (lambda ((K4 code_integer)) (@ (@ (@ if_Pro5737122678794959658eger_o (= K4 zero_z3403309356797280102nteger)) (@ (@ produc6677183202524767010eger_o zero_z3403309356797280102nteger) false)) (@ (@ produc9125791028180074456eger_o (lambda ((R4 code_integer) (S6 code_integer)) (@ (@ produc6677183202524767010eger_o (@ (@ (@ if_Code_integer (@ (@ ord_le6747313008572928689nteger zero_z3403309356797280102nteger) K4)) R4) (@ (@ minus_8373710615458151222nteger (@ uminus1351360451143612070nteger R4)) S6))) (= S6 one_one_Code_integer)))) (@ (@ code_divmod_abs K4) (@ numera6620942414471956472nteger (@ bit0 one))))))) (forall ((P6 assn) (Q6 assn) (M2 list_P8527749157015355191n_assn) (Ps2 assn) (Up2 assn) (Qs assn) (Uq2 assn) (F4 assn)) (let ((_let_1 (@ times_times_assn Qs))) (let ((_let_2 (@ times_times_assn Ps2))) (=> (@ (@ entails P6) Q6) (=> (@ (@ (@ (@ (@ (@ fi (@ (@ cons_P2971678138204555879n_assn (@ (@ produc118845697133431529n_assn P6) Q6)) M2)) (@ _let_2 Up2)) (@ _let_1 Uq2)) sln) sln) F4) (@ (@ (@ (@ (@ (@ fi M2) (@ _let_2 P6)) (@ _let_1 Q6)) Up2) Uq2) F4)))))) (forall ((T nat)) (exists ((Z4 nat)) (forall ((X7 nat)) (=> (@ (@ ord_less_nat X7) Z4) (not (@ (@ ord_less_nat T) X7)))))) (= bot_bo2099793752762293965at_nat (@ collec3392354462482085612at_nat bot_bo482883023278783056_nat_o)) (forall ((X nat) (Xs list_nat)) (= (@ distinct_nat (@ (@ insert_nat X) Xs)) (@ distinct_nat Xs))) (forall ((X produc5834231552977413017st_int)) (=> (forall ((P5 (-> int int Bool))) (not (= X (@ (@ produc8618682346314911123st_int P5) nil_int)))) (=> (forall ((P5 (-> int int Bool)) (X3 int)) (not (= X (@ (@ produc8618682346314911123st_int P5) (@ (@ cons_int X3) nil_int))))) (not (forall ((P5 (-> int int Bool)) (X3 int) (Y2 int) (Xs2 list_int)) (not (= X (@ (@ produc8618682346314911123st_int P5) (@ (@ cons_int X3) (@ (@ cons_int Y2) Xs2)))))))))) (forall ((B2 assn) (X assn) (A2 assn)) (=> (@ (@ ord_less_assn B2) X) (@ (@ ord_less_assn (@ (@ inf_inf_assn A2) B2)) X))) (forall ((A2 nat) (B2 nat) (C nat)) (=> (@ (@ ord_less_nat zero_zero_nat) A2) (=> (@ (@ ord_less_eq_nat B2) C) (@ (@ ord_less_nat B2) (@ (@ plus_plus_nat A2) C))))) (= (lambda ((Y4 list_c) (Z2 list_c)) (= Y4 Z2)) (lambda ((Xs3 list_c) (Ys3 list_c)) (and (forall ((I4 nat)) (=> (@ (@ ord_less_nat I4) (@ size_size_list_c Xs3)) (= (@ (@ nth_c Xs3) I4) (@ (@ nth_c Ys3) I4)))) (= (@ size_size_list_c Xs3) (@ size_size_list_c Ys3))))) (forall ((D int) (T int) (B set_int)) (=> (@ (@ ord_less_int zero_zero_int) D) (=> (@ (@ member_int (@ (@ minus_minus_int T) one_one_int)) B) (forall ((X7 int)) (let ((_let_1 (@ ord_less_eq_int T))) (=> (forall ((Xa3 int)) (=> (@ (@ member_int Xa3) (@ (@ set_or1266510415728281911st_int one_one_int) D)) (forall ((Xb3 int)) (=> (@ (@ member_int Xb3) B) (not (= X7 (@ (@ plus_plus_int Xb3) Xa3))))))) (=> (@ _let_1 X7) (@ _let_1 (@ (@ minus_minus_int X7) D))))))))) (forall ((A2 filter_nat) (B2 filter_nat) (C filter_nat) (D2 filter_nat)) (=> (= A2 B2) (=> (@ (@ ord_le2510731241096832064er_nat B2) C) (=> (= C D2) (@ (@ ord_le2510731241096832064er_nat A2) D2))))) (forall ((P (-> code_integer Bool)) (D code_integer) (Q (-> code_integer Bool))) (=> (forall ((X3 code_integer) (K code_integer)) (= (@ P X3) (@ P (@ (@ minus_8373710615458151222nteger X3) (@ (@ times_3573771949741848930nteger K) D))))) (=> (forall ((X3 code_integer) (K code_integer)) (= (@ Q X3) (@ Q (@ (@ minus_8373710615458151222nteger X3) (@ (@ times_3573771949741848930nteger K) D))))) (forall ((X7 code_integer) (K2 code_integer)) (let ((_let_1 (@ (@ minus_8373710615458151222nteger X7) (@ (@ times_3573771949741848930nteger K2) D)))) (= (and (@ P X7) (@ Q X7)) (and (@ P _let_1) (@ Q _let_1)))))))) (forall ((A set_Pr4329608150637261639at_nat) (B set_Pr4329608150637261639at_nat)) (let ((_let_1 (@ sup_su5525570899277871387at_nat A))) (let ((_let_2 (@ _let_1 B))) (= (@ _let_1 _let_2) _let_2)))) (forall ((C filter_nat) (B2 filter_nat) (A2 filter_nat)) (let ((_let_1 (@ ord_le2510731241096832064er_nat C))) (=> (@ _let_1 B2) (@ _let_1 (@ (@ sup_sup_filter_nat A2) B2))))) (forall ((F4 (-> produc1908205239877642774nteger Bool)) (A2 (-> produc6241069584506657477e_term option6357759511663192854e_term)) (B2 produc8923325533196201883nteger)) (=> (@ F4 (@ (@ produc8603105652947943368nteger A2) B2)) (@ (@ (@ produc1217013493180205570eger_o F4) A2) B2))) (= ord_less_set_nat (lambda ((B3 set_nat) (A3 set_nat)) (and (not (= A3 B3)) (= A3 (@ (@ sup_sup_set_nat A3) B3))))) (forall ((A2 set_int) (A7 set_int) (B2 set_int) (B6 set_int)) (=> (@ (@ ord_less_eq_set_int A2) A7) (=> (@ (@ ord_less_eq_set_int B2) B6) (=> (= (@ (@ inf_inf_set_int A7) B6) bot_bot_set_int) (= (@ (@ inf_inf_set_int A2) B2) bot_bot_set_int))))) (forall ((X code_integer) (Y code_integer)) (= (@ (@ ord_le3102999989581377725nteger (@ (@ plus_p5714425477246183910nteger (@ (@ times_3573771949741848930nteger X) X)) (@ (@ times_3573771949741848930nteger Y) Y))) zero_z3403309356797280102nteger) (and (= X zero_z3403309356797280102nteger) (= Y zero_z3403309356797280102nteger)))) (forall ((A set_Pr4329608150637261639at_nat) (B set_Pr4329608150637261639at_nat) (C2 set_Pr4329608150637261639at_nat)) (let ((_let_1 (@ sup_su5525570899277871387at_nat A))) (= (@ _let_1 (@ (@ inf_in7913087082777306421at_nat B) C2)) (@ (@ inf_in7913087082777306421at_nat (@ _let_1 B)) (@ _let_1 C2))))) (= (lambda ((Y4 filter_nat) (Z2 filter_nat)) (= Y4 Z2)) (lambda ((A3 filter_nat) (B3 filter_nat)) (and (@ (@ ord_le2510731241096832064er_nat B3) A3) (@ (@ ord_le2510731241096832064er_nat A3) B3)))) _let_25 (forall ((N nat) (Xs list_d)) (let ((_let_1 (@ butlast_d Xs))) (=> (@ (@ ord_less_nat N) (@ size_size_list_d _let_1)) (= (@ (@ nth_d _let_1) N) (@ (@ nth_d Xs) N))))) (forall ((L list_num)) (= (@ (@ sorted_wrt_num ord_less_num) L) (and (@ (@ sorted_wrt_num ord_less_eq_num) L) (@ distinct_num L)))) (forall ((P (-> nat Bool)) (I nat) (J nat)) (= (@ (@ list_all_nat P) (@ (@ upt I) J)) (@ (@ (@ all_interval_nat P) I) J))) (forall ((Xs list_c) (Ys list_d) (Zs list_c) (P (-> list_c list_d list_c Bool))) (let ((_let_1 (@ size_size_list_d Ys))) (=> (= (@ size_size_list_c Xs) _let_1) (=> (= _let_1 (@ size_size_list_c Zs)) (=> (@ (@ (@ P nil_c) nil_d) nil_c) (=> (forall ((X3 c) (Xs2 list_c) (Y2 d) (Ys5 list_d) (Z4 c) (Zs2 list_c)) (let ((_let_1 (@ size_size_list_d Ys5))) (=> (= (@ size_size_list_c Xs2) _let_1) (=> (= _let_1 (@ size_size_list_c Zs2)) (=> (@ (@ (@ P Xs2) Ys5) Zs2) (@ (@ (@ P (@ (@ cons_c X3) Xs2)) (@ (@ cons_d Y2) Ys5)) (@ (@ cons_c Z4) Zs2))))))) (@ (@ (@ P Xs) Ys) Zs))))))) (forall ((N nat)) (@ (@ ord_less_nat N) (@ suc N))) (forall ((P (-> nat nat Bool)) (M2 nat) (N nat)) (=> (forall ((M6 nat)) (@ (@ P M6) zero_zero_nat)) (=> (forall ((M6 nat) (N5 nat)) (=> (@ (@ ord_less_nat zero_zero_nat) N5) (=> (@ (@ P N5) (@ (@ modulo_modulo_nat M6) N5)) (@ (@ P M6) N5)))) (@ (@ P M2) N)))) (forall ((C int) (A set_int) (B set_int)) (let ((_let_1 (@ member_int C))) (= (@ _let_1 (@ (@ sup_sup_set_int A) B)) (or (@ _let_1 B) (@ _let_1 A))))) (forall ((B2 set_Pr4329608150637261639at_nat) (A2 set_Pr4329608150637261639at_nat)) (=> (@ (@ ord_le1268244103169919719at_nat B2) A2) (= A2 (@ (@ sup_su5525570899277871387at_nat A2) B2)))) (forall ((I nat) (L list_P5464809261938338413at_nat) (X produc3843707927480180839at_nat) (Y produc3843707927480180839at_nat)) (=> (@ (@ ord_less_nat I) (@ size_s1588839187904960729at_nat L)) (= (@ (@ member8757157785044589968at_nat X) (@ set_Pr3765526544606949372at_nat (@ (@ (@ 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B2))) (forall ((L12 list_nat) (L23 list_c)) (=> (= (@ size_size_list_nat L12) (@ size_size_list_c L23)) (= (@ (@ (@ zipf_n5773672615478942615_nat_c product_Pair_nat_c) L12) L23) (@ (@ zip_nat_c L12) L23)))) (forall ((A2 int) (B2 int) (C int) (D2 int)) (let ((_let_1 (@ ord_less_eq_int zero_zero_int))) (=> (@ (@ ord_less_eq_int A2) B2) (=> (@ (@ ord_less_eq_int C) D2) (=> (@ _let_1 B2) (=> (@ _let_1 C) (@ (@ ord_less_eq_int (@ (@ times_times_int A2) C)) (@ (@ times_times_int B2) D2)))))))) (forall ((X nat) (Y nat)) (@ (@ ord_less_eq_nat X) (@ (@ sup_sup_nat X) Y))) (forall ((A2 code_integer) (F4 (-> assn code_integer)) (B2 assn) (C assn)) (let ((_let_1 (@ ord_le6747313008572928689nteger A2))) (=> (@ _let_1 (@ F4 B2)) (=> (@ (@ ord_less_eq_assn B2) C) (=> (forall ((X3 assn) (Y2 assn)) (=> (@ (@ ord_less_eq_assn X3) Y2) (@ (@ ord_le3102999989581377725nteger (@ F4 X3)) (@ F4 Y2)))) (@ _let_1 (@ F4 C))))))) (forall ((C int) (A2 int) (B2 int)) (let ((_let_1 (@ ord_less_eq_int C))) (=> (@ 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(@ F4 B2)) (=> (@ (@ ord_less_assn B2) C) (=> (forall ((X3 assn) (Y2 assn)) (=> (@ (@ ord_less_assn X3) Y2) (@ (@ ord_less_num (@ F4 X3)) (@ F4 Y2)))) (@ (@ ord_less_num A2) (@ F4 C)))))) (forall ((X produc254973753779126261st_nat)) (=> (forall ((P5 (-> nat nat Bool))) (not (= X (@ (@ produc4727192421694094319st_nat P5) nil_nat)))) (not (forall ((P5 (-> nat nat Bool)) (X3 nat) (Ys5 list_nat)) (not (= X (@ (@ produc4727192421694094319st_nat P5) (@ (@ cons_nat X3) Ys5)))))))) (forall ((Xs list_int) (Ys list_int) (R2 set_Pr958786334691620121nt_int) (N nat)) (=> (@ (@ member6698963635872716290st_int (@ (@ produc364263696895485585st_int Xs) Ys)) (@ (@ lexn_int R2) N)) (and (= (@ size_size_list_int Xs) N) (= (@ size_size_list_int Ys) N)))) (forall ((Y set_nat) (Z set_nat) (X set_nat)) (= (@ (@ inf_inf_set_nat (@ (@ sup_sup_set_nat Y) Z)) X) (@ (@ sup_sup_set_nat (@ (@ inf_inf_set_nat Y) X)) (@ (@ inf_inf_set_nat Z) X)))) (forall ((A2 set_nat) (B2 set_nat)) (= (not (@ (@ ord_less_set_nat A2) B2)) (or (not (@ (@ ord_less_eq_set_nat A2) B2)) (= A2 B2)))) _let_24 (= one_one_rat (@ abs_Rat _let_23)) (forall ((A2 int) (B2 int)) (= (@ (@ minus_minus_int (@ (@ plus_plus_int A2) B2)) B2) A2)) (forall ((Ax (-> produc6241069584506657477e_term option6357759511663192854e_term)) (Ay produc8923325533196201883nteger) (Bx (-> produc6241069584506657477e_term option6357759511663192854e_term)) (By produc8923325533196201883nteger) (R2 set_Pr1722956316086891245nteger) (P (-> (-> produc6241069584506657477e_term option6357759511663192854e_term) produc8923325533196201883nteger Bool))) (=> (@ (@ member2446009503569356342nteger (@ (@ produc7954516348491987909nteger (@ (@ produc8603105652947943368nteger Ax) Ay)) (@ (@ produc8603105652947943368nteger Bx) By))) (@ transi6228740973808232501nteger R2)) (=> (forall ((A4 (-> produc6241069584506657477e_term option6357759511663192854e_term)) (B4 produc8923325533196201883nteger)) (=> (@ (@ member2446009503569356342nteger (@ (@ produc7954516348491987909nteger (@ (@ produc8603105652947943368nteger Ax) Ay)) (@ (@ produc8603105652947943368nteger A4) B4))) R2) (@ (@ P A4) B4))) (=> (forall ((A4 (-> produc6241069584506657477e_term option6357759511663192854e_term)) (B4 produc8923325533196201883nteger) (Aa (-> produc6241069584506657477e_term option6357759511663192854e_term)) (Ba produc8923325533196201883nteger)) (let ((_let_1 (@ (@ produc8603105652947943368nteger A4) B4))) (=> (@ (@ member2446009503569356342nteger (@ (@ produc7954516348491987909nteger (@ (@ produc8603105652947943368nteger Ax) Ay)) _let_1)) (@ transi6228740973808232501nteger R2)) (=> (@ (@ member2446009503569356342nteger (@ (@ produc7954516348491987909nteger _let_1) (@ (@ produc8603105652947943368nteger Aa) Ba))) R2) (=> (@ (@ P A4) B4) (@ (@ P Aa) Ba)))))) (@ (@ P Bx) By))))) (forall ((P (-> int int assn)) (L3 list_int)) (= (@ (@ (@ vEBT_L74593716426352029nt_int P) nil_int) L3) (@ pure_assn (= L3 nil_int)))) (forall ((X produc3843707927480180839at_nat) (Xs 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((X produc6575502325842934193n_assn)) (= (@ (@ remove1670527618125605709n_assn X) nil_Pr5671120429643327159n_assn) nil_Pr5671120429643327159n_assn)) (forall ((P Bool) (Q Bool)) (= (= (@ pure_assn P) (@ pure_assn Q)) (= P Q))) (forall ((X produc6575502325842934193n_assn) (Xs list_P8527749157015355191n_assn) (Ys list_P8527749157015355191n_assn) (R2 set_Pr8116311503512020807n_assn)) (=> (@ (@ member3994142547374651152n_assn (@ (@ produc3014731801419794263n_assn (@ (@ cons_P2971678138204555879n_assn X) Xs)) Ys)) (@ listre4270255209692100112n_assn R2)) (=> (forall ((Y2 produc6575502325842934193n_assn)) (=> (= Ys (@ (@ cons_P2971678138204555879n_assn Y2) Xs)) (not (@ (@ member4743710847862083984n_assn (@ (@ produc6128706242671166167n_assn X) Y2)) R2)))) (not (forall ((Zs2 list_P8527749157015355191n_assn)) (=> (= Ys (@ (@ cons_P2971678138204555879n_assn X) Zs2)) (not (@ (@ member3994142547374651152n_assn (@ (@ produc3014731801419794263n_assn Xs) Zs2)) (@ listre4270255209692100112n_assn R2))))))))) (forall ((A set_Pr4329608150637261639at_nat)) (= (@ (@ sup_su5525570899277871387at_nat A) bot_bo228742789529271731at_nat) A)) (= ord_less_eq_assn (lambda ((B3 assn) (A3 assn)) (= (@ (@ sup_sup_assn A3) B3) A3))) (forall ((B2 filter_nat) (A2 filter_nat)) (=> (@ (@ ord_le2510731241096832064er_nat B2) A2) (= (@ (@ sup_sup_filter_nat A2) B2) A2))) (forall ((N nat) (M2 nat)) (let ((_let_1 (@ ord_less_nat N))) (=> (not (@ _let_1 M2)) (= (@ _let_1 (@ suc M2)) (= N M2))))) (forall ((A2 set_Pr1261947904930325089at_nat) (C set_Pr1261947904930325089at_nat) (B2 set_Pr1261947904930325089at_nat)) (=> (@ (@ ord_le7866589430770878221at_nat A2) C) (@ (@ ord_le7866589430770878221at_nat (@ (@ inf_in2572325071724192079at_nat A2) B2)) C))) (forall ((A2 int) (B2 int)) (= (@ (@ minus_minus_int (@ (@ plus_plus_int A2) B2)) B2) A2)) (forall ((I nat) (Xs list_c) (Ys list_d)) (let ((_let_1 (@ ord_less_nat I))) (=> (@ _let_1 (@ size_size_list_c Xs)) (=> (@ _let_1 (@ size_size_list_d Ys)) (= (@ (@ 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(@ (@ produc3014731801419794263n_assn Ms) Ns)) _let_3)) (and (= _let_2 _let_1) (@ (@ member4743710847862083984n_assn (@ (@ produc6128706242671166167n_assn M2) N)) R2)) (@ (@ ord_less_nat _let_2) _let_1))))))) (forall ((Xs list_P5464809261938338413at_nat) (P (-> produc3843707927480180839at_nat Bool)) (X produc3843707927480180839at_nat)) (=> (forall ((I5 nat)) (=> (@ (@ ord_less_nat I5) (@ size_s1588839187904960729at_nat Xs)) (@ P (@ (@ nth_Pr1239524528086697198at_nat Xs) I5)))) (=> (@ (@ member8757157785044589968at_nat X) (@ set_Pr3765526544606949372at_nat Xs)) (@ P X)))) (forall ((A2 filter_nat) (B2 filter_nat) (C filter_nat)) (=> (= A2 B2) (=> (@ (@ ord_le2510731241096832064er_nat B2) C) (@ (@ ord_le2510731241096832064er_nat A2) C)))) (forall ((A multis2468970476368604999at_nat) (B multis2468970476368604999at_nat) (M5 multis2468970476368604999at_nat) (N7 multis2468970476368604999at_nat)) (=> (= (@ (@ plus_p7104986032573967614at_nat A) B) (@ (@ plus_p7104986032573967614at_nat M5) N7)) (not (forall ((Am multis2468970476368604999at_nat) (An multis2468970476368604999at_nat)) (=> (= A (@ (@ plus_p7104986032573967614at_nat Am) An)) (forall ((Bm multis2468970476368604999at_nat) (Bn multis2468970476368604999at_nat)) (=> (= B (@ (@ plus_p7104986032573967614at_nat Bm) Bn)) (=> (= M5 (@ (@ plus_p7104986032573967614at_nat Am) Bm)) (not (= N7 (@ (@ plus_p7104986032573967614at_nat An) Bn))))))))))) (forall ((M2 nat) (N nat)) (let ((_let_1 (@ minus_minus_nat N))) (=> (@ (@ ord_less_eq_nat M2) N) (=> (@ (@ ord_less_nat one_one_nat) M2) (= (@ suc (@ _let_1 M2)) (@ _let_1 (@ (@ minus_minus_nat M2) one_one_nat))))))) (forall ((C (-> produc3658429121746597890et_nat Bool)) (B set_Pr4532377907799695533_nat_o) (A set_Pr4532377907799695533_nat_o)) (let ((_let_1 (@ member6576561426505652726_nat_o C))) (=> (=> (not (@ _let_1 B)) (@ _let_1 A)) (@ _let_1 (@ (@ sup_su5209123915105501825_nat_o A) B))))) (forall ((Y num) (X num)) (=> (@ (@ ord_less_eq_num Y) X) (not (@ (@ ord_less_num X) Y)))) 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produc3658429121746597890et_nat)) (=> (@ (@ (@ produc6216949301066131538_nat_o F4) A2) B2) (@ F4 (@ (@ produc5001842942810119800et_nat A2) B2)))) (forall ((Xs list_c) (P (-> c c Bool))) (=> (@ (@ ord_less_eq_nat (@ size_size_list_c Xs)) one_one_nat) (@ (@ sorted_wrt_c P) Xs))) (forall ((N nat) (Xs list_d)) (= (@ size_s457006183821432778_nat_d (@ (@ enumerate_d N) Xs)) (@ size_size_list_d Xs))) (forall ((X assn) (Y assn) (Z assn)) (let ((_let_1 (@ inf_inf_assn X))) (= (@ (@ inf_inf_assn (@ _let_1 Y)) Z) (@ _let_1 (@ (@ inf_inf_assn Y) Z))))) (forall ((Xs list_c) (Ys list_c) (R2 set_Product_prod_c_c)) (= (@ (@ member7012247553653173456list_c (@ (@ produc5515445818230282391list_c Xs) Ys)) (@ listrel1_c R2)) (exists ((Y5 c) (N2 nat)) (and (@ (@ member5074992359041316560od_c_c (@ (@ product_Pair_c_c (@ (@ nth_c Xs) N2)) Y5)) R2) (= Ys (@ (@ (@ list_update_c Xs) N2) Y5)) (@ (@ ord_less_nat N2) (@ size_size_list_c Xs)))))) (forall ((A2 nat) (B2 nat) (C nat) (D2 nat)) (=> (@ (@ ord_less_nat 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Zs))))))) (forall ((R2 set_Pr8536935166611901872et_nat) (S3 set_Pr8536935166611901872et_nat)) (=> (forall ((X3 (-> produc3658429121746597890et_nat Bool)) (Y2 produc3925858234332021118et_nat)) (let ((_let_1 (@ member6124377750444531601et_nat (@ (@ produc2245416461498447860et_nat X3) Y2)))) (=> (@ _let_1 R2) (@ _let_1 S3)))) (@ (@ ord_le4763372923235995152et_nat R2) S3))) (= (@ rotate1_nat nil_nat) nil_nat) (forall ((X (-> produc6575502325842934193n_assn int assn)) (Xa list_P8527749157015355191n_assn) (Xb list_int) (Y assn)) (let ((_let_1 (not (= Y bot_bot_assn)))) (let ((_let_2 (= Xa nil_Pr5671120429643327159n_assn))) (let ((_let_3 (= Xb nil_int))) (=> (= (@ (@ (@ vEBT_L4760345170377931482sn_int X) Xa) Xb) Y) (=> (=> _let_2 (=> _let_3 (not (= Y one_one_assn)))) (=> (forall ((A4 produc6575502325842934193n_assn) (As list_P8527749157015355191n_assn)) (=> (= Xa (@ (@ cons_P2971678138204555879n_assn A4) As)) (forall ((C4 int) (Cs2 list_int)) (=> (= Xb (@ (@ cons_int C4) Cs2)) (not (= Y (@ (@ 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A2))) (forall ((X produc3658429121746597890et_nat) (Y Bool)) (=> (= (@ in_range X) Y) (not (forall ((H heap_e7401611519738050253t_unit) (As set_nat)) (=> (= X (@ (@ produc7507926704131184380et_nat H) As)) (= Y (not (forall ((X2 nat)) (=> (@ (@ member_nat X2) As) (@ (@ ord_less_nat X2) (@ lim_Product_unit H))))))))))) (forall ((A2 nat) (B2 nat) (R2 set_Pr1261947904930325089at_nat) (P (-> nat Bool))) (=> (@ (@ member8440522571783428010at_nat (@ (@ product_Pair_nat_nat A2) B2)) (@ transi6264000038957366511cl_nat R2)) (=> (forall ((Y2 nat)) (=> (@ (@ member8440522571783428010at_nat (@ (@ product_Pair_nat_nat A2) Y2)) R2) (@ P Y2))) (=> (forall ((Y2 nat) (Z4 nat)) (=> (@ (@ member8440522571783428010at_nat (@ (@ product_Pair_nat_nat A2) Y2)) (@ transi6264000038957366511cl_nat R2)) (=> (@ (@ member8440522571783428010at_nat (@ (@ product_Pair_nat_nat Y2) Z4)) R2) (=> (@ P Y2) (@ P Z4))))) (@ P B2))))) (forall ((X rat) (A2 rat) (Y rat) (U rat) (V2 rat)) (let ((_let_1 (@ ord_less_eq_rat 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((_let_1 (@ (@ produc7507926704131184380et_nat H2) bot_bot_set_nat))) (= (@ (@ rep_assn (@ (@ times_times_assn P) Q)) _let_1) (and (@ (@ rep_assn Q) _let_1) (@ (@ rep_assn P) _let_1))))) (forall ((N filter_nat) (M2 filter_nat)) (let ((_let_1 (@ (@ ord_min_filter_nat M2) N))) (= (@ (@ ord_le2510731241096832064er_nat N) _let_1) (= _let_1 N)))) (forall ((X21 d) (X222 list_d)) (= (@ size_size_list_d (@ (@ cons_d X21) X222)) (@ (@ plus_plus_nat (@ size_size_list_d X222)) (@ suc zero_zero_nat)))) (forall ((K3 int)) (=> (not (= K3 zero_zero_int)) (=> (forall ((N5 nat)) (=> (= K3 (@ semiri1314217659103216013at_int N5)) (not (@ (@ ord_less_nat zero_zero_nat) N5)))) (not (forall ((N5 nat)) (=> (= K3 (@ uminus_uminus_int (@ semiri1314217659103216013at_int N5))) (not (@ (@ ord_less_nat zero_zero_nat) N5)))))))) (forall ((Xs list_P8527749157015355191n_assn) (P (-> produc6575502325842934193n_assn Bool))) (= (forall ((X2 produc6575502325842934193n_assn)) (=> (@ (@ member7957490590177025114n_assn X2) 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ord_le2965882846123202637_nat_o (@ (@ insert5175938949040314269_nat_o X) A)) B) (and (@ (@ ord_le2965882846123202637_nat_o A) B) (@ (@ member6576561426505652726_nat_o X) B)))) (forall ((A2 nat) (B2 nat) (C nat) (D2 nat)) (=> (= A2 B2) (=> (@ (@ ord_less_eq_nat B2) C) (=> (= C D2) (@ (@ ord_less_eq_nat A2) D2))))) (forall ((P (-> code_integer Bool)) (P3 (-> code_integer Bool)) (Q (-> code_integer Bool)) (Q3 (-> code_integer Bool))) (=> (exists ((Z3 code_integer)) (forall ((X3 code_integer)) (=> (@ (@ ord_le6747313008572928689nteger Z3) X3) (= (@ P X3) (@ P3 X3))))) (=> (exists ((Z3 code_integer)) (forall ((X3 code_integer)) (=> (@ (@ ord_le6747313008572928689nteger Z3) X3) (= (@ Q X3) (@ Q3 X3))))) (exists ((Z4 code_integer)) (forall ((X7 code_integer)) (=> (@ (@ ord_le6747313008572928689nteger Z4) X7) (= (and (@ P X7) (@ Q X7)) (and (@ P3 X7) (@ Q3 X7))))))))) (forall ((A2 assn) (B2 assn)) (=> (@ (@ ord_less_eq_assn A2) B2) (=> (not (= A2 B2)) (@ (@ ord_less_assn A2) B2)))) (forall ((X21 int) (X222 list_int) (Y21 int) (Y222 list_int)) (= (= (@ (@ cons_int X21) X222) (@ (@ cons_int Y21) Y222)) (and (= X21 Y21) (= X222 Y222)))) (forall ((M2 list_P8527749157015355191n_assn) (P6 assn) (Up2 assn) (Q6 assn) (Uq2 assn) (F4 assn)) (=> (@ (@ (@ (@ fI_RESULT M2) (@ (@ times_times_assn P6) Up2)) (@ (@ times_times_assn Q6) Uq2)) F4) (@ (@ (@ (@ (@ (@ fi M2) P6) Q6) Up2) Uq2) F4))) (forall ((X nat) (Y nat) (Zs list_nat)) (let ((_let_1 (@ (@ cons_nat Y) Zs))) (let ((_let_2 (@ sorted_wrt_nat ord_less_eq_nat))) (= (@ _let_2 (@ (@ cons_nat X) _let_1)) (and (@ _let_2 _let_1) (@ (@ ord_less_eq_nat X) Y)))))) (forall ((P (-> d d Bool)) (Xs list_d) (I nat) (J nat)) (let ((_let_1 (@ nth_d Xs))) (=> (@ (@ sorted_wrt_d P) Xs) (=> (@ (@ ord_less_nat I) J) (=> (@ (@ ord_less_nat J) (@ size_size_list_d Xs)) (@ (@ P (@ _let_1 I)) (@ _let_1 J))))))) (forall ((A2 multis2468970476368604999at_nat) (B2 multis2468970476368604999at_nat) (C multis2468970476368604999at_nat)) (let ((_let_1 (@ minus_4286766774447292334at_nat A2))) (= (@ (@ minus_4286766774447292334at_nat (@ _let_1 B2)) C) (@ _let_1 (@ (@ plus_p7104986032573967614at_nat B2) C))))) (forall ((From nat) (To nat) (Xs list_c) (I nat)) (=> (@ (@ ord_less_nat From) To) (=> (@ (@ ord_less_eq_nat To) (@ size_size_list_c Xs)) (=> (@ (@ ord_less_nat I) (@ (@ minus_minus_nat To) From)) (= (@ (@ nth_c (@ (@ (@ slice_c From) To) Xs)) I) (@ (@ nth_c Xs) (@ (@ plus_plus_nat From) I))))))) (forall ((B2 int) (A2 int)) (= (= (@ (@ plus_plus_int B2) A2) A2) (= B2 zero_zero_int))) (forall ((Z int)) (= (@ (@ ord_less_nat zero_zero_nat) (@ nat2 Z)) (@ (@ ord_less_int zero_zero_int) Z))) (forall ((S set_Pr1261947904930325089at_nat) (T3 set_Pr1261947904930325089at_nat)) (= (@ (@ sup_su6327502436637775413at_nat S) (@ (@ inf_in2572325071724192079at_nat S) T3)) S)) (forall ((A2 rat) (B2 rat)) (= (= A2 (@ (@ plus_plus_rat B2) A2)) (= B2 zero_zero_rat))) (forall ((From nat) (To nat) (Xs list_nat) (I nat)) (=> (@ (@ ord_less_nat From) To) (=> (@ (@ ord_less_eq_nat To) (@ size_size_list_nat Xs)) (=> (@ (@ ord_less_nat I) (@ (@ minus_minus_nat To) From)) (= (@ (@ nth_nat (@ (@ (@ slice_nat From) To) Xs)) I) (@ (@ nth_nat Xs) (@ (@ plus_plus_nat From) I))))))) (forall ((A2 code_integer) (B2 code_integer) (F4 (-> code_integer code_integer)) (C code_integer)) (=> (@ (@ ord_le6747313008572928689nteger A2) B2) (=> (= (@ F4 B2) C) (=> (forall ((X3 code_integer) (Y2 code_integer)) (=> (@ (@ ord_le6747313008572928689nteger X3) Y2) (@ (@ ord_le6747313008572928689nteger (@ F4 X3)) (@ F4 Y2)))) (@ (@ ord_le6747313008572928689nteger (@ F4 A2)) C))))) (forall ((A2 rat) (E rat) (C rat) (B2 rat) (D2 rat)) (= (= (@ (@ plus_plus_rat (@ (@ times_times_rat A2) E)) C) (@ (@ plus_plus_rat (@ (@ times_times_rat B2) E)) D2)) (= C (@ (@ plus_plus_rat (@ (@ times_times_rat (@ (@ minus_minus_rat B2) A2)) E)) D2)))) (forall ((N nat) (Xs list_d)) (let ((_let_1 (@ size_size_list_d Xs))) (=> (@ (@ ord_less_nat N) _let_1) (= (@ (@ nth_d (@ rev_d Xs)) N) (@ (@ nth_d Xs) (@ (@ minus_minus_nat _let_1) (@ suc N))))))) (forall ((Y (-> produc3658429121746597890et_nat Bool)) (X (-> produc3658429121746597890et_nat Bool)) (Xs list_P7985473006766602707_nat_o)) (let ((_let_1 (@ member6576561426505652726_nat_o Y))) (=> (@ _let_1 (@ set_Pr400311997697478754_nat_o (@ (@ cons_P6219271836124797827_nat_o X) Xs))) (or (= Y X) (@ _let_1 (@ set_Pr400311997697478754_nat_o Xs)))))) (forall ((Xs list_c)) (= (@ size_size_list_c (@ butlast_c Xs)) (@ (@ minus_minus_nat (@ size_size_list_c Xs)) one_one_nat))) _let_21 (forall ((B2 filter_nat) (A2 filter_nat)) (=> (@ (@ ord_le2510731241096832064er_nat B2) A2) (= (@ (@ inf_inf_filter_nat A2) B2) B2))) (forall ((N nat) (Xs list_c)) (= (@ size_s385972143775086793_nat_c (@ (@ enumerate_c N) Xs)) (@ size_size_list_c Xs))) (forall ((A2 set_Pr4329608150637261639at_nat) (C set_Pr4329608150637261639at_nat) (B2 set_Pr4329608150637261639at_nat) (D2 set_Pr4329608150637261639at_nat)) (=> (@ (@ ord_le1268244103169919719at_nat A2) C) (=> (@ (@ ord_le1268244103169919719at_nat B2) D2) (@ (@ ord_le1268244103169919719at_nat (@ (@ sup_su5525570899277871387at_nat A2) B2)) (@ (@ sup_su5525570899277871387at_nat C) D2))))) (= ord_le2510731241096832064er_nat (lambda ((B3 filter_nat) (A3 filter_nat)) (or (@ (@ ord_less_filter_nat B3) A3) (= A3 B3)))) (forall ((A set_nat) (C2 set_nat) (B set_nat) (D set_nat)) (=> (@ (@ ord_less_eq_set_nat A) C2) (=> (@ (@ ord_less_eq_set_nat B) D) (@ (@ ord_less_eq_set_nat (@ (@ sup_sup_set_nat A) B)) (@ (@ sup_sup_set_nat C2) D))))) (forall ((A2 code_integer) (B2 code_integer) (C code_integer)) (=> (@ (@ ord_le6747313008572928689nteger A2) B2) (@ (@ ord_le6747313008572928689nteger (@ (@ plus_p5714425477246183910nteger A2) C)) (@ (@ plus_p5714425477246183910nteger B2) C)))) (forall ((M2 nat) (N nat)) (= (= (@ (@ divide_divide_nat M2) N) zero_zero_nat) (or (@ (@ ord_less_nat M2) N) (= N zero_zero_nat)))) (forall ((Xs list_P6011104703257516679at_nat)) (= (= bot_bo2099793752762293965at_nat (@ set_Pr5648618587558075414at_nat Xs)) (= Xs nil_Pr5478986624290739719at_nat))) (forall ((A assn) (M5 assn) (B assn)) (=> (@ (@ entailst A) M5) (=> (@ (@ entailst B) M5) (@ (@ entailst (@ (@ sup_sup_assn A) B)) M5)))) (forall ((L list_nat) (I nat) (J nat)) (let ((_let_1 (@ ord_less_nat I))) (let ((_let_2 (@ nth_nat L))) (let ((_let_3 (@ size_size_list_nat L))) (=> (@ distinct_nat L) (=> (@ (@ sorted_wrt_nat ord_less_eq_nat) L) (=> (@ _let_1 _let_3) (=> (@ (@ ord_less_nat J) _let_3) (= (@ (@ ord_less_nat (@ _let_2 I)) (@ _let_2 J)) (@ _let_1 J)))))))))) (not (= top_top_assn bot_bot_assn)) (@ (@ ord_less_nat i2) _let_20) (forall ((A2 produc3843707927480180839at_nat) (A set_Pr4329608150637261639at_nat) (B set_Pr4329608150637261639at_nat)) (let ((_let_1 (@ inf_in7913087082777306421at_nat A))) (=> (not (@ (@ member8757157785044589968at_nat A2) A)) (= (@ _let_1 (@ (@ insert9069300056098147895at_nat A2) B)) (@ _let_1 B))))) (forall ((J code_integer)) (= (@ (@ code_divmod_abs zero_z3403309356797280102nteger) J) (@ (@ produc1086072967326762835nteger zero_z3403309356797280102nteger) zero_z3403309356797280102nteger))) (forall ((I nat) (J nat) (K3 nat)) (let ((_let_1 (@ times_times_nat K3))) (=> (@ (@ ord_less_nat I) J) (=> (@ (@ ord_less_nat zero_zero_nat) K3) (@ (@ ord_less_nat (@ _let_1 I)) (@ _let_1 J)))))) (forall ((A2 code_integer) (B2 code_integer)) (=> (@ (@ ord_le3102999989581377725nteger A2) zero_z3403309356797280102nteger) (=> (@ (@ ord_le3102999989581377725nteger B2) zero_z3403309356797280102nteger) (@ (@ ord_le3102999989581377725nteger zero_z3403309356797280102nteger) (@ (@ times_3573771949741848930nteger A2) B2))))) (forall ((From nat) (To nat) (Xs list_d)) (=> (@ (@ ord_less_eq_nat From) To) (=> (@ (@ ord_less_eq_nat To) (@ size_size_list_d Xs)) (= (@ size_size_list_d (@ (@ (@ slice_d From) To) Xs)) (@ (@ minus_minus_nat To) From))))) (forall ((A2 list_d) (B2 list_int) (A7 list_d) (B6 list_int)) (=> (= (@ size_size_list_d A2) (@ size_size_list_int B2)) (=> (= (@ size_size_list_d A7) (@ size_size_list_int B6)) (=> (= (@ (@ zip_d_int A2) B2) (@ (@ zip_d_int A7) B6)) (and (= B2 B6) (= A2 A7)))))) (forall ((X rat) (Y rat)) (not (@ (@ ord_less_rat (@ (@ plus_plus_rat (@ (@ times_times_rat X) X)) (@ (@ times_times_rat Y) Y))) zero_zero_rat))) (= ord_le6747313008572928689nteger (lambda ((A3 code_integer) (B3 code_integer)) (@ (@ ord_le6747313008572928689nteger (@ (@ minus_8373710615458151222nteger A3) B3)) zero_z3403309356797280102nteger))) (forall ((C int) (B2 int) (A2 int)) (let ((_let_1 (@ ord_less_eq_int C))) (=> (@ _let_1 B2) (@ _let_1 (@ (@ sup_sup_int A2) B2))))) (forall ((B set_Pr4329608150637261639at_nat) (A2 produc3843707927480180839at_nat) (A set_Pr4329608150637261639at_nat)) (let ((_let_1 (@ inf_in7913087082777306421at_nat B))) (= (= (@ _let_1 (@ (@ insert9069300056098147895at_nat A2) A)) bot_bo228742789529271731at_nat) (and (not (@ (@ member8757157785044589968at_nat A2) B)) (= (@ _let_1 A) bot_bo228742789529271731at_nat))))) (forall ((A2 product_prod_nat_nat) (B set_Pr1261947904930325089at_nat) (C2 set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ insert8211810215607154385at_nat A2))) (= (@ (@ sup_su6327502436637775413at_nat (@ _let_1 B)) C2) (@ _let_1 (@ (@ sup_su6327502436637775413at_nat B) C2))))) (forall ((A2 nat) (B2 nat) (C nat)) (let ((_let_1 (@ times_times_nat A2))) (= (@ _let_1 (@ (@ plus_plus_nat B2) C)) (@ (@ plus_plus_nat (@ _let_1 B2)) (@ _let_1 C))))) (forall ((X produc3843707927480180839at_nat) (Xs list_P5464809261938338413at_nat)) (let ((_let_1 (@ member8757157785044589968at_nat X))) (=> (@ _let_1 (@ set_Pr3765526544606949372at_nat (@ butlas2561766218336428473at_nat Xs))) (@ _let_1 (@ set_Pr3765526544606949372at_nat Xs))))) (forall ((M2 nat) (Xs list_nat) (N nat)) (=> (@ (@ ord_less_nat M2) (@ size_size_list_nat Xs)) (= (@ (@ nth_Pr7617993195940197384at_nat (@ (@ enumerate_nat N) Xs)) M2) (@ (@ product_Pair_nat_nat (@ (@ plus_plus_nat N) M2)) (@ (@ nth_nat Xs) M2))))) _let_19 (forall ((J nat) (I nat)) (not (@ (@ ord_less_nat (@ (@ plus_plus_nat J) I)) I))) (forall ((A2 nat) (B2 nat) (C nat)) (=> (@ (@ ord_less_eq_nat A2) B2) (=> (@ (@ ord_less_nat B2) C) (@ (@ ord_less_nat A2) C)))) (forall ((L list_Code_integer) (I nat) (J nat)) (let ((_let_1 (@ ord_less_nat I))) (let ((_let_2 (@ nth_Code_integer L))) (let ((_let_3 (@ size_s3445333598471063425nteger L))) (=> (@ distin1543349897113766820nteger L) (=> (@ (@ sorted710888440204495920nteger ord_le3102999989581377725nteger) L) (=> (@ _let_1 _let_3) (=> (@ (@ ord_less_nat J) _let_3) (= (@ (@ ord_le6747313008572928689nteger (@ _let_2 I)) (@ _let_2 J)) (@ _let_1 J)))))))))) (= (lambda ((Y4 list_d) (Z2 list_d)) (= Y4 Z2)) (lambda ((Xs3 list_d) (Ys3 list_d)) (and (= (@ size_size_list_d Xs3) (@ size_size_list_d Ys3)) (forall ((I4 nat)) (=> (@ (@ ord_less_nat I4) (@ size_size_list_d Xs3)) (= (@ (@ nth_d Xs3) I4) (@ (@ nth_d Ys3) I4))))))) (forall ((M2 nat) (N nat)) (=> (@ (@ ord_less_nat zero_zero_nat) M2) (=> (@ (@ ord_less_nat M2) N) (@ (@ ord_less_nat (@ semiri1408675320244567234ct_nat M2)) (@ semiri1408675320244567234ct_nat N))))) (forall ((P (-> nat Bool)) (I nat)) (@ finite_finite_nat (@ collect_nat (lambda ((K4 nat)) (and (@ P K4) (@ (@ ord_less_nat K4) I)))))) (forall ((X set_Pr1261947904930325089at_nat) (Y set_Pr1261947904930325089at_nat) (Xs list_s1210847774152347623at_nat) (Ys list_s1210847774152347623at_nat)) (=> (@ (@ member8757157785044589968at_nat (@ (@ produc2922128104949294807at_nat X) Y)) (@ set_Pr3765526544606949372at_nat (@ (@ zip_se5600341670672612855at_nat Xs) Ys))) (@ (@ member2643936169264416010at_nat Y) (@ set_se5049602875457034614at_nat Ys)))) (forall ((X nat) (Y nat)) (=> (@ (@ ord_less_nat X) Y) (not (= X Y)))) (forall ((A2 rat) (B2 rat) (C rat)) (=> (@ (@ ord_less_rat zero_zero_rat) A2) (=> (@ (@ ord_less_eq_rat B2) C) (@ (@ ord_less_rat B2) (@ (@ plus_plus_rat A2) C))))) (forall ((N nat)) (= (not (@ (@ ord_less_nat zero_zero_nat) N)) (= N zero_zero_nat))) (forall ((L12 list_c) (L23 list_int)) (=> (= (@ size_size_list_c L12) (@ size_size_list_int L23)) (= (@ (@ (@ zipf_c230841880303976139_c_int product_Pair_c_int) L12) L23) (@ (@ zip_c_int L12) L23)))) (forall ((A2 nat) (B set_nat) (B2 nat)) (let ((_let_1 (@ member_nat A2))) (=> (@ _let_1 B) (@ _let_1 (@ (@ insert_nat2 B2) B))))) (forall ((A2 nat) (N nat)) (let ((_let_1 (@ power_power_nat A2))) (= (@ _let_1 (@ suc N)) (@ (@ times_times_nat A2) (@ _let_1 N))))) (= ord_less_eq_int (lambda ((A3 int) (B3 int)) (= (@ (@ inf_inf_int A3) B3) A3))) (forall ((A set_nat) (B set_nat)) (@ (@ ord_less_eq_set_nat A) (@ (@ sup_sup_set_nat A) B))) (= sup_sup_set_nat (lambda ((A5 set_nat) (B7 set_nat)) (@ (@ sup_sup_set_nat B7) A5))) (forall ((A2 list_c) (B2 list_d) (A7 list_c) (B6 list_d)) (=> (= (@ size_size_list_c A2) (@ size_size_list_d B2)) (=> (= (@ size_size_list_c A7) (@ size_size_list_d B6)) (=> (= (@ (@ zip_c_d A2) B2) (@ (@ zip_c_d A7) B6)) (and (= B2 B6) (= A2 A7)))))) (forall ((I nat) (J nat) (L list_num) (X num)) (let ((_let_1 (@ nth_num L))) (=> (@ (@ ord_less_eq_nat zero_zero_nat) I) (=> (@ (@ ord_less_nat I) J) (=> (@ (@ ord_less_nat J) (@ size_size_list_num L)) (=> (@ (@ sorted_wrt_num ord_less_eq_num) L) (=> (@ (@ ord_less_eq_num (@ _let_1 I)) X) (=> (@ (@ ord_less_num X) (@ _let_1 J)) (not (forall ((K nat)) (let ((_let_1 (@ nth_num L))) (=> (@ (@ ord_less_eq_nat I) K) (=> (@ (@ ord_less_nat K) J) (=> (@ (@ ord_less_eq_num (@ _let_1 K)) X) (not (@ (@ ord_less_num X) (@ _let_1 (@ (@ plus_plus_nat K) one_one_nat)))))))))))))))))) (forall ((I int) (J int)) (let ((_let_1 (@ (@ upto I) J))) (let ((_let_2 (@ (@ ord_less_eq_int I) J))) (=> (@ (@ accp_P1096762738010456898nt_int upto_rel) (@ (@ product_Pair_int_int I) J)) (and (=> _let_2 (= _let_1 (@ (@ cons_int I) (@ (@ upto (@ (@ plus_plus_int I) one_one_int)) J)))) (=> (not _let_2) (= _let_1 nil_int))))))) (forall ((I int)) (= (@ (@ upto I) I) (@ (@ cons_int I) nil_int))) (forall ((X num) (Y num)) (=> (@ (@ ord_less_num X) Y) (not (= X Y)))) (forall ((A2 assn) (B2 assn) (F4 (-> assn nat)) (C nat)) (=> (@ (@ ord_less_eq_assn A2) B2) (=> (@ (@ ord_less_nat (@ F4 B2)) C) (=> (forall ((X3 assn) (Y2 assn)) (=> (@ (@ ord_less_eq_assn X3) Y2) (@ (@ ord_less_eq_nat (@ F4 X3)) (@ F4 Y2)))) (@ (@ ord_less_nat (@ F4 A2)) C))))) (forall ((A2 assn) (B2 assn) (F4 (-> assn int)) (C int)) (=> (@ (@ ord_less_assn A2) B2) (=> (@ (@ ord_less_int (@ F4 B2)) C) (=> (forall ((X3 assn) (Y2 assn)) (=> (@ (@ ord_less_assn X3) Y2) (@ (@ ord_less_int (@ F4 X3)) (@ F4 Y2)))) (@ (@ ord_less_int (@ F4 A2)) C))))) (forall ((B2 int) (A2 int)) (=> (@ (@ member_int B2) (@ (@ insert_int2 A2) bot_bot_set_int)) (= B2 A2))) (forall ((A set_Pr4329608150637261639at_nat) (B set_Pr4329608150637261639at_nat)) (= (@ (@ inf_in7913087082777306421at_nat (@ (@ inf_in7913087082777306421at_nat A) B)) (@ (@ minus_3314409938677909166at_nat A) B)) bot_bo228742789529271731at_nat)) (forall ((A2 nat)) (= (@ (@ minus_minus_nat A2) A2) zero_zero_nat)) (forall ((A2 num) (B2 num)) (=> (not (= A2 B2)) (=> (@ (@ ord_less_eq_num A2) B2) (@ (@ ord_less_num A2) B2)))) (forall ((A2 code_integer)) (= (@ (@ ord_le3102999989581377725nteger (@ (@ plus_p5714425477246183910nteger A2) A2)) zero_z3403309356797280102nteger) (@ (@ ord_le3102999989581377725nteger A2) zero_z3403309356797280102nteger))) (@ (@ _let_18 (@ produc27273713700761075at_nat (lambda ((X2 nat) (Y5 nat) (__flatten_var_0 product_prod_nat_nat)) (@ (@ produc2626176000494625587at_nat (lambda ((U4 nat) (V4 nat)) (let ((_let_1 (@ times_times_nat Y5))) (let ((_let_2 (@ times_times_nat X2))) (@ (@ product_Pair_nat_nat (@ (@ plus_plus_nat (@ _let_2 U4)) (@ _let_1 V4))) (@ (@ plus_plus_nat (@ _let_2 V4)) (@ _let_1 U4))))))) __flatten_var_0)))) times_times_int) (forall ((A set_Pr4329608150637261639at_nat) (A2 produc3843707927480180839at_nat) (B set_Pr4329608150637261639at_nat)) (let ((_let_1 (@ insert9069300056098147895at_nat A2))) (let ((_let_2 (@ minus_3314409938677909166at_nat A))) (= (@ _let_2 (@ _let_1 B)) (@ (@ minus_3314409938677909166at_nat (@ _let_2 (@ _let_1 bot_bo228742789529271731at_nat))) B))))) (forall ((A multis2468970476368604999at_nat) (B multis2468970476368604999at_nat) (Z6 multis2468970476368604999at_nat)) (let ((_let_1 (@ plus_p7104986032573967614at_nat Z6))) (=> (or (and (= B zero_z1048942125864253310at_nat) (= A zero_z1048942125864253310at_nat)) (@ (@ member8757157785044589968at_nat (@ (@ produc2922128104949294807at_nat (@ set_ms8126754132646256062at_nat A)) (@ set_ms8126754132646256062at_nat B))) fun_max_strict)) (@ (@ member6689249552917799696at_nat (@ (@ produc4348348721325984599at_nat (@ _let_1 A)) (@ _let_1 B))) ms_weak)))) (forall ((X product_prod_nat_nat) (XS set_Pr1261947904930325089at_nat) (Y product_prod_nat_nat) (YS set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ produc2922128104949294807at_nat XS))) (=> (@ (@ member8440522571783428010at_nat X) XS) (=> (@ (@ member8206827879206165904at_nat (@ (@ produc6161850002892822231at_nat X) Y)) fun_pair_less) (=> (@ (@ member8757157785044589968at_nat (@ _let_1 YS)) fun_min_strict) (@ (@ member8757157785044589968at_nat (@ _let_1 (@ (@ insert8211810215607154385at_nat Y) YS))) fun_min_strict)))))) (forall ((A2 nat) (B2 nat) (F4 (-> nat nat)) (C nat)) (=> (@ (@ ord_less_eq_nat A2) B2) (=> (= (@ F4 B2) C) (=> (forall ((X3 nat) (Y2 nat)) (=> (@ (@ ord_less_eq_nat X3) Y2) (@ (@ ord_less_eq_nat (@ F4 X3)) (@ F4 Y2)))) (@ (@ ord_less_eq_nat (@ F4 A2)) C))))) (forall ((A set_Pr4329608150637261639at_nat)) (= (forall ((X2 produc3843707927480180839at_nat)) (not (@ (@ member8757157785044589968at_nat X2) A))) (= A bot_bo228742789529271731at_nat))) (forall ((A set_Pr4329608150637261639at_nat) (B set_Pr4329608150637261639at_nat) (C2 set_Pr4329608150637261639at_nat)) (let ((_let_1 (@ minus_3314409938677909166at_nat A))) (= (@ (@ minus_3314409938677909166at_nat (@ _let_1 B)) C2) (@ _let_1 (@ (@ sup_su5525570899277871387at_nat B) C2))))) (forall ((X (-> 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((A4 (-> int option6357759511663192854e_term)) (B4 int) (C4 int)) (not (= Y (@ (@ produc4305682042979456191nt_int A4) (@ (@ product_Pair_int_int B4) C4))))))) (forall ((Y set_nat) (X set_nat) (Z set_nat)) (=> (@ (@ ord_less_eq_set_nat Y) X) (=> (@ (@ ord_less_eq_set_nat Z) X) (@ (@ ord_less_eq_set_nat (@ (@ sup_sup_set_nat Y) Z)) X)))) (forall ((A set_Pr4532377907799695533_nat_o) (B set_Pr4532377907799695533_nat_o)) (=> (@ (@ ord_le2453136405763929_nat_o A) B) (exists ((B4 (-> produc3658429121746597890et_nat Bool))) (@ (@ member6576561426505652726_nat_o B4) (@ (@ minus_1801376950450012436_nat_o B) A))))) (forall ((U2 set_Pr1261947904930325089at_nat) (V set_Pr1261947904930325089at_nat) (X product_prod_nat_nat)) (let ((_let_1 (@ member8440522571783428010at_nat X))) (=> (@ (@ ord_le3146513528884898305at_nat U2) V) (=> (@ _let_1 (@ transi6264000038957366511cl_nat U2)) (@ _let_1 (@ transi6264000038957366511cl_nat V)))))) (forall ((A2 int) (B2 int)) (=> (@ (@ ord_less_eq_int A2) B2) (=> (@ 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filter_nat)) (=> (@ (@ ord_le2510731241096832064er_nat A2) C) (@ (@ ord_le2510731241096832064er_nat (@ (@ inf_inf_filter_nat A2) B2)) C))) (forall ((A2 rat) (B2 rat) (C rat) (D2 rat)) (let ((_let_1 (@ ord_less_eq_rat zero_zero_rat))) (=> (@ (@ ord_less_rat A2) B2) (=> (@ (@ ord_less_rat C) D2) (=> (@ _let_1 A2) (=> (@ _let_1 C) (@ (@ ord_less_rat (@ (@ times_times_rat A2) C)) (@ (@ times_times_rat B2) D2)))))))) (forall ((A set_Pr1261947904930325089at_nat) (B set_Pr1261947904930325089at_nat)) (=> (@ (@ ord_le3146513528884898305at_nat A) B) (= (@ (@ minus_1356011639430497352at_nat A) B) bot_bo2099793752762293965at_nat))) (forall ((A2 code_integer)) (= (@ (@ plus_p5714425477246183910nteger A2) zero_z3403309356797280102nteger) A2)) (forall ((A2 int) (X int) (B2 int)) (=> (@ (@ ord_less_eq_int A2) X) (=> (@ (@ ord_less_eq_int B2) X) (@ (@ ord_less_eq_int (@ (@ sup_sup_int A2) B2)) X)))) (forall ((P (-> produc2285326912895808259nt_int Bool)) (P6 produc2285326912895808259nt_int)) (=> (forall ((A4 (-> produc8551481072490612790e_term option6357759511663192854e_term)) (B4 product_prod_int_int)) (@ P (@ (@ produc5700946648718959541nt_int A4) B4))) (@ P P6))) (forall ((Xs list_nat)) (= (@ (@ sorted_wrt_nat ord_less_eq_nat) Xs) (forall ((I4 nat)) (let ((_let_1 (@ suc I4))) (let ((_let_2 (@ nth_nat Xs))) (=> (@ (@ ord_less_nat _let_1) (@ size_size_list_nat Xs)) (@ (@ ord_less_eq_nat (@ _let_2 I4)) (@ _let_2 _let_1)))))))) (forall ((A2 nat) (B2 nat) (F4 (-> nat assn)) (C assn)) (=> (@ (@ ord_less_eq_nat A2) B2) (=> (@ (@ ord_less_assn (@ F4 B2)) C) (=> (forall ((X3 nat) (Y2 nat)) (=> (@ (@ ord_less_eq_nat X3) Y2) (@ (@ ord_less_eq_assn (@ F4 X3)) (@ F4 Y2)))) (@ (@ ord_less_assn (@ F4 A2)) C))))) _let_10 (forall ((C code_integer) (B2 code_integer)) (= (@ (@ ord_le3102999989581377725nteger C) (@ (@ times_3573771949741848930nteger C) B2)) (and (=> (@ (@ ord_le6747313008572928689nteger zero_z3403309356797280102nteger) C) (@ (@ ord_le3102999989581377725nteger one_one_Code_integer) B2)) (=> (@ (@ ord_le6747313008572928689nteger C) zero_z3403309356797280102nteger) (@ (@ ord_le3102999989581377725nteger B2) one_one_Code_integer))))) (forall ((N nat)) (=> (@ (@ ord_less_nat zero_zero_nat) N) (= N (@ suc (@ (@ minus_minus_nat N) one_one_nat))))) (forall ((X code_integer) (Y code_integer)) (let ((_let_1 (@ ord_le3102999989581377725nteger zero_z3403309356797280102nteger))) (=> (@ _let_1 X) (=> (@ _let_1 Y) (= (@ (@ ord_less_nat (@ code_nat_of_integer X)) (@ code_nat_of_integer Y)) (@ (@ ord_le6747313008572928689nteger X) Y)))))) (forall ((A2 assn) (B2 assn) (C assn)) (let ((_let_1 (@ ord_less_eq_assn A2))) (=> (@ _let_1 B2) (=> (= B2 C) (@ _let_1 C))))) (forall ((X nat) (Y nat) (Xs list_nat)) (let ((_let_1 (@ remove1_nat X))) (let ((_let_2 (@ cons_nat Y))) (let ((_let_3 (@ _let_1 (@ _let_2 Xs)))) (let ((_let_4 (= X Y))) (and (=> _let_4 (= _let_3 Xs)) (=> (not _let_4) (= _let_3 (@ _let_2 (@ _let_1 Xs)))))))))) (= ord_less_num (lambda ((A3 num) (B3 num)) (and (@ (@ ord_less_eq_num A3) B3) (not (= A3 B3))))) (forall ((N1 nat) (R1 list_nat) (N22 nat) (R22 list_nat)) (=> (= (@ (@ cons_nat N1) R1) (@ (@ cons_nat N22) R22)) (and (= R1 R22) (= N1 N22)))) (forall ((A set_o)) (= (@ (@ minus_minus_set_o A) bot_bot_set_o) A)) (forall ((A2 rat) (B2 rat) (C rat)) (= (@ (@ minus_minus_rat A2) (@ (@ minus_minus_rat B2) C)) (@ (@ minus_minus_rat (@ (@ plus_plus_rat A2) C)) B2))) (forall ((Y nat) (X222 list_nat) (X21 nat)) (let ((_let_1 (@ member_nat Y))) (=> (@ _let_1 (@ set_nat2 X222)) (@ _let_1 (@ set_nat2 (@ (@ cons_nat X21) X222)))))) (forall ((Xs list_nat) (I nat)) (= (@ (@ (@ list_update_nat Xs) I) (@ (@ nth_nat Xs) I)) Xs)) (forall ((A2 nat)) (= (@ (@ times_times_nat zero_zero_nat) A2) zero_zero_nat)) (forall ((A2 code_integer) (M2 nat) (N nat)) (let ((_let_1 (@ power_8256067586552552935nteger A2))) (=> (@ (@ ord_le6747313008572928689nteger one_one_Code_integer) A2) (= (= (@ _let_1 M2) (@ _let_1 N)) (= M2 N))))) (= ord_less_eq_set_nat (lambda ((B3 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cons_P2971678138204555879n_assn X) Xs)) (@ (@ cons_nat Y) Ys)) (@ (@ cons_P110449348784310650sn_nat (@ (@ produc6456381919915743786sn_nat X) Y)) (@ (@ zip_Pr1018045463562677002sn_nat Xs) Ys)))) (forall ((A2 rat) (B2 rat)) (let ((_let_1 (@ ord_less_rat zero_zero_rat))) (=> (@ _let_1 A2) (=> (@ (@ ord_less_eq_rat zero_zero_rat) B2) (@ _let_1 (@ (@ plus_plus_rat A2) B2)))))) (forall ((Xs list_P8527749157015355191n_assn) (Ys list_P8527749157015355191n_assn)) (= (= nil_Pr4327835960982145133n_assn (@ (@ zip_Pr8806919808394484215n_assn Xs) Ys)) (or (= Ys nil_Pr5671120429643327159n_assn) (= Xs nil_Pr5671120429643327159n_assn)))) (forall ((A2 int) (A set_int)) (=> (@ (@ member_int A2) A) (exists ((B5 set_int)) (and (not (@ (@ member_int A2) B5)) (= A (@ (@ insert_int2 A2) B5)))))) (forall ((I code_integer) (J code_integer) (K3 code_integer) (L code_integer)) (=> (and (@ (@ ord_le6747313008572928689nteger K3) L) (@ (@ ord_le3102999989581377725nteger I) J)) (@ (@ ord_le6747313008572928689nteger (@ (@ plus_p5714425477246183910nteger I) K3)) (@ (@ plus_p5714425477246183910nteger J) L)))) (forall ((A set_nat) (B set_nat) (C2 set_nat)) (let ((_let_1 (@ ord_less_eq_set_nat A))) (=> (@ _let_1 B) (=> (@ (@ ord_less_eq_set_nat B) C2) (@ _let_1 C2))))) (forall ((X int) (Y int) (Z int)) (=> (@ (@ ord_less_eq_int X) Y) (=> (@ (@ ord_less_int Y) Z) (@ (@ ord_less_int X) Z)))) (forall ((A2 code_integer) (B2 code_integer)) (=> (not (= A2 B2)) (=> (@ (@ ord_le3102999989581377725nteger A2) B2) (@ (@ ord_le6747313008572928689nteger A2) B2)))) (forall ((C int)) (not (@ (@ member_int C) bot_bot_set_int))) (forall ((B2 set_nat) (C set_nat) (A2 set_nat)) (=> (@ (@ ord_less_eq_set_nat (@ (@ sup_sup_set_nat B2) C)) A2) (not (=> (@ (@ ord_less_eq_set_nat B2) A2) (not (@ (@ ord_less_eq_set_nat C) A2)))))) (forall ((X (-> produc3658429121746597890et_nat Bool)) (Xs list_P7985473006766602707_nat_o)) (let ((_let_1 (@ size_s8908918004648414271_nat_o Xs))) (let ((_let_2 (@ size_s8908918004648414271_nat_o (@ (@ remove4235003712227595625_nat_o X) Xs)))) (let ((_let_3 (@ (@ member6576561426505652726_nat_o X) (@ set_Pr400311997697478754_nat_o Xs)))) (and (=> _let_3 (= _let_2 (@ (@ minus_minus_nat _let_1) one_one_nat))) (=> (not _let_3) (= _let_2 _let_1))))))) (forall ((A set_Pr1261947904930325089at_nat) (B set_Pr1261947904930325089at_nat)) (@ (@ ord_le3146513528884898305at_nat (@ (@ inf_in2572325071724192079at_nat A) B)) B)) _let_8 (forall ((X num)) (@ (@ ord_less_nat zero_zero_nat) (@ nat_of_num X))) (not (@ _let_7 zero_zero_int)) (forall ((P (-> int Bool)) (I int) (J int)) (= (@ (@ list_all_int P) (@ (@ upto I) J)) (@ (@ (@ all_interval_int P) I) J))) (forall ((X int) (Y int) (Z int)) (= (@ (@ plus_plus_int (@ (@ ord_min_int X) Y)) Z) (@ (@ ord_min_int (@ (@ plus_plus_int X) Z)) (@ (@ plus_plus_int Y) Z)))) (forall ((D int) (T int) (A set_int)) (=> (@ (@ ord_less_int zero_zero_int) D) (=> (@ (@ member_int (@ (@ plus_plus_int T) one_one_int)) A) (forall ((X7 int)) (=> (forall ((Xa3 int)) (=> (@ (@ member_int Xa3) (@ (@ set_or1266510415728281911st_int one_one_int) D)) (forall ((Xb3 int)) (=> (@ (@ member_int Xb3) A) (not (= X7 (@ (@ minus_minus_int Xb3) Xa3))))))) (=> (= X7 T) (= (@ (@ plus_plus_int X7) D) T))))))) (forall ((K3 int) (L int) (Q6 int) (R2 int)) (=> (@ (@ (@ eucl_rel_int K3) L) (@ (@ product_Pair_int_int Q6) R2)) (= (@ (@ divide_divide_int K3) L) Q6))) (forall ((A2 set_nat) (B2 set_nat)) (=> (@ (@ ord_less_eq_set_nat A2) B2) (= (@ (@ sup_sup_set_nat A2) B2) B2))) (forall ((F4 (-> produc3925858234332021118et_nat Bool)) (A2 (-> produc3658429121746597890et_nat Bool)) (B2 produc3658429121746597890et_nat)) (=> (@ F4 (@ (@ produc5001842942810119800et_nat A2) B2)) (@ (@ (@ produc6216949301066131538_nat_o F4) A2) B2))) (forall ((N nat) (P (-> nat Bool))) (=> (=> (forall ((N3 nat)) (=> (@ (@ ord_less_nat N3) N) (not (@ P N3)))) (@ P N)) (exists ((N4 nat)) (and (@ P N4) (@ (@ ord_less_eq_nat N4) N))))) (= upto_aux (lambda ((I4 int) (J2 int) (Js list_int)) (@ (@ (@ 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(@ (@ times_times_assn (@ (@ P A2) C)) (@ (@ _let_1 As2) Cs))))) (forall ((Xs list_int) (Xs4 list_int) (Xsi list_P8527749157015355191n_assn) (Xsi2 list_P8527749157015355191n_assn) (A (-> int produc6575502325842934193n_assn assn)) (A6 (-> int produc6575502325842934193n_assn assn))) (=> (= Xs Xs4) (=> (= Xsi Xsi2) (=> (forall ((X3 int) (Xi produc6575502325842934193n_assn)) (=> (@ (@ member_int X3) (@ set_int2 Xs4)) (=> (@ (@ member7957490590177025114n_assn Xi) (@ set_Pr1139785259514867910n_assn Xsi2)) (= (@ (@ A X3) Xi) (@ (@ A6 X3) Xi))))) (= (@ (@ (@ vEBT_L1620274777744359680n_assn A) Xs) Xsi) (@ (@ (@ vEBT_L1620274777744359680n_assn A6) Xs4) Xsi2)))))) (forall ((B nat) (K3 nat) (B2 nat) (A2 nat)) (let ((_let_1 (@ plus_plus_nat A2))) (let ((_let_2 (@ plus_plus_nat K3))) (=> (= B (@ _let_2 B2)) (= (@ _let_1 B) (@ _let_2 (@ _let_1 B2))))))) (forall ((A2 int) (B2 int)) (=> (@ (@ ord_less_eq_int A2) B2) (= A2 (@ (@ inf_inf_int A2) B2)))) (forall ((M2 set_Pr1261947904930325089at_nat) (Ms list_s1210847774152347623at_nat) (N set_Pr1261947904930325089at_nat) (Ns list_s1210847774152347623at_nat) (R2 set_Pr4329608150637261639at_nat)) (let ((_let_1 (@ lenlex1357538814655152620at_nat R2))) (let ((_let_2 (@ size_s8736152011456118867at_nat Ns))) (let ((_let_3 (@ size_s8736152011456118867at_nat Ms))) (= (@ (@ member4080735728053443344at_nat (@ (@ produc7536900900485677911at_nat (@ (@ cons_s6881495754146722583at_nat M2) Ms)) (@ (@ cons_s6881495754146722583at_nat N) Ns))) _let_1) (or (@ (@ ord_less_nat _let_3) _let_2) (and (@ (@ member8757157785044589968at_nat (@ (@ produc2922128104949294807at_nat M2) N)) R2) (= _let_3 _let_2)) (and (@ (@ member4080735728053443344at_nat (@ (@ produc7536900900485677911at_nat Ms) Ns)) _let_1) (= M2 N)))))))) (forall ((A2 assn) (B2 assn) (F4 (-> assn num)) (C num)) (=> (@ (@ ord_less_assn A2) B2) (=> (@ (@ ord_less_eq_num (@ F4 B2)) C) (=> (forall ((X3 assn) (Y2 assn)) (=> (@ (@ ord_less_assn X3) Y2) (@ (@ ord_less_num (@ F4 X3)) (@ F4 Y2)))) (@ (@ ord_less_num (@ F4 A2)) C))))) (forall ((R2 int) (L int) (K3 int) (Q6 int)) (=> (= (@ sgn_sgn_int R2) (@ sgn_sgn_int L)) (=> (@ (@ ord_less_int (@ abs_abs_int R2)) (@ abs_abs_int L)) (=> (= K3 (@ (@ plus_plus_int (@ (@ times_times_int Q6) L)) R2)) (@ (@ (@ eucl_rel_int K3) L) (@ (@ product_Pair_int_int Q6) R2)))))) (forall ((F4 (-> nat assn)) (N nat) (M2 nat)) (=> (forall ((N5 nat)) (@ (@ ord_less_assn (@ F4 N5)) (@ F4 (@ suc N5)))) (= (@ (@ ord_less_assn (@ F4 N)) (@ F4 M2)) (@ (@ ord_less_nat N) M2)))) (forall ((I nat) (L list_d) (X d)) (=> (@ (@ ord_less_nat I) (@ size_size_list_d L)) (= (@ (@ insert_d (@ (@ nth_d L) I)) (@ set_d2 (@ (@ (@ list_update_d L) I) X))) (@ (@ insert_d X) (@ set_d2 L))))) (forall ((A2 nat) (B2 nat) (C nat) (D2 nat)) (=> (@ (@ ord_less_nat A2) B2) (=> (@ (@ ord_less_nat C) D2) (=> (@ (@ ord_less_nat zero_zero_nat) B2) (=> (@ (@ ord_less_eq_nat zero_zero_nat) C) (@ (@ ord_less_nat (@ (@ times_times_nat A2) C)) (@ (@ times_times_nat B2) D2))))))) (forall ((A2 assn) (F4 (-> nat assn)) (B2 nat) (C nat)) (let ((_let_1 (@ ord_less_assn A2))) (=> (@ _let_1 (@ F4 B2)) (=> (@ (@ ord_less_nat B2) C) (=> (forall ((X3 nat) (Y2 nat)) (=> (@ (@ ord_less_nat X3) Y2) (@ (@ ord_less_assn (@ F4 X3)) (@ F4 Y2)))) (@ _let_1 (@ F4 C))))))) (forall ((S set_Pr4532377907799695533_nat_o)) (=> (not (= S bot_bo7824918357723582233_nat_o)) (not (forall ((X3 (-> produc3658429121746597890et_nat Bool))) (not (@ (@ member6576561426505652726_nat_o X3) S)))))) (forall ((C produc3843707927480180839at_nat) (B set_Pr4329608150637261639at_nat) (A set_Pr4329608150637261639at_nat)) (let ((_let_1 (@ member8757157785044589968at_nat C))) (=> (=> (not (@ _let_1 B)) (@ _let_1 A)) (@ _let_1 (@ (@ sup_su5525570899277871387at_nat A) B))))) (forall ((Xs list_nat) (N nat) (X nat)) (=> (@ distinct_nat Xs) (=> (@ (@ ord_less_nat N) (@ size_size_list_nat Xs)) (= (@ set_nat2 (@ (@ (@ list_update_nat Xs) N) X)) (@ (@ insert_nat2 X) (@ (@ minus_minus_set_nat (@ set_nat2 Xs)) (@ (@ insert_nat2 (@ (@ nth_nat Xs) N)) bot_bot_set_nat))))))) (forall ((I nat) (I3 set_nat) (Xs list_int) (A (-> int nat assn)) (Xsi list_nat)) (=> (not (@ (@ member_nat I) I3)) (=> (@ (@ ord_less_nat I) (@ size_size_list_int Xs)) (= (@ (@ (@ (@ vEBT_L8891422820522952478nt_nat (@ (@ insert_nat2 I) I3)) A) Xs) Xsi) (@ (@ times_times_assn (@ (@ A (@ (@ nth_int Xs) I)) (@ (@ nth_nat Xsi) I))) (@ (@ (@ (@ vEBT_L8891422820522952478nt_nat I3) A) Xs) Xsi)))))) (forall ((A2 set_nat) (B2 set_nat)) (@ (@ ord_less_eq_set_nat (@ (@ inf_inf_set_nat A2) B2)) B2)) (forall ((B2 nat) (A2 nat) (C nat)) (let ((_let_1 (@ times_times_nat B2))) (let ((_let_2 (@ times_times_nat A2))) (= (@ _let_1 (@ _let_2 C)) (@ _let_2 (@ _let_1 C)))))) (forall ((L12 list_c) (L23 list_nat)) (=> (= (@ size_size_list_c L12) (@ size_size_list_nat L23)) (= (@ (@ (@ zipf_c7084520048314076179_c_nat product_Pair_c_nat) L12) L23) (@ (@ zip_c_nat L12) L23)))) (forall ((X produc6575502325842934193n_assn) (Y produc6575502325842934193n_assn) (R2 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plus_p7104986032573967614at_nat Z7) B))) ms_weak)))) (forall ((A2 set_nat) (X set_nat) (B2 set_nat)) (=> (@ (@ ord_less_eq_set_nat A2) X) (@ (@ ord_less_eq_set_nat (@ (@ inf_inf_set_nat A2) B2)) X))) (forall ((A2 code_integer) (C code_integer) (B2 code_integer)) (= (@ (@ ord_le6747313008572928689nteger (@ (@ times_3573771949741848930nteger A2) C)) (@ (@ times_3573771949741848930nteger B2) C)) (and (=> (@ (@ ord_le3102999989581377725nteger zero_z3403309356797280102nteger) C) (@ (@ ord_le6747313008572928689nteger A2) B2)) (=> (@ (@ ord_le3102999989581377725nteger C) zero_z3403309356797280102nteger) (@ (@ ord_le6747313008572928689nteger B2) A2))))) (forall ((D2 int) (Z int) (X int)) (=> (@ (@ ord_less_int zero_zero_int) D2) (@ (@ ord_less_int Z) (@ (@ plus_plus_int X) (@ (@ times_times_int (@ (@ plus_plus_int (@ abs_abs_int (@ (@ minus_minus_int X) Z))) one_one_int)) D2))))) (forall ((A2 rat)) (= (@ (@ minus_minus_rat A2) A2) zero_zero_rat)) (forall ((A2 set_Pr1261947904930325089at_nat) (X set_Pr1261947904930325089at_nat) (B2 set_Pr1261947904930325089at_nat)) (=> (@ (@ ord_le3146513528884898305at_nat A2) X) (@ (@ ord_le3146513528884898305at_nat (@ (@ inf_in2572325071724192079at_nat A2) B2)) X))) (forall ((A2 nat) (B2 nat)) (=> (@ (@ ord_less_nat A2) zero_zero_nat) (=> (@ (@ ord_less_eq_nat B2) zero_zero_nat) (@ (@ ord_less_nat (@ (@ plus_plus_nat A2) B2)) zero_zero_nat)))) (forall ((Xs list_assn) (Ys list_assn) (Xy produc6575502325842934193n_assn) (Xys list_P8527749157015355191n_assn)) (=> (= (@ (@ zip_assn_assn Xs) Ys) (@ (@ cons_P2971678138204555879n_assn Xy) Xys)) (not (forall ((X3 assn) (Xs5 list_assn)) (=> (= Xs (@ (@ cons_assn X3) Xs5)) (forall ((Y2 assn) (Ys4 list_assn)) (=> (= Ys (@ (@ cons_assn Y2) Ys4)) (=> (= Xy (@ (@ produc118845697133431529n_assn X3) Y2)) (not (= Xys (@ (@ zip_assn_assn Xs5) Ys4))))))))))) (forall ((B2 int) (C int) (A2 int)) (=> (@ (@ ord_less_int B2) C) (@ (@ ord_less_int (@ (@ inf_inf_int A2) B2)) C))) (forall ((A2 rat) (B2 rat)) (=> (@ (@ ord_less_rat A2) zero_zero_rat) (=> (@ (@ ord_less_rat B2) zero_zero_rat) (@ (@ ord_less_rat zero_zero_rat) (@ (@ times_times_rat A2) B2))))) (forall ((A set_nat) (A2 nat)) (=> (= A bot_bot_set_nat) (not (@ (@ member_nat A2) A)))) _let_6 (forall ((X produc6575502325842934193n_assn) (Y produc6575502325842934193n_assn) (Xs list_P8527749157015355191n_assn)) (let ((_let_1 (@ remove1763081955827946941n_assn X))) (let ((_let_2 (@ _let_1 Xs))) (let ((_let_3 (@ cons_P2971678138204555879n_assn Y))) (let ((_let_4 (@ _let_1 (@ _let_3 Xs)))) (let ((_let_5 (= X Y))) (and (=> _let_5 (= _let_4 _let_2)) (=> (not _let_5) (= _let_4 (@ _let_3 _let_2)))))))))) (forall ((H2 heap_e7401611519738050253t_unit) (As2 set_nat) (Q assn) (R assn)) (let ((_let_1 (@ (@ produc7507926704131184380et_nat H2) As2))) (=> (@ in_range _let_1) (=> (forall ((H5 heap_e7401611519738050253t_unit) (As4 set_nat)) (let ((_let_1 (@ produc7507926704131184380et_nat H5))) (=> (= (@ (@ inf_inf_set_nat As2) As4) bot_bot_set_nat) (=> (@ (@ (@ relH As2) H2) H5) (=> (@ in_range (@ _let_1 As2)) (=> (@ (@ rep_assn Q) (@ _let_1 As4)) (@ (@ rep_assn R) (@ _let_1 (@ (@ sup_sup_set_nat As2) As4))))))))) (@ (@ rep_assn (@ (@ wand_assn Q) R)) _let_1))))) (forall ((A2 nat) (B2 nat)) (=> (@ (@ ord_less_eq_nat A2) B2) (= (@ (@ plus_plus_nat (@ (@ minus_minus_nat B2) A2)) A2) B2))) (= ord_le2510731241096832064er_nat (lambda ((A3 filter_nat) (B3 filter_nat)) (or (@ (@ ord_less_filter_nat A3) B3) (= A3 B3)))) (forall ((Xa product_prod_nat_nat) (X product_prod_nat_nat)) (= (@ (@ times_times_int (@ abs_Integ Xa)) (@ abs_Integ X)) (@ abs_Integ (@ (@ (@ produc27273713700761075at_nat (lambda ((X2 nat) (Y5 nat) (__flatten_var_0 product_prod_nat_nat)) (@ (@ produc2626176000494625587at_nat (lambda ((U4 nat) (V4 nat)) (let ((_let_1 (@ times_times_nat Y5))) (let ((_let_2 (@ times_times_nat X2))) (@ (@ product_Pair_nat_nat (@ (@ plus_plus_nat (@ _let_2 U4)) (@ _let_1 V4))) (@ (@ plus_plus_nat (@ _let_2 V4)) (@ _let_1 U4))))))) __flatten_var_0))) Xa) X)))) (forall ((X nat) (Y nat)) (=> (@ (@ ord_less_eq_nat X) Y) (= (@ (@ ord_min_nat X) Y) X))) (forall ((Xs list_P8527749157015355191n_assn)) (= (= nil_Pr5671120429643327159n_assn (@ rev_Pr4855572775806611735n_assn Xs)) (= Xs nil_Pr5671120429643327159n_assn))) (forall ((X code_integer) (Y code_integer)) (=> (not (= X Y)) (=> (not (@ (@ ord_le6747313008572928689nteger X) Y)) (@ (@ ord_le6747313008572928689nteger Y) X)))) (forall ((N nat) (M2 nat)) (let ((_let_1 (@ ord_less_nat N))) (=> (not (@ _let_1 M2)) (=> (@ _let_1 (@ suc M2)) (= M2 N))))) (forall ((A2 nat) (B2 nat) (C nat)) (let ((_let_1 (@ times_times_nat C))) (=> (@ (@ ord_less_nat A2) B2) (=> (@ (@ ord_less_nat zero_zero_nat) C) (@ (@ ord_less_nat (@ _let_1 A2)) (@ _let_1 B2)))))) (forall ((X c) (Xs list_c)) (=> (@ (@ member_c X) (@ set_c2 Xs)) (@ (@ ord_less_nat zero_zero_nat) (@ size_size_list_c Xs)))) (forall ((T int)) (exists ((Z4 int)) (forall ((X7 int)) (=> (@ (@ ord_less_int X7) Z4) (not (= X7 T)))))) (forall ((F4 (-> int nat int))) (= (@ (@ (@ zipf_int_nat_int F4) nil_int) nil_nat) nil_int)) _let_5 (forall ((A2 set_nat) (B2 set_nat)) (=> (@ (@ ord_less_set_nat A2) B2) (= (@ (@ inf_inf_set_nat A2) B2) A2))) (forall ((N nat)) (let ((_let_1 (@ ord_less_nat zero_zero_nat))) (= (@ _let_1 (@ bit_se2002935070580805687sk_nat N)) (@ _let_1 N)))) (forall ((A2 int) (B2 int)) (=> (@ (@ ord_less_int A2) B2) (= (@ (@ inf_inf_int A2) B2) A2))) (forall ((D int) (P (-> int Bool)) (P3 (-> int Bool)) (A set_int)) (=> (@ (@ ord_less_int zero_zero_int) D) (=> (exists ((Z3 int)) (forall ((X3 int)) (=> (@ (@ ord_less_int Z3) X3) (= (@ P X3) (@ P3 X3))))) (=> (forall ((X3 int)) (=> (forall ((Xa2 int)) (=> (@ (@ member_int Xa2) (@ (@ set_or1266510415728281911st_int one_one_int) D)) (forall ((Xb2 int)) (=> (@ (@ member_int Xb2) A) (not (= X3 (@ (@ minus_minus_int Xb2) Xa2))))))) (=> (@ P X3) (@ P (@ (@ plus_plus_int X3) D))))) (=> (forall ((X3 int) (K int)) (= (@ P3 X3) (@ P3 (@ (@ minus_minus_int X3) (@ (@ times_times_int K) D))))) (= (exists ((X8 int)) (@ P X8)) (or (exists ((X2 int)) (and (@ (@ member_int X2) (@ (@ set_or1266510415728281911st_int one_one_int) D)) (exists ((Y5 int)) (and (@ (@ member_int Y5) A) (@ P (@ (@ minus_minus_int Y5) X2)))))) (exists ((X2 int)) (and (@ P3 X2) (@ (@ member_int X2) (@ (@ set_or1266510415728281911st_int one_one_int) D))))))))))) (forall ((A2 nat) (B2 nat)) (let ((_let_1 (@ ord_less_nat zero_zero_nat))) (=> (@ _let_1 A2) (=> (@ (@ ord_less_eq_nat zero_zero_nat) B2) (@ _let_1 (@ (@ plus_plus_nat A2) B2)))))) (forall ((A2 num) (F4 (-> int num)) (B2 int) (C int)) (=> (@ (@ ord_less_eq_num A2) (@ F4 B2)) (=> (@ (@ ord_less_int B2) C) (=> (forall ((X3 int) (Y2 int)) (=> (@ (@ ord_less_int X3) Y2) (@ (@ ord_less_num (@ F4 X3)) (@ F4 Y2)))) (@ (@ ord_less_num A2) (@ F4 C)))))) (forall ((Xs list_P8527749157015355191n_assn) (A set_Pr5949110396991348497n_assn) (X produc6575502325842934193n_assn) (I nat)) (=> (@ (@ ord_le171416862856029873n_assn (@ set_Pr1139785259514867910n_assn Xs)) A) (=> (@ (@ member7957490590177025114n_assn X) A) (@ (@ ord_le171416862856029873n_assn (@ set_Pr1139785259514867910n_assn (@ (@ (@ list_u4534839942911652127n_assn Xs) I) X))) A)))) (forall ((Xs list_P1743416141875011707e_term) (I nat) (X (-> produc8551481072490612790e_term option6357759511663192854e_term)) (Ys list_P5707943133018811711nt_int) (Y product_prod_int_int)) (= (@ (@ zip_Pr4168994715204986005nt_int (@ (@ (@ list_u3533491785856317309e_term Xs) I) X)) (@ (@ (@ list_u3002344382305578791nt_int Ys) I) Y)) (@ (@ (@ list_u7736365598306452245nt_int (@ (@ zip_Pr4168994715204986005nt_int Xs) Ys)) I) (@ (@ produc5700946648718959541nt_int X) Y)))) (forall ((X assn)) (= (@ (@ inf_inf_assn X) bot_bot_assn) bot_bot_assn)) (forall ((C2 set_Pr1261947904930325089at_nat) (D set_Pr1261947904930325089at_nat) (A2 product_prod_nat_nat)) (let ((_let_1 (@ insert8211810215607154385at_nat A2))) (=> (@ (@ ord_le3146513528884898305at_nat C2) D) (@ (@ ord_le3146513528884898305at_nat (@ _let_1 C2)) (@ _let_1 D))))) (forall ((A set_Pr4329608150637261639at_nat) (X produc3843707927480180839at_nat)) (let ((_let_1 (@ (@ insert9069300056098147895at_nat X) bot_bo228742789529271731at_nat))) (=> (@ (@ ord_le1268244103169919719at_nat A) _let_1) (or (= A bot_bo228742789529271731at_nat) (= A _let_1))))) (forall ((X nat) (Xs list_nat)) (@ (@ ord_less_eq_set_nat (@ set_nat2 (@ (@ remove1_nat X) Xs))) (@ set_nat2 Xs))) (= sup_sup_set_nat (lambda ((X2 set_nat) (Y5 set_nat)) (@ (@ sup_sup_set_nat Y5) X2))) (forall ((N nat)) (exists ((Xs2 list_d)) (= (@ size_size_list_d Xs2) N))) (forall ((A2 assn) (B2 assn)) (let ((_let_1 (@ (@ inf_inf_assn A2) B2))) (= (@ (@ inf_inf_assn _let_1) B2) _let_1))) (forall ((N nat) (Xs list_P8527749157015355191n_assn) (P (-> produc6575502325842934193n_assn Bool))) (=> (@ (@ ord_less_nat N) (@ size_s6829681357464350627n_assn Xs)) (=> (forall ((X3 produc6575502325842934193n_assn)) (=> (@ (@ member7957490590177025114n_assn X3) (@ set_Pr1139785259514867910n_assn Xs)) (@ P X3))) (@ P (@ (@ nth_Pr1769885009046257848n_assn Xs) N))))) (forall ((Xs list_c)) (= (@ size_size_list_c (@ rotate1_c Xs)) (@ size_size_list_c Xs))) (forall ((A2 set_nat)) (= (@ (@ sup_sup_set_nat A2) bot_bot_set_nat) A2)) (forall ((A2 int) (B2 int) (C int)) (=> (@ (@ ord_less_int A2) B2) (=> (@ (@ ord_less_int zero_zero_int) C) (@ (@ ord_less_int (@ (@ times_times_int A2) C)) (@ (@ times_times_int B2) C))))) (forall ((A2 set_int)) (= (@ (@ sup_sup_set_int A2) bot_bot_set_int) A2)) (forall ((C set_nat) (A2 set_nat) (B2 set_nat)) (let ((_let_1 (@ ord_less_set_nat C))) (=> (@ _let_1 A2) (@ _let_1 (@ (@ sup_sup_set_nat A2) B2))))) (forall ((A2 rat) (B2 rat) (C rat) (D2 rat)) (=> (@ (@ ord_less_eq_rat A2) B2) (=> (@ (@ ord_less_eq_rat C) D2) (@ (@ ord_less_eq_rat (@ (@ plus_plus_rat A2) C)) (@ (@ plus_plus_rat B2) D2))))) (forall ((A2 set_o)) (= (@ (@ sup_sup_set_o A2) bot_bot_set_o) A2)) (forall ((Xa product_prod_int_int) (X product_prod_int_int)) (let ((_let_1 (@ product_snd_int_int X))) (let ((_let_2 (@ product_snd_int_int Xa))) (=> (@ (@ ratrel Xa) Xa) (=> (@ (@ ratrel X) X) (= (@ (@ plus_plus_rat (@ abs_Rat Xa)) (@ abs_Rat X)) (@ abs_Rat (@ (@ product_Pair_int_int (@ (@ plus_plus_int (@ (@ times_times_int (@ product_fst_int_int Xa)) _let_1)) (@ (@ times_times_int (@ product_fst_int_int X)) _let_2))) (@ (@ times_times_int _let_2) _let_1))))))))) (forall ((A set_nat) (A2 nat) (B set_nat)) (let ((_let_1 (@ insert_nat2 A2))) (let ((_let_2 (@ minus_minus_set_nat A))) (= (@ _let_2 (@ _let_1 B)) (@ (@ minus_minus_set_nat (@ _let_2 (@ _let_1 bot_bot_set_nat))) B))))) (= zero_zero_rat (@ abs_Rat _let_4)) (forall ((B2 int) (A2 int) (C int)) (let ((_let_1 (@ ord_less_int C))) (=> (@ (@ ord_less_int B2) A2) (=> (@ _let_1 B2) (@ _let_1 A2))))) (= ord_less_int (lambda ((B3 int) (A3 int)) (and (@ (@ ord_less_eq_int B3) A3) (not (= A3 B3))))) (forall ((Xs list_c) (Ys list_d) (Zs list_int) (P (-> list_c list_d list_int Bool))) (let ((_let_1 (@ size_size_list_d Ys))) (=> (= (@ size_size_list_c Xs) _let_1) (=> (= _let_1 (@ size_size_list_int Zs)) (=> (@ (@ (@ P nil_c) nil_d) nil_int) (=> (forall ((X3 c) (Xs2 list_c) (Y2 d) (Ys5 list_d) (Z4 int) (Zs2 list_int)) (let ((_let_1 (@ size_size_list_d Ys5))) (=> (= (@ size_size_list_c Xs2) _let_1) (=> (= _let_1 (@ size_size_list_int Zs2)) (=> (@ (@ (@ P Xs2) Ys5) Zs2) (@ (@ (@ P (@ (@ cons_c X3) Xs2)) (@ (@ cons_d Y2) Ys5)) (@ (@ cons_int Z4) Zs2))))))) (@ (@ (@ P Xs) Ys) Zs))))))) (forall ((M2 nat) (I nat) (N nat)) (=> (@ (@ ord_less_nat M2) (@ (@ times_times_nat I) N)) (@ (@ ord_less_nat (@ (@ divide_divide_nat M2) N)) I))) (forall ((P (-> list_nat list_P8527749157015355191n_assn Bool)) (R (-> nat produc6575502325842934193n_assn Bool)) (Xs list_nat) (Ys list_P8527749157015355191n_assn)) (=> (forall ((Xs2 list_nat)) (@ (@ P Xs2) nil_Pr5671120429643327159n_assn)) (=> (forall ((X_1 list_P8527749157015355191n_assn)) (@ (@ P nil_nat) X_1)) (=> (forall ((X3 nat) (Xs2 list_nat) (Y2 produc6575502325842934193n_assn) (Ys5 list_P8527749157015355191n_assn)) (let ((_let_1 (@ (@ cons_P2971678138204555879n_assn Y2) Ys5))) (=> (@ (@ R X3) Y2) (=> (@ (@ P Xs2) _let_1) (@ (@ P (@ (@ cons_nat X3) Xs2)) _let_1))))) (=> (forall ((X3 nat) (Xs2 list_nat) (Y2 produc6575502325842934193n_assn) (Ys5 list_P8527749157015355191n_assn)) (let ((_let_1 (@ P (@ (@ cons_nat X3) Xs2)))) (=> (not (@ (@ R X3) Y2)) (=> (@ _let_1 Ys5) (@ _let_1 (@ (@ cons_P2971678138204555879n_assn Y2) Ys5)))))) (@ (@ P Xs) Ys)))))) (forall ((A2 nat) (F4 (-> nat nat)) (B2 nat) (C nat)) (let ((_let_1 (@ ord_less_nat A2))) (=> (@ _let_1 (@ F4 B2)) (=> (@ (@ ord_less_eq_nat B2) C) (=> (forall ((X3 nat) (Y2 nat)) (=> (@ (@ ord_less_eq_nat X3) Y2) (@ (@ ord_less_eq_nat (@ F4 X3)) (@ F4 Y2)))) (@ _let_1 (@ F4 C))))))) (forall ((I nat) (I3 set_nat) (Xs list_c) (A (-> c nat assn)) (Xsi list_nat)) (=> (not (@ (@ member_nat I) I3)) (=> (@ (@ ord_less_nat I) (@ size_size_list_c Xs)) (= (@ (@ (@ (@ vEBT_L6585172037124793648_c_nat (@ (@ insert_nat2 I) I3)) A) Xs) Xsi) (@ (@ times_times_assn (@ (@ A (@ (@ nth_c Xs) I)) (@ (@ nth_nat Xsi) I))) (@ (@ (@ (@ vEBT_L6585172037124793648_c_nat I3) A) Xs) Xsi)))))) (forall ((A2 nat) (B2 nat) (C nat)) (=> (@ (@ ord_less_nat A2) B2) (=> (@ (@ ord_less_eq_nat C) A2) (@ (@ ord_less_nat (@ (@ minus_minus_nat A2) C)) (@ (@ minus_minus_nat B2) C))))) (forall ((L list_c) (P (-> c Bool))) (= (forall ((X2 c)) (=> (@ (@ member_c X2) (@ set_c2 L)) (@ P X2))) (forall ((I4 nat)) (=> (@ (@ ord_less_nat I4) (@ size_size_list_c L)) (@ P (@ (@ nth_c L) I4)))))) (forall ((C int) (A2 int) (B2 int)) (=> (@ (@ ord_less_eq_int C) zero_zero_int) (=> (@ (@ ord_less_eq_int A2) B2) (@ (@ ord_less_eq_int (@ (@ plus_plus_int A2) C)) B2)))) (forall ((C nat) (A2 nat) (B2 nat)) (let ((_let_1 (@ ord_less_nat C))) (=> (@ _let_1 A2) (@ _let_1 (@ (@ sup_sup_nat A2) B2))))) (= ord_less_eq_nat (lambda ((X2 nat) (Y5 nat)) (= (@ (@ inf_inf_nat X2) Y5) X2))) (forall ((A2 int) (B2 int) (C int)) (=> (@ (@ ord_less_eq_int A2) B2) (=> (@ (@ ord_less_int B2) C) (@ (@ ord_less_int A2) C)))) (forall ((A2 set_nat)) (= (@ (@ ord_less_eq_set_nat A2) bot_bot_set_nat) (= A2 bot_bot_set_nat))) _let_3 (forall ((X produc3843707927480180839at_nat)) (= (@ the_el221668144340439132at_nat (@ (@ insert9069300056098147895at_nat X) bot_bo228742789529271731at_nat)) X)) (forall ((A2 int) (B2 int)) (= (@ quotient_of (@ (@ fract A2) B2)) (@ normalize (@ (@ product_Pair_int_int A2) B2)))) (forall ((N nat)) (not (@ (@ ord_less_nat N) zero_zero_nat))) (forall ((X produc3658429121746597890et_nat)) (not (forall ((H heap_e7401611519738050253t_unit) (As set_nat)) (not (= X (@ (@ produc7507926704131184380et_nat H) As)))))) (forall ((A2 filter_nat) (X filter_nat) (B2 filter_nat)) (=> (@ (@ ord_le2510731241096832064er_nat A2) X) (@ (@ ord_le2510731241096832064er_nat (@ (@ inf_inf_filter_nat A2) B2)) X))) (forall ((A2 assn) (B2 assn) (F4 (-> assn filter_nat)) (C filter_nat)) (=> (@ (@ 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(or (and (@ (@ ord_less_rat B2) A2) (@ (@ ord_less_rat C) zero_zero_rat)) (and (@ (@ ord_less_rat A2) B2) (@ (@ ord_less_rat zero_zero_rat) C))))) (forall ((Xs list_nat) (Ys list_nat)) (=> (@ distinct_nat Xs) (=> (@ distinct_nat Ys) (@ distin6923225563576452346at_nat (@ (@ product_nat_nat Xs) Ys))))) (forall ((A2 rat) (B2 rat) (C rat)) (let ((_let_1 (@ ord_less_eq_rat B2))) (=> (@ (@ ord_less_eq_rat zero_zero_rat) A2) (=> (@ _let_1 C) (@ _let_1 (@ (@ plus_plus_rat A2) C)))))) (forall ((L nat) (H2 nat) (Is1 list_nat) (I nat) (Is2 list_nat)) (let ((_let_1 (@ upt L))) (= (= (@ _let_1 H2) (@ (@ append_nat Is1) (@ (@ cons_nat I) Is2))) (and (= Is2 (@ (@ upt (@ suc I)) H2)) (@ (@ ord_less_nat I) H2) (@ (@ ord_less_eq_nat L) I) (= Is1 (@ _let_1 I)))))) (forall ((Xs list_int) (P (-> int int Bool))) (=> (@ (@ ord_less_eq_nat (@ size_size_list_int Xs)) one_one_nat) (@ (@ sorted_wrt_int P) Xs))) (forall ((Y set_Pr1261947904930325089at_nat) (Z set_Pr1261947904930325089at_nat) (X 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C))) (=> (@ (@ ord_le3102999989581377725nteger (@ _let_1 A2)) (@ _let_1 B2)) (=> (@ (@ ord_le6747313008572928689nteger zero_z3403309356797280102nteger) C) (@ (@ ord_le3102999989581377725nteger A2) B2))))) (forall ((A2 list_d) (B2 list_c) (A7 list_d) (B6 list_c)) (=> (= (@ size_size_list_d A2) (@ size_size_list_c B2)) (=> (= (@ size_size_list_d A7) (@ size_size_list_c B6)) (=> (= (@ (@ zip_d_c A2) B2) (@ (@ zip_d_c A7) B6)) (and (= A2 A7) (= B2 B6)))))) (forall ((X assn) (A2 assn) (B2 assn)) (let ((_let_1 (@ ord_less_eq_assn X))) (=> (@ _let_1 A2) (@ _let_1 (@ (@ sup_sup_assn A2) B2))))) (forall ((M2 nat) (N nat)) (let ((_let_1 (@ (@ ord_min_nat M2) N))) (= (not (@ (@ ord_less_nat _let_1) M2)) (= _let_1 M2)))) (forall ((A2 int) (B2 int)) (let ((_let_1 (@ ord_less_int zero_zero_int))) (=> (@ _let_1 A2) (=> (@ (@ ord_less_eq_int zero_zero_int) B2) (@ _let_1 (@ (@ plus_plus_int A2) B2)))))) (forall ((Xs list_nat)) (= (@ set_nat2 (@ rotate1_nat Xs)) (@ set_nat2 Xs))) (forall ((P (-> nat Bool)) (N nat)) (=> (@ P N) (=> (not (@ P zero_zero_nat)) (exists ((K nat)) (and (@ (@ ord_less_eq_nat K) N) (forall ((I6 nat)) (=> (@ (@ ord_less_nat I6) K) (not (@ P I6)))) (@ P K)))))) (forall ((A2 int) (B2 int)) (let ((_let_1 (@ ord_less_int zero_zero_int))) (= (@ (@ ord_less_int (@ (@ times_times_int A2) B2)) zero_zero_int) (or (and (@ (@ ord_less_int B2) zero_zero_int) (@ _let_1 A2)) (and (@ _let_1 B2) (@ (@ ord_less_int A2) zero_zero_int)))))) (forall ((M2 nat) (N nat)) (= (@ (@ member8440522571783428010at_nat (@ (@ product_Pair_nat_nat M2) N)) (@ transi6264000038957366511cl_nat pred_nat)) (@ (@ ord_less_nat M2) N))) (forall ((A2 Bool) (A set_o)) (let ((_let_1 (@ insert_o2 A2))) (=> (@ (@ member_o A2) A) (= (@ _let_1 (@ (@ minus_minus_set_o A) (@ _let_1 bot_bot_set_o))) A)))) (forall ((A set_int)) (not (@ (@ ord_less_set_int A) bot_bot_set_int))) (forall ((W int) (Y int) (X int) (Z int)) (let ((_let_1 (@ times_times_int X))) (let ((_let_2 (@ times_times_int W))) (= (= (@ (@ plus_plus_int (@ _let_2 Y)) (@ _let_1 Z)) (@ (@ plus_plus_int (@ _let_2 Z)) (@ _let_1 Y))) (or (= W X) (= Y Z)))))) (forall ((A set_nat)) (= (@ (@ minus_minus_set_nat bot_bot_set_nat) A) bot_bot_set_nat)) (forall ((A set_Pr1261947904930325089at_nat)) (= (@ (@ minus_1356011639430497352at_nat A) bot_bo2099793752762293965at_nat) A)) (forall ((A2 Bool) (A set_o)) (=> (@ (@ member_o A2) A) (exists ((B5 set_o)) (and (= A (@ (@ insert_o2 A2) B5)) (not (@ (@ member_o A2) B5)))))) (forall ((A2 code_integer) (E code_integer) (C code_integer) (B2 code_integer) (D2 code_integer)) (= (@ (@ ord_le3102999989581377725nteger (@ (@ plus_p5714425477246183910nteger (@ (@ times_3573771949741848930nteger A2) E)) C)) (@ (@ plus_p5714425477246183910nteger (@ (@ times_3573771949741848930nteger B2) E)) D2)) (@ (@ ord_le3102999989581377725nteger (@ (@ plus_p5714425477246183910nteger (@ (@ times_3573771949741848930nteger (@ (@ minus_8373710615458151222nteger A2) B2)) E)) C)) D2))) (forall ((A2 set_Pr4329608150637261639at_nat) (B2 set_Pr4329608150637261639at_nat)) (=> (@ (@ ord_le1268244103169919719at_nat A2) B2) (= (@ (@ sup_su5525570899277871387at_nat A2) B2) B2))) (forall ((A2 int) (B2 int)) (=> (@ (@ ord_less_int A2) zero_zero_int) (=> (@ (@ ord_less_int zero_zero_int) B2) (@ (@ ord_less_int (@ (@ times_times_int A2) B2)) zero_zero_int)))) (forall ((B2 nat) (C nat) (A2 nat)) (=> (@ (@ ord_less_eq_nat B2) C) (@ (@ ord_less_eq_nat (@ (@ ord_min_nat A2) B2)) C))) (forall ((A set_Pr4329608150637261639at_nat)) (= (@ (@ minus_3314409938677909166at_nat A) bot_bo228742789529271731at_nat) A)) (forall ((A2 nat) (B2 nat) (A set_nat)) (let ((_let_1 (@ member_nat A2))) (= (@ _let_1 (@ (@ insert_nat2 B2) A)) (or (@ _let_1 A) (= A2 B2))))) (forall ((B set_nat) (A2 nat)) (@ (@ ord_less_eq_set_nat B) (@ (@ insert_nat2 A2) B))) (forall ((K3 nat) (M2 nat) (N nat)) (let ((_let_1 (@ times_times_nat (@ suc K3)))) (= (@ (@ ord_less_nat (@ _let_1 M2)) (@ _let_1 N)) (@ (@ ord_less_nat M2) N)))) (forall ((X product_prod_nat_nat) (S set_Pr1261947904930325089at_nat)) (=> (@ (@ member8440522571783428010at_nat X) S) (@ (@ ord_le7866589430770878221at_nat (@ (@ minus_1356011639430497352at_nat S) (@ (@ insert8211810215607154385at_nat X) bot_bo2099793752762293965at_nat))) S))) (forall ((A2 (-> produc3658429121746597890et_nat Bool)) (B2 produc3925858234332021118et_nat) (A7 (-> produc3658429121746597890et_nat Bool)) (B6 produc3925858234332021118et_nat)) (=> (= (@ (@ produc2245416461498447860et_nat A2) B2) (@ (@ produc2245416461498447860et_nat A7) B6)) (not (=> (= A2 A7) (not (= B2 B6)))))) (forall ((A2 rat) (C rat)) (= (@ (@ ord_less_rat (@ (@ times_times_rat A2) C)) C) (and (=> (@ (@ ord_less_eq_rat C) zero_zero_rat) (@ (@ ord_less_rat one_one_rat) A2)) (=> (@ (@ ord_less_eq_rat zero_zero_rat) C) (@ (@ ord_less_rat A2) one_one_rat))))) (forall ((P (-> nat Bool)) (Xs list_nat)) (let ((_let_1 (@ list_ex_nat P))) (= (@ _let_1 (@ rev_nat Xs)) (@ _let_1 Xs)))) (forall ((I nat) (Xs list_int) (J nat) (X int)) (let ((_let_1 (@ (@ nth_int (@ (@ (@ list_update_int Xs) I) X)) J))) (let ((_let_2 (= I J))) (=> (@ (@ ord_less_nat I) (@ size_size_list_int Xs)) (and (=> _let_2 (= _let_1 X)) (=> (not _let_2) (= _let_1 (@ (@ nth_int Xs) J)))))))) (forall ((C multis2468970476368604999at_nat) (B2 multis2468970476368604999at_nat) (A2 multis2468970476368604999at_nat)) (=> (= (@ (@ plus_p7104986032573967614at_nat C) B2) A2) (= C (@ (@ minus_4286766774447292334at_nat A2) B2)))) (forall ((Xs list_int) (Ys list_int) (R2 set_Pr958786334691620121nt_int)) (=> (@ (@ member6698963635872716290st_int (@ (@ produc364263696895485585st_int Xs) Ys)) (@ listrel1_int R2)) (= (@ size_size_list_int Xs) (@ size_size_list_int Ys)))) (forall ((A2 code_integer)) (not (@ (@ ord_le6747313008572928689nteger (@ (@ times_3573771949741848930nteger A2) A2)) zero_z3403309356797280102nteger))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
10.21/10.40	% SZS output end Proof for theBenchmark
10.21/10.40	EOF