0.08/0.13 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.08/0.14 % Command : do_cvc5 %s %d 0.15/0.35 % Computer : n025.cluster.edu 0.15/0.35 % Model : x86_64 x86_64 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.15/0.35 % Memory : 8042.1875MB 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64 0.15/0.35 % CPULimit : 960 0.15/0.35 % WCLimit : 120 0.15/0.36 % DateTime : Tue Aug 9 06:43:41 EDT 2022 0.15/0.36 % CPUTime : 0.99/1.22 %----Proving TH0 10.16/10.40 ------- cvc5-thf casc j11 : /export/starexec/sandbox2/benchmark/theBenchmark.p at /export/starexec/sandbox2/benchmark/theBenchmark.p... 10.16/10.40 --- Run --ho-elim --full-saturate-quant at 10... 10.16/10.40 % SZS status Theorem for theBenchmark 10.16/10.40 % SZS output start Proof for theBenchmark 10.16/10.40 (let ((_let_1 (= produc3946833401584108663at_nat (lambda ((P3 produc3843707927480180839at_nat)) (@ (@ produc2922128104949294807at_nat (@ produc2937545259423399429at_nat P3)) (@ produc6011863565407846595at_nat P3)))))) (let ((_let_2 (@ produc6842872674320459806at_nat minus_minus_nat))) (let ((_let_3 (= produc7726050920695093128at_nat (lambda ((A6 set_se7855581050983116737at_nat) (B6 (-> set_Pr1261947904930325089at_nat set_se7855581050983116737at_nat))) (@ comple4364388969068068532at_nat (@ (@ image_6898982319499645995at_nat (lambda ((X4 set_Pr1261947904930325089at_nat)) (@ comple4364388969068068532at_nat (@ (@ image_6898982319499645995at_nat (lambda ((Y5 set_Pr1261947904930325089at_nat)) (@ (@ insert9069300056098147895at_nat (@ (@ produc2922128104949294807at_nat X4) Y5)) bot_bo228742789529271731at_nat))) (@ B6 X4))))) A6)))))) (let ((_let_4 (@ image_num_num id_num))) (let ((_let_5 (= sup_su718114333110466843at_nat (lambda ((A6 set_Pr8693737435421807431at_nat) (B6 set_Pr8693737435421807431at_nat)) (@ comple2748534634209756852at_nat (@ (@ image_8493167801588156084at_nat (lambda ((B4 Bool)) (@ (@ (@ if_set1508868558775481357at_nat B4) A6) B6))) top_top_set_o)))))) (let ((_let_6 (@ (@ produc9045269283572012658at_rat top_top_set_nat) (lambda ((Uu nat)) top_top_set_rat)))) (let ((_let_7 (= _let_6 top_to7513191607651882425at_rat))) (let ((_let_8 (= quotient_rat_int (lambda ((R6 (-> rat rat Bool)) (Abs4 (-> rat int)) (Rep4 (-> int rat)) (T4 (-> rat int Bool))) (let ((_let_1 (@ conversep_rat_int T4))) (and (@ (@ ord_le3222257882335906850_int_o T4) (@ (@ bNF_Grp_rat_int top_top_set_rat) Abs4)) (@ (@ ord_le8236914709048111138_rat_o (@ (@ bNF_Grp_int_rat top_top_set_int) Rep4)) _let_1) (= R6 (@ (@ relcompp_rat_int_rat T4) _let_1)))))))) (let ((_let_9 (@ (@ bNF_re7400052026677387805at_int pcr_int) pcr_int))) (let ((_let_10 (= quotient_rat_char (lambda ((R6 (-> rat rat Bool)) (Abs4 (-> rat char)) (Rep4 (-> char rat)) (T4 (-> rat char Bool))) (let ((_let_1 (@ conversep_rat_char T4))) (and (= R6 (@ (@ relcom1505247221262953652ar_rat T4) _let_1)) (@ (@ ord_le4891902658761385405_rat_o (@ (@ bNF_Grp_char_rat top_top_set_char) Rep4)) _let_1) (@ (@ ord_le6546876390139131069char_o T4) (@ (@ bNF_Grp_rat_char top_top_set_rat) Abs4)))))))) (let ((_let_11 (not thesis))) (let ((_let_12 (@ (@ bNF_re2241393799969408733at_nat intrel) intrel))) (let ((_let_13 (@ (@ bNF_re3099431351363272937at_nat intrel) _let_12))) (let ((_let_14 (= bot_bot_nat_num_o (lambda ((X4 nat) (Y5 num)) (@ (@ member9148766508732265716at_num (@ (@ product_Pair_nat_num X4) Y5)) bot_bo7038385379056416535at_num))))) (let ((_let_15 (= comple90263536869209701_set_o (lambda ((A6 set_set_o)) (@ collect_o (lambda ((X4 Bool)) (@ complete_Sup_Sup_o (@ (@ image_set_o_o (@ member_o X4)) A6)))))))) (let ((_let_16 (= bNF_re7408651293131936558nt_int (lambda ((R6 (-> product_prod_nat_nat int Bool)) (S4 (-> (-> product_prod_nat_nat product_prod_nat_nat) (-> int int) Bool)) (F2 (-> product_prod_nat_nat product_prod_nat_nat product_prod_nat_nat)) (G3 (-> int int int))) (@ (@ ord_le2484784447047653514_int_o (@ (@ (@ bNF_Gr1354378531936274772nt_int F2) G3) R6)) S4))))) (let ((_let_17 (@ (@ produc1839366721759504235ar_nat top_top_set_char) (lambda ((Uu char)) top_top_set_nat)))) (let ((_let_18 (= _let_17 top_to5594287848199751986ar_nat))) (let ((_let_19 (@ collec3392354462482085612at_nat (@ produc6081775807080527818_nat_o ord_less_nat)))) (let ((_let_20 (= bNF_Ca8459412986667044542atLess _let_19))) (let ((_let_21 (= comple3628384868704368283et_int (lambda ((A6 set_set_int)) (@ collect_int (lambda ((X4 int)) (@ complete_Inf_Inf_o (@ (@ image_set_int_o (@ member_int X4)) A6)))))))) (let ((_let_22 (= finite4703585013658510744_o_nat (lambda ((S4 set_o) (F2 (-> Bool nat nat))) (forall ((X4 Bool) (Y5 Bool)) (let ((_let_1 (@ F2 Y5))) (let ((_let_2 (@ F2 X4))) (=> (@ (@ member_o X4) S4) (=> (@ (@ member_o Y5) S4) (= (@ (@ comp_nat_nat_nat _let_1) _let_2) (@ (@ comp_nat_nat_nat _let_2) _let_1))))))))))) (let ((_let_23 (@ (@ image_17660834435998945t_unit produc1126150082675451753t_unit) top_to2503719809363509323t_unit))) (let ((_let_24 (= _let_23 top_to3956321331435058429t_unit))) (let ((_let_25 (= comple2584293577114468500t_unit (lambda ((Uu2 set_Product_unit)) product_Unity)))) (let ((_let_26 (= order_1960202971199294558of_int (lambda ((P4 (-> int int Bool)) (A6 set_int)) (@ collec213857154873943460nt_int (@ produc4947309494688390418_int_o (lambda ((A5 int) (B4 int)) (and (@ (@ member5262025264175285858nt_int (@ (@ product_Pair_int_int A5) B4)) (@ (@ produc1453890548195736866nt_int A6) (lambda ((Uu int)) A6))) (@ (@ P4 A5) B4))))))))) (let ((_let_27 (@ (@ comp_int_nat_int nat2) abs_abs_int))) (let ((_let_28 (= total_7212417256332265445at_nat (lambda ((A6 set_se7855581050983116737at_nat) (R5 set_Pr4329608150637261639at_nat)) (forall ((X4 set_Pr1261947904930325089at_nat)) (=> (@ (@ member2643936169264416010at_nat X4) A6) (forall ((Y5 set_Pr1261947904930325089at_nat)) (=> (@ (@ member2643936169264416010at_nat Y5) A6) (=> (not (= X4 Y5)) (or (@ (@ member8757157785044589968at_nat (@ (@ produc2922128104949294807at_nat Y5) X4)) R5) (@ (@ member8757157785044589968at_nat (@ (@ produc2922128104949294807at_nat X4) Y5)) R5))))))))))) (let ((_let_29 (@ comp_nat_nat_nat id_nat))) (let ((_let_30 (= _let_29 id_nat_nat))) (let ((_let_31 (= top_top_int_int_o (lambda ((X4 int) (Y5 int)) (@ (@ member5262025264175285858nt_int (@ (@ product_Pair_int_int X4) Y5)) top_to4366644338036079209nt_int))))) (let ((_let_32 (= comple2433913294995299363_num_o (lambda ((S4 set_nat_num_o) (X4 nat) (Y5 num)) (@ (@ member9148766508732265716at_num (@ (@ product_Pair_nat_num X4) Y5)) (@ comple6868718957223342258at_num (@ (@ image_6580737572886966642at_num collec4100598399430923318at_num) (@ (@ image_8484515203959327177_num_o produc4927758841916487424_num_o) S4)))))))) (let ((_let_33 (= order_2442354982230848562at_nat (lambda ((R5 set_Pr7459493094073627847at_nat) (A5 set_Pr4329608150637261639at_nat)) (@ collec4573900263915890866at_nat (lambda ((B4 set_Pr4329608150637261639at_nat)) (and (@ (@ member1466754251312161552at_nat (@ (@ produc9060074326276436823at_nat A5) B4)) R5) (not (= B4 A5))))))))) (let ((_let_34 (@ (@ set_or4665077453230672383an_nat zero_zero_nat) (@ numeral_numeral_nat (@ bit0 (@ bit0 (@ bit0 (@ bit0 (@ bit0 (@ bit0 (@ bit0 (@ bit0 one)))))))))))) (let ((_let_35 (= top_top_set_char (@ (@ image_nat_char unique3096191561947761185of_nat) _let_34)))) (let ((_let_36 (= code_pcr_integer (@ (@ relcom967497705283160040nteger (lambda ((Y2 int) (Z int)) (= Y2 Z))) code_cr_integer)))) (let ((_let_37 (= top_top_nat_nat_o (lambda ((X4 nat) (Y5 nat)) (@ (@ member8440522571783428010at_nat (@ (@ product_Pair_nat_nat X4) Y5)) top_to4669805908274784177at_nat))))) (let ((_let_38 (= code_divmod_integer (lambda ((K5 code_integer) (L3 code_integer)) (let ((_let_1 (@ (@ code_divmod_abs K5) L3))) (let ((_let_2 (@ produc1086072967326762835nteger zero_z3403309356797280102nteger))) (let ((_let_3 (@ ord_le6747313008572928689nteger zero_z3403309356797280102nteger))) (@ (@ (@ if_Pro6119634080678213985nteger (= K5 zero_z3403309356797280102nteger)) (@ _let_2 zero_z3403309356797280102nteger)) (@ (@ (@ if_Pro6119634080678213985nteger (@ _let_3 L3)) (@ (@ (@ if_Pro6119634080678213985nteger (@ _let_3 K5)) _let_1) (@ (@ produc6916734918728496179nteger (lambda ((R5 code_integer) (S code_integer)) (let ((_let_1 (@ uminus1351360451143612070nteger R5))) (@ (@ (@ if_Pro6119634080678213985nteger (= S zero_z3403309356797280102nteger)) (@ (@ produc1086072967326762835nteger _let_1) zero_z3403309356797280102nteger)) (@ (@ produc1086072967326762835nteger (@ (@ minus_8373710615458151222nteger _let_1) one_one_Code_integer)) (@ (@ minus_8373710615458151222nteger L3) S)))))) _let_1))) (@ (@ (@ if_Pro6119634080678213985nteger (= L3 zero_z3403309356797280102nteger)) (@ _let_2 K5)) (@ (@ produc6499014454317279255nteger uminus1351360451143612070nteger) (@ (@ (@ if_Pro6119634080678213985nteger (@ (@ ord_le6747313008572928689nteger K5) zero_z3403309356797280102nteger)) _let_1) (@ (@ produc6916734918728496179nteger (lambda ((R5 code_integer) (S code_integer)) (let ((_let_1 (@ uminus1351360451143612070nteger R5))) (@ (@ (@ if_Pro6119634080678213985nteger (= S zero_z3403309356797280102nteger)) (@ (@ produc1086072967326762835nteger _let_1) zero_z3403309356797280102nteger)) (@ (@ produc1086072967326762835nteger (@ (@ minus_8373710615458151222nteger _let_1) one_one_Code_integer)) (@ (@ minus_8373710615458151222nteger (@ uminus1351360451143612070nteger L3)) S)))))) _let_1))))))))))))) (let ((_let_39 (= comp_C8797469213163452608nteger (lambda ((F2 (-> (-> code_integer code_integer) produc8923325533196201883nteger produc8923325533196201883nteger)) (G3 (-> code_integer code_integer code_integer)) (X4 code_integer) (__flatten_var_0 produc8923325533196201883nteger)) (@ (@ F2 (@ G3 X4)) __flatten_var_0))))) (let ((_let_40 (= fun_in6812141508599261570at_nat (lambda ((R6 set_Pr7459493094073627847at_nat) (X4 set_Pr4329608150637261639at_nat) (Y5 set_Pr4329608150637261639at_nat)) (@ (@ member1466754251312161552at_nat (@ (@ produc9060074326276436823at_nat X4) Y5)) R6))))) (let ((_let_41 (= finite2110315540964234241at_nat (lambda ((S4 set_Pr1261947904930325089at_nat) (F2 (-> product_prod_nat_nat nat nat))) (forall ((X4 product_prod_nat_nat) (Y5 product_prod_nat_nat)) (let ((_let_1 (@ F2 Y5))) (let ((_let_2 (@ F2 X4))) (=> (@ (@ member8440522571783428010at_nat X4) S4) (=> (@ (@ member8440522571783428010at_nat Y5) S4) (= (@ (@ comp_nat_nat_nat _let_1) _let_2) (@ (@ comp_nat_nat_nat _let_2) _let_1))))))))))) (let ((_let_42 (= id_on_num (lambda ((A6 set_num)) (@ (@ bNF_Gr_num_num A6) id_num))))) (let ((_let_43 (= refl_o6272981002401706822at_nat (lambda ((A6 set_se5479201105039950375at_nat) (R5 set_Pr7459493094073627847at_nat)) (and (@ (@ ord_le5997549366648089703at_nat R5) (@ (@ produc6258361011560675592at_nat A6) (lambda ((Uu set_Pr4329608150637261639at_nat)) A6))) (forall ((X4 set_Pr4329608150637261639at_nat)) (=> (@ (@ member6273874620674182256at_nat X4) A6) (@ (@ member1466754251312161552at_nat (@ (@ produc9060074326276436823at_nat X4) X4)) R5)))))))) (let ((_let_44 (= comple8317665133742190828_nat_o (lambda ((S4 set_nat_o) (X4 nat)) (@ (@ member_nat X4) (@ comple7399068483239264473et_nat (@ (@ image_nat_o_set_nat collect_nat) S4))))))) (let ((_let_45 (= comple6265855634338933877_nat_o (lambda ((S4 set_Pr5582243495563764594_nat_o) (X4 product_prod_nat_nat)) (@ (@ member8440522571783428010at_nat X4) (@ comple1930127330929219688at_nat (@ (@ image_7124889717316225246at_nat collec3392354462482085612at_nat) S4))))))) (let ((_let_46 (= bNF_Ca333620267926924494at_rat (lambda ((R5 set_Pr1261947904930325089at_nat) (As (-> nat rat))) (forall ((I2 nat) (J nat)) (=> (@ (@ member8440522571783428010at_nat (@ (@ product_Pair_nat_nat I2) J)) R5) (@ (@ ord_less_eq_rat (@ As I2)) (@ As J)))))))) (let ((_let_47 (= inv_im2900519150384625825at_int (lambda ((R5 set_Pr7459493094073627847at_nat) (F2 (-> int set_Pr4329608150637261639at_nat))) (@ collec213857154873943460nt_int (@ produc4947309494688390418_int_o (lambda ((X4 int) (Y5 int)) (@ (@ member1466754251312161552at_nat (@ (@ produc9060074326276436823at_nat (@ F2 X4)) (@ F2 Y5))) R5)))))))) (let ((_let_48 (= id_on_nat (lambda ((A6 set_nat)) (@ (@ bNF_Gr_nat_nat A6) id_nat))))) (let ((_let_49 (= bot_bo3364206721330744218_nat_o (lambda ((X4 set_Pr4329608150637261639at_nat) (Y5 set_Pr4329608150637261639at_nat)) (@ (@ member1466754251312161552at_nat (@ (@ produc9060074326276436823at_nat X4) Y5)) bot_bo4948859079157340979at_nat))))) (let ((_let_50 (= basic_685971451221398055t_unit (lambda ((P3 produc7812382424243267045t_unit)) (@ (@ insert_ref_a (@ produc473321116828791851t_unit P3)) bot_bot_set_ref_a))))) (let ((_let_51 (= bNF_re717283939379294677_int_o (lambda ((R6 (-> product_prod_nat_nat int Bool)) (S4 (-> (-> product_prod_nat_nat Bool) (-> int Bool) Bool)) (F2 (-> product_prod_nat_nat product_prod_nat_nat Bool)) (G3 (-> int int Bool))) (@ (@ ord_le2932013042137311317nt_o_o (@ (@ (@ bNF_Gr364077372107685167_int_o F2) G3) R6)) S4))))) (let ((_let_52 (@ bNF_re3666534408544137501at_o_o intrel))) (let ((_let_53 (@ bNF_re4202695980764964119_nat_o intrel))) (let ((_let_54 (= comple3592611370556534995_nat_o (lambda ((S4 set_nat_nat_o) (X4 nat) (Y5 nat)) (@ (@ member8440522571783428010at_nat (@ (@ product_Pair_nat_nat X4) Y5)) (@ comple5685304695842803022at_nat (@ (@ image_7124889717316225246at_nat collec3392354462482085612at_nat) (@ (@ image_7429393840292777309_nat_o produc6081775807080527818_nat_o) S4)))))))) (let ((_let_55 (= order_aboveS_nat (lambda ((R5 set_Pr1261947904930325089at_nat) (A5 nat)) (@ collect_nat (lambda ((B4 nat)) (and (not (= B4 A5)) (@ (@ member8440522571783428010at_nat (@ (@ product_Pair_nat_nat A5) B4)) R5)))))))) (let ((_let_56 (= code_bit_cut_integer (lambda ((K5 code_integer)) (@ (@ (@ if_Pro5737122678794959658eger_o (= K5 zero_z3403309356797280102nteger)) (@ (@ produc6677183202524767010eger_o zero_z3403309356797280102nteger) false)) (@ (@ produc9125791028180074456eger_o (lambda ((R5 code_integer) (S code_integer)) (@ (@ produc6677183202524767010eger_o (@ (@ (@ if_Code_integer (@ (@ ord_le6747313008572928689nteger zero_z3403309356797280102nteger) K5)) R5) (@ (@ minus_8373710615458151222nteger (@ uminus1351360451143612070nteger R5)) S))) (= S one_one_Code_integer)))) (@ (@ code_divmod_abs K5) (@ numera6620942414471956472nteger (@ bit0 one))))))))) (let ((_let_57 (= top_to8903224817164384382_nat_o (lambda ((X4 set_Pr1261947904930325089at_nat) (Y5 set_Pr1261947904930325089at_nat)) (@ (@ member8757157785044589968at_nat (@ (@ produc2922128104949294807at_nat X4) Y5)) top_to6833984726390702231at_nat))))) (let ((_let_58 (= produc4245557441103728435nt_int (lambda ((F2 (-> int int product_prod_int_int)) (Prod3 product_prod_int_int)) (@ (@ F2 (@ product_fst_int_int Prod3)) (@ product_snd_int_int Prod3)))))) (let ((_let_59 (= id_on_3275838214495744996at_nat (lambda ((A6 set_se5479201105039950375at_nat)) (@ comple7342073961973170484at_nat (@ (@ image_1124969593608450885at_nat (lambda ((X4 set_Pr4329608150637261639at_nat)) (@ (@ insert291458823148189367at_nat (@ (@ produc9060074326276436823at_nat X4) X4)) bot_bo4948859079157340979at_nat))) A6)))))) (let ((_let_60 (= comple7806235888213564991et_nat (lambda ((A6 set_set_nat)) (@ collect_nat (lambda ((X4 nat)) (@ complete_Inf_Inf_o (@ (@ image_set_nat_o (@ member_nat X4)) A6)))))))) (let ((_let_61 (= basic_1496934909540232809t_unit (lambda ((P3 produc7812382424243267045t_unit)) (@ (@ insert8563697753282147485t_unit (@ produc1126150082675451753t_unit P3)) bot_bo3686245532977126937t_unit))))) (let ((_let_62 (@ produc4245557441103728435nt_int product_Pair_int_int))) (let ((_let_63 (= _let_62 id_Pro4381231610383771306nt_int))) (let ((_let_64 (@ (@ produc1836876251250453959ar_int top_top_set_char) (lambda ((Uu char)) top_top_set_int)))) (let ((_let_65 (= _let_64 top_to3104204703268025230ar_int))) (let ((_let_66 (= refl_on_int (lambda ((A6 set_int) (R5 set_Pr958786334691620121nt_int)) (and (@ (@ ord_le2843351958646193337nt_int R5) (@ (@ produc1453890548195736866nt_int A6) (lambda ((Uu int)) A6))) (forall ((X4 int)) (=> (@ (@ member_int X4) A6) (@ (@ member5262025264175285858nt_int (@ (@ product_Pair_int_int X4) X4)) R5)))))))) (let ((_let_67 (= gcd_Gcd_int (lambda ((K3 set_int)) (@ semiri1314217659103216013at_int (@ gcd_Gcd_nat (@ (@ image_int_nat (@ (@ comp_int_nat_int nat2) abs_abs_int)) K3))))))) (let ((_let_68 (= produc929334515565554804at_nat (lambda ((A6 set_nat) (B6 set_nat)) (@ (@ produc457027306803732586at_nat A6) (lambda ((Uu nat)) B6)))))) (let ((_let_69 (= inv_im4437241714082187487at_nat (lambda ((R5 set_Pr4329608150637261639at_nat) (F2 (-> nat set_Pr1261947904930325089at_nat))) (@ collec3392354462482085612at_nat (@ produc6081775807080527818_nat_o (lambda ((X4 nat) (Y5 nat)) (@ (@ member8757157785044589968at_nat (@ (@ produc2922128104949294807at_nat (@ F2 X4)) (@ F2 Y5))) R5)))))))) (let ((_let_70 (= inv_image_int_int (lambda ((R5 set_Pr958786334691620121nt_int) (F2 (-> int int))) (@ collec213857154873943460nt_int (@ produc4947309494688390418_int_o (lambda ((X4 int) (Y5 int)) (@ (@ member5262025264175285858nt_int (@ (@ product_Pair_int_int (@ F2 X4)) (@ F2 Y5))) R5)))))))) (let ((_let_71 (= inv_im2903009620893676101at_nat (lambda ((R5 set_Pr7459493094073627847at_nat) (F2 (-> nat set_Pr4329608150637261639at_nat))) (@ collec3392354462482085612at_nat (@ produc6081775807080527818_nat_o (lambda ((X4 nat) (Y5 nat)) (@ (@ member1466754251312161552at_nat (@ (@ produc9060074326276436823at_nat (@ F2 X4)) (@ F2 Y5))) R5)))))))) (let ((_let_72 (= produc297006045350968285nt_int produc4245557441103728435nt_int))) (let ((_let_73 (= bNF_re4555766996558763186at_nat (lambda ((R6 (-> product_prod_nat_nat int Bool)) (S4 (-> nat nat Bool)) (F2 (-> product_prod_nat_nat nat)) (G3 (-> int nat))) (@ (@ ord_le129227817499904167_int_o R6) (@ (@ (@ bNF_vi5493721401438417730_nat_o F2) G3) S4)))))) (let ((_let_74 (= bot_bot_int_int_o (lambda ((X4 int) (Y5 int)) (@ (@ member5262025264175285858nt_int (@ (@ product_Pair_int_int X4) Y5)) bot_bo1796632182523588997nt_int))))) (let ((_let_75 (@ (@ bNF_re7408651293131936558nt_int pcr_int) _let_9))) (let ((_let_76 (forall ((P2 Bool)) (and (=> (not P2) (= (@ collec6321179662152712658at_nat (@ produc410239310623530412_nat_o (lambda ((A5 set_Pr1261947904930325089at_nat) (B4 set_Pr1261947904930325089at_nat)) P2))) bot_bo228742789529271731at_nat)) (=> P2 (= (@ collec6321179662152712658at_nat (@ produc410239310623530412_nat_o (lambda ((A5 set_Pr1261947904930325089at_nat) (B4 set_Pr1261947904930325089at_nat)) P2))) top_to6833984726390702231at_nat)))))) (let ((_let_77 (= int_ge_less_than2 (lambda ((D3 int)) (@ collec213857154873943460nt_int (@ produc4947309494688390418_int_o (lambda ((Z6 int) (Z4 int)) (and (@ (@ ord_less_int Z6) Z4) (@ (@ ord_less_eq_int D3) Z4))))))))) (let ((_let_78 (= (@ produc7548845685434208379at_nat produc2922128104949294807at_nat) id_Pro8722402698821300696at_nat))) (let ((_let_79 (= produc8005341501107743676_int_o produc4947309494688390418_int_o))) (let ((_let_80 (= fun_in_rel_nat_num (lambda ((R6 set_Pr6200539531224447659at_num) (X4 nat) (Y5 num)) (@ (@ member9148766508732265716at_num (@ (@ product_Pair_nat_num X4) Y5)) R6))))) (let ((_let_81 (= (@ produc49306077274653107at_num product_Pair_nat_num) id_Pro8267972854940751164at_num))) (let ((_let_82 (= bNF_Ca4949091444211332621at_nat (lambda ((R5 set_Pr4329608150637261639at_nat) (As (-> set_Pr1261947904930325089at_nat nat))) (forall ((I2 set_Pr1261947904930325089at_nat) (J set_Pr1261947904930325089at_nat)) (=> (@ (@ member8757157785044589968at_nat (@ (@ produc2922128104949294807at_nat I2) J)) R5) (@ (@ ord_less_eq_nat (@ As I2)) (@ As J)))))))) (let ((_let_83 (= unique4921790084139445826nteger (lambda ((L3 num) (__flatten_var_0 produc8923325533196201883nteger)) (@ (@ produc6916734918728496179nteger (lambda ((Q3 code_integer) (R5 code_integer)) (let ((_let_1 (@ (@ times_3573771949741848930nteger (@ numera6620942414471956472nteger (@ bit0 one))) Q3))) (let ((_let_2 (@ numera6620942414471956472nteger L3))) (@ (@ (@ if_Pro6119634080678213985nteger (@ (@ ord_le3102999989581377725nteger _let_2) R5)) (@ (@ produc1086072967326762835nteger (@ (@ plus_p5714425477246183910nteger _let_1) one_one_Code_integer)) (@ (@ minus_8373710615458151222nteger R5) _let_2))) (@ (@ produc1086072967326762835nteger _let_1) R5)))))) __flatten_var_0))))) (let ((_let_84 (@ comp_P1287623958910499840t_unit produc6369869760173755749_ref_a))) (let ((_let_85 (@ _let_84 (@ produc2058451029528183389_ref_a (lambda ((X4 ref_a) (Y5 heap_e7401611519738050253t_unit)) (@ (@ produc2564672488694626579_ref_a Y5) X4)))))) (let ((_let_86 (= produc473321116828791851t_unit _let_85))) (let ((_let_87 (= total_3592101749530773125at_nat (lambda ((A6 set_Pr1261947904930325089at_nat) (R5 set_Pr8693737435421807431at_nat)) (forall ((X4 product_prod_nat_nat)) (=> (@ (@ member8440522571783428010at_nat X4) A6) (forall ((Y5 product_prod_nat_nat)) (=> (@ (@ member8440522571783428010at_nat Y5) A6) (=> (not (= X4 Y5)) (or (@ (@ member8206827879206165904at_nat (@ (@ produc6161850002892822231at_nat Y5) X4)) R5) (@ (@ member8206827879206165904at_nat (@ (@ produc6161850002892822231at_nat X4) Y5)) R5))))))))))) (let ((_let_88 (@ bNF_re6644619430987730960nt_o_o pcr_int))) (let ((_let_89 (@ bNF_re717283939379294677_int_o pcr_int))) (let ((_let_90 (= sup_su5525570899277871387at_nat (lambda ((A6 set_Pr4329608150637261639at_nat) (B6 set_Pr4329608150637261639at_nat)) (@ comple4364388969068068532at_nat (@ (@ image_2496312346330513076at_nat (lambda ((B4 Bool)) (@ (@ (@ if_set3208018901896979469at_nat B4) A6) B6))) top_top_set_o)))))) (let ((_let_91 (@ (@ insert9069300056098147895at_nat (@ (@ produc2922128104949294807at_nat bot_bo2099793752762293965at_nat) bot_bo2099793752762293965at_nat)) bot_bo228742789529271731at_nat))) (let ((_let_92 (= fun_max_weak (@ (@ sup_su5525570899277871387at_nat (@ max_ex8135407076693332796at_nat fun_pair_leq)) _let_91)))) (let ((_let_93 (= relcom967497705283160040nteger (lambda ((R6 (-> int int Bool)) (S4 (-> int code_integer Bool)) (A5 int) (C4 code_integer)) (exists ((B4 int)) (and (@ (@ S4 B4) C4) (@ (@ R6 A5) B4))))))) (let ((_let_94 (= _let_4 id_set_num))) (let ((_let_95 (@ (@ map_fu3667384564859982768at_int rep_Integ) abs_Integ))) (let ((_let_96 (@ (@ map_fu4960017516451851995nt_int rep_Integ) _let_95))) (let ((_let_97 (= plus_plus_int (@ _let_96 (@ produc27273713700761075at_nat (lambda ((X4 nat) (Y5 nat) (__flatten_var_0 product_prod_nat_nat)) (@ (@ produc2626176000494625587at_nat (lambda ((U3 nat) (V3 nat)) (@ (@ product_Pair_nat_nat (@ (@ plus_plus_nat X4) U3)) (@ (@ plus_plus_nat Y5) V3)))) __flatten_var_0))))))) (let ((_let_98 (= bNF_vi7331807916455492308_int_o (lambda ((F2 (-> nat int)) (G3 (-> code_integer int)) (P4 (-> int int Bool)) (__flatten_var_0 nat) (__flatten_var_1 code_integer)) (@ (@ (@ (@ relcom3277315637376110988nteger (@ (@ bNF_Grp_nat_int top_top_set_nat) F2)) (@ (@ relcom967497705283160040nteger P4) (@ conver1462408618118490240er_int (@ (@ bNF_Gr6045950513751025625er_int top_to4645266643341252675nteger) G3)))) __flatten_var_0) __flatten_var_1))))) (let ((_let_99 (@ produc6499014454317279255nteger id_Code_integer))) (let ((_let_100 (= _let_99 id_Pro2309048762231606924nteger))) (let ((_let_101 (= comple4364388969068068532at_nat (lambda ((A6 set_se5479201105039950375at_nat)) (@ collec6321179662152712658at_nat (lambda ((X4 produc3843707927480180839at_nat)) (@ complete_Sup_Sup_o (@ (@ image_3568060456209098518_nat_o (@ member8757157785044589968at_nat X4)) A6)))))))) (let ((_let_102 (= inv_im4434751243573137211at_int (lambda ((R5 set_Pr4329608150637261639at_nat) (F2 (-> int set_Pr1261947904930325089at_nat))) (@ collec213857154873943460nt_int (@ produc4947309494688390418_int_o (lambda ((X4 int) (Y5 int)) (@ (@ member8757157785044589968at_nat (@ (@ produc2922128104949294807at_nat (@ F2 X4)) (@ F2 Y5))) R5)))))))) (let ((_let_103 (= order_1962693441708344834of_nat (lambda ((P4 (-> nat nat Bool)) (A6 set_nat)) (@ collec3392354462482085612at_nat (@ produc6081775807080527818_nat_o (lambda ((A5 nat) (B4 nat)) (and (@ (@ member8440522571783428010at_nat (@ (@ product_Pair_nat_nat A5) B4)) (@ (@ produc457027306803732586at_nat A6) (lambda ((Uu nat)) A6))) (@ (@ P4 A5) B4))))))))) (let ((_let_104 (= quotient_char_nat (lambda ((R6 (-> char char Bool)) (Abs4 (-> char nat)) (Rep4 (-> nat char)) (T4 (-> char nat Bool))) (let ((_let_1 (@ conversep_char_nat T4))) (and (@ (@ ord_le5641337153896221125_nat_o T4) (@ (@ bNF_Grp_char_nat top_top_set_char) Abs4)) (@ (@ ord_le4878496333587278021char_o (@ (@ bNF_Grp_nat_char top_top_set_nat) Rep4)) _let_1) (= R6 (@ (@ relcom6755291642603558309t_char T4) _let_1)))))))) (let ((_let_105 (= code_negative (@ (@ comp_C3531382070062128313er_num uminus1351360451143612070nteger) numera6620942414471956472nteger)))) (let ((_let_106 (= (@ (@ produc1427039474575272051t_char top_top_set_rat) (lambda ((Uu rat)) top_top_set_char)) top_to3221206985699244474t_char))) (let ((_let_107 (= bNF_vi2997284877290766385_nat_o (lambda ((F2 (-> rat product_prod_nat_nat)) (G3 (-> int product_prod_nat_nat)) (P4 (-> product_prod_nat_nat product_prod_nat_nat Bool)) (__flatten_var_0 rat) (__flatten_var_1 int)) (@ (@ (@ (@ relcom1211213461163567844at_int (@ (@ bNF_Gr6883301533820405721at_nat top_top_set_rat) F2)) (@ (@ relcom8911704206367525917at_int P4) (@ conver1866313717161370910at_nat (@ (@ bNF_Gr6591314147588017797at_nat top_top_set_int) G3)))) __flatten_var_0) __flatten_var_1))))) (let ((_let_108 (@ (@ comp_nat_num_int num_of_nat) nat2))) (let ((_let_109 (= comple6496622788309502864_int_o (lambda ((S4 set_int_o) (X4 int)) (@ (@ member_int X4) (@ comple3221217463730067765et_int (@ (@ image_int_o_set_int collect_int) S4))))))) (let ((_let_110 (@ alloc_a x))) (let ((_let_111 (@ _let_110 h))) (let ((_let_112 (=> (= r (@ produc473321116828791851t_unit _let_111)) (=> (= h2 (@ produc1126150082675451753t_unit _let_111)) thesis)))) (let ((_let_113 (= comple4350791933526045961_num_o (lambda ((S4 set_nat_num_o) (X4 nat) (Y5 num)) (@ (@ member9148766508732265716at_num (@ (@ product_Pair_nat_num X4) Y5)) (@ comple1400524285282149784at_num (@ (@ image_6580737572886966642at_num collec4100598399430923318at_num) (@ (@ image_8484515203959327177_num_o produc4927758841916487424_num_o) S4)))))))) (let ((_let_114 (= comple1901448594430626575_nat_o (lambda ((S4 set_Pr5582243495563764594_nat_o) (X4 product_prod_nat_nat)) (@ (@ member8440522571783428010at_nat X4) (@ comple5685304695842803022at_nat (@ (@ image_7124889717316225246at_nat collec3392354462482085612at_nat) S4))))))) (let ((_let_115 (= id_int2 (@ collec213857154873943460nt_int (lambda ((X4 product_prod_int_int)) (= (@ product_fst_int_int X4) (@ product_snd_int_int X4))))))) (let ((_let_116 (@ (@ map_fu1227494855608507351um_num code_int_of_integer) id_num))) (let ((_let_117 (= code_num_of_integer (@ _let_116 _let_108)))) (let ((_let_118 (= product_swap_nat_nat (lambda ((P3 product_prod_nat_nat)) (@ (@ product_Pair_nat_nat (@ product_snd_nat_nat P3)) (@ product_fst_nat_nat P3)))))) (let ((_let_119 (forall ((P2 Bool)) (and (=> (not P2) (= (@ collec3392354462482085612at_nat (@ produc6081775807080527818_nat_o (lambda ((A5 nat) (B4 nat)) P2))) bot_bo2099793752762293965at_nat)) (=> P2 (= (@ collec3392354462482085612at_nat (@ produc6081775807080527818_nat_o (lambda ((A5 nat) (B4 nat)) P2))) top_to4669805908274784177at_nat)))))) (let ((_let_120 (= bNF_Ca4946600973702282345at_int (lambda ((R5 set_Pr4329608150637261639at_nat) (As (-> set_Pr1261947904930325089at_nat int))) (forall ((I2 set_Pr1261947904930325089at_nat) (J set_Pr1261947904930325089at_nat)) (=> (@ (@ member8757157785044589968at_nat (@ (@ produc2922128104949294807at_nat I2) J)) R5) (@ (@ ord_less_eq_int (@ As I2)) (@ As J)))))))) (let ((_let_121 (= top_to1996260823553986621t_unit (@ (@ insert_Product_unit product_Unity) bot_bo3957492148770167129t_unit)))) (let ((_let_122 (= bNF_re6718328864250387230um_num (lambda ((R6 (-> int code_integer Bool)) (S4 (-> num num Bool)) (F2 (-> int num)) (G3 (-> code_integer num))) (@ (@ ord_le996066559646421213eger_o R6) (@ (@ (@ bNF_vi2326032003723069084_num_o F2) G3) S4)))))) (let ((_let_123 (= bNF_vi728936465572800120_nat_o (lambda ((F2 (-> char product_prod_nat_nat)) (G3 (-> int product_prod_nat_nat)) (P4 (-> product_prod_nat_nat product_prod_nat_nat Bool)) (__flatten_var_0 char) (__flatten_var_1 int)) (@ (@ (@ (@ relcom7879471502873553579at_int (@ (@ bNF_Gr8982933507515605408at_nat top_top_set_char) F2)) (@ (@ relcom8911704206367525917at_int P4) (@ conver1866313717161370910at_nat (@ (@ bNF_Gr6591314147588017797at_nat top_top_set_int) G3)))) __flatten_var_0) __flatten_var_1))))) (let ((_let_124 (= comple5307621999477653941_nat_o (lambda ((S4 set_se7255092946006855566_nat_o) (X4 set_Pr4329608150637261639at_nat) (Y5 set_Pr4329608150637261639at_nat)) (@ (@ member1466754251312161552at_nat (@ (@ produc9060074326276436823at_nat X4) Y5)) (@ comple4403251139954110286at_nat (@ (@ image_5694205205332509994at_nat collec7872792499061297490at_nat) (@ (@ image_5235725667318448191_nat_o produc9020218426428501292_nat_o) S4)))))))) (let ((_let_125 (@ image_int_int id_int))) (let ((_let_126 (= produc6036585564866528938nt_int (lambda ((F2 (-> int int)) (G3 (-> int int)) (__flatten_var_0 product_prod_int_int)) (@ (@ produc4245557441103728435nt_int (lambda ((X4 int) (Y5 int)) (@ (@ product_Pair_int_int (@ F2 X4)) (@ G3 Y5)))) __flatten_var_0))))) (let ((_let_127 (= comple493620192902636699_nat_o (lambda ((S4 set_se9180647916752606350_nat_o) (X4 set_Pr1261947904930325089at_nat) (Y5 set_Pr1261947904930325089at_nat)) (@ (@ member8757157785044589968at_nat (@ (@ produc2922128104949294807at_nat X4) Y5)) (@ comple4364388969068068532at_nat (@ (@ image_4902389024228248874at_nat collec6321179662152712658at_nat) (@ (@ image_6226802281960588479_nat_o produc410239310623530412_nat_o) S4)))))))) (let ((_let_128 (= nat_prod_encode (@ produc6842872674320459806at_nat (lambda ((M5 nat) (N4 nat)) (@ (@ plus_plus_nat (@ nat_triangle (@ (@ plus_plus_nat M5) N4))) M5)))))) (let ((_let_129 (= defaul566961228789861419t_unit product_Unity))) (let ((_let_130 (= pred_nat (@ collec3392354462482085612at_nat (@ produc6081775807080527818_nat_o (lambda ((M5 nat) (N4 nat)) (= N4 (@ suc M5)))))))) (let ((_let_131 (= comple8183010123678664591_nat_o (lambda ((S4 set_Pr7010166363911110284_nat_o) (X4 produc3843707927480180839at_nat)) (@ (@ member8757157785044589968at_nat X4) (@ comple6751905152567503566at_nat (@ (@ image_4902389024228248874at_nat collec6321179662152712658at_nat) S4))))))) (let ((_let_132 (= ref_a2 (lambda ((V3 a)) (@ heap_heap_ref_a (@ alloc_a V3)))))) (let ((_let_133 (= quotient_nat_char (lambda ((R6 (-> nat nat Bool)) (Abs4 (-> nat char)) (Rep4 (-> char nat)) (T4 (-> nat char Bool))) (let ((_let_1 (@ conversep_nat_char T4))) (and (= R6 (@ (@ relcom8112501251453913252ar_nat T4) _let_1)) (@ (@ ord_le5641337153896221125_nat_o (@ (@ bNF_Grp_char_nat top_top_set_char) Rep4)) _let_1) (@ (@ ord_le4878496333587278021char_o T4) (@ (@ bNF_Grp_nat_char top_top_set_nat) Abs4)))))))) (let ((_let_134 (= product_swap_num_nat (lambda ((P3 product_prod_num_nat)) (@ (@ product_Pair_nat_num (@ product_snd_num_nat P3)) (@ product_fst_num_nat P3)))))) (let ((_let_135 (= id_on_o (lambda ((A6 set_o)) (@ (@ bNF_Gr_o_o A6) id_o))))) (let ((_let_136 (= uminus2952777764628376836t_unit (lambda ((Uu2 product_unit)) product_Unity)))) (let ((_let_137 (= bNF_Ca1965613569405424510nt_int (lambda ((R5 set_Pr958786334691620121nt_int) (As (-> int int))) (forall ((I2 int) (J int)) (=> (@ (@ member5262025264175285858nt_int (@ (@ product_Pair_int_int I2) J)) R5) (@ (@ ord_less_eq_int (@ As I2)) (@ As J)))))))) (let ((_let_138 (= comple6751905152567503566at_nat (lambda ((A6 set_se5479201105039950375at_nat)) (@ collec6321179662152712658at_nat (lambda ((X4 produc3843707927480180839at_nat)) (@ complete_Inf_Inf_o (@ (@ image_3568060456209098518_nat_o (@ member8757157785044589968at_nat X4)) A6)))))))) (let ((_let_139 (= int_ge_less_than (lambda ((D3 int)) (@ collec213857154873943460nt_int (@ produc4947309494688390418_int_o (lambda ((Z6 int) (Z4 int)) (and (@ (@ ord_less_eq_int D3) Z6) (@ (@ ord_less_int Z6) Z4))))))))) (let ((_let_140 (= complete_Inf_Inf_o_o (lambda ((S4 set_o_o) (X4 Bool)) (@ (@ member_o X4) (@ comple3063163877087187839_set_o (@ (@ image_o_o_set_o collect_o) S4))))))) (let ((_let_141 (= ref_a3 ref_a2))) (let ((_let_142 (= produc6499014454317279255nteger (@ produc1802105962441033582nteger id_Code_integer)))) (let ((_let_143 (= quotient_char_rat (lambda ((R6 (-> char char Bool)) (Abs4 (-> char rat)) (Rep4 (-> rat char)) (T4 (-> char rat Bool))) (let ((_let_1 (@ conversep_char_rat T4))) (and (@ (@ ord_le4891902658761385405_rat_o T4) (@ (@ bNF_Grp_char_rat top_top_set_char) Abs4)) (@ (@ ord_le6546876390139131069char_o (@ (@ bNF_Grp_rat_char top_top_set_rat) Rep4)) _let_1) (= R6 (@ (@ relcom3428143170894750637t_char T4) _let_1)))))))) (let ((_let_144 (= bNF_vi467646977814820164_int_o (lambda ((F2 (-> list_nat int)) (G3 (-> code_integer int)) (P4 (-> int int Bool)) (__flatten_var_0 list_nat) (__flatten_var_1 code_integer)) (@ (@ (@ (@ relcom7887202796854296604nteger (@ (@ bNF_Grp_list_nat_int top_top_set_list_nat) F2)) (@ (@ relcom967497705283160040nteger P4) (@ conver1462408618118490240er_int (@ (@ bNF_Gr6045950513751025625er_int top_to4645266643341252675nteger) G3)))) __flatten_var_0) __flatten_var_1))))) (let ((_let_145 (= bNF_Ca30959104405961555nteger (lambda ((R5 set_Pr1261947904930325089at_nat) (As (-> nat code_integer))) (forall ((I2 nat) (J nat)) (=> (@ (@ member8440522571783428010at_nat (@ (@ product_Pair_nat_nat I2) J)) R5) (@ (@ ord_le3102999989581377725nteger (@ As I2)) (@ As J)))))))) (let ((_let_146 (= fun_max_strict (@ max_ex8135407076693332796at_nat fun_pair_less)))) (let ((_let_147 (= fun_pair_leq (@ (@ sup_su718114333110466843at_nat fun_pair_less) id_Pro2258643101195443293at_nat)))) (let ((_let_148 (= top_to1326704617074743934_nat_o (lambda ((X4 set_Pr4329608150637261639at_nat) (Y5 set_Pr4329608150637261639at_nat)) (@ (@ member1466754251312161552at_nat (@ (@ produc9060074326276436823at_nat X4) Y5)) top_to5281548843312042519at_nat))))) (let ((_let_149 (= finite8619596206551965927at_nat (lambda ((S4 set_Pr4329608150637261639at_nat) (F2 (-> produc3843707927480180839at_nat nat nat))) (forall ((X4 produc3843707927480180839at_nat) (Y5 produc3843707927480180839at_nat)) (let ((_let_1 (@ F2 Y5))) (let ((_let_2 (@ F2 X4))) (=> (@ (@ member8757157785044589968at_nat X4) S4) (=> (@ (@ member8757157785044589968at_nat Y5) S4) (= (@ (@ comp_nat_nat_nat _let_1) _let_2) (@ (@ comp_nat_nat_nat _let_2) _let_1))))))))))) (let ((_let_150 (= unique5024387138958732305ep_int (lambda ((L3 num) (__flatten_var_0 product_prod_int_int)) (@ (@ produc4245557441103728435nt_int (lambda ((Q3 int) (R5 int)) (let ((_let_1 (@ (@ times_times_int (@ numeral_numeral_int (@ bit0 one))) Q3))) (let ((_let_2 (@ numeral_numeral_int L3))) (@ (@ (@ if_Pro3027730157355071871nt_int (@ (@ ord_less_eq_int _let_2) R5)) (@ (@ product_Pair_int_int (@ (@ plus_plus_int _let_1) one_one_int)) (@ (@ minus_minus_int R5) _let_2))) (@ (@ product_Pair_int_int _let_1) R5)))))) __flatten_var_0))))) (let ((_let_151 (= produc1453890548195736866nt_int (lambda ((A6 set_int) (B6 (-> int set_int))) (@ comple5382143125604098054nt_int (@ (@ image_8635204845542730022nt_int (lambda ((X4 int)) (@ comple5382143125604098054nt_int (@ (@ image_8635204845542730022nt_int (lambda ((Y5 int)) (@ (@ insert5033312907999012233nt_int (@ (@ product_Pair_int_int X4) Y5)) bot_bo1796632182523588997nt_int))) (@ B6 X4))))) A6)))))) (let ((_let_152 (= bNF_vi2125572119366604152_int_o (lambda ((F2 (-> int int)) (G3 (-> code_integer int)) (P4 (-> int int Bool)) (__flatten_var_0 int) (__flatten_var_1 code_integer)) (@ (@ (@ (@ relcom967497705283160040nteger (@ (@ bNF_Grp_int_int top_top_set_int) F2)) (@ (@ relcom967497705283160040nteger P4) (@ conver1462408618118490240er_int (@ (@ bNF_Gr6045950513751025625er_int top_to4645266643341252675nteger) G3)))) __flatten_var_0) __flatten_var_1))))) (let ((_let_153 (@ comp_o_o_nat id_o))) (let ((_let_154 (= _let_153 id_nat_o))) (let ((_let_155 (= finite4582259249640653518nt_nat (lambda ((S4 set_int) (F2 (-> int nat nat))) (forall ((X4 int) (Y5 int)) (let ((_let_1 (@ F2 Y5))) (let ((_let_2 (@ F2 X4))) (=> (@ (@ member_int X4) S4) (=> (@ (@ member_int Y5) S4) (= (@ (@ comp_nat_nat_nat _let_1) _let_2) (@ (@ comp_nat_nat_nat _let_2) _let_1))))))))))) (let ((_let_156 (@ comp_P3239167524078694454t_unit produc5717040794327095847_ref_a))) (let ((_let_157 (@ _let_156 (@ produc2058451029528183389_ref_a (lambda ((X4 ref_a) (Y5 heap_e7401611519738050253t_unit)) (@ (@ produc2564672488694626579_ref_a Y5) X4)))))) (let ((_let_158 (= produc1126150082675451753t_unit _let_157))) (let ((_let_159 (= product_snd_num_nat (@ (@ comp_P8336958949797789649um_nat product_fst_nat_num) (@ produc5219324331026901427at_num (lambda ((X4 num) (Y5 nat)) (@ (@ product_Pair_nat_num Y5) X4))))))) (let ((_let_160 (= bNF_vi7262943168399475603_int_o (lambda ((F2 (-> char int)) (G3 (-> code_integer int)) (P4 (-> int int Bool)) (__flatten_var_0 char) (__flatten_var_1 code_integer)) (@ (@ (@ (@ relcom5819909836510906509nteger (@ (@ bNF_Grp_char_int top_top_set_char) F2)) (@ (@ relcom967497705283160040nteger P4) (@ conver1462408618118490240er_int (@ (@ bNF_Gr6045950513751025625er_int top_to4645266643341252675nteger) G3)))) __flatten_var_0) __flatten_var_1))))) (let ((_let_161 (= bNF_re7626690874201225453um_num (lambda ((R6 (-> int int Bool)) (S4 (-> num num Bool)) (F2 (-> int num)) (G3 (-> int num))) (@ (@ ord_le6124364862034508274_num_o (@ (@ (@ bNF_Gr7020624548710275655nt_num F2) G3) R6)) S4))))) (let ((_let_162 (= comple3221217463730067765et_int (lambda ((A6 set_set_int)) (@ collect_int (lambda ((X4 int)) (@ complete_Sup_Sup_o (@ (@ image_set_int_o (@ member_int X4)) A6)))))))) (let ((_let_163 (= fun_pair_less (@ (@ lex_prod_nat_nat less_than) less_than)))) (let ((_let_164 (= refl_on_nat (lambda ((A6 set_nat) (R5 set_Pr1261947904930325089at_nat)) (and (@ (@ ord_le3146513528884898305at_nat R5) (@ (@ produc457027306803732586at_nat A6) (lambda ((Uu nat)) A6))) (forall ((X4 nat)) (=> (@ (@ member_nat X4) A6) (@ (@ member8440522571783428010at_nat (@ (@ product_Pair_nat_nat X4) X4)) R5)))))))) (let ((_let_165 (= euclid4774559944035922753ze_int _let_27))) (let ((_let_166 (= order_4940263126897443436at_nat (lambda ((R5 set_Pr8693737435421807431at_nat) (A5 product_prod_nat_nat)) (@ collec3392354462482085612at_nat (lambda ((B4 product_prod_nat_nat)) (and (not (= B4 A5)) (@ (@ member8206827879206165904at_nat (@ (@ produc6161850002892822231at_nat A5) B4)) R5)))))))) (let ((_let_167 (= produc27273713700761075at_nat (lambda ((F2 (-> nat nat product_prod_nat_nat product_prod_nat_nat)) (X4 product_prod_nat_nat) (__flatten_var_0 product_prod_nat_nat)) (@ (@ (@ F2 (@ product_fst_nat_nat X4)) (@ product_snd_nat_nat X4)) __flatten_var_0))))) (let ((_let_168 (= produc4947309494688390418_int_o (lambda ((F2 (-> int int Bool)) (Prod3 product_prod_int_int)) (@ (@ F2 (@ product_fst_int_int Prod3)) (@ product_snd_int_int Prod3)))))) (let ((_let_169 (= (@ produc5456455677105495163at_nat produc9060074326276436823at_nat) id_Pro6043886709289754456at_nat))) (let ((_let_170 (= (@ (@ image_nat_int nat_int_decode) top_top_set_nat) top_top_set_int))) (let ((_let_171 (= comp_o_o_nat (lambda ((F2 (-> Bool Bool)) (G3 (-> nat Bool)) (X4 nat)) (@ F2 (@ G3 X4)))))) (let ((_let_172 (= comp_nat_num_int (lambda ((F2 (-> nat num)) (G3 (-> int nat)) (X4 int)) (@ F2 (@ G3 X4)))))) (let ((_let_173 (= id_Pro2258643101195443293at_nat (@ collec7088162979684241874at_nat (lambda ((X4 produc859450856879609959at_nat)) (= (@ produc3213797794245857475at_nat X4) (@ produc6408287024330202629at_nat X4))))))) (let ((_let_174 (= order_8308734813930759573at_nat (lambda ((P4 (-> set_Pr4329608150637261639at_nat set_Pr4329608150637261639at_nat Bool)) (A6 set_se5479201105039950375at_nat)) (@ collec7872792499061297490at_nat (@ produc9020218426428501292_nat_o (lambda ((A5 set_Pr4329608150637261639at_nat) (B4 set_Pr4329608150637261639at_nat)) (and (@ (@ P4 A5) B4) (@ (@ member1466754251312161552at_nat (@ (@ produc9060074326276436823at_nat A5) B4)) (@ (@ produc6258361011560675592at_nat A6) (lambda ((Uu set_Pr4329608150637261639at_nat)) A6))))))))))) (let ((_let_175 (= relcom8911704206367525917at_int (lambda ((R6 (-> product_prod_nat_nat product_prod_nat_nat Bool)) (S4 (-> product_prod_nat_nat int Bool)) (A5 product_prod_nat_nat) (C4 int)) (exists ((B4 product_prod_nat_nat)) (and (@ (@ R6 A5) B4) (@ (@ S4 B4) C4))))))) (let ((_let_176 (= fun_in_rel_int_int (lambda ((R6 set_Pr958786334691620121nt_int) (X4 int) (Y5 int)) (@ (@ member5262025264175285858nt_int (@ (@ product_Pair_int_int X4) Y5)) R6))))) (let ((_let_177 (= comp_nat_nat_nat (lambda ((F2 (-> nat nat)) (G3 (-> nat nat)) (X4 nat)) (@ F2 (@ G3 X4)))))) (let ((_let_178 (= produc8739625826339149834_nat_o (lambda ((F2 (-> nat nat product_prod_nat_nat Bool)) (X4 product_prod_nat_nat) (Y5 product_prod_nat_nat)) (@ (@ produc6081775807080527818_nat_o (lambda ((L3 nat) (R5 nat)) (@ (@ (@ F2 L3) R5) Y5))) X4))))) (let ((_let_179 (= comple3063163877087187839_set_o (lambda ((A6 set_set_o)) (@ collect_o (lambda ((X4 Bool)) (@ complete_Inf_Inf_o (@ (@ image_set_o_o (@ member_o X4)) A6)))))))) (let ((_let_180 (= product_fst_num_nat (@ (@ comp_P5051845089628979463um_nat product_snd_nat_num) (@ produc5219324331026901427at_num (lambda ((X4 num) (Y5 nat)) (@ (@ product_Pair_nat_num Y5) X4))))))) (let ((_let_181 (= produc1854806715440696265at_nat produc27273713700761075at_nat))) (let ((_let_182 (= order_1761765819289301284nt_int (lambda ((R5 set_Pr2560585780119916871nt_int) (A5 product_prod_int_int)) (@ collec213857154873943460nt_int (lambda ((B4 product_prod_int_int)) (and (@ (@ member8566619992076573584nt_int (@ (@ produc3646306378393792727nt_int A5) B4)) R5) (not (= B4 A5))))))))) (let ((_let_183 (@ (@ produc1204236661673008499ar_rat top_top_set_char) (lambda ((Uu char)) top_top_set_rat)))) (let ((_let_184 (= _let_183 top_to8437673547576850234ar_rat))) (let ((_let_185 (= (@ (@ image_list_nat_nat nat_list_encode) top_top_set_list_nat) top_top_set_nat))) (let ((_let_186 (= comple7399068483239264473et_nat (lambda ((A6 set_set_nat)) (@ collect_nat (lambda ((X4 nat)) (@ complete_Sup_Sup_o (@ (@ image_set_nat_o (@ member_nat X4)) A6)))))))) (let ((_let_187 (= produc6237731129814287028at_num (lambda ((A6 set_nat) (B6 (-> nat set_num))) (@ comple1400524285282149784at_num (@ (@ image_2893549341467670548at_num (lambda ((X4 nat)) (@ comple1400524285282149784at_num (@ (@ image_4778453735051108682at_num (lambda ((Y5 num)) (@ (@ insert8920054152555992091at_num (@ (@ product_Pair_nat_num X4) Y5)) bot_bo7038385379056416535at_num))) (@ B6 X4))))) A6)))))) (let ((_let_188 (= refl_o6955724340487615712at_nat (lambda ((A6 set_se7855581050983116737at_nat) (R5 set_Pr4329608150637261639at_nat)) (and (@ (@ ord_le1268244103169919719at_nat R5) (@ (@ produc7726050920695093128at_nat A6) (lambda ((Uu set_Pr1261947904930325089at_nat)) A6))) (forall ((X4 set_Pr1261947904930325089at_nat)) (=> (@ (@ member2643936169264416010at_nat X4) A6) (@ (@ member8757157785044589968at_nat (@ (@ produc2922128104949294807at_nat X4) X4)) R5)))))))) (let ((_let_189 (= ord_less_eq_int (lambda ((X4 int) (Xa3 int)) (@ (@ (@ produc8739625826339149834_nat_o (lambda ((Y5 nat) (Z4 nat) (__flatten_var_0 product_prod_nat_nat)) (@ (@ produc6081775807080527818_nat_o (lambda ((U3 nat) (V3 nat)) (@ (@ ord_less_eq_nat (@ (@ plus_plus_nat Y5) V3)) (@ (@ plus_plus_nat U3) Z4)))) __flatten_var_0))) (@ rep_Integ X4)) (@ rep_Integ Xa3)))))) (let ((_let_190 (= (@ (@ produc8728714639637146746at_rat top_top_set_rat) (lambda ((Uu rat)) top_top_set_rat)) top_to3112507417142880193at_rat))) (let ((_let_191 (= lookup_a (lambda ((R5 ref_a)) (@ heap_tap_a (lambda ((H5 heap_e7401611519738050253t_unit)) (@ (@ get_a H5) R5))))))) (let ((_let_192 (= bNF_vi508398028314858188_int_o (lambda ((F2 (-> rat int)) (G3 (-> code_integer int)) (P4 (-> int int Bool)) (__flatten_var_0 rat) (__flatten_var_1 code_integer)) (@ (@ (@ (@ relcom3409376902655092628nteger (@ (@ bNF_Grp_rat_int top_top_set_rat) F2)) (@ (@ relcom967497705283160040nteger P4) (@ conver1462408618118490240er_int (@ (@ bNF_Gr6045950513751025625er_int top_to4645266643341252675nteger) G3)))) __flatten_var_0) __flatten_var_1))))) (let ((_let_193 (@ image_nat_nat id_nat))) (let ((_let_194 (= total_on_nat (lambda ((A6 set_nat) (R5 set_Pr1261947904930325089at_nat)) (forall ((X4 nat)) (=> (@ (@ member_nat X4) A6) (forall ((Y5 nat)) (=> (@ (@ member_nat Y5) A6) (=> (not (= X4 Y5)) (or (@ (@ member8440522571783428010at_nat (@ (@ product_Pair_nat_nat Y5) X4)) R5) (@ (@ member8440522571783428010at_nat (@ (@ product_Pair_nat_nat X4) Y5)) R5))))))))))) (let ((_let_195 (= inv_image_nat_nat (lambda ((R5 set_Pr1261947904930325089at_nat) (F2 (-> nat nat))) (@ collec3392354462482085612at_nat (@ produc6081775807080527818_nat_o (lambda ((X4 nat) (Y5 nat)) (@ (@ member8440522571783428010at_nat (@ (@ product_Pair_nat_nat (@ F2 X4)) (@ F2 Y5))) R5)))))))) (let ((_let_196 (= uminus_uminus_int (@ _let_95 (@ produc2626176000494625587at_nat (lambda ((X4 nat) (Y5 nat)) (@ (@ product_Pair_nat_nat Y5) X4))))))) (let ((_let_197 (= comple5770381748412298549_int_o (lambda ((S4 set_int_int_o) (X4 int) (Y5 int)) (@ (@ member5262025264175285858nt_int (@ (@ product_Pair_int_int X4) Y5)) (@ comple1626965760690514720nt_int (@ (@ image_4447441447610994254nt_int collec213857154873943460nt_int) (@ (@ image_1365644804893650413_int_o produc4947309494688390418_int_o) S4)))))))) (let ((_let_198 (= inf_inf_Product_unit (lambda ((Uu2 product_unit) (Uv2 product_unit)) product_Unity)))) (let ((_let_199 (= complete_Inf_Inf_int (lambda ((X9 set_int)) (@ uminus_uminus_int (@ complete_Sup_Sup_int (@ (@ image_int_int uminus_uminus_int) X9))))))) (let ((_let_200 (= comple4707286699709038525_int_o (lambda ((S4 set_Pr8049984349381595834_int_o) (X4 product_prod_int_int)) (@ (@ member5262025264175285858nt_int X4) (@ comple1626965760690514720nt_int (@ (@ image_4447441447610994254nt_int collec213857154873943460nt_int) S4))))))) (let ((_let_201 (= nat2 (lambda ((X4 int)) (@ (@ produc6842872674320459806at_nat minus_minus_nat) (@ rep_Integ X4)))))) (let ((_let_202 (= produc6258361011560675592at_nat (lambda ((A6 set_se5479201105039950375at_nat) (B6 (-> set_Pr4329608150637261639at_nat set_se5479201105039950375at_nat))) (@ comple7342073961973170484at_nat (@ (@ image_1124969593608450885at_nat (lambda ((X4 set_Pr4329608150637261639at_nat)) (@ comple7342073961973170484at_nat (@ (@ image_1124969593608450885at_nat (lambda ((Y5 set_Pr4329608150637261639at_nat)) (@ (@ insert291458823148189367at_nat (@ (@ produc9060074326276436823at_nat X4) Y5)) bot_bo4948859079157340979at_nat))) (@ B6 X4))))) A6)))))) (let ((_let_203 (@ (@ image_int_int abs_abs_int) top_top_set_int))) (let ((_let_204 (= _let_203 semiring_1_Nats_int))) (let ((_let_205 (= quotient_char_char (lambda ((R6 (-> char char Bool)) (Abs4 (-> char char)) (Rep4 (-> char char)) (T4 (-> char char Bool))) (let ((_let_1 (@ conversep_char_char T4))) (let ((_let_2 (@ bNF_Grp_char_char top_top_set_char))) (and (@ (@ ord_le2540245887939449860char_o T4) (@ _let_2 Abs4)) (@ (@ ord_le2540245887939449860char_o (@ _let_2 Rep4)) _let_1) (= R6 (@ (@ relcom5872928454965100966r_char T4) _let_1))))))))) (let ((_let_206 (= product_snd_int_int (@ produc8211389475949308722nt_int (lambda ((X12 int) (X23 int)) X23))))) (let ((_let_207 (= adjust_div (@ produc8211389475949308722nt_int (lambda ((Q3 int) (R5 int)) (@ (@ plus_plus_int Q3) (@ zero_n2684676970156552555ol_int (not (= R5 zero_zero_int))))))))) (let ((_let_208 (= id_nat2 (@ collec3392354462482085612at_nat (lambda ((X4 product_prod_nat_nat)) (= (@ product_fst_nat_nat X4) (@ product_snd_nat_nat X4))))))) (let ((_let_209 (= minus_minus_int (@ _let_96 (@ produc27273713700761075at_nat (lambda ((X4 nat) (Y5 nat) (__flatten_var_0 product_prod_nat_nat)) (@ (@ produc2626176000494625587at_nat (lambda ((U3 nat) (V3 nat)) (@ (@ product_Pair_nat_nat (@ (@ plus_plus_nat X4) V3)) (@ (@ plus_plus_nat Y5) U3)))) __flatten_var_0))))))) (let ((_let_210 (= fun_in8056734985859589634at_nat (lambda ((R6 set_Pr4329608150637261639at_nat) (X4 set_Pr1261947904930325089at_nat) (Y5 set_Pr1261947904930325089at_nat)) (@ (@ member8757157785044589968at_nat (@ (@ produc2922128104949294807at_nat X4) Y5)) R6))))) (let ((_let_211 (= (@ produc2626176000494625587at_nat product_Pair_nat_nat) id_Pro7559728917991913458at_nat))) (let ((_let_212 (= produc970745769005243767t_unit (lambda ((P3 produc7812382424243267045t_unit)) (@ (@ produc2564672488694626579_ref_a (@ produc1126150082675451753t_unit P3)) (@ produc473321116828791851t_unit P3)))))) (let ((_let_213 (= inv_image_nat_int (lambda ((R5 set_Pr1261947904930325089at_nat) (F2 (-> int nat))) (@ collec213857154873943460nt_int (@ produc4947309494688390418_int_o (lambda ((X4 int) (Y5 int)) (@ (@ member8440522571783428010at_nat (@ (@ product_Pair_nat_nat (@ F2 X4)) (@ F2 Y5))) R5)))))))) (let ((_let_214 (= product_fst_nat_nat (@ (@ comp_P1567445206330693457at_nat product_snd_nat_nat) (@ produc2626176000494625587at_nat (lambda ((X4 nat) (Y5 nat)) (@ (@ product_Pair_nat_nat Y5) X4))))))) (let ((_let_215 (@ (@ map_fu434086159418415080_int_o rep_Integ) (@ (@ map_fu4826362097070443709at_o_o rep_Integ) id_o)))) (let ((_let_216 (= comple8322679762649017525_nat_o (lambda ((S4 set_se9180647916752606350_nat_o) (X4 set_Pr1261947904930325089at_nat) (Y5 set_Pr1261947904930325089at_nat)) (@ (@ member8757157785044589968at_nat (@ (@ produc2922128104949294807at_nat X4) Y5)) (@ comple6751905152567503566at_nat (@ (@ image_4902389024228248874at_nat collec6321179662152712658at_nat) (@ (@ image_6226802281960588479_nat_o produc410239310623530412_nat_o) S4)))))))) (let ((_let_217 (= sup_sup_set_nat (lambda ((A6 set_nat) (B6 set_nat)) (@ comple7399068483239264473et_nat (@ (@ image_o_set_nat (lambda ((B4 Bool)) (@ (@ (@ if_set_nat B4) A6) B6))) top_top_set_o)))))) (let ((_let_218 (= top_top_nat_num_o (lambda ((X4 nat) (Y5 num)) (@ (@ member9148766508732265716at_num (@ (@ product_Pair_nat_num X4) Y5)) top_to385025497714130939at_num))))) (let ((_let_219 (= nat_to_rat_surj (lambda ((N4 nat)) (@ (@ produc6207742614233964070at_rat (lambda ((A5 nat) (B4 nat)) (@ (@ fract (@ nat_int_decode A5)) (@ nat_int_decode B4)))) (@ nat_prod_decode N4)))))) (let ((_let_220 (= bNF_Ca5157130669891357211al_int (lambda ((A6 set_int) (R5 set_Pr958786334691620121nt_int)) (forall ((X4 int)) (=> (@ (@ member_int X4) (@ field_int R5)) (exists ((Y5 int)) (and (@ (@ member_int Y5) A6) (@ (@ member5262025264175285858nt_int (@ (@ product_Pair_int_int X4) Y5)) R5) (not (= X4 Y5)))))))))) (let ((_let_221 (= comple1675732732025788397_nat_o (lambda ((S4 set_nat_nat_o) (X4 nat) (Y5 nat)) (@ (@ member8440522571783428010at_nat (@ (@ product_Pair_nat_nat X4) Y5)) (@ comple1930127330929219688at_nat (@ (@ image_7124889717316225246at_nat collec3392354462482085612at_nat) (@ (@ image_7429393840292777309_nat_o produc6081775807080527818_nat_o) S4)))))))) (let ((_let_222 (= bNF_vi5202502398764838569_nat_o (lambda ((F2 (-> list_nat product_prod_nat_nat)) (G3 (-> int product_prod_nat_nat)) (P4 (-> product_prod_nat_nat product_prod_nat_nat Bool)) (__flatten_var_0 list_nat) (__flatten_var_1 int)) (@ (@ (@ (@ relcom170568170053003356at_int (@ (@ bNF_Gr4119388860389678161at_nat top_top_set_list_nat) F2)) (@ (@ relcom8911704206367525917at_int P4) (@ conver1866313717161370910at_nat (@ (@ bNF_Gr6591314147588017797at_nat top_top_set_int) G3)))) __flatten_var_0) __flatten_var_1))))) (let ((_let_223 (= product_swap_int_int (lambda ((P3 product_prod_int_int)) (@ (@ product_Pair_int_int (@ product_snd_int_int P3)) (@ product_fst_int_int P3)))))) (let ((_let_224 (@ (@ image_nat_rat nat_to_rat_surj) top_top_set_nat))) (let ((_let_225 (= field_6020823756834552118ts_rat _let_224))) (let ((_let_226 (= ord_less_int (@ _let_215 (@ produc8739625826339149834_nat_o (lambda ((X4 nat) (Y5 nat) (__flatten_var_0 product_prod_nat_nat)) (@ (@ produc6081775807080527818_nat_o (lambda ((U3 nat) (V3 nat)) (@ (@ ord_less_nat (@ (@ plus_plus_nat X4) V3)) (@ (@ plus_plus_nat U3) Y5)))) __flatten_var_0))))))) (let ((_let_227 (= comp_int_nat_int (lambda ((F2 (-> int nat)) (G3 (-> int int)) (X4 int)) (@ F2 (@ G3 X4)))))) (let ((_let_228 (= comple5382143125604098054nt_int (lambda ((A6 set_se6260736226359567993nt_int)) (@ collec213857154873943460nt_int (lambda ((X4 product_prod_int_int)) (@ complete_Sup_Sup_o (@ (@ image_701744273176368580_int_o (@ member5262025264175285858nt_int X4)) A6)))))))) (let ((_let_229 (= bNF_Ca966259857504369954at_int (lambda ((R5 set_Pr1261947904930325089at_nat) (As (-> nat int))) (forall ((I2 nat) (J nat)) (=> (@ (@ member8440522571783428010at_nat (@ (@ product_Pair_nat_nat I2) J)) R5) (@ (@ ord_less_eq_int (@ As I2)) (@ As J)))))))) (let ((_let_230 (= top_top_Product_unit product_Unity))) (let ((_let_231 (= ord_less_rat (lambda ((P3 rat) (Q3 rat)) (@ (@ produc4947309494688390418_int_o (lambda ((A5 int) (C4 int)) (@ (@ produc4947309494688390418_int_o (lambda ((B4 int) (D3 int)) (@ (@ ord_less_int (@ (@ times_times_int A5) D3)) (@ (@ times_times_int C4) B4)))) (@ quotient_of Q3)))) (@ quotient_of P3)))))) (let ((_let_232 (= fun_min_strict (@ min_ex6901939911449802026at_nat fun_pair_less)))) (let ((_let_233 (= bNF_Ca1968104039914474786nt_nat (lambda ((R5 set_Pr958786334691620121nt_int) (As (-> int nat))) (forall ((I2 int) (J int)) (=> (@ (@ member5262025264175285858nt_int (@ (@ product_Pair_int_int I2) J)) R5) (@ (@ ord_less_eq_nat (@ As I2)) (@ As J)))))))) (let ((_let_234 (= quotient_rat_rat (lambda ((R6 (-> rat rat Bool)) (Abs4 (-> rat rat)) (Rep4 (-> rat rat)) (T4 (-> rat rat Bool))) (let ((_let_1 (@ bNF_Grp_rat_rat top_top_set_rat))) (let ((_let_2 (@ conversep_rat_rat T4))) (and (= R6 (@ (@ relcompp_rat_rat_rat T4) _let_2)) (@ (@ ord_le4717968354871517046_rat_o (@ _let_1 Rep4)) _let_2) (@ (@ ord_le4717968354871517046_rat_o T4) (@ _let_1 Abs4))))))))) (let ((_let_235 (= bNF_vi1204582724742824157_nat_o (lambda ((F2 (-> int product_prod_nat_nat)) (G3 (-> int product_prod_nat_nat)) (P4 (-> product_prod_nat_nat product_prod_nat_nat Bool)) (__flatten_var_0 int) (__flatten_var_1 int)) (let ((_let_1 (@ bNF_Gr6591314147588017797at_nat top_top_set_int))) (@ (@ (@ (@ relcom1106208330880909712at_int (@ _let_1 F2)) (@ (@ relcom8911704206367525917at_int P4) (@ conver1866313717161370910at_nat (@ _let_1 G3)))) __flatten_var_0) __flatten_var_1)))))) (let ((_let_236 (= comple4393433247856107946_int_o (lambda ((S4 set_int_o) (X4 int)) (@ (@ member_int X4) (@ comple3628384868704368283et_int (@ (@ image_int_o_set_int collect_int) S4))))))) (let ((_let_237 (= order_8809246210994205103at_nat (lambda ((P4 (-> set_Pr1261947904930325089at_nat set_Pr1261947904930325089at_nat Bool)) (A6 set_se7855581050983116737at_nat)) (@ collec6321179662152712658at_nat (@ produc410239310623530412_nat_o (lambda ((A5 set_Pr1261947904930325089at_nat) (B4 set_Pr1261947904930325089at_nat)) (and (@ (@ P4 A5) B4) (@ (@ member8757157785044589968at_nat (@ (@ produc2922128104949294807at_nat A5) B4)) (@ (@ produc7726050920695093128at_nat A6) (lambda ((Uu set_Pr1261947904930325089at_nat)) A6))))))))))) (let ((_let_238 (@ image_o_o id_o))) (let ((_let_239 (= _let_238 id_set_o))) (let ((_let_240 (= quotient_char_int (lambda ((R6 (-> char char Bool)) (Abs4 (-> char int)) (Rep4 (-> int char)) (T4 (-> char int Bool))) (let ((_let_1 (@ conversep_char_int T4))) (and (@ (@ ord_le3396192186225775209_int_o T4) (@ (@ bNF_Grp_char_int top_top_set_char) Abs4)) (= R6 (@ (@ relcom750623199913152513t_char T4) _let_1)) (@ (@ ord_le7608100903186094441char_o (@ (@ bNF_Grp_int_char top_top_set_int) Rep4)) _let_1))))))) (let ((_let_241 (= quotient_nat_rat (lambda ((R6 (-> nat nat Bool)) (Abs4 (-> nat rat)) (Rep4 (-> rat nat)) (T4 (-> nat rat Bool))) (let ((_let_1 (@ conversep_nat_rat T4))) (and (@ (@ ord_le5467402850006352766_nat_o (@ (@ bNF_Grp_rat_nat top_top_set_rat) Rep4)) _let_1) (= R6 (@ (@ relcompp_nat_rat_nat T4) _let_1)) (@ (@ ord_le1897120724991155070_rat_o T4) (@ (@ bNF_Grp_nat_rat top_top_set_nat) Abs4)))))))) (let ((_let_242 (@ (@ produc4754187946284079723t_char top_top_set_nat) (lambda ((Uu nat)) top_top_set_char)))) (let ((_let_243 (= _let_242 top_to7107842681480589234t_char))) (let ((_let_244 (forall ((F (-> heap_e7401611519738050253t_unit produc7812382424243267045t_unit)) (H heap_e7401611519738050253t_unit) (H2 heap_e7401611519738050253t_unit) (R ref_a)) (let ((_let_1 (@ F H))) (=> (@ (@ (@ (@ heap_effect_ref_a (@ heap_heap_ref_a F)) H) H2) R) (not (=> (= H2 (@ produc1126150082675451753t_unit _let_1)) (not (= R (@ produc473321116828791851t_unit _let_1)))))))))) (let ((_let_245 (= _let_193 id_set_nat))) (let ((_let_246 (@ comple7806235888213564991et_nat (@ (@ image_nat_set_nat set_or1210151606488870762an_nat) top_top_set_nat)))) (let ((_let_247 (= _let_246 bot_bot_set_nat))) (let ((_let_248 (= bNF_Ca5159621140400407487al_nat (lambda ((A6 set_nat) (R5 set_Pr1261947904930325089at_nat)) (forall ((X4 nat)) (=> (@ (@ member_nat X4) (@ field_nat R5)) (exists ((Y5 nat)) (and (not (= X4 Y5)) (@ (@ member8440522571783428010at_nat (@ (@ product_Pair_nat_nat X4) Y5)) R5) (@ (@ member_nat Y5) A6))))))))) (let ((_let_249 (= bot_bot_Product_unit product_Unity))) (let ((_let_250 (= pcr_int (@ (@ relcom8911704206367525917at_int (@ (@ basic_5328504652464829177at_nat (lambda ((Y2 nat) (Z nat)) (= Y2 Z))) (lambda ((Y2 nat) (Z nat)) (= Y2 Z)))) cr_int)))) (let ((_let_251 (= produc7926200574084438792nt_int produc8211389475949308722nt_int))) (let ((_let_252 (= produc5396952528824381687at_nat (lambda ((P3 produc1319942482725812455at_nat)) (@ (@ produc9060074326276436823at_nat (@ produc826222791318859909at_nat P3)) (@ produc4486455499028916547at_nat P3)))))) (let ((_let_253 (= comple1930127330929219688at_nat (lambda ((A6 set_se7855581050983116737at_nat)) (@ collec3392354462482085612at_nat (lambda ((X4 product_prod_nat_nat)) (@ complete_Inf_Inf_o (@ (@ image_7457375456213313148_nat_o (@ member8440522571783428010at_nat X4)) A6)))))))) (let ((_let_254 (= produc2937545259423399429at_nat (@ (@ comp_P4974406650942564362at_nat produc6011863565407846595at_nat) (@ produc7548845685434208379at_nat (lambda ((X4 set_Pr1261947904930325089at_nat) (Y5 set_Pr1261947904930325089at_nat)) (@ (@ produc2922128104949294807at_nat Y5) X4))))))) (let ((_let_255 (@ (@ image_7136766188234240905_ref_a produc473321116828791851t_unit) top_to2503719809363509323t_unit))) (let ((_let_256 (= _let_255 top_top_set_ref_a))) (let ((_let_257 (= sup_sup_Product_unit (lambda ((Uu2 product_unit) (Uv2 product_unit)) product_Unity)))) (let ((_let_258 (= bNF_Ca8448034394003515314at_nat (lambda ((A6 set_se7855581050983116737at_nat) (R5 set_Pr4329608150637261639at_nat)) (forall ((X4 set_Pr1261947904930325089at_nat)) (=> (@ (@ member2643936169264416010at_nat X4) (@ field_3145993188331922222at_nat R5)) (exists ((Y5 set_Pr1261947904930325089at_nat)) (and (@ (@ member2643936169264416010at_nat Y5) A6) (not (= X4 Y5)) (@ (@ member8757157785044589968at_nat (@ (@ produc2922128104949294807at_nat X4) Y5)) R5))))))))) (let ((_let_259 (@ (@ image_678696785212003926at_nat nat_sum_decode) top_top_set_nat))) (let ((_let_260 (= _let_259 top_to6661820994512907621at_nat))) (let ((_let_261 (= order_aboveS_int (lambda ((R5 set_Pr958786334691620121nt_int) (A5 int)) (@ collect_int (lambda ((B4 int)) (and (@ (@ member5262025264175285858nt_int (@ (@ product_Pair_int_int A5) B4)) R5) (not (= B4 A5))))))))) (let ((_let_262 (= comple1177764198577243945_nat_o (lambda ((S4 set_Pr7010166363911110284_nat_o) (X4 produc3843707927480180839at_nat)) (@ (@ member8757157785044589968at_nat X4) (@ comple4364388969068068532at_nat (@ (@ image_4902389024228248874at_nat collec6321179662152712658at_nat) S4))))))) (let ((_let_263 (= fun_in_rel_nat_nat (lambda ((R6 set_Pr1261947904930325089at_nat) (X4 nat) (Y5 nat)) (@ (@ member8440522571783428010at_nat (@ (@ product_Pair_nat_nat X4) Y5)) R6))))) (let ((_let_264 (= produc457027306803732586at_nat (lambda ((A6 set_nat) (B6 (-> nat set_nat))) (@ comple5685304695842803022at_nat (@ (@ image_7178329752028323786at_nat (lambda ((X4 nat)) (@ comple5685304695842803022at_nat (@ (@ image_7178329752028323786at_nat (lambda ((Y5 nat)) (@ (@ insert8211810215607154385at_nat (@ (@ product_Pair_nat_nat X4) Y5)) bot_bo2099793752762293965at_nat))) (@ B6 X4))))) A6)))))) (let ((_let_265 (= bNF_Ca8665028551170535155natLeq (@ collec3392354462482085612at_nat (@ produc6081775807080527818_nat_o ord_less_eq_nat))))) (let ((_let_266 (= bNF_Ca6037544080215331608at_nat (lambda ((A6 set_se5479201105039950375at_nat) (R5 set_Pr7459493094073627847at_nat)) (forall ((X4 set_Pr4329608150637261639at_nat)) (=> (@ (@ member6273874620674182256at_nat X4) (@ field_1428494348145443988at_nat R5)) (exists ((Y5 set_Pr4329608150637261639at_nat)) (and (@ (@ member6273874620674182256at_nat Y5) A6) (@ (@ member1466754251312161552at_nat (@ (@ produc9060074326276436823at_nat X4) Y5)) R5) (not (= X4 Y5)))))))))) (let ((_let_267 (@ (@ produc137982192359816398at_int top_top_set_rat) (lambda ((Uu rat)) top_top_set_int)))) (let ((_let_268 (= _let_267 top_to7002410609688830997at_int))) (let ((_let_269 (= comple342879659800731223_int_o (lambda ((S4 set_Pr8049984349381595834_int_o) (X4 product_prod_int_int)) (@ (@ member5262025264175285858nt_int X4) (@ comple5382143125604098054nt_int (@ (@ image_4447441447610994254nt_int collec213857154873943460nt_int) S4))))))) (let ((_let_270 (= order_4440095836999870412at_nat (lambda ((R5 set_Pr4329608150637261639at_nat) (A5 set_Pr1261947904930325089at_nat)) (@ collec5514110066124741708at_nat (lambda ((B4 set_Pr1261947904930325089at_nat)) (and (not (= B4 A5)) (@ (@ member8757157785044589968at_nat (@ (@ produc2922128104949294807at_nat A5) B4)) R5)))))))) (let ((_let_271 (= inv_image_int_nat (lambda ((R5 set_Pr958786334691620121nt_int) (F2 (-> nat int))) (@ collec3392354462482085612at_nat (@ produc6081775807080527818_nat_o (lambda ((X4 nat) (Y5 nat)) (@ (@ member5262025264175285858nt_int (@ (@ product_Pair_int_int (@ F2 X4)) (@ F2 Y5))) R5)))))))) (let ((_let_272 (= complete_Sup_Sup_o_o (lambda ((S4 set_o_o) (X4 Bool)) (@ (@ member_o X4) (@ comple90263536869209701_set_o (@ (@ image_o_o_set_o collect_o) S4))))))) (let ((_let_273 (= comple4502628867940267931_nat_o (lambda ((S4 set_se7255092946006855566_nat_o) (X4 set_Pr4329608150637261639at_nat) (Y5 set_Pr4329608150637261639at_nat)) (@ (@ member1466754251312161552at_nat (@ (@ produc9060074326276436823at_nat X4) Y5)) (@ comple7342073961973170484at_nat (@ (@ image_5694205205332509994at_nat collec7872792499061297490at_nat) (@ (@ image_5235725667318448191_nat_o produc9020218426428501292_nat_o) S4)))))))) (let ((_let_274 (= intrel (@ produc8739625826339149834_nat_o (lambda ((X4 nat) (Y5 nat) (__flatten_var_0 product_prod_nat_nat)) (@ (@ produc6081775807080527818_nat_o (lambda ((U3 nat) (V3 nat)) (= (@ (@ plus_plus_nat X4) V3) (@ (@ plus_plus_nat U3) Y5)))) __flatten_var_0)))))) (let ((_let_275 (forall ((P2 Bool)) (and (=> P2 (= (@ collec213857154873943460nt_int (@ produc4947309494688390418_int_o (lambda ((A5 int) (B4 int)) P2))) top_to4366644338036079209nt_int)) (=> (not P2) (= (@ collec213857154873943460nt_int (@ produc4947309494688390418_int_o (lambda ((A5 int) (B4 int)) P2))) bot_bo1796632182523588997nt_int)))))) (let ((_let_276 (= bNF_vi190728152058600505_nat_o (lambda ((F2 (-> nat product_prod_nat_nat)) (G3 (-> int product_prod_nat_nat)) (P4 (-> product_prod_nat_nat product_prod_nat_nat Bool)) (__flatten_var_0 nat) (__flatten_var_1 int)) (@ (@ (@ (@ relcom8569543703982574316at_int (@ (@ bNF_Gr3553472063123884001at_nat top_top_set_nat) F2)) (@ (@ relcom8911704206367525917at_int P4) (@ conver1866313717161370910at_nat (@ (@ bNF_Gr6591314147588017797at_nat top_top_set_int) G3)))) __flatten_var_0) __flatten_var_1))))) (let ((_let_277 (= bNF_Ca1332973979827979050nt_rat (lambda ((R5 set_Pr958786334691620121nt_int) (As (-> int rat))) (forall ((I2 int) (J int)) (=> (@ (@ member5262025264175285858nt_int (@ (@ product_Pair_int_int I2) J)) R5) (@ (@ ord_less_eq_rat (@ As I2)) (@ As J)))))))) (let ((_let_278 (= ord_less_eq_rat (lambda ((P3 rat) (Q3 rat)) (@ (@ produc4947309494688390418_int_o (lambda ((A5 int) (C4 int)) (@ (@ produc4947309494688390418_int_o (lambda ((B4 int) (D3 int)) (@ (@ ord_less_eq_int (@ (@ times_times_int A5) D3)) (@ (@ times_times_int C4) B4)))) (@ quotient_of Q3)))) (@ quotient_of P3)))))) (let ((_let_279 (= times_times_int (@ _let_96 (@ produc27273713700761075at_nat (lambda ((X4 nat) (Y5 nat) (__flatten_var_0 product_prod_nat_nat)) (@ (@ produc2626176000494625587at_nat (lambda ((U3 nat) (V3 nat)) (let ((_let_1 (@ times_times_nat Y5))) (let ((_let_2 (@ times_times_nat X4))) (@ (@ product_Pair_nat_nat (@ (@ plus_plus_nat (@ _let_2 U3)) (@ _let_1 V3))) (@ (@ plus_plus_nat (@ _let_2 V3)) (@ _let_1 U3))))))) __flatten_var_0))))))) (let ((_let_280 (@ (@ produc140472662868866674at_nat top_top_set_rat) (lambda ((Uu rat)) top_top_set_nat)))) (let ((_let_281 (= _let_280 top_to269121717765781945at_nat))) (let ((_let_282 (@ (@ comp_nat_nat_nat suc) suc))) (let ((_let_283 (= produc826222791318859909at_nat (@ (@ comp_P3728553842126764068at_nat produc4486455499028916547at_nat) (@ produc5456455677105495163at_nat (lambda ((X4 set_Pr4329608150637261639at_nat) (Y5 set_Pr4329608150637261639at_nat)) (@ (@ produc9060074326276436823at_nat Y5) X4))))))) (let ((_let_284 (= gcd_Lcm_int (lambda ((K3 set_int)) (@ semiri1314217659103216013at_int (@ gcd_Lcm_nat (@ (@ image_int_nat (@ (@ comp_int_nat_int nat2) abs_abs_int)) K3))))))) (let ((_let_285 (= archim3151403230148437115or_rat (lambda ((P3 rat)) (@ (@ produc8211389475949308722nt_int divide_divide_int) (@ quotient_of P3)))))) (let ((_let_286 (= id_on_int (lambda ((A6 set_int)) (@ comple5382143125604098054nt_int (@ (@ image_8635204845542730022nt_int (lambda ((X4 int)) (@ (@ insert5033312907999012233nt_int (@ (@ product_Pair_int_int X4) X4)) bot_bo1796632182523588997nt_int))) A6)))))) (let ((_let_287 (= produc4780622933104268256_nat_o produc8739625826339149834_nat_o))) (let ((_let_288 (= quotient_rat_nat (lambda ((R6 (-> rat rat Bool)) (Abs4 (-> rat nat)) (Rep4 (-> nat rat)) (T4 (-> rat nat Bool))) (let ((_let_1 (@ conversep_rat_nat T4))) (and (= R6 (@ (@ relcompp_rat_nat_rat T4) _let_1)) (@ (@ ord_le1897120724991155070_rat_o (@ (@ bNF_Grp_nat_rat top_top_set_nat) Rep4)) _let_1) (@ (@ ord_le5467402850006352766_nat_o T4) (@ (@ bNF_Grp_rat_nat top_top_set_rat) Abs4)))))))) (let ((_let_289 (= bot_bo394778441745866138_nat_o (lambda ((X4 set_Pr1261947904930325089at_nat) (Y5 set_Pr1261947904930325089at_nat)) (@ (@ member8757157785044589968at_nat (@ (@ produc2922128104949294807at_nat X4) Y5)) bot_bo228742789529271731at_nat))))) (let ((_let_290 (= comple4687483117567863418t_unit (lambda ((Uu2 set_Product_unit)) product_Unity)))) (let ((_let_291 (@ (@ produc2936396906406871148r_char top_top_set_char) (lambda ((Uu char)) top_top_set_char)))) (let ((_let_292 (= _let_291 top_to1235241553633177651r_char))) (let ((_let_293 (= bNF_Ca968750328013420230at_nat (lambda ((R5 set_Pr1261947904930325089at_nat) (As (-> nat nat))) (forall ((I2 nat) (J nat)) (=> (@ (@ member8440522571783428010at_nat (@ (@ product_Pair_nat_nat I2) J)) R5) (@ (@ ord_less_eq_nat (@ As I2)) (@ As J)))))))) (let ((_let_294 (= comple5685304695842803022at_nat (lambda ((A6 set_se7855581050983116737at_nat)) (@ collec3392354462482085612at_nat (lambda ((X4 product_prod_nat_nat)) (@ complete_Sup_Sup_o (@ (@ image_7457375456213313148_nat_o (@ member8440522571783428010at_nat X4)) A6)))))))) (let ((_let_295 (= bot_bot_nat_nat_o (lambda ((X4 nat) (Y5 nat)) (@ (@ member8440522571783428010at_nat (@ (@ product_Pair_nat_nat X4) Y5)) bot_bo2099793752762293965at_nat))))) (let ((_let_296 (= _let_224 top_top_set_rat))) (let ((_let_297 (= total_5117575981256876747at_nat (lambda ((A6 set_se5479201105039950375at_nat) (R5 set_Pr7459493094073627847at_nat)) (forall ((X4 set_Pr4329608150637261639at_nat)) (=> (@ (@ member6273874620674182256at_nat X4) A6) (forall ((Y5 set_Pr4329608150637261639at_nat)) (=> (@ (@ member6273874620674182256at_nat Y5) A6) (=> (not (= X4 Y5)) (or (@ (@ member1466754251312161552at_nat (@ (@ produc9060074326276436823at_nat X4) Y5)) R5) (@ (@ member1466754251312161552at_nat (@ (@ produc9060074326276436823at_nat Y5) X4)) R5))))))))))) (let ((_let_298 (= product_fst_int_int (@ produc8211389475949308722nt_int (lambda ((X12 int) (X23 int)) X12))))) (let ((_let_299 (= product_Unity (@ product_Abs_unit true)))) (let ((_let_300 (= total_on_int (lambda ((A6 set_int) (R5 set_Pr958786334691620121nt_int)) (forall ((X4 int)) (=> (@ (@ member_int X4) A6) (forall ((Y5 int)) (=> (@ (@ member_int Y5) A6) (=> (not (= X4 Y5)) (or (@ (@ member5262025264175285858nt_int (@ (@ product_Pair_int_int Y5) X4)) R5) (@ (@ member5262025264175285858nt_int (@ (@ product_Pair_int_int X4) Y5)) R5))))))))))) (let ((_let_301 (= random6974930770145893639ompred (lambda ((P4 (-> produc7822875418678951345atural produc4675096598859438275atural)) (S produc7822875418678951345atural)) (@ (@ produc6665183775751917029atural (lambda ((P5 pred_Product_unit) (S7 produc7822875418678951345atural)) (@ (@ (@ if_Pro3444522238938527101atural (@ (@ eval_Product_unit P5) product_Unity)) (@ (@ produc5069803637994805237atural bot_bo2717538794563056311t_unit) S7)) (@ (@ produc5069803637994805237atural (@ single_Product_unit product_Unity)) S7)))) (@ P4 S)))))) (let ((_let_302 (@ (@ (@ (@ heap_effect_ref_a (@ ref_a2 x)) h) h2) r))) (let ((_let_303 (= fun_min_weak (@ (@ sup_su5525570899277871387at_nat (@ min_ex6901939911449802026at_nat fun_pair_leq)) _let_91)))) (let ((_let_304 (= finite3582905537739598962at_nat (lambda ((S4 set_nat) (F2 (-> nat nat nat))) (forall ((X4 nat) (Y5 nat)) (let ((_let_1 (@ F2 Y5))) (let ((_let_2 (@ F2 X4))) (=> (@ (@ member_nat X4) S4) (=> (@ (@ member_nat Y5) S4) (= (@ (@ comp_nat_nat_nat _let_1) _let_2) (@ (@ comp_nat_nat_nat _let_2) _let_1))))))))))) (let ((_let_305 (= bNF_Ca402612664642806191nteger (lambda ((R5 set_Pr958786334691620121nt_int) (As (-> int code_integer))) (forall ((I2 int) (J int)) (=> (@ (@ member5262025264175285858nt_int (@ (@ product_Pair_int_int I2) J)) R5) (@ (@ ord_le3102999989581377725nteger (@ As I2)) (@ As J)))))))) (let ((_let_306 (= comple1626965760690514720nt_int (lambda ((A6 set_se6260736226359567993nt_int)) (@ collec213857154873943460nt_int (lambda ((X4 product_prod_int_int)) (@ complete_Inf_Inf_o (@ (@ image_701744273176368580_int_o (@ member5262025264175285858nt_int X4)) A6)))))))) (let ((_let_307 (= id_on_6713504163309144702at_nat (lambda ((A6 set_se7855581050983116737at_nat)) (@ comple4364388969068068532at_nat (@ (@ image_6898982319499645995at_nat (lambda ((X4 set_Pr1261947904930325089at_nat)) (@ (@ insert9069300056098147895at_nat (@ (@ produc2922128104949294807at_nat X4) X4)) bot_bo228742789529271731at_nat))) A6)))))) (let ((_let_308 (= comple6214475593288795910_nat_o (lambda ((S4 set_nat_o) (X4 nat)) (@ (@ member_nat X4) (@ comple7806235888213564991et_nat (@ (@ image_nat_o_set_nat collect_nat) S4))))))) (let ((_let_309 (= unique5026877609467782581ep_nat (lambda ((L3 num) (__flatten_var_0 product_prod_nat_nat)) (@ (@ produc2626176000494625587at_nat (lambda ((Q3 nat) (R5 nat)) (let ((_let_1 (@ (@ times_times_nat (@ numeral_numeral_nat (@ bit0 one))) Q3))) (let ((_let_2 (@ numeral_numeral_nat L3))) (@ (@ (@ if_Pro6206227464963214023at_nat (@ (@ ord_less_eq_nat _let_2) R5)) (@ (@ product_Pair_nat_nat (@ (@ 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SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_337 (EQ_RESOLVE (ASSUME :args (_let_189)) (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) :args ((= _let_189 (= ord_less_eq_int (lambda ((X4 int) (Xa3 int)) (@ (@ produc6081775807080527818_nat_o (lambda ((BOUND_VARIABLE_133418 nat) (BOUND_VARIABLE_133419 nat)) (@ (@ produc6081775807080527818_nat_o (lambda ((BOUND_VARIABLE_133420 nat) (BOUND_VARIABLE_133421 nat)) (@ (@ ord_less_eq_nat (@ (@ plus_plus_nat BOUND_VARIABLE_133418) BOUND_VARIABLE_133421)) (@ (@ plus_plus_nat BOUND_VARIABLE_133420) BOUND_VARIABLE_133419)))) (@ rep_Integ Xa3)))) (@ rep_Integ X4)))))))))) (let ((_let_338 (SYMM (ASSUME :args (_let_190))))) (let ((_let_339 (ASSUME :args (_let_192)))) (let ((_let_340 (EQ_RESOLVE (ASSUME :args (_let_194)) (MACRO_SR_EQ_INTRO :args (_let_194 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_341 (ASSUME :args (_let_140)))) (let ((_let_342 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:args ((= code_divmod_integer (lambda ((K5 code_integer) (L3 code_integer)) (let ((_let_1 (@ (@ code_divmod_abs K5) L3))) (let ((_let_2 (@ produc1086072967326762835nteger zero_z3403309356797280102nteger))) (let ((_let_3 (@ ord_le6747313008572928689nteger zero_z3403309356797280102nteger))) (@ (@ (@ if_Pro6119634080678213985nteger (= zero_z3403309356797280102nteger K5)) (@ _let_2 zero_z3403309356797280102nteger)) (@ (@ (@ if_Pro6119634080678213985nteger (@ _let_3 L3)) (@ (@ (@ if_Pro6119634080678213985nteger (@ _let_3 K5)) _let_1) (@ (@ produc6916734918728496179nteger (lambda ((R5 code_integer) (S code_integer)) (let ((_let_1 (@ uminus1351360451143612070nteger R5))) (@ (@ (@ if_Pro6119634080678213985nteger (= zero_z3403309356797280102nteger S)) (@ (@ produc1086072967326762835nteger _let_1) zero_z3403309356797280102nteger)) (@ (@ produc1086072967326762835nteger (@ (@ minus_8373710615458151222nteger _let_1) one_one_Code_integer)) (@ (@ minus_8373710615458151222nteger L3) S)))))) _let_1))) (@ (@ (@ if_Pro6119634080678213985nteger (= zero_z3403309356797280102nteger L3)) (@ _let_2 K5)) (@ (@ produc6499014454317279255nteger uminus1351360451143612070nteger) (@ (@ (@ if_Pro6119634080678213985nteger (@ (@ ord_le6747313008572928689nteger K5) zero_z3403309356797280102nteger)) _let_1) (@ (@ produc6916734918728496179nteger (lambda ((R5 code_integer) (S code_integer)) (let ((_let_1 (@ uminus1351360451143612070nteger R5))) (@ (@ (@ if_Pro6119634080678213985nteger (= zero_z3403309356797280102nteger S)) (@ (@ produc1086072967326762835nteger _let_1) zero_z3403309356797280102nteger)) (@ (@ produc1086072967326762835nteger (@ (@ minus_8373710615458151222nteger _let_1) one_one_Code_integer)) (@ (@ minus_8373710615458151222nteger (@ uminus1351360451143612070nteger L3)) S)))))) _let_1))))))))))) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_353 (ASSUME :args (_let_218)))) (let ((_let_354 (EQ_RESOLVE (ASSUME :args (_let_123)) (MACRO_SR_EQ_INTRO (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) :args (_let_123 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_355 (ASSUME :args (_let_5)))) (let ((_let_356 (SYMM (ASSUME :args (_let_185))))) (let ((_let_357 (0))) (let ((_let_358 (EQ_RESOLVE (ASSUME :args (_let_119)) (MACRO_SR_EQ_INTRO :args (_let_119 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_359 (AND_ELIM _let_358 :args _let_357))) (let ((_let_360 (1))) (let ((_let_361 (AND_ELIM _let_358 :args _let_360))) (let ((_let_362 (ASSUME :args (_let_115)))) (let ((_let_363 (ASSUME :args (_let_177)))) (let ((_let_364 (ASSUME :args (_let_197)))) (let ((_let_365 (ASSUME :args (_let_198)))) (let ((_let_366 (EQ_RESOLVE (ASSUME :args (_let_152)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_365 _let_364 _let_363 _let_362 _let_361 _let_359 _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) :args (_let_152 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_367 (ASSUME :args (_let_124)))) (let ((_let_368 (ASSUME :args (_let_195)))) (let ((_let_369 (ASSUME :args (_let_128)))) (let ((_let_370 (ASSUME :args (_let_227)))) (let ((_let_371 (ASSUME :args (_let_206)))) (let ((_let_372 (SYMM (ASSUME :args (_let_106))))) (let ((_let_373 (ASSUME :args (_let_200)))) (let ((_let_374 (ASSUME :args (_let_3)))) (let ((_let_375 (EQ_RESOLVE (EQ_RESOLVE (ASSUME :args (_let_120)) (MACRO_SR_EQ_INTRO :args (_let_120 SB_DEFAULT SBA_FIXPOINT))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_374 _let_373 _let_372 _let_371 _let_370 _let_369 _let_368 _let_367 _let_366 _let_365 _let_364 _let_363 _let_362 _let_361 _let_359 _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) :args ((= bNF_Ca4946600973702282345at_int (lambda ((R5 set_Pr4329608150637261639at_nat) (As (-> set_Pr1261947904930325089at_nat int))) (forall ((I2 set_Pr1261947904930325089at_nat) (J set_Pr1261947904930325089at_nat)) (or (not (@ (@ member8757157785044589968at_nat (@ (@ produc2922128104949294807at_nat I2) J)) R5)) (@ (@ ord_less_eq_int (@ As I2)) (@ As J)))))) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_376 (SYMM (ASSUME :args (_let_78))))) (let ((_let_377 (ASSUME :args (_let_121)))) (let ((_let_378 (ASSUME :args (_let_214)))) (let ((_let_379 (ASSUME :args (_let_109)))) (let ((_let_380 (ASSUME :args (_let_162)))) (let ((_let_381 (SYMM (ASSUME :args (_let_211))))) (let ((_let_382 (ASSUME :args (_let_219)))) (let ((_let_383 (EQ_RESOLVE (ASSUME :args (_let_58)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_382 _let_381 _let_380 _let_379 _let_378 _let_377 _let_376 _let_375 _let_374 _let_373 _let_372 _let_371 _let_370 _let_369 _let_368 _let_367 _let_366 _let_365 _let_364 _let_363 _let_362 _let_361 _let_359 _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) :args (_let_58 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_384 (EQ_RESOLVE (ASSUME :args (_let_220)) (MACRO_SR_EQ_INTRO :args (_let_220 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_385 (EQ_RESOLVE (ASSUME :args (_let_118)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_384 _let_383 _let_382 _let_381 _let_380 _let_379 _let_378 _let_377 _let_376 _let_375 _let_374 _let_373 _let_372 _let_371 _let_370 _let_369 _let_368 _let_367 _let_366 _let_365 _let_364 _let_363 _let_362 _let_361 _let_359 _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) :args (_let_118 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_386 (ASSUME :args (_let_205)))) (let ((_let_387 (ASSUME :args (_let_210)))) (let ((_let_388 (EQ_RESOLVE (ASSUME :args (_let_168)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_387 _let_386 _let_385 _let_384 _let_383 _let_382 _let_381 _let_380 _let_379 _let_378 _let_377 _let_376 _let_375 _let_374 _let_373 _let_372 _let_371 _let_370 _let_369 _let_368 _let_367 _let_366 _let_365 _let_364 _let_363 _let_362 _let_361 _let_359 _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) :args (_let_168 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_389 (EQ_RESOLVE (ASSUME :args (_let_213)) (TRUST_SUBS_MAP (AND_INTRO _let_388 _let_387 _let_386 _let_385 _let_384 _let_383 _let_382 _let_381 _let_380 _let_379 _let_378 _let_377 _let_376 _let_375 _let_374 _let_373 _let_372 _let_371 _let_370 _let_369 _let_368 _let_367 _let_366 _let_365 _let_364 _let_363 _let_362 _let_361 _let_359 _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) :args ((= _let_213 (= inv_image_nat_int (lambda ((R5 set_Pr1261947904930325089at_nat) (F2 (-> int nat))) (@ collec213857154873943460nt_int (lambda ((BOUND_VARIABLE_137484 product_prod_int_int)) (@ (@ member8440522571783428010at_nat (@ (@ product_Pair_nat_nat (@ F2 (@ product_fst_int_int BOUND_VARIABLE_137484))) (@ F2 (@ (@ produc8211389475949308722nt_int (lambda ((BOUND_VARIABLE_137485 int) (BOUND_VARIABLE_137486 int)) BOUND_VARIABLE_137486)) BOUND_VARIABLE_137484)))) R5))))))))))) (let ((_let_390 (EQ_RESOLVE (ASSUME :args (_let_225)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_389 _let_388 _let_387 _let_386 _let_385 _let_384 _let_383 _let_382 _let_381 _let_380 _let_379 _let_378 _let_377 _let_376 _let_375 _let_374 _let_373 _let_372 _let_371 _let_370 _let_369 _let_368 _let_367 _let_366 _let_365 _let_364 _let_363 _let_362 _let_361 _let_359 _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) :args (_let_225 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_391 (EQ_RESOLVE (EQ_RESOLVE (ASSUME :args (_let_229)) (MACRO_SR_EQ_INTRO :args (_let_229 SB_DEFAULT SBA_FIXPOINT))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_390 _let_389 _let_388 _let_387 _let_386 _let_385 _let_384 _let_383 _let_382 _let_381 _let_380 _let_379 _let_378 _let_377 _let_376 _let_375 _let_374 _let_373 _let_372 _let_371 _let_370 _let_369 _let_368 _let_367 _let_366 _let_365 _let_364 _let_363 _let_362 _let_361 _let_359 _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) :args ((= bNF_Ca966259857504369954at_int (lambda ((R5 set_Pr1261947904930325089at_nat) (As (-> nat int))) (forall ((I2 nat) (J nat)) (or (not (@ (@ member8440522571783428010at_nat (@ (@ product_Pair_nat_nat I2) J)) R5)) (@ (@ ord_less_eq_int (@ As I2)) (@ As J)))))) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_392 (EQ_RESOLVE (ASSUME :args (_let_146)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_391 _let_390 _let_389 _let_388 _let_387 _let_386 _let_385 _let_384 _let_383 _let_382 _let_381 _let_380 _let_379 _let_378 _let_377 _let_376 _let_375 _let_374 _let_373 _let_372 _let_371 _let_370 _let_369 _let_368 _let_367 _let_366 _let_365 _let_364 _let_363 _let_362 _let_361 _let_359 _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) :args (_let_146 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_393 (ASSUME :args (_let_143)))) (let ((_let_394 (ASSUME :args (_let_173)))) (let ((_let_395 (ASSUME :args (_let_136)))) (let ((_let_396 (EQ_RESOLVE (ASSUME :args (_let_175)) (MACRO_SR_EQ_INTRO :args (_let_175 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_397 (EQ_RESOLVE (ASSUME :args (_let_131)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_396 _let_395 _let_394 _let_393 _let_392 _let_391 _let_390 _let_389 _let_388 _let_387 _let_386 _let_385 _let_384 _let_383 _let_382 _let_381 _let_380 _let_379 _let_378 _let_377 _let_376 _let_375 _let_374 _let_373 _let_372 _let_371 _let_370 _let_369 _let_368 _let_367 _let_366 _let_365 _let_364 _let_363 _let_362 _let_361 _let_359 _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) :args (_let_131 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_398 (EQ_RESOLVE (ASSUME :args (_let_117)) (TRUST_SUBS_MAP (AND_INTRO _let_397 _let_396 _let_395 _let_394 _let_393 _let_392 _let_391 _let_390 _let_389 _let_388 _let_387 _let_386 _let_385 _let_384 _let_383 _let_382 _let_381 _let_380 _let_379 _let_378 _let_377 _let_376 _let_375 _let_374 _let_373 _let_372 _let_371 _let_370 _let_369 _let_368 _let_367 _let_366 _let_365 _let_364 _let_363 _let_362 _let_361 _let_359 _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) :args ((= _let_117 (= code_num_of_integer (@ _let_116 (lambda ((BOUND_VARIABLE_138373 int)) (@ num_of_nat (@ nat2 BOUND_VARIABLE_138373))))))))))) (let ((_let_399 (ASSUME :args (_let_161)))) (let ((_let_400 (EQ_RESOLVE (ASSUME :args (_let_231)) (TRUST_SUBS_MAP (AND_INTRO _let_399 _let_398 _let_397 _let_396 _let_395 _let_394 _let_393 _let_392 _let_391 _let_390 _let_389 _let_388 _let_387 _let_386 _let_385 _let_384 _let_383 _let_382 _let_381 _let_380 _let_379 _let_378 _let_377 _let_376 _let_375 _let_374 _let_373 _let_372 _let_371 _let_370 _let_369 _let_368 _let_367 _let_366 _let_365 _let_364 _let_363 _let_362 _let_361 _let_359 _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) :args ((= _let_231 (= ord_less_rat (lambda ((P3 rat) (Q3 rat)) (let ((_let_1 (@ quotient_of Q3))) (let ((_let_2 (@ quotient_of P3))) (@ (@ ord_less_int (@ (@ times_times_int (@ product_fst_int_int _let_2)) (@ (@ produc8211389475949308722nt_int (lambda ((BOUND_VARIABLE_138959 int) (BOUND_VARIABLE_138960 int)) BOUND_VARIABLE_138960)) _let_1))) (@ (@ times_times_int (@ (@ produc8211389475949308722nt_int (lambda ((BOUND_VARIABLE_138951 int) (BOUND_VARIABLE_138952 int)) BOUND_VARIABLE_138952)) _let_2)) (@ product_fst_int_int _let_1))))))))))))) (let ((_let_401 (ASSUME :args (_let_113)))) (let ((_let_402 (EQ_RESOLVE (ASSUME :args (_let_107)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_401 _let_400 _let_399 _let_398 _let_397 _let_396 _let_395 _let_394 _let_393 _let_392 _let_391 _let_390 _let_389 _let_388 _let_387 _let_386 _let_385 _let_384 _let_383 _let_382 _let_381 _let_380 _let_379 _let_378 _let_377 _let_376 _let_375 _let_374 _let_373 _let_372 _let_371 _let_370 _let_369 _let_368 _let_367 _let_366 _let_365 _let_364 _let_363 _let_362 _let_361 _let_359 _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) :args (_let_107 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_403 (EQ_RESOLVE (ASSUME :args (_let_47)) (TRUST_SUBS_MAP (AND_INTRO _let_402 _let_401 _let_400 _let_399 _let_398 _let_397 _let_396 _let_395 _let_394 _let_393 _let_392 _let_391 _let_390 _let_389 _let_388 _let_387 _let_386 _let_385 _let_384 _let_383 _let_382 _let_381 _let_380 _let_379 _let_378 _let_377 _let_376 _let_375 _let_374 _let_373 _let_372 _let_371 _let_370 _let_369 _let_368 _let_367 _let_366 _let_365 _let_364 _let_363 _let_362 _let_361 _let_359 _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) :args ((= _let_47 (= inv_im2900519150384625825at_int (lambda ((R5 set_Pr7459493094073627847at_nat) (F2 (-> int set_Pr4329608150637261639at_nat))) (@ collec213857154873943460nt_int (lambda ((BOUND_VARIABLE_139594 product_prod_int_int)) (@ (@ member1466754251312161552at_nat (@ (@ produc9060074326276436823at_nat (@ F2 (@ product_fst_int_int BOUND_VARIABLE_139594))) (@ F2 (@ (@ produc8211389475949308722nt_int (lambda ((BOUND_VARIABLE_139595 int) (BOUND_VARIABLE_139596 int)) BOUND_VARIABLE_139596)) BOUND_VARIABLE_139594)))) R5))))))))))) (let ((_let_404 (EQ_RESOLVE (ASSUME :args (_let_28)) (MACRO_SR_EQ_INTRO :args (_let_28 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_405 (EQ_RESOLVE (ASSUME :args (_let_209)) (TRUST_SUBS_MAP (AND_INTRO _let_404 _let_403 _let_402 _let_401 _let_400 _let_399 _let_398 _let_397 _let_396 _let_395 _let_394 _let_393 _let_392 _let_391 _let_390 _let_389 _let_388 _let_387 _let_386 _let_385 _let_384 _let_383 _let_382 _let_381 _let_380 _let_379 _let_378 _let_377 _let_376 _let_375 _let_374 _let_373 _let_372 _let_371 _let_370 _let_369 _let_368 _let_367 _let_366 _let_365 _let_364 _let_363 _let_362 _let_361 _let_359 _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) :args ((= _let_209 (= minus_minus_int (@ _let_96 (lambda ((BOUND_VARIABLE_139775 product_prod_nat_nat) (BOUND_VARIABLE_139776 product_prod_nat_nat)) (@ (@ produc2626176000494625587at_nat (lambda ((BOUND_VARIABLE_139845 nat) (BOUND_VARIABLE_139846 nat)) (@ (@ product_Pair_nat_nat (@ (@ plus_plus_nat (@ (@ (@ comp_P1567445206330693457at_nat product_snd_nat_nat) (@ produc2626176000494625587at_nat (lambda ((BOUND_VARIABLE_139848 nat) (BOUND_VARIABLE_139849 nat)) (@ (@ product_Pair_nat_nat BOUND_VARIABLE_139849) BOUND_VARIABLE_139848)))) BOUND_VARIABLE_139775)) BOUND_VARIABLE_139846)) (@ (@ plus_plus_nat (@ product_snd_nat_nat BOUND_VARIABLE_139775)) BOUND_VARIABLE_139845)))) BOUND_VARIABLE_139776)))))))))) (let ((_let_406 (ASSUME :args (_let_103)))) (let ((_let_407 (ASSUME :args (_let_101)))) (let ((_let_408 (EQ_RESOLVE (ASSUME :args (_let_98)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_407 _let_406 _let_405 _let_404 _let_403 _let_402 _let_401 _let_400 _let_399 _let_398 _let_397 _let_396 _let_395 _let_394 _let_393 _let_392 _let_391 _let_390 _let_389 _let_388 _let_387 _let_386 _let_385 _let_384 _let_383 _let_382 _let_381 _let_380 _let_379 _let_378 _let_377 _let_376 _let_375 _let_374 _let_373 _let_372 _let_371 _let_370 _let_369 _let_368 _let_367 _let_366 _let_365 _let_364 _let_363 _let_362 _let_361 _let_359 _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) :args (_let_98 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_409 (EQ_RESOLVE (ASSUME :args (_let_97)) (TRUST_SUBS_MAP (AND_INTRO _let_408 _let_407 _let_406 _let_405 _let_404 _let_403 _let_402 _let_401 _let_400 _let_399 _let_398 _let_397 _let_396 _let_395 _let_394 _let_393 _let_392 _let_391 _let_390 _let_389 _let_388 _let_387 _let_386 _let_385 _let_384 _let_383 _let_382 _let_381 _let_380 _let_379 _let_378 _let_377 _let_376 _let_375 _let_374 _let_373 _let_372 _let_371 _let_370 _let_369 _let_368 _let_367 _let_366 _let_365 _let_364 _let_363 _let_362 _let_361 _let_359 _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) :args ((= _let_97 (= plus_plus_int (@ _let_96 (lambda ((BOUND_VARIABLE_140318 product_prod_nat_nat) (BOUND_VARIABLE_140319 product_prod_nat_nat)) (@ (@ produc2626176000494625587at_nat (lambda ((BOUND_VARIABLE_140388 nat) (BOUND_VARIABLE_140389 nat)) (@ (@ product_Pair_nat_nat (@ (@ plus_plus_nat (@ (@ (@ comp_P1567445206330693457at_nat product_snd_nat_nat) (@ produc2626176000494625587at_nat (lambda ((BOUND_VARIABLE_140391 nat) (BOUND_VARIABLE_140392 nat)) (@ (@ product_Pair_nat_nat BOUND_VARIABLE_140392) BOUND_VARIABLE_140391)))) BOUND_VARIABLE_140318)) BOUND_VARIABLE_140388)) (@ (@ plus_plus_nat (@ product_snd_nat_nat BOUND_VARIABLE_140318)) BOUND_VARIABLE_140389)))) BOUND_VARIABLE_140319)))))))))) (let ((_let_410 (ASSUME :args (_let_20)))) (let ((_let_411 (ASSUME :args (_let_83)))) (let ((_let_412 (ASSUME :args (_let_74)))) (let ((_let_413 (ASSUME :args (_let_73)))) (let ((_let_414 (EQ_RESOLVE (ASSUME :args (_let_164)) (MACRO_SR_EQ_INTRO :args (_let_164 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_415 (ASSUME :args (_let_51)))) (let ((_let_416 (EQ_RESOLVE (ASSUME :args (_let_70)) (TRUST_SUBS_MAP (AND_INTRO _let_415 _let_414 _let_413 _let_412 _let_411 _let_410 _let_409 _let_408 _let_407 _let_406 _let_405 _let_404 _let_403 _let_402 _let_401 _let_400 _let_399 _let_398 _let_397 _let_396 _let_395 _let_394 _let_393 _let_392 _let_391 _let_390 _let_389 _let_388 _let_387 _let_386 _let_385 _let_384 _let_383 _let_382 _let_381 _let_380 _let_379 _let_378 _let_377 _let_376 _let_375 _let_374 _let_373 _let_372 _let_371 _let_370 _let_369 _let_368 _let_367 _let_366 _let_365 _let_364 _let_363 _let_362 _let_361 _let_359 _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) :args ((= _let_70 (= inv_image_int_int (lambda ((R5 set_Pr958786334691620121nt_int) (F2 (-> int int))) (@ collec213857154873943460nt_int (lambda ((BOUND_VARIABLE_142518 product_prod_int_int)) (@ (@ member5262025264175285858nt_int (@ (@ product_Pair_int_int (@ F2 (@ product_fst_int_int BOUND_VARIABLE_142518))) (@ F2 (@ (@ produc8211389475949308722nt_int (lambda ((BOUND_VARIABLE_142519 int) (BOUND_VARIABLE_142520 int)) BOUND_VARIABLE_142520)) BOUND_VARIABLE_142518)))) R5))))))))))) (let ((_let_417 (EQ_RESOLVE (ASSUME :args (_let_82)) (MACRO_SR_EQ_INTRO :args (_let_82 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_418 (ASSUME :args (_let_40)))) (let ((_let_419 (EQ_RESOLVE (ASSUME :args (_let_67)) (TRUST_SUBS_MAP (AND_INTRO _let_418 _let_417 _let_416 _let_415 _let_414 _let_413 _let_412 _let_411 _let_410 _let_409 _let_408 _let_407 _let_406 _let_405 _let_404 _let_403 _let_402 _let_401 _let_400 _let_399 _let_398 _let_397 _let_396 _let_395 _let_394 _let_393 _let_392 _let_391 _let_390 _let_389 _let_388 _let_387 _let_386 _let_385 _let_384 _let_383 _let_382 _let_381 _let_380 _let_379 _let_378 _let_377 _let_376 _let_375 _let_374 _let_373 _let_372 _let_371 _let_370 _let_369 _let_368 _let_367 _let_366 _let_365 _let_364 _let_363 _let_362 _let_361 _let_359 _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) :args ((= _let_67 (= gcd_Gcd_int (lambda ((K3 set_int)) (@ semiri1314217659103216013at_int (@ gcd_Gcd_nat (@ (@ image_int_nat (lambda ((BOUND_VARIABLE_142734 int)) (@ nat2 (@ abs_abs_int BOUND_VARIABLE_142734)))) K3))))))))))) (let ((_let_420 (EQ_RESOLVE (SYMM (ASSUME :args (_let_65))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_419 _let_418 _let_417 _let_416 _let_415 _let_414 _let_413 _let_412 _let_411 _let_410 _let_409 _let_408 _let_407 _let_406 _let_405 _let_404 _let_403 _let_402 _let_401 _let_400 _let_399 _let_398 _let_397 _let_396 _let_395 _let_394 _let_393 _let_392 _let_391 _let_390 _let_389 _let_388 _let_387 _let_386 _let_385 _let_384 _let_383 _let_382 _let_381 _let_380 _let_379 _let_378 _let_377 _let_376 _let_375 _let_374 _let_373 _let_372 _let_371 _let_370 _let_369 _let_368 _let_367 _let_366 _let_365 _let_364 _let_363 _let_362 _let_361 _let_359 _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) :args ((= top_to3104204703268025230ar_int _let_64) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_421 (EQ_RESOLVE (SYMM (ASSUME :args (_let_63))) (TRUST_SUBS_MAP (AND_INTRO _let_420 _let_419 _let_418 _let_417 _let_416 _let_415 _let_414 _let_413 _let_412 _let_411 _let_410 _let_409 _let_408 _let_407 _let_406 _let_405 _let_404 _let_403 _let_402 _let_401 _let_400 _let_399 _let_398 _let_397 _let_396 _let_395 _let_394 _let_393 _let_392 _let_391 _let_390 _let_389 _let_388 _let_387 _let_386 _let_385 _let_384 _let_383 _let_382 _let_381 _let_380 _let_379 _let_378 _let_377 _let_376 _let_375 _let_374 _let_373 _let_372 _let_371 _let_370 _let_369 _let_368 _let_367 _let_366 _let_365 _let_364 _let_363 _let_362 _let_361 _let_359 _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) :args ((= (= id_Pro4381231610383771306nt_int _let_62) (= id_Pro4381231610383771306nt_int (lambda ((BOUND_VARIABLE_143169 product_prod_int_int)) (@ (@ product_Pair_int_int (@ product_fst_int_int BOUND_VARIABLE_143169)) (@ (@ produc8211389475949308722nt_int (lambda ((BOUND_VARIABLE_143170 int) (BOUND_VARIABLE_143171 int)) BOUND_VARIABLE_143171)) BOUND_VARIABLE_143169)))))))))) (let ((_let_422 (ASSUME :args (_let_61)))) (let ((_let_423 (ASSUME :args (_let_60)))) (let ((_let_424 (ASSUME :args (_let_59)))) (let ((_let_425 (EQ_RESOLVE (ASSUME :args (_let_199)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_424 _let_423 _let_422 _let_421 _let_420 _let_419 _let_418 _let_417 _let_416 _let_415 _let_414 _let_413 _let_412 _let_411 _let_410 _let_409 _let_408 _let_407 _let_406 _let_405 _let_404 _let_403 _let_402 _let_401 _let_400 _let_399 _let_398 _let_397 _let_396 _let_395 _let_394 _let_393 _let_392 _let_391 _let_390 _let_389 _let_388 _let_387 _let_386 _let_385 _let_384 _let_383 _let_382 _let_381 _let_380 _let_379 _let_378 _let_377 _let_376 _let_375 _let_374 _let_373 _let_372 _let_371 _let_370 _let_369 _let_368 _let_367 _let_366 _let_365 _let_364 _let_363 _let_362 _let_361 _let_359 _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) :args (_let_199 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_426 (EQ_RESOLVE (ASSUME :args (_let_37)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_425 _let_424 _let_423 _let_422 _let_421 _let_420 _let_419 _let_418 _let_417 _let_416 _let_415 _let_414 _let_413 _let_412 _let_411 _let_410 _let_409 _let_408 _let_407 _let_406 _let_405 _let_404 _let_403 _let_402 _let_401 _let_400 _let_399 _let_398 _let_397 _let_396 _let_395 _let_394 _let_393 _let_392 _let_391 _let_390 _let_389 _let_388 _let_387 _let_386 _let_385 _let_384 _let_383 _let_382 _let_381 _let_380 _let_379 _let_378 _let_377 _let_376 _let_375 _let_374 _let_373 _let_372 _let_371 _let_370 _let_369 _let_368 _let_367 _let_366 _let_365 _let_364 _let_363 _let_362 _let_361 _let_359 _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) :args (_let_37 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_427 (EQ_RESOLVE (ASSUME :args (_let_56)) (MACRO_SR_EQ_INTRO :args (_let_56 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_428 (ASSUME :args (_let_54)))) (let ((_let_429 (EQ_RESOLVE (ASSUME :args (_let_150)) (TRUST_SUBS_MAP (AND_INTRO _let_428 _let_427 _let_426 _let_425 _let_424 _let_423 _let_422 _let_421 _let_420 _let_419 _let_418 _let_417 _let_416 _let_415 _let_414 _let_413 _let_412 _let_411 _let_410 _let_409 _let_408 _let_407 _let_406 _let_405 _let_404 _let_403 _let_402 _let_401 _let_400 _let_399 _let_398 _let_397 _let_396 _let_395 _let_394 _let_393 _let_392 _let_391 _let_390 _let_389 _let_388 _let_387 _let_386 _let_385 _let_384 _let_383 _let_382 _let_381 _let_380 _let_379 _let_378 _let_377 _let_376 _let_375 _let_374 _let_373 _let_372 _let_371 _let_370 _let_369 _let_368 _let_367 _let_366 _let_365 _let_364 _let_363 _let_362 _let_361 _let_359 _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) :args ((= _let_150 (= unique5024387138958732305ep_int (lambda ((L3 num) (__flatten_var_0 product_prod_int_int)) (let ((_let_1 (@ (@ produc8211389475949308722nt_int (lambda ((BOUND_VARIABLE_144503 int) (BOUND_VARIABLE_144504 int)) BOUND_VARIABLE_144504)) __flatten_var_0))) (let ((_let_2 (@ (@ times_times_int (@ numeral_numeral_int (@ bit0 one))) (@ product_fst_int_int __flatten_var_0)))) (let ((_let_3 (@ numeral_numeral_int L3))) (let ((_let_4 (@ (@ map_fu4960017516451851995nt_int rep_Integ) (@ (@ map_fu3667384564859982768at_int rep_Integ) abs_Integ)))) (@ (@ (@ if_Pro3027730157355071871nt_int (@ (@ produc6081775807080527818_nat_o (lambda ((BOUND_VARIABLE_144573 nat) (BOUND_VARIABLE_144574 nat)) (@ (@ produc6081775807080527818_nat_o (lambda ((BOUND_VARIABLE_144576 nat) (BOUND_VARIABLE_144577 nat)) (@ (@ ord_less_eq_nat (@ (@ plus_plus_nat BOUND_VARIABLE_144573) BOUND_VARIABLE_144577)) (@ (@ plus_plus_nat BOUND_VARIABLE_144576) BOUND_VARIABLE_144574)))) (@ rep_Integ (@ (@ produc8211389475949308722nt_int (lambda ((BOUND_VARIABLE_144503 int) (BOUND_VARIABLE_144504 int)) BOUND_VARIABLE_144504)) __flatten_var_0))))) (@ rep_Integ _let_3))) (@ (@ product_Pair_int_int (@ (@ (@ _let_4 (lambda ((BOUND_VARIABLE_144542 product_prod_nat_nat) (BOUND_VARIABLE_144543 product_prod_nat_nat)) (@ (@ produc2626176000494625587at_nat (lambda ((BOUND_VARIABLE_144544 nat) (BOUND_VARIABLE_144545 nat)) (@ (@ product_Pair_nat_nat (@ (@ plus_plus_nat (@ (@ (@ comp_P1567445206330693457at_nat product_snd_nat_nat) (@ produc2626176000494625587at_nat (lambda ((BOUND_VARIABLE_144549 nat) (BOUND_VARIABLE_144550 nat)) (@ (@ product_Pair_nat_nat BOUND_VARIABLE_144550) BOUND_VARIABLE_144549)))) BOUND_VARIABLE_144542)) BOUND_VARIABLE_144544)) (@ (@ plus_plus_nat (@ product_snd_nat_nat BOUND_VARIABLE_144542)) BOUND_VARIABLE_144545)))) BOUND_VARIABLE_144543))) _let_2) one_one_int)) (@ (@ (@ _let_4 (lambda ((BOUND_VARIABLE_144513 product_prod_nat_nat) (BOUND_VARIABLE_144514 product_prod_nat_nat)) (@ (@ produc2626176000494625587at_nat (lambda ((BOUND_VARIABLE_144515 nat) (BOUND_VARIABLE_144516 nat)) (@ (@ product_Pair_nat_nat (@ (@ plus_plus_nat (@ (@ (@ comp_P1567445206330693457at_nat product_snd_nat_nat) (@ produc2626176000494625587at_nat (lambda ((BOUND_VARIABLE_144520 nat) (BOUND_VARIABLE_144521 nat)) (@ (@ product_Pair_nat_nat BOUND_VARIABLE_144521) BOUND_VARIABLE_144520)))) BOUND_VARIABLE_144513)) BOUND_VARIABLE_144516)) (@ (@ plus_plus_nat (@ product_snd_nat_nat BOUND_VARIABLE_144513)) BOUND_VARIABLE_144515)))) BOUND_VARIABLE_144514))) _let_1) _let_3))) (@ (@ product_Pair_int_int _let_2) _let_1)))))))))))))) (let ((_let_430 (EQ_RESOLVE (ASSUME :args (_let_79)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_429 _let_428 _let_427 _let_426 _let_425 _let_424 _let_423 _let_422 _let_421 _let_420 _let_419 _let_418 _let_417 _let_416 _let_415 _let_414 _let_413 _let_412 _let_411 _let_410 _let_409 _let_408 _let_407 _let_406 _let_405 _let_404 _let_403 _let_402 _let_401 _let_400 _let_399 _let_398 _let_397 _let_396 _let_395 _let_394 _let_393 _let_392 _let_391 _let_390 _let_389 _let_388 _let_387 _let_386 _let_385 _let_384 _let_383 _let_382 _let_381 _let_380 _let_379 _let_378 _let_377 _let_376 _let_375 _let_374 _let_373 _let_372 _let_371 _let_370 _let_369 _let_368 _let_367 _let_366 _let_365 _let_364 _let_363 _let_362 _let_361 _let_359 _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) :args (_let_79 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_431 (ASSUME :args (_let_50)))) (let ((_let_432 (ASSUME :args (_let_49)))) (let ((_let_433 (EQ_RESOLVE (ASSUME :args (_let_77)) (TRUST_SUBS_MAP (AND_INTRO _let_432 _let_431 _let_430 _let_429 _let_428 _let_427 _let_426 _let_425 _let_424 _let_423 _let_422 _let_421 _let_420 _let_419 _let_418 _let_417 _let_416 _let_415 _let_414 _let_413 _let_412 _let_411 _let_410 _let_409 _let_408 _let_407 _let_406 _let_405 _let_404 _let_403 _let_402 _let_401 _let_400 _let_399 _let_398 _let_397 _let_396 _let_395 _let_394 _let_393 _let_392 _let_391 _let_390 _let_389 _let_388 _let_387 _let_386 _let_385 _let_384 _let_383 _let_382 _let_381 _let_380 _let_379 _let_378 _let_377 _let_376 _let_375 _let_374 _let_373 _let_372 _let_371 _let_370 _let_369 _let_368 _let_367 _let_366 _let_365 _let_364 _let_363 _let_362 _let_361 _let_359 _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) :args ((= _let_77 (= int_ge_less_than2 (lambda ((D3 int)) (@ collec213857154873943460nt_int (lambda ((BOUND_VARIABLE_145340 product_prod_int_int)) (and (@ (@ ord_less_int (@ product_fst_int_int BOUND_VARIABLE_145340)) (@ (@ produc8211389475949308722nt_int (lambda ((BOUND_VARIABLE_145341 int) (BOUND_VARIABLE_145342 int)) BOUND_VARIABLE_145342)) BOUND_VARIABLE_145340)) (@ (@ produc6081775807080527818_nat_o (lambda ((BOUND_VARIABLE_145384 nat) (BOUND_VARIABLE_145385 nat)) (@ (@ produc6081775807080527818_nat_o (lambda ((BOUND_VARIABLE_145387 nat) (BOUND_VARIABLE_145388 nat)) (@ (@ ord_less_eq_nat (@ (@ plus_plus_nat BOUND_VARIABLE_145384) BOUND_VARIABLE_145388)) (@ (@ plus_plus_nat BOUND_VARIABLE_145387) BOUND_VARIABLE_145385)))) (@ rep_Integ (@ (@ produc8211389475949308722nt_int (lambda ((BOUND_VARIABLE_145341 int) (BOUND_VARIABLE_145342 int)) BOUND_VARIABLE_145342)) BOUND_VARIABLE_145340))))) (@ rep_Integ D3))))))))))))) (let ((_let_434 (ASSUME :args (_let_48)))) (let ((_let_435 (EQ_RESOLVE (ASSUME :args (_let_72)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_434 _let_433 _let_432 _let_431 _let_430 _let_429 _let_428 _let_427 _let_426 _let_425 _let_424 _let_423 _let_422 _let_421 _let_420 _let_419 _let_418 _let_417 _let_416 _let_415 _let_414 _let_413 _let_412 _let_411 _let_410 _let_409 _let_408 _let_407 _let_406 _let_405 _let_404 _let_403 _let_402 _let_401 _let_400 _let_399 _let_398 _let_397 _let_396 _let_395 _let_394 _let_393 _let_392 _let_391 _let_390 _let_389 _let_388 _let_387 _let_386 _let_385 _let_384 _let_383 _let_382 _let_381 _let_380 _let_379 _let_378 _let_377 _let_376 _let_375 _let_374 _let_373 _let_372 _let_371 _let_370 _let_369 _let_368 _let_367 _let_366 _let_365 _let_364 _let_363 _let_362 _let_361 _let_359 _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) :args (_let_72 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_436 (SYMM (ASSUME :args (_let_94))))) (let ((_let_437 (ASSUME :args (_let_45)))) (let ((_let_438 (EQ_RESOLVE (SYMM (ASSUME :args (_let_154))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_437 _let_436 _let_435 _let_434 _let_433 _let_432 _let_431 _let_430 _let_429 _let_428 _let_427 _let_426 _let_425 _let_424 _let_423 _let_422 _let_421 _let_420 _let_419 _let_418 _let_417 _let_416 _let_415 _let_414 _let_413 _let_412 _let_411 _let_410 _let_409 _let_408 _let_407 _let_406 _let_405 _let_404 _let_403 _let_402 _let_401 _let_400 _let_399 _let_398 _let_397 _let_396 _let_395 _let_394 _let_393 _let_392 _let_391 _let_390 _let_389 _let_388 _let_387 _let_386 _let_385 _let_384 _let_383 _let_382 _let_381 _let_380 _let_379 _let_378 _let_377 _let_376 _let_375 _let_374 _let_373 _let_372 _let_371 _let_370 _let_369 _let_368 _let_367 _let_366 _let_365 _let_364 _let_363 _let_362 _let_361 _let_359 _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) :args ((= id_nat_o _let_153) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_439 (EQ_RESOLVE (ASSUME :args (_let_43)) (MACRO_SR_EQ_INTRO :args (_let_43 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_440 (ASSUME :args (_let_134)))) (let ((_let_441 (ASSUME :args (_let_201)))) (let ((_let_442 (ASSUME :args (_let_39)))) (let ((_let_443 (ASSUME :args (_let_221)))) (let ((_let_444 (ASSUME :args (_let_36)))) (let ((_let_445 (ASSUME :args (_let_230)))) (let ((_let_446 (EQ_RESOLVE (ASSUME :args (_let_46)) (MACRO_SR_EQ_INTRO :args (_let_46 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_447 (EQ_RESOLVE (ASSUME :args (_let_33)) (MACRO_SR_EQ_INTRO :args (_let_33 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_448 (ASSUME :args (_let_186)))) (let ((_let_449 (ASSUME :args (_let_35)))) (let ((_let_450 (ASSUME :args (_let_31)))) (let ((_let_451 (ASSUME :args (_let_180)))) (let ((_let_452 (EQ_RESOLVE (ASSUME :args (_let_102)) (TRUST_SUBS_MAP (AND_INTRO _let_451 _let_450 _let_449 _let_448 _let_447 _let_446 _let_445 _let_444 _let_443 _let_442 _let_441 _let_440 _let_439 _let_438 _let_437 _let_436 _let_435 _let_434 _let_433 _let_432 _let_431 _let_430 _let_429 _let_428 _let_427 _let_426 _let_425 _let_424 _let_423 _let_422 _let_421 _let_420 _let_419 _let_418 _let_417 _let_416 _let_415 _let_414 _let_413 _let_412 _let_411 _let_410 _let_409 _let_408 _let_407 _let_406 _let_405 _let_404 _let_403 _let_402 _let_401 _let_400 _let_399 _let_398 _let_397 _let_396 _let_395 _let_394 _let_393 _let_392 _let_391 _let_390 _let_389 _let_388 _let_387 _let_386 _let_385 _let_384 _let_383 _let_382 _let_381 _let_380 _let_379 _let_378 _let_377 _let_376 _let_375 _let_374 _let_373 _let_372 _let_371 _let_370 _let_369 _let_368 _let_367 _let_366 _let_365 _let_364 _let_363 _let_362 _let_361 _let_359 _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) :args ((= _let_102 (= inv_im4434751243573137211at_int (lambda ((R5 set_Pr4329608150637261639at_nat) (F2 (-> int set_Pr1261947904930325089at_nat))) (@ collec213857154873943460nt_int (lambda ((BOUND_VARIABLE_150246 product_prod_int_int)) (@ (@ member8757157785044589968at_nat (@ (@ produc2922128104949294807at_nat (@ F2 (@ product_fst_int_int BOUND_VARIABLE_150246))) (@ F2 (@ (@ produc8211389475949308722nt_int (lambda ((BOUND_VARIABLE_150247 int) (BOUND_VARIABLE_150248 int)) BOUND_VARIABLE_150248)) BOUND_VARIABLE_150246)))) R5))))))))))) (let ((_let_453 (EQ_RESOLVE (SYMM (ASSUME :args (_let_30))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_452 _let_451 _let_450 _let_449 _let_448 _let_447 _let_446 _let_445 _let_444 _let_443 _let_442 _let_441 _let_440 _let_439 _let_438 _let_437 _let_436 _let_435 _let_434 _let_433 _let_432 _let_431 _let_430 _let_429 _let_428 _let_427 _let_426 _let_425 _let_424 _let_423 _let_422 _let_421 _let_420 _let_419 _let_418 _let_417 _let_416 _let_415 _let_414 _let_413 _let_412 _let_411 _let_410 _let_409 _let_408 _let_407 _let_406 _let_405 _let_404 _let_403 _let_402 _let_401 _let_400 _let_399 _let_398 _let_397 _let_396 _let_395 _let_394 _let_393 _let_392 _let_391 _let_390 _let_389 _let_388 _let_387 _let_386 _let_385 _let_384 _let_383 _let_382 _let_381 _let_380 _let_379 _let_378 _let_377 _let_376 _let_375 _let_374 _let_373 _let_372 _let_371 _let_370 _let_369 _let_368 _let_367 _let_366 _let_365 _let_364 _let_363 _let_362 _let_361 _let_359 _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) :args ((= id_nat_nat _let_29) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_454 (ASSUME :args (_let_135)))) (let ((_let_455 (EQ_RESOLVE (ASSUME :args (_let_232)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_454 _let_453 _let_452 _let_451 _let_450 _let_449 _let_448 _let_447 _let_446 _let_445 _let_444 _let_443 _let_442 _let_441 _let_440 _let_439 _let_438 _let_437 _let_436 _let_435 _let_434 _let_433 _let_432 _let_431 _let_430 _let_429 _let_428 _let_427 _let_426 _let_425 _let_424 _let_423 _let_422 _let_421 _let_420 _let_419 _let_418 _let_417 _let_416 _let_415 _let_414 _let_413 _let_412 _let_411 _let_410 _let_409 _let_408 _let_407 _let_406 _let_405 _let_404 _let_403 _let_402 _let_401 _let_400 _let_399 _let_398 _let_397 _let_396 _let_395 _let_394 _let_393 _let_392 _let_391 _let_390 _let_389 _let_388 _let_387 _let_386 _let_385 _let_384 _let_383 _let_382 _let_381 _let_380 _let_379 _let_378 _let_377 _let_376 _let_375 _let_374 _let_373 _let_372 _let_371 _let_370 _let_369 _let_368 _let_367 _let_366 _let_365 _let_364 _let_363 _let_362 _let_361 _let_359 _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) :args (_let_232 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_456 (EQ_RESOLVE (ASSUME :args (_let_87)) (MACRO_SR_EQ_INTRO :args (_let_87 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_457 (EQ_RESOLVE (SYMM (ASSUME :args (_let_7))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_456 _let_455 _let_454 _let_453 _let_452 _let_451 _let_450 _let_449 _let_448 _let_447 _let_446 _let_445 _let_444 _let_443 _let_442 _let_441 _let_440 _let_439 _let_438 _let_437 _let_436 _let_435 _let_434 _let_433 _let_432 _let_431 _let_430 _let_429 _let_428 _let_427 _let_426 _let_425 _let_424 _let_423 _let_422 _let_421 _let_420 _let_419 _let_418 _let_417 _let_416 _let_415 _let_414 _let_413 _let_412 _let_411 _let_410 _let_409 _let_408 _let_407 _let_406 _let_405 _let_404 _let_403 _let_402 _let_401 _let_400 _let_399 _let_398 _let_397 _let_396 _let_395 _let_394 _let_393 _let_392 _let_391 _let_390 _let_389 _let_388 _let_387 _let_386 _let_385 _let_384 _let_383 _let_382 _let_381 _let_380 _let_379 _let_378 _let_377 _let_376 _let_375 _let_374 _let_373 _let_372 _let_371 _let_370 _let_369 _let_368 _let_367 _let_366 _let_365 _let_364 _let_363 _let_362 _let_361 _let_359 _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) :args ((= top_to7513191607651882425at_rat _let_6) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_458 (ASSUME :args (_let_86)))) (let ((_let_459 (EQ_RESOLVE (ASSUME :args (_let_90)) (TRUST_SUBS_MAP (AND_INTRO _let_458 _let_457 _let_456 _let_455 _let_454 _let_453 _let_452 _let_451 _let_450 _let_449 _let_448 _let_447 _let_446 _let_445 _let_444 _let_443 _let_442 _let_441 _let_440 _let_439 _let_438 _let_437 _let_436 _let_435 _let_434 _let_433 _let_432 _let_431 _let_430 _let_429 _let_428 _let_427 _let_426 _let_425 _let_424 _let_423 _let_422 _let_421 _let_420 _let_419 _let_418 _let_417 _let_416 _let_415 _let_414 _let_413 _let_412 _let_411 _let_410 _let_409 _let_408 _let_407 _let_406 _let_405 _let_404 _let_403 _let_402 _let_401 _let_400 _let_399 _let_398 _let_397 _let_396 _let_395 _let_394 _let_393 _let_392 _let_391 _let_390 _let_389 _let_388 _let_387 _let_386 _let_385 _let_384 _let_383 _let_382 _let_381 _let_380 _let_379 _let_378 _let_377 _let_376 _let_375 _let_374 _let_373 _let_372 _let_371 _let_370 _let_369 _let_368 _let_367 _let_366 _let_365 _let_364 _let_363 _let_362 _let_361 _let_359 _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) :args ((= _let_90 (= sup_su5525570899277871387at_nat (lambda ((A6 set_Pr4329608150637261639at_nat) (B6 set_Pr4329608150637261639at_nat)) (@ collec6321179662152712658at_nat (lambda ((BOUND_VARIABLE_151104 produc3843707927480180839at_nat)) (@ complete_Sup_Sup_o (@ (@ image_3568060456209098518_nat_o (@ member8757157785044589968at_nat BOUND_VARIABLE_151104)) (@ (@ image_2496312346330513076at_nat (lambda ((B4 Bool)) (@ (@ (@ if_set3208018901896979469at_nat B4) A6) B6))) top_top_set_o))))))))))))) (let ((_let_460 (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_459 _let_458 _let_457 _let_456 _let_455 _let_454 _let_453 _let_452 _let_451 _let_450 _let_449 _let_448 _let_447 _let_446 _let_445 _let_444 _let_443 _let_442 _let_441 _let_440 _let_439 _let_438 _let_437 _let_436 _let_435 _let_434 _let_433 _let_432 _let_431 _let_430 _let_429 _let_428 _let_427 _let_426 _let_425 _let_424 _let_423 _let_422 _let_421 _let_420 _let_419 _let_418 _let_417 _let_416 _let_415 _let_414 _let_413 _let_412 _let_411 _let_410 _let_409 _let_408 _let_407 _let_406 _let_405 _let_404 _let_403 _let_402 _let_401 _let_400 _let_399 _let_398 _let_397 _let_396 _let_395 _let_394 _let_393 _let_392 _let_391 _let_390 _let_389 _let_388 _let_387 _let_386 _let_385 _let_384 _let_383 _let_382 _let_381 _let_380 _let_379 _let_378 _let_377 _let_376 _let_375 _let_374 _let_373 _let_372 _let_371 _let_370 _let_369 _let_368 _let_367 _let_366 _let_365 _let_364 _let_363 _let_362 _let_361 _let_359 _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) :args ((= finite4703585013658510744_o_nat (lambda ((S4 set_o) (F2 (-> Bool nat nat))) (forall ((X4 Bool) (Y5 Bool)) (let ((_let_1 (@ F2 Y5))) (let ((_let_2 (@ F2 X4))) (or (not (@ (@ member_o X4) S4)) (not (@ (@ member_o Y5) S4)) (= (@ (@ comp_nat_nat_nat _let_1) _let_2) (@ (@ comp_nat_nat_nat _let_2) _let_1)))))))) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_461 (EQ_RESOLVE (SYMM (ASSUME :args (_let_18))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_460 _let_459 _let_458 _let_457 _let_456 _let_455 _let_454 _let_453 _let_452 _let_451 _let_450 _let_449 _let_448 _let_447 _let_446 _let_445 _let_444 _let_443 _let_442 _let_441 _let_440 _let_439 _let_438 _let_437 _let_436 _let_435 _let_434 _let_433 _let_432 _let_431 _let_430 _let_429 _let_428 _let_427 _let_426 _let_425 _let_424 _let_423 _let_422 _let_421 _let_420 _let_419 _let_418 _let_417 _let_416 _let_415 _let_414 _let_413 _let_412 _let_411 _let_410 _let_409 _let_408 _let_407 _let_406 _let_405 _let_404 _let_403 _let_402 _let_401 _let_400 _let_399 _let_398 _let_397 _let_396 _let_395 _let_394 _let_393 _let_392 _let_391 _let_390 _let_389 _let_388 _let_387 _let_386 _let_385 _let_384 _let_383 _let_382 _let_381 _let_380 _let_379 _let_378 _let_377 _let_376 _let_375 _let_374 _let_373 _let_372 _let_371 _let_370 _let_369 _let_368 _let_367 _let_366 _let_365 _let_364 _let_363 _let_362 _let_361 _let_359 _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) :args ((= top_to5594287848199751986ar_nat _let_17) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_462 (ASSUME :args (_let_16)))) (let ((_let_463 (EQ_RESOLVE (ASSUME :args (_let_226)) (TRUST_SUBS_MAP (AND_INTRO _let_462 _let_461 _let_460 _let_459 _let_458 _let_457 _let_456 _let_455 _let_454 _let_453 _let_452 _let_451 _let_450 _let_449 _let_448 _let_447 _let_446 _let_445 _let_444 _let_443 _let_442 _let_441 _let_440 _let_439 _let_438 _let_437 _let_436 _let_435 _let_434 _let_433 _let_432 _let_431 _let_430 _let_429 _let_428 _let_427 _let_426 _let_425 _let_424 _let_423 _let_422 _let_421 _let_420 _let_419 _let_418 _let_417 _let_416 _let_415 _let_414 _let_413 _let_412 _let_411 _let_410 _let_409 _let_408 _let_407 _let_406 _let_405 _let_404 _let_403 _let_402 _let_401 _let_400 _let_399 _let_398 _let_397 _let_396 _let_395 _let_394 _let_393 _let_392 _let_391 _let_390 _let_389 _let_388 _let_387 _let_386 _let_385 _let_384 _let_383 _let_382 _let_381 _let_380 _let_379 _let_378 _let_377 _let_376 _let_375 _let_374 _let_373 _let_372 _let_371 _let_370 _let_369 _let_368 _let_367 _let_366 _let_365 _let_364 _let_363 _let_362 _let_361 _let_359 _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) :args ((= _let_226 (= ord_less_int (@ _let_215 (lambda ((BOUND_VARIABLE_152334 product_prod_nat_nat) (BOUND_VARIABLE_152335 product_prod_nat_nat)) (@ (@ produc6081775807080527818_nat_o (lambda ((BOUND_VARIABLE_152336 nat) (BOUND_VARIABLE_152337 nat)) (@ (@ produc6081775807080527818_nat_o (lambda ((BOUND_VARIABLE_152386 nat) (BOUND_VARIABLE_152387 nat)) (@ (@ ord_less_nat (@ (@ plus_plus_nat BOUND_VARIABLE_152336) BOUND_VARIABLE_152387)) (@ (@ plus_plus_nat BOUND_VARIABLE_152386) BOUND_VARIABLE_152337)))) BOUND_VARIABLE_152335))) BOUND_VARIABLE_152334)))))))))) (let ((_let_464 (EQ_RESOLVE (ASSUME :args (_let_26)) (TRUST_SUBS_MAP (AND_INTRO _let_463 _let_462 _let_461 _let_460 _let_459 _let_458 _let_457 _let_456 _let_455 _let_454 _let_453 _let_452 _let_451 _let_450 _let_449 _let_448 _let_447 _let_446 _let_445 _let_444 _let_443 _let_442 _let_441 _let_440 _let_439 _let_438 _let_437 _let_436 _let_435 _let_434 _let_433 _let_432 _let_431 _let_430 _let_429 _let_428 _let_427 _let_426 _let_425 _let_424 _let_423 _let_422 _let_421 _let_420 _let_419 _let_418 _let_417 _let_416 _let_415 _let_414 _let_413 _let_412 _let_411 _let_410 _let_409 _let_408 _let_407 _let_406 _let_405 _let_404 _let_403 _let_402 _let_401 _let_400 _let_399 _let_398 _let_397 _let_396 _let_395 _let_394 _let_393 _let_392 _let_391 _let_390 _let_389 _let_388 _let_387 _let_386 _let_385 _let_384 _let_383 _let_382 _let_381 _let_380 _let_379 _let_378 _let_377 _let_376 _let_375 _let_374 _let_373 _let_372 _let_371 _let_370 _let_369 _let_368 _let_367 _let_366 _let_365 _let_364 _let_363 _let_362 _let_361 _let_359 _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) :args ((= _let_26 (= order_1960202971199294558of_int (lambda ((P4 (-> int int Bool)) (A6 set_int)) (@ collec213857154873943460nt_int (lambda ((BOUND_VARIABLE_152696 product_prod_int_int)) (let ((_let_1 (@ (@ produc8211389475949308722nt_int (lambda ((BOUND_VARIABLE_152697 int) (BOUND_VARIABLE_152698 int)) BOUND_VARIABLE_152698)) BOUND_VARIABLE_152696))) (let ((_let_2 (@ product_fst_int_int BOUND_VARIABLE_152696))) (and (@ (@ member5262025264175285858nt_int (@ (@ product_Pair_int_int _let_2) _let_1)) (@ (@ produc1453890548195736866nt_int A6) (lambda ((BOUND_VARIABLE_152727 int)) A6))) (@ (@ P4 _let_2) _let_1)))))))))))))) (let ((_let_465 (ASSUME :args (_let_80)))) (let ((_let_466 (ASSUME :args (_let_14)))) (let ((_let_467 (EQ_RESOLVE (ASSUME :args (_let_133)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_466 _let_465 _let_464 _let_463 _let_462 _let_461 _let_460 _let_459 _let_458 _let_457 _let_456 _let_455 _let_454 _let_453 _let_452 _let_451 _let_450 _let_449 _let_448 _let_447 _let_446 _let_445 _let_444 _let_443 _let_442 _let_441 _let_440 _let_439 _let_438 _let_437 _let_436 _let_435 _let_434 _let_433 _let_432 _let_431 _let_430 _let_429 _let_428 _let_427 _let_426 _let_425 _let_424 _let_423 _let_422 _let_421 _let_420 _let_419 _let_418 _let_417 _let_416 _let_415 _let_414 _let_413 _let_412 _let_411 _let_410 _let_409 _let_408 _let_407 _let_406 _let_405 _let_404 _let_403 _let_402 _let_401 _let_400 _let_399 _let_398 _let_397 _let_396 _let_395 _let_394 _let_393 _let_392 _let_391 _let_390 _let_389 _let_388 _let_387 _let_386 _let_385 _let_384 _let_383 _let_382 _let_381 _let_380 _let_379 _let_378 _let_377 _let_376 _let_375 _let_374 _let_373 _let_372 _let_371 _let_370 _let_369 _let_368 _let_367 _let_366 _let_365 _let_364 _let_363 _let_362 _let_361 _let_359 _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) :args (_let_133 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_468 (EQ_RESOLVE (ASSUME :args (_let_93)) (MACRO_SR_EQ_INTRO :args (_let_93 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_469 (EQ_RESOLVE (ASSUME :args (_let_222)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_468 _let_467 _let_466 _let_465 _let_464 _let_463 _let_462 _let_461 _let_460 _let_459 _let_458 _let_457 _let_456 _let_455 _let_454 _let_453 _let_452 _let_451 _let_450 _let_449 _let_448 _let_447 _let_446 _let_445 _let_444 _let_443 _let_442 _let_441 _let_440 _let_439 _let_438 _let_437 _let_436 _let_435 _let_434 _let_433 _let_432 _let_431 _let_430 _let_429 _let_428 _let_427 _let_426 _let_425 _let_424 _let_423 _let_422 _let_421 _let_420 _let_419 _let_418 _let_417 _let_416 _let_415 _let_414 _let_413 _let_412 _let_411 _let_410 _let_409 _let_408 _let_407 _let_406 _let_405 _let_404 _let_403 _let_402 _let_401 _let_400 _let_399 _let_398 _let_397 _let_396 _let_395 _let_394 _let_393 _let_392 _let_391 _let_390 _let_389 _let_388 _let_387 _let_386 _let_385 _let_384 _let_383 _let_382 _let_381 _let_380 _let_379 _let_378 _let_377 _let_376 _let_375 _let_374 _let_373 _let_372 _let_371 _let_370 _let_369 _let_368 _let_367 _let_366 _let_365 _let_364 _let_363 _let_362 _let_361 _let_359 _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) :args (_let_222 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_470 (EQ_RESOLVE (ASSUME :args (_let_92)) (TRUST_SUBS_MAP (AND_INTRO _let_469 _let_468 _let_467 _let_466 _let_465 _let_464 _let_463 _let_462 _let_461 _let_460 _let_459 _let_458 _let_457 _let_456 _let_455 _let_454 _let_453 _let_452 _let_451 _let_450 _let_449 _let_448 _let_447 _let_446 _let_445 _let_444 _let_443 _let_442 _let_441 _let_440 _let_439 _let_438 _let_437 _let_436 _let_435 _let_434 _let_433 _let_432 _let_431 _let_430 _let_429 _let_428 _let_427 _let_426 _let_425 _let_424 _let_423 _let_422 _let_421 _let_420 _let_419 _let_418 _let_417 _let_416 _let_415 _let_414 _let_413 _let_412 _let_411 _let_410 _let_409 _let_408 _let_407 _let_406 _let_405 _let_404 _let_403 _let_402 _let_401 _let_400 _let_399 _let_398 _let_397 _let_396 _let_395 _let_394 _let_393 _let_392 _let_391 _let_390 _let_389 _let_388 _let_387 _let_386 _let_385 _let_384 _let_383 _let_382 _let_381 _let_380 _let_379 _let_378 _let_377 _let_376 _let_375 _let_374 _let_373 _let_372 _let_371 _let_370 _let_369 _let_368 _let_367 _let_366 _let_365 _let_364 _let_363 _let_362 _let_361 _let_359 _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) :args ((= _let_92 (= fun_max_weak (@ collec6321179662152712658at_nat (lambda ((BOUND_VARIABLE_155332 produc3843707927480180839at_nat)) (@ complete_Sup_Sup_o (@ (@ image_3568060456209098518_nat_o (@ member8757157785044589968at_nat BOUND_VARIABLE_155332)) (@ (@ image_2496312346330513076at_nat (lambda ((BOUND_VARIABLE_155333 Bool)) (let ((_let_1 (@ collec3392354462482085612at_nat (@ produc6081775807080527818_nat_o (lambda ((BOUND_VARIABLE_259197 nat) (BOUND_VARIABLE_259199 nat)) false))))) (@ (@ (@ if_set3208018901896979469at_nat BOUND_VARIABLE_155333) (@ max_ex8135407076693332796at_nat (@ comple2748534634209756852at_nat (@ (@ image_8493167801588156084at_nat (lambda ((BOUND_VARIABLE_155334 Bool)) (@ (@ (@ if_set1508868558775481357at_nat BOUND_VARIABLE_155334) (@ (@ lex_prod_nat_nat less_than) less_than)) (@ collec7088162979684241874at_nat (lambda ((BOUND_VARIABLE_155335 produc859450856879609959at_nat)) (= (@ produc6408287024330202629at_nat BOUND_VARIABLE_155335) (@ produc3213797794245857475at_nat BOUND_VARIABLE_155335))))))) top_top_set_o)))) (@ (@ insert9069300056098147895at_nat (@ (@ produc2922128104949294807at_nat _let_1) _let_1)) bot_bo228742789529271731at_nat))))) top_top_set_o)))))))))))) (let ((_let_471 (EQ_RESOLVE (ASSUME :args (_let_217)) (TRUST_SUBS_MAP (AND_INTRO _let_470 _let_469 _let_468 _let_467 _let_466 _let_465 _let_464 _let_463 _let_462 _let_461 _let_460 _let_459 _let_458 _let_457 _let_456 _let_455 _let_454 _let_453 _let_452 _let_451 _let_450 _let_449 _let_448 _let_447 _let_446 _let_445 _let_444 _let_443 _let_442 _let_441 _let_440 _let_439 _let_438 _let_437 _let_436 _let_435 _let_434 _let_433 _let_432 _let_431 _let_430 _let_429 _let_428 _let_427 _let_426 _let_425 _let_424 _let_423 _let_422 _let_421 _let_420 _let_419 _let_418 _let_417 _let_416 _let_415 _let_414 _let_413 _let_412 _let_411 _let_410 _let_409 _let_408 _let_407 _let_406 _let_405 _let_404 _let_403 _let_402 _let_401 _let_400 _let_399 _let_398 _let_397 _let_396 _let_395 _let_394 _let_393 _let_392 _let_391 _let_390 _let_389 _let_388 _let_387 _let_386 _let_385 _let_384 _let_383 _let_382 _let_381 _let_380 _let_379 _let_378 _let_377 _let_376 _let_375 _let_374 _let_373 _let_372 _let_371 _let_370 _let_369 _let_368 _let_367 _let_366 _let_365 _let_364 _let_363 _let_362 _let_361 _let_359 _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) :args ((= _let_217 (= sup_sup_set_nat (lambda ((A6 set_nat) (B6 set_nat)) (@ collect_nat (lambda ((BOUND_VARIABLE_155399 nat)) (@ complete_Sup_Sup_o (@ (@ image_set_nat_o (@ member_nat BOUND_VARIABLE_155399)) (@ (@ image_o_set_nat (lambda ((B4 Bool)) (@ (@ (@ if_set_nat B4) A6) B6))) top_top_set_o))))))))))))) (let ((_let_472 (ASSUME :args (_let_1)))) (let ((_let_473 (ASSUME :args (_let_202)))) (let ((_let_474 (ASSUME :args (_let_122)))) (let ((_let_475 (ASSUME :args (_let_158)))) (let ((_let_476 (EQ_RESOLVE (EQ_RESOLVE (ASSUME :args (_let_207)) (MACRO_SR_EQ_INTRO :args (_let_207 SB_DEFAULT SBA_FIXPOINT))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_475 _let_474 _let_473 _let_472 _let_471 _let_470 _let_469 _let_468 _let_467 _let_466 _let_465 _let_464 _let_463 _let_462 _let_461 _let_460 _let_459 _let_458 _let_457 _let_456 _let_455 _let_454 _let_453 _let_452 _let_451 _let_450 _let_449 _let_448 _let_447 _let_446 _let_445 _let_444 _let_443 _let_442 _let_441 _let_440 _let_439 _let_438 _let_437 _let_436 _let_435 _let_434 _let_433 _let_432 _let_431 _let_430 _let_429 _let_428 _let_427 _let_426 _let_425 _let_424 _let_423 _let_422 _let_421 _let_420 _let_419 _let_418 _let_417 _let_416 _let_415 _let_414 _let_413 _let_412 _let_411 _let_410 _let_409 _let_408 _let_407 _let_406 _let_405 _let_404 _let_403 _let_402 _let_401 _let_400 _let_399 _let_398 _let_397 _let_396 _let_395 _let_394 _let_393 _let_392 _let_391 _let_390 _let_389 _let_388 _let_387 _let_386 _let_385 _let_384 _let_383 _let_382 _let_381 _let_380 _let_379 _let_378 _let_377 _let_376 _let_375 _let_374 _let_373 _let_372 _let_371 _let_370 _let_369 _let_368 _let_367 _let_366 _let_365 _let_364 _let_363 _let_362 _let_361 _let_359 _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) :args ((= adjust_div (@ produc8211389475949308722nt_int (lambda ((Q3 int) (R5 int)) (@ (@ plus_plus_int Q3) (@ zero_n2684676970156552555ol_int (not (= zero_zero_int R5))))))) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_477 (SYMM (ASSUME :args (_let_81))))) (let ((_let_478 (EQ_RESOLVE (EQ_RESOLVE (ASSUME :args (_let_41)) (MACRO_SR_EQ_INTRO :args (_let_41 SB_DEFAULT SBA_FIXPOINT))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_477 _let_476 _let_475 _let_474 _let_473 _let_472 _let_471 _let_470 _let_469 _let_468 _let_467 _let_466 _let_465 _let_464 _let_463 _let_462 _let_461 _let_460 _let_459 _let_458 _let_457 _let_456 _let_455 _let_454 _let_453 _let_452 _let_451 _let_450 _let_449 _let_448 _let_447 _let_446 _let_445 _let_444 _let_443 _let_442 _let_441 _let_440 _let_439 _let_438 _let_437 _let_436 _let_435 _let_434 _let_433 _let_432 _let_431 _let_430 _let_429 _let_428 _let_427 _let_426 _let_425 _let_424 _let_423 _let_422 _let_421 _let_420 _let_419 _let_418 _let_417 _let_416 _let_415 _let_414 _let_413 _let_412 _let_411 _let_410 _let_409 _let_408 _let_407 _let_406 _let_405 _let_404 _let_403 _let_402 _let_401 _let_400 _let_399 _let_398 _let_397 _let_396 _let_395 _let_394 _let_393 _let_392 _let_391 _let_390 _let_389 _let_388 _let_387 _let_386 _let_385 _let_384 _let_383 _let_382 _let_381 _let_380 _let_379 _let_378 _let_377 _let_376 _let_375 _let_374 _let_373 _let_372 _let_371 _let_370 _let_369 _let_368 _let_367 _let_366 _let_365 _let_364 _let_363 _let_362 _let_361 _let_359 _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) :args ((= finite2110315540964234241at_nat (lambda ((S4 set_Pr1261947904930325089at_nat) (F2 (-> product_prod_nat_nat nat nat))) (forall ((X4 product_prod_nat_nat) (Y5 product_prod_nat_nat)) (let ((_let_1 (@ F2 Y5))) (let ((_let_2 (@ F2 X4))) (or (not (@ (@ member8440522571783428010at_nat X4) S4)) (not (@ (@ member8440522571783428010at_nat Y5) S4)) (= (@ (@ comp_nat_nat_nat _let_1) _let_2) (@ (@ comp_nat_nat_nat _let_2) _let_1)))))))) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_479 (EQ_RESOLVE (ASSUME :args (_let_233)) (MACRO_SR_EQ_INTRO :args (_let_233 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_480 (ASSUME :args (_let_234)))) (let ((_let_481 (ASSUME :args (_let_69)))) (let ((_let_482 (EQ_RESOLVE (ASSUME :args (_let_181)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_481 _let_480 _let_479 _let_478 _let_477 _let_476 _let_475 _let_474 _let_473 _let_472 _let_471 _let_470 _let_469 _let_468 _let_467 _let_466 _let_465 _let_464 _let_463 _let_462 _let_461 _let_460 _let_459 _let_458 _let_457 _let_456 _let_455 _let_454 _let_453 _let_452 _let_451 _let_450 _let_449 _let_448 _let_447 _let_446 _let_445 _let_444 _let_443 _let_442 _let_441 _let_440 _let_439 _let_438 _let_437 _let_436 _let_435 _let_434 _let_433 _let_432 _let_431 _let_430 _let_429 _let_428 _let_427 _let_426 _let_425 _let_424 _let_423 _let_422 _let_421 _let_420 _let_419 _let_418 _let_417 _let_416 _let_415 _let_414 _let_413 _let_412 _let_411 _let_410 _let_409 _let_408 _let_407 _let_406 _let_405 _let_404 _let_403 _let_402 _let_401 _let_400 _let_399 _let_398 _let_397 _let_396 _let_395 _let_394 _let_393 _let_392 _let_391 _let_390 _let_389 _let_388 _let_387 _let_386 _let_385 _let_384 _let_383 _let_382 _let_381 _let_380 _let_379 _let_378 _let_377 _let_376 _let_375 _let_374 _let_373 _let_372 _let_371 _let_370 _let_369 _let_368 _let_367 _let_366 _let_365 _let_364 _let_363 _let_362 _let_361 _let_359 _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) :args (_let_181 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_483 (ASSUME :args (_let_114)))) (let ((_let_484 (EQ_RESOLVE (ASSUME :args (_let_235)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_483 _let_482 _let_481 _let_480 _let_479 _let_478 _let_477 _let_476 _let_475 _let_474 _let_473 _let_472 _let_471 _let_470 _let_469 _let_468 _let_467 _let_466 _let_465 _let_464 _let_463 _let_462 _let_461 _let_460 _let_459 _let_458 _let_457 _let_456 _let_455 _let_454 _let_453 _let_452 _let_451 _let_450 _let_449 _let_448 _let_447 _let_446 _let_445 _let_444 _let_443 _let_442 _let_441 _let_440 _let_439 _let_438 _let_437 _let_436 _let_435 _let_434 _let_433 _let_432 _let_431 _let_430 _let_429 _let_428 _let_427 _let_426 _let_425 _let_424 _let_423 _let_422 _let_421 _let_420 _let_419 _let_418 _let_417 _let_416 _let_415 _let_414 _let_413 _let_412 _let_411 _let_410 _let_409 _let_408 _let_407 _let_406 _let_405 _let_404 _let_403 _let_402 _let_401 _let_400 _let_399 _let_398 _let_397 _let_396 _let_395 _let_394 _let_393 _let_392 _let_391 _let_390 _let_389 _let_388 _let_387 _let_386 _let_385 _let_384 _let_383 _let_382 _let_381 _let_380 _let_379 _let_378 _let_377 _let_376 _let_375 _let_374 _let_373 _let_372 _let_371 _let_370 _let_369 _let_368 _let_367 _let_366 _let_365 _let_364 _let_363 _let_362 _let_361 _let_359 _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) :args (_let_235 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_485 (EQ_RESOLVE (SYMM (ASSUME :args (_let_184))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_484 _let_483 _let_482 _let_481 _let_480 _let_479 _let_478 _let_477 _let_476 _let_475 _let_474 _let_473 _let_472 _let_471 _let_470 _let_469 _let_468 _let_467 _let_466 _let_465 _let_464 _let_463 _let_462 _let_461 _let_460 _let_459 _let_458 _let_457 _let_456 _let_455 _let_454 _let_453 _let_452 _let_451 _let_450 _let_449 _let_448 _let_447 _let_446 _let_445 _let_444 _let_443 _let_442 _let_441 _let_440 _let_439 _let_438 _let_437 _let_436 _let_435 _let_434 _let_433 _let_432 _let_431 _let_430 _let_429 _let_428 _let_427 _let_426 _let_425 _let_424 _let_423 _let_422 _let_421 _let_420 _let_419 _let_418 _let_417 _let_416 _let_415 _let_414 _let_413 _let_412 _let_411 _let_410 _let_409 _let_408 _let_407 _let_406 _let_405 _let_404 _let_403 _let_402 _let_401 _let_400 _let_399 _let_398 _let_397 _let_396 _let_395 _let_394 _let_393 _let_392 _let_391 _let_390 _let_389 _let_388 _let_387 _let_386 _let_385 _let_384 _let_383 _let_382 _let_381 _let_380 _let_379 _let_378 _let_377 _let_376 _let_375 _let_374 _let_373 _let_372 _let_371 _let_370 _let_369 _let_368 _let_367 _let_366 _let_365 _let_364 _let_363 _let_362 _let_361 _let_359 _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) :args ((= top_to8437673547576850234ar_rat _let_183) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_486 (EQ_RESOLVE (ASSUME :args (_let_139)) (TRUST_SUBS_MAP (AND_INTRO _let_485 _let_484 _let_483 _let_482 _let_481 _let_480 _let_479 _let_478 _let_477 _let_476 _let_475 _let_474 _let_473 _let_472 _let_471 _let_470 _let_469 _let_468 _let_467 _let_466 _let_465 _let_464 _let_463 _let_462 _let_461 _let_460 _let_459 _let_458 _let_457 _let_456 _let_455 _let_454 _let_453 _let_452 _let_451 _let_450 _let_449 _let_448 _let_447 _let_446 _let_445 _let_444 _let_443 _let_442 _let_441 _let_440 _let_439 _let_438 _let_437 _let_436 _let_435 _let_434 _let_433 _let_432 _let_431 _let_430 _let_429 _let_428 _let_427 _let_426 _let_425 _let_424 _let_423 _let_422 _let_421 _let_420 _let_419 _let_418 _let_417 _let_416 _let_415 _let_414 _let_413 _let_412 _let_411 _let_410 _let_409 _let_408 _let_407 _let_406 _let_405 _let_404 _let_403 _let_402 _let_401 _let_400 _let_399 _let_398 _let_397 _let_396 _let_395 _let_394 _let_393 _let_392 _let_391 _let_390 _let_389 _let_388 _let_387 _let_386 _let_385 _let_384 _let_383 _let_382 _let_381 _let_380 _let_379 _let_378 _let_377 _let_376 _let_375 _let_374 _let_373 _let_372 _let_371 _let_370 _let_369 _let_368 _let_367 _let_366 _let_365 _let_364 _let_363 _let_362 _let_361 _let_359 _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) :args ((= _let_139 (= int_ge_less_than (lambda ((D3 int)) (@ collec213857154873943460nt_int (lambda ((BOUND_VARIABLE_158404 product_prod_int_int)) (and (@ (@ produc6081775807080527818_nat_o (lambda ((BOUND_VARIABLE_158502 nat) (BOUND_VARIABLE_158503 nat)) (@ (@ produc6081775807080527818_nat_o (lambda ((BOUND_VARIABLE_158504 nat) (BOUND_VARIABLE_158505 nat)) (@ (@ ord_less_eq_nat (@ (@ plus_plus_nat BOUND_VARIABLE_158502) BOUND_VARIABLE_158505)) (@ (@ plus_plus_nat BOUND_VARIABLE_158504) BOUND_VARIABLE_158503)))) (@ rep_Integ (@ product_fst_int_int BOUND_VARIABLE_158404))))) (@ rep_Integ D3)) (@ (@ (@ (@ (@ map_fu434086159418415080_int_o rep_Integ) (@ (@ map_fu4826362097070443709at_o_o rep_Integ) id_o)) (lambda ((BOUND_VARIABLE_158477 product_prod_nat_nat) (BOUND_VARIABLE_158478 product_prod_nat_nat)) (@ (@ produc6081775807080527818_nat_o (lambda ((BOUND_VARIABLE_158479 nat) (BOUND_VARIABLE_158480 nat)) (@ (@ produc6081775807080527818_nat_o (lambda ((BOUND_VARIABLE_158481 nat) (BOUND_VARIABLE_158482 nat)) (@ (@ ord_less_nat (@ (@ plus_plus_nat BOUND_VARIABLE_158479) BOUND_VARIABLE_158482)) (@ (@ plus_plus_nat BOUND_VARIABLE_158481) BOUND_VARIABLE_158480)))) BOUND_VARIABLE_158478))) BOUND_VARIABLE_158477))) (@ product_fst_int_int BOUND_VARIABLE_158404)) (@ (@ produc8211389475949308722nt_int (lambda ((BOUND_VARIABLE_158405 int) (BOUND_VARIABLE_158406 int)) BOUND_VARIABLE_158406)) BOUND_VARIABLE_158404))))))))))))) (let ((_let_487 (ASSUME :args (_let_236)))) (let ((_let_488 (EQ_RESOLVE (ASSUME :args (_let_237)) (TRUST_SUBS_MAP (AND_INTRO _let_487 _let_486 _let_485 _let_484 _let_483 _let_482 _let_481 _let_480 _let_479 _let_478 _let_477 _let_476 _let_475 _let_474 _let_473 _let_472 _let_471 _let_470 _let_469 _let_468 _let_467 _let_466 _let_465 _let_464 _let_463 _let_462 _let_461 _let_460 _let_459 _let_458 _let_457 _let_456 _let_455 _let_454 _let_453 _let_452 _let_451 _let_450 _let_449 _let_448 _let_447 _let_446 _let_445 _let_444 _let_443 _let_442 _let_441 _let_440 _let_439 _let_438 _let_437 _let_436 _let_435 _let_434 _let_433 _let_432 _let_431 _let_430 _let_429 _let_428 _let_427 _let_426 _let_425 _let_424 _let_423 _let_422 _let_421 _let_420 _let_419 _let_418 _let_417 _let_416 _let_415 _let_414 _let_413 _let_412 _let_411 _let_410 _let_409 _let_408 _let_407 _let_406 _let_405 _let_404 _let_403 _let_402 _let_401 _let_400 _let_399 _let_398 _let_397 _let_396 _let_395 _let_394 _let_393 _let_392 _let_391 _let_390 _let_389 _let_388 _let_387 _let_386 _let_385 _let_384 _let_383 _let_382 _let_381 _let_380 _let_379 _let_378 _let_377 _let_376 _let_375 _let_374 _let_373 _let_372 _let_371 _let_370 _let_369 _let_368 _let_367 _let_366 _let_365 _let_364 _let_363 _let_362 _let_361 _let_359 _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) :args ((= _let_237 (= order_8809246210994205103at_nat (lambda ((P4 (-> set_Pr1261947904930325089at_nat set_Pr1261947904930325089at_nat Bool)) (A6 set_se7855581050983116737at_nat)) (@ collec6321179662152712658at_nat (@ produc410239310623530412_nat_o (lambda ((A5 set_Pr1261947904930325089at_nat) (B4 set_Pr1261947904930325089at_nat)) (and (@ (@ P4 A5) B4) (@ (@ member8757157785044589968at_nat (@ (@ produc2922128104949294807at_nat A5) B4)) (@ collec6321179662152712658at_nat (lambda ((BOUND_VARIABLE_159328 produc3843707927480180839at_nat)) (@ complete_Sup_Sup_o (@ (@ image_3568060456209098518_nat_o (@ member8757157785044589968at_nat BOUND_VARIABLE_159328)) (@ (@ image_6898982319499645995at_nat (lambda ((BOUND_VARIABLE_159329 set_Pr1261947904930325089at_nat)) (@ collec6321179662152712658at_nat (lambda ((BOUND_VARIABLE_159330 produc3843707927480180839at_nat)) (@ complete_Sup_Sup_o (@ (@ image_3568060456209098518_nat_o (@ member8757157785044589968at_nat BOUND_VARIABLE_159330)) (@ (@ image_6898982319499645995at_nat (lambda ((BOUND_VARIABLE_159332 set_Pr1261947904930325089at_nat)) (@ (@ insert9069300056098147895at_nat (@ (@ produc2922128104949294807at_nat BOUND_VARIABLE_159329) BOUND_VARIABLE_159332)) bot_bo228742789529271731at_nat))) A6))))))) A6)))))))))))))))))) (let ((_let_489 (SYMM (ASSUME :args (_let_239))))) (let ((_let_490 (EQ_RESOLVE (ASSUME :args (_let_240)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_489 _let_488 _let_487 _let_486 _let_485 _let_484 _let_483 _let_482 _let_481 _let_480 _let_479 _let_478 _let_477 _let_476 _let_475 _let_474 _let_473 _let_472 _let_471 _let_470 _let_469 _let_468 _let_467 _let_466 _let_465 _let_464 _let_463 _let_462 _let_461 _let_460 _let_459 _let_458 _let_457 _let_456 _let_455 _let_454 _let_453 _let_452 _let_451 _let_450 _let_449 _let_448 _let_447 _let_446 _let_445 _let_444 _let_443 _let_442 _let_441 _let_440 _let_439 _let_438 _let_437 _let_436 _let_435 _let_434 _let_433 _let_432 _let_431 _let_430 _let_429 _let_428 _let_427 _let_426 _let_425 _let_424 _let_423 _let_422 _let_421 _let_420 _let_419 _let_418 _let_417 _let_416 _let_415 _let_414 _let_413 _let_412 _let_411 _let_410 _let_409 _let_408 _let_407 _let_406 _let_405 _let_404 _let_403 _let_402 _let_401 _let_400 _let_399 _let_398 _let_397 _let_396 _let_395 _let_394 _let_393 _let_392 _let_391 _let_390 _let_389 _let_388 _let_387 _let_386 _let_385 _let_384 _let_383 _let_382 _let_381 _let_380 _let_379 _let_378 _let_377 _let_376 _let_375 _let_374 _let_373 _let_372 _let_371 _let_370 _let_369 _let_368 _let_367 _let_366 _let_365 _let_364 _let_363 _let_362 _let_361 _let_359 _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) :args (_let_240 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_491 (EQ_RESOLVE (ASSUME :args (_let_241)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_490 _let_489 _let_488 _let_487 _let_486 _let_485 _let_484 _let_483 _let_482 _let_481 _let_480 _let_479 _let_478 _let_477 _let_476 _let_475 _let_474 _let_473 _let_472 _let_471 _let_470 _let_469 _let_468 _let_467 _let_466 _let_465 _let_464 _let_463 _let_462 _let_461 _let_460 _let_459 _let_458 _let_457 _let_456 _let_455 _let_454 _let_453 _let_452 _let_451 _let_450 _let_449 _let_448 _let_447 _let_446 _let_445 _let_444 _let_443 _let_442 _let_441 _let_440 _let_439 _let_438 _let_437 _let_436 _let_435 _let_434 _let_433 _let_432 _let_431 _let_430 _let_429 _let_428 _let_427 _let_426 _let_425 _let_424 _let_423 _let_422 _let_421 _let_420 _let_419 _let_418 _let_417 _let_416 _let_415 _let_414 _let_413 _let_412 _let_411 _let_410 _let_409 _let_408 _let_407 _let_406 _let_405 _let_404 _let_403 _let_402 _let_401 _let_400 _let_399 _let_398 _let_397 _let_396 _let_395 _let_394 _let_393 _let_392 _let_391 _let_390 _let_389 _let_388 _let_387 _let_386 _let_385 _let_384 _let_383 _let_382 _let_381 _let_380 _let_379 _let_378 _let_377 _let_376 _let_375 _let_374 _let_373 _let_372 _let_371 _let_370 _let_369 _let_368 _let_367 _let_366 _let_365 _let_364 _let_363 _let_362 _let_361 _let_359 _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) :args (_let_241 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_492 (AND_INTRO _let_491 _let_490 _let_489 _let_488 _let_487 _let_486 _let_485 _let_484 _let_483 _let_482 _let_481 _let_480 _let_479 _let_478 _let_477 _let_476 _let_475 _let_474 _let_473 _let_472 _let_471 _let_470 _let_469 _let_468 _let_467 _let_466 _let_465 _let_464 _let_463 _let_462 _let_461 _let_460 _let_459 _let_458 _let_457 _let_456 _let_455 _let_454 _let_453 _let_452 _let_451 _let_450 _let_449 _let_448 _let_447 _let_446 _let_445 _let_444 _let_443 _let_442 _let_441 _let_440 _let_439 _let_438 _let_437 _let_436 _let_435 _let_434 _let_433 _let_432 _let_431 _let_430 _let_429 _let_428 _let_427 _let_426 _let_425 _let_424 _let_423 _let_422 _let_421 _let_420 _let_419 _let_418 _let_417 _let_416 _let_415 _let_414 _let_413 _let_412 _let_411 _let_410 _let_409 _let_408 _let_407 _let_406 _let_405 _let_404 _let_403 _let_402 _let_401 _let_400 _let_399 _let_398 _let_397 _let_396 _let_395 _let_394 _let_393 _let_392 _let_391 _let_390 _let_389 _let_388 _let_387 _let_386 _let_385 _let_384 _let_383 _let_382 _let_381 _let_380 _let_379 _let_378 _let_377 _let_376 _let_375 _let_374 _let_373 _let_372 _let_371 _let_370 _let_369 _let_368 _let_367 _let_366 _let_365 _let_364 _let_363 _let_362 _let_361 _let_359 _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 ((_let_493 (EQ_RESOLVE (ASSUME :args (_let_244)) (TRANS (MACRO_SR_EQ_INTRO :args (_let_244 SB_DEFAULT SBA_FIXPOINT)) (MACRO_SR_EQ_INTRO _let_492 :args ((forall ((F (-> heap_e7401611519738050253t_unit produc7812382424243267045t_unit)) (H heap_e7401611519738050253t_unit) (H2 heap_e7401611519738050253t_unit) (R ref_a)) (let ((_let_1 (@ F H))) (or (not (@ (@ (@ (@ heap_effect_ref_a (@ heap_heap_ref_a F)) H) H2) R)) (and (= H2 (@ produc1126150082675451753t_unit _let_1)) (= R (@ produc473321116828791851t_unit _let_1)))))) SB_DEFAULT SBA_FIXPOINT)) (PREPROCESS :args ((= (forall ((F (-> heap_e7401611519738050253t_unit produc7812382424243267045t_unit)) (H heap_e7401611519738050253t_unit) (H2 heap_e7401611519738050253t_unit) (R ref_a)) (let ((_let_1 (@ F H))) (or (not (@ (@ (@ (@ heap_effect_ref_a (@ heap_heap_ref_a F)) H) H2) R)) (and (= H2 (@ (@ (@ comp_P3239167524078694454t_unit produc5717040794327095847_ref_a) (@ produc2058451029528183389_ref_a (lambda ((X4 ref_a) (Y5 heap_e7401611519738050253t_unit)) (@ (@ produc2564672488694626579_ref_a Y5) X4)))) _let_1)) (= R (@ (@ (@ comp_P1287623958910499840t_unit produc6369869760173755749_ref_a) (@ produc2058451029528183389_ref_a (lambda ((X4 ref_a) (Y5 heap_e7401611519738050253t_unit)) (@ (@ produc2564672488694626579_ref_a Y5) X4)))) _let_1)))))) _let_321))) (PREPROCESS :args ((= _let_321 _let_320))))))) (let ((_let_494 (EQ_RESOLVE (ASSUME :args (_let_174)) (MACRO_SR_EQ_INTRO _let_492 :args (_let_174 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_495 (SYMM (ASSUME :args (_let_245))))) (let ((_let_496 (EQ_RESOLVE (SYMM (ASSUME :args (_let_247))) (TRUST_SUBS_MAP (AND_INTRO _let_495 _let_494 _let_491 _let_490 _let_489 _let_488 _let_487 _let_486 _let_485 _let_484 _let_483 _let_482 _let_481 _let_480 _let_479 _let_478 _let_477 _let_476 _let_475 _let_474 _let_473 _let_472 _let_471 _let_470 _let_469 _let_468 _let_467 _let_466 _let_465 _let_464 _let_463 _let_462 _let_461 _let_460 _let_459 _let_458 _let_457 _let_456 _let_455 _let_454 _let_453 _let_452 _let_451 _let_450 _let_449 _let_448 _let_447 _let_446 _let_445 _let_444 _let_443 _let_442 _let_441 _let_440 _let_439 _let_438 _let_437 _let_436 _let_435 _let_434 _let_433 _let_432 _let_431 _let_430 _let_429 _let_428 _let_427 _let_426 _let_425 _let_424 _let_423 _let_422 _let_421 _let_420 _let_419 _let_418 _let_417 _let_416 _let_415 _let_414 _let_413 _let_412 _let_411 _let_410 _let_409 _let_408 _let_407 _let_406 _let_405 _let_404 _let_403 _let_402 _let_401 _let_400 _let_399 _let_398 _let_397 _let_396 _let_395 _let_394 _let_393 _let_392 _let_391 _let_390 _let_389 _let_388 _let_387 _let_386 _let_385 _let_384 _let_383 _let_382 _let_381 _let_380 _let_379 _let_378 _let_377 _let_376 _let_375 _let_374 _let_373 _let_372 _let_371 _let_370 _let_369 _let_368 _let_367 _let_366 _let_365 _let_364 _let_363 _let_362 _let_361 _let_359 _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) :args ((= (= bot_bot_set_nat _let_246) (= bot_bot_set_nat (@ collect_nat (lambda ((BOUND_VARIABLE_161496 nat)) (@ complete_Inf_Inf_o (@ (@ image_set_nat_o (@ member_nat BOUND_VARIABLE_161496)) (@ (@ image_nat_set_nat set_or1210151606488870762an_nat) (@ (@ image_list_nat_nat nat_list_encode) top_top_set_list_nat))))))))))))) (let ((_let_497 (EQ_RESOLVE (ASSUME :args (_let_248)) (MACRO_SR_EQ_INTRO :args (_let_248 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_498 (EQ_RESOLVE (ASSUME :args (_let_250)) (TRUST_SUBS_MAP (AND_INTRO _let_497 _let_496 _let_495 _let_494 _let_491 _let_490 _let_489 _let_488 _let_487 _let_486 _let_485 _let_484 _let_483 _let_482 _let_481 _let_480 _let_479 _let_478 _let_477 _let_476 _let_475 _let_474 _let_473 _let_472 _let_471 _let_470 _let_469 _let_468 _let_467 _let_466 _let_465 _let_464 _let_463 _let_462 _let_461 _let_460 _let_459 _let_458 _let_457 _let_456 _let_455 _let_454 _let_453 _let_452 _let_451 _let_450 _let_449 _let_448 _let_447 _let_446 _let_445 _let_444 _let_443 _let_442 _let_441 _let_440 _let_439 _let_438 _let_437 _let_436 _let_435 _let_434 _let_433 _let_432 _let_431 _let_430 _let_429 _let_428 _let_427 _let_426 _let_425 _let_424 _let_423 _let_422 _let_421 _let_420 _let_419 _let_418 _let_417 _let_416 _let_415 _let_414 _let_413 _let_412 _let_411 _let_410 _let_409 _let_408 _let_407 _let_406 _let_405 _let_404 _let_403 _let_402 _let_401 _let_400 _let_399 _let_398 _let_397 _let_396 _let_395 _let_394 _let_393 _let_392 _let_391 _let_390 _let_389 _let_388 _let_387 _let_386 _let_385 _let_384 _let_383 _let_382 _let_381 _let_380 _let_379 _let_378 _let_377 _let_376 _let_375 _let_374 _let_373 _let_372 _let_371 _let_370 _let_369 _let_368 _let_367 _let_366 _let_365 _let_364 _let_363 _let_362 _let_361 _let_359 _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) :args ((= _let_250 (= pcr_int (lambda ((BOUND_VARIABLE_162072 product_prod_nat_nat) (BOUND_VARIABLE_162073 int)) (not (forall ((BOUND_VARIABLE_162074 product_prod_nat_nat)) (or (not (@ (@ (@ (@ basic_5328504652464829177at_nat (lambda ((BOUND_VARIABLE_162083 nat) (BOUND_VARIABLE_162084 nat)) (= BOUND_VARIABLE_162083 BOUND_VARIABLE_162084))) (lambda ((BOUND_VARIABLE_162078 nat) (BOUND_VARIABLE_162079 nat)) (= BOUND_VARIABLE_162078 BOUND_VARIABLE_162079))) BOUND_VARIABLE_162072) BOUND_VARIABLE_162074)) (not (@ (@ cr_int BOUND_VARIABLE_162074) BOUND_VARIABLE_162073))))))))))))) (let ((_let_499 (ASSUME :args (_let_105)))) (let ((_let_500 (ASSUME :args (_let_251)))) (let ((_let_501 (ASSUME :args (_let_252)))) (let ((_let_502 (ASSUME :args (_let_253)))) (let ((_let_503 (ASSUME :args (_let_132)))) (let ((_let_504 (EQ_RESOLVE (SYMM (ASSUME :args (_let_24))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_503 _let_502 _let_501 _let_500 _let_499 _let_498 _let_497 _let_496 _let_495 _let_494 _let_491 _let_490 _let_489 _let_488 _let_487 _let_486 _let_485 _let_484 _let_483 _let_482 _let_481 _let_480 _let_479 _let_478 _let_477 _let_476 _let_475 _let_474 _let_473 _let_472 _let_471 _let_470 _let_469 _let_468 _let_467 _let_466 _let_465 _let_464 _let_463 _let_462 _let_461 _let_460 _let_459 _let_458 _let_457 _let_456 _let_455 _let_454 _let_453 _let_452 _let_451 _let_450 _let_449 _let_448 _let_447 _let_446 _let_445 _let_444 _let_443 _let_442 _let_441 _let_440 _let_439 _let_438 _let_437 _let_436 _let_435 _let_434 _let_433 _let_432 _let_431 _let_430 _let_429 _let_428 _let_427 _let_426 _let_425 _let_424 _let_423 _let_422 _let_421 _let_420 _let_419 _let_418 _let_417 _let_416 _let_415 _let_414 _let_413 _let_412 _let_411 _let_410 _let_409 _let_408 _let_407 _let_406 _let_405 _let_404 _let_403 _let_402 _let_401 _let_400 _let_399 _let_398 _let_397 _let_396 _let_395 _let_394 _let_393 _let_392 _let_391 _let_390 _let_389 _let_388 _let_387 _let_386 _let_385 _let_384 _let_383 _let_382 _let_381 _let_380 _let_379 _let_378 _let_377 _let_376 _let_375 _let_374 _let_373 _let_372 _let_371 _let_370 _let_369 _let_368 _let_367 _let_366 _let_365 _let_364 _let_363 _let_362 _let_361 _let_359 _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) :args ((= top_to3956321331435058429t_unit _let_23) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_505 (ASSUME :args (_let_32)))) (let ((_let_506 (EQ_RESOLVE (ASSUME :args (_let_258)) (MACRO_SR_EQ_INTRO :args (_let_258 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_507 (EQ_RESOLVE (ASSUME :args (_let_166)) (MACRO_SR_EQ_INTRO :args (_let_166 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_508 (ASSUME :args (_let_263)))) (let ((_let_509 (EQ_RESOLVE (ASSUME :args (_let_76)) (MACRO_SR_EQ_INTRO :args (_let_76 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_510 (AND_ELIM _let_509 :args _let_357))) (let ((_let_511 (AND_ELIM _let_509 :args _let_360))) (let ((_let_512 (EQ_RESOLVE (ASSUME :args (_let_264)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_511 _let_510 _let_508 _let_507 _let_506 _let_505 _let_504 _let_503 _let_502 _let_501 _let_500 _let_499 _let_498 _let_497 _let_496 _let_495 _let_494 _let_491 _let_490 _let_489 _let_488 _let_487 _let_486 _let_485 _let_484 _let_483 _let_482 _let_481 _let_480 _let_479 _let_478 _let_477 _let_476 _let_475 _let_474 _let_473 _let_472 _let_471 _let_470 _let_469 _let_468 _let_467 _let_466 _let_465 _let_464 _let_463 _let_462 _let_461 _let_460 _let_459 _let_458 _let_457 _let_456 _let_455 _let_454 _let_453 _let_452 _let_451 _let_450 _let_449 _let_448 _let_447 _let_446 _let_445 _let_444 _let_443 _let_442 _let_441 _let_440 _let_439 _let_438 _let_437 _let_436 _let_435 _let_434 _let_433 _let_432 _let_431 _let_430 _let_429 _let_428 _let_427 _let_426 _let_425 _let_424 _let_423 _let_422 _let_421 _let_420 _let_419 _let_418 _let_417 _let_416 _let_415 _let_414 _let_413 _let_412 _let_411 _let_410 _let_409 _let_408 _let_407 _let_406 _let_405 _let_404 _let_403 _let_402 _let_401 _let_400 _let_399 _let_398 _let_397 _let_396 _let_395 _let_394 _let_393 _let_392 _let_391 _let_390 _let_389 _let_388 _let_387 _let_386 _let_385 _let_384 _let_383 _let_382 _let_381 _let_380 _let_379 _let_378 _let_377 _let_376 _let_375 _let_374 _let_373 _let_372 _let_371 _let_370 _let_369 _let_368 _let_367 _let_366 _let_365 _let_364 _let_363 _let_362 _let_361 _let_359 _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) :args (_let_264 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_513 (ASSUME :args (_let_265)))) (let ((_let_514 (EQ_RESOLVE (ASSUME :args (_let_266)) (MACRO_SR_EQ_INTRO :args (_let_266 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_515 (EQ_RESOLVE (SYMM (ASSUME :args (_let_268))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_514 _let_513 _let_512 _let_511 _let_510 _let_508 _let_507 _let_506 _let_505 _let_504 _let_503 _let_502 _let_501 _let_500 _let_499 _let_498 _let_497 _let_496 _let_495 _let_494 _let_491 _let_490 _let_489 _let_488 _let_487 _let_486 _let_485 _let_484 _let_483 _let_482 _let_481 _let_480 _let_479 _let_478 _let_477 _let_476 _let_475 _let_474 _let_473 _let_472 _let_471 _let_470 _let_469 _let_468 _let_467 _let_466 _let_465 _let_464 _let_463 _let_462 _let_461 _let_460 _let_459 _let_458 _let_457 _let_456 _let_455 _let_454 _let_453 _let_452 _let_451 _let_450 _let_449 _let_448 _let_447 _let_446 _let_445 _let_444 _let_443 _let_442 _let_441 _let_440 _let_439 _let_438 _let_437 _let_436 _let_435 _let_434 _let_433 _let_432 _let_431 _let_430 _let_429 _let_428 _let_427 _let_426 _let_425 _let_424 _let_423 _let_422 _let_421 _let_420 _let_419 _let_418 _let_417 _let_416 _let_415 _let_414 _let_413 _let_412 _let_411 _let_410 _let_409 _let_408 _let_407 _let_406 _let_405 _let_404 _let_403 _let_402 _let_401 _let_400 _let_399 _let_398 _let_397 _let_396 _let_395 _let_394 _let_393 _let_392 _let_391 _let_390 _let_389 _let_388 _let_387 _let_386 _let_385 _let_384 _let_383 _let_382 _let_381 _let_380 _let_379 _let_378 _let_377 _let_376 _let_375 _let_374 _let_373 _let_372 _let_371 _let_370 _let_369 _let_368 _let_367 _let_366 _let_365 _let_364 _let_363 _let_362 _let_361 _let_359 _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) :args ((= top_to7002410609688830997at_int _let_267) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_516 (EQ_RESOLVE (ASSUME :args (_let_55)) (MACRO_SR_EQ_INTRO :args (_let_55 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_517 (ASSUME :args (_let_21)))) (let ((_let_518 (ASSUME :args (_let_269)))) (let ((_let_519 (EQ_RESOLVE (ASSUME :args (_let_126)) (TRUST_SUBS_MAP (AND_INTRO _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_510 _let_508 _let_507 _let_506 _let_505 _let_504 _let_503 _let_502 _let_501 _let_500 _let_499 _let_498 _let_497 _let_496 _let_495 _let_494 _let_491 _let_490 _let_489 _let_488 _let_487 _let_486 _let_485 _let_484 _let_483 _let_482 _let_481 _let_480 _let_479 _let_478 _let_477 _let_476 _let_475 _let_474 _let_473 _let_472 _let_471 _let_470 _let_469 _let_468 _let_467 _let_466 _let_465 _let_464 _let_463 _let_462 _let_461 _let_460 _let_459 _let_458 _let_457 _let_456 _let_455 _let_454 _let_453 _let_452 _let_451 _let_450 _let_449 _let_448 _let_447 _let_446 _let_445 _let_444 _let_443 _let_442 _let_441 _let_440 _let_439 _let_438 _let_437 _let_436 _let_435 _let_434 _let_433 _let_432 _let_431 _let_430 _let_429 _let_428 _let_427 _let_426 _let_425 _let_424 _let_423 _let_422 _let_421 _let_420 _let_419 _let_418 _let_417 _let_416 _let_415 _let_414 _let_413 _let_412 _let_411 _let_410 _let_409 _let_408 _let_407 _let_406 _let_405 _let_404 _let_403 _let_402 _let_401 _let_400 _let_399 _let_398 _let_397 _let_396 _let_395 _let_394 _let_393 _let_392 _let_391 _let_390 _let_389 _let_388 _let_387 _let_386 _let_385 _let_384 _let_383 _let_382 _let_381 _let_380 _let_379 _let_378 _let_377 _let_376 _let_375 _let_374 _let_373 _let_372 _let_371 _let_370 _let_369 _let_368 _let_367 _let_366 _let_365 _let_364 _let_363 _let_362 _let_361 _let_359 _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) :args ((= _let_126 (= produc6036585564866528938nt_int (lambda ((F2 (-> int int)) (G3 (-> int int)) (__flatten_var_0 product_prod_int_int)) (@ (@ product_Pair_int_int (@ F2 (@ product_fst_int_int __flatten_var_0))) (@ G3 (@ (@ produc8211389475949308722nt_int (lambda ((BOUND_VARIABLE_168369 int) (BOUND_VARIABLE_168370 int)) BOUND_VARIABLE_168370)) __flatten_var_0))))))))))) (let ((_let_520 (EQ_RESOLVE (ASSUME :args (_let_270)) (MACRO_SR_EQ_INTRO :args (_let_270 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_521 (ASSUME :args (_let_271)))) (let ((_let_522 (ASSUME :args (_let_272)))) (let ((_let_523 (ASSUME :args (_let_273)))) (let ((_let_524 (EQ_RESOLVE (ASSUME :args (_let_274)) (TRUST_SUBS_MAP (AND_INTRO _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_510 _let_508 _let_507 _let_506 _let_505 _let_504 _let_503 _let_502 _let_501 _let_500 _let_499 _let_498 _let_497 _let_496 _let_495 _let_494 _let_491 _let_490 _let_489 _let_488 _let_487 _let_486 _let_485 _let_484 _let_483 _let_482 _let_481 _let_480 _let_479 _let_478 _let_477 _let_476 _let_475 _let_474 _let_473 _let_472 _let_471 _let_470 _let_469 _let_468 _let_467 _let_466 _let_465 _let_464 _let_463 _let_462 _let_461 _let_460 _let_459 _let_458 _let_457 _let_456 _let_455 _let_454 _let_453 _let_452 _let_451 _let_450 _let_449 _let_448 _let_447 _let_446 _let_445 _let_444 _let_443 _let_442 _let_441 _let_440 _let_439 _let_438 _let_437 _let_436 _let_435 _let_434 _let_433 _let_432 _let_431 _let_430 _let_429 _let_428 _let_427 _let_426 _let_425 _let_424 _let_423 _let_422 _let_421 _let_420 _let_419 _let_418 _let_417 _let_416 _let_415 _let_414 _let_413 _let_412 _let_411 _let_410 _let_409 _let_408 _let_407 _let_406 _let_405 _let_404 _let_403 _let_402 _let_401 _let_400 _let_399 _let_398 _let_397 _let_396 _let_395 _let_394 _let_393 _let_392 _let_391 _let_390 _let_389 _let_388 _let_387 _let_386 _let_385 _let_384 _let_383 _let_382 _let_381 _let_380 _let_379 _let_378 _let_377 _let_376 _let_375 _let_374 _let_373 _let_372 _let_371 _let_370 _let_369 _let_368 _let_367 _let_366 _let_365 _let_364 _let_363 _let_362 _let_361 _let_359 _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) :args ((= _let_274 (= intrel (lambda ((BOUND_VARIABLE_169852 product_prod_nat_nat) (BOUND_VARIABLE_169853 product_prod_nat_nat)) (@ (@ produc6081775807080527818_nat_o (lambda ((BOUND_VARIABLE_169854 nat) (BOUND_VARIABLE_169855 nat)) (@ (@ produc6081775807080527818_nat_o (lambda ((BOUND_VARIABLE_169913 nat) (BOUND_VARIABLE_169914 nat)) (= (@ (@ plus_plus_nat BOUND_VARIABLE_169913) BOUND_VARIABLE_169855) (@ (@ plus_plus_nat BOUND_VARIABLE_169854) BOUND_VARIABLE_169914)))) BOUND_VARIABLE_169853))) BOUND_VARIABLE_169852))))))))) (let ((_let_525 (EQ_RESOLVE (ASSUME :args (_let_275)) (MACRO_SR_EQ_INTRO :args (_let_275 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_526 (EQ_RESOLVE (AND_ELIM _let_525 :args _let_357) (MACRO_SR_EQ_INTRO (AND_INTRO _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_510 _let_508 _let_507 _let_506 _let_505 _let_504 _let_503 _let_502 _let_501 _let_500 _let_499 _let_498 _let_497 _let_496 _let_495 _let_494 _let_491 _let_490 _let_489 _let_488 _let_487 _let_486 _let_485 _let_484 _let_483 _let_482 _let_481 _let_480 _let_479 _let_478 _let_477 _let_476 _let_475 _let_474 _let_473 _let_472 _let_471 _let_470 _let_469 _let_468 _let_467 _let_466 _let_465 _let_464 _let_463 _let_462 _let_461 _let_460 _let_459 _let_458 _let_457 _let_456 _let_455 _let_454 _let_453 _let_452 _let_451 _let_450 _let_449 _let_448 _let_447 _let_446 _let_445 _let_444 _let_443 _let_442 _let_441 _let_440 _let_439 _let_438 _let_437 _let_436 _let_435 _let_434 _let_433 _let_432 _let_431 _let_430 _let_429 _let_428 _let_427 _let_426 _let_425 _let_424 _let_423 _let_422 _let_421 _let_420 _let_419 _let_418 _let_417 _let_416 _let_415 _let_414 _let_413 _let_412 _let_411 _let_410 _let_409 _let_408 _let_407 _let_406 _let_405 _let_404 _let_403 _let_402 _let_401 _let_400 _let_399 _let_398 _let_397 _let_396 _let_395 _let_394 _let_393 _let_392 _let_391 _let_390 _let_389 _let_388 _let_387 _let_386 _let_385 _let_384 _let_383 _let_382 _let_381 _let_380 _let_379 _let_378 _let_377 _let_376 _let_375 _let_374 _let_373 _let_372 _let_371 _let_370 _let_369 _let_368 _let_367 _let_366 _let_365 _let_364 _let_363 _let_362 _let_361 _let_359 _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) :args ((= top_to4366644338036079209nt_int (@ collec213857154873943460nt_int (@ produc4947309494688390418_int_o (lambda ((BOUND_VARIABLE_153233 int) (BOUND_VARIABLE_153235 int)) true)))) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_527 (EQ_RESOLVE (AND_ELIM _let_525 :args _let_360) (MACRO_SR_EQ_INTRO (AND_INTRO _let_526 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_510 _let_508 _let_507 _let_506 _let_505 _let_504 _let_503 _let_502 _let_501 _let_500 _let_499 _let_498 _let_497 _let_496 _let_495 _let_494 _let_491 _let_490 _let_489 _let_488 _let_487 _let_486 _let_485 _let_484 _let_483 _let_482 _let_481 _let_480 _let_479 _let_478 _let_477 _let_476 _let_475 _let_474 _let_473 _let_472 _let_471 _let_470 _let_469 _let_468 _let_467 _let_466 _let_465 _let_464 _let_463 _let_462 _let_461 _let_460 _let_459 _let_458 _let_457 _let_456 _let_455 _let_454 _let_453 _let_452 _let_451 _let_450 _let_449 _let_448 _let_447 _let_446 _let_445 _let_444 _let_443 _let_442 _let_441 _let_440 _let_439 _let_438 _let_437 _let_436 _let_435 _let_434 _let_433 _let_432 _let_431 _let_430 _let_429 _let_428 _let_427 _let_426 _let_425 _let_424 _let_423 _let_422 _let_421 _let_420 _let_419 _let_418 _let_417 _let_416 _let_415 _let_414 _let_413 _let_412 _let_411 _let_410 _let_409 _let_408 _let_407 _let_406 _let_405 _let_404 _let_403 _let_402 _let_401 _let_400 _let_399 _let_398 _let_397 _let_396 _let_395 _let_394 _let_393 _let_392 _let_391 _let_390 _let_389 _let_388 _let_387 _let_386 _let_385 _let_384 _let_383 _let_382 _let_381 _let_380 _let_379 _let_378 _let_377 _let_376 _let_375 _let_374 _let_373 _let_372 _let_371 _let_370 _let_369 _let_368 _let_367 _let_366 _let_365 _let_364 _let_363 _let_362 _let_361 _let_359 _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) :args ((= bot_bo1796632182523588997nt_int (@ collec213857154873943460nt_int (@ produc4947309494688390418_int_o (lambda ((BOUND_VARIABLE_170337 int) (BOUND_VARIABLE_170339 int)) false)))) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_528 (EQ_RESOLVE (ASSUME :args (_let_261)) (MACRO_SR_EQ_INTRO :args (_let_261 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_529 (EQ_RESOLVE (ASSUME :args (_let_276)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_528 _let_527 _let_526 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_510 _let_508 _let_507 _let_506 _let_505 _let_504 _let_503 _let_502 _let_501 _let_500 _let_499 _let_498 _let_497 _let_496 _let_495 _let_494 _let_491 _let_490 _let_489 _let_488 _let_487 _let_486 _let_485 _let_484 _let_483 _let_482 _let_481 _let_480 _let_479 _let_478 _let_477 _let_476 _let_475 _let_474 _let_473 _let_472 _let_471 _let_470 _let_469 _let_468 _let_467 _let_466 _let_465 _let_464 _let_463 _let_462 _let_461 _let_460 _let_459 _let_458 _let_457 _let_456 _let_455 _let_454 _let_453 _let_452 _let_451 _let_450 _let_449 _let_448 _let_447 _let_446 _let_445 _let_444 _let_443 _let_442 _let_441 _let_440 _let_439 _let_438 _let_437 _let_436 _let_435 _let_434 _let_433 _let_432 _let_431 _let_430 _let_429 _let_428 _let_427 _let_426 _let_425 _let_424 _let_423 _let_422 _let_421 _let_420 _let_419 _let_418 _let_417 _let_416 _let_415 _let_414 _let_413 _let_412 _let_411 _let_410 _let_409 _let_408 _let_407 _let_406 _let_405 _let_404 _let_403 _let_402 _let_401 _let_400 _let_399 _let_398 _let_397 _let_396 _let_395 _let_394 _let_393 _let_392 _let_391 _let_390 _let_389 _let_388 _let_387 _let_386 _let_385 _let_384 _let_383 _let_382 _let_381 _let_380 _let_379 _let_378 _let_377 _let_376 _let_375 _let_374 _let_373 _let_372 _let_371 _let_370 _let_369 _let_368 _let_367 _let_366 _let_365 _let_364 _let_363 _let_362 _let_361 _let_359 _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) :args (_let_276 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_530 (EQ_RESOLVE (ASSUME :args (_let_8)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_529 _let_528 _let_527 _let_526 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_510 _let_508 _let_507 _let_506 _let_505 _let_504 _let_503 _let_502 _let_501 _let_500 _let_499 _let_498 _let_497 _let_496 _let_495 _let_494 _let_491 _let_490 _let_489 _let_488 _let_487 _let_486 _let_485 _let_484 _let_483 _let_482 _let_481 _let_480 _let_479 _let_478 _let_477 _let_476 _let_475 _let_474 _let_473 _let_472 _let_471 _let_470 _let_469 _let_468 _let_467 _let_466 _let_465 _let_464 _let_463 _let_462 _let_461 _let_460 _let_459 _let_458 _let_457 _let_456 _let_455 _let_454 _let_453 _let_452 _let_451 _let_450 _let_449 _let_448 _let_447 _let_446 _let_445 _let_444 _let_443 _let_442 _let_441 _let_440 _let_439 _let_438 _let_437 _let_436 _let_435 _let_434 _let_433 _let_432 _let_431 _let_430 _let_429 _let_428 _let_427 _let_426 _let_425 _let_424 _let_423 _let_422 _let_421 _let_420 _let_419 _let_418 _let_417 _let_416 _let_415 _let_414 _let_413 _let_412 _let_411 _let_410 _let_409 _let_408 _let_407 _let_406 _let_405 _let_404 _let_403 _let_402 _let_401 _let_400 _let_399 _let_398 _let_397 _let_396 _let_395 _let_394 _let_393 _let_392 _let_391 _let_390 _let_389 _let_388 _let_387 _let_386 _let_385 _let_384 _let_383 _let_382 _let_381 _let_380 _let_379 _let_378 _let_377 _let_376 _let_375 _let_374 _let_373 _let_372 _let_371 _let_370 _let_369 _let_368 _let_367 _let_366 _let_365 _let_364 _let_363 _let_362 _let_361 _let_359 _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) :args (_let_8 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_531 (EQ_RESOLVE (ASSUME :args (_let_104)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_530 _let_529 _let_528 _let_527 _let_526 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_510 _let_508 _let_507 _let_506 _let_505 _let_504 _let_503 _let_502 _let_501 _let_500 _let_499 _let_498 _let_497 _let_496 _let_495 _let_494 _let_491 _let_490 _let_489 _let_488 _let_487 _let_486 _let_485 _let_484 _let_483 _let_482 _let_481 _let_480 _let_479 _let_478 _let_477 _let_476 _let_475 _let_474 _let_473 _let_472 _let_471 _let_470 _let_469 _let_468 _let_467 _let_466 _let_465 _let_464 _let_463 _let_462 _let_461 _let_460 _let_459 _let_458 _let_457 _let_456 _let_455 _let_454 _let_453 _let_452 _let_451 _let_450 _let_449 _let_448 _let_447 _let_446 _let_445 _let_444 _let_443 _let_442 _let_441 _let_440 _let_439 _let_438 _let_437 _let_436 _let_435 _let_434 _let_433 _let_432 _let_431 _let_430 _let_429 _let_428 _let_427 _let_426 _let_425 _let_424 _let_423 _let_422 _let_421 _let_420 _let_419 _let_418 _let_417 _let_416 _let_415 _let_414 _let_413 _let_412 _let_411 _let_410 _let_409 _let_408 _let_407 _let_406 _let_405 _let_404 _let_403 _let_402 _let_401 _let_400 _let_399 _let_398 _let_397 _let_396 _let_395 _let_394 _let_393 _let_392 _let_391 _let_390 _let_389 _let_388 _let_387 _let_386 _let_385 _let_384 _let_383 _let_382 _let_381 _let_380 _let_379 _let_378 _let_377 _let_376 _let_375 _let_374 _let_373 _let_372 _let_371 _let_370 _let_369 _let_368 _let_367 _let_366 _let_365 _let_364 _let_363 _let_362 _let_361 _let_359 _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) :args (_let_104 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_532 (EQ_RESOLVE (ASSUME :args (_let_277)) (MACRO_SR_EQ_INTRO :args (_let_277 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_533 (EQ_RESOLVE (ASSUME :args (_let_68)) (TRUST_SUBS_MAP (AND_INTRO _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_510 _let_508 _let_507 _let_506 _let_505 _let_504 _let_503 _let_502 _let_501 _let_500 _let_499 _let_498 _let_497 _let_496 _let_495 _let_494 _let_491 _let_490 _let_489 _let_488 _let_487 _let_486 _let_485 _let_484 _let_483 _let_482 _let_481 _let_480 _let_479 _let_478 _let_477 _let_476 _let_475 _let_474 _let_473 _let_472 _let_471 _let_470 _let_469 _let_468 _let_467 _let_466 _let_465 _let_464 _let_463 _let_462 _let_461 _let_460 _let_459 _let_458 _let_457 _let_456 _let_455 _let_454 _let_453 _let_452 _let_451 _let_450 _let_449 _let_448 _let_447 _let_446 _let_445 _let_444 _let_443 _let_442 _let_441 _let_440 _let_439 _let_438 _let_437 _let_436 _let_435 _let_434 _let_433 _let_432 _let_431 _let_430 _let_429 _let_428 _let_427 _let_426 _let_425 _let_424 _let_423 _let_422 _let_421 _let_420 _let_419 _let_418 _let_417 _let_416 _let_415 _let_414 _let_413 _let_412 _let_411 _let_410 _let_409 _let_408 _let_407 _let_406 _let_405 _let_404 _let_403 _let_402 _let_401 _let_400 _let_399 _let_398 _let_397 _let_396 _let_395 _let_394 _let_393 _let_392 _let_391 _let_390 _let_389 _let_388 _let_387 _let_386 _let_385 _let_384 _let_383 _let_382 _let_381 _let_380 _let_379 _let_378 _let_377 _let_376 _let_375 _let_374 _let_373 _let_372 _let_371 _let_370 _let_369 _let_368 _let_367 _let_366 _let_365 _let_364 _let_363 _let_362 _let_361 _let_359 _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) :args ((= _let_68 (= produc929334515565554804at_nat (lambda ((A6 set_nat) (B6 set_nat)) (@ comple5685304695842803022at_nat (@ (@ image_7178329752028323786at_nat (lambda ((BOUND_VARIABLE_172998 nat)) (@ comple5685304695842803022at_nat (@ (@ image_7178329752028323786at_nat (lambda ((BOUND_VARIABLE_173000 nat)) (@ (@ insert8211810215607154385at_nat (@ (@ product_Pair_nat_nat BOUND_VARIABLE_172998) BOUND_VARIABLE_173000)) (@ collec3392354462482085612at_nat (@ produc6081775807080527818_nat_o (lambda ((BOUND_VARIABLE_259197 nat) (BOUND_VARIABLE_259199 nat)) false)))))) B6)))) A6)))))))))) (let ((_let_534 (EQ_RESOLVE (ASSUME :args (_let_278)) (TRUST_SUBS_MAP (AND_INTRO _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_510 _let_508 _let_507 _let_506 _let_505 _let_504 _let_503 _let_502 _let_501 _let_500 _let_499 _let_498 _let_497 _let_496 _let_495 _let_494 _let_491 _let_490 _let_489 _let_488 _let_487 _let_486 _let_485 _let_484 _let_483 _let_482 _let_481 _let_480 _let_479 _let_478 _let_477 _let_476 _let_475 _let_474 _let_473 _let_472 _let_471 _let_470 _let_469 _let_468 _let_467 _let_466 _let_465 _let_464 _let_463 _let_462 _let_461 _let_460 _let_459 _let_458 _let_457 _let_456 _let_455 _let_454 _let_453 _let_452 _let_451 _let_450 _let_449 _let_448 _let_447 _let_446 _let_445 _let_444 _let_443 _let_442 _let_441 _let_440 _let_439 _let_438 _let_437 _let_436 _let_435 _let_434 _let_433 _let_432 _let_431 _let_430 _let_429 _let_428 _let_427 _let_426 _let_425 _let_424 _let_423 _let_422 _let_421 _let_420 _let_419 _let_418 _let_417 _let_416 _let_415 _let_414 _let_413 _let_412 _let_411 _let_410 _let_409 _let_408 _let_407 _let_406 _let_405 _let_404 _let_403 _let_402 _let_401 _let_400 _let_399 _let_398 _let_397 _let_396 _let_395 _let_394 _let_393 _let_392 _let_391 _let_390 _let_389 _let_388 _let_387 _let_386 _let_385 _let_384 _let_383 _let_382 _let_381 _let_380 _let_379 _let_378 _let_377 _let_376 _let_375 _let_374 _let_373 _let_372 _let_371 _let_370 _let_369 _let_368 _let_367 _let_366 _let_365 _let_364 _let_363 _let_362 _let_361 _let_359 _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) :args ((= _let_278 (= ord_less_eq_rat (lambda ((P3 rat) (Q3 rat)) (@ (@ produc6081775807080527818_nat_o (lambda ((BOUND_VARIABLE_173323 nat) (BOUND_VARIABLE_173324 nat)) (@ (@ produc6081775807080527818_nat_o (lambda ((BOUND_VARIABLE_173334 nat) (BOUND_VARIABLE_173335 nat)) (@ (@ ord_less_eq_nat (@ (@ plus_plus_nat BOUND_VARIABLE_173323) BOUND_VARIABLE_173335)) (@ (@ plus_plus_nat BOUND_VARIABLE_173334) BOUND_VARIABLE_173324)))) (@ rep_Integ (@ (@ times_times_int (@ (@ produc8211389475949308722nt_int (lambda ((BOUND_VARIABLE_173325 int) (BOUND_VARIABLE_173326 int)) BOUND_VARIABLE_173326)) (@ quotient_of P3))) (@ product_fst_int_int (@ quotient_of Q3))))))) (@ rep_Integ (@ (@ times_times_int (@ product_fst_int_int (@ quotient_of P3))) (@ (@ produc8211389475949308722nt_int (lambda ((BOUND_VARIABLE_173313 int) (BOUND_VARIABLE_173314 int)) BOUND_VARIABLE_173314)) (@ quotient_of Q3))))))))))))) (let ((_let_535 (EQ_RESOLVE (ASSUME :args (_let_279)) (TRUST_SUBS_MAP (AND_INTRO _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_510 _let_508 _let_507 _let_506 _let_505 _let_504 _let_503 _let_502 _let_501 _let_500 _let_499 _let_498 _let_497 _let_496 _let_495 _let_494 _let_491 _let_490 _let_489 _let_488 _let_487 _let_486 _let_485 _let_484 _let_483 _let_482 _let_481 _let_480 _let_479 _let_478 _let_477 _let_476 _let_475 _let_474 _let_473 _let_472 _let_471 _let_470 _let_469 _let_468 _let_467 _let_466 _let_465 _let_464 _let_463 _let_462 _let_461 _let_460 _let_459 _let_458 _let_457 _let_456 _let_455 _let_454 _let_453 _let_452 _let_451 _let_450 _let_449 _let_448 _let_447 _let_446 _let_445 _let_444 _let_443 _let_442 _let_441 _let_440 _let_439 _let_438 _let_437 _let_436 _let_435 _let_434 _let_433 _let_432 _let_431 _let_430 _let_429 _let_428 _let_427 _let_426 _let_425 _let_424 _let_423 _let_422 _let_421 _let_420 _let_419 _let_418 _let_417 _let_416 _let_415 _let_414 _let_413 _let_412 _let_411 _let_410 _let_409 _let_408 _let_407 _let_406 _let_405 _let_404 _let_403 _let_402 _let_401 _let_400 _let_399 _let_398 _let_397 _let_396 _let_395 _let_394 _let_393 _let_392 _let_391 _let_390 _let_389 _let_388 _let_387 _let_386 _let_385 _let_384 _let_383 _let_382 _let_381 _let_380 _let_379 _let_378 _let_377 _let_376 _let_375 _let_374 _let_373 _let_372 _let_371 _let_370 _let_369 _let_368 _let_367 _let_366 _let_365 _let_364 _let_363 _let_362 _let_361 _let_359 _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) :args ((= _let_279 (= times_times_int (@ _let_96 (lambda ((BOUND_VARIABLE_173364 product_prod_nat_nat) (BOUND_VARIABLE_173365 product_prod_nat_nat)) (@ (@ produc2626176000494625587at_nat (lambda ((BOUND_VARIABLE_173447 nat) (BOUND_VARIABLE_173448 nat)) (let ((_let_1 (@ times_times_nat (@ product_snd_nat_nat BOUND_VARIABLE_173364)))) (let ((_let_2 (@ times_times_nat (@ (@ (@ comp_P1567445206330693457at_nat product_snd_nat_nat) (@ produc2626176000494625587at_nat (lambda ((BOUND_VARIABLE_173450 nat) (BOUND_VARIABLE_173451 nat)) (@ (@ product_Pair_nat_nat BOUND_VARIABLE_173451) BOUND_VARIABLE_173450)))) BOUND_VARIABLE_173364)))) (@ (@ product_Pair_nat_nat (@ (@ plus_plus_nat (@ _let_2 BOUND_VARIABLE_173447)) (@ _let_1 BOUND_VARIABLE_173448))) (@ (@ plus_plus_nat (@ _let_2 BOUND_VARIABLE_173448)) (@ _let_1 BOUND_VARIABLE_173447))))))) BOUND_VARIABLE_173365)))))))))) (let ((_let_536 (EQ_RESOLVE (SYMM (ASSUME :args (_let_281))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_510 _let_508 _let_507 _let_506 _let_505 _let_504 _let_503 _let_502 _let_501 _let_500 _let_499 _let_498 _let_497 _let_496 _let_495 _let_494 _let_491 _let_490 _let_489 _let_488 _let_487 _let_486 _let_485 _let_484 _let_483 _let_482 _let_481 _let_480 _let_479 _let_478 _let_477 _let_476 _let_475 _let_474 _let_473 _let_472 _let_471 _let_470 _let_469 _let_468 _let_467 _let_466 _let_465 _let_464 _let_463 _let_462 _let_461 _let_460 _let_459 _let_458 _let_457 _let_456 _let_455 _let_454 _let_453 _let_452 _let_451 _let_450 _let_449 _let_448 _let_447 _let_446 _let_445 _let_444 _let_443 _let_442 _let_441 _let_440 _let_439 _let_438 _let_437 _let_436 _let_435 _let_434 _let_433 _let_432 _let_431 _let_430 _let_429 _let_428 _let_427 _let_426 _let_425 _let_424 _let_423 _let_422 _let_421 _let_420 _let_419 _let_418 _let_417 _let_416 _let_415 _let_414 _let_413 _let_412 _let_411 _let_410 _let_409 _let_408 _let_407 _let_406 _let_405 _let_404 _let_403 _let_402 _let_401 _let_400 _let_399 _let_398 _let_397 _let_396 _let_395 _let_394 _let_393 _let_392 _let_391 _let_390 _let_389 _let_388 _let_387 _let_386 _let_385 _let_384 _let_383 _let_382 _let_381 _let_380 _let_379 _let_378 _let_377 _let_376 _let_375 _let_374 _let_373 _let_372 _let_371 _let_370 _let_369 _let_368 _let_367 _let_366 _let_365 _let_364 _let_363 _let_362 _let_361 _let_359 _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) :args ((= top_to269121717765781945at_nat _let_280) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_537 (ASSUME :args (_let_254)))) (let ((_let_538 (EQ_RESOLVE (SYMM (ASSUME :args (_let_243))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_510 _let_508 _let_507 _let_506 _let_505 _let_504 _let_503 _let_502 _let_501 _let_500 _let_499 _let_498 _let_497 _let_496 _let_495 _let_494 _let_491 _let_490 _let_489 _let_488 _let_487 _let_486 _let_485 _let_484 _let_483 _let_482 _let_481 _let_480 _let_479 _let_478 _let_477 _let_476 _let_475 _let_474 _let_473 _let_472 _let_471 _let_470 _let_469 _let_468 _let_467 _let_466 _let_465 _let_464 _let_463 _let_462 _let_461 _let_460 _let_459 _let_458 _let_457 _let_456 _let_455 _let_454 _let_453 _let_452 _let_451 _let_450 _let_449 _let_448 _let_447 _let_446 _let_445 _let_444 _let_443 _let_442 _let_441 _let_440 _let_439 _let_438 _let_437 _let_436 _let_435 _let_434 _let_433 _let_432 _let_431 _let_430 _let_429 _let_428 _let_427 _let_426 _let_425 _let_424 _let_423 _let_422 _let_421 _let_420 _let_419 _let_418 _let_417 _let_416 _let_415 _let_414 _let_413 _let_412 _let_411 _let_410 _let_409 _let_408 _let_407 _let_406 _let_405 _let_404 _let_403 _let_402 _let_401 _let_400 _let_399 _let_398 _let_397 _let_396 _let_395 _let_394 _let_393 _let_392 _let_391 _let_390 _let_389 _let_388 _let_387 _let_386 _let_385 _let_384 _let_383 _let_382 _let_381 _let_380 _let_379 _let_378 _let_377 _let_376 _let_375 _let_374 _let_373 _let_372 _let_371 _let_370 _let_369 _let_368 _let_367 _let_366 _let_365 _let_364 _let_363 _let_362 _let_361 _let_359 _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) :args ((= top_to7107842681480589234t_char _let_242) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_539 (EQ_RESOLVE (ASSUME :args (_let_284)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_510 _let_508 _let_507 _let_506 _let_505 _let_504 _let_503 _let_502 _let_501 _let_500 _let_499 _let_498 _let_497 _let_496 _let_495 _let_494 _let_491 _let_490 _let_489 _let_488 _let_487 _let_486 _let_485 _let_484 _let_483 _let_482 _let_481 _let_480 _let_479 _let_478 _let_477 _let_476 _let_475 _let_474 _let_473 _let_472 _let_471 _let_470 _let_469 _let_468 _let_467 _let_466 _let_465 _let_464 _let_463 _let_462 _let_461 _let_460 _let_459 _let_458 _let_457 _let_456 _let_455 _let_454 _let_453 _let_452 _let_451 _let_450 _let_449 _let_448 _let_447 _let_446 _let_445 _let_444 _let_443 _let_442 _let_441 _let_440 _let_439 _let_438 _let_437 _let_436 _let_435 _let_434 _let_433 _let_432 _let_431 _let_430 _let_429 _let_428 _let_427 _let_426 _let_425 _let_424 _let_423 _let_422 _let_421 _let_420 _let_419 _let_418 _let_417 _let_416 _let_415 _let_414 _let_413 _let_412 _let_411 _let_410 _let_409 _let_408 _let_407 _let_406 _let_405 _let_404 _let_403 _let_402 _let_401 _let_400 _let_399 _let_398 _let_397 _let_396 _let_395 _let_394 _let_393 _let_392 _let_391 _let_390 _let_389 _let_388 _let_387 _let_386 _let_385 _let_384 _let_383 _let_382 _let_381 _let_380 _let_379 _let_378 _let_377 _let_376 _let_375 _let_374 _let_373 _let_372 _let_371 _let_370 _let_369 _let_368 _let_367 _let_366 _let_365 _let_364 _let_363 _let_362 _let_361 _let_359 _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) :args (_let_284 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_540 (ASSUME :args (_let_159)))) (let ((_let_541 (EQ_RESOLVE (ASSUME :args (_let_57)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_540 _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_510 _let_508 _let_507 _let_506 _let_505 _let_504 _let_503 _let_502 _let_501 _let_500 _let_499 _let_498 _let_497 _let_496 _let_495 _let_494 _let_491 _let_490 _let_489 _let_488 _let_487 _let_486 _let_485 _let_484 _let_483 _let_482 _let_481 _let_480 _let_479 _let_478 _let_477 _let_476 _let_475 _let_474 _let_473 _let_472 _let_471 _let_470 _let_469 _let_468 _let_467 _let_466 _let_465 _let_464 _let_463 _let_462 _let_461 _let_460 _let_459 _let_458 _let_457 _let_456 _let_455 _let_454 _let_453 _let_452 _let_451 _let_450 _let_449 _let_448 _let_447 _let_446 _let_445 _let_444 _let_443 _let_442 _let_441 _let_440 _let_439 _let_438 _let_437 _let_436 _let_435 _let_434 _let_433 _let_432 _let_431 _let_430 _let_429 _let_428 _let_427 _let_426 _let_425 _let_424 _let_423 _let_422 _let_421 _let_420 _let_419 _let_418 _let_417 _let_416 _let_415 _let_414 _let_413 _let_412 _let_411 _let_410 _let_409 _let_408 _let_407 _let_406 _let_405 _let_404 _let_403 _let_402 _let_401 _let_400 _let_399 _let_398 _let_397 _let_396 _let_395 _let_394 _let_393 _let_392 _let_391 _let_390 _let_389 _let_388 _let_387 _let_386 _let_385 _let_384 _let_383 _let_382 _let_381 _let_380 _let_379 _let_378 _let_377 _let_376 _let_375 _let_374 _let_373 _let_372 _let_371 _let_370 _let_369 _let_368 _let_367 _let_366 _let_365 _let_364 _let_363 _let_362 _let_361 _let_359 _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) :args (_let_57 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_542 (EQ_RESOLVE (SYMM (ASSUME :args (_let_260))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_541 _let_540 _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_510 _let_508 _let_507 _let_506 _let_505 _let_504 _let_503 _let_502 _let_501 _let_500 _let_499 _let_498 _let_497 _let_496 _let_495 _let_494 _let_491 _let_490 _let_489 _let_488 _let_487 _let_486 _let_485 _let_484 _let_483 _let_482 _let_481 _let_480 _let_479 _let_478 _let_477 _let_476 _let_475 _let_474 _let_473 _let_472 _let_471 _let_470 _let_469 _let_468 _let_467 _let_466 _let_465 _let_464 _let_463 _let_462 _let_461 _let_460 _let_459 _let_458 _let_457 _let_456 _let_455 _let_454 _let_453 _let_452 _let_451 _let_450 _let_449 _let_448 _let_447 _let_446 _let_445 _let_444 _let_443 _let_442 _let_441 _let_440 _let_439 _let_438 _let_437 _let_436 _let_435 _let_434 _let_433 _let_432 _let_431 _let_430 _let_429 _let_428 _let_427 _let_426 _let_425 _let_424 _let_423 _let_422 _let_421 _let_420 _let_419 _let_418 _let_417 _let_416 _let_415 _let_414 _let_413 _let_412 _let_411 _let_410 _let_409 _let_408 _let_407 _let_406 _let_405 _let_404 _let_403 _let_402 _let_401 _let_400 _let_399 _let_398 _let_397 _let_396 _let_395 _let_394 _let_393 _let_392 _let_391 _let_390 _let_389 _let_388 _let_387 _let_386 _let_385 _let_384 _let_383 _let_382 _let_381 _let_380 _let_379 _let_378 _let_377 _let_376 _let_375 _let_374 _let_373 _let_372 _let_371 _let_370 _let_369 _let_368 _let_367 _let_366 _let_365 _let_364 _let_363 _let_362 _let_361 _let_359 _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) :args ((= top_to6661820994512907621at_nat _let_259) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_543 (ASSUME :args (_let_285)))) (let ((_let_544 (EQ_RESOLVE (ASSUME :args (_let_286)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_543 _let_542 _let_541 _let_540 _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_510 _let_508 _let_507 _let_506 _let_505 _let_504 _let_503 _let_502 _let_501 _let_500 _let_499 _let_498 _let_497 _let_496 _let_495 _let_494 _let_491 _let_490 _let_489 _let_488 _let_487 _let_486 _let_485 _let_484 _let_483 _let_482 _let_481 _let_480 _let_479 _let_478 _let_477 _let_476 _let_475 _let_474 _let_473 _let_472 _let_471 _let_470 _let_469 _let_468 _let_467 _let_466 _let_465 _let_464 _let_463 _let_462 _let_461 _let_460 _let_459 _let_458 _let_457 _let_456 _let_455 _let_454 _let_453 _let_452 _let_451 _let_450 _let_449 _let_448 _let_447 _let_446 _let_445 _let_444 _let_443 _let_442 _let_441 _let_440 _let_439 _let_438 _let_437 _let_436 _let_435 _let_434 _let_433 _let_432 _let_431 _let_430 _let_429 _let_428 _let_427 _let_426 _let_425 _let_424 _let_423 _let_422 _let_421 _let_420 _let_419 _let_418 _let_417 _let_416 _let_415 _let_414 _let_413 _let_412 _let_411 _let_410 _let_409 _let_408 _let_407 _let_406 _let_405 _let_404 _let_403 _let_402 _let_401 _let_400 _let_399 _let_398 _let_397 _let_396 _let_395 _let_394 _let_393 _let_392 _let_391 _let_390 _let_389 _let_388 _let_387 _let_386 _let_385 _let_384 _let_383 _let_382 _let_381 _let_380 _let_379 _let_378 _let_377 _let_376 _let_375 _let_374 _let_373 _let_372 _let_371 _let_370 _let_369 _let_368 _let_367 _let_366 _let_365 _let_364 _let_363 _let_362 _let_361 _let_359 _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) :args (_let_286 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_545 (EQ_RESOLVE (ASSUME :args (_let_287)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_544 _let_543 _let_542 _let_541 _let_540 _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_510 _let_508 _let_507 _let_506 _let_505 _let_504 _let_503 _let_502 _let_501 _let_500 _let_499 _let_498 _let_497 _let_496 _let_495 _let_494 _let_491 _let_490 _let_489 _let_488 _let_487 _let_486 _let_485 _let_484 _let_483 _let_482 _let_481 _let_480 _let_479 _let_478 _let_477 _let_476 _let_475 _let_474 _let_473 _let_472 _let_471 _let_470 _let_469 _let_468 _let_467 _let_466 _let_465 _let_464 _let_463 _let_462 _let_461 _let_460 _let_459 _let_458 _let_457 _let_456 _let_455 _let_454 _let_453 _let_452 _let_451 _let_450 _let_449 _let_448 _let_447 _let_446 _let_445 _let_444 _let_443 _let_442 _let_441 _let_440 _let_439 _let_438 _let_437 _let_436 _let_435 _let_434 _let_433 _let_432 _let_431 _let_430 _let_429 _let_428 _let_427 _let_426 _let_425 _let_424 _let_423 _let_422 _let_421 _let_420 _let_419 _let_418 _let_417 _let_416 _let_415 _let_414 _let_413 _let_412 _let_411 _let_410 _let_409 _let_408 _let_407 _let_406 _let_405 _let_404 _let_403 _let_402 _let_401 _let_400 _let_399 _let_398 _let_397 _let_396 _let_395 _let_394 _let_393 _let_392 _let_391 _let_390 _let_389 _let_388 _let_387 _let_386 _let_385 _let_384 _let_383 _let_382 _let_381 _let_380 _let_379 _let_378 _let_377 _let_376 _let_375 _let_374 _let_373 _let_372 _let_371 _let_370 _let_369 _let_368 _let_367 _let_366 _let_365 _let_364 _let_363 _let_362 _let_361 _let_359 _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) :args (_let_287 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_546 (EQ_RESOLVE (ASSUME :args (_let_66)) (MACRO_SR_EQ_INTRO :args (_let_66 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_547 (ASSUME :args (_let_228)))) (let ((_let_548 (EQ_RESOLVE (ASSUME :args (_let_223)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_547 _let_546 _let_545 _let_544 _let_543 _let_542 _let_541 _let_540 _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_510 _let_508 _let_507 _let_506 _let_505 _let_504 _let_503 _let_502 _let_501 _let_500 _let_499 _let_498 _let_497 _let_496 _let_495 _let_494 _let_491 _let_490 _let_489 _let_488 _let_487 _let_486 _let_485 _let_484 _let_483 _let_482 _let_481 _let_480 _let_479 _let_478 _let_477 _let_476 _let_475 _let_474 _let_473 _let_472 _let_471 _let_470 _let_469 _let_468 _let_467 _let_466 _let_465 _let_464 _let_463 _let_462 _let_461 _let_460 _let_459 _let_458 _let_457 _let_456 _let_455 _let_454 _let_453 _let_452 _let_451 _let_450 _let_449 _let_448 _let_447 _let_446 _let_445 _let_444 _let_443 _let_442 _let_441 _let_440 _let_439 _let_438 _let_437 _let_436 _let_435 _let_434 _let_433 _let_432 _let_431 _let_430 _let_429 _let_428 _let_427 _let_426 _let_425 _let_424 _let_423 _let_422 _let_421 _let_420 _let_419 _let_418 _let_417 _let_416 _let_415 _let_414 _let_413 _let_412 _let_411 _let_410 _let_409 _let_408 _let_407 _let_406 _let_405 _let_404 _let_403 _let_402 _let_401 _let_400 _let_399 _let_398 _let_397 _let_396 _let_395 _let_394 _let_393 _let_392 _let_391 _let_390 _let_389 _let_388 _let_387 _let_386 _let_385 _let_384 _let_383 _let_382 _let_381 _let_380 _let_379 _let_378 _let_377 _let_376 _let_375 _let_374 _let_373 _let_372 _let_371 _let_370 _let_369 _let_368 _let_367 _let_366 _let_365 _let_364 _let_363 _let_362 _let_361 _let_359 _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) :args (_let_223 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_549 (EQ_RESOLVE (ASSUME :args (_let_288)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_548 _let_547 _let_546 _let_545 _let_544 _let_543 _let_542 _let_541 _let_540 _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_510 _let_508 _let_507 _let_506 _let_505 _let_504 _let_503 _let_502 _let_501 _let_500 _let_499 _let_498 _let_497 _let_496 _let_495 _let_494 _let_491 _let_490 _let_489 _let_488 _let_487 _let_486 _let_485 _let_484 _let_483 _let_482 _let_481 _let_480 _let_479 _let_478 _let_477 _let_476 _let_475 _let_474 _let_473 _let_472 _let_471 _let_470 _let_469 _let_468 _let_467 _let_466 _let_465 _let_464 _let_463 _let_462 _let_461 _let_460 _let_459 _let_458 _let_457 _let_456 _let_455 _let_454 _let_453 _let_452 _let_451 _let_450 _let_449 _let_448 _let_447 _let_446 _let_445 _let_444 _let_443 _let_442 _let_441 _let_440 _let_439 _let_438 _let_437 _let_436 _let_435 _let_434 _let_433 _let_432 _let_431 _let_430 _let_429 _let_428 _let_427 _let_426 _let_425 _let_424 _let_423 _let_422 _let_421 _let_420 _let_419 _let_418 _let_417 _let_416 _let_415 _let_414 _let_413 _let_412 _let_411 _let_410 _let_409 _let_408 _let_407 _let_406 _let_405 _let_404 _let_403 _let_402 _let_401 _let_400 _let_399 _let_398 _let_397 _let_396 _let_395 _let_394 _let_393 _let_392 _let_391 _let_390 _let_389 _let_388 _let_387 _let_386 _let_385 _let_384 _let_383 _let_382 _let_381 _let_380 _let_379 _let_378 _let_377 _let_376 _let_375 _let_374 _let_373 _let_372 _let_371 _let_370 _let_369 _let_368 _let_367 _let_366 _let_365 _let_364 _let_363 _let_362 _let_361 _let_359 _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) :args (_let_288 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_550 (EQ_RESOLVE (ASSUME :args (_let_289)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_549 _let_548 _let_547 _let_546 _let_545 _let_544 _let_543 _let_542 _let_541 _let_540 _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_510 _let_508 _let_507 _let_506 _let_505 _let_504 _let_503 _let_502 _let_501 _let_500 _let_499 _let_498 _let_497 _let_496 _let_495 _let_494 _let_491 _let_490 _let_489 _let_488 _let_487 _let_486 _let_485 _let_484 _let_483 _let_482 _let_481 _let_480 _let_479 _let_478 _let_477 _let_476 _let_475 _let_474 _let_473 _let_472 _let_471 _let_470 _let_469 _let_468 _let_467 _let_466 _let_465 _let_464 _let_463 _let_462 _let_461 _let_460 _let_459 _let_458 _let_457 _let_456 _let_455 _let_454 _let_453 _let_452 _let_451 _let_450 _let_449 _let_448 _let_447 _let_446 _let_445 _let_444 _let_443 _let_442 _let_441 _let_440 _let_439 _let_438 _let_437 _let_436 _let_435 _let_434 _let_433 _let_432 _let_431 _let_430 _let_429 _let_428 _let_427 _let_426 _let_425 _let_424 _let_423 _let_422 _let_421 _let_420 _let_419 _let_418 _let_417 _let_416 _let_415 _let_414 _let_413 _let_412 _let_411 _let_410 _let_409 _let_408 _let_407 _let_406 _let_405 _let_404 _let_403 _let_402 _let_401 _let_400 _let_399 _let_398 _let_397 _let_396 _let_395 _let_394 _let_393 _let_392 _let_391 _let_390 _let_389 _let_388 _let_387 _let_386 _let_385 _let_384 _let_383 _let_382 _let_381 _let_380 _let_379 _let_378 _let_377 _let_376 _let_375 _let_374 _let_373 _let_372 _let_371 _let_370 _let_369 _let_368 _let_367 _let_366 _let_365 _let_364 _let_363 _let_362 _let_361 _let_359 _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) :args (_let_289 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_551 (EQ_RESOLVE (ASSUME :args (_let_151)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_550 _let_549 _let_548 _let_547 _let_546 _let_545 _let_544 _let_543 _let_542 _let_541 _let_540 _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_510 _let_508 _let_507 _let_506 _let_505 _let_504 _let_503 _let_502 _let_501 _let_500 _let_499 _let_498 _let_497 _let_496 _let_495 _let_494 _let_491 _let_490 _let_489 _let_488 _let_487 _let_486 _let_485 _let_484 _let_483 _let_482 _let_481 _let_480 _let_479 _let_478 _let_477 _let_476 _let_475 _let_474 _let_473 _let_472 _let_471 _let_470 _let_469 _let_468 _let_467 _let_466 _let_465 _let_464 _let_463 _let_462 _let_461 _let_460 _let_459 _let_458 _let_457 _let_456 _let_455 _let_454 _let_453 _let_452 _let_451 _let_450 _let_449 _let_448 _let_447 _let_446 _let_445 _let_444 _let_443 _let_442 _let_441 _let_440 _let_439 _let_438 _let_437 _let_436 _let_435 _let_434 _let_433 _let_432 _let_431 _let_430 _let_429 _let_428 _let_427 _let_426 _let_425 _let_424 _let_423 _let_422 _let_421 _let_420 _let_419 _let_418 _let_417 _let_416 _let_415 _let_414 _let_413 _let_412 _let_411 _let_410 _let_409 _let_408 _let_407 _let_406 _let_405 _let_404 _let_403 _let_402 _let_401 _let_400 _let_399 _let_398 _let_397 _let_396 _let_395 _let_394 _let_393 _let_392 _let_391 _let_390 _let_389 _let_388 _let_387 _let_386 _let_385 _let_384 _let_383 _let_382 _let_381 _let_380 _let_379 _let_378 _let_377 _let_376 _let_375 _let_374 _let_373 _let_372 _let_371 _let_370 _let_369 _let_368 _let_367 _let_366 _let_365 _let_364 _let_363 _let_362 _let_361 _let_359 _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) :args (_let_151 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_552 (ASSUME :args (_let_290)))) (let ((_let_553 (EQ_RESOLVE (SYMM (ASSUME :args (_let_292))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546 _let_545 _let_544 _let_543 _let_542 _let_541 _let_540 _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_510 _let_508 _let_507 _let_506 _let_505 _let_504 _let_503 _let_502 _let_501 _let_500 _let_499 _let_498 _let_497 _let_496 _let_495 _let_494 _let_491 _let_490 _let_489 _let_488 _let_487 _let_486 _let_485 _let_484 _let_483 _let_482 _let_481 _let_480 _let_479 _let_478 _let_477 _let_476 _let_475 _let_474 _let_473 _let_472 _let_471 _let_470 _let_469 _let_468 _let_467 _let_466 _let_465 _let_464 _let_463 _let_462 _let_461 _let_460 _let_459 _let_458 _let_457 _let_456 _let_455 _let_454 _let_453 _let_452 _let_451 _let_450 _let_449 _let_448 _let_447 _let_446 _let_445 _let_444 _let_443 _let_442 _let_441 _let_440 _let_439 _let_438 _let_437 _let_436 _let_435 _let_434 _let_433 _let_432 _let_431 _let_430 _let_429 _let_428 _let_427 _let_426 _let_425 _let_424 _let_423 _let_422 _let_421 _let_420 _let_419 _let_418 _let_417 _let_416 _let_415 _let_414 _let_413 _let_412 _let_411 _let_410 _let_409 _let_408 _let_407 _let_406 _let_405 _let_404 _let_403 _let_402 _let_401 _let_400 _let_399 _let_398 _let_397 _let_396 _let_395 _let_394 _let_393 _let_392 _let_391 _let_390 _let_389 _let_388 _let_387 _let_386 _let_385 _let_384 _let_383 _let_382 _let_381 _let_380 _let_379 _let_378 _let_377 _let_376 _let_375 _let_374 _let_373 _let_372 _let_371 _let_370 _let_369 _let_368 _let_367 _let_366 _let_365 _let_364 _let_363 _let_362 _let_361 _let_359 _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) :args ((= top_to1235241553633177651r_char _let_291) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_554 (EQ_RESOLVE (ASSUME :args (_let_293)) (MACRO_SR_EQ_INTRO :args (_let_293 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_555 (EQ_RESOLVE (ASSUME :args (_let_295)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546 _let_545 _let_544 _let_543 _let_542 _let_541 _let_540 _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_510 _let_508 _let_507 _let_506 _let_505 _let_504 _let_503 _let_502 _let_501 _let_500 _let_499 _let_498 _let_497 _let_496 _let_495 _let_494 _let_491 _let_490 _let_489 _let_488 _let_487 _let_486 _let_485 _let_484 _let_483 _let_482 _let_481 _let_480 _let_479 _let_478 _let_477 _let_476 _let_475 _let_474 _let_473 _let_472 _let_471 _let_470 _let_469 _let_468 _let_467 _let_466 _let_465 _let_464 _let_463 _let_462 _let_461 _let_460 _let_459 _let_458 _let_457 _let_456 _let_455 _let_454 _let_453 _let_452 _let_451 _let_450 _let_449 _let_448 _let_447 _let_446 _let_445 _let_444 _let_443 _let_442 _let_441 _let_440 _let_439 _let_438 _let_437 _let_436 _let_435 _let_434 _let_433 _let_432 _let_431 _let_430 _let_429 _let_428 _let_427 _let_426 _let_425 _let_424 _let_423 _let_422 _let_421 _let_420 _let_419 _let_418 _let_417 _let_416 _let_415 _let_414 _let_413 _let_412 _let_411 _let_410 _let_409 _let_408 _let_407 _let_406 _let_405 _let_404 _let_403 _let_402 _let_401 _let_400 _let_399 _let_398 _let_397 _let_396 _let_395 _let_394 _let_393 _let_392 _let_391 _let_390 _let_389 _let_388 _let_387 _let_386 _let_385 _let_384 _let_383 _let_382 _let_381 _let_380 _let_379 _let_378 _let_377 _let_376 _let_375 _let_374 _let_373 _let_372 _let_371 _let_370 _let_369 _let_368 _let_367 _let_366 _let_365 _let_364 _let_363 _let_362 _let_361 _let_359 _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) :args (_let_295 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_556 (EQ_RESOLVE (ASSUME :args (_let_208)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546 _let_545 _let_544 _let_543 _let_542 _let_541 _let_540 _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_510 _let_508 _let_507 _let_506 _let_505 _let_504 _let_503 _let_502 _let_501 _let_500 _let_499 _let_498 _let_497 _let_496 _let_495 _let_494 _let_491 _let_490 _let_489 _let_488 _let_487 _let_486 _let_485 _let_484 _let_483 _let_482 _let_481 _let_480 _let_479 _let_478 _let_477 _let_476 _let_475 _let_474 _let_473 _let_472 _let_471 _let_470 _let_469 _let_468 _let_467 _let_466 _let_465 _let_464 _let_463 _let_462 _let_461 _let_460 _let_459 _let_458 _let_457 _let_456 _let_455 _let_454 _let_453 _let_452 _let_451 _let_450 _let_449 _let_448 _let_447 _let_446 _let_445 _let_444 _let_443 _let_442 _let_441 _let_440 _let_439 _let_438 _let_437 _let_436 _let_435 _let_434 _let_433 _let_432 _let_431 _let_430 _let_429 _let_428 _let_427 _let_426 _let_425 _let_424 _let_423 _let_422 _let_421 _let_420 _let_419 _let_418 _let_417 _let_416 _let_415 _let_414 _let_413 _let_412 _let_411 _let_410 _let_409 _let_408 _let_407 _let_406 _let_405 _let_404 _let_403 _let_402 _let_401 _let_400 _let_399 _let_398 _let_397 _let_396 _let_395 _let_394 _let_393 _let_392 _let_391 _let_390 _let_389 _let_388 _let_387 _let_386 _let_385 _let_384 _let_383 _let_382 _let_381 _let_380 _let_379 _let_378 _let_377 _let_376 _let_375 _let_374 _let_373 _let_372 _let_371 _let_370 _let_369 _let_368 _let_367 _let_366 _let_365 _let_364 _let_363 _let_362 _let_361 _let_359 _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) :args (_let_208 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_557 (EQ_RESOLVE (ASSUME :args (_let_297)) (MACRO_SR_EQ_INTRO :args (_let_297 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_558 (ASSUME :args (_let_298)))) (let ((_let_559 (EQ_RESOLVE (ASSUME :args (_let_262)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546 _let_545 _let_544 _let_543 _let_542 _let_541 _let_540 _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_510 _let_508 _let_507 _let_506 _let_505 _let_504 _let_503 _let_502 _let_501 _let_500 _let_499 _let_498 _let_497 _let_496 _let_495 _let_494 _let_491 _let_490 _let_489 _let_488 _let_487 _let_486 _let_485 _let_484 _let_483 _let_482 _let_481 _let_480 _let_479 _let_478 _let_477 _let_476 _let_475 _let_474 _let_473 _let_472 _let_471 _let_470 _let_469 _let_468 _let_467 _let_466 _let_465 _let_464 _let_463 _let_462 _let_461 _let_460 _let_459 _let_458 _let_457 _let_456 _let_455 _let_454 _let_453 _let_452 _let_451 _let_450 _let_449 _let_448 _let_447 _let_446 _let_445 _let_444 _let_443 _let_442 _let_441 _let_440 _let_439 _let_438 _let_437 _let_436 _let_435 _let_434 _let_433 _let_432 _let_431 _let_430 _let_429 _let_428 _let_427 _let_426 _let_425 _let_424 _let_423 _let_422 _let_421 _let_420 _let_419 _let_418 _let_417 _let_416 _let_415 _let_414 _let_413 _let_412 _let_411 _let_410 _let_409 _let_408 _let_407 _let_406 _let_405 _let_404 _let_403 _let_402 _let_401 _let_400 _let_399 _let_398 _let_397 _let_396 _let_395 _let_394 _let_393 _let_392 _let_391 _let_390 _let_389 _let_388 _let_387 _let_386 _let_385 _let_384 _let_383 _let_382 _let_381 _let_380 _let_379 _let_378 _let_377 _let_376 _let_375 _let_374 _let_373 _let_372 _let_371 _let_370 _let_369 _let_368 _let_367 _let_366 _let_365 _let_364 _let_363 _let_362 _let_361 _let_359 _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) :args (_let_262 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_560 (EQ_RESOLVE (ASSUME :args (_let_127)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546 _let_545 _let_544 _let_543 _let_542 _let_541 _let_540 _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_510 _let_508 _let_507 _let_506 _let_505 _let_504 _let_503 _let_502 _let_501 _let_500 _let_499 _let_498 _let_497 _let_496 _let_495 _let_494 _let_491 _let_490 _let_489 _let_488 _let_487 _let_486 _let_485 _let_484 _let_483 _let_482 _let_481 _let_480 _let_479 _let_478 _let_477 _let_476 _let_475 _let_474 _let_473 _let_472 _let_471 _let_470 _let_469 _let_468 _let_467 _let_466 _let_465 _let_464 _let_463 _let_462 _let_461 _let_460 _let_459 _let_458 _let_457 _let_456 _let_455 _let_454 _let_453 _let_452 _let_451 _let_450 _let_449 _let_448 _let_447 _let_446 _let_445 _let_444 _let_443 _let_442 _let_441 _let_440 _let_439 _let_438 _let_437 _let_436 _let_435 _let_434 _let_433 _let_432 _let_431 _let_430 _let_429 _let_428 _let_427 _let_426 _let_425 _let_424 _let_423 _let_422 _let_421 _let_420 _let_419 _let_418 _let_417 _let_416 _let_415 _let_414 _let_413 _let_412 _let_411 _let_410 _let_409 _let_408 _let_407 _let_406 _let_405 _let_404 _let_403 _let_402 _let_401 _let_400 _let_399 _let_398 _let_397 _let_396 _let_395 _let_394 _let_393 _let_392 _let_391 _let_390 _let_389 _let_388 _let_387 _let_386 _let_385 _let_384 _let_383 _let_382 _let_381 _let_380 _let_379 _let_378 _let_377 _let_376 _let_375 _let_374 _let_373 _let_372 _let_371 _let_370 _let_369 _let_368 _let_367 _let_366 _let_365 _let_364 _let_363 _let_362 _let_361 _let_359 _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) :args (_let_127 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_561 (ASSUME :args (_let_299)))) (let ((_let_562 (EQ_RESOLVE (ASSUME :args (_let_300)) (MACRO_SR_EQ_INTRO :args (_let_300 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_563 (EQ_RESOLVE (ASSUME :args (_let_212)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546 _let_545 _let_544 _let_543 _let_542 _let_541 _let_540 _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_510 _let_508 _let_507 _let_506 _let_505 _let_504 _let_503 _let_502 _let_501 _let_500 _let_499 _let_498 _let_497 _let_496 _let_495 _let_494 _let_491 _let_490 _let_489 _let_488 _let_487 _let_486 _let_485 _let_484 _let_483 _let_482 _let_481 _let_480 _let_479 _let_478 _let_477 _let_476 _let_475 _let_474 _let_473 _let_472 _let_471 _let_470 _let_469 _let_468 _let_467 _let_466 _let_465 _let_464 _let_463 _let_462 _let_461 _let_460 _let_459 _let_458 _let_457 _let_456 _let_455 _let_454 _let_453 _let_452 _let_451 _let_450 _let_449 _let_448 _let_447 _let_446 _let_445 _let_444 _let_443 _let_442 _let_441 _let_440 _let_439 _let_438 _let_437 _let_436 _let_435 _let_434 _let_433 _let_432 _let_431 _let_430 _let_429 _let_428 _let_427 _let_426 _let_425 _let_424 _let_423 _let_422 _let_421 _let_420 _let_419 _let_418 _let_417 _let_416 _let_415 _let_414 _let_413 _let_412 _let_411 _let_410 _let_409 _let_408 _let_407 _let_406 _let_405 _let_404 _let_403 _let_402 _let_401 _let_400 _let_399 _let_398 _let_397 _let_396 _let_395 _let_394 _let_393 _let_392 _let_391 _let_390 _let_389 _let_388 _let_387 _let_386 _let_385 _let_384 _let_383 _let_382 _let_381 _let_380 _let_379 _let_378 _let_377 _let_376 _let_375 _let_374 _let_373 _let_372 _let_371 _let_370 _let_369 _let_368 _let_367 _let_366 _let_365 _let_364 _let_363 _let_362 _let_361 _let_359 _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) :args (_let_212 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_564 (EQ_RESOLVE (SYMM (ASSUME :args (_let_100))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546 _let_545 _let_544 _let_543 _let_542 _let_541 _let_540 _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_510 _let_508 _let_507 _let_506 _let_505 _let_504 _let_503 _let_502 _let_501 _let_500 _let_499 _let_498 _let_497 _let_496 _let_495 _let_494 _let_491 _let_490 _let_489 _let_488 _let_487 _let_486 _let_485 _let_484 _let_483 _let_482 _let_481 _let_480 _let_479 _let_478 _let_477 _let_476 _let_475 _let_474 _let_473 _let_472 _let_471 _let_470 _let_469 _let_468 _let_467 _let_466 _let_465 _let_464 _let_463 _let_462 _let_461 _let_460 _let_459 _let_458 _let_457 _let_456 _let_455 _let_454 _let_453 _let_452 _let_451 _let_450 _let_449 _let_448 _let_447 _let_446 _let_445 _let_444 _let_443 _let_442 _let_441 _let_440 _let_439 _let_438 _let_437 _let_436 _let_435 _let_434 _let_433 _let_432 _let_431 _let_430 _let_429 _let_428 _let_427 _let_426 _let_425 _let_424 _let_423 _let_422 _let_421 _let_420 _let_419 _let_418 _let_417 _let_416 _let_415 _let_414 _let_413 _let_412 _let_411 _let_410 _let_409 _let_408 _let_407 _let_406 _let_405 _let_404 _let_403 _let_402 _let_401 _let_400 _let_399 _let_398 _let_397 _let_396 _let_395 _let_394 _let_393 _let_392 _let_391 _let_390 _let_389 _let_388 _let_387 _let_386 _let_385 _let_384 _let_383 _let_382 _let_381 _let_380 _let_379 _let_378 _let_377 _let_376 _let_375 _let_374 _let_373 _let_372 _let_371 _let_370 _let_369 _let_368 _let_367 _let_366 _let_365 _let_364 _let_363 _let_362 _let_361 _let_359 _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) :args ((= id_Pro2309048762231606924nteger _let_99) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_565 (EQ_RESOLVE (EQ_RESOLVE (ASSUME :args (_let_137)) (MACRO_SR_EQ_INTRO :args (_let_137 SB_DEFAULT SBA_FIXPOINT))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_564 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546 _let_545 _let_544 _let_543 _let_542 _let_541 _let_540 _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_510 _let_508 _let_507 _let_506 _let_505 _let_504 _let_503 _let_502 _let_501 _let_500 _let_499 _let_498 _let_497 _let_496 _let_495 _let_494 _let_491 _let_490 _let_489 _let_488 _let_487 _let_486 _let_485 _let_484 _let_483 _let_482 _let_481 _let_480 _let_479 _let_478 _let_477 _let_476 _let_475 _let_474 _let_473 _let_472 _let_471 _let_470 _let_469 _let_468 _let_467 _let_466 _let_465 _let_464 _let_463 _let_462 _let_461 _let_460 _let_459 _let_458 _let_457 _let_456 _let_455 _let_454 _let_453 _let_452 _let_451 _let_450 _let_449 _let_448 _let_447 _let_446 _let_445 _let_444 _let_443 _let_442 _let_441 _let_440 _let_439 _let_438 _let_437 _let_436 _let_435 _let_434 _let_433 _let_432 _let_431 _let_430 _let_429 _let_428 _let_427 _let_426 _let_425 _let_424 _let_423 _let_422 _let_421 _let_420 _let_419 _let_418 _let_417 _let_416 _let_415 _let_414 _let_413 _let_412 _let_411 _let_410 _let_409 _let_408 _let_407 _let_406 _let_405 _let_404 _let_403 _let_402 _let_401 _let_400 _let_399 _let_398 _let_397 _let_396 _let_395 _let_394 _let_393 _let_392 _let_391 _let_390 _let_389 _let_388 _let_387 _let_386 _let_385 _let_384 _let_383 _let_382 _let_381 _let_380 _let_379 _let_378 _let_377 _let_376 _let_375 _let_374 _let_373 _let_372 _let_371 _let_370 _let_369 _let_368 _let_367 _let_366 _let_365 _let_364 _let_363 _let_362 _let_361 _let_359 _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) :args ((= bNF_Ca1965613569405424510nt_int (lambda ((R5 set_Pr958786334691620121nt_int) (As (-> int int))) (forall ((I2 int) (J int)) (or (not (@ (@ member5262025264175285858nt_int (@ (@ product_Pair_int_int I2) J)) R5)) (@ (@ ord_less_eq_int (@ As I2)) (@ As J)))))) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_566 (ASSUME :args (_let_294)))) (let ((_let_567 (EQ_RESOLVE (SYMM (ASSUME :args (_let_256))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_566 _let_565 _let_564 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546 _let_545 _let_544 _let_543 _let_542 _let_541 _let_540 _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_510 _let_508 _let_507 _let_506 _let_505 _let_504 _let_503 _let_502 _let_501 _let_500 _let_499 _let_498 _let_497 _let_496 _let_495 _let_494 _let_491 _let_490 _let_489 _let_488 _let_487 _let_486 _let_485 _let_484 _let_483 _let_482 _let_481 _let_480 _let_479 _let_478 _let_477 _let_476 _let_475 _let_474 _let_473 _let_472 _let_471 _let_470 _let_469 _let_468 _let_467 _let_466 _let_465 _let_464 _let_463 _let_462 _let_461 _let_460 _let_459 _let_458 _let_457 _let_456 _let_455 _let_454 _let_453 _let_452 _let_451 _let_450 _let_449 _let_448 _let_447 _let_446 _let_445 _let_444 _let_443 _let_442 _let_441 _let_440 _let_439 _let_438 _let_437 _let_436 _let_435 _let_434 _let_433 _let_432 _let_431 _let_430 _let_429 _let_428 _let_427 _let_426 _let_425 _let_424 _let_423 _let_422 _let_421 _let_420 _let_419 _let_418 _let_417 _let_416 _let_415 _let_414 _let_413 _let_412 _let_411 _let_410 _let_409 _let_408 _let_407 _let_406 _let_405 _let_404 _let_403 _let_402 _let_401 _let_400 _let_399 _let_398 _let_397 _let_396 _let_395 _let_394 _let_393 _let_392 _let_391 _let_390 _let_389 _let_388 _let_387 _let_386 _let_385 _let_384 _let_383 _let_382 _let_381 _let_380 _let_379 _let_378 _let_377 _let_376 _let_375 _let_374 _let_373 _let_372 _let_371 _let_370 _let_369 _let_368 _let_367 _let_366 _let_365 _let_364 _let_363 _let_362 _let_361 _let_359 _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) :args ((= top_top_set_ref_a _let_255) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_568 (EQ_RESOLVE (ASSUME :args (_let_301)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_567 _let_566 _let_565 _let_564 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546 _let_545 _let_544 _let_543 _let_542 _let_541 _let_540 _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_510 _let_508 _let_507 _let_506 _let_505 _let_504 _let_503 _let_502 _let_501 _let_500 _let_499 _let_498 _let_497 _let_496 _let_495 _let_494 _let_491 _let_490 _let_489 _let_488 _let_487 _let_486 _let_485 _let_484 _let_483 _let_482 _let_481 _let_480 _let_479 _let_478 _let_477 _let_476 _let_475 _let_474 _let_473 _let_472 _let_471 _let_470 _let_469 _let_468 _let_467 _let_466 _let_465 _let_464 _let_463 _let_462 _let_461 _let_460 _let_459 _let_458 _let_457 _let_456 _let_455 _let_454 _let_453 _let_452 _let_451 _let_450 _let_449 _let_448 _let_447 _let_446 _let_445 _let_444 _let_443 _let_442 _let_441 _let_440 _let_439 _let_438 _let_437 _let_436 _let_435 _let_434 _let_433 _let_432 _let_431 _let_430 _let_429 _let_428 _let_427 _let_426 _let_425 _let_424 _let_423 _let_422 _let_421 _let_420 _let_419 _let_418 _let_417 _let_416 _let_415 _let_414 _let_413 _let_412 _let_411 _let_410 _let_409 _let_408 _let_407 _let_406 _let_405 _let_404 _let_403 _let_402 _let_401 _let_400 _let_399 _let_398 _let_397 _let_396 _let_395 _let_394 _let_393 _let_392 _let_391 _let_390 _let_389 _let_388 _let_387 _let_386 _let_385 _let_384 _let_383 _let_382 _let_381 _let_380 _let_379 _let_378 _let_377 _let_376 _let_375 _let_374 _let_373 _let_372 _let_371 _let_370 _let_369 _let_368 _let_367 _let_366 _let_365 _let_364 _let_363 _let_362 _let_361 _let_359 _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) :args (_let_301 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_569 (EQ_RESOLVE (SYMM (ASSUME :args (_let_296))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_568 _let_567 _let_566 _let_565 _let_564 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546 _let_545 _let_544 _let_543 _let_542 _let_541 _let_540 _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_510 _let_508 _let_507 _let_506 _let_505 _let_504 _let_503 _let_502 _let_501 _let_500 _let_499 _let_498 _let_497 _let_496 _let_495 _let_494 _let_491 _let_490 _let_489 _let_488 _let_487 _let_486 _let_485 _let_484 _let_483 _let_482 _let_481 _let_480 _let_479 _let_478 _let_477 _let_476 _let_475 _let_474 _let_473 _let_472 _let_471 _let_470 _let_469 _let_468 _let_467 _let_466 _let_465 _let_464 _let_463 _let_462 _let_461 _let_460 _let_459 _let_458 _let_457 _let_456 _let_455 _let_454 _let_453 _let_452 _let_451 _let_450 _let_449 _let_448 _let_447 _let_446 _let_445 _let_444 _let_443 _let_442 _let_441 _let_440 _let_439 _let_438 _let_437 _let_436 _let_435 _let_434 _let_433 _let_432 _let_431 _let_430 _let_429 _let_428 _let_427 _let_426 _let_425 _let_424 _let_423 _let_422 _let_421 _let_420 _let_419 _let_418 _let_417 _let_416 _let_415 _let_414 _let_413 _let_412 _let_411 _let_410 _let_409 _let_408 _let_407 _let_406 _let_405 _let_404 _let_403 _let_402 _let_401 _let_400 _let_399 _let_398 _let_397 _let_396 _let_395 _let_394 _let_393 _let_392 _let_391 _let_390 _let_389 _let_388 _let_387 _let_386 _let_385 _let_384 _let_383 _let_382 _let_381 _let_380 _let_379 _let_378 _let_377 _let_376 _let_375 _let_374 _let_373 _let_372 _let_371 _let_370 _let_369 _let_368 _let_367 _let_366 _let_365 _let_364 _let_363 _let_362 _let_361 _let_359 _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) :args ((= top_top_set_rat _let_224) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_570 (ASSUME :args (_let_283)))) (let ((_let_571 (ASSUME :args (_let_176)))) (let ((_let_572 (EQ_RESOLVE (ASSUME :args (_let_257)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_564 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546 _let_545 _let_544 _let_543 _let_542 _let_541 _let_540 _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_510 _let_508 _let_507 _let_506 _let_505 _let_504 _let_503 _let_502 _let_501 _let_500 _let_499 _let_498 _let_497 _let_496 _let_495 _let_494 _let_491 _let_490 _let_489 _let_488 _let_487 _let_486 _let_485 _let_484 _let_483 _let_482 _let_481 _let_480 _let_479 _let_478 _let_477 _let_476 _let_475 _let_474 _let_473 _let_472 _let_471 _let_470 _let_469 _let_468 _let_467 _let_466 _let_465 _let_464 _let_463 _let_462 _let_461 _let_460 _let_459 _let_458 _let_457 _let_456 _let_455 _let_454 _let_453 _let_452 _let_451 _let_450 _let_449 _let_448 _let_447 _let_446 _let_445 _let_444 _let_443 _let_442 _let_441 _let_440 _let_439 _let_438 _let_437 _let_436 _let_435 _let_434 _let_433 _let_432 _let_431 _let_430 _let_429 _let_428 _let_427 _let_426 _let_425 _let_424 _let_423 _let_422 _let_421 _let_420 _let_419 _let_418 _let_417 _let_416 _let_415 _let_414 _let_413 _let_412 _let_411 _let_410 _let_409 _let_408 _let_407 _let_406 _let_405 _let_404 _let_403 _let_402 _let_401 _let_400 _let_399 _let_398 _let_397 _let_396 _let_395 _let_394 _let_393 _let_392 _let_391 _let_390 _let_389 _let_388 _let_387 _let_386 _let_385 _let_384 _let_383 _let_382 _let_381 _let_380 _let_379 _let_378 _let_377 _let_376 _let_375 _let_374 _let_373 _let_372 _let_371 _let_370 _let_369 _let_368 _let_367 _let_366 _let_365 _let_364 _let_363 _let_362 _let_361 _let_359 _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) :args (_let_257 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_573 (ASSUME :args (_let_71)))) (let ((_let_574 (ASSUME :args (_let_179)))) (let ((_let_575 (EQ_RESOLVE (ASSUME :args (_let_303)) (TRUST_SUBS_MAP (AND_INTRO _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_564 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546 _let_545 _let_544 _let_543 _let_542 _let_541 _let_540 _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_510 _let_508 _let_507 _let_506 _let_505 _let_504 _let_503 _let_502 _let_501 _let_500 _let_499 _let_498 _let_497 _let_496 _let_495 _let_494 _let_491 _let_490 _let_489 _let_488 _let_487 _let_486 _let_485 _let_484 _let_483 _let_482 _let_481 _let_480 _let_479 _let_478 _let_477 _let_476 _let_475 _let_474 _let_473 _let_472 _let_471 _let_470 _let_469 _let_468 _let_467 _let_466 _let_465 _let_464 _let_463 _let_462 _let_461 _let_460 _let_459 _let_458 _let_457 _let_456 _let_455 _let_454 _let_453 _let_452 _let_451 _let_450 _let_449 _let_448 _let_447 _let_446 _let_445 _let_444 _let_443 _let_442 _let_441 _let_440 _let_439 _let_438 _let_437 _let_436 _let_435 _let_434 _let_433 _let_432 _let_431 _let_430 _let_429 _let_428 _let_427 _let_426 _let_425 _let_424 _let_423 _let_422 _let_421 _let_420 _let_419 _let_418 _let_417 _let_416 _let_415 _let_414 _let_413 _let_412 _let_411 _let_410 _let_409 _let_408 _let_407 _let_406 _let_405 _let_404 _let_403 _let_402 _let_401 _let_400 _let_399 _let_398 _let_397 _let_396 _let_395 _let_394 _let_393 _let_392 _let_391 _let_390 _let_389 _let_388 _let_387 _let_386 _let_385 _let_384 _let_383 _let_382 _let_381 _let_380 _let_379 _let_378 _let_377 _let_376 _let_375 _let_374 _let_373 _let_372 _let_371 _let_370 _let_369 _let_368 _let_367 _let_366 _let_365 _let_364 _let_363 _let_362 _let_361 _let_359 _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) :args ((= _let_303 (= fun_min_weak (@ collec6321179662152712658at_nat (lambda ((BOUND_VARIABLE_189883 produc3843707927480180839at_nat)) (@ complete_Sup_Sup_o (@ (@ image_3568060456209098518_nat_o (@ member8757157785044589968at_nat BOUND_VARIABLE_189883)) (@ (@ image_2496312346330513076at_nat (lambda ((BOUND_VARIABLE_189884 Bool)) (let ((_let_1 (@ collec3392354462482085612at_nat (@ produc6081775807080527818_nat_o (lambda ((BOUND_VARIABLE_259197 nat) (BOUND_VARIABLE_259199 nat)) false))))) (@ (@ (@ if_set3208018901896979469at_nat BOUND_VARIABLE_189884) (@ min_ex6901939911449802026at_nat (@ comple2748534634209756852at_nat (@ (@ image_8493167801588156084at_nat (lambda ((BOUND_VARIABLE_189885 Bool)) (@ (@ (@ if_set1508868558775481357at_nat BOUND_VARIABLE_189885) (@ (@ lex_prod_nat_nat less_than) less_than)) (@ collec7088162979684241874at_nat (lambda ((BOUND_VARIABLE_189886 produc859450856879609959at_nat)) (= (@ produc6408287024330202629at_nat BOUND_VARIABLE_189886) (@ produc3213797794245857475at_nat BOUND_VARIABLE_189886))))))) top_top_set_o)))) (@ (@ insert9069300056098147895at_nat (@ (@ produc2922128104949294807at_nat _let_1) _let_1)) (@ collec6321179662152712658at_nat (@ produc410239310623530412_nat_o (lambda ((BOUND_VARIABLE_257674 set_Pr1261947904930325089at_nat) (BOUND_VARIABLE_257676 set_Pr1261947904930325089at_nat)) false)))))))) top_top_set_o)))))))))))) (let ((_let_576 (EQ_RESOLVE (EQ_RESOLVE (ASSUME :args (_let_304)) (MACRO_SR_EQ_INTRO :args (_let_304 SB_DEFAULT SBA_FIXPOINT))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_564 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546 _let_545 _let_544 _let_543 _let_542 _let_541 _let_540 _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_510 _let_508 _let_507 _let_506 _let_505 _let_504 _let_503 _let_502 _let_501 _let_500 _let_499 _let_498 _let_497 _let_496 _let_495 _let_494 _let_491 _let_490 _let_489 _let_488 _let_487 _let_486 _let_485 _let_484 _let_483 _let_482 _let_481 _let_480 _let_479 _let_478 _let_477 _let_476 _let_475 _let_474 _let_473 _let_472 _let_471 _let_470 _let_469 _let_468 _let_467 _let_466 _let_465 _let_464 _let_463 _let_462 _let_461 _let_460 _let_459 _let_458 _let_457 _let_456 _let_455 _let_454 _let_453 _let_452 _let_451 _let_450 _let_449 _let_448 _let_447 _let_446 _let_445 _let_444 _let_443 _let_442 _let_441 _let_440 _let_439 _let_438 _let_437 _let_436 _let_435 _let_434 _let_433 _let_432 _let_431 _let_430 _let_429 _let_428 _let_427 _let_426 _let_425 _let_424 _let_423 _let_422 _let_421 _let_420 _let_419 _let_418 _let_417 _let_416 _let_415 _let_414 _let_413 _let_412 _let_411 _let_410 _let_409 _let_408 _let_407 _let_406 _let_405 _let_404 _let_403 _let_402 _let_401 _let_400 _let_399 _let_398 _let_397 _let_396 _let_395 _let_394 _let_393 _let_392 _let_391 _let_390 _let_389 _let_388 _let_387 _let_386 _let_385 _let_384 _let_383 _let_382 _let_381 _let_380 _let_379 _let_378 _let_377 _let_376 _let_375 _let_374 _let_373 _let_372 _let_371 _let_370 _let_369 _let_368 _let_367 _let_366 _let_365 _let_364 _let_363 _let_362 _let_361 _let_359 _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) :args ((= finite3582905537739598962at_nat (lambda ((S4 set_nat) (F2 (-> nat nat nat))) (forall ((X4 nat) (Y5 nat)) (let ((_let_1 (@ F2 Y5))) (let ((_let_2 (@ F2 X4))) (or (not (@ (@ member_nat X4) S4)) (not (@ (@ member_nat Y5) S4)) (= (@ (@ comp_nat_nat_nat _let_1) _let_2) (@ (@ comp_nat_nat_nat _let_2) _let_1)))))))) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_577 (EQ_RESOLVE (ASSUME :args (_let_25)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_564 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546 _let_545 _let_544 _let_543 _let_542 _let_541 _let_540 _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_510 _let_508 _let_507 _let_506 _let_505 _let_504 _let_503 _let_502 _let_501 _let_500 _let_499 _let_498 _let_497 _let_496 _let_495 _let_494 _let_491 _let_490 _let_489 _let_488 _let_487 _let_486 _let_485 _let_484 _let_483 _let_482 _let_481 _let_480 _let_479 _let_478 _let_477 _let_476 _let_475 _let_474 _let_473 _let_472 _let_471 _let_470 _let_469 _let_468 _let_467 _let_466 _let_465 _let_464 _let_463 _let_462 _let_461 _let_460 _let_459 _let_458 _let_457 _let_456 _let_455 _let_454 _let_453 _let_452 _let_451 _let_450 _let_449 _let_448 _let_447 _let_446 _let_445 _let_444 _let_443 _let_442 _let_441 _let_440 _let_439 _let_438 _let_437 _let_436 _let_435 _let_434 _let_433 _let_432 _let_431 _let_430 _let_429 _let_428 _let_427 _let_426 _let_425 _let_424 _let_423 _let_422 _let_421 _let_420 _let_419 _let_418 _let_417 _let_416 _let_415 _let_414 _let_413 _let_412 _let_411 _let_410 _let_409 _let_408 _let_407 _let_406 _let_405 _let_404 _let_403 _let_402 _let_401 _let_400 _let_399 _let_398 _let_397 _let_396 _let_395 _let_394 _let_393 _let_392 _let_391 _let_390 _let_389 _let_388 _let_387 _let_386 _let_385 _let_384 _let_383 _let_382 _let_381 _let_380 _let_379 _let_378 _let_377 _let_376 _let_375 _let_374 _let_373 _let_372 _let_371 _let_370 _let_369 _let_368 _let_367 _let_366 _let_365 _let_364 _let_363 _let_362 _let_361 _let_359 _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) :args (_let_25 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_578 (EQ_RESOLVE (ASSUME :args (_let_305)) (MACRO_SR_EQ_INTRO :args (_let_305 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_579 (SYMM (ASSUME :args (_let_169))))) (let ((_let_580 (EQ_RESOLVE (SYMM (ASSUME :args (_let_204))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_564 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546 _let_545 _let_544 _let_543 _let_542 _let_541 _let_540 _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_510 _let_508 _let_507 _let_506 _let_505 _let_504 _let_503 _let_502 _let_501 _let_500 _let_499 _let_498 _let_497 _let_496 _let_495 _let_494 _let_491 _let_490 _let_489 _let_488 _let_487 _let_486 _let_485 _let_484 _let_483 _let_482 _let_481 _let_480 _let_479 _let_478 _let_477 _let_476 _let_475 _let_474 _let_473 _let_472 _let_471 _let_470 _let_469 _let_468 _let_467 _let_466 _let_465 _let_464 _let_463 _let_462 _let_461 _let_460 _let_459 _let_458 _let_457 _let_456 _let_455 _let_454 _let_453 _let_452 _let_451 _let_450 _let_449 _let_448 _let_447 _let_446 _let_445 _let_444 _let_443 _let_442 _let_441 _let_440 _let_439 _let_438 _let_437 _let_436 _let_435 _let_434 _let_433 _let_432 _let_431 _let_430 _let_429 _let_428 _let_427 _let_426 _let_425 _let_424 _let_423 _let_422 _let_421 _let_420 _let_419 _let_418 _let_417 _let_416 _let_415 _let_414 _let_413 _let_412 _let_411 _let_410 _let_409 _let_408 _let_407 _let_406 _let_405 _let_404 _let_403 _let_402 _let_401 _let_400 _let_399 _let_398 _let_397 _let_396 _let_395 _let_394 _let_393 _let_392 _let_391 _let_390 _let_389 _let_388 _let_387 _let_386 _let_385 _let_384 _let_383 _let_382 _let_381 _let_380 _let_379 _let_378 _let_377 _let_376 _let_375 _let_374 _let_373 _let_372 _let_371 _let_370 _let_369 _let_368 _let_367 _let_366 _let_365 _let_364 _let_363 _let_362 _let_361 _let_359 _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) :args ((= semiring_1_Nats_int _let_203) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_581 (ASSUME :args (_let_306)))) (let ((_let_582 (EQ_RESOLVE (ASSUME :args (_let_307)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_564 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546 _let_545 _let_544 _let_543 _let_542 _let_541 _let_540 _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_510 _let_508 _let_507 _let_506 _let_505 _let_504 _let_503 _let_502 _let_501 _let_500 _let_499 _let_498 _let_497 _let_496 _let_495 _let_494 _let_491 _let_490 _let_489 _let_488 _let_487 _let_486 _let_485 _let_484 _let_483 _let_482 _let_481 _let_480 _let_479 _let_478 _let_477 _let_476 _let_475 _let_474 _let_473 _let_472 _let_471 _let_470 _let_469 _let_468 _let_467 _let_466 _let_465 _let_464 _let_463 _let_462 _let_461 _let_460 _let_459 _let_458 _let_457 _let_456 _let_455 _let_454 _let_453 _let_452 _let_451 _let_450 _let_449 _let_448 _let_447 _let_446 _let_445 _let_444 _let_443 _let_442 _let_441 _let_440 _let_439 _let_438 _let_437 _let_436 _let_435 _let_434 _let_433 _let_432 _let_431 _let_430 _let_429 _let_428 _let_427 _let_426 _let_425 _let_424 _let_423 _let_422 _let_421 _let_420 _let_419 _let_418 _let_417 _let_416 _let_415 _let_414 _let_413 _let_412 _let_411 _let_410 _let_409 _let_408 _let_407 _let_406 _let_405 _let_404 _let_403 _let_402 _let_401 _let_400 _let_399 _let_398 _let_397 _let_396 _let_395 _let_394 _let_393 _let_392 _let_391 _let_390 _let_389 _let_388 _let_387 _let_386 _let_385 _let_384 _let_383 _let_382 _let_381 _let_380 _let_379 _let_378 _let_377 _let_376 _let_375 _let_374 _let_373 _let_372 _let_371 _let_370 _let_369 _let_368 _let_367 _let_366 _let_365 _let_364 _let_363 _let_362 _let_361 _let_359 _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) :args (_let_307 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_583 (ASSUME :args (_let_15)))) (let ((_let_584 (EQ_RESOLVE (ASSUME :args (_let_308)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_564 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546 _let_545 _let_544 _let_543 _let_542 _let_541 _let_540 _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_510 _let_508 _let_507 _let_506 _let_505 _let_504 _let_503 _let_502 _let_501 _let_500 _let_499 _let_498 _let_497 _let_496 _let_495 _let_494 _let_491 _let_490 _let_489 _let_488 _let_487 _let_486 _let_485 _let_484 _let_483 _let_482 _let_481 _let_480 _let_479 _let_478 _let_477 _let_476 _let_475 _let_474 _let_473 _let_472 _let_471 _let_470 _let_469 _let_468 _let_467 _let_466 _let_465 _let_464 _let_463 _let_462 _let_461 _let_460 _let_459 _let_458 _let_457 _let_456 _let_455 _let_454 _let_453 _let_452 _let_451 _let_450 _let_449 _let_448 _let_447 _let_446 _let_445 _let_444 _let_443 _let_442 _let_441 _let_440 _let_439 _let_438 _let_437 _let_436 _let_435 _let_434 _let_433 _let_432 _let_431 _let_430 _let_429 _let_428 _let_427 _let_426 _let_425 _let_424 _let_423 _let_422 _let_421 _let_420 _let_419 _let_418 _let_417 _let_416 _let_415 _let_414 _let_413 _let_412 _let_411 _let_410 _let_409 _let_408 _let_407 _let_406 _let_405 _let_404 _let_403 _let_402 _let_401 _let_400 _let_399 _let_398 _let_397 _let_396 _let_395 _let_394 _let_393 _let_392 _let_391 _let_390 _let_389 _let_388 _let_387 _let_386 _let_385 _let_384 _let_383 _let_382 _let_381 _let_380 _let_379 _let_378 _let_377 _let_376 _let_375 _let_374 _let_373 _let_372 _let_371 _let_370 _let_369 _let_368 _let_367 _let_366 _let_365 _let_364 _let_363 _let_362 _let_361 _let_359 _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) :args (_let_308 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_585 (ASSUME :args (_let_309)))) (let ((_let_586 (EQ_RESOLVE (ASSUME :args (_let_216)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_564 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546 _let_545 _let_544 _let_543 _let_542 _let_541 _let_540 _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_510 _let_508 _let_507 _let_506 _let_505 _let_504 _let_503 _let_502 _let_501 _let_500 _let_499 _let_498 _let_497 _let_496 _let_495 _let_494 _let_491 _let_490 _let_489 _let_488 _let_487 _let_486 _let_485 _let_484 _let_483 _let_482 _let_481 _let_480 _let_479 _let_478 _let_477 _let_476 _let_475 _let_474 _let_473 _let_472 _let_471 _let_470 _let_469 _let_468 _let_467 _let_466 _let_465 _let_464 _let_463 _let_462 _let_461 _let_460 _let_459 _let_458 _let_457 _let_456 _let_455 _let_454 _let_453 _let_452 _let_451 _let_450 _let_449 _let_448 _let_447 _let_446 _let_445 _let_444 _let_443 _let_442 _let_441 _let_440 _let_439 _let_438 _let_437 _let_436 _let_435 _let_434 _let_433 _let_432 _let_431 _let_430 _let_429 _let_428 _let_427 _let_426 _let_425 _let_424 _let_423 _let_422 _let_421 _let_420 _let_419 _let_418 _let_417 _let_416 _let_415 _let_414 _let_413 _let_412 _let_411 _let_410 _let_409 _let_408 _let_407 _let_406 _let_405 _let_404 _let_403 _let_402 _let_401 _let_400 _let_399 _let_398 _let_397 _let_396 _let_395 _let_394 _let_393 _let_392 _let_391 _let_390 _let_389 _let_388 _let_387 _let_386 _let_385 _let_384 _let_383 _let_382 _let_381 _let_380 _let_379 _let_378 _let_377 _let_376 _let_375 _let_374 _let_373 _let_372 _let_371 _let_370 _let_369 _let_368 _let_367 _let_366 _let_365 _let_364 _let_363 _let_362 _let_361 _let_359 _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) :args (_let_216 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_587 (EQ_RESOLVE (ASSUME :args (_let_310)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_564 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546 _let_545 _let_544 _let_543 _let_542 _let_541 _let_540 _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_510 _let_508 _let_507 _let_506 _let_505 _let_504 _let_503 _let_502 _let_501 _let_500 _let_499 _let_498 _let_497 _let_496 _let_495 _let_494 _let_491 _let_490 _let_489 _let_488 _let_487 _let_486 _let_485 _let_484 _let_483 _let_482 _let_481 _let_480 _let_479 _let_478 _let_477 _let_476 _let_475 _let_474 _let_473 _let_472 _let_471 _let_470 _let_469 _let_468 _let_467 _let_466 _let_465 _let_464 _let_463 _let_462 _let_461 _let_460 _let_459 _let_458 _let_457 _let_456 _let_455 _let_454 _let_453 _let_452 _let_451 _let_450 _let_449 _let_448 _let_447 _let_446 _let_445 _let_444 _let_443 _let_442 _let_441 _let_440 _let_439 _let_438 _let_437 _let_436 _let_435 _let_434 _let_433 _let_432 _let_431 _let_430 _let_429 _let_428 _let_427 _let_426 _let_425 _let_424 _let_423 _let_422 _let_421 _let_420 _let_419 _let_418 _let_417 _let_416 _let_415 _let_414 _let_413 _let_412 _let_411 _let_410 _let_409 _let_408 _let_407 _let_406 _let_405 _let_404 _let_403 _let_402 _let_401 _let_400 _let_399 _let_398 _let_397 _let_396 _let_395 _let_394 _let_393 _let_392 _let_391 _let_390 _let_389 _let_388 _let_387 _let_386 _let_385 _let_384 _let_383 _let_382 _let_381 _let_380 _let_379 _let_378 _let_377 _let_376 _let_375 _let_374 _let_373 _let_372 _let_371 _let_370 _let_369 _let_368 _let_367 _let_366 _let_365 _let_364 _let_363 _let_362 _let_361 _let_359 _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) :args (_let_310 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_588 (EQ_RESOLVE (ASSUME :args (_let_10)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_564 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546 _let_545 _let_544 _let_543 _let_542 _let_541 _let_540 _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_510 _let_508 _let_507 _let_506 _let_505 _let_504 _let_503 _let_502 _let_501 _let_500 _let_499 _let_498 _let_497 _let_496 _let_495 _let_494 _let_491 _let_490 _let_489 _let_488 _let_487 _let_486 _let_485 _let_484 _let_483 _let_482 _let_481 _let_480 _let_479 _let_478 _let_477 _let_476 _let_475 _let_474 _let_473 _let_472 _let_471 _let_470 _let_469 _let_468 _let_467 _let_466 _let_465 _let_464 _let_463 _let_462 _let_461 _let_460 _let_459 _let_458 _let_457 _let_456 _let_455 _let_454 _let_453 _let_452 _let_451 _let_450 _let_449 _let_448 _let_447 _let_446 _let_445 _let_444 _let_443 _let_442 _let_441 _let_440 _let_439 _let_438 _let_437 _let_436 _let_435 _let_434 _let_433 _let_432 _let_431 _let_430 _let_429 _let_428 _let_427 _let_426 _let_425 _let_424 _let_423 _let_422 _let_421 _let_420 _let_419 _let_418 _let_417 _let_416 _let_415 _let_414 _let_413 _let_412 _let_411 _let_410 _let_409 _let_408 _let_407 _let_406 _let_405 _let_404 _let_403 _let_402 _let_401 _let_400 _let_399 _let_398 _let_397 _let_396 _let_395 _let_394 _let_393 _let_392 _let_391 _let_390 _let_389 _let_388 _let_387 _let_386 _let_385 _let_384 _let_383 _let_382 _let_381 _let_380 _let_379 _let_378 _let_377 _let_376 _let_375 _let_374 _let_373 _let_372 _let_371 _let_370 _let_369 _let_368 _let_367 _let_366 _let_365 _let_364 _let_363 _let_362 _let_361 _let_359 _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) :args (_let_10 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_589 (SYMM (ASSUME :args (_let_311))))) (let ((_let_590 (AND_INTRO _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_564 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546 _let_545 _let_544 _let_543 _let_542 _let_541 _let_540 _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_510 _let_508 _let_507 _let_506 _let_505 _let_504 _let_503 _let_502 _let_501 _let_500 _let_499 _let_498 _let_497 _let_496 _let_495 _let_494 _let_491 _let_490 _let_489 _let_488 _let_487 _let_486 _let_485 _let_484 _let_483 _let_482 _let_481 _let_480 _let_479 _let_478 _let_477 _let_476 _let_475 _let_474 _let_473 _let_472 _let_471 _let_470 _let_469 _let_468 _let_467 _let_466 _let_465 _let_464 _let_463 _let_462 _let_461 _let_460 _let_459 _let_458 _let_457 _let_456 _let_455 _let_454 _let_453 _let_452 _let_451 _let_450 _let_449 _let_448 _let_447 _let_446 _let_445 _let_444 _let_443 _let_442 _let_441 _let_440 _let_439 _let_438 _let_437 _let_436 _let_435 _let_434 _let_433 _let_432 _let_431 _let_430 _let_429 _let_428 _let_427 _let_426 _let_425 _let_424 _let_423 _let_422 _let_421 _let_420 _let_419 _let_418 _let_417 _let_416 _let_415 _let_414 _let_413 _let_412 _let_411 _let_410 _let_409 _let_408 _let_407 _let_406 _let_405 _let_404 _let_403 _let_402 _let_401 _let_400 _let_399 _let_398 _let_397 _let_396 _let_395 _let_394 _let_393 _let_392 _let_391 _let_390 _let_389 _let_388 _let_387 _let_386 _let_385 _let_384 _let_383 _let_382 _let_381 _let_380 _let_379 _let_378 _let_377 _let_376 _let_375 _let_374 _let_373 _let_372 _let_371 _let_370 _let_369 _let_368 _let_367 _let_366 _let_365 _let_364 _let_363 _let_362 _let_361 _let_359 _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 ((_let_591 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_319)) :args ((or _let_318 _let_316 (not _let_319)))) (EQ_RESOLVE (ASSUME :args (_let_302)) (TRANS (MACRO_SR_EQ_INTRO _let_590 :args (_let_302 SB_DEFAULT SBA_FIXPOINT)) (PREPROCESS :args ((= (@ (@ (@ (@ heap_effect_ref_a (@ heap_heap_ref_a _let_110)) h) h2) r) _let_317))))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_493 :args (_let_312 h h2 r QUANTIFIERS_INST_CBQI_CONFLICT)) :args (_let_320))) _let_493 :args (_let_319 false _let_320)) :args (_let_316 false _let_317 false _let_319)))) (let ((_let_592 (not _let_316))) (let ((_let_593 (not _let_314))) (let ((_let_594 (=> (= r (@ (@ _let_84 (@ produc2058451029528183389_ref_a ll_36)) _let_111)) (not (= h2 (@ (@ _let_156 (@ produc2058451029528183389_ref_a ll_37)) _let_111)))))) (let ((_let_595 (EQ_RESOLVE (SYMM (ASSUME :args (_let_141))) (MACRO_SR_EQ_INTRO _let_590 :args ((= ref_a2 ref_a3) SB_DEFAULT SBA_FIXPOINT))))) (SCOPE (MACRO_RESOLUTION_TRUST (REORDERING (IMPLIES_ELIM (EQ_RESOLVE (ASSUME :args (_let_112)) (TRANS (MACRO_SR_EQ_INTRO (AND_INTRO (MACRO_SR_PRED_TRANSFORM (ASSUME :args (_let_11)) :args ((= thesis false))) (EQ_RESOLVE (ASSUME :args (_let_249)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_595 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_564 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546 _let_545 _let_544 _let_543 _let_542 _let_541 _let_540 _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_510 _let_508 _let_507 _let_506 _let_505 _let_504 _let_503 _let_502 _let_501 _let_500 _let_499 _let_498 _let_497 _let_496 _let_495 _let_494 _let_491 _let_490 _let_489 _let_488 _let_487 _let_486 _let_485 _let_484 _let_483 _let_482 _let_481 _let_480 _let_479 _let_478 _let_477 _let_476 _let_475 _let_474 _let_473 _let_472 _let_471 _let_470 _let_469 _let_468 _let_467 _let_466 _let_465 _let_464 _let_463 _let_462 _let_461 _let_460 _let_459 _let_458 _let_457 _let_456 _let_455 _let_454 _let_453 _let_452 _let_451 _let_450 _let_449 _let_448 _let_447 _let_446 _let_445 _let_444 _let_443 _let_442 _let_441 _let_440 _let_439 _let_438 _let_437 _let_436 _let_435 _let_434 _let_433 _let_432 _let_431 _let_430 _let_429 _let_428 _let_427 _let_426 _let_425 _let_424 _let_423 _let_422 _let_421 _let_420 _let_419 _let_418 _let_417 _let_416 _let_415 _let_414 _let_413 _let_412 _let_411 _let_410 _let_409 _let_408 _let_407 _let_406 _let_405 _let_404 _let_403 _let_402 _let_401 _let_400 _let_399 _let_398 _let_397 _let_396 _let_395 _let_394 _let_393 _let_392 _let_391 _let_390 _let_389 _let_388 _let_387 _let_386 _let_385 _let_384 _let_383 _let_382 _let_381 _let_380 _let_379 _let_378 _let_377 _let_376 _let_375 _let_374 _let_373 _let_372 _let_371 _let_370 _let_369 _let_368 _let_367 _let_366 _let_365 _let_364 _let_363 _let_362 _let_361 _let_359 _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) :args (_let_249 SB_DEFAULT SBA_FIXPOINT))) _let_595 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_564 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546 _let_545 _let_544 _let_543 _let_542 _let_541 _let_540 _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_510 _let_508 _let_507 _let_506 _let_505 _let_504 _let_503 _let_502 _let_501 _let_500 _let_499 _let_498 _let_497 _let_496 _let_495 _let_494 _let_491 _let_490 _let_489 _let_488 _let_487 _let_486 _let_485 _let_484 _let_483 _let_482 _let_481 _let_480 _let_479 _let_478 _let_477 _let_476 _let_475 _let_474 _let_473 _let_472 _let_471 _let_470 _let_469 _let_468 _let_467 _let_466 _let_465 _let_464 _let_463 _let_462 _let_461 _let_460 _let_459 _let_458 _let_457 _let_456 _let_455 _let_454 _let_453 _let_452 _let_451 _let_450 _let_449 _let_448 _let_447 _let_446 _let_445 _let_444 _let_443 _let_442 _let_441 _let_440 _let_439 _let_438 _let_437 _let_436 _let_435 _let_434 _let_433 _let_432 _let_431 _let_430 _let_429 _let_428 _let_427 _let_426 _let_425 _let_424 _let_423 _let_422 _let_421 _let_420 _let_419 _let_418 _let_417 _let_416 _let_415 _let_414 _let_413 _let_412 _let_411 _let_410 _let_409 _let_408 _let_407 _let_406 _let_405 _let_404 _let_403 _let_402 _let_401 _let_400 _let_399 _let_398 _let_397 _let_396 _let_395 _let_394 _let_393 _let_392 _let_391 _let_390 _let_389 _let_388 _let_387 _let_386 _let_385 _let_384 _let_383 _let_382 _let_381 _let_380 _let_379 _let_378 _let_377 _let_376 _let_375 _let_374 _let_373 _let_372 _let_371 _let_370 _let_369 _let_368 _let_367 _let_366 _let_365 _let_364 _let_363 _let_362 _let_361 _let_359 _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) :args (_let_112 SB_DEFAULT SBA_FIXPOINT)) (PREPROCESS :args ((= (=> (= r (@ _let_85 _let_111)) (not (= h2 (@ _let_157 _let_111)))) _let_594))) (PREPROCESS :args ((= _let_594 (=> _let_315 _let_593))))))) :args ((or _let_593 (not _let_315)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_316 1)) :args ((or _let_315 _let_592))) _let_591 :args (_let_315 false _let_316)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_316 0)) :args ((or _let_314 _let_592))) _let_591 :args (_let_314 false _let_316)) :args (false false _let_315 false _let_314)) :args ((forall ((F (-> int int)) (A4 set_int) (G (-> int int)) (B5 set_int)) (=> (@ (@ inj_on_int_int F) A4) (=> (@ (@ inj_on_int_int G) B5) (=> (= (@ (@ inf_inf_set_int (@ (@ image_int_int F) A4)) (@ (@ image_int_int G) B5)) bot_bot_set_int) (@ (@ inj_on_int_int (lambda ((X4 int)) (@ (@ (@ if_int (@ (@ member_int X4) A4)) (@ F X4)) (@ G X4)))) (@ (@ sup_sup_set_int A4) B5)))))) (forall ((S5 set_nat)) (=> (not (@ finite_finite_nat S5)) (exists ((F5 (-> nat nat))) (and (@ (@ inj_on_nat_nat F5) top_top_set_nat) (@ (@ ord_less_eq_set_nat (@ (@ image_nat_nat F5) top_top_set_nat)) S5))))) (forall ((F (-> nat num)) (G (-> nat nat)) (X2 nat)) (= (@ (@ (@ comp_P5371577678113413053at_nat (@ (@ produc4918694523301289860at_nat F) id_nat)) (@ (@ bNF_co805650143699787099at_nat id_nat) G)) X2) (@ (@ (@ bNF_co8159352583862032293um_nat (@ (@ comp_num_num_nat id_num) F)) G) X2))) (forall ((F (-> int nat)) (A4 set_int) (P2 (-> nat Bool))) (=> (forall ((X nat)) (=> (@ (@ member_nat X) (@ (@ image_int_nat F) A4)) (@ P2 X))) (forall ((X6 int)) (=> (@ (@ member_int X6) A4) (@ P2 (@ F X6)))))) (forall ((F (-> int int)) (A4 set_int) (P2 (-> int Bool))) (= (@ collect_int (lambda ((X4 int)) (and (@ P2 X4) (@ (@ member_int X4) (@ (@ image_int_int F) A4))))) (@ (@ image_int_int F) (@ collect_int (lambda ((X4 int)) (and (@ P2 (@ F X4)) (@ (@ member_int X4) A4))))))) (forall ((F (-> int int)) (A4 set_int)) (=> (@ (@ inj_on_int_int F) A4) (@ (@ inj_on_int_int (@ (@ the_inv_into_int_int A4) F)) (@ (@ image_int_int F) A4)))) (= code_int_of_integer (lambda ((K5 code_integer)) (@ (@ (@ if_int (@ (@ ord_le6747313008572928689nteger K5) zero_z3403309356797280102nteger)) (@ uminus_uminus_int (@ code_int_of_integer (@ uminus1351360451143612070nteger K5)))) (@ (@ (@ if_int (= K5 zero_z3403309356797280102nteger)) zero_zero_int) (@ (@ produc1553301316500091796er_int (lambda ((L3 code_integer) (J code_integer)) (let ((_let_1 (@ (@ times_times_int (@ numeral_numeral_int (@ bit0 one))) (@ code_int_of_integer L3)))) (@ (@ (@ if_int (= J zero_z3403309356797280102nteger)) _let_1) (@ (@ plus_plus_int _let_1) one_one_int))))) (@ (@ code_divmod_integer K5) (@ numera6620942414471956472nteger (@ bit0 one)))))))) (forall ((X2 product_unit)) (= (@ (@ image_8730104196221521654t_unit (lambda ((Uu nat)) X2)) top_top_set_nat) (@ (@ insert_Product_unit X2) bot_bo3957492148770167129t_unit))) (forall ((A4 set_o) (F (-> Bool Bool))) (= (@ (@ bNF_re4705727531993890431at_o_o (lambda ((Y2 nat) (Z nat)) (= Y2 Z))) (@ (@ bNF_Grp_o_o A4) F)) (@ (@ bNF_Grp_nat_o_nat_o (@ collect_nat_o (lambda ((X4 (-> nat Bool))) (@ (@ ord_less_eq_set_o (@ (@ image_nat_o X4) top_top_set_nat)) A4)))) (@ comp_o_o_nat F)))) (forall ((C produc3843707927480180839at_nat) (A4 set_se7855581050983116737at_nat)) (=> (@ (@ member8757157785044589968at_nat C) (@ id_on_6713504163309144702at_nat A4)) (not (forall ((X set_Pr1261947904930325089at_nat)) (=> (@ (@ member2643936169264416010at_nat X) A4) (not (= C (@ (@ produc2922128104949294807at_nat X) X)))))))) (= code_nat_of_integer (lambda ((K5 code_integer)) (@ (@ (@ if_nat (@ (@ ord_le3102999989581377725nteger K5) zero_z3403309356797280102nteger)) zero_zero_nat) (@ (@ produc1555791787009142072er_nat (lambda ((L3 code_integer) (J code_integer)) (let ((_let_1 (@ code_nat_of_integer L3))) (let ((_let_2 (@ (@ plus_plus_nat _let_1) _let_1))) (@ (@ (@ if_nat (= J zero_z3403309356797280102nteger)) _let_2) (@ (@ plus_plus_nat _let_2) one_one_nat)))))) (@ (@ code_divmod_integer K5) (@ numera6620942414471956472nteger (@ bit0 one))))))) (forall ((A4 set_int)) (= (@ complete_Sup_Sup_int (@ (@ image_int_int (lambda ((X4 int)) X4)) A4)) (@ complete_Sup_Sup_int A4))) (forall ((F (-> int int)) (G (-> int int))) (=> (@ order_6722886889984875411nt_int F) (=> (= (@ (@ image_int_int F) top_top_set_int) top_top_set_int) (=> (forall ((X int)) (= (@ G (@ F X)) X)) (@ order_6722886889984875411nt_int G))))) (forall ((A4 set_o) (F (-> Bool nat)) (M nat)) (=> (not (= A4 bot_bot_set_o)) (=> (forall ((X Bool)) (=> (@ (@ member_o X) A4) (@ (@ ord_less_eq_nat (@ F X)) M))) (@ (@ ord_less_eq_nat (@ complete_Sup_Sup_nat (@ (@ image_o_nat F) A4))) M)))) (forall ((F (-> product_prod_nat_nat product_prod_nat_nat)) (A4 set_Pr1261947904930325089at_nat)) (=> (@ (@ inj_on8969904277767023793at_nat F) A4) (= (@ finite6177210948735845034at_nat (@ (@ image_5168914502847457605at_nat F) A4)) (@ finite6177210948735845034at_nat A4)))) (forall ((A4 set_nat) (B5 set_rat)) (=> (@ finite_finite_nat A4) (=> (@ finite_finite_rat B5) (= (exists ((F2 (-> nat rat))) (and (@ (@ inj_on_nat_rat F2) A4) (@ (@ ord_less_eq_set_rat (@ (@ image_nat_rat F2) A4)) B5))) (@ (@ ord_less_eq_nat (@ finite_card_nat A4)) (@ finite_card_rat B5)))))) (forall ((F (-> nat nat)) (G (-> nat nat)) (X2 nat) (F3 (-> nat nat)) (G2 (-> nat nat)) (X3 nat)) (=> (= (@ F (@ G X2)) (@ F3 (@ G2 X3))) (= (@ (@ (@ comp_nat_nat_nat F) G) X2) (@ (@ (@ comp_nat_nat_nat F3) G2) X3)))) (= (@ _let_238 top_top_set_o) top_top_set_o) (forall ((X2 product_prod_int_int) (Y3 int) (Z2 int)) (=> (= X2 (@ (@ product_Pair_int_int Y3) Z2)) (= (@ product_fst_int_int X2) Y3))) (forall ((Sa (-> num num Bool)) (X2 (-> int num)) (G (-> nat num)) (Y3 (-> int nat))) (= (@ (@ (@ (@ bNF_re7626690874201225453um_num (lambda ((Y2 int) (Z int)) (= Y2 Z))) Sa) X2) (@ (@ comp_nat_num_int G) Y3)) (@ (@ (@ (@ bNF_re1845987051190671011um_nat (lambda ((Y2 int) (Z int)) (= Y2 Z))) (lambda ((X4 num) (Y5 nat)) (@ (@ Sa X4) (@ G Y5)))) X2) Y3))) (forall ((R3 (-> nat nat Bool))) (= (@ (@ bNF_re3734335887435638179at_nat (lambda ((Y2 char) (Z char)) (= Y2 Z))) R3) (@ (@ relcom8141925468094106422ar_nat (@ conver5210974729819302706ar_nat (@ (@ bNF_Gr1779741795384719769ar_nat (@ collec1683818095804863890at_nat (lambda ((X4 (-> char product_prod_nat_nat))) (@ (@ ord_le3146513528884898305at_nat (@ (@ image_8382823969816519465at_nat X4) top_top_set_char)) (@ collec3392354462482085612at_nat (@ produc6081775807080527818_nat_o R3)))))) (@ comp_P1491501995297412481t_char product_fst_nat_nat)))) (@ (@ bNF_Gr1779741795384719769ar_nat (@ collec1683818095804863890at_nat (lambda ((X4 (-> char product_prod_nat_nat))) (@ (@ ord_le3146513528884898305at_nat (@ (@ image_8382823969816519465at_nat X4) top_top_set_char)) (@ collec3392354462482085612at_nat (@ produc6081775807080527818_nat_o R3)))))) (@ comp_P1491501995297412481t_char product_snd_nat_nat))))) (forall ((Rep (-> num Bool)) (Abs (-> Bool num)) (Rep2 (-> num Bool)) (Abs2 (-> Bool num)) (Rep3 (-> int nat)) (Abs3 (-> nat int)) (M (-> nat Bool)) (M1 (-> Bool Bool)) (M2 (-> nat Bool))) (=> (@ (@ (@ type_d9070036042389994064_num_o Rep) Abs) top_top_set_o) (=> (@ (@ (@ type_d9070036042389994064_num_o Rep2) Abs2) top_top_set_o) (=> (@ (@ (@ type_d7249847660678803242nt_nat Rep3) Abs3) top_top_set_nat) (=> (= (@ (@ comp_nat_num_int (@ (@ comp_o_num_nat Abs2) M)) Rep3) (@ (@ comp_num_num_int (@ (@ comp_o_num_num (@ (@ comp_o_num_o Abs2) M1)) Rep)) (@ (@ comp_nat_num_int (@ (@ comp_o_num_nat Abs) M2)) Rep3))) (= (@ (@ comp_o_o_nat M1) M2) M)))))) (forall ((B5 set_int) (F (-> nat int)) (A4 set_nat) (G (-> int int))) (let ((_let_1 (@ (@ image_nat_int F) A4))) (=> (not (= B5 bot_bot_set_int)) (=> (@ condit1735850657277959132ow_int _let_1) (=> (forall ((M4 int)) (=> (@ (@ member_int M4) B5) (exists ((X6 nat)) (and (@ (@ ord_less_eq_int (@ F X6)) (@ G M4)) (@ (@ member_nat X6) A4))))) (@ (@ ord_less_eq_int (@ complete_Inf_Inf_int _let_1)) (@ complete_Inf_Inf_int (@ (@ image_int_int G) B5)))))))) (forall ((V a) (H heap_e7401611519738050253t_unit) (V2 a)) (let ((_let_1 (@ (@ alloc_a V) H))) (= (@ (@ (@ set_a (@ produc473321116828791851t_unit _let_1)) V2) (@ produc1126150082675451753t_unit _let_1)) (@ produc1126150082675451753t_unit (@ (@ alloc_a V2) H))))) _let_311 (forall ((F (-> product_prod_nat_nat nat)) (A4 set_Pr1261947904930325089at_nat)) (=> (@ (@ inj_on2178005380612969504at_nat F) A4) (= (@ finite_finite_nat (@ (@ image_2486076414777270412at_nat F) A4)) (@ finite6177210948735845034at_nat A4)))) (forall ((I3 set_Product_unit) (X2 product_unit) (F (-> product_unit product_unit))) (=> (not (= I3 bot_bo3957492148770167129t_unit)) (= (@ comple2584293577114468500t_unit (@ (@ image_405062704495631173t_unit (lambda ((I2 product_unit)) (@ (@ inf_inf_Product_unit X2) (@ F I2)))) I3)) (@ (@ inf_inf_Product_unit X2) (@ comple2584293577114468500t_unit (@ (@ image_405062704495631173t_unit F) I3)))))) (forall ((A4 set_o) (F (-> Bool int)) (M int)) (=> (not (= A4 bot_bot_set_o)) (=> (forall ((X Bool)) (=> (@ (@ member_o X) A4) (@ (@ ord_less_eq_int (@ F X)) M))) (@ (@ ord_less_eq_int (@ complete_Sup_Sup_int (@ (@ image_o_int F) A4))) M)))) (forall ((F (-> nat num Bool)) (A nat) (B num)) (=> (@ (@ produc4927758841916487424_num_o F) (@ (@ product_Pair_nat_num A) B)) (@ (@ F A) B))) (forall ((A4 set_Pr1261947904930325089at_nat) (B5 set_Pr1261947904930325089at_nat) (F (-> product_prod_nat_nat product_prod_nat_nat)) (G (-> product_prod_nat_nat int))) (=> (= A4 B5) (= (@ (@ relcom8911704206367525917at_int (@ conver6965824823119931701at_nat (@ (@ bNF_Gr7275288873855648526at_nat A4) F))) (@ (@ bNF_Gr190934199572118623at_int A4) G)) (@ (@ relcom8911704206367525917at_int (@ conver6965824823119931701at_nat (@ (@ bNF_Gr7275288873855648526at_nat B5) F))) (@ (@ bNF_Gr190934199572118623at_int B5) G))))) (forall ((F (-> code_integer code_integer)) (X2 produc8923325533196201883nteger)) (= (@ produc6174133586879617921nteger (@ (@ produc6499014454317279255nteger F) X2)) (@ F (@ produc6174133586879617921nteger X2)))) (forall ((A4 set_Pr4329608150637261639at_nat) (F (-> produc3843707927480180839at_nat product_unit)) (X2 product_unit)) (=> (forall ((I4 produc3843707927480180839at_nat)) (=> (@ (@ member8757157785044589968at_nat I4) A4) (@ (@ ord_le3221252021190050221t_unit (@ F I4)) X2))) (=> (forall ((Y product_unit)) (=> (forall ((I5 produc3843707927480180839at_nat)) (=> (@ (@ member8757157785044589968at_nat I5) A4) (@ (@ ord_le3221252021190050221t_unit (@ F I5)) Y))) (@ (@ ord_le3221252021190050221t_unit X2) Y))) (= (@ comple4687483117567863418t_unit (@ (@ image_7082456443403096939t_unit F) A4)) X2)))) (forall ((I3 set_Pr1261947904930325089at_nat) (C set_nat) (F (-> product_prod_nat_nat set_nat))) (=> (not (= I3 bot_bo2099793752762293965at_nat)) (=> (forall ((I4 product_prod_nat_nat)) (=> (@ (@ member8440522571783428010at_nat I4) I3) (@ (@ ord_less_eq_set_nat C) (@ F I4)))) (= (= (@ comple7399068483239264473et_nat (@ (@ image_15824709712370754et_nat F) I3)) C) (forall ((X4 product_prod_nat_nat)) (=> (@ (@ member8440522571783428010at_nat X4) I3) (= (@ F X4) C))))))) _let_310 (forall ((H (-> char int)) (F4 set_int)) (=> (@ finite_finite_char (@ (@ vimage_char_int H) F4)) (=> (= (@ (@ image_char_int H) top_top_set_char) top_top_set_int) (@ finite_finite_int F4)))) (forall ((B5 (-> product_unit set_nat)) (A product_unit) (A4 set_Product_unit)) (let ((_let_1 (@ image_8173849991827986510et_nat B5))) (= (@ comple7399068483239264473et_nat (@ _let_1 (@ (@ insert_Product_unit A) A4))) (@ (@ sup_sup_set_nat (@ B5 A)) (@ comple7399068483239264473et_nat (@ _let_1 A4)))))) _let_309 (forall ((F (-> int int Bool)) (P product_prod_int_int)) (= (@ (@ produc4947309494688390418_int_o (lambda ((Y5 int) (X4 int)) (@ (@ F X4) Y5))) (@ product_swap_int_int P)) (@ (@ produc4947309494688390418_int_o F) P))) (forall ((F (-> char Bool)) (A char) (A4 set_char)) (=> (@ (@ inj_on_char_o F) top_top_set_char) (= (@ (@ member_o (@ F A)) (@ (@ image_char_o F) A4)) (@ (@ member_char A) A4)))) (= produc4947309494688390418_int_o (lambda ((F2 (-> int int Bool)) (X4 product_prod_int_int)) (@ (@ F2 (@ product_fst_int_int X4)) (@ product_snd_int_int X4)))) (forall ((F (-> int nat)) (A4 set_int) (P2 (-> set_nat Bool))) (= (forall ((B6 set_nat)) (=> (@ (@ ord_less_eq_set_nat B6) (@ (@ image_int_nat F) A4)) (@ P2 B6))) (forall ((B6 set_int)) (=> (@ (@ ord_less_eq_set_int B6) A4) (@ P2 (@ (@ image_int_nat F) B6)))))) (forall ((F (-> Bool product_unit)) (A4 set_o) (X2 Bool)) (let ((_let_1 (@ (@ image_o_Product_unit F) A4))) (=> (@ condit9161856309968323677t_unit _let_1) (=> (@ (@ member_o X2) A4) (@ (@ ord_le3221252021190050221t_unit (@ comple2584293577114468500t_unit _let_1)) (@ F X2)))))) (forall ((Sb (-> num num Bool)) (I (-> nat num)) (X2 (-> int nat)) (Y3 (-> int num))) (= (@ (@ (@ (@ bNF_re7626690874201225453um_num (lambda ((Y2 int) (Z int)) (= Y2 Z))) Sb) (@ (@ comp_nat_num_int I) X2)) Y3) (@ (@ (@ (@ bNF_re272988434038980259at_num (lambda ((Y2 int) (Z int)) (= Y2 Z))) (lambda ((X4 nat) (__flatten_var_0 num)) (@ (@ Sb (@ I X4)) __flatten_var_0))) X2) Y3))) _let_308 (forall ((C3 set_o) (A4 (-> Bool set_int)) (B5 set_int)) (let ((_let_1 (= C3 bot_bot_set_o))) (and (=> _let_1 (= (@ comple3628384868704368283et_int (@ (@ image_o_set_int (lambda ((X4 Bool)) (@ (@ inf_inf_set_int (@ A4 X4)) B5))) C3)) top_top_set_int)) (=> (not _let_1) (= (@ comple3628384868704368283et_int (@ (@ image_o_set_int (lambda ((X4 Bool)) (@ (@ inf_inf_set_int (@ A4 X4)) B5))) C3)) (@ (@ inf_inf_set_int (@ comple3628384868704368283et_int (@ (@ image_o_set_int A4) C3))) B5)))))) (forall ((F (-> int nat)) (A4 set_int)) (=> (@ order_mono_int_nat F) (=> (@ condit1735850657277959132ow_int A4) (=> (not (= A4 bot_bot_set_int)) (@ (@ ord_less_eq_nat (@ F (@ complete_Inf_Inf_int A4))) (@ complete_Inf_Inf_nat (@ (@ image_int_nat F) A4))))))) (forall ((Q product_prod_int_int) (F (-> int int Bool)) (G (-> int int Bool)) (P product_prod_int_int)) (=> (forall ((X int) (Y int)) (=> (= (@ (@ product_Pair_int_int X) Y) Q) (= (@ (@ F X) Y) (@ (@ G X) Y)))) (=> (= P Q) (= (@ (@ produc4947309494688390418_int_o F) P) (@ (@ produc4947309494688390418_int_o G) Q))))) (forall ((A4 set_nat) (C set_o)) (let ((_let_1 (= A4 bot_bot_set_nat))) (and (=> (not _let_1) (= (@ comple90263536869209701_set_o (@ (@ image_nat_set_o (lambda ((Y5 nat)) C)) A4)) C)) (=> _let_1 (= (@ comple90263536869209701_set_o (@ (@ image_nat_set_o (lambda ((Y5 nat)) C)) A4)) bot_bot_set_o))))) (forall ((Z2 nat) (F (-> int nat)) (A4 set_int)) (= (@ (@ member_nat Z2) (@ (@ image_int_nat F) A4)) (exists ((X4 int)) (and (= Z2 (@ F X4)) (@ (@ member_int X4) A4))))) (forall ((F (-> nat product_prod_nat_nat)) (A4 set_nat) (B5 set_Pr1261947904930325089at_nat) (G (-> product_prod_nat_nat nat))) (=> (@ (@ inj_on5538052773655684606at_nat F) A4) (=> (@ (@ ord_le3146513528884898305at_nat (@ (@ image_5846123807819985514at_nat F) A4)) B5) (=> (@ (@ inj_on2178005380612969504at_nat G) B5) (=> (@ (@ ord_less_eq_set_nat (@ (@ image_2486076414777270412at_nat G) B5)) A4) (=> (@ finite_finite_nat A4) (=> (@ finite6177210948735845034at_nat B5) (= (@ finite_card_nat A4) (@ finite711546835091564841at_nat B5))))))))) (forall ((A4 set_int) (C nat)) (=> (not (= A4 bot_bot_set_int)) (= (@ complete_Inf_Inf_nat (@ (@ image_int_nat (lambda ((X4 int)) C)) A4)) C))) (forall ((F (-> nat rat)) (B5 set_nat) (A nat) (A4 set_nat)) (let ((_let_1 (@ member_nat A))) (=> (@ (@ inj_on_nat_rat F) B5) (=> (@ _let_1 B5) (=> (@ (@ ord_less_eq_set_nat A4) B5) (= (@ (@ member_rat (@ F A)) (@ (@ image_nat_rat F) A4)) (@ _let_1 A4))))))) (forall ((F (-> list_nat list_nat))) (=> (@ finite8100373058378681591st_nat top_top_set_list_nat) (=> (= (@ (@ image_7976474329151083847st_nat F) top_top_set_list_nat) top_top_set_list_nat) (@ (@ inj_on3049792774292151987st_nat F) top_top_set_list_nat)))) (= comp_nat_num_int (lambda ((F2 (-> nat num)) (G3 (-> int nat)) (X4 int)) (@ F2 (@ G3 X4)))) (forall ((B5 (-> nat set_nat)) (F (-> nat nat)) (A4 set_nat)) (= (@ comple7806235888213564991et_nat (@ (@ image_nat_set_nat (lambda ((A5 nat)) (@ B5 (@ F A5)))) A4)) (@ comple7806235888213564991et_nat (@ (@ image_nat_set_nat B5) (@ (@ image_nat_nat F) A4))))) (forall ((C (-> int int Bool)) (P product_prod_int_int)) (=> (@ (@ produc4947309494688390418_int_o C) P) (not (forall ((X int) (Y int)) (=> (= P (@ (@ product_Pair_int_int X) Y)) (not (@ (@ C X) Y))))))) (forall ((Rep (-> int nat)) (Abs (-> nat int)) (G (-> int int)) (P2 (-> int Bool)) (H (-> int int))) (=> (@ (@ (@ type_d7249847660678803242nt_nat Rep) Abs) top_top_set_nat) (= (@ (@ (@ bNF_vi3197508430158922565_int_o G) Abs) (@ (@ bNF_Grp_int_int (@ collect_int P2)) H)) (@ (@ bNF_Grp_int_nat (@ collect_int (lambda ((X4 int)) (@ P2 (@ G X4))))) (@ (@ comp_int_nat_int (@ (@ comp_int_nat_int Rep) H)) G))))) (forall ((X2 produc7812382424243267045t_unit)) (= (@ produc5717040794327095847_ref_a (@ produc970745769005243767t_unit X2)) (@ produc1126150082675451753t_unit X2))) (forall ((C3 set_o) (A4 set_rat) (B5 (-> Bool set_rat))) (let ((_let_1 (= C3 bot_bot_set_o))) (and (=> _let_1 (= (@ comple4298007329820168263et_rat (@ (@ image_o_set_rat (lambda ((X4 Bool)) (@ (@ minus_minus_set_rat A4) (@ B5 X4)))) C3)) top_top_set_rat)) (=> (not _let_1) (= (@ comple4298007329820168263et_rat (@ (@ image_o_set_rat (lambda ((X4 Bool)) (@ (@ minus_minus_set_rat A4) (@ B5 X4)))) C3)) (@ (@ minus_minus_set_rat A4) (@ comple3890839924845867745et_rat (@ (@ image_o_set_rat B5) C3)))))))) (forall ((R set_Pr5564308138774400199at_nat) (A4 set_Pr4329608150637261639at_nat)) (=> (@ (@ ord_le3091953645718357095at_nat R) (@ (@ produc4441300235185154312at_nat A4) (lambda ((Uu produc3843707927480180839at_nat)) A4))) (=> (forall ((X produc3843707927480180839at_nat)) (=> (@ (@ member8757157785044589968at_nat X) A4) (@ (@ member6009668390874684176at_nat (@ (@ produc2335810615602371415at_nat X) X)) R))) (@ (@ refl_o7446464703481863270at_nat A4) R)))) (= (@ (@ image_1320371278474632150at_nat nat_sum_encode) top_to6661820994512907621at_nat) top_top_set_nat) (forall ((F (-> int nat)) (A4 set_int)) (=> (@ (@ inj_on_int_nat F) A4) (@ (@ inj_on1389844818000382683et_nat (@ image_int_nat F)) (@ finite_Fpow_int A4)))) (forall ((Rep (-> int product_prod_nat_nat)) (Abs (-> product_prod_nat_nat int)) (F (-> int product_prod_nat_nat)) (G (-> code_integer int)) (R3 (-> product_prod_nat_nat product_prod_nat_nat Bool)) (S5 (-> product_prod_nat_nat int Bool))) (=> (@ (@ (@ type_d7732240953928457511at_nat Rep) Abs) top_to4669805908274784177at_nat) (= (@ (@ (@ bNF_vi2881549544236934259_int_o F) G) (@ (@ relcom8911704206367525917at_int (@ conver6965824823119931701at_nat R3)) S5)) (@ (@ relcom967497705283160040nteger (@ conversep_int_int (@ (@ (@ bNF_vi1204582724742824157_nat_o Rep) F) R3))) (@ (@ (@ bNF_vi2881549544236934259_int_o Rep) G) S5))))) (forall ((X2 product_unit) (Y3 product_unit)) (= (@ (@ (@ if_Product_unit false) X2) Y3) Y3)) (forall ((A produc3843707927480180839at_nat) (A4 set_Pr4329608150637261639at_nat) (F (-> produc3843707927480180839at_nat set_nat)) (C set_nat)) (=> (@ (@ member8757157785044589968at_nat A) A4) (=> (forall ((X produc3843707927480180839at_nat)) (=> (@ (@ member8757157785044589968at_nat X) A4) (= (@ F X) C))) (= (@ comple7399068483239264473et_nat (@ (@ image_3160451284896210088et_nat F) A4)) C)))) (forall ((F (-> (-> code_integer code_integer) produc8923325533196201883nteger produc8923325533196201883nteger)) (G (-> (-> code_integer code_integer) produc8923325533196201883nteger produc8923325533196201883nteger)) (H (-> code_integer code_integer code_integer))) (= (@ (@ comp_C6484513282182537548nteger (@ (@ bNF_co1764293801198077070nteger F) G)) H) (@ (@ bNF_co3156833790671340178nteger (@ (@ comp_C8797469213163452608nteger F) H)) (@ (@ comp_C8797469213163452608nteger G) H)))) (forall ((F (-> Bool int)) (A4 set_o) (X2 Bool) (U int)) (let ((_let_1 (@ (@ image_o_int F) A4))) (let ((_let_2 (@ ord_less_eq_int U))) (=> (@ condit2212336002400062152ve_int _let_1) (=> (@ (@ member_o X2) A4) (=> (@ _let_2 (@ F X2)) (@ _let_2 (@ complete_Sup_Sup_int _let_1)))))))) (forall ((U Bool) (A4 set_o) (A Bool) (B5 (-> Bool set_o))) (=> (@ (@ member_o U) A4) (= (@ comple3063163877087187839_set_o (@ (@ image_o_set_o (lambda ((X4 Bool)) (@ (@ insert_o A) (@ B5 X4)))) A4)) (@ (@ insert_o A) (@ comple3063163877087187839_set_o (@ (@ image_o_set_o B5) A4)))))) (forall ((A4 set_int) (F (-> int Bool)) (B5 set_o)) (=> (forall ((X int)) (=> (@ (@ member_int X) A4) (@ (@ member_o (@ F X)) B5))) (@ (@ ord_less_eq_set_o (@ (@ image_int_o F) A4)) B5))) (forall ((C3 set_nat) (A4 set_nat) (B5 (-> nat set_nat))) (let ((_let_1 (@ (@ sup_sup_set_nat A4) (@ comple7399068483239264473et_nat (@ (@ image_nat_set_nat B5) C3))))) (let ((_let_2 (= C3 bot_bot_set_nat))) (and (=> (not _let_2) (= _let_1 (@ comple7399068483239264473et_nat (@ (@ image_nat_set_nat (lambda ((X4 nat)) (@ (@ sup_sup_set_nat A4) (@ B5 X4)))) C3)))) (=> _let_2 (= _let_1 A4)))))) (forall ((B5 set_nat) (A4 set_nat)) (let ((_let_1 (@ produc457027306803732586at_nat A4))) (let ((_let_2 (@ image_2486076414777270412at_nat product_fst_nat_nat))) (let ((_let_3 (= B5 bot_bot_set_nat))) (and (=> (not _let_3) (= (@ _let_2 (@ _let_1 (lambda ((Uu nat)) B5))) A4)) (=> _let_3 (= (@ _let_2 (@ _let_1 (lambda ((Uu nat)) B5))) bot_bot_set_nat))))))) (= produc6011863565407846595at_nat (@ (@ comp_P4974406650942564362at_nat produc2937545259423399429at_nat) (@ produc7548845685434208379at_nat (lambda ((X4 set_Pr1261947904930325089at_nat) (Y5 set_Pr1261947904930325089at_nat)) (@ (@ produc2922128104949294807at_nat Y5) X4))))) (forall ((X2 a) (H heap_e7401611519738050253t_unit) (X3 a)) (= (@ (@ get_a (@ produc1126150082675451753t_unit (@ (@ alloc_a X2) H))) (@ produc473321116828791851t_unit (@ (@ alloc_a X3) H))) X2)) (forall ((U int) (A4 set_int) (A Bool) (B5 (-> int set_o))) (=> (@ (@ member_int U) A4) (= (@ comple3063163877087187839_set_o (@ (@ image_int_set_o (lambda ((X4 int)) (@ (@ insert_o A) (@ B5 X4)))) A4)) (@ (@ insert_o A) (@ comple3063163877087187839_set_o (@ (@ image_int_set_o B5) A4)))))) (forall ((B5 (-> nat int Bool)) (C3 (-> num nat Bool)) (A4 (-> int int Bool))) (@ (@ (@ (@ bNF_re5843449549409830101nt_nat (@ (@ bNF_re4155804983283621959um_nat B5) C3)) (@ (@ bNF_re3642433447925381491nt_nat (@ (@ bNF_re3713166177374151349at_int A4) B5)) (@ (@ bNF_re1845987051190671011um_nat A4) C3))) comp_nat_num_int) comp_int_nat_int)) _let_307 _let_306 (forall ((A4 set_nat) (C3 set_o) (B5 set_nat) (D set_o)) (= (@ (@ ord_le7519981659162375251_nat_o (@ (@ product_Sigma_nat_o A4) (lambda ((Uu nat)) C3))) (@ (@ product_Sigma_nat_o B5) (lambda ((Uu nat)) D))) (or (= A4 bot_bot_set_nat) (and (@ (@ ord_less_eq_set_nat A4) B5) (@ (@ ord_less_eq_set_o C3) D)) (= C3 bot_bot_set_o)))) (forall ((G (-> int nat)) (C3 set_int) (B5 set_int) (X2 int)) (let ((_let_1 (@ (@ sup_sup_set_int B5) (@ (@ insert_int X2) bot_bot_set_int)))) (=> (@ (@ inj_on_int_nat G) C3) (=> (@ (@ ord_less_eq_set_int C3) _let_1) (@ (@ member_nat_int (lambda ((I2 nat)) (@ (@ (@ if_int (@ (@ member_nat I2) (@ (@ image_int_nat G) C3))) (@ (@ (@ the_inv_into_int_nat C3) G) I2)) X2))) (@ (@ bNF_We7538026264050006418at_int top_top_set_nat) _let_1)))))) (= divmod_nat (lambda ((M5 nat) (N4 nat)) (@ (@ (@ if_Pro6206227464963214023at_nat (or (= N4 zero_zero_nat) (@ (@ ord_less_nat M5) N4))) (@ (@ product_Pair_nat_nat zero_zero_nat) M5)) (@ (@ produc2626176000494625587at_nat (lambda ((Q3 nat) (__flatten_var_0 nat)) (@ (@ product_Pair_nat_nat (@ suc Q3)) __flatten_var_0))) (@ (@ divmod_nat (@ (@ minus_minus_nat M5) N4)) N4))))) (forall ((F (-> nat rat)) (C3 set_nat) (A4 set_o) (B5 (-> Bool set_nat)) (J4 Bool)) (=> (@ (@ inj_on_nat_rat F) C3) (=> (forall ((X Bool)) (=> (@ (@ member_o X) A4) (@ (@ ord_less_eq_set_nat (@ B5 X)) C3))) (=> (@ (@ member_o J4) A4) (= (@ (@ image_nat_rat F) (@ comple7806235888213564991et_nat (@ (@ image_o_set_nat B5) A4))) (@ comple4298007329820168263et_rat (@ (@ image_o_set_rat (lambda ((X4 Bool)) (@ (@ image_nat_rat F) (@ B5 X4)))) A4))))))) (forall ((A4 set_int) (B5 (-> int set_nat))) (= (@ (@ image_2855239504505064772at_int product_fst_int_nat) (@ (@ produc1456381018704787142nt_nat A4) B5)) (@ collect_int (lambda ((X4 int)) (and (not (= (@ B5 X4) bot_bot_set_nat)) (@ (@ member_int X4) A4)))))) (forall ((P produc3843707927480180839at_nat) (C (-> set_Pr1261947904930325089at_nat set_Pr1261947904930325089at_nat Bool))) (=> (forall ((A3 set_Pr1261947904930325089at_nat) (B3 set_Pr1261947904930325089at_nat)) (=> (= P (@ (@ produc2922128104949294807at_nat A3) B3)) (@ (@ C A3) B3))) (@ (@ produc410239310623530412_nat_o C) P))) (= (@ (@ image_nat_list_nat nat_list_decode) top_top_set_nat) top_top_set_list_nat) (forall ((S5 set_nat) (F (-> int nat)) (T3 set_int)) (= (@ (@ ord_less_eq_set_nat S5) (@ (@ image_int_nat F) T3)) (exists ((U2 set_int)) (and (@ (@ ord_less_eq_set_int U2) T3) (= S5 (@ (@ image_int_nat F) U2)) (@ (@ inj_on_int_nat F) U2))))) (forall ((A Bool) (A4 set_o) (B5 (-> Bool set_nat))) (=> (@ (@ member_o A) A4) (@ (@ ord_less_eq_set_nat (@ comple7806235888213564991et_nat (@ (@ image_o_set_nat B5) A4))) (@ B5 A)))) (forall ((F (-> nat nat)) (A4 set_nat) (Y3 nat)) (=> (@ (@ inj_on_nat_nat F) A4) (=> (@ (@ member_nat Y3) (@ (@ image_nat_nat F) A4)) (= (@ F (@ (@ (@ the_inv_into_nat_nat A4) F) Y3)) Y3)))) (forall ((I3 set_int) (F (-> int set_nat)) (X2 set_nat)) (=> (not (= I3 bot_bot_set_int)) (=> (forall ((I4 int)) (=> (@ (@ member_int I4) I3) (= (@ F I4) X2))) (= (@ comple7399068483239264473et_nat (@ (@ image_int_set_nat F) I3)) X2)))) (forall ((A nat) (B nat)) (= (@ (@ image_nat_int semiri1314217659103216013at_int) (@ (@ set_or1269000886237332187st_nat A) B)) (@ (@ set_or1266510415728281911st_int (@ semiri1314217659103216013at_int A)) (@ semiri1314217659103216013at_int B)))) (forall ((F (-> int int)) (A4 set_int)) (=> (@ (@ inj_on_int_int F) A4) (= (@ (@ image_int_int (@ (@ the_inv_into_int_int A4) F)) (@ (@ image_int_int F) A4)) A4))) (forall ((A4 set_o) (F (-> Bool Bool)) (B5 set_o)) (=> (forall ((X Bool)) (=> (@ (@ member_o X) A4) (@ (@ member_o (@ F X)) B5))) (@ (@ ord_less_eq_set_o (@ (@ image_o_o F) A4)) B5))) (forall ((R set_Product_prod_o_o) (A Bool) (B Bool)) (let ((_let_1 (@ field_o R))) (=> (@ (@ order_6238756238976269133r_on_o _let_1) R) (=> (@ (@ member_o A) _let_1) (=> (@ (@ member_o B) _let_1) (= (@ (@ member7466972457876170832od_o_o (@ (@ product_Pair_o_o A) B)) R) (not (@ (@ member7466972457876170832od_o_o (@ (@ product_Pair_o_o B) A)) (@ (@ minus_7052513330764642158od_o_o R) id_o2))))))))) (forall ((X2 Bool)) (= (@ (@ image_char_o (lambda ((Uu char)) X2)) top_top_set_char) (@ (@ insert_o X2) bot_bot_set_o))) (forall ((A4 set_se5479201105039950375at_nat) (R set_Pr7459493094073627847at_nat) (X2 set_Pr4329608150637261639at_nat) (Y3 set_Pr4329608150637261639at_nat)) (=> (@ (@ refl_o6272981002401706822at_nat A4) R) (=> (@ (@ member1466754251312161552at_nat (@ (@ produc9060074326276436823at_nat X2) Y3)) R) (@ (@ member6273874620674182256at_nat Y3) A4)))) (forall ((A set_Pr4329608150637261639at_nat) (B set_Pr4329608150637261639at_nat)) (= (@ (@ member1466754251312161552at_nat (@ (@ produc9060074326276436823at_nat A) B)) id_set4888139568991089827at_nat) (= A B))) (forall ((F (-> product_unit set_nat))) (= (@ comple7399068483239264473et_nat (@ (@ image_8173849991827986510et_nat F) bot_bo3957492148770167129t_unit)) bot_bot_set_nat)) (forall ((F (-> char nat)) (A char) (A4 set_char)) (=> (@ (@ inj_on_char_nat F) top_top_set_char) (= (@ (@ member_nat (@ F A)) (@ (@ image_char_nat F) A4)) (@ (@ member_char A) A4)))) (forall ((F (-> char nat)) (B5 set_nat) (A4 set_char)) (let ((_let_1 (@ image_char_nat F))) (=> (= (@ _let_1 top_top_set_char) top_top_set_nat) (=> (@ (@ ord_less_eq_set_char (@ (@ vimage_char_nat F) B5)) A4) (@ (@ ord_less_eq_set_nat B5) (@ _let_1 A4)))))) (forall ((Rep (-> num char)) (Abs (-> char num)) (S5 (-> char set_nat)) (M (-> nat char)) (F (-> nat nat)) (S6 (-> nat set_nat)) (G (-> int nat))) (let ((_let_1 (@ image_nat_nat F))) (=> (@ (@ (@ type_d4396077731765706521m_char Rep) Abs) top_top_set_char) (=> (= (@ (@ comp_c915470459090449932at_nat S5) M) (@ (@ comp_s3433241188411525313at_nat _let_1) S6)) (= (@ (@ comp_num_set_nat_int (@ (@ comp_c6696174282101004374at_num S5) Rep)) (@ (@ comp_nat_num_int (@ (@ comp_char_num_nat Abs) M)) G)) (@ (@ comp_s3430750717902475037at_int _let_1) (@ (@ comp_nat_set_nat_int S6) G))))))) (forall ((I3 set_Product_unit) (F (-> product_unit set_nat)) (X2 set_nat)) (=> (not (= I3 bot_bo3957492148770167129t_unit)) (= (@ comple7806235888213564991et_nat (@ (@ image_8173849991827986510et_nat (lambda ((I2 product_unit)) (@ (@ inf_inf_set_nat (@ F I2)) X2))) I3)) (@ (@ inf_inf_set_nat (@ comple7806235888213564991et_nat (@ (@ image_8173849991827986510et_nat F) I3))) X2)))) (forall ((R3 (-> nat nat Bool))) (= (@ (@ bNF_re3715656647883201625at_nat (lambda ((Y2 int) (Z int)) (= Y2 Z))) R3) (@ (@ relcom2406850561174050523nt_nat (@ conver1572571282669976050nt_nat (@ (@ bNF_Gr1462982377596425817nt_nat (@ collec2532482545165550967at_nat (lambda ((X4 (-> int product_prod_nat_nat))) (@ (@ ord_le3146513528884898305at_nat (@ (@ image_8883965892284119310at_nat X4) top_top_set_int)) (@ collec3392354462482085612at_nat (@ produc6081775807080527818_nat_o R3)))))) (@ comp_P1953119740877977564at_int product_fst_nat_nat)))) (@ (@ bNF_Gr1462982377596425817nt_nat (@ collec2532482545165550967at_nat (lambda ((X4 (-> int product_prod_nat_nat))) (@ (@ ord_le3146513528884898305at_nat (@ (@ image_8883965892284119310at_nat X4) top_top_set_int)) (@ collec3392354462482085612at_nat (@ produc6081775807080527818_nat_o R3)))))) (@ comp_P1953119740877977564at_int product_snd_nat_nat))))) _let_305 (forall ((B5 set_Product_unit) (F (-> int nat)) (A4 set_int) (G (-> product_unit nat))) (let ((_let_1 (@ (@ image_int_nat F) A4))) (=> (not (= B5 bot_bo3957492148770167129t_unit)) (=> (@ condit1738341127787009408ow_nat _let_1) (=> (forall ((M4 product_unit)) (=> (@ (@ member_Product_unit M4) B5) (exists ((X6 int)) (and (@ (@ member_int X6) A4) (@ (@ ord_less_eq_nat (@ F X6)) (@ G M4)))))) (@ (@ ord_less_eq_nat (@ complete_Inf_Inf_nat _let_1)) (@ complete_Inf_Inf_nat (@ (@ image_875570014554754200it_nat G) B5)))))))) (forall ((X2 nat) (Y3 nat) (R set_Pr958786334691620121nt_int) (F (-> nat int))) (= (@ (@ member8440522571783428010at_nat (@ (@ product_Pair_nat_nat X2) Y3)) (@ (@ inv_image_int_nat R) F)) (@ (@ member5262025264175285858nt_int (@ (@ product_Pair_int_int (@ F X2)) (@ F Y3))) R))) (forall ((A4 set_Pr4329608150637261639at_nat) (F set_nat)) (=> (not (= A4 bot_bo228742789529271731at_nat)) (= (@ comple7399068483239264473et_nat (@ (@ image_3160451284896210088et_nat (lambda ((I2 produc3843707927480180839at_nat)) F)) A4)) F))) (forall ((P2 (-> nat nat Bool)) (Y3 nat) (X2 nat)) (let ((_let_1 (@ (@ product_Pair_nat_nat X2) Y3))) (=> (@ (@ P2 Y3) X2) (@ (@ P2 (@ product_snd_nat_nat _let_1)) (@ product_fst_nat_nat _let_1))))) (forall ((F (-> ref_a ref_a)) (G (-> heap_e7401611519738050253t_unit heap_e7401611519738050253t_unit)) (X2 produc7812382424243267045t_unit)) (= (@ produc473321116828791851t_unit (@ (@ (@ produc3456481717235892722t_unit F) G) X2)) (@ F (@ produc473321116828791851t_unit X2)))) (forall ((F (-> nat nat)) (X5 set_nat) (G1 (-> nat nat)) (G22 (-> nat nat))) (=> (= (@ (@ image_nat_nat F) X5) top_top_set_nat) (=> (forall ((X nat)) (=> (@ (@ member_nat X) X5) (= (@ (@ (@ comp_nat_nat_nat G1) F) X) (@ (@ (@ comp_nat_nat_nat G22) F) X)))) (= G1 G22)))) (forall ((P2 (-> int Bool)) (Q2 (-> int Bool))) (= (@ collec213857154873943460nt_int (@ produc4947309494688390418_int_o (lambda ((A5 int) (B4 int)) (and (@ Q2 B4) (@ P2 A5))))) (@ (@ produc1453890548195736866nt_int (@ collect_int P2)) (lambda ((Uu int)) (@ collect_int Q2))))) (forall ((F (-> set_nat set_nat)) (A4 set_set_nat)) (=> (@ order_1005506198798982270et_nat F) (@ (@ ord_less_eq_set_nat (@ comple7399068483239264473et_nat (@ (@ image_7916887816326733075et_nat F) A4))) (@ F (@ comple7399068483239264473et_nat A4))))) (forall ((F (-> (-> code_integer code_integer) produc8923325533196201883nteger produc8923325533196201883nteger)) (G (-> code_integer code_integer code_integer))) (=> (@ (@ inj_on3998011822705705585nteger F) top_to3804862627464599871nteger) (=> (@ (@ inj_on108595395805848489nteger G) top_to4645266643341252675nteger) (@ (@ inj_on7031512951821619701nteger (@ (@ comp_C8797469213163452608nteger F) G)) top_to4645266643341252675nteger)))) _let_304 (forall ((F (-> nat rat)) (A4 set_rat)) (let ((_let_1 (@ image_nat_rat F))) (=> (= (@ _let_1 top_top_set_nat) top_top_set_rat) (= (@ _let_1 (@ (@ vimage_nat_rat F) A4)) A4)))) (forall ((F (-> nat rat)) (B5 set_rat) (I nat)) (=> (@ (@ ord_less_eq_set_rat (@ (@ image_nat_rat F) top_top_set_nat)) B5) (@ (@ member_rat (@ F I)) B5))) (forall ((F (-> Bool product_unit)) (A4 set_o) (A Bool)) (let ((_let_1 (@ (@ image_o_Product_unit F) A4))) (let ((_let_2 (@ comple2584293577114468500t_unit _let_1))) (=> (= (@ comple4687483117567863418t_unit _let_1) _let_2) (=> (@ condit2080475194861589617t_unit _let_1) (=> (@ condit9161856309968323677t_unit _let_1) (=> (@ (@ member_o A) A4) (= (@ F A) _let_2)))))))) (forall ((F (-> Bool Bool)) (G (-> nat num)) (H (-> nat Bool)) (I (-> int nat))) (= (@ (@ comp_P9057111047297513408at_int (@ (@ produc3628557804203378146at_num F) G)) (@ (@ produc8250590009387450446nt_nat H) I)) (@ (@ produc4807921795543229080nt_num (@ (@ comp_o_o_nat F) H)) (@ (@ comp_nat_num_int G) I)))) (forall ((F (-> Bool Bool)) (G (-> Bool nat)) (X2 Bool)) (= (@ (@ (@ comp_P1422407636550552773_nat_o (@ (@ produc7071226018047599512at_nat F) id_nat)) (@ (@ bNF_convol_o_o_nat id_o) G)) X2) (@ (@ (@ bNF_convol_o_o_nat (@ (@ comp_o_o_o id_o) F)) G) X2))) (forall ((X2 set_Product_unit) (Y3 set_Product_unit)) (= (@ (@ (@ if_set_Product_unit false) X2) Y3) Y3)) (forall ((A4 set_Product_unit) (F (-> product_unit product_unit)) (U product_unit)) (let ((_let_1 (@ (@ image_405062704495631173t_unit F) A4))) (=> (not (= A4 bot_bo3957492148770167129t_unit)) (=> (@ condit2080475194861589617t_unit _let_1) (= (@ (@ ord_le3221252021190050221t_unit (@ comple4687483117567863418t_unit _let_1)) U) (forall ((X4 product_unit)) (=> (@ (@ member_Product_unit X4) A4) (@ (@ ord_le3221252021190050221t_unit (@ F X4)) U)))))))) (forall ((A heap_e7401611519738050253t_unit) (P produc7812382424243267045t_unit)) (=> (@ (@ member242389114213480694t_unit A) (@ basic_1496934909540232809t_unit P)) (= A (@ produc1126150082675451753t_unit P)))) (forall ((F (-> nat int)) (A4 set_set_nat)) (=> (@ (@ inj_on_nat_int F) (@ comple7399068483239264473et_nat A4)) (@ (@ inj_on426556184350386907et_int (@ image_nat_int F)) A4))) (forall ((A Bool) (A4 set_o) (B int) (B5 (-> Bool set_int))) (=> (@ (@ member_o A) A4) (=> (@ (@ member_int B) (@ B5 A)) (@ (@ member7847949116333733898_o_int (@ (@ product_Pair_o_int A) B)) (@ (@ product_Sigma_o_int A4) B5))))) (forall ((A (-> nat nat)) (B (-> nat nat)) (C (-> nat nat)) (V nat)) (=> (= (@ (@ comp_nat_nat_nat A) B) C) (= (@ A (@ B V)) (@ C V)))) (forall ((H heap_e7401611519738050253t_unit) (R ref_a) (R2 ref_a)) (let ((_let_1 (@ present_a H))) (=> (@ _let_1 R) (=> (not (@ _let_1 R2)) (@ (@ noteq_a_a R) R2))))) (forall ((C3 set_Product_unit) (A4 (-> product_unit set_Product_unit)) (B5 set_Product_unit)) (let ((_let_1 (= C3 bot_bo3957492148770167129t_unit))) (and (=> _let_1 (= (@ comple3349607820504768346t_unit (@ (@ image_7778121751606633509t_unit (lambda ((X4 product_unit)) (@ (@ sup_su793286257634532545t_unit (@ A4 X4)) B5))) C3)) bot_bo3957492148770167129t_unit)) (=> (not _let_1) (= (@ comple3349607820504768346t_unit (@ (@ image_7778121751606633509t_unit (lambda ((X4 product_unit)) (@ (@ sup_su793286257634532545t_unit (@ A4 X4)) B5))) C3)) (@ (@ sup_su793286257634532545t_unit (@ comple3349607820504768346t_unit (@ (@ image_7778121751606633509t_unit A4) C3))) B5)))))) (forall ((F (-> (-> product_prod_nat_nat int Bool) produc4196048018000912732at_int Bool)) (P2 (-> product_prod_nat_nat product_prod_nat_nat Bool)) (Q2 (-> product_prod_nat_nat int Bool))) (@ (@ (@ (@ (@ bNF_cs7194553038297458973at_int (@ collec2851339944984316337at_int (@ F (@ (@ relcom8911704206367525917at_int P2) Q2)))) produc6408287024330202629at_nat) produc4619704898428564714at_int) (@ (@ bNF_fs6342258632037972510at_int P2) Q2)) (@ (@ bNF_sn649997494946348640at_int P2) Q2))) (forall ((H (-> char char)) (F4 set_char)) (=> (@ finite_finite_char (@ (@ vimage_char_char H) F4)) (=> (= (@ (@ image_char_char H) top_top_set_char) top_top_set_char) (@ finite_finite_char F4)))) (forall ((F (-> nat rat)) (A nat) (A4 set_nat)) (let ((_let_1 (@ insert_nat A))) (let ((_let_2 (@ inj_on_nat_rat F))) (= (@ _let_2 (@ _let_1 A4)) (and (@ _let_2 A4) (not (@ (@ member_rat (@ F A)) (@ (@ image_nat_rat F) (@ (@ minus_minus_set_nat A4) (@ _let_1 bot_bot_set_nat)))))))))) (forall ((R1 (-> int int Bool)) (R22 (-> int int Bool)) (P2 (-> int int Bool)) (Q2 (-> int int Bool)) (A product_prod_int_int) (A4 set_Pr958786334691620121nt_int) (B product_prod_int_int) (B5 set_Pr958786334691620121nt_int)) (=> (@ (@ (@ (@ bNF_re3403563459893282935_int_o R1) (@ (@ bNF_re5089333283451836215nt_o_o R22) (lambda ((Y2 Bool) (Z Bool)) (= Y2 Z)))) P2) Q2) (=> (@ (@ member5262025264175285858nt_int A) A4) (=> (@ (@ member5262025264175285858nt_int B) B5) (=> (@ (@ ord_le2843351958646193337nt_int A4) (@ collec213857154873943460nt_int (@ produc4947309494688390418_int_o R1))) (=> (@ (@ ord_le2843351958646193337nt_int B5) (@ collec213857154873943460nt_int (@ produc4947309494688390418_int_o R22))) (= (@ (@ P2 (@ product_fst_int_int A)) (@ product_fst_int_int B)) (@ (@ Q2 (@ product_snd_int_int A)) (@ product_snd_int_int B))))))))) (forall ((A4 set_Pr4329608150637261639at_nat) (X2 product_unit) (F (-> produc3843707927480180839at_nat product_unit))) (=> (forall ((I4 produc3843707927480180839at_nat)) (=> (@ (@ member8757157785044589968at_nat I4) A4) (@ (@ ord_le3221252021190050221t_unit X2) (@ F I4)))) (=> (forall ((Y product_unit)) (=> (forall ((I5 produc3843707927480180839at_nat)) (=> (@ (@ member8757157785044589968at_nat I5) A4) (@ (@ ord_le3221252021190050221t_unit Y) (@ F I5)))) (@ (@ ord_le3221252021190050221t_unit Y) X2))) (= (@ comple2584293577114468500t_unit (@ (@ image_7082456443403096939t_unit F) A4)) X2)))) (forall ((X2 int) (A4 set_int) (F (-> int set_Product_unit))) (let ((_let_1 (@ (@ vimage4422279681566046568t_unit (@ produc550872421827702152t_unit X2)) (@ (@ produc2622961094310184599t_unit A4) F)))) (let ((_let_2 (@ (@ member_int X2) A4))) (and (=> _let_2 (= _let_1 (@ F X2))) (=> (not _let_2) (= _let_1 bot_bo3957492148770167129t_unit)))))) _let_303 (forall ((F (-> char char)) (G (-> nat char))) (=> (= (@ (@ image_char_char F) top_top_set_char) top_top_set_char) (=> (= (@ (@ image_nat_char G) top_top_set_nat) top_top_set_char) (= (@ (@ image_5973708714899544198r_char (@ (@ produc8759894717825771837t_char F) G)) top_to5594287848199751986ar_nat) top_to1235241553633177651r_char)))) (forall ((I Bool) (A4 set_o) (U product_unit) (F (-> Bool product_unit))) (let ((_let_1 (@ ord_le3221252021190050221t_unit U))) (=> (@ (@ member_o I) A4) (=> (@ _let_1 (@ F I)) (@ _let_1 (@ comple4687483117567863418t_unit (@ (@ image_o_Product_unit F) A4))))))) (forall ((F (-> product_unit Bool)) (A product_unit) (B5 set_Product_unit)) (let ((_let_1 (@ image_Product_unit_o F))) (= (@ _let_1 (@ (@ insert_Product_unit A) B5)) (@ (@ insert_o (@ F A)) (@ _let_1 B5))))) (forall ((A4 set_se7855581050983116737at_nat) (R set_Pr4329608150637261639at_nat) (A set_Pr1261947904930325089at_nat) (B set_Pr1261947904930325089at_nat)) (=> (@ (@ refl_o6955724340487615712at_nat A4) R) (=> (@ (@ member8757157785044589968at_nat (@ (@ produc2922128104949294807at_nat A) B)) R) (and (@ (@ member2643936169264416010at_nat B) A4) (@ (@ member2643936169264416010at_nat A) A4))))) (forall ((F (-> nat rat)) (V (-> rat nat))) (= (@ (@ image_rat_rat (@ (@ comp_nat_rat_rat F) V)) top_top_set_rat) (@ (@ image_nat_rat F) (@ (@ image_rat_nat V) top_top_set_rat)))) (forall ((A4 set_Pr958786334691620121nt_int) (F (-> product_prod_int_int nat))) (=> (not (@ finite2998713641127702882nt_int A4)) (=> (@ finite_finite_nat (@ (@ image_5044651549707136836nt_nat F) A4)) (exists ((X product_prod_int_int)) (and (not (@ finite2998713641127702882nt_int (@ collec213857154873943460nt_int (lambda ((A5 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nat)) (F22 (-> nat nat)) (G1 (-> nat num)) (G22 (-> int nat))) (= (@ (@ produc4534572193387464160nt_num (@ (@ comp_nat_nat_nat F1) F22)) (@ (@ comp_nat_num_int G1) G22)) (@ (@ comp_P6334688330072917552at_int (@ (@ produc3535218481486409604at_num F1) G1)) (@ (@ produc7977240407231685526nt_nat F22) G22)))) (forall ((T2 produc1319942482725812455at_nat)) (= T2 (@ (@ produc9060074326276436823at_nat (@ produc4486455499028916547at_nat T2)) (@ produc826222791318859909at_nat T2)))) (forall ((R set_Pr4329608150637261639at_nat) (A4 set_se7855581050983116737at_nat)) (=> (@ (@ ord_le1268244103169919719at_nat R) (@ (@ produc7726050920695093128at_nat A4) (lambda ((Uu set_Pr1261947904930325089at_nat)) A4))) (=> (forall ((X set_Pr1261947904930325089at_nat)) (=> (@ (@ member2643936169264416010at_nat X) A4) (@ (@ member8757157785044589968at_nat (@ (@ produc2922128104949294807at_nat X) X)) R))) (@ (@ refl_o6955724340487615712at_nat A4) R)))) (forall ((F (-> int nat)) (A4 (-> nat int)) (I3 set_nat)) (let ((_let_1 (@ (@ image_nat_int A4) I3))) (=> (@ order_mono_int_nat F) (=> (@ condit2212336002400062152ve_int _let_1) (=> (not (= I3 bot_bot_set_nat)) (@ (@ ord_less_eq_nat (@ complete_Sup_Sup_nat (@ (@ image_nat_nat (lambda ((X4 nat)) (@ F (@ A4 X4)))) I3))) (@ F (@ complete_Sup_Sup_int _let_1)))))))) (forall ((X2 produc3843707927480180839at_nat)) (@ (@ refl_o7446464703481863270at_nat (@ (@ insert9069300056098147895at_nat X2) bot_bo228742789529271731at_nat)) (@ (@ insert398606708087465655at_nat (@ (@ produc2335810615602371415at_nat X2) X2)) bot_bo7193250159860175667at_nat))) (forall ((A4 set_Pr8693737435421807431at_nat) (B5 set_se6425085446898223655at_nat)) (let ((_let_1 (@ sup_su718114333110466843at_nat A4))) (= (@ _let_1 (@ comple6332534001959699150at_nat B5)) (@ comple6332534001959699150at_nat (@ (@ image_1013614488123988933at_nat _let_1) B5))))) (forall ((X2 int) (A4 set_int) (C product_unit)) (=> (@ (@ member_int X2) A4) (= (@ (@ image_5846526143423701914t_unit (lambda ((X4 int)) C)) A4) (@ (@ insert_Product_unit C) bot_bo3957492148770167129t_unit)))) (forall ((F (-> int nat)) (A4 set_int)) (=> (@ finite_finite_nat (@ (@ image_int_nat F) A4)) (=> (not (@ finite_finite_int A4)) (exists ((X nat)) (and (@ (@ member_nat X) (@ (@ image_int_nat F) A4)) (not (@ finite_finite_int (@ (@ vimage_int_nat F) (@ (@ insert_nat X) bot_bot_set_nat))))))))) (forall ((F (-> int nat)) (G (-> nat num)) (X2 set_num)) (= (@ (@ vimage_int_nat F) (@ (@ vimage_nat_num G) X2)) (@ (@ vimage_int_num (@ (@ comp_nat_num_int G) F)) X2))) (= bNF_re717283939379294677_int_o (lambda ((R6 (-> product_prod_nat_nat int Bool)) (S4 (-> (-> product_prod_nat_nat Bool) (-> int Bool) Bool)) (F2 (-> product_prod_nat_nat product_prod_nat_nat Bool)) (G3 (-> int int Bool))) (@ (@ ord_le129227817499904167_int_o R6) (@ (@ (@ bNF_vi5082502771524357669nt_o_o F2) G3) S4)))) (forall ((A4 set_o) (F (-> Bool nat))) (=> (not (@ finite_finite_o A4)) (=> (@ finite_finite_nat (@ (@ image_o_nat F) A4)) (exists ((X Bool)) (and (@ (@ member_o X) A4) (not (@ finite_finite_o (@ collect_o (lambda ((A5 Bool)) (and (= (@ F A5) (@ F X)) (@ (@ member_o A5) A4))))))))))) (forall ((B nat) (F (-> int nat)) (X2 int) (C nat) (G (-> int nat)) (A4 set_int)) (=> (= B (@ F X2)) (=> (= C (@ G X2)) (=> (@ (@ member_int X2) A4) (@ (@ member8440522571783428010at_nat (@ (@ product_Pair_nat_nat B) C)) (@ (@ (@ bNF_Gr7689810333322530600at_nat A4) F) G)))))) (forall ((F (-> Bool nat))) (= (@ (@ image_o_nat F) bot_bot_set_o) bot_bot_set_nat)) (forall ((A4 set_Pr4329608150637261639at_nat) (F (-> produc3843707927480180839at_nat set_nat)) (X2 set_nat)) (=> (forall ((I4 produc3843707927480180839at_nat)) (=> (@ (@ member8757157785044589968at_nat I4) A4) (@ (@ ord_less_eq_set_nat (@ F I4)) X2))) (=> (forall ((Y set_nat)) (=> (forall ((I5 produc3843707927480180839at_nat)) (=> (@ (@ member8757157785044589968at_nat I5) A4) (@ (@ ord_less_eq_set_nat (@ F I5)) Y))) (@ (@ ord_less_eq_set_nat X2) Y))) (= (@ comple7399068483239264473et_nat (@ (@ image_3160451284896210088et_nat F) A4)) X2)))) (forall ((T3 (-> int product_prod_nat_nat Bool)) (R3 (-> product_prod_nat_nat product_prod_nat_nat Bool))) (=> (@ left_u1182257597767569412at_nat T3) (=> (@ (@ ord_le5604493270027003598_nat_o R3) (lambda ((Y2 product_prod_nat_nat) (Z product_prod_nat_nat)) (= Y2 Z))) (@ (@ ord_le6741204236512500942_int_o (@ (@ relcom1106208330880909712at_int T3) (@ (@ relcom8911704206367525917at_int R3) (@ conver1866313717161370910at_nat T3)))) (lambda ((Y2 int) (Z int)) (= Y2 Z)))))) (forall ((A4 set_nat) (C set_char)) (let ((_let_1 (= A4 bot_bot_set_nat))) (and (=> (not _let_1) (= (@ comple7965528767983648192t_char (@ (@ image_nat_set_char (lambda ((Y5 nat)) C)) A4)) C)) (=> _let_1 (= (@ comple7965528767983648192t_char (@ (@ image_nat_set_char (lambda ((Y5 nat)) C)) A4)) top_top_set_char))))) (forall ((Rep (-> int Bool)) (Abs (-> Bool int)) (Rep2 (-> nat Bool)) (Abs2 (-> Bool nat)) (Rep3 (-> int nat)) (Abs3 (-> nat int)) (M (-> nat Bool)) (M1 (-> Bool Bool)) (M2 (-> nat Bool))) (=> (@ (@ (@ type_d8403010662121346494_int_o Rep) Abs) top_top_set_o) (=> (@ (@ (@ type_d1000680970699258650_nat_o Rep2) Abs2) top_top_set_o) (=> (@ (@ (@ type_d7249847660678803242nt_nat Rep3) Abs3) top_top_set_nat) (=> (= (@ (@ comp_nat_nat_int (@ (@ comp_o_nat_nat Abs2) M)) Rep3) (@ (@ comp_int_nat_int (@ (@ comp_o_nat_int (@ (@ comp_o_nat_o Abs2) M1)) Rep)) (@ (@ comp_nat_int_int (@ (@ comp_o_int_nat Abs) M2)) Rep3))) (= (@ (@ comp_o_o_nat M1) M2) M)))))) (forall ((G (-> int nat)) (H (-> int int)) (R (-> int nat)) (F (-> nat num))) (let ((_let_1 (@ comp_nat_num_int F))) (=> (= (@ (@ comp_int_nat_int G) H) R) (= (@ (@ comp_int_num_int (@ _let_1 G)) H) (@ _let_1 R))))) (forall ((A4 set_Product_unit) (C set_nat)) (let ((_let_1 (= A4 bot_bo3957492148770167129t_unit))) (and (=> _let_1 (= (@ comple7806235888213564991et_nat (@ (@ image_8173849991827986510et_nat (lambda ((Y5 product_unit)) C)) A4)) top_top_set_nat)) (=> (not _let_1) (= (@ comple7806235888213564991et_nat (@ (@ image_8173849991827986510et_nat (lambda ((Y5 product_unit)) C)) A4)) C))))) (forall ((F (-> nat rat)) (A4 set_nat)) (=> (@ order_2045666486212196060at_rat F) (=> (@ condit2214826472909112428ve_nat A4) (@ condit1103211067700513672ow_rat (@ (@ image_nat_rat F) A4))))) (forall ((Y3 product_prod_nat_nat) (YS set_Pr1261947904930325089at_nat) (X2 product_prod_nat_nat) (XS set_Pr1261947904930325089at_nat)) (=> (@ (@ member8440522571783428010at_nat Y3) YS) (=> (@ (@ member8206827879206165904at_nat (@ (@ produc6161850002892822231at_nat X2) Y3)) fun_pair_leq) (=> (@ (@ member8757157785044589968at_nat (@ (@ produc2922128104949294807at_nat XS) YS)) fun_max_weak) (@ (@ member8757157785044589968at_nat (@ (@ produc2922128104949294807at_nat (@ (@ insert8211810215607154385at_nat X2) XS)) YS)) fun_max_weak))))) (forall ((M set_nat) (N set_nat) (F (-> nat nat)) (G (-> nat nat))) (=> (= M N) (=> (forall ((X nat)) (=> (@ (@ member_nat X) N) (= (@ F X) (@ G X)))) (= (@ (@ image_nat_nat F) M) (@ (@ image_nat_nat G) N))))) (forall ((F (-> char char)) (G (-> char char))) (=> (= (@ (@ image_char_char F) top_top_set_char) top_top_set_char) (=> (= (@ (@ image_char_char G) top_top_set_char) top_top_set_char) (= (@ (@ image_char_char (@ (@ comp_char_char_char G) F)) top_top_set_char) top_top_set_char)))) (forall ((A4 set_o) (F (-> Bool int)) (G (-> Bool int))) (let ((_let_1 (@ (@ image_o_int G) A4))) (let ((_let_2 (@ (@ image_o_int F) A4))) (=> (not (= A4 bot_bot_set_o)) (=> (@ condit2212336002400062152ve_int _let_2) (=> (@ condit2212336002400062152ve_int _let_1) (= (@ (@ sup_sup_int (@ complete_Sup_Sup_int _let_2)) (@ complete_Sup_Sup_int _let_1)) (@ complete_Sup_Sup_int (@ (@ image_o_int (lambda ((A5 Bool)) (@ (@ sup_sup_int (@ F A5)) (@ G A5)))) A4))))))))) (forall ((A4 set_o) (B5 (-> Bool set_Product_unit))) (= (@ (@ image_8742399529945250561unit_o produc5219655352205527288t_unit) (@ (@ produc411009820408249917t_unit A4) B5)) (@ collect_o (lambda ((X4 Bool)) (and (not (= (@ B5 X4) bot_bo3957492148770167129t_unit)) (@ (@ member_o X4) A4)))))) (= ord_less_int (lambda ((X4 int) (Xa3 int)) (@ (@ (@ produc8739625826339149834_nat_o (lambda ((Y5 nat) (Z4 nat) (__flatten_var_0 product_prod_nat_nat)) (@ (@ produc6081775807080527818_nat_o (lambda ((U3 nat) (V3 nat)) (@ (@ ord_less_nat (@ (@ plus_plus_nat Y5) V3)) (@ (@ plus_plus_nat U3) Z4)))) __flatten_var_0))) (@ rep_Integ X4)) (@ rep_Integ Xa3)))) (forall ((X2 num) (Y3 nat)) (= (@ product_swap_num_nat (@ (@ product_Pair_num_nat X2) Y3)) (@ (@ product_Pair_nat_num Y3) X2))) (forall ((A4 set_Pr1261947904930325089at_nat) (R set_Pr8693737435421807431at_nat) (A product_prod_nat_nat)) (=> (@ (@ refl_o7122697186039111552at_nat A4) R) (=> (@ (@ member8440522571783428010at_nat A) A4) (@ (@ member8206827879206165904at_nat (@ (@ produc6161850002892822231at_nat A) A)) R)))) (forall ((A4 set_nat) (F (-> nat nat))) (=> (@ finite_finite_nat A4) (=> (@ (@ ord_less_eq_set_nat A4) (@ (@ image_nat_nat F) A4)) (@ (@ inj_on_nat_nat F) A4)))) (forall ((F (-> int int)) (A4 set_int) (Y3 int) (X2 int)) (=> (@ (@ inj_on_int_int F) A4) (=> (not (@ (@ member_int Y3) (@ (@ image_int_int F) A4))) (@ (@ inj_on_int_int (@ (@ (@ fun_upd_int_int F) X2) Y3)) A4)))) (forall ((F (-> code_integer code_integer)) (A4 set_Code_integer)) (= (@ (@ inj_on20428373856169009nteger (@ produc6499014454317279255nteger F)) (@ (@ produc5882431272649516420nteger top_to4645266643341252675nteger) (lambda ((Uu code_integer)) A4))) (@ (@ inj_on1158064722259180589nteger F) A4))) (forall ((A product_unit) (A4 set_Product_unit)) (let ((_let_1 (@ pow_Product_unit A4))) (let ((_let_2 (@ insert_Product_unit A))) (= (@ pow_Product_unit (@ _let_2 A4)) (@ (@ sup_su5975557051335651745t_unit _let_1) (@ (@ image_4019945301284682565t_unit _let_2) _let_1)))))) (forall ((C3 set_nat) (A Bool) (B5 (-> nat set_o))) (let ((_let_1 (@ insert_o A))) (let ((_let_2 (@ _let_1 (@ comple90263536869209701_set_o (@ (@ image_nat_set_o B5) C3))))) (let ((_let_3 (= C3 bot_bot_set_nat))) (and (=> (not _let_3) (= _let_2 (@ comple90263536869209701_set_o (@ (@ image_nat_set_o (lambda ((X4 nat)) (@ (@ insert_o A) (@ B5 X4)))) C3)))) (=> _let_3 (= _let_2 (@ _let_1 bot_bot_set_o)))))))) (forall ((S5 set_int) (F (-> int nat nat)) (X2 int)) (let ((_let_1 (@ F X2))) (=> (@ (@ finite8981753823465611337nt_nat S5) F) (=> (@ (@ member_int X2) S5) (= (@ (@ comp_nat_nat_nat _let_1) _let_1) _let_1))))) (forall ((B Bool) (F (-> rat Bool))) (=> (@ (@ member_o B) (@ (@ image_rat_o F) top_top_set_rat)) (not (forall ((X rat)) (= B (not (@ F X))))))) (forall ((R3 (-> int int Bool))) (= (@ (@ bNF_re7554818335971813481nt_int (lambda ((Y2 rat) (Z rat)) (= Y2 Z))) R3) (@ (@ relcom2810802720173317863at_int (@ conver6967689361887734790at_int (@ (@ bNF_Gr6858100456814184557at_int (@ collec2521308361159233923nt_int (lambda ((X4 (-> rat product_prod_int_int))) (@ (@ ord_le2843351958646193337nt_int (@ (@ image_5997455970908365082nt_int X4) top_top_set_rat)) (@ collec213857154873943460nt_int (@ produc4947309494688390418_int_o R3)))))) (@ comp_P6018825582104210588nt_rat product_fst_int_int)))) (@ (@ bNF_Gr6858100456814184557at_int (@ collec2521308361159233923nt_int (lambda ((X4 (-> rat product_prod_int_int))) (@ (@ ord_le2843351958646193337nt_int (@ (@ image_5997455970908365082nt_int X4) top_top_set_rat)) (@ collec213857154873943460nt_int (@ produc4947309494688390418_int_o R3)))))) (@ comp_P6018825582104210588nt_rat product_snd_int_int))))) (forall ((X2 nat) (Y3 num)) (= (@ product_swap_nat_num (@ (@ product_Pair_nat_num X2) Y3)) (@ (@ product_Pair_num_nat Y3) X2))) (forall ((F (-> nat int)) (A4 set_nat) (B5 set_nat)) (let ((_let_1 (@ image_nat_int F))) (@ (@ ord_less_eq_set_int (@ _let_1 (@ (@ inf_inf_set_nat A4) B5))) (@ (@ inf_inf_set_int (@ _let_1 A4)) (@ _let_1 B5))))) (forall ((X2 (-> char int)) (Ra (-> int int Bool))) (=> (forall ((Z3 int)) (=> (@ (@ member_int Z3) (@ (@ image_char_int X2) top_top_set_char)) (@ (@ Ra Z3) Z3))) (@ (@ (@ (@ bNF_re4731199128827642459nt_int (lambda ((Y2 char) (Z char)) (= Y2 Z))) Ra) X2) X2))) (forall ((A4 set_ref_a) (B5 (-> ref_a set_he8644174446132254637t_unit))) (= (@ (@ image_7136766188234240905_ref_a produc473321116828791851t_unit) (@ (@ produc3946373962484743846t_unit A4) B5)) (@ collect_ref_a (lambda ((X4 ref_a)) (and (@ (@ member_ref_a X4) A4) (not (= (@ B5 X4) bot_bo3686245532977126937t_unit))))))) (forall ((B5 set_o) (A4 set_o) (P2 (-> Bool Bool))) (let ((_let_1 (@ ord_less_eq_set_o B5))) (=> (@ _let_1 A4) (= (@ _let_1 (@ collect_o (lambda ((X4 Bool)) (and (@ (@ member_o X4) A4) (@ P2 X4))))) (forall ((X4 Bool)) (=> (@ (@ member_o X4) B5) (@ P2 X4))))))) (forall ((R ref_a) (H2 heap_e7401611519738050253t_unit) (V a) (H heap_e7401611519738050253t_unit)) (=> (= (@ (@ produc6544324848051098391t_unit R) H2) (@ (@ alloc_a V) H)) (@ (@ (@ (@ heap_effect_ref_a (@ ref_a2 V)) H) H2) R))) (forall ((X2 product_unit)) (not (forall ((Y Bool)) (=> (= X2 (@ product_Abs_unit Y)) (not (@ (@ member_o Y) (@ (@ insert_o true) bot_bot_set_o))))))) (forall ((H (-> nat nat product_prod_nat_nat product_prod_nat_nat)) (F (-> nat nat)) (G (-> nat nat)) (X2 product_prod_nat_nat)) (= (@ (@ produc27273713700761075at_nat H) (@ (@ (@ produc6977886695330630970at_nat F) G) X2)) (@ (@ produc27273713700761075at_nat (lambda ((L3 nat) (R5 nat) (__flatten_var_0 product_prod_nat_nat)) (@ (@ (@ H (@ F L3)) (@ G R5)) __flatten_var_0))) X2))) (forall ((R3 (-> int int Bool)) (X2 (-> char int)) (Y3 (-> char int)) (Ra (-> int int Bool))) (=> (@ (@ (@ (@ bNF_re4731199128827642459nt_int (lambda ((Y2 char) (Z char)) (= Y2 Z))) R3) X2) Y3) (=> (forall ((Z3 int) (Yb int)) (=> (@ (@ member_int Z3) (@ (@ image_char_int X2) top_top_set_char)) (=> (@ (@ member_int Yb) (@ (@ image_char_int Y3) top_top_set_char)) (=> (@ (@ R3 Z3) Yb) (@ (@ Ra Z3) Yb))))) (@ (@ (@ (@ bNF_re4731199128827642459nt_int (lambda ((Y2 char) (Z char)) (= Y2 Z))) Ra) X2) Y3)))) (forall ((H heap_e7401611519738050253t_unit) (H2 heap_e7401611519738050253t_unit) (X2 ref_a)) (=> (= H H2) (@ (@ (@ (@ heap_effect_ref_a (@ heap_return_ref_a X2)) H) H2) X2))) (forall ((P product_prod_nat_nat) (Z2 Bool) (C (-> nat nat set_o))) (=> (forall ((A3 nat) (B3 nat)) (=> (= P (@ (@ product_Pair_nat_nat A3) B3)) (@ (@ member_o Z2) (@ (@ C A3) B3)))) (@ (@ member_o Z2) (@ (@ produc59986286002894506_set_o C) P)))) (forall ((A4 set_Product_unit) (C set_Product_unit)) (let ((_let_1 (= A4 bot_bo3957492148770167129t_unit))) (and (=> _let_1 (= (@ comple3349607820504768346t_unit (@ (@ image_7778121751606633509t_unit (lambda ((Y5 product_unit)) C)) A4)) bot_bo3957492148770167129t_unit)) (=> (not _let_1) (= (@ comple3349607820504768346t_unit (@ (@ image_7778121751606633509t_unit (lambda ((Y5 product_unit)) C)) A4)) C))))) (forall ((B rat) (F (-> nat rat)) (X2 nat)) (=> (= B (@ F X2)) (@ (@ member_rat B) (@ (@ image_nat_rat F) top_top_set_nat)))) (forall ((A4 set_nat) (B5 set_rat) (F (-> nat rat))) (=> (@ finite_finite_nat A4) (=> (@ (@ ord_less_eq_set_rat B5) (@ (@ image_nat_rat F) A4)) (@ (@ ord_less_eq_nat (@ finite_card_rat B5)) (@ finite_card_nat A4))))) (forall ((F (-> nat rat))) (= (@ (@ image_nat_rat F) bot_bot_set_nat) bot_bot_set_rat)) (forall ((R1 (-> int code_integer Bool))) (let ((_let_1 (@ bNF_re6718328864250387230um_num R1))) (@ (@ (@ (@ bNF_re4105200416192800571er_num (lambda ((Y2 (-> num num)) (Z (-> num num))) (= Y2 Z))) (@ (@ bNF_re6292805115969292119er_num (@ _let_1 (lambda ((Y2 num) (Z num)) (= Y2 Z)))) (@ _let_1 (lambda ((Y2 num) (Z num)) (= Y2 Z))))) comp_num_num_int) comp_n8557746072492896886nteger))) (forall ((I product_prod_nat_nat) (A4 set_Pr1261947904930325089at_nat) (F (-> product_prod_nat_nat set_nat))) (=> (@ (@ member8440522571783428010at_nat I) A4) (@ (@ ord_less_eq_set_nat (@ comple7806235888213564991et_nat (@ (@ image_15824709712370754et_nat F) A4))) (@ F I)))) (forall ((A nat) (B num) (A4 set_Pr6200539531224447659at_num) (F (-> nat num Bool))) (=> (@ (@ member9148766508732265716at_num (@ (@ product_Pair_nat_num A) B)) A4) (@ (@ member_o (@ (@ F A) B)) (@ (@ image_4451812852358507538_num_o (@ produc4927758841916487424_num_o F)) A4)))) (forall ((Rep (-> nat rat)) (Abs (-> rat nat)) (F (-> nat nat)) (P2 (-> nat Bool)) (H (-> nat rat))) (=> (@ (@ (@ type_d5615363888691252950at_rat Rep) Abs) top_top_set_rat) (= (@ (@ (@ bNF_vi2930123780028963665_rat_o F) Rep) (@ (@ bNF_Grp_nat_rat (@ collect_nat P2)) H)) (@ (@ bNF_Grp_nat_nat (@ collect_nat (lambda ((X4 nat)) (@ P2 (@ F X4))))) (@ (@ comp_nat_nat_nat (@ (@ comp_rat_nat_nat Abs) H)) F))))) (forall ((F (-> nat nat)) (G (-> nat nat)) (H (-> nat nat))) (= (@ (@ comp_n8574565218330151774at_nat (@ (@ bNF_co805650143699787099at_nat F) G)) H) (@ (@ bNF_co805650143699787099at_nat (@ (@ comp_nat_nat_nat F) H)) (@ (@ comp_nat_nat_nat G) H)))) (forall ((F (-> nat nat)) (G (-> nat num)) (A nat) (B nat)) (= (@ (@ (@ produc3535218481486409604at_num F) G) (@ (@ product_Pair_nat_nat A) B)) (@ (@ product_Pair_nat_num (@ F A)) (@ G B)))) (forall ((H (-> Bool int)) (F (-> int int Bool)) (Prod product_prod_int_int)) (= (@ H (@ (@ produc4947309494688390418_int_o F) Prod)) (@ (@ produc8211389475949308722nt_int (lambda ((X12 int) (X23 int)) (@ H (@ (@ F X12) X23)))) Prod))) (forall ((F (-> product_prod_nat_nat Bool)) (A nat) (B nat)) (=> (@ F (@ (@ product_Pair_nat_nat A) B)) (@ (@ (@ produc1310100445399344235_nat_o F) A) B))) (forall ((Z2 int) (C (-> nat num set_int)) (P product_prod_nat_num)) (=> (@ (@ member_int Z2) (@ (@ produc9175805072616146554et_int C) P)) (not (forall ((X nat) (Y num)) (=> (= P (@ (@ product_Pair_nat_num X) Y)) (not (@ (@ member_int Z2) (@ (@ C X) Y)))))))) (forall ((F (-> rat rat))) (=> (@ finite_finite_rat top_top_set_rat) (=> (= (@ (@ image_rat_rat F) top_top_set_rat) top_top_set_rat) (@ (@ inj_on_rat_rat F) top_top_set_rat)))) (forall ((F (-> rat nat)) (B5 set_nat) (A4 set_rat)) (let ((_let_1 (@ image_rat_nat F))) (=> (= (@ _let_1 top_top_set_rat) top_top_set_nat) (=> (@ (@ ord_less_eq_set_rat (@ (@ vimage_rat_nat F) B5)) A4) (@ (@ ord_less_eq_set_nat B5) (@ _let_1 A4)))))) (forall ((X2 int) (A4 set_int) (G (-> int int))) (=> (@ (@ member_int X2) A4) (@ (@ member5262025264175285858nt_int (@ (@ (@ bNF_co2174166945328636015nt_int id_int) G) X2)) (@ collec213857154873943460nt_int (@ produc4947309494688390418_int_o (@ (@ bNF_Grp_int_int A4) G)))))) _let_301 (forall ((Z2 set_Pr1261947904930325089at_nat)) (= (@ (@ (@ comp_P4528037747288561284at_nat produc2937545259423399429at_nat) (lambda ((X4 set_Pr1261947904930325089at_nat)) (@ (@ produc2922128104949294807at_nat X4) X4))) Z2) (@ id_set2334057505560298834at_nat Z2))) (forall ((Rep (-> Bool Bool)) (Abs (-> Bool Bool)) (Rep2 (-> Bool Bool)) (Abs2 (-> Bool Bool)) (Rep3 (-> nat nat)) (Abs3 (-> nat nat)) (M (-> nat Bool)) (M1 (-> Bool Bool)) (M2 (-> nat Bool))) (=> (@ (@ (@ type_definition_o_o Rep) Abs) top_top_set_o) (=> (@ (@ (@ type_definition_o_o Rep2) Abs2) top_top_set_o) (=> (@ (@ (@ type_d6250493948777748686at_nat Rep3) Abs3) top_top_set_nat) (=> (= (@ (@ comp_nat_o_nat (@ (@ comp_o_o_nat Abs2) M)) Rep3) (@ (@ comp_o_o_nat (@ (@ comp_o_o_o (@ (@ comp_o_o_o Abs2) M1)) Rep)) (@ (@ comp_nat_o_nat (@ (@ comp_o_o_nat Abs) M2)) Rep3))) (= (@ (@ comp_o_o_nat M1) M2) M)))))) (forall ((A4 set_nat)) (= (@ complete_Inf_Inf_nat (@ (@ image_nat_nat (lambda ((X4 nat)) X4)) A4)) (@ complete_Inf_Inf_nat A4))) (forall ((A int) (P product_prod_int_int)) (= (= A (@ product_fst_int_int P)) (exists ((B4 int)) (= P (@ (@ product_Pair_int_int A) B4))))) (forall ((M (-> produc3843707927480180839at_nat product_unit)) (A4 set_Pr4329608150637261639at_nat) (B5 set_Pr4329608150637261639at_nat)) (let ((_let_1 (@ image_7082456443403096939t_unit M))) (= (@ comple2584293577114468500t_unit (@ _let_1 (@ (@ sup_su5525570899277871387at_nat A4) B5))) (@ (@ inf_inf_Product_unit (@ comple2584293577114468500t_unit (@ _let_1 A4))) (@ comple2584293577114468500t_unit (@ _let_1 B5)))))) (forall ((A4 set_nat) (B5 set_int)) (=> (@ finite_finite_nat A4) (=> (@ finite_finite_int B5) (= (exists ((F2 (-> nat int))) (and (@ (@ ord_less_eq_set_int (@ (@ image_nat_int F2) A4)) B5) (@ (@ inj_on_nat_int F2) A4))) (@ (@ ord_less_eq_nat (@ finite_card_nat A4)) (@ finite_card_int B5)))))) (forall ((C3 set_o) (A4 set_char) (B5 (-> Bool set_char))) (let ((_let_1 (= C3 bot_bot_set_o))) (and (=> (not _let_1) (= (@ comple7965528767983648192t_char (@ (@ image_o_set_char (lambda ((X4 Bool)) (@ (@ inf_inf_set_char A4) (@ B5 X4)))) C3)) (@ (@ inf_inf_set_char A4) (@ comple7965528767983648192t_char (@ (@ image_o_set_char B5) C3))))) (=> _let_1 (= (@ comple7965528767983648192t_char (@ (@ image_o_set_char (lambda ((X4 Bool)) (@ (@ inf_inf_set_char A4) (@ B5 X4)))) C3)) top_top_set_char))))) (forall ((B Bool) (F (-> rat Bool)) (X2 rat)) (=> (= B (@ F X2)) (@ (@ member_o B) (@ (@ image_rat_o F) top_top_set_rat)))) (forall ((I3 set_Pr1261947904930325089at_nat) (A4 (-> product_prod_nat_nat set_nat))) (=> (@ finite6177210948735845034at_nat I3) (= (@ condit2214826472909112428ve_nat (@ comple7399068483239264473et_nat (@ (@ image_15824709712370754et_nat A4) I3))) (forall ((X4 product_prod_nat_nat)) (=> (@ (@ member8440522571783428010at_nat X4) I3) (@ condit2214826472909112428ve_nat (@ A4 X4))))))) (forall ((C3 set_Product_unit) (A4 (-> product_unit set_Pr8693737435421807431at_nat)) (B5 set_Pr8693737435421807431at_nat)) (let ((_let_1 (@ (@ sup_su718114333110466843at_nat (@ comple2748534634209756852at_nat (@ (@ image_7288820656315755647at_nat A4) C3))) B5))) (let ((_let_2 (= C3 bot_bo3957492148770167129t_unit))) (and (=> (not _let_2) (= _let_1 (@ comple2748534634209756852at_nat (@ (@ image_7288820656315755647at_nat (lambda ((X4 product_unit)) (@ (@ sup_su718114333110466843at_nat (@ A4 X4)) B5))) C3)))) (=> _let_2 (= _let_1 B5)))))) (forall ((F (-> product_prod_int_int Bool)) (A int) (B int)) (=> (@ (@ (@ produc175634133007206835_int_o F) A) B) (@ F (@ (@ product_Pair_int_int A) B)))) (forall ((A4 set_Product_unit) (M3 nat) (F (-> product_unit nat))) (=> (not (= A4 bot_bo3957492148770167129t_unit)) (=> (forall ((X product_unit)) (=> (@ (@ member_Product_unit X) A4) (@ (@ ord_less_eq_nat M3) (@ F X)))) (@ (@ ord_less_eq_nat M3) (@ complete_Inf_Inf_nat (@ (@ image_875570014554754200it_nat F) A4)))))) (forall ((G (-> char nat)) (F (-> nat nat))) (=> (@ finite_finite_nat (@ (@ image_char_nat G) top_top_set_char)) (@ finite_finite_nat (@ (@ image_char_nat (lambda ((X4 char)) (@ F (@ G X4)))) top_top_set_char)))) (forall ((I3 set_Product_unit) (F (-> product_unit product_unit)) (X2 product_unit)) (=> (not (= I3 bot_bo3957492148770167129t_unit)) (= (@ comple2584293577114468500t_unit (@ (@ image_405062704495631173t_unit (lambda ((I2 product_unit)) (@ (@ inf_inf_Product_unit (@ F I2)) X2))) I3)) (@ (@ inf_inf_Product_unit (@ comple2584293577114468500t_unit (@ (@ image_405062704495631173t_unit F) I3))) X2)))) (forall ((A4 set_nat) (C3 set_nat) (B5 (-> nat set_nat))) (=> (forall ((X nat)) (=> (@ (@ member_nat X) A4) (@ (@ ord_less_eq_set_nat C3) (@ B5 X)))) (@ (@ ord_less_eq_set_nat C3) (@ comple7806235888213564991et_nat (@ (@ image_nat_set_nat B5) A4))))) (forall ((U Bool) (A4 set_o) (A nat) (B5 (-> Bool set_nat))) (=> (@ (@ member_o U) A4) (= (@ comple7399068483239264473et_nat (@ (@ image_o_set_nat (lambda ((X4 Bool)) (@ (@ insert_nat A) (@ B5 X4)))) A4)) (@ (@ insert_nat A) (@ comple7399068483239264473et_nat (@ (@ image_o_set_nat B5) A4)))))) (forall ((B5 (-> Bool Bool Bool)) (C3 (-> Bool Bool Bool)) (A4 (-> nat nat Bool))) (let ((_let_1 (@ bNF_re4705727531993890431at_o_o A4))) (@ (@ (@ (@ bNF_re6580757339198446453_nat_o (@ (@ bNF_rel_fun_o_o_o_o B5) C3)) (@ (@ bNF_re2697311982885662685_nat_o (@ _let_1 B5)) (@ _let_1 C3))) comp_o_o_nat) comp_o_o_nat))) (forall ((K Bool) (I3 set_o) (A4 (-> Bool set_Pr4329608150637261639at_nat))) (let ((_let_1 (@ comple4364388969068068532at_nat (@ (@ image_2496312346330513076at_nat A4) I3)))) (=> (@ (@ member_o K) I3) (= (@ (@ 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bNF_re1982657550219213441nt_nat (@ (@ bNF_re8207659476513966505_o_int R1) R22)) (@ (@ bNF_re8210149947023016781_o_nat R1) R32))) comp_o_o_nat) comp_int_nat_int)) (forall ((F (-> (-> code_integer code_integer) produc8923325533196201883nteger produc8923325533196201883nteger)) (G (-> code_integer code_integer code_integer)) (L (-> code_integer produc8923325533196201883nteger produc8923325533196201883nteger)) (H (-> code_integer code_integer))) (let ((_let_1 (@ comp_C8797469213163452608nteger F))) (=> (= (@ _let_1 G) L) (= (@ _let_1 (@ (@ comp_C2931745410781319416nteger G) H)) (@ (@ comp_C1593894019821074884nteger L) H))))) (forall ((F (-> product_unit Bool))) (= (@ (@ image_Product_unit_o F) bot_bo3957492148770167129t_unit) bot_bot_set_o)) (forall ((F (-> nat rat)) (X2 nat)) (@ (@ member_rat (@ F X2)) (@ (@ image_nat_rat F) top_top_set_nat))) (forall ((F (-> product_unit product_unit)) (A product_unit) (B5 set_Product_unit)) (let ((_let_1 (@ image_405062704495631173t_unit F))) (= (@ _let_1 (@ (@ insert_Product_unit A) B5)) (@ (@ insert_Product_unit (@ F A)) (@ _let_1 B5))))) (forall ((C3 set_Product_unit) (A4 (-> product_unit set_nat)) (B5 set_nat)) (let ((_let_1 (= C3 bot_bo3957492148770167129t_unit))) (and (=> _let_1 (= (@ comple7806235888213564991et_nat (@ (@ image_8173849991827986510et_nat (lambda ((X4 product_unit)) (@ (@ minus_minus_set_nat (@ A4 X4)) B5))) C3)) top_top_set_nat)) (=> (not _let_1) (= (@ comple7806235888213564991et_nat (@ (@ image_8173849991827986510et_nat (lambda ((X4 product_unit)) (@ (@ minus_minus_set_nat (@ A4 X4)) B5))) C3)) (@ (@ minus_minus_set_nat (@ comple7806235888213564991et_nat (@ (@ image_8173849991827986510et_nat A4) C3))) B5)))))) (forall ((R3 (-> int int Bool)) (A (-> rat int)) (B (-> rat int))) (= (@ (@ (@ (@ bNF_re7554818335971813481nt_int (lambda ((Y2 rat) (Z rat)) (= Y2 Z))) R3) A) B) (exists ((Z4 (-> rat product_prod_int_int))) (and (@ (@ member546649419593416001nt_int Z4) (@ collec2521308361159233923nt_int (lambda ((X4 (-> rat product_prod_int_int))) (@ (@ ord_le2843351958646193337nt_int (@ (@ image_5997455970908365082nt_int X4) top_top_set_rat)) (@ collec213857154873943460nt_int (@ produc4947309494688390418_int_o R3)))))) (= (@ (@ comp_P6018825582104210588nt_rat product_fst_int_int) Z4) A) (= (@ (@ comp_P6018825582104210588nt_rat product_snd_int_int) Z4) B))))) (forall ((A4 set_o) (G (-> Bool nat)) (B5 set_o) (F (-> Bool nat))) (let ((_let_1 (@ (@ image_o_nat G) B5))) (=> (not (= A4 bot_bot_set_o)) (=> (@ condit1738341127787009408ow_nat _let_1) (=> (@ (@ ord_less_eq_set_o A4) B5) (=> (forall ((X Bool)) (=> (@ (@ member_o X) B5) (@ (@ ord_less_eq_nat (@ G X)) (@ F X)))) (@ (@ ord_less_eq_nat (@ complete_Inf_Inf_nat _let_1)) (@ complete_Inf_Inf_nat (@ (@ image_o_nat F) A4))))))))) (forall ((F (-> int nat)) (A4 set_int) (X2 int) (U nat)) (let ((_let_1 (@ (@ image_int_nat F) A4))) (let ((_let_2 (@ ord_less_eq_nat U))) (=> (@ condit2214826472909112428ve_nat _let_1) (=> (@ (@ member_int X2) A4) (=> (@ _let_2 (@ F X2)) (@ _let_2 (@ complete_Sup_Sup_nat _let_1)))))))) (forall ((F (-> nat rat)) (A4 set_nat) (B5 set_rat) (G (-> rat nat))) (=> (@ (@ inj_on_nat_rat F) A4) (=> (@ (@ ord_less_eq_set_rat (@ (@ image_nat_rat F) A4)) B5) (=> (@ (@ inj_on_rat_nat G) B5) (=> (@ (@ ord_less_eq_set_nat (@ (@ image_rat_nat G) B5)) A4) (=> (@ finite_finite_nat A4) (=> (@ finite_finite_rat B5) (= (@ finite_card_nat A4) (@ finite_card_rat B5))))))))) (forall ((F (-> int nat)) (A int) (B5 set_int)) (let ((_let_1 (@ image_int_nat F))) (= (@ _let_1 (@ (@ insert_int A) B5)) (@ (@ insert_nat (@ F A)) (@ _let_1 B5))))) (forall ((A4 set_o) (F (-> Bool nat)) (M nat)) (=> (forall ((X Bool)) (=> (@ (@ member_o X) A4) (@ (@ ord_less_eq_nat (@ F X)) M))) (@ condit2214826472909112428ve_nat (@ (@ image_o_nat F) A4)))) (forall ((R1 (-> int int Bool)) (R22 (-> nat nat Bool)) (P2 (-> int nat Bool)) (Q2 (-> int nat Bool)) (A product_prod_int_int) (A4 set_Pr958786334691620121nt_int) (B product_prod_nat_nat) (B5 set_Pr1261947904930325089at_nat)) (=> (@ (@ (@ (@ bNF_re3376528473927230327_nat_o R1) (@ (@ bNF_re4705727531993890431at_o_o R22) (lambda ((Y2 Bool) (Z Bool)) (= Y2 Z)))) P2) Q2) (=> (@ (@ member5262025264175285858nt_int A) A4) (=> (@ (@ member8440522571783428010at_nat B) B5) (=> (@ (@ ord_le2843351958646193337nt_int A4) (@ collec213857154873943460nt_int (@ produc4947309494688390418_int_o R1))) (=> (@ (@ ord_le3146513528884898305at_nat B5) (@ collec3392354462482085612at_nat (@ produc6081775807080527818_nat_o R22))) (= (@ (@ P2 (@ product_fst_int_int A)) (@ product_fst_nat_nat B)) (@ (@ Q2 (@ product_snd_int_int A)) (@ product_snd_nat_nat B))))))))) (= vimage6435164912253009178at_nat (lambda ((F2 (-> nat produc3843707927480180839at_nat)) (B6 set_Pr4329608150637261639at_nat)) (@ comple7399068483239264473et_nat (@ (@ image_3160451284896210088et_nat (lambda ((Y5 produc3843707927480180839at_nat)) (@ (@ vimage6435164912253009178at_nat F2) (@ (@ insert9069300056098147895at_nat Y5) bot_bo228742789529271731at_nat)))) B6)))) (forall ((A rat)) (= (@ (@ image_rat_rat (lambda ((X4 rat)) (@ (@ minus_minus_rat X4) A))) top_top_set_rat) top_top_set_rat)) (forall ((A4 set_Pr1261947904930325089at_nat) (B5 set_Pr1261947904930325089at_nat) (F (-> product_prod_nat_nat set_nat)) (G (-> product_prod_nat_nat set_nat))) (=> (@ (@ ord_le3146513528884898305at_nat A4) B5) (=> (forall ((X product_prod_nat_nat)) (=> (@ (@ member8440522571783428010at_nat X) A4) (@ (@ ord_less_eq_set_nat (@ F X)) (@ G X)))) (@ (@ ord_less_eq_set_nat (@ comple7399068483239264473et_nat (@ (@ image_15824709712370754et_nat F) A4))) (@ comple7399068483239264473et_nat (@ (@ image_15824709712370754et_nat G) B5)))))) (forall ((R3 (-> int int Bool))) (= (@ (@ bNF_re4712519889275205905nt_int (lambda ((Y2 int) (Z int)) (= Y2 Z))) R3) (@ (@ relcom6733878598652036755nt_int (@ conver1062113817206378758nt_int (@ (@ bNF_Gr952524912132828525nt_int (@ collec2229320974926845999nt_int (lambda ((X4 (-> int product_prod_int_int))) (@ (@ ord_le2843351958646193337nt_int (@ (@ image_5705468584675977158nt_int X4) top_top_set_int)) (@ collec213857154873943460nt_int (@ produc4947309494688390418_int_o R3)))))) (@ comp_P6651465171681656048nt_int product_fst_int_int)))) (@ (@ bNF_Gr952524912132828525nt_int (@ collec2229320974926845999nt_int (lambda ((X4 (-> int product_prod_int_int))) (@ (@ ord_le2843351958646193337nt_int (@ (@ image_5705468584675977158nt_int X4) top_top_set_int)) (@ collec213857154873943460nt_int (@ produc4947309494688390418_int_o R3)))))) (@ comp_P6651465171681656048nt_int product_snd_int_int))))) (forall ((Rep (-> num nat)) (Abs (-> nat num))) (=> (@ (@ (@ type_d4380824352085218072um_nat Rep) Abs) top_top_set_nat) (= (@ (@ comp_nat_num_num Abs) Rep) id_num))) (forall ((Rep (-> Bool nat)) (Abs (-> nat Bool))) (=> (@ (@ (@ type_d7121381646445849148_o_nat Rep) Abs) top_top_set_nat) (= (@ (@ comp_nat_o_o Abs) Rep) id_o))) (forall ((F (-> int int)) (A4 set_int)) (=> (@ order_mono_int_int F) (=> (@ condit1735850657277959132ow_int A4) (=> (not (= A4 bot_bot_set_int)) (@ (@ ord_less_eq_int (@ F (@ complete_Inf_Inf_int A4))) (@ complete_Inf_Inf_int (@ (@ image_int_int F) A4))))))) (forall ((A int) (A4 set_int) (B int) (B5 (-> int set_int))) (let ((_let_1 (@ member_int B))) (=> (@ (@ member_int A) A4) (=> (@ _let_1 (@ B5 A)) (@ _let_1 (@ comple3221217463730067765et_int (@ (@ image_int_set_int B5) A4))))))) (forall ((F (-> code_integer code_integer code_integer)) (G (-> (-> code_integer code_integer) produc8923325533196201883nteger produc8923325533196201883nteger))) (= (@ (@ comp_s4786119426940707554nteger (@ vimage6029918387083761651nteger F)) (@ vimage4289680085338140859nteger G)) (@ vimage6839621282666897215nteger (@ (@ comp_C8797469213163452608nteger G) F)))) (forall ((X2 Bool) (A4 set_o) (F (-> Bool int))) (let ((_let_1 (@ (@ image_o_int F) A4))) (=> (@ (@ member_o X2) A4) (=> (@ condit2212336002400062152ve_int _let_1) (@ (@ ord_less_eq_int (@ F X2)) (@ complete_Sup_Sup_int _let_1)))))) (forall ((P rat) (Q rat)) (= (@ quotient_of (@ (@ times_times_rat P) Q)) (@ (@ produc4245557441103728435nt_int (lambda ((A5 int) (C4 int)) (@ (@ produc4245557441103728435nt_int (lambda ((B4 int) (D3 int)) (@ normalize (@ (@ product_Pair_int_int (@ (@ times_times_int A5) B4)) (@ (@ times_times_int C4) D3))))) (@ quotient_of Q)))) (@ quotient_of P)))) (forall ((X2 product_unit)) (= (@ (@ image_2327579789247107822t_unit (lambda ((Uu rat)) X2)) top_top_set_rat) (@ (@ insert_Product_unit X2) bot_bo3957492148770167129t_unit))) (forall ((B5 (-> rat set_nat)) (F (-> nat rat)) (A4 set_nat)) (= (@ comple7806235888213564991et_nat (@ (@ image_nat_set_nat (lambda ((A5 nat)) (@ B5 (@ F A5)))) A4)) (@ comple7806235888213564991et_nat (@ (@ image_rat_set_nat B5) (@ (@ image_nat_rat F) A4))))) (forall ((F (-> nat Bool)) (B Bool)) (=> (@ (@ inj_on_nat_o F) top_top_set_nat) (= (@ (@ member_o B) (@ (@ image_nat_o F) top_top_set_nat)) (exists ((X4 nat)) (and (forall ((Y5 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B5)))))) (forall ((R1 (-> nat nat Bool)) (Abs1 (-> nat nat)) (Rep1 (-> nat nat)) (T1 (-> nat nat Bool)) (R22 (-> nat nat Bool)) (Abs22 (-> nat nat)) (Rep22 (-> nat nat)) (T22 (-> nat nat Bool))) (let ((_let_1 (@ relcompp_nat_nat_nat T1))) (=> (@ (@ (@ (@ quotient_nat_nat R1) Abs1) Rep1) T1) (=> (@ (@ (@ (@ quotient_nat_nat R22) Abs22) Rep22) T22) (@ (@ (@ (@ quotient_nat_nat (@ _let_1 (@ (@ relcompp_nat_nat_nat R22) (@ conversep_nat_nat T1)))) (@ (@ comp_nat_nat_nat Abs22) Abs1)) (@ (@ comp_nat_nat_nat Rep1) Rep22)) (@ _let_1 T22)))))) (forall ((R (-> int int Bool)) (S2 (-> int code_integer Bool)) (A1 int) (A22 code_integer)) (=> (@ (@ (@ (@ relcom967497705283160040nteger R) S2) A1) A22) (not (forall ((B3 int)) (=> (@ (@ R A1) B3) (not (@ (@ S2 B3) A22))))))) _let_300 (forall ((R set_Pr4329608150637261639at_nat) (S2 set_Pr4329608150637261639at_nat) (R3 set_Pr7459493094073627847at_nat) (S3 set_Pr4329608150637261639at_nat)) (let ((_let_1 (@ produc9060074326276436823at_nat R))) (=> (@ (@ member1466754251312161552at_nat (@ _let_1 S2)) R3) (=> (= S3 S2) (@ (@ member1466754251312161552at_nat (@ _let_1 S3)) R3))))) _let_299 (forall ((C3 set_nat) (A4 (-> nat set_nat)) (B5 set_nat)) (let ((_let_1 (@ (@ sup_sup_set_nat (@ comple7399068483239264473et_nat (@ (@ image_nat_set_nat A4) C3))) B5))) (let ((_let_2 (= C3 bot_bot_set_nat))) (and (=> _let_2 (= _let_1 B5)) (=> (not _let_2) (= _let_1 (@ comple7399068483239264473et_nat (@ (@ image_nat_set_nat (lambda ((X4 nat)) (@ (@ sup_sup_set_nat (@ A4 X4)) B5))) C3)))))))) (forall ((F (-> nat Bool)) (A4 set_nat)) (=> (@ finite_finite_o (@ (@ image_nat_o F) A4)) (=> (not (@ finite_finite_nat A4)) (exists ((X Bool)) (and (not (@ finite_finite_nat (@ (@ inf_inf_set_nat (@ (@ vimage_nat_o F) (@ (@ insert_o X) bot_bot_set_o))) A4))) (@ (@ member_o X) (@ (@ image_nat_o F) A4))))))) (forall ((A4 set_o) (F (-> Bool int)) (A Bool)) (let ((_let_1 (@ image_o_int F))) (let ((_let_2 (@ _let_1 A4))) (=> (not (= A4 bot_bot_set_o)) (=> (@ 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H))))) (forall ((P2 (-> ref_a heap_e7401611519738050253t_unit Bool))) (= (@ the_Pr5012129486825234846t_unit (@ produc4924168586796184916unit_o P2)) (@ the_Pr5012129486825234846t_unit (lambda ((Xy produc7812382424243267045t_unit)) (@ (@ P2 (@ produc473321116828791851t_unit Xy)) (@ produc1126150082675451753t_unit Xy)))))) (forall ((F (-> rat int)) (G (-> int rat))) (=> (@ order_5406978534148954943at_int F) (=> (= (@ (@ image_rat_int F) top_top_set_rat) top_top_set_int) (=> (forall ((X rat)) (= (@ G (@ F X)) X)) (@ order_6090247300407429951nt_rat G))))) (forall ((X2 num) (Y3 num)) (=> (= X2 Y3) (@ (@ (@ (@ bNF_Grp_num_num top_top_set_num) id_num) X2) Y3))) (forall ((A4 set_Product_unit) (B5 set_Product_unit)) (let ((_let_1 (@ produc6121607364029222536t_unit A4))) (let ((_let_2 (@ image_262127665112854123t_unit produc6786084904866402309t_unit))) (let ((_let_3 (= A4 bot_bo3957492148770167129t_unit))) (and (=> _let_3 (= (@ _let_2 (@ _let_1 (lambda ((Uu product_unit)) B5))) bot_bo3957492148770167129t_unit)) (=> (not _let_3) (= (@ _let_2 (@ _let_1 (lambda ((Uu product_unit)) B5))) B5))))))) (forall ((A4 set_Product_unit) (C set_Product_unit)) (let ((_let_1 (= A4 bot_bo3957492148770167129t_unit))) (and (=> (not _let_1) (= (@ comple3349607820504768346t_unit (@ (@ image_7778121751606633509t_unit (lambda ((Y5 product_unit)) C)) A4)) C)) (=> _let_1 (= (@ comple3349607820504768346t_unit (@ (@ image_7778121751606633509t_unit (lambda ((Y5 product_unit)) C)) A4)) bot_bo3957492148770167129t_unit))))) (forall ((R set_Pr958786334691620121nt_int)) (=> (@ (@ total_on_int (@ field_int R)) R) (=> (@ (@ ord_le2843351958646193337nt_int R) id_int2) (or (exists ((A3 int)) (= R (@ (@ insert5033312907999012233nt_int (@ (@ product_Pair_int_int A3) A3)) bot_bo1796632182523588997nt_int))) (= R bot_bo1796632182523588997nt_int))))) (= (@ comple7399068483239264473et_nat (@ (@ image_nat_set_nat set_ord_atMost_nat) top_top_set_nat)) top_top_set_nat) (forall ((F (-> nat nat))) (=> (@ finite_finite_nat top_top_set_nat) (=> (= (@ (@ image_nat_nat F) top_top_set_nat) top_top_set_nat) (@ (@ inj_on_nat_nat F) top_top_set_nat)))) (forall ((X2 int) (A4 set_int) (F (-> int nat))) (=> (@ (@ member_int X2) A4) (@ (@ member_nat (@ F X2)) (@ (@ image_int_nat F) A4)))) (forall ((F (-> Bool Bool)) (G (-> nat num)) (H (-> nat Bool)) (I (-> int nat)) (Prod product_prod_nat_int)) (= (@ (@ (@ produc3628557804203378146at_num F) G) (@ (@ (@ produc8250590009387450446nt_nat H) I) Prod)) (@ (@ (@ produc4807921795543229080nt_num (@ (@ comp_o_o_nat F) H)) (@ (@ comp_nat_num_int G) I)) Prod))) (forall ((X2 Bool)) (@ (@ refl_on_o (@ (@ insert_o X2) bot_bot_set_o)) (@ (@ insert6201435330877294327od_o_o (@ (@ product_Pair_o_o X2) X2)) bot_bo7073875226086086771od_o_o))) (forall ((F (-> nat rat))) (let ((_let_1 (@ image_nat_rat F))) (= (@ (@ comp_s703482200030188019et_nat comple3890839924845867745et_rat) (@ image_4408659257933336347et_rat _let_1)) (@ (@ comp_s6435139744279249717et_nat _let_1) comple7399068483239264473et_nat)))) (forall ((G1 (-> Bool Bool)) (G22 (-> nat nat)) (F1 (-> nat Bool)) (F22 (-> nat nat)) (V product_prod_nat_nat)) (= (@ (@ (@ produc7071226018047599512at_nat G1) G22) (@ (@ (@ produc7251236297486395890at_nat F1) F22) V)) (@ (@ (@ produc7251236297486395890at_nat (@ (@ comp_o_o_nat G1) F1)) (@ (@ comp_nat_nat_nat G22) F22)) V))) (forall ((X2 nat) (A4 set_nat) (F (-> nat product_unit))) (let ((_let_1 (@ (@ image_8730104196221521654t_unit F) A4))) (=> (@ (@ member_nat X2) A4) (=> (@ condit2080475194861589617t_unit _let_1) (@ (@ ord_le3221252021190050221t_unit (@ F X2)) (@ comple4687483117567863418t_unit _let_1)))))) (forall ((F (-> product_unit product_unit)) (A product_unit) (A4 set_Product_unit)) (let ((_let_1 (@ image_405062704495631173t_unit F))) (= (@ comple4687483117567863418t_unit (@ _let_1 (@ (@ insert_Product_unit A) A4))) (@ (@ sup_sup_Product_unit (@ F A)) (@ comple4687483117567863418t_unit (@ _let_1 A4)))))) (forall ((F (-> nat product_unit)) (G (-> nat nat)) (A4 set_nat)) (= (@ (@ image_3978134465758882403it_nat (lambda ((X4 nat)) (@ (@ produc4803288329813530246it_nat (@ F X4)) (@ G X4)))) A4) (@ (@ produc6875377002296012693it_nat (@ (@ image_8730104196221521654t_unit F) A4)) (lambda ((X4 product_unit)) (@ (@ image_nat_nat G) (@ (@ inf_inf_set_nat (@ (@ vimage4884490618288580032t_unit F) (@ (@ insert_Product_unit X4) bot_bo3957492148770167129t_unit))) A4)))))) (forall ((F (-> Bool set_Pr8693737435421807431at_nat)) (A Bool) (B5 set_o)) (let ((_let_1 (@ image_8493167801588156084at_nat F))) (= (@ comple2748534634209756852at_nat (@ _let_1 (@ (@ insert_o A) B5))) (@ (@ sup_su718114333110466843at_nat (@ F A)) (@ comple2748534634209756852at_nat (@ _let_1 B5)))))) (forall ((X2 int) (Y3 int) (R set_Pr1261947904930325089at_nat) (F (-> int nat))) (= (@ (@ member5262025264175285858nt_int (@ (@ product_Pair_int_int X2) Y3)) (@ (@ inv_image_nat_int R) F)) (@ (@ member8440522571783428010at_nat (@ (@ product_Pair_nat_nat (@ F X2)) (@ F Y3))) R))) (forall ((B5 (-> int set_nat)) (F (-> int int)) (A4 set_int)) (= (@ comple7806235888213564991et_nat (@ (@ image_int_set_nat (lambda ((A5 int)) (@ B5 (@ F A5)))) A4)) (@ comple7806235888213564991et_nat (@ (@ image_int_set_nat B5) (@ (@ image_int_int F) A4))))) (forall ((C3 set_o) (A Bool) (B5 (-> Bool set_o))) (let ((_let_1 (@ insert_o A))) (let ((_let_2 (@ _let_1 (@ comple90263536869209701_set_o (@ (@ image_o_set_o B5) C3))))) (let ((_let_3 (= C3 bot_bot_set_o))) (and (=> (not _let_3) (= _let_2 (@ comple90263536869209701_set_o (@ (@ image_o_set_o (lambda ((X4 Bool)) (@ (@ insert_o A) (@ B5 X4)))) C3)))) (=> _let_3 (= _let_2 (@ _let_1 bot_bot_set_o)))))))) (forall ((A product_prod_nat_nat) (B product_prod_nat_nat) (A4 set_Pr1261947904930325089at_nat)) (=> (= A B) (=> (@ (@ member8440522571783428010at_nat A) A4) (@ (@ member8206827879206165904at_nat (@ (@ produc6161850002892822231at_nat A) B)) (@ id_on_2554058798563519774at_nat A4))))) (forall ((A4 set_o) (C Bool)) (let ((_let_1 (= A4 bot_bot_set_o))) (and (=> _let_1 (= (@ (@ image_o_o (lambda ((X4 Bool)) C)) A4) bot_bot_set_o)) (=> (not _let_1) (= (@ (@ image_o_o (lambda ((X4 Bool)) C)) A4) (@ (@ insert_o C) bot_bot_set_o)))))) (forall ((A nat) (B nat)) (=> (@ (@ member8440522571783428010at_nat (@ (@ product_Pair_nat_nat A) B)) id_nat2) (= A B))) (forall ((C3 set_Product_unit) (A4 set_Product_unit) (B5 (-> product_unit set_Product_unit))) (let ((_let_1 (= C3 bot_bo3957492148770167129t_unit))) (and (=> (not _let_1) (= (@ comple3349607820504768346t_unit (@ (@ image_7778121751606633509t_unit (lambda ((X4 product_unit)) (@ (@ sup_su793286257634532545t_unit A4) (@ B5 X4)))) C3)) (@ (@ sup_su793286257634532545t_unit A4) (@ comple3349607820504768346t_unit (@ (@ image_7778121751606633509t_unit B5) C3))))) (=> _let_1 (= (@ comple3349607820504768346t_unit (@ (@ image_7778121751606633509t_unit (lambda ((X4 product_unit)) (@ (@ sup_su793286257634532545t_unit A4) (@ B5 X4)))) C3)) bot_bo3957492148770167129t_unit))))) (forall ((R1 (-> nat nat Bool)) (Abs1 (-> nat Bool)) (Rep1 (-> Bool nat)) (T1 (-> nat Bool Bool)) (R22 (-> Bool Bool Bool)) (Abs22 (-> Bool Bool)) (Rep22 (-> Bool Bool)) (T22 (-> Bool Bool Bool))) (=> (@ (@ (@ (@ quotient_nat_o R1) Abs1) Rep1) T1) (=> (@ (@ (@ (@ quotient_o_o R22) Abs22) Rep22) T22) (@ (@ (@ (@ quotient_nat_o (@ (@ relcompp_nat_o_nat T1) (@ (@ relcompp_o_o_nat R22) (@ conversep_nat_o T1)))) (@ (@ comp_o_o_nat Abs22) Abs1)) (@ (@ comp_o_nat_o Rep1) Rep22)) (@ (@ relcompp_nat_o_o T1) T22))))) (forall ((R set_Pr1261947904930325089at_nat) (S2 set_Pr1261947904930325089at_nat)) (=> (forall ((X nat) (Y nat)) (let ((_let_1 (@ member8440522571783428010at_nat (@ (@ product_Pair_nat_nat X) Y)))) (=> (@ _let_1 R) (@ _let_1 S2)))) (@ (@ ord_le3146513528884898305at_nat R) S2))) (forall ((A4 set_int) (B5 set_int) (C3 (-> int nat)) (D (-> int nat))) (=> (= A4 B5) (=> (forall ((X int)) (=> (@ (@ member_int X) B5) (= (@ C3 X) (@ D X)))) (= (@ 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(@ (@ image_2486076414777270412at_nat (@ produc6842872674320459806at_nat F)) A4)))) _let_298 (forall ((F (-> char int)) (Y3 int)) (=> (= (@ (@ image_char_int F) top_top_set_char) top_top_set_int) (exists ((X char)) (= Y3 (@ F X))))) (forall ((A4 set_int) (B5 (-> int set_int)) (F (-> int int))) (=> (not (= A4 bot_bot_set_int)) (=> (forall ((X int)) (=> (@ (@ member_int X) A4) (not (= (@ B5 X) bot_bot_set_int)))) (=> (@ condit1735850657277959132ow_int (@ comple3221217463730067765et_int (@ (@ image_int_set_int (lambda ((X4 int)) (@ (@ image_int_int F) (@ B5 X4)))) A4))) (= (@ complete_Inf_Inf_int (@ (@ image_int_int F) (@ comple3221217463730067765et_int (@ (@ image_int_set_int B5) A4)))) (@ complete_Inf_Inf_int (@ (@ image_int_int (lambda ((X4 int)) (@ complete_Inf_Inf_int (@ (@ image_int_int F) (@ B5 X4))))) A4))))))) (forall ((X2 int) (Fx int) (A4 set_int) (F (-> int int))) (=> (@ (@ member5262025264175285858nt_int (@ (@ product_Pair_int_int X2) Fx)) (@ (@ bNF_Gr_int_int A4) F)) (@ (@ 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(@ produc1453890548195736866nt_int A4) (lambda ((Uu int)) B5))) (and (@ (@ member_int (@ product_snd_int_int X2)) B5) (@ (@ member_int (@ product_fst_int_int X2)) A4)))) (forall ((F (-> Bool int)) (A4 set_o) (X2 int) (B5 set_o)) (=> (@ (@ inj_on_o_int F) A4) (=> (@ (@ member_int X2) (@ (@ image_o_int F) A4)) (=> (@ (@ ord_less_eq_set_o A4) B5) (@ (@ member_o (@ (@ (@ the_inv_into_o_int A4) F) X2)) B5))))) (forall ((F (-> nat num)) (G (-> nat nat)) (L (-> nat num)) (H (-> int nat))) (=> (= (@ (@ comp_nat_num_nat F) G) L) (= (@ (@ comp_nat_num_int F) (@ (@ comp_nat_nat_int G) H)) (@ (@ comp_nat_num_int L) H)))) (forall ((A4 set_Pr4329608150637261639at_nat) (C3 set_nat) (B5 (-> produc3843707927480180839at_nat set_nat))) (=> (forall ((X produc3843707927480180839at_nat)) (=> (@ (@ member8757157785044589968at_nat X) A4) (@ (@ ord_less_eq_set_nat C3) (@ B5 X)))) (@ (@ ord_less_eq_set_nat C3) (@ comple7806235888213564991et_nat (@ (@ image_3160451284896210088et_nat B5) A4))))) (forall ((G (-> 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(@ (@ produc457027306803732586at_nat A4) B5)) (not (forall ((X nat)) (=> (@ (@ member_nat X) A4) (forall ((Y nat)) (=> (@ (@ member_nat Y) (@ B5 X)) (not (= C (@ (@ product_Pair_nat_nat X) Y)))))))))) (forall ((A4 set_o) (B5 set_Product_unit)) (= (= (@ (@ produc411009820408249917t_unit A4) (lambda ((Uu Bool)) B5)) bot_bo4402188677660116584t_unit) (or (= B5 bot_bo3957492148770167129t_unit) (= A4 bot_bot_set_o)))) (forall ((C product_prod_o_nat) (A4 set_o) (B5 (-> Bool set_nat))) (=> (@ (@ member2802428098988154798_o_nat C) (@ (@ product_Sigma_o_nat A4) B5)) (not (forall ((X Bool)) (=> (@ (@ member_o X) A4) (forall ((Y nat)) (=> (@ (@ member_nat Y) (@ B5 X)) (not (= C (@ (@ product_Pair_o_nat X) Y)))))))))) (forall ((F (-> int nat)) (A4 set_int)) (=> (@ (@ inj_on_int_nat F) A4) (= (@ finite_finite_nat (@ (@ image_int_nat F) A4)) (@ finite_finite_int A4)))) (forall ((B5 set_int) (F (-> nat int)) (A4 set_nat)) (=> (@ (@ ord_less_eq_set_int B5) (@ (@ image_nat_int F) A4)) (not (forall ((C2 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((A4 (-> Bool set_Pr4329608150637261639at_nat))) (= (@ comple4364388969068068532at_nat (@ (@ image_2496312346330513076at_nat A4) top_top_set_o)) (@ (@ sup_su5525570899277871387at_nat (@ A4 true)) (@ A4 false)))) (forall ((X2 int) (A4 set_int) (F (-> int set_nat))) (let ((_let_1 (@ (@ vimage9012682431555523728nt_nat (@ product_Pair_int_nat X2)) (@ (@ produc1456381018704787142nt_nat A4) F)))) (let ((_let_2 (@ (@ member_int X2) A4))) (and (=> _let_2 (= _let_1 (@ F X2))) (=> (not _let_2) (= _let_1 bot_bot_set_nat)))))) (forall ((A4 set_nat) (F (-> nat product_unit)) (G (-> nat product_unit))) (let ((_let_1 (@ (@ image_8730104196221521654t_unit G) A4))) (let ((_let_2 (@ (@ image_8730104196221521654t_unit F) A4))) (=> (not (= A4 bot_bot_set_nat)) (=> (@ condit2080475194861589617t_unit _let_2) (=> (@ condit2080475194861589617t_unit _let_1) (= (@ (@ sup_sup_Product_unit (@ comple4687483117567863418t_unit _let_2)) (@ comple4687483117567863418t_unit _let_1)) (@ comple4687483117567863418t_unit (@ (@ image_8730104196221521654t_unit (lambda ((A5 nat)) (@ (@ sup_sup_Product_unit (@ F A5)) (@ G A5)))) A4))))))))) _let_294 (forall ((A4 (-> product_prod_nat_nat int Bool)) (B5 (-> (-> product_prod_nat_nat Bool) (-> int Bool) Bool)) (F (-> product_prod_nat_nat product_prod_nat_nat Bool)) (G (-> int int Bool)) (X5 set_Pr49084382684228242at_int) (X2 produc4196048018000912732at_int)) (=> (@ (@ (@ (@ bNF_re717283939379294677_int_o A4) B5) F) G) (=> (@ (@ ord_le4604737605482584818at_int X5) (@ collec2851339944984316337at_int (@ produc6937227050501860053_int_o A4))) (=> (@ (@ member8394280151737582451at_int X2) X5) (@ (@ B5 (@ (@ (@ comp_P7900071416159368952at_int F) produc4619704898428564714at_int) X2)) (@ (@ (@ comp_i653165354545908656at_int G) produc3064508320661873192at_int) X2)))))) (forall ((F3 (-> nat nat)) (F (-> nat nat)) (A4 set_nat)) (=> (@ (@ inj_on_nat_nat (@ (@ comp_nat_nat_nat F3) F)) A4) (@ (@ inj_on_nat_nat F) A4))) _let_293 (forall ((A4 set_nat) (F (-> nat rat))) (=> (@ finite_finite_nat A4) (@ (@ ord_less_eq_nat (@ finite_card_rat (@ (@ image_nat_rat F) A4))) (@ finite_card_nat A4)))) (forall ((A4 set_o)) (=> (forall ((X Bool)) (not (@ (@ member_o X) A4))) (@ (@ ord_less_eq_set_o A4) bot_bot_set_o))) (forall ((F (-> nat num)) (G (-> Bool Bool)) (H (-> int nat)) (I (-> nat Bool)) (Prod product_prod_int_nat)) (= (@ (@ (@ produc3264868786340801506um_o_o F) G) (@ (@ (@ produc8298419091753553490_nat_o H) I) Prod)) (@ (@ (@ produc9074608839065728392_nat_o (@ (@ comp_nat_num_int F) H)) (@ (@ comp_o_o_nat G) I)) Prod))) _let_292 (forall ((A4 set_Pr1261947904930325089at_nat) (B5 set_Pr1261947904930325089at_nat) (F (-> product_prod_nat_nat product_unit)) (G (-> product_prod_nat_nat product_unit))) (=> (@ (@ ord_le3146513528884898305at_nat A4) B5) (=> (forall ((X product_prod_nat_nat)) (=> (@ (@ member8440522571783428010at_nat X) A4) (@ (@ ord_le3221252021190050221t_unit (@ F X)) (@ G X)))) (@ (@ ord_le3221252021190050221t_unit (@ comple4687483117567863418t_unit (@ (@ image_6169909464789311569t_unit F) A4))) (@ comple4687483117567863418t_unit (@ (@ image_6169909464789311569t_unit G) B5)))))) (forall ((A rat) (S2 set_rat) (T2 set_rat)) (= (@ (@ image_rat_rat (lambda ((X4 rat)) (@ (@ minus_minus_rat X4) A))) (@ (@ minus_minus_set_rat S2) T2)) (@ (@ minus_minus_set_rat (@ (@ image_rat_rat (lambda ((X4 rat)) (@ (@ minus_minus_rat X4) A))) S2)) (@ (@ image_rat_rat (lambda ((X4 rat)) (@ (@ minus_minus_rat X4) A))) T2)))) (forall ((A4 set_Pr4329608150637261639at_nat)) (= (@ collec6321179662152712658at_nat (lambda ((X4 produc3843707927480180839at_nat)) (@ (@ member8757157785044589968at_nat X4) A4))) A4)) (forall ((B int) (F (-> Bool int)) (A4 set_o)) (=> (@ (@ member_int B) (@ (@ image_o_int F) A4)) (not (forall ((X Bool)) (=> (= B (@ F X)) (not (@ (@ member_o X) A4))))))) (forall ((F (-> nat num Bool)) (A nat) (B num)) (=> (@ (@ F A) B) (@ (@ produc4927758841916487424_num_o F) (@ (@ product_Pair_nat_num A) B)))) (forall ((F (-> char int)) (Y3 int)) (=> (= (@ (@ image_char_int F) top_top_set_char) top_top_set_int) (not (forall ((X char)) (not (= Y3 (@ F X))))))) (forall ((Rep (-> product_unit Bool)) (Abs (-> Bool product_unit)) (G (-> nat nat)) (P2 (-> nat Bool)) (H (-> nat product_unit))) (=> (@ (@ (@ type_d6188575255521822967unit_o Rep) Abs) top_top_set_o) (= (@ (@ (@ bNF_vi1443435967014148806unit_o G) Abs) (@ (@ bNF_Gr1993012052113314029t_unit (@ collect_nat P2)) H)) (@ (@ bNF_Grp_nat_o (@ collect_nat (lambda ((X4 nat)) (@ P2 (@ G X4))))) (@ (@ comp_nat_o_nat (@ (@ comp_P4985893458130756478_o_nat Rep) H)) G))))) (forall ((F (-> int int)) (A4 set_int)) (= (= (@ (@ image_int_int F) A4) bot_bot_set_int) (= A4 bot_bot_set_int))) (forall ((F (-> heap_e7401611519738050253t_unit heap_e7401611519738050253t_unit))) (= (@ (@ comp_P4044372497395451596t_unit produc473321116828791851t_unit) (@ produc3038839249364385243_ref_a F)) produc473321116828791851t_unit)) (forall ((F (-> nat rat)) (A4 set_nat) (G (-> nat rat)) (B5 set_nat) (H (-> rat rat))) (let ((_let_1 (@ comp_rat_rat_nat H))) (=> (= (@ (@ image_nat_rat F) A4) (@ (@ image_nat_rat G) B5)) (= (@ (@ image_nat_rat (@ _let_1 F)) A4) (@ (@ image_nat_rat (@ _let_1 G)) B5))))) _let_290 (forall ((G (-> nat nat)) (F (-> int nat)) (A4 set_int)) (= (@ complete_Inf_Inf_nat (@ (@ image_nat_nat G) (@ (@ image_int_nat F) A4))) (@ complete_Inf_Inf_nat (@ (@ image_int_nat (@ (@ comp_nat_nat_int G) F)) A4)))) (forall ((F (-> int nat)) (A4 set_int) (B5 set_nat)) (= (@ (@ ord_less_eq_set_nat (@ (@ image_int_nat F) A4)) B5) (@ (@ ord_less_eq_set_int A4) (@ (@ vimage_int_nat F) B5)))) (forall ((G (-> int int)) (F (-> nat int)) (A4 set_nat)) (= (@ complete_Sup_Sup_int (@ (@ image_int_int G) (@ (@ image_nat_int F) A4))) (@ complete_Sup_Sup_int (@ (@ image_nat_int (@ (@ comp_int_int_nat G) F)) A4)))) (forall ((C product_prod_o_o) (A4 set_o) (B5 (-> Bool set_o))) (=> (@ (@ member7466972457876170832od_o_o C) (@ (@ product_Sigma_o_o A4) B5)) (not (forall ((X Bool)) (=> (@ (@ member_o X) A4) (forall ((Y Bool)) (=> (@ (@ member_o Y) (@ B5 X)) (not (= C (@ (@ product_Pair_o_o X) Y)))))))))) (forall ((X2 produc7812382424243267045t_unit)) (= (@ produc6369869760173755749_ref_a (@ produc970745769005243767t_unit X2)) (@ produc473321116828791851t_unit X2))) (forall ((I produc3843707927480180839at_nat) (A4 set_Pr4329608150637261639at_nat) (U set_nat) (F (-> produc3843707927480180839at_nat set_nat))) (let ((_let_1 (@ ord_less_eq_set_nat U))) (=> (@ (@ member8757157785044589968at_nat I) A4) (=> (@ _let_1 (@ F I)) (@ _let_1 (@ comple7399068483239264473et_nat (@ (@ image_3160451284896210088et_nat F) A4))))))) (forall ((Rep (-> num Bool)) (Abs (-> Bool num)) (M (-> nat Bool)) (M1 (-> Bool Bool)) (M2 (-> nat Bool)) (F (-> Bool num)) (G (-> int nat))) (=> (@ (@ (@ type_d9070036042389994064_num_o Rep) Abs) top_top_set_o) (=> (= M (@ (@ comp_o_o_nat M1) M2)) (= (@ (@ comp_nat_num_int (@ (@ comp_o_num_nat F) M)) G) (@ (@ comp_num_num_int (@ (@ comp_o_num_num (@ (@ comp_o_num_o F) M1)) Rep)) (@ (@ comp_nat_num_int (@ (@ comp_o_num_nat Abs) M2)) G)))))) (forall ((S5 set_nat) (F (-> nat nat nat)) (X2 nat) (Y3 nat) (G (-> nat nat))) (let ((_let_1 (@ comp_nat_nat_nat (@ F Y3)))) (let ((_let_2 (@ comp_nat_nat_nat (@ F X2)))) (=> (@ (@ finite3582905537739598962at_nat S5) F) (=> (@ (@ member_nat X2) S5) (=> (@ (@ member_nat Y3) S5) (= (@ _let_1 (@ _let_2 G)) (@ _let_2 (@ _let_1 G))))))))) (forall ((B5 (-> nat set_Pr8693737435421807431at_nat)) (A nat) (A4 set_nat)) (let ((_let_1 (@ image_4592875511192039216at_nat B5))) (= (@ comple2748534634209756852at_nat (@ _let_1 (@ (@ insert_nat A) A4))) (@ (@ sup_su718114333110466843at_nat (@ B5 A)) (@ comple2748534634209756852at_nat (@ _let_1 A4)))))) (forall ((A4 set_nat) (C3 set_Product_unit) (B5 set_nat) (D set_Product_unit)) (= (@ (@ ord_le1468274181084648008t_unit (@ (@ produc5506539147108004339t_unit A4) (lambda ((Uu nat)) C3))) (@ (@ produc5506539147108004339t_unit B5) (lambda ((Uu nat)) D))) (or (= A4 bot_bot_set_nat) (= C3 bot_bo3957492148770167129t_unit) (and (@ (@ ord_less_eq_set_nat A4) B5) (@ (@ ord_le3507040750410214029t_unit C3) D))))) (forall ((R3 set_Pr958786334691620121nt_int) (S5 set_Pr958786334691620121nt_int)) (= (@ (@ inf_inf_int_int_o (lambda ((X4 int) (Y5 int)) (@ (@ member5262025264175285858nt_int (@ (@ product_Pair_int_int X4) Y5)) R3))) (lambda ((X4 int) (Y5 int)) (@ (@ member5262025264175285858nt_int (@ (@ product_Pair_int_int X4) Y5)) S5))) (lambda ((X4 int) (Y5 int)) (@ (@ member5262025264175285858nt_int (@ (@ product_Pair_int_int X4) Y5)) (@ (@ inf_in2269163501485487111nt_int R3) S5))))) (forall ((A product_prod_nat_nat) (A4 set_Pr1261947904930325089at_nat) (F (-> product_prod_nat_nat set_nat)) (C set_nat)) (=> (@ (@ member8440522571783428010at_nat A) A4) (=> (forall ((X product_prod_nat_nat)) (=> (@ (@ member8440522571783428010at_nat X) A4) (= (@ F X) C))) (= (@ comple7399068483239264473et_nat (@ (@ image_15824709712370754et_nat F) A4)) C)))) (forall ((R3 (-> int int Bool)) (R7 (-> int code_integer Bool)) (S5 (-> num num Bool)) (S6 (-> num num Bool))) (=> (@ left_unique_int_int R3) (=> (@ right_total_int_int R3) (=> (@ right_8475562212078014689nteger R7) (=> (@ left_t2374113004080657585nteger R7) (@ (@ ord_le6931201860925936491_num_o (@ (@ bNF_re6718328864250387230um_num (@ (@ relcom967497705283160040nteger R3) R7)) (@ (@ relcompp_num_num_num S5) S6))) (@ (@ relcom1533066287727470739er_num (@ (@ bNF_re7626690874201225453um_num R3) S5)) (@ (@ bNF_re6718328864250387230um_num R7) S6)))))))) (forall ((F (-> nat rat)) (A4 set_nat)) (=> (@ (@ inj_on_nat_rat F) A4) (= (@ (@ image_rat_nat (@ (@ the_inv_into_nat_rat A4) F)) (@ (@ image_nat_rat F) A4)) A4))) _let_289 (forall ((F (-> Bool set_nat)) (A Bool) (B5 set_o)) (let ((_let_1 (@ image_o_set_nat F))) (= (@ comple7399068483239264473et_nat (@ _let_1 (@ (@ insert_o A) B5))) (@ (@ sup_sup_set_nat (@ F A)) (@ comple7399068483239264473et_nat (@ _let_1 B5)))))) (forall ((A set_Pr1261947904930325089at_nat) (B set_Pr1261947904930325089at_nat)) (=> (@ (@ member8757157785044589968at_nat (@ (@ produc2922128104949294807at_nat A) B)) id_set1796276052702428605at_nat) (= A B))) (forall ((A4 set_int) (R set_Pr958786334691620121nt_int) (A int) (B int)) (=> (@ (@ refl_on_int A4) R) (=> (@ (@ member5262025264175285858nt_int (@ (@ product_Pair_int_int A) B)) R) (and (@ (@ member_int A) A4) (@ (@ member_int B) A4))))) (forall ((K produc3843707927480180839at_nat) (I3 set_Pr4329608150637261639at_nat) (A4 (-> produc3843707927480180839at_nat set_nat))) (let ((_let_1 (@ comple7806235888213564991et_nat (@ (@ image_3160451284896210088et_nat A4) I3)))) (=> (@ (@ member8757157785044589968at_nat K) I3) (= (@ (@ inf_inf_set_nat (@ A4 K)) _let_1) _let_1)))) (forall ((F (-> product_unit set_Pr1261947904930325089at_nat)) (A product_unit) (A4 set_Product_unit)) (let ((_let_1 (@ image_3617315916088684441at_nat F))) (= (@ comple1930127330929219688at_nat (@ _let_1 (@ (@ insert_Product_unit A) A4))) (@ (@ inf_in2572325071724192079at_nat (@ F A)) (@ comple1930127330929219688at_nat (@ _let_1 A4)))))) (forall ((R3 (-> num num Bool))) (= (@ (@ bNF_re7626690874201225453um_num (lambda ((Y2 int) (Z int)) (= Y2 Z))) R3) (@ (@ relcom1697847500783689711nt_num (@ conver5699786650113435344nt_num (@ (@ bNF_Gr5590197745039885111nt_num (@ collec266097228571071243um_num (lambda ((X4 (-> int product_prod_num_num))) (@ (@ ord_le880128212290418581um_num (@ (@ image_7722540232540426402um_num X4) top_top_set_int)) (@ collec2230928802738392704um_num (@ produc5703948589228662326_num_o R3)))))) (@ comp_P4305060815297604026um_int product_fst_num_num)))) (@ (@ bNF_Gr5590197745039885111nt_num (@ collec266097228571071243um_num (lambda ((X4 (-> int product_prod_num_num))) (@ (@ ord_le880128212290418581um_num (@ (@ image_7722540232540426402um_num X4) top_top_set_int)) (@ collec2230928802738392704um_num (@ produc5703948589228662326_num_o R3)))))) (@ comp_P4305060815297604026um_int product_snd_num_num))))) (forall ((F (-> char char)) (G (-> char rat))) (=> (= (@ (@ image_char_char F) top_top_set_char) top_top_set_char) (=> (= (@ (@ image_char_rat G) top_top_set_char) top_top_set_rat) (= (@ (@ image_7275072250160737868ar_rat (@ (@ produc5209943433214700613ar_rat F) G)) top_to1235241553633177651r_char) top_to8437673547576850234ar_rat)))) (forall ((X2 nat) (Y3 nat)) (= (@ the_Pr7557018466319803784at_nat (@ produc6081775807080527818_nat_o (lambda ((X7 nat) (Y6 nat)) (and (= X2 X7) (= Y3 Y6))))) (@ (@ product_Pair_nat_nat X2) Y3))) (forall ((F (-> char nat)) (G (-> nat rat))) (=> (= (@ (@ image_char_nat F) top_top_set_char) top_top_set_nat) (=> (= (@ (@ image_nat_rat G) top_top_set_nat) top_top_set_rat) (= (@ (@ image_char_rat (@ (@ comp_nat_rat_char G) F)) top_top_set_char) top_top_set_rat)))) (forall ((I produc3843707927480180839at_nat) (A4 set_Pr4329608150637261639at_nat) (F (-> produc3843707927480180839at_nat product_unit))) (=> (@ (@ member8757157785044589968at_nat I) A4) (@ (@ ord_le3221252021190050221t_unit (@ comple2584293577114468500t_unit (@ (@ image_7082456443403096939t_unit F) A4))) (@ F I)))) (forall ((K Bool) (I3 set_o) (A4 (-> Bool product_unit))) (let ((_let_1 (@ comple4687483117567863418t_unit (@ (@ image_o_Product_unit A4) I3)))) (=> (@ (@ member_o K) I3) (= (@ (@ sup_sup_Product_unit (@ A4 K)) _let_1) _let_1)))) (forall ((A set_Pr4329608150637261639at_nat) (B set_Pr4329608150637261639at_nat) (A4 set_se5479201105039950375at_nat) (B5 (-> set_Pr4329608150637261639at_nat set_se5479201105039950375at_nat))) (=> (@ (@ member1466754251312161552at_nat (@ (@ produc9060074326276436823at_nat A) B)) (@ (@ produc6258361011560675592at_nat A4) B5)) (@ (@ member6273874620674182256at_nat B) (@ B5 A)))) (forall ((R3 set_Pr7459493094073627847at_nat) (S5 set_Pr7459493094073627847at_nat)) (= (= (lambda ((X4 set_Pr4329608150637261639at_nat) (Y5 set_Pr4329608150637261639at_nat)) (@ (@ member1466754251312161552at_nat (@ (@ produc9060074326276436823at_nat X4) Y5)) R3)) (lambda ((X4 set_Pr4329608150637261639at_nat) (Y5 set_Pr4329608150637261639at_nat)) (@ (@ member1466754251312161552at_nat (@ (@ produc9060074326276436823at_nat X4) Y5)) S5))) (= R3 S5))) _let_288 (forall ((A (-> nat nat)) (B (-> nat nat)) (C (-> nat nat)) (D2 (-> nat nat))) (=> (= (@ (@ comp_nat_nat_nat A) B) (@ (@ comp_nat_nat_nat C) D2)) (forall ((V4 nat)) (= (@ A (@ B V4)) (@ C (@ D2 V4)))))) (forall ((C3 set_nat) (A product_unit) (B5 (-> nat set_Product_unit))) (let ((_let_1 (= C3 bot_bot_set_nat))) (and (=> _let_1 (= (@ comple3349607820504768346t_unit (@ (@ image_4824033694279209942t_unit (lambda ((X4 nat)) (@ (@ insert_Product_unit A) (@ B5 X4)))) C3)) bot_bo3957492148770167129t_unit)) (=> (not _let_1) (= (@ comple3349607820504768346t_unit (@ (@ image_4824033694279209942t_unit (lambda ((X4 nat)) (@ (@ insert_Product_unit A) (@ B5 X4)))) C3)) (@ (@ insert_Product_unit A) (@ comple3349607820504768346t_unit (@ (@ image_4824033694279209942t_unit B5) C3)))))))) (forall ((A4 set_int) (R set_Pr958786334691620121nt_int)) (=> (forall ((X int) (Y int)) (=> (@ (@ member_int X) A4) (=> (@ (@ member_int Y) A4) (=> (not (= X Y)) (or (@ (@ member5262025264175285858nt_int (@ (@ product_Pair_int_int X) Y)) R) (@ (@ member5262025264175285858nt_int (@ (@ product_Pair_int_int Y) X)) R)))))) (@ (@ total_on_int A4) R))) (forall ((F (-> product_unit rat)) (A4 set_rat)) (=> (= (@ (@ image_240439954468258464it_rat F) top_to1996260823553986621t_unit) top_top_set_rat) (= (= (@ (@ vimage5618198413390092650it_rat F) A4) bot_bo3957492148770167129t_unit) (= A4 bot_bot_set_rat)))) (forall ((X2 product_prod_nat_nat) (Y3 product_prod_nat_nat) (A4 set_Pr1261947904930325089at_nat)) (= (@ (@ member8206827879206165904at_nat (@ (@ produc6161850002892822231at_nat X2) Y3)) (@ id_on_2554058798563519774at_nat A4)) (and (@ (@ member8440522571783428010at_nat X2) A4) (= X2 Y3)))) (forall ((M (-> produc3843707927480180839at_nat set_Pr8693737435421807431at_nat)) (A4 set_Pr4329608150637261639at_nat) (B5 set_Pr4329608150637261639at_nat)) (let ((_let_1 (@ image_7260680879217540773at_nat M))) (= (@ comple2748534634209756852at_nat (@ _let_1 (@ (@ sup_su5525570899277871387at_nat A4) B5))) (@ (@ sup_su718114333110466843at_nat (@ comple2748534634209756852at_nat (@ _let_1 A4))) (@ comple2748534634209756852at_nat (@ _let_1 B5)))))) (forall ((A4 set_o) (C3 set_nat) (B5 set_o) (D set_nat)) (= (@ (@ ord_le6472378536984071597_o_nat (@ (@ product_Sigma_o_nat A4) (lambda ((Uu Bool)) C3))) (@ (@ product_Sigma_o_nat B5) (lambda ((Uu Bool)) D))) (or (= C3 bot_bot_set_nat) (and (@ (@ ord_less_eq_set_nat C3) D) (@ (@ ord_less_eq_set_o A4) B5)) (= A4 bot_bot_set_o)))) (forall ((Prod produc1319942482725812455at_nat)) (= (@ (@ produc9060074326276436823at_nat (@ produc4486455499028916547at_nat Prod)) (@ produc826222791318859909at_nat Prod)) Prod)) (@ (@ _let_75 (@ produc27273713700761075at_nat (lambda ((X4 nat) (Y5 nat) (__flatten_var_0 product_prod_nat_nat)) (@ (@ produc2626176000494625587at_nat (lambda ((U3 nat) (V3 nat)) (@ (@ product_Pair_nat_nat (@ (@ plus_plus_nat X4) V3)) (@ (@ plus_plus_nat Y5) U3)))) __flatten_var_0)))) minus_minus_int) (forall ((I3 set_se7855581050983116737at_nat) (A4 (-> set_Pr1261947904930325089at_nat set_se7855581050983116737at_nat)) (B5 (-> set_Pr1261947904930325089at_nat set_se7855581050983116737at_nat))) (let ((_let_1 (@ produc7726050920695093128at_nat I3))) (= (@ _let_1 (lambda ((I2 set_Pr1261947904930325089at_nat)) (@ (@ sup_su3642409539654194069at_nat (@ A4 I2)) (@ B5 I2)))) (@ (@ sup_su5525570899277871387at_nat (@ _let_1 A4)) (@ _let_1 B5))))) (forall ((R set_Pr1261947904930325089at_nat) (S2 set_Pr1261947904930325089at_nat) (R3 set_Pr4329608150637261639at_nat) (S3 set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ produc2922128104949294807at_nat R))) (=> (@ (@ member8757157785044589968at_nat (@ _let_1 S2)) R3) (=> (= S3 S2) (@ (@ member8757157785044589968at_nat (@ _let_1 S3)) R3))))) (forall ((B5 (-> product_unit set_Pr8693737435421807431at_nat)) (A product_unit) (A4 set_Product_unit)) (let ((_let_1 (@ image_7288820656315755647at_nat B5))) (= (@ comple2748534634209756852at_nat (@ _let_1 (@ (@ insert_Product_unit A) A4))) (@ (@ sup_su718114333110466843at_nat (@ B5 A)) (@ comple2748534634209756852at_nat (@ _let_1 A4)))))) (= (@ (@ image_2486076414777270412at_nat nat_prod_encode) top_to4669805908274784177at_nat) top_top_set_nat) (forall ((A4 set_Product_unit) (C set_int)) (let ((_let_1 (= A4 bot_bo3957492148770167129t_unit))) (and (=> _let_1 (= (@ comple3628384868704368283et_int (@ (@ image_3995998972318789802et_int (lambda ((Y5 product_unit)) C)) A4)) top_top_set_int)) (=> (not _let_1) (= (@ comple3628384868704368283et_int (@ (@ image_3995998972318789802et_int (lambda ((Y5 product_unit)) C)) A4)) C))))) (forall ((A4 set_Product_unit) (F (-> product_unit int)) (U int)) (let ((_let_1 (@ (@ image_873079544045703924it_int F) A4))) (=> (not (= A4 bot_bo3957492148770167129t_unit)) (=> (@ condit2212336002400062152ve_int _let_1) (= (@ (@ ord_less_eq_int (@ complete_Sup_Sup_int _let_1)) U) (forall ((X4 product_unit)) (=> (@ (@ member_Product_unit X4) A4) (@ (@ ord_less_eq_int (@ F X4)) U)))))))) (forall ((F (-> product_unit product_unit))) (= (@ comple4687483117567863418t_unit (@ (@ image_405062704495631173t_unit F) bot_bo3957492148770167129t_unit)) bot_bot_Product_unit)) (forall ((B5 (-> set_Pr1261947904930325089at_nat set_se7855581050983116737at_nat))) (= (@ (@ produc7726050920695093128at_nat bot_bo3083307316010499117at_nat) B5) bot_bo228742789529271731at_nat)) (forall ((X2 set_Pr4329608150637261639at_nat) (Y3 set_Pr4329608150637261639at_nat)) (= (@ basic_1274512288150691911at_nat (@ (@ produc9060074326276436823at_nat X2) Y3)) (@ (@ insert2290795007606087959at_nat X2) bot_bo1534825418459847827at_nat))) (forall ((B5 (-> nat set_nat)) (A4 set_set_nat)) (= (@ comple7806235888213564991et_nat (@ (@ image_7916887816326733075et_nat (lambda ((Y5 set_nat)) (@ comple7806235888213564991et_nat (@ (@ image_nat_set_nat B5) Y5)))) A4)) (@ comple7806235888213564991et_nat (@ (@ image_nat_set_nat B5) (@ comple7399068483239264473et_nat A4))))) (forall ((B5 (-> product_unit set_Pr4329608150637261639at_nat)) (A product_unit) (A4 set_Product_unit)) (let ((_let_1 (@ image_5172358348707908735at_nat B5))) (= (@ comple4364388969068068532at_nat (@ _let_1 (@ (@ insert_Product_unit A) A4))) (@ (@ sup_su5525570899277871387at_nat (@ B5 A)) (@ comple4364388969068068532at_nat (@ _let_1 A4)))))) (forall ((F (-> nat rat)) (A4 set_nat) (P2 (-> rat Bool))) (= (@ collect_rat (lambda ((X4 rat)) (and (@ (@ member_rat X4) (@ (@ image_nat_rat F) A4)) (@ P2 X4)))) (@ (@ image_nat_rat F) (@ collect_nat (lambda ((X4 nat)) (and (@ (@ member_nat X4) A4) (@ P2 (@ F X4)))))))) (forall ((P2 (-> char int product_unit))) (= (@ comple2584293577114468500t_unit (@ (@ image_5846526143423701914t_unit (lambda ((Y5 int)) (@ comple4687483117567863418t_unit (@ (@ image_4337914935673063477t_unit (lambda ((X4 char)) (@ (@ P2 X4) Y5))) top_top_set_char)))) top_top_set_int)) (@ comple4687483117567863418t_unit (@ (@ image_4409302170498516394t_unit (lambda ((F2 (-> int char))) (@ comple2584293577114468500t_unit (@ (@ image_5846526143423701914t_unit (lambda ((X4 int)) (@ (@ P2 (@ F2 X4)) X4))) top_top_set_int)))) top_top_set_int_char)))) (forall ((X2 (-> nat Bool)) (Xa2 (-> nat Bool)) (F (-> Bool Bool)) (Fa (-> Bool Bool))) (=> (forall ((Z3 Bool) (Za Bool)) (=> (@ (@ member_o Z3) (@ (@ image_nat_o X2) top_top_set_nat)) (=> (@ (@ member_o Za) (@ (@ image_nat_o Xa2) top_top_set_nat)) (=> (= (@ F Z3) (@ Fa Za)) (= Z3 Za))))) (=> (= (@ (@ comp_o_o_nat F) X2) (@ (@ comp_o_o_nat Fa) Xa2)) (= X2 Xa2)))) _let_287 (= produc27273713700761075at_nat (lambda ((F2 (-> nat nat product_prod_nat_nat product_prod_nat_nat)) (X4 product_prod_nat_nat) (Y5 product_prod_nat_nat)) (@ (@ produc2626176000494625587at_nat (lambda ((L3 nat) (R5 nat)) (@ (@ (@ F2 L3) R5) Y5))) X4))) (forall ((F (-> int nat)) (A4 set_int) (B5 set_int)) (let ((_let_1 (@ image_int_nat F))) (=> (@ (@ inj_on_int_nat F) top_top_set_int) (= (= (@ _let_1 A4) (@ _let_1 B5)) (= A4 B5))))) (forall ((R1 (-> ref_a heap_e7401611519738050253t_unit Bool)) (R22 (-> nat nat Bool)) (P2 (-> ref_a nat Bool)) (Q2 (-> heap_e7401611519738050253t_unit nat Bool)) (A produc7812382424243267045t_unit) (A4 set_Pr1133966238863718811t_unit) (B product_prod_nat_nat) (B5 set_Pr1261947904930325089at_nat)) (=> (@ (@ (@ (@ bNF_re9202112420002600977_nat_o R1) (@ (@ bNF_re4705727531993890431at_o_o R22) (lambda ((Y2 Bool) (Z Bool)) (= Y2 Z)))) P2) Q2) (=> (@ (@ member7849944260330398460t_unit A) A4) (=> (@ (@ member8440522571783428010at_nat B) B5) (=> (@ (@ ord_le5525191956872776187t_unit A4) (@ collec3252306575900995386t_unit (@ produc4924168586796184916unit_o R1))) (=> (@ (@ ord_le3146513528884898305at_nat B5) (@ collec3392354462482085612at_nat (@ produc6081775807080527818_nat_o R22))) (= (@ (@ P2 (@ produc473321116828791851t_unit A)) (@ product_fst_nat_nat B)) (@ (@ Q2 (@ produc1126150082675451753t_unit A)) (@ product_snd_nat_nat B))))))))) _let_286 (= comp_int_nat_int (lambda ((F2 (-> int nat)) (G3 (-> int int)) (X4 int)) (@ F2 (@ G3 X4)))) (forall ((F (-> Bool Bool)) (G (-> Bool Bool)) (X2 Bool)) (= (@ (@ (@ comp_P551574746845053877_o_o_o (@ (@ produc1928436952130685430_o_o_o F) id_o)) (@ (@ bNF_convol_o_o_o id_o) G)) X2) (@ (@ (@ bNF_convol_o_o_o (@ (@ comp_o_o_o id_o) F)) G) X2))) (forall ((C3 set_o) (A4 (-> Bool set_int)) (B5 set_int)) (let ((_let_1 (= C3 bot_bot_set_o))) (and (=> _let_1 (= (@ comple3628384868704368283et_int (@ (@ image_o_set_int (lambda ((X4 Bool)) (@ (@ minus_minus_set_int (@ A4 X4)) B5))) C3)) top_top_set_int)) (=> (not _let_1) (= (@ comple3628384868704368283et_int (@ (@ image_o_set_int (lambda ((X4 Bool)) (@ (@ minus_minus_set_int (@ A4 X4)) B5))) C3)) (@ (@ minus_minus_set_int (@ comple3628384868704368283et_int (@ (@ image_o_set_int A4) C3))) B5)))))) (forall ((A nat) (B Bool) (A4 set_nat) (B5 (-> nat set_o))) (= (@ (@ member6310962623043647828_nat_o (@ (@ product_Pair_nat_o A) B)) (@ (@ product_Sigma_nat_o A4) B5)) (and (@ (@ member_nat A) A4) (@ (@ member_o B) (@ B5 A))))) (forall ((F (-> int int)) (A4 set_int) (X2 int) (U int)) (let ((_let_1 (@ (@ image_int_int F) A4))) (=> (@ condit1735850657277959132ow_int _let_1) (=> (@ (@ member_int X2) A4) (=> (@ (@ ord_less_eq_int (@ F X2)) U) (@ (@ ord_less_eq_int (@ complete_Inf_Inf_int _let_1)) U)))))) (forall ((X2 num) (Y3 num)) (= (@ (@ (@ if_num false) X2) Y3) Y3)) (forall ((Rep (-> int int)) (Abs (-> int int)) (A4 set_int)) (=> (@ (@ (@ type_d7247357190169752966nt_int Rep) Abs) A4) (= (@ (@ image_int_int Rep) top_top_set_int) A4))) _let_285 (forall ((X2 nat) (A4 set_nat) (F (-> nat Bool))) (let ((_let_1 (@ (@ image_nat_o F) A4))) (=> (@ (@ member_nat X2) A4) (= (@ (@ insert_o (@ F X2)) _let_1) _let_1)))) (forall ((A4 set_o) (C3 set_nat) (B5 (-> Bool set_nat))) (=> (forall ((X Bool)) (=> (@ (@ member_o X) A4) (@ (@ ord_less_eq_set_nat C3) (@ B5 X)))) (@ (@ ord_less_eq_set_nat C3) (@ comple7806235888213564991et_nat (@ (@ image_o_set_nat B5) A4))))) (forall ((B5 set_Pr1261947904930325089at_nat) (F (-> nat product_prod_nat_nat)) (A4 set_nat)) (=> (@ finite6177210948735845034at_nat B5) (=> (@ (@ ord_le3146513528884898305at_nat B5) (@ (@ image_5846123807819985514at_nat F) A4)) (exists ((C2 set_nat)) (and (@ finite_finite_nat C2) (= B5 (@ (@ image_5846123807819985514at_nat F) C2)) (@ (@ ord_less_eq_set_nat C2) A4)))))) (forall ((F (-> int int)) (A4 set_int) (F3 (-> int nat))) (=> (@ (@ inj_on_int_int F) A4) (= (@ (@ inj_on_int_nat F3) (@ (@ image_int_int F) A4)) (@ (@ inj_on_int_nat (@ (@ comp_int_nat_int F3) F)) A4)))) (forall ((R22 (-> nat nat Bool)) (R32 (-> nat num Bool)) (R1 (-> nat int Bool))) (@ (@ (@ (@ bNF_re584878643992547173nt_num (@ (@ bNF_re2211152805895086571at_num R22) R32)) (@ (@ bNF_re8622501330148003679nt_num (@ (@ bNF_re6025474579976152573at_nat R1) R22)) (@ (@ bNF_re2582806366131931207at_num R1) R32))) comp_nat_nat_nat) comp_nat_num_int)) (forall ((I3 set_o) (F (-> Bool product_unit)) (C product_unit)) (=> (not (= I3 bot_bot_set_o)) (=> (forall ((I4 Bool)) (=> (@ (@ member_o I4) I3) (@ (@ ord_le3221252021190050221t_unit (@ F I4)) C))) (= (= (@ comple2584293577114468500t_unit (@ (@ image_o_Product_unit F) I3)) C) (forall ((X4 Bool)) (=> (@ (@ member_o X4) I3) (= (@ F X4) C))))))) (forall ((F (-> nat int)) (A4 set_nat)) (=> (@ (@ inj_on_nat_int F) A4) (= (@ (@ image_int_nat (@ (@ the_inv_into_nat_int A4) F)) (@ (@ image_nat_int F) A4)) A4))) (forall ((A4 set_nat) (F (-> nat nat)) (A nat)) (let ((_let_1 (@ image_nat_nat F))) (let ((_let_2 (@ _let_1 A4))) (=> (not (= A4 bot_bot_set_nat)) (=> (@ condit2214826472909112428ve_nat _let_2) (= (@ complete_Sup_Sup_nat (@ _let_1 (@ (@ insert_nat A) A4))) (@ (@ sup_sup_nat (@ F A)) (@ complete_Sup_Sup_nat _let_2)))))))) (forall ((I nat) (A4 set_nat) (U set_nat) (F (-> nat set_nat))) (let ((_let_1 (@ ord_less_eq_set_nat U))) (=> (@ (@ member_nat I) A4) (=> (@ _let_1 (@ F I)) (@ _let_1 (@ comple7399068483239264473et_nat (@ (@ image_nat_set_nat F) A4))))))) (forall ((I3 set_nat) (F (-> nat set_nat)) (X2 set_nat)) (=> (not (= I3 bot_bot_set_nat)) (=> (forall ((I4 nat)) (=> (@ (@ member_nat I4) I3) (= (@ F I4) X2))) (= (@ comple7806235888213564991et_nat (@ (@ image_nat_set_nat F) I3)) X2)))) (forall ((P2 (-> int Bool)) (F (-> int int int)) (Prod product_prod_int_int)) (let ((_let_1 (@ product_snd_int_int Prod))) (let ((_let_2 (@ product_fst_int_int Prod))) (= (@ P2 (@ (@ produc8211389475949308722nt_int F) Prod)) (=> (= Prod (@ (@ product_Pair_int_int _let_2) _let_1)) (@ P2 (@ (@ F _let_2) _let_1))))))) (forall ((P2 (-> (-> product_prod_nat_nat Bool) Bool)) (F (-> nat nat product_prod_nat_nat Bool)) (Prod product_prod_nat_nat)) (let ((_let_1 (@ product_snd_nat_nat Prod))) (let ((_let_2 (@ product_fst_nat_nat Prod))) (= (@ P2 (@ (@ produc8739625826339149834_nat_o F) Prod)) (not (and (= Prod (@ (@ product_Pair_nat_nat _let_2) _let_1)) (not (@ P2 (@ (@ F _let_2) _let_1))))))))) (forall ((C Bool) (T2 heap_Heap_ref_a) (E heap_Heap_ref_a) (H heap_e7401611519738050253t_unit) (H2 heap_e7401611519738050253t_unit) (R ref_a)) (=> (@ (@ (@ (@ heap_effect_ref_a (@ (@ (@ if_Heap_Heap_ref_a C) T2) E)) H) H2) R) (=> (=> C (not (@ (@ (@ (@ heap_effect_ref_a T2) H) H2) R))) (not (=> (not C) (not (@ (@ (@ (@ heap_effect_ref_a E) H) H2) R))))))) (forall ((A4 set_int) (F (-> int int)) (G (-> int int))) (let ((_let_1 (@ (@ image_int_int G) A4))) (let ((_let_2 (@ (@ image_int_int F) A4))) (=> (not (= A4 bot_bot_set_int)) (=> (@ condit2212336002400062152ve_int _let_2) (=> (@ condit2212336002400062152ve_int _let_1) (= (@ (@ sup_sup_int (@ complete_Sup_Sup_int _let_2)) (@ complete_Sup_Sup_int _let_1)) (@ complete_Sup_Sup_int (@ (@ image_int_int (lambda ((A5 int)) (@ (@ sup_sup_int (@ F A5)) (@ G A5)))) A4))))))))) (forall ((X2 (-> int int)) (Xa2 (-> int int)) (F (-> int nat)) (Fa (-> int nat))) (=> (forall ((Z3 int) (Za int)) (=> (@ (@ member_int Z3) (@ (@ image_int_int X2) top_top_set_int)) (=> (@ (@ member_int Za) (@ (@ image_int_int Xa2) top_top_set_int)) (=> (= (@ F Z3) (@ Fa Za)) (= Z3 Za))))) (=> (= (@ (@ comp_int_nat_int F) X2) (@ (@ comp_int_nat_int Fa) Xa2)) (= X2 Xa2)))) (forall ((A4 set_Pr1261947904930325089at_nat) (F (-> product_prod_nat_nat set_nat))) (let ((_let_1 (@ (@ image_15824709712370754et_nat F) A4))) (=> (not (= A4 bot_bo2099793752762293965at_nat)) (@ (@ ord_less_eq_set_nat (@ comple7806235888213564991et_nat _let_1)) (@ comple7399068483239264473et_nat _let_1))))) (forall ((A4 set_ref_a)) (= (@ (@ vimage2910454108108208703_ref_a produc473321116828791851t_unit) A4) (@ (@ produc3946373962484743846t_unit A4) (lambda ((Uu ref_a)) top_to3956321331435058429t_unit)))) (forall ((F (-> nat set_rat))) (= (@ comple4298007329820168263et_rat (@ (@ image_nat_set_rat F) bot_bot_set_nat)) top_top_set_rat)) (forall ((K nat) (I3 set_nat) (A4 (-> nat set_nat))) (let ((_let_1 (@ comple7806235888213564991et_nat (@ (@ image_nat_set_nat A4) I3)))) (=> (@ (@ member_nat K) I3) (= (@ (@ inf_inf_set_nat (@ A4 K)) _let_1) _let_1)))) (forall ((F (-> int int)) (C3 set_int) (A4 set_o) (B5 (-> Bool set_int)) (J4 Bool)) (=> (@ (@ inj_on_int_int F) C3) (=> (forall ((X Bool)) (=> (@ (@ member_o X) A4) (@ (@ ord_less_eq_set_int (@ B5 X)) C3))) (=> (@ (@ member_o J4) A4) (= (@ (@ image_int_int F) (@ comple3628384868704368283et_int (@ (@ image_o_set_int B5) A4))) (@ comple3628384868704368283et_int (@ (@ image_o_set_int (lambda ((X4 Bool)) (@ (@ image_int_int F) (@ B5 X4)))) A4))))))) (forall ((F (-> int nat)) (A4 set_int) (B5 set_int)) (let ((_let_1 (@ image_int_nat F))) (=> (@ (@ inj_on_int_nat F) (@ (@ sup_sup_set_int A4) B5)) (= (= (@ _let_1 A4) (@ _let_1 B5)) (= A4 B5))))) (forall ((Z2 produc7812382424243267045t_unit) (A4 set_ref_a) (F (-> ref_a heap_e7401611519738050253t_unit))) (=> (@ (@ member7849944260330398460t_unit Z2) (@ collec3252306575900995386t_unit (@ produc4924168586796184916unit_o (@ (@ bNF_Gr6510375311308651680t_unit A4) F)))) (= (@ (@ (@ comp_r3604920825623061426t_unit F) produc473321116828791851t_unit) Z2) (@ produc1126150082675451753t_unit Z2)))) (forall ((F (-> rat int)) (Y3 int)) (=> (= (@ (@ image_rat_int F) top_top_set_rat) top_top_set_int) (exists ((X rat)) (= Y3 (@ F X))))) (forall ((G (-> int nat)) (F (-> nat int)) (A4 set_nat)) (= (@ complete_Inf_Inf_nat (@ (@ image_int_nat G) (@ (@ image_nat_int F) A4))) (@ complete_Inf_Inf_nat (@ (@ image_nat_nat (@ (@ comp_int_nat_nat G) F)) A4)))) (forall ((R set_Pr7459493094073627847at_nat)) (=> (@ (@ total_5117575981256876747at_nat (@ field_1428494348145443988at_nat R)) R) (=> (@ (@ ord_le5997549366648089703at_nat R) id_set4888139568991089827at_nat) (or (exists ((A3 set_Pr4329608150637261639at_nat)) (= R (@ (@ insert291458823148189367at_nat (@ (@ produc9060074326276436823at_nat A3) A3)) bot_bo4948859079157340979at_nat))) (= R bot_bo4948859079157340979at_nat))))) (forall ((R3 set_Pr1261947904930325089at_nat) (S5 set_Pr1261947904930325089at_nat)) (= (@ (@ inf_inf_nat_nat_o (lambda ((X4 nat) (Y5 nat)) (@ (@ member8440522571783428010at_nat (@ (@ product_Pair_nat_nat X4) Y5)) R3))) (lambda ((X4 nat) (Y5 nat)) (@ (@ member8440522571783428010at_nat (@ (@ product_Pair_nat_nat X4) Y5)) S5))) (lambda ((X4 nat) (Y5 nat)) (@ (@ member8440522571783428010at_nat (@ (@ product_Pair_nat_nat X4) Y5)) (@ (@ inf_in2572325071724192079at_nat R3) S5))))) (forall ((F (-> set_Pr1261947904930325089at_nat set_Pr1261947904930325089at_nat)) (X2 set_Pr1261947904930325089at_nat) (Y3 set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ produc2922128104949294807at_nat X2))) (= (@ (@ produc6468969725218530979at_nat F) (@ _let_1 Y3)) (@ _let_1 (@ F Y3))))) (forall ((A4 set_nat) (B5 set_int)) (=> (@ finite_finite_nat A4) (=> (@ finite_finite_int B5) (=> (@ (@ ord_less_eq_nat (@ finite_card_nat A4)) (@ finite_card_int B5)) (exists ((F5 (-> nat int))) (and (@ (@ ord_less_eq_set_int (@ (@ image_nat_int F5) A4)) B5) (@ (@ inj_on_nat_int F5) A4))))))) (forall ((F (-> int nat)) (V (-> rat int))) (= (@ (@ image_rat_nat (@ (@ comp_int_nat_rat F) V)) top_top_set_rat) (@ (@ image_int_nat F) (@ (@ image_rat_int V) top_top_set_rat)))) (forall ((F (-> int nat)) (C3 set_int) (A4 set_o) (B5 (-> Bool set_int)) (J4 Bool)) (=> (@ (@ inj_on_int_nat F) C3) (=> (forall ((X Bool)) (=> (@ (@ member_o X) A4) (@ (@ ord_less_eq_set_int (@ B5 X)) C3))) (=> (@ (@ member_o J4) A4) (= (@ (@ image_int_nat F) (@ comple3628384868704368283et_int (@ (@ image_o_set_int B5) A4))) (@ comple7806235888213564991et_nat (@ (@ image_o_set_nat (lambda ((X4 Bool)) (@ (@ image_int_nat F) (@ B5 X4)))) A4))))))) (forall ((C3 set_Product_unit) (A Bool) (B5 (-> product_unit set_o))) (let ((_let_1 (@ insert_o A))) (let ((_let_2 (@ _let_1 (@ comple90263536869209701_set_o (@ (@ image_6930536745178679216_set_o B5) C3))))) (let ((_let_3 (= C3 bot_bo3957492148770167129t_unit))) (and (=> (not _let_3) (= _let_2 (@ comple90263536869209701_set_o (@ (@ image_6930536745178679216_set_o (lambda ((X4 product_unit)) (@ (@ insert_o A) (@ B5 X4)))) C3)))) (=> _let_3 (= _let_2 (@ _let_1 bot_bot_set_o)))))))) (forall ((B5 (-> nat set_nat)) (F (-> int nat)) (A4 set_int)) (= (@ comple7399068483239264473et_nat (@ (@ image_int_set_nat (lambda ((A5 int)) (@ B5 (@ F A5)))) A4)) (@ comple7399068483239264473et_nat (@ (@ image_nat_set_nat B5) (@ (@ image_int_nat F) A4))))) (forall ((A4 set_Pr1133966238863718811t_unit)) (@ (@ ord_le5525191956872776187t_unit A4) (@ (@ produc3946373962484743846t_unit (@ (@ image_7136766188234240905_ref_a produc473321116828791851t_unit) A4)) (lambda ((Uu ref_a)) (@ (@ image_17660834435998945t_unit produc1126150082675451753t_unit) A4))))) (forall ((A4 set_nat) (B5 set_rat) (F (-> nat rat))) (=> (@ finite_finite_nat A4) (=> (@ (@ ord_less_eq_set_rat B5) (@ (@ image_nat_rat F) A4)) (@ finite_finite_rat B5)))) (forall ((A4 set_Product_unit) (C Bool)) (let ((_let_1 (= A4 bot_bo3957492148770167129t_unit))) (and (=> _let_1 (= (@ (@ image_Product_unit_o (lambda ((X4 product_unit)) C)) A4) bot_bot_set_o)) (=> (not _let_1) (= (@ (@ image_Product_unit_o (lambda ((X4 product_unit)) C)) A4) (@ (@ insert_o C) bot_bot_set_o)))))) (forall ((F (-> int int)) (X5 set_int)) (@ (@ inj_on5397397550511676250nt_int (lambda ((X4 int)) (@ (@ product_Pair_int_int X4) (@ F X4)))) X5)) (forall ((I3 set_se7855581050983116737at_nat) (J3 set_se7855581050983116737at_nat) (C3 (-> set_Pr1261947904930325089at_nat set_se7855581050983116737at_nat))) (= (@ (@ produc7726050920695093128at_nat (@ (@ sup_su3642409539654194069at_nat I3) J3)) C3) (@ (@ sup_su5525570899277871387at_nat (@ (@ produc7726050920695093128at_nat I3) C3)) (@ (@ produc7726050920695093128at_nat J3) C3)))) (forall ((B5 (-> product_unit set_rat))) (= (@ comple4298007329820168263et_rat (@ (@ image_4665621433434589782et_rat B5) bot_bo3957492148770167129t_unit)) top_top_set_rat)) (forall ((A4 set_int) (B5 set_int) (C3 (-> int int)) (D (-> int int)) (Sup (-> set_int int))) (=> (= A4 B5) (=> (forall ((X int)) (=> (@ (@ member_int X) B5) (= (@ C3 X) (@ D X)))) (= (@ Sup (@ (@ image_int_int C3) A4)) (@ Sup (@ (@ image_int_int D) B5)))))) (forall ((P2 (-> product_prod_nat_nat Bool)) (Q2 (-> nat Bool))) (= (@ collec7029190964493513045at_nat (@ produc8758269395934548017_nat_o (lambda ((A5 product_prod_nat_nat) (B4 nat)) (and (@ P2 A5) (@ Q2 B4))))) (@ (@ produc7672662199629908489at_nat (@ collec3392354462482085612at_nat P2)) (lambda ((Uu product_prod_nat_nat)) (@ collect_nat Q2))))) (forall ((A4 set_Product_unit)) (= (@ comple4687483117567863418t_unit (@ (@ image_405062704495631173t_unit (lambda ((X4 product_unit)) X4)) A4)) (@ comple4687483117567863418t_unit A4))) _let_284 _let_283 (forall ((C produc1906917888121415911at_nat) (A4 set_Pr4329608150637261639at_nat)) (=> (@ (@ member6009668390874684176at_nat C) (@ id_on_7869290023980668164at_nat A4)) (not (forall ((X produc3843707927480180839at_nat)) (=> (@ (@ member8757157785044589968at_nat X) A4) (not (= C (@ (@ produc2335810615602371415at_nat X) X)))))))) (forall ((A4 set_int) (M int) (F (-> int int))) (=> (forall ((X int)) (=> (@ (@ member_int X) A4) (@ (@ ord_less_eq_int M) (@ F X)))) (@ condit1735850657277959132ow_int (@ (@ image_int_int F) A4)))) (forall ((X2 nat) (Y3 list_nat)) (let ((_let_1 (@ accp_nat nat_list_decode_rel))) (=> (= (@ nat_list_decode X2) Y3) (=> (@ _let_1 X2) (=> (=> (= X2 zero_zero_nat) (=> (= Y3 nil_nat) (not (@ _let_1 zero_zero_nat)))) (not (forall ((N2 nat)) (let ((_let_1 (@ suc N2))) (=> (= X2 _let_1) (=> (= Y3 (@ (@ produc2761476792215241774st_nat (lambda ((X4 nat) (Y5 nat)) (@ (@ cons_nat X4) (@ nat_list_decode Y5)))) (@ nat_prod_decode N2))) (not (@ (@ accp_nat nat_list_decode_rel) _let_1)))))))))))) (forall ((S5 set_rat)) (=> (not (@ finite_finite_rat S5)) (exists ((F5 (-> nat rat))) (and (@ (@ ord_less_eq_set_rat (@ (@ image_nat_rat F5) top_top_set_nat)) S5) (@ (@ inj_on_nat_rat F5) top_top_set_nat))))) (forall ((F (-> produc1319942482725812455at_nat Bool)) (A set_Pr4329608150637261639at_nat) (B set_Pr4329608150637261639at_nat)) (=> (@ (@ (@ produc447603880154497357_nat_o F) A) B) (@ F (@ (@ produc9060074326276436823at_nat A) B)))) (forall ((X2 int) (A4 set_int) (F (-> int int))) (=> (@ (@ member_int X2) A4) (@ (@ member_int (@ F X2)) (@ (@ image_int_int F) A4)))) (forall ((A4 set_o) (M3 int) (F (-> Bool int))) (=> (not (= A4 bot_bot_set_o)) (=> (forall ((X Bool)) (=> (@ (@ member_o X) A4) (@ (@ ord_less_eq_int M3) (@ F X)))) (@ (@ ord_less_eq_int M3) (@ complete_Inf_Inf_int (@ (@ image_o_int F) A4)))))) (forall ((I set_Pr1261947904930325089at_nat) (J4 set_Pr1261947904930325089at_nat) (R3 set_Pr4329608150637261639at_nat)) (=> (@ (@ member8757157785044589968at_nat (@ (@ produc2922128104949294807at_nat I) J4)) R3) (@ (@ member2643936169264416010at_nat I) (@ field_3145993188331922222at_nat R3)))) (forall ((F (-> rat int)) (B5 set_int) (I rat)) (=> (@ (@ ord_less_eq_set_int (@ (@ image_rat_int F) top_top_set_rat)) B5) (@ (@ member_int (@ F I)) B5))) (forall ((Inf (-> set_rat rat)) (G (-> int rat)) (F (-> nat int)) (A4 set_nat)) (= (@ Inf (@ (@ image_int_rat G) (@ (@ image_nat_int F) A4))) (@ Inf (@ (@ image_nat_rat (@ (@ comp_int_rat_nat G) F)) A4)))) (forall ((C3 set_Product_unit) (A4 (-> product_unit set_int)) (B5 set_int)) (let ((_let_1 (@ (@ minus_minus_set_int (@ comple3628384868704368283et_int (@ (@ image_3995998972318789802et_int A4) C3))) B5))) (let ((_let_2 (= C3 bot_bo3957492148770167129t_unit))) (and (=> _let_2 (= _let_1 (@ (@ minus_minus_set_int top_top_set_int) B5))) (=> (not _let_2) (= _let_1 (@ comple3628384868704368283et_int (@ (@ image_3995998972318789802et_int (lambda ((X4 product_unit)) (@ (@ minus_minus_set_int (@ A4 X4)) B5))) C3)))))))) (forall ((I int) (A4 set_int) (U set_nat) (F (-> int set_nat))) (let ((_let_1 (@ ord_less_eq_set_nat U))) (=> (@ (@ member_int I) A4) (=> (@ _let_1 (@ F I)) (@ _let_1 (@ comple7399068483239264473et_nat (@ (@ image_int_set_nat F) A4))))))) (forall ((Rep (-> int int)) (Abs (-> int int)) (A4 set_int)) (=> (@ (@ (@ type_d7247357190169752966nt_int Rep) Abs) A4) (= (@ (@ image_int_int Abs) A4) top_top_set_int))) (forall ((A4 set_o) (B5 set_nat) (C3 set_o) (D set_nat)) (= (= (@ (@ product_Sigma_o_nat A4) (lambda ((Uu Bool)) B5)) (@ (@ product_Sigma_o_nat C3) (lambda ((Uu Bool)) D))) (or (and (= B5 D) (= A4 C3)) (and (or (= B5 bot_bot_set_nat) (= A4 bot_bot_set_o)) (or (= D bot_bot_set_nat) (= C3 bot_bot_set_o)))))) (forall ((F (-> product_prod_nat_nat product_prod_nat_nat)) (A4 set_Pr1261947904930325089at_nat) (B5 set_Pr1261947904930325089at_nat)) (=> (@ (@ inj_on8969904277767023793at_nat F) A4) (=> (@ (@ ord_le3146513528884898305at_nat (@ (@ image_5168914502847457605at_nat F) A4)) B5) (=> (@ finite6177210948735845034at_nat B5) (@ finite6177210948735845034at_nat A4))))) (forall ((F (-> Bool int)) (A4 set_o) (P2 (-> int Bool))) (= (@ collect_int (lambda ((X4 int)) (and (@ (@ member_int X4) (@ (@ image_o_int F) A4)) (@ P2 X4)))) (@ (@ image_o_int F) (@ collect_o (lambda ((X4 Bool)) (and (@ (@ member_o X4) A4) (@ P2 (@ F X4)))))))) (forall ((F (-> nat product_unit)) (A4 set_nat)) (=> (@ finite4290736615968046902t_unit (@ (@ image_8730104196221521654t_unit F) A4)) (=> (not (@ finite_finite_nat A4)) (exists ((X product_unit)) (and (@ (@ member_Product_unit X) (@ (@ image_8730104196221521654t_unit F) A4)) (not (@ finite_finite_nat (@ (@ vimage4884490618288580032t_unit F) (@ (@ insert_Product_unit X) bot_bo3957492148770167129t_unit))))))))) (forall ((A4 set_int)) (= (@ collect_int (lambda ((X4 int)) (@ (@ member_int X4) A4))) A4)) (forall ((H (-> int Bool)) (F (-> int int int)) (Prod product_prod_int_int)) (= (@ H (@ (@ produc8211389475949308722nt_int F) Prod)) (@ (@ produc4947309494688390418_int_o (lambda ((X12 int) (X23 int)) (@ H (@ (@ F X12) X23)))) Prod))) (forall ((F (-> product_prod_nat_nat nat)) (A4 set_Pr1261947904930325089at_nat)) (=> (@ finite_finite_nat (@ (@ image_2486076414777270412at_nat F) A4)) (=> (@ (@ inj_on2178005380612969504at_nat F) A4) (@ finite6177210948735845034at_nat A4)))) (forall ((P2 (-> product_unit Bool)) (X2 product_unit)) (=> (forall ((Y Bool)) (=> (@ (@ member_o Y) (@ (@ insert_o true) bot_bot_set_o)) (@ P2 (@ product_Abs_unit Y)))) (@ P2 X2))) (forall ((F (-> nat rat)) (G (-> nat int)) (A4 set_nat)) (= (@ (@ image_1351718144375922894at_int (lambda ((X4 nat)) (@ (@ product_Pair_rat_int (@ F X4)) (@ G X4)))) A4) (@ (@ produc137982192359816398at_int (@ (@ image_nat_rat F) A4)) (lambda ((X4 rat)) (@ (@ image_nat_int G) (@ (@ inf_inf_set_nat (@ (@ vimage_nat_rat F) (@ (@ insert_rat X4) bot_bot_set_rat))) A4)))))) (forall ((B Bool) (B5 (-> nat set_o)) (A4 set_nat) (A nat)) (let ((_let_1 (@ member_o B))) (=> (@ _let_1 (@ comple3063163877087187839_set_o (@ (@ image_nat_set_o B5) A4))) (=> (not (@ _let_1 (@ B5 A))) (not (@ (@ member_nat A) A4)))))) (forall ((F (-> nat product_prod_nat_nat)) (A4 set_nat)) (=> (@ finite6177210948735845034at_nat (@ (@ image_5846123807819985514at_nat F) A4)) (=> (@ (@ inj_on5538052773655684606at_nat F) A4) (@ finite_finite_nat A4)))) (forall ((X2 rat) (Y3 rat)) (=> (= X2 Y3) (@ (@ (@ (@ bNF_Grp_rat_rat top_top_set_rat) id_rat) X2) Y3))) (forall ((R3 (-> product_prod_nat_nat product_prod_nat_nat Bool)) (S5 (-> product_prod_nat_nat int Bool))) (=> (@ left_u7296345956935681743at_nat R3) (=> (@ left_u4005249686606446046at_int S5) (@ left_u4005249686606446046at_int (@ (@ relcom8911704206367525917at_int R3) S5))))) (= (@ (@ comp_P8237986404257982958t_unit produc2762368996035445955t_unit) (@ (@ comp_h5940001671827863714t_unit (lambda ((X4 heap_e7401611519738050253t_unit)) (@ (@ produc8256076736985659095t_unit X4) X4))) produc1126150082675451753t_unit)) produc1126150082675451753t_unit) (forall ((F (-> nat nat)) (G (-> nat nat)) (R set_nat)) (= (@ (@ image_nat_nat F) (@ (@ image_nat_nat G) R)) (@ (@ image_nat_nat (@ (@ comp_nat_nat_nat F) G)) R))) (forall ((S5 set_Pr1261947904930325089at_nat) (T3 set_nat) (F (-> product_prod_nat_nat nat))) (=> (@ finite6177210948735845034at_nat S5) (=> (@ finite_finite_nat T3) (=> (= (@ finite711546835091564841at_nat S5) (@ finite_card_nat T3)) (=> (@ (@ ord_less_eq_set_nat (@ (@ image_2486076414777270412at_nat F) S5)) T3) (= (forall ((X4 nat)) (=> (@ (@ member_nat X4) T3) (exists ((Y5 product_prod_nat_nat)) (and (@ (@ member8440522571783428010at_nat Y5) S5) (= (@ F Y5) X4))))) (@ (@ inj_on2178005380612969504at_nat F) S5))))))) (forall ((X2 nat) (A4 set_nat) (B Bool) (F (-> nat Bool))) (=> (@ (@ member_nat X2) A4) (=> (= B (@ F X2)) (@ (@ member_o B) (@ (@ image_nat_o F) A4))))) (forall ((P2 (-> Bool Bool)) (F (-> int int Bool)) (Prod product_prod_int_int)) (let ((_let_1 (@ product_snd_int_int Prod))) (let ((_let_2 (@ product_fst_int_int Prod))) (= (@ P2 (@ (@ produc4947309494688390418_int_o F) Prod)) (not (and (not (@ P2 (@ (@ F _let_2) _let_1))) (= Prod (@ (@ product_Pair_int_int _let_2) _let_1)))))))) (forall ((F1 (-> nat int)) (A13 set_nat) (B1 set_int) (F22 (-> int nat)) (B22 set_int) (A24 set_nat)) (=> (= (@ (@ image_nat_int F1) A13) B1) (=> (@ (@ inj_on_int_nat F22) B22) (=> (@ (@ ord_less_eq_set_nat (@ (@ image_int_nat F22) B22)) A24) (=> (=> (= B22 bot_bot_set_int) (= A24 bot_bot_set_nat)) (= (@ (@ bNF_We8537379975951060974nt_int B22) B1) (@ (@ image_26857530455967037nt_int (@ (@ (@ bNF_We1895166106483946404nt_nat B22) F1) F22)) (@ (@ bNF_We7540516734559056694at_nat A24) A13)))))))) (forall ((A nat) (B nat) (R3 set_Pr1261947904930325089at_nat) (F (-> nat nat)) (G (-> nat num))) (=> (@ (@ member8440522571783428010at_nat (@ (@ product_Pair_nat_nat A) B)) R3) (@ (@ member9148766508732265716at_num (@ (@ product_Pair_nat_num (@ F A)) (@ G B))) (@ (@ image_5877158439796295311at_num (@ (@ produc3535218481486409604at_num F) G)) R3)))) (forall ((B int) (F (-> nat int)) (A4 set_nat)) (=> (@ (@ member_int B) (@ (@ image_nat_int F) A4)) (not (forall ((X nat)) (=> (= B (@ F X)) (not (@ (@ member_nat X) A4))))))) (forall ((A4 set_Product_unit) (G (-> product_unit int)) (B5 set_Product_unit) (F (-> product_unit int))) (let ((_let_1 (@ (@ image_873079544045703924it_int G) B5))) (=> (not (= A4 bot_bo3957492148770167129t_unit)) (=> (@ condit1735850657277959132ow_int _let_1) (=> (@ (@ ord_le3507040750410214029t_unit A4) B5) (=> (forall ((X product_unit)) (=> (@ (@ member_Product_unit X) B5) (@ (@ ord_less_eq_int (@ G X)) (@ F X)))) (@ (@ ord_less_eq_int (@ complete_Inf_Inf_int _let_1)) (@ complete_Inf_Inf_int (@ (@ image_873079544045703924it_int F) A4))))))))) (forall ((F1 (-> Bool Bool)) (F22 (-> nat Bool)) (G1 (-> int nat)) (G22 (-> int int))) (= (@ (@ produc8250590009387450446nt_nat (@ (@ comp_o_o_nat F1) F22)) (@ (@ comp_int_nat_int G1) G22)) (@ (@ comp_P465755969289462830at_int (@ (@ produc8070579729948654068nt_nat F1) G1)) (@ (@ produc8248099538878400170nt_int F22) G22)))) (forall ((M (-> nat nat)) (G (-> int nat)) (X2 int) (N (-> int nat)) (H (-> int int)) (F (-> nat nat))) (=> (= (@ M (@ G X2)) (@ N (@ H X2))) (= (@ (@ (@ comp_nat_nat_int (@ (@ comp_nat_nat_nat F) M)) G) X2) (@ (@ (@ comp_int_nat_int (@ (@ comp_nat_nat_int F) N)) H) X2)))) (forall ((A nat) (A4 set_nat) (B int) (B5 (-> nat set_int))) (let ((_let_1 (@ member_int B))) (=> (@ (@ member_nat A) A4) (=> (@ _let_1 (@ B5 A)) (@ _let_1 (@ comple3221217463730067765et_int (@ (@ image_nat_set_int B5) A4))))))) (forall ((P2 (-> product_prod_int_int Bool)) (F (-> int int product_prod_int_int)) (Prod product_prod_int_int)) (let ((_let_1 (@ product_snd_int_int Prod))) (let ((_let_2 (@ product_fst_int_int Prod))) (= (@ P2 (@ (@ produc4245557441103728435nt_int F) Prod)) (=> (= Prod (@ (@ product_Pair_int_int _let_2) _let_1)) (@ P2 (@ (@ F _let_2) _let_1))))))) (forall ((F (-> product_prod_nat_nat product_prod_nat_nat)) (A4 set_Pr1261947904930325089at_nat) (B5 set_Pr1261947904930325089at_nat) (G (-> product_prod_nat_nat product_prod_nat_nat))) (=> (@ (@ inj_on8969904277767023793at_nat F) A4) (=> (@ (@ ord_le3146513528884898305at_nat (@ (@ image_5168914502847457605at_nat F) A4)) B5) (=> (@ (@ inj_on8969904277767023793at_nat G) B5) (=> (@ (@ ord_le3146513528884898305at_nat (@ (@ image_5168914502847457605at_nat G) B5)) A4) (=> (@ finite6177210948735845034at_nat A4) (=> (@ finite6177210948735845034at_nat B5) (= (@ finite711546835091564841at_nat A4) (@ finite711546835091564841at_nat B5))))))))) (forall ((F (-> nat rat)) (G (-> int nat)) (R set_int)) (= (@ (@ image_nat_rat F) (@ (@ image_int_nat G) R)) (@ (@ image_int_rat (@ (@ comp_nat_rat_int F) G)) R))) (forall ((B int) (F (-> nat int)) (X2 nat) (A4 set_nat)) (=> (= B (@ F X2)) (=> (@ (@ member_nat X2) A4) (@ (@ member_int B) (@ (@ image_nat_int F) A4))))) (= _let_282 _let_282) (forall ((A4 set_o) (B nat) (B5 (-> Bool set_nat))) (=> (forall ((X Bool)) (=> (@ (@ member_o X) A4) (@ (@ member_nat B) (@ B5 X)))) (@ (@ member_nat B) (@ comple7806235888213564991et_nat (@ (@ image_o_set_nat B5) A4))))) (forall ((P2 (-> set_Pr4329608150637261639at_nat set_Pr4329608150637261639at_nat Bool)) (Y3 set_Pr4329608150637261639at_nat) (X2 set_Pr4329608150637261639at_nat)) (let ((_let_1 (@ (@ produc9060074326276436823at_nat X2) Y3))) (=> (@ (@ P2 Y3) X2) (@ (@ P2 (@ produc826222791318859909at_nat _let_1)) (@ produc4486455499028916547at_nat _let_1))))) _let_281 (forall ((A int) (S2 set_int) (T2 set_int)) (= (@ (@ image_int_int (lambda ((X4 int)) (@ (@ minus_minus_int X4) A))) (@ (@ minus_minus_set_int S2) T2)) (@ (@ minus_minus_set_int (@ (@ image_int_int (lambda ((X4 int)) (@ (@ minus_minus_int X4) A))) S2)) (@ (@ image_int_int (lambda ((X4 int)) (@ (@ minus_minus_int X4) A))) T2)))) (forall ((X2 nat) (C3 set_nat) (A4 set_nat) (B5 set_nat)) (=> (@ (@ member_nat X2) C3) (= (@ (@ ord_le3146513528884898305at_nat (@ (@ produc457027306803732586at_nat A4) (lambda ((Uu nat)) C3))) (@ (@ produc457027306803732586at_nat B5) (lambda ((Uu nat)) C3))) (@ (@ ord_less_eq_set_nat A4) B5)))) (forall ((G1 (-> nat num)) (G22 (-> nat num)) (F1 (-> int nat)) (F22 (-> int nat)) (V product_prod_int_int)) (= (@ (@ (@ produc1476026309457068494at_num G1) G22) (@ (@ (@ produc5667422475138734578nt_nat F1) F22) V)) (@ (@ (@ produc165562089265172102nt_num (@ (@ comp_nat_num_int G1) F1)) (@ (@ comp_nat_num_int G22) F22)) V))) _let_279 _let_278 (forall ((A4 set_nat)) (= (@ comple7399068483239264473et_nat (@ (@ image_nat_set_nat (lambda ((X4 nat)) (@ (@ insert_nat X4) bot_bot_set_nat))) A4)) A4)) (forall ((A4 (-> product_prod_nat_nat product_prod_nat_nat Bool)) (B5 (-> product_prod_nat_nat int Bool))) (=> (@ right_1383565826979811350at_nat A4) (=> (@ right_8621877368619751767at_int B5) (@ right_8621877368619751767at_int (@ (@ relcom8911704206367525917at_int A4) B5))))) _let_277 (forall ((H (-> rat int)) (F4 set_int)) (=> (@ finite_finite_rat (@ (@ vimage_rat_int H) F4)) (=> (= (@ (@ image_rat_int H) top_top_set_rat) top_top_set_int) (@ finite_finite_int F4)))) (forall ((B int) (B5 (-> nat set_int)) (A4 set_nat) (A nat)) (let ((_let_1 (@ member_int B))) (=> (@ _let_1 (@ comple3628384868704368283et_int (@ (@ image_nat_set_int B5) A4))) (=> (not (@ _let_1 (@ B5 A))) (not (@ (@ member_nat A) A4)))))) (forall ((X2 set_Pr1261947904930325089at_nat) (Y3 set_Pr1261947904930325089at_nat) (A set_Pr1261947904930325089at_nat)) (=> (= (@ produc6011863565407846595at_nat (@ (@ produc2922128104949294807at_nat X2) Y3)) A) (= X2 A))) (forall ((Sup (-> set_rat rat)) (G (-> int rat)) (F (-> nat int)) (A4 set_nat)) (= (@ Sup (@ (@ image_int_rat G) (@ (@ image_nat_int F) A4))) (@ Sup (@ (@ image_nat_rat (@ (@ comp_int_rat_nat G) F)) A4)))) (forall ((I nat) (A4 set_nat) (F (-> nat set_nat)) (U set_nat)) (=> (@ (@ member_nat I) A4) (=> (@ (@ ord_less_eq_set_nat (@ F I)) U) (@ (@ ord_less_eq_set_nat (@ comple7806235888213564991et_nat (@ (@ image_nat_set_nat F) A4))) U)))) (forall ((Xa2 product_prod_nat_nat) (X2 product_prod_nat_nat)) (= (@ (@ times_times_int (@ abs_Integ Xa2)) (@ abs_Integ X2)) (@ abs_Integ (@ (@ (@ produc27273713700761075at_nat (lambda ((X4 nat) (Y5 nat) (__flatten_var_0 product_prod_nat_nat)) (@ (@ produc2626176000494625587at_nat (lambda ((U3 nat) (V3 nat)) (let ((_let_1 (@ times_times_nat Y5))) (let ((_let_2 (@ times_times_nat X4))) (@ (@ product_Pair_nat_nat (@ (@ plus_plus_nat (@ _let_2 U3)) (@ _let_1 V3))) (@ (@ plus_plus_nat (@ _let_2 V3)) (@ _let_1 U3))))))) __flatten_var_0))) Xa2) X2)))) (forall ((F (-> nat nat)) (G (-> nat nat)) (X2 nat)) (=> (= (@ (@ comp_nat_nat_nat F) G) id_nat) (= (@ F (@ G X2)) X2))) (forall ((P2 (-> nat Bool)) (P nat) (Q2 (-> nat Bool)) (Q nat)) (let ((_let_1 (@ (@ product_Pair_nat_nat P) Q))) (=> (@ P2 P) (=> (@ Q2 Q) (and (@ Q2 (@ product_snd_nat_nat _let_1)) (@ P2 (@ product_fst_nat_nat _let_1))))))) (forall ((Sup (-> set_o Bool)) (G (-> Bool Bool)) (F (-> nat Bool)) (A4 set_nat)) (= (@ Sup (@ (@ image_o_o G) (@ (@ image_nat_o F) A4))) (@ Sup (@ (@ image_nat_o (@ (@ comp_o_o_nat G) F)) A4)))) (forall ((F (-> nat int)) (V (-> rat nat))) (= (@ (@ image_rat_int (@ (@ comp_nat_int_rat F) V)) top_top_set_rat) (@ (@ image_nat_int F) (@ (@ image_rat_nat V) top_top_set_rat)))) (forall ((A4 (-> Bool set_Product_unit)) (I Bool) (B5 set_Product_unit) (J3 set_o)) (= (@ comple3349607820504768346t_unit (@ (@ image_663195431845683034t_unit (@ (@ (@ fun_up4718931970374059986t_unit A4) I) B5)) J3)) (@ (@ sup_su793286257634532545t_unit (@ comple3349607820504768346t_unit (@ (@ image_663195431845683034t_unit A4) (@ (@ minus_minus_set_o J3) (@ (@ insert_o I) bot_bot_set_o))))) (@ (@ (@ if_set_Product_unit (@ (@ member_o I) J3)) B5) bot_bo3957492148770167129t_unit)))) (forall ((F (-> int rat)) (G (-> nat int)) (R set_nat)) (= (@ (@ image_int_rat F) (@ (@ image_nat_int G) R)) (@ (@ image_nat_rat (@ (@ comp_int_rat_nat F) G)) R))) (forall ((F (-> int rat)) (A4 set_int) (G (-> nat rat)) (B5 set_nat) (H (-> rat nat))) (=> (= (@ (@ image_int_rat F) A4) (@ (@ image_nat_rat G) B5)) (= (@ (@ image_int_nat (@ (@ comp_rat_nat_int H) F)) A4) (@ (@ image_nat_nat (@ (@ comp_rat_nat_nat H) G)) B5)))) (forall ((F (-> Bool Bool)) (G (-> Bool Bool)) (L (-> Bool Bool)) (H (-> nat Bool))) (=> (= (@ (@ comp_o_o_o F) G) L) (= (@ (@ comp_o_o_nat F) (@ (@ comp_o_o_nat G) H)) (@ (@ comp_o_o_nat L) H)))) (= comp_o_o_nat (lambda ((F2 (-> Bool Bool)) (G3 (-> nat Bool)) (X4 nat)) (@ F2 (@ G3 X4)))) (forall ((F (-> nat int)) (S5 set_set_nat)) (let ((_let_1 (@ image_nat_int F))) (= (@ _let_1 (@ comple7399068483239264473et_nat S5)) (@ comple3221217463730067765et_int (@ (@ image_3739036796817536367et_int _let_1) S5))))) (forall ((F (-> Bool nat)) (B5 set_o) (A Bool) (A4 set_o)) (let ((_let_1 (@ member_o A))) (=> (@ (@ inj_on_o_nat F) B5) (=> (@ _let_1 B5) (=> (@ (@ ord_less_eq_set_o A4) B5) (= (@ (@ member_nat (@ F A)) (@ (@ image_o_nat F) A4)) (@ _let_1 A4))))))) (forall ((F (-> product_prod_int_int Bool))) (= (@ produc4947309494688390418_int_o (@ produc175634133007206835_int_o F)) F)) (forall ((F (-> Bool product_unit))) (= (@ (@ image_o_Product_unit F) bot_bot_set_o) bot_bo3957492148770167129t_unit)) (forall ((G (-> nat nat)) (H (-> int nat)) (R (-> int nat)) (F (-> nat num))) (=> (= (@ (@ comp_nat_nat_int G) H) R) (= (@ (@ comp_nat_num_int (@ (@ comp_nat_num_nat F) G)) H) (@ (@ comp_nat_num_int F) R)))) (forall ((Rep (-> nat num)) (Abs (-> num nat)) (G (-> nat int)) (P2 (-> int Bool)) (H (-> int nat))) (=> (@ (@ (@ type_d2807825734933527320at_num Rep) Abs) top_top_set_num) (= (@ (@ (@ bNF_vi1731478210338170163_nat_o G) Abs) (@ (@ bNF_Grp_int_nat (@ collect_int P2)) H)) (@ (@ bNF_Grp_nat_num (@ collect_nat (lambda ((X4 nat)) (@ P2 (@ G X4))))) (@ (@ comp_int_num_nat (@ (@ comp_nat_num_int Rep) H)) G))))) (forall ((A4 set_int) (M3 nat) (F (-> int nat))) (=> (not (= A4 bot_bot_set_int)) (=> (forall ((X int)) (=> (@ (@ member_int X) A4) (@ (@ ord_less_eq_nat M3) (@ F X)))) (@ (@ ord_less_eq_nat M3) (@ complete_Inf_Inf_nat (@ (@ image_int_nat F) A4)))))) (forall ((R3 (-> nat nat Bool)) (A (-> list_nat nat)) (B (-> list_nat nat))) (= (@ (@ (@ (@ bNF_re4629543205785817921at_nat (lambda ((Y2 list_nat) (Z list_nat)) (= Y2 Z))) R3) A) B) (exists ((Z4 (-> list_nat product_prod_nat_nat))) (and (@ (@ member3963856813518191233at_nat Z4) (@ collec3092956710985254339at_nat (lambda ((X4 (-> list_nat product_prod_nat_nat))) (@ (@ ord_le3146513528884898305at_nat (@ (@ image_2795870212791037530at_nat X4) top_top_set_list_nat)) (@ collec3392354462482085612at_nat (@ produc6081775807080527818_nat_o R3)))))) (= (@ (@ comp_P5292260908303971472st_nat product_snd_nat_nat) Z4) B) (= (@ (@ comp_P5292260908303971472st_nat product_fst_nat_nat) Z4) A))))) (forall ((B5 set_se6425085446898223655at_nat) (A set_Pr8693737435421807431at_nat)) (= (@ (@ sup_su718114333110466843at_nat (@ comple6332534001959699150at_nat B5)) A) (@ comple6332534001959699150at_nat (@ (@ image_1013614488123988933at_nat (lambda ((B4 set_Pr8693737435421807431at_nat)) (@ (@ sup_su718114333110466843at_nat B4) A))) B5)))) (forall ((C3 set_nat) (A Bool) (B5 (-> nat set_o))) (let ((_let_1 (= C3 bot_bot_set_nat))) (and (=> (not _let_1) (= (@ comple90263536869209701_set_o (@ (@ image_nat_set_o (lambda ((X4 nat)) (@ (@ insert_o A) (@ B5 X4)))) C3)) (@ (@ insert_o A) (@ comple90263536869209701_set_o (@ (@ image_nat_set_o B5) C3))))) (=> _let_1 (= (@ comple90263536869209701_set_o (@ (@ image_nat_set_o (lambda ((X4 nat)) (@ (@ insert_o A) (@ B5 X4)))) C3)) bot_bot_set_o))))) (forall ((R3 (-> product_prod_nat_nat int Bool)) (R7 (-> int int Bool)) (S5 (-> nat nat Bool)) (S6 (-> nat nat Bool))) (=> (@ left_u4005249686606446046at_int R3) (=> (@ right_1157779049177982926at_int R3) (=> (@ right_unique_int_int R7) (=> (@ left_total_int_int R7) (@ (@ ord_le1714508135640884727_nat_o (@ (@ bNF_re4555766996558763186at_nat (@ (@ relcom2949942408940504938nt_int R3) R7)) (@ (@ relcompp_nat_nat_nat S5) S6))) (@ (@ relcom4272412204205018633nt_nat (@ (@ bNF_re4555766996558763186at_nat R3) S5)) (@ (@ bNF_re3715656647883201625at_nat R7) S6)))))))) (forall ((I3 set_Product_unit) (X2 set_Pr1261947904930325089at_nat) (F (-> product_unit set_Pr1261947904930325089at_nat))) (=> (not (= I3 bot_bo3957492148770167129t_unit)) (= (@ comple1930127330929219688at_nat (@ (@ image_3617315916088684441at_nat (lambda ((I2 product_unit)) (@ (@ inf_in2572325071724192079at_nat X2) (@ F I2)))) I3)) (@ (@ inf_in2572325071724192079at_nat X2) (@ comple1930127330929219688at_nat (@ (@ image_3617315916088684441at_nat F) I3)))))) (forall ((C3 set_Product_unit) (A product_unit) (B5 (-> product_unit set_Product_unit))) (let ((_let_1 (@ insert_Product_unit A))) (let ((_let_2 (@ _let_1 (@ comple3349607820504768346t_unit (@ (@ image_7778121751606633509t_unit B5) C3))))) (let ((_let_3 (= C3 bot_bo3957492148770167129t_unit))) (and (=> (not _let_3) (= _let_2 (@ comple3349607820504768346t_unit (@ (@ image_7778121751606633509t_unit (lambda ((X4 product_unit)) (@ (@ insert_Product_unit A) (@ B5 X4)))) C3)))) (=> _let_3 (= _let_2 (@ _let_1 bot_bo3957492148770167129t_unit)))))))) (forall ((G (-> nat nat)) (F (-> nat nat)) (V (-> nat nat))) (let ((_let_1 (@ comp_nat_nat_nat G))) (= (@ _let_1 (@ (@ comp_nat_nat_nat F) V)) (@ (@ comp_nat_nat_nat (@ _let_1 F)) V)))) (forall ((X2 product_prod_int_nat) (A4 set_int) (B5 set_nat)) (= (@ (@ member216504246829706758nt_nat X2) (@ (@ produc1456381018704787142nt_nat A4) (lambda ((Uu int)) B5))) (and (@ (@ member_int (@ product_fst_int_nat X2)) A4) (@ (@ member_nat (@ product_snd_int_nat X2)) B5)))) (forall ((P2 (-> nat nat Bool)) (X2 nat) (Y3 nat) (A product_prod_nat_nat)) (=> (@ (@ P2 X2) Y3) (=> (= A (@ (@ product_Pair_nat_nat X2) Y3)) (@ (@ P2 (@ product_fst_nat_nat A)) (@ product_snd_nat_nat A))))) (forall ((A4 set_nat) (C product_unit)) (=> (not (= A4 bot_bot_set_nat)) (= (@ comple2584293577114468500t_unit (@ (@ image_8730104196221521654t_unit (lambda ((X4 nat)) C)) A4)) C))) (forall ((X2 (-> char nat)) (Ra (-> nat nat Bool))) (=> (forall ((Z3 nat)) (=> (@ (@ member_nat Z3) (@ (@ image_char_nat X2) top_top_set_char)) (@ (@ Ra Z3) Z3))) (@ (@ (@ (@ bNF_re3734335887435638179at_nat (lambda ((Y2 char) (Z char)) (= Y2 Z))) Ra) X2) X2))) (forall ((G (-> rat nat)) (F (-> nat rat))) (=> (forall ((X nat)) (= (@ G (@ F X)) X)) (= (@ (@ image_rat_nat G) top_top_set_rat) top_top_set_nat))) _let_276 (forall ((A4 set_se5479201105039950375at_nat) (R set_Pr7459493094073627847at_nat) (A set_Pr4329608150637261639at_nat) (B set_Pr4329608150637261639at_nat)) (=> (@ (@ refl_o6272981002401706822at_nat A4) R) (=> (@ (@ member1466754251312161552at_nat (@ (@ produc9060074326276436823at_nat A) B)) R) (and (@ (@ member6273874620674182256at_nat A) A4) (@ (@ member6273874620674182256at_nat B) A4))))) (forall ((F (-> char int)) (B int)) (=> (@ (@ inj_on_char_int F) top_top_set_char) (= (@ (@ member_int B) (@ (@ image_char_int F) top_top_set_char)) (exists ((X4 char)) (and (forall ((Y5 char)) (=> (= B (@ F Y5)) (= Y5 X4))) (= B (@ F X4))))))) (forall ((S5 (-> product_prod_nat_nat product_prod_nat_nat Bool)) (T3 (-> product_prod_nat_nat product_prod_nat_nat Bool)) (R3 (-> product_prod_nat_nat int Bool))) (= (@ (@ relcom8911704206367525917at_int (@ (@ sup_su362511073950362882_nat_o S5) T3)) R3) (@ (@ sup_su5231854730092680051_int_o (@ (@ relcom8911704206367525917at_int S5) R3)) (@ (@ relcom8911704206367525917at_int T3) R3)))) (forall ((B5 set_o) (A4 set_o) (F (-> Bool product_unit)) (G (-> Bool product_unit))) (=> (@ (@ ord_less_eq_set_o B5) A4) (=> (forall ((X Bool)) (=> (@ (@ member_o X) B5) (@ (@ ord_le3221252021190050221t_unit (@ F X)) (@ G X)))) (@ (@ ord_le3221252021190050221t_unit (@ comple2584293577114468500t_unit (@ (@ image_o_Product_unit F) A4))) (@ comple2584293577114468500t_unit (@ (@ image_o_Product_unit G) B5)))))) (forall ((P2 (-> rat int product_unit))) (= (@ comple2584293577114468500t_unit (@ (@ image_5846526143423701914t_unit (lambda ((Y5 int)) (@ comple4687483117567863418t_unit (@ (@ image_2327579789247107822t_unit (lambda ((X4 rat)) (@ (@ P2 X4) Y5))) top_top_set_rat)))) top_top_set_int)) (@ comple4687483117567863418t_unit (@ (@ image_4174709274675160035t_unit (lambda ((F2 (-> int rat))) (@ comple2584293577114468500t_unit (@ (@ image_5846526143423701914t_unit (lambda ((X4 int)) (@ (@ P2 (@ F2 X4)) X4))) top_top_set_int)))) top_top_set_int_rat)))) (= produc6369869760173755749_ref_a (@ (@ comp_P7254561687666694144_ref_a produc473321116828791851t_unit) (@ produc4426278547552487717t_unit (lambda ((X4 heap_e7401611519738050253t_unit) (Y5 ref_a)) (@ (@ produc6544324848051098391t_unit Y5) X4))))) (forall ((I int) (A4 set_int) (U product_unit) (F (-> int product_unit))) (let ((_let_1 (@ ord_le3221252021190050221t_unit U))) (=> (@ (@ member_int I) A4) (=> (@ _let_1 (@ F I)) (@ _let_1 (@ comple4687483117567863418t_unit (@ (@ image_5846526143423701914t_unit F) A4))))))) (forall ((R ref_a) (X2 a) (Y3 a) (H heap_e7401611519738050253t_unit)) (let ((_let_1 (@ set_a R))) (let ((_let_2 (@ _let_1 X2))) (= (@ _let_2 (@ (@ _let_1 Y3) H)) (@ _let_2 H))))) (forall ((S5 set_se5479201105039950375at_nat)) (= (@ comple8183010123678664591_nat_o (@ (@ image_4859512832475012440_nat_o (lambda ((I2 set_Pr4329608150637261639at_nat) (X4 produc3843707927480180839at_nat)) (@ (@ member8757157785044589968at_nat X4) I2))) S5)) (lambda ((X4 produc3843707927480180839at_nat)) (@ (@ member8757157785044589968at_nat X4) (@ comple6751905152567503566at_nat S5))))) (forall ((F (-> product_prod_nat_nat set_nat)) (A product_prod_nat_nat) (A4 set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ image_15824709712370754et_nat F))) (= (@ comple7399068483239264473et_nat (@ _let_1 (@ (@ insert8211810215607154385at_nat A) A4))) (@ (@ sup_sup_set_nat (@ F A)) (@ comple7399068483239264473et_nat (@ _let_1 A4)))))) (forall ((A4 set_nat) (B5 set_nat) (C3 (-> nat rat)) (D (-> nat rat)) (Sup (-> set_rat rat))) (=> (= A4 B5) (=> (forall ((X nat)) (=> (@ (@ member_nat X) B5) (= (@ C3 X) (@ D X)))) (= (@ Sup (@ (@ image_nat_rat C3) A4)) (@ Sup (@ (@ image_nat_rat D) B5)))))) (forall ((F (-> (-> code_integer code_integer) produc8923325533196201883nteger produc8923325533196201883nteger)) (G (-> code_integer code_integer code_integer)) (H (-> code_integer code_integer))) (let ((_let_1 (@ comp_C8797469213163452608nteger F))) (= (@ (@ comp_C1593894019821074884nteger (@ _let_1 G)) H) (@ _let_1 (@ (@ comp_C2931745410781319416nteger G) H))))) (forall ((Sa (-> num num Bool)) (X2 (-> int num)) (G (-> num num)) (Y3 (-> int num))) (= (@ (@ (@ (@ bNF_re7626690874201225453um_num (lambda ((Y2 int) (Z int)) (= Y2 Z))) Sa) X2) (@ (@ comp_num_num_int G) Y3)) (@ (@ (@ (@ bNF_re7626690874201225453um_num (lambda ((Y2 int) (Z int)) (= Y2 Z))) (lambda ((X4 num) (Y5 num)) (@ (@ Sa X4) (@ G Y5)))) X2) Y3))) (forall ((B5 set_nat) (A4 set_o)) (let ((_let_1 (@ product_Sigma_o_nat A4))) (let ((_let_2 (@ image_8105710389281276538_nat_o product_fst_o_nat))) (let ((_let_3 (= B5 bot_bot_set_nat))) (and (=> _let_3 (= (@ _let_2 (@ _let_1 (lambda ((Uu Bool)) B5))) bot_bot_set_o)) (=> (not _let_3) (= (@ _let_2 (@ _let_1 (lambda ((Uu Bool)) B5))) A4))))))) (forall ((F (-> Bool product_unit)) (A4 set_o) (X2 Bool) (U product_unit)) (let ((_let_1 (@ (@ image_o_Product_unit F) A4))) (=> (@ condit9161856309968323677t_unit _let_1) (=> (@ (@ member_o X2) A4) (=> (@ (@ ord_le3221252021190050221t_unit (@ F X2)) U) (@ (@ ord_le3221252021190050221t_unit (@ comple2584293577114468500t_unit _let_1)) U)))))) (forall ((X2 int) (Y3 int) (A int)) (=> (= (@ product_fst_int_int (@ (@ product_Pair_int_int X2) Y3)) A) (= X2 A))) (forall ((K4 set_int)) (= (@ gcd_Gcd_int (@ (@ image_int_int abs_abs_int) K4)) (@ gcd_Gcd_int K4))) (forall ((R1 (-> int int Bool))) (@ (@ (@ (@ bNF_re6307232852808291833nt_nat (lambda ((Y2 (-> int nat)) (Z (-> int nat))) (= Y2 Z))) (@ (@ bNF_re2034674868506727813nt_nat (@ (@ bNF_re4712519889275205905nt_int R1) (lambda ((Y2 int) (Z int)) (= Y2 Z)))) (@ (@ bNF_re3715656647883201625at_nat R1) (lambda ((Y2 nat) (Z nat)) (= Y2 Z))))) comp_int_nat_int) comp_int_nat_int)) (forall ((B5 (-> product_unit set_int))) (= (@ comple3628384868704368283et_int (@ (@ image_3995998972318789802et_int B5) bot_bo3957492148770167129t_unit)) top_top_set_int)) (forall ((I3 set_nat) (F (-> nat set_nat)) (X2 set_nat)) (=> (not (= I3 bot_bot_set_nat)) (=> (forall ((I4 nat)) (=> (@ (@ member_nat I4) I3) (= (@ F I4) X2))) (= (@ comple7399068483239264473et_nat (@ (@ image_nat_set_nat F) I3)) X2)))) (forall ((C (-> set_Pr4329608150637261639at_nat set_Pr4329608150637261639at_nat Bool)) (P produc1319942482725812455at_nat)) (=> (@ (@ produc9020218426428501292_nat_o C) P) (not (forall ((X set_Pr4329608150637261639at_nat) (Y set_Pr4329608150637261639at_nat)) (=> (= P (@ (@ produc9060074326276436823at_nat X) Y)) (not (@ (@ C X) Y))))))) (forall ((F (-> int int)) (A4 set_int)) (=> (@ (@ inj_on_int_int F) A4) (= (@ finite_card_int (@ (@ image_int_int F) A4)) (@ finite_card_int A4)))) (forall ((A4 set_nat) (F set_nat)) (=> (not (= A4 bot_bot_set_nat)) (= (@ comple7806235888213564991et_nat (@ (@ image_nat_set_nat (lambda ((I2 nat)) F)) A4)) F))) (forall ((A4 set_o) (C product_unit)) (let ((_let_1 (= A4 bot_bot_set_o))) (and (=> (not _let_1) (= (@ comple2584293577114468500t_unit (@ (@ image_o_Product_unit (lambda ((Y5 Bool)) C)) A4)) C)) (=> _let_1 (= (@ comple2584293577114468500t_unit (@ (@ image_o_Product_unit (lambda ((Y5 Bool)) C)) A4)) top_top_Product_unit))))) (forall ((X2 nat) (Y3 num) (A num)) (=> (= (@ product_snd_nat_num (@ (@ product_Pair_nat_num X2) Y3)) A) (= Y3 A))) (forall ((G (-> nat num)) (F (-> int nat)) (A4 set_int)) (=> (@ (@ inj_on_int_num (@ (@ comp_nat_num_int G) F)) A4) (@ (@ inj_on_nat_num G) (@ (@ image_int_nat F) A4)))) (forall ((S5 set_se5479201105039950375at_nat)) (= (@ comple493620192902636699_nat_o (@ (@ image_6595146019508340652_nat_o (lambda ((I2 set_Pr4329608150637261639at_nat) (X4 set_Pr1261947904930325089at_nat) (Y5 set_Pr1261947904930325089at_nat)) (@ (@ member8757157785044589968at_nat (@ (@ produc2922128104949294807at_nat X4) Y5)) I2))) S5)) (lambda ((X4 set_Pr1261947904930325089at_nat) (Y5 set_Pr1261947904930325089at_nat)) (@ (@ member8757157785044589968at_nat (@ (@ produc2922128104949294807at_nat X4) Y5)) (@ comple4364388969068068532at_nat S5))))) (forall ((F (-> int int product_prod_int_int))) (= (@ produc8249235968001453780nt_int (@ produc4245557441103728435nt_int F)) F)) (forall ((F (-> code_integer code_integer))) (= (@ (@ comp_P3428181540658402820nteger produc6174133586879617921nteger) (@ produc6499014454317279255nteger F)) (@ (@ comp_C1043215000170864188nteger F) produc6174133586879617921nteger))) (forall ((A4 set_Pr1261947904930325089at_nat) (R set_Pr8693737435421807431at_nat) (X2 product_prod_nat_nat) (Y3 product_prod_nat_nat)) (=> (@ (@ refl_o7122697186039111552at_nat A4) R) (=> (@ (@ member8206827879206165904at_nat (@ (@ produc6161850002892822231at_nat X2) Y3)) R) (@ (@ member8440522571783428010at_nat Y3) A4)))) (forall ((A4 set_int) (G (-> int product_unit)) (B5 set_int) (F (-> int product_unit))) (let ((_let_1 (@ (@ image_5846526143423701914t_unit G) B5))) (=> (not (= A4 bot_bot_set_int)) (=> (@ condit9161856309968323677t_unit _let_1) (=> (@ (@ ord_less_eq_set_int A4) B5) (=> (forall ((X int)) (=> (@ (@ member_int X) B5) (@ (@ ord_le3221252021190050221t_unit (@ G X)) (@ F X)))) (@ (@ ord_le3221252021190050221t_unit (@ comple2584293577114468500t_unit _let_1)) (@ comple2584293577114468500t_unit (@ (@ image_5846526143423701914t_unit F) A4))))))))) (forall ((A4 set_Product_unit) (C set_char)) (let ((_let_1 (= A4 bot_bo3957492148770167129t_unit))) (and (=> (not _let_1) (= (@ comple7965528767983648192t_char (@ (@ image_5325685772115642575t_char (lambda ((Y5 product_unit)) C)) A4)) C)) (=> _let_1 (= (@ comple7965528767983648192t_char (@ (@ image_5325685772115642575t_char (lambda ((Y5 product_unit)) C)) A4)) top_top_set_char))))) (forall ((P product_prod_nat_nat) (Z2 int) (C (-> nat nat set_int))) (=> (forall ((A3 nat) (B3 nat)) (=> (= P (@ (@ product_Pair_nat_nat A3) B3)) (@ (@ member_int Z2) (@ (@ C A3) B3)))) (@ (@ member_int Z2) (@ (@ produc2011625207790711856et_int C) P)))) (forall ((X2 product_prod_int_int) (Y3 product_prod_int_int)) (= (@ (@ (@ if_Pro3027730157355071871nt_int false) X2) Y3) Y3)) (forall ((F (-> nat int)) (C3 set_nat) (A4 set_nat) (B5 (-> nat set_nat)) (J4 nat)) (=> (@ (@ inj_on_nat_int F) C3) (=> (forall ((X nat)) (=> (@ (@ member_nat X) A4) (@ (@ ord_less_eq_set_nat (@ B5 X)) C3))) (=> (@ (@ member_nat J4) A4) (= (@ (@ image_nat_int F) (@ comple7806235888213564991et_nat (@ (@ image_nat_set_nat B5) A4))) (@ comple3628384868704368283et_int (@ (@ image_nat_set_int (lambda ((X4 nat)) (@ (@ image_nat_int F) (@ B5 X4)))) A4))))))) (forall ((F (-> int Bool)) (A4 set_int) (X2 Bool) (B5 set_o)) (=> (@ (@ inj_on_int_o F) A4) (=> (not (@ (@ member_o X2) B5)) (=> (= (@ (@ insert_o X2) B5) (@ (@ image_int_o F) A4)) (not (forall ((X8 int) (A8 set_int)) (=> (not (@ (@ member_int X8) A8)) (=> (= A4 (@ (@ insert_int X8) A8)) (=> (= X2 (@ F X8)) (not (= B5 (@ (@ image_int_o F) A8)))))))))))) (forall ((R set_Pr958786334691620121nt_int) (A4 set_int)) (=> (@ (@ ord_le2843351958646193337nt_int R) (@ (@ produc1453890548195736866nt_int A4) (lambda ((Uu int)) A4))) (=> (forall ((X int)) (=> (@ (@ member_int X) A4) (@ (@ member5262025264175285858nt_int (@ (@ product_Pair_int_int X) X)) R))) (@ (@ refl_on_int A4) R)))) (forall ((X2 int) (Y3 int) (R set_Pr958786334691620121nt_int) (F (-> int int))) (= (@ (@ member5262025264175285858nt_int (@ (@ product_Pair_int_int X2) Y3)) (@ (@ inv_image_int_int R) F)) (@ (@ member5262025264175285858nt_int (@ (@ product_Pair_int_int (@ F X2)) (@ F Y3))) R))) (forall ((A4 set_num) (F (-> num num))) (= (@ (@ bNF_re7626690874201225453um_num (lambda ((Y2 int) (Z int)) (= Y2 Z))) (@ (@ bNF_Grp_num_num A4) F)) (@ (@ bNF_Gr318824752125099290nt_num (@ collect_int_num (lambda ((X4 (-> int num))) (@ (@ ord_less_eq_set_num (@ (@ image_int_num X4) top_top_set_int)) A4)))) (@ comp_num_num_int F)))) (forall ((Rep (-> nat char)) (Abs (-> char nat)) (S5 (-> char set_nat)) (M (-> int char)) (F (-> nat nat)) (S6 (-> int set_nat)) (G (-> int int))) (let ((_let_1 (@ comp_s3430750717902475037at_int (@ image_nat_nat F)))) (=> (@ (@ (@ type_d5945782884131516111t_char Rep) Abs) top_top_set_char) (=> (= (@ (@ comp_c912979988581399656at_int S5) M) (@ _let_1 S6)) (= (@ (@ comp_nat_set_nat_int (@ (@ comp_c915470459090449932at_nat S5) Rep)) (@ (@ comp_int_nat_int (@ (@ comp_char_nat_int Abs) M)) G)) (@ _let_1 (@ (@ comp_int_set_nat_int S6) G))))))) (forall ((F (-> int int)) (V (-> rat int))) (= (@ (@ image_rat_int (@ (@ comp_int_int_rat F) V)) top_top_set_rat) (@ (@ image_int_int F) (@ (@ image_rat_int V) top_top_set_rat)))) (forall ((F (-> num nat)) (X2 nat) (Y3 num)) (= (@ (@ produc1035573138926686394at_nat F) (@ (@ product_Pair_nat_num X2) Y3)) (@ (@ product_Pair_nat_nat X2) (@ F Y3)))) (forall ((F (-> int nat)) (A4 (-> int int)) (I3 set_int)) (let ((_let_1 (@ (@ image_int_int A4) I3))) (=> (@ order_mono_int_nat F) (=> (@ condit1735850657277959132ow_int _let_1) (=> (not (= I3 bot_bot_set_int)) (@ (@ ord_less_eq_nat (@ F (@ complete_Inf_Inf_int _let_1))) (@ complete_Inf_Inf_nat (@ (@ image_int_nat (lambda ((X4 int)) (@ F (@ A4 X4)))) I3)))))))) (forall ((F (-> Bool Bool))) (= (@ (@ image_o_o F) bot_bot_set_o) bot_bot_set_o)) (forall ((A4 set_int) (F (-> int int)) (B5 set_int)) (let ((_let_1 (@ image_int_int F))) (let ((_let_2 (@ _let_1 B5))) (let ((_let_3 (@ _let_1 A4))) (=> (not (= A4 bot_bot_set_int)) (=> (@ condit2212336002400062152ve_int _let_3) (=> (not (= B5 bot_bot_set_int)) (=> (@ condit2212336002400062152ve_int _let_2) (= (@ complete_Sup_Sup_int (@ _let_1 (@ (@ sup_sup_set_int A4) B5))) (@ (@ sup_sup_int (@ complete_Sup_Sup_int _let_3)) (@ complete_Sup_Sup_int _let_2))))))))))) _let_275 (forall ((C3 set_Product_unit) (A product_prod_nat_nat) (B5 (-> product_unit set_Pr1261947904930325089at_nat))) (let ((_let_1 (= C3 bot_bo3957492148770167129t_unit))) (and (=> (not _let_1) (= (@ comple5685304695842803022at_nat (@ (@ image_3617315916088684441at_nat (lambda ((X4 product_unit)) (@ (@ insert8211810215607154385at_nat A) (@ B5 X4)))) C3)) (@ (@ insert8211810215607154385at_nat A) (@ comple5685304695842803022at_nat (@ (@ image_3617315916088684441at_nat B5) C3))))) (=> _let_1 (= (@ comple5685304695842803022at_nat (@ (@ image_3617315916088684441at_nat (lambda ((X4 product_unit)) (@ (@ insert8211810215607154385at_nat A) (@ B5 X4)))) C3)) bot_bo2099793752762293965at_nat))))) (forall ((A product_unit) (A4 set_Product_unit) (B product_unit) (B5 set_Product_unit)) (let ((_let_1 (@ produc6121607364029222536t_unit (@ (@ insert_Product_unit A) A4)))) (= (@ _let_1 (lambda ((Uu product_unit)) (@ (@ insert_Product_unit B) B5))) (@ (@ insert4616891024742550839t_unit (@ (@ produc5692694829384537815t_unit A) B)) (@ (@ sup_su6481247232241170203t_unit (@ (@ produc6121607364029222536t_unit A4) (lambda ((Uu product_unit)) (@ (@ insert_Product_unit B) B5)))) (@ _let_1 (lambda ((Uu product_unit)) B5))))))) (forall ((A nat) (A4 set_nat) (B nat) (B5 (-> nat set_nat))) (=> (@ (@ member_nat A) A4) (=> (@ (@ member_nat B) (@ B5 A)) (@ (@ member8440522571783428010at_nat (@ (@ product_Pair_nat_nat A) B)) (@ (@ produc457027306803732586at_nat A4) B5))))) (forall ((C num) (F (-> int nat))) (= (@ (@ comp_nat_num_int (lambda ((X4 nat)) C)) F) (lambda ((X4 int)) C))) (forall ((B product_prod_nat_nat) (B5 (-> Bool set_Pr1261947904930325089at_nat)) (A4 set_o) (A Bool)) (let ((_let_1 (@ member8440522571783428010at_nat B))) (=> (@ _let_1 (@ comple1930127330929219688at_nat (@ (@ image_7077428525161401678at_nat B5) A4))) (=> (not (@ _let_1 (@ B5 A))) (not (@ (@ member_o A) A4)))))) (forall ((B5 set_int) (F (-> int int)) (A4 set_int)) (= (@ (@ ord_less_eq_set_int B5) (@ (@ image_int_int F) A4)) (exists ((AA set_int)) (and (@ (@ ord_less_eq_set_int AA) A4) (= B5 (@ (@ image_int_int F) AA)))))) (forall ((F (-> int nat)) (G (-> nat rat)) (A4 set_int) (B5 set_nat)) (= (@ (@ image_3420722608207172081at_rat (@ produc877984105854340063at_rat (lambda ((X4 int) (Y5 nat)) (@ (@ product_Pair_nat_rat (@ F X4)) (@ G Y5))))) (@ (@ produc1456381018704787142nt_nat A4) (lambda ((Uu int)) B5))) (@ (@ produc9045269283572012658at_rat (@ (@ image_int_nat F) A4)) (lambda ((Uu nat)) (@ (@ image_nat_rat G) B5))))) (forall ((F (-> produc3843707927480180839at_nat Bool)) (A set_Pr1261947904930325089at_nat) (B set_Pr1261947904930325089at_nat)) (=> (@ F (@ (@ produc2922128104949294807at_nat A) B)) (@ (@ (@ produc7820828192191229133_nat_o F) A) B))) (forall ((F (-> nat int)) (A4 set_int)) (@ (@ ord_less_eq_set_int (@ (@ image_nat_int F) (@ (@ vimage_nat_int F) A4))) A4)) (forall ((F (-> product_unit set_rat))) (= (@ comple4298007329820168263et_rat (@ (@ image_4665621433434589782et_rat F) bot_bo3957492148770167129t_unit)) top_top_set_rat)) (forall ((A4 set_nat) (F (-> nat int)) (U int)) (let ((_let_1 (@ (@ image_nat_int F) A4))) (=> (not (= A4 bot_bot_set_nat)) (=> (@ condit2212336002400062152ve_int _let_1) (= (@ (@ ord_less_eq_int (@ complete_Sup_Sup_int _let_1)) U) (forall ((X4 nat)) (=> (@ (@ member_nat X4) A4) (@ (@ ord_less_eq_int (@ F X4)) U)))))))) (forall ((X2 produc8923325533196201883nteger) (Y3 produc8923325533196201883nteger)) (= (@ (@ (@ if_Pro6119634080678213985nteger false) X2) Y3) Y3)) (forall ((S5 set_se4826145725398303499at_num)) (= (@ comple4350791933526045961_num_o (@ (@ image_2055017250723459638_num_o (lambda ((I2 set_Pr6200539531224447659at_num) (X4 nat) (Y5 num)) (@ (@ member9148766508732265716at_num (@ (@ product_Pair_nat_num X4) Y5)) I2))) S5)) (lambda ((X4 nat) (Y5 num)) (@ (@ member9148766508732265716at_num (@ (@ product_Pair_nat_num X4) Y5)) (@ comple1400524285282149784at_num S5))))) (forall ((F (-> nat nat)) (A4 set_nat) (B5 set_nat)) (let ((_let_1 (@ image_nat_nat F))) (@ (@ ord_less_eq_set_nat (@ (@ minus_minus_set_nat (@ _let_1 A4)) (@ _let_1 B5))) (@ _let_1 (@ (@ minus_minus_set_nat A4) B5))))) _let_274 (forall ((A4 (-> product_prod_nat_nat int Bool)) (B5 (-> nat nat Bool)) (F (-> product_prod_nat_nat nat)) (G (-> int nat))) (=> (forall ((X product_prod_nat_nat) (Y int)) (=> (@ (@ A4 X) Y) (@ (@ B5 (@ F X)) (@ G Y)))) (@ (@ (@ (@ bNF_re4555766996558763186at_nat A4) B5) F) G))) (forall ((F (-> nat nat)) (G (-> char nat))) (= (@ (@ image_char_nat (lambda ((X4 char)) (@ F (@ G X4)))) top_top_set_char) (@ (@ image_nat_nat F) (@ (@ image_char_nat G) top_top_set_char)))) (forall ((B nat) (F (-> nat nat))) (=> (@ (@ member_nat B) (@ (@ image_nat_nat F) top_top_set_nat)) (not (forall ((X nat)) (not (= B (@ F X))))))) (forall ((H1 (-> Bool Bool)) (H22 (-> nat nat)) (F (-> nat Bool)) (G (-> nat nat))) (= (@ (@ comp_P1391661485614827491at_nat (@ (@ produc7071226018047599512at_nat H1) H22)) (@ (@ bNF_convol_nat_o_nat F) G)) (@ (@ bNF_convol_nat_o_nat (@ (@ comp_o_o_nat H1) F)) (@ (@ comp_nat_nat_nat H22) G)))) (forall ((R3 (-> int int Bool)) (S5 (-> int code_integer Bool))) (=> (@ left_total_int_int R3) (=> (@ left_t2374113004080657585nteger S5) (@ left_t2374113004080657585nteger (@ (@ relcom967497705283160040nteger R3) S5))))) (forall ((P2 (-> int int Bool))) (= (@ the_Pr4378521158711661632nt_int (@ produc4947309494688390418_int_o P2)) (@ the_Pr4378521158711661632nt_int (lambda ((Xy product_prod_int_int)) (@ (@ P2 (@ product_fst_int_int Xy)) (@ product_snd_int_int Xy)))))) (forall ((M (-> int int)) (G (-> nat int)) (X2 nat) (N (-> nat int)) (H (-> nat nat)) (F (-> int nat))) (=> (= (@ M (@ G X2)) (@ N (@ H X2))) (= (@ (@ (@ comp_int_nat_nat (@ (@ comp_int_nat_int F) M)) G) X2) (@ (@ (@ comp_nat_nat_nat (@ (@ comp_int_nat_nat F) N)) H) X2)))) (forall ((F (-> int int)) (A4 set_int) (B5 set_int)) (=> (@ (@ inj_on_int_int F) A4) (=> (@ (@ ord_less_eq_set_int (@ (@ image_int_int F) A4)) B5) (=> (@ finite_finite_int B5) (@ finite_finite_int A4))))) (forall ((A4 set_nat) (F (-> nat nat)) (G (-> nat nat))) (let ((_let_1 (@ (@ image_nat_nat G) A4))) (let ((_let_2 (@ (@ image_nat_nat F) A4))) (=> (not (= A4 bot_bot_set_nat)) (=> (@ condit1738341127787009408ow_nat _let_2) (=> (@ condit1738341127787009408ow_nat _let_1) (= (@ (@ inf_inf_nat (@ complete_Inf_Inf_nat _let_2)) (@ complete_Inf_Inf_nat _let_1)) (@ complete_Inf_Inf_nat (@ (@ image_nat_nat (lambda ((A5 nat)) (@ (@ inf_inf_nat (@ F A5)) (@ G A5)))) A4))))))))) _let_273 (forall ((Z2 produc3843707927480180839at_nat) (A4 set_se7855581050983116737at_nat) (F (-> set_Pr1261947904930325089at_nat set_Pr1261947904930325089at_nat))) (=> (@ (@ member8757157785044589968at_nat Z2) (@ collec6321179662152712658at_nat (@ produc410239310623530412_nat_o (@ (@ bNF_Gr6677838525845560078at_nat A4) F)))) (= (@ (@ (@ comp_s7355055891894327172at_nat F) produc6011863565407846595at_nat) Z2) (@ produc2937545259423399429at_nat Z2)))) (= produc4486455499028916547at_nat (@ (@ comp_P3728553842126764068at_nat produc826222791318859909at_nat) (@ produc5456455677105495163at_nat (lambda ((X4 set_Pr4329608150637261639at_nat) (Y5 set_Pr4329608150637261639at_nat)) (@ (@ produc9060074326276436823at_nat Y5) X4))))) (forall ((F (-> int nat)) (A4 set_int) (B5 set_nat)) (let ((_let_1 (@ image_int_nat F))) (=> (= (@ _let_1 A4) B5) (= (@ (@ image_4702325430467532143et_nat _let_1) (@ pow_int A4)) (@ pow_nat B5))))) (forall ((V a) (H heap_e7401611519738050253t_unit) (H2 heap_e7401611519738050253t_unit) (R ref_a)) (=> (@ (@ (@ (@ heap_effect_ref_a (@ ref_a2 V)) H) H2) R) (not (=> (= (@ (@ get_a H2) R) V) (=> (@ (@ present_a H2) R) (@ (@ present_a H) R)))))) (forall ((F (-> nat num)) (G (-> int nat))) (=> (@ (@ inj_on_nat_num F) top_top_set_nat) (=> (@ (@ inj_on_int_nat G) top_top_set_int) (@ (@ inj_on_int_num (@ (@ comp_nat_num_int F) G)) top_top_set_int)))) (forall ((F (-> nat product_unit)) (A4 set_nat)) (=> (@ order_5727276828720722763t_unit F) (=> (@ condit2214826472909112428ve_nat A4) (=> (not (= A4 bot_bot_set_nat)) (@ (@ ord_le3221252021190050221t_unit (@ comple4687483117567863418t_unit (@ (@ image_8730104196221521654t_unit F) A4))) (@ F (@ complete_Sup_Sup_nat A4))))))) _let_272 (forall ((C3 set_nat) (A4 set_nat) (B5 (-> nat set_nat))) (let ((_let_1 (= C3 bot_bot_set_nat))) (and (=> _let_1 (= (@ comple7399068483239264473et_nat (@ (@ image_nat_set_nat (lambda ((X4 nat)) (@ (@ sup_sup_set_nat A4) (@ B5 X4)))) C3)) bot_bot_set_nat)) (=> (not _let_1) (= (@ comple7399068483239264473et_nat (@ (@ image_nat_set_nat (lambda ((X4 nat)) (@ (@ sup_sup_set_nat A4) (@ B5 X4)))) C3)) (@ (@ sup_sup_set_nat A4) (@ comple7399068483239264473et_nat (@ (@ image_nat_set_nat B5) C3)))))))) (= product_snd_nat_nat (@ (@ comp_P1567445206330693457at_nat product_fst_nat_nat) (@ produc2626176000494625587at_nat (lambda ((X4 nat) (Y5 nat)) (@ (@ product_Pair_nat_nat Y5) X4))))) (= vimage_nat_nat (lambda ((F2 (-> nat nat)) (B6 set_nat)) (@ comple7399068483239264473et_nat (@ (@ image_nat_set_nat (lambda ((Y5 nat)) (@ (@ vimage_nat_nat F2) (@ (@ insert_nat Y5) bot_bot_set_nat)))) B6)))) (forall ((F (-> int nat)) (B5 set_int) (A int) (A4 set_int)) (let ((_let_1 (@ member_int A))) (=> (@ (@ inj_on_int_nat F) B5) (=> (@ _let_1 B5) (=> (@ (@ ord_less_eq_set_int A4) B5) (= (@ (@ member_nat (@ F A)) (@ (@ image_int_nat F) A4)) (@ _let_1 A4))))))) (forall ((F (-> Bool Bool)) (G (-> nat nat)) (H (-> nat Bool)) (I (-> nat nat)) (Prod product_prod_nat_nat)) (= (@ (@ (@ produc7071226018047599512at_nat F) G) (@ (@ (@ produc7251236297486395890at_nat H) I) Prod)) (@ (@ (@ produc7251236297486395890at_nat (@ (@ comp_o_o_nat F) H)) (@ (@ comp_nat_nat_nat G) I)) Prod))) (forall ((X2 product_unit)) (@ (@ order_888282469287196226t_unit (@ (@ insert_Product_unit X2) bot_bo3957492148770167129t_unit)) (@ (@ insert4616891024742550839t_unit (@ (@ produc5692694829384537815t_unit X2) X2)) bot_bo1654022762305692595t_unit))) (forall ((F (-> product_prod_nat_num Bool)) (A nat) (B num)) (=> (@ F (@ (@ product_Pair_nat_num A) B)) (@ (@ (@ produc156083480235303841_num_o F) A) B))) (forall ((A4 set_Product_unit) (C3 set_Pr1261947904930325089at_nat) (B5 set_Product_unit) (D set_Pr1261947904930325089at_nat)) (= (@ (@ ord_le8681960759543468507at_nat (@ (@ produc3904733337175673596at_nat A4) (lambda ((Uu product_unit)) C3))) (@ (@ produc3904733337175673596at_nat B5) (lambda ((Uu product_unit)) D))) (or (= A4 bot_bo3957492148770167129t_unit) (and (@ (@ ord_le3146513528884898305at_nat C3) D) (@ (@ ord_le3507040750410214029t_unit A4) B5)) (= C3 bot_bo2099793752762293965at_nat)))) (forall ((A4 set_o) (B int) (B5 (-> Bool set_int))) (=> (forall ((X Bool)) (=> (@ (@ member_o X) A4) (@ (@ member_int B) (@ B5 X)))) (@ (@ member_int B) (@ comple3628384868704368283et_int (@ (@ image_o_set_int B5) A4))))) (forall ((F (-> list_nat list_nat))) (let ((_let_1 (@ (@ bNF_Gr600725020315365264st_nat top_top_set_list_nat) F))) (=> (= F id_list_nat) (= (@ (@ relcom8030397737370142931st_nat (@ conver909888920752868663st_nat _let_1)) _let_1) _let_1)))) (forall ((Z2 product_prod_int_int) (A4 set_int) (F (-> int int))) (=> (@ (@ member5262025264175285858nt_int Z2) (@ collec213857154873943460nt_int (@ produc4947309494688390418_int_o (@ (@ bNF_Grp_int_int A4) F)))) (= (@ (@ (@ comp_i4330622015127193916nt_int F) product_fst_int_int) Z2) (@ product_snd_int_int Z2)))) (forall ((B5 (-> nat set_rat))) (= (@ comple4298007329820168263et_rat (@ (@ image_nat_set_rat B5) bot_bot_set_nat)) top_top_set_rat)) (forall ((A4 set_int) (B5 set_int) (C3 (-> int int)) (D (-> int int)) (Inf (-> set_int int))) (=> (= A4 B5) (=> (forall ((X int)) (=> (@ (@ member_int X) B5) (= (@ C3 X) (@ D X)))) (= (@ Inf (@ (@ image_int_int C3) A4)) (@ Inf (@ (@ image_int_int D) B5)))))) (forall ((X2 product_prod_nat_nat) (Y3 nat) (Z2 nat)) (=> (= X2 (@ (@ product_Pair_nat_nat Y3) Z2)) (= (@ product_fst_nat_nat X2) Y3))) (forall ((A4 set_Product_unit) (C product_unit)) (=> (not (= A4 bot_bo3957492148770167129t_unit)) (= (@ comple4687483117567863418t_unit (@ (@ image_405062704495631173t_unit (lambda ((X4 product_unit)) C)) A4)) C))) (forall ((F (-> (-> int code_integer Bool) produc2963269191615333738nteger Bool)) (P2 (-> int int Bool)) (Q2 (-> int code_integer Bool))) (@ (@ (@ (@ (@ bNF_cs4943907971211754724nteger (@ collec7215431352809750357nteger (@ F (@ (@ relcom967497705283160040nteger P2) Q2)))) product_snd_int_int) produc45500017171379470nteger) (@ (@ bNF_fs4543836202474805097nteger P2) Q2)) (@ (@ bNF_sn8000174127721201323nteger P2) Q2))) (forall ((A int) (B int) (R set_Pr958786334691620121nt_int)) (= (@ field_int (@ (@ insert5033312907999012233nt_int (@ (@ product_Pair_int_int A) B)) R)) (@ (@ sup_sup_set_int (@ (@ insert_int A) (@ (@ insert_int B) bot_bot_set_int))) (@ field_int R)))) (forall ((Q product_prod_nat_nat) (F (-> nat nat product_prod_nat_nat Bool)) (G (-> nat nat product_prod_nat_nat Bool)) (P product_prod_nat_nat)) (=> (forall ((X nat) (Y nat)) (=> (= (@ (@ product_Pair_nat_nat X) Y) Q) (= (@ (@ F X) Y) (@ (@ G X) Y)))) (=> (= P Q) (= (@ (@ produc8739625826339149834_nat_o F) P) (@ (@ produc8739625826339149834_nat_o G) Q))))) (forall ((H1 (-> Bool Bool)) (H22 (-> Bool Bool)) (F (-> nat Bool)) (G (-> nat Bool))) (= (@ (@ comp_P7034811116587396339_o_nat (@ (@ produc1928436952130685430_o_o_o H1) H22)) (@ (@ bNF_convol_nat_o_o F) G)) (@ (@ bNF_convol_nat_o_o (@ (@ comp_o_o_nat H1) F)) (@ (@ comp_o_o_nat H22) G)))) (forall ((R22 (-> nat Bool Bool)) (R32 (-> nat Bool Bool)) (R1 (-> nat nat Bool))) (let ((_let_1 (@ bNF_re1402873238235875719_nat_o R1))) (@ (@ (@ (@ bNF_re3930744952143938759_nat_o (@ (@ bNF_re439150893885221597_nat_o R22) R32)) (@ (@ bNF_re7744223787735169245_nat_o (@ _let_1 R22)) (@ _let_1 R32))) comp_nat_nat_nat) comp_o_o_nat))) (forall ((G (-> nat Bool)) (C3 set_nat) (B5 set_nat) (X2 nat)) (let ((_let_1 (@ (@ sup_sup_set_nat B5) (@ (@ insert_nat X2) bot_bot_set_nat)))) (=> (@ (@ inj_on_nat_o G) C3) (=> (@ (@ ord_less_eq_set_nat C3) _let_1) (@ (@ member_o_nat (lambda ((I2 Bool)) (@ (@ (@ if_nat (@ (@ member_o I2) (@ (@ image_nat_o G) C3))) (@ (@ (@ the_inv_into_nat_o C3) G) I2)) X2))) (@ (@ bNF_We6830391624356636116_o_nat top_top_set_o) _let_1)))))) (forall ((A4 set_nat) (B5 (-> nat set_Pr1261947904930325089at_nat))) (=> (@ finite_finite_nat A4) (= (@ finite6177210948735845034at_nat (@ comple5685304695842803022at_nat (@ (@ image_7178329752028323786at_nat B5) A4))) (forall ((X4 nat)) (=> (@ (@ member_nat X4) A4) (@ finite6177210948735845034at_nat (@ B5 X4))))))) (forall ((X2 (-> rat Bool)) (Ra (-> Bool Bool Bool))) (=> (forall ((Z3 Bool)) (=> (@ (@ member_o Z3) (@ (@ image_rat_o X2) top_top_set_rat)) (@ (@ Ra Z3) Z3))) (@ (@ (@ (@ bNF_re1865807574169326223at_o_o (lambda ((Y2 rat) (Z rat)) (= Y2 Z))) Ra) X2) X2))) (forall ((F (-> nat rat)) (A4 set_nat) (B5 set_nat)) (let ((_let_1 (@ image_nat_rat F))) (@ (@ ord_less_eq_set_rat (@ _let_1 (@ (@ inf_inf_set_nat A4) B5))) (@ (@ inf_inf_set_rat (@ _let_1 A4)) (@ _let_1 B5))))) (forall ((U nat) (A4 set_nat) (A nat) (B5 (-> nat set_nat))) (=> (@ (@ member_nat U) A4) (= (@ comple7806235888213564991et_nat (@ (@ image_nat_set_nat (lambda ((X4 nat)) (@ (@ insert_nat A) (@ B5 X4)))) A4)) (@ (@ insert_nat A) (@ comple7806235888213564991et_nat (@ (@ image_nat_set_nat B5) A4)))))) _let_271 _let_270 (forall ((C3 set_Product_unit) (A4 set_Pr4329608150637261639at_nat) (B5 (-> product_unit set_Pr4329608150637261639at_nat))) (let ((_let_1 (@ (@ sup_su5525570899277871387at_nat A4) (@ comple4364388969068068532at_nat (@ (@ image_5172358348707908735at_nat B5) C3))))) (let ((_let_2 (= C3 bot_bo3957492148770167129t_unit))) (and (=> (not _let_2) (= _let_1 (@ comple4364388969068068532at_nat (@ (@ image_5172358348707908735at_nat (lambda ((X4 product_unit)) (@ (@ sup_su5525570899277871387at_nat A4) (@ B5 X4)))) C3)))) (=> _let_2 (= _let_1 A4)))))) (forall ((Y4 set_int)) (= (@ (@ image_int_int (lambda ((X4 int)) X4)) Y4) Y4)) (forall ((X2 (-> char Bool)) (Ya (-> char Bool)) (Y3 (-> char int)) (Xa2 (-> char int)) (R3 (-> Bool int Bool)) (Ra (-> Bool int Bool))) (=> (= X2 Ya) (=> (= Y3 Xa2) (=> (forall ((Z3 Bool) (Yb int)) (=> (@ (@ member_o Z3) (@ (@ image_char_o Ya) top_top_set_char)) (=> (@ (@ member_int Yb) (@ (@ image_char_int Xa2) top_top_set_char)) (= (@ (@ R3 Z3) Yb) (@ (@ Ra Z3) Yb))))) (= (@ (@ (@ (@ bNF_re4780507660726531203_o_int (lambda ((Y2 char) (Z char)) (= Y2 Z))) R3) X2) Y3) (@ (@ (@ (@ bNF_re4780507660726531203_o_int (lambda ((Y2 char) (Z char)) (= Y2 Z))) Ra) Ya) Xa2)))))) (forall ((P2 (-> nat Bool)) (F (-> nat product_prod_nat_nat)) (B5 set_Pr1261947904930325089at_nat)) (=> (forall ((X nat)) (=> (@ P2 X) (@ (@ member8440522571783428010at_nat (@ F X)) B5))) (@ (@ ord_le3146513528884898305at_nat (@ (@ image_5846123807819985514at_nat F) (@ collect_nat P2))) B5))) (forall ((P2 Bool)) (or (= P2 true) (= P2 false))) (forall ((F (-> nat nat))) (let ((_let_1 (@ image_nat_nat F))) (= (@ (@ comp_s174380336271864291et_nat comple7399068483239264473et_nat) (@ image_7916887816326733075et_nat _let_1)) (@ (@ comp_s6993074788030935341et_nat _let_1) comple7399068483239264473et_nat)))) (forall ((A4 set_nat)) (= (@ complete_Inf_Inf_nat (@ (@ image_nat_nat id_nat) A4)) (@ complete_Inf_Inf_nat A4))) (forall ((F (-> nat Bool)) (B5 set_o) (I nat)) (=> (@ (@ ord_less_eq_set_o (@ (@ image_nat_o F) top_top_set_nat)) B5) (@ (@ member_o (@ F I)) B5))) (forall ((C3 set_Product_unit) (A4 (-> product_unit set_o)) (B5 set_o)) (let ((_let_1 (= C3 bot_bo3957492148770167129t_unit))) (and (=> _let_1 (= (@ comple90263536869209701_set_o (@ (@ image_6930536745178679216_set_o (lambda ((X4 product_unit)) (@ (@ sup_sup_set_o (@ A4 X4)) B5))) C3)) bot_bot_set_o)) (=> (not _let_1) (= (@ comple90263536869209701_set_o (@ (@ image_6930536745178679216_set_o (lambda ((X4 product_unit)) (@ (@ sup_sup_set_o (@ A4 X4)) B5))) C3)) (@ (@ sup_sup_set_o (@ comple90263536869209701_set_o (@ (@ image_6930536745178679216_set_o A4) C3))) B5)))))) (forall ((F (-> nat int)) (A4 set_nat) (G (-> nat int)) (B5 set_nat)) (=> (@ (@ inj_on_nat_int F) A4) (=> (@ (@ inj_on_nat_int G) B5) (=> (= (@ (@ inf_inf_set_int (@ (@ image_nat_int F) A4)) (@ (@ image_nat_int G) B5)) bot_bot_set_int) (@ (@ inj_on_nat_int (lambda ((X4 nat)) (@ (@ (@ if_int (@ (@ member_nat X4) A4)) (@ F X4)) (@ G X4)))) (@ (@ sup_sup_set_nat A4) B5)))))) (forall ((F (-> int nat)) (G (-> nat num)) (Set set_num)) (= (@ (@ vimage_int_nat F) (@ (@ vimage_nat_num G) Set)) (@ (@ vimage_int_num (@ (@ comp_nat_num_int G) F)) Set))) (forall ((N3 nat)) (= (@ (@ image_nat_nat suc) (@ set_ord_atMost_nat N3)) (@ (@ set_or1269000886237332187st_nat one_one_nat) (@ suc N3)))) (forall ((Z2 nat)) (= (@ (@ (@ comp_P1955610211387027840at_nat product_snd_nat_nat) (lambda ((X4 nat)) (@ (@ product_Pair_nat_nat X4) X4))) Z2) (@ id_nat Z2))) _let_269 (forall ((A4 set_int) (B5 set_int) (F (-> int product_unit)) (G (-> int product_unit))) (=> (@ (@ ord_less_eq_set_int A4) B5) (=> (forall ((X int)) (=> (@ (@ member_int X) A4) (@ (@ ord_le3221252021190050221t_unit (@ F X)) (@ G X)))) (@ (@ ord_le3221252021190050221t_unit (@ comple4687483117567863418t_unit (@ (@ image_5846526143423701914t_unit F) A4))) (@ comple4687483117567863418t_unit (@ (@ image_5846526143423701914t_unit G) B5)))))) (forall ((P2 (-> produc3843707927480180839at_nat Bool)) (P produc3843707927480180839at_nat)) (=> (forall ((A3 set_Pr1261947904930325089at_nat) (B3 set_Pr1261947904930325089at_nat)) (@ P2 (@ (@ produc2922128104949294807at_nat A3) B3))) (@ P2 P))) (forall ((F (-> ref_a ref_a)) (G (-> heap_e7401611519738050253t_unit heap_e7401611519738050253t_unit))) (= (@ (@ comp_P4044372497395451596t_unit produc473321116828791851t_unit) (@ (@ produc3456481717235892722t_unit F) G)) (@ (@ comp_r2143332150499412868t_unit F) produc473321116828791851t_unit))) (forall ((F (-> nat int)) (X2 nat)) (@ (@ member_int (@ F X2)) (@ (@ image_nat_int F) top_top_set_nat))) (= (@ (@ image_int_nat nat_int_encode) top_top_set_int) top_top_set_nat) (forall ((F (-> rat nat)) (Y3 nat)) (=> (= (@ (@ image_rat_nat F) top_top_set_rat) top_top_set_nat) (exists ((X rat)) (= Y3 (@ F X))))) (forall ((F (-> Bool int)) (A4 set_o)) (=> (@ order_mono_o_int F) (=> (@ condit5413489452508810728elow_o A4) (=> (not (= A4 bot_bot_set_o)) (@ (@ ord_less_eq_int (@ F (@ complete_Inf_Inf_o A4))) (@ complete_Inf_Inf_int (@ (@ image_o_int F) A4))))))) (forall ((G (-> nat nat)) (H (-> int nat)) (R12 (-> int nat)) (R23 (-> int int)) (F (-> nat nat)) (L (-> int nat))) (=> (= (@ (@ comp_nat_nat_int G) H) (@ (@ comp_int_nat_int R12) R23)) (=> (= (@ (@ comp_nat_nat_int F) R12) L) (= (@ (@ comp_nat_nat_int (@ (@ comp_nat_nat_nat F) G)) H) (@ (@ comp_int_nat_int L) R23))))) (forall ((X2 nat) (Y3 list_nat)) (=> (= (@ nat_list_decode X2) Y3) (=> (=> (= X2 zero_zero_nat) (not (= Y3 nil_nat))) (not (forall ((N2 nat)) (=> (= X2 (@ suc N2)) (not (= Y3 (@ (@ produc2761476792215241774st_nat (lambda ((X4 nat) (Y5 nat)) (@ (@ cons_nat X4) (@ nat_list_decode Y5)))) (@ nat_prod_decode N2)))))))))) (forall ((G (-> int nat)) (H (-> nat int)) (R12 (-> nat nat)) (R23 (-> nat nat)) (F (-> nat num)) (L (-> nat num))) (=> (= (@ (@ comp_int_nat_nat G) H) (@ (@ comp_nat_nat_nat R12) R23)) (=> (= (@ (@ comp_nat_num_nat F) R12) L) (= (@ (@ comp_int_num_nat (@ (@ comp_nat_num_int F) G)) H) (@ (@ comp_nat_num_nat L) R23))))) (forall ((A4 set_o) (C product_unit)) (=> (not (= A4 bot_bot_set_o)) (= (@ comple4687483117567863418t_unit (@ (@ image_o_Product_unit (lambda ((X4 Bool)) C)) A4)) C))) (forall ((F (-> int nat)) (A4 set_nat)) (@ (@ ord_less_eq_set_nat (@ (@ image_int_nat F) (@ (@ vimage_int_nat F) A4))) A4)) (forall ((F (-> int nat)) (A4 (-> int int)) (I3 set_int)) (let ((_let_1 (@ (@ image_int_int A4) I3))) (=> (@ order_mono_int_nat F) (=> (@ condit2212336002400062152ve_int _let_1) (=> (not (= I3 bot_bot_set_int)) (@ (@ ord_less_eq_nat (@ complete_Sup_Sup_nat (@ (@ image_int_nat (lambda ((X4 int)) (@ F (@ A4 X4)))) I3))) (@ F (@ complete_Sup_Sup_int _let_1)))))))) (forall ((A4 set_o) (F (-> Bool product_unit))) (let ((_let_1 (@ (@ image_o_Product_unit F) A4))) (=> (not (= A4 bot_bot_set_o)) (@ (@ ord_le3221252021190050221t_unit (@ comple2584293577114468500t_unit _let_1)) (@ comple4687483117567863418t_unit _let_1))))) (forall ((F (-> int int)) (A4 set_int) (B5 set_int)) (let ((_let_1 (@ image_int_int F))) (=> (@ (@ inj_on_int_int F) top_top_set_int) (= (@ _let_1 (@ (@ minus_minus_set_int A4) B5)) (@ (@ minus_minus_set_int (@ _let_1 A4)) (@ _let_1 B5)))))) (forall ((X2 (-> nat Bool)) (Ra (-> Bool Bool Bool))) (=> (forall ((Z3 Bool)) (=> (@ (@ member_o Z3) (@ (@ image_nat_o X2) top_top_set_nat)) (@ (@ Ra Z3) Z3))) (@ (@ (@ (@ bNF_re4705727531993890431at_o_o (lambda ((Y2 nat) (Z nat)) (= Y2 Z))) Ra) X2) X2))) (forall ((X2 (-> nat Bool)) (F (-> Bool Bool)) (G (-> Bool Bool))) (=> (forall ((Z3 Bool)) (=> (@ (@ member_o Z3) (@ (@ image_nat_o X2) top_top_set_nat)) (= (@ F Z3) (@ G Z3)))) (= (@ (@ comp_o_o_nat F) X2) (@ (@ comp_o_o_nat G) X2)))) (forall ((F (-> nat int)) (A4 set_nat)) (=> (@ finite_finite_int (@ (@ image_nat_int F) A4)) (=> (not (@ finite_finite_nat A4)) (not (forall ((Y int)) (=> (@ (@ member_int Y) (@ (@ image_nat_int F) A4)) (@ finite_finite_nat (@ (@ inf_inf_set_nat (@ (@ vimage_nat_int F) (@ (@ insert_int Y) bot_bot_set_int))) A4)))))))) (forall ((C3 set_Product_unit) (A4 set_o) (B5 (-> product_unit set_o))) (let ((_let_1 (= C3 bot_bo3957492148770167129t_unit))) (and (=> _let_1 (= (@ comple90263536869209701_set_o (@ (@ image_6930536745178679216_set_o (lambda ((X4 product_unit)) (@ (@ sup_sup_set_o A4) (@ B5 X4)))) C3)) bot_bot_set_o)) (=> (not _let_1) (= (@ comple90263536869209701_set_o (@ (@ image_6930536745178679216_set_o (lambda ((X4 product_unit)) (@ (@ sup_sup_set_o A4) (@ B5 X4)))) C3)) (@ (@ sup_sup_set_o A4) (@ comple90263536869209701_set_o (@ (@ image_6930536745178679216_set_o B5) C3)))))))) (forall ((A4 set_Pr4329608150637261639at_nat) (F (-> produc3843707927480180839at_nat set_nat))) (let ((_let_1 (@ (@ image_3160451284896210088et_nat F) A4))) (=> (not (= A4 bot_bo228742789529271731at_nat)) (@ (@ ord_less_eq_set_nat (@ comple7806235888213564991et_nat _let_1)) (@ comple7399068483239264473et_nat _let_1))))) (forall ((K nat) (I3 set_nat) (A4 (-> nat set_Pr8693737435421807431at_nat))) (let ((_let_1 (@ comple2748534634209756852at_nat (@ (@ image_4592875511192039216at_nat A4) I3)))) (=> (@ (@ member_nat K) I3) (= (@ (@ sup_su718114333110466843at_nat (@ A4 K)) _let_1) _let_1)))) (forall ((Rep (-> nat rat)) (Abs (-> rat nat)) (F (-> int int)) (P2 (-> int Bool)) (H (-> int rat))) (=> (@ (@ (@ type_d5615363888691252950at_rat Rep) Abs) top_top_set_rat) (= (@ (@ (@ bNF_vi1281217848275042457_rat_o F) Rep) (@ (@ bNF_Grp_int_rat (@ collect_int P2)) H)) (@ (@ bNF_Grp_int_nat (@ collect_int (lambda ((X4 int)) (@ P2 (@ F X4))))) (@ (@ comp_int_nat_int (@ (@ comp_rat_nat_int Abs) H)) F))))) (forall ((G (-> nat Bool)) (H (-> nat nat)) (R12 (-> Bool Bool)) (R23 (-> nat Bool)) (F (-> Bool nat)) (L (-> Bool nat))) (=> (= (@ (@ comp_nat_o_nat G) H) (@ (@ comp_o_o_nat R12) R23)) (=> (= (@ (@ comp_o_nat_o F) R12) L) (= (@ (@ comp_nat_nat_nat (@ (@ comp_o_nat_nat F) G)) H) (@ (@ comp_o_nat_nat L) R23))))) (forall ((A4 set_o) (B5 set_o)) (= (= (@ (@ product_Sigma_o_o A4) (lambda ((Uu Bool)) B5)) bot_bo7073875226086086771od_o_o) (or (= B5 bot_bot_set_o) (= A4 bot_bot_set_o)))) (forall ((F (-> Bool int)) (A4 set_o) (X2 Bool) (U int)) (let ((_let_1 (@ (@ image_o_int F) A4))) (=> (@ condit1735850657277959132ow_int _let_1) (=> (@ (@ member_o X2) A4) (=> (@ (@ ord_less_eq_int (@ F X2)) U) (@ (@ ord_less_eq_int (@ complete_Inf_Inf_int _let_1)) U)))))) (= (@ comple7399068483239264473et_nat (@ (@ image_nat_set_nat set_ord_lessThan_nat) top_top_set_nat)) top_top_set_nat) (forall ((A4 set_int) (F (-> int nat))) (=> (@ finite_finite_int A4) (= (@ (@ inj_on_int_nat F) A4) (= (@ finite_card_nat (@ (@ image_int_nat F) A4)) (@ finite_card_int A4))))) (forall ((I nat) (A4 set_nat) (F (-> nat set_nat))) (=> (@ (@ member_nat I) A4) (@ (@ ord_less_eq_set_nat (@ comple7806235888213564991et_nat (@ (@ image_nat_set_nat F) A4))) (@ F I)))) (forall ((A nat) (A4 set_nat) (B num) (B5 (-> nat set_num))) (=> (@ (@ member_nat A) A4) (=> (@ (@ member_num B) (@ B5 A)) (@ (@ member9148766508732265716at_num (@ (@ product_Pair_nat_num A) B)) (@ (@ produc6237731129814287028at_num A4) B5))))) (forall ((P2 (-> rat rat product_unit))) (= (@ comple2584293577114468500t_unit (@ (@ image_2327579789247107822t_unit (lambda ((Y5 rat)) (@ comple4687483117567863418t_unit (@ (@ image_2327579789247107822t_unit (lambda ((X4 rat)) (@ (@ P2 X4) Y5))) top_top_set_rat)))) top_top_set_rat)) (@ comple4687483117567863418t_unit (@ (@ image_1193274288206594871t_unit (lambda ((F2 (-> rat rat))) (@ comple2584293577114468500t_unit (@ (@ image_2327579789247107822t_unit (lambda ((X4 rat)) (@ (@ P2 (@ F2 X4)) X4))) top_top_set_rat)))) top_top_set_rat_rat)))) (forall ((X2 set_Pr1261947904930325089at_nat) (Y3 set_Pr1261947904930325089at_nat) (R set_Pr4329608150637261639at_nat) (F (-> set_Pr1261947904930325089at_nat set_Pr1261947904930325089at_nat))) (= (@ (@ member8757157785044589968at_nat (@ (@ produc2922128104949294807at_nat X2) Y3)) (@ (@ inv_im7023619800666061458at_nat R) F)) (@ (@ member8757157785044589968at_nat (@ (@ produc2922128104949294807at_nat (@ F X2)) (@ F Y3))) R))) (forall ((F (-> nat nat)) (A4 set_nat)) (@ (@ ord_less_eq_set_nat (@ (@ image_nat_nat F) (@ (@ vimage_nat_nat F) A4))) A4)) (forall ((F (-> int nat)) (A4 set_int) (Y3 nat) (X2 int)) (=> (@ (@ inj_on_int_nat F) A4) (=> (not (@ (@ member_nat Y3) (@ (@ image_int_nat F) A4))) (@ (@ inj_on_int_nat (@ (@ (@ fun_upd_int_nat F) X2) Y3)) A4)))) _let_268 (forall ((X2 set_nat) (Y3 set_nat)) (= (@ (@ (@ if_set_nat false) X2) Y3) Y3)) (forall ((X2 product_prod_nat_nat) (XS set_Pr1261947904930325089at_nat) (Y3 product_prod_nat_nat) (YS set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ produc2922128104949294807at_nat XS))) (=> (@ (@ member8440522571783428010at_nat X2) XS) (=> (@ (@ member8206827879206165904at_nat (@ (@ produc6161850002892822231at_nat X2) Y3)) fun_pair_leq) (=> (@ (@ member8757157785044589968at_nat (@ _let_1 YS)) fun_min_weak) (@ (@ member8757157785044589968at_nat (@ _let_1 (@ (@ insert8211810215607154385at_nat Y3) YS))) fun_min_weak)))))) (forall ((R3 (-> nat nat Bool)) (A (-> char nat)) (B (-> char nat))) (= (@ (@ (@ (@ bNF_re3734335887435638179at_nat (lambda ((Y2 char) (Z char)) (= Y2 Z))) R3) A) B) (exists ((Z4 (-> char product_prod_nat_nat))) (and (@ (@ member3295615932019376976at_nat Z4) (@ collec1683818095804863890at_nat (lambda ((X4 (-> char product_prod_nat_nat))) (@ (@ ord_le3146513528884898305at_nat (@ (@ image_8382823969816519465at_nat X4) top_top_set_char)) (@ collec3392354462482085612at_nat (@ produc6081775807080527818_nat_o R3)))))) (= (@ (@ comp_P1491501995297412481t_char product_fst_nat_nat) Z4) A) (= (@ (@ comp_P1491501995297412481t_char product_snd_nat_nat) Z4) B))))) (forall ((Prod produc7812382424243267045t_unit)) (= (@ (@ produc6544324848051098391t_unit (@ produc473321116828791851t_unit Prod)) (@ produc1126150082675451753t_unit Prod)) Prod)) _let_266 (forall ((F (-> nat Bool)) (B5 set_nat) (A nat) (A4 set_nat)) (let ((_let_1 (@ member_nat A))) (=> (@ (@ inj_on_nat_o F) B5) (=> (@ _let_1 B5) (=> (@ (@ ord_less_eq_set_nat A4) B5) (= (@ (@ member_o (@ F A)) (@ (@ image_nat_o F) A4)) (@ _let_1 A4))))))) (forall ((G (-> nat nat)) (H (-> int nat)) (R12 (-> int nat)) (R23 (-> int int)) (F (-> nat num)) (L (-> int num))) (=> (= (@ (@ comp_nat_nat_int G) H) (@ (@ comp_int_nat_int R12) R23)) (=> (= (@ (@ comp_nat_num_int F) R12) L) (= (@ (@ comp_nat_num_int (@ (@ comp_nat_num_nat F) G)) H) (@ (@ comp_int_num_int L) R23))))) (forall ((F (-> nat rat)) (G (-> nat nat)) (A4 set_nat) (X2 rat)) (let ((_let_1 (@ (@ image_nat_nat G) A4))) (=> (@ (@ inj_on_nat_rat F) _let_1) (=> (@ (@ inj_on_nat_nat G) A4) (=> (@ (@ member_rat X2) (@ (@ image_nat_rat F) _let_1)) (= (@ (@ (@ the_inv_into_nat_rat A4) (@ (@ comp_nat_rat_nat F) G)) X2) (@ (@ (@ comp_nat_nat_rat (@ (@ the_inv_into_nat_nat A4) G)) (@ (@ the_inv_into_nat_rat _let_1) F)) X2))))))) (forall ((B nat) (F (-> int nat)) (X2 int) (A4 set_int)) (=> (= B (@ F X2)) (=> (@ (@ member_int X2) A4) (@ (@ member_nat B) (@ (@ image_int_nat F) A4))))) (forall ((K product_prod_nat_nat) (I3 set_Pr1261947904930325089at_nat) (A4 (-> product_prod_nat_nat set_Pr8693737435421807431at_nat))) (let ((_let_1 (@ comple2748534634209756852at_nat (@ (@ image_5803077947706746251at_nat A4) I3)))) (=> (@ (@ member8440522571783428010at_nat K) I3) (= (@ (@ sup_su718114333110466843at_nat (@ A4 K)) _let_1) _let_1)))) (forall ((S5 set_Co726186806682698383nteger) (F (-> (-> code_integer code_integer) produc8923325533196201883nteger produc8923325533196201883nteger)) (G (-> code_integer code_integer code_integer)) (R3 set_Code_integer)) (=> (@ (@ finite954763878425697269nteger S5) F) (=> (@ (@ ord_le348599935723844335nteger (@ (@ image_2177946750938214461nteger G) top_to4645266643341252675nteger)) S5) (@ (@ finite917065715488314481nteger R3) (@ (@ comp_C8797469213163452608nteger F) G))))) _let_265 (forall ((P produc859450856879609959at_nat)) (=> (@ (@ member8206827879206165904at_nat P) id_Pro2258643101195443293at_nat) (not (forall ((X product_prod_nat_nat)) (not (= P (@ (@ produc6161850002892822231at_nat X) X))))))) (forall ((X2 int) (A4 set_int) (B Bool) (F (-> int Bool))) (=> (@ (@ member_int X2) A4) (=> (= B (@ F X2)) (@ (@ member_o B) (@ (@ image_int_o F) A4))))) (forall ((F (-> nat nat)) (A4 (-> int nat)) (I3 set_int)) (let ((_let_1 (@ (@ image_int_nat A4) I3))) (=> (@ order_mono_nat_nat F) (=> (@ condit1738341127787009408ow_nat _let_1) (=> (not (= I3 bot_bot_set_int)) (@ (@ ord_less_eq_nat (@ F (@ complete_Inf_Inf_nat _let_1))) (@ complete_Inf_Inf_nat (@ (@ image_int_nat (lambda ((X4 int)) (@ F (@ A4 X4)))) I3)))))))) (forall ((A Bool) (A4 set_o) (B Bool) (B5 set_o)) (let ((_let_1 (@ product_Sigma_o_o (@ (@ insert_o A) A4)))) (= (@ _let_1 (lambda ((Uu Bool)) (@ (@ insert_o B) B5))) (@ (@ insert6201435330877294327od_o_o (@ (@ product_Pair_o_o A) B)) (@ (@ sup_su5769328420594410459od_o_o (@ (@ product_Sigma_o_o A4) (lambda ((Uu Bool)) (@ (@ insert_o B) B5)))) (@ _let_1 (lambda ((Uu Bool)) B5))))))) (forall ((F (-> num num)) (G (-> num nat)) (X2 num)) (= (@ (@ (@ comp_P480327259280165693at_num (@ (@ produc2149532328386841038at_nat F) id_nat)) (@ (@ bNF_co6100160411832691183um_nat id_num) G)) X2) (@ (@ (@ bNF_co6100160411832691183um_nat (@ (@ comp_num_num_num id_num) F)) G) X2))) (= comp_C8797469213163452608nteger (lambda ((F2 (-> (-> code_integer code_integer) produc8923325533196201883nteger produc8923325533196201883nteger)) (G3 (-> code_integer code_integer code_integer)) (X4 code_integer) (__flatten_var_0 produc8923325533196201883nteger)) (@ (@ F2 (@ G3 X4)) __flatten_var_0))) (forall ((Y3 product_unit)) (= Y3 product_Unity)) (forall ((F (-> int int)) (A4 set_int)) (=> (@ order_mono_int_int F) (=> (@ condit2212336002400062152ve_int A4) (@ condit2212336002400062152ve_int (@ (@ image_int_int F) A4))))) (forall ((X2 nat) (A4 set_nat) (F (-> nat nat))) (=> (@ (@ member_nat X2) A4) (@ (@ member_nat (@ F X2)) (@ (@ image_nat_nat F) A4)))) (forall ((A4 set_Pr1261947904930325089at_nat) (U set_nat) (F (-> product_prod_nat_nat set_nat))) (=> (forall ((I4 product_prod_nat_nat)) (=> (@ (@ member8440522571783428010at_nat I4) A4) (@ (@ ord_less_eq_set_nat U) (@ F I4)))) (@ (@ ord_less_eq_set_nat U) (@ comple7806235888213564991et_nat (@ (@ image_15824709712370754et_nat F) A4))))) (forall ((C3 set_Product_unit) (A product_prod_nat_nat) (B5 (-> product_unit set_Pr1261947904930325089at_nat))) (let ((_let_1 (@ insert8211810215607154385at_nat A))) (let ((_let_2 (@ _let_1 (@ comple5685304695842803022at_nat (@ (@ image_3617315916088684441at_nat B5) C3))))) (let ((_let_3 (= C3 bot_bo3957492148770167129t_unit))) (and (=> _let_3 (= _let_2 (@ _let_1 bot_bo2099793752762293965at_nat))) (=> (not _let_3) (= _let_2 (@ comple5685304695842803022at_nat (@ (@ image_3617315916088684441at_nat (lambda ((X4 product_unit)) (@ (@ insert8211810215607154385at_nat A) (@ B5 X4)))) C3))))))))) (forall ((S5 set_se7855581050983116737at_nat)) (= (@ comple6265855634338933877_nat_o (@ (@ image_5253903537071781336_nat_o (lambda ((I2 set_Pr1261947904930325089at_nat) (X4 product_prod_nat_nat)) (@ (@ member8440522571783428010at_nat X4) I2))) S5)) (lambda ((X4 product_prod_nat_nat)) (@ (@ member8440522571783428010at_nat X4) (@ comple1930127330929219688at_nat S5))))) (forall ((A4 set_o) (F set_nat)) (=> (not (= A4 bot_bot_set_o)) (= (@ comple7399068483239264473et_nat (@ (@ image_o_set_nat (lambda ((I2 Bool)) F)) A4)) F))) (forall ((C3 set_nat) (A nat) (B5 (-> nat set_nat))) (let ((_let_1 (= C3 bot_bot_set_nat))) (and (=> _let_1 (= (@ comple7399068483239264473et_nat (@ (@ image_nat_set_nat (lambda ((X4 nat)) (@ (@ insert_nat A) (@ B5 X4)))) C3)) bot_bot_set_nat)) (=> (not _let_1) (= (@ comple7399068483239264473et_nat (@ (@ image_nat_set_nat (lambda ((X4 nat)) (@ (@ insert_nat A) (@ B5 X4)))) C3)) (@ (@ insert_nat A) (@ comple7399068483239264473et_nat (@ (@ image_nat_set_nat B5) C3)))))))) (forall ((F (-> product_unit set_nat)) (A4 set_Product_unit)) (=> (@ order_509894322932672675et_nat F) (@ (@ ord_less_eq_set_nat (@ comple7399068483239264473et_nat (@ (@ image_8173849991827986510et_nat F) A4))) (@ F (@ comple4687483117567863418t_unit A4))))) (forall ((X2 nat) (Y3 nat) (Z2 nat)) (let ((_let_1 (@ product_Pair_nat_nat X2))) (= (@ (@ member8206827879206165904at_nat (@ (@ produc6161850002892822231at_nat (@ _let_1 Y3)) (@ _let_1 Z2))) fun_pair_less) (@ (@ ord_less_nat Y3) Z2)))) (forall ((A4 set_Product_unit) (C set_Pr1261947904930325089at_nat)) (let ((_let_1 (= A4 bot_bo3957492148770167129t_unit))) (and (=> (not _let_1) (= (@ comple5685304695842803022at_nat (@ (@ image_3617315916088684441at_nat (lambda ((Y5 product_unit)) C)) A4)) C)) (=> _let_1 (= (@ comple5685304695842803022at_nat (@ (@ image_3617315916088684441at_nat (lambda ((Y5 product_unit)) C)) A4)) bot_bo2099793752762293965at_nat))))) (forall ((F (-> ref_a int)) (G (-> heap_e7401611519738050253t_unit int)) (X2 produc7812382424243267045t_unit)) (= (@ (@ produc6143945040009431475nt_int F) (@ (@ produc3558794870892339738_ref_a G) X2)) (@ (@ product_Pair_int_int (@ F (@ produc473321116828791851t_unit X2))) (@ G (@ produc1126150082675451753t_unit X2))))) _let_264 (forall ((C (-> set_Pr1261947904930325089at_nat set_Pr1261947904930325089at_nat Bool)) (P produc3843707927480180839at_nat)) (=> (@ (@ produc410239310623530412_nat_o C) P) (not (forall ((X set_Pr1261947904930325089at_nat) (Y set_Pr1261947904930325089at_nat)) (=> (= P (@ (@ produc2922128104949294807at_nat X) Y)) (not (@ (@ C X) Y))))))) (forall ((Rep (-> int Bool)) (Abs (-> Bool int)) (M (-> nat Bool)) (M1 (-> Bool Bool)) (M2 (-> nat Bool)) (F (-> Bool nat)) (G (-> int nat))) (=> (@ (@ (@ type_d8403010662121346494_int_o Rep) Abs) top_top_set_o) (=> (= M (@ (@ comp_o_o_nat M1) M2)) (= (@ (@ comp_nat_nat_int (@ (@ comp_o_nat_nat F) M)) G) (@ (@ comp_int_nat_int (@ (@ comp_o_nat_int (@ (@ comp_o_nat_o F) M1)) Rep)) (@ (@ comp_nat_int_int (@ (@ comp_o_int_nat Abs) M2)) G)))))) (forall ((F (-> char char))) (=> (@ finite_finite_char top_top_set_char) (=> (@ (@ inj_on_char_char F) top_top_set_char) (= (@ (@ image_char_char F) top_top_set_char) top_top_set_char)))) (forall ((I3 set_nat) (C set_nat) (F (-> nat set_nat))) (=> (not (= I3 bot_bot_set_nat)) (=> (forall ((I4 nat)) (=> (@ (@ member_nat I4) I3) (@ (@ ord_less_eq_set_nat C) (@ F I4)))) (= (= (@ comple7399068483239264473et_nat (@ (@ image_nat_set_nat F) I3)) C) (forall ((X4 nat)) (=> (@ (@ member_nat X4) I3) (= (@ F X4) C))))))) (forall ((F (-> int nat)) (A4 set_int)) (=> (@ order_3680150258199746352nt_nat F) (=> (@ condit2212336002400062152ve_int A4) (@ condit1738341127787009408ow_nat (@ (@ image_int_nat F) A4))))) (forall ((F (-> Bool Bool))) (=> (@ (@ inj_on_o_o F) top_top_set_o) (@ (@ inj_on_nat_o_nat_o (@ comp_o_o_nat F)) top_top_set_nat_o))) (forall ((A (-> Bool Bool)) (B (-> nat Bool)) (C (-> Bool Bool)) (D2 (-> nat Bool))) (=> (= (@ (@ comp_o_o_nat A) B) (@ (@ comp_o_o_nat C) D2)) (forall ((V4 nat)) (= (@ A (@ B V4)) (@ C (@ D2 V4)))))) (@ (@ (@ (@ bNF_re8246922863344978751at_nat intrel) (lambda ((Y2 nat) (Z nat)) (= Y2 Z))) _let_2) _let_2) (forall ((C3 set_nat) (A4 (-> nat set_rat)) (B5 set_rat)) (let ((_let_1 (= C3 bot_bot_set_nat))) (and (=> _let_1 (= (@ comple4298007329820168263et_rat (@ (@ image_nat_set_rat (lambda ((X4 nat)) (@ (@ minus_minus_set_rat (@ A4 X4)) B5))) C3)) top_top_set_rat)) (=> (not _let_1) (= (@ comple4298007329820168263et_rat (@ (@ image_nat_set_rat (lambda ((X4 nat)) (@ (@ minus_minus_set_rat (@ A4 X4)) B5))) C3)) (@ (@ minus_minus_set_rat (@ comple4298007329820168263et_rat (@ (@ image_nat_set_rat A4) C3))) B5)))))) (forall ((P2 (-> int int Bool)) (P product_prod_int_int) (Q2 (-> Bool Bool)) (F (-> int int Bool))) (=> (@ (@ P2 (@ product_snd_int_int P)) (@ product_fst_int_int P)) (=> (forall ((X int) (Y int)) (=> (@ (@ P2 Y) X) (@ Q2 (@ (@ F X) Y)))) (@ Q2 (@ (@ produc4947309494688390418_int_o F) P))))) (forall ((S5 set_int) (F (-> int nat nat))) (=> (forall ((X int) (Y int)) (let ((_let_1 (@ F Y))) (let ((_let_2 (@ F X))) (=> (@ (@ member_int X) S5) (=> (@ (@ member_int Y) S5) (= (@ (@ comp_nat_nat_nat _let_1) _let_2) (@ (@ comp_nat_nat_nat _let_2) _let_1))))))) (@ (@ finite4582259249640653518nt_nat S5) F))) (forall ((Y3 produc3843707927480180839at_nat)) (not (forall ((A3 set_Pr1261947904930325089at_nat) (B3 set_Pr1261947904930325089at_nat)) (not (= Y3 (@ (@ produc2922128104949294807at_nat A3) B3)))))) (forall ((C product_prod_int_int) (A4 set_int) (B5 (-> int set_int))) (=> (@ (@ member5262025264175285858nt_int C) (@ (@ produc1453890548195736866nt_int A4) B5)) (not (forall ((X int)) (=> (@ (@ member_int X) A4) (forall ((Y int)) (=> (@ (@ member_int Y) (@ B5 X)) (not (= C (@ (@ product_Pair_int_int X) Y)))))))))) (forall ((B5 set_Pr4329608150637261639at_nat) (A4 set_Pr4329608150637261639at_nat) (Q2 (-> produc3843707927480180839at_nat Bool)) (P2 (-> produc3843707927480180839at_nat Bool))) (=> (@ (@ ord_le1268244103169919719at_nat B5) A4) (=> (forall ((X produc3843707927480180839at_nat)) (=> (@ (@ member8757157785044589968at_nat X) B5) (=> (@ Q2 X) (@ P2 X)))) (@ (@ ord_le1268244103169919719at_nat (@ collec6321179662152712658at_nat (lambda ((X4 produc3843707927480180839at_nat)) (and (@ (@ member8757157785044589968at_nat X4) B5) (@ Q2 X4))))) (@ collec6321179662152712658at_nat (lambda ((X4 produc3843707927480180839at_nat)) (and (@ (@ member8757157785044589968at_nat X4) A4) (@ P2 X4)))))))) (forall ((F (-> int int)) (A int) (A4 set_int)) (let ((_let_1 (@ inj_on_int_int F))) (let ((_let_2 (@ insert_int A))) (= (@ _let_1 (@ _let_2 A4)) (and (not (@ (@ member_int (@ F A)) (@ (@ image_int_int F) (@ (@ minus_minus_set_int A4) (@ _let_2 bot_bot_set_int))))) (@ _let_1 A4)))))) (forall ((F (-> int int)) (A4 set_int)) (=> (@ (@ inj_on_int_int F) top_top_set_int) (=> (@ (@ ord_less_eq_set_int A4) (@ (@ image_int_int F) top_top_set_int)) (= (@ finite_card_int (@ (@ vimage_int_int F) A4)) (@ finite_card_int A4))))) (forall ((A int) (A4 set_int) (B int) (B5 set_int)) (let ((_let_1 (@ produc1453890548195736866nt_int (@ (@ insert_int A) A4)))) (= (@ _let_1 (lambda ((Uu int)) (@ (@ insert_int B) B5))) (@ (@ insert5033312907999012233nt_int (@ (@ product_Pair_int_int A) B)) (@ (@ sup_su6024340866399070445nt_int (@ (@ produc1453890548195736866nt_int A4) (lambda ((Uu int)) (@ (@ insert_int B) B5)))) (@ _let_1 (lambda ((Uu int)) B5))))))) (forall ((F (-> produc3843707927480180839at_nat product_unit)) (A4 set_Pr4329608150637261639at_nat) (B5 set_Pr4329608150637261639at_nat)) (let ((_let_1 (@ inj_on3108384905993948887t_unit F))) (let ((_let_2 (@ image_7082456443403096939t_unit F))) (= (@ _let_1 (@ (@ sup_su5525570899277871387at_nat A4) B5)) (and (@ _let_1 B5) (= (@ (@ inf_in4660618365625256667t_unit (@ _let_2 (@ (@ minus_3314409938677909166at_nat A4) B5))) (@ _let_2 (@ (@ minus_3314409938677909166at_nat B5) A4))) bot_bo3957492148770167129t_unit) (@ _let_1 A4)))))) (forall ((Rep (-> product_unit Bool)) (Abs (-> Bool product_unit))) (=> (@ (@ (@ type_d6188575255521822967unit_o Rep) Abs) top_top_set_o) (= (@ (@ comp_P5156358013004227690it_o_o Rep) Abs) id_o))) (forall ((F (-> nat int)) (A4 set_nat) (B5 set_nat)) (let ((_let_1 (@ image_nat_int F))) (=> (@ (@ inj_on_nat_int F) (@ (@ sup_sup_set_nat A4) B5)) (= (= (@ _let_1 A4) (@ _let_1 B5)) (= A4 B5))))) (forall ((Y3 product_prod_nat_nat) (Y4 set_Pr1261947904930325089at_nat) (X2 product_prod_nat_nat) (X5 set_Pr1261947904930325089at_nat)) (=> (@ (@ member8440522571783428010at_nat Y3) Y4) (=> (@ (@ member8206827879206165904at_nat (@ (@ produc6161850002892822231at_nat X2) Y3)) fun_pair_less) (=> (@ (@ member8757157785044589968at_nat (@ (@ produc2922128104949294807at_nat X5) Y4)) fun_max_strict) (@ (@ member8757157785044589968at_nat (@ (@ produc2922128104949294807at_nat (@ (@ insert8211810215607154385at_nat X2) X5)) Y4)) fun_max_strict))))) (forall ((F (-> nat nat)) (A4 set_nat) (B5 set_nat)) (let ((_let_1 (@ image_nat_nat F))) (@ (@ ord_less_eq_set_nat (@ _let_1 (@ (@ inf_inf_set_nat A4) B5))) (@ (@ inf_inf_set_nat (@ _let_1 A4)) (@ _let_1 B5))))) (forall ((C3 set_nat) (A4 set_o) (B5 (-> nat set_o))) (let ((_let_1 (= C3 bot_bot_set_nat))) (and (=> (not _let_1) (= (@ comple90263536869209701_set_o (@ (@ image_nat_set_o (lambda ((X4 nat)) (@ (@ sup_sup_set_o A4) (@ B5 X4)))) C3)) (@ (@ sup_sup_set_o A4) (@ comple90263536869209701_set_o (@ (@ image_nat_set_o B5) C3))))) (=> _let_1 (= (@ comple90263536869209701_set_o (@ (@ image_nat_set_o (lambda ((X4 nat)) (@ (@ sup_sup_set_o A4) (@ B5 X4)))) C3)) bot_bot_set_o))))) (forall ((F (-> nat rat)) (A4 set_nat)) (= (= (@ (@ image_nat_rat F) A4) bot_bot_set_rat) (= A4 bot_bot_set_nat))) (forall ((F (-> int nat)) (A4 set_int)) (=> (@ finite_finite_nat (@ (@ image_int_nat F) A4)) (=> (@ (@ inj_on_int_nat F) A4) (@ finite_finite_int A4)))) (forall ((A4 set_nat) (B5 set_o) (G (-> Bool product_unit)) (F (-> nat product_unit))) (=> (forall ((I4 nat)) (=> (@ (@ member_nat I4) A4) (exists ((X6 Bool)) (and (@ (@ member_o X6) B5) (@ (@ ord_le3221252021190050221t_unit (@ G X6)) (@ F I4)))))) (=> (forall ((J2 Bool)) (=> (@ (@ member_o J2) B5) (exists ((X6 nat)) (and (@ (@ member_nat X6) A4) (@ (@ ord_le3221252021190050221t_unit (@ F X6)) (@ G J2)))))) (= (@ comple2584293577114468500t_unit (@ (@ image_8730104196221521654t_unit F) A4)) (@ comple2584293577114468500t_unit (@ (@ image_o_Product_unit G) B5)))))) (forall ((B nat) (F (-> nat nat)) (X2 nat) (A4 set_nat)) (=> (= B (@ F X2)) (=> (@ (@ member_nat X2) A4) (@ (@ member_nat B) (@ (@ image_nat_nat F) A4))))) (forall ((K Bool) (I3 set_o) (A4 (-> Bool set_nat))) (let ((_let_1 (@ comple7399068483239264473et_nat (@ (@ image_o_set_nat A4) I3)))) (=> (@ (@ member_o K) I3) (= (@ (@ sup_sup_set_nat (@ A4 K)) _let_1) _let_1)))) (forall ((F (-> nat rat)) (B rat)) (=> (@ (@ inj_on_nat_rat F) top_top_set_nat) (= (@ (@ member_rat B) (@ (@ image_nat_rat F) top_top_set_nat)) (exists ((X4 nat)) (and (forall ((Y5 nat)) (=> (= B (@ F Y5)) (= Y5 X4))) (= B (@ F X4))))))) (forall ((A4 set_nat) (X2 set_nat) (F (-> nat set_nat))) (=> (forall ((I4 nat)) (=> (@ (@ member_nat I4) A4) (@ (@ ord_less_eq_set_nat X2) (@ F I4)))) (=> (forall ((Y set_nat)) (=> (forall ((I5 nat)) (=> (@ (@ member_nat I5) A4) (@ (@ ord_less_eq_set_nat Y) (@ F I5)))) (@ (@ ord_less_eq_set_nat Y) X2))) (= (@ comple7806235888213564991et_nat (@ (@ image_nat_set_nat F) A4)) X2)))) (forall ((F (-> char product_unit)) (A product_unit) (X2 char)) (=> (= (@ (@ image_4337914935673063477t_unit F) top_top_set_char) (@ (@ insert_Product_unit A) bot_bo3957492148770167129t_unit)) (= (@ F X2) A))) (= produc8739625826339149834_nat_o (lambda ((F2 (-> nat nat product_prod_nat_nat Bool)) (P3 product_prod_nat_nat) (__flatten_var_0 product_prod_nat_nat)) (@ (@ (@ F2 (@ 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nat)) (not (= Y3 (@ (@ product_Pair_nat_nat A3) B3)))))) (forall ((A4 set_Pr4329608150637261639at_nat) (X2 set_nat) (F (-> produc3843707927480180839at_nat set_nat))) (=> (forall ((I4 produc3843707927480180839at_nat)) (=> (@ (@ member8757157785044589968at_nat I4) A4) (@ (@ ord_less_eq_set_nat X2) (@ F I4)))) (=> (forall ((Y set_nat)) (=> (forall ((I5 produc3843707927480180839at_nat)) (=> (@ (@ member8757157785044589968at_nat I5) A4) (@ (@ ord_less_eq_set_nat Y) (@ F I5)))) (@ (@ ord_less_eq_set_nat Y) X2))) (= (@ comple7806235888213564991et_nat (@ (@ image_3160451284896210088et_nat F) A4)) X2)))) (forall ((I3 set_int) (F (-> int product_unit)) (X2 product_unit)) (=> (not (= I3 bot_bot_set_int)) (=> (forall ((I4 int)) (=> (@ (@ member_int I4) I3) (= (@ F I4) X2))) (= (@ comple4687483117567863418t_unit (@ (@ image_5846526143423701914t_unit F) I3)) X2)))) (forall ((X2 Bool) (A4 set_o) (F (-> Bool set_nat))) (let ((_let_1 (@ (@ image_o_set_nat F) A4))) (=> (@ (@ member_o X2) A4) (=> (@ condit5477540289124974626et_nat _let_1) (@ (@ ord_less_eq_set_nat (@ F X2)) (@ comple7399068483239264473et_nat _let_1)))))) (forall ((A4 set_nat) (A7 set_rat)) (=> (not (= A4 bot_bot_set_nat)) (= (exists ((F2 (-> nat rat))) (and (@ (@ inj_on_nat_rat F2) A4) (@ (@ ord_less_eq_set_rat (@ (@ image_nat_rat F2) A4)) A7))) (exists ((G3 (-> rat nat))) (= (@ (@ image_rat_nat G3) A7) A4))))) (forall ((P product_prod_int_int)) (= (@ (@ produc4245557441103728435nt_int product_Pair_int_int) P) P)) (forall ((A4 set_Product_unit) (B5 set_Product_unit) (C3 set_Product_unit) (D set_Product_unit)) (= (= (@ (@ produc6121607364029222536t_unit A4) (lambda ((Uu product_unit)) B5)) (@ (@ produc6121607364029222536t_unit C3) (lambda ((Uu product_unit)) D))) (or (and (= B5 D) (= A4 C3)) (and (or (= B5 bot_bo3957492148770167129t_unit) (= A4 bot_bo3957492148770167129t_unit)) (or (= C3 bot_bo3957492148770167129t_unit) (= D bot_bo3957492148770167129t_unit)))))) _let_262 (forall ((C3 set_o) (A4 (-> Bool set_rat)) (B5 set_rat)) (let ((_let_1 (@ (@ minus_minus_set_rat (@ comple4298007329820168263et_rat (@ (@ image_o_set_rat A4) C3))) B5))) (let ((_let_2 (= C3 bot_bot_set_o))) (and (=> (not _let_2) (= _let_1 (@ comple4298007329820168263et_rat (@ (@ image_o_set_rat (lambda ((X4 Bool)) (@ (@ minus_minus_set_rat (@ A4 X4)) B5))) C3)))) (=> _let_2 (= _let_1 (@ (@ minus_minus_set_rat top_top_set_rat) B5))))))) (forall ((F (-> int product_unit)) (A4 set_int) (G (-> int product_unit)) (B5 set_int)) (=> (@ (@ inj_on4178023183795006766t_unit F) A4) (=> (@ (@ inj_on4178023183795006766t_unit G) B5) (=> (= (@ (@ inf_in4660618365625256667t_unit (@ (@ image_5846526143423701914t_unit F) A4)) (@ (@ image_5846526143423701914t_unit G) B5)) bot_bo3957492148770167129t_unit) (@ (@ inj_on4178023183795006766t_unit (lambda ((X4 int)) (@ (@ (@ if_Product_unit (@ (@ member_int X4) A4)) (@ F X4)) (@ G X4)))) (@ (@ sup_sup_set_int A4) B5)))))) (forall ((F (-> nat product_unit)) (A4 (-> nat nat)) (I3 set_nat)) (let ((_let_1 (@ (@ image_nat_nat A4) I3))) (=> (@ order_5727276828720722763t_unit F) (=> (@ condit1738341127787009408ow_nat _let_1) (=> (not (= I3 bot_bot_set_nat)) (@ (@ ord_le3221252021190050221t_unit (@ F (@ complete_Inf_Inf_nat _let_1))) (@ comple2584293577114468500t_unit (@ (@ image_8730104196221521654t_unit (lambda ((X4 nat)) (@ F (@ A4 X4)))) I3)))))))) (forall ((Xa2 product_prod_nat_nat) (X2 product_prod_nat_nat)) (= (@ (@ plus_plus_int (@ abs_Integ Xa2)) (@ abs_Integ X2)) (@ abs_Integ (@ (@ (@ produc27273713700761075at_nat (lambda ((X4 nat) (Y5 nat) (__flatten_var_0 product_prod_nat_nat)) (@ (@ produc2626176000494625587at_nat (lambda ((U3 nat) (V3 nat)) (@ (@ product_Pair_nat_nat (@ (@ plus_plus_nat X4) U3)) (@ (@ plus_plus_nat Y5) V3)))) __flatten_var_0))) Xa2) X2)))) _let_261 (forall ((A4 set_o)) (= (@ complete_Inf_Inf_o (@ (@ image_o_o id_o) A4)) (@ complete_Inf_Inf_o A4))) (forall ((X1 ref_a) (X22 heap_e7401611519738050253t_unit)) (= (@ produc1126150082675451753t_unit (@ (@ produc6544324848051098391t_unit X1) X22)) X22)) _let_260 (forall ((F (-> char int)) (B5 set_int) (I char)) (=> (@ (@ ord_less_eq_set_int (@ (@ image_char_int F) top_top_set_char)) B5) (@ (@ member_int (@ F I)) B5))) (forall ((A4 set_Pr1261947904930325089at_nat) (B5 set_nat)) (=> (@ finite6177210948735845034at_nat A4) (=> (@ finite_finite_nat B5) (=> (@ (@ ord_less_eq_nat (@ finite711546835091564841at_nat A4)) (@ finite_card_nat B5)) (exists ((F5 (-> product_prod_nat_nat nat))) (and (@ (@ ord_less_eq_set_nat (@ (@ image_2486076414777270412at_nat F5) A4)) B5) (@ (@ inj_on2178005380612969504at_nat F5) A4))))))) (forall ((A4 set_Pr1261947904930325089at_nat) (B5 (-> product_prod_nat_nat set_nat)) (C3 set_nat)) (=> (forall ((X product_prod_nat_nat)) (=> (@ (@ member8440522571783428010at_nat X) A4) (@ (@ ord_less_eq_set_nat (@ B5 X)) C3))) (@ (@ ord_less_eq_set_nat (@ comple7399068483239264473et_nat (@ (@ image_15824709712370754et_nat B5) A4))) C3))) (forall ((B Bool) (F (-> nat Bool)) (X2 nat) (A4 set_nat)) (=> (= B (@ F X2)) (=> (@ (@ member_nat X2) A4) (@ (@ member_o B) (@ (@ image_nat_o F) A4))))) (forall ((R7 (-> int code_integer Bool)) (S6 (-> num num Bool)) (R3 (-> int int Bool)) (S5 (-> num num Bool))) (=> (@ right_8475562212078014689nteger R7) (=> (@ left_t2374113004080657585nteger R7) (=> (@ left_unique_num_num S6) (=> (@ right_total_num_num S6) (@ (@ ord_le6931201860925936491_num_o (@ (@ bNF_re6718328864250387230um_num (@ (@ relcom967497705283160040nteger R3) R7)) (@ (@ relcompp_num_num_num S5) S6))) (@ (@ relcom1533066287727470739er_num (@ (@ bNF_re7626690874201225453um_num R3) S5)) (@ (@ bNF_re6718328864250387230um_num R7) S6)))))))) (forall ((F (-> nat rat)) (A4 set_nat)) (=> (@ order_mono_nat_rat F) (=> (@ condit1738341127787009408ow_nat A4) (@ condit1103211067700513672ow_rat (@ (@ image_nat_rat F) A4))))) _let_258 (forall ((F (-> nat nat)) (A4 set_nat) (P2 (-> set_nat Bool))) (= (forall ((B6 set_nat)) (=> (@ (@ ord_less_eq_set_nat B6) (@ (@ image_nat_nat F) A4)) (@ P2 B6))) (forall ((B6 set_nat)) (=> (@ (@ ord_less_eq_set_nat B6) A4) (@ P2 (@ (@ image_nat_nat F) B6)))))) (forall ((C3 set_Pr1261947904930325089at_nat) (A4 set_nat) (B5 (-> product_prod_nat_nat set_nat))) (let ((_let_1 (@ (@ sup_sup_set_nat A4) (@ comple7399068483239264473et_nat (@ (@ image_15824709712370754et_nat B5) C3))))) (let ((_let_2 (= C3 bot_bo2099793752762293965at_nat))) (and (=> (not _let_2) (= _let_1 (@ comple7399068483239264473et_nat (@ (@ image_15824709712370754et_nat (lambda ((X4 product_prod_nat_nat)) (@ (@ sup_sup_set_nat A4) (@ B5 X4)))) C3)))) (=> _let_2 (= _let_1 A4)))))) (forall ((M (-> produc859450856879609959at_nat set_Pr8693737435421807431at_nat)) (A4 set_Pr8693737435421807431at_nat) (B5 set_Pr8693737435421807431at_nat)) (let ((_let_1 (@ image_6654316230217496229at_nat M))) (= (@ comple2748534634209756852at_nat (@ _let_1 (@ (@ sup_su718114333110466843at_nat A4) B5))) (@ (@ sup_su718114333110466843at_nat (@ comple2748534634209756852at_nat (@ _let_1 A4))) (@ comple2748534634209756852at_nat (@ _let_1 B5)))))) (forall ((A4 set_int) (F (-> int nat)) (U nat)) (let ((_let_1 (@ (@ image_int_nat F) A4))) (=> (not (= A4 bot_bot_set_int)) (=> (@ condit2214826472909112428ve_nat _let_1) (= (@ (@ ord_less_eq_nat (@ complete_Sup_Sup_nat _let_1)) U) (forall ((X4 int)) (=> (@ (@ member_int X4) A4) (@ (@ ord_less_eq_nat (@ F X4)) U)))))))) (forall ((F4 set_nat) (H (-> nat rat))) (=> (@ finite_finite_nat F4) (@ finite_finite_rat (@ (@ image_nat_rat H) F4)))) (forall ((C3 set_o) (A4 (-> Bool set_rat)) (B5 set_rat)) (let ((_let_1 (= C3 bot_bot_set_o))) (and (=> (not _let_1) (= (@ comple4298007329820168263et_rat (@ (@ image_o_set_rat (lambda ((X4 Bool)) (@ (@ minus_minus_set_rat (@ A4 X4)) B5))) C3)) (@ (@ minus_minus_set_rat (@ comple4298007329820168263et_rat (@ (@ image_o_set_rat A4) C3))) B5))) (=> _let_1 (= (@ comple4298007329820168263et_rat (@ (@ image_o_set_rat (lambda ((X4 Bool)) (@ (@ minus_minus_set_rat (@ A4 X4)) B5))) C3)) top_top_set_rat))))) (forall ((F (-> int nat)) (G (-> int int)) (L (-> int nat)) (H (-> int int))) (let ((_let_1 (@ comp_int_nat_int F))) (=> (= (@ _let_1 G) L) (= (@ _let_1 (@ (@ comp_int_int_int G) H)) (@ (@ comp_int_nat_int L) H))))) (forall ((F (-> nat nat)) (A4 set_nat) (Y3 nat) (X2 nat)) (=> (@ (@ inj_on_nat_nat F) A4) (=> (not (@ (@ member_nat Y3) (@ (@ image_nat_nat F) A4))) (@ (@ inj_on_nat_nat (@ (@ (@ fun_upd_nat_nat F) X2) Y3)) A4)))) (forall ((P2 (-> int int Bool)) (P product_prod_int_int) (Q2 (-> product_prod_int_int Bool)) (F (-> int int product_prod_int_int))) (=> (@ (@ P2 (@ product_snd_int_int P)) (@ product_fst_int_int P)) (=> (forall ((X int) (Y int)) (=> (@ (@ P2 Y) X) (@ Q2 (@ (@ F X) Y)))) (@ Q2 (@ (@ produc4245557441103728435nt_int F) P))))) (forall ((F (-> product_unit Bool)) (A4 set_Product_unit) (X2 Bool) (B5 set_o)) (=> (@ (@ inj_on8854722734121536060unit_o F) A4) (=> (not (@ (@ member_o X2) B5)) (=> (= (@ (@ insert_o X2) B5) (@ (@ image_Product_unit_o F) A4)) (not (forall ((X8 product_unit) (A8 set_Product_unit)) (=> (not (@ (@ member_Product_unit X8) A8)) (=> (= A4 (@ (@ insert_Product_unit X8) A8)) (=> (= X2 (@ F X8)) (not (= B5 (@ (@ image_Product_unit_o F) A8)))))))))))) (forall ((F (-> nat int)) (A4 set_nat) (B5 set_int)) (= (@ (@ ord_less_eq_set_int (@ (@ image_nat_int F) A4)) B5) (@ (@ ord_less_eq_set_nat A4) (@ (@ vimage_nat_int F) B5)))) (forall ((N3 nat)) (@ bNF_We3818239936649020644el_nat (@ collec3392354462482085612at_nat (@ produc6081775807080527818_nat_o (lambda ((X4 nat) (Y5 nat)) (and (@ (@ ord_less_eq_nat X4) Y5) (@ (@ ord_less_nat Y5) N3) (@ (@ ord_less_nat X4) N3))))))) (forall ((N3 nat)) (= (@ nat_list_decode (@ suc N3)) (@ (@ produc2761476792215241774st_nat (lambda ((X4 nat) (Y5 nat)) (@ (@ cons_nat X4) (@ nat_list_decode Y5)))) (@ nat_prod_decode N3)))) (forall ((F (-> Bool Bool)) (G (-> nat Bool))) (=> (@ (@ inj_on_o_o F) top_top_set_o) (=> (@ (@ inj_on_nat_o G) top_top_set_nat) (@ (@ inj_on_nat_o (@ (@ comp_o_o_nat F) G)) top_top_set_nat)))) (forall ((K int) (I3 set_int) (A4 (-> int product_unit))) (let ((_let_1 (@ comple4687483117567863418t_unit (@ (@ image_5846526143423701914t_unit A4) I3)))) (=> (@ (@ member_int K) I3) (= (@ (@ sup_sup_Product_unit (@ A4 K)) _let_1) _let_1)))) (forall ((Rb (-> nat nat Bool)) (Sd (-> nat nat Bool))) (@ (@ (@ (@ bNF_re3262823321055862553at_nat (@ (@ bNF_re5653821019739307937at_nat Rb) Sd)) (@ (@ bNF_re239970166668089693at_nat (@ (@ bNF_re5653821019739307937at_nat (lambda ((Y2 nat) (Z nat)) (= Y2 Z))) Rb)) (@ (@ bNF_re5653821019739307937at_nat (lambda ((Y2 nat) (Z nat)) (= Y2 Z))) Sd))) comp_nat_nat_nat) comp_nat_nat_nat)) _let_257 (forall ((B5 set_rat) (F (-> nat rat)) (A4 set_nat)) (=> (@ finite_finite_rat B5) (=> (@ (@ ord_less_eq_set_rat B5) (@ (@ image_nat_rat F) A4)) (exists ((C2 set_nat)) (and (@ (@ ord_less_eq_set_nat C2) A4) (= B5 (@ (@ image_nat_rat F) C2)) (@ finite_finite_nat C2)))))) (forall ((C3 set_o) (A product_unit) (B5 (-> Bool set_Product_unit))) (let ((_let_1 (@ insert_Product_unit A))) (let ((_let_2 (@ _let_1 (@ comple3349607820504768346t_unit (@ (@ image_663195431845683034t_unit B5) C3))))) (let ((_let_3 (= C3 bot_bot_set_o))) (and (=> (not _let_3) (= _let_2 (@ comple3349607820504768346t_unit (@ (@ image_663195431845683034t_unit (lambda ((X4 Bool)) (@ (@ insert_Product_unit A) (@ B5 X4)))) C3)))) (=> _let_3 (= _let_2 (@ _let_1 bot_bo3957492148770167129t_unit)))))))) (forall ((P2 (-> product_prod_int_int Bool)) (P product_prod_int_int)) (=> (forall ((A3 int) (B3 int)) (@ P2 (@ (@ product_Pair_int_int A3) B3))) (@ P2 P))) (forall ((A4 set_nat) (C set_int)) (let ((_let_1 (= A4 bot_bot_set_nat))) (and (=> _let_1 (= (@ comple3628384868704368283et_int (@ (@ image_nat_set_int (lambda ((Y5 nat)) C)) A4)) top_top_set_int)) (=> (not _let_1) (= (@ comple3628384868704368283et_int (@ (@ image_nat_set_int (lambda ((Y5 nat)) C)) A4)) C))))) (forall ((Prod produc3843707927480180839at_nat)) (= Prod (@ (@ produc2922128104949294807at_nat (@ produc6011863565407846595at_nat Prod)) (@ produc2937545259423399429at_nat Prod)))) (forall ((X2 (-> int int)) (Ya (-> int int)) (F (-> int nat)) (G (-> int nat))) (=> (= X2 Ya) (=> (forall ((Z3 int)) (=> (@ (@ member_int Z3) (@ (@ image_int_int Ya) top_top_set_int)) (= (@ F Z3) (@ G Z3)))) (= (@ (@ comp_int_nat_int F) X2) (@ (@ comp_int_nat_int G) Ya))))) (forall ((B set_Pr4329608150637261639at_nat) (P produc1319942482725812455at_nat)) (= (= B (@ produc826222791318859909at_nat P)) (exists ((A5 set_Pr4329608150637261639at_nat)) (= P (@ (@ produc9060074326276436823at_nat A5) B))))) (forall ((S5 set_se7592288975875140775at_nat)) (= (@ comple4502628867940267931_nat_o (@ (@ image_5337237954834410540_nat_o (lambda ((I2 set_Pr7459493094073627847at_nat) (X4 set_Pr4329608150637261639at_nat) (Y5 set_Pr4329608150637261639at_nat)) (@ (@ member1466754251312161552at_nat (@ (@ produc9060074326276436823at_nat X4) Y5)) I2))) S5)) (lambda ((X4 set_Pr4329608150637261639at_nat) (Y5 set_Pr4329608150637261639at_nat)) (@ (@ member1466754251312161552at_nat (@ (@ produc9060074326276436823at_nat X4) Y5)) (@ comple7342073961973170484at_nat S5))))) (forall ((F (-> int int)) (A4 set_int)) (@ (@ ord_less_eq_set_int (@ (@ image_int_int F) (@ (@ vimage_int_int F) A4))) A4)) (forall ((A (-> int nat)) (B (-> int int)) (C (-> int nat)) (V int)) (=> (= (@ (@ comp_int_nat_int A) B) (@ (@ comp_nat_nat_int id_nat) C)) (= (@ A (@ B V)) (@ C V)))) (forall ((Rep (-> int nat)) (Abs (-> nat int)) (A4 set_nat)) (=> (@ (@ (@ type_d7249847660678803242nt_nat Rep) Abs) A4) (= (@ (@ image_int_nat Rep) top_top_set_int) A4))) (forall ((A produc3843707927480180839at_nat) (A4 set_Pr4329608150637261639at_nat)) (let ((_let_1 (@ pow_Pr1023649790151954692at_nat A4))) (let ((_let_2 (@ insert9069300056098147895at_nat A))) (= (@ pow_Pr1023649790151954692at_nat (@ _let_2 A4)) (@ (@ sup_su474284620922681339at_nat _let_1) (@ (@ image_4303274092540115909at_nat _let_2) _let_1)))))) (@ (@ (@ _let_89 (@ _let_88 (lambda ((Y2 Bool) (Z Bool)) (= Y2 Z)))) (@ produc8739625826339149834_nat_o (lambda ((X4 nat) (Y5 nat) (__flatten_var_0 product_prod_nat_nat)) (@ (@ produc6081775807080527818_nat_o (lambda ((U3 nat) (V3 nat)) (@ (@ ord_less_eq_nat (@ (@ plus_plus_nat X4) V3)) (@ (@ plus_plus_nat U3) Y5)))) __flatten_var_0)))) ord_less_eq_int) (forall ((Ac produc4196048018000912732at_int) (P2 (-> product_prod_nat_nat product_prod_nat_nat Bool)) (Q2 (-> product_prod_nat_nat int Bool))) (=> (@ (@ member8394280151737582451at_int Ac) (@ collec2851339944984316337at_int (@ produc6937227050501860053_int_o (@ (@ relcom8911704206367525917at_int P2) Q2)))) (@ (@ member8206827879206165904at_nat (@ (@ (@ bNF_fs6342258632037972510at_int P2) Q2) Ac)) (@ collec7088162979684241874at_nat (@ produc6590410687421337004_nat_o P2))))) (forall ((A4 (-> int int Bool)) (B5 (-> num num Bool)) (F (-> int num)) (G (-> int num)) (X2 int) (Y3 int)) (=> (@ (@ (@ (@ 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refl_o7446464703481863270at_nat A4) R) (=> (@ (@ member6009668390874684176at_nat (@ (@ produc2335810615602371415at_nat A) B)) R) (and (@ (@ member8757157785044589968at_nat A) A4) (@ (@ member8757157785044589968at_nat B) A4))))) (forall ((F (-> nat rat)) (A4 set_nat) (B5 set_rat)) (=> (@ (@ inj_on_nat_rat F) A4) (=> (@ (@ ord_less_eq_set_rat (@ (@ image_nat_rat F) A4)) B5) (=> (@ finite_finite_rat B5) (@ finite_finite_nat A4))))) (forall ((F (-> heap_e7401611519738050253t_unit int)) (G (-> ref_a int)) (X2 produc7812382424243267045t_unit)) (= (@ (@ produc6768910348387636265nt_int F) (@ (@ produc5845103964736263686t_unit G) X2)) (@ (@ product_Pair_int_int (@ G (@ produc473321116828791851t_unit X2))) (@ F (@ produc1126150082675451753t_unit X2))))) (forall ((C3 set_Product_unit) (A Bool) (B5 (-> product_unit set_o))) (let ((_let_1 (= C3 bot_bo3957492148770167129t_unit))) (and (=> (not _let_1) (= (@ comple90263536869209701_set_o (@ (@ image_6930536745178679216_set_o (lambda ((X4 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set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ image_6169909464789311569t_unit F))) (= (@ comple2584293577114468500t_unit (@ _let_1 (@ (@ insert8211810215607154385at_nat A) A4))) (@ (@ inf_inf_Product_unit (@ F A)) (@ comple2584293577114468500t_unit (@ _let_1 A4)))))) (forall ((F (-> nat nat)) (G (-> nat nat)) (R3 (-> nat nat Bool))) (@ (@ ord_le3146513528884898305at_nat (@ (@ image_5168914502847457605at_nat (@ (@ bNF_co8276296344278409722at_nat (@ (@ comp_n2711240574518091068at_nat F) product_fst_nat_nat)) (@ (@ comp_n2711240574518091068at_nat G) product_snd_nat_nat))) (@ collec3392354462482085612at_nat (@ produc6081775807080527818_nat_o (@ (@ (@ bNF_vi6667456707345531737_nat_o F) G) R3))))) (@ collec3392354462482085612at_nat (@ produc6081775807080527818_nat_o R3)))) (forall ((A4 set_Product_unit) (G (-> product_unit nat)) (B5 set_Product_unit) (F (-> product_unit nat))) (let ((_let_1 (@ (@ image_875570014554754200it_nat G) B5))) (=> (not (= A4 bot_bo3957492148770167129t_unit)) (=> (@ condit1738341127787009408ow_nat _let_1) (=> (@ (@ ord_le3507040750410214029t_unit A4) B5) (=> (forall ((X product_unit)) (=> (@ (@ member_Product_unit X) B5) (@ (@ ord_less_eq_nat (@ G X)) (@ F X)))) (@ (@ ord_less_eq_nat (@ complete_Inf_Inf_nat _let_1)) (@ complete_Inf_Inf_nat (@ (@ image_875570014554754200it_nat F) A4))))))))) (forall ((A product_prod_nat_nat) (A4 set_Pr1261947904930325089at_nat) (B5 (-> product_prod_nat_nat set_nat))) (=> (@ (@ member8440522571783428010at_nat A) A4) (@ (@ ord_less_eq_set_nat (@ B5 A)) (@ comple7399068483239264473et_nat (@ (@ image_15824709712370754et_nat B5) A4))))) (forall ((X2 product_prod_nat_nat) (A4 set_Pr1261947904930325089at_nat) (X5 set_Pr1261947904930325089at_nat)) (=> (@ (@ member8440522571783428010at_nat X2) A4) (=> (@ (@ ord_le3146513528884898305at_nat X5) A4) (@ (@ ord_le3146513528884898305at_nat (@ (@ insert8211810215607154385at_nat X2) X5)) A4)))) (forall ((A4 set_int) (B5 set_int) (F (-> int set_nat)) (G (-> int set_nat))) (=> (@ (@ ord_less_eq_set_int A4) B5) (=> (forall ((X int)) (=> (@ (@ member_int X) A4) (@ (@ ord_less_eq_set_nat (@ F X)) (@ G X)))) (@ (@ ord_less_eq_set_nat (@ comple7399068483239264473et_nat (@ (@ image_int_set_nat F) A4))) (@ comple7399068483239264473et_nat (@ (@ image_int_set_nat G) B5)))))) (forall ((A4 set_int) (B5 (-> int set_Product_unit)) (F (-> product_unit int))) (=> (not (= A4 bot_bot_set_int)) (=> (forall ((X int)) (=> (@ (@ member_int X) A4) (not (= (@ B5 X) bot_bo3957492148770167129t_unit)))) (=> (@ condit1735850657277959132ow_int (@ comple3221217463730067765et_int (@ (@ image_int_set_int (lambda ((X4 int)) (@ (@ image_873079544045703924it_int F) (@ B5 X4)))) A4))) (= (@ complete_Inf_Inf_int (@ (@ image_873079544045703924it_int F) (@ comple3349607820504768346t_unit (@ (@ image_8658272795163236474t_unit B5) A4)))) (@ complete_Inf_Inf_int (@ (@ image_int_int (lambda ((X4 int)) (@ complete_Inf_Inf_int (@ (@ image_873079544045703924it_int F) (@ B5 X4))))) A4))))))) (forall ((A4 set_o) (F (-> Bool product_unit)) (U product_unit)) (let ((_let_1 (@ (@ image_o_Product_unit F) A4))) (=> (not (= A4 bot_bot_set_o)) (=> (@ condit9161856309968323677t_unit _let_1) (= (@ (@ ord_le3221252021190050221t_unit U) (@ comple2584293577114468500t_unit _let_1)) (forall ((X4 Bool)) (=> (@ (@ member_o X4) A4) (@ (@ ord_le3221252021190050221t_unit U) (@ F X4))))))))) (forall ((B5 set_set_nat) (A set_nat)) (= (@ (@ inf_inf_set_nat (@ comple7399068483239264473et_nat B5)) A) (@ comple7399068483239264473et_nat (@ (@ image_7916887816326733075et_nat (lambda ((B4 set_nat)) (@ (@ inf_inf_set_nat B4) A))) B5)))) (forall ((A4 set_int) (B5 (-> int set_o)) (F (-> Bool int))) (=> (not (= A4 bot_bot_set_int)) (=> (forall ((X int)) (=> (@ (@ member_int X) A4) (not (= (@ B5 X) bot_bot_set_o)))) (=> (@ condit1735850657277959132ow_int (@ comple3221217463730067765et_int (@ (@ image_int_set_int (lambda ((X4 int)) (@ (@ image_o_int F) (@ B5 X4)))) A4))) (= (@ complete_Inf_Inf_int (@ (@ image_o_int F) (@ comple90263536869209701_set_o (@ (@ image_int_set_o B5) A4)))) (@ complete_Inf_Inf_int (@ (@ image_int_int (lambda ((X4 int)) (@ complete_Inf_Inf_int (@ (@ image_o_int F) (@ B5 X4))))) A4))))))) (forall ((A nat) (A4 set_nat) (B product_unit) (B5 set_Product_unit)) (let ((_let_1 (@ produc5506539147108004339t_unit (@ (@ insert_nat A) A4)))) (= (@ _let_1 (lambda ((Uu nat)) (@ (@ insert_Product_unit B) B5))) (@ (@ insert6804906068341198690t_unit (@ (@ produc3434450474625521892t_unit A) B)) (@ (@ sup_su4209953369189666580t_unit (@ (@ produc5506539147108004339t_unit A4) (lambda ((Uu nat)) (@ (@ insert_Product_unit B) B5)))) (@ _let_1 (lambda ((Uu nat)) B5))))))) (forall ((I int) (A4 set_int) (F (-> int product_unit))) (=> (@ (@ member_int I) A4) (@ (@ ord_le3221252021190050221t_unit (@ comple2584293577114468500t_unit (@ (@ image_5846526143423701914t_unit F) A4))) (@ F I)))) (forall ((B5 (-> nat set_Product_unit))) (= (@ comple3349607820504768346t_unit (@ (@ image_4824033694279209942t_unit B5) bot_bot_set_nat)) bot_bo3957492148770167129t_unit)) (forall ((A4 set_set_nat)) (= (@ comple7399068483239264473et_nat (@ (@ image_7916887816326733075et_nat (lambda ((X4 set_nat)) X4)) A4)) (@ comple7399068483239264473et_nat A4))) (forall ((A4 set_o) (B5 set_o) (G (-> Bool product_unit)) (F (-> Bool product_unit))) (=> (forall ((I4 Bool)) (=> (@ (@ member_o I4) A4) (exists ((X6 Bool)) (and (@ (@ ord_le3221252021190050221t_unit (@ G X6)) (@ F I4)) (@ (@ member_o X6) B5))))) (=> (forall ((J2 Bool)) (=> (@ (@ member_o J2) B5) (exists ((X6 Bool)) (and (@ (@ member_o X6) A4) (@ (@ ord_le3221252021190050221t_unit (@ F X6)) (@ G J2)))))) (= (@ comple2584293577114468500t_unit (@ (@ image_o_Product_unit F) A4)) (@ comple2584293577114468500t_unit (@ (@ image_o_Product_unit G) B5)))))) (forall ((A4 set_nat) (G (-> nat int)) (B5 set_nat) (F (-> nat int))) (let ((_let_1 (@ (@ image_nat_int G) B5))) (=> (not (= A4 bot_bot_set_nat)) (=> (@ condit2212336002400062152ve_int _let_1) (=> (@ (@ ord_less_eq_set_nat A4) B5) (=> (forall ((X nat)) (=> (@ (@ member_nat X) A4) (@ (@ ord_less_eq_int (@ F X)) (@ G X)))) (@ (@ ord_less_eq_int (@ complete_Sup_Sup_int (@ (@ image_nat_int F) A4))) (@ complete_Sup_Sup_int _let_1)))))))) (@ fun_re2478310338295953701at_nat (@ (@ produc9060074326276436823at_nat fun_min_strict) fun_min_weak)) _let_256 (forall ((Prod product_prod_int_int)) (= (@ (@ product_Pair_int_int (@ product_fst_int_int Prod)) (@ product_snd_int_int Prod)) Prod)) (forall ((B5 (-> nat set_char))) (= (@ comple7965528767983648192t_char (@ (@ image_nat_set_char B5) bot_bot_set_nat)) top_top_set_char)) (forall ((A4 set_o) (C set_nat)) (let ((_let_1 (= A4 bot_bot_set_o))) (and (=> (not _let_1) (= (@ comple7399068483239264473et_nat (@ (@ image_o_set_nat (lambda ((Y5 Bool)) C)) A4)) C)) (=> _let_1 (= (@ comple7399068483239264473et_nat (@ (@ image_o_set_nat (lambda ((Y5 Bool)) C)) A4)) bot_bot_set_nat))))) _let_254 (forall ((A4 set_int) (B5 set_o) (G (-> Bool product_unit)) (F (-> int product_unit))) (=> (forall ((I4 int)) (=> (@ (@ member_int I4) A4) (exists ((X6 Bool)) (and (@ (@ ord_le3221252021190050221t_unit (@ G X6)) (@ F I4)) (@ (@ member_o X6) B5))))) (=> (forall ((J2 Bool)) (=> (@ (@ member_o J2) B5) (exists ((X6 int)) (and (@ (@ member_int X6) A4) (@ (@ ord_le3221252021190050221t_unit (@ F X6)) (@ G J2)))))) (= (@ comple2584293577114468500t_unit (@ (@ image_5846526143423701914t_unit F) A4)) (@ comple2584293577114468500t_unit (@ (@ image_o_Product_unit G) B5)))))) (forall ((F3 (-> nat num)) (F (-> int nat)) (A4 set_int)) (=> (@ (@ inj_on_int_num (@ (@ comp_nat_num_int F3) F)) A4) (@ (@ inj_on_int_nat F) A4))) (forall ((B5 set_set_o) (X2 Bool) (A4 set_o)) (let ((_let_1 (@ insert_o X2))) (=> (forall ((C2 set_o)) (=> (@ (@ member_set_o C2) B5) (not (@ (@ member_o X2) C2)))) (= (@ (@ member_set_o A4) (@ (@ image_set_o_set_o _let_1) B5)) (and (@ (@ member_set_o (@ (@ minus_minus_set_o A4) (@ _let_1 bot_bot_set_o))) B5) (@ (@ member_o X2) A4)))))) (forall ((F (-> product_prod_nat_nat nat)) (A4 set_Pr1261947904930325089at_nat) (B5 set_nat)) (=> (@ (@ inj_on2178005380612969504at_nat F) A4) (=> (@ (@ ord_less_eq_set_nat (@ (@ image_2486076414777270412at_nat F) A4)) B5) (=> (@ finite_finite_nat B5) (@ finite6177210948735845034at_nat A4))))) (forall ((Rep (-> nat char)) (Abs (-> char nat)) (S5 (-> char set_rat)) (M (-> int char)) (F (-> nat rat)) (S6 (-> int set_nat)) (G (-> int int))) (let ((_let_1 (@ comp_s8253438564248248613at_int (@ image_nat_rat F)))) (=> (@ (@ (@ type_d5945782884131516111t_char Rep) Abs) top_top_set_char) (=> (= (@ (@ comp_c5735667834927173232at_int S5) M) (@ _let_1 S6)) (= (@ (@ comp_nat_set_rat_int (@ (@ comp_c5738158305436223508at_nat S5) Rep)) (@ (@ comp_int_nat_int (@ (@ comp_char_nat_int Abs) M)) G)) (@ _let_1 (@ (@ comp_int_set_nat_int S6) G))))))) (forall ((K nat) (I3 set_nat) (A4 (-> nat set_Pr4329608150637261639at_nat))) (let ((_let_1 (@ comple4364388969068068532at_nat (@ (@ image_1087905878993176368at_nat A4) I3)))) (=> (@ (@ member_nat K) I3) (= (@ (@ sup_su5525570899277871387at_nat (@ A4 K)) _let_1) _let_1)))) (forall ((R (-> int product_prod_nat_nat Bool)) (S2 (-> product_prod_nat_nat product_prod_nat_nat Bool))) (= (@ conver1866313717161370910at_nat (@ (@ relcom716700242784427165at_nat R) S2)) (@ (@ relcom8911704206367525917at_int (@ conver6965824823119931701at_nat S2)) (@ conver1866313717161370910at_nat R)))) (forall ((T2 (-> nat nat))) (= (@ (@ comp_nat_nat_nat id_nat) T2) T2)) (forall ((P rat)) (= (@ quotient_of (@ uminus_uminus_rat P)) (@ (@ produc4245557441103728435nt_int (lambda ((A5 int) (__flatten_var_0 int)) (@ (@ product_Pair_int_int (@ uminus_uminus_int A5)) __flatten_var_0))) (@ quotient_of P)))) (forall ((F4 set_nat) (H (-> nat product_prod_nat_nat))) (=> (@ finite_finite_nat F4) (@ finite6177210948735845034at_nat (@ (@ image_5846123807819985514at_nat H) F4)))) (forall ((F (-> nat nat)) (G (-> Bool Bool)) (H (-> nat nat)) (I (-> nat Bool)) (Prod product_prod_nat_nat)) (= (@ (@ (@ produc2001155298098703512at_o_o F) G) (@ (@ (@ produc4787215299218314158_nat_o H) I) Prod)) (@ (@ (@ produc4787215299218314158_nat_o (@ (@ comp_nat_nat_nat F) H)) (@ (@ comp_o_o_nat G) I)) Prod))) (forall ((A4 set_Pr4329608150637261639at_nat) (F (-> produc3843707927480180839at_nat set_nat)) (U set_nat)) (=> (forall ((I4 produc3843707927480180839at_nat)) (=> (@ (@ member8757157785044589968at_nat I4) A4) (@ (@ ord_less_eq_set_nat (@ F I4)) U))) (@ (@ ord_less_eq_set_nat (@ comple7399068483239264473et_nat (@ (@ image_3160451284896210088et_nat F) A4))) U))) (forall ((I3 set_o) (C product_unit) (F (-> Bool product_unit))) (=> (not (= I3 bot_bot_set_o)) (=> (forall ((I4 Bool)) (=> (@ (@ member_o I4) I3) (@ (@ ord_le3221252021190050221t_unit C) (@ F I4)))) (= (= (@ comple4687483117567863418t_unit (@ (@ image_o_Product_unit F) I3)) C) (forall ((X4 Bool)) (=> (@ (@ member_o X4) I3) (= (@ F X4) C))))))) (forall ((R3 (-> Bool int Bool)) (X2 (-> char Bool)) (Y3 (-> char int)) (Ra (-> Bool int Bool))) (=> (@ (@ (@ (@ bNF_re4780507660726531203_o_int (lambda ((Y2 char) (Z char)) (= Y2 Z))) R3) X2) Y3) (=> (forall ((Z3 Bool) (Yb int)) (=> (@ (@ member_o Z3) (@ (@ image_char_o X2) top_top_set_char)) (=> (@ (@ member_int Yb) (@ (@ image_char_int Y3) top_top_set_char)) (=> (@ (@ R3 Z3) Yb) (@ (@ Ra Z3) Yb))))) (@ (@ (@ (@ bNF_re4780507660726531203_o_int (lambda ((Y2 char) (Z char)) (= Y2 Z))) Ra) X2) Y3)))) (forall ((F (-> nat nat)) (B nat)) (=> (@ (@ inj_on_nat_nat F) top_top_set_nat) (= (@ (@ member_nat B) (@ (@ image_nat_nat F) top_top_set_nat)) (exists ((X4 nat)) (and (forall ((Y5 nat)) (=> (= B (@ F Y5)) (= Y5 X4))) (= B (@ F X4))))))) (forall ((Y3 product_prod_int_int)) (not (forall ((A3 int) (B3 int)) (not (= Y3 (@ (@ product_Pair_int_int A3) B3)))))) (forall ((R3 (-> int int Bool)) (A (-> char int)) (B (-> char int))) (= (@ (@ (@ (@ bNF_re4731199128827642459nt_int (lambda ((Y2 char) (Z char)) (= Y2 Z))) R3) A) B) (exists ((Z4 (-> char product_prod_int_int))) (and (@ (@ member2992454361780672008nt_int Z4) (@ collec1380656525566158922nt_int (lambda ((X4 (-> char product_prod_int_int))) (@ (@ ord_le2843351958646193337nt_int (@ (@ image_5204326662208377313nt_int X4) top_top_set_char)) (@ collec213857154873943460nt_int (@ produc4947309494688390418_int_o R3)))))) (= (@ (@ comp_P4161745170962941589t_char product_fst_int_int) Z4) A) (= (@ (@ comp_P4161745170962941589t_char product_snd_int_int) Z4) B))))) _let_253 (forall ((Sup (-> set_rat rat)) (G (-> rat rat)) (F (-> nat rat)) (A4 set_nat)) (= (@ Sup (@ (@ image_rat_rat G) (@ (@ image_nat_rat F) A4))) (@ Sup (@ (@ image_nat_rat (@ (@ comp_rat_rat_nat G) F)) A4)))) (forall ((F (-> int nat)) (A4 set_int) (B5 set_int)) (let ((_let_1 (@ image_int_nat F))) (=> (@ (@ inj_on_int_nat F) top_top_set_int) (= (@ _let_1 (@ (@ minus_minus_set_int A4) B5)) (@ (@ minus_minus_set_nat (@ _let_1 A4)) (@ _let_1 B5)))))) (forall ((X2 set_Pr4329608150637261639at_nat) (Y3 set_Pr4329608150637261639at_nat)) (= (@ produc5396952528824381687at_nat (@ (@ produc9060074326276436823at_nat X2) Y3)) (@ (@ produc9060074326276436823at_nat Y3) X2))) (forall ((F (-> product_unit nat)) (A4 set_Product_unit) (X2 nat) (B5 set_nat)) (=> (@ (@ inj_on8430439091780834860it_nat F) A4) (=> (not (@ (@ member_nat X2) B5)) (=> (= (@ (@ insert_nat X2) B5) (@ (@ image_875570014554754200it_nat F) A4)) (not (forall ((X8 product_unit) (A8 set_Product_unit)) (=> (not (@ (@ member_Product_unit X8) A8)) (=> (= A4 (@ (@ insert_Product_unit X8) A8)) (=> (= X2 (@ F X8)) (not (= B5 (@ (@ image_875570014554754200it_nat F) A8)))))))))))) (forall ((F (-> int nat)) (G (-> int int))) (=> (@ (@ inj_on_int_nat F) top_top_set_int) (=> (@ (@ inj_on_int_int G) top_top_set_int) (@ (@ inj_on_int_nat (@ (@ comp_int_nat_int F) G)) top_top_set_int)))) (forall ((F (-> Bool Bool)) (G (-> nat Bool)) (H (-> nat nat))) (let ((_let_1 (@ comp_o_o_nat F))) (= (@ (@ comp_nat_o_nat (@ _let_1 G)) H) (@ _let_1 (@ (@ comp_nat_o_nat G) H))))) _let_252 (forall ((F (-> nat nat)) (A4 set_nat)) (=> (@ finite_finite_nat (@ (@ image_nat_nat F) A4)) (=> (not (@ finite_finite_nat A4)) (not (forall ((Y nat)) (=> (@ (@ member_nat Y) (@ (@ image_nat_nat F) A4)) (@ finite_finite_nat (@ (@ inf_inf_set_nat (@ (@ vimage_nat_nat F) (@ (@ insert_nat Y) bot_bot_set_nat))) A4)))))))) (forall ((F (-> nat rat)) (A4 set_nat) (A7 set_rat) (G (-> int nat)) (B5 set_int) (B7 set_nat)) (=> (= (@ (@ image_nat_rat F) A4) A7) (=> (= (@ (@ image_int_nat G) B5) B7) (= (@ (@ image_3755276878268593137at_nat (@ (@ produc8749313216793205150nt_nat F) G)) (@ (@ produc454536836294682310at_int A4) (lambda ((Uu nat)) B5))) (@ (@ produc140472662868866674at_nat A7) (lambda ((Uu rat)) B7)))))) (forall ((F (-> nat nat)) (A4 set_nat) (B5 set_nat)) (let ((_let_1 (@ inj_on_nat_nat F))) (let ((_let_2 (@ image_nat_nat F))) (= (@ _let_1 (@ (@ sup_sup_set_nat A4) B5)) (and (@ _let_1 A4) (= (@ (@ 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((S5 set_int) (F (-> nat int)) (T3 set_nat)) (= (@ (@ ord_less_eq_set_int S5) (@ (@ image_nat_int F) T3)) (exists ((U2 set_nat)) (and (@ (@ ord_less_eq_set_nat U2) T3) (@ (@ inj_on_nat_int F) U2) (= S5 (@ (@ image_nat_int F) U2)))))) (forall ((A4 set_nat) (B5 set_o) (C3 set_nat) (D set_o)) (= (= (@ (@ product_Sigma_nat_o A4) (lambda ((Uu nat)) B5)) (@ (@ product_Sigma_nat_o C3) (lambda ((Uu nat)) D))) (or (and (= A4 C3) (= B5 D)) (and (or (= D bot_bot_set_o) (= C3 bot_bot_set_nat)) (or (= B5 bot_bot_set_o) (= A4 bot_bot_set_nat)))))) (forall ((F (-> nat nat)) (G (-> nat nat)) (A4 set_nat)) (= (@ (@ image_nat_nat F) (@ (@ image_nat_nat G) A4)) (@ (@ image_nat_nat (lambda ((X4 nat)) (@ F (@ G X4)))) A4))) (forall ((P2 (-> product_prod_nat_nat Bool)) (Q2 (-> product_prod_nat_nat product_prod_int_int Bool))) (= (@ collec6785001409445536906nt_int (@ produc5031841752791441652_int_o (lambda ((X4 product_prod_nat_nat) (Y5 product_prod_int_int)) (and (@ (@ Q2 X4) Y5) (@ P2 X4))))) (@ (@ 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set_int)) (= (= bot_bot_set_int (@ (@ image_int_int F) A4)) (= A4 bot_bot_set_int))) (= produc4245557441103728435nt_int (lambda ((C4 (-> int int product_prod_int_int)) (P3 product_prod_int_int)) (@ (@ C4 (@ product_fst_int_int P3)) (@ product_snd_int_int P3)))) (forall ((A (-> Bool Bool)) (B (-> nat Bool)) (C (-> nat Bool)) (V nat)) (=> (= (@ (@ comp_o_o_nat A) B) C) (= (@ A (@ B V)) (@ C V)))) (forall ((F (-> Bool rat)) (A4 set_rat)) (=> (= (@ (@ image_o_rat F) top_top_set_o) top_top_set_rat) (= (= (@ (@ vimage_o_rat F) A4) bot_bot_set_o) (= A4 bot_bot_set_rat)))) (forall ((A4 set_nat) (M3 nat) (F (-> nat nat))) (=> (forall ((X nat)) (=> (@ (@ member_nat X) A4) (@ (@ ord_less_eq_nat M3) (@ F X)))) (@ condit1738341127787009408ow_nat (@ (@ image_nat_nat F) A4)))) (forall ((F (-> nat product_unit))) (= (@ comple2584293577114468500t_unit (@ (@ image_8730104196221521654t_unit F) bot_bot_set_nat)) top_top_Product_unit)) (forall ((A4 set_Pr4329608150637261639at_nat) (R set_Pr5564308138774400199at_nat) (X2 produc3843707927480180839at_nat) (Y3 produc3843707927480180839at_nat)) (=> (@ (@ refl_o7446464703481863270at_nat A4) R) (=> (@ (@ member6009668390874684176at_nat (@ (@ produc2335810615602371415at_nat X2) Y3)) R) (@ (@ member8757157785044589968at_nat X2) A4)))) (forall ((F1 (-> int int)) (A13 set_int) (B1 set_int) (F22 (-> int nat)) (B22 set_int) (A24 set_nat)) (=> (= (@ (@ image_int_int F1) A13) B1) (=> (@ (@ inj_on_int_nat F22) B22) (=> (@ (@ ord_less_eq_set_nat (@ (@ image_int_nat F22) B22)) A24) (=> (=> (= B22 bot_bot_set_int) (= A24 bot_bot_set_nat)) (= (@ (@ bNF_We8537379975951060974nt_int B22) B1) (@ (@ image_5437939712159429529nt_int (@ (@ (@ bNF_We2266819666720791040nt_nat B22) F1) F22)) (@ (@ bNF_We7538026264050006418at_int A24) A13)))))))) (forall ((F (-> nat rat)) (A rat) (X2 nat)) (=> (= (@ (@ image_nat_rat F) top_top_set_nat) (@ (@ insert_rat A) bot_bot_set_rat)) (= (@ F X2) A))) (= produc4947309494688390418_int_o (lambda ((C4 (-> int 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comp_nat_nat_nat))) (forall ((B5 (-> int set_nat)) (F (-> nat int)) (A4 set_nat)) (= (@ comple7399068483239264473et_nat (@ (@ image_nat_set_nat (lambda ((A5 nat)) (@ B5 (@ F A5)))) A4)) (@ comple7399068483239264473et_nat (@ (@ image_int_set_nat B5) (@ (@ image_nat_int F) A4))))) (forall ((F (-> nat int)) (G (-> nat nat)) (A4 set_nat)) (= (@ (@ image_6845477519721040070nt_nat (lambda ((X4 nat)) (@ (@ product_Pair_int_nat (@ F X4)) (@ G X4)))) A4) (@ (@ produc1456381018704787142nt_nat (@ (@ image_nat_int F) A4)) (lambda ((X4 int)) (@ (@ image_nat_nat G) (@ (@ inf_inf_set_nat (@ (@ vimage_nat_int F) (@ (@ insert_int X4) bot_bot_set_int))) A4)))))) (forall ((A4 set_nat) (B5 set_Product_unit) (C3 set_nat) (D set_Product_unit)) (= (= (@ (@ produc5506539147108004339t_unit A4) (lambda ((Uu nat)) B5)) (@ (@ produc5506539147108004339t_unit C3) (lambda ((Uu nat)) D))) (or (and (= B5 D) (= A4 C3)) (and (or (= C3 bot_bot_set_nat) (= D bot_bo3957492148770167129t_unit)) (or (= B5 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ord_le5525191956872776187t_unit B5) (@ collec3252306575900995386t_unit (@ produc4924168586796184916unit_o R22))) (= (@ (@ P2 (@ produc473321116828791851t_unit A)) (@ produc473321116828791851t_unit B)) (@ (@ Q2 (@ produc1126150082675451753t_unit A)) (@ produc1126150082675451753t_unit B))))))))) (forall ((A4 set_Pr958786334691620121nt_int)) (= (@ collec213857154873943460nt_int (lambda ((X4 product_prod_int_int)) (@ (@ member5262025264175285858nt_int X4) A4))) A4)) (forall ((X2 produc3843707927480180839at_nat) (Y3 set_Pr1261947904930325089at_nat) (Z2 set_Pr1261947904930325089at_nat)) (=> (= X2 (@ (@ produc2922128104949294807at_nat Y3) Z2)) (= (@ produc2937545259423399429at_nat X2) Z2))) (forall ((K4 set_int)) (= (@ gcd_Lcm_nat (@ (@ image_int_nat (lambda ((K5 int)) (@ nat2 (@ abs_abs_int K5)))) K4)) (@ nat2 (@ gcd_Lcm_int K4)))) (= (lambda ((Y2 rat) (Z rat)) (= Y2 Z)) (@ (@ bNF_Grp_rat_rat top_top_set_rat) id_rat)) (forall ((A4 set_nat) (F product_unit)) (=> (not (= A4 bot_bot_set_nat)) (= (@ comple4687483117567863418t_unit (@ (@ image_8730104196221521654t_unit (lambda ((I2 nat)) F)) A4)) F))) (forall ((A4 set_o) (C set_o)) (let ((_let_1 (= A4 bot_bot_set_o))) (and (=> (not _let_1) (= (@ comple90263536869209701_set_o (@ (@ image_o_set_o (lambda ((Y5 Bool)) C)) A4)) C)) (=> _let_1 (= (@ comple90263536869209701_set_o (@ (@ image_o_set_o (lambda ((Y5 Bool)) C)) A4)) bot_bot_set_o))))) (forall ((X2 set_nat) (Y3 set_nat)) (= (@ (@ (@ if_set_nat true) X2) Y3) X2)) _let_250 (forall ((F (-> product_prod_nat_nat product_prod_nat_nat))) (=> (@ finite6177210948735845034at_nat top_to4669805908274784177at_nat) (=> (= (@ (@ image_5168914502847457605at_nat F) top_to4669805908274784177at_nat) top_to4669805908274784177at_nat) (@ (@ inj_on8969904277767023793at_nat F) top_to4669805908274784177at_nat)))) (forall ((Sup (-> set_rat rat)) (G (-> nat rat)) (F (-> int nat)) (A4 set_int)) (= (@ Sup (@ (@ image_nat_rat G) (@ (@ image_int_nat F) A4))) (@ Sup (@ (@ image_int_rat (@ (@ comp_nat_rat_int G) F)) A4)))) _let_249 (forall ((F (-> int nat)) (A4 set_int) (Y3 nat)) (=> (@ (@ inj_on_int_nat F) A4) (=> (@ (@ member_nat Y3) (@ (@ image_int_nat F) A4)) (= (@ F (@ (@ (@ the_inv_into_int_nat A4) F) Y3)) Y3)))) (forall ((A4 set_int) (B5 set_int) (C3 (-> int product_unit)) (D (-> int product_unit))) (=> (= A4 B5) (=> (forall ((X int)) (=> (@ (@ member_int X) B5) (= (@ C3 X) (@ D X)))) (= (@ comple2584293577114468500t_unit (@ (@ image_5846526143423701914t_unit C3) A4)) (@ comple2584293577114468500t_unit (@ (@ image_5846526143423701914t_unit D) B5)))))) (forall ((X2 (-> nat rat)) (Ra (-> rat rat Bool))) (=> (forall ((Z3 rat)) (=> (@ (@ member_rat Z3) (@ (@ image_nat_rat X2) top_top_set_nat)) (@ (@ Ra Z3) Z3))) (@ (@ (@ (@ bNF_re4702136315717946289at_rat (lambda ((Y2 nat) (Z nat)) (= Y2 Z))) Ra) X2) X2))) (forall ((F (-> nat product_unit))) (= (@ comple4687483117567863418t_unit (@ (@ image_8730104196221521654t_unit F) bot_bot_set_nat)) bot_bot_Product_unit)) (forall ((G (-> nat int)) (F (-> int rat))) (=> (@ finite_finite_int (@ (@ image_nat_int G) top_top_set_nat)) (@ finite_finite_rat (@ (@ image_nat_rat (lambda ((X4 nat)) (@ F (@ G X4)))) top_top_set_nat)))) (forall ((Z2 nat)) (= (@ (@ (@ comp_P1955610211387027840at_nat product_fst_nat_nat) (lambda ((X4 nat)) (@ (@ product_Pair_nat_nat X4) X4))) Z2) (@ id_nat Z2))) (forall ((F (-> product_unit product_unit)) (A4 set_Product_unit)) (=> (@ order_4454465170704313136t_unit F) (@ (@ ord_le3221252021190050221t_unit (@ F (@ comple2584293577114468500t_unit A4))) (@ comple2584293577114468500t_unit (@ (@ image_405062704495631173t_unit F) A4))))) (forall ((Rep (-> nat nat)) (Abs (-> nat nat)) (A4 set_nat)) (=> (@ (@ (@ type_d6250493948777748686at_nat Rep) Abs) A4) (= (@ (@ image_nat_nat Abs) A4) top_top_set_nat))) (forall ((Prod produc1319942482725812455at_nat)) (= Prod (@ (@ produc9060074326276436823at_nat (@ produc4486455499028916547at_nat Prod)) (@ produc826222791318859909at_nat Prod)))) (forall ((X1 set_Pr4329608150637261639at_nat) (X22 set_Pr4329608150637261639at_nat) (Y1 set_Pr4329608150637261639at_nat) (Y22 set_Pr4329608150637261639at_nat)) (= (= (@ (@ produc9060074326276436823at_nat X1) X22) (@ (@ produc9060074326276436823at_nat Y1) Y22)) (and (= X1 Y1) (= X22 Y22)))) (forall ((C product_prod_nat_num) (F (-> nat nat)) (G (-> nat num)) (R3 set_Pr1261947904930325089at_nat)) (=> (@ (@ member9148766508732265716at_num C) (@ (@ image_5877158439796295311at_num (@ (@ produc3535218481486409604at_num F) G)) R3)) (not (forall ((X nat) (Y nat)) (=> (= C (@ (@ product_Pair_nat_num (@ F X)) (@ G Y))) (not (@ (@ member8440522571783428010at_nat (@ (@ product_Pair_nat_nat X) Y)) R3))))))) (forall ((F (-> nat nat))) (let ((_let_1 (@ (@ bNF_Grp_nat_nat top_top_set_nat) F))) (=> (= F id_nat) (= (@ (@ relcompp_nat_nat_nat (@ conversep_nat_nat _let_1)) _let_1) _let_1)))) (forall ((B nat) (F (-> int nat)) (A4 set_int)) (=> (@ (@ member_nat B) (@ (@ image_int_nat F) A4)) (not (forall ((X int)) (=> (= 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(@ (@ produc2335810615602371415at_nat Y) X)) R)))))) (@ (@ total_1513685709984341995at_nat A4) R))) (forall ((A4 set_int) (B5 set_int)) (=> (@ finite_finite_int A4) (=> (@ finite_finite_int B5) (= (exists ((F2 (-> int int))) (and (@ (@ ord_less_eq_set_int (@ (@ image_int_int F2) A4)) B5) (@ (@ inj_on_int_int F2) A4))) (@ (@ ord_less_eq_nat (@ finite_card_int A4)) (@ finite_card_int B5)))))) (forall ((A (-> (-> code_integer code_integer) produc8923325533196201883nteger produc8923325533196201883nteger)) (B (-> code_integer code_integer code_integer)) (C (-> code_integer produc8923325533196201883nteger produc8923325533196201883nteger)) (V code_integer)) (=> (= (@ (@ comp_C8797469213163452608nteger A) B) (@ (@ comp_P3928908779438215820nteger id_Pro496765588584934260nteger) C)) (= (@ A (@ B V)) (@ C V)))) (forall ((Rep (-> nat int)) (Abs (-> int nat))) (=> (@ (@ (@ type_d6248003478268698410at_int Rep) Abs) top_top_set_int) (= (@ (@ comp_int_nat_nat Abs) Rep) id_nat))) (forall ((F (-> int 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Y3)))) (forall ((A int) (B int) (R3 set_Pr958786334691620121nt_int) (F (-> int int)) (G (-> int int))) (=> (@ (@ member5262025264175285858nt_int (@ (@ product_Pair_int_int A) B)) R3) (@ (@ member5262025264175285858nt_int (@ (@ product_Pair_int_int (@ F A)) (@ G B))) (@ (@ image_2653370878348428101nt_int (@ (@ produc6036585564866528938nt_int F) G)) R3)))) (forall ((P2 (-> product_prod_nat_nat Bool)) (Q2 (-> product_prod_int_int Bool))) (= (@ collec6785001409445536906nt_int (@ produc5031841752791441652_int_o (lambda ((A5 product_prod_nat_nat) (B4 product_prod_int_int)) (and (@ Q2 B4) (@ P2 A5))))) (@ (@ produc8806266479013559872nt_int (@ collec3392354462482085612at_nat P2)) (lambda ((Uu product_prod_nat_nat)) (@ collec213857154873943460nt_int Q2))))) (forall ((H2 heap_e7401611519738050253t_unit) (R ref_a) (V a) (H heap_e7401611519738050253t_unit) (X2 product_unit)) (=> (= H2 (@ (@ (@ set_a R) V) H)) (@ (@ (@ (@ heap_e2830298082929533060t_unit (@ (@ update_a R) V)) H) H2) X2))) (forall ((R3 set_Pr1261947904930325089at_nat) (S5 set_Pr1261947904930325089at_nat)) (= (@ (@ sup_sup_nat_nat_o (lambda ((X4 nat) (Y5 nat)) (@ (@ member8440522571783428010at_nat (@ (@ product_Pair_nat_nat X4) Y5)) R3))) (lambda ((X4 nat) (Y5 nat)) (@ (@ member8440522571783428010at_nat (@ (@ product_Pair_nat_nat X4) Y5)) S5))) (lambda ((X4 nat) (Y5 nat)) (@ (@ member8440522571783428010at_nat (@ (@ product_Pair_nat_nat X4) Y5)) (@ (@ sup_su6327502436637775413at_nat R3) S5))))) (forall ((R1 (-> product_prod_nat_nat int Bool))) (@ (@ (@ (@ bNF_re2742285375668209089nt_num (lambda ((Y2 (-> nat num)) (Z (-> nat num))) (= Y2 Z))) (@ (@ bNF_re2682547871993127601nt_num (@ (@ bNF_re4555766996558763186at_nat R1) (lambda ((Y2 nat) (Z nat)) (= Y2 Z)))) (@ (@ bNF_re8466801222876787014um_num R1) (lambda ((Y2 num) (Z num)) (= Y2 Z))))) comp_n8649498751204056690at_nat) comp_nat_num_int)) (forall ((F (-> Bool set_nat)) (A Bool) (A4 set_o)) (let ((_let_1 (@ image_o_set_nat F))) (= (@ 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top_top_set_char) (=> (@ (@ ord_less_eq_set_char (@ (@ vimage_char_char F) B5)) A4) (@ (@ ord_less_eq_set_char B5) (@ _let_1 A4)))))) (forall ((A4 set_se5479201105039950375at_nat) (R set_Pr7459493094073627847at_nat)) (=> (forall ((X set_Pr4329608150637261639at_nat) (Y set_Pr4329608150637261639at_nat)) (=> (@ (@ member6273874620674182256at_nat X) A4) (=> (@ (@ member6273874620674182256at_nat Y) A4) (=> (not (= X Y)) (or (@ (@ member1466754251312161552at_nat (@ (@ produc9060074326276436823at_nat Y) X)) R) (@ (@ member1466754251312161552at_nat (@ (@ produc9060074326276436823at_nat X) Y)) R)))))) (@ (@ total_5117575981256876747at_nat A4) R))) (forall ((A nat) (B num) (A4 set_nat) (B5 (-> nat set_num))) (=> (@ (@ member9148766508732265716at_num (@ (@ product_Pair_nat_num A) B)) (@ (@ produc6237731129814287028at_num A4) B5)) (@ (@ member_nat A) A4))) (forall ((X2 product_prod_o_nat) (A4 set_o) (B5 set_nat)) (= (@ (@ member2802428098988154798_o_nat X2) (@ (@ product_Sigma_o_nat A4) (lambda ((Uu Bool)) B5))) (and (@ (@ member_nat (@ product_snd_o_nat X2)) B5) (@ (@ member_o (@ product_fst_o_nat X2)) A4)))) (forall ((F (-> nat rat)) (A4 set_nat) (B5 set_nat)) (let ((_let_1 (@ image_nat_rat F))) (@ (@ ord_less_eq_set_rat (@ (@ minus_minus_set_rat (@ _let_1 A4)) (@ _let_1 B5))) (@ _let_1 (@ (@ minus_minus_set_nat A4) B5))))) (forall ((F (-> nat rat)) (A4 set_nat) (P2 (-> set_rat Bool))) (= (forall ((B6 set_rat)) (=> (@ (@ ord_less_eq_set_rat B6) (@ (@ image_nat_rat F) A4)) (@ P2 B6))) (forall ((B6 set_nat)) (=> (@ (@ ord_less_eq_set_nat B6) A4) (@ P2 (@ (@ image_nat_rat F) B6)))))) (forall ((Prod product_prod_nat_nat)) (= (@ (@ product_Pair_nat_nat (@ product_fst_nat_nat Prod)) (@ product_snd_nat_nat Prod)) Prod)) (forall ((A4 set_int) (B5 set_nat)) (=> (@ finite_finite_int A4) (=> (@ finite_finite_nat B5) (= (exists ((F2 (-> int nat))) (and (@ (@ ord_less_eq_set_nat (@ (@ image_int_nat F2) A4)) B5) (@ (@ inj_on_int_nat F2) A4))) (@ (@ ord_less_eq_nat (@ finite_card_int A4)) (@ finite_card_nat B5)))))) (forall ((F (-> ref_a nat)) (G (-> heap_e7401611519738050253t_unit nat)) (X2 produc7812382424243267045t_unit)) (= (@ (@ produc5147081798617427195at_nat F) (@ (@ produc8366372614399963582_ref_a G) X2)) (@ (@ product_Pair_nat_nat (@ F (@ produc473321116828791851t_unit X2))) (@ G (@ produc1126150082675451753t_unit X2))))) (forall ((A4 set_o) (B5 (-> Bool set_Pr1261947904930325089at_nat))) (=> (@ finite_finite_o A4) (=> (forall ((A3 Bool)) (=> (@ (@ member_o A3) A4) (@ finite6177210948735845034at_nat (@ B5 A3)))) (@ finite6177210948735845034at_nat (@ comple5685304695842803022at_nat (@ (@ image_7077428525161401678at_nat B5) A4)))))) _let_248 (forall ((Rep (-> nat Bool)) (Abs (-> Bool nat)) (M (-> Bool Bool))) (=> (@ (@ (@ type_d1000680970699258650_nat_o Rep) Abs) top_top_set_o) (=> (= M id_o) (= (@ (@ comp_o_nat_nat (@ (@ comp_o_nat_o Abs) M)) Rep) id_nat)))) (forall ((F (-> code_integer code_integer)) (X2 produc8923325533196201883nteger) (G (-> code_integer code_integer))) (let ((_let_1 (@ produc6174133586879617921nteger X2))) (= (= (@ (@ produc6499014454317279255nteger F) X2) (@ (@ produc6499014454317279255nteger G) X2)) (= (@ F _let_1) (@ G _let_1))))) (forall ((C3 set_nat) (A product_unit) (B5 (-> nat set_Product_unit))) (let ((_let_1 (@ insert_Product_unit A))) (let ((_let_2 (@ _let_1 (@ comple3349607820504768346t_unit (@ (@ image_4824033694279209942t_unit B5) C3))))) (let ((_let_3 (= C3 bot_bot_set_nat))) (and (=> (not _let_3) (= _let_2 (@ comple3349607820504768346t_unit (@ (@ image_4824033694279209942t_unit (lambda ((X4 nat)) (@ (@ insert_Product_unit A) (@ B5 X4)))) C3)))) (=> _let_3 (= _let_2 (@ _let_1 bot_bo3957492148770167129t_unit)))))))) _let_247 (forall ((F (-> int nat)) (G (-> nat num))) (= (@ (@ comp_s6458263553158497821et_num (@ vimage_int_nat F)) (@ vimage_nat_num G)) (@ vimage_int_num (@ (@ comp_nat_num_int G) F)))) (forall ((Z2 int) (F (-> int int)) (A4 set_int)) (= (@ (@ member_int Z2) (@ (@ image_int_int F) A4)) (exists ((X4 int)) (and (= Z2 (@ F X4)) (@ (@ member_int X4) A4))))) (forall ((A4 set_nat) (B5 set_nat) (C3 set_nat)) (= (@ (@ produc457027306803732586at_nat (@ (@ minus_minus_set_nat A4) B5)) (lambda ((Uu nat)) C3)) (@ (@ minus_1356011639430497352at_nat (@ (@ produc457027306803732586at_nat A4) (lambda ((Uu nat)) C3))) (@ (@ produc457027306803732586at_nat B5) (lambda ((Uu nat)) C3))))) (forall ((B nat) (B5 (-> int set_nat)) (A4 set_int)) (=> (@ (@ member_nat B) (@ comple7399068483239264473et_nat (@ (@ image_int_set_nat B5) A4))) (not (forall ((X int)) (=> (@ (@ member_int X) A4) (not (@ (@ member_nat B) (@ B5 X)))))))) (forall ((B5 (-> Bool nat Bool)) (C3 (-> Bool num Bool)) (A4 (-> nat int Bool))) (@ (@ (@ (@ bNF_re7387973359137000979nt_num (@ (@ bNF_re766437678722298023_o_num B5) C3)) (@ (@ bNF_re4102725726183926567nt_num (@ (@ bNF_re8210149947023016781_o_nat A4) B5)) (@ (@ bNF_re4767481733178795415_o_num A4) C3))) comp_o_o_nat) comp_nat_num_int)) (forall ((K product_prod_nat_nat) (I3 set_Pr1261947904930325089at_nat) (A4 (-> product_prod_nat_nat set_nat))) (let ((_let_1 (@ comple7806235888213564991et_nat (@ (@ image_15824709712370754et_nat A4) I3)))) (=> (@ (@ member8440522571783428010at_nat K) I3) (= (@ (@ inf_inf_set_nat (@ A4 K)) _let_1) _let_1)))) (forall ((A4 set_o) (F (-> Bool product_unit)) (A Bool)) (let ((_let_1 (@ image_o_Product_unit F))) (let ((_let_2 (@ _let_1 A4))) (=> (not (= A4 bot_bot_set_o)) (=> (@ condit9161856309968323677t_unit _let_2) (= (@ comple2584293577114468500t_unit (@ _let_1 (@ (@ insert_o A) A4))) (@ (@ inf_inf_Product_unit (@ F A)) (@ comple2584293577114468500t_unit _let_2)))))))) (forall ((P2 (-> nat nat Bool)) (P product_prod_nat_nat) (Q2 (-> (-> product_prod_nat_nat Bool) Bool)) (F (-> nat nat product_prod_nat_nat Bool))) (=> (@ (@ P2 (@ product_snd_nat_nat P)) (@ product_fst_nat_nat P)) (=> (forall ((X nat) (Y nat)) (=> (@ (@ P2 Y) X) (@ Q2 (@ (@ F X) Y)))) (@ Q2 (@ (@ produc8739625826339149834_nat_o F) P))))) (forall ((A4 set_nat) (F (-> nat rat))) (=> (@ finite_finite_nat A4) (= (@ (@ inj_on_nat_rat F) A4) (= (@ finite_card_rat (@ (@ image_nat_rat F) A4)) (@ finite_card_nat A4))))) (forall ((F (-> ref_a ref_a)) (G (-> heap_e7401611519738050253t_unit heap_e7401611519738050253t_unit)) (X2 produc7812382424243267045t_unit)) (= (@ produc1126150082675451753t_unit (@ (@ (@ produc3456481717235892722t_unit F) G) X2)) (@ G (@ produc1126150082675451753t_unit X2)))) (forall ((F (-> nat rat)) (C3 set_nat) (A4 set_nat) (B5 set_nat)) (let ((_let_1 (@ image_nat_rat F))) (=> (@ (@ inj_on_nat_rat F) C3) (=> (@ (@ ord_less_eq_set_nat A4) C3) (=> (@ (@ ord_less_eq_set_nat B5) C3) (= (@ _let_1 (@ (@ inf_inf_set_nat A4) B5)) (@ (@ inf_inf_set_rat (@ _let_1 A4)) (@ _let_1 B5)))))))) (forall ((C product_prod_int_int) (F (-> nat int)) (G (-> num int)) (R3 set_Pr6200539531224447659at_num)) (=> (@ (@ member5262025264175285858nt_int C) (@ (@ image_1039142661021589043nt_int (@ (@ produc5477380188365894716um_int F) G)) R3)) (not (forall ((X nat) (Y num)) (=> (= C (@ (@ product_Pair_int_int (@ F X)) (@ G Y))) (not (@ (@ member9148766508732265716at_num (@ (@ product_Pair_nat_num X) Y)) R3))))))) (forall ((F (-> Bool set_nat)) (A4 set_o) (A Bool)) (let ((_let_1 (@ (@ image_o_set_nat F) A4))) (let ((_let_2 (@ comple7806235888213564991et_nat _let_1))) (=> (= (@ comple7399068483239264473et_nat _let_1) _let_2) (=> (@ condit5477540289124974626et_nat _let_1) (=> (@ condit68592940725977398et_nat _let_1) (=> (@ (@ member_o A) A4) (= (@ F A) _let_2)))))))) (forall ((F (-> int nat)) (A4 set_int) (P2 (-> set_nat Bool))) (= (exists ((B6 set_nat)) (and (@ finite_finite_nat B6) (@ P2 B6) (@ (@ ord_less_eq_set_nat B6) (@ (@ image_int_nat F) A4)))) (exists ((B6 set_int)) (and (@ finite_finite_int B6) (@ (@ ord_less_eq_set_int B6) A4) (@ P2 (@ (@ image_int_nat F) B6)))))) (forall ((A int) (P2 (-> int Bool))) (= (@ (@ member_int A) (@ collect_int P2)) (@ P2 A))) (forall ((Rep (-> num char)) (Abs (-> char num)) (M (-> char char))) (=> (@ (@ (@ type_d4396077731765706521m_char Rep) Abs) top_top_set_char) (=> (= M id_char) (= (@ (@ comp_char_num_num (@ (@ comp_char_num_char Abs) M)) Rep) id_num)))) (forall ((B int) (F (-> rat int)) (X2 rat)) (=> (= B (@ F X2)) (@ (@ member_int B) (@ (@ image_rat_int F) top_top_set_rat)))) (forall ((F (-> nat nat)) (A4 set_nat) (B5 set_nat) (G (-> nat nat))) (=> (@ (@ inj_on_nat_nat F) A4) (=> (@ (@ ord_less_eq_set_nat (@ (@ image_nat_nat F) A4)) B5) (=> (@ (@ inj_on_nat_nat G) B5) (=> (@ (@ ord_less_eq_set_nat (@ (@ image_nat_nat G) B5)) A4) (=> (@ finite_finite_nat A4) (=> (@ finite_finite_nat B5) (= (@ finite_card_nat A4) (@ finite_card_nat B5))))))))) (forall ((A nat) (B nat) (R set_Pr1261947904930325089at_nat)) (= (@ field_nat (@ (@ insert8211810215607154385at_nat (@ (@ product_Pair_nat_nat A) B)) R)) (@ (@ sup_sup_set_nat (@ (@ insert_nat A) (@ (@ insert_nat B) bot_bot_set_nat))) (@ field_nat R)))) (forall ((A4 set_Product_unit)) (= (@ comple4687483117567863418t_unit (@ (@ image_405062704495631173t_unit id_Product_unit) A4)) (@ comple4687483117567863418t_unit A4))) (forall ((A4 set_o) (U set_nat) (F (-> Bool set_nat))) (=> (forall ((I4 Bool)) (=> (@ (@ member_o I4) A4) (@ (@ ord_less_eq_set_nat U) (@ F I4)))) (@ (@ ord_less_eq_set_nat U) (@ comple7806235888213564991et_nat (@ (@ image_o_set_nat F) A4))))) (forall ((A4 set_Product_unit) (M3 product_unit) (F (-> product_unit product_unit))) (=> (not (= A4 bot_bo3957492148770167129t_unit)) (=> (forall ((X product_unit)) (=> (@ (@ member_Product_unit X) A4) (@ (@ ord_le3221252021190050221t_unit M3) (@ F X)))) (@ (@ ord_le3221252021190050221t_unit M3) (@ comple2584293577114468500t_unit (@ (@ image_405062704495631173t_unit F) A4)))))) (forall ((B5 set_Product_unit) (A4 set_nat)) (let ((_let_1 (@ produc5506539147108004339t_unit A4))) (let ((_let_2 (@ image_3884712837920099081it_nat produc3800628931346975736t_unit))) (let ((_let_3 (= B5 bot_bo3957492148770167129t_unit))) (and (=> (not _let_3) (= (@ _let_2 (@ _let_1 (lambda ((Uu nat)) B5))) A4)) (=> _let_3 (= (@ _let_2 (@ _let_1 (lambda ((Uu nat)) B5))) bot_bot_set_nat))))))) (forall ((G (-> rat nat)) (F (-> nat rat)) (A4 set_nat)) (= (@ complete_Sup_Sup_nat (@ (@ image_rat_nat G) (@ (@ image_nat_rat F) A4))) (@ complete_Sup_Sup_nat (@ (@ image_nat_nat (@ (@ comp_rat_nat_nat G) F)) A4)))) (forall ((A4 set_int) (C nat)) (=> (not (= A4 bot_bot_set_int)) (= (@ complete_Sup_Sup_nat (@ (@ image_int_nat (lambda ((X4 int)) C)) A4)) C))) _let_245 (forall ((S5 set_Pr4329608150637261639at_nat) (F (-> produc3843707927480180839at_nat nat nat)) (X2 produc3843707927480180839at_nat)) (let ((_let_1 (@ F X2))) (=> (@ (@ finite352855791390415404at_nat S5) F) (=> (@ (@ member8757157785044589968at_nat X2) S5) (= (@ (@ comp_nat_nat_nat _let_1) _let_1) _let_1))))) (forall ((A nat) (B nat) (A4 set_Pr1261947904930325089at_nat) (F (-> nat nat Bool))) (=> (@ (@ member8440522571783428010at_nat (@ (@ product_Pair_nat_nat A) B)) A4) (@ (@ member_o (@ (@ F A) B)) (@ (@ image_3693632289388996572_nat_o (@ produc6081775807080527818_nat_o F)) A4)))) (forall ((A Bool) (B int) (A4 set_o) (B5 (-> Bool set_int))) (=> (@ (@ member7847949116333733898_o_int (@ (@ product_Pair_o_int A) B)) (@ (@ product_Sigma_o_int A4) B5)) (not (=> (@ (@ member_o A) A4) (not (@ (@ member_int B) (@ B5 A))))))) (forall ((A4 set_Product_unit) (C set_nat)) (=> (not (= A4 bot_bo3957492148770167129t_unit)) (= (@ comple7806235888213564991et_nat (@ (@ image_8173849991827986510et_nat (lambda ((X4 product_unit)) C)) A4)) C))) (forall ((F (-> nat product_unit)) (A4 set_nat)) (= (= (@ (@ image_8730104196221521654t_unit F) A4) bot_bo3957492148770167129t_unit) (= A4 bot_bot_set_nat))) (forall ((B nat) (F (-> Bool nat)) (X2 Bool) (A4 set_o)) (=> (= B (@ F X2)) (=> (@ (@ member_o X2) A4) (@ (@ member_nat B) (@ (@ image_o_nat F) A4))))) (forall ((C product_prod_int_int) (F (-> nat int)) (G (-> nat int)) (R3 set_Pr1261947904930325089at_nat)) (=> (@ (@ member5262025264175285858nt_int C) (@ (@ image_1990417195239315453nt_int (@ (@ produc7347049785058425330at_int F) G)) R3)) (not (forall ((X nat) (Y nat)) (=> (= C (@ (@ product_Pair_int_int (@ F X)) (@ G Y))) (not (@ (@ member8440522571783428010at_nat (@ (@ product_Pair_nat_nat X) Y)) R3))))))) (forall ((A4 set_Product_unit) (F (-> product_unit product_unit)) (B5 set_Product_unit)) (let ((_let_1 (@ image_405062704495631173t_unit F))) (let ((_let_2 (@ _let_1 B5))) (let ((_let_3 (@ _let_1 A4))) (=> (not (= A4 bot_bo3957492148770167129t_unit)) (=> (@ condit2080475194861589617t_unit _let_3) (=> (not (= B5 bot_bo3957492148770167129t_unit)) (=> (@ condit2080475194861589617t_unit _let_2) (= (@ comple4687483117567863418t_unit (@ _let_1 (@ (@ sup_su793286257634532545t_unit A4) B5))) (@ (@ sup_sup_Product_unit (@ comple4687483117567863418t_unit _let_3)) (@ comple4687483117567863418t_unit _let_2))))))))))) (forall ((C product_prod_nat_num) (F (-> int nat)) (G (-> int num)) (R3 set_Pr958786334691620121nt_int)) (=> (@ (@ member9148766508732265716at_num C) (@ (@ image_6540112122905407959at_num (@ (@ produc2224754261294513212nt_num F) G)) R3)) (not (forall ((X int) (Y int)) (=> (= C (@ (@ product_Pair_nat_num (@ F X)) (@ G Y))) (not (@ (@ member5262025264175285858nt_int (@ (@ product_Pair_int_int X) Y)) R3))))))) (forall ((Prod produc7812382424243267045t_unit) (Prod2 produc7812382424243267045t_unit)) (=> (and (= (@ produc473321116828791851t_unit Prod) (@ produc473321116828791851t_unit Prod2)) (= (@ produc1126150082675451753t_unit Prod) (@ produc1126150082675451753t_unit Prod2))) (= Prod Prod2))) (forall ((A int) (B int) (A4 set_int) (B5 (-> int set_int))) (=> (@ (@ member5262025264175285858nt_int (@ (@ product_Pair_int_int A) B)) (@ (@ produc1453890548195736866nt_int A4) B5)) (@ (@ member_int A) A4))) (= bNF_re6718328864250387230um_num (lambda ((R6 (-> int code_integer Bool)) (S4 (-> num num Bool)) (F2 (-> int num)) (G3 (-> code_integer num))) (@ (@ ord_le6124364862034508274_num_o (@ (@ (@ bNF_Gr166583433173494904er_num F2) G3) R6)) S4))) (forall ((Rep (-> Bool Bool)) (Abs (-> Bool Bool)) (Rep2 (-> num Bool)) (Abs2 (-> Bool num)) (Rep3 (-> int nat)) (Abs3 (-> nat int)) (M (-> nat Bool)) (M1 (-> Bool Bool)) (M2 (-> nat Bool))) (=> (@ (@ (@ type_definition_o_o Rep) Abs) top_top_set_o) (=> (@ (@ (@ type_d9070036042389994064_num_o Rep2) Abs2) top_top_set_o) (=> (@ (@ (@ type_d7249847660678803242nt_nat Rep3) Abs3) top_top_set_nat) (=> (= (@ (@ comp_nat_num_int (@ (@ comp_o_num_nat Abs2) M)) Rep3) (@ (@ comp_o_num_int (@ (@ comp_o_num_o (@ (@ comp_o_num_o Abs2) M1)) Rep)) (@ (@ comp_nat_o_int (@ (@ comp_o_o_nat Abs) M2)) Rep3))) (= (@ (@ comp_o_o_nat M1) M2) M)))))) (forall ((X2 nat) (A4 set_nat) (B rat) (F (-> nat rat))) (=> (@ (@ member_nat X2) A4) (=> (= B (@ F X2)) (@ (@ member_rat B) (@ (@ image_nat_rat F) A4))))) (forall ((A4 set_nat) (X2 product_unit) (F (-> nat product_unit))) (=> (forall ((I4 nat)) (=> (@ (@ member_nat I4) A4) (@ (@ ord_le3221252021190050221t_unit X2) (@ F I4)))) (=> (forall ((Y product_unit)) (=> (forall ((I5 nat)) (=> (@ (@ member_nat I5) A4) (@ (@ ord_le3221252021190050221t_unit Y) (@ F I5)))) (@ (@ ord_le3221252021190050221t_unit Y) X2))) (= (@ comple2584293577114468500t_unit (@ (@ image_8730104196221521654t_unit F) A4)) X2)))) (= bit_take_bit_num (lambda ((N4 nat) (M5 num)) (@ (@ produc478579273971653890on_num (lambda ((A5 nat) (X4 num)) (@ (@ (@ case_nat_option_num none_num) (lambda ((O nat)) (@ (@ (@ (@ case_num_option_num (@ some_num one)) (lambda ((P3 num)) (@ (@ (@ case_o6005452278849405969um_num none_num) (lambda ((Q3 num)) (@ some_num (@ bit0 Q3)))) (@ (@ bit_take_bit_num O) P3)))) (lambda ((P3 num)) (@ some_num (@ (@ (@ case_option_num_num one) bit1) (@ (@ bit_take_bit_num O) P3))))) X4))) A5))) (@ (@ product_Pair_nat_num N4) M5)))) (forall ((F (-> nat nat))) (=> (@ finite_finite_nat top_top_set_nat) (=> (@ (@ inj_on_nat_nat F) top_top_set_nat) (= (@ (@ image_nat_nat F) top_top_set_nat) top_top_set_nat)))) (forall ((F (-> int int)) (A4 set_int) (Y3 int)) (=> (@ (@ inj_on_int_int F) A4) (=> (@ (@ member_int Y3) (@ (@ image_int_int F) A4)) (= (@ F (@ (@ (@ the_inv_into_int_int A4) F) Y3)) Y3)))) (forall ((F (-> product_unit product_unit)) (A4 set_Product_unit)) (= (= (@ (@ image_405062704495631173t_unit F) A4) bot_bo3957492148770167129t_unit) (= A4 bot_bo3957492148770167129t_unit))) (forall ((A4 set_int) (F (-> int int)) (B5 set_int)) (let ((_let_1 (@ image_int_int F))) (let ((_let_2 (@ _let_1 B5))) (let ((_let_3 (@ _let_1 A4))) (=> (not (= A4 bot_bot_set_int)) (=> (@ condit1735850657277959132ow_int _let_3) (=> (not (= B5 bot_bot_set_int)) (=> (@ condit1735850657277959132ow_int _let_2) (= (@ complete_Inf_Inf_int (@ _let_1 (@ (@ sup_sup_set_int A4) B5))) (@ (@ inf_inf_int (@ complete_Inf_Inf_int _let_3)) (@ complete_Inf_Inf_int _let_2))))))))))) (forall ((P2 (-> char rat product_unit))) (= (@ comple4687483117567863418t_unit (@ (@ image_2327579789247107822t_unit (lambda ((Y5 rat)) (@ comple2584293577114468500t_unit (@ (@ image_4337914935673063477t_unit (lambda ((X4 char)) (@ (@ P2 X4) Y5))) top_top_set_char)))) top_top_set_rat)) (@ comple2584293577114468500t_unit (@ (@ image_6940606515012899070t_unit (lambda ((X4 (-> rat char))) (@ comple4687483117567863418t_unit (@ (@ image_2327579789247107822t_unit (lambda ((Y5 rat)) (@ (@ P2 (@ X4 Y5)) Y5))) top_top_set_rat)))) top_top_set_rat_char)))) (forall ((I nat) (A4 set_nat) (F (-> nat product_unit)) (U product_unit)) (=> (@ (@ member_nat I) A4) (=> (@ (@ ord_le3221252021190050221t_unit (@ F I)) U) (@ (@ ord_le3221252021190050221t_unit (@ comple2584293577114468500t_unit (@ (@ image_8730104196221521654t_unit F) A4))) U)))) (forall ((F (-> list_nat product_prod_nat_nat)) (A4 set_list_nat) (B5 set_list_nat)) (let ((_let_1 (@ image_2795870212791037530at_nat F))) (=> (@ (@ inj_on7574789179980466158at_nat F) top_top_set_list_nat) (= (@ _let_1 (@ (@ inf_inf_set_list_nat A4) B5)) (@ (@ inf_in2572325071724192079at_nat (@ _let_1 A4)) (@ _let_1 B5)))))) (forall ((N set_nat)) (= (@ gcd_Gcd_int (@ (@ image_nat_int semiri1314217659103216013at_int) N)) (@ semiri1314217659103216013at_int (@ gcd_Gcd_nat N)))) _let_244 (forall ((Z2 Bool) (C (-> nat nat set_o)) (P product_prod_nat_nat)) (=> (@ (@ member_o Z2) (@ (@ produc59986286002894506_set_o C) P)) (not (forall ((X nat) (Y nat)) (=> (= P (@ (@ product_Pair_nat_nat X) Y)) (not (@ (@ member_o Z2) (@ (@ C X) Y)))))))) (forall ((F (-> nat product_unit)) (A4 set_nat) (X2 nat)) (let ((_let_1 (@ (@ image_8730104196221521654t_unit F) A4))) (=> (@ condit9161856309968323677t_unit _let_1) (=> (@ (@ member_nat X2) A4) (@ (@ ord_le3221252021190050221t_unit (@ comple2584293577114468500t_unit _let_1)) (@ F X2)))))) (= nat2 (@ (@ (@ map_fu2345160673673942751at_nat rep_Integ) id_nat) _let_2)) (forall ((T2 (-> nat Bool))) (= (@ (@ comp_o_o_nat id_o) T2) T2)) (forall ((G (-> num num)) (F (-> nat num)) (V (-> int nat))) (= (@ (@ comp_num_num_int G) (@ (@ comp_nat_num_int F) V)) (@ (@ comp_nat_num_int (@ (@ comp_num_num_nat G) F)) V))) (forall ((F (-> int int)) (A int) (B5 set_int)) (let ((_let_1 (@ image_int_int F))) (= (@ _let_1 (@ (@ insert_int A) B5)) (@ (@ insert_int (@ F A)) (@ _let_1 B5))))) (forall ((A int) (B Bool) (A4 set_int) (B5 (-> int set_o))) (= (@ (@ member4489920277610959864_int_o (@ (@ product_Pair_int_o A) B)) (@ (@ product_Sigma_int_o A4) B5)) (and (@ (@ member_int A) A4) (@ (@ member_o B) (@ B5 A))))) (forall ((I3 set_nat) (F (-> nat product_unit)) (C product_unit)) (=> (not (= I3 bot_bot_set_nat)) (=> (forall ((I4 nat)) (=> (@ (@ member_nat I4) I3) (@ (@ ord_le3221252021190050221t_unit (@ F I4)) C))) (= (= (@ comple2584293577114468500t_unit (@ (@ image_8730104196221521654t_unit F) I3)) C) (forall ((X4 nat)) (=> (@ (@ member_nat X4) I3) (= (@ F X4) C))))))) (forall ((B5 set_se7855581050983116737at_nat) (A4 set_Pr1261947904930325089at_nat)) (= (@ (@ inf_in2572325071724192079at_nat (@ comple5685304695842803022at_nat B5)) A4) (@ comple5685304695842803022at_nat (@ (@ image_3684629450409544005at_nat (lambda ((C5 set_Pr1261947904930325089at_nat)) (@ (@ inf_in2572325071724192079at_nat C5) A4))) B5)))) (forall ((F (-> Bool Bool)) (A4 set_o) (X2 Bool) (B5 set_o)) (=> (@ (@ inj_on_o_o F) A4) (=> (@ (@ member_o X2) (@ (@ image_o_o F) A4)) (=> (@ (@ ord_less_eq_set_o A4) B5) (@ (@ member_o (@ (@ (@ the_inv_into_o_o A4) F) X2)) B5))))) (forall ((I nat) (J4 nat) (R3 set_Pr1261947904930325089at_nat)) (=> (@ (@ member8440522571783428010at_nat (@ (@ product_Pair_nat_nat I) J4)) R3) (@ (@ member_nat I) (@ field_nat R3)))) _let_243 (forall ((X2 produc3843707927480180839at_nat) (Z5 set_Pr4329608150637261639at_nat) (X5 set_Pr4329608150637261639at_nat) (P2 (-> produc3843707927480180839at_nat Bool))) (=> (@ (@ member8757157785044589968at_nat X2) Z5) (=> (@ (@ ord_le1268244103169919719at_nat Z5) (@ collec6321179662152712658at_nat (lambda ((X4 produc3843707927480180839at_nat)) (and (@ (@ member8757157785044589968at_nat X4) X5) (@ P2 X4))))) (@ P2 X2)))) _let_241 (forall ((R1 (-> (-> produc8923325533196201883nteger produc8923325533196201883nteger) (-> produc8923325533196201883nteger produc8923325533196201883nteger) Bool)) (Abs1 (-> (-> produc8923325533196201883nteger produc8923325533196201883nteger) code_integer code_integer)) (Rep1 (-> (-> code_integer code_integer) produc8923325533196201883nteger produc8923325533196201883nteger)) (T1 (-> (-> produc8923325533196201883nteger produc8923325533196201883nteger) (-> code_integer code_integer) Bool)) (R22 (-> (-> code_integer code_integer) (-> code_integer code_integer) Bool)) (Abs22 (-> (-> code_integer code_integer) code_integer)) (Rep22 (-> code_integer code_integer code_integer)) (T22 (-> (-> code_integer code_integer) code_integer Bool))) (=> (@ (@ (@ (@ quotie8207154290130328982nteger R1) Abs1) Rep1) T1) (=> (@ (@ (@ (@ quotie9062115205763428814nteger R22) Abs22) Rep22) T22) (@ (@ (@ (@ quotie8803226531959296410nteger (@ (@ relcom458776940982682326nteger T1) (@ (@ relcom1820845089908643850nteger R22) (@ conver3229387634306789365nteger T1)))) (@ (@ comp_C7826480081638475456nteger Abs22) Abs1)) (@ (@ comp_C8797469213163452608nteger Rep1) Rep22)) (@ (@ relcom4829277440228594702nteger T1) T22))))) (forall ((Rep (-> nat nat)) (Abs (-> nat nat)) (A4 set_nat)) (=> (@ (@ (@ type_d6250493948777748686at_nat Rep) Abs) A4) (= (@ (@ image_nat_nat Rep) top_top_set_nat) A4))) (forall ((X1 nat) (X22 nat)) (= (@ product_snd_nat_nat (@ (@ product_Pair_nat_nat X1) X22)) X22)) (forall ((A int) (A4 set_int) (B5 (-> int set_nat))) (=> (@ (@ member_int A) A4) (@ (@ ord_less_eq_set_nat (@ B5 A)) (@ comple7399068483239264473et_nat (@ (@ image_int_set_nat B5) A4))))) (forall ((A4 (-> Bool set_nat))) (= (@ comple7399068483239264473et_nat (@ (@ image_o_set_nat A4) top_top_set_o)) (@ (@ sup_sup_set_nat (@ A4 true)) (@ A4 false)))) (forall ((F4 set_int) (H (-> int int))) (=> (@ finite_finite_int F4) (@ finite_finite_int (@ (@ image_int_int H) F4)))) (forall ((F (-> int 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_let_2 bot_bo3957492148770167129t_unit))))) (@ _let_1 A4)))))) (forall ((X2 nat) (Z5 set_nat) (X5 set_nat) (P2 (-> nat Bool))) (=> (@ (@ member_nat X2) Z5) (=> (@ (@ ord_less_eq_set_nat Z5) (@ collect_nat (lambda ((X4 nat)) (and (@ P2 X4) (@ (@ member_nat X4) X5))))) (@ P2 X2)))) (forall ((F (-> product_unit nat)) (A product_unit) (A4 set_Product_unit)) (let ((_let_1 (@ insert_Product_unit A))) (let ((_let_2 (@ inj_on8430439091780834860it_nat F))) (= (@ _let_2 (@ _let_1 A4)) (and (@ _let_2 A4) (not (@ (@ member_nat (@ F A)) (@ (@ image_875570014554754200it_nat F) (@ (@ minus_6452836326544984404t_unit A4) (@ _let_1 bot_bo3957492148770167129t_unit)))))))))) (forall ((X2 Bool) (A4 set_o) (F (-> Bool Bool))) (=> (@ (@ member_o X2) A4) (@ (@ member_o (@ F X2)) (@ (@ image_o_o F) A4)))) (= code_num_of_integer (lambda ((K5 code_integer)) (@ (@ (@ if_num (@ (@ ord_le3102999989581377725nteger K5) one_one_Code_integer)) one) (@ (@ produc7336495610019696514er_num (lambda ((L3 code_integer) (J code_integer)) (let ((_let_1 (@ code_num_of_integer L3))) (let ((_let_2 (@ (@ plus_plus_num _let_1) _let_1))) (@ (@ (@ if_num (= J zero_z3403309356797280102nteger)) _let_2) (@ (@ plus_plus_num _let_2) one)))))) (@ (@ code_divmod_integer K5) (@ numera6620942414471956472nteger (@ bit0 one))))))) (forall ((A4 set_o) (C set_int)) (let ((_let_1 (= A4 bot_bot_set_o))) (and (=> _let_1 (= (@ comple3628384868704368283et_int (@ (@ image_o_set_int (lambda ((Y5 Bool)) C)) A4)) top_top_set_int)) (=> (not _let_1) (= (@ comple3628384868704368283et_int (@ (@ image_o_set_int (lambda ((Y5 Bool)) C)) A4)) C))))) (forall ((X2 int) (Y3 int) (A4 set_int)) (= (@ (@ member5262025264175285858nt_int (@ (@ product_Pair_int_int X2) Y3)) (@ id_on_int A4)) (and (@ (@ member_int X2) A4) (= X2 Y3)))) (forall ((A4 set_nat) (C product_unit)) (let ((_let_1 (= A4 bot_bot_set_nat))) (and (=> (not _let_1) (= (@ comple2584293577114468500t_unit (@ (@ image_8730104196221521654t_unit (lambda ((Y5 nat)) C)) A4)) C)) (=> _let_1 (= (@ comple2584293577114468500t_unit (@ (@ image_8730104196221521654t_unit (lambda ((Y5 nat)) C)) A4)) top_top_Product_unit))))) (forall ((G (-> nat char)) (C3 set_nat) (B5 set_nat) (X2 nat)) (let ((_let_1 (@ (@ sup_sup_set_nat B5) (@ (@ insert_nat X2) bot_bot_set_nat)))) (=> (@ (@ inj_on_nat_char G) C3) (=> (@ (@ ord_less_eq_set_nat C3) _let_1) (@ (@ member_char_nat (lambda ((I2 char)) (@ (@ (@ if_nat (@ (@ member_char I2) (@ (@ image_nat_char G) C3))) (@ (@ (@ the_in9023905271258939222t_char C3) G) I2)) X2))) (@ (@ bNF_We935846424581991991ar_nat top_top_set_char) _let_1)))))) (forall ((Z2 nat) (C (-> nat num set_nat)) (A nat) (B num)) (let ((_let_1 (@ member_nat Z2))) (=> (@ _let_1 (@ (@ C A) B)) (@ _let_1 (@ (@ produc4130284055270567454et_nat C) (@ (@ product_Pair_nat_num A) B)))))) (forall ((X2 literal) (H heap_e7401611519738050253t_unit) (H2 heap_e7401611519738050253t_unit) (R ref_a)) (not (@ (@ (@ (@ heap_effect_ref_a (@ heap_raise_ref_a X2)) H) H2) R))) (forall ((A4 set_Pr1261947904930325089at_nat) (F set_nat)) (=> (not (= A4 bot_bo2099793752762293965at_nat)) (= (@ comple7806235888213564991et_nat (@ (@ image_15824709712370754et_nat (lambda ((I2 product_prod_nat_nat)) F)) A4)) F))) (forall ((F heap_Heap_ref_a) (H heap_e7401611519738050253t_unit) (H2 heap_e7401611519738050253t_unit) (A ref_a) (H3 heap_e7401611519738050253t_unit) (B ref_a)) (let ((_let_1 (@ (@ heap_effect_ref_a F) H))) (=> (@ (@ _let_1 H2) A) (=> (@ (@ _let_1 H3) B) (= A B))))) (= produc27273713700761075at_nat (lambda ((F2 (-> nat nat product_prod_nat_nat product_prod_nat_nat)) (P3 product_prod_nat_nat) (__flatten_var_0 product_prod_nat_nat)) (@ (@ (@ F2 (@ product_fst_nat_nat P3)) (@ product_snd_nat_nat P3)) __flatten_var_0))) (forall ((A4 set_nat) (F (-> nat rat))) (=> (not (@ finite_finite_nat A4)) (=> (@ finite_finite_rat (@ (@ image_nat_rat F) A4)) (exists ((X nat)) (and (not (@ finite_finite_nat (@ collect_nat (lambda ((A5 nat)) (and (= (@ F A5) (@ F X)) (@ (@ member_nat A5) A4)))))) (@ (@ member_nat X) A4)))))) (forall ((A4 set_nat) (F (-> nat Bool)) (B5 set_o)) (=> (forall ((X nat)) (=> (@ (@ member_nat X) A4) (@ (@ member_o (@ F X)) B5))) (@ (@ ord_less_eq_set_o (@ (@ image_nat_o F) A4)) B5))) (forall ((I Bool) (A4 set_o) (F (-> Bool product_unit)) (U product_unit)) (=> (@ (@ member_o I) A4) (=> (@ (@ ord_le3221252021190050221t_unit (@ F I)) U) (@ (@ ord_le3221252021190050221t_unit (@ comple2584293577114468500t_unit (@ (@ image_o_Product_unit F) A4))) U)))) (forall ((F (-> int int)) (G (-> int nat)) (Set set_nat)) (= (@ (@ vimage_int_int F) (@ (@ vimage_int_nat G) Set)) (@ (@ vimage_int_nat (@ (@ comp_int_nat_int G) F)) Set))) (forall ((I3 set_o) (F (-> Bool set_nat)) (X2 set_nat)) (=> (not (= I3 bot_bot_set_o)) (= (@ comple7806235888213564991et_nat (@ (@ image_o_set_nat (lambda ((I2 Bool)) (@ (@ inf_inf_set_nat (@ F I2)) X2))) I3)) (@ (@ inf_inf_set_nat (@ comple7806235888213564991et_nat (@ (@ image_o_set_nat F) I3))) X2)))) (forall ((M set_int) (N set_int) (F (-> int nat)) (G (-> int nat))) (=> (= M N) (=> (forall ((X int)) (=> (@ (@ member_int X) N) (= (@ F X) (@ G X)))) (= (@ (@ image_int_nat F) M) (@ (@ image_int_nat G) N))))) (forall ((C3 set_Product_unit) (A4 set_nat) (B5 (-> product_unit set_nat))) (let ((_let_1 (= C3 bot_bo3957492148770167129t_unit))) (and (=> (not _let_1) (= (@ comple7806235888213564991et_nat (@ (@ image_8173849991827986510et_nat (lambda ((X4 product_unit)) (@ (@ minus_minus_set_nat A4) (@ B5 X4)))) C3)) (@ (@ minus_minus_set_nat A4) (@ comple7399068483239264473et_nat (@ (@ image_8173849991827986510et_nat B5) C3))))) (=> _let_1 (= (@ comple7806235888213564991et_nat (@ (@ image_8173849991827986510et_nat (lambda ((X4 product_unit)) (@ (@ minus_minus_set_nat A4) (@ B5 X4)))) C3)) top_top_set_nat))))) (forall ((A4 set_nat) (C nat)) (=> (not (= A4 bot_bot_set_nat)) (= (@ complete_Inf_Inf_nat (@ (@ image_nat_nat (lambda ((X4 nat)) C)) A4)) C))) (forall ((F (-> int nat)) (A4 (-> Bool int)) (I3 set_o)) (let ((_let_1 (@ (@ image_o_int A4) I3))) (=> (@ order_mono_int_nat F) (=> (@ condit1735850657277959132ow_int _let_1) (=> (not (= I3 bot_bot_set_o)) (@ (@ ord_less_eq_nat (@ F (@ complete_Inf_Inf_int _let_1))) (@ complete_Inf_Inf_nat (@ (@ image_o_nat (lambda ((X4 Bool)) (@ F (@ A4 X4)))) I3)))))))) (forall ((A produc859450856879609959at_nat) (B produc859450856879609959at_nat) (R set_Pr553994874890374343at_nat)) (= (@ field_3044959742847878580at_nat (@ (@ insert5475735164933346999at_nat (@ (@ produc4662710985925991255at_nat A) B)) R)) (@ (@ sup_su718114333110466843at_nat (@ (@ insert5050368324300391991at_nat A) (@ (@ insert5050368324300391991at_nat B) bot_bo5327735625951526323at_nat))) (@ field_3044959742847878580at_nat R)))) (forall ((A4 (-> product_prod_nat_nat int Bool)) (B5 (-> nat nat Bool)) (F (-> product_prod_nat_nat nat)) (G (-> int nat)) (X5 set_Pr49084382684228242at_int) (X2 produc4196048018000912732at_int)) (=> (@ (@ (@ (@ bNF_re4555766996558763186at_nat A4) B5) F) G) (=> (@ (@ ord_le4604737605482584818at_int X5) (@ collec2851339944984316337at_int (@ produc6937227050501860053_int_o A4))) (=> (@ (@ member8394280151737582451at_int X2) X5) (@ (@ B5 (@ (@ (@ comp_P8635049891247748876at_int F) produc4619704898428564714at_int) X2)) (@ (@ (@ comp_i5627883460353289149at_int G) produc3064508320661873192at_int) X2)))))) (forall ((Sb (-> num num Bool)) (I (-> num num)) (X2 (-> int num)) (Y3 (-> int num))) (= (@ (@ (@ (@ bNF_re7626690874201225453um_num (lambda ((Y2 int) (Z int)) (= Y2 Z))) Sb) (@ (@ comp_num_num_int I) X2)) Y3) (@ (@ (@ (@ bNF_re7626690874201225453um_num (lambda ((Y2 int) (Z int)) (= Y2 Z))) (lambda ((X4 num) (__flatten_var_0 num)) (@ (@ Sb (@ I X4)) __flatten_var_0))) X2) Y3))) (forall ((F (-> nat int)) (A4 set_nat) (B5 set_nat)) (let ((_let_1 (@ image_nat_int F))) (=> (@ (@ inj_on_nat_int F) top_top_set_nat) (= (@ (@ ord_less_eq_set_int (@ _let_1 A4)) (@ _let_1 B5)) (@ (@ ord_less_eq_set_nat A4) B5))))) (forall ((A4 set_o) (B5 set_Product_unit)) (let ((_let_1 (@ produc411009820408249917t_unit A4))) (let ((_let_2 (@ image_4419268941131634678t_unit produc2875488738488844090t_unit))) (let ((_let_3 (= A4 bot_bot_set_o))) (and (=> _let_3 (= (@ _let_2 (@ _let_1 (lambda ((Uu Bool)) B5))) bot_bo3957492148770167129t_unit)) (=> (not _let_3) (= (@ _let_2 (@ _let_1 (lambda ((Uu Bool)) B5))) B5))))))) (forall ((G (-> nat nat)) (F (-> nat nat)) (A4 set_nat)) (=> (@ (@ inj_on_nat_nat (@ (@ comp_nat_nat_nat G) F)) A4) (@ (@ inj_on_nat_nat G) (@ (@ image_nat_nat F) A4)))) (forall ((A4 (-> nat set_o)) (I nat) (B5 set_o) (J3 set_nat)) (= (@ comple90263536869209701_set_o (@ (@ image_nat_set_o (@ (@ (@ fun_upd_nat_set_o A4) I) B5)) J3)) (@ (@ sup_sup_set_o (@ comple90263536869209701_set_o (@ (@ image_nat_set_o A4) (@ (@ minus_minus_set_nat J3) (@ (@ insert_nat I) bot_bot_set_nat))))) (@ (@ (@ if_set_o (@ (@ member_nat I) J3)) B5) bot_bot_set_o)))) (forall ((A nat) (B nat) (A4 set_Pr1261947904930325089at_nat) (F (-> nat nat int))) (=> (@ (@ member8440522571783428010at_nat (@ (@ product_Pair_nat_nat A) B)) A4) (@ (@ member_int (@ (@ F A) B)) (@ (@ image_2483585944268220136at_int (@ produc6840382203811409530at_int F)) A4)))) (forall ((B5 set_rat) (F (-> nat rat)) (A4 set_nat)) (= (@ (@ ord_less_eq_set_rat B5) (@ (@ image_nat_rat F) A4)) (exists ((AA set_nat)) (and (= B5 (@ (@ image_nat_rat F) AA)) (@ (@ ord_less_eq_set_nat AA) A4))))) (forall ((X2 set_Pr1261947904930325089at_nat) (Y3 set_Pr1261947904930325089at_nat)) (= (@ basic_484852565060450053at_nat (@ (@ produc2922128104949294807at_nat X2) Y3)) (@ (@ insert9200635055090092081at_nat Y3) bot_bo3083307316010499117at_nat))) (forall ((P2 (-> set_Pr4329608150637261639at_nat Bool)) (P set_Pr4329608150637261639at_nat) (Q2 (-> set_Pr4329608150637261639at_nat Bool)) (Q set_Pr4329608150637261639at_nat)) (let ((_let_1 (@ (@ produc9060074326276436823at_nat P) Q))) (=> (@ P2 P) (=> (@ Q2 Q) (and (@ P2 (@ produc4486455499028916547at_nat _let_1)) (@ Q2 (@ produc826222791318859909at_nat _let_1))))))) (forall ((F (-> int nat)) (A4 set_int) (X2 nat) (B5 set_int)) (=> (@ (@ inj_on_int_nat F) A4) (=> (@ (@ member_nat X2) (@ (@ image_int_nat F) A4)) (=> (@ (@ ord_less_eq_set_int A4) B5) (@ (@ member_int (@ (@ (@ the_inv_into_int_nat A4) F) X2)) B5))))) (forall ((F (-> nat Bool)) (A4 set_nat) (F3 (-> Bool Bool))) (=> (@ (@ inj_on_nat_o F) A4) (= (@ (@ inj_on_o_o F3) (@ (@ image_nat_o F) A4)) (@ (@ inj_on_nat_o (@ (@ comp_o_o_nat F3) F)) A4)))) (forall ((B nat) (B5 (-> nat set_nat)) (A4 set_nat)) (=> (@ (@ member_nat B) (@ comple7399068483239264473et_nat (@ (@ image_nat_set_nat B5) A4))) (not (forall ((X nat)) (=> (@ (@ member_nat X) A4) (not (@ (@ member_nat B) (@ B5 X)))))))) (forall ((A4 set_nat) (R set_Pr1261947904930325089at_nat) (A nat) (B nat)) (=> (@ (@ refl_on_nat A4) R) (=> (@ (@ member8440522571783428010at_nat (@ (@ product_Pair_nat_nat A) B)) R) (and (@ (@ member_nat A) A4) (@ (@ member_nat B) A4))))) (forall ((A4 set_int) (G (-> nat nat)) (B5 set_nat) (F (-> int nat))) (let ((_let_1 (@ (@ image_nat_nat G) B5))) (=> (not (= A4 bot_bot_set_int)) (=> (@ condit2214826472909112428ve_nat _let_1) (=> (forall ((N2 int)) (=> (@ (@ member_int N2) A4) (exists ((X6 nat)) (and (@ (@ member_nat X6) B5) (@ (@ ord_less_eq_nat (@ F N2)) (@ G X6)))))) (@ (@ ord_less_eq_nat (@ complete_Sup_Sup_nat (@ (@ image_int_nat F) A4))) (@ complete_Sup_Sup_nat _let_1))))))) (forall ((C3 set_o) (A4 (-> Bool set_o)) (B5 set_o)) (let ((_let_1 (= C3 bot_bot_set_o))) (and (=> _let_1 (= (@ comple90263536869209701_set_o (@ (@ image_o_set_o (lambda ((X4 Bool)) (@ (@ sup_sup_set_o (@ A4 X4)) B5))) C3)) bot_bot_set_o)) (=> (not _let_1) (= (@ comple90263536869209701_set_o (@ (@ image_o_set_o (lambda ((X4 Bool)) (@ (@ sup_sup_set_o (@ A4 X4)) B5))) C3)) (@ (@ sup_sup_set_o (@ comple90263536869209701_set_o (@ (@ image_o_set_o A4) C3))) B5)))))) _let_239 (forall ((B5 set_Pr958786334691620121nt_int) (A4 set_Pr958786334691620121nt_int) (P2 (-> product_prod_int_int Bool))) (let ((_let_1 (@ ord_le2843351958646193337nt_int B5))) (=> (@ _let_1 A4) (= (@ _let_1 (@ collec213857154873943460nt_int (lambda ((X4 product_prod_int_int)) (and (@ (@ member5262025264175285858nt_int X4) A4) (@ P2 X4))))) (forall ((X4 product_prod_int_int)) (=> (@ (@ member5262025264175285858nt_int X4) B5) (@ P2 X4))))))) (forall ((R3 (-> int int Bool)) (A (-> nat int)) (B (-> nat int))) (= (@ (@ (@ (@ bNF_re6650684261131312217nt_int (lambda ((Y2 nat) (Z nat)) (= Y2 Z))) R3) A) B) (exists ((Z4 (-> nat product_prod_int_int))) (and (@ (@ member6440191985751670089nt_int Z4) (@ collec8414850927317488011nt_int (lambda ((X4 (-> nat product_prod_int_int))) (@ (@ ord_le2843351958646193337nt_int (@ (@ image_2667626500211843362nt_int X4) top_top_set_nat)) (@ collec213857154873943460nt_int (@ produc4947309494688390418_int_o R3)))))) (= (@ (@ comp_P6653955642190706324nt_nat product_snd_int_int) Z4) B) (= (@ (@ comp_P6653955642190706324nt_nat product_fst_int_int) Z4) A))))) (forall ((C product_prod_int_o) (A4 set_int) (B5 (-> int set_o))) (=> (@ (@ member4489920277610959864_int_o C) (@ (@ product_Sigma_int_o A4) B5)) (not (forall ((X int)) (=> (@ (@ member_int X) A4) (forall ((Y Bool)) (=> (@ (@ member_o Y) (@ B5 X)) (not (= C (@ (@ product_Pair_int_o X) Y)))))))))) (= produc473321116828791851t_unit (@ produc4846201513286513633_ref_a (lambda ((X12 ref_a) (X23 heap_e7401611519738050253t_unit)) X12))) _let_237 (forall ((F (-> nat nat))) (= (@ (@ comp_nat_nat_nat F) id_nat) F)) (forall ((R3 (-> product_prod_nat_nat int Bool)) (S5 (-> nat nat Bool)) (R7 (-> int int Bool)) (S6 (-> nat nat Bool))) (@ (@ ord_le1714508135640884727_nat_o (@ (@ relcom4272412204205018633nt_nat (@ (@ bNF_re4555766996558763186at_nat R3) S5)) (@ (@ bNF_re3715656647883201625at_nat R7) S6))) (@ (@ bNF_re4555766996558763186at_nat (@ (@ relcom2949942408940504938nt_int R3) R7)) (@ (@ relcompp_nat_nat_nat S5) S6)))) (forall ((F (-> int nat)) (G (-> int int)) (X2 int) (Y3 int)) (let ((_let_1 (@ comp_int_nat_int F))) (= (@ _let_1 (@ (@ (@ fun_upd_int_int G) X2) Y3)) (@ (@ (@ fun_upd_int_nat (@ _let_1 G)) X2) (@ F Y3))))) (forall ((C3 set_nat) (A4 set_char) (B5 (-> nat set_char))) (let ((_let_1 (= C3 bot_bot_set_nat))) (and (=> (not _let_1) (= (@ comple7965528767983648192t_char (@ (@ image_nat_set_char (lambda ((X4 nat)) (@ (@ inf_inf_set_char A4) (@ B5 X4)))) C3)) (@ (@ inf_inf_set_char A4) (@ comple7965528767983648192t_char (@ (@ image_nat_set_char B5) C3))))) (=> _let_1 (= (@ comple7965528767983648192t_char (@ (@ image_nat_set_char (lambda ((X4 nat)) (@ (@ inf_inf_set_char A4) (@ B5 X4)))) C3)) top_top_set_char))))) (forall ((M (-> nat Bool)) (G (-> nat nat)) (X2 nat) (N (-> Bool Bool)) (H (-> nat Bool)) (F (-> Bool Bool))) (=> (= (@ M (@ G X2)) (@ N (@ H X2))) (= (@ (@ (@ comp_nat_o_nat (@ (@ comp_o_o_nat F) M)) G) X2) (@ (@ (@ comp_o_o_nat (@ (@ comp_o_o_o F) N)) H) X2)))) (forall ((A4 set_nat) (F (-> nat int)) (M int)) (=> (not (= A4 bot_bot_set_nat)) (=> (forall ((X nat)) (=> (@ (@ member_nat X) A4) (@ (@ ord_less_eq_int (@ F X)) M))) (@ (@ ord_less_eq_int (@ complete_Sup_Sup_int (@ (@ image_nat_int F) A4))) M)))) (forall ((A4 set_int) (M3 int) (F (-> int int))) (=> (forall ((X int)) (=> (@ (@ member_int X) A4) (@ (@ ord_less_eq_int M3) (@ F X)))) (@ condit1735850657277959132ow_int (@ (@ image_int_int F) A4)))) (forall ((F (-> nat int)) (A4 set_nat)) (= (@ comple3221217463730067765et_int (@ (@ image_nat_set_int (lambda ((X4 nat)) (@ (@ insert_int (@ F X4)) bot_bot_set_int))) A4)) (@ (@ image_nat_int F) A4))) (forall ((B5 (-> nat set_int))) (= (@ comple3628384868704368283et_int (@ (@ image_nat_set_int B5) bot_bot_set_nat)) top_top_set_int)) (forall ((S5 set_Pr1261947904930325089at_nat) (F (-> product_prod_nat_nat nat nat)) (X2 product_prod_nat_nat) (Y3 product_prod_nat_nat)) (let ((_let_1 (@ F Y3))) (let ((_let_2 (@ F X2))) (=> (@ (@ finite2110315540964234241at_nat S5) F) (=> (@ (@ member8440522571783428010at_nat X2) S5) (=> (@ (@ member8440522571783428010at_nat Y3) S5) (= (@ (@ comp_nat_nat_nat _let_1) _let_2) (@ (@ comp_nat_nat_nat _let_2) _let_1)))))))) (forall ((I3 set_o) (F (-> Bool set_nat)) (C set_nat)) (=> (not (= I3 bot_bot_set_o)) (=> (forall ((I4 Bool)) (=> (@ (@ member_o I4) I3) (@ (@ ord_less_eq_set_nat (@ F I4)) C))) (= (= (@ comple7806235888213564991et_nat (@ (@ image_o_set_nat F) I3)) C) (forall ((X4 Bool)) (=> (@ (@ member_o X4) I3) (= (@ F X4) C))))))) (forall ((I product_prod_nat_nat) (A4 set_Pr1261947904930325089at_nat) (F (-> product_prod_nat_nat set_nat)) (U set_nat)) (=> (@ (@ member8440522571783428010at_nat I) A4) (=> (@ (@ ord_less_eq_set_nat (@ F I)) U) (@ (@ ord_less_eq_set_nat (@ comple7806235888213564991et_nat (@ (@ image_15824709712370754et_nat F) A4))) U)))) (forall ((F (-> nat int)) (A4 set_nat)) (=> (@ (@ inj_on_nat_int F) A4) (= (@ finite_card_int (@ (@ image_nat_int F) A4)) (@ finite_card_nat A4)))) (forall ((Rb (-> nat int Bool)) (Sd (-> num nat Bool))) (@ (@ (@ (@ bNF_re5843449549409830101nt_nat (@ (@ bNF_re4155804983283621959um_nat Rb) Sd)) (@ (@ bNF_re3642433447925381491nt_nat (@ (@ bNF_re3713166177374151349at_int (lambda ((Y2 int) (Z int)) (= Y2 Z))) Rb)) (@ (@ bNF_re1845987051190671011um_nat (lambda ((Y2 int) (Z int)) (= Y2 Z))) Sd))) comp_nat_num_int) comp_int_nat_int)) (forall ((X2 Bool) (A4 set_o) (F (-> Bool product_unit))) (let ((_let_1 (@ (@ image_o_Product_unit F) A4))) (=> (@ (@ member_o X2) A4) (= (@ (@ insert_Product_unit (@ F X2)) _let_1) _let_1)))) (forall ((A4 set_Pr3280342998896498603um_nat) (R3 (-> nat num Bool))) (=> (@ (@ ord_le5164908622851071819um_nat A4) (@ collec1522684865789554998um_nat (@ produc6857965554392702720_nat_o (@ conversep_nat_num R3)))) (@ (@ ord_le8085105155179020875at_num (@ (@ image_7762062833379733445at_num (@ produc5219324331026901427at_num (lambda ((X4 num) (Y5 nat)) (@ (@ product_Pair_nat_num Y5) X4)))) A4)) (@ collec4100598399430923318at_num (@ produc4927758841916487424_num_o R3))))) (forall ((X2 Bool) (A4 set_o) (F (-> Bool nat)) (Y3 nat)) (let ((_let_1 (@ image_o_nat F))) (let ((_let_2 (@ (@ image_o_nat (@ (@ (@ fun_upd_o_nat F) X2) Y3)) A4))) (let ((_let_3 (@ (@ member_o X2) A4))) (and (=> (not _let_3) (= _let_2 (@ _let_1 A4))) (=> _let_3 (= _let_2 (@ (@ insert_nat Y3) (@ _let_1 (@ (@ minus_minus_set_o A4) (@ (@ insert_o X2) bot_bot_set_o))))))))))) (@ (@ _let_13 (@ produc27273713700761075at_nat (lambda ((X4 nat) (Y5 nat) (__flatten_var_0 product_prod_nat_nat)) (@ (@ produc2626176000494625587at_nat (lambda ((U3 nat) (V3 nat)) (@ (@ product_Pair_nat_nat (@ (@ plus_plus_nat X4) U3)) (@ (@ plus_plus_nat Y5) V3)))) __flatten_var_0)))) (@ produc27273713700761075at_nat (lambda ((X4 nat) (Y5 nat) (__flatten_var_0 product_prod_nat_nat)) (@ (@ produc2626176000494625587at_nat (lambda ((U3 nat) (V3 nat)) (@ (@ product_Pair_nat_nat (@ (@ plus_plus_nat X4) U3)) (@ (@ plus_plus_nat Y5) V3)))) __flatten_var_0)))) (forall ((F (-> rat rat)) (G (-> nat rat)) (R set_nat)) (= (@ (@ 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(=> (@ (@ ord_le996066559646421213eger_o (@ (@ relcom967497705283160040nteger R3) S5)) T3) (@ (@ ord_le129227817499904167_int_o (@ (@ relcom8911704206367525917at_int (@ (@ (@ bNF_vi2682369418337388893_int_o F) G) R3)) (@ (@ (@ bNF_vi33923956287962137eger_o G) H) S5))) (@ (@ (@ bNF_vi33923956287962137eger_o F) H) T3)))) (forall ((A4 set_o) (C product_unit)) (let ((_let_1 (= A4 bot_bot_set_o))) (and (=> _let_1 (= (@ (@ image_o_Product_unit (lambda ((X4 Bool)) C)) A4) bot_bo3957492148770167129t_unit)) (=> (not _let_1) (= (@ (@ image_o_Product_unit (lambda ((X4 Bool)) C)) A4) (@ (@ insert_Product_unit C) bot_bo3957492148770167129t_unit)))))) (forall ((I product_prod_nat_nat) (A4 set_Pr1261947904930325089at_nat) (U product_unit) (F (-> product_prod_nat_nat product_unit))) (let ((_let_1 (@ ord_le3221252021190050221t_unit U))) (=> (@ (@ member8440522571783428010at_nat I) A4) (=> (@ _let_1 (@ F I)) (@ _let_1 (@ comple4687483117567863418t_unit (@ (@ image_6169909464789311569t_unit F) A4))))))) (forall ((F (-> int nat)) (A4 set_int) (A int)) (let ((_let_1 (@ (@ image_int_nat F) A4))) (let ((_let_2 (@ complete_Inf_Inf_nat _let_1))) (=> (= (@ complete_Sup_Sup_nat _let_1) _let_2) (=> (@ condit2214826472909112428ve_nat _let_1) (=> (@ condit1738341127787009408ow_nat _let_1) (=> (@ (@ member_int A) A4) (= (@ F A) _let_2)))))))) (forall ((A (-> (-> code_integer code_integer) produc8923325533196201883nteger produc8923325533196201883nteger)) (B (-> code_integer code_integer code_integer)) (C (-> (-> code_integer code_integer) produc8923325533196201883nteger produc8923325533196201883nteger)) (D2 (-> code_integer code_integer code_integer))) (=> (= (@ (@ comp_C8797469213163452608nteger A) B) (@ (@ comp_C8797469213163452608nteger C) D2)) (forall ((V4 code_integer)) (= (@ A (@ B V4)) (@ C (@ D2 V4)))))) (forall ((A4 set_int) (B5 (-> int set_nat)) (C3 set_nat)) (=> (forall ((X int)) (=> (@ (@ member_int X) A4) (@ (@ ord_less_eq_set_nat (@ B5 X)) C3))) (@ (@ ord_less_eq_set_nat (@ 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type_d5945782884131516111t_char Rep) Abs) top_top_set_char) (= (@ (@ (@ bNF_vi9149698133064535136char_o F) Rep) (@ (@ bNF_Grp_int_char (@ collect_int P2)) H)) (@ (@ bNF_Grp_int_nat (@ collect_int (lambda ((X4 int)) (@ P2 (@ F X4))))) (@ (@ comp_int_nat_int (@ (@ comp_char_nat_int Abs) H)) F))))) (forall ((F (-> nat int)) (A nat) (B5 set_nat)) (let ((_let_1 (@ image_nat_int F))) (= (@ _let_1 (@ (@ insert_nat A) B5)) (@ (@ insert_int (@ F A)) (@ _let_1 B5))))) (forall ((A4 set_int) (G (-> int nat)) (B5 set_int) (F (-> int nat))) (let ((_let_1 (@ (@ image_int_nat G) B5))) (=> (not (= A4 bot_bot_set_int)) (=> (@ condit2214826472909112428ve_nat _let_1) (=> (forall ((N2 int)) (=> (@ (@ member_int N2) A4) (exists ((X6 int)) (and (@ (@ ord_less_eq_nat (@ F N2)) (@ G X6)) (@ (@ member_int X6) B5))))) (@ (@ ord_less_eq_nat (@ complete_Sup_Sup_nat (@ (@ image_int_nat F) A4))) (@ complete_Sup_Sup_nat _let_1))))))) (forall ((A4 set_nat) (B nat) (B5 (-> nat set_nat))) (=> (forall ((X nat)) (=> (@ (@ 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member8440522571783428010at_nat C) (@ (@ image_5831868185956570253at_nat (@ (@ produc5667422475138734578nt_nat F) G)) R3)) (not (forall ((X int) (Y int)) (=> (= C (@ (@ product_Pair_nat_nat (@ F X)) (@ G Y))) (not (@ (@ member5262025264175285858nt_int (@ (@ product_Pair_int_int X) Y)) R3))))))) (forall ((A int) (B int) (R3 set_Pr958786334691620121nt_int) (F (-> int nat)) (G (-> int nat))) (=> (@ (@ member5262025264175285858nt_int (@ (@ product_Pair_int_int A) B)) R3) (@ (@ member8440522571783428010at_nat (@ (@ product_Pair_nat_nat (@ F A)) (@ G B))) (@ (@ image_5831868185956570253at_nat (@ (@ produc5667422475138734578nt_nat F) G)) R3)))) (forall ((K4 set_int)) (= (@ gcd_Lcm_int (@ (@ image_int_int abs_abs_int) K4)) (@ gcd_Lcm_int K4))) (forall ((F heap_Heap_ref_a) (H heap_e7401611519738050253t_unit) (H2 heap_e7401611519738050253t_unit) (R ref_a) (G (-> ref_a heap_Heap_ref_a)) (H3 heap_e7401611519738050253t_unit) (R2 ref_a)) (=> (@ (@ (@ (@ heap_effect_ref_a F) H) H2) R) (=> (@ (@ (@ (@ 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G) I2)) X2))) (@ (@ bNF_We8730861560085513481t_unit top_top_set_o) _let_1)))))) (forall ((P2 (-> product_prod_nat_nat Bool)) (F (-> product_prod_nat_nat produc859450856879609959at_nat)) (G (-> product_prod_nat_nat produc859450856879609959at_nat)) (S5 set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ inf_in2572325071724192079at_nat S5))) (= (@ (@ image_1119892238107900587at_nat (lambda ((X4 product_prod_nat_nat)) (@ (@ (@ if_Pro4507677147265585453at_nat (@ P2 X4)) (@ F X4)) (@ G X4)))) S5) (@ (@ sup_su718114333110466843at_nat (@ (@ image_1119892238107900587at_nat F) (@ _let_1 (@ collec3392354462482085612at_nat P2)))) (@ (@ image_1119892238107900587at_nat G) (@ _let_1 (@ collec3392354462482085612at_nat (lambda ((X4 product_prod_nat_nat)) (not (@ P2 X4)))))))))) (forall ((I3 set_Pr1261947904930325089at_nat) (J3 set_Pr1261947904930325089at_nat) (C3 (-> product_prod_nat_nat set_Pr1261947904930325089at_nat))) (= (@ (@ produc2761391749766926216at_nat (@ (@ sup_su6327502436637775413at_nat I3) J3)) C3) (@ (@ sup_su718114333110466843at_nat (@ (@ produc2761391749766926216at_nat I3) C3)) (@ (@ produc2761391749766926216at_nat J3) C3)))) (forall ((F (-> nat nat product_prod_nat_nat Bool))) (= (@ produc3704529784387675049_nat_o (@ produc8739625826339149834_nat_o F)) F)) (forall ((A nat) (B nat)) (= (@ (@ image_nat_int semiri1314217659103216013at_int) (@ (@ set_or4665077453230672383an_nat A) B)) (@ (@ set_or4662586982721622107an_int (@ semiri1314217659103216013at_int A)) (@ semiri1314217659103216013at_int B)))) (forall ((X5 (-> int int Bool))) (= (@ fun_in_rel_int_int (@ collec213857154873943460nt_int (@ produc4947309494688390418_int_o X5))) X5)) _let_233 (forall ((B5 set_Product_unit) (A product_unit)) (= (@ (@ inf_inf_Product_unit (@ comple4687483117567863418t_unit B5)) A) (@ comple4687483117567863418t_unit (@ (@ image_405062704495631173t_unit (lambda ((B4 product_unit)) (@ (@ inf_inf_Product_unit B4) A))) B5)))) (forall ((A4 set_se7855581050983116737at_nat) (R set_Pr4329608150637261639at_nat) (A set_Pr1261947904930325089at_nat) (B set_Pr1261947904930325089at_nat)) (=> (@ (@ order_1968183844437341695at_nat A4) R) (=> (@ (@ member8757157785044589968at_nat (@ (@ produc2922128104949294807at_nat A) B)) R) (and (@ (@ member2643936169264416010at_nat B) A4) (@ (@ member2643936169264416010at_nat A) A4))))) (forall ((Prod product_prod_nat_nat)) (= Prod (@ (@ product_Pair_nat_nat (@ product_fst_nat_nat Prod)) (@ product_snd_nat_nat Prod)))) (forall ((F (-> int int)) (A4 set_int) (B5 set_int)) (let ((_let_1 (@ image_int_int F))) (=> (@ (@ ord_less_eq_set_int (@ _let_1 A4)) B5) (@ (@ ord_le4403425263959731960et_int (@ (@ image_524474410958335435et_int _let_1) (@ pow_int A4))) (@ pow_int B5))))) (forall ((R3 set_Pr958786334691620121nt_int) (S5 set_Pr958786334691620121nt_int)) (= (@ (@ ord_le6741204236512500942_int_o (lambda ((X4 int) (Y5 int)) (@ (@ member5262025264175285858nt_int (@ (@ product_Pair_int_int X4) Y5)) R3))) (lambda ((X4 int) (Y5 int)) (@ (@ 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(@ (@ member_rat A) A4)))) _let_232 (forall ((A4 set_int) (B5 set_int) (F (-> int int))) (=> (@ finite_finite_int A4) (=> (@ (@ ord_less_eq_set_int B5) (@ (@ image_int_int F) A4)) (@ finite_finite_int B5)))) _let_231 (forall ((A4 set_o) (B5 set_o) (F (-> Bool set_nat)) (G (-> Bool set_nat))) (=> (@ (@ ord_less_eq_set_o A4) B5) (=> (forall ((X Bool)) (=> (@ (@ member_o X) A4) (@ (@ ord_less_eq_set_nat (@ F X)) (@ G X)))) (@ (@ ord_less_eq_set_nat (@ comple7399068483239264473et_nat (@ (@ image_o_set_nat F) A4))) (@ comple7399068483239264473et_nat (@ (@ image_o_set_nat G) B5)))))) (forall ((S5 set_o) (F (-> Bool Bool Bool)) (X2 Bool) (Y3 Bool) (G (-> nat Bool))) (let ((_let_1 (@ comp_o_o_nat (@ F Y3)))) (let ((_let_2 (@ comp_o_o_nat (@ F X2)))) (=> (@ (@ finite7905178416053733328on_o_o S5) F) (=> (@ (@ member_o X2) S5) (=> (@ (@ member_o Y3) S5) (= (@ _let_1 (@ _let_2 G)) (@ _let_2 (@ _let_1 G))))))))) (forall ((F (-> nat nat product_prod_nat_nat product_prod_nat_nat)) (P 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(A4 set_nat)) (=> (@ (@ inj_on_nat_int F) A4) (= (@ finite_finite_int (@ (@ image_nat_int F) A4)) (@ finite_finite_nat A4)))) _let_230 (forall ((X2 heap_Heap_ref_a) (Y3 heap_Heap_ref_a)) (= (@ (@ (@ if_Heap_Heap_ref_a true) X2) Y3) X2)) (forall ((K int) (I3 set_int) (A4 (-> int product_unit))) (let ((_let_1 (@ comple2584293577114468500t_unit (@ (@ image_5846526143423701914t_unit A4) I3)))) (=> (@ (@ member_int K) I3) (= (@ (@ inf_inf_Product_unit (@ A4 K)) _let_1) _let_1)))) (forall ((H (-> Bool Bool)) (F (-> int int Bool)) (Prod product_prod_int_int)) (= (@ H (@ (@ produc4947309494688390418_int_o F) Prod)) (@ (@ produc4947309494688390418_int_o (lambda ((X12 int) (X23 int)) (@ H (@ (@ F X12) X23)))) Prod))) (forall ((C (-> nat nat product_prod_nat_nat Bool)) (P product_prod_nat_nat) (Z2 product_prod_nat_nat)) (=> (@ (@ (@ produc8739625826339149834_nat_o C) P) Z2) (not (forall ((X nat) (Y nat)) (=> (= P (@ (@ product_Pair_nat_nat X) Y)) (not (@ (@ (@ C X) Y) Z2))))))) (forall ((Inf (-> 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heap_e7401611519738050253t_unit num)) (X2 produc7812382424243267045t_unit)) (= (@ (@ produc1704413584773205829at_num F) (@ (@ produc7633249859560231688_ref_a G) X2)) (@ (@ product_Pair_nat_num (@ F (@ produc473321116828791851t_unit X2))) (@ G (@ produc1126150082675451753t_unit X2))))) (forall ((B int) (F (-> char int))) (=> (@ (@ member_int B) (@ (@ image_char_int F) top_top_set_char)) (not (forall ((X char)) (not (= B (@ F X))))))) (forall ((A4 set_int) (F (-> int int))) (=> (not (@ finite_finite_int A4)) (=> (@ finite_finite_int (@ (@ image_int_int F) A4)) (exists ((X int)) (and (@ (@ member_int X) A4) (not (@ finite_finite_int (@ collect_int (lambda ((A5 int)) (and (= (@ F A5) (@ F X)) (@ (@ member_int A5) A4))))))))))) (forall ((Y3 product_prod_nat_num)) (not (forall ((A3 nat) (B3 num)) (not (= Y3 (@ (@ product_Pair_nat_num A3) B3)))))) (forall ((B5 set_set_Product_unit) (X2 product_unit) (A4 set_Product_unit)) (let ((_let_1 (@ insert_Product_unit X2))) (=> (forall ((C2 set_Product_unit)) (=> (@ (@ member5877623283571906838t_unit C2) B5) (not (@ (@ member_Product_unit X2) C2)))) (= (@ (@ member5877623283571906838t_unit A4) (@ (@ image_4019945301284682565t_unit _let_1) B5)) (and (@ (@ member5877623283571906838t_unit (@ (@ minus_6452836326544984404t_unit A4) (@ _let_1 bot_bo3957492148770167129t_unit))) B5) (@ (@ member_Product_unit X2) A4)))))) (forall ((Z2 nat) (C (-> nat num set_nat)) (P product_prod_nat_num)) (=> (@ (@ member_nat Z2) (@ (@ produc4130284055270567454et_nat C) P)) (not (forall ((X nat) (Y num)) (=> (= P (@ (@ product_Pair_nat_num X) Y)) (not (@ (@ member_nat Z2) (@ (@ C X) Y)))))))) (forall ((Q product_prod_int_int) (F (-> int int product_prod_int_int)) (G (-> int int product_prod_int_int)) (P product_prod_int_int)) (=> (forall ((X int) (Y int)) (=> (= (@ (@ product_Pair_int_int X) Y) Q) (= (@ (@ F X) Y) (@ (@ G X) Y)))) (=> (= P Q) (= (@ (@ produc4245557441103728435nt_int F) P) (@ (@ produc4245557441103728435nt_int G) Q))))) (forall ((C3 set_nat) (A4 set_rat) (B5 (-> nat set_rat))) (let ((_let_1 (= C3 bot_bot_set_nat))) (and (=> (not _let_1) (= (@ comple4298007329820168263et_rat (@ (@ image_nat_set_rat (lambda ((X4 nat)) (@ (@ minus_minus_set_rat A4) (@ B5 X4)))) C3)) (@ (@ minus_minus_set_rat A4) (@ comple3890839924845867745et_rat (@ (@ image_nat_set_rat B5) C3))))) (=> _let_1 (= (@ comple4298007329820168263et_rat (@ (@ image_nat_set_rat (lambda ((X4 nat)) (@ (@ minus_minus_set_rat A4) (@ B5 X4)))) C3)) top_top_set_rat))))) (forall ((F (-> char char)) (G (-> char rat))) (=> (= (@ (@ image_char_char F) top_top_set_char) top_top_set_char) (=> (= (@ (@ image_char_rat G) top_top_set_char) top_top_set_rat) (= (@ (@ image_char_rat (@ (@ comp_char_rat_char G) F)) top_top_set_char) top_top_set_rat)))) (forall ((M (-> int nat)) (G (-> int int)) (X2 int) (N (-> nat nat)) (H (-> int nat)) (F (-> nat num))) (=> (= (@ M (@ G X2)) (@ N (@ H X2))) (= (@ (@ (@ comp_int_num_int (@ (@ comp_nat_num_int F) M)) G) X2) (@ (@ (@ comp_nat_num_int (@ (@ comp_nat_num_nat F) N)) H) X2)))) (forall ((X2 int) (A4 set_int) (F (-> int int))) (let ((_let_1 (@ (@ image_int_int F) A4))) (=> (@ (@ member_int X2) A4) (= (@ (@ insert_int (@ F X2)) _let_1) _let_1)))) (forall ((Z2 int) (C (-> nat nat set_int)) (P product_prod_nat_nat)) (=> (@ (@ member_int Z2) (@ (@ produc2011625207790711856et_int C) P)) (not (forall ((X nat) (Y nat)) (=> (= P (@ (@ product_Pair_nat_nat X) Y)) (not (@ (@ member_int Z2) (@ (@ C X) Y)))))))) (forall ((F (-> nat product_unit)) (A4 set_nat) (X2 nat) (U product_unit)) (let ((_let_1 (@ (@ image_8730104196221521654t_unit F) A4))) (=> (@ condit9161856309968323677t_unit _let_1) (=> (@ (@ member_nat X2) A4) (=> (@ (@ ord_le3221252021190050221t_unit (@ F X2)) U) (@ (@ ord_le3221252021190050221t_unit (@ comple2584293577114468500t_unit _let_1)) U)))))) (forall ((A4 set_o) (C set_rat)) (let ((_let_1 (= A4 bot_bot_set_o))) (and (=> (not _let_1) (= (@ comple4298007329820168263et_rat (@ (@ image_o_set_rat (lambda ((Y5 Bool)) C)) A4)) C)) (=> _let_1 (= (@ comple4298007329820168263et_rat (@ (@ image_o_set_rat (lambda ((Y5 Bool)) C)) A4)) top_top_set_rat))))) (forall ((F (-> nat num)) (G (-> int nat)) (R set_int)) (= (@ (@ image_nat_num F) (@ (@ image_int_nat G) R)) (@ (@ image_int_num (@ (@ comp_nat_num_int F) G)) R))) (forall ((F (-> nat Bool)) (G (-> int nat)) (A4 set_int) (X2 Bool)) (let ((_let_1 (@ (@ image_int_nat G) A4))) (=> (@ (@ inj_on_nat_o F) _let_1) (=> (@ (@ inj_on_int_nat G) A4) (=> (@ (@ member_o X2) (@ (@ image_nat_o F) _let_1)) (= (@ (@ (@ the_inv_into_int_o A4) (@ (@ comp_nat_o_int F) G)) X2) (@ (@ (@ comp_nat_int_o (@ (@ the_inv_into_int_nat A4) G)) (@ (@ the_inv_into_nat_o _let_1) F)) X2))))))) (forall ((A4 set_Pr4329608150637261639at_nat) (B5 set_Pr4329608150637261639at_nat) (F (-> produc3843707927480180839at_nat set_nat)) (G (-> produc3843707927480180839at_nat set_nat))) (=> (@ (@ ord_le1268244103169919719at_nat A4) B5) (=> (forall ((X produc3843707927480180839at_nat)) (=> (@ (@ member8757157785044589968at_nat X) A4) (@ (@ ord_less_eq_set_nat (@ F X)) (@ G X)))) (@ (@ ord_less_eq_set_nat (@ comple7399068483239264473et_nat (@ (@ image_3160451284896210088et_nat F) A4))) (@ comple7399068483239264473et_nat (@ (@ image_3160451284896210088et_nat G) B5)))))) _let_229 _let_228 _let_227 (forall ((F (-> int Bool)) (A4 set_int) (P2 (-> Bool Bool))) (= (@ collect_o (lambda ((X4 Bool)) (and (@ (@ member_o X4) (@ (@ image_int_o F) A4)) (@ P2 X4)))) (@ (@ image_int_o F) (@ collect_int (lambda ((X4 int)) (and (@ (@ member_int X4) A4) (@ P2 (@ F X4)))))))) (forall ((F (-> nat nat)) (G (-> int nat)) (L (-> int nat)) (H (-> int int))) (let ((_let_1 (@ comp_nat_nat_int F))) (=> (= (@ _let_1 G) L) (= (@ _let_1 (@ (@ comp_int_nat_int G) H)) (@ (@ comp_int_nat_int L) H))))) (forall ((F (-> set_nat set_nat)) (A4 set_set_nat)) (=> (@ order_1005506198798982270et_nat F) (@ (@ ord_less_eq_set_nat (@ F (@ comple7806235888213564991et_nat A4))) (@ comple7806235888213564991et_nat (@ (@ image_7916887816326733075et_nat F) A4))))) (forall ((I3 set_o) (C set_nat) (F (-> Bool set_nat))) (=> (not (= I3 bot_bot_set_o)) (=> (forall ((I4 Bool)) (=> (@ (@ member_o I4) I3) (@ (@ ord_less_eq_set_nat C) (@ F I4)))) (= (= (@ comple7399068483239264473et_nat (@ (@ image_o_set_nat F) I3)) C) (forall ((X4 Bool)) (=> (@ (@ member_o X4) I3) (= (@ F X4) C))))))) (forall ((A4 set_o) (C product_unit)) (=> (not (= A4 bot_bot_set_o)) (= (@ comple2584293577114468500t_unit (@ (@ image_o_Product_unit (lambda ((X4 Bool)) C)) A4)) C))) (forall ((F (-> nat rat)) (A4 set_nat) (B5 set_nat)) (let ((_let_1 (@ image_nat_rat F))) (=> (@ (@ inj_on_nat_rat F) top_top_set_nat) (= (@ _let_1 (@ (@ inf_inf_set_nat A4) B5)) (@ (@ inf_inf_set_rat (@ _let_1 A4)) (@ _let_1 B5)))))) (forall ((F (-> nat product_prod_nat_nat)) (A4 set_nat)) (=> (@ (@ inj_on5538052773655684606at_nat F) A4) (= (@ finite6177210948735845034at_nat (@ (@ image_5846123807819985514at_nat F) A4)) (@ finite_finite_nat A4)))) (forall ((R3 set_Pr4329608150637261639at_nat) (S5 set_Pr4329608150637261639at_nat)) (= (= (lambda ((X4 set_Pr1261947904930325089at_nat) (Y5 set_Pr1261947904930325089at_nat)) (@ (@ member8757157785044589968at_nat (@ (@ produc2922128104949294807at_nat X4) Y5)) R3)) (lambda ((X4 set_Pr1261947904930325089at_nat) (Y5 set_Pr1261947904930325089at_nat)) (@ (@ member8757157785044589968at_nat (@ (@ produc2922128104949294807at_nat X4) Y5)) S5))) (= R3 S5))) (forall ((F (-> product_prod_nat_nat Bool)) (A4 set_Pr1261947904930325089at_nat)) (=> (@ finite_finite_o (@ (@ image_3693632289388996572_nat_o F) A4)) (=> (not (@ finite6177210948735845034at_nat A4)) (exists ((X Bool)) (and (not (@ finite6177210948735845034at_nat (@ (@ vimage2444243245536687506_nat_o F) (@ (@ insert_o X) bot_bot_set_o)))) (@ (@ member_o X) (@ (@ image_3693632289388996572_nat_o F) A4))))))) (forall ((F (-> int product_unit)) (A4 set_int) (X2 int)) (let ((_let_1 (@ (@ image_5846526143423701914t_unit F) A4))) (=> (@ condit9161856309968323677t_unit _let_1) (=> (@ (@ member_int X2) A4) (@ (@ ord_le3221252021190050221t_unit (@ comple2584293577114468500t_unit _let_1)) (@ F X2)))))) (forall ((F (-> nat rat)) (A4 set_nat) (P2 (-> set_rat Bool))) (= (forall ((B6 set_rat)) (=> (and (@ finite_finite_rat B6) (@ (@ ord_less_eq_set_rat B6) (@ (@ image_nat_rat F) A4))) (@ P2 B6))) (forall ((B6 set_nat)) (=> (and (@ (@ ord_less_eq_set_nat B6) A4) (@ finite_finite_nat B6)) (@ P2 (@ (@ image_nat_rat F) B6)))))) (forall ((A nat) (P product_prod_nat_nat)) (= (= A (@ product_fst_nat_nat P)) (exists ((B4 nat)) (= P (@ (@ product_Pair_nat_nat A) B4))))) (forall ((G (-> (-> code_integer code_integer) code_integer code_integer)) (H (-> code_integer code_integer code_integer)) (R (-> code_integer code_integer code_integer)) (F (-> (-> code_integer code_integer) produc8923325533196201883nteger produc8923325533196201883nteger))) (=> (= (@ (@ comp_C2822359487432382964nteger G) H) R) (= (@ (@ comp_C8797469213163452608nteger (@ (@ comp_C3983183376822107068nteger F) G)) H) (@ (@ comp_C8797469213163452608nteger F) R)))) _let_226 (forall ((M (-> produc859450856879609959at_nat product_unit)) (A4 set_Pr8693737435421807431at_nat) (B5 set_Pr8693737435421807431at_nat)) (let ((_let_1 (@ image_8487516615895632747t_unit M))) (= (@ comple2584293577114468500t_unit (@ _let_1 (@ (@ sup_su718114333110466843at_nat A4) B5))) (@ (@ inf_inf_Product_unit (@ comple2584293577114468500t_unit (@ _let_1 A4))) (@ comple2584293577114468500t_unit (@ _let_1 B5)))))) (forall ((N3 nat)) (let ((_let_1 (@ suc N3))) (=> (@ (@ accp_nat nat_list_decode_rel) _let_1) (= (@ nat_list_decode _let_1) (@ (@ produc2761476792215241774st_nat (lambda ((X4 nat) (Y5 nat)) (@ (@ cons_nat X4) (@ nat_list_decode Y5)))) (@ nat_prod_decode N3)))))) _let_225 (forall ((G (-> rat int)) (F (-> nat rat)) (A4 set_nat)) (= (@ complete_Inf_Inf_int (@ (@ image_rat_int G) (@ (@ image_nat_rat F) A4))) (@ complete_Inf_Inf_int (@ (@ image_nat_int (@ (@ comp_rat_int_nat G) F)) A4)))) (forall ((F (-> int int Bool))) (= (@ produc175634133007206835_int_o (@ produc4947309494688390418_int_o F)) F)) (forall ((F (-> nat num)) (G (-> nat num)) (H (-> int nat))) (= (@ (@ comp_n8531277669757933902um_int (@ (@ bNF_co4716684370017810927um_num F) G)) H) (@ (@ bNF_co5088337930254655563um_num (@ (@ comp_nat_num_int F) H)) (@ (@ comp_nat_num_int G) H)))) (forall ((C3 set_Product_unit) (A4 set_nat) (B5 (-> product_unit set_nat))) (let ((_let_1 (@ (@ minus_minus_set_nat A4) (@ comple7399068483239264473et_nat (@ (@ image_8173849991827986510et_nat B5) C3))))) (let ((_let_2 (= C3 bot_bo3957492148770167129t_unit))) (and (=> (not _let_2) (= _let_1 (@ comple7806235888213564991et_nat (@ (@ image_8173849991827986510et_nat (lambda ((X4 product_unit)) (@ (@ minus_minus_set_nat A4) (@ B5 X4)))) C3)))) (=> _let_2 (= _let_1 A4)))))) (forall ((B5 set_set_nat) (X2 nat) (A4 set_nat)) (let ((_let_1 (@ insert_nat X2))) (=> (forall ((C2 set_nat)) (=> (@ (@ member_set_nat C2) B5) (not (@ (@ member_nat X2) C2)))) (= (@ (@ member_set_nat A4) (@ (@ image_7916887816326733075et_nat _let_1) B5)) (and (@ (@ member_nat X2) A4) (@ (@ member_set_nat (@ (@ minus_minus_set_nat A4) (@ _let_1 bot_bot_set_nat))) B5)))))) (forall ((R1 (-> int int Bool))) (@ (@ (@ (@ bNF_re3846787885862361009nt_num (lambda ((Y2 (-> nat num)) (Z (-> nat num))) (= Y2 Z))) (@ (@ bNF_re9099949428469764705nt_num (@ (@ bNF_re3715656647883201625at_nat R1) (lambda ((Y2 nat) (Z nat)) (= Y2 Z)))) (@ (@ bNF_re7626690874201225453um_num R1) (lambda ((Y2 num) (Z num)) (= Y2 Z))))) comp_nat_num_int) comp_nat_num_int)) _let_223 (forall ((S5 set_se7855581050983116737at_nat)) (= (@ comple1901448594430626575_nat_o (@ (@ image_5253903537071781336_nat_o (lambda ((I2 set_Pr1261947904930325089at_nat) (X4 product_prod_nat_nat)) (@ (@ member8440522571783428010at_nat X4) I2))) S5)) (lambda ((X4 product_prod_nat_nat)) (@ (@ member8440522571783428010at_nat X4) (@ comple5685304695842803022at_nat S5))))) (forall ((R3 (-> int int Bool)) (S5 (-> int code_integer Bool))) (=> (@ left_unique_int_int R3) (=> (@ left_u6795595883297946906nteger S5) (@ left_u6795595883297946906nteger (@ (@ relcom967497705283160040nteger R3) S5))))) (forall ((A4 set_nat) (B5 set_nat)) (= (= (@ (@ produc457027306803732586at_nat A4) (lambda ((Uu nat)) B5)) bot_bo2099793752762293965at_nat) (or (= B5 bot_bot_set_nat) (= A4 bot_bot_set_nat)))) (forall ((X2 Bool) (A4 set_o) (F (-> Bool Bool))) (let ((_let_1 (@ (@ image_o_o F) A4))) (=> (@ (@ member_o X2) A4) (= (@ (@ insert_o (@ F X2)) _let_1) _let_1)))) (forall ((A4 set_int) (R set_Pr958786334691620121nt_int) (A int) (B int)) (=> (@ (@ order_2886507596567047182on_int A4) R) (=> (@ (@ member5262025264175285858nt_int (@ (@ product_Pair_int_int A) B)) R) (and (@ (@ member_int B) A4) (@ (@ member_int A) A4))))) (forall ((A4 set_nat) (B5 set_nat)) (let ((_let_1 (@ produc457027306803732586at_nat A4))) (let ((_let_2 (@ image_2486076414777270412at_nat product_snd_nat_nat))) (let ((_let_3 (= A4 bot_bot_set_nat))) (and (=> (not _let_3) (= (@ _let_2 (@ _let_1 (lambda ((Uu nat)) B5))) B5)) (=> _let_3 (= (@ _let_2 (@ _let_1 (lambda ((Uu nat)) B5))) bot_bot_set_nat))))))) (forall ((A4 set_Pr4329608150637261639at_nat) (R set_Pr5564308138774400199at_nat) (A produc3843707927480180839at_nat)) (=> (@ (@ refl_o7446464703481863270at_nat A4) R) (=> (@ (@ member8757157785044589968at_nat A) A4) (@ (@ member6009668390874684176at_nat (@ (@ produc2335810615602371415at_nat A) A)) R)))) (forall ((F (-> product_unit Bool)) (A4 set_o)) (=> (= (@ (@ image_Product_unit_o F) top_to1996260823553986621t_unit) top_top_set_o) (= (= (@ (@ vimage8808348054653608838unit_o F) A4) bot_bo3957492148770167129t_unit) (= A4 bot_bot_set_o)))) (forall ((R3 set_Pr7459493094073627847at_nat) (S5 set_Pr7459493094073627847at_nat)) (= (@ (@ sup_su6164525874564267778_nat_o (lambda ((X4 set_Pr4329608150637261639at_nat) (Y5 set_Pr4329608150637261639at_nat)) (@ (@ member1466754251312161552at_nat (@ (@ produc9060074326276436823at_nat X4) Y5)) R3))) (lambda ((X4 set_Pr4329608150637261639at_nat) (Y5 set_Pr4329608150637261639at_nat)) (@ (@ member1466754251312161552at_nat (@ (@ produc9060074326276436823at_nat X4) Y5)) S5))) (lambda ((X4 set_Pr4329608150637261639at_nat) (Y5 set_Pr4329608150637261639at_nat)) (@ (@ member1466754251312161552at_nat (@ (@ produc9060074326276436823at_nat X4) Y5)) (@ (@ sup_su5395584912770621083at_nat R3) S5))))) (forall ((C3 set_Pr1261947904930325089at_nat) (A4 set_nat) (B5 (-> product_prod_nat_nat set_nat))) (let ((_let_1 (@ (@ inf_inf_set_nat A4) (@ comple7806235888213564991et_nat (@ (@ image_15824709712370754et_nat B5) C3))))) (let ((_let_2 (= C3 bot_bo2099793752762293965at_nat))) (and (=> (not _let_2) (= _let_1 (@ comple7806235888213564991et_nat (@ (@ image_15824709712370754et_nat (lambda ((X4 product_prod_nat_nat)) (@ (@ inf_inf_set_nat A4) (@ B5 X4)))) C3)))) (=> _let_2 (= _let_1 A4)))))) (forall ((I3 set_Pr1261947904930325089at_nat) (F (-> product_prod_nat_nat set_nat)) (X2 set_nat)) (=> (not (= I3 bot_bo2099793752762293965at_nat)) (=> (forall ((I4 product_prod_nat_nat)) (=> (@ (@ member8440522571783428010at_nat I4) I3) (= (@ F I4) X2))) (= (@ comple7399068483239264473et_nat (@ (@ image_15824709712370754et_nat F) I3)) X2)))) _let_222 (forall ((F (-> int int)) (V (-> char int))) (= (@ (@ image_char_int (@ (@ comp_int_int_char F) V)) top_top_set_char) (@ (@ image_int_int F) (@ (@ image_char_int V) top_top_set_char)))) (forall ((A4 set_o) (B5 (-> Bool set_nat))) (= (@ (@ image_8105710389281276538_nat_o product_fst_o_nat) (@ (@ product_Sigma_o_nat A4) B5)) (@ collect_o (lambda ((X4 Bool)) (and (not (= (@ B5 X4) bot_bot_set_nat)) (@ (@ member_o X4) A4)))))) (forall ((X1 ref_a) (X22 heap_e7401611519738050253t_unit)) (= (@ produc473321116828791851t_unit (@ (@ produc6544324848051098391t_unit X1) X22)) X1)) _let_221 (@ (@ inj_on7039184780174133295nt_int (lambda ((F2 (-> int int))) (@ collec213857154873943460nt_int (@ produc4947309494688390418_int_o (lambda ((X4 int) (Y5 int)) (= Y5 (@ F2 X4))))))) top_top_set_int_int) (forall ((F (-> product_prod_int_int int))) (= (@ produc8211389475949308722nt_int (@ produc1016772743285680337nt_int F)) F)) (forall ((S5 set_set_nat)) (= (@ comple8317665133742190828_nat_o (@ (@ image_set_nat_nat_o (lambda ((I2 set_nat) (X4 nat)) (@ (@ member_nat X4) I2))) S5)) (lambda ((X4 nat)) (@ (@ member_nat X4) (@ comple7399068483239264473et_nat S5))))) (forall ((F (-> rat nat)) (X2 rat)) (@ (@ member_nat (@ F X2)) (@ (@ image_rat_nat F) top_top_set_rat))) (forall ((Z2 int) (C (-> nat num set_int)) (A nat) (B num)) (let ((_let_1 (@ member_int Z2))) (=> (@ _let_1 (@ (@ C A) B)) (@ _let_1 (@ (@ produc9175805072616146554et_int C) (@ (@ product_Pair_nat_num A) B)))))) (forall ((R3 (-> int int Bool)) (S5 (-> product_prod_nat_nat product_prod_nat_nat Bool)) (R7 (-> int code_integer Bool)) (S6 (-> product_prod_nat_nat int Bool))) (@ (@ ord_le8615040745438789472_int_o (@ (@ relcom2127790875031262553er_int (@ (@ bNF_re8766404587435608311at_nat R3) S5)) (@ (@ bNF_re2828929484557863493at_int R7) S6))) (@ (@ bNF_re2828929484557863493at_int (@ (@ relcom967497705283160040nteger R3) R7)) (@ (@ relcom8911704206367525917at_int S5) S6)))) (forall ((F3 (-> int nat)) (F (-> int int)) (A4 set_int)) (=> (@ (@ inj_on_int_nat (@ (@ comp_int_nat_int F3) F)) A4) (@ (@ inj_on_int_int F) A4))) (forall ((A4 set_nat) (F (-> nat nat)) (G (-> nat nat))) (let ((_let_1 (@ (@ image_nat_nat G) A4))) (let ((_let_2 (@ (@ image_nat_nat F) A4))) (=> (not (= A4 bot_bot_set_nat)) (=> (@ condit2214826472909112428ve_nat _let_2) (=> (@ condit2214826472909112428ve_nat _let_1) (= (@ (@ sup_sup_nat (@ complete_Sup_Sup_nat _let_2)) (@ complete_Sup_Sup_nat _let_1)) (@ complete_Sup_Sup_nat (@ (@ image_nat_nat (lambda ((A5 nat)) (@ (@ sup_sup_nat (@ F A5)) (@ G A5)))) A4))))))))) (forall ((Rep (-> Bool char)) (Abs (-> char Bool)) (S5 (-> char 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(=> (@ left_total_int_int R7) (=> (@ left_unique_nat_nat S6) (=> (@ right_total_nat_nat S6) (@ (@ ord_le1714508135640884727_nat_o (@ (@ bNF_re4555766996558763186at_nat (@ (@ relcom2949942408940504938nt_int R3) R7)) (@ (@ relcompp_nat_nat_nat S5) S6))) (@ (@ relcom4272412204205018633nt_nat (@ (@ bNF_re4555766996558763186at_nat R3) S5)) (@ (@ bNF_re3715656647883201625at_nat R7) S6)))))))) (forall ((H (-> int int)) (F (-> int int int)) (Prod product_prod_int_int)) (= (@ H (@ (@ produc8211389475949308722nt_int F) Prod)) (@ (@ produc8211389475949308722nt_int (lambda ((X12 int) (X23 int)) (@ H (@ (@ F X12) X23)))) Prod))) (forall ((F (-> nat nat)) (G (-> nat nat)) (Set set_nat)) (= (@ (@ vimage_nat_nat F) (@ (@ vimage_nat_nat G) Set)) (@ (@ vimage_nat_nat (@ (@ comp_nat_nat_nat G) F)) Set))) (forall ((Prod produc7812382424243267045t_unit)) (= Prod (@ (@ produc6544324848051098391t_unit (@ produc473321116828791851t_unit Prod)) (@ produc1126150082675451753t_unit Prod)))) (forall ((Y3 Bool) (P2 (-> Bool Bool))) (=> (@ (@ member_o Y3) (@ (@ insert_o true) bot_bot_set_o)) (=> (forall ((X product_unit)) (@ P2 (@ product_Rep_unit X))) (@ P2 Y3)))) (forall ((A set_Pr1261947904930325089at_nat) (B set_Pr1261947904930325089at_nat)) (= (@ (@ member8757157785044589968at_nat (@ (@ produc2922128104949294807at_nat A) B)) id_set1796276052702428605at_nat) (= A B))) _let_220 (forall ((I3 set_Pr1261947904930325089at_nat) (A4 (-> product_prod_nat_nat set_nat))) (=> (@ finite6177210948735845034at_nat I3) (= (@ condit1738341127787009408ow_nat (@ comple7399068483239264473et_nat (@ (@ image_15824709712370754et_nat A4) I3))) (forall ((X4 product_prod_nat_nat)) (=> (@ (@ member8440522571783428010at_nat X4) I3) (@ condit1738341127787009408ow_nat (@ A4 X4))))))) (forall ((P2 (-> product_prod_int_int Bool)) (F (-> product_prod_int_int produc3843707927480180839at_nat)) (G (-> product_prod_int_int produc3843707927480180839at_nat)) (S5 set_Pr958786334691620121nt_int)) (let ((_let_1 (@ 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(-> nat product_prod_nat_nat))) (=> (@ finite_finite_nat A4) (=> (@ (@ ord_le3146513528884898305at_nat B5) (@ (@ image_5846123807819985514at_nat F) A4)) (@ finite6177210948735845034at_nat B5)))) (forall ((Z2 set_Pr4329608150637261639at_nat)) (= (@ (@ (@ comp_P8235817900121468292at_nat produc826222791318859909at_nat) (lambda ((X4 set_Pr4329608150637261639at_nat)) (@ (@ produc9060074326276436823at_nat X4) X4))) Z2) (@ id_set7849613212452405432at_nat Z2))) (forall ((Z2 Bool) (C (-> nat num set_o)) (A nat) (B num)) (let ((_let_1 (@ member_o Z2))) (=> (@ _let_1 (@ (@ C A) B)) (@ _let_1 (@ (@ produc836176033315069408_set_o C) (@ (@ product_Pair_nat_num A) B)))))) (forall ((P product_prod_int_int) (C (-> int int Bool))) (=> (forall ((A3 int) (B3 int)) (=> (= P (@ (@ product_Pair_int_int A3) B3)) (@ (@ C A3) B3))) (@ (@ produc4947309494688390418_int_o C) P))) (forall ((X5 set_Pr958786334691620121nt_int) (Y4 set_Pr958786334691620121nt_int)) (let ((_let_1 (@ ord_le2843351958646193337nt_int X5))) (=> (@ _let_1 Y4) (@ _let_1 (@ collec213857154873943460nt_int (@ produc4947309494688390418_int_o (@ fun_in_rel_int_int Y4))))))) (forall ((Inf (-> set_int int)) (A4 set_int)) (= (@ Inf (@ (@ image_int_int (lambda ((X4 int)) X4)) A4)) (@ Inf A4))) (forall ((F (-> char rat)) (G (-> rat int))) (=> (= (@ (@ image_char_rat F) top_top_set_char) top_top_set_rat) (=> (= (@ (@ image_rat_int G) top_top_set_rat) top_top_set_int) (= (@ (@ image_char_int (@ (@ comp_rat_int_char G) F)) top_top_set_char) top_top_set_int)))) (forall ((S5 set_se6260736226359567993nt_int)) (= (@ comple5770381748412298549_int_o (@ (@ image_4446226961036766042_int_o (lambda ((I2 set_Pr958786334691620121nt_int) (X4 int) (Y5 int)) (@ (@ member5262025264175285858nt_int (@ (@ product_Pair_int_int X4) Y5)) I2))) S5)) (lambda ((X4 int) (Y5 int)) (@ (@ member5262025264175285858nt_int (@ (@ product_Pair_int_int X4) Y5)) (@ comple1626965760690514720nt_int S5))))) (forall ((P produc3843707927480180839at_nat)) (exists ((X 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nat)) (A4 set_nat) (X2 nat) (B5 set_nat)) (=> (@ (@ inj_on_nat_nat F) A4) (=> (@ (@ member_nat X2) (@ (@ image_nat_nat F) A4)) (=> (@ (@ ord_less_eq_set_nat A4) B5) (@ (@ member_nat (@ (@ (@ the_inv_into_nat_nat A4) F) X2)) B5))))) _let_219 (forall ((Rep (-> nat char)) (Abs (-> char nat)) (S5 (-> char set_rat)) (M (-> nat char)) (F (-> nat rat)) (S6 (-> nat set_nat)) (G (-> nat nat))) (let ((_let_1 (@ comp_s8255929034757298889at_nat (@ image_nat_rat F)))) (let ((_let_2 (@ comp_c5738158305436223508at_nat S5))) (=> (@ (@ (@ type_d5945782884131516111t_char Rep) Abs) top_top_set_char) (=> (= (@ _let_2 M) (@ _let_1 S6)) (= (@ (@ comp_nat_set_rat_nat (@ _let_2 Rep)) (@ (@ comp_nat_nat_nat (@ (@ comp_char_nat_nat Abs) M)) G)) (@ _let_1 (@ (@ comp_nat_set_nat_nat S6) G)))))))) (forall ((X2 nat)) (@ (@ refl_on_nat (@ (@ insert_nat X2) bot_bot_set_nat)) (@ (@ insert8211810215607154385at_nat (@ (@ product_Pair_nat_nat X2) X2)) bot_bo2099793752762293965at_nat))) (forall ((I produc3843707927480180839at_nat) (J4 produc3843707927480180839at_nat) (R3 set_Pr5564308138774400199at_nat)) (=> (@ (@ member6009668390874684176at_nat (@ (@ produc2335810615602371415at_nat I) J4)) R3) (@ (@ member8757157785044589968at_nat I) (@ field_2862844103579723188at_nat R3)))) (forall ((R3 (-> nat nat Bool)) (A (-> nat nat)) (B (-> nat nat))) (= (@ (@ (@ (@ bNF_re5653821019739307937at_nat (lambda ((Y2 nat) (Z nat)) (= Y2 Z))) R3) A) B) (exists ((Z4 (-> nat product_prod_nat_nat))) (and (= (@ (@ comp_P1955610211387027840at_nat product_fst_nat_nat) Z4) A) (= (@ (@ comp_P1955610211387027840at_nat product_snd_nat_nat) Z4) B) (@ (@ member6743353555990375057at_nat Z4) (@ collec8718012497556192979at_nat (lambda ((X4 (-> nat product_prod_nat_nat))) (@ (@ ord_le3146513528884898305at_nat (@ (@ image_5846123807819985514at_nat X4) top_top_set_nat)) (@ collec3392354462482085612at_nat (@ produc6081775807080527818_nat_o R3)))))))))) (forall ((P2 (-> product_prod_int_int Bool)) (Q2 (-> 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(lambda ((X4 nat)) (and (@ P2 X4) (@ (@ member_nat X4) (@ (@ image_nat_nat F) A4))))) (@ (@ image_nat_nat F) (@ collect_nat (lambda ((X4 nat)) (and (@ (@ member_nat X4) A4) (@ P2 (@ F X4)))))))) (forall ((C product_prod_nat_num) (F (-> nat nat)) (G (-> num num)) (R3 set_Pr6200539531224447659at_num)) (=> (@ (@ member9148766508732265716at_num C) (@ (@ image_4925883905578568901at_num (@ (@ produc1665548884793878990um_num F) G)) R3)) (not (forall ((X nat) (Y num)) (=> (= C (@ (@ product_Pair_nat_num (@ F X)) (@ G Y))) (not (@ (@ member9148766508732265716at_num (@ (@ product_Pair_nat_num X) Y)) R3))))))) (forall ((X2 product_prod_nat_nat)) (@ (@ total_3592101749530773125at_nat (@ (@ insert8211810215607154385at_nat X2) bot_bo2099793752762293965at_nat)) (@ (@ insert5050368324300391991at_nat (@ (@ produc6161850002892822231at_nat X2) X2)) bot_bo5327735625951526323at_nat))) (forall ((A set_nat) (B5 set_set_nat)) (let ((_let_1 (@ sup_sup_set_nat A))) (= (@ _let_1 (@ 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I3)))))) (forall ((X2 int) (Y3 int)) (= (@ product_swap_int_int (@ (@ product_Pair_int_int X2) Y3)) (@ (@ product_Pair_int_int Y3) X2))) (forall ((P2 (-> product_prod_int_int Bool)) (Q2 (-> product_prod_int_int Bool))) (= (@ collec7447955092554649554nt_int (@ produc1676490119946744748_int_o (lambda ((A5 product_prod_int_int) (B4 product_prod_int_int)) (and (@ P2 A5) (@ Q2 B4))))) (@ (@ produc245848125267896712nt_int (@ collec213857154873943460nt_int P2)) (lambda ((Uu product_prod_int_int)) (@ collec213857154873943460nt_int Q2))))) (forall ((A nat) (A4 set_nat) (B Bool) (B5 set_o)) (let ((_let_1 (@ product_Sigma_nat_o (@ (@ insert_nat A) A4)))) (= (@ _let_1 (lambda ((Uu nat)) (@ (@ insert_o B) B5))) (@ (@ insert2233377226759017069_nat_o (@ (@ product_Pair_nat_o A) B)) (@ (@ sup_su503371503184139039_nat_o (@ (@ product_Sigma_nat_o A4) (lambda ((Uu nat)) (@ (@ insert_o B) B5)))) (@ _let_1 (lambda ((Uu nat)) B5))))))) (forall ((F (-> Bool product_unit)) (A4 set_o)) (=> (@ 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produc8250590009387450446nt_nat (@ (@ comp_o_o_nat F) H)) (@ (@ comp_int_nat_int G) I)))) (forall ((N3 nat)) (= (@ set_ord_atMost_nat (@ suc N3)) (@ (@ insert_nat zero_zero_nat) (@ (@ image_nat_nat suc) (@ set_ord_atMost_nat N3))))) (forall ((B nat) (F (-> nat nat)) (X2 nat) (C num) (G (-> nat num)) (A4 set_nat)) (=> (= B (@ F X2)) (=> (= C (@ G X2)) (=> (@ (@ member_nat X2) A4) (@ (@ member9148766508732265716at_num (@ (@ product_Pair_nat_num B) C)) (@ (@ (@ bNF_Gr3875488559241464598at_num A4) F) G)))))) (forall ((B5 (-> nat Bool Bool)) (C3 (-> nat Bool Bool)) (A4 (-> nat nat Bool))) (let ((_let_1 (@ bNF_re1402873238235875719_nat_o A4))) (@ (@ (@ (@ bNF_re3930744952143938759_nat_o (@ (@ bNF_re439150893885221597_nat_o B5) C3)) (@ (@ bNF_re7744223787735169245_nat_o (@ _let_1 B5)) (@ _let_1 C3))) comp_nat_nat_nat) comp_o_o_nat))) (forall ((A4 (-> product_prod_nat_nat int Bool)) (B5 (-> (-> product_prod_nat_nat Bool) (-> int Bool) Bool)) (F (-> product_prod_nat_nat product_prod_nat_nat Bool)) (G (-> int int Bool))) (=> (forall ((X product_prod_nat_nat) (Y int)) (=> (@ (@ A4 X) Y) (@ (@ B5 (@ F X)) (@ G Y)))) (@ (@ (@ (@ bNF_re717283939379294677_int_o A4) B5) F) G))) (forall ((R1 (-> product_prod_nat_nat int Bool)) (R22 (-> product_prod_nat_nat int Bool)) (P2 (-> product_prod_nat_nat product_prod_nat_nat Bool)) (Q2 (-> int int Bool)) (A produc4196048018000912732at_int) (A4 set_Pr49084382684228242at_int) (B produc4196048018000912732at_int) (B5 set_Pr49084382684228242at_int)) (=> (@ (@ (@ (@ bNF_re717283939379294677_int_o R1) (@ (@ bNF_re6644619430987730960nt_o_o R22) (lambda ((Y2 Bool) (Z Bool)) (= Y2 Z)))) P2) Q2) (=> (@ (@ member8394280151737582451at_int A) A4) (=> (@ (@ member8394280151737582451at_int B) B5) (=> (@ (@ ord_le4604737605482584818at_int A4) (@ collec2851339944984316337at_int (@ produc6937227050501860053_int_o R1))) (=> (@ (@ ord_le4604737605482584818at_int B5) (@ collec2851339944984316337at_int (@ produc6937227050501860053_int_o R22))) (= (@ (@ P2 (@ produc4619704898428564714at_int A)) (@ produc4619704898428564714at_int B)) (@ (@ Q2 (@ produc3064508320661873192at_int A)) (@ produc3064508320661873192at_int B))))))))) _let_218 (forall ((P2 (-> nat Bool)) (F (-> nat produc3843707927480180839at_nat)) (G (-> nat produc3843707927480180839at_nat)) (S5 set_nat)) (let ((_let_1 (@ inf_inf_set_nat S5))) (= (@ (@ image_2499013659892586576at_nat (lambda ((X4 nat)) (@ (@ (@ if_Pro3594990065127090477at_nat (@ P2 X4)) (@ F X4)) (@ G X4)))) S5) (@ (@ sup_su5525570899277871387at_nat (@ (@ image_2499013659892586576at_nat F) (@ _let_1 (@ collect_nat P2)))) (@ (@ image_2499013659892586576at_nat G) (@ _let_1 (@ collect_nat (lambda ((X4 nat)) (not (@ P2 X4)))))))))) (forall ((A4 set_Pr4329608150637261639at_nat) (B5 set_se5479201105039950375at_nat)) (let ((_let_1 (@ sup_su5525570899277871387at_nat A4))) (= (@ _let_1 (@ comple6751905152567503566at_nat B5)) (@ comple6751905152567503566at_nat (@ (@ image_4303274092540115909at_nat _let_1) B5))))) (forall ((A4 set_int) (F (-> int product_unit)) (U product_unit)) (=> (forall ((I4 int)) (=> (@ (@ member_int I4) A4) (@ (@ ord_le3221252021190050221t_unit (@ F I4)) U))) (@ (@ ord_le3221252021190050221t_unit (@ comple4687483117567863418t_unit (@ (@ image_5846526143423701914t_unit F) A4))) U))) (forall ((A4 set_o) (F (-> Bool product_prod_nat_nat))) (=> (not (@ finite_finite_o A4)) (=> (@ finite6177210948735845034at_nat (@ (@ image_3855930084881510382at_nat F) A4)) (exists ((X Bool)) (and (@ (@ member_o X) A4) (not (@ finite_finite_o (@ collect_o (lambda ((A5 Bool)) (and (= (@ F A5) (@ F X)) (@ (@ member_o A5) A4))))))))))) (forall ((I3 set_nat) (A4 (-> nat set_nat)) (B5 (-> nat set_nat))) (let ((_let_1 (@ produc457027306803732586at_nat I3))) (= (@ _let_1 (lambda ((I2 nat)) (@ (@ sup_sup_set_nat (@ A4 I2)) (@ B5 I2)))) (@ (@ sup_su6327502436637775413at_nat (@ _let_1 A4)) (@ _let_1 B5))))) (forall ((N3 nat)) (= (@ (@ inf_in2572325071724192079at_nat bNF_Ca8665028551170535155natLeq) (@ (@ produc457027306803732586at_nat (@ collect_nat (lambda ((X4 nat)) (@ (@ ord_less_nat X4) N3)))) (lambda ((Uu nat)) (@ collect_nat (lambda ((X4 nat)) (@ (@ ord_less_nat X4) N3)))))) (@ collec3392354462482085612at_nat (@ produc6081775807080527818_nat_o (lambda ((X4 nat) (Y5 nat)) (and (@ (@ ord_less_nat Y5) N3) (@ (@ ord_less_eq_nat X4) Y5) (@ (@ ord_less_nat X4) N3))))))) (forall ((F (-> nat set_nat)) (A nat) (A4 set_nat)) (let ((_let_1 (@ image_nat_set_nat F))) (= (@ comple7399068483239264473et_nat (@ _let_1 (@ (@ insert_nat A) A4))) (@ (@ sup_sup_set_nat (@ F A)) (@ comple7399068483239264473et_nat (@ _let_1 A4)))))) (forall ((A4 set_Pr4329608150637261639at_nat) (U product_unit) (F (-> produc3843707927480180839at_nat product_unit))) (=> (forall ((I4 produc3843707927480180839at_nat)) (=> (@ (@ member8757157785044589968at_nat I4) A4) (@ (@ ord_le3221252021190050221t_unit U) (@ F I4)))) (@ (@ ord_le3221252021190050221t_unit U) (@ comple2584293577114468500t_unit (@ (@ image_7082456443403096939t_unit F) A4))))) (forall ((C3 set_Product_unit) (A4 set_Pr1261947904930325089at_nat) (B5 (-> product_unit set_Pr1261947904930325089at_nat))) (let ((_let_1 (@ (@ inf_in2572325071724192079at_nat A4) (@ comple1930127330929219688at_nat (@ (@ image_3617315916088684441at_nat B5) C3))))) (let ((_let_2 (= C3 bot_bo3957492148770167129t_unit))) (and (=> (not _let_2) (= _let_1 (@ comple1930127330929219688at_nat (@ (@ image_3617315916088684441at_nat (lambda ((X4 product_unit)) (@ (@ inf_in2572325071724192079at_nat A4) (@ B5 X4)))) C3)))) (=> _let_2 (= _let_1 A4)))))) (forall ((F (-> set_Pr1261947904930325089at_nat set_Pr1261947904930325089at_nat Bool)) (A set_Pr1261947904930325089at_nat) (B set_Pr1261947904930325089at_nat)) (=> (@ (@ F A) B) (@ (@ produc410239310623530412_nat_o F) (@ (@ produc2922128104949294807at_nat A) B)))) (forall ((R22 (-> nat int Bool)) (R32 (-> num nat Bool)) (R1 (-> int int Bool))) (@ (@ (@ (@ bNF_re5843449549409830101nt_nat (@ (@ bNF_re4155804983283621959um_nat R22) R32)) (@ (@ bNF_re3642433447925381491nt_nat (@ (@ bNF_re3713166177374151349at_int R1) R22)) (@ (@ bNF_re1845987051190671011um_nat R1) R32))) comp_nat_num_int) comp_int_nat_int)) (forall ((A4 set_nat) (B5 (-> nat set_nat))) (=> (@ finite_finite_nat A4) (=> (forall ((A3 nat)) (=> (@ (@ member_nat A3) A4) (@ finite_finite_nat (@ B5 A3)))) (@ finite_finite_nat (@ comple7399068483239264473et_nat (@ (@ image_nat_set_nat B5) A4)))))) _let_217 (forall ((G1 (-> nat nat)) (G22 (-> Bool Bool)) (F1 (-> nat nat)) (F22 (-> nat Bool)) (V product_prod_nat_nat)) (= (@ (@ (@ produc2001155298098703512at_o_o G1) G22) (@ (@ (@ produc4787215299218314158_nat_o F1) F22) V)) (@ (@ (@ produc4787215299218314158_nat_o (@ (@ comp_nat_nat_nat G1) F1)) (@ (@ comp_o_o_nat G22) F22)) V))) (forall ((B nat) (F (-> nat nat)) (X2 nat)) (=> (= B (@ F X2)) (@ (@ member_nat B) (@ (@ image_nat_nat F) top_top_set_nat)))) (forall ((A nat) (B num) (A4 set_Pr6200539531224447659at_num) (F (-> nat num nat))) (=> (@ (@ member9148766508732265716at_num (@ (@ product_Pair_nat_num A) B)) A4) (@ (@ member_nat (@ (@ F A) B)) (@ (@ image_4504471508743443926um_nat (@ produc4973203077627929192um_nat F)) A4)))) (forall ((R3 (-> int code_integer Bool)) (R7 (-> code_integer int Bool)) (S5 (-> num num Bool)) (S6 (-> num num Bool))) (=> (@ left_u6795595883297946906nteger R3) (=> (@ right_7281159819619925802nteger R3) (=> (@ right_7836862732553076961er_int R7) (=> (@ left_t1735413524555719857er_int R7) (@ (@ ord_le4541714130423454556_num_o (@ (@ bNF_re7626690874201225453um_num (@ (@ relcom328798225758222312er_int R3) R7)) (@ (@ relcompp_num_num_num S5) S6))) (@ (@ relcom7779292856395800339nt_num (@ (@ bNF_re6718328864250387230um_num R3) S5)) (@ (@ bNF_re8313794964846168862um_num R7) S6)))))))) (forall ((I3 set_Pr1261947904930325089at_nat) (A4 (-> product_prod_nat_nat set_Pr1261947904930325089at_nat)) (B5 (-> product_prod_nat_nat set_Pr1261947904930325089at_nat))) (let ((_let_1 (@ produc2761391749766926216at_nat I3))) (= (@ _let_1 (lambda ((I2 product_prod_nat_nat)) (@ (@ sup_su6327502436637775413at_nat (@ A4 I2)) (@ B5 I2)))) (@ (@ sup_su718114333110466843at_nat (@ _let_1 A4)) (@ _let_1 B5))))) (forall ((S5 set_Co726186806682698383nteger) (F (-> (-> code_integer code_integer) produc8923325533196201883nteger produc8923325533196201883nteger)) (G (-> code_integer code_integer code_integer)) (R3 set_Code_integer)) (=> (@ (@ finite6756937295472016048nteger S5) F) (=> (@ (@ ord_le348599935723844335nteger (@ (@ image_2177946750938214461nteger G) top_to4645266643341252675nteger)) S5) (@ (@ finite366418920864469932nteger R3) (@ (@ comp_C8797469213163452608nteger F) G))))) _let_216 (forall ((F (-> nat rat)) (A4 set_nat) (P2 (-> set_rat Bool))) (= (exists ((B6 set_rat)) (and (@ P2 B6) (@ (@ ord_less_eq_set_rat B6) (@ (@ image_nat_rat F) A4)) (@ finite_finite_rat B6))) (exists ((B6 set_nat)) (and (@ (@ ord_less_eq_set_nat B6) A4) (@ P2 (@ (@ image_nat_rat F) B6)) (@ finite_finite_nat B6))))) (forall ((C3 set_o) (A4 set_Pr8693737435421807431at_nat) (B5 (-> Bool set_Pr8693737435421807431at_nat))) (let ((_let_1 (@ (@ sup_su718114333110466843at_nat A4) (@ comple2748534634209756852at_nat (@ (@ image_8493167801588156084at_nat B5) C3))))) (let ((_let_2 (= C3 bot_bot_set_o))) (and (=> _let_2 (= _let_1 A4)) (=> (not _let_2) (= _let_1 (@ comple2748534634209756852at_nat (@ (@ image_8493167801588156084at_nat (lambda ((X4 Bool)) (@ (@ sup_su718114333110466843at_nat A4) (@ B5 X4)))) C3)))))))) (forall ((C3 set_Pr4329608150637261639at_nat) (A4 (-> produc3843707927480180839at_nat set_Pr1261947904930325089at_nat)) (B5 set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ (@ inf_in2572325071724192079at_nat (@ comple1930127330929219688at_nat (@ (@ image_7979982168039674559at_nat A4) C3))) B5))) (let ((_let_2 (= C3 bot_bo228742789529271731at_nat))) (and (=> _let_2 (= _let_1 B5)) (=> (not _let_2) (= _let_1 (@ comple1930127330929219688at_nat (@ (@ image_7979982168039674559at_nat (lambda ((X4 produc3843707927480180839at_nat)) (@ (@ inf_in2572325071724192079at_nat (@ A4 X4)) B5))) C3)))))))) (forall ((A set_Pr4329608150637261639at_nat) (B set_Pr4329608150637261639at_nat)) (=> (@ (@ member1466754251312161552at_nat (@ (@ produc9060074326276436823at_nat A) B)) id_set4888139568991089827at_nat) (= A B))) (forall ((F (-> int nat)) (A4 set_nat)) (=> (@ (@ inj_on_int_nat F) top_top_set_int) (=> (@ (@ ord_less_eq_set_nat A4) (@ (@ image_int_nat F) top_top_set_int)) (= (@ finite_card_int (@ (@ vimage_int_nat F) A4)) (@ finite_card_nat A4))))) (forall ((A4 set_o) (U product_unit) (F (-> Bool product_unit))) (=> (forall ((I4 Bool)) (=> (@ (@ member_o I4) A4) (@ (@ ord_le3221252021190050221t_unit U) (@ F I4)))) (@ (@ ord_le3221252021190050221t_unit U) (@ comple2584293577114468500t_unit (@ (@ image_o_Product_unit F) A4))))) (forall ((X2 Bool) (A4 set_o) (B Bool) (F (-> Bool Bool))) (=> (@ (@ member_o X2) A4) (=> (= B (@ F X2)) (@ (@ member_o B) (@ (@ image_o_o F) A4))))) (forall ((F (-> rat rat)) (Y3 rat)) (=> (= (@ (@ image_rat_rat F) top_top_set_rat) top_top_set_rat) (exists ((X rat)) (= Y3 (@ F X))))) (forall ((C3 set_nat) (A4 (-> nat set_rat)) (B5 set_rat)) (let ((_let_1 (= C3 bot_bot_set_nat))) (and (=> _let_1 (= (@ comple4298007329820168263et_rat (@ (@ image_nat_set_rat (lambda ((X4 nat)) (@ (@ inf_inf_set_rat (@ A4 X4)) B5))) C3)) top_top_set_rat)) (=> (not _let_1) (= (@ comple4298007329820168263et_rat (@ (@ image_nat_set_rat (lambda ((X4 nat)) (@ (@ inf_inf_set_rat (@ A4 X4)) B5))) C3)) (@ (@ inf_inf_set_rat (@ comple4298007329820168263et_rat (@ (@ image_nat_set_rat A4) C3))) B5)))))) (forall ((B nat) (B5 (-> Bool set_nat)) (A4 set_o) (A Bool)) (let ((_let_1 (@ member_nat B))) (=> (@ _let_1 (@ comple7806235888213564991et_nat (@ (@ image_o_set_nat B5) A4))) (=> (@ (@ member_o A) A4) (@ _let_1 (@ B5 A)))))) (forall ((F (-> nat int)) (A4 set_nat) (A7 set_int) (G (-> int nat)) (B5 set_int) (B7 set_nat)) (=> (= (@ (@ image_nat_int F) A4) A7) (=> (= (@ (@ image_int_nat G) B5) B7) (= (@ (@ image_5071185234104513605nt_nat (@ (@ produc8348893967468530162nt_nat F) G)) (@ (@ produc454536836294682310at_int A4) (lambda ((Uu nat)) B5))) (@ (@ produc1456381018704787142nt_nat A7) (lambda ((Uu int)) B7)))))) (forall ((A4 set_o) (B5 set_o) (F (-> Bool product_unit)) (G (-> Bool product_unit))) (=> (forall ((I4 Bool)) (=> (@ (@ member_o I4) A4) (exists ((X6 Bool)) (and (@ (@ member_o X6) B5) (@ (@ ord_le3221252021190050221t_unit (@ F I4)) (@ G X6)))))) (=> (forall ((J2 Bool)) (=> (@ (@ member_o J2) B5) (exists ((X6 Bool)) (and (@ (@ ord_le3221252021190050221t_unit (@ G J2)) (@ F X6)) (@ (@ member_o X6) A4))))) (= (@ comple4687483117567863418t_unit (@ (@ image_o_Product_unit F) A4)) (@ comple4687483117567863418t_unit (@ (@ image_o_Product_unit G) B5)))))) (= ord_less_eq_int (@ _let_215 (@ produc8739625826339149834_nat_o (lambda ((X4 nat) (Y5 nat) (__flatten_var_0 product_prod_nat_nat)) (@ (@ produc6081775807080527818_nat_o (lambda ((U3 nat) (V3 nat)) (@ (@ ord_less_eq_nat (@ (@ plus_plus_nat X4) V3)) (@ (@ plus_plus_nat U3) Y5)))) __flatten_var_0))))) (forall ((U int) (A4 set_int) (A nat) (B5 (-> int set_nat))) (=> (@ (@ member_int U) A4) (= (@ comple7399068483239264473et_nat (@ (@ image_int_set_nat (lambda ((X4 int)) (@ (@ insert_nat A) (@ B5 X4)))) A4)) (@ (@ insert_nat A) (@ comple7399068483239264473et_nat (@ (@ image_int_set_nat B5) A4)))))) (forall ((A4 set_nat) (F (-> nat product_unit))) (let ((_let_1 (@ (@ image_8730104196221521654t_unit F) A4))) (=> (not (= A4 bot_bot_set_nat)) (@ (@ ord_le3221252021190050221t_unit (@ comple2584293577114468500t_unit _let_1)) (@ comple4687483117567863418t_unit _let_1))))) (forall ((A4 set_Product_unit) (C3 set_Product_unit) (B5 set_Product_unit) (D set_Product_unit)) (= (@ (@ ord_le930853871177014503t_unit (@ (@ produc6121607364029222536t_unit A4) (lambda ((Uu product_unit)) C3))) (@ (@ produc6121607364029222536t_unit B5) (lambda ((Uu product_unit)) D))) (or (and (@ (@ ord_le3507040750410214029t_unit A4) B5) (@ (@ ord_le3507040750410214029t_unit C3) D)) (= C3 bot_bo3957492148770167129t_unit) (= A4 bot_bo3957492148770167129t_unit)))) (forall ((H (-> nat rat)) (F4 set_rat)) (=> (@ finite_finite_nat (@ (@ vimage_nat_rat H) F4)) (=> (= (@ (@ image_nat_rat H) top_top_set_nat) top_top_set_rat) (@ finite_finite_rat F4)))) (forall ((A4 set_o) (B5 set_nat)) (= (= (@ (@ product_Sigma_o_nat A4) (lambda ((Uu Bool)) B5)) bot_bo66526543525301729_o_nat) (or (= A4 bot_bot_set_o) (= B5 bot_bot_set_nat)))) (= (@ (@ comp_P9134237804721252988t_unit produc6942380573175061695_ref_a) (@ (@ comp_r6154141770783548544t_unit (lambda ((X4 ref_a)) (@ (@ produc1340070678782110931_ref_a X4) X4))) produc473321116828791851t_unit)) produc473321116828791851t_unit) _let_214 _let_213 (forall ((Q product_prod_nat_num) (F (-> nat nat)) (P product_prod_nat_num)) (=> (= Q (@ (@ produc6767424583952363640at_num F) P)) (not (forall ((X nat) (Y num)) (=> (= P (@ (@ product_Pair_nat_num X) Y)) (not (= Q (@ (@ product_Pair_nat_num (@ F X)) Y)))))))) (forall ((A4 set_int) (F (-> int nat)) (B5 set_int)) (let ((_let_1 (@ image_int_nat F))) (let ((_let_2 (@ _let_1 B5))) (let ((_let_3 (@ _let_1 A4))) (=> (not (= A4 bot_bot_set_int)) (=> (@ condit1738341127787009408ow_nat _let_3) (=> (not (= B5 bot_bot_set_int)) (=> (@ condit1738341127787009408ow_nat _let_2) (= (@ complete_Inf_Inf_nat (@ _let_1 (@ (@ sup_sup_set_int A4) B5))) (@ (@ inf_inf_nat (@ complete_Inf_Inf_nat _let_3)) (@ complete_Inf_Inf_nat _let_2))))))))))) (forall ((A int) (A4 set_int) (B Bool) (B5 (-> int set_o))) (let ((_let_1 (@ member_o B))) (=> (@ (@ member_int A) A4) (=> (@ _let_1 (@ B5 A)) (@ _let_1 (@ comple90263536869209701_set_o (@ (@ image_int_set_o B5) A4))))))) (forall ((X2 (-> char nat)) (Ya (-> char nat)) (Y3 (-> char Bool)) (Xa2 (-> char Bool)) (R3 (-> nat Bool Bool)) (Ra (-> nat Bool Bool))) (=> (= X2 Ya) (=> (= Y3 Xa2) (=> (forall ((Z3 nat) (Yb Bool)) (=> (@ (@ member_nat Z3) (@ (@ image_char_nat Ya) top_top_set_char)) (=> (@ (@ member_o Yb) (@ (@ image_char_o Xa2) top_top_set_char)) (= (@ (@ R3 Z3) Yb) (@ (@ Ra Z3) Yb))))) (= (@ (@ (@ (@ bNF_re7885669492343766789_nat_o (lambda ((Y2 char) (Z char)) (= Y2 Z))) R3) X2) Y3) (@ (@ (@ (@ bNF_re7885669492343766789_nat_o (lambda ((Y2 char) (Z char)) (= Y2 Z))) Ra) Ya) Xa2)))))) (forall ((A4 set_o) (F (-> Bool int)) (B5 set_o)) (let ((_let_1 (@ image_o_int F))) (let ((_let_2 (@ _let_1 B5))) (let ((_let_3 (@ _let_1 A4))) (=> (not (= A4 bot_bot_set_o)) (=> (@ condit2212336002400062152ve_int _let_3) (=> (not (= B5 bot_bot_set_o)) (=> (@ condit2212336002400062152ve_int _let_2) (= (@ complete_Sup_Sup_int (@ _let_1 (@ (@ sup_sup_set_o A4) B5))) (@ (@ sup_sup_int (@ complete_Sup_Sup_int _let_3)) (@ complete_Sup_Sup_int _let_2))))))))))) (forall ((A set_Pr8693737435421807431at_nat) (B5 set_se6425085446898223655at_nat)) (let ((_let_1 (@ sup_su718114333110466843at_nat A))) (= (@ _let_1 (@ comple6332534001959699150at_nat B5)) (@ comple6332534001959699150at_nat (@ (@ image_1013614488123988933at_nat _let_1) B5))))) (forall ((R1 (-> nat nat Bool))) (let ((_let_1 (@ bNF_re5653821019739307937at_nat R1))) (@ (@ (@ (@ bNF_re3262823321055862553at_nat (lambda ((Y2 (-> nat nat)) (Z (-> nat nat))) (= Y2 Z))) (@ (@ bNF_re239970166668089693at_nat (@ _let_1 (lambda ((Y2 nat) (Z nat)) (= Y2 Z)))) (@ _let_1 (lambda ((Y2 nat) (Z nat)) (= Y2 Z))))) comp_nat_nat_nat) comp_nat_nat_nat))) (forall ((X2 product_prod_nat_nat)) (@ (@ refl_o7122697186039111552at_nat (@ (@ insert8211810215607154385at_nat X2) bot_bo2099793752762293965at_nat)) (@ (@ insert5050368324300391991at_nat (@ (@ produc6161850002892822231at_nat X2) X2)) bot_bo5327735625951526323at_nat))) (forall ((F (-> int nat)) (X5 set_int) (G1 (-> nat num)) (G22 (-> nat num))) (=> (= (@ (@ image_int_nat F) X5) top_top_set_nat) (=> (forall ((X int)) (=> (@ (@ member_int X) X5) (= (@ (@ (@ comp_nat_num_int G1) F) X) (@ (@ (@ comp_nat_num_int G22) F) X)))) (= G1 G22)))) (forall ((C3 set_Product_unit) (A4 set_char) (B5 (-> product_unit set_char))) (let ((_let_1 (= C3 bot_bo3957492148770167129t_unit))) (and (=> _let_1 (= (@ comple7965528767983648192t_char (@ (@ image_5325685772115642575t_char (lambda ((X4 product_unit)) (@ (@ minus_minus_set_char A4) (@ B5 X4)))) C3)) top_top_set_char)) (=> (not _let_1) (= (@ comple7965528767983648192t_char (@ (@ image_5325685772115642575t_char (lambda ((X4 product_unit)) (@ (@ minus_minus_set_char A4) (@ B5 X4)))) C3)) (@ (@ minus_minus_set_char A4) (@ comple4338141846124676698t_char (@ (@ image_5325685772115642575t_char B5) C3)))))))) (forall ((C3 set_Product_unit) (A4 set_nat) (B5 (-> product_unit set_nat))) (let ((_let_1 (@ (@ sup_sup_set_nat A4) (@ comple7399068483239264473et_nat (@ (@ image_8173849991827986510et_nat B5) C3))))) (let ((_let_2 (= C3 bot_bo3957492148770167129t_unit))) (and (=> _let_2 (= _let_1 A4)) (=> (not _let_2) (= _let_1 (@ comple7399068483239264473et_nat (@ (@ image_8173849991827986510et_nat (lambda ((X4 product_unit)) (@ (@ sup_sup_set_nat A4) (@ B5 X4)))) C3)))))))) (forall ((A4 set_nat) (C rat)) (let ((_let_1 (= A4 bot_bot_set_nat))) (and (=> _let_1 (= (@ (@ image_nat_rat (lambda ((X4 nat)) C)) A4) bot_bot_set_rat)) (=> (not _let_1) (= (@ (@ image_nat_rat (lambda ((X4 nat)) C)) A4) (@ (@ insert_rat C) bot_bot_set_rat)))))) (forall ((A4 set_o) (F (-> Bool int)) (A Bool)) (let ((_let_1 (@ image_o_int F))) (let ((_let_2 (@ _let_1 A4))) (=> (not (= A4 bot_bot_set_o)) (=> (@ condit1735850657277959132ow_int _let_2) (= (@ complete_Inf_Inf_int (@ _let_1 (@ (@ insert_o A) A4))) (@ (@ inf_inf_int (@ F A)) (@ complete_Inf_Inf_int _let_2)))))))) (forall ((B5 (-> product_unit set_Pr1261947904930325089at_nat))) (= (@ comple5685304695842803022at_nat (@ (@ image_3617315916088684441at_nat B5) bot_bo3957492148770167129t_unit)) bot_bo2099793752762293965at_nat)) (forall ((A4 set_nat) (B5 set_nat) (C3 (-> nat int)) (D (-> nat int)) (Sup (-> set_int int))) (=> (= A4 B5) (=> (forall ((X nat)) (=> (@ (@ member_nat X) B5) (= (@ C3 X) (@ D X)))) (= (@ Sup (@ (@ image_nat_int C3) A4)) (@ Sup (@ (@ image_nat_int D) B5)))))) (forall ((N3 nat)) (=> (@ (@ ord_less_nat zero_zero_nat) N3) (= (@ (@ image_nat_nat (lambda ((M5 nat)) (@ (@ modulo_modulo_nat M5) N3))) top_top_set_nat) (@ (@ set_or4665077453230672383an_nat zero_zero_nat) N3)))) (forall ((A4 set_se7855581050983116737at_nat) (R set_Pr4329608150637261639at_nat) (A set_Pr1261947904930325089at_nat)) (=> (@ (@ refl_o6955724340487615712at_nat A4) R) (=> (@ (@ member2643936169264416010at_nat A) A4) (@ (@ member8757157785044589968at_nat (@ (@ produc2922128104949294807at_nat A) A)) R)))) (forall ((F (-> int int Bool)) (X1 int) (X22 int)) (= (@ (@ produc4947309494688390418_int_o F) (@ (@ product_Pair_int_int X1) X22)) (@ (@ F X1) X22))) (forall ((R3 (-> Bool nat Bool)) (X2 (-> char Bool)) (Y3 (-> char nat)) (Ra (-> Bool nat Bool))) (=> (@ (@ (@ (@ bNF_re4782998131235581479_o_nat (lambda ((Y2 char) (Z char)) (= Y2 Z))) R3) X2) Y3) (=> (forall ((Z3 Bool) (Yb nat)) (=> (@ (@ member_o Z3) (@ (@ image_char_o X2) top_top_set_char)) (=> (@ (@ member_nat Yb) (@ (@ image_char_nat Y3) top_top_set_char)) (=> (@ (@ R3 Z3) Yb) (@ (@ Ra Z3) Yb))))) (@ (@ (@ (@ bNF_re4782998131235581479_o_nat (lambda ((Y2 char) (Z char)) (= Y2 Z))) Ra) X2) Y3)))) (forall ((I3 set_o) (F (-> Bool product_unit)) (X2 product_unit)) (=> (not (= I3 bot_bot_set_o)) (=> (forall ((I4 Bool)) (=> (@ (@ member_o I4) I3) (= (@ F I4) X2))) (= (@ comple4687483117567863418t_unit (@ (@ image_o_Product_unit F) I3)) X2)))) (forall ((A4 set_nat) (B5 set_int) (F (-> nat product_unit)) (G (-> int product_unit))) (=> (forall ((I4 nat)) (=> (@ (@ member_nat I4) A4) (exists ((X6 int)) (and (@ (@ ord_le3221252021190050221t_unit (@ F I4)) (@ G X6)) (@ (@ member_int X6) B5))))) (=> (forall ((J2 int)) (=> (@ (@ member_int J2) B5) (exists ((X6 nat)) (and (@ (@ member_nat X6) A4) (@ (@ ord_le3221252021190050221t_unit (@ G J2)) (@ F X6)))))) (= (@ comple4687483117567863418t_unit (@ (@ image_8730104196221521654t_unit F) A4)) (@ comple4687483117567863418t_unit (@ (@ image_5846526143423701914t_unit G) B5)))))) (forall ((F (-> nat rat)) (A4 set_nat)) (=> (@ (@ inj_on_nat_rat F) A4) (= (@ finite_finite_rat (@ (@ image_nat_rat F) A4)) (@ finite_finite_nat A4)))) (forall ((F (-> nat nat)) (B5 set_nat) (A4 set_nat)) (=> (@ (@ inj_on_nat_nat F) top_top_set_nat) (=> (@ (@ ord_less_eq_set_nat B5) (@ (@ image_nat_nat F) A4)) (@ (@ ord_less_eq_set_nat (@ (@ vimage_nat_nat F) B5)) A4)))) (forall ((A4 set_nat) (B5 set_int) (F (-> nat int))) (=> (@ finite_finite_nat A4) (=> (@ (@ ord_less_eq_set_int B5) (@ (@ image_nat_int F) A4)) (@ (@ ord_less_eq_nat (@ finite_card_int B5)) (@ finite_card_nat A4))))) (forall ((P2 (-> product_prod_int_int Bool)) (Q2 (-> nat Bool))) (= (@ collec364394062568603661nt_nat (@ produc5441891513209881465_nat_o (lambda ((A5 product_prod_int_int) (B4 nat)) (and (@ P2 A5) (@ Q2 B4))))) (@ (@ produc1007865297704999105nt_nat (@ collec213857154873943460nt_int P2)) (lambda ((Uu product_prod_int_int)) (@ collect_nat Q2))))) (forall ((X2 product_prod_nat_nat) (XS set_Pr1261947904930325089at_nat) (Y3 product_prod_nat_nat) (YS set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ produc2922128104949294807at_nat XS))) (=> (@ (@ member8440522571783428010at_nat X2) XS) (=> (@ (@ member8206827879206165904at_nat (@ (@ produc6161850002892822231at_nat X2) Y3)) fun_pair_less) (=> (@ (@ member8757157785044589968at_nat (@ _let_1 YS)) fun_min_strict) (@ (@ member8757157785044589968at_nat (@ _let_1 (@ (@ insert8211810215607154385at_nat Y3) YS))) fun_min_strict)))))) (forall ((F (-> nat nat)) (A4 set_nat) (B5 set_nat)) (let ((_let_1 (@ image_nat_nat F))) (=> (@ (@ inj_on_nat_nat F) (@ (@ sup_sup_set_nat A4) B5)) (= (= (@ _let_1 A4) (@ _let_1 B5)) (= A4 B5))))) (forall ((C3 set_Product_unit) (A4 set_nat) (B5 (-> product_unit set_nat))) (let ((_let_1 (= C3 bot_bo3957492148770167129t_unit))) (and (=> (not _let_1) (= (@ comple7806235888213564991et_nat (@ (@ image_8173849991827986510et_nat (lambda ((X4 product_unit)) (@ (@ inf_inf_set_nat A4) (@ B5 X4)))) C3)) (@ (@ inf_inf_set_nat A4) (@ comple7806235888213564991et_nat (@ (@ image_8173849991827986510et_nat B5) C3))))) (=> _let_1 (= (@ comple7806235888213564991et_nat (@ (@ image_8173849991827986510et_nat (lambda ((X4 product_unit)) (@ (@ inf_inf_set_nat A4) (@ B5 X4)))) C3)) top_top_set_nat))))) (forall ((A4 set_int) (B5 (-> int set_Pr1261947904930325089at_nat))) (=> (@ finite_finite_int A4) (=> (forall ((A3 int)) (=> (@ (@ member_int A3) A4) (@ finite6177210948735845034at_nat (@ B5 A3)))) (@ finite6177210948735845034at_nat (@ comple5685304695842803022at_nat (@ (@ image_8938366415781434990at_nat B5) A4)))))) (forall ((A4 set_int) (F (-> int int)) (U int)) (let ((_let_1 (@ (@ image_int_int F) A4))) (=> (not (= A4 bot_bot_set_int)) (=> (@ condit1735850657277959132ow_int _let_1) (= (@ (@ ord_less_eq_int U) (@ complete_Inf_Inf_int _let_1)) (forall ((X4 int)) (=> (@ (@ member_int X4) A4) (@ (@ ord_less_eq_int U) (@ F X4))))))))) (forall ((F1 (-> nat nat)) (F22 (-> nat nat)) (G1 (-> Bool Bool)) (G22 (-> nat Bool))) (= (@ (@ produc4787215299218314158_nat_o (@ (@ comp_nat_nat_nat F1) F22)) (@ (@ comp_o_o_nat G1) G22)) (@ (@ comp_P8901546994122883554at_nat (@ (@ produc2001155298098703512at_o_o F1) G1)) (@ (@ produc4787215299218314158_nat_o F22) G22)))) (forall ((G (-> rat int)) (F (-> nat rat)) (A4 set_nat)) (= (@ complete_Sup_Sup_int (@ (@ image_rat_int G) (@ (@ image_nat_rat F) A4))) (@ complete_Sup_Sup_int (@ (@ image_nat_int (@ (@ comp_rat_int_nat G) F)) A4)))) (forall ((A nat) (B int) (A4 set_nat) (B5 (-> nat set_int))) (= (@ (@ member4262671552274231302at_int (@ (@ product_Pair_nat_int A) B)) (@ (@ produc454536836294682310at_int A4) B5)) (and (@ (@ member_nat A) A4) (@ (@ member_int B) (@ B5 A))))) (forall ((B5 set_set_nat) (A4 set_nat)) (= (@ (@ inf_inf_set_nat (@ comple7399068483239264473et_nat B5)) A4) (@ 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((L3 nat) (R5 nat) (__flatten_var_0 product_prod_nat_nat)) (@ (@ (@ F (@ G1 L3)) (@ G22 R5)) __flatten_var_0))))) (forall ((Prod product_prod_nat_num)) (= (@ (@ product_Pair_nat_num (@ product_fst_nat_num Prod)) (@ product_snd_nat_num Prod)) Prod)) (forall ((A4 set_int) (B5 set_int)) (=> (@ finite_finite_int A4) (=> (@ finite_finite_int B5) (=> (@ (@ ord_less_eq_nat (@ finite_card_int A4)) (@ finite_card_int B5)) (exists ((F5 (-> int int))) (and (@ (@ ord_less_eq_set_int (@ (@ image_int_int F5) A4)) B5) (@ (@ inj_on_int_int F5) A4))))))) (forall ((X5 set_ref_a) (A4 set_Pr1133966238863718811t_unit) (Y4 set_he8644174446132254637t_unit) (P2 (-> ref_a heap_e7401611519738050253t_unit Bool)) (Q2 (-> ref_a heap_e7401611519738050253t_unit Bool))) (let ((_let_1 (@ ord_le5525191956872776187t_unit A4))) (=> (= X5 (@ (@ image_7136766188234240905_ref_a produc473321116828791851t_unit) A4)) (=> (= Y4 (@ (@ image_17660834435998945t_unit produc1126150082675451753t_unit) A4)) (=> (forall ((X ref_a)) (=> (@ (@ member_ref_a X) X5) (forall ((Xa heap_e7401611519738050253t_unit)) (=> (@ (@ member242389114213480694t_unit Xa) Y4) (=> (@ (@ P2 X) Xa) (@ (@ Q2 X) Xa)))))) (=> (@ _let_1 (@ collec3252306575900995386t_unit (@ produc4924168586796184916unit_o P2))) (@ _let_1 (@ collec3252306575900995386t_unit (@ produc4924168586796184916unit_o Q2))))))))) (forall ((R ref_a) (R2 ref_a) (X2 a) (X3 a) (H heap_e7401611519738050253t_unit)) (let ((_let_1 (@ (@ set_a R) X2))) (let ((_let_2 (@ (@ set_a R2) X3))) (=> (@ (@ noteq_a_a R) R2) (= (@ _let_1 (@ _let_2 H)) (@ _let_2 (@ _let_1 H))))))) (forall ((A4 set_nat) (B5 set_nat)) (=> (@ finite_finite_nat A4) (=> (@ finite_finite_nat B5) (= (exists ((F2 (-> nat nat))) (and (@ (@ inj_on_nat_nat F2) A4) (@ (@ ord_less_eq_set_nat (@ (@ image_nat_nat F2) A4)) B5))) (@ (@ ord_less_eq_nat (@ finite_card_nat A4)) (@ finite_card_nat B5)))))) (forall ((F (-> int nat)) (A4 set_int) (A7 set_nat) (G (-> int int)) (B5 set_int) (B7 set_int)) (=> (= (@ (@ image_int_nat F) A4) A7) (=> (= (@ (@ image_int_int G) B5) B7) (= (@ (@ image_1654017166447373545at_int (@ (@ produc5664932004629684302nt_int F) G)) (@ (@ produc1453890548195736866nt_int A4) (lambda ((Uu int)) B5))) (@ (@ produc454536836294682310at_int A7) (lambda ((Uu nat)) B7)))))) (forall ((H (-> nat nat product_prod_nat_nat Bool)) (F (-> nat nat)) (G (-> nat nat)) (X2 product_prod_nat_nat)) (= (@ (@ produc8739625826339149834_nat_o H) (@ (@ (@ produc6977886695330630970at_nat F) G) X2)) (@ (@ produc8739625826339149834_nat_o (lambda ((L3 nat) (R5 nat) (__flatten_var_0 product_prod_nat_nat)) (@ (@ (@ H (@ F L3)) (@ G R5)) __flatten_var_0))) X2))) (forall ((F (-> heap_e7401611519738050253t_unit nat)) (G (-> ref_a nat)) (X2 produc7812382424243267045t_unit)) (= (@ (@ produc5772047106995631985at_nat F) (@ (@ produc6942186945380262242t_unit G) X2)) (@ (@ product_Pair_nat_nat (@ G (@ produc473321116828791851t_unit X2))) (@ F (@ produc1126150082675451753t_unit X2))))) (forall ((A nat) (B num) (R3 set_Pr6200539531224447659at_num) (F (-> nat nat)) (G (-> num nat))) (=> (@ (@ member9148766508732265716at_num (@ (@ product_Pair_nat_num A) B)) R3) (@ (@ member8440522571783428010at_nat (@ (@ product_Pair_nat_nat (@ F A)) (@ G B))) (@ (@ image_4217639968629731195at_nat (@ (@ produc5108217098638100356um_nat F) G)) R3)))) (forall ((M set_nat) (N set_nat) (F (-> nat int)) (G (-> nat int))) (=> (= M N) (=> (forall ((X nat)) (=> (@ (@ member_nat X) N) (= (@ F X) (@ G X)))) (= (@ (@ image_nat_int F) M) (@ (@ image_nat_int G) N))))) (= produc4947309494688390418_int_o (lambda ((F2 (-> int int Bool)) (P3 product_prod_int_int)) (@ (@ F2 (@ product_fst_int_int P3)) (@ product_snd_int_int P3)))) (forall ((B int) (B5 (-> Bool set_int)) (A4 set_o) (A Bool)) (let ((_let_1 (@ member_int B))) (=> (@ _let_1 (@ comple3628384868704368283et_int (@ (@ image_o_set_int B5) A4))) (=> (not (@ _let_1 (@ B5 A))) (not (@ (@ member_o A) A4)))))) (forall ((H2 heap_e7401611519738050253t_unit) (H heap_e7401611519738050253t_unit) (R ref_a) (F (-> heap_e7401611519738050253t_unit ref_a))) (=> (= H2 H) (=> (= R (@ F H)) (@ (@ (@ (@ heap_effect_ref_a (@ heap_tap_ref_a F)) H) H2) R)))) (forall ((F (-> nat set_Pr1261947904930325089at_nat)) (A nat) (A4 set_nat)) (let ((_let_1 (@ image_7178329752028323786at_nat F))) (= (@ comple1930127330929219688at_nat (@ _let_1 (@ (@ insert_nat A) A4))) (@ (@ inf_in2572325071724192079at_nat (@ F A)) (@ comple1930127330929219688at_nat (@ _let_1 A4)))))) (forall ((F1 (-> nat rat)) (A13 set_nat) (B1 set_rat) (F22 (-> int int)) (B22 set_int) (A24 set_int)) (=> (= (@ (@ image_nat_rat F1) A13) B1) (=> (@ (@ inj_on_int_int F22) B22) (=> (@ (@ ord_less_eq_set_int (@ (@ image_int_int F22) B22)) A24) (=> (=> (= B22 bot_bot_set_int) (= A24 bot_bot_set_int)) (= (@ (@ bNF_We7904740386373615514nt_rat B22) B1) (@ (@ image_1904597124500147013nt_rat (@ (@ (@ bNF_We576767280138975660at_int B22) F1) F22)) (@ (@ bNF_We8539870446460111250nt_nat A24) A13)))))))) (forall ((A4 set_se7855581050983116737at_nat) (R set_Pr4329608150637261639at_nat)) (=> (forall ((X set_Pr1261947904930325089at_nat) (Y set_Pr1261947904930325089at_nat)) (=> (@ (@ member2643936169264416010at_nat X) A4) (=> (@ (@ member2643936169264416010at_nat Y) A4) (=> (not (= X Y)) (or (@ (@ member8757157785044589968at_nat (@ (@ produc2922128104949294807at_nat Y) X)) R) (@ (@ member8757157785044589968at_nat (@ (@ produc2922128104949294807at_nat X) Y)) R)))))) (@ (@ total_7212417256332265445at_nat A4) R))) (forall ((X2 produc3843707927480180839at_nat) (Y3 produc3843707927480180839at_nat) (A4 set_Pr4329608150637261639at_nat)) (= (@ (@ member6009668390874684176at_nat (@ (@ produc2335810615602371415at_nat X2) Y3)) (@ id_on_7869290023980668164at_nat A4)) (and (@ (@ member8757157785044589968at_nat X2) A4) (= X2 Y3)))) (forall ((S5 set_nat) (F (-> nat Bool Bool)) (X2 nat) (Y3 nat) (G (-> nat Bool))) (let ((_let_1 (@ comp_o_o_nat (@ F Y3)))) (let ((_let_2 (@ comp_o_o_nat (@ F X2)))) (=> (@ (@ finite7806256374766696054_nat_o S5) F) (=> (@ (@ member_nat X2) S5) (=> (@ (@ member_nat Y3) S5) (= (@ _let_1 (@ _let_2 G)) (@ _let_2 (@ _let_1 G))))))))) (= (@ (@ image_7976474329151083847st_nat id_list_nat) top_top_set_list_nat) top_top_set_list_nat) (forall ((F (-> produc859450856879609959at_nat produc3843707927480180839at_nat)) (A4 set_Pr8693737435421807431at_nat) (B5 set_Pr8693737435421807431at_nat)) (let ((_let_1 (@ image_7637461350386011077at_nat F))) (= (@ _let_1 (@ (@ sup_su718114333110466843at_nat A4) B5)) (@ (@ sup_su5525570899277871387at_nat (@ _let_1 A4)) (@ _let_1 B5))))) (forall ((A4 set_Product_unit) (F (-> product_unit int)) (A product_unit)) (let ((_let_1 (@ image_873079544045703924it_int F))) (let ((_let_2 (@ _let_1 A4))) (=> (not (= A4 bot_bo3957492148770167129t_unit)) (=> (@ condit1735850657277959132ow_int _let_2) (= (@ complete_Inf_Inf_int (@ _let_1 (@ (@ insert_Product_unit A) A4))) (@ (@ inf_inf_int (@ F A)) (@ complete_Inf_Inf_int _let_2)))))))) (forall ((P2 (-> product_prod_int_int Bool)) (F (-> int int product_prod_int_int)) (Prod product_prod_int_int)) (let ((_let_1 (@ product_snd_int_int Prod))) (let ((_let_2 (@ product_fst_int_int Prod))) (= (@ P2 (@ (@ produc4245557441103728435nt_int F) Prod)) (not (and (not (@ P2 (@ (@ F _let_2) _let_1))) (= Prod (@ (@ product_Pair_int_int _let_2) _let_1)))))))) (forall ((H (-> rat rat)) (F4 set_rat)) (=> (@ finite_finite_rat (@ (@ vimage_rat_rat H) F4)) (=> (= (@ (@ image_rat_rat H) top_top_set_rat) top_top_set_rat) (@ finite_finite_rat F4)))) (forall ((U Bool) (A4 set_o) (A product_unit) (B5 (-> Bool set_Product_unit))) (=> (@ (@ member_o U) A4) (= (@ comple3349607820504768346t_unit (@ (@ image_663195431845683034t_unit (lambda ((X4 Bool)) (@ (@ insert_Product_unit A) (@ B5 X4)))) A4)) (@ (@ insert_Product_unit A) (@ comple3349607820504768346t_unit (@ (@ image_663195431845683034t_unit B5) A4)))))) (forall ((F (-> product_prod_nat_num Bool)) (A nat) (B num)) (=> (@ (@ (@ produc156083480235303841_num_o F) A) B) (@ F (@ (@ product_Pair_nat_num A) B)))) (forall ((K Bool) (I3 set_o) (A4 (-> Bool set_Pr1261947904930325089at_nat))) (let ((_let_1 (@ comple1930127330929219688at_nat (@ (@ image_7077428525161401678at_nat A4) I3)))) (=> (@ (@ member_o K) I3) (= (@ (@ inf_in2572325071724192079at_nat (@ A4 K)) _let_1) _let_1)))) (forall ((F (-> nat nat)) (A4 set_nat) (A7 set_nat) (G (-> int int)) (B5 set_int) (B7 set_int)) (=> (= (@ (@ image_nat_nat F) A4) A7) (=> (= (@ (@ image_int_int G) B5) B7) (= (@ (@ image_9117352539549038149at_int (@ (@ produc7974749936722635250nt_int F) G)) (@ (@ produc454536836294682310at_int A4) (lambda ((Uu nat)) B5))) (@ (@ produc454536836294682310at_int A7) (lambda ((Uu nat)) B7)))))) _let_212 _let_211 (forall ((B5 (-> Bool int Bool)) (C3 (-> Bool nat Bool)) (A4 (-> nat int Bool))) (@ (@ (@ (@ bNF_re7413876800493218871nt_nat (@ (@ bNF_re4895681925607069953_o_nat B5) C3)) (@ (@ bNF_re1982657550219213441nt_nat (@ (@ 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(@ (@ member8440522571783428010at_nat U) A4) (= (@ comple7216939928495492468t_unit (@ (@ image_121980125215734065t_unit (lambda ((X4 product_prod_nat_nat)) (@ (@ insert_Product_unit A) (@ B5 X4)))) A4)) (@ (@ insert_Product_unit A) (@ comple7216939928495492468t_unit (@ (@ image_121980125215734065t_unit B5) A4)))))) (forall ((A4 set_nat) (B5 set_nat) (C3 set_nat) (D set_nat)) (= (@ (@ inf_in2572325071724192079at_nat (@ (@ produc457027306803732586at_nat A4) (lambda ((Uu nat)) B5))) (@ (@ produc457027306803732586at_nat C3) (lambda ((Uu nat)) D))) (@ (@ produc457027306803732586at_nat (@ (@ inf_inf_set_nat A4) C3)) (lambda ((Uu nat)) (@ (@ inf_inf_set_nat B5) D))))) (forall ((F (-> nat int)) (G (-> nat int)) (A4 set_nat)) (= (@ condit1735850657277959132ow_int (@ (@ image_nat_int (lambda ((X4 nat)) (@ (@ inf_inf_int (@ F X4)) (@ G X4)))) A4)) (and (@ condit1735850657277959132ow_int (@ (@ image_nat_int G) A4)) (@ condit1735850657277959132ow_int (@ (@ image_nat_int F) A4))))) (forall ((A4 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((X4 product_unit)) (=> (@ (@ member_Product_unit X4) I3) (= (@ F X4) C))))))) (forall ((A4 set_int) (C int)) (=> (not (= A4 bot_bot_set_int)) (= (@ complete_Inf_Inf_int (@ (@ image_int_int (lambda ((X4 int)) C)) A4)) C))) (forall ((A4 set_nat) (F (-> nat int)) (B5 set_int)) (= (@ (@ ord_le656430383953171549at_int (@ (@ bNF_Gr_nat_int A4) F)) (@ (@ produc454536836294682310at_int A4) (lambda ((Uu nat)) B5))) (@ (@ ord_less_eq_set_int (@ (@ image_nat_int F) A4)) B5))) _let_210 (forall ((R set_Pr8693737435421807431at_nat)) (let ((_let_1 (@ field_4706345496283612622at_nat R))) (=> (@ (@ order_7480980593162297270at_nat _let_1) R) (= (@ (@ order_8331247224601271455at_nat _let_1) R) (forall ((A6 set_Pr1261947904930325089at_nat)) (=> (@ (@ ord_le3146513528884898305at_nat A6) (@ field_4706345496283612622at_nat R)) (=> (not (= A6 bot_bo2099793752762293965at_nat)) (exists ((X4 product_prod_nat_nat)) (and (forall ((Y5 product_prod_nat_nat)) (=> (@ (@ member8440522571783428010at_nat Y5) A6) (@ (@ 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(lambda ((X4 Bool)) (@ complete_Inf_Inf_int (@ (@ image_int_int F) (@ B5 X4))))) A4))))))) (forall ((F (-> char int)) (A char) (A4 set_char)) (=> (@ (@ inj_on_char_int F) top_top_set_char) (= (@ (@ member_int (@ F A)) (@ (@ image_char_int F) A4)) (@ (@ member_char A) A4)))) (forall ((X2 produc3843707927480180839at_nat) (Y3 produc3843707927480180839at_nat)) (= (@ (@ (@ if_Pro3594990065127090477at_nat true) X2) Y3) X2)) (forall ((S5 set_int) (F (-> int Bool Bool)) (X2 int) (Y3 int) (G (-> nat Bool))) (let ((_let_1 (@ comp_o_o_nat (@ F Y3)))) (let ((_let_2 (@ comp_o_o_nat (@ F X2)))) (=> (@ (@ finite5985214029334008090_int_o S5) F) (=> (@ (@ member_int X2) S5) (=> (@ (@ member_int Y3) S5) (= (@ _let_1 (@ _let_2 G)) (@ _let_2 (@ _let_1 G))))))))) (forall ((C3 set_o) (A4 set_rat) (B5 (-> Bool set_rat))) (let ((_let_1 (= C3 bot_bot_set_o))) (and (=> (not _let_1) (= (@ comple4298007329820168263et_rat (@ (@ image_o_set_rat (lambda ((X4 Bool)) (@ (@ inf_inf_set_rat A4) (@ B5 X4)))) C3)) (@ (@ 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image_8173849991827986510et_nat B5) C3))))) (let ((_let_3 (= C3 bot_bo3957492148770167129t_unit))) (and (=> _let_3 (= _let_2 (@ _let_1 bot_bot_set_nat))) (=> (not _let_3) (= _let_2 (@ comple7399068483239264473et_nat (@ (@ image_8173849991827986510et_nat (lambda ((X4 product_unit)) (@ (@ insert_nat A) (@ B5 X4)))) C3))))))))) (forall ((X2 (-> nat nat)) (Xa2 (-> nat nat)) (F (-> nat nat)) (Fa (-> nat nat))) (=> (forall ((Z3 nat) (Za nat)) (=> (@ (@ member_nat Z3) (@ (@ image_nat_nat X2) top_top_set_nat)) (=> (@ (@ member_nat Za) (@ (@ image_nat_nat Xa2) top_top_set_nat)) (=> (= (@ F Z3) (@ Fa Za)) (= Z3 Za))))) (=> (= (@ (@ comp_nat_nat_nat F) X2) (@ (@ comp_nat_nat_nat Fa) Xa2)) (= X2 Xa2)))) (forall ((C3 set_nat) (A4 set_Product_unit) (B5 (-> nat set_Product_unit))) (let ((_let_1 (= C3 bot_bot_set_nat))) (and (=> _let_1 (= (@ comple3349607820504768346t_unit (@ (@ image_4824033694279209942t_unit (lambda ((X4 nat)) (@ (@ sup_su793286257634532545t_unit A4) (@ B5 X4)))) C3)) bot_bo3957492148770167129t_unit)) (=> (not _let_1) (= (@ comple3349607820504768346t_unit (@ (@ image_4824033694279209942t_unit (lambda ((X4 nat)) (@ (@ sup_su793286257634532545t_unit A4) (@ B5 X4)))) C3)) (@ (@ sup_su793286257634532545t_unit A4) (@ comple3349607820504768346t_unit (@ (@ image_4824033694279209942t_unit B5) C3)))))))) (forall ((F (-> set_Pr1261947904930325089at_nat set_Pr1261947904930325089at_nat Bool)) (A set_Pr1261947904930325089at_nat) (B set_Pr1261947904930325089at_nat)) (=> (@ (@ produc410239310623530412_nat_o F) (@ (@ produc2922128104949294807at_nat A) B)) (@ (@ F A) B))) (forall ((S5 set_o) (F (-> Bool nat nat)) (X2 Bool)) (let ((_let_1 (@ F X2))) (=> (@ (@ finite2426395113773319005_o_nat S5) F) (=> (@ (@ member_o X2) S5) (= (@ (@ comp_nat_nat_nat _let_1) _let_1) _let_1))))) (forall ((A4 set_Pr4329608150637261639at_nat) (R set_Pr5564308138774400199at_nat) (A produc3843707927480180839at_nat) (B produc3843707927480180839at_nat)) (=> (@ (@ order_2339240034117818117at_nat A4) R) (=> (@ (@ member6009668390874684176at_nat (@ (@ produc2335810615602371415at_nat A) B)) R) (and (@ (@ member8757157785044589968at_nat B) A4) (@ (@ member8757157785044589968at_nat A) A4))))) (forall ((B heap_e7401611519738050253t_unit) (P produc7812382424243267045t_unit)) (= (= B (@ produc1126150082675451753t_unit P)) (exists ((A5 ref_a)) (= P (@ (@ produc6544324848051098391t_unit A5) B))))) (forall ((X2 Bool) (Y3 Bool)) (=> (= X2 Y3) (@ (@ (@ (@ bNF_Grp_o_o top_top_set_o) id_o) X2) Y3))) (forall ((Sup (-> set_int int)) (A4 set_int)) (= (@ Sup (@ (@ image_int_int id_int) A4)) (@ Sup A4))) (forall ((A4 set_se5479201105039950375at_nat) (B5 set_se5479201105039950375at_nat)) (= (@ (@ image_3313167189156628421at_nat (@ produc5456455677105495163at_nat (lambda ((I2 set_Pr4329608150637261639at_nat) (J set_Pr4329608150637261639at_nat)) (@ (@ produc9060074326276436823at_nat J) I2)))) (@ (@ produc6258361011560675592at_nat A4) (lambda ((Uu 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(forall ((R7 (-> int code_integer Bool)) (S6 (-> int code_integer Bool)) (R3 (-> int int Bool)) (S5 (-> int int Bool))) (=> (@ right_8475562212078014689nteger R7) (=> (@ left_t2374113004080657585nteger R7) (=> (@ left_u6795595883297946906nteger S6) (=> (@ right_7281159819619925802nteger S6) (@ (@ ord_le7522433683449569238eger_o (@ (@ bNF_re3379532845092657523nteger (@ (@ relcom967497705283160040nteger R3) R7)) (@ (@ relcom967497705283160040nteger S5) S6))) (@ (@ relcom7212586982944386682nteger (@ (@ bNF_re4712519889275205905nt_int R3) S5)) (@ (@ bNF_re3379532845092657523nteger R7) S6)))))))) (forall ((R1 (-> int int Bool)) (Abs1 (-> int nat)) (Rep1 (-> nat int)) (T1 (-> int nat Bool)) (R22 (-> nat nat Bool)) (Abs22 (-> nat num)) (Rep22 (-> num nat)) (T22 (-> nat num Bool))) (=> (@ (@ (@ (@ quotient_int_nat R1) Abs1) Rep1) T1) (=> (@ (@ (@ (@ quotient_nat_num R22) Abs22) Rep22) T22) (@ (@ (@ (@ quotient_int_num (@ (@ relcompp_int_nat_int T1) (@ (@ relcompp_nat_nat_int R22) (@ conversep_int_nat T1)))) (@ (@ comp_nat_num_int Abs22) Abs1)) (@ (@ comp_nat_int_num Rep1) Rep22)) (@ (@ relcompp_int_nat_num T1) T22))))) (forall ((X2 int) (Y3 int)) (= (@ (@ (@ if_int false) X2) Y3) Y3)) (forall ((F (-> int int)) (G (-> nat nat)) (A4 set_int) (B5 set_nat)) (= (@ (@ image_7928304878501623365nt_nat (@ produc5385566376148791347nt_nat (lambda ((X4 int) (Y5 nat)) (@ (@ product_Pair_int_nat (@ F X4)) (@ G Y5))))) (@ (@ produc1456381018704787142nt_nat A4) (lambda ((Uu int)) B5))) (@ (@ produc1456381018704787142nt_nat (@ (@ image_int_int F) A4)) (lambda ((Uu int)) (@ (@ image_nat_nat G) B5))))) (forall ((R3 (-> nat Bool Bool)) (X2 (-> char nat)) (Y3 (-> char Bool)) (Ra (-> nat Bool Bool))) (=> (@ (@ (@ (@ bNF_re7885669492343766789_nat_o (lambda ((Y2 char) (Z char)) (= Y2 Z))) R3) X2) Y3) (=> (forall ((Z3 nat) (Yb Bool)) (=> (@ (@ member_nat Z3) (@ (@ image_char_nat X2) top_top_set_char)) (=> (@ (@ member_o Yb) (@ (@ image_char_o Y3) top_top_set_char)) (=> (@ (@ R3 Z3) Yb) (@ (@ Ra Z3) Yb))))) (@ (@ (@ (@ bNF_re7885669492343766789_nat_o (lambda ((Y2 char) (Z char)) (= Y2 Z))) Ra) X2) Y3)))) (forall ((S5 set_set_o)) (= (@ complete_Sup_Sup_o_o (@ (@ image_set_o_o_o (lambda ((I2 set_o) (X4 Bool)) (@ (@ member_o X4) I2))) S5)) (lambda ((X4 Bool)) (@ (@ member_o X4) (@ comple90263536869209701_set_o S5))))) (forall ((B5 (-> Bool set_nat))) (= (@ comple7399068483239264473et_nat (@ (@ image_o_set_nat B5) bot_bot_set_o)) bot_bot_set_nat)) (forall ((F (-> int int)) (A4 set_int) (P2 (-> set_int Bool))) (= (forall ((B6 set_int)) (=> (@ (@ ord_less_eq_set_int B6) (@ (@ image_int_int F) A4)) (@ P2 B6))) (forall ((B6 set_int)) (=> (@ (@ ord_less_eq_set_int B6) A4) (@ P2 (@ (@ image_int_int F) B6)))))) (forall ((A4 set_o) (C3 set_Product_unit) (B5 set_o) (D set_Product_unit)) (= (@ (@ ord_le518195775913581980t_unit (@ (@ produc411009820408249917t_unit A4) (lambda ((Uu Bool)) C3))) (@ (@ produc411009820408249917t_unit B5) (lambda ((Uu Bool)) D))) (or (= C3 bot_bo3957492148770167129t_unit) (and (@ (@ ord_le3507040750410214029t_unit C3) D) (@ (@ ord_less_eq_set_o A4) B5)) (= A4 bot_bot_set_o)))) (forall ((C3 set_o) (A Bool) (B5 (-> Bool set_o))) (let ((_let_1 (= C3 bot_bot_set_o))) (and (=> _let_1 (= (@ comple90263536869209701_set_o (@ (@ image_o_set_o (lambda ((X4 Bool)) (@ (@ insert_o A) (@ B5 X4)))) C3)) bot_bot_set_o)) (=> (not _let_1) (= (@ comple90263536869209701_set_o (@ (@ image_o_set_o (lambda ((X4 Bool)) (@ (@ insert_o A) (@ B5 X4)))) C3)) (@ (@ insert_o A) (@ comple90263536869209701_set_o (@ (@ image_o_set_o B5) C3)))))))) (= (lambda ((Y2 num) (Z num)) (= Y2 Z)) (@ (@ bNF_Grp_num_num top_top_set_num) id_num)) (forall ((Rep (-> nat Bool)) (Abs (-> Bool nat)) (Rep2 (-> Bool Bool)) (Abs2 (-> Bool Bool)) (Rep3 (-> nat nat)) (Abs3 (-> nat nat)) (M (-> nat Bool)) (M1 (-> Bool Bool)) (M2 (-> nat Bool))) (=> (@ (@ (@ type_d1000680970699258650_nat_o Rep) Abs) top_top_set_o) (=> (@ (@ (@ type_definition_o_o Rep2) Abs2) top_top_set_o) (=> (@ (@ (@ type_d6250493948777748686at_nat Rep3) Abs3) top_top_set_nat) (=> (= (@ (@ comp_nat_o_nat (@ (@ comp_o_o_nat Abs2) M)) Rep3) (@ (@ comp_nat_o_nat (@ (@ comp_o_o_nat (@ (@ comp_o_o_o Abs2) M1)) Rep)) (@ (@ comp_nat_nat_nat (@ (@ comp_o_nat_nat Abs) M2)) Rep3))) (= (@ (@ comp_o_o_nat M1) M2) M)))))) (forall ((F (-> product_prod_nat_nat product_prod_nat_nat)) (A4 set_Pr1261947904930325089at_nat) (P2 (-> set_Pr1261947904930325089at_nat Bool))) (= (exists ((B6 set_Pr1261947904930325089at_nat)) (and (@ P2 B6) (@ (@ ord_le3146513528884898305at_nat B6) (@ (@ image_5168914502847457605at_nat F) A4)) (@ finite6177210948735845034at_nat B6))) (exists ((B6 set_Pr1261947904930325089at_nat)) (and (@ finite6177210948735845034at_nat B6) (@ P2 (@ (@ image_5168914502847457605at_nat F) B6)) (@ (@ ord_le3146513528884898305at_nat B6) A4))))) (forall ((F (-> nat nat)) (Fa (-> int nat)) (G (-> nat nat)) (Ga (-> int int))) (= (@ (@ comp_P397146161216181329at_int (@ (@ basic_873636322600132658at_int F) Fa)) (@ (@ produc7974749936722635250nt_int G) Ga)) (@ (@ basic_873636322600132658at_int (@ (@ comp_nat_nat_nat F) G)) (@ (@ comp_int_nat_int Fa) Ga)))) (forall ((X2 set_Pr8693737435421807431at_nat) (Y3 set_Pr8693737435421807431at_nat)) (= (@ (@ (@ if_set1508868558775481357at_nat false) X2) Y3) Y3)) (forall ((I Bool) (A4 set_o) (F (-> Bool set_nat))) (=> (@ (@ member_o I) A4) (@ (@ ord_less_eq_set_nat (@ comple7806235888213564991et_nat (@ (@ image_o_set_nat F) A4))) (@ F I)))) (forall ((F (-> int nat)) (A4 set_int) (P2 (-> nat Bool))) (=> (exists ((X6 nat)) (and (@ P2 X6) (@ (@ member_nat X6) (@ (@ image_int_nat F) A4)))) (exists ((X int)) (and (@ P2 (@ F X)) (@ (@ member_int X) A4))))) (forall ((Z2 rat) (F (-> nat rat)) (A4 set_nat)) (= (@ (@ member_rat Z2) (@ (@ image_nat_rat F) A4)) (exists ((X4 nat)) (and (@ (@ member_nat X4) A4) (= Z2 (@ F X4)))))) (forall ((F (-> int nat)) (A4 set_int)) (=> (@ finite_finite_nat (@ (@ image_int_nat F) A4)) (=> (not (@ finite_finite_int A4)) (not (forall ((Y nat)) (=> (@ (@ member_nat Y) (@ (@ image_int_nat F) A4)) (@ finite_finite_int (@ (@ inf_inf_set_int (@ (@ vimage_int_nat F) (@ (@ insert_nat Y) bot_bot_set_nat))) A4)))))))) (forall ((F (-> nat nat)) (Z2 nat)) (=> (@ (@ inj_on_nat_nat F) top_top_set_nat) (= (@ (@ (@ comp_nat_nat_nat (@ (@ the_inv_into_nat_nat top_top_set_nat) F)) F) Z2) (@ id_nat Z2)))) (forall ((X2 Bool) (A4 set_o) (X5 set_o)) (=> (@ (@ member_o X2) A4) (=> (@ (@ ord_less_eq_set_o X5) A4) (@ (@ ord_less_eq_set_o (@ (@ insert_o X2) X5)) A4)))) (forall ((Rb (-> nat nat Bool)) (Sd (-> num num Bool))) (@ (@ (@ (@ bNF_re3846787885862361009nt_num (@ (@ bNF_re341483209202555957um_num Rb) Sd)) (@ (@ bNF_re9099949428469764705nt_num (@ (@ bNF_re3715656647883201625at_nat (lambda ((Y2 int) (Z int)) (= Y2 Z))) Rb)) (@ (@ bNF_re7626690874201225453um_num (lambda ((Y2 int) (Z int)) (= Y2 Z))) Sd))) comp_nat_num_int) comp_nat_num_int)) (forall ((C product_prod_nat_nat) (F (-> nat nat)) (G (-> num nat)) (R3 set_Pr6200539531224447659at_num)) (=> (@ (@ member8440522571783428010at_nat C) (@ (@ image_4217639968629731195at_nat (@ (@ produc5108217098638100356um_nat F) G)) R3)) (not (forall ((X nat) (Y num)) (=> (= C (@ (@ product_Pair_nat_nat (@ F X)) (@ G Y))) (not (@ (@ member9148766508732265716at_num (@ (@ product_Pair_nat_num X) Y)) R3))))))) (forall ((Z2 product_prod_nat_nat) (A4 set_nat) (F (-> nat nat))) (=> (@ (@ member8440522571783428010at_nat Z2) (@ collec3392354462482085612at_nat (@ produc6081775807080527818_nat_o (@ (@ bNF_Grp_nat_nat A4) F)))) (@ (@ member_nat (@ product_fst_nat_nat Z2)) A4))) (forall ((I nat) (C3 set_nat) (G (-> nat Bool)) (X2 nat)) (=> (@ (@ member_nat I) C3) (=> (@ (@ inj_on_nat_o G) C3) (= (@ (@ (@ comp_o_nat_nat (lambda ((I2 Bool)) (@ (@ (@ if_nat (@ (@ member_o I2) (@ (@ image_nat_o G) C3))) (@ (@ (@ the_inv_into_nat_o C3) G) I2)) X2))) G) I) (@ id_nat I))))) (forall ((A4 (-> Bool set_Pr1261947904930325089at_nat))) (= (@ comple1930127330929219688at_nat (@ (@ image_7077428525161401678at_nat A4) top_top_set_o)) (@ (@ inf_in2572325071724192079at_nat (@ A4 true)) (@ A4 false)))) (forall ((X2 ref_a) (Y3 heap_e7401611519738050253t_unit) (A heap_e7401611519738050253t_unit)) (=> (= (@ produc1126150082675451753t_unit (@ (@ produc6544324848051098391t_unit X2) Y3)) A) (= Y3 A))) (forall ((S5 set_o) (F (-> Bool nat nat)) (X2 Bool) (Y3 Bool) (G (-> nat nat))) (let ((_let_1 (@ comp_nat_nat_nat (@ F Y3)))) (let ((_let_2 (@ comp_nat_nat_nat (@ F X2)))) (=> (@ (@ finite4703585013658510744_o_nat S5) F) (=> (@ (@ member_o X2) S5) (=> (@ (@ member_o Y3) S5) (= (@ _let_1 (@ _let_2 G)) (@ _let_2 (@ _let_1 G))))))))) (forall ((G (-> nat int)) (F (-> nat nat)) (A4 set_nat)) (= (@ complete_Sup_Sup_int (@ (@ image_nat_int G) (@ (@ image_nat_nat F) A4))) (@ complete_Sup_Sup_int (@ (@ image_nat_int (@ (@ comp_nat_int_nat G) F)) A4)))) (forall ((F (-> nat num)) (G (-> nat num)) (H (-> int nat)) (I (-> int nat))) (= (@ (@ comp_P9218946435557410242nt_int (@ (@ produc1476026309457068494at_num F) G)) (@ (@ produc5667422475138734578nt_nat H) I)) (@ (@ produc165562089265172102nt_num (@ (@ comp_nat_num_int F) H)) (@ (@ comp_nat_num_int G) I)))) (forall ((B5 (-> nat set_Pr1261947904930325089at_nat)) (A nat) (A4 set_nat)) (let ((_let_1 (@ image_7178329752028323786at_nat B5))) (= (@ comple1930127330929219688at_nat (@ _let_1 (@ (@ insert_nat A) A4))) (@ (@ inf_in2572325071724192079at_nat (@ B5 A)) (@ comple1930127330929219688at_nat (@ _let_1 A4)))))) (forall ((B5 (-> produc3843707927480180839at_nat set_nat)) (A produc3843707927480180839at_nat) (A4 set_Pr4329608150637261639at_nat)) (let ((_let_1 (@ image_3160451284896210088et_nat B5))) (= (@ comple7806235888213564991et_nat (@ _let_1 (@ (@ insert9069300056098147895at_nat A) A4))) (@ (@ inf_inf_set_nat (@ B5 A)) (@ comple7806235888213564991et_nat (@ _let_1 A4)))))) (forall ((A4 set_nat) (B5 set_nat) (F (-> nat set_nat)) (G (-> nat set_nat))) (=> (@ (@ ord_less_eq_set_nat A4) B5) (=> (forall ((X nat)) (=> (@ (@ member_nat X) A4) (@ (@ ord_less_eq_set_nat (@ F X)) (@ G X)))) (@ (@ ord_less_eq_set_nat (@ comple7399068483239264473et_nat (@ (@ image_nat_set_nat F) A4))) (@ comple7399068483239264473et_nat (@ (@ image_nat_set_nat G) B5)))))) (forall ((F (-> nat rat)) (A4 set_nat)) (= (= bot_bot_set_rat (@ (@ image_nat_rat F) A4)) (= A4 bot_bot_set_nat))) (forall ((X2 (-> char nat)) (Ya (-> char nat)) (Y3 (-> char int)) (Xa2 (-> char int)) (R3 (-> nat int Bool)) (Ra (-> nat int Bool))) (=> (= X2 Ya) (=> (= Y3 Xa2) (=> (forall ((Z3 nat) (Yb int)) (=> (@ (@ member_nat Z3) (@ (@ image_char_nat Ya) top_top_set_char)) (=> (@ (@ member_int Yb) (@ (@ image_char_int Xa2) top_top_set_char)) (= (@ (@ R3 Z3) Yb) (@ (@ Ra Z3) Yb))))) (= (@ (@ (@ (@ bNF_re3731845416926587903at_int (lambda ((Y2 char) (Z char)) (= Y2 Z))) R3) X2) Y3) (@ (@ (@ (@ bNF_re3731845416926587903at_int (lambda ((Y2 char) (Z char)) (= Y2 Z))) Ra) Ya) Xa2)))))) (forall ((F (-> nat rat)) (Y3 rat)) (=> (= (@ (@ image_nat_rat F) top_top_set_nat) top_top_set_rat) (exists ((X nat)) (= Y3 (@ F X))))) (forall ((C3 set_nat) (A4 (-> nat set_o)) (B5 set_o)) (let ((_let_1 (= C3 bot_bot_set_nat))) (and (=> (not _let_1) (= (@ comple90263536869209701_set_o (@ (@ image_nat_set_o (lambda ((X4 nat)) (@ (@ sup_sup_set_o (@ A4 X4)) B5))) C3)) (@ (@ sup_sup_set_o (@ comple90263536869209701_set_o (@ (@ image_nat_set_o A4) C3))) B5))) (=> _let_1 (= (@ comple90263536869209701_set_o (@ (@ image_nat_set_o (lambda ((X4 nat)) (@ (@ sup_sup_set_o (@ A4 X4)) B5))) C3)) bot_bot_set_o))))) (forall ((F (-> nat product_prod_nat_nat)) (A4 set_nat)) (=> (@ finite6177210948735845034at_nat (@ (@ image_5846123807819985514at_nat F) A4)) (=> (not (@ finite_finite_nat A4)) (exists ((X product_prod_nat_nat)) (and (not (@ finite_finite_nat (@ (@ inf_inf_set_nat (@ (@ vimage8013328719654469172at_nat F) (@ (@ insert8211810215607154385at_nat X) bot_bo2099793752762293965at_nat))) A4))) (@ (@ member8440522571783428010at_nat X) (@ (@ image_5846123807819985514at_nat F) A4))))))) (forall ((F (-> rat int)) (X2 rat)) (@ (@ member_int (@ F X2)) (@ (@ image_rat_int F) top_top_set_rat))) (forall ((G (-> nat nat)) (H (-> nat nat)) (R (-> nat nat)) (F (-> nat nat))) (let ((_let_1 (@ comp_nat_nat_nat F))) (=> (= (@ (@ comp_nat_nat_nat G) H) R) (= (@ (@ comp_nat_nat_nat (@ _let_1 G)) H) (@ _let_1 R))))) (= produc1126150082675451753t_unit (@ produc2552614499379209865t_unit (lambda ((X12 ref_a) (X23 heap_e7401611519738050253t_unit)) X23))) (forall ((B5 set_nat) (A4 set_nat) (F (-> nat product_unit)) (G (-> nat product_unit))) (=> (@ (@ ord_less_eq_set_nat B5) A4) (=> (forall ((X nat)) (=> (@ (@ member_nat X) B5) (@ (@ ord_le3221252021190050221t_unit (@ F X)) (@ G X)))) (@ (@ ord_le3221252021190050221t_unit (@ comple2584293577114468500t_unit (@ (@ image_8730104196221521654t_unit F) A4))) (@ comple2584293577114468500t_unit (@ (@ image_8730104196221521654t_unit G) B5)))))) (forall ((R3 set_Pr1261947904930325089at_nat) (S5 set_Pr1261947904930325089at_nat)) (= (@ (@ ord_le2646555220125990790_nat_o (lambda ((X4 nat) (Y5 nat)) (@ (@ member8440522571783428010at_nat (@ (@ product_Pair_nat_nat X4) Y5)) R3))) (lambda ((X4 nat) (Y5 nat)) (@ (@ member8440522571783428010at_nat (@ (@ product_Pair_nat_nat X4) Y5)) S5))) (@ (@ ord_le3146513528884898305at_nat R3) S5))) (forall ((R3 (-> nat nat Bool))) (= (@ (@ bNF_re5653821019739307937at_nat (lambda ((Y2 nat) (Z nat)) (= Y2 Z))) R3) (@ (@ relcom8186637903969514807at_nat (@ conver3498139987538047730at_nat (@ (@ bNF_Gr3388551082464497497at_nat (@ collec8718012497556192979at_nat (lambda ((X4 (-> nat product_prod_nat_nat))) (@ (@ ord_le3146513528884898305at_nat (@ (@ image_5846123807819985514at_nat X4) top_top_set_nat)) (@ collec3392354462482085612at_nat (@ produc6081775807080527818_nat_o R3)))))) (@ comp_P1955610211387027840at_nat product_fst_nat_nat)))) (@ (@ bNF_Gr3388551082464497497at_nat (@ collec8718012497556192979at_nat (lambda ((X4 (-> nat product_prod_nat_nat))) (@ (@ ord_le3146513528884898305at_nat (@ (@ image_5846123807819985514at_nat X4) top_top_set_nat)) (@ collec3392354462482085612at_nat (@ produc6081775807080527818_nat_o R3)))))) (@ comp_P1955610211387027840at_nat product_snd_nat_nat))))) (forall ((Ac product_prod_nat_nat) (P2 (-> nat nat Bool)) (Q2 (-> nat nat Bool))) (=> (@ (@ member8440522571783428010at_nat Ac) (@ collec3392354462482085612at_nat (@ produc6081775807080527818_nat_o (@ (@ relcompp_nat_nat_nat P2) Q2)))) (@ (@ member8440522571783428010at_nat (@ (@ (@ bNF_fs6799373675401686564at_nat P2) Q2) Ac)) (@ collec3392354462482085612at_nat (@ produc6081775807080527818_nat_o P2))))) (forall ((A product_unit) (A4 set_Product_unit) (B nat) (B5 set_nat)) (let ((_let_1 (@ produc6875377002296012693it_nat (@ (@ insert_Product_unit A) A4)))) (= (@ _let_1 (lambda ((Uu product_unit)) (@ (@ insert_nat B) B5))) (@ (@ insert6879346373837673660it_nat (@ (@ produc4803288329813530246it_nat A) B)) (@ (@ sup_su1639320892072265582it_nat (@ (@ 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order_2678306075789641520at_int F) (=> (@ condit2214826472909112428ve_nat A4) (@ condit1735850657277959132ow_int (@ (@ image_nat_int F) A4))))) (forall ((S5 set_Pr4329608150637261639at_nat) (F (-> produc3843707927480180839at_nat nat nat)) (X2 produc3843707927480180839at_nat) (Y3 produc3843707927480180839at_nat)) (let ((_let_1 (@ F Y3))) (let ((_let_2 (@ F X2))) (=> (@ (@ finite8619596206551965927at_nat S5) F) (=> (@ (@ member8757157785044589968at_nat X2) S5) (=> (@ (@ member8757157785044589968at_nat Y3) S5) (= (@ (@ comp_nat_nat_nat _let_1) _let_2) (@ (@ comp_nat_nat_nat _let_2) _let_1)))))))) (forall ((B int) (F (-> nat int)) (X2 nat) (C int) (G (-> nat int)) (A4 set_nat)) (=> (= B (@ F X2)) (=> (= C (@ G X2)) (=> (@ (@ member_nat X2) A4) (@ (@ member5262025264175285858nt_int (@ (@ product_Pair_int_int B) C)) (@ (@ (@ bNF_Gr8315020014477690244nt_int A4) F) G)))))) (forall ((C3 set_o) (A nat) (B5 (-> Bool set_nat))) (let ((_let_1 (@ insert_nat A))) (let ((_let_2 (@ _let_1 (@ comple7399068483239264473et_nat (@ (@ image_o_set_nat B5) C3))))) (let ((_let_3 (= C3 bot_bot_set_o))) (and (=> (not _let_3) (= _let_2 (@ comple7399068483239264473et_nat (@ (@ image_o_set_nat (lambda ((X4 Bool)) (@ (@ insert_nat A) (@ B5 X4)))) C3)))) (=> _let_3 (= _let_2 (@ _let_1 bot_bot_set_nat)))))))) (forall ((F (-> nat Bool)) (A4 set_nat)) (= (= (@ (@ image_nat_o F) A4) bot_bot_set_o) (= A4 bot_bot_set_nat))) (= code_divmod_integer (lambda ((K5 code_integer) (L3 code_integer)) (let ((_let_1 (@ (@ code_divmod_abs K5) L3))) (let ((_let_2 (@ produc1086072967326762835nteger zero_z3403309356797280102nteger))) (@ (@ (@ if_Pro6119634080678213985nteger (= K5 zero_z3403309356797280102nteger)) (@ _let_2 zero_z3403309356797280102nteger)) (@ (@ (@ if_Pro6119634080678213985nteger (= L3 zero_z3403309356797280102nteger)) (@ _let_2 K5)) (@ (@ (@ (@ comp_C1593894019821074884nteger (@ (@ comp_C8797469213163452608nteger produc6499014454317279255nteger) times_3573771949741848930nteger)) sgn_sgn_Code_integer) L3) (@ (@ (@ if_Pro6119634080678213985nteger (= (@ sgn_sgn_Code_integer K5) (@ sgn_sgn_Code_integer L3))) _let_1) (@ (@ produc6916734918728496179nteger (lambda ((R5 code_integer) (S code_integer)) (let ((_let_1 (@ uminus1351360451143612070nteger R5))) (@ (@ (@ if_Pro6119634080678213985nteger (= S zero_z3403309356797280102nteger)) (@ (@ produc1086072967326762835nteger _let_1) zero_z3403309356797280102nteger)) (@ (@ produc1086072967326762835nteger (@ (@ minus_8373710615458151222nteger _let_1) one_one_Code_integer)) (@ (@ minus_8373710615458151222nteger (@ abs_abs_Code_integer L3)) S)))))) _let_1))))))))) (forall ((C product_prod_nat_num) (A4 set_nat) (B5 (-> nat set_num))) (=> (@ (@ member9148766508732265716at_num C) (@ (@ produc6237731129814287028at_num A4) B5)) (not (forall ((X nat)) (=> (@ (@ member_nat X) A4) (forall ((Y num)) (=> (@ (@ member_num Y) (@ B5 X)) (not (= C (@ (@ product_Pair_nat_num X) Y)))))))))) (forall ((F (-> num num)) (X2 nat) (Y3 num)) (let ((_let_1 (@ product_Pair_nat_num X2))) (= (@ (@ produc8389275579088931588um_nat F) (@ _let_1 Y3)) (@ _let_1 (@ F Y3))))) (forall ((A4 set_Product_unit) (F (-> product_unit set_nat)) (B5 set_Product_unit)) (let ((_let_1 (@ image_8173849991827986510et_nat F))) (let ((_let_2 (@ _let_1 B5))) (let ((_let_3 (@ _let_1 A4))) (=> (not (= A4 bot_bo3957492148770167129t_unit)) (=> (@ condit5477540289124974626et_nat _let_3) (=> (not (= B5 bot_bo3957492148770167129t_unit)) (=> (@ condit5477540289124974626et_nat _let_2) (= (@ comple7399068483239264473et_nat (@ _let_1 (@ (@ sup_su793286257634532545t_unit A4) B5))) (@ (@ sup_sup_set_nat (@ comple7399068483239264473et_nat _let_3)) (@ comple7399068483239264473et_nat _let_2))))))))))) (forall ((F (-> nat nat)) (G (-> nat nat)) (L (-> nat nat)) (H (-> nat nat))) (let ((_let_1 (@ comp_nat_nat_nat F))) (=> (= (@ _let_1 G) L) (= (@ _let_1 (@ (@ comp_nat_nat_nat G) H)) (@ (@ comp_nat_nat_nat L) H))))) (forall ((B Bool) (F (-> nat Bool)) (X2 nat)) (=> (= B (@ F X2)) (@ (@ member_o B) (@ (@ image_nat_o F) top_top_set_nat)))) (forall ((B5 (-> Bool nat Bool)) (C3 (-> Bool nat Bool)) (A4 (-> nat nat Bool))) (let ((_let_1 (@ bNF_re7523573913982466217_o_nat A4))) (@ (@ (@ (@ bNF_re1515921786380824775at_nat (@ (@ bNF_re4209105892566519389_o_nat B5) C3)) (@ (@ bNF_re2144779315220482269at_nat (@ _let_1 B5)) (@ _let_1 C3))) comp_o_o_nat) comp_nat_nat_nat))) (forall ((Inf (-> set_o Bool)) (G (-> Bool Bool)) (F (-> nat Bool)) (A4 set_nat)) (= (@ Inf (@ (@ image_o_o G) (@ (@ image_nat_o F) A4))) (@ Inf (@ (@ image_nat_o (@ (@ comp_o_o_nat G) F)) A4)))) (forall ((F (-> int int)) (S5 set_set_int)) (let ((_let_1 (@ image_int_int F))) (= (@ _let_1 (@ comple3221217463730067765et_int S5)) (@ comple3221217463730067765et_int (@ (@ image_524474410958335435et_int _let_1) S5))))) (forall ((I produc3843707927480180839at_nat) (A4 set_Pr4329608150637261639at_nat) (F (-> produc3843707927480180839at_nat product_unit)) (U product_unit)) (=> (@ (@ member8757157785044589968at_nat I) A4) (=> (@ (@ ord_le3221252021190050221t_unit (@ F I)) U) (@ (@ ord_le3221252021190050221t_unit (@ comple2584293577114468500t_unit (@ (@ image_7082456443403096939t_unit F) A4))) U)))) (forall ((G1 (-> nat num)) (G22 (-> int nat)) (F1 (-> int nat)) (F22 (-> int int)) (V product_prod_int_int)) (= (@ (@ (@ produc5918048235202344416nt_nat G1) G22) (@ (@ (@ produc5664932004629684302nt_int F1) F22) V)) (@ (@ (@ produc3608230303109393468nt_nat (@ (@ comp_nat_num_int G1) F1)) (@ (@ comp_int_nat_int G22) F22)) V))) (forall ((R3 (-> product_prod_nat_nat int Bool))) (= (@ (@ relcom8911704206367525917at_int bot_bo4898103413517107610_nat_o) R3) bot_bo5438875203632553179_int_o)) (forall ((A set_Pr1261947904930325089at_nat) (B set_Pr1261947904930325089at_nat) (A4 set_se7855581050983116737at_nat) (B5 (-> set_Pr1261947904930325089at_nat set_se7855581050983116737at_nat))) (=> (@ (@ member8757157785044589968at_nat (@ (@ produc2922128104949294807at_nat A) B)) (@ (@ produc7726050920695093128at_nat A4) B5)) (@ (@ member2643936169264416010at_nat A) A4))) (forall ((N3 nat) (P2 (-> nat Bool)) (M3 nat)) (=> (forall ((K2 nat)) (=> (@ (@ ord_less_nat N3) K2) (@ P2 K2))) (=> (forall ((K2 nat)) (=> (@ (@ ord_less_eq_nat K2) N3) (=> (forall ((I5 nat)) (=> (@ (@ ord_less_nat K2) I5) (@ P2 I5))) (@ P2 K2)))) (@ P2 M3)))) (forall ((X2 (-> char Bool)) (Ya (-> char Bool)) (Y3 (-> char Bool)) (Xa2 (-> char Bool)) (R3 (-> Bool Bool Bool)) (Ra (-> Bool Bool Bool))) (=> (= X2 Ya) (=> (= Y3 Xa2) (=> (forall ((Z3 Bool) (Yb Bool)) (=> (@ (@ member_o Z3) (@ (@ image_char_o Ya) top_top_set_char)) (=> (@ (@ member_o Yb) (@ (@ image_char_o Xa2) top_top_set_char)) (= (@ (@ R3 Z3) Yb) (@ (@ Ra Z3) Yb))))) (= (@ (@ (@ (@ bNF_re1692451286490762625ar_o_o (lambda ((Y2 char) (Z char)) (= Y2 Z))) R3) X2) Y3) (@ (@ (@ (@ bNF_re1692451286490762625ar_o_o (lambda ((Y2 char) (Z char)) (= Y2 Z))) Ra) Ya) Xa2)))))) (forall ((F (-> code_integer code_integer code_integer)) (A4 set_Code_integer) (G (-> (-> code_integer code_integer) produc8923325533196201883nteger produc8923325533196201883nteger))) (=> (@ (@ inj_on108595395805848489nteger F) A4) (=> (@ (@ inj_on3998011822705705585nteger G) (@ (@ image_2177946750938214461nteger F) A4)) (@ (@ inj_on7031512951821619701nteger (@ (@ comp_C8797469213163452608nteger G) F)) A4)))) (forall ((G (-> nat nat)) (F (-> int nat)) (V (-> int int))) (let ((_let_1 (@ comp_nat_nat_int G))) (= (@ _let_1 (@ (@ comp_int_nat_int F) V)) (@ (@ comp_int_nat_int (@ _let_1 F)) V)))) (forall ((F (-> int int)) (G (-> char int))) (= (@ (@ image_char_int (lambda ((X4 char)) (@ F (@ G X4)))) top_top_set_char) (@ (@ image_int_int F) (@ (@ image_char_int G) top_top_set_char)))) (forall ((X2 int) (A4 set_int) (C int)) (=> (@ (@ member_int X2) A4) (= (@ (@ image_int_int (lambda ((X4 int)) C)) A4) (@ (@ insert_int C) bot_bot_set_int)))) _let_208 (forall ((P2 Bool) (Q2 (-> int int Bool))) (= (@ produc4947309494688390418_int_o (lambda ((A5 int) (B4 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((F (-> nat int))) (let ((_let_1 (@ image_nat_int F))) (= (@ (@ comp_s1975749275458958491et_nat comple3221217463730067765et_int) (@ image_3739036796817536367et_int _let_1)) (@ (@ comp_s3768223441818958217et_nat _let_1) comple7399068483239264473et_nat)))) (forall ((F (-> char Bool)) (A Bool) (X2 char)) (=> (= (@ (@ image_char_o F) top_top_set_char) (@ (@ insert_o A) bot_bot_set_o)) (= (@ F X2) A))) (forall ((F (-> int int int)) (G1 (-> int int)) (G22 (-> int int))) (= (@ (@ comp_P5356232565778667509nt_int (@ produc8211389475949308722nt_int F)) (@ (@ produc6036585564866528938nt_int G1) G22)) (@ produc8211389475949308722nt_int (lambda ((L3 int) (R5 int)) (@ (@ F (@ G1 L3)) (@ G22 R5)))))) (forall ((C product_prod_int_int) (A4 set_int)) (=> (@ (@ member5262025264175285858nt_int C) (@ id_on_int A4)) (not (forall ((X int)) (=> (@ (@ member_int X) A4) (not (= C (@ (@ product_Pair_int_int X) X)))))))) (forall ((A4 set_int) (B5 set_int)) (= (@ (@ image_2653370878348428101nt_int (@ produc4245557441103728435nt_int (lambda ((I2 int) (J int)) (@ (@ product_Pair_int_int J) I2)))) (@ (@ produc1453890548195736866nt_int A4) (lambda ((Uu int)) B5))) (@ (@ produc1453890548195736866nt_int B5) (lambda ((Uu int)) A4)))) (forall ((C3 set_o) (A4 (-> Bool set_int)) (B5 set_int)) (let ((_let_1 (@ (@ minus_minus_set_int (@ comple3628384868704368283et_int (@ (@ image_o_set_int A4) C3))) B5))) (let ((_let_2 (= C3 bot_bot_set_o))) (and (=> _let_2 (= _let_1 (@ (@ minus_minus_set_int top_top_set_int) B5))) (=> (not _let_2) (= _let_1 (@ comple3628384868704368283et_int (@ (@ image_o_set_int (lambda ((X4 Bool)) (@ (@ minus_minus_set_int (@ A4 X4)) B5))) C3)))))))) (forall ((A4 set_int) (B5 set_nat) (F (-> int nat))) (=> (@ finite_finite_int A4) (=> (@ (@ ord_less_eq_set_nat B5) (@ (@ image_int_nat F) A4)) (@ finite_finite_nat B5)))) (forall ((A4 set_Pr1261947904930325089at_nat)) (@ (@ total_3592101749530773125at_nat A4) fun_pair_less)) (forall ((R3 (-> int int Bool)) (S5 (-> num num 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(-> nat set_o))) (let ((_let_1 (@ (@ vimage6125388955539849434_nat_o (@ product_Pair_nat_o X2)) (@ (@ product_Sigma_nat_o A4) F)))) (let ((_let_2 (@ (@ member_nat X2) A4))) (and (=> (not _let_2) (= _let_1 bot_bot_set_o)) (=> _let_2 (= _let_1 (@ F X2))))))) (forall ((F (-> nat nat)) (G (-> int nat)) (R set_int)) (= (@ (@ image_nat_nat F) (@ (@ image_int_nat G) R)) (@ (@ image_int_nat (@ (@ comp_nat_nat_int F) G)) R))) (forall ((S5 set_nat) (F (-> nat nat)) (T3 set_nat)) (= (@ (@ ord_less_eq_set_nat S5) (@ (@ image_nat_nat F) T3)) (exists ((U2 set_nat)) (and (@ (@ inj_on_nat_nat F) U2) (= S5 (@ (@ image_nat_nat F) U2)) (@ (@ ord_less_eq_set_nat U2) T3))))) (forall ((X2 nat) (Fx nat) (A4 set_nat) (F (-> nat nat))) (=> (@ (@ member8440522571783428010at_nat (@ (@ product_Pair_nat_nat X2) Fx)) (@ (@ bNF_Gr_nat_nat A4) F)) (= (@ F X2) Fx))) (forall ((B5 set_nat) (F (-> nat nat)) (A4 set_nat) (G (-> nat nat))) (let ((_let_1 (@ (@ image_nat_nat F) A4))) (=> (not (= B5 bot_bot_set_nat)) (=> (@ condit1738341127787009408ow_nat _let_1) (=> (forall ((M4 nat)) (=> (@ (@ member_nat M4) B5) (exists ((X6 nat)) (and (@ (@ ord_less_eq_nat (@ F X6)) (@ G M4)) (@ (@ member_nat X6) A4))))) (@ (@ ord_less_eq_nat (@ complete_Inf_Inf_nat _let_1)) (@ complete_Inf_Inf_nat (@ (@ image_nat_nat G) B5)))))))) _let_206 (forall ((Sup (-> set_num num)) (A4 set_num)) (= (@ Sup (@ (@ image_num_num id_num) A4)) (@ Sup A4))) (= produc8739625826339149834_nat_o (lambda ((C4 (-> nat nat product_prod_nat_nat Bool)) (P3 product_prod_nat_nat) (__flatten_var_0 product_prod_nat_nat)) (@ (@ (@ C4 (@ product_fst_nat_nat P3)) (@ product_snd_nat_nat P3)) __flatten_var_0))) (@ (@ _let_12 (@ produc2626176000494625587at_nat (lambda ((X4 nat) (Y5 nat)) (@ (@ product_Pair_nat_nat Y5) X4)))) (@ produc2626176000494625587at_nat (lambda ((X4 nat) (Y5 nat)) (@ (@ product_Pair_nat_nat Y5) X4)))) (forall ((F (-> rat nat)) (A rat) (A4 set_rat)) (=> (@ (@ inj_on_rat_nat F) top_top_set_rat) (= (@ (@ member_nat (@ F A)) (@ (@ 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int nat))) (= (@ (@ produc165562089265172102nt_num (@ (@ comp_nat_num_int F1) F22)) (@ (@ comp_nat_num_int G1) G22)) (@ (@ comp_P9218946435557410242nt_int (@ (@ produc1476026309457068494at_num F1) G1)) (@ (@ produc5667422475138734578nt_nat F22) G22)))) _let_201 (forall ((X5 (-> int code_integer Bool)) (A4 (-> num num Bool)) (F (-> int num)) (G (-> code_integer num)) (Y4 (-> int code_integer Bool)) (B5 (-> num num Bool))) (=> (@ (@ (@ (@ bNF_re6718328864250387230um_num X5) A4) F) G) (=> (forall ((X int) (Y code_integer)) (=> (@ (@ Y4 X) Y) (@ (@ X5 X) Y))) (=> (forall ((X num) (Y num)) (=> (@ (@ A4 X) Y) (@ (@ B5 X) Y))) (@ (@ (@ (@ bNF_re6718328864250387230um_num Y4) B5) F) G))))) (forall ((B5 set_nat) (F (-> product_prod_nat_nat nat)) (A4 set_Pr1261947904930325089at_nat)) (=> (@ finite_finite_nat B5) (=> (@ (@ ord_less_eq_set_nat B5) (@ (@ image_2486076414777270412at_nat F) A4)) (exists ((C2 set_Pr1261947904930325089at_nat)) (and (@ (@ ord_le3146513528884898305at_nat C2) A4) (= B5 (@ (@ image_2486076414777270412at_nat F) C2)) (@ finite6177210948735845034at_nat C2)))))) (forall ((X2 set_Pr1261947904930325089at_nat) (Y3 set_Pr1261947904930325089at_nat)) (= (@ the_Pr4604535484834969198at_nat (@ produc410239310623530412_nat_o (lambda ((X7 set_Pr1261947904930325089at_nat) (Y6 set_Pr1261947904930325089at_nat)) (and (= Y3 Y6) (= X2 X7))))) (@ (@ produc2922128104949294807at_nat X2) Y3))) (forall ((S5 set_set_int)) (= (@ comple6496622788309502864_int_o (@ (@ image_set_int_int_o (lambda ((I2 set_int) (X4 int)) (@ (@ member_int X4) I2))) S5)) (lambda ((X4 int)) (@ (@ member_int X4) (@ comple3221217463730067765et_int S5))))) (forall ((F (-> rat nat)) (A4 set_nat)) (let ((_let_1 (@ image_rat_nat F))) (=> (= (@ _let_1 top_top_set_rat) top_top_set_nat) (= (@ _let_1 (@ (@ vimage_rat_nat F) A4)) A4)))) (forall ((A4 set_nat) (F (-> nat set_nat))) (= (@ (@ sup_sup_set_nat A4) (@ comple7399068483239264473et_nat (@ (@ image_nat_set_nat F) bot_bot_set_nat))) A4)) (forall ((I nat) (C3 set_nat) (G (-> nat nat)) (X2 nat)) (=> (@ (@ member_nat I) C3) (=> (@ (@ inj_on_nat_nat G) C3) (= (@ (@ (@ comp_nat_nat_nat (lambda ((I2 nat)) (@ (@ (@ if_nat (@ (@ member_nat I2) (@ (@ image_nat_nat G) C3))) (@ (@ (@ the_inv_into_nat_nat C3) G) I2)) X2))) G) I) (@ id_nat I))))) (= produc8211389475949308722nt_int (lambda ((F2 (-> int int int)) (X4 product_prod_int_int)) (@ (@ F2 (@ product_fst_int_int X4)) (@ product_snd_int_int X4)))) (forall ((R set_Pr8693737435421807431at_nat) (A product_prod_nat_nat) (B product_prod_nat_nat)) (let ((_let_1 (@ field_4706345496283612622at_nat R))) (=> (@ (@ order_7480980593162297270at_nat _let_1) R) (=> (@ (@ member8440522571783428010at_nat A) _let_1) (=> (@ (@ member8440522571783428010at_nat B) _let_1) (= (@ (@ member8206827879206165904at_nat (@ (@ produc6161850002892822231at_nat A) B)) R) (not (@ (@ member8206827879206165904at_nat (@ (@ produc6161850002892822231at_nat B) A)) (@ (@ minus_8321449233255521966at_nat R) id_Pro2258643101195443293at_nat))))))))) (forall ((F (-> int nat)) (C3 set_int) (A4 set_int) (B5 (-> int set_int)) (J4 int)) (=> (@ (@ inj_on_int_nat F) C3) (=> (forall ((X int)) (=> (@ (@ member_int X) A4) (@ (@ ord_less_eq_set_int (@ B5 X)) C3))) (=> (@ (@ member_int J4) A4) (= (@ (@ image_int_nat F) (@ comple3628384868704368283et_int (@ (@ image_int_set_int B5) A4))) (@ comple7806235888213564991et_nat (@ (@ image_int_set_nat (lambda ((X4 int)) (@ (@ image_int_nat F) (@ B5 X4)))) A4))))))) (forall ((C3 set_o) (A4 set_nat) (B5 (-> Bool set_nat))) (let ((_let_1 (@ (@ inf_inf_set_nat A4) (@ comple7806235888213564991et_nat (@ (@ image_o_set_nat B5) C3))))) (let ((_let_2 (= C3 bot_bot_set_o))) (and (=> (not _let_2) (= _let_1 (@ comple7806235888213564991et_nat (@ (@ image_o_set_nat (lambda ((X4 Bool)) (@ (@ inf_inf_set_nat A4) (@ B5 X4)))) C3)))) (=> _let_2 (= _let_1 A4)))))) (forall ((F (-> nat product_prod_nat_nat)) (A4 set_nat)) (=> (@ finite6177210948735845034at_nat (@ (@ image_5846123807819985514at_nat F) A4)) (=> (not (@ finite_finite_nat A4)) (exists ((X product_prod_nat_nat)) (and (not (@ finite_finite_nat (@ (@ vimage8013328719654469172at_nat F) (@ (@ insert8211810215607154385at_nat X) bot_bo2099793752762293965at_nat)))) (@ (@ member8440522571783428010at_nat X) (@ (@ image_5846123807819985514at_nat F) A4))))))) (forall ((A4 set_int) (F (-> int int)) (M int)) (=> (forall ((X int)) (=> (@ (@ member_int X) A4) (@ (@ ord_less_eq_int (@ F X)) M))) (@ condit2212336002400062152ve_int (@ (@ image_int_int F) A4)))) (forall ((T2 product_prod_nat_num)) (= T2 (@ (@ product_Pair_nat_num (@ product_fst_nat_num T2)) (@ product_snd_nat_num T2)))) (forall ((F (-> Bool Bool)) (A4 set_o)) (= (= (@ (@ image_o_o F) A4) bot_bot_set_o) (= A4 bot_bot_set_o))) (forall ((C (-> produc8923325533196201883nteger produc8923325533196201883nteger)) (F (-> code_integer code_integer code_integer))) (= (@ (@ comp_C8797469213163452608nteger (lambda ((X4 (-> code_integer code_integer)) (__flatten_var_0 produc8923325533196201883nteger)) (@ C __flatten_var_0))) F) (lambda ((X4 code_integer) (__flatten_var_0 produc8923325533196201883nteger)) (@ C __flatten_var_0)))) (forall ((X2 produc8923325533196201883nteger) (Y3 produc8923325533196201883nteger)) (= (@ (@ (@ if_Pro6119634080678213985nteger true) X2) Y3) X2)) (forall ((M (-> produc859450856879609959at_nat set_Pr1261947904930325089at_nat)) (A4 set_Pr8693737435421807431at_nat) (B5 set_Pr8693737435421807431at_nat)) (let ((_let_1 (@ image_1384942819424619199at_nat M))) (= (@ comple1930127330929219688at_nat (@ _let_1 (@ (@ sup_su718114333110466843at_nat A4) B5))) (@ (@ inf_in2572325071724192079at_nat (@ comple1930127330929219688at_nat (@ _let_1 A4))) (@ comple1930127330929219688at_nat (@ _let_1 B5)))))) _let_200 (forall ((Xa2 product_prod_nat_nat) (X2 product_prod_nat_nat)) (= (@ (@ minus_minus_int (@ abs_Integ Xa2)) (@ abs_Integ X2)) (@ abs_Integ (@ (@ (@ produc27273713700761075at_nat (lambda ((X4 nat) (Y5 nat) (__flatten_var_0 product_prod_nat_nat)) (@ (@ produc2626176000494625587at_nat (lambda ((U3 nat) (V3 nat)) (@ (@ product_Pair_nat_nat (@ (@ plus_plus_nat X4) V3)) (@ (@ plus_plus_nat Y5) U3)))) __flatten_var_0))) Xa2) X2)))) (forall ((F (-> char rat)) (G (-> rat nat))) (=> (= (@ (@ image_char_rat F) top_top_set_char) top_top_set_rat) (=> (= (@ (@ image_rat_nat G) top_top_set_rat) top_top_set_nat) (= (@ (@ image_char_nat (@ (@ comp_rat_nat_char G) F)) top_top_set_char) top_top_set_nat)))) (forall ((A4 set_Product_unit) (G (-> product_unit product_unit)) (B5 set_Product_unit) (F (-> product_unit product_unit))) (let ((_let_1 (@ (@ image_405062704495631173t_unit G) B5))) (=> (not (= A4 bot_bo3957492148770167129t_unit)) (=> (@ condit2080475194861589617t_unit _let_1) (=> (@ (@ ord_le3507040750410214029t_unit A4) B5) (=> (forall ((X product_unit)) (=> (@ (@ member_Product_unit X) A4) (@ (@ ord_le3221252021190050221t_unit (@ F X)) (@ G X)))) (@ (@ ord_le3221252021190050221t_unit (@ comple4687483117567863418t_unit (@ (@ image_405062704495631173t_unit F) A4))) (@ comple4687483117567863418t_unit _let_1)))))))) (forall ((A int) (B int) (A4 set_Pr958786334691620121nt_int) (F (-> int int Bool))) (=> (@ (@ member5262025264175285858nt_int (@ (@ product_Pair_int_int A) B)) A4) (@ (@ member_o (@ (@ F A) B)) (@ (@ image_2135063354759101220_int_o (@ produc4947309494688390418_int_o F)) A4)))) _let_199 (forall ((A int) (B int) (A4 set_Pr958786334691620121nt_int) (F (-> int int int))) (=> (@ (@ member5262025264175285858nt_int (@ (@ product_Pair_int_int A) B)) A4) (@ (@ member_int (@ (@ F A) B)) (@ (@ image_5042161079198086560nt_int (@ produc8211389475949308722nt_int F)) A4)))) (forall ((A int) (B int) (R3 set_Pr958786334691620121nt_int) (F (-> int nat)) (G (-> int num))) (=> (@ (@ member5262025264175285858nt_int (@ (@ product_Pair_int_int A) B)) R3) (@ (@ member9148766508732265716at_num (@ (@ product_Pair_nat_num (@ F A)) (@ G B))) (@ (@ image_6540112122905407959at_num (@ (@ produc2224754261294513212nt_num F) G)) R3)))) (forall ((A4 set_Product_unit) (B5 (-> product_unit set_Product_unit)) (F (-> product_unit int))) (=> (not (= A4 bot_bo3957492148770167129t_unit)) (=> (forall ((X product_unit)) (=> (@ (@ member_Product_unit X) A4) (not (= (@ B5 X) bot_bo3957492148770167129t_unit)))) (=> (@ condit2212336002400062152ve_int (@ comple3221217463730067765et_int (@ (@ image_3995998972318789802et_int (lambda ((X4 product_unit)) (@ (@ image_873079544045703924it_int F) (@ B5 X4)))) A4))) (= (@ complete_Sup_Sup_int (@ (@ image_873079544045703924it_int F) (@ comple3349607820504768346t_unit (@ (@ image_7778121751606633509t_unit B5) A4)))) (@ complete_Sup_Sup_int (@ (@ image_873079544045703924it_int (lambda ((X4 product_unit)) (@ complete_Sup_Sup_int (@ (@ image_873079544045703924it_int F) (@ B5 X4))))) A4))))))) (forall ((X2 int) (A4 set_int) (F (-> int set_int))) (let ((_let_1 (@ (@ vimage7872673496510460816nt_int (@ product_Pair_int_int X2)) (@ (@ produc1453890548195736866nt_int A4) F)))) (let ((_let_2 (@ (@ member_int X2) A4))) (and (=> _let_2 (= _let_1 (@ F X2))) (=> (not _let_2) (= _let_1 bot_bot_set_int)))))) (forall ((F (-> Bool nat)) (A Bool) (A4 set_o)) (=> (@ (@ inj_on_o_nat F) top_top_set_o) (= (@ (@ member_nat (@ F A)) (@ (@ image_o_nat F) A4)) (@ (@ member_o A) A4)))) (forall ((K product_prod_nat_nat) (I3 set_Pr1261947904930325089at_nat) (A4 (-> product_prod_nat_nat set_nat))) (let ((_let_1 (@ comple7399068483239264473et_nat (@ (@ image_15824709712370754et_nat A4) I3)))) (=> (@ (@ member8440522571783428010at_nat K) I3) (= (@ (@ sup_sup_set_nat (@ A4 K)) _let_1) _let_1)))) (forall ((S5 set_nat) (F (-> nat nat nat)) (X2 nat)) (let ((_let_1 (@ F X2))) (=> (@ (@ finite7982400111564556781at_nat S5) F) (=> (@ (@ member_nat X2) S5) (= (@ (@ comp_nat_nat_nat _let_1) _let_1) _let_1))))) (= produc8211389475949308722nt_int (lambda ((C4 (-> int int int)) (P3 product_prod_int_int)) (@ (@ C4 (@ product_fst_int_int P3)) (@ product_snd_int_int P3)))) (forall ((F (-> Bool Bool)) (G (-> nat nat)) (H (-> nat Bool)) (I (-> nat nat))) (= (@ (@ comp_P4962864564169660718at_nat (@ (@ produc7071226018047599512at_nat F) G)) (@ (@ produc7251236297486395890at_nat H) I)) (@ (@ produc7251236297486395890at_nat (@ (@ comp_o_o_nat F) H)) (@ (@ comp_nat_nat_nat G) I)))) (forall ((G (-> code_integer code_integer code_integer)) (H (-> code_integer code_integer)) (R (-> code_integer code_integer code_integer)) (F (-> (-> code_integer code_integer) produc8923325533196201883nteger produc8923325533196201883nteger))) (let ((_let_1 (@ comp_C8797469213163452608nteger F))) (=> (= (@ (@ comp_C2931745410781319416nteger G) H) R) (= (@ (@ comp_C1593894019821074884nteger (@ _let_1 G)) H) (@ _let_1 R))))) (forall ((A4 set_int) (F (-> int nat))) (=> (@ finite_finite_int A4) (=> (= (@ finite_card_nat (@ (@ image_int_nat F) A4)) (@ finite_card_int A4)) (@ (@ inj_on_int_nat F) A4)))) (forall ((B5 (-> nat set_nat)) (A4 set_set_nat)) (= (@ comple7399068483239264473et_nat (@ (@ image_7916887816326733075et_nat (lambda ((Y5 set_nat)) (@ comple7399068483239264473et_nat (@ (@ image_nat_set_nat B5) Y5)))) A4)) (@ comple7399068483239264473et_nat (@ (@ image_nat_set_nat B5) (@ comple7399068483239264473et_nat A4))))) (forall ((R set_Pr7459493094073627847at_nat)) (let ((_let_1 (@ field_1428494348145443988at_nat R))) (=> (@ (@ order_1878278401035043452at_nat _let_1) R) (= (@ (@ order_423636163458052581at_nat _let_1) R) (forall ((A6 set_se5479201105039950375at_nat)) (=> (@ (@ ord_le7966958417815640519at_nat A6) (@ field_1428494348145443988at_nat R)) (=> (not (= A6 bot_bo1534825418459847827at_nat)) (exists ((X4 set_Pr4329608150637261639at_nat)) (and (forall ((Y5 set_Pr4329608150637261639at_nat)) (=> (@ (@ member6273874620674182256at_nat Y5) A6) (@ (@ member1466754251312161552at_nat (@ (@ produc9060074326276436823at_nat X4) Y5)) R))) (@ (@ member6273874620674182256at_nat X4) A6)))))))))) (forall ((F (-> nat nat)) (A4 set_nat)) (=> (@ (@ inj_on_nat_nat F) A4) (@ (@ inj_on4604407203859583615et_nat (@ image_nat_nat F)) (@ finite_Fpow_nat A4)))) (forall ((F (-> nat int)) (A4 set_int)) (=> (@ (@ inj_on_nat_int F) top_top_set_nat) (=> (@ (@ ord_less_eq_set_int A4) (@ (@ image_nat_int F) top_top_set_nat)) (= (@ finite_card_nat (@ (@ vimage_nat_int F) A4)) (@ finite_card_int A4))))) (forall ((F (-> nat rat)) (G (-> nat nat)) (A4 set_nat)) (= (@ (@ image_nat_rat F) (@ (@ image_nat_nat G) A4)) (@ (@ image_nat_rat (lambda ((X4 nat)) (@ F (@ G X4)))) A4))) (forall ((F (-> nat rat)) (A4 set_nat) (B5 set_rat)) (let ((_let_1 (@ image_nat_rat F))) (=> (= (@ _let_1 A4) B5) (= (@ (@ image_4408659257933336347et_rat _let_1) (@ pow_nat A4)) (@ pow_rat B5))))) _let_198 (forall ((A4 set_Pr1261947904930325089at_nat) (F (-> product_prod_nat_nat product_prod_nat_nat))) (let ((_let_1 (@ (@ image_5168914502847457605at_nat F) A4))) (=> (@ finite6177210948735845034at_nat A4) (=> (@ (@ ord_le3146513528884898305at_nat _let_1) A4) (=> (@ (@ inj_on8969904277767023793at_nat F) A4) (= _let_1 A4)))))) (forall ((A4 set_nat) (B5 (-> nat set_Product_unit))) (= (@ (@ image_3884712837920099081it_nat produc3800628931346975736t_unit) (@ (@ produc5506539147108004339t_unit A4) B5)) (@ collect_nat (lambda ((X4 nat)) (and (not (= (@ B5 X4) bot_bo3957492148770167129t_unit)) (@ (@ member_nat X4) A4)))))) (forall ((Sup (-> set_nat nat)) (A4 set_nat)) (= (@ Sup (@ (@ image_nat_nat id_nat) A4)) (@ Sup A4))) (forall ((A4 set_Pr4329608150637261639at_nat) (B5 (-> produc3843707927480180839at_nat set_Pr1261947904930325089at_nat))) (=> (@ finite4343798906461161616at_nat A4) (=> (forall ((A3 produc3843707927480180839at_nat)) (=> (@ (@ member8757157785044589968at_nat A3) A4) (@ finite6177210948735845034at_nat (@ B5 A3)))) (@ finite6177210948735845034at_nat (@ comple5685304695842803022at_nat (@ (@ image_7979982168039674559at_nat B5) A4)))))) (forall ((F (-> int nat)) (G (-> int num)) (A int) (B int)) (= (@ (@ (@ produc2224754261294513212nt_num F) G) (@ (@ product_Pair_int_int A) B)) (@ (@ product_Pair_nat_num (@ F A)) (@ G B)))) (forall ((B nat) (F (-> Bool nat)) (A4 set_o)) (=> (@ (@ member_nat B) (@ (@ image_o_nat F) A4)) (not (forall ((X Bool)) (=> (= B (@ F X)) (not (@ (@ member_o X) A4))))))) _let_197 (forall ((F (-> num nat)) (G (-> num nat)) (X2 num)) (= (@ (@ (@ comp_P2539519431309506803at_num (@ (@ produc4208724500416182148at_nat F) id_nat)) (@ (@ bNF_co6100160411832691183um_nat id_num) G)) X2) (@ (@ (@ bNF_co7969830008525221797at_nat (@ (@ comp_nat_nat_num id_nat) F)) G) X2))) _let_196 (forall ((F (-> Bool product_unit)) (A4 set_o) (G (-> Bool product_unit)) (B5 set_o)) (=> (@ (@ inj_on4268752236855399398t_unit F) A4) (=> (@ (@ inj_on4268752236855399398t_unit G) B5) (=> (= (@ (@ inf_in4660618365625256667t_unit (@ (@ image_o_Product_unit F) A4)) (@ (@ image_o_Product_unit G) B5)) bot_bo3957492148770167129t_unit) (@ (@ inj_on4268752236855399398t_unit (lambda ((X4 Bool)) (@ (@ (@ if_Product_unit (@ (@ member_o X4) A4)) (@ F X4)) (@ G X4)))) (@ (@ sup_sup_set_o A4) B5)))))) (forall ((B int) (B5 (-> nat set_int)) (A4 set_nat) (A nat)) (let ((_let_1 (@ member_int B))) (=> (@ _let_1 (@ comple3628384868704368283et_int (@ (@ image_nat_set_int B5) A4))) (=> (@ (@ member_nat A) A4) (@ _let_1 (@ B5 A)))))) (forall ((X2 int) (A4 set_int) (F (-> int Bool)) (Y3 Bool)) (let ((_let_1 (@ image_int_o F))) (let ((_let_2 (@ (@ image_int_o (@ (@ (@ fun_upd_int_o F) X2) Y3)) A4))) (let ((_let_3 (@ (@ member_int X2) A4))) (and (=> (not _let_3) (= _let_2 (@ _let_1 A4))) (=> _let_3 (= _let_2 (@ (@ insert_o Y3) (@ _let_1 (@ (@ minus_minus_set_int A4) (@ (@ insert_int X2) bot_bot_set_int))))))))))) (= bNF_re7626690874201225453um_num (lambda ((R6 (-> int int Bool)) (S4 (-> num num Bool)) (F2 (-> int num)) (G3 (-> int num))) (@ (@ ord_le6741204236512500942_int_o R6) (@ (@ (@ bNF_vi2107963681178519309_num_o F2) G3) S4)))) (forall ((X2 nat) (Y3 num)) (= (@ basic_snds_nat_num (@ (@ product_Pair_nat_num X2) Y3)) (@ (@ insert_num Y3) bot_bot_set_num))) (forall ((A4 set_nat) (B5 set_nat) (C3 (-> nat set_nat)) (D (-> nat set_nat))) (=> (= A4 B5) (=> (forall ((X nat)) (=> (@ (@ member_nat X) B5) (= (@ C3 X) (@ D X)))) (= (@ comple7399068483239264473et_nat (@ (@ image_nat_set_nat C3) A4)) (@ comple7399068483239264473et_nat (@ (@ image_nat_set_nat D) B5)))))) (forall ((A4 set_Pr1261947904930325089at_nat) (B5 set_Pr1261947904930325089at_nat) (C3 set_Pr1261947904930325089at_nat) (D set_Pr1261947904930325089at_nat)) (= (@ (@ inf_in4302113700860409141at_nat (@ (@ produc2761391749766926216at_nat A4) (lambda ((Uu product_prod_nat_nat)) B5))) (@ (@ produc2761391749766926216at_nat C3) (lambda ((Uu product_prod_nat_nat)) D))) (@ (@ produc2761391749766926216at_nat (@ (@ inf_in2572325071724192079at_nat A4) C3)) (lambda ((Uu product_prod_nat_nat)) (@ (@ inf_in2572325071724192079at_nat B5) D))))) (forall ((F (-> Bool nat)) (A4 set_o) (X2 Bool) (U nat)) (let ((_let_1 (@ (@ image_o_nat F) A4))) (=> (@ condit1738341127787009408ow_nat _let_1) (=> (@ (@ member_o X2) A4) (=> (@ (@ ord_less_eq_nat (@ F X2)) U) (@ (@ ord_less_eq_nat (@ complete_Inf_Inf_nat _let_1)) U)))))) (forall ((F (-> rat char)) (Y3 char)) (=> (= (@ (@ image_rat_char F) top_top_set_rat) top_top_set_char) (not (forall ((X rat)) (not (= Y3 (@ F X))))))) (forall ((N3 nat)) (= (@ (@ inf_in2572325071724192079at_nat bNF_Ca8665028551170535155natLeq) (@ (@ produc457027306803732586at_nat (@ (@ order_underS_nat bNF_Ca8665028551170535155natLeq) N3)) (lambda ((Uu nat)) (@ (@ order_underS_nat bNF_Ca8665028551170535155natLeq) N3)))) (@ collec3392354462482085612at_nat (@ produc6081775807080527818_nat_o (lambda ((X4 nat) (Y5 nat)) (and (@ (@ ord_less_eq_nat X4) Y5) (@ (@ ord_less_nat Y5) N3) (@ (@ ord_less_nat X4) N3))))))) (forall ((F (-> int nat)) (A4 set_int)) (=> (@ order_3680150258199746352nt_nat F) (=> (@ condit1735850657277959132ow_int A4) (@ condit2214826472909112428ve_nat (@ (@ image_int_nat F) A4))))) (forall ((A4 set_Pr4329608150637261639at_nat) (B5 set_Pr4329608150637261639at_nat) (F (-> produc3843707927480180839at_nat set_nat)) (G (-> produc3843707927480180839at_nat set_nat))) (=> (@ (@ ord_le1268244103169919719at_nat A4) B5) (=> (forall ((X produc3843707927480180839at_nat)) (=> (@ (@ member8757157785044589968at_nat X) A4) (@ (@ ord_less_eq_set_nat (@ F X)) (@ G X)))) (@ (@ ord_less_eq_set_nat (@ comple7806235888213564991et_nat (@ (@ image_3160451284896210088et_nat F) B5))) (@ comple7806235888213564991et_nat (@ (@ image_3160451284896210088et_nat G) A4)))))) (forall ((G (-> nat int)) (F (-> nat nat)) (A4 set_nat)) (= (@ complete_Inf_Inf_int (@ (@ image_nat_int G) (@ (@ image_nat_nat F) A4))) (@ complete_Inf_Inf_int (@ (@ image_nat_int (@ (@ comp_nat_int_nat G) F)) A4)))) (forall ((A4 set_Pr1261947904930325089at_nat)) (@ (@ ord_le3146513528884898305at_nat A4) (@ (@ produc457027306803732586at_nat (@ (@ image_2486076414777270412at_nat product_fst_nat_nat) A4)) (lambda ((Uu nat)) (@ (@ image_2486076414777270412at_nat product_snd_nat_nat) A4))))) (forall ((A4 set_nat)) (= (@ (@ vimage4653281326611754070at_nat product_fst_nat_nat) A4) (@ (@ produc457027306803732586at_nat A4) (lambda ((Uu nat)) top_top_set_nat)))) (forall ((R3 (-> ref_a heap_e7401611519738050253t_unit Bool))) (let ((_let_1 (@ collec3252306575900995386t_unit (@ produc4924168586796184916unit_o R3)))) (= (@ (@ relcom3136146828236442456t_unit (@ conver4368408235330554745_ref_a (@ (@ bNF_Gr5964920315653434322_ref_a _let_1) produc473321116828791851t_unit))) (@ (@ bNF_Gr5237703264515865432t_unit _let_1) produc1126150082675451753t_unit)) R3))) (forall ((F1 (-> Bool Bool)) (F22 (-> nat Bool)) (G1 (-> nat nat)) (G22 (-> nat nat))) (= (@ (@ produc7251236297486395890at_nat (@ (@ comp_o_o_nat F1) F22)) (@ (@ comp_nat_nat_nat G1) G22)) (@ (@ comp_P4962864564169660718at_nat (@ (@ produc7071226018047599512at_nat F1) G1)) (@ (@ produc7251236297486395890at_nat F22) G22)))) (forall ((F (-> heap_e7401611519738050253t_unit heap_e7401611519738050253t_unit)) (X2 produc7812382424243267045t_unit)) (= (@ produc473321116828791851t_unit (@ (@ produc3038839249364385243_ref_a F) X2)) (@ produc473321116828791851t_unit X2))) (forall ((I produc3843707927480180839at_nat) (J4 produc3843707927480180839at_nat) (R3 set_Pr5564308138774400199at_nat)) (=> (@ (@ member6009668390874684176at_nat (@ (@ produc2335810615602371415at_nat I) J4)) R3) (@ (@ member8757157785044589968at_nat J4) (@ field_2862844103579723188at_nat R3)))) (forall ((A4 set_o) (B5 set_o) (F (-> Bool set_nat)) (G (-> Bool set_nat))) (=> (forall ((I4 Bool)) (=> (@ (@ member_o I4) A4) (exists ((X6 Bool)) (and (@ (@ member_o X6) B5) (@ (@ ord_less_eq_set_nat (@ F I4)) (@ G X6)))))) (=> (forall ((J2 Bool)) (=> (@ (@ member_o J2) B5) (exists ((X6 Bool)) (and (@ (@ member_o X6) A4) (@ (@ ord_less_eq_set_nat (@ G J2)) (@ F X6)))))) (= (@ comple7399068483239264473et_nat (@ (@ image_o_set_nat F) A4)) (@ comple7399068483239264473et_nat (@ (@ image_o_set_nat G) B5)))))) (forall ((R2 ref_a) (V a) (H heap_e7401611519738050253t_unit) (H2 heap_e7401611519738050253t_unit) (R product_unit)) (=> (@ (@ (@ (@ heap_e2830298082929533060t_unit (@ (@ update_a R2) V)) H) H2) R) (= H2 (@ (@ (@ set_a R2) V) H)))) (= produc8211389475949308722nt_int (lambda ((F2 (-> int int int)) (Prod3 product_prod_int_int)) (@ (@ F2 (@ product_fst_int_int Prod3)) (@ product_snd_int_int Prod3)))) (forall ((A4 set_int) (F (-> int int)) (M int)) (=> (not (= A4 bot_bot_set_int)) (=> (forall ((X int)) (=> (@ (@ member_int X) A4) (@ (@ ord_less_eq_int (@ F X)) M))) (@ (@ ord_less_eq_int (@ complete_Sup_Sup_int (@ (@ image_int_int F) A4))) M)))) (forall ((C3 set_Product_unit) (A4 (-> product_unit set_rat)) (B5 set_rat)) (let ((_let_1 (@ (@ minus_minus_set_rat (@ comple4298007329820168263et_rat (@ (@ image_4665621433434589782et_rat A4) C3))) B5))) (let ((_let_2 (= C3 bot_bo3957492148770167129t_unit))) (and (=> _let_2 (= _let_1 (@ (@ minus_minus_set_rat top_top_set_rat) B5))) (=> (not _let_2) (= _let_1 (@ comple4298007329820168263et_rat (@ (@ image_4665621433434589782et_rat (lambda ((X4 product_unit)) (@ (@ minus_minus_set_rat (@ A4 X4)) B5))) C3)))))))) (forall ((F (-> Bool nat)) (A4 set_o) (X2 Bool)) (let ((_let_1 (@ (@ image_o_nat F) A4))) (=> (@ condit1738341127787009408ow_nat _let_1) (=> (@ (@ member_o X2) A4) (@ (@ ord_less_eq_nat (@ complete_Inf_Inf_nat _let_1)) (@ F X2)))))) (forall ((A4 set_nat) (F (-> nat nat)) (U nat)) (let ((_let_1 (@ (@ image_nat_nat F) A4))) (=> (not (= A4 bot_bot_set_nat)) (=> (@ condit2214826472909112428ve_nat _let_1) (= (@ (@ ord_less_eq_nat (@ complete_Sup_Sup_nat _let_1)) U) (forall ((X4 nat)) (=> (@ (@ member_nat X4) A4) (@ (@ ord_less_eq_nat (@ F X4)) U)))))))) (forall ((F (-> int int)) (A4 set_int) (B5 set_int)) (let ((_let_1 (@ image_int_int F))) (=> (@ (@ inj_on_int_int F) (@ (@ sup_sup_set_int A4) B5)) (= (= (@ _let_1 A4) (@ _let_1 B5)) (= A4 B5))))) (forall ((A4 set_nat) (C set_Product_unit)) (let ((_let_1 (= A4 bot_bot_set_nat))) (and (=> (not _let_1) (= (@ comple3349607820504768346t_unit (@ (@ image_4824033694279209942t_unit (lambda ((Y5 nat)) C)) A4)) C)) (=> _let_1 (= (@ comple3349607820504768346t_unit (@ (@ image_4824033694279209942t_unit (lambda ((Y5 nat)) C)) A4)) bot_bo3957492148770167129t_unit))))) (forall ((F (-> char char)) (Y3 char)) (=> (= (@ (@ image_char_char F) top_top_set_char) top_top_set_char) (exists ((X char)) (= Y3 (@ F X))))) (forall ((F (-> ref_a nat)) (G (-> heap_e7401611519738050253t_unit nat)) (R3 (-> nat nat Bool))) (@ (@ ord_le3146513528884898305at_nat (@ (@ image_4710180989675653397at_nat (@ (@ bNF_co5610825919353547504at_nat (@ (@ comp_r8155216869944865719t_unit F) produc473321116828791851t_unit)) (@ (@ comp_h8354993580257045729t_unit G) produc1126150082675451753t_unit))) (@ collec3252306575900995386t_unit (@ produc4924168586796184916unit_o (@ (@ (@ bNF_vi4623496019404053219_nat_o F) G) R3))))) (@ collec3392354462482085612at_nat (@ produc6081775807080527818_nat_o R3)))) (forall ((F (-> list_nat product_prod_nat_nat)) (A4 set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ image_2795870212791037530at_nat F))) (= (@ _let_1 (@ (@ vimage8527374361057053988at_nat F) A4)) (@ (@ inf_in2572325071724192079at_nat A4) (@ _let_1 top_top_set_list_nat))))) (forall ((C3 set_Pr1261947904930325089at_nat) (A4 (-> product_prod_nat_nat set_nat)) (B5 set_nat)) (let ((_let_1 (@ (@ inf_inf_set_nat (@ comple7806235888213564991et_nat (@ (@ image_15824709712370754et_nat A4) C3))) B5))) (let ((_let_2 (= C3 bot_bo2099793752762293965at_nat))) (and (=> (not _let_2) (= _let_1 (@ comple7806235888213564991et_nat (@ (@ image_15824709712370754et_nat (lambda ((X4 product_prod_nat_nat)) (@ (@ inf_inf_set_nat (@ A4 X4)) B5))) C3)))) (=> _let_2 (= _let_1 B5)))))) (forall ((A4 set_o) (B5 set_o) (C3 (-> Bool int)) (D (-> Bool int))) (=> (= A4 B5) (=> (forall ((X Bool)) (=> (@ (@ member_o X) B5) (= (@ C3 X) (@ D X)))) (= (@ complete_Inf_Inf_int (@ (@ image_o_int C3) A4)) (@ complete_Inf_Inf_int (@ (@ image_o_int D) B5)))))) (forall ((A4 set_nat) (F (-> nat product_unit)) (B5 set_nat)) (let ((_let_1 (@ image_8730104196221521654t_unit F))) (let ((_let_2 (@ _let_1 B5))) (let ((_let_3 (@ _let_1 A4))) (=> (not (= A4 bot_bot_set_nat)) (=> (@ condit9161856309968323677t_unit _let_3) (=> (not (= B5 bot_bot_set_nat)) (=> (@ condit9161856309968323677t_unit _let_2) (= (@ comple2584293577114468500t_unit (@ _let_1 (@ (@ sup_sup_set_nat A4) B5))) (@ (@ inf_inf_Product_unit (@ comple2584293577114468500t_unit _let_3)) (@ comple2584293577114468500t_unit _let_2))))))))))) (forall ((A4 set_Product_unit) (C set_rat)) (let ((_let_1 (= A4 bot_bo3957492148770167129t_unit))) (and (=> _let_1 (= (@ comple4298007329820168263et_rat (@ (@ image_4665621433434589782et_rat (lambda ((Y5 product_unit)) C)) A4)) top_top_set_rat)) (=> (not _let_1) (= (@ comple4298007329820168263et_rat (@ (@ image_4665621433434589782et_rat (lambda ((Y5 product_unit)) C)) A4)) C))))) (forall ((Y4 (-> int code_integer Bool)) (X5 (-> int code_integer Bool)) (A4 (-> num num Bool)) (B5 (-> num num Bool)) (F (-> int num)) (G (-> code_integer num))) (=> (forall ((X int) (Y code_integer)) (=> (@ (@ Y4 X) Y) (@ (@ X5 X) Y))) (=> (forall ((X num) (Y num)) (=> (@ (@ A4 X) Y) (@ (@ B5 X) Y))) (=> (@ (@ (@ (@ bNF_re6718328864250387230um_num X5) A4) F) G) (@ (@ (@ (@ bNF_re6718328864250387230um_num Y4) B5) F) G))))) (forall ((F (-> rat nat)) (G (-> nat rat))) (=> (@ order_5409469004658005219at_nat F) (=> (= (@ (@ image_rat_nat F) top_top_set_rat) top_top_set_nat) (=> (forall ((X rat)) (= (@ G (@ F X)) X)) (@ order_5090893588506375395at_rat G))))) (forall ((A4 set_int) (F (-> int product_unit)) (X2 product_unit)) (=> (forall ((I4 int)) (=> (@ (@ member_int I4) A4) (@ (@ ord_le3221252021190050221t_unit (@ F I4)) X2))) (=> (forall ((Y product_unit)) (=> (forall ((I5 int)) (=> (@ (@ member_int I5) A4) (@ (@ ord_le3221252021190050221t_unit (@ F I5)) Y))) (@ (@ ord_le3221252021190050221t_unit X2) Y))) (= (@ comple4687483117567863418t_unit (@ (@ image_5846526143423701914t_unit F) A4)) X2)))) (forall ((A4 set_Product_unit) (C set_nat)) (let ((_let_1 (= A4 bot_bo3957492148770167129t_unit))) (and (=> _let_1 (= (@ comple7399068483239264473et_nat (@ (@ image_8173849991827986510et_nat (lambda ((Y5 product_unit)) C)) A4)) bot_bot_set_nat)) (=> (not _let_1) (= (@ comple7399068483239264473et_nat (@ (@ image_8173849991827986510et_nat (lambda ((Y5 product_unit)) C)) A4)) C))))) (forall ((M (-> produc3843707927480180839at_nat set_nat)) (A4 set_Pr4329608150637261639at_nat) (B5 set_Pr4329608150637261639at_nat)) (let ((_let_1 (@ image_3160451284896210088et_nat M))) (= (@ comple7806235888213564991et_nat (@ _let_1 (@ (@ sup_su5525570899277871387at_nat A4) B5))) (@ (@ inf_inf_set_nat (@ comple7806235888213564991et_nat (@ _let_1 A4))) (@ comple7806235888213564991et_nat (@ _let_1 B5)))))) (forall ((P2 (-> product_prod_nat_nat Bool)) (Q2 (-> product_prod_nat_nat Bool))) (=> (forall ((X product_prod_nat_nat)) (= (@ P2 X) (@ Q2 X))) (= (@ collec3392354462482085612at_nat P2) (@ collec3392354462482085612at_nat Q2)))) (forall ((A product_prod_nat_nat) (B product_prod_nat_nat)) (= (@ (@ member8206827879206165904at_nat (@ (@ produc6161850002892822231at_nat A) B)) id_Pro2258643101195443293at_nat) (= A B))) (forall ((X2 product_unit)) (@ (@ member_o (@ product_Rep_unit X2)) (@ (@ insert_o true) bot_bot_set_o))) (forall ((X2 set_Pr4329608150637261639at_nat) (Y3 set_Pr4329608150637261639at_nat)) (= (@ (@ (@ if_set3208018901896979469at_nat true) X2) Y3) X2)) (forall ((X5 (-> nat nat Bool))) (= (@ fun_in_rel_nat_nat (@ collec3392354462482085612at_nat (@ produc6081775807080527818_nat_o X5))) X5)) (forall ((F (-> product_unit set_o))) (= (@ comple90263536869209701_set_o (@ (@ image_6930536745178679216_set_o F) bot_bo3957492148770167129t_unit)) bot_bot_set_o)) (forall ((C3 set_nat) (A4 set_char) (B5 (-> nat set_char))) (let ((_let_1 (= C3 bot_bot_set_nat))) (and (=> (not _let_1) (= (@ comple7965528767983648192t_char (@ (@ image_nat_set_char (lambda ((X4 nat)) (@ (@ minus_minus_set_char A4) (@ B5 X4)))) C3)) (@ (@ minus_minus_set_char A4) (@ comple4338141846124676698t_char (@ (@ image_nat_set_char B5) C3))))) (=> _let_1 (= (@ comple7965528767983648192t_char (@ (@ image_nat_set_char (lambda ((X4 nat)) (@ (@ minus_minus_set_char A4) (@ B5 X4)))) C3)) top_top_set_char))))) _let_195 (forall ((F (-> char nat)) (X2 char)) (@ (@ member_nat (@ F X2)) (@ (@ image_char_nat F) top_top_set_char))) (forall ((X2 product_prod_nat_nat) (Y3 nat) (Z2 nat)) (=> (= X2 (@ (@ product_Pair_nat_nat Y3) Z2)) (= (@ product_snd_nat_nat X2) Z2))) (forall ((Q2 (-> int Bool)) (P2 (-> int int int)) (Z2 product_prod_int_int)) (=> (@ Q2 (@ (@ produc8211389475949308722nt_int P2) Z2)) (not (forall ((X int) (Y int)) (=> (= Z2 (@ (@ product_Pair_int_int X) Y)) (not (@ Q2 (@ (@ P2 X) Y)))))))) (forall ((R set_Pr958786334691620121nt_int)) (let ((_let_1 (@ field_int R))) (=> (@ (@ order_4471489696718655927on_int _let_1) R) (= (@ (@ order_2886507596567047182on_int _let_1) R) (forall ((A6 set_int)) (=> (@ (@ ord_less_eq_set_int A6) (@ field_int R)) (=> (not (= A6 bot_bot_set_int)) (exists ((X4 int)) (and (forall ((Y5 int)) (=> (@ (@ member_int Y5) A6) (@ (@ member5262025264175285858nt_int (@ (@ product_Pair_int_int X4) Y5)) R))) (@ (@ member_int X4) A6)))))))))) (forall ((R3 (-> product_prod_nat_nat product_prod_nat_nat Bool)) (S5 (-> nat nat Bool)) (R7 (-> product_prod_nat_nat int Bool)) (S6 (-> nat nat Bool))) (@ (@ ord_le1714508135640884727_nat_o (@ (@ relcom531901107642208332nt_nat (@ (@ bNF_re8246922863344978751at_nat R3) S5)) (@ (@ bNF_re4555766996558763186at_nat R7) S6))) (@ (@ bNF_re4555766996558763186at_nat (@ (@ relcom8911704206367525917at_int R3) R7)) (@ (@ relcompp_nat_nat_nat S5) S6)))) (forall ((F (-> int int)) (A4 set_int) (B5 set_int)) (= (@ (@ ord_less_eq_set_int (@ (@ image_int_int F) A4)) B5) (forall ((X4 int)) (=> (@ (@ member_int X4) A4) (@ (@ member_int (@ F X4)) B5))))) (forall ((F (-> nat rat)) (C3 set_nat) (A4 set_nat) (B5 set_nat)) (let ((_let_1 (@ image_nat_rat F))) (=> (@ (@ inj_on_nat_rat F) C3) (=> (@ (@ ord_less_eq_set_nat A4) C3) (=> (@ (@ ord_less_eq_set_nat B5) C3) (= (= (@ _let_1 A4) (@ _let_1 B5)) (= A4 B5))))))) (forall ((A4 set_int) (B5 set_nat)) (=> (@ finite_finite_int A4) (=> (@ finite_finite_nat B5) (=> (@ (@ ord_less_eq_nat (@ finite_card_int A4)) (@ finite_card_nat B5)) (exists ((F5 (-> int nat))) (and (@ (@ inj_on_int_nat F5) A4) (@ (@ ord_less_eq_set_nat (@ (@ image_int_nat F5) A4)) B5))))))) (forall ((A4 set_int) (B5 set_int) (C3 (-> int nat)) (D (-> int nat))) (=> (= A4 B5) (=> (forall ((X int)) (=> (@ (@ member_int X) B5) (= (@ C3 X) (@ D X)))) (= (@ complete_Sup_Sup_nat (@ (@ image_int_nat C3) A4)) (@ complete_Sup_Sup_nat (@ (@ image_int_nat D) B5)))))) (forall ((F (-> nat nat)) (B5 set_nat) (I nat)) (=> (@ (@ ord_less_eq_set_nat (@ (@ image_nat_nat F) top_top_set_nat)) B5) (@ (@ member_nat (@ F I)) B5))) _let_194 (forall ((S5 set_nat) (F (-> nat nat nat))) (=> (forall ((X nat) (Y nat)) (let ((_let_1 (@ F Y))) (let ((_let_2 (@ F X))) (=> (@ (@ member_nat X) S5) (=> (@ (@ member_nat Y) S5) (= (@ (@ comp_nat_nat_nat _let_1) _let_2) (@ (@ comp_nat_nat_nat _let_2) _let_1))))))) (@ (@ finite3582905537739598962at_nat S5) F))) (forall ((B5 set_o) (F (-> nat nat)) (A4 set_nat) (G (-> Bool nat))) (let ((_let_1 (@ (@ image_nat_nat F) A4))) (=> (not (= B5 bot_bot_set_o)) (=> (@ condit1738341127787009408ow_nat _let_1) (=> (forall ((M4 Bool)) (=> (@ (@ member_o M4) B5) (exists ((X6 nat)) (and (@ (@ ord_less_eq_nat (@ F X6)) (@ G M4)) (@ (@ member_nat X6) A4))))) (@ (@ ord_less_eq_nat (@ complete_Inf_Inf_nat _let_1)) (@ complete_Inf_Inf_nat (@ (@ image_o_nat G) B5)))))))) (forall ((F (-> product_prod_nat_nat Bool)) (A nat) (B nat)) (=> (@ (@ (@ produc1310100445399344235_nat_o F) A) B) (@ F (@ (@ product_Pair_nat_nat A) B)))) (forall ((F (-> nat rat)) (A4 set_rat)) (let ((_let_1 (@ 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P2 (@ product_snd_int_int P)) (@ product_fst_int_int P)) (=> (forall ((X int) (Y int)) (=> (@ (@ P2 Y) X) (@ Q2 (@ (@ F X) Y)))) (@ Q2 (@ (@ produc8211389475949308722nt_int F) P))))) (forall ((F (-> product_unit set_nat)) (A product_unit) (B5 set_Product_unit)) (let ((_let_1 (@ image_8173849991827986510et_nat F))) (= (@ comple7399068483239264473et_nat (@ _let_1 (@ (@ insert_Product_unit A) B5))) (@ (@ sup_sup_set_nat (@ F A)) (@ comple7399068483239264473et_nat (@ _let_1 B5)))))) (forall ((P produc1319942482725812455at_nat) (C (-> set_Pr4329608150637261639at_nat set_Pr4329608150637261639at_nat Bool))) (=> (forall ((A3 set_Pr4329608150637261639at_nat) (B3 set_Pr4329608150637261639at_nat)) (=> (= P (@ (@ produc9060074326276436823at_nat A3) B3)) (@ (@ C A3) B3))) (@ (@ produc9020218426428501292_nat_o C) P))) (forall ((F (-> nat int)) (B5 set_int) (A4 set_nat)) (=> (@ (@ inj_on_nat_int F) top_top_set_nat) (=> (@ (@ ord_less_eq_set_int B5) (@ (@ image_nat_int F) A4)) (@ (@ 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(forall ((F (-> int nat)) (A4 set_int)) (=> (@ (@ inj_on_int_nat F) A4) (@ (@ inj_on_nat_int (@ (@ the_inv_into_int_nat A4) F)) (@ (@ image_int_nat F) A4)))) (forall ((F (-> nat int)) (A4 set_nat) (B5 set_nat)) (let ((_let_1 (@ image_nat_int F))) (=> (@ (@ inj_on_nat_int F) top_top_set_nat) (= (@ _let_1 (@ (@ inf_inf_set_nat A4) B5)) (@ (@ inf_inf_set_int (@ _let_1 A4)) (@ _let_1 B5)))))) (forall ((P2 (-> nat Bool)) (F (-> nat int)) (G (-> nat int)) (S5 set_nat)) (let ((_let_1 (@ inf_inf_set_nat S5))) (= (@ (@ image_nat_int (lambda ((X4 nat)) (@ (@ (@ if_int (@ P2 X4)) (@ F X4)) (@ G X4)))) S5) (@ (@ sup_sup_set_int (@ (@ image_nat_int F) (@ _let_1 (@ collect_nat P2)))) (@ (@ image_nat_int G) (@ _let_1 (@ collect_nat (lambda ((X4 nat)) (not (@ P2 X4)))))))))) (forall ((F (-> int int)) (A4 set_int)) (=> (@ (@ inj_on_int_int F) A4) (= (@ finite_finite_int (@ (@ image_int_int F) A4)) (@ finite_finite_int A4)))) (forall ((A4 set_o) (B5 set_o)) (let ((_let_1 (@ product_Sigma_o_o A4))) (let ((_let_2 (@ image_7896445794123959606_o_o_o product_snd_o_o))) (let ((_let_3 (= A4 bot_bot_set_o))) (and (=> (not _let_3) (= (@ _let_2 (@ _let_1 (lambda ((Uu Bool)) B5))) B5)) (=> _let_3 (= (@ _let_2 (@ _let_1 (lambda ((Uu Bool)) B5))) bot_bot_set_o))))))) (forall ((Rep (-> num Bool)) (Abs (-> Bool num)) (M (-> nat Bool)) (M1 (-> Bool Bool)) (M2 (-> nat Bool)) (F (-> Bool Bool)) (G (-> int nat))) (=> (@ (@ (@ type_d9070036042389994064_num_o Rep) Abs) top_top_set_o) (=> (= M (@ (@ comp_o_o_nat M1) M2)) (= (@ (@ comp_nat_o_int (@ (@ comp_o_o_nat F) M)) G) (@ (@ comp_num_o_int (@ (@ comp_o_o_num (@ (@ comp_o_o_o F) M1)) Rep)) (@ (@ comp_nat_num_int (@ (@ comp_o_num_nat Abs) M2)) G)))))) (forall ((Rep (-> Bool rat)) (Abs (-> rat Bool))) (=> (@ (@ (@ type_d6486251586359353412_o_rat Rep) Abs) top_top_set_rat) (= (@ (@ comp_rat_o_o Abs) Rep) id_o))) (forall ((F (-> nat nat Bool)) (A nat) (B nat)) (=> (@ (@ produc6081775807080527818_nat_o F) (@ (@ product_Pair_nat_nat A) B)) (@ (@ F A) B))) (forall ((A int) (B Bool) (A4 set_int) (B5 (-> int set_o))) (=> (@ (@ member4489920277610959864_int_o (@ (@ product_Pair_int_o A) B)) (@ (@ product_Sigma_int_o A4) B5)) (not (=> (@ (@ member_int A) A4) (not (@ (@ member_o B) (@ B5 A))))))) (forall ((P2 (-> product_prod_nat_nat Bool)) (Q2 (-> product_prod_nat_nat Bool))) (= (@ collec7088162979684241874at_nat (@ produc6590410687421337004_nat_o (lambda ((A5 product_prod_nat_nat) (B4 product_prod_nat_nat)) (and (@ Q2 B4) (@ P2 A5))))) (@ (@ produc2761391749766926216at_nat (@ collec3392354462482085612at_nat P2)) (lambda ((Uu product_prod_nat_nat)) (@ collec3392354462482085612at_nat Q2))))) (forall ((F (-> nat nat)) (G (-> nat nat)) (X2 nat) (F3 (-> int nat)) (G2 (-> int int)) (X3 int)) (=> (= (@ F (@ G X2)) (@ F3 (@ G2 X3))) (= (@ (@ (@ comp_nat_nat_nat F) G) X2) (@ (@ (@ comp_int_nat_int F3) G2) X3)))) (forall ((A4 set_nat) (U product_unit) (F (-> nat product_unit))) (=> (forall ((I4 nat)) (=> (@ (@ member_nat I4) A4) (@ (@ 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(forall ((X2 Bool) (Y3 Bool)) (let ((_let_1 (@ (@ insert_o true) bot_bot_set_o))) (=> (@ (@ member_o X2) _let_1) (=> (@ (@ member_o Y3) _let_1) (= (= (@ product_Abs_unit X2) (@ product_Abs_unit Y3)) (= X2 Y3)))))) (forall ((A product_prod_nat_nat) (A4 set_Pr1261947904930325089at_nat)) (=> (@ (@ member8440522571783428010at_nat A) A4) (@ (@ member8206827879206165904at_nat (@ (@ produc6161850002892822231at_nat A) A)) (@ id_on_2554058798563519774at_nat A4)))) (forall ((T3 (-> int product_prod_nat_nat Bool)) (R3 (-> product_prod_nat_nat product_prod_nat_nat Bool))) (=> (@ left_t8261381459436684205at_nat T3) (=> (@ (@ ord_le5604493270027003598_nat_o (lambda ((Y2 product_prod_nat_nat) (Z product_prod_nat_nat)) (= Y2 Z))) R3) (@ (@ ord_le6741204236512500942_int_o (lambda ((Y2 int) (Z int)) (= Y2 Z))) (@ (@ relcom1106208330880909712at_int T3) (@ (@ relcom8911704206367525917at_int R3) (@ conver1866313717161370910at_nat T3))))))) (forall ((I product_prod_nat_nat) (A4 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product_prod_nat_nat) (C num) (G (-> product_prod_nat_nat num)) (A4 set_Pr1261947904930325089at_nat)) (=> (= B (@ F X2)) (=> (= C (@ G X2)) (=> (@ (@ member8440522571783428010at_nat X2) A4) (@ (@ member9148766508732265716at_num (@ (@ product_Pair_nat_num B) C)) (@ (@ (@ bNF_Gr5511461681843259283at_num A4) F) G)))))) (forall ((F (-> product_prod_int_int int))) (= (@ produc8211389475949308722nt_int (lambda ((X4 int) (Y5 int)) (@ F (@ (@ product_Pair_int_int X4) Y5)))) F)) (forall ((C3 set_Product_unit) (A4 set_nat) (B5 (-> product_unit set_nat))) (let ((_let_1 (= C3 bot_bo3957492148770167129t_unit))) (and (=> (not _let_1) (= (@ comple7399068483239264473et_nat (@ (@ image_8173849991827986510et_nat (lambda ((X4 product_unit)) (@ (@ sup_sup_set_nat A4) (@ B5 X4)))) C3)) (@ (@ sup_sup_set_nat A4) (@ comple7399068483239264473et_nat (@ (@ image_8173849991827986510et_nat B5) C3))))) (=> _let_1 (= (@ comple7399068483239264473et_nat (@ (@ image_8173849991827986510et_nat (lambda ((X4 product_unit)) (@ (@ sup_sup_set_nat A4) (@ B5 X4)))) C3)) bot_bot_set_nat))))) (forall ((X1 int) (X22 int)) (= (@ product_snd_int_int (@ (@ product_Pair_int_int X1) X22)) X22)) (forall ((A4 (-> nat Bool))) (= (@ id_on_nat (@ collect_nat A4)) (@ collec3392354462482085612at_nat (@ produc6081775807080527818_nat_o (lambda ((X4 nat) (Y5 nat)) (and (= X4 Y5) (@ A4 X4))))))) (forall ((A4 set_nat) (F (-> nat rat)) (X2 nat)) (=> (not (= A4 bot_bot_set_nat)) (=> (forall ((Y nat)) (=> (@ (@ member_nat Y) A4) (= (@ F Y) (@ F X2)))) (= (@ the_elem_rat (@ (@ image_nat_rat F) A4)) (@ F X2))))) (forall ((F (-> nat int)) (A4 set_nat) (P2 (-> int Bool))) (=> (exists ((X6 int)) (and (@ (@ member_int X6) (@ (@ image_nat_int F) A4)) (@ P2 X6))) (exists ((X nat)) (and (@ (@ member_nat X) A4) (@ P2 (@ F X)))))) (forall ((H1 (-> nat nat)) (H22 (-> Bool Bool)) (F (-> nat nat)) (G (-> nat Bool))) (= (@ (@ comp_P5799945282029801519_o_nat (@ (@ produc2001155298098703512at_o_o H1) H22)) (@ (@ bNF_convol_nat_nat_o F) G)) (@ (@ bNF_convol_nat_nat_o (@ (@ comp_nat_nat_nat H1) F)) (@ (@ comp_o_o_nat H22) G)))) (forall ((R1 (-> int code_integer Bool))) (@ (@ (@ (@ bNF_re2655444144887082515er_num (lambda ((Y2 (-> nat num)) (Z (-> nat num))) (= Y2 Z))) (@ (@ bNF_re5502197115626545091er_num (@ (@ bNF_re2807294637932363402at_nat R1) (lambda ((Y2 nat) (Z nat)) (= Y2 Z)))) (@ (@ bNF_re6718328864250387230um_num R1) (lambda ((Y2 num) (Z num)) (= Y2 Z))))) comp_nat_num_int) comp_n2103536230552569900nteger)) (forall ((X2 Bool) (A4 set_o) (F (-> Bool nat))) (let ((_let_1 (@ (@ image_o_nat F) A4))) (=> (@ (@ member_o X2) A4) (=> (@ condit2214826472909112428ve_nat _let_1) (@ (@ ord_less_eq_nat (@ F X2)) (@ complete_Sup_Sup_nat _let_1)))))) (forall ((Sup (-> set_nat nat)) (G (-> nat nat)) (F (-> nat nat)) (A4 set_nat)) (= (@ Sup (@ (@ image_nat_nat G) (@ (@ image_nat_nat F) A4))) (@ Sup (@ (@ image_nat_nat (@ (@ comp_nat_nat_nat G) F)) A4)))) (forall ((F (-> nat int)) (A4 set_nat) (B5 set_int)) (let ((_let_1 (@ image_nat_int F))) (=> (= (@ _let_1 A4) B5) (= (@ (@ image_3739036796817536367et_int _let_1) (@ pow_nat A4)) (@ pow_int B5))))) (forall ((A4 set_Product_unit) (C set_int)) (let ((_let_1 (= A4 bot_bo3957492148770167129t_unit))) (and (=> (not _let_1) (= (@ comple3628384868704368283et_int (@ (@ image_3995998972318789802et_int (lambda ((Y5 product_unit)) C)) A4)) C)) (=> _let_1 (= (@ comple3628384868704368283et_int (@ (@ image_3995998972318789802et_int (lambda ((Y5 product_unit)) C)) A4)) top_top_set_int))))) _let_189 _let_188 (forall ((B5 set_o) (A4 set_o) (F (-> Bool set_nat)) (G (-> Bool set_nat))) (=> (@ (@ ord_less_eq_set_o B5) A4) (=> (forall ((X Bool)) (=> (@ (@ member_o X) B5) (@ (@ ord_less_eq_set_nat (@ F X)) (@ G X)))) (@ (@ ord_less_eq_set_nat (@ comple7806235888213564991et_nat (@ (@ image_o_set_nat F) A4))) (@ comple7806235888213564991et_nat (@ (@ image_o_set_nat G) B5)))))) (forall ((P2 (-> int int Bool)) (X2 int) (Y3 int) (A product_prod_int_int)) (=> (@ (@ P2 X2) Y3) (=> (= A (@ (@ product_Pair_int_int X2) Y3)) (@ (@ P2 (@ product_fst_int_int A)) (@ product_snd_int_int A))))) (forall ((A set_Pr4329608150637261639at_nat) (A4 set_se5479201105039950375at_nat)) (=> (@ (@ member6273874620674182256at_nat A) A4) (@ (@ member1466754251312161552at_nat (@ (@ produc9060074326276436823at_nat A) A)) (@ id_on_3275838214495744996at_nat A4)))) (forall ((H (-> rat nat)) (F4 set_nat)) (=> (@ finite_finite_rat (@ (@ vimage_rat_nat H) F4)) (=> (= (@ (@ image_rat_nat H) top_top_set_rat) top_top_set_nat) (@ finite_finite_nat F4)))) (forall ((F (-> Bool set_rat))) (= (@ comple4298007329820168263et_rat (@ (@ image_o_set_rat F) bot_bot_set_o)) top_top_set_rat)) (forall ((A nat) (A4 set_nat)) (=> (@ (@ member_nat A) A4) (@ (@ member8440522571783428010at_nat (@ (@ product_Pair_nat_nat A) A)) (@ id_on_nat A4)))) (forall ((X2 nat) (A4 set_nat) (G (-> nat nat))) (=> (@ (@ member_nat X2) A4) (@ (@ member8440522571783428010at_nat (@ (@ (@ bNF_co805650143699787099at_nat id_nat) G) X2)) (@ collec3392354462482085612at_nat (@ produc6081775807080527818_nat_o (@ (@ bNF_Grp_nat_nat A4) G)))))) (forall ((C product_prod_nat_nat) (A4 set_nat)) (=> (@ (@ member8440522571783428010at_nat C) (@ id_on_nat A4)) (not (forall ((X nat)) (=> (@ (@ member_nat X) A4) (not (= C (@ (@ product_Pair_nat_nat X) X)))))))) _let_187 (forall ((I nat) (C3 set_nat) (G (-> nat int)) (X2 nat)) (=> (@ (@ member_nat I) C3) (=> (@ (@ inj_on_nat_int G) C3) (= (@ (@ (@ comp_int_nat_nat (lambda ((I2 int)) (@ (@ (@ if_nat (@ (@ member_int I2) (@ (@ image_nat_int G) C3))) (@ (@ (@ the_inv_into_nat_int C3) G) I2)) X2))) G) I) (@ id_nat I))))) (forall ((C Bool) (T2 heap_Heap_ref_a) (H heap_e7401611519738050253t_unit) (H2 heap_e7401611519738050253t_unit) (R ref_a) (E heap_Heap_ref_a)) (=> (=> C (@ (@ (@ (@ heap_effect_ref_a T2) H) H2) R)) (=> (=> (not C) (@ (@ (@ (@ heap_effect_ref_a E) H) H2) R)) (@ (@ (@ (@ heap_effect_ref_a (@ (@ (@ if_Heap_Heap_ref_a C) T2) E)) H) H2) R)))) (forall ((A4 set_int) (F (-> int nat))) (=> (not (@ finite_finite_int A4)) (=> (@ finite_finite_nat (@ (@ image_int_nat F) A4)) (exists ((X int)) (and (@ (@ member_int X) A4) (not (@ finite_finite_int (@ collect_int (lambda ((A5 int)) (and (@ (@ member_int A5) A4) (= (@ F A5) (@ F X)))))))))))) (forall ((X2 product_prod_nat_num) (Y3 nat) (Z2 num)) (=> (= X2 (@ (@ product_Pair_nat_num Y3) Z2)) (= (@ product_snd_nat_num X2) Z2))) (forall ((F (-> nat Bool)) (A nat) (B5 set_nat)) (let ((_let_1 (@ image_nat_o F))) (= (@ _let_1 (@ (@ insert_nat A) B5)) (@ (@ insert_o (@ F A)) (@ _let_1 B5))))) (forall ((A4 (-> nat set_nat)) (I3 set_nat)) (exists ((F5 (-> nat product_prod_nat_nat))) (let ((_let_1 (@ comple7399068483239264473et_nat (@ (@ image_nat_set_nat A4) I3)))) (and (@ (@ ord_le3146513528884898305at_nat (@ (@ image_5846123807819985514at_nat F5) _let_1)) (@ (@ produc457027306803732586at_nat I3) A4)) (@ (@ inj_on5538052773655684606at_nat F5) _let_1))))) (forall ((B8 set_se7855581050983116737at_nat) (A4 set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ (@ inf_in2572325071724192079at_nat (@ comple1930127330929219688at_nat B8)) A4))) (let ((_let_2 (= B8 bot_bo3083307316010499117at_nat))) (and (=> (not _let_2) (= _let_1 (@ comple1930127330929219688at_nat (@ (@ image_3684629450409544005at_nat (lambda ((B6 set_Pr1261947904930325089at_nat)) (@ (@ inf_in2572325071724192079at_nat B6) A4))) B8)))) (=> _let_2 (= _let_1 A4)))))) (forall ((B5 (-> int set_nat)) (F (-> nat int)) (A4 set_nat)) (= (@ comple7806235888213564991et_nat (@ (@ image_nat_set_nat (lambda ((A5 nat)) (@ B5 (@ F A5)))) A4)) (@ comple7806235888213564991et_nat (@ (@ image_int_set_nat B5) (@ (@ image_nat_int F) A4))))) (forall ((A4 set_Pr1261947904930325089at_nat) (B5 set_Pr1261947904930325089at_nat)) (=> (@ finite6177210948735845034at_nat A4) (=> (@ finite6177210948735845034at_nat B5) (= (exists ((F2 (-> product_prod_nat_nat product_prod_nat_nat))) (and (@ (@ inj_on8969904277767023793at_nat F2) A4) (@ (@ 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id_Pro5428700290092274115at_nat))))))))) (forall ((C3 set_nat) (A4 (-> nat set_Pr8693737435421807431at_nat)) (B5 set_Pr8693737435421807431at_nat)) (let ((_let_1 (@ (@ sup_su718114333110466843at_nat (@ comple2748534634209756852at_nat (@ (@ image_4592875511192039216at_nat A4) C3))) B5))) (let ((_let_2 (= C3 bot_bot_set_nat))) (and (=> _let_2 (= _let_1 B5)) (=> (not _let_2) (= _let_1 (@ comple2748534634209756852at_nat (@ (@ image_4592875511192039216at_nat (lambda ((X4 nat)) (@ (@ sup_su718114333110466843at_nat (@ A4 X4)) B5))) C3)))))))) (forall ((A4 set_Product_unit) (C int)) (=> (not (= A4 bot_bo3957492148770167129t_unit)) (= (@ complete_Sup_Sup_int (@ (@ image_873079544045703924it_int (lambda ((X4 product_unit)) C)) A4)) C))) (forall ((X2 set_Pr1261947904930325089at_nat) (Fx set_Pr1261947904930325089at_nat) (A4 set_se7855581050983116737at_nat) (F (-> set_Pr1261947904930325089at_nat set_Pr1261947904930325089at_nat))) (=> (@ (@ member8757157785044589968at_nat (@ (@ produc2922128104949294807at_nat X2) Fx)) (@ (@ bNF_Gr1527221351080490466at_nat A4) F)) (@ (@ member2643936169264416010at_nat X2) A4))) (forall ((C3 set_Product_unit) (A4 set_nat) (B5 (-> product_unit set_nat))) (let ((_let_1 (@ (@ inf_inf_set_nat A4) (@ comple7806235888213564991et_nat (@ (@ image_8173849991827986510et_nat B5) C3))))) (let ((_let_2 (= C3 bot_bo3957492148770167129t_unit))) (and (=> (not _let_2) (= _let_1 (@ comple7806235888213564991et_nat (@ (@ image_8173849991827986510et_nat (lambda ((X4 product_unit)) (@ (@ inf_inf_set_nat A4) (@ B5 X4)))) C3)))) (=> _let_2 (= _let_1 A4)))))) (forall ((Rep (-> product_unit Bool)) (Abs (-> Bool product_unit)) (X2 Bool) (S5 (-> Bool set_o)) (Y3 Bool)) (let ((_let_1 (@ member_o X2))) (=> (@ (@ (@ type_d6188575255521822967unit_o Rep) Abs) top_top_set_o) (=> (@ _let_1 (@ (@ (@ comp_o6895741221744486154t_unit S5) Rep) (@ Abs Y3))) (@ _let_1 (@ S5 Y3)))))) (forall ((Z2 produc3843707927480180839at_nat) (A4 set_se7855581050983116737at_nat) (F (-> set_Pr1261947904930325089at_nat set_Pr1261947904930325089at_nat))) (=> (@ (@ member8757157785044589968at_nat Z2) (@ collec6321179662152712658at_nat (@ produc410239310623530412_nat_o (@ (@ bNF_Gr6677838525845560078at_nat A4) F)))) (@ (@ member2643936169264416010at_nat (@ produc6011863565407846595at_nat Z2)) A4))) (forall ((C heap_Heap_ref_a) (H heap_e7401611519738050253t_unit)) (=> (@ (@ heap_success_ref_a C) H) (not (forall ((R4 ref_a) (H4 heap_e7401611519738050253t_unit)) (not (@ (@ (@ (@ heap_effect_ref_a C) H) H4) R4)))))) (forall ((F (-> int nat)) (Fa (-> int nat)) (G (-> int int)) (Ga (-> int int))) (= (@ (@ comp_P2318390481314533713nt_int (@ (@ basic_1872990034501187214nt_int F) Fa)) (@ (@ produc6036585564866528938nt_int G) Ga)) (@ (@ basic_1872990034501187214nt_int (@ (@ comp_int_nat_int F) G)) (@ (@ comp_int_nat_int Fa) Ga)))) (forall ((X2 Bool) (A4 set_o) (F (-> Bool product_unit))) (let ((_let_1 (@ (@ image_o_Product_unit F) A4))) (=> (@ (@ member_o X2) A4) (=> (@ 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member5262025264175285858nt_int (@ (@ (@ bNF_fs8167890477030535480nt_int P2) Q2) Ac)) (@ collec213857154873943460nt_int (@ produc4947309494688390418_int_o P2))))) (forall ((X2 (-> code_integer code_integer code_integer)) (Xa2 (-> code_integer code_integer code_integer)) (F (-> (-> code_integer code_integer) produc8923325533196201883nteger produc8923325533196201883nteger)) (Fa (-> (-> code_integer code_integer) produc8923325533196201883nteger produc8923325533196201883nteger))) (=> (forall ((Z3 (-> code_integer code_integer)) (Za (-> code_integer code_integer))) (=> (@ (@ member2790140394383616496nteger Z3) (@ (@ image_2177946750938214461nteger X2) top_to4645266643341252675nteger)) (=> (@ (@ member2790140394383616496nteger Za) (@ (@ image_2177946750938214461nteger Xa2) top_to4645266643341252675nteger)) (=> (= (@ F Z3) (@ Fa Za)) (= Z3 Za))))) (=> (= (@ (@ comp_C8797469213163452608nteger F) X2) (@ (@ comp_C8797469213163452608nteger Fa) Xa2)) (= X2 Xa2)))) (forall ((P2 (-> (-> product_prod_nat_nat product_prod_nat_nat) Bool)) (F (-> nat nat product_prod_nat_nat product_prod_nat_nat)) (Prod product_prod_nat_nat)) (let ((_let_1 (@ product_snd_nat_nat Prod))) (let ((_let_2 (@ product_fst_nat_nat Prod))) (= (@ P2 (@ (@ produc27273713700761075at_nat F) Prod)) (=> (= Prod (@ (@ product_Pair_nat_nat _let_2) _let_1)) (@ P2 (@ (@ F _let_2) _let_1))))))) (forall ((B5 set_Product_unit) (F (-> nat nat)) (A4 set_nat) (G (-> product_unit nat))) (let ((_let_1 (@ (@ image_nat_nat F) A4))) (=> (not (= B5 bot_bo3957492148770167129t_unit)) (=> (@ condit1738341127787009408ow_nat _let_1) (=> (forall ((M4 product_unit)) (=> (@ (@ member_Product_unit M4) B5) (exists ((X6 nat)) (and (@ (@ member_nat X6) A4) (@ (@ ord_less_eq_nat (@ F X6)) (@ G M4)))))) (@ (@ ord_less_eq_nat (@ complete_Inf_Inf_nat _let_1)) (@ complete_Inf_Inf_nat (@ (@ image_875570014554754200it_nat G) B5)))))))) (forall ((A nat) (A4 set_nat)) (let ((_let_1 (@ pow_nat A4))) (let ((_let_2 (@ insert_nat A))) (= (@ pow_nat (@ _let_2 A4)) (@ (@ sup_sup_set_set_nat _let_1) (@ (@ image_7916887816326733075et_nat _let_2) _let_1)))))) _let_186 (forall ((K nat) (I3 set_nat) (A4 (-> nat set_Pr1261947904930325089at_nat))) (let ((_let_1 (@ comple1930127330929219688at_nat (@ (@ image_7178329752028323786at_nat A4) I3)))) (=> (@ (@ member_nat K) I3) (= (@ (@ inf_in2572325071724192079at_nat (@ A4 K)) _let_1) _let_1)))) (forall ((F (-> product_unit set_nat)) (A4 set_Product_unit)) (=> (@ order_509894322932672675et_nat F) (@ (@ ord_less_eq_set_nat (@ F (@ comple2584293577114468500t_unit A4))) (@ comple7806235888213564991et_nat (@ (@ image_8173849991827986510et_nat F) A4))))) _let_185 (forall ((X2 set_Pr4329608150637261639at_nat) (Y3 set_Pr4329608150637261639at_nat) (A set_Pr4329608150637261639at_nat)) (=> (= (@ produc826222791318859909at_nat (@ (@ produc9060074326276436823at_nat X2) Y3)) A) (= Y3 A))) (forall ((M (-> produc859450856879609959at_nat product_unit)) (A4 set_Pr8693737435421807431at_nat) (B5 set_Pr8693737435421807431at_nat)) (let ((_let_1 (@ image_8487516615895632747t_unit M))) (= (@ comple4687483117567863418t_unit (@ _let_1 (@ (@ sup_su718114333110466843at_nat A4) B5))) (@ (@ sup_sup_Product_unit (@ comple4687483117567863418t_unit (@ _let_1 A4))) (@ comple4687483117567863418t_unit (@ _let_1 B5)))))) (forall ((A4 set_int) (M3 nat) (F (-> int nat))) (=> (forall ((X int)) (=> (@ (@ member_int X) A4) (@ (@ ord_less_eq_nat M3) (@ F X)))) (@ condit1738341127787009408ow_nat (@ (@ image_int_nat F) A4)))) (forall ((K int) (I3 set_int) (A4 (-> int set_Pr1261947904930325089at_nat))) (let ((_let_1 (@ comple1930127330929219688at_nat (@ (@ image_8938366415781434990at_nat A4) I3)))) (=> (@ (@ member_int K) I3) (= (@ (@ inf_in2572325071724192079at_nat (@ A4 K)) _let_1) _let_1)))) (forall ((F (-> a a)) (R2 ref_a) (H heap_e7401611519738050253t_unit) (H2 heap_e7401611519738050253t_unit) (R a)) (let ((_let_1 (@ F (@ (@ get_a H) R2)))) (=> (@ (@ (@ (@ heap_effect_a (@ (@ change_a F) R2)) H) H2) R) (not (=> (= H2 (@ (@ (@ set_a R2) _let_1) H)) (not (= R _let_1))))))) (forall ((F (-> int nat)) (G (-> int nat)) (A4 set_int)) (= (@ condit1738341127787009408ow_nat (@ (@ image_int_nat (lambda ((X4 int)) (@ (@ inf_inf_nat (@ F X4)) (@ G X4)))) A4)) (and (@ condit1738341127787009408ow_nat (@ (@ image_int_nat G) A4)) (@ condit1738341127787009408ow_nat (@ (@ image_int_nat F) A4))))) _let_184 (forall ((C3 set_nat) (A4 (-> nat set_int)) (B5 set_int)) (let ((_let_1 (= C3 bot_bot_set_nat))) (and (=> (not _let_1) (= (@ comple3628384868704368283et_int (@ (@ image_nat_set_int (lambda ((X4 nat)) (@ (@ minus_minus_set_int (@ A4 X4)) B5))) C3)) (@ (@ minus_minus_set_int (@ comple3628384868704368283et_int (@ (@ image_nat_set_int A4) C3))) B5))) (=> _let_1 (= (@ comple3628384868704368283et_int (@ (@ image_nat_set_int (lambda ((X4 nat)) (@ (@ minus_minus_set_int (@ A4 X4)) B5))) C3)) top_top_set_int))))) (forall ((A Bool) (A4 set_o)) (=> (@ (@ member_o A) A4) (@ (@ member7466972457876170832od_o_o (@ (@ product_Pair_o_o A) A)) (@ id_on_o A4)))) (forall ((F (-> product_prod_nat_nat product_prod_nat_nat)) (C3 set_Pr1261947904930325089at_nat) (A4 set_Pr1261947904930325089at_nat) (B5 set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ image_5168914502847457605at_nat F))) (=> (@ (@ inj_on8969904277767023793at_nat F) C3) (=> (@ (@ ord_le3146513528884898305at_nat A4) C3) (=> (@ (@ ord_le3146513528884898305at_nat B5) C3) (= (@ _let_1 (@ (@ inf_in2572325071724192079at_nat A4) B5)) (@ (@ inf_in2572325071724192079at_nat (@ _let_1 A4)) (@ _let_1 B5)))))))) (forall ((F (-> int int)) (G (-> int int)) (A4 set_int)) (= (@ condit2212336002400062152ve_int (@ (@ image_int_int (lambda ((X4 int)) (@ (@ sup_sup_int (@ F X4)) (@ G X4)))) A4)) (and (@ condit2212336002400062152ve_int (@ (@ image_int_int G) A4)) (@ condit2212336002400062152ve_int (@ (@ image_int_int F) A4))))) (forall ((S5 set_int) (T3 set_nat) (F (-> int nat))) (=> (@ finite_finite_int S5) (=> (@ finite_finite_nat T3) (=> (= (@ finite_card_int S5) (@ finite_card_nat T3)) (=> (@ (@ ord_less_eq_set_nat (@ (@ image_int_nat F) S5)) T3) (= (forall ((X4 nat)) (=> (@ (@ member_nat X4) T3) (exists ((Y5 int)) (and (@ (@ member_int Y5) S5) (= (@ F Y5) X4))))) (@ (@ inj_on_int_nat F) S5))))))) (forall ((F (-> nat Bool)) (G (-> nat nat)) (A4 set_nat) (X2 Bool)) (let ((_let_1 (@ (@ image_nat_nat G) A4))) (=> (@ (@ inj_on_nat_o F) _let_1) (=> (@ (@ inj_on_nat_nat G) A4) (=> (@ (@ member_o X2) (@ (@ image_nat_o F) _let_1)) (= (@ (@ (@ the_inv_into_nat_o A4) (@ (@ comp_nat_o_nat F) G)) X2) (@ (@ (@ comp_nat_nat_o (@ (@ the_inv_into_nat_nat A4) G)) (@ (@ the_inv_into_nat_o _let_1) F)) X2))))))) (forall ((F (-> int nat)) (A4 set_int) (B5 set_int)) (let ((_let_1 (@ image_int_nat F))) (@ (@ ord_less_eq_set_nat (@ (@ minus_minus_set_nat (@ _let_1 A4)) (@ _let_1 B5))) (@ _let_1 (@ (@ minus_minus_set_int A4) B5))))) (forall ((A4 set_Pr4329608150637261639at_nat) (B5 (-> produc3843707927480180839at_nat set_nat))) (=> (@ finite4343798906461161616at_nat A4) (=> (forall ((A3 produc3843707927480180839at_nat)) (=> (@ (@ member8757157785044589968at_nat A3) A4) (@ finite_finite_nat (@ B5 A3)))) (@ finite_finite_nat (@ comple7399068483239264473et_nat (@ (@ image_3160451284896210088et_nat B5) A4)))))) (forall ((A4 set_int) (F (-> int nat)) (M nat)) (=> (not (= A4 bot_bot_set_int)) (=> (forall ((X int)) (=> (@ (@ member_int X) A4) (@ (@ ord_less_eq_nat (@ F X)) M))) (@ (@ ord_less_eq_nat (@ complete_Sup_Sup_nat (@ (@ image_int_nat F) A4))) M)))) (forall ((R set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ field_nat R))) (=> (@ (@ order_4473980167227706203on_nat _let_1) R) (= (@ (@ order_2888998067076097458on_nat _let_1) R) (forall ((A6 set_nat)) (=> (@ (@ ord_less_eq_set_nat A6) (@ field_nat R)) (=> (not (= A6 bot_bot_set_nat)) (exists ((X4 nat)) (and (@ (@ member_nat X4) A6) (forall ((Y5 nat)) (=> (@ (@ member_nat Y5) A6) (@ (@ member8440522571783428010at_nat (@ (@ product_Pair_nat_nat X4) Y5)) R)))))))))))) (forall ((F (-> Bool nat)) (A4 set_o) (P2 (-> nat Bool))) (= (@ collect_nat (lambda ((X4 nat)) (and (@ P2 X4) (@ (@ member_nat X4) (@ (@ image_o_nat F) A4))))) (@ (@ image_o_nat F) (@ collect_o (lambda ((X4 Bool)) (and (@ (@ member_o X4) A4) (@ P2 (@ F X4)))))))) (forall ((A4 set_nat) (C set_Product_unit)) (let ((_let_1 (= A4 bot_bot_set_nat))) (and (=> (not _let_1) (= (@ comple3349607820504768346t_unit (@ (@ image_4824033694279209942t_unit (lambda ((Y5 nat)) C)) A4)) C)) (=> _let_1 (= (@ comple3349607820504768346t_unit (@ (@ image_4824033694279209942t_unit (lambda ((Y5 nat)) C)) A4)) bot_bo3957492148770167129t_unit))))) (forall ((R3 set_Pr7459493094073627847at_nat) (S5 set_Pr7459493094073627847at_nat)) (= (@ (@ ord_le3072208448688395470_nat_o (lambda ((X4 set_Pr4329608150637261639at_nat) (Y5 set_Pr4329608150637261639at_nat)) (@ (@ member1466754251312161552at_nat (@ (@ produc9060074326276436823at_nat X4) Y5)) R3))) (lambda ((X4 set_Pr4329608150637261639at_nat) (Y5 set_Pr4329608150637261639at_nat)) (@ (@ member1466754251312161552at_nat (@ (@ produc9060074326276436823at_nat X4) Y5)) S5))) (@ (@ ord_le5997549366648089703at_nat R3) S5))) (forall ((A4 set_o) (R set_Product_prod_o_o) (A Bool) (B Bool)) (=> (@ (@ order_2615775362358406454r_on_o A4) R) (=> (@ (@ member7466972457876170832od_o_o (@ (@ product_Pair_o_o A) B)) R) (and (@ (@ member_o A) A4) (@ (@ member_o B) A4))))) (forall ((G1 (-> Bool Bool)) (G22 (-> nat num)) (F1 (-> nat Bool)) (F22 (-> int nat)) (V product_prod_nat_int)) (= (@ (@ (@ produc3628557804203378146at_num G1) G22) (@ (@ (@ produc8250590009387450446nt_nat F1) F22) V)) (@ (@ (@ produc4807921795543229080nt_num (@ (@ comp_o_o_nat G1) F1)) (@ (@ comp_nat_num_int G22) F22)) V))) (= produc5717040794327095847_ref_a (@ (@ comp_P2006160480335490974_ref_a produc1126150082675451753t_unit) (@ produc4426278547552487717t_unit (lambda ((X4 heap_e7401611519738050253t_unit) (Y5 ref_a)) (@ (@ produc6544324848051098391t_unit Y5) X4))))) (forall ((C3 set_Product_unit) (A4 (-> product_unit set_int)) (B5 set_int)) (let ((_let_1 (= C3 bot_bo3957492148770167129t_unit))) (and (=> (not _let_1) (= (@ comple3628384868704368283et_int (@ (@ image_3995998972318789802et_int (lambda ((X4 product_unit)) (@ (@ inf_inf_set_int (@ A4 X4)) B5))) C3)) (@ (@ inf_inf_set_int (@ comple3628384868704368283et_int (@ (@ image_3995998972318789802et_int A4) C3))) B5))) (=> _let_1 (= (@ comple3628384868704368283et_int (@ (@ image_3995998972318789802et_int (lambda ((X4 product_unit)) (@ (@ inf_inf_set_int (@ A4 X4)) B5))) C3)) top_top_set_int))))) (forall ((R1 (-> ref_a heap_e7401611519738050253t_unit Bool)) (R22 (-> int int Bool)) (P2 (-> ref_a int Bool)) (Q2 (-> heap_e7401611519738050253t_unit int Bool)) (A produc7812382424243267045t_unit) (A4 set_Pr1133966238863718811t_unit) (B product_prod_int_int) (B5 set_Pr958786334691620121nt_int)) (=> (@ (@ (@ (@ bNF_re5775369113877777_int_o R1) (@ (@ bNF_re5089333283451836215nt_o_o R22) (lambda ((Y2 Bool) (Z Bool)) (= Y2 Z)))) P2) Q2) (=> (@ (@ member7849944260330398460t_unit A) A4) (=> (@ (@ member5262025264175285858nt_int B) B5) (=> (@ (@ ord_le5525191956872776187t_unit A4) (@ collec3252306575900995386t_unit (@ produc4924168586796184916unit_o R1))) (=> (@ (@ ord_le2843351958646193337nt_int B5) (@ collec213857154873943460nt_int (@ produc4947309494688390418_int_o R22))) (= (@ (@ P2 (@ produc473321116828791851t_unit A)) (@ product_fst_int_int B)) (@ (@ Q2 (@ produc1126150082675451753t_unit A)) (@ product_snd_int_int B))))))))) (forall ((F (-> nat nat)) (A4 set_nat) (P2 (-> nat Bool))) (=> (exists ((X6 nat)) (and (@ (@ member_nat X6) (@ (@ image_nat_nat F) A4)) (@ P2 X6))) (exists ((X nat)) (and (@ P2 (@ F X)) (@ (@ member_nat X) A4))))) (forall ((A4 (-> int int Bool)) (B5 (-> num num Bool)) (F (-> int num)) (G (-> int num)) (X5 set_Pr958786334691620121nt_int) (X2 product_prod_int_int)) (=> (@ (@ (@ (@ bNF_re7626690874201225453um_num A4) B5) F) G) (=> (@ (@ ord_le2843351958646193337nt_int X5) (@ collec213857154873943460nt_int (@ produc4947309494688390418_int_o A4))) (=> (@ (@ member5262025264175285858nt_int X2) X5) (@ (@ B5 (@ (@ (@ comp_i7231038107349025742nt_int F) product_fst_int_int) X2)) (@ (@ (@ comp_i7231038107349025742nt_int G) product_snd_int_int) X2)))))) (forall ((A4 set_o) (G (-> int nat)) (B5 set_int) (F (-> Bool nat))) (let ((_let_1 (@ (@ image_int_nat G) B5))) (=> (not (= A4 bot_bot_set_o)) (=> (@ condit2214826472909112428ve_nat _let_1) (=> (forall ((N2 Bool)) (=> (@ (@ member_o N2) A4) (exists ((X6 int)) (and (@ (@ member_int X6) B5) (@ (@ ord_less_eq_nat (@ F N2)) (@ G X6)))))) (@ (@ ord_less_eq_nat (@ complete_Sup_Sup_nat (@ (@ image_o_nat F) A4))) (@ complete_Sup_Sup_nat _let_1))))))) (forall ((A (-> nat num)) (B (-> int nat)) (C (-> nat num)) (D2 (-> int nat)) (V int)) (=> (= (@ (@ comp_nat_num_int A) B) (@ (@ comp_nat_num_int C) D2)) (= (@ A (@ B V)) (@ C (@ D2 V))))) (forall ((F (-> nat rat)) (A4 set_nat)) (=> (@ (@ inj_on_nat_rat F) top_top_set_nat) (= (@ (@ vimage_nat_rat F) (@ (@ image_nat_rat F) A4)) A4))) (forall ((X2 Bool) (A4 set_o) (B int) (F (-> Bool int))) (=> (@ (@ member_o X2) A4) (=> (= B (@ F X2)) (@ (@ member_int B) (@ (@ image_o_int F) A4))))) _let_182 (forall ((F (-> int nat)) (A4 set_int)) (=> (@ order_mono_int_nat F) (=> (@ condit2212336002400062152ve_int A4) (=> (not (= A4 bot_bot_set_int)) (@ (@ ord_less_eq_nat (@ complete_Sup_Sup_nat (@ (@ image_int_nat F) A4))) (@ F (@ complete_Sup_Sup_int A4))))))) (forall ((H2 heap_e7401611519738050253t_unit) (H heap_e7401611519738050253t_unit) (X2 ref_a) (R ref_ref_a)) (=> (= H2 H) (=> (= X2 (@ (@ get_ref_a H) R)) (@ (@ (@ (@ heap_effect_ref_a (@ lookup_ref_a R)) H) H2) X2)))) (forall ((F (-> product_prod_nat_nat product_unit)) (A product_prod_nat_nat) (A4 set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ image_6169909464789311569t_unit F))) (= (@ comple4687483117567863418t_unit (@ _let_1 (@ (@ insert8211810215607154385at_nat A) A4))) (@ (@ 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((X4 nat)) (and (= Z2 (@ F X4)) (@ (@ member_nat X4) A4))))) (forall ((F (-> nat set_nat)) (A nat) (B5 set_nat)) (let ((_let_1 (@ image_nat_set_nat F))) (= (@ comple7399068483239264473et_nat (@ _let_1 (@ (@ insert_nat A) B5))) (@ (@ sup_sup_set_nat (@ F A)) (@ comple7399068483239264473et_nat (@ _let_1 B5)))))) (forall ((F (-> int Bool)) (G (-> int int)) (A4 set_int) (X2 Bool)) (let ((_let_1 (@ (@ image_int_int G) A4))) (=> (@ (@ inj_on_int_o F) _let_1) (=> (@ (@ inj_on_int_int G) A4) (=> (@ (@ member_o X2) (@ (@ image_int_o F) _let_1)) (= (@ (@ (@ the_inv_into_int_o A4) (@ (@ comp_int_o_int F) G)) X2) (@ (@ (@ comp_int_int_o (@ (@ the_inv_into_int_int A4) G)) (@ (@ the_inv_into_int_o _let_1) F)) X2))))))) (forall ((I3 set_nat) (F (-> nat set_nat)) (X2 set_nat)) (=> (not (= I3 bot_bot_set_nat)) (= (@ comple7806235888213564991et_nat (@ (@ image_nat_set_nat (lambda ((I2 nat)) (@ (@ inf_inf_set_nat (@ F I2)) X2))) I3)) (@ (@ inf_inf_set_nat (@ comple7806235888213564991et_nat (@ (@ 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image_3755276878268593137at_nat (@ produc5347463441023893471at_nat (lambda ((X4 nat) (Y5 int)) (@ (@ product_Pair_rat_nat (@ F X4)) (@ G Y5))))) (@ (@ produc454536836294682310at_int A4) (lambda ((Uu nat)) B5))) (@ (@ produc140472662868866674at_nat (@ (@ image_nat_rat F) A4)) (lambda ((Uu rat)) (@ (@ image_int_nat G) B5))))) (forall ((A set_Pr4329608150637261639at_nat) (B set_Pr4329608150637261639at_nat) (A2 set_Pr4329608150637261639at_nat) (B2 set_Pr4329608150637261639at_nat)) (= (= (@ (@ produc9060074326276436823at_nat A) B) (@ (@ produc9060074326276436823at_nat A2) B2)) (and (= A A2) (= B B2)))) (forall ((A4 set_o) (G (-> nat nat)) (B5 set_nat) (F (-> Bool nat))) (let ((_let_1 (@ (@ image_nat_nat G) B5))) (=> (not (= A4 bot_bot_set_o)) (=> (@ condit2214826472909112428ve_nat _let_1) (=> (forall ((N2 Bool)) (=> (@ (@ member_o N2) A4) (exists ((X6 nat)) (and (@ (@ member_nat X6) B5) (@ (@ ord_less_eq_nat (@ F N2)) (@ G X6)))))) (@ (@ ord_less_eq_nat (@ complete_Sup_Sup_nat (@ (@ image_o_nat F) A4))) (@ complete_Sup_Sup_nat _let_1))))))) _let_181 (forall ((X5 set_Pr4329608150637261639at_nat) (P2 (-> produc3843707927480180839at_nat Bool))) (@ (@ ord_le1268244103169919719at_nat (@ collec6321179662152712658at_nat (lambda ((X4 produc3843707927480180839at_nat)) (and (@ P2 X4) (@ (@ member8757157785044589968at_nat X4) X5))))) X5)) (forall ((F (-> num Bool)) (G (-> nat num)) (L1 (-> Bool Bool)) (L2 (-> nat Bool)) (H (-> int nat)) (R (-> int Bool))) (=> (= (@ (@ comp_num_o_nat F) G) (@ (@ comp_o_o_nat L1) L2)) (=> (= (@ (@ comp_nat_o_int L2) H) R) (= (@ (@ comp_num_o_int F) (@ (@ comp_nat_num_int G) H)) (@ (@ comp_o_o_int L1) R))))) _let_180 (forall ((F (-> nat nat)) (A4 set_nat)) (=> (@ (@ inj_on_nat_nat F) A4) (= (@ (@ image_nat_nat (@ (@ the_inv_into_nat_nat A4) F)) (@ (@ image_nat_nat F) A4)) A4))) (forall ((F (-> nat rat)) (G (-> nat rat)) (A4 set_nat)) (= (@ (@ image_2021340605491722874at_rat (lambda ((X4 nat)) (@ (@ product_Pair_rat_rat (@ F X4)) (@ G X4)))) A4) (@ (@ produc8728714639637146746at_rat (@ (@ image_nat_rat F) A4)) (lambda ((X4 rat)) (@ (@ image_nat_rat G) (@ (@ inf_inf_set_nat (@ (@ vimage_nat_rat F) (@ (@ insert_rat X4) bot_bot_set_rat))) A4)))))) _let_179 (forall ((F (-> nat set_nat)) (A nat) (A4 set_nat)) (let ((_let_1 (@ image_nat_set_nat F))) (= (@ comple7806235888213564991et_nat (@ _let_1 (@ (@ insert_nat A) A4))) (@ (@ inf_inf_set_nat (@ F A)) (@ comple7806235888213564991et_nat (@ _let_1 A4)))))) (forall ((R7 (-> int int Bool)) (S6 (-> num num Bool)) (R3 (-> int int Bool)) (S5 (-> num num Bool))) (=> (@ right_unique_int_int R7) (=> (@ left_total_int_int R7) (=> (@ left_unique_num_num S6) (=> (@ right_total_num_num S6) (@ (@ ord_le4541714130423454556_num_o (@ (@ bNF_re7626690874201225453um_num (@ (@ relcompp_int_int_int R3) R7)) (@ (@ relcompp_num_num_num S5) S6))) (@ (@ relcom9025577121137075810nt_num (@ (@ bNF_re7626690874201225453um_num R3) S5)) (@ (@ bNF_re7626690874201225453um_num R7) S6)))))))) (forall ((R3 set_Pr6200539531224447659at_num) (S5 set_Pr6200539531224447659at_num)) (= (@ (@ sup_sup_nat_num_o (lambda ((X4 nat) (Y5 num)) (@ (@ member9148766508732265716at_num (@ (@ product_Pair_nat_num X4) Y5)) R3))) (lambda ((X4 nat) (Y5 num)) (@ (@ member9148766508732265716at_num (@ (@ product_Pair_nat_num X4) Y5)) S5))) (lambda ((X4 nat) (Y5 num)) (@ (@ member9148766508732265716at_num (@ (@ product_Pair_nat_num X4) Y5)) (@ (@ sup_su2042722026077122175at_num R3) S5))))) (forall ((F (-> produc3843707927480180839at_nat produc3843707927480180839at_nat)) (A4 set_Pr4329608150637261639at_nat) (B5 set_Pr4329608150637261639at_nat)) (let ((_let_1 (@ image_960689587819713477at_nat F))) (= (@ _let_1 (@ (@ sup_su5525570899277871387at_nat A4) B5)) (@ (@ sup_su5525570899277871387at_nat (@ _let_1 A4)) (@ _let_1 B5))))) (forall ((F (-> int nat)) (G (-> int int)) (A4 set_int) (B5 set_int)) (= (@ (@ image_1654017166447373545at_int (@ produc3246203729202673879at_int (lambda ((X4 int) (Y5 int)) (@ (@ product_Pair_nat_int (@ F X4)) (@ G Y5))))) (@ (@ produc1453890548195736866nt_int A4) (lambda ((Uu int)) B5))) (@ (@ produc454536836294682310at_int (@ (@ image_int_nat F) A4)) (lambda ((Uu nat)) (@ (@ image_int_int G) B5))))) (forall ((A4 set_Pr1261947904930325089at_nat) (F (-> product_prod_nat_nat product_unit)) (U product_unit)) (=> (forall ((I4 product_prod_nat_nat)) (=> (@ (@ member8440522571783428010at_nat I4) A4) (@ (@ ord_le3221252021190050221t_unit (@ F I4)) U))) (@ (@ ord_le3221252021190050221t_unit (@ comple4687483117567863418t_unit (@ (@ image_6169909464789311569t_unit F) A4))) U))) _let_178 (forall ((H (-> Bool product_prod_int_int)) (F (-> int int Bool)) (Prod product_prod_int_int)) (= (@ H (@ (@ produc4947309494688390418_int_o F) Prod)) (@ (@ produc4245557441103728435nt_int (lambda ((X12 int) (X23 int)) (@ H (@ (@ F X12) X23)))) Prod))) (forall ((F (-> int int)) (X5 set_int) (G1 (-> int nat)) (G22 (-> int nat))) (=> (= (@ (@ image_int_int F) X5) top_top_set_int) (=> (forall ((X int)) (=> (@ (@ member_int X) X5) (= (@ (@ (@ comp_int_nat_int G1) F) X) (@ (@ (@ comp_int_nat_int G22) F) X)))) (= G1 G22)))) (forall ((X2 nat)) (= (@ (@ image_char_nat (lambda ((Uu char)) X2)) top_top_set_char) (@ (@ insert_nat X2) bot_bot_set_nat))) (forall ((A4 set_Product_unit) (C product_unit)) (let ((_let_1 (= A4 bot_bo3957492148770167129t_unit))) (and (=> (not _let_1) (= (@ (@ image_405062704495631173t_unit (lambda ((X4 product_unit)) C)) A4) (@ (@ insert_Product_unit C) bot_bo3957492148770167129t_unit))) (=> _let_1 (= (@ (@ image_405062704495631173t_unit (lambda ((X4 product_unit)) C)) A4) bot_bo3957492148770167129t_unit))))) (forall ((A4 set_nat) (B5 set_nat) (G (-> nat product_unit)) (F (-> nat product_unit))) (=> (forall ((I4 nat)) (=> (@ (@ member_nat I4) A4) (exists ((X6 nat)) (and (@ (@ member_nat X6) B5) (@ (@ ord_le3221252021190050221t_unit (@ G X6)) (@ F I4)))))) (=> (forall ((J2 nat)) (=> (@ (@ member_nat J2) B5) (exists ((X6 nat)) (and (@ (@ 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A4)))) (forall ((A4 set_o) (G (-> Bool int)) (B5 set_o) (F (-> Bool int))) (let ((_let_1 (@ (@ image_o_int G) B5))) (=> (not (= A4 bot_bot_set_o)) (=> (@ condit1735850657277959132ow_int _let_1) (=> (@ (@ ord_less_eq_set_o A4) B5) (=> (forall ((X Bool)) (=> (@ (@ member_o X) B5) (@ (@ ord_less_eq_int (@ G X)) (@ F X)))) (@ (@ ord_less_eq_int (@ complete_Inf_Inf_int _let_1)) (@ complete_Inf_Inf_int (@ (@ image_o_int F) A4))))))))) (forall ((X2 nat) (Y3 nat)) (= (@ basic_snds_nat_nat (@ (@ product_Pair_nat_nat X2) Y3)) (@ (@ insert_nat Y3) bot_bot_set_nat))) _let_177 (forall ((F (-> nat nat)) (A4 set_nat) (F3 (-> nat nat))) (=> (@ (@ inj_on_nat_nat F) A4) (= (@ (@ inj_on_nat_nat F3) (@ (@ image_nat_nat F) A4)) (@ (@ inj_on_nat_nat (@ (@ comp_nat_nat_nat F3) F)) A4)))) (forall ((P2 (-> int Bool)) (Q2 (-> int int Bool))) (= (@ collec213857154873943460nt_int (@ produc4947309494688390418_int_o (lambda ((X4 int) (Y5 int)) (and (@ (@ Q2 X4) Y5) (@ P2 X4))))) (@ (@ 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((_let_1 (@ (@ bNF_Grp_rat_rat top_top_set_rat) F))) (=> (= F id_rat) (= (@ (@ relcompp_rat_rat_rat (@ conversep_rat_rat _let_1)) _let_1) _let_1)))) (forall ((B5 (-> product_unit set_char))) (= (@ comple7965528767983648192t_char (@ (@ image_5325685772115642575t_char B5) bot_bo3957492148770167129t_unit)) top_top_set_char)) (forall ((K int) (I3 set_int) (A4 (-> int set_nat))) (let ((_let_1 (@ comple7806235888213564991et_nat (@ (@ image_int_set_nat A4) I3)))) (=> (@ (@ member_int K) I3) (= (@ (@ inf_inf_set_nat (@ A4 K)) _let_1) _let_1)))) (forall ((F (-> int int)) (B5 set_int) (A int) (A4 set_int)) (let ((_let_1 (@ member_int A))) (=> (@ (@ inj_on_int_int F) B5) (=> (@ _let_1 B5) (=> (@ (@ ord_less_eq_set_int A4) B5) (= (@ (@ member_int (@ F A)) (@ (@ image_int_int F) A4)) (@ _let_1 A4))))))) (forall ((F (-> Bool set_nat)) (A4 set_o) (X2 Bool)) (let ((_let_1 (@ (@ image_o_set_nat F) A4))) (=> (@ condit68592940725977398et_nat _let_1) (=> (@ (@ member_o X2) A4) (@ (@ ord_less_eq_set_nat (@ 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produc8923325533196201883nteger)) (G (-> code_integer code_integer code_integer)) (X2 code_integer) (F3 (-> (-> code_integer code_integer) produc8923325533196201883nteger produc8923325533196201883nteger)) (G2 (-> code_integer code_integer code_integer)) (X3 code_integer)) (=> (= (@ F (@ G X2)) (@ F3 (@ G2 X3))) (= (@ (@ (@ comp_C8797469213163452608nteger F) G) X2) (@ (@ (@ comp_C8797469213163452608nteger F3) G2) X3)))) (forall ((A4 set_o) (C3 set_o) (B5 set_o) (D set_o)) (= (@ (@ ord_le192195778054999463od_o_o (@ (@ product_Sigma_o_o A4) (lambda ((Uu Bool)) C3))) (@ (@ product_Sigma_o_o B5) (lambda ((Uu Bool)) D))) (or (= A4 bot_bot_set_o) (= C3 bot_bot_set_o) (and (@ (@ ord_less_eq_set_o C3) D) (@ (@ ord_less_eq_set_o A4) B5))))) (forall ((A4 set_o) (B5 (-> Bool set_Product_unit)) (F (-> product_unit int))) (=> (not (= A4 bot_bot_set_o)) (=> (forall ((X Bool)) (=> (@ (@ member_o X) A4) (not (= (@ B5 X) bot_bo3957492148770167129t_unit)))) (=> (@ condit2212336002400062152ve_int (@ comple3221217463730067765et_int (@ (@ image_o_set_int (lambda ((X4 Bool)) (@ (@ image_873079544045703924it_int F) (@ B5 X4)))) A4))) (= (@ complete_Sup_Sup_int (@ (@ image_873079544045703924it_int F) (@ comple3349607820504768346t_unit (@ (@ image_663195431845683034t_unit B5) A4)))) (@ complete_Sup_Sup_int (@ (@ image_o_int (lambda ((X4 Bool)) (@ complete_Sup_Sup_int (@ (@ image_873079544045703924it_int F) (@ B5 X4))))) A4))))))) (forall ((A4 set_o) (B5 set_o) (F (-> Bool set_nat)) (G (-> Bool set_nat))) (=> (@ (@ ord_less_eq_set_o A4) B5) (=> (forall ((X Bool)) (=> (@ (@ member_o X) A4) (@ (@ ord_less_eq_set_nat (@ F X)) (@ G X)))) (@ (@ ord_less_eq_set_nat (@ comple7806235888213564991et_nat (@ (@ image_o_set_nat F) B5))) (@ comple7806235888213564991et_nat (@ (@ image_o_set_nat G) A4)))))) (forall ((F (-> nat nat)) (A4 (-> nat nat)) (I3 set_nat)) (let ((_let_1 (@ (@ image_nat_nat A4) I3))) (=> (@ order_mono_nat_nat F) (=> (@ condit1738341127787009408ow_nat _let_1) (=> (not (= I3 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(@ (@ image_int_set_nat F) A4))) U))) (forall ((A product_unit) (B5 set_Product_unit)) (let ((_let_1 (@ inf_inf_Product_unit A))) (= (@ _let_1 (@ comple4687483117567863418t_unit B5)) (@ comple4687483117567863418t_unit (@ (@ image_405062704495631173t_unit _let_1) B5))))) (forall ((A4 set_nat)) (= (@ collect_nat (lambda ((X4 nat)) (@ (@ member_nat X4) A4))) A4)) _let_176 (@ (@ (@ _let_53 (@ _let_52 (lambda ((Y2 Bool) (Z Bool)) (= Y2 Z)))) (@ produc8739625826339149834_nat_o (lambda ((X4 nat) (Y5 nat) (__flatten_var_0 product_prod_nat_nat)) (@ (@ produc6081775807080527818_nat_o (lambda ((U3 nat) (V3 nat)) (@ (@ ord_less_nat (@ (@ plus_plus_nat X4) V3)) (@ (@ plus_plus_nat U3) Y5)))) __flatten_var_0)))) (@ produc8739625826339149834_nat_o (lambda ((X4 nat) (Y5 nat) (__flatten_var_0 product_prod_nat_nat)) (@ (@ produc6081775807080527818_nat_o (lambda ((U3 nat) (V3 nat)) (@ (@ ord_less_nat (@ (@ plus_plus_nat X4) V3)) (@ (@ plus_plus_nat U3) Y5)))) __flatten_var_0)))) (forall ((F (-> nat nat)) (A4 set_nat)) (=> (@ (@ inj_on_nat_nat F) A4) (= (@ finite_finite_nat (@ (@ image_nat_nat F) A4)) (@ finite_finite_nat A4)))) (forall ((A4 set_nat) (F (-> nat num))) (= (@ (@ bNF_re272988434038980259at_num (lambda ((Y2 int) (Z int)) (= Y2 Z))) (@ (@ bNF_Grp_nat_num A4) F)) (@ (@ bNF_Gr6763702254253555408nt_num (@ collect_int_nat (lambda ((X4 (-> int nat))) (@ (@ ord_less_eq_set_nat (@ (@ image_int_nat X4) top_top_set_int)) A4)))) (@ comp_nat_num_int F)))) (forall ((F (-> rat nat)) (A nat) (X2 rat)) (=> (= (@ (@ image_rat_nat F) top_top_set_rat) (@ (@ insert_nat A) bot_bot_set_nat)) (= (@ F X2) A))) (forall ((S5 set_Pr1261947904930325089at_nat) (F (-> product_prod_nat_nat Bool Bool)) (X2 product_prod_nat_nat) (Y3 product_prod_nat_nat) (G (-> nat Bool))) (let ((_let_1 (@ comp_o_o_nat (@ F Y3)))) (let ((_let_2 (@ comp_o_o_nat (@ F X2)))) (=> (@ (@ finite1496024664758132007_nat_o S5) F) (=> (@ (@ member8440522571783428010at_nat X2) S5) (=> (@ (@ member8440522571783428010at_nat Y3) S5) (= (@ _let_1 (@ _let_2 G)) (@ _let_2 (@ _let_1 G))))))))) _let_175 (forall ((A Bool) (B nat) (A4 set_o) (B5 (-> Bool set_nat))) (=> (@ (@ member2802428098988154798_o_nat (@ (@ product_Pair_o_nat A) B)) (@ (@ product_Sigma_o_nat A4) B5)) (not (=> (@ (@ member_o A) A4) (not (@ (@ member_nat B) (@ B5 A))))))) (forall ((A Bool) (A4 set_o) (B Bool) (B5 (-> Bool set_o))) (=> (@ (@ member_o A) A4) (=> (@ (@ member_o B) (@ B5 A)) (@ (@ member7466972457876170832od_o_o (@ (@ product_Pair_o_o A) B)) (@ (@ product_Sigma_o_o A4) B5))))) (forall ((Ac produc4196048018000912732at_int) (P2 (-> product_prod_nat_nat product_prod_nat_nat Bool)) (Q2 (-> product_prod_nat_nat int Bool))) (=> (@ (@ member8394280151737582451at_int Ac) (@ collec2851339944984316337at_int (@ produc6937227050501860053_int_o (@ (@ relcom8911704206367525917at_int P2) Q2)))) (@ (@ member8394280151737582451at_int (@ (@ (@ bNF_sn649997494946348640at_int P2) Q2) Ac)) (@ collec2851339944984316337at_int (@ produc6937227050501860053_int_o Q2))))) (forall ((A4 set_Product_unit) (F (-> product_unit set_nat)) (B5 set_Product_unit)) (let ((_let_1 (@ image_8173849991827986510et_nat F))) (let ((_let_2 (@ _let_1 B5))) (let ((_let_3 (@ _let_1 A4))) (=> (not (= A4 bot_bo3957492148770167129t_unit)) (=> (@ condit68592940725977398et_nat _let_3) (=> (not (= B5 bot_bo3957492148770167129t_unit)) (=> (@ condit68592940725977398et_nat _let_2) (= (@ comple7806235888213564991et_nat (@ _let_1 (@ (@ sup_su793286257634532545t_unit A4) B5))) (@ (@ inf_inf_set_nat (@ comple7806235888213564991et_nat _let_3)) (@ comple7806235888213564991et_nat _let_2))))))))))) (forall ((P2 (-> nat Bool)) (Q2 (-> nat nat Bool))) (= (@ collec3392354462482085612at_nat (@ produc6081775807080527818_nat_o (lambda ((X4 nat) (Y5 nat)) (and (@ P2 X4) (@ (@ Q2 X4) Y5))))) (@ (@ produc457027306803732586at_nat (@ collect_nat P2)) (lambda ((X4 nat)) (@ collect_nat (@ Q2 X4)))))) (forall ((R (-> product_prod_nat_nat product_prod_nat_nat Bool)) (S2 (-> product_prod_nat_nat 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(@ minus_minus_set_int A4) (@ comple3221217463730067765et_int (@ (@ image_nat_set_int B5) C3))))) (=> _let_1 (= (@ comple3628384868704368283et_int (@ (@ image_nat_set_int (lambda ((X4 nat)) (@ (@ minus_minus_set_int A4) (@ B5 X4)))) C3)) top_top_set_int))))) (forall ((C heap_Heap_ref_a) (H heap_e7401611519738050253t_unit) (H2 heap_e7401611519738050253t_unit) (R ref_a)) (=> (@ (@ (@ (@ heap_effect_ref_a C) H) H2) R) (@ (@ heap_success_ref_a C) H))) (forall ((C3 set_nat) (A4 (-> nat set_rat)) (B5 set_rat)) (let ((_let_1 (@ (@ minus_minus_set_rat (@ comple4298007329820168263et_rat (@ (@ image_nat_set_rat A4) C3))) B5))) (let ((_let_2 (= C3 bot_bot_set_nat))) (and (=> (not _let_2) (= _let_1 (@ comple4298007329820168263et_rat (@ (@ image_nat_set_rat (lambda ((X4 nat)) (@ (@ minus_minus_set_rat (@ A4 X4)) B5))) C3)))) (=> _let_2 (= _let_1 (@ (@ minus_minus_set_rat top_top_set_rat) B5))))))) (forall ((P2 (-> int Bool)) (F (-> int nat)) (B5 set_nat)) (=> (forall ((X int)) (=> (@ P2 X) (@ (@ 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(@ (@ produc8256076736985659095t_unit X4) X4))) produc1126150082675451753t_unit)) produc1126150082675451753t_unit) (forall ((F (-> product_unit set_Pr4329608150637261639at_nat)) (A product_unit) (B5 set_Product_unit)) (let ((_let_1 (@ image_5172358348707908735at_nat F))) (= (@ comple4364388969068068532at_nat (@ _let_1 (@ (@ insert_Product_unit A) B5))) (@ (@ sup_su5525570899277871387at_nat (@ F A)) (@ comple4364388969068068532at_nat (@ _let_1 B5)))))) (forall ((B int) (F (-> int int)) (X2 int) (C int) (G (-> int int)) (A4 set_int)) (=> (= B (@ F X2)) (=> (= C (@ G X2)) (=> (@ (@ member_int X2) A4) (@ (@ member5262025264175285858nt_int (@ (@ product_Pair_int_int B) C)) (@ (@ (@ bNF_Gr8686673574714534880nt_int A4) F) G)))))) (forall ((C3 set_nat) (A4 set_rat) (B5 (-> nat set_rat))) (let ((_let_1 (= C3 bot_bot_set_nat))) (and (=> _let_1 (= (@ comple4298007329820168263et_rat (@ (@ image_nat_set_rat (lambda ((X4 nat)) (@ (@ inf_inf_set_rat A4) (@ B5 X4)))) C3)) top_top_set_rat)) (=> (not _let_1) (= (@ comple4298007329820168263et_rat (@ (@ image_nat_set_rat (lambda ((X4 nat)) (@ (@ inf_inf_set_rat A4) (@ B5 X4)))) C3)) (@ (@ inf_inf_set_rat A4) (@ comple4298007329820168263et_rat (@ (@ image_nat_set_rat B5) C3)))))))) (forall ((F (-> heap_e7401611519738050253t_unit set_Pr4329608150637261639at_nat)) (G (-> ref_a set_Pr4329608150637261639at_nat)) (X2 produc7812382424243267045t_unit)) (= (@ (@ produc5990651871820846223at_nat F) (@ (@ produc5988837738927868575t_unit G) X2)) (@ (@ produc9060074326276436823at_nat (@ G (@ produc473321116828791851t_unit X2))) (@ F (@ produc1126150082675451753t_unit X2))))) _let_173 (forall ((R3 (-> num num Bool)) (S5 (-> num num Bool))) (= (@ (@ bNF_re7626690874201225453um_num (lambda ((Y2 int) (Z int)) (= Y2 Z))) (@ (@ relcompp_num_num_num R3) S5)) (@ (@ relcom9025577121137075810nt_num (@ (@ bNF_re7626690874201225453um_num (lambda ((Y2 int) (Z int)) (= Y2 Z))) R3)) (@ (@ bNF_re7626690874201225453um_num (lambda ((Y2 int) (Z int)) (= Y2 Z))) S5)))) (forall ((P2 (-> heap_e7401611519738050253t_unit Bool)) (H heap_e7401611519738050253t_unit) (H2 heap_e7401611519738050253t_unit) (F (-> heap_e7401611519738050253t_unit produc7812382424243267045t_unit)) (R ref_a)) (let ((_let_1 (@ F H))) (=> (@ P2 H) (=> (= H2 (@ produc1126150082675451753t_unit _let_1)) (=> (= R (@ produc473321116828791851t_unit _let_1)) (@ (@ (@ (@ heap_effect_ref_a (@ (@ heap_guard_ref_a P2) F)) H) H2) R)))))) (forall ((F (-> product_prod_int_int product_prod_int_int))) (= (@ produc4245557441103728435nt_int (@ produc8249235968001453780nt_int F)) F)) (forall ((F (-> char rat)) (Y3 rat)) (=> (= (@ (@ image_char_rat F) top_top_set_char) top_top_set_rat) (exists ((X char)) (= Y3 (@ F X))))) (forall ((Rep (-> nat Bool)) (Abs (-> Bool nat)) (M (-> nat Bool)) (M1 (-> Bool Bool)) (M2 (-> nat Bool)) (F (-> Bool Bool)) (G (-> nat nat))) (=> (@ (@ (@ type_d1000680970699258650_nat_o Rep) Abs) top_top_set_o) (=> (= M (@ (@ comp_o_o_nat M1) M2)) (= (@ (@ comp_nat_o_nat (@ (@ comp_o_o_nat F) M)) G) (@ (@ comp_nat_o_nat (@ (@ comp_o_o_nat (@ (@ comp_o_o_o F) M1)) Rep)) (@ (@ comp_nat_nat_nat (@ (@ comp_o_nat_nat Abs) M2)) G)))))) (forall ((P2 (-> int int Bool)) (Q2 (-> int code_integer Bool)) (A int) (C code_integer)) (let ((_let_1 (@ (@ (@ (@ bNF_pi4515785505327359899nteger P2) Q2) A) C))) (=> (@ (@ (@ (@ relcom967497705283160040nteger P2) Q2) A) C) (and (@ (@ Q2 _let_1) C) (@ (@ P2 A) _let_1))))) (forall ((M (-> produc3843707927480180839at_nat set_nat)) (A4 set_Pr4329608150637261639at_nat) (B5 set_Pr4329608150637261639at_nat)) (let ((_let_1 (@ image_3160451284896210088et_nat M))) (= (@ comple7806235888213564991et_nat (@ _let_1 (@ (@ sup_su5525570899277871387at_nat A4) B5))) (@ (@ inf_inf_set_nat (@ comple7806235888213564991et_nat (@ _let_1 A4))) (@ comple7806235888213564991et_nat (@ _let_1 B5)))))) (forall ((P2 (-> nat Bool)) (P nat) (Q2 (-> num Bool)) (Q num)) (let ((_let_1 (@ (@ product_Pair_nat_num P) Q))) (=> (@ P2 P) (=> (@ Q2 Q) (and (@ Q2 (@ 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set_Pr1261947904930325089at_nat) (B Bool) (B5 (-> product_prod_nat_nat set_o))) (=> (forall ((X product_prod_nat_nat)) (=> (@ (@ member8440522571783428010at_nat X) A4) (@ (@ member_o B) (@ B5 X)))) (@ (@ member_o B) (@ comple3063163877087187839_set_o (@ (@ image_501298686397505212_set_o B5) A4))))) (forall ((F (-> Bool product_unit)) (A4 set_o)) (=> (@ order_7782127260464396005t_unit F) (=> (@ condit5413489452508810728elow_o A4) (=> (not (= A4 bot_bot_set_o)) (@ (@ ord_le3221252021190050221t_unit (@ F (@ complete_Inf_Inf_o A4))) (@ comple2584293577114468500t_unit (@ (@ image_o_Product_unit F) A4))))))) (forall ((F (-> int int)) (A4 set_int) (B5 set_int)) (let ((_let_1 (@ image_int_int F))) (=> (@ (@ ord_less_eq_set_int (@ _let_1 A4)) B5) (@ (@ ord_le4403425263959731960et_int (@ (@ image_524474410958335435et_int _let_1) (@ finite_Fpow_int A4))) (@ finite_Fpow_int B5))))) (forall ((M (-> Bool Bool)) (G (-> nat Bool)) (X2 nat) (N (-> nat Bool)) (H (-> nat nat)) (F (-> Bool Bool))) (=> (= (@ M (@ G X2)) (@ N (@ H X2))) (= (@ (@ (@ comp_o_o_nat (@ (@ comp_o_o_o F) M)) G) X2) (@ (@ (@ comp_nat_o_nat (@ (@ comp_o_o_nat F) N)) H) X2)))) (forall ((R3 (-> product_prod_nat_nat product_prod_nat_nat Bool)) (S5 (-> int int Bool)) (R7 (-> product_prod_nat_nat int Bool)) (S6 (-> int code_integer Bool))) (@ (@ ord_le6141271677531915726eger_o (@ (@ relcom4574826104943343961nteger (@ (@ bNF_re20414067882207223nt_int R3) S5)) (@ (@ bNF_re6202762543029211035nteger R7) S6))) (@ (@ bNF_re6202762543029211035nteger (@ (@ relcom8911704206367525917at_int R3) R7)) (@ (@ relcom967497705283160040nteger S5) S6)))) (forall ((I3 set_Product_unit) (F (-> product_unit set_Pr1261947904930325089at_nat)) (X2 set_Pr1261947904930325089at_nat)) (=> (not (= I3 bot_bo3957492148770167129t_unit)) (= (@ comple1930127330929219688at_nat (@ (@ image_3617315916088684441at_nat (lambda ((I2 product_unit)) (@ (@ inf_in2572325071724192079at_nat (@ F I2)) X2))) I3)) (@ (@ inf_in2572325071724192079at_nat (@ comple1930127330929219688at_nat (@ (@ image_3617315916088684441at_nat F) I3))) X2)))) (forall ((F (-> nat nat product_prod_nat_nat Bool)) (G (-> product_prod_nat_nat product_prod_nat_nat Bool))) (=> (forall ((X nat) (Y nat)) (= (@ (@ F X) Y) (@ G (@ (@ product_Pair_nat_nat X) Y)))) (= (@ produc8739625826339149834_nat_o F) G))) (forall ((G (-> char int)) (F (-> int char))) (=> (forall ((X int)) (= (@ G (@ F X)) X)) (= (@ (@ image_char_int G) top_top_set_char) top_top_set_int))) _let_171 (forall ((F (-> int nat)) (A4 set_int) (B5 set_int)) (let ((_let_1 (@ inj_on_int_nat F))) (let ((_let_2 (@ image_int_nat F))) (= (@ _let_1 (@ (@ sup_sup_set_int A4) B5)) (and (@ _let_1 A4) (= (@ (@ inf_inf_set_nat (@ _let_2 (@ (@ minus_minus_set_int A4) B5))) (@ _let_2 (@ (@ minus_minus_set_int B5) A4))) bot_bot_set_nat) (@ _let_1 B5)))))) (forall ((S5 set_int) (F (-> int nat nat)) (X2 int) (Y3 int) (G (-> nat nat))) (let ((_let_1 (@ comp_nat_nat_nat (@ F Y3)))) (let ((_let_2 (@ comp_nat_nat_nat (@ F X2)))) (=> (@ (@ finite4582259249640653518nt_nat S5) F) (=> (@ (@ member_int X2) S5) (=> (@ (@ member_int Y3) S5) (= (@ _let_1 (@ _let_2 G)) (@ _let_2 (@ _let_1 G))))))))) (= (@ comple7399068483239264473et_nat (@ (@ image_nat_set_nat set_ord_atLeast_nat) top_top_set_nat)) top_top_set_nat) (forall ((H1 (-> int nat)) (H22 (-> int nat)) (F (-> int int)) (G (-> int int))) (= (@ (@ comp_P2134349925370910487at_int (@ (@ produc5667422475138734578nt_nat H1) H22)) (@ (@ bNF_co2174166945328636015nt_int F) G)) (@ (@ bNF_co1177303703936631735at_nat (@ (@ comp_int_nat_int H1) F)) (@ (@ comp_int_nat_int H22) G)))) (forall ((A4 set_nat) (F (-> nat rat)) (B5 set_rat)) (=> (forall ((X nat)) (=> (@ (@ member_nat X) A4) (@ (@ member_rat (@ F X)) B5))) (@ (@ ord_less_eq_set_rat (@ (@ image_nat_rat F) A4)) B5))) (forall ((F (-> Bool Bool)) (G (-> nat Bool)) (X2 nat) (Y3 Bool)) (let ((_let_1 (@ comp_o_o_nat F))) (= (@ _let_1 (@ (@ (@ fun_upd_nat_o G) X2) Y3)) (@ (@ (@ fun_upd_nat_o (@ _let_1 G)) X2) (@ F Y3))))) (forall ((K Bool) (I3 set_o) (A4 (-> Bool set_Pr8693737435421807431at_nat))) (let ((_let_1 (@ comple2748534634209756852at_nat (@ (@ image_8493167801588156084at_nat A4) I3)))) (=> (@ (@ member_o K) I3) (= (@ (@ sup_su718114333110466843at_nat (@ A4 K)) _let_1) _let_1)))) (forall ((F (-> int nat)) (A4 set_int)) (=> (@ order_mono_int_nat F) (=> (@ condit1735850657277959132ow_int A4) (@ condit1738341127787009408ow_nat (@ (@ image_int_nat F) A4))))) (forall ((A4 set_int) (F (-> int int)) (A int)) (let ((_let_1 (@ image_int_int F))) (let ((_let_2 (@ _let_1 A4))) (=> (not (= A4 bot_bot_set_int)) (=> (@ condit1735850657277959132ow_int _let_2) (= (@ complete_Inf_Inf_int (@ _let_1 (@ (@ insert_int A) A4))) (@ (@ inf_inf_int (@ F A)) (@ complete_Inf_Inf_int _let_2)))))))) (forall ((B5 set_nat) (A4 set_Product_unit)) (let ((_let_1 (@ produc6875377002296012693it_nat A4))) (let ((_let_2 (@ image_7474191388529947450t_unit produc5169466786534984090it_nat))) (let ((_let_3 (= B5 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(exists ((C2 set_int)) (and (@ finite_finite_int C2) (= B5 (@ (@ image_int_nat F) C2)) (@ (@ ord_less_eq_set_int C2) A4)))))) (forall ((U nat) (A4 set_nat) (A Bool) (B5 (-> nat set_o))) (=> (@ (@ member_nat U) A4) (= (@ comple3063163877087187839_set_o (@ (@ image_nat_set_o (lambda ((X4 nat)) (@ (@ insert_o A) (@ B5 X4)))) A4)) (@ (@ insert_o A) (@ comple3063163877087187839_set_o (@ (@ image_nat_set_o B5) A4)))))) (forall ((M (-> produc3843707927480180839at_nat set_nat)) (A4 set_Pr4329608150637261639at_nat) (B5 set_Pr4329608150637261639at_nat)) (let ((_let_1 (@ image_3160451284896210088et_nat M))) (= (@ comple7399068483239264473et_nat (@ _let_1 (@ (@ sup_su5525570899277871387at_nat A4) B5))) (@ (@ sup_sup_set_nat (@ comple7399068483239264473et_nat (@ _let_1 A4))) (@ comple7399068483239264473et_nat (@ _let_1 B5)))))) (forall ((A int) (B int) (A2 int) (B2 int)) (= (= (@ (@ product_Pair_int_int A) B) (@ (@ product_Pair_int_int A2) B2)) (and (= A A2) (= B B2)))) (forall ((Rep (-> nat Bool)) (Abs (-> Bool nat)) (Rep2 (-> nat Bool)) (Abs2 (-> Bool nat)) (Rep3 (-> nat nat)) (Abs3 (-> nat nat)) (M (-> nat Bool)) (M1 (-> Bool Bool)) (M2 (-> nat Bool))) (=> (@ (@ (@ type_d1000680970699258650_nat_o Rep) Abs) top_top_set_o) (=> (@ (@ (@ type_d1000680970699258650_nat_o Rep2) Abs2) top_top_set_o) (=> (@ (@ (@ type_d6250493948777748686at_nat Rep3) Abs3) top_top_set_nat) (=> (= (@ (@ comp_nat_nat_nat (@ (@ comp_o_nat_nat Abs2) M)) Rep3) (@ (@ comp_nat_nat_nat (@ (@ comp_o_nat_nat (@ (@ comp_o_nat_o Abs2) M1)) Rep)) (@ (@ comp_nat_nat_nat (@ (@ comp_o_nat_nat Abs) M2)) Rep3))) (= (@ (@ comp_o_o_nat M1) M2) M)))))) (forall ((R set_Pr1261947904930325089at_nat)) (=> (@ (@ total_on_nat (@ field_nat R)) R) (=> (@ (@ ord_le3146513528884898305at_nat R) id_nat2) (or (exists ((A3 nat)) (= R (@ (@ insert8211810215607154385at_nat (@ (@ product_Pair_nat_nat A3) A3)) bot_bo2099793752762293965at_nat))) (= R bot_bo2099793752762293965at_nat))))) (forall ((X2 set_Pr1261947904930325089at_nat) (Fx set_Pr1261947904930325089at_nat) (A4 set_se7855581050983116737at_nat) (F (-> set_Pr1261947904930325089at_nat set_Pr1261947904930325089at_nat))) (=> (@ (@ member8757157785044589968at_nat (@ (@ produc2922128104949294807at_nat X2) Fx)) (@ (@ bNF_Gr1527221351080490466at_nat A4) F)) (= (@ F X2) Fx))) (forall ((A4 (-> product_prod_nat_nat int Bool)) (B5 (-> (-> product_prod_nat_nat Bool) (-> int Bool) Bool)) (F (-> product_prod_nat_nat product_prod_nat_nat Bool)) (G (-> int int Bool)) (X2 product_prod_nat_nat) (Y3 int)) (=> (@ (@ (@ (@ bNF_re717283939379294677_int_o A4) B5) F) G) (=> (@ (@ A4 X2) Y3) (@ (@ B5 (@ F X2)) (@ G Y3))))) (forall ((A4 set_Product_unit) (C set_nat)) (=> (not (= A4 bot_bo3957492148770167129t_unit)) (= (@ comple7399068483239264473et_nat (@ (@ image_8173849991827986510et_nat (lambda ((X4 product_unit)) C)) A4)) C))) _let_168 (forall ((U nat) (A4 set_nat) (A Bool) (B5 (-> nat set_o))) (=> (@ (@ member_nat U) A4) (= (@ comple90263536869209701_set_o (@ (@ image_nat_set_o (lambda ((X4 nat)) (@ (@ insert_o A) (@ B5 X4)))) A4)) (@ (@ insert_o A) (@ comple90263536869209701_set_o (@ (@ image_nat_set_o B5) A4)))))) (forall ((F (-> product_prod_nat_nat product_unit)) (A4 set_Pr1261947904930325089at_nat)) (=> (@ finite4290736615968046902t_unit (@ (@ image_6169909464789311569t_unit F) A4)) (=> (not (@ finite6177210948735845034at_nat A4)) (exists ((X product_unit)) (and (not (@ finite6177210948735845034at_nat (@ (@ inf_in2572325071724192079at_nat (@ (@ vimage3104651464403166471t_unit F) (@ (@ insert_Product_unit X) bot_bo3957492148770167129t_unit))) A4))) (@ (@ member_Product_unit X) (@ (@ image_6169909464789311569t_unit F) A4))))))) (forall ((A4 set_int) (B5 (-> int set_o))) (= (@ (@ image_90517134139374612_o_int product_fst_int_o) (@ (@ product_Sigma_int_o A4) B5)) (@ collect_int (lambda ((X4 int)) (and (@ (@ member_int X4) A4) (not (= (@ B5 X4) bot_bot_set_o))))))) (forall ((A4 set_nat) (C product_unit)) (let ((_let_1 (= A4 bot_bot_set_nat))) (and (=> (not _let_1) (= (@ comple4687483117567863418t_unit (@ (@ image_8730104196221521654t_unit (lambda ((Y5 nat)) C)) A4)) C)) (=> _let_1 (= (@ comple4687483117567863418t_unit (@ (@ image_8730104196221521654t_unit (lambda ((Y5 nat)) C)) A4)) bot_bot_Product_unit))))) (forall ((B5 (-> product_unit set_Product_unit))) (= (@ comple3349607820504768346t_unit (@ (@ image_7778121751606633509t_unit B5) bot_bo3957492148770167129t_unit)) bot_bo3957492148770167129t_unit)) (forall ((M (-> produc859450856879609959at_nat set_nat)) (A4 set_Pr8693737435421807431at_nat) (B5 set_Pr8693737435421807431at_nat)) (let ((_let_1 (@ image_2819269535336293544et_nat M))) (= (@ comple7806235888213564991et_nat (@ _let_1 (@ (@ sup_su718114333110466843at_nat A4) B5))) (@ (@ inf_inf_set_nat (@ comple7806235888213564991et_nat (@ _let_1 A4))) (@ comple7806235888213564991et_nat (@ _let_1 B5)))))) (forall ((F (-> product_prod_nat_nat product_prod_nat_nat product_prod_nat_nat))) (= (@ produc27273713700761075at_nat (@ produc3610074571335452306at_nat F)) F)) (forall ((A4 set_o) (M nat) (F (-> Bool nat))) (=> (forall ((X Bool)) (=> (@ (@ member_o X) A4) (@ (@ ord_less_eq_nat M) (@ F X)))) (@ condit1738341127787009408ow_nat (@ (@ image_o_nat F) A4)))) (forall ((F (-> char char)) (G (-> rat char))) (=> (= (@ (@ image_char_char F) top_top_set_char) top_top_set_char) (=> (= (@ (@ image_rat_char G) top_top_set_rat) top_top_set_char) (= (@ (@ image_8036680598759533694r_char (@ (@ produc5432746246116964165t_char F) G)) top_to8437673547576850234ar_rat) top_to1235241553633177651r_char)))) (forall ((F (-> nat nat)) (A4 set_nat)) (let ((_let_1 (@ image_nat_nat F))) (= (@ _let_1 (@ (@ vimage_nat_nat F) A4)) (@ (@ inf_inf_set_nat A4) (@ _let_1 top_top_set_nat))))) (forall ((A4 set_int) (B5 set_int) (F (-> int int))) (=> (@ finite_finite_int A4) (=> (@ (@ ord_less_eq_set_int B5) (@ (@ image_int_int F) A4)) (@ (@ ord_less_eq_nat (@ finite_card_int B5)) (@ finite_card_int A4))))) (forall ((R (-> int int Bool)) (S2 (-> int code_integer Bool)) (A int) (C code_integer)) (=> (@ (@ (@ (@ relcom967497705283160040nteger R) S2) A) C) (not (forall ((B3 int)) (=> (@ (@ R A) B3) (not (@ (@ S2 B3) C))))))) _let_167 (forall ((F (-> nat int)) (C3 set_nat) (A4 set_nat) (B5 set_nat)) (let ((_let_1 (@ image_nat_int F))) (=> (@ (@ inj_on_nat_int F) C3) (=> (@ (@ ord_less_eq_set_nat A4) C3) (=> (@ (@ ord_less_eq_set_nat B5) C3) (= (@ _let_1 (@ (@ inf_inf_set_nat A4) B5)) (@ (@ inf_inf_set_int (@ _let_1 A4)) (@ _let_1 B5)))))))) (forall ((P2 (-> rat char product_unit))) (= (@ comple4687483117567863418t_unit (@ (@ image_4337914935673063477t_unit (lambda ((Y5 char)) (@ comple2584293577114468500t_unit (@ (@ image_2327579789247107822t_unit (lambda ((X4 rat)) (@ (@ P2 X4) Y5))) top_top_set_rat)))) top_top_set_char)) (@ comple2584293577114468500t_unit (@ (@ image_7615136836863079294t_unit (lambda ((X4 (-> char rat))) (@ comple4687483117567863418t_unit (@ (@ image_4337914935673063477t_unit (lambda ((Y5 char)) (@ (@ P2 (@ X4 Y5)) Y5))) top_top_set_char)))) top_top_set_char_rat)))) (forall ((F (-> nat nat)) (X2 nat)) (@ (@ member_nat (@ F X2)) (@ (@ image_nat_nat F) top_top_set_nat))) (forall ((U int) (A4 set_int) (A product_unit) (B5 (-> int set_Product_unit))) (=> (@ (@ member_int U) A4) (= (@ comple3349607820504768346t_unit (@ (@ image_8658272795163236474t_unit (lambda ((X4 int)) (@ (@ insert_Product_unit A) (@ B5 X4)))) A4)) (@ (@ insert_Product_unit A) (@ comple3349607820504768346t_unit (@ (@ image_8658272795163236474t_unit B5) A4)))))) (forall ((A int) (B int) (A4 set_int) (B5 (-> int set_int))) (=> (@ (@ member5262025264175285858nt_int (@ (@ product_Pair_int_int A) B)) (@ (@ produc1453890548195736866nt_int A4) B5)) (not (=> (@ (@ member_int A) A4) (not (@ (@ member_int B) (@ B5 A))))))) (forall ((A int) (A4 set_int) (B nat) (B5 (-> int set_nat))) (let ((_let_1 (@ member_nat B))) (=> (@ (@ member_int A) A4) (=> (@ _let_1 (@ B5 A)) (@ _let_1 (@ comple7399068483239264473et_nat (@ (@ image_int_set_nat B5) A4))))))) (forall ((A4 set_nat) (F (-> nat nat))) (= (@ (@ bNF_re5653821019739307937at_nat (lambda ((Y2 nat) (Z nat)) (= Y2 Z))) (@ (@ bNF_Grp_nat_nat A4) F)) (@ (@ bNF_Gr3847987472475283150at_nat (@ collect_nat_nat (lambda ((X4 (-> nat nat))) (@ (@ ord_less_eq_set_nat (@ (@ image_nat_nat X4) top_top_set_nat)) A4)))) (@ comp_nat_nat_nat F)))) (forall ((A4 set_nat) (B5 (-> nat set_o))) (= (@ (@ image_8629803608462650132_o_nat product_fst_nat_o) (@ (@ product_Sigma_nat_o A4) B5)) (@ collect_nat (lambda ((X4 nat)) (and (@ (@ member_nat X4) A4) (not (= (@ B5 X4) bot_bot_set_o))))))) (forall ((U int)) (=> (@ (@ ord_less_eq_int zero_zero_int) U) (= (@ (@ set_or4662586982721622107an_int zero_zero_int) U) (@ (@ image_nat_int semiri1314217659103216013at_int) (@ set_ord_lessThan_nat (@ nat2 U)))))) (forall ((A4 set_nat) (F (-> nat set_nat))) (let ((_let_1 (@ (@ image_nat_set_nat F) A4))) (=> (not (= A4 bot_bot_set_nat)) (@ (@ ord_less_eq_set_nat (@ comple7806235888213564991et_nat _let_1)) (@ comple7399068483239264473et_nat _let_1))))) (forall ((Xa2 product_prod_nat_nat) (X2 product_prod_nat_nat)) (= (@ (@ ord_less_eq_int (@ abs_Integ Xa2)) (@ abs_Integ X2)) (@ (@ (@ produc8739625826339149834_nat_o (lambda ((X4 nat) (Y5 nat) (__flatten_var_0 product_prod_nat_nat)) (@ (@ produc6081775807080527818_nat_o (lambda ((U3 nat) (V3 nat)) (@ (@ ord_less_eq_nat (@ (@ plus_plus_nat X4) V3)) (@ (@ plus_plus_nat U3) Y5)))) __flatten_var_0))) Xa2) X2))) (forall ((A4 set_nat) (B5 set_nat) (F (-> nat nat))) (let ((_let_1 (@ image_nat_nat F))) (=> (@ (@ ord_less_eq_set_nat A4) B5) (@ (@ ord_less_eq_set_nat (@ _let_1 A4)) (@ _let_1 B5))))) (forall ((H1 (-> nat num)) (H22 (-> int nat)) (F (-> int nat)) (G (-> int int))) (= (@ (@ comp_P8376639181999047357at_int (@ (@ produc5918048235202344416nt_nat H1) H22)) (@ (@ bNF_co1174813233427581459at_int F) G)) (@ (@ bNF_co8531006144098876929um_nat (@ (@ comp_nat_num_int H1) F)) (@ (@ comp_int_nat_int H22) G)))) _let_166 (forall ((Rep (-> Bool Bool)) (Abs (-> Bool Bool)) (M (-> nat nat)) (M1 (-> Bool nat)) (M2 (-> nat Bool)) (F (-> nat nat)) (G (-> nat nat))) (=> (@ (@ (@ type_definition_o_o Rep) Abs) top_top_set_o) (=> (= M (@ (@ comp_o_nat_nat M1) M2)) (= (@ (@ comp_nat_nat_nat (@ (@ comp_nat_nat_nat F) M)) G) (@ (@ comp_o_nat_nat (@ (@ comp_o_nat_o (@ (@ comp_nat_nat_o F) M1)) Rep)) (@ (@ comp_nat_o_nat (@ (@ comp_o_o_nat Abs) M2)) G)))))) (forall ((A product_unit) (A4 set_Product_unit) (B Bool) (B5 set_o)) (let ((_let_1 (@ produc4996980317674386579unit_o (@ (@ insert_Product_unit A) A4)))) (= (@ _let_1 (lambda ((Uu product_unit)) (@ (@ insert_o B) B5))) (@ (@ insert3586912282507785154unit_o (@ (@ produc8487917018914037602unit_o A) B)) (@ (@ sup_su2851927382625014182unit_o (@ (@ produc4996980317674386579unit_o A4) (lambda ((Uu product_unit)) (@ (@ insert_o B) B5)))) (@ _let_1 (lambda ((Uu product_unit)) B5))))))) (forall ((A4 set_Pr1261947904930325089at_nat) (B5 (-> product_prod_nat_nat set_Pr1261947904930325089at_nat))) (=> (@ 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top_top_set_char) (= (@ (@ member_nat B) (@ (@ image_char_nat F) top_top_set_char)) (exists ((X4 char)) (and (forall ((Y5 char)) (=> (= B (@ F Y5)) (= Y5 X4))) (= B (@ F X4))))))) (forall ((A product_unit) (B product_unit) (R set_Pr5094982260447487303t_unit)) (= (@ field_Product_unit (@ (@ insert4616891024742550839t_unit (@ (@ produc5692694829384537815t_unit A) B)) R)) (@ (@ sup_su793286257634532545t_unit (@ (@ insert_Product_unit A) (@ (@ insert_Product_unit B) bot_bo3957492148770167129t_unit))) (@ field_Product_unit R)))) (forall ((F (-> int int Bool)) (A int) (B int)) (=> (@ (@ produc4947309494688390418_int_o F) (@ (@ product_Pair_int_int A) B)) (@ (@ F A) B))) (forall ((F (-> nat rat)) (A4 set_nat)) (=> (@ (@ inj_on_nat_rat F) A4) (= (@ finite_card_rat (@ (@ image_nat_rat F) A4)) (@ finite_card_nat A4)))) _let_164 (forall ((A nat) (B num) (R3 set_Pr6200539531224447659at_num) (F (-> nat nat)) (G (-> num num))) (=> (@ (@ member9148766508732265716at_num (@ (@ product_Pair_nat_num A) B)) R3) (@ (@ member9148766508732265716at_num (@ (@ product_Pair_nat_num (@ F A)) (@ G B))) (@ (@ image_4925883905578568901at_num (@ (@ produc1665548884793878990um_num F) G)) R3)))) (forall ((F (-> nat rat)) (A4 set_rat)) (=> (@ (@ inj_on_nat_rat F) top_top_set_nat) (=> (@ (@ ord_less_eq_set_rat A4) (@ (@ image_nat_rat F) top_top_set_nat)) (= (@ finite_card_nat (@ (@ vimage_nat_rat F) A4)) (@ finite_card_rat A4))))) (forall ((P2 (-> nat Bool)) (F (-> nat nat)) (G (-> nat nat)) (S5 set_nat)) (let ((_let_1 (@ inf_inf_set_nat S5))) (= (@ (@ image_nat_nat (lambda ((X4 nat)) (@ (@ (@ if_nat (@ P2 X4)) (@ F X4)) (@ G X4)))) S5) (@ (@ sup_sup_set_nat (@ (@ image_nat_nat F) (@ _let_1 (@ collect_nat P2)))) (@ (@ image_nat_nat G) (@ _let_1 (@ collect_nat (lambda ((X4 nat)) (not (@ P2 X4)))))))))) (forall ((Rep (-> num char)) (Abs (-> char num))) (=> (@ (@ (@ type_d4396077731765706521m_char Rep) Abs) top_top_set_char) (= (@ (@ comp_char_num_num Abs) Rep) id_num))) (forall ((R 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comple7806235888213564991et_nat (@ (@ image_7916887816326733075et_nat id_set_nat) A4)) (@ comple7806235888213564991et_nat A4))) (forall ((F (-> char nat)) (A4 set_nat)) (let ((_let_1 (@ image_char_nat F))) (=> (= (@ _let_1 top_top_set_char) top_top_set_nat) (= (@ _let_1 (@ (@ vimage_char_nat F) A4)) A4)))) (forall ((A set_Pr4329608150637261639at_nat) (P produc1319942482725812455at_nat)) (= (= A (@ produc4486455499028916547at_nat P)) (exists ((B4 set_Pr4329608150637261639at_nat)) (= P (@ (@ produc9060074326276436823at_nat A) B4))))) (forall ((A4 set_int) (F (-> int rat)) (M rat)) (=> (forall ((X int)) (=> (@ (@ member_int X) A4) (@ (@ ord_less_eq_rat (@ F X)) M))) (@ condit1579696412822616692ve_rat (@ (@ image_int_rat F) A4)))) (forall ((X2 int)) (@ (@ refl_on_int (@ (@ insert_int X2) bot_bot_set_int)) (@ (@ insert5033312907999012233nt_int (@ (@ product_Pair_int_int X2) X2)) bot_bo1796632182523588997nt_int))) (@ (@ (@ (@ bNF_re6718328864250387230um_num code_pcr_integer) (lambda ((Y2 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image_nat_nat F) A4)))) (forall ((R3 (-> product_prod_nat_nat int Bool)) (F (-> product_prod_nat_nat product_prod_nat_nat Bool)) (G (-> int int Bool))) (@ (@ (@ (@ bNF_re717283939379294677_int_o R3) (@ (@ (@ bNF_Gr364077372107685167_int_o F) G) R3)) F) G)) (forall ((I set_Pr4329608150637261639at_nat) (J4 set_Pr4329608150637261639at_nat) (R3 set_Pr7459493094073627847at_nat)) (=> (@ (@ member1466754251312161552at_nat (@ (@ produc9060074326276436823at_nat I) J4)) R3) (@ (@ member6273874620674182256at_nat J4) (@ field_1428494348145443988at_nat R3)))) (forall ((G (-> int num)) (H (-> int int)) (R12 (-> nat num)) (R23 (-> int nat)) (F (-> num nat)) (L (-> nat nat))) (=> (= (@ (@ comp_int_num_int G) H) (@ (@ comp_nat_num_int R12) R23)) (=> (= (@ (@ comp_num_nat_nat F) R12) L) (= (@ (@ comp_int_nat_int (@ (@ comp_num_nat_int F) G)) H) (@ (@ comp_nat_nat_int L) R23))))) (forall ((F (-> nat product_unit)) (G (-> nat rat)) (A4 set_nat)) (= (@ (@ image_469905907365485675it_rat (lambda ((X4 nat)) (@ (@ produc4168158269727034510it_rat (@ F X4)) (@ G X4)))) A4) (@ (@ produc6240246942209516957it_rat (@ (@ image_8730104196221521654t_unit F) A4)) (lambda ((X4 product_unit)) (@ (@ image_nat_rat G) (@ (@ inf_inf_set_nat (@ (@ vimage4884490618288580032t_unit F) (@ (@ insert_Product_unit X4) bot_bo3957492148770167129t_unit))) A4)))))) (forall ((F (-> rat nat)) (B5 set_nat) (I rat)) (=> (@ (@ ord_less_eq_set_nat (@ (@ image_rat_nat F) top_top_set_rat)) B5) (@ (@ member_nat (@ F I)) B5))) (forall ((Rep (-> product_unit Bool)) (Abs (-> Bool product_unit)) (X2 produc3843707927480180839at_nat) (S5 (-> Bool set_Pr4329608150637261639at_nat)) (Y3 Bool)) (let ((_let_1 (@ member8757157785044589968at_nat X2))) (=> (@ (@ (@ type_d6188575255521822967unit_o Rep) Abs) top_top_set_o) (=> (@ _let_1 (@ (@ (@ comp_o4913564575355137019t_unit S5) Rep) (@ Abs Y3))) (@ _let_1 (@ S5 Y3)))))) (forall ((M (-> produc859450856879609959at_nat set_Pr4329608150637261639at_nat)) (A4 set_Pr8693737435421807431at_nat) (B5 set_Pr8693737435421807431at_nat)) (let ((_let_1 (@ image_3876558564303283877at_nat M))) (= (@ comple4364388969068068532at_nat (@ _let_1 (@ (@ sup_su718114333110466843at_nat A4) B5))) (@ (@ sup_su5525570899277871387at_nat (@ comple4364388969068068532at_nat (@ _let_1 A4))) (@ comple4364388969068068532at_nat (@ _let_1 B5)))))) (forall ((X2 set_Pr1261947904930325089at_nat)) (@ (@ total_7212417256332265445at_nat (@ (@ insert9200635055090092081at_nat X2) bot_bo3083307316010499117at_nat)) (@ (@ insert9069300056098147895at_nat (@ (@ produc2922128104949294807at_nat X2) X2)) bot_bo228742789529271731at_nat))) (forall ((M set_nat) (N set_nat) (F (-> nat rat)) (G (-> nat rat))) (=> (= M N) (=> (forall ((X nat)) (=> (@ (@ member_nat X) N) (= (@ F X) (@ G X)))) (= (@ (@ image_nat_rat F) M) (@ (@ image_nat_rat G) N))))) (forall ((Inf (-> set_nat nat)) (A4 set_nat)) (= (@ Inf (@ (@ image_nat_nat (lambda ((X4 nat)) X4)) A4)) (@ Inf A4))) (forall ((A Bool) (B int) (A4 set_o) (B5 (-> Bool set_int))) (= (@ (@ member7847949116333733898_o_int (@ (@ product_Pair_o_int A) B)) (@ (@ product_Sigma_o_int A4) B5)) (and (@ (@ member_o A) A4) (@ (@ member_int B) (@ B5 A))))) (forall ((F (-> nat product_unit)) (A4 (-> int nat)) (I3 set_int)) (let ((_let_1 (@ (@ image_int_nat A4) I3))) (=> (@ order_5727276828720722763t_unit F) (=> (@ condit1738341127787009408ow_nat _let_1) (=> (not (= I3 bot_bot_set_int)) (@ (@ ord_le3221252021190050221t_unit (@ F (@ complete_Inf_Inf_nat _let_1))) (@ comple2584293577114468500t_unit (@ (@ image_5846526143423701914t_unit (lambda ((X4 int)) (@ F (@ A4 X4)))) I3)))))))) (forall ((X5 set_Pr958786334691620121nt_int) (Y4 set_Pr958786334691620121nt_int)) (let ((_let_1 (@ ord_le2843351958646193337nt_int X5))) (=> (@ _let_1 (@ collec213857154873943460nt_int (@ produc4947309494688390418_int_o (@ fun_in_rel_int_int Y4)))) (@ _let_1 Y4)))) (forall ((B rat) (F (-> nat rat))) (=> (@ (@ member_rat B) (@ (@ image_nat_rat F) top_top_set_nat)) (not (forall ((X nat)) (not (= B (@ F X))))))) (forall ((F (-> nat int)) (C3 set_nat) (A4 set_nat) (B5 set_nat)) (let ((_let_1 (@ image_nat_int F))) (let ((_let_2 (@ (@ minus_minus_set_nat A4) B5))) (=> (@ (@ inj_on_nat_int F) C3) (=> (@ (@ ord_less_eq_set_nat _let_2) C3) (=> (@ (@ ord_less_eq_set_nat B5) C3) (= (@ _let_1 _let_2) (@ (@ minus_minus_set_int (@ _let_1 A4)) (@ _let_1 B5))))))))) (forall ((A4 set_Product_unit) (B5 (-> product_unit set_o)) (F (-> Bool int))) (=> (not (= A4 bot_bo3957492148770167129t_unit)) (=> (forall ((X product_unit)) (=> (@ (@ member_Product_unit X) A4) (not (= (@ B5 X) bot_bot_set_o)))) (=> (@ condit1735850657277959132ow_int (@ comple3221217463730067765et_int (@ (@ image_3995998972318789802et_int (lambda ((X4 product_unit)) (@ (@ image_o_int F) (@ B5 X4)))) A4))) (= (@ complete_Inf_Inf_int (@ (@ image_o_int F) (@ comple90263536869209701_set_o (@ (@ image_6930536745178679216_set_o B5) A4)))) (@ complete_Inf_Inf_int (@ (@ image_873079544045703924it_int (lambda ((X4 product_unit)) (@ 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produc1126150082675451753t_unit _let_1)) (=> (= R (@ produc473321116828791851t_unit _let_1)) (@ (@ (@ (@ heap_effect_ref_a (@ heap_heap_ref_a F)) H) H2) R))))) (forall ((H (-> rat char)) (F4 set_char)) (=> (@ finite_finite_rat (@ (@ vimage_rat_char H) F4)) (=> (= (@ (@ image_rat_char H) top_top_set_rat) top_top_set_char) (@ finite_finite_char F4)))) (forall ((F (-> Bool product_unit)) (A Bool) (A4 set_o)) (let ((_let_1 (@ image_o_Product_unit F))) (= (@ comple4687483117567863418t_unit (@ _let_1 (@ (@ insert_o A) A4))) (@ (@ sup_sup_Product_unit (@ F A)) (@ comple4687483117567863418t_unit (@ _let_1 A4)))))) (forall ((T2 (-> nat Bool))) (= (@ (@ comp_o_o_nat (lambda ((X4 Bool)) X4)) T2) T2)) (forall ((A4 set_Pr1261947904930325089at_nat) (B5 (-> product_prod_nat_nat set_Pr1261947904930325089at_nat))) (=> (@ finite6177210948735845034at_nat A4) (= (@ finite6177210948735845034at_nat (@ comple5685304695842803022at_nat (@ (@ image_5423882813909314213at_nat B5) A4))) (forall ((X4 product_prod_nat_nat)) (=> (@ (@ member8440522571783428010at_nat X4) A4) (@ finite6177210948735845034at_nat (@ B5 X4))))))) _let_163 (forall ((A int) (B int) (A4 set_int)) (=> (= A B) (=> (@ (@ member_int A) A4) (@ (@ member5262025264175285858nt_int (@ (@ product_Pair_int_int A) B)) (@ id_on_int A4))))) _let_162 (forall ((F (-> int int)) (A4 set_int) (B5 set_int)) (let ((_let_1 (@ image_int_int F))) (=> (= (@ _let_1 A4) B5) (= (@ (@ image_524474410958335435et_int _let_1) (@ pow_int A4)) (@ pow_int B5))))) (forall ((P2 (-> set_Pr1261947904930325089at_nat set_Pr1261947904930325089at_nat Bool)) (Y3 set_Pr1261947904930325089at_nat) (X2 set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ (@ produc2922128104949294807at_nat X2) Y3))) (=> (@ (@ P2 Y3) X2) (@ (@ P2 (@ produc2937545259423399429at_nat _let_1)) (@ produc6011863565407846595at_nat _let_1))))) (forall ((A4 set_nat) (B5 set_nat) (F (-> nat product_unit)) (G (-> nat product_unit))) (=> (forall ((I4 nat)) (=> (@ (@ member_nat I4) A4) (exists ((X6 nat)) (and (@ (@ ord_le3221252021190050221t_unit (@ F I4)) (@ G X6)) (@ (@ member_nat X6) B5))))) (=> (forall ((J2 nat)) (=> (@ (@ member_nat J2) B5) (exists ((X6 nat)) (and (@ (@ member_nat X6) A4) (@ (@ ord_le3221252021190050221t_unit (@ G J2)) (@ F X6)))))) (= (@ comple4687483117567863418t_unit (@ (@ image_8730104196221521654t_unit F) A4)) (@ comple4687483117567863418t_unit (@ (@ image_8730104196221521654t_unit G) B5)))))) (forall ((F (-> nat nat)) (C3 set_nat) (A4 set_nat) (B5 set_nat)) (let ((_let_1 (@ image_nat_nat F))) (=> (@ (@ inj_on_nat_nat F) C3) (=> (@ (@ ord_less_eq_set_nat A4) C3) (=> (@ (@ ord_less_eq_set_nat B5) C3) (= (= (@ _let_1 A4) (@ _let_1 B5)) (= A4 B5))))))) (forall ((F (-> nat Bool)) (G (-> Bool Bool)) (X2 set_o)) (= (@ (@ vimage_nat_o F) (@ (@ vimage_o_o G) X2)) (@ (@ vimage_nat_o (@ (@ comp_o_o_nat G) F)) X2))) (forall ((Rep (-> Bool rat)) (Abs (-> rat Bool)) (F (-> nat Bool)) (P2 (-> Bool Bool)) (H (-> Bool rat))) (=> (@ (@ (@ type_d6486251586359353412_o_rat Rep) Abs) top_top_set_rat) (= (@ (@ (@ bNF_vi3868162310295888627_rat_o F) Rep) (@ (@ bNF_Grp_o_rat (@ collect_o P2)) H)) (@ (@ bNF_Grp_nat_o (@ collect_nat (lambda ((X4 nat)) (@ P2 (@ F X4))))) (@ (@ comp_o_o_nat (@ (@ comp_rat_o_o Abs) H)) F))))) (forall ((A4 set_Pr1261947904930325089at_nat)) (@ (@ inj_on8969904277767023793at_nat (@ produc2626176000494625587at_nat (lambda ((I2 nat) (J nat)) (@ (@ product_Pair_nat_nat J) I2)))) A4)) (forall ((A4 set_Product_unit) (C3 set_nat) (B5 set_Product_unit) (D set_nat)) (= (@ (@ ord_le8121013740822022818it_nat (@ (@ produc6875377002296012693it_nat A4) (lambda ((Uu product_unit)) C3))) (@ (@ produc6875377002296012693it_nat B5) (lambda ((Uu product_unit)) D))) (or (= C3 bot_bot_set_nat) (and (@ (@ ord_less_eq_set_nat C3) D) (@ (@ ord_le3507040750410214029t_unit A4) B5)) (= A4 bot_bo3957492148770167129t_unit)))) (forall ((I3 set_nat) (F (-> nat set_Pr1261947904930325089at_nat)) (X2 set_Pr1261947904930325089at_nat)) (=> (not (= I3 bot_bot_set_nat)) (= (@ comple1930127330929219688at_nat (@ (@ image_7178329752028323786at_nat (lambda ((I2 nat)) (@ (@ inf_in2572325071724192079at_nat (@ F I2)) X2))) I3)) (@ (@ inf_in2572325071724192079at_nat (@ comple1930127330929219688at_nat (@ (@ image_7178329752028323786at_nat F) I3))) X2)))) (forall ((A4 set_Product_unit) (G (-> int nat)) (B5 set_int) (F (-> product_unit nat))) (let ((_let_1 (@ (@ image_int_nat G) B5))) (=> (not (= A4 bot_bo3957492148770167129t_unit)) (=> (@ condit2214826472909112428ve_nat _let_1) (=> (forall ((N2 product_unit)) (=> (@ (@ member_Product_unit N2) A4) (exists ((X6 int)) (and (@ (@ ord_less_eq_nat (@ F N2)) (@ G X6)) (@ (@ member_int X6) B5))))) (@ (@ ord_less_eq_nat (@ complete_Sup_Sup_nat (@ (@ image_875570014554754200it_nat F) A4))) (@ complete_Sup_Sup_nat _let_1))))))) (forall ((Rep (-> Bool Bool)) (Abs (-> Bool Bool)) (M (-> nat Bool)) (M1 (-> Bool Bool)) (M2 (-> nat Bool)) (F (-> Bool num)) (G (-> int nat))) (=> (@ (@ (@ type_definition_o_o Rep) Abs) top_top_set_o) (=> (= M (@ (@ comp_o_o_nat M1) M2)) (= (@ (@ comp_nat_num_int (@ (@ comp_o_num_nat F) M)) G) (@ (@ comp_o_num_int (@ (@ comp_o_num_o (@ (@ comp_o_num_o F) M1)) Rep)) (@ (@ comp_nat_o_int (@ (@ comp_o_o_nat Abs) M2)) G)))))) (forall ((X2 product_prod_int_o) (A4 set_int) (B5 set_o)) (= (@ (@ member4489920277610959864_int_o X2) (@ (@ product_Sigma_int_o A4) (lambda ((Uu int)) B5))) (and (@ (@ member_int (@ product_fst_int_o X2)) A4) (@ (@ member_o (@ product_snd_int_o X2)) B5)))) (forall ((F (-> nat nat)) (G (-> nat nat))) (=> (@ (@ inj_on_nat_nat F) top_top_set_nat) (=> (@ (@ inj_on_nat_nat G) top_top_set_nat) (@ (@ inj_on_nat_nat (@ (@ comp_nat_nat_nat F) G)) top_top_set_nat)))) (forall ((X2 int) (A4 set_int) (F (-> int set_o))) (let ((_let_1 (@ (@ vimage4304346610107161470_int_o (@ product_Pair_int_o X2)) (@ (@ product_Sigma_int_o A4) F)))) (let ((_let_2 (@ (@ member_int X2) A4))) (and (=> _let_2 (= _let_1 (@ F X2))) (=> (not _let_2) (= _let_1 bot_bot_set_o)))))) (forall ((F (-> int nat)) (C3 set_int) (A4 set_int) (B5 set_int)) (let ((_let_1 (@ image_int_nat F))) (=> (@ (@ inj_on_int_nat F) C3) (=> (@ (@ ord_less_eq_set_int A4) C3) (=> (@ (@ ord_less_eq_set_int B5) C3) (= (= (@ _let_1 A4) (@ _let_1 B5)) (= A4 B5))))))) (forall ((A4 set_Product_unit) (B5 set_Pr1261947904930325089at_nat) (C3 set_Product_unit) (D set_Pr1261947904930325089at_nat)) (= (= (@ (@ produc3904733337175673596at_nat A4) (lambda ((Uu product_unit)) B5)) (@ (@ produc3904733337175673596at_nat C3) (lambda ((Uu product_unit)) D))) (or (and (= B5 D) (= A4 C3)) (and (or (= C3 bot_bo3957492148770167129t_unit) (= D bot_bo2099793752762293965at_nat)) (or (= A4 bot_bo3957492148770167129t_unit) (= B5 bot_bo2099793752762293965at_nat)))))) (forall ((R set_Pr1261947904930325089at_nat) (A nat) (B nat)) (let ((_let_1 (@ field_nat R))) (=> (@ (@ order_4473980167227706203on_nat _let_1) R) (=> (@ (@ member_nat A) _let_1) (=> (@ (@ member_nat B) _let_1) (= (@ (@ member8440522571783428010at_nat (@ (@ product_Pair_nat_nat A) B)) R) (not (@ (@ member8440522571783428010at_nat (@ (@ product_Pair_nat_nat B) A)) (@ (@ minus_1356011639430497352at_nat R) id_nat2))))))))) (forall ((C3 set_nat) (A4 (-> nat set_char)) (B5 set_char)) (let ((_let_1 (@ (@ minus_minus_set_char (@ comple7965528767983648192t_char (@ (@ image_nat_set_char A4) C3))) B5))) (let ((_let_2 (= C3 bot_bot_set_nat))) (and (=> (not _let_2) (= _let_1 (@ comple7965528767983648192t_char (@ (@ image_nat_set_char (lambda ((X4 nat)) (@ (@ minus_minus_set_char (@ A4 X4)) B5))) C3)))) (=> _let_2 (= _let_1 (@ (@ minus_minus_set_char top_top_set_char) B5))))))) (= vimage_nat_o (lambda ((F2 (-> nat Bool)) (B6 set_o)) (@ comple7399068483239264473et_nat (@ (@ image_o_set_nat (lambda ((Y5 Bool)) (@ (@ vimage_nat_o F2) (@ (@ insert_o Y5) bot_bot_set_o)))) B6)))) (forall ((A4 set_Product_unit) (F (-> product_unit int)) (B5 set_Product_unit)) (let ((_let_1 (@ image_873079544045703924it_int F))) (let ((_let_2 (@ _let_1 B5))) (let ((_let_3 (@ _let_1 A4))) (=> (not (= A4 bot_bo3957492148770167129t_unit)) (=> (@ condit1735850657277959132ow_int _let_3) (=> (not (= B5 bot_bo3957492148770167129t_unit)) (=> (@ condit1735850657277959132ow_int _let_2) (= (@ complete_Inf_Inf_int (@ _let_1 (@ (@ sup_su793286257634532545t_unit A4) B5))) (@ (@ inf_inf_int (@ complete_Inf_Inf_int _let_3)) (@ complete_Inf_Inf_int _let_2))))))))))) (forall ((F (-> product_prod_nat_nat nat)) (A4 set_Pr1261947904930325089at_nat)) (=> (@ finite_finite_nat (@ (@ image_2486076414777270412at_nat F) A4)) (=> (not (@ finite6177210948735845034at_nat A4)) (exists ((X nat)) (and (@ (@ member_nat X) (@ (@ image_2486076414777270412at_nat F) A4)) (not (@ finite6177210948735845034at_nat (@ (@ vimage4653281326611754070at_nat F) (@ (@ insert_nat X) bot_bot_set_nat))))))))) (forall ((F (-> Bool nat)) (G (-> Bool Bool)) (X2 Bool)) (= (@ (@ (@ comp_P1471321874221585045at_o_o (@ (@ produc9141321880750005618at_o_o F) id_o)) (@ (@ bNF_convol_o_o_o id_o) G)) X2) (@ (@ (@ bNF_convol_o_nat_o (@ (@ comp_nat_nat_o id_nat) F)) G) X2))) (forall ((A4 set_o) (B5 set_o) (C3 (-> Bool int)) (D (-> Bool int))) (=> (= A4 B5) (=> (forall ((X Bool)) (=> (@ (@ member_o X) B5) (= (@ C3 X) (@ D X)))) (= (@ complete_Sup_Sup_int (@ (@ image_o_int C3) A4)) (@ complete_Sup_Sup_int (@ (@ image_o_int D) B5)))))) (forall ((F (-> nat int)) (A4 set_nat) (P2 (-> set_int Bool))) (= (forall ((B6 set_int)) (=> (and (@ (@ ord_less_eq_set_int B6) (@ (@ image_nat_int F) A4)) (@ finite_finite_int B6)) (@ P2 B6))) (forall ((B6 set_nat)) (=> (and (@ finite_finite_nat B6) (@ (@ ord_less_eq_set_nat B6) A4)) (@ P2 (@ (@ image_nat_int F) B6)))))) (forall ((F (-> char rat))) (= (= (@ (@ image_char_rat F) top_top_set_char) top_top_set_rat) (forall ((Y5 rat)) (exists ((X4 char)) (= Y5 (@ F X4)))))) (forall ((F (-> char rat)) (B5 set_rat) (A4 set_char)) (let ((_let_1 (@ image_char_rat F))) (=> (= (@ _let_1 top_top_set_char) top_top_set_rat) (=> (@ (@ ord_less_eq_set_char (@ (@ vimage_char_rat F) B5)) A4) (@ (@ ord_less_eq_set_rat B5) (@ _let_1 A4)))))) (forall ((P2 (-> nat char product_unit))) (= (@ comple4687483117567863418t_unit (@ (@ image_4337914935673063477t_unit (lambda ((Y5 char)) (@ comple2584293577114468500t_unit (@ (@ image_8730104196221521654t_unit (lambda ((X4 nat)) (@ (@ P2 X4) Y5))) top_top_set_nat)))) top_top_set_char)) (@ comple2584293577114468500t_unit (@ (@ image_108929247839792006t_unit (lambda ((X4 (-> char nat))) (@ comple4687483117567863418t_unit (@ (@ image_4337914935673063477t_unit (lambda ((Y5 char)) (@ (@ P2 (@ X4 Y5)) Y5))) top_top_set_char)))) top_top_set_char_nat)))) _let_161 (forall ((Ac produc3843707927480180839at_nat) (P2 (-> set_Pr1261947904930325089at_nat set_Pr1261947904930325089at_nat Bool)) (Q2 (-> set_Pr1261947904930325089at_nat set_Pr1261947904930325089at_nat Bool))) (=> (@ (@ member8757157785044589968at_nat Ac) (@ collec6321179662152712658at_nat (@ produc410239310623530412_nat_o (@ (@ relcom8363394528208558896at_nat P2) Q2)))) (@ (@ member8757157785044589968at_nat (@ (@ (@ bNF_sn1857951156667551021at_nat P2) Q2) Ac)) (@ collec6321179662152712658at_nat (@ produc410239310623530412_nat_o Q2))))) (forall ((Y3 nat) (X2 num) (A4 set_Pr3280342998896498603um_nat)) (= (@ (@ member9148766508732265716at_num (@ (@ product_Pair_nat_num Y3) X2)) (@ (@ image_7762062833379733445at_num product_swap_num_nat) A4)) (@ (@ member6570852975090897396um_nat (@ (@ product_Pair_num_nat X2) Y3)) A4))) (forall ((C3 set_Product_unit) (A4 (-> product_unit set_nat)) (B5 set_nat)) (let ((_let_1 (= C3 bot_bo3957492148770167129t_unit))) (and (=> (not _let_1) (= (@ comple7806235888213564991et_nat (@ (@ image_8173849991827986510et_nat (lambda ((X4 product_unit)) (@ (@ inf_inf_set_nat (@ A4 X4)) B5))) C3)) (@ (@ inf_inf_set_nat (@ comple7806235888213564991et_nat (@ (@ image_8173849991827986510et_nat A4) C3))) B5))) (=> _let_1 (= (@ comple7806235888213564991et_nat (@ (@ image_8173849991827986510et_nat (lambda ((X4 product_unit)) (@ (@ inf_inf_set_nat (@ A4 X4)) B5))) C3)) top_top_set_nat))))) (forall ((M (-> produc3843707927480180839at_nat set_Pr1261947904930325089at_nat)) (A4 set_Pr4329608150637261639at_nat) (B5 set_Pr4329608150637261639at_nat)) (let ((_let_1 (@ image_7979982168039674559at_nat M))) (= (@ comple1930127330929219688at_nat (@ _let_1 (@ (@ sup_su5525570899277871387at_nat A4) B5))) (@ (@ inf_in2572325071724192079at_nat (@ comple1930127330929219688at_nat (@ _let_1 A4))) (@ comple1930127330929219688at_nat (@ _let_1 B5)))))) (forall ((F (-> nat rat)) (A4 set_nat) (B5 set_rat)) (=> (@ (@ inj_on_nat_rat F) A4) (=> (@ (@ ord_less_eq_set_rat (@ (@ image_nat_rat F) A4)) B5) (=> (@ finite_finite_rat B5) (@ (@ ord_less_eq_nat (@ finite_card_nat A4)) (@ finite_card_rat B5)))))) (forall ((F (-> heap_e7401611519738050253t_unit set_Pr1261947904930325089at_nat)) (G (-> ref_a set_Pr1261947904930325089at_nat)) (X2 produc7812382424243267045t_unit)) (= (@ (@ produc8705118745468743695at_nat F) (@ (@ produc5323809043756447493t_unit G) X2)) (@ (@ produc2922128104949294807at_nat (@ G (@ produc473321116828791851t_unit X2))) (@ F (@ produc1126150082675451753t_unit X2))))) (forall ((C3 set_Product_unit) (A4 set_rat) (B5 (-> product_unit set_rat))) (let ((_let_1 (= C3 bot_bo3957492148770167129t_unit))) (and (=> (not _let_1) (= (@ comple4298007329820168263et_rat (@ (@ image_4665621433434589782et_rat (lambda ((X4 product_unit)) (@ (@ minus_minus_set_rat A4) (@ B5 X4)))) C3)) (@ (@ minus_minus_set_rat A4) (@ comple3890839924845867745et_rat (@ (@ image_4665621433434589782et_rat B5) C3))))) (=> _let_1 (= (@ comple4298007329820168263et_rat (@ (@ image_4665621433434589782et_rat (lambda ((X4 product_unit)) (@ (@ minus_minus_set_rat A4) (@ B5 X4)))) C3)) top_top_set_rat))))) (forall ((F (-> Bool Bool)) (G (-> Bool Bool)) (H (-> nat Bool))) (= (@ (@ comp_o_o_nat (@ (@ comp_o_o_o F) G)) H) (@ (@ comp_o_o_nat F) (@ (@ comp_o_o_nat G) H)))) (forall ((P product_prod_int_int)) (exists ((X int) (Y int)) (= P (@ (@ product_Pair_int_int X) Y)))) (forall ((F (-> char char)) (Y3 char)) (=> (= (@ (@ image_char_char F) top_top_set_char) top_top_set_char) (not (forall ((X char)) (not (= Y3 (@ F X))))))) (forall ((B5 set_int) (A4 set_int) (P2 (-> int Bool))) (let ((_let_1 (@ ord_less_eq_set_int B5))) (=> (@ _let_1 A4) (= (@ _let_1 (@ collect_int (lambda ((X4 int)) (and (@ (@ member_int X4) A4) (@ P2 X4))))) (forall ((X4 int)) (=> (@ (@ member_int X4) B5) (@ P2 X4))))))) _let_160 (forall ((B5 set_o) (F (-> int nat)) (A4 set_int) (G (-> Bool nat))) (let ((_let_1 (@ (@ image_int_nat F) A4))) (=> (not (= B5 bot_bot_set_o)) (=> (@ condit1738341127787009408ow_nat _let_1) (=> (forall ((M4 Bool)) (=> (@ (@ member_o M4) B5) (exists ((X6 int)) (and (@ (@ member_int X6) A4) (@ (@ ord_less_eq_nat (@ F X6)) (@ G M4)))))) (@ (@ ord_less_eq_nat (@ complete_Inf_Inf_nat _let_1)) (@ complete_Inf_Inf_nat (@ (@ image_o_nat G) B5)))))))) (forall ((Q produc3843707927480180839at_nat) (F (-> set_Pr1261947904930325089at_nat set_Pr1261947904930325089at_nat)) (P produc3843707927480180839at_nat)) (=> (= Q (@ (@ produc5380969780118646373at_nat F) P)) (not (forall ((X set_Pr1261947904930325089at_nat) (Y set_Pr1261947904930325089at_nat)) (=> (= P (@ (@ produc2922128104949294807at_nat X) Y)) (not (= Q (@ (@ produc2922128104949294807at_nat (@ F X)) Y)))))))) (forall ((X2 set_Pr8693737435421807431at_nat) (Y3 set_Pr8693737435421807431at_nat)) (= (@ (@ (@ if_set1508868558775481357at_nat true) X2) Y3) X2)) (forall ((X2 (-> int nat)) (F (-> nat num)) (G (-> nat num))) (=> (forall ((Z3 nat)) (=> (@ (@ member_nat Z3) (@ (@ image_int_nat X2) top_top_set_int)) (= (@ F Z3) (@ G Z3)))) (= (@ (@ comp_nat_num_int F) X2) (@ (@ comp_nat_num_int G) X2)))) (forall ((A4 set_nat) (F (-> nat nat)) (A nat)) (let ((_let_1 (@ image_nat_nat F))) (let ((_let_2 (@ _let_1 A4))) (=> (not (= A4 bot_bot_set_nat)) (=> (@ condit1738341127787009408ow_nat _let_2) (= (@ complete_Inf_Inf_nat (@ _let_1 (@ (@ insert_nat A) A4))) (@ (@ inf_inf_nat (@ F A)) (@ complete_Inf_Inf_nat _let_2)))))))) (forall ((F (-> char nat)) (Y3 nat)) (=> (= (@ (@ image_char_nat F) top_top_set_char) top_top_set_nat) (exists ((X char)) (= Y3 (@ F X))))) (forall ((Rep (-> nat char)) (Abs (-> char nat)) (S5 (-> char set_nat)) (M (-> nat char)) (F (-> nat nat)) (S6 (-> nat set_nat)) (G (-> nat nat))) (let ((_let_1 (@ comp_s3433241188411525313at_nat (@ image_nat_nat F)))) (let ((_let_2 (@ comp_c915470459090449932at_nat S5))) (=> (@ (@ (@ type_d5945782884131516111t_char Rep) Abs) top_top_set_char) (=> (= (@ _let_2 M) (@ _let_1 S6)) (= (@ (@ comp_nat_set_nat_nat (@ _let_2 Rep)) (@ (@ comp_nat_nat_nat (@ (@ comp_char_nat_nat Abs) M)) G)) (@ _let_1 (@ (@ comp_nat_set_nat_nat S6) G)))))))) (forall ((F (-> product_prod_nat_nat nat)) (A4 set_Pr1261947904930325089at_nat) (P2 (-> set_nat Bool))) (= (exists ((B6 set_nat)) (and (@ P2 B6) (@ (@ ord_less_eq_set_nat B6) (@ (@ image_2486076414777270412at_nat F) A4)) (@ finite_finite_nat B6))) (exists ((B6 set_Pr1261947904930325089at_nat)) (and (@ P2 (@ (@ image_2486076414777270412at_nat F) B6)) (@ (@ ord_le3146513528884898305at_nat B6) A4) (@ finite6177210948735845034at_nat B6))))) (forall ((F (-> num num)) (G (-> nat num)) (H (-> int nat))) (= (@ (@ comp_nat_num_int (@ (@ comp_num_num_nat F) G)) H) (@ (@ comp_num_num_int F) (@ (@ comp_nat_num_int G) H)))) (forall ((F (-> nat nat)) (S5 set_set_nat)) (let ((_let_1 (@ image_nat_nat F))) (= (@ _let_1 (@ comple7399068483239264473et_nat S5)) (@ comple7399068483239264473et_nat (@ (@ image_7916887816326733075et_nat _let_1) S5))))) (forall ((Z2 set_Pr4329608150637261639at_nat)) (= (@ (@ (@ comp_P8235817900121468292at_nat produc4486455499028916547at_nat) (lambda ((X4 set_Pr4329608150637261639at_nat)) (@ (@ produc9060074326276436823at_nat X4) X4))) Z2) (@ id_set7849613212452405432at_nat Z2))) (forall ((F (-> nat rat)) (G (-> int nat)) (A4 set_int) (X2 rat)) (let ((_let_1 (@ (@ image_int_nat G) A4))) (=> (@ (@ inj_on_nat_rat F) _let_1) (=> (@ (@ inj_on_int_nat G) A4) (=> (@ (@ member_rat X2) (@ (@ image_nat_rat F) _let_1)) (= (@ (@ (@ the_inv_into_int_rat A4) (@ (@ comp_nat_rat_int F) G)) X2) (@ (@ (@ comp_nat_int_rat (@ (@ the_inv_into_int_nat A4) G)) (@ (@ the_inv_into_nat_rat _let_1) F)) X2))))))) (forall ((A4 set_Product_unit) (B5 set_Pr1261947904930325089at_nat)) (= (= (@ (@ produc3904733337175673596at_nat A4) (lambda ((Uu product_unit)) B5)) bot_bo6659885642593197735at_nat) (or (= A4 bot_bo3957492148770167129t_unit) (= B5 bot_bo2099793752762293965at_nat)))) (forall ((X2 product_prod_nat_nat) (A4 (-> nat nat Bool))) (=> (@ (@ member8440522571783428010at_nat X2) (@ collec3392354462482085612at_nat (@ produc6081775807080527818_nat_o A4))) (@ (@ A4 (@ product_fst_nat_nat X2)) (@ product_snd_nat_nat X2)))) _let_159 (forall ((R3 (-> int int Bool))) (let ((_let_1 (@ bNF_Gr2749509334501985047nt_int (@ collec213857154873943460nt_int (@ produc4947309494688390418_int_o R3))))) (= (@ (@ relcom3664783465810776136nt_int (@ conver7247880940930113968nt_int (@ _let_1 product_fst_int_int))) (@ _let_1 product_snd_int_int)) R3))) (forall ((F (-> product_prod_int_int product_prod_int_int))) (= (@ produc4245557441103728435nt_int (lambda ((X4 int) (Y5 int)) (@ F (@ (@ product_Pair_int_int X4) Y5)))) F)) (forall ((A4 set_nat) (B5 set_rat)) (=> (@ finite_finite_nat A4) (=> (@ finite_finite_rat B5) (=> (@ (@ ord_less_eq_nat (@ finite_card_nat A4)) (@ finite_card_rat B5)) (exists ((F5 (-> nat rat))) (and (@ (@ inj_on_nat_rat F5) A4) (@ (@ ord_less_eq_set_rat (@ (@ image_nat_rat F5) A4)) B5))))))) (forall ((R ref_a) (H heap_e7401611519738050253t_unit) (H2 heap_e7401611519738050253t_unit) (X2 a)) (=> (@ (@ (@ (@ heap_effect_a (@ lookup_a R)) H) H2) X2) (not (=> (= H2 H) (not (= X2 (@ (@ get_a H) R))))))) (forall ((A4 set_int) (R set_Pr958786334691620121nt_int) (A int)) (=> (@ (@ refl_on_int A4) R) (=> (@ (@ member_int A) A4) (@ (@ member5262025264175285858nt_int (@ (@ 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set_set_nat)) (let ((_let_1 (@ image_nat_rat F))) (= (@ _let_1 (@ comple7399068483239264473et_nat S5)) (@ comple3890839924845867745et_rat (@ (@ image_4408659257933336347et_rat _let_1) S5))))) (forall ((A4 set_o) (R set_Product_prod_o_o) (A Bool) (B Bool)) (=> (@ (@ refl_on_o A4) R) (=> (@ (@ member7466972457876170832od_o_o (@ (@ product_Pair_o_o A) B)) R) (and (@ (@ member_o B) A4) (@ (@ member_o A) A4))))) (forall ((X1 nat) (X22 num) (Y1 nat) (Y22 num)) (= (= (@ (@ product_Pair_nat_num X1) X22) (@ (@ product_Pair_nat_num Y1) Y22)) (and (= X1 Y1) (= X22 Y22)))) (forall ((F (-> int int)) (A4 set_int) (B5 set_int)) (let ((_let_1 (@ image_int_int F))) (@ (@ ord_less_eq_set_int (@ _let_1 (@ (@ inf_inf_set_int A4) B5))) (@ (@ inf_inf_set_int (@ _let_1 A4)) (@ _let_1 B5))))) (forall ((B5 set_nat) (F (-> int nat)) (A4 set_int)) (= (@ (@ ord_less_eq_set_nat B5) (@ (@ image_int_nat F) A4)) (exists ((AA set_int)) (and (= B5 (@ (@ image_int_nat F) AA)) (@ (@ ord_less_eq_set_int AA) A4))))) (forall ((B5 set_int) (A4 set_int) (F (-> int set_nat)) (G (-> int set_nat))) (=> (@ (@ ord_less_eq_set_int B5) A4) (=> (forall ((X int)) (=> (@ (@ member_int X) B5) (@ (@ ord_less_eq_set_nat (@ F X)) (@ G X)))) (@ (@ ord_less_eq_set_nat (@ comple7806235888213564991et_nat (@ (@ image_int_set_nat F) A4))) (@ comple7806235888213564991et_nat (@ (@ image_int_set_nat G) B5)))))) (forall ((X1 set_Pr1261947904930325089at_nat) (X22 set_Pr1261947904930325089at_nat) (Y1 set_Pr1261947904930325089at_nat) (Y22 set_Pr1261947904930325089at_nat)) (= (= (@ (@ produc2922128104949294807at_nat X1) X22) (@ (@ produc2922128104949294807at_nat Y1) Y22)) (and (= X1 Y1) (= X22 Y22)))) (forall ((A4 set_Pr1261947904930325089at_nat) (R set_Pr8693737435421807431at_nat)) (=> (forall ((X product_prod_nat_nat) (Y product_prod_nat_nat)) (=> (@ (@ member8440522571783428010at_nat X) A4) (=> (@ (@ member8440522571783428010at_nat Y) A4) (=> (not (= X Y)) (or (@ (@ member8206827879206165904at_nat (@ (@ produc6161850002892822231at_nat Y) X)) R) (@ (@ member8206827879206165904at_nat (@ (@ produc6161850002892822231at_nat X) Y)) R)))))) (@ (@ total_3592101749530773125at_nat A4) R))) (forall ((A4 set_int) (F (-> int int)) (X2 int)) (=> (not (= A4 bot_bot_set_int)) (=> (forall ((Y int)) (=> (@ (@ member_int Y) A4) (= (@ F Y) (@ F X2)))) (= (@ the_elem_int (@ (@ image_int_int F) A4)) (@ F X2))))) (forall ((G (-> product_unit char)) (C3 set_Product_unit) (B5 set_Product_unit) (X2 product_unit)) (let ((_let_1 (@ (@ sup_su793286257634532545t_unit B5) (@ (@ insert_Product_unit X2) bot_bo3957492148770167129t_unit)))) (=> (@ (@ inj_on1959294024837303853t_char G) C3) (=> (@ (@ ord_le3507040750410214029t_unit C3) _let_1) (@ (@ member379592906918970460t_unit (lambda ((I2 char)) (@ (@ (@ if_Product_unit (@ (@ member_char I2) (@ (@ image_7248553556944771225t_char G) C3))) (@ (@ (@ the_in3194898024646563179t_char C3) G) I2)) X2))) (@ (@ bNF_We7396736742984212070t_unit top_top_set_char) _let_1)))))) (forall ((S5 set_se7592288975875140775at_nat)) (= (@ comple5307621999477653941_nat_o (@ (@ image_5337237954834410540_nat_o (lambda ((I2 set_Pr7459493094073627847at_nat) (X4 set_Pr4329608150637261639at_nat) (Y5 set_Pr4329608150637261639at_nat)) (@ (@ member1466754251312161552at_nat (@ (@ produc9060074326276436823at_nat X4) Y5)) I2))) S5)) (lambda ((X4 set_Pr4329608150637261639at_nat) (Y5 set_Pr4329608150637261639at_nat)) (@ (@ member1466754251312161552at_nat (@ (@ produc9060074326276436823at_nat X4) Y5)) (@ comple4403251139954110286at_nat S5))))) (forall ((F1 (-> nat nat)) (A13 set_nat) (B1 set_nat) (F22 (-> int int)) (B22 set_int) (A24 set_int)) (=> (= (@ (@ image_nat_nat F1) A13) B1) (=> (@ (@ inj_on_int_int F22) B22) (=> (@ (@ ord_less_eq_set_int (@ (@ image_int_int F22) B22)) A24) (=> (=> (= B22 bot_bot_set_int) (= A24 bot_bot_set_int)) (= (@ (@ bNF_We8539870446460111250nt_nat B22) B1) (@ (@ image_5412825682893543741nt_nat (@ (@ (@ bNF_We893321924073841572at_int B22) F1) F22)) (@ (@ bNF_We8539870446460111250nt_nat A24) A13)))))))) (forall ((F (-> nat nat)) (A4 set_nat) (B5 set_nat)) (let ((_let_1 (@ image_nat_nat F))) (=> (@ (@ inj_on_nat_nat F) top_top_set_nat) (= (@ _let_1 (@ (@ minus_minus_set_nat A4) B5)) (@ (@ minus_minus_set_nat (@ _let_1 A4)) (@ _let_1 B5)))))) (forall ((F (-> int product_unit)) (A4 set_int)) (=> (@ order_2843698775922903023t_unit F) (=> (@ condit1735850657277959132ow_int A4) (=> (not (= A4 bot_bot_set_int)) (@ (@ ord_le3221252021190050221t_unit (@ F (@ complete_Inf_Inf_int A4))) (@ comple2584293577114468500t_unit (@ (@ image_5846526143423701914t_unit F) A4))))))) (forall ((Rep (-> product_unit Bool)) (Abs (-> Bool product_unit)) (X2 product_prod_nat_nat) (S5 (-> Bool set_Pr1261947904930325089at_nat)) (Y3 Bool)) (let ((_let_1 (@ member8440522571783428010at_nat X2))) (=> (@ (@ (@ type_d6188575255521822967unit_o Rep) Abs) top_top_set_o) (=> (@ _let_1 (@ (@ (@ comp_o2254869825208929t_unit S5) Rep) (@ Abs Y3))) (@ _let_1 (@ S5 Y3)))))) _let_158 (forall ((A nat) (B nat) (A4 set_nat) (B5 (-> nat set_nat))) (= (@ (@ member8440522571783428010at_nat (@ (@ product_Pair_nat_nat A) B)) (@ (@ produc457027306803732586at_nat A4) B5)) (and (@ (@ member_nat A) A4) (@ (@ member_nat B) (@ B5 A))))) (forall ((C3 set_nat) (A4 (-> nat set_char)) (B5 set_char)) (let ((_let_1 (= C3 bot_bot_set_nat))) (and (=> (not _let_1) (= (@ comple7965528767983648192t_char (@ (@ image_nat_set_char (lambda ((X4 nat)) (@ (@ minus_minus_set_char (@ A4 X4)) B5))) C3)) (@ (@ minus_minus_set_char (@ comple7965528767983648192t_char (@ (@ image_nat_set_char A4) C3))) B5))) (=> _let_1 (= (@ comple7965528767983648192t_char (@ (@ image_nat_set_char (lambda ((X4 nat)) (@ (@ minus_minus_set_char (@ A4 X4)) B5))) C3)) top_top_set_char))))) (forall ((Rep (-> Bool char)) (Abs (-> char Bool)) (S5 (-> char set_rat)) (M (-> Bool char)) (F (-> nat rat)) (S6 (-> Bool set_nat)) (G (-> nat Bool))) (let ((_let_1 (@ image_nat_rat F))) (let ((_let_2 (@ comp_char_set_rat_o S5))) (=> (@ (@ (@ type_d9076672964931703357o_char Rep) Abs) top_top_set_char) (=> (= (@ _let_2 M) (@ (@ comp_s8507027185284273247_rat_o _let_1) S6)) (= (@ (@ comp_o_set_rat_nat (@ _let_2 Rep)) (@ (@ comp_o_o_nat (@ (@ comp_char_o_o Abs) M)) G)) (@ (@ comp_s8255929034757298889at_nat _let_1) (@ (@ comp_o_set_nat_nat S6) G)))))))) (forall ((A4 set_o) (M3 nat) (F (-> Bool nat))) (=> (not (= A4 bot_bot_set_o)) (=> (forall ((X Bool)) (=> (@ (@ member_o X) A4) (@ (@ ord_less_eq_nat M3) (@ F X)))) (@ (@ ord_less_eq_nat M3) (@ complete_Inf_Inf_nat (@ (@ image_o_nat F) A4)))))) (forall ((P2 (-> product_prod_int_int Bool)) (Q2 (-> product_prod_int_int product_prod_int_int Bool))) (= (@ collec7447955092554649554nt_int (@ produc1676490119946744748_int_o (lambda ((X4 product_prod_int_int) (Y5 product_prod_int_int)) (and (@ P2 X4) (@ (@ Q2 X4) Y5))))) (@ (@ produc245848125267896712nt_int (@ collec213857154873943460nt_int P2)) (lambda ((X4 product_prod_int_int)) (@ collec213857154873943460nt_int (@ Q2 X4)))))) _let_155 (forall ((F (-> nat Bool)) (A4 set_nat) (G (-> Bool Bool))) (=> (@ (@ inj_on_nat_o F) A4) (=> (@ (@ inj_on_o_o G) (@ (@ image_nat_o F) A4)) (@ (@ inj_on_nat_o (@ (@ comp_o_o_nat G) F)) A4)))) (forall ((X2 nat) (A4 set_nat) (C int)) (=> (@ (@ member_nat X2) A4) (= (@ (@ image_nat_int (lambda ((X4 nat)) C)) A4) (@ (@ insert_int C) bot_bot_set_int)))) _let_154 _let_152 (forall ((A Bool) (A4 set_o) (B int) (B5 (-> Bool set_int))) (let ((_let_1 (@ member_int B))) (=> (@ (@ member_o A) A4) (=> (@ _let_1 (@ B5 A)) (@ _let_1 (@ comple3221217463730067765et_int (@ (@ image_o_set_int B5) A4))))))) (forall ((X2 nat) (C3 set_nat) (A4 set_nat) (B5 set_nat)) (=> (@ (@ member_nat X2) C3) (= (= (@ (@ produc457027306803732586at_nat A4) (lambda ((Uu nat)) C3)) (@ (@ produc457027306803732586at_nat B5) (lambda ((Uu nat)) C3))) (= A4 B5)))) (forall ((B5 set_nat) (A4 set_nat) (Q2 (-> nat Bool)) (P2 (-> nat Bool))) (=> (@ (@ ord_less_eq_set_nat B5) A4) (=> (forall ((X nat)) (=> (@ (@ member_nat X) B5) (=> (@ Q2 X) (@ P2 X)))) (@ (@ ord_less_eq_set_nat (@ collect_nat (lambda ((X4 nat)) (and (@ Q2 X4) (@ (@ member_nat X4) B5))))) (@ collect_nat (lambda ((X4 nat)) (and (@ P2 X4) (@ (@ member_nat X4) A4)))))))) _let_151 (forall ((F (-> product_unit int)) (A4 set_Product_unit)) (=> (@ order_7093624213399680841it_int F) (=> (@ condit2080475194861589617t_unit A4) (=> (not (= A4 bot_bo3957492148770167129t_unit)) (@ (@ ord_less_eq_int (@ complete_Sup_Sup_int (@ (@ image_873079544045703924it_int F) A4))) (@ F (@ comple4687483117567863418t_unit A4))))))) (forall ((F (-> nat int)) (A4 set_nat) (P2 (-> set_int Bool))) (= (exists ((B6 set_int)) (and (@ finite_finite_int B6) (@ (@ ord_less_eq_set_int B6) (@ (@ image_nat_int F) A4)) (@ P2 B6))) (exists ((B6 set_nat)) (and (@ finite_finite_nat B6) (@ (@ ord_less_eq_set_nat B6) A4) (@ P2 (@ (@ image_nat_int F) B6)))))) (forall ((A4 (-> nat set_Product_unit)) (I nat) (B5 set_Product_unit) (J3 set_nat)) (= (@ comple3349607820504768346t_unit (@ (@ image_4824033694279209942t_unit (@ (@ (@ fun_up1220017903161424222t_unit A4) I) B5)) J3)) (@ (@ sup_su793286257634532545t_unit (@ comple3349607820504768346t_unit (@ (@ image_4824033694279209942t_unit A4) (@ (@ minus_minus_set_nat J3) (@ (@ insert_nat I) bot_bot_set_nat))))) (@ (@ (@ if_set_Product_unit (@ (@ member_nat I) J3)) B5) bot_bo3957492148770167129t_unit)))) (forall ((Sup (-> set_nat nat)) (G (-> nat nat)) (F (-> int nat)) (A4 set_int)) (= (@ Sup (@ (@ image_nat_nat G) (@ (@ image_int_nat F) A4))) (@ Sup (@ (@ image_int_nat (@ (@ comp_nat_nat_int G) F)) A4)))) (forall ((C product_prod_o_o) (A4 set_o)) (=> (@ (@ member7466972457876170832od_o_o C) (@ id_on_o A4)) (not (forall ((X Bool)) (=> (@ (@ member_o X) A4) (not (= C (@ (@ product_Pair_o_o X) X)))))))) (forall ((B5 set_he8644174446132254637t_unit) (A4 set_ref_a)) (let ((_let_1 (@ produc3946373962484743846t_unit A4))) (let ((_let_2 (@ image_7136766188234240905_ref_a produc473321116828791851t_unit))) (let ((_let_3 (= B5 bot_bo3686245532977126937t_unit))) (and (=> (not _let_3) (= (@ _let_2 (@ _let_1 (lambda ((Uu ref_a)) B5))) A4)) (=> _let_3 (= (@ _let_2 (@ _let_1 (lambda ((Uu ref_a)) B5))) bot_bot_set_ref_a))))))) _let_150 (forall ((C3 set_o) (A4 set_int) (B5 (-> Bool set_int))) (let ((_let_1 (= C3 bot_bot_set_o))) (and (=> _let_1 (= (@ comple3628384868704368283et_int (@ (@ image_o_set_int (lambda ((X4 Bool)) (@ (@ inf_inf_set_int A4) (@ B5 X4)))) C3)) top_top_set_int)) (=> (not _let_1) (= (@ comple3628384868704368283et_int (@ (@ image_o_set_int (lambda ((X4 Bool)) (@ (@ inf_inf_set_int A4) (@ B5 X4)))) C3)) (@ (@ inf_inf_set_int A4) (@ comple3628384868704368283et_int (@ (@ image_o_set_int B5) C3)))))))) (forall ((A4 set_nat) (F (-> nat product_unit)) (G (-> nat product_unit))) (let ((_let_1 (@ (@ image_8730104196221521654t_unit G) A4))) (let ((_let_2 (@ (@ image_8730104196221521654t_unit F) A4))) (=> (not (= A4 bot_bot_set_nat)) (=> (@ condit9161856309968323677t_unit _let_2) (=> (@ condit9161856309968323677t_unit _let_1) (= (@ (@ inf_inf_Product_unit (@ comple2584293577114468500t_unit _let_2)) (@ comple2584293577114468500t_unit _let_1)) (@ comple2584293577114468500t_unit (@ (@ image_8730104196221521654t_unit (lambda ((A5 nat)) (@ (@ inf_inf_Product_unit (@ F A5)) (@ G A5)))) A4))))))))) (forall ((A Bool) (B Bool) (A4 set_o)) (=> (= A B) (=> (@ (@ member_o A) A4) (@ (@ member7466972457876170832od_o_o (@ (@ product_Pair_o_o A) B)) (@ id_on_o A4))))) (forall ((A4 set_Pr8693737435421807431at_nat) (F (-> product_unit set_Pr8693737435421807431at_nat))) (= (@ (@ sup_su718114333110466843at_nat A4) (@ comple2748534634209756852at_nat (@ (@ image_7288820656315755647at_nat F) bot_bo3957492148770167129t_unit))) A4)) (forall ((C3 set_o) (A4 (-> Bool set_Pr8693737435421807431at_nat)) (B5 set_Pr8693737435421807431at_nat)) (let ((_let_1 (@ (@ sup_su718114333110466843at_nat (@ comple2748534634209756852at_nat (@ (@ image_8493167801588156084at_nat A4) C3))) B5))) (let ((_let_2 (= C3 bot_bot_set_o))) (and (=> _let_2 (= _let_1 B5)) (=> (not _let_2) (= _let_1 (@ comple2748534634209756852at_nat (@ (@ image_8493167801588156084at_nat (lambda ((X4 Bool)) (@ (@ sup_su718114333110466843at_nat (@ A4 X4)) B5))) C3)))))))) (forall ((F (-> rat nat)) (G (-> nat rat)) (A4 set_nat)) (= (@ (@ image_rat_nat F) (@ (@ image_nat_rat G) A4)) (@ (@ image_nat_nat (lambda ((X4 nat)) (@ F (@ G X4)))) A4))) (forall ((C (-> nat num Bool)) (P product_prod_nat_num)) (=> (@ (@ produc4927758841916487424_num_o C) P) (not (forall ((X nat) (Y num)) (=> (= P (@ (@ product_Pair_nat_num X) Y)) (not (@ (@ C X) Y))))))) (forall ((A4 set_Pr4329608150637261639at_nat)) (=> (forall ((X produc3843707927480180839at_nat)) (not (@ (@ member8757157785044589968at_nat X) A4))) (@ (@ ord_le1268244103169919719at_nat A4) bot_bo228742789529271731at_nat))) (forall ((R (-> code_integer int Bool)) (S2 (-> int int Bool))) (= (@ conver1462408618118490240er_int (@ (@ relcom3789353511612409832nt_int R) S2)) (@ (@ relcom967497705283160040nteger (@ conversep_int_int S2)) (@ conver1462408618118490240er_int R)))) (forall ((F (-> code_integer code_integer code_integer)) (X5 set_Code_integer) (G1 (-> (-> code_integer code_integer) produc8923325533196201883nteger produc8923325533196201883nteger)) (G22 (-> (-> code_integer code_integer) produc8923325533196201883nteger produc8923325533196201883nteger))) (=> (= (@ (@ image_2177946750938214461nteger F) X5) top_to3804862627464599871nteger) (=> (forall ((X code_integer)) (=> (@ (@ member_Code_integer X) X5) (= (@ (@ (@ comp_C8797469213163452608nteger G1) F) X) (@ (@ (@ comp_C8797469213163452608nteger G22) F) X)))) (= G1 G22)))) (forall ((X5 (-> int int Bool)) (A4 (-> num num Bool)) (F (-> int num)) (G (-> int num)) (Y4 (-> int int Bool)) (B5 (-> num num Bool))) (=> (@ (@ (@ (@ bNF_re7626690874201225453um_num X5) A4) F) G) (=> (forall ((X int) (Y int)) (=> (@ (@ Y4 X) Y) (@ (@ X5 X) Y))) (=> (forall ((X num) (Y num)) (=> (@ (@ A4 X) Y) (@ (@ B5 X) Y))) (@ (@ (@ (@ bNF_re7626690874201225453um_num Y4) B5) F) G))))) _let_149 (forall ((F (-> product_prod_nat_nat set_nat)) (A product_prod_nat_nat) (B5 set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ image_15824709712370754et_nat F))) (= (@ comple7399068483239264473et_nat (@ _let_1 (@ (@ insert8211810215607154385at_nat A) B5))) (@ (@ sup_sup_set_nat (@ F A)) (@ comple7399068483239264473et_nat (@ _let_1 B5)))))) (forall ((A int) (A4 set_int) (B Bool) (B5 (-> int set_o))) (=> (@ (@ member_int A) A4) (=> (@ (@ member_o B) (@ B5 A)) (@ (@ member4489920277610959864_int_o (@ (@ product_Pair_int_o A) B)) (@ (@ product_Sigma_int_o A4) B5))))) _let_148 (forall ((P2 (-> produc1319942482725812455at_nat Bool)) (P produc1319942482725812455at_nat)) (=> (forall ((A3 set_Pr4329608150637261639at_nat) (B3 set_Pr4329608150637261639at_nat)) (@ P2 (@ (@ produc9060074326276436823at_nat A3) B3))) (@ P2 P))) (forall ((X2 (-> char int)) (Ya (-> char int)) (Y3 (-> char int)) (Xa2 (-> char int)) (R3 (-> int int Bool)) (Ra (-> int int Bool))) (=> (= X2 Ya) (=> (= Y3 Xa2) (=> (forall ((Z3 int) (Yb int)) (=> (@ (@ member_int Z3) (@ (@ image_char_int Ya) top_top_set_char)) (=> (@ (@ member_int Yb) (@ (@ image_char_int Xa2) top_top_set_char)) (= (@ (@ R3 Z3) Yb) (@ (@ Ra Z3) Yb))))) (= (@ (@ (@ (@ bNF_re4731199128827642459nt_int (lambda ((Y2 char) (Z char)) (= Y2 Z))) R3) X2) Y3) (@ (@ (@ (@ bNF_re4731199128827642459nt_int (lambda ((Y2 char) (Z char)) (= Y2 Z))) Ra) Ya) Xa2)))))) (forall ((R1 (-> product_prod_nat_nat int Bool))) (let ((_let_1 (@ bNF_re4555766996558763186at_nat R1))) (@ (@ (@ (@ bNF_re1160762158786734233nt_nat (lambda ((Y2 (-> nat nat)) (Z (-> nat nat))) (= Y2 Z))) (@ (@ bNF_re8419181437172746013nt_nat (@ _let_1 (lambda ((Y2 nat) (Z nat)) (= Y2 Z)))) (@ _let_1 (lambda ((Y2 nat) (Z nat)) (= Y2 Z))))) comp_n2711240574518091068at_nat) comp_nat_nat_int))) (forall ((A4 set_int) (M3 int) (F (-> int int))) (=> (not (= A4 bot_bot_set_int)) (=> (forall ((X int)) (=> (@ (@ member_int X) A4) (@ (@ 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(forall ((A4 set_o) (B5 set_int) (F (-> Bool product_unit)) (G (-> int product_unit))) (=> (forall ((I4 Bool)) (=> (@ (@ member_o I4) A4) (exists ((X6 int)) (and (@ (@ ord_le3221252021190050221t_unit (@ F I4)) (@ G X6)) (@ (@ member_int X6) B5))))) (=> (forall ((J2 int)) (=> (@ (@ member_int J2) B5) (exists ((X6 Bool)) (and (@ (@ member_o X6) A4) (@ (@ ord_le3221252021190050221t_unit (@ G J2)) (@ F X6)))))) (= (@ comple4687483117567863418t_unit (@ (@ image_o_Product_unit F) A4)) (@ comple4687483117567863418t_unit (@ (@ image_5846526143423701914t_unit G) B5)))))) (forall ((R3 (-> product_prod_nat_nat product_prod_nat_nat Bool)) (S5 (-> product_prod_nat_nat product_prod_nat_nat Bool)) (R7 (-> product_prod_nat_nat int Bool)) (S6 (-> product_prod_nat_nat int Bool))) (@ (@ ord_le2484784447047653514_int_o (@ (@ relcom4982215633375716084nt_int (@ (@ bNF_re2241393799969408733at_nat R3) S5)) (@ (@ bNF_re7400052026677387805at_int R7) S6))) (@ (@ bNF_re7400052026677387805at_int (@ (@ 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image_663195431845683034t_unit B5) C3))))) (=> _let_1 (= (@ comple3349607820504768346t_unit (@ (@ image_663195431845683034t_unit (lambda ((X4 Bool)) (@ (@ sup_su793286257634532545t_unit A4) (@ B5 X4)))) C3)) bot_bo3957492148770167129t_unit))))) (forall ((B5 set_nat) (A4 set_nat) (F (-> nat set_nat)) (G (-> nat set_nat))) (=> (@ (@ ord_less_eq_set_nat B5) A4) (=> (forall ((X nat)) (=> (@ (@ member_nat X) B5) (@ (@ ord_less_eq_set_nat (@ F X)) (@ G X)))) (@ (@ ord_less_eq_set_nat (@ comple7806235888213564991et_nat (@ (@ image_nat_set_nat F) A4))) (@ comple7806235888213564991et_nat (@ (@ image_nat_set_nat G) B5)))))) (forall ((K int) (I3 set_int) (A4 (-> int set_nat))) (let ((_let_1 (@ comple7399068483239264473et_nat (@ (@ image_int_set_nat A4) I3)))) (=> (@ (@ member_int K) I3) (= (@ (@ sup_sup_set_nat (@ A4 K)) _let_1) _let_1)))) (forall ((B5 (-> nat nat Bool)) (C3 (-> num nat Bool)) (A4 (-> int nat Bool))) (@ (@ (@ (@ bNF_re6524732562925676389at_nat (@ (@ 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sup_sup_set_nat A4))) (= (@ _let_1 (@ comple7806235888213564991et_nat B5)) (@ comple7806235888213564991et_nat (@ (@ image_7916887816326733075et_nat _let_1) B5))))) (forall ((B5 set_int) (A4 set_int) (Q2 (-> int Bool)) (P2 (-> int Bool))) (=> (@ (@ ord_less_eq_set_int B5) A4) (=> (forall ((X int)) (=> (@ (@ member_int X) B5) (=> (@ Q2 X) (@ P2 X)))) (@ (@ ord_less_eq_set_int (@ collect_int (lambda ((X4 int)) (and (@ (@ member_int X4) B5) (@ Q2 X4))))) (@ collect_int (lambda ((X4 int)) (and (@ P2 X4) (@ (@ member_int X4) A4)))))))) _let_144 (forall ((C3 set_Pr4329608150637261639at_nat) (A4 (-> produc3843707927480180839at_nat set_nat)) (B5 set_nat)) (let ((_let_1 (@ (@ inf_inf_set_nat (@ comple7806235888213564991et_nat (@ (@ image_3160451284896210088et_nat A4) C3))) B5))) (let ((_let_2 (= C3 bot_bo228742789529271731at_nat))) (and (=> _let_2 (= _let_1 B5)) (=> (not _let_2) (= _let_1 (@ comple7806235888213564991et_nat (@ (@ image_3160451284896210088et_nat (lambda ((X4 produc3843707927480180839at_nat)) (@ (@ inf_inf_set_nat (@ A4 X4)) B5))) C3)))))))) (forall ((S5 set_se6260736226359567993nt_int)) (= (@ comple7687260386943045147_int_o (@ (@ image_4446226961036766042_int_o (lambda ((I2 set_Pr958786334691620121nt_int) (X4 int) (Y5 int)) (@ (@ member5262025264175285858nt_int (@ (@ product_Pair_int_int X4) Y5)) I2))) S5)) (lambda ((X4 int) (Y5 int)) (@ (@ member5262025264175285858nt_int (@ (@ product_Pair_int_int X4) Y5)) (@ comple5382143125604098054nt_int S5))))) (forall ((F (-> produc859450856879609959at_nat product_unit)) (A4 set_Pr8693737435421807431at_nat) (B5 set_Pr8693737435421807431at_nat)) (let ((_let_1 (@ image_8487516615895632747t_unit F))) (let ((_let_2 (@ inj_on1041401102088758999t_unit F))) (= (@ _let_2 (@ (@ sup_su718114333110466843at_nat A4) B5)) (and (@ _let_2 A4) (@ _let_2 B5) (= (@ (@ inf_in4660618365625256667t_unit (@ _let_1 (@ (@ minus_8321449233255521966at_nat A4) B5))) (@ _let_1 (@ (@ minus_8321449233255521966at_nat B5) A4))) bot_bo3957492148770167129t_unit)))))) (forall ((F (-> rat nat))) (= (= (@ (@ image_rat_nat F) top_top_set_rat) top_top_set_nat) (forall ((Y5 nat)) (exists ((X4 rat)) (= Y5 (@ F X4)))))) (forall ((F (-> char char)) (G (-> rat int))) (=> (= (@ (@ image_char_char F) top_top_set_char) top_top_set_char) (=> (= (@ (@ image_rat_int G) top_top_set_rat) top_top_set_int) (= (@ (@ image_4975014655635759961ar_int (@ (@ produc1863155021832019360at_int F) G)) top_to8437673547576850234ar_rat) top_to3104204703268025230ar_int)))) (forall ((B5 (-> nat set_nat))) (= (@ comple7399068483239264473et_nat (@ (@ image_nat_set_nat B5) bot_bot_set_nat)) bot_bot_set_nat)) (forall ((X2 set_Pr1261947904930325089at_nat) (Y3 set_Pr1261947904930325089at_nat) (R set_Pr1261947904930325089at_nat) (F (-> set_Pr1261947904930325089at_nat nat))) (= (@ (@ member8757157785044589968at_nat (@ (@ produc2922128104949294807at_nat X2) Y3)) (@ (@ inv_im6750873321330482877at_nat R) F)) (@ (@ member8440522571783428010at_nat (@ (@ product_Pair_nat_nat (@ F X2)) (@ F Y3))) R))) _let_143 (forall ((R3 (-> int int Bool)) (S5 (-> num num Bool)) (R7 (-> int int Bool)) (S6 (-> num num Bool))) (@ (@ ord_le4541714130423454556_num_o (@ (@ relcom9025577121137075810nt_num (@ (@ bNF_re7626690874201225453um_num R3) S5)) (@ (@ bNF_re7626690874201225453um_num R7) S6))) (@ (@ bNF_re7626690874201225453um_num (@ (@ relcompp_int_int_int R3) R7)) (@ (@ relcompp_num_num_num S5) S6)))) (forall ((P2 (-> int Bool)) (F (-> int nat)) (G (-> int nat)) (S5 set_int)) (let ((_let_1 (@ inf_inf_set_int S5))) (= (@ (@ image_int_nat (lambda ((X4 int)) (@ (@ (@ if_nat (@ P2 X4)) (@ F X4)) (@ G X4)))) S5) (@ (@ sup_sup_set_nat (@ (@ image_int_nat F) (@ _let_1 (@ collect_int P2)))) (@ (@ image_int_nat G) (@ _let_1 (@ collect_int (lambda ((X4 int)) (not (@ P2 X4)))))))))) (forall ((Prod produc3843707927480180839at_nat)) (= (@ (@ produc2922128104949294807at_nat (@ produc6011863565407846595at_nat Prod)) (@ produc2937545259423399429at_nat Prod)) Prod)) (forall ((F (-> nat nat)) (A4 set_nat) (B5 set_nat)) (let ((_let_1 (@ image_nat_nat F))) (=> (@ (@ ord_less_eq_set_nat (@ _let_1 A4)) B5) (@ (@ ord_le6893508408891458716et_nat (@ (@ image_7916887816326733075et_nat _let_1) (@ pow_nat A4))) (@ pow_nat B5))))) (forall ((F (-> code_integer code_integer)) (G (-> code_integer code_integer)) (X2 produc8923325533196201883nteger)) (= (@ (@ produc6499014454317279255nteger F) (@ (@ produc6499014454317279255nteger G) X2)) (@ (@ produc6499014454317279255nteger (@ (@ comp_C7449957260575251196nteger F) G)) X2))) (forall ((B5 set_nat) (F (-> nat nat)) (A4 set_nat)) (=> (@ finite_finite_nat B5) (=> (@ (@ ord_less_eq_set_nat B5) (@ (@ image_nat_nat F) A4)) (exists ((C2 set_nat)) (and (= B5 (@ (@ image_nat_nat F) C2)) (@ finite_finite_nat C2) (@ (@ ord_less_eq_set_nat C2) A4)))))) (forall ((I3 set_nat) (A4 (-> nat set_nat))) (=> (@ finite_finite_nat I3) (= (@ condit1738341127787009408ow_nat (@ comple7399068483239264473et_nat (@ (@ image_nat_set_nat A4) 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(-> rat rat))) (=> (@ finite_finite_rat top_top_set_rat) (=> (@ (@ inj_on_rat_rat F) top_top_set_rat) (= (@ (@ image_rat_rat F) top_top_set_rat) top_top_set_rat)))) (forall ((A4 set_o) (B Bool) (B5 (-> Bool set_o))) (=> (forall ((X Bool)) (=> (@ (@ member_o X) A4) (@ (@ member_o B) (@ B5 X)))) (@ (@ member_o B) (@ comple3063163877087187839_set_o (@ (@ image_o_set_o B5) A4))))) (forall ((N set_nat)) (= (@ gcd_Lcm_int (@ (@ image_nat_int semiri1314217659103216013at_int) N)) (@ semiri1314217659103216013at_int (@ gcd_Lcm_nat N)))) (forall ((P2 (-> int Bool)) (F (-> int int)) (B5 set_int)) (=> (forall ((X int)) (=> (@ P2 X) (@ (@ member_int (@ F X)) B5))) (@ (@ ord_less_eq_set_int (@ (@ image_int_int F) (@ collect_int P2))) B5))) (forall ((F (-> int nat)) (A4 set_int) (B5 set_nat)) (= (@ (@ ord_less_eq_set_nat (@ (@ image_int_nat F) A4)) B5) (forall ((X4 int)) (=> (@ (@ member_int X4) A4) (@ (@ member_nat (@ F X4)) B5))))) (forall ((Q2 (-> (-> product_prod_nat_nat product_prod_nat_nat) 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(B5 set_nat)) (= (@ (@ ord_less_eq_set_nat (@ (@ image_nat_nat F) A4)) B5) (@ (@ ord_less_eq_set_nat A4) (@ (@ vimage_nat_nat F) B5)))) (forall ((X2 nat) (Y3 nat) (R set_Pr1261947904930325089at_nat) (F (-> nat nat))) (= (@ (@ member8440522571783428010at_nat (@ (@ product_Pair_nat_nat X2) Y3)) (@ (@ inv_image_nat_nat R) F)) (@ (@ member8440522571783428010at_nat (@ (@ product_Pair_nat_nat (@ F X2)) (@ F Y3))) R))) (forall ((Inf (-> set_o Bool)) (A4 set_o)) (= (@ Inf (@ (@ image_o_o id_o) A4)) (@ Inf A4))) (forall ((A4 set_int) (F (-> int nat)) (B5 set_nat)) (=> (forall ((X int)) (=> (@ (@ member_int X) A4) (@ (@ member_nat (@ F X)) B5))) (@ (@ ord_less_eq_set_nat (@ (@ image_int_nat F) A4)) B5))) (forall ((P2 (-> product_prod_nat_num Bool)) (P product_prod_nat_num)) (=> (forall ((A3 nat) (B3 num)) (@ P2 (@ (@ product_Pair_nat_num A3) B3))) (@ P2 P))) (forall ((A4 set_nat)) (= (@ (@ produc457027306803732586at_nat A4) (lambda ((Uu nat)) bot_bot_set_nat)) bot_bo2099793752762293965at_nat)) (forall ((A4 set_nat) (C set_o)) (let ((_let_1 (= A4 bot_bot_set_nat))) (and (=> (not _let_1) (= (@ comple90263536869209701_set_o (@ (@ image_nat_set_o (lambda ((Y5 nat)) C)) A4)) C)) (=> _let_1 (= (@ comple90263536869209701_set_o (@ (@ image_nat_set_o (lambda ((Y5 nat)) C)) A4)) bot_bot_set_o))))) (forall ((A4 set_int) (G (-> int product_unit)) (B5 set_int) (F (-> int product_unit))) (let ((_let_1 (@ (@ image_5846526143423701914t_unit G) B5))) (=> (not (= A4 bot_bot_set_int)) (=> (@ condit2080475194861589617t_unit _let_1) (=> (@ (@ ord_less_eq_set_int A4) B5) (=> (forall ((X int)) (=> (@ (@ member_int X) A4) (@ (@ ord_le3221252021190050221t_unit (@ F X)) (@ G X)))) (@ (@ ord_le3221252021190050221t_unit (@ comple4687483117567863418t_unit (@ (@ image_5846526143423701914t_unit F) A4))) (@ comple4687483117567863418t_unit _let_1)))))))) (forall ((A code_integer) (S2 set_Code_integer) (T2 set_Code_integer)) (= (@ (@ image_4470545334726330049nteger (lambda ((X4 code_integer)) (@ (@ 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member8440522571783428010at_nat X) S5) (=> (@ (@ member8440522571783428010at_nat Y) S5) (= (@ (@ comp_nat_nat_nat _let_1) _let_2) (@ (@ comp_nat_nat_nat _let_2) _let_1))))))) (@ (@ finite2110315540964234241at_nat S5) F))) (forall ((F (-> int nat)) (A4 set_int)) (=> (@ finite_finite_nat (@ (@ image_int_nat F) A4)) (=> (not (@ finite_finite_int A4)) (exists ((X nat)) (and (not (@ finite_finite_int (@ (@ inf_inf_set_int (@ (@ vimage_int_nat F) (@ (@ insert_nat X) bot_bot_set_nat))) A4))) (@ (@ member_nat X) (@ (@ image_int_nat F) A4))))))) _let_140 (forall ((F (-> nat Bool)) (A4 set_nat) (P2 (-> Bool Bool))) (= (@ collect_o (lambda ((X4 Bool)) (and (@ (@ member_o X4) (@ (@ image_nat_o F) A4)) (@ P2 X4)))) (@ (@ image_nat_o F) (@ collect_nat (lambda ((X4 nat)) (and (@ (@ member_nat X4) A4) (@ P2 (@ F X4)))))))) (forall ((A4 (-> Bool set_Pr4329608150637261639at_nat))) (= (@ comple4364388969068068532at_nat (@ (@ image_2496312346330513076at_nat A4) top_top_set_o)) (@ (@ 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product_prod_nat_nat Bool)) (S5 (-> product_prod_nat_nat int Bool))) (=> (@ (@ (@ type_d281131942595027436at_nat Rep) Abs) top_to4669805908274784177at_nat) (= (@ (@ (@ bNF_vi5426221348228882691_int_o F) G) (@ (@ relcom8911704206367525917at_int (@ conver6965824823119931701at_nat R3)) S5)) (@ (@ relcom8911704206367525917at_int (@ conver6965824823119931701at_nat (@ (@ (@ bNF_vi763171854521451549_nat_o Rep) F) R3))) (@ (@ (@ bNF_vi5426221348228882691_int_o Rep) G) S5))))) (forall ((B5 set_int) (F (-> nat nat)) (A4 set_nat) (G (-> int nat))) (let ((_let_1 (@ (@ image_nat_nat F) A4))) (=> (not (= B5 bot_bot_set_int)) (=> (@ condit1738341127787009408ow_nat _let_1) (=> (forall ((M4 int)) (=> (@ (@ member_int M4) B5) (exists ((X6 nat)) (and (@ (@ ord_less_eq_nat (@ F X6)) (@ G M4)) (@ (@ member_nat X6) A4))))) (@ (@ ord_less_eq_nat (@ complete_Inf_Inf_nat _let_1)) (@ complete_Inf_Inf_nat (@ (@ image_int_nat G) B5)))))))) (forall ((P2 (-> nat Bool)) (F (-> nat rat)) (G (-> nat rat)) (S5 set_nat)) (let ((_let_1 (@ inf_inf_set_nat S5))) (= (@ (@ image_nat_rat (lambda ((X4 nat)) (@ (@ (@ if_rat (@ P2 X4)) (@ F X4)) (@ G X4)))) S5) (@ (@ sup_sup_set_rat (@ (@ image_nat_rat F) (@ _let_1 (@ collect_nat P2)))) (@ (@ image_nat_rat G) (@ _let_1 (@ collect_nat (lambda ((X4 nat)) (not (@ P2 X4)))))))))) (forall ((A4 set_int) (F (-> int nat)) (A int)) (let ((_let_1 (@ image_int_nat F))) (let ((_let_2 (@ _let_1 A4))) (=> (not (= A4 bot_bot_set_int)) (=> (@ condit2214826472909112428ve_nat _let_2) (= (@ complete_Sup_Sup_nat (@ _let_1 (@ (@ insert_int A) A4))) (@ (@ sup_sup_nat (@ F A)) (@ complete_Sup_Sup_nat _let_2)))))))) (forall ((B nat) (B5 (-> Bool set_nat)) (A4 set_o)) (=> (@ (@ member_nat B) (@ comple7399068483239264473et_nat (@ (@ image_o_set_nat B5) A4))) (not (forall ((X Bool)) (=> (@ (@ member_o X) A4) (not (@ (@ member_nat B) (@ B5 X)))))))) (= produc27273713700761075at_nat (lambda ((F2 (-> nat nat product_prod_nat_nat product_prod_nat_nat)) (Prod3 product_prod_nat_nat) (__flatten_var_0 product_prod_nat_nat)) (@ (@ (@ F2 (@ product_fst_nat_nat Prod3)) (@ product_snd_nat_nat Prod3)) __flatten_var_0))) (forall ((I3 set_o) (F (-> Bool set_nat)) (X2 set_nat)) (=> (not (= I3 bot_bot_set_o)) (=> (forall ((I4 Bool)) (=> (@ (@ member_o I4) I3) (= (@ F I4) X2))) (= (@ comple7399068483239264473et_nat (@ (@ image_o_set_nat F) I3)) X2)))) (forall ((A4 set_Pr4329608150637261639at_nat) (F (-> produc3843707927480180839at_nat product_unit)) (U product_unit)) (=> (forall ((I4 produc3843707927480180839at_nat)) (=> (@ (@ member8757157785044589968at_nat I4) A4) (@ (@ ord_le3221252021190050221t_unit (@ F I4)) U))) (@ (@ ord_le3221252021190050221t_unit (@ comple4687483117567863418t_unit (@ (@ image_7082456443403096939t_unit F) A4))) U))) (forall ((B5 (-> nat set_o))) (= (@ comple90263536869209701_set_o (@ (@ image_nat_set_o B5) bot_bot_set_nat)) bot_bot_set_o)) (forall ((B nat) (B5 (-> Bool set_nat)) (A4 set_o) (A Bool)) (let ((_let_1 (@ member_nat B))) (=> (@ _let_1 (@ 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inv_im8510909985083594081at_nat R) F)) (@ (@ member5262025264175285858nt_int (@ (@ product_Pair_int_int (@ F X2)) (@ F Y3))) R))) (forall ((Rep (-> num Bool)) (Abs (-> Bool num)) (M (-> Bool Bool))) (=> (@ (@ (@ type_d9070036042389994064_num_o Rep) Abs) top_top_set_o) (=> (= M id_o) (= (@ (@ comp_o_num_num (@ (@ comp_o_num_o Abs) M)) Rep) id_num)))) (forall ((A4 set_o) (C set_Product_unit)) (let ((_let_1 (= A4 bot_bot_set_o))) (and (=> _let_1 (= (@ comple3349607820504768346t_unit (@ (@ image_663195431845683034t_unit (lambda ((Y5 Bool)) C)) A4)) bot_bo3957492148770167129t_unit)) (=> (not _let_1) (= (@ comple3349607820504768346t_unit (@ (@ image_663195431845683034t_unit (lambda ((Y5 Bool)) C)) A4)) C))))) (forall ((F (-> nat nat)) (A4 set_nat)) (=> (@ order_mono_nat_nat F) (=> (@ condit1738341127787009408ow_nat A4) (=> (not (= A4 bot_bot_set_nat)) (@ (@ ord_less_eq_nat (@ F (@ complete_Inf_Inf_nat A4))) (@ complete_Inf_Inf_nat (@ (@ image_nat_nat F) A4))))))) (forall ((X2 product_unit)) (@ (@ total_5665700600833547665t_unit (@ (@ insert_Product_unit X2) bot_bo3957492148770167129t_unit)) (@ (@ insert4616891024742550839t_unit (@ (@ produc5692694829384537815t_unit X2) X2)) bot_bo1654022762305692595t_unit))) (forall ((C3 set_Product_unit) (A nat) (B5 (-> product_unit set_nat))) (let ((_let_1 (= C3 bot_bo3957492148770167129t_unit))) (and (=> _let_1 (= (@ comple7399068483239264473et_nat (@ (@ image_8173849991827986510et_nat (lambda ((X4 product_unit)) (@ (@ insert_nat A) (@ B5 X4)))) C3)) bot_bot_set_nat)) (=> (not _let_1) (= (@ comple7399068483239264473et_nat (@ (@ image_8173849991827986510et_nat (lambda ((X4 product_unit)) (@ (@ insert_nat A) (@ B5 X4)))) C3)) (@ (@ insert_nat A) (@ comple7399068483239264473et_nat (@ (@ image_8173849991827986510et_nat B5) C3)))))))) (forall ((A nat)) (@ (@ member8440522571783428010at_nat (@ (@ product_Pair_nat_nat A) A)) id_nat2)) (forall ((Rep (-> nat rat)) (Abs (-> rat nat)) (A4 set_rat)) (=> (@ (@ (@ type_d5615363888691252950at_rat Rep) Abs) A4) (= (@ (@ image_nat_rat Rep) top_top_set_nat) A4))) (forall ((F (-> ref_a ref_a))) (= (@ (@ comp_P8019343326919024234t_unit produc1126150082675451753t_unit) (@ produc4508741384315284437t_unit F)) produc1126150082675451753t_unit)) (forall ((F (-> nat int)) (G (-> num int)) (A nat) (B num)) (= (@ (@ (@ produc5477380188365894716um_int F) G) (@ (@ product_Pair_nat_num A) B)) (@ (@ product_Pair_int_int (@ F A)) (@ G B)))) (forall ((C produc3843707927480180839at_nat) (F (-> nat set_Pr1261947904930325089at_nat)) (G (-> num set_Pr1261947904930325089at_nat)) (R3 set_Pr6200539531224447659at_num)) (=> (@ (@ member8757157785044589968at_nat C) (@ (@ image_2708129733610033121at_nat (@ (@ produc170006858110003436at_nat F) G)) R3)) (not (forall ((X nat) (Y num)) (=> (= C (@ (@ produc2922128104949294807at_nat (@ F X)) (@ G Y))) (not (@ (@ member9148766508732265716at_num (@ (@ product_Pair_nat_num X) Y)) R3))))))) (forall ((I Bool) (C3 set_o) (G (-> Bool nat)) (X2 Bool)) (=> (@ (@ member_o I) C3) (=> (@ (@ inj_on_o_nat G) C3) (= (@ (@ (@ comp_nat_o_o (lambda ((I2 nat)) (let ((_let_1 (@ (@ member_nat I2) (@ (@ image_o_nat G) C3)))) (and (=> (not _let_1) X2) (=> _let_1 (@ (@ (@ the_inv_into_o_nat C3) G) I2)))))) G) I) (@ id_o I))))) (forall ((F (-> nat nat)) (G (-> int nat)) (A4 set_int)) (= (@ (@ image_nat_nat F) (@ (@ image_int_nat G) A4)) (@ (@ image_int_nat (lambda ((X4 int)) (@ F (@ G X4)))) A4))) (forall ((Z2 int) (C (-> int int set_int)) (A int) (B int)) (let ((_let_1 (@ member_int Z2))) (=> (@ _let_1 (@ (@ C A) B)) (@ _let_1 (@ (@ produc73460835934605544et_int C) (@ (@ product_Pair_int_int A) B)))))) (forall ((F (-> nat nat)) (A4 set_nat) (X2 nat) (U nat)) (let ((_let_1 (@ (@ image_nat_nat F) A4))) (=> (@ condit1738341127787009408ow_nat _let_1) (=> (@ (@ member_nat X2) A4) (=> (@ (@ ord_less_eq_nat (@ F X2)) U) (@ (@ ord_less_eq_nat (@ complete_Inf_Inf_nat _let_1)) U)))))) (forall ((P product_prod_nat_num)) (exists ((X nat) (Y num)) (= P (@ (@ product_Pair_nat_num X) Y)))) (forall ((A4 (-> Bool set_nat))) (= (@ comple7806235888213564991et_nat (@ (@ image_o_set_nat A4) top_top_set_o)) (@ (@ inf_inf_set_nat (@ A4 true)) (@ A4 false)))) (forall ((A4 set_Product_unit) (F (-> product_unit nat)) (U nat)) (let ((_let_1 (@ (@ image_875570014554754200it_nat F) A4))) (=> (not (= A4 bot_bo3957492148770167129t_unit)) (=> (@ condit2214826472909112428ve_nat _let_1) (= (@ (@ ord_less_eq_nat (@ complete_Sup_Sup_nat _let_1)) U) (forall ((X4 product_unit)) (=> (@ (@ member_Product_unit X4) A4) (@ (@ ord_less_eq_nat (@ F X4)) U)))))))) (forall ((A4 set_nat) (M3 int) (F (-> nat int))) (=> (forall ((X nat)) (=> (@ (@ member_nat X) A4) (@ (@ ord_less_eq_int M3) (@ F X)))) (@ condit1735850657277959132ow_int (@ (@ image_nat_int F) A4)))) (forall ((A4 set_Product_unit) (F set_nat)) (=> (not (= A4 bot_bo3957492148770167129t_unit)) (= (@ comple7399068483239264473et_nat (@ (@ image_8173849991827986510et_nat (lambda ((I2 product_unit)) F)) A4)) F))) (forall ((A nat) (A4 set_nat) (B Bool) (B5 (-> nat set_o))) (let ((_let_1 (@ member_o B))) (=> (@ (@ member_nat A) A4) (=> (@ _let_1 (@ B5 A)) (@ _let_1 (@ comple90263536869209701_set_o (@ (@ image_nat_set_o B5) A4))))))) (forall ((R3 (-> product_prod_nat_nat product_prod_nat_nat Bool)) (S5 (-> product_prod_nat_nat int Bool))) (=> (@ left_t5646938096895998950at_nat R3) (=> (@ left_t1861001511420785031at_int S5) (@ left_t1861001511420785031at_int (@ (@ relcom8911704206367525917at_int R3) S5))))) (forall ((F (-> int int)) (A4 set_int)) (=> (@ order_3677659787690696076nt_int F) (=> (@ condit1735850657277959132ow_int A4) (@ condit2212336002400062152ve_int (@ (@ image_int_int F) A4))))) (forall ((A4 set_o) (B5 set_o) (C3 set_o) (D set_o)) (= (= (@ (@ product_Sigma_o_o A4) (lambda ((Uu Bool)) B5)) (@ (@ product_Sigma_o_o C3) (lambda ((Uu Bool)) D))) (or (and (or (= D bot_bot_set_o) (= C3 bot_bot_set_o)) (or (= B5 bot_bot_set_o) (= A4 bot_bot_set_o))) (and (= A4 C3) (= B5 D))))) (forall ((B5 (-> Bool set_int))) (= (@ comple3628384868704368283et_int (@ (@ image_o_set_int B5) bot_bot_set_o)) top_top_set_int)) (forall ((A set_Pr4329608150637261639at_nat) (B set_Pr4329608150637261639at_nat) (A4 set_se5479201105039950375at_nat) (B5 (-> set_Pr4329608150637261639at_nat set_se5479201105039950375at_nat))) (=> (@ (@ member1466754251312161552at_nat (@ (@ produc9060074326276436823at_nat A) B)) (@ (@ produc6258361011560675592at_nat A4) B5)) (@ (@ member6273874620674182256at_nat A) A4))) (forall ((F (-> nat int)) (A4 set_nat)) (=> (@ finite_finite_int (@ (@ image_nat_int F) A4)) (=> (not (@ finite_finite_nat A4)) (exists ((X int)) (and (@ (@ member_int X) (@ (@ image_nat_int F) A4)) (not (@ finite_finite_nat (@ (@ inf_inf_set_nat (@ (@ vimage_nat_int F) (@ (@ insert_int X) bot_bot_set_int))) A4)))))))) (forall ((A4 set_nat) (C set_nat)) (let ((_let_1 (= A4 bot_bot_set_nat))) (and (=> (not _let_1) (= (@ comple7399068483239264473et_nat (@ (@ image_nat_set_nat (lambda ((Y5 nat)) C)) A4)) C)) (=> _let_1 (= (@ comple7399068483239264473et_nat (@ (@ image_nat_set_nat (lambda ((Y5 nat)) C)) A4)) bot_bot_set_nat))))) (forall ((A4 set_int) (B5 set_int) (F (-> int int)) (G (-> int code_integer))) (=> (= A4 B5) (= (@ (@ relcom967497705283160040nteger (@ conversep_int_int (@ (@ bNF_Grp_int_int A4) F))) (@ (@ bNF_Gr6684649993275963353nteger A4) G)) (@ (@ relcom967497705283160040nteger (@ conversep_int_int (@ (@ bNF_Grp_int_int B5) F))) (@ (@ bNF_Gr6684649993275963353nteger B5) G))))) (forall ((X2 (-> nat nat)) (Ya (-> nat nat)) (F (-> nat nat)) (G (-> nat nat))) (=> (= X2 Ya) (=> (forall ((Z3 nat)) (=> (@ (@ member_nat Z3) (@ (@ image_nat_nat Ya) top_top_set_nat)) (= (@ F Z3) (@ G Z3)))) (= (@ (@ comp_nat_nat_nat F) X2) (@ (@ comp_nat_nat_nat G) Ya))))) (forall ((F (-> char char)) (G (-> char nat))) (=> (= (@ (@ image_char_char F) top_top_set_char) top_top_set_char) (=> (= (@ (@ image_char_nat G) top_top_set_char) top_top_set_nat) (= (@ (@ image_1559928771699358788ar_nat (@ (@ 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collec266097228571071243um_num (lambda ((X4 (-> int product_prod_num_num))) (@ (@ ord_le880128212290418581um_num (@ (@ image_7722540232540426402um_num X4) top_top_set_int)) (@ collec2230928802738392704um_num (@ produc5703948589228662326_num_o R3)))))) (= (@ (@ comp_P4305060815297604026um_int product_snd_num_num) Z4) B) (= (@ (@ comp_P4305060815297604026um_int product_fst_num_num) Z4) A))))) (forall ((F (-> char char))) (let ((_let_1 (@ (@ bNF_Grp_char_char top_top_set_char) F))) (=> (= F id_char) (= (@ (@ relcom5872928454965100966r_char (@ conversep_char_char _let_1)) _let_1) _let_1)))) (forall ((M (-> produc859450856879609959at_nat set_nat)) (A4 set_Pr8693737435421807431at_nat) (B5 set_Pr8693737435421807431at_nat)) (let ((_let_1 (@ image_2819269535336293544et_nat M))) (= (@ comple7399068483239264473et_nat (@ _let_1 (@ (@ sup_su718114333110466843at_nat A4) B5))) (@ (@ sup_sup_set_nat (@ comple7399068483239264473et_nat (@ _let_1 A4))) (@ comple7399068483239264473et_nat (@ _let_1 B5)))))) (forall ((I num) (C3 set_num) (G (-> num Bool)) (X2 num)) (=> (@ (@ member_num I) C3) (=> (@ (@ inj_on_num_o G) C3) (= (@ (@ (@ comp_o_num_num (lambda ((I2 Bool)) (@ (@ (@ if_num (@ (@ member_o I2) (@ (@ image_num_o G) C3))) (@ (@ (@ the_inv_into_num_o C3) G) I2)) X2))) G) I) (@ id_num I))))) (forall ((F (-> nat int)) (G (-> nat nat)) (A4 set_nat)) (= (@ (@ image_nat_int F) (@ (@ image_nat_nat G) A4)) (@ (@ image_nat_int (lambda ((X4 nat)) (@ F (@ G X4)))) A4))) (forall ((F (-> nat set_o))) (= (@ comple90263536869209701_set_o (@ (@ image_nat_set_o F) bot_bot_set_nat)) bot_bot_set_o)) (forall ((C produc1319942482725812455at_nat) (A4 set_se5479201105039950375at_nat)) (=> (@ (@ member1466754251312161552at_nat C) (@ id_on_3275838214495744996at_nat A4)) (not (forall ((X set_Pr4329608150637261639at_nat)) (=> (@ (@ member6273874620674182256at_nat X) A4) (not (= C (@ (@ produc9060074326276436823at_nat X) X)))))))) (forall ((A int) (B int)) (= (@ (@ member5262025264175285858nt_int (@ 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((_let_1 (@ comple7399068483239264473et_nat (@ (@ image_15824709712370754et_nat A4) I3)))) (=> (@ (@ member8440522571783428010at_nat K) I3) (= (@ (@ sup_sup_set_nat (@ A4 K)) _let_1) _let_1)))) (forall ((F (-> nat nat)) (A4 set_nat)) (=> (@ (@ inj_on_nat_nat F) top_top_set_nat) (= (@ (@ vimage_nat_nat F) (@ (@ image_nat_nat F) A4)) A4))) (forall ((F (-> nat rat)) (A4 set_set_nat)) (=> (@ (@ inj_on_nat_rat F) (@ comple7399068483239264473et_nat A4)) (@ (@ inj_on1096178645466186887et_rat (@ image_nat_rat F)) A4))) (forall ((P2 (-> nat Bool)) (Q2 (-> product_prod_int_int Bool))) (= (@ collec5600542410287506995nt_int (@ produc4306188689235752475_int_o (lambda ((A5 nat) (B4 product_prod_int_int)) (and (@ Q2 B4) (@ P2 A5))))) (@ (@ produc7854212285064481439nt_int (@ collect_nat P2)) (lambda ((Uu nat)) (@ collec213857154873943460nt_int Q2))))) (forall ((F (-> nat nat)) (A4 set_nat) (B5 set_nat)) (=> (@ (@ inj_on_nat_nat F) A4) (=> (@ (@ ord_less_eq_set_nat (@ (@ image_nat_nat F) A4)) B5) (=> (@ finite_finite_nat B5) (@ finite_finite_nat A4))))) (forall ((I Bool) (A4 set_o) (F (-> Bool set_nat))) (=> (@ (@ member_o I) A4) (@ (@ ord_less_eq_set_nat (@ F I)) (@ comple7399068483239264473et_nat (@ (@ image_o_set_nat F) A4))))) (forall ((A4 set_Product_unit) (G (-> product_unit nat)) (B5 set_Product_unit) (F (-> product_unit nat))) (let ((_let_1 (@ (@ image_875570014554754200it_nat G) B5))) (=> (not (= A4 bot_bo3957492148770167129t_unit)) (=> (@ condit2214826472909112428ve_nat _let_1) (=> (@ (@ ord_le3507040750410214029t_unit A4) B5) (=> (forall ((X product_unit)) (=> (@ (@ member_Product_unit X) A4) (@ (@ ord_less_eq_nat (@ F X)) (@ G X)))) (@ (@ ord_less_eq_nat (@ complete_Sup_Sup_nat (@ (@ image_875570014554754200it_nat F) A4))) (@ complete_Sup_Sup_nat _let_1)))))))) (forall ((A set_Pr4329608150637261639at_nat) (B set_Pr4329608150637261639at_nat) (A2 set_Pr4329608150637261639at_nat) (B2 set_Pr4329608150637261639at_nat)) (=> (= (@ (@ produc9060074326276436823at_nat A) B) (@ (@ 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(= _let_1 (@ comple7806235888213564991et_nat (@ (@ image_8173849991827986510et_nat (lambda ((X4 product_unit)) (@ (@ minus_minus_set_nat (@ A4 X4)) B5))) C3)))) (=> _let_2 (= _let_1 (@ (@ minus_minus_set_nat top_top_set_nat) B5))))))) (forall ((G (-> (-> code_integer code_integer) produc8923325533196201883nteger produc8923325533196201883nteger)) (F (-> code_integer code_integer code_integer)) (A4 set_Code_integer)) (=> (@ (@ inj_on7031512951821619701nteger (@ (@ comp_C8797469213163452608nteger G) F)) A4) (@ (@ inj_on3998011822705705585nteger G) (@ (@ image_2177946750938214461nteger F) A4)))) (forall ((F (-> int int)) (G (-> int nat)) (A4 set_int)) (= (@ (@ image_659947567330398058nt_nat (lambda ((X4 int)) (@ (@ product_Pair_int_nat (@ F X4)) (@ G X4)))) A4) (@ (@ produc1456381018704787142nt_nat (@ (@ image_int_int F) A4)) (lambda ((X4 int)) (@ (@ image_int_nat G) (@ (@ inf_inf_set_int (@ (@ vimage_int_int F) (@ (@ insert_int X4) bot_bot_set_int))) A4)))))) (forall ((A4 set_int) (F (-> 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((A4 set_Pr7459493094073627847at_nat)) (@ (@ inj_on3942866938762682161at_nat (@ produc5456455677105495163at_nat (lambda ((I2 set_Pr4329608150637261639at_nat) (J set_Pr4329608150637261639at_nat)) (@ (@ produc9060074326276436823at_nat J) I2)))) A4)) (forall ((R3 set_Pr1261947904930325089at_nat) (S5 set_Pr1261947904930325089at_nat)) (= (= (lambda ((X4 nat) (Y5 nat)) (@ (@ member8440522571783428010at_nat (@ (@ product_Pair_nat_nat X4) Y5)) R3)) (lambda ((X4 nat) (Y5 nat)) (@ (@ member8440522571783428010at_nat (@ (@ product_Pair_nat_nat X4) Y5)) S5))) (= R3 S5))) (forall ((F (-> nat int)) (A4 set_nat)) (=> (@ order_2678306075789641520at_int F) (=> (@ condit1738341127787009408ow_nat A4) (@ condit2212336002400062152ve_int (@ (@ image_nat_int F) A4))))) (forall ((A set_Pr4329608150637261639at_nat)) (@ (@ member1466754251312161552at_nat (@ (@ produc9060074326276436823at_nat A) A)) id_set4888139568991089827at_nat)) (forall ((F (-> set_Pr4329608150637261639at_nat set_Pr4329608150637261639at_nat)) (X2 set_Pr4329608150637261639at_nat) (Y3 set_Pr4329608150637261639at_nat)) (let ((_let_1 (@ produc9060074326276436823at_nat X2))) (= (@ (@ produc8057050257526108681at_nat F) (@ _let_1 Y3)) (@ _let_1 (@ F Y3))))) (forall ((F (-> nat int)) (A4 set_nat)) (=> (@ finite_finite_int (@ (@ image_nat_int F) A4)) (=> (@ (@ inj_on_nat_int F) A4) (@ finite_finite_nat A4)))) (forall ((S5 (-> int int Bool)) (T3 (-> int int Bool)) (R3 (-> int code_integer Bool))) (= (@ (@ relcom967497705283160040nteger (@ (@ sup_sup_int_int_o S5) T3)) R3) (@ (@ sup_su1544571744061072657eger_o (@ (@ relcom967497705283160040nteger S5) R3)) (@ (@ relcom967497705283160040nteger T3) R3)))) (forall ((A4 set_Pr1261947904930325089at_nat) (R3 (-> nat nat Bool))) (=> (@ (@ ord_le3146513528884898305at_nat A4) (@ collec3392354462482085612at_nat (@ produc6081775807080527818_nat_o (@ conversep_nat_nat R3)))) (@ (@ ord_le3146513528884898305at_nat (@ (@ image_5168914502847457605at_nat (@ produc2626176000494625587at_nat (lambda ((X4 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comp_nat_num_num (lambda ((I2 nat)) (@ (@ (@ if_num (@ (@ member_nat I2) (@ (@ image_num_nat G) C3))) (@ (@ (@ the_inv_into_num_nat C3) G) I2)) X2))) G) I) (@ id_num I))))) (forall ((I3 set_nat) (X2 product_unit) (F (-> nat product_unit))) (=> (not (= I3 bot_bot_set_nat)) (= (@ comple2584293577114468500t_unit (@ (@ image_8730104196221521654t_unit (lambda ((I2 nat)) (@ (@ inf_inf_Product_unit X2) (@ F I2)))) I3)) (@ (@ inf_inf_Product_unit X2) (@ comple2584293577114468500t_unit (@ (@ image_8730104196221521654t_unit F) I3)))))) (forall ((B8 set_set_nat) (A4 set_nat)) (let ((_let_1 (@ (@ inf_inf_set_nat (@ comple7806235888213564991et_nat B8)) A4))) (let ((_let_2 (= B8 bot_bot_set_set_nat))) (and (=> _let_2 (= _let_1 A4)) (=> (not _let_2) (= _let_1 (@ comple7806235888213564991et_nat (@ (@ image_7916887816326733075et_nat (lambda ((B6 set_nat)) (@ (@ inf_inf_set_nat B6) A4))) B8)))))))) (forall ((F (-> rat rat)) (A4 set_rat)) (let ((_let_1 (@ image_rat_rat F))) (=> (= (@ _let_1 top_top_set_rat) top_top_set_rat) (= (@ _let_1 (@ (@ vimage_rat_rat F) A4)) A4)))) (forall ((A4 set_nat) (B5 (-> nat set_int)) (F (-> int int))) (=> (not (= A4 bot_bot_set_nat)) (=> (forall ((X nat)) (=> (@ (@ member_nat X) A4) (not (= (@ B5 X) bot_bot_set_int)))) (=> (@ condit2212336002400062152ve_int (@ comple3221217463730067765et_int (@ (@ image_nat_set_int (lambda ((X4 nat)) (@ (@ image_int_int F) (@ B5 X4)))) A4))) (= (@ complete_Sup_Sup_int (@ (@ image_int_int F) (@ comple3221217463730067765et_int (@ (@ image_nat_set_int B5) A4)))) (@ complete_Sup_Sup_int (@ (@ image_nat_int (lambda ((X4 nat)) (@ complete_Sup_Sup_int (@ (@ image_int_int F) (@ B5 X4))))) A4))))))) (forall ((A4 set_Product_unit) (B5 set_o)) (= (= (@ (@ produc4996980317674386579unit_o A4) (lambda ((Uu product_unit)) B5)) bot_bo3195362268743713342unit_o) (or (= B5 bot_bot_set_o) (= A4 bot_bo3957492148770167129t_unit)))) (forall ((X2 (-> char int)) (Ya (-> char int)) (Y3 (-> char Bool)) (Xa2 (-> char Bool)) (R3 (-> int Bool Bool)) (Ra (-> int Bool Bool))) (=> (= X2 Ya) (=> (= Y3 Xa2) (=> (forall ((Z3 int) (Yb Bool)) (=> (@ (@ member_int Z3) (@ (@ image_char_int Ya) top_top_set_char)) (=> (@ (@ member_o Yb) (@ (@ image_char_o Xa2) top_top_set_char)) (= (@ (@ R3 Z3) Yb) (@ (@ Ra Z3) Yb))))) (= (@ (@ (@ (@ bNF_re6064627146911078825_int_o (lambda ((Y2 char) (Z char)) (= Y2 Z))) R3) X2) Y3) (@ (@ (@ (@ bNF_re6064627146911078825_int_o (lambda ((Y2 char) (Z char)) (= Y2 Z))) Ra) Ya) Xa2)))))) (forall ((F (-> nat int)) (A4 set_nat)) (= (= bot_bot_set_int (@ (@ image_nat_int F) A4)) (= A4 bot_bot_set_nat))) (forall ((Z2 Bool) (C (-> int int set_o)) (A int) (B int)) (let ((_let_1 (@ member_o Z2))) (=> (@ _let_1 (@ (@ C A) B)) (@ _let_1 (@ (@ produc4257766111578684402_set_o C) (@ (@ product_Pair_int_int A) B)))))) (forall ((X2 nat) (Y3 num) (A nat)) (=> (= (@ product_fst_nat_num (@ (@ product_Pair_nat_num X2) Y3)) A) (= X2 A))) (forall ((F (-> char char))) (=> (@ finite_finite_char top_top_set_char) (=> (= (@ (@ image_char_char F) top_top_set_char) top_top_set_char) (@ (@ inj_on_char_char F) top_top_set_char)))) _let_133 _let_132 (forall ((P product_prod_nat_nat) (C (-> nat nat product_prod_nat_nat Bool)) (X2 product_prod_nat_nat)) (=> (forall ((A3 nat) (B3 nat)) (=> (= (@ (@ product_Pair_nat_nat A3) B3) P) (@ (@ (@ C A3) B3) X2))) (@ (@ (@ produc8739625826339149834_nat_o C) P) X2))) (forall ((X2 set_Pr1261947904930325089at_nat) (Y3 set_Pr1261947904930325089at_nat)) (= (@ produc3946833401584108663at_nat (@ (@ produc2922128104949294807at_nat X2) Y3)) (@ (@ produc2922128104949294807at_nat Y3) X2))) (forall ((C produc859450856879609959at_nat) (A4 set_Pr1261947904930325089at_nat)) (=> (@ (@ member8206827879206165904at_nat C) (@ id_on_2554058798563519774at_nat A4)) (not (forall ((X product_prod_nat_nat)) (=> (@ (@ member8440522571783428010at_nat X) A4) (not (= C (@ (@ produc6161850002892822231at_nat X) X)))))))) (forall ((A4 set_Product_unit) (B5 set_nat)) (let ((_let_1 (@ produc6875377002296012693it_nat A4))) (let ((_let_2 (@ image_6725568594985674851at_nat produc996414825743149016it_nat))) (let ((_let_3 (= A4 bot_bo3957492148770167129t_unit))) (and (=> (not _let_3) (= (@ _let_2 (@ _let_1 (lambda ((Uu product_unit)) B5))) B5)) (=> _let_3 (= (@ _let_2 (@ _let_1 (lambda ((Uu product_unit)) B5))) bot_bot_set_nat))))))) (forall ((Rep (-> num char)) (Abs (-> char num)) (S5 (-> char set_int)) (M (-> nat char)) (F (-> nat int)) (S6 (-> nat set_nat)) (G (-> int nat))) (let ((_let_1 (@ image_nat_int F))) (=> (@ (@ (@ type_d4396077731765706521m_char Rep) Abs) top_top_set_char) (=> (= (@ (@ comp_c3102392033783471720nt_nat S5) M) (@ (@ comp_s5620162763104547101nt_nat _let_1) S6)) (= (@ (@ comp_num_set_int_int (@ (@ comp_c8883095856794026162nt_num S5) Rep)) (@ (@ comp_nat_num_int (@ (@ comp_char_num_nat Abs) M)) G)) (@ (@ comp_s5617672292595496825nt_int _let_1) (@ (@ comp_nat_set_nat_int S6) G))))))) (forall ((I int) (J4 int) (R3 set_Pr958786334691620121nt_int)) (=> (@ (@ member5262025264175285858nt_int (@ (@ product_Pair_int_int I) J4)) R3) (@ (@ member_int J4) (@ field_int R3)))) (forall ((S5 set_se5479201105039950375at_nat)) (= (@ comple1177764198577243945_nat_o (@ (@ image_4859512832475012440_nat_o (lambda ((I2 set_Pr4329608150637261639at_nat) (X4 produc3843707927480180839at_nat)) (@ (@ member8757157785044589968at_nat X4) I2))) S5)) (lambda ((X4 produc3843707927480180839at_nat)) (@ (@ member8757157785044589968at_nat X4) (@ comple4364388969068068532at_nat S5))))) (forall ((F (-> set_Pr1261947904930325089at_nat set_Pr1261947904930325089at_nat)) (X2 set_Pr1261947904930325089at_nat) (Y3 set_Pr1261947904930325089at_nat)) (= (@ (@ produc5380969780118646373at_nat F) (@ (@ produc2922128104949294807at_nat X2) Y3)) (@ (@ produc2922128104949294807at_nat (@ F X2)) Y3))) (forall ((F (-> product_unit set_int))) (= (@ comple3628384868704368283et_int (@ (@ image_3995998972318789802et_int F) bot_bo3957492148770167129t_unit)) top_top_set_int)) (forall ((A4 set_int) (G (-> int nat)) (B5 set_int) (F (-> int nat))) (let ((_let_1 (@ (@ image_int_nat G) B5))) (=> (not (= A4 bot_bot_set_int)) (=> (@ condit2214826472909112428ve_nat _let_1) (=> (@ (@ ord_less_eq_set_int A4) B5) (=> (forall ((X int)) (=> (@ (@ member_int X) A4) (@ (@ ord_less_eq_nat (@ F X)) (@ G X)))) (@ (@ ord_less_eq_nat (@ complete_Sup_Sup_nat (@ (@ image_int_nat F) A4))) (@ complete_Sup_Sup_nat _let_1)))))))) (forall ((A4 set_Pr4329608150637261639at_nat) (F product_unit)) (=> (not (= A4 bot_bo228742789529271731at_nat)) (= (@ comple2584293577114468500t_unit (@ (@ image_7082456443403096939t_unit (lambda ((I2 produc3843707927480180839at_nat)) F)) A4)) F))) (forall ((R set_Pr958786334691620121nt_int) (A int) (B int)) (let ((_let_1 (@ field_int R))) (=> (@ (@ order_4471489696718655927on_int _let_1) R) (=> (@ (@ member_int A) _let_1) (=> (@ (@ member_int B) _let_1) (= (@ (@ member5262025264175285858nt_int (@ (@ product_Pair_int_int A) B)) R) (not (@ (@ member5262025264175285858nt_int (@ (@ product_Pair_int_int B) A)) (@ (@ minus_1052850069191792384nt_int R) id_int2))))))))) (forall ((I3 set_Pr1261947904930325089at_nat) (X2 product_unit) (F (-> product_prod_nat_nat product_unit))) (=> (not (= I3 bot_bo2099793752762293965at_nat)) (= (@ comple2584293577114468500t_unit (@ (@ image_6169909464789311569t_unit (lambda ((I2 product_prod_nat_nat)) (@ (@ inf_inf_Product_unit X2) (@ F I2)))) I3)) (@ (@ inf_inf_Product_unit X2) (@ comple2584293577114468500t_unit (@ (@ image_6169909464789311569t_unit F) I3)))))) (forall ((A4 set_Product_unit) (F (-> product_unit product_unit)) (U product_unit)) (let ((_let_1 (@ (@ image_405062704495631173t_unit F) A4))) (=> (not (= A4 bot_bo3957492148770167129t_unit)) (=> (@ condit9161856309968323677t_unit _let_1) (= (@ (@ ord_le3221252021190050221t_unit U) (@ comple2584293577114468500t_unit _let_1)) (forall ((X4 product_unit)) (=> (@ (@ member_Product_unit X4) A4) (@ (@ ord_le3221252021190050221t_unit U) (@ F X4))))))))) (forall ((F (-> int nat)) (A4 set_int) (B5 set_int)) (let ((_let_1 (@ image_int_nat F))) (= (@ _let_1 (@ (@ sup_sup_set_int A4) B5)) (@ (@ sup_sup_set_nat (@ _let_1 A4)) (@ _let_1 B5))))) _let_131 (forall ((X2 Bool) (A4 set_o) (C nat)) (=> (@ (@ member_o X2) A4) (= (@ (@ image_o_nat (lambda ((X4 Bool)) C)) A4) (@ (@ insert_nat C) bot_bot_set_nat)))) (forall ((B5 set_int) (F (-> int int)) (A4 set_int)) (=> (@ finite_finite_int B5) (=> (@ (@ ord_less_eq_set_int B5) (@ (@ image_int_int F) A4)) (exists ((C2 set_int)) (and (@ (@ ord_less_eq_set_int C2) A4) (= B5 (@ (@ image_int_int F) C2)) (@ finite_finite_int C2)))))) (forall ((F (-> int int)) (A4 set_int)) (=> (@ (@ inj_on_int_int F) A4) (@ (@ inj_on6435365835345961783et_int (@ image_int_int F)) (@ finite_Fpow_int A4)))) (forall ((A4 set_o) (B5 set_int) (G (-> int product_unit)) (F (-> Bool product_unit))) (=> (forall ((I4 Bool)) (=> (@ (@ member_o I4) A4) (exists ((X6 int)) (and (@ (@ ord_le3221252021190050221t_unit (@ G X6)) (@ F I4)) (@ (@ member_int X6) B5))))) (=> (forall ((J2 int)) (=> (@ (@ member_int J2) B5) (exists ((X6 Bool)) (and (@ (@ member_o X6) A4) (@ (@ ord_le3221252021190050221t_unit (@ F X6)) (@ G J2)))))) (= (@ comple2584293577114468500t_unit (@ (@ image_o_Product_unit F) A4)) (@ comple2584293577114468500t_unit (@ (@ image_5846526143423701914t_unit G) B5)))))) (forall ((F (-> produc1319942482725812455at_nat Bool)) (A set_Pr4329608150637261639at_nat) (B set_Pr4329608150637261639at_nat)) (=> (@ (@ (@ produc447603880154497357_nat_o F) A) B) (@ F (@ (@ produc9060074326276436823at_nat A) B)))) (forall ((F (-> nat int)) (G (-> nat int)) (A4 set_nat)) (= (@ condit2212336002400062152ve_int (@ (@ image_nat_int (lambda ((X4 nat)) (@ (@ sup_sup_int (@ F X4)) (@ G X4)))) A4)) (and (@ condit2212336002400062152ve_int (@ (@ image_nat_int G) A4)) (@ condit2212336002400062152ve_int (@ (@ image_nat_int F) A4))))) (forall ((F (-> Bool nat)) (A4 set_o) (X2 nat) (B5 set_o)) (=> (@ (@ inj_on_o_nat F) A4) (=> (@ (@ member_nat X2) (@ (@ image_o_nat F) A4)) (=> (@ (@ ord_less_eq_set_o A4) B5) (@ (@ member_o (@ (@ (@ the_inv_into_o_nat A4) F) X2)) B5))))) (forall ((I3 set_nat) (F (-> nat product_unit)) (X2 product_unit)) (=> (not (= I3 bot_bot_set_nat)) (=> (forall ((I4 nat)) (=> (@ (@ member_nat I4) I3) (= (@ F I4) X2))) (= (@ comple4687483117567863418t_unit (@ (@ image_8730104196221521654t_unit F) I3)) X2)))) (forall ((Inf (-> set_num num)) (G (-> nat num)) (F (-> int nat)) (A4 set_int)) (= (@ Inf (@ (@ image_nat_num G) (@ (@ image_int_nat F) A4))) (@ Inf (@ (@ image_int_num (@ (@ comp_nat_num_int G) F)) A4)))) (forall ((F (-> int nat)) (A4 (-> nat int)) (I3 set_nat)) (let ((_let_1 (@ (@ image_nat_int A4) I3))) (=> (@ order_mono_int_nat F) (=> (@ condit1735850657277959132ow_int _let_1) (=> (not (= I3 bot_bot_set_nat)) (@ (@ ord_less_eq_nat (@ F (@ complete_Inf_Inf_int _let_1))) (@ complete_Inf_Inf_nat (@ (@ image_nat_nat (lambda ((X4 nat)) (@ F (@ A4 X4)))) I3)))))))) (forall ((F (-> int nat)) (A4 set_int) (B5 set_nat)) (let ((_let_1 (@ image_int_nat F))) (=> (@ (@ ord_less_eq_set_nat (@ _let_1 A4)) B5) (@ (@ ord_le6893508408891458716et_nat (@ (@ image_4702325430467532143et_nat _let_1) (@ finite_Fpow_int A4))) (@ finite_Fpow_nat B5))))) (forall ((A4 set_Pr1261947904930325089at_nat)) (= (@ collec3392354462482085612at_nat (lambda ((X4 product_prod_nat_nat)) (@ (@ member8440522571783428010at_nat X4) A4))) A4)) (forall ((F (-> int nat)) (G (-> int nat)) (A4 set_int)) (= (@ condit2214826472909112428ve_nat (@ (@ image_int_nat (lambda ((X4 int)) (@ (@ sup_sup_nat (@ F X4)) (@ G X4)))) A4)) (and (@ condit2214826472909112428ve_nat (@ (@ image_int_nat G) A4)) (@ condit2214826472909112428ve_nat (@ (@ image_int_nat F) A4))))) (forall ((F (-> char product_prod_nat_nat)) (A4 set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ image_8382823969816519465at_nat F))) (= (@ _let_1 (@ (@ vimage8942442433166402803at_nat F) A4)) (@ (@ inf_in2572325071724192079at_nat A4) (@ _let_1 top_top_set_char))))) (forall ((F (-> nat nat product_prod_nat_nat product_prod_nat_nat)) (A nat) (B nat)) (= (@ (@ produc27273713700761075at_nat F) (@ (@ product_Pair_nat_nat A) B)) (@ (@ F A) B))) (forall ((G (-> nat nat)) (F (-> nat nat)) (A4 set_nat)) (= (@ complete_Inf_Inf_nat (@ (@ image_nat_nat G) (@ (@ image_nat_nat F) A4))) (@ complete_Inf_Inf_nat (@ (@ image_nat_nat (@ (@ comp_nat_nat_nat G) F)) A4)))) (forall ((A4 set_Pr8693737435421807431at_nat) (F (-> nat set_Pr8693737435421807431at_nat))) (= (@ (@ sup_su718114333110466843at_nat A4) (@ comple2748534634209756852at_nat (@ (@ image_4592875511192039216at_nat F) bot_bot_set_nat))) A4)) (forall ((Z2 product_prod_nat_nat) (C (-> nat num set_Pr1261947904930325089at_nat)) (P product_prod_nat_num)) (=> (@ (@ member8440522571783428010at_nat Z2) (@ (@ produc859037500352796105at_nat C) P)) (not (forall ((X nat) (Y num)) (=> (= P (@ (@ product_Pair_nat_num X) Y)) (not (@ (@ member8440522571783428010at_nat Z2) (@ (@ C X) Y)))))))) (forall ((Rep (-> nat rat)) (Abs (-> rat nat)) (M (-> rat rat))) (=> (@ (@ (@ type_d5615363888691252950at_rat Rep) Abs) top_top_set_rat) (=> (= M id_rat) (= (@ (@ comp_rat_nat_nat (@ (@ comp_rat_nat_rat Abs) M)) Rep) id_nat)))) _let_130 (forall ((F (-> product_prod_nat_nat product_prod_nat_nat product_prod_nat_nat))) (= (@ produc27273713700761075at_nat (lambda ((X4 nat) (Y5 nat) (__flatten_var_0 product_prod_nat_nat)) (@ (@ F (@ (@ product_Pair_nat_nat X4) Y5)) __flatten_var_0))) F)) (forall ((P2 (-> set_Pr1261947904930325089at_nat set_Pr1261947904930325089at_nat Bool)) (X2 set_Pr1261947904930325089at_nat) (Y3 set_Pr1261947904930325089at_nat) (A produc3843707927480180839at_nat)) (=> (@ (@ P2 X2) Y3) (=> (= A (@ (@ produc2922128104949294807at_nat X2) Y3)) (@ (@ P2 (@ produc6011863565407846595at_nat A)) (@ produc2937545259423399429at_nat A))))) (forall ((F (-> char int)) (X2 char)) (@ (@ member_int (@ F X2)) (@ (@ image_char_int F) top_top_set_char))) (forall ((B Bool) (F (-> char Bool)) (X2 char)) (=> (= B (@ F X2)) (@ (@ member_o B) (@ (@ image_char_o F) top_top_set_char)))) _let_129 (forall ((G (-> Bool rat)) (C3 set_o) (B5 set_o) (X2 Bool)) (let ((_let_1 (@ (@ sup_sup_set_o B5) (@ (@ insert_o X2) bot_bot_set_o)))) (=> (@ (@ inj_on_o_rat G) C3) (=> (@ (@ ord_less_eq_set_o C3) _let_1) (@ (@ member_rat_o (lambda ((I2 rat)) (let ((_let_1 (@ (@ member_rat I2) (@ (@ image_o_rat G) C3)))) (and (=> (not _let_1) X2) (=> _let_1 (@ (@ (@ the_inv_into_o_rat C3) G) I2)))))) (@ (@ bNF_We6195730058148253354_rat_o top_top_set_rat) _let_1)))))) (forall ((F (-> nat int)) (A4 set_nat) (B5 set_nat)) (let ((_let_1 (@ image_nat_int F))) (=> (@ (@ inj_on_nat_int F) top_top_set_nat) (= (= (@ _let_1 A4) (@ _let_1 B5)) (= A4 B5))))) (= id_on_nat (lambda ((A6 set_nat)) (@ comple5685304695842803022at_nat (@ (@ image_7178329752028323786at_nat (lambda ((X4 nat)) (@ (@ insert8211810215607154385at_nat (@ (@ product_Pair_nat_nat X4) X4)) bot_bo2099793752762293965at_nat))) A6)))) (forall ((A set_nat) (B5 set_set_nat)) (let ((_let_1 (@ inf_inf_set_nat A))) (= (@ _let_1 (@ comple7399068483239264473et_nat B5)) (@ comple7399068483239264473et_nat (@ (@ image_7916887816326733075et_nat _let_1) B5))))) (forall ((X2 rat) (Y3 rat)) (= (@ (@ (@ if_rat true) X2) Y3) X2)) _let_128 (forall ((F (-> int int int)) (G (-> product_prod_int_int int))) (=> (forall ((X int) (Y int)) (= (@ (@ F X) Y) (@ G (@ (@ product_Pair_int_int X) Y)))) (= (@ produc8211389475949308722nt_int F) G))) (forall ((X2 nat) (A4 set_nat) (F (-> nat nat))) (let ((_let_1 (@ (@ image_nat_nat F) A4))) (=> (@ (@ member_nat X2) A4) (=> (@ condit2214826472909112428ve_nat _let_1) (@ (@ ord_less_eq_nat (@ F X2)) (@ complete_Sup_Sup_nat _let_1)))))) (forall ((F (-> char nat)) (A nat) (X2 char)) (=> (= (@ (@ image_char_nat F) top_top_set_char) (@ (@ insert_nat A) bot_bot_set_nat)) (= (@ F X2) A))) (forall ((B Bool) (F (-> nat Bool)) (A4 set_nat)) (=> (@ (@ member_o B) (@ (@ image_nat_o F) A4)) (not (forall ((X nat)) (=> (= B (@ F X)) (not (@ (@ member_nat X) A4))))))) (forall ((F (-> nat Bool)) (G (-> nat nat)) (L1 (-> Bool Bool)) (L2 (-> nat Bool)) (H (-> nat nat)) (R (-> nat Bool))) (let ((_let_1 (@ comp_o_o_nat L1))) (let ((_let_2 (@ comp_nat_o_nat F))) (=> (= (@ _let_2 G) (@ _let_1 L2)) (=> (= (@ (@ comp_nat_o_nat L2) H) R) (= (@ _let_2 (@ (@ comp_nat_nat_nat G) H)) (@ _let_1 R))))))) (forall ((A4 set_nat)) (= (@ complete_Sup_Sup_nat (@ (@ image_nat_nat (lambda ((X4 nat)) X4)) A4)) (@ complete_Sup_Sup_nat A4))) (forall ((B rat) (F (-> nat rat)) (A4 set_nat)) (=> (@ (@ member_rat B) (@ (@ image_nat_rat F) A4)) (not (forall ((X nat)) (=> (= B (@ F X)) (not (@ (@ member_nat X) A4))))))) (forall ((X2 (-> nat Bool)) (Ya (-> nat Bool)) (F (-> Bool Bool)) (G (-> Bool Bool))) (=> (= X2 Ya) (=> (forall ((Z3 Bool)) (=> (@ (@ member_o Z3) (@ (@ image_nat_o Ya) top_top_set_nat)) (= (@ F Z3) (@ G Z3)))) (= (@ (@ comp_o_o_nat F) X2) (@ (@ comp_o_o_nat G) Ya))))) (forall ((B5 set_Pr1261947904930325089at_nat) (A4 set_Pr1261947904930325089at_nat) (P2 (-> product_prod_nat_nat Bool))) (let ((_let_1 (@ ord_le3146513528884898305at_nat B5))) (=> (@ _let_1 A4) (= (@ _let_1 (@ collec3392354462482085612at_nat (lambda ((X4 product_prod_nat_nat)) (and (@ P2 X4) (@ (@ member8440522571783428010at_nat X4) A4))))) (forall ((X4 product_prod_nat_nat)) (=> (@ (@ member8440522571783428010at_nat X4) B5) (@ P2 X4))))))) _let_127 (forall ((X5 set_nat) (P2 (-> nat Bool))) (@ (@ ord_less_eq_set_nat (@ collect_nat (lambda ((X4 nat)) (and (@ (@ member_nat X4) X5) (@ P2 X4))))) X5)) (forall ((F (-> nat nat)) (A4 set_nat) (B5 set_nat)) (let ((_let_1 (@ image_nat_nat F))) (=> (@ (@ inj_on_nat_nat F) top_top_set_nat) (= (@ (@ ord_less_eq_set_nat (@ _let_1 A4)) (@ _let_1 B5)) (@ (@ ord_less_eq_set_nat A4) B5))))) (forall ((A set_Pr1261947904930325089at_nat) (B5 set_se7855581050983116737at_nat)) (let ((_let_1 (@ inf_in2572325071724192079at_nat A))) (= (@ _let_1 (@ comple5685304695842803022at_nat B5)) (@ comple5685304695842803022at_nat (@ (@ image_3684629450409544005at_nat _let_1) B5))))) (forall ((Z2 nat) (C (-> int int set_nat)) (P product_prod_int_int)) (=> (@ (@ member_nat Z2) (@ (@ produc4251311855443802252et_nat C) P)) (not (forall ((X int) (Y int)) (=> (= P (@ (@ product_Pair_int_int X) Y)) (not (@ (@ member_nat Z2) (@ (@ C X) Y)))))))) (forall ((Rep (-> product_unit Bool)) (Abs (-> Bool product_unit)) (X2 nat) (S5 (-> Bool set_nat)) (Y3 Bool)) (let ((_let_1 (@ member_nat X2))) (=> (@ (@ (@ type_d6188575255521822967unit_o Rep) Abs) top_top_set_o) (=> (@ _let_1 (@ (@ (@ comp_o9190160103024335696t_unit S5) Rep) (@ Abs Y3))) (@ _let_1 (@ S5 Y3)))))) (forall ((A4 set_nat) (B5 set_Pr1261947904930325089at_nat)) (=> (@ finite_finite_nat A4) (=> (@ finite6177210948735845034at_nat B5) (=> (@ (@ ord_less_eq_nat (@ finite_card_nat A4)) (@ finite711546835091564841at_nat B5)) (exists ((F5 (-> nat product_prod_nat_nat))) (and (@ (@ ord_le3146513528884898305at_nat (@ (@ 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(forall ((A4 set_nat) (B5 (-> nat set_Pr1261947904930325089at_nat))) (=> (@ finite_finite_nat A4) (=> (forall ((A3 nat)) (=> (@ (@ member_nat A3) A4) (@ finite6177210948735845034at_nat (@ B5 A3)))) (@ finite6177210948735845034at_nat (@ comple5685304695842803022at_nat (@ (@ image_7178329752028323786at_nat B5) A4)))))) (forall ((K nat) (I3 set_nat) (A4 (-> nat set_nat))) (let ((_let_1 (@ comple7399068483239264473et_nat (@ (@ image_nat_set_nat A4) I3)))) (=> (@ (@ member_nat K) I3) (= (@ (@ sup_sup_set_nat (@ A4 K)) _let_1) _let_1)))) (forall ((G (-> nat nat)) (F (-> nat nat)) (A4 set_nat)) (= (@ complete_Sup_Sup_nat (@ (@ image_nat_nat G) (@ (@ image_nat_nat F) A4))) (@ complete_Sup_Sup_nat (@ (@ image_nat_nat (@ (@ comp_nat_nat_nat G) F)) A4)))) (= (@ _let_125 top_top_set_int) top_top_set_int) (forall ((A product_prod_nat_nat) (P2 (-> product_prod_nat_nat Bool))) (= (@ (@ member8440522571783428010at_nat A) (@ collec3392354462482085612at_nat P2)) (@ P2 A))) (forall ((S5 set_nat) (T3 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(=> (= (@ (@ comp_num_num_nat F) G) L) (= (@ (@ comp_num_num_int F) (@ (@ comp_nat_num_int G) H)) (@ (@ comp_nat_num_int L) H)))) (forall ((A4 set_o) (F (-> Bool int)) (M int)) (=> (forall ((X Bool)) (=> (@ (@ member_o X) A4) (@ (@ ord_less_eq_int (@ F X)) M))) (@ condit2212336002400062152ve_int (@ (@ image_o_int F) A4)))) (forall ((U Bool) (A4 set_o) (A nat) (B5 (-> Bool set_nat))) (=> (@ (@ member_o U) A4) (= (@ comple7806235888213564991et_nat (@ (@ image_o_set_nat (lambda ((X4 Bool)) (@ (@ insert_nat A) (@ B5 X4)))) A4)) (@ (@ insert_nat A) (@ comple7806235888213564991et_nat (@ (@ image_o_set_nat B5) A4)))))) (forall ((F (-> int nat)) (Fa (-> nat nat)) (G (-> int int)) (Ga (-> nat nat))) (= (@ (@ comp_P3488689526429045841nt_nat (@ (@ basic_1875480505010237490nt_nat F) Fa)) (@ (@ produc5039722323474524658at_nat G) Ga)) (@ (@ basic_1875480505010237490nt_nat (@ (@ comp_int_nat_int F) G)) (@ (@ comp_nat_nat_nat Fa) Ga)))) (forall ((A4 set_nat) (B5 (-> nat set_int)) (F (-> int int))) (=> 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(@ (@ product_Pair_int_int A) A)) id_int2)) (forall ((B5 set_int) (F (-> nat int)) (A4 set_nat)) (=> (@ finite_finite_int B5) (=> (@ (@ ord_less_eq_set_int B5) (@ (@ image_nat_int F) A4)) (exists ((C2 set_nat)) (and (@ finite_finite_nat C2) (= B5 (@ (@ image_nat_int F) C2)) (@ (@ ord_less_eq_set_nat C2) A4)))))) (forall ((A4 set_Pr1261947904930325089at_nat) (F (-> product_prod_nat_nat product_unit)) (X2 product_unit)) (=> (forall ((I4 product_prod_nat_nat)) (=> (@ (@ member8440522571783428010at_nat I4) A4) (@ (@ ord_le3221252021190050221t_unit (@ F I4)) X2))) (=> (forall ((Y product_unit)) (=> (forall ((I5 product_prod_nat_nat)) (=> (@ (@ member8440522571783428010at_nat I5) A4) (@ (@ ord_le3221252021190050221t_unit (@ F I5)) Y))) (@ (@ ord_le3221252021190050221t_unit X2) Y))) (= (@ comple4687483117567863418t_unit (@ (@ image_6169909464789311569t_unit F) A4)) X2)))) (forall ((I3 set_int) (C product_unit) (F (-> int product_unit))) (=> (not (= I3 bot_bot_set_int)) (=> (forall ((I4 int)) (=> (@ (@ member_int I4) I3) (@ (@ ord_le3221252021190050221t_unit C) (@ F I4)))) (= (= (@ comple4687483117567863418t_unit (@ (@ image_5846526143423701914t_unit F) I3)) C) (forall ((X4 int)) (=> (@ (@ member_int X4) I3) (= (@ F X4) C))))))) (forall ((F (-> int int))) (= (@ (@ image_int_int F) bot_bot_set_int) bot_bot_set_int)) (forall ((F (-> rat rat))) (= (= (@ (@ image_rat_rat F) top_top_set_rat) top_top_set_rat) (forall ((Y5 rat)) (exists ((X4 rat)) (= Y5 (@ F X4)))))) (forall ((F (-> nat set_Product_unit))) (= (@ comple3349607820504768346t_unit (@ (@ image_4824033694279209942t_unit F) bot_bot_set_nat)) bot_bo3957492148770167129t_unit)) (forall ((X2 nat) (Y3 nat)) (= (@ basic_fsts_nat_nat (@ (@ product_Pair_nat_nat X2) Y3)) (@ (@ insert_nat X2) bot_bot_set_nat))) (forall ((G (-> nat Bool)) (H (-> nat nat)) (R12 (-> Bool Bool)) (R23 (-> nat Bool)) (F (-> Bool Bool)) (L (-> Bool Bool))) (=> (= (@ (@ comp_nat_o_nat G) H) (@ (@ comp_o_o_nat R12) R23)) (=> (= (@ (@ comp_o_o_o F) R12) L) (= (@ (@ comp_nat_o_nat (@ (@ comp_o_o_nat F) G)) H) (@ (@ comp_o_o_nat L) R23))))) (forall ((A4 set_int) (B5 (-> int set_nat))) (=> (@ finite_finite_int A4) (=> (forall ((A3 int)) (=> (@ (@ member_int A3) A4) (@ finite_finite_nat (@ B5 A3)))) (@ finite_finite_nat (@ comple7399068483239264473et_nat (@ (@ image_int_set_nat B5) A4)))))) (forall ((F (-> int int)) (A4 set_int)) (= (@ comple3221217463730067765et_int (@ (@ image_int_set_int (lambda ((X4 int)) (@ (@ insert_int (@ F X4)) bot_bot_set_int))) A4)) (@ (@ image_int_int F) A4))) (forall ((I int) (A4 set_int) (F (-> int product_unit)) (U product_unit)) (=> (@ (@ member_int I) A4) (=> (@ (@ ord_le3221252021190050221t_unit (@ F I)) U) (@ (@ ord_le3221252021190050221t_unit (@ comple2584293577114468500t_unit (@ (@ image_5846526143423701914t_unit F) A4))) U)))) _let_124 (forall ((A4 set_o) (B5 (-> Bool set_Product_unit)) (F (-> product_unit int))) (=> (not (= A4 bot_bot_set_o)) (=> (forall ((X Bool)) (=> (@ (@ member_o X) A4) (not (= (@ 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set_Pr1261947904930325089at_nat num))) (=> (@ (@ member8757157785044589968at_nat (@ (@ produc2922128104949294807at_nat A) B)) R3) (@ (@ member9148766508732265716at_num (@ (@ product_Pair_nat_num (@ F A)) (@ G B))) (@ (@ image_8033574621161215657at_num (@ (@ produc3932168101365401472at_num F) G)) R3)))) (forall ((A4 (-> product_prod_nat_nat product_prod_nat_nat Bool)) (B5 (-> product_prod_nat_nat int Bool))) (=> (@ right_4094035864313884895at_nat A4) (=> (@ right_1157779049177982926at_int B5) (@ right_1157779049177982926at_int (@ (@ relcom8911704206367525917at_int A4) B5))))) (forall ((F (-> produc859450856879609959at_nat Bool)) (A4 set_Pr8693737435421807431at_nat) (B5 set_Pr8693737435421807431at_nat)) (let ((_let_1 (@ inj_on991952103320416098_nat_o F))) (let ((_let_2 (@ image_3275415580317762038_nat_o F))) (= (@ _let_1 (@ (@ sup_su718114333110466843at_nat A4) B5)) (and (@ _let_1 B5) (= (@ (@ inf_inf_set_o (@ _let_2 (@ (@ minus_8321449233255521966at_nat A4) B5))) (@ _let_2 (@ (@ 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refl_on_nat A4) R)))) (forall ((X2 nat) (Y3 nat)) (= (@ product_swap_nat_nat (@ (@ product_Pair_nat_nat X2) Y3)) (@ (@ product_Pair_nat_nat Y3) X2))) (forall ((P2 (-> ref_a ref_a Bool)) (Q2 (-> ref_a heap_e7401611519738050253t_unit Bool))) (= produc1126150082675451753t_unit (@ (@ comp_P8019343326919024234t_unit produc1126150082675451753t_unit) (@ (@ bNF_sn8323453914685745821t_unit P2) Q2)))) (forall ((A4 set_int) (C nat)) (let ((_let_1 (= A4 bot_bot_set_int))) (and (=> _let_1 (= (@ (@ image_int_nat (lambda ((X4 int)) C)) A4) bot_bot_set_nat)) (=> (not _let_1) (= (@ (@ image_int_nat (lambda ((X4 int)) C)) A4) (@ (@ insert_nat C) bot_bot_set_nat)))))) _let_122 _let_121 (forall ((C3 set_o) (A4 set_o) (B5 (-> Bool set_o))) (let ((_let_1 (= C3 bot_bot_set_o))) (and (=> (not _let_1) (= (@ comple90263536869209701_set_o (@ (@ image_o_set_o (lambda ((X4 Bool)) (@ (@ sup_sup_set_o A4) (@ B5 X4)))) C3)) (@ (@ sup_sup_set_o A4) (@ comple90263536869209701_set_o (@ (@ image_o_set_o B5) C3))))) (=> _let_1 (= (@ comple90263536869209701_set_o (@ (@ image_o_set_o (lambda ((X4 Bool)) (@ (@ sup_sup_set_o A4) (@ B5 X4)))) C3)) bot_bot_set_o))))) (forall ((A4 set_Pr8693737435421807431at_nat) (F (-> Bool set_Pr8693737435421807431at_nat))) (= (@ (@ sup_su718114333110466843at_nat A4) (@ comple2748534634209756852at_nat (@ (@ image_8493167801588156084at_nat F) bot_bot_set_o))) A4)) (forall ((F (-> Bool nat)) (G (-> Bool Bool)) (L1 (-> nat nat)) (L2 (-> Bool nat)) (H (-> nat Bool)) (R (-> nat nat))) (=> (= (@ (@ comp_o_nat_o F) G) (@ (@ comp_nat_nat_o L1) L2)) (=> (= (@ (@ comp_o_nat_nat L2) H) R) (= (@ (@ comp_o_nat_nat F) (@ (@ comp_o_o_nat G) H)) (@ (@ comp_nat_nat_nat L1) R))))) (forall ((C3 set_o) (A4 (-> Bool set_Product_unit)) (B5 set_Product_unit)) (let ((_let_1 (= C3 bot_bot_set_o))) (and (=> (not _let_1) (= (@ comple3349607820504768346t_unit (@ (@ image_663195431845683034t_unit (lambda ((X4 Bool)) (@ (@ sup_su793286257634532545t_unit (@ A4 X4)) B5))) C3)) (@ (@ sup_su793286257634532545t_unit (@ comple3349607820504768346t_unit (@ (@ image_663195431845683034t_unit A4) C3))) B5))) (=> _let_1 (= (@ comple3349607820504768346t_unit (@ (@ image_663195431845683034t_unit (lambda ((X4 Bool)) (@ (@ sup_su793286257634532545t_unit (@ A4 X4)) B5))) C3)) bot_bo3957492148770167129t_unit))))) (forall ((F (-> nat product_unit)) (A4 set_nat)) (= (= bot_bo3957492148770167129t_unit (@ (@ image_8730104196221521654t_unit F) A4)) (= A4 bot_bot_set_nat))) (forall ((R (-> product_prod_nat_nat product_prod_nat_nat Bool)) (S2 (-> product_prod_nat_nat int Bool)) (T2 (-> int int Bool))) (let ((_let_1 (@ relcom8911704206367525917at_int R))) (= (@ (@ relcom2949942408940504938nt_int (@ _let_1 S2)) T2) (@ _let_1 (@ (@ relcom2949942408940504938nt_int S2) T2))))) _let_120 (forall ((F (-> product_unit product_unit))) (= (@ (@ image_405062704495631173t_unit F) bot_bo3957492148770167129t_unit) bot_bo3957492148770167129t_unit)) (forall ((S5 set_se5479201105039950375at_nat)) (= (@ comple8322679762649017525_nat_o (@ (@ image_6595146019508340652_nat_o (lambda ((I2 set_Pr4329608150637261639at_nat) (X4 set_Pr1261947904930325089at_nat) (Y5 set_Pr1261947904930325089at_nat)) (@ (@ member8757157785044589968at_nat (@ (@ produc2922128104949294807at_nat X4) Y5)) I2))) S5)) (lambda ((X4 set_Pr1261947904930325089at_nat) (Y5 set_Pr1261947904930325089at_nat)) (@ (@ member8757157785044589968at_nat (@ (@ produc2922128104949294807at_nat X4) Y5)) (@ comple6751905152567503566at_nat S5))))) (forall ((C3 set_o) (A4 set_nat) (B5 (-> Bool set_nat))) (let ((_let_1 (@ (@ minus_minus_set_nat A4) (@ comple7399068483239264473et_nat (@ (@ image_o_set_nat B5) C3))))) (let ((_let_2 (= C3 bot_bot_set_o))) (and (=> (not _let_2) (= _let_1 (@ comple7806235888213564991et_nat (@ (@ image_o_set_nat (lambda ((X4 Bool)) (@ (@ minus_minus_set_nat A4) (@ B5 X4)))) C3)))) (=> _let_2 (= _let_1 A4)))))) (forall ((X2 int) (Y3 int) (A int)) (=> (= (@ product_snd_int_int (@ (@ product_Pair_int_int X2) Y3)) A) (= Y3 A))) _let_119 (forall ((N3 nat)) (let ((_let_1 (@ set_or4665077453230672383an_nat zero_zero_nat))) (= (@ _let_1 (@ suc N3)) (@ (@ insert_nat zero_zero_nat) (@ (@ image_nat_nat suc) (@ _let_1 N3)))))) (forall ((F (-> nat rat)) (G (-> int nat)) (A4 set_int)) (= (@ (@ image_nat_rat F) (@ (@ image_int_nat G) A4)) (@ (@ image_int_rat (lambda ((X4 int)) (@ F (@ G X4)))) A4))) (forall ((F (-> product_unit nat)) (A4 (-> Bool product_unit)) (I3 set_o)) (let ((_let_1 (@ (@ image_o_Product_unit A4) I3))) (=> (@ order_7096114683908731117it_nat F) (=> (@ condit2080475194861589617t_unit _let_1) (=> (not (= I3 bot_bot_set_o)) (@ (@ ord_less_eq_nat (@ complete_Sup_Sup_nat (@ (@ image_o_nat (lambda ((X4 Bool)) (@ F (@ A4 X4)))) I3))) (@ F (@ comple4687483117567863418t_unit _let_1)))))))) (forall ((I Bool) (C3 set_o) (G (-> Bool int)) (X2 Bool)) (=> (@ (@ member_o I) C3) (=> (@ (@ inj_on_o_int G) C3) (= (@ (@ (@ comp_int_o_o (lambda ((I2 int)) (let ((_let_1 (@ (@ member_int I2) (@ (@ image_o_int G) C3)))) (and (=> (not _let_1) X2) (=> _let_1 (@ (@ (@ the_inv_into_o_int C3) G) I2)))))) G) I) (@ id_o I))))) (forall ((Inf (-> set_rat rat)) (G (-> nat rat)) (F (-> int nat)) (A4 set_int)) (= (@ Inf (@ (@ image_nat_rat G) (@ (@ image_int_nat F) A4))) (@ Inf (@ (@ image_int_rat (@ (@ comp_nat_rat_int G) F)) A4)))) (forall ((X2 produc3843707927480180839at_nat)) (@ (@ total_1513685709984341995at_nat (@ (@ insert9069300056098147895at_nat X2) bot_bo228742789529271731at_nat)) (@ (@ insert398606708087465655at_nat (@ (@ produc2335810615602371415at_nat X2) X2)) bot_bo7193250159860175667at_nat))) (forall ((F (-> Bool Bool)) (G (-> nat Bool)) (A4 set_nat) (X2 Bool)) (let ((_let_1 (@ (@ image_nat_o G) A4))) (let ((_let_2 (@ the_inv_into_nat_o A4))) (=> (@ (@ inj_on_o_o F) _let_1) (=> (@ (@ inj_on_nat_o G) A4) (=> (@ (@ member_o X2) (@ (@ image_o_o F) _let_1)) (= (@ (@ _let_2 (@ (@ comp_o_o_nat F) G)) X2) (@ (@ (@ comp_o_nat_o (@ _let_2 G)) (@ (@ the_inv_into_o_o _let_1) F)) X2)))))))) _let_118 (forall ((K Bool) (I3 set_o) (A4 (-> Bool set_Pr1261947904930325089at_nat))) (let ((_let_1 (@ comple1930127330929219688at_nat (@ (@ image_7077428525161401678at_nat A4) I3)))) (=> (@ (@ member_o K) I3) (= (@ (@ inf_in2572325071724192079at_nat (@ A4 K)) _let_1) _let_1)))) (forall ((P2 (-> nat Bool)) (F (-> nat produc859450856879609959at_nat)) (G (-> nat produc859450856879609959at_nat)) (S5 set_nat)) (let ((_let_1 (@ inf_inf_set_nat S5))) (= (@ (@ image_3276603626957510736at_nat (lambda ((X4 nat)) (@ (@ (@ if_Pro4507677147265585453at_nat (@ P2 X4)) (@ F X4)) (@ G X4)))) S5) (@ (@ sup_su718114333110466843at_nat (@ (@ image_3276603626957510736at_nat F) (@ _let_1 (@ collect_nat P2)))) (@ (@ image_3276603626957510736at_nat G) (@ _let_1 (@ collect_nat (lambda ((X4 nat)) (not (@ P2 X4)))))))))) (forall ((A nat) (B nat) (A2 nat) (B2 nat)) (= (= (@ (@ product_Pair_nat_nat A) B) (@ (@ product_Pair_nat_nat A2) B2)) (and (= B B2) (= A A2)))) (forall ((X2 int) (A4 set_int) (F (-> int nat)) (Y3 nat)) (let ((_let_1 (@ image_int_nat F))) (let ((_let_2 (@ (@ image_int_nat (@ (@ (@ fun_upd_int_nat F) X2) Y3)) A4))) (let ((_let_3 (@ (@ member_int X2) A4))) (and (=> (not _let_3) (= _let_2 (@ _let_1 A4))) (=> _let_3 (= _let_2 (@ (@ insert_nat Y3) (@ _let_1 (@ (@ minus_minus_set_int A4) (@ (@ insert_int X2) bot_bot_set_int))))))))))) (forall ((B5 (-> rat set_nat)) (F (-> nat rat)) (A4 set_nat)) (= (@ comple7399068483239264473et_nat (@ (@ image_nat_set_nat (lambda ((A5 nat)) (@ B5 (@ F A5)))) A4)) (@ comple7399068483239264473et_nat (@ (@ image_rat_set_nat B5) (@ (@ image_nat_rat F) A4))))) (forall ((F (-> rat int)) (B int)) (=> (@ (@ inj_on_rat_int F) top_top_set_rat) (= (@ (@ member_int B) (@ (@ image_rat_int F) top_top_set_rat)) (exists ((X4 rat)) (and (= B (@ F X4)) (forall ((Y5 rat)) (=> (= B (@ F Y5)) (= Y5 X4)))))))) (= product_fst_int_int (@ (@ comp_P5356232565778667509nt_int product_snd_int_int) (@ produc4245557441103728435nt_int (lambda ((X4 int) (Y5 int)) (@ (@ 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the_Pr8265262403268641490at_num (@ produc4927758841916487424_num_o (lambda ((X7 nat) (Y6 num)) (and (= X2 X7) (= Y3 Y6))))) (@ (@ product_Pair_nat_num X2) Y3))) (forall ((F1 (-> nat num)) (F22 (-> int nat)) (G1 (-> nat nat)) (G22 (-> nat nat))) (= (@ (@ produc2608876591208338912at_nat (@ (@ comp_nat_num_int F1) F22)) (@ (@ comp_nat_nat_nat G1) G22)) (@ (@ comp_P5124699952429557552nt_nat (@ (@ produc4918694523301289860at_nat F1) G1)) (@ (@ produc4668068763237680022at_nat F22) G22)))) (forall ((X2 produc3843707927480180839at_nat)) (@ (@ order_2711500226769404828at_nat (@ (@ insert9069300056098147895at_nat X2) bot_bo228742789529271731at_nat)) (@ (@ insert398606708087465655at_nat (@ (@ produc2335810615602371415at_nat X2) X2)) bot_bo7193250159860175667at_nat))) (forall ((F (-> nat nat)) (A4 set_nat) (B5 set_nat)) (let ((_let_1 (@ image_nat_nat F))) (=> (@ (@ ord_less_eq_set_nat (@ _let_1 A4)) B5) (@ (@ ord_le6893508408891458716et_nat (@ (@ image_7916887816326733075et_nat _let_1) (@ finite_Fpow_nat A4))) (@ finite_Fpow_nat B5))))) (forall ((F (-> nat product_prod_nat_nat)) (A4 set_nat) (B5 set_Pr1261947904930325089at_nat)) (=> (@ (@ inj_on5538052773655684606at_nat F) A4) (=> (@ (@ ord_le3146513528884898305at_nat (@ (@ image_5846123807819985514at_nat F) A4)) B5) (=> (@ finite6177210948735845034at_nat B5) (@ finite_finite_nat A4))))) (forall ((A4 set_o) (M3 nat) (F (-> Bool nat))) (=> (forall ((X Bool)) (=> (@ (@ member_o X) A4) (@ (@ ord_less_eq_nat M3) (@ F X)))) (@ condit1738341127787009408ow_nat (@ (@ image_o_nat F) A4)))) (forall ((A4 set_o) (F set_nat)) (=> (not (= A4 bot_bot_set_o)) (= (@ comple7806235888213564991et_nat (@ (@ image_o_set_nat (lambda ((I2 Bool)) F)) A4)) F))) (forall ((A4 set_int) (F (-> int int))) (=> (@ finite_finite_int A4) (=> (@ (@ ord_less_eq_set_int A4) (@ (@ image_int_int F) A4)) (@ (@ inj_on_int_int F) A4)))) (forall ((B5 (-> product_unit set_nat))) (= (@ comple7806235888213564991et_nat (@ (@ image_8173849991827986510et_nat B5) bot_bo3957492148770167129t_unit)) top_top_set_nat)) (forall ((F (-> Bool nat)) (A4 set_o)) (=> (@ order_mono_o_nat F) (=> (@ condit5488710616941104124bove_o A4) (=> (not (= A4 bot_bot_set_o)) (@ (@ ord_less_eq_nat (@ complete_Sup_Sup_nat (@ (@ image_o_nat F) A4))) (@ F (@ complete_Sup_Sup_o A4))))))) (forall ((B Bool) (B5 (-> Bool set_o)) (A4 set_o) (A Bool)) (let ((_let_1 (@ member_o B))) (=> (@ _let_1 (@ comple3063163877087187839_set_o (@ (@ image_o_set_o B5) A4))) (=> (@ (@ member_o A) A4) (@ _let_1 (@ B5 A)))))) (forall ((F (-> nat rat)) (Y3 rat)) (=> (= (@ (@ image_nat_rat F) top_top_set_nat) top_top_set_rat) (not (forall ((X nat)) (not (= Y3 (@ F X))))))) (forall ((Rep (-> Bool Bool)) (Abs (-> Bool Bool)) (Rep2 (-> nat Bool)) (Abs2 (-> Bool nat)) (Rep3 (-> nat nat)) (Abs3 (-> nat nat)) (M (-> nat Bool)) (M1 (-> Bool Bool)) (M2 (-> nat Bool))) (=> (@ (@ (@ type_definition_o_o Rep) Abs) top_top_set_o) (=> (@ (@ (@ type_d1000680970699258650_nat_o Rep2) Abs2) top_top_set_o) (=> (@ (@ (@ type_d6250493948777748686at_nat Rep3) Abs3) top_top_set_nat) (=> (= (@ (@ comp_nat_nat_nat (@ (@ comp_o_nat_nat Abs2) M)) Rep3) (@ (@ comp_o_nat_nat (@ (@ comp_o_nat_o (@ (@ comp_o_nat_o Abs2) M1)) Rep)) (@ (@ comp_nat_o_nat (@ (@ comp_o_o_nat Abs) M2)) Rep3))) (= (@ (@ comp_o_o_nat M1) M2) M)))))) (forall ((A4 set_Product_unit) (F (-> product_unit int)) (G (-> product_unit int))) (let ((_let_1 (@ (@ image_873079544045703924it_int G) A4))) (let ((_let_2 (@ (@ image_873079544045703924it_int F) A4))) (=> (not (= A4 bot_bo3957492148770167129t_unit)) (=> (@ condit2212336002400062152ve_int _let_2) (=> (@ condit2212336002400062152ve_int _let_1) (= (@ (@ sup_sup_int (@ complete_Sup_Sup_int _let_2)) (@ complete_Sup_Sup_int _let_1)) (@ complete_Sup_Sup_int (@ (@ image_873079544045703924it_int (lambda ((A5 product_unit)) (@ (@ sup_sup_int (@ F A5)) (@ G A5)))) A4))))))))) (forall ((A nat) (B num) (R3 set_Pr6200539531224447659at_num) (F (-> nat int)) (G (-> num int))) (=> (@ (@ member9148766508732265716at_num (@ (@ product_Pair_nat_num A) B)) R3) (@ (@ member5262025264175285858nt_int (@ (@ product_Pair_int_int (@ F A)) (@ G B))) (@ (@ image_1039142661021589043nt_int (@ (@ produc5477380188365894716um_int F) G)) R3)))) (forall ((A4 (-> Bool set_Pr1261947904930325089at_nat))) (= (@ comple1930127330929219688at_nat (@ (@ image_7077428525161401678at_nat A4) top_top_set_o)) (@ (@ inf_in2572325071724192079at_nat (@ A4 true)) (@ A4 false)))) (forall ((F (-> nat nat)) (A4 set_nat)) (=> (@ order_2680796546298691796at_nat F) (=> (@ condit2214826472909112428ve_nat A4) (@ condit1738341127787009408ow_nat (@ (@ image_nat_nat F) A4))))) (forall ((F (-> int int)) (A4 set_int) (B5 set_int)) (let ((_let_1 (@ inj_on_int_int F))) (let ((_let_2 (@ image_int_int F))) (= (@ _let_1 (@ (@ sup_sup_set_int A4) B5)) (and (@ _let_1 A4) (= (@ (@ inf_inf_set_int (@ _let_2 (@ (@ minus_minus_set_int A4) B5))) (@ _let_2 (@ (@ minus_minus_set_int B5) A4))) bot_bot_set_int) (@ _let_1 B5)))))) (forall ((F (-> (-> code_integer code_integer) produc8923325533196201883nteger produc8923325533196201883nteger)) (G (-> code_integer code_integer code_integer)) (X2 code_integer) (H (-> (-> code_integer code_integer) produc8923325533196201883nteger produc8923325533196201883nteger)) (K (-> code_integer code_integer code_integer))) (=> (= (@ F (@ G X2)) (@ H (@ K X2))) (= (@ (@ (@ comp_C8797469213163452608nteger F) G) X2) (@ (@ (@ comp_C8797469213163452608nteger H) K) X2)))) (forall ((F (-> produc3843707927480180839at_nat Bool)) (A set_Pr1261947904930325089at_nat) (B set_Pr1261947904930325089at_nat)) (=> (@ (@ (@ produc7820828192191229133_nat_o F) A) B) (@ F (@ (@ produc2922128104949294807at_nat A) B)))) (forall ((R set_Pr7459493094073627847at_nat) (S2 set_Pr7459493094073627847at_nat)) (=> (forall ((X set_Pr4329608150637261639at_nat) (Y set_Pr4329608150637261639at_nat)) (let ((_let_1 (@ member1466754251312161552at_nat (@ (@ produc9060074326276436823at_nat X) Y)))) (=> (@ _let_1 R) (@ _let_1 S2)))) (@ (@ ord_le5997549366648089703at_nat R) S2))) (forall ((X2 product_prod_nat_int) (A4 set_nat) (B5 set_int)) (= (@ (@ member4262671552274231302at_int X2) (@ (@ produc454536836294682310at_int A4) (lambda ((Uu nat)) B5))) (and (@ (@ member_nat (@ product_fst_nat_int X2)) A4) (@ (@ member_int (@ product_snd_nat_int X2)) B5)))) (forall ((M (-> produc859450856879609959at_nat set_Pr4329608150637261639at_nat)) (A4 set_Pr8693737435421807431at_nat) (B5 set_Pr8693737435421807431at_nat)) (let ((_let_1 (@ image_3876558564303283877at_nat M))) (= (@ comple4364388969068068532at_nat (@ _let_1 (@ (@ sup_su718114333110466843at_nat A4) B5))) (@ (@ sup_su5525570899277871387at_nat (@ comple4364388969068068532at_nat (@ _let_1 A4))) (@ comple4364388969068068532at_nat (@ _let_1 B5)))))) (forall ((F (-> nat Bool)) (A4 set_nat) (G (-> nat Bool)) (B5 set_nat)) (=> (@ (@ inj_on_nat_o F) A4) (=> (@ (@ inj_on_nat_o G) B5) (=> (= (@ (@ inf_inf_set_o (@ (@ image_nat_o F) A4)) (@ (@ image_nat_o G) B5)) bot_bot_set_o) (@ (@ inj_on_nat_o (lambda ((X4 nat)) (let ((_let_1 (@ (@ member_nat X4) A4))) (and (=> _let_1 (@ F X4)) (=> (not _let_1) (@ G X4)))))) (@ (@ sup_sup_set_nat A4) B5)))))) (forall ((X2 num) (Y3 num)) (= (@ (@ (@ if_num true) X2) Y3) X2)) (forall ((R3 (-> nat nat Bool)) (X2 (-> char nat)) (Y3 (-> char nat)) (Ra (-> nat nat Bool))) (=> (@ (@ (@ (@ bNF_re3734335887435638179at_nat (lambda ((Y2 char) (Z char)) (= Y2 Z))) R3) X2) Y3) (=> (forall ((Z3 nat) (Yb nat)) (=> (@ (@ member_nat Z3) (@ (@ image_char_nat X2) top_top_set_char)) (=> (@ (@ member_nat Yb) (@ (@ image_char_nat Y3) top_top_set_char)) (=> (@ (@ R3 Z3) Yb) (@ (@ Ra Z3) Yb))))) (@ (@ (@ (@ bNF_re3734335887435638179at_nat (lambda ((Y2 char) (Z char)) (= Y2 Z))) Ra) X2) Y3)))) (forall ((F (-> nat int)) (A4 set_nat)) (=> (@ (@ inj_on_nat_int F) A4) (@ (@ inj_on426556184350386907et_int (@ image_nat_int F)) (@ pow_nat A4)))) (forall ((A ref_a) (P produc7812382424243267045t_unit)) (= (= A (@ produc473321116828791851t_unit P)) (exists ((B4 heap_e7401611519738050253t_unit)) (= P (@ (@ produc6544324848051098391t_unit A) B4))))) (forall ((S5 set_Pr1261947904930325089at_nat) (T3 set_Pr1261947904930325089at_nat) (F (-> product_prod_nat_nat product_prod_nat_nat))) (=> (@ finite6177210948735845034at_nat S5) (=> (@ finite6177210948735845034at_nat T3) (=> (= (@ finite711546835091564841at_nat S5) (@ finite711546835091564841at_nat T3)) (=> (@ (@ ord_le3146513528884898305at_nat (@ (@ image_5168914502847457605at_nat F) S5)) T3) (= (forall ((X4 product_prod_nat_nat)) (=> (@ (@ member8440522571783428010at_nat X4) T3) (exists ((Y5 product_prod_nat_nat)) (and (@ (@ member8440522571783428010at_nat Y5) S5) (= (@ F Y5) X4))))) (@ (@ inj_on8969904277767023793at_nat F) S5))))))) (forall ((C3 set_Product_unit) (A4 (-> product_unit set_Pr4329608150637261639at_nat)) (B5 set_Pr4329608150637261639at_nat)) (let ((_let_1 (@ (@ sup_su5525570899277871387at_nat (@ comple4364388969068068532at_nat (@ (@ image_5172358348707908735at_nat A4) C3))) B5))) (let ((_let_2 (= C3 bot_bo3957492148770167129t_unit))) (and (=> (not _let_2) (= _let_1 (@ comple4364388969068068532at_nat (@ (@ image_5172358348707908735at_nat (lambda ((X4 product_unit)) (@ (@ sup_su5525570899277871387at_nat (@ A4 X4)) B5))) C3)))) (=> _let_2 (= _let_1 B5)))))) (forall ((F (-> Bool Bool)) (A4 set_o) (G (-> Bool Bool)) (B5 set_o)) (=> (@ (@ inj_on_o_o F) A4) (=> (@ (@ inj_on_o_o G) B5) (=> (= (@ (@ inf_inf_set_o (@ (@ image_o_o F) A4)) (@ (@ image_o_o G) B5)) bot_bot_set_o) (@ (@ inj_on_o_o (lambda ((X4 Bool)) (let ((_let_1 (@ (@ member_o X4) A4))) (and (=> _let_1 (@ F X4)) (=> (not _let_1) (@ G X4)))))) (@ (@ sup_sup_set_o A4) B5)))))) (forall ((A (-> Bool Bool)) (B (-> nat Bool)) (C (-> nat Bool)) (V nat)) (=> (= (@ (@ comp_o_o_nat A) B) (@ (@ comp_o_o_nat id_o) C)) (= (@ A (@ B V)) (@ C V)))) (forall ((X2 product_prod_int_int) (Y3 product_prod_int_int)) (= (@ (@ (@ if_Pro3027730157355071871nt_int true) X2) Y3) X2)) (forall ((M (-> produc859450856879609959at_nat set_Pr1261947904930325089at_nat)) (A4 set_Pr8693737435421807431at_nat) (B5 set_Pr8693737435421807431at_nat)) (let ((_let_1 (@ image_1384942819424619199at_nat M))) (= (@ comple1930127330929219688at_nat (@ _let_1 (@ (@ sup_su718114333110466843at_nat A4) B5))) (@ (@ inf_in2572325071724192079at_nat (@ comple1930127330929219688at_nat (@ _let_1 A4))) (@ comple1930127330929219688at_nat (@ _let_1 B5)))))) (forall ((F (-> nat num)) (G (-> nat nat)) (H (-> int nat)) (I (-> nat nat)) (Prod product_prod_int_nat)) (= (@ (@ (@ produc4918694523301289860at_nat F) G) (@ (@ (@ produc4668068763237680022at_nat H) I) Prod)) (@ (@ (@ produc2608876591208338912at_nat (@ (@ comp_nat_num_int F) H)) (@ (@ comp_nat_nat_nat G) I)) Prod))) (forall ((A4 set_Pr1261947904930325089at_nat) (R set_Pr8693737435421807431at_nat) (A product_prod_nat_nat) (B product_prod_nat_nat)) (=> (@ (@ order_8331247224601271455at_nat A4) R) (=> (@ (@ member8206827879206165904at_nat (@ (@ produc6161850002892822231at_nat A) B)) R) (and (@ (@ member8440522571783428010at_nat B) A4) (@ (@ member8440522571783428010at_nat A) A4))))) (forall ((K product_prod_nat_nat) (I3 set_Pr1261947904930325089at_nat) (A4 (-> product_prod_nat_nat product_unit))) (let ((_let_1 (@ comple2584293577114468500t_unit (@ (@ image_6169909464789311569t_unit A4) I3)))) (=> (@ (@ member8440522571783428010at_nat K) I3) (= (@ (@ inf_inf_Product_unit (@ A4 K)) _let_1) _let_1)))) (forall ((A4 set_Product_unit) (B5 (-> product_unit set_int)) (F (-> int int))) (=> (not (= A4 bot_bo3957492148770167129t_unit)) (=> (forall ((X product_unit)) (=> (@ (@ member_Product_unit X) A4) (not (= (@ B5 X) bot_bot_set_int)))) (=> (@ condit2212336002400062152ve_int (@ comple3221217463730067765et_int (@ (@ image_3995998972318789802et_int (lambda ((X4 product_unit)) (@ (@ image_int_int F) (@ B5 X4)))) A4))) (= (@ complete_Sup_Sup_int (@ (@ image_int_int F) (@ comple3221217463730067765et_int (@ (@ 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((X4 nat) (Y5 num)) (@ (@ member9148766508732265716at_num (@ (@ product_Pair_nat_num X4) Y5)) S5))) (= R3 S5))) (forall ((Z2 product_prod_int_int) (A4 set_int) (F (-> int int))) (=> (@ (@ member5262025264175285858nt_int Z2) (@ collec213857154873943460nt_int (@ produc4947309494688390418_int_o (@ (@ bNF_Grp_int_int A4) F)))) (@ (@ member_int (@ product_fst_int_int Z2)) A4))) (forall ((A4 set_int) (U set_nat) (F (-> int set_nat))) (=> (forall ((I4 int)) (=> (@ (@ member_int I4) A4) (@ (@ ord_less_eq_set_nat U) (@ F I4)))) (@ (@ ord_less_eq_set_nat U) (@ comple7806235888213564991et_nat (@ (@ image_int_set_nat F) A4))))) (forall ((F (-> Bool product_unit))) (= (@ comple2584293577114468500t_unit (@ (@ image_o_Product_unit F) bot_bot_set_o)) top_top_Product_unit)) (forall ((F (-> int int Bool)) (G (-> product_prod_int_int Bool))) (=> (forall ((X int) (Y int)) (= (@ (@ F X) Y) (@ G (@ (@ product_Pair_int_int X) Y)))) (= (@ produc4947309494688390418_int_o F) G))) (forall ((A4 set_int) (B5 set_nat) (F (-> int product_unit)) (G (-> nat product_unit))) (=> (forall ((I4 int)) (=> (@ (@ member_int I4) A4) (exists ((X6 nat)) (and (@ (@ ord_le3221252021190050221t_unit (@ F I4)) (@ G X6)) (@ (@ member_nat X6) B5))))) (=> (forall ((J2 nat)) (=> (@ (@ member_nat J2) B5) (exists ((X6 int)) (and (@ (@ ord_le3221252021190050221t_unit (@ G J2)) (@ F X6)) (@ (@ member_int X6) A4))))) (= (@ comple4687483117567863418t_unit (@ (@ image_5846526143423701914t_unit F) A4)) (@ comple4687483117567863418t_unit (@ (@ image_8730104196221521654t_unit G) B5)))))) (forall ((A4 set_nat) (G (-> nat nat)) (B5 set_nat) (F (-> nat nat))) (let ((_let_1 (@ (@ image_nat_nat G) B5))) (=> (not (= A4 bot_bot_set_nat)) (=> (@ condit2214826472909112428ve_nat _let_1) (=> (forall ((N2 nat)) (=> (@ (@ member_nat N2) A4) (exists ((X6 nat)) (and (@ (@ ord_less_eq_nat (@ F N2)) (@ G X6)) (@ (@ member_nat X6) B5))))) (@ (@ ord_less_eq_nat (@ complete_Sup_Sup_nat (@ (@ image_nat_nat F) A4))) (@ complete_Sup_Sup_nat _let_1))))))) (forall ((A (-> int nat)) (B (-> int int)) (C (-> int nat)) (D2 (-> int int)) (V int)) (=> (= (@ (@ comp_int_nat_int A) B) (@ (@ comp_int_nat_int C) D2)) (= (@ A (@ B V)) (@ C (@ D2 V))))) (forall ((A set_Pr1261947904930325089at_nat) (B set_Pr1261947904930325089at_nat) (A2 set_Pr1261947904930325089at_nat) (B2 set_Pr1261947904930325089at_nat)) (=> (= (@ (@ produc2922128104949294807at_nat A) B) (@ (@ produc2922128104949294807at_nat A2) B2)) (not (=> (= A A2) (not (= B B2)))))) (forall ((F (-> nat product_unit)) (A nat) (A4 set_nat)) (let ((_let_1 (@ image_8730104196221521654t_unit F))) (= (@ comple4687483117567863418t_unit (@ _let_1 (@ (@ insert_nat A) A4))) (@ (@ sup_sup_Product_unit (@ F A)) (@ comple4687483117567863418t_unit (@ _let_1 A4)))))) (forall ((I int) (A4 set_int) (F (-> int set_nat))) (=> (@ (@ member_int I) A4) (@ (@ ord_less_eq_set_nat (@ comple7806235888213564991et_nat (@ (@ image_int_set_nat F) A4))) (@ F I)))) (forall ((F (-> Bool nat)) (A4 set_o)) (=> (@ order_mono_o_nat F) (=> (@ condit5413489452508810728elow_o A4) (=> (not (= A4 bot_bot_set_o)) (@ (@ ord_less_eq_nat (@ F (@ complete_Inf_Inf_o A4))) (@ complete_Inf_Inf_nat (@ (@ image_o_nat F) A4))))))) (forall ((Rep (-> nat char)) (Abs (-> char nat)) (F (-> nat nat)) (P2 (-> nat Bool)) (H (-> nat char))) (=> (@ (@ (@ type_d5945782884131516111t_char Rep) Abs) top_top_set_char) (= (@ (@ (@ bNF_vi8943400373106913048char_o F) Rep) (@ (@ bNF_Grp_nat_char (@ collect_nat P2)) H)) (@ (@ bNF_Grp_nat_nat (@ collect_nat (lambda ((X4 nat)) (@ P2 (@ F X4))))) (@ (@ comp_nat_nat_nat (@ (@ comp_char_nat_nat Abs) H)) F))))) (forall ((A4 set_o)) (= (@ complete_Sup_Sup_o (@ (@ image_o_o id_o) A4)) (@ complete_Sup_Sup_o A4))) (forall ((M (-> produc3843707927480180839at_nat set_Pr4329608150637261639at_nat)) (A4 set_Pr4329608150637261639at_nat) (B5 set_Pr4329608150637261639at_nat)) (let ((_let_1 (@ image_7364710425340685989at_nat M))) (= (@ comple4364388969068068532at_nat (@ _let_1 (@ (@ sup_su5525570899277871387at_nat A4) B5))) (@ (@ sup_su5525570899277871387at_nat (@ comple4364388969068068532at_nat (@ _let_1 A4))) (@ comple4364388969068068532at_nat (@ _let_1 B5)))))) (forall ((F (-> char char)) (G (-> rat rat))) (=> (= (@ (@ image_char_char F) top_top_set_char) top_top_set_char) (=> (= (@ (@ image_rat_rat G) top_top_set_rat) top_top_set_rat) (= (@ (@ image_5644637116751559941ar_rat (@ (@ produc1230515432254573900at_rat F) G)) top_to8437673547576850234ar_rat) top_to8437673547576850234ar_rat)))) (forall ((A4 set_Pr1261947904930325089at_nat) (F set_nat)) (=> (not (= A4 bot_bo2099793752762293965at_nat)) (= (@ comple7399068483239264473et_nat (@ (@ image_15824709712370754et_nat (lambda ((I2 product_prod_nat_nat)) F)) A4)) F))) _let_117 (forall ((C3 set_Product_unit) (A4 set_Pr1261947904930325089at_nat) (B5 (-> product_unit set_Pr1261947904930325089at_nat))) (let ((_let_1 (= C3 bot_bo3957492148770167129t_unit))) (and (=> (not _let_1) (= (@ comple5685304695842803022at_nat (@ (@ image_3617315916088684441at_nat (lambda ((X4 product_unit)) (@ (@ sup_su6327502436637775413at_nat A4) (@ B5 X4)))) C3)) (@ (@ sup_su6327502436637775413at_nat A4) (@ comple5685304695842803022at_nat (@ (@ image_3617315916088684441at_nat B5) C3))))) (=> _let_1 (= (@ comple5685304695842803022at_nat (@ (@ image_3617315916088684441at_nat (lambda ((X4 product_unit)) (@ (@ sup_su6327502436637775413at_nat A4) (@ B5 X4)))) C3)) bot_bo2099793752762293965at_nat))))) (forall ((B int) (B5 (-> Bool set_int)) (A4 set_o)) (=> (@ (@ member_int B) (@ comple3221217463730067765et_int (@ (@ image_o_set_int B5) A4))) (not (forall ((X Bool)) (=> (@ (@ member_o X) A4) (not (@ (@ member_int B) (@ B5 X)))))))) (forall ((R3 (-> Bool Bool Bool)) (X2 (-> char Bool)) (Y3 (-> char Bool)) (Ra (-> Bool Bool Bool))) (=> (@ (@ (@ (@ bNF_re1692451286490762625ar_o_o (lambda ((Y2 char) (Z char)) (= Y2 Z))) R3) X2) Y3) (=> (forall ((Z3 Bool) (Yb Bool)) (=> (@ (@ member_o Z3) (@ (@ image_char_o X2) top_top_set_char)) (=> (@ (@ member_o Yb) (@ (@ image_char_o Y3) top_top_set_char)) (=> (@ (@ R3 Z3) Yb) (@ (@ Ra Z3) Yb))))) (@ (@ (@ (@ bNF_re1692451286490762625ar_o_o (lambda ((Y2 char) (Z char)) (= Y2 Z))) Ra) X2) Y3)))) (forall ((F (-> int product_unit)) (A4 set_int) (A int)) (let ((_let_1 (@ (@ image_5846526143423701914t_unit F) A4))) (let ((_let_2 (@ comple2584293577114468500t_unit _let_1))) (=> (= (@ comple4687483117567863418t_unit _let_1) _let_2) (=> (@ condit2080475194861589617t_unit _let_1) (=> (@ condit9161856309968323677t_unit _let_1) (=> (@ (@ member_int A) A4) (= (@ F A) _let_2)))))))) (forall ((Q product_prod_int_int) (F (-> int int)) (P product_prod_int_int)) (=> (= Q (@ (@ produc2355237562570658114nt_int F) P)) (not (forall ((X int) (Y int)) (=> (= P (@ (@ product_Pair_int_int X) Y)) (not (= Q (@ (@ product_Pair_int_int (@ F X)) Y)))))))) (forall ((A4 set_Product_unit) (F (-> product_unit product_unit))) (let ((_let_1 (@ (@ image_405062704495631173t_unit F) A4))) (=> (not (= A4 bot_bo3957492148770167129t_unit)) (@ (@ ord_le3221252021190050221t_unit (@ comple2584293577114468500t_unit _let_1)) (@ comple4687483117567863418t_unit _let_1))))) (forall ((A4 set_rat) (A7 set_nat)) (=> (not (= A4 bot_bot_set_rat)) (= (exists ((F2 (-> rat nat))) (and (@ (@ ord_less_eq_set_nat (@ (@ image_rat_nat F2) A4)) A7) (@ (@ inj_on_rat_nat F2) A4))) (exists ((G3 (-> nat rat))) (= (@ (@ image_nat_rat G3) A7) A4))))) (forall ((B5 (-> nat set_nat)) (F (-> int nat)) (A4 set_int)) (= (@ comple7806235888213564991et_nat (@ (@ image_int_set_nat (lambda ((A5 int)) (@ B5 (@ F A5)))) A4)) (@ comple7806235888213564991et_nat (@ (@ image_nat_set_nat B5) (@ (@ image_int_nat F) A4))))) _let_115 (forall ((Rep (-> Bool char)) (Abs (-> char Bool)) (M (-> char char))) (=> (@ (@ (@ type_d9076672964931703357o_char Rep) Abs) top_top_set_char) (=> (= M id_char) (= (@ (@ comp_char_o_o (@ (@ comp_char_o_char Abs) M)) Rep) id_o)))) (forall ((P2 (-> int int Bool)) (Y3 int) (X2 int)) (let ((_let_1 (@ (@ product_Pair_int_int X2) Y3))) (=> (@ (@ P2 Y3) X2) (@ (@ P2 (@ product_snd_int_int _let_1)) (@ product_fst_int_int _let_1))))) (forall ((A nat) (B num) (A4 set_Pr6200539531224447659at_num) (F (-> nat num int))) (=> (@ (@ member9148766508732265716at_num (@ (@ product_Pair_nat_num A) B)) A4) (@ (@ member_int (@ (@ F A) B)) (@ (@ image_4501981038234393650um_int (@ produc4970712607118878916um_int F)) A4)))) (forall ((Rep (-> nat num)) (Abs (-> num nat)) (G (-> product_prod_nat_nat int)) (P2 (-> int Bool)) (H (-> int nat))) (=> (@ (@ (@ type_d2807825734933527320at_num Rep) Abs) top_top_set_num) (= (@ (@ (@ bNF_vi9094538908245281400_nat_o G) Abs) (@ (@ bNF_Grp_int_nat (@ collect_int P2)) H)) (@ (@ bNF_Gr5974128493091723341at_num (@ collec3392354462482085612at_nat (lambda ((X4 product_prod_nat_nat)) (@ P2 (@ G X4))))) (@ (@ comp_i1186163378102392086at_nat (@ (@ comp_nat_num_int Rep) H)) G))))) (forall ((R set_Pr4329608150637261639at_nat)) (=> (@ (@ total_7212417256332265445at_nat (@ field_3145993188331922222at_nat R)) R) (=> (@ (@ ord_le1268244103169919719at_nat R) id_set1796276052702428605at_nat) (or (exists ((A3 set_Pr1261947904930325089at_nat)) (= R (@ (@ insert9069300056098147895at_nat (@ (@ produc2922128104949294807at_nat A3) A3)) bot_bo228742789529271731at_nat))) (= R bot_bo228742789529271731at_nat))))) (forall ((F (-> nat int)) (A4 (-> int nat)) (I3 set_int)) (let ((_let_1 (@ (@ image_int_nat A4) I3))) (=> (@ order_mono_nat_int F) (=> (@ condit1738341127787009408ow_nat _let_1) (=> (not (= I3 bot_bot_set_int)) (@ (@ ord_less_eq_int (@ F (@ complete_Inf_Inf_nat _let_1))) (@ complete_Inf_Inf_int (@ (@ image_int_int (lambda ((X4 int)) (@ F (@ A4 X4)))) I3)))))))) (forall ((A4 (-> Bool set_Pr8693737435421807431at_nat))) (= (@ comple2748534634209756852at_nat (@ (@ image_8493167801588156084at_nat A4) top_top_set_o)) (@ (@ sup_su718114333110466843at_nat (@ A4 true)) (@ A4 false)))) (forall ((F (-> int nat)) (C3 set_int) (A4 set_int) (B5 set_int)) (let ((_let_1 (@ image_int_nat F))) (=> (@ (@ inj_on_int_nat F) C3) (=> (@ (@ ord_less_eq_set_int A4) C3) (=> (@ (@ ord_less_eq_set_int B5) C3) (= (@ _let_1 (@ (@ inf_inf_set_int A4) B5)) (@ (@ inf_inf_set_nat (@ _let_1 A4)) (@ _let_1 B5)))))))) (forall ((A4 set_nat) (B5 set_Pr1261947904930325089at_nat)) (=> (@ finite_finite_nat A4) (=> (@ finite6177210948735845034at_nat B5) (= (exists ((F2 (-> nat product_prod_nat_nat))) (and (@ (@ inj_on5538052773655684606at_nat F2) A4) (@ (@ ord_le3146513528884898305at_nat (@ (@ image_5846123807819985514at_nat F2) A4)) B5))) (@ (@ ord_less_eq_nat (@ finite_card_nat A4)) (@ finite711546835091564841at_nat B5)))))) (forall ((G (-> nat nat)) (F (-> nat int))) (=> (@ finite_finite_nat (@ (@ image_nat_nat G) top_top_set_nat)) (@ finite_finite_int (@ (@ image_nat_int (lambda ((X4 nat)) (@ F (@ G X4)))) top_top_set_nat)))) (forall ((F (-> nat nat)) (X2 nat) (Y3 nat)) (= (@ (@ produc986720760941809198at_nat F) (@ (@ product_Pair_nat_nat X2) Y3)) (@ (@ product_Pair_nat_nat (@ F X2)) Y3))) (forall ((C3 set_o) (A4 (-> Bool set_Pr1261947904930325089at_nat)) (B5 set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ (@ inf_in2572325071724192079at_nat (@ comple1930127330929219688at_nat (@ (@ image_7077428525161401678at_nat A4) C3))) B5))) (let ((_let_2 (= C3 bot_bot_set_o))) (and (=> (not _let_2) (= _let_1 (@ comple1930127330929219688at_nat (@ (@ image_7077428525161401678at_nat (lambda ((X4 Bool)) (@ (@ inf_in2572325071724192079at_nat (@ A4 X4)) B5))) C3)))) (=> _let_2 (= _let_1 B5)))))) (forall ((M (-> produc3843707927480180839at_nat set_Pr1261947904930325089at_nat)) (A4 set_Pr4329608150637261639at_nat) (B5 set_Pr4329608150637261639at_nat)) (let ((_let_1 (@ image_7979982168039674559at_nat M))) (= (@ comple1930127330929219688at_nat (@ _let_1 (@ (@ sup_su5525570899277871387at_nat A4) B5))) (@ (@ inf_in2572325071724192079at_nat (@ comple1930127330929219688at_nat (@ _let_1 A4))) (@ comple1930127330929219688at_nat (@ _let_1 B5)))))) (forall ((F (-> char product_prod_nat_nat)) (A4 set_char) (B5 set_char)) (let ((_let_1 (@ image_8382823969816519465at_nat F))) (=> (@ (@ inj_on1021528964648911549at_nat F) top_top_set_char) (= (@ _let_1 (@ (@ inf_inf_set_char A4) B5)) (@ (@ inf_in2572325071724192079at_nat (@ _let_1 A4)) (@ _let_1 B5)))))) (forall ((F (-> nat nat)) (A4 set_nat) (G (-> nat nat))) (=> (@ (@ inj_on_nat_nat F) A4) (=> (@ (@ inj_on_nat_nat G) (@ (@ image_nat_nat F) A4)) (@ (@ inj_on_nat_nat (@ (@ comp_nat_nat_nat G) F)) A4)))) (forall ((F (-> nat int)) (A4 set_nat) (B5 set_nat)) (let ((_let_1 (@ image_nat_int F))) (=> (@ (@ inj_on_nat_int F) top_top_set_nat) (= (@ _let_1 (@ (@ minus_minus_set_nat A4) B5)) (@ (@ minus_minus_set_int (@ _let_1 A4)) (@ _let_1 B5)))))) (forall ((X2 set_Pr4329608150637261639at_nat) (Y3 set_Pr4329608150637261639at_nat) (A4 set_se5479201105039950375at_nat)) (= (@ (@ member1466754251312161552at_nat (@ (@ produc9060074326276436823at_nat X2) Y3)) (@ id_on_3275838214495744996at_nat A4)) (and (@ (@ member6273874620674182256at_nat X2) A4) (= X2 Y3)))) (forall ((F (-> int nat)) (A4 set_int)) (=> (@ order_mono_int_nat F) (=> (@ condit2212336002400062152ve_int A4) (@ condit2214826472909112428ve_nat (@ (@ image_int_nat F) A4))))) (forall ((Z2 Bool) (C (-> int int set_o)) (P product_prod_int_int)) (=> (@ (@ member_o Z2) (@ (@ produc4257766111578684402_set_o C) P)) (not (forall ((X int) (Y int)) (=> (= P (@ (@ product_Pair_int_int X) Y)) (not (@ (@ member_o Z2) (@ (@ C X) Y)))))))) (forall ((A4 set_nat) (B5 set_nat) (C3 (-> nat int)) (D (-> nat int)) (Inf (-> set_int int))) (=> (= A4 B5) (=> (forall ((X nat)) (=> (@ (@ member_nat X) B5) (= (@ C3 X) (@ D X)))) (= (@ Inf (@ (@ image_nat_int C3) A4)) (@ Inf (@ (@ image_nat_int D) B5)))))) (forall ((A4 set_int) (G (-> nat int)) (B5 set_nat) (F (-> int int))) (let ((_let_1 (@ (@ image_nat_int G) B5))) (=> (not (= A4 bot_bot_set_int)) (=> (@ condit2212336002400062152ve_int _let_1) (=> (forall ((N2 int)) (=> (@ (@ member_int N2) A4) (exists ((X6 nat)) (and (@ (@ member_nat X6) B5) (@ (@ ord_less_eq_int (@ F N2)) (@ G X6)))))) (@ (@ ord_less_eq_int (@ complete_Sup_Sup_int (@ (@ image_int_int F) A4))) (@ complete_Sup_Sup_int _let_1))))))) (forall ((A4 set_int) (B5 set_nat) (F (-> int nat))) (=> (@ finite_finite_int A4) (=> (@ (@ ord_less_eq_set_nat B5) (@ (@ image_int_nat F) A4)) (@ (@ ord_less_eq_nat (@ finite_card_nat B5)) (@ finite_card_int A4))))) _let_114 (forall ((F (-> nat num)) (G (-> nat nat)) (L1 (-> num num)) (L2 (-> nat num)) (H (-> int nat)) (R (-> int num))) (=> (= (@ (@ comp_nat_num_nat F) G) (@ (@ comp_num_num_nat L1) L2)) (=> (= (@ (@ comp_nat_num_int L2) H) R) (= (@ (@ comp_nat_num_int F) (@ (@ comp_nat_nat_int G) H)) (@ (@ comp_num_num_int L1) R))))) (forall ((F (-> int nat)) (G (-> int int)) (X2 int) (H (-> int nat)) (K (-> int int))) (=> (= (@ F (@ G X2)) (@ H (@ K X2))) (= (@ (@ (@ comp_int_nat_int F) G) X2) (@ (@ (@ comp_int_nat_int H) K) X2)))) (forall ((S5 set_int) (T3 set_int) (F (-> int int))) (=> (@ finite_finite_int S5) (=> (@ finite_finite_int T3) (=> (= (@ finite_card_int S5) (@ finite_card_int T3)) (=> (@ (@ ord_less_eq_set_int (@ (@ image_int_int F) S5)) T3) (= (forall ((X4 int)) (=> (@ (@ member_int X4) T3) (exists ((Y5 int)) (and (@ (@ member_int Y5) S5) (= (@ F Y5) X4))))) (@ (@ inj_on_int_int F) S5))))))) (forall ((A nat) (B nat) (R3 set_Pr1261947904930325089at_nat) (F (-> nat int)) (G (-> nat int))) (=> (@ (@ member8440522571783428010at_nat (@ (@ product_Pair_nat_nat A) B)) R3) (@ (@ member5262025264175285858nt_int (@ (@ product_Pair_int_int (@ F A)) (@ G B))) (@ (@ image_1990417195239315453nt_int (@ (@ produc7347049785058425330at_int F) G)) R3)))) (forall ((H heap_e7401611519738050253t_unit) (V a)) (not (@ (@ present_a H) (@ produc473321116828791851t_unit (@ (@ alloc_a V) H))))) (forall ((A4 set_Product_unit) (F (-> product_unit nat)) (U nat)) (let ((_let_1 (@ (@ image_875570014554754200it_nat F) A4))) (=> (not (= A4 bot_bo3957492148770167129t_unit)) (=> (@ condit1738341127787009408ow_nat _let_1) (= (@ (@ ord_less_eq_nat U) (@ complete_Inf_Inf_nat _let_1)) (forall ((X4 product_unit)) (=> (@ (@ member_Product_unit X4) A4) (@ (@ ord_less_eq_nat U) (@ F X4))))))))) (forall ((F (-> product_unit product_unit)) (A4 set_Product_unit)) (=> (= (@ (@ image_405062704495631173t_unit F) top_to1996260823553986621t_unit) top_to1996260823553986621t_unit) (= (= (@ (@ vimage7995052115951654139t_unit F) A4) bot_bo3957492148770167129t_unit) (= A4 bot_bo3957492148770167129t_unit)))) (forall ((A4 set_se7855581050983116737at_nat) (R set_Pr4329608150637261639at_nat) (X2 set_Pr1261947904930325089at_nat) (Y3 set_Pr1261947904930325089at_nat)) (=> (@ (@ refl_o6955724340487615712at_nat A4) R) (=> (@ (@ member8757157785044589968at_nat (@ (@ produc2922128104949294807at_nat X2) Y3)) R) (@ (@ member2643936169264416010at_nat X2) A4)))) _let_113 (forall ((P2 (-> rat nat product_unit))) (= (@ comple4687483117567863418t_unit (@ (@ image_8730104196221521654t_unit (lambda ((Y5 nat)) (@ comple2584293577114468500t_unit (@ (@ image_2327579789247107822t_unit (lambda ((X4 rat)) (@ (@ P2 X4) Y5))) top_top_set_rat)))) top_top_set_nat)) (@ comple2584293577114468500t_unit (@ (@ image_340470173791133503t_unit (lambda ((X4 (-> nat rat))) (@ comple4687483117567863418t_unit (@ (@ image_8730104196221521654t_unit (lambda ((Y5 nat)) (@ (@ P2 (@ X4 Y5)) Y5))) top_top_set_nat)))) top_top_set_nat_rat)))) (forall ((A4 (-> int set_nat)) (I int) (B5 set_nat) (J3 set_int)) (= (@ comple7399068483239264473et_nat (@ (@ image_int_set_nat (@ (@ (@ fun_upd_int_set_nat A4) I) B5)) J3)) (@ (@ sup_sup_set_nat (@ comple7399068483239264473et_nat (@ (@ image_int_set_nat A4) (@ (@ minus_minus_set_int J3) (@ (@ insert_int I) bot_bot_set_int))))) (@ (@ (@ if_set_nat (@ (@ member_int I) J3)) B5) bot_bot_set_nat)))) (forall ((A4 set_nat) (B5 set_nat) (F (-> nat nat))) (=> (@ finite_finite_nat A4) (=> (@ (@ ord_less_eq_set_nat B5) (@ (@ image_nat_nat F) A4)) (@ (@ ord_less_eq_nat (@ finite_card_nat B5)) (@ finite_card_nat A4))))) (forall ((F (-> rat int)) (Y3 int)) (=> (= (@ (@ image_rat_int F) top_top_set_rat) top_top_set_int) (not (forall ((X rat)) (not (= Y3 (@ F X))))))) (forall ((P produc3843707927480180839at_nat)) (= (@ (@ produc7548845685434208379at_nat produc2922128104949294807at_nat) P) P)) (forall ((R (-> product_prod_nat_nat product_prod_nat_nat Bool)) (S2 (-> product_prod_nat_nat int Bool))) (= (@ conver4689305806000247544at_int (@ (@ relcom8911704206367525917at_int R) S2)) (@ (@ relcom716700242784427165at_nat (@ conver4689305806000247544at_int S2)) (@ conver6965824823119931701at_nat R)))) (forall ((F (-> num nat)) (G (-> nat num)) (L1 (-> int nat)) (L2 (-> nat int)) (H (-> int nat)) (R (-> int int))) (=> (= (@ (@ comp_num_nat_nat F) G) (@ (@ comp_int_nat_nat L1) L2)) (=> (= (@ (@ comp_nat_int_int L2) H) R) (= (@ (@ comp_num_nat_int F) (@ (@ comp_nat_num_int G) H)) (@ (@ comp_int_nat_int L1) R))))) (forall ((Z2 nat) (C (-> int int set_nat)) (A int) (B int)) (let ((_let_1 (@ member_nat Z2))) (=> (@ _let_1 (@ (@ C A) B)) (@ _let_1 (@ (@ produc4251311855443802252et_nat C) (@ (@ product_Pair_int_int A) B)))))) (forall ((A4 set_Pr1261947904930325089at_nat) (F (-> product_prod_nat_nat set_nat)) (U set_nat)) (=> (forall ((I4 product_prod_nat_nat)) (=> (@ (@ member8440522571783428010at_nat I4) A4) (@ (@ ord_less_eq_set_nat (@ F I4)) U))) (@ (@ ord_less_eq_set_nat (@ comple7399068483239264473et_nat (@ (@ image_15824709712370754et_nat F) A4))) U))) (forall ((R3 (-> int code_integer Bool)) (S5 (-> num num Bool)) (R7 (-> code_integer int Bool)) (S6 (-> num num Bool))) (@ (@ ord_le4541714130423454556_num_o (@ (@ relcom7779292856395800339nt_num (@ (@ bNF_re6718328864250387230um_num R3) S5)) (@ (@ bNF_re8313794964846168862um_num R7) S6))) (@ (@ bNF_re7626690874201225453um_num (@ (@ relcom328798225758222312er_int R3) R7)) (@ (@ relcompp_num_num_num S5) S6)))) (forall ((F (-> nat num)) (G (-> nat nat)) (H (-> int nat))) (= (@ (@ comp_nat_num_int (@ (@ comp_nat_num_nat F) G)) H) (@ (@ comp_nat_num_int F) (@ (@ comp_nat_nat_int G) H)))) (forall ((X2 set_Pr1261947904930325089at_nat) (Y3 set_Pr1261947904930325089at_nat) (A4 set_se7855581050983116737at_nat)) (= (@ (@ member8757157785044589968at_nat (@ (@ produc2922128104949294807at_nat X2) Y3)) (@ id_on_6713504163309144702at_nat A4)) (and (= X2 Y3) (@ (@ member2643936169264416010at_nat X2) A4)))) (forall ((P2 (-> nat rat product_unit))) (= (@ comple2584293577114468500t_unit (@ (@ image_2327579789247107822t_unit (lambda ((Y5 rat)) (@ comple4687483117567863418t_unit (@ (@ image_8730104196221521654t_unit (lambda ((X4 nat)) (@ (@ P2 X4) Y5))) top_top_set_nat)))) top_top_set_rat)) (@ comple4687483117567863418t_unit (@ (@ image_2910438736038083391t_unit (lambda ((F2 (-> rat nat))) (@ comple2584293577114468500t_unit (@ (@ image_2327579789247107822t_unit (lambda ((X4 rat)) (@ (@ P2 (@ F2 X4)) X4))) top_top_set_rat)))) top_top_set_rat_nat)))) (forall ((F (-> set_Pr4329608150637261639at_nat set_Pr4329608150637261639at_nat Bool)) (A set_Pr4329608150637261639at_nat) (B set_Pr4329608150637261639at_nat)) (=> (@ (@ F A) B) (@ (@ produc9020218426428501292_nat_o F) (@ (@ produc9060074326276436823at_nat A) B)))) (forall ((X2 produc1319942482725812455at_nat) (Y3 set_Pr4329608150637261639at_nat) (Z2 set_Pr4329608150637261639at_nat)) (=> (= X2 (@ (@ produc9060074326276436823at_nat Y3) Z2)) (= (@ produc4486455499028916547at_nat X2) Y3))) (forall ((R3 (-> int Bool Bool)) (X2 (-> char int)) (Y3 (-> char Bool)) (Ra (-> int Bool Bool))) (=> (@ (@ (@ (@ bNF_re6064627146911078825_int_o (lambda ((Y2 char) (Z char)) (= Y2 Z))) R3) X2) Y3) (=> (forall ((Z3 int) (Yb Bool)) (=> (@ (@ member_int Z3) (@ (@ image_char_int X2) top_top_set_char)) (=> (@ (@ member_o Yb) (@ (@ image_char_o Y3) top_top_set_char)) (=> (@ (@ R3 Z3) Yb) (@ (@ Ra Z3) Yb))))) (@ (@ (@ (@ bNF_re6064627146911078825_int_o (lambda ((Y2 char) (Z char)) (= Y2 Z))) Ra) X2) Y3)))) (forall ((A4 set_Product_unit)) (=> (forall ((X product_unit)) (not (@ (@ member_Product_unit X) A4))) (@ (@ ord_le3507040750410214029t_unit A4) bot_bo3957492148770167129t_unit))) (forall ((R1 (-> int int Bool)) (Abs1 (-> int int)) (Rep1 (-> int int)) (T1 (-> int int Bool)) (R22 (-> int int Bool)) (Abs22 (-> int nat)) (Rep22 (-> nat int)) (T22 (-> int nat Bool))) (=> (@ (@ (@ (@ quotient_int_int R1) Abs1) Rep1) T1) (=> (@ (@ (@ (@ quotient_int_nat R22) Abs22) Rep22) T22) (@ (@ (@ (@ quotient_int_nat (@ (@ relcompp_int_int_int T1) (@ (@ relcompp_int_int_int R22) (@ conversep_int_int T1)))) (@ (@ comp_int_nat_int Abs22) Abs1)) (@ (@ comp_int_int_nat Rep1) Rep22)) (@ (@ relcompp_int_int_nat T1) T22))))) (forall ((A4 set_Product_unit) (F (-> product_unit nat)) (M nat)) (=> (not (= A4 bot_bo3957492148770167129t_unit)) (=> (forall ((X product_unit)) (=> (@ (@ member_Product_unit X) A4) (@ (@ ord_less_eq_nat (@ F X)) M))) (@ (@ ord_less_eq_nat (@ complete_Sup_Sup_nat (@ (@ image_875570014554754200it_nat F) A4))) M)))) (forall ((F (-> Bool nat)) (A4 set_o) (X2 Bool) (U nat)) (let ((_let_1 (@ (@ image_o_nat F) A4))) (let ((_let_2 (@ ord_less_eq_nat U))) (=> (@ condit2214826472909112428ve_nat _let_1) (=> (@ (@ member_o X2) A4) (=> (@ _let_2 (@ F X2)) (@ _let_2 (@ complete_Sup_Sup_nat _let_1)))))))) (forall ((A4 set_int) (B5 set_nat) (G (-> nat product_unit)) (F (-> int product_unit))) (=> (forall ((I4 int)) (=> (@ (@ member_int I4) A4) (exists ((X6 nat)) (and (@ (@ member_nat X6) B5) (@ (@ ord_le3221252021190050221t_unit (@ G X6)) (@ F I4)))))) (=> (forall ((J2 nat)) (=> (@ (@ member_nat J2) B5) (exists ((X6 int)) (and (@ (@ member_int X6) A4) (@ (@ ord_le3221252021190050221t_unit (@ F X6)) (@ G J2)))))) (= (@ comple2584293577114468500t_unit (@ (@ image_5846526143423701914t_unit F) A4)) (@ comple2584293577114468500t_unit (@ (@ image_8730104196221521654t_unit G) B5)))))) _let_112 (= produc8739625826339149834_nat_o (lambda ((F2 (-> nat nat product_prod_nat_nat Bool)) (X4 product_prod_nat_nat) (__flatten_var_0 product_prod_nat_nat)) (@ (@ (@ F2 (@ product_fst_nat_nat X4)) (@ product_snd_nat_nat X4)) __flatten_var_0))) (forall ((F (-> nat Bool)) (A4 set_nat)) (=> (@ finite_finite_o (@ (@ image_nat_o F) A4)) (=> (not (@ finite_finite_nat A4)) (exists ((X Bool)) (and (@ (@ member_o X) (@ (@ image_nat_o F) A4)) (not (@ finite_finite_nat (@ (@ vimage_nat_o F) (@ (@ insert_o X) bot_bot_set_o))))))))) (forall ((F (-> int int)) (A4 set_int)) (=> (@ (@ inj_on_int_int F) A4) (@ (@ inj_on6435365835345961783et_int (@ image_int_int F)) (@ pow_int A4)))) (forall ((F (-> int int))) (let ((_let_1 (@ (@ bNF_Grp_int_int top_top_set_int) F))) (=> (= F id_int) (= (@ (@ relcompp_int_int_int (@ conversep_int_int _let_1)) _let_1) _let_1)))) (forall ((X2 product_prod_o_o) (A4 set_o) (B5 set_o)) (= (@ (@ member7466972457876170832od_o_o X2) (@ (@ product_Sigma_o_o A4) (lambda ((Uu Bool)) B5))) (and (@ (@ member_o (@ product_fst_o_o X2)) A4) (@ (@ member_o (@ product_snd_o_o X2)) B5)))) (forall ((M (-> nat int)) (G (-> nat nat)) (X2 nat) (N (-> int int)) (H (-> nat int)) (F (-> int nat))) (=> (= (@ M (@ G X2)) (@ N (@ H X2))) (= (@ (@ (@ comp_nat_nat_nat (@ (@ comp_int_nat_nat F) M)) G) X2) (@ (@ (@ comp_int_nat_nat (@ (@ comp_int_nat_int F) N)) H) X2)))) (@ wf_nat _let_19) (forall ((B product_prod_nat_nat) (B5 (-> Bool set_Pr1261947904930325089at_nat)) (A4 set_o) (A Bool)) (let ((_let_1 (@ member8440522571783428010at_nat B))) (=> (@ _let_1 (@ comple1930127330929219688at_nat (@ (@ image_7077428525161401678at_nat B5) A4))) (=> (@ (@ member_o A) A4) (@ _let_1 (@ B5 A)))))) (forall ((F (-> product_unit nat)) (A4 set_Product_unit)) (=> (@ order_7096114683908731117it_nat F) (=> (@ condit2080475194861589617t_unit A4) (=> (not (= A4 bot_bo3957492148770167129t_unit)) (@ (@ ord_less_eq_nat (@ complete_Sup_Sup_nat (@ (@ image_875570014554754200it_nat F) A4))) (@ F (@ comple4687483117567863418t_unit A4))))))) (forall ((A4 set_set_nat)) (= (@ comple7399068483239264473et_nat (@ (@ image_7916887816326733075et_nat id_set_nat) A4)) (@ comple7399068483239264473et_nat A4))) (forall ((M (-> nat nat)) (G (-> nat nat)) (X2 nat) (N (-> nat nat)) (H (-> nat nat)) (F (-> nat nat))) (let ((_let_1 (@ comp_nat_nat_nat F))) (=> (= (@ M (@ G X2)) (@ N (@ H X2))) (= (@ (@ (@ comp_nat_nat_nat (@ _let_1 M)) G) X2) (@ (@ (@ comp_nat_nat_nat (@ _let_1 N)) H) X2))))) _let_109 (@ (@ (@ (@ bNF_re7626690874201225453um_num (lambda ((Y2 int) (Z int)) (= Y2 Z))) (lambda ((Y2 num) (Z num)) (= Y2 Z))) _let_108) _let_108) (forall ((F (-> nat int)) (A4 set_nat) (B5 set_int)) (let ((_let_1 (@ image_nat_int F))) (=> (@ (@ ord_less_eq_set_int (@ _let_1 A4)) B5) (@ (@ ord_le4403425263959731960et_int (@ (@ image_3739036796817536367et_int _let_1) (@ finite_Fpow_nat A4))) (@ finite_Fpow_int B5))))) (forall ((F (-> int nat)) (V (-> char int))) (= (@ (@ image_char_nat (@ (@ comp_int_nat_char F) V)) top_top_set_char) (@ (@ image_int_nat F) (@ (@ image_char_int V) top_top_set_char)))) (forall ((C nat) (F (-> nat nat))) (= (@ (@ comp_nat_nat_nat (lambda ((X4 nat)) C)) F) (lambda ((X4 nat)) C))) (forall ((G (-> int nat)) (F (-> int int)) (A4 set_int)) (=> (@ (@ inj_on_int_nat (@ (@ comp_int_nat_int G) F)) A4) (@ (@ inj_on_int_nat G) (@ (@ image_int_int F) A4)))) (forall ((A4 set_Pr4329608150637261639at_nat) (U set_nat) (F (-> produc3843707927480180839at_nat set_nat))) (=> (forall ((I4 produc3843707927480180839at_nat)) (=> (@ (@ member8757157785044589968at_nat I4) A4) (@ (@ ord_less_eq_set_nat U) (@ F I4)))) (@ (@ ord_less_eq_set_nat U) (@ comple7806235888213564991et_nat (@ (@ image_3160451284896210088et_nat F) A4))))) (forall ((X5 set_int) (P2 (-> int Bool))) (@ (@ ord_less_eq_set_int (@ collect_int (lambda ((X4 int)) (and (@ P2 X4) (@ (@ member_int X4) X5))))) X5)) (forall ((H (-> int int product_prod_int_int)) (F (-> int int)) (G (-> int int)) (X2 product_prod_int_int)) (= (@ (@ produc4245557441103728435nt_int H) (@ (@ (@ produc6036585564866528938nt_int F) G) X2)) (@ (@ 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(forall ((G (-> nat nat))) (= (@ (@ comp_nat_nat_nat id_nat) G) G)) (forall ((I produc3843707927480180839at_nat) (A4 set_Pr4329608150637261639at_nat) (F (-> produc3843707927480180839at_nat set_nat))) (=> (@ (@ member8757157785044589968at_nat I) A4) (@ (@ ord_less_eq_set_nat (@ comple7806235888213564991et_nat (@ (@ image_3160451284896210088et_nat F) A4))) (@ F I)))) (forall ((G (-> int nat)) (F (-> int int)) (A4 set_int)) (= (@ complete_Inf_Inf_nat (@ (@ image_int_nat G) (@ (@ image_int_int F) A4))) (@ complete_Inf_Inf_nat (@ (@ image_int_nat (@ (@ comp_int_nat_int G) F)) A4)))) _let_107 (forall ((Z2 produc7812382424243267045t_unit) (A4 set_ref_a) (F (-> ref_a heap_e7401611519738050253t_unit))) (=> (@ (@ member7849944260330398460t_unit Z2) (@ collec3252306575900995386t_unit (@ produc4924168586796184916unit_o (@ (@ bNF_Gr6510375311308651680t_unit A4) F)))) (@ (@ member_ref_a (@ produc473321116828791851t_unit Z2)) A4))) (forall ((F (-> char char)) (G (-> char int))) (=> (= (@ (@ image_char_char F) top_top_set_char) top_top_set_char) (=> (= (@ (@ image_char_int G) top_top_set_char) top_top_set_int) (= (@ (@ image_6605449789044937888ar_int (@ (@ produc5842583022792146073ar_int F) G)) top_to1235241553633177651r_char) top_to3104204703268025230ar_int)))) (forall ((C3 set_nat) (A4 set_nat) (B5 (-> nat set_nat))) (let ((_let_1 (@ (@ minus_minus_set_nat A4) (@ comple7399068483239264473et_nat (@ (@ image_nat_set_nat B5) C3))))) (let ((_let_2 (= C3 bot_bot_set_nat))) (and (=> _let_2 (= _let_1 A4)) (=> (not _let_2) (= _let_1 (@ comple7806235888213564991et_nat (@ (@ image_nat_set_nat (lambda ((X4 nat)) (@ (@ minus_minus_set_nat A4) (@ B5 X4)))) C3)))))))) (forall ((F (-> rat int)) (G (-> nat rat)) (A4 set_nat)) (= (@ (@ image_rat_int F) (@ (@ image_nat_rat G) A4)) (@ (@ image_nat_int (lambda ((X4 nat)) (@ F (@ G X4)))) A4))) (forall ((F (-> nat nat)) (A4 set_nat)) (=> (@ (@ inj_on_nat_nat F) A4) (= (@ finite_card_nat (@ (@ image_nat_nat F) A4)) (@ finite_card_nat A4)))) (forall ((A4 set_o) (F (-> Bool nat)) (U nat)) (let ((_let_1 (@ (@ image_o_nat F) A4))) (=> (not (= A4 bot_bot_set_o)) (=> (@ condit2214826472909112428ve_nat _let_1) (= (@ (@ ord_less_eq_nat (@ complete_Sup_Sup_nat _let_1)) U) (forall ((X4 Bool)) (=> (@ (@ member_o X4) A4) (@ (@ ord_less_eq_nat (@ F X4)) U)))))))) (forall ((C3 set_o) (A4 set_nat) (B5 (-> Bool set_nat))) (let ((_let_1 (= C3 bot_bot_set_o))) (and (=> _let_1 (= (@ comple7399068483239264473et_nat (@ (@ image_o_set_nat (lambda ((X4 Bool)) (@ (@ sup_sup_set_nat A4) (@ B5 X4)))) C3)) bot_bot_set_nat)) (=> (not _let_1) (= (@ comple7399068483239264473et_nat (@ (@ image_o_set_nat (lambda ((X4 Bool)) (@ (@ sup_sup_set_nat A4) (@ B5 X4)))) C3)) (@ (@ sup_sup_set_nat A4) (@ comple7399068483239264473et_nat (@ (@ image_o_set_nat B5) C3)))))))) (forall ((R3 set_Pr4329608150637261639at_nat) (S5 set_Pr4329608150637261639at_nat)) (= (@ (@ ord_le3935385432712749774_nat_o (lambda ((X4 set_Pr1261947904930325089at_nat) (Y5 set_Pr1261947904930325089at_nat)) (@ (@ member8757157785044589968at_nat (@ (@ produc2922128104949294807at_nat X4) Y5)) R3))) (lambda ((X4 set_Pr1261947904930325089at_nat) (Y5 set_Pr1261947904930325089at_nat)) (@ (@ member8757157785044589968at_nat (@ (@ produc2922128104949294807at_nat X4) Y5)) S5))) (@ (@ ord_le1268244103169919719at_nat R3) S5))) (forall ((U nat) (A4 set_nat) (A nat) (B5 (-> nat set_nat))) (=> (@ (@ member_nat U) A4) (= (@ comple7399068483239264473et_nat (@ (@ image_nat_set_nat (lambda ((X4 nat)) (@ (@ insert_nat A) (@ B5 X4)))) A4)) (@ (@ insert_nat A) (@ comple7399068483239264473et_nat (@ (@ image_nat_set_nat B5) A4)))))) (forall ((A4 set_nat) (B5 (-> nat set_nat))) (=> (@ finite_finite_nat A4) (= (@ finite_finite_nat (@ comple7399068483239264473et_nat (@ (@ image_nat_set_nat B5) A4))) (forall ((X4 nat)) (=> (@ (@ member_nat X4) A4) (@ finite_finite_nat (@ B5 X4))))))) (forall ((R3 (-> int code_integer Bool))) (= (@ (@ relcom967497705283160040nteger (lambda ((Y2 int) (Z int)) (= Y2 Z))) R3) R3)) (forall ((X2 nat)) (@ (@ total_on_nat (@ (@ insert_nat X2) bot_bot_set_nat)) (@ (@ insert8211810215607154385at_nat (@ (@ product_Pair_nat_nat X2) X2)) bot_bo2099793752762293965at_nat))) (forall ((M (-> nat nat)) (G (-> int nat)) (X2 int) (N (-> int nat)) (H (-> int int)) (F (-> nat num))) (=> (= (@ M (@ G X2)) (@ N (@ H X2))) (= (@ (@ (@ comp_nat_num_int (@ (@ comp_nat_num_nat F) M)) G) X2) (@ (@ (@ comp_int_num_int (@ (@ comp_nat_num_int F) N)) H) X2)))) (forall ((A4 set_nat) (B5 set_nat) (F (-> nat int))) (let ((_let_1 (@ image_nat_int F))) (=> (@ (@ ord_less_eq_set_nat A4) B5) (@ (@ ord_less_eq_set_int (@ _let_1 A4)) (@ _let_1 B5))))) (forall ((P2 (-> product_prod_nat_nat Bool)) (Q2 (-> product_prod_nat_nat product_prod_nat_nat Bool))) (= (@ collec7088162979684241874at_nat (@ produc6590410687421337004_nat_o (lambda ((X4 product_prod_nat_nat) (Y5 product_prod_nat_nat)) (and (@ (@ Q2 X4) Y5) (@ P2 X4))))) (@ (@ produc2761391749766926216at_nat (@ collec3392354462482085612at_nat P2)) (lambda ((X4 product_prod_nat_nat)) (@ collec3392354462482085612at_nat (@ Q2 X4)))))) (forall ((R1 (-> Bool Bool Bool)) (Abs1 (-> Bool Bool)) (Rep1 (-> Bool Bool)) (T1 (-> Bool Bool Bool)) (R22 (-> Bool Bool Bool)) (Abs22 (-> Bool nat)) (Rep22 (-> nat Bool)) (T22 (-> Bool nat Bool))) (=> (@ (@ (@ (@ quotient_o_o R1) Abs1) Rep1) T1) (=> (@ (@ (@ (@ quotient_o_nat R22) Abs22) Rep22) T22) (@ (@ (@ (@ quotient_o_nat (@ (@ relcompp_o_o_o T1) (@ (@ relcompp_o_o_o R22) (@ conversep_o_o T1)))) (@ (@ comp_o_nat_o Abs22) Abs1)) (@ (@ comp_o_o_nat Rep1) Rep22)) (@ (@ relcompp_o_o_nat T1) T22))))) (forall ((A4 set_Pr1261947904930325089at_nat) (B5 set_Pr1261947904930325089at_nat)) (=> (@ finite6177210948735845034at_nat A4) (=> (@ finite6177210948735845034at_nat B5) (=> (@ (@ ord_less_eq_nat (@ finite711546835091564841at_nat A4)) (@ finite711546835091564841at_nat B5)) (exists ((F5 (-> product_prod_nat_nat product_prod_nat_nat))) (and (@ (@ inj_on8969904277767023793at_nat F5) A4) (@ (@ ord_le3146513528884898305at_nat (@ (@ image_5168914502847457605at_nat F5) A4)) B5))))))) (forall ((A4 set_nat) (F (-> nat nat))) (let ((_let_1 (@ (@ image_nat_nat F) A4))) (=> (@ finite_finite_nat A4) (=> (@ (@ ord_less_eq_set_nat _let_1) A4) (=> (@ (@ inj_on_nat_nat F) A4) (= _let_1 A4)))))) (forall ((F (-> produc3843707927480180839at_nat Bool)) (A set_Pr1261947904930325089at_nat) (B set_Pr1261947904930325089at_nat)) (=> (@ (@ (@ produc7820828192191229133_nat_o F) A) B) (@ F (@ (@ produc2922128104949294807at_nat A) B)))) (forall ((X5 set_Pr1261947904930325089at_nat) (Y4 set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ ord_le3146513528884898305at_nat X5))) (=> (@ _let_1 Y4) (@ _let_1 (@ collec3392354462482085612at_nat (@ produc6081775807080527818_nat_o (@ fun_in_rel_nat_nat Y4))))))) (forall ((G (-> nat num)) (H (-> int nat)) (R (-> int num)) (F (-> num num))) (=> (= (@ (@ comp_nat_num_int G) H) R) (= (@ (@ comp_nat_num_int (@ (@ 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(@ bNF_re1865807574169326223at_o_o (lambda ((Y2 rat) (Z rat)) (= Y2 Z))) R3) X2) Y3) (@ (@ (@ (@ bNF_re1865807574169326223at_o_o (lambda ((Y2 rat) (Z rat)) (= Y2 Z))) Ra) Ya) Xa2)))))) (forall ((Prod product_prod_int_int)) (@ (@ produc4947309494688390418_int_o (lambda ((Uu int) (Uv int)) true)) Prod)) (forall ((A (-> nat num)) (B (-> int nat)) (C (-> int num)) (V int)) (=> (= (@ (@ comp_nat_num_int A) B) C) (= (@ A (@ B V)) (@ C V)))) _let_106 (forall ((F (-> Bool product_unit)) (A4 set_o)) (= (= (@ (@ image_o_Product_unit F) A4) bot_bo3957492148770167129t_unit) (= A4 bot_bot_set_o))) (forall ((F (-> int nat)) (A4 set_int)) (=> (@ (@ inj_on_int_nat F) A4) (@ (@ inj_on1389844818000382683et_nat (@ image_int_nat F)) (@ pow_int A4)))) (forall ((A product_prod_nat_nat) (A4 set_Pr1261947904930325089at_nat) (B5 (-> product_prod_nat_nat set_nat))) (=> (@ (@ member8440522571783428010at_nat A) A4) (@ (@ ord_less_eq_set_nat (@ comple7806235888213564991et_nat (@ (@ image_15824709712370754et_nat B5) A4))) (@ B5 A)))) (forall ((F (-> nat product_unit)) (A nat) (B5 set_nat)) (let ((_let_1 (@ image_8730104196221521654t_unit F))) (= (@ _let_1 (@ (@ insert_nat A) B5)) (@ (@ insert_Product_unit (@ F A)) (@ _let_1 B5))))) (forall ((X2 product_prod_int_int) (A4 (-> int int Bool))) (=> (@ (@ member5262025264175285858nt_int X2) (@ collec213857154873943460nt_int (@ produc4947309494688390418_int_o A4))) (@ (@ A4 (@ product_fst_int_int X2)) (@ product_snd_int_int X2)))) (forall ((A4 set_Product_unit) (B5 set_o) (C3 set_Product_unit) (D set_o)) (= (= (@ (@ produc4996980317674386579unit_o A4) (lambda ((Uu product_unit)) B5)) (@ (@ produc4996980317674386579unit_o C3) (lambda ((Uu product_unit)) D))) (or (and (= A4 C3) (= B5 D)) (and (or (= C3 bot_bo3957492148770167129t_unit) (= D bot_bot_set_o)) (or (= A4 bot_bo3957492148770167129t_unit) (= B5 bot_bot_set_o)))))) (forall ((X2 ref_a) (Y3 heap_e7401611519738050253t_unit) (A ref_a)) (=> (= (@ produc473321116828791851t_unit (@ (@ 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T2)) (@ (@ inf_inf_set_rat (@ (@ image_rat_rat (lambda ((X4 rat)) (@ (@ minus_minus_rat X4) A))) S2)) (@ (@ image_rat_rat (lambda ((X4 rat)) (@ (@ minus_minus_rat X4) A))) T2)))) (forall ((K product_prod_nat_nat) (I3 set_Pr1261947904930325089at_nat) (A4 (-> product_prod_nat_nat set_Pr1261947904930325089at_nat))) (let ((_let_1 (@ comple1930127330929219688at_nat (@ (@ image_5423882813909314213at_nat A4) I3)))) (=> (@ (@ member8440522571783428010at_nat K) I3) (= (@ (@ inf_in2572325071724192079at_nat (@ A4 K)) _let_1) _let_1)))) (forall ((C product_prod_o_int) (A4 set_o) (B5 (-> Bool set_int))) (=> (@ (@ member7847949116333733898_o_int C) (@ (@ product_Sigma_o_int A4) B5)) (not (forall ((X Bool)) (=> (@ (@ member_o X) A4) (forall ((Y int)) (=> (@ (@ member_int Y) (@ B5 X)) (not (= C (@ (@ product_Pair_o_int X) Y)))))))))) (forall ((X2 produc1799199577659733785_ref_a)) (= (@ produc473321116828791851t_unit (@ produc6214465446503547763_ref_a X2)) (@ produc6369869760173755749_ref_a X2))) (forall ((A nat) (B num) (A2 nat) (B2 num)) (=> (= (@ (@ product_Pair_nat_num A) B) (@ (@ product_Pair_nat_num A2) B2)) (not (=> (= A A2) (not (= B B2)))))) (forall ((Ac produc2963269191615333738nteger) (P2 (-> int int Bool)) (Q2 (-> int code_integer Bool))) (=> (@ (@ member4345257455949424659nteger Ac) (@ collec7215431352809750357nteger (@ produc540600059291021473eger_o (@ (@ relcom967497705283160040nteger P2) Q2)))) (@ (@ member4345257455949424659nteger (@ (@ (@ bNF_sn8000174127721201323nteger P2) Q2) Ac)) (@ collec7215431352809750357nteger (@ produc540600059291021473eger_o Q2))))) (forall ((A4 set_Product_unit) (C int)) (=> (not (= A4 bot_bo3957492148770167129t_unit)) (= (@ complete_Inf_Inf_int (@ (@ image_873079544045703924it_int (lambda ((X4 product_unit)) C)) A4)) C))) (forall ((P2 (-> product_prod_nat_nat product_prod_nat_nat Bool)) (Q2 (-> product_prod_nat_nat int Bool)) (A product_prod_nat_nat) (C int)) (let ((_let_1 (@ (@ (@ (@ bNF_pi770922605693484880at_int P2) Q2) A) C))) (=> (@ (@ (@ (@ relcom8911704206367525917at_int P2) Q2) A) C) (and (@ (@ P2 A) _let_1) (@ (@ Q2 _let_1) C))))) (forall ((A4 set_nat) (C set_rat)) (let ((_let_1 (= A4 bot_bot_set_nat))) (and (=> _let_1 (= (@ comple4298007329820168263et_rat (@ (@ image_nat_set_rat (lambda ((Y5 nat)) C)) A4)) top_top_set_rat)) (=> (not _let_1) (= (@ comple4298007329820168263et_rat (@ (@ image_nat_set_rat (lambda ((Y5 nat)) C)) A4)) C))))) (forall ((A code_integer)) (= (@ (@ image_4470545334726330049nteger (lambda ((X4 code_integer)) (@ (@ minus_8373710615458151222nteger X4) A))) top_to4645266643341252675nteger) top_to4645266643341252675nteger)) (forall ((F (-> int nat)) (G (-> nat int)) (A4 set_int) (B5 set_nat)) (= (@ (@ image_2751100147091372101at_int (@ produc208361644738540083at_int (lambda ((X4 int) (Y5 nat)) (@ (@ product_Pair_nat_int (@ F X4)) (@ G Y5))))) (@ (@ produc1456381018704787142nt_nat A4) (lambda ((Uu int)) B5))) (@ (@ produc454536836294682310at_int (@ (@ image_int_nat F) A4)) (lambda ((Uu nat)) (@ (@ image_nat_int G) B5))))) (forall ((B5 set_Pr4329608150637261639at_nat) (A4 set_Pr4329608150637261639at_nat) (F (-> produc3843707927480180839at_nat set_nat)) (G (-> produc3843707927480180839at_nat set_nat))) (=> (@ (@ ord_le1268244103169919719at_nat B5) A4) (=> (forall ((X produc3843707927480180839at_nat)) (=> (@ (@ member8757157785044589968at_nat X) B5) (@ (@ ord_less_eq_set_nat (@ F X)) (@ G X)))) (@ (@ ord_less_eq_set_nat (@ comple7806235888213564991et_nat (@ (@ image_3160451284896210088et_nat F) A4))) (@ comple7806235888213564991et_nat (@ (@ image_3160451284896210088et_nat G) B5)))))) (forall ((I product_prod_nat_nat) (A4 set_Pr1261947904930325089at_nat) (F (-> product_prod_nat_nat product_unit))) (=> (@ (@ member8440522571783428010at_nat I) A4) (@ (@ ord_le3221252021190050221t_unit (@ F I)) (@ comple4687483117567863418t_unit (@ (@ image_6169909464789311569t_unit F) A4))))) (forall ((F (-> int int)) (A4 set_int) (B5 set_int)) (let ((_let_1 (@ image_int_int F))) (=> (@ (@ inj_on_int_int F) top_top_set_int) (= (@ (@ ord_less_eq_set_int (@ _let_1 A4)) (@ _let_1 B5)) (@ (@ ord_less_eq_set_int A4) B5))))) (forall ((F (-> int nat)) (A4 set_int) (F3 (-> nat num))) (=> (@ (@ inj_on_int_nat F) A4) (= (@ (@ inj_on_nat_num F3) (@ (@ image_int_nat F) A4)) (@ (@ inj_on_int_num (@ (@ comp_nat_num_int F3) F)) A4)))) (forall ((S5 set_Pr4329608150637261639at_nat) (F (-> produc3843707927480180839at_nat Bool Bool)) (X2 produc3843707927480180839at_nat) (Y3 produc3843707927480180839at_nat) (G (-> nat Bool))) (let ((_let_1 (@ comp_o_o_nat (@ F Y3)))) (let ((_let_2 (@ comp_o_o_nat (@ F X2)))) (=> (@ (@ finite2818816984019561153_nat_o S5) F) (=> (@ (@ member8757157785044589968at_nat X2) S5) (=> (@ (@ member8757157785044589968at_nat Y3) S5) (= (@ _let_1 (@ _let_2 G)) (@ _let_2 (@ _let_1 G))))))))) (forall ((A4 set_o) (F (-> Bool nat)) (B5 set_nat)) (=> (forall ((X Bool)) (=> (@ (@ member_o X) A4) (@ (@ member_nat (@ F X)) B5))) (@ (@ ord_less_eq_set_nat (@ (@ image_o_nat F) A4)) B5))) (forall ((F (-> product_prod_nat_nat produc7812382424243267045t_unit)) (A4 set_ref_a) (B5 set_he8644174446132254637t_unit)) (= (@ (@ vimage4308919176130087787t_unit F) (@ (@ produc3946373962484743846t_unit A4) (lambda ((Uu ref_a)) B5))) (@ (@ inf_in2572325071724192079at_nat (@ (@ vimage7322659125625010723_ref_a (@ (@ comp_P7986581389989349338at_nat produc473321116828791851t_unit) F)) A4)) (@ (@ vimage1024995831485383111t_unit (@ (@ comp_P6390991081591698364at_nat produc1126150082675451753t_unit) F)) B5)))) (forall ((P2 (-> int Bool)) (F (-> int int)) (G (-> int int)) (S5 set_int)) (let ((_let_1 (@ inf_inf_set_int S5))) (= (@ (@ image_int_int (lambda ((X4 int)) (@ (@ (@ if_int (@ P2 X4)) (@ F X4)) (@ G X4)))) S5) (@ (@ sup_sup_set_int (@ (@ image_int_int F) (@ _let_1 (@ collect_int P2)))) (@ (@ image_int_int G) (@ _let_1 (@ collect_int (lambda ((X4 int)) (not (@ P2 X4)))))))))) (forall ((B Bool) (F (-> Bool Bool)) (X2 Bool) (A4 set_o)) (=> (= B (@ F X2)) (=> (@ (@ member_o X2) A4) (@ (@ member_o B) (@ (@ image_o_o F) A4))))) (forall ((A4 set_o) (B5 set_o) (C3 (-> Bool product_unit)) (D (-> Bool product_unit))) (=> (= A4 B5) (=> (forall ((X Bool)) (=> (@ (@ member_o X) B5) (= (@ C3 X) (@ D X)))) (= (@ comple4687483117567863418t_unit (@ (@ image_o_Product_unit C3) A4)) (@ comple4687483117567863418t_unit (@ (@ image_o_Product_unit D) B5)))))) (forall ((A4 set_ref_a) (B5 set_he8644174446132254637t_unit)) (let ((_let_1 (@ produc3946373962484743846t_unit A4))) (let ((_let_2 (@ image_17660834435998945t_unit produc1126150082675451753t_unit))) (let ((_let_3 (= A4 bot_bot_set_ref_a))) (and (=> _let_3 (= (@ _let_2 (@ _let_1 (lambda ((Uu ref_a)) B5))) bot_bo3686245532977126937t_unit)) (=> (not _let_3) (= (@ _let_2 (@ _let_1 (lambda ((Uu ref_a)) B5))) B5))))))) (forall ((F (-> product_unit Bool)) (A4 set_Product_unit)) (= (= (@ (@ image_Product_unit_o F) A4) bot_bot_set_o) (= A4 bot_bo3957492148770167129t_unit))) (forall ((F (-> nat nat)) (B5 set_nat) (A nat) (A4 set_nat)) (let ((_let_1 (@ member_nat A))) (=> (@ (@ inj_on_nat_nat F) B5) (=> (@ _let_1 B5) (=> (@ (@ ord_less_eq_set_nat A4) B5) (= (@ (@ member_nat (@ F A)) (@ (@ image_nat_nat F) A4)) (@ _let_1 A4))))))) (forall ((A4 set_int) (G (-> int int)) (B5 set_int) (F (-> int int))) (let ((_let_1 (@ (@ image_int_int G) B5))) (=> (not (= A4 bot_bot_set_int)) (=> (@ condit1735850657277959132ow_int _let_1) (=> (@ (@ ord_less_eq_set_int A4) B5) (=> (forall ((X int)) (=> (@ (@ member_int X) B5) (@ (@ ord_less_eq_int (@ G X)) (@ F X)))) (@ (@ ord_less_eq_int (@ complete_Inf_Inf_int _let_1)) (@ complete_Inf_Inf_int (@ (@ image_int_int F) A4))))))))) (forall ((G (-> int nat)) (F (-> int int)) (A4 set_int)) (= (@ complete_Sup_Sup_nat (@ (@ image_int_nat G) (@ (@ image_int_int F) A4))) (@ complete_Sup_Sup_nat (@ (@ image_int_nat (@ (@ comp_int_nat_int G) F)) A4)))) (forall ((A4 (-> int int Bool)) (B5 (-> int code_integer Bool))) (=> (@ right_total_int_int A4) (=> (@ right_7281159819619925802nteger B5) (@ right_7281159819619925802nteger (@ (@ relcom967497705283160040nteger A4) B5))))) (forall ((P2 (-> product_prod_nat_nat Bool)) (F (-> product_prod_nat_nat Bool)) (B5 set_o)) (=> (forall ((X product_prod_nat_nat)) (=> (@ P2 X) (@ (@ member_o (@ F X)) B5))) (@ (@ ord_less_eq_set_o (@ (@ image_3693632289388996572_nat_o F) (@ collec3392354462482085612at_nat P2))) B5))) (forall ((C product_prod_int_int) (F (-> int int)) (G (-> int int)) (R3 set_Pr958786334691620121nt_int)) (=> (@ (@ member5262025264175285858nt_int C) (@ (@ image_2653370878348428101nt_int (@ (@ produc6036585564866528938nt_int F) G)) R3)) (not (forall ((X int) (Y int)) (=> (= C (@ (@ product_Pair_int_int (@ F X)) (@ G Y))) (not (@ (@ member5262025264175285858nt_int (@ (@ product_Pair_int_int X) Y)) R3))))))) (forall ((A4 set_nat) (B5 set_nat) (C3 (-> nat nat)) (D (-> nat nat))) (=> (= A4 B5) (=> (forall ((X nat)) (=> (@ (@ member_nat X) B5) (= (@ C3 X) (@ D X)))) (= (@ complete_Sup_Sup_nat (@ (@ image_nat_nat C3) A4)) (@ complete_Sup_Sup_nat (@ (@ image_nat_nat D) B5)))))) (forall ((C3 set_o) (A4 set_nat) (B5 (-> Bool set_nat))) (let ((_let_1 (@ (@ sup_sup_set_nat A4) (@ comple7399068483239264473et_nat (@ (@ image_o_set_nat B5) C3))))) (let ((_let_2 (= C3 bot_bot_set_o))) (and (=> (not _let_2) (= _let_1 (@ comple7399068483239264473et_nat (@ (@ image_o_set_nat (lambda ((X4 Bool)) (@ (@ sup_sup_set_nat A4) (@ B5 X4)))) C3)))) (=> _let_2 (= _let_1 A4)))))) (forall ((P rat) (Q rat)) (= (@ quotient_of (@ (@ divide_divide_rat P) Q)) (@ (@ produc4245557441103728435nt_int (lambda ((A5 int) (C4 int)) (@ (@ produc4245557441103728435nt_int (lambda ((B4 int) (D3 int)) (@ normalize (@ (@ product_Pair_int_int (@ (@ times_times_int A5) D3)) (@ (@ times_times_int C4) B4))))) (@ quotient_of Q)))) (@ quotient_of P)))) (forall ((P product_prod_nat_num) (Z2 Bool) (C (-> nat num set_o))) (=> (forall ((A3 nat) (B3 num)) (=> (= P (@ (@ product_Pair_nat_num A3) B3)) (@ (@ member_o Z2) (@ (@ C A3) B3)))) (@ (@ member_o Z2) (@ (@ produc836176033315069408_set_o C) P)))) (forall ((A ref_a) (P produc7812382424243267045t_unit)) (= (@ (@ member_ref_a A) (@ basic_685971451221398055t_unit P)) (= A (@ produc473321116828791851t_unit P)))) (forall ((A4 set_nat) (F (-> nat product_unit)) (A nat)) (let ((_let_1 (@ image_8730104196221521654t_unit F))) (let ((_let_2 (@ _let_1 A4))) (=> (not (= A4 bot_bot_set_nat)) (=> (@ condit9161856309968323677t_unit _let_2) (= (@ comple2584293577114468500t_unit (@ _let_1 (@ (@ insert_nat A) A4))) (@ (@ inf_inf_Product_unit (@ F A)) (@ comple2584293577114468500t_unit _let_2)))))))) (forall ((R2 (-> int int Bool)) (R (-> int int Bool)) (S3 (-> int code_integer Bool)) (S2 (-> int code_integer Bool))) (=> (@ (@ ord_le6741204236512500942_int_o R2) R) (=> (@ (@ ord_le996066559646421213eger_o S3) S2) (@ (@ ord_le996066559646421213eger_o (@ (@ relcom967497705283160040nteger R2) S3)) (@ (@ relcom967497705283160040nteger R) S2))))) (forall ((F (-> nat nat)) (A4 set_nat) (B5 set_nat)) (let ((_let_1 (@ image_nat_nat F))) (=> (@ (@ inj_on_nat_nat F) top_top_set_nat) (= (= (@ _let_1 A4) (@ _let_1 B5)) (= A4 B5))))) (forall ((F (-> nat int)) (G (-> nat rat)) (A4 set_nat)) (= (@ (@ image_3337248961327643342nt_rat (lambda ((X4 nat)) (@ (@ product_Pair_int_rat (@ F X4)) (@ G X4)))) A4) (@ (@ produc821250958618291406nt_rat (@ (@ image_nat_int F) A4)) (lambda ((X4 int)) (@ (@ image_nat_rat G) (@ (@ inf_inf_set_nat (@ (@ vimage_nat_int F) (@ (@ insert_int X4) bot_bot_set_int))) A4)))))) (forall ((S5 set_Pr1261947904930325089at_nat) (F (-> product_prod_nat_nat nat nat)) (X2 product_prod_nat_nat) (Y3 product_prod_nat_nat) (G (-> nat nat))) (let ((_let_1 (@ comp_nat_nat_nat (@ F Y3)))) (let ((_let_2 (@ comp_nat_nat_nat (@ F X2)))) (=> (@ (@ finite2110315540964234241at_nat S5) F) (=> (@ (@ member8440522571783428010at_nat X2) S5) (=> (@ (@ member8440522571783428010at_nat Y3) S5) (= (@ _let_1 (@ _let_2 G)) (@ _let_2 (@ _let_1 G))))))))) (forall ((B8 set_set_nat) (A4 set_nat)) (let ((_let_1 (@ inf_inf_set_nat A4))) (let ((_let_2 (@ _let_1 (@ comple7806235888213564991et_nat B8)))) (let ((_let_3 (= B8 bot_bot_set_set_nat))) (and (=> (not _let_3) (= _let_2 (@ comple7806235888213564991et_nat (@ (@ image_7916887816326733075et_nat _let_1) B8)))) (=> _let_3 (= _let_2 A4))))))) (forall ((X2 code_integer) (Y3 code_integer)) (= (@ (@ (@ if_Code_integer false) X2) Y3) Y3)) (forall ((F (-> Bool Bool)) (G (-> nat Bool)) (R set_nat)) (= (@ (@ image_o_o F) (@ (@ image_nat_o G) R)) (@ (@ image_nat_o (@ (@ comp_o_o_nat F) G)) R))) (forall ((F (-> product_prod_nat_nat product_prod_nat_nat)) (A4 set_Pr1261947904930325089at_nat) (B5 set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ image_5168914502847457605at_nat F))) (@ (@ ord_le3146513528884898305at_nat (@ _let_1 (@ (@ inf_in2572325071724192079at_nat A4) B5))) (@ (@ inf_in2572325071724192079at_nat (@ _let_1 A4)) (@ _let_1 B5))))) (forall ((X2 product_prod_nat_nat)) (= (@ nat2 (@ abs_Integ X2)) (@ (@ produc6842872674320459806at_nat minus_minus_nat) X2))) (forall ((P2 (-> ref_a heap_e7401611519738050253t_unit Bool)) (X2 ref_a) (Y3 heap_e7401611519738050253t_unit) (A produc7812382424243267045t_unit)) (=> (@ (@ P2 X2) Y3) (=> (= A (@ (@ produc6544324848051098391t_unit X2) Y3)) (@ (@ P2 (@ produc473321116828791851t_unit A)) (@ produc1126150082675451753t_unit A))))) (forall ((X2 nat) (Y3 nat)) (=> (= X2 Y3) (@ (@ (@ (@ bNF_Grp_nat_nat top_top_set_nat) id_nat) X2) Y3))) (forall ((X2 Bool) (A4 set_o) (C Bool)) (=> (@ (@ member_o X2) A4) (= (@ (@ image_o_o (lambda ((X4 Bool)) C)) A4) (@ (@ insert_o C) bot_bot_set_o)))) _let_105 (forall ((A4 set_Pr1261947904930325089at_nat) (F (-> product_prod_nat_nat nat))) (=> (not (@ finite6177210948735845034at_nat A4)) (=> (@ finite_finite_nat (@ (@ image_2486076414777270412at_nat F) A4)) (exists ((X product_prod_nat_nat)) (and (not (@ finite6177210948735845034at_nat (@ collec3392354462482085612at_nat (lambda ((A5 product_prod_nat_nat)) (and (@ (@ member8440522571783428010at_nat A5) A4) (= (@ F A5) (@ F X))))))) (@ (@ member8440522571783428010at_nat X) A4)))))) _let_104 _let_103 (forall ((I3 set_o) (F (-> Bool set_nat)) (X2 set_nat)) (=> (not (= I3 bot_bot_set_o)) (=> (forall ((I4 Bool)) (=> (@ (@ member_o I4) I3) (= (@ F I4) X2))) (= (@ comple7806235888213564991et_nat (@ (@ image_o_set_nat F) I3)) X2)))) (= relcom8911704206367525917at_int (lambda ((R5 (-> product_prod_nat_nat product_prod_nat_nat Bool)) (S (-> product_prod_nat_nat int Bool)) (A12 product_prod_nat_nat) (A23 int)) (exists ((A5 product_prod_nat_nat) (B4 product_prod_nat_nat) (C4 int)) (and (= A12 A5) (= A23 C4) (@ (@ S B4) C4) (@ (@ R5 A5) B4))))) (forall ((F (-> nat nat)) (A4 set_nat)) (=> (@ finite_finite_nat (@ (@ image_nat_nat F) A4)) (=> (not (@ finite_finite_nat A4)) (exists ((X nat)) (and (not (@ finite_finite_nat (@ (@ inf_inf_set_nat (@ (@ vimage_nat_nat F) (@ (@ insert_nat X) bot_bot_set_nat))) A4))) (@ (@ member_nat X) (@ (@ image_nat_nat F) A4))))))) _let_102 _let_101 (forall ((A4 set_int) (B int) (B5 (-> int set_int))) (=> (forall ((X int)) (=> (@ (@ member_int X) A4) (@ (@ member_int B) (@ B5 X)))) (@ (@ member_int B) (@ comple3628384868704368283et_int (@ (@ image_int_set_int B5) A4))))) _let_100 (forall ((A4 set_nat) (B5 set_set_nat)) (let ((_let_1 (@ inf_inf_set_nat A4))) (= (@ _let_1 (@ comple7399068483239264473et_nat B5)) (@ comple7399068483239264473et_nat (@ (@ image_7916887816326733075et_nat _let_1) B5))))) _let_98 (forall ((Y3 num) (X2 nat) (A4 set_Pr6200539531224447659at_num)) (= (@ (@ member6570852975090897396um_nat (@ (@ product_Pair_num_nat Y3) X2)) (@ (@ image_2347970371937200581um_nat product_swap_nat_num) A4)) (@ (@ member9148766508732265716at_num (@ (@ product_Pair_nat_num X2) Y3)) A4))) (forall ((F (-> nat nat)) (A4 set_set_nat)) (let ((_let_1 (@ vimage_nat_nat F))) (= (@ _let_1 (@ comple7399068483239264473et_nat A4)) (@ comple7399068483239264473et_nat (@ (@ image_7916887816326733075et_nat _let_1) A4))))) (forall ((P product_prod_nat_nat)) (=> (@ (@ member8440522571783428010at_nat P) id_nat2) (not (forall ((X nat)) (not (= P (@ (@ product_Pair_nat_nat X) X))))))) _let_97 (forall ((G (-> nat int)) (F (-> int nat))) (=> (@ finite_finite_int (@ (@ image_nat_int G) top_top_set_nat)) (@ finite_finite_nat (@ (@ image_nat_nat (lambda ((X4 nat)) (@ F (@ G X4)))) top_top_set_nat)))) (forall ((X2 nat) (A4 set_nat) (B int) (F (-> nat int))) (=> (@ (@ member_nat X2) A4) (=> (= B (@ F X2)) (@ (@ member_int B) (@ (@ image_nat_int F) A4))))) (forall ((X2 (-> char Bool)) (Ya (-> char Bool)) (Y3 (-> char nat)) (Xa2 (-> char nat)) (R3 (-> Bool nat Bool)) (Ra (-> Bool nat Bool))) (=> (= X2 Ya) (=> (= Y3 Xa2) (=> (forall ((Z3 Bool) (Yb nat)) (=> (@ (@ member_o Z3) (@ (@ image_char_o Ya) top_top_set_char)) (=> (@ (@ member_nat Yb) (@ (@ image_char_nat Xa2) top_top_set_char)) (= (@ (@ R3 Z3) Yb) (@ (@ Ra Z3) Yb))))) (= (@ (@ (@ (@ bNF_re4782998131235581479_o_nat (lambda ((Y2 char) (Z char)) (= Y2 Z))) R3) X2) Y3) (@ (@ (@ (@ bNF_re4782998131235581479_o_nat (lambda ((Y2 char) (Z char)) (= Y2 Z))) Ra) Ya) Xa2)))))) _let_94 (forall ((P2 (-> rat int product_unit))) (= (@ comple4687483117567863418t_unit (@ (@ image_5846526143423701914t_unit (lambda ((Y5 int)) (@ comple2584293577114468500t_unit (@ (@ image_2327579789247107822t_unit (lambda ((X4 rat)) (@ (@ P2 X4) Y5))) top_top_set_rat)))) top_top_set_int)) (@ comple2584293577114468500t_unit (@ (@ image_4174709274675160035t_unit (lambda ((X4 (-> int rat))) (@ comple4687483117567863418t_unit (@ (@ image_5846526143423701914t_unit (lambda ((Y5 int)) (@ (@ P2 (@ X4 Y5)) Y5))) top_top_set_int)))) top_top_set_int_rat)))) (forall ((F (-> nat num)) (G (-> int nat)) (H (-> int nat)) (I (-> int int))) (= (@ (@ comp_P3772045228931366376nt_int (@ (@ produc5918048235202344416nt_nat F) G)) (@ (@ produc5664932004629684302nt_int H) I)) (@ (@ produc3608230303109393468nt_nat (@ (@ comp_nat_num_int F) H)) (@ (@ comp_int_nat_int G) I)))) (forall ((B5 set_nat) (F (-> int 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Y5) bot_bo3957492148770167129t_unit)))) B6)))) (forall ((F (-> int nat)) (A4 set_int)) (= (= (@ (@ image_int_nat F) A4) bot_bot_set_nat) (= A4 bot_bot_set_int))) (forall ((X2 nat) (Y3 nat)) (= (@ (@ (@ if_nat false) X2) Y3) Y3)) (forall ((P2 (-> nat Bool)) (Q2 (-> product_prod_nat_nat Bool))) (= (@ collec5903703980526211963at_nat (@ produc5864757623865647827_nat_o (lambda ((A5 nat) (B4 product_prod_nat_nat)) (and (@ P2 A5) (@ Q2 B4))))) (@ (@ produc1809337555817847783at_nat (@ collect_nat P2)) (lambda ((Uu nat)) (@ collec3392354462482085612at_nat Q2))))) (forall ((B nat) (B5 (-> nat set_nat)) (A4 set_nat) (A nat)) (let ((_let_1 (@ member_nat B))) (=> (@ _let_1 (@ comple7806235888213564991et_nat (@ (@ image_nat_set_nat B5) A4))) (=> (@ (@ member_nat A) A4) (@ _let_1 (@ B5 A)))))) _let_92 (forall ((A4 set_nat) (F (-> nat nat))) (=> (@ finite_finite_nat A4) (=> (= (@ finite_card_nat (@ (@ image_nat_nat F) A4)) (@ finite_card_nat A4)) (@ (@ inj_on_nat_nat F) A4)))) (forall ((A nat) (A4 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Bool))) (= (forall ((B6 set_nat)) (=> (and (@ (@ ord_less_eq_set_nat B6) (@ (@ image_2486076414777270412at_nat F) A4)) (@ finite_finite_nat B6)) (@ P2 B6))) (forall ((B6 set_Pr1261947904930325089at_nat)) (=> (and (@ finite6177210948735845034at_nat B6) (@ (@ ord_le3146513528884898305at_nat B6) A4)) (@ P2 (@ (@ image_2486076414777270412at_nat F) B6)))))) _let_90 (forall ((F (-> Bool Bool)) (A Bool) (A4 set_o)) (=> (@ (@ inj_on_o_o F) top_top_set_o) (= (@ (@ member_o (@ F A)) (@ (@ image_o_o F) A4)) (@ (@ member_o A) A4)))) (forall ((M (-> int int)) (G (-> int int)) (X2 int) (N (-> int int)) (H (-> int int)) (F (-> int nat))) (let ((_let_1 (@ comp_int_nat_int F))) (=> (= (@ M (@ G X2)) (@ N (@ H X2))) (= (@ (@ (@ comp_int_nat_int (@ _let_1 M)) G) X2) (@ (@ (@ comp_int_nat_int (@ _let_1 N)) H) X2))))) (forall ((F (-> nat nat)) (A4 set_nat) (G (-> nat nat)) (B5 set_nat) (H (-> nat nat))) (let ((_let_1 (@ comp_nat_nat_nat H))) (=> (= (@ (@ image_nat_nat F) A4) (@ (@ image_nat_nat G) B5)) (= (@ (@ image_nat_nat (@ _let_1 F)) A4) (@ (@ image_nat_nat (@ _let_1 G)) B5))))) (forall ((I produc3843707927480180839at_nat) (A4 set_Pr4329608150637261639at_nat) (F (-> produc3843707927480180839at_nat product_unit))) (=> (@ (@ member8757157785044589968at_nat I) A4) (@ (@ ord_le3221252021190050221t_unit (@ F I)) (@ comple4687483117567863418t_unit (@ (@ image_7082456443403096939t_unit F) A4))))) (forall ((A4 set_nat) (C int)) (=> (not (= A4 bot_bot_set_nat)) (= (@ complete_Inf_Inf_int (@ (@ image_nat_int (lambda ((X4 nat)) C)) A4)) C))) (forall ((F (-> rat rat)) (B5 set_rat) (A4 set_rat)) (let ((_let_1 (@ image_rat_rat F))) (=> (= (@ _let_1 top_top_set_rat) top_top_set_rat) (=> (@ (@ ord_less_eq_set_rat (@ (@ vimage_rat_rat F) B5)) A4) (@ (@ ord_less_eq_set_rat B5) (@ _let_1 A4)))))) (forall ((M set_nat)) (=> (@ finite_finite_nat M) (=> (not (= M bot_bot_set_nat)) (=> (not (@ (@ member_nat zero_zero_nat) M)) (= (@ gcd_Gcd_nat M) (@ lattic8265883725875713057ax_nat (@ 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image_o_set_nat D) B5)))))) (forall ((A4 (-> product_unit set_Product_unit)) (I product_unit) (B5 set_Product_unit) (J3 set_Product_unit)) (= (@ comple3349607820504768346t_unit (@ (@ image_7778121751606633509t_unit (@ (@ (@ fun_up488859312337516701t_unit A4) I) B5)) J3)) (@ (@ sup_su793286257634532545t_unit (@ comple3349607820504768346t_unit (@ (@ image_7778121751606633509t_unit A4) (@ (@ minus_6452836326544984404t_unit J3) (@ (@ insert_Product_unit I) bot_bo3957492148770167129t_unit))))) (@ (@ (@ if_set_Product_unit (@ (@ member_Product_unit I) J3)) B5) bot_bo3957492148770167129t_unit)))) (forall ((C3 set_nat) (A4 (-> nat set_int)) (B5 set_int)) (let ((_let_1 (= C3 bot_bot_set_nat))) (and (=> _let_1 (= (@ comple3628384868704368283et_int (@ (@ image_nat_set_int (lambda ((X4 nat)) (@ (@ inf_inf_set_int (@ A4 X4)) B5))) C3)) top_top_set_int)) (=> (not _let_1) (= (@ comple3628384868704368283et_int (@ (@ image_nat_set_int (lambda ((X4 nat)) (@ (@ inf_inf_set_int (@ A4 X4)) B5))) C3)) (@ (@ 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right_8475562212078014689nteger R7) (=> (@ left_t2374113004080657585nteger R7) (=> (@ left_u4005249686606446046at_int S6) (=> (@ right_1157779049177982926at_int S6) (@ (@ ord_le8615040745438789472_int_o (@ (@ bNF_re2828929484557863493at_int (@ (@ relcom967497705283160040nteger R3) R7)) (@ (@ relcom8911704206367525917at_int S5) S6))) (@ (@ relcom2127790875031262553er_int (@ (@ bNF_re8766404587435608311at_nat R3) S5)) (@ (@ bNF_re2828929484557863493at_int R7) S6)))))))) _let_87 (forall ((F (-> Bool Bool)) (A4 set_o) (P2 (-> Bool Bool))) (= (@ collect_o (lambda ((X4 Bool)) (and (@ P2 X4) (@ (@ member_o X4) (@ (@ image_o_o F) A4))))) (@ (@ image_o_o F) (@ collect_o (lambda ((X4 Bool)) (and (@ (@ member_o X4) A4) (@ P2 (@ F X4)))))))) (forall ((K Bool) (I3 set_o) (A4 (-> Bool set_nat))) (let ((_let_1 (@ comple7806235888213564991et_nat (@ (@ image_o_set_nat A4) I3)))) (=> (@ (@ member_o K) I3) (= (@ (@ inf_inf_set_nat (@ A4 K)) _let_1) _let_1)))) (= (lambda ((Y2 nat) (Z nat)) (= Y2 Z)) (@ (@ 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comple2584293577114468500t_unit _let_2)) (@ comple2584293577114468500t_unit _let_1)) (@ comple2584293577114468500t_unit (@ (@ image_o_Product_unit (lambda ((A5 Bool)) (@ (@ inf_inf_Product_unit (@ F A5)) (@ G A5)))) A4))))))))) (forall ((A4 set_nat) (B5 set_int) (F (-> nat int))) (=> (@ finite_finite_nat A4) (=> (@ (@ ord_less_eq_set_int B5) (@ (@ image_nat_int F) A4)) (@ finite_finite_int B5)))) (forall ((X2 Bool) (A4 set_o) (C product_unit)) (=> (@ (@ member_o X2) A4) (= (@ (@ image_o_Product_unit (lambda ((X4 Bool)) C)) A4) (@ (@ insert_Product_unit C) bot_bo3957492148770167129t_unit)))) (forall ((F (-> nat rat)) (A4 set_nat) (G (-> nat rat)) (B5 set_nat) (H (-> rat int))) (let ((_let_1 (@ comp_rat_int_nat H))) (=> (= (@ (@ image_nat_rat F) A4) (@ (@ image_nat_rat G) B5)) (= (@ (@ image_nat_int (@ _let_1 F)) A4) (@ (@ image_nat_int (@ _let_1 G)) B5))))) (forall ((R3 set_Pr958786334691620121nt_int) (S5 set_Pr958786334691620121nt_int)) (= (= (lambda ((X4 int) (Y5 int)) (@ (@ member5262025264175285858nt_int (@ (@ product_Pair_int_int X4) Y5)) R3)) (lambda ((X4 int) (Y5 int)) (@ (@ member5262025264175285858nt_int (@ (@ product_Pair_int_int X4) Y5)) S5))) (= R3 S5))) (forall ((F (-> rat rat)) (G (-> nat rat)) (A4 set_nat)) (= (@ (@ image_rat_rat F) (@ (@ image_nat_rat G) A4)) (@ (@ image_nat_rat (lambda ((X4 nat)) (@ F (@ G X4)))) A4))) (forall ((A4 set_nat) (B5 (-> nat set_nat))) (= (@ (@ image_2486076414777270412at_nat product_fst_nat_nat) (@ (@ produc457027306803732586at_nat A4) B5)) (@ collect_nat (lambda ((X4 nat)) (and (not (= (@ B5 X4) bot_bot_set_nat)) (@ (@ member_nat X4) A4)))))) (forall ((C3 set_o) (A4 (-> Bool set_nat)) (B5 set_nat)) (let ((_let_1 (@ (@ sup_sup_set_nat (@ comple7399068483239264473et_nat (@ (@ image_o_set_nat A4) C3))) B5))) (let ((_let_2 (= C3 bot_bot_set_o))) (and (=> _let_2 (= _let_1 B5)) (=> (not _let_2) (= _let_1 (@ comple7399068483239264473et_nat (@ (@ image_o_set_nat (lambda ((X4 Bool)) (@ (@ sup_sup_set_nat (@ A4 X4)) B5))) C3)))))))) (forall ((R (-> product_prod_nat_nat product_prod_nat_nat Bool)) (S2 (-> product_prod_nat_nat int Bool)) (A product_prod_nat_nat) (C int)) (=> (@ (@ (@ (@ relcom8911704206367525917at_int R) S2) A) C) (not (forall ((B3 product_prod_nat_nat)) (=> (@ (@ R A) B3) (not (@ (@ S2 B3) C))))))) (forall ((Y3 set_Pr4329608150637261639at_nat) (X2 set_Pr4329608150637261639at_nat) (A4 set_Pr7459493094073627847at_nat)) (= (@ (@ member1466754251312161552at_nat (@ (@ produc9060074326276436823at_nat Y3) X2)) (@ (@ image_3313167189156628421at_nat produc5396952528824381687at_nat) A4)) (@ (@ member1466754251312161552at_nat (@ (@ produc9060074326276436823at_nat X2) Y3)) A4))) (forall ((R22 (-> Bool nat Bool)) (R32 (-> Bool nat Bool)) (R1 (-> nat nat Bool))) (let ((_let_1 (@ bNF_re7523573913982466217_o_nat R1))) (@ (@ (@ (@ bNF_re1515921786380824775at_nat (@ (@ bNF_re4209105892566519389_o_nat R22) R32)) (@ (@ bNF_re2144779315220482269at_nat (@ _let_1 R22)) (@ _let_1 R32))) comp_o_o_nat) comp_nat_nat_nat))) _let_86 (forall ((F (-> Bool product_unit))) (= (@ comple4687483117567863418t_unit (@ (@ image_o_Product_unit F) bot_bot_set_o)) bot_bot_Product_unit)) (forall ((F (-> int int)) (A4 set_int)) (=> (@ finite_finite_int (@ (@ image_int_int F) A4)) (=> (@ (@ inj_on_int_int F) A4) (@ finite_finite_int A4)))) (forall ((I3 set_nat) (C product_unit) (F (-> nat product_unit))) (=> (not (= I3 bot_bot_set_nat)) (=> (forall ((I4 nat)) (=> (@ (@ member_nat I4) I3) (@ (@ ord_le3221252021190050221t_unit C) (@ F I4)))) (= (= (@ comple4687483117567863418t_unit (@ (@ image_8730104196221521654t_unit F) I3)) C) (forall ((X4 nat)) (=> (@ (@ member_nat X4) I3) (= (@ F X4) C))))))) (forall ((X2 nat) (Y3 nat)) (= (@ (@ (@ if_nat true) X2) Y3) X2)) (forall ((A4 set_nat) (F (-> nat int)) (B5 set_int)) (=> (forall ((X nat)) (=> (@ (@ member_nat X) A4) (@ (@ member_int (@ F X)) B5))) (@ (@ ord_less_eq_set_int (@ (@ image_nat_int F) A4)) B5))) (forall ((F (-> nat rat)) (A4 set_nat) (G (-> nat rat)) (B5 set_nat)) (=> (@ (@ inj_on_nat_rat F) A4) (=> (@ (@ inj_on_nat_rat G) B5) (=> (= (@ (@ inf_inf_set_rat (@ (@ image_nat_rat F) A4)) (@ (@ image_nat_rat G) B5)) bot_bot_set_rat) (@ (@ inj_on_nat_rat (lambda ((X4 nat)) (@ (@ (@ if_rat (@ (@ member_nat X4) A4)) (@ F X4)) (@ G X4)))) (@ (@ sup_sup_set_nat A4) B5)))))) (forall ((A (-> int nat)) (B (-> int int)) (C (-> int nat)) (D2 (-> int int))) (=> (= (@ (@ comp_int_nat_int A) B) (@ (@ comp_int_nat_int C) D2)) (forall ((V4 int)) (= (@ A (@ B V4)) (@ C (@ D2 V4)))))) (forall ((A4 set_int) (F (-> int nat))) (=> (@ finite_finite_int A4) (@ (@ ord_less_eq_nat (@ finite_card_nat (@ (@ image_int_nat F) A4))) (@ finite_card_int A4)))) (forall ((A4 (-> int code_integer Bool)) (B5 (-> num num Bool)) (F (-> int num)) (G (-> code_integer num))) (=> (forall ((X int) (Y code_integer)) (=> (@ (@ A4 X) Y) (@ (@ B5 (@ F X)) (@ G Y)))) (@ (@ (@ (@ bNF_re6718328864250387230um_num A4) B5) F) G))) (forall ((F (-> int int)) (A4 set_int) (P2 (-> set_int Bool))) (= (forall ((B6 set_int)) (=> (and (@ finite_finite_int B6) (@ (@ ord_less_eq_set_int B6) (@ (@ image_int_int F) A4))) (@ P2 B6))) (forall ((B6 set_int)) (=> (and (@ finite_finite_int B6) (@ (@ ord_less_eq_set_int B6) A4)) (@ P2 (@ (@ image_int_int F) B6)))))) (forall ((X2 set_Pr4329608150637261639at_nat) (Y3 set_Pr4329608150637261639at_nat)) (= (@ basic_5713354656523905413at_nat (@ (@ produc9060074326276436823at_nat X2) Y3)) (@ (@ insert2290795007606087959at_nat Y3) bot_bo1534825418459847827at_nat))) (forall ((X1 nat) (X22 num)) (= (@ product_snd_nat_num (@ (@ product_Pair_nat_num X1) X22)) X22)) (forall ((F (-> int nat)) (G (-> rat int))) (= (@ (@ image_rat_nat (lambda ((X4 rat)) (@ F (@ G X4)))) top_top_set_rat) (@ (@ image_int_nat F) (@ (@ image_rat_int G) top_top_set_rat)))) _let_83 (forall ((F (-> int int)) (A4 set_int) (B5 set_int)) (let ((_let_1 (@ image_int_int F))) (= (@ _let_1 (@ (@ sup_sup_set_int A4) B5)) (@ (@ sup_sup_set_int (@ _let_1 A4)) (@ _let_1 B5))))) (forall ((S5 set_se7855581050983116737at_nat)) (= (@ comple3592611370556534995_nat_o (@ (@ image_6923511907955291850_nat_o (lambda ((I2 set_Pr1261947904930325089at_nat) (X4 nat) (Y5 nat)) (@ (@ member8440522571783428010at_nat (@ (@ product_Pair_nat_nat X4) Y5)) I2))) S5)) (lambda ((X4 nat) (Y5 nat)) (@ (@ member8440522571783428010at_nat (@ (@ product_Pair_nat_nat X4) Y5)) (@ comple5685304695842803022at_nat S5))))) (forall ((A4 set_o) (B5 (-> Bool set_o)) (F (-> Bool int))) (=> (not (= A4 bot_bot_set_o)) (=> (forall ((X Bool)) (=> (@ (@ member_o X) A4) (not (= (@ B5 X) bot_bot_set_o)))) (=> (@ condit1735850657277959132ow_int (@ comple3221217463730067765et_int (@ (@ image_o_set_int (lambda ((X4 Bool)) (@ (@ image_o_int F) (@ B5 X4)))) A4))) (= (@ complete_Inf_Inf_int (@ (@ image_o_int F) (@ comple90263536869209701_set_o (@ (@ image_o_set_o B5) A4)))) (@ complete_Inf_Inf_int (@ (@ image_o_int (lambda ((X4 Bool)) (@ complete_Inf_Inf_int (@ (@ image_o_int F) (@ B5 X4))))) A4))))))) (forall ((A4 set_int) (F (-> int int))) (=> (@ finite_finite_int A4) (= (@ (@ inj_on_int_int F) A4) (= (@ finite_card_int (@ (@ image_int_int F) A4)) (@ finite_card_int A4))))) (forall ((G (-> rat char)) (F (-> char rat))) (=> (forall ((X char)) (= (@ G (@ F X)) X)) (= (@ (@ image_rat_char G) top_top_set_rat) top_top_set_char))) (@ (@ (@ type_d6188575255521822967unit_o product_Rep_unit) product_Abs_unit) (@ (@ insert_o true) bot_bot_set_o)) (forall ((F (-> code_integer code_integer code_integer)) (A4 set_Code_integer) (F3 (-> (-> code_integer code_integer) produc8923325533196201883nteger produc8923325533196201883nteger))) (=> (@ (@ inj_on108595395805848489nteger F) A4) (= (@ (@ inj_on3998011822705705585nteger F3) (@ (@ image_2177946750938214461nteger F) A4)) (@ (@ inj_on7031512951821619701nteger (@ (@ comp_C8797469213163452608nteger F3) F)) A4)))) (forall ((A4 set_o) (F (-> Bool int)) (B5 set_o)) (let ((_let_1 (@ image_o_int F))) (let ((_let_2 (@ _let_1 B5))) (let ((_let_3 (@ _let_1 A4))) (=> (not (= A4 bot_bot_set_o)) (=> (@ condit1735850657277959132ow_int _let_3) (=> (not (= B5 bot_bot_set_o)) (=> (@ condit1735850657277959132ow_int _let_2) (= (@ complete_Inf_Inf_int (@ _let_1 (@ (@ sup_sup_set_o A4) B5))) (@ (@ inf_inf_int (@ complete_Inf_Inf_int _let_3)) (@ complete_Inf_Inf_int _let_2))))))))))) _let_82 (forall ((Z2 nat) (F (-> nat nat)) (A4 set_nat)) (= (@ (@ member_nat Z2) (@ (@ image_nat_nat F) A4)) (exists ((X4 nat)) (and (@ (@ member_nat X4) A4) (= Z2 (@ F X4)))))) (forall ((F (-> nat nat)) (A4 set_nat) (P2 (-> nat Bool))) (=> (forall ((X nat)) (=> (@ (@ member_nat X) (@ (@ image_nat_nat F) A4)) (@ P2 X))) (forall ((X6 nat)) (=> (@ (@ member_nat X6) A4) (@ P2 (@ F X6)))))) (forall ((Z2 nat) (C (-> nat nat set_nat)) (P product_prod_nat_nat)) (=> (@ (@ member_nat Z2) (@ (@ produc6189476227299908564et_nat C) P)) (not (forall ((X nat) (Y nat)) (=> (= P (@ (@ product_Pair_nat_nat X) Y)) (not (@ (@ member_nat Z2) (@ (@ C X) Y)))))))) (forall ((Inf (-> set_rat rat)) (G (-> nat rat)) (F (-> nat nat)) (A4 set_nat)) (= (@ Inf (@ (@ image_nat_rat G) (@ (@ image_nat_nat F) A4))) (@ Inf (@ (@ image_nat_rat (@ (@ comp_nat_rat_nat G) F)) A4)))) (forall ((Ac produc2963269191615333738nteger) (P2 (-> int int Bool)) (Q2 (-> int code_integer Bool))) (=> (@ (@ member4345257455949424659nteger Ac) (@ collec7215431352809750357nteger (@ produc540600059291021473eger_o (@ (@ relcom967497705283160040nteger P2) Q2)))) (@ (@ member5262025264175285858nt_int (@ (@ (@ bNF_fs4543836202474805097nteger P2) Q2) Ac)) (@ collec213857154873943460nt_int (@ produc4947309494688390418_int_o P2))))) (forall ((Inf (-> set_nat nat)) (G (-> nat nat)) (F (-> int nat)) (A4 set_int)) (= (@ Inf (@ (@ image_nat_nat G) (@ (@ image_int_nat F) A4))) (@ Inf (@ (@ image_int_nat (@ (@ comp_nat_nat_int G) F)) A4)))) (forall ((P2 (-> num nat Bool)) (Y3 num) (X2 nat)) (let ((_let_1 (@ (@ product_Pair_nat_num X2) Y3))) (=> (@ (@ P2 Y3) X2) (@ (@ P2 (@ product_snd_nat_num _let_1)) (@ product_fst_nat_num _let_1))))) _let_81 (forall ((A4 set_int) (A7 set_int)) (=> (not (= A4 bot_bot_set_int)) (= (exists ((F2 (-> int int))) (and (@ (@ ord_less_eq_set_int (@ (@ image_int_int F2) A4)) A7) (@ (@ inj_on_int_int F2) A4))) (exists ((G3 (-> int int))) (= (@ (@ image_int_int G3) A7) A4))))) (forall ((X2 nat) (Fx num) (A4 set_nat) (F (-> nat num))) (=> (@ (@ member9148766508732265716at_num (@ (@ product_Pair_nat_num X2) Fx)) (@ (@ bNF_Gr_nat_num A4) F)) (= (@ F X2) Fx))) _let_80 (forall ((X2 produc3843707927480180839at_nat) (Y3 set_Pr1261947904930325089at_nat) (Z2 set_Pr1261947904930325089at_nat)) (=> (= X2 (@ (@ produc2922128104949294807at_nat Y3) Z2)) (= (@ produc6011863565407846595at_nat X2) Y3))) (forall ((Rep (-> nat Bool)) (Abs (-> Bool nat)) (Rep2 (-> Bool char)) (Abs2 (-> char Bool)) (Rep3 (-> nat Bool)) (Abs3 (-> Bool nat)) (M (-> Bool char)) (M1 (-> Bool char)) (M2 (-> Bool Bool))) (let ((_let_1 (@ comp_char_o_o Abs2))) (=> (@ (@ (@ type_d1000680970699258650_nat_o Rep) Abs) top_top_set_o) (=> (@ (@ (@ type_d9076672964931703357o_char Rep2) Abs2) top_top_set_char) (=> (@ (@ (@ type_d1000680970699258650_nat_o Rep3) Abs3) top_top_set_o) (=> (= (@ (@ comp_o_o_nat (@ _let_1 M)) Rep3) (@ (@ comp_nat_o_nat (@ (@ comp_o_o_nat (@ _let_1 M1)) Rep)) (@ (@ comp_o_nat_nat (@ (@ comp_o_nat_o Abs) M2)) Rep3))) (= (@ (@ comp_o_char_o M1) M2) M))))))) (forall ((F (-> int nat)) (A4 set_int) (B5 set_nat)) (let ((_let_1 (@ image_int_nat F))) (=> (@ (@ ord_less_eq_set_nat (@ _let_1 A4)) B5) (@ (@ ord_le6893508408891458716et_nat (@ (@ image_4702325430467532143et_nat _let_1) (@ pow_int A4))) (@ pow_nat B5))))) _let_79 (forall ((M (-> produc859450856879609959at_nat set_nat)) (A4 set_Pr8693737435421807431at_nat) (B5 set_Pr8693737435421807431at_nat)) (let ((_let_1 (@ image_2819269535336293544et_nat M))) (= (@ comple7806235888213564991et_nat (@ _let_1 (@ (@ sup_su718114333110466843at_nat A4) B5))) (@ (@ inf_inf_set_nat (@ comple7806235888213564991et_nat (@ _let_1 A4))) (@ comple7806235888213564991et_nat (@ _let_1 B5)))))) (forall ((R3 (-> product_prod_nat_nat int Bool))) (= (@ (@ relcom8911704206367525917at_int (lambda ((Y2 product_prod_nat_nat) (Z product_prod_nat_nat)) (= Y2 Z))) R3) R3)) (forall ((F (-> Bool Bool)) (B5 set_o) (A Bool) (A4 set_o)) (let ((_let_1 (@ member_o A))) (=> (@ (@ inj_on_o_o F) B5) (=> (@ _let_1 B5) (=> (@ (@ ord_less_eq_set_o A4) B5) (= (@ (@ member_o (@ F A)) (@ (@ image_o_o F) A4)) (@ _let_1 A4))))))) (forall ((K nat) (I3 set_nat) (A4 (-> nat product_unit))) (let ((_let_1 (@ comple2584293577114468500t_unit (@ (@ image_8730104196221521654t_unit A4) I3)))) (=> (@ (@ member_nat K) I3) (= (@ (@ inf_inf_Product_unit (@ A4 K)) _let_1) _let_1)))) (forall ((F (-> Bool set_Pr1261947904930325089at_nat)) (A Bool) (A4 set_o)) (let ((_let_1 (@ image_7077428525161401678at_nat F))) (= (@ comple1930127330929219688at_nat (@ _let_1 (@ (@ insert_o A) A4))) (@ (@ inf_in2572325071724192079at_nat (@ F A)) (@ comple1930127330929219688at_nat (@ _let_1 A4)))))) (forall ((A4 set_int) (B5 set_int) (F (-> int set_nat)) (G (-> int set_nat))) (=> (@ (@ ord_less_eq_set_int A4) B5) (=> (forall ((X int)) (=> (@ (@ member_int X) A4) (@ (@ ord_less_eq_set_nat (@ F X)) (@ G X)))) (@ (@ ord_less_eq_set_nat (@ comple7806235888213564991et_nat (@ (@ image_int_set_nat F) B5))) (@ comple7806235888213564991et_nat (@ (@ image_int_set_nat G) A4)))))) (forall ((F (-> nat int))) (= (@ (@ image_nat_int F) bot_bot_set_nat) bot_bot_set_int)) (forall ((C3 set_Product_unit) (A4 (-> product_unit set_Pr1261947904930325089at_nat)) (B5 set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ (@ inf_in2572325071724192079at_nat (@ comple1930127330929219688at_nat (@ (@ image_3617315916088684441at_nat A4) C3))) B5))) (let ((_let_2 (= C3 bot_bo3957492148770167129t_unit))) (and (=> (not _let_2) (= _let_1 (@ comple1930127330929219688at_nat (@ (@ image_3617315916088684441at_nat (lambda ((X4 product_unit)) (@ (@ inf_in2572325071724192079at_nat (@ A4 X4)) B5))) C3)))) (=> _let_2 (= _let_1 B5)))))) _let_78 (forall ((A4 set_o) (B5 (-> Bool set_nat)) (C3 set_nat)) (=> (forall ((X Bool)) (=> (@ (@ member_o X) A4) (@ (@ ord_less_eq_set_nat (@ B5 X)) C3))) (@ (@ ord_less_eq_set_nat (@ comple7399068483239264473et_nat (@ (@ image_o_set_nat B5) A4))) C3))) (forall ((F (-> rat rat)) (G (-> rat rat))) (=> (@ order_4774338944571509483at_rat F) (=> (= (@ (@ image_rat_rat F) top_top_set_rat) top_top_set_rat) (=> (forall ((X rat)) (= (@ G (@ F X)) X)) (@ order_4774338944571509483at_rat G))))) (forall ((A4 set_se5479201105039950375at_nat) (R set_Pr7459493094073627847at_nat) (X2 set_Pr4329608150637261639at_nat) (Y3 set_Pr4329608150637261639at_nat)) (=> (@ (@ refl_o6272981002401706822at_nat A4) R) (=> (@ (@ member1466754251312161552at_nat (@ (@ produc9060074326276436823at_nat X2) Y3)) R) (@ (@ member6273874620674182256at_nat X2) A4)))) (forall ((C3 set_Product_unit) (A4 set_rat) (B5 (-> product_unit set_rat))) (let ((_let_1 (= C3 bot_bo3957492148770167129t_unit))) (and (=> (not _let_1) (= (@ comple4298007329820168263et_rat (@ (@ image_4665621433434589782et_rat (lambda ((X4 product_unit)) (@ (@ inf_inf_set_rat A4) (@ B5 X4)))) C3)) (@ (@ inf_inf_set_rat A4) (@ comple4298007329820168263et_rat (@ (@ image_4665621433434589782et_rat B5) C3))))) (=> _let_1 (= (@ comple4298007329820168263et_rat (@ (@ image_4665621433434589782et_rat (lambda ((X4 product_unit)) (@ (@ inf_inf_set_rat A4) (@ B5 X4)))) C3)) top_top_set_rat))))) (forall ((B5 set_set_int) (X2 int) (A4 set_int)) (let ((_let_1 (@ insert_int X2))) (=> (forall ((C2 set_int)) (=> (@ (@ member_set_int C2) B5) (not (@ (@ member_int X2) C2)))) (= (@ (@ member_set_int A4) (@ (@ image_524474410958335435et_int _let_1) B5)) (and (@ (@ member_set_int (@ (@ minus_minus_set_int A4) (@ _let_1 bot_bot_set_int))) B5) (@ (@ member_int X2) A4)))))) (forall ((B5 set_se7855581050983116737at_nat) (A set_Pr1261947904930325089at_nat)) (= (@ (@ inf_in2572325071724192079at_nat (@ comple5685304695842803022at_nat B5)) A) (@ comple5685304695842803022at_nat (@ (@ image_3684629450409544005at_nat (lambda ((B4 set_Pr1261947904930325089at_nat)) (@ (@ inf_in2572325071724192079at_nat B4) A))) B5)))) (= produc27273713700761075at_nat (lambda ((C4 (-> nat nat product_prod_nat_nat product_prod_nat_nat)) (P3 product_prod_nat_nat) (__flatten_var_0 product_prod_nat_nat)) (@ (@ (@ C4 (@ product_fst_nat_nat P3)) (@ product_snd_nat_nat P3)) __flatten_var_0))) (forall ((B5 set_nat) (A4 set_nat) (P2 (-> nat Bool))) (let ((_let_1 (@ ord_less_eq_set_nat B5))) (=> (@ _let_1 A4) (= (@ _let_1 (@ collect_nat (lambda ((X4 nat)) (and (@ (@ member_nat X4) A4) (@ P2 X4))))) (forall ((X4 nat)) (=> (@ (@ member_nat X4) B5) (@ P2 X4))))))) (forall ((B5 (-> Bool set_Pr8693737435421807431at_nat)) (A Bool) (A4 set_o)) (let ((_let_1 (@ image_8493167801588156084at_nat B5))) (= (@ comple2748534634209756852at_nat (@ _let_1 (@ (@ insert_o A) A4))) (@ (@ sup_su718114333110466843at_nat (@ B5 A)) (@ comple2748534634209756852at_nat (@ _let_1 A4)))))) (forall ((F (-> nat nat)) (G (-> nat nat))) (=> (@ order_5726023648592871131at_nat F) (=> (= (@ (@ image_nat_nat F) top_top_set_nat) top_top_set_nat) (=> (forall ((X nat)) (= (@ G (@ F X)) X)) (@ order_5726023648592871131at_nat G))))) (forall ((F (-> rat nat)) (A4 set_rat) (B5 set_nat) (G (-> nat rat))) (=> (@ (@ inj_on_rat_nat F) A4) (=> (@ (@ ord_less_eq_set_nat (@ (@ image_rat_nat F) A4)) B5) (=> (@ (@ inj_on_nat_rat G) B5) (=> (@ (@ ord_less_eq_set_rat (@ (@ image_nat_rat G) B5)) A4) (=> (@ finite_finite_rat A4) (=> (@ finite_finite_nat B5) (= (@ finite_card_rat A4) (@ finite_card_nat B5))))))))) _let_77 (forall ((F (-> nat nat)) (C3 set_nat) (A4 set_nat) (B5 set_nat)) (let ((_let_1 (@ image_nat_nat F))) (=> (@ (@ inj_on_nat_nat F) C3) (=> (@ (@ ord_less_eq_set_nat A4) C3) (=> (@ (@ ord_less_eq_set_nat B5) C3) (= (@ _let_1 (@ (@ inf_inf_set_nat A4) B5)) (@ (@ inf_inf_set_nat (@ _let_1 A4)) (@ _let_1 B5)))))))) (forall ((F (-> Bool Bool))) (let ((_let_1 (@ (@ bNF_Grp_o_o top_top_set_o) F))) (=> (= F id_o) (= (@ (@ relcompp_o_o_o (@ conversep_o_o _let_1)) _let_1) _let_1)))) _let_76 (forall ((F (-> ref_a ref_a)) (G (-> heap_e7401611519738050253t_unit heap_e7401611519738050253t_unit))) (= (@ (@ comp_P8019343326919024234t_unit produc1126150082675451753t_unit) (@ (@ produc3456481717235892722t_unit F) G)) (@ (@ comp_h4837689053573563144t_unit G) produc1126150082675451753t_unit))) (forall ((X2 produc1319942482725812455at_nat) (Y3 set_Pr4329608150637261639at_nat) (Z2 set_Pr4329608150637261639at_nat)) (=> (= X2 (@ (@ produc9060074326276436823at_nat Y3) Z2)) (= (@ produc826222791318859909at_nat X2) Z2))) (forall ((F (-> produc1319942482725812455at_nat Bool)) (A set_Pr4329608150637261639at_nat) (B set_Pr4329608150637261639at_nat)) (=> (@ F (@ (@ produc9060074326276436823at_nat A) B)) (@ (@ (@ produc447603880154497357_nat_o F) A) B))) (forall ((A4 set_nat) (F product_unit)) (=> (not (= A4 bot_bot_set_nat)) (= (@ comple2584293577114468500t_unit (@ (@ image_8730104196221521654t_unit (lambda ((I2 nat)) F)) A4)) F))) (forall ((F (-> nat num)) (X5 set_nat)) (@ (@ inj_on6246296710604522312at_num (lambda ((X4 nat)) (@ (@ product_Pair_nat_num X4) (@ F X4)))) X5)) (@ (@ _let_75 (@ produc27273713700761075at_nat (lambda ((X4 nat) (Y5 nat) (__flatten_var_0 product_prod_nat_nat)) (@ (@ produc2626176000494625587at_nat (lambda ((U3 nat) (V3 nat)) (let ((_let_1 (@ times_times_nat Y5))) (let ((_let_2 (@ times_times_nat X4))) (@ (@ product_Pair_nat_nat (@ (@ plus_plus_nat (@ _let_2 U3)) (@ _let_1 V3))) (@ (@ plus_plus_nat (@ _let_2 V3)) (@ _let_1 U3))))))) __flatten_var_0)))) times_times_int) _let_74 (forall ((F (-> nat nat)) (A4 set_nat)) (= (@ comple7399068483239264473et_nat (@ (@ image_nat_set_nat (lambda ((X4 nat)) (@ (@ insert_nat (@ F X4)) bot_bot_set_nat))) A4)) (@ (@ image_nat_nat F) A4))) (forall ((F (-> Bool Bool)) (G (-> Bool Bool)) (H (-> nat Bool)) (I (-> nat Bool))) (= (@ (@ comp_P4785046977597218846at_nat (@ (@ produc1928436952130685430_o_o_o F) G)) (@ (@ produc6957950696844810486_nat_o H) I)) (@ (@ produc6957950696844810486_nat_o (@ (@ comp_o_o_nat F) H)) (@ (@ comp_o_o_nat G) I)))) (forall ((X2 set_Pr1261947904930325089at_nat) (Y3 set_Pr1261947904930325089at_nat)) (= (@ basic_3661821009137050567at_nat (@ (@ produc2922128104949294807at_nat X2) Y3)) (@ (@ insert9200635055090092081at_nat X2) bot_bo3083307316010499117at_nat))) (forall ((G1 (-> nat num)) (G22 (-> nat nat)) (F1 (-> int nat)) (F22 (-> nat nat)) (V product_prod_int_nat)) (= (@ (@ (@ produc4918694523301289860at_nat G1) G22) (@ (@ (@ produc4668068763237680022at_nat F1) F22) V)) (@ (@ (@ produc2608876591208338912at_nat (@ (@ comp_nat_num_int G1) F1)) (@ (@ comp_nat_nat_nat G22) F22)) V))) (forall ((A nat) (A4 set_nat) (B5 (-> nat set_nat))) (=> (@ (@ member_nat A) A4) (@ (@ ord_less_eq_set_nat (@ comple7806235888213564991et_nat (@ (@ image_nat_set_nat B5) A4))) (@ B5 A)))) (forall ((B5 set_se5479201105039950375at_nat) (X2 produc3843707927480180839at_nat) (A4 set_Pr4329608150637261639at_nat)) (let ((_let_1 (@ insert9069300056098147895at_nat X2))) (=> (forall ((C2 set_Pr4329608150637261639at_nat)) (=> (@ (@ member6273874620674182256at_nat C2) B5) (not (@ (@ member8757157785044589968at_nat X2) C2)))) (= (@ (@ member6273874620674182256at_nat A4) (@ (@ image_4303274092540115909at_nat _let_1) B5)) (and (@ (@ member8757157785044589968at_nat X2) A4) (@ (@ member6273874620674182256at_nat (@ (@ minus_3314409938677909166at_nat A4) (@ _let_1 bot_bo228742789529271731at_nat))) B5)))))) (forall ((F (-> int product_unit)) (A4 set_int) (X2 int) (U product_unit)) (let ((_let_1 (@ (@ image_5846526143423701914t_unit F) A4))) (=> (@ condit9161856309968323677t_unit _let_1) (=> (@ (@ member_int X2) A4) (=> (@ (@ ord_le3221252021190050221t_unit (@ F X2)) U) (@ (@ ord_le3221252021190050221t_unit (@ comple2584293577114468500t_unit _let_1)) U)))))) (forall ((P2 (-> nat rat product_unit))) (= (@ comple4687483117567863418t_unit (@ (@ image_2327579789247107822t_unit (lambda ((Y5 rat)) (@ comple2584293577114468500t_unit (@ (@ image_8730104196221521654t_unit (lambda ((X4 nat)) (@ (@ P2 X4) Y5))) top_top_set_nat)))) top_top_set_rat)) (@ comple2584293577114468500t_unit (@ (@ image_2910438736038083391t_unit (lambda ((X4 (-> rat nat))) (@ comple4687483117567863418t_unit (@ (@ image_2327579789247107822t_unit (lambda ((Y5 rat)) (@ (@ P2 (@ X4 Y5)) Y5))) top_top_set_rat)))) top_top_set_rat_nat)))) (= (@ (@ image_5846123807819985514at_nat nat_prod_decode) top_top_set_nat) top_to4669805908274784177at_nat) _let_73 (forall ((F (-> nat nat)) (A4 set_nat)) (=> (@ (@ inj_on_nat_nat F) A4) (@ (@ inj_on_nat_nat (@ (@ the_inv_into_nat_nat A4) F)) (@ (@ image_nat_nat F) A4)))) (forall ((Rep (-> nat char)) (Abs (-> char nat))) (=> (@ (@ (@ type_d5945782884131516111t_char Rep) Abs) top_top_set_char) (= (@ (@ comp_char_nat_nat Abs) Rep) id_nat))) (forall ((R3 (-> int int Bool)) (S5 (-> int code_integer Bool)) (T3 (-> int code_integer Bool))) (let ((_let_1 (@ relcom967497705283160040nteger R3))) (= (@ _let_1 (@ (@ sup_su1544571744061072657eger_o S5) T3)) (@ (@ sup_su1544571744061072657eger_o (@ _let_1 S5)) (@ _let_1 T3))))) (forall ((A set_Pr1261947904930325089at_nat) (P produc3843707927480180839at_nat)) (= (= A (@ produc6011863565407846595at_nat P)) (exists ((B4 set_Pr1261947904930325089at_nat)) (= P (@ (@ produc2922128104949294807at_nat A) B4))))) (forall ((G (-> nat rat)) (F (-> rat int))) (=> (@ finite_finite_rat (@ (@ image_nat_rat G) top_top_set_nat)) (@ finite_finite_int (@ (@ image_nat_int (lambda ((X4 nat)) (@ F (@ G X4)))) top_top_set_nat)))) (forall ((A nat) (B nat) (S2 nat) (T2 nat)) (=> (@ (@ ord_less_eq_nat A) B) (=> (@ (@ ord_less_eq_nat S2) T2) (@ (@ member8206827879206165904at_nat (@ (@ produc6161850002892822231at_nat (@ (@ product_Pair_nat_nat A) S2)) (@ (@ product_Pair_nat_nat B) T2))) fun_pair_leq)))) (forall ((B int) (B5 (-> int set_int)) (A4 set_int)) (=> (@ (@ member_int B) (@ comple3221217463730067765et_int (@ (@ image_int_set_int B5) A4))) (not (forall ((X int)) (=> (@ (@ member_int X) A4) (not (@ (@ member_int B) (@ B5 X)))))))) (forall ((F (-> int int)) (C3 set_int) (A4 set_int) (B5 (-> int set_int)) (J4 int)) (=> (@ (@ inj_on_int_int F) C3) (=> (forall ((X int)) (=> (@ (@ member_int X) A4) (@ (@ ord_less_eq_set_int (@ B5 X)) C3))) (=> (@ (@ member_int J4) A4) (= (@ (@ image_int_int F) (@ comple3628384868704368283et_int (@ (@ image_int_set_int B5) A4))) (@ comple3628384868704368283et_int (@ (@ image_int_set_int (lambda ((X4 int)) (@ (@ image_int_int F) (@ B5 X4)))) A4))))))) (forall ((Z2 int)) (= (@ (@ (@ comp_P6651465171681656048nt_int product_fst_int_int) (lambda ((X4 int)) (@ (@ product_Pair_int_int X4) X4))) Z2) (@ id_int Z2))) (forall ((A4 (-> product_prod_nat_nat Bool))) (= (@ id_on_2554058798563519774at_nat (@ collec3392354462482085612at_nat A4)) (@ collec7088162979684241874at_nat (@ produc6590410687421337004_nat_o (lambda ((X4 product_prod_nat_nat) (Y5 product_prod_nat_nat)) (and (= X4 Y5) (@ A4 X4))))))) (forall ((C3 set_Pr1261947904930325089at_nat) (A4 (-> product_prod_nat_nat set_Pr8693737435421807431at_nat)) (B5 set_Pr8693737435421807431at_nat)) (let ((_let_1 (@ (@ sup_su718114333110466843at_nat (@ comple2748534634209756852at_nat (@ (@ image_5803077947706746251at_nat A4) C3))) B5))) (let ((_let_2 (= C3 bot_bo2099793752762293965at_nat))) (and (=> _let_2 (= _let_1 B5)) (=> (not _let_2) (= _let_1 (@ comple2748534634209756852at_nat (@ (@ image_5803077947706746251at_nat (lambda ((X4 product_prod_nat_nat)) (@ (@ sup_su718114333110466843at_nat (@ A4 X4)) B5))) C3)))))))) (forall ((F (-> int int)) (G (-> int int)) (R3 (-> int int Bool))) (@ (@ ord_le2843351958646193337nt_int (@ (@ image_2653370878348428101nt_int (@ (@ bNF_co3748779267718262122nt_int (@ (@ comp_i4330622015127193916nt_int F) product_fst_int_int)) (@ (@ comp_i4330622015127193916nt_int G) product_snd_int_int))) (@ collec213857154873943460nt_int (@ produc4947309494688390418_int_o (@ (@ (@ bNF_vi3884084463199473129_int_o F) G) R3))))) (@ collec213857154873943460nt_int (@ produc4947309494688390418_int_o R3)))) (forall ((R1 (-> product_prod_nat_nat int Bool))) (@ (@ (@ (@ bNF_re4099335476084980305nt_nat (lambda ((Y2 (-> int nat)) (Z (-> int nat))) (= Y2 Z))) (@ (@ bNF_re3284331099615978085nt_nat (@ (@ bNF_re5552630237950767466nt_int R1) (lambda ((Y2 int) (Z int)) (= Y2 Z)))) (@ (@ bNF_re4555766996558763186at_nat R1) (lambda ((Y2 nat) (Z nat)) (= Y2 Z))))) comp_i4471277238271202272at_nat) comp_int_nat_int)) (@ (@ _let_13 (@ produc27273713700761075at_nat (lambda ((X4 nat) (Y5 nat) (__flatten_var_0 product_prod_nat_nat)) (@ (@ produc2626176000494625587at_nat (lambda ((U3 nat) (V3 nat)) (let ((_let_1 (@ times_times_nat Y5))) (let ((_let_2 (@ times_times_nat X4))) (@ (@ product_Pair_nat_nat (@ (@ plus_plus_nat (@ _let_2 U3)) (@ _let_1 V3))) (@ (@ plus_plus_nat (@ _let_2 V3)) (@ _let_1 U3))))))) __flatten_var_0)))) (@ produc27273713700761075at_nat (lambda ((X4 nat) (Y5 nat) (__flatten_var_0 product_prod_nat_nat)) (@ (@ produc2626176000494625587at_nat (lambda ((U3 nat) (V3 nat)) (let ((_let_1 (@ times_times_nat Y5))) (let ((_let_2 (@ times_times_nat X4))) (@ (@ product_Pair_nat_nat (@ (@ plus_plus_nat (@ _let_2 U3)) (@ _let_1 V3))) (@ (@ plus_plus_nat (@ _let_2 V3)) (@ _let_1 U3))))))) __flatten_var_0)))) (forall ((F (-> rat char)) (B5 set_char) (A4 set_rat)) (let ((_let_1 (@ image_rat_char F))) (=> (= (@ _let_1 top_top_set_rat) top_top_set_char) (=> (@ (@ ord_less_eq_set_rat (@ (@ vimage_rat_char F) B5)) A4) (@ (@ ord_less_eq_set_char B5) (@ _let_1 A4)))))) (forall ((F (-> Bool Bool)) (G (-> int nat)) (H (-> nat Bool)) (I (-> int int)) (Prod product_prod_nat_int)) (= (@ (@ (@ produc8070579729948654068nt_nat F) G) (@ (@ (@ produc8248099538878400170nt_int H) I) Prod)) (@ (@ (@ produc8250590009387450446nt_nat (@ (@ comp_o_o_nat F) H)) (@ (@ comp_int_nat_int G) I)) Prod))) (forall ((A4 set_nat) (C set_rat)) (let ((_let_1 (= A4 bot_bot_set_nat))) (and (=> _let_1 (= (@ comple4298007329820168263et_rat (@ (@ image_nat_set_rat (lambda ((Y5 nat)) C)) A4)) top_top_set_rat)) (=> (not _let_1) (= (@ comple4298007329820168263et_rat (@ (@ image_nat_set_rat (lambda ((Y5 nat)) C)) A4)) C))))) (forall ((H (-> product_prod_int_int product_prod_int_int)) (F (-> int int product_prod_int_int)) (Prod product_prod_int_int)) (= (@ H (@ (@ produc4245557441103728435nt_int F) Prod)) (@ (@ produc4245557441103728435nt_int (lambda ((X12 int) (X23 int)) (@ H (@ (@ F X12) X23)))) Prod))) (forall ((Rep (-> num Bool)) (Abs (-> Bool num)) (Rep2 (-> Bool Bool)) (Abs2 (-> Bool Bool)) (Rep3 (-> int nat)) (Abs3 (-> nat int)) (M (-> nat Bool)) (M1 (-> Bool Bool)) (M2 (-> nat Bool))) (=> (@ (@ (@ type_d9070036042389994064_num_o Rep) Abs) top_top_set_o) (=> (@ (@ (@ type_definition_o_o Rep2) Abs2) top_top_set_o) (=> (@ (@ (@ type_d7249847660678803242nt_nat Rep3) Abs3) top_top_set_nat) (=> (= (@ (@ comp_nat_o_int (@ (@ comp_o_o_nat Abs2) M)) Rep3) (@ (@ comp_num_o_int (@ (@ comp_o_o_num (@ (@ comp_o_o_o Abs2) M1)) Rep)) (@ (@ comp_nat_num_int (@ (@ comp_o_num_nat Abs) M2)) Rep3))) (= (@ (@ comp_o_o_nat M1) M2) M)))))) _let_72 (forall ((Rep (-> num rat)) (Abs (-> rat num)) (F (-> int nat)) (P2 (-> nat Bool)) (H (-> nat rat))) (=> (@ (@ (@ type_d3745694291998722336um_rat Rep) Abs) top_top_set_rat) (= (@ (@ (@ bNF_vi7769575839906753835_rat_o F) Rep) (@ (@ bNF_Grp_nat_rat (@ collect_nat P2)) H)) (@ (@ bNF_Grp_int_num (@ collect_int (lambda ((X4 int)) (@ P2 (@ F X4))))) (@ (@ comp_nat_num_int (@ (@ comp_rat_num_nat Abs) H)) F))))) (forall ((B5 set_o) (A4 set_o)) (let ((_let_1 (@ product_Sigma_o_o A4))) (let ((_let_2 (@ image_7896445794123959606_o_o_o product_fst_o_o))) (let ((_let_3 (= B5 bot_bot_set_o))) (and (=> (not _let_3) (= (@ _let_2 (@ _let_1 (lambda ((Uu Bool)) B5))) A4)) (=> _let_3 (= (@ _let_2 (@ _let_1 (lambda ((Uu Bool)) B5))) bot_bot_set_o))))))) (forall ((H (-> product_prod_int_int int)) (F (-> int int product_prod_int_int)) (Prod product_prod_int_int)) (= (@ H (@ (@ produc4245557441103728435nt_int F) Prod)) (@ (@ produc8211389475949308722nt_int (lambda ((X12 int) (X23 int)) (@ H (@ (@ F X12) X23)))) Prod))) (forall ((A4 set_o) (B5 set_nat) (F (-> Bool product_unit)) (G (-> nat product_unit))) (=> (forall ((I4 Bool)) (=> (@ (@ member_o I4) A4) (exists ((X6 nat)) (and (@ (@ member_nat X6) B5) (@ (@ ord_le3221252021190050221t_unit (@ F I4)) (@ G X6)))))) (=> (forall ((J2 nat)) (=> (@ (@ member_nat J2) B5) (exists ((X6 Bool)) (and (@ (@ member_o X6) A4) (@ (@ ord_le3221252021190050221t_unit (@ G J2)) (@ F X6)))))) (= (@ comple4687483117567863418t_unit (@ (@ image_o_Product_unit F) A4)) (@ comple4687483117567863418t_unit (@ (@ image_8730104196221521654t_unit G) B5)))))) _let_71 (forall ((F (-> rat Bool)) (X2 rat)) (@ (@ member_o (@ F X2)) (@ (@ image_rat_o F) top_top_set_rat))) (forall ((X1 set_Pr1261947904930325089at_nat) (X22 set_Pr1261947904930325089at_nat)) (= (@ produc6011863565407846595at_nat (@ (@ produc2922128104949294807at_nat X1) X22)) X1)) (forall ((X2 int) (A4 set_int) (F (-> int nat))) (let ((_let_1 (@ (@ image_int_nat F) A4))) (=> (@ (@ member_int X2) A4) (=> (@ condit2214826472909112428ve_nat _let_1) (@ (@ ord_less_eq_nat (@ F X2)) (@ complete_Sup_Sup_nat _let_1)))))) (= produc4245557441103728435nt_int (lambda ((F2 (-> int int product_prod_int_int)) (P3 product_prod_int_int)) (@ (@ F2 (@ product_fst_int_int P3)) (@ product_snd_int_int P3)))) (forall ((F (-> nat rat)) (A4 set_nat) (P2 (-> rat Bool))) (=> (exists ((X6 rat)) (and (@ (@ member_rat X6) (@ (@ image_nat_rat F) A4)) (@ P2 X6))) (exists ((X nat)) (and (@ P2 (@ F X)) (@ (@ member_nat X) A4))))) (forall ((H2 heap_e7401611519738050253t_unit) (R ref_a) (F (-> a a)) (H heap_e7401611519738050253t_unit) (X2 a)) (let ((_let_1 (@ F (@ (@ get_a H) R)))) (=> (= H2 (@ (@ (@ set_a R) _let_1) H)) (=> (= X2 _let_1) (@ (@ (@ (@ heap_effect_a (@ (@ change_a F) R)) H) H2) X2))))) (forall ((F (-> Bool int)) (A Bool) (A4 set_o)) (let ((_let_1 (@ insert_o A))) (let ((_let_2 (@ inj_on_o_int F))) (= (@ _let_2 (@ _let_1 A4)) (and (@ _let_2 A4) (not (@ (@ member_int (@ F A)) (@ (@ image_o_int F) (@ (@ minus_minus_set_o A4) (@ _let_1 bot_bot_set_o)))))))))) (forall ((A Bool) (A4 set_o) (B5 (-> Bool set_nat))) (=> (@ (@ member_o A) A4) (@ (@ ord_less_eq_set_nat (@ B5 A)) (@ comple7399068483239264473et_nat (@ (@ image_o_set_nat B5) A4))))) (forall ((R1 (-> nat nat Bool)) (R22 (-> int int Bool)) (P2 (-> nat int Bool)) (Q2 (-> nat int Bool)) (A product_prod_nat_nat) (A4 set_Pr1261947904930325089at_nat) (B product_prod_int_int) (B5 set_Pr958786334691620121nt_int)) (=> (@ (@ (@ (@ bNF_re605504016728627135_int_o R1) (@ (@ bNF_re5089333283451836215nt_o_o R22) (lambda ((Y2 Bool) (Z Bool)) (= Y2 Z)))) P2) Q2) (=> (@ (@ member8440522571783428010at_nat A) A4) (=> (@ (@ member5262025264175285858nt_int B) B5) (=> (@ (@ ord_le3146513528884898305at_nat A4) (@ collec3392354462482085612at_nat (@ produc6081775807080527818_nat_o R1))) (=> (@ (@ ord_le2843351958646193337nt_int B5) (@ collec213857154873943460nt_int (@ produc4947309494688390418_int_o R22))) (= (@ (@ P2 (@ product_fst_nat_nat A)) (@ product_fst_int_int B)) (@ (@ Q2 (@ product_snd_nat_nat A)) (@ product_snd_int_int B))))))))) (forall ((X2 produc3843707927480180839at_nat) (A4 set_se7855581050983116737at_nat) (B5 set_se7855581050983116737at_nat)) (let ((_let_1 (@ member8757157785044589968at_nat X2))) (= (@ _let_1 (@ (@ produc3241716407206042770at_nat A4) B5)) (@ _let_1 (@ (@ produc7726050920695093128at_nat A4) (lambda ((Uu set_Pr1261947904930325089at_nat)) B5)))))) (forall ((B5 set_Pr1261947904930325089at_nat) (F (-> product_prod_nat_nat product_prod_nat_nat)) (A4 set_Pr1261947904930325089at_nat)) (=> (@ finite6177210948735845034at_nat B5) (=> (@ (@ ord_le3146513528884898305at_nat B5) (@ (@ image_5168914502847457605at_nat F) A4)) (exists ((C2 set_Pr1261947904930325089at_nat)) (and (@ (@ ord_le3146513528884898305at_nat C2) A4) (@ finite6177210948735845034at_nat C2) (= B5 (@ (@ image_5168914502847457605at_nat F) C2))))))) (forall ((F (-> nat char)) (Y3 char)) (=> (= (@ (@ image_nat_char F) top_top_set_nat) top_top_set_char) (exists ((X nat)) (= Y3 (@ F X))))) (forall ((F (-> rat product_prod_nat_nat)) (A4 set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ image_9175953278516507234at_nat F))) (= (@ _let_1 (@ (@ vimage2119786153496215084at_nat F) A4)) (@ (@ inf_in2572325071724192079at_nat A4) (@ _let_1 top_top_set_rat))))) (forall ((A4 set_nat) (B5 set_nat) (F (-> nat product_unit)) (G (-> nat product_unit))) (=> (@ (@ ord_less_eq_set_nat A4) B5) (=> (forall ((X nat)) (=> (@ (@ member_nat X) A4) (@ (@ ord_le3221252021190050221t_unit (@ F X)) (@ G X)))) (@ (@ ord_le3221252021190050221t_unit (@ comple4687483117567863418t_unit (@ (@ image_8730104196221521654t_unit F) A4))) (@ comple4687483117567863418t_unit (@ (@ image_8730104196221521654t_unit G) B5)))))) (forall ((F (-> nat nat)) (G (-> rat nat))) (= (@ (@ image_rat_nat (lambda ((X4 rat)) (@ F (@ G X4)))) top_top_set_rat) (@ (@ image_nat_nat F) (@ (@ image_rat_nat G) top_top_set_rat)))) (forall ((X2 produc4675096598859438275atural) (Y3 produc4675096598859438275atural)) (= (@ (@ (@ if_Pro3444522238938527101atural false) X2) Y3) Y3)) (forall ((F (-> char char)) (G (-> nat rat))) (=> (= (@ (@ image_char_char F) top_top_set_char) top_top_set_char) (=> (= (@ (@ image_nat_rat G) top_top_set_nat) top_top_set_rat) (= (@ (@ image_2699825501378146573ar_rat (@ (@ produc1547070076189439812at_rat F) G)) top_to5594287848199751986ar_nat) top_to8437673547576850234ar_rat)))) (forall ((F (-> nat nat)) (G (-> nat nat))) (= (@ (@ comp_s8964582002068861047et_nat (@ vimage_nat_nat F)) (@ vimage_nat_nat G)) (@ vimage_nat_nat (@ (@ comp_nat_nat_nat G) F)))) (forall ((F (-> int nat)) (A4 set_int) (A7 set_nat) (G (-> nat int)) (B5 set_nat) (B7 set_int)) (=> (= (@ (@ image_int_nat F) A4) A7) (=> (= (@ (@ image_nat_int G) B5) B7) (= (@ (@ image_2751100147091372101at_int (@ (@ produc4665578292728629746at_int F) G)) (@ (@ produc1456381018704787142nt_nat A4) (lambda ((Uu int)) B5))) (@ (@ produc454536836294682310at_int A7) (lambda ((Uu nat)) B7)))))) (forall ((A4 set_o) (F (-> Bool int)) (U int)) (let ((_let_1 (@ (@ image_o_int F) A4))) (=> (not (= A4 bot_bot_set_o)) (=> (@ condit1735850657277959132ow_int _let_1) (= (@ (@ ord_less_eq_int U) (@ complete_Inf_Inf_int _let_1)) (forall ((X4 Bool)) (=> (@ (@ member_o X4) A4) (@ (@ ord_less_eq_int U) (@ F X4))))))))) (forall ((F (-> code_integer code_integer code_integer)) (G (-> (-> code_integer code_integer) produc8923325533196201883nteger produc8923325533196201883nteger)) (X2 set_Pr4111642102156807771nteger)) (= (@ (@ vimage6029918387083761651nteger F) (@ (@ vimage4289680085338140859nteger G) X2)) (@ (@ vimage6839621282666897215nteger (@ (@ comp_C8797469213163452608nteger G) F)) X2))) (forall ((I3 set_o) (X2 product_unit) (F (-> Bool product_unit))) (=> (not (= I3 bot_bot_set_o)) (= (@ comple2584293577114468500t_unit (@ (@ image_o_Product_unit (lambda ((I2 Bool)) (@ (@ inf_inf_Product_unit X2) (@ F I2)))) I3)) (@ (@ inf_inf_Product_unit X2) (@ comple2584293577114468500t_unit (@ (@ image_o_Product_unit F) I3)))))) (forall ((Q product_prod_nat_nat) (F (-> nat nat)) (P product_prod_nat_nat)) (=> (= Q (@ (@ produc986720760941809198at_nat F) P)) (not (forall ((X nat) (Y nat)) (=> (= P (@ (@ product_Pair_nat_nat X) Y)) (not (= Q (@ (@ product_Pair_nat_nat (@ F X)) Y)))))))) (forall ((R ref_a) (S2 ref_a) (X2 a) (H heap_e7401611519738050253t_unit)) (=> (@ (@ noteq_a_a R) S2) (= (@ (@ get_a (@ (@ (@ set_a S2) X2) H)) R) (@ (@ get_a H) R)))) (forall ((P2 (-> nat Bool)) (Q2 (-> nat Bool))) (= (@ collec3392354462482085612at_nat (@ produc6081775807080527818_nat_o (lambda ((A5 nat) (B4 nat)) (and (@ Q2 B4) (@ P2 A5))))) (@ (@ produc457027306803732586at_nat (@ collect_nat P2)) (lambda ((Uu nat)) (@ collect_nat Q2))))) (forall ((G (-> rat nat)) (F (-> nat nat))) (=> (@ finite_finite_nat (@ (@ image_rat_nat G) top_top_set_rat)) (@ finite_finite_nat (@ (@ image_rat_nat (lambda ((X4 rat)) (@ F (@ G X4)))) top_top_set_rat)))) (forall ((R1 (-> nat nat Bool))) (let ((_let_1 (@ bNF_re4705727531993890431at_o_o R1))) (@ (@ (@ (@ bNF_re6580757339198446453_nat_o (lambda ((Y2 (-> Bool Bool)) (Z (-> Bool Bool))) (= Y2 Z))) (@ (@ bNF_re2697311982885662685_nat_o (@ _let_1 (lambda ((Y2 Bool) (Z Bool)) (= Y2 Z)))) (@ _let_1 (lambda ((Y2 Bool) (Z Bool)) (= Y2 Z))))) comp_o_o_nat) comp_o_o_nat))) (forall ((M (-> produc3843707927480180839at_nat set_Pr8693737435421807431at_nat)) (A4 set_Pr4329608150637261639at_nat) (B5 set_Pr4329608150637261639at_nat)) (let ((_let_1 (@ image_7260680879217540773at_nat M))) (= (@ comple2748534634209756852at_nat (@ _let_1 (@ (@ sup_su5525570899277871387at_nat A4) B5))) (@ (@ sup_su718114333110466843at_nat (@ comple2748534634209756852at_nat (@ _let_1 A4))) (@ comple2748534634209756852at_nat (@ _let_1 B5)))))) (forall ((K produc3843707927480180839at_nat) (I3 set_Pr4329608150637261639at_nat) (A4 (-> produc3843707927480180839at_nat set_Pr1261947904930325089at_nat))) (let ((_let_1 (@ comple1930127330929219688at_nat (@ (@ image_7979982168039674559at_nat A4) I3)))) (=> (@ (@ member8757157785044589968at_nat K) I3) (= (@ (@ inf_in2572325071724192079at_nat (@ A4 K)) _let_1) _let_1)))) (forall ((B5 (-> Bool set_nat)) (A Bool) (A4 set_o)) (let ((_let_1 (@ image_o_set_nat B5))) (= (@ comple7399068483239264473et_nat (@ _let_1 (@ (@ insert_o A) A4))) (@ (@ sup_sup_set_nat (@ B5 A)) (@ comple7399068483239264473et_nat (@ _let_1 A4)))))) (forall ((F (-> nat rat)) (A4 set_rat)) (@ (@ ord_less_eq_set_rat (@ (@ image_nat_rat F) (@ (@ vimage_nat_rat F) A4))) A4)) (forall ((A4 set_int) (M nat) (F (-> int nat))) (=> (forall ((X int)) (=> (@ (@ member_int X) A4) (@ (@ ord_less_eq_nat M) (@ F X)))) (@ condit1738341127787009408ow_nat (@ (@ image_int_nat F) A4)))) (forall ((C3 set_Product_unit) (A4 (-> product_unit set_char)) (B5 set_char)) (let ((_let_1 (@ (@ minus_minus_set_char (@ comple7965528767983648192t_char (@ (@ image_5325685772115642575t_char A4) C3))) B5))) (let ((_let_2 (= C3 bot_bo3957492148770167129t_unit))) (and (=> (not _let_2) (= _let_1 (@ comple7965528767983648192t_char (@ (@ image_5325685772115642575t_char (lambda ((X4 product_unit)) (@ (@ minus_minus_set_char (@ A4 X4)) B5))) C3)))) (=> _let_2 (= _let_1 (@ (@ minus_minus_set_char top_top_set_char) B5))))))) (forall ((A4 set_o) (F (-> Bool int)) (G (-> Bool int))) (let ((_let_1 (@ (@ image_o_int G) A4))) (let ((_let_2 (@ (@ image_o_int F) A4))) (=> (not (= A4 bot_bot_set_o)) (=> (@ condit1735850657277959132ow_int _let_2) (=> (@ condit1735850657277959132ow_int _let_1) (= (@ (@ inf_inf_int (@ complete_Inf_Inf_int _let_2)) (@ complete_Inf_Inf_int _let_1)) (@ complete_Inf_Inf_int (@ (@ image_o_int (lambda ((A5 Bool)) (@ (@ inf_inf_int (@ F A5)) (@ G A5)))) A4))))))))) (forall ((S5 set_rat)) (= (not (@ finite_finite_rat S5)) (exists ((F2 (-> nat rat))) (and (@ (@ ord_less_eq_set_rat (@ (@ image_nat_rat F2) top_top_set_nat)) S5) (@ (@ inj_on_nat_rat F2) top_top_set_nat))))) (forall ((F (-> int int)) (G (-> int int)) (A4 set_int)) (= (@ (@ image_5705468584675977158nt_int (lambda ((X4 int)) (@ (@ product_Pair_int_int (@ F X4)) (@ G X4)))) A4) (@ (@ produc1453890548195736866nt_int (@ (@ image_int_int F) A4)) (lambda ((X4 int)) (@ (@ image_int_int G) (@ (@ inf_inf_set_int (@ (@ vimage_int_int F) (@ (@ insert_int X4) bot_bot_set_int))) A4)))))) (forall ((I Bool) (J4 Bool) (R3 set_Product_prod_o_o)) (=> (@ (@ member7466972457876170832od_o_o (@ (@ product_Pair_o_o I) J4)) R3) (@ (@ member_o J4) (@ field_o R3)))) (forall ((S5 set_int)) (=> (not (@ finite_finite_int S5)) (exists ((F5 (-> nat int))) (and (@ (@ ord_less_eq_set_int (@ (@ image_nat_int F5) top_top_set_nat)) S5) (@ (@ inj_on_nat_int F5) top_top_set_nat))))) (forall ((R7 (-> product_prod_nat_nat int Bool)) (S6 (-> int code_integer Bool)) (R3 (-> product_prod_nat_nat product_prod_nat_nat Bool)) (S5 (-> int int Bool))) (=> (@ right_8621877368619751767at_int R7) (=> (@ left_t1861001511420785031at_int R7) (=> (@ left_u6795595883297946906nteger S6) (=> (@ right_7281159819619925802nteger S6) (@ (@ ord_le6141271677531915726eger_o (@ (@ bNF_re6202762543029211035nteger (@ (@ relcom8911704206367525917at_int R3) R7)) (@ (@ relcom967497705283160040nteger S5) S6))) (@ (@ relcom4574826104943343961nteger (@ (@ bNF_re20414067882207223nt_int R3) S5)) (@ (@ bNF_re6202762543029211035nteger R7) S6)))))))) (forall ((P product_prod_nat_nat) (Z2 nat) (C (-> nat nat set_nat))) (=> (forall ((A3 nat) (B3 nat)) (=> (= P (@ (@ product_Pair_nat_nat A3) B3)) (@ (@ member_nat Z2) (@ (@ C A3) B3)))) (@ (@ member_nat Z2) (@ (@ produc6189476227299908564et_nat C) P)))) (forall ((A nat) (B nat) (A2 nat) (B2 nat)) (=> (= (@ (@ product_Pair_nat_nat A) B) (@ (@ product_Pair_nat_nat A2) B2)) (not (=> (= A A2) (not (= B B2)))))) (= produc8211389475949308722nt_int (lambda ((F2 (-> int int int)) (P3 product_prod_int_int)) (@ (@ F2 (@ product_fst_int_int P3)) (@ product_snd_int_int P3)))) (forall ((F (-> nat rat)) (A4 set_nat) (B5 set_rat)) (let ((_let_1 (@ image_nat_rat F))) (=> (@ (@ ord_less_eq_set_rat (@ _let_1 A4)) B5) (@ (@ ord_le513522071413781156et_rat (@ (@ image_4408659257933336347et_rat _let_1) (@ finite_Fpow_nat A4))) (@ finite_Fpow_rat B5))))) _let_70 (forall ((A produc3843707927480180839at_nat) (A4 set_Pr4329608150637261639at_nat) (B5 (-> produc3843707927480180839at_nat set_nat))) (=> (@ (@ member8757157785044589968at_nat A) A4) (@ (@ ord_less_eq_set_nat (@ B5 A)) (@ comple7399068483239264473et_nat (@ (@ image_3160451284896210088et_nat B5) A4))))) (forall ((X2 (-> char Bool)) (Ra (-> Bool Bool Bool))) (=> (forall ((Z3 Bool)) (=> (@ (@ member_o Z3) (@ (@ image_char_o X2) top_top_set_char)) (@ (@ Ra Z3) Z3))) (@ (@ (@ (@ bNF_re1692451286490762625ar_o_o (lambda ((Y2 char) (Z char)) (= Y2 Z))) Ra) X2) X2))) (forall ((A4 set_Product_unit) (C set_rat)) (let ((_let_1 (= A4 bot_bo3957492148770167129t_unit))) (and (=> _let_1 (= (@ comple4298007329820168263et_rat (@ (@ image_4665621433434589782et_rat (lambda ((Y5 product_unit)) C)) A4)) top_top_set_rat)) (=> (not _let_1) (= (@ comple4298007329820168263et_rat (@ (@ image_4665621433434589782et_rat (lambda ((Y5 product_unit)) C)) A4)) C))))) (forall ((P2 (-> product_prod_nat_nat Bool)) (F (-> product_prod_nat_nat int)) (B5 set_int)) (=> (forall ((X product_prod_nat_nat)) (=> (@ P2 X) (@ (@ member_int (@ F X)) B5))) (@ (@ ord_less_eq_set_int (@ (@ image_2483585944268220136at_int F) (@ collec3392354462482085612at_nat P2))) B5))) (forall ((B5 set_nat) (F (-> nat nat)) (A4 set_nat)) (=> (@ (@ ord_less_eq_set_nat B5) (@ (@ image_nat_nat F) A4)) (not (forall ((C2 set_nat)) (=> (@ (@ ord_less_eq_set_nat C2) A4) (not (= B5 (@ (@ image_nat_nat F) C2)))))))) (forall ((A4 set_o) (F (-> Bool set_nat)) (X2 set_nat)) (=> (forall ((I4 Bool)) (=> (@ (@ member_o I4) A4) (@ (@ ord_less_eq_set_nat (@ F I4)) X2))) (=> (forall ((Y set_nat)) (=> (forall ((I5 Bool)) (=> (@ (@ member_o I5) A4) (@ (@ ord_less_eq_set_nat (@ F I5)) Y))) (@ (@ ord_less_eq_set_nat X2) Y))) (= (@ comple7399068483239264473et_nat (@ (@ image_o_set_nat F) A4)) X2)))) (forall ((B5 (-> product_prod_nat_nat set_nat)) (A product_prod_nat_nat) (A4 set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ image_15824709712370754et_nat B5))) (= (@ comple7806235888213564991et_nat (@ _let_1 (@ (@ insert8211810215607154385at_nat A) A4))) (@ (@ inf_inf_set_nat (@ B5 A)) (@ comple7806235888213564991et_nat (@ _let_1 A4)))))) (forall ((X2 int) (A4 set_int) (F (-> int int)) (Y3 int)) (let ((_let_1 (@ image_int_int F))) (let ((_let_2 (@ (@ image_int_int (@ (@ (@ fun_upd_int_int F) X2) Y3)) A4))) (let ((_let_3 (@ (@ member_int X2) A4))) (and (=> (not _let_3) (= _let_2 (@ _let_1 A4))) (=> _let_3 (= _let_2 (@ (@ insert_int Y3) (@ _let_1 (@ (@ minus_minus_set_int A4) (@ (@ insert_int X2) bot_bot_set_int))))))))))) (forall ((A4 set_int)) (= (@ complete_Sup_Sup_int (@ (@ image_int_int id_int) A4)) (@ complete_Sup_Sup_int A4))) (forall ((F (-> char char)) (A4 set_char)) (let ((_let_1 (@ image_char_char F))) (=> (= (@ _let_1 top_top_set_char) top_top_set_char) (= (@ _let_1 (@ (@ vimage_char_char F) A4)) A4)))) (forall ((A4 set_Pr4329608150637261639at_nat) (F (-> Bool set_Pr4329608150637261639at_nat))) (= (@ (@ sup_su5525570899277871387at_nat A4) (@ comple4364388969068068532at_nat (@ (@ image_2496312346330513076at_nat F) bot_bot_set_o))) A4)) _let_69 (forall ((A4 set_o) (F (-> Bool nat)) (U nat)) (let ((_let_1 (@ (@ image_o_nat F) A4))) (=> (not (= A4 bot_bot_set_o)) (=> (@ condit1738341127787009408ow_nat _let_1) (= (@ (@ ord_less_eq_nat U) (@ complete_Inf_Inf_nat _let_1)) (forall ((X4 Bool)) (=> (@ (@ member_o X4) A4) (@ (@ ord_less_eq_nat U) (@ F X4))))))))) (forall ((A Bool) (A4 set_o) (B product_unit) (B5 set_Product_unit)) (let ((_let_1 (@ produc411009820408249917t_unit (@ (@ insert_o A) A4)))) (= (@ _let_1 (lambda ((Uu Bool)) (@ (@ insert_Product_unit B) B5))) (@ (@ insert9112848208840649964t_unit (@ (@ produc3901946521647900940t_unit A) B)) (@ (@ sup_su4058753791541417424t_unit (@ (@ produc411009820408249917t_unit A4) (lambda ((Uu Bool)) (@ (@ insert_Product_unit B) B5)))) (@ _let_1 (lambda ((Uu Bool)) B5))))))) (forall ((F (-> int product_unit)) (A4 set_int) (X2 int) (U product_unit)) (let ((_let_1 (@ (@ image_5846526143423701914t_unit F) A4))) (let ((_let_2 (@ ord_le3221252021190050221t_unit U))) (=> (@ condit2080475194861589617t_unit _let_1) (=> (@ (@ member_int X2) A4) (=> (@ _let_2 (@ F X2)) (@ _let_2 (@ comple4687483117567863418t_unit _let_1)))))))) (forall ((Rb (-> int nat Bool)) (Sd (-> nat num Bool))) (@ (@ (@ (@ bNF_re4310571189260822741nt_num (@ (@ bNF_re9124706910656911431at_num Rb) Sd)) (@ (@ bNF_re7492190849051111027nt_num (@ (@ bNF_re4715010359784256181nt_nat (lambda ((Y2 int) (Z int)) (= Y2 Z))) Rb)) (@ (@ bNF_re272988434038980259at_num (lambda ((Y2 int) (Z int)) (= Y2 Z))) Sd))) comp_int_nat_int) comp_nat_num_int)) (forall ((F (-> nat num)) (G (-> int nat)) (A4 set_int) (X2 num)) (let ((_let_1 (@ (@ image_int_nat G) A4))) (=> (@ (@ inj_on_nat_num F) _let_1) (=> (@ (@ inj_on_int_nat G) A4) (=> (@ (@ member_num X2) (@ (@ image_nat_num F) _let_1)) (= (@ (@ (@ the_inv_into_int_num A4) (@ (@ comp_nat_num_int F) G)) X2) (@ (@ (@ comp_nat_int_num (@ (@ the_inv_into_int_nat A4) G)) (@ (@ the_inv_into_nat_num _let_1) F)) X2))))))) (forall ((F (-> nat int)) (C3 set_nat) (A4 set_nat) (B5 set_nat)) (let ((_let_1 (@ image_nat_int F))) (=> (@ (@ inj_on_nat_int F) C3) (=> (@ (@ ord_less_eq_set_nat A4) C3) (=> (@ (@ ord_less_eq_set_nat B5) C3) (= (= (@ _let_1 A4) (@ _let_1 B5)) (= A4 B5))))))) (forall ((A4 set_int) (F (-> int product_prod_nat_nat))) (=> (not (@ finite_finite_int A4)) (=> (@ finite6177210948735845034at_nat (@ (@ image_8883965892284119310at_nat F) A4)) (exists ((X int)) (and (@ (@ member_int X) A4) (not (@ finite_finite_int (@ collect_int (lambda ((A5 int)) (and (= (@ F A5) (@ F X)) (@ (@ member_int A5) A4))))))))))) (forall ((F (-> nat nat)) (G (-> int nat)) (H (-> int int))) (let ((_let_1 (@ comp_nat_nat_int F))) (= (@ (@ comp_int_nat_int (@ _let_1 G)) H) (@ _let_1 (@ (@ comp_int_nat_int G) H))))) (forall ((F (-> int nat)) (A4 set_int) (P2 (-> nat Bool))) (= (@ collect_nat (lambda ((X4 nat)) (and (@ P2 X4) (@ (@ member_nat X4) (@ (@ image_int_nat F) A4))))) (@ (@ image_int_nat F) (@ collect_int (lambda ((X4 int)) (and (@ P2 (@ F X4)) (@ (@ member_int X4) A4))))))) (forall ((A4 set_Product_unit) (F (-> product_unit product_unit)) (G (-> product_unit product_unit))) (let ((_let_1 (@ (@ image_405062704495631173t_unit G) A4))) (let ((_let_2 (@ (@ image_405062704495631173t_unit F) A4))) (=> (not (= A4 bot_bo3957492148770167129t_unit)) (=> (@ condit9161856309968323677t_unit _let_2) (=> (@ condit9161856309968323677t_unit _let_1) (= (@ (@ inf_inf_Product_unit (@ comple2584293577114468500t_unit _let_2)) (@ comple2584293577114468500t_unit _let_1)) (@ comple2584293577114468500t_unit (@ (@ image_405062704495631173t_unit (lambda ((A5 product_unit)) (@ (@ inf_inf_Product_unit (@ F A5)) (@ G A5)))) A4))))))))) (forall ((A4 set_nat) (F (-> nat int)) (A nat)) (let ((_let_1 (@ image_nat_int F))) (let ((_let_2 (@ _let_1 A4))) (=> (not (= A4 bot_bot_set_nat)) (=> (@ condit1735850657277959132ow_int _let_2) (= (@ complete_Inf_Inf_int (@ _let_1 (@ (@ insert_nat A) A4))) (@ (@ inf_inf_int (@ F A)) (@ complete_Inf_Inf_int _let_2)))))))) (forall ((F (-> nat rat)) (G (-> rat nat))) (= (@ (@ image_rat_rat (lambda ((X4 rat)) (@ F (@ G X4)))) top_top_set_rat) (@ (@ image_nat_rat F) (@ (@ image_rat_nat G) top_top_set_rat)))) (forall ((B5 set_int) (A4 set_int) (F (-> int product_unit)) (G (-> int product_unit))) (=> (@ (@ ord_less_eq_set_int B5) A4) (=> (forall ((X int)) (=> (@ (@ member_int X) B5) (@ (@ ord_le3221252021190050221t_unit (@ F X)) (@ G X)))) (@ (@ ord_le3221252021190050221t_unit (@ comple2584293577114468500t_unit (@ (@ image_5846526143423701914t_unit F) A4))) (@ comple2584293577114468500t_unit (@ (@ image_5846526143423701914t_unit G) B5)))))) _let_68 (forall ((R (-> product_prod_nat_nat product_prod_nat_nat Bool)) (A product_prod_nat_nat) (B product_prod_nat_nat) (S2 (-> product_prod_nat_nat int Bool)) (C int)) (=> (@ (@ R A) B) (=> (@ (@ S2 B) C) (@ (@ (@ (@ relcom8911704206367525917at_int R) S2) A) C)))) (forall ((P2 (-> char nat product_unit))) (= (@ comple4687483117567863418t_unit (@ (@ image_8730104196221521654t_unit (lambda ((Y5 nat)) (@ comple2584293577114468500t_unit (@ (@ image_4337914935673063477t_unit (lambda ((X4 char)) (@ (@ P2 X4) Y5))) top_top_set_char)))) top_top_set_nat)) (@ comple2584293577114468500t_unit (@ (@ image_4600008085730780422t_unit (lambda ((X4 (-> nat char))) (@ comple4687483117567863418t_unit (@ (@ image_8730104196221521654t_unit (lambda ((Y5 nat)) (@ (@ P2 (@ X4 Y5)) Y5))) top_top_set_nat)))) top_top_set_nat_char)))) (forall ((I nat) (J4 nat)) (= (@ (@ image_nat_nat suc) (@ (@ set_or4665077453230672383an_nat I) J4)) (@ (@ set_or4665077453230672383an_nat (@ suc I)) (@ suc J4)))) (forall ((B nat) (B5 (-> nat set_nat)) (A4 set_nat) (A nat)) (let ((_let_1 (@ member_nat B))) (=> (@ _let_1 (@ comple7806235888213564991et_nat (@ (@ image_nat_set_nat B5) A4))) (=> (not (@ _let_1 (@ B5 A))) (not (@ (@ member_nat A) A4)))))) (forall ((A4 set_Pr1261947904930325089at_nat) (B5 (-> product_prod_nat_nat set_nat))) (=> (@ finite6177210948735845034at_nat A4) (=> (forall ((A3 product_prod_nat_nat)) (=> (@ (@ member8440522571783428010at_nat A3) A4) (@ finite_finite_nat (@ B5 A3)))) (@ finite_finite_nat (@ comple7399068483239264473et_nat (@ (@ image_15824709712370754et_nat B5) A4)))))) (forall ((X2 product_prod_nat_nat) (Y3 product_prod_nat_nat)) (= (@ (@ (@ if_Pro6206227464963214023at_nat true) X2) Y3) X2)) _let_67 (forall ((F (-> ref_a ref_a)) (R2 ref_ref_a) (H heap_e7401611519738050253t_unit) (H2 heap_e7401611519738050253t_unit) (R ref_a)) (let ((_let_1 (@ F (@ (@ get_ref_a H) R2)))) (=> (@ (@ (@ (@ heap_effect_ref_a (@ (@ change_ref_a F) R2)) H) H2) R) (not (=> (= H2 (@ (@ (@ set_ref_a2 R2) _let_1) H)) (not (= R _let_1))))))) (forall ((F (-> nat num))) (=> (@ (@ inj_on_nat_num F) top_top_set_nat) (@ (@ inj_on5377432224680912883nt_num (@ comp_nat_num_int F)) top_top_set_int_nat))) (= bNF_re4555766996558763186at_nat (lambda ((R6 (-> product_prod_nat_nat int Bool)) (S4 (-> nat nat Bool)) (F2 (-> product_prod_nat_nat nat)) (G3 (-> int nat))) (@ (@ ord_le2646555220125990790_nat_o (@ (@ (@ bNF_Gr6955563364113978072nt_nat F2) G3) R6)) S4))) (forall ((B5 set_Pr4329608150637261639at_nat) (A4 set_Pr4329608150637261639at_nat) (F (-> produc3843707927480180839at_nat product_unit)) (G (-> produc3843707927480180839at_nat product_unit))) (=> (@ (@ ord_le1268244103169919719at_nat B5) A4) (=> (forall ((X produc3843707927480180839at_nat)) (=> (@ (@ member8757157785044589968at_nat X) B5) (@ (@ ord_le3221252021190050221t_unit (@ F X)) (@ G X)))) (@ (@ ord_le3221252021190050221t_unit (@ comple2584293577114468500t_unit (@ (@ image_7082456443403096939t_unit F) A4))) (@ comple2584293577114468500t_unit (@ (@ image_7082456443403096939t_unit G) B5)))))) (forall ((X2 Bool)) (@ (@ total_on_o (@ (@ insert_o X2) bot_bot_set_o)) (@ (@ insert6201435330877294327od_o_o (@ (@ product_Pair_o_o X2) X2)) bot_bo7073875226086086771od_o_o))) (forall ((F (-> nat int)) (A4 set_nat)) (= (= (@ (@ image_nat_int F) A4) bot_bot_set_int) (= A4 bot_bot_set_nat))) _let_66 _let_65 (forall ((B5 (-> nat nat Bool)) (C3 (-> nat num Bool)) (A4 (-> nat int Bool))) (@ (@ (@ (@ bNF_re584878643992547173nt_num (@ (@ bNF_re2211152805895086571at_num B5) C3)) (@ (@ bNF_re8622501330148003679nt_num (@ (@ bNF_re6025474579976152573at_nat A4) B5)) (@ (@ bNF_re2582806366131931207at_num A4) C3))) comp_nat_nat_nat) comp_nat_num_int)) (forall ((Rep (-> nat num)) (Abs (-> num nat)) (G (-> product_prod_int_int int)) (P2 (-> int Bool)) (H (-> int nat))) (=> (@ (@ (@ type_d2807825734933527320at_num Rep) Abs) top_top_set_num) (= (@ (@ (@ bNF_vi1633389952966819264_nat_o G) Abs) (@ (@ bNF_Grp_int_nat (@ collect_int P2)) H)) (@ (@ bNF_Gr8532703628021589765nt_num (@ collec213857154873943460nt_int (lambda ((X4 product_prod_int_int)) (@ P2 (@ G X4))))) (@ (@ comp_i7231038107349025742nt_int (@ (@ comp_nat_num_int Rep) H)) G))))) (forall ((F (-> product_unit nat)) (A4 (-> product_unit product_unit)) (I3 set_Product_unit)) (let ((_let_1 (@ (@ image_405062704495631173t_unit A4) I3))) (=> (@ order_7096114683908731117it_nat F) (=> (@ condit2080475194861589617t_unit _let_1) (=> (not (= I3 bot_bo3957492148770167129t_unit)) (@ (@ ord_less_eq_nat (@ complete_Sup_Sup_nat (@ (@ image_875570014554754200it_nat (lambda ((X4 product_unit)) (@ F (@ A4 X4)))) I3))) (@ F (@ comple4687483117567863418t_unit _let_1)))))))) (forall ((P2 produc1319942482725812455at_nat) (F (-> set_Pr1261947904930325089at_nat set_Pr1261947904930325089at_nat))) (=> (@ fun_re2478310338295953701at_nat P2) (@ fun_re2478310338295953701at_nat (@ (@ fun_rp8445993449185644698at_nat P2) F)))) (forall ((A4 set_o) (M3 rat) (F (-> Bool rat))) (=> (forall ((X Bool)) (=> (@ (@ member_o X) A4) (@ (@ ord_less_eq_rat M3) (@ F X)))) (@ condit1103211067700513672ow_rat (@ (@ image_o_rat F) A4)))) (forall ((R1 (-> int int Bool))) (let ((_let_1 (@ bNF_re7626690874201225453um_num R1))) (@ (@ (@ (@ bNF_re5446066262214944985nt_num (lambda ((Y2 (-> num num)) (Z (-> num num))) (= Y2 Z))) (@ (@ bNF_re4768042542643474933nt_num (@ _let_1 (lambda ((Y2 num) (Z num)) (= Y2 Z)))) (@ _let_1 (lambda ((Y2 num) (Z num)) (= Y2 Z))))) comp_num_num_int) comp_num_num_int))) (forall ((X2 produc859450856879609959at_nat) (Y3 produc859450856879609959at_nat)) (= (@ (@ (@ if_Pro4507677147265585453at_nat true) X2) Y3) X2)) (forall ((F (-> int int)) (A4 set_int) (X2 int) (U int)) (let ((_let_1 (@ (@ image_int_int F) A4))) (let ((_let_2 (@ ord_less_eq_int U))) (=> (@ condit2212336002400062152ve_int _let_1) (=> (@ (@ member_int X2) A4) (=> (@ _let_2 (@ F X2)) (@ _let_2 (@ complete_Sup_Sup_int _let_1)))))))) (forall ((F (-> int int)) (A4 set_int)) (=> (@ order_mono_int_int F) (=> (@ condit1735850657277959132ow_int A4) (@ condit1735850657277959132ow_int (@ (@ image_int_int F) A4))))) (forall ((F (-> int int)) (X2 int) (Y3 int)) (= (@ (@ produc2355237562570658114nt_int F) (@ (@ product_Pair_int_int X2) Y3)) (@ (@ product_Pair_int_int (@ F X2)) Y3))) (forall ((F (-> nat rat)) (A4 set_nat)) (=> (@ (@ inj_on_nat_rat F) A4) (@ (@ inj_on_rat_nat (@ (@ the_inv_into_nat_rat A4) F)) (@ (@ image_nat_rat F) A4)))) _let_63 (forall ((K Bool) (I3 set_o) (A4 (-> Bool set_Pr8693737435421807431at_nat))) (let ((_let_1 (@ comple2748534634209756852at_nat (@ (@ image_8493167801588156084at_nat A4) I3)))) (=> (@ (@ member_o K) I3) (= (@ (@ sup_su718114333110466843at_nat (@ A4 K)) _let_1) _let_1)))) (forall ((F (-> int Bool)) (A4 set_int) (G (-> int Bool)) (B5 set_int)) (=> (@ (@ inj_on_int_o F) A4) (=> (@ (@ inj_on_int_o G) B5) (=> (= (@ (@ inf_inf_set_o (@ (@ image_int_o F) A4)) (@ (@ image_int_o G) B5)) bot_bot_set_o) (@ (@ inj_on_int_o (lambda ((X4 int)) (let ((_let_1 (@ (@ member_int X4) A4))) (and (=> _let_1 (@ F X4)) (=> (not _let_1) (@ G X4)))))) (@ (@ sup_sup_set_int A4) B5)))))) (forall ((X2 product_prod_nat_nat) (Z5 set_Pr1261947904930325089at_nat) (X5 set_Pr1261947904930325089at_nat) (P2 (-> product_prod_nat_nat Bool))) (=> (@ (@ member8440522571783428010at_nat X2) Z5) (=> (@ (@ ord_le3146513528884898305at_nat Z5) (@ collec3392354462482085612at_nat (lambda ((X4 product_prod_nat_nat)) (and (@ P2 X4) (@ (@ member8440522571783428010at_nat X4) X5))))) (@ P2 X2)))) (forall ((X2 nat) (Y3 nat) (R set_Pr4329608150637261639at_nat) (F (-> nat set_Pr1261947904930325089at_nat))) (= (@ (@ member8440522571783428010at_nat (@ (@ product_Pair_nat_nat X2) Y3)) (@ (@ inv_im4437241714082187487at_nat R) F)) (@ (@ member8757157785044589968at_nat (@ (@ produc2922128104949294807at_nat (@ F X2)) (@ F Y3))) R))) (forall ((F1 (-> nat num)) (F22 (-> int nat)) (G1 (-> int nat)) (G22 (-> int int))) (= (@ (@ produc3608230303109393468nt_nat (@ (@ comp_nat_num_int F1) F22)) (@ (@ comp_int_nat_int G1) G22)) (@ (@ comp_P3772045228931366376nt_int (@ (@ produc5918048235202344416nt_nat F1) G1)) (@ (@ produc5664932004629684302nt_int F22) G22)))) (forall ((R3 (-> product_prod_nat_nat product_prod_nat_nat Bool)) (R7 (-> product_prod_nat_nat int Bool)) (S5 (-> product_prod_nat_nat product_prod_nat_nat Bool)) (S6 (-> product_prod_nat_nat int Bool))) (=> (@ left_u7296345956935681743at_nat R3) (=> (@ right_4094035864313884895at_nat R3) (=> (@ right_8621877368619751767at_int R7) (=> (@ left_t1861001511420785031at_int R7) (@ (@ ord_le2484784447047653514_int_o (@ (@ bNF_re7400052026677387805at_int (@ (@ relcom8911704206367525917at_int R3) R7)) (@ (@ relcom8911704206367525917at_int S5) S6))) (@ (@ relcom4982215633375716084nt_int (@ (@ bNF_re2241393799969408733at_nat R3) S5)) (@ (@ bNF_re7400052026677387805at_int R7) S6)))))))) (forall ((A4 set_o) (F (-> Bool rat)) (M rat)) (=> (forall ((X Bool)) (=> (@ (@ member_o X) A4) (@ (@ ord_less_eq_rat (@ F X)) M))) (@ condit1579696412822616692ve_rat (@ (@ image_o_rat F) A4)))) (forall ((F (-> Bool product_unit)) (A Bool) (A4 set_o)) (let ((_let_1 (@ image_o_Product_unit F))) (= (@ comple2584293577114468500t_unit (@ _let_1 (@ (@ insert_o A) A4))) (@ (@ inf_inf_Product_unit (@ F A)) (@ comple2584293577114468500t_unit (@ _let_1 A4)))))) (forall ((X1 nat) (X22 nat)) (= (@ product_fst_nat_nat (@ (@ product_Pair_nat_nat X1) X22)) X1)) (forall ((R3 (-> nat nat Bool)) (A (-> rat nat)) (B (-> rat nat))) (= (@ (@ (@ (@ bNF_re6557955094579809201at_nat (lambda ((Y2 rat) (Z rat)) (= Y2 Z))) R3) A) B) (exists ((Z4 (-> rat product_prod_nat_nat))) (and (@ (@ member849810989832120969at_nat Z4) (@ collec2824469931397938891at_nat (lambda ((X4 (-> rat product_prod_nat_nat))) (@ (@ ord_le3146513528884898305at_nat (@ (@ image_9175953278516507234at_nat X4) top_top_set_rat)) (@ collec3392354462482085612at_nat (@ produc6081775807080527818_nat_o R3)))))) (= (@ (@ comp_P1320480151300532104at_rat product_snd_nat_nat) Z4) B) (= (@ (@ comp_P1320480151300532104at_rat product_fst_nat_nat) Z4) A))))) (forall ((X5 set_Pr958786334691620121nt_int) (P2 (-> product_prod_int_int Bool))) (@ (@ ord_le2843351958646193337nt_int (@ collec213857154873943460nt_int (lambda ((X4 product_prod_int_int)) (and (@ (@ member5262025264175285858nt_int X4) X5) (@ P2 X4))))) X5)) (forall ((A4 set_nat) (C int)) (let ((_let_1 (= A4 bot_bot_set_nat))) (and (=> (not _let_1) (= (@ (@ image_nat_int (lambda ((X4 nat)) C)) A4) (@ (@ insert_int C) bot_bot_set_int))) (=> _let_1 (= (@ (@ image_nat_int (lambda ((X4 nat)) C)) A4) bot_bot_set_int))))) (forall ((A int) (A4 set_int) (F (-> int set_nat)) (C set_nat)) (=> (@ (@ member_int A) A4) (=> (forall ((X int)) (=> (@ (@ member_int X) A4) (= (@ F X) C))) (= (@ comple7399068483239264473et_nat (@ (@ image_int_set_nat F) A4)) C)))) (forall ((A4 set_nat) (B5 set_Product_unit)) (= (= (@ (@ produc5506539147108004339t_unit A4) (lambda ((Uu nat)) B5)) bot_bo5043309098482578556t_unit) (or (= B5 bot_bo3957492148770167129t_unit) (= A4 bot_bot_set_nat)))) (forall ((C3 set_nat) (A4 (-> nat set_char)) (B5 set_char)) (let ((_let_1 (= C3 bot_bot_set_nat))) (and (=> _let_1 (= (@ comple7965528767983648192t_char (@ (@ image_nat_set_char (lambda ((X4 nat)) (@ (@ inf_inf_set_char (@ A4 X4)) B5))) C3)) top_top_set_char)) (=> (not _let_1) (= (@ comple7965528767983648192t_char (@ (@ image_nat_set_char (lambda ((X4 nat)) (@ (@ inf_inf_set_char (@ A4 X4)) B5))) C3)) (@ (@ inf_inf_set_char (@ comple7965528767983648192t_char (@ (@ image_nat_set_char A4) C3))) B5)))))) (forall ((F (-> rat nat)) (G (-> nat rat)) (R set_nat)) (= (@ (@ image_rat_nat F) (@ (@ image_nat_rat G) R)) (@ (@ image_nat_nat (@ (@ comp_rat_nat_nat F) G)) R))) (forall ((A4 set_o) (F product_unit)) (=> (not (= A4 bot_bot_set_o)) (= (@ comple2584293577114468500t_unit (@ (@ image_o_Product_unit (lambda ((I2 Bool)) F)) A4)) F))) (forall ((X2 produc6271795597528267376eger_o) (Y3 produc6271795597528267376eger_o)) (= (@ (@ (@ if_Pro5737122678794959658eger_o false) X2) Y3) Y3)) _let_61 (forall ((C (-> nat nat Bool)) (P product_prod_nat_nat)) (=> (@ (@ produc6081775807080527818_nat_o C) P) (not (forall ((X nat) (Y nat)) (=> (= P (@ (@ product_Pair_nat_nat X) Y)) (not (@ (@ C X) Y))))))) (forall ((R1 (-> nat nat Bool)) (Abs1 (-> nat int)) (Rep1 (-> int nat)) (T1 (-> nat int Bool)) (R22 (-> int int Bool)) (Abs22 (-> int int)) (Rep22 (-> int int)) (T22 (-> int int Bool))) (=> (@ (@ (@ (@ quotient_nat_int R1) Abs1) Rep1) T1) (=> (@ (@ (@ (@ quotient_int_int R22) Abs22) Rep22) T22) (@ (@ (@ (@ quotient_nat_int (@ (@ relcompp_nat_int_nat T1) (@ (@ relcompp_int_int_nat R22) (@ conversep_nat_int T1)))) (@ (@ comp_int_int_nat Abs22) Abs1)) (@ (@ comp_int_nat_int Rep1) Rep22)) (@ (@ relcompp_nat_int_int T1) T22))))) (forall ((F (-> int int product_prod_int_int)) (X1 int) (X22 int)) (= (@ (@ produc4245557441103728435nt_int F) (@ (@ product_Pair_int_int X1) X22)) (@ (@ F X1) X22))) (forall ((F4 set_Pr1261947904930325089at_nat) (H (-> product_prod_nat_nat product_prod_nat_nat))) (=> (@ finite6177210948735845034at_nat F4) (@ finite6177210948735845034at_nat (@ (@ image_5168914502847457605at_nat H) F4)))) (forall ((A set_Pr1261947904930325089at_nat) (B set_Pr1261947904930325089at_nat) (R set_Pr4329608150637261639at_nat)) (= (@ field_3145993188331922222at_nat (@ (@ insert9069300056098147895at_nat (@ (@ produc2922128104949294807at_nat A) B)) R)) (@ (@ sup_su3642409539654194069at_nat (@ (@ insert9200635055090092081at_nat A) (@ (@ insert9200635055090092081at_nat B) bot_bo3083307316010499117at_nat))) (@ field_3145993188331922222at_nat R)))) (forall ((F (-> nat char)) (Y3 char)) (=> (= (@ (@ image_nat_char F) top_top_set_nat) top_top_set_char) (not (forall ((X nat)) (not (= Y3 (@ F X))))))) (forall ((F1 (-> nat nat)) (A13 set_nat) (B1 set_nat) (F22 (-> int nat)) (B22 set_int) (A24 set_nat)) (=> (= (@ (@ image_nat_nat F1) A13) B1) (=> (@ (@ inj_on_int_nat F22) B22) (=> (@ (@ ord_less_eq_set_nat (@ (@ image_int_nat F22) B22)) A24) (=> (=> (= B22 bot_bot_set_int) (= A24 bot_bot_set_nat)) (= (@ (@ bNF_We8539870446460111250nt_nat B22) B1) (@ (@ image_4204708549965163745nt_nat (@ (@ (@ bNF_We895812394582891848at_nat B22) F1) F22)) (@ (@ bNF_We7540516734559056694at_nat A24) A13)))))))) (forall ((H1 (-> int nat)) (H22 (-> nat num)) (F (-> int int)) (G (-> int nat))) (= (@ (@ comp_P1145193044942399421um_int (@ (@ produc1225400549393458656at_num H1) H22)) (@ (@ bNF_co2176657415837686291nt_nat F) G)) (@ (@ bNF_co6958007526947186177at_num (@ (@ comp_int_nat_int H1) F)) (@ (@ comp_nat_num_int H22) G)))) (forall ((A4 set_int)) (=> (forall ((X int)) (not (@ (@ member_int X) A4))) (@ (@ ord_less_eq_set_int A4) bot_bot_set_int))) _let_60 (forall ((A4 set_int) (F (-> int nat)) (A int)) (let ((_let_1 (@ image_int_nat F))) (let ((_let_2 (@ _let_1 A4))) (=> (not (= A4 bot_bot_set_int)) (=> (@ condit1738341127787009408ow_nat _let_2) (= (@ complete_Inf_Inf_nat (@ _let_1 (@ (@ insert_int A) A4))) (@ (@ inf_inf_nat (@ F A)) (@ complete_Inf_Inf_nat _let_2)))))))) _let_59 (forall ((A4 set_nat) (F (-> product_unit set_nat))) (= (@ (@ sup_sup_set_nat A4) (@ comple7399068483239264473et_nat (@ (@ image_8173849991827986510et_nat F) bot_bo3957492148770167129t_unit))) A4)) (forall ((Rep (-> Bool Bool)) (Abs (-> Bool Bool)) (M (-> Bool Bool))) (=> (@ (@ (@ type_definition_o_o Rep) Abs) top_top_set_o) (=> (= M id_o) (= (@ (@ comp_o_o_o (@ (@ comp_o_o_o Abs) M)) Rep) id_o)))) (forall ((Rep (-> nat char)) (Abs (-> char nat)) (M (-> char char))) (=> (@ (@ (@ type_d5945782884131516111t_char Rep) Abs) top_top_set_char) (=> (= M id_char) (= (@ (@ comp_char_nat_nat (@ (@ comp_char_nat_char Abs) M)) Rep) id_nat)))) (forall ((Y4 set_Pr1261947904930325089at_nat)) (=> (@ finite6177210948735845034at_nat Y4) (=> (not (= Y4 bot_bo2099793752762293965at_nat)) (@ (@ member8757157785044589968at_nat (@ (@ produc2922128104949294807at_nat bot_bo2099793752762293965at_nat) Y4)) fun_max_strict)))) (forall ((X2 nat) (Fx nat) (A4 set_nat) (F (-> nat nat))) (=> (@ (@ member8440522571783428010at_nat (@ (@ product_Pair_nat_nat X2) Fx)) (@ (@ bNF_Gr_nat_nat A4) F)) (@ (@ member_nat X2) A4))) (= (@ (@ image_char_nat comm_s629917340098488124ar_nat) top_top_set_char) _let_34) _let_58 (forall ((F (-> nat rat)) (B5 set_rat) (A4 set_nat)) (=> (@ (@ inj_on_nat_rat F) top_top_set_nat) (=> (@ (@ ord_less_eq_set_rat B5) (@ (@ image_nat_rat F) A4)) (@ (@ ord_less_eq_set_nat (@ (@ vimage_nat_rat F) B5)) A4)))) _let_57 (forall ((F (-> set_nat product_unit)) (A4 set_set_nat)) (=> (@ order_7928700340835332885t_unit F) (@ (@ ord_le3221252021190050221t_unit (@ comple4687483117567863418t_unit (@ (@ image_6369283972875870912t_unit F) A4))) (@ F (@ comple7399068483239264473et_nat A4))))) (forall ((A4 set_o) (B5 set_o) (F (-> Bool set_nat)) (G (-> Bool set_nat))) (=> (@ (@ ord_less_eq_set_o A4) B5) (=> (forall ((X Bool)) (=> (@ (@ member_o X) A4) (@ (@ ord_less_eq_set_nat (@ F X)) (@ G X)))) (@ (@ ord_less_eq_set_nat (@ comple7399068483239264473et_nat (@ (@ image_o_set_nat F) A4))) (@ comple7399068483239264473et_nat (@ (@ image_o_set_nat G) B5)))))) (forall ((F (-> ref_a set_Pr1261947904930325089at_nat)) (G (-> heap_e7401611519738050253t_unit set_Pr1261947904930325089at_nat)) (X2 produc7812382424243267045t_unit)) (= (@ (@ produc4016808307611786905at_nat F) (@ (@ produc2928627021203296111_ref_a G) X2)) (@ (@ produc2922128104949294807at_nat (@ F (@ produc473321116828791851t_unit X2))) (@ G (@ produc1126150082675451753t_unit X2))))) (forall ((A4 set_int) (B5 (-> int set_int)) (F (-> int int))) (=> (not (= A4 bot_bot_set_int)) (=> (forall ((X int)) (=> (@ (@ member_int X) A4) (not (= (@ B5 X) bot_bot_set_int)))) (=> (@ condit2212336002400062152ve_int (@ comple3221217463730067765et_int (@ (@ image_int_set_int (lambda ((X4 int)) (@ (@ image_int_int F) (@ B5 X4)))) A4))) (= (@ complete_Sup_Sup_int (@ (@ image_int_int F) (@ comple3221217463730067765et_int (@ (@ image_int_set_int B5) A4)))) (@ complete_Sup_Sup_int (@ (@ image_int_int (lambda ((X4 int)) (@ complete_Sup_Sup_int (@ (@ image_int_int F) (@ B5 X4))))) A4))))))) (forall ((R7 (-> product_prod_nat_nat int Bool)) (S6 (-> product_prod_nat_nat int Bool)) (R3 (-> product_prod_nat_nat product_prod_nat_nat Bool)) (S5 (-> product_prod_nat_nat product_prod_nat_nat Bool))) (=> (@ right_8621877368619751767at_int R7) (=> (@ left_t1861001511420785031at_int R7) (=> (@ left_u4005249686606446046at_int S6) (=> (@ right_1157779049177982926at_int S6) (@ (@ ord_le2484784447047653514_int_o (@ (@ bNF_re7400052026677387805at_int (@ (@ relcom8911704206367525917at_int R3) R7)) (@ (@ relcom8911704206367525917at_int S5) S6))) (@ (@ relcom4982215633375716084nt_int (@ (@ bNF_re2241393799969408733at_nat R3) S5)) (@ (@ bNF_re7400052026677387805at_int R7) S6)))))))) (forall ((X2 (-> rat nat)) (Ra (-> nat nat Bool))) (=> (forall ((Z3 nat)) (=> (@ (@ member_nat Z3) (@ (@ image_rat_nat X2) top_top_set_rat)) (@ (@ Ra Z3) Z3))) (@ (@ (@ (@ bNF_re6557955094579809201at_nat (lambda ((Y2 rat) (Z rat)) (= Y2 Z))) Ra) X2) X2))) (forall ((F (-> nat nat product_prod_nat_nat Bool)) (P product_prod_nat_nat)) (= (@ (@ produc8739625826339149834_nat_o (lambda ((Y5 nat) (X4 nat) (__flatten_var_0 product_prod_nat_nat)) (@ (@ (@ F X4) Y5) __flatten_var_0))) (@ product_swap_nat_nat P)) (@ (@ produc8739625826339149834_nat_o F) P))) (forall ((F (-> rat product_unit)) (A product_unit) (X2 rat)) (=> (= (@ (@ image_2327579789247107822t_unit F) top_top_set_rat) (@ (@ insert_Product_unit A) bot_bo3957492148770167129t_unit)) (= (@ F X2) A))) (forall ((A4 set_int) (F (-> int int))) (let ((_let_1 (@ (@ image_int_int F) A4))) (=> (@ finite_finite_int A4) (=> (@ (@ ord_less_eq_set_int _let_1) A4) (=> (@ (@ inj_on_int_int F) A4) (= _let_1 A4)))))) (forall ((C3 set_Product_unit) (A4 (-> 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set_Pr1261947904930325089at_nat) (B Bool) (B5 (-> product_prod_nat_nat set_o))) (let ((_let_1 (@ member_o B))) (=> (@ (@ member8440522571783428010at_nat A) A4) (=> (@ _let_1 (@ B5 A)) (@ _let_1 (@ comple90263536869209701_set_o (@ (@ image_501298686397505212_set_o B5) A4))))))) (forall ((A set_Pr1261947904930325089at_nat)) (@ (@ member8757157785044589968at_nat (@ (@ produc2922128104949294807at_nat A) A)) id_set1796276052702428605at_nat)) (forall ((F (-> nat Bool)) (A4 set_nat) (X2 Bool) (B5 set_o)) (=> (@ (@ inj_on_nat_o F) A4) (=> (not (@ (@ member_o X2) B5)) (=> (= (@ (@ insert_o X2) B5) (@ (@ image_nat_o F) A4)) (not (forall ((X8 nat) (A8 set_nat)) (=> (not (@ (@ member_nat X8) A8)) (=> (= A4 (@ (@ insert_nat X8) A8)) (=> (= X2 (@ F X8)) (not (= B5 (@ (@ image_nat_o F) A8)))))))))))) (forall ((A4 set_nat) (F (-> nat int))) (=> (@ finite_finite_nat A4) (= (@ (@ inj_on_nat_int F) A4) (= (@ finite_card_int (@ (@ image_nat_int F) A4)) (@ finite_card_nat A4))))) (forall ((C3 set_Product_unit) (A4 (-> product_unit set_nat)) (B5 set_nat)) (let ((_let_1 (= C3 bot_bo3957492148770167129t_unit))) (and (=> (not _let_1) (= (@ comple7399068483239264473et_nat (@ (@ image_8173849991827986510et_nat (lambda ((X4 product_unit)) (@ (@ sup_sup_set_nat (@ A4 X4)) B5))) C3)) (@ (@ sup_sup_set_nat (@ comple7399068483239264473et_nat (@ (@ image_8173849991827986510et_nat A4) C3))) B5))) (=> _let_1 (= (@ comple7399068483239264473et_nat (@ (@ image_8173849991827986510et_nat (lambda ((X4 product_unit)) (@ (@ sup_sup_set_nat (@ A4 X4)) B5))) C3)) bot_bot_set_nat))))) (forall ((Ac product_prod_int_int) (P2 (-> int int Bool)) (Q2 (-> int int Bool))) (=> (@ (@ member5262025264175285858nt_int Ac) (@ collec213857154873943460nt_int (@ produc4947309494688390418_int_o (@ (@ relcompp_int_int_int P2) Q2)))) (@ (@ member5262025264175285858nt_int (@ (@ (@ bNF_sn1062102010912252026nt_int P2) Q2) Ac)) (@ collec213857154873943460nt_int (@ produc4947309494688390418_int_o Q2))))) (forall ((Z2 Bool) (C (-> nat nat set_o)) (A nat) (B nat)) (let ((_let_1 (@ member_o Z2))) (=> (@ _let_1 (@ (@ C A) B)) (@ _let_1 (@ (@ produc59986286002894506_set_o C) (@ (@ product_Pair_nat_nat A) B)))))) (forall ((A4 set_nat) (F (-> nat nat)) (X2 nat)) (=> (not (= A4 bot_bot_set_nat)) (=> (forall ((Y nat)) (=> (@ (@ member_nat Y) A4) (= (@ F Y) (@ F X2)))) (= (@ the_elem_nat (@ (@ image_nat_nat F) A4)) (@ F X2))))) (forall ((P2 (-> nat Bool)) (Q2 (-> nat product_prod_int_int Bool))) (= (@ collec5600542410287506995nt_int (@ produc4306188689235752475_int_o (lambda ((X4 nat) (Y5 product_prod_int_int)) (and (@ P2 X4) (@ (@ Q2 X4) Y5))))) (@ (@ produc7854212285064481439nt_int (@ collect_nat P2)) (lambda ((X4 nat)) (@ collec213857154873943460nt_int (@ Q2 X4)))))) (forall ((A4 set_Pr1261947904930325089at_nat) (B5 set_Pr1261947904930325089at_nat) (F (-> product_prod_nat_nat product_prod_nat_nat))) (=> (@ finite6177210948735845034at_nat A4) (=> (@ (@ ord_le3146513528884898305at_nat B5) (@ (@ image_5168914502847457605at_nat F) A4)) (@ finite6177210948735845034at_nat B5)))) (forall ((A4 set_nat) (B5 set_nat) (C3 set_nat)) (= (@ (@ produc457027306803732586at_nat (@ (@ sup_sup_set_nat A4) B5)) (lambda ((Uu nat)) C3)) (@ (@ sup_su6327502436637775413at_nat (@ (@ produc457027306803732586at_nat A4) (lambda ((Uu nat)) C3))) (@ (@ produc457027306803732586at_nat B5) (lambda ((Uu nat)) C3))))) _let_56 (forall ((N3 nat)) (@ (@ member_int (@ semiri1314217659103216013at_int N3)) (@ (@ image_int_int abs_abs_int) top_top_set_int))) (forall ((A4 set_Pr4329608150637261639at_nat) (B5 set_Pr4329608150637261639at_nat) (F (-> produc3843707927480180839at_nat set_nat)) (G (-> produc3843707927480180839at_nat set_nat))) (=> (@ (@ ord_le1268244103169919719at_nat A4) B5) (=> (forall ((X produc3843707927480180839at_nat)) (=> (@ (@ member8757157785044589968at_nat X) A4) (@ (@ ord_less_eq_set_nat (@ F X)) (@ G X)))) (@ (@ ord_less_eq_set_nat (@ comple7399068483239264473et_nat (@ (@ image_3160451284896210088et_nat F) A4))) (@ comple7399068483239264473et_nat (@ (@ image_3160451284896210088et_nat G) B5)))))) (forall ((F (-> nat Bool)) (A nat) (A4 set_nat)) (let ((_let_1 (@ insert_nat A))) (let ((_let_2 (@ inj_on_nat_o F))) (= (@ _let_2 (@ _let_1 A4)) (and (@ _let_2 A4) (not (@ (@ member_o (@ F A)) (@ (@ image_nat_o F) (@ (@ minus_minus_set_nat A4) (@ _let_1 bot_bot_set_nat)))))))))) (forall ((F (-> int nat))) (= (@ (@ comp_int_nat_int F) id_int) F)) (forall ((F (-> nat rat)) (A4 set_nat) (B5 set_nat)) (let ((_let_1 (@ image_nat_rat F))) (=> (@ (@ inj_on_nat_rat F) top_top_set_nat) (= (@ _let_1 (@ (@ minus_minus_set_nat A4) B5)) (@ (@ minus_minus_set_rat (@ _let_1 A4)) (@ _let_1 B5)))))) (forall ((A nat) (B nat) (A4 set_nat)) (=> (= A B) (=> (@ (@ member_nat A) A4) (@ (@ member8440522571783428010at_nat (@ (@ product_Pair_nat_nat A) B)) (@ id_on_nat A4))))) _let_55 _let_54 (forall ((A nat) (B nat) (R3 set_Pr1261947904930325089at_nat) (F (-> nat nat)) (G (-> nat nat))) (=> (@ (@ member8440522571783428010at_nat (@ (@ product_Pair_nat_nat A) B)) R3) (@ (@ member8440522571783428010at_nat (@ (@ product_Pair_nat_nat (@ F A)) (@ G B))) (@ (@ image_5168914502847457605at_nat (@ (@ produc6977886695330630970at_nat F) G)) R3)))) (forall ((F (-> char nat)) (G (-> nat char))) (=> (= (@ (@ image_char_nat F) top_top_set_char) top_top_set_nat) (=> (= (@ (@ image_nat_char G) top_top_set_nat) top_top_set_char) (= (@ (@ image_char_char (@ (@ comp_nat_char_char G) F)) top_top_set_char) top_top_set_char)))) (forall ((A4 set_int) (F (-> int nat)) (G (-> int nat))) (let ((_let_1 (@ (@ image_int_nat G) A4))) (let ((_let_2 (@ (@ image_int_nat F) A4))) (=> (not (= A4 bot_bot_set_int)) (=> (@ condit2214826472909112428ve_nat _let_2) (=> (@ condit2214826472909112428ve_nat _let_1) (= (@ (@ sup_sup_nat (@ complete_Sup_Sup_nat _let_2)) (@ complete_Sup_Sup_nat _let_1)) (@ complete_Sup_Sup_nat (@ (@ image_int_nat (lambda ((A5 int)) (@ (@ sup_sup_nat (@ F A5)) (@ G A5)))) A4))))))))) (forall ((P2 (-> rat nat product_unit))) (= (@ comple2584293577114468500t_unit (@ (@ image_8730104196221521654t_unit (lambda ((Y5 nat)) (@ comple4687483117567863418t_unit (@ (@ image_2327579789247107822t_unit (lambda ((X4 rat)) (@ (@ P2 X4) Y5))) top_top_set_rat)))) top_top_set_nat)) (@ comple4687483117567863418t_unit (@ (@ image_340470173791133503t_unit (lambda ((F2 (-> nat rat))) (@ comple2584293577114468500t_unit (@ (@ image_8730104196221521654t_unit (lambda ((X4 nat)) (@ (@ P2 (@ F2 X4)) X4))) top_top_set_nat)))) top_top_set_nat_rat)))) (forall ((H1 (-> nat num)) (H22 (-> nat num)) (F (-> int nat)) (G (-> int nat))) (= (@ (@ comp_P7387482301570536291um_int (@ (@ produc1476026309457068494at_num H1) H22)) (@ (@ bNF_co1177303703936631735at_nat F) G)) (@ (@ bNF_co5088337930254655563um_num (@ (@ comp_nat_num_int H1) F)) (@ (@ comp_nat_num_int H22) G)))) (forall ((F (-> nat num)) (X2 nat) (Y3 nat)) (= (@ (@ produc1225095714263496890um_nat F) (@ (@ product_Pair_nat_nat X2) Y3)) (@ (@ product_Pair_nat_num X2) (@ F Y3)))) (@ (@ (@ _let_53 (@ _let_52 (lambda ((Y2 Bool) (Z Bool)) (= Y2 Z)))) (@ produc8739625826339149834_nat_o (lambda ((X4 nat) (Y5 nat) (__flatten_var_0 product_prod_nat_nat)) (@ (@ produc6081775807080527818_nat_o (lambda ((U3 nat) (V3 nat)) (@ (@ ord_less_eq_nat (@ (@ plus_plus_nat X4) V3)) (@ (@ plus_plus_nat U3) Y5)))) __flatten_var_0)))) (@ produc8739625826339149834_nat_o (lambda ((X4 nat) (Y5 nat) (__flatten_var_0 product_prod_nat_nat)) (@ (@ produc6081775807080527818_nat_o (lambda ((U3 nat) (V3 nat)) (@ (@ ord_less_eq_nat (@ (@ plus_plus_nat X4) V3)) (@ (@ plus_plus_nat U3) Y5)))) __flatten_var_0)))) (forall ((F (-> nat int)) (A4 set_nat) (B5 set_int) (G (-> int nat))) (=> (@ (@ inj_on_nat_int F) A4) (=> (@ (@ ord_less_eq_set_int (@ (@ image_nat_int F) A4)) B5) (=> (@ (@ inj_on_int_nat G) B5) (=> (@ (@ ord_less_eq_set_nat (@ (@ image_int_nat G) B5)) A4) (=> (@ finite_finite_nat A4) (=> (@ finite_finite_int B5) (= (@ finite_card_nat A4) (@ 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condit2212336002400062152ve_int (@ comple3221217463730067765et_int (@ (@ image_o_set_int (lambda ((X4 Bool)) (@ (@ image_o_int F) (@ B5 X4)))) A4))) (= (@ complete_Sup_Sup_int (@ (@ image_o_int F) (@ comple90263536869209701_set_o (@ (@ image_o_set_o B5) A4)))) (@ complete_Sup_Sup_int (@ (@ image_o_int (lambda ((X4 Bool)) (@ complete_Sup_Sup_int (@ (@ image_o_int F) (@ B5 X4))))) A4))))))) (forall ((P2 (-> nat Bool)) (F (-> nat nat)) (B5 set_nat)) (=> (forall ((X nat)) (=> (@ P2 X) (@ (@ member_nat (@ F X)) B5))) (@ (@ ord_less_eq_set_nat (@ (@ image_nat_nat F) (@ collect_nat P2))) B5))) (forall ((Rep (-> nat int)) (Abs (-> int nat)) (A4 set_int)) (=> (@ (@ (@ type_d6248003478268698410at_int Rep) Abs) A4) (= (@ (@ image_nat_int Rep) top_top_set_nat) A4))) (forall ((F (-> int nat)) (A4 set_int) (B5 set_nat)) (=> (@ (@ inj_on_int_nat F) A4) (=> (@ (@ ord_less_eq_set_nat (@ (@ image_int_nat F) A4)) B5) (=> (@ finite_finite_nat B5) (@ finite_finite_int A4))))) (forall ((F (-> nat rat)) (G (-> nat rat)) (A4 set_nat)) (= (@ condit1103211067700513672ow_rat (@ (@ image_nat_rat (lambda ((X4 nat)) (@ (@ inf_inf_rat (@ F X4)) (@ G X4)))) A4)) (and (@ condit1103211067700513672ow_rat (@ (@ image_nat_rat G) A4)) (@ condit1103211067700513672ow_rat (@ (@ image_nat_rat F) A4))))) (forall ((X1 int) (X22 int) (Y1 int) (Y22 int)) (= (= (@ (@ product_Pair_int_int X1) X22) (@ (@ product_Pair_int_int Y1) Y22)) (and (= X1 Y1) (= X22 Y22)))) (forall ((A4 set_nat) (B5 set_nat)) (= (@ (@ image_5168914502847457605at_nat (@ produc2626176000494625587at_nat (lambda ((I2 nat) (J nat)) (@ (@ product_Pair_nat_nat J) I2)))) (@ (@ produc457027306803732586at_nat A4) (lambda ((Uu nat)) B5))) (@ (@ produc457027306803732586at_nat B5) (lambda ((Uu nat)) A4)))) (forall ((F (-> int int product_prod_int_int)) (P product_prod_int_int)) (= (@ (@ produc4245557441103728435nt_int (lambda ((Y5 int) (X4 int)) (@ (@ F X4) Y5))) (@ product_swap_int_int P)) (@ (@ produc4245557441103728435nt_int F) P))) (forall ((F (-> product_prod_nat_nat product_prod_nat_nat))) (=> (@ finite6177210948735845034at_nat top_to4669805908274784177at_nat) (=> (@ (@ inj_on8969904277767023793at_nat F) top_to4669805908274784177at_nat) (= (@ (@ image_5168914502847457605at_nat F) top_to4669805908274784177at_nat) top_to4669805908274784177at_nat)))) (forall ((A4 set_nat) (G (-> nat nat)) (B5 set_nat) (F (-> nat nat))) (let ((_let_1 (@ (@ image_nat_nat G) B5))) (=> (not (= A4 bot_bot_set_nat)) (=> (@ condit1738341127787009408ow_nat _let_1) (=> (@ (@ ord_less_eq_set_nat A4) B5) (=> (forall ((X nat)) (=> (@ (@ member_nat X) B5) (@ (@ ord_less_eq_nat (@ G X)) (@ F X)))) (@ (@ ord_less_eq_nat (@ complete_Inf_Inf_nat _let_1)) (@ complete_Inf_Inf_nat (@ (@ image_nat_nat F) A4))))))))) (forall ((C nat) (Y3 nat) (X2 nat)) (let ((_let_1 (@ (@ set_or4665077453230672383an_nat X2) Y3))) (let ((_let_2 (@ (@ ord_less_nat X2) Y3))) (let ((_let_3 (@ (@ ord_less_nat C) Y3))) (and (=> _let_3 (= (@ (@ image_nat_nat (lambda ((I2 nat)) (@ (@ 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set_Pr958786334691620121nt_int) (S3 int)) (let ((_let_1 (@ product_Pair_int_int R))) (=> (@ (@ member5262025264175285858nt_int (@ _let_1 S2)) R3) (=> (= S3 S2) (@ (@ member5262025264175285858nt_int (@ _let_1 S3)) R3))))) _let_51 (forall ((F (-> nat rat)) (A4 set_nat)) (=> (@ (@ inj_on_nat_rat F) A4) (@ (@ inj_on1096178645466186887et_rat (@ image_nat_rat F)) (@ pow_nat A4)))) (forall ((A4 set_Product_unit) (B5 set_nat) (C3 set_Product_unit) (D set_nat)) (= (= (@ (@ produc6875377002296012693it_nat A4) (lambda ((Uu product_unit)) B5)) (@ (@ produc6875377002296012693it_nat C3) (lambda ((Uu product_unit)) D))) (or (and (or (= B5 bot_bot_set_nat) (= A4 bot_bo3957492148770167129t_unit)) (or (= D bot_bot_set_nat) (= C3 bot_bo3957492148770167129t_unit))) (and (= A4 C3) (= B5 D))))) (forall ((F (-> nat int)) (A int) (X2 nat)) (=> (= (@ (@ image_nat_int F) top_top_set_nat) (@ (@ insert_int A) bot_bot_set_int)) (= (@ F X2) A))) (forall ((F (-> int nat)) (A4 set_int) (B5 set_nat)) (=> (@ (@ inj_on_int_nat F) A4) (=> (@ (@ ord_less_eq_set_nat (@ (@ image_int_nat F) A4)) B5) (=> (@ finite_finite_nat B5) (@ (@ ord_less_eq_nat (@ finite_card_int A4)) (@ finite_card_nat B5)))))) (forall ((A4 set_o) (R set_Product_prod_o_o) (X2 Bool) (Y3 Bool)) (=> (@ (@ refl_on_o A4) R) (=> (@ (@ member7466972457876170832od_o_o (@ (@ product_Pair_o_o X2) Y3)) R) (@ (@ member_o Y3) A4)))) (forall ((A4 set_Pr4329608150637261639at_nat) (B5 set_Pr4329608150637261639at_nat) (F (-> produc3843707927480180839at_nat product_unit)) (G (-> produc3843707927480180839at_nat product_unit))) (=> (@ (@ ord_le1268244103169919719at_nat A4) B5) (=> (forall ((X produc3843707927480180839at_nat)) (=> (@ (@ member8757157785044589968at_nat X) A4) (@ (@ ord_le3221252021190050221t_unit (@ F X)) (@ G X)))) (@ (@ ord_le3221252021190050221t_unit (@ comple4687483117567863418t_unit (@ (@ image_7082456443403096939t_unit F) A4))) (@ comple4687483117567863418t_unit (@ (@ image_7082456443403096939t_unit G) B5)))))) (forall ((F (-> nat char))) (= (= (@ (@ image_nat_char F) top_top_set_nat) top_top_set_char) (forall ((Y5 char)) (exists ((X4 nat)) (= Y5 (@ F X4)))))) (forall ((A set_Pr4329608150637261639at_nat) (B5 set_se5479201105039950375at_nat)) (let ((_let_1 (@ sup_su5525570899277871387at_nat A))) (= (@ _let_1 (@ comple6751905152567503566at_nat B5)) (@ comple6751905152567503566at_nat (@ (@ image_4303274092540115909at_nat _let_1) B5))))) (forall ((Y3 Bool)) (=> (@ (@ member_o Y3) (@ (@ insert_o true) bot_bot_set_o)) (= (@ product_Rep_unit (@ product_Abs_unit Y3)) Y3))) (forall ((Q2 (-> Bool Bool)) (P2 (-> int int Bool)) (Z2 product_prod_int_int)) (=> (@ Q2 (@ (@ produc4947309494688390418_int_o P2) Z2)) (not (forall ((X int) (Y int)) (=> (= Z2 (@ (@ product_Pair_int_int X) Y)) (not (@ Q2 (@ (@ P2 X) Y)))))))) (forall ((I product_prod_nat_nat) (J4 product_prod_nat_nat) (R3 set_Pr8693737435421807431at_nat)) (=> (@ (@ member8206827879206165904at_nat (@ (@ produc6161850002892822231at_nat I) J4)) R3) (@ (@ member8440522571783428010at_nat J4) (@ field_4706345496283612622at_nat R3)))) (forall ((F (-> int product_prod_nat_nat)) (A4 set_int) (B5 set_int)) (let ((_let_1 (@ image_8883965892284119310at_nat F))) (=> (@ (@ inj_on8575894858119818402at_nat F) top_top_set_int) (= (@ _let_1 (@ (@ inf_inf_set_int A4) B5)) (@ (@ inf_in2572325071724192079at_nat (@ _let_1 A4)) (@ _let_1 B5)))))) (forall ((I3 set_nat) (J3 set_nat) (C3 (-> nat set_nat))) (= (@ (@ produc457027306803732586at_nat (@ (@ inf_inf_set_nat I3) J3)) C3) (@ (@ inf_in2572325071724192079at_nat (@ (@ produc457027306803732586at_nat I3) C3)) (@ (@ produc457027306803732586at_nat J3) C3)))) (forall ((F (-> product_unit product_unit)) (A4 set_Product_unit)) (=> (@ order_4454465170704313136t_unit F) (@ (@ ord_le3221252021190050221t_unit (@ comple4687483117567863418t_unit (@ (@ image_405062704495631173t_unit F) A4))) (@ F (@ comple4687483117567863418t_unit A4))))) (forall ((X5 set_Pr1261947904930325089at_nat)) (=> (not (= X5 bot_bo2099793752762293965at_nat)) (@ (@ member8757157785044589968at_nat (@ (@ produc2922128104949294807at_nat X5) bot_bo2099793752762293965at_nat)) fun_min_strict))) (forall ((P2 (-> char char product_unit))) (= (@ comple4687483117567863418t_unit (@ (@ image_4337914935673063477t_unit (lambda ((Y5 char)) (@ comple2584293577114468500t_unit (@ (@ image_4337914935673063477t_unit (lambda ((X4 char)) (@ (@ P2 X4) Y5))) top_top_set_char)))) top_top_set_char)) (@ comple2584293577114468500t_unit (@ (@ image_8077363282794994245t_unit (lambda ((X4 (-> char char))) (@ comple4687483117567863418t_unit (@ (@ image_4337914935673063477t_unit (lambda ((Y5 char)) (@ (@ P2 (@ X4 Y5)) Y5))) top_top_set_char)))) top_to8079350907815874599r_char)))) (forall ((R22 (-> nat nat Bool)) (R32 (-> num nat Bool)) (R1 (-> int nat Bool))) (@ (@ (@ (@ bNF_re6524732562925676389at_nat (@ (@ bNF_re3784151423046777323um_nat R22) R32)) (@ (@ bNF_re717418264989850719at_nat (@ (@ bNF_re3344003087646356989at_nat R1) R22)) (@ (@ bNF_re1474333490953826375um_nat R1) R32))) comp_nat_num_int) comp_nat_nat_nat)) (forall ((C3 set_o) (A4 (-> Bool set_rat)) (B5 set_rat)) (let ((_let_1 (= C3 bot_bot_set_o))) (and (=> _let_1 (= (@ comple4298007329820168263et_rat (@ (@ image_o_set_rat (lambda ((X4 Bool)) (@ (@ inf_inf_set_rat (@ A4 X4)) B5))) C3)) top_top_set_rat)) (=> (not _let_1) (= (@ comple4298007329820168263et_rat (@ (@ image_o_set_rat (lambda ((X4 Bool)) (@ (@ inf_inf_set_rat (@ A4 X4)) B5))) C3)) (@ (@ inf_inf_set_rat (@ comple4298007329820168263et_rat (@ (@ image_o_set_rat A4) C3))) B5)))))) (forall ((Rep (-> nat Bool)) (Abs (-> Bool nat)) (M (-> nat Bool)) (M1 (-> Bool Bool)) (M2 (-> nat Bool)) (F (-> Bool nat)) (G (-> nat nat))) (=> (@ (@ (@ type_d1000680970699258650_nat_o Rep) Abs) top_top_set_o) (=> (= M (@ (@ comp_o_o_nat M1) M2)) (= (@ (@ comp_nat_nat_nat (@ (@ comp_o_nat_nat F) M)) G) (@ (@ comp_nat_nat_nat (@ (@ comp_o_nat_nat (@ (@ comp_o_nat_o F) M1)) Rep)) (@ (@ comp_nat_nat_nat (@ (@ comp_o_nat_nat Abs) M2)) G)))))) (forall ((P produc7812382424243267045t_unit)) (@ (@ member242389114213480694t_unit (@ produc1126150082675451753t_unit P)) (@ basic_1496934909540232809t_unit P))) (forall ((I product_prod_nat_nat) (A4 set_Pr1261947904930325089at_nat) (F (-> product_prod_nat_nat product_unit))) (=> (@ (@ member8440522571783428010at_nat I) A4) (@ (@ ord_le3221252021190050221t_unit (@ comple2584293577114468500t_unit (@ (@ image_6169909464789311569t_unit F) A4))) (@ F I)))) (forall ((A (-> nat nat)) (B (-> nat nat)) (C (-> nat nat)) (D2 (-> nat nat)) (V nat)) (=> (= (@ (@ comp_nat_nat_nat A) B) (@ (@ comp_nat_nat_nat C) D2)) (= (@ A (@ B V)) (@ C (@ D2 V))))) (forall ((I3 set_Pr1261947904930325089at_nat) (F (-> product_prod_nat_nat product_unit)) (X2 product_unit)) (=> (not (= I3 bot_bo2099793752762293965at_nat)) (=> (forall ((I4 product_prod_nat_nat)) (=> (@ (@ member8440522571783428010at_nat I4) I3) (= (@ F I4) X2))) (= (@ comple2584293577114468500t_unit (@ (@ image_6169909464789311569t_unit F) I3)) X2)))) (forall ((A4 set_Product_unit) (F (-> product_unit int)) (U int)) (let ((_let_1 (@ (@ image_873079544045703924it_int F) A4))) (=> (not (= A4 bot_bo3957492148770167129t_unit)) (=> (@ condit1735850657277959132ow_int _let_1) (= (@ (@ ord_less_eq_int U) (@ complete_Inf_Inf_int _let_1)) (forall ((X4 product_unit)) (=> (@ (@ member_Product_unit X4) A4) (@ (@ ord_less_eq_int U) (@ F X4))))))))) _let_50 (forall ((X2 Bool) (A4 set_o) (B nat) (F (-> Bool nat))) (=> (@ (@ member_o X2) A4) (=> (= B (@ F X2)) (@ (@ member_nat B) (@ (@ image_o_nat F) A4))))) (forall ((Y3 int) (X2 int) (A4 set_Pr958786334691620121nt_int)) (= (@ (@ member5262025264175285858nt_int (@ (@ product_Pair_int_int Y3) X2)) (@ (@ image_2653370878348428101nt_int product_swap_int_int) A4)) (@ (@ member5262025264175285858nt_int (@ (@ product_Pair_int_int X2) Y3)) A4))) (forall ((P2 (-> product_prod_int_int Bool)) (F (-> product_prod_int_int produc859450856879609959at_nat)) (G (-> product_prod_int_int produc859450856879609959at_nat)) (S5 set_Pr958786334691620121nt_int)) (let ((_let_1 (@ inf_in2269163501485487111nt_int S5))) (= (@ (@ image_8858061497167895027at_nat (lambda ((X4 product_prod_int_int)) (@ (@ (@ if_Pro4507677147265585453at_nat (@ P2 X4)) (@ F X4)) (@ G X4)))) S5) (@ (@ sup_su718114333110466843at_nat (@ (@ image_8858061497167895027at_nat F) (@ _let_1 (@ collec213857154873943460nt_int P2)))) (@ (@ image_8858061497167895027at_nat G) (@ _let_1 (@ collec213857154873943460nt_int (lambda ((X4 product_prod_int_int)) (not (@ P2 X4)))))))))) (forall ((A Bool) (A4 set_o) (B nat) (B5 (-> Bool set_nat))) (let ((_let_1 (@ member_nat B))) (=> (@ (@ member_o A) A4) (=> (@ _let_1 (@ B5 A)) (@ _let_1 (@ comple7399068483239264473et_nat (@ (@ image_o_set_nat B5) A4))))))) (forall ((A4 (-> product_prod_nat_nat int Bool)) (B5 (-> nat nat Bool)) (F (-> product_prod_nat_nat nat)) (G (-> int nat)) (X2 product_prod_nat_nat) (Y3 int)) (=> (@ (@ (@ (@ bNF_re4555766996558763186at_nat A4) B5) F) G) (=> (@ (@ A4 X2) Y3) (@ (@ B5 (@ F X2)) (@ G Y3))))) (forall ((X2 Bool) (A4 set_o) (F (-> Bool product_unit)) (Y3 product_unit)) (let ((_let_1 (@ image_o_Product_unit F))) (let ((_let_2 (@ (@ image_o_Product_unit (@ (@ (@ fun_up846054379331416818t_unit F) X2) Y3)) A4))) (let ((_let_3 (@ (@ member_o X2) A4))) (and (=> _let_3 (= _let_2 (@ (@ insert_Product_unit Y3) (@ _let_1 (@ (@ minus_minus_set_o A4) (@ (@ insert_o X2) bot_bot_set_o)))))) (=> (not _let_3) (= _let_2 (@ _let_1 A4)))))))) (forall ((X2 nat) (A4 set_nat) (F (-> nat int))) (let ((_let_1 (@ (@ image_nat_int F) A4))) (=> (@ (@ member_nat X2) A4) (=> (@ condit2212336002400062152ve_int _let_1) (@ (@ ord_less_eq_int (@ F X2)) (@ complete_Sup_Sup_int _let_1)))))) (forall ((I3 set_Product_unit) (F (-> product_unit product_unit)) (X2 product_unit)) (=> (not (= I3 bot_bo3957492148770167129t_unit)) (=> (forall ((I4 product_unit)) (=> (@ (@ member_Product_unit I4) I3) (= (@ F I4) X2))) (= (@ comple4687483117567863418t_unit (@ (@ image_405062704495631173t_unit F) I3)) X2)))) (forall ((A4 set_o) (R set_Product_prod_o_o) (A Bool)) (=> (@ (@ refl_on_o A4) R) (=> (@ (@ member_o A) A4) (@ (@ member7466972457876170832od_o_o (@ (@ product_Pair_o_o A) A)) R)))) (forall ((F (-> nat int)) (A4 set_nat)) (=> (@ (@ inj_on_nat_int F) A4) (@ (@ inj_on_int_nat (@ (@ the_inv_into_nat_int A4) F)) (@ (@ image_nat_int F) A4)))) (forall ((R3 (-> product_prod_nat_nat product_prod_nat_nat Bool)) (S5 (-> product_prod_nat_nat int Bool)) (T3 (-> product_prod_nat_nat int Bool)) (F (-> product_prod_nat_nat product_prod_nat_nat)) (G (-> product_prod_nat_nat product_prod_nat_nat)) (H (-> int int))) (=> (@ (@ ord_le129227817499904167_int_o (@ (@ relcom8911704206367525917at_int R3) S5)) T3) (@ (@ ord_le129227817499904167_int_o (@ (@ relcom8911704206367525917at_int (@ (@ (@ bNF_vi763171854521451549_nat_o F) G) R3)) (@ (@ (@ bNF_vi5426221348228882691_int_o G) H) S5))) (@ (@ (@ bNF_vi5426221348228882691_int_o F) H) T3)))) (forall ((Rep (-> nat nat)) (Abs (-> nat nat)) (G (-> nat nat)) (P2 (-> nat Bool)) (H (-> nat nat))) (=> (@ (@ (@ type_d6250493948777748686at_nat Rep) Abs) top_top_set_nat) (= (@ (@ (@ bNF_vi6667456707345531737_nat_o G) Abs) (@ (@ bNF_Grp_nat_nat (@ collect_nat P2)) H)) (@ (@ bNF_Grp_nat_nat (@ collect_nat (lambda ((X4 nat)) (@ P2 (@ G X4))))) (@ (@ comp_nat_nat_nat (@ (@ comp_nat_nat_nat Rep) H)) G))))) (forall ((B5 (-> nat set_nat))) (= (@ (@ produc457027306803732586at_nat bot_bot_set_nat) B5) bot_bo2099793752762293965at_nat)) _let_49 (forall ((F (-> nat nat)) (A4 set_nat)) (=> (@ order_mono_nat_nat F) (=> (@ condit2214826472909112428ve_nat A4) (@ condit2214826472909112428ve_nat (@ (@ image_nat_nat F) A4))))) (forall ((F1 (-> Bool Bool)) (F22 (-> nat Bool)) (G1 (-> Bool Bool)) (G22 (-> nat Bool))) (= (@ (@ produc6957950696844810486_nat_o (@ (@ comp_o_o_nat F1) F22)) (@ (@ comp_o_o_nat G1) G22)) (@ (@ comp_P4785046977597218846at_nat (@ (@ produc1928436952130685430_o_o_o F1) G1)) (@ (@ produc6957950696844810486_nat_o F22) G22)))) (forall ((X2 nat) (A4 set_nat) (X5 set_nat)) (=> (@ (@ member_nat X2) A4) (=> (@ (@ ord_less_eq_set_nat X5) A4) (@ (@ ord_less_eq_set_nat (@ (@ insert_nat X2) X5)) A4)))) (forall ((R1 (-> int int Bool)) (Abs1 (-> int int)) (Rep1 (-> int int)) (T1 (-> int int Bool)) (R22 (-> int int Bool)) (Abs22 (-> int code_integer)) (Rep22 (-> code_integer int)) (T22 (-> int code_integer Bool))) (=> (@ (@ (@ (@ quotient_int_int R1) Abs1) Rep1) T1) (=> (@ (@ (@ (@ quotie2291698863146621601nteger R22) Abs22) Rep22) T22) (@ (@ (@ (@ quotie2291698863146621601nteger (@ (@ relcompp_int_int_int T1) (@ (@ relcompp_int_int_int R22) (@ conversep_int_int T1)))) (@ (@ comp_i1585864551200866970er_int Abs22) Abs1)) (@ (@ comp_i2224564030725804698nteger Rep1) Rep22)) (@ (@ relcom967497705283160040nteger T1) T22))))) (forall ((A4 set_Product_unit) (C3 set_o) (B5 set_Product_unit) (D set_o)) (= (@ (@ ord_le8534741403851954546unit_o (@ (@ produc4996980317674386579unit_o A4) (lambda ((Uu product_unit)) C3))) (@ (@ produc4996980317674386579unit_o B5) (lambda ((Uu product_unit)) D))) (or (= C3 bot_bot_set_o) (and (@ (@ ord_less_eq_set_o C3) D) (@ (@ ord_le3507040750410214029t_unit A4) B5)) (= A4 bot_bo3957492148770167129t_unit)))) (forall ((A4 set_Pr7459493094073627847at_nat) (R3 (-> set_Pr4329608150637261639at_nat set_Pr4329608150637261639at_nat Bool))) (=> (@ (@ ord_le5997549366648089703at_nat A4) (@ collec7872792499061297490at_nat (@ produc9020218426428501292_nat_o (@ conver9095369822871743413at_nat R3)))) (@ (@ ord_le5997549366648089703at_nat (@ (@ image_3313167189156628421at_nat (@ produc5456455677105495163at_nat (lambda ((X4 set_Pr4329608150637261639at_nat) (Y5 set_Pr4329608150637261639at_nat)) (@ (@ produc9060074326276436823at_nat Y5) X4)))) A4)) (@ collec7872792499061297490at_nat (@ produc9020218426428501292_nat_o R3))))) (forall ((F (-> nat product_prod_nat_nat)) (A4 set_nat)) (=> (@ finite6177210948735845034at_nat (@ (@ image_5846123807819985514at_nat F) A4)) (=> (not (@ finite_finite_nat A4)) (not (forall ((Y product_prod_nat_nat)) (=> (@ (@ member8440522571783428010at_nat Y) (@ (@ image_5846123807819985514at_nat F) A4)) (@ finite_finite_nat (@ (@ inf_inf_set_nat (@ (@ vimage8013328719654469172at_nat F) (@ (@ insert8211810215607154385at_nat Y) bot_bo2099793752762293965at_nat))) A4)))))))) (forall ((R3 (-> int int Bool)) (A (-> int int)) (B (-> int int))) (= (@ (@ (@ (@ bNF_re4712519889275205905nt_int (lambda ((Y2 int) (Z int)) (= Y2 Z))) R3) A) B) (exists ((Z4 (-> int product_prod_int_int))) (and (= (@ (@ comp_P6651465171681656048nt_int product_fst_int_int) Z4) A) (= (@ (@ comp_P6651465171681656048nt_int product_snd_int_int) Z4) B) (@ (@ member254662033361028077nt_int Z4) (@ collec2229320974926845999nt_int (lambda ((X4 (-> int product_prod_int_int))) (@ (@ ord_le2843351958646193337nt_int (@ (@ image_5705468584675977158nt_int X4) top_top_set_int)) (@ collec213857154873943460nt_int (@ produc4947309494688390418_int_o R3)))))))))) (forall ((A4 set_se7855581050983116737at_nat) (B5 set_se7855581050983116737at_nat) (C3 set_se7855581050983116737at_nat)) (= (@ (@ produc7726050920695093128at_nat (@ (@ sup_su3642409539654194069at_nat A4) B5)) (lambda ((Uu set_Pr1261947904930325089at_nat)) C3)) (@ (@ sup_su5525570899277871387at_nat (@ (@ produc7726050920695093128at_nat A4) (lambda ((Uu set_Pr1261947904930325089at_nat)) C3))) (@ (@ produc7726050920695093128at_nat B5) (lambda ((Uu set_Pr1261947904930325089at_nat)) C3))))) (forall ((F (-> nat nat)) (G (-> nat nat)) (A nat) (B nat)) (= (@ (@ (@ produc6977886695330630970at_nat F) G) (@ (@ product_Pair_nat_nat A) B)) (@ (@ product_Pair_nat_nat (@ F A)) (@ G B)))) (forall ((S5 set_int)) (= (not (@ finite_finite_int S5)) (exists ((F2 (-> nat int))) (and (@ (@ inj_on_nat_int F2) top_top_set_nat) (@ (@ ord_less_eq_set_int (@ (@ image_nat_int F2) top_top_set_nat)) S5))))) (forall ((K int) (I3 set_int) (A4 (-> int set_Pr1261947904930325089at_nat))) (let ((_let_1 (@ comple1930127330929219688at_nat (@ (@ image_8938366415781434990at_nat A4) I3)))) (=> (@ (@ member_int K) I3) (= (@ (@ inf_in2572325071724192079at_nat (@ A4 K)) _let_1) _let_1)))) (forall ((B5 set_set_nat) (A set_nat)) (= (@ (@ sup_sup_set_nat (@ comple7806235888213564991et_nat B5)) A) (@ comple7806235888213564991et_nat (@ (@ image_7916887816326733075et_nat (lambda ((B4 set_nat)) (@ (@ sup_sup_set_nat B4) A))) B5)))) (forall ((I3 set_o) (F (-> Bool product_unit)) (X2 product_unit)) (=> (not (= I3 bot_bot_set_o)) (=> (forall ((I4 Bool)) (=> (@ (@ member_o I4) I3) (= (@ F I4) X2))) (= (@ comple2584293577114468500t_unit (@ (@ image_o_Product_unit F) I3)) X2)))) (forall ((A4 set_nat) (M nat) (F (-> nat nat))) (=> (forall ((X nat)) (=> (@ (@ member_nat X) A4) (@ (@ ord_less_eq_nat M) (@ F X)))) (@ condit1738341127787009408ow_nat (@ (@ image_nat_nat F) A4)))) (forall ((F (-> int Bool)) (A4 set_int) (X2 Bool) (B5 set_int)) (=> (@ (@ inj_on_int_o F) A4) (=> (@ (@ member_o X2) (@ (@ image_int_o F) A4)) (=> (@ (@ ord_less_eq_set_int A4) B5) (@ (@ member_int (@ (@ (@ the_inv_into_int_o A4) F) X2)) B5))))) (forall ((F (-> int rat)) (A4 set_int) (G (-> nat rat)) (B5 set_nat) (H (-> rat int))) (=> (= (@ (@ image_int_rat F) A4) (@ (@ image_nat_rat G) B5)) (= (@ (@ image_int_int (@ (@ comp_rat_int_int H) F)) A4) (@ (@ image_nat_int (@ (@ comp_rat_int_nat H) G)) B5)))) (forall ((A4 set_nat) (B5 set_nat) (C3 (-> nat product_unit)) (D (-> nat product_unit))) (=> (= A4 B5) (=> (forall ((X nat)) (=> (@ (@ member_nat X) B5) (= (@ C3 X) (@ D X)))) (= (@ comple2584293577114468500t_unit (@ (@ image_8730104196221521654t_unit C3) A4)) (@ comple2584293577114468500t_unit (@ (@ image_8730104196221521654t_unit D) B5)))))) (forall ((F (-> nat rat)) (G (-> nat rat)) (A4 set_nat)) (= (@ condit1579696412822616692ve_rat (@ (@ image_nat_rat (lambda ((X4 nat)) (@ (@ sup_sup_rat (@ F X4)) (@ G X4)))) A4)) (and (@ condit1579696412822616692ve_rat (@ (@ image_nat_rat G) A4)) (@ condit1579696412822616692ve_rat (@ (@ image_nat_rat F) A4))))) (forall ((A int) (B nat) (A4 set_int) (B5 (-> int set_nat))) (=> (@ (@ member216504246829706758nt_nat (@ (@ product_Pair_int_nat A) B)) (@ (@ produc1456381018704787142nt_nat A4) B5)) (not (=> (@ (@ member_int A) A4) (not (@ (@ member_nat B) (@ B5 A))))))) (forall ((F (-> char char)) (G (-> rat nat))) (=> (= (@ (@ image_char_char F) top_top_set_char) top_top_set_char) (=> (= (@ (@ image_rat_nat G) top_top_set_rat) top_top_set_nat) (= (@ (@ image_9152865675144956669ar_nat (@ (@ produc1865645492341069636at_nat F) G)) top_to8437673547576850234ar_rat) top_to5594287848199751986ar_nat)))) (forall ((T2 produc3843707927480180839at_nat)) (= T2 (@ (@ produc2922128104949294807at_nat (@ produc6011863565407846595at_nat T2)) (@ produc2937545259423399429at_nat T2)))) (forall ((F (-> Bool product_unit)) (A4 set_Product_unit)) (=> (= (@ (@ image_o_Product_unit F) top_top_set_o) top_to1996260823553986621t_unit) (= (= (@ (@ vimage4222377557387472176t_unit F) A4) bot_bot_set_o) (= A4 bot_bo3957492148770167129t_unit)))) (forall ((A4 set_se7855581050983116737at_nat)) (= (@ (@ produc7726050920695093128at_nat A4) (lambda ((Uu set_Pr1261947904930325089at_nat)) bot_bo3083307316010499117at_nat)) bot_bo228742789529271731at_nat)) (forall ((A4 set_nat) (C nat)) (=> (not (= A4 bot_bot_set_nat)) (= (@ complete_Sup_Sup_nat (@ (@ image_nat_nat (lambda ((X4 nat)) C)) A4)) C))) (forall ((C3 set_Product_unit) (A4 set_int) (B5 (-> product_unit set_int))) (let ((_let_1 (= C3 bot_bo3957492148770167129t_unit))) (and (=> _let_1 (= (@ comple3628384868704368283et_int (@ (@ image_3995998972318789802et_int (lambda ((X4 product_unit)) (@ (@ inf_inf_set_int A4) (@ B5 X4)))) C3)) top_top_set_int)) (=> (not _let_1) (= (@ comple3628384868704368283et_int (@ (@ image_3995998972318789802et_int (lambda ((X4 product_unit)) (@ (@ inf_inf_set_int A4) (@ B5 X4)))) C3)) (@ (@ inf_inf_set_int A4) (@ comple3628384868704368283et_int (@ (@ image_3995998972318789802et_int B5) C3)))))))) (forall ((F (-> nat nat)) (G (-> int int)) (A4 set_nat) (B5 set_int)) (= (@ (@ image_9117352539549038149at_int (@ produc1486167065449562675at_int (lambda ((X4 nat) (Y5 int)) (@ (@ product_Pair_nat_int (@ F X4)) (@ G Y5))))) (@ (@ produc454536836294682310at_int A4) (lambda ((Uu nat)) B5))) (@ (@ produc454536836294682310at_int (@ (@ image_nat_nat F) A4)) (lambda ((Uu nat)) (@ (@ image_int_int G) B5))))) (forall ((A4 set_Product_unit) (G (-> product_unit int)) (B5 set_Product_unit) (F (-> product_unit int))) (let ((_let_1 (@ (@ image_873079544045703924it_int G) B5))) (=> (not (= A4 bot_bo3957492148770167129t_unit)) (=> (@ condit2212336002400062152ve_int _let_1) (=> (@ (@ ord_le3507040750410214029t_unit A4) B5) (=> (forall ((X product_unit)) (=> (@ (@ member_Product_unit X) A4) (@ (@ ord_less_eq_int (@ F X)) (@ G X)))) (@ (@ ord_less_eq_int (@ complete_Sup_Sup_int (@ (@ image_873079544045703924it_int F) A4))) (@ complete_Sup_Sup_int _let_1)))))))) (forall ((F (-> char Bool)) (B Bool)) (=> (@ (@ inj_on_char_o F) top_top_set_char) (= (@ (@ member_o B) (@ (@ image_char_o F) top_top_set_char)) (exists ((X4 char)) (and (= B (@ F X4)) (forall ((Y5 char)) (=> (= B (@ F Y5)) (= Y5 X4)))))))) (forall ((S5 set_Pr1261947904930325089at_nat)) (=> (not (@ finite6177210948735845034at_nat S5)) (exists ((F5 (-> nat product_prod_nat_nat))) (and (@ (@ ord_le3146513528884898305at_nat (@ (@ image_5846123807819985514at_nat F5) top_top_set_nat)) S5) (@ (@ inj_on5538052773655684606at_nat F5) top_top_set_nat))))) (forall ((Rep (-> product_unit Bool)) (Abs (-> Bool product_unit)) (G (-> nat Bool)) (P2 (-> Bool Bool)) (H (-> Bool product_unit))) (=> (@ (@ (@ type_d6188575255521822967unit_o Rep) Abs) top_top_set_o) (= (@ (@ (@ bNF_vi5856767400800367702unit_o G) Abs) (@ (@ bNF_Gr395642070819736771t_unit (@ collect_o P2)) H)) (@ (@ bNF_Grp_nat_o (@ collect_nat (lambda ((X4 nat)) (@ P2 (@ G X4))))) (@ (@ comp_o_o_nat (@ (@ comp_P5156358013004227690it_o_o Rep) H)) G))))) (forall ((G (-> rat int)) (F (-> int rat))) (=> (forall ((X int)) (= (@ G (@ F X)) X)) (= (@ (@ image_rat_int G) top_top_set_rat) top_top_set_int))) (forall ((F (-> set_Pr1261947904930325089at_nat nat)) (G (-> set_Pr1261947904930325089at_nat num)) (A set_Pr1261947904930325089at_nat) (B set_Pr1261947904930325089at_nat)) (= (@ (@ (@ produc3932168101365401472at_num F) G) (@ (@ produc2922128104949294807at_nat A) B)) (@ (@ product_Pair_nat_num (@ F A)) (@ G B)))) (forall ((A4 set_Product_unit) (F (-> product_unit set_nat)) (A product_unit)) (let ((_let_1 (@ image_8173849991827986510et_nat F))) (let ((_let_2 (@ _let_1 A4))) (=> (not (= A4 bot_bo3957492148770167129t_unit)) (=> (@ condit5477540289124974626et_nat _let_2) (= (@ comple7399068483239264473et_nat (@ _let_1 (@ (@ insert_Product_unit A) A4))) (@ (@ sup_sup_set_nat (@ F A)) (@ comple7399068483239264473et_nat _let_2)))))))) (forall ((A4 set_nat) (F (-> product_prod_nat_nat set_nat))) (= (@ (@ sup_sup_set_nat A4) (@ comple7399068483239264473et_nat (@ (@ image_15824709712370754et_nat F) bot_bo2099793752762293965at_nat))) A4)) (forall ((R3 (-> product_prod_nat_nat product_prod_nat_nat Bool))) (= (@ (@ relcom8911704206367525917at_int R3) bot_bo5438875203632553179_int_o) bot_bo5438875203632553179_int_o)) _let_48 (forall ((G1 (-> Bool Bool)) (G22 (-> Bool Bool)) (F1 (-> nat Bool)) (F22 (-> nat Bool)) (V product_prod_nat_nat)) (= (@ (@ (@ produc1928436952130685430_o_o_o G1) G22) (@ (@ (@ produc6957950696844810486_nat_o F1) F22) V)) (@ (@ (@ produc6957950696844810486_nat_o (@ (@ comp_o_o_nat G1) F1)) (@ (@ comp_o_o_nat G22) F22)) V))) (forall ((A4 set_o) (B5 set_nat)) (let ((_let_1 (@ product_Sigma_o_nat A4))) (let ((_let_2 (@ image_4888532181312399726at_nat product_snd_o_nat))) (let ((_let_3 (= A4 bot_bot_set_o))) (and (=> _let_3 (= (@ _let_2 (@ _let_1 (lambda ((Uu Bool)) B5))) bot_bot_set_nat)) (=> (not _let_3) (= (@ _let_2 (@ _let_1 (lambda ((Uu Bool)) B5))) B5))))))) (forall ((G (-> nat rat)) (C3 set_nat) (B5 set_nat) (X2 nat)) (let ((_let_1 (@ (@ sup_sup_set_nat B5) (@ (@ insert_nat X2) bot_bot_set_nat)))) (=> (@ (@ inj_on_nat_rat G) C3) (=> (@ (@ ord_less_eq_set_nat C3) _let_1) (@ (@ member_rat_nat (lambda ((I2 rat)) (@ (@ (@ if_nat (@ (@ member_rat I2) (@ (@ image_nat_rat G) C3))) (@ (@ (@ the_inv_into_nat_rat C3) G) I2)) X2))) (@ (@ bNF_We7223962090624190782at_nat top_top_set_rat) _let_1)))))) (forall ((F (-> nat int)) (A4 set_nat)) (=> (@ order_mono_nat_int F) (=> (@ condit2214826472909112428ve_nat A4) (@ condit2212336002400062152ve_int (@ (@ image_nat_int F) A4))))) (forall ((I int) (J4 int) (R3 set_Pr958786334691620121nt_int)) (=> (@ (@ member5262025264175285858nt_int (@ (@ product_Pair_int_int I) J4)) R3) (@ (@ member_int I) (@ field_int R3)))) (forall ((R set_Pr7459493094073627847at_nat) (A4 set_se5479201105039950375at_nat)) (=> (@ (@ ord_le5997549366648089703at_nat R) (@ (@ produc6258361011560675592at_nat A4) (lambda ((Uu set_Pr4329608150637261639at_nat)) A4))) (=> (forall ((X set_Pr4329608150637261639at_nat)) (=> (@ (@ member6273874620674182256at_nat X) A4) (@ (@ member1466754251312161552at_nat (@ (@ produc9060074326276436823at_nat X) X)) R))) (@ (@ refl_o6272981002401706822at_nat A4) R)))) (forall ((A4 set_Product_unit) (C nat)) (let ((_let_1 (= A4 bot_bo3957492148770167129t_unit))) (and (=> _let_1 (= (@ (@ image_875570014554754200it_nat (lambda ((X4 product_unit)) C)) A4) bot_bot_set_nat)) (=> (not _let_1) (= (@ (@ image_875570014554754200it_nat (lambda ((X4 product_unit)) C)) A4) (@ (@ insert_nat C) bot_bot_set_nat)))))) (forall ((S5 set_int) (F (-> int nat nat)) (X2 int) (Y3 int)) (let ((_let_1 (@ F Y3))) (let ((_let_2 (@ F X2))) (=> (@ (@ finite4582259249640653518nt_nat S5) F) (=> (@ (@ member_int X2) S5) (=> (@ (@ member_int Y3) S5) (= (@ (@ comp_nat_nat_nat _let_1) _let_2) (@ (@ comp_nat_nat_nat _let_2) _let_1)))))))) (forall ((C3 set_o) (A4 set_Pr1261947904930325089at_nat) (B5 (-> Bool set_Pr1261947904930325089at_nat))) (let ((_let_1 (@ (@ inf_in2572325071724192079at_nat A4) (@ comple1930127330929219688at_nat (@ (@ image_7077428525161401678at_nat B5) C3))))) (let ((_let_2 (= C3 bot_bot_set_o))) (and (=> _let_2 (= _let_1 A4)) (=> (not _let_2) (= _let_1 (@ comple1930127330929219688at_nat (@ (@ image_7077428525161401678at_nat (lambda ((X4 Bool)) (@ (@ inf_in2572325071724192079at_nat A4) (@ B5 X4)))) C3)))))))) (forall ((Sup (-> set_nat nat)) (G (-> rat nat)) (F (-> nat rat)) (A4 set_nat)) (= (@ Sup (@ (@ image_rat_nat G) (@ (@ image_nat_rat F) A4))) (@ Sup (@ (@ image_nat_nat (@ (@ comp_rat_nat_nat G) F)) A4)))) (forall ((Xa2 product_prod_nat_nat) (X2 product_prod_nat_nat)) (= (@ (@ ord_less_int (@ abs_Integ Xa2)) (@ abs_Integ X2)) (@ (@ (@ produc8739625826339149834_nat_o (lambda ((X4 nat) (Y5 nat) (__flatten_var_0 product_prod_nat_nat)) (@ (@ produc6081775807080527818_nat_o (lambda ((U3 nat) (V3 nat)) (@ (@ ord_less_nat (@ (@ plus_plus_nat X4) V3)) (@ (@ plus_plus_nat U3) Y5)))) __flatten_var_0))) Xa2) X2))) (forall ((S5 set_Pr1261947904930325089at_nat)) (= (not (@ finite6177210948735845034at_nat S5)) (exists ((F2 (-> nat product_prod_nat_nat))) (and (@ (@ ord_le3146513528884898305at_nat (@ (@ image_5846123807819985514at_nat F2) top_top_set_nat)) S5) (@ (@ inj_on5538052773655684606at_nat F2) top_top_set_nat))))) (forall ((F (-> product_prod_nat_nat Bool)) (A4 set_Pr1261947904930325089at_nat)) (=> (@ finite_finite_o (@ (@ image_3693632289388996572_nat_o F) A4)) (=> (not (@ finite6177210948735845034at_nat A4)) (exists ((X Bool)) (and (not (@ finite6177210948735845034at_nat (@ (@ inf_in2572325071724192079at_nat (@ (@ vimage2444243245536687506_nat_o F) (@ (@ insert_o X) bot_bot_set_o))) A4))) (@ (@ member_o X) (@ (@ image_3693632289388996572_nat_o F) A4))))))) (forall ((A4 set_nat) (C product_unit)) (=> (not (= A4 bot_bot_set_nat)) (= (@ comple4687483117567863418t_unit (@ (@ image_8730104196221521654t_unit (lambda ((X4 nat)) C)) A4)) C))) (forall ((Y3 nat) (X2 nat) (A4 set_Pr1261947904930325089at_nat)) (= (@ (@ member8440522571783428010at_nat (@ (@ product_Pair_nat_nat Y3) X2)) (@ (@ image_5168914502847457605at_nat product_swap_nat_nat) A4)) (@ (@ member8440522571783428010at_nat (@ (@ product_Pair_nat_nat X2) Y3)) A4))) (forall ((Rep (-> nat rat)) (Abs (-> rat nat))) (=> (@ (@ (@ type_d5615363888691252950at_rat Rep) Abs) top_top_set_rat) (= (@ (@ comp_rat_nat_nat Abs) Rep) id_nat))) (forall ((B int) (F (-> int int)) (A4 set_int)) (=> (@ (@ member_int B) (@ (@ image_int_int F) A4)) (not (forall ((X int)) (=> (= B (@ F X)) (not (@ (@ member_int X) A4))))))) (@ trans_4347625901269045472at_nat fun_pair_less) (forall ((X2 char) (Y3 char)) (=> (= X2 Y3) (@ (@ (@ (@ bNF_Grp_char_char top_top_set_char) id_char) X2) Y3))) (forall ((A4 set_o) (C set_char)) (let ((_let_1 (= A4 bot_bot_set_o))) (and (=> _let_1 (= (@ comple7965528767983648192t_char (@ (@ image_o_set_char (lambda ((Y5 Bool)) C)) A4)) top_top_set_char)) (=> (not _let_1) (= (@ comple7965528767983648192t_char (@ (@ image_o_set_char (lambda ((Y5 Bool)) C)) A4)) C))))) (forall ((X2 Bool) (A4 set_o) (F (-> Bool nat))) (=> (@ (@ member_o X2) A4) (@ (@ member_nat (@ F X2)) (@ (@ image_o_nat F) A4)))) (forall ((A4 set_nat) (B5 set_int) (G (-> int product_unit)) (F (-> nat product_unit))) (=> (forall ((I4 nat)) (=> (@ (@ member_nat I4) A4) (exists ((X6 int)) (and (@ (@ member_int X6) B5) (@ (@ ord_le3221252021190050221t_unit (@ G X6)) (@ F I4)))))) (=> (forall ((J2 int)) (=> (@ (@ member_int J2) B5) (exists ((X6 nat)) (and (@ (@ ord_le3221252021190050221t_unit (@ F X6)) (@ G J2)) (@ (@ member_nat X6) A4))))) (= (@ comple2584293577114468500t_unit (@ (@ image_8730104196221521654t_unit F) A4)) (@ comple2584293577114468500t_unit (@ (@ image_5846526143423701914t_unit G) B5)))))) (forall ((F (-> nat nat)) (A4 set_nat)) (=> (@ (@ inj_on_nat_nat F) A4) (@ (@ inj_on4604407203859583615et_nat (@ image_nat_nat F)) (@ pow_nat A4)))) (forall ((F (-> product_unit Bool)) (A4 set_Product_unit)) (= (= bot_bot_set_o (@ (@ image_Product_unit_o F) A4)) (= A4 bot_bo3957492148770167129t_unit))) (forall ((A code_integer) (S2 set_Code_integer) (T2 set_Code_integer)) (= (@ (@ image_4470545334726330049nteger (lambda ((X4 code_integer)) (@ (@ minus_8373710615458151222nteger X4) A))) (@ (@ inf_in1364745209274528805nteger S2) T2)) (@ (@ inf_in1364745209274528805nteger (@ (@ image_4470545334726330049nteger (lambda ((X4 code_integer)) (@ (@ minus_8373710615458151222nteger X4) A))) S2)) (@ (@ image_4470545334726330049nteger (lambda ((X4 code_integer)) (@ (@ minus_8373710615458151222nteger X4) A))) T2)))) (forall ((A4 (-> int set_Product_unit)) (I int) (B5 set_Product_unit) (J3 set_int)) (= (@ comple3349607820504768346t_unit (@ (@ image_8658272795163236474t_unit (@ (@ (@ fun_up5054257004045450754t_unit A4) I) B5)) J3)) (@ (@ sup_su793286257634532545t_unit (@ comple3349607820504768346t_unit (@ (@ image_8658272795163236474t_unit A4) (@ (@ minus_minus_set_int J3) (@ (@ insert_int I) bot_bot_set_int))))) (@ (@ (@ if_set_Product_unit (@ (@ member_int I) J3)) B5) bot_bo3957492148770167129t_unit)))) (forall ((F (-> char nat)) (B5 set_nat) (I char)) (=> (@ (@ ord_less_eq_set_nat (@ (@ image_char_nat F) top_top_set_char)) B5) (@ (@ member_nat (@ F I)) B5))) (forall ((X5 set_Pr1261947904930325089at_nat)) (@ (@ member8757157785044589968at_nat (@ (@ produc2922128104949294807at_nat X5) bot_bo2099793752762293965at_nat)) fun_min_weak)) _let_47 (forall ((A product_prod_nat_nat) (A4 set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ pow_Pr3466873192417945886at_nat A4))) (let ((_let_2 (@ insert8211810215607154385at_nat A))) (= (@ pow_Pr3466873192417945886at_nat (@ _let_2 A4)) (@ (@ sup_su3642409539654194069at_nat _let_1) (@ (@ image_3684629450409544005at_nat _let_2) _let_1)))))) (forall ((R3 (-> product_prod_nat_nat product_prod_nat_nat Bool)) (S5 (-> product_prod_nat_nat int Bool)) (T3 (-> product_prod_nat_nat int Bool)) (F (-> int product_prod_nat_nat)) (G (-> int product_prod_nat_nat)) (H (-> code_integer int))) (=> (@ (@ ord_le129227817499904167_int_o (@ (@ relcom8911704206367525917at_int R3) S5)) T3) (@ (@ ord_le996066559646421213eger_o (@ (@ relcom967497705283160040nteger (@ (@ (@ bNF_vi1204582724742824157_nat_o F) G) R3)) (@ (@ (@ bNF_vi2881549544236934259_int_o G) H) S5))) (@ (@ (@ bNF_vi2881549544236934259_int_o F) H) T3)))) _let_46 (forall ((F (-> int nat)) (A4 set_int)) (=> (@ (@ inj_on_int_nat F) A4) (= (@ (@ image_nat_int (@ (@ the_inv_into_int_nat A4) F)) (@ (@ image_int_nat F) A4)) A4))) (forall ((F (-> int int)) (A4 set_int)) (=> (@ order_3677659787690696076nt_int F) (=> (@ condit2212336002400062152ve_int A4) (@ condit1735850657277959132ow_int (@ (@ image_int_int F) A4))))) (forall ((S5 set_nat) (T3 set_int) (F (-> nat int))) (=> (@ finite_finite_nat S5) (=> (@ finite_finite_int T3) (=> (= (@ finite_card_nat S5) (@ finite_card_int T3)) (=> (@ (@ ord_less_eq_set_int (@ (@ image_nat_int F) S5)) T3) (= (forall ((X4 int)) (=> (@ (@ member_int X4) T3) (exists ((Y5 nat)) (and (@ (@ member_nat Y5) S5) (= (@ F Y5) X4))))) (@ (@ inj_on_nat_int F) S5))))))) _let_45 _let_44 (forall ((X2 (-> char int)) (Ya (-> char int)) (Y3 (-> char nat)) (Xa2 (-> char nat)) (R3 (-> int nat Bool)) (Ra (-> int nat Bool))) (=> (= X2 Ya) (=> (= Y3 Xa2) (=> (forall ((Z3 int) (Yb nat)) (=> (@ (@ member_int Z3) (@ (@ image_char_int Ya) top_top_set_char)) (=> (@ (@ member_nat Yb) (@ (@ image_char_nat Xa2) top_top_set_char)) (= (@ (@ R3 Z3) Yb) (@ (@ Ra Z3) Yb))))) (= (@ (@ (@ (@ bNF_re4733689599336692735nt_nat (lambda ((Y2 char) (Z char)) (= Y2 Z))) R3) X2) Y3) (@ (@ (@ (@ bNF_re4733689599336692735nt_nat (lambda ((Y2 char) (Z char)) (= Y2 Z))) Ra) Ya) Xa2)))))) (forall ((A4 set_nat) (F (-> nat product_unit)) (A nat)) (let ((_let_1 (@ image_8730104196221521654t_unit F))) (let ((_let_2 (@ _let_1 A4))) (=> (not (= A4 bot_bot_set_nat)) (=> (@ condit2080475194861589617t_unit _let_2) (= (@ 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B))))))))) (forall ((R1 (-> int int Bool)) (R22 (-> ref_a heap_e7401611519738050253t_unit Bool)) (P2 (-> int ref_a Bool)) (Q2 (-> int heap_e7401611519738050253t_unit Bool)) (A product_prod_int_int) (A4 set_Pr958786334691620121nt_int) (B produc7812382424243267045t_unit) (B5 set_Pr1133966238863718811t_unit)) (=> (@ (@ (@ (@ bNF_re5404797796594736747unit_o R1) (@ (@ bNF_re1850668159662942673it_o_o R22) (lambda ((Y2 Bool) (Z Bool)) (= Y2 Z)))) P2) Q2) (=> (@ (@ member5262025264175285858nt_int A) A4) (=> (@ (@ member7849944260330398460t_unit B) B5) (=> (@ (@ ord_le2843351958646193337nt_int A4) (@ collec213857154873943460nt_int (@ produc4947309494688390418_int_o R1))) (=> (@ (@ ord_le5525191956872776187t_unit B5) (@ collec3252306575900995386t_unit (@ produc4924168586796184916unit_o R22))) (= (@ (@ P2 (@ product_fst_int_int A)) (@ produc473321116828791851t_unit B)) (@ (@ Q2 (@ product_snd_int_int A)) (@ produc1126150082675451753t_unit B))))))))) (forall ((A4 set_nat) (F (-> nat int)) (U int)) (let ((_let_1 (@ (@ image_nat_int F) A4))) (=> (not (= A4 bot_bot_set_nat)) (=> (@ condit1735850657277959132ow_int _let_1) (= (@ (@ ord_less_eq_int U) (@ complete_Inf_Inf_int _let_1)) (forall ((X4 nat)) (=> (@ (@ member_nat X4) A4) (@ (@ ord_less_eq_int U) (@ F X4))))))))) (forall ((S5 set_Pr1261947904930325089at_nat) (F (-> product_prod_nat_nat nat nat)) (X2 product_prod_nat_nat)) (let ((_let_1 (@ F X2))) (=> (@ (@ finite5150387867909132486at_nat S5) F) (=> (@ (@ member8440522571783428010at_nat X2) S5) (= (@ (@ comp_nat_nat_nat _let_1) _let_1) _let_1))))) (forall ((B num) (P product_prod_nat_num)) (= (= B (@ product_snd_nat_num P)) (exists ((A5 nat)) (= P (@ (@ product_Pair_nat_num A5) B))))) (forall ((A4 set_nat) (F (-> nat nat)) (B5 set_nat)) (let ((_let_1 (@ image_nat_nat F))) (let ((_let_2 (@ _let_1 B5))) (let ((_let_3 (@ _let_1 A4))) (=> (not (= A4 bot_bot_set_nat)) (=> (@ condit2214826472909112428ve_nat _let_3) (=> (not (= B5 bot_bot_set_nat)) (=> (@ 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(@ inj_on_o_int F) top_top_set_o) (= (@ (@ member_int (@ F A)) (@ (@ image_o_int F) A4)) (@ (@ member_o A) A4)))) (forall ((R7 (-> code_integer int Bool)) (S6 (-> num num Bool)) (R3 (-> int code_integer Bool)) (S5 (-> num num Bool))) (=> (@ right_7836862732553076961er_int R7) (=> (@ left_t1735413524555719857er_int R7) (=> (@ left_unique_num_num S6) (=> (@ right_total_num_num S6) (@ (@ ord_le4541714130423454556_num_o (@ (@ bNF_re7626690874201225453um_num (@ (@ relcom328798225758222312er_int R3) R7)) (@ (@ relcompp_num_num_num S5) S6))) (@ (@ relcom7779292856395800339nt_num (@ (@ bNF_re6718328864250387230um_num R3) S5)) (@ (@ bNF_re8313794964846168862um_num R7) S6)))))))) (forall ((A Bool) (A4 set_o) (B nat) (B5 (-> Bool set_nat))) (=> (@ (@ member_o A) A4) (=> (@ (@ member_nat B) (@ B5 A)) (@ (@ member2802428098988154798_o_nat (@ (@ product_Pair_o_nat A) B)) (@ (@ product_Sigma_o_nat A4) B5))))) _let_39 (forall ((Y4 (-> product_prod_nat_nat int Bool)) (X5 (-> product_prod_nat_nat int 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(= (@ (@ member1466754251312161552at_nat (@ (@ produc9060074326276436823at_nat A) B)) R) (not (@ (@ member1466754251312161552at_nat (@ (@ produc9060074326276436823at_nat B) A)) (@ (@ minus_8674369445256047406at_nat R) id_set4888139568991089827at_nat))))))))) _let_38 (forall ((G (-> int int)) (F (-> nat int)) (A4 set_nat)) (= (@ complete_Inf_Inf_int (@ (@ image_int_int G) (@ (@ image_nat_int F) A4))) (@ complete_Inf_Inf_int (@ (@ image_nat_int (@ (@ comp_int_int_nat G) F)) A4)))) (forall ((C3 set_o) (A4 (-> Bool set_char)) (B5 set_char)) (let ((_let_1 (= C3 bot_bot_set_o))) (and (=> _let_1 (= (@ comple7965528767983648192t_char (@ (@ image_o_set_char (lambda ((X4 Bool)) (@ (@ minus_minus_set_char (@ A4 X4)) B5))) C3)) top_top_set_char)) (=> (not _let_1) (= (@ comple7965528767983648192t_char (@ (@ image_o_set_char (lambda ((X4 Bool)) (@ (@ minus_minus_set_char (@ A4 X4)) B5))) C3)) (@ (@ minus_minus_set_char (@ comple7965528767983648192t_char (@ (@ image_o_set_char A4) C3))) B5)))))) (forall ((P2 (-> rat char product_unit))) (= (@ comple2584293577114468500t_unit (@ (@ image_4337914935673063477t_unit (lambda ((Y5 char)) (@ comple4687483117567863418t_unit (@ (@ image_2327579789247107822t_unit (lambda ((X4 rat)) (@ (@ P2 X4) Y5))) top_top_set_rat)))) top_top_set_char)) (@ comple4687483117567863418t_unit (@ (@ image_7615136836863079294t_unit (lambda ((F2 (-> char rat))) (@ comple2584293577114468500t_unit (@ (@ image_4337914935673063477t_unit (lambda ((X4 char)) (@ (@ P2 (@ F2 X4)) X4))) top_top_set_char)))) top_top_set_char_rat)))) (forall ((F (-> nat rat)) (A4 set_nat) (G (-> nat rat)) (B5 set_nat) (H (-> rat nat))) (let ((_let_1 (@ comp_rat_nat_nat H))) (=> (= (@ (@ image_nat_rat F) A4) (@ (@ image_nat_rat G) B5)) (= (@ (@ image_nat_nat (@ _let_1 F)) A4) (@ (@ image_nat_nat (@ _let_1 G)) B5))))) (forall ((X5 set_Pr1261947904930325089at_nat) (P2 (-> product_prod_nat_nat Bool))) (@ (@ ord_le3146513528884898305at_nat (@ collec3392354462482085612at_nat (lambda ((X4 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product_unit)) (B5 set_nat)) (let ((_let_1 (@ image_8730104196221521654t_unit F))) (let ((_let_2 (@ _let_1 B5))) (let ((_let_3 (@ _let_1 A4))) (=> (not (= A4 bot_bot_set_nat)) (=> (@ condit2080475194861589617t_unit _let_3) (=> (not (= B5 bot_bot_set_nat)) (=> (@ condit2080475194861589617t_unit _let_2) (= (@ comple4687483117567863418t_unit (@ _let_1 (@ (@ sup_sup_set_nat A4) B5))) (@ (@ sup_sup_Product_unit (@ comple4687483117567863418t_unit _let_3)) (@ comple4687483117567863418t_unit _let_2))))))))))) (forall ((A4 set_int) (M3 rat) (F (-> int rat))) (=> (forall ((X int)) (=> (@ (@ member_int X) A4) (@ (@ ord_less_eq_rat M3) (@ F X)))) (@ condit1103211067700513672ow_rat (@ (@ image_int_rat F) A4)))) (forall ((F (-> nat rat)) (A4 set_nat)) (=> (@ (@ inj_on_nat_rat F) A4) (@ (@ inj_on1096178645466186887et_rat (@ image_nat_rat F)) (@ finite_Fpow_nat A4)))) (forall ((F (-> nat nat)) (A4 set_nat)) (=> (@ order_mono_nat_nat F) (=> (@ condit1738341127787009408ow_nat A4) (@ condit1738341127787009408ow_nat (@ (@ image_nat_nat F) A4))))) (forall ((F (-> heap_e7401611519738050253t_unit num)) (G (-> ref_a nat)) (X2 produc7812382424243267045t_unit)) (= (@ (@ produc3902377510303101371um_nat F) (@ (@ produc6942186945380262242t_unit G) X2)) (@ (@ product_Pair_nat_num (@ G (@ produc473321116828791851t_unit X2))) (@ F (@ produc1126150082675451753t_unit X2))))) (forall ((A4 set_Pr1261947904930325089at_nat) (B5 (-> product_prod_nat_nat set_nat))) (=> (@ finite6177210948735845034at_nat A4) (= (@ finite_finite_nat (@ comple7399068483239264473et_nat (@ (@ image_15824709712370754et_nat B5) A4))) (forall ((X4 product_prod_nat_nat)) (=> (@ (@ member8440522571783428010at_nat X4) A4) (@ finite_finite_nat (@ B5 X4))))))) (forall ((F (-> nat rat)) (A4 set_nat) (B5 set_nat)) (let ((_let_1 (@ image_nat_rat F))) (=> (@ (@ inj_on_nat_rat F) (@ (@ sup_sup_set_nat A4) B5)) (= (= (@ _let_1 A4) (@ _let_1 B5)) (= A4 B5))))) (forall ((A4 set_o) (C nat)) (let ((_let_1 (= A4 bot_bot_set_o))) (and (=> (not _let_1) (= (@ (@ image_o_nat (lambda ((X4 Bool)) C)) A4) (@ (@ insert_nat C) bot_bot_set_nat))) (=> _let_1 (= (@ (@ image_o_nat (lambda ((X4 Bool)) C)) A4) bot_bot_set_nat))))) (forall ((H1 (-> (-> code_integer code_integer) produc8923325533196201883nteger produc8923325533196201883nteger)) (H22 (-> (-> code_integer code_integer) produc8923325533196201883nteger produc8923325533196201883nteger)) (F (-> code_integer code_integer code_integer)) (G (-> code_integer code_integer code_integer))) (= (@ (@ comp_P8564252314792299288nteger (@ (@ produc4724772261320961782nteger H1) H22)) (@ (@ bNF_co6169604788974073338nteger F) G)) (@ (@ bNF_co3156833790671340178nteger (@ (@ comp_C8797469213163452608nteger H1) F)) (@ (@ comp_C8797469213163452608nteger H22) G)))) (forall ((R set_Pr5564308138774400199at_nat)) (let ((_let_1 (@ field_2862844103579723188at_nat R))) (=> (@ (@ order_2711500226769404828at_nat _let_1) R) (= (@ (@ order_2339240034117818117at_nat _let_1) R) (forall ((A6 set_Pr4329608150637261639at_nat)) (=> (@ (@ ord_le1268244103169919719at_nat A6) (@ field_2862844103579723188at_nat R)) (=> (not (= A6 bot_bo228742789529271731at_nat)) (exists ((X4 produc3843707927480180839at_nat)) (and (@ (@ member8757157785044589968at_nat X4) A6) (forall ((Y5 produc3843707927480180839at_nat)) (=> (@ (@ member8757157785044589968at_nat Y5) A6) (@ (@ member6009668390874684176at_nat (@ (@ produc2335810615602371415at_nat X4) Y5)) R)))))))))))) (forall ((I nat) (C3 set_nat) (G (-> nat rat)) (X2 nat)) (=> (@ (@ member_nat I) C3) (=> (@ (@ inj_on_nat_rat G) C3) (= (@ (@ (@ comp_rat_nat_nat (lambda ((I2 rat)) (@ (@ (@ if_nat (@ (@ member_rat I2) (@ (@ image_nat_rat G) C3))) (@ (@ (@ the_inv_into_nat_rat C3) G) I2)) X2))) G) I) (@ id_nat I))))) (forall ((Z2 product_prod_nat_nat) (A4 set_nat) (F (-> nat nat))) (=> (@ (@ member8440522571783428010at_nat Z2) (@ collec3392354462482085612at_nat (@ produc6081775807080527818_nat_o (@ (@ bNF_Grp_nat_nat A4) F)))) (= (@ (@ (@ comp_n2711240574518091068at_nat F) product_fst_nat_nat) Z2) (@ product_snd_nat_nat Z2)))) _let_37 (forall ((I3 set_se7855581050983116737at_nat) (X5 (-> set_Pr1261947904930325089at_nat set_se7855581050983116737at_nat))) (= (= (@ (@ produc7726050920695093128at_nat I3) X5) bot_bo228742789529271731at_nat) (forall ((X4 set_Pr1261947904930325089at_nat)) (=> (@ (@ member2643936169264416010at_nat X4) I3) (= (@ X5 X4) bot_bo3083307316010499117at_nat))))) (forall ((A set_Pr1261947904930325089at_nat) (B set_Pr1261947904930325089at_nat) (A4 set_se7855581050983116737at_nat)) (=> (= A B) (=> (@ (@ member2643936169264416010at_nat A) A4) (@ (@ member8757157785044589968at_nat (@ (@ produc2922128104949294807at_nat A) B)) (@ id_on_6713504163309144702at_nat A4))))) (forall ((A4 set_nat) (B5 set_nat) (C3 (-> nat nat)) (D (-> nat nat))) (=> (= A4 B5) (=> (forall ((X nat)) (=> (@ (@ member_nat X) B5) (= (@ C3 X) (@ D X)))) (= (@ complete_Inf_Inf_nat (@ (@ image_nat_nat C3) A4)) (@ complete_Inf_Inf_nat (@ (@ image_nat_nat D) B5)))))) (forall ((R3 set_Pr4329608150637261639at_nat) (S5 set_Pr4329608150637261639at_nat)) (= (@ (@ sup_su7519161239522478338_nat_o (lambda ((X4 set_Pr1261947904930325089at_nat) (Y5 set_Pr1261947904930325089at_nat)) (@ (@ member8757157785044589968at_nat (@ (@ produc2922128104949294807at_nat X4) Y5)) R3))) (lambda ((X4 set_Pr1261947904930325089at_nat) (Y5 set_Pr1261947904930325089at_nat)) (@ (@ member8757157785044589968at_nat (@ (@ produc2922128104949294807at_nat X4) Y5)) S5))) (lambda ((X4 set_Pr1261947904930325089at_nat) (Y5 set_Pr1261947904930325089at_nat)) (@ (@ member8757157785044589968at_nat (@ (@ produc2922128104949294807at_nat X4) Y5)) (@ (@ sup_su5525570899277871387at_nat R3) S5))))) (forall ((P rat)) (= (@ quotient_of (@ inverse_inverse_rat P)) (@ (@ produc4245557441103728435nt_int (lambda ((A5 int) (B4 int)) (@ (@ (@ if_Pro3027730157355071871nt_int (= A5 zero_zero_int)) (@ (@ product_Pair_int_int zero_zero_int) one_one_int)) (@ (@ product_Pair_int_int (@ (@ times_times_int (@ sgn_sgn_int A5)) B4)) (@ abs_abs_int A5))))) (@ quotient_of P)))) _let_36 (forall ((A4 set_ref_a) (B5 (-> ref_a set_he8644174446132254637t_unit))) (= (@ (@ image_17660834435998945t_unit produc1126150082675451753t_unit) (@ (@ produc3946373962484743846t_unit A4) B5)) (@ comple6989579708249578522t_unit (@ (@ image_5570573867351727369t_unit B5) A4)))) (forall ((B5 set_rat) (F (-> nat rat)) (A4 set_nat)) (=> (@ (@ ord_less_eq_set_rat B5) (@ (@ image_nat_rat F) A4)) (not (forall ((C2 set_nat)) (=> (@ (@ ord_less_eq_set_nat C2) A4) (not (= B5 (@ (@ image_nat_rat F) C2)))))))) (forall ((F (-> Bool int)) (A4 set_o) (X2 Bool)) (let ((_let_1 (@ (@ image_o_int F) A4))) (=> (@ condit1735850657277959132ow_int _let_1) (=> (@ (@ member_o X2) A4) (@ (@ ord_less_eq_int (@ complete_Inf_Inf_int _let_1)) (@ F X2)))))) (forall ((F (-> Bool set_nat)) (A4 set_o) (X2 Bool) (U set_nat)) (let ((_let_1 (@ (@ image_o_set_nat F) A4))) (let ((_let_2 (@ ord_less_eq_set_nat U))) (=> (@ condit5477540289124974626et_nat _let_1) (=> (@ (@ member_o X2) A4) (=> (@ _let_2 (@ F X2)) (@ _let_2 (@ comple7399068483239264473et_nat _let_1)))))))) (forall ((F (-> int int)) (A4 set_set_int)) (=> (@ (@ inj_on_int_int F) (@ comple3221217463730067765et_int A4)) (@ (@ inj_on6435365835345961783et_int (@ image_int_int F)) A4))) (forall ((F (-> nat int)) (V (-> char nat))) (= (@ (@ image_char_int (@ (@ comp_nat_int_char F) V)) top_top_set_char) (@ (@ image_nat_int F) (@ (@ image_char_nat V) top_top_set_char)))) (forall ((A4 (-> int Bool))) (= (@ id_on_int (@ collect_int A4)) (@ collec213857154873943460nt_int (@ produc4947309494688390418_int_o (lambda ((X4 int) (Y5 int)) (and (@ A4 X4) (= X4 Y5))))))) (forall ((R3 (-> nat nat Bool))) (= (@ (@ bNF_re4629543205785817921at_nat (lambda ((Y2 list_nat) (Z list_nat)) (= Y2 Z))) R3) (@ (@ relcom5920149085449455271at_nat (@ conver6066198818478722162at_nat (@ (@ bNF_Gr1532745923208276441at_nat (@ collec3092956710985254339at_nat (lambda ((X4 (-> list_nat product_prod_nat_nat))) (@ (@ ord_le3146513528884898305at_nat (@ (@ image_2795870212791037530at_nat X4) top_top_set_list_nat)) (@ collec3392354462482085612at_nat (@ produc6081775807080527818_nat_o R3)))))) (@ comp_P5292260908303971472st_nat product_fst_nat_nat)))) (@ (@ bNF_Gr1532745923208276441at_nat (@ collec3092956710985254339at_nat (lambda ((X4 (-> list_nat product_prod_nat_nat))) (@ (@ ord_le3146513528884898305at_nat (@ (@ image_2795870212791037530at_nat X4) top_top_set_list_nat)) (@ collec3392354462482085612at_nat (@ produc6081775807080527818_nat_o R3)))))) (@ comp_P5292260908303971472st_nat product_snd_nat_nat))))) (forall ((B5 (-> nat set_Pr4329608150637261639at_nat)) (A nat) (A4 set_nat)) (let ((_let_1 (@ image_1087905878993176368at_nat B5))) (= (@ comple4364388969068068532at_nat (@ _let_1 (@ (@ insert_nat A) A4))) (@ (@ sup_su5525570899277871387at_nat (@ B5 A)) (@ comple4364388969068068532at_nat (@ _let_1 A4)))))) (forall ((X2 produc7812382424243267045t_unit) (A4 (-> ref_a heap_e7401611519738050253t_unit Bool))) (=> (@ (@ member7849944260330398460t_unit X2) (@ collec3252306575900995386t_unit (@ produc4924168586796184916unit_o A4))) (@ (@ A4 (@ produc473321116828791851t_unit X2)) (@ produc1126150082675451753t_unit X2)))) (forall ((K Bool) (I3 set_o) (A4 (-> Bool set_nat))) (let ((_let_1 (@ comple7399068483239264473et_nat (@ (@ image_o_set_nat A4) I3)))) (=> (@ (@ member_o K) I3) (= (@ (@ sup_sup_set_nat (@ A4 K)) _let_1) _let_1)))) (forall ((F (-> (-> code_integer code_integer) produc8923325533196201883nteger produc8923325533196201883nteger))) (=> (@ (@ inj_on3998011822705705585nteger F) top_to3804862627464599871nteger) (@ (@ inj_on5500977043710295017nteger (@ comp_C8797469213163452608nteger F)) top_to3639204395728341691nteger))) (forall ((F (-> int int)) (A4 set_int) (B5 set_int)) (let ((_let_1 (@ image_int_int F))) (=> (@ (@ inj_on_int_int F) top_top_set_int) (= (@ _let_1 (@ (@ inf_inf_set_int A4) B5)) (@ (@ inf_inf_set_int (@ _let_1 A4)) (@ _let_1 B5)))))) (forall ((P2 (-> char nat product_unit))) (= (@ comple2584293577114468500t_unit (@ (@ image_8730104196221521654t_unit (lambda ((Y5 nat)) (@ comple4687483117567863418t_unit (@ (@ image_4337914935673063477t_unit (lambda ((X4 char)) (@ (@ P2 X4) Y5))) top_top_set_char)))) top_top_set_nat)) (@ comple4687483117567863418t_unit (@ (@ image_4600008085730780422t_unit (lambda ((F2 (-> nat char))) (@ comple2584293577114468500t_unit (@ (@ image_8730104196221521654t_unit (lambda ((X4 nat)) (@ (@ P2 (@ F2 X4)) X4))) top_top_set_nat)))) top_top_set_nat_char)))) (forall ((R3 (-> Bool Bool Bool)) (X2 (-> rat Bool)) (Y3 (-> rat Bool)) (Ra (-> Bool Bool Bool))) (=> (@ (@ (@ (@ bNF_re1865807574169326223at_o_o (lambda ((Y2 rat) (Z rat)) (= Y2 Z))) R3) X2) Y3) (=> (forall ((Z3 Bool) (Yb Bool)) (=> (@ (@ member_o Z3) (@ (@ image_rat_o X2) top_top_set_rat)) (=> (@ (@ member_o Yb) (@ (@ image_rat_o Y3) top_top_set_rat)) (=> (@ (@ R3 Z3) Yb) (@ (@ Ra Z3) Yb))))) (@ (@ (@ (@ bNF_re1865807574169326223at_o_o (lambda ((Y2 rat) (Z rat)) (= Y2 Z))) Ra) X2) Y3)))) (forall ((F (-> nat Bool)) (A4 set_nat) (X2 Bool) (B5 set_nat)) (=> (@ (@ inj_on_nat_o F) A4) (=> (@ (@ member_o X2) (@ (@ image_nat_o F) A4)) (=> (@ (@ ord_less_eq_set_nat A4) B5) (@ (@ member_nat (@ (@ (@ the_inv_into_nat_o A4) F) X2)) B5))))) (forall ((Rep (-> int nat)) (Abs (-> nat int)) (A4 set_nat)) (=> (@ (@ (@ type_d7249847660678803242nt_nat Rep) Abs) A4) (= (@ (@ image_nat_int Abs) A4) top_top_set_int))) (forall ((A4 set_o) (F (-> Bool set_nat))) (let ((_let_1 (@ (@ image_o_set_nat F) A4))) (=> (not (= A4 bot_bot_set_o)) (@ (@ ord_less_eq_set_nat (@ comple7806235888213564991et_nat _let_1)) (@ comple7399068483239264473et_nat _let_1))))) (forall ((A4 set_int) (B5 set_int) (G (-> int product_unit)) (F (-> int product_unit))) (=> (forall ((I4 int)) (=> (@ (@ member_int I4) A4) (exists ((X6 int)) (and (@ (@ member_int X6) B5) (@ (@ ord_le3221252021190050221t_unit (@ G X6)) (@ F I4)))))) (=> (forall ((J2 int)) (=> (@ (@ member_int J2) B5) (exists ((X6 int)) (and (@ (@ ord_le3221252021190050221t_unit (@ F X6)) (@ G J2)) (@ (@ member_int X6) A4))))) (= (@ comple2584293577114468500t_unit (@ (@ image_5846526143423701914t_unit F) A4)) (@ comple2584293577114468500t_unit (@ (@ image_5846526143423701914t_unit G) B5)))))) (forall ((A4 set_se7855581050983116737at_nat) (B5 set_se7855581050983116737at_nat)) (= (@ (@ image_960689587819713477at_nat (@ produc7548845685434208379at_nat (lambda ((I2 set_Pr1261947904930325089at_nat) (J set_Pr1261947904930325089at_nat)) (@ (@ produc2922128104949294807at_nat J) I2)))) (@ (@ produc7726050920695093128at_nat A4) (lambda ((Uu set_Pr1261947904930325089at_nat)) B5))) (@ (@ produc7726050920695093128at_nat B5) (lambda ((Uu set_Pr1261947904930325089at_nat)) A4)))) (forall ((Rep (-> nat nat)) (Abs (-> nat nat))) (=> (@ (@ (@ type_d6250493948777748686at_nat Rep) Abs) top_top_set_nat) (= (@ (@ comp_nat_nat_nat Abs) Rep) id_nat))) (forall ((H (-> char nat)) (F4 set_nat)) (=> (@ finite_finite_char (@ (@ vimage_char_nat H) F4)) (=> (= (@ (@ image_char_nat H) top_top_set_char) top_top_set_nat) (@ finite_finite_nat F4)))) (forall ((I produc3843707927480180839at_nat) (A4 set_Pr4329608150637261639at_nat) (F (-> produc3843707927480180839at_nat set_nat))) (=> (@ (@ member8757157785044589968at_nat I) A4) (@ (@ ord_less_eq_set_nat (@ F I)) (@ comple7399068483239264473et_nat (@ (@ image_3160451284896210088et_nat F) A4))))) (forall ((A nat) (A4 set_nat) (B int) (B5 (-> nat set_int))) (=> (@ (@ member_nat A) A4) (=> (@ (@ member_int B) (@ B5 A)) (@ (@ member4262671552274231302at_int (@ (@ product_Pair_nat_int A) B)) (@ (@ produc454536836294682310at_int A4) B5))))) (forall ((K Bool) (I3 set_o) (A4 (-> Bool product_unit))) (let ((_let_1 (@ comple2584293577114468500t_unit (@ (@ image_o_Product_unit A4) I3)))) (=> (@ (@ member_o K) I3) (= (@ (@ inf_inf_Product_unit (@ A4 K)) _let_1) _let_1)))) (forall ((F (-> int int))) (=> (@ finite_finite_int top_top_set_int) (=> (@ (@ inj_on_int_int F) top_top_set_int) (= (@ (@ image_int_int F) top_top_set_int) top_top_set_int)))) (forall ((X2 (-> int int)) (F (-> int nat)) (G (-> int nat))) (=> (forall ((Z3 int)) (=> (@ (@ member_int Z3) (@ (@ image_int_int X2) top_top_set_int)) (= (@ F Z3) (@ G Z3)))) (= (@ (@ comp_int_nat_int F) X2) (@ (@ comp_int_nat_int G) X2)))) (forall ((X2 produc3843707927480180839at_nat) (Y3 produc3843707927480180839at_nat)) (= (@ (@ (@ if_Pro3594990065127090477at_nat false) X2) Y3) Y3)) (forall ((R3 (-> product_prod_nat_nat int Bool)) (F (-> product_prod_nat_nat nat)) (G (-> int nat))) (@ (@ (@ (@ bNF_re4555766996558763186at_nat R3) (@ (@ (@ bNF_Gr6955563364113978072nt_nat F) G) R3)) F) G)) (forall ((F (-> nat nat product_prod_nat_nat product_prod_nat_nat)) (G (-> product_prod_nat_nat product_prod_nat_nat product_prod_nat_nat))) (=> (forall ((X nat) (Y nat)) (= (@ (@ F X) Y) (@ G (@ (@ product_Pair_nat_nat X) Y)))) (= (@ produc27273713700761075at_nat F) G))) (forall ((F (-> rat int))) (= (= (@ (@ image_rat_int F) top_top_set_rat) top_top_set_int) (forall ((Y5 int)) (exists ((X4 rat)) (= Y5 (@ F X4)))))) (forall ((A4 set_Product_unit) (F (-> product_unit product_unit)) (G (-> product_unit product_unit))) (let ((_let_1 (@ (@ image_405062704495631173t_unit G) A4))) (let ((_let_2 (@ (@ image_405062704495631173t_unit F) A4))) (=> (not (= A4 bot_bo3957492148770167129t_unit)) (=> (@ condit2080475194861589617t_unit _let_2) (=> (@ condit2080475194861589617t_unit _let_1) (= (@ (@ sup_sup_Product_unit (@ comple4687483117567863418t_unit _let_2)) (@ comple4687483117567863418t_unit _let_1)) (@ comple4687483117567863418t_unit (@ (@ image_405062704495631173t_unit (lambda ((A5 product_unit)) (@ (@ sup_sup_Product_unit (@ F A5)) (@ G A5)))) A4))))))))) (forall ((F (-> nat Bool)) (G (-> Bool Bool))) (= (@ (@ comp_s9189197539837705563_set_o (@ vimage_nat_o F)) (@ vimage_o_o G)) (@ vimage_nat_o (@ (@ comp_o_o_nat G) F)))) (forall ((A4 set_set_nat)) (= (@ comple7806235888213564991et_nat (@ (@ image_7916887816326733075et_nat (lambda ((X4 set_nat)) X4)) A4)) (@ comple7806235888213564991et_nat A4))) (forall ((F (-> nat nat)) (G (-> Bool nat)) (L1 (-> Bool nat)) (L2 (-> Bool Bool)) (H (-> nat Bool)) (R (-> nat Bool))) (=> (= (@ (@ comp_nat_nat_o F) G) (@ (@ comp_o_nat_o L1) L2)) (=> (= (@ (@ comp_o_o_nat L2) H) R) (= (@ (@ comp_nat_nat_nat F) (@ (@ comp_o_nat_nat G) H)) (@ (@ comp_o_nat_nat L1) R))))) (forall ((Rb (-> int code_integer Bool)) (Sd (-> num num Bool))) (@ (@ (@ (@ bNF_re7839584876883444355nt_num (@ (@ bNF_re6718328864250387230um_num Rb) Sd)) (@ (@ bNF_re2961086658867094474nt_num (@ (@ bNF_re982302072995117890nteger (lambda ((Y2 int) (Z int)) (= Y2 Z))) Rb)) (@ (@ bNF_re7626690874201225453um_num (lambda ((Y2 int) (Z int)) (= Y2 Z))) Sd))) comp_int_num_int) comp_C2177396528461469320um_int)) (forall ((C3 set_Pr4329608150637261639at_nat) (A4 set_nat) (B5 (-> produc3843707927480180839at_nat set_nat))) (let ((_let_1 (@ (@ 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(forall ((X2 (-> nat nat)) (F (-> nat nat)) (G (-> nat nat))) (=> (forall ((Z3 nat)) (=> (@ (@ member_nat Z3) (@ (@ image_nat_nat X2) top_top_set_nat)) (= (@ F Z3) (@ G Z3)))) (= (@ (@ comp_nat_nat_nat F) X2) (@ (@ comp_nat_nat_nat G) X2)))) (forall ((F (-> nat rat)) (A nat) (B5 set_nat)) (let ((_let_1 (@ image_nat_rat F))) (= (@ _let_1 (@ (@ insert_nat A) B5)) (@ (@ insert_rat (@ F A)) (@ _let_1 B5))))) (forall ((X2 set_Pr4329608150637261639at_nat) (Y3 set_Pr4329608150637261639at_nat) (A set_Pr4329608150637261639at_nat)) (=> (= (@ produc4486455499028916547at_nat (@ (@ produc9060074326276436823at_nat X2) Y3)) A) (= X2 A))) (forall ((X5 set_o) (P2 (-> Bool Bool))) (@ (@ ord_less_eq_set_o (@ collect_o (lambda ((X4 Bool)) (and (@ (@ member_o X4) X5) (@ P2 X4))))) X5)) (forall ((F (-> product_unit char)) (A4 set_char)) (=> (= (@ (@ image_7248553556944771225t_char F) top_to1996260823553986621t_unit) top_top_set_char) (= (= (@ (@ vimage2648087219933717859t_char F) A4) 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(lambda ((Y2 nat) (Z nat)) (= Y2 Z))) R3) (@ (@ relcom3290293904592725231at_int (@ conver2987682522074450438at_int (@ (@ bNF_Gr2878093617000900205at_int (@ collec8414850927317488011nt_int (lambda ((X4 (-> nat product_prod_int_int))) (@ (@ ord_le2843351958646193337nt_int (@ (@ image_2667626500211843362nt_int X4) top_top_set_nat)) (@ collec213857154873943460nt_int (@ produc4947309494688390418_int_o R3)))))) (@ comp_P6653955642190706324nt_nat product_fst_int_int)))) (@ (@ bNF_Gr2878093617000900205at_int (@ collec8414850927317488011nt_int (lambda ((X4 (-> nat product_prod_int_int))) (@ (@ ord_le2843351958646193337nt_int (@ (@ image_2667626500211843362nt_int X4) top_top_set_nat)) (@ collec213857154873943460nt_int (@ produc4947309494688390418_int_o R3)))))) (@ comp_P6653955642190706324nt_nat product_snd_int_int))))) (forall ((R3 (-> int int Bool))) (= (@ (@ bNF_re4731199128827642459nt_int (lambda ((Y2 char) (Z char)) (= Y2 Z))) R3) (@ (@ relcom4417706183330134766ar_int (@ conver1155128050257070662ar_int (@ (@ bNF_Gr6947267152677263533ar_int (@ collec1380656525566158922nt_int (lambda ((X4 (-> char product_prod_int_int))) (@ (@ ord_le2843351958646193337nt_int (@ (@ image_5204326662208377313nt_int X4) top_top_set_char)) (@ collec213857154873943460nt_int (@ produc4947309494688390418_int_o R3)))))) (@ comp_P4161745170962941589t_char product_fst_int_int)))) (@ (@ bNF_Gr6947267152677263533ar_int (@ collec1380656525566158922nt_int (lambda ((X4 (-> char product_prod_int_int))) (@ (@ ord_le2843351958646193337nt_int (@ (@ image_5204326662208377313nt_int X4) top_top_set_char)) (@ collec213857154873943460nt_int (@ produc4947309494688390418_int_o R3)))))) (@ comp_P4161745170962941589t_char product_snd_int_int))))) (forall ((A4 set_Product_unit) (F (-> product_unit product_unit)) (A product_unit)) (let ((_let_1 (@ image_405062704495631173t_unit F))) (let ((_let_2 (@ _let_1 A4))) (=> (not (= A4 bot_bo3957492148770167129t_unit)) (=> (@ condit2080475194861589617t_unit _let_2) (= (@ comple4687483117567863418t_unit (@ _let_1 (@ (@ insert_Product_unit A) A4))) (@ (@ sup_sup_Product_unit (@ F A)) (@ comple4687483117567863418t_unit _let_2)))))))) (forall ((F (-> nat set_nat)) (A4 set_nat) (A nat)) (let ((_let_1 (@ (@ image_nat_set_nat F) A4))) (let ((_let_2 (@ comple7806235888213564991et_nat _let_1))) (=> (= (@ comple7399068483239264473et_nat _let_1) _let_2) (=> (@ condit5477540289124974626et_nat _let_1) (=> (@ condit68592940725977398et_nat _let_1) (=> (@ (@ member_nat A) A4) (= (@ F A) _let_2)))))))) _let_33 (forall ((I3 set_Product_unit) (F (-> product_unit set_nat)) (X2 set_nat)) (=> (not (= I3 bot_bo3957492148770167129t_unit)) (=> (forall ((I4 product_unit)) (=> (@ (@ member_Product_unit I4) I3) (= (@ F I4) X2))) (= (@ comple7806235888213564991et_nat (@ (@ image_8173849991827986510et_nat F) I3)) X2)))) (forall ((X5 set_Pr1261947904930325089at_nat)) (=> (@ finite6177210948735845034at_nat X5) (@ (@ member8757157785044589968at_nat (@ (@ produc2922128104949294807at_nat bot_bo2099793752762293965at_nat) X5)) fun_max_weak))) (forall ((F (-> nat nat)) (A4 set_nat) (X2 nat) (U nat)) (let ((_let_1 (@ (@ image_nat_nat F) A4))) (let ((_let_2 (@ ord_less_eq_nat U))) (=> (@ condit2214826472909112428ve_nat _let_1) (=> (@ (@ member_nat X2) A4) (=> (@ _let_2 (@ F X2)) (@ _let_2 (@ complete_Sup_Sup_nat _let_1)))))))) (forall ((B5 (-> Bool set_rat))) (= (@ comple4298007329820168263et_rat (@ (@ image_o_set_rat B5) bot_bot_set_o)) top_top_set_rat)) (forall ((A4 set_o) (C set_Product_unit)) (let ((_let_1 (= A4 bot_bot_set_o))) (and (=> (not _let_1) (= (@ comple3349607820504768346t_unit (@ (@ image_663195431845683034t_unit (lambda ((Y5 Bool)) C)) A4)) C)) (=> _let_1 (= (@ comple3349607820504768346t_unit (@ (@ image_663195431845683034t_unit (lambda ((Y5 Bool)) C)) A4)) bot_bo3957492148770167129t_unit))))) (forall ((Rep (-> Bool char)) (Abs (-> char Bool)) (F (-> nat Bool)) (P2 (-> Bool Bool)) (H (-> Bool char))) (=> (@ (@ (@ type_d9076672964931703357o_char Rep) Abs) top_top_set_char) (= (@ (@ (@ bNF_vi8816436626763797690char_o F) Rep) (@ (@ bNF_Grp_o_char (@ collect_o P2)) H)) (@ (@ bNF_Grp_nat_o (@ collect_nat (lambda ((X4 nat)) (@ P2 (@ F X4))))) (@ (@ comp_o_o_nat (@ (@ comp_char_o_o Abs) H)) F))))) (forall ((X2 rat)) (= (@ (@ image_nat_rat (lambda ((Uu nat)) X2)) top_top_set_nat) (@ (@ insert_rat X2) bot_bot_set_rat))) (forall ((F1 (-> nat rat)) (A13 set_nat) (B1 set_rat) (F22 (-> int nat)) (B22 set_int) (A24 set_nat)) (=> (= (@ (@ image_nat_rat F1) A13) B1) (=> (@ (@ inj_on_int_nat F22) B22) (=> (@ (@ ord_less_eq_set_nat (@ (@ image_int_nat F22) B22)) A24) (=> (=> (= B22 bot_bot_set_int) (= A24 bot_bot_set_nat)) (= (@ (@ bNF_We7904740386373615514nt_rat B22) B1) (@ (@ image_696479991571767017nt_rat (@ (@ (@ bNF_We579257750648025936at_nat B22) F1) F22)) (@ (@ bNF_We7540516734559056694at_nat A24) A13)))))))) (forall ((A4 (-> int code_integer Bool)) (B5 (-> num num Bool)) (F (-> int num)) (G (-> code_integer num)) (X5 set_Pr8415741480598773322nteger) (X2 produc2963269191615333738nteger)) (=> (@ (@ (@ (@ bNF_re6718328864250387230um_num A4) B5) F) G) (=> (@ (@ ord_le2638047946463454698nteger X5) (@ collec7215431352809750357nteger (@ produc540600059291021473eger_o A4))) (=> (@ (@ member4345257455949424659nteger X2) X5) (@ (@ B5 (@ (@ (@ comp_i3846818780818535807nteger F) produc45500017171379470nteger) X2)) (@ (@ (@ comp_C8580465762518603278nteger G) produc2153544567185597776nteger) X2)))))) (forall ((F (-> nat int)) (A4 (-> nat nat)) (I3 set_nat)) (let ((_let_1 (@ (@ image_nat_nat A4) I3))) (=> (@ order_mono_nat_int F) (=> (@ condit1738341127787009408ow_nat _let_1) (=> (not (= I3 bot_bot_set_nat)) (@ (@ ord_less_eq_int (@ F (@ complete_Inf_Inf_nat _let_1))) (@ complete_Inf_Inf_int (@ (@ image_nat_int (lambda ((X4 nat)) (@ F (@ A4 X4)))) I3)))))))) (forall ((A4 set_nat) (M3 nat) (F (-> nat nat))) (=> (not (= A4 bot_bot_set_nat)) (=> (forall ((X nat)) (=> (@ (@ member_nat X) A4) (@ (@ ord_less_eq_nat M3) (@ F X)))) (@ (@ ord_less_eq_nat M3) (@ complete_Inf_Inf_nat (@ (@ image_nat_nat F) A4)))))) (forall ((F (-> nat produc3843707927480180839at_nat)) (A4 set_nat)) (=> (@ finite4343798906461161616at_nat (@ (@ image_2499013659892586576at_nat F) A4)) (=> (not (@ finite_finite_nat A4)) (exists ((X produc3843707927480180839at_nat)) (and (not (@ finite_finite_nat (@ (@ vimage6435164912253009178at_nat F) (@ (@ insert9069300056098147895at_nat X) bot_bo228742789529271731at_nat)))) (@ (@ member8757157785044589968at_nat X) (@ (@ image_2499013659892586576at_nat F) A4))))))) (forall ((A nat) (B nat) (S2 nat) (T2 nat)) (=> (@ (@ ord_less_nat A) B) (@ (@ member8206827879206165904at_nat (@ (@ produc6161850002892822231at_nat (@ (@ product_Pair_nat_nat A) S2)) (@ (@ product_Pair_nat_nat B) T2))) fun_pair_leq))) (forall ((F (-> heap_e7401611519738050253t_unit heap_e7401611519738050253t_unit))) (= (@ (@ comp_P8019343326919024234t_unit produc1126150082675451753t_unit) (@ produc3038839249364385243_ref_a F)) (@ (@ comp_h4837689053573563144t_unit F) produc1126150082675451753t_unit))) (forall ((R3 (-> int int Bool)) (S5 (-> int code_integer Bool)) (T3 (-> int code_integer Bool)) (F (-> int int)) (G (-> int int)) (H (-> code_integer code_integer))) (=> (@ (@ ord_le996066559646421213eger_o (@ (@ relcom967497705283160040nteger R3) S5)) T3) (@ (@ ord_le996066559646421213eger_o (@ (@ relcom967497705283160040nteger (@ (@ (@ bNF_vi3884084463199473129_int_o F) G) R3)) (@ (@ (@ bNF_vi699694178825965831eger_o G) H) S5))) (@ (@ (@ bNF_vi699694178825965831eger_o F) H) T3)))) (forall ((A int) (S2 set_int) (T2 set_int)) (= (@ (@ image_int_int (lambda ((X4 int)) (@ (@ minus_minus_int X4) A))) (@ (@ inf_inf_set_int S2) T2)) (@ (@ inf_inf_set_int (@ (@ image_int_int (lambda ((X4 int)) (@ (@ minus_minus_int X4) A))) S2)) (@ (@ image_int_int (lambda ((X4 int)) (@ (@ minus_minus_int X4) A))) T2)))) (forall ((X2 (-> rat int)) (Ra (-> int int Bool))) (=> (forall ((Z3 int)) (=> (@ (@ member_int Z3) (@ (@ image_rat_int X2) top_top_set_rat)) (@ (@ Ra Z3) Z3))) (@ (@ (@ (@ bNF_re7554818335971813481nt_int (lambda ((Y2 rat) (Z rat)) (= Y2 Z))) Ra) X2) X2))) (forall ((I3 set_nat) (A4 (-> nat set_nat)) (B5 (-> nat set_nat))) (let ((_let_1 (@ produc457027306803732586at_nat I3))) (= (@ _let_1 (lambda ((I2 nat)) (@ (@ inf_inf_set_nat (@ A4 I2)) (@ B5 I2)))) (@ (@ inf_in2572325071724192079at_nat (@ _let_1 A4)) (@ _let_1 B5))))) (forall ((B nat) (F (-> Bool nat)) (X2 Bool) (C num) (G (-> Bool num)) (A4 set_o)) (=> (= B (@ F X2)) (=> (= C (@ G X2)) (=> (@ (@ member_o X2) A4) (@ (@ member9148766508732265716at_num (@ (@ product_Pair_nat_num B) C)) (@ (@ (@ bNF_Gr7727518618234538026at_num A4) F) G)))))) (forall ((A4 set_o) (R set_Product_prod_o_o)) (=> (forall ((X Bool) (Y Bool)) (=> (@ (@ member_o X) A4) (=> (@ (@ member_o Y) A4) (=> (not (= X Y)) (or (@ (@ member7466972457876170832od_o_o (@ (@ product_Pair_o_o X) Y)) R) (@ (@ member7466972457876170832od_o_o (@ (@ product_Pair_o_o Y) X)) R)))))) (@ (@ total_on_o A4) R))) (forall ((A4 set_nat) (G (-> nat int)) (B5 set_nat) (F (-> nat int))) (let ((_let_1 (@ (@ image_nat_int G) B5))) (=> (not (= A4 bot_bot_set_nat)) (=> (@ condit1735850657277959132ow_int _let_1) (=> (@ (@ ord_less_eq_set_nat A4) B5) (=> (forall ((X nat)) (=> (@ (@ member_nat X) B5) (@ (@ ord_less_eq_int (@ G X)) (@ F X)))) (@ (@ ord_less_eq_int (@ complete_Inf_Inf_int _let_1)) (@ complete_Inf_Inf_int (@ (@ image_nat_int F) A4))))))))) (forall ((A nat) (B nat) (A4 set_nat) (B5 (-> nat set_nat))) (=> (@ (@ member8440522571783428010at_nat (@ (@ product_Pair_nat_nat A) B)) (@ (@ produc457027306803732586at_nat A4) B5)) (not (=> (@ (@ member_nat A) A4) (not (@ (@ member_nat B) (@ B5 A))))))) (forall ((F (-> nat nat)) (X2 nat) (Y3 nat)) (let ((_let_1 (@ product_Pair_nat_nat X2))) (= (@ (@ produc3094765310956027504at_nat F) (@ _let_1 Y3)) (@ _let_1 (@ F Y3))))) (forall ((F (-> product_unit product_unit))) (= (@ comple2584293577114468500t_unit (@ (@ image_405062704495631173t_unit F) bot_bo3957492148770167129t_unit)) top_top_Product_unit)) (forall ((Z2 num)) (= (@ (@ (@ comp_P864883071962432936um_num product_snd_num_num) (lambda ((X4 num)) (@ (@ product_Pair_num_num X4) X4))) Z2) (@ id_num Z2))) (forall ((F (-> int int)) (G (-> nat rat)) (A4 set_int) (B5 set_nat)) (= (@ (@ image_4420076320108226637nt_rat (@ produc1877337817755394619nt_rat (lambda ((X4 int) (Y5 nat)) (@ (@ product_Pair_int_rat (@ F X4)) (@ G Y5))))) (@ (@ produc1456381018704787142nt_nat A4) (lambda ((Uu int)) B5))) (@ (@ produc821250958618291406nt_rat (@ (@ image_int_int F) A4)) (lambda ((Uu int)) (@ (@ image_nat_rat G) B5))))) (forall ((A4 set_o) (M code_integer) (F (-> Bool code_integer))) (=> (forall ((X Bool)) (=> (@ (@ member_o X) A4) (@ (@ ord_le3102999989581377725nteger M) (@ F X)))) (@ condit4933233095834890765nteger (@ (@ image_o_Code_integer F) A4)))) (forall ((A4 set_int) (B5 set_int) (F (-> int product_unit)) (G (-> int product_unit))) (=> (forall ((I4 int)) (=> (@ (@ member_int I4) A4) (exists ((X6 int)) (and (@ (@ ord_le3221252021190050221t_unit (@ F I4)) (@ G X6)) (@ (@ member_int X6) B5))))) (=> (forall ((J2 int)) (=> (@ (@ member_int J2) B5) (exists ((X6 int)) (and (@ (@ ord_le3221252021190050221t_unit (@ G J2)) (@ F X6)) (@ (@ member_int X6) A4))))) (= (@ comple4687483117567863418t_unit (@ (@ image_5846526143423701914t_unit F) A4)) (@ comple4687483117567863418t_unit (@ (@ image_5846526143423701914t_unit G) B5)))))) (forall ((A4 set_o) (C set_char)) (let ((_let_1 (= A4 bot_bot_set_o))) (and (=> (not _let_1) (= (@ comple7965528767983648192t_char (@ (@ image_o_set_char (lambda ((Y5 Bool)) C)) A4)) C)) (=> _let_1 (= (@ comple7965528767983648192t_char (@ (@ image_o_set_char (lambda ((Y5 Bool)) C)) A4)) top_top_set_char))))) (forall ((A4 set_int) (B5 set_int) (C3 (-> int product_unit)) (D (-> int product_unit))) (=> (= A4 B5) (=> (forall ((X int)) (=> (@ (@ member_int X) B5) (= (@ C3 X) (@ D X)))) (= (@ comple4687483117567863418t_unit (@ (@ image_5846526143423701914t_unit C3) A4)) (@ comple4687483117567863418t_unit (@ (@ image_5846526143423701914t_unit D) B5)))))) (forall ((P produc1319942482725812455at_nat)) (=> (@ (@ member1466754251312161552at_nat P) id_set4888139568991089827at_nat) (not (forall ((X set_Pr4329608150637261639at_nat)) (not (= P (@ (@ produc9060074326276436823at_nat X) X))))))) _let_32 (forall ((A4 set_int) (F (-> int int))) (=> (@ finite_finite_int A4) (=> (= (@ finite_card_int (@ (@ image_int_int F) A4)) (@ finite_card_int A4)) (@ (@ inj_on_int_int F) A4)))) (forall ((F (-> (-> code_integer code_integer) produc8923325533196201883nteger produc8923325533196201883nteger)) (G (-> code_integer code_integer code_integer)) (X2 code_integer) (Y3 (-> code_integer code_integer))) (let ((_let_1 (@ comp_C8797469213163452608nteger F))) (= (@ _let_1 (@ (@ (@ fun_up8056716234270145717nteger G) X2) Y3)) (@ (@ (@ fun_up8139772397987072257nteger (@ _let_1 G)) X2) (@ F Y3))))) (forall ((F (-> code_integer code_integer))) (= (@ (@ comp_P3428181540658402820nteger produc8508995932063986495nteger) (@ produc6499014454317279255nteger F)) produc8508995932063986495nteger)) (forall ((U Bool) (A4 set_o) (A Bool) (B5 (-> Bool set_o))) (=> (@ (@ member_o U) A4) (= (@ comple90263536869209701_set_o (@ (@ image_o_set_o (lambda ((X4 Bool)) (@ (@ insert_o A) (@ B5 X4)))) A4)) (@ (@ insert_o A) (@ comple90263536869209701_set_o (@ (@ image_o_set_o B5) A4)))))) (forall ((A4 set_num) (B5 set_nat)) (= (@ (@ image_7762062833379733445at_num (@ produc5219324331026901427at_num (lambda ((I2 num) (J nat)) (@ (@ product_Pair_nat_num J) I2)))) (@ (@ produc7810729746965977780um_nat A4) (lambda ((Uu num)) B5))) (@ (@ produc6237731129814287028at_num B5) (lambda ((Uu nat)) A4)))) (forall ((R3 (-> product_prod_nat_nat product_prod_nat_nat Bool)) (S5 (-> product_prod_nat_nat int Bool)) (T3 (-> product_prod_nat_nat int Bool))) (let ((_let_1 (@ relcom8911704206367525917at_int R3))) (= (@ _let_1 (@ (@ sup_su5231854730092680051_int_o S5) T3)) (@ (@ sup_su5231854730092680051_int_o (@ _let_1 S5)) (@ _let_1 T3))))) (forall ((F (-> nat int)) (A4 set_nat) (B5 set_int)) (= (@ (@ ord_less_eq_set_int (@ (@ image_nat_int F) A4)) B5) (forall ((X4 nat)) (=> (@ (@ member_nat X4) A4) (@ (@ member_int (@ F X4)) B5))))) (forall ((A4 (-> nat nat Bool)) (B5 (-> nat nat Bool))) (=> (@ (@ ord_le2646555220125990790_nat_o A4) B5) (@ (@ ord_le3146513528884898305at_nat (@ collec3392354462482085612at_nat (@ produc6081775807080527818_nat_o A4))) (@ collec3392354462482085612at_nat (@ produc6081775807080527818_nat_o B5))))) (forall ((P2 (-> char char product_unit))) (= (@ comple2584293577114468500t_unit (@ (@ image_4337914935673063477t_unit (lambda ((Y5 char)) (@ comple4687483117567863418t_unit (@ (@ image_4337914935673063477t_unit (lambda ((X4 char)) (@ (@ P2 X4) Y5))) top_top_set_char)))) top_top_set_char)) (@ comple4687483117567863418t_unit (@ (@ image_8077363282794994245t_unit (lambda ((F2 (-> char char))) (@ comple2584293577114468500t_unit (@ (@ image_4337914935673063477t_unit (lambda ((X4 char)) (@ (@ P2 (@ F2 X4)) X4))) top_top_set_char)))) top_to8079350907815874599r_char)))) (forall ((F (-> rat Bool)) (B Bool)) (=> (@ (@ inj_on_rat_o F) top_top_set_rat) (= (@ (@ member_o B) (@ (@ image_rat_o F) top_top_set_rat)) (exists ((X4 rat)) (and (forall ((Y5 rat)) (=> (= B (@ F Y5)) (= Y5 X4))) (= B (@ F X4))))))) (forall ((K Bool) (I3 set_o) (A4 (-> Bool set_nat))) (let ((_let_1 (@ comple7806235888213564991et_nat (@ (@ image_o_set_nat A4) I3)))) (=> (@ (@ member_o K) I3) (= (@ (@ inf_inf_set_nat (@ A4 K)) _let_1) _let_1)))) (forall ((F (-> nat nat product_prod_nat_nat Bool)) (X1 nat) (X22 nat)) (= (@ (@ produc8739625826339149834_nat_o F) (@ (@ product_Pair_nat_nat X1) X22)) (@ (@ F X1) X22))) (forall ((A int) (B nat) (A4 set_int) (B5 (-> int set_nat))) (= (@ (@ member216504246829706758nt_nat (@ (@ product_Pair_int_nat A) B)) (@ (@ produc1456381018704787142nt_nat A4) B5)) (and (@ (@ member_int A) A4) (@ (@ member_nat B) (@ B5 A))))) (forall ((A4 set_o) (B5 (-> Bool set_nat))) (=> (@ finite_finite_o A4) (=> (forall ((A3 Bool)) (=> (@ (@ member_o A3) A4) (@ finite_finite_nat (@ B5 A3)))) (@ finite_finite_nat (@ comple7399068483239264473et_nat (@ (@ image_o_set_nat B5) A4)))))) (forall ((Inf (-> set_num num)) (A4 set_num)) (= (@ Inf (@ (@ image_num_num id_num) A4)) (@ Inf A4))) (forall ((B int) (F (-> int int)) (X2 int) (A4 set_int)) (=> (= B (@ F X2)) (=> (@ (@ member_int X2) A4) (@ (@ member_int B) (@ (@ image_int_int F) A4))))) (forall ((S5 set_o) (F (-> Bool nat nat))) (=> (forall ((X Bool) (Y Bool)) (let ((_let_1 (@ F Y))) (let ((_let_2 (@ F X))) (=> (@ (@ member_o X) S5) (=> (@ (@ member_o Y) S5) (= (@ (@ comp_nat_nat_nat _let_1) _let_2) (@ (@ comp_nat_nat_nat _let_2) _let_1))))))) (@ (@ finite4703585013658510744_o_nat S5) F))) (forall ((A4 set_Product_unit) (B5 set_o)) (let ((_let_1 (@ produc4996980317674386579unit_o A4))) (let ((_let_2 (@ image_1801747192096393899it_o_o produc7461459235754980752unit_o))) (let ((_let_3 (= A4 bot_bo3957492148770167129t_unit))) (and (=> (not _let_3) (= (@ _let_2 (@ _let_1 (lambda ((Uu product_unit)) B5))) B5)) (=> _let_3 (= (@ _let_2 (@ _let_1 (lambda ((Uu product_unit)) B5))) bot_bot_set_o))))))) (forall ((X1 set_Pr4329608150637261639at_nat) (X22 set_Pr4329608150637261639at_nat)) (= (@ produc826222791318859909at_nat (@ (@ produc9060074326276436823at_nat X1) X22)) X22)) (forall ((F (-> nat nat)) (A4 set_nat) (A nat)) (let ((_let_1 (@ (@ image_nat_nat F) A4))) (let ((_let_2 (@ complete_Inf_Inf_nat _let_1))) (=> (= (@ complete_Sup_Sup_nat _let_1) _let_2) (=> (@ condit2214826472909112428ve_nat _let_1) (=> (@ condit1738341127787009408ow_nat _let_1) (=> (@ (@ member_nat A) A4) (= (@ F A) _let_2)))))))) (forall ((G (-> nat int)) (H (-> nat nat)) (R12 (-> int int)) (R23 (-> nat int)) (F (-> int nat)) (L (-> int nat))) (=> (= (@ (@ comp_nat_int_nat G) H) (@ (@ comp_int_int_nat R12) R23)) (=> (= (@ (@ comp_int_nat_int F) R12) L) (= (@ (@ comp_nat_nat_nat (@ (@ comp_int_nat_nat F) G)) H) (@ (@ comp_int_nat_nat L) R23))))) (forall ((A4 set_Pr1261947904930325089at_nat) (B5 set_nat) (F (-> product_prod_nat_nat nat))) (=> (@ finite6177210948735845034at_nat A4) (=> (@ (@ ord_less_eq_set_nat B5) (@ (@ image_2486076414777270412at_nat F) A4)) (@ finite_finite_nat B5)))) (forall ((A4 set_int) (U product_unit) (F (-> int product_unit))) (=> (forall ((I4 int)) (=> (@ (@ member_int I4) A4) (@ (@ ord_le3221252021190050221t_unit U) (@ F I4)))) (@ (@ ord_le3221252021190050221t_unit U) (@ comple2584293577114468500t_unit (@ (@ image_5846526143423701914t_unit F) A4))))) (forall ((X2 int) (Z5 set_int) (X5 set_int) (P2 (-> int Bool))) (=> (@ (@ member_int X2) Z5) (=> (@ (@ ord_less_eq_set_int Z5) (@ collect_int (lambda ((X4 int)) (and (@ P2 X4) (@ (@ member_int X4) X5))))) (@ P2 X2)))) (forall ((A4 set_Pr958786334691620121nt_int) (R3 (-> int int Bool))) (=> (@ (@ ord_le2843351958646193337nt_int A4) (@ collec213857154873943460nt_int (@ produc4947309494688390418_int_o (@ conversep_int_int R3)))) (@ (@ ord_le2843351958646193337nt_int (@ (@ image_2653370878348428101nt_int (@ produc4245557441103728435nt_int (lambda ((X4 int) (Y5 int)) (@ (@ product_Pair_int_int Y5) X4)))) A4)) (@ collec213857154873943460nt_int (@ produc4947309494688390418_int_o R3))))) (forall ((A Bool) (B Bool) (A4 set_o) (B5 (-> Bool set_o))) (= (@ (@ member7466972457876170832od_o_o (@ (@ product_Pair_o_o A) B)) (@ (@ product_Sigma_o_o A4) B5)) (and (@ (@ member_o A) A4) (@ (@ member_o B) (@ B5 A))))) (forall ((I3 set_int) (F (-> int product_unit)) (X2 product_unit)) (=> (not (= I3 bot_bot_set_int)) (=> (forall ((I4 int)) (=> (@ (@ member_int I4) I3) (= (@ F I4) X2))) (= (@ comple2584293577114468500t_unit (@ (@ image_5846526143423701914t_unit F) I3)) X2)))) (forall ((F (-> ref_a ref_a)) (X2 produc7812382424243267045t_unit)) (= (@ produc1126150082675451753t_unit (@ (@ produc4508741384315284437t_unit F) X2)) (@ produc1126150082675451753t_unit X2))) (forall ((A produc3843707927480180839at_nat) (B produc3843707927480180839at_nat) (R set_Pr5564308138774400199at_nat)) (= (@ field_2862844103579723188at_nat (@ (@ insert398606708087465655at_nat (@ (@ produc2335810615602371415at_nat A) B)) R)) (@ (@ sup_su5525570899277871387at_nat (@ (@ insert9069300056098147895at_nat A) (@ (@ insert9069300056098147895at_nat B) bot_bo228742789529271731at_nat))) (@ field_2862844103579723188at_nat R)))) (forall ((Q2 (-> product_prod_int_int Bool)) (P2 (-> int int product_prod_int_int)) (Z2 product_prod_int_int)) (=> (@ Q2 (@ (@ produc4245557441103728435nt_int P2) Z2)) (not (forall ((X int) (Y int)) (=> (= Z2 (@ (@ product_Pair_int_int X) Y)) (not (@ Q2 (@ (@ P2 X) Y)))))))) (forall ((B5 (-> Bool set_nat)) (A Bool) (A4 set_o)) (let ((_let_1 (@ image_o_set_nat B5))) (= (@ comple7806235888213564991et_nat (@ _let_1 (@ (@ insert_o A) A4))) (@ (@ inf_inf_set_nat (@ B5 A)) (@ comple7806235888213564991et_nat (@ _let_1 A4)))))) (forall ((A nat) (B num) (A2 nat) (B2 num)) (= (= (@ (@ product_Pair_nat_num A) B) (@ (@ product_Pair_nat_num A2) B2)) (and (= A A2) (= B B2)))) (forall ((X2 set_Product_unit) (Y3 set_Product_unit)) (= (@ (@ (@ if_set_Product_unit true) X2) Y3) X2)) (forall ((C3 set_Product_unit) (A4 (-> product_unit set_char)) (B5 set_char)) (let ((_let_1 (= C3 bot_bo3957492148770167129t_unit))) (and (=> _let_1 (= (@ comple7965528767983648192t_char (@ (@ image_5325685772115642575t_char (lambda ((X4 product_unit)) (@ (@ inf_inf_set_char (@ A4 X4)) B5))) C3)) top_top_set_char)) (=> (not _let_1) (= (@ comple7965528767983648192t_char (@ (@ image_5325685772115642575t_char (lambda ((X4 product_unit)) (@ (@ inf_inf_set_char (@ A4 X4)) B5))) C3)) (@ (@ inf_inf_set_char (@ comple7965528767983648192t_char (@ (@ image_5325685772115642575t_char A4) C3))) B5)))))) (forall ((P rat)) (= (@ quotient_of (@ abs_abs_rat P)) (@ (@ produc4245557441103728435nt_int (lambda ((A5 int) (__flatten_var_0 int)) (@ (@ product_Pair_int_int (@ abs_abs_int A5)) __flatten_var_0))) (@ quotient_of P)))) (forall ((M (-> int nat)) (G (-> int int)) (X2 int) (N (-> nat nat)) (H (-> int nat)) (F (-> nat nat))) (=> (= (@ M (@ G X2)) (@ N (@ H X2))) (= (@ (@ (@ comp_int_nat_int (@ (@ comp_nat_nat_int F) M)) G) X2) (@ (@ (@ comp_nat_nat_int (@ (@ comp_nat_nat_nat F) N)) H) X2)))) (forall ((C3 set_Pr1261947904930325089at_nat) (A4 (-> product_prod_nat_nat set_nat)) (B5 set_nat)) (let ((_let_1 (@ (@ sup_sup_set_nat (@ comple7399068483239264473et_nat (@ (@ image_15824709712370754et_nat A4) C3))) B5))) (let ((_let_2 (= C3 bot_bo2099793752762293965at_nat))) (and (=> _let_2 (= _let_1 B5)) (=> (not _let_2) (= _let_1 (@ comple7399068483239264473et_nat (@ (@ image_15824709712370754et_nat (lambda ((X4 product_prod_nat_nat)) (@ (@ sup_sup_set_nat (@ A4 X4)) B5))) C3)))))))) (forall ((C3 set_nat) (A4 set_Pr8693737435421807431at_nat) (B5 (-> nat set_Pr8693737435421807431at_nat))) (let ((_let_1 (@ (@ sup_su718114333110466843at_nat A4) (@ comple2748534634209756852at_nat (@ (@ image_4592875511192039216at_nat B5) C3))))) (let ((_let_2 (= C3 bot_bot_set_nat))) (and (=> (not _let_2) (= _let_1 (@ comple2748534634209756852at_nat (@ (@ image_4592875511192039216at_nat (lambda ((X4 nat)) (@ (@ sup_su718114333110466843at_nat A4) (@ B5 X4)))) C3)))) (=> _let_2 (= _let_1 A4)))))) (forall ((F (-> nat int)) (A4 set_nat)) (=> (@ order_mono_nat_int F) (=> (@ condit1738341127787009408ow_nat A4) (=> (not (= A4 bot_bot_set_nat)) (@ (@ ord_less_eq_int (@ F (@ complete_Inf_Inf_nat A4))) (@ complete_Inf_Inf_int (@ (@ image_nat_int F) A4))))))) (forall ((F (-> Bool set_nat)) (A4 set_o) (X2 Bool) (U set_nat)) (let ((_let_1 (@ (@ image_o_set_nat F) A4))) (=> (@ condit68592940725977398et_nat _let_1) (=> (@ (@ member_o X2) A4) (=> (@ (@ ord_less_eq_set_nat (@ F X2)) U) (@ (@ ord_less_eq_set_nat (@ comple7806235888213564991et_nat _let_1)) U)))))) (forall ((C3 set_Pr4329608150637261639at_nat) (A4 set_nat) (B5 (-> produc3843707927480180839at_nat set_nat))) (let ((_let_1 (@ (@ inf_inf_set_nat A4) (@ comple7806235888213564991et_nat (@ (@ image_3160451284896210088et_nat B5) C3))))) (let ((_let_2 (= C3 bot_bo228742789529271731at_nat))) (and (=> (not _let_2) (= _let_1 (@ comple7806235888213564991et_nat (@ (@ image_3160451284896210088et_nat (lambda ((X4 produc3843707927480180839at_nat)) (@ (@ inf_inf_set_nat A4) (@ B5 X4)))) C3)))) (=> _let_2 (= _let_1 A4)))))) (forall ((X2 (-> char nat)) (Ya (-> char nat)) (Y3 (-> char nat)) (Xa2 (-> char nat)) (R3 (-> nat nat Bool)) (Ra (-> nat nat Bool))) (=> (= X2 Ya) (=> (= Y3 Xa2) (=> (forall ((Z3 nat) (Yb nat)) (=> (@ (@ member_nat Z3) (@ (@ image_char_nat Ya) top_top_set_char)) (=> (@ (@ member_nat Yb) (@ (@ image_char_nat Xa2) top_top_set_char)) (= (@ (@ R3 Z3) Yb) (@ (@ Ra Z3) Yb))))) (= (@ (@ (@ (@ bNF_re3734335887435638179at_nat (lambda ((Y2 char) (Z char)) (= Y2 Z))) R3) X2) Y3) (@ (@ (@ (@ bNF_re3734335887435638179at_nat (lambda ((Y2 char) (Z char)) (= Y2 Z))) Ra) Ya) Xa2)))))) (forall ((B nat) (F (-> nat nat)) (A4 set_nat)) (=> (@ (@ member_nat B) (@ (@ image_nat_nat F) A4)) (not (forall ((X nat)) (=> (= B (@ F X)) (not (@ (@ member_nat X) A4))))))) (forall ((F (-> ref_a ref_a)) (X2 produc7812382424243267045t_unit)) (= (@ produc473321116828791851t_unit (@ (@ produc4508741384315284437t_unit F) X2)) (@ F (@ produc473321116828791851t_unit X2)))) (forall ((F (-> int nat)) (A4 set_int)) (=> (@ (@ inj_on_int_nat F) A4) (= (@ finite_card_nat (@ (@ image_int_nat F) A4)) (@ finite_card_int A4)))) (forall ((A4 set_Product_unit) (B5 (-> product_unit set_int)) (F (-> int int))) (=> (not (= A4 bot_bo3957492148770167129t_unit)) (=> (forall ((X product_unit)) (=> (@ (@ member_Product_unit X) A4) (not (= (@ B5 X) bot_bot_set_int)))) (=> (@ condit1735850657277959132ow_int (@ comple3221217463730067765et_int (@ (@ image_3995998972318789802et_int (lambda ((X4 product_unit)) (@ (@ image_int_int F) (@ B5 X4)))) A4))) (= (@ complete_Inf_Inf_int (@ (@ image_int_int F) (@ comple3221217463730067765et_int (@ (@ image_3995998972318789802et_int B5) A4)))) (@ complete_Inf_Inf_int (@ (@ image_873079544045703924it_int (lambda ((X4 product_unit)) (@ complete_Inf_Inf_int (@ (@ image_int_int F) (@ B5 X4))))) A4))))))) (forall ((A nat) (B num) (A4 set_nat) (B5 (-> nat set_num))) (= (@ (@ member9148766508732265716at_num (@ (@ product_Pair_nat_num A) B)) (@ (@ produc6237731129814287028at_num A4) B5)) (and (@ (@ member_num B) (@ B5 A)) (@ (@ member_nat A) A4)))) (forall ((S5 set_nat) (T3 set_Pr1261947904930325089at_nat) (F (-> nat product_prod_nat_nat))) (=> (@ finite_finite_nat S5) (=> (@ finite6177210948735845034at_nat T3) (=> (= (@ finite_card_nat S5) (@ finite711546835091564841at_nat T3)) (=> (@ (@ ord_le3146513528884898305at_nat (@ (@ image_5846123807819985514at_nat F) S5)) T3) (= (forall ((X4 product_prod_nat_nat)) (=> (@ (@ member8440522571783428010at_nat X4) T3) (exists ((Y5 nat)) (and (= (@ F Y5) X4) (@ (@ member_nat Y5) S5))))) (@ (@ inj_on5538052773655684606at_nat F) S5))))))) (forall ((A ref_a) (P produc7812382424243267045t_unit)) (=> (@ (@ member_ref_a A) (@ basic_685971451221398055t_unit P)) (= A (@ produc473321116828791851t_unit P)))) (forall ((B nat) (F (-> nat nat)) (X2 nat) (C nat) (G (-> nat nat)) (A4 set_nat)) (=> (= B (@ F X2)) (=> (= C (@ G X2)) (=> (@ (@ member_nat X2) A4) (@ (@ member8440522571783428010at_nat (@ (@ product_Pair_nat_nat B) C)) (@ (@ (@ bNF_Gr7318156773085685964at_nat A4) F) G)))))) (forall ((C Bool) (F (-> nat Bool))) (= (@ (@ comp_o_o_nat (lambda ((X4 Bool)) C)) F) (lambda ((X4 nat)) C))) (forall ((F (-> int int)) (C3 set_int) (A4 set_int) (B5 set_int)) (let ((_let_1 (@ image_int_int F))) (let ((_let_2 (@ (@ minus_minus_set_int A4) B5))) (=> (@ (@ inj_on_int_int F) C3) (=> (@ (@ ord_less_eq_set_int _let_2) C3) (=> (@ (@ ord_less_eq_set_int B5) C3) (= (@ _let_1 _let_2) (@ (@ minus_minus_set_int (@ _let_1 A4)) (@ _let_1 B5))))))))) (forall ((Rep (-> nat int)) (Abs (-> int nat)) (A4 set_int)) (=> (@ (@ (@ type_d6248003478268698410at_int Rep) Abs) A4) (= (@ (@ image_int_nat Abs) A4) top_top_set_nat))) (forall ((X2 int) (Fx int) (A4 set_int) (F (-> int int))) (=> (@ (@ member5262025264175285858nt_int (@ (@ product_Pair_int_int X2) Fx)) (@ (@ bNF_Gr_int_int A4) F)) (= (@ F X2) Fx))) (forall ((C3 set_nat) (A4 (-> nat set_nat)) (B5 set_nat)) (let ((_let_1 (@ (@ inf_inf_set_nat (@ comple7806235888213564991et_nat (@ (@ image_nat_set_nat A4) C3))) B5))) (let ((_let_2 (= C3 bot_bot_set_nat))) (and (=> _let_2 (= _let_1 B5)) (=> (not _let_2) (= _let_1 (@ comple7806235888213564991et_nat (@ (@ image_nat_set_nat (lambda ((X4 nat)) (@ (@ inf_inf_set_nat (@ A4 X4)) B5))) C3)))))))) (forall ((X2 set_Pr1261947904930325089at_nat)) (@ (@ order_5942792088423767318at_nat (@ (@ insert9200635055090092081at_nat X2) bot_bo3083307316010499117at_nat)) (@ (@ insert9069300056098147895at_nat (@ (@ produc2922128104949294807at_nat X2) X2)) bot_bo228742789529271731at_nat))) (forall ((F (-> nat int)) (G (-> int nat))) (=> (@ order_5723533178083820855at_int F) (=> (= (@ (@ image_nat_int F) top_top_set_nat) top_top_set_int) (=> (forall ((X nat)) (= (@ G (@ F X)) X)) (@ order_6725377360493925687nt_nat G))))) _let_31 (forall ((A4 set_nat) (M rat) (F (-> nat rat))) (=> (forall ((X nat)) (=> (@ (@ member_nat X) A4) (@ (@ ord_less_eq_rat M) (@ F X)))) (@ condit1103211067700513672ow_rat (@ (@ image_nat_rat F) A4)))) (forall ((F (-> int int int)) (P product_prod_int_int)) (= (@ (@ produc8211389475949308722nt_int (lambda ((Y5 int) (X4 int)) (@ (@ F X4) Y5))) (@ product_swap_int_int P)) (@ (@ produc8211389475949308722nt_int F) P))) (forall ((X5 set_nat) (A4 set_Pr1261947904930325089at_nat) (Y4 set_nat) (P2 (-> nat nat Bool)) (Q2 (-> nat nat Bool))) (let ((_let_1 (@ ord_le3146513528884898305at_nat A4))) (=> (= X5 (@ (@ image_2486076414777270412at_nat product_fst_nat_nat) A4)) (=> (= Y4 (@ (@ image_2486076414777270412at_nat product_snd_nat_nat) A4)) (=> (forall ((X nat)) (=> (@ (@ member_nat X) X5) (forall ((Xa nat)) (=> (@ (@ member_nat Xa) Y4) (=> (@ (@ P2 X) Xa) (@ (@ Q2 X) Xa)))))) (=> (@ _let_1 (@ collec3392354462482085612at_nat (@ produc6081775807080527818_nat_o P2))) (@ _let_1 (@ collec3392354462482085612at_nat (@ produc6081775807080527818_nat_o Q2))))))))) (forall ((P rat) (Q rat)) (= (@ quotient_of (@ (@ plus_plus_rat P) Q)) (@ (@ produc4245557441103728435nt_int (lambda ((A5 int) (C4 int)) (@ (@ produc4245557441103728435nt_int (lambda ((B4 int) (D3 int)) (@ normalize (@ (@ product_Pair_int_int (@ (@ plus_plus_int (@ (@ times_times_int A5) D3)) (@ (@ times_times_int B4) C4))) (@ (@ times_times_int C4) D3))))) (@ quotient_of Q)))) (@ quotient_of P)))) (forall ((R set_Pr5094982260447487303t_unit)) (let ((_let_1 (@ field_Product_unit R))) (=> (@ (@ order_888282469287196226t_unit _let_1) R) (= (@ (@ order_3164716736300062379t_unit _let_1) R) (forall ((A6 set_Product_unit)) (=> (@ (@ ord_le3507040750410214029t_unit A6) (@ field_Product_unit R)) (=> (not (= A6 bot_bo3957492148770167129t_unit)) (exists ((X4 product_unit)) (and (@ (@ member_Product_unit X4) A6) (forall ((Y5 product_unit)) (=> (@ (@ member_Product_unit Y5) A6) (@ (@ member7821138191923116944t_unit (@ (@ produc5692694829384537815t_unit X4) Y5)) R)))))))))))) _let_30 (forall ((F (-> nat num)) (G (-> int nat)) (X2 int) (F3 (-> nat num)) (G2 (-> int nat)) (X3 int)) (=> (= (@ F (@ G X2)) (@ F3 (@ G2 X3))) (= (@ (@ (@ comp_nat_num_int F) G) X2) (@ (@ (@ comp_nat_num_int F3) G2) X3)))) (forall ((R ref_a) (V a) (H heap_e7401611519738050253t_unit)) (= (@ present_a (@ (@ (@ set_a R) V) H)) (@ present_a H))) (forall ((F (-> code_integer code_integer)) (X2 produc8923325533196201883nteger)) (= (@ produc8508995932063986495nteger (@ (@ produc6499014454317279255nteger F) X2)) (@ produc8508995932063986495nteger X2))) (forall ((X2 int) (Y3 int)) (=> (= X2 Y3) (@ (@ (@ (@ bNF_Grp_int_int top_top_set_int) id_int) X2) Y3))) (forall ((F (-> nat nat)) (G (-> nat nat)) (X2 nat) (Y3 nat)) (let ((_let_1 (@ comp_nat_nat_nat F))) (= (@ _let_1 (@ (@ (@ fun_upd_nat_nat G) X2) Y3)) (@ (@ (@ fun_upd_nat_nat (@ _let_1 G)) X2) (@ F Y3))))) (forall ((P2 (-> (-> product_prod_nat_nat Bool) Bool)) (F (-> nat nat product_prod_nat_nat Bool)) (Prod product_prod_nat_nat)) (let ((_let_1 (@ product_snd_nat_nat Prod))) (let ((_let_2 (@ product_fst_nat_nat Prod))) (= (@ P2 (@ (@ produc8739625826339149834_nat_o F) Prod)) (=> (= Prod (@ (@ product_Pair_nat_nat _let_2) _let_1)) (@ P2 (@ (@ F _let_2) _let_1))))))) (forall ((F (-> nat nat)) (A4 set_nat) (P2 (-> set_nat Bool))) (= (exists ((B6 set_nat)) (and (@ finite_finite_nat B6) (@ (@ ord_less_eq_set_nat B6) (@ (@ image_nat_nat F) A4)) (@ P2 B6))) (exists ((B6 set_nat)) (and (@ finite_finite_nat B6) (@ (@ ord_less_eq_set_nat B6) A4) (@ P2 (@ (@ image_nat_nat F) B6)))))) (forall ((F (-> product_unit nat)) (A4 (-> nat product_unit)) (I3 set_nat)) (let ((_let_1 (@ (@ image_8730104196221521654t_unit A4) I3))) (=> (@ order_7096114683908731117it_nat F) (=> (@ condit2080475194861589617t_unit _let_1) (=> (not (= I3 bot_bot_set_nat)) (@ (@ ord_less_eq_nat (@ complete_Sup_Sup_nat (@ (@ image_nat_nat (lambda ((X4 nat)) (@ F (@ A4 X4)))) I3))) (@ F (@ comple4687483117567863418t_unit _let_1)))))))) (forall ((A4 set_nat)) (= (@ (@ vimage4653281326611754070at_nat product_snd_nat_nat) A4) (@ (@ produc457027306803732586at_nat top_top_set_nat) (lambda ((Uu nat)) A4)))) _let_28 (forall ((F (-> int int))) (=> (@ finite_finite_int top_top_set_int) (=> (= (@ (@ image_int_int F) top_top_set_int) top_top_set_int) (@ (@ inj_on_int_int F) top_top_set_int)))) (forall ((P2 (-> product_prod_int_int Bool)) (Q2 (-> product_prod_int_int product_prod_nat_nat Bool))) (= (@ collec7751116662793354522at_nat (@ produc3235059054576640100_nat_o (lambda ((X4 product_prod_int_int) (Y5 product_prod_nat_nat)) (and (@ (@ Q2 X4) Y5) (@ P2 X4))))) (@ (@ produc3424345432876038864at_nat (@ collec213857154873943460nt_int P2)) (lambda ((X4 product_prod_int_int)) (@ 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image_nat_set_nat F) A4)) C)))) (forall ((C product_prod_nat_o) (A4 set_nat) (B5 (-> nat set_o))) (=> (@ (@ member6310962623043647828_nat_o C) (@ (@ product_Sigma_nat_o A4) B5)) (not (forall ((X nat)) (=> (@ (@ member_nat X) A4) (forall ((Y Bool)) (=> (@ (@ member_o Y) (@ B5 X)) (not (= C (@ (@ product_Pair_nat_o X) Y)))))))))) (@ fun_is_measure_int _let_27) (forall ((G (-> int int)) (H (-> int int)) (R (-> int int)) (F (-> int nat))) (let ((_let_1 (@ comp_int_nat_int F))) (=> (= (@ (@ comp_int_int_int G) H) R) (= (@ (@ comp_int_nat_int (@ _let_1 G)) H) (@ _let_1 R))))) (forall ((F (-> int int)) (C3 set_int) (A4 set_int) (B5 set_int)) (let ((_let_1 (@ image_int_int F))) (=> (@ (@ inj_on_int_int F) C3) (=> (@ (@ ord_less_eq_set_int A4) C3) (=> (@ (@ ord_less_eq_set_int B5) C3) (= (@ _let_1 (@ (@ inf_inf_set_int A4) B5)) (@ (@ inf_inf_set_int (@ _let_1 A4)) (@ _let_1 B5)))))))) (forall ((X2 set_Pr1261947904930325089at_nat) (Y3 set_Pr1261947904930325089at_nat) (A set_Pr1261947904930325089at_nat)) (=> (= (@ produc2937545259423399429at_nat (@ (@ produc2922128104949294807at_nat X2) Y3)) A) (= Y3 A))) (forall ((A4 set_nat) (F (-> nat int)) (M int)) (=> (forall ((X nat)) (=> (@ (@ member_nat X) A4) (@ (@ ord_less_eq_int (@ F X)) M))) (@ condit2212336002400062152ve_int (@ (@ image_nat_int F) A4)))) (forall ((Rep (-> num char)) (Abs (-> char num)) (S5 (-> char set_rat)) (M (-> nat char)) (F (-> nat rat)) (S6 (-> nat set_nat)) (G (-> int nat))) (let ((_let_1 (@ image_nat_rat F))) (=> (@ (@ (@ type_d4396077731765706521m_char Rep) Abs) top_top_set_char) (=> (= (@ (@ comp_c5738158305436223508at_nat S5) M) (@ (@ comp_s8255929034757298889at_nat _let_1) S6)) (= (@ (@ comp_num_set_rat_int (@ (@ comp_c2295490091592002142at_num S5) Rep)) (@ (@ comp_nat_num_int (@ (@ comp_char_num_nat Abs) M)) G)) (@ (@ comp_s8253438564248248613at_int _let_1) (@ (@ comp_nat_set_nat_int S6) G))))))) (forall ((A4 set_o) (C set_rat)) (let ((_let_1 (= A4 bot_bot_set_o))) (and (=> _let_1 (= (@ comple4298007329820168263et_rat (@ (@ image_o_set_rat (lambda ((Y5 Bool)) C)) A4)) top_top_set_rat)) (=> (not _let_1) (= (@ comple4298007329820168263et_rat (@ (@ image_o_set_rat (lambda ((Y5 Bool)) C)) A4)) C))))) (forall ((F (-> nat int)) (A4 set_nat) (X2 nat) (U int)) (let ((_let_1 (@ (@ image_nat_int F) A4))) (=> (@ condit1735850657277959132ow_int _let_1) (=> (@ (@ member_nat X2) A4) (=> (@ (@ ord_less_eq_int (@ F X2)) U) (@ (@ ord_less_eq_int (@ complete_Inf_Inf_int _let_1)) U)))))) (forall ((A4 (-> Bool set_nat))) (= (@ comple7399068483239264473et_nat (@ (@ image_o_set_nat A4) top_top_set_o)) (@ (@ sup_sup_set_nat (@ A4 true)) (@ A4 false)))) (forall ((A4 set_o) (F product_unit)) (=> (not (= A4 bot_bot_set_o)) (= (@ comple4687483117567863418t_unit (@ (@ image_o_Product_unit (lambda ((I2 Bool)) F)) A4)) F))) (forall ((A4 set_he8644174446132254637t_unit)) (= (@ (@ vimage6116673589273818795t_unit produc1126150082675451753t_unit) A4) (@ (@ produc3946373962484743846t_unit top_top_set_ref_a) (lambda ((Uu ref_a)) A4)))) (forall ((F (-> int int)) (G (-> int nat)) (X2 set_nat)) (= (@ (@ vimage_int_int F) (@ (@ vimage_int_nat G) X2)) (@ (@ vimage_int_nat (@ (@ comp_int_nat_int G) F)) X2))) (forall ((A4 set_int) (B5 set_int) (C3 (-> int nat)) (D (-> int nat)) (Inf (-> set_nat nat))) (=> (= A4 B5) (=> (forall ((X int)) (=> (@ (@ member_int X) B5) (= (@ C3 X) (@ D X)))) (= (@ Inf (@ (@ image_int_nat C3) A4)) (@ Inf (@ (@ image_int_nat D) B5)))))) (forall ((X2 Bool) (A4 set_o) (F (-> Bool int))) (=> (@ (@ member_o X2) A4) (@ (@ member_int (@ F X2)) (@ (@ image_o_int F) A4)))) (forall ((R3 (-> nat nat Bool))) (let ((_let_1 (@ bNF_Gr193424670081168899at_nat (@ collec3392354462482085612at_nat (@ produc6081775807080527818_nat_o R3))))) (= (@ (@ relcom8572034174491624592at_nat (@ conver4691796276509297820at_nat (@ _let_1 product_fst_nat_nat))) (@ _let_1 product_snd_nat_nat)) R3))) (forall ((A4 set_Product_unit) (C set_o)) (let ((_let_1 (= A4 bot_bo3957492148770167129t_unit))) (and (=> (not _let_1) (= (@ comple90263536869209701_set_o (@ (@ image_6930536745178679216_set_o (lambda ((Y5 product_unit)) C)) A4)) C)) (=> _let_1 (= (@ comple90263536869209701_set_o (@ (@ image_6930536745178679216_set_o (lambda ((Y5 product_unit)) C)) A4)) bot_bot_set_o))))) (forall ((F (-> Bool set_nat)) (A Bool) (A4 set_o)) (let ((_let_1 (@ image_o_set_nat F))) (= (@ comple7399068483239264473et_nat (@ _let_1 (@ (@ insert_o A) A4))) (@ (@ sup_sup_set_nat (@ F A)) (@ comple7399068483239264473et_nat (@ _let_1 A4)))))) (forall ((A4 set_Pr4329608150637261639at_nat) (R set_Pr5564308138774400199at_nat) (X2 produc3843707927480180839at_nat) (Y3 produc3843707927480180839at_nat)) (=> (@ (@ refl_o7446464703481863270at_nat A4) R) (=> (@ (@ member6009668390874684176at_nat (@ (@ produc2335810615602371415at_nat X2) Y3)) R) (@ (@ member8757157785044589968at_nat Y3) A4)))) (forall ((I3 set_int) (F (-> int set_nat)) (X2 set_nat)) (=> (not (= I3 bot_bot_set_int)) (=> (forall ((I4 int)) (=> (@ (@ member_int I4) I3) (= (@ F I4) X2))) (= (@ comple7806235888213564991et_nat (@ (@ image_int_set_nat F) I3)) X2)))) (forall ((F (-> Bool product_unit)) (A4 set_o) (X2 Bool) (U product_unit)) (let ((_let_1 (@ (@ image_o_Product_unit F) A4))) (let ((_let_2 (@ ord_le3221252021190050221t_unit U))) (=> (@ condit2080475194861589617t_unit _let_1) (=> (@ (@ member_o X2) A4) (=> (@ _let_2 (@ F X2)) (@ _let_2 (@ comple4687483117567863418t_unit _let_1)))))))) (forall ((C3 set_o) (A nat) (B5 (-> Bool set_nat))) (let ((_let_1 (= C3 bot_bot_set_o))) (and (=> _let_1 (= (@ comple7399068483239264473et_nat (@ (@ image_o_set_nat (lambda ((X4 Bool)) (@ (@ insert_nat A) (@ B5 X4)))) C3)) bot_bot_set_nat)) (=> (not _let_1) (= (@ comple7399068483239264473et_nat (@ (@ image_o_set_nat (lambda ((X4 Bool)) (@ (@ insert_nat A) (@ B5 X4)))) C3)) (@ (@ insert_nat A) (@ comple7399068483239264473et_nat (@ (@ image_o_set_nat B5) C3)))))))) (forall ((A4 set_Product_unit) (C product_unit)) (=> (not (= A4 bot_bo3957492148770167129t_unit)) (= (@ comple2584293577114468500t_unit (@ (@ image_405062704495631173t_unit (lambda ((X4 product_unit)) C)) A4)) C))) (forall ((A nat) (B nat)) (= (@ (@ member8440522571783428010at_nat (@ (@ product_Pair_nat_nat A) B)) id_nat2) (= A B))) (forall ((P2 (-> (-> product_prod_nat_nat product_prod_nat_nat) Bool)) (F (-> nat nat product_prod_nat_nat product_prod_nat_nat)) (Prod product_prod_nat_nat)) (let ((_let_1 (@ product_snd_nat_nat Prod))) (let ((_let_2 (@ product_fst_nat_nat Prod))) (= (@ P2 (@ (@ produc27273713700761075at_nat F) Prod)) (not (and (= Prod (@ (@ product_Pair_nat_nat _let_2) _let_1)) (not (@ P2 (@ (@ F _let_2) _let_1))))))))) _let_26 (forall ((B5 set_nat) (F (-> nat nat)) (A4 set_nat)) (= (@ (@ ord_less_eq_set_nat B5) (@ (@ image_nat_nat F) A4)) (exists ((AA set_nat)) (and (@ (@ ord_less_eq_set_nat AA) A4) (= B5 (@ (@ image_nat_nat F) AA)))))) (forall ((A4 set_Product_unit) (F product_unit)) (=> (not (= A4 bot_bo3957492148770167129t_unit)) (= (@ comple4687483117567863418t_unit (@ (@ image_405062704495631173t_unit (lambda ((I2 product_unit)) F)) A4)) F))) (forall ((C3 set_Product_unit) (A4 (-> product_unit set_Pr1261947904930325089at_nat)) (B5 set_Pr1261947904930325089at_nat)) (let ((_let_1 (= C3 bot_bo3957492148770167129t_unit))) (and (=> (not _let_1) (= (@ comple5685304695842803022at_nat (@ (@ image_3617315916088684441at_nat (lambda ((X4 product_unit)) (@ (@ sup_su6327502436637775413at_nat (@ A4 X4)) B5))) C3)) (@ (@ sup_su6327502436637775413at_nat (@ comple5685304695842803022at_nat (@ (@ image_3617315916088684441at_nat A4) C3))) B5))) (=> _let_1 (= (@ comple5685304695842803022at_nat (@ (@ image_3617315916088684441at_nat (lambda ((X4 product_unit)) (@ (@ sup_su6327502436637775413at_nat (@ A4 X4)) B5))) C3)) bot_bo2099793752762293965at_nat))))) (forall ((A4 set_Product_unit) (C set_char)) (let ((_let_1 (= A4 bot_bo3957492148770167129t_unit))) (and (=> (not _let_1) (= (@ comple7965528767983648192t_char (@ (@ image_5325685772115642575t_char (lambda ((Y5 product_unit)) C)) A4)) C)) (=> _let_1 (= (@ comple7965528767983648192t_char (@ (@ image_5325685772115642575t_char (lambda ((Y5 product_unit)) C)) A4)) top_top_set_char))))) (forall ((A4 set_o) (B5 set_Product_unit) (C3 set_o) (D set_Product_unit)) (= (= (@ (@ produc411009820408249917t_unit A4) (lambda ((Uu Bool)) B5)) (@ (@ produc411009820408249917t_unit C3) (lambda ((Uu Bool)) D))) (or (and (or (= B5 bot_bo3957492148770167129t_unit) (= A4 bot_bot_set_o)) (or (= C3 bot_bot_set_o) (= D bot_bo3957492148770167129t_unit))) (and (= B5 D) (= A4 C3))))) (forall ((R nat) (S2 num) (R3 set_Pr6200539531224447659at_num) (S3 num)) (let ((_let_1 (@ product_Pair_nat_num R))) (=> (@ (@ member9148766508732265716at_num (@ _let_1 S2)) R3) (=> (= S3 S2) (@ (@ member9148766508732265716at_num (@ _let_1 S3)) R3))))) (forall ((I3 set_o) (F (-> Bool product_unit)) (X2 product_unit)) (=> (not (= I3 bot_bot_set_o)) (= (@ comple2584293577114468500t_unit (@ (@ image_o_Product_unit (lambda ((I2 Bool)) (@ (@ inf_inf_Product_unit (@ F I2)) X2))) I3)) (@ (@ inf_inf_Product_unit (@ comple2584293577114468500t_unit (@ (@ image_o_Product_unit F) I3))) X2)))) (forall ((F (-> nat nat product_prod_nat_nat product_prod_nat_nat))) (= (@ produc3610074571335452306at_nat (@ produc27273713700761075at_nat F)) F)) (forall ((S5 set_int) (F (-> int int)) (T3 set_int)) (= (@ (@ ord_less_eq_set_int S5) (@ (@ image_int_int F) T3)) (exists ((U2 set_int)) (and (= S5 (@ (@ image_int_int F) U2)) (@ (@ inj_on_int_int F) U2) (@ (@ ord_less_eq_set_int U2) T3))))) _let_25 (forall ((X2 produc652263959640188542_nat_o) (A4 set_Pr1261947904930325089at_nat) (B5 set_o)) (= (@ (@ member2200362271989506215_nat_o X2) (@ (@ produc203973861852599583_nat_o A4) (lambda ((Uu product_prod_nat_nat)) B5))) (and (@ (@ member8440522571783428010at_nat (@ produc6435950281062462810_nat_o X2)) A4) (@ (@ member_o (@ produc668916169454083228_nat_o X2)) B5)))) (forall ((G (-> rat rat)) (F (-> rat rat))) (=> (forall ((X rat)) (= (@ G (@ F X)) X)) (= (@ (@ image_rat_rat G) top_top_set_rat) top_top_set_rat))) (forall ((A4 set_int) (C3 set_nat) (B5 (-> int set_nat))) (=> (forall ((X int)) (=> (@ (@ member_int X) A4) (@ (@ ord_less_eq_set_nat C3) (@ B5 X)))) (@ (@ ord_less_eq_set_nat C3) (@ comple7806235888213564991et_nat (@ (@ image_int_set_nat B5) A4))))) (forall ((F (-> nat nat)) (G (-> num num)) (A nat) (B num)) (= (@ (@ (@ produc1665548884793878990um_num F) G) (@ (@ product_Pair_nat_num A) B)) (@ (@ product_Pair_nat_num (@ F A)) (@ G B)))) _let_24 (forall ((A Bool) (B Bool) (A4 set_o) (B5 (-> Bool set_o))) (=> (@ (@ member7466972457876170832od_o_o (@ (@ product_Pair_o_o A) B)) (@ (@ product_Sigma_o_o A4) B5)) (not (=> (@ (@ member_o A) A4) (not (@ (@ member_o B) (@ B5 A))))))) (forall ((M (-> produc3843707927480180839at_nat set_nat)) (A4 set_Pr4329608150637261639at_nat) (B5 set_Pr4329608150637261639at_nat)) (let ((_let_1 (@ image_3160451284896210088et_nat M))) (= (@ comple7399068483239264473et_nat (@ _let_1 (@ (@ sup_su5525570899277871387at_nat A4) B5))) (@ (@ sup_sup_set_nat (@ comple7399068483239264473et_nat (@ _let_1 A4))) (@ comple7399068483239264473et_nat (@ _let_1 B5)))))) (forall ((Z2 Bool)) (= (@ (@ (@ comp_P2137996956111167876_o_o_o product_snd_o_o) (lambda ((X4 Bool)) (@ (@ product_Pair_o_o X4) X4))) Z2) (@ id_o Z2))) (forall ((I3 set_o) (F (-> Bool set_Pr1261947904930325089at_nat)) (X2 set_Pr1261947904930325089at_nat)) (=> (not (= I3 bot_bot_set_o)) (= (@ comple1930127330929219688at_nat (@ (@ image_7077428525161401678at_nat (lambda ((I2 Bool)) (@ (@ inf_in2572325071724192079at_nat (@ F I2)) X2))) I3)) (@ (@ inf_in2572325071724192079at_nat (@ comple1930127330929219688at_nat (@ (@ image_7077428525161401678at_nat F) I3))) X2)))) (forall ((A4 set_o) (B5 set_o) (C3 (-> Bool product_unit)) (D (-> Bool product_unit))) (=> (= A4 B5) (=> (forall ((X Bool)) (=> (@ (@ member_o X) B5) (= (@ C3 X) (@ D X)))) (= (@ comple2584293577114468500t_unit (@ (@ image_o_Product_unit C3) A4)) (@ comple2584293577114468500t_unit (@ (@ image_o_Product_unit D) B5)))))) (forall ((H (-> int product_prod_int_int)) (F (-> int int int)) (Prod product_prod_int_int)) (= (@ H (@ (@ produc8211389475949308722nt_int F) Prod)) (@ (@ produc4245557441103728435nt_int (lambda ((X12 int) (X23 int)) (@ H (@ (@ F X12) X23)))) Prod))) (forall ((F (-> rat char)) (A4 set_char)) (let ((_let_1 (@ image_rat_char F))) (=> (= (@ _let_1 top_top_set_rat) top_top_set_char) (= (@ _let_1 (@ (@ vimage_rat_char F) A4)) A4)))) (forall ((R set_Pr8693737435421807431at_nat)) (=> (@ (@ total_3592101749530773125at_nat (@ field_4706345496283612622at_nat R)) R) (=> (@ (@ ord_le3000389064537975527at_nat R) id_Pro2258643101195443293at_nat) (or (exists ((A3 product_prod_nat_nat)) (= R (@ (@ insert5050368324300391991at_nat (@ (@ produc6161850002892822231at_nat A3) A3)) bot_bo5327735625951526323at_nat))) (= R bot_bo5327735625951526323at_nat))))) (forall ((A int) (B int) (A2 int) (B2 int)) (=> (= (@ (@ product_Pair_int_int A) B) (@ (@ product_Pair_int_int A2) B2)) (not (=> (= A A2) (not (= B B2)))))) (forall ((A4 set_o) (F (-> Bool product_unit)) (B5 set_o)) (let ((_let_1 (@ image_o_Product_unit F))) (let ((_let_2 (@ _let_1 B5))) (let ((_let_3 (@ _let_1 A4))) (=> (not (= A4 bot_bot_set_o)) (=> (@ condit9161856309968323677t_unit _let_3) (=> (not (= B5 bot_bot_set_o)) (=> (@ condit9161856309968323677t_unit _let_2) (= (@ comple2584293577114468500t_unit (@ _let_1 (@ (@ sup_sup_set_o A4) B5))) (@ (@ inf_inf_Product_unit (@ comple2584293577114468500t_unit _let_3)) (@ comple2584293577114468500t_unit _let_2))))))))))) _let_22 (forall ((C3 set_o) (A4 (-> Bool set_nat)) (B5 set_nat)) (let ((_let_1 (= C3 bot_bot_set_o))) (and (=> (not _let_1) (= (@ comple7399068483239264473et_nat (@ (@ image_o_set_nat (lambda ((X4 Bool)) (@ (@ sup_sup_set_nat (@ A4 X4)) B5))) C3)) (@ (@ sup_sup_set_nat (@ comple7399068483239264473et_nat (@ (@ image_o_set_nat A4) C3))) B5))) (=> _let_1 (= (@ comple7399068483239264473et_nat (@ (@ image_o_set_nat (lambda ((X4 Bool)) (@ (@ sup_sup_set_nat (@ A4 X4)) B5))) C3)) bot_bot_set_nat))))) (forall ((F (-> nat nat))) (=> (@ (@ inj_on_nat_nat F) top_top_set_nat) (@ (@ inj_on2461717442902640625at_nat (@ comp_nat_nat_nat F)) top_top_set_nat_nat))) (forall ((Prod product_prod_int_int)) (= Prod (@ (@ product_Pair_int_int (@ product_fst_int_int Prod)) (@ product_snd_int_int Prod)))) (forall ((F (-> nat product_unit)) (A4 set_nat) (G (-> nat product_unit)) (B5 set_nat)) (=> (@ (@ inj_on7061601236592826506t_unit F) A4) (=> (@ (@ inj_on7061601236592826506t_unit G) B5) (=> (= (@ (@ inf_in4660618365625256667t_unit (@ (@ image_8730104196221521654t_unit F) A4)) (@ (@ image_8730104196221521654t_unit G) B5)) bot_bo3957492148770167129t_unit) (@ (@ inj_on7061601236592826506t_unit (lambda ((X4 nat)) (@ (@ (@ if_Product_unit (@ (@ member_nat X4) A4)) (@ F X4)) (@ G X4)))) (@ (@ sup_sup_set_nat A4) B5)))))) (forall ((F (-> product_unit set_Pr8693737435421807431at_nat)) (A product_unit) (B5 set_Product_unit)) (let ((_let_1 (@ image_7288820656315755647at_nat F))) (= (@ comple2748534634209756852at_nat (@ _let_1 (@ (@ insert_Product_unit A) B5))) (@ (@ sup_su718114333110466843at_nat (@ F A)) (@ comple2748534634209756852at_nat (@ _let_1 B5)))))) (forall ((X2 nat) (Y3 nat) (A4 set_nat)) (= (@ (@ member8440522571783428010at_nat (@ (@ product_Pair_nat_nat X2) Y3)) (@ id_on_nat A4)) (and (@ (@ member_nat X2) A4) (= X2 Y3)))) (forall ((A int) (A4 set_int)) (=> (@ (@ member_int A) A4) (@ (@ member5262025264175285858nt_int (@ (@ product_Pair_int_int A) A)) (@ id_on_int A4)))) (forall ((X2 product_unit) (A4 set_Product_unit) (F (-> product_unit nat)) (Y3 nat)) (let ((_let_1 (@ image_875570014554754200it_nat F))) (let ((_let_2 (@ (@ image_875570014554754200it_nat (@ (@ (@ fun_up6473050886840373792it_nat F) X2) Y3)) A4))) (let ((_let_3 (@ (@ member_Product_unit X2) A4))) (and (=> _let_3 (= _let_2 (@ (@ insert_nat Y3) (@ _let_1 (@ (@ minus_6452836326544984404t_unit A4) (@ (@ insert_Product_unit X2) bot_bo3957492148770167129t_unit)))))) (=> (not _let_3) (= _let_2 (@ _let_1 A4)))))))) (forall ((F (-> char char)) (G (-> char char))) (=> (= (@ (@ image_char_char F) top_top_set_char) top_top_set_char) (=> (= (@ (@ image_char_char G) top_top_set_char) top_top_set_char) (= (@ (@ image_7676512070627423941r_char (@ (@ produc7830753070125841726r_char F) G)) top_to1235241553633177651r_char) top_to1235241553633177651r_char)))) (forall ((A4 set_Product_unit) (F (-> product_unit set_nat)) (G (-> product_unit set_nat))) (let ((_let_1 (@ (@ image_8173849991827986510et_nat G) A4))) (let ((_let_2 (@ (@ image_8173849991827986510et_nat F) A4))) (=> (not (= A4 bot_bo3957492148770167129t_unit)) (=> (@ condit5477540289124974626et_nat _let_2) (=> (@ condit5477540289124974626et_nat _let_1) (= (@ (@ sup_sup_set_nat (@ comple7399068483239264473et_nat _let_2)) (@ comple7399068483239264473et_nat _let_1)) (@ comple7399068483239264473et_nat (@ (@ image_8173849991827986510et_nat (lambda ((A5 product_unit)) (@ (@ sup_sup_set_nat (@ F A5)) (@ G A5)))) A4))))))))) (= (@ set_or1210151606488870762an_nat zero_zero_nat) (@ (@ image_nat_nat suc) top_top_set_nat)) (forall ((F (-> nat rat)) (A4 set_nat) (B5 set_rat)) (= (@ (@ ord_less_eq_set_rat (@ (@ image_nat_rat F) A4)) B5) (forall ((X4 nat)) (=> (@ (@ member_nat X4) A4) (@ (@ member_rat (@ F X4)) B5))))) (forall ((R3 (-> int int Bool)) (F (-> int num)) (G (-> int num))) (@ (@ (@ (@ bNF_re7626690874201225453um_num R3) (@ (@ (@ bNF_Gr7020624548710275655nt_num F) G) R3)) F) G)) (forall ((F (-> int int product_prod_int_int)) (G (-> product_prod_int_int product_prod_int_int))) (=> (forall ((X int) (Y int)) (= (@ (@ F X) Y) (@ G (@ (@ product_Pair_int_int X) Y)))) (= (@ produc4245557441103728435nt_int F) G))) (forall ((K nat) (I3 set_nat) (A4 (-> nat set_Pr1261947904930325089at_nat))) (let ((_let_1 (@ comple1930127330929219688at_nat (@ (@ image_7178329752028323786at_nat A4) I3)))) (=> (@ (@ member_nat K) I3) (= (@ (@ inf_in2572325071724192079at_nat (@ A4 K)) _let_1) _let_1)))) (forall ((S5 set_nat) (T3 set_rat) (F (-> nat rat))) (=> (@ finite_finite_nat S5) (=> (@ finite_finite_rat T3) (=> (= (@ finite_card_nat S5) (@ finite_card_rat T3)) (=> (@ (@ ord_less_eq_set_rat (@ (@ image_nat_rat F) S5)) T3) (= (forall ((X4 rat)) (=> (@ (@ member_rat X4) T3) (exists ((Y5 nat)) (and (@ (@ member_nat Y5) S5) (= (@ F Y5) X4))))) (@ (@ inj_on_nat_rat F) S5))))))) (forall ((A4 set_nat) (B5 set_nat)) (= (@ (@ image_5168914502847457605at_nat product_swap_nat_nat) (@ (@ produc457027306803732586at_nat A4) (lambda ((Uu nat)) B5))) (@ (@ produc457027306803732586at_nat B5) (lambda ((Uu nat)) A4)))) _let_21 (forall ((F (-> nat Bool)) (G (-> Bool Bool)) (Set set_o)) (= (@ (@ vimage_nat_o F) (@ (@ vimage_o_o G) Set)) (@ (@ vimage_nat_o (@ (@ comp_o_o_nat G) F)) Set))) _let_20 (forall ((S5 set_se7855581050983116737at_nat)) (= (@ comple1675732732025788397_nat_o (@ (@ image_6923511907955291850_nat_o (lambda ((I2 set_Pr1261947904930325089at_nat) (X4 nat) (Y5 nat)) (@ (@ member8440522571783428010at_nat (@ (@ product_Pair_nat_nat X4) Y5)) I2))) S5)) (lambda ((X4 nat) (Y5 nat)) (@ (@ member8440522571783428010at_nat (@ (@ product_Pair_nat_nat X4) Y5)) (@ comple1930127330929219688at_nat S5))))) (forall ((P2 (-> heap_e7401611519738050253t_unit Bool)) (F (-> heap_e7401611519738050253t_unit produc7812382424243267045t_unit)) (H heap_e7401611519738050253t_unit) (H2 heap_e7401611519738050253t_unit) (R ref_a)) (let ((_let_1 (@ F H))) (=> (@ (@ (@ (@ heap_effect_ref_a (@ (@ heap_guard_ref_a P2) F)) H) H2) R) (not (=> (= H2 (@ produc1126150082675451753t_unit _let_1)) (=> (= R (@ produc473321116828791851t_unit _let_1)) (not (@ P2 H)))))))) (forall ((C3 set_Pr1261947904930325089at_nat) (A4 set_nat) (B5 (-> product_prod_nat_nat set_nat))) (let ((_let_1 (@ (@ minus_minus_set_nat A4) (@ comple7399068483239264473et_nat (@ (@ image_15824709712370754et_nat B5) C3))))) (let ((_let_2 (= C3 bot_bo2099793752762293965at_nat))) (and (=> _let_2 (= _let_1 A4)) (=> (not _let_2) (= _let_1 (@ comple7806235888213564991et_nat (@ (@ image_15824709712370754et_nat (lambda ((X4 product_prod_nat_nat)) (@ (@ minus_minus_set_nat A4) (@ B5 X4)))) C3)))))))) (forall ((F (-> nat rat)) (A4 set_nat)) (=> (@ finite_finite_rat (@ (@ image_nat_rat F) A4)) (=> (@ (@ inj_on_nat_rat F) A4) (@ finite_finite_nat A4)))) (forall ((X5 set_int) (A4 set_Pr958786334691620121nt_int) (Y4 set_int) (P2 (-> int int Bool)) (Q2 (-> int int Bool))) (let ((_let_1 (@ ord_le2843351958646193337nt_int A4))) (=> (= X5 (@ (@ image_5042161079198086560nt_int product_fst_int_int) A4)) (=> (= Y4 (@ (@ image_5042161079198086560nt_int product_snd_int_int) A4)) (=> (forall ((X int)) (=> (@ (@ member_int X) X5) (forall ((Xa int)) (=> (@ (@ member_int Xa) Y4) (=> (@ (@ P2 X) Xa) (@ (@ Q2 X) Xa)))))) (=> (@ _let_1 (@ collec213857154873943460nt_int (@ produc4947309494688390418_int_o P2))) (@ _let_1 (@ collec213857154873943460nt_int (@ produc4947309494688390418_int_o Q2))))))))) (forall ((F (-> Bool Bool)) (G (-> nat Bool)) (X2 nat) (H (-> Bool Bool)) (K (-> nat Bool))) (=> (= (@ F (@ G X2)) (@ H (@ K X2))) (= (@ (@ (@ comp_o_o_nat F) G) X2) (@ (@ (@ comp_o_o_nat H) K) X2)))) (forall ((F (-> int nat)) (A4 set_nat)) (let ((_let_1 (@ image_int_nat F))) (= (@ _let_1 (@ (@ vimage_int_nat F) A4)) (@ (@ inf_inf_set_nat A4) (@ _let_1 top_top_set_int))))) (forall ((A int) (B int) (A4 set_int) (B5 (-> int set_int))) (=> (@ (@ member5262025264175285858nt_int (@ (@ product_Pair_int_int A) B)) (@ (@ produc1453890548195736866nt_int A4) B5)) (@ (@ member_int B) (@ B5 A)))) (= (@ (@ image_char_char id_char) top_top_set_char) top_top_set_char) (forall ((U product_prod_nat_nat) (A4 set_Pr1261947904930325089at_nat) (A product_unit) (B5 (-> product_prod_nat_nat set_Product_unit))) (=> (@ (@ member8440522571783428010at_nat U) A4) (= (@ comple3349607820504768346t_unit (@ (@ image_121980125215734065t_unit (lambda ((X4 product_prod_nat_nat)) (@ (@ insert_Product_unit A) (@ B5 X4)))) A4)) (@ (@ insert_Product_unit A) (@ comple3349607820504768346t_unit (@ (@ image_121980125215734065t_unit B5) A4)))))) (forall ((A4 set_nat) (F (-> nat nat)) (U nat)) (let ((_let_1 (@ (@ image_nat_nat F) A4))) (=> (not (= A4 bot_bot_set_nat)) (=> (@ condit1738341127787009408ow_nat _let_1) (= (@ (@ ord_less_eq_nat U) (@ complete_Inf_Inf_nat _let_1)) (forall ((X4 nat)) (=> (@ (@ member_nat X4) A4) (@ (@ ord_less_eq_nat U) (@ F X4))))))))) (forall ((X2 heap_Heap_ref_a) (Y3 heap_Heap_ref_a)) (= (@ (@ (@ if_Heap_Heap_ref_a false) X2) Y3) Y3)) (forall ((F (-> heap_e7401611519738050253t_unit heap_e7401611519738050253t_unit)) (X2 produc7812382424243267045t_unit)) (= (@ produc1126150082675451753t_unit (@ (@ produc3038839249364385243_ref_a F) X2)) (@ F (@ produc1126150082675451753t_unit X2)))) (forall ((A Bool) (A4 set_o)) (let ((_let_1 (@ pow_o A4))) (let ((_let_2 (@ insert_o A))) (= (@ pow_o (@ _let_2 A4)) (@ (@ sup_sup_set_set_o _let_1) (@ (@ image_set_o_set_o _let_2) _let_1)))))) (forall ((P produc1319942482725812455at_nat)) (exists ((X set_Pr4329608150637261639at_nat) (Y set_Pr4329608150637261639at_nat)) (= P (@ (@ produc9060074326276436823at_nat X) Y)))) (= bNF_re7408651293131936558nt_int (lambda ((R6 (-> product_prod_nat_nat int Bool)) (S4 (-> (-> product_prod_nat_nat product_prod_nat_nat) (-> int int) Bool)) (F2 (-> product_prod_nat_nat product_prod_nat_nat product_prod_nat_nat)) (G3 (-> int int int))) (@ (@ ord_le129227817499904167_int_o R6) (@ (@ (@ bNF_vi8966365312794588230_int_o F2) G3) S4)))) (forall ((A (-> nat num)) (B (-> int nat)) (C (-> int num)) (V int)) (=> (= (@ (@ comp_nat_num_int A) B) (@ (@ comp_num_num_int id_num) C)) (= (@ A (@ B V)) (@ C V)))) (forall ((X2 produc7812382424243267045t_unit) (Y3 ref_a) (Z2 heap_e7401611519738050253t_unit)) (=> (= X2 (@ (@ produc6544324848051098391t_unit Y3) Z2)) (= (@ produc473321116828791851t_unit X2) Y3))) (forall ((B5 (-> nat Bool Bool)) (C3 (-> num Bool Bool)) (A4 (-> int nat Bool))) (@ (@ (@ (@ bNF_re3931674169038344211_nat_o (@ (@ bNF_re8508505965575957011_num_o B5) C3)) (@ (@ bNF_re7435575058205011731_nat_o (@ (@ bNF_re4914077030771115051_nat_o A4) B5)) (@ (@ bNF_re3760060065607074657_num_o A4) C3))) comp_nat_num_int) comp_o_o_nat)) (forall ((A4 set_nat) (B5 set_nat) (C3 (-> nat rat)) (D (-> nat rat)) (Inf (-> set_rat rat))) (=> (= A4 B5) (=> (forall ((X nat)) (=> (@ (@ member_nat X) B5) (= (@ C3 X) (@ D X)))) (= (@ Inf (@ (@ image_nat_rat C3) A4)) (@ Inf (@ (@ image_nat_rat D) B5)))))) (forall ((C3 set_nat) (A4 (-> nat set_Product_unit)) (B5 set_Product_unit)) (let ((_let_1 (= C3 bot_bot_set_nat))) (and (=> _let_1 (= (@ comple3349607820504768346t_unit (@ (@ image_4824033694279209942t_unit (lambda ((X4 nat)) (@ (@ sup_su793286257634532545t_unit (@ A4 X4)) B5))) C3)) bot_bo3957492148770167129t_unit)) (=> (not _let_1) (= (@ comple3349607820504768346t_unit (@ (@ image_4824033694279209942t_unit (lambda ((X4 nat)) (@ (@ sup_su793286257634532545t_unit (@ A4 X4)) B5))) C3)) (@ (@ sup_su793286257634532545t_unit (@ comple3349607820504768346t_unit (@ (@ image_4824033694279209942t_unit A4) C3))) B5)))))) (forall ((B5 set_Product_unit) (A product_unit)) (= (@ (@ sup_sup_Product_unit (@ comple2584293577114468500t_unit B5)) A) (@ comple2584293577114468500t_unit (@ (@ image_405062704495631173t_unit (lambda ((B4 product_unit)) (@ (@ sup_sup_Product_unit B4) A))) B5)))) (forall ((F (-> nat rat)) (A4 set_nat) (A7 set_rat) (G (-> int int)) (B5 set_int) (B7 set_int)) (=> (= (@ (@ image_nat_rat F) A4) A7) (=> (= (@ (@ image_int_int G) B5) B7) (= (@ (@ image_8800797895614172237at_int (@ (@ produc8746822746284154874nt_int F) G)) (@ (@ produc454536836294682310at_int A4) (lambda ((Uu nat)) B5))) (@ (@ produc137982192359816398at_int A7) (lambda ((Uu rat)) B7)))))) (forall ((F (-> nat product_unit)) (A4 set_nat)) (=> (@ finite4290736615968046902t_unit (@ (@ image_8730104196221521654t_unit F) A4)) (=> (not (@ finite_finite_nat A4)) (not (forall ((Y product_unit)) (=> (@ (@ member_Product_unit Y) (@ (@ image_8730104196221521654t_unit F) A4)) (@ finite_finite_nat (@ (@ inf_inf_set_nat (@ (@ vimage4884490618288580032t_unit F) (@ (@ insert_Product_unit Y) bot_bo3957492148770167129t_unit))) A4)))))))) (forall ((C product_prod_nat_nat) (F (-> nat nat)) (G (-> nat nat)) (R3 set_Pr1261947904930325089at_nat)) (=> (@ (@ member8440522571783428010at_nat C) (@ (@ image_5168914502847457605at_nat (@ (@ produc6977886695330630970at_nat F) G)) R3)) (not (forall ((X nat) (Y nat)) (=> (= C (@ (@ product_Pair_nat_nat (@ F X)) (@ G Y))) (not (@ (@ member8440522571783428010at_nat (@ (@ product_Pair_nat_nat X) Y)) R3))))))) (forall ((B product_prod_nat_nat) (B5 (-> Bool set_Pr1261947904930325089at_nat)) (A4 set_o)) (=> (@ (@ member8440522571783428010at_nat B) (@ comple5685304695842803022at_nat (@ (@ image_7077428525161401678at_nat B5) A4))) (not (forall ((X Bool)) (=> (@ (@ member_o X) A4) (not (@ (@ member8440522571783428010at_nat B) (@ B5 X)))))))) (forall ((F (-> product_prod_nat_nat set_Pr8693737435421807431at_nat)) (A product_prod_nat_nat) (B5 set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ image_5803077947706746251at_nat F))) (= (@ comple2748534634209756852at_nat (@ _let_1 (@ (@ insert8211810215607154385at_nat A) B5))) (@ (@ sup_su718114333110466843at_nat (@ F A)) (@ comple2748534634209756852at_nat (@ _let_1 B5)))))) (forall ((G (-> nat int)) (F (-> int nat)) (A4 set_int)) (= (@ complete_Inf_Inf_int (@ (@ image_nat_int G) (@ (@ image_int_nat F) A4))) (@ complete_Inf_Inf_int (@ (@ image_int_int (@ (@ comp_nat_int_int G) F)) A4)))) (forall ((H heap_e7401611519738050253t_unit) (R ref_a) (V a)) (=> (@ (@ present_a H) R) (@ (@ noteq_a_a R) (@ produc473321116828791851t_unit (@ (@ alloc_a V) H))))) (forall ((X2 Bool) (A4 set_o) (F (-> Bool set_nat))) (let ((_let_1 (@ (@ vimage5656379182745576100_o_nat (@ product_Pair_o_nat X2)) (@ (@ product_Sigma_o_nat A4) F)))) (let ((_let_2 (@ (@ member_o X2) A4))) (and (=> _let_2 (= _let_1 (@ F X2))) (=> (not _let_2) (= _let_1 bot_bot_set_nat)))))) (forall ((A4 set_Pr1261947904930325089at_nat)) (= (@ comple5685304695842803022at_nat (@ (@ image_5423882813909314213at_nat (lambda ((X4 product_prod_nat_nat)) (@ (@ insert8211810215607154385at_nat X4) bot_bo2099793752762293965at_nat))) A4)) A4)) (forall ((X2 nat) (A4 set_nat) (F (-> nat Bool))) (=> (@ (@ member_nat X2) A4) (@ (@ member_o (@ F X2)) (@ (@ image_nat_o F) A4)))) (forall ((P2 (-> nat Bool)) (F (-> nat Bool)) (B5 set_o)) (=> (forall ((X nat)) (=> (@ P2 X) (@ (@ member_o (@ F X)) B5))) (@ (@ ord_less_eq_set_o (@ (@ image_nat_o F) (@ collect_nat P2))) B5))) _let_18 _let_16 (forall ((I produc3843707927480180839at_nat) (A4 set_Pr4329608150637261639at_nat) (F (-> produc3843707927480180839at_nat set_nat)) (U set_nat)) (=> (@ (@ member8757157785044589968at_nat I) A4) (=> (@ (@ ord_less_eq_set_nat (@ F I)) U) (@ (@ ord_less_eq_set_nat (@ comple7806235888213564991et_nat (@ (@ image_3160451284896210088et_nat F) A4))) U)))) (forall ((A4 set_int) (G (-> int int)) (B5 set_int) (F (-> int int))) (let ((_let_1 (@ (@ image_int_int G) B5))) (=> (not (= A4 bot_bot_set_int)) (=> (@ condit2212336002400062152ve_int _let_1) (=> (@ (@ ord_less_eq_set_int A4) B5) (=> (forall ((X int)) (=> (@ (@ member_int X) A4) (@ (@ ord_less_eq_int (@ F X)) (@ G X)))) (@ (@ ord_less_eq_int (@ complete_Sup_Sup_int (@ (@ image_int_int F) A4))) (@ complete_Sup_Sup_int _let_1)))))))) (forall ((F (-> int int)) (A4 set_int) (A7 set_int) (G (-> nat rat)) (B5 set_nat) (B7 set_rat)) (=> (= (@ (@ image_int_int F) A4) A7) (=> (= (@ (@ image_nat_rat G) B5) B7) (= (@ (@ image_4420076320108226637nt_rat (@ (@ produc4404592263388028922at_rat F) G)) (@ (@ produc1456381018704787142nt_nat A4) (lambda ((Uu int)) B5))) (@ (@ produc821250958618291406nt_rat A7) (lambda ((Uu int)) B7)))))) (forall ((X2 produc4675096598859438275atural) (Y3 produc4675096598859438275atural)) (= (@ (@ (@ if_Pro3444522238938527101atural true) X2) Y3) X2)) (forall ((X2 nat) (A4 set_nat) (C Bool)) (=> (@ (@ member_nat X2) A4) (= (@ (@ image_nat_o (lambda ((X4 nat)) C)) A4) (@ (@ insert_o C) bot_bot_set_o)))) (forall ((F (-> int int)) (A4 set_int) (P2 (-> set_int Bool))) (= (exists ((B6 set_int)) (and (@ finite_finite_int B6) (@ (@ ord_less_eq_set_int B6) (@ (@ image_int_int F) A4)) (@ P2 B6))) (exists ((B6 set_int)) (and (@ (@ ord_less_eq_set_int B6) A4) (@ P2 (@ (@ image_int_int F) B6)) (@ finite_finite_int B6))))) (forall ((A4 set_Product_unit) (C product_unit)) (let ((_let_1 (= A4 bot_bo3957492148770167129t_unit))) (and (=> (not _let_1) (= (@ comple4687483117567863418t_unit (@ (@ image_405062704495631173t_unit (lambda ((Y5 product_unit)) C)) A4)) C)) (=> _let_1 (= (@ comple4687483117567863418t_unit (@ (@ image_405062704495631173t_unit (lambda ((Y5 product_unit)) C)) A4)) bot_bot_Product_unit))))) (forall ((A4 set_Pr4329608150637261639at_nat) (B5 (-> produc3843707927480180839at_nat set_nat)) (C3 set_nat)) (=> (forall ((X produc3843707927480180839at_nat)) (=> (@ (@ member8757157785044589968at_nat X) A4) (@ (@ ord_less_eq_set_nat (@ B5 X)) C3))) (@ (@ ord_less_eq_set_nat (@ comple7399068483239264473et_nat (@ (@ image_3160451284896210088et_nat B5) A4))) C3))) (forall ((B Bool) (B5 (-> int set_o)) (A4 set_int)) (=> (@ (@ member_o B) (@ comple90263536869209701_set_o (@ (@ image_int_set_o B5) A4))) (not (forall ((X int)) (=> (@ (@ member_int X) A4) (not (@ (@ member_o B) (@ B5 X)))))))) (forall ((U int) (A4 set_int) (A Bool) (B5 (-> int set_o))) (=> (@ (@ member_int U) A4) (= (@ comple90263536869209701_set_o (@ (@ image_int_set_o (lambda ((X4 int)) (@ (@ insert_o A) (@ B5 X4)))) A4)) (@ (@ insert_o A) (@ comple90263536869209701_set_o (@ (@ image_int_set_o B5) A4)))))) (forall ((F4 set_nat) (H (-> nat int))) (=> (@ finite_finite_nat F4) (@ finite_finite_int (@ (@ image_nat_int H) F4)))) (forall ((F heap_Heap_ref_a) (H heap_e7401611519738050253t_unit) (H2 heap_e7401611519738050253t_unit) (A ref_a) (H3 heap_e7401611519738050253t_unit) (B ref_a)) (let ((_let_1 (@ (@ heap_effect_ref_a F) H))) (=> (@ (@ _let_1 H2) A) (=> (@ (@ _let_1 H3) B) (= H2 H3))))) (forall ((F (-> nat rat)) (A4 set_nat) (P2 (-> rat Bool))) (=> (forall ((X rat)) (=> (@ (@ member_rat X) (@ (@ image_nat_rat F) A4)) (@ P2 X))) (forall ((X6 nat)) (=> (@ (@ member_nat X6) A4) (@ P2 (@ F X6)))))) (forall ((F (-> rat int)) (B5 set_int) (A4 set_rat)) (let ((_let_1 (@ image_rat_int F))) (=> (= (@ _let_1 top_top_set_rat) top_top_set_int) (=> (@ (@ ord_less_eq_set_rat (@ (@ vimage_rat_int F) B5)) A4) (@ (@ ord_less_eq_set_int B5) (@ _let_1 A4)))))) (forall ((Z2 product_prod_nat_nat) (C (-> nat num set_Pr1261947904930325089at_nat)) (A nat) (B num)) (let ((_let_1 (@ member8440522571783428010at_nat Z2))) (=> (@ _let_1 (@ (@ C A) B)) (@ _let_1 (@ (@ produc859037500352796105at_nat C) (@ (@ product_Pair_nat_num A) B)))))) (forall ((B int) (F (-> rat int))) (=> (@ (@ member_int B) (@ (@ image_rat_int F) top_top_set_rat)) (not (forall ((X rat)) (not (= B (@ F X))))))) (forall ((I Bool) (J4 Bool) (R3 set_Product_prod_o_o)) (=> (@ (@ member7466972457876170832od_o_o (@ (@ product_Pair_o_o I) J4)) R3) (@ (@ member_o I) (@ field_o R3)))) (forall ((X2 code_integer) (Y3 code_integer)) (= (@ (@ (@ if_Code_integer true) X2) Y3) X2)) (forall ((H (-> product_prod_int_int Bool)) (F (-> int int product_prod_int_int)) (Prod product_prod_int_int)) (= (@ H (@ (@ produc4245557441103728435nt_int F) Prod)) (@ (@ produc4947309494688390418_int_o (lambda ((X12 int) (X23 int)) (@ H (@ (@ F X12) X23)))) Prod))) (forall ((F (-> nat nat)) (A4 set_nat) (P2 (-> set_nat Bool))) (= (forall ((B6 set_nat)) (=> (and (@ (@ ord_less_eq_set_nat B6) (@ (@ image_nat_nat F) A4)) (@ finite_finite_nat B6)) (@ P2 B6))) (forall ((B6 set_nat)) (=> (and (@ (@ ord_less_eq_set_nat B6) A4) (@ finite_finite_nat B6)) (@ P2 (@ (@ image_nat_nat F) B6)))))) (forall ((Rb (-> Bool nat Bool)) (Sd (-> Bool nat Bool))) (@ (@ (@ (@ bNF_re1515921786380824775at_nat (@ (@ bNF_re4209105892566519389_o_nat Rb) Sd)) (@ (@ bNF_re2144779315220482269at_nat (@ (@ bNF_re7523573913982466217_o_nat (lambda ((Y2 nat) (Z nat)) (= Y2 Z))) Rb)) (@ (@ bNF_re7523573913982466217_o_nat (lambda ((Y2 nat) (Z nat)) (= Y2 Z))) Sd))) comp_o_o_nat) comp_nat_nat_nat)) (forall ((X2 product_unit) (Y3 product_unit)) (= (@ (@ (@ if_Product_unit true) X2) Y3) X2)) (forall ((A nat) (P2 (-> nat Bool))) (= (@ (@ member_nat A) (@ collect_nat P2)) (@ P2 A))) (= (@ (@ image_rat_rat id_rat) top_top_set_rat) top_top_set_rat) (= produc8739625826339149834_nat_o (lambda ((F2 (-> nat nat product_prod_nat_nat Bool)) (Prod3 product_prod_nat_nat) (__flatten_var_0 product_prod_nat_nat)) (@ (@ (@ F2 (@ product_fst_nat_nat Prod3)) (@ product_snd_nat_nat Prod3)) __flatten_var_0))) _let_15 (forall ((F (-> nat rat)) (A4 set_nat) (G (-> int rat)) (B5 set_int) (H (-> rat int))) (=> (= (@ (@ image_nat_rat F) A4) (@ (@ image_int_rat G) B5)) (= (@ (@ image_nat_int (@ (@ comp_rat_int_nat H) F)) A4) (@ (@ image_int_int (@ (@ comp_rat_int_int H) G)) B5)))) (forall ((F (-> Bool set_o))) (= (@ comple90263536869209701_set_o (@ (@ image_o_set_o F) bot_bot_set_o)) bot_bot_set_o)) (forall ((X2 product_prod_nat_nat)) (@ (@ order_7480980593162297270at_nat (@ (@ insert8211810215607154385at_nat X2) bot_bo2099793752762293965at_nat)) (@ (@ insert5050368324300391991at_nat (@ (@ produc6161850002892822231at_nat X2) X2)) bot_bo5327735625951526323at_nat))) (forall ((G (-> int nat)) (F (-> nat int)) (A4 set_nat)) (= (@ complete_Sup_Sup_nat (@ (@ image_int_nat G) (@ (@ image_nat_int F) A4))) (@ complete_Sup_Sup_nat (@ (@ image_nat_nat (@ (@ comp_int_nat_nat G) F)) A4)))) (forall ((A4 set_Pr4329608150637261639at_nat)) (@ (@ inj_on8430303779476321073at_nat (@ produc7548845685434208379at_nat (lambda ((I2 set_Pr1261947904930325089at_nat) (J set_Pr1261947904930325089at_nat)) (@ (@ 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image_o_set_int (lambda ((X4 Bool)) (@ (@ image_int_int F) (@ B5 X4)))) A4))) (= (@ complete_Sup_Sup_int (@ (@ image_int_int F) (@ comple3221217463730067765et_int (@ (@ image_o_set_int B5) A4)))) (@ complete_Sup_Sup_int (@ (@ image_o_int (lambda ((X4 Bool)) (@ complete_Sup_Sup_int (@ (@ image_int_int F) (@ B5 X4))))) A4))))))) (forall ((A4 set_int) (F (-> int nat)) (U nat)) (let ((_let_1 (@ (@ image_int_nat F) A4))) (=> (not (= A4 bot_bot_set_int)) (=> (@ condit1738341127787009408ow_nat _let_1) (= (@ (@ ord_less_eq_nat U) (@ complete_Inf_Inf_nat _let_1)) (forall ((X4 int)) (=> (@ (@ member_int X4) A4) (@ (@ ord_less_eq_nat U) (@ F X4))))))))) (forall ((I3 set_nat) (J3 set_nat) (C3 (-> nat set_nat))) (= (@ (@ produc457027306803732586at_nat (@ (@ minus_minus_set_nat I3) J3)) C3) (@ (@ minus_1356011639430497352at_nat (@ (@ produc457027306803732586at_nat I3) C3)) (@ (@ produc457027306803732586at_nat J3) C3)))) (forall ((F (-> nat rat)) (C3 set_nat) (A4 set_nat) (B5 set_nat)) (let ((_let_1 (@ image_nat_rat F))) (let ((_let_2 (@ (@ minus_minus_set_nat A4) B5))) (=> (@ (@ inj_on_nat_rat F) C3) (=> (@ (@ ord_less_eq_set_nat _let_2) C3) (=> (@ (@ ord_less_eq_set_nat B5) C3) (= (@ _let_1 _let_2) (@ (@ minus_minus_set_rat (@ _let_1 A4)) (@ _let_1 B5))))))))) (forall ((F (-> int nat)) (A4 set_int) (B5 set_int)) (let ((_let_1 (@ image_int_nat F))) (=> (@ (@ inj_on_int_nat F) top_top_set_int) (= (@ (@ ord_less_eq_set_nat (@ _let_1 A4)) (@ _let_1 B5)) (@ (@ ord_less_eq_set_int A4) B5))))) (@ (@ _let_13 (@ produc27273713700761075at_nat (lambda ((X4 nat) (Y5 nat) (__flatten_var_0 product_prod_nat_nat)) (@ (@ produc2626176000494625587at_nat (lambda ((U3 nat) (V3 nat)) (@ (@ product_Pair_nat_nat (@ (@ plus_plus_nat X4) V3)) (@ (@ plus_plus_nat Y5) U3)))) __flatten_var_0)))) (@ produc27273713700761075at_nat (lambda ((X4 nat) (Y5 nat) (__flatten_var_0 product_prod_nat_nat)) (@ (@ produc2626176000494625587at_nat (lambda ((U3 nat) (V3 nat)) (@ (@ product_Pair_nat_nat (@ (@ plus_plus_nat X4) V3)) (@ (@ plus_plus_nat Y5) U3)))) __flatten_var_0)))) (forall ((F (-> char int)) (A4 set_int)) (let ((_let_1 (@ image_char_int F))) (=> (= (@ _let_1 top_top_set_char) top_top_set_int) (= (@ _let_1 (@ (@ vimage_char_int F) A4)) A4)))) (forall ((P product_prod_int_int) (Z2 int) (C (-> int int set_int))) (=> (forall ((A3 int) (B3 int)) (=> (= P (@ (@ product_Pair_int_int A3) B3)) (@ (@ member_int Z2) (@ (@ C A3) B3)))) (@ (@ member_int Z2) (@ (@ produc73460835934605544et_int C) P)))) (forall ((F (-> nat Bool)) (A4 set_nat)) (=> (@ finite_finite_o (@ (@ image_nat_o F) A4)) (=> (not (@ finite_finite_nat A4)) (not (forall ((Y Bool)) (=> (@ (@ member_o Y) (@ (@ image_nat_o F) A4)) (@ finite_finite_nat (@ (@ inf_inf_set_nat (@ (@ vimage_nat_o F) (@ (@ insert_o Y) bot_bot_set_o))) A4)))))))) (forall ((I nat) (J4 nat)) (= (@ (@ image_nat_nat suc) (@ (@ set_or1269000886237332187st_nat I) J4)) (@ (@ set_or1269000886237332187st_nat (@ suc I)) (@ suc J4)))) (forall ((Rep (-> num char)) (Abs (-> char num)) (F (-> int nat)) (P2 (-> nat Bool)) (H (-> nat char))) (=> (@ (@ (@ type_d4396077731765706521m_char Rep) Abs) top_top_set_char) (= (@ (@ (@ bNF_vi1300075849944819442char_o F) Rep) (@ (@ bNF_Grp_nat_char (@ collect_nat P2)) H)) (@ (@ bNF_Grp_int_num (@ collect_int (lambda ((X4 int)) (@ P2 (@ F X4))))) (@ (@ comp_nat_num_int (@ (@ comp_char_num_nat Abs) H)) F))))) (forall ((R3 (-> int int Bool)) (R7 (-> int int Bool)) (S5 (-> num num Bool)) (S6 (-> num num Bool))) (=> (@ left_unique_int_int R3) (=> (@ right_total_int_int R3) (=> (@ right_unique_int_int R7) (=> (@ left_total_int_int R7) (@ (@ ord_le4541714130423454556_num_o (@ (@ bNF_re7626690874201225453um_num (@ (@ relcompp_int_int_int R3) R7)) (@ (@ relcompp_num_num_num S5) S6))) (@ (@ relcom9025577121137075810nt_num (@ (@ bNF_re7626690874201225453um_num R3) S5)) (@ (@ bNF_re7626690874201225453um_num R7) S6)))))))) (forall ((C3 set_Pr1261947904930325089at_nat) (A4 set_Pr1261947904930325089at_nat) (B5 (-> 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(=> (@ (@ P2 X2) Y3) (=> (= A (@ (@ produc9060074326276436823at_nat X2) Y3)) (@ (@ P2 (@ produc4486455499028916547at_nat A)) (@ produc826222791318859909at_nat A))))) (forall ((A int)) (= (@ (@ image_int_int (lambda ((X4 int)) (@ (@ minus_minus_int X4) A))) top_top_set_int) top_top_set_int)) (forall ((G (-> nat Bool)) (H (-> nat nat)) (R (-> nat Bool)) (F (-> Bool Bool))) (let ((_let_1 (@ comp_o_o_nat F))) (=> (= (@ (@ comp_nat_o_nat G) H) R) (= (@ (@ comp_nat_o_nat (@ _let_1 G)) H) (@ _let_1 R))))) (forall ((F (-> int nat)) (A4 set_int)) (= (@ comple7399068483239264473et_nat (@ (@ image_int_set_nat (lambda ((X4 int)) (@ (@ insert_nat (@ F X4)) bot_bot_set_nat))) A4)) (@ (@ image_int_nat F) A4))) (forall ((A4 set_Pr4329608150637261639at_nat) (F set_nat)) (=> (not (= A4 bot_bo228742789529271731at_nat)) (= (@ comple7806235888213564991et_nat (@ (@ image_3160451284896210088et_nat (lambda ((I2 produc3843707927480180839at_nat)) F)) A4)) F))) (forall ((F (-> nat int)) (A4 set_nat) (X2 nat)) (let ((_let_1 (@ (@ image_nat_int F) A4))) (=> (@ condit1735850657277959132ow_int _let_1) (=> (@ (@ member_nat X2) A4) (@ (@ ord_less_eq_int (@ complete_Inf_Inf_int _let_1)) (@ F X2)))))) (forall ((I3 set_Product_unit) (F (-> product_unit product_unit)) (X2 product_unit)) (=> (not (= I3 bot_bo3957492148770167129t_unit)) (=> (forall ((I4 product_unit)) (=> (@ (@ member_Product_unit I4) I3) (= (@ F I4) X2))) (= (@ comple2584293577114468500t_unit (@ (@ image_405062704495631173t_unit F) I3)) X2)))) (forall ((G (-> int nat)) (H (-> int int)) (R (-> int nat)) (F (-> nat nat))) (let ((_let_1 (@ comp_nat_nat_int F))) (=> (= (@ (@ comp_int_nat_int G) H) R) (= (@ (@ comp_int_nat_int (@ _let_1 G)) H) (@ _let_1 R))))) (forall ((F (-> int int)) (B5 set_int) (A4 set_int)) (=> (@ (@ inj_on_int_int F) top_top_set_int) (=> (@ (@ ord_less_eq_set_int B5) (@ (@ image_int_int F) A4)) (@ (@ ord_less_eq_set_int (@ (@ vimage_int_int F) B5)) A4)))) (forall ((T3 (-> code_integer int Bool)) (R3 (-> int int Bool))) (=> (@ left_t1735413524555719857er_int T3) (=> (@ (@ ord_le6741204236512500942_int_o (lambda ((Y2 int) (Z int)) (= Y2 Z))) R3) (@ (@ ord_le3602516367967493612eger_o (lambda ((Y2 code_integer) (Z code_integer)) (= Y2 Z))) (@ (@ relcom692387321444912665nteger T3) (@ (@ relcom967497705283160040nteger R3) (@ conver1462408618118490240er_int T3))))))) (forall ((F (-> nat num)) (G (-> int nat)) (H (-> int nat)) (I (-> int int)) (Prod product_prod_int_int)) (= (@ (@ (@ produc5918048235202344416nt_nat F) G) (@ (@ (@ produc5664932004629684302nt_int H) I) Prod)) (@ (@ (@ produc3608230303109393468nt_nat (@ (@ comp_nat_num_int F) H)) (@ (@ comp_int_nat_int G) I)) Prod))) (forall ((A4 set_o) (C set_o)) (let ((_let_1 (= A4 bot_bot_set_o))) (and (=> (not _let_1) (= (@ comple90263536869209701_set_o (@ (@ image_o_set_o (lambda ((Y5 Bool)) C)) A4)) C)) (=> _let_1 (= (@ comple90263536869209701_set_o (@ (@ image_o_set_o (lambda ((Y5 Bool)) C)) A4)) bot_bot_set_o))))) (forall ((F (-> nat nat)) (A4 (-> int nat)) (I3 set_int)) (let ((_let_1 (@ (@ image_int_nat A4) I3))) (=> (@ order_mono_nat_nat F) (=> (@ condit2214826472909112428ve_nat _let_1) (=> (not (= I3 bot_bot_set_int)) (@ (@ ord_less_eq_nat (@ complete_Sup_Sup_nat (@ (@ image_int_nat (lambda ((X4 int)) (@ F (@ A4 X4)))) I3))) (@ F (@ complete_Sup_Sup_nat _let_1)))))))) (forall ((F (-> nat int)) (A4 set_nat) (P2 (-> set_int Bool))) (= (forall ((B6 set_int)) (=> (@ (@ ord_less_eq_set_int B6) (@ (@ image_nat_int F) A4)) (@ P2 B6))) (forall ((B6 set_nat)) (=> (@ (@ ord_less_eq_set_nat B6) A4) (@ P2 (@ (@ image_nat_int F) B6)))))) (forall ((P product_prod_nat_num) (Z2 nat) (C (-> nat num set_nat))) (=> (forall ((A3 nat) (B3 num)) (=> (= P (@ (@ product_Pair_nat_num A3) B3)) (@ (@ member_nat Z2) (@ (@ C A3) B3)))) (@ (@ member_nat Z2) (@ (@ produc4130284055270567454et_nat C) P)))) (forall ((C3 set_Pr1261947904930325089at_nat) (A4 (-> product_prod_nat_nat set_Pr1261947904930325089at_nat)) (B5 set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ (@ inf_in2572325071724192079at_nat (@ comple1930127330929219688at_nat (@ (@ image_5423882813909314213at_nat A4) C3))) B5))) (let ((_let_2 (= C3 bot_bo2099793752762293965at_nat))) (and (=> _let_2 (= _let_1 B5)) (=> (not _let_2) (= _let_1 (@ comple1930127330929219688at_nat (@ (@ image_5423882813909314213at_nat (lambda ((X4 product_prod_nat_nat)) (@ (@ inf_in2572325071724192079at_nat (@ A4 X4)) B5))) C3)))))))) (forall ((S5 set_o) (F (-> Bool nat nat)) (X2 Bool) (Y3 Bool)) (let ((_let_1 (@ F Y3))) (let ((_let_2 (@ F X2))) (=> (@ (@ finite4703585013658510744_o_nat S5) F) (=> (@ (@ member_o X2) S5) (=> (@ (@ member_o Y3) S5) (= (@ (@ comp_nat_nat_nat _let_1) _let_2) (@ (@ comp_nat_nat_nat _let_2) _let_1)))))))) (forall ((F (-> num num)) (G (-> nat num)) (L1 (-> nat num)) (L2 (-> nat nat)) (H (-> int nat)) (R (-> int nat))) (=> (= (@ (@ comp_num_num_nat F) G) (@ (@ comp_nat_num_nat L1) L2)) (=> (= (@ (@ comp_nat_nat_int L2) H) R) (= (@ (@ comp_num_num_int F) (@ (@ comp_nat_num_int G) H)) (@ (@ comp_nat_num_int L1) R))))) (forall ((F (-> nat int)) (A4 set_nat) (B5 set_int)) (=> (@ (@ inj_on_nat_int F) A4) (=> (@ (@ ord_less_eq_set_int (@ (@ image_nat_int F) A4)) B5) (=> (@ finite_finite_int B5) (@ (@ ord_less_eq_nat (@ finite_card_nat A4)) (@ finite_card_int B5)))))) (forall ((R3 (-> int int Bool)) (S5 (-> int int Bool)) (R7 (-> int code_integer Bool)) (S6 (-> int code_integer Bool))) (@ (@ ord_le7522433683449569238eger_o (@ (@ relcom7212586982944386682nteger (@ (@ bNF_re4712519889275205905nt_int R3) S5)) (@ (@ bNF_re3379532845092657523nteger R7) S6))) (@ (@ bNF_re3379532845092657523nteger (@ (@ relcom967497705283160040nteger R3) R7)) (@ (@ relcom967497705283160040nteger S5) S6)))) (forall ((A4 set_Product_unit) (B5 set_nat)) (= (= (@ (@ produc6875377002296012693it_nat A4) (lambda ((Uu product_unit)) B5)) bot_bo2472676621365177558it_nat) (or (= B5 bot_bot_set_nat) (= A4 bot_bo3957492148770167129t_unit)))) (forall ((F (-> int nat)) (C3 set_int) (A4 set_nat) (B5 (-> nat set_int)) (J4 nat)) (=> (@ (@ inj_on_int_nat F) C3) (=> (forall ((X nat)) (=> (@ (@ member_nat X) A4) (@ (@ ord_less_eq_set_int (@ B5 X)) C3))) (=> (@ (@ member_nat J4) A4) (= (@ (@ image_int_nat F) (@ comple3628384868704368283et_int (@ (@ image_nat_set_int B5) A4))) (@ comple7806235888213564991et_nat (@ (@ image_nat_set_nat (lambda ((X4 nat)) (@ (@ image_int_nat F) (@ B5 X4)))) A4))))))) (forall ((C3 set_nat) (A nat) (B5 (-> nat set_nat))) (let ((_let_1 (@ insert_nat A))) (let ((_let_2 (@ _let_1 (@ comple7399068483239264473et_nat (@ (@ image_nat_set_nat B5) C3))))) (let ((_let_3 (= C3 bot_bot_set_nat))) (and (=> _let_3 (= _let_2 (@ _let_1 bot_bot_set_nat))) (=> (not _let_3) (= _let_2 (@ comple7399068483239264473et_nat (@ (@ image_nat_set_nat (lambda ((X4 nat)) (@ (@ insert_nat A) (@ B5 X4)))) C3))))))))) (forall ((B nat) (B5 (-> int set_nat)) (A4 set_int) (A int)) (let ((_let_1 (@ member_nat B))) (=> (@ _let_1 (@ comple7806235888213564991et_nat (@ (@ 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(forall ((Rb (-> nat Bool Bool)) (Sd (-> nat Bool Bool))) (@ (@ (@ (@ bNF_re3930744952143938759_nat_o (@ (@ bNF_re439150893885221597_nat_o Rb) Sd)) (@ (@ bNF_re7744223787735169245_nat_o (@ (@ bNF_re1402873238235875719_nat_o (lambda ((Y2 nat) (Z nat)) (= Y2 Z))) Rb)) (@ (@ bNF_re1402873238235875719_nat_o (lambda ((Y2 nat) (Z nat)) (= Y2 Z))) Sd))) comp_nat_nat_nat) comp_o_o_nat)) (forall ((F (-> (-> code_integer code_integer) produc8923325533196201883nteger produc8923325533196201883nteger)) (G (-> code_integer code_integer code_integer)) (X2 produc3346328345660746739nteger)) (= (@ (@ produc4281629032016041417nteger (@ (@ comp_C8797469213163452608nteger F) G)) X2) (@ (@ F (@ G (@ produc1861665112190112313nteger X2))) (@ produc7955729907432593271nteger X2)))) (forall ((A Bool) (P2 (-> Bool Bool))) (= (@ (@ member_o A) (@ collect_o P2)) (@ P2 A))) (forall ((K nat) (I3 set_nat) (A4 (-> nat set_nat))) (let ((_let_1 (@ comple7399068483239264473et_nat (@ (@ image_nat_set_nat A4) I3)))) (=> (@ 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(@ (@ image_405062704495631173t_unit F) A4)) (= A4 bot_bo3957492148770167129t_unit))) (= (@ _let_4 top_top_set_num) top_top_set_num) _let_3 (forall ((B5 set_o) (A4 set_nat)) (let ((_let_1 (@ product_Sigma_nat_o A4))) (let ((_let_2 (@ image_8629803608462650132_o_nat product_fst_nat_o))) (let ((_let_3 (= B5 bot_bot_set_o))) (and (=> (not _let_3) (= (@ _let_2 (@ _let_1 (lambda ((Uu nat)) B5))) A4)) (=> _let_3 (= (@ _let_2 (@ _let_1 (lambda ((Uu nat)) B5))) bot_bot_set_nat))))))) (forall ((F (-> int rat)) (G (-> nat int)) (A4 set_nat)) (= (@ (@ image_int_rat F) (@ (@ image_nat_int G) A4)) (@ (@ image_nat_rat (lambda ((X4 nat)) (@ F (@ G X4)))) A4))) (forall ((F (-> char nat)) (Y3 nat)) (=> (= (@ (@ image_char_nat F) top_top_set_char) top_top_set_nat) (not (forall ((X char)) (not (= Y3 (@ F X))))))) (forall ((A4 (-> product_unit set_o)) (I product_unit) (B5 set_o) (J3 set_Product_unit)) (= (@ comple90263536869209701_set_o (@ (@ image_6930536745178679216_set_o (@ (@ (@ 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Bool)) (B5 set_o) (I char)) (=> (@ (@ ord_less_eq_set_o (@ (@ image_char_o F) top_top_set_char)) B5) (@ (@ member_o (@ F I)) B5))) (forall ((X2 Bool) (Z5 set_o) (X5 set_o) (P2 (-> Bool Bool))) (=> (@ (@ member_o X2) Z5) (=> (@ (@ ord_less_eq_set_o Z5) (@ collect_o (lambda ((X4 Bool)) (and (@ P2 X4) (@ (@ member_o X4) X5))))) (@ P2 X2)))) (forall ((A product_prod_nat_nat)) (@ (@ member8206827879206165904at_nat (@ (@ produc6161850002892822231at_nat A) A)) id_Pro2258643101195443293at_nat)) (forall ((S5 set_rat) (F (-> nat rat)) (T3 set_nat)) (= (@ (@ ord_less_eq_set_rat S5) (@ (@ image_nat_rat F) T3)) (exists ((U2 set_nat)) (and (@ (@ ord_less_eq_set_nat U2) T3) (= S5 (@ (@ image_nat_rat F) U2)) (@ (@ inj_on_nat_rat F) U2))))) (forall ((A4 set_Pr1261947904930325089at_nat) (B5 set_Pr1261947904930325089at_nat) (F (-> product_prod_nat_nat set_nat)) (G (-> product_prod_nat_nat set_nat))) (=> (@ (@ ord_le3146513528884898305at_nat A4) B5) (=> (forall ((X product_prod_nat_nat)) (=> (@ (@ 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(Z nat)) (= Y2 Z))) _let_2) nat2) (forall ((A int) (B int) (A4 set_Pr958786334691620121nt_int) (F (-> int int nat))) (=> (@ (@ member5262025264175285858nt_int (@ (@ product_Pair_int_int A) B)) A4) (@ (@ member_nat (@ (@ F A) B)) (@ (@ image_5044651549707136836nt_nat (@ produc8213879946458358998nt_nat F)) A4)))) (forall ((G (-> nat rat)) (F (-> rat nat))) (=> (@ finite_finite_rat (@ (@ image_nat_rat G) top_top_set_nat)) (@ finite_finite_nat (@ (@ image_nat_nat (lambda ((X4 nat)) (@ F (@ G X4)))) top_top_set_nat)))) (forall ((A int) (A4 set_int) (B int) (B5 (-> int set_int))) (=> (@ (@ member_int A) A4) (=> (@ (@ member_int B) (@ B5 A)) (@ (@ member5262025264175285858nt_int (@ (@ product_Pair_int_int A) B)) (@ (@ produc1453890548195736866nt_int A4) B5))))) (forall ((F (-> product_unit set_nat)) (A product_unit) (A4 set_Product_unit)) (let ((_let_1 (@ image_8173849991827986510et_nat F))) (= (@ comple7399068483239264473et_nat (@ _let_1 (@ (@ insert_Product_unit A) A4))) (@ (@ 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int Bool)) (X5 (-> product_prod_nat_nat int Bool)) (A4 (-> (-> product_prod_nat_nat product_prod_nat_nat) (-> int int) Bool)) (B5 (-> (-> product_prod_nat_nat product_prod_nat_nat) (-> int int) Bool)) (F (-> product_prod_nat_nat product_prod_nat_nat product_prod_nat_nat)) (G (-> int int int))) (=> (forall ((X product_prod_nat_nat) (Y int)) (=> (@ (@ Y4 X) Y) (@ (@ X5 X) Y))) (=> (forall ((X (-> product_prod_nat_nat product_prod_nat_nat)) (Y (-> int int))) (=> (@ (@ A4 X) Y) (@ (@ B5 X) Y))) (=> (@ (@ (@ (@ bNF_re7408651293131936558nt_int X5) A4) F) G) (@ (@ (@ (@ bNF_re7408651293131936558nt_int Y4) B5) F) G))))) (forall ((F (-> nat set_Pr4329608150637261639at_nat)) (A nat) (B5 set_nat)) (let ((_let_1 (@ image_1087905878993176368at_nat F))) (= (@ comple4364388969068068532at_nat (@ _let_1 (@ (@ insert_nat A) B5))) (@ (@ sup_su5525570899277871387at_nat (@ F A)) (@ comple4364388969068068532at_nat (@ _let_1 B5)))))) (forall ((R3 (-> int nat Bool)) (X2 (-> char int)) (Y3 (-> char nat)) (Ra (-> int nat Bool))) (=> (@ (@ (@ (@ bNF_re4733689599336692735nt_nat (lambda ((Y2 char) (Z char)) (= Y2 Z))) R3) X2) Y3) (=> (forall ((Z3 int) (Yb nat)) (=> (@ (@ member_int Z3) (@ (@ image_char_int X2) top_top_set_char)) (=> (@ (@ member_nat Yb) (@ (@ image_char_nat Y3) top_top_set_char)) (=> (@ (@ R3 Z3) Yb) (@ (@ Ra Z3) Yb))))) (@ (@ (@ (@ bNF_re4733689599336692735nt_nat (lambda ((Y2 char) (Z char)) (= Y2 Z))) Ra) X2) Y3)))) (forall ((F (-> nat int)) (B int)) (=> (@ (@ inj_on_nat_int F) top_top_set_nat) (= (@ (@ member_int B) (@ (@ image_nat_int F) top_top_set_nat)) (exists ((X4 nat)) (and (forall ((Y5 nat)) (=> (= B (@ F Y5)) (= Y5 X4))) (= B (@ F X4))))))) (forall ((F (-> nat int)) (A4 set_nat) (P2 (-> int Bool))) (=> (forall ((X int)) (=> (@ (@ member_int X) (@ (@ image_nat_int F) A4)) (@ P2 X))) (forall ((X6 nat)) (=> (@ (@ member_nat X6) A4) (@ P2 (@ F X6)))))) (forall ((A4 set_Product_unit) (B5 set_Product_unit)) (= (= (@ (@ produc6121607364029222536t_unit A4) (lambda ((Uu product_unit)) B5)) bot_bo1654022762305692595t_unit) (or (= B5 bot_bo3957492148770167129t_unit) (= A4 bot_bo3957492148770167129t_unit)))) _let_1 (forall ((F (-> Bool Bool)) (G (-> Bool Bool)) (H (-> nat Bool))) (= (@ (@ comp_o7658611401268416066_o_nat (@ (@ bNF_convol_o_o_o F) G)) H) (@ (@ bNF_convol_nat_o_o (@ (@ comp_o_o_nat F) H)) (@ (@ comp_o_o_nat G) H)))) (forall ((C product_prod_nat_int) (A4 set_nat) (B5 (-> nat set_int))) (=> (@ (@ member4262671552274231302at_int C) (@ (@ produc454536836294682310at_int A4) B5)) (not (forall ((X nat)) (=> (@ (@ member_nat X) A4) (forall ((Y int)) (=> (@ (@ member_int Y) (@ B5 X)) (not (= C (@ (@ product_Pair_nat_int X) Y)))))))))) (forall ((B int) (B5 (-> Bool set_int)) (A4 set_o) (A Bool)) (let ((_let_1 (@ member_int B))) (=> (@ _let_1 (@ comple3628384868704368283et_int (@ (@ image_o_set_int B5) A4))) (=> (@ (@ member_o A) A4) (@ _let_1 (@ B5 A)))))) (forall ((X2 int) (A4 set_int) (C Bool)) (=> (@ (@ member_int X2) A4) (= (@ (@ image_int_o (lambda ((X4 int)) C)) A4) (@ (@ insert_o C) bot_bot_set_o)))) (forall ((A4 set_Product_unit) (C set_nat)) (let ((_let_1 (= A4 bot_bo3957492148770167129t_unit))) (and (=> _let_1 (= (@ comple7399068483239264473et_nat (@ (@ image_8173849991827986510et_nat (lambda ((Y5 product_unit)) C)) A4)) bot_bot_set_nat)) (=> (not _let_1) (= (@ comple7399068483239264473et_nat (@ (@ image_8173849991827986510et_nat (lambda ((Y5 product_unit)) C)) A4)) C))))) (forall ((X1 set_Pr4329608150637261639at_nat) (X22 set_Pr4329608150637261639at_nat)) (= (@ produc4486455499028916547at_nat (@ (@ produc9060074326276436823at_nat X1) X22)) X1)) (forall ((X1 set_Pr1261947904930325089at_nat) (X22 set_Pr1261947904930325089at_nat)) (= (@ produc2937545259423399429at_nat (@ (@ produc2922128104949294807at_nat X1) X22)) X22)) (forall ((F (-> nat nat)) (A4 set_nat) (B5 set_nat)) (let ((_let_1 (@ image_nat_nat F))) (=> (= (@ _let_1 A4) B5) (= (@ (@ image_7916887816326733075et_nat _let_1) (@ pow_nat A4)) (@ pow_nat B5))))) (forall ((R22 (-> Bool nat Bool)) (R32 (-> Bool num Bool)) (R1 (-> nat int Bool))) (@ (@ (@ (@ bNF_re7387973359137000979nt_num (@ (@ bNF_re766437678722298023_o_num R22) R32)) (@ (@ bNF_re4102725726183926567nt_num (@ (@ bNF_re8210149947023016781_o_nat R1) R22)) (@ (@ bNF_re4767481733178795415_o_num R1) R32))) comp_o_o_nat) comp_nat_num_int)) (forall ((P produc7812382424243267045t_unit) (Q produc7812382424243267045t_unit)) (=> (= (@ produc473321116828791851t_unit P) (@ produc473321116828791851t_unit Q)) (=> (= (@ produc1126150082675451753t_unit P) (@ produc1126150082675451753t_unit Q)) (= P Q)))) (forall ((Rep (-> nat nat)) (Abs (-> nat nat))) (=> (@ (@ (@ type_d6250493948777748686at_nat Rep) Abs) top_top_set_nat) (= (@ (@ comp_nat_nat_nat Rep) Abs) id_nat))) (forall ((A Bool) (A4 set_o) (B Bool) (B5 (-> Bool set_o))) (let ((_let_1 (@ member_o B))) (=> (@ (@ member_o A) A4) (=> (@ _let_1 (@ B5 A)) (@ _let_1 (@ comple90263536869209701_set_o (@ (@ image_o_set_o B5) A4))))))) (forall ((G (-> Bool Bool)) (F (-> nat Bool)) (A4 set_nat)) (= (@ complete_Inf_Inf_o (@ (@ image_o_o G) (@ (@ image_nat_o F) A4))) (@ complete_Inf_Inf_o (@ (@ image_nat_o (@ (@ comp_o_o_nat G) F)) A4)))) (forall ((S5 set_Pr4329608150637261639at_nat) (F (-> produc3843707927480180839at_nat nat nat)) (X2 produc3843707927480180839at_nat) (Y3 produc3843707927480180839at_nat) (G (-> nat nat))) (let ((_let_1 (@ comp_nat_nat_nat (@ F Y3)))) (let ((_let_2 (@ comp_nat_nat_nat (@ F X2)))) (=> (@ (@ finite8619596206551965927at_nat S5) F) (=> (@ (@ member8757157785044589968at_nat X2) S5) (=> (@ (@ member8757157785044589968at_nat Y3) S5) (= (@ _let_1 (@ _let_2 G)) (@ _let_2 (@ _let_1 G))))))))) (forall ((A4 set_nat) (F (-> nat int))) (=> (@ finite_finite_nat A4) (@ (@ ord_less_eq_nat (@ finite_card_int (@ (@ image_nat_int F) A4))) (@ finite_card_nat A4)))) (= product_snd_int_int (@ (@ comp_P5356232565778667509nt_int product_fst_int_int) (@ produc4245557441103728435nt_int (lambda ((X4 int) (Y5 int)) (@ (@ 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((Inf (-> set_int int)) (A4 set_int)) (= (@ Inf (@ (@ image_int_int id_int) A4)) (@ Inf A4))) (forall ((G1 (-> nat num)) (G22 (-> Bool Bool)) (F1 (-> int nat)) (F22 (-> nat Bool)) (V product_prod_int_nat)) (= (@ (@ (@ produc3264868786340801506um_o_o G1) G22) (@ (@ (@ produc8298419091753553490_nat_o F1) F22) V)) (@ (@ (@ produc9074608839065728392_nat_o (@ (@ comp_nat_num_int G1) F1)) (@ (@ comp_o_o_nat G22) F22)) V))) (forall ((B int) (P product_prod_int_int)) (= (= B (@ product_snd_int_int P)) (exists ((A5 int)) (= P (@ (@ product_Pair_int_int A5) B))))) (forall ((B rat) (F (-> nat rat)) (X2 nat) (A4 set_nat)) (=> (= B (@ F X2)) (=> (@ (@ member_nat X2) A4) (@ (@ member_rat B) (@ (@ image_nat_rat F) A4))))) (forall ((A4 set_o) (X2 product_unit) (F (-> Bool product_unit))) (=> (forall ((I4 Bool)) (=> (@ (@ member_o I4) A4) (@ (@ ord_le3221252021190050221t_unit X2) (@ F I4)))) (=> (forall ((Y product_unit)) (=> (forall ((I5 Bool)) (=> (@ (@ member_o I5) A4) (@ (@ ord_le3221252021190050221t_unit Y) (@ F I5)))) (@ (@ ord_le3221252021190050221t_unit Y) X2))) (= (@ comple2584293577114468500t_unit (@ (@ image_o_Product_unit F) A4)) X2)))) (forall ((F (-> rat Bool)) (G (-> nat rat)) (A4 set_nat) (X2 Bool)) (let ((_let_1 (@ (@ image_nat_rat G) A4))) (=> (@ (@ inj_on_rat_o F) _let_1) (=> (@ (@ inj_on_nat_rat G) A4) (=> (@ (@ member_o X2) (@ (@ image_rat_o F) _let_1)) (= (@ (@ (@ the_inv_into_nat_o A4) (@ (@ comp_rat_o_nat F) G)) X2) (@ (@ (@ comp_rat_nat_o (@ (@ the_inv_into_nat_rat A4) G)) (@ (@ the_inv_into_rat_o _let_1) F)) X2))))))) (forall ((X2 int)) (= (@ (@ image_nat_int (lambda ((Uu nat)) X2)) top_top_set_nat) (@ (@ insert_int X2) bot_bot_set_int))) (forall ((F1 (-> int nat)) (A13 set_int) (B1 set_nat) (F22 (-> int nat)) (B22 set_int) (A24 set_nat)) (=> (= (@ (@ image_int_nat F1) A13) B1) (=> (@ (@ inj_on_int_nat F22) B22) (=> (@ (@ ord_less_eq_set_nat (@ (@ image_int_nat F22) B22)) A24) (=> (=> (= B22 bot_bot_set_int) (= A24 bot_bot_set_nat)) (= (@ (@ bNF_We8539870446460111250nt_nat B22) B1) (@ (@ image_392418694813850429nt_nat (@ (@ (@ bNF_We1267465954819736484at_nat B22) F1) F22)) (@ (@ bNF_We7538026264050006418at_int A24) A13)))))))) (forall ((X2 product_unit)) (= (@ (@ image_4337914935673063477t_unit (lambda ((Uu char)) X2)) top_top_set_char) (@ (@ insert_Product_unit X2) bot_bo3957492148770167129t_unit))) (forall ((A4 set_int) (F (-> int int)) (A int)) (let ((_let_1 (@ image_int_int F))) (let ((_let_2 (@ _let_1 A4))) (=> (not (= A4 bot_bot_set_int)) (=> (@ condit2212336002400062152ve_int _let_2) (= (@ complete_Sup_Sup_int (@ _let_1 (@ (@ insert_int A) A4))) (@ (@ sup_sup_int (@ F A)) (@ complete_Sup_Sup_int _let_2)))))))) (forall ((A4 set_nat) (C set_char)) (let ((_let_1 (= A4 bot_bot_set_nat))) (and (=> (not _let_1) (= (@ comple7965528767983648192t_char (@ (@ image_nat_set_char (lambda ((Y5 nat)) C)) A4)) C)) (=> _let_1 (= (@ comple7965528767983648192t_char (@ (@ image_nat_set_char (lambda ((Y5 nat)) C)) A4)) top_top_set_char))))) (forall ((F (-> nat rat)) (A4 set_nat) (B5 set_nat)) (let ((_let_1 (@ image_nat_rat F))) (=> (@ (@ inj_on_nat_rat F) top_top_set_nat) (= (@ (@ ord_less_eq_set_rat (@ _let_1 A4)) (@ _let_1 B5)) (@ (@ ord_less_eq_set_nat A4) B5))))) (forall ((X2 Bool) (A4 set_o) (F (-> Bool Bool)) (Y3 Bool)) (let ((_let_1 (@ image_o_o F))) (let ((_let_2 (@ (@ image_o_o (@ (@ (@ fun_upd_o_o F) X2) Y3)) A4))) (let ((_let_3 (@ (@ member_o X2) A4))) (and (=> _let_3 (= _let_2 (@ (@ insert_o Y3) (@ _let_1 (@ (@ minus_minus_set_o A4) (@ (@ insert_o X2) bot_bot_set_o)))))) (=> (not _let_3) (= _let_2 (@ _let_1 A4)))))))) (forall ((A4 set_nat) (B5 set_nat) (C3 (-> nat nat)) (D (-> nat nat)) (Inf (-> set_nat nat))) (=> (= A4 B5) (=> (forall ((X nat)) (=> (@ (@ member_nat X) B5) (= (@ C3 X) (@ D X)))) (= (@ Inf (@ (@ image_nat_nat C3) A4)) (@ Inf (@ (@ image_nat_nat D) B5)))))) (forall ((A4 set_nat) (F (-> nat nat)) (B5 set_nat)) (= (@ (@ ord_le3146513528884898305at_nat (@ (@ bNF_Gr_nat_nat A4) F)) (@ (@ produc457027306803732586at_nat A4) (lambda ((Uu nat)) B5))) (@ (@ ord_less_eq_set_nat (@ (@ image_nat_nat F) A4)) B5))) (forall ((Rep (-> Bool Bool)) (Abs (-> Bool Bool)) (M (-> nat Bool)) (M1 (-> Bool Bool)) (M2 (-> nat Bool)) (F (-> Bool Bool)) (G (-> nat nat))) (=> (@ (@ (@ type_definition_o_o Rep) Abs) top_top_set_o) (=> (= M (@ (@ comp_o_o_nat M1) M2)) (= (@ (@ comp_nat_o_nat (@ (@ comp_o_o_nat F) M)) G) (@ (@ comp_o_o_nat (@ (@ comp_o_o_o (@ (@ comp_o_o_o F) M1)) Rep)) (@ (@ comp_nat_o_nat (@ (@ comp_o_o_nat Abs) M2)) G)))))) (forall ((A4 (-> Bool set_Pr8693737435421807431at_nat))) (= (@ comple2748534634209756852at_nat (@ (@ image_8493167801588156084at_nat A4) top_top_set_o)) (@ (@ sup_su718114333110466843at_nat (@ A4 true)) (@ A4 false)))) (forall ((I int) (A4 set_int) (F (-> int set_nat)) (U set_nat)) (=> (@ (@ member_int I) A4) (=> (@ (@ ord_less_eq_set_nat (@ F I)) U) (@ (@ ord_less_eq_set_nat (@ comple7806235888213564991et_nat (@ (@ image_int_set_nat F) A4))) U))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) 10.23/10.44 % SZS output end Proof for theBenchmark 10.23/10.44 EOF