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% This file was generated by Isabelle (most likely Sledgehammer)
% 2020-12-16 14:19:25.787

% Could-be-implicit typings (21)
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% Explicit typings (75)
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thf(sy_c_DefAss_OhyperUn_001t__List__Olist_It__String__Ochar_J, type,
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thf(sy_c_DefAss_Ohyper__subset_001t__List__Olist_It__String__Ochar_J, type,
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thf(sy_c_Exceptions_Opreallocated, type,
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thf(sy_c_Expr_Oexp_OFAcc_001t__List__Olist_It__String__Ochar_J, type,
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thf(sy_c_Objects_Oinit__fields, type,
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thf(sy_c_Orderings_Obot__class_Obot_001_062_I_062_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_M_062_I_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_M_Eo_J_J, type,
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thf(sy_c_Orderings_Obot__class_Obot_001_062_It__List__Olist_It__String__Ochar_J_M_062_I_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_M_Eo_J_J, type,
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thf(sy_c_Orderings_Obot__class_Obot_001_062_It__List__Olist_It__String__Ochar_J_M_062_It__List__Olist_It__String__Ochar_J_M_Eo_J_J, type,
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thf(sy_c_member_001t__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_M_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_J, type,
    member652041809on_val : produc515445032on_val > set_Pr723149704on_val > $o).
thf(sy_c_member_001t__Product____Type__Oprod_It__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_Mt__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_M_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J, type,
    member1888679917on_val : produc1097884484on_val > set_Pr556513572on_val > $o).
thf(sy_c_member_001t__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J, type,
    member1296415951on_val : produc266837688on_val > set_Pr2075231726on_val > $o).
thf(sy_c_member_001t__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J, type,
    member89690956t_char : produc1257910179t_char > set_Pr164112643t_char > $o).
thf(sy_c_member_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_Mt__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_M_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_Mt__Product____Type__Oprod_It__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_Mt__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_M_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J, type,
    member354538064on_val : produc1172664615on_val > set_Pr1189492743on_val > $o).
thf(sy_v_C, type,
    c : list_char).
thf(sy_v_FDTs, type,
    fDTs : list_P1991792281har_ty).
thf(sy_v_P, type,
    p : list_P1234162913t_char).
thf(sy_v_a, type,
    a : nat).
thf(sy_v_h_Ha, type,
    h_a : nat > option2118145160on_val).
thf(sy_v_ha, type,
    ha : nat > option2118145160on_val).
thf(sy_v_la, type,
    la : list_char > option_val).

% Relevant facts (185)
thf(fact_0_exp_Oinject_I1_J, axiom,
    ((![X1 : list_char, Y1 : list_char]: (((new_list_char @ X1) = (new_list_char @ Y1)) = (X1 = Y1))))). % exp.inject(1)
thf(fact_1_val_Oinject_I3_J, axiom,
    ((![X5 : nat, Y5 : nat]: (((addr @ X5) = (addr @ Y5)) = (X5 = Y5))))). % val.inject(3)
thf(fact_2_fun__upd__upd, axiom,
    ((![F : nat > option2118145160on_val, X : nat, Y : option2118145160on_val, Z : option2118145160on_val]: ((fun_up262443479on_val @ (fun_up262443479on_val @ F @ X @ Y) @ X @ Z) = (fun_up262443479on_val @ F @ X @ Z))))). % fun_upd_upd
thf(fact_3_fun__upd__triv, axiom,
    ((![F : nat > option2118145160on_val, X : nat]: ((fun_up262443479on_val @ F @ X @ (F @ X)) = F)))). % fun_upd_triv
thf(fact_4_fun__upd__apply, axiom,
    ((fun_up262443479on_val = (^[F2 : nat > option2118145160on_val]: (^[X2 : nat]: (^[Y2 : option2118145160on_val]: (^[Z2 : nat]: (if_opt451925058on_val @ (Z2 = X2) @ Y2 @ (F2 @ Z2))))))))). % fun_upd_apply
thf(fact_5_sqUn__lem, axiom,
    ((![A : option_set_list_char, A2 : option_set_list_char, B : option_set_list_char]: ((hyper_1448788648t_char @ A @ A2) => (hyper_1448788648t_char @ (hyperUn_list_char @ A @ B) @ (hyperUn_list_char @ A2 @ B)))))). % sqUn_lem
thf(fact_6_exp_Oinject_I3_J, axiom,
    ((![X3 : val, Y3 : val]: (((val_list_char @ X3) = (val_list_char @ Y3)) = (X3 = Y3))))). % exp.inject(3)
thf(fact_7_option_Oinject, axiom,
    ((![X22 : nat, Y22 : nat]: (((some_nat @ X22) = (some_nat @ Y22)) = (X22 = Y22))))). % option.inject
thf(fact_8_option_Oinject, axiom,
    ((![X22 : produc266837688on_val, Y22 : produc266837688on_val]: (((some_P1299442195on_val @ X22) = (some_P1299442195on_val @ Y22)) = (X22 = Y22))))). % option.inject
thf(fact_9_option_Oinject, axiom,
    ((![X22 : set_list_char, Y22 : set_list_char]: (((some_set_list_char @ X22) = (some_set_list_char @ Y22)) = (X22 = Y22))))). % option.inject
thf(fact_10_option_Oinject, axiom,
    ((![X22 : val, Y22 : val]: (((some_val @ X22) = (some_val @ Y22)) = (X22 = Y22))))). % option.inject
thf(fact_11_prod_Oinject, axiom,
    ((![X1 : list_char, X22 : produc1257910179t_char > option_val, Y1 : list_char, Y22 : produc1257910179t_char > option_val]: (((produc904988266on_val @ X1 @ X22) = (produc904988266on_val @ Y1 @ Y22)) = (((X1 = Y1)) & ((X22 = Y22))))))). % prod.inject
thf(fact_12_prod_Oinject, axiom,
    ((![X1 : produc1097884484on_val, X22 : produc1097884484on_val, Y1 : produc1097884484on_val, Y22 : produc1097884484on_val]: (((produc1069526295on_val @ X1 @ X22) = (produc1069526295on_val @ Y1 @ Y22)) = (((X1 = Y1)) & ((X22 = Y22))))))). % prod.inject
thf(fact_13_prod_Oinject, axiom,
    ((![X1 : exp_list_char, X22 : produc515445032on_val, Y1 : exp_list_char, Y22 : produc515445032on_val]: (((produc2023458740on_val @ X1 @ X22) = (produc2023458740on_val @ Y1 @ Y22)) = (((X1 = Y1)) & ((X22 = Y22))))))). % prod.inject
thf(fact_14_prod_Oinject, axiom,
    ((![X1 : nat > option2118145160on_val, X22 : list_char > option_val, Y1 : nat > option2118145160on_val, Y22 : list_char > option_val]: (((produc52622304on_val @ X1 @ X22) = (produc52622304on_val @ Y1 @ Y22)) = (((X1 = Y1)) & ((X22 = Y22))))))). % prod.inject
thf(fact_15_prod_Oinject, axiom,
    ((![X1 : list_char, X22 : list_char, Y1 : list_char, Y22 : list_char]: (((produc1304532571t_char @ X1 @ X22) = (produc1304532571t_char @ Y1 @ Y22)) = (((X1 = Y1)) & ((X22 = Y22))))))). % prod.inject
thf(fact_16_old_Oprod_Oinject, axiom,
    ((![A3 : list_char, B2 : produc1257910179t_char > option_val, A4 : list_char, B3 : produc1257910179t_char > option_val]: (((produc904988266on_val @ A3 @ B2) = (produc904988266on_val @ A4 @ B3)) = (((A3 = A4)) & ((B2 = B3))))))). % old.prod.inject
thf(fact_17_old_Oprod_Oinject, axiom,
    ((![A3 : produc1097884484on_val, B2 : produc1097884484on_val, A4 : produc1097884484on_val, B3 : produc1097884484on_val]: (((produc1069526295on_val @ A3 @ B2) = (produc1069526295on_val @ A4 @ B3)) = (((A3 = A4)) & ((B2 = B3))))))). % old.prod.inject
thf(fact_18_old_Oprod_Oinject, axiom,
    ((![A3 : exp_list_char, B2 : produc515445032on_val, A4 : exp_list_char, B3 : produc515445032on_val]: (((produc2023458740on_val @ A3 @ B2) = (produc2023458740on_val @ A4 @ B3)) = (((A3 = A4)) & ((B2 = B3))))))). % old.prod.inject
thf(fact_19_old_Oprod_Oinject, axiom,
    ((![A3 : nat > option2118145160on_val, B2 : list_char > option_val, A4 : nat > option2118145160on_val, B3 : list_char > option_val]: (((produc52622304on_val @ A3 @ B2) = (produc52622304on_val @ A4 @ B3)) = (((A3 = A4)) & ((B2 = B3))))))). % old.prod.inject
thf(fact_20_old_Oprod_Oinject, axiom,
    ((![A3 : list_char, B2 : list_char, A4 : list_char, B3 : list_char]: (((produc1304532571t_char @ A3 @ B2) = (produc1304532571t_char @ A4 @ B3)) = (((A3 = A4)) & ((B2 = B3))))))). % old.prod.inject
thf(fact_21_domD, axiom,
    ((![A3 : produc1172664615on_val, M : produc1172664615on_val > option_nat]: ((member354538064on_val @ A3 @ (dom_Pr691387813al_nat @ M)) => (?[B4 : nat]: ((M @ A3) = (some_nat @ B4))))))). % domD
thf(fact_22_domD, axiom,
    ((![A3 : produc1172664615on_val, M : produc1172664615on_val > option2118145160on_val]: ((member354538064on_val @ A3 @ (dom_Pr269338893on_val @ M)) => (?[B4 : produc266837688on_val]: ((M @ A3) = (some_P1299442195on_val @ B4))))))). % domD
thf(fact_23_domD, axiom,
    ((![A3 : produc1172664615on_val, M : produc1172664615on_val > option_set_list_char]: ((member354538064on_val @ A3 @ (dom_Pr1335625324t_char @ M)) => (?[B4 : set_list_char]: ((M @ A3) = (some_set_list_char @ B4))))))). % domD
thf(fact_24_domD, axiom,
    ((![A3 : list_char, M : list_char > option_val]: ((member_list_char @ A3 @ (dom_list_char_val @ M)) => (?[B4 : val]: ((M @ A3) = (some_val @ B4))))))). % domD
thf(fact_25_domD, axiom,
    ((![A3 : produc1172664615on_val, M : produc1172664615on_val > option_val]: ((member354538064on_val @ A3 @ (dom_Pr162898261al_val @ M)) => (?[B4 : val]: ((M @ A3) = (some_val @ B4))))))). % domD
thf(fact_26_domI, axiom,
    ((![M : produc1172664615on_val > option_nat, A3 : produc1172664615on_val, B2 : nat]: (((M @ A3) = (some_nat @ B2)) => (member354538064on_val @ A3 @ (dom_Pr691387813al_nat @ M)))))). % domI
thf(fact_27_domI, axiom,
    ((![M : produc1172664615on_val > option2118145160on_val, A3 : produc1172664615on_val, B2 : produc266837688on_val]: (((M @ A3) = (some_P1299442195on_val @ B2)) => (member354538064on_val @ A3 @ (dom_Pr269338893on_val @ M)))))). % domI
thf(fact_28_domI, axiom,
    ((![M : produc1172664615on_val > option_set_list_char, A3 : produc1172664615on_val, B2 : set_list_char]: (((M @ A3) = (some_set_list_char @ B2)) => (member354538064on_val @ A3 @ (dom_Pr1335625324t_char @ M)))))). % domI
thf(fact_29_domI, axiom,
    ((![M : list_char > option_val, A3 : list_char, B2 : val]: (((M @ A3) = (some_val @ B2)) => (member_list_char @ A3 @ (dom_list_char_val @ M)))))). % domI
thf(fact_30_domI, axiom,
    ((![M : produc1172664615on_val > option_val, A3 : produc1172664615on_val, B2 : val]: (((M @ A3) = (some_val @ B2)) => (member354538064on_val @ A3 @ (dom_Pr162898261al_val @ M)))))). % domI
thf(fact_31_old_Oprod_Oinducts, axiom,
    ((![P : produc266837688on_val > $o, Prod : produc266837688on_val]: ((![A5 : list_char, B4 : produc1257910179t_char > option_val]: (P @ (produc904988266on_val @ A5 @ B4))) => (P @ Prod))))). % old.prod.inducts
thf(fact_32_old_Oprod_Oinducts, axiom,
    ((![P : produc1172664615on_val > $o, Prod : produc1172664615on_val]: ((![A5 : produc1097884484on_val, B4 : produc1097884484on_val]: (P @ (produc1069526295on_val @ A5 @ B4))) => (P @ Prod))))). % old.prod.inducts
thf(fact_33_old_Oprod_Oinducts, axiom,
    ((![P : produc1097884484on_val > $o, Prod : produc1097884484on_val]: ((![A5 : exp_list_char, B4 : produc515445032on_val]: (P @ (produc2023458740on_val @ A5 @ B4))) => (P @ Prod))))). % old.prod.inducts
thf(fact_34_old_Oprod_Oinducts, axiom,
    ((![P : produc515445032on_val > $o, Prod : produc515445032on_val]: ((![A5 : nat > option2118145160on_val, B4 : list_char > option_val]: (P @ (produc52622304on_val @ A5 @ B4))) => (P @ Prod))))). % old.prod.inducts
thf(fact_35_old_Oprod_Oinducts, axiom,
    ((![P : produc1257910179t_char > $o, Prod : produc1257910179t_char]: ((![A5 : list_char, B4 : list_char]: (P @ (produc1304532571t_char @ A5 @ B4))) => (P @ Prod))))). % old.prod.inducts
thf(fact_36_old_Oprod_Oexhaust, axiom,
    ((![Y : produc266837688on_val]: (~ ((![A5 : list_char, B4 : produc1257910179t_char > option_val]: (~ ((Y = (produc904988266on_val @ A5 @ B4)))))))))). % old.prod.exhaust
thf(fact_37_old_Oprod_Oexhaust, axiom,
    ((![Y : produc1172664615on_val]: (~ ((![A5 : produc1097884484on_val, B4 : produc1097884484on_val]: (~ ((Y = (produc1069526295on_val @ A5 @ B4)))))))))). % old.prod.exhaust
thf(fact_38_old_Oprod_Oexhaust, axiom,
    ((![Y : produc1097884484on_val]: (~ ((![A5 : exp_list_char, B4 : produc515445032on_val]: (~ ((Y = (produc2023458740on_val @ A5 @ B4)))))))))). % old.prod.exhaust
thf(fact_39_old_Oprod_Oexhaust, axiom,
    ((![Y : produc515445032on_val]: (~ ((![A5 : nat > option2118145160on_val, B4 : list_char > option_val]: (~ ((Y = (produc52622304on_val @ A5 @ B4)))))))))). % old.prod.exhaust
thf(fact_40_old_Oprod_Oexhaust, axiom,
    ((![Y : produc1257910179t_char]: (~ ((![A5 : list_char, B4 : list_char]: (~ ((Y = (produc1304532571t_char @ A5 @ B4)))))))))). % old.prod.exhaust
thf(fact_41_prod__induct4, axiom,
    ((![P : produc1172664615on_val > $o, X : produc1172664615on_val]: ((![A5 : produc1097884484on_val, B4 : exp_list_char, C : nat > option2118145160on_val, D : list_char > option_val]: (P @ (produc1069526295on_val @ A5 @ (produc2023458740on_val @ B4 @ (produc52622304on_val @ C @ D))))) => (P @ X))))). % prod_induct4
thf(fact_42_prod__induct3, axiom,
    ((![P : produc1172664615on_val > $o, X : produc1172664615on_val]: ((![A5 : produc1097884484on_val, B4 : exp_list_char, C : produc515445032on_val]: (P @ (produc1069526295on_val @ A5 @ (produc2023458740on_val @ B4 @ C)))) => (P @ X))))). % prod_induct3
thf(fact_43_prod__induct3, axiom,
    ((![P : produc1097884484on_val > $o, X : produc1097884484on_val]: ((![A5 : exp_list_char, B4 : nat > option2118145160on_val, C : list_char > option_val]: (P @ (produc2023458740on_val @ A5 @ (produc52622304on_val @ B4 @ C)))) => (P @ X))))). % prod_induct3
thf(fact_44_prod__cases4, axiom,
    ((![Y : produc1172664615on_val]: (~ ((![A5 : produc1097884484on_val, B4 : exp_list_char, C : nat > option2118145160on_val, D : list_char > option_val]: (~ ((Y = (produc1069526295on_val @ A5 @ (produc2023458740on_val @ B4 @ (produc52622304on_val @ C @ D)))))))))))). % prod_cases4
thf(fact_45_prod__cases3, axiom,
    ((![Y : produc1172664615on_val]: (~ ((![A5 : produc1097884484on_val, B4 : exp_list_char, C : produc515445032on_val]: (~ ((Y = (produc1069526295on_val @ A5 @ (produc2023458740on_val @ B4 @ C))))))))))). % prod_cases3
thf(fact_46_prod__cases3, axiom,
    ((![Y : produc1097884484on_val]: (~ ((![A5 : exp_list_char, B4 : nat > option2118145160on_val, C : list_char > option_val]: (~ ((Y = (produc2023458740on_val @ A5 @ (produc52622304on_val @ B4 @ C))))))))))). % prod_cases3
thf(fact_47_Pair__inject, axiom,
    ((![A3 : list_char, B2 : produc1257910179t_char > option_val, A4 : list_char, B3 : produc1257910179t_char > option_val]: (((produc904988266on_val @ A3 @ B2) = (produc904988266on_val @ A4 @ B3)) => (~ (((A3 = A4) => (~ ((B2 = B3)))))))))). % Pair_inject
thf(fact_48_Pair__inject, axiom,
    ((![A3 : produc1097884484on_val, B2 : produc1097884484on_val, A4 : produc1097884484on_val, B3 : produc1097884484on_val]: (((produc1069526295on_val @ A3 @ B2) = (produc1069526295on_val @ A4 @ B3)) => (~ (((A3 = A4) => (~ ((B2 = B3)))))))))). % Pair_inject
thf(fact_49_Pair__inject, axiom,
    ((![A3 : exp_list_char, B2 : produc515445032on_val, A4 : exp_list_char, B3 : produc515445032on_val]: (((produc2023458740on_val @ A3 @ B2) = (produc2023458740on_val @ A4 @ B3)) => (~ (((A3 = A4) => (~ ((B2 = B3)))))))))). % Pair_inject
thf(fact_50_Pair__inject, axiom,
    ((![A3 : nat > option2118145160on_val, B2 : list_char > option_val, A4 : nat > option2118145160on_val, B3 : list_char > option_val]: (((produc52622304on_val @ A3 @ B2) = (produc52622304on_val @ A4 @ B3)) => (~ (((A3 = A4) => (~ ((B2 = B3)))))))))). % Pair_inject
thf(fact_51_Pair__inject, axiom,
    ((![A3 : list_char, B2 : list_char, A4 : list_char, B3 : list_char]: (((produc1304532571t_char @ A3 @ B2) = (produc1304532571t_char @ A4 @ B3)) => (~ (((A3 = A4) => (~ ((B2 = B3)))))))))). % Pair_inject
thf(fact_52_prod__cases, axiom,
    ((![P : produc266837688on_val > $o, P2 : produc266837688on_val]: ((![A5 : list_char, B4 : produc1257910179t_char > option_val]: (P @ (produc904988266on_val @ A5 @ B4))) => (P @ P2))))). % prod_cases
thf(fact_53_prod__cases, axiom,
    ((![P : produc1172664615on_val > $o, P2 : produc1172664615on_val]: ((![A5 : produc1097884484on_val, B4 : produc1097884484on_val]: (P @ (produc1069526295on_val @ A5 @ B4))) => (P @ P2))))). % prod_cases
thf(fact_54_prod__cases, axiom,
    ((![P : produc1097884484on_val > $o, P2 : produc1097884484on_val]: ((![A5 : exp_list_char, B4 : produc515445032on_val]: (P @ (produc2023458740on_val @ A5 @ B4))) => (P @ P2))))). % prod_cases
thf(fact_55_prod__cases, axiom,
    ((![P : produc515445032on_val > $o, P2 : produc515445032on_val]: ((![A5 : nat > option2118145160on_val, B4 : list_char > option_val]: (P @ (produc52622304on_val @ A5 @ B4))) => (P @ P2))))). % prod_cases
thf(fact_56_prod__cases, axiom,
    ((![P : produc1257910179t_char > $o, P2 : produc1257910179t_char]: ((![A5 : list_char, B4 : list_char]: (P @ (produc1304532571t_char @ A5 @ B4))) => (P @ P2))))). % prod_cases
thf(fact_57_surj__pair, axiom,
    ((![P2 : produc266837688on_val]: (?[X4 : list_char, Y4 : produc1257910179t_char > option_val]: (P2 = (produc904988266on_val @ X4 @ Y4)))))). % surj_pair
thf(fact_58_surj__pair, axiom,
    ((![P2 : produc1172664615on_val]: (?[X4 : produc1097884484on_val, Y4 : produc1097884484on_val]: (P2 = (produc1069526295on_val @ X4 @ Y4)))))). % surj_pair
thf(fact_59_surj__pair, axiom,
    ((![P2 : produc1097884484on_val]: (?[X4 : exp_list_char, Y4 : produc515445032on_val]: (P2 = (produc2023458740on_val @ X4 @ Y4)))))). % surj_pair
thf(fact_60_surj__pair, axiom,
    ((![P2 : produc515445032on_val]: (?[X4 : nat > option2118145160on_val, Y4 : list_char > option_val]: (P2 = (produc52622304on_val @ X4 @ Y4)))))). % surj_pair
thf(fact_61_surj__pair, axiom,
    ((![P2 : produc1257910179t_char]: (?[X4 : list_char, Y4 : list_char]: (P2 = (produc1304532571t_char @ X4 @ Y4)))))). % surj_pair
thf(fact_62_fun__upd__idem__iff, axiom,
    ((![F : nat > option2118145160on_val, X : nat, Y : option2118145160on_val]: (((fun_up262443479on_val @ F @ X @ Y) = F) = ((F @ X) = Y))))). % fun_upd_idem_iff
thf(fact_63_fun__upd__twist, axiom,
    ((![A3 : nat, C2 : nat, M : nat > option2118145160on_val, B2 : option2118145160on_val, D2 : option2118145160on_val]: ((~ ((A3 = C2))) => ((fun_up262443479on_val @ (fun_up262443479on_val @ M @ A3 @ B2) @ C2 @ D2) = (fun_up262443479on_val @ (fun_up262443479on_val @ M @ C2 @ D2) @ A3 @ B2)))))). % fun_upd_twist
thf(fact_64_fun__upd__other, axiom,
    ((![Z : nat, X : nat, F : nat > option2118145160on_val, Y : option2118145160on_val]: ((~ ((Z = X))) => ((fun_up262443479on_val @ F @ X @ Y @ Z) = (F @ Z)))))). % fun_upd_other
thf(fact_65_fun__upd__same, axiom,
    ((![F : nat > option2118145160on_val, X : nat, Y : option2118145160on_val]: ((fun_up262443479on_val @ F @ X @ Y @ X) = Y)))). % fun_upd_same
thf(fact_66_fun__upd__idem, axiom,
    ((![F : nat > option2118145160on_val, X : nat, Y : option2118145160on_val]: (((F @ X) = Y) => ((fun_up262443479on_val @ F @ X @ Y) = F))))). % fun_upd_idem
thf(fact_67_fun__upd__eqD, axiom,
    ((![F : nat > option2118145160on_val, X : nat, Y : option2118145160on_val, G : nat > option2118145160on_val, Z : option2118145160on_val]: (((fun_up262443479on_val @ F @ X @ Y) = (fun_up262443479on_val @ G @ X @ Z)) => (Y = Z))))). % fun_upd_eqD
thf(fact_68_fun__upd__def, axiom,
    ((fun_up262443479on_val = (^[F2 : nat > option2118145160on_val]: (^[A6 : nat]: (^[B5 : option2118145160on_val]: (^[X2 : nat]: (if_opt451925058on_val @ (X2 = A6) @ B5 @ (F2 @ X2))))))))). % fun_upd_def
thf(fact_69_hyperUn__assoc, axiom,
    ((![A : option_set_list_char, B : option_set_list_char, C3 : option_set_list_char]: ((hyperUn_list_char @ (hyperUn_list_char @ A @ B) @ C3) = (hyperUn_list_char @ A @ (hyperUn_list_char @ B @ C3)))))). % hyperUn_assoc
thf(fact_70_map__upd__Some__unfold, axiom,
    ((![M : nat > option2118145160on_val, A3 : nat, B2 : produc266837688on_val, X : nat, Y : produc266837688on_val]: (((fun_up262443479on_val @ M @ A3 @ (some_P1299442195on_val @ B2) @ X) = (some_P1299442195on_val @ Y)) = (((((X = A3)) & ((B2 = Y)))) | ((((~ ((X = A3)))) & (((M @ X) = (some_P1299442195on_val @ Y)))))))))). % map_upd_Some_unfold
thf(fact_71_map__upd__triv, axiom,
    ((![T : nat > option2118145160on_val, K : nat, X : produc266837688on_val]: (((T @ K) = (some_P1299442195on_val @ X)) => ((fun_up262443479on_val @ T @ K @ (some_P1299442195on_val @ X)) = T))))). % map_upd_triv
thf(fact_72_map__upd__eqD1, axiom,
    ((![M : nat > option2118145160on_val, A3 : nat, X : produc266837688on_val, N : nat > option2118145160on_val, Y : produc266837688on_val]: (((fun_up262443479on_val @ M @ A3 @ (some_P1299442195on_val @ X)) = (fun_up262443479on_val @ N @ A3 @ (some_P1299442195on_val @ Y))) => (X = Y))))). % map_upd_eqD1
thf(fact_73_exp_Odistinct_I3_J, axiom,
    ((![X1 : list_char, X3 : val]: (~ (((new_list_char @ X1) = (val_list_char @ X3))))))). % exp.distinct(3)
thf(fact_74_red__reds_ORedNew, axiom,
    ((![H : nat > option2118145160on_val, A3 : nat, P : list_P1234162913t_char, C3 : list_char, FDTs : list_P1991792281har_ty, H2 : nat > option2118145160on_val, L : list_char > option_val]: (((new_Addr @ H) = (some_nat @ A3)) => ((fields1441617180t_char @ P @ C3 @ FDTs) => ((H2 = (fun_up262443479on_val @ H @ A3 @ (some_P1299442195on_val @ (produc904988266on_val @ C3 @ (init_fields @ FDTs))))) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (new_list_char @ C3) @ (produc52622304on_val @ H @ L)) @ (produc2023458740on_val @ (val_list_char @ (addr @ A3)) @ (produc52622304on_val @ H2 @ L))) @ (red @ P)))))))). % red_reds.RedNew
thf(fact_75_redp__redsp_ORedNew, axiom,
    ((![H : nat > option2118145160on_val, A3 : nat, P : list_P1234162913t_char, C3 : list_char, FDTs : list_P1991792281har_ty, H2 : nat > option2118145160on_val, L : list_char > option_val]: (((new_Addr @ H) = (some_nat @ A3)) => ((fields1441617180t_char @ P @ C3 @ FDTs) => ((H2 = (fun_up262443479on_val @ H @ A3 @ (some_P1299442195on_val @ (produc904988266on_val @ C3 @ (init_fields @ FDTs))))) => (redp @ P @ (new_list_char @ C3) @ (produc52622304on_val @ H @ L) @ (val_list_char @ (addr @ A3)) @ (produc52622304on_val @ H2 @ L)))))))). % redp_redsp.RedNew
thf(fact_76_New, axiom,
    ((![H : nat > option2118145160on_val, A3 : nat, P : list_P1234162913t_char, C3 : list_char, FDTs : list_P1991792281har_ty, H2 : nat > option2118145160on_val, L : list_char > option_val]: (((new_Addr @ H) = (some_nat @ A3)) => ((fields1441617180t_char @ P @ C3 @ FDTs) => ((H2 = (fun_up262443479on_val @ H @ A3 @ (some_P1299442195on_val @ (produc904988266on_val @ C3 @ (init_fields @ FDTs))))) => (eval @ P @ (new_list_char @ C3) @ (produc52622304on_val @ H @ L) @ (val_list_char @ (addr @ A3)) @ (produc52622304on_val @ H2 @ L)))))))). % New
thf(fact_77_the__Addr_Osimps, axiom,
    ((![A3 : nat]: ((the_Addr @ (addr @ A3)) = A3)))). % the_Addr.simps
thf(fact_78_pred__equals__eq2, axiom,
    ((![R : set_Pr2075231726on_val, S : set_Pr2075231726on_val]: (((^[X2 : list_char]: (^[Y2 : produc1257910179t_char > option_val]: (member1296415951on_val @ (produc904988266on_val @ X2 @ Y2) @ R))) = (^[X2 : list_char]: (^[Y2 : produc1257910179t_char > option_val]: (member1296415951on_val @ (produc904988266on_val @ X2 @ Y2) @ S)))) = (R = S))))). % pred_equals_eq2
thf(fact_79_pred__equals__eq2, axiom,
    ((![R : set_Pr1189492743on_val, S : set_Pr1189492743on_val]: (((^[X2 : produc1097884484on_val]: (^[Y2 : produc1097884484on_val]: (member354538064on_val @ (produc1069526295on_val @ X2 @ Y2) @ R))) = (^[X2 : produc1097884484on_val]: (^[Y2 : produc1097884484on_val]: (member354538064on_val @ (produc1069526295on_val @ X2 @ Y2) @ S)))) = (R = S))))). % pred_equals_eq2
thf(fact_80_pred__equals__eq2, axiom,
    ((![R : set_Pr556513572on_val, S : set_Pr556513572on_val]: (((^[X2 : exp_list_char]: (^[Y2 : produc515445032on_val]: (member1888679917on_val @ (produc2023458740on_val @ X2 @ Y2) @ R))) = (^[X2 : exp_list_char]: (^[Y2 : produc515445032on_val]: (member1888679917on_val @ (produc2023458740on_val @ X2 @ Y2) @ S)))) = (R = S))))). % pred_equals_eq2
thf(fact_81_pred__equals__eq2, axiom,
    ((![R : set_Pr723149704on_val, S : set_Pr723149704on_val]: (((^[X2 : nat > option2118145160on_val]: (^[Y2 : list_char > option_val]: (member652041809on_val @ (produc52622304on_val @ X2 @ Y2) @ R))) = (^[X2 : nat > option2118145160on_val]: (^[Y2 : list_char > option_val]: (member652041809on_val @ (produc52622304on_val @ X2 @ Y2) @ S)))) = (R = S))))). % pred_equals_eq2
thf(fact_82_pred__equals__eq2, axiom,
    ((![R : set_Pr164112643t_char, S : set_Pr164112643t_char]: (((^[X2 : list_char]: (^[Y2 : list_char]: (member89690956t_char @ (produc1304532571t_char @ X2 @ Y2) @ R))) = (^[X2 : list_char]: (^[Y2 : list_char]: (member89690956t_char @ (produc1304532571t_char @ X2 @ Y2) @ S)))) = (R = S))))). % pred_equals_eq2
thf(fact_83_mem__Collect__eq, axiom,
    ((![A3 : produc1172664615on_val, P : produc1172664615on_val > $o]: ((member354538064on_val @ A3 @ (collec2055896722on_val @ P)) = (P @ A3))))). % mem_Collect_eq
thf(fact_84_Collect__mem__eq, axiom,
    ((![A : set_Pr1189492743on_val]: ((collec2055896722on_val @ (^[X2 : produc1172664615on_val]: (member354538064on_val @ X2 @ A))) = A)))). % Collect_mem_eq
thf(fact_85_has__fields__fun, axiom,
    ((![P : list_P1234162913t_char, C3 : list_char, FDTs : list_P1991792281har_ty, FDTs2 : list_P1991792281har_ty]: ((fields1441617180t_char @ P @ C3 @ FDTs) => ((fields1441617180t_char @ P @ C3 @ FDTs2) => (FDTs2 = FDTs)))))). % has_fields_fun
thf(fact_86__092_060A_062_Osimps_I1_J, axiom,
    ((![C3 : list_char]: ((a_list_char @ (new_list_char @ C3)) = (some_set_list_char @ bot_bo1263509675t_char))))). % \<A>.simps(1)
thf(fact_87_oconf__init__fields, axiom,
    ((![P : list_P1234162913t_char, C3 : list_char, FDTs : list_P1991792281har_ty, H : nat > option2118145160on_val]: ((fields1441617180t_char @ P @ C3 @ FDTs) => (oconf_454120169t_char @ P @ H @ (produc904988266on_val @ C3 @ (init_fields @ FDTs))))))). % oconf_init_fields
thf(fact_88_redp__red__eq, axiom,
    ((redp = (^[P3 : list_P1234162913t_char]: (^[X2 : exp_list_char]: (^[Y2 : produc515445032on_val]: (^[Z2 : exp_list_char]: (^[Aa : produc515445032on_val]: (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ X2 @ Y2) @ (produc2023458740on_val @ Z2 @ Aa)) @ (red @ P3)))))))))). % redp_red_eq
thf(fact_89_eval__cases_I2_J, axiom,
    ((![P : list_P1234162913t_char, V : val, S2 : produc515445032on_val, E : exp_list_char, S3 : produc515445032on_val]: ((eval @ P @ (val_list_char @ V) @ S2 @ E @ S3) => (~ (((E = (val_list_char @ V)) => (~ ((S3 = S2)))))))))). % eval_cases(2)
thf(fact_90_Val, axiom,
    ((![P : list_P1234162913t_char, V : val, S2 : produc515445032on_val]: (eval @ P @ (val_list_char @ V) @ S2 @ (val_list_char @ V) @ S2)))). % Val
thf(fact_91__092_060A_062_Osimps_I3_J, axiom,
    ((![V : val]: ((a_list_char @ (val_list_char @ V)) = (some_set_list_char @ bot_bo1263509675t_char))))). % \<A>.simps(3)
thf(fact_92_all__not__in__conv, axiom,
    ((![A : set_Pr1189492743on_val]: ((![X2 : produc1172664615on_val]: (~ ((member354538064on_val @ X2 @ A)))) = (A = bot_bo1575563891on_val))))). % all_not_in_conv
thf(fact_93_empty__iff, axiom,
    ((![C2 : produc1172664615on_val]: (~ ((member354538064on_val @ C2 @ bot_bo1575563891on_val)))))). % empty_iff
thf(fact_94_bot__empty__eq, axiom,
    ((bot_bo824611882_val_o = (^[X2 : produc1172664615on_val]: (member354538064on_val @ X2 @ bot_bo1575563891on_val))))). % bot_empty_eq
thf(fact_95_bot__empty__eq2, axiom,
    ((bot_bo352882861_val_o = (^[X2 : list_char]: (^[Y2 : produc1257910179t_char > option_val]: (member1296415951on_val @ (produc904988266on_val @ X2 @ Y2) @ bot_bo932848258on_val)))))). % bot_empty_eq2
thf(fact_96_bot__empty__eq2, axiom,
    ((bot_bo1918180954_val_o = (^[X2 : produc1097884484on_val]: (^[Y2 : produc1097884484on_val]: (member354538064on_val @ (produc1069526295on_val @ X2 @ Y2) @ bot_bo1575563891on_val)))))). % bot_empty_eq2
thf(fact_97_bot__empty__eq2, axiom,
    ((bot_bo1487430909_val_o = (^[X2 : exp_list_char]: (^[Y2 : produc515445032on_val]: (member1888679917on_val @ (produc2023458740on_val @ X2 @ Y2) @ bot_bo1575411088on_val)))))). % bot_empty_eq2
thf(fact_98_bot__empty__eq2, axiom,
    ((bot_bo1949275371_val_o = (^[X2 : nat > option2118145160on_val]: (^[Y2 : list_char > option_val]: (member652041809on_val @ (produc52622304on_val @ X2 @ Y2) @ bot_bo923954676on_val)))))). % bot_empty_eq2
thf(fact_99_bot__empty__eq2, axiom,
    ((bot_bo1359030064char_o = (^[X2 : list_char]: (^[Y2 : list_char]: (member89690956t_char @ (produc1304532571t_char @ X2 @ Y2) @ bot_bo346063215t_char)))))). % bot_empty_eq2
thf(fact_100_emptyE, axiom,
    ((![A3 : produc1172664615on_val]: (~ ((member354538064on_val @ A3 @ bot_bo1575563891on_val)))))). % emptyE
thf(fact_101_equals0D, axiom,
    ((![A : set_Pr1189492743on_val, A3 : produc1172664615on_val]: ((A = bot_bo1575563891on_val) => (~ ((member354538064on_val @ A3 @ A))))))). % equals0D
thf(fact_102_equals0I, axiom,
    ((![A : set_Pr1189492743on_val]: ((![Y4 : produc1172664615on_val]: (~ ((member354538064on_val @ Y4 @ A)))) => (A = bot_bo1575563891on_val))))). % equals0I
thf(fact_103_ex__in__conv, axiom,
    ((![A : set_Pr1189492743on_val]: ((?[X2 : produc1172664615on_val]: (member354538064on_val @ X2 @ A)) = (~ ((A = bot_bo1575563891on_val))))))). % ex_in_conv
thf(fact_104_fields__def2, axiom,
    ((![P : list_P1234162913t_char, C3 : list_char, FDTs : list_P1991792281har_ty]: ((fields1441617180t_char @ P @ C3 @ FDTs) => ((fields1811926268t_char @ P @ C3) = FDTs))))). % fields_def2
thf(fact_105_FAcc, axiom,
    ((![P : list_P1234162913t_char, E2 : exp_list_char, S_0 : produc515445032on_val, A3 : nat, H : nat > option2118145160on_val, L : list_char > option_val, C3 : list_char, Fs : produc1257910179t_char > option_val, F3 : list_char, D3 : list_char, V : val]: ((eval @ P @ E2 @ S_0 @ (val_list_char @ (addr @ A3)) @ (produc52622304on_val @ H @ L)) => (((H @ A3) = (some_P1299442195on_val @ (produc904988266on_val @ C3 @ Fs))) => (((Fs @ (produc1304532571t_char @ F3 @ D3)) = (some_val @ V)) => (eval @ P @ (fAcc_list_char @ E2 @ F3 @ D3) @ S_0 @ (val_list_char @ V) @ (produc52622304on_val @ H @ L)))))))). % FAcc
thf(fact_106_red__lcl__incr, axiom,
    ((![E2 : exp_list_char, H_0 : nat > option2118145160on_val, L_0 : list_char > option_val, E : exp_list_char, H_1 : nat > option2118145160on_val, L_1 : list_char > option_val, P : list_P1234162913t_char]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E2 @ (produc52622304on_val @ H_0 @ L_0)) @ (produc2023458740on_val @ E @ (produc52622304on_val @ H_1 @ L_1))) @ (red @ P)) => (ord_le1836582007t_char @ (dom_list_char_val @ L_0) @ (dom_list_char_val @ L_1)))))). % red_lcl_incr
thf(fact_107_red__hext__incr, axiom,
    ((![E2 : exp_list_char, H : nat > option2118145160on_val, L : list_char > option_val, E : exp_list_char, H2 : nat > option2118145160on_val, L2 : list_char > option_val, P : list_P1234162913t_char]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E2 @ (produc52622304on_val @ H @ L)) @ (produc2023458740on_val @ E @ (produc52622304on_val @ H2 @ L2))) @ (red @ P)) => (hext @ H @ H2))))). % red_hext_incr
thf(fact_108_order__refl, axiom,
    ((![X : set_list_char]: (ord_le1836582007t_char @ X @ X)))). % order_refl
thf(fact_109_subsetI, axiom,
    ((![A : set_Pr1189492743on_val, B : set_Pr1189492743on_val]: ((![X4 : produc1172664615on_val]: ((member354538064on_val @ X4 @ A) => (member354538064on_val @ X4 @ B))) => (ord_le837504935on_val @ A @ B))))). % subsetI
thf(fact_110_subsetI, axiom,
    ((![A : set_list_char, B : set_list_char]: ((![X4 : list_char]: ((member_list_char @ X4 @ A) => (member_list_char @ X4 @ B))) => (ord_le1836582007t_char @ A @ B))))). % subsetI
thf(fact_111_subset__antisym, axiom,
    ((![A : set_list_char, B : set_list_char]: ((ord_le1836582007t_char @ A @ B) => ((ord_le1836582007t_char @ B @ A) => (A = B)))))). % subset_antisym
thf(fact_112_exp_Oinject_I7_J, axiom,
    ((![X71 : exp_list_char, X72 : list_char, X73 : list_char, Y71 : exp_list_char, Y72 : list_char, Y73 : list_char]: (((fAcc_list_char @ X71 @ X72 @ X73) = (fAcc_list_char @ Y71 @ Y72 @ Y73)) = (((X71 = Y71)) & ((((X72 = Y72)) & ((X73 = Y73))))))))). % exp.inject(7)
thf(fact_113_subset__empty, axiom,
    ((![A : set_list_char]: ((ord_le1836582007t_char @ A @ bot_bo1263509675t_char) = (A = bot_bo1263509675t_char))))). % subset_empty
thf(fact_114_empty__subsetI, axiom,
    ((![A : set_list_char]: (ord_le1836582007t_char @ bot_bo1263509675t_char @ A)))). % empty_subsetI
thf(fact_115_bot_Oextremum__uniqueI, axiom,
    ((![A3 : set_list_char]: ((ord_le1836582007t_char @ A3 @ bot_bo1263509675t_char) => (A3 = bot_bo1263509675t_char))))). % bot.extremum_uniqueI
thf(fact_116_bot_Oextremum__unique, axiom,
    ((![A3 : set_list_char]: ((ord_le1836582007t_char @ A3 @ bot_bo1263509675t_char) = (A3 = bot_bo1263509675t_char))))). % bot.extremum_unique
thf(fact_117_bot_Oextremum, axiom,
    ((![A3 : set_list_char]: (ord_le1836582007t_char @ bot_bo1263509675t_char @ A3)))). % bot.extremum
thf(fact_118_in__mono, axiom,
    ((![A : set_Pr1189492743on_val, B : set_Pr1189492743on_val, X : produc1172664615on_val]: ((ord_le837504935on_val @ A @ B) => ((member354538064on_val @ X @ A) => (member354538064on_val @ X @ B)))))). % in_mono
thf(fact_119_in__mono, axiom,
    ((![A : set_list_char, B : set_list_char, X : list_char]: ((ord_le1836582007t_char @ A @ B) => ((member_list_char @ X @ A) => (member_list_char @ X @ B)))))). % in_mono
thf(fact_120_subsetD, axiom,
    ((![A : set_Pr1189492743on_val, B : set_Pr1189492743on_val, C2 : produc1172664615on_val]: ((ord_le837504935on_val @ A @ B) => ((member354538064on_val @ C2 @ A) => (member354538064on_val @ C2 @ B)))))). % subsetD
thf(fact_121_subsetD, axiom,
    ((![A : set_list_char, B : set_list_char, C2 : list_char]: ((ord_le1836582007t_char @ A @ B) => ((member_list_char @ C2 @ A) => (member_list_char @ C2 @ B)))))). % subsetD
thf(fact_122_equalityE, axiom,
    ((![A : set_list_char, B : set_list_char]: ((A = B) => (~ (((ord_le1836582007t_char @ A @ B) => (~ ((ord_le1836582007t_char @ B @ A)))))))))). % equalityE
thf(fact_123_subset__eq, axiom,
    ((ord_le837504935on_val = (^[A7 : set_Pr1189492743on_val]: (^[B6 : set_Pr1189492743on_val]: (![X2 : produc1172664615on_val]: (((member354538064on_val @ X2 @ A7)) => ((member354538064on_val @ X2 @ B6))))))))). % subset_eq
thf(fact_124_subset__eq, axiom,
    ((ord_le1836582007t_char = (^[A7 : set_list_char]: (^[B6 : set_list_char]: (![X2 : list_char]: (((member_list_char @ X2 @ A7)) => ((member_list_char @ X2 @ B6))))))))). % subset_eq
thf(fact_125_equalityD1, axiom,
    ((![A : set_list_char, B : set_list_char]: ((A = B) => (ord_le1836582007t_char @ A @ B))))). % equalityD1
thf(fact_126_equalityD2, axiom,
    ((![A : set_list_char, B : set_list_char]: ((A = B) => (ord_le1836582007t_char @ B @ A))))). % equalityD2
thf(fact_127_subset__iff, axiom,
    ((ord_le837504935on_val = (^[A7 : set_Pr1189492743on_val]: (^[B6 : set_Pr1189492743on_val]: (![T2 : produc1172664615on_val]: (((member354538064on_val @ T2 @ A7)) => ((member354538064on_val @ T2 @ B6))))))))). % subset_iff
thf(fact_128_subset__iff, axiom,
    ((ord_le1836582007t_char = (^[A7 : set_list_char]: (^[B6 : set_list_char]: (![T2 : list_char]: (((member_list_char @ T2 @ A7)) => ((member_list_char @ T2 @ B6))))))))). % subset_iff
thf(fact_129_subset__refl, axiom,
    ((![A : set_list_char]: (ord_le1836582007t_char @ A @ A)))). % subset_refl
thf(fact_130_Collect__mono, axiom,
    ((![P : list_char > $o, Q : list_char > $o]: ((![X4 : list_char]: ((P @ X4) => (Q @ X4))) => (ord_le1836582007t_char @ (collect_list_char @ P) @ (collect_list_char @ Q)))))). % Collect_mono
thf(fact_131_subset__trans, axiom,
    ((![A : set_list_char, B : set_list_char, C3 : set_list_char]: ((ord_le1836582007t_char @ A @ B) => ((ord_le1836582007t_char @ B @ C3) => (ord_le1836582007t_char @ A @ C3)))))). % subset_trans
thf(fact_132_set__eq__subset, axiom,
    (((^[Y6 : set_list_char]: (^[Z3 : set_list_char]: (Y6 = Z3))) = (^[A7 : set_list_char]: (^[B6 : set_list_char]: (((ord_le1836582007t_char @ A7 @ B6)) & ((ord_le1836582007t_char @ B6 @ A7)))))))). % set_eq_subset
thf(fact_133_Collect__subset, axiom,
    ((![A : set_Pr1189492743on_val, P : produc1172664615on_val > $o]: (ord_le837504935on_val @ (collec2055896722on_val @ (^[X2 : produc1172664615on_val]: (((member354538064on_val @ X2 @ A)) & ((P @ X2))))) @ A)))). % Collect_subset
thf(fact_134_Collect__subset, axiom,
    ((![A : set_list_char, P : list_char > $o]: (ord_le1836582007t_char @ (collect_list_char @ (^[X2 : list_char]: (((member_list_char @ X2 @ A)) & ((P @ X2))))) @ A)))). % Collect_subset
thf(fact_135_Collect__mono__iff, axiom,
    ((![P : list_char > $o, Q : list_char > $o]: ((ord_le1836582007t_char @ (collect_list_char @ P) @ (collect_list_char @ Q)) = (![X2 : list_char]: (((P @ X2)) => ((Q @ X2)))))))). % Collect_mono_iff
thf(fact_136_order__subst1, axiom,
    ((![A3 : set_list_char, F : set_list_char > set_list_char, B2 : set_list_char, C2 : set_list_char]: ((ord_le1836582007t_char @ A3 @ (F @ B2)) => ((ord_le1836582007t_char @ B2 @ C2) => ((![X4 : set_list_char, Y4 : set_list_char]: ((ord_le1836582007t_char @ X4 @ Y4) => (ord_le1836582007t_char @ (F @ X4) @ (F @ Y4)))) => (ord_le1836582007t_char @ A3 @ (F @ C2)))))))). % order_subst1
thf(fact_137_order__subst2, axiom,
    ((![A3 : set_list_char, B2 : set_list_char, F : set_list_char > set_list_char, C2 : set_list_char]: ((ord_le1836582007t_char @ A3 @ B2) => ((ord_le1836582007t_char @ (F @ B2) @ C2) => ((![X4 : set_list_char, Y4 : set_list_char]: ((ord_le1836582007t_char @ X4 @ Y4) => (ord_le1836582007t_char @ (F @ X4) @ (F @ Y4)))) => (ord_le1836582007t_char @ (F @ A3) @ C2))))))). % order_subst2
thf(fact_138_ord__eq__le__subst, axiom,
    ((![A3 : set_list_char, F : set_list_char > set_list_char, B2 : set_list_char, C2 : set_list_char]: ((A3 = (F @ B2)) => ((ord_le1836582007t_char @ B2 @ C2) => ((![X4 : set_list_char, Y4 : set_list_char]: ((ord_le1836582007t_char @ X4 @ Y4) => (ord_le1836582007t_char @ (F @ X4) @ (F @ Y4)))) => (ord_le1836582007t_char @ A3 @ (F @ C2)))))))). % ord_eq_le_subst
thf(fact_139_ord__le__eq__subst, axiom,
    ((![A3 : set_list_char, B2 : set_list_char, F : set_list_char > set_list_char, C2 : set_list_char]: ((ord_le1836582007t_char @ A3 @ B2) => (((F @ B2) = C2) => ((![X4 : set_list_char, Y4 : set_list_char]: ((ord_le1836582007t_char @ X4 @ Y4) => (ord_le1836582007t_char @ (F @ X4) @ (F @ Y4)))) => (ord_le1836582007t_char @ (F @ A3) @ C2))))))). % ord_le_eq_subst
thf(fact_140_eq__iff, axiom,
    (((^[Y6 : set_list_char]: (^[Z3 : set_list_char]: (Y6 = Z3))) = (^[X2 : set_list_char]: (^[Y2 : set_list_char]: (((ord_le1836582007t_char @ X2 @ Y2)) & ((ord_le1836582007t_char @ Y2 @ X2)))))))). % eq_iff
thf(fact_141_antisym, axiom,
    ((![X : set_list_char, Y : set_list_char]: ((ord_le1836582007t_char @ X @ Y) => ((ord_le1836582007t_char @ Y @ X) => (X = Y)))))). % antisym
thf(fact_142_eq__refl, axiom,
    ((![X : set_list_char, Y : set_list_char]: ((X = Y) => (ord_le1836582007t_char @ X @ Y))))). % eq_refl
thf(fact_143_order_Otrans, axiom,
    ((![A3 : set_list_char, B2 : set_list_char, C2 : set_list_char]: ((ord_le1836582007t_char @ A3 @ B2) => ((ord_le1836582007t_char @ B2 @ C2) => (ord_le1836582007t_char @ A3 @ C2)))))). % order.trans
thf(fact_144_antisym__conv, axiom,
    ((![Y : set_list_char, X : set_list_char]: ((ord_le1836582007t_char @ Y @ X) => ((ord_le1836582007t_char @ X @ Y) = (X = Y)))))). % antisym_conv
thf(fact_145_order__class_Oorder_Oeq__iff, axiom,
    (((^[Y6 : set_list_char]: (^[Z3 : set_list_char]: (Y6 = Z3))) = (^[A6 : set_list_char]: (^[B5 : set_list_char]: (((ord_le1836582007t_char @ A6 @ B5)) & ((ord_le1836582007t_char @ B5 @ A6)))))))). % order_class.order.eq_iff
thf(fact_146_ord__eq__le__trans, axiom,
    ((![A3 : set_list_char, B2 : set_list_char, C2 : set_list_char]: ((A3 = B2) => ((ord_le1836582007t_char @ B2 @ C2) => (ord_le1836582007t_char @ A3 @ C2)))))). % ord_eq_le_trans
thf(fact_147_ord__le__eq__trans, axiom,
    ((![A3 : set_list_char, B2 : set_list_char, C2 : set_list_char]: ((ord_le1836582007t_char @ A3 @ B2) => ((B2 = C2) => (ord_le1836582007t_char @ A3 @ C2)))))). % ord_le_eq_trans
thf(fact_148_order__class_Oorder_Oantisym, axiom,
    ((![A3 : set_list_char, B2 : set_list_char]: ((ord_le1836582007t_char @ A3 @ B2) => ((ord_le1836582007t_char @ B2 @ A3) => (A3 = B2)))))). % order_class.order.antisym
thf(fact_149_order__trans, axiom,
    ((![X : set_list_char, Y : set_list_char, Z : set_list_char]: ((ord_le1836582007t_char @ X @ Y) => ((ord_le1836582007t_char @ Y @ Z) => (ord_le1836582007t_char @ X @ Z)))))). % order_trans
thf(fact_150_dual__order_Orefl, axiom,
    ((![A3 : set_list_char]: (ord_le1836582007t_char @ A3 @ A3)))). % dual_order.refl
thf(fact_151_dual__order_Otrans, axiom,
    ((![B2 : set_list_char, A3 : set_list_char, C2 : set_list_char]: ((ord_le1836582007t_char @ B2 @ A3) => ((ord_le1836582007t_char @ C2 @ B2) => (ord_le1836582007t_char @ C2 @ A3)))))). % dual_order.trans
thf(fact_152_dual__order_Oeq__iff, axiom,
    (((^[Y6 : set_list_char]: (^[Z3 : set_list_char]: (Y6 = Z3))) = (^[A6 : set_list_char]: (^[B5 : set_list_char]: (((ord_le1836582007t_char @ B5 @ A6)) & ((ord_le1836582007t_char @ A6 @ B5)))))))). % dual_order.eq_iff
thf(fact_153_dual__order_Oantisym, axiom,
    ((![B2 : set_list_char, A3 : set_list_char]: ((ord_le1836582007t_char @ B2 @ A3) => ((ord_le1836582007t_char @ A3 @ B2) => (A3 = B2)))))). % dual_order.antisym
thf(fact_154_redp__redsp_OFAccRed, axiom,
    ((![P : list_P1234162913t_char, E2 : exp_list_char, S2 : produc515445032on_val, E : exp_list_char, S3 : produc515445032on_val, F3 : list_char, D3 : list_char]: ((redp @ P @ E2 @ S2 @ E @ S3) => (redp @ P @ (fAcc_list_char @ E2 @ F3 @ D3) @ S2 @ (fAcc_list_char @ E @ F3 @ D3) @ S3))))). % redp_redsp.FAccRed
thf(fact_155_exp_Odistinct_I61_J, axiom,
    ((![X3 : val, X71 : exp_list_char, X72 : list_char, X73 : list_char]: (~ (((val_list_char @ X3) = (fAcc_list_char @ X71 @ X72 @ X73))))))). % exp.distinct(61)
thf(fact_156_exp_Odistinct_I11_J, axiom,
    ((![X1 : list_char, X71 : exp_list_char, X72 : list_char, X73 : list_char]: (~ (((new_list_char @ X1) = (fAcc_list_char @ X71 @ X72 @ X73))))))). % exp.distinct(11)
thf(fact_157__092_060A_062_Osimps_I7_J, axiom,
    ((![E2 : exp_list_char, F3 : list_char, D3 : list_char]: ((a_list_char @ (fAcc_list_char @ E2 @ F3 @ D3)) = (a_list_char @ E2))))). % \<A>.simps(7)
thf(fact_158_eval__hext, axiom,
    ((![P : list_P1234162913t_char, E2 : exp_list_char, H : nat > option2118145160on_val, L : list_char > option_val, E : exp_list_char, H2 : nat > option2118145160on_val, L2 : list_char > option_val]: ((eval @ P @ E2 @ (produc52622304on_val @ H @ L) @ E @ (produc52622304on_val @ H2 @ L2)) => (hext @ H @ H2))))). % eval_hext
thf(fact_159_red__reds_OFAccRed, axiom,
    ((![E2 : exp_list_char, S2 : produc515445032on_val, E : exp_list_char, S3 : produc515445032on_val, P : list_P1234162913t_char, F3 : list_char, D3 : list_char]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E2 @ S2) @ (produc2023458740on_val @ E @ S3)) @ (red @ P)) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (fAcc_list_char @ E2 @ F3 @ D3) @ S2) @ (produc2023458740on_val @ (fAcc_list_char @ E @ F3 @ D3) @ S3)) @ (red @ P)))))). % red_reds.FAccRed
thf(fact_160_eval__lcl__incr, axiom,
    ((![P : list_P1234162913t_char, E2 : exp_list_char, H_0 : nat > option2118145160on_val, L_0 : list_char > option_val, E : exp_list_char, H_1 : nat > option2118145160on_val, L_1 : list_char > option_val]: ((eval @ P @ E2 @ (produc52622304on_val @ H_0 @ L_0) @ E @ (produc52622304on_val @ H_1 @ L_1)) => (ord_le1836582007t_char @ (dom_list_char_val @ L_0) @ (dom_list_char_val @ L_1)))))). % eval_lcl_incr
thf(fact_161_preallocated__upd__obj, axiom,
    ((![H : nat > option2118145160on_val, A3 : nat, C3 : list_char, Fs : produc1257910179t_char > option_val, Fs2 : produc1257910179t_char > option_val]: ((preallocated @ H) => (((H @ A3) = (some_P1299442195on_val @ (produc904988266on_val @ C3 @ Fs))) => (preallocated @ (fun_up262443479on_val @ H @ A3 @ (some_P1299442195on_val @ (produc904988266on_val @ C3 @ Fs2))))))))). % preallocated_upd_obj
thf(fact_162_hext__upd__obj, axiom,
    ((![H : nat > option2118145160on_val, A3 : nat, C3 : list_char, Fs : produc1257910179t_char > option_val, Fs2 : produc1257910179t_char > option_val]: (((H @ A3) = (some_P1299442195on_val @ (produc904988266on_val @ C3 @ Fs))) => (hext @ H @ (fun_up262443479on_val @ H @ A3 @ (some_P1299442195on_val @ (produc904988266on_val @ C3 @ Fs2)))))))). % hext_upd_obj
thf(fact_163_red__reds_ORedFAcc, axiom,
    ((![S2 : produc515445032on_val, A3 : nat, C3 : list_char, Fs : produc1257910179t_char > option_val, F3 : list_char, D3 : list_char, V : val, P : list_P1234162913t_char]: (((hp @ S2 @ A3) = (some_P1299442195on_val @ (produc904988266on_val @ C3 @ Fs))) => (((Fs @ (produc1304532571t_char @ F3 @ D3)) = (some_val @ V)) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (fAcc_list_char @ (val_list_char @ (addr @ A3)) @ F3 @ D3) @ S2) @ (produc2023458740on_val @ (val_list_char @ V) @ S2)) @ (red @ P))))))). % red_reds.RedFAcc
thf(fact_164_redp__redsp_ORedFAcc, axiom,
    ((![S2 : produc515445032on_val, A3 : nat, C3 : list_char, Fs : produc1257910179t_char > option_val, F3 : list_char, D3 : list_char, V : val, P : list_P1234162913t_char]: (((hp @ S2 @ A3) = (some_P1299442195on_val @ (produc904988266on_val @ C3 @ Fs))) => (((Fs @ (produc1304532571t_char @ F3 @ D3)) = (some_val @ V)) => (redp @ P @ (fAcc_list_char @ (val_list_char @ (addr @ A3)) @ F3 @ D3) @ S2 @ (val_list_char @ V) @ S2)))))). % redp_redsp.RedFAcc
thf(fact_165_hext__refl, axiom,
    ((![H : nat > option2118145160on_val]: (hext @ H @ H)))). % hext_refl
thf(fact_166_pred__subset__eq2, axiom,
    ((![R : set_Pr2075231726on_val, S : set_Pr2075231726on_val]: ((ord_le1192209529_val_o @ (^[X2 : list_char]: (^[Y2 : produc1257910179t_char > option_val]: (member1296415951on_val @ (produc904988266on_val @ X2 @ Y2) @ R))) @ (^[X2 : list_char]: (^[Y2 : produc1257910179t_char > option_val]: (member1296415951on_val @ (produc904988266on_val @ X2 @ Y2) @ S)))) = (ord_le1071216206on_val @ R @ S))))). % pred_subset_eq2
thf(fact_167_pred__subset__eq2, axiom,
    ((![R : set_Pr1189492743on_val, S : set_Pr1189492743on_val]: ((ord_le1677030286_val_o @ (^[X2 : produc1097884484on_val]: (^[Y2 : produc1097884484on_val]: (member354538064on_val @ (produc1069526295on_val @ X2 @ Y2) @ R))) @ (^[X2 : produc1097884484on_val]: (^[Y2 : produc1097884484on_val]: (member354538064on_val @ (produc1069526295on_val @ X2 @ Y2) @ S)))) = (ord_le837504935on_val @ R @ S))))). % pred_subset_eq2
thf(fact_168_pred__subset__eq2, axiom,
    ((![R : set_Pr556513572on_val, S : set_Pr556513572on_val]: ((ord_le383107121_val_o @ (^[X2 : exp_list_char]: (^[Y2 : produc515445032on_val]: (member1888679917on_val @ (produc2023458740on_val @ X2 @ Y2) @ R))) @ (^[X2 : exp_list_char]: (^[Y2 : produc515445032on_val]: (member1888679917on_val @ (produc2023458740on_val @ X2 @ Y2) @ S)))) = (ord_le131203268on_val @ R @ S))))). % pred_subset_eq2
thf(fact_169_pred__subset__eq2, axiom,
    ((![R : set_Pr723149704on_val, S : set_Pr723149704on_val]: ((ord_le752245279_val_o @ (^[X2 : nat > option2118145160on_val]: (^[Y2 : list_char > option_val]: (member652041809on_val @ (produc52622304on_val @ X2 @ Y2) @ R))) @ (^[X2 : nat > option2118145160on_val]: (^[Y2 : list_char > option_val]: (member652041809on_val @ (produc52622304on_val @ X2 @ Y2) @ S)))) = (ord_le930806568on_val @ R @ S))))). % pred_subset_eq2
thf(fact_170_pred__subset__eq2, axiom,
    ((![R : set_Pr164112643t_char, S : set_Pr164112643t_char]: ((ord_le2024582756char_o @ (^[X2 : list_char]: (^[Y2 : list_char]: (member89690956t_char @ (produc1304532571t_char @ X2 @ Y2) @ R))) @ (^[X2 : list_char]: (^[Y2 : list_char]: (member89690956t_char @ (produc1304532571t_char @ X2 @ Y2) @ S)))) = (ord_le167891107t_char @ R @ S))))). % pred_subset_eq2
thf(fact_171_subrelI, axiom,
    ((![R2 : set_Pr2075231726on_val, S2 : set_Pr2075231726on_val]: ((![X4 : list_char, Y4 : produc1257910179t_char > option_val]: ((member1296415951on_val @ (produc904988266on_val @ X4 @ Y4) @ R2) => (member1296415951on_val @ (produc904988266on_val @ X4 @ Y4) @ S2))) => (ord_le1071216206on_val @ R2 @ S2))))). % subrelI
thf(fact_172_subrelI, axiom,
    ((![R2 : set_Pr1189492743on_val, S2 : set_Pr1189492743on_val]: ((![X4 : produc1097884484on_val, Y4 : produc1097884484on_val]: ((member354538064on_val @ (produc1069526295on_val @ X4 @ Y4) @ R2) => (member354538064on_val @ (produc1069526295on_val @ X4 @ Y4) @ S2))) => (ord_le837504935on_val @ R2 @ S2))))). % subrelI
thf(fact_173_subrelI, axiom,
    ((![R2 : set_Pr556513572on_val, S2 : set_Pr556513572on_val]: ((![X4 : exp_list_char, Y4 : produc515445032on_val]: ((member1888679917on_val @ (produc2023458740on_val @ X4 @ Y4) @ R2) => (member1888679917on_val @ (produc2023458740on_val @ X4 @ Y4) @ S2))) => (ord_le131203268on_val @ R2 @ S2))))). % subrelI
thf(fact_174_subrelI, axiom,
    ((![R2 : set_Pr723149704on_val, S2 : set_Pr723149704on_val]: ((![X4 : nat > option2118145160on_val, Y4 : list_char > option_val]: ((member652041809on_val @ (produc52622304on_val @ X4 @ Y4) @ R2) => (member652041809on_val @ (produc52622304on_val @ X4 @ Y4) @ S2))) => (ord_le930806568on_val @ R2 @ S2))))). % subrelI
thf(fact_175_subrelI, axiom,
    ((![R2 : set_Pr164112643t_char, S2 : set_Pr164112643t_char]: ((![X4 : list_char, Y4 : list_char]: ((member89690956t_char @ (produc1304532571t_char @ X4 @ Y4) @ R2) => (member89690956t_char @ (produc1304532571t_char @ X4 @ Y4) @ S2))) => (ord_le167891107t_char @ R2 @ S2))))). % subrelI
thf(fact_176_less__eq__set__def, axiom,
    ((ord_le837504935on_val = (^[A7 : set_Pr1189492743on_val]: (^[B6 : set_Pr1189492743on_val]: (ord_le14618614_val_o @ (^[X2 : produc1172664615on_val]: (member354538064on_val @ X2 @ A7)) @ (^[X2 : produc1172664615on_val]: (member354538064on_val @ X2 @ B6)))))))). % less_eq_set_def
thf(fact_177_less__eq__set__def, axiom,
    ((ord_le1836582007t_char = (^[A7 : set_list_char]: (^[B6 : set_list_char]: (ord_le1945897678char_o @ (^[X2 : list_char]: (member_list_char @ X2 @ A7)) @ (^[X2 : list_char]: (member_list_char @ X2 @ B6)))))))). % less_eq_set_def
thf(fact_178_pred__subset__eq, axiom,
    ((![R : set_Pr1189492743on_val, S : set_Pr1189492743on_val]: ((ord_le14618614_val_o @ (^[X2 : produc1172664615on_val]: (member354538064on_val @ X2 @ R)) @ (^[X2 : produc1172664615on_val]: (member354538064on_val @ X2 @ S))) = (ord_le837504935on_val @ R @ S))))). % pred_subset_eq
thf(fact_179_pred__subset__eq, axiom,
    ((![R : set_list_char, S : set_list_char]: ((ord_le1945897678char_o @ (^[X2 : list_char]: (member_list_char @ X2 @ R)) @ (^[X2 : list_char]: (member_list_char @ X2 @ S))) = (ord_le1836582007t_char @ R @ S))))). % pred_subset_eq
thf(fact_180_hext__trans, axiom,
    ((![H : nat > option2118145160on_val, H2 : nat > option2118145160on_val, H3 : nat > option2118145160on_val]: ((hext @ H @ H2) => ((hext @ H2 @ H3) => (hext @ H @ H3)))))). % hext_trans
thf(fact_181_preallocated__hext, axiom,
    ((![H : nat > option2118145160on_val, H2 : nat > option2118145160on_val]: ((preallocated @ H) => ((hext @ H @ H2) => (preallocated @ H2)))))). % preallocated_hext
thf(fact_182_hext__objD, axiom,
    ((![H : nat > option2118145160on_val, H2 : nat > option2118145160on_val, A3 : nat, C3 : list_char, Fs : produc1257910179t_char > option_val]: ((hext @ H @ H2) => (((H @ A3) = (some_P1299442195on_val @ (produc904988266on_val @ C3 @ Fs))) => (?[Fs3 : produc1257910179t_char > option_val]: ((H2 @ A3) = (some_P1299442195on_val @ (produc904988266on_val @ C3 @ Fs3))))))))). % hext_objD
thf(fact_183_hext__def, axiom,
    ((hext = (^[H4 : nat > option2118145160on_val]: (^[H5 : nat > option2118145160on_val]: (![A6 : nat]: (![C4 : list_char]: (![Fs4 : produc1257910179t_char > option_val]: ((((H4 @ A6) = (some_P1299442195on_val @ (produc904988266on_val @ C4 @ Fs4)))) => ((?[Fs5 : produc1257910179t_char > option_val]: ((H5 @ A6) = (some_P1299442195on_val @ (produc904988266on_val @ C4 @ Fs5)))))))))))))). % hext_def
thf(fact_184_hextI, axiom,
    ((![H : nat > option2118145160on_val, H2 : nat > option2118145160on_val]: ((![A5 : nat, C5 : list_char, Fs6 : produc1257910179t_char > option_val]: (((H @ A5) = (some_P1299442195on_val @ (produc904988266on_val @ C5 @ Fs6))) => (?[Fs7 : produc1257910179t_char > option_val]: ((H2 @ A5) = (some_P1299442195on_val @ (produc904988266on_val @ C5 @ Fs7)))))) => (hext @ H @ H2))))). % hextI

% Helper facts (3)
thf(help_If_3_1_If_001t__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_T, axiom,
    ((![P : $o]: ((P = $true) | (P = $false))))).
thf(help_If_2_1_If_001t__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_T, axiom,
    ((![X : option2118145160on_val, Y : option2118145160on_val]: ((if_opt451925058on_val @ $false @ X @ Y) = Y)))).
thf(help_If_1_1_If_001t__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_T, axiom,
    ((![X : option2118145160on_val, Y : option2118145160on_val]: ((if_opt451925058on_val @ $true @ X @ Y) = X)))).

% Conjectures (4)
thf(conj_0, hypothesis,
    (((new_Addr @ ha) = (some_nat @ a)))).
thf(conj_1, hypothesis,
    ((fields1441617180t_char @ p @ c @ fDTs))).
thf(conj_2, hypothesis,
    ((h_a = (fun_up262443479on_val @ ha @ a @ (some_P1299442195on_val @ (produc904988266on_val @ c @ (init_fields @ fDTs))))))).
thf(conj_3, conjecture,
    ((hyper_1448788648t_char @ (hyperUn_list_char @ (some_set_list_char @ (dom_list_char_val @ la)) @ (a_list_char @ (new_list_char @ c))) @ (hyperUn_list_char @ (some_set_list_char @ (dom_list_char_val @ la)) @ (a_list_char @ (val_list_char @ (addr @ a))))))).
