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% Explicit typings (91)
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thf(sy_c_Expr_Oexp_OVal_001t__List__Olist_It__String__Ochar_J, type,
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thf(sy_c_Expr_Oexp_OWhile_001t__List__Olist_It__String__Ochar_J, type,
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thf(sy_c_List_Oappend_001t__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J, type,
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    produc746553401on_val : (list_char > option_val) > (list_char > option_val) > produc1335728385on_val).
thf(sy_c_Product__Type_OPair_001_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_001_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J, type,
    produc52622304on_val : (nat > option2118145160on_val) > (list_char > option_val) > produc515445032on_val).
thf(sy_c_Product__Type_OPair_001_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_001_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, type,
    produc1392944775on_val : (nat > option2118145160on_val) > (nat > option2118145160on_val) > produc1914020559on_val).
thf(sy_c_Product__Type_OPair_001t__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_001t__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J, type,
    produc240508503t_char : exp_list_char > exp_list_char > produc677445863t_char).
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thf(sy_c_Product__Type_OPair_001t__List__Olist_It__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_J_001t__List__Olist_It__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_J, type,
    produc1721801175t_char : list_exp_list_char > list_exp_list_char > produc1813212775t_char).
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thf(sy_c_member_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__Product____Type__Oprod_It__List__Olist_It__Expr__Oexp_It__List__Olist_It__String__Ochar_J_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_Mt__Product____Type__Oprod_It__Product____Type__Oprod_It__List__Olist_It__Expr__Oexp_It__List__Olist_It__String__Ochar_J_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_J, type,
    member939451536on_val : produc1931033447on_val > set_Pr655264327on_val > $o).
thf(sy_c_member_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__Product____Type__Oprod_It__List__Olist_It__Expr__Oexp_It__List__Olist_It__String__Ochar_J_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__List__Olist_It__Expr__Oexp_It__List__Olist_It__String__Ochar_J_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_Mt__Product____Type__Oprod_It__Product____Type__Oprod_It__List__Olist_It__Expr__Oexp_It__List__Olist_It__String__Ochar_J_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__List__Olist_It__Expr__Oexp_It__List__Olist_It__String__Ochar_J_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_J, type,
    member1743964944on_val : produc1428501223on_val > set_Pr1301890247on_val > $o).
thf(sy_v_E, type,
    e : list_char > option_ty).
thf(sy_v_P, type,
    p : list_P1234162913t_char).
thf(sy_v_T, type,
    t : ty).
thf(sy_v_e, type,
    e2 : exp_list_char).
thf(sy_v_e_H, type,
    e3 : exp_list_char).
thf(sy_v_h, type,
    h : nat > option2118145160on_val).
thf(sy_v_h_H, type,
    h2 : nat > option2118145160on_val).
thf(sy_v_l, type,
    l : list_char > option_val).
thf(sy_v_l_H, type,
    l2 : list_char > option_val).

% Relevant facts (241)
thf(fact_0_prod__cases4, axiom,
    ((![Y : produc1172664615on_val]: (~ ((![A : produc1097884484on_val, B : exp_list_char, C : nat > option2118145160on_val, D : list_char > option_val]: (~ ((Y = (produc1069526295on_val @ A @ (produc2023458740on_val @ B @ (produc52622304on_val @ C @ D)))))))))))). % prod_cases4
thf(fact_1_prod__cases4, axiom,
    ((![Y : produc655058983on_val]: (~ ((![A : produc335961278on_val, B : list_exp_list_char, C : nat > option2118145160on_val, D : list_char > option_val]: (~ ((Y = (produc245869591on_val @ A @ (produc1725134254on_val @ B @ (produc52622304on_val @ C @ D)))))))))))). % prod_cases4
thf(fact_2_prod__induct4, axiom,
    ((![P : produc1172664615on_val > $o, X : produc1172664615on_val]: ((![A : produc1097884484on_val, B : exp_list_char, C : nat > option2118145160on_val, D : list_char > option_val]: (P @ (produc1069526295on_val @ A @ (produc2023458740on_val @ B @ (produc52622304on_val @ C @ D))))) => (P @ X))))). % prod_induct4
thf(fact_3_prod__induct4, axiom,
    ((![P : produc655058983on_val > $o, X : produc655058983on_val]: ((![A : produc335961278on_val, B : list_exp_list_char, C : nat > option2118145160on_val, D : list_char > option_val]: (P @ (produc245869591on_val @ A @ (produc1725134254on_val @ B @ (produc52622304on_val @ C @ D))))) => (P @ X))))). % prod_induct4
thf(fact_4_prod_Oinject, axiom,
    ((![X1 : produc1097884484on_val, X2 : produc1097884484on_val, Y1 : produc1097884484on_val, Y2 : produc1097884484on_val]: (((produc1069526295on_val @ X1 @ X2) = (produc1069526295on_val @ Y1 @ Y2)) = (((X1 = Y1)) & ((X2 = Y2))))))). % prod.inject
thf(fact_5_prod_Oinject, axiom,
    ((![X1 : exp_list_char, X2 : produc515445032on_val, Y1 : exp_list_char, Y2 : produc515445032on_val]: (((produc2023458740on_val @ X1 @ X2) = (produc2023458740on_val @ Y1 @ Y2)) = (((X1 = Y1)) & ((X2 = Y2))))))). % prod.inject
thf(fact_6_prod_Oinject, axiom,
    ((![X1 : nat > option2118145160on_val, X2 : list_char > option_val, Y1 : nat > option2118145160on_val, Y2 : list_char > option_val]: (((produc52622304on_val @ X1 @ X2) = (produc52622304on_val @ Y1 @ Y2)) = (((X1 = Y1)) & ((X2 = Y2))))))). % prod.inject
thf(fact_7_prod_Oinject, axiom,
    ((![X1 : produc335961278on_val, X2 : produc335961278on_val, Y1 : produc335961278on_val, Y2 : produc335961278on_val]: (((produc245869591on_val @ X1 @ X2) = (produc245869591on_val @ Y1 @ Y2)) = (((X1 = Y1)) & ((X2 = Y2))))))). % prod.inject
thf(fact_8_prod_Oinject, axiom,
    ((![X1 : list_exp_list_char, X2 : produc515445032on_val, Y1 : list_exp_list_char, Y2 : produc515445032on_val]: (((produc1725134254on_val @ X1 @ X2) = (produc1725134254on_val @ Y1 @ Y2)) = (((X1 = Y1)) & ((X2 = Y2))))))). % prod.inject
thf(fact_9_old_Oprod_Oinject, axiom,
    ((![A2 : produc1097884484on_val, B2 : produc1097884484on_val, A3 : produc1097884484on_val, B3 : produc1097884484on_val]: (((produc1069526295on_val @ A2 @ B2) = (produc1069526295on_val @ A3 @ B3)) = (((A2 = A3)) & ((B2 = B3))))))). % old.prod.inject
thf(fact_10_old_Oprod_Oinject, axiom,
    ((![A2 : exp_list_char, B2 : produc515445032on_val, A3 : exp_list_char, B3 : produc515445032on_val]: (((produc2023458740on_val @ A2 @ B2) = (produc2023458740on_val @ A3 @ B3)) = (((A2 = A3)) & ((B2 = B3))))))). % old.prod.inject
thf(fact_11_old_Oprod_Oinject, axiom,
    ((![A2 : nat > option2118145160on_val, B2 : list_char > option_val, A3 : nat > option2118145160on_val, B3 : list_char > option_val]: (((produc52622304on_val @ A2 @ B2) = (produc52622304on_val @ A3 @ B3)) = (((A2 = A3)) & ((B2 = B3))))))). % old.prod.inject
thf(fact_12_old_Oprod_Oinject, axiom,
    ((![A2 : produc335961278on_val, B2 : produc335961278on_val, A3 : produc335961278on_val, B3 : produc335961278on_val]: (((produc245869591on_val @ A2 @ B2) = (produc245869591on_val @ A3 @ B3)) = (((A2 = A3)) & ((B2 = B3))))))). % old.prod.inject
thf(fact_13_old_Oprod_Oinject, axiom,
    ((![A2 : list_exp_list_char, B2 : produc515445032on_val, A3 : list_exp_list_char, B3 : produc515445032on_val]: (((produc1725134254on_val @ A2 @ B2) = (produc1725134254on_val @ A3 @ B3)) = (((A2 = A3)) & ((B2 = B3))))))). % old.prod.inject
thf(fact_14_prod__cases3, axiom,
    ((![Y : produc1172664615on_val]: (~ ((![A : produc1097884484on_val, B : exp_list_char, C : produc515445032on_val]: (~ ((Y = (produc1069526295on_val @ A @ (produc2023458740on_val @ B @ C))))))))))). % prod_cases3
thf(fact_15_prod__cases3, axiom,
    ((![Y : produc1097884484on_val]: (~ ((![A : exp_list_char, B : nat > option2118145160on_val, C : list_char > option_val]: (~ ((Y = (produc2023458740on_val @ A @ (produc52622304on_val @ B @ C))))))))))). % prod_cases3
thf(fact_16_prod__cases3, axiom,
    ((![Y : produc655058983on_val]: (~ ((![A : produc335961278on_val, B : list_exp_list_char, C : produc515445032on_val]: (~ ((Y = (produc245869591on_val @ A @ (produc1725134254on_val @ B @ C))))))))))). % prod_cases3
thf(fact_17_prod__cases3, axiom,
    ((![Y : produc335961278on_val]: (~ ((![A : list_exp_list_char, B : nat > option2118145160on_val, C : list_char > option_val]: (~ ((Y = (produc1725134254on_val @ A @ (produc52622304on_val @ B @ C))))))))))). % prod_cases3
thf(fact_18_prod__induct3, axiom,
    ((![P : produc1172664615on_val > $o, X : produc1172664615on_val]: ((![A : produc1097884484on_val, B : exp_list_char, C : produc515445032on_val]: (P @ (produc1069526295on_val @ A @ (produc2023458740on_val @ B @ C)))) => (P @ X))))). % prod_induct3
thf(fact_19_prod__induct3, axiom,
    ((![P : produc1097884484on_val > $o, X : produc1097884484on_val]: ((![A : exp_list_char, B : nat > option2118145160on_val, C : list_char > option_val]: (P @ (produc2023458740on_val @ A @ (produc52622304on_val @ B @ C)))) => (P @ X))))). % prod_induct3
thf(fact_20_prod__induct3, axiom,
    ((![P : produc655058983on_val > $o, X : produc655058983on_val]: ((![A : produc335961278on_val, B : list_exp_list_char, C : produc515445032on_val]: (P @ (produc245869591on_val @ A @ (produc1725134254on_val @ B @ C)))) => (P @ X))))). % prod_induct3
thf(fact_21_prod__induct3, axiom,
    ((![P : produc335961278on_val > $o, X : produc335961278on_val]: ((![A : list_exp_list_char, B : nat > option2118145160on_val, C : list_char > option_val]: (P @ (produc1725134254on_val @ A @ (produc52622304on_val @ B @ C)))) => (P @ X))))). % prod_induct3
thf(fact_22_old_Oprod_Oinducts, axiom,
    ((![P : produc1172664615on_val > $o, Prod : produc1172664615on_val]: ((![A : produc1097884484on_val, B : produc1097884484on_val]: (P @ (produc1069526295on_val @ A @ B))) => (P @ Prod))))). % old.prod.inducts
thf(fact_23_old_Oprod_Oinducts, axiom,
    ((![P : produc1097884484on_val > $o, Prod : produc1097884484on_val]: ((![A : exp_list_char, B : produc515445032on_val]: (P @ (produc2023458740on_val @ A @ B))) => (P @ Prod))))). % old.prod.inducts
thf(fact_24_old_Oprod_Oinducts, axiom,
    ((![P : produc515445032on_val > $o, Prod : produc515445032on_val]: ((![A : nat > option2118145160on_val, B : list_char > option_val]: (P @ (produc52622304on_val @ A @ B))) => (P @ Prod))))). % old.prod.inducts
thf(fact_25_old_Oprod_Oinducts, axiom,
    ((![P : produc655058983on_val > $o, Prod : produc655058983on_val]: ((![A : produc335961278on_val, B : produc335961278on_val]: (P @ (produc245869591on_val @ A @ B))) => (P @ Prod))))). % old.prod.inducts
thf(fact_26_old_Oprod_Oinducts, axiom,
    ((![P : produc335961278on_val > $o, Prod : produc335961278on_val]: ((![A : list_exp_list_char, B : produc515445032on_val]: (P @ (produc1725134254on_val @ A @ B))) => (P @ Prod))))). % old.prod.inducts
thf(fact_27_old_Oprod_Oexhaust, axiom,
    ((![Y : produc1172664615on_val]: (~ ((![A : produc1097884484on_val, B : produc1097884484on_val]: (~ ((Y = (produc1069526295on_val @ A @ B)))))))))). % old.prod.exhaust
thf(fact_28_old_Oprod_Oexhaust, axiom,
    ((![Y : produc1097884484on_val]: (~ ((![A : exp_list_char, B : produc515445032on_val]: (~ ((Y = (produc2023458740on_val @ A @ B)))))))))). % old.prod.exhaust
thf(fact_29_old_Oprod_Oexhaust, axiom,
    ((![Y : produc515445032on_val]: (~ ((![A : nat > option2118145160on_val, B : list_char > option_val]: (~ ((Y = (produc52622304on_val @ A @ B)))))))))). % old.prod.exhaust
thf(fact_30_old_Oprod_Oexhaust, axiom,
    ((![Y : produc655058983on_val]: (~ ((![A : produc335961278on_val, B : produc335961278on_val]: (~ ((Y = (produc245869591on_val @ A @ B)))))))))). % old.prod.exhaust
thf(fact_31_old_Oprod_Oexhaust, axiom,
    ((![Y : produc335961278on_val]: (~ ((![A : list_exp_list_char, B : produc515445032on_val]: (~ ((Y = (produc1725134254on_val @ A @ B)))))))))). % old.prod.exhaust
thf(fact_32_Pair__inject, axiom,
    ((![A2 : produc1097884484on_val, B2 : produc1097884484on_val, A3 : produc1097884484on_val, B3 : produc1097884484on_val]: (((produc1069526295on_val @ A2 @ B2) = (produc1069526295on_val @ A3 @ B3)) => (~ (((A2 = A3) => (~ ((B2 = B3)))))))))). % Pair_inject
thf(fact_33_Pair__inject, axiom,
    ((![A2 : exp_list_char, B2 : produc515445032on_val, A3 : exp_list_char, B3 : produc515445032on_val]: (((produc2023458740on_val @ A2 @ B2) = (produc2023458740on_val @ A3 @ B3)) => (~ (((A2 = A3) => (~ ((B2 = B3)))))))))). % Pair_inject
thf(fact_34_Pair__inject, axiom,
    ((![A2 : nat > option2118145160on_val, B2 : list_char > option_val, A3 : nat > option2118145160on_val, B3 : list_char > option_val]: (((produc52622304on_val @ A2 @ B2) = (produc52622304on_val @ A3 @ B3)) => (~ (((A2 = A3) => (~ ((B2 = B3)))))))))). % Pair_inject
thf(fact_35_Pair__inject, axiom,
    ((![A2 : produc335961278on_val, B2 : produc335961278on_val, A3 : produc335961278on_val, B3 : produc335961278on_val]: (((produc245869591on_val @ A2 @ B2) = (produc245869591on_val @ A3 @ B3)) => (~ (((A2 = A3) => (~ ((B2 = B3)))))))))). % Pair_inject
thf(fact_36_Pair__inject, axiom,
    ((![A2 : list_exp_list_char, B2 : produc515445032on_val, A3 : list_exp_list_char, B3 : produc515445032on_val]: (((produc1725134254on_val @ A2 @ B2) = (produc1725134254on_val @ A3 @ B3)) => (~ (((A2 = A3) => (~ ((B2 = B3)))))))))). % Pair_inject
thf(fact_37_prod__cases, axiom,
    ((![P : produc1172664615on_val > $o, P2 : produc1172664615on_val]: ((![A : produc1097884484on_val, B : produc1097884484on_val]: (P @ (produc1069526295on_val @ A @ B))) => (P @ P2))))). % prod_cases
thf(fact_38_prod__cases, axiom,
    ((![P : produc1097884484on_val > $o, P2 : produc1097884484on_val]: ((![A : exp_list_char, B : produc515445032on_val]: (P @ (produc2023458740on_val @ A @ B))) => (P @ P2))))). % prod_cases
thf(fact_39_prod__cases, axiom,
    ((![P : produc515445032on_val > $o, P2 : produc515445032on_val]: ((![A : nat > option2118145160on_val, B : list_char > option_val]: (P @ (produc52622304on_val @ A @ B))) => (P @ P2))))). % prod_cases
thf(fact_40_prod__cases, axiom,
    ((![P : produc655058983on_val > $o, P2 : produc655058983on_val]: ((![A : produc335961278on_val, B : produc335961278on_val]: (P @ (produc245869591on_val @ A @ B))) => (P @ P2))))). % prod_cases
thf(fact_41_prod__cases, axiom,
    ((![P : produc335961278on_val > $o, P2 : produc335961278on_val]: ((![A : list_exp_list_char, B : produc515445032on_val]: (P @ (produc1725134254on_val @ A @ B))) => (P @ P2))))). % prod_cases
thf(fact_42_surj__pair, axiom,
    ((![P2 : produc1172664615on_val]: (?[X3 : produc1097884484on_val, Y3 : produc1097884484on_val]: (P2 = (produc1069526295on_val @ X3 @ Y3)))))). % surj_pair
thf(fact_43_surj__pair, axiom,
    ((![P2 : produc1097884484on_val]: (?[X3 : exp_list_char, Y3 : produc515445032on_val]: (P2 = (produc2023458740on_val @ X3 @ Y3)))))). % surj_pair
thf(fact_44_surj__pair, axiom,
    ((![P2 : produc515445032on_val]: (?[X3 : nat > option2118145160on_val, Y3 : list_char > option_val]: (P2 = (produc52622304on_val @ X3 @ Y3)))))). % surj_pair
thf(fact_45_surj__pair, axiom,
    ((![P2 : produc655058983on_val]: (?[X3 : produc335961278on_val, Y3 : produc335961278on_val]: (P2 = (produc245869591on_val @ X3 @ Y3)))))). % surj_pair
thf(fact_46_surj__pair, axiom,
    ((![P2 : produc335961278on_val]: (?[X3 : list_exp_list_char, Y3 : produc515445032on_val]: (P2 = (produc1725134254on_val @ X3 @ Y3)))))). % surj_pair
thf(fact_47_same__fstI, axiom,
    ((![P : (nat > option2118145160on_val) > $o, X : nat > option2118145160on_val, Y4 : list_char > option_val, Y : list_char > option_val, R : (nat > option2118145160on_val) > set_Pr1104486497on_val]: ((P @ X) => ((member1177709994on_val @ (produc746553401on_val @ Y4 @ Y) @ (R @ X)) => (member2027247312on_val @ (produc2106877847on_val @ (produc52622304on_val @ X @ Y4) @ (produc52622304on_val @ X @ Y)) @ (same_f1752972725on_val @ P @ R))))))). % same_fstI
thf(fact_48_same__fstI, axiom,
    ((![P : exp_list_char > $o, X : exp_list_char, Y4 : produc515445032on_val, Y : produc515445032on_val, R : exp_list_char > set_Pr148564103on_val]: ((P @ X) => ((member2027247312on_val @ (produc2106877847on_val @ Y4 @ Y) @ (R @ X)) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ X @ Y4) @ (produc2023458740on_val @ X @ Y)) @ (same_f366220041on_val @ P @ R))))))). % same_fstI
thf(fact_49_same__fstI, axiom,
    ((![P : list_exp_list_char > $o, X : list_exp_list_char, Y4 : produc515445032on_val, Y : produc515445032on_val, R : list_exp_list_char > set_Pr148564103on_val]: ((P @ X) => ((member2027247312on_val @ (produc2106877847on_val @ Y4 @ Y) @ (R @ X)) => (member1689761872on_val @ (produc245869591on_val @ (produc1725134254on_val @ X @ Y4) @ (produc1725134254on_val @ X @ Y)) @ (same_f1555812995on_val @ P @ R))))))). % same_fstI
thf(fact_50_same__fstI, axiom,
    ((![P : produc1097884484on_val > $o, X : produc1097884484on_val, Y4 : produc1097884484on_val, Y : produc1097884484on_val, R : produc1097884484on_val > set_Pr1189492743on_val]: ((P @ X) => ((member354538064on_val @ (produc1069526295on_val @ Y4 @ Y) @ (R @ X)) => (member208988944on_val @ (produc564964183on_val @ (produc1069526295on_val @ X @ Y4) @ (produc1069526295on_val @ X @ Y)) @ (same_f962657004on_val @ P @ R))))))). % same_fstI
thf(fact_51_same__fstI, axiom,
    ((![P : produc335961278on_val > $o, X : produc335961278on_val, Y4 : produc335961278on_val, Y : produc335961278on_val, R : produc335961278on_val > set_Pr208351751on_val]: ((P @ X) => ((member1689761872on_val @ (produc245869591on_val @ Y4 @ Y) @ (R @ X)) => (member1743964944on_val @ (produc1802175319on_val @ (produc245869591on_val @ X @ Y4) @ (produc245869591on_val @ X @ Y)) @ (same_f1147886828on_val @ P @ R))))))). % same_fstI
thf(fact_52_red__hext__incr, axiom,
    ((![E : exp_list_char, H : nat > option2118145160on_val, L : list_char > option_val, E2 : exp_list_char, H2 : nat > option2118145160on_val, L2 : list_char > option_val, P : list_P1234162913t_char]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E @ (produc52622304on_val @ H @ L)) @ (produc2023458740on_val @ E2 @ (produc52622304on_val @ H2 @ L2))) @ (red @ P)) => (hext @ H @ H2))))). % red_hext_incr
thf(fact_53_ssubst__Pair__rhs, axiom,
    ((![R2 : produc1097884484on_val, S : produc1097884484on_val, R : set_Pr1189492743on_val, S2 : produc1097884484on_val]: ((member354538064on_val @ (produc1069526295on_val @ R2 @ S) @ R) => ((S2 = S) => (member354538064on_val @ (produc1069526295on_val @ R2 @ S2) @ R)))))). % ssubst_Pair_rhs
thf(fact_54_ssubst__Pair__rhs, axiom,
    ((![R2 : exp_list_char, S : produc515445032on_val, R : set_Pr556513572on_val, S2 : produc515445032on_val]: ((member1888679917on_val @ (produc2023458740on_val @ R2 @ S) @ R) => ((S2 = S) => (member1888679917on_val @ (produc2023458740on_val @ R2 @ S2) @ R)))))). % ssubst_Pair_rhs
thf(fact_55_ssubst__Pair__rhs, axiom,
    ((![R2 : nat > option2118145160on_val, S : list_char > option_val, R : set_Pr723149704on_val, S2 : list_char > option_val]: ((member652041809on_val @ (produc52622304on_val @ R2 @ S) @ R) => ((S2 = S) => (member652041809on_val @ (produc52622304on_val @ R2 @ S2) @ R)))))). % ssubst_Pair_rhs
thf(fact_56_ssubst__Pair__rhs, axiom,
    ((![R2 : produc335961278on_val, S : produc335961278on_val, R : set_Pr208351751on_val, S2 : produc335961278on_val]: ((member1689761872on_val @ (produc245869591on_val @ R2 @ S) @ R) => ((S2 = S) => (member1689761872on_val @ (produc245869591on_val @ R2 @ S2) @ R)))))). % ssubst_Pair_rhs
thf(fact_57_ssubst__Pair__rhs, axiom,
    ((![R2 : list_exp_list_char, S : produc515445032on_val, R : set_Pr1511552798on_val, S2 : produc515445032on_val]: ((member184158439on_val @ (produc1725134254on_val @ R2 @ S) @ R) => ((S2 = S) => (member184158439on_val @ (produc1725134254on_val @ R2 @ S2) @ R)))))). % ssubst_Pair_rhs
thf(fact_58_red__lcl__add, axiom,
    ((![E : exp_list_char, H : nat > option2118145160on_val, L : list_char > option_val, E2 : exp_list_char, H2 : nat > option2118145160on_val, L2 : list_char > option_val, P : list_P1234162913t_char, L_0 : list_char > option_val]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E @ (produc52622304on_val @ H @ L)) @ (produc2023458740on_val @ E2 @ (produc52622304on_val @ H2 @ L2))) @ (red @ P)) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E @ (produc52622304on_val @ H @ (map_ad1615113112ar_val @ L_0 @ L))) @ (produc2023458740on_val @ E2 @ (produc52622304on_val @ H2 @ (map_ad1615113112ar_val @ L_0 @ L2)))) @ (red @ P)))))). % red_lcl_add
thf(fact_59_in__lex__prod, axiom,
    ((![A2 : produc1097884484on_val, B2 : produc335961278on_val, A3 : produc1097884484on_val, B3 : produc335961278on_val, R2 : set_Pr1189492743on_val, S : set_Pr208351751on_val]: ((member1284182416on_val @ (produc625175255on_val @ (produc367337745on_val @ A2 @ B2) @ (produc367337745on_val @ A3 @ B3)) @ (lex_pr511103273on_val @ R2 @ S)) = (((member354538064on_val @ (produc1069526295on_val @ A2 @ A3) @ R2)) | ((((A2 = A3)) & ((member1689761872on_val @ (produc245869591on_val @ B2 @ B3) @ S))))))))). % in_lex_prod
thf(fact_60_in__lex__prod, axiom,
    ((![A2 : produc335961278on_val, B2 : produc1097884484on_val, A3 : produc335961278on_val, B3 : produc1097884484on_val, R2 : set_Pr208351751on_val, S : set_Pr1189492743on_val]: ((member939451536on_val @ (produc1914110935on_val @ (produc974123805on_val @ A2 @ B2) @ (produc974123805on_val @ A3 @ B3)) @ (lex_pr1117889333on_val @ R2 @ S)) = (((member1689761872on_val @ (produc245869591on_val @ A2 @ A3) @ R2)) | ((((A2 = A3)) & ((member354538064on_val @ (produc1069526295on_val @ B2 @ B3) @ S))))))))). % in_lex_prod
thf(fact_61_in__lex__prod, axiom,
    ((![A2 : produc1097884484on_val, B2 : produc1097884484on_val, A3 : produc1097884484on_val, B3 : produc1097884484on_val, R2 : set_Pr1189492743on_val, S : set_Pr1189492743on_val]: ((member208988944on_val @ (produc564964183on_val @ (produc1069526295on_val @ A2 @ B2) @ (produc1069526295on_val @ A3 @ B3)) @ (lex_pr186272047on_val @ R2 @ S)) = (((member354538064on_val @ (produc1069526295on_val @ A2 @ A3) @ R2)) | ((((A2 = A3)) & ((member354538064on_val @ (produc1069526295on_val @ B2 @ B3) @ S))))))))). % in_lex_prod
thf(fact_62_in__lex__prod, axiom,
    ((![A2 : nat > option2118145160on_val, B2 : list_char > option_val, A3 : nat > option2118145160on_val, B3 : list_char > option_val, R2 : set_Pr1465729071on_val, S : set_Pr1104486497on_val]: ((member2027247312on_val @ (produc2106877847on_val @ (produc52622304on_val @ A2 @ B2) @ (produc52622304on_val @ A3 @ B3)) @ (lex_pr683585528on_val @ R2 @ S)) = (((member78096504on_val @ (produc1392944775on_val @ A2 @ A3) @ R2)) | ((((A2 = A3)) & ((member1177709994on_val @ (produc746553401on_val @ B2 @ B3) @ S))))))))). % in_lex_prod
thf(fact_63_in__lex__prod, axiom,
    ((![A2 : produc335961278on_val, B2 : produc335961278on_val, A3 : produc335961278on_val, B3 : produc335961278on_val, R2 : set_Pr208351751on_val, S : set_Pr208351751on_val]: ((member1743964944on_val @ (produc1802175319on_val @ (produc245869591on_val @ A2 @ B2) @ (produc245869591on_val @ A3 @ B3)) @ (lex_pr601255983on_val @ R2 @ S)) = (((member1689761872on_val @ (produc245869591on_val @ A2 @ A3) @ R2)) | ((((A2 = A3)) & ((member1689761872on_val @ (produc245869591on_val @ B2 @ B3) @ S))))))))). % in_lex_prod
thf(fact_64_in__lex__prod, axiom,
    ((![A2 : exp_list_char, B2 : produc515445032on_val, A3 : exp_list_char, B3 : produc515445032on_val, R2 : set_Pr224372167t_char, S : set_Pr148564103on_val]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ A2 @ B2) @ (produc2023458740on_val @ A3 @ B3)) @ (lex_pr1764546508on_val @ R2 @ S)) = (((member1699993616t_char @ (produc240508503t_char @ A2 @ A3) @ R2)) | ((((A2 = A3)) & ((member2027247312on_val @ (produc2106877847on_val @ B2 @ B3) @ S))))))))). % in_lex_prod
thf(fact_65_in__lex__prod, axiom,
    ((![A2 : list_exp_list_char, B2 : produc515445032on_val, A3 : list_exp_list_char, B3 : produc515445032on_val, R2 : set_Pr1932514887t_char, S : set_Pr148564103on_val]: ((member1689761872on_val @ (produc245869591on_val @ (produc1725134254on_val @ A2 @ B2) @ (produc1725134254on_val @ A3 @ B3)) @ (lex_pr263313862on_val @ R2 @ S)) = (((member462435472t_char @ (produc1721801175t_char @ A2 @ A3) @ R2)) | ((((A2 = A3)) & ((member2027247312on_val @ (produc2106877847on_val @ B2 @ B3) @ S))))))))). % in_lex_prod
thf(fact_66_converse__rtrancl__induct__red, axiom,
    ((![E : exp_list_char, H : nat > option2118145160on_val, L : list_char > option_val, E2 : exp_list_char, H2 : nat > option2118145160on_val, L2 : list_char > option_val, P : list_P1234162913t_char, R : exp_list_char > (nat > option2118145160on_val) > (list_char > option_val) > exp_list_char > (nat > option2118145160on_val) > (list_char > option_val) > $o]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E @ (produc52622304on_val @ H @ L)) @ (produc2023458740on_val @ E2 @ (produc52622304on_val @ H2 @ L2))) @ (transi111096263on_val @ (red @ P))) => ((![E3 : exp_list_char, H3 : nat > option2118145160on_val, L3 : list_char > option_val]: (R @ E3 @ H3 @ L3 @ E3 @ H3 @ L3)) => ((![E_0 : exp_list_char, H_0 : nat > option2118145160on_val, L_02 : list_char > option_val, E_1 : exp_list_char, H_1 : nat > option2118145160on_val, L_1 : list_char > option_val, E4 : exp_list_char, H4 : nat > option2118145160on_val, L4 : list_char > option_val]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E_0 @ (produc52622304on_val @ H_0 @ L_02)) @ (produc2023458740on_val @ E_1 @ (produc52622304on_val @ H_1 @ L_1))) @ (red @ P)) => ((R @ E_1 @ H_1 @ L_1 @ E4 @ H4 @ L4) => (R @ E_0 @ H_0 @ L_02 @ E4 @ H4 @ L4)))) => (R @ E @ H @ L @ E2 @ H2 @ L2))))))). % converse_rtrancl_induct_red
thf(fact_67_curryI, axiom,
    ((![F : produc1172664615on_val > $o, A2 : produc1097884484on_val, B2 : produc1097884484on_val]: ((F @ (produc1069526295on_val @ A2 @ B2)) => (produc360843917_val_o @ F @ A2 @ B2))))). % curryI
thf(fact_68_curryI, axiom,
    ((![F : produc1097884484on_val > $o, A2 : exp_list_char, B2 : produc515445032on_val]: ((F @ (produc2023458740on_val @ A2 @ B2)) => (produc699483184_val_o @ F @ A2 @ B2))))). % curryI
thf(fact_69_curryI, axiom,
    ((![F : produc515445032on_val > $o, A2 : nat > option2118145160on_val, B2 : list_char > option_val]: ((F @ (produc52622304on_val @ A2 @ B2)) => (produc761261956_val_o @ F @ A2 @ B2))))). % curryI
thf(fact_70_curryI, axiom,
    ((![F : produc655058983on_val > $o, A2 : produc335961278on_val, B2 : produc335961278on_val]: ((F @ (produc245869591on_val @ A2 @ B2)) => (produc1990203021_val_o @ F @ A2 @ B2))))). % curryI
thf(fact_71_curryI, axiom,
    ((![F : produc335961278on_val > $o, A2 : list_exp_list_char, B2 : produc515445032on_val]: ((F @ (produc1725134254on_val @ A2 @ B2)) => (produc1199911222_val_o @ F @ A2 @ B2))))). % curryI
thf(fact_72_Red__lcl__add, axiom,
    ((![E : exp_list_char, H : nat > option2118145160on_val, L : list_char > option_val, E2 : exp_list_char, H2 : nat > option2118145160on_val, L2 : list_char > option_val, P : list_P1234162913t_char, L_0 : list_char > option_val]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E @ (produc52622304on_val @ H @ L)) @ (produc2023458740on_val @ E2 @ (produc52622304on_val @ H2 @ L2))) @ (transi111096263on_val @ (red @ P))) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E @ (produc52622304on_val @ H @ (map_ad1615113112ar_val @ L_0 @ L))) @ (produc2023458740on_val @ E2 @ (produc52622304on_val @ H2 @ (map_ad1615113112ar_val @ L_0 @ L2)))) @ (transi111096263on_val @ (red @ P))))))). % Red_lcl_add
thf(fact_73_curryD, axiom,
    ((![F : produc1172664615on_val > $o, A2 : produc1097884484on_val, B2 : produc1097884484on_val]: ((produc360843917_val_o @ F @ A2 @ B2) => (F @ (produc1069526295on_val @ A2 @ B2)))))). % curryD
thf(fact_74_curryD, axiom,
    ((![F : produc1097884484on_val > $o, A2 : exp_list_char, B2 : produc515445032on_val]: ((produc699483184_val_o @ F @ A2 @ B2) => (F @ (produc2023458740on_val @ A2 @ B2)))))). % curryD
thf(fact_75_curryD, axiom,
    ((![F : produc515445032on_val > $o, A2 : nat > option2118145160on_val, B2 : list_char > option_val]: ((produc761261956_val_o @ F @ A2 @ B2) => (F @ (produc52622304on_val @ A2 @ B2)))))). % curryD
thf(fact_76_curryD, axiom,
    ((![F : produc655058983on_val > $o, A2 : produc335961278on_val, B2 : produc335961278on_val]: ((produc1990203021_val_o @ F @ A2 @ B2) => (F @ (produc245869591on_val @ A2 @ B2)))))). % curryD
thf(fact_77_curryD, axiom,
    ((![F : produc335961278on_val > $o, A2 : list_exp_list_char, B2 : produc515445032on_val]: ((produc1199911222_val_o @ F @ A2 @ B2) => (F @ (produc1725134254on_val @ A2 @ B2)))))). % curryD
thf(fact_78_curryE, axiom,
    ((![F : produc1172664615on_val > $o, A2 : produc1097884484on_val, B2 : produc1097884484on_val]: ((produc360843917_val_o @ F @ A2 @ B2) => (F @ (produc1069526295on_val @ A2 @ B2)))))). % curryE
thf(fact_79_curryE, axiom,
    ((![F : produc1097884484on_val > $o, A2 : exp_list_char, B2 : produc515445032on_val]: ((produc699483184_val_o @ F @ A2 @ B2) => (F @ (produc2023458740on_val @ A2 @ B2)))))). % curryE
thf(fact_80_curryE, axiom,
    ((![F : produc515445032on_val > $o, A2 : nat > option2118145160on_val, B2 : list_char > option_val]: ((produc761261956_val_o @ F @ A2 @ B2) => (F @ (produc52622304on_val @ A2 @ B2)))))). % curryE
thf(fact_81_curryE, axiom,
    ((![F : produc655058983on_val > $o, A2 : produc335961278on_val, B2 : produc335961278on_val]: ((produc1990203021_val_o @ F @ A2 @ B2) => (F @ (produc245869591on_val @ A2 @ B2)))))). % curryE
thf(fact_82_curryE, axiom,
    ((![F : produc335961278on_val > $o, A2 : list_exp_list_char, B2 : produc515445032on_val]: ((produc1199911222_val_o @ F @ A2 @ B2) => (F @ (produc1725134254on_val @ A2 @ B2)))))). % curryE
thf(fact_83_hext__refl, axiom,
    ((![H : nat > option2118145160on_val]: (hext @ H @ H)))). % hext_refl
thf(fact_84_rtrancl__induct2, axiom,
    ((![Ax : produc1097884484on_val, Ay : produc1097884484on_val, Bx : produc1097884484on_val, By : produc1097884484on_val, R2 : set_Pr1368603847on_val, P : produc1097884484on_val > produc1097884484on_val > $o]: ((member208988944on_val @ (produc564964183on_val @ (produc1069526295on_val @ Ax @ Ay) @ (produc1069526295on_val @ Bx @ By)) @ (transi100378922on_val @ R2)) => ((P @ Ax @ Ay) => ((![A : produc1097884484on_val, B : produc1097884484on_val, Aa : produc1097884484on_val, Ba : produc1097884484on_val]: ((member208988944on_val @ (produc564964183on_val @ (produc1069526295on_val @ Ax @ Ay) @ (produc1069526295on_val @ A @ B)) @ (transi100378922on_val @ R2)) => ((member208988944on_val @ (produc564964183on_val @ (produc1069526295on_val @ A @ B) @ (produc1069526295on_val @ Aa @ Ba)) @ R2) => ((P @ A @ B) => (P @ Aa @ Ba))))) => (P @ Bx @ By))))))). % rtrancl_induct2
thf(fact_85_rtrancl__induct2, axiom,
    ((![Ax : nat > option2118145160on_val, Ay : list_char > option_val, Bx : nat > option2118145160on_val, By : list_char > option_val, R2 : set_Pr148564103on_val, P : (nat > option2118145160on_val) > (list_char > option_val) > $o]: ((member2027247312on_val @ (produc2106877847on_val @ (produc52622304on_val @ Ax @ Ay) @ (produc52622304on_val @ Bx @ By)) @ (transi432893227on_val @ R2)) => ((P @ Ax @ Ay) => ((![A : nat > option2118145160on_val, B : list_char > option_val, Aa : nat > option2118145160on_val, Ba : list_char > option_val]: ((member2027247312on_val @ (produc2106877847on_val @ (produc52622304on_val @ Ax @ Ay) @ (produc52622304on_val @ A @ B)) @ (transi432893227on_val @ R2)) => ((member2027247312on_val @ (produc2106877847on_val @ (produc52622304on_val @ A @ B) @ (produc52622304on_val @ Aa @ Ba)) @ R2) => ((P @ A @ B) => (P @ Aa @ Ba))))) => (P @ Bx @ By))))))). % rtrancl_induct2
thf(fact_86_rtrancl__induct2, axiom,
    ((![Ax : produc335961278on_val, Ay : produc335961278on_val, Bx : produc335961278on_val, By : produc335961278on_val, R2 : set_Pr1301890247on_val, P : produc335961278on_val > produc335961278on_val > $o]: ((member1743964944on_val @ (produc1802175319on_val @ (produc245869591on_val @ Ax @ Ay) @ (produc245869591on_val @ Bx @ By)) @ (transi159622442on_val @ R2)) => ((P @ Ax @ Ay) => ((![A : produc335961278on_val, B : produc335961278on_val, Aa : produc335961278on_val, Ba : produc335961278on_val]: ((member1743964944on_val @ (produc1802175319on_val @ (produc245869591on_val @ Ax @ Ay) @ (produc245869591on_val @ A @ B)) @ (transi159622442on_val @ R2)) => ((member1743964944on_val @ (produc1802175319on_val @ (produc245869591on_val @ A @ B) @ (produc245869591on_val @ Aa @ Ba)) @ R2) => ((P @ A @ B) => (P @ Aa @ Ba))))) => (P @ Bx @ By))))))). % rtrancl_induct2
thf(fact_87_rtrancl__induct2, axiom,
    ((![Ax : exp_list_char, Ay : produc515445032on_val, Bx : exp_list_char, By : produc515445032on_val, R2 : set_Pr1189492743on_val, P : exp_list_char > produc515445032on_val > $o]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ Ax @ Ay) @ (produc2023458740on_val @ Bx @ By)) @ (transi111096263on_val @ R2)) => ((P @ Ax @ Ay) => ((![A : exp_list_char, B : produc515445032on_val, Aa : exp_list_char, Ba : produc515445032on_val]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ Ax @ Ay) @ (produc2023458740on_val @ A @ B)) @ (transi111096263on_val @ R2)) => ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ A @ B) @ (produc2023458740on_val @ Aa @ Ba)) @ R2) => ((P @ A @ B) => (P @ Aa @ Ba))))) => (P @ Bx @ By))))))). % rtrancl_induct2
thf(fact_88_rtrancl__induct2, axiom,
    ((![Ax : list_exp_list_char, Ay : produc515445032on_val, Bx : list_exp_list_char, By : produc515445032on_val, R2 : set_Pr208351751on_val, P : list_exp_list_char > produc515445032on_val > $o]: ((member1689761872on_val @ (produc245869591on_val @ (produc1725134254on_val @ Ax @ Ay) @ (produc1725134254on_val @ Bx @ By)) @ (transi325225921on_val @ R2)) => ((P @ Ax @ Ay) => ((![A : list_exp_list_char, B : produc515445032on_val, Aa : list_exp_list_char, Ba : produc515445032on_val]: ((member1689761872on_val @ (produc245869591on_val @ (produc1725134254on_val @ Ax @ Ay) @ (produc1725134254on_val @ A @ B)) @ (transi325225921on_val @ R2)) => ((member1689761872on_val @ (produc245869591on_val @ (produc1725134254on_val @ A @ B) @ (produc1725134254on_val @ Aa @ Ba)) @ R2) => ((P @ A @ B) => (P @ Aa @ Ba))))) => (P @ Bx @ By))))))). % rtrancl_induct2
thf(fact_89_converse__rtranclE2, axiom,
    ((![Xa : produc1097884484on_val, Xb : produc1097884484on_val, Za : produc1097884484on_val, Zb : produc1097884484on_val, R2 : set_Pr1368603847on_val]: ((member208988944on_val @ (produc564964183on_val @ (produc1069526295on_val @ Xa @ Xb) @ (produc1069526295on_val @ Za @ Zb)) @ (transi100378922on_val @ R2)) => ((~ (((produc1069526295on_val @ Xa @ Xb) = (produc1069526295on_val @ Za @ Zb)))) => (~ ((![A : produc1097884484on_val, B : produc1097884484on_val]: ((member208988944on_val @ (produc564964183on_val @ (produc1069526295on_val @ Xa @ Xb) @ (produc1069526295on_val @ A @ B)) @ R2) => (~ ((member208988944on_val @ (produc564964183on_val @ (produc1069526295on_val @ A @ B) @ (produc1069526295on_val @ Za @ Zb)) @ (transi100378922on_val @ R2))))))))))))). % converse_rtranclE2
thf(fact_90_converse__rtranclE2, axiom,
    ((![Xa : nat > option2118145160on_val, Xb : list_char > option_val, Za : nat > option2118145160on_val, Zb : list_char > option_val, R2 : set_Pr148564103on_val]: ((member2027247312on_val @ (produc2106877847on_val @ (produc52622304on_val @ Xa @ Xb) @ (produc52622304on_val @ Za @ Zb)) @ (transi432893227on_val @ R2)) => ((~ (((produc52622304on_val @ Xa @ Xb) = (produc52622304on_val @ Za @ Zb)))) => (~ ((![A : nat > option2118145160on_val, B : list_char > option_val]: ((member2027247312on_val @ (produc2106877847on_val @ (produc52622304on_val @ Xa @ Xb) @ (produc52622304on_val @ A @ B)) @ R2) => (~ ((member2027247312on_val @ (produc2106877847on_val @ (produc52622304on_val @ A @ B) @ (produc52622304on_val @ Za @ Zb)) @ (transi432893227on_val @ R2))))))))))))). % converse_rtranclE2
thf(fact_91_converse__rtranclE2, axiom,
    ((![Xa : produc335961278on_val, Xb : produc335961278on_val, Za : produc335961278on_val, Zb : produc335961278on_val, R2 : set_Pr1301890247on_val]: ((member1743964944on_val @ (produc1802175319on_val @ (produc245869591on_val @ Xa @ Xb) @ (produc245869591on_val @ Za @ Zb)) @ (transi159622442on_val @ R2)) => ((~ (((produc245869591on_val @ Xa @ Xb) = (produc245869591on_val @ Za @ Zb)))) => (~ ((![A : produc335961278on_val, B : produc335961278on_val]: ((member1743964944on_val @ (produc1802175319on_val @ (produc245869591on_val @ Xa @ Xb) @ (produc245869591on_val @ A @ B)) @ R2) => (~ ((member1743964944on_val @ (produc1802175319on_val @ (produc245869591on_val @ A @ B) @ (produc245869591on_val @ Za @ Zb)) @ (transi159622442on_val @ R2))))))))))))). % converse_rtranclE2
thf(fact_92_converse__rtranclE2, axiom,
    ((![Xa : exp_list_char, Xb : produc515445032on_val, Za : exp_list_char, Zb : produc515445032on_val, R2 : set_Pr1189492743on_val]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ Xa @ Xb) @ (produc2023458740on_val @ Za @ Zb)) @ (transi111096263on_val @ R2)) => ((~ (((produc2023458740on_val @ Xa @ Xb) = (produc2023458740on_val @ Za @ Zb)))) => (~ ((![A : exp_list_char, B : produc515445032on_val]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ Xa @ Xb) @ (produc2023458740on_val @ A @ B)) @ R2) => (~ ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ A @ B) @ (produc2023458740on_val @ Za @ Zb)) @ (transi111096263on_val @ R2))))))))))))). % converse_rtranclE2
thf(fact_93_converse__rtranclE2, axiom,
    ((![Xa : list_exp_list_char, Xb : produc515445032on_val, Za : list_exp_list_char, Zb : produc515445032on_val, R2 : set_Pr208351751on_val]: ((member1689761872on_val @ (produc245869591on_val @ (produc1725134254on_val @ Xa @ Xb) @ (produc1725134254on_val @ Za @ Zb)) @ (transi325225921on_val @ R2)) => ((~ (((produc1725134254on_val @ Xa @ Xb) = (produc1725134254on_val @ Za @ Zb)))) => (~ ((![A : list_exp_list_char, B : produc515445032on_val]: ((member1689761872on_val @ (produc245869591on_val @ (produc1725134254on_val @ Xa @ Xb) @ (produc1725134254on_val @ A @ B)) @ R2) => (~ ((member1689761872on_val @ (produc245869591on_val @ (produc1725134254on_val @ A @ B) @ (produc1725134254on_val @ Za @ Zb)) @ (transi325225921on_val @ R2))))))))))))). % converse_rtranclE2
thf(fact_94_converse__rtrancl__induct2, axiom,
    ((![Ax : produc1097884484on_val, Ay : produc1097884484on_val, Bx : produc1097884484on_val, By : produc1097884484on_val, R2 : set_Pr1368603847on_val, P : produc1097884484on_val > produc1097884484on_val > $o]: ((member208988944on_val @ (produc564964183on_val @ (produc1069526295on_val @ Ax @ Ay) @ (produc1069526295on_val @ Bx @ By)) @ (transi100378922on_val @ R2)) => ((P @ Bx @ By) => ((![A : produc1097884484on_val, B : produc1097884484on_val, Aa : produc1097884484on_val, Ba : produc1097884484on_val]: ((member208988944on_val @ (produc564964183on_val @ (produc1069526295on_val @ A @ B) @ (produc1069526295on_val @ Aa @ Ba)) @ R2) => ((member208988944on_val @ (produc564964183on_val @ (produc1069526295on_val @ Aa @ Ba) @ (produc1069526295on_val @ Bx @ By)) @ (transi100378922on_val @ R2)) => ((P @ Aa @ Ba) => (P @ A @ B))))) => (P @ Ax @ Ay))))))). % converse_rtrancl_induct2
thf(fact_95_converse__rtrancl__induct2, axiom,
    ((![Ax : nat > option2118145160on_val, Ay : list_char > option_val, Bx : nat > option2118145160on_val, By : list_char > option_val, R2 : set_Pr148564103on_val, P : (nat > option2118145160on_val) > (list_char > option_val) > $o]: ((member2027247312on_val @ (produc2106877847on_val @ (produc52622304on_val @ Ax @ Ay) @ (produc52622304on_val @ Bx @ By)) @ (transi432893227on_val @ R2)) => ((P @ Bx @ By) => ((![A : nat > option2118145160on_val, B : list_char > option_val, Aa : nat > option2118145160on_val, Ba : list_char > option_val]: ((member2027247312on_val @ (produc2106877847on_val @ (produc52622304on_val @ A @ B) @ (produc52622304on_val @ Aa @ Ba)) @ R2) => ((member2027247312on_val @ (produc2106877847on_val @ (produc52622304on_val @ Aa @ Ba) @ (produc52622304on_val @ Bx @ By)) @ (transi432893227on_val @ R2)) => ((P @ Aa @ Ba) => (P @ A @ B))))) => (P @ Ax @ Ay))))))). % converse_rtrancl_induct2
thf(fact_96_converse__rtrancl__induct2, axiom,
    ((![Ax : produc335961278on_val, Ay : produc335961278on_val, Bx : produc335961278on_val, By : produc335961278on_val, R2 : set_Pr1301890247on_val, P : produc335961278on_val > produc335961278on_val > $o]: ((member1743964944on_val @ (produc1802175319on_val @ (produc245869591on_val @ Ax @ Ay) @ (produc245869591on_val @ Bx @ By)) @ (transi159622442on_val @ R2)) => ((P @ Bx @ By) => ((![A : produc335961278on_val, B : produc335961278on_val, Aa : produc335961278on_val, Ba : produc335961278on_val]: ((member1743964944on_val @ (produc1802175319on_val @ (produc245869591on_val @ A @ B) @ (produc245869591on_val @ Aa @ Ba)) @ R2) => ((member1743964944on_val @ (produc1802175319on_val @ (produc245869591on_val @ Aa @ Ba) @ (produc245869591on_val @ Bx @ By)) @ (transi159622442on_val @ R2)) => ((P @ Aa @ Ba) => (P @ A @ B))))) => (P @ Ax @ Ay))))))). % converse_rtrancl_induct2
thf(fact_97_converse__rtrancl__induct2, axiom,
    ((![Ax : exp_list_char, Ay : produc515445032on_val, Bx : exp_list_char, By : produc515445032on_val, R2 : set_Pr1189492743on_val, P : exp_list_char > produc515445032on_val > $o]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ Ax @ Ay) @ (produc2023458740on_val @ Bx @ By)) @ (transi111096263on_val @ R2)) => ((P @ Bx @ By) => ((![A : exp_list_char, B : produc515445032on_val, Aa : exp_list_char, Ba : produc515445032on_val]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ A @ B) @ (produc2023458740on_val @ Aa @ Ba)) @ R2) => ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ Aa @ Ba) @ (produc2023458740on_val @ Bx @ By)) @ (transi111096263on_val @ R2)) => ((P @ Aa @ Ba) => (P @ A @ B))))) => (P @ Ax @ Ay))))))). % converse_rtrancl_induct2
thf(fact_98_converse__rtrancl__induct2, axiom,
    ((![Ax : list_exp_list_char, Ay : produc515445032on_val, Bx : list_exp_list_char, By : produc515445032on_val, R2 : set_Pr208351751on_val, P : list_exp_list_char > produc515445032on_val > $o]: ((member1689761872on_val @ (produc245869591on_val @ (produc1725134254on_val @ Ax @ Ay) @ (produc1725134254on_val @ Bx @ By)) @ (transi325225921on_val @ R2)) => ((P @ Bx @ By) => ((![A : list_exp_list_char, B : produc515445032on_val, Aa : list_exp_list_char, Ba : produc515445032on_val]: ((member1689761872on_val @ (produc245869591on_val @ (produc1725134254on_val @ A @ B) @ (produc1725134254on_val @ Aa @ Ba)) @ R2) => ((member1689761872on_val @ (produc245869591on_val @ (produc1725134254on_val @ Aa @ Ba) @ (produc1725134254on_val @ Bx @ By)) @ (transi325225921on_val @ R2)) => ((P @ Aa @ Ba) => (P @ A @ B))))) => (P @ Ax @ Ay))))))). % converse_rtrancl_induct2
thf(fact_99_map__add__assoc, axiom,
    ((![M1 : list_char > option_val, M2 : list_char > option_val, M3 : list_char > option_val]: ((map_ad1615113112ar_val @ M1 @ (map_ad1615113112ar_val @ M2 @ M3)) = (map_ad1615113112ar_val @ (map_ad1615113112ar_val @ M1 @ M2) @ M3))))). % map_add_assoc
thf(fact_100_r__into__rtrancl, axiom,
    ((![P2 : produc1172664615on_val, R2 : set_Pr1189492743on_val]: ((member354538064on_val @ P2 @ R2) => (member354538064on_val @ P2 @ (transi111096263on_val @ R2)))))). % r_into_rtrancl
thf(fact_101_r__into__rtrancl, axiom,
    ((![P2 : produc655058983on_val, R2 : set_Pr208351751on_val]: ((member1689761872on_val @ P2 @ R2) => (member1689761872on_val @ P2 @ (transi325225921on_val @ R2)))))). % r_into_rtrancl
thf(fact_102_rtrancl__idemp, axiom,
    ((![R2 : set_Pr1189492743on_val]: ((transi111096263on_val @ (transi111096263on_val @ R2)) = (transi111096263on_val @ R2))))). % rtrancl_idemp
thf(fact_103_rtrancl__idemp, axiom,
    ((![R2 : set_Pr208351751on_val]: ((transi325225921on_val @ (transi325225921on_val @ R2)) = (transi325225921on_val @ R2))))). % rtrancl_idemp
thf(fact_104_WTrt__hext__mono, axiom,
    ((![P : list_P1234162913t_char, H : nat > option2118145160on_val, E5 : list_char > option_ty, E : exp_list_char, T : ty, H2 : nat > option2118145160on_val]: ((wTrt @ P @ H @ E5 @ E @ T) => ((hext @ H @ H2) => (wTrt @ P @ H2 @ E5 @ E @ T)))))). % WTrt_hext_mono
thf(fact_105_hext__trans, axiom,
    ((![H : nat > option2118145160on_val, H2 : nat > option2118145160on_val, H5 : nat > option2118145160on_val]: ((hext @ H @ H2) => ((hext @ H2 @ H5) => (hext @ H @ H5)))))). % hext_trans
thf(fact_106_rtranclE, axiom,
    ((![A2 : produc1097884484on_val, B2 : produc1097884484on_val, R2 : set_Pr1189492743on_val]: ((member354538064on_val @ (produc1069526295on_val @ A2 @ B2) @ (transi111096263on_val @ R2)) => ((~ ((A2 = B2))) => (~ ((![Y3 : produc1097884484on_val]: ((member354538064on_val @ (produc1069526295on_val @ A2 @ Y3) @ (transi111096263on_val @ R2)) => (~ ((member354538064on_val @ (produc1069526295on_val @ Y3 @ B2) @ R2)))))))))))). % rtranclE
thf(fact_107_rtranclE, axiom,
    ((![A2 : produc335961278on_val, B2 : produc335961278on_val, R2 : set_Pr208351751on_val]: ((member1689761872on_val @ (produc245869591on_val @ A2 @ B2) @ (transi325225921on_val @ R2)) => ((~ ((A2 = B2))) => (~ ((![Y3 : produc335961278on_val]: ((member1689761872on_val @ (produc245869591on_val @ A2 @ Y3) @ (transi325225921on_val @ R2)) => (~ ((member1689761872on_val @ (produc245869591on_val @ Y3 @ B2) @ R2)))))))))))). % rtranclE
thf(fact_108_rtrancl_Ocases, axiom,
    ((![A1 : produc1097884484on_val, A22 : produc1097884484on_val, R2 : set_Pr1189492743on_val]: ((member354538064on_val @ (produc1069526295on_val @ A1 @ A22) @ (transi111096263on_val @ R2)) => ((~ ((A22 = A1))) => (~ ((![B : produc1097884484on_val]: ((member354538064on_val @ (produc1069526295on_val @ A1 @ B) @ (transi111096263on_val @ R2)) => (~ ((member354538064on_val @ (produc1069526295on_val @ B @ A22) @ R2)))))))))))). % rtrancl.cases
thf(fact_109_rtrancl_Ocases, axiom,
    ((![A1 : produc335961278on_val, A22 : produc335961278on_val, R2 : set_Pr208351751on_val]: ((member1689761872on_val @ (produc245869591on_val @ A1 @ A22) @ (transi325225921on_val @ R2)) => ((~ ((A22 = A1))) => (~ ((![B : produc335961278on_val]: ((member1689761872on_val @ (produc245869591on_val @ A1 @ B) @ (transi325225921on_val @ R2)) => (~ ((member1689761872on_val @ (produc245869591on_val @ B @ A22) @ R2)))))))))))). % rtrancl.cases
thf(fact_110_rtrancl_Osimps, axiom,
    ((![A1 : produc1097884484on_val, A22 : produc1097884484on_val, R2 : set_Pr1189492743on_val]: ((member354538064on_val @ (produc1069526295on_val @ A1 @ A22) @ (transi111096263on_val @ R2)) = (((?[A4 : produc1097884484on_val]: (((A1 = A4)) & ((A22 = A4))))) | ((?[A4 : produc1097884484on_val]: (?[B4 : produc1097884484on_val]: (?[C2 : produc1097884484on_val]: (((A1 = A4)) & ((((A22 = C2)) & ((((member354538064on_val @ (produc1069526295on_val @ A4 @ B4) @ (transi111096263on_val @ R2))) & ((member354538064on_val @ (produc1069526295on_val @ B4 @ C2) @ R2)))))))))))))))). % rtrancl.simps
thf(fact_111_rtrancl_Osimps, axiom,
    ((![A1 : produc335961278on_val, A22 : produc335961278on_val, R2 : set_Pr208351751on_val]: ((member1689761872on_val @ (produc245869591on_val @ A1 @ A22) @ (transi325225921on_val @ R2)) = (((?[A4 : produc335961278on_val]: (((A1 = A4)) & ((A22 = A4))))) | ((?[A4 : produc335961278on_val]: (?[B4 : produc335961278on_val]: (?[C2 : produc335961278on_val]: (((A1 = A4)) & ((((A22 = C2)) & ((((member1689761872on_val @ (produc245869591on_val @ A4 @ B4) @ (transi325225921on_val @ R2))) & ((member1689761872on_val @ (produc245869591on_val @ B4 @ C2) @ R2)))))))))))))))). % rtrancl.simps
thf(fact_112_rtrancl__trans, axiom,
    ((![X : produc1097884484on_val, Y : produc1097884484on_val, R2 : set_Pr1189492743on_val, Z : produc1097884484on_val]: ((member354538064on_val @ (produc1069526295on_val @ X @ Y) @ (transi111096263on_val @ R2)) => ((member354538064on_val @ (produc1069526295on_val @ Y @ Z) @ (transi111096263on_val @ R2)) => (member354538064on_val @ (produc1069526295on_val @ X @ Z) @ (transi111096263on_val @ R2))))))). % rtrancl_trans
thf(fact_113_rtrancl__trans, axiom,
    ((![X : produc335961278on_val, Y : produc335961278on_val, R2 : set_Pr208351751on_val, Z : produc335961278on_val]: ((member1689761872on_val @ (produc245869591on_val @ X @ Y) @ (transi325225921on_val @ R2)) => ((member1689761872on_val @ (produc245869591on_val @ Y @ Z) @ (transi325225921on_val @ R2)) => (member1689761872on_val @ (produc245869591on_val @ X @ Z) @ (transi325225921on_val @ R2))))))). % rtrancl_trans
thf(fact_114_rtrancl__induct, axiom,
    ((![A2 : produc1097884484on_val, B2 : produc1097884484on_val, R2 : set_Pr1189492743on_val, P : produc1097884484on_val > $o]: ((member354538064on_val @ (produc1069526295on_val @ A2 @ B2) @ (transi111096263on_val @ R2)) => ((P @ A2) => ((![Y3 : produc1097884484on_val, Z2 : produc1097884484on_val]: ((member354538064on_val @ (produc1069526295on_val @ A2 @ Y3) @ (transi111096263on_val @ R2)) => ((member354538064on_val @ (produc1069526295on_val @ Y3 @ Z2) @ R2) => ((P @ Y3) => (P @ Z2))))) => (P @ B2))))))). % rtrancl_induct
thf(fact_115_rtrancl__induct, axiom,
    ((![A2 : produc335961278on_val, B2 : produc335961278on_val, R2 : set_Pr208351751on_val, P : produc335961278on_val > $o]: ((member1689761872on_val @ (produc245869591on_val @ A2 @ B2) @ (transi325225921on_val @ R2)) => ((P @ A2) => ((![Y3 : produc335961278on_val, Z2 : produc335961278on_val]: ((member1689761872on_val @ (produc245869591on_val @ A2 @ Y3) @ (transi325225921on_val @ R2)) => ((member1689761872on_val @ (produc245869591on_val @ Y3 @ Z2) @ R2) => ((P @ Y3) => (P @ Z2))))) => (P @ B2))))))). % rtrancl_induct
thf(fact_116_rtrancl_Oinducts, axiom,
    ((![X1 : produc1097884484on_val, X2 : produc1097884484on_val, R2 : set_Pr1189492743on_val, P : produc1097884484on_val > produc1097884484on_val > $o]: ((member354538064on_val @ (produc1069526295on_val @ X1 @ X2) @ (transi111096263on_val @ R2)) => ((![A : produc1097884484on_val]: (P @ A @ A)) => ((![A : produc1097884484on_val, B : produc1097884484on_val, C : produc1097884484on_val]: ((member354538064on_val @ (produc1069526295on_val @ A @ B) @ (transi111096263on_val @ R2)) => ((P @ A @ B) => ((member354538064on_val @ (produc1069526295on_val @ B @ C) @ R2) => (P @ A @ C))))) => (P @ X1 @ X2))))))). % rtrancl.inducts
thf(fact_117_rtrancl_Oinducts, axiom,
    ((![X1 : produc335961278on_val, X2 : produc335961278on_val, R2 : set_Pr208351751on_val, P : produc335961278on_val > produc335961278on_val > $o]: ((member1689761872on_val @ (produc245869591on_val @ X1 @ X2) @ (transi325225921on_val @ R2)) => ((![A : produc335961278on_val]: (P @ A @ A)) => ((![A : produc335961278on_val, B : produc335961278on_val, C : produc335961278on_val]: ((member1689761872on_val @ (produc245869591on_val @ A @ B) @ (transi325225921on_val @ R2)) => ((P @ A @ B) => ((member1689761872on_val @ (produc245869591on_val @ B @ C) @ R2) => (P @ A @ C))))) => (P @ X1 @ X2))))))). % rtrancl.inducts
thf(fact_118_mem__Collect__eq, axiom,
    ((![A2 : produc1172664615on_val, P : produc1172664615on_val > $o]: ((member354538064on_val @ A2 @ (collec2055896722on_val @ P)) = (P @ A2))))). % mem_Collect_eq
thf(fact_119_mem__Collect__eq, axiom,
    ((![A2 : produc655058983on_val, P : produc655058983on_val > $o]: ((member1689761872on_val @ A2 @ (collec105960082on_val @ P)) = (P @ A2))))). % mem_Collect_eq
thf(fact_120_Collect__mem__eq, axiom,
    ((![A5 : set_Pr1189492743on_val]: ((collec2055896722on_val @ (^[X4 : produc1172664615on_val]: (member354538064on_val @ X4 @ A5))) = A5)))). % Collect_mem_eq
thf(fact_121_Collect__mem__eq, axiom,
    ((![A5 : set_Pr208351751on_val]: ((collec105960082on_val @ (^[X4 : produc655058983on_val]: (member1689761872on_val @ X4 @ A5))) = A5)))). % Collect_mem_eq
thf(fact_122_converse__rtranclE, axiom,
    ((![X : produc1097884484on_val, Z : produc1097884484on_val, R2 : set_Pr1189492743on_val]: ((member354538064on_val @ (produc1069526295on_val @ X @ Z) @ (transi111096263on_val @ R2)) => ((~ ((X = Z))) => (~ ((![Y3 : produc1097884484on_val]: ((member354538064on_val @ (produc1069526295on_val @ X @ Y3) @ R2) => (~ ((member354538064on_val @ (produc1069526295on_val @ Y3 @ Z) @ (transi111096263on_val @ R2))))))))))))). % converse_rtranclE
thf(fact_123_converse__rtranclE, axiom,
    ((![X : produc335961278on_val, Z : produc335961278on_val, R2 : set_Pr208351751on_val]: ((member1689761872on_val @ (produc245869591on_val @ X @ Z) @ (transi325225921on_val @ R2)) => ((~ ((X = Z))) => (~ ((![Y3 : produc335961278on_val]: ((member1689761872on_val @ (produc245869591on_val @ X @ Y3) @ R2) => (~ ((member1689761872on_val @ (produc245869591on_val @ Y3 @ Z) @ (transi325225921on_val @ R2))))))))))))). % converse_rtranclE
thf(fact_124_rtrancl_Ortrancl__refl, axiom,
    ((![A2 : produc1097884484on_val, R2 : set_Pr1189492743on_val]: (member354538064on_val @ (produc1069526295on_val @ A2 @ A2) @ (transi111096263on_val @ R2))))). % rtrancl.rtrancl_refl
thf(fact_125_rtrancl_Ortrancl__refl, axiom,
    ((![A2 : produc335961278on_val, R2 : set_Pr208351751on_val]: (member1689761872on_val @ (produc245869591on_val @ A2 @ A2) @ (transi325225921on_val @ R2))))). % rtrancl.rtrancl_refl
thf(fact_126_converse__rtrancl__induct, axiom,
    ((![A2 : produc1097884484on_val, B2 : produc1097884484on_val, R2 : set_Pr1189492743on_val, P : produc1097884484on_val > $o]: ((member354538064on_val @ (produc1069526295on_val @ A2 @ B2) @ (transi111096263on_val @ R2)) => ((P @ B2) => ((![Y3 : produc1097884484on_val, Z2 : produc1097884484on_val]: ((member354538064on_val @ (produc1069526295on_val @ Y3 @ Z2) @ R2) => ((member354538064on_val @ (produc1069526295on_val @ Z2 @ B2) @ (transi111096263on_val @ R2)) => ((P @ Z2) => (P @ Y3))))) => (P @ A2))))))). % converse_rtrancl_induct
thf(fact_127_converse__rtrancl__induct, axiom,
    ((![A2 : produc335961278on_val, B2 : produc335961278on_val, R2 : set_Pr208351751on_val, P : produc335961278on_val > $o]: ((member1689761872on_val @ (produc245869591on_val @ A2 @ B2) @ (transi325225921on_val @ R2)) => ((P @ B2) => ((![Y3 : produc335961278on_val, Z2 : produc335961278on_val]: ((member1689761872on_val @ (produc245869591on_val @ Y3 @ Z2) @ R2) => ((member1689761872on_val @ (produc245869591on_val @ Z2 @ B2) @ (transi325225921on_val @ R2)) => ((P @ Z2) => (P @ Y3))))) => (P @ A2))))))). % converse_rtrancl_induct
thf(fact_128_rtrancl_Ortrancl__into__rtrancl, axiom,
    ((![A2 : produc1097884484on_val, B2 : produc1097884484on_val, R2 : set_Pr1189492743on_val, C3 : produc1097884484on_val]: ((member354538064on_val @ (produc1069526295on_val @ A2 @ B2) @ (transi111096263on_val @ R2)) => ((member354538064on_val @ (produc1069526295on_val @ B2 @ C3) @ R2) => (member354538064on_val @ (produc1069526295on_val @ A2 @ C3) @ (transi111096263on_val @ R2))))))). % rtrancl.rtrancl_into_rtrancl
thf(fact_129_rtrancl_Ortrancl__into__rtrancl, axiom,
    ((![A2 : produc335961278on_val, B2 : produc335961278on_val, R2 : set_Pr208351751on_val, C3 : produc335961278on_val]: ((member1689761872on_val @ (produc245869591on_val @ A2 @ B2) @ (transi325225921on_val @ R2)) => ((member1689761872on_val @ (produc245869591on_val @ B2 @ C3) @ R2) => (member1689761872on_val @ (produc245869591on_val @ A2 @ C3) @ (transi325225921on_val @ R2))))))). % rtrancl.rtrancl_into_rtrancl
thf(fact_130_converse__rtrancl__into__rtrancl, axiom,
    ((![A2 : produc1097884484on_val, B2 : produc1097884484on_val, R2 : set_Pr1189492743on_val, C3 : produc1097884484on_val]: ((member354538064on_val @ (produc1069526295on_val @ A2 @ B2) @ R2) => ((member354538064on_val @ (produc1069526295on_val @ B2 @ C3) @ (transi111096263on_val @ R2)) => (member354538064on_val @ (produc1069526295on_val @ A2 @ C3) @ (transi111096263on_val @ R2))))))). % converse_rtrancl_into_rtrancl
thf(fact_131_converse__rtrancl__into__rtrancl, axiom,
    ((![A2 : produc335961278on_val, B2 : produc335961278on_val, R2 : set_Pr208351751on_val, C3 : produc335961278on_val]: ((member1689761872on_val @ (produc245869591on_val @ A2 @ B2) @ R2) => ((member1689761872on_val @ (produc245869591on_val @ B2 @ C3) @ (transi325225921on_val @ R2)) => (member1689761872on_val @ (produc245869591on_val @ A2 @ C3) @ (transi325225921on_val @ R2))))))). % converse_rtrancl_into_rtrancl
thf(fact_132_reds__hext__incr, axiom,
    ((![Es : list_exp_list_char, H : nat > option2118145160on_val, L : list_char > option_val, Es2 : list_exp_list_char, H2 : nat > option2118145160on_val, L2 : list_char > option_val, P : list_P1234162913t_char]: ((member1689761872on_val @ (produc245869591on_val @ (produc1725134254on_val @ Es @ (produc52622304on_val @ H @ L)) @ (produc1725134254on_val @ Es2 @ (produc52622304on_val @ H2 @ L2))) @ (reds @ P)) => (hext @ H @ H2))))). % reds_hext_incr
thf(fact_133_single__valued__confluent, axiom,
    ((![R2 : set_Pr1189492743on_val, X : produc1097884484on_val, Y : produc1097884484on_val, Z : produc1097884484on_val]: ((single747474179on_val @ R2) => ((member354538064on_val @ (produc1069526295on_val @ X @ Y) @ (transi111096263on_val @ R2)) => ((member354538064on_val @ (produc1069526295on_val @ X @ Z) @ (transi111096263on_val @ R2)) => ((member354538064on_val @ (produc1069526295on_val @ Y @ Z) @ (transi111096263on_val @ R2)) | (member354538064on_val @ (produc1069526295on_val @ Z @ Y) @ (transi111096263on_val @ R2))))))))). % single_valued_confluent
thf(fact_134_single__valued__confluent, axiom,
    ((![R2 : set_Pr208351751on_val, X : produc335961278on_val, Y : produc335961278on_val, Z : produc335961278on_val]: ((single965918723on_val @ R2) => ((member1689761872on_val @ (produc245869591on_val @ X @ Y) @ (transi325225921on_val @ R2)) => ((member1689761872on_val @ (produc245869591on_val @ X @ Z) @ (transi325225921on_val @ R2)) => ((member1689761872on_val @ (produc245869591on_val @ Y @ Z) @ (transi325225921on_val @ R2)) | (member1689761872on_val @ (produc245869591on_val @ Z @ Y) @ (transi325225921on_val @ R2))))))))). % single_valued_confluent
thf(fact_135_red__reds_OThrowThrow, axiom,
    ((![E : exp_list_char, S : produc515445032on_val, P : list_P1234162913t_char]: (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (throw_list_char @ (throw_list_char @ E)) @ S) @ (produc2023458740on_val @ (throw_list_char @ E) @ S)) @ (red @ P))))). % red_reds.ThrowThrow
thf(fact_136_red__reds_OThrowRed, axiom,
    ((![E : exp_list_char, S : produc515445032on_val, E2 : exp_list_char, S2 : produc515445032on_val, P : list_P1234162913t_char]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E @ S) @ (produc2023458740on_val @ E2 @ S2)) @ (red @ P)) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (throw_list_char @ E) @ S) @ (produc2023458740on_val @ (throw_list_char @ E2) @ S2)) @ (red @ P)))))). % red_reds.ThrowRed
thf(fact_137_red__reds_OTryRed, axiom,
    ((![E : exp_list_char, S : produc515445032on_val, E2 : exp_list_char, S2 : produc515445032on_val, P : list_P1234162913t_char, C4 : list_char, V : list_char, E_2 : exp_list_char]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E @ S) @ (produc2023458740on_val @ E2 @ S2)) @ (red @ P)) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (tryCatch_list_char @ E @ C4 @ V @ E_2) @ S) @ (produc2023458740on_val @ (tryCatch_list_char @ E2 @ C4 @ V @ E_2) @ S2)) @ (red @ P)))))). % red_reds.TryRed
thf(fact_138_red__reds_OFAccRed, axiom,
    ((![E : exp_list_char, S : produc515445032on_val, E2 : exp_list_char, S2 : produc515445032on_val, P : list_P1234162913t_char, F2 : list_char, D2 : list_char]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E @ S) @ (produc2023458740on_val @ E2 @ S2)) @ (red @ P)) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (fAcc_list_char @ E @ F2 @ D2) @ S) @ (produc2023458740on_val @ (fAcc_list_char @ E2 @ F2 @ D2) @ S2)) @ (red @ P)))))). % red_reds.FAccRed
thf(fact_139_red__reds_OCastRed, axiom,
    ((![E : exp_list_char, S : produc515445032on_val, E2 : exp_list_char, S2 : produc515445032on_val, P : list_P1234162913t_char, C4 : list_char]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E @ S) @ (produc2023458740on_val @ E2 @ S2)) @ (red @ P)) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (cast_list_char @ C4 @ E) @ S) @ (produc2023458740on_val @ (cast_list_char @ C4 @ E2) @ S2)) @ (red @ P)))))). % red_reds.CastRed
thf(fact_140_red__reds_OCastThrow, axiom,
    ((![C4 : list_char, E : exp_list_char, S : produc515445032on_val, P : list_P1234162913t_char]: (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (cast_list_char @ C4 @ (throw_list_char @ E)) @ S) @ (produc2023458740on_val @ (throw_list_char @ E) @ S)) @ (red @ P))))). % red_reds.CastThrow
thf(fact_141_red__reds_OFAccThrow, axiom,
    ((![E : exp_list_char, F2 : list_char, D2 : list_char, S : produc515445032on_val, P : list_P1234162913t_char]: (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (fAcc_list_char @ (throw_list_char @ E) @ F2 @ D2) @ S) @ (produc2023458740on_val @ (throw_list_char @ E) @ S)) @ (red @ P))))). % red_reds.FAccThrow
thf(fact_142_FAccRedsThrow, axiom,
    ((![E : exp_list_char, S : produc515445032on_val, A2 : exp_list_char, S2 : produc515445032on_val, P : list_P1234162913t_char, F2 : list_char, D2 : list_char]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E @ S) @ (produc2023458740on_val @ (throw_list_char @ A2) @ S2)) @ (transi111096263on_val @ (red @ P))) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (fAcc_list_char @ E @ F2 @ D2) @ S) @ (produc2023458740on_val @ (throw_list_char @ A2) @ S2)) @ (transi111096263on_val @ (red @ P))))))). % FAccRedsThrow
thf(fact_143_CastRedsThrow, axiom,
    ((![E : exp_list_char, S : produc515445032on_val, A2 : exp_list_char, S2 : produc515445032on_val, P : list_P1234162913t_char, C4 : list_char]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E @ S) @ (produc2023458740on_val @ (throw_list_char @ A2) @ S2)) @ (transi111096263on_val @ (red @ P))) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (cast_list_char @ C4 @ E) @ S) @ (produc2023458740on_val @ (throw_list_char @ A2) @ S2)) @ (transi111096263on_val @ (red @ P))))))). % CastRedsThrow
thf(fact_144_TryReds, axiom,
    ((![E : exp_list_char, S : produc515445032on_val, E2 : exp_list_char, S2 : produc515445032on_val, P : list_P1234162913t_char, C4 : list_char, V : list_char, E_2 : exp_list_char]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E @ S) @ (produc2023458740on_val @ E2 @ S2)) @ (transi111096263on_val @ (red @ P))) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (tryCatch_list_char @ E @ C4 @ V @ E_2) @ S) @ (produc2023458740on_val @ (tryCatch_list_char @ E2 @ C4 @ V @ E_2) @ S2)) @ (transi111096263on_val @ (red @ P))))))). % TryReds
thf(fact_145_FAccReds, axiom,
    ((![E : exp_list_char, S : produc515445032on_val, E2 : exp_list_char, S2 : produc515445032on_val, P : list_P1234162913t_char, F2 : list_char, D2 : list_char]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E @ S) @ (produc2023458740on_val @ E2 @ S2)) @ (transi111096263on_val @ (red @ P))) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (fAcc_list_char @ E @ F2 @ D2) @ S) @ (produc2023458740on_val @ (fAcc_list_char @ E2 @ F2 @ D2) @ S2)) @ (transi111096263on_val @ (red @ P))))))). % FAccReds
thf(fact_146_CastReds, axiom,
    ((![E : exp_list_char, S : produc515445032on_val, E2 : exp_list_char, S2 : produc515445032on_val, P : list_P1234162913t_char, C4 : list_char]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E @ S) @ (produc2023458740on_val @ E2 @ S2)) @ (transi111096263on_val @ (red @ P))) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (cast_list_char @ C4 @ E) @ S) @ (produc2023458740on_val @ (cast_list_char @ C4 @ E2) @ S2)) @ (transi111096263on_val @ (red @ P))))))). % CastReds
thf(fact_147_ThrowRedsThrow, axiom,
    ((![E : exp_list_char, S : produc515445032on_val, A2 : exp_list_char, S2 : produc515445032on_val, P : list_P1234162913t_char]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E @ S) @ (produc2023458740on_val @ (throw_list_char @ A2) @ S2)) @ (transi111096263on_val @ (red @ P))) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (throw_list_char @ E) @ S) @ (produc2023458740on_val @ (throw_list_char @ A2) @ S2)) @ (transi111096263on_val @ (red @ P))))))). % ThrowRedsThrow
thf(fact_148_ThrowReds, axiom,
    ((![E : exp_list_char, S : produc515445032on_val, E2 : exp_list_char, S2 : produc515445032on_val, P : list_P1234162913t_char]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E @ S) @ (produc2023458740on_val @ E2 @ S2)) @ (transi111096263on_val @ (red @ P))) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (throw_list_char @ E) @ S) @ (produc2023458740on_val @ (throw_list_char @ E2) @ S2)) @ (transi111096263on_val @ (red @ P))))))). % ThrowReds
thf(fact_149_exp_Oinject_I15_J, axiom,
    ((![X151 : exp_list_char, X152 : list_char, X153 : list_char, X154 : exp_list_char, Y151 : exp_list_char, Y152 : list_char, Y153 : list_char, Y154 : exp_list_char]: (((tryCatch_list_char @ X151 @ X152 @ X153 @ X154) = (tryCatch_list_char @ Y151 @ Y152 @ Y153 @ Y154)) = (((X151 = Y151)) & ((((X152 = Y152)) & ((((X153 = Y153)) & ((X154 = Y154))))))))))). % exp.inject(15)
thf(fact_150_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_151_exp_Oinject_I2_J, axiom,
    ((![X21 : list_char, X22 : exp_list_char, Y21 : list_char, Y22 : exp_list_char]: (((cast_list_char @ X21 @ X22) = (cast_list_char @ Y21 @ Y22)) = (((X21 = Y21)) & ((X22 = Y22))))))). % exp.inject(2)
thf(fact_152_exp_Oinject_I14_J, axiom,
    ((![X14 : exp_list_char, Y14 : exp_list_char]: (((throw_list_char @ X14) = (throw_list_char @ Y14)) = (X14 = Y14))))). % exp.inject(14)
thf(fact_153_ListReds1, axiom,
    ((![E : exp_list_char, S : produc515445032on_val, E2 : exp_list_char, S2 : produc515445032on_val, P : list_P1234162913t_char, Es : list_exp_list_char]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E @ S) @ (produc2023458740on_val @ E2 @ S2)) @ (transi111096263on_val @ (red @ P))) => (member1689761872on_val @ (produc245869591on_val @ (produc1725134254on_val @ (cons_exp_list_char @ E @ Es) @ S) @ (produc1725134254on_val @ (cons_exp_list_char @ E2 @ Es) @ S2)) @ (transi325225921on_val @ (reds @ P))))))). % ListReds1
thf(fact_154_red__reds_OListRed1, axiom,
    ((![E : exp_list_char, S : produc515445032on_val, E2 : exp_list_char, S2 : produc515445032on_val, P : list_P1234162913t_char, Es : list_exp_list_char]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E @ S) @ (produc2023458740on_val @ E2 @ S2)) @ (red @ P)) => (member1689761872on_val @ (produc245869591on_val @ (produc1725134254on_val @ (cons_exp_list_char @ E @ Es) @ S) @ (produc1725134254on_val @ (cons_exp_list_char @ E2 @ Es) @ S2)) @ (reds @ P)))))). % red_reds.ListRed1
thf(fact_155_exp_Odistinct_I51_J, axiom,
    ((![X21 : list_char, X22 : exp_list_char, X14 : exp_list_char]: (~ (((cast_list_char @ X21 @ X22) = (throw_list_char @ X14))))))). % exp.distinct(51)
thf(fact_156_exp_Odistinct_I151_J, axiom,
    ((![X71 : exp_list_char, X72 : list_char, X73 : list_char, X14 : exp_list_char]: (~ (((fAcc_list_char @ X71 @ X72 @ X73) = (throw_list_char @ X14))))))). % exp.distinct(151)
thf(fact_157_exp_Odistinct_I209_J, axiom,
    ((![X14 : exp_list_char, X151 : exp_list_char, X152 : list_char, X153 : list_char, X154 : exp_list_char]: (~ (((throw_list_char @ X14) = (tryCatch_list_char @ X151 @ X152 @ X153 @ X154))))))). % exp.distinct(209)
thf(fact_158_exp_Odistinct_I37_J, axiom,
    ((![X21 : list_char, X22 : exp_list_char, X71 : exp_list_char, X72 : list_char, X73 : list_char]: (~ (((cast_list_char @ X21 @ X22) = (fAcc_list_char @ X71 @ X72 @ X73))))))). % exp.distinct(37)
thf(fact_159_exp_Odistinct_I53_J, axiom,
    ((![X21 : list_char, X22 : exp_list_char, X151 : exp_list_char, X152 : list_char, X153 : list_char, X154 : exp_list_char]: (~ (((cast_list_char @ X21 @ X22) = (tryCatch_list_char @ X151 @ X152 @ X153 @ X154))))))). % exp.distinct(53)
thf(fact_160_exp_Odistinct_I153_J, axiom,
    ((![X71 : exp_list_char, X72 : list_char, X73 : list_char, X151 : exp_list_char, X152 : list_char, X153 : list_char, X154 : exp_list_char]: (~ (((fAcc_list_char @ X71 @ X72 @ X73) = (tryCatch_list_char @ X151 @ X152 @ X153 @ X154))))))). % exp.distinct(153)
thf(fact_161_ListRedsVal, axiom,
    ((![E : exp_list_char, S_0 : produc515445032on_val, V2 : val, S_1 : produc515445032on_val, P : list_P1234162913t_char, Es : list_exp_list_char, Es2 : list_exp_list_char, S_2 : produc515445032on_val]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E @ S_0) @ (produc2023458740on_val @ (val_list_char @ V2) @ S_1)) @ (transi111096263on_val @ (red @ P))) => ((member1689761872on_val @ (produc245869591on_val @ (produc1725134254on_val @ Es @ S_1) @ (produc1725134254on_val @ Es2 @ S_2)) @ (transi325225921on_val @ (reds @ P))) => (member1689761872on_val @ (produc245869591on_val @ (produc1725134254on_val @ (cons_exp_list_char @ E @ Es) @ S_0) @ (produc1725134254on_val @ (cons_exp_list_char @ (val_list_char @ V2) @ Es2) @ S_2)) @ (transi325225921on_val @ (reds @ P)))))))). % ListRedsVal
thf(fact_162_single__valued__def, axiom,
    ((single747474179on_val = (^[R3 : set_Pr1189492743on_val]: (![X4 : produc1097884484on_val]: (![Y5 : produc1097884484on_val]: (((member354538064on_val @ (produc1069526295on_val @ X4 @ Y5) @ R3)) => ((![Z3 : produc1097884484on_val]: (((member354538064on_val @ (produc1069526295on_val @ X4 @ Z3) @ R3)) => ((Y5 = Z3)))))))))))). % single_valued_def
thf(fact_163_single__valued__def, axiom,
    ((single1293603232on_val = (^[R3 : set_Pr556513572on_val]: (![X4 : exp_list_char]: (![Y5 : produc515445032on_val]: (((member1888679917on_val @ (produc2023458740on_val @ X4 @ Y5) @ R3)) => ((![Z3 : produc515445032on_val]: (((member1888679917on_val @ (produc2023458740on_val @ X4 @ Z3) @ R3)) => ((Y5 = Z3)))))))))))). % single_valued_def
thf(fact_164_single__valued__def, axiom,
    ((single2124932044on_val = (^[R3 : set_Pr723149704on_val]: (![X4 : nat > option2118145160on_val]: (![Y5 : list_char > option_val]: (((member652041809on_val @ (produc52622304on_val @ X4 @ Y5) @ R3)) => ((![Z3 : list_char > option_val]: (((member652041809on_val @ (produc52622304on_val @ X4 @ Z3) @ R3)) => ((Y5 = Z3)))))))))))). % single_valued_def
thf(fact_165_single__valued__def, axiom,
    ((single965918723on_val = (^[R3 : set_Pr208351751on_val]: (![X4 : produc335961278on_val]: (![Y5 : produc335961278on_val]: (((member1689761872on_val @ (produc245869591on_val @ X4 @ Y5) @ R3)) => ((![Z3 : produc335961278on_val]: (((member1689761872on_val @ (produc245869591on_val @ X4 @ Z3) @ R3)) => ((Y5 = Z3)))))))))))). % single_valued_def
thf(fact_166_single__valued__def, axiom,
    ((single1942935962on_val = (^[R3 : set_Pr1511552798on_val]: (![X4 : list_exp_list_char]: (![Y5 : produc515445032on_val]: (((member184158439on_val @ (produc1725134254on_val @ X4 @ Y5) @ R3)) => ((![Z3 : produc515445032on_val]: (((member184158439on_val @ (produc1725134254on_val @ X4 @ Z3) @ R3)) => ((Y5 = Z3)))))))))))). % single_valued_def
thf(fact_167_single__valuedI, axiom,
    ((![R2 : set_Pr1189492743on_val]: ((![X3 : produc1097884484on_val, Y3 : produc1097884484on_val, Z2 : produc1097884484on_val]: ((member354538064on_val @ (produc1069526295on_val @ X3 @ Y3) @ R2) => ((member354538064on_val @ (produc1069526295on_val @ X3 @ Z2) @ R2) => (Y3 = Z2)))) => (single747474179on_val @ R2))))). % single_valuedI
thf(fact_168_single__valuedI, axiom,
    ((![R2 : set_Pr556513572on_val]: ((![X3 : exp_list_char, Y3 : produc515445032on_val, Z2 : produc515445032on_val]: ((member1888679917on_val @ (produc2023458740on_val @ X3 @ Y3) @ R2) => ((member1888679917on_val @ (produc2023458740on_val @ X3 @ Z2) @ R2) => (Y3 = Z2)))) => (single1293603232on_val @ R2))))). % single_valuedI
thf(fact_169_single__valuedI, axiom,
    ((![R2 : set_Pr723149704on_val]: ((![X3 : nat > option2118145160on_val, Y3 : list_char > option_val, Z2 : list_char > option_val]: ((member652041809on_val @ (produc52622304on_val @ X3 @ Y3) @ R2) => ((member652041809on_val @ (produc52622304on_val @ X3 @ Z2) @ R2) => (Y3 = Z2)))) => (single2124932044on_val @ R2))))). % single_valuedI
thf(fact_170_single__valuedI, axiom,
    ((![R2 : set_Pr208351751on_val]: ((![X3 : produc335961278on_val, Y3 : produc335961278on_val, Z2 : produc335961278on_val]: ((member1689761872on_val @ (produc245869591on_val @ X3 @ Y3) @ R2) => ((member1689761872on_val @ (produc245869591on_val @ X3 @ Z2) @ R2) => (Y3 = Z2)))) => (single965918723on_val @ R2))))). % single_valuedI
thf(fact_171_single__valuedI, axiom,
    ((![R2 : set_Pr1511552798on_val]: ((![X3 : list_exp_list_char, Y3 : produc515445032on_val, Z2 : produc515445032on_val]: ((member184158439on_val @ (produc1725134254on_val @ X3 @ Y3) @ R2) => ((member184158439on_val @ (produc1725134254on_val @ X3 @ Z2) @ R2) => (Y3 = Z2)))) => (single1942935962on_val @ R2))))). % single_valuedI
thf(fact_172_single__valuedD, axiom,
    ((![R2 : set_Pr1189492743on_val, X : produc1097884484on_val, Y : produc1097884484on_val, Z : produc1097884484on_val]: ((single747474179on_val @ R2) => ((member354538064on_val @ (produc1069526295on_val @ X @ Y) @ R2) => ((member354538064on_val @ (produc1069526295on_val @ X @ Z) @ R2) => (Y = Z))))))). % single_valuedD
thf(fact_173_single__valuedD, axiom,
    ((![R2 : set_Pr556513572on_val, X : exp_list_char, Y : produc515445032on_val, Z : produc515445032on_val]: ((single1293603232on_val @ R2) => ((member1888679917on_val @ (produc2023458740on_val @ X @ Y) @ R2) => ((member1888679917on_val @ (produc2023458740on_val @ X @ Z) @ R2) => (Y = Z))))))). % single_valuedD
thf(fact_174_single__valuedD, axiom,
    ((![R2 : set_Pr723149704on_val, X : nat > option2118145160on_val, Y : list_char > option_val, Z : list_char > option_val]: ((single2124932044on_val @ R2) => ((member652041809on_val @ (produc52622304on_val @ X @ Y) @ R2) => ((member652041809on_val @ (produc52622304on_val @ X @ Z) @ R2) => (Y = Z))))))). % single_valuedD
thf(fact_175_single__valuedD, axiom,
    ((![R2 : set_Pr208351751on_val, X : produc335961278on_val, Y : produc335961278on_val, Z : produc335961278on_val]: ((single965918723on_val @ R2) => ((member1689761872on_val @ (produc245869591on_val @ X @ Y) @ R2) => ((member1689761872on_val @ (produc245869591on_val @ X @ Z) @ R2) => (Y = Z))))))). % single_valuedD
thf(fact_176_single__valuedD, axiom,
    ((![R2 : set_Pr1511552798on_val, X : list_exp_list_char, Y : produc515445032on_val, Z : produc515445032on_val]: ((single1942935962on_val @ R2) => ((member184158439on_val @ (produc1725134254on_val @ X @ Y) @ R2) => ((member184158439on_val @ (produc1725134254on_val @ X @ Z) @ R2) => (Y = Z))))))). % single_valuedD
thf(fact_177_exp_Odistinct_I77_J, axiom,
    ((![X32 : val, X151 : exp_list_char, X152 : list_char, X153 : list_char, X154 : exp_list_char]: (~ (((val_list_char @ X32) = (tryCatch_list_char @ X151 @ X152 @ X153 @ X154))))))). % exp.distinct(77)
thf(fact_178_exp_Odistinct_I75_J, axiom,
    ((![X32 : val, X14 : exp_list_char]: (~ (((val_list_char @ X32) = (throw_list_char @ X14))))))). % exp.distinct(75)
thf(fact_179_exp_Odistinct_I61_J, axiom,
    ((![X32 : val, X71 : exp_list_char, X72 : list_char, X73 : list_char]: (~ (((val_list_char @ X32) = (fAcc_list_char @ X71 @ X72 @ X73))))))). % exp.distinct(61)
thf(fact_180_exp_Odistinct_I29_J, axiom,
    ((![X21 : list_char, X22 : exp_list_char, X32 : val]: (~ (((cast_list_char @ X21 @ X22) = (val_list_char @ X32))))))). % exp.distinct(29)
thf(fact_181_red__reds_ORedTry, axiom,
    ((![V2 : val, C4 : list_char, V : list_char, E_2 : exp_list_char, S : produc515445032on_val, P : list_P1234162913t_char]: (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (tryCatch_list_char @ (val_list_char @ V2) @ C4 @ V @ E_2) @ S) @ (produc2023458740on_val @ (val_list_char @ V2) @ S)) @ (red @ P))))). % red_reds.RedTry
thf(fact_182_red__reds_OListRed2, axiom,
    ((![Es : list_exp_list_char, S : produc515445032on_val, Es2 : list_exp_list_char, S2 : produc515445032on_val, P : list_P1234162913t_char, V2 : val]: ((member1689761872on_val @ (produc245869591on_val @ (produc1725134254on_val @ Es @ S) @ (produc1725134254on_val @ Es2 @ S2)) @ (reds @ P)) => (member1689761872on_val @ (produc245869591on_val @ (produc1725134254on_val @ (cons_exp_list_char @ (val_list_char @ V2) @ Es) @ S) @ (produc1725134254on_val @ (cons_exp_list_char @ (val_list_char @ V2) @ Es2) @ S2)) @ (reds @ P)))))). % red_reds.ListRed2
thf(fact_183_TryRedsVal, axiom,
    ((![E : exp_list_char, S : produc515445032on_val, V2 : val, S2 : produc515445032on_val, P : list_P1234162913t_char, C4 : list_char, V : list_char, E_2 : exp_list_char]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E @ S) @ (produc2023458740on_val @ (val_list_char @ V2) @ S2)) @ (transi111096263on_val @ (red @ P))) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (tryCatch_list_char @ E @ C4 @ V @ E_2) @ S) @ (produc2023458740on_val @ (val_list_char @ V2) @ S2)) @ (transi111096263on_val @ (red @ P))))))). % TryRedsVal
thf(fact_184_ListReds2, axiom,
    ((![Es : list_exp_list_char, S : produc515445032on_val, Es2 : list_exp_list_char, S2 : produc515445032on_val, P : list_P1234162913t_char, V2 : val]: ((member1689761872on_val @ (produc245869591on_val @ (produc1725134254on_val @ Es @ S) @ (produc1725134254on_val @ Es2 @ S2)) @ (transi325225921on_val @ (reds @ P))) => (member1689761872on_val @ (produc245869591on_val @ (produc1725134254on_val @ (cons_exp_list_char @ (val_list_char @ V2) @ Es) @ S) @ (produc1725134254on_val @ (cons_exp_list_char @ (val_list_char @ V2) @ Es2) @ S2)) @ (transi325225921on_val @ (reds @ P))))))). % ListReds2
thf(fact_185_reds_Osimps, axiom,
    ((![A1 : list_exp_list_char, A22 : produc515445032on_val, A32 : list_exp_list_char, A42 : produc515445032on_val, P : list_P1234162913t_char]: ((member1689761872on_val @ (produc245869591on_val @ (produc1725134254on_val @ A1 @ A22) @ (produc1725134254on_val @ A32 @ A42)) @ (reds @ P)) = (((?[E6 : exp_list_char]: (?[S3 : produc515445032on_val]: (?[E7 : exp_list_char]: (?[S4 : produc515445032on_val]: (?[Es3 : list_exp_list_char]: (((A1 = (cons_exp_list_char @ E6 @ Es3))) & ((((A22 = S3)) & ((((A32 = (cons_exp_list_char @ E7 @ Es3))) & ((((A42 = S4)) & ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E6 @ S3) @ (produc2023458740on_val @ E7 @ S4)) @ (red @ P)))))))))))))))) | ((?[Es3 : list_exp_list_char]: (?[S3 : produc515445032on_val]: (?[Es4 : list_exp_list_char]: (?[S4 : produc515445032on_val]: (?[V3 : val]: (((A1 = (cons_exp_list_char @ (val_list_char @ V3) @ Es3))) & ((((A22 = S3)) & ((((A32 = (cons_exp_list_char @ (val_list_char @ V3) @ Es4))) & ((((A42 = S4)) & ((member1689761872on_val @ (produc245869591on_val @ (produc1725134254on_val @ Es3 @ S3) @ (produc1725134254on_val @ Es4 @ S4)) @ (reds @ P))))))))))))))))))))). % reds.simps
thf(fact_186_reds_Ocases, axiom,
    ((![A1 : list_exp_list_char, A22 : produc515445032on_val, A32 : list_exp_list_char, A42 : produc515445032on_val, P : list_P1234162913t_char]: ((member1689761872on_val @ (produc245869591on_val @ (produc1725134254on_val @ A1 @ A22) @ (produc1725134254on_val @ A32 @ A42)) @ (reds @ P)) => ((![E3 : exp_list_char, S5 : produc515445032on_val, E4 : exp_list_char, S6 : produc515445032on_val, Es5 : list_exp_list_char]: ((A1 = (cons_exp_list_char @ E3 @ Es5)) => ((A22 = S5) => ((A32 = (cons_exp_list_char @ E4 @ Es5)) => ((A42 = S6) => (~ ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E3 @ S5) @ (produc2023458740on_val @ E4 @ S6)) @ (red @ P))))))))) => (~ ((![Es5 : list_exp_list_char, S5 : produc515445032on_val, Es6 : list_exp_list_char, S6 : produc515445032on_val, V4 : val]: ((A1 = (cons_exp_list_char @ (val_list_char @ V4) @ Es5)) => ((A22 = S5) => ((A32 = (cons_exp_list_char @ (val_list_char @ V4) @ Es6)) => ((A42 = S6) => (~ ((member1689761872on_val @ (produc245869591on_val @ (produc1725134254on_val @ Es5 @ S5) @ (produc1725134254on_val @ Es6 @ S6)) @ (reds @ P)))))))))))))))). % reds.cases
thf(fact_187_CallRedsParams, axiom,
    ((![Es : list_exp_list_char, S : produc515445032on_val, Es2 : list_exp_list_char, S2 : produc515445032on_val, P : list_P1234162913t_char, V2 : val, M : list_char]: ((member1689761872on_val @ (produc245869591on_val @ (produc1725134254on_val @ Es @ S) @ (produc1725134254on_val @ Es2 @ S2)) @ (transi325225921on_val @ (reds @ P))) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (call_list_char @ (val_list_char @ V2) @ M @ Es) @ S) @ (produc2023458740on_val @ (call_list_char @ (val_list_char @ V2) @ M @ Es2) @ S2)) @ (transi111096263on_val @ (red @ P))))))). % CallRedsParams
thf(fact_188_CastRedsNull, axiom,
    ((![E : exp_list_char, S : produc515445032on_val, S2 : produc515445032on_val, P : list_P1234162913t_char, C4 : list_char]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E @ S) @ (produc2023458740on_val @ (val_list_char @ null) @ S2)) @ (transi111096263on_val @ (red @ P))) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (cast_list_char @ C4 @ E) @ S) @ (produc2023458740on_val @ (val_list_char @ null) @ S2)) @ (transi111096263on_val @ (red @ P))))))). % CastRedsNull
thf(fact_189_red__reds_OCallParams, axiom,
    ((![Es : list_exp_list_char, S : produc515445032on_val, Es2 : list_exp_list_char, S2 : produc515445032on_val, P : list_P1234162913t_char, V2 : val, M : list_char]: ((member1689761872on_val @ (produc245869591on_val @ (produc1725134254on_val @ Es @ S) @ (produc1725134254on_val @ Es2 @ S2)) @ (reds @ P)) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (call_list_char @ (val_list_char @ V2) @ M @ Es) @ S) @ (produc2023458740on_val @ (call_list_char @ (val_list_char @ V2) @ M @ Es2) @ S2)) @ (red @ P)))))). % red_reds.CallParams
thf(fact_190_red__reds_ORedCastNull, axiom,
    ((![C4 : list_char, S : produc515445032on_val, P : list_P1234162913t_char]: (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (cast_list_char @ C4 @ (val_list_char @ null)) @ S) @ (produc2023458740on_val @ (val_list_char @ null) @ S)) @ (red @ P))))). % red_reds.RedCastNull
thf(fact_191_exp_Odistinct_I41_J, axiom,
    ((![X21 : list_char, X22 : exp_list_char, X91 : exp_list_char, X92 : list_char, X93 : list_exp_list_char]: (~ (((cast_list_char @ X21 @ X22) = (call_list_char @ X91 @ X92 @ X93))))))). % exp.distinct(41)
thf(fact_192_exp_Odistinct_I141_J, axiom,
    ((![X71 : exp_list_char, X72 : list_char, X73 : list_char, X91 : exp_list_char, X92 : list_char, X93 : list_exp_list_char]: (~ (((fAcc_list_char @ X71 @ X72 @ X73) = (call_list_char @ X91 @ X92 @ X93))))))). % exp.distinct(141)
thf(fact_193_exp_Odistinct_I177_J, axiom,
    ((![X91 : exp_list_char, X92 : list_char, X93 : list_exp_list_char, X14 : exp_list_char]: (~ (((call_list_char @ X91 @ X92 @ X93) = (throw_list_char @ X14))))))). % exp.distinct(177)
thf(fact_194_exp_Odistinct_I179_J, axiom,
    ((![X91 : exp_list_char, X92 : list_char, X93 : list_exp_list_char, X151 : exp_list_char, X152 : list_char, X153 : list_char, X154 : exp_list_char]: (~ (((call_list_char @ X91 @ X92 @ X93) = (tryCatch_list_char @ X151 @ X152 @ X153 @ X154))))))). % exp.distinct(179)
thf(fact_195_red__reds_OCallObj, axiom,
    ((![E : exp_list_char, S : produc515445032on_val, E2 : exp_list_char, S2 : produc515445032on_val, P : list_P1234162913t_char, M : list_char, Es : list_exp_list_char]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E @ S) @ (produc2023458740on_val @ E2 @ S2)) @ (red @ P)) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (call_list_char @ E @ M @ Es) @ S) @ (produc2023458740on_val @ (call_list_char @ E2 @ M @ Es) @ S2)) @ (red @ P)))))). % red_reds.CallObj
thf(fact_196_red__reds_OCallThrowObj, axiom,
    ((![E : exp_list_char, M : list_char, Es : list_exp_list_char, S : produc515445032on_val, P : list_P1234162913t_char]: (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (call_list_char @ (throw_list_char @ E) @ M @ Es) @ S) @ (produc2023458740on_val @ (throw_list_char @ E) @ S)) @ (red @ P))))). % red_reds.CallThrowObj
thf(fact_197_CallRedsObj, axiom,
    ((![E : exp_list_char, S : produc515445032on_val, E2 : exp_list_char, S2 : produc515445032on_val, P : list_P1234162913t_char, M : list_char, Es : list_exp_list_char]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E @ S) @ (produc2023458740on_val @ E2 @ S2)) @ (transi111096263on_val @ (red @ P))) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (call_list_char @ E @ M @ Es) @ S) @ (produc2023458740on_val @ (call_list_char @ E2 @ M @ Es) @ S2)) @ (transi111096263on_val @ (red @ P))))))). % CallRedsObj
thf(fact_198_CallRedsThrowObj, axiom,
    ((![E : exp_list_char, S0 : produc515445032on_val, A2 : exp_list_char, S_1 : produc515445032on_val, P : list_P1234162913t_char, M : list_char, Es : list_exp_list_char]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E @ S0) @ (produc2023458740on_val @ (throw_list_char @ A2) @ S_1)) @ (transi111096263on_val @ (red @ P))) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (call_list_char @ E @ M @ Es) @ S0) @ (produc2023458740on_val @ (throw_list_char @ A2) @ S_1)) @ (transi111096263on_val @ (red @ P))))))). % CallRedsThrowObj
thf(fact_199_CallRedsThrowParams, axiom,
    ((![E : exp_list_char, S0 : produc515445032on_val, V2 : val, S_1 : produc515445032on_val, P : list_P1234162913t_char, Es : list_exp_list_char, Vs_1 : list_val, A2 : exp_list_char, Es_2 : list_exp_list_char, S_2 : produc515445032on_val, M : list_char]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E @ S0) @ (produc2023458740on_val @ (val_list_char @ V2) @ S_1)) @ (transi111096263on_val @ (red @ P))) => ((member1689761872on_val @ (produc245869591on_val @ (produc1725134254on_val @ Es @ S_1) @ (produc1725134254on_val @ (append_exp_list_char @ (map_va1515327237t_char @ val_list_char @ Vs_1) @ (cons_exp_list_char @ (throw_list_char @ A2) @ Es_2)) @ S_2)) @ (transi325225921on_val @ (reds @ P))) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (call_list_char @ E @ M @ Es) @ S0) @ (produc2023458740on_val @ (throw_list_char @ A2) @ S_2)) @ (transi111096263on_val @ (red @ P)))))))). % CallRedsThrowParams
thf(fact_200_BinOpRedsThrow2, axiom,
    ((![E_12 : exp_list_char, S_0 : produc515445032on_val, V_1 : val, S_1 : produc515445032on_val, P : list_P1234162913t_char, E_2 : exp_list_char, E : exp_list_char, S_2 : produc515445032on_val, Bop : bop]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E_12 @ S_0) @ (produc2023458740on_val @ (val_list_char @ V_1) @ S_1)) @ (transi111096263on_val @ (red @ P))) => ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E_2 @ S_1) @ (produc2023458740on_val @ (throw_list_char @ E) @ S_2)) @ (transi111096263on_val @ (red @ P))) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (binOp_list_char @ E_12 @ Bop @ E_2) @ S_0) @ (produc2023458740on_val @ (throw_list_char @ E) @ S_2)) @ (transi111096263on_val @ (red @ P)))))))). % BinOpRedsThrow2
thf(fact_201_FAssRedsThrow2, axiom,
    ((![E_12 : exp_list_char, S_0 : produc515445032on_val, V2 : val, S_1 : produc515445032on_val, P : list_P1234162913t_char, E_2 : exp_list_char, E : exp_list_char, S_2 : produc515445032on_val, F2 : list_char, D2 : list_char]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E_12 @ S_0) @ (produc2023458740on_val @ (val_list_char @ V2) @ S_1)) @ (transi111096263on_val @ (red @ P))) => ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E_2 @ S_1) @ (produc2023458740on_val @ (throw_list_char @ E) @ S_2)) @ (transi111096263on_val @ (red @ P))) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (fAss_list_char @ E_12 @ F2 @ D2 @ E_2) @ S_0) @ (produc2023458740on_val @ (throw_list_char @ E) @ S_2)) @ (transi111096263on_val @ (red @ P)))))))). % FAssRedsThrow2
thf(fact_202_exp_Odistinct_I167_J, axiom,
    ((![X81 : exp_list_char, X82 : list_char, X83 : list_char, X84 : exp_list_char, X151 : exp_list_char, X152 : list_char, X153 : list_char, X154 : exp_list_char]: (~ (((fAss_list_char @ X81 @ X82 @ X83 @ X84) = (tryCatch_list_char @ X151 @ X152 @ X153 @ X154))))))). % exp.distinct(167)
thf(fact_203_exp_Odistinct_I165_J, axiom,
    ((![X81 : exp_list_char, X82 : list_char, X83 : list_char, X84 : exp_list_char, X14 : exp_list_char]: (~ (((fAss_list_char @ X81 @ X82 @ X83 @ X84) = (throw_list_char @ X14))))))). % exp.distinct(165)
thf(fact_204_exp_Odistinct_I139_J, axiom,
    ((![X71 : exp_list_char, X72 : list_char, X73 : list_char, X81 : exp_list_char, X82 : list_char, X83 : list_char, X84 : exp_list_char]: (~ (((fAcc_list_char @ X71 @ X72 @ X73) = (fAss_list_char @ X81 @ X82 @ X83 @ X84))))))). % exp.distinct(139)
thf(fact_205_exp_Odistinct_I99_J, axiom,
    ((![X41 : exp_list_char, X42 : bop, X43 : exp_list_char, X151 : exp_list_char, X152 : list_char, X153 : list_char, X154 : exp_list_char]: (~ (((binOp_list_char @ X41 @ X42 @ X43) = (tryCatch_list_char @ X151 @ X152 @ X153 @ X154))))))). % exp.distinct(99)
thf(fact_206_exp_Odistinct_I97_J, axiom,
    ((![X41 : exp_list_char, X42 : bop, X43 : exp_list_char, X14 : exp_list_char]: (~ (((binOp_list_char @ X41 @ X42 @ X43) = (throw_list_char @ X14))))))). % exp.distinct(97)
thf(fact_207_exp_Odistinct_I83_J, axiom,
    ((![X41 : exp_list_char, X42 : bop, X43 : exp_list_char, X71 : exp_list_char, X72 : list_char, X73 : list_char]: (~ (((binOp_list_char @ X41 @ X42 @ X43) = (fAcc_list_char @ X71 @ X72 @ X73))))))). % exp.distinct(83)
thf(fact_208_exp_Odistinct_I39_J, axiom,
    ((![X21 : list_char, X22 : exp_list_char, X81 : exp_list_char, X82 : list_char, X83 : list_char, X84 : exp_list_char]: (~ (((cast_list_char @ X21 @ X22) = (fAss_list_char @ X81 @ X82 @ X83 @ X84))))))). % exp.distinct(39)
thf(fact_209_exp_Odistinct_I31_J, axiom,
    ((![X21 : list_char, X22 : exp_list_char, X41 : exp_list_char, X42 : bop, X43 : exp_list_char]: (~ (((cast_list_char @ X21 @ X22) = (binOp_list_char @ X41 @ X42 @ X43))))))). % exp.distinct(31)
thf(fact_210_red__reds_OFAssRed1, axiom,
    ((![E : exp_list_char, S : produc515445032on_val, E2 : exp_list_char, S2 : produc515445032on_val, P : list_P1234162913t_char, F2 : list_char, D2 : list_char, E_2 : exp_list_char]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E @ S) @ (produc2023458740on_val @ E2 @ S2)) @ (red @ P)) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (fAss_list_char @ E @ F2 @ D2 @ E_2) @ S) @ (produc2023458740on_val @ (fAss_list_char @ E2 @ F2 @ D2 @ E_2) @ S2)) @ (red @ P)))))). % red_reds.FAssRed1
thf(fact_211_red__reds_OBinOpRed1, axiom,
    ((![E : exp_list_char, S : produc515445032on_val, E2 : exp_list_char, S2 : produc515445032on_val, P : list_P1234162913t_char, Bop : bop, E_2 : exp_list_char]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E @ S) @ (produc2023458740on_val @ E2 @ S2)) @ (red @ P)) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (binOp_list_char @ E @ Bop @ E_2) @ S) @ (produc2023458740on_val @ (binOp_list_char @ E2 @ Bop @ E_2) @ S2)) @ (red @ P)))))). % red_reds.BinOpRed1
thf(fact_212_red__reds_OCallThrowParams, axiom,
    ((![Es : list_exp_list_char, Vs : list_val, E : exp_list_char, Es2 : list_exp_list_char, V2 : val, M : list_char, S : produc515445032on_val, P : list_P1234162913t_char]: ((Es = (append_exp_list_char @ (map_va1515327237t_char @ val_list_char @ Vs) @ (cons_exp_list_char @ (throw_list_char @ E) @ Es2))) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (call_list_char @ (val_list_char @ V2) @ M @ Es) @ S) @ (produc2023458740on_val @ (throw_list_char @ E) @ S)) @ (red @ P)))))). % red_reds.CallThrowParams
thf(fact_213_red__reds_OFAssRed2, axiom,
    ((![E : exp_list_char, S : produc515445032on_val, E2 : exp_list_char, S2 : produc515445032on_val, P : list_P1234162913t_char, V2 : val, F2 : list_char, D2 : list_char]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E @ S) @ (produc2023458740on_val @ E2 @ S2)) @ (red @ P)) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (fAss_list_char @ (val_list_char @ V2) @ F2 @ D2 @ E) @ S) @ (produc2023458740on_val @ (fAss_list_char @ (val_list_char @ V2) @ F2 @ D2 @ E2) @ S2)) @ (red @ P)))))). % red_reds.FAssRed2
thf(fact_214_red__reds_OFAssThrow1, axiom,
    ((![E : exp_list_char, F2 : list_char, D2 : list_char, E_2 : exp_list_char, S : produc515445032on_val, P : list_P1234162913t_char]: (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (fAss_list_char @ (throw_list_char @ E) @ F2 @ D2 @ E_2) @ S) @ (produc2023458740on_val @ (throw_list_char @ E) @ S)) @ (red @ P))))). % red_reds.FAssThrow1
thf(fact_215_red__reds_OBinOpRed2, axiom,
    ((![E : exp_list_char, S : produc515445032on_val, E2 : exp_list_char, S2 : produc515445032on_val, P : list_P1234162913t_char, V_1 : val, Bop : bop]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E @ S) @ (produc2023458740on_val @ E2 @ S2)) @ (red @ P)) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (binOp_list_char @ (val_list_char @ V_1) @ Bop @ E) @ S) @ (produc2023458740on_val @ (binOp_list_char @ (val_list_char @ V_1) @ Bop @ E2) @ S2)) @ (red @ P)))))). % red_reds.BinOpRed2
thf(fact_216_red__reds_OBinOpThrow1, axiom,
    ((![E : exp_list_char, Bop : bop, E_2 : exp_list_char, S : produc515445032on_val, P : list_P1234162913t_char]: (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (binOp_list_char @ (throw_list_char @ E) @ Bop @ E_2) @ S) @ (produc2023458740on_val @ (throw_list_char @ E) @ S)) @ (red @ P))))). % red_reds.BinOpThrow1
thf(fact_217_FAssReds1, axiom,
    ((![E : exp_list_char, S : produc515445032on_val, E2 : exp_list_char, S2 : produc515445032on_val, P : list_P1234162913t_char, F2 : list_char, D2 : list_char, E_2 : exp_list_char]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E @ S) @ (produc2023458740on_val @ E2 @ S2)) @ (transi111096263on_val @ (red @ P))) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (fAss_list_char @ E @ F2 @ D2 @ E_2) @ S) @ (produc2023458740on_val @ (fAss_list_char @ E2 @ F2 @ D2 @ E_2) @ S2)) @ (transi111096263on_val @ (red @ P))))))). % FAssReds1
thf(fact_218_BinOp1Reds, axiom,
    ((![E : exp_list_char, S : produc515445032on_val, E2 : exp_list_char, S2 : produc515445032on_val, P : list_P1234162913t_char, Bop : bop, E_2 : exp_list_char]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E @ S) @ (produc2023458740on_val @ E2 @ S2)) @ (transi111096263on_val @ (red @ P))) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (binOp_list_char @ E @ Bop @ E_2) @ S) @ (produc2023458740on_val @ (binOp_list_char @ E2 @ Bop @ E_2) @ S2)) @ (transi111096263on_val @ (red @ P))))))). % BinOp1Reds
thf(fact_219_red__reds_OFAssThrow2, axiom,
    ((![V2 : val, F2 : list_char, D2 : list_char, E : exp_list_char, S : produc515445032on_val, P : list_P1234162913t_char]: (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (fAss_list_char @ (val_list_char @ V2) @ F2 @ D2 @ (throw_list_char @ E)) @ S) @ (produc2023458740on_val @ (throw_list_char @ E) @ S)) @ (red @ P))))). % red_reds.FAssThrow2
thf(fact_220_red__reds_OBinOpThrow2, axiom,
    ((![V_1 : val, Bop : bop, E : exp_list_char, S : produc515445032on_val, P : list_P1234162913t_char]: (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (binOp_list_char @ (val_list_char @ V_1) @ Bop @ (throw_list_char @ E)) @ S) @ (produc2023458740on_val @ (throw_list_char @ E) @ S)) @ (red @ P))))). % red_reds.BinOpThrow2
thf(fact_221_FAssReds2, axiom,
    ((![E : exp_list_char, S : produc515445032on_val, E2 : exp_list_char, S2 : produc515445032on_val, P : list_P1234162913t_char, V2 : val, F2 : list_char, D2 : list_char]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E @ S) @ (produc2023458740on_val @ E2 @ S2)) @ (transi111096263on_val @ (red @ P))) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (fAss_list_char @ (val_list_char @ V2) @ F2 @ D2 @ E) @ S) @ (produc2023458740on_val @ (fAss_list_char @ (val_list_char @ V2) @ F2 @ D2 @ E2) @ S2)) @ (transi111096263on_val @ (red @ P))))))). % FAssReds2
thf(fact_222_FAssRedsThrow1, axiom,
    ((![E : exp_list_char, S : produc515445032on_val, E2 : exp_list_char, S2 : produc515445032on_val, P : list_P1234162913t_char, F2 : list_char, D2 : list_char, E_2 : exp_list_char]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E @ S) @ (produc2023458740on_val @ (throw_list_char @ E2) @ S2)) @ (transi111096263on_val @ (red @ P))) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (fAss_list_char @ E @ F2 @ D2 @ E_2) @ S) @ (produc2023458740on_val @ (throw_list_char @ E2) @ S2)) @ (transi111096263on_val @ (red @ P))))))). % FAssRedsThrow1
thf(fact_223_BinOp2Reds, axiom,
    ((![E : exp_list_char, S : produc515445032on_val, E2 : exp_list_char, S2 : produc515445032on_val, P : list_P1234162913t_char, V2 : val, Bop : bop]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E @ S) @ (produc2023458740on_val @ E2 @ S2)) @ (transi111096263on_val @ (red @ P))) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (binOp_list_char @ (val_list_char @ V2) @ Bop @ E) @ S) @ (produc2023458740on_val @ (binOp_list_char @ (val_list_char @ V2) @ Bop @ E2) @ S2)) @ (transi111096263on_val @ (red @ P))))))). % BinOp2Reds
thf(fact_224_BinOpRedsThrow1, axiom,
    ((![E : exp_list_char, S : produc515445032on_val, E2 : exp_list_char, S2 : produc515445032on_val, P : list_P1234162913t_char, Bop : bop, E_2 : exp_list_char]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E @ S) @ (produc2023458740on_val @ (throw_list_char @ E2) @ S2)) @ (transi111096263on_val @ (red @ P))) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (binOp_list_char @ E @ Bop @ E_2) @ S) @ (produc2023458740on_val @ (throw_list_char @ E2) @ S2)) @ (transi111096263on_val @ (red @ P))))))). % BinOpRedsThrow1
thf(fact_225_redp__redsp_OCallThrowParams, axiom,
    ((![Es : list_exp_list_char, Vs : list_val, E : exp_list_char, Es2 : list_exp_list_char, P : list_P1234162913t_char, V2 : val, M : list_char, S : produc515445032on_val]: ((Es = (append_exp_list_char @ (map_va1515327237t_char @ val_list_char @ Vs) @ (cons_exp_list_char @ (throw_list_char @ E) @ Es2))) => (redp @ P @ (call_list_char @ (val_list_char @ V2) @ M @ Es) @ S @ (throw_list_char @ E) @ S))))). % redp_redsp.CallThrowParams
thf(fact_226_CallRedsNull, axiom,
    ((![E : exp_list_char, S_0 : produc515445032on_val, S_1 : produc515445032on_val, P : list_P1234162913t_char, Es : list_exp_list_char, Vs : list_val, S_2 : produc515445032on_val, M : list_char]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E @ S_0) @ (produc2023458740on_val @ (val_list_char @ null) @ S_1)) @ (transi111096263on_val @ (red @ P))) => ((member1689761872on_val @ (produc245869591on_val @ (produc1725134254on_val @ Es @ S_1) @ (produc1725134254on_val @ (map_va1515327237t_char @ val_list_char @ Vs) @ S_2)) @ (transi325225921on_val @ (reds @ P))) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (call_list_char @ E @ M @ Es) @ S_0) @ (produc2023458740on_val @ (throw_list_char @ (val_list_char @ (addr @ (addr_of_sys_xcpt @ nullPointer)))) @ S_2)) @ (transi111096263on_val @ (red @ P)))))))). % CallRedsNull
thf(fact_227_WhileRedsThrow, axiom,
    ((![B2 : exp_list_char, S : produc515445032on_val, E : exp_list_char, S2 : produc515445032on_val, P : list_P1234162913t_char, C3 : exp_list_char]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ B2 @ S) @ (produc2023458740on_val @ (throw_list_char @ E) @ S2)) @ (transi111096263on_val @ (red @ P))) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (while_list_char @ B2 @ C3) @ S) @ (produc2023458740on_val @ (throw_list_char @ E) @ S2)) @ (transi111096263on_val @ (red @ P))))))). % WhileRedsThrow
thf(fact_228_redp__redsp_ORedFAssNull, axiom,
    ((![P : list_P1234162913t_char, F2 : list_char, D2 : list_char, V2 : val, S : produc515445032on_val]: (redp @ P @ (fAss_list_char @ (val_list_char @ null) @ F2 @ D2 @ (val_list_char @ V2)) @ S @ (throw_list_char @ (val_list_char @ (addr @ (addr_of_sys_xcpt @ nullPointer)))) @ S)))). % redp_redsp.RedFAssNull
thf(fact_229_redp__redsp_ORedCallNull, axiom,
    ((![P : list_P1234162913t_char, M : list_char, Vs : list_val, S : produc515445032on_val]: (redp @ P @ (call_list_char @ (val_list_char @ null) @ M @ (map_va1515327237t_char @ val_list_char @ Vs)) @ S @ (throw_list_char @ (val_list_char @ (addr @ (addr_of_sys_xcpt @ nullPointer)))) @ S)))). % redp_redsp.RedCallNull
thf(fact_230_redp__redsp_OBinOpRed2, axiom,
    ((![P : list_P1234162913t_char, E : exp_list_char, S : produc515445032on_val, E2 : exp_list_char, S2 : produc515445032on_val, V_1 : val, Bop : bop]: ((redp @ P @ E @ S @ E2 @ S2) => (redp @ P @ (binOp_list_char @ (val_list_char @ V_1) @ Bop @ E) @ S @ (binOp_list_char @ (val_list_char @ V_1) @ Bop @ E2) @ S2))))). % redp_redsp.BinOpRed2
thf(fact_231_redp__redsp_OFAssRed2, axiom,
    ((![P : list_P1234162913t_char, E : exp_list_char, S : produc515445032on_val, E2 : exp_list_char, S2 : produc515445032on_val, V2 : val, F2 : list_char, D2 : list_char]: ((redp @ P @ E @ S @ E2 @ S2) => (redp @ P @ (fAss_list_char @ (val_list_char @ V2) @ F2 @ D2 @ E) @ S @ (fAss_list_char @ (val_list_char @ V2) @ F2 @ D2 @ E2) @ S2))))). % redp_redsp.FAssRed2
thf(fact_232_redp__redsp_OCallObj, axiom,
    ((![P : list_P1234162913t_char, E : exp_list_char, S : produc515445032on_val, E2 : exp_list_char, S2 : produc515445032on_val, M : list_char, Es : list_exp_list_char]: ((redp @ P @ E @ S @ E2 @ S2) => (redp @ P @ (call_list_char @ E @ M @ Es) @ S @ (call_list_char @ E2 @ M @ Es) @ S2))))). % redp_redsp.CallObj
thf(fact_233_redp__redsp_OBinOpThrow1, axiom,
    ((![P : list_P1234162913t_char, E : exp_list_char, Bop : bop, E_2 : exp_list_char, S : produc515445032on_val]: (redp @ P @ (binOp_list_char @ (throw_list_char @ E) @ Bop @ E_2) @ S @ (throw_list_char @ E) @ S)))). % redp_redsp.BinOpThrow1
thf(fact_234_redp__redsp_OFAssThrow1, axiom,
    ((![P : list_P1234162913t_char, E : exp_list_char, F2 : list_char, D2 : list_char, E_2 : exp_list_char, S : produc515445032on_val]: (redp @ P @ (fAss_list_char @ (throw_list_char @ E) @ F2 @ D2 @ E_2) @ S @ (throw_list_char @ E) @ S)))). % redp_redsp.FAssThrow1
thf(fact_235_redp__redsp_OBinOpRed1, axiom,
    ((![P : list_P1234162913t_char, E : exp_list_char, S : produc515445032on_val, E2 : exp_list_char, S2 : produc515445032on_val, Bop : bop, E_2 : exp_list_char]: ((redp @ P @ E @ S @ E2 @ S2) => (redp @ P @ (binOp_list_char @ E @ Bop @ E_2) @ S @ (binOp_list_char @ E2 @ Bop @ E_2) @ S2))))). % redp_redsp.BinOpRed1
thf(fact_236_redp__redsp_OFAssRed1, axiom,
    ((![P : list_P1234162913t_char, E : exp_list_char, S : produc515445032on_val, E2 : exp_list_char, S2 : produc515445032on_val, F2 : list_char, D2 : list_char, E_2 : exp_list_char]: ((redp @ P @ E @ S @ E2 @ S2) => (redp @ P @ (fAss_list_char @ E @ F2 @ D2 @ E_2) @ S @ (fAss_list_char @ E2 @ F2 @ D2 @ E_2) @ S2))))). % redp_redsp.FAssRed1
thf(fact_237_redp__redsp_OCallThrowObj, axiom,
    ((![P : list_P1234162913t_char, E : exp_list_char, M : list_char, Es : list_exp_list_char, S : produc515445032on_val]: (redp @ P @ (call_list_char @ (throw_list_char @ E) @ M @ Es) @ S @ (throw_list_char @ E) @ S)))). % redp_redsp.CallThrowObj
thf(fact_238_redp__redsp_OCastThrow, axiom,
    ((![P : list_P1234162913t_char, C4 : list_char, E : exp_list_char, S : produc515445032on_val]: (redp @ P @ (cast_list_char @ C4 @ (throw_list_char @ E)) @ S @ (throw_list_char @ E) @ S)))). % redp_redsp.CastThrow
thf(fact_239_redp__redsp_ORedTry, axiom,
    ((![P : list_P1234162913t_char, V2 : val, C4 : list_char, V : list_char, E_2 : exp_list_char, S : produc515445032on_val]: (redp @ P @ (tryCatch_list_char @ (val_list_char @ V2) @ C4 @ V @ E_2) @ S @ (val_list_char @ V2) @ S)))). % redp_redsp.RedTry
thf(fact_240_redp__redsp_OFAccThrow, axiom,
    ((![P : list_P1234162913t_char, E : exp_list_char, F2 : list_char, D2 : list_char, S : produc515445032on_val]: (redp @ P @ (fAcc_list_char @ (throw_list_char @ E) @ F2 @ D2) @ S @ (throw_list_char @ E) @ S)))). % redp_redsp.FAccThrow

% Conjectures (4)
thf(conj_0, hypothesis,
    ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ e2 @ (produc52622304on_val @ h @ l)) @ (produc2023458740on_val @ e3 @ (produc52622304on_val @ h2 @ l2))) @ (red @ p)))).
thf(conj_1, hypothesis,
    ((wTrt @ p @ h @ e @ e2 @ t))).
thf(conj_2, hypothesis,
    ((hconf_1244167010t_char @ p @ h))).
thf(conj_3, conjecture,
    ((hconf_1244167010t_char @ p @ h2))).
