% TIMEFORMAT='%3R'; { time (exec 2>&1; /home/martin/bin/satallax -E /home/martin/.isabelle/contrib/e-2.5-1/x86_64-linux/eprover -p tstp -t 5 /home/martin/judgement-day/tptp-thf/tptp/TypeSafe/prob_41__5332214_1 ) ; }
% This file was generated by Isabelle (most likely Sledgehammer)
% 2020-12-16 14:18:54.155

% Could-be-implicit typings (27)
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thf(ty_n_t__Type__Oty, type,
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% Explicit typings (72)
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thf(sy_c_Exceptions_Opreallocated, type,
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thf(sy_c_Expr_Oexp_OFAcc_001t__List__Olist_It__String__Ochar_J, type,
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thf(sy_c_Expr_Oexp_OFAss_001t__List__Olist_It__String__Ochar_J, type,
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thf(sy_c_Expr_Oexp_OLAss_001t__List__Olist_It__String__Ochar_J, type,
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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_Fun_Ofun__upd_001t__Nat__Onat_001t__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J, type,
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thf(sy_c_Option_Ooption_ONone_001t__Type__Oty, type,
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thf(sy_c_Option_Ooption_ONone_001t__Value__Oval, type,
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thf(sy_c_member_001t__Product____Type__Oprod_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_Mt__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, type,
    member197592058on_val : produc1085126737on_val > set_Pr2110063281on_val > $o).
thf(sy_c_member_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_J, type,
    member803902992t_char : produc442406631t_char > set_Pr729957319t_char > $o).
thf(sy_c_member_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__Product____Type__Oprod_It__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_Mt__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_M_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_Mt__Product____Type__Oprod_It__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_Mt__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_M_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_Mt__Product____Type__Oprod_It__Product____Type__Oprod_It__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_Mt__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_M_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_Mt__Product____Type__Oprod_It__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_Mt__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_M_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_J, type,
    member208988944on_val : produc1161703655on_val > set_Pr1368603847on_val > $o).
thf(sy_v_C____, type,
    c : list_char).
thf(sy_v_D____, type,
    d : list_char).
thf(sy_v_E____, type,
    e : list_char > option_ty).
thf(sy_v_F____, type,
    f : list_char).
thf(sy_v_P, type,
    p : list_P1234162913t_char).
thf(sy_v_TF____, type,
    tf : ty).
thf(sy_v_T____, type,
    t : ty).
thf(sy_v_Tv____, type,
    tv : ty).
thf(sy_v_a____, type,
    a : nat).
thf(sy_v_fs____, type,
    fs : produc1257910179t_char > option_val).
thf(sy_v_ha____, type,
    ha : nat > option2118145160on_val).
thf(sy_v_v____, type,
    v : val).

% Relevant facts (248)
thf(fact_0_hconf, axiom,
    ((hconf_1244167010t_char @ p @ ha))). % hconf
thf(fact_1_ha, axiom,
    (((ha @ a) = (some_P1299442195on_val @ (produc904988266on_val @ c @ fs))))). % ha
thf(fact_2_prod_Oinject, axiom,
    ((![X1 : list_char, X2 : produc1257910179t_char > option_val, Y1 : list_char, Y2 : produc1257910179t_char > option_val]: (((produc904988266on_val @ X1 @ X2) = (produc904988266on_val @ Y1 @ Y2)) = (((X1 = Y1)) & ((X2 = Y2))))))). % prod.inject
thf(fact_3_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_4_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_5_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_6_prod_Oinject, axiom,
    ((![X1 : list_char, X2 : list_char, Y1 : list_char, Y2 : list_char]: (((produc1304532571t_char @ X1 @ X2) = (produc1304532571t_char @ Y1 @ Y2)) = (((X1 = Y1)) & ((X2 = Y2))))))). % prod.inject
thf(fact_7_old_Oprod_Oinject, axiom,
    ((![A : list_char, B : produc1257910179t_char > option_val, A2 : list_char, B2 : produc1257910179t_char > option_val]: (((produc904988266on_val @ A @ B) = (produc904988266on_val @ A2 @ B2)) = (((A = A2)) & ((B = B2))))))). % old.prod.inject
thf(fact_8_old_Oprod_Oinject, axiom,
    ((![A : produc1097884484on_val, B : produc1097884484on_val, A2 : produc1097884484on_val, B2 : produc1097884484on_val]: (((produc1069526295on_val @ A @ B) = (produc1069526295on_val @ A2 @ B2)) = (((A = A2)) & ((B = B2))))))). % old.prod.inject
thf(fact_9_old_Oprod_Oinject, axiom,
    ((![A : exp_list_char, B : produc515445032on_val, A2 : exp_list_char, B2 : produc515445032on_val]: (((produc2023458740on_val @ A @ B) = (produc2023458740on_val @ A2 @ B2)) = (((A = A2)) & ((B = B2))))))). % old.prod.inject
thf(fact_10_old_Oprod_Oinject, axiom,
    ((![A : nat > option2118145160on_val, B : list_char > option_val, A2 : nat > option2118145160on_val, B2 : list_char > option_val]: (((produc52622304on_val @ A @ B) = (produc52622304on_val @ A2 @ B2)) = (((A = A2)) & ((B = B2))))))). % old.prod.inject
thf(fact_11_old_Oprod_Oinject, axiom,
    ((![A : list_char, B : list_char, A2 : list_char, B2 : list_char]: (((produc1304532571t_char @ A @ B) = (produc1304532571t_char @ A2 @ B2)) = (((A = A2)) & ((B = B2))))))). % old.prod.inject
thf(fact_12_has, axiom,
    ((has_fi599584195t_char @ p @ c @ f @ tf @ d))). % has
thf(fact_13_RedFAss_Oprems_I2_J, axiom,
    ((hconf_1244167010t_char @ p @ ha))). % RedFAss.prems(2)
thf(fact_14_sub, axiom,
    ((widen_917054840t_char @ p @ tv @ tf))). % sub
thf(fact_15_surj__pair, axiom,
    ((![P : produc266837688on_val]: (?[X : list_char, Y : produc1257910179t_char > option_val]: (P = (produc904988266on_val @ X @ Y)))))). % surj_pair
thf(fact_16_surj__pair, axiom,
    ((![P : produc1172664615on_val]: (?[X : produc1097884484on_val, Y : produc1097884484on_val]: (P = (produc1069526295on_val @ X @ Y)))))). % surj_pair
thf(fact_17_surj__pair, axiom,
    ((![P : produc1097884484on_val]: (?[X : exp_list_char, Y : produc515445032on_val]: (P = (produc2023458740on_val @ X @ Y)))))). % surj_pair
thf(fact_18_surj__pair, axiom,
    ((![P : produc515445032on_val]: (?[X : nat > option2118145160on_val, Y : list_char > option_val]: (P = (produc52622304on_val @ X @ Y)))))). % surj_pair
thf(fact_19_surj__pair, axiom,
    ((![P : produc1257910179t_char]: (?[X : list_char, Y : list_char]: (P = (produc1304532571t_char @ X @ Y)))))). % surj_pair
thf(fact_20_prod__cases, axiom,
    ((![P2 : produc266837688on_val > $o, P : produc266837688on_val]: ((![A3 : list_char, B3 : produc1257910179t_char > option_val]: (P2 @ (produc904988266on_val @ A3 @ B3))) => (P2 @ P))))). % prod_cases
thf(fact_21_prod__cases, axiom,
    ((![P2 : produc1172664615on_val > $o, P : produc1172664615on_val]: ((![A3 : produc1097884484on_val, B3 : produc1097884484on_val]: (P2 @ (produc1069526295on_val @ A3 @ B3))) => (P2 @ P))))). % prod_cases
thf(fact_22_prod__cases, axiom,
    ((![P2 : produc1097884484on_val > $o, P : produc1097884484on_val]: ((![A3 : exp_list_char, B3 : produc515445032on_val]: (P2 @ (produc2023458740on_val @ A3 @ B3))) => (P2 @ P))))). % prod_cases
thf(fact_23_prod__cases, axiom,
    ((![P2 : produc515445032on_val > $o, P : produc515445032on_val]: ((![A3 : nat > option2118145160on_val, B3 : list_char > option_val]: (P2 @ (produc52622304on_val @ A3 @ B3))) => (P2 @ P))))). % prod_cases
thf(fact_24_prod__cases, axiom,
    ((![P2 : produc1257910179t_char > $o, P : produc1257910179t_char]: ((![A3 : list_char, B3 : list_char]: (P2 @ (produc1304532571t_char @ A3 @ B3))) => (P2 @ P))))). % prod_cases
thf(fact_25_Pair__inject, axiom,
    ((![A : list_char, B : produc1257910179t_char > option_val, A2 : list_char, B2 : produc1257910179t_char > option_val]: (((produc904988266on_val @ A @ B) = (produc904988266on_val @ A2 @ B2)) => (~ (((A = A2) => (~ ((B = B2)))))))))). % Pair_inject
thf(fact_26_Pair__inject, axiom,
    ((![A : produc1097884484on_val, B : produc1097884484on_val, A2 : produc1097884484on_val, B2 : produc1097884484on_val]: (((produc1069526295on_val @ A @ B) = (produc1069526295on_val @ A2 @ B2)) => (~ (((A = A2) => (~ ((B = B2)))))))))). % Pair_inject
thf(fact_27_Pair__inject, axiom,
    ((![A : exp_list_char, B : produc515445032on_val, A2 : exp_list_char, B2 : produc515445032on_val]: (((produc2023458740on_val @ A @ B) = (produc2023458740on_val @ A2 @ B2)) => (~ (((A = A2) => (~ ((B = B2)))))))))). % Pair_inject
thf(fact_28_Pair__inject, axiom,
    ((![A : nat > option2118145160on_val, B : list_char > option_val, A2 : nat > option2118145160on_val, B2 : list_char > option_val]: (((produc52622304on_val @ A @ B) = (produc52622304on_val @ A2 @ B2)) => (~ (((A = A2) => (~ ((B = B2)))))))))). % Pair_inject
thf(fact_29_Pair__inject, axiom,
    ((![A : list_char, B : list_char, A2 : list_char, B2 : list_char]: (((produc1304532571t_char @ A @ B) = (produc1304532571t_char @ A2 @ B2)) => (~ (((A = A2) => (~ ((B = B2)))))))))). % Pair_inject
thf(fact_30_prod__cases3, axiom,
    ((![Y3 : produc1172664615on_val]: (~ ((![A3 : produc1097884484on_val, B3 : exp_list_char, C : produc515445032on_val]: (~ ((Y3 = (produc1069526295on_val @ A3 @ (produc2023458740on_val @ B3 @ C))))))))))). % prod_cases3
thf(fact_31_prod__cases3, axiom,
    ((![Y3 : produc1097884484on_val]: (~ ((![A3 : exp_list_char, B3 : nat > option2118145160on_val, C : list_char > option_val]: (~ ((Y3 = (produc2023458740on_val @ A3 @ (produc52622304on_val @ B3 @ C))))))))))). % prod_cases3
thf(fact_32_prod__cases4, axiom,
    ((![Y3 : produc1172664615on_val]: (~ ((![A3 : produc1097884484on_val, B3 : exp_list_char, C : nat > option2118145160on_val, D : list_char > option_val]: (~ ((Y3 = (produc1069526295on_val @ A3 @ (produc2023458740on_val @ B3 @ (produc52622304on_val @ C @ D)))))))))))). % prod_cases4
thf(fact_33_old_Oprod_Oinducts, axiom,
    ((![P2 : produc266837688on_val > $o, Prod : produc266837688on_val]: ((![A3 : list_char, B3 : produc1257910179t_char > option_val]: (P2 @ (produc904988266on_val @ A3 @ B3))) => (P2 @ Prod))))). % old.prod.inducts
thf(fact_34_old_Oprod_Oinducts, axiom,
    ((![P2 : produc1172664615on_val > $o, Prod : produc1172664615on_val]: ((![A3 : produc1097884484on_val, B3 : produc1097884484on_val]: (P2 @ (produc1069526295on_val @ A3 @ B3))) => (P2 @ Prod))))). % old.prod.inducts
thf(fact_35_old_Oprod_Oinducts, axiom,
    ((![P2 : produc1097884484on_val > $o, Prod : produc1097884484on_val]: ((![A3 : exp_list_char, B3 : produc515445032on_val]: (P2 @ (produc2023458740on_val @ A3 @ B3))) => (P2 @ Prod))))). % old.prod.inducts
thf(fact_36_old_Oprod_Oinducts, axiom,
    ((![P2 : produc515445032on_val > $o, Prod : produc515445032on_val]: ((![A3 : nat > option2118145160on_val, B3 : list_char > option_val]: (P2 @ (produc52622304on_val @ A3 @ B3))) => (P2 @ Prod))))). % old.prod.inducts
thf(fact_37_old_Oprod_Oinducts, axiom,
    ((![P2 : produc1257910179t_char > $o, Prod : produc1257910179t_char]: ((![A3 : list_char, B3 : list_char]: (P2 @ (produc1304532571t_char @ A3 @ B3))) => (P2 @ Prod))))). % old.prod.inducts
thf(fact_38_old_Oprod_Oexhaust, axiom,
    ((![Y3 : produc266837688on_val]: (~ ((![A3 : list_char, B3 : produc1257910179t_char > option_val]: (~ ((Y3 = (produc904988266on_val @ A3 @ B3)))))))))). % old.prod.exhaust
thf(fact_39_old_Oprod_Oexhaust, axiom,
    ((![Y3 : produc1172664615on_val]: (~ ((![A3 : produc1097884484on_val, B3 : produc1097884484on_val]: (~ ((Y3 = (produc1069526295on_val @ A3 @ B3)))))))))). % old.prod.exhaust
thf(fact_40_old_Oprod_Oexhaust, axiom,
    ((![Y3 : produc1097884484on_val]: (~ ((![A3 : exp_list_char, B3 : produc515445032on_val]: (~ ((Y3 = (produc2023458740on_val @ A3 @ B3)))))))))). % old.prod.exhaust
thf(fact_41_old_Oprod_Oexhaust, axiom,
    ((![Y3 : produc515445032on_val]: (~ ((![A3 : nat > option2118145160on_val, B3 : list_char > option_val]: (~ ((Y3 = (produc52622304on_val @ A3 @ B3)))))))))). % old.prod.exhaust
thf(fact_42_old_Oprod_Oexhaust, axiom,
    ((![Y3 : produc1257910179t_char]: (~ ((![A3 : list_char, B3 : list_char]: (~ ((Y3 = (produc1304532571t_char @ A3 @ B3)))))))))). % old.prod.exhaust
thf(fact_43_prod__induct4, axiom,
    ((![P2 : produc1172664615on_val > $o, X3 : produc1172664615on_val]: ((![A3 : produc1097884484on_val, B3 : exp_list_char, C : nat > option2118145160on_val, D : list_char > option_val]: (P2 @ (produc1069526295on_val @ A3 @ (produc2023458740on_val @ B3 @ (produc52622304on_val @ C @ D))))) => (P2 @ X3))))). % prod_induct4
thf(fact_44_prod__induct3, axiom,
    ((![P2 : produc1172664615on_val > $o, X3 : produc1172664615on_val]: ((![A3 : produc1097884484on_val, B3 : exp_list_char, C : produc515445032on_val]: (P2 @ (produc1069526295on_val @ A3 @ (produc2023458740on_val @ B3 @ C)))) => (P2 @ X3))))). % prod_induct3
thf(fact_45_prod__induct3, axiom,
    ((![P2 : produc1097884484on_val > $o, X3 : produc1097884484on_val]: ((![A3 : exp_list_char, B3 : nat > option2118145160on_val, C : list_char > option_val]: (P2 @ (produc2023458740on_val @ A3 @ (produc52622304on_val @ B3 @ C)))) => (P2 @ X3))))). % prod_induct3
thf(fact_46_hconfD, axiom,
    ((![P2 : list_P1234162913t_char, H : nat > option2118145160on_val, A : nat, Obj : produc266837688on_val]: ((hconf_1244167010t_char @ P2 @ H) => (((H @ A) = (some_P1299442195on_val @ Obj)) => (oconf_454120169t_char @ P2 @ H @ Obj)))))). % hconfD
thf(fact_47_option_Oinject, axiom,
    ((![X2 : produc266837688on_val, Y2 : produc266837688on_val]: (((some_P1299442195on_val @ X2) = (some_P1299442195on_val @ Y2)) = (X2 = Y2))))). % option.inject
thf(fact_48_option_Oinject, axiom,
    ((![X2 : ty, Y2 : ty]: (((some_ty @ X2) = (some_ty @ Y2)) = (X2 = Y2))))). % option.inject
thf(fact_49_option_Oinject, axiom,
    ((![X2 : val, Y2 : val]: (((some_val @ X2) = (some_val @ Y2)) = (X2 = Y2))))). % option.inject
thf(fact_50__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062TF_ATv_O_A_092_060lbrakk_062typeof_092_060_094bsub_062h_092_060_094esub_062_Av_A_061_A_092_060lfloor_062Tv_092_060rfloor_062_059_AP_A_092_060turnstile_062_AC_Ahas_AF_058TF_Ain_AD_059_AP_A_092_060turnstile_062_ATv_A_092_060le_062_ATF_092_060rbrakk_062_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062, axiom,
    ((~ ((![TF : ty, Tv : ty]: (((typeof_h @ ha @ v) = (some_ty @ Tv)) => ((has_fi599584195t_char @ p @ c @ f @ TF @ d) => (~ ((widen_917054840t_char @ p @ Tv @ TF)))))))))). % \<open>\<And>thesis. (\<And>TF Tv. \<lbrakk>typeof\<^bsub>h\<^esub> v = \<lfloor>Tv\<rfloor>; P \<turnstile> C has F:TF in D; P \<turnstile> Tv \<le> TF\<rbrakk> \<Longrightarrow> thesis) \<Longrightarrow> thesis\<close>
thf(fact_51_pred__equals__eq2, axiom,
    ((![R : set_Pr2075231726on_val, S : set_Pr2075231726on_val]: (((^[X4 : list_char]: (^[Y4 : produc1257910179t_char > option_val]: (member1296415951on_val @ (produc904988266on_val @ X4 @ Y4) @ R))) = (^[X4 : list_char]: (^[Y4 : produc1257910179t_char > option_val]: (member1296415951on_val @ (produc904988266on_val @ X4 @ Y4) @ S)))) = (R = S))))). % pred_equals_eq2
thf(fact_52_pred__equals__eq2, axiom,
    ((![R : set_Pr1189492743on_val, S : set_Pr1189492743on_val]: (((^[X4 : produc1097884484on_val]: (^[Y4 : produc1097884484on_val]: (member354538064on_val @ (produc1069526295on_val @ X4 @ Y4) @ R))) = (^[X4 : produc1097884484on_val]: (^[Y4 : produc1097884484on_val]: (member354538064on_val @ (produc1069526295on_val @ X4 @ Y4) @ S)))) = (R = S))))). % pred_equals_eq2
thf(fact_53_pred__equals__eq2, axiom,
    ((![R : set_Pr556513572on_val, S : set_Pr556513572on_val]: (((^[X4 : exp_list_char]: (^[Y4 : produc515445032on_val]: (member1888679917on_val @ (produc2023458740on_val @ X4 @ Y4) @ R))) = (^[X4 : exp_list_char]: (^[Y4 : produc515445032on_val]: (member1888679917on_val @ (produc2023458740on_val @ X4 @ Y4) @ S)))) = (R = S))))). % pred_equals_eq2
thf(fact_54_pred__equals__eq2, axiom,
    ((![R : set_Pr723149704on_val, S : set_Pr723149704on_val]: (((^[X4 : nat > option2118145160on_val]: (^[Y4 : list_char > option_val]: (member652041809on_val @ (produc52622304on_val @ X4 @ Y4) @ R))) = (^[X4 : nat > option2118145160on_val]: (^[Y4 : list_char > option_val]: (member652041809on_val @ (produc52622304on_val @ X4 @ Y4) @ S)))) = (R = S))))). % pred_equals_eq2
thf(fact_55_pred__equals__eq2, axiom,
    ((![R : set_Pr164112643t_char, S : set_Pr164112643t_char]: (((^[X4 : list_char]: (^[Y4 : list_char]: (member89690956t_char @ (produc1304532571t_char @ X4 @ Y4) @ R))) = (^[X4 : list_char]: (^[Y4 : list_char]: (member89690956t_char @ (produc1304532571t_char @ X4 @ Y4) @ S)))) = (R = S))))). % pred_equals_eq2
thf(fact_56_typeofv, axiom,
    (((typeof_h @ ha @ v) = (some_ty @ tv)))). % typeofv
thf(fact_57_widen__trans, axiom,
    ((![P2 : list_P1234162913t_char, S : ty, U : ty, T : ty]: ((widen_917054840t_char @ P2 @ S @ U) => ((widen_917054840t_char @ P2 @ U @ T) => (widen_917054840t_char @ P2 @ S @ T)))))). % widen_trans
thf(fact_58_widen__refl, axiom,
    ((![P2 : list_P1234162913t_char, T : ty]: (widen_917054840t_char @ P2 @ T @ T)))). % widen_refl
thf(fact_59_hconf__def, axiom,
    ((hconf_1244167010t_char = (^[P3 : list_P1234162913t_char]: (^[H2 : nat > option2118145160on_val]: (((![A4 : nat]: (![Obj2 : produc266837688on_val]: ((((H2 @ A4) = (some_P1299442195on_val @ Obj2))) => ((oconf_454120169t_char @ P3 @ H2 @ Obj2)))))) & ((preallocated @ H2)))))))). % hconf_def
thf(fact_60_hconf__upd__obj, axiom,
    ((![P2 : list_P1234162913t_char, H : nat > option2118145160on_val, A : nat, C2 : list_char, Fs : produc1257910179t_char > option_val, Fs2 : produc1257910179t_char > option_val]: ((hconf_1244167010t_char @ P2 @ H) => (((H @ A) = (some_P1299442195on_val @ (produc904988266on_val @ C2 @ Fs))) => ((oconf_454120169t_char @ P2 @ H @ (produc904988266on_val @ C2 @ Fs2)) => (hconf_1244167010t_char @ P2 @ (fun_up262443479on_val @ H @ A @ (some_P1299442195on_val @ (produc904988266on_val @ C2 @ Fs2)))))))))). % hconf_upd_obj
thf(fact_61_conf__def, axiom,
    ((conf_P93989998t_char = (^[P3 : list_P1234162913t_char]: (^[H2 : nat > option2118145160on_val]: (^[V : val]: (^[T2 : ty]: (?[T3 : ty]: ((((typeof_h @ H2 @ V) = (some_ty @ T3))) & ((widen_917054840t_char @ P3 @ T3 @ T2))))))))))). % conf_def
thf(fact_62_RedFAss_Oprems_I1_J, axiom,
    ((wTrt @ p @ ha @ e @ (fAss_list_char @ (val_list_char @ (addr @ a)) @ f @ d @ (val_list_char @ v)) @ t))). % RedFAss.prems(1)
thf(fact_63_oconf__upd__obj, axiom,
    ((![P2 : list_P1234162913t_char, H : nat > option2118145160on_val, Obj : produc266837688on_val, A : nat, C2 : list_char, Fs : produc1257910179t_char > option_val, Fs2 : produc1257910179t_char > option_val]: ((oconf_454120169t_char @ P2 @ H @ Obj) => (((H @ A) = (some_P1299442195on_val @ (produc904988266on_val @ C2 @ Fs))) => (oconf_454120169t_char @ P2 @ (fun_up262443479on_val @ H @ A @ (some_P1299442195on_val @ (produc904988266on_val @ C2 @ Fs2))) @ Obj)))))). % oconf_upd_obj
thf(fact_64_ssubst__Pair__rhs, axiom,
    ((![R2 : list_char, S2 : produc1257910179t_char > option_val, R : set_Pr2075231726on_val, S3 : produc1257910179t_char > option_val]: ((member1296415951on_val @ (produc904988266on_val @ R2 @ S2) @ R) => ((S3 = S2) => (member1296415951on_val @ (produc904988266on_val @ R2 @ S3) @ R)))))). % ssubst_Pair_rhs
thf(fact_65_ssubst__Pair__rhs, axiom,
    ((![R2 : produc1097884484on_val, S2 : produc1097884484on_val, R : set_Pr1189492743on_val, S3 : produc1097884484on_val]: ((member354538064on_val @ (produc1069526295on_val @ R2 @ S2) @ R) => ((S3 = S2) => (member354538064on_val @ (produc1069526295on_val @ R2 @ S3) @ R)))))). % ssubst_Pair_rhs
thf(fact_66_ssubst__Pair__rhs, axiom,
    ((![R2 : exp_list_char, S2 : produc515445032on_val, R : set_Pr556513572on_val, S3 : produc515445032on_val]: ((member1888679917on_val @ (produc2023458740on_val @ R2 @ S2) @ R) => ((S3 = S2) => (member1888679917on_val @ (produc2023458740on_val @ R2 @ S3) @ R)))))). % ssubst_Pair_rhs
thf(fact_67_ssubst__Pair__rhs, axiom,
    ((![R2 : nat > option2118145160on_val, S2 : list_char > option_val, R : set_Pr723149704on_val, S3 : list_char > option_val]: ((member652041809on_val @ (produc52622304on_val @ R2 @ S2) @ R) => ((S3 = S2) => (member652041809on_val @ (produc52622304on_val @ R2 @ S3) @ R)))))). % ssubst_Pair_rhs
thf(fact_68_ssubst__Pair__rhs, axiom,
    ((![R2 : list_char, S2 : list_char, R : set_Pr164112643t_char, S3 : list_char]: ((member89690956t_char @ (produc1304532571t_char @ R2 @ S2) @ R) => ((S3 = S2) => (member89690956t_char @ (produc1304532571t_char @ R2 @ S3) @ R)))))). % ssubst_Pair_rhs
thf(fact_69_curryI, axiom,
    ((![F : produc266837688on_val > $o, A : list_char, B : produc1257910179t_char > option_val]: ((F @ (produc904988266on_val @ A @ B)) => (produc988598624_val_o @ F @ A @ B))))). % curryI
thf(fact_70_curryI, axiom,
    ((![F : produc1172664615on_val > $o, A : produc1097884484on_val, B : produc1097884484on_val]: ((F @ (produc1069526295on_val @ A @ B)) => (produc360843917_val_o @ F @ A @ B))))). % curryI
thf(fact_71_curryI, axiom,
    ((![F : produc1097884484on_val > $o, A : exp_list_char, B : produc515445032on_val]: ((F @ (produc2023458740on_val @ A @ B)) => (produc699483184_val_o @ F @ A @ B))))). % curryI
thf(fact_72_curryI, axiom,
    ((![F : produc515445032on_val > $o, A : nat > option2118145160on_val, B : list_char > option_val]: ((F @ (produc52622304on_val @ A @ B)) => (produc761261956_val_o @ F @ A @ B))))). % curryI
thf(fact_73_curryI, axiom,
    ((![F : produc1257910179t_char > $o, A : list_char, B : list_char]: ((F @ (produc1304532571t_char @ A @ B)) => (produc239457481char_o @ F @ A @ B))))). % curryI
thf(fact_74_wt, axiom,
    ((wTrt @ p @ ha @ e @ (fAss_list_char @ (val_list_char @ (addr @ a)) @ f @ d @ (val_list_char @ v)) @ t))). % wt
thf(fact_75_conf__widen, axiom,
    ((![P2 : list_P1234162913t_char, H : nat > option2118145160on_val, V2 : val, T : ty, T4 : ty]: ((conf_P93989998t_char @ P2 @ H @ V2 @ T) => ((widen_917054840t_char @ P2 @ T @ T4) => (conf_P93989998t_char @ P2 @ H @ V2 @ T4)))))). % conf_widen
thf(fact_76_curryE, axiom,
    ((![F : produc266837688on_val > $o, A : list_char, B : produc1257910179t_char > option_val]: ((produc988598624_val_o @ F @ A @ B) => (F @ (produc904988266on_val @ A @ B)))))). % curryE
thf(fact_77_curryE, axiom,
    ((![F : produc1172664615on_val > $o, A : produc1097884484on_val, B : produc1097884484on_val]: ((produc360843917_val_o @ F @ A @ B) => (F @ (produc1069526295on_val @ A @ B)))))). % curryE
thf(fact_78_curryE, axiom,
    ((![F : produc1097884484on_val > $o, A : exp_list_char, B : produc515445032on_val]: ((produc699483184_val_o @ F @ A @ B) => (F @ (produc2023458740on_val @ A @ B)))))). % curryE
thf(fact_79_curryE, axiom,
    ((![F : produc515445032on_val > $o, A : nat > option2118145160on_val, B : list_char > option_val]: ((produc761261956_val_o @ F @ A @ B) => (F @ (produc52622304on_val @ A @ B)))))). % curryE
thf(fact_80_curryE, axiom,
    ((![F : produc1257910179t_char > $o, A : list_char, B : list_char]: ((produc239457481char_o @ F @ A @ B) => (F @ (produc1304532571t_char @ A @ B)))))). % curryE
thf(fact_81_mem__Collect__eq, axiom,
    ((![A : produc1172664615on_val, P2 : produc1172664615on_val > $o]: ((member354538064on_val @ A @ (collec2055896722on_val @ P2)) = (P2 @ A))))). % mem_Collect_eq
thf(fact_82_Collect__mem__eq, axiom,
    ((![A5 : set_Pr1189492743on_val]: ((collec2055896722on_val @ (^[X4 : produc1172664615on_val]: (member354538064on_val @ X4 @ A5))) = A5)))). % Collect_mem_eq
thf(fact_83_curryD, axiom,
    ((![F : produc266837688on_val > $o, A : list_char, B : produc1257910179t_char > option_val]: ((produc988598624_val_o @ F @ A @ B) => (F @ (produc904988266on_val @ A @ B)))))). % curryD
thf(fact_84_curryD, axiom,
    ((![F : produc1172664615on_val > $o, A : produc1097884484on_val, B : produc1097884484on_val]: ((produc360843917_val_o @ F @ A @ B) => (F @ (produc1069526295on_val @ A @ B)))))). % curryD
thf(fact_85_curryD, axiom,
    ((![F : produc1097884484on_val > $o, A : exp_list_char, B : produc515445032on_val]: ((produc699483184_val_o @ F @ A @ B) => (F @ (produc2023458740on_val @ A @ B)))))). % curryD
thf(fact_86_curryD, axiom,
    ((![F : produc515445032on_val > $o, A : nat > option2118145160on_val, B : list_char > option_val]: ((produc761261956_val_o @ F @ A @ B) => (F @ (produc52622304on_val @ A @ B)))))). % curryD
thf(fact_87_curryD, axiom,
    ((![F : produc1257910179t_char > $o, A : list_char, B : list_char]: ((produc239457481char_o @ F @ A @ B) => (F @ (produc1304532571t_char @ A @ B)))))). % curryD
thf(fact_88_preallocated__upd__obj, axiom,
    ((![H : nat > option2118145160on_val, A : nat, C2 : list_char, Fs : produc1257910179t_char > option_val, Fs2 : produc1257910179t_char > option_val]: ((preallocated @ H) => (((H @ A) = (some_P1299442195on_val @ (produc904988266on_val @ C2 @ Fs))) => (preallocated @ (fun_up262443479on_val @ H @ A @ (some_P1299442195on_val @ (produc904988266on_val @ C2 @ Fs2))))))))). % preallocated_upd_obj
thf(fact_89_WTrtVal, axiom,
    ((![H : nat > option2118145160on_val, V2 : val, T : ty, P2 : list_P1234162913t_char, E : list_char > option_ty]: (((typeof_h @ H @ V2) = (some_ty @ T)) => (wTrt @ P2 @ H @ E @ (val_list_char @ V2) @ T))))). % WTrtVal
thf(fact_90_exp_Oinject_I8_J, axiom,
    ((![X81 : exp_list_char, X82 : list_char, X83 : list_char, X84 : exp_list_char, Y81 : exp_list_char, Y82 : list_char, Y83 : list_char, Y84 : exp_list_char]: (((fAss_list_char @ X81 @ X82 @ X83 @ X84) = (fAss_list_char @ Y81 @ Y82 @ Y83 @ Y84)) = (((X81 = Y81)) & ((((X82 = Y82)) & ((((X83 = Y83)) & ((X84 = Y84))))))))))). % exp.inject(8)
thf(fact_91_val_Oinject_I3_J, axiom,
    ((![X5 : nat, Y5 : nat]: (((addr @ X5) = (addr @ Y5)) = (X5 = Y5))))). % val.inject(3)
thf(fact_92_fun__upd__upd, axiom,
    ((![F : nat > option2118145160on_val, X3 : nat, Y3 : option2118145160on_val, Z : option2118145160on_val]: ((fun_up262443479on_val @ (fun_up262443479on_val @ F @ X3 @ Y3) @ X3 @ Z) = (fun_up262443479on_val @ F @ X3 @ Z))))). % fun_upd_upd
thf(fact_93_fun__upd__upd, axiom,
    ((![F : produc1257910179t_char > option_val, X3 : produc1257910179t_char, Y3 : option_val, Z : option_val]: ((fun_up356838326on_val @ (fun_up356838326on_val @ F @ X3 @ Y3) @ X3 @ Z) = (fun_up356838326on_val @ F @ X3 @ Z))))). % fun_upd_upd
thf(fact_94_fun__upd__upd, axiom,
    ((![F : list_char > option_val, X3 : list_char, Y3 : option_val, Z : option_val]: ((fun_up1252458416on_val @ (fun_up1252458416on_val @ F @ X3 @ Y3) @ X3 @ Z) = (fun_up1252458416on_val @ F @ X3 @ Z))))). % fun_upd_upd
thf(fact_95_fun__upd__triv, axiom,
    ((![F : nat > option2118145160on_val, X3 : nat]: ((fun_up262443479on_val @ F @ X3 @ (F @ X3)) = F)))). % fun_upd_triv
thf(fact_96_fun__upd__triv, axiom,
    ((![F : produc1257910179t_char > option_val, X3 : produc1257910179t_char]: ((fun_up356838326on_val @ F @ X3 @ (F @ X3)) = F)))). % fun_upd_triv
thf(fact_97_fun__upd__triv, axiom,
    ((![F : list_char > option_val, X3 : list_char]: ((fun_up1252458416on_val @ F @ X3 @ (F @ X3)) = F)))). % fun_upd_triv
thf(fact_98_fun__upd__apply, axiom,
    ((fun_up262443479on_val = (^[F2 : nat > option2118145160on_val]: (^[X4 : nat]: (^[Y4 : option2118145160on_val]: (^[Z2 : nat]: (if_opt451925058on_val @ (Z2 = X4) @ Y4 @ (F2 @ Z2))))))))). % fun_upd_apply
thf(fact_99_fun__upd__apply, axiom,
    ((fun_up356838326on_val = (^[F2 : produc1257910179t_char > option_val]: (^[X4 : produc1257910179t_char]: (^[Y4 : option_val]: (^[Z2 : produc1257910179t_char]: (if_option_val @ (Z2 = X4) @ Y4 @ (F2 @ Z2))))))))). % fun_upd_apply
thf(fact_100_fun__upd__apply, axiom,
    ((fun_up1252458416on_val = (^[F2 : list_char > option_val]: (^[X4 : list_char]: (^[Y4 : option_val]: (^[Z2 : list_char]: (if_option_val @ (Z2 = X4) @ Y4 @ (F2 @ Z2))))))))). % fun_upd_apply
thf(fact_101_exp_Oinject_I3_J, axiom,
    ((![X32 : val, Y32 : val]: (((val_list_char @ X32) = (val_list_char @ Y32)) = (X32 = Y32))))). % exp.inject(3)
thf(fact_102_fun__upd__idem__iff, axiom,
    ((![F : nat > option2118145160on_val, X3 : nat, Y3 : option2118145160on_val]: (((fun_up262443479on_val @ F @ X3 @ Y3) = F) = ((F @ X3) = Y3))))). % fun_upd_idem_iff
thf(fact_103_fun__upd__idem__iff, axiom,
    ((![F : produc1257910179t_char > option_val, X3 : produc1257910179t_char, Y3 : option_val]: (((fun_up356838326on_val @ F @ X3 @ Y3) = F) = ((F @ X3) = Y3))))). % fun_upd_idem_iff
thf(fact_104_fun__upd__idem__iff, axiom,
    ((![F : list_char > option_val, X3 : list_char, Y3 : option_val]: (((fun_up1252458416on_val @ F @ X3 @ Y3) = F) = ((F @ X3) = Y3))))). % fun_upd_idem_iff
thf(fact_105_fun__upd__twist, axiom,
    ((![A : nat, C3 : nat, M : nat > option2118145160on_val, B : option2118145160on_val, D2 : option2118145160on_val]: ((~ ((A = C3))) => ((fun_up262443479on_val @ (fun_up262443479on_val @ M @ A @ B) @ C3 @ D2) = (fun_up262443479on_val @ (fun_up262443479on_val @ M @ C3 @ D2) @ A @ B)))))). % fun_upd_twist
thf(fact_106_fun__upd__twist, axiom,
    ((![A : produc1257910179t_char, C3 : produc1257910179t_char, M : produc1257910179t_char > option_val, B : option_val, D2 : option_val]: ((~ ((A = C3))) => ((fun_up356838326on_val @ (fun_up356838326on_val @ M @ A @ B) @ C3 @ D2) = (fun_up356838326on_val @ (fun_up356838326on_val @ M @ C3 @ D2) @ A @ B)))))). % fun_upd_twist
thf(fact_107_fun__upd__twist, axiom,
    ((![A : list_char, C3 : list_char, M : list_char > option_val, B : option_val, D2 : option_val]: ((~ ((A = C3))) => ((fun_up1252458416on_val @ (fun_up1252458416on_val @ M @ A @ B) @ C3 @ D2) = (fun_up1252458416on_val @ (fun_up1252458416on_val @ M @ C3 @ D2) @ A @ B)))))). % fun_upd_twist
thf(fact_108_fun__upd__other, axiom,
    ((![Z : nat, X3 : nat, F : nat > option2118145160on_val, Y3 : option2118145160on_val]: ((~ ((Z = X3))) => ((fun_up262443479on_val @ F @ X3 @ Y3 @ Z) = (F @ Z)))))). % fun_upd_other
thf(fact_109_fun__upd__other, axiom,
    ((![Z : produc1257910179t_char, X3 : produc1257910179t_char, F : produc1257910179t_char > option_val, Y3 : option_val]: ((~ ((Z = X3))) => ((fun_up356838326on_val @ F @ X3 @ Y3 @ Z) = (F @ Z)))))). % fun_upd_other
thf(fact_110_fun__upd__other, axiom,
    ((![Z : list_char, X3 : list_char, F : list_char > option_val, Y3 : option_val]: ((~ ((Z = X3))) => ((fun_up1252458416on_val @ F @ X3 @ Y3 @ Z) = (F @ Z)))))). % fun_upd_other
thf(fact_111_fun__upd__same, axiom,
    ((![F : nat > option2118145160on_val, X3 : nat, Y3 : option2118145160on_val]: ((fun_up262443479on_val @ F @ X3 @ Y3 @ X3) = Y3)))). % fun_upd_same
thf(fact_112_fun__upd__same, axiom,
    ((![F : produc1257910179t_char > option_val, X3 : produc1257910179t_char, Y3 : option_val]: ((fun_up356838326on_val @ F @ X3 @ Y3 @ X3) = Y3)))). % fun_upd_same
thf(fact_113_fun__upd__same, axiom,
    ((![F : list_char > option_val, X3 : list_char, Y3 : option_val]: ((fun_up1252458416on_val @ F @ X3 @ Y3 @ X3) = Y3)))). % fun_upd_same
thf(fact_114_fun__upd__idem, axiom,
    ((![F : nat > option2118145160on_val, X3 : nat, Y3 : option2118145160on_val]: (((F @ X3) = Y3) => ((fun_up262443479on_val @ F @ X3 @ Y3) = F))))). % fun_upd_idem
thf(fact_115_fun__upd__idem, axiom,
    ((![F : produc1257910179t_char > option_val, X3 : produc1257910179t_char, Y3 : option_val]: (((F @ X3) = Y3) => ((fun_up356838326on_val @ F @ X3 @ Y3) = F))))). % fun_upd_idem
thf(fact_116_fun__upd__idem, axiom,
    ((![F : list_char > option_val, X3 : list_char, Y3 : option_val]: (((F @ X3) = Y3) => ((fun_up1252458416on_val @ F @ X3 @ Y3) = F))))). % fun_upd_idem
thf(fact_117_fun__upd__eqD, axiom,
    ((![F : nat > option2118145160on_val, X3 : nat, Y3 : option2118145160on_val, G : nat > option2118145160on_val, Z : option2118145160on_val]: (((fun_up262443479on_val @ F @ X3 @ Y3) = (fun_up262443479on_val @ G @ X3 @ Z)) => (Y3 = Z))))). % fun_upd_eqD
thf(fact_118_fun__upd__eqD, axiom,
    ((![F : produc1257910179t_char > option_val, X3 : produc1257910179t_char, Y3 : option_val, G : produc1257910179t_char > option_val, Z : option_val]: (((fun_up356838326on_val @ F @ X3 @ Y3) = (fun_up356838326on_val @ G @ X3 @ Z)) => (Y3 = Z))))). % fun_upd_eqD
thf(fact_119_fun__upd__eqD, axiom,
    ((![F : list_char > option_val, X3 : list_char, Y3 : option_val, G : list_char > option_val, Z : option_val]: (((fun_up1252458416on_val @ F @ X3 @ Y3) = (fun_up1252458416on_val @ G @ X3 @ Z)) => (Y3 = Z))))). % fun_upd_eqD
thf(fact_120_fun__upd__def, axiom,
    ((fun_up262443479on_val = (^[F2 : nat > option2118145160on_val]: (^[A4 : nat]: (^[B4 : option2118145160on_val]: (^[X4 : nat]: (if_opt451925058on_val @ (X4 = A4) @ B4 @ (F2 @ X4))))))))). % fun_upd_def
thf(fact_121_fun__upd__def, axiom,
    ((fun_up356838326on_val = (^[F2 : produc1257910179t_char > option_val]: (^[A4 : produc1257910179t_char]: (^[B4 : option_val]: (^[X4 : produc1257910179t_char]: (if_option_val @ (X4 = A4) @ B4 @ (F2 @ X4))))))))). % fun_upd_def
thf(fact_122_fun__upd__def, axiom,
    ((fun_up1252458416on_val = (^[F2 : list_char > option_val]: (^[A4 : list_char]: (^[B4 : option_val]: (^[X4 : list_char]: (if_option_val @ (X4 = A4) @ B4 @ (F2 @ X4))))))))). % fun_upd_def
thf(fact_123_oconf__fupd, axiom,
    ((![P2 : list_P1234162913t_char, C2 : list_char, F3 : list_char, T : ty, D3 : list_char, H : nat > option2118145160on_val, V2 : val, Fs : produc1257910179t_char > option_val]: ((has_fi599584195t_char @ P2 @ C2 @ F3 @ T @ D3) => ((conf_P93989998t_char @ P2 @ H @ V2 @ T) => ((oconf_454120169t_char @ P2 @ H @ (produc904988266on_val @ C2 @ Fs)) => (oconf_454120169t_char @ P2 @ H @ (produc904988266on_val @ C2 @ (fun_up356838326on_val @ Fs @ (produc1304532571t_char @ F3 @ D3) @ (some_val @ V2)))))))))). % oconf_fupd
thf(fact_124_exp_Odistinct_I63_J, axiom,
    ((![X32 : val, X81 : exp_list_char, X82 : list_char, X83 : list_char, X84 : exp_list_char]: (~ (((val_list_char @ X32) = (fAss_list_char @ X81 @ X82 @ X83 @ X84))))))). % exp.distinct(63)
thf(fact_125_map__upd__eqD1, axiom,
    ((![M : nat > option2118145160on_val, A : nat, X3 : produc266837688on_val, N : nat > option2118145160on_val, Y3 : produc266837688on_val]: (((fun_up262443479on_val @ M @ A @ (some_P1299442195on_val @ X3)) = (fun_up262443479on_val @ N @ A @ (some_P1299442195on_val @ Y3))) => (X3 = Y3))))). % map_upd_eqD1
thf(fact_126_map__upd__eqD1, axiom,
    ((![M : produc1257910179t_char > option_val, A : produc1257910179t_char, X3 : val, N : produc1257910179t_char > option_val, Y3 : val]: (((fun_up356838326on_val @ M @ A @ (some_val @ X3)) = (fun_up356838326on_val @ N @ A @ (some_val @ Y3))) => (X3 = Y3))))). % map_upd_eqD1
thf(fact_127_map__upd__eqD1, axiom,
    ((![M : list_char > option_val, A : list_char, X3 : val, N : list_char > option_val, Y3 : val]: (((fun_up1252458416on_val @ M @ A @ (some_val @ X3)) = (fun_up1252458416on_val @ N @ A @ (some_val @ Y3))) => (X3 = Y3))))). % map_upd_eqD1
thf(fact_128_map__upd__triv, axiom,
    ((![T5 : nat > option2118145160on_val, K : nat, X3 : produc266837688on_val]: (((T5 @ K) = (some_P1299442195on_val @ X3)) => ((fun_up262443479on_val @ T5 @ K @ (some_P1299442195on_val @ X3)) = T5))))). % map_upd_triv
thf(fact_129_map__upd__triv, axiom,
    ((![T5 : produc1257910179t_char > option_val, K : produc1257910179t_char, X3 : val]: (((T5 @ K) = (some_val @ X3)) => ((fun_up356838326on_val @ T5 @ K @ (some_val @ X3)) = T5))))). % map_upd_triv
thf(fact_130_map__upd__triv, axiom,
    ((![T5 : list_char > option_val, K : list_char, X3 : val]: (((T5 @ K) = (some_val @ X3)) => ((fun_up1252458416on_val @ T5 @ K @ (some_val @ X3)) = T5))))). % map_upd_triv
thf(fact_131_map__upd__Some__unfold, axiom,
    ((![M : nat > option2118145160on_val, A : nat, B : produc266837688on_val, X3 : nat, Y3 : produc266837688on_val]: (((fun_up262443479on_val @ M @ A @ (some_P1299442195on_val @ B) @ X3) = (some_P1299442195on_val @ Y3)) = (((((X3 = A)) & ((B = Y3)))) | ((((~ ((X3 = A)))) & (((M @ X3) = (some_P1299442195on_val @ Y3)))))))))). % map_upd_Some_unfold
thf(fact_132_map__upd__Some__unfold, axiom,
    ((![M : produc1257910179t_char > option_val, A : produc1257910179t_char, B : val, X3 : produc1257910179t_char, Y3 : val]: (((fun_up356838326on_val @ M @ A @ (some_val @ B) @ X3) = (some_val @ Y3)) = (((((X3 = A)) & ((B = Y3)))) | ((((~ ((X3 = A)))) & (((M @ X3) = (some_val @ Y3)))))))))). % map_upd_Some_unfold
thf(fact_133_map__upd__Some__unfold, axiom,
    ((![M : list_char > option_val, A : list_char, B : val, X3 : list_char, Y3 : val]: (((fun_up1252458416on_val @ M @ A @ (some_val @ B) @ X3) = (some_val @ Y3)) = (((((X3 = A)) & ((B = Y3)))) | ((((~ ((X3 = A)))) & (((M @ X3) = (some_val @ Y3)))))))))). % map_upd_Some_unfold
thf(fact_134_the__Addr_Osimps, axiom,
    ((![A : nat]: ((the_Addr @ (addr @ A)) = A)))). % the_Addr.simps
thf(fact_135_hconf__new, axiom,
    ((![P2 : list_P1234162913t_char, H : nat > option2118145160on_val, A : nat, Obj : produc266837688on_val]: ((hconf_1244167010t_char @ P2 @ H) => (((H @ A) = none_P1535574167on_val) => ((oconf_454120169t_char @ P2 @ H @ Obj) => (hconf_1244167010t_char @ P2 @ (fun_up262443479on_val @ H @ A @ (some_P1299442195on_val @ Obj))))))))). % hconf_new
thf(fact_136_not__Some__eq, axiom,
    ((![X3 : option2118145160on_val]: ((![Y4 : produc266837688on_val]: (~ ((X3 = (some_P1299442195on_val @ Y4))))) = (X3 = none_P1535574167on_val))))). % not_Some_eq
thf(fact_137_not__Some__eq, axiom,
    ((![X3 : option_ty]: ((![Y4 : ty]: (~ ((X3 = (some_ty @ Y4))))) = (X3 = none_ty))))). % not_Some_eq
thf(fact_138_not__Some__eq, axiom,
    ((![X3 : option_val]: ((![Y4 : val]: (~ ((X3 = (some_val @ Y4))))) = (X3 = none_val))))). % not_Some_eq
thf(fact_139_not__None__eq, axiom,
    ((![X3 : option2118145160on_val]: ((~ ((X3 = none_P1535574167on_val))) = (?[Y4 : produc266837688on_val]: (X3 = (some_P1299442195on_val @ Y4))))))). % not_None_eq
thf(fact_140_not__None__eq, axiom,
    ((![X3 : option_ty]: ((~ ((X3 = none_ty))) = (?[Y4 : ty]: (X3 = (some_ty @ Y4))))))). % not_None_eq
thf(fact_141_not__None__eq, axiom,
    ((![X3 : option_val]: ((~ ((X3 = none_val))) = (?[Y4 : val]: (X3 = (some_val @ Y4))))))). % not_None_eq
thf(fact_142_empty__upd__none, axiom,
    ((![X3 : produc1257910179t_char]: ((fun_up356838326on_val @ (^[X4 : produc1257910179t_char]: none_val) @ X3 @ none_val) = (^[X4 : produc1257910179t_char]: none_val))))). % empty_upd_none
thf(fact_143_empty__upd__none, axiom,
    ((![X3 : list_char]: ((fun_up1252458416on_val @ (^[X4 : list_char]: none_val) @ X3 @ none_val) = (^[X4 : list_char]: none_val))))). % empty_upd_none
thf(fact_144_empty__upd__none, axiom,
    ((![X3 : nat]: ((fun_up262443479on_val @ (^[X4 : nat]: none_P1535574167on_val) @ X3 @ none_P1535574167on_val) = (^[X4 : nat]: none_P1535574167on_val))))). % empty_upd_none
thf(fact_145_option_Odistinct_I1_J, axiom,
    ((![X2 : produc266837688on_val]: (~ ((none_P1535574167on_val = (some_P1299442195on_val @ X2))))))). % option.distinct(1)
thf(fact_146_option_Odistinct_I1_J, axiom,
    ((![X2 : ty]: (~ ((none_ty = (some_ty @ X2))))))). % option.distinct(1)
thf(fact_147_option_Odistinct_I1_J, axiom,
    ((![X2 : val]: (~ ((none_val = (some_val @ X2))))))). % option.distinct(1)
thf(fact_148_option_OdiscI, axiom,
    ((![Option : option2118145160on_val, X2 : produc266837688on_val]: ((Option = (some_P1299442195on_val @ X2)) => (~ ((Option = none_P1535574167on_val))))))). % option.discI
thf(fact_149_option_OdiscI, axiom,
    ((![Option : option_ty, X2 : ty]: ((Option = (some_ty @ X2)) => (~ ((Option = none_ty))))))). % option.discI
thf(fact_150_option_OdiscI, axiom,
    ((![Option : option_val, X2 : val]: ((Option = (some_val @ X2)) => (~ ((Option = none_val))))))). % option.discI
thf(fact_151_option_Oexhaust, axiom,
    ((![Y3 : option2118145160on_val]: ((~ ((Y3 = none_P1535574167on_val))) => (~ ((![X22 : produc266837688on_val]: (~ ((Y3 = (some_P1299442195on_val @ X22))))))))))). % option.exhaust
thf(fact_152_option_Oexhaust, axiom,
    ((![Y3 : option_ty]: ((~ ((Y3 = none_ty))) => (~ ((![X22 : ty]: (~ ((Y3 = (some_ty @ X22))))))))))). % option.exhaust
thf(fact_153_option_Oexhaust, axiom,
    ((![Y3 : option_val]: ((~ ((Y3 = none_val))) => (~ ((![X22 : val]: (~ ((Y3 = (some_val @ X22))))))))))). % option.exhaust
thf(fact_154_option_Oinducts, axiom,
    ((![P2 : option2118145160on_val > $o, Option : option2118145160on_val]: ((P2 @ none_P1535574167on_val) => ((![X : produc266837688on_val]: (P2 @ (some_P1299442195on_val @ X))) => (P2 @ Option)))))). % option.inducts
thf(fact_155_option_Oinducts, axiom,
    ((![P2 : option_ty > $o, Option : option_ty]: ((P2 @ none_ty) => ((![X : ty]: (P2 @ (some_ty @ X))) => (P2 @ Option)))))). % option.inducts
thf(fact_156_option_Oinducts, axiom,
    ((![P2 : option_val > $o, Option : option_val]: ((P2 @ none_val) => ((![X : val]: (P2 @ (some_val @ X))) => (P2 @ Option)))))). % option.inducts
thf(fact_157_split__option__ex, axiom,
    (((^[P4 : option2118145160on_val > $o]: (?[X6 : option2118145160on_val]: (P4 @ X6))) = (^[P3 : option2118145160on_val > $o]: (((P3 @ none_P1535574167on_val)) | ((?[X4 : produc266837688on_val]: (P3 @ (some_P1299442195on_val @ X4))))))))). % split_option_ex
thf(fact_158_split__option__ex, axiom,
    (((^[P4 : option_ty > $o]: (?[X6 : option_ty]: (P4 @ X6))) = (^[P3 : option_ty > $o]: (((P3 @ none_ty)) | ((?[X4 : ty]: (P3 @ (some_ty @ X4))))))))). % split_option_ex
thf(fact_159_split__option__ex, axiom,
    (((^[P4 : option_val > $o]: (?[X6 : option_val]: (P4 @ X6))) = (^[P3 : option_val > $o]: (((P3 @ none_val)) | ((?[X4 : val]: (P3 @ (some_val @ X4))))))))). % split_option_ex
thf(fact_160_split__option__all, axiom,
    (((^[P4 : option2118145160on_val > $o]: (![X6 : option2118145160on_val]: (P4 @ X6))) = (^[P3 : option2118145160on_val > $o]: (((P3 @ none_P1535574167on_val)) & ((![X4 : produc266837688on_val]: (P3 @ (some_P1299442195on_val @ X4))))))))). % split_option_all
thf(fact_161_split__option__all, axiom,
    (((^[P4 : option_ty > $o]: (![X6 : option_ty]: (P4 @ X6))) = (^[P3 : option_ty > $o]: (((P3 @ none_ty)) & ((![X4 : ty]: (P3 @ (some_ty @ X4))))))))). % split_option_all
thf(fact_162_split__option__all, axiom,
    (((^[P4 : option_val > $o]: (![X6 : option_val]: (P4 @ X6))) = (^[P3 : option_val > $o]: (((P3 @ none_val)) & ((![X4 : val]: (P3 @ (some_val @ X4))))))))). % split_option_all
thf(fact_163_combine__options__cases, axiom,
    ((![X3 : option2118145160on_val, P2 : option2118145160on_val > option2118145160on_val > $o, Y3 : option2118145160on_val]: (((X3 = none_P1535574167on_val) => (P2 @ X3 @ Y3)) => (((Y3 = none_P1535574167on_val) => (P2 @ X3 @ Y3)) => ((![A3 : produc266837688on_val, B3 : produc266837688on_val]: ((X3 = (some_P1299442195on_val @ A3)) => ((Y3 = (some_P1299442195on_val @ B3)) => (P2 @ X3 @ Y3)))) => (P2 @ X3 @ Y3))))))). % combine_options_cases
thf(fact_164_combine__options__cases, axiom,
    ((![X3 : option2118145160on_val, P2 : option2118145160on_val > option_ty > $o, Y3 : option_ty]: (((X3 = none_P1535574167on_val) => (P2 @ X3 @ Y3)) => (((Y3 = none_ty) => (P2 @ X3 @ Y3)) => ((![A3 : produc266837688on_val, B3 : ty]: ((X3 = (some_P1299442195on_val @ A3)) => ((Y3 = (some_ty @ B3)) => (P2 @ X3 @ Y3)))) => (P2 @ X3 @ Y3))))))). % combine_options_cases
thf(fact_165_combine__options__cases, axiom,
    ((![X3 : option2118145160on_val, P2 : option2118145160on_val > option_val > $o, Y3 : option_val]: (((X3 = none_P1535574167on_val) => (P2 @ X3 @ Y3)) => (((Y3 = none_val) => (P2 @ X3 @ Y3)) => ((![A3 : produc266837688on_val, B3 : val]: ((X3 = (some_P1299442195on_val @ A3)) => ((Y3 = (some_val @ B3)) => (P2 @ X3 @ Y3)))) => (P2 @ X3 @ Y3))))))). % combine_options_cases
thf(fact_166_combine__options__cases, axiom,
    ((![X3 : option_ty, P2 : option_ty > option2118145160on_val > $o, Y3 : option2118145160on_val]: (((X3 = none_ty) => (P2 @ X3 @ Y3)) => (((Y3 = none_P1535574167on_val) => (P2 @ X3 @ Y3)) => ((![A3 : ty, B3 : produc266837688on_val]: ((X3 = (some_ty @ A3)) => ((Y3 = (some_P1299442195on_val @ B3)) => (P2 @ X3 @ Y3)))) => (P2 @ X3 @ Y3))))))). % combine_options_cases
thf(fact_167_combine__options__cases, axiom,
    ((![X3 : option_ty, P2 : option_ty > option_ty > $o, Y3 : option_ty]: (((X3 = none_ty) => (P2 @ X3 @ Y3)) => (((Y3 = none_ty) => (P2 @ X3 @ Y3)) => ((![A3 : ty, B3 : ty]: ((X3 = (some_ty @ A3)) => ((Y3 = (some_ty @ B3)) => (P2 @ X3 @ Y3)))) => (P2 @ X3 @ Y3))))))). % combine_options_cases
thf(fact_168_combine__options__cases, axiom,
    ((![X3 : option_ty, P2 : option_ty > option_val > $o, Y3 : option_val]: (((X3 = none_ty) => (P2 @ X3 @ Y3)) => (((Y3 = none_val) => (P2 @ X3 @ Y3)) => ((![A3 : ty, B3 : val]: ((X3 = (some_ty @ A3)) => ((Y3 = (some_val @ B3)) => (P2 @ X3 @ Y3)))) => (P2 @ X3 @ Y3))))))). % combine_options_cases
thf(fact_169_combine__options__cases, axiom,
    ((![X3 : option_val, P2 : option_val > option2118145160on_val > $o, Y3 : option2118145160on_val]: (((X3 = none_val) => (P2 @ X3 @ Y3)) => (((Y3 = none_P1535574167on_val) => (P2 @ X3 @ Y3)) => ((![A3 : val, B3 : produc266837688on_val]: ((X3 = (some_val @ A3)) => ((Y3 = (some_P1299442195on_val @ B3)) => (P2 @ X3 @ Y3)))) => (P2 @ X3 @ Y3))))))). % combine_options_cases
thf(fact_170_combine__options__cases, axiom,
    ((![X3 : option_val, P2 : option_val > option_ty > $o, Y3 : option_ty]: (((X3 = none_val) => (P2 @ X3 @ Y3)) => (((Y3 = none_ty) => (P2 @ X3 @ Y3)) => ((![A3 : val, B3 : ty]: ((X3 = (some_val @ A3)) => ((Y3 = (some_ty @ B3)) => (P2 @ X3 @ Y3)))) => (P2 @ X3 @ Y3))))))). % combine_options_cases
thf(fact_171_combine__options__cases, axiom,
    ((![X3 : option_val, P2 : option_val > option_val > $o, Y3 : option_val]: (((X3 = none_val) => (P2 @ X3 @ Y3)) => (((Y3 = none_val) => (P2 @ X3 @ Y3)) => ((![A3 : val, B3 : val]: ((X3 = (some_val @ A3)) => ((Y3 = (some_val @ B3)) => (P2 @ X3 @ Y3)))) => (P2 @ X3 @ Y3))))))). % combine_options_cases
thf(fact_172_map__upd__nonempty, axiom,
    ((![T5 : nat > option2118145160on_val, K : nat, X3 : produc266837688on_val]: (~ (((fun_up262443479on_val @ T5 @ K @ (some_P1299442195on_val @ X3)) = (^[X4 : nat]: none_P1535574167on_val))))))). % map_upd_nonempty
thf(fact_173_map__upd__nonempty, axiom,
    ((![T5 : produc1257910179t_char > option_val, K : produc1257910179t_char, X3 : val]: (~ (((fun_up356838326on_val @ T5 @ K @ (some_val @ X3)) = (^[X4 : produc1257910179t_char]: none_val))))))). % map_upd_nonempty
thf(fact_174_map__upd__nonempty, axiom,
    ((![T5 : list_char > option_val, K : list_char, X3 : val]: (~ (((fun_up1252458416on_val @ T5 @ K @ (some_val @ X3)) = (^[X4 : list_char]: none_val))))))). % map_upd_nonempty
thf(fact_175_preallocated__new, axiom,
    ((![H : nat > option2118145160on_val, A : nat, X3 : produc266837688on_val]: ((preallocated @ H) => (((H @ A) = none_P1535574167on_val) => (preallocated @ (fun_up262443479on_val @ H @ A @ (some_P1299442195on_val @ X3)))))))). % preallocated_new
thf(fact_176_oconf__new, axiom,
    ((![P2 : list_P1234162913t_char, H : nat > option2118145160on_val, Obj : produc266837688on_val, A : nat, X3 : produc266837688on_val]: ((oconf_454120169t_char @ P2 @ H @ Obj) => (((H @ A) = none_P1535574167on_val) => (oconf_454120169t_char @ P2 @ (fun_up262443479on_val @ H @ A @ (some_P1299442195on_val @ X3)) @ Obj)))))). % oconf_new
thf(fact_177_typeof__lit__typeof, axiom,
    ((![V2 : val, T : ty, H : nat > option2118145160on_val]: (((typeof_h @ (^[X4 : nat]: none_P1535574167on_val) @ V2) = (some_ty @ T)) => ((typeof_h @ H @ V2) = (some_ty @ T)))))). % typeof_lit_typeof
thf(fact_178_red__reds_ORedFAss, axiom,
    ((![H : nat > option2118145160on_val, A : nat, C2 : list_char, Fs : produc1257910179t_char > option_val, F3 : list_char, D3 : list_char, V2 : val, L : list_char > option_val, P2 : list_P1234162913t_char]: (((H @ A) = (some_P1299442195on_val @ (produc904988266on_val @ C2 @ Fs))) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (fAss_list_char @ (val_list_char @ (addr @ A)) @ F3 @ D3 @ (val_list_char @ V2)) @ (produc52622304on_val @ H @ L)) @ (produc2023458740on_val @ (val_list_char @ unit) @ (produc52622304on_val @ (fun_up262443479on_val @ H @ A @ (some_P1299442195on_val @ (produc904988266on_val @ C2 @ (fun_up356838326on_val @ Fs @ (produc1304532571t_char @ F3 @ D3) @ (some_val @ V2))))) @ L))) @ (red @ P2)))))). % red_reds.RedFAss
thf(fact_179_red__reds_OFAssRed2, axiom,
    ((![E2 : exp_list_char, S2 : produc515445032on_val, E3 : exp_list_char, S3 : produc515445032on_val, P2 : list_P1234162913t_char, V2 : val, F3 : list_char, D3 : list_char]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E2 @ S2) @ (produc2023458740on_val @ E3 @ S3)) @ (red @ P2)) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (fAss_list_char @ (val_list_char @ V2) @ F3 @ D3 @ E2) @ S2) @ (produc2023458740on_val @ (fAss_list_char @ (val_list_char @ V2) @ F3 @ D3 @ E3) @ S3)) @ (red @ P2)))))). % red_reds.FAssRed2
thf(fact_180_red__reds_OFAssRed1, axiom,
    ((![E2 : exp_list_char, S2 : produc515445032on_val, E3 : exp_list_char, S3 : produc515445032on_val, P2 : list_P1234162913t_char, F3 : list_char, D3 : list_char, E_2 : exp_list_char]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E2 @ S2) @ (produc2023458740on_val @ E3 @ S3)) @ (red @ P2)) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (fAss_list_char @ E2 @ F3 @ D3 @ E_2) @ S2) @ (produc2023458740on_val @ (fAss_list_char @ E3 @ F3 @ D3 @ E_2) @ S3)) @ (red @ P2)))))). % red_reds.FAssRed1
thf(fact_181_val_Odistinct_I7_J, axiom,
    ((![X5 : nat]: (~ ((unit = (addr @ X5))))))). % val.distinct(7)
thf(fact_182_redp__redsp_ORedFAss, axiom,
    ((![H : nat > option2118145160on_val, A : nat, C2 : list_char, Fs : produc1257910179t_char > option_val, P2 : list_P1234162913t_char, F3 : list_char, D3 : list_char, V2 : val, L : list_char > option_val]: (((H @ A) = (some_P1299442195on_val @ (produc904988266on_val @ C2 @ Fs))) => (redp @ P2 @ (fAss_list_char @ (val_list_char @ (addr @ A)) @ F3 @ D3 @ (val_list_char @ V2)) @ (produc52622304on_val @ H @ L) @ (val_list_char @ unit) @ (produc52622304on_val @ (fun_up262443479on_val @ H @ A @ (some_P1299442195on_val @ (produc904988266on_val @ C2 @ (fun_up356838326on_val @ Fs @ (produc1304532571t_char @ F3 @ D3) @ (some_val @ V2))))) @ L)))))). % redp_redsp.RedFAss
thf(fact_183_FAssRedsVal, axiom,
    ((![E_1 : exp_list_char, S_0 : produc515445032on_val, A : nat, S_1 : produc515445032on_val, P2 : list_P1234162913t_char, E_2 : exp_list_char, V2 : val, H_2 : nat > option2118145160on_val, L_2 : list_char > option_val, C2 : list_char, Fs : produc1257910179t_char > option_val, F3 : list_char, D3 : list_char]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E_1 @ S_0) @ (produc2023458740on_val @ (val_list_char @ (addr @ A)) @ S_1)) @ (transi111096263on_val @ (red @ P2))) => ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E_2 @ S_1) @ (produc2023458740on_val @ (val_list_char @ V2) @ (produc52622304on_val @ H_2 @ L_2))) @ (transi111096263on_val @ (red @ P2))) => (((some_P1299442195on_val @ (produc904988266on_val @ C2 @ Fs)) = (H_2 @ A)) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (fAss_list_char @ E_1 @ F3 @ D3 @ E_2) @ S_0) @ (produc2023458740on_val @ (val_list_char @ unit) @ (produc52622304on_val @ (fun_up262443479on_val @ H_2 @ A @ (some_P1299442195on_val @ (produc904988266on_val @ C2 @ (fun_up356838326on_val @ Fs @ (produc1304532571t_char @ F3 @ D3) @ (some_val @ V2))))) @ L_2))) @ (transi111096263on_val @ (red @ P2))))))))). % FAssRedsVal
thf(fact_184_FAss, axiom,
    ((![P2 : list_P1234162913t_char, E_1 : exp_list_char, S_0 : produc515445032on_val, A : nat, S_1 : produc515445032on_val, E_2 : exp_list_char, V2 : val, H_2 : nat > option2118145160on_val, L_2 : list_char > option_val, C2 : list_char, Fs : produc1257910179t_char > option_val, Fs2 : produc1257910179t_char > option_val, F3 : list_char, D3 : list_char, H_22 : nat > option2118145160on_val]: ((eval @ P2 @ E_1 @ S_0 @ (val_list_char @ (addr @ A)) @ S_1) => ((eval @ P2 @ E_2 @ S_1 @ (val_list_char @ V2) @ (produc52622304on_val @ H_2 @ L_2)) => (((H_2 @ A) = (some_P1299442195on_val @ (produc904988266on_val @ C2 @ Fs))) => ((Fs2 = (fun_up356838326on_val @ Fs @ (produc1304532571t_char @ F3 @ D3) @ (some_val @ V2))) => ((H_22 = (fun_up262443479on_val @ H_2 @ A @ (some_P1299442195on_val @ (produc904988266on_val @ C2 @ Fs2)))) => (eval @ P2 @ (fAss_list_char @ E_1 @ F3 @ D3 @ E_2) @ S_0 @ (val_list_char @ unit) @ (produc52622304on_val @ H_22 @ L_2)))))))))). % FAss
thf(fact_185_redp__redsp_OFAssRed1, axiom,
    ((![P2 : list_P1234162913t_char, E2 : exp_list_char, S2 : produc515445032on_val, E3 : exp_list_char, S3 : produc515445032on_val, F3 : list_char, D3 : list_char, E_2 : exp_list_char]: ((redp @ P2 @ E2 @ S2 @ E3 @ S3) => (redp @ P2 @ (fAss_list_char @ E2 @ F3 @ D3 @ E_2) @ S2 @ (fAss_list_char @ E3 @ F3 @ D3 @ E_2) @ S3))))). % redp_redsp.FAssRed1
thf(fact_186_Val, axiom,
    ((![P2 : list_P1234162913t_char, V2 : val, S2 : produc515445032on_val]: (eval @ P2 @ (val_list_char @ V2) @ S2 @ (val_list_char @ V2) @ S2)))). % Val
thf(fact_187_eval__cases_I2_J, axiom,
    ((![P2 : list_P1234162913t_char, V2 : val, S2 : produc515445032on_val, E3 : exp_list_char, S3 : produc515445032on_val]: ((eval @ P2 @ (val_list_char @ V2) @ S2 @ E3 @ S3) => (~ (((E3 = (val_list_char @ V2)) => (~ ((S3 = S2)))))))))). % eval_cases(2)
thf(fact_188_redp__redsp_OFAssRed2, axiom,
    ((![P2 : list_P1234162913t_char, E2 : exp_list_char, S2 : produc515445032on_val, E3 : exp_list_char, S3 : produc515445032on_val, V2 : val, F3 : list_char, D3 : list_char]: ((redp @ P2 @ E2 @ S2 @ E3 @ S3) => (redp @ P2 @ (fAss_list_char @ (val_list_char @ V2) @ F3 @ D3 @ E2) @ S2 @ (fAss_list_char @ (val_list_char @ V2) @ F3 @ D3 @ E3) @ S3))))). % redp_redsp.FAssRed2
thf(fact_189_FAssReds1, axiom,
    ((![E2 : exp_list_char, S2 : produc515445032on_val, E3 : exp_list_char, S3 : produc515445032on_val, P2 : list_P1234162913t_char, F3 : list_char, D3 : list_char, E_2 : exp_list_char]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E2 @ S2) @ (produc2023458740on_val @ E3 @ S3)) @ (transi111096263on_val @ (red @ P2))) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (fAss_list_char @ E2 @ F3 @ D3 @ E_2) @ S2) @ (produc2023458740on_val @ (fAss_list_char @ E3 @ F3 @ D3 @ E_2) @ S3)) @ (transi111096263on_val @ (red @ P2))))))). % FAssReds1
thf(fact_190_FAssReds2, axiom,
    ((![E2 : exp_list_char, S2 : produc515445032on_val, E3 : exp_list_char, S3 : produc515445032on_val, P2 : list_P1234162913t_char, V2 : val, F3 : list_char, D3 : list_char]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E2 @ S2) @ (produc2023458740on_val @ E3 @ S3)) @ (transi111096263on_val @ (red @ P2))) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (fAss_list_char @ (val_list_char @ V2) @ F3 @ D3 @ E2) @ S2) @ (produc2023458740on_val @ (fAss_list_char @ (val_list_char @ V2) @ F3 @ D3 @ E3) @ S3)) @ (transi111096263on_val @ (red @ P2))))))). % FAssReds2
thf(fact_191_redp__red__eq, axiom,
    ((redp = (^[P3 : list_P1234162913t_char]: (^[X4 : exp_list_char]: (^[Y4 : produc515445032on_val]: (^[Z2 : exp_list_char]: (^[Aa : produc515445032on_val]: (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ X4 @ Y4) @ (produc2023458740on_val @ Z2 @ Aa)) @ (red @ P3)))))))))). % redp_red_eq
thf(fact_192_converse__rtrancl__induct__red, axiom,
    ((![E2 : exp_list_char, H : nat > option2118145160on_val, L : list_char > option_val, E3 : exp_list_char, H3 : nat > option2118145160on_val, L2 : list_char > option_val, P2 : 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 @ E2 @ (produc52622304on_val @ H @ L)) @ (produc2023458740on_val @ E3 @ (produc52622304on_val @ H3 @ L2))) @ (transi111096263on_val @ (red @ P2))) => ((![E4 : exp_list_char, H4 : nat > option2118145160on_val, L3 : list_char > option_val]: (R @ E4 @ H4 @ L3 @ E4 @ H4 @ L3)) => ((![E_0 : exp_list_char, H_0 : nat > option2118145160on_val, L_0 : list_char > option_val, E_12 : exp_list_char, H_1 : nat > option2118145160on_val, L_1 : list_char > option_val, E5 : exp_list_char, H5 : nat > option2118145160on_val, L4 : list_char > option_val]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E_0 @ (produc52622304on_val @ H_0 @ L_0)) @ (produc2023458740on_val @ E_12 @ (produc52622304on_val @ H_1 @ L_1))) @ (red @ P2)) => ((R @ E_12 @ H_1 @ L_1 @ E5 @ H5 @ L4) => (R @ E_0 @ H_0 @ L_0 @ E5 @ H5 @ L4)))) => (R @ E2 @ H @ L @ E3 @ H3 @ L2))))))). % converse_rtrancl_induct_red
thf(fact_193_rtrancl__induct2, axiom,
    ((![Ax : list_char, Ay : produc1257910179t_char > option_val, Bx : list_char, By : produc1257910179t_char > option_val, R2 : set_Pr2110063281on_val, P2 : list_char > (produc1257910179t_char > option_val) > $o]: ((member197592058on_val @ (produc881885833on_val @ (produc904988266on_val @ Ax @ Ay) @ (produc904988266on_val @ Bx @ By)) @ (transi2071064181on_val @ R2)) => ((P2 @ Ax @ Ay) => ((![A3 : list_char, B3 : produc1257910179t_char > option_val, Aa2 : list_char, Ba : produc1257910179t_char > option_val]: ((member197592058on_val @ (produc881885833on_val @ (produc904988266on_val @ Ax @ Ay) @ (produc904988266on_val @ A3 @ B3)) @ (transi2071064181on_val @ R2)) => ((member197592058on_val @ (produc881885833on_val @ (produc904988266on_val @ A3 @ B3) @ (produc904988266on_val @ Aa2 @ Ba)) @ R2) => ((P2 @ A3 @ B3) => (P2 @ Aa2 @ Ba))))) => (P2 @ Bx @ By))))))). % rtrancl_induct2
thf(fact_194_rtrancl__induct2, axiom,
    ((![Ax : produc1097884484on_val, Ay : produc1097884484on_val, Bx : produc1097884484on_val, By : produc1097884484on_val, R2 : set_Pr1368603847on_val, P2 : produc1097884484on_val > produc1097884484on_val > $o]: ((member208988944on_val @ (produc564964183on_val @ (produc1069526295on_val @ Ax @ Ay) @ (produc1069526295on_val @ Bx @ By)) @ (transi100378922on_val @ R2)) => ((P2 @ Ax @ Ay) => ((![A3 : produc1097884484on_val, B3 : produc1097884484on_val, Aa2 : produc1097884484on_val, Ba : produc1097884484on_val]: ((member208988944on_val @ (produc564964183on_val @ (produc1069526295on_val @ Ax @ Ay) @ (produc1069526295on_val @ A3 @ B3)) @ (transi100378922on_val @ R2)) => ((member208988944on_val @ (produc564964183on_val @ (produc1069526295on_val @ A3 @ B3) @ (produc1069526295on_val @ Aa2 @ Ba)) @ R2) => ((P2 @ A3 @ B3) => (P2 @ Aa2 @ Ba))))) => (P2 @ Bx @ By))))))). % rtrancl_induct2
thf(fact_195_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, P2 : (nat > option2118145160on_val) > (list_char > option_val) > $o]: ((member2027247312on_val @ (produc2106877847on_val @ (produc52622304on_val @ Ax @ Ay) @ (produc52622304on_val @ Bx @ By)) @ (transi432893227on_val @ R2)) => ((P2 @ Ax @ Ay) => ((![A3 : nat > option2118145160on_val, B3 : list_char > option_val, Aa2 : nat > option2118145160on_val, Ba : list_char > option_val]: ((member2027247312on_val @ (produc2106877847on_val @ (produc52622304on_val @ Ax @ Ay) @ (produc52622304on_val @ A3 @ B3)) @ (transi432893227on_val @ R2)) => ((member2027247312on_val @ (produc2106877847on_val @ (produc52622304on_val @ A3 @ B3) @ (produc52622304on_val @ Aa2 @ Ba)) @ R2) => ((P2 @ A3 @ B3) => (P2 @ Aa2 @ Ba))))) => (P2 @ Bx @ By))))))). % rtrancl_induct2
thf(fact_196_rtrancl__induct2, axiom,
    ((![Ax : list_char, Ay : list_char, Bx : list_char, By : list_char, R2 : set_Pr729957319t_char, P2 : list_char > list_char > $o]: ((member803902992t_char @ (produc395356247t_char @ (produc1304532571t_char @ Ax @ Ay) @ (produc1304532571t_char @ Bx @ By)) @ (transi858104614t_char @ R2)) => ((P2 @ Ax @ Ay) => ((![A3 : list_char, B3 : list_char, Aa2 : list_char, Ba : list_char]: ((member803902992t_char @ (produc395356247t_char @ (produc1304532571t_char @ Ax @ Ay) @ (produc1304532571t_char @ A3 @ B3)) @ (transi858104614t_char @ R2)) => ((member803902992t_char @ (produc395356247t_char @ (produc1304532571t_char @ A3 @ B3) @ (produc1304532571t_char @ Aa2 @ Ba)) @ R2) => ((P2 @ A3 @ B3) => (P2 @ Aa2 @ Ba))))) => (P2 @ Bx @ By))))))). % rtrancl_induct2
thf(fact_197_rtrancl__induct2, axiom,
    ((![Ax : exp_list_char, Ay : produc515445032on_val, Bx : exp_list_char, By : produc515445032on_val, R2 : set_Pr1189492743on_val, P2 : exp_list_char > produc515445032on_val > $o]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ Ax @ Ay) @ (produc2023458740on_val @ Bx @ By)) @ (transi111096263on_val @ R2)) => ((P2 @ Ax @ Ay) => ((![A3 : exp_list_char, B3 : produc515445032on_val, Aa2 : exp_list_char, Ba : produc515445032on_val]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ Ax @ Ay) @ (produc2023458740on_val @ A3 @ B3)) @ (transi111096263on_val @ R2)) => ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ A3 @ B3) @ (produc2023458740on_val @ Aa2 @ Ba)) @ R2) => ((P2 @ A3 @ B3) => (P2 @ Aa2 @ Ba))))) => (P2 @ Bx @ By))))))). % rtrancl_induct2
thf(fact_198_converse__rtranclE2, axiom,
    ((![Xa : list_char, Xb : produc1257910179t_char > option_val, Za : list_char, Zb : produc1257910179t_char > option_val, R2 : set_Pr2110063281on_val]: ((member197592058on_val @ (produc881885833on_val @ (produc904988266on_val @ Xa @ Xb) @ (produc904988266on_val @ Za @ Zb)) @ (transi2071064181on_val @ R2)) => ((~ (((produc904988266on_val @ Xa @ Xb) = (produc904988266on_val @ Za @ Zb)))) => (~ ((![A3 : list_char, B3 : produc1257910179t_char > option_val]: ((member197592058on_val @ (produc881885833on_val @ (produc904988266on_val @ Xa @ Xb) @ (produc904988266on_val @ A3 @ B3)) @ R2) => (~ ((member197592058on_val @ (produc881885833on_val @ (produc904988266on_val @ A3 @ B3) @ (produc904988266on_val @ Za @ Zb)) @ (transi2071064181on_val @ R2))))))))))))). % converse_rtranclE2
thf(fact_199_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)))) => (~ ((![A3 : produc1097884484on_val, B3 : produc1097884484on_val]: ((member208988944on_val @ (produc564964183on_val @ (produc1069526295on_val @ Xa @ Xb) @ (produc1069526295on_val @ A3 @ B3)) @ R2) => (~ ((member208988944on_val @ (produc564964183on_val @ (produc1069526295on_val @ A3 @ B3) @ (produc1069526295on_val @ Za @ Zb)) @ (transi100378922on_val @ R2))))))))))))). % converse_rtranclE2
thf(fact_200_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)))) => (~ ((![A3 : nat > option2118145160on_val, B3 : list_char > option_val]: ((member2027247312on_val @ (produc2106877847on_val @ (produc52622304on_val @ Xa @ Xb) @ (produc52622304on_val @ A3 @ B3)) @ R2) => (~ ((member2027247312on_val @ (produc2106877847on_val @ (produc52622304on_val @ A3 @ B3) @ (produc52622304on_val @ Za @ Zb)) @ (transi432893227on_val @ R2))))))))))))). % converse_rtranclE2
thf(fact_201_converse__rtranclE2, axiom,
    ((![Xa : list_char, Xb : list_char, Za : list_char, Zb : list_char, R2 : set_Pr729957319t_char]: ((member803902992t_char @ (produc395356247t_char @ (produc1304532571t_char @ Xa @ Xb) @ (produc1304532571t_char @ Za @ Zb)) @ (transi858104614t_char @ R2)) => ((~ (((produc1304532571t_char @ Xa @ Xb) = (produc1304532571t_char @ Za @ Zb)))) => (~ ((![A3 : list_char, B3 : list_char]: ((member803902992t_char @ (produc395356247t_char @ (produc1304532571t_char @ Xa @ Xb) @ (produc1304532571t_char @ A3 @ B3)) @ R2) => (~ ((member803902992t_char @ (produc395356247t_char @ (produc1304532571t_char @ A3 @ B3) @ (produc1304532571t_char @ Za @ Zb)) @ (transi858104614t_char @ R2))))))))))))). % converse_rtranclE2
thf(fact_202_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)))) => (~ ((![A3 : exp_list_char, B3 : produc515445032on_val]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ Xa @ Xb) @ (produc2023458740on_val @ A3 @ B3)) @ R2) => (~ ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ A3 @ B3) @ (produc2023458740on_val @ Za @ Zb)) @ (transi111096263on_val @ R2))))))))))))). % converse_rtranclE2
thf(fact_203_converse__rtrancl__induct2, axiom,
    ((![Ax : list_char, Ay : produc1257910179t_char > option_val, Bx : list_char, By : produc1257910179t_char > option_val, R2 : set_Pr2110063281on_val, P2 : list_char > (produc1257910179t_char > option_val) > $o]: ((member197592058on_val @ (produc881885833on_val @ (produc904988266on_val @ Ax @ Ay) @ (produc904988266on_val @ Bx @ By)) @ (transi2071064181on_val @ R2)) => ((P2 @ Bx @ By) => ((![A3 : list_char, B3 : produc1257910179t_char > option_val, Aa2 : list_char, Ba : produc1257910179t_char > option_val]: ((member197592058on_val @ (produc881885833on_val @ (produc904988266on_val @ A3 @ B3) @ (produc904988266on_val @ Aa2 @ Ba)) @ R2) => ((member197592058on_val @ (produc881885833on_val @ (produc904988266on_val @ Aa2 @ Ba) @ (produc904988266on_val @ Bx @ By)) @ (transi2071064181on_val @ R2)) => ((P2 @ Aa2 @ Ba) => (P2 @ A3 @ B3))))) => (P2 @ Ax @ Ay))))))). % converse_rtrancl_induct2
thf(fact_204_converse__rtrancl__induct2, axiom,
    ((![Ax : produc1097884484on_val, Ay : produc1097884484on_val, Bx : produc1097884484on_val, By : produc1097884484on_val, R2 : set_Pr1368603847on_val, P2 : produc1097884484on_val > produc1097884484on_val > $o]: ((member208988944on_val @ (produc564964183on_val @ (produc1069526295on_val @ Ax @ Ay) @ (produc1069526295on_val @ Bx @ By)) @ (transi100378922on_val @ R2)) => ((P2 @ Bx @ By) => ((![A3 : produc1097884484on_val, B3 : produc1097884484on_val, Aa2 : produc1097884484on_val, Ba : produc1097884484on_val]: ((member208988944on_val @ (produc564964183on_val @ (produc1069526295on_val @ A3 @ B3) @ (produc1069526295on_val @ Aa2 @ Ba)) @ R2) => ((member208988944on_val @ (produc564964183on_val @ (produc1069526295on_val @ Aa2 @ Ba) @ (produc1069526295on_val @ Bx @ By)) @ (transi100378922on_val @ R2)) => ((P2 @ Aa2 @ Ba) => (P2 @ A3 @ B3))))) => (P2 @ Ax @ Ay))))))). % converse_rtrancl_induct2
thf(fact_205_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, P2 : (nat > option2118145160on_val) > (list_char > option_val) > $o]: ((member2027247312on_val @ (produc2106877847on_val @ (produc52622304on_val @ Ax @ Ay) @ (produc52622304on_val @ Bx @ By)) @ (transi432893227on_val @ R2)) => ((P2 @ Bx @ By) => ((![A3 : nat > option2118145160on_val, B3 : list_char > option_val, Aa2 : nat > option2118145160on_val, Ba : list_char > option_val]: ((member2027247312on_val @ (produc2106877847on_val @ (produc52622304on_val @ A3 @ B3) @ (produc52622304on_val @ Aa2 @ Ba)) @ R2) => ((member2027247312on_val @ (produc2106877847on_val @ (produc52622304on_val @ Aa2 @ Ba) @ (produc52622304on_val @ Bx @ By)) @ (transi432893227on_val @ R2)) => ((P2 @ Aa2 @ Ba) => (P2 @ A3 @ B3))))) => (P2 @ Ax @ Ay))))))). % converse_rtrancl_induct2
thf(fact_206_converse__rtrancl__induct2, axiom,
    ((![Ax : list_char, Ay : list_char, Bx : list_char, By : list_char, R2 : set_Pr729957319t_char, P2 : list_char > list_char > $o]: ((member803902992t_char @ (produc395356247t_char @ (produc1304532571t_char @ Ax @ Ay) @ (produc1304532571t_char @ Bx @ By)) @ (transi858104614t_char @ R2)) => ((P2 @ Bx @ By) => ((![A3 : list_char, B3 : list_char, Aa2 : list_char, Ba : list_char]: ((member803902992t_char @ (produc395356247t_char @ (produc1304532571t_char @ A3 @ B3) @ (produc1304532571t_char @ Aa2 @ Ba)) @ R2) => ((member803902992t_char @ (produc395356247t_char @ (produc1304532571t_char @ Aa2 @ Ba) @ (produc1304532571t_char @ Bx @ By)) @ (transi858104614t_char @ R2)) => ((P2 @ Aa2 @ Ba) => (P2 @ A3 @ B3))))) => (P2 @ Ax @ Ay))))))). % converse_rtrancl_induct2
thf(fact_207_converse__rtrancl__induct2, axiom,
    ((![Ax : exp_list_char, Ay : produc515445032on_val, Bx : exp_list_char, By : produc515445032on_val, R2 : set_Pr1189492743on_val, P2 : exp_list_char > produc515445032on_val > $o]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ Ax @ Ay) @ (produc2023458740on_val @ Bx @ By)) @ (transi111096263on_val @ R2)) => ((P2 @ Bx @ By) => ((![A3 : exp_list_char, B3 : produc515445032on_val, Aa2 : exp_list_char, Ba : produc515445032on_val]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ A3 @ B3) @ (produc2023458740on_val @ Aa2 @ Ba)) @ R2) => ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ Aa2 @ Ba) @ (produc2023458740on_val @ Bx @ By)) @ (transi111096263on_val @ R2)) => ((P2 @ Aa2 @ Ba) => (P2 @ A3 @ B3))))) => (P2 @ Ax @ Ay))))))). % converse_rtrancl_induct2
thf(fact_208_converse__rtrancl__into__rtrancl, axiom,
    ((![A : list_char, B : list_char, R2 : set_Pr164112643t_char, C3 : list_char]: ((member89690956t_char @ (produc1304532571t_char @ A @ B) @ R2) => ((member89690956t_char @ (produc1304532571t_char @ B @ C3) @ (transi1879726366t_char @ R2)) => (member89690956t_char @ (produc1304532571t_char @ A @ C3) @ (transi1879726366t_char @ R2))))))). % converse_rtrancl_into_rtrancl
thf(fact_209_converse__rtrancl__into__rtrancl, axiom,
    ((![A : produc1097884484on_val, B : produc1097884484on_val, R2 : set_Pr1189492743on_val, C3 : produc1097884484on_val]: ((member354538064on_val @ (produc1069526295on_val @ A @ B) @ R2) => ((member354538064on_val @ (produc1069526295on_val @ B @ C3) @ (transi111096263on_val @ R2)) => (member354538064on_val @ (produc1069526295on_val @ A @ C3) @ (transi111096263on_val @ R2))))))). % converse_rtrancl_into_rtrancl
thf(fact_210_rtrancl_Ortrancl__into__rtrancl, axiom,
    ((![A : list_char, B : list_char, R2 : set_Pr164112643t_char, C3 : list_char]: ((member89690956t_char @ (produc1304532571t_char @ A @ B) @ (transi1879726366t_char @ R2)) => ((member89690956t_char @ (produc1304532571t_char @ B @ C3) @ R2) => (member89690956t_char @ (produc1304532571t_char @ A @ C3) @ (transi1879726366t_char @ R2))))))). % rtrancl.rtrancl_into_rtrancl
thf(fact_211_rtrancl_Ortrancl__into__rtrancl, axiom,
    ((![A : produc1097884484on_val, B : produc1097884484on_val, R2 : set_Pr1189492743on_val, C3 : produc1097884484on_val]: ((member354538064on_val @ (produc1069526295on_val @ A @ B) @ (transi111096263on_val @ R2)) => ((member354538064on_val @ (produc1069526295on_val @ B @ C3) @ R2) => (member354538064on_val @ (produc1069526295on_val @ A @ C3) @ (transi111096263on_val @ R2))))))). % rtrancl.rtrancl_into_rtrancl
thf(fact_212_converse__rtrancl__induct, axiom,
    ((![A : list_char, B : list_char, R2 : set_Pr164112643t_char, P2 : list_char > $o]: ((member89690956t_char @ (produc1304532571t_char @ A @ B) @ (transi1879726366t_char @ R2)) => ((P2 @ B) => ((![Y : list_char, Z3 : list_char]: ((member89690956t_char @ (produc1304532571t_char @ Y @ Z3) @ R2) => ((member89690956t_char @ (produc1304532571t_char @ Z3 @ B) @ (transi1879726366t_char @ R2)) => ((P2 @ Z3) => (P2 @ Y))))) => (P2 @ A))))))). % converse_rtrancl_induct
thf(fact_213_converse__rtrancl__induct, axiom,
    ((![A : produc1097884484on_val, B : produc1097884484on_val, R2 : set_Pr1189492743on_val, P2 : produc1097884484on_val > $o]: ((member354538064on_val @ (produc1069526295on_val @ A @ B) @ (transi111096263on_val @ R2)) => ((P2 @ B) => ((![Y : produc1097884484on_val, Z3 : produc1097884484on_val]: ((member354538064on_val @ (produc1069526295on_val @ Y @ Z3) @ R2) => ((member354538064on_val @ (produc1069526295on_val @ Z3 @ B) @ (transi111096263on_val @ R2)) => ((P2 @ Z3) => (P2 @ Y))))) => (P2 @ A))))))). % converse_rtrancl_induct
thf(fact_214_rtrancl_Ortrancl__refl, axiom,
    ((![A : list_char, R2 : set_Pr164112643t_char]: (member89690956t_char @ (produc1304532571t_char @ A @ A) @ (transi1879726366t_char @ R2))))). % rtrancl.rtrancl_refl
thf(fact_215_rtrancl_Ortrancl__refl, axiom,
    ((![A : produc1097884484on_val, R2 : set_Pr1189492743on_val]: (member354538064on_val @ (produc1069526295on_val @ A @ A) @ (transi111096263on_val @ R2))))). % rtrancl.rtrancl_refl
thf(fact_216_converse__rtranclE, axiom,
    ((![X3 : list_char, Z : list_char, R2 : set_Pr164112643t_char]: ((member89690956t_char @ (produc1304532571t_char @ X3 @ Z) @ (transi1879726366t_char @ R2)) => ((~ ((X3 = Z))) => (~ ((![Y : list_char]: ((member89690956t_char @ (produc1304532571t_char @ X3 @ Y) @ R2) => (~ ((member89690956t_char @ (produc1304532571t_char @ Y @ Z) @ (transi1879726366t_char @ R2))))))))))))). % converse_rtranclE
thf(fact_217_converse__rtranclE, axiom,
    ((![X3 : produc1097884484on_val, Z : produc1097884484on_val, R2 : set_Pr1189492743on_val]: ((member354538064on_val @ (produc1069526295on_val @ X3 @ Z) @ (transi111096263on_val @ R2)) => ((~ ((X3 = Z))) => (~ ((![Y : produc1097884484on_val]: ((member354538064on_val @ (produc1069526295on_val @ X3 @ Y) @ R2) => (~ ((member354538064on_val @ (produc1069526295on_val @ Y @ Z) @ (transi111096263on_val @ R2))))))))))))). % converse_rtranclE
thf(fact_218_rtrancl_Oinducts, axiom,
    ((![X1 : list_char, X2 : list_char, R2 : set_Pr164112643t_char, P2 : list_char > list_char > $o]: ((member89690956t_char @ (produc1304532571t_char @ X1 @ X2) @ (transi1879726366t_char @ R2)) => ((![A3 : list_char]: (P2 @ A3 @ A3)) => ((![A3 : list_char, B3 : list_char, C : list_char]: ((member89690956t_char @ (produc1304532571t_char @ A3 @ B3) @ (transi1879726366t_char @ R2)) => ((P2 @ A3 @ B3) => ((member89690956t_char @ (produc1304532571t_char @ B3 @ C) @ R2) => (P2 @ A3 @ C))))) => (P2 @ X1 @ X2))))))). % rtrancl.inducts
thf(fact_219_rtrancl_Oinducts, axiom,
    ((![X1 : produc1097884484on_val, X2 : produc1097884484on_val, R2 : set_Pr1189492743on_val, P2 : produc1097884484on_val > produc1097884484on_val > $o]: ((member354538064on_val @ (produc1069526295on_val @ X1 @ X2) @ (transi111096263on_val @ R2)) => ((![A3 : produc1097884484on_val]: (P2 @ A3 @ A3)) => ((![A3 : produc1097884484on_val, B3 : produc1097884484on_val, C : produc1097884484on_val]: ((member354538064on_val @ (produc1069526295on_val @ A3 @ B3) @ (transi111096263on_val @ R2)) => ((P2 @ A3 @ B3) => ((member354538064on_val @ (produc1069526295on_val @ B3 @ C) @ R2) => (P2 @ A3 @ C))))) => (P2 @ X1 @ X2))))))). % rtrancl.inducts
thf(fact_220_rtrancl__induct, axiom,
    ((![A : list_char, B : list_char, R2 : set_Pr164112643t_char, P2 : list_char > $o]: ((member89690956t_char @ (produc1304532571t_char @ A @ B) @ (transi1879726366t_char @ R2)) => ((P2 @ A) => ((![Y : list_char, Z3 : list_char]: ((member89690956t_char @ (produc1304532571t_char @ A @ Y) @ (transi1879726366t_char @ R2)) => ((member89690956t_char @ (produc1304532571t_char @ Y @ Z3) @ R2) => ((P2 @ Y) => (P2 @ Z3))))) => (P2 @ B))))))). % rtrancl_induct
thf(fact_221_rtrancl__induct, axiom,
    ((![A : produc1097884484on_val, B : produc1097884484on_val, R2 : set_Pr1189492743on_val, P2 : produc1097884484on_val > $o]: ((member354538064on_val @ (produc1069526295on_val @ A @ B) @ (transi111096263on_val @ R2)) => ((P2 @ A) => ((![Y : produc1097884484on_val, Z3 : produc1097884484on_val]: ((member354538064on_val @ (produc1069526295on_val @ A @ Y) @ (transi111096263on_val @ R2)) => ((member354538064on_val @ (produc1069526295on_val @ Y @ Z3) @ R2) => ((P2 @ Y) => (P2 @ Z3))))) => (P2 @ B))))))). % rtrancl_induct
thf(fact_222_rtrancl__trans, axiom,
    ((![X3 : list_char, Y3 : list_char, R2 : set_Pr164112643t_char, Z : list_char]: ((member89690956t_char @ (produc1304532571t_char @ X3 @ Y3) @ (transi1879726366t_char @ R2)) => ((member89690956t_char @ (produc1304532571t_char @ Y3 @ Z) @ (transi1879726366t_char @ R2)) => (member89690956t_char @ (produc1304532571t_char @ X3 @ Z) @ (transi1879726366t_char @ R2))))))). % rtrancl_trans
thf(fact_223_rtrancl__trans, axiom,
    ((![X3 : produc1097884484on_val, Y3 : produc1097884484on_val, R2 : set_Pr1189492743on_val, Z : produc1097884484on_val]: ((member354538064on_val @ (produc1069526295on_val @ X3 @ Y3) @ (transi111096263on_val @ R2)) => ((member354538064on_val @ (produc1069526295on_val @ Y3 @ Z) @ (transi111096263on_val @ R2)) => (member354538064on_val @ (produc1069526295on_val @ X3 @ Z) @ (transi111096263on_val @ R2))))))). % rtrancl_trans
thf(fact_224_rtrancl_Osimps, axiom,
    ((![A1 : list_char, A22 : list_char, R2 : set_Pr164112643t_char]: ((member89690956t_char @ (produc1304532571t_char @ A1 @ A22) @ (transi1879726366t_char @ R2)) = (((?[A4 : list_char]: (((A1 = A4)) & ((A22 = A4))))) | ((?[A4 : list_char]: (?[B4 : list_char]: (?[C4 : list_char]: (((A1 = A4)) & ((((A22 = C4)) & ((((member89690956t_char @ (produc1304532571t_char @ A4 @ B4) @ (transi1879726366t_char @ R2))) & ((member89690956t_char @ (produc1304532571t_char @ B4 @ C4) @ R2)))))))))))))))). % rtrancl.simps
thf(fact_225_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]: (?[C4 : produc1097884484on_val]: (((A1 = A4)) & ((((A22 = C4)) & ((((member354538064on_val @ (produc1069526295on_val @ A4 @ B4) @ (transi111096263on_val @ R2))) & ((member354538064on_val @ (produc1069526295on_val @ B4 @ C4) @ R2)))))))))))))))). % rtrancl.simps
thf(fact_226_rtrancl_Ocases, axiom,
    ((![A1 : list_char, A22 : list_char, R2 : set_Pr164112643t_char]: ((member89690956t_char @ (produc1304532571t_char @ A1 @ A22) @ (transi1879726366t_char @ R2)) => ((~ ((A22 = A1))) => (~ ((![B3 : list_char]: ((member89690956t_char @ (produc1304532571t_char @ A1 @ B3) @ (transi1879726366t_char @ R2)) => (~ ((member89690956t_char @ (produc1304532571t_char @ B3 @ A22) @ R2)))))))))))). % rtrancl.cases
thf(fact_227_rtrancl_Ocases, axiom,
    ((![A1 : produc1097884484on_val, A22 : produc1097884484on_val, R2 : set_Pr1189492743on_val]: ((member354538064on_val @ (produc1069526295on_val @ A1 @ A22) @ (transi111096263on_val @ R2)) => ((~ ((A22 = A1))) => (~ ((![B3 : produc1097884484on_val]: ((member354538064on_val @ (produc1069526295on_val @ A1 @ B3) @ (transi111096263on_val @ R2)) => (~ ((member354538064on_val @ (produc1069526295on_val @ B3 @ A22) @ R2)))))))))))). % rtrancl.cases
thf(fact_228_rtranclE, axiom,
    ((![A : list_char, B : list_char, R2 : set_Pr164112643t_char]: ((member89690956t_char @ (produc1304532571t_char @ A @ B) @ (transi1879726366t_char @ R2)) => ((~ ((A = B))) => (~ ((![Y : list_char]: ((member89690956t_char @ (produc1304532571t_char @ A @ Y) @ (transi1879726366t_char @ R2)) => (~ ((member89690956t_char @ (produc1304532571t_char @ Y @ B) @ R2)))))))))))). % rtranclE
thf(fact_229_rtranclE, axiom,
    ((![A : produc1097884484on_val, B : produc1097884484on_val, R2 : set_Pr1189492743on_val]: ((member354538064on_val @ (produc1069526295on_val @ A @ B) @ (transi111096263on_val @ R2)) => ((~ ((A = B))) => (~ ((![Y : produc1097884484on_val]: ((member354538064on_val @ (produc1069526295on_val @ A @ Y) @ (transi111096263on_val @ R2)) => (~ ((member354538064on_val @ (produc1069526295on_val @ Y @ B) @ R2)))))))))))). % rtranclE
thf(fact_230_LAssRedsVal, axiom,
    ((![E2 : exp_list_char, S2 : produc515445032on_val, V2 : val, H3 : nat > option2118145160on_val, L2 : list_char > option_val, P2 : list_P1234162913t_char, V3 : list_char]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E2 @ S2) @ (produc2023458740on_val @ (val_list_char @ V2) @ (produc52622304on_val @ H3 @ L2))) @ (transi111096263on_val @ (red @ P2))) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (lAss_list_char @ V3 @ E2) @ S2) @ (produc2023458740on_val @ (val_list_char @ unit) @ (produc52622304on_val @ H3 @ (fun_up1252458416on_val @ L2 @ V3 @ (some_val @ V2))))) @ (transi111096263on_val @ (red @ P2))))))). % LAssRedsVal
thf(fact_231_FAcc, axiom,
    ((![P2 : list_P1234162913t_char, E2 : exp_list_char, S_0 : produc515445032on_val, A : nat, H : nat > option2118145160on_val, L : list_char > option_val, C2 : list_char, Fs : produc1257910179t_char > option_val, F3 : list_char, D3 : list_char, V2 : val]: ((eval @ P2 @ E2 @ S_0 @ (val_list_char @ (addr @ A)) @ (produc52622304on_val @ H @ L)) => (((H @ A) = (some_P1299442195on_val @ (produc904988266on_val @ C2 @ Fs))) => (((Fs @ (produc1304532571t_char @ F3 @ D3)) = (some_val @ V2)) => (eval @ P2 @ (fAcc_list_char @ E2 @ F3 @ D3) @ S_0 @ (val_list_char @ V2) @ (produc52622304on_val @ H @ L)))))))). % FAcc
thf(fact_232_exp_Oinject_I6_J, axiom,
    ((![X61 : list_char, X62 : exp_list_char, Y61 : list_char, Y62 : exp_list_char]: (((lAss_list_char @ X61 @ X62) = (lAss_list_char @ Y61 @ Y62)) = (((X61 = Y61)) & ((X62 = Y62))))))). % exp.inject(6)
thf(fact_233_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_234_exp_Odistinct_I59_J, axiom,
    ((![X32 : val, X61 : list_char, X62 : exp_list_char]: (~ (((val_list_char @ X32) = (lAss_list_char @ X61 @ X62))))))). % exp.distinct(59)
thf(fact_235_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_236_exp_Odistinct_I123_J, axiom,
    ((![X61 : list_char, X62 : exp_list_char, X81 : exp_list_char, X82 : list_char, X83 : list_char, X84 : exp_list_char]: (~ (((lAss_list_char @ X61 @ X62) = (fAss_list_char @ X81 @ X82 @ X83 @ X84))))))). % exp.distinct(123)
thf(fact_237_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_238_red__reds_OLAssRed, axiom,
    ((![E2 : exp_list_char, S2 : produc515445032on_val, E3 : exp_list_char, S3 : produc515445032on_val, P2 : list_P1234162913t_char, V3 : list_char]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E2 @ S2) @ (produc2023458740on_val @ E3 @ S3)) @ (red @ P2)) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (lAss_list_char @ V3 @ E2) @ S2) @ (produc2023458740on_val @ (lAss_list_char @ V3 @ E3) @ S3)) @ (red @ P2)))))). % red_reds.LAssRed
thf(fact_239_red__reds_OFAccRed, axiom,
    ((![E2 : exp_list_char, S2 : produc515445032on_val, E3 : exp_list_char, S3 : produc515445032on_val, P2 : list_P1234162913t_char, F3 : list_char, D3 : list_char]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E2 @ S2) @ (produc2023458740on_val @ E3 @ S3)) @ (red @ P2)) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (fAcc_list_char @ E2 @ F3 @ D3) @ S2) @ (produc2023458740on_val @ (fAcc_list_char @ E3 @ F3 @ D3) @ S3)) @ (red @ P2)))))). % red_reds.FAccRed
thf(fact_240_LAssReds, axiom,
    ((![E2 : exp_list_char, S2 : produc515445032on_val, E3 : exp_list_char, S3 : produc515445032on_val, P2 : list_P1234162913t_char, V3 : list_char]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E2 @ S2) @ (produc2023458740on_val @ E3 @ S3)) @ (transi111096263on_val @ (red @ P2))) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (lAss_list_char @ V3 @ E2) @ S2) @ (produc2023458740on_val @ (lAss_list_char @ V3 @ E3) @ S3)) @ (transi111096263on_val @ (red @ P2))))))). % LAssReds
thf(fact_241_FAccReds, axiom,
    ((![E2 : exp_list_char, S2 : produc515445032on_val, E3 : exp_list_char, S3 : produc515445032on_val, P2 : list_P1234162913t_char, F3 : list_char, D3 : list_char]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E2 @ S2) @ (produc2023458740on_val @ E3 @ S3)) @ (transi111096263on_val @ (red @ P2))) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (fAcc_list_char @ E2 @ F3 @ D3) @ S2) @ (produc2023458740on_val @ (fAcc_list_char @ E3 @ F3 @ D3) @ S3)) @ (transi111096263on_val @ (red @ P2))))))). % FAccReds
thf(fact_242_LAss, axiom,
    ((![P2 : list_P1234162913t_char, E2 : exp_list_char, S_0 : produc515445032on_val, V2 : val, H : nat > option2118145160on_val, L : list_char > option_val, L2 : list_char > option_val, V3 : list_char]: ((eval @ P2 @ E2 @ S_0 @ (val_list_char @ V2) @ (produc52622304on_val @ H @ L)) => ((L2 = (fun_up1252458416on_val @ L @ V3 @ (some_val @ V2))) => (eval @ P2 @ (lAss_list_char @ V3 @ E2) @ S_0 @ (val_list_char @ unit) @ (produc52622304on_val @ H @ L2))))))). % LAss
thf(fact_243_redp__redsp_ORedLAss, axiom,
    ((![P2 : list_P1234162913t_char, V3 : list_char, V2 : val, H : nat > option2118145160on_val, L : list_char > option_val]: (redp @ P2 @ (lAss_list_char @ V3 @ (val_list_char @ V2)) @ (produc52622304on_val @ H @ L) @ (val_list_char @ unit) @ (produc52622304on_val @ H @ (fun_up1252458416on_val @ L @ V3 @ (some_val @ V2))))))). % redp_redsp.RedLAss
thf(fact_244_red__reds_ORedLAss, axiom,
    ((![V3 : list_char, V2 : val, H : nat > option2118145160on_val, L : list_char > option_val, P2 : list_P1234162913t_char]: (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (lAss_list_char @ V3 @ (val_list_char @ V2)) @ (produc52622304on_val @ H @ L)) @ (produc2023458740on_val @ (val_list_char @ unit) @ (produc52622304on_val @ H @ (fun_up1252458416on_val @ L @ V3 @ (some_val @ V2))))) @ (red @ P2))))). % red_reds.RedLAss
thf(fact_245_FAccRedsVal, axiom,
    ((![E2 : exp_list_char, S2 : produc515445032on_val, A : nat, S3 : produc515445032on_val, P2 : list_P1234162913t_char, C2 : list_char, Fs : produc1257910179t_char > option_val, F3 : list_char, D3 : list_char, V2 : val]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E2 @ S2) @ (produc2023458740on_val @ (val_list_char @ (addr @ A)) @ S3)) @ (transi111096263on_val @ (red @ P2))) => (((hp @ S3 @ A) = (some_P1299442195on_val @ (produc904988266on_val @ C2 @ Fs))) => (((Fs @ (produc1304532571t_char @ F3 @ D3)) = (some_val @ V2)) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (fAcc_list_char @ E2 @ F3 @ D3) @ S2) @ (produc2023458740on_val @ (val_list_char @ V2) @ S3)) @ (transi111096263on_val @ (red @ P2))))))))). % FAccRedsVal
thf(fact_246_red__reds_ORedFAcc, axiom,
    ((![S2 : produc515445032on_val, A : nat, C2 : list_char, Fs : produc1257910179t_char > option_val, F3 : list_char, D3 : list_char, V2 : val, P2 : list_P1234162913t_char]: (((hp @ S2 @ A) = (some_P1299442195on_val @ (produc904988266on_val @ C2 @ Fs))) => (((Fs @ (produc1304532571t_char @ F3 @ D3)) = (some_val @ V2)) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (fAcc_list_char @ (val_list_char @ (addr @ A)) @ F3 @ D3) @ S2) @ (produc2023458740on_val @ (val_list_char @ V2) @ S2)) @ (red @ P2))))))). % red_reds.RedFAcc
thf(fact_247_redp__redsp_ORedFAcc, axiom,
    ((![S2 : produc515445032on_val, A : nat, C2 : list_char, Fs : produc1257910179t_char > option_val, F3 : list_char, D3 : list_char, V2 : val, P2 : list_P1234162913t_char]: (((hp @ S2 @ A) = (some_P1299442195on_val @ (produc904988266on_val @ C2 @ Fs))) => (((Fs @ (produc1304532571t_char @ F3 @ D3)) = (some_val @ V2)) => (redp @ P2 @ (fAcc_list_char @ (val_list_char @ (addr @ A)) @ F3 @ D3) @ S2 @ (val_list_char @ V2) @ S2)))))). % redp_redsp.RedFAcc

% Helper facts (5)
thf(help_If_2_1_If_001t__Option__Ooption_It__Value__Oval_J_T, axiom,
    ((![X3 : option_val, Y3 : option_val]: ((if_option_val @ $false @ X3 @ Y3) = Y3)))).
thf(help_If_1_1_If_001t__Option__Ooption_It__Value__Oval_J_T, axiom,
    ((![X3 : option_val, Y3 : option_val]: ((if_option_val @ $true @ X3 @ Y3) = X3)))).
thf(help_If_3_1_If_001t__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_T, axiom,
    ((![P2 : $o]: ((P2 = $true) | (P2 = $false))))).
thf(help_If_2_1_If_001t__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_T, axiom,
    ((![X3 : option2118145160on_val, Y3 : option2118145160on_val]: ((if_opt451925058on_val @ $false @ X3 @ Y3) = Y3)))).
thf(help_If_1_1_If_001t__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_T, axiom,
    ((![X3 : option2118145160on_val, Y3 : option2118145160on_val]: ((if_opt451925058on_val @ $true @ X3 @ Y3) = X3)))).

% Conjectures (1)
thf(conj_0, conjecture,
    ((oconf_454120169t_char @ p @ ha @ (produc904988266on_val @ c @ fs)))).
