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% This file was generated by Isabelle (most likely Sledgehammer)
% 2020-12-16 14:22:30.537

% Could-be-implicit typings (25)
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% Explicit typings (66)
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% Relevant facts (191)
thf(fact_0_TryRed_Oprems_I1_J, axiom,
    ((typeSa1777264139_sconf @ p @ e @ (produc52622304on_val @ a @ b)))). % TryRed.prems(1)
thf(fact_1_TryRed_Ohyps_I2_J, axiom,
    ((![E : list_char > option_ty, T : ty]: ((typeSa1777264139_sconf @ p @ E @ (produc52622304on_val @ a @ b)) => ((wTrt @ p @ a @ E @ ea @ T) => (?[T2 : ty]: ((wTrt @ p @ aa @ E @ e_a @ T2) & (widen_917054840t_char @ p @ T2 @ T)))))))). % TryRed.hyps(2)
thf(fact_2_TryRed_Oprems_I2_J, axiom,
    ((wTrt @ p @ a @ e @ (tryCatch_list_char @ ea @ c @ v @ e_2) @ t))). % TryRed.prems(2)
thf(fact_3_TryRed_Ohyps_I1_J, axiom,
    ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ ea @ (produc52622304on_val @ a @ b)) @ (produc2023458740on_val @ e_a @ (produc52622304on_val @ aa @ ba))) @ (red @ p)))). % TryRed.hyps(1)
thf(fact_4_exp_Oinject_I15_J, axiom,
    ((![X151 : exp_list_char, X152 : list_char, X153 : list_char, X154 : exp_list_char, Y151 : exp_list_char, Y152 : list_char, Y153 : list_char, Y154 : exp_list_char]: (((tryCatch_list_char @ X151 @ X152 @ X153 @ X154) = (tryCatch_list_char @ Y151 @ Y152 @ Y153 @ Y154)) = (((X151 = Y151)) & ((((X152 = Y152)) & ((((X153 = Y153)) & ((X154 = Y154))))))))))). % exp.inject(15)
thf(fact_5_local_Owf, axiom,
    ((wf_pro1229751607t_char @ wf_J_mdecl @ p))). % local.wf
thf(fact_6_widen__trans, axiom,
    ((![P : list_P1234162913t_char, S : ty, U : ty, T : ty]: ((widen_917054840t_char @ P @ S @ U) => ((widen_917054840t_char @ P @ U @ T) => (widen_917054840t_char @ P @ S @ T)))))). % widen_trans
thf(fact_7_widen__refl, axiom,
    ((![P : list_P1234162913t_char, T : ty]: (widen_917054840t_char @ P @ T @ T)))). % widen_refl
thf(fact_8_red__reds_OTryRed, axiom,
    ((![E2 : exp_list_char, S2 : produc515445032on_val, E3 : exp_list_char, S3 : produc515445032on_val, P : list_P1234162913t_char, C : list_char, V : list_char, E_2 : exp_list_char]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E2 @ S2) @ (produc2023458740on_val @ E3 @ S3)) @ (red @ P)) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (tryCatch_list_char @ E2 @ C @ V @ E_2) @ S2) @ (produc2023458740on_val @ (tryCatch_list_char @ E3 @ C @ V @ E_2) @ S3)) @ (red @ P)))))). % red_reds.TryRed
thf(fact_9_WTrt__elim__cases_I2_J, axiom,
    ((![P : list_P1234162913t_char, H : nat > option2118145160on_val, E : list_char > option_ty, E2 : exp_list_char, E_1 : exp_list_char, E_2 : exp_list_char, T : ty]: ((wTrt @ P @ H @ E @ (cond_list_char @ E2 @ E_1 @ E_2) @ T) => (~ (((wTrt @ P @ H @ E @ E2 @ boolean) => (![T_1 : ty]: ((wTrt @ P @ H @ E @ E_1 @ T_1) => (![T_2 : ty]: ((wTrt @ P @ H @ E @ E_2 @ T_2) => (((widen_917054840t_char @ P @ T_1 @ T_2) | (widen_917054840t_char @ P @ T_2 @ T_1)) => (((widen_917054840t_char @ P @ T_1 @ T_2) => (T = T_2)) => (~ (((widen_917054840t_char @ P @ T_2 @ T_1) => (T = T_1))))))))))))))))). % WTrt_elim_cases(2)
thf(fact_10_WTrtCond, axiom,
    ((![P : list_P1234162913t_char, H : nat > option2118145160on_val, E : list_char > option_ty, E2 : exp_list_char, E_1 : exp_list_char, T_12 : ty, E_2 : exp_list_char, T_22 : ty, T : ty]: ((wTrt @ P @ H @ E @ E2 @ boolean) => ((wTrt @ P @ H @ E @ E_1 @ T_12) => ((wTrt @ P @ H @ E @ E_2 @ T_22) => (((widen_917054840t_char @ P @ T_12 @ T_22) | (widen_917054840t_char @ P @ T_22 @ T_12)) => (((widen_917054840t_char @ P @ T_12 @ T_22) => (T = T_22)) => (((widen_917054840t_char @ P @ T_22 @ T_12) => (T = T_12)) => (wTrt @ P @ H @ E @ (cond_list_char @ E2 @ E_1 @ E_2) @ T)))))))))). % WTrtCond
thf(fact_11_WTrt__hext__mono, axiom,
    ((![P : list_P1234162913t_char, H : nat > option2118145160on_val, E : list_char > option_ty, E2 : exp_list_char, T : ty, H2 : nat > option2118145160on_val]: ((wTrt @ P @ H @ E @ E2 @ T) => ((hext @ H @ H2) => (wTrt @ P @ H2 @ E @ E2 @ T)))))). % WTrt_hext_mono
thf(fact_12_exp_Opred__inject_I15_J, axiom,
    ((![P : list_char > $o, A : exp_list_char, Aa : list_char, Ab : list_char, Ac : exp_list_char]: ((pred_exp_list_char @ P @ (tryCatch_list_char @ A @ Aa @ Ab @ Ac)) = (((pred_exp_list_char @ P @ A)) & ((((P @ Ab)) & ((pred_exp_list_char @ P @ Ac))))))))). % exp.pred_inject(15)
thf(fact_13_WTrt__elim__cases_I5_J, axiom,
    ((![P : list_P1234162913t_char, H : nat > option2118145160on_val, E : list_char > option_ty, E_1 : exp_list_char, C : list_char, V : list_char, E_2 : exp_list_char, T : ty]: ((wTrt @ P @ H @ E @ (tryCatch_list_char @ E_1 @ C @ V @ E_2) @ T) => (~ ((![T_1 : ty]: ((wTrt @ P @ H @ E @ E_1 @ T_1) => ((wTrt @ P @ H @ (fun_up9191ion_ty @ E @ V @ (some_ty @ (class @ C))) @ E_2 @ T) => (~ ((widen_917054840t_char @ P @ T_1 @ T)))))))))))). % WTrt_elim_cases(5)
thf(fact_14_WTrtTry, axiom,
    ((![P : list_P1234162913t_char, H : nat > option2118145160on_val, E : list_char > option_ty, E_1 : exp_list_char, T_12 : ty, V : list_char, C : list_char, E_2 : exp_list_char, T_22 : ty]: ((wTrt @ P @ H @ E @ E_1 @ T_12) => ((wTrt @ P @ H @ (fun_up9191ion_ty @ E @ V @ (some_ty @ (class @ C))) @ E_2 @ T_22) => ((widen_917054840t_char @ P @ T_12 @ T_22) => (wTrt @ P @ H @ E @ (tryCatch_list_char @ E_1 @ C @ V @ E_2) @ T_22))))))). % WTrtTry
thf(fact_15_exp_Oinject_I12_J, axiom,
    ((![X121 : exp_list_char, X122 : exp_list_char, X123 : exp_list_char, Y121 : exp_list_char, Y122 : exp_list_char, Y123 : exp_list_char]: (((cond_list_char @ X121 @ X122 @ X123) = (cond_list_char @ Y121 @ Y122 @ Y123)) = (((X121 = Y121)) & ((((X122 = Y122)) & ((X123 = Y123))))))))). % exp.inject(12)
thf(fact_16_exp_Opred__inject_I12_J, axiom,
    ((![P : list_char > $o, A : exp_list_char, Aa : exp_list_char, Ab : exp_list_char]: ((pred_exp_list_char @ P @ (cond_list_char @ A @ Aa @ Ab)) = (((pred_exp_list_char @ P @ A)) & ((((pred_exp_list_char @ P @ Aa)) & ((pred_exp_list_char @ P @ Ab))))))))). % exp.pred_inject(12)
thf(fact_17_red__hext__incr, axiom,
    ((![E2 : exp_list_char, H : nat > option2118145160on_val, L : list_char > option_val, E3 : exp_list_char, H2 : nat > option2118145160on_val, L2 : list_char > option_val, P : list_P1234162913t_char]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E2 @ (produc52622304on_val @ H @ L)) @ (produc2023458740on_val @ E3 @ (produc52622304on_val @ H2 @ L2))) @ (red @ P)) => (hext @ H @ H2))))). % red_hext_incr
thf(fact_18_red__reds_OCondRed, axiom,
    ((![E2 : exp_list_char, S2 : produc515445032on_val, E3 : exp_list_char, S3 : produc515445032on_val, P : list_P1234162913t_char, E_1 : exp_list_char, E_2 : exp_list_char]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E2 @ S2) @ (produc2023458740on_val @ E3 @ S3)) @ (red @ P)) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (cond_list_char @ E2 @ E_1 @ E_2) @ S2) @ (produc2023458740on_val @ (cond_list_char @ E3 @ E_1 @ E_2) @ S3)) @ (red @ P)))))). % red_reds.CondRed
thf(fact_19_Class__widen, axiom,
    ((![P : list_P1234162913t_char, C : list_char, T : ty]: ((widen_917054840t_char @ P @ (class @ C) @ T) => (?[D : list_char]: (T = (class @ D))))))). % Class_widen
thf(fact_20_exp_Odistinct_I203_J, axiom,
    ((![X121 : exp_list_char, X122 : exp_list_char, X123 : exp_list_char, X151 : exp_list_char, X152 : list_char, X153 : list_char, X154 : exp_list_char]: (~ (((cond_list_char @ X121 @ X122 @ X123) = (tryCatch_list_char @ X151 @ X152 @ X153 @ X154))))))). % exp.distinct(203)
thf(fact_21_hext__refl, axiom,
    ((![H : nat > option2118145160on_val]: (hext @ H @ H)))). % hext_refl
thf(fact_22_prod__cases4, axiom,
    ((![Y : produc1172664615on_val]: (~ ((![A2 : produc1097884484on_val, B : exp_list_char, C2 : nat > option2118145160on_val, D2 : list_char > option_val]: (~ ((Y = (produc1069526295on_val @ A2 @ (produc2023458740on_val @ B @ (produc52622304on_val @ C2 @ D2)))))))))))). % prod_cases4
thf(fact_23_prod__induct4, axiom,
    ((![P : produc1172664615on_val > $o, X : produc1172664615on_val]: ((![A2 : produc1097884484on_val, B : exp_list_char, C2 : nat > option2118145160on_val, D2 : list_char > option_val]: (P @ (produc1069526295on_val @ A2 @ (produc2023458740on_val @ B @ (produc52622304on_val @ C2 @ D2))))) => (P @ X))))). % prod_induct4
thf(fact_24_old_Oprod_Oinject, axiom,
    ((![A : nat > option2118145160on_val, B2 : list_char > option_val, A3 : nat > option2118145160on_val, B3 : list_char > option_val]: (((produc52622304on_val @ A @ B2) = (produc52622304on_val @ A3 @ B3)) = (((A = A3)) & ((B2 = B3))))))). % old.prod.inject
thf(fact_25_old_Oprod_Oinject, axiom,
    ((![A : produc1097884484on_val, B2 : produc1097884484on_val, A3 : produc1097884484on_val, B3 : produc1097884484on_val]: (((produc1069526295on_val @ A @ B2) = (produc1069526295on_val @ A3 @ B3)) = (((A = A3)) & ((B2 = B3))))))). % old.prod.inject
thf(fact_26_old_Oprod_Oinject, axiom,
    ((![A : exp_list_char, B2 : produc515445032on_val, A3 : exp_list_char, B3 : produc515445032on_val]: (((produc2023458740on_val @ A @ B2) = (produc2023458740on_val @ A3 @ B3)) = (((A = A3)) & ((B2 = B3))))))). % old.prod.inject
thf(fact_27_old_Oprod_Oinject, axiom,
    ((![A : list_char, B2 : produc1257910179t_char > option_val, A3 : list_char, B3 : produc1257910179t_char > option_val]: (((produc904988266on_val @ A @ B2) = (produc904988266on_val @ A3 @ B3)) = (((A = A3)) & ((B2 = B3))))))). % old.prod.inject
thf(fact_28_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_29_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_30_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_31_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_32_old_Oprod_Oinducts, axiom,
    ((![P : produc515445032on_val > $o, Prod : produc515445032on_val]: ((![A2 : nat > option2118145160on_val, B : list_char > option_val]: (P @ (produc52622304on_val @ A2 @ B))) => (P @ Prod))))). % old.prod.inducts
thf(fact_33_old_Oprod_Oinducts, axiom,
    ((![P : produc1172664615on_val > $o, Prod : produc1172664615on_val]: ((![A2 : produc1097884484on_val, B : produc1097884484on_val]: (P @ (produc1069526295on_val @ A2 @ B))) => (P @ Prod))))). % old.prod.inducts
thf(fact_34_old_Oprod_Oinducts, axiom,
    ((![P : produc1097884484on_val > $o, Prod : produc1097884484on_val]: ((![A2 : exp_list_char, B : produc515445032on_val]: (P @ (produc2023458740on_val @ A2 @ B))) => (P @ Prod))))). % old.prod.inducts
thf(fact_35_old_Oprod_Oinducts, axiom,
    ((![P : produc266837688on_val > $o, Prod : produc266837688on_val]: ((![A2 : list_char, B : produc1257910179t_char > option_val]: (P @ (produc904988266on_val @ A2 @ B))) => (P @ Prod))))). % old.prod.inducts
thf(fact_36_old_Oprod_Oexhaust, axiom,
    ((![Y : produc515445032on_val]: (~ ((![A2 : nat > option2118145160on_val, B : list_char > option_val]: (~ ((Y = (produc52622304on_val @ A2 @ B)))))))))). % old.prod.exhaust
thf(fact_37_old_Oprod_Oexhaust, axiom,
    ((![Y : produc1172664615on_val]: (~ ((![A2 : produc1097884484on_val, B : produc1097884484on_val]: (~ ((Y = (produc1069526295on_val @ A2 @ B)))))))))). % old.prod.exhaust
thf(fact_38_old_Oprod_Oexhaust, axiom,
    ((![Y : produc1097884484on_val]: (~ ((![A2 : exp_list_char, B : produc515445032on_val]: (~ ((Y = (produc2023458740on_val @ A2 @ B)))))))))). % old.prod.exhaust
thf(fact_39_old_Oprod_Oexhaust, axiom,
    ((![Y : produc266837688on_val]: (~ ((![A2 : list_char, B : produc1257910179t_char > option_val]: (~ ((Y = (produc904988266on_val @ A2 @ B)))))))))). % old.prod.exhaust
thf(fact_40_Pair__inject, axiom,
    ((![A : nat > option2118145160on_val, B2 : list_char > option_val, A3 : nat > option2118145160on_val, B3 : list_char > option_val]: (((produc52622304on_val @ A @ B2) = (produc52622304on_val @ A3 @ B3)) => (~ (((A = A3) => (~ ((B2 = B3)))))))))). % Pair_inject
thf(fact_41_Pair__inject, axiom,
    ((![A : produc1097884484on_val, B2 : produc1097884484on_val, A3 : produc1097884484on_val, B3 : produc1097884484on_val]: (((produc1069526295on_val @ A @ B2) = (produc1069526295on_val @ A3 @ B3)) => (~ (((A = A3) => (~ ((B2 = B3)))))))))). % Pair_inject
thf(fact_42_Pair__inject, axiom,
    ((![A : exp_list_char, B2 : produc515445032on_val, A3 : exp_list_char, B3 : produc515445032on_val]: (((produc2023458740on_val @ A @ B2) = (produc2023458740on_val @ A3 @ B3)) => (~ (((A = A3) => (~ ((B2 = B3)))))))))). % Pair_inject
thf(fact_43_Pair__inject, axiom,
    ((![A : list_char, B2 : produc1257910179t_char > option_val, A3 : list_char, B3 : produc1257910179t_char > option_val]: (((produc904988266on_val @ A @ B2) = (produc904988266on_val @ A3 @ B3)) => (~ (((A = A3) => (~ ((B2 = B3)))))))))). % Pair_inject
thf(fact_44_prod__cases, axiom,
    ((![P : produc515445032on_val > $o, P2 : produc515445032on_val]: ((![A2 : nat > option2118145160on_val, B : list_char > option_val]: (P @ (produc52622304on_val @ A2 @ B))) => (P @ P2))))). % prod_cases
thf(fact_45_prod__cases, axiom,
    ((![P : produc1172664615on_val > $o, P2 : produc1172664615on_val]: ((![A2 : produc1097884484on_val, B : produc1097884484on_val]: (P @ (produc1069526295on_val @ A2 @ B))) => (P @ P2))))). % prod_cases
thf(fact_46_prod__cases, axiom,
    ((![P : produc1097884484on_val > $o, P2 : produc1097884484on_val]: ((![A2 : exp_list_char, B : produc515445032on_val]: (P @ (produc2023458740on_val @ A2 @ B))) => (P @ P2))))). % prod_cases
thf(fact_47_prod__cases, axiom,
    ((![P : produc266837688on_val > $o, P2 : produc266837688on_val]: ((![A2 : list_char, B : produc1257910179t_char > option_val]: (P @ (produc904988266on_val @ A2 @ B))) => (P @ P2))))). % prod_cases
thf(fact_48_surj__pair, axiom,
    ((![P2 : produc515445032on_val]: (?[X3 : nat > option2118145160on_val, Y3 : list_char > option_val]: (P2 = (produc52622304on_val @ X3 @ Y3)))))). % surj_pair
thf(fact_49_surj__pair, axiom,
    ((![P2 : produc1172664615on_val]: (?[X3 : produc1097884484on_val, Y3 : produc1097884484on_val]: (P2 = (produc1069526295on_val @ X3 @ Y3)))))). % surj_pair
thf(fact_50_surj__pair, axiom,
    ((![P2 : produc1097884484on_val]: (?[X3 : exp_list_char, Y3 : produc515445032on_val]: (P2 = (produc2023458740on_val @ X3 @ Y3)))))). % surj_pair
thf(fact_51_surj__pair, axiom,
    ((![P2 : produc266837688on_val]: (?[X3 : list_char, Y3 : produc1257910179t_char > option_val]: (P2 = (produc904988266on_val @ X3 @ Y3)))))). % surj_pair
thf(fact_52_hext__trans, axiom,
    ((![H : nat > option2118145160on_val, H2 : nat > option2118145160on_val, H3 : nat > option2118145160on_val]: ((hext @ H @ H2) => ((hext @ H2 @ H3) => (hext @ H @ H3)))))). % hext_trans
thf(fact_53_prod__induct3, axiom,
    ((![P : produc1172664615on_val > $o, X : produc1172664615on_val]: ((![A2 : produc1097884484on_val, B : exp_list_char, C2 : produc515445032on_val]: (P @ (produc1069526295on_val @ A2 @ (produc2023458740on_val @ B @ C2)))) => (P @ X))))). % prod_induct3
thf(fact_54_prod__induct3, axiom,
    ((![P : produc1097884484on_val > $o, X : produc1097884484on_val]: ((![A2 : exp_list_char, B : nat > option2118145160on_val, C2 : list_char > option_val]: (P @ (produc2023458740on_val @ A2 @ (produc52622304on_val @ B @ C2)))) => (P @ X))))). % prod_induct3
thf(fact_55_prod__cases3, axiom,
    ((![Y : produc1172664615on_val]: (~ ((![A2 : produc1097884484on_val, B : exp_list_char, C2 : produc515445032on_val]: (~ ((Y = (produc1069526295on_val @ A2 @ (produc2023458740on_val @ B @ C2))))))))))). % prod_cases3
thf(fact_56_prod__cases3, axiom,
    ((![Y : produc1097884484on_val]: (~ ((![A2 : exp_list_char, B : nat > option2118145160on_val, C2 : list_char > option_val]: (~ ((Y = (produc2023458740on_val @ A2 @ (produc52622304on_val @ B @ C2))))))))))). % prod_cases3
thf(fact_57_mem__Collect__eq, axiom,
    ((![A : produc1172664615on_val, P : produc1172664615on_val > $o]: ((member354538064on_val @ A @ (collec2055896722on_val @ P)) = (P @ A))))). % mem_Collect_eq
thf(fact_58_Collect__mem__eq, axiom,
    ((![A4 : set_Pr1189492743on_val]: ((collec2055896722on_val @ (^[X4 : produc1172664615on_val]: (member354538064on_val @ X4 @ A4))) = A4)))). % Collect_mem_eq
thf(fact_59_ty_Oinject, axiom,
    ((![X5 : list_char, Y5 : list_char]: (((class @ X5) = (class @ Y5)) = (X5 = Y5))))). % ty.inject
thf(fact_60_fun__upd__apply, axiom,
    ((fun_up9191ion_ty = (^[F : list_char > option_ty]: (^[X4 : list_char]: (^[Y4 : option_ty]: (^[Z : list_char]: (if_option_ty @ (Z = X4) @ Y4 @ (F @ Z))))))))). % fun_upd_apply
thf(fact_61_fun__upd__apply, axiom,
    ((fun_up262443479on_val = (^[F : nat > option2118145160on_val]: (^[X4 : nat]: (^[Y4 : option2118145160on_val]: (^[Z : nat]: (if_opt451925058on_val @ (Z = X4) @ Y4 @ (F @ Z))))))))). % fun_upd_apply
thf(fact_62_fun__upd__triv, axiom,
    ((![F2 : list_char > option_ty, X : list_char]: ((fun_up9191ion_ty @ F2 @ X @ (F2 @ X)) = F2)))). % fun_upd_triv
thf(fact_63_fun__upd__triv, axiom,
    ((![F2 : nat > option2118145160on_val, X : nat]: ((fun_up262443479on_val @ F2 @ X @ (F2 @ X)) = F2)))). % fun_upd_triv
thf(fact_64_fun__upd__upd, axiom,
    ((![F2 : list_char > option_ty, X : list_char, Y : option_ty, Z2 : option_ty]: ((fun_up9191ion_ty @ (fun_up9191ion_ty @ F2 @ X @ Y) @ X @ Z2) = (fun_up9191ion_ty @ F2 @ X @ Z2))))). % fun_upd_upd
thf(fact_65_fun__upd__upd, axiom,
    ((![F2 : nat > option2118145160on_val, X : nat, Y : option2118145160on_val, Z2 : option2118145160on_val]: ((fun_up262443479on_val @ (fun_up262443479on_val @ F2 @ X @ Y) @ X @ Z2) = (fun_up262443479on_val @ F2 @ X @ Z2))))). % fun_upd_upd
thf(fact_66_option_Oinject, axiom,
    ((![X2 : ty, Y2 : ty]: (((some_ty @ X2) = (some_ty @ Y2)) = (X2 = Y2))))). % option.inject
thf(fact_67_option_Oinject, axiom,
    ((![X2 : produc266837688on_val, Y2 : produc266837688on_val]: (((some_P1299442195on_val @ X2) = (some_P1299442195on_val @ Y2)) = (X2 = Y2))))). % option.inject
thf(fact_68_red__preserves__hconf, axiom,
    ((![E2 : exp_list_char, H : nat > option2118145160on_val, L : list_char > option_val, E3 : exp_list_char, H2 : nat > option2118145160on_val, L2 : list_char > option_val, P : list_P1234162913t_char, E : list_char > option_ty, T : ty]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E2 @ (produc52622304on_val @ H @ L)) @ (produc2023458740on_val @ E3 @ (produc52622304on_val @ H2 @ L2))) @ (red @ P)) => ((wTrt @ P @ H @ E @ E2 @ T) => ((hconf_1244167010t_char @ P @ H) => (hconf_1244167010t_char @ P @ H2))))))). % red_preserves_hconf
thf(fact_69_hext__upd__obj, axiom,
    ((![H : nat > option2118145160on_val, A : nat, C : list_char, Fs : produc1257910179t_char > option_val, Fs2 : produc1257910179t_char > option_val]: (((H @ A) = (some_P1299442195on_val @ (produc904988266on_val @ C @ Fs))) => (hext @ H @ (fun_up262443479on_val @ H @ A @ (some_P1299442195on_val @ (produc904988266on_val @ C @ Fs2)))))))). % hext_upd_obj
thf(fact_70_hext__objD, axiom,
    ((![H : nat > option2118145160on_val, H2 : nat > option2118145160on_val, A : nat, C : list_char, Fs : produc1257910179t_char > option_val]: ((hext @ H @ H2) => (((H @ A) = (some_P1299442195on_val @ (produc904988266on_val @ C @ Fs))) => (?[Fs3 : produc1257910179t_char > option_val]: ((H2 @ A) = (some_P1299442195on_val @ (produc904988266on_val @ C @ Fs3))))))))). % hext_objD
thf(fact_71_hext__def, axiom,
    ((hext = (^[H4 : nat > option2118145160on_val]: (^[H5 : nat > option2118145160on_val]: (![A5 : nat]: (![C3 : list_char]: (![Fs4 : produc1257910179t_char > option_val]: ((((H4 @ A5) = (some_P1299442195on_val @ (produc904988266on_val @ C3 @ Fs4)))) => ((?[Fs5 : produc1257910179t_char > option_val]: ((H5 @ A5) = (some_P1299442195on_val @ (produc904988266on_val @ C3 @ Fs5)))))))))))))). % hext_def
thf(fact_72_hextI, axiom,
    ((![H : nat > option2118145160on_val, H2 : nat > option2118145160on_val]: ((![A2 : nat, C4 : list_char, Fs6 : produc1257910179t_char > option_val]: (((H @ A2) = (some_P1299442195on_val @ (produc904988266on_val @ C4 @ Fs6))) => (?[Fs7 : produc1257910179t_char > option_val]: ((H2 @ A2) = (some_P1299442195on_val @ (produc904988266on_val @ C4 @ Fs7)))))) => (hext @ H @ H2))))). % hextI
thf(fact_73_fun__upd__def, axiom,
    ((fun_up9191ion_ty = (^[F : list_char > option_ty]: (^[A5 : list_char]: (^[B4 : option_ty]: (^[X4 : list_char]: (if_option_ty @ (X4 = A5) @ B4 @ (F @ X4))))))))). % fun_upd_def
thf(fact_74_fun__upd__def, axiom,
    ((fun_up262443479on_val = (^[F : nat > option2118145160on_val]: (^[A5 : nat]: (^[B4 : option2118145160on_val]: (^[X4 : nat]: (if_opt451925058on_val @ (X4 = A5) @ B4 @ (F @ X4))))))))). % fun_upd_def
thf(fact_75_fun__upd__eqD, axiom,
    ((![F2 : list_char > option_ty, X : list_char, Y : option_ty, G : list_char > option_ty, Z2 : option_ty]: (((fun_up9191ion_ty @ F2 @ X @ Y) = (fun_up9191ion_ty @ G @ X @ Z2)) => (Y = Z2))))). % fun_upd_eqD
thf(fact_76_fun__upd__eqD, axiom,
    ((![F2 : nat > option2118145160on_val, X : nat, Y : option2118145160on_val, G : nat > option2118145160on_val, Z2 : option2118145160on_val]: (((fun_up262443479on_val @ F2 @ X @ Y) = (fun_up262443479on_val @ G @ X @ Z2)) => (Y = Z2))))). % fun_upd_eqD
thf(fact_77_fun__upd__idem, axiom,
    ((![F2 : list_char > option_ty, X : list_char, Y : option_ty]: (((F2 @ X) = Y) => ((fun_up9191ion_ty @ F2 @ X @ Y) = F2))))). % fun_upd_idem
thf(fact_78_fun__upd__idem, axiom,
    ((![F2 : nat > option2118145160on_val, X : nat, Y : option2118145160on_val]: (((F2 @ X) = Y) => ((fun_up262443479on_val @ F2 @ X @ Y) = F2))))). % fun_upd_idem
thf(fact_79_fun__upd__same, axiom,
    ((![F2 : list_char > option_ty, X : list_char, Y : option_ty]: ((fun_up9191ion_ty @ F2 @ X @ Y @ X) = Y)))). % fun_upd_same
thf(fact_80_fun__upd__same, axiom,
    ((![F2 : nat > option2118145160on_val, X : nat, Y : option2118145160on_val]: ((fun_up262443479on_val @ F2 @ X @ Y @ X) = Y)))). % fun_upd_same
thf(fact_81_fun__upd__other, axiom,
    ((![Z2 : list_char, X : list_char, F2 : list_char > option_ty, Y : option_ty]: ((~ ((Z2 = X))) => ((fun_up9191ion_ty @ F2 @ X @ Y @ Z2) = (F2 @ Z2)))))). % fun_upd_other
thf(fact_82_fun__upd__other, axiom,
    ((![Z2 : nat, X : nat, F2 : nat > option2118145160on_val, Y : option2118145160on_val]: ((~ ((Z2 = X))) => ((fun_up262443479on_val @ F2 @ X @ Y @ Z2) = (F2 @ Z2)))))). % fun_upd_other
thf(fact_83_fun__upd__twist, axiom,
    ((![A : list_char, C5 : list_char, M : list_char > option_ty, B2 : option_ty, D3 : option_ty]: ((~ ((A = C5))) => ((fun_up9191ion_ty @ (fun_up9191ion_ty @ M @ A @ B2) @ C5 @ D3) = (fun_up9191ion_ty @ (fun_up9191ion_ty @ M @ C5 @ D3) @ A @ B2)))))). % fun_upd_twist
thf(fact_84_fun__upd__twist, axiom,
    ((![A : nat, C5 : nat, M : nat > option2118145160on_val, B2 : option2118145160on_val, D3 : option2118145160on_val]: ((~ ((A = C5))) => ((fun_up262443479on_val @ (fun_up262443479on_val @ M @ A @ B2) @ C5 @ D3) = (fun_up262443479on_val @ (fun_up262443479on_val @ M @ C5 @ D3) @ A @ B2)))))). % fun_upd_twist
thf(fact_85_fun__upd__idem__iff, axiom,
    ((![F2 : list_char > option_ty, X : list_char, Y : option_ty]: (((fun_up9191ion_ty @ F2 @ X @ Y) = F2) = ((F2 @ X) = Y))))). % fun_upd_idem_iff
thf(fact_86_fun__upd__idem__iff, axiom,
    ((![F2 : nat > option2118145160on_val, X : nat, Y : option2118145160on_val]: (((fun_up262443479on_val @ F2 @ X @ Y) = F2) = ((F2 @ X) = Y))))). % fun_upd_idem_iff
thf(fact_87_ty_Odistinct_I13_J, axiom,
    ((![X5 : list_char]: (~ ((boolean = (class @ X5))))))). % ty.distinct(13)
thf(fact_88_red__preserves__lconf, axiom,
    ((![E2 : exp_list_char, H : nat > option2118145160on_val, L : list_char > option_val, E3 : exp_list_char, H2 : nat > option2118145160on_val, L2 : list_char > option_val, P : list_P1234162913t_char, E : list_char > option_ty, T : ty]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E2 @ (produc52622304on_val @ H @ L)) @ (produc2023458740on_val @ E3 @ (produc52622304on_val @ H2 @ L2))) @ (red @ P)) => ((wTrt @ P @ H @ E @ E2 @ T) => ((lconf_485928294t_char @ P @ H @ L @ E) => (lconf_485928294t_char @ P @ H2 @ L2 @ E))))))). % red_preserves_lconf
thf(fact_89_red__preserves__sconf, axiom,
    ((![E2 : exp_list_char, S2 : produc515445032on_val, E3 : exp_list_char, S3 : produc515445032on_val, P : list_P1234162913t_char, E : list_char > option_ty, T : ty]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E2 @ S2) @ (produc2023458740on_val @ E3 @ S3)) @ (red @ P)) => ((wTrt @ P @ (hp @ S2) @ E @ E2 @ T) => ((typeSa1777264139_sconf @ P @ E @ S2) => (typeSa1777264139_sconf @ P @ E @ S3))))))). % red_preserves_sconf
thf(fact_90_map__upd__eqD1, axiom,
    ((![M : list_char > option_ty, A : list_char, X : ty, N : list_char > option_ty, Y : ty]: (((fun_up9191ion_ty @ M @ A @ (some_ty @ X)) = (fun_up9191ion_ty @ N @ A @ (some_ty @ Y))) => (X = Y))))). % map_upd_eqD1
thf(fact_91_map__upd__eqD1, axiom,
    ((![M : nat > option2118145160on_val, A : nat, X : produc266837688on_val, N : nat > option2118145160on_val, Y : produc266837688on_val]: (((fun_up262443479on_val @ M @ A @ (some_P1299442195on_val @ X)) = (fun_up262443479on_val @ N @ A @ (some_P1299442195on_val @ Y))) => (X = Y))))). % map_upd_eqD1
thf(fact_92_map__upd__triv, axiom,
    ((![T3 : list_char > option_ty, K : list_char, X : ty]: (((T3 @ K) = (some_ty @ X)) => ((fun_up9191ion_ty @ T3 @ K @ (some_ty @ X)) = T3))))). % map_upd_triv
thf(fact_93_map__upd__triv, axiom,
    ((![T3 : nat > option2118145160on_val, K : nat, X : produc266837688on_val]: (((T3 @ K) = (some_P1299442195on_val @ X)) => ((fun_up262443479on_val @ T3 @ K @ (some_P1299442195on_val @ X)) = T3))))). % map_upd_triv
thf(fact_94_map__upd__Some__unfold, axiom,
    ((![M : list_char > option_ty, A : list_char, B2 : ty, X : list_char, Y : ty]: (((fun_up9191ion_ty @ M @ A @ (some_ty @ B2) @ X) = (some_ty @ Y)) = (((((X = A)) & ((B2 = Y)))) | ((((~ ((X = A)))) & (((M @ X) = (some_ty @ Y)))))))))). % map_upd_Some_unfold
thf(fact_95_map__upd__Some__unfold, axiom,
    ((![M : nat > option2118145160on_val, A : nat, B2 : produc266837688on_val, X : nat, Y : produc266837688on_val]: (((fun_up262443479on_val @ M @ A @ (some_P1299442195on_val @ B2) @ X) = (some_P1299442195on_val @ Y)) = (((((X = A)) & ((B2 = Y)))) | ((((~ ((X = A)))) & (((M @ X) = (some_P1299442195on_val @ Y)))))))))). % map_upd_Some_unfold
thf(fact_96_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_97_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_98_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_99_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_100_lconf__hext, axiom,
    ((![P : list_P1234162913t_char, H : nat > option2118145160on_val, L : list_char > option_val, E : list_char > option_ty, H2 : nat > option2118145160on_val]: ((lconf_485928294t_char @ P @ H @ L @ E) => ((hext @ H @ H2) => (lconf_485928294t_char @ P @ H2 @ L @ E)))))). % lconf_hext
thf(fact_101_hconf__upd__obj, axiom,
    ((![P : list_P1234162913t_char, H : nat > option2118145160on_val, A : nat, C : list_char, Fs : produc1257910179t_char > option_val, Fs2 : produc1257910179t_char > option_val]: ((hconf_1244167010t_char @ P @ H) => (((H @ A) = (some_P1299442195on_val @ (produc904988266on_val @ C @ Fs))) => ((oconf_454120169t_char @ P @ H @ (produc904988266on_val @ C @ Fs2)) => (hconf_1244167010t_char @ P @ (fun_up262443479on_val @ H @ A @ (some_P1299442195on_val @ (produc904988266on_val @ C @ Fs2)))))))))). % hconf_upd_obj
thf(fact_102_red__lcl__add, axiom,
    ((![E2 : exp_list_char, H : nat > option2118145160on_val, L : list_char > option_val, E3 : exp_list_char, H2 : nat > option2118145160on_val, L2 : list_char > option_val, P : list_P1234162913t_char, L_0 : list_char > option_val]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E2 @ (produc52622304on_val @ H @ L)) @ (produc2023458740on_val @ E3 @ (produc52622304on_val @ H2 @ L2))) @ (red @ P)) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E2 @ (produc52622304on_val @ H @ (map_ad1615113112ar_val @ L_0 @ L))) @ (produc2023458740on_val @ E3 @ (produc52622304on_val @ H2 @ (map_ad1615113112ar_val @ L_0 @ L2)))) @ (red @ P)))))). % red_lcl_add
thf(fact_103_map__add__assoc, axiom,
    ((![M1 : list_char > option_val, M2 : list_char > option_val, M3 : list_char > option_val]: ((map_ad1615113112ar_val @ M1 @ (map_ad1615113112ar_val @ M2 @ M3)) = (map_ad1615113112ar_val @ (map_ad1615113112ar_val @ M1 @ M2) @ M3))))). % map_add_assoc
thf(fact_104_map__add__find__right, axiom,
    ((![N : list_char > option_val, K : list_char, Xx : val, M : list_char > option_val]: (((N @ K) = (some_val @ Xx)) => ((map_ad1615113112ar_val @ M @ N @ K) = (some_val @ Xx)))))). % map_add_find_right
thf(fact_105_map__add__upd, axiom,
    ((![F2 : list_char > option_val, G : list_char > option_val, X : list_char, Y : val]: ((map_ad1615113112ar_val @ F2 @ (fun_up1252458416on_val @ G @ X @ (some_val @ Y))) = (fun_up1252458416on_val @ (map_ad1615113112ar_val @ F2 @ G) @ X @ (some_val @ Y)))))). % map_add_upd
thf(fact_106_map__add__upd, axiom,
    ((![F2 : list_char > option_ty, G : list_char > option_ty, X : list_char, Y : ty]: ((map_add_list_char_ty @ F2 @ (fun_up9191ion_ty @ G @ X @ (some_ty @ Y))) = (fun_up9191ion_ty @ (map_add_list_char_ty @ F2 @ G) @ X @ (some_ty @ Y)))))). % map_add_upd
thf(fact_107_map__add__upd, axiom,
    ((![F2 : nat > option2118145160on_val, G : nat > option2118145160on_val, X : nat, Y : produc266837688on_val]: ((map_ad109059391on_val @ F2 @ (fun_up262443479on_val @ G @ X @ (some_P1299442195on_val @ Y))) = (fun_up262443479on_val @ (map_ad109059391on_val @ F2 @ G) @ X @ (some_P1299442195on_val @ Y)))))). % map_add_upd
thf(fact_108_hconfD, axiom,
    ((![P : list_P1234162913t_char, H : nat > option2118145160on_val, A : nat, Obj : produc266837688on_val]: ((hconf_1244167010t_char @ P @ H) => (((H @ A) = (some_P1299442195on_val @ Obj)) => (oconf_454120169t_char @ P @ H @ Obj)))))). % hconfD
thf(fact_109_hconf__def, axiom,
    ((hconf_1244167010t_char = (^[P3 : list_P1234162913t_char]: (^[H4 : nat > option2118145160on_val]: (((![A5 : nat]: (![Obj2 : produc266837688on_val]: ((((H4 @ A5) = (some_P1299442195on_val @ Obj2))) => ((oconf_454120169t_char @ P3 @ H4 @ Obj2)))))) & ((preallocated @ H4)))))))). % hconf_def
thf(fact_110_Red__lcl__add, axiom,
    ((![E2 : exp_list_char, H : nat > option2118145160on_val, L : list_char > option_val, E3 : exp_list_char, H2 : nat > option2118145160on_val, L2 : list_char > option_val, P : list_P1234162913t_char, L_0 : list_char > option_val]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E2 @ (produc52622304on_val @ H @ L)) @ (produc2023458740on_val @ E3 @ (produc52622304on_val @ H2 @ L2))) @ (transi111096263on_val @ (red @ P))) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E2 @ (produc52622304on_val @ H @ (map_ad1615113112ar_val @ L_0 @ L))) @ (produc2023458740on_val @ E3 @ (produc52622304on_val @ H2 @ (map_ad1615113112ar_val @ L_0 @ L2)))) @ (transi111096263on_val @ (red @ P))))))). % Red_lcl_add
thf(fact_111_hconf__new, axiom,
    ((![P : list_P1234162913t_char, H : nat > option2118145160on_val, A : nat, Obj : produc266837688on_val]: ((hconf_1244167010t_char @ P @ H) => (((H @ A) = none_P1535574167on_val) => ((oconf_454120169t_char @ P @ H @ Obj) => (hconf_1244167010t_char @ P @ (fun_up262443479on_val @ H @ A @ (some_P1299442195on_val @ Obj))))))))). % hconf_new
thf(fact_112_lconf__upd2, axiom,
    ((![P : list_P1234162913t_char, H : nat > option2118145160on_val, L : list_char > option_val, E : list_char > option_ty, V2 : val, T : ty, V : list_char]: ((lconf_485928294t_char @ P @ H @ L @ E) => ((conf_P93989998t_char @ P @ H @ V2 @ T) => (lconf_485928294t_char @ P @ H @ (fun_up1252458416on_val @ L @ V @ (some_val @ V2)) @ (fun_up9191ion_ty @ E @ V @ (some_ty @ T)))))))). % lconf_upd2
thf(fact_113_not__Some__eq, axiom,
    ((![X : option_ty]: ((![Y4 : ty]: (~ ((X = (some_ty @ Y4))))) = (X = none_ty))))). % not_Some_eq
thf(fact_114_not__Some__eq, axiom,
    ((![X : option2118145160on_val]: ((![Y4 : produc266837688on_val]: (~ ((X = (some_P1299442195on_val @ Y4))))) = (X = none_P1535574167on_val))))). % not_Some_eq
thf(fact_115_not__None__eq, axiom,
    ((![X : option_ty]: ((~ ((X = none_ty))) = (?[Y4 : ty]: (X = (some_ty @ Y4))))))). % not_None_eq
thf(fact_116_not__None__eq, axiom,
    ((![X : option2118145160on_val]: ((~ ((X = none_P1535574167on_val))) = (?[Y4 : produc266837688on_val]: (X = (some_P1299442195on_val @ Y4))))))). % not_None_eq
thf(fact_117_map__add__None, axiom,
    ((![M : list_char > option_val, N : list_char > option_val, K : list_char]: (((map_ad1615113112ar_val @ M @ N @ K) = none_val) = ((((N @ K) = none_val)) & (((M @ K) = none_val))))))). % map_add_None
thf(fact_118_map__add__eq__empty__iff, axiom,
    ((![F2 : list_char > option_val, G : list_char > option_val]: (((map_ad1615113112ar_val @ F2 @ G) = (^[X4 : list_char]: none_val)) = (((F2 = (^[X4 : list_char]: none_val))) & ((G = (^[X4 : list_char]: none_val)))))))). % map_add_eq_empty_iff
thf(fact_119_empty__upd__none, axiom,
    ((![X : list_char]: ((fun_up9191ion_ty @ (^[X4 : list_char]: none_ty) @ X @ none_ty) = (^[X4 : list_char]: none_ty))))). % empty_upd_none
thf(fact_120_empty__upd__none, axiom,
    ((![X : nat]: ((fun_up262443479on_val @ (^[X4 : nat]: none_P1535574167on_val) @ X @ none_P1535574167on_val) = (^[X4 : nat]: none_P1535574167on_val))))). % empty_upd_none
thf(fact_121_empty__map__add, axiom,
    ((![M : list_char > option_val]: ((map_ad1615113112ar_val @ (^[X4 : list_char]: none_val) @ M) = M)))). % empty_map_add
thf(fact_122_map__add__empty, axiom,
    ((![M : list_char > option_val]: ((map_ad1615113112ar_val @ M @ (^[X4 : list_char]: none_val)) = M)))). % map_add_empty
thf(fact_123_empty__eq__map__add__iff, axiom,
    ((![F2 : list_char > option_val, G : list_char > option_val]: (((^[X4 : list_char]: none_val) = (map_ad1615113112ar_val @ F2 @ G)) = (((F2 = (^[X4 : list_char]: none_val))) & ((G = (^[X4 : list_char]: none_val)))))))). % empty_eq_map_add_iff
thf(fact_124_combine__options__cases, axiom,
    ((![X : option_ty, P : option_ty > option_ty > $o, Y : option_ty]: (((X = none_ty) => (P @ X @ Y)) => (((Y = none_ty) => (P @ X @ Y)) => ((![A2 : ty, B : ty]: ((X = (some_ty @ A2)) => ((Y = (some_ty @ B)) => (P @ X @ Y)))) => (P @ X @ Y))))))). % combine_options_cases
thf(fact_125_combine__options__cases, axiom,
    ((![X : option_ty, P : option_ty > option2118145160on_val > $o, Y : option2118145160on_val]: (((X = none_ty) => (P @ X @ Y)) => (((Y = none_P1535574167on_val) => (P @ X @ Y)) => ((![A2 : ty, B : produc266837688on_val]: ((X = (some_ty @ A2)) => ((Y = (some_P1299442195on_val @ B)) => (P @ X @ Y)))) => (P @ X @ Y))))))). % combine_options_cases
thf(fact_126_combine__options__cases, axiom,
    ((![X : option2118145160on_val, P : option2118145160on_val > option_ty > $o, Y : option_ty]: (((X = none_P1535574167on_val) => (P @ X @ Y)) => (((Y = none_ty) => (P @ X @ Y)) => ((![A2 : produc266837688on_val, B : ty]: ((X = (some_P1299442195on_val @ A2)) => ((Y = (some_ty @ B)) => (P @ X @ Y)))) => (P @ X @ Y))))))). % combine_options_cases
thf(fact_127_combine__options__cases, axiom,
    ((![X : option2118145160on_val, P : option2118145160on_val > option2118145160on_val > $o, Y : option2118145160on_val]: (((X = none_P1535574167on_val) => (P @ X @ Y)) => (((Y = none_P1535574167on_val) => (P @ X @ Y)) => ((![A2 : produc266837688on_val, B : produc266837688on_val]: ((X = (some_P1299442195on_val @ A2)) => ((Y = (some_P1299442195on_val @ B)) => (P @ X @ Y)))) => (P @ X @ Y))))))). % combine_options_cases
thf(fact_128_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_129_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_130_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_131_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_132_option_Oinducts, axiom,
    ((![P : option_ty > $o, Option : option_ty]: ((P @ none_ty) => ((![X3 : ty]: (P @ (some_ty @ X3))) => (P @ Option)))))). % option.inducts
thf(fact_133_option_Oinducts, axiom,
    ((![P : option2118145160on_val > $o, Option : option2118145160on_val]: ((P @ none_P1535574167on_val) => ((![X3 : produc266837688on_val]: (P @ (some_P1299442195on_val @ X3))) => (P @ Option)))))). % option.inducts
thf(fact_134_option_Oexhaust, axiom,
    ((![Y : option_ty]: ((~ ((Y = none_ty))) => (~ ((![X22 : ty]: (~ ((Y = (some_ty @ X22))))))))))). % option.exhaust
thf(fact_135_option_Oexhaust, axiom,
    ((![Y : option2118145160on_val]: ((~ ((Y = none_P1535574167on_val))) => (~ ((![X22 : produc266837688on_val]: (~ ((Y = (some_P1299442195on_val @ X22))))))))))). % option.exhaust
thf(fact_136_option_OdiscI, axiom,
    ((![Option : option_ty, X2 : ty]: ((Option = (some_ty @ X2)) => (~ ((Option = none_ty))))))). % option.discI
thf(fact_137_option_OdiscI, axiom,
    ((![Option : option2118145160on_val, X2 : produc266837688on_val]: ((Option = (some_P1299442195on_val @ X2)) => (~ ((Option = none_P1535574167on_val))))))). % option.discI
thf(fact_138_option_Odistinct_I1_J, axiom,
    ((![X2 : ty]: (~ ((none_ty = (some_ty @ X2))))))). % option.distinct(1)
thf(fact_139_option_Odistinct_I1_J, axiom,
    ((![X2 : produc266837688on_val]: (~ ((none_P1535574167on_val = (some_P1299442195on_val @ X2))))))). % option.distinct(1)
thf(fact_140_conf__widen, axiom,
    ((![P : list_P1234162913t_char, H : nat > option2118145160on_val, V2 : val, T : ty, T4 : ty]: ((conf_P93989998t_char @ P @ H @ V2 @ T) => ((widen_917054840t_char @ P @ T @ T4) => (conf_P93989998t_char @ P @ H @ V2 @ T4)))))). % conf_widen
thf(fact_141_map__upd__nonempty, axiom,
    ((![T3 : list_char > option_ty, K : list_char, X : ty]: (~ (((fun_up9191ion_ty @ T3 @ K @ (some_ty @ X)) = (^[X4 : list_char]: none_ty))))))). % map_upd_nonempty
thf(fact_142_map__upd__nonempty, axiom,
    ((![T3 : nat > option2118145160on_val, K : nat, X : produc266837688on_val]: (~ (((fun_up262443479on_val @ T3 @ K @ (some_P1299442195on_val @ X)) = (^[X4 : nat]: none_P1535574167on_val))))))). % map_upd_nonempty
thf(fact_143_map__add__SomeD, axiom,
    ((![M : list_char > option_val, N : list_char > option_val, K : list_char, X : val]: (((map_ad1615113112ar_val @ M @ N @ K) = (some_val @ X)) => (((N @ K) = (some_val @ X)) | (((N @ K) = none_val) & ((M @ K) = (some_val @ X)))))))). % map_add_SomeD
thf(fact_144_map__add__Some__iff, axiom,
    ((![M : list_char > option_val, N : list_char > option_val, K : list_char, X : val]: (((map_ad1615113112ar_val @ M @ N @ K) = (some_val @ X)) = ((((N @ K) = (some_val @ X))) | (((((N @ K) = none_val)) & (((M @ K) = (some_val @ X)))))))))). % map_add_Some_iff
thf(fact_145_lconf__upd, axiom,
    ((![P : list_P1234162913t_char, H : nat > option2118145160on_val, L : list_char > option_val, E : list_char > option_ty, V2 : val, T : ty, V : list_char]: ((lconf_485928294t_char @ P @ H @ L @ E) => ((conf_P93989998t_char @ P @ H @ V2 @ T) => (((E @ V) = (some_ty @ T)) => (lconf_485928294t_char @ P @ H @ (fun_up1252458416on_val @ L @ V @ (some_val @ V2)) @ E))))))). % lconf_upd
thf(fact_146_lconf__def, axiom,
    ((lconf_485928294t_char = (^[P3 : list_P1234162913t_char]: (^[H4 : nat > option2118145160on_val]: (^[L3 : list_char > option_val]: (^[E4 : list_char > option_ty]: (![V3 : list_char]: (![V4 : val]: ((((L3 @ V3) = (some_val @ V4))) => ((?[T5 : ty]: ((((E4 @ V3) = (some_ty @ T5))) & ((conf_P93989998t_char @ P3 @ H4 @ V4 @ T5))))))))))))))). % lconf_def
thf(fact_147_hext__new, axiom,
    ((![H : nat > option2118145160on_val, A : nat, X : produc266837688on_val]: (((H @ A) = none_P1535574167on_val) => (hext @ H @ (fun_up262443479on_val @ H @ A @ (some_P1299442195on_val @ X))))))). % hext_new
thf(fact_148_converse__rtrancl__induct__red, axiom,
    ((![E2 : exp_list_char, H : nat > option2118145160on_val, L : list_char > option_val, E3 : exp_list_char, H2 : nat > option2118145160on_val, L2 : list_char > option_val, P : list_P1234162913t_char, R : exp_list_char > (nat > option2118145160on_val) > (list_char > option_val) > exp_list_char > (nat > option2118145160on_val) > (list_char > option_val) > $o]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E2 @ (produc52622304on_val @ H @ L)) @ (produc2023458740on_val @ E3 @ (produc52622304on_val @ H2 @ L2))) @ (transi111096263on_val @ (red @ P))) => ((![E5 : exp_list_char, H6 : nat > option2118145160on_val, L4 : list_char > option_val]: (R @ E5 @ H6 @ L4 @ E5 @ H6 @ L4)) => ((![E_0 : exp_list_char, H_0 : nat > option2118145160on_val, L_02 : list_char > option_val, E_12 : exp_list_char, H_1 : nat > option2118145160on_val, L_1 : list_char > option_val, E6 : exp_list_char, H7 : nat > option2118145160on_val, L5 : list_char > option_val]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E_0 @ (produc52622304on_val @ H_0 @ L_02)) @ (produc2023458740on_val @ E_12 @ (produc52622304on_val @ H_1 @ L_1))) @ (red @ P)) => ((R @ E_12 @ H_1 @ L_1 @ E6 @ H7 @ L5) => (R @ E_0 @ H_0 @ L_02 @ E6 @ H7 @ L5)))) => (R @ E2 @ H @ L @ E3 @ H2 @ L2))))))). % converse_rtrancl_induct_red
thf(fact_149_TryReds, axiom,
    ((![E2 : exp_list_char, S2 : produc515445032on_val, E3 : exp_list_char, S3 : produc515445032on_val, P : list_P1234162913t_char, C : list_char, V : list_char, E_2 : exp_list_char]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E2 @ S2) @ (produc2023458740on_val @ E3 @ S3)) @ (transi111096263on_val @ (red @ P))) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (tryCatch_list_char @ E2 @ C @ V @ E_2) @ S2) @ (produc2023458740on_val @ (tryCatch_list_char @ E3 @ C @ V @ E_2) @ S3)) @ (transi111096263on_val @ (red @ P))))))). % TryReds
thf(fact_150_CondReds, axiom,
    ((![E2 : exp_list_char, S2 : produc515445032on_val, E3 : exp_list_char, S3 : produc515445032on_val, P : list_P1234162913t_char, E_1 : exp_list_char, E_2 : exp_list_char]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E2 @ S2) @ (produc2023458740on_val @ E3 @ S3)) @ (transi111096263on_val @ (red @ P))) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (cond_list_char @ E2 @ E_1 @ E_2) @ S2) @ (produc2023458740on_val @ (cond_list_char @ E3 @ E_1 @ E_2) @ S3)) @ (transi111096263on_val @ (red @ P))))))). % CondReds
thf(fact_151_preallocated__new, axiom,
    ((![H : nat > option2118145160on_val, A : nat, X : produc266837688on_val]: ((preallocated @ H) => (((H @ A) = none_P1535574167on_val) => (preallocated @ (fun_up262443479on_val @ H @ A @ (some_P1299442195on_val @ X)))))))). % preallocated_new
thf(fact_152_lconf__empty, axiom,
    ((![P : list_P1234162913t_char, H : nat > option2118145160on_val, E : list_char > option_ty]: (lconf_485928294t_char @ P @ H @ (^[X4 : list_char]: none_val) @ E)))). % lconf_empty
thf(fact_153_preallocated__hext, axiom,
    ((![H : nat > option2118145160on_val, H2 : nat > option2118145160on_val]: ((preallocated @ H) => ((hext @ H @ H2) => (preallocated @ H2)))))). % preallocated_hext
thf(fact_154_preallocated__upd__obj, axiom,
    ((![H : nat > option2118145160on_val, A : nat, C : list_char, Fs : produc1257910179t_char > option_val, Fs2 : produc1257910179t_char > option_val]: ((preallocated @ H) => (((H @ A) = (some_P1299442195on_val @ (produc904988266on_val @ C @ Fs))) => (preallocated @ (fun_up262443479on_val @ H @ A @ (some_P1299442195on_val @ (produc904988266on_val @ C @ Fs2))))))))). % preallocated_upd_obj
thf(fact_155_converse__rtrancl__induct2, axiom,
    ((![Ax : nat > option2118145160on_val, Ay : list_char > option_val, Bx : nat > option2118145160on_val, By : list_char > option_val, R2 : set_Pr148564103on_val, P : (nat > option2118145160on_val) > (list_char > option_val) > $o]: ((member2027247312on_val @ (produc2106877847on_val @ (produc52622304on_val @ Ax @ Ay) @ (produc52622304on_val @ Bx @ By)) @ (transi432893227on_val @ R2)) => ((P @ Bx @ By) => ((![A2 : nat > option2118145160on_val, B : list_char > option_val, Aa2 : nat > option2118145160on_val, Ba : list_char > option_val]: ((member2027247312on_val @ (produc2106877847on_val @ (produc52622304on_val @ A2 @ B) @ (produc52622304on_val @ Aa2 @ Ba)) @ R2) => ((member2027247312on_val @ (produc2106877847on_val @ (produc52622304on_val @ Aa2 @ Ba) @ (produc52622304on_val @ Bx @ By)) @ (transi432893227on_val @ R2)) => ((P @ Aa2 @ Ba) => (P @ A2 @ B))))) => (P @ Ax @ Ay))))))). % converse_rtrancl_induct2
thf(fact_156_converse__rtrancl__induct2, axiom,
    ((![Ax : produc1097884484on_val, Ay : produc1097884484on_val, Bx : produc1097884484on_val, By : produc1097884484on_val, R2 : set_Pr1368603847on_val, P : produc1097884484on_val > produc1097884484on_val > $o]: ((member208988944on_val @ (produc564964183on_val @ (produc1069526295on_val @ Ax @ Ay) @ (produc1069526295on_val @ Bx @ By)) @ (transi100378922on_val @ R2)) => ((P @ Bx @ By) => ((![A2 : produc1097884484on_val, B : produc1097884484on_val, Aa2 : produc1097884484on_val, Ba : produc1097884484on_val]: ((member208988944on_val @ (produc564964183on_val @ (produc1069526295on_val @ A2 @ B) @ (produc1069526295on_val @ Aa2 @ Ba)) @ R2) => ((member208988944on_val @ (produc564964183on_val @ (produc1069526295on_val @ Aa2 @ Ba) @ (produc1069526295on_val @ Bx @ By)) @ (transi100378922on_val @ R2)) => ((P @ Aa2 @ Ba) => (P @ A2 @ B))))) => (P @ Ax @ Ay))))))). % converse_rtrancl_induct2
thf(fact_157_converse__rtrancl__induct2, axiom,
    ((![Ax : list_char, Ay : produc1257910179t_char > option_val, Bx : list_char, By : produc1257910179t_char > option_val, R2 : set_Pr2110063281on_val, P : list_char > (produc1257910179t_char > option_val) > $o]: ((member197592058on_val @ (produc881885833on_val @ (produc904988266on_val @ Ax @ Ay) @ (produc904988266on_val @ Bx @ By)) @ (transi2071064181on_val @ R2)) => ((P @ Bx @ By) => ((![A2 : list_char, B : produc1257910179t_char > option_val, Aa2 : list_char, Ba : produc1257910179t_char > option_val]: ((member197592058on_val @ (produc881885833on_val @ (produc904988266on_val @ A2 @ B) @ (produc904988266on_val @ Aa2 @ Ba)) @ R2) => ((member197592058on_val @ (produc881885833on_val @ (produc904988266on_val @ Aa2 @ Ba) @ (produc904988266on_val @ Bx @ By)) @ (transi2071064181on_val @ R2)) => ((P @ Aa2 @ Ba) => (P @ A2 @ B))))) => (P @ Ax @ Ay))))))). % converse_rtrancl_induct2
thf(fact_158_converse__rtrancl__induct2, axiom,
    ((![Ax : exp_list_char, Ay : produc515445032on_val, Bx : exp_list_char, By : produc515445032on_val, R2 : set_Pr1189492743on_val, P : exp_list_char > produc515445032on_val > $o]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ Ax @ Ay) @ (produc2023458740on_val @ Bx @ By)) @ (transi111096263on_val @ R2)) => ((P @ Bx @ By) => ((![A2 : exp_list_char, B : produc515445032on_val, Aa2 : exp_list_char, Ba : produc515445032on_val]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ A2 @ B) @ (produc2023458740on_val @ Aa2 @ Ba)) @ R2) => ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ Aa2 @ Ba) @ (produc2023458740on_val @ Bx @ By)) @ (transi111096263on_val @ R2)) => ((P @ Aa2 @ Ba) => (P @ A2 @ B))))) => (P @ Ax @ Ay))))))). % converse_rtrancl_induct2
thf(fact_159_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)))) => (~ ((![A2 : nat > option2118145160on_val, B : list_char > option_val]: ((member2027247312on_val @ (produc2106877847on_val @ (produc52622304on_val @ Xa @ Xb) @ (produc52622304on_val @ A2 @ B)) @ R2) => (~ ((member2027247312on_val @ (produc2106877847on_val @ (produc52622304on_val @ A2 @ B) @ (produc52622304on_val @ Za @ Zb)) @ (transi432893227on_val @ R2))))))))))))). % converse_rtranclE2
thf(fact_160_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)))) => (~ ((![A2 : produc1097884484on_val, B : produc1097884484on_val]: ((member208988944on_val @ (produc564964183on_val @ (produc1069526295on_val @ Xa @ Xb) @ (produc1069526295on_val @ A2 @ B)) @ R2) => (~ ((member208988944on_val @ (produc564964183on_val @ (produc1069526295on_val @ A2 @ B) @ (produc1069526295on_val @ Za @ Zb)) @ (transi100378922on_val @ R2))))))))))))). % converse_rtranclE2
thf(fact_161_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)))) => (~ ((![A2 : list_char, B : produc1257910179t_char > option_val]: ((member197592058on_val @ (produc881885833on_val @ (produc904988266on_val @ Xa @ Xb) @ (produc904988266on_val @ A2 @ B)) @ R2) => (~ ((member197592058on_val @ (produc881885833on_val @ (produc904988266on_val @ A2 @ B) @ (produc904988266on_val @ Za @ Zb)) @ (transi2071064181on_val @ R2))))))))))))). % converse_rtranclE2
thf(fact_162_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)))) => (~ ((![A2 : exp_list_char, B : produc515445032on_val]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ Xa @ Xb) @ (produc2023458740on_val @ A2 @ B)) @ R2) => (~ ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ A2 @ B) @ (produc2023458740on_val @ Za @ Zb)) @ (transi111096263on_val @ R2))))))))))))). % converse_rtranclE2
thf(fact_163_rtranclE, axiom,
    ((![A : produc1097884484on_val, B2 : produc1097884484on_val, R2 : set_Pr1189492743on_val]: ((member354538064on_val @ (produc1069526295on_val @ A @ B2) @ (transi111096263on_val @ R2)) => ((~ ((A = B2))) => (~ ((![Y3 : produc1097884484on_val]: ((member354538064on_val @ (produc1069526295on_val @ A @ Y3) @ (transi111096263on_val @ R2)) => (~ ((member354538064on_val @ (produc1069526295on_val @ Y3 @ B2) @ R2)))))))))))). % rtranclE
thf(fact_164_rtrancl_Ocases, axiom,
    ((![A1 : produc1097884484on_val, A22 : produc1097884484on_val, R2 : set_Pr1189492743on_val]: ((member354538064on_val @ (produc1069526295on_val @ A1 @ A22) @ (transi111096263on_val @ R2)) => ((~ ((A22 = A1))) => (~ ((![B : produc1097884484on_val]: ((member354538064on_val @ (produc1069526295on_val @ A1 @ B) @ (transi111096263on_val @ R2)) => (~ ((member354538064on_val @ (produc1069526295on_val @ B @ A22) @ R2)))))))))))). % rtrancl.cases
thf(fact_165_rtrancl_Osimps, axiom,
    ((![A1 : produc1097884484on_val, A22 : produc1097884484on_val, R2 : set_Pr1189492743on_val]: ((member354538064on_val @ (produc1069526295on_val @ A1 @ A22) @ (transi111096263on_val @ R2)) = (((?[A5 : produc1097884484on_val]: (((A1 = A5)) & ((A22 = A5))))) | ((?[A5 : produc1097884484on_val]: (?[B4 : produc1097884484on_val]: (?[C6 : produc1097884484on_val]: (((A1 = A5)) & ((((A22 = C6)) & ((((member354538064on_val @ (produc1069526295on_val @ A5 @ B4) @ (transi111096263on_val @ R2))) & ((member354538064on_val @ (produc1069526295on_val @ B4 @ C6) @ R2)))))))))))))))). % rtrancl.simps
thf(fact_166_rtrancl__trans, axiom,
    ((![X : produc1097884484on_val, Y : produc1097884484on_val, R2 : set_Pr1189492743on_val, Z2 : produc1097884484on_val]: ((member354538064on_val @ (produc1069526295on_val @ X @ Y) @ (transi111096263on_val @ R2)) => ((member354538064on_val @ (produc1069526295on_val @ Y @ Z2) @ (transi111096263on_val @ R2)) => (member354538064on_val @ (produc1069526295on_val @ X @ Z2) @ (transi111096263on_val @ R2))))))). % rtrancl_trans
thf(fact_167_rtrancl__induct, axiom,
    ((![A : produc1097884484on_val, B2 : produc1097884484on_val, R2 : set_Pr1189492743on_val, P : produc1097884484on_val > $o]: ((member354538064on_val @ (produc1069526295on_val @ A @ B2) @ (transi111096263on_val @ R2)) => ((P @ A) => ((![Y3 : produc1097884484on_val, Z3 : produc1097884484on_val]: ((member354538064on_val @ (produc1069526295on_val @ A @ Y3) @ (transi111096263on_val @ R2)) => ((member354538064on_val @ (produc1069526295on_val @ Y3 @ Z3) @ R2) => ((P @ Y3) => (P @ Z3))))) => (P @ B2))))))). % rtrancl_induct
thf(fact_168_rtrancl_Oinducts, axiom,
    ((![X1 : produc1097884484on_val, X2 : produc1097884484on_val, R2 : set_Pr1189492743on_val, P : produc1097884484on_val > produc1097884484on_val > $o]: ((member354538064on_val @ (produc1069526295on_val @ X1 @ X2) @ (transi111096263on_val @ R2)) => ((![A2 : produc1097884484on_val]: (P @ A2 @ A2)) => ((![A2 : produc1097884484on_val, B : produc1097884484on_val, C2 : produc1097884484on_val]: ((member354538064on_val @ (produc1069526295on_val @ A2 @ B) @ (transi111096263on_val @ R2)) => ((P @ A2 @ B) => ((member354538064on_val @ (produc1069526295on_val @ B @ C2) @ R2) => (P @ A2 @ C2))))) => (P @ X1 @ X2))))))). % rtrancl.inducts
thf(fact_169_converse__rtranclE, axiom,
    ((![X : produc1097884484on_val, Z2 : produc1097884484on_val, R2 : set_Pr1189492743on_val]: ((member354538064on_val @ (produc1069526295on_val @ X @ Z2) @ (transi111096263on_val @ R2)) => ((~ ((X = Z2))) => (~ ((![Y3 : produc1097884484on_val]: ((member354538064on_val @ (produc1069526295on_val @ X @ Y3) @ R2) => (~ ((member354538064on_val @ (produc1069526295on_val @ Y3 @ Z2) @ (transi111096263on_val @ R2))))))))))))). % converse_rtranclE
thf(fact_170_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_171_converse__rtrancl__induct, axiom,
    ((![A : produc1097884484on_val, B2 : produc1097884484on_val, R2 : set_Pr1189492743on_val, P : produc1097884484on_val > $o]: ((member354538064on_val @ (produc1069526295on_val @ A @ B2) @ (transi111096263on_val @ R2)) => ((P @ B2) => ((![Y3 : produc1097884484on_val, Z3 : produc1097884484on_val]: ((member354538064on_val @ (produc1069526295on_val @ Y3 @ Z3) @ R2) => ((member354538064on_val @ (produc1069526295on_val @ Z3 @ B2) @ (transi111096263on_val @ R2)) => ((P @ Z3) => (P @ Y3))))) => (P @ A))))))). % converse_rtrancl_induct
thf(fact_172_rtrancl_Ortrancl__into__rtrancl, axiom,
    ((![A : produc1097884484on_val, B2 : produc1097884484on_val, R2 : set_Pr1189492743on_val, C5 : produc1097884484on_val]: ((member354538064on_val @ (produc1069526295on_val @ A @ B2) @ (transi111096263on_val @ R2)) => ((member354538064on_val @ (produc1069526295on_val @ B2 @ C5) @ R2) => (member354538064on_val @ (produc1069526295on_val @ A @ C5) @ (transi111096263on_val @ R2))))))). % rtrancl.rtrancl_into_rtrancl
thf(fact_173_converse__rtrancl__into__rtrancl, axiom,
    ((![A : produc1097884484on_val, B2 : produc1097884484on_val, R2 : set_Pr1189492743on_val, C5 : produc1097884484on_val]: ((member354538064on_val @ (produc1069526295on_val @ A @ B2) @ R2) => ((member354538064on_val @ (produc1069526295on_val @ B2 @ C5) @ (transi111096263on_val @ R2)) => (member354538064on_val @ (produc1069526295on_val @ A @ C5) @ (transi111096263on_val @ R2))))))). % converse_rtrancl_into_rtrancl
thf(fact_174_rtrancl__induct2, axiom,
    ((![Ax : nat > option2118145160on_val, Ay : list_char > option_val, Bx : nat > option2118145160on_val, By : list_char > option_val, R2 : set_Pr148564103on_val, P : (nat > option2118145160on_val) > (list_char > option_val) > $o]: ((member2027247312on_val @ (produc2106877847on_val @ (produc52622304on_val @ Ax @ Ay) @ (produc52622304on_val @ Bx @ By)) @ (transi432893227on_val @ R2)) => ((P @ Ax @ Ay) => ((![A2 : nat > option2118145160on_val, B : list_char > option_val, Aa2 : nat > option2118145160on_val, Ba : list_char > option_val]: ((member2027247312on_val @ (produc2106877847on_val @ (produc52622304on_val @ Ax @ Ay) @ (produc52622304on_val @ A2 @ B)) @ (transi432893227on_val @ R2)) => ((member2027247312on_val @ (produc2106877847on_val @ (produc52622304on_val @ A2 @ B) @ (produc52622304on_val @ Aa2 @ Ba)) @ R2) => ((P @ A2 @ B) => (P @ Aa2 @ Ba))))) => (P @ Bx @ By))))))). % rtrancl_induct2
thf(fact_175_rtrancl__induct2, axiom,
    ((![Ax : produc1097884484on_val, Ay : produc1097884484on_val, Bx : produc1097884484on_val, By : produc1097884484on_val, R2 : set_Pr1368603847on_val, P : produc1097884484on_val > produc1097884484on_val > $o]: ((member208988944on_val @ (produc564964183on_val @ (produc1069526295on_val @ Ax @ Ay) @ (produc1069526295on_val @ Bx @ By)) @ (transi100378922on_val @ R2)) => ((P @ Ax @ Ay) => ((![A2 : produc1097884484on_val, B : produc1097884484on_val, Aa2 : produc1097884484on_val, Ba : produc1097884484on_val]: ((member208988944on_val @ (produc564964183on_val @ (produc1069526295on_val @ Ax @ Ay) @ (produc1069526295on_val @ A2 @ B)) @ (transi100378922on_val @ R2)) => ((member208988944on_val @ (produc564964183on_val @ (produc1069526295on_val @ A2 @ B) @ (produc1069526295on_val @ Aa2 @ Ba)) @ R2) => ((P @ A2 @ B) => (P @ Aa2 @ Ba))))) => (P @ Bx @ By))))))). % rtrancl_induct2
thf(fact_176_rtrancl__induct2, axiom,
    ((![Ax : list_char, Ay : produc1257910179t_char > option_val, Bx : list_char, By : produc1257910179t_char > option_val, R2 : set_Pr2110063281on_val, P : list_char > (produc1257910179t_char > option_val) > $o]: ((member197592058on_val @ (produc881885833on_val @ (produc904988266on_val @ Ax @ Ay) @ (produc904988266on_val @ Bx @ By)) @ (transi2071064181on_val @ R2)) => ((P @ Ax @ Ay) => ((![A2 : list_char, B : produc1257910179t_char > option_val, Aa2 : list_char, Ba : produc1257910179t_char > option_val]: ((member197592058on_val @ (produc881885833on_val @ (produc904988266on_val @ Ax @ Ay) @ (produc904988266on_val @ A2 @ B)) @ (transi2071064181on_val @ R2)) => ((member197592058on_val @ (produc881885833on_val @ (produc904988266on_val @ A2 @ B) @ (produc904988266on_val @ Aa2 @ Ba)) @ R2) => ((P @ A2 @ B) => (P @ Aa2 @ Ba))))) => (P @ Bx @ By))))))). % rtrancl_induct2
thf(fact_177_rtrancl__induct2, axiom,
    ((![Ax : exp_list_char, Ay : produc515445032on_val, Bx : exp_list_char, By : produc515445032on_val, R2 : set_Pr1189492743on_val, P : exp_list_char > produc515445032on_val > $o]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ Ax @ Ay) @ (produc2023458740on_val @ Bx @ By)) @ (transi111096263on_val @ R2)) => ((P @ Ax @ Ay) => ((![A2 : exp_list_char, B : produc515445032on_val, Aa2 : exp_list_char, Ba : produc515445032on_val]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ Ax @ Ay) @ (produc2023458740on_val @ A2 @ B)) @ (transi111096263on_val @ R2)) => ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ A2 @ B) @ (produc2023458740on_val @ Aa2 @ Ba)) @ R2) => ((P @ A2 @ B) => (P @ Aa2 @ Ba))))) => (P @ Bx @ By))))))). % rtrancl_induct2
thf(fact_178_TryRedsVal, axiom,
    ((![E2 : exp_list_char, S2 : produc515445032on_val, V2 : val, S3 : produc515445032on_val, P : list_P1234162913t_char, C : list_char, V : list_char, E_2 : exp_list_char]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E2 @ S2) @ (produc2023458740on_val @ (val_list_char @ V2) @ S3)) @ (transi111096263on_val @ (red @ P))) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (tryCatch_list_char @ E2 @ C @ V @ E_2) @ S2) @ (produc2023458740on_val @ (val_list_char @ V2) @ S3)) @ (transi111096263on_val @ (red @ P))))))). % TryRedsVal
thf(fact_179_exp_Oinject_I3_J, axiom,
    ((![X32 : val, Y32 : val]: (((val_list_char @ X32) = (val_list_char @ Y32)) = (X32 = Y32))))). % exp.inject(3)
thf(fact_180_exp_Odistinct_I71_J, axiom,
    ((![X32 : val, X121 : exp_list_char, X122 : exp_list_char, X123 : exp_list_char]: (~ (((val_list_char @ X32) = (cond_list_char @ X121 @ X122 @ X123))))))). % exp.distinct(71)
thf(fact_181_exp_Odistinct_I77_J, axiom,
    ((![X32 : val, X151 : exp_list_char, X152 : list_char, X153 : list_char, X154 : exp_list_char]: (~ (((val_list_char @ X32) = (tryCatch_list_char @ X151 @ X152 @ X153 @ X154))))))). % exp.distinct(77)
thf(fact_182_red__reds_ORedTry, axiom,
    ((![V2 : val, C : list_char, V : list_char, E_2 : exp_list_char, S2 : produc515445032on_val, P : list_P1234162913t_char]: (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (tryCatch_list_char @ (val_list_char @ V2) @ C @ V @ E_2) @ S2) @ (produc2023458740on_val @ (val_list_char @ V2) @ S2)) @ (red @ P))))). % red_reds.RedTry
thf(fact_183_CondReds2T, axiom,
    ((![E2 : exp_list_char, S_0 : produc515445032on_val, S_1 : produc515445032on_val, P : list_P1234162913t_char, E_1 : exp_list_char, E3 : exp_list_char, S_2 : produc515445032on_val, E_2 : exp_list_char]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E2 @ S_0) @ (produc2023458740on_val @ (val_list_char @ (bool @ $true)) @ S_1)) @ (transi111096263on_val @ (red @ P))) => ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E_1 @ S_1) @ (produc2023458740on_val @ E3 @ S_2)) @ (transi111096263on_val @ (red @ P))) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (cond_list_char @ E2 @ E_1 @ E_2) @ S_0) @ (produc2023458740on_val @ E3 @ S_2)) @ (transi111096263on_val @ (red @ P)))))))). % CondReds2T
thf(fact_184_CondReds2F, axiom,
    ((![E2 : exp_list_char, S_0 : produc515445032on_val, S_1 : produc515445032on_val, P : list_P1234162913t_char, E_2 : exp_list_char, E3 : exp_list_char, S_2 : produc515445032on_val, E_1 : exp_list_char]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E2 @ S_0) @ (produc2023458740on_val @ (val_list_char @ (bool @ $false)) @ S_1)) @ (transi111096263on_val @ (red @ P))) => ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E_2 @ S_1) @ (produc2023458740on_val @ E3 @ S_2)) @ (transi111096263on_val @ (red @ P))) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (cond_list_char @ E2 @ E_1 @ E_2) @ S_0) @ (produc2023458740on_val @ E3 @ S_2)) @ (transi111096263on_val @ (red @ P)))))))). % CondReds2F
thf(fact_185_red__reds_ORedCondT, axiom,
    ((![E_1 : exp_list_char, E_2 : exp_list_char, S2 : produc515445032on_val, P : list_P1234162913t_char]: (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (cond_list_char @ (val_list_char @ (bool @ $true)) @ E_1 @ E_2) @ S2) @ (produc2023458740on_val @ E_1 @ S2)) @ (red @ P))))). % red_reds.RedCondT
thf(fact_186_red__reds_ORedCondF, axiom,
    ((![E_1 : exp_list_char, E_2 : exp_list_char, S2 : produc515445032on_val, P : list_P1234162913t_char]: (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (cond_list_char @ (val_list_char @ (bool @ $false)) @ E_1 @ E_2) @ S2) @ (produc2023458740on_val @ E_2 @ S2)) @ (red @ P))))). % red_reds.RedCondF
thf(fact_187_WhileTReds, axiom,
    ((![B2 : exp_list_char, S_0 : produc515445032on_val, S_1 : produc515445032on_val, P : list_P1234162913t_char, C5 : exp_list_char, V_1 : val, S_2 : produc515445032on_val, E2 : exp_list_char, S_3 : produc515445032on_val]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ B2 @ S_0) @ (produc2023458740on_val @ (val_list_char @ (bool @ $true)) @ S_1)) @ (transi111096263on_val @ (red @ P))) => ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ C5 @ S_1) @ (produc2023458740on_val @ (val_list_char @ V_1) @ S_2)) @ (transi111096263on_val @ (red @ P))) => ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (while_list_char @ B2 @ C5) @ S_2) @ (produc2023458740on_val @ E2 @ S_3)) @ (transi111096263on_val @ (red @ P))) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (while_list_char @ B2 @ C5) @ S_0) @ (produc2023458740on_val @ E2 @ S_3)) @ (transi111096263on_val @ (red @ P))))))))). % WhileTReds
thf(fact_188_exp_Oinject_I13_J, axiom,
    ((![X131 : exp_list_char, X132 : exp_list_char, Y131 : exp_list_char, Y132 : exp_list_char]: (((while_list_char @ X131 @ X132) = (while_list_char @ Y131 @ Y132)) = (((X131 = Y131)) & ((X132 = Y132))))))). % exp.inject(13)
thf(fact_189_exp_Opred__inject_I13_J, axiom,
    ((![P : list_char > $o, A : exp_list_char, Aa : exp_list_char]: ((pred_exp_list_char @ P @ (while_list_char @ A @ Aa)) = (((pred_exp_list_char @ P @ A)) & ((pred_exp_list_char @ P @ Aa))))))). % exp.pred_inject(13)
thf(fact_190_exp_Odistinct_I73_J, axiom,
    ((![X32 : val, X131 : exp_list_char, X132 : exp_list_char]: (~ (((val_list_char @ X32) = (while_list_char @ X131 @ X132))))))). % exp.distinct(73)

% Helper facts (5)
thf(help_If_2_1_If_001t__Option__Ooption_It__Type__Oty_J_T, axiom,
    ((![X : option_ty, Y : option_ty]: ((if_option_ty @ $false @ X @ Y) = Y)))).
thf(help_If_1_1_If_001t__Option__Ooption_It__Type__Oty_J_T, axiom,
    ((![X : option_ty, Y : option_ty]: ((if_option_ty @ $true @ X @ Y) = X)))).
thf(help_If_3_1_If_001t__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_T, axiom,
    ((![P : $o]: ((P = $true) | (P = $false))))).
thf(help_If_2_1_If_001t__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_T, axiom,
    ((![X : option2118145160on_val, Y : option2118145160on_val]: ((if_opt451925058on_val @ $false @ X @ Y) = Y)))).
thf(help_If_1_1_If_001t__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_T, axiom,
    ((![X : option2118145160on_val, Y : option2118145160on_val]: ((if_opt451925058on_val @ $true @ X @ Y) = X)))).

% Conjectures (1)
thf(conj_0, conjecture,
    ((?[T6 : ty]: ((wTrt @ p @ aa @ e @ (tryCatch_list_char @ e_a @ c @ v @ e_2) @ T6) & (widen_917054840t_char @ p @ T6 @ t))))).
