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% This file was generated by Isabelle (most likely Sledgehammer)
% 2020-12-16 14:20:14.040

% Could-be-implicit typings (25)
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thf(ty_n_t__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J, type,
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thf(ty_n_t__Option__Ooption_It__Value__Oval_J, type,
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thf(ty_n_t__Option__Ooption_It__Type__Oty_J, type,
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thf(ty_n_t__List__Olist_It__String__Ochar_J, type,
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thf(ty_n_t__Value__Oval, type,
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thf(ty_n_t__Type__Oty, type,
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thf(ty_n_t__Nat__Onat, type,
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% Explicit typings (61)
thf(sy_c_BigStep_Oeval, type,
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thf(sy_c_BigStep_Ofinal_001t__List__Olist_It__String__Ochar_J, type,
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thf(sy_c_Conform_Ohconf_001t__Product____Type__Oprod_It__List__Olist_It__List__Olist_It__String__Ochar_J_J_Mt__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_J, type,
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thf(sy_c_Conform_Olconf_001t__Product____Type__Oprod_It__List__Olist_It__List__Olist_It__String__Ochar_J_J_Mt__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_J, type,
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thf(sy_c_Exceptions_OClassCast, type,
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thf(sy_c_Exceptions_ONullPointer, type,
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thf(sy_c_Exceptions_Oaddr__of__sys__xcpt, type,
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thf(sy_c_Expr_Oexp_OCast_001t__List__Olist_It__String__Ochar_J, 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_OTryCatch_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_Expr_Oexp_Othrow_001t__List__Olist_It__String__Ochar_J, type,
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thf(sy_c_Fun_Ofun__upd_001t__List__Olist_It__String__Ochar_J_001t__Option__Ooption_It__Value__Oval_J, type,
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thf(sy_c_If_001t__Option__Ooption_It__Value__Oval_J, type,
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thf(sy_c_JWellForm_Owf__J__mdecl, type,
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thf(sy_c_Option_Ooption_OSome_001t__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J, type,
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thf(sy_c_Option_Ooption_OSome_001t__Value__Oval, type,
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thf(sy_c_Product__Type_OPair_001_062_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_001_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J, type,
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thf(sy_c_Product__Type_OPair_001t__List__Olist_It__String__Ochar_J_001_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, type,
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thf(sy_c_Product__Type_OPair_001t__List__Olist_It__String__Ochar_J_001t__List__Olist_It__String__Ochar_J, type,
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thf(sy_c_Value_Oval_OAddr, type,
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thf(sy_c_Value_Oval_ONull, type,
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thf(sy_c_WWellForm_Owwf__J__mdecl, type,
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thf(sy_c_WellTypeRT_OWTrt, type,
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    member197592058on_val : produc1085126737on_val > set_Pr2110063281on_val > $o).
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thf(sy_v_D______, type,
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thf(sy_v_E____, type,
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thf(sy_v_P, type,
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thf(sy_v_T____, type,
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thf(sy_v_a______, type,
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thf(sy_v_aa______, type,
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% Relevant facts (199)
thf(fact_0_RedCastFail_Ohyps_I2_J, axiom,
    ((~ ((member89690956t_char @ (produc1304532571t_char @ d @ c) @ (transi1879726366t_char @ (subcls880436836t_char @ p))))))). % RedCastFail.hyps(2)
thf(fact_1_RedCastFail_Oprems_I1_J, axiom,
    ((typeSa1777264139_sconf @ p @ e @ (produc52622304on_val @ a @ b)))). % RedCastFail.prems(1)
thf(fact_2_RedCastFail_Ohyps_I1_J, axiom,
    (((hp @ (produc52622304on_val @ a @ b) @ aa) = (some_P1299442195on_val @ (produc904988266on_val @ d @ fs))))). % RedCastFail.hyps(1)
thf(fact_3_RedCastFail_Oprems_I2_J, axiom,
    ((wTrt @ p @ a @ e @ (cast_list_char @ c @ (val_list_char @ (addr @ aa))) @ t))). % RedCastFail.prems(2)
thf(fact_4_val_Oinject_I3_J, axiom,
    ((![X5 : nat, Y5 : nat]: (((addr @ X5) = (addr @ Y5)) = (X5 = Y5))))). % val.inject(3)
thf(fact_5_exp_Oinject_I14_J, axiom,
    ((![X14 : exp_list_char, Y14 : exp_list_char]: (((throw_list_char @ X14) = (throw_list_char @ Y14)) = (X14 = Y14))))). % exp.inject(14)
thf(fact_6_exp_Oinject_I3_J, axiom,
    ((![X3 : val, Y3 : val]: (((val_list_char @ X3) = (val_list_char @ Y3)) = (X3 = Y3))))). % exp.inject(3)
thf(fact_7_local_Owf, axiom,
    ((wf_pro1229751607t_char @ wf_J_mdecl @ p))). % local.wf
thf(fact_8_exp_Odistinct_I75_J, axiom,
    ((![X3 : val, X14 : exp_list_char]: (~ (((val_list_char @ X3) = (throw_list_char @ X14))))))). % exp.distinct(75)
thf(fact_9_finalE, axiom,
    ((![E : exp_list_char]: ((final_list_char @ E) => ((![V : val]: (~ ((E = (val_list_char @ V))))) => (~ ((![A : nat]: (~ ((E = (throw_list_char @ (val_list_char @ (addr @ A)))))))))))))). % finalE
thf(fact_10_final__def, axiom,
    ((final_list_char = (^[E2 : exp_list_char]: (((?[V2 : val]: (E2 = (val_list_char @ V2)))) | ((?[A2 : nat]: (E2 = (throw_list_char @ (val_list_char @ (addr @ A2))))))))))). % final_def
thf(fact_11_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_12_widen__refl, axiom,
    ((![P : list_P1234162913t_char, T : ty]: (widen_917054840t_char @ P @ T @ T)))). % widen_refl
thf(fact_13_WTrt__elim__cases_I4_J, axiom,
    ((![P : list_P1234162913t_char, H : nat > option2118145160on_val, E3 : list_char > option_ty, E : exp_list_char, T : ty]: ((wTrt @ P @ H @ E3 @ (throw_list_char @ E) @ T) => (~ ((![T_r : ty]: ((wTrt @ P @ H @ E3 @ E @ T_r) => (~ ((is_refT @ T_r))))))))))). % WTrt_elim_cases(4)
thf(fact_14_WTrtThrow, axiom,
    ((![P : list_P1234162913t_char, H : nat > option2118145160on_val, E3 : list_char > option_ty, E : exp_list_char, T_r2 : ty, T : ty]: ((wTrt @ P @ H @ E3 @ E @ T_r2) => ((is_refT @ T_r2) => (wTrt @ P @ H @ E3 @ (throw_list_char @ E) @ T)))))). % WTrtThrow
thf(fact_15_Throw, axiom,
    ((![P : list_P1234162913t_char, E : exp_list_char, S_0 : produc515445032on_val, A3 : nat, S_1 : produc515445032on_val]: ((eval @ P @ E @ S_0 @ (val_list_char @ (addr @ A3)) @ S_1) => (eval @ P @ (throw_list_char @ E) @ S_0 @ (throw_list_char @ (val_list_char @ (addr @ A3))) @ S_1))))). % Throw
thf(fact_16_exp_Oinject_I2_J, axiom,
    ((![X21 : list_char, X22 : exp_list_char, Y21 : list_char, Y22 : exp_list_char]: (((cast_list_char @ X21 @ X22) = (cast_list_char @ Y21 @ Y22)) = (((X21 = Y21)) & ((X22 = Y22))))))). % exp.inject(2)
thf(fact_17_eval__final, axiom,
    ((![P : list_P1234162913t_char, E : exp_list_char, S2 : produc515445032on_val, E4 : exp_list_char, S3 : produc515445032on_val]: ((eval @ P @ E @ S2 @ E4 @ S3) => (final_list_char @ E4))))). % eval_final
thf(fact_18_eval__finalId, axiom,
    ((![E : exp_list_char, P : list_P1234162913t_char, S2 : produc515445032on_val]: ((final_list_char @ E) => (eval @ P @ E @ S2 @ E @ S2))))). % eval_finalId
thf(fact_19_eval__evals_OCastThrow, axiom,
    ((![P : list_P1234162913t_char, E : exp_list_char, S_0 : produc515445032on_val, E4 : exp_list_char, S_1 : produc515445032on_val, C : list_char]: ((eval @ P @ E @ S_0 @ (throw_list_char @ E4) @ S_1) => (eval @ P @ (cast_list_char @ C @ E) @ S_0 @ (throw_list_char @ E4) @ S_1))))). % eval_evals.CastThrow
thf(fact_20_Cast, axiom,
    ((![P : list_P1234162913t_char, E : exp_list_char, S_0 : produc515445032on_val, A3 : nat, H : nat > option2118145160on_val, L : list_char > option_val, D : list_char, Fs : produc1257910179t_char > option_val, C : list_char]: ((eval @ P @ E @ S_0 @ (val_list_char @ (addr @ A3)) @ (produc52622304on_val @ H @ L)) => (((H @ A3) = (some_P1299442195on_val @ (produc904988266on_val @ D @ Fs))) => ((member89690956t_char @ (produc1304532571t_char @ D @ C) @ (transi1879726366t_char @ (subcls880436836t_char @ P))) => (eval @ P @ (cast_list_char @ C @ E) @ S_0 @ (val_list_char @ (addr @ A3)) @ (produc52622304on_val @ H @ L)))))))). % Cast
thf(fact_21_Val, axiom,
    ((![P : list_P1234162913t_char, V3 : val, S2 : produc515445032on_val]: (eval @ P @ (val_list_char @ V3) @ S2 @ (val_list_char @ V3) @ S2)))). % Val
thf(fact_22_eval__cases_I2_J, axiom,
    ((![P : list_P1234162913t_char, V3 : val, S2 : produc515445032on_val, E4 : exp_list_char, S3 : produc515445032on_val]: ((eval @ P @ (val_list_char @ V3) @ S2 @ E4 @ S3) => (~ (((E4 = (val_list_char @ V3)) => (~ ((S3 = S2)))))))))). % eval_cases(2)
thf(fact_23_eval__evals_OThrowThrow, axiom,
    ((![P : list_P1234162913t_char, E : exp_list_char, S_0 : produc515445032on_val, E4 : exp_list_char, S_1 : produc515445032on_val]: ((eval @ P @ E @ S_0 @ (throw_list_char @ E4) @ S_1) => (eval @ P @ (throw_list_char @ E) @ S_0 @ (throw_list_char @ E4) @ S_1))))). % eval_evals.ThrowThrow
thf(fact_24_CastFail, axiom,
    ((![P : list_P1234162913t_char, E : exp_list_char, S_0 : produc515445032on_val, A3 : nat, H : nat > option2118145160on_val, L : list_char > option_val, D : list_char, Fs : produc1257910179t_char > option_val, C : list_char]: ((eval @ P @ E @ S_0 @ (val_list_char @ (addr @ A3)) @ (produc52622304on_val @ H @ L)) => (((H @ A3) = (some_P1299442195on_val @ (produc904988266on_val @ D @ Fs))) => ((~ ((member89690956t_char @ (produc1304532571t_char @ D @ C) @ (transi1879726366t_char @ (subcls880436836t_char @ P))))) => (eval @ P @ (cast_list_char @ C @ E) @ S_0 @ (throw_list_char @ (val_list_char @ (addr @ (addr_of_sys_xcpt @ classCast)))) @ (produc52622304on_val @ H @ L)))))))). % CastFail
thf(fact_25_exp_Odistinct_I29_J, axiom,
    ((![X21 : list_char, X22 : exp_list_char, X3 : val]: (~ (((cast_list_char @ X21 @ X22) = (val_list_char @ X3))))))). % exp.distinct(29)
thf(fact_26_exp_Odistinct_I51_J, axiom,
    ((![X21 : list_char, X22 : exp_list_char, X14 : exp_list_char]: (~ (((cast_list_char @ X21 @ X22) = (throw_list_char @ X14))))))). % exp.distinct(51)
thf(fact_27_TryThrow, axiom,
    ((![P : list_P1234162913t_char, E_1 : exp_list_char, S_0 : produc515445032on_val, A3 : nat, H_1 : nat > option2118145160on_val, L_1 : list_char > option_val, D : list_char, Fs : produc1257910179t_char > option_val, C : list_char, V4 : list_char, E_2 : exp_list_char]: ((eval @ P @ E_1 @ S_0 @ (throw_list_char @ (val_list_char @ (addr @ A3))) @ (produc52622304on_val @ H_1 @ L_1)) => (((H_1 @ A3) = (some_P1299442195on_val @ (produc904988266on_val @ D @ Fs))) => ((~ ((member89690956t_char @ (produc1304532571t_char @ D @ C) @ (transi1879726366t_char @ (subcls880436836t_char @ P))))) => (eval @ P @ (tryCatch_list_char @ E_1 @ C @ V4 @ E_2) @ S_0 @ (throw_list_char @ (val_list_char @ (addr @ A3))) @ (produc52622304on_val @ H_1 @ L_1)))))))). % TryThrow
thf(fact_28_rtrancl__idemp, axiom,
    ((![R : set_Pr164112643t_char]: ((transi1879726366t_char @ (transi1879726366t_char @ R)) = (transi1879726366t_char @ R))))). % rtrancl_idemp
thf(fact_29_rtrancl__idemp, axiom,
    ((![R : set_Pr1189492743on_val]: ((transi111096263on_val @ (transi111096263on_val @ R)) = (transi111096263on_val @ R))))). % rtrancl_idemp
thf(fact_30_r__into__rtrancl, axiom,
    ((![P2 : produc1257910179t_char, R : set_Pr164112643t_char]: ((member89690956t_char @ P2 @ R) => (member89690956t_char @ P2 @ (transi1879726366t_char @ R)))))). % r_into_rtrancl
thf(fact_31_r__into__rtrancl, axiom,
    ((![P2 : produc1172664615on_val, R : set_Pr1189492743on_val]: ((member354538064on_val @ P2 @ R) => (member354538064on_val @ P2 @ (transi111096263on_val @ R)))))). % r_into_rtrancl
thf(fact_32_option_Oinject, axiom,
    ((![X2 : produc266837688on_val, Y2 : produc266837688on_val]: (((some_P1299442195on_val @ X2) = (some_P1299442195on_val @ Y2)) = (X2 = Y2))))). % option.inject
thf(fact_33_option_Oinject, axiom,
    ((![X2 : val, Y2 : val]: (((some_val @ X2) = (some_val @ Y2)) = (X2 = Y2))))). % option.inject
thf(fact_34_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_35_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_36_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_37_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_38_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_39_old_Oprod_Oinject, axiom,
    ((![A3 : list_char, B : list_char, A4 : list_char, B2 : list_char]: (((produc1304532571t_char @ A3 @ B) = (produc1304532571t_char @ A4 @ B2)) = (((A3 = A4)) & ((B = B2))))))). % old.prod.inject
thf(fact_40_old_Oprod_Oinject, axiom,
    ((![A3 : nat > option2118145160on_val, B : list_char > option_val, A4 : nat > option2118145160on_val, B2 : list_char > option_val]: (((produc52622304on_val @ A3 @ B) = (produc52622304on_val @ A4 @ B2)) = (((A3 = A4)) & ((B = B2))))))). % old.prod.inject
thf(fact_41_old_Oprod_Oinject, axiom,
    ((![A3 : list_char, B : produc1257910179t_char > option_val, A4 : list_char, B2 : produc1257910179t_char > option_val]: (((produc904988266on_val @ A3 @ B) = (produc904988266on_val @ A4 @ B2)) = (((A3 = A4)) & ((B = B2))))))). % old.prod.inject
thf(fact_42_old_Oprod_Oinject, axiom,
    ((![A3 : produc1097884484on_val, B : produc1097884484on_val, A4 : produc1097884484on_val, B2 : produc1097884484on_val]: (((produc1069526295on_val @ A3 @ B) = (produc1069526295on_val @ A4 @ B2)) = (((A3 = A4)) & ((B = B2))))))). % old.prod.inject
thf(fact_43_old_Oprod_Oinject, axiom,
    ((![A3 : exp_list_char, B : produc515445032on_val, A4 : exp_list_char, B2 : produc515445032on_val]: (((produc2023458740on_val @ A3 @ B) = (produc2023458740on_val @ A4 @ B2)) = (((A3 = A4)) & ((B = B2))))))). % old.prod.inject
thf(fact_44_rtranclE, axiom,
    ((![A3 : list_char, B : list_char, R : set_Pr164112643t_char]: ((member89690956t_char @ (produc1304532571t_char @ A3 @ B) @ (transi1879726366t_char @ R)) => ((~ ((A3 = B))) => (~ ((![Y : list_char]: ((member89690956t_char @ (produc1304532571t_char @ A3 @ Y) @ (transi1879726366t_char @ R)) => (~ ((member89690956t_char @ (produc1304532571t_char @ Y @ B) @ R)))))))))))). % rtranclE
thf(fact_45_rtranclE, axiom,
    ((![A3 : produc1097884484on_val, B : produc1097884484on_val, R : set_Pr1189492743on_val]: ((member354538064on_val @ (produc1069526295on_val @ A3 @ B) @ (transi111096263on_val @ R)) => ((~ ((A3 = B))) => (~ ((![Y : produc1097884484on_val]: ((member354538064on_val @ (produc1069526295on_val @ A3 @ Y) @ (transi111096263on_val @ R)) => (~ ((member354538064on_val @ (produc1069526295on_val @ Y @ B) @ R)))))))))))). % rtranclE
thf(fact_46_rtrancl_Ocases, axiom,
    ((![A1 : list_char, A22 : list_char, R : set_Pr164112643t_char]: ((member89690956t_char @ (produc1304532571t_char @ A1 @ A22) @ (transi1879726366t_char @ R)) => ((~ ((A22 = A1))) => (~ ((![B3 : list_char]: ((member89690956t_char @ (produc1304532571t_char @ A1 @ B3) @ (transi1879726366t_char @ R)) => (~ ((member89690956t_char @ (produc1304532571t_char @ B3 @ A22) @ R)))))))))))). % rtrancl.cases
thf(fact_47_rtrancl_Ocases, axiom,
    ((![A1 : produc1097884484on_val, A22 : produc1097884484on_val, R : set_Pr1189492743on_val]: ((member354538064on_val @ (produc1069526295on_val @ A1 @ A22) @ (transi111096263on_val @ R)) => ((~ ((A22 = A1))) => (~ ((![B3 : produc1097884484on_val]: ((member354538064on_val @ (produc1069526295on_val @ A1 @ B3) @ (transi111096263on_val @ R)) => (~ ((member354538064on_val @ (produc1069526295on_val @ B3 @ A22) @ R)))))))))))). % rtrancl.cases
thf(fact_48_rtrancl_Osimps, axiom,
    ((![A1 : list_char, A22 : list_char, R : set_Pr164112643t_char]: ((member89690956t_char @ (produc1304532571t_char @ A1 @ A22) @ (transi1879726366t_char @ R)) = (((?[A2 : list_char]: (((A1 = A2)) & ((A22 = A2))))) | ((?[A2 : list_char]: (?[B4 : list_char]: (?[C2 : list_char]: (((A1 = A2)) & ((((A22 = C2)) & ((((member89690956t_char @ (produc1304532571t_char @ A2 @ B4) @ (transi1879726366t_char @ R))) & ((member89690956t_char @ (produc1304532571t_char @ B4 @ C2) @ R)))))))))))))))). % rtrancl.simps
thf(fact_49_rtrancl_Osimps, axiom,
    ((![A1 : produc1097884484on_val, A22 : produc1097884484on_val, R : set_Pr1189492743on_val]: ((member354538064on_val @ (produc1069526295on_val @ A1 @ A22) @ (transi111096263on_val @ R)) = (((?[A2 : produc1097884484on_val]: (((A1 = A2)) & ((A22 = A2))))) | ((?[A2 : produc1097884484on_val]: (?[B4 : produc1097884484on_val]: (?[C2 : produc1097884484on_val]: (((A1 = A2)) & ((((A22 = C2)) & ((((member354538064on_val @ (produc1069526295on_val @ A2 @ B4) @ (transi111096263on_val @ R))) & ((member354538064on_val @ (produc1069526295on_val @ B4 @ C2) @ R)))))))))))))))). % rtrancl.simps
thf(fact_50_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_51_rtrancl__induct2, axiom,
    ((![Ax : list_char, Ay : list_char, Bx : list_char, By : list_char, R : set_Pr729957319t_char, P : list_char > list_char > $o]: ((member803902992t_char @ (produc395356247t_char @ (produc1304532571t_char @ Ax @ Ay) @ (produc1304532571t_char @ Bx @ By)) @ (transi858104614t_char @ R)) => ((P @ Ax @ Ay) => ((![A : list_char, B3 : list_char, Aa : list_char, Ba : list_char]: ((member803902992t_char @ (produc395356247t_char @ (produc1304532571t_char @ Ax @ Ay) @ (produc1304532571t_char @ A @ B3)) @ (transi858104614t_char @ R)) => ((member803902992t_char @ (produc395356247t_char @ (produc1304532571t_char @ A @ B3) @ (produc1304532571t_char @ Aa @ Ba)) @ R) => ((P @ A @ B3) => (P @ Aa @ Ba))))) => (P @ Bx @ By))))))). % rtrancl_induct2
thf(fact_52_rtrancl__induct2, axiom,
    ((![Ax : nat > option2118145160on_val, Ay : list_char > option_val, Bx : nat > option2118145160on_val, By : list_char > option_val, R : 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 @ R)) => ((P @ Ax @ Ay) => ((![A : nat > option2118145160on_val, B3 : list_char > option_val, Aa : nat > option2118145160on_val, Ba : list_char > option_val]: ((member2027247312on_val @ (produc2106877847on_val @ (produc52622304on_val @ Ax @ Ay) @ (produc52622304on_val @ A @ B3)) @ (transi432893227on_val @ R)) => ((member2027247312on_val @ (produc2106877847on_val @ (produc52622304on_val @ A @ B3) @ (produc52622304on_val @ Aa @ Ba)) @ R) => ((P @ A @ B3) => (P @ Aa @ Ba))))) => (P @ Bx @ By))))))). % rtrancl_induct2
thf(fact_53_rtrancl__induct2, axiom,
    ((![Ax : list_char, Ay : produc1257910179t_char > option_val, Bx : list_char, By : produc1257910179t_char > option_val, R : 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 @ R)) => ((P @ Ax @ Ay) => ((![A : list_char, B3 : produc1257910179t_char > option_val, Aa : list_char, Ba : produc1257910179t_char > option_val]: ((member197592058on_val @ (produc881885833on_val @ (produc904988266on_val @ Ax @ Ay) @ (produc904988266on_val @ A @ B3)) @ (transi2071064181on_val @ R)) => ((member197592058on_val @ (produc881885833on_val @ (produc904988266on_val @ A @ B3) @ (produc904988266on_val @ Aa @ Ba)) @ R) => ((P @ A @ B3) => (P @ Aa @ Ba))))) => (P @ Bx @ By))))))). % rtrancl_induct2
thf(fact_54_rtrancl__induct2, axiom,
    ((![Ax : produc1097884484on_val, Ay : produc1097884484on_val, Bx : produc1097884484on_val, By : produc1097884484on_val, R : set_Pr1368603847on_val, P : produc1097884484on_val > produc1097884484on_val > $o]: ((member208988944on_val @ (produc564964183on_val @ (produc1069526295on_val @ Ax @ Ay) @ (produc1069526295on_val @ Bx @ By)) @ (transi100378922on_val @ R)) => ((P @ Ax @ Ay) => ((![A : produc1097884484on_val, B3 : produc1097884484on_val, Aa : produc1097884484on_val, Ba : produc1097884484on_val]: ((member208988944on_val @ (produc564964183on_val @ (produc1069526295on_val @ Ax @ Ay) @ (produc1069526295on_val @ A @ B3)) @ (transi100378922on_val @ R)) => ((member208988944on_val @ (produc564964183on_val @ (produc1069526295on_val @ A @ B3) @ (produc1069526295on_val @ Aa @ Ba)) @ R) => ((P @ A @ B3) => (P @ Aa @ Ba))))) => (P @ Bx @ By))))))). % rtrancl_induct2
thf(fact_55_rtrancl__induct2, axiom,
    ((![Ax : exp_list_char, Ay : produc515445032on_val, Bx : exp_list_char, By : produc515445032on_val, R : set_Pr1189492743on_val, P : exp_list_char > produc515445032on_val > $o]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ Ax @ Ay) @ (produc2023458740on_val @ Bx @ By)) @ (transi111096263on_val @ R)) => ((P @ Ax @ Ay) => ((![A : exp_list_char, B3 : produc515445032on_val, Aa : exp_list_char, Ba : produc515445032on_val]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ Ax @ Ay) @ (produc2023458740on_val @ A @ B3)) @ (transi111096263on_val @ R)) => ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ A @ B3) @ (produc2023458740on_val @ Aa @ Ba)) @ R) => ((P @ A @ B3) => (P @ Aa @ Ba))))) => (P @ Bx @ By))))))). % rtrancl_induct2
thf(fact_56_converse__rtranclE2, axiom,
    ((![Xa : list_char, Xb : list_char, Za : list_char, Zb : list_char, R : set_Pr729957319t_char]: ((member803902992t_char @ (produc395356247t_char @ (produc1304532571t_char @ Xa @ Xb) @ (produc1304532571t_char @ Za @ Zb)) @ (transi858104614t_char @ R)) => ((~ (((produc1304532571t_char @ Xa @ Xb) = (produc1304532571t_char @ Za @ Zb)))) => (~ ((![A : list_char, B3 : list_char]: ((member803902992t_char @ (produc395356247t_char @ (produc1304532571t_char @ Xa @ Xb) @ (produc1304532571t_char @ A @ B3)) @ R) => (~ ((member803902992t_char @ (produc395356247t_char @ (produc1304532571t_char @ A @ B3) @ (produc1304532571t_char @ Za @ Zb)) @ (transi858104614t_char @ R))))))))))))). % converse_rtranclE2
thf(fact_57_converse__rtranclE2, axiom,
    ((![Xa : nat > option2118145160on_val, Xb : list_char > option_val, Za : nat > option2118145160on_val, Zb : list_char > option_val, R : set_Pr148564103on_val]: ((member2027247312on_val @ (produc2106877847on_val @ (produc52622304on_val @ Xa @ Xb) @ (produc52622304on_val @ Za @ Zb)) @ (transi432893227on_val @ R)) => ((~ (((produc52622304on_val @ Xa @ Xb) = (produc52622304on_val @ Za @ Zb)))) => (~ ((![A : nat > option2118145160on_val, B3 : list_char > option_val]: ((member2027247312on_val @ (produc2106877847on_val @ (produc52622304on_val @ Xa @ Xb) @ (produc52622304on_val @ A @ B3)) @ R) => (~ ((member2027247312on_val @ (produc2106877847on_val @ (produc52622304on_val @ A @ B3) @ (produc52622304on_val @ Za @ Zb)) @ (transi432893227on_val @ R))))))))))))). % converse_rtranclE2
thf(fact_58_converse__rtranclE2, axiom,
    ((![Xa : list_char, Xb : produc1257910179t_char > option_val, Za : list_char, Zb : produc1257910179t_char > option_val, R : set_Pr2110063281on_val]: ((member197592058on_val @ (produc881885833on_val @ (produc904988266on_val @ Xa @ Xb) @ (produc904988266on_val @ Za @ Zb)) @ (transi2071064181on_val @ R)) => ((~ (((produc904988266on_val @ Xa @ Xb) = (produc904988266on_val @ Za @ Zb)))) => (~ ((![A : list_char, B3 : produc1257910179t_char > option_val]: ((member197592058on_val @ (produc881885833on_val @ (produc904988266on_val @ Xa @ Xb) @ (produc904988266on_val @ A @ B3)) @ R) => (~ ((member197592058on_val @ (produc881885833on_val @ (produc904988266on_val @ A @ B3) @ (produc904988266on_val @ Za @ Zb)) @ (transi2071064181on_val @ R))))))))))))). % converse_rtranclE2
thf(fact_59_converse__rtranclE2, axiom,
    ((![Xa : produc1097884484on_val, Xb : produc1097884484on_val, Za : produc1097884484on_val, Zb : produc1097884484on_val, R : set_Pr1368603847on_val]: ((member208988944on_val @ (produc564964183on_val @ (produc1069526295on_val @ Xa @ Xb) @ (produc1069526295on_val @ Za @ Zb)) @ (transi100378922on_val @ R)) => ((~ (((produc1069526295on_val @ Xa @ Xb) = (produc1069526295on_val @ Za @ Zb)))) => (~ ((![A : produc1097884484on_val, B3 : produc1097884484on_val]: ((member208988944on_val @ (produc564964183on_val @ (produc1069526295on_val @ Xa @ Xb) @ (produc1069526295on_val @ A @ B3)) @ R) => (~ ((member208988944on_val @ (produc564964183on_val @ (produc1069526295on_val @ A @ B3) @ (produc1069526295on_val @ Za @ Zb)) @ (transi100378922on_val @ R))))))))))))). % converse_rtranclE2
thf(fact_60_converse__rtranclE2, axiom,
    ((![Xa : exp_list_char, Xb : produc515445032on_val, Za : exp_list_char, Zb : produc515445032on_val, R : set_Pr1189492743on_val]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ Xa @ Xb) @ (produc2023458740on_val @ Za @ Zb)) @ (transi111096263on_val @ R)) => ((~ (((produc2023458740on_val @ Xa @ Xb) = (produc2023458740on_val @ Za @ Zb)))) => (~ ((![A : exp_list_char, B3 : produc515445032on_val]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ Xa @ Xb) @ (produc2023458740on_val @ A @ B3)) @ R) => (~ ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ A @ B3) @ (produc2023458740on_val @ Za @ Zb)) @ (transi111096263on_val @ R))))))))))))). % converse_rtranclE2
thf(fact_61_converse__rtrancl__induct2, axiom,
    ((![Ax : list_char, Ay : list_char, Bx : list_char, By : list_char, R : set_Pr729957319t_char, P : list_char > list_char > $o]: ((member803902992t_char @ (produc395356247t_char @ (produc1304532571t_char @ Ax @ Ay) @ (produc1304532571t_char @ Bx @ By)) @ (transi858104614t_char @ R)) => ((P @ Bx @ By) => ((![A : list_char, B3 : list_char, Aa : list_char, Ba : list_char]: ((member803902992t_char @ (produc395356247t_char @ (produc1304532571t_char @ A @ B3) @ (produc1304532571t_char @ Aa @ Ba)) @ R) => ((member803902992t_char @ (produc395356247t_char @ (produc1304532571t_char @ Aa @ Ba) @ (produc1304532571t_char @ Bx @ By)) @ (transi858104614t_char @ R)) => ((P @ Aa @ Ba) => (P @ A @ B3))))) => (P @ Ax @ Ay))))))). % converse_rtrancl_induct2
thf(fact_62_converse__rtrancl__induct2, axiom,
    ((![Ax : nat > option2118145160on_val, Ay : list_char > option_val, Bx : nat > option2118145160on_val, By : list_char > option_val, R : 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 @ R)) => ((P @ Bx @ By) => ((![A : nat > option2118145160on_val, B3 : list_char > option_val, Aa : nat > option2118145160on_val, Ba : list_char > option_val]: ((member2027247312on_val @ (produc2106877847on_val @ (produc52622304on_val @ A @ B3) @ (produc52622304on_val @ Aa @ Ba)) @ R) => ((member2027247312on_val @ (produc2106877847on_val @ (produc52622304on_val @ Aa @ Ba) @ (produc52622304on_val @ Bx @ By)) @ (transi432893227on_val @ R)) => ((P @ Aa @ Ba) => (P @ A @ B3))))) => (P @ Ax @ Ay))))))). % converse_rtrancl_induct2
thf(fact_63_converse__rtrancl__induct2, axiom,
    ((![Ax : list_char, Ay : produc1257910179t_char > option_val, Bx : list_char, By : produc1257910179t_char > option_val, R : 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 @ R)) => ((P @ Bx @ By) => ((![A : list_char, B3 : produc1257910179t_char > option_val, Aa : list_char, Ba : produc1257910179t_char > option_val]: ((member197592058on_val @ (produc881885833on_val @ (produc904988266on_val @ A @ B3) @ (produc904988266on_val @ Aa @ Ba)) @ R) => ((member197592058on_val @ (produc881885833on_val @ (produc904988266on_val @ Aa @ Ba) @ (produc904988266on_val @ Bx @ By)) @ (transi2071064181on_val @ R)) => ((P @ Aa @ Ba) => (P @ A @ B3))))) => (P @ Ax @ Ay))))))). % converse_rtrancl_induct2
thf(fact_64_converse__rtrancl__induct2, axiom,
    ((![Ax : produc1097884484on_val, Ay : produc1097884484on_val, Bx : produc1097884484on_val, By : produc1097884484on_val, R : set_Pr1368603847on_val, P : produc1097884484on_val > produc1097884484on_val > $o]: ((member208988944on_val @ (produc564964183on_val @ (produc1069526295on_val @ Ax @ Ay) @ (produc1069526295on_val @ Bx @ By)) @ (transi100378922on_val @ R)) => ((P @ Bx @ By) => ((![A : produc1097884484on_val, B3 : produc1097884484on_val, Aa : produc1097884484on_val, Ba : produc1097884484on_val]: ((member208988944on_val @ (produc564964183on_val @ (produc1069526295on_val @ A @ B3) @ (produc1069526295on_val @ Aa @ Ba)) @ R) => ((member208988944on_val @ (produc564964183on_val @ (produc1069526295on_val @ Aa @ Ba) @ (produc1069526295on_val @ Bx @ By)) @ (transi100378922on_val @ R)) => ((P @ Aa @ Ba) => (P @ A @ B3))))) => (P @ Ax @ Ay))))))). % converse_rtrancl_induct2
thf(fact_65_converse__rtrancl__induct2, axiom,
    ((![Ax : exp_list_char, Ay : produc515445032on_val, Bx : exp_list_char, By : produc515445032on_val, R : set_Pr1189492743on_val, P : exp_list_char > produc515445032on_val > $o]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ Ax @ Ay) @ (produc2023458740on_val @ Bx @ By)) @ (transi111096263on_val @ R)) => ((P @ Bx @ By) => ((![A : exp_list_char, B3 : produc515445032on_val, Aa : exp_list_char, Ba : produc515445032on_val]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ A @ B3) @ (produc2023458740on_val @ Aa @ Ba)) @ R) => ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ Aa @ Ba) @ (produc2023458740on_val @ Bx @ By)) @ (transi111096263on_val @ R)) => ((P @ Aa @ Ba) => (P @ A @ B3))))) => (P @ Ax @ Ay))))))). % converse_rtrancl_induct2
thf(fact_66_exp_Odistinct_I77_J, axiom,
    ((![X3 : val, X151 : exp_list_char, X152 : list_char, X153 : list_char, X154 : exp_list_char]: (~ (((val_list_char @ X3) = (tryCatch_list_char @ X151 @ X152 @ X153 @ X154))))))). % exp.distinct(77)
thf(fact_67_exp_Odistinct_I209_J, axiom,
    ((![X14 : exp_list_char, X151 : exp_list_char, X152 : list_char, X153 : list_char, X154 : exp_list_char]: (~ (((throw_list_char @ X14) = (tryCatch_list_char @ X151 @ X152 @ X153 @ X154))))))). % exp.distinct(209)
thf(fact_68_exp_Odistinct_I53_J, axiom,
    ((![X21 : list_char, X22 : exp_list_char, X151 : exp_list_char, X152 : list_char, X153 : list_char, X154 : exp_list_char]: (~ (((cast_list_char @ X21 @ X22) = (tryCatch_list_char @ X151 @ X152 @ X153 @ X154))))))). % exp.distinct(53)
thf(fact_69_Try, axiom,
    ((![P : list_P1234162913t_char, E_1 : exp_list_char, S_0 : produc515445032on_val, V_1 : val, S_1 : produc515445032on_val, C : list_char, V4 : list_char, E_2 : exp_list_char]: ((eval @ P @ E_1 @ S_0 @ (val_list_char @ V_1) @ S_1) => (eval @ P @ (tryCatch_list_char @ E_1 @ C @ V4 @ E_2) @ S_0 @ (val_list_char @ V_1) @ S_1))))). % Try
thf(fact_70_old_Oprod_Oinducts, axiom,
    ((![P : produc1257910179t_char > $o, Prod : produc1257910179t_char]: ((![A : list_char, B3 : list_char]: (P @ (produc1304532571t_char @ A @ B3))) => (P @ Prod))))). % old.prod.inducts
thf(fact_71_old_Oprod_Oinducts, axiom,
    ((![P : produc515445032on_val > $o, Prod : produc515445032on_val]: ((![A : nat > option2118145160on_val, B3 : list_char > option_val]: (P @ (produc52622304on_val @ A @ B3))) => (P @ Prod))))). % old.prod.inducts
thf(fact_72_old_Oprod_Oinducts, axiom,
    ((![P : produc266837688on_val > $o, Prod : produc266837688on_val]: ((![A : list_char, B3 : produc1257910179t_char > option_val]: (P @ (produc904988266on_val @ A @ B3))) => (P @ Prod))))). % old.prod.inducts
thf(fact_73_old_Oprod_Oinducts, axiom,
    ((![P : produc1172664615on_val > $o, Prod : produc1172664615on_val]: ((![A : produc1097884484on_val, B3 : produc1097884484on_val]: (P @ (produc1069526295on_val @ A @ B3))) => (P @ Prod))))). % old.prod.inducts
thf(fact_74_old_Oprod_Oinducts, axiom,
    ((![P : produc1097884484on_val > $o, Prod : produc1097884484on_val]: ((![A : exp_list_char, B3 : produc515445032on_val]: (P @ (produc2023458740on_val @ A @ B3))) => (P @ Prod))))). % old.prod.inducts
thf(fact_75_mem__Collect__eq, axiom,
    ((![A3 : produc1257910179t_char, P : produc1257910179t_char > $o]: ((member89690956t_char @ A3 @ (collec768236686t_char @ P)) = (P @ A3))))). % mem_Collect_eq
thf(fact_76_mem__Collect__eq, axiom,
    ((![A3 : produc1172664615on_val, P : produc1172664615on_val > $o]: ((member354538064on_val @ A3 @ (collec2055896722on_val @ P)) = (P @ A3))))). % mem_Collect_eq
thf(fact_77_Collect__mem__eq, axiom,
    ((![A5 : set_Pr164112643t_char]: ((collec768236686t_char @ (^[X : produc1257910179t_char]: (member89690956t_char @ X @ A5))) = A5)))). % Collect_mem_eq
thf(fact_78_Collect__mem__eq, axiom,
    ((![A5 : set_Pr1189492743on_val]: ((collec2055896722on_val @ (^[X : produc1172664615on_val]: (member354538064on_val @ X @ A5))) = A5)))). % Collect_mem_eq
thf(fact_79_old_Oprod_Oexhaust, axiom,
    ((![Y4 : produc1257910179t_char]: (~ ((![A : list_char, B3 : list_char]: (~ ((Y4 = (produc1304532571t_char @ A @ B3)))))))))). % old.prod.exhaust
thf(fact_80_old_Oprod_Oexhaust, axiom,
    ((![Y4 : produc515445032on_val]: (~ ((![A : nat > option2118145160on_val, B3 : list_char > option_val]: (~ ((Y4 = (produc52622304on_val @ A @ B3)))))))))). % old.prod.exhaust
thf(fact_81_old_Oprod_Oexhaust, axiom,
    ((![Y4 : produc266837688on_val]: (~ ((![A : list_char, B3 : produc1257910179t_char > option_val]: (~ ((Y4 = (produc904988266on_val @ A @ B3)))))))))). % old.prod.exhaust
thf(fact_82_old_Oprod_Oexhaust, axiom,
    ((![Y4 : produc1172664615on_val]: (~ ((![A : produc1097884484on_val, B3 : produc1097884484on_val]: (~ ((Y4 = (produc1069526295on_val @ A @ B3)))))))))). % old.prod.exhaust
thf(fact_83_old_Oprod_Oexhaust, axiom,
    ((![Y4 : produc1097884484on_val]: (~ ((![A : exp_list_char, B3 : produc515445032on_val]: (~ ((Y4 = (produc2023458740on_val @ A @ B3)))))))))). % old.prod.exhaust
thf(fact_84_prod__induct4, axiom,
    ((![P : produc1172664615on_val > $o, X4 : produc1172664615on_val]: ((![A : produc1097884484on_val, B3 : exp_list_char, C3 : nat > option2118145160on_val, D2 : list_char > option_val]: (P @ (produc1069526295on_val @ A @ (produc2023458740on_val @ B3 @ (produc52622304on_val @ C3 @ D2))))) => (P @ X4))))). % prod_induct4
thf(fact_85_prod__induct3, axiom,
    ((![P : produc1172664615on_val > $o, X4 : produc1172664615on_val]: ((![A : produc1097884484on_val, B3 : exp_list_char, C3 : produc515445032on_val]: (P @ (produc1069526295on_val @ A @ (produc2023458740on_val @ B3 @ C3)))) => (P @ X4))))). % prod_induct3
thf(fact_86_prod__induct3, axiom,
    ((![P : produc1097884484on_val > $o, X4 : produc1097884484on_val]: ((![A : exp_list_char, B3 : nat > option2118145160on_val, C3 : list_char > option_val]: (P @ (produc2023458740on_val @ A @ (produc52622304on_val @ B3 @ C3)))) => (P @ X4))))). % prod_induct3
thf(fact_87_prod__cases4, axiom,
    ((![Y4 : produc1172664615on_val]: (~ ((![A : produc1097884484on_val, B3 : exp_list_char, C3 : nat > option2118145160on_val, D2 : list_char > option_val]: (~ ((Y4 = (produc1069526295on_val @ A @ (produc2023458740on_val @ B3 @ (produc52622304on_val @ C3 @ D2)))))))))))). % prod_cases4
thf(fact_88_prod__cases3, axiom,
    ((![Y4 : produc1172664615on_val]: (~ ((![A : produc1097884484on_val, B3 : exp_list_char, C3 : produc515445032on_val]: (~ ((Y4 = (produc1069526295on_val @ A @ (produc2023458740on_val @ B3 @ C3))))))))))). % prod_cases3
thf(fact_89_prod__cases3, axiom,
    ((![Y4 : produc1097884484on_val]: (~ ((![A : exp_list_char, B3 : nat > option2118145160on_val, C3 : list_char > option_val]: (~ ((Y4 = (produc2023458740on_val @ A @ (produc52622304on_val @ B3 @ C3))))))))))). % prod_cases3
thf(fact_90_Pair__inject, axiom,
    ((![A3 : list_char, B : list_char, A4 : list_char, B2 : list_char]: (((produc1304532571t_char @ A3 @ B) = (produc1304532571t_char @ A4 @ B2)) => (~ (((A3 = A4) => (~ ((B = B2)))))))))). % Pair_inject
thf(fact_91_Pair__inject, axiom,
    ((![A3 : nat > option2118145160on_val, B : list_char > option_val, A4 : nat > option2118145160on_val, B2 : list_char > option_val]: (((produc52622304on_val @ A3 @ B) = (produc52622304on_val @ A4 @ B2)) => (~ (((A3 = A4) => (~ ((B = B2)))))))))). % Pair_inject
thf(fact_92_Pair__inject, axiom,
    ((![A3 : list_char, B : produc1257910179t_char > option_val, A4 : list_char, B2 : produc1257910179t_char > option_val]: (((produc904988266on_val @ A3 @ B) = (produc904988266on_val @ A4 @ B2)) => (~ (((A3 = A4) => (~ ((B = B2)))))))))). % Pair_inject
thf(fact_93_Pair__inject, axiom,
    ((![A3 : produc1097884484on_val, B : produc1097884484on_val, A4 : produc1097884484on_val, B2 : produc1097884484on_val]: (((produc1069526295on_val @ A3 @ B) = (produc1069526295on_val @ A4 @ B2)) => (~ (((A3 = A4) => (~ ((B = B2)))))))))). % Pair_inject
thf(fact_94_Pair__inject, axiom,
    ((![A3 : exp_list_char, B : produc515445032on_val, A4 : exp_list_char, B2 : produc515445032on_val]: (((produc2023458740on_val @ A3 @ B) = (produc2023458740on_val @ A4 @ B2)) => (~ (((A3 = A4) => (~ ((B = B2)))))))))). % Pair_inject
thf(fact_95_prod__cases, axiom,
    ((![P : produc1257910179t_char > $o, P2 : produc1257910179t_char]: ((![A : list_char, B3 : list_char]: (P @ (produc1304532571t_char @ A @ B3))) => (P @ P2))))). % prod_cases
thf(fact_96_prod__cases, axiom,
    ((![P : produc515445032on_val > $o, P2 : produc515445032on_val]: ((![A : nat > option2118145160on_val, B3 : list_char > option_val]: (P @ (produc52622304on_val @ A @ B3))) => (P @ P2))))). % prod_cases
thf(fact_97_prod__cases, axiom,
    ((![P : produc266837688on_val > $o, P2 : produc266837688on_val]: ((![A : list_char, B3 : produc1257910179t_char > option_val]: (P @ (produc904988266on_val @ A @ B3))) => (P @ P2))))). % prod_cases
thf(fact_98_prod__cases, axiom,
    ((![P : produc1172664615on_val > $o, P2 : produc1172664615on_val]: ((![A : produc1097884484on_val, B3 : produc1097884484on_val]: (P @ (produc1069526295on_val @ A @ B3))) => (P @ P2))))). % prod_cases
thf(fact_99_prod__cases, axiom,
    ((![P : produc1097884484on_val > $o, P2 : produc1097884484on_val]: ((![A : exp_list_char, B3 : produc515445032on_val]: (P @ (produc2023458740on_val @ A @ B3))) => (P @ P2))))). % prod_cases
thf(fact_100_surj__pair, axiom,
    ((![P2 : produc1257910179t_char]: (?[X6 : list_char, Y : list_char]: (P2 = (produc1304532571t_char @ X6 @ Y)))))). % surj_pair
thf(fact_101_surj__pair, axiom,
    ((![P2 : produc515445032on_val]: (?[X6 : nat > option2118145160on_val, Y : list_char > option_val]: (P2 = (produc52622304on_val @ X6 @ Y)))))). % surj_pair
thf(fact_102_surj__pair, axiom,
    ((![P2 : produc266837688on_val]: (?[X6 : list_char, Y : produc1257910179t_char > option_val]: (P2 = (produc904988266on_val @ X6 @ Y)))))). % surj_pair
thf(fact_103_surj__pair, axiom,
    ((![P2 : produc1172664615on_val]: (?[X6 : produc1097884484on_val, Y : produc1097884484on_val]: (P2 = (produc1069526295on_val @ X6 @ Y)))))). % surj_pair
thf(fact_104_surj__pair, axiom,
    ((![P2 : produc1097884484on_val]: (?[X6 : exp_list_char, Y : produc515445032on_val]: (P2 = (produc2023458740on_val @ X6 @ Y)))))). % surj_pair
thf(fact_105_converse__rtrancl__into__rtrancl, axiom,
    ((![A3 : list_char, B : list_char, R : set_Pr164112643t_char, C4 : list_char]: ((member89690956t_char @ (produc1304532571t_char @ A3 @ B) @ R) => ((member89690956t_char @ (produc1304532571t_char @ B @ C4) @ (transi1879726366t_char @ R)) => (member89690956t_char @ (produc1304532571t_char @ A3 @ C4) @ (transi1879726366t_char @ R))))))). % converse_rtrancl_into_rtrancl
thf(fact_106_converse__rtrancl__into__rtrancl, axiom,
    ((![A3 : produc1097884484on_val, B : produc1097884484on_val, R : set_Pr1189492743on_val, C4 : produc1097884484on_val]: ((member354538064on_val @ (produc1069526295on_val @ A3 @ B) @ R) => ((member354538064on_val @ (produc1069526295on_val @ B @ C4) @ (transi111096263on_val @ R)) => (member354538064on_val @ (produc1069526295on_val @ A3 @ C4) @ (transi111096263on_val @ R))))))). % converse_rtrancl_into_rtrancl
thf(fact_107_rtrancl_Ortrancl__into__rtrancl, axiom,
    ((![A3 : list_char, B : list_char, R : set_Pr164112643t_char, C4 : list_char]: ((member89690956t_char @ (produc1304532571t_char @ A3 @ B) @ (transi1879726366t_char @ R)) => ((member89690956t_char @ (produc1304532571t_char @ B @ C4) @ R) => (member89690956t_char @ (produc1304532571t_char @ A3 @ C4) @ (transi1879726366t_char @ R))))))). % rtrancl.rtrancl_into_rtrancl
thf(fact_108_rtrancl_Ortrancl__into__rtrancl, axiom,
    ((![A3 : produc1097884484on_val, B : produc1097884484on_val, R : set_Pr1189492743on_val, C4 : produc1097884484on_val]: ((member354538064on_val @ (produc1069526295on_val @ A3 @ B) @ (transi111096263on_val @ R)) => ((member354538064on_val @ (produc1069526295on_val @ B @ C4) @ R) => (member354538064on_val @ (produc1069526295on_val @ A3 @ C4) @ (transi111096263on_val @ R))))))). % rtrancl.rtrancl_into_rtrancl
thf(fact_109_converse__rtrancl__induct, axiom,
    ((![A3 : list_char, B : list_char, R : set_Pr164112643t_char, P : list_char > $o]: ((member89690956t_char @ (produc1304532571t_char @ A3 @ B) @ (transi1879726366t_char @ R)) => ((P @ B) => ((![Y : list_char, Z : list_char]: ((member89690956t_char @ (produc1304532571t_char @ Y @ Z) @ R) => ((member89690956t_char @ (produc1304532571t_char @ Z @ B) @ (transi1879726366t_char @ R)) => ((P @ Z) => (P @ Y))))) => (P @ A3))))))). % converse_rtrancl_induct
thf(fact_110_converse__rtrancl__induct, axiom,
    ((![A3 : produc1097884484on_val, B : produc1097884484on_val, R : set_Pr1189492743on_val, P : produc1097884484on_val > $o]: ((member354538064on_val @ (produc1069526295on_val @ A3 @ B) @ (transi111096263on_val @ R)) => ((P @ B) => ((![Y : produc1097884484on_val, Z : produc1097884484on_val]: ((member354538064on_val @ (produc1069526295on_val @ Y @ Z) @ R) => ((member354538064on_val @ (produc1069526295on_val @ Z @ B) @ (transi111096263on_val @ R)) => ((P @ Z) => (P @ Y))))) => (P @ A3))))))). % converse_rtrancl_induct
thf(fact_111_rtrancl_Ortrancl__refl, axiom,
    ((![A3 : list_char, R : set_Pr164112643t_char]: (member89690956t_char @ (produc1304532571t_char @ A3 @ A3) @ (transi1879726366t_char @ R))))). % rtrancl.rtrancl_refl
thf(fact_112_rtrancl_Ortrancl__refl, axiom,
    ((![A3 : produc1097884484on_val, R : set_Pr1189492743on_val]: (member354538064on_val @ (produc1069526295on_val @ A3 @ A3) @ (transi111096263on_val @ R))))). % rtrancl.rtrancl_refl
thf(fact_113_converse__rtranclE, axiom,
    ((![X4 : list_char, Z2 : list_char, R : set_Pr164112643t_char]: ((member89690956t_char @ (produc1304532571t_char @ X4 @ Z2) @ (transi1879726366t_char @ R)) => ((~ ((X4 = Z2))) => (~ ((![Y : list_char]: ((member89690956t_char @ (produc1304532571t_char @ X4 @ Y) @ R) => (~ ((member89690956t_char @ (produc1304532571t_char @ Y @ Z2) @ (transi1879726366t_char @ R))))))))))))). % converse_rtranclE
thf(fact_114_converse__rtranclE, axiom,
    ((![X4 : produc1097884484on_val, Z2 : produc1097884484on_val, R : set_Pr1189492743on_val]: ((member354538064on_val @ (produc1069526295on_val @ X4 @ Z2) @ (transi111096263on_val @ R)) => ((~ ((X4 = Z2))) => (~ ((![Y : produc1097884484on_val]: ((member354538064on_val @ (produc1069526295on_val @ X4 @ Y) @ R) => (~ ((member354538064on_val @ (produc1069526295on_val @ Y @ Z2) @ (transi111096263on_val @ R))))))))))))). % converse_rtranclE
thf(fact_115_rtrancl_Oinducts, axiom,
    ((![X1 : list_char, X2 : list_char, R : set_Pr164112643t_char, P : list_char > list_char > $o]: ((member89690956t_char @ (produc1304532571t_char @ X1 @ X2) @ (transi1879726366t_char @ R)) => ((![A : list_char]: (P @ A @ A)) => ((![A : list_char, B3 : list_char, C3 : list_char]: ((member89690956t_char @ (produc1304532571t_char @ A @ B3) @ (transi1879726366t_char @ R)) => ((P @ A @ B3) => ((member89690956t_char @ (produc1304532571t_char @ B3 @ C3) @ R) => (P @ A @ C3))))) => (P @ X1 @ X2))))))). % rtrancl.inducts
thf(fact_116_rtrancl_Oinducts, axiom,
    ((![X1 : produc1097884484on_val, X2 : produc1097884484on_val, R : set_Pr1189492743on_val, P : produc1097884484on_val > produc1097884484on_val > $o]: ((member354538064on_val @ (produc1069526295on_val @ X1 @ X2) @ (transi111096263on_val @ R)) => ((![A : produc1097884484on_val]: (P @ A @ A)) => ((![A : produc1097884484on_val, B3 : produc1097884484on_val, C3 : produc1097884484on_val]: ((member354538064on_val @ (produc1069526295on_val @ A @ B3) @ (transi111096263on_val @ R)) => ((P @ A @ B3) => ((member354538064on_val @ (produc1069526295on_val @ B3 @ C3) @ R) => (P @ A @ C3))))) => (P @ X1 @ X2))))))). % rtrancl.inducts
thf(fact_117_rtrancl__induct, axiom,
    ((![A3 : list_char, B : list_char, R : set_Pr164112643t_char, P : list_char > $o]: ((member89690956t_char @ (produc1304532571t_char @ A3 @ B) @ (transi1879726366t_char @ R)) => ((P @ A3) => ((![Y : list_char, Z : list_char]: ((member89690956t_char @ (produc1304532571t_char @ A3 @ Y) @ (transi1879726366t_char @ R)) => ((member89690956t_char @ (produc1304532571t_char @ Y @ Z) @ R) => ((P @ Y) => (P @ Z))))) => (P @ B))))))). % rtrancl_induct
thf(fact_118_rtrancl__induct, axiom,
    ((![A3 : produc1097884484on_val, B : produc1097884484on_val, R : set_Pr1189492743on_val, P : produc1097884484on_val > $o]: ((member354538064on_val @ (produc1069526295on_val @ A3 @ B) @ (transi111096263on_val @ R)) => ((P @ A3) => ((![Y : produc1097884484on_val, Z : produc1097884484on_val]: ((member354538064on_val @ (produc1069526295on_val @ A3 @ Y) @ (transi111096263on_val @ R)) => ((member354538064on_val @ (produc1069526295on_val @ Y @ Z) @ R) => ((P @ Y) => (P @ Z))))) => (P @ B))))))). % rtrancl_induct
thf(fact_119_rtrancl__trans, axiom,
    ((![X4 : list_char, Y4 : list_char, R : set_Pr164112643t_char, Z2 : list_char]: ((member89690956t_char @ (produc1304532571t_char @ X4 @ Y4) @ (transi1879726366t_char @ R)) => ((member89690956t_char @ (produc1304532571t_char @ Y4 @ Z2) @ (transi1879726366t_char @ R)) => (member89690956t_char @ (produc1304532571t_char @ X4 @ Z2) @ (transi1879726366t_char @ R))))))). % rtrancl_trans
thf(fact_120_rtrancl__trans, axiom,
    ((![X4 : produc1097884484on_val, Y4 : produc1097884484on_val, R : set_Pr1189492743on_val, Z2 : produc1097884484on_val]: ((member354538064on_val @ (produc1069526295on_val @ X4 @ Y4) @ (transi111096263on_val @ R)) => ((member354538064on_val @ (produc1069526295on_val @ Y4 @ Z2) @ (transi111096263on_val @ R)) => (member354538064on_val @ (produc1069526295on_val @ X4 @ Z2) @ (transi111096263on_val @ R))))))). % rtrancl_trans
thf(fact_121_TryCatch, axiom,
    ((![P : list_P1234162913t_char, E_1 : exp_list_char, S_0 : produc515445032on_val, A3 : nat, H_1 : nat > option2118145160on_val, L_1 : list_char > option_val, D : list_char, Fs : produc1257910179t_char > option_val, C : list_char, E_2 : exp_list_char, V4 : list_char, E_22 : exp_list_char, H_2 : nat > option2118145160on_val, L_2 : list_char > option_val]: ((eval @ P @ E_1 @ S_0 @ (throw_list_char @ (val_list_char @ (addr @ A3))) @ (produc52622304on_val @ H_1 @ L_1)) => (((H_1 @ A3) = (some_P1299442195on_val @ (produc904988266on_val @ D @ Fs))) => ((member89690956t_char @ (produc1304532571t_char @ D @ C) @ (transi1879726366t_char @ (subcls880436836t_char @ P))) => ((eval @ P @ E_2 @ (produc52622304on_val @ H_1 @ (fun_up1252458416on_val @ L_1 @ V4 @ (some_val @ (addr @ A3)))) @ E_22 @ (produc52622304on_val @ H_2 @ L_2)) => (eval @ P @ (tryCatch_list_char @ E_1 @ C @ V4 @ E_2) @ S_0 @ E_22 @ (produc52622304on_val @ H_2 @ (fun_up1252458416on_val @ L_2 @ V4 @ (L_1 @ V4))))))))))). % TryCatch
thf(fact_122_CastRedsFail, axiom,
    ((![E : exp_list_char, S2 : produc515445032on_val, A3 : nat, S3 : produc515445032on_val, P : list_P1234162913t_char, D : list_char, Fs : produc1257910179t_char > option_val, C : list_char]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E @ S2) @ (produc2023458740on_val @ (val_list_char @ (addr @ A3)) @ S3)) @ (transi111096263on_val @ (red @ P))) => (((hp @ S3 @ A3) = (some_P1299442195on_val @ (produc904988266on_val @ D @ Fs))) => ((~ ((member89690956t_char @ (produc1304532571t_char @ D @ C) @ (transi1879726366t_char @ (subcls880436836t_char @ P))))) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (cast_list_char @ C @ E) @ S2) @ (produc2023458740on_val @ (throw_list_char @ (val_list_char @ (addr @ (addr_of_sys_xcpt @ classCast)))) @ S3)) @ (transi111096263on_val @ (red @ P))))))))). % CastRedsFail
thf(fact_123_red__reds_ORedCastFail, axiom,
    ((![S2 : produc515445032on_val, A3 : nat, D : list_char, Fs : produc1257910179t_char > option_val, C : list_char, P : list_P1234162913t_char]: (((hp @ S2 @ A3) = (some_P1299442195on_val @ (produc904988266on_val @ D @ Fs))) => ((~ ((member89690956t_char @ (produc1304532571t_char @ D @ C) @ (transi1879726366t_char @ (subcls880436836t_char @ P))))) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (cast_list_char @ C @ (val_list_char @ (addr @ A3))) @ S2) @ (produc2023458740on_val @ (throw_list_char @ (val_list_char @ (addr @ (addr_of_sys_xcpt @ classCast)))) @ S2)) @ (red @ P))))))). % red_reds.RedCastFail
thf(fact_124_red__reds_ORedTryFail, axiom,
    ((![S2 : produc515445032on_val, A3 : nat, D : list_char, Fs : produc1257910179t_char > option_val, C : list_char, P : list_P1234162913t_char, V4 : list_char, E_2 : exp_list_char]: (((hp @ S2 @ A3) = (some_P1299442195on_val @ (produc904988266on_val @ D @ Fs))) => ((~ ((member89690956t_char @ (produc1304532571t_char @ D @ C) @ (transi1879726366t_char @ (subcls880436836t_char @ P))))) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (tryCatch_list_char @ (throw_list_char @ (val_list_char @ (addr @ A3))) @ C @ V4 @ E_2) @ S2) @ (produc2023458740on_val @ (throw_list_char @ (val_list_char @ (addr @ A3))) @ S2)) @ (red @ P))))))). % red_reds.RedTryFail
thf(fact_125_TryRedsFail, axiom,
    ((![E_1 : exp_list_char, S2 : produc515445032on_val, A3 : nat, H : nat > option2118145160on_val, L : list_char > option_val, P : list_P1234162913t_char, D : list_char, Fs : produc1257910179t_char > option_val, C : list_char, V4 : list_char, E_2 : exp_list_char]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E_1 @ S2) @ (produc2023458740on_val @ (throw_list_char @ (val_list_char @ (addr @ A3))) @ (produc52622304on_val @ H @ L))) @ (transi111096263on_val @ (red @ P))) => (((H @ A3) = (some_P1299442195on_val @ (produc904988266on_val @ D @ Fs))) => ((~ ((member89690956t_char @ (produc1304532571t_char @ D @ C) @ (transi1879726366t_char @ (subcls880436836t_char @ P))))) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (tryCatch_list_char @ E_1 @ C @ V4 @ E_2) @ S2) @ (produc2023458740on_val @ (throw_list_char @ (val_list_char @ (addr @ A3))) @ (produc52622304on_val @ H @ L))) @ (transi111096263on_val @ (red @ P))))))))). % TryRedsFail
thf(fact_126_CastRedsAddr, axiom,
    ((![E : exp_list_char, S2 : produc515445032on_val, A3 : nat, S3 : produc515445032on_val, P : list_P1234162913t_char, D : list_char, Fs : produc1257910179t_char > option_val, C : list_char]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E @ S2) @ (produc2023458740on_val @ (val_list_char @ (addr @ A3)) @ S3)) @ (transi111096263on_val @ (red @ P))) => (((hp @ S3 @ A3) = (some_P1299442195on_val @ (produc904988266on_val @ D @ Fs))) => ((member89690956t_char @ (produc1304532571t_char @ D @ C) @ (transi1879726366t_char @ (subcls880436836t_char @ P))) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (cast_list_char @ C @ E) @ S2) @ (produc2023458740on_val @ (val_list_char @ (addr @ A3)) @ S3)) @ (transi111096263on_val @ (red @ P))))))))). % CastRedsAddr
thf(fact_127_TryReds, axiom,
    ((![E : exp_list_char, S2 : produc515445032on_val, E4 : exp_list_char, S3 : produc515445032on_val, P : list_P1234162913t_char, C : list_char, V4 : list_char, E_2 : exp_list_char]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E @ S2) @ (produc2023458740on_val @ E4 @ S3)) @ (transi111096263on_val @ (red @ P))) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (tryCatch_list_char @ E @ C @ V4 @ E_2) @ S2) @ (produc2023458740on_val @ (tryCatch_list_char @ E4 @ C @ V4 @ E_2) @ S3)) @ (transi111096263on_val @ (red @ P))))))). % TryReds
thf(fact_128_CastReds, axiom,
    ((![E : exp_list_char, S2 : produc515445032on_val, E4 : exp_list_char, S3 : produc515445032on_val, P : list_P1234162913t_char, C : list_char]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E @ S2) @ (produc2023458740on_val @ E4 @ S3)) @ (transi111096263on_val @ (red @ P))) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (cast_list_char @ C @ E) @ S2) @ (produc2023458740on_val @ (cast_list_char @ C @ E4) @ S3)) @ (transi111096263on_val @ (red @ P))))))). % CastReds
thf(fact_129_ThrowReds, axiom,
    ((![E : exp_list_char, S2 : produc515445032on_val, E4 : exp_list_char, S3 : produc515445032on_val, P : list_P1234162913t_char]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E @ S2) @ (produc2023458740on_val @ E4 @ S3)) @ (transi111096263on_val @ (red @ P))) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (throw_list_char @ E) @ S2) @ (produc2023458740on_val @ (throw_list_char @ E4) @ S3)) @ (transi111096263on_val @ (red @ P))))))). % ThrowReds
thf(fact_130_red__reds_OTryRed, axiom,
    ((![E : exp_list_char, S2 : produc515445032on_val, E4 : exp_list_char, S3 : produc515445032on_val, P : list_P1234162913t_char, C : list_char, V4 : list_char, E_2 : exp_list_char]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E @ S2) @ (produc2023458740on_val @ E4 @ S3)) @ (red @ P)) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (tryCatch_list_char @ E @ C @ V4 @ E_2) @ S2) @ (produc2023458740on_val @ (tryCatch_list_char @ E4 @ C @ V4 @ E_2) @ S3)) @ (red @ P)))))). % red_reds.TryRed
thf(fact_131_ThrowRedsThrow, axiom,
    ((![E : exp_list_char, S2 : produc515445032on_val, A3 : exp_list_char, S3 : produc515445032on_val, P : list_P1234162913t_char]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E @ S2) @ (produc2023458740on_val @ (throw_list_char @ A3) @ S3)) @ (transi111096263on_val @ (red @ P))) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (throw_list_char @ E) @ S2) @ (produc2023458740on_val @ (throw_list_char @ A3) @ S3)) @ (transi111096263on_val @ (red @ P))))))). % ThrowRedsThrow
thf(fact_132_red__reds_OCastRed, axiom,
    ((![E : exp_list_char, S2 : produc515445032on_val, E4 : exp_list_char, S3 : produc515445032on_val, P : list_P1234162913t_char, C : list_char]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E @ S2) @ (produc2023458740on_val @ E4 @ S3)) @ (red @ P)) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (cast_list_char @ C @ E) @ S2) @ (produc2023458740on_val @ (cast_list_char @ C @ E4) @ S3)) @ (red @ P)))))). % red_reds.CastRed
thf(fact_133_red__reds_OThrowRed, axiom,
    ((![E : exp_list_char, S2 : produc515445032on_val, E4 : exp_list_char, S3 : produc515445032on_val, P : list_P1234162913t_char]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E @ S2) @ (produc2023458740on_val @ E4 @ S3)) @ (red @ P)) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (throw_list_char @ E) @ S2) @ (produc2023458740on_val @ (throw_list_char @ E4) @ S3)) @ (red @ P)))))). % red_reds.ThrowRed
thf(fact_134_red__reds_OThrowThrow, axiom,
    ((![E : exp_list_char, S2 : produc515445032on_val, P : list_P1234162913t_char]: (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (throw_list_char @ (throw_list_char @ E)) @ S2) @ (produc2023458740on_val @ (throw_list_char @ E) @ S2)) @ (red @ P))))). % red_reds.ThrowThrow
thf(fact_135_converse__rtrancl__induct__red, axiom,
    ((![E : exp_list_char, H : nat > option2118145160on_val, L : list_char > option_val, E4 : exp_list_char, H2 : nat > option2118145160on_val, L2 : list_char > option_val, P : list_P1234162913t_char, R2 : exp_list_char > (nat > option2118145160on_val) > (list_char > option_val) > exp_list_char > (nat > option2118145160on_val) > (list_char > option_val) > $o]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E @ (produc52622304on_val @ H @ L)) @ (produc2023458740on_val @ E4 @ (produc52622304on_val @ H2 @ L2))) @ (transi111096263on_val @ (red @ P))) => ((![E5 : exp_list_char, H3 : nat > option2118145160on_val, L3 : list_char > option_val]: (R2 @ E5 @ H3 @ L3 @ E5 @ H3 @ L3)) => ((![E_0 : exp_list_char, H_0 : nat > option2118145160on_val, L_0 : list_char > option_val, E_12 : exp_list_char, H_12 : nat > option2118145160on_val, L_12 : list_char > option_val, E6 : exp_list_char, H4 : nat > option2118145160on_val, L4 : list_char > option_val]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E_0 @ (produc52622304on_val @ H_0 @ L_0)) @ (produc2023458740on_val @ E_12 @ (produc52622304on_val @ H_12 @ L_12))) @ (red @ P)) => ((R2 @ E_12 @ H_12 @ L_12 @ E6 @ H4 @ L4) => (R2 @ E_0 @ H_0 @ L_0 @ E6 @ H4 @ L4)))) => (R2 @ E @ H @ L @ E4 @ H2 @ L2))))))). % converse_rtrancl_induct_red
thf(fact_136_red__reds_OCastThrow, axiom,
    ((![C : list_char, E : exp_list_char, S2 : produc515445032on_val, P : list_P1234162913t_char]: (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (cast_list_char @ C @ (throw_list_char @ E)) @ S2) @ (produc2023458740on_val @ (throw_list_char @ E) @ S2)) @ (red @ P))))). % red_reds.CastThrow
thf(fact_137_CastRedsThrow, axiom,
    ((![E : exp_list_char, S2 : produc515445032on_val, A3 : exp_list_char, S3 : produc515445032on_val, P : list_P1234162913t_char, C : list_char]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E @ S2) @ (produc2023458740on_val @ (throw_list_char @ A3) @ S3)) @ (transi111096263on_val @ (red @ P))) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (cast_list_char @ C @ E) @ S2) @ (produc2023458740on_val @ (throw_list_char @ A3) @ S3)) @ (transi111096263on_val @ (red @ P))))))). % CastRedsThrow
thf(fact_138_red__reds_ORedTry, axiom,
    ((![V3 : val, C : list_char, V4 : 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 @ V3) @ C @ V4 @ E_2) @ S2) @ (produc2023458740on_val @ (val_list_char @ V3) @ S2)) @ (red @ P))))). % red_reds.RedTry
thf(fact_139_TryRedsVal, axiom,
    ((![E : exp_list_char, S2 : produc515445032on_val, V3 : val, S3 : produc515445032on_val, P : list_P1234162913t_char, C : list_char, V4 : list_char, E_2 : exp_list_char]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E @ S2) @ (produc2023458740on_val @ (val_list_char @ V3) @ S3)) @ (transi111096263on_val @ (red @ P))) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (tryCatch_list_char @ E @ C @ V4 @ E_2) @ S2) @ (produc2023458740on_val @ (val_list_char @ V3) @ S3)) @ (transi111096263on_val @ (red @ P))))))). % TryRedsVal
thf(fact_140_red__preserves__sconf, axiom,
    ((![E : exp_list_char, S2 : produc515445032on_val, E4 : exp_list_char, S3 : produc515445032on_val, P : list_P1234162913t_char, E3 : list_char > option_ty, T : ty]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E @ S2) @ (produc2023458740on_val @ E4 @ S3)) @ (red @ P)) => ((wTrt @ P @ (hp @ S2) @ E3 @ E @ T) => ((typeSa1777264139_sconf @ P @ E3 @ S2) => (typeSa1777264139_sconf @ P @ E3 @ S3))))))). % red_preserves_sconf
thf(fact_141_TryCatchRedsFinal, axiom,
    ((![E_1 : exp_list_char, S_0 : produc515445032on_val, A3 : nat, H_1 : nat > option2118145160on_val, L_1 : list_char > option_val, P : list_P1234162913t_char, D : list_char, Fs : produc1257910179t_char > option_val, C : list_char, E_2 : exp_list_char, V4 : list_char, E_22 : exp_list_char, H_2 : nat > option2118145160on_val, L_2 : list_char > option_val]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E_1 @ S_0) @ (produc2023458740on_val @ (throw_list_char @ (val_list_char @ (addr @ A3))) @ (produc52622304on_val @ H_1 @ L_1))) @ (transi111096263on_val @ (red @ P))) => (((H_1 @ A3) = (some_P1299442195on_val @ (produc904988266on_val @ D @ Fs))) => ((member89690956t_char @ (produc1304532571t_char @ D @ C) @ (transi1879726366t_char @ (subcls880436836t_char @ P))) => ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E_2 @ (produc52622304on_val @ H_1 @ (fun_up1252458416on_val @ L_1 @ V4 @ (some_val @ (addr @ A3))))) @ (produc2023458740on_val @ E_22 @ (produc52622304on_val @ H_2 @ L_2))) @ (transi111096263on_val @ (red @ P))) => ((final_list_char @ E_22) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (tryCatch_list_char @ E_1 @ C @ V4 @ E_2) @ S_0) @ (produc2023458740on_val @ E_22 @ (produc52622304on_val @ H_2 @ (fun_up1252458416on_val @ L_2 @ V4 @ (L_1 @ V4))))) @ (transi111096263on_val @ (red @ P))))))))))). % TryCatchRedsFinal
thf(fact_142_red__reds_ORedCast, axiom,
    ((![S2 : produc515445032on_val, A3 : nat, D : list_char, Fs : produc1257910179t_char > option_val, C : list_char, P : list_P1234162913t_char]: (((hp @ S2 @ A3) = (some_P1299442195on_val @ (produc904988266on_val @ D @ Fs))) => ((member89690956t_char @ (produc1304532571t_char @ D @ C) @ (transi1879726366t_char @ (subcls880436836t_char @ P))) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (cast_list_char @ C @ (val_list_char @ (addr @ A3))) @ S2) @ (produc2023458740on_val @ (val_list_char @ (addr @ A3)) @ S2)) @ (red @ P))))))). % red_reds.RedCast
thf(fact_143_big__iff__small, axiom,
    ((![P : list_P1234162913t_char, E : exp_list_char, S2 : produc515445032on_val, E4 : exp_list_char, S3 : produc515445032on_val]: ((wf_pro1229751607t_char @ wwf_J_mdecl @ P) => ((eval @ P @ E @ S2 @ E4 @ S3) = (((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E @ S2) @ (produc2023458740on_val @ E4 @ S3)) @ (transi111096263on_val @ (red @ P)))) & ((final_list_char @ E4)))))))). % big_iff_small
thf(fact_144_small__by__big, axiom,
    ((![P : list_P1234162913t_char, E : exp_list_char, S2 : produc515445032on_val, E4 : exp_list_char, S3 : produc515445032on_val]: ((wf_pro1229751607t_char @ wwf_J_mdecl @ P) => ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E @ S2) @ (produc2023458740on_val @ E4 @ S3)) @ (transi111096263on_val @ (red @ P))) => ((final_list_char @ E4) => (eval @ P @ E @ S2 @ E4 @ S3))))))). % small_by_big
thf(fact_145_FAccRedsVal, axiom,
    ((![E : exp_list_char, S2 : produc515445032on_val, A3 : nat, S3 : produc515445032on_val, P : list_P1234162913t_char, C : list_char, Fs : produc1257910179t_char > option_val, F : list_char, D : list_char, V3 : val]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E @ S2) @ (produc2023458740on_val @ (val_list_char @ (addr @ A3)) @ S3)) @ (transi111096263on_val @ (red @ P))) => (((hp @ S3 @ A3) = (some_P1299442195on_val @ (produc904988266on_val @ C @ Fs))) => (((Fs @ (produc1304532571t_char @ F @ D)) = (some_val @ V3)) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (fAcc_list_char @ E @ F @ D) @ S2) @ (produc2023458740on_val @ (val_list_char @ V3) @ S3)) @ (transi111096263on_val @ (red @ P))))))))). % FAccRedsVal
thf(fact_146_red__reds_ORedFAcc, axiom,
    ((![S2 : produc515445032on_val, A3 : nat, C : list_char, Fs : produc1257910179t_char > option_val, F : list_char, D : list_char, V3 : val, P : list_P1234162913t_char]: (((hp @ S2 @ A3) = (some_P1299442195on_val @ (produc904988266on_val @ C @ Fs))) => (((Fs @ (produc1304532571t_char @ F @ D)) = (some_val @ V3)) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (fAcc_list_char @ (val_list_char @ (addr @ A3)) @ F @ D) @ S2) @ (produc2023458740on_val @ (val_list_char @ V3) @ S2)) @ (red @ P))))))). % red_reds.RedFAcc
thf(fact_147_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_148_exp_Odistinct_I61_J, axiom,
    ((![X3 : val, X71 : exp_list_char, X72 : list_char, X73 : list_char]: (~ (((val_list_char @ X3) = (fAcc_list_char @ X71 @ X72 @ X73))))))). % exp.distinct(61)
thf(fact_149_exp_Odistinct_I151_J, axiom,
    ((![X71 : exp_list_char, X72 : list_char, X73 : list_char, X14 : exp_list_char]: (~ (((fAcc_list_char @ X71 @ X72 @ X73) = (throw_list_char @ X14))))))). % exp.distinct(151)
thf(fact_150_exp_Odistinct_I37_J, axiom,
    ((![X21 : list_char, X22 : exp_list_char, X71 : exp_list_char, X72 : list_char, X73 : list_char]: (~ (((cast_list_char @ X21 @ X22) = (fAcc_list_char @ X71 @ X72 @ X73))))))). % exp.distinct(37)
thf(fact_151_exp_Odistinct_I153_J, axiom,
    ((![X71 : exp_list_char, X72 : list_char, X73 : list_char, X151 : exp_list_char, X152 : list_char, X153 : list_char, X154 : exp_list_char]: (~ (((fAcc_list_char @ X71 @ X72 @ X73) = (tryCatch_list_char @ X151 @ X152 @ X153 @ X154))))))). % exp.distinct(153)
thf(fact_152_eval__evals_OFAccThrow, axiom,
    ((![P : list_P1234162913t_char, E : exp_list_char, S_0 : produc515445032on_val, E4 : exp_list_char, S_1 : produc515445032on_val, F : list_char, D : list_char]: ((eval @ P @ E @ S_0 @ (throw_list_char @ E4) @ S_1) => (eval @ P @ (fAcc_list_char @ E @ F @ D) @ S_0 @ (throw_list_char @ E4) @ S_1))))). % eval_evals.FAccThrow
thf(fact_153_red__reds_OFAccRed, axiom,
    ((![E : exp_list_char, S2 : produc515445032on_val, E4 : exp_list_char, S3 : produc515445032on_val, P : list_P1234162913t_char, F : list_char, D : list_char]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E @ S2) @ (produc2023458740on_val @ E4 @ S3)) @ (red @ P)) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (fAcc_list_char @ E @ F @ D) @ S2) @ (produc2023458740on_val @ (fAcc_list_char @ E4 @ F @ D) @ S3)) @ (red @ P)))))). % red_reds.FAccRed
thf(fact_154_red__reds_OFAccThrow, axiom,
    ((![E : exp_list_char, F : list_char, D : list_char, S2 : produc515445032on_val, P : list_P1234162913t_char]: (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (fAcc_list_char @ (throw_list_char @ E) @ F @ D) @ S2) @ (produc2023458740on_val @ (throw_list_char @ E) @ S2)) @ (red @ P))))). % red_reds.FAccThrow
thf(fact_155_FAccReds, axiom,
    ((![E : exp_list_char, S2 : produc515445032on_val, E4 : exp_list_char, S3 : produc515445032on_val, P : list_P1234162913t_char, F : list_char, D : list_char]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E @ S2) @ (produc2023458740on_val @ E4 @ S3)) @ (transi111096263on_val @ (red @ P))) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (fAcc_list_char @ E @ F @ D) @ S2) @ (produc2023458740on_val @ (fAcc_list_char @ E4 @ F @ D) @ S3)) @ (transi111096263on_val @ (red @ P))))))). % FAccReds
thf(fact_156_FAccRedsThrow, axiom,
    ((![E : exp_list_char, S2 : produc515445032on_val, A3 : exp_list_char, S3 : produc515445032on_val, P : list_P1234162913t_char, F : list_char, D : list_char]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E @ S2) @ (produc2023458740on_val @ (throw_list_char @ A3) @ S3)) @ (transi111096263on_val @ (red @ P))) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (fAcc_list_char @ E @ F @ D) @ S2) @ (produc2023458740on_val @ (throw_list_char @ A3) @ S3)) @ (transi111096263on_val @ (red @ P))))))). % FAccRedsThrow
thf(fact_157_extend__1__eval, axiom,
    ((![P : list_P1234162913t_char, E : exp_list_char, S2 : produc515445032on_val, E7 : exp_list_char, S4 : produc515445032on_val, E4 : exp_list_char, S3 : produc515445032on_val]: ((wf_pro1229751607t_char @ wwf_J_mdecl @ P) => ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E @ S2) @ (produc2023458740on_val @ E7 @ S4)) @ (red @ P)) => ((eval @ P @ E7 @ S4 @ E4 @ S3) => (eval @ P @ E @ S2 @ E4 @ S3))))))). % extend_1_eval
thf(fact_158_FAcc, axiom,
    ((![P : list_P1234162913t_char, E : exp_list_char, S_0 : produc515445032on_val, A3 : nat, H : nat > option2118145160on_val, L : list_char > option_val, C : list_char, Fs : produc1257910179t_char > option_val, F : list_char, D : list_char, V3 : val]: ((eval @ P @ E @ S_0 @ (val_list_char @ (addr @ A3)) @ (produc52622304on_val @ H @ L)) => (((H @ A3) = (some_P1299442195on_val @ (produc904988266on_val @ C @ Fs))) => (((Fs @ (produc1304532571t_char @ F @ D)) = (some_val @ V3)) => (eval @ P @ (fAcc_list_char @ E @ F @ D) @ S_0 @ (val_list_char @ V3) @ (produc52622304on_val @ H @ L)))))))). % FAcc
thf(fact_159_extend__eval, axiom,
    ((![P : list_P1234162913t_char, E : exp_list_char, S2 : produc515445032on_val, E7 : exp_list_char, S4 : produc515445032on_val, E4 : exp_list_char, S3 : produc515445032on_val]: ((wf_pro1229751607t_char @ wwf_J_mdecl @ P) => ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E @ S2) @ (produc2023458740on_val @ E7 @ S4)) @ (transi111096263on_val @ (red @ P))) => ((eval @ P @ E7 @ S4 @ E4 @ S3) => (eval @ P @ E @ S2 @ E4 @ S3))))))). % extend_eval
thf(fact_160_big__by__small, axiom,
    ((![P : list_P1234162913t_char, E : exp_list_char, S2 : produc515445032on_val, E4 : exp_list_char, S3 : produc515445032on_val]: ((wf_pro1229751607t_char @ wwf_J_mdecl @ P) => ((eval @ P @ E @ S2 @ E4 @ S3) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E @ S2) @ (produc2023458740on_val @ E4 @ S3)) @ (transi111096263on_val @ (red @ P)))))))). % big_by_small
thf(fact_161_wf__prog__wwf__prog, axiom,
    ((![P : list_P1234162913t_char]: ((wf_pro1229751607t_char @ wf_J_mdecl @ P) => (wf_pro1229751607t_char @ wwf_J_mdecl @ P))))). % wf_prog_wwf_prog
thf(fact_162_wf__mdecl__wwf__mdecl, axiom,
    ((![P : list_P1234162913t_char, C : list_char, Md : produc1259892823t_char]: ((wf_J_mdecl @ P @ C @ Md) => (wwf_J_mdecl @ P @ C @ Md))))). % wf_mdecl_wwf_mdecl
thf(fact_163_fun__upd__apply, axiom,
    ((fun_up1252458416on_val = (^[F2 : list_char > option_val]: (^[X : list_char]: (^[Y6 : option_val]: (^[Z3 : list_char]: (if_option_val @ (Z3 = X) @ Y6 @ (F2 @ Z3))))))))). % fun_upd_apply
thf(fact_164_fun__upd__upd, axiom,
    ((![F3 : list_char > option_val, X4 : list_char, Y4 : option_val, Z2 : option_val]: ((fun_up1252458416on_val @ (fun_up1252458416on_val @ F3 @ X4 @ Y4) @ X4 @ Z2) = (fun_up1252458416on_val @ F3 @ X4 @ Z2))))). % fun_upd_upd
thf(fact_165_fun__upd__triv, axiom,
    ((![F3 : list_char > option_val, X4 : list_char]: ((fun_up1252458416on_val @ F3 @ X4 @ (F3 @ X4)) = F3)))). % fun_upd_triv
thf(fact_166_fun__upd__def, axiom,
    ((fun_up1252458416on_val = (^[F2 : list_char > option_val]: (^[A2 : list_char]: (^[B4 : option_val]: (^[X : list_char]: (if_option_val @ (X = A2) @ B4 @ (F2 @ X))))))))). % fun_upd_def
thf(fact_167_fun__upd__eqD, axiom,
    ((![F3 : list_char > option_val, X4 : list_char, Y4 : option_val, G : list_char > option_val, Z2 : option_val]: (((fun_up1252458416on_val @ F3 @ X4 @ Y4) = (fun_up1252458416on_val @ G @ X4 @ Z2)) => (Y4 = Z2))))). % fun_upd_eqD
thf(fact_168_fun__upd__idem, axiom,
    ((![F3 : list_char > option_val, X4 : list_char, Y4 : option_val]: (((F3 @ X4) = Y4) => ((fun_up1252458416on_val @ F3 @ X4 @ Y4) = F3))))). % fun_upd_idem
thf(fact_169_fun__upd__same, axiom,
    ((![F3 : list_char > option_val, X4 : list_char, Y4 : option_val]: ((fun_up1252458416on_val @ F3 @ X4 @ Y4 @ X4) = Y4)))). % fun_upd_same
thf(fact_170_fun__upd__other, axiom,
    ((![Z2 : list_char, X4 : list_char, F3 : list_char > option_val, Y4 : option_val]: ((~ ((Z2 = X4))) => ((fun_up1252458416on_val @ F3 @ X4 @ Y4 @ Z2) = (F3 @ Z2)))))). % fun_upd_other
thf(fact_171_fun__upd__twist, axiom,
    ((![A3 : list_char, C4 : list_char, M : list_char > option_val, B : option_val, D3 : option_val]: ((~ ((A3 = C4))) => ((fun_up1252458416on_val @ (fun_up1252458416on_val @ M @ A3 @ B) @ C4 @ D3) = (fun_up1252458416on_val @ (fun_up1252458416on_val @ M @ C4 @ D3) @ A3 @ B)))))). % fun_upd_twist
thf(fact_172_fun__upd__idem__iff, axiom,
    ((![F3 : list_char > option_val, X4 : list_char, Y4 : option_val]: (((fun_up1252458416on_val @ F3 @ X4 @ Y4) = F3) = ((F3 @ X4) = Y4))))). % fun_upd_idem_iff
thf(fact_173_redp__redsp_ORedFAcc, axiom,
    ((![S2 : produc515445032on_val, A3 : nat, C : list_char, Fs : produc1257910179t_char > option_val, F : list_char, D : list_char, V3 : val, P : list_P1234162913t_char]: (((hp @ S2 @ A3) = (some_P1299442195on_val @ (produc904988266on_val @ C @ Fs))) => (((Fs @ (produc1304532571t_char @ F @ D)) = (some_val @ V3)) => (redp @ P @ (fAcc_list_char @ (val_list_char @ (addr @ A3)) @ F @ D) @ S2 @ (val_list_char @ V3) @ S2)))))). % redp_redsp.RedFAcc
thf(fact_174_red__preserves__hconf, axiom,
    ((![E : exp_list_char, H : nat > option2118145160on_val, L : list_char > option_val, E4 : exp_list_char, H2 : nat > option2118145160on_val, L2 : list_char > option_val, P : list_P1234162913t_char, E3 : list_char > option_ty, T : ty]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E @ (produc52622304on_val @ H @ L)) @ (produc2023458740on_val @ E4 @ (produc52622304on_val @ H2 @ L2))) @ (red @ P)) => ((wTrt @ P @ H @ E3 @ E @ T) => ((hconf_1244167010t_char @ P @ H) => (hconf_1244167010t_char @ P @ H2))))))). % red_preserves_hconf
thf(fact_175_redp__redsp_OFAccRed, axiom,
    ((![P : list_P1234162913t_char, E : exp_list_char, S2 : produc515445032on_val, E4 : exp_list_char, S3 : produc515445032on_val, F : list_char, D : list_char]: ((redp @ P @ E @ S2 @ E4 @ S3) => (redp @ P @ (fAcc_list_char @ E @ F @ D) @ S2 @ (fAcc_list_char @ E4 @ F @ D) @ S3))))). % redp_redsp.FAccRed
thf(fact_176_redp__redsp_OCastThrow, axiom,
    ((![P : list_P1234162913t_char, C : list_char, E : exp_list_char, S2 : produc515445032on_val]: (redp @ P @ (cast_list_char @ C @ (throw_list_char @ E)) @ S2 @ (throw_list_char @ E) @ S2)))). % redp_redsp.CastThrow
thf(fact_177_redp__redsp_ORedTry, axiom,
    ((![P : list_P1234162913t_char, V3 : val, C : list_char, V4 : list_char, E_2 : exp_list_char, S2 : produc515445032on_val]: (redp @ P @ (tryCatch_list_char @ (val_list_char @ V3) @ C @ V4 @ E_2) @ S2 @ (val_list_char @ V3) @ S2)))). % redp_redsp.RedTry
thf(fact_178_redp__redsp_OFAccThrow, axiom,
    ((![P : list_P1234162913t_char, E : exp_list_char, F : list_char, D : list_char, S2 : produc515445032on_val]: (redp @ P @ (fAcc_list_char @ (throw_list_char @ E) @ F @ D) @ S2 @ (throw_list_char @ E) @ S2)))). % redp_redsp.FAccThrow
thf(fact_179_redp__redsp_OTryRed, axiom,
    ((![P : list_P1234162913t_char, E : exp_list_char, S2 : produc515445032on_val, E4 : exp_list_char, S3 : produc515445032on_val, C : list_char, V4 : list_char, E_2 : exp_list_char]: ((redp @ P @ E @ S2 @ E4 @ S3) => (redp @ P @ (tryCatch_list_char @ E @ C @ V4 @ E_2) @ S2 @ (tryCatch_list_char @ E4 @ C @ V4 @ E_2) @ S3))))). % redp_redsp.TryRed
thf(fact_180_redp__redsp_OThrowRed, axiom,
    ((![P : list_P1234162913t_char, E : exp_list_char, S2 : produc515445032on_val, E4 : exp_list_char, S3 : produc515445032on_val]: ((redp @ P @ E @ S2 @ E4 @ S3) => (redp @ P @ (throw_list_char @ E) @ S2 @ (throw_list_char @ E4) @ S3))))). % redp_redsp.ThrowRed
thf(fact_181_redp__redsp_OThrowThrow, axiom,
    ((![P : list_P1234162913t_char, E : exp_list_char, S2 : produc515445032on_val]: (redp @ P @ (throw_list_char @ (throw_list_char @ E)) @ S2 @ (throw_list_char @ E) @ S2)))). % redp_redsp.ThrowThrow
thf(fact_182_redp__redsp_OCastRed, axiom,
    ((![P : list_P1234162913t_char, E : exp_list_char, S2 : produc515445032on_val, E4 : exp_list_char, S3 : produc515445032on_val, C : list_char]: ((redp @ P @ E @ S2 @ E4 @ S3) => (redp @ P @ (cast_list_char @ C @ E) @ S2 @ (cast_list_char @ C @ E4) @ S3))))). % redp_redsp.CastRed
thf(fact_183_redp__red__eq, axiom,
    ((redp = (^[P3 : list_P1234162913t_char]: (^[X : exp_list_char]: (^[Y6 : produc515445032on_val]: (^[Z3 : exp_list_char]: (^[Aa2 : produc515445032on_val]: (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ X @ Y6) @ (produc2023458740on_val @ Z3 @ Aa2)) @ (red @ P3)))))))))). % redp_red_eq
thf(fact_184_red__preserves__lconf, axiom,
    ((![E : exp_list_char, H : nat > option2118145160on_val, L : list_char > option_val, E4 : exp_list_char, H2 : nat > option2118145160on_val, L2 : list_char > option_val, P : list_P1234162913t_char, E3 : list_char > option_ty, T : ty]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E @ (produc52622304on_val @ H @ L)) @ (produc2023458740on_val @ E4 @ (produc52622304on_val @ H2 @ L2))) @ (red @ P)) => ((wTrt @ P @ H @ E3 @ E @ T) => ((lconf_485928294t_char @ P @ H @ L @ E3) => (lconf_485928294t_char @ P @ H2 @ L2 @ E3))))))). % red_preserves_lconf
thf(fact_185_map__upd__Some__unfold, axiom,
    ((![M : list_char > option_val, A3 : list_char, B : val, X4 : list_char, Y4 : val]: (((fun_up1252458416on_val @ M @ A3 @ (some_val @ B) @ X4) = (some_val @ Y4)) = (((((X4 = A3)) & ((B = Y4)))) | ((((~ ((X4 = A3)))) & (((M @ X4) = (some_val @ Y4)))))))))). % map_upd_Some_unfold
thf(fact_186_map__upd__eqD1, axiom,
    ((![M : list_char > option_val, A3 : list_char, X4 : val, N : list_char > option_val, Y4 : val]: (((fun_up1252458416on_val @ M @ A3 @ (some_val @ X4)) = (fun_up1252458416on_val @ N @ A3 @ (some_val @ Y4))) => (X4 = Y4))))). % map_upd_eqD1
thf(fact_187_map__upd__triv, axiom,
    ((![T2 : list_char > option_val, K : list_char, X4 : val]: (((T2 @ K) = (some_val @ X4)) => ((fun_up1252458416on_val @ T2 @ K @ (some_val @ X4)) = T2))))). % map_upd_triv
thf(fact_188_eval__cases_I5_J, axiom,
    ((![P : list_P1234162913t_char, E : exp_list_char, F : list_char, D : list_char, S2 : produc515445032on_val, E4 : exp_list_char, S3 : produc515445032on_val]: ((eval @ P @ (fAcc_list_char @ E @ F @ D) @ S2 @ E4 @ S3) => ((![A : nat, H3 : nat > option2118145160on_val, L3 : list_char > option_val, C5 : list_char, Fs2 : produc1257910179t_char > option_val, V : val]: ((E4 = (val_list_char @ V)) => ((S3 = (produc52622304on_val @ H3 @ L3)) => ((eval @ P @ E @ S2 @ (val_list_char @ (addr @ A)) @ (produc52622304on_val @ H3 @ L3)) => (((H3 @ A) = (some_P1299442195on_val @ (produc904988266on_val @ C5 @ Fs2))) => (~ (((Fs2 @ (produc1304532571t_char @ F @ D)) = (some_val @ V))))))))) => (((E4 = (throw_list_char @ (val_list_char @ (addr @ (addr_of_sys_xcpt @ nullPointer))))) => (~ ((eval @ P @ E @ S2 @ (val_list_char @ null) @ S3)))) => (~ ((![E6 : exp_list_char]: ((E4 = (throw_list_char @ E6)) => (~ ((eval @ P @ E @ S2 @ (throw_list_char @ E6) @ S3))))))))))))). % eval_cases(5)
thf(fact_189_CastRedsNull, axiom,
    ((![E : exp_list_char, S2 : produc515445032on_val, S3 : produc515445032on_val, P : list_P1234162913t_char, C : list_char]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E @ S2) @ (produc2023458740on_val @ (val_list_char @ null) @ S3)) @ (transi111096263on_val @ (red @ P))) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (cast_list_char @ C @ E) @ S2) @ (produc2023458740on_val @ (val_list_char @ null) @ S3)) @ (transi111096263on_val @ (red @ P))))))). % CastRedsNull
thf(fact_190_val_Odistinct_I13_J, axiom,
    ((![X5 : nat]: (~ ((null = (addr @ X5))))))). % val.distinct(13)
thf(fact_191_eval__cases_I12_J, axiom,
    ((![P : list_P1234162913t_char, E : exp_list_char, S2 : produc515445032on_val, E4 : exp_list_char, S3 : produc515445032on_val]: ((eval @ P @ (throw_list_char @ E) @ S2 @ E4 @ S3) => ((![A : nat]: ((E4 = (throw_list_char @ (val_list_char @ (addr @ A)))) => (~ ((eval @ P @ E @ S2 @ (val_list_char @ (addr @ A)) @ S3))))) => (((E4 = (throw_list_char @ (val_list_char @ (addr @ (addr_of_sys_xcpt @ nullPointer))))) => (~ ((eval @ P @ E @ S2 @ (val_list_char @ null) @ S3)))) => (~ ((![E6 : exp_list_char]: ((E4 = (throw_list_char @ E6)) => (~ ((eval @ P @ E @ S2 @ (throw_list_char @ E6) @ S3))))))))))))). % eval_cases(12)
thf(fact_192_ThrowNull, axiom,
    ((![P : list_P1234162913t_char, E : exp_list_char, S_0 : produc515445032on_val, S_1 : produc515445032on_val]: ((eval @ P @ E @ S_0 @ (val_list_char @ null) @ S_1) => (eval @ P @ (throw_list_char @ E) @ S_0 @ (throw_list_char @ (val_list_char @ (addr @ (addr_of_sys_xcpt @ nullPointer)))) @ S_1))))). % ThrowNull
thf(fact_193_redp__redsp_ORedThrowNull, axiom,
    ((![P : list_P1234162913t_char, S2 : produc515445032on_val]: (redp @ P @ (throw_list_char @ (val_list_char @ null)) @ S2 @ (throw_list_char @ (val_list_char @ (addr @ (addr_of_sys_xcpt @ nullPointer)))) @ S2)))). % redp_redsp.RedThrowNull
thf(fact_194_CastNull, axiom,
    ((![P : list_P1234162913t_char, E : exp_list_char, S_0 : produc515445032on_val, S_1 : produc515445032on_val, C : list_char]: ((eval @ P @ E @ S_0 @ (val_list_char @ null) @ S_1) => (eval @ P @ (cast_list_char @ C @ E) @ S_0 @ (val_list_char @ null) @ S_1))))). % CastNull
thf(fact_195_redp__redsp_ORedCastNull, axiom,
    ((![P : list_P1234162913t_char, C : list_char, S2 : produc515445032on_val]: (redp @ P @ (cast_list_char @ C @ (val_list_char @ null)) @ S2 @ (val_list_char @ null) @ S2)))). % redp_redsp.RedCastNull
thf(fact_196_FAccNull, axiom,
    ((![P : list_P1234162913t_char, E : exp_list_char, S_0 : produc515445032on_val, S_1 : produc515445032on_val, F : list_char, D : list_char]: ((eval @ P @ E @ S_0 @ (val_list_char @ null) @ S_1) => (eval @ P @ (fAcc_list_char @ E @ F @ D) @ S_0 @ (throw_list_char @ (val_list_char @ (addr @ (addr_of_sys_xcpt @ nullPointer)))) @ S_1))))). % FAccNull
thf(fact_197_redp__redsp_ORedFAccNull, axiom,
    ((![P : list_P1234162913t_char, F : list_char, D : list_char, S2 : produc515445032on_val]: (redp @ P @ (fAcc_list_char @ (val_list_char @ null) @ F @ D) @ S2 @ (throw_list_char @ (val_list_char @ (addr @ (addr_of_sys_xcpt @ nullPointer)))) @ S2)))). % redp_redsp.RedFAccNull
thf(fact_198_red__reds_ORedThrowNull, axiom,
    ((![S2 : produc515445032on_val, P : list_P1234162913t_char]: (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (throw_list_char @ (val_list_char @ null)) @ S2) @ (produc2023458740on_val @ (throw_list_char @ (val_list_char @ (addr @ (addr_of_sys_xcpt @ nullPointer)))) @ S2)) @ (red @ P))))). % red_reds.RedThrowNull

% Helper facts (3)
thf(help_If_3_1_If_001t__Option__Ooption_It__Value__Oval_J_T, axiom,
    ((![P : $o]: ((P = $true) | (P = $false))))).
thf(help_If_2_1_If_001t__Option__Ooption_It__Value__Oval_J_T, axiom,
    ((![X4 : option_val, Y4 : option_val]: ((if_option_val @ $false @ X4 @ Y4) = Y4)))).
thf(help_If_1_1_If_001t__Option__Ooption_It__Value__Oval_J_T, axiom,
    ((![X4 : option_val, Y4 : option_val]: ((if_option_val @ $true @ X4 @ Y4) = X4)))).

% Conjectures (1)
thf(conj_0, conjecture,
    ((?[T3 : ty]: ((wTrt @ p @ a @ e @ (throw_list_char @ (val_list_char @ (addr @ (addr_of_sys_xcpt @ classCast)))) @ T3) & (widen_917054840t_char @ p @ T3 @ t))))).
