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% This file was generated by Isabelle (most likely Sledgehammer)
% 2020-12-16 14:20:40.197

% Could-be-implicit typings (25)
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% Explicit typings (65)
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thf(sy_c_SmallStep_Ored, type,
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thf(sy_c_State_Ohp, type,
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thf(sy_c_Transitive__Closure_Ortrancl_001t__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_M_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_J, type,
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    transi100378922on_val : set_Pr1368603847on_val > set_Pr1368603847on_val).
thf(sy_c_TypeRel_Owiden_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,
    widen_917054840t_char : list_P1234162913t_char > ty > ty > $o).
thf(sy_c_TypeSafe__Mirabelle__osrwgqrerx_Osconf, type,
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thf(sy_c_Type_Oty_OBoolean, type,
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thf(sy_c_Type_Oty_OVoid, type,
    void : ty).
thf(sy_c_WellForm_Owf__prog_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,
    wf_pro1229751607t_char : (list_P1234162913t_char > list_char > produc1259892823t_char > $o) > list_P1234162913t_char > $o).
thf(sy_c_WellTypeRT_OWTrt, type,
    wTrt : list_P1234162913t_char > (nat > option2118145160on_val) > (list_char > option_ty) > exp_list_char > ty > $o).
thf(sy_c_member_001t__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_M_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_J, type,
    member652041809on_val : produc515445032on_val > set_Pr723149704on_val > $o).
thf(sy_c_member_001t__Product____Type__Oprod_It__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_Mt__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_M_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J, type,
    member1888679917on_val : produc1097884484on_val > set_Pr556513572on_val > $o).
thf(sy_c_member_001t__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J, type,
    member1296415951on_val : produc266837688on_val > set_Pr2075231726on_val > $o).
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    member2027247312on_val : produc744932519on_val > set_Pr148564103on_val > $o).
thf(sy_c_member_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_Mt__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_M_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_Mt__Product____Type__Oprod_It__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_Mt__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_M_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J, type,
    member354538064on_val : produc1172664615on_val > set_Pr1189492743on_val > $o).
thf(sy_c_member_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_Mt__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J, type,
    member197592058on_val : produc1085126737on_val > set_Pr2110063281on_val > $o).
thf(sy_c_member_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__Product____Type__Oprod_It__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_Mt__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_M_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_Mt__Product____Type__Oprod_It__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_Mt__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_M_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_Mt__Product____Type__Oprod_It__Product____Type__Oprod_It__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_Mt__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_M_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_Mt__Product____Type__Oprod_It__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_Mt__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_M_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_J, type,
    member208988944on_val : produc1161703655on_val > set_Pr1368603847on_val > $o).
thf(sy_v_E____, type,
    e : list_char > option_ty).
thf(sy_v_P, type,
    p : list_P1234162913t_char).
thf(sy_v_T____, type,
    t : ty).
thf(sy_v_V______, type,
    v : list_char).
thf(sy_v_a______, type,
    a : nat > option2118145160on_val).
thf(sy_v_aa______, type,
    aa : nat > option2118145160on_val).
thf(sy_v_b______, type,
    b : list_char > option_val).
thf(sy_v_ba______, type,
    ba : list_char > option_val).
thf(sy_v_e_Ha______, type,
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thf(sy_v_ea______, type,
    ea : exp_list_char).

% Relevant facts (188)
thf(fact_0_LAssRed_Oprems_I1_J, axiom,
    ((typeSa1777264139_sconf @ p @ e @ (produc52622304on_val @ a @ b)))). % LAssRed.prems(1)
thf(fact_1_LAssRed_Oprems_I2_J, axiom,
    ((wTrt @ p @ a @ e @ (lAss_list_char @ v @ ea) @ t))). % LAssRed.prems(2)
thf(fact_2_LAssRed_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)))))))). % LAssRed.hyps(2)
thf(fact_3_LAssRed_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)))). % LAssRed.hyps(1)
thf(fact_4_exp_Oinject_I6_J, axiom,
    ((![X61 : list_char, X62 : exp_list_char, Y61 : list_char, Y62 : exp_list_char]: (((lAss_list_char @ X61 @ X62) = (lAss_list_char @ Y61 @ Y62)) = (((X61 = Y61)) & ((X62 = Y62))))))). % exp.inject(6)
thf(fact_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_WTrt__elim__cases_I1_J, axiom,
    ((![P : list_P1234162913t_char, H : nat > option2118145160on_val, E : list_char > option_ty, V : list_char, E2 : exp_list_char, T : ty]: ((wTrt @ P @ H @ E @ (lAss_list_char @ V @ E2) @ T) => (~ (((T = void) => (![T3 : ty]: (((E @ V) = (some_ty @ T3)) => (![T2 : ty]: ((wTrt @ P @ H @ E @ E2 @ T2) => (~ ((widen_917054840t_char @ P @ T2 @ T3)))))))))))))). % WTrt_elim_cases(1)
thf(fact_9_WTrtLAss, axiom,
    ((![E : list_char > option_ty, V2 : list_char, T : ty, P : list_P1234162913t_char, H : nat > option2118145160on_val, E2 : exp_list_char, T4 : ty]: (((E @ V2) = (some_ty @ T)) => ((wTrt @ P @ H @ E @ E2 @ T4) => ((widen_917054840t_char @ P @ T4 @ T) => (wTrt @ P @ H @ E @ (lAss_list_char @ V2 @ E2) @ void))))))). % WTrtLAss
thf(fact_10_red__reds_OLAssRed, axiom,
    ((![E2 : exp_list_char, S2 : produc515445032on_val, E3 : exp_list_char, S3 : produc515445032on_val, P : list_P1234162913t_char, V2 : list_char]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E2 @ S2) @ (produc2023458740on_val @ E3 @ S3)) @ (red @ P)) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (lAss_list_char @ V2 @ E2) @ S2) @ (produc2023458740on_val @ (lAss_list_char @ V2 @ E3) @ S3)) @ (red @ P)))))). % red_reds.LAssRed
thf(fact_11_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_12_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_13_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_14_exp_Opred__inject_I6_J, axiom,
    ((![P : list_char > $o, A : list_char, Aa : exp_list_char]: ((pred_exp_list_char @ P @ (lAss_list_char @ A @ Aa)) = (((P @ A)) & ((pred_exp_list_char @ P @ Aa))))))). % exp.pred_inject(6)
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_exp_Odistinct_I131_J, axiom,
    ((![X61 : list_char, X62 : exp_list_char, X121 : exp_list_char, X122 : exp_list_char, X123 : exp_list_char]: (~ (((lAss_list_char @ X61 @ X62) = (cond_list_char @ X121 @ X122 @ X123))))))). % exp.distinct(131)
thf(fact_20_hext__refl, axiom,
    ((![H : nat > option2118145160on_val]: (hext @ H @ H)))). % hext_refl
thf(fact_21_prod__cases4, axiom,
    ((![Y : produc1172664615on_val]: (~ ((![A2 : produc1097884484on_val, B : exp_list_char, C : nat > option2118145160on_val, D : list_char > option_val]: (~ ((Y = (produc1069526295on_val @ A2 @ (produc2023458740on_val @ B @ (produc52622304on_val @ C @ D)))))))))))). % prod_cases4
thf(fact_22_prod__induct4, axiom,
    ((![P : produc1172664615on_val > $o, X : produc1172664615on_val]: ((![A2 : produc1097884484on_val, B : exp_list_char, C : nat > option2118145160on_val, D : list_char > option_val]: (P @ (produc1069526295on_val @ A2 @ (produc2023458740on_val @ B @ (produc52622304on_val @ C @ D))))) => (P @ X))))). % prod_induct4
thf(fact_23_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_24_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_25_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_26_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_27_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_28_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_29_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_30_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_31_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_32_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_33_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_34_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_35_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_36_old_Oprod_Oexhaust, axiom,
    ((![Y : produc1172664615on_val]: (~ ((![A2 : produc1097884484on_val, B : produc1097884484on_val]: (~ ((Y = (produc1069526295on_val @ A2 @ B)))))))))). % old.prod.exhaust
thf(fact_37_old_Oprod_Oexhaust, axiom,
    ((![Y : produc1097884484on_val]: (~ ((![A2 : exp_list_char, B : produc515445032on_val]: (~ ((Y = (produc2023458740on_val @ A2 @ B)))))))))). % old.prod.exhaust
thf(fact_38_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_39_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_40_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_41_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_42_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_43_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_44_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_45_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_46_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_47_surj__pair, axiom,
    ((![P2 : produc515445032on_val]: (?[X3 : nat > option2118145160on_val, Y3 : list_char > option_val]: (P2 = (produc52622304on_val @ X3 @ Y3)))))). % surj_pair
thf(fact_48_surj__pair, axiom,
    ((![P2 : produc1172664615on_val]: (?[X3 : produc1097884484on_val, Y3 : produc1097884484on_val]: (P2 = (produc1069526295on_val @ X3 @ Y3)))))). % surj_pair
thf(fact_49_surj__pair, axiom,
    ((![P2 : produc1097884484on_val]: (?[X3 : exp_list_char, Y3 : produc515445032on_val]: (P2 = (produc2023458740on_val @ X3 @ Y3)))))). % surj_pair
thf(fact_50_surj__pair, axiom,
    ((![P2 : produc266837688on_val]: (?[X3 : list_char, Y3 : produc1257910179t_char > option_val]: (P2 = (produc904988266on_val @ X3 @ Y3)))))). % surj_pair
thf(fact_51_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_52_prod__induct3, axiom,
    ((![P : produc1172664615on_val > $o, X : produc1172664615on_val]: ((![A2 : produc1097884484on_val, B : exp_list_char, C : produc515445032on_val]: (P @ (produc1069526295on_val @ A2 @ (produc2023458740on_val @ B @ C)))) => (P @ X))))). % prod_induct3
thf(fact_53_prod__induct3, axiom,
    ((![P : produc1097884484on_val > $o, X : produc1097884484on_val]: ((![A2 : exp_list_char, B : nat > option2118145160on_val, C : list_char > option_val]: (P @ (produc2023458740on_val @ A2 @ (produc52622304on_val @ B @ C)))) => (P @ X))))). % prod_induct3
thf(fact_54_prod__cases3, axiom,
    ((![Y : produc1172664615on_val]: (~ ((![A2 : produc1097884484on_val, B : exp_list_char, C : produc515445032on_val]: (~ ((Y = (produc1069526295on_val @ A2 @ (produc2023458740on_val @ B @ C))))))))))). % prod_cases3
thf(fact_55_prod__cases3, axiom,
    ((![Y : produc1097884484on_val]: (~ ((![A2 : exp_list_char, B : nat > option2118145160on_val, C : list_char > option_val]: (~ ((Y = (produc2023458740on_val @ A2 @ (produc52622304on_val @ B @ C))))))))))). % prod_cases3
thf(fact_56_option_Oinject, axiom,
    ((![X2 : ty, Y2 : ty]: (((some_ty @ X2) = (some_ty @ Y2)) = (X2 = Y2))))). % option.inject
thf(fact_57_option_Oinject, axiom,
    ((![X2 : produc266837688on_val, Y2 : produc266837688on_val]: (((some_P1299442195on_val @ X2) = (some_P1299442195on_val @ Y2)) = (X2 = Y2))))). % option.inject
thf(fact_58_mem__Collect__eq, axiom,
    ((![A : produc1172664615on_val, P : produc1172664615on_val > $o]: ((member354538064on_val @ A @ (collec2055896722on_val @ P)) = (P @ A))))). % mem_Collect_eq
thf(fact_59_Collect__mem__eq, axiom,
    ((![A4 : set_Pr1189492743on_val]: ((collec2055896722on_val @ (^[X4 : produc1172664615on_val]: (member354538064on_val @ X4 @ A4))) = A4)))). % Collect_mem_eq
thf(fact_60_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_61_ty_Odistinct_I1_J, axiom,
    ((~ ((void = boolean))))). % ty.distinct(1)
thf(fact_62_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_63_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_64_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_65_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_66_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_67_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_68_hext__objD, axiom,
    ((![H : nat > option2118145160on_val, H2 : nat > option2118145160on_val, A : nat, C2 : list_char, Fs : produc1257910179t_char > option_val]: ((hext @ H @ H2) => (((H @ A) = (some_P1299442195on_val @ (produc904988266on_val @ C2 @ Fs))) => (?[Fs2 : produc1257910179t_char > option_val]: ((H2 @ A) = (some_P1299442195on_val @ (produc904988266on_val @ C2 @ Fs2))))))))). % hext_objD
thf(fact_69_hext__def, axiom,
    ((hext = (^[H4 : nat > option2118145160on_val]: (^[H5 : nat > option2118145160on_val]: (![A5 : nat]: (![C3 : list_char]: (![Fs3 : produc1257910179t_char > option_val]: ((((H4 @ A5) = (some_P1299442195on_val @ (produc904988266on_val @ C3 @ Fs3)))) => ((?[Fs4 : produc1257910179t_char > option_val]: ((H5 @ A5) = (some_P1299442195on_val @ (produc904988266on_val @ C3 @ Fs4)))))))))))))). % hext_def
thf(fact_70_hextI, axiom,
    ((![H : nat > option2118145160on_val, H2 : nat > option2118145160on_val]: ((![A2 : nat, C4 : list_char, Fs5 : produc1257910179t_char > option_val]: (((H @ A2) = (some_P1299442195on_val @ (produc904988266on_val @ C4 @ Fs5))) => (?[Fs6 : produc1257910179t_char > option_val]: ((H2 @ A2) = (some_P1299442195on_val @ (produc904988266on_val @ C4 @ Fs6)))))) => (hext @ H @ H2))))). % hextI
thf(fact_71_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_72_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_73_sconf__def, axiom,
    ((typeSa1777264139_sconf = (^[P3 : list_P1234162913t_char]: (^[E4 : list_char > option_ty]: (produc99536995_val_o @ (^[H4 : nat > option2118145160on_val]: (^[L3 : list_char > option_val]: (((hconf_1244167010t_char @ P3 @ H4)) & ((lconf_485928294t_char @ P3 @ H4 @ L3 @ E4))))))))))). % sconf_def
thf(fact_74_red__reds_OCondThrow, axiom,
    ((![E2 : exp_list_char, 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 @ (throw_list_char @ E2) @ E_1 @ E_2) @ S2) @ (produc2023458740on_val @ (throw_list_char @ E2) @ S2)) @ (red @ P))))). % red_reds.CondThrow
thf(fact_75_red__reds_OLAssThrow, axiom,
    ((![V2 : list_char, E2 : exp_list_char, S2 : produc515445032on_val, P : list_P1234162913t_char]: (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (lAss_list_char @ V2 @ (throw_list_char @ E2)) @ S2) @ (produc2023458740on_val @ (throw_list_char @ E2) @ S2)) @ (red @ P))))). % red_reds.LAssThrow
thf(fact_76_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_77_split__part, axiom,
    ((![P : $o, Q : (nat > option2118145160on_val) > (list_char > option_val) > $o]: ((produc99536995_val_o @ (^[A5 : nat > option2118145160on_val]: (^[B4 : list_char > option_val]: ((P) & ((Q @ A5 @ B4)))))) = (^[Ab2 : produc515445032on_val]: ((P) & ((produc99536995_val_o @ Q @ Ab2)))))))). % split_part
thf(fact_78_exp_Opred__inject_I14_J, axiom,
    ((![P : list_char > $o, A : exp_list_char]: ((pred_exp_list_char @ P @ (throw_list_char @ A)) = (pred_exp_list_char @ P @ A))))). % exp.pred_inject(14)
thf(fact_79_case__prod__conv, axiom,
    ((![F : (nat > option2118145160on_val) > (list_char > option_val) > $o, A : nat > option2118145160on_val, B2 : list_char > option_val]: ((produc99536995_val_o @ F @ (produc52622304on_val @ A @ B2)) = (F @ A @ B2))))). % case_prod_conv
thf(fact_80_case__prodI2, axiom,
    ((![P2 : produc1172664615on_val, C5 : produc1097884484on_val > produc1097884484on_val > $o]: ((![A2 : produc1097884484on_val, B : produc1097884484on_val]: ((P2 = (produc1069526295on_val @ A2 @ B)) => (C5 @ A2 @ B))) => (produc50362220_val_o @ C5 @ P2))))). % case_prodI2
thf(fact_81_case__prodI2, axiom,
    ((![P2 : produc1097884484on_val, C5 : exp_list_char > produc515445032on_val > $o]: ((![A2 : exp_list_char, B : produc515445032on_val]: ((P2 = (produc2023458740on_val @ A2 @ B)) => (C5 @ A2 @ B))) => (produc199145871_val_o @ C5 @ P2))))). % case_prodI2
thf(fact_82_case__prodI2, axiom,
    ((![P2 : produc266837688on_val, C5 : list_char > (produc1257910179t_char > option_val) > $o]: ((![A2 : list_char, B : produc1257910179t_char > option_val]: ((P2 = (produc904988266on_val @ A2 @ B)) => (C5 @ A2 @ B))) => (produc1336856385_val_o @ C5 @ P2))))). % case_prodI2
thf(fact_83_case__prodI2, axiom,
    ((![P2 : produc515445032on_val, C5 : (nat > option2118145160on_val) > (list_char > option_val) > $o]: ((![A2 : nat > option2118145160on_val, B : list_char > option_val]: ((P2 = (produc52622304on_val @ A2 @ B)) => (C5 @ A2 @ B))) => (produc99536995_val_o @ C5 @ P2))))). % case_prodI2
thf(fact_84_case__prodI, axiom,
    ((![F : produc1097884484on_val > produc1097884484on_val > $o, A : produc1097884484on_val, B2 : produc1097884484on_val]: ((F @ A @ B2) => (produc50362220_val_o @ F @ (produc1069526295on_val @ A @ B2)))))). % case_prodI
thf(fact_85_case__prodI, axiom,
    ((![F : exp_list_char > produc515445032on_val > $o, A : exp_list_char, B2 : produc515445032on_val]: ((F @ A @ B2) => (produc199145871_val_o @ F @ (produc2023458740on_val @ A @ B2)))))). % case_prodI
thf(fact_86_case__prodI, axiom,
    ((![F : list_char > (produc1257910179t_char > option_val) > $o, A : list_char, B2 : produc1257910179t_char > option_val]: ((F @ A @ B2) => (produc1336856385_val_o @ F @ (produc904988266on_val @ A @ B2)))))). % case_prodI
thf(fact_87_case__prodI, axiom,
    ((![F : (nat > option2118145160on_val) > (list_char > option_val) > $o, A : nat > option2118145160on_val, B2 : list_char > option_val]: ((F @ A @ B2) => (produc99536995_val_o @ F @ (produc52622304on_val @ A @ B2)))))). % case_prodI
thf(fact_88_prod_Ocase__distrib, axiom,
    ((![H : $o > $o, F : (nat > option2118145160on_val) > (list_char > option_val) > $o, Prod : produc515445032on_val]: ((H @ (produc99536995_val_o @ F @ Prod)) = (produc99536995_val_o @ (^[X12 : nat > option2118145160on_val]: (^[X22 : list_char > option_val]: (H @ (F @ X12 @ X22)))) @ Prod))))). % prod.case_distrib
thf(fact_89_prod_Odisc__eq__case, axiom,
    ((![Prod : produc515445032on_val]: (produc99536995_val_o @ (^[Uu : nat > option2118145160on_val]: (^[Uv : list_char > option_val]: $true)) @ Prod)))). % prod.disc_eq_case
thf(fact_90_internal__case__prod__def, axiom,
    ((produc563955725_val_o = produc99536995_val_o))). % internal_case_prod_def
thf(fact_91_old_Oprod_Ocase, axiom,
    ((![F : (nat > option2118145160on_val) > (list_char > option_val) > $o, X1 : nat > option2118145160on_val, X2 : list_char > option_val]: ((produc99536995_val_o @ F @ (produc52622304on_val @ X1 @ X2)) = (F @ X1 @ X2))))). % old.prod.case
thf(fact_92_exp_Odistinct_I135_J, axiom,
    ((![X61 : list_char, X62 : exp_list_char, X14 : exp_list_char]: (~ (((lAss_list_char @ X61 @ X62) = (throw_list_char @ X14))))))). % exp.distinct(135)
thf(fact_93_exp_Odistinct_I201_J, axiom,
    ((![X121 : exp_list_char, X122 : exp_list_char, X123 : exp_list_char, X14 : exp_list_char]: (~ (((cond_list_char @ X121 @ X122 @ X123) = (throw_list_char @ X14))))))). % exp.distinct(201)
thf(fact_94_case__prodE, axiom,
    ((![C5 : produc1097884484on_val > produc1097884484on_val > $o, P2 : produc1172664615on_val]: ((produc50362220_val_o @ C5 @ P2) => (~ ((![X3 : produc1097884484on_val, Y3 : produc1097884484on_val]: ((P2 = (produc1069526295on_val @ X3 @ Y3)) => (~ ((C5 @ X3 @ Y3))))))))))). % case_prodE
thf(fact_95_case__prodE, axiom,
    ((![C5 : exp_list_char > produc515445032on_val > $o, P2 : produc1097884484on_val]: ((produc199145871_val_o @ C5 @ P2) => (~ ((![X3 : exp_list_char, Y3 : produc515445032on_val]: ((P2 = (produc2023458740on_val @ X3 @ Y3)) => (~ ((C5 @ X3 @ Y3))))))))))). % case_prodE
thf(fact_96_case__prodE, axiom,
    ((![C5 : list_char > (produc1257910179t_char > option_val) > $o, P2 : produc266837688on_val]: ((produc1336856385_val_o @ C5 @ P2) => (~ ((![X3 : list_char, Y3 : produc1257910179t_char > option_val]: ((P2 = (produc904988266on_val @ X3 @ Y3)) => (~ ((C5 @ X3 @ Y3))))))))))). % case_prodE
thf(fact_97_case__prodE, axiom,
    ((![C5 : (nat > option2118145160on_val) > (list_char > option_val) > $o, P2 : produc515445032on_val]: ((produc99536995_val_o @ C5 @ P2) => (~ ((![X3 : nat > option2118145160on_val, Y3 : list_char > option_val]: ((P2 = (produc52622304on_val @ X3 @ Y3)) => (~ ((C5 @ X3 @ Y3))))))))))). % case_prodE
thf(fact_98_case__prodD, axiom,
    ((![F : produc1097884484on_val > produc1097884484on_val > $o, A : produc1097884484on_val, B2 : produc1097884484on_val]: ((produc50362220_val_o @ F @ (produc1069526295on_val @ A @ B2)) => (F @ A @ B2))))). % case_prodD
thf(fact_99_case__prodD, axiom,
    ((![F : exp_list_char > produc515445032on_val > $o, A : exp_list_char, B2 : produc515445032on_val]: ((produc199145871_val_o @ F @ (produc2023458740on_val @ A @ B2)) => (F @ A @ B2))))). % case_prodD
thf(fact_100_case__prodD, axiom,
    ((![F : list_char > (produc1257910179t_char > option_val) > $o, A : list_char, B2 : produc1257910179t_char > option_val]: ((produc1336856385_val_o @ F @ (produc904988266on_val @ A @ B2)) => (F @ A @ B2))))). % case_prodD
thf(fact_101_case__prodD, axiom,
    ((![F : (nat > option2118145160on_val) > (list_char > option_val) > $o, A : nat > option2118145160on_val, B2 : list_char > option_val]: ((produc99536995_val_o @ F @ (produc52622304on_val @ A @ B2)) => (F @ A @ B2))))). % case_prodD
thf(fact_102_cond__case__prod__eta, axiom,
    ((![F : (nat > option2118145160on_val) > (list_char > option_val) > $o, G : produc515445032on_val > $o]: ((![X3 : nat > option2118145160on_val, Y3 : list_char > option_val]: ((F @ X3 @ Y3) = (G @ (produc52622304on_val @ X3 @ Y3)))) => ((produc99536995_val_o @ F) = G))))). % cond_case_prod_eta
thf(fact_103_case__prod__eta, axiom,
    ((![F : produc515445032on_val > $o]: ((produc99536995_val_o @ (^[X4 : nat > option2118145160on_val]: (^[Y4 : list_char > option_val]: (F @ (produc52622304on_val @ X4 @ Y4))))) = F)))). % case_prod_eta
thf(fact_104_case__prodE2, axiom,
    ((![Q : $o > $o, P : (nat > option2118145160on_val) > (list_char > option_val) > $o, Z : produc515445032on_val]: ((Q @ (produc99536995_val_o @ P @ Z)) => (~ ((![X3 : nat > option2118145160on_val, Y3 : list_char > option_val]: ((Z = (produc52622304on_val @ X3 @ Y3)) => (~ ((Q @ (P @ X3 @ Y3)))))))))))). % case_prodE2
thf(fact_105_red__reds_OThrowThrow, axiom,
    ((![E2 : exp_list_char, S2 : produc515445032on_val, P : list_P1234162913t_char]: (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (throw_list_char @ (throw_list_char @ E2)) @ S2) @ (produc2023458740on_val @ (throw_list_char @ E2) @ S2)) @ (red @ P))))). % red_reds.ThrowThrow
thf(fact_106_red__reds_OThrowRed, axiom,
    ((![E2 : exp_list_char, S2 : produc515445032on_val, E3 : exp_list_char, S3 : produc515445032on_val, P : list_P1234162913t_char]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E2 @ S2) @ (produc2023458740on_val @ E3 @ S3)) @ (red @ P)) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (throw_list_char @ E2) @ S2) @ (produc2023458740on_val @ (throw_list_char @ E3) @ S3)) @ (red @ P)))))). % red_reds.ThrowRed
thf(fact_107_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_108_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_109_split__cong, axiom,
    ((![Q2 : produc515445032on_val, F : (nat > option2118145160on_val) > (list_char > option_val) > $o, G : (nat > option2118145160on_val) > (list_char > option_val) > $o, P2 : produc515445032on_val]: ((![X3 : nat > option2118145160on_val, Y3 : list_char > option_val]: (((produc52622304on_val @ X3 @ Y3) = Q2) => ((F @ X3 @ Y3) = (G @ X3 @ Y3)))) => ((P2 = Q2) => ((produc99536995_val_o @ F @ P2) = (produc99536995_val_o @ G @ Q2))))))). % split_cong
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_mem__case__prodI, axiom,
    ((![Z : produc1172664615on_val, C5 : (nat > option2118145160on_val) > (list_char > option_val) > set_Pr1189492743on_val, A : nat > option2118145160on_val, B2 : list_char > option_val]: ((member354538064on_val @ Z @ (C5 @ A @ B2)) => (member354538064on_val @ Z @ (produc1919805778on_val @ C5 @ (produc52622304on_val @ A @ B2))))))). % mem_case_prodI
thf(fact_112_mem__case__prodI, axiom,
    ((![Z : produc1172664615on_val, C5 : produc1097884484on_val > produc1097884484on_val > set_Pr1189492743on_val, A : produc1097884484on_val, B2 : produc1097884484on_val]: ((member354538064on_val @ Z @ (C5 @ A @ B2)) => (member354538064on_val @ Z @ (produc493625819on_val @ C5 @ (produc1069526295on_val @ A @ B2))))))). % mem_case_prodI
thf(fact_113_mem__case__prodI, axiom,
    ((![Z : produc1172664615on_val, C5 : exp_list_char > produc515445032on_val > set_Pr1189492743on_val, A : exp_list_char, B2 : produc515445032on_val]: ((member354538064on_val @ Z @ (C5 @ A @ B2)) => (member354538064on_val @ Z @ (produc848217214on_val @ C5 @ (produc2023458740on_val @ A @ B2))))))). % mem_case_prodI
thf(fact_114_mem__case__prodI, axiom,
    ((![Z : produc1172664615on_val, C5 : list_char > (produc1257910179t_char > option_val) > set_Pr1189492743on_val, A : list_char, B2 : produc1257910179t_char > option_val]: ((member354538064on_val @ Z @ (C5 @ A @ B2)) => (member354538064on_val @ Z @ (produc535686448on_val @ C5 @ (produc904988266on_val @ A @ B2))))))). % mem_case_prodI
thf(fact_115_mem__case__prodI2, axiom,
    ((![P2 : produc515445032on_val, Z : produc1172664615on_val, C5 : (nat > option2118145160on_val) > (list_char > option_val) > set_Pr1189492743on_val]: ((![A2 : nat > option2118145160on_val, B : list_char > option_val]: ((P2 = (produc52622304on_val @ A2 @ B)) => (member354538064on_val @ Z @ (C5 @ A2 @ B)))) => (member354538064on_val @ Z @ (produc1919805778on_val @ C5 @ P2)))))). % mem_case_prodI2
thf(fact_116_mem__case__prodI2, axiom,
    ((![P2 : produc1172664615on_val, Z : produc1172664615on_val, C5 : produc1097884484on_val > produc1097884484on_val > set_Pr1189492743on_val]: ((![A2 : produc1097884484on_val, B : produc1097884484on_val]: ((P2 = (produc1069526295on_val @ A2 @ B)) => (member354538064on_val @ Z @ (C5 @ A2 @ B)))) => (member354538064on_val @ Z @ (produc493625819on_val @ C5 @ P2)))))). % mem_case_prodI2
thf(fact_117_mem__case__prodI2, axiom,
    ((![P2 : produc1097884484on_val, Z : produc1172664615on_val, C5 : exp_list_char > produc515445032on_val > set_Pr1189492743on_val]: ((![A2 : exp_list_char, B : produc515445032on_val]: ((P2 = (produc2023458740on_val @ A2 @ B)) => (member354538064on_val @ Z @ (C5 @ A2 @ B)))) => (member354538064on_val @ Z @ (produc848217214on_val @ C5 @ P2)))))). % mem_case_prodI2
thf(fact_118_mem__case__prodI2, axiom,
    ((![P2 : produc266837688on_val, Z : produc1172664615on_val, C5 : list_char > (produc1257910179t_char > option_val) > set_Pr1189492743on_val]: ((![A2 : list_char, B : produc1257910179t_char > option_val]: ((P2 = (produc904988266on_val @ A2 @ B)) => (member354538064on_val @ Z @ (C5 @ A2 @ B)))) => (member354538064on_val @ Z @ (produc535686448on_val @ C5 @ P2)))))). % mem_case_prodI2
thf(fact_119_case__prod__Pair__iden, axiom,
    ((![P2 : produc515445032on_val]: ((produc2088825459on_val @ produc52622304on_val @ P2) = P2)))). % case_prod_Pair_iden
thf(fact_120_case__prod__Pair__iden, axiom,
    ((![P2 : produc1172664615on_val]: ((produc64793339on_val @ produc1069526295on_val @ P2) = P2)))). % case_prod_Pair_iden
thf(fact_121_case__prod__Pair__iden, axiom,
    ((![P2 : produc1097884484on_val]: ((produc1537230907on_val @ produc2023458740on_val @ P2) = P2)))). % case_prod_Pair_iden
thf(fact_122_case__prod__Pair__iden, axiom,
    ((![P2 : produc266837688on_val]: ((produc1336886479on_val @ produc904988266on_val @ P2) = P2)))). % case_prod_Pair_iden
thf(fact_123_mem__case__prodE, axiom,
    ((![Z : produc1172664615on_val, C5 : (nat > option2118145160on_val) > (list_char > option_val) > set_Pr1189492743on_val, P2 : produc515445032on_val]: ((member354538064on_val @ Z @ (produc1919805778on_val @ C5 @ P2)) => (~ ((![X3 : nat > option2118145160on_val, Y3 : list_char > option_val]: ((P2 = (produc52622304on_val @ X3 @ Y3)) => (~ ((member354538064on_val @ Z @ (C5 @ X3 @ Y3)))))))))))). % mem_case_prodE
thf(fact_124_mem__case__prodE, axiom,
    ((![Z : produc1172664615on_val, C5 : produc1097884484on_val > produc1097884484on_val > set_Pr1189492743on_val, P2 : produc1172664615on_val]: ((member354538064on_val @ Z @ (produc493625819on_val @ C5 @ P2)) => (~ ((![X3 : produc1097884484on_val, Y3 : produc1097884484on_val]: ((P2 = (produc1069526295on_val @ X3 @ Y3)) => (~ ((member354538064on_val @ Z @ (C5 @ X3 @ Y3)))))))))))). % mem_case_prodE
thf(fact_125_mem__case__prodE, axiom,
    ((![Z : produc1172664615on_val, C5 : exp_list_char > produc515445032on_val > set_Pr1189492743on_val, P2 : produc1097884484on_val]: ((member354538064on_val @ Z @ (produc848217214on_val @ C5 @ P2)) => (~ ((![X3 : exp_list_char, Y3 : produc515445032on_val]: ((P2 = (produc2023458740on_val @ X3 @ Y3)) => (~ ((member354538064on_val @ Z @ (C5 @ X3 @ Y3)))))))))))). % mem_case_prodE
thf(fact_126_mem__case__prodE, axiom,
    ((![Z : produc1172664615on_val, C5 : list_char > (produc1257910179t_char > option_val) > set_Pr1189492743on_val, P2 : produc266837688on_val]: ((member354538064on_val @ Z @ (produc535686448on_val @ C5 @ P2)) => (~ ((![X3 : list_char, Y3 : produc1257910179t_char > option_val]: ((P2 = (produc904988266on_val @ X3 @ Y3)) => (~ ((member354538064on_val @ Z @ (C5 @ X3 @ Y3)))))))))))). % mem_case_prodE
thf(fact_127_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_128_CondRedsThrow, axiom,
    ((![E2 : exp_list_char, S2 : produc515445032on_val, A : 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 @ (throw_list_char @ A) @ S3)) @ (transi111096263on_val @ (red @ P))) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (cond_list_char @ E2 @ E_1 @ E_2) @ S2) @ (produc2023458740on_val @ (throw_list_char @ A) @ S3)) @ (transi111096263on_val @ (red @ P))))))). % CondRedsThrow
thf(fact_129_LAssRedsThrow, axiom,
    ((![E2 : exp_list_char, S2 : produc515445032on_val, A : exp_list_char, S3 : produc515445032on_val, P : list_P1234162913t_char, V2 : list_char]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E2 @ S2) @ (produc2023458740on_val @ (throw_list_char @ A) @ S3)) @ (transi111096263on_val @ (red @ P))) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (lAss_list_char @ V2 @ E2) @ S2) @ (produc2023458740on_val @ (throw_list_char @ A) @ S3)) @ (transi111096263on_val @ (red @ P))))))). % LAssRedsThrow
thf(fact_130_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_131_ThrowRedsThrow, axiom,
    ((![E2 : exp_list_char, S2 : produc515445032on_val, A : exp_list_char, S3 : produc515445032on_val, P : list_P1234162913t_char]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E2 @ S2) @ (produc2023458740on_val @ (throw_list_char @ A) @ S3)) @ (transi111096263on_val @ (red @ P))) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (throw_list_char @ E2) @ S2) @ (produc2023458740on_val @ (throw_list_char @ A) @ S3)) @ (transi111096263on_val @ (red @ P))))))). % ThrowRedsThrow
thf(fact_132_ThrowReds, axiom,
    ((![E2 : exp_list_char, S2 : produc515445032on_val, E3 : exp_list_char, S3 : produc515445032on_val, P : list_P1234162913t_char]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E2 @ S2) @ (produc2023458740on_val @ E3 @ S3)) @ (transi111096263on_val @ (red @ P))) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (throw_list_char @ E2) @ S2) @ (produc2023458740on_val @ (throw_list_char @ E3) @ S3)) @ (transi111096263on_val @ (red @ P))))))). % ThrowReds
thf(fact_133_LAssReds, axiom,
    ((![E2 : exp_list_char, S2 : produc515445032on_val, E3 : exp_list_char, S3 : produc515445032on_val, P : list_P1234162913t_char, V2 : list_char]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E2 @ S2) @ (produc2023458740on_val @ E3 @ S3)) @ (transi111096263on_val @ (red @ P))) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (lAss_list_char @ V2 @ E2) @ S2) @ (produc2023458740on_val @ (lAss_list_char @ V2 @ E3) @ S3)) @ (transi111096263on_val @ (red @ P))))))). % LAssReds
thf(fact_134_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_135_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_136_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_137_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_138_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_139_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_140_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_141_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_142_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_143_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_144_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_145_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_146_rtrancl__idemp, axiom,
    ((![R2 : set_Pr1189492743on_val]: ((transi111096263on_val @ (transi111096263on_val @ R2)) = (transi111096263on_val @ R2))))). % rtrancl_idemp
thf(fact_147_r__into__rtrancl, axiom,
    ((![P2 : produc1172664615on_val, R2 : set_Pr1189492743on_val]: ((member354538064on_val @ P2 @ R2) => (member354538064on_val @ P2 @ (transi111096263on_val @ R2)))))). % r_into_rtrancl
thf(fact_148_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_149_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_150_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, Z2 : produc1097884484on_val]: ((member354538064on_val @ (produc1069526295on_val @ Y3 @ Z2) @ R2) => ((member354538064on_val @ (produc1069526295on_val @ Z2 @ B2) @ (transi111096263on_val @ R2)) => ((P @ Z2) => (P @ Y3))))) => (P @ A))))))). % converse_rtrancl_induct
thf(fact_151_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_152_converse__rtranclE, axiom,
    ((![X : produc1097884484on_val, Z : produc1097884484on_val, R2 : set_Pr1189492743on_val]: ((member354538064on_val @ (produc1069526295on_val @ X @ Z) @ (transi111096263on_val @ R2)) => ((~ ((X = Z))) => (~ ((![Y3 : produc1097884484on_val]: ((member354538064on_val @ (produc1069526295on_val @ X @ Y3) @ R2) => (~ ((member354538064on_val @ (produc1069526295on_val @ Y3 @ Z) @ (transi111096263on_val @ R2))))))))))))). % converse_rtranclE
thf(fact_153_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, C : produc1097884484on_val]: ((member354538064on_val @ (produc1069526295on_val @ A2 @ B) @ (transi111096263on_val @ R2)) => ((P @ A2 @ B) => ((member354538064on_val @ (produc1069526295on_val @ B @ C) @ R2) => (P @ A2 @ C))))) => (P @ X1 @ X2))))))). % rtrancl.inducts
thf(fact_154_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, Z2 : produc1097884484on_val]: ((member354538064on_val @ (produc1069526295on_val @ A @ Y3) @ (transi111096263on_val @ R2)) => ((member354538064on_val @ (produc1069526295on_val @ Y3 @ Z2) @ R2) => ((P @ Y3) => (P @ Z2))))) => (P @ B2))))))). % rtrancl_induct
thf(fact_155_rtrancl__trans, axiom,
    ((![X : produc1097884484on_val, Y : produc1097884484on_val, R2 : set_Pr1189492743on_val, Z : produc1097884484on_val]: ((member354538064on_val @ (produc1069526295on_val @ X @ Y) @ (transi111096263on_val @ R2)) => ((member354538064on_val @ (produc1069526295on_val @ Y @ Z) @ (transi111096263on_val @ R2)) => (member354538064on_val @ (produc1069526295on_val @ X @ Z) @ (transi111096263on_val @ R2))))))). % rtrancl_trans
thf(fact_156_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_157_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_158_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_159_WhileRedsThrow, axiom,
    ((![B2 : exp_list_char, S2 : produc515445032on_val, E2 : exp_list_char, S3 : produc515445032on_val, P : list_P1234162913t_char, C5 : exp_list_char]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ B2 @ S2) @ (produc2023458740on_val @ (throw_list_char @ E2) @ S3)) @ (transi111096263on_val @ (red @ P))) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (while_list_char @ B2 @ C5) @ S2) @ (produc2023458740on_val @ (throw_list_char @ E2) @ S3)) @ (transi111096263on_val @ (red @ P))))))). % WhileRedsThrow
thf(fact_160_FAccRedsThrow, axiom,
    ((![E2 : exp_list_char, S2 : produc515445032on_val, A : exp_list_char, S3 : produc515445032on_val, P : list_P1234162913t_char, F2 : list_char, D2 : list_char]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E2 @ S2) @ (produc2023458740on_val @ (throw_list_char @ A) @ S3)) @ (transi111096263on_val @ (red @ P))) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (fAcc_list_char @ E2 @ F2 @ D2) @ S2) @ (produc2023458740on_val @ (throw_list_char @ A) @ S3)) @ (transi111096263on_val @ (red @ P))))))). % FAccRedsThrow
thf(fact_161_CastRedsThrow, axiom,
    ((![E2 : exp_list_char, S2 : produc515445032on_val, A : exp_list_char, S3 : produc515445032on_val, P : list_P1234162913t_char, C2 : list_char]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E2 @ S2) @ (produc2023458740on_val @ (throw_list_char @ A) @ S3)) @ (transi111096263on_val @ (red @ P))) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (cast_list_char @ C2 @ E2) @ S2) @ (produc2023458740on_val @ (throw_list_char @ A) @ S3)) @ (transi111096263on_val @ (red @ P))))))). % CastRedsThrow
thf(fact_162_exp_Oinject_I2_J, axiom,
    ((![X21 : list_char, X222 : exp_list_char, Y21 : list_char, Y22 : exp_list_char]: (((cast_list_char @ X21 @ X222) = (cast_list_char @ Y21 @ Y22)) = (((X21 = Y21)) & ((X222 = Y22))))))). % exp.inject(2)
thf(fact_163_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_164_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_165_exp_Opred__inject_I2_J, axiom,
    ((![P : list_char > $o, A : list_char, Aa : exp_list_char]: ((pred_exp_list_char @ P @ (cast_list_char @ A @ Aa)) = (pred_exp_list_char @ P @ Aa))))). % exp.pred_inject(2)
thf(fact_166_exp_Opred__inject_I7_J, axiom,
    ((![P : list_char > $o, A : exp_list_char, Aa : list_char, Ab : list_char]: ((pred_exp_list_char @ P @ (fAcc_list_char @ A @ Aa @ Ab)) = (pred_exp_list_char @ P @ A))))). % exp.pred_inject(7)
thf(fact_167_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_168_exp_Odistinct_I205_J, axiom,
    ((![X131 : exp_list_char, X132 : exp_list_char, X14 : exp_list_char]: (~ (((while_list_char @ X131 @ X132) = (throw_list_char @ X14))))))). % exp.distinct(205)
thf(fact_169_exp_Odistinct_I51_J, axiom,
    ((![X21 : list_char, X222 : exp_list_char, X14 : exp_list_char]: (~ (((cast_list_char @ X21 @ X222) = (throw_list_char @ X14))))))). % exp.distinct(51)
thf(fact_170_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_171_exp_Odistinct_I133_J, axiom,
    ((![X61 : list_char, X62 : exp_list_char, X131 : exp_list_char, X132 : exp_list_char]: (~ (((lAss_list_char @ X61 @ X62) = (while_list_char @ X131 @ X132))))))). % exp.distinct(133)
thf(fact_172_exp_Odistinct_I35_J, axiom,
    ((![X21 : list_char, X222 : exp_list_char, X61 : list_char, X62 : exp_list_char]: (~ (((cast_list_char @ X21 @ X222) = (lAss_list_char @ X61 @ X62))))))). % exp.distinct(35)
thf(fact_173_exp_Odistinct_I121_J, axiom,
    ((![X61 : list_char, X62 : exp_list_char, X71 : exp_list_char, X72 : list_char, X73 : list_char]: (~ (((lAss_list_char @ X61 @ X62) = (fAcc_list_char @ X71 @ X72 @ X73))))))). % exp.distinct(121)
thf(fact_174_exp_Odistinct_I199_J, axiom,
    ((![X121 : exp_list_char, X122 : exp_list_char, X123 : exp_list_char, X131 : exp_list_char, X132 : exp_list_char]: (~ (((cond_list_char @ X121 @ X122 @ X123) = (while_list_char @ X131 @ X132))))))). % exp.distinct(199)
thf(fact_175_exp_Odistinct_I147_J, axiom,
    ((![X71 : exp_list_char, X72 : list_char, X73 : list_char, X121 : exp_list_char, X122 : exp_list_char, X123 : exp_list_char]: (~ (((fAcc_list_char @ X71 @ X72 @ X73) = (cond_list_char @ X121 @ X122 @ X123))))))). % exp.distinct(147)
thf(fact_176_exp_Odistinct_I47_J, axiom,
    ((![X21 : list_char, X222 : exp_list_char, X121 : exp_list_char, X122 : exp_list_char, X123 : exp_list_char]: (~ (((cast_list_char @ X21 @ X222) = (cond_list_char @ X121 @ X122 @ X123))))))). % exp.distinct(47)
thf(fact_177_exp_Odistinct_I149_J, axiom,
    ((![X71 : exp_list_char, X72 : list_char, X73 : list_char, X131 : exp_list_char, X132 : exp_list_char]: (~ (((fAcc_list_char @ X71 @ X72 @ X73) = (while_list_char @ X131 @ X132))))))). % exp.distinct(149)
thf(fact_178_exp_Odistinct_I49_J, axiom,
    ((![X21 : list_char, X222 : exp_list_char, X131 : exp_list_char, X132 : exp_list_char]: (~ (((cast_list_char @ X21 @ X222) = (while_list_char @ X131 @ X132))))))). % exp.distinct(49)
thf(fact_179_exp_Odistinct_I37_J, axiom,
    ((![X21 : list_char, X222 : exp_list_char, X71 : exp_list_char, X72 : list_char, X73 : list_char]: (~ (((cast_list_char @ X21 @ X222) = (fAcc_list_char @ X71 @ X72 @ X73))))))). % exp.distinct(37)
thf(fact_180_red__reds_OCastRed, axiom,
    ((![E2 : exp_list_char, S2 : produc515445032on_val, E3 : exp_list_char, S3 : produc515445032on_val, P : list_P1234162913t_char, C2 : list_char]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E2 @ S2) @ (produc2023458740on_val @ E3 @ S3)) @ (red @ P)) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (cast_list_char @ C2 @ E2) @ S2) @ (produc2023458740on_val @ (cast_list_char @ C2 @ E3) @ S3)) @ (red @ P)))))). % red_reds.CastRed
thf(fact_181_red__reds_OFAccRed, axiom,
    ((![E2 : exp_list_char, S2 : produc515445032on_val, E3 : exp_list_char, S3 : produc515445032on_val, P : list_P1234162913t_char, F2 : list_char, D2 : list_char]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E2 @ S2) @ (produc2023458740on_val @ E3 @ S3)) @ (red @ P)) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (fAcc_list_char @ E2 @ F2 @ D2) @ S2) @ (produc2023458740on_val @ (fAcc_list_char @ E3 @ F2 @ D2) @ S3)) @ (red @ P)))))). % red_reds.FAccRed
thf(fact_182_WTrtWhile, axiom,
    ((![P : list_P1234162913t_char, H : nat > option2118145160on_val, E : list_char > option_ty, E2 : exp_list_char, C5 : exp_list_char, T : ty]: ((wTrt @ P @ H @ E @ E2 @ boolean) => ((wTrt @ P @ H @ E @ C5 @ T) => (wTrt @ P @ H @ E @ (while_list_char @ E2 @ C5) @ void)))))). % WTrtWhile
thf(fact_183_WTrt__elim__cases_I3_J, axiom,
    ((![P : list_P1234162913t_char, H : nat > option2118145160on_val, E : list_char > option_ty, E2 : exp_list_char, C5 : exp_list_char, T : ty]: ((wTrt @ P @ H @ E @ (while_list_char @ E2 @ C5) @ T) => (~ (((T = void) => ((wTrt @ P @ H @ E @ E2 @ boolean) => (![T3 : ty]: (~ ((wTrt @ P @ H @ E @ C5 @ T3)))))))))))). % WTrt_elim_cases(3)
thf(fact_184_red__reds_OCastThrow, axiom,
    ((![C2 : list_char, E2 : exp_list_char, S2 : produc515445032on_val, P : list_P1234162913t_char]: (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (cast_list_char @ C2 @ (throw_list_char @ E2)) @ S2) @ (produc2023458740on_val @ (throw_list_char @ E2) @ S2)) @ (red @ P))))). % red_reds.CastThrow
thf(fact_185_red__reds_OFAccThrow, axiom,
    ((![E2 : exp_list_char, F2 : list_char, D2 : list_char, S2 : produc515445032on_val, P : list_P1234162913t_char]: (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (fAcc_list_char @ (throw_list_char @ E2) @ F2 @ D2) @ S2) @ (produc2023458740on_val @ (throw_list_char @ E2) @ S2)) @ (red @ P))))). % red_reds.FAccThrow
thf(fact_186_CastReds, axiom,
    ((![E2 : exp_list_char, S2 : produc515445032on_val, E3 : exp_list_char, S3 : produc515445032on_val, P : list_P1234162913t_char, C2 : list_char]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E2 @ S2) @ (produc2023458740on_val @ E3 @ S3)) @ (transi111096263on_val @ (red @ P))) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (cast_list_char @ C2 @ E2) @ S2) @ (produc2023458740on_val @ (cast_list_char @ C2 @ E3) @ S3)) @ (transi111096263on_val @ (red @ P))))))). % CastReds
thf(fact_187_FAccReds, axiom,
    ((![E2 : exp_list_char, S2 : produc515445032on_val, E3 : exp_list_char, S3 : produc515445032on_val, P : list_P1234162913t_char, F2 : list_char, D2 : list_char]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E2 @ S2) @ (produc2023458740on_val @ E3 @ S3)) @ (transi111096263on_val @ (red @ P))) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (fAcc_list_char @ E2 @ F2 @ D2) @ S2) @ (produc2023458740on_val @ (fAcc_list_char @ E3 @ F2 @ D2) @ S3)) @ (transi111096263on_val @ (red @ P))))))). % FAccReds

% Conjectures (1)
thf(conj_0, conjecture,
    ((?[T5 : ty]: ((wTrt @ p @ aa @ e @ (lAss_list_char @ v @ e_a) @ T5) & (widen_917054840t_char @ p @ T5 @ t))))).
