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% This file was generated by Isabelle (most likely Sledgehammer)
% 2020-12-16 14:21:11.033

% Could-be-implicit typings (25)
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% Explicit typings (63)
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thf(sy_c_Type_Ois__refT, type,
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thf(sy_c_Type_Oty_OClass, type,
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thf(sy_c_Type_Oty_ONT, type,
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thf(sy_c_Type_Oty_OVoid, type,
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% Relevant facts (192)
thf(fact_0_UClass, axiom,
    ((u = (class @ c)))). % UClass
thf(fact_1_void, axiom,
    ((t = void))). % void
thf(fact_2_sub, axiom,
    ((widen_917054840t_char @ p @ t_2 @ tf))). % sub
thf(fact_3__092_060open_062P_A_092_060turnstile_062_AC_H_Ahas_AF_058TF_Ain_AD_092_060close_062, axiom,
    ((has_fi599584195t_char @ p @ c @ f @ tf @ d))). % \<open>P \<turnstile> C' has F:TF in D\<close>
thf(fact_4_wt_092_060_094sub_0622_H, axiom,
    ((wTrt2 @ p @ h_a @ e @ e_2 @ t_2))). % wt\<^sub>2'
thf(fact_5__092_060open_062P_ME_Mh_H_A_092_060turnstile_062_Ae_H_A_058_AClass_AC_H_092_060close_062, axiom,
    ((wTrt2 @ p @ h_a @ e @ e_a @ (class @ c)))). % \<open>P,E,h' \<turnstile> e' : Class C'\<close>
thf(fact_6_wt_092_060_094sub_0621_H, axiom,
    ((wTrt2 @ p @ h_a @ e @ e_a @ u))). % wt\<^sub>1'
thf(fact_7_has, axiom,
    ((has_fi599584195t_char @ p @ c2 @ f @ tf @ d))). % has
thf(fact_8_wt_092_060_094sub_0622, axiom,
    ((wTrt2 @ p @ ha @ e @ e_2 @ t_2))). % wt\<^sub>2
thf(fact_9__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062U_O_A_092_060lbrakk_062P_ME_Mh_H_A_092_060turnstile_062_Ae_H_A_058_AU_059_AP_A_092_060turnstile_062_AU_A_092_060le_062_AClass_AC_092_060rbrakk_062_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062, axiom,
    ((~ ((![U : ty]: ((wTrt2 @ p @ h_a @ e @ e_a @ U) => (~ ((widen_917054840t_char @ p @ U @ (class @ c2)))))))))). % \<open>\<And>thesis. (\<And>U. \<lbrakk>P,E,h' \<turnstile> e' : U; P \<turnstile> U \<le> Class C\<rbrakk> \<Longrightarrow> thesis) \<Longrightarrow> thesis\<close>
thf(fact_10_FAssRed1_Oprems_I2_J, axiom,
    ((wTrt2 @ p @ ha @ e @ (fAss_list_char @ ea @ f @ d @ e_2) @ t))). % FAssRed1.prems(2)
thf(fact_11__092_060open_062U_A_061_ANT_A_092_060Longrightarrow_062_A_092_060exists_062T_H_O_AP_ME_Mh_H_A_092_060turnstile_062_Ae_H_092_060bullet_062F_123D_125_A_058_061_Ae_092_060_094sub_0622_A_058_AT_H_A_092_060and_062_AP_A_092_060turnstile_062_AT_H_A_092_060le_062_AT_092_060close_062, axiom,
    (((u = nt) => (?[T : ty]: ((wTrt2 @ p @ h_a @ e @ (fAss_list_char @ e_a @ f @ d @ e_2) @ T) & (widen_917054840t_char @ p @ T @ t)))))). % \<open>U = NT \<Longrightarrow> \<exists>T'. P,E,h' \<turnstile> e'\<bullet>F{D} := e\<^sub>2 : T' \<and> P \<turnstile> T' \<le> T\<close>
thf(fact_12_wt, axiom,
    ((wTrt2 @ p @ ha @ e @ (fAss_list_char @ ea @ f @ d @ e_2) @ t))). % wt
thf(fact_13_UsubC, axiom,
    ((widen_917054840t_char @ p @ u @ (class @ c2)))). % UsubC
thf(fact_14__092_060open_062P_ME_Mh_A_092_060turnstile_062_Ae_A_058_ANT_A_092_060Longrightarrow_062_A_092_060exists_062T_H_O_AP_ME_Mh_H_A_092_060turnstile_062_Ae_H_092_060bullet_062F_123D_125_A_058_061_Ae_092_060_094sub_0622_A_058_AT_H_A_092_060and_062_AP_A_092_060turnstile_062_AT_H_A_092_060le_062_AT_092_060close_062, axiom,
    (((wTrt2 @ p @ ha @ e @ ea @ nt) => (?[T : ty]: ((wTrt2 @ p @ h_a @ e @ (fAss_list_char @ e_a @ f @ d @ e_2) @ T) & (widen_917054840t_char @ p @ T @ t)))))). % \<open>P,E,h \<turnstile> e : NT \<Longrightarrow> \<exists>T'. P,E,h' \<turnstile> e'\<bullet>F{D} := e\<^sub>2 : T' \<and> P \<turnstile> T' \<le> T\<close>
thf(fact_15_exp_Oinject_I8_J, axiom,
    ((![X81 : exp_list_char, X82 : list_char, X83 : list_char, X84 : exp_list_char, Y81 : exp_list_char, Y82 : list_char, Y83 : list_char, Y84 : exp_list_char]: (((fAss_list_char @ X81 @ X82 @ X83 @ X84) = (fAss_list_char @ Y81 @ Y82 @ Y83 @ Y84)) = (((X81 = Y81)) & ((((X82 = Y82)) & ((((X83 = Y83)) & ((X84 = Y84))))))))))). % exp.inject(8)
thf(fact_16_local_Owf, axiom,
    ((wf_pro1229751607t_char @ wf_J_mdecl @ p))). % local.wf
thf(fact_17_widen__trans, axiom,
    ((![P : list_P1234162913t_char, S : ty, U2 : ty, T2 : ty]: ((widen_917054840t_char @ P @ S @ U2) => ((widen_917054840t_char @ P @ U2 @ T2) => (widen_917054840t_char @ P @ S @ T2)))))). % widen_trans
thf(fact_18_widen__refl, axiom,
    ((![P : list_P1234162913t_char, T2 : ty]: (widen_917054840t_char @ P @ T2 @ T2)))). % widen_refl
thf(fact_19_wt_092_060_094sub_0621, axiom,
    ((wTrt2 @ p @ ha @ e @ ea @ (class @ c2)))). % wt\<^sub>1
thf(fact_20_WTrtFAss, axiom,
    ((![P : list_P1234162913t_char, H : nat > option2118145160on_val, E : list_char > option_ty, E_1 : exp_list_char, C : list_char, F : list_char, T2 : ty, D : list_char, E_2 : exp_list_char, T_2 : ty]: ((wTrt2 @ P @ H @ E @ E_1 @ (class @ C)) => ((has_fi599584195t_char @ P @ C @ F @ T2 @ D) => ((wTrt2 @ P @ H @ E @ E_2 @ T_2) => ((widen_917054840t_char @ P @ T_2 @ T2) => (wTrt2 @ P @ H @ E @ (fAss_list_char @ E_1 @ F @ D @ E_2) @ void)))))))). % WTrtFAss
thf(fact_21_widen__null, axiom,
    ((![P : list_P1234162913t_char, C : list_char]: (widen_917054840t_char @ P @ nt @ (class @ C))))). % widen_null
thf(fact_22_WTrtFAssNT, axiom,
    ((![P : list_P1234162913t_char, H : nat > option2118145160on_val, E : list_char > option_ty, E_1 : exp_list_char, E_2 : exp_list_char, T_2 : ty, F : list_char, D : list_char]: ((wTrt2 @ P @ H @ E @ E_1 @ nt) => ((wTrt2 @ P @ H @ E @ E_2 @ T_2) => (wTrt2 @ P @ H @ E @ (fAss_list_char @ E_1 @ F @ D @ E_2) @ void)))))). % WTrtFAssNT
thf(fact_23_WTrt__elim__cases_I8_J, axiom,
    ((![P : list_P1234162913t_char, H : nat > option2118145160on_val, E : list_char > option_ty, E2 : exp_list_char, F : list_char, D : list_char, V : exp_list_char, T2 : ty]: ((wTrt2 @ P @ H @ E @ (fAss_list_char @ E2 @ F @ D @ V) @ T2) => (((T2 = void) => (![C2 : list_char]: ((wTrt2 @ P @ H @ E @ E2 @ (class @ C2)) => (![T3 : ty]: ((has_fi599584195t_char @ P @ C2 @ F @ T3 @ D) => (![T_22 : ty]: ((wTrt2 @ P @ H @ E @ V @ T_22) => (~ ((widen_917054840t_char @ P @ T_22 @ T3)))))))))) => (~ (((T2 = void) => ((wTrt2 @ P @ H @ E @ E2 @ nt) => (![T_22 : ty]: (~ ((wTrt2 @ P @ H @ E @ V @ T_22))))))))))))). % WTrt_elim_cases(8)
thf(fact_24_Class__widen, axiom,
    ((![P : list_P1234162913t_char, C : list_char, T2 : ty]: ((widen_917054840t_char @ P @ (class @ C) @ T2) => (?[D2 : list_char]: (T2 = (class @ D2))))))). % Class_widen
thf(fact_25_ty_Oinject, axiom,
    ((![X5 : list_char, Y5 : list_char]: (((class @ X5) = (class @ Y5)) = (X5 = Y5))))). % ty.inject
thf(fact_26_ty_Odistinct_I5_J, axiom,
    ((~ ((void = nt))))). % ty.distinct(5)
thf(fact_27_ty_Odistinct_I19_J, axiom,
    ((![X5 : list_char]: (~ ((nt = (class @ X5))))))). % ty.distinct(19)
thf(fact_28_ty_Odistinct_I7_J, axiom,
    ((![X5 : list_char]: (~ ((void = (class @ X5))))))). % ty.distinct(7)
thf(fact_29_FAssRed1_Ohyps_I2_J, axiom,
    ((![E : list_char > option_ty, T2 : ty]: ((typeSa1777264139_sconf @ p @ E @ (produc52622304on_val @ ha @ la)) => ((wTrt2 @ p @ ha @ E @ ea @ T2) => (?[T : ty]: ((wTrt2 @ p @ h_a @ E @ e_a @ T) & (widen_917054840t_char @ p @ T @ T2)))))))). % FAssRed1.hyps(2)
thf(fact_30_IH, axiom,
    ((![E : list_char > option_ty, T2 : ty]: ((typeSa1777264139_sconf @ p @ E @ (produc52622304on_val @ ha @ la)) => ((wTrt2 @ p @ ha @ E @ ea @ T2) => (?[U : ty]: ((wTrt2 @ p @ h_a @ E @ e_a @ U) & (widen_917054840t_char @ p @ U @ T2)))))))). % IH
thf(fact_31_FAssRed1_Oprems_I1_J, axiom,
    ((typeSa1777264139_sconf @ p @ e @ (produc52622304on_val @ ha @ la)))). % FAssRed1.prems(1)
thf(fact_32_WTrt__elim__cases_I7_J, axiom,
    ((![P : list_P1234162913t_char, H : nat > option2118145160on_val, E : list_char > option_ty, E2 : exp_list_char, F : list_char, D : list_char, T2 : ty]: ((wTrt2 @ P @ H @ E @ (fAcc_list_char @ E2 @ F @ D) @ T2) => ((![C2 : list_char]: ((wTrt2 @ P @ H @ E @ E2 @ (class @ C2)) => (~ ((has_fi599584195t_char @ P @ C2 @ F @ T2 @ D))))) => (wTrt2 @ P @ H @ E @ E2 @ nt)))))). % WTrt_elim_cases(7)
thf(fact_33_WTrt_H__WTrts_H_Ointros_I10_J, axiom,
    ((![P : list_P1234162913t_char, H : nat > option2118145160on_val, E : list_char > option_ty, E_1 : exp_list_char, C : list_char, F : list_char, T2 : ty, D : list_char, E_2 : exp_list_char, T_2 : ty]: ((wTrt @ P @ H @ E @ E_1 @ (class @ C)) => ((has_fi599584195t_char @ P @ C @ F @ T2 @ D) => ((wTrt @ P @ H @ E @ E_2 @ T_2) => ((widen_917054840t_char @ P @ T_2 @ T2) => (wTrt @ P @ H @ E @ (fAss_list_char @ E_1 @ F @ D @ E_2) @ void)))))))). % WTrt'_WTrts'.intros(10)
thf(fact_34_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_35_conf, axiom,
    ((typeSa1777264139_sconf @ p @ e @ (produc52622304on_val @ ha @ la)))). % conf
thf(fact_36_WTrt_H__WTrts_H_Ointros_I9_J, axiom,
    ((![P : list_P1234162913t_char, H : nat > option2118145160on_val, E : list_char > option_ty, E2 : exp_list_char, F : list_char, D : list_char, T2 : ty]: ((wTrt @ P @ H @ E @ E2 @ nt) => (wTrt @ P @ H @ E @ (fAcc_list_char @ E2 @ F @ D) @ T2))))). % WTrt'_WTrts'.intros(9)
thf(fact_37_wt_H__wt, axiom,
    ((![P : list_P1234162913t_char, H : nat > option2118145160on_val, E : list_char > option_ty, E2 : exp_list_char, T2 : ty]: ((wTrt @ P @ H @ E @ E2 @ T2) => (wTrt2 @ P @ H @ E @ E2 @ T2))))). % wt'_wt
thf(fact_38_wt__wt_H, axiom,
    ((![P : list_P1234162913t_char, H : nat > option2118145160on_val, E : list_char > option_ty, E2 : exp_list_char, T2 : ty]: ((wTrt2 @ P @ H @ E @ E2 @ T2) => (wTrt @ P @ H @ E @ E2 @ T2))))). % wt_wt'
thf(fact_39_wt_H__iff__wt, axiom,
    ((wTrt = wTrt2))). % wt'_iff_wt
thf(fact_40_WTrt_H__WTrts_H_Ointros_I8_J, axiom,
    ((![P : list_P1234162913t_char, H : nat > option2118145160on_val, E : list_char > option_ty, E2 : exp_list_char, C : list_char, F : list_char, T2 : ty, D : list_char]: ((wTrt @ P @ H @ E @ E2 @ (class @ C)) => ((has_fi599584195t_char @ P @ C @ F @ T2 @ D) => (wTrt @ P @ H @ E @ (fAcc_list_char @ E2 @ F @ D) @ T2)))))). % WTrt'_WTrts'.intros(8)
thf(fact_41_exp_Odistinct_I139_J, axiom,
    ((![X71 : exp_list_char, X72 : list_char, X73 : list_char, X81 : exp_list_char, X82 : list_char, X83 : list_char, X84 : exp_list_char]: (~ (((fAcc_list_char @ X71 @ X72 @ X73) = (fAss_list_char @ X81 @ X82 @ X83 @ X84))))))). % exp.distinct(139)
thf(fact_42_WTrtFAccNT, axiom,
    ((![P : list_P1234162913t_char, H : nat > option2118145160on_val, E : list_char > option_ty, E2 : exp_list_char, F : list_char, D : list_char, T2 : ty]: ((wTrt2 @ P @ H @ E @ E2 @ nt) => (wTrt2 @ P @ H @ E @ (fAcc_list_char @ E2 @ F @ D) @ T2))))). % WTrtFAccNT
thf(fact_43_WTrt_H__WTrts_H_Ointros_I11_J, axiom,
    ((![P : list_P1234162913t_char, H : nat > option2118145160on_val, E : list_char > option_ty, E_1 : exp_list_char, E_2 : exp_list_char, T_2 : ty, F : list_char, D : list_char]: ((wTrt @ P @ H @ E @ E_1 @ nt) => ((wTrt @ P @ H @ E @ E_2 @ T_2) => (wTrt @ P @ H @ E @ (fAss_list_char @ E_1 @ F @ D @ E_2) @ void)))))). % WTrt'_WTrts'.intros(11)
thf(fact_44_WTrtFAcc, axiom,
    ((![P : list_P1234162913t_char, H : nat > option2118145160on_val, E : list_char > option_ty, E2 : exp_list_char, C : list_char, F : list_char, T2 : ty, D : list_char]: ((wTrt2 @ P @ H @ E @ E2 @ (class @ C)) => ((has_fi599584195t_char @ P @ C @ F @ T2 @ D) => (wTrt2 @ P @ H @ E @ (fAcc_list_char @ E2 @ F @ D) @ T2)))))). % WTrtFAcc
thf(fact_45_mem__Collect__eq, axiom,
    ((![A : produc1172664615on_val, P : produc1172664615on_val > $o]: ((member354538064on_val @ A @ (collec2055896722on_val @ P)) = (P @ A))))). % mem_Collect_eq
thf(fact_46_mem__Collect__eq, axiom,
    ((![A : produc1257910179t_char, P : produc1257910179t_char > $o]: ((member89690956t_char @ A @ (collec768236686t_char @ P)) = (P @ A))))). % mem_Collect_eq
thf(fact_47_Collect__mem__eq, axiom,
    ((![A2 : set_Pr1189492743on_val]: ((collec2055896722on_val @ (^[X : produc1172664615on_val]: (member354538064on_val @ X @ A2))) = A2)))). % Collect_mem_eq
thf(fact_48_Collect__mem__eq, axiom,
    ((![A2 : set_Pr164112643t_char]: ((collec768236686t_char @ (^[X : produc1257910179t_char]: (member89690956t_char @ X @ A2))) = A2)))). % Collect_mem_eq
thf(fact_49_old_Oprod_Oinject, axiom,
    ((![A : nat > option2118145160on_val, B : list_char > option_val, A3 : nat > option2118145160on_val, B2 : list_char > option_val]: (((produc52622304on_val @ A @ B) = (produc52622304on_val @ A3 @ B2)) = (((A = A3)) & ((B = B2))))))). % old.prod.inject
thf(fact_50_old_Oprod_Oinject, axiom,
    ((![A : produc1097884484on_val, B : produc1097884484on_val, A3 : produc1097884484on_val, B2 : produc1097884484on_val]: (((produc1069526295on_val @ A @ B) = (produc1069526295on_val @ A3 @ B2)) = (((A = A3)) & ((B = B2))))))). % old.prod.inject
thf(fact_51_old_Oprod_Oinject, axiom,
    ((![A : exp_list_char, B : produc515445032on_val, A3 : exp_list_char, B2 : produc515445032on_val]: (((produc2023458740on_val @ A @ B) = (produc2023458740on_val @ A3 @ B2)) = (((A = A3)) & ((B = B2))))))). % old.prod.inject
thf(fact_52_old_Oprod_Oinject, axiom,
    ((![A : list_char, B : list_char, A3 : list_char, B2 : list_char]: (((produc1304532571t_char @ A @ B) = (produc1304532571t_char @ A3 @ B2)) = (((A = A3)) & ((B = B2))))))). % old.prod.inject
thf(fact_53_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_54_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_55_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_56_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_57_red, axiom,
    ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ ea @ (produc52622304on_val @ ha @ la)) @ (produc2023458740on_val @ e_a @ (produc52622304on_val @ h_a @ l_a))) @ (red @ p)))). % red
thf(fact_58_pred__equals__eq2, axiom,
    ((![R : set_Pr723149704on_val, S : set_Pr723149704on_val]: (((^[X : nat > option2118145160on_val]: (^[Y : list_char > option_val]: (member652041809on_val @ (produc52622304on_val @ X @ Y) @ R))) = (^[X : nat > option2118145160on_val]: (^[Y : list_char > option_val]: (member652041809on_val @ (produc52622304on_val @ X @ Y) @ S)))) = (R = S))))). % pred_equals_eq2
thf(fact_59_pred__equals__eq2, axiom,
    ((![R : set_Pr1189492743on_val, S : set_Pr1189492743on_val]: (((^[X : produc1097884484on_val]: (^[Y : produc1097884484on_val]: (member354538064on_val @ (produc1069526295on_val @ X @ Y) @ R))) = (^[X : produc1097884484on_val]: (^[Y : produc1097884484on_val]: (member354538064on_val @ (produc1069526295on_val @ X @ Y) @ S)))) = (R = S))))). % pred_equals_eq2
thf(fact_60_pred__equals__eq2, axiom,
    ((![R : set_Pr556513572on_val, S : set_Pr556513572on_val]: (((^[X : exp_list_char]: (^[Y : produc515445032on_val]: (member1888679917on_val @ (produc2023458740on_val @ X @ Y) @ R))) = (^[X : exp_list_char]: (^[Y : produc515445032on_val]: (member1888679917on_val @ (produc2023458740on_val @ X @ Y) @ S)))) = (R = S))))). % pred_equals_eq2
thf(fact_61_pred__equals__eq2, axiom,
    ((![R : set_Pr164112643t_char, S : set_Pr164112643t_char]: (((^[X : list_char]: (^[Y : list_char]: (member89690956t_char @ (produc1304532571t_char @ X @ Y) @ R))) = (^[X : list_char]: (^[Y : list_char]: (member89690956t_char @ (produc1304532571t_char @ X @ Y) @ S)))) = (R = S))))). % pred_equals_eq2
thf(fact_62_is__refT__def, axiom,
    ((is_refT = (^[T4 : ty]: (((T4 = nt)) | ((?[C3 : list_char]: (T4 = (class @ C3))))))))). % is_refT_def
thf(fact_63_refTE, axiom,
    ((![T2 : ty]: ((is_refT @ T2) => ((~ ((T2 = nt))) => (~ ((![C2 : list_char]: (~ ((T2 = (class @ C2)))))))))))). % refTE
thf(fact_64__Csubclass_C, axiom,
    ((member89690956t_char @ (produc1304532571t_char @ c @ c2) @ (transi1879726366t_char @ (subcls880436836t_char @ p))))). % "subclass"
thf(fact_65_Class__widen__Class, axiom,
    ((![P : list_P1234162913t_char, C : list_char, D : list_char]: ((widen_917054840t_char @ P @ (class @ C) @ (class @ D)) = (member89690956t_char @ (produc1304532571t_char @ C @ D) @ (transi1879726366t_char @ (subcls880436836t_char @ P))))))). % Class_widen_Class
thf(fact_66_has__field__mono, axiom,
    ((![P : list_P1234162913t_char, C : list_char, F : list_char, T2 : ty, D : list_char, C4 : list_char]: ((has_fi599584195t_char @ P @ C @ F @ T2 @ D) => ((member89690956t_char @ (produc1304532571t_char @ C4 @ C) @ (transi1879726366t_char @ (subcls880436836t_char @ P))) => (has_fi599584195t_char @ P @ C4 @ F @ T2 @ D)))))). % has_field_mono
thf(fact_67_widen__subcls, axiom,
    ((![C : list_char, D : list_char, P : list_P1234162913t_char]: ((member89690956t_char @ (produc1304532571t_char @ C @ D) @ (transi1879726366t_char @ (subcls880436836t_char @ P))) => (widen_917054840t_char @ P @ (class @ C) @ (class @ D)))))). % widen_subcls
thf(fact_68_widen_Ocases, axiom,
    ((![P : list_P1234162913t_char, A1 : ty, A22 : ty]: ((widen_917054840t_char @ P @ A1 @ A22) => ((~ ((A22 = A1))) => ((![C2 : list_char]: ((A1 = (class @ C2)) => (![D2 : list_char]: ((A22 = (class @ D2)) => (~ ((member89690956t_char @ (produc1304532571t_char @ C2 @ D2) @ (transi1879726366t_char @ (subcls880436836t_char @ P))))))))) => (~ (((A1 = nt) => (![C2 : list_char]: (~ ((A22 = (class @ C2)))))))))))))). % widen.cases
thf(fact_69_widen_Osimps, axiom,
    ((widen_917054840t_char = (^[P2 : list_P1234162913t_char]: (^[A12 : ty]: (^[A23 : ty]: (((?[T4 : ty]: (((A12 = T4)) & ((A23 = T4))))) | ((((?[C3 : list_char]: (?[D3 : list_char]: (((A12 = (class @ C3))) & ((((A23 = (class @ D3))) & ((member89690956t_char @ (produc1304532571t_char @ C3 @ D3) @ (transi1879726366t_char @ (subcls880436836t_char @ P2)))))))))) | ((?[C3 : list_char]: (((A12 = nt)) & ((A23 = (class @ C3))))))))))))))). % widen.simps
thf(fact_70_widen__Class, axiom,
    ((![P : list_P1234162913t_char, T2 : ty, C : list_char]: ((widen_917054840t_char @ P @ T2 @ (class @ C)) = (((T2 = nt)) | ((?[D3 : list_char]: (((T2 = (class @ D3))) & ((member89690956t_char @ (produc1304532571t_char @ D3 @ C) @ (transi1879726366t_char @ (subcls880436836t_char @ P)))))))))))). % widen_Class
thf(fact_71_widen_Oinducts, axiom,
    ((![P : list_P1234162913t_char, X1 : ty, X2 : ty, Pa : ty > ty > $o]: ((widen_917054840t_char @ P @ X1 @ X2) => ((![T3 : ty]: (Pa @ T3 @ T3)) => ((![C2 : list_char, D2 : list_char]: ((member89690956t_char @ (produc1304532571t_char @ C2 @ D2) @ (transi1879726366t_char @ (subcls880436836t_char @ P))) => (Pa @ (class @ C2) @ (class @ D2)))) => ((![C2 : list_char]: (Pa @ nt @ (class @ C2))) => (Pa @ X1 @ X2)))))))). % widen.inducts
thf(fact_72_surj__pair, axiom,
    ((![P3 : produc515445032on_val]: (?[X3 : nat > option2118145160on_val, Y3 : list_char > option_val]: (P3 = (produc52622304on_val @ X3 @ Y3)))))). % surj_pair
thf(fact_73_surj__pair, axiom,
    ((![P3 : produc1172664615on_val]: (?[X3 : produc1097884484on_val, Y3 : produc1097884484on_val]: (P3 = (produc1069526295on_val @ X3 @ Y3)))))). % surj_pair
thf(fact_74_surj__pair, axiom,
    ((![P3 : produc1097884484on_val]: (?[X3 : exp_list_char, Y3 : produc515445032on_val]: (P3 = (produc2023458740on_val @ X3 @ Y3)))))). % surj_pair
thf(fact_75_surj__pair, axiom,
    ((![P3 : produc1257910179t_char]: (?[X3 : list_char, Y3 : list_char]: (P3 = (produc1304532571t_char @ X3 @ Y3)))))). % surj_pair
thf(fact_76_prod__cases, axiom,
    ((![P : produc515445032on_val > $o, P3 : produc515445032on_val]: ((![A4 : nat > option2118145160on_val, B3 : list_char > option_val]: (P @ (produc52622304on_val @ A4 @ B3))) => (P @ P3))))). % prod_cases
thf(fact_77_prod__cases, axiom,
    ((![P : produc1172664615on_val > $o, P3 : produc1172664615on_val]: ((![A4 : produc1097884484on_val, B3 : produc1097884484on_val]: (P @ (produc1069526295on_val @ A4 @ B3))) => (P @ P3))))). % prod_cases
thf(fact_78_prod__cases, axiom,
    ((![P : produc1097884484on_val > $o, P3 : produc1097884484on_val]: ((![A4 : exp_list_char, B3 : produc515445032on_val]: (P @ (produc2023458740on_val @ A4 @ B3))) => (P @ P3))))). % prod_cases
thf(fact_79_prod__cases, axiom,
    ((![P : produc1257910179t_char > $o, P3 : produc1257910179t_char]: ((![A4 : list_char, B3 : list_char]: (P @ (produc1304532571t_char @ A4 @ B3))) => (P @ P3))))). % prod_cases
thf(fact_80_Pair__inject, axiom,
    ((![A : nat > option2118145160on_val, B : list_char > option_val, A3 : nat > option2118145160on_val, B2 : list_char > option_val]: (((produc52622304on_val @ A @ B) = (produc52622304on_val @ A3 @ B2)) => (~ (((A = A3) => (~ ((B = B2)))))))))). % Pair_inject
thf(fact_81_Pair__inject, axiom,
    ((![A : produc1097884484on_val, B : produc1097884484on_val, A3 : produc1097884484on_val, B2 : produc1097884484on_val]: (((produc1069526295on_val @ A @ B) = (produc1069526295on_val @ A3 @ B2)) => (~ (((A = A3) => (~ ((B = B2)))))))))). % Pair_inject
thf(fact_82_Pair__inject, axiom,
    ((![A : exp_list_char, B : produc515445032on_val, A3 : exp_list_char, B2 : produc515445032on_val]: (((produc2023458740on_val @ A @ B) = (produc2023458740on_val @ A3 @ B2)) => (~ (((A = A3) => (~ ((B = B2)))))))))). % Pair_inject
thf(fact_83_Pair__inject, axiom,
    ((![A : list_char, B : list_char, A3 : list_char, B2 : list_char]: (((produc1304532571t_char @ A @ B) = (produc1304532571t_char @ A3 @ B2)) => (~ (((A = A3) => (~ ((B = B2)))))))))). % Pair_inject
thf(fact_84_prod__cases3, axiom,
    ((![Y4 : produc1172664615on_val]: (~ ((![A4 : produc1097884484on_val, B3 : exp_list_char, C5 : produc515445032on_val]: (~ ((Y4 = (produc1069526295on_val @ A4 @ (produc2023458740on_val @ B3 @ C5))))))))))). % prod_cases3
thf(fact_85_prod__cases3, axiom,
    ((![Y4 : produc1097884484on_val]: (~ ((![A4 : exp_list_char, B3 : nat > option2118145160on_val, C5 : list_char > option_val]: (~ ((Y4 = (produc2023458740on_val @ A4 @ (produc52622304on_val @ B3 @ C5))))))))))). % prod_cases3
thf(fact_86_prod__cases4, axiom,
    ((![Y4 : produc1172664615on_val]: (~ ((![A4 : produc1097884484on_val, B3 : exp_list_char, C5 : nat > option2118145160on_val, D4 : list_char > option_val]: (~ ((Y4 = (produc1069526295on_val @ A4 @ (produc2023458740on_val @ B3 @ (produc52622304on_val @ C5 @ D4)))))))))))). % prod_cases4
thf(fact_87_prod__induct3, axiom,
    ((![P : produc1172664615on_val > $o, X4 : produc1172664615on_val]: ((![A4 : produc1097884484on_val, B3 : exp_list_char, C5 : produc515445032on_val]: (P @ (produc1069526295on_val @ A4 @ (produc2023458740on_val @ B3 @ C5)))) => (P @ X4))))). % prod_induct3
thf(fact_88_prod__induct3, axiom,
    ((![P : produc1097884484on_val > $o, X4 : produc1097884484on_val]: ((![A4 : exp_list_char, B3 : nat > option2118145160on_val, C5 : list_char > option_val]: (P @ (produc2023458740on_val @ A4 @ (produc52622304on_val @ B3 @ C5)))) => (P @ X4))))). % prod_induct3
thf(fact_89_prod__induct4, axiom,
    ((![P : produc1172664615on_val > $o, X4 : produc1172664615on_val]: ((![A4 : produc1097884484on_val, B3 : exp_list_char, C5 : nat > option2118145160on_val, D4 : list_char > option_val]: (P @ (produc1069526295on_val @ A4 @ (produc2023458740on_val @ B3 @ (produc52622304on_val @ C5 @ D4))))) => (P @ X4))))). % prod_induct4
thf(fact_90_old_Oprod_Oexhaust, axiom,
    ((![Y4 : produc515445032on_val]: (~ ((![A4 : nat > option2118145160on_val, B3 : list_char > option_val]: (~ ((Y4 = (produc52622304on_val @ A4 @ B3)))))))))). % old.prod.exhaust
thf(fact_91_old_Oprod_Oexhaust, axiom,
    ((![Y4 : produc1172664615on_val]: (~ ((![A4 : produc1097884484on_val, B3 : produc1097884484on_val]: (~ ((Y4 = (produc1069526295on_val @ A4 @ B3)))))))))). % old.prod.exhaust
thf(fact_92_old_Oprod_Oexhaust, axiom,
    ((![Y4 : produc1097884484on_val]: (~ ((![A4 : exp_list_char, B3 : produc515445032on_val]: (~ ((Y4 = (produc2023458740on_val @ A4 @ B3)))))))))). % old.prod.exhaust
thf(fact_93_old_Oprod_Oexhaust, axiom,
    ((![Y4 : produc1257910179t_char]: (~ ((![A4 : list_char, B3 : list_char]: (~ ((Y4 = (produc1304532571t_char @ A4 @ B3)))))))))). % old.prod.exhaust
thf(fact_94_old_Oprod_Oinducts, axiom,
    ((![P : produc515445032on_val > $o, Prod : produc515445032on_val]: ((![A4 : nat > option2118145160on_val, B3 : list_char > option_val]: (P @ (produc52622304on_val @ A4 @ B3))) => (P @ Prod))))). % old.prod.inducts
thf(fact_95_old_Oprod_Oinducts, axiom,
    ((![P : produc1172664615on_val > $o, Prod : produc1172664615on_val]: ((![A4 : produc1097884484on_val, B3 : produc1097884484on_val]: (P @ (produc1069526295on_val @ A4 @ B3))) => (P @ Prod))))). % old.prod.inducts
thf(fact_96_old_Oprod_Oinducts, axiom,
    ((![P : produc1097884484on_val > $o, Prod : produc1097884484on_val]: ((![A4 : exp_list_char, B3 : produc515445032on_val]: (P @ (produc2023458740on_val @ A4 @ B3))) => (P @ Prod))))). % old.prod.inducts
thf(fact_97_old_Oprod_Oinducts, axiom,
    ((![P : produc1257910179t_char > $o, Prod : produc1257910179t_char]: ((![A4 : list_char, B3 : list_char]: (P @ (produc1304532571t_char @ A4 @ B3))) => (P @ Prod))))). % old.prod.inducts
thf(fact_98_red__reds_OFAccRed, axiom,
    ((![E2 : exp_list_char, S2 : produc515445032on_val, E3 : exp_list_char, S3 : produc515445032on_val, P : list_P1234162913t_char, F : list_char, D : 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 @ F @ D) @ S2) @ (produc2023458740on_val @ (fAcc_list_char @ E3 @ F @ D) @ S3)) @ (red @ P)))))). % red_reds.FAccRed
thf(fact_99_red__reds_OFAssRed1, axiom,
    ((![E2 : exp_list_char, S2 : produc515445032on_val, E3 : exp_list_char, S3 : produc515445032on_val, P : list_P1234162913t_char, F : list_char, D : 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 @ (fAss_list_char @ E2 @ F @ D @ E_2) @ S2) @ (produc2023458740on_val @ (fAss_list_char @ E3 @ F @ D @ E_2) @ S3)) @ (red @ P)))))). % red_reds.FAssRed1
thf(fact_100_rtrancl__idemp, axiom,
    ((![R2 : set_Pr164112643t_char]: ((transi1879726366t_char @ (transi1879726366t_char @ R2)) = (transi1879726366t_char @ R2))))). % rtrancl_idemp
thf(fact_101_rtrancl__idemp, axiom,
    ((![R2 : set_Pr1189492743on_val]: ((transi111096263on_val @ (transi111096263on_val @ R2)) = (transi111096263on_val @ R2))))). % rtrancl_idemp
thf(fact_102_r__into__rtrancl, axiom,
    ((![P3 : produc1257910179t_char, R2 : set_Pr164112643t_char]: ((member89690956t_char @ P3 @ R2) => (member89690956t_char @ P3 @ (transi1879726366t_char @ R2)))))). % r_into_rtrancl
thf(fact_103_r__into__rtrancl, axiom,
    ((![P3 : produc1172664615on_val, R2 : set_Pr1189492743on_val]: ((member354538064on_val @ P3 @ R2) => (member354538064on_val @ P3 @ (transi111096263on_val @ R2)))))). % r_into_rtrancl
thf(fact_104_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) => ((![A4 : 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 @ A4 @ B3)) @ (transi432893227on_val @ R2)) => ((member2027247312on_val @ (produc2106877847on_val @ (produc52622304on_val @ A4 @ B3) @ (produc52622304on_val @ Aa @ Ba)) @ R2) => ((P @ A4 @ B3) => (P @ Aa @ Ba))))) => (P @ Bx @ By))))))). % rtrancl_induct2
thf(fact_105_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) => ((![A4 : produc1097884484on_val, B3 : produc1097884484on_val, Aa : produc1097884484on_val, Ba : produc1097884484on_val]: ((member208988944on_val @ (produc564964183on_val @ (produc1069526295on_val @ Ax @ Ay) @ (produc1069526295on_val @ A4 @ B3)) @ (transi100378922on_val @ R2)) => ((member208988944on_val @ (produc564964183on_val @ (produc1069526295on_val @ A4 @ B3) @ (produc1069526295on_val @ Aa @ Ba)) @ R2) => ((P @ A4 @ B3) => (P @ Aa @ Ba))))) => (P @ Bx @ By))))))). % rtrancl_induct2
thf(fact_106_rtrancl__induct2, axiom,
    ((![Ax : list_char, Ay : list_char, Bx : list_char, By : list_char, R2 : set_Pr729957319t_char, P : list_char > list_char > $o]: ((member803902992t_char @ (produc395356247t_char @ (produc1304532571t_char @ Ax @ Ay) @ (produc1304532571t_char @ Bx @ By)) @ (transi858104614t_char @ R2)) => ((P @ Ax @ Ay) => ((![A4 : list_char, B3 : list_char, Aa : list_char, Ba : list_char]: ((member803902992t_char @ (produc395356247t_char @ (produc1304532571t_char @ Ax @ Ay) @ (produc1304532571t_char @ A4 @ B3)) @ (transi858104614t_char @ R2)) => ((member803902992t_char @ (produc395356247t_char @ (produc1304532571t_char @ A4 @ B3) @ (produc1304532571t_char @ Aa @ Ba)) @ R2) => ((P @ A4 @ B3) => (P @ Aa @ Ba))))) => (P @ Bx @ By))))))). % rtrancl_induct2
thf(fact_107_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) => ((![A4 : exp_list_char, B3 : produc515445032on_val, Aa : exp_list_char, Ba : produc515445032on_val]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ Ax @ Ay) @ (produc2023458740on_val @ A4 @ B3)) @ (transi111096263on_val @ R2)) => ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ A4 @ B3) @ (produc2023458740on_val @ Aa @ Ba)) @ R2) => ((P @ A4 @ B3) => (P @ Aa @ Ba))))) => (P @ Bx @ By))))))). % rtrancl_induct2
thf(fact_108_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)))) => (~ ((![A4 : nat > option2118145160on_val, B3 : list_char > option_val]: ((member2027247312on_val @ (produc2106877847on_val @ (produc52622304on_val @ Xa @ Xb) @ (produc52622304on_val @ A4 @ B3)) @ R2) => (~ ((member2027247312on_val @ (produc2106877847on_val @ (produc52622304on_val @ A4 @ B3) @ (produc52622304on_val @ Za @ Zb)) @ (transi432893227on_val @ R2))))))))))))). % converse_rtranclE2
thf(fact_109_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)))) => (~ ((![A4 : produc1097884484on_val, B3 : produc1097884484on_val]: ((member208988944on_val @ (produc564964183on_val @ (produc1069526295on_val @ Xa @ Xb) @ (produc1069526295on_val @ A4 @ B3)) @ R2) => (~ ((member208988944on_val @ (produc564964183on_val @ (produc1069526295on_val @ A4 @ B3) @ (produc1069526295on_val @ Za @ Zb)) @ (transi100378922on_val @ R2))))))))))))). % converse_rtranclE2
thf(fact_110_converse__rtranclE2, axiom,
    ((![Xa : list_char, Xb : list_char, Za : list_char, Zb : list_char, R2 : set_Pr729957319t_char]: ((member803902992t_char @ (produc395356247t_char @ (produc1304532571t_char @ Xa @ Xb) @ (produc1304532571t_char @ Za @ Zb)) @ (transi858104614t_char @ R2)) => ((~ (((produc1304532571t_char @ Xa @ Xb) = (produc1304532571t_char @ Za @ Zb)))) => (~ ((![A4 : list_char, B3 : list_char]: ((member803902992t_char @ (produc395356247t_char @ (produc1304532571t_char @ Xa @ Xb) @ (produc1304532571t_char @ A4 @ B3)) @ R2) => (~ ((member803902992t_char @ (produc395356247t_char @ (produc1304532571t_char @ A4 @ B3) @ (produc1304532571t_char @ Za @ Zb)) @ (transi858104614t_char @ R2))))))))))))). % converse_rtranclE2
thf(fact_111_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)))) => (~ ((![A4 : exp_list_char, B3 : produc515445032on_val]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ Xa @ Xb) @ (produc2023458740on_val @ A4 @ B3)) @ R2) => (~ ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ A4 @ B3) @ (produc2023458740on_val @ Za @ Zb)) @ (transi111096263on_val @ R2))))))))))))). % converse_rtranclE2
thf(fact_112_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) => ((![A4 : nat > option2118145160on_val, B3 : list_char > option_val, Aa : nat > option2118145160on_val, Ba : list_char > option_val]: ((member2027247312on_val @ (produc2106877847on_val @ (produc52622304on_val @ A4 @ B3) @ (produc52622304on_val @ Aa @ Ba)) @ R2) => ((member2027247312on_val @ (produc2106877847on_val @ (produc52622304on_val @ Aa @ Ba) @ (produc52622304on_val @ Bx @ By)) @ (transi432893227on_val @ R2)) => ((P @ Aa @ Ba) => (P @ A4 @ B3))))) => (P @ Ax @ Ay))))))). % converse_rtrancl_induct2
thf(fact_113_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) => ((![A4 : produc1097884484on_val, B3 : produc1097884484on_val, Aa : produc1097884484on_val, Ba : produc1097884484on_val]: ((member208988944on_val @ (produc564964183on_val @ (produc1069526295on_val @ A4 @ B3) @ (produc1069526295on_val @ Aa @ Ba)) @ R2) => ((member208988944on_val @ (produc564964183on_val @ (produc1069526295on_val @ Aa @ Ba) @ (produc1069526295on_val @ Bx @ By)) @ (transi100378922on_val @ R2)) => ((P @ Aa @ Ba) => (P @ A4 @ B3))))) => (P @ Ax @ Ay))))))). % converse_rtrancl_induct2
thf(fact_114_converse__rtrancl__induct2, axiom,
    ((![Ax : list_char, Ay : list_char, Bx : list_char, By : list_char, R2 : set_Pr729957319t_char, P : list_char > list_char > $o]: ((member803902992t_char @ (produc395356247t_char @ (produc1304532571t_char @ Ax @ Ay) @ (produc1304532571t_char @ Bx @ By)) @ (transi858104614t_char @ R2)) => ((P @ Bx @ By) => ((![A4 : list_char, B3 : list_char, Aa : list_char, Ba : list_char]: ((member803902992t_char @ (produc395356247t_char @ (produc1304532571t_char @ A4 @ B3) @ (produc1304532571t_char @ Aa @ Ba)) @ R2) => ((member803902992t_char @ (produc395356247t_char @ (produc1304532571t_char @ Aa @ Ba) @ (produc1304532571t_char @ Bx @ By)) @ (transi858104614t_char @ R2)) => ((P @ Aa @ Ba) => (P @ A4 @ B3))))) => (P @ Ax @ Ay))))))). % converse_rtrancl_induct2
thf(fact_115_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) => ((![A4 : exp_list_char, B3 : produc515445032on_val, Aa : exp_list_char, Ba : produc515445032on_val]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ A4 @ B3) @ (produc2023458740on_val @ Aa @ Ba)) @ R2) => ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ Aa @ Ba) @ (produc2023458740on_val @ Bx @ By)) @ (transi111096263on_val @ R2)) => ((P @ Aa @ Ba) => (P @ A4 @ B3))))) => (P @ Ax @ Ay))))))). % converse_rtrancl_induct2
thf(fact_116_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))) => ((![E4 : exp_list_char, H3 : nat > option2118145160on_val, L3 : list_char > option_val]: (R @ E4 @ H3 @ L3 @ E4 @ H3 @ L3)) => ((![E_0 : exp_list_char, H_0 : nat > option2118145160on_val, L_0 : list_char > option_val, E_12 : exp_list_char, H_1 : nat > option2118145160on_val, L_1 : list_char > option_val, E5 : exp_list_char, 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_1 @ L_1))) @ (red @ P)) => ((R @ E_12 @ H_1 @ L_1 @ E5 @ H4 @ L4) => (R @ E_0 @ H_0 @ L_0 @ E5 @ H4 @ L4)))) => (R @ E2 @ H @ L @ E3 @ H2 @ L2))))))). % converse_rtrancl_induct_red
thf(fact_117_rtranclE, axiom,
    ((![A : list_char, B : list_char, R2 : set_Pr164112643t_char]: ((member89690956t_char @ (produc1304532571t_char @ A @ B) @ (transi1879726366t_char @ R2)) => ((~ ((A = B))) => (~ ((![Y3 : list_char]: ((member89690956t_char @ (produc1304532571t_char @ A @ Y3) @ (transi1879726366t_char @ R2)) => (~ ((member89690956t_char @ (produc1304532571t_char @ Y3 @ B) @ R2)))))))))))). % rtranclE
thf(fact_118_rtranclE, axiom,
    ((![A : produc1097884484on_val, B : produc1097884484on_val, R2 : set_Pr1189492743on_val]: ((member354538064on_val @ (produc1069526295on_val @ A @ B) @ (transi111096263on_val @ R2)) => ((~ ((A = B))) => (~ ((![Y3 : produc1097884484on_val]: ((member354538064on_val @ (produc1069526295on_val @ A @ Y3) @ (transi111096263on_val @ R2)) => (~ ((member354538064on_val @ (produc1069526295on_val @ Y3 @ B) @ R2)))))))))))). % rtranclE
thf(fact_119_rtrancl_Ocases, axiom,
    ((![A1 : list_char, A22 : list_char, R2 : set_Pr164112643t_char]: ((member89690956t_char @ (produc1304532571t_char @ A1 @ A22) @ (transi1879726366t_char @ R2)) => ((~ ((A22 = A1))) => (~ ((![B3 : list_char]: ((member89690956t_char @ (produc1304532571t_char @ A1 @ B3) @ (transi1879726366t_char @ R2)) => (~ ((member89690956t_char @ (produc1304532571t_char @ B3 @ A22) @ R2)))))))))))). % rtrancl.cases
thf(fact_120_rtrancl_Ocases, axiom,
    ((![A1 : produc1097884484on_val, A22 : produc1097884484on_val, R2 : set_Pr1189492743on_val]: ((member354538064on_val @ (produc1069526295on_val @ A1 @ A22) @ (transi111096263on_val @ R2)) => ((~ ((A22 = A1))) => (~ ((![B3 : produc1097884484on_val]: ((member354538064on_val @ (produc1069526295on_val @ A1 @ B3) @ (transi111096263on_val @ R2)) => (~ ((member354538064on_val @ (produc1069526295on_val @ B3 @ A22) @ R2)))))))))))). % rtrancl.cases
thf(fact_121_rtrancl_Osimps, axiom,
    ((![A1 : list_char, A22 : list_char, R2 : set_Pr164112643t_char]: ((member89690956t_char @ (produc1304532571t_char @ A1 @ A22) @ (transi1879726366t_char @ R2)) = (((?[A5 : list_char]: (((A1 = A5)) & ((A22 = A5))))) | ((?[A5 : list_char]: (?[B4 : list_char]: (?[C6 : list_char]: (((A1 = A5)) & ((((A22 = C6)) & ((((member89690956t_char @ (produc1304532571t_char @ A5 @ B4) @ (transi1879726366t_char @ R2))) & ((member89690956t_char @ (produc1304532571t_char @ B4 @ C6) @ R2)))))))))))))))). % rtrancl.simps
thf(fact_122_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_123_rtrancl__trans, axiom,
    ((![X4 : list_char, Y4 : list_char, R2 : set_Pr164112643t_char, Z : list_char]: ((member89690956t_char @ (produc1304532571t_char @ X4 @ Y4) @ (transi1879726366t_char @ R2)) => ((member89690956t_char @ (produc1304532571t_char @ Y4 @ Z) @ (transi1879726366t_char @ R2)) => (member89690956t_char @ (produc1304532571t_char @ X4 @ Z) @ (transi1879726366t_char @ R2))))))). % rtrancl_trans
thf(fact_124_rtrancl__trans, axiom,
    ((![X4 : produc1097884484on_val, Y4 : produc1097884484on_val, R2 : set_Pr1189492743on_val, Z : produc1097884484on_val]: ((member354538064on_val @ (produc1069526295on_val @ X4 @ Y4) @ (transi111096263on_val @ R2)) => ((member354538064on_val @ (produc1069526295on_val @ Y4 @ Z) @ (transi111096263on_val @ R2)) => (member354538064on_val @ (produc1069526295on_val @ X4 @ Z) @ (transi111096263on_val @ R2))))))). % rtrancl_trans
thf(fact_125_rtrancl__induct, axiom,
    ((![A : list_char, B : list_char, R2 : set_Pr164112643t_char, P : list_char > $o]: ((member89690956t_char @ (produc1304532571t_char @ A @ B) @ (transi1879726366t_char @ R2)) => ((P @ A) => ((![Y3 : list_char, Z2 : list_char]: ((member89690956t_char @ (produc1304532571t_char @ A @ Y3) @ (transi1879726366t_char @ R2)) => ((member89690956t_char @ (produc1304532571t_char @ Y3 @ Z2) @ R2) => ((P @ Y3) => (P @ Z2))))) => (P @ B))))))). % rtrancl_induct
thf(fact_126_rtrancl__induct, axiom,
    ((![A : produc1097884484on_val, B : produc1097884484on_val, R2 : set_Pr1189492743on_val, P : produc1097884484on_val > $o]: ((member354538064on_val @ (produc1069526295on_val @ A @ B) @ (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 @ B))))))). % rtrancl_induct
thf(fact_127_rtrancl_Oinducts, axiom,
    ((![X1 : list_char, X2 : list_char, R2 : set_Pr164112643t_char, P : list_char > list_char > $o]: ((member89690956t_char @ (produc1304532571t_char @ X1 @ X2) @ (transi1879726366t_char @ R2)) => ((![A4 : list_char]: (P @ A4 @ A4)) => ((![A4 : list_char, B3 : list_char, C5 : list_char]: ((member89690956t_char @ (produc1304532571t_char @ A4 @ B3) @ (transi1879726366t_char @ R2)) => ((P @ A4 @ B3) => ((member89690956t_char @ (produc1304532571t_char @ B3 @ C5) @ R2) => (P @ A4 @ C5))))) => (P @ X1 @ X2))))))). % rtrancl.inducts
thf(fact_128_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)) => ((![A4 : produc1097884484on_val]: (P @ A4 @ A4)) => ((![A4 : produc1097884484on_val, B3 : produc1097884484on_val, C5 : produc1097884484on_val]: ((member354538064on_val @ (produc1069526295on_val @ A4 @ B3) @ (transi111096263on_val @ R2)) => ((P @ A4 @ B3) => ((member354538064on_val @ (produc1069526295on_val @ B3 @ C5) @ R2) => (P @ A4 @ C5))))) => (P @ X1 @ X2))))))). % rtrancl.inducts
thf(fact_129_converse__rtranclE, axiom,
    ((![X4 : list_char, Z : list_char, R2 : set_Pr164112643t_char]: ((member89690956t_char @ (produc1304532571t_char @ X4 @ Z) @ (transi1879726366t_char @ R2)) => ((~ ((X4 = Z))) => (~ ((![Y3 : list_char]: ((member89690956t_char @ (produc1304532571t_char @ X4 @ Y3) @ R2) => (~ ((member89690956t_char @ (produc1304532571t_char @ Y3 @ Z) @ (transi1879726366t_char @ R2))))))))))))). % converse_rtranclE
thf(fact_130_converse__rtranclE, axiom,
    ((![X4 : produc1097884484on_val, Z : produc1097884484on_val, R2 : set_Pr1189492743on_val]: ((member354538064on_val @ (produc1069526295on_val @ X4 @ Z) @ (transi111096263on_val @ R2)) => ((~ ((X4 = Z))) => (~ ((![Y3 : produc1097884484on_val]: ((member354538064on_val @ (produc1069526295on_val @ X4 @ Y3) @ R2) => (~ ((member354538064on_val @ (produc1069526295on_val @ Y3 @ Z) @ (transi111096263on_val @ R2))))))))))))). % converse_rtranclE
thf(fact_131_rtrancl_Ortrancl__refl, axiom,
    ((![A : list_char, R2 : set_Pr164112643t_char]: (member89690956t_char @ (produc1304532571t_char @ A @ A) @ (transi1879726366t_char @ R2))))). % rtrancl.rtrancl_refl
thf(fact_132_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_133_converse__rtrancl__induct, axiom,
    ((![A : list_char, B : list_char, R2 : set_Pr164112643t_char, P : list_char > $o]: ((member89690956t_char @ (produc1304532571t_char @ A @ B) @ (transi1879726366t_char @ R2)) => ((P @ B) => ((![Y3 : list_char, Z2 : list_char]: ((member89690956t_char @ (produc1304532571t_char @ Y3 @ Z2) @ R2) => ((member89690956t_char @ (produc1304532571t_char @ Z2 @ B) @ (transi1879726366t_char @ R2)) => ((P @ Z2) => (P @ Y3))))) => (P @ A))))))). % converse_rtrancl_induct
thf(fact_134_converse__rtrancl__induct, axiom,
    ((![A : produc1097884484on_val, B : produc1097884484on_val, R2 : set_Pr1189492743on_val, P : produc1097884484on_val > $o]: ((member354538064on_val @ (produc1069526295on_val @ A @ B) @ (transi111096263on_val @ R2)) => ((P @ B) => ((![Y3 : produc1097884484on_val, Z2 : produc1097884484on_val]: ((member354538064on_val @ (produc1069526295on_val @ Y3 @ Z2) @ R2) => ((member354538064on_val @ (produc1069526295on_val @ Z2 @ B) @ (transi111096263on_val @ R2)) => ((P @ Z2) => (P @ Y3))))) => (P @ A))))))). % converse_rtrancl_induct
thf(fact_135_rtrancl_Ortrancl__into__rtrancl, axiom,
    ((![A : list_char, B : list_char, R2 : set_Pr164112643t_char, C7 : list_char]: ((member89690956t_char @ (produc1304532571t_char @ A @ B) @ (transi1879726366t_char @ R2)) => ((member89690956t_char @ (produc1304532571t_char @ B @ C7) @ R2) => (member89690956t_char @ (produc1304532571t_char @ A @ C7) @ (transi1879726366t_char @ R2))))))). % rtrancl.rtrancl_into_rtrancl
thf(fact_136_rtrancl_Ortrancl__into__rtrancl, axiom,
    ((![A : produc1097884484on_val, B : produc1097884484on_val, R2 : set_Pr1189492743on_val, C7 : produc1097884484on_val]: ((member354538064on_val @ (produc1069526295on_val @ A @ B) @ (transi111096263on_val @ R2)) => ((member354538064on_val @ (produc1069526295on_val @ B @ C7) @ R2) => (member354538064on_val @ (produc1069526295on_val @ A @ C7) @ (transi111096263on_val @ R2))))))). % rtrancl.rtrancl_into_rtrancl
thf(fact_137_converse__rtrancl__into__rtrancl, axiom,
    ((![A : list_char, B : list_char, R2 : set_Pr164112643t_char, C7 : list_char]: ((member89690956t_char @ (produc1304532571t_char @ A @ B) @ R2) => ((member89690956t_char @ (produc1304532571t_char @ B @ C7) @ (transi1879726366t_char @ R2)) => (member89690956t_char @ (produc1304532571t_char @ A @ C7) @ (transi1879726366t_char @ R2))))))). % converse_rtrancl_into_rtrancl
thf(fact_138_converse__rtrancl__into__rtrancl, axiom,
    ((![A : produc1097884484on_val, B : produc1097884484on_val, R2 : set_Pr1189492743on_val, C7 : produc1097884484on_val]: ((member354538064on_val @ (produc1069526295on_val @ A @ B) @ R2) => ((member354538064on_val @ (produc1069526295on_val @ B @ C7) @ (transi111096263on_val @ R2)) => (member354538064on_val @ (produc1069526295on_val @ A @ C7) @ (transi111096263on_val @ R2))))))). % converse_rtrancl_into_rtrancl
thf(fact_139_FAccReds, axiom,
    ((![E2 : exp_list_char, S2 : produc515445032on_val, E3 : exp_list_char, S3 : produc515445032on_val, P : list_P1234162913t_char, F : list_char, D : 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 @ F @ D) @ S2) @ (produc2023458740on_val @ (fAcc_list_char @ E3 @ F @ D) @ S3)) @ (transi111096263on_val @ (red @ P))))))). % FAccReds
thf(fact_140_FAssReds1, axiom,
    ((![E2 : exp_list_char, S2 : produc515445032on_val, E3 : exp_list_char, S3 : produc515445032on_val, P : list_P1234162913t_char, F : list_char, D : 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 @ (fAss_list_char @ E2 @ F @ D @ E_2) @ S2) @ (produc2023458740on_val @ (fAss_list_char @ E3 @ F @ D @ E_2) @ S3)) @ (transi111096263on_val @ (red @ P))))))). % FAssReds1
thf(fact_141_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, T2 : ty]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E2 @ (produc52622304on_val @ H @ L)) @ (produc2023458740on_val @ E3 @ (produc52622304on_val @ H2 @ L2))) @ (red @ P)) => ((wTrt2 @ P @ H @ E @ E2 @ T2) => ((hconf_1244167010t_char @ P @ H) => (hconf_1244167010t_char @ P @ H2))))))). % red_preserves_hconf
thf(fact_142_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, T2 : ty]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E2 @ (produc52622304on_val @ H @ L)) @ (produc2023458740on_val @ E3 @ (produc52622304on_val @ H2 @ L2))) @ (red @ P)) => ((wTrt2 @ P @ H @ E @ E2 @ T2) => ((lconf_485928294t_char @ P @ H @ L @ E) => (lconf_485928294t_char @ P @ H2 @ L2 @ E))))))). % red_preserves_lconf
thf(fact_143_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, T2 : ty]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E2 @ S2) @ (produc2023458740on_val @ E3 @ S3)) @ (red @ P)) => ((wTrt2 @ P @ (hp @ S2) @ E @ E2 @ T2) => ((typeSa1777264139_sconf @ P @ E @ S2) => (typeSa1777264139_sconf @ P @ E @ S3))))))). % red_preserves_sconf
thf(fact_144_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_02 : 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_02 @ L))) @ (produc2023458740on_val @ E3 @ (produc52622304on_val @ H2 @ (map_ad1615113112ar_val @ L_02 @ L2)))) @ (transi111096263on_val @ (red @ P))))))). % Red_lcl_add
thf(fact_145_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_146_WTrt__hext__mono, axiom,
    ((![P : list_P1234162913t_char, H : nat > option2118145160on_val, E : list_char > option_ty, E2 : exp_list_char, T2 : ty, H2 : nat > option2118145160on_val]: ((wTrt2 @ P @ H @ E @ E2 @ T2) => ((hext @ H @ H2) => (wTrt2 @ P @ H2 @ E @ E2 @ T2)))))). % WTrt_hext_mono
thf(fact_147_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_02 : 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_02 @ L))) @ (produc2023458740on_val @ E3 @ (produc52622304on_val @ H2 @ (map_ad1615113112ar_val @ L_02 @ L2)))) @ (red @ P)))))). % red_lcl_add
thf(fact_148_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_149_FAssReds2, axiom,
    ((![E2 : exp_list_char, S2 : produc515445032on_val, E3 : exp_list_char, S3 : produc515445032on_val, P : list_P1234162913t_char, V : val, F : list_char, D : list_char]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E2 @ S2) @ (produc2023458740on_val @ E3 @ S3)) @ (transi111096263on_val @ (red @ P))) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (fAss_list_char @ (val_list_char @ V) @ F @ D @ E2) @ S2) @ (produc2023458740on_val @ (fAss_list_char @ (val_list_char @ V) @ F @ D @ E3) @ S3)) @ (transi111096263on_val @ (red @ P))))))). % FAssReds2
thf(fact_150_FAccRedsThrow, axiom,
    ((![E2 : exp_list_char, S2 : produc515445032on_val, A : exp_list_char, S3 : produc515445032on_val, P : list_P1234162913t_char, F : list_char, D : 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 @ F @ D) @ S2) @ (produc2023458740on_val @ (throw_list_char @ A) @ S3)) @ (transi111096263on_val @ (red @ P))))))). % FAccRedsThrow
thf(fact_151_exp_Oinject_I3_J, axiom,
    ((![X32 : val, Y32 : val]: (((val_list_char @ X32) = (val_list_char @ Y32)) = (X32 = Y32))))). % exp.inject(3)
thf(fact_152_exp_Oinject_I14_J, axiom,
    ((![X14 : exp_list_char, Y14 : exp_list_char]: (((throw_list_char @ X14) = (throw_list_char @ Y14)) = (X14 = Y14))))). % exp.inject(14)
thf(fact_153_red__reds_OFAssThrow2, axiom,
    ((![V : val, F : list_char, D : list_char, E2 : exp_list_char, S2 : produc515445032on_val, P : list_P1234162913t_char]: (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (fAss_list_char @ (val_list_char @ V) @ F @ D @ (throw_list_char @ E2)) @ S2) @ (produc2023458740on_val @ (throw_list_char @ E2) @ S2)) @ (red @ P))))). % red_reds.FAssThrow2
thf(fact_154_exp_Odistinct_I63_J, axiom,
    ((![X32 : val, X81 : exp_list_char, X82 : list_char, X83 : list_char, X84 : exp_list_char]: (~ (((val_list_char @ X32) = (fAss_list_char @ X81 @ X82 @ X83 @ X84))))))). % exp.distinct(63)
thf(fact_155_exp_Odistinct_I61_J, axiom,
    ((![X32 : val, X71 : exp_list_char, X72 : list_char, X73 : list_char]: (~ (((val_list_char @ X32) = (fAcc_list_char @ X71 @ X72 @ X73))))))). % exp.distinct(61)
thf(fact_156_exp_Odistinct_I165_J, axiom,
    ((![X81 : exp_list_char, X82 : list_char, X83 : list_char, X84 : exp_list_char, X14 : exp_list_char]: (~ (((fAss_list_char @ X81 @ X82 @ X83 @ X84) = (throw_list_char @ X14))))))). % exp.distinct(165)
thf(fact_157_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_158_exp_Odistinct_I75_J, axiom,
    ((![X32 : val, X14 : exp_list_char]: (~ (((val_list_char @ X32) = (throw_list_char @ X14))))))). % exp.distinct(75)
thf(fact_159_WTrt__elim__cases_I4_J, axiom,
    ((![P : list_P1234162913t_char, H : nat > option2118145160on_val, E : list_char > option_ty, E2 : exp_list_char, T2 : ty]: ((wTrt2 @ P @ H @ E @ (throw_list_char @ E2) @ T2) => (~ ((![T_r : ty]: ((wTrt2 @ P @ H @ E @ E2 @ T_r) => (~ ((is_refT @ T_r))))))))))). % WTrt_elim_cases(4)
thf(fact_160_WTrtThrow, axiom,
    ((![P : list_P1234162913t_char, H : nat > option2118145160on_val, E : list_char > option_ty, E2 : exp_list_char, T_r2 : ty, T2 : ty]: ((wTrt2 @ P @ H @ E @ E2 @ T_r2) => ((is_refT @ T_r2) => (wTrt2 @ P @ H @ E @ (throw_list_char @ E2) @ T2)))))). % WTrtThrow
thf(fact_161_FAssRedsThrow2, axiom,
    ((![E_1 : exp_list_char, S_0 : produc515445032on_val, V : val, S_1 : produc515445032on_val, P : list_P1234162913t_char, E_2 : exp_list_char, E2 : exp_list_char, S_2 : produc515445032on_val, F : list_char, D : list_char]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E_1 @ S_0) @ (produc2023458740on_val @ (val_list_char @ V) @ S_1)) @ (transi111096263on_val @ (red @ P))) => ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E_2 @ S_1) @ (produc2023458740on_val @ (throw_list_char @ E2) @ S_2)) @ (transi111096263on_val @ (red @ P))) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (fAss_list_char @ E_1 @ F @ D @ E_2) @ S_0) @ (produc2023458740on_val @ (throw_list_char @ E2) @ S_2)) @ (transi111096263on_val @ (red @ P)))))))). % FAssRedsThrow2
thf(fact_162_WTrt_H__WTrts_H_Ointros_I21_J, axiom,
    ((![P : list_P1234162913t_char, H : nat > option2118145160on_val, E : list_char > option_ty, E2 : exp_list_char, T_r2 : ty, T2 : ty]: ((wTrt @ P @ H @ E @ E2 @ T_r2) => ((is_refT @ T_r2) => (wTrt @ P @ H @ E @ (throw_list_char @ E2) @ T2)))))). % WTrt'_WTrts'.intros(21)
thf(fact_163_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_164_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_165_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_166_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_167_red__reds_OFAssThrow1, axiom,
    ((![E2 : exp_list_char, F : list_char, D : list_char, E_2 : exp_list_char, S2 : produc515445032on_val, P : list_P1234162913t_char]: (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (fAss_list_char @ (throw_list_char @ E2) @ F @ D @ E_2) @ S2) @ (produc2023458740on_val @ (throw_list_char @ E2) @ S2)) @ (red @ P))))). % red_reds.FAssThrow1
thf(fact_168_red__reds_OFAccThrow, axiom,
    ((![E2 : 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 @ E2) @ F @ D) @ S2) @ (produc2023458740on_val @ (throw_list_char @ E2) @ S2)) @ (red @ P))))). % red_reds.FAccThrow
thf(fact_169_red__reds_OFAssRed2, axiom,
    ((![E2 : exp_list_char, S2 : produc515445032on_val, E3 : exp_list_char, S3 : produc515445032on_val, P : list_P1234162913t_char, V : val, F : list_char, D : list_char]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E2 @ S2) @ (produc2023458740on_val @ E3 @ S3)) @ (red @ P)) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (fAss_list_char @ (val_list_char @ V) @ F @ D @ E2) @ S2) @ (produc2023458740on_val @ (fAss_list_char @ (val_list_char @ V) @ F @ D @ E3) @ S3)) @ (red @ P)))))). % red_reds.FAssRed2
thf(fact_170_FAssRedsThrow1, axiom,
    ((![E2 : exp_list_char, S2 : produc515445032on_val, E3 : exp_list_char, S3 : produc515445032on_val, P : list_P1234162913t_char, F : list_char, D : list_char, E_2 : exp_list_char]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E2 @ S2) @ (produc2023458740on_val @ (throw_list_char @ E3) @ S3)) @ (transi111096263on_val @ (red @ P))) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (fAss_list_char @ E2 @ F @ D @ E_2) @ S2) @ (produc2023458740on_val @ (throw_list_char @ E3) @ S3)) @ (transi111096263on_val @ (red @ P))))))). % FAssRedsThrow1
thf(fact_171_BinOpRedsThrow2, axiom,
    ((![E_1 : exp_list_char, S_0 : produc515445032on_val, V_1 : val, S_1 : produc515445032on_val, P : list_P1234162913t_char, E_2 : exp_list_char, E2 : exp_list_char, S_2 : produc515445032on_val, Bop : bop]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E_1 @ S_0) @ (produc2023458740on_val @ (val_list_char @ V_1) @ S_1)) @ (transi111096263on_val @ (red @ P))) => ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E_2 @ S_1) @ (produc2023458740on_val @ (throw_list_char @ E2) @ S_2)) @ (transi111096263on_val @ (red @ P))) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (binOp_list_char @ E_1 @ Bop @ E_2) @ S_0) @ (produc2023458740on_val @ (throw_list_char @ E2) @ S_2)) @ (transi111096263on_val @ (red @ P)))))))). % BinOpRedsThrow2
thf(fact_172_WhileRedsThrow, axiom,
    ((![B : exp_list_char, S2 : produc515445032on_val, E2 : exp_list_char, S3 : produc515445032on_val, P : list_P1234162913t_char, C7 : exp_list_char]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ B @ S2) @ (produc2023458740on_val @ (throw_list_char @ E2) @ S3)) @ (transi111096263on_val @ (red @ P))) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (while_list_char @ B @ C7) @ S2) @ (produc2023458740on_val @ (throw_list_char @ E2) @ S3)) @ (transi111096263on_val @ (red @ P))))))). % WhileRedsThrow
thf(fact_173_TryRedsVal, axiom,
    ((![E2 : exp_list_char, S2 : produc515445032on_val, V : val, S3 : produc515445032on_val, P : list_P1234162913t_char, C : list_char, V2 : list_char, E_2 : exp_list_char]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E2 @ S2) @ (produc2023458740on_val @ (val_list_char @ V) @ S3)) @ (transi111096263on_val @ (red @ P))) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (tryCatch_list_char @ E2 @ C @ V2 @ E_2) @ S2) @ (produc2023458740on_val @ (val_list_char @ V) @ S3)) @ (transi111096263on_val @ (red @ P))))))). % TryRedsVal
thf(fact_174_exp_Oinject_I4_J, axiom,
    ((![X41 : exp_list_char, X42 : bop, X43 : exp_list_char, Y41 : exp_list_char, Y42 : bop, Y43 : exp_list_char]: (((binOp_list_char @ X41 @ X42 @ X43) = (binOp_list_char @ Y41 @ Y42 @ Y43)) = (((X41 = Y41)) & ((((X42 = Y42)) & ((X43 = Y43))))))))). % exp.inject(4)
thf(fact_175_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_176_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_177_exp_Odistinct_I55_J, axiom,
    ((![X32 : val, X41 : exp_list_char, X42 : bop, X43 : exp_list_char]: (~ (((val_list_char @ X32) = (binOp_list_char @ X41 @ X42 @ X43))))))). % exp.distinct(55)
thf(fact_178_exp_Odistinct_I73_J, axiom,
    ((![X32 : val, X131 : exp_list_char, X132 : exp_list_char]: (~ (((val_list_char @ X32) = (while_list_char @ X131 @ X132))))))). % exp.distinct(73)
thf(fact_179_exp_Odistinct_I77_J, axiom,
    ((![X32 : val, X151 : exp_list_char, X152 : list_char, X153 : list_char, X154 : exp_list_char]: (~ (((val_list_char @ X32) = (tryCatch_list_char @ X151 @ X152 @ X153 @ X154))))))). % exp.distinct(77)
thf(fact_180_exp_Odistinct_I97_J, axiom,
    ((![X41 : exp_list_char, X42 : bop, X43 : exp_list_char, X14 : exp_list_char]: (~ (((binOp_list_char @ X41 @ X42 @ X43) = (throw_list_char @ X14))))))). % exp.distinct(97)
thf(fact_181_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_182_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_183_exp_Odistinct_I207_J, axiom,
    ((![X131 : exp_list_char, X132 : exp_list_char, X151 : exp_list_char, X152 : list_char, X153 : list_char, X154 : exp_list_char]: (~ (((while_list_char @ X131 @ X132) = (tryCatch_list_char @ X151 @ X152 @ X153 @ X154))))))). % exp.distinct(207)
thf(fact_184_exp_Odistinct_I99_J, axiom,
    ((![X41 : exp_list_char, X42 : bop, X43 : exp_list_char, X151 : exp_list_char, X152 : list_char, X153 : list_char, X154 : exp_list_char]: (~ (((binOp_list_char @ X41 @ X42 @ X43) = (tryCatch_list_char @ X151 @ X152 @ X153 @ X154))))))). % exp.distinct(99)
thf(fact_185_exp_Odistinct_I95_J, axiom,
    ((![X41 : exp_list_char, X42 : bop, X43 : exp_list_char, X131 : exp_list_char, X132 : exp_list_char]: (~ (((binOp_list_char @ X41 @ X42 @ X43) = (while_list_char @ X131 @ X132))))))). % exp.distinct(95)
thf(fact_186_exp_Odistinct_I83_J, axiom,
    ((![X41 : exp_list_char, X42 : bop, X43 : exp_list_char, X71 : exp_list_char, X72 : list_char, X73 : list_char]: (~ (((binOp_list_char @ X41 @ X42 @ X43) = (fAcc_list_char @ X71 @ X72 @ X73))))))). % exp.distinct(83)
thf(fact_187_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_188_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_189_exp_Odistinct_I85_J, axiom,
    ((![X41 : exp_list_char, X42 : bop, X43 : exp_list_char, X81 : exp_list_char, X82 : list_char, X83 : list_char, X84 : exp_list_char]: (~ (((binOp_list_char @ X41 @ X42 @ X43) = (fAss_list_char @ X81 @ X82 @ X83 @ X84))))))). % exp.distinct(85)
thf(fact_190_exp_Odistinct_I163_J, axiom,
    ((![X81 : exp_list_char, X82 : list_char, X83 : list_char, X84 : exp_list_char, X131 : exp_list_char, X132 : exp_list_char]: (~ (((fAss_list_char @ X81 @ X82 @ X83 @ X84) = (while_list_char @ X131 @ X132))))))). % exp.distinct(163)
thf(fact_191_exp_Odistinct_I167_J, axiom,
    ((![X81 : exp_list_char, X82 : list_char, X83 : list_char, X84 : exp_list_char, X151 : exp_list_char, X152 : list_char, X153 : list_char, X154 : exp_list_char]: (~ (((fAss_list_char @ X81 @ X82 @ X83 @ X84) = (tryCatch_list_char @ X151 @ X152 @ X153 @ X154))))))). % exp.distinct(167)

% Conjectures (1)
thf(conj_0, conjecture,
    ((?[T5 : ty]: ((wTrt2 @ p @ h_a @ e @ (fAss_list_char @ e_a @ f @ d @ e_2) @ T5) & (widen_917054840t_char @ p @ T5 @ t))))).
