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% This file was generated by Isabelle (most likely Sledgehammer)
% 2020-12-16 14:20:19.509

% Could-be-implicit typings (23)
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% Explicit typings (63)
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thf(sy_c_Expr_Oexp_OBinOp_001t__List__Olist_It__String__Ochar_J, type,
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thf(sy_c_Expr_Oexp_OCond_001t__List__Olist_It__String__Ochar_J, type,
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thf(sy_c_Expr_Oexp_OFAss_001t__List__Olist_It__String__Ochar_J, type,
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thf(sy_c_WellTypeRT_OWTrt, type,
    wTrt : list_P1234162913t_char > (nat > option2118145160on_val) > (list_char > option_ty) > exp_list_char > ty > $o).
thf(sy_c_WellType_OWT, type,
    wt : list_P1234162913t_char > (list_char > option_ty) > exp_list_char > ty > $o).
thf(sy_c_Wfrec_Osame__fst_001_062_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_001_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J, type,
    same_f1752972725on_val : ((nat > option2118145160on_val) > $o) > ((nat > option2118145160on_val) > set_Pr1104486497on_val) > set_Pr148564103on_val).
thf(sy_c_Wfrec_Osame__fst_001t__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_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,
    same_f366220041on_val : (exp_list_char > $o) > (exp_list_char > set_Pr148564103on_val) > set_Pr1189492743on_val).
thf(sy_c_Wfrec_Osame__fst_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_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,
    same_f962657004on_val : (produc1097884484on_val > $o) > (produc1097884484on_val > set_Pr1189492743on_val) > set_Pr1368603847on_val).
thf(sy_c_member_001t__Product____Type__Oprod_I_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_M_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_J, type,
    member1177709994on_val : produc1335728385on_val > set_Pr1104486497on_val > $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__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_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,
    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__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_092_060_094sub_0621____, type,
    t_1 : ty).
thf(sy_v_T_092_060_094sub_0622____, type,
    t_2 : ty).
thf(sy_v_T____, type,
    t : ty).
thf(sy_v_bop____, type,
    bop2 : bop).
thf(sy_v_e_092_060_094sub_0621_H____, type,
    e_1 : exp_list_char).
thf(sy_v_e_092_060_094sub_0621____, type,
    e_12 : exp_list_char).
thf(sy_v_e_092_060_094sub_0622____, type,
    e_2 : exp_list_char).
thf(sy_v_h_Ha____, type,
    h_a : nat > option2118145160on_val).
thf(sy_v_ha____, type,
    ha : nat > option2118145160on_val).
thf(sy_v_l_Ha____, type,
    l_a : list_char > option_val).
thf(sy_v_la____, type,
    la : list_char > option_val).

% Relevant facts (173)
thf(fact_0__092_060open_062P_ME_Mh_H_A_092_060turnstile_062_Ae_092_060_094sub_0622_A_058_AT_092_060_094sub_0622_092_060close_062, axiom,
    ((wTrt @ p @ h_a @ e @ e_2 @ t_2))). % \<open>P,E,h' \<turnstile> e\<^sub>2 : T\<^sub>2\<close>
thf(fact_1__092_060open_062_092_060exists_062U_O_AP_ME_Mh_H_A_092_060turnstile_062_Ae_092_060_094sub_0621_H_A_058_AU_A_092_060and_062_AP_A_092_060turnstile_062_AU_A_092_060le_062_AT_092_060_094sub_0621_092_060close_062, axiom,
    ((?[U : ty]: ((wTrt @ p @ h_a @ e @ e_1 @ U) & (widen_917054840t_char @ p @ U @ t_1))))). % \<open>\<exists>U. P,E,h' \<turnstile> e\<^sub>1' : U \<and> P \<turnstile> U \<le> T\<^sub>1\<close>
thf(fact_2_wt_092_060_094sub_0622, axiom,
    ((wTrt @ p @ ha @ e @ e_2 @ t_2))). % wt\<^sub>2
thf(fact_3_wt, axiom,
    ((wTrt @ p @ ha @ e @ (binOp_list_char @ e_12 @ bop2 @ e_2) @ t))). % wt
thf(fact_4_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_5_wt_092_060_094sub_0621, axiom,
    ((wTrt @ p @ ha @ e @ e_12 @ t_1))). % wt\<^sub>1
thf(fact_6_local_Owf, axiom,
    ((wf_pro1229751607t_char @ wf_J_mdecl @ p))). % local.wf
thf(fact_7__092_060open_062bop_A_061_AEq_092_060close_062, axiom,
    ((bop2 = c_Expr_Obop_OEq))). % \<open>bop = Eq\<close>
thf(fact_8__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062T_092_060_094sub_0621_AT_092_060_094sub_0622_O_A_092_060lbrakk_062T_A_061_ABoolean_059_AP_ME_Mh_A_092_060turnstile_062_Ae_092_060_094sub_0621_A_058_AT_092_060_094sub_0621_059_AP_ME_Mh_A_092_060turnstile_062_Ae_092_060_094sub_0622_A_058_AT_092_060_094sub_0622_092_060rbrakk_062_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062, axiom,
    ((~ (((t = boolean) => ((?[X_1 : ty]: (wTrt @ p @ ha @ e @ e_12 @ X_1)) => (![T_2 : ty]: (~ ((wTrt @ p @ ha @ e @ e_2 @ T_2)))))))))). % \<open>\<And>thesis. (\<And>T\<^sub>1 T\<^sub>2. \<lbrakk>T = Boolean; P,E,h \<turnstile> e\<^sub>1 : T\<^sub>1; P,E,h \<turnstile> e\<^sub>2 : T\<^sub>2\<rbrakk> \<Longrightarrow> thesis) \<Longrightarrow> thesis\<close>
thf(fact_9_BinOpRed1_Oprems_I2_J, axiom,
    ((wTrt @ p @ ha @ e @ (binOp_list_char @ e_12 @ bop2 @ e_2) @ t))). % BinOpRed1.prems(2)
thf(fact_10__092_060open_062T_A_061_ABoolean_092_060close_062, axiom,
    ((t = boolean))). % \<open>T = Boolean\<close>
thf(fact_11_IH, axiom,
    ((![E : list_char > option_ty, T : ty]: ((typeSa1777264139_sconf @ p @ E @ (produc52622304on_val @ ha @ la)) => ((wTrt @ p @ ha @ E @ e_12 @ T) => (?[U : ty]: ((wTrt @ p @ h_a @ E @ e_1 @ U) & (widen_917054840t_char @ p @ U @ T)))))))). % IH
thf(fact_12_conf, axiom,
    ((typeSa1777264139_sconf @ p @ e @ (produc52622304on_val @ ha @ la)))). % conf
thf(fact_13_BinOpRed1_Ohyps_I2_J, axiom,
    ((![E : list_char > option_ty, T : ty]: ((typeSa1777264139_sconf @ p @ E @ (produc52622304on_val @ ha @ la)) => ((wTrt @ p @ ha @ E @ e_12 @ T) => (?[T2 : ty]: ((wTrt @ p @ h_a @ E @ e_1 @ T2) & (widen_917054840t_char @ p @ T2 @ T)))))))). % BinOpRed1.hyps(2)
thf(fact_14_WTrtBinOpEq, axiom,
    ((![P : list_P1234162913t_char, H : nat > option2118145160on_val, E : list_char > option_ty, E_1 : exp_list_char, T_1 : ty, E_2 : exp_list_char, T_22 : ty]: ((wTrt @ P @ H @ E @ E_1 @ T_1) => ((wTrt @ P @ H @ E @ E_2 @ T_22) => (wTrt @ P @ H @ E @ (binOp_list_char @ E_1 @ c_Expr_Obop_OEq @ E_2) @ boolean)))))). % WTrtBinOpEq
thf(fact_15_BinOpRed1_Oprems_I1_J, axiom,
    ((typeSa1777264139_sconf @ p @ e @ (produc52622304on_val @ ha @ la)))). % BinOpRed1.prems(1)
thf(fact_16_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_17_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_18_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_19_old_Oprod_Oinject, axiom,
    ((![A : nat > option2118145160on_val, B : list_char > option_val, A2 : nat > option2118145160on_val, B2 : list_char > option_val]: (((produc52622304on_val @ A @ B) = (produc52622304on_val @ A2 @ B2)) = (((A = A2)) & ((B = B2))))))). % old.prod.inject
thf(fact_20_old_Oprod_Oinject, axiom,
    ((![A : produc1097884484on_val, B : produc1097884484on_val, A2 : produc1097884484on_val, B2 : produc1097884484on_val]: (((produc1069526295on_val @ A @ B) = (produc1069526295on_val @ A2 @ B2)) = (((A = A2)) & ((B = B2))))))). % old.prod.inject
thf(fact_21_old_Oprod_Oinject, axiom,
    ((![A : exp_list_char, B : produc515445032on_val, A2 : exp_list_char, B2 : produc515445032on_val]: (((produc2023458740on_val @ A @ B) = (produc2023458740on_val @ A2 @ B2)) = (((A = A2)) & ((B = B2))))))). % old.prod.inject
thf(fact_22_red, axiom,
    ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ e_12 @ (produc52622304on_val @ ha @ la)) @ (produc2023458740on_val @ e_1 @ (produc52622304on_val @ h_a @ l_a))) @ (red @ p)))). % red
thf(fact_23_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_24_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_25_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_26_widen__trans, axiom,
    ((![P : list_P1234162913t_char, S : ty, U2 : ty, T : ty]: ((widen_917054840t_char @ P @ S @ U2) => ((widen_917054840t_char @ P @ U2 @ T) => (widen_917054840t_char @ P @ S @ T)))))). % widen_trans
thf(fact_27_widen__refl, axiom,
    ((![P : list_P1234162913t_char, T : ty]: (widen_917054840t_char @ P @ T @ T)))). % widen_refl
thf(fact_28_WTBinOpEq, axiom,
    ((![P : list_P1234162913t_char, E : list_char > option_ty, E_1 : exp_list_char, T_1 : ty, E_2 : exp_list_char, T_22 : ty]: ((wt @ P @ E @ E_1 @ T_1) => ((wt @ P @ E @ E_2 @ T_22) => (((widen_917054840t_char @ P @ T_1 @ T_22) | (widen_917054840t_char @ P @ T_22 @ T_1)) => (wt @ P @ E @ (binOp_list_char @ E_1 @ c_Expr_Obop_OEq @ E_2) @ boolean))))))). % WTBinOpEq
thf(fact_29_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_12 : ty]: ((wTrt @ P @ H @ E @ E_1 @ T_12) => (![T_2 : ty]: ((wTrt @ P @ H @ E @ E_2 @ T_2) => (((widen_917054840t_char @ P @ T_12 @ T_2) | (widen_917054840t_char @ P @ T_2 @ T_12)) => (((widen_917054840t_char @ P @ T_12 @ T_2) => (T = T_2)) => (~ (((widen_917054840t_char @ P @ T_2 @ T_12) => (T = T_12))))))))))))))))). % WTrt_elim_cases(2)
thf(fact_30_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_31_WTCond, axiom,
    ((![P : list_P1234162913t_char, E : list_char > option_ty, E2 : exp_list_char, E_1 : exp_list_char, T_1 : ty, E_2 : exp_list_char, T_22 : ty, T : ty]: ((wt @ P @ E @ E2 @ boolean) => ((wt @ P @ E @ E_1 @ T_1) => ((wt @ P @ E @ E_2 @ T_22) => (((widen_917054840t_char @ P @ T_1 @ T_22) | (widen_917054840t_char @ P @ T_22 @ T_1)) => (((widen_917054840t_char @ P @ T_1 @ T_22) => (T = T_22)) => (((widen_917054840t_char @ P @ T_22 @ T_1) => (T = T_1)) => (wt @ P @ E @ (cond_list_char @ E2 @ E_1 @ E_2) @ T)))))))))). % WTCond
thf(fact_32_WT__elim__cases_I2_J, axiom,
    ((![P : list_P1234162913t_char, E : list_char > option_ty, E2 : exp_list_char, E_1 : exp_list_char, E_2 : exp_list_char, T : ty]: ((wt @ P @ E @ (cond_list_char @ E2 @ E_1 @ E_2) @ T) => (~ (((wt @ P @ E @ E2 @ boolean) => (![T_12 : ty]: ((wt @ P @ E @ E_1 @ T_12) => (![T_2 : ty]: ((wt @ P @ E @ E_2 @ T_2) => (((widen_917054840t_char @ P @ T_12 @ T_2) | (widen_917054840t_char @ P @ T_2 @ T_12)) => (((widen_917054840t_char @ P @ T_12 @ T_2) => (T = T_2)) => (~ (((widen_917054840t_char @ P @ T_2 @ T_12) => (T = T_12))))))))))))))))). % WT_elim_cases(2)
thf(fact_33_WT__implies__WTrt, axiom,
    ((![P : list_P1234162913t_char, E : list_char > option_ty, E2 : exp_list_char, T : ty, H : nat > option2118145160on_val]: ((wt @ P @ E @ E2 @ T) => (wTrt @ P @ H @ E @ E2 @ T))))). % WT_implies_WTrt
thf(fact_34_exp_Odistinct_I93_J, axiom,
    ((![X41 : exp_list_char, X42 : bop, X43 : exp_list_char, X121 : exp_list_char, X122 : exp_list_char, X123 : exp_list_char]: (~ (((binOp_list_char @ X41 @ X42 @ X43) = (cond_list_char @ X121 @ X122 @ X123))))))). % exp.distinct(93)
thf(fact_35_old_Oprod_Oinducts, axiom,
    ((![P : produc515445032on_val > $o, Prod : produc515445032on_val]: ((![A3 : nat > option2118145160on_val, B3 : list_char > option_val]: (P @ (produc52622304on_val @ A3 @ B3))) => (P @ Prod))))). % old.prod.inducts
thf(fact_36_old_Oprod_Oinducts, axiom,
    ((![P : produc1172664615on_val > $o, Prod : produc1172664615on_val]: ((![A3 : produc1097884484on_val, B3 : produc1097884484on_val]: (P @ (produc1069526295on_val @ A3 @ B3))) => (P @ Prod))))). % old.prod.inducts
thf(fact_37_old_Oprod_Oinducts, axiom,
    ((![P : produc1097884484on_val > $o, Prod : produc1097884484on_val]: ((![A3 : exp_list_char, B3 : produc515445032on_val]: (P @ (produc2023458740on_val @ A3 @ B3))) => (P @ Prod))))). % old.prod.inducts
thf(fact_38_old_Oprod_Oexhaust, axiom,
    ((![Y3 : produc515445032on_val]: (~ ((![A3 : nat > option2118145160on_val, B3 : list_char > option_val]: (~ ((Y3 = (produc52622304on_val @ A3 @ B3)))))))))). % old.prod.exhaust
thf(fact_39_old_Oprod_Oexhaust, axiom,
    ((![Y3 : produc1172664615on_val]: (~ ((![A3 : produc1097884484on_val, B3 : produc1097884484on_val]: (~ ((Y3 = (produc1069526295on_val @ A3 @ B3)))))))))). % old.prod.exhaust
thf(fact_40_old_Oprod_Oexhaust, axiom,
    ((![Y3 : produc1097884484on_val]: (~ ((![A3 : exp_list_char, B3 : produc515445032on_val]: (~ ((Y3 = (produc2023458740on_val @ A3 @ B3)))))))))). % old.prod.exhaust
thf(fact_41_prod__induct4, axiom,
    ((![P : produc1172664615on_val > $o, X3 : produc1172664615on_val]: ((![A3 : produc1097884484on_val, B3 : exp_list_char, C : nat > option2118145160on_val, D : list_char > option_val]: (P @ (produc1069526295on_val @ A3 @ (produc2023458740on_val @ B3 @ (produc52622304on_val @ C @ D))))) => (P @ X3))))). % prod_induct4
thf(fact_42_prod__induct3, axiom,
    ((![P : produc1172664615on_val > $o, X3 : produc1172664615on_val]: ((![A3 : produc1097884484on_val, B3 : exp_list_char, C : produc515445032on_val]: (P @ (produc1069526295on_val @ A3 @ (produc2023458740on_val @ B3 @ C)))) => (P @ X3))))). % prod_induct3
thf(fact_43_prod__induct3, axiom,
    ((![P : produc1097884484on_val > $o, X3 : produc1097884484on_val]: ((![A3 : exp_list_char, B3 : nat > option2118145160on_val, C : list_char > option_val]: (P @ (produc2023458740on_val @ A3 @ (produc52622304on_val @ B3 @ C)))) => (P @ X3))))). % prod_induct3
thf(fact_44_prod__cases4, axiom,
    ((![Y3 : produc1172664615on_val]: (~ ((![A3 : produc1097884484on_val, B3 : exp_list_char, C : nat > option2118145160on_val, D : list_char > option_val]: (~ ((Y3 = (produc1069526295on_val @ A3 @ (produc2023458740on_val @ B3 @ (produc52622304on_val @ C @ D)))))))))))). % prod_cases4
thf(fact_45_prod__cases3, axiom,
    ((![Y3 : produc1172664615on_val]: (~ ((![A3 : produc1097884484on_val, B3 : exp_list_char, C : produc515445032on_val]: (~ ((Y3 = (produc1069526295on_val @ A3 @ (produc2023458740on_val @ B3 @ C))))))))))). % prod_cases3
thf(fact_46_prod__cases3, axiom,
    ((![Y3 : produc1097884484on_val]: (~ ((![A3 : exp_list_char, B3 : nat > option2118145160on_val, C : list_char > option_val]: (~ ((Y3 = (produc2023458740on_val @ A3 @ (produc52622304on_val @ B3 @ C))))))))))). % prod_cases3
thf(fact_47_Pair__inject, axiom,
    ((![A : nat > option2118145160on_val, B : list_char > option_val, A2 : nat > option2118145160on_val, B2 : list_char > option_val]: (((produc52622304on_val @ A @ B) = (produc52622304on_val @ A2 @ B2)) => (~ (((A = A2) => (~ ((B = B2)))))))))). % Pair_inject
thf(fact_48_Pair__inject, axiom,
    ((![A : produc1097884484on_val, B : produc1097884484on_val, A2 : produc1097884484on_val, B2 : produc1097884484on_val]: (((produc1069526295on_val @ A @ B) = (produc1069526295on_val @ A2 @ B2)) => (~ (((A = A2) => (~ ((B = B2)))))))))). % Pair_inject
thf(fact_49_Pair__inject, axiom,
    ((![A : exp_list_char, B : produc515445032on_val, A2 : exp_list_char, B2 : produc515445032on_val]: (((produc2023458740on_val @ A @ B) = (produc2023458740on_val @ A2 @ B2)) => (~ (((A = A2) => (~ ((B = B2)))))))))). % Pair_inject
thf(fact_50_mem__Collect__eq, axiom,
    ((![A : produc1172664615on_val, P : produc1172664615on_val > $o]: ((member354538064on_val @ A @ (collec2055896722on_val @ P)) = (P @ A))))). % mem_Collect_eq
thf(fact_51_Collect__mem__eq, axiom,
    ((![A4 : set_Pr1189492743on_val]: ((collec2055896722on_val @ (^[X : produc1172664615on_val]: (member354538064on_val @ X @ A4))) = A4)))). % Collect_mem_eq
thf(fact_52_prod__cases, axiom,
    ((![P : produc515445032on_val > $o, P2 : produc515445032on_val]: ((![A3 : nat > option2118145160on_val, B3 : list_char > option_val]: (P @ (produc52622304on_val @ A3 @ B3))) => (P @ P2))))). % prod_cases
thf(fact_53_prod__cases, axiom,
    ((![P : produc1172664615on_val > $o, P2 : produc1172664615on_val]: ((![A3 : produc1097884484on_val, B3 : produc1097884484on_val]: (P @ (produc1069526295on_val @ A3 @ B3))) => (P @ P2))))). % prod_cases
thf(fact_54_prod__cases, axiom,
    ((![P : produc1097884484on_val > $o, P2 : produc1097884484on_val]: ((![A3 : exp_list_char, B3 : produc515445032on_val]: (P @ (produc2023458740on_val @ A3 @ B3))) => (P @ P2))))). % prod_cases
thf(fact_55_surj__pair, axiom,
    ((![P2 : produc515445032on_val]: (?[X4 : nat > option2118145160on_val, Y4 : list_char > option_val]: (P2 = (produc52622304on_val @ X4 @ Y4)))))). % surj_pair
thf(fact_56_surj__pair, axiom,
    ((![P2 : produc1172664615on_val]: (?[X4 : produc1097884484on_val, Y4 : produc1097884484on_val]: (P2 = (produc1069526295on_val @ X4 @ Y4)))))). % surj_pair
thf(fact_57_surj__pair, axiom,
    ((![P2 : produc1097884484on_val]: (?[X4 : exp_list_char, Y4 : produc515445032on_val]: (P2 = (produc2023458740on_val @ X4 @ Y4)))))). % surj_pair
thf(fact_58_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_1 : ty, E_2 : exp_list_char, T_22 : ty, T : ty]: ((wTrt @ P @ H @ E @ E2 @ boolean) => ((wTrt @ P @ H @ E @ E_1 @ T_1) => ((wTrt @ P @ H @ E @ E_2 @ T_22) => (((widen_917054840t_char @ P @ T_1 @ T_22) | (widen_917054840t_char @ P @ T_22 @ T_1)) => (((widen_917054840t_char @ P @ T_1 @ T_22) => (T = T_22)) => (((widen_917054840t_char @ P @ T_22 @ T_1) => (T = T_1)) => (wTrt @ P @ H @ E @ (cond_list_char @ E2 @ E_1 @ E_2) @ T)))))))))). % WTrtCond
thf(fact_59_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_60_red__reds_OBinOpRed1, axiom,
    ((![E2 : exp_list_char, S2 : produc515445032on_val, E3 : exp_list_char, S3 : produc515445032on_val, P : list_P1234162913t_char, Bop : bop, 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 @ (binOp_list_char @ E2 @ Bop @ E_2) @ S2) @ (produc2023458740on_val @ (binOp_list_char @ E3 @ Bop @ E_2) @ S3)) @ (red @ P)))))). % red_reds.BinOpRed1
thf(fact_61_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_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_same__fstI, axiom,
    ((![P : (nat > option2118145160on_val) > $o, X3 : nat > option2118145160on_val, Y5 : list_char > option_val, Y3 : list_char > option_val, R : (nat > option2118145160on_val) > set_Pr1104486497on_val]: ((P @ X3) => ((member1177709994on_val @ (produc746553401on_val @ Y5 @ Y3) @ (R @ X3)) => (member2027247312on_val @ (produc2106877847on_val @ (produc52622304on_val @ X3 @ Y5) @ (produc52622304on_val @ X3 @ Y3)) @ (same_f1752972725on_val @ P @ R))))))). % same_fstI
thf(fact_65_same__fstI, axiom,
    ((![P : exp_list_char > $o, X3 : exp_list_char, Y5 : produc515445032on_val, Y3 : produc515445032on_val, R : exp_list_char > set_Pr148564103on_val]: ((P @ X3) => ((member2027247312on_val @ (produc2106877847on_val @ Y5 @ Y3) @ (R @ X3)) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ X3 @ Y5) @ (produc2023458740on_val @ X3 @ Y3)) @ (same_f366220041on_val @ P @ R))))))). % same_fstI
thf(fact_66_same__fstI, axiom,
    ((![P : produc1097884484on_val > $o, X3 : produc1097884484on_val, Y5 : produc1097884484on_val, Y3 : produc1097884484on_val, R : produc1097884484on_val > set_Pr1189492743on_val]: ((P @ X3) => ((member354538064on_val @ (produc1069526295on_val @ Y5 @ Y3) @ (R @ X3)) => (member208988944on_val @ (produc564964183on_val @ (produc1069526295on_val @ X3 @ Y5) @ (produc1069526295on_val @ X3 @ Y3)) @ (same_f962657004on_val @ P @ R))))))). % same_fstI
thf(fact_67_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_68_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_69_sconf__def, axiom,
    ((typeSa1777264139_sconf = (^[P3 : list_P1234162913t_char]: (^[E4 : list_char > option_ty]: (produc99536995_val_o @ (^[H3 : nat > option2118145160on_val]: (^[L3 : list_char > option_val]: (((hconf_1244167010t_char @ P3 @ H3)) & ((lconf_485928294t_char @ P3 @ H3 @ L3 @ E4))))))))))). % sconf_def
thf(fact_70_red__reds_OBinOpRed2, axiom,
    ((![E2 : exp_list_char, S2 : produc515445032on_val, E3 : exp_list_char, S3 : produc515445032on_val, P : list_P1234162913t_char, V_1 : val, Bop : bop]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E2 @ S2) @ (produc2023458740on_val @ E3 @ S3)) @ (red @ P)) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (binOp_list_char @ (val_list_char @ V_1) @ Bop @ E2) @ S2) @ (produc2023458740on_val @ (binOp_list_char @ (val_list_char @ V_1) @ Bop @ E3) @ S3)) @ (red @ P)))))). % red_reds.BinOpRed2
thf(fact_71_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_72_exp_Oinject_I3_J, axiom,
    ((![X32 : val, Y32 : val]: (((val_list_char @ X32) = (val_list_char @ Y32)) = (X32 = Y32))))). % exp.inject(3)
thf(fact_73_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_74_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)))))) = (^[Ab : produc515445032on_val]: ((P) & ((produc99536995_val_o @ Q @ Ab)))))))). % split_part
thf(fact_75_case__prod__conv, axiom,
    ((![F : (nat > option2118145160on_val) > (list_char > option_val) > $o, A : nat > option2118145160on_val, B : list_char > option_val]: ((produc99536995_val_o @ F @ (produc52622304on_val @ A @ B)) = (F @ A @ B))))). % case_prod_conv
thf(fact_76_case__prodI2, axiom,
    ((![P2 : produc1172664615on_val, C2 : produc1097884484on_val > produc1097884484on_val > $o]: ((![A3 : produc1097884484on_val, B3 : produc1097884484on_val]: ((P2 = (produc1069526295on_val @ A3 @ B3)) => (C2 @ A3 @ B3))) => (produc50362220_val_o @ C2 @ P2))))). % case_prodI2
thf(fact_77_case__prodI2, axiom,
    ((![P2 : produc1097884484on_val, C2 : exp_list_char > produc515445032on_val > $o]: ((![A3 : exp_list_char, B3 : produc515445032on_val]: ((P2 = (produc2023458740on_val @ A3 @ B3)) => (C2 @ A3 @ B3))) => (produc199145871_val_o @ C2 @ P2))))). % case_prodI2
thf(fact_78_case__prodI2, axiom,
    ((![P2 : produc515445032on_val, C2 : (nat > option2118145160on_val) > (list_char > option_val) > $o]: ((![A3 : nat > option2118145160on_val, B3 : list_char > option_val]: ((P2 = (produc52622304on_val @ A3 @ B3)) => (C2 @ A3 @ B3))) => (produc99536995_val_o @ C2 @ P2))))). % case_prodI2
thf(fact_79_case__prodI, axiom,
    ((![F : produc1097884484on_val > produc1097884484on_val > $o, A : produc1097884484on_val, B : produc1097884484on_val]: ((F @ A @ B) => (produc50362220_val_o @ F @ (produc1069526295on_val @ A @ B)))))). % case_prodI
thf(fact_80_case__prodI, axiom,
    ((![F : exp_list_char > produc515445032on_val > $o, A : exp_list_char, B : produc515445032on_val]: ((F @ A @ B) => (produc199145871_val_o @ F @ (produc2023458740on_val @ A @ B)))))). % case_prodI
thf(fact_81_case__prodI, axiom,
    ((![F : (nat > option2118145160on_val) > (list_char > option_val) > $o, A : nat > option2118145160on_val, B : list_char > option_val]: ((F @ A @ B) => (produc99536995_val_o @ F @ (produc52622304on_val @ A @ B)))))). % case_prodI
thf(fact_82_exp_Odistinct_I75_J, axiom,
    ((![X32 : val, X14 : exp_list_char]: (~ (((val_list_char @ X32) = (throw_list_char @ X14))))))). % exp.distinct(75)
thf(fact_83_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_84_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_85_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_86_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_87_exp_Odistinct_I71_J, axiom,
    ((![X32 : val, X121 : exp_list_char, X122 : exp_list_char, X123 : exp_list_char]: (~ (((val_list_char @ X32) = (cond_list_char @ X121 @ X122 @ X123))))))). % exp.distinct(71)
thf(fact_88_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_89_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_90_case__prodE, axiom,
    ((![C2 : produc1097884484on_val > produc1097884484on_val > $o, P2 : produc1172664615on_val]: ((produc50362220_val_o @ C2 @ P2) => (~ ((![X4 : produc1097884484on_val, Y4 : produc1097884484on_val]: ((P2 = (produc1069526295on_val @ X4 @ Y4)) => (~ ((C2 @ X4 @ Y4))))))))))). % case_prodE
thf(fact_91_case__prodE, axiom,
    ((![C2 : exp_list_char > produc515445032on_val > $o, P2 : produc1097884484on_val]: ((produc199145871_val_o @ C2 @ P2) => (~ ((![X4 : exp_list_char, Y4 : produc515445032on_val]: ((P2 = (produc2023458740on_val @ X4 @ Y4)) => (~ ((C2 @ X4 @ Y4))))))))))). % case_prodE
thf(fact_92_case__prodE, axiom,
    ((![C2 : (nat > option2118145160on_val) > (list_char > option_val) > $o, P2 : produc515445032on_val]: ((produc99536995_val_o @ C2 @ P2) => (~ ((![X4 : nat > option2118145160on_val, Y4 : list_char > option_val]: ((P2 = (produc52622304on_val @ X4 @ Y4)) => (~ ((C2 @ X4 @ Y4))))))))))). % case_prodE
thf(fact_93_case__prodD, axiom,
    ((![F : produc1097884484on_val > produc1097884484on_val > $o, A : produc1097884484on_val, B : produc1097884484on_val]: ((produc50362220_val_o @ F @ (produc1069526295on_val @ A @ B)) => (F @ A @ B))))). % case_prodD
thf(fact_94_case__prodD, axiom,
    ((![F : exp_list_char > produc515445032on_val > $o, A : exp_list_char, B : produc515445032on_val]: ((produc199145871_val_o @ F @ (produc2023458740on_val @ A @ B)) => (F @ A @ B))))). % case_prodD
thf(fact_95_case__prodD, axiom,
    ((![F : (nat > option2118145160on_val) > (list_char > option_val) > $o, A : nat > option2118145160on_val, B : list_char > option_val]: ((produc99536995_val_o @ F @ (produc52622304on_val @ A @ B)) => (F @ A @ B))))). % case_prodD
thf(fact_96_cond__case__prod__eta, axiom,
    ((![F : (nat > option2118145160on_val) > (list_char > option_val) > $o, G : produc515445032on_val > $o]: ((![X4 : nat > option2118145160on_val, Y4 : list_char > option_val]: ((F @ X4 @ Y4) = (G @ (produc52622304on_val @ X4 @ Y4)))) => ((produc99536995_val_o @ F) = G))))). % cond_case_prod_eta
thf(fact_97_case__prod__eta, axiom,
    ((![F : produc515445032on_val > $o]: ((produc99536995_val_o @ (^[X : nat > option2118145160on_val]: (^[Y : list_char > option_val]: (F @ (produc52622304on_val @ X @ Y))))) = F)))). % case_prod_eta
thf(fact_98_case__prodE2, axiom,
    ((![Q : $o > $o, P : (nat > option2118145160on_val) > (list_char > option_val) > $o, Z : produc515445032on_val]: ((Q @ (produc99536995_val_o @ P @ Z)) => (~ ((![X4 : nat > option2118145160on_val, Y4 : list_char > option_val]: ((Z = (produc52622304on_val @ X4 @ Y4)) => (~ ((Q @ (P @ X4 @ Y4)))))))))))). % case_prodE2
thf(fact_99_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_100_red__reds_OBinOpThrow2, axiom,
    ((![V_1 : val, Bop : bop, E2 : exp_list_char, S2 : produc515445032on_val, P : list_P1234162913t_char]: (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (binOp_list_char @ (val_list_char @ V_1) @ Bop @ (throw_list_char @ E2)) @ S2) @ (produc2023458740on_val @ (throw_list_char @ E2) @ S2)) @ (red @ P))))). % red_reds.BinOpThrow2
thf(fact_101_internal__case__prod__def, axiom,
    ((produc563955725_val_o = produc99536995_val_o))). % internal_case_prod_def
thf(fact_102_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_103_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_104_red__reds_OBinOpThrow1, axiom,
    ((![E2 : exp_list_char, Bop : bop, E_2 : exp_list_char, S2 : produc515445032on_val, P : list_P1234162913t_char]: (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (binOp_list_char @ (throw_list_char @ E2) @ Bop @ E_2) @ S2) @ (produc2023458740on_val @ (throw_list_char @ E2) @ S2)) @ (red @ P))))). % red_reds.BinOpThrow1
thf(fact_105_hext__refl, axiom,
    ((![H : nat > option2118145160on_val]: (hext @ H @ H)))). % hext_refl
thf(fact_106_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_107_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_108_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]: ((![X4 : nat > option2118145160on_val, Y4 : list_char > option_val]: (((produc52622304on_val @ X4 @ Y4) = Q2) => ((F @ X4 @ Y4) = (G @ X4 @ Y4)))) => ((P2 = Q2) => ((produc99536995_val_o @ F @ P2) = (produc99536995_val_o @ G @ Q2))))))). % split_cong
thf(fact_109_red__reds_ORedCondF, axiom,
    ((![E_1 : exp_list_char, E_2 : exp_list_char, S2 : produc515445032on_val, P : list_P1234162913t_char]: (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (cond_list_char @ (val_list_char @ (bool @ $false)) @ E_1 @ E_2) @ S2) @ (produc2023458740on_val @ E_2 @ S2)) @ (red @ P))))). % red_reds.RedCondF
thf(fact_110_mem__case__prodI, axiom,
    ((![Z : produc1172664615on_val, C2 : (nat > option2118145160on_val) > (list_char > option_val) > set_Pr1189492743on_val, A : nat > option2118145160on_val, B : list_char > option_val]: ((member354538064on_val @ Z @ (C2 @ A @ B)) => (member354538064on_val @ Z @ (produc1919805778on_val @ C2 @ (produc52622304on_val @ A @ B))))))). % mem_case_prodI
thf(fact_111_mem__case__prodI, axiom,
    ((![Z : produc1172664615on_val, C2 : produc1097884484on_val > produc1097884484on_val > set_Pr1189492743on_val, A : produc1097884484on_val, B : produc1097884484on_val]: ((member354538064on_val @ Z @ (C2 @ A @ B)) => (member354538064on_val @ Z @ (produc493625819on_val @ C2 @ (produc1069526295on_val @ A @ B))))))). % mem_case_prodI
thf(fact_112_mem__case__prodI, axiom,
    ((![Z : produc1172664615on_val, C2 : exp_list_char > produc515445032on_val > set_Pr1189492743on_val, A : exp_list_char, B : produc515445032on_val]: ((member354538064on_val @ Z @ (C2 @ A @ B)) => (member354538064on_val @ Z @ (produc848217214on_val @ C2 @ (produc2023458740on_val @ A @ B))))))). % mem_case_prodI
thf(fact_113_mem__case__prodI2, axiom,
    ((![P2 : produc515445032on_val, Z : produc1172664615on_val, C2 : (nat > option2118145160on_val) > (list_char > option_val) > set_Pr1189492743on_val]: ((![A3 : nat > option2118145160on_val, B3 : list_char > option_val]: ((P2 = (produc52622304on_val @ A3 @ B3)) => (member354538064on_val @ Z @ (C2 @ A3 @ B3)))) => (member354538064on_val @ Z @ (produc1919805778on_val @ C2 @ P2)))))). % mem_case_prodI2
thf(fact_114_mem__case__prodI2, axiom,
    ((![P2 : produc1172664615on_val, Z : produc1172664615on_val, C2 : produc1097884484on_val > produc1097884484on_val > set_Pr1189492743on_val]: ((![A3 : produc1097884484on_val, B3 : produc1097884484on_val]: ((P2 = (produc1069526295on_val @ A3 @ B3)) => (member354538064on_val @ Z @ (C2 @ A3 @ B3)))) => (member354538064on_val @ Z @ (produc493625819on_val @ C2 @ P2)))))). % mem_case_prodI2
thf(fact_115_mem__case__prodI2, axiom,
    ((![P2 : produc1097884484on_val, Z : produc1172664615on_val, C2 : exp_list_char > produc515445032on_val > set_Pr1189492743on_val]: ((![A3 : exp_list_char, B3 : produc515445032on_val]: ((P2 = (produc2023458740on_val @ A3 @ B3)) => (member354538064on_val @ Z @ (C2 @ A3 @ B3)))) => (member354538064on_val @ Z @ (produc848217214on_val @ C2 @ P2)))))). % mem_case_prodI2
thf(fact_116_mem__case__prodE, axiom,
    ((![Z : produc1172664615on_val, C2 : (nat > option2118145160on_val) > (list_char > option_val) > set_Pr1189492743on_val, P2 : produc515445032on_val]: ((member354538064on_val @ Z @ (produc1919805778on_val @ C2 @ P2)) => (~ ((![X4 : nat > option2118145160on_val, Y4 : list_char > option_val]: ((P2 = (produc52622304on_val @ X4 @ Y4)) => (~ ((member354538064on_val @ Z @ (C2 @ X4 @ Y4)))))))))))). % mem_case_prodE
thf(fact_117_mem__case__prodE, axiom,
    ((![Z : produc1172664615on_val, C2 : produc1097884484on_val > produc1097884484on_val > set_Pr1189492743on_val, P2 : produc1172664615on_val]: ((member354538064on_val @ Z @ (produc493625819on_val @ C2 @ P2)) => (~ ((![X4 : produc1097884484on_val, Y4 : produc1097884484on_val]: ((P2 = (produc1069526295on_val @ X4 @ Y4)) => (~ ((member354538064on_val @ Z @ (C2 @ X4 @ Y4)))))))))))). % mem_case_prodE
thf(fact_118_mem__case__prodE, axiom,
    ((![Z : produc1172664615on_val, C2 : exp_list_char > produc515445032on_val > set_Pr1189492743on_val, P2 : produc1097884484on_val]: ((member354538064on_val @ Z @ (produc848217214on_val @ C2 @ P2)) => (~ ((![X4 : exp_list_char, Y4 : produc515445032on_val]: ((P2 = (produc2023458740on_val @ X4 @ Y4)) => (~ ((member354538064on_val @ Z @ (C2 @ X4 @ Y4)))))))))))). % mem_case_prodE
thf(fact_119_hext__trans, axiom,
    ((![H : nat > option2118145160on_val, H2 : nat > option2118145160on_val, H4 : nat > option2118145160on_val]: ((hext @ H @ H2) => ((hext @ H2 @ H4) => (hext @ H @ H4)))))). % hext_trans
thf(fact_120_same__fst__def, axiom,
    ((same_f1752972725on_val = (^[P3 : (nat > option2118145160on_val) > $o]: (^[R2 : (nat > option2118145160on_val) > set_Pr1104486497on_val]: (collec1161811218on_val @ (produc271780076_val_o @ (produc1588213706_val_o @ (^[X5 : nat > option2118145160on_val]: (^[Y6 : list_char > option_val]: (produc99536995_val_o @ (^[X : nat > option2118145160on_val]: (^[Y : list_char > option_val]: (((X5 = X)) & ((((P3 @ X)) & ((member1177709994on_val @ (produc746553401on_val @ Y6 @ Y) @ (R2 @ X))))))))))))))))))). % same_fst_def
thf(fact_121_red__reds_ORedCondT, axiom,
    ((![E_1 : exp_list_char, E_2 : exp_list_char, S2 : produc515445032on_val, P : list_P1234162913t_char]: (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (cond_list_char @ (val_list_char @ (bool @ $true)) @ E_1 @ E_2) @ S2) @ (produc2023458740on_val @ E_1 @ S2)) @ (red @ P))))). % red_reds.RedCondT
thf(fact_122_val_Oinject_I1_J, axiom,
    ((![X32 : $o, Y32 : $o]: (((bool @ X32) = (bool @ Y32)) = (X32 = Y32))))). % val.inject(1)
thf(fact_123_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_124_red__reds_OFAssThrow2, axiom,
    ((![V : val, F2 : list_char, D2 : 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) @ F2 @ D2 @ (throw_list_char @ E2)) @ S2) @ (produc2023458740on_val @ (throw_list_char @ E2) @ S2)) @ (red @ P))))). % red_reds.FAssThrow2
thf(fact_125_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_126_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_127_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_128_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_129_exp_Odistinct_I161_J, axiom,
    ((![X81 : exp_list_char, X82 : list_char, X83 : list_char, X84 : exp_list_char, X121 : exp_list_char, X122 : exp_list_char, X123 : exp_list_char]: (~ (((fAss_list_char @ X81 @ X82 @ X83 @ X84) = (cond_list_char @ X121 @ X122 @ X123))))))). % exp.distinct(161)
thf(fact_130_red__reds_OFAssRed1, 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, 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 @ F2 @ D2 @ E_2) @ S2) @ (produc2023458740on_val @ (fAss_list_char @ E3 @ F2 @ D2 @ E_2) @ S3)) @ (red @ P)))))). % red_reds.FAssRed1
thf(fact_131_red__reds_OFAssRed2, axiom,
    ((![E2 : exp_list_char, S2 : produc515445032on_val, E3 : exp_list_char, S3 : produc515445032on_val, P : list_P1234162913t_char, V : val, 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 @ (fAss_list_char @ (val_list_char @ V) @ F2 @ D2 @ E2) @ S2) @ (produc2023458740on_val @ (fAss_list_char @ (val_list_char @ V) @ F2 @ D2 @ E3) @ S3)) @ (red @ P)))))). % red_reds.FAssRed2
thf(fact_132_red__reds_OFAssThrow1, axiom,
    ((![E2 : exp_list_char, F2 : list_char, D2 : 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) @ F2 @ D2 @ E_2) @ S2) @ (produc2023458740on_val @ (throw_list_char @ E2) @ S2)) @ (red @ P))))). % red_reds.FAssThrow1
thf(fact_133_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, H5 : nat > option2118145160on_val, L4 : list_char > option_val]: (R @ E5 @ H5 @ L4 @ E5 @ H5 @ 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, H6 : 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 @ H6 @ L5) => (R @ E_0 @ H_0 @ L_02 @ E6 @ H6 @ L5)))) => (R @ E2 @ H @ L @ E3 @ H2 @ L2))))))). % converse_rtrancl_induct_red
thf(fact_134_CondReds2T, axiom,
    ((![E2 : exp_list_char, S_0 : produc515445032on_val, S_1 : produc515445032on_val, P : list_P1234162913t_char, E_1 : exp_list_char, E3 : exp_list_char, S_2 : produc515445032on_val, E_2 : exp_list_char]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E2 @ S_0) @ (produc2023458740on_val @ (val_list_char @ (bool @ $true)) @ S_1)) @ (transi111096263on_val @ (red @ P))) => ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E_1 @ S_1) @ (produc2023458740on_val @ E3 @ S_2)) @ (transi111096263on_val @ (red @ P))) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (cond_list_char @ E2 @ E_1 @ E_2) @ S_0) @ (produc2023458740on_val @ E3 @ S_2)) @ (transi111096263on_val @ (red @ P)))))))). % CondReds2T
thf(fact_135_CondReds2F, axiom,
    ((![E2 : exp_list_char, S_0 : produc515445032on_val, S_1 : produc515445032on_val, P : list_P1234162913t_char, E_2 : exp_list_char, E3 : exp_list_char, S_2 : produc515445032on_val, E_1 : exp_list_char]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E2 @ S_0) @ (produc2023458740on_val @ (val_list_char @ (bool @ $false)) @ S_1)) @ (transi111096263on_val @ (red @ P))) => ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E_2 @ S_1) @ (produc2023458740on_val @ E3 @ S_2)) @ (transi111096263on_val @ (red @ P))) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (cond_list_char @ E2 @ E_1 @ E_2) @ S_0) @ (produc2023458740on_val @ E3 @ S_2)) @ (transi111096263on_val @ (red @ P)))))))). % CondReds2F
thf(fact_136_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, F2 : list_char, D2 : 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 @ F2 @ D2 @ E_2) @ S_0) @ (produc2023458740on_val @ (throw_list_char @ E2) @ S_2)) @ (transi111096263on_val @ (red @ P)))))))). % FAssRedsThrow2
thf(fact_137_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_138_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_139_BinOp1Reds, axiom,
    ((![E2 : exp_list_char, S2 : produc515445032on_val, E3 : exp_list_char, S3 : produc515445032on_val, P : list_P1234162913t_char, Bop : bop, 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 @ (binOp_list_char @ E2 @ Bop @ E_2) @ S2) @ (produc2023458740on_val @ (binOp_list_char @ E3 @ Bop @ E_2) @ S3)) @ (transi111096263on_val @ (red @ P))))))). % BinOp1Reds
thf(fact_140_FAssReds1, 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, 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 @ F2 @ D2 @ E_2) @ S2) @ (produc2023458740on_val @ (fAss_list_char @ E3 @ F2 @ D2 @ E_2) @ S3)) @ (transi111096263on_val @ (red @ P))))))). % FAssReds1
thf(fact_141_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_142_BinOp2Reds, axiom,
    ((![E2 : exp_list_char, S2 : produc515445032on_val, E3 : exp_list_char, S3 : produc515445032on_val, P : list_P1234162913t_char, V : val, Bop : bop]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E2 @ S2) @ (produc2023458740on_val @ E3 @ S3)) @ (transi111096263on_val @ (red @ P))) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (binOp_list_char @ (val_list_char @ V) @ Bop @ E2) @ S2) @ (produc2023458740on_val @ (binOp_list_char @ (val_list_char @ V) @ Bop @ E3) @ S3)) @ (transi111096263on_val @ (red @ P))))))). % BinOp2Reds
thf(fact_143_FAssReds2, axiom,
    ((![E2 : exp_list_char, S2 : produc515445032on_val, E3 : exp_list_char, S3 : produc515445032on_val, P : list_P1234162913t_char, V : val, 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 @ (fAss_list_char @ (val_list_char @ V) @ F2 @ D2 @ E2) @ S2) @ (produc2023458740on_val @ (fAss_list_char @ (val_list_char @ V) @ F2 @ D2 @ E3) @ S3)) @ (transi111096263on_val @ (red @ P))))))). % FAssReds2
thf(fact_144_BinOpRedsThrow1, axiom,
    ((![E2 : exp_list_char, S2 : produc515445032on_val, E3 : exp_list_char, S3 : produc515445032on_val, P : list_P1234162913t_char, Bop : bop, 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 @ (binOp_list_char @ E2 @ Bop @ E_2) @ S2) @ (produc2023458740on_val @ (throw_list_char @ E3) @ S3)) @ (transi111096263on_val @ (red @ P))))))). % BinOpRedsThrow1
thf(fact_145_FAssRedsThrow1, 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, 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 @ F2 @ D2 @ E_2) @ S2) @ (produc2023458740on_val @ (throw_list_char @ E3) @ S3)) @ (transi111096263on_val @ (red @ P))))))). % FAssRedsThrow1
thf(fact_146_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_147_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_148_rtrancl__induct2, axiom,
    ((![Ax : nat > option2118145160on_val, Ay : list_char > option_val, Bx : nat > option2118145160on_val, By : list_char > option_val, R3 : 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 @ R3)) => ((P @ Ax @ Ay) => ((![A3 : 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 @ A3 @ B3)) @ (transi432893227on_val @ R3)) => ((member2027247312on_val @ (produc2106877847on_val @ (produc52622304on_val @ A3 @ B3) @ (produc52622304on_val @ Aa @ Ba)) @ R3) => ((P @ A3 @ B3) => (P @ Aa @ Ba))))) => (P @ Bx @ By))))))). % rtrancl_induct2
thf(fact_149_rtrancl__induct2, axiom,
    ((![Ax : produc1097884484on_val, Ay : produc1097884484on_val, Bx : produc1097884484on_val, By : produc1097884484on_val, R3 : set_Pr1368603847on_val, P : produc1097884484on_val > produc1097884484on_val > $o]: ((member208988944on_val @ (produc564964183on_val @ (produc1069526295on_val @ Ax @ Ay) @ (produc1069526295on_val @ Bx @ By)) @ (transi100378922on_val @ R3)) => ((P @ Ax @ Ay) => ((![A3 : produc1097884484on_val, B3 : produc1097884484on_val, Aa : produc1097884484on_val, Ba : produc1097884484on_val]: ((member208988944on_val @ (produc564964183on_val @ (produc1069526295on_val @ Ax @ Ay) @ (produc1069526295on_val @ A3 @ B3)) @ (transi100378922on_val @ R3)) => ((member208988944on_val @ (produc564964183on_val @ (produc1069526295on_val @ A3 @ B3) @ (produc1069526295on_val @ Aa @ Ba)) @ R3) => ((P @ A3 @ B3) => (P @ Aa @ Ba))))) => (P @ Bx @ By))))))). % rtrancl_induct2
thf(fact_150_rtrancl__induct2, axiom,
    ((![Ax : exp_list_char, Ay : produc515445032on_val, Bx : exp_list_char, By : produc515445032on_val, R3 : set_Pr1189492743on_val, P : exp_list_char > produc515445032on_val > $o]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ Ax @ Ay) @ (produc2023458740on_val @ Bx @ By)) @ (transi111096263on_val @ R3)) => ((P @ Ax @ Ay) => ((![A3 : exp_list_char, B3 : produc515445032on_val, Aa : exp_list_char, Ba : produc515445032on_val]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ Ax @ Ay) @ (produc2023458740on_val @ A3 @ B3)) @ (transi111096263on_val @ R3)) => ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ A3 @ B3) @ (produc2023458740on_val @ Aa @ Ba)) @ R3) => ((P @ A3 @ B3) => (P @ Aa @ Ba))))) => (P @ Bx @ By))))))). % rtrancl_induct2
thf(fact_151_converse__rtranclE2, axiom,
    ((![Xa : nat > option2118145160on_val, Xb : list_char > option_val, Za : nat > option2118145160on_val, Zb : list_char > option_val, R3 : set_Pr148564103on_val]: ((member2027247312on_val @ (produc2106877847on_val @ (produc52622304on_val @ Xa @ Xb) @ (produc52622304on_val @ Za @ Zb)) @ (transi432893227on_val @ R3)) => ((~ (((produc52622304on_val @ Xa @ Xb) = (produc52622304on_val @ Za @ Zb)))) => (~ ((![A3 : nat > option2118145160on_val, B3 : list_char > option_val]: ((member2027247312on_val @ (produc2106877847on_val @ (produc52622304on_val @ Xa @ Xb) @ (produc52622304on_val @ A3 @ B3)) @ R3) => (~ ((member2027247312on_val @ (produc2106877847on_val @ (produc52622304on_val @ A3 @ B3) @ (produc52622304on_val @ Za @ Zb)) @ (transi432893227on_val @ R3))))))))))))). % converse_rtranclE2
thf(fact_152_converse__rtranclE2, axiom,
    ((![Xa : produc1097884484on_val, Xb : produc1097884484on_val, Za : produc1097884484on_val, Zb : produc1097884484on_val, R3 : set_Pr1368603847on_val]: ((member208988944on_val @ (produc564964183on_val @ (produc1069526295on_val @ Xa @ Xb) @ (produc1069526295on_val @ Za @ Zb)) @ (transi100378922on_val @ R3)) => ((~ (((produc1069526295on_val @ Xa @ Xb) = (produc1069526295on_val @ Za @ Zb)))) => (~ ((![A3 : produc1097884484on_val, B3 : produc1097884484on_val]: ((member208988944on_val @ (produc564964183on_val @ (produc1069526295on_val @ Xa @ Xb) @ (produc1069526295on_val @ A3 @ B3)) @ R3) => (~ ((member208988944on_val @ (produc564964183on_val @ (produc1069526295on_val @ A3 @ B3) @ (produc1069526295on_val @ Za @ Zb)) @ (transi100378922on_val @ R3))))))))))))). % converse_rtranclE2
thf(fact_153_converse__rtranclE2, axiom,
    ((![Xa : exp_list_char, Xb : produc515445032on_val, Za : exp_list_char, Zb : produc515445032on_val, R3 : set_Pr1189492743on_val]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ Xa @ Xb) @ (produc2023458740on_val @ Za @ Zb)) @ (transi111096263on_val @ R3)) => ((~ (((produc2023458740on_val @ Xa @ Xb) = (produc2023458740on_val @ Za @ Zb)))) => (~ ((![A3 : exp_list_char, B3 : produc515445032on_val]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ Xa @ Xb) @ (produc2023458740on_val @ A3 @ B3)) @ R3) => (~ ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ A3 @ B3) @ (produc2023458740on_val @ Za @ Zb)) @ (transi111096263on_val @ R3))))))))))))). % converse_rtranclE2
thf(fact_154_rtranclE, axiom,
    ((![A : produc1097884484on_val, B : produc1097884484on_val, R3 : set_Pr1189492743on_val]: ((member354538064on_val @ (produc1069526295on_val @ A @ B) @ (transi111096263on_val @ R3)) => ((~ ((A = B))) => (~ ((![Y4 : produc1097884484on_val]: ((member354538064on_val @ (produc1069526295on_val @ A @ Y4) @ (transi111096263on_val @ R3)) => (~ ((member354538064on_val @ (produc1069526295on_val @ Y4 @ B) @ R3)))))))))))). % rtranclE
thf(fact_155_rtrancl_Ocases, axiom,
    ((![A1 : produc1097884484on_val, A22 : produc1097884484on_val, R3 : set_Pr1189492743on_val]: ((member354538064on_val @ (produc1069526295on_val @ A1 @ A22) @ (transi111096263on_val @ R3)) => ((~ ((A22 = A1))) => (~ ((![B3 : produc1097884484on_val]: ((member354538064on_val @ (produc1069526295on_val @ A1 @ B3) @ (transi111096263on_val @ R3)) => (~ ((member354538064on_val @ (produc1069526295on_val @ B3 @ A22) @ R3)))))))))))). % rtrancl.cases
thf(fact_156_rtrancl_Osimps, axiom,
    ((![A1 : produc1097884484on_val, A22 : produc1097884484on_val, R3 : set_Pr1189492743on_val]: ((member354538064on_val @ (produc1069526295on_val @ A1 @ A22) @ (transi111096263on_val @ R3)) = (((?[A5 : produc1097884484on_val]: (((A1 = A5)) & ((A22 = A5))))) | ((?[A5 : produc1097884484on_val]: (?[B4 : produc1097884484on_val]: (?[C3 : produc1097884484on_val]: (((A1 = A5)) & ((((A22 = C3)) & ((((member354538064on_val @ (produc1069526295on_val @ A5 @ B4) @ (transi111096263on_val @ R3))) & ((member354538064on_val @ (produc1069526295on_val @ B4 @ C3) @ R3)))))))))))))))). % rtrancl.simps
thf(fact_157_rtrancl__trans, axiom,
    ((![X3 : produc1097884484on_val, Y3 : produc1097884484on_val, R3 : set_Pr1189492743on_val, Z : produc1097884484on_val]: ((member354538064on_val @ (produc1069526295on_val @ X3 @ Y3) @ (transi111096263on_val @ R3)) => ((member354538064on_val @ (produc1069526295on_val @ Y3 @ Z) @ (transi111096263on_val @ R3)) => (member354538064on_val @ (produc1069526295on_val @ X3 @ Z) @ (transi111096263on_val @ R3))))))). % rtrancl_trans
thf(fact_158_rtrancl__induct, axiom,
    ((![A : produc1097884484on_val, B : produc1097884484on_val, R3 : set_Pr1189492743on_val, P : produc1097884484on_val > $o]: ((member354538064on_val @ (produc1069526295on_val @ A @ B) @ (transi111096263on_val @ R3)) => ((P @ A) => ((![Y4 : produc1097884484on_val, Z2 : produc1097884484on_val]: ((member354538064on_val @ (produc1069526295on_val @ A @ Y4) @ (transi111096263on_val @ R3)) => ((member354538064on_val @ (produc1069526295on_val @ Y4 @ Z2) @ R3) => ((P @ Y4) => (P @ Z2))))) => (P @ B))))))). % rtrancl_induct
thf(fact_159_rtrancl_Oinducts, axiom,
    ((![X1 : produc1097884484on_val, X2 : produc1097884484on_val, R3 : set_Pr1189492743on_val, P : produc1097884484on_val > produc1097884484on_val > $o]: ((member354538064on_val @ (produc1069526295on_val @ X1 @ X2) @ (transi111096263on_val @ R3)) => ((![A3 : produc1097884484on_val]: (P @ A3 @ A3)) => ((![A3 : produc1097884484on_val, B3 : produc1097884484on_val, C : produc1097884484on_val]: ((member354538064on_val @ (produc1069526295on_val @ A3 @ B3) @ (transi111096263on_val @ R3)) => ((P @ A3 @ B3) => ((member354538064on_val @ (produc1069526295on_val @ B3 @ C) @ R3) => (P @ A3 @ C))))) => (P @ X1 @ X2))))))). % rtrancl.inducts
thf(fact_160_converse__rtranclE, axiom,
    ((![X3 : produc1097884484on_val, Z : produc1097884484on_val, R3 : set_Pr1189492743on_val]: ((member354538064on_val @ (produc1069526295on_val @ X3 @ Z) @ (transi111096263on_val @ R3)) => ((~ ((X3 = Z))) => (~ ((![Y4 : produc1097884484on_val]: ((member354538064on_val @ (produc1069526295on_val @ X3 @ Y4) @ R3) => (~ ((member354538064on_val @ (produc1069526295on_val @ Y4 @ Z) @ (transi111096263on_val @ R3))))))))))))). % converse_rtranclE
thf(fact_161_rtrancl_Ortrancl__refl, axiom,
    ((![A : produc1097884484on_val, R3 : set_Pr1189492743on_val]: (member354538064on_val @ (produc1069526295on_val @ A @ A) @ (transi111096263on_val @ R3))))). % rtrancl.rtrancl_refl
thf(fact_162_converse__rtrancl__induct, axiom,
    ((![A : produc1097884484on_val, B : produc1097884484on_val, R3 : set_Pr1189492743on_val, P : produc1097884484on_val > $o]: ((member354538064on_val @ (produc1069526295on_val @ A @ B) @ (transi111096263on_val @ R3)) => ((P @ B) => ((![Y4 : produc1097884484on_val, Z2 : produc1097884484on_val]: ((member354538064on_val @ (produc1069526295on_val @ Y4 @ Z2) @ R3) => ((member354538064on_val @ (produc1069526295on_val @ Z2 @ B) @ (transi111096263on_val @ R3)) => ((P @ Z2) => (P @ Y4))))) => (P @ A))))))). % converse_rtrancl_induct
thf(fact_163_rtrancl_Ortrancl__into__rtrancl, axiom,
    ((![A : produc1097884484on_val, B : produc1097884484on_val, R3 : set_Pr1189492743on_val, C2 : produc1097884484on_val]: ((member354538064on_val @ (produc1069526295on_val @ A @ B) @ (transi111096263on_val @ R3)) => ((member354538064on_val @ (produc1069526295on_val @ B @ C2) @ R3) => (member354538064on_val @ (produc1069526295on_val @ A @ C2) @ (transi111096263on_val @ R3))))))). % rtrancl.rtrancl_into_rtrancl
thf(fact_164_converse__rtrancl__into__rtrancl, axiom,
    ((![A : produc1097884484on_val, B : produc1097884484on_val, R3 : set_Pr1189492743on_val, C2 : produc1097884484on_val]: ((member354538064on_val @ (produc1069526295on_val @ A @ B) @ R3) => ((member354538064on_val @ (produc1069526295on_val @ B @ C2) @ (transi111096263on_val @ R3)) => (member354538064on_val @ (produc1069526295on_val @ A @ C2) @ (transi111096263on_val @ R3))))))). % converse_rtrancl_into_rtrancl
thf(fact_165_converse__rtrancl__induct2, axiom,
    ((![Ax : nat > option2118145160on_val, Ay : list_char > option_val, Bx : nat > option2118145160on_val, By : list_char > option_val, R3 : 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 @ R3)) => ((P @ Bx @ By) => ((![A3 : nat > option2118145160on_val, B3 : list_char > option_val, Aa : nat > option2118145160on_val, Ba : list_char > option_val]: ((member2027247312on_val @ (produc2106877847on_val @ (produc52622304on_val @ A3 @ B3) @ (produc52622304on_val @ Aa @ Ba)) @ R3) => ((member2027247312on_val @ (produc2106877847on_val @ (produc52622304on_val @ Aa @ Ba) @ (produc52622304on_val @ Bx @ By)) @ (transi432893227on_val @ R3)) => ((P @ Aa @ Ba) => (P @ A3 @ B3))))) => (P @ Ax @ Ay))))))). % converse_rtrancl_induct2
thf(fact_166_converse__rtrancl__induct2, axiom,
    ((![Ax : produc1097884484on_val, Ay : produc1097884484on_val, Bx : produc1097884484on_val, By : produc1097884484on_val, R3 : set_Pr1368603847on_val, P : produc1097884484on_val > produc1097884484on_val > $o]: ((member208988944on_val @ (produc564964183on_val @ (produc1069526295on_val @ Ax @ Ay) @ (produc1069526295on_val @ Bx @ By)) @ (transi100378922on_val @ R3)) => ((P @ Bx @ By) => ((![A3 : produc1097884484on_val, B3 : produc1097884484on_val, Aa : produc1097884484on_val, Ba : produc1097884484on_val]: ((member208988944on_val @ (produc564964183on_val @ (produc1069526295on_val @ A3 @ B3) @ (produc1069526295on_val @ Aa @ Ba)) @ R3) => ((member208988944on_val @ (produc564964183on_val @ (produc1069526295on_val @ Aa @ Ba) @ (produc1069526295on_val @ Bx @ By)) @ (transi100378922on_val @ R3)) => ((P @ Aa @ Ba) => (P @ A3 @ B3))))) => (P @ Ax @ Ay))))))). % converse_rtrancl_induct2
thf(fact_167_converse__rtrancl__induct2, axiom,
    ((![Ax : exp_list_char, Ay : produc515445032on_val, Bx : exp_list_char, By : produc515445032on_val, R3 : set_Pr1189492743on_val, P : exp_list_char > produc515445032on_val > $o]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ Ax @ Ay) @ (produc2023458740on_val @ Bx @ By)) @ (transi111096263on_val @ R3)) => ((P @ Bx @ By) => ((![A3 : exp_list_char, B3 : produc515445032on_val, Aa : exp_list_char, Ba : produc515445032on_val]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ A3 @ B3) @ (produc2023458740on_val @ Aa @ Ba)) @ R3) => ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ Aa @ Ba) @ (produc2023458740on_val @ Bx @ By)) @ (transi111096263on_val @ R3)) => ((P @ Aa @ Ba) => (P @ A3 @ B3))))) => (P @ Ax @ Ay))))))). % converse_rtrancl_induct2
thf(fact_168_WhileTRedsThrow, axiom,
    ((![B : exp_list_char, S_0 : produc515445032on_val, S_1 : produc515445032on_val, P : list_P1234162913t_char, C2 : exp_list_char, E2 : exp_list_char, S_2 : produc515445032on_val]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ B @ S_0) @ (produc2023458740on_val @ (val_list_char @ (bool @ $true)) @ S_1)) @ (transi111096263on_val @ (red @ P))) => ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ C2 @ S_1) @ (produc2023458740on_val @ (throw_list_char @ E2) @ S_2)) @ (transi111096263on_val @ (red @ P))) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (while_list_char @ B @ C2) @ S_0) @ (produc2023458740on_val @ (throw_list_char @ E2) @ S_2)) @ (transi111096263on_val @ (red @ P)))))))). % WhileTRedsThrow
thf(fact_169_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_170_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_171_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_172_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)

% Conjectures (1)
thf(conj_0, conjecture,
    ((wTrt @ p @ h_a @ e @ (binOp_list_char @ e_1 @ bop2 @ e_2) @ t))).
