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% This file was generated by Isabelle (most likely Sledgehammer)
% 2020-12-16 14:21:21.933

% Could-be-implicit typings (21)
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% Explicit typings (55)
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thf(sy_c_Expr_Oexp_OFAcc_001t__List__Olist_It__String__Ochar_J, type,
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thf(sy_c_Expr_Oexp_OVal_001t__List__Olist_It__String__Ochar_J, type,
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thf(sy_c_Expr_Oexp_OWhile_001t__List__Olist_It__String__Ochar_J, type,
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thf(sy_c_Expr_Oexp_Othrow_001t__List__Olist_It__String__Ochar_J, type,
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thf(sy_c_JWellForm_Owf__J__mdecl, type,
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thf(sy_c_Map_Omap__add_001t__List__Olist_It__String__Ochar_J_001t__Value__Oval, type,
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    wTrt : list_P1234162913t_char > (nat > option2118145160on_val) > (list_char > option_ty) > exp_list_char > ty > $o).
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    collec2055896722on_val : (produc1172664615on_val > $o) > set_Pr1189492743on_val).
thf(sy_c_SmallStep_Ored, type,
    red : list_P1234162913t_char > set_Pr1189492743on_val).
thf(sy_c_State_Ohp, type,
    hp : produc515445032on_val > nat > option2118145160on_val).
thf(sy_c_Transitive__Closure_Ortrancl_001t__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_M_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_J, type,
    transi432893227on_val : set_Pr148564103on_val > set_Pr148564103on_val).
thf(sy_c_Transitive__Closure_Ortrancl_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,
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    transi100378922on_val : set_Pr1368603847on_val > set_Pr1368603847on_val).
thf(sy_c_TypeRel_Ohas__field_001t__Product____Type__Oprod_It__List__Olist_It__List__Olist_It__String__Ochar_J_J_Mt__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_J, type,
    has_fi599584195t_char : list_P1234162913t_char > list_char > list_char > ty > list_char > $o).
thf(sy_c_TypeRel_Owiden_001t__Product____Type__Oprod_It__List__Olist_It__List__Olist_It__String__Ochar_J_J_Mt__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_J, type,
    widen_917054840t_char : list_P1234162913t_char > ty > ty > $o).
thf(sy_c_TypeSafe__Mirabelle__osrwgqrerx_Osconf, type,
    typeSa1777264139_sconf : list_P1234162913t_char > (list_char > option_ty) > produc515445032on_val > $o).
thf(sy_c_Type_Ois__refT, type,
    is_refT : ty > $o).
thf(sy_c_Type_Oty_OClass, type,
    class : list_char > ty).
thf(sy_c_Type_Oty_ONT, type,
    nt : ty).
thf(sy_c_Type_Oty_OVoid, type,
    void : ty).
thf(sy_c_Value_Oval_OBool, type,
    bool : $o > val).
thf(sy_c_WellForm_Owf__prog_001t__Product____Type__Oprod_It__List__Olist_It__List__Olist_It__String__Ochar_J_J_Mt__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_J, type,
    wf_pro1229751607t_char : (list_P1234162913t_char > list_char > produc1259892823t_char > $o) > list_P1234162913t_char > $o).
thf(sy_c_WellTypeRT_OWTrt, type,
    wTrt2 : list_P1234162913t_char > (nat > option2118145160on_val) > (list_char > option_ty) > exp_list_char > ty > $o).
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    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,
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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_C____, type,
    c : list_char).
thf(sy_v_D____, type,
    d : list_char).
thf(sy_v_E____, type,
    e : list_char > option_ty).
thf(sy_v_F____, type,
    f : list_char).
thf(sy_v_P, type,
    p : list_P1234162913t_char).
thf(sy_v_TF____, type,
    tf : ty).
thf(sy_v_T_092_060_094sub_0622_H____, type,
    t_2 : ty).
thf(sy_v_T_092_060_094sub_0622____, type,
    t_22 : ty).
thf(sy_v_T____, type,
    t : ty).
thf(sy_v_e_092_060_094sub_0622_H____, type,
    e_2 : exp_list_char).
thf(sy_v_e_092_060_094sub_0622____, type,
    e_22 : 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).
thf(sy_v_v____, type,
    v : val).

% Relevant facts (165)
thf(fact_0_wt_092_060_094sub_0622_H, axiom,
    ((wTrt2 @ p @ h_a @ e @ e_2 @ t_2))). % wt\<^sub>2'
thf(fact_1_has, axiom,
    ((has_fi599584195t_char @ p @ c @ f @ tf @ d))). % has
thf(fact_2_wt_092_060_094sub_0621_H, axiom,
    ((wTrt2 @ p @ h_a @ e @ (val_list_char @ v) @ (class @ c)))). % wt\<^sub>1'
thf(fact_3_wt, axiom,
    ((wTrt2 @ p @ ha @ e @ (fAss_list_char @ (val_list_char @ v) @ f @ d @ e_22) @ t))). % wt
thf(fact_4__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062T_092_060_094sub_0622_H_O_A_092_060lbrakk_062P_ME_Mh_H_A_092_060turnstile_062_Ae_092_060_094sub_0622_H_A_058_AT_092_060_094sub_0622_H_059_AP_A_092_060turnstile_062_AT_092_060_094sub_0622_H_A_092_060le_062_AT_092_060_094sub_0622_092_060rbrakk_062_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062, axiom,
    ((~ ((![T_2 : ty]: ((wTrt2 @ p @ h_a @ e @ e_2 @ T_2) => (~ ((widen_917054840t_char @ p @ T_2 @ t_22))))))))). % \<open>\<And>thesis. (\<And>T\<^sub>2'. \<lbrakk>P,E,h' \<turnstile> e\<^sub>2' : T\<^sub>2'; P \<turnstile> T\<^sub>2' \<le> T\<^sub>2\<rbrakk> \<Longrightarrow> thesis) \<Longrightarrow> thesis\<close>
thf(fact_5_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_6_exp_Oinject_I3_J, axiom,
    ((![X3 : val, Y3 : val]: (((val_list_char @ X3) = (val_list_char @ Y3)) = (X3 = Y3))))). % exp.inject(3)
thf(fact_7_exp_Odistinct_I63_J, axiom,
    ((![X3 : val, X81 : exp_list_char, X82 : list_char, X83 : list_char, X84 : exp_list_char]: (~ (((val_list_char @ X3) = (fAss_list_char @ X81 @ X82 @ X83 @ X84))))))). % exp.distinct(63)
thf(fact_8_wt_092_060_094sub_0621, axiom,
    ((wTrt2 @ p @ ha @ e @ (val_list_char @ v) @ (class @ c)))). % wt\<^sub>1
thf(fact_9_local_Owf, axiom,
    ((wf_pro1229751607t_char @ wf_J_mdecl @ p))). % local.wf
thf(fact_10_wt_092_060_094sub_0622, axiom,
    ((wTrt2 @ p @ ha @ e @ e_22 @ t_22))). % wt\<^sub>2
thf(fact_11_FAssRed2_Oprems_I2_J, axiom,
    ((wTrt2 @ p @ ha @ e @ (fAss_list_char @ (val_list_char @ v) @ f @ d @ e_22) @ t))). % FAssRed2.prems(2)
thf(fact_12__092_060open_062T_A_061_AVoid_092_060close_062, axiom,
    ((t = void))). % \<open>T = Void\<close>
thf(fact_13_TsubTF, axiom,
    ((widen_917054840t_char @ p @ t_22 @ tf))). % TsubTF
thf(fact_14_T_HsubT, axiom,
    ((widen_917054840t_char @ p @ t_2 @ t_22))). % T'subT
thf(fact_15_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, T : ty, D : list_char, E_2 : exp_list_char, T_22 : ty]: ((wTrt2 @ P @ H @ E @ E_1 @ (class @ C)) => ((has_fi599584195t_char @ P @ C @ F @ T @ D) => ((wTrt2 @ P @ H @ E @ E_2 @ T_22) => ((widen_917054840t_char @ P @ T_22 @ T) => (wTrt2 @ P @ H @ E @ (fAss_list_char @ E_1 @ F @ D @ E_2) @ void)))))))). % WTrtFAss
thf(fact_16_ty_Oinject, axiom,
    ((![X5 : list_char, Y5 : list_char]: (((class @ X5) = (class @ Y5)) = (X5 = Y5))))). % ty.inject
thf(fact_17_FAssRed2_Ohyps_I2_J, axiom,
    ((![E : list_char > option_ty, T : ty]: ((typeSa1777264139_sconf @ p @ E @ (produc52622304on_val @ ha @ la)) => ((wTrt2 @ p @ ha @ E @ e_22 @ T) => (?[T2 : ty]: ((wTrt2 @ p @ h_a @ E @ e_2 @ T2) & (widen_917054840t_char @ p @ T2 @ T)))))))). % FAssRed2.hyps(2)
thf(fact_18_ty_Odistinct_I7_J, axiom,
    ((![X5 : list_char]: (~ ((void = (class @ X5))))))). % ty.distinct(7)
thf(fact_19_IH, axiom,
    ((![E : list_char > option_ty, T : ty]: ((typeSa1777264139_sconf @ p @ E @ (produc52622304on_val @ ha @ la)) => ((wTrt2 @ p @ ha @ E @ e_22 @ T) => (?[U : ty]: ((wTrt2 @ p @ h_a @ E @ e_2 @ U) & (widen_917054840t_char @ p @ U @ T)))))))). % IH
thf(fact_20_Class__widen, axiom,
    ((![P : list_P1234162913t_char, C : list_char, T : ty]: ((widen_917054840t_char @ P @ (class @ C) @ T) => (?[D2 : list_char]: (T = (class @ D2))))))). % Class_widen
thf(fact_21_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, T : ty]: ((wTrt2 @ P @ H @ E @ (fAss_list_char @ E2 @ F @ D @ V) @ T) => (((T = void) => (![C2 : list_char]: ((wTrt2 @ P @ H @ E @ E2 @ (class @ C2)) => (![T3 : ty]: ((has_fi599584195t_char @ P @ C2 @ F @ T3 @ D) => (![T_23 : ty]: ((wTrt2 @ P @ H @ E @ V @ T_23) => (~ ((widen_917054840t_char @ P @ T_23 @ T3)))))))))) => (~ (((T = void) => ((wTrt2 @ P @ H @ E @ E2 @ nt) => (![T_23 : ty]: (~ ((wTrt2 @ P @ H @ E @ V @ T_23))))))))))))). % WTrt_elim_cases(8)
thf(fact_22_FAssRed2_Oprems_I1_J, axiom,
    ((typeSa1777264139_sconf @ p @ e @ (produc52622304on_val @ ha @ la)))). % FAssRed2.prems(1)
thf(fact_23_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, T : ty, D : list_char, E_2 : exp_list_char, T_22 : ty]: ((wTrt @ P @ H @ E @ E_1 @ (class @ C)) => ((has_fi599584195t_char @ P @ C @ F @ T @ D) => ((wTrt @ P @ H @ E @ E_2 @ T_22) => ((widen_917054840t_char @ P @ T_22 @ T) => (wTrt @ P @ H @ E @ (fAss_list_char @ E_1 @ F @ D @ E_2) @ void)))))))). % WTrt'_WTrts'.intros(10)
thf(fact_24_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_25_conf, axiom,
    ((typeSa1777264139_sconf @ p @ e @ (produc52622304on_val @ ha @ la)))). % conf
thf(fact_26_wt_H__wt, axiom,
    ((![P : list_P1234162913t_char, H : nat > option2118145160on_val, E : list_char > option_ty, E2 : exp_list_char, T : ty]: ((wTrt @ P @ H @ E @ E2 @ T) => (wTrt2 @ P @ H @ E @ E2 @ T))))). % wt'_wt
thf(fact_27_wt__wt_H, axiom,
    ((![P : list_P1234162913t_char, H : nat > option2118145160on_val, E : list_char > option_ty, E2 : exp_list_char, T : ty]: ((wTrt2 @ P @ H @ E @ E2 @ T) => (wTrt @ P @ H @ E @ E2 @ T))))). % wt_wt'
thf(fact_28_wt_H__iff__wt, axiom,
    ((wTrt = wTrt2))). % wt'_iff_wt
thf(fact_29_ty_Odistinct_I19_J, axiom,
    ((![X5 : list_char]: (~ ((nt = (class @ X5))))))). % ty.distinct(19)
thf(fact_30_ty_Odistinct_I5_J, axiom,
    ((~ ((void = nt))))). % ty.distinct(5)
thf(fact_31_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_22 : ty, F : list_char, D : list_char]: ((wTrt @ P @ H @ E @ E_1 @ nt) => ((wTrt @ P @ H @ E @ E_2 @ T_22) => (wTrt @ P @ H @ E @ (fAss_list_char @ E_1 @ F @ D @ E_2) @ void)))))). % WTrt'_WTrts'.intros(11)
thf(fact_32_widen__null, axiom,
    ((![P : list_P1234162913t_char, C : list_char]: (widen_917054840t_char @ P @ nt @ (class @ C))))). % widen_null
thf(fact_33_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_22 : ty, F : list_char, D : list_char]: ((wTrt2 @ P @ H @ E @ E_1 @ nt) => ((wTrt2 @ P @ H @ E @ E_2 @ T_22) => (wTrt2 @ P @ H @ E @ (fAss_list_char @ E_1 @ F @ D @ E_2) @ void)))))). % WTrtFAssNT
thf(fact_34_widen__refl, axiom,
    ((![P : list_P1234162913t_char, T : ty]: (widen_917054840t_char @ P @ T @ T)))). % widen_refl
thf(fact_35_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_36_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_37_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_38_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_39_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_40_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_41_red, axiom,
    ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ e_22 @ (produc52622304on_val @ ha @ la)) @ (produc2023458740on_val @ e_2 @ (produc52622304on_val @ h_a @ l_a))) @ (red @ p)))). % red
thf(fact_42_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, T : ty]: ((wTrt2 @ P @ H @ E @ (fAcc_list_char @ E2 @ F @ D) @ T) => ((![C2 : list_char]: ((wTrt2 @ P @ H @ E @ E2 @ (class @ C2)) => (~ ((has_fi599584195t_char @ P @ C2 @ F @ T @ D))))) => (wTrt2 @ P @ H @ E @ E2 @ nt)))))). % WTrt_elim_cases(7)
thf(fact_43_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_44_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_45_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_46_refTE, axiom,
    ((![T : ty]: ((is_refT @ T) => ((~ ((T = nt))) => (~ ((![C2 : list_char]: (~ ((T = (class @ C2)))))))))))). % refTE
thf(fact_47_is__refT__def, axiom,
    ((is_refT = (^[T4 : ty]: (((T4 = nt)) | ((?[C3 : list_char]: (T4 = (class @ C3))))))))). % is_refT_def
thf(fact_48_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, T : ty, D : list_char]: ((wTrt @ P @ H @ E @ E2 @ (class @ C)) => ((has_fi599584195t_char @ P @ C @ F @ T @ D) => (wTrt @ P @ H @ E @ (fAcc_list_char @ E2 @ F @ D) @ T)))))). % WTrt'_WTrts'.intros(8)
thf(fact_49_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_50_exp_Odistinct_I61_J, axiom,
    ((![X3 : val, X71 : exp_list_char, X72 : list_char, X73 : list_char]: (~ (((val_list_char @ X3) = (fAcc_list_char @ X71 @ X72 @ X73))))))). % exp.distinct(61)
thf(fact_51_mem__Collect__eq, axiom,
    ((![A : produc1172664615on_val, P : produc1172664615on_val > $o]: ((member354538064on_val @ A @ (collec2055896722on_val @ P)) = (P @ A))))). % mem_Collect_eq
thf(fact_52_Collect__mem__eq, axiom,
    ((![A3 : set_Pr1189492743on_val]: ((collec2055896722on_val @ (^[X : produc1172664615on_val]: (member354538064on_val @ X @ A3))) = A3)))). % Collect_mem_eq
thf(fact_53_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_54_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, T : ty]: ((wTrt2 @ P @ H @ E @ E2 @ nt) => (wTrt2 @ P @ H @ E @ (fAcc_list_char @ E2 @ F @ D) @ T))))). % WTrtFAccNT
thf(fact_55_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, T : ty]: ((wTrt @ P @ H @ E @ E2 @ nt) => (wTrt @ P @ H @ E @ (fAcc_list_char @ E2 @ F @ D) @ T))))). % WTrt'_WTrts'.intros(9)
thf(fact_56_surj__pair, axiom,
    ((![P2 : produc515445032on_val]: (?[X4 : nat > option2118145160on_val, Y4 : list_char > option_val]: (P2 = (produc52622304on_val @ X4 @ Y4)))))). % surj_pair
thf(fact_57_surj__pair, axiom,
    ((![P2 : produc1172664615on_val]: (?[X4 : produc1097884484on_val, Y4 : produc1097884484on_val]: (P2 = (produc1069526295on_val @ X4 @ Y4)))))). % surj_pair
thf(fact_58_surj__pair, axiom,
    ((![P2 : produc1097884484on_val]: (?[X4 : exp_list_char, Y4 : produc515445032on_val]: (P2 = (produc2023458740on_val @ X4 @ Y4)))))). % surj_pair
thf(fact_59_prod__cases, axiom,
    ((![P : produc515445032on_val > $o, P2 : produc515445032on_val]: ((![A4 : nat > option2118145160on_val, B3 : list_char > option_val]: (P @ (produc52622304on_val @ A4 @ B3))) => (P @ P2))))). % prod_cases
thf(fact_60_prod__cases, axiom,
    ((![P : produc1172664615on_val > $o, P2 : produc1172664615on_val]: ((![A4 : produc1097884484on_val, B3 : produc1097884484on_val]: (P @ (produc1069526295on_val @ A4 @ B3))) => (P @ P2))))). % prod_cases
thf(fact_61_prod__cases, axiom,
    ((![P : produc1097884484on_val > $o, P2 : produc1097884484on_val]: ((![A4 : exp_list_char, B3 : produc515445032on_val]: (P @ (produc2023458740on_val @ A4 @ B3))) => (P @ P2))))). % prod_cases
thf(fact_62_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_63_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_64_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_65_prod__cases3, axiom,
    ((![Y6 : produc1172664615on_val]: (~ ((![A4 : produc1097884484on_val, B3 : exp_list_char, C4 : produc515445032on_val]: (~ ((Y6 = (produc1069526295on_val @ A4 @ (produc2023458740on_val @ B3 @ C4))))))))))). % prod_cases3
thf(fact_66_prod__cases3, axiom,
    ((![Y6 : produc1097884484on_val]: (~ ((![A4 : exp_list_char, B3 : nat > option2118145160on_val, C4 : list_char > option_val]: (~ ((Y6 = (produc2023458740on_val @ A4 @ (produc52622304on_val @ B3 @ C4))))))))))). % prod_cases3
thf(fact_67_prod__cases4, axiom,
    ((![Y6 : produc1172664615on_val]: (~ ((![A4 : produc1097884484on_val, B3 : exp_list_char, C4 : nat > option2118145160on_val, D3 : list_char > option_val]: (~ ((Y6 = (produc1069526295on_val @ A4 @ (produc2023458740on_val @ B3 @ (produc52622304on_val @ C4 @ D3)))))))))))). % prod_cases4
thf(fact_68_prod__induct3, axiom,
    ((![P : produc1172664615on_val > $o, X6 : produc1172664615on_val]: ((![A4 : produc1097884484on_val, B3 : exp_list_char, C4 : produc515445032on_val]: (P @ (produc1069526295on_val @ A4 @ (produc2023458740on_val @ B3 @ C4)))) => (P @ X6))))). % prod_induct3
thf(fact_69_prod__induct3, axiom,
    ((![P : produc1097884484on_val > $o, X6 : produc1097884484on_val]: ((![A4 : exp_list_char, B3 : nat > option2118145160on_val, C4 : list_char > option_val]: (P @ (produc2023458740on_val @ A4 @ (produc52622304on_val @ B3 @ C4)))) => (P @ X6))))). % prod_induct3
thf(fact_70_prod__induct4, axiom,
    ((![P : produc1172664615on_val > $o, X6 : produc1172664615on_val]: ((![A4 : produc1097884484on_val, B3 : exp_list_char, C4 : nat > option2118145160on_val, D3 : list_char > option_val]: (P @ (produc1069526295on_val @ A4 @ (produc2023458740on_val @ B3 @ (produc52622304on_val @ C4 @ D3))))) => (P @ X6))))). % prod_induct4
thf(fact_71_old_Oprod_Oexhaust, axiom,
    ((![Y6 : produc515445032on_val]: (~ ((![A4 : nat > option2118145160on_val, B3 : list_char > option_val]: (~ ((Y6 = (produc52622304on_val @ A4 @ B3)))))))))). % old.prod.exhaust
thf(fact_72_old_Oprod_Oexhaust, axiom,
    ((![Y6 : produc1172664615on_val]: (~ ((![A4 : produc1097884484on_val, B3 : produc1097884484on_val]: (~ ((Y6 = (produc1069526295on_val @ A4 @ B3)))))))))). % old.prod.exhaust
thf(fact_73_old_Oprod_Oexhaust, axiom,
    ((![Y6 : produc1097884484on_val]: (~ ((![A4 : exp_list_char, B3 : produc515445032on_val]: (~ ((Y6 = (produc2023458740on_val @ A4 @ B3)))))))))). % old.prod.exhaust
thf(fact_74_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_75_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_76_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_77_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, T : ty, D : list_char]: ((wTrt2 @ P @ H @ E @ E2 @ (class @ C)) => ((has_fi599584195t_char @ P @ C @ F @ T @ D) => (wTrt2 @ P @ H @ E @ (fAcc_list_char @ E2 @ F @ D) @ T)))))). % WTrtFAcc
thf(fact_78_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_79_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_80_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_81_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)) => ((wTrt2 @ P @ H @ E @ E2 @ T) => ((hconf_1244167010t_char @ P @ H) => (hconf_1244167010t_char @ P @ H2))))))). % red_preserves_hconf
thf(fact_82_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)) => ((wTrt2 @ P @ H @ E @ E2 @ T) => ((lconf_485928294t_char @ P @ H @ L @ E) => (lconf_485928294t_char @ P @ H2 @ L2 @ E))))))). % red_preserves_lconf
thf(fact_83_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)) => ((wTrt2 @ P @ (hp @ S2) @ E @ E2 @ T) => ((typeSa1777264139_sconf @ P @ E @ S2) => (typeSa1777264139_sconf @ P @ E @ S3))))))). % red_preserves_sconf
thf(fact_84_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_85_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_86_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_87_exp_Odistinct_I75_J, axiom,
    ((![X3 : val, X14 : exp_list_char]: (~ (((val_list_char @ X3) = (throw_list_char @ X14))))))). % exp.distinct(75)
thf(fact_88_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_89_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_90_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]: ((wTrt2 @ P @ H @ E @ E2 @ T) => ((hext @ H @ H2) => (wTrt2 @ P @ H2 @ E @ E2 @ T)))))). % WTrt_hext_mono
thf(fact_91_WTrt__elim__cases_I4_J, axiom,
    ((![P : list_P1234162913t_char, H : nat > option2118145160on_val, E : list_char > option_ty, E2 : exp_list_char, T : ty]: ((wTrt2 @ P @ H @ E @ (throw_list_char @ E2) @ T) => (~ ((![T_r : ty]: ((wTrt2 @ P @ H @ E @ E2 @ T_r) => (~ ((is_refT @ T_r))))))))))). % WTrt_elim_cases(4)
thf(fact_92_WTrtThrow, axiom,
    ((![P : list_P1234162913t_char, H : nat > option2118145160on_val, E : list_char > option_ty, E2 : exp_list_char, T_r2 : ty, T : ty]: ((wTrt2 @ P @ H @ E @ E2 @ T_r2) => ((is_refT @ T_r2) => (wTrt2 @ P @ H @ E @ (throw_list_char @ E2) @ T)))))). % WTrtThrow
thf(fact_93_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, T : ty]: ((wTrt @ P @ H @ E @ E2 @ T_r2) => ((is_refT @ T_r2) => (wTrt @ P @ H @ E @ (throw_list_char @ E2) @ T)))))). % WTrt'_WTrts'.intros(21)
thf(fact_94_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_95_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_96_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_97_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_98_hext__refl, axiom,
    ((![H : nat > option2118145160on_val]: (hext @ H @ H)))). % hext_refl
thf(fact_99_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_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_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_102_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_103_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_104_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_105_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_106_exp_Odistinct_I55_J, axiom,
    ((![X3 : val, X41 : exp_list_char, X42 : bop, X43 : exp_list_char]: (~ (((val_list_char @ X3) = (binOp_list_char @ X41 @ X42 @ X43))))))). % exp.distinct(55)
thf(fact_107_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_108_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_109_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_110_hext__trans, axiom,
    ((![H : nat > option2118145160on_val, H2 : nat > option2118145160on_val, H3 : nat > option2118145160on_val]: ((hext @ H @ H2) => ((hext @ H2 @ H3) => (hext @ H @ H3)))))). % hext_trans
thf(fact_111_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_112_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_113_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_114_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_115_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_116_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_117_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_118_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_119_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_120_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_121_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_122_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_123_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_124_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, H4 : nat > option2118145160on_val, L3 : list_char > option_val]: (R @ E4 @ H4 @ L3 @ E4 @ H4 @ L3)) => ((![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, E5 : exp_list_char, H5 : nat > option2118145160on_val, L4 : 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 @ E5 @ H5 @ L4) => (R @ E_0 @ H_0 @ L_02 @ E5 @ H5 @ L4)))) => (R @ E2 @ H @ L @ E3 @ H2 @ L2))))))). % converse_rtrancl_induct_red
thf(fact_125_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_126_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_127_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_128_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_129_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_130_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_131_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_132_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_133_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_134_rtranclE, axiom,
    ((![A : produc1097884484on_val, B : produc1097884484on_val, R2 : set_Pr1189492743on_val]: ((member354538064on_val @ (produc1069526295on_val @ A @ B) @ (transi111096263on_val @ R2)) => ((~ ((A = B))) => (~ ((![Y4 : produc1097884484on_val]: ((member354538064on_val @ (produc1069526295on_val @ A @ Y4) @ (transi111096263on_val @ R2)) => (~ ((member354538064on_val @ (produc1069526295on_val @ Y4 @ B) @ R2)))))))))))). % rtranclE
thf(fact_135_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_136_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]: (?[C5 : produc1097884484on_val]: (((A1 = A5)) & ((((A22 = C5)) & ((((member354538064on_val @ (produc1069526295on_val @ A5 @ B4) @ (transi111096263on_val @ R2))) & ((member354538064on_val @ (produc1069526295on_val @ B4 @ C5) @ R2)))))))))))))))). % rtrancl.simps
thf(fact_137_rtrancl__trans, axiom,
    ((![X6 : produc1097884484on_val, Y6 : produc1097884484on_val, R2 : set_Pr1189492743on_val, Z : produc1097884484on_val]: ((member354538064on_val @ (produc1069526295on_val @ X6 @ Y6) @ (transi111096263on_val @ R2)) => ((member354538064on_val @ (produc1069526295on_val @ Y6 @ Z) @ (transi111096263on_val @ R2)) => (member354538064on_val @ (produc1069526295on_val @ X6 @ Z) @ (transi111096263on_val @ R2))))))). % rtrancl_trans
thf(fact_138_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) => ((![Y4 : produc1097884484on_val, Z2 : produc1097884484on_val]: ((member354538064on_val @ (produc1069526295on_val @ A @ Y4) @ (transi111096263on_val @ R2)) => ((member354538064on_val @ (produc1069526295on_val @ Y4 @ Z2) @ R2) => ((P @ Y4) => (P @ Z2))))) => (P @ B))))))). % rtrancl_induct
thf(fact_139_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, C4 : produc1097884484on_val]: ((member354538064on_val @ (produc1069526295on_val @ A4 @ B3) @ (transi111096263on_val @ R2)) => ((P @ A4 @ B3) => ((member354538064on_val @ (produc1069526295on_val @ B3 @ C4) @ R2) => (P @ A4 @ C4))))) => (P @ X1 @ X2))))))). % rtrancl.inducts
thf(fact_140_converse__rtranclE, axiom,
    ((![X6 : produc1097884484on_val, Z : produc1097884484on_val, R2 : set_Pr1189492743on_val]: ((member354538064on_val @ (produc1069526295on_val @ X6 @ Z) @ (transi111096263on_val @ R2)) => ((~ ((X6 = Z))) => (~ ((![Y4 : produc1097884484on_val]: ((member354538064on_val @ (produc1069526295on_val @ X6 @ Y4) @ R2) => (~ ((member354538064on_val @ (produc1069526295on_val @ Y4 @ Z) @ (transi111096263on_val @ R2))))))))))))). % converse_rtranclE
thf(fact_141_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_142_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) => ((![Y4 : produc1097884484on_val, Z2 : produc1097884484on_val]: ((member354538064on_val @ (produc1069526295on_val @ Y4 @ Z2) @ R2) => ((member354538064on_val @ (produc1069526295on_val @ Z2 @ B) @ (transi111096263on_val @ R2)) => ((P @ Z2) => (P @ Y4))))) => (P @ A))))))). % converse_rtrancl_induct
thf(fact_143_rtrancl_Ortrancl__into__rtrancl, axiom,
    ((![A : produc1097884484on_val, B : produc1097884484on_val, R2 : set_Pr1189492743on_val, C6 : produc1097884484on_val]: ((member354538064on_val @ (produc1069526295on_val @ A @ B) @ (transi111096263on_val @ R2)) => ((member354538064on_val @ (produc1069526295on_val @ B @ C6) @ R2) => (member354538064on_val @ (produc1069526295on_val @ A @ C6) @ (transi111096263on_val @ R2))))))). % rtrancl.rtrancl_into_rtrancl
thf(fact_144_converse__rtrancl__into__rtrancl, axiom,
    ((![A : produc1097884484on_val, B : produc1097884484on_val, R2 : set_Pr1189492743on_val, C6 : produc1097884484on_val]: ((member354538064on_val @ (produc1069526295on_val @ A @ B) @ R2) => ((member354538064on_val @ (produc1069526295on_val @ B @ C6) @ (transi111096263on_val @ R2)) => (member354538064on_val @ (produc1069526295on_val @ A @ C6) @ (transi111096263on_val @ R2))))))). % converse_rtrancl_into_rtrancl
thf(fact_145_WhileRedsThrow, axiom,
    ((![B : exp_list_char, S2 : produc515445032on_val, E2 : exp_list_char, S3 : produc515445032on_val, P : list_P1234162913t_char, C6 : 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 @ C6) @ S2) @ (produc2023458740on_val @ (throw_list_char @ E2) @ S3)) @ (transi111096263on_val @ (red @ P))))))). % WhileRedsThrow
thf(fact_146_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_147_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_148_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_149_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_150_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_151_exp_Odistinct_I77_J, axiom,
    ((![X3 : val, X151 : exp_list_char, X152 : list_char, X153 : list_char, X154 : exp_list_char]: (~ (((val_list_char @ X3) = (tryCatch_list_char @ X151 @ X152 @ X153 @ X154))))))). % exp.distinct(77)
thf(fact_152_exp_Odistinct_I73_J, axiom,
    ((![X3 : val, X131 : exp_list_char, X132 : exp_list_char]: (~ (((val_list_char @ X3) = (while_list_char @ X131 @ X132))))))). % exp.distinct(73)
thf(fact_153_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)
thf(fact_154_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_155_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_156_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_157_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_158_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_159_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_160_red__reds_OTryRed, axiom,
    ((![E2 : exp_list_char, S2 : produc515445032on_val, E3 : exp_list_char, S3 : produc515445032on_val, P : list_P1234162913t_char, C : list_char, V2 : list_char, E_2 : exp_list_char]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E2 @ S2) @ (produc2023458740on_val @ E3 @ S3)) @ (red @ P)) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (tryCatch_list_char @ E2 @ C @ V2 @ E_2) @ S2) @ (produc2023458740on_val @ (tryCatch_list_char @ E3 @ C @ V2 @ E_2) @ S3)) @ (red @ P)))))). % red_reds.TryRed
thf(fact_161_red__reds_ORedTry, axiom,
    ((![V : val, C : list_char, V2 : list_char, E_2 : exp_list_char, S2 : produc515445032on_val, P : list_P1234162913t_char]: (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (tryCatch_list_char @ (val_list_char @ V) @ C @ V2 @ E_2) @ S2) @ (produc2023458740on_val @ (val_list_char @ V) @ S2)) @ (red @ P))))). % red_reds.RedTry
thf(fact_162_TryReds, axiom,
    ((![E2 : exp_list_char, S2 : produc515445032on_val, E3 : exp_list_char, 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 @ E3 @ S3)) @ (transi111096263on_val @ (red @ P))) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (tryCatch_list_char @ E2 @ C @ V2 @ E_2) @ S2) @ (produc2023458740on_val @ (tryCatch_list_char @ E3 @ C @ V2 @ E_2) @ S3)) @ (transi111096263on_val @ (red @ P))))))). % TryReds
thf(fact_163_WhileTRedsThrow, axiom,
    ((![B : exp_list_char, S_0 : produc515445032on_val, S_1 : produc515445032on_val, P : list_P1234162913t_char, C6 : 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 @ C6 @ S_1) @ (produc2023458740on_val @ (throw_list_char @ E2) @ S_2)) @ (transi111096263on_val @ (red @ P))) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (while_list_char @ B @ C6) @ S_0) @ (produc2023458740on_val @ (throw_list_char @ E2) @ S_2)) @ (transi111096263on_val @ (red @ P)))))))). % WhileTRedsThrow
thf(fact_164_WhileTReds, axiom,
    ((![B : exp_list_char, S_0 : produc515445032on_val, S_1 : produc515445032on_val, P : list_P1234162913t_char, C6 : exp_list_char, V_1 : val, S_2 : produc515445032on_val, E2 : exp_list_char, S_3 : 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 @ C6 @ S_1) @ (produc2023458740on_val @ (val_list_char @ V_1) @ S_2)) @ (transi111096263on_val @ (red @ P))) => ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (while_list_char @ B @ C6) @ S_2) @ (produc2023458740on_val @ E2 @ S_3)) @ (transi111096263on_val @ (red @ P))) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (while_list_char @ B @ C6) @ S_0) @ (produc2023458740on_val @ E2 @ S_3)) @ (transi111096263on_val @ (red @ P))))))))). % WhileTReds

% Conjectures (1)
thf(conj_0, conjecture,
    ((wTrt2 @ p @ h_a @ e @ (fAss_list_char @ (val_list_char @ v) @ f @ d @ e_2) @ void))).
