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thf(ty_n_t__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J, type,
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thf(ty_n_t__List__Olist_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__Type__Oty_J_J, type,
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thf(ty_n_t__List__Olist_It__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_J, type,
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thf(ty_n_t__List__Olist_It__List__Olist_It__String__Ochar_J_J, type,
    list_list_char : $tType).
thf(ty_n_t__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J, type,
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thf(ty_n_t__Option__Ooption_It__Value__Oval_J, type,
    option_val : $tType).
thf(ty_n_t__Option__Ooption_It__Type__Oty_J, type,
    option_ty : $tType).
thf(ty_n_t__List__Olist_It__String__Ochar_J, type,
    list_char : $tType).
thf(ty_n_t__List__Olist_It__Type__Oty_J, type,
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thf(ty_n_t__Set__Oset_It__Type__Oty_J, type,
    set_ty : $tType).
thf(ty_n_t__Type__Oty, type,
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thf(ty_n_t__Nat__Onat, type,
    nat : $tType).

% Explicit typings (105)
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thf(sy_c_Decl_Ois__type_001t__Product____Type__Oprod_It__List__Olist_It__List__Olist_It__String__Ochar_J_J_Mt__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_J, type,
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thf(sy_c_Expr_Oexp_OCall_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_List_Olist_Olist__all2_001t__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_001t__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J, type,
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thf(sy_c_List_Olist_Olist__all2_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_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,
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thf(sy_c_List_Olist_Olist__all2_001t__Type__Oty_001t__Type__Oty, type,
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thf(sy_c_List_Olist_Oset_001t__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J, type,
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thf(sy_c_List_Olist_Oset_001t__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__Product____Type__Oprod_It__List__Olist_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__Type__Oty_J_J_Mt__List__Olist_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__Product____Type__Oprod_It__List__Olist_It__Type__Oty_J_Mt__Product____Type__Oprod_It__Type__Oty_Mt__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_J_J_J_J_J_J_J, type,
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thf(sy_c_List_Olist_Oset_001t__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__Product____Type__Oprod_It__List__Olist_It__Type__Oty_J_Mt__Product____Type__Oprod_It__Type__Oty_Mt__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_J_J_J, type,
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thf(sy_c_List_Olist_Oset_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,
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thf(sy_c_List_Olist_Oset_001t__Type__Oty, 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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thf(sy_c_Orderings_Obot__class_Obot_001_062_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_I_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_M_Eo_J_J, type,
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thf(sy_c_Orderings_Obot__class_Obot_001_062_It__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_M_062_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_M_Eo_J_J, type,
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thf(sy_c_Orderings_Obot__class_Obot_001_062_It__List__Olist_It__List__Olist_It__String__Ochar_J_J_M_062_It__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_M_Eo_J_J, type,
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thf(sy_c_Orderings_Obot__class_Obot_001_062_It__List__Olist_It__String__Ochar_J_M_062_It__List__Olist_It__String__Ochar_J_M_Eo_J_J, type,
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thf(sy_c_Orderings_Obot__class_Obot_001_062_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_M_062_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_M_Eo_J_J, type,
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thf(sy_c_Orderings_Obot__class_Obot_001_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_M_Eo_J, type,
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thf(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_It__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_J, type,
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thf(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_J, type,
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thf(sy_c_Product__Type_OPair_001_062_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_001_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J, type,
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    c : list_char).
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    c2 : list_char).
thf(sy_v_D_H____, type,
    d : list_char).
thf(sy_v_D____, type,
    d2 : list_char).
thf(sy_v_E____, type,
    e : list_char > option_ty).
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    m : list_char).
thf(sy_v_P, type,
    p : list_P1234162913t_char).
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    t : ty).
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    t2 : ty).
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    ts : list_ty).
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    ts2 : list_ty).
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    u : ty).
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    us : list_ty).
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    body : exp_list_char).
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    body2 : exp_list_char).
thf(sy_v_e_Ha____, type,
    e_a : exp_list_char).
thf(sy_v_ea____, type,
    ea : exp_list_char).
thf(sy_v_esa____, type,
    esa : list_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).
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    pns : list_list_char).
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    pns2 : list_list_char).

% Relevant facts (208)
thf(fact_0_UClass, axiom,
    ((u = (class @ c)))). % UClass
thf(fact_1_subs_H, axiom,
    ((list_all2_ty_ty @ (widen_917054840t_char @ p) @ ts2 @ ts))). % subs'
thf(fact_2_subs, axiom,
    ((list_all2_ty_ty @ (widen_917054840t_char @ p) @ us @ ts2))). % subs
thf(fact_3_sub_H, axiom,
    ((widen_917054840t_char @ p @ t @ t2))). % sub'
thf(fact_4__092_060open_062P_ME_Mh_H_A_092_060turnstile_062_Aes_A_091_058_093_AUs_092_060close_062, axiom,
    ((wTrts @ p @ h_a @ e @ esa @ us))). % \<open>P,E,h' \<turnstile> es [:] Us\<close>
thf(fact_5_method_H, axiom,
    ((method297381284t_char @ p @ c @ m @ ts @ t @ (produc713467969t_char @ pns @ body) @ d))). % method'
thf(fact_6__092_060open_062P_ME_Mh_H_A_092_060turnstile_062_Ae_H_A_058_AClass_AC_H_092_060close_062, axiom,
    ((wTrt @ p @ h_a @ e @ e_a @ (class @ c)))). % \<open>P,E,h' \<turnstile> e' : Class C'\<close>
thf(fact_7_wte_H, axiom,
    ((wTrt @ p @ h_a @ e @ e_a @ u))). % wte'
thf(fact_8_wtes, axiom,
    ((wTrts @ p @ ha @ e @ esa @ us))). % wtes
thf(fact_9__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062U_O_A_092_060lbrakk_062P_ME_Mh_H_A_092_060turnstile_062_Ae_H_A_058_AU_059_AP_A_092_060turnstile_062_AU_A_092_060le_062_AClass_AC_092_060rbrakk_062_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062, axiom,
    ((~ ((![U : ty]: ((wTrt @ p @ h_a @ e @ e_a @ U) => (~ ((widen_917054840t_char @ p @ U @ (class @ c2)))))))))). % \<open>\<And>thesis. (\<And>U. \<lbrakk>P,E,h' \<turnstile> e' : U; P \<turnstile> U \<le> Class C\<rbrakk> \<Longrightarrow> thesis) \<Longrightarrow> thesis\<close>
thf(fact_10_CallObj_Oprems_I2_J, axiom,
    ((wTrt @ p @ ha @ e @ (call_list_char @ ea @ m @ esa) @ t2))). % CallObj.prems(2)
thf(fact_11__092_060open_062U_A_061_ANT_A_092_060Longrightarrow_062_A_092_060exists_062T_H_O_AP_ME_Mh_H_A_092_060turnstile_062_Ae_H_092_060bullet_062M_Ies_J_A_058_AT_H_A_092_060and_062_AP_A_092_060turnstile_062_AT_H_A_092_060le_062_AT_092_060close_062, axiom,
    (((u = nt) => (?[T : ty]: ((wTrt @ p @ h_a @ e @ (call_list_char @ e_a @ m @ esa) @ T) & (widen_917054840t_char @ p @ T @ t2)))))). % \<open>U = NT \<Longrightarrow> \<exists>T'. P,E,h' \<turnstile> e'\<bullet>M(es) : T' \<and> P \<turnstile> T' \<le> T\<close>
thf(fact_12__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062Ts_H_AT_H_Apns_H_Abody_H_AD_H_O_A_092_060lbrakk_062P_A_092_060turnstile_062_AC_H_Asees_AM_058_ATs_H_092_060rightarrow_062T_H_A_061_A_Ipns_H_M_Abody_H_J_Ain_AD_H_059_AP_A_092_060turnstile_062_ATs_A_091_092_060le_062_093_ATs_H_059_AP_A_092_060turnstile_062_AT_H_A_092_060le_062_AT_092_060rbrakk_062_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062, axiom,
    ((~ ((![Ts : list_ty, T : ty]: ((?[Pns : list_list_char, Body : exp_list_char, X_1 : list_char]: (method297381284t_char @ p @ c @ m @ Ts @ T @ (produc713467969t_char @ Pns @ Body) @ X_1)) => ((list_all2_ty_ty @ (widen_917054840t_char @ p) @ ts2 @ Ts) => (~ ((widen_917054840t_char @ p @ T @ t2)))))))))). % \<open>\<And>thesis. (\<And>Ts' T' pns' body' D'. \<lbrakk>P \<turnstile> C' sees M: Ts'\<rightarrow>T' = (pns', body') in D'; P \<turnstile> Ts [\<le>] Ts'; P \<turnstile> T' \<le> T\<rbrakk> \<Longrightarrow> thesis) \<Longrightarrow> thesis\<close>
thf(fact_13_wt, axiom,
    ((wTrt @ p @ ha @ e @ (call_list_char @ ea @ m @ esa) @ t2))). % wt
thf(fact_14_UsubC, axiom,
    ((widen_917054840t_char @ p @ u @ (class @ c2)))). % UsubC
thf(fact_15_exp_Oinject_I9_J, axiom,
    ((![X91 : exp_list_char, X92 : list_char, X93 : list_exp_list_char, Y91 : exp_list_char, Y92 : list_char, Y93 : list_exp_list_char]: (((call_list_char @ X91 @ X92 @ X93) = (call_list_char @ Y91 @ Y92 @ Y93)) = (((X91 = Y91)) & ((((X92 = Y92)) & ((X93 = Y93))))))))). % exp.inject(9)
thf(fact_16__092_060open_062_092_060And_062Ts_O_A_092_060lbrakk_062P_ME_Mh_A_092_060turnstile_062_Ae_A_058_ANT_059_AP_ME_Mh_A_092_060turnstile_062_Aes_A_091_058_093_ATs_092_060rbrakk_062_A_092_060Longrightarrow_062_A_092_060exists_062T_H_O_AP_ME_Mh_H_A_092_060turnstile_062_Ae_H_092_060bullet_062M_Ies_J_A_058_AT_H_A_092_060and_062_AP_A_092_060turnstile_062_AT_H_A_092_060le_062_AT_092_060close_062, axiom,
    ((![Ts2 : list_ty]: ((wTrt @ p @ ha @ e @ ea @ nt) => ((wTrts @ p @ ha @ e @ esa @ Ts2) => (?[T : ty]: ((wTrt @ p @ h_a @ e @ (call_list_char @ e_a @ m @ esa) @ T) & (widen_917054840t_char @ p @ T @ t2)))))))). % \<open>\<And>Ts. \<lbrakk>P,E,h \<turnstile> e : NT; P,E,h \<turnstile> es [:] Ts\<rbrakk> \<Longrightarrow> \<exists>T'. P,E,h' \<turnstile> e'\<bullet>M(es) : T' \<and> P \<turnstile> T' \<le> T\<close>
thf(fact_17_method, axiom,
    ((method297381284t_char @ p @ c2 @ m @ ts2 @ t2 @ (produc713467969t_char @ pns2 @ body2) @ d2))). % method
thf(fact_18_local_Owf, axiom,
    ((wf_pro1229751607t_char @ wf_J_mdecl @ p))). % local.wf
thf(fact_19_widen__trans, axiom,
    ((![P : list_P1234162913t_char, S : ty, U2 : ty, T2 : ty]: ((widen_917054840t_char @ P @ S @ U2) => ((widen_917054840t_char @ P @ U2 @ T2) => (widen_917054840t_char @ P @ S @ T2)))))). % widen_trans
thf(fact_20_wte, axiom,
    ((wTrt @ p @ ha @ e @ ea @ (class @ c2)))). % wte
thf(fact_21_widens__refl, axiom,
    ((![P : list_P1234162913t_char, Xs : list_ty]: (list_all2_ty_ty @ (widen_917054840t_char @ P) @ Xs @ Xs)))). % widens_refl
thf(fact_22_sees__method__fun, axiom,
    ((![P : list_P1234162913t_char, C : list_char, M : list_char, TS : list_ty, T2 : ty, M2 : produc1294284815t_char, D : list_char, TS2 : list_ty, T3 : ty, M3 : produc1294284815t_char, D2 : list_char]: ((method297381284t_char @ P @ C @ M @ TS @ T2 @ M2 @ D) => ((method297381284t_char @ P @ C @ M @ TS2 @ T3 @ M3 @ D2) => ((TS2 = TS) & ((T3 = T2) & ((M3 = M2) & (D2 = D))))))))). % sees_method_fun
thf(fact_23_sees__method__idemp, axiom,
    ((![P : list_P1234162913t_char, C : list_char, M : list_char, Ts2 : list_ty, T2 : ty, M2 : produc1294284815t_char, D : list_char]: ((method297381284t_char @ P @ C @ M @ Ts2 @ T2 @ M2 @ D) => (method297381284t_char @ P @ D @ M @ Ts2 @ T2 @ M2 @ D))))). % sees_method_idemp
thf(fact_24_widen__null, axiom,
    ((![P : list_P1234162913t_char, C : list_char]: (widen_917054840t_char @ P @ nt @ (class @ C))))). % widen_null
thf(fact_25_widens__trans, axiom,
    ((![P : list_P1234162913t_char, Ss : list_ty, Ts2 : list_ty, Us : list_ty]: ((list_all2_ty_ty @ (widen_917054840t_char @ P) @ Ss @ Ts2) => ((list_all2_ty_ty @ (widen_917054840t_char @ P) @ Ts2 @ Us) => (list_all2_ty_ty @ (widen_917054840t_char @ P) @ Ss @ Us)))))). % widens_trans
thf(fact_26_Class__widen, axiom,
    ((![P : list_P1234162913t_char, C : list_char, T2 : ty]: ((widen_917054840t_char @ P @ (class @ C) @ T2) => (?[D3 : list_char]: (T2 = (class @ D3))))))). % Class_widen
thf(fact_27_widen__refl, axiom,
    ((![P : list_P1234162913t_char, T2 : ty]: (widen_917054840t_char @ P @ T2 @ T2)))). % widen_refl
thf(fact_28_WTrtCall, axiom,
    ((![P : list_P1234162913t_char, H : nat > option2118145160on_val, E : list_char > option_ty, E2 : exp_list_char, C : list_char, M : list_char, Ts2 : list_ty, T2 : ty, Pns2 : list_list_char, Body2 : exp_list_char, D : list_char, Es : list_exp_list_char, Ts3 : list_ty]: ((wTrt @ P @ H @ E @ E2 @ (class @ C)) => ((method297381284t_char @ P @ C @ M @ Ts2 @ T2 @ (produc713467969t_char @ Pns2 @ Body2) @ D) => ((wTrts @ P @ H @ E @ Es @ Ts3) => ((list_all2_ty_ty @ (widen_917054840t_char @ P) @ Ts3 @ Ts2) => (wTrt @ P @ H @ E @ (call_list_char @ E2 @ M @ Es) @ T2)))))))). % WTrtCall
thf(fact_29_WTrtCallNT, axiom,
    ((![P : list_P1234162913t_char, H : nat > option2118145160on_val, E : list_char > option_ty, E2 : exp_list_char, Es : list_exp_list_char, Ts2 : list_ty, M : list_char, T2 : ty]: ((wTrt @ P @ H @ E @ E2 @ nt) => ((wTrts @ P @ H @ E @ Es @ Ts2) => (wTrt @ P @ H @ E @ (call_list_char @ E2 @ M @ Es) @ T2)))))). % WTrtCallNT
thf(fact_30_ty_Oinject, axiom,
    ((![X5 : list_char, Y5 : list_char]: (((class @ X5) = (class @ Y5)) = (X5 = Y5))))). % ty.inject
thf(fact_31_has__method__def, axiom,
    ((has_me170134744t_char = (^[P2 : list_P1234162913t_char]: (^[C2 : list_char]: (^[M4 : list_char]: (?[Ts4 : list_ty]: (?[T4 : ty]: (?[M5 : produc1294284815t_char]: (?[X : list_char]: (method297381284t_char @ P2 @ C2 @ M4 @ Ts4 @ T4 @ M5 @ X))))))))))). % has_method_def
thf(fact_32_prod_Oinject, axiom,
    ((![X1 : list_list_char, X2 : exp_list_char, Y1 : list_list_char, Y2 : exp_list_char]: (((produc713467969t_char @ X1 @ X2) = (produc713467969t_char @ Y1 @ Y2)) = (((X1 = Y1)) & ((X2 = Y2))))))). % prod.inject
thf(fact_33_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_34_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_35_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_36_prod_Oinject, axiom,
    ((![X1 : list_char, X2 : list_char, Y1 : list_char, Y2 : list_char]: (((produc1304532571t_char @ X1 @ X2) = (produc1304532571t_char @ Y1 @ Y2)) = (((X1 = Y1)) & ((X2 = Y2))))))). % prod.inject
thf(fact_37_old_Oprod_Oinject, axiom,
    ((![A : list_list_char, B : exp_list_char, A2 : list_list_char, B2 : exp_list_char]: (((produc713467969t_char @ A @ B) = (produc713467969t_char @ A2 @ B2)) = (((A = A2)) & ((B = B2))))))). % old.prod.inject
thf(fact_38_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_39_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_40_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_41_old_Oprod_Oinject, axiom,
    ((![A : list_char, B : list_char, A2 : list_char, B2 : list_char]: (((produc1304532571t_char @ A @ B) = (produc1304532571t_char @ A2 @ B2)) = (((A = A2)) & ((B = B2))))))). % old.prod.inject
thf(fact_42_ty_Odistinct_I19_J, axiom,
    ((![X5 : list_char]: (~ ((nt = (class @ X5))))))). % ty.distinct(19)
thf(fact_43_CallObj_Ohyps_I2_J, axiom,
    ((![E : list_char > option_ty, T2 : ty]: ((typeSa1777264139_sconf @ p @ E @ (produc52622304on_val @ ha @ la)) => ((wTrt @ p @ ha @ E @ ea @ T2) => (?[T : ty]: ((wTrt @ p @ h_a @ E @ e_a @ T) & (widen_917054840t_char @ p @ T @ T2)))))))). % CallObj.hyps(2)
thf(fact_44_IH, axiom,
    ((![E : list_char > option_ty, T2 : ty]: ((typeSa1777264139_sconf @ p @ E @ (produc52622304on_val @ ha @ la)) => ((wTrt @ p @ ha @ E @ ea @ T2) => (?[U : ty]: ((wTrt @ p @ h_a @ E @ e_a @ U) & (widen_917054840t_char @ p @ U @ T2)))))))). % IH
thf(fact_45_CallObj_Oprems_I1_J, axiom,
    ((typeSa1777264139_sconf @ p @ e @ (produc52622304on_val @ ha @ la)))). % CallObj.prems(1)
thf(fact_46_conf, axiom,
    ((typeSa1777264139_sconf @ p @ e @ (produc52622304on_val @ ha @ la)))). % conf
thf(fact_47_old_Oprod_Oinducts, axiom,
    ((![P : produc1294284815t_char > $o, Prod : produc1294284815t_char]: ((![A3 : list_list_char, B3 : exp_list_char]: (P @ (produc713467969t_char @ A3 @ B3))) => (P @ Prod))))). % old.prod.inducts
thf(fact_48_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_49_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_50_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_51_old_Oprod_Oinducts, axiom,
    ((![P : produc1257910179t_char > $o, Prod : produc1257910179t_char]: ((![A3 : list_char, B3 : list_char]: (P @ (produc1304532571t_char @ A3 @ B3))) => (P @ Prod))))). % old.prod.inducts
thf(fact_52_old_Oprod_Oexhaust, axiom,
    ((![Y : produc1294284815t_char]: (~ ((![A3 : list_list_char, B3 : exp_list_char]: (~ ((Y = (produc713467969t_char @ A3 @ B3)))))))))). % old.prod.exhaust
thf(fact_53_old_Oprod_Oexhaust, axiom,
    ((![Y : produc515445032on_val]: (~ ((![A3 : nat > option2118145160on_val, B3 : list_char > option_val]: (~ ((Y = (produc52622304on_val @ A3 @ B3)))))))))). % old.prod.exhaust
thf(fact_54_old_Oprod_Oexhaust, axiom,
    ((![Y : produc1172664615on_val]: (~ ((![A3 : produc1097884484on_val, B3 : produc1097884484on_val]: (~ ((Y = (produc1069526295on_val @ A3 @ B3)))))))))). % old.prod.exhaust
thf(fact_55_old_Oprod_Oexhaust, axiom,
    ((![Y : produc1097884484on_val]: (~ ((![A3 : exp_list_char, B3 : produc515445032on_val]: (~ ((Y = (produc2023458740on_val @ A3 @ B3)))))))))). % old.prod.exhaust
thf(fact_56_old_Oprod_Oexhaust, axiom,
    ((![Y : produc1257910179t_char]: (~ ((![A3 : list_char, B3 : list_char]: (~ ((Y = (produc1304532571t_char @ A3 @ B3)))))))))). % old.prod.exhaust
thf(fact_57_prod__induct4, axiom,
    ((![P : produc1172664615on_val > $o, X3 : produc1172664615on_val]: ((![A3 : produc1097884484on_val, B3 : exp_list_char, C3 : nat > option2118145160on_val, D4 : list_char > option_val]: (P @ (produc1069526295on_val @ A3 @ (produc2023458740on_val @ B3 @ (produc52622304on_val @ C3 @ D4))))) => (P @ X3))))). % prod_induct4
thf(fact_58_mem__Collect__eq, axiom,
    ((![A : produc1172664615on_val, P : produc1172664615on_val > $o]: ((member354538064on_val @ A @ (collec2055896722on_val @ P)) = (P @ A))))). % mem_Collect_eq
thf(fact_59_mem__Collect__eq, axiom,
    ((![A : produc1257910179t_char, P : produc1257910179t_char > $o]: ((member89690956t_char @ A @ (collec768236686t_char @ P)) = (P @ A))))). % mem_Collect_eq
thf(fact_60_Collect__mem__eq, axiom,
    ((![A4 : set_Pr1189492743on_val]: ((collec2055896722on_val @ (^[X4 : produc1172664615on_val]: (member354538064on_val @ X4 @ A4))) = A4)))). % Collect_mem_eq
thf(fact_61_Collect__mem__eq, axiom,
    ((![A4 : set_Pr164112643t_char]: ((collec768236686t_char @ (^[X4 : produc1257910179t_char]: (member89690956t_char @ X4 @ A4))) = A4)))). % Collect_mem_eq
thf(fact_62_prod__induct3, axiom,
    ((![P : produc1172664615on_val > $o, X3 : produc1172664615on_val]: ((![A3 : produc1097884484on_val, B3 : exp_list_char, C3 : produc515445032on_val]: (P @ (produc1069526295on_val @ A3 @ (produc2023458740on_val @ B3 @ C3)))) => (P @ X3))))). % prod_induct3
thf(fact_63_prod__induct3, axiom,
    ((![P : produc1097884484on_val > $o, X3 : produc1097884484on_val]: ((![A3 : exp_list_char, B3 : nat > option2118145160on_val, C3 : list_char > option_val]: (P @ (produc2023458740on_val @ A3 @ (produc52622304on_val @ B3 @ C3)))) => (P @ X3))))). % prod_induct3
thf(fact_64_prod__cases4, axiom,
    ((![Y : produc1172664615on_val]: (~ ((![A3 : produc1097884484on_val, B3 : exp_list_char, C3 : nat > option2118145160on_val, D4 : list_char > option_val]: (~ ((Y = (produc1069526295on_val @ A3 @ (produc2023458740on_val @ B3 @ (produc52622304on_val @ C3 @ D4)))))))))))). % prod_cases4
thf(fact_65_prod__cases3, axiom,
    ((![Y : produc1172664615on_val]: (~ ((![A3 : produc1097884484on_val, B3 : exp_list_char, C3 : produc515445032on_val]: (~ ((Y = (produc1069526295on_val @ A3 @ (produc2023458740on_val @ B3 @ C3))))))))))). % prod_cases3
thf(fact_66_prod__cases3, axiom,
    ((![Y : produc1097884484on_val]: (~ ((![A3 : exp_list_char, B3 : nat > option2118145160on_val, C3 : list_char > option_val]: (~ ((Y = (produc2023458740on_val @ A3 @ (produc52622304on_val @ B3 @ C3))))))))))). % prod_cases3
thf(fact_67_Pair__inject, axiom,
    ((![A : list_list_char, B : exp_list_char, A2 : list_list_char, B2 : exp_list_char]: (((produc713467969t_char @ A @ B) = (produc713467969t_char @ A2 @ B2)) => (~ (((A = A2) => (~ ((B = B2)))))))))). % Pair_inject
thf(fact_68_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_69_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_70_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_71_Pair__inject, axiom,
    ((![A : list_char, B : list_char, A2 : list_char, B2 : list_char]: (((produc1304532571t_char @ A @ B) = (produc1304532571t_char @ A2 @ B2)) => (~ (((A = A2) => (~ ((B = B2)))))))))). % Pair_inject
thf(fact_72_prod__cases, axiom,
    ((![P : produc1294284815t_char > $o, P3 : produc1294284815t_char]: ((![A3 : list_list_char, B3 : exp_list_char]: (P @ (produc713467969t_char @ A3 @ B3))) => (P @ P3))))). % prod_cases
thf(fact_73_prod__cases, axiom,
    ((![P : produc515445032on_val > $o, P3 : produc515445032on_val]: ((![A3 : nat > option2118145160on_val, B3 : list_char > option_val]: (P @ (produc52622304on_val @ A3 @ B3))) => (P @ P3))))). % prod_cases
thf(fact_74_prod__cases, axiom,
    ((![P : produc1172664615on_val > $o, P3 : produc1172664615on_val]: ((![A3 : produc1097884484on_val, B3 : produc1097884484on_val]: (P @ (produc1069526295on_val @ A3 @ B3))) => (P @ P3))))). % prod_cases
thf(fact_75_prod__cases, axiom,
    ((![P : produc1097884484on_val > $o, P3 : produc1097884484on_val]: ((![A3 : exp_list_char, B3 : produc515445032on_val]: (P @ (produc2023458740on_val @ A3 @ B3))) => (P @ P3))))). % prod_cases
thf(fact_76_prod__cases, axiom,
    ((![P : produc1257910179t_char > $o, P3 : produc1257910179t_char]: ((![A3 : list_char, B3 : list_char]: (P @ (produc1304532571t_char @ A3 @ B3))) => (P @ P3))))). % prod_cases
thf(fact_77_surj__pair, axiom,
    ((![P3 : produc1294284815t_char]: (?[X6 : list_list_char, Y3 : exp_list_char]: (P3 = (produc713467969t_char @ X6 @ Y3)))))). % surj_pair
thf(fact_78_surj__pair, axiom,
    ((![P3 : produc515445032on_val]: (?[X6 : nat > option2118145160on_val, Y3 : list_char > option_val]: (P3 = (produc52622304on_val @ X6 @ Y3)))))). % surj_pair
thf(fact_79_surj__pair, axiom,
    ((![P3 : produc1172664615on_val]: (?[X6 : produc1097884484on_val, Y3 : produc1097884484on_val]: (P3 = (produc1069526295on_val @ X6 @ Y3)))))). % surj_pair
thf(fact_80_surj__pair, axiom,
    ((![P3 : produc1097884484on_val]: (?[X6 : exp_list_char, Y3 : produc515445032on_val]: (P3 = (produc2023458740on_val @ X6 @ Y3)))))). % surj_pair
thf(fact_81_surj__pair, axiom,
    ((![P3 : produc1257910179t_char]: (?[X6 : list_char, Y3 : list_char]: (P3 = (produc1304532571t_char @ X6 @ Y3)))))). % surj_pair
thf(fact_82_red, axiom,
    ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ ea @ (produc52622304on_val @ ha @ la)) @ (produc2023458740on_val @ e_a @ (produc52622304on_val @ h_a @ l_a))) @ (red @ p)))). % red
thf(fact_83_method__def2, axiom,
    ((![P : list_P1234162913t_char, C : list_char, M : list_char, Ts2 : list_ty, T2 : ty, M2 : produc1294284815t_char, D : list_char]: ((method297381284t_char @ P @ C @ M @ Ts2 @ T2 @ M2 @ D) => ((method667690372t_char @ P @ C @ M) = (produc1238538255t_char @ D @ (produc1730359111t_char @ Ts2 @ (produc248075743t_char @ T2 @ M2)))))))). % method_def2
thf(fact_84__Csubclass_C, axiom,
    ((member89690956t_char @ (produc1304532571t_char @ c @ c2) @ (transi1879726366t_char @ (subcls880436836t_char @ p))))). % "subclass"
thf(fact_85_pred__equals__eq2, axiom,
    ((![R : set_Pr2063914181t_char, S : set_Pr2063914181t_char]: (((^[X4 : list_list_char]: (^[Y4 : exp_list_char]: (member605104934t_char @ (produc713467969t_char @ X4 @ Y4) @ R))) = (^[X4 : list_list_char]: (^[Y4 : exp_list_char]: (member605104934t_char @ (produc713467969t_char @ X4 @ Y4) @ S)))) = (R = S))))). % pred_equals_eq2
thf(fact_86_pred__equals__eq2, axiom,
    ((![R : set_Pr723149704on_val, S : set_Pr723149704on_val]: (((^[X4 : nat > option2118145160on_val]: (^[Y4 : list_char > option_val]: (member652041809on_val @ (produc52622304on_val @ X4 @ Y4) @ R))) = (^[X4 : nat > option2118145160on_val]: (^[Y4 : list_char > option_val]: (member652041809on_val @ (produc52622304on_val @ X4 @ Y4) @ S)))) = (R = S))))). % pred_equals_eq2
thf(fact_87_pred__equals__eq2, axiom,
    ((![R : set_Pr1189492743on_val, S : set_Pr1189492743on_val]: (((^[X4 : produc1097884484on_val]: (^[Y4 : produc1097884484on_val]: (member354538064on_val @ (produc1069526295on_val @ X4 @ Y4) @ R))) = (^[X4 : produc1097884484on_val]: (^[Y4 : produc1097884484on_val]: (member354538064on_val @ (produc1069526295on_val @ X4 @ Y4) @ S)))) = (R = S))))). % pred_equals_eq2
thf(fact_88_pred__equals__eq2, axiom,
    ((![R : set_Pr556513572on_val, S : set_Pr556513572on_val]: (((^[X4 : exp_list_char]: (^[Y4 : produc515445032on_val]: (member1888679917on_val @ (produc2023458740on_val @ X4 @ Y4) @ R))) = (^[X4 : exp_list_char]: (^[Y4 : produc515445032on_val]: (member1888679917on_val @ (produc2023458740on_val @ X4 @ Y4) @ S)))) = (R = S))))). % pred_equals_eq2
thf(fact_89_pred__equals__eq2, axiom,
    ((![R : set_Pr164112643t_char, S : set_Pr164112643t_char]: (((^[X4 : list_char]: (^[Y4 : list_char]: (member89690956t_char @ (produc1304532571t_char @ X4 @ Y4) @ R))) = (^[X4 : list_char]: (^[Y4 : list_char]: (member89690956t_char @ (produc1304532571t_char @ X4 @ Y4) @ S)))) = (R = S))))). % pred_equals_eq2
thf(fact_90_Class__widen__Class, axiom,
    ((![P : list_P1234162913t_char, C : list_char, D : list_char]: ((widen_917054840t_char @ P @ (class @ C) @ (class @ D)) = (member89690956t_char @ (produc1304532571t_char @ C @ D) @ (transi1879726366t_char @ (subcls880436836t_char @ P))))))). % Class_widen_Class
thf(fact_91_sees__method__decl__mono, axiom,
    ((![C4 : list_char, C : list_char, P : list_P1234162913t_char, M : list_char, Ts2 : list_ty, T2 : ty, M2 : produc1294284815t_char, D : list_char, Ts3 : list_ty, T3 : ty, M3 : produc1294284815t_char, D2 : list_char]: ((member89690956t_char @ (produc1304532571t_char @ C4 @ C) @ (transi1879726366t_char @ (subcls880436836t_char @ P))) => ((method297381284t_char @ P @ C @ M @ Ts2 @ T2 @ M2 @ D) => ((method297381284t_char @ P @ C4 @ M @ Ts3 @ T3 @ M3 @ D2) => (member89690956t_char @ (produc1304532571t_char @ D2 @ D) @ (transi1879726366t_char @ (subcls880436836t_char @ P))))))))). % sees_method_decl_mono
thf(fact_92_sees__method__decl__above, axiom,
    ((![P : list_P1234162913t_char, C : list_char, M : list_char, Ts2 : list_ty, T2 : ty, M2 : produc1294284815t_char, D : list_char]: ((method297381284t_char @ P @ C @ M @ Ts2 @ T2 @ M2 @ D) => (member89690956t_char @ (produc1304532571t_char @ C @ D) @ (transi1879726366t_char @ (subcls880436836t_char @ P))))))). % sees_method_decl_above
thf(fact_93_widen__subcls, axiom,
    ((![C : list_char, D : list_char, P : list_P1234162913t_char]: ((member89690956t_char @ (produc1304532571t_char @ C @ D) @ (transi1879726366t_char @ (subcls880436836t_char @ P))) => (widen_917054840t_char @ P @ (class @ C) @ (class @ D)))))). % widen_subcls
thf(fact_94_widen_Ocases, axiom,
    ((![P : list_P1234162913t_char, A1 : ty, A22 : ty]: ((widen_917054840t_char @ P @ A1 @ A22) => ((~ ((A22 = A1))) => ((![C5 : list_char]: ((A1 = (class @ C5)) => (![D3 : list_char]: ((A22 = (class @ D3)) => (~ ((member89690956t_char @ (produc1304532571t_char @ C5 @ D3) @ (transi1879726366t_char @ (subcls880436836t_char @ P))))))))) => (~ (((A1 = nt) => (![C5 : list_char]: (~ ((A22 = (class @ C5)))))))))))))). % widen.cases
thf(fact_95_widen_Osimps, axiom,
    ((widen_917054840t_char = (^[P2 : list_P1234162913t_char]: (^[A12 : ty]: (^[A23 : ty]: (((?[T4 : ty]: (((A12 = T4)) & ((A23 = T4))))) | ((((?[C2 : list_char]: (?[D5 : list_char]: (((A12 = (class @ C2))) & ((((A23 = (class @ D5))) & ((member89690956t_char @ (produc1304532571t_char @ C2 @ D5) @ (transi1879726366t_char @ (subcls880436836t_char @ P2)))))))))) | ((?[C2 : list_char]: (((A12 = nt)) & ((A23 = (class @ C2))))))))))))))). % widen.simps
thf(fact_96_widen__Class, axiom,
    ((![P : list_P1234162913t_char, T2 : ty, C : list_char]: ((widen_917054840t_char @ P @ T2 @ (class @ C)) = (((T2 = nt)) | ((?[D5 : list_char]: (((T2 = (class @ D5))) & ((member89690956t_char @ (produc1304532571t_char @ D5 @ C) @ (transi1879726366t_char @ (subcls880436836t_char @ P)))))))))))). % widen_Class
thf(fact_97_widen_Oinducts, axiom,
    ((![P : list_P1234162913t_char, X1 : ty, X2 : ty, Pa : ty > ty > $o]: ((widen_917054840t_char @ P @ X1 @ X2) => ((![T5 : ty]: (Pa @ T5 @ T5)) => ((![C5 : list_char, D3 : list_char]: ((member89690956t_char @ (produc1304532571t_char @ C5 @ D3) @ (transi1879726366t_char @ (subcls880436836t_char @ P))) => (Pa @ (class @ C5) @ (class @ D3)))) => ((![C5 : list_char]: (Pa @ nt @ (class @ C5))) => (Pa @ X1 @ X2)))))))). % widen.inducts
thf(fact_98_sees__method__mono, axiom,
    ((![C4 : list_char, C : list_char, P : list_P1234162913t_char, Wf_md : list_P1234162913t_char > list_char > produc1259892823t_char > $o, M : list_char, Ts2 : list_ty, T2 : ty, M2 : produc1294284815t_char, D : list_char]: ((member89690956t_char @ (produc1304532571t_char @ C4 @ C) @ (transi1879726366t_char @ (subcls880436836t_char @ P))) => ((wf_pro1229751607t_char @ Wf_md @ P) => ((method297381284t_char @ P @ C @ M @ Ts2 @ T2 @ M2 @ D) => (?[D6 : list_char, Ts : list_ty, T : ty, M6 : produc1294284815t_char]: ((method297381284t_char @ P @ C4 @ M @ Ts @ T @ M6 @ D6) & ((list_all2_ty_ty @ (widen_917054840t_char @ P) @ Ts2 @ Ts) & (widen_917054840t_char @ P @ T @ T2)))))))))). % sees_method_mono
thf(fact_99_sees__method__mono2, axiom,
    ((![C4 : list_char, C : list_char, P : list_P1234162913t_char, Wf_md : list_P1234162913t_char > list_char > produc1259892823t_char > $o, M : list_char, Ts2 : list_ty, T2 : ty, M2 : produc1294284815t_char, D : list_char, Ts3 : list_ty, T3 : ty, M3 : produc1294284815t_char, D2 : list_char]: ((member89690956t_char @ (produc1304532571t_char @ C4 @ C) @ (transi1879726366t_char @ (subcls880436836t_char @ P))) => ((wf_pro1229751607t_char @ Wf_md @ P) => ((method297381284t_char @ P @ C @ M @ Ts2 @ T2 @ M2 @ D) => ((method297381284t_char @ P @ C4 @ M @ Ts3 @ T3 @ M3 @ D2) => ((list_all2_ty_ty @ (widen_917054840t_char @ P) @ Ts2 @ Ts3) & (widen_917054840t_char @ P @ T3 @ T2))))))))). % sees_method_mono2
thf(fact_100_singletonI, axiom,
    ((![A : produc1172664615on_val]: (member354538064on_val @ A @ (insert1971494647on_val @ A @ bot_bo1575563891on_val))))). % singletonI
thf(fact_101_singletonI, axiom,
    ((![A : produc1257910179t_char]: (member89690956t_char @ A @ (insert1354671475t_char @ A @ bot_bo346063215t_char))))). % singletonI
thf(fact_102_all__not__in__conv, axiom,
    ((![A4 : set_Pr1189492743on_val]: ((![X4 : produc1172664615on_val]: (~ ((member354538064on_val @ X4 @ A4)))) = (A4 = bot_bo1575563891on_val))))). % all_not_in_conv
thf(fact_103_all__not__in__conv, axiom,
    ((![A4 : set_Pr164112643t_char]: ((![X4 : produc1257910179t_char]: (~ ((member89690956t_char @ X4 @ A4)))) = (A4 = bot_bo346063215t_char))))). % all_not_in_conv
thf(fact_104_empty__iff, axiom,
    ((![C6 : produc1172664615on_val]: (~ ((member354538064on_val @ C6 @ bot_bo1575563891on_val)))))). % empty_iff
thf(fact_105_empty__iff, axiom,
    ((![C6 : produc1257910179t_char]: (~ ((member89690956t_char @ C6 @ bot_bo346063215t_char)))))). % empty_iff
thf(fact_106_insert__iff, axiom,
    ((![A : produc1172664615on_val, B : produc1172664615on_val, A4 : set_Pr1189492743on_val]: ((member354538064on_val @ A @ (insert1971494647on_val @ B @ A4)) = (((A = B)) | ((member354538064on_val @ A @ A4))))))). % insert_iff
thf(fact_107_insert__iff, axiom,
    ((![A : produc1257910179t_char, B : produc1257910179t_char, A4 : set_Pr164112643t_char]: ((member89690956t_char @ A @ (insert1354671475t_char @ B @ A4)) = (((A = B)) | ((member89690956t_char @ A @ A4))))))). % insert_iff
thf(fact_108_insertCI, axiom,
    ((![A : produc1172664615on_val, B4 : set_Pr1189492743on_val, B : produc1172664615on_val]: (((~ ((member354538064on_val @ A @ B4))) => (A = B)) => (member354538064on_val @ A @ (insert1971494647on_val @ B @ B4)))))). % insertCI
thf(fact_109_insertCI, axiom,
    ((![A : produc1257910179t_char, B4 : set_Pr164112643t_char, B : produc1257910179t_char]: (((~ ((member89690956t_char @ A @ B4))) => (A = B)) => (member89690956t_char @ A @ (insert1354671475t_char @ B @ B4)))))). % insertCI
thf(fact_110_ex__in__conv, axiom,
    ((![A4 : set_Pr1189492743on_val]: ((?[X4 : produc1172664615on_val]: (member354538064on_val @ X4 @ A4)) = (~ ((A4 = bot_bo1575563891on_val))))))). % ex_in_conv
thf(fact_111_ex__in__conv, axiom,
    ((![A4 : set_Pr164112643t_char]: ((?[X4 : produc1257910179t_char]: (member89690956t_char @ X4 @ A4)) = (~ ((A4 = bot_bo346063215t_char))))))). % ex_in_conv
thf(fact_112_equals0I, axiom,
    ((![A4 : set_Pr1189492743on_val]: ((![Y3 : produc1172664615on_val]: (~ ((member354538064on_val @ Y3 @ A4)))) => (A4 = bot_bo1575563891on_val))))). % equals0I
thf(fact_113_equals0I, axiom,
    ((![A4 : set_Pr164112643t_char]: ((![Y3 : produc1257910179t_char]: (~ ((member89690956t_char @ Y3 @ A4)))) => (A4 = bot_bo346063215t_char))))). % equals0I
thf(fact_114_equals0D, axiom,
    ((![A4 : set_Pr1189492743on_val, A : produc1172664615on_val]: ((A4 = bot_bo1575563891on_val) => (~ ((member354538064on_val @ A @ A4))))))). % equals0D
thf(fact_115_equals0D, axiom,
    ((![A4 : set_Pr164112643t_char, A : produc1257910179t_char]: ((A4 = bot_bo346063215t_char) => (~ ((member89690956t_char @ A @ A4))))))). % equals0D
thf(fact_116_emptyE, axiom,
    ((![A : produc1172664615on_val]: (~ ((member354538064on_val @ A @ bot_bo1575563891on_val)))))). % emptyE
thf(fact_117_emptyE, axiom,
    ((![A : produc1257910179t_char]: (~ ((member89690956t_char @ A @ bot_bo346063215t_char)))))). % emptyE
thf(fact_118_mk__disjoint__insert, axiom,
    ((![A : produc1172664615on_val, A4 : set_Pr1189492743on_val]: ((member354538064on_val @ A @ A4) => (?[B5 : set_Pr1189492743on_val]: ((A4 = (insert1971494647on_val @ A @ B5)) & (~ ((member354538064on_val @ A @ B5))))))))). % mk_disjoint_insert
thf(fact_119_mk__disjoint__insert, axiom,
    ((![A : produc1257910179t_char, A4 : set_Pr164112643t_char]: ((member89690956t_char @ A @ A4) => (?[B5 : set_Pr164112643t_char]: ((A4 = (insert1354671475t_char @ A @ B5)) & (~ ((member89690956t_char @ A @ B5))))))))). % mk_disjoint_insert
thf(fact_120_insert__eq__iff, axiom,
    ((![A : produc1172664615on_val, A4 : set_Pr1189492743on_val, B : produc1172664615on_val, B4 : set_Pr1189492743on_val]: ((~ ((member354538064on_val @ A @ A4))) => ((~ ((member354538064on_val @ B @ B4))) => (((insert1971494647on_val @ A @ A4) = (insert1971494647on_val @ B @ B4)) = (((((A = B)) => ((A4 = B4)))) & ((((~ ((A = B)))) => ((?[C2 : set_Pr1189492743on_val]: (((A4 = (insert1971494647on_val @ B @ C2))) & ((((~ ((member354538064on_val @ B @ C2)))) & ((((B4 = (insert1971494647on_val @ A @ C2))) & ((~ ((member354538064on_val @ A @ C2)))))))))))))))))))). % insert_eq_iff
thf(fact_121_insert__eq__iff, axiom,
    ((![A : produc1257910179t_char, A4 : set_Pr164112643t_char, B : produc1257910179t_char, B4 : set_Pr164112643t_char]: ((~ ((member89690956t_char @ A @ A4))) => ((~ ((member89690956t_char @ B @ B4))) => (((insert1354671475t_char @ A @ A4) = (insert1354671475t_char @ B @ B4)) = (((((A = B)) => ((A4 = B4)))) & ((((~ ((A = B)))) => ((?[C2 : set_Pr164112643t_char]: (((A4 = (insert1354671475t_char @ B @ C2))) & ((((~ ((member89690956t_char @ B @ C2)))) & ((((B4 = (insert1354671475t_char @ A @ C2))) & ((~ ((member89690956t_char @ A @ C2)))))))))))))))))))). % insert_eq_iff
thf(fact_122_insert__absorb, axiom,
    ((![A : produc1172664615on_val, A4 : set_Pr1189492743on_val]: ((member354538064on_val @ A @ A4) => ((insert1971494647on_val @ A @ A4) = A4))))). % insert_absorb
thf(fact_123_insert__absorb, axiom,
    ((![A : produc1257910179t_char, A4 : set_Pr164112643t_char]: ((member89690956t_char @ A @ A4) => ((insert1354671475t_char @ A @ A4) = A4))))). % insert_absorb
thf(fact_124_insert__ident, axiom,
    ((![X3 : produc1172664615on_val, A4 : set_Pr1189492743on_val, B4 : set_Pr1189492743on_val]: ((~ ((member354538064on_val @ X3 @ A4))) => ((~ ((member354538064on_val @ X3 @ B4))) => (((insert1971494647on_val @ X3 @ A4) = (insert1971494647on_val @ X3 @ B4)) = (A4 = B4))))))). % insert_ident
thf(fact_125_insert__ident, axiom,
    ((![X3 : produc1257910179t_char, A4 : set_Pr164112643t_char, B4 : set_Pr164112643t_char]: ((~ ((member89690956t_char @ X3 @ A4))) => ((~ ((member89690956t_char @ X3 @ B4))) => (((insert1354671475t_char @ X3 @ A4) = (insert1354671475t_char @ X3 @ B4)) = (A4 = B4))))))). % insert_ident
thf(fact_126_Set_Oset__insert, axiom,
    ((![X3 : produc1172664615on_val, A4 : set_Pr1189492743on_val]: ((member354538064on_val @ X3 @ A4) => (~ ((![B5 : set_Pr1189492743on_val]: ((A4 = (insert1971494647on_val @ X3 @ B5)) => (member354538064on_val @ X3 @ B5))))))))). % Set.set_insert
thf(fact_127_Set_Oset__insert, axiom,
    ((![X3 : produc1257910179t_char, A4 : set_Pr164112643t_char]: ((member89690956t_char @ X3 @ A4) => (~ ((![B5 : set_Pr164112643t_char]: ((A4 = (insert1354671475t_char @ X3 @ B5)) => (member89690956t_char @ X3 @ B5))))))))). % Set.set_insert
thf(fact_128_insertI2, axiom,
    ((![A : produc1172664615on_val, B4 : set_Pr1189492743on_val, B : produc1172664615on_val]: ((member354538064on_val @ A @ B4) => (member354538064on_val @ A @ (insert1971494647on_val @ B @ B4)))))). % insertI2
thf(fact_129_insertI2, axiom,
    ((![A : produc1257910179t_char, B4 : set_Pr164112643t_char, B : produc1257910179t_char]: ((member89690956t_char @ A @ B4) => (member89690956t_char @ A @ (insert1354671475t_char @ B @ B4)))))). % insertI2
thf(fact_130_insertI1, axiom,
    ((![A : produc1172664615on_val, B4 : set_Pr1189492743on_val]: (member354538064on_val @ A @ (insert1971494647on_val @ A @ B4))))). % insertI1
thf(fact_131_insertI1, axiom,
    ((![A : produc1257910179t_char, B4 : set_Pr164112643t_char]: (member89690956t_char @ A @ (insert1354671475t_char @ A @ B4))))). % insertI1
thf(fact_132_insertE, axiom,
    ((![A : produc1172664615on_val, B : produc1172664615on_val, A4 : set_Pr1189492743on_val]: ((member354538064on_val @ A @ (insert1971494647on_val @ B @ A4)) => ((~ ((A = B))) => (member354538064on_val @ A @ A4)))))). % insertE
thf(fact_133_insertE, axiom,
    ((![A : produc1257910179t_char, B : produc1257910179t_char, A4 : set_Pr164112643t_char]: ((member89690956t_char @ A @ (insert1354671475t_char @ B @ A4)) => ((~ ((A = B))) => (member89690956t_char @ A @ A4)))))). % insertE
thf(fact_134_insert__compr, axiom,
    ((insert1971494647on_val = (^[A5 : produc1172664615on_val]: (^[B6 : set_Pr1189492743on_val]: (collec2055896722on_val @ (^[X4 : produc1172664615on_val]: (((X4 = A5)) | ((member354538064on_val @ X4 @ B6)))))))))). % insert_compr
thf(fact_135_insert__compr, axiom,
    ((insert1354671475t_char = (^[A5 : produc1257910179t_char]: (^[B6 : set_Pr164112643t_char]: (collec768236686t_char @ (^[X4 : produc1257910179t_char]: (((X4 = A5)) | ((member89690956t_char @ X4 @ B6)))))))))). % insert_compr
thf(fact_136_singleton__iff, axiom,
    ((![B : produc1172664615on_val, A : produc1172664615on_val]: ((member354538064on_val @ B @ (insert1971494647on_val @ A @ bot_bo1575563891on_val)) = (B = A))))). % singleton_iff
thf(fact_137_singleton__iff, axiom,
    ((![B : produc1257910179t_char, A : produc1257910179t_char]: ((member89690956t_char @ B @ (insert1354671475t_char @ A @ bot_bo346063215t_char)) = (B = A))))). % singleton_iff
thf(fact_138_singletonD, axiom,
    ((![B : produc1172664615on_val, A : produc1172664615on_val]: ((member354538064on_val @ B @ (insert1971494647on_val @ A @ bot_bo1575563891on_val)) => (B = A))))). % singletonD
thf(fact_139_singletonD, axiom,
    ((![B : produc1257910179t_char, A : produc1257910179t_char]: ((member89690956t_char @ B @ (insert1354671475t_char @ A @ bot_bo346063215t_char)) => (B = A))))). % singletonD
thf(fact_140_sees__wf__mdecl, axiom,
    ((![Wf_md : list_P1234162913t_char > list_char > produc1259892823t_char > $o, P : list_P1234162913t_char, C : list_char, M : list_char, Ts2 : list_ty, T2 : ty, M2 : produc1294284815t_char, D : list_char]: ((wf_pro1229751607t_char @ Wf_md @ P) => ((method297381284t_char @ P @ C @ M @ Ts2 @ T2 @ M2 @ D) => (wf_mde297024346t_char @ Wf_md @ P @ D @ (produc1238538255t_char @ M @ (produc1730359111t_char @ Ts2 @ (produc248075743t_char @ T2 @ M2))))))))). % sees_wf_mdecl
thf(fact_141_red__reds_OCallObj, axiom,
    ((![E2 : exp_list_char, S2 : produc515445032on_val, E3 : exp_list_char, S3 : produc515445032on_val, P : list_P1234162913t_char, M : list_char, Es : list_exp_list_char]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E2 @ S2) @ (produc2023458740on_val @ E3 @ S3)) @ (red @ P)) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (call_list_char @ E2 @ M @ Es) @ S2) @ (produc2023458740on_val @ (call_list_char @ E3 @ M @ Es) @ S3)) @ (red @ P)))))). % red_reds.CallObj
thf(fact_142_r__into__rtrancl, axiom,
    ((![P3 : produc1257910179t_char, R2 : set_Pr164112643t_char]: ((member89690956t_char @ P3 @ R2) => (member89690956t_char @ P3 @ (transi1879726366t_char @ R2)))))). % r_into_rtrancl
thf(fact_143_r__into__rtrancl, axiom,
    ((![P3 : produc1172664615on_val, R2 : set_Pr1189492743on_val]: ((member354538064on_val @ P3 @ R2) => (member354538064on_val @ P3 @ (transi111096263on_val @ R2)))))). % r_into_rtrancl
thf(fact_144_rtrancl__idemp, axiom,
    ((![R2 : set_Pr164112643t_char]: ((transi1879726366t_char @ (transi1879726366t_char @ R2)) = (transi1879726366t_char @ R2))))). % rtrancl_idemp
thf(fact_145_rtrancl__idemp, axiom,
    ((![R2 : set_Pr1189492743on_val]: ((transi111096263on_val @ (transi111096263on_val @ R2)) = (transi111096263on_val @ R2))))). % rtrancl_idemp
thf(fact_146_converse__rtrancl__induct2, axiom,
    ((![Ax : list_list_char, Ay : exp_list_char, Bx : list_list_char, By : exp_list_char, R2 : set_Pr1060756575t_char, P : list_list_char > exp_list_char > $o]: ((member1392938152t_char @ (produc618657463t_char @ (produc713467969t_char @ Ax @ Ay) @ (produc713467969t_char @ Bx @ By)) @ (transi1892282060t_char @ R2)) => ((P @ Bx @ By) => ((![A3 : list_list_char, B3 : exp_list_char, Aa : list_list_char, Ba : exp_list_char]: ((member1392938152t_char @ (produc618657463t_char @ (produc713467969t_char @ A3 @ B3) @ (produc713467969t_char @ Aa @ Ba)) @ R2) => ((member1392938152t_char @ (produc618657463t_char @ (produc713467969t_char @ Aa @ Ba) @ (produc713467969t_char @ Bx @ By)) @ (transi1892282060t_char @ R2)) => ((P @ Aa @ Ba) => (P @ A3 @ B3))))) => (P @ Ax @ Ay))))))). % converse_rtrancl_induct2
thf(fact_147_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) => ((![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)) @ R2) => ((member2027247312on_val @ (produc2106877847on_val @ (produc52622304on_val @ Aa @ Ba) @ (produc52622304on_val @ Bx @ By)) @ (transi432893227on_val @ R2)) => ((P @ Aa @ Ba) => (P @ A3 @ B3))))) => (P @ Ax @ Ay))))))). % converse_rtrancl_induct2
thf(fact_148_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) => ((![A3 : produc1097884484on_val, B3 : produc1097884484on_val, Aa : produc1097884484on_val, Ba : produc1097884484on_val]: ((member208988944on_val @ (produc564964183on_val @ (produc1069526295on_val @ A3 @ 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 @ A3 @ B3))))) => (P @ Ax @ Ay))))))). % converse_rtrancl_induct2
thf(fact_149_converse__rtrancl__induct2, axiom,
    ((![Ax : list_char, Ay : list_char, Bx : list_char, By : list_char, R2 : set_Pr729957319t_char, P : list_char > list_char > $o]: ((member803902992t_char @ (produc395356247t_char @ (produc1304532571t_char @ Ax @ Ay) @ (produc1304532571t_char @ Bx @ By)) @ (transi858104614t_char @ R2)) => ((P @ Bx @ By) => ((![A3 : list_char, B3 : list_char, Aa : list_char, Ba : list_char]: ((member803902992t_char @ (produc395356247t_char @ (produc1304532571t_char @ A3 @ B3) @ (produc1304532571t_char @ Aa @ Ba)) @ R2) => ((member803902992t_char @ (produc395356247t_char @ (produc1304532571t_char @ Aa @ Ba) @ (produc1304532571t_char @ Bx @ By)) @ (transi858104614t_char @ R2)) => ((P @ Aa @ Ba) => (P @ A3 @ B3))))) => (P @ Ax @ Ay))))))). % converse_rtrancl_induct2
thf(fact_150_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) => ((![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)) @ R2) => ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ Aa @ Ba) @ (produc2023458740on_val @ Bx @ By)) @ (transi111096263on_val @ R2)) => ((P @ Aa @ Ba) => (P @ A3 @ B3))))) => (P @ Ax @ Ay))))))). % converse_rtrancl_induct2
thf(fact_151_converse__rtranclE2, axiom,
    ((![Xa : list_list_char, Xb : exp_list_char, Za : list_list_char, Zb : exp_list_char, R2 : set_Pr1060756575t_char]: ((member1392938152t_char @ (produc618657463t_char @ (produc713467969t_char @ Xa @ Xb) @ (produc713467969t_char @ Za @ Zb)) @ (transi1892282060t_char @ R2)) => ((~ (((produc713467969t_char @ Xa @ Xb) = (produc713467969t_char @ Za @ Zb)))) => (~ ((![A3 : list_list_char, B3 : exp_list_char]: ((member1392938152t_char @ (produc618657463t_char @ (produc713467969t_char @ Xa @ Xb) @ (produc713467969t_char @ A3 @ B3)) @ R2) => (~ ((member1392938152t_char @ (produc618657463t_char @ (produc713467969t_char @ A3 @ B3) @ (produc713467969t_char @ Za @ Zb)) @ (transi1892282060t_char @ R2))))))))))))). % converse_rtranclE2
thf(fact_152_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)))) => (~ ((![A3 : nat > option2118145160on_val, B3 : list_char > option_val]: ((member2027247312on_val @ (produc2106877847on_val @ (produc52622304on_val @ Xa @ Xb) @ (produc52622304on_val @ A3 @ B3)) @ R2) => (~ ((member2027247312on_val @ (produc2106877847on_val @ (produc52622304on_val @ A3 @ B3) @ (produc52622304on_val @ Za @ Zb)) @ (transi432893227on_val @ R2))))))))))))). % converse_rtranclE2
thf(fact_153_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)))) => (~ ((![A3 : produc1097884484on_val, B3 : produc1097884484on_val]: ((member208988944on_val @ (produc564964183on_val @ (produc1069526295on_val @ Xa @ Xb) @ (produc1069526295on_val @ A3 @ B3)) @ R2) => (~ ((member208988944on_val @ (produc564964183on_val @ (produc1069526295on_val @ A3 @ B3) @ (produc1069526295on_val @ Za @ Zb)) @ (transi100378922on_val @ R2))))))))))))). % converse_rtranclE2
thf(fact_154_converse__rtranclE2, axiom,
    ((![Xa : list_char, Xb : list_char, Za : list_char, Zb : list_char, R2 : set_Pr729957319t_char]: ((member803902992t_char @ (produc395356247t_char @ (produc1304532571t_char @ Xa @ Xb) @ (produc1304532571t_char @ Za @ Zb)) @ (transi858104614t_char @ R2)) => ((~ (((produc1304532571t_char @ Xa @ Xb) = (produc1304532571t_char @ Za @ Zb)))) => (~ ((![A3 : list_char, B3 : list_char]: ((member803902992t_char @ (produc395356247t_char @ (produc1304532571t_char @ Xa @ Xb) @ (produc1304532571t_char @ A3 @ B3)) @ R2) => (~ ((member803902992t_char @ (produc395356247t_char @ (produc1304532571t_char @ A3 @ B3) @ (produc1304532571t_char @ Za @ Zb)) @ (transi858104614t_char @ R2))))))))))))). % converse_rtranclE2
thf(fact_155_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)))) => (~ ((![A3 : exp_list_char, B3 : produc515445032on_val]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ Xa @ Xb) @ (produc2023458740on_val @ A3 @ B3)) @ R2) => (~ ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ A3 @ B3) @ (produc2023458740on_val @ Za @ Zb)) @ (transi111096263on_val @ R2))))))))))))). % converse_rtranclE2
thf(fact_156_rtrancl__induct2, axiom,
    ((![Ax : list_list_char, Ay : exp_list_char, Bx : list_list_char, By : exp_list_char, R2 : set_Pr1060756575t_char, P : list_list_char > exp_list_char > $o]: ((member1392938152t_char @ (produc618657463t_char @ (produc713467969t_char @ Ax @ Ay) @ (produc713467969t_char @ Bx @ By)) @ (transi1892282060t_char @ R2)) => ((P @ Ax @ Ay) => ((![A3 : list_list_char, B3 : exp_list_char, Aa : list_list_char, Ba : exp_list_char]: ((member1392938152t_char @ (produc618657463t_char @ (produc713467969t_char @ Ax @ Ay) @ (produc713467969t_char @ A3 @ B3)) @ (transi1892282060t_char @ R2)) => ((member1392938152t_char @ (produc618657463t_char @ (produc713467969t_char @ A3 @ B3) @ (produc713467969t_char @ Aa @ Ba)) @ R2) => ((P @ A3 @ B3) => (P @ Aa @ Ba))))) => (P @ Bx @ By))))))). % rtrancl_induct2
thf(fact_157_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) => ((![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 @ R2)) => ((member2027247312on_val @ (produc2106877847on_val @ (produc52622304on_val @ A3 @ B3) @ (produc52622304on_val @ Aa @ Ba)) @ R2) => ((P @ A3 @ B3) => (P @ Aa @ Ba))))) => (P @ Bx @ By))))))). % rtrancl_induct2
thf(fact_158_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) => ((![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 @ R2)) => ((member208988944on_val @ (produc564964183on_val @ (produc1069526295on_val @ A3 @ B3) @ (produc1069526295on_val @ Aa @ Ba)) @ R2) => ((P @ A3 @ B3) => (P @ Aa @ Ba))))) => (P @ Bx @ By))))))). % rtrancl_induct2
thf(fact_159_rtrancl__induct2, axiom,
    ((![Ax : list_char, Ay : list_char, Bx : list_char, By : list_char, R2 : set_Pr729957319t_char, P : list_char > list_char > $o]: ((member803902992t_char @ (produc395356247t_char @ (produc1304532571t_char @ Ax @ Ay) @ (produc1304532571t_char @ Bx @ By)) @ (transi858104614t_char @ R2)) => ((P @ Ax @ Ay) => ((![A3 : list_char, B3 : list_char, Aa : list_char, Ba : list_char]: ((member803902992t_char @ (produc395356247t_char @ (produc1304532571t_char @ Ax @ Ay) @ (produc1304532571t_char @ A3 @ B3)) @ (transi858104614t_char @ R2)) => ((member803902992t_char @ (produc395356247t_char @ (produc1304532571t_char @ A3 @ B3) @ (produc1304532571t_char @ Aa @ Ba)) @ R2) => ((P @ A3 @ B3) => (P @ Aa @ Ba))))) => (P @ Bx @ By))))))). % rtrancl_induct2
thf(fact_160_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) => ((![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 @ R2)) => ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ A3 @ B3) @ (produc2023458740on_val @ Aa @ Ba)) @ R2) => ((P @ A3 @ B3) => (P @ Aa @ Ba))))) => (P @ Bx @ By))))))). % rtrancl_induct2
thf(fact_161_converse__rtrancl__induct__red, axiom,
    ((![E2 : exp_list_char, H : nat > option2118145160on_val, L : list_char > option_val, E3 : exp_list_char, H2 : nat > option2118145160on_val, L2 : list_char > option_val, P : list_P1234162913t_char, R : exp_list_char > (nat > option2118145160on_val) > (list_char > option_val) > exp_list_char > (nat > option2118145160on_val) > (list_char > option_val) > $o]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E2 @ (produc52622304on_val @ H @ L)) @ (produc2023458740on_val @ E3 @ (produc52622304on_val @ H2 @ L2))) @ (transi111096263on_val @ (red @ P))) => ((![E4 : exp_list_char, H3 : nat > option2118145160on_val, L3 : list_char > option_val]: (R @ E4 @ H3 @ L3 @ E4 @ H3 @ L3)) => ((![E_0 : exp_list_char, H_0 : nat > option2118145160on_val, L_0 : list_char > option_val, E_1 : exp_list_char, H_1 : nat > option2118145160on_val, L_1 : list_char > option_val, E5 : exp_list_char, H4 : nat > option2118145160on_val, L4 : list_char > option_val]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E_0 @ (produc52622304on_val @ H_0 @ L_0)) @ (produc2023458740on_val @ E_1 @ (produc52622304on_val @ H_1 @ L_1))) @ (red @ P)) => ((R @ E_1 @ H_1 @ L_1 @ E5 @ H4 @ L4) => (R @ E_0 @ H_0 @ L_0 @ E5 @ H4 @ L4)))) => (R @ E2 @ H @ L @ E3 @ H2 @ L2))))))). % converse_rtrancl_induct_red
thf(fact_162_rtranclE, axiom,
    ((![A : list_char, B : list_char, R2 : set_Pr164112643t_char]: ((member89690956t_char @ (produc1304532571t_char @ A @ B) @ (transi1879726366t_char @ R2)) => ((~ ((A = B))) => (~ ((![Y3 : list_char]: ((member89690956t_char @ (produc1304532571t_char @ A @ Y3) @ (transi1879726366t_char @ R2)) => (~ ((member89690956t_char @ (produc1304532571t_char @ Y3 @ B) @ R2)))))))))))). % rtranclE
thf(fact_163_rtranclE, axiom,
    ((![A : produc1097884484on_val, B : produc1097884484on_val, R2 : set_Pr1189492743on_val]: ((member354538064on_val @ (produc1069526295on_val @ A @ B) @ (transi111096263on_val @ R2)) => ((~ ((A = B))) => (~ ((![Y3 : produc1097884484on_val]: ((member354538064on_val @ (produc1069526295on_val @ A @ Y3) @ (transi111096263on_val @ R2)) => (~ ((member354538064on_val @ (produc1069526295on_val @ Y3 @ B) @ R2)))))))))))). % rtranclE
thf(fact_164_rtrancl_Ocases, axiom,
    ((![A1 : list_char, A22 : list_char, R2 : set_Pr164112643t_char]: ((member89690956t_char @ (produc1304532571t_char @ A1 @ A22) @ (transi1879726366t_char @ R2)) => ((~ ((A22 = A1))) => (~ ((![B3 : list_char]: ((member89690956t_char @ (produc1304532571t_char @ A1 @ B3) @ (transi1879726366t_char @ R2)) => (~ ((member89690956t_char @ (produc1304532571t_char @ B3 @ A22) @ R2)))))))))))). % rtrancl.cases
thf(fact_165_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_166_rtrancl_Osimps, axiom,
    ((![A1 : list_char, A22 : list_char, R2 : set_Pr164112643t_char]: ((member89690956t_char @ (produc1304532571t_char @ A1 @ A22) @ (transi1879726366t_char @ R2)) = (((?[A5 : list_char]: (((A1 = A5)) & ((A22 = A5))))) | ((?[A5 : list_char]: (?[B7 : list_char]: (?[C7 : list_char]: (((A1 = A5)) & ((((A22 = C7)) & ((((member89690956t_char @ (produc1304532571t_char @ A5 @ B7) @ (transi1879726366t_char @ R2))) & ((member89690956t_char @ (produc1304532571t_char @ B7 @ C7) @ R2)))))))))))))))). % rtrancl.simps
thf(fact_167_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]: (?[B7 : produc1097884484on_val]: (?[C7 : produc1097884484on_val]: (((A1 = A5)) & ((((A22 = C7)) & ((((member354538064on_val @ (produc1069526295on_val @ A5 @ B7) @ (transi111096263on_val @ R2))) & ((member354538064on_val @ (produc1069526295on_val @ B7 @ C7) @ R2)))))))))))))))). % rtrancl.simps
thf(fact_168_rtrancl__trans, axiom,
    ((![X3 : list_char, Y : list_char, R2 : set_Pr164112643t_char, Z : list_char]: ((member89690956t_char @ (produc1304532571t_char @ X3 @ Y) @ (transi1879726366t_char @ R2)) => ((member89690956t_char @ (produc1304532571t_char @ Y @ Z) @ (transi1879726366t_char @ R2)) => (member89690956t_char @ (produc1304532571t_char @ X3 @ Z) @ (transi1879726366t_char @ R2))))))). % rtrancl_trans
thf(fact_169_rtrancl__trans, axiom,
    ((![X3 : produc1097884484on_val, Y : produc1097884484on_val, R2 : set_Pr1189492743on_val, Z : produc1097884484on_val]: ((member354538064on_val @ (produc1069526295on_val @ X3 @ Y) @ (transi111096263on_val @ R2)) => ((member354538064on_val @ (produc1069526295on_val @ Y @ Z) @ (transi111096263on_val @ R2)) => (member354538064on_val @ (produc1069526295on_val @ X3 @ Z) @ (transi111096263on_val @ R2))))))). % rtrancl_trans
thf(fact_170_rtrancl__induct, axiom,
    ((![A : list_char, B : list_char, R2 : set_Pr164112643t_char, P : list_char > $o]: ((member89690956t_char @ (produc1304532571t_char @ A @ B) @ (transi1879726366t_char @ R2)) => ((P @ A) => ((![Y3 : list_char, Z2 : list_char]: ((member89690956t_char @ (produc1304532571t_char @ A @ Y3) @ (transi1879726366t_char @ R2)) => ((member89690956t_char @ (produc1304532571t_char @ Y3 @ Z2) @ R2) => ((P @ Y3) => (P @ Z2))))) => (P @ B))))))). % rtrancl_induct
thf(fact_171_rtrancl__induct, axiom,
    ((![A : produc1097884484on_val, B : produc1097884484on_val, R2 : set_Pr1189492743on_val, P : produc1097884484on_val > $o]: ((member354538064on_val @ (produc1069526295on_val @ A @ B) @ (transi111096263on_val @ R2)) => ((P @ A) => ((![Y3 : produc1097884484on_val, Z2 : produc1097884484on_val]: ((member354538064on_val @ (produc1069526295on_val @ A @ Y3) @ (transi111096263on_val @ R2)) => ((member354538064on_val @ (produc1069526295on_val @ Y3 @ Z2) @ R2) => ((P @ Y3) => (P @ Z2))))) => (P @ B))))))). % rtrancl_induct
thf(fact_172_rtrancl_Oinducts, axiom,
    ((![X1 : list_char, X2 : list_char, R2 : set_Pr164112643t_char, P : list_char > list_char > $o]: ((member89690956t_char @ (produc1304532571t_char @ X1 @ X2) @ (transi1879726366t_char @ R2)) => ((![A3 : list_char]: (P @ A3 @ A3)) => ((![A3 : list_char, B3 : list_char, C3 : list_char]: ((member89690956t_char @ (produc1304532571t_char @ A3 @ B3) @ (transi1879726366t_char @ R2)) => ((P @ A3 @ B3) => ((member89690956t_char @ (produc1304532571t_char @ B3 @ C3) @ R2) => (P @ A3 @ C3))))) => (P @ X1 @ X2))))))). % rtrancl.inducts
thf(fact_173_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)) => ((![A3 : produc1097884484on_val]: (P @ A3 @ A3)) => ((![A3 : produc1097884484on_val, B3 : produc1097884484on_val, C3 : produc1097884484on_val]: ((member354538064on_val @ (produc1069526295on_val @ A3 @ B3) @ (transi111096263on_val @ R2)) => ((P @ A3 @ B3) => ((member354538064on_val @ (produc1069526295on_val @ B3 @ C3) @ R2) => (P @ A3 @ C3))))) => (P @ X1 @ X2))))))). % rtrancl.inducts
thf(fact_174_converse__rtranclE, axiom,
    ((![X3 : list_char, Z : list_char, R2 : set_Pr164112643t_char]: ((member89690956t_char @ (produc1304532571t_char @ X3 @ Z) @ (transi1879726366t_char @ R2)) => ((~ ((X3 = Z))) => (~ ((![Y3 : list_char]: ((member89690956t_char @ (produc1304532571t_char @ X3 @ Y3) @ R2) => (~ ((member89690956t_char @ (produc1304532571t_char @ Y3 @ Z) @ (transi1879726366t_char @ R2))))))))))))). % converse_rtranclE
thf(fact_175_converse__rtranclE, axiom,
    ((![X3 : produc1097884484on_val, Z : produc1097884484on_val, R2 : set_Pr1189492743on_val]: ((member354538064on_val @ (produc1069526295on_val @ X3 @ Z) @ (transi111096263on_val @ R2)) => ((~ ((X3 = Z))) => (~ ((![Y3 : produc1097884484on_val]: ((member354538064on_val @ (produc1069526295on_val @ X3 @ Y3) @ R2) => (~ ((member354538064on_val @ (produc1069526295on_val @ Y3 @ Z) @ (transi111096263on_val @ R2))))))))))))). % converse_rtranclE
thf(fact_176_rtrancl_Ortrancl__refl, axiom,
    ((![A : list_char, R2 : set_Pr164112643t_char]: (member89690956t_char @ (produc1304532571t_char @ A @ A) @ (transi1879726366t_char @ R2))))). % rtrancl.rtrancl_refl
thf(fact_177_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_178_converse__rtrancl__induct, axiom,
    ((![A : list_char, B : list_char, R2 : set_Pr164112643t_char, P : list_char > $o]: ((member89690956t_char @ (produc1304532571t_char @ A @ B) @ (transi1879726366t_char @ R2)) => ((P @ B) => ((![Y3 : list_char, Z2 : list_char]: ((member89690956t_char @ (produc1304532571t_char @ Y3 @ Z2) @ R2) => ((member89690956t_char @ (produc1304532571t_char @ Z2 @ B) @ (transi1879726366t_char @ R2)) => ((P @ Z2) => (P @ Y3))))) => (P @ A))))))). % converse_rtrancl_induct
thf(fact_179_converse__rtrancl__induct, axiom,
    ((![A : produc1097884484on_val, B : produc1097884484on_val, R2 : set_Pr1189492743on_val, P : produc1097884484on_val > $o]: ((member354538064on_val @ (produc1069526295on_val @ A @ B) @ (transi111096263on_val @ R2)) => ((P @ B) => ((![Y3 : produc1097884484on_val, Z2 : produc1097884484on_val]: ((member354538064on_val @ (produc1069526295on_val @ Y3 @ Z2) @ R2) => ((member354538064on_val @ (produc1069526295on_val @ Z2 @ B) @ (transi111096263on_val @ R2)) => ((P @ Z2) => (P @ Y3))))) => (P @ A))))))). % converse_rtrancl_induct
thf(fact_180_rtrancl_Ortrancl__into__rtrancl, axiom,
    ((![A : list_char, B : list_char, R2 : set_Pr164112643t_char, C6 : list_char]: ((member89690956t_char @ (produc1304532571t_char @ A @ B) @ (transi1879726366t_char @ R2)) => ((member89690956t_char @ (produc1304532571t_char @ B @ C6) @ R2) => (member89690956t_char @ (produc1304532571t_char @ A @ C6) @ (transi1879726366t_char @ R2))))))). % rtrancl.rtrancl_into_rtrancl
thf(fact_181_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_182_converse__rtrancl__into__rtrancl, axiom,
    ((![A : list_char, B : list_char, R2 : set_Pr164112643t_char, C6 : list_char]: ((member89690956t_char @ (produc1304532571t_char @ A @ B) @ R2) => ((member89690956t_char @ (produc1304532571t_char @ B @ C6) @ (transi1879726366t_char @ R2)) => (member89690956t_char @ (produc1304532571t_char @ A @ C6) @ (transi1879726366t_char @ R2))))))). % converse_rtrancl_into_rtrancl
thf(fact_183_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_184_CallRedsObj, axiom,
    ((![E2 : exp_list_char, S2 : produc515445032on_val, E3 : exp_list_char, S3 : produc515445032on_val, P : list_P1234162913t_char, M : list_char, Es : list_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 @ (call_list_char @ E2 @ M @ Es) @ S2) @ (produc2023458740on_val @ (call_list_char @ E3 @ M @ Es) @ S3)) @ (transi111096263on_val @ (red @ P))))))). % CallRedsObj
thf(fact_185_red__preserves__hconf, axiom,
    ((![E2 : exp_list_char, H : nat > option2118145160on_val, L : list_char > option_val, E3 : exp_list_char, H2 : nat > option2118145160on_val, L2 : list_char > option_val, P : list_P1234162913t_char, E : list_char > option_ty, T2 : ty]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E2 @ (produc52622304on_val @ H @ L)) @ (produc2023458740on_val @ E3 @ (produc52622304on_val @ H2 @ L2))) @ (red @ P)) => ((wTrt @ P @ H @ E @ E2 @ T2) => ((hconf_1244167010t_char @ P @ H) => (hconf_1244167010t_char @ P @ H2))))))). % red_preserves_hconf
thf(fact_186_bot__empty__eq2, axiom,
    ((bot_bo1821121046char_o = (^[X4 : list_list_char]: (^[Y4 : exp_list_char]: (member605104934t_char @ (produc713467969t_char @ X4 @ Y4) @ bot_bo1987439961t_char)))))). % bot_empty_eq2
thf(fact_187_bot__empty__eq2, axiom,
    ((bot_bo1949275371_val_o = (^[X4 : nat > option2118145160on_val]: (^[Y4 : list_char > option_val]: (member652041809on_val @ (produc52622304on_val @ X4 @ Y4) @ bot_bo923954676on_val)))))). % bot_empty_eq2
thf(fact_188_bot__empty__eq2, axiom,
    ((bot_bo1918180954_val_o = (^[X4 : produc1097884484on_val]: (^[Y4 : produc1097884484on_val]: (member354538064on_val @ (produc1069526295on_val @ X4 @ Y4) @ bot_bo1575563891on_val)))))). % bot_empty_eq2
thf(fact_189_bot__empty__eq2, axiom,
    ((bot_bo1487430909_val_o = (^[X4 : exp_list_char]: (^[Y4 : produc515445032on_val]: (member1888679917on_val @ (produc2023458740on_val @ X4 @ Y4) @ bot_bo1575411088on_val)))))). % bot_empty_eq2
thf(fact_190_bot__empty__eq2, axiom,
    ((bot_bo1359030064char_o = (^[X4 : list_char]: (^[Y4 : list_char]: (member89690956t_char @ (produc1304532571t_char @ X4 @ Y4) @ bot_bo346063215t_char)))))). % bot_empty_eq2
thf(fact_191_bot__empty__eq, axiom,
    ((bot_bo824611882_val_o = (^[X4 : produc1172664615on_val]: (member354538064on_val @ X4 @ bot_bo1575563891on_val))))). % bot_empty_eq
thf(fact_192_bot__empty__eq, axiom,
    ((bot_bo2060516910char_o = (^[X4 : produc1257910179t_char]: (member89690956t_char @ X4 @ bot_bo346063215t_char))))). % bot_empty_eq
thf(fact_193_red__preserves__lconf, axiom,
    ((![E2 : exp_list_char, H : nat > option2118145160on_val, L : list_char > option_val, E3 : exp_list_char, H2 : nat > option2118145160on_val, L2 : list_char > option_val, P : list_P1234162913t_char, E : list_char > option_ty, T2 : ty]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E2 @ (produc52622304on_val @ H @ L)) @ (produc2023458740on_val @ E3 @ (produc52622304on_val @ H2 @ L2))) @ (red @ P)) => ((wTrt @ P @ H @ E @ E2 @ T2) => ((lconf_485928294t_char @ P @ H @ L @ E) => (lconf_485928294t_char @ P @ H2 @ L2 @ E))))))). % red_preserves_lconf
thf(fact_194_is__singletonI_H, axiom,
    ((![A4 : set_Pr1189492743on_val]: ((~ ((A4 = bot_bo1575563891on_val))) => ((![X6 : produc1172664615on_val, Y3 : produc1172664615on_val]: ((member354538064on_val @ X6 @ A4) => ((member354538064on_val @ Y3 @ A4) => (X6 = Y3)))) => (is_sin1880980507on_val @ A4)))))). % is_singletonI'
thf(fact_195_is__singletonI_H, axiom,
    ((![A4 : set_Pr164112643t_char]: ((~ ((A4 = bot_bo346063215t_char))) => ((![X6 : produc1257910179t_char, Y3 : produc1257910179t_char]: ((member89690956t_char @ X6 @ A4) => ((member89690956t_char @ Y3 @ A4) => (X6 = Y3)))) => (is_sin1522322583t_char @ A4)))))). % is_singletonI'
thf(fact_196_red__preserves__sconf, axiom,
    ((![E2 : exp_list_char, S2 : produc515445032on_val, E3 : exp_list_char, S3 : produc515445032on_val, P : list_P1234162913t_char, E : list_char > option_ty, T2 : ty]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E2 @ S2) @ (produc2023458740on_val @ E3 @ S3)) @ (red @ P)) => ((wTrt @ P @ (hp @ S2) @ E @ E2 @ T2) => ((typeSa1777264139_sconf @ P @ E @ S2) => (typeSa1777264139_sconf @ P @ E @ S3))))))). % red_preserves_sconf
thf(fact_197_Call__lemma, axiom,
    ((![P : list_P1234162913t_char, C : list_char, M : list_char, Ts2 : list_ty, T2 : ty, M2 : produc1294284815t_char, D : list_char, C4 : list_char, Wf_md : list_P1234162913t_char > list_char > produc1259892823t_char > $o]: ((method297381284t_char @ P @ C @ M @ Ts2 @ T2 @ M2 @ D) => ((member89690956t_char @ (produc1304532571t_char @ C4 @ C) @ (transi1879726366t_char @ (subcls880436836t_char @ P))) => ((wf_pro1229751607t_char @ Wf_md @ P) => (?[D6 : list_char, Ts : list_ty, T : ty, M6 : produc1294284815t_char]: ((method297381284t_char @ P @ C4 @ M @ Ts @ T @ M6 @ D6) & ((list_all2_ty_ty @ (widen_917054840t_char @ P) @ Ts2 @ Ts) & ((widen_917054840t_char @ P @ T @ T2) & ((member89690956t_char @ (produc1304532571t_char @ C4 @ D6) @ (transi1879726366t_char @ (subcls880436836t_char @ P))) & ((is_typ250416522t_char @ P @ T) & ((![X7 : ty]: ((member_ty @ X7 @ (set_ty2 @ Ts)) => (is_typ250416522t_char @ P @ X7))) & (Wf_md @ P @ D6 @ (produc1238538255t_char @ M @ (produc1730359111t_char @ Ts @ (produc248075743t_char @ T @ M6))))))))))))))))). % Call_lemma
thf(fact_198_Red__lcl__add, axiom,
    ((![E2 : exp_list_char, H : nat > option2118145160on_val, L : list_char > option_val, E3 : exp_list_char, H2 : nat > option2118145160on_val, L2 : list_char > option_val, P : list_P1234162913t_char, L_02 : list_char > option_val]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E2 @ (produc52622304on_val @ H @ L)) @ (produc2023458740on_val @ E3 @ (produc52622304on_val @ H2 @ L2))) @ (transi111096263on_val @ (red @ P))) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E2 @ (produc52622304on_val @ H @ (map_ad1615113112ar_val @ L_02 @ L))) @ (produc2023458740on_val @ E3 @ (produc52622304on_val @ H2 @ (map_ad1615113112ar_val @ L_02 @ L2)))) @ (transi111096263on_val @ (red @ P))))))). % Red_lcl_add
thf(fact_199_red__lcl__add, axiom,
    ((![E2 : exp_list_char, H : nat > option2118145160on_val, L : list_char > option_val, E3 : exp_list_char, H2 : nat > option2118145160on_val, L2 : list_char > option_val, P : list_P1234162913t_char, L_02 : list_char > option_val]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E2 @ (produc52622304on_val @ H @ L)) @ (produc2023458740on_val @ E3 @ (produc52622304on_val @ H2 @ L2))) @ (red @ P)) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E2 @ (produc52622304on_val @ H @ (map_ad1615113112ar_val @ L_02 @ L))) @ (produc2023458740on_val @ E3 @ (produc52622304on_val @ H2 @ (map_ad1615113112ar_val @ L_02 @ L2)))) @ (red @ P)))))). % red_lcl_add
thf(fact_200_list__all2__same, axiom,
    ((![P : ty > ty > $o, Xs : list_ty]: ((list_all2_ty_ty @ P @ Xs @ Xs) = (![X4 : ty]: (((member_ty @ X4 @ (set_ty2 @ Xs))) => ((P @ X4 @ X4)))))))). % list_all2_same
thf(fact_201_list_Orel__cong, axiom,
    ((![X3 : list_P942933805on_val, Ya : list_P942933805on_val, Y : list_P942933805on_val, Xa : list_P942933805on_val, R : produc1172664615on_val > produc1172664615on_val > $o, Ra : produc1172664615on_val > produc1172664615on_val > $o]: ((X3 = Ya) => ((Y = Xa) => ((![Z2 : produc1172664615on_val, Yb : produc1172664615on_val]: ((member354538064on_val @ Z2 @ (set_Pr348738748on_val @ Ya)) => ((member354538064on_val @ Yb @ (set_Pr348738748on_val @ Xa)) => ((R @ Z2 @ Yb) = (Ra @ Z2 @ Yb))))) => ((list_a1344266055on_val @ R @ X3 @ Y) = (list_a1344266055on_val @ Ra @ Ya @ Xa)))))))). % list.rel_cong
thf(fact_202_list_Orel__cong, axiom,
    ((![X3 : list_P942933805on_val, Ya : list_P942933805on_val, Y : list_P757710633t_char, Xa : list_P757710633t_char, R : produc1172664615on_val > produc1257910179t_char > $o, Ra : produc1172664615on_val > produc1257910179t_char > $o]: ((X3 = Ya) => ((Y = Xa) => ((![Z2 : produc1172664615on_val, Yb : produc1257910179t_char]: ((member354538064on_val @ Z2 @ (set_Pr348738748on_val @ Ya)) => ((member89690956t_char @ Yb @ (set_Pr1342796728t_char @ Xa)) => ((R @ Z2 @ Yb) = (Ra @ Z2 @ Yb))))) => ((list_a1606905283t_char @ R @ X3 @ Y) = (list_a1606905283t_char @ Ra @ Ya @ Xa)))))))). % list.rel_cong
thf(fact_203_list_Orel__cong, axiom,
    ((![X3 : list_P757710633t_char, Ya : list_P757710633t_char, Y : list_P942933805on_val, Xa : list_P942933805on_val, R : produc1257910179t_char > produc1172664615on_val > $o, Ra : produc1257910179t_char > produc1172664615on_val > $o]: ((X3 = Ya) => ((Y = Xa) => ((![Z2 : produc1257910179t_char, Yb : produc1172664615on_val]: ((member89690956t_char @ Z2 @ (set_Pr1342796728t_char @ Ya)) => ((member354538064on_val @ Yb @ (set_Pr348738748on_val @ Xa)) => ((R @ Z2 @ Yb) = (Ra @ Z2 @ Yb))))) => ((list_a56902603on_val @ R @ X3 @ Y) = (list_a56902603on_val @ Ra @ Ya @ Xa)))))))). % list.rel_cong
thf(fact_204_list_Orel__cong, axiom,
    ((![X3 : list_P757710633t_char, Ya : list_P757710633t_char, Y : list_P757710633t_char, Xa : list_P757710633t_char, R : produc1257910179t_char > produc1257910179t_char > $o, Ra : produc1257910179t_char > produc1257910179t_char > $o]: ((X3 = Ya) => ((Y = Xa) => ((![Z2 : produc1257910179t_char, Yb : produc1257910179t_char]: ((member89690956t_char @ Z2 @ (set_Pr1342796728t_char @ Ya)) => ((member89690956t_char @ Yb @ (set_Pr1342796728t_char @ Xa)) => ((R @ Z2 @ Yb) = (Ra @ Z2 @ Yb))))) => ((list_a1368132679t_char @ R @ X3 @ Y) = (list_a1368132679t_char @ Ra @ Ya @ Xa)))))))). % list.rel_cong
thf(fact_205_list_Orel__cong, axiom,
    ((![X3 : list_ty, Ya : list_ty, Y : list_ty, Xa : list_ty, R : ty > ty > $o, Ra : ty > ty > $o]: ((X3 = Ya) => ((Y = Xa) => ((![Z2 : ty, Yb : ty]: ((member_ty @ Z2 @ (set_ty2 @ Ya)) => ((member_ty @ Yb @ (set_ty2 @ Xa)) => ((R @ Z2 @ Yb) = (Ra @ Z2 @ Yb))))) => ((list_all2_ty_ty @ R @ X3 @ Y) = (list_all2_ty_ty @ Ra @ Ya @ Xa)))))))). % list.rel_cong
thf(fact_206_mdecl__visible, axiom,
    ((![Wf_md : list_P1234162913t_char > list_char > produc1259892823t_char > $o, P : list_P1234162913t_char, C : list_char, S : list_char, Fs : list_P1126587903har_ty, Ms : list_P1653548253t_char, M : list_char, Ts2 : list_ty, T2 : ty, M2 : produc1294284815t_char]: ((wf_pro1229751607t_char @ Wf_md @ P) => ((member958036996t_char @ (produc1548560403t_char @ C @ (produc1972337867t_char @ S @ (produc1107711029t_char @ Fs @ Ms))) @ (set_Pr1611739760t_char @ P)) => ((member397625600t_char @ (produc1238538255t_char @ M @ (produc1730359111t_char @ Ts2 @ (produc248075743t_char @ T2 @ M2))) @ (set_Pr1045701996t_char @ Ms)) => (method297381284t_char @ P @ C @ M @ Ts2 @ T2 @ M2 @ C))))))). % mdecl_visible
thf(fact_207_list__all2__eq, axiom,
    (((^[Y6 : list_ty]: (^[Z3 : list_ty]: (Y6 = Z3))) = (list_all2_ty_ty @ (^[Y6 : ty]: (^[Z3 : ty]: (Y6 = Z3))))))). % list_all2_eq

% Conjectures (1)
thf(conj_0, conjecture,
    ((?[T6 : ty]: ((wTrt @ p @ h_a @ e @ (call_list_char @ e_a @ m @ esa) @ T6) & (widen_917054840t_char @ p @ T6 @ t2))))).
