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thf(sy_c_TypeRel_OMethod_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,
    method297381284t_char : list_P1234162913t_char > list_char > list_char > list_ty > ty > produc1294284815t_char > list_char > $o).
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_Ohas__method_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_me170134744t_char : list_P1234162913t_char > list_char > list_char > $o).
thf(sy_c_TypeRel_Omethod_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,
    method667690372t_char : list_P1234162913t_char > list_char > list_char > produc1259892823t_char).
thf(sy_c_TypeRel_Osubcls1_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,
    subcls880436836t_char : list_P1234162913t_char > set_Pr164112643t_char).
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_Oty_OClass, type,
    class : list_char > ty).
thf(sy_c_Type_Oty_ONT, type,
    nt : ty).
thf(sy_c_WellForm_Owf__mdecl_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_mde297024346t_char : (list_P1234162913t_char > list_char > produc1259892823t_char > $o) > list_P1234162913t_char > list_char > produc1259892823t_char > $o).
thf(sy_c_WellForm_Owf__prog_001t__Product____Type__Oprod_It__List__Olist_It__List__Olist_It__String__Ochar_J_J_Mt__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_J, type,
    wf_pro1229751607t_char : (list_P1234162913t_char > list_char > produc1259892823t_char > $o) > list_P1234162913t_char > $o).
thf(sy_c_WellTypeRT_OWTrt, type,
    wTrt : list_P1234162913t_char > (nat > option2118145160on_val) > (list_char > option_ty) > exp_list_char > ty > $o).
thf(sy_c_WellTypeRT_OWTrts, type,
    wTrts : list_P1234162913t_char > (nat > option2118145160on_val) > (list_char > option_ty) > list_exp_list_char > list_ty > $o).
thf(sy_c_member_001t__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_M_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_J, type,
    member652041809on_val : produc515445032on_val > set_Pr723149704on_val > $o).
thf(sy_c_member_001t__Product____Type__Oprod_It__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_Mt__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_M_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J, type,
    member1888679917on_val : produc1097884484on_val > set_Pr556513572on_val > $o).
thf(sy_c_member_001t__Product____Type__Oprod_It__List__Olist_It__List__Olist_It__String__Ochar_J_J_Mt__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_J, type,
    member605104934t_char : produc1294284815t_char > set_Pr2063914181t_char > $o).
thf(sy_c_member_001t__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J, type,
    member89690956t_char : produc1257910179t_char > set_Pr164112643t_char > $o).
thf(sy_c_member_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,
    member958036996t_char : produc1777519579t_char > set_Pr2090064827t_char > $o).
thf(sy_c_member_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,
    member397625600t_char : produc1259892823t_char > set_Pr1344692407t_char > $o).
thf(sy_c_member_001t__Product____Type__Oprod_It__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_M_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_Mt__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_M_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J, type,
    member2027247312on_val : produc744932519on_val > set_Pr148564103on_val > $o).
thf(sy_c_member_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_Mt__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_M_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_Mt__Product____Type__Oprod_It__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_Mt__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_M_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J, type,
    member354538064on_val : produc1172664615on_val > set_Pr1189492743on_val > $o).
thf(sy_c_member_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__List__Olist_It__List__Olist_It__String__Ochar_J_J_Mt__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_J_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, type,
    member1392938152t_char : produc1689611007t_char > set_Pr1060756575t_char > $o).
thf(sy_c_member_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_J, type,
    member803902992t_char : produc442406631t_char > set_Pr729957319t_char > $o).
thf(sy_c_member_001t__Product____Type__Oprod_It__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_Mt__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_J, type,
    member395678224t_char : produc1741765095t_char > set_Pr1592888263t_char > $o).
thf(sy_c_member_001t__Type__Oty, type,
    member_ty : ty > set_ty > $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_M____, type,
    m : list_char).
thf(sy_v_P, type,
    p : list_P1234162913t_char).
thf(sy_v_T____, type,
    t : ty).
thf(sy_v_Ts____, type,
    ts : list_ty).
thf(sy_v_U____, type,
    u : ty).
thf(sy_v_Us____, type,
    us : list_ty).
thf(sy_v_body____, type,
    body : 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).
thf(sy_v_pns____, type,
    pns : list_list_char).

% Relevant facts (249)
thf(fact_0_UsubC, axiom,
    ((widen_917054840t_char @ p @ u @ (class @ c)))). % UsubC
thf(fact_1_wte_H, axiom,
    ((wTrt @ p @ h_a @ e @ e_a @ u))). % wte'
thf(fact_2__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 @ t)))))). % \<open>U = NT \<Longrightarrow> \<exists>T'. P,E,h' \<turnstile> e'\<bullet>M(es) : T' \<and> P \<turnstile> T' \<le> T\<close>
thf(fact_3__092_060open_062_092_060And_062C_H_O_A_092_060lbrakk_062U_A_061_AClass_AC_H_059_AP_A_092_060turnstile_062_AC_H_A_092_060preceq_062_092_060_094sup_062_K_AC_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,
    ((![C : list_char]: ((u = (class @ C)) => ((member89690956t_char @ (produc1304532571t_char @ C @ c) @ (transi1879726366t_char @ (subcls880436836t_char @ p))) => (?[T : ty]: ((wTrt @ p @ h_a @ e @ (call_list_char @ e_a @ m @ esa) @ T) & (widen_917054840t_char @ p @ T @ t)))))))). % \<open>\<And>C'. \<lbrakk>U = Class C'; P \<turnstile> C' \<preceq>\<^sup>* C\<rbrakk> \<Longrightarrow> \<exists>T'. P,E,h' \<turnstile> e'\<bullet>M(es) : T' \<and> P \<turnstile> T' \<le> T\<close>
thf(fact_4__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 @ c)))))))))). % \<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_5_CallObj_Oprems_I2_J, axiom,
    ((wTrt @ p @ ha @ e @ (call_list_char @ ea @ m @ esa) @ t))). % CallObj.prems(2)
thf(fact_6_wt, axiom,
    ((wTrt @ p @ ha @ e @ (call_list_char @ ea @ m @ esa) @ t))). % wt
thf(fact_7_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_8__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,
    ((![Ts : list_ty]: ((wTrt @ p @ ha @ e @ ea @ nt) => ((wTrts @ p @ ha @ e @ esa @ Ts) => (?[T : ty]: ((wTrt @ p @ h_a @ e @ (call_list_char @ e_a @ m @ esa) @ T) & (widen_917054840t_char @ p @ T @ t)))))))). % \<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_9_local_Owf, axiom,
    ((wf_pro1229751607t_char @ wf_J_mdecl @ p))). % local.wf
thf(fact_10_wtes, axiom,
    ((wTrts @ p @ ha @ e @ esa @ us))). % wtes
thf(fact_11_wte, axiom,
    ((wTrt @ p @ ha @ e @ ea @ (class @ c)))). % wte
thf(fact_12_subs, axiom,
    ((list_all2_ty_ty @ (widen_917054840t_char @ p) @ us @ ts))). % subs
thf(fact_13_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_14_widen__refl, axiom,
    ((![P : list_P1234162913t_char, T2 : ty]: (widen_917054840t_char @ P @ T2 @ T2)))). % widen_refl
thf(fact_15_method, axiom,
    ((method297381284t_char @ p @ c @ m @ ts @ t @ (produc713467969t_char @ pns @ body) @ d))). % method
thf(fact_16_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_17_CallObj_Oprems_I1_J, axiom,
    ((typeSa1777264139_sconf @ p @ e @ (produc52622304on_val @ ha @ la)))). % CallObj.prems(1)
thf(fact_18_widens__refl, axiom,
    ((![P : list_P1234162913t_char, Xs : list_ty]: (list_all2_ty_ty @ (widen_917054840t_char @ P) @ Xs @ Xs)))). % widens_refl
thf(fact_19_conf, axiom,
    ((typeSa1777264139_sconf @ p @ e @ (produc52622304on_val @ ha @ la)))). % conf
thf(fact_20_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_21_Class__widen__Class, axiom,
    ((![P : list_P1234162913t_char, C2 : list_char, D : list_char]: ((widen_917054840t_char @ P @ (class @ C2) @ (class @ D)) = (member89690956t_char @ (produc1304532571t_char @ C2 @ D) @ (transi1879726366t_char @ (subcls880436836t_char @ P))))))). % Class_widen_Class
thf(fact_22_sees__method__fun, axiom,
    ((![P : list_P1234162913t_char, C2 : 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 @ C2 @ M @ TS @ T2 @ M2 @ D) => ((method297381284t_char @ P @ C2 @ 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, C2 : list_char, M : list_char, Ts : list_ty, T2 : ty, M2 : produc1294284815t_char, D : list_char]: ((method297381284t_char @ P @ C2 @ M @ Ts @ T2 @ M2 @ D) => (method297381284t_char @ P @ D @ M @ Ts @ T2 @ M2 @ D))))). % sees_method_idemp
thf(fact_24_sees__method__decl__mono, axiom,
    ((![C : list_char, C2 : list_char, P : list_P1234162913t_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]: ((member89690956t_char @ (produc1304532571t_char @ C @ C2) @ (transi1879726366t_char @ (subcls880436836t_char @ P))) => ((method297381284t_char @ P @ C2 @ M @ Ts @ T2 @ M2 @ D) => ((method297381284t_char @ P @ C @ M @ Ts2 @ T3 @ M3 @ D2) => (member89690956t_char @ (produc1304532571t_char @ D2 @ D) @ (transi1879726366t_char @ (subcls880436836t_char @ P))))))))). % sees_method_decl_mono
thf(fact_25_sees__method__decl__above, axiom,
    ((![P : list_P1234162913t_char, C2 : list_char, M : list_char, Ts : list_ty, T2 : ty, M2 : produc1294284815t_char, D : list_char]: ((method297381284t_char @ P @ C2 @ M @ Ts @ T2 @ M2 @ D) => (member89690956t_char @ (produc1304532571t_char @ C2 @ D) @ (transi1879726366t_char @ (subcls880436836t_char @ P))))))). % sees_method_decl_above
thf(fact_26_widen_Oinducts, axiom,
    ((![P : list_P1234162913t_char, X1 : ty, X2 : ty, Pa : ty > ty > $o]: ((widen_917054840t_char @ P @ X1 @ X2) => ((![T4 : ty]: (Pa @ T4 @ T4)) => ((![C3 : list_char, D3 : list_char]: ((member89690956t_char @ (produc1304532571t_char @ C3 @ D3) @ (transi1879726366t_char @ (subcls880436836t_char @ P))) => (Pa @ (class @ C3) @ (class @ D3)))) => ((![C3 : list_char]: (Pa @ nt @ (class @ C3))) => (Pa @ X1 @ X2)))))))). % widen.inducts
thf(fact_27_widen__Class, axiom,
    ((![P : list_P1234162913t_char, T2 : ty, C2 : list_char]: ((widen_917054840t_char @ P @ T2 @ (class @ C2)) = (((T2 = nt)) | ((?[D4 : list_char]: (((T2 = (class @ D4))) & ((member89690956t_char @ (produc1304532571t_char @ D4 @ C2) @ (transi1879726366t_char @ (subcls880436836t_char @ P)))))))))))). % widen_Class
thf(fact_28_widen_Osimps, axiom,
    ((widen_917054840t_char = (^[P2 : list_P1234162913t_char]: (^[A1 : ty]: (^[A2 : ty]: (((?[T5 : ty]: (((A1 = T5)) & ((A2 = T5))))) | ((((?[C4 : list_char]: (?[D4 : list_char]: (((A1 = (class @ C4))) & ((((A2 = (class @ D4))) & ((member89690956t_char @ (produc1304532571t_char @ C4 @ D4) @ (transi1879726366t_char @ (subcls880436836t_char @ P2)))))))))) | ((?[C4 : list_char]: (((A1 = nt)) & ((A2 = (class @ C4))))))))))))))). % widen.simps
thf(fact_29_widen_Ocases, axiom,
    ((![P : list_P1234162913t_char, A12 : ty, A22 : ty]: ((widen_917054840t_char @ P @ A12 @ A22) => ((~ ((A22 = A12))) => ((![C3 : list_char]: ((A12 = (class @ C3)) => (![D3 : list_char]: ((A22 = (class @ D3)) => (~ ((member89690956t_char @ (produc1304532571t_char @ C3 @ D3) @ (transi1879726366t_char @ (subcls880436836t_char @ P))))))))) => (~ (((A12 = nt) => (![C3 : list_char]: (~ ((A22 = (class @ C3)))))))))))))). % widen.cases
thf(fact_30_widens__trans, axiom,
    ((![P : list_P1234162913t_char, Ss : list_ty, Ts : list_ty, Us : list_ty]: ((list_all2_ty_ty @ (widen_917054840t_char @ P) @ Ss @ Ts) => ((list_all2_ty_ty @ (widen_917054840t_char @ P) @ Ts @ Us) => (list_all2_ty_ty @ (widen_917054840t_char @ P) @ Ss @ Us)))))). % widens_trans
thf(fact_31_widen__subcls, axiom,
    ((![C2 : list_char, D : list_char, P : list_P1234162913t_char]: ((member89690956t_char @ (produc1304532571t_char @ C2 @ D) @ (transi1879726366t_char @ (subcls880436836t_char @ P))) => (widen_917054840t_char @ P @ (class @ C2) @ (class @ D)))))). % widen_subcls
thf(fact_32_widen__null, axiom,
    ((![P : list_P1234162913t_char, C2 : list_char]: (widen_917054840t_char @ P @ nt @ (class @ C2))))). % widen_null
thf(fact_33_Class__widen, axiom,
    ((![P : list_P1234162913t_char, C2 : list_char, T2 : ty]: ((widen_917054840t_char @ P @ (class @ C2) @ T2) => (?[D3 : list_char]: (T2 = (class @ D3))))))). % Class_widen
thf(fact_34_WTrtCall, axiom,
    ((![P : list_P1234162913t_char, H : nat > option2118145160on_val, E : list_char > option_ty, E2 : exp_list_char, C2 : list_char, M : list_char, Ts : list_ty, T2 : ty, Pns : list_list_char, Body : exp_list_char, D : list_char, Es : list_exp_list_char, Ts2 : list_ty]: ((wTrt @ P @ H @ E @ E2 @ (class @ C2)) => ((method297381284t_char @ P @ C2 @ M @ Ts @ T2 @ (produc713467969t_char @ Pns @ Body) @ D) => ((wTrts @ P @ H @ E @ Es @ Ts2) => ((list_all2_ty_ty @ (widen_917054840t_char @ P) @ Ts2 @ Ts) => (wTrt @ P @ H @ E @ (call_list_char @ E2 @ M @ Es) @ T2)))))))). % WTrtCall
thf(fact_35_sees__method__mono, axiom,
    ((![C : list_char, C2 : list_char, P : list_P1234162913t_char, Wf_md : list_P1234162913t_char > list_char > produc1259892823t_char > $o, M : list_char, Ts : list_ty, T2 : ty, M2 : produc1294284815t_char, D : list_char]: ((member89690956t_char @ (produc1304532571t_char @ C @ C2) @ (transi1879726366t_char @ (subcls880436836t_char @ P))) => ((wf_pro1229751607t_char @ Wf_md @ P) => ((method297381284t_char @ P @ C2 @ M @ Ts @ T2 @ M2 @ D) => (?[D5 : list_char, Ts3 : list_ty, T : ty, M4 : produc1294284815t_char]: ((method297381284t_char @ P @ C @ M @ Ts3 @ T @ M4 @ D5) & ((list_all2_ty_ty @ (widen_917054840t_char @ P) @ Ts @ Ts3) & (widen_917054840t_char @ P @ T @ T2)))))))))). % sees_method_mono
thf(fact_36_sees__method__mono2, axiom,
    ((![C : list_char, C2 : list_char, P : list_P1234162913t_char, Wf_md : list_P1234162913t_char > list_char > produc1259892823t_char > $o, 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]: ((member89690956t_char @ (produc1304532571t_char @ C @ C2) @ (transi1879726366t_char @ (subcls880436836t_char @ P))) => ((wf_pro1229751607t_char @ Wf_md @ P) => ((method297381284t_char @ P @ C2 @ M @ Ts @ T2 @ M2 @ D) => ((method297381284t_char @ P @ C @ M @ Ts2 @ T3 @ M3 @ D2) => ((list_all2_ty_ty @ (widen_917054840t_char @ P) @ Ts @ Ts2) & (widen_917054840t_char @ P @ T3 @ T2))))))))). % sees_method_mono2
thf(fact_37_WTrtCallNT, axiom,
    ((![P : list_P1234162913t_char, H : nat > option2118145160on_val, E : list_char > option_ty, E2 : exp_list_char, Es : list_exp_list_char, Ts : list_ty, M : list_char, T2 : ty]: ((wTrt @ P @ H @ E @ E2 @ nt) => ((wTrts @ P @ H @ E @ Es @ Ts) => (wTrt @ P @ H @ E @ (call_list_char @ E2 @ M @ Es) @ T2)))))). % WTrtCallNT
thf(fact_38_ty_Oinject, axiom,
    ((![X5 : list_char, Y5 : list_char]: (((class @ X5) = (class @ Y5)) = (X5 = Y5))))). % ty.inject
thf(fact_39_has__method__def, axiom,
    ((has_me170134744t_char = (^[P2 : list_P1234162913t_char]: (^[C4 : list_char]: (^[M5 : list_char]: (?[Ts4 : list_ty]: (?[T5 : ty]: (?[M6 : produc1294284815t_char]: (?[X : list_char]: (method297381284t_char @ P2 @ C4 @ M5 @ Ts4 @ T5 @ M6 @ X))))))))))). % has_method_def
thf(fact_40_rtrancl__idemp, axiom,
    ((![R : set_Pr164112643t_char]: ((transi1879726366t_char @ (transi1879726366t_char @ R)) = (transi1879726366t_char @ R))))). % rtrancl_idemp
thf(fact_41_rtrancl__idemp, axiom,
    ((![R : set_Pr1189492743on_val]: ((transi111096263on_val @ (transi111096263on_val @ R)) = (transi111096263on_val @ R))))). % rtrancl_idemp
thf(fact_42_r__into__rtrancl, axiom,
    ((![P3 : produc1257910179t_char, R : set_Pr164112643t_char]: ((member89690956t_char @ P3 @ R) => (member89690956t_char @ P3 @ (transi1879726366t_char @ R)))))). % r_into_rtrancl
thf(fact_43_r__into__rtrancl, axiom,
    ((![P3 : produc1172664615on_val, R : set_Pr1189492743on_val]: ((member354538064on_val @ P3 @ R) => (member354538064on_val @ P3 @ (transi111096263on_val @ R)))))). % r_into_rtrancl
thf(fact_44_prod_Oinject, axiom,
    ((![X1 : list_char, X2 : produc1675325977t_char, Y1 : list_char, Y2 : produc1675325977t_char]: (((produc1548560403t_char @ X1 @ X2) = (produc1548560403t_char @ Y1 @ Y2)) = (((X1 = Y1)) & ((X2 = Y2))))))). % prod.inject
thf(fact_45_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_46_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_47_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_48_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_49_old_Oprod_Oinject, axiom,
    ((![A : list_char, B : produc1675325977t_char, A3 : list_char, B2 : produc1675325977t_char]: (((produc1548560403t_char @ A @ B) = (produc1548560403t_char @ A3 @ B2)) = (((A = A3)) & ((B = B2))))))). % old.prod.inject
thf(fact_50_old_Oprod_Oinject, axiom,
    ((![A : list_char, B : list_char, A3 : list_char, B2 : list_char]: (((produc1304532571t_char @ A @ B) = (produc1304532571t_char @ A3 @ B2)) = (((A = A3)) & ((B = B2))))))). % old.prod.inject
thf(fact_51_old_Oprod_Oinject, axiom,
    ((![A : list_list_char, B : exp_list_char, A3 : list_list_char, B2 : exp_list_char]: (((produc713467969t_char @ A @ B) = (produc713467969t_char @ A3 @ B2)) = (((A = A3)) & ((B = B2))))))). % old.prod.inject
thf(fact_52_old_Oprod_Oinject, axiom,
    ((![A : exp_list_char, B : produc515445032on_val, A3 : exp_list_char, B2 : produc515445032on_val]: (((produc2023458740on_val @ A @ B) = (produc2023458740on_val @ A3 @ B2)) = (((A = A3)) & ((B = B2))))))). % old.prod.inject
thf(fact_53_old_Oprod_Oinject, axiom,
    ((![A : nat > option2118145160on_val, B : list_char > option_val, A3 : nat > option2118145160on_val, B2 : list_char > option_val]: (((produc52622304on_val @ A @ B) = (produc52622304on_val @ A3 @ B2)) = (((A = A3)) & ((B = B2))))))). % old.prod.inject
thf(fact_54_rtrancl__induct2, axiom,
    ((![Ax : list_char, Ay : produc1675325977t_char, Bx : list_char, By : produc1675325977t_char, R : set_Pr1592888263t_char, P : list_char > produc1675325977t_char > $o]: ((member395678224t_char @ (produc1207395415t_char @ (produc1548560403t_char @ Ax @ Ay) @ (produc1548560403t_char @ Bx @ By)) @ (transi1072703710t_char @ R)) => ((P @ Ax @ Ay) => ((![A4 : list_char, B3 : produc1675325977t_char, Aa : list_char, Ba : produc1675325977t_char]: ((member395678224t_char @ (produc1207395415t_char @ (produc1548560403t_char @ Ax @ Ay) @ (produc1548560403t_char @ A4 @ B3)) @ (transi1072703710t_char @ R)) => ((member395678224t_char @ (produc1207395415t_char @ (produc1548560403t_char @ A4 @ B3) @ (produc1548560403t_char @ Aa @ Ba)) @ R) => ((P @ A4 @ B3) => (P @ Aa @ Ba))))) => (P @ Bx @ By))))))). % rtrancl_induct2
thf(fact_55_rtrancl__induct2, axiom,
    ((![Ax : list_char, Ay : list_char, Bx : list_char, By : list_char, R : set_Pr729957319t_char, P : list_char > list_char > $o]: ((member803902992t_char @ (produc395356247t_char @ (produc1304532571t_char @ Ax @ Ay) @ (produc1304532571t_char @ Bx @ By)) @ (transi858104614t_char @ R)) => ((P @ Ax @ Ay) => ((![A4 : list_char, B3 : list_char, Aa : list_char, Ba : list_char]: ((member803902992t_char @ (produc395356247t_char @ (produc1304532571t_char @ Ax @ Ay) @ (produc1304532571t_char @ A4 @ B3)) @ (transi858104614t_char @ R)) => ((member803902992t_char @ (produc395356247t_char @ (produc1304532571t_char @ A4 @ B3) @ (produc1304532571t_char @ Aa @ Ba)) @ R) => ((P @ A4 @ B3) => (P @ Aa @ Ba))))) => (P @ Bx @ By))))))). % rtrancl_induct2
thf(fact_56_rtrancl__induct2, axiom,
    ((![Ax : list_list_char, Ay : exp_list_char, Bx : list_list_char, By : exp_list_char, R : 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 @ R)) => ((P @ Ax @ Ay) => ((![A4 : 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 @ A4 @ B3)) @ (transi1892282060t_char @ R)) => ((member1392938152t_char @ (produc618657463t_char @ (produc713467969t_char @ A4 @ B3) @ (produc713467969t_char @ Aa @ Ba)) @ R) => ((P @ A4 @ B3) => (P @ Aa @ Ba))))) => (P @ Bx @ By))))))). % rtrancl_induct2
thf(fact_57_rtrancl__induct2, axiom,
    ((![Ax : nat > option2118145160on_val, Ay : list_char > option_val, Bx : nat > option2118145160on_val, By : list_char > option_val, R : 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 @ R)) => ((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 @ R)) => ((member2027247312on_val @ (produc2106877847on_val @ (produc52622304on_val @ A4 @ B3) @ (produc52622304on_val @ Aa @ Ba)) @ R) => ((P @ A4 @ B3) => (P @ Aa @ Ba))))) => (P @ Bx @ By))))))). % rtrancl_induct2
thf(fact_58_rtrancl__induct2, axiom,
    ((![Ax : exp_list_char, Ay : produc515445032on_val, Bx : exp_list_char, By : produc515445032on_val, R : set_Pr1189492743on_val, P : exp_list_char > produc515445032on_val > $o]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ Ax @ Ay) @ (produc2023458740on_val @ Bx @ By)) @ (transi111096263on_val @ R)) => ((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 @ R)) => ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ A4 @ B3) @ (produc2023458740on_val @ Aa @ Ba)) @ R) => ((P @ A4 @ B3) => (P @ Aa @ Ba))))) => (P @ Bx @ By))))))). % rtrancl_induct2
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_mem__Collect__eq, axiom,
    ((![A : produc1172664615on_val, P : produc1172664615on_val > $o]: ((member354538064on_val @ A @ (collec2055896722on_val @ P)) = (P @ A))))). % mem_Collect_eq
thf(fact_61_mem__Collect__eq, axiom,
    ((![A : produc1777519579t_char, P : produc1777519579t_char > $o]: ((member958036996t_char @ A @ (collec178542150t_char @ P)) = (P @ A))))). % mem_Collect_eq
thf(fact_62_mem__Collect__eq, axiom,
    ((![A : produc1259892823t_char, P : produc1259892823t_char > $o]: ((member397625600t_char @ A @ (collec1549347906t_char @ P)) = (P @ A))))). % mem_Collect_eq
thf(fact_63_Collect__mem__eq, axiom,
    ((![A5 : set_Pr164112643t_char]: ((collec768236686t_char @ (^[X3 : produc1257910179t_char]: (member89690956t_char @ X3 @ A5))) = A5)))). % Collect_mem_eq
thf(fact_64_Collect__mem__eq, axiom,
    ((![A5 : set_Pr1189492743on_val]: ((collec2055896722on_val @ (^[X3 : produc1172664615on_val]: (member354538064on_val @ X3 @ A5))) = A5)))). % Collect_mem_eq
thf(fact_65_Collect__mem__eq, axiom,
    ((![A5 : set_Pr2090064827t_char]: ((collec178542150t_char @ (^[X3 : produc1777519579t_char]: (member958036996t_char @ X3 @ A5))) = A5)))). % Collect_mem_eq
thf(fact_66_Collect__mem__eq, axiom,
    ((![A5 : set_Pr1344692407t_char]: ((collec1549347906t_char @ (^[X3 : produc1259892823t_char]: (member397625600t_char @ X3 @ A5))) = A5)))). % Collect_mem_eq
thf(fact_67_converse__rtranclE2, axiom,
    ((![Xa : list_char, Xb : produc1675325977t_char, Za : list_char, Zb : produc1675325977t_char, R : set_Pr1592888263t_char]: ((member395678224t_char @ (produc1207395415t_char @ (produc1548560403t_char @ Xa @ Xb) @ (produc1548560403t_char @ Za @ Zb)) @ (transi1072703710t_char @ R)) => ((~ (((produc1548560403t_char @ Xa @ Xb) = (produc1548560403t_char @ Za @ Zb)))) => (~ ((![A4 : list_char, B3 : produc1675325977t_char]: ((member395678224t_char @ (produc1207395415t_char @ (produc1548560403t_char @ Xa @ Xb) @ (produc1548560403t_char @ A4 @ B3)) @ R) => (~ ((member395678224t_char @ (produc1207395415t_char @ (produc1548560403t_char @ A4 @ B3) @ (produc1548560403t_char @ Za @ Zb)) @ (transi1072703710t_char @ R))))))))))))). % converse_rtranclE2
thf(fact_68_converse__rtranclE2, axiom,
    ((![Xa : list_char, Xb : list_char, Za : list_char, Zb : list_char, R : set_Pr729957319t_char]: ((member803902992t_char @ (produc395356247t_char @ (produc1304532571t_char @ Xa @ Xb) @ (produc1304532571t_char @ Za @ Zb)) @ (transi858104614t_char @ R)) => ((~ (((produc1304532571t_char @ Xa @ Xb) = (produc1304532571t_char @ Za @ Zb)))) => (~ ((![A4 : list_char, B3 : list_char]: ((member803902992t_char @ (produc395356247t_char @ (produc1304532571t_char @ Xa @ Xb) @ (produc1304532571t_char @ A4 @ B3)) @ R) => (~ ((member803902992t_char @ (produc395356247t_char @ (produc1304532571t_char @ A4 @ B3) @ (produc1304532571t_char @ Za @ Zb)) @ (transi858104614t_char @ R))))))))))))). % converse_rtranclE2
thf(fact_69_converse__rtranclE2, axiom,
    ((![Xa : list_list_char, Xb : exp_list_char, Za : list_list_char, Zb : exp_list_char, R : set_Pr1060756575t_char]: ((member1392938152t_char @ (produc618657463t_char @ (produc713467969t_char @ Xa @ Xb) @ (produc713467969t_char @ Za @ Zb)) @ (transi1892282060t_char @ R)) => ((~ (((produc713467969t_char @ Xa @ Xb) = (produc713467969t_char @ Za @ Zb)))) => (~ ((![A4 : list_list_char, B3 : exp_list_char]: ((member1392938152t_char @ (produc618657463t_char @ (produc713467969t_char @ Xa @ Xb) @ (produc713467969t_char @ A4 @ B3)) @ R) => (~ ((member1392938152t_char @ (produc618657463t_char @ (produc713467969t_char @ A4 @ B3) @ (produc713467969t_char @ Za @ Zb)) @ (transi1892282060t_char @ R))))))))))))). % converse_rtranclE2
thf(fact_70_converse__rtranclE2, axiom,
    ((![Xa : nat > option2118145160on_val, Xb : list_char > option_val, Za : nat > option2118145160on_val, Zb : list_char > option_val, R : set_Pr148564103on_val]: ((member2027247312on_val @ (produc2106877847on_val @ (produc52622304on_val @ Xa @ Xb) @ (produc52622304on_val @ Za @ Zb)) @ (transi432893227on_val @ R)) => ((~ (((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)) @ R) => (~ ((member2027247312on_val @ (produc2106877847on_val @ (produc52622304on_val @ A4 @ B3) @ (produc52622304on_val @ Za @ Zb)) @ (transi432893227on_val @ R))))))))))))). % converse_rtranclE2
thf(fact_71_converse__rtranclE2, axiom,
    ((![Xa : exp_list_char, Xb : produc515445032on_val, Za : exp_list_char, Zb : produc515445032on_val, R : set_Pr1189492743on_val]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ Xa @ Xb) @ (produc2023458740on_val @ Za @ Zb)) @ (transi111096263on_val @ R)) => ((~ (((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)) @ R) => (~ ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ A4 @ B3) @ (produc2023458740on_val @ Za @ Zb)) @ (transi111096263on_val @ R))))))))))))). % converse_rtranclE2
thf(fact_72_converse__rtrancl__induct2, axiom,
    ((![Ax : list_char, Ay : produc1675325977t_char, Bx : list_char, By : produc1675325977t_char, R : set_Pr1592888263t_char, P : list_char > produc1675325977t_char > $o]: ((member395678224t_char @ (produc1207395415t_char @ (produc1548560403t_char @ Ax @ Ay) @ (produc1548560403t_char @ Bx @ By)) @ (transi1072703710t_char @ R)) => ((P @ Bx @ By) => ((![A4 : list_char, B3 : produc1675325977t_char, Aa : list_char, Ba : produc1675325977t_char]: ((member395678224t_char @ (produc1207395415t_char @ (produc1548560403t_char @ A4 @ B3) @ (produc1548560403t_char @ Aa @ Ba)) @ R) => ((member395678224t_char @ (produc1207395415t_char @ (produc1548560403t_char @ Aa @ Ba) @ (produc1548560403t_char @ Bx @ By)) @ (transi1072703710t_char @ R)) => ((P @ Aa @ Ba) => (P @ A4 @ B3))))) => (P @ Ax @ Ay))))))). % converse_rtrancl_induct2
thf(fact_73_converse__rtrancl__induct2, axiom,
    ((![Ax : list_char, Ay : list_char, Bx : list_char, By : list_char, R : set_Pr729957319t_char, P : list_char > list_char > $o]: ((member803902992t_char @ (produc395356247t_char @ (produc1304532571t_char @ Ax @ Ay) @ (produc1304532571t_char @ Bx @ By)) @ (transi858104614t_char @ R)) => ((P @ Bx @ By) => ((![A4 : list_char, B3 : list_char, Aa : list_char, Ba : list_char]: ((member803902992t_char @ (produc395356247t_char @ (produc1304532571t_char @ A4 @ B3) @ (produc1304532571t_char @ Aa @ Ba)) @ R) => ((member803902992t_char @ (produc395356247t_char @ (produc1304532571t_char @ Aa @ Ba) @ (produc1304532571t_char @ Bx @ By)) @ (transi858104614t_char @ R)) => ((P @ Aa @ Ba) => (P @ A4 @ B3))))) => (P @ Ax @ Ay))))))). % converse_rtrancl_induct2
thf(fact_74_converse__rtrancl__induct2, axiom,
    ((![Ax : list_list_char, Ay : exp_list_char, Bx : list_list_char, By : exp_list_char, R : 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 @ R)) => ((P @ Bx @ By) => ((![A4 : list_list_char, B3 : exp_list_char, Aa : list_list_char, Ba : exp_list_char]: ((member1392938152t_char @ (produc618657463t_char @ (produc713467969t_char @ A4 @ B3) @ (produc713467969t_char @ Aa @ Ba)) @ R) => ((member1392938152t_char @ (produc618657463t_char @ (produc713467969t_char @ Aa @ Ba) @ (produc713467969t_char @ Bx @ By)) @ (transi1892282060t_char @ R)) => ((P @ Aa @ Ba) => (P @ A4 @ B3))))) => (P @ Ax @ Ay))))))). % converse_rtrancl_induct2
thf(fact_75_converse__rtrancl__induct2, axiom,
    ((![Ax : nat > option2118145160on_val, Ay : list_char > option_val, Bx : nat > option2118145160on_val, By : list_char > option_val, R : 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 @ R)) => ((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)) @ R) => ((member2027247312on_val @ (produc2106877847on_val @ (produc52622304on_val @ Aa @ Ba) @ (produc52622304on_val @ Bx @ By)) @ (transi432893227on_val @ R)) => ((P @ Aa @ Ba) => (P @ A4 @ B3))))) => (P @ Ax @ Ay))))))). % converse_rtrancl_induct2
thf(fact_76_converse__rtrancl__induct2, axiom,
    ((![Ax : exp_list_char, Ay : produc515445032on_val, Bx : exp_list_char, By : produc515445032on_val, R : set_Pr1189492743on_val, P : exp_list_char > produc515445032on_val > $o]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ Ax @ Ay) @ (produc2023458740on_val @ Bx @ By)) @ (transi111096263on_val @ R)) => ((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)) @ R) => ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ Aa @ Ba) @ (produc2023458740on_val @ Bx @ By)) @ (transi111096263on_val @ R)) => ((P @ Aa @ Ba) => (P @ A4 @ B3))))) => (P @ Ax @ Ay))))))). % converse_rtrancl_induct2
thf(fact_77_old_Oprod_Oinducts, axiom,
    ((![P : produc1777519579t_char > $o, Prod : produc1777519579t_char]: ((![A4 : list_char, B3 : produc1675325977t_char]: (P @ (produc1548560403t_char @ A4 @ B3))) => (P @ Prod))))). % old.prod.inducts
thf(fact_78_old_Oprod_Oinducts, axiom,
    ((![P : produc1257910179t_char > $o, Prod : produc1257910179t_char]: ((![A4 : list_char, B3 : list_char]: (P @ (produc1304532571t_char @ A4 @ B3))) => (P @ Prod))))). % old.prod.inducts
thf(fact_79_old_Oprod_Oinducts, axiom,
    ((![P : produc1294284815t_char > $o, Prod : produc1294284815t_char]: ((![A4 : list_list_char, B3 : exp_list_char]: (P @ (produc713467969t_char @ A4 @ B3))) => (P @ Prod))))). % old.prod.inducts
thf(fact_80_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_81_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_82_old_Oprod_Oexhaust, axiom,
    ((![Y : produc1777519579t_char]: (~ ((![A4 : list_char, B3 : produc1675325977t_char]: (~ ((Y = (produc1548560403t_char @ A4 @ B3)))))))))). % old.prod.exhaust
thf(fact_83_old_Oprod_Oexhaust, axiom,
    ((![Y : produc1257910179t_char]: (~ ((![A4 : list_char, B3 : list_char]: (~ ((Y = (produc1304532571t_char @ A4 @ B3)))))))))). % old.prod.exhaust
thf(fact_84_old_Oprod_Oexhaust, axiom,
    ((![Y : produc1294284815t_char]: (~ ((![A4 : list_list_char, B3 : exp_list_char]: (~ ((Y = (produc713467969t_char @ A4 @ B3)))))))))). % old.prod.exhaust
thf(fact_85_old_Oprod_Oexhaust, axiom,
    ((![Y : produc1097884484on_val]: (~ ((![A4 : exp_list_char, B3 : produc515445032on_val]: (~ ((Y = (produc2023458740on_val @ A4 @ B3)))))))))). % old.prod.exhaust
thf(fact_86_old_Oprod_Oexhaust, axiom,
    ((![Y : produc515445032on_val]: (~ ((![A4 : nat > option2118145160on_val, B3 : list_char > option_val]: (~ ((Y = (produc52622304on_val @ A4 @ B3)))))))))). % old.prod.exhaust
thf(fact_87_prod__induct4, axiom,
    ((![P : produc1777519579t_char > $o, X4 : produc1777519579t_char]: ((![A4 : list_char, B3 : list_char, C5 : list_P1126587903har_ty, D6 : list_P1653548253t_char]: (P @ (produc1548560403t_char @ A4 @ (produc1972337867t_char @ B3 @ (produc1107711029t_char @ C5 @ D6))))) => (P @ X4))))). % prod_induct4
thf(fact_88_prod__induct3, axiom,
    ((![P : produc1777519579t_char > $o, X4 : produc1777519579t_char]: ((![A4 : list_char, B3 : list_char, C5 : produc443281733t_char]: (P @ (produc1548560403t_char @ A4 @ (produc1972337867t_char @ B3 @ C5)))) => (P @ X4))))). % prod_induct3
thf(fact_89_prod__induct3, axiom,
    ((![P : produc1097884484on_val > $o, X4 : produc1097884484on_val]: ((![A4 : exp_list_char, B3 : nat > option2118145160on_val, C5 : list_char > option_val]: (P @ (produc2023458740on_val @ A4 @ (produc52622304on_val @ B3 @ C5)))) => (P @ X4))))). % prod_induct3
thf(fact_90_prod__cases4, axiom,
    ((![Y : produc1777519579t_char]: (~ ((![A4 : list_char, B3 : list_char, C5 : list_P1126587903har_ty, D6 : list_P1653548253t_char]: (~ ((Y = (produc1548560403t_char @ A4 @ (produc1972337867t_char @ B3 @ (produc1107711029t_char @ C5 @ D6)))))))))))). % prod_cases4
thf(fact_91_prod__cases3, axiom,
    ((![Y : produc1777519579t_char]: (~ ((![A4 : list_char, B3 : list_char, C5 : produc443281733t_char]: (~ ((Y = (produc1548560403t_char @ A4 @ (produc1972337867t_char @ B3 @ C5))))))))))). % prod_cases3
thf(fact_92_prod__cases3, axiom,
    ((![Y : produc1097884484on_val]: (~ ((![A4 : exp_list_char, B3 : nat > option2118145160on_val, C5 : list_char > option_val]: (~ ((Y = (produc2023458740on_val @ A4 @ (produc52622304on_val @ B3 @ C5))))))))))). % prod_cases3
thf(fact_93_Pair__inject, axiom,
    ((![A : list_char, B : produc1675325977t_char, A3 : list_char, B2 : produc1675325977t_char]: (((produc1548560403t_char @ A @ B) = (produc1548560403t_char @ A3 @ B2)) => (~ (((A = A3) => (~ ((B = B2)))))))))). % Pair_inject
thf(fact_94_Pair__inject, axiom,
    ((![A : list_char, B : list_char, A3 : list_char, B2 : list_char]: (((produc1304532571t_char @ A @ B) = (produc1304532571t_char @ A3 @ B2)) => (~ (((A = A3) => (~ ((B = B2)))))))))). % Pair_inject
thf(fact_95_Pair__inject, axiom,
    ((![A : list_list_char, B : exp_list_char, A3 : list_list_char, B2 : exp_list_char]: (((produc713467969t_char @ A @ B) = (produc713467969t_char @ A3 @ B2)) => (~ (((A = A3) => (~ ((B = B2)))))))))). % Pair_inject
thf(fact_96_Pair__inject, axiom,
    ((![A : exp_list_char, B : produc515445032on_val, A3 : exp_list_char, B2 : produc515445032on_val]: (((produc2023458740on_val @ A @ B) = (produc2023458740on_val @ A3 @ B2)) => (~ (((A = A3) => (~ ((B = B2)))))))))). % Pair_inject
thf(fact_97_Pair__inject, axiom,
    ((![A : nat > option2118145160on_val, B : list_char > option_val, A3 : nat > option2118145160on_val, B2 : list_char > option_val]: (((produc52622304on_val @ A @ B) = (produc52622304on_val @ A3 @ B2)) => (~ (((A = A3) => (~ ((B = B2)))))))))). % Pair_inject
thf(fact_98_prod__cases, axiom,
    ((![P : produc1777519579t_char > $o, P3 : produc1777519579t_char]: ((![A4 : list_char, B3 : produc1675325977t_char]: (P @ (produc1548560403t_char @ A4 @ B3))) => (P @ P3))))). % prod_cases
thf(fact_99_prod__cases, axiom,
    ((![P : produc1257910179t_char > $o, P3 : produc1257910179t_char]: ((![A4 : list_char, B3 : list_char]: (P @ (produc1304532571t_char @ A4 @ B3))) => (P @ P3))))). % prod_cases
thf(fact_100_prod__cases, axiom,
    ((![P : produc1294284815t_char > $o, P3 : produc1294284815t_char]: ((![A4 : list_list_char, B3 : exp_list_char]: (P @ (produc713467969t_char @ A4 @ B3))) => (P @ P3))))). % prod_cases
thf(fact_101_prod__cases, axiom,
    ((![P : produc1097884484on_val > $o, P3 : produc1097884484on_val]: ((![A4 : exp_list_char, B3 : produc515445032on_val]: (P @ (produc2023458740on_val @ A4 @ B3))) => (P @ P3))))). % prod_cases
thf(fact_102_prod__cases, axiom,
    ((![P : produc515445032on_val > $o, P3 : produc515445032on_val]: ((![A4 : nat > option2118145160on_val, B3 : list_char > option_val]: (P @ (produc52622304on_val @ A4 @ B3))) => (P @ P3))))). % prod_cases
thf(fact_103_surj__pair, axiom,
    ((![P3 : produc1777519579t_char]: (?[X6 : list_char, Y3 : produc1675325977t_char]: (P3 = (produc1548560403t_char @ X6 @ Y3)))))). % surj_pair
thf(fact_104_surj__pair, axiom,
    ((![P3 : produc1257910179t_char]: (?[X6 : list_char, Y3 : list_char]: (P3 = (produc1304532571t_char @ X6 @ Y3)))))). % surj_pair
thf(fact_105_surj__pair, axiom,
    ((![P3 : produc1294284815t_char]: (?[X6 : list_list_char, Y3 : exp_list_char]: (P3 = (produc713467969t_char @ X6 @ Y3)))))). % surj_pair
thf(fact_106_surj__pair, axiom,
    ((![P3 : produc1097884484on_val]: (?[X6 : exp_list_char, Y3 : produc515445032on_val]: (P3 = (produc2023458740on_val @ X6 @ Y3)))))). % surj_pair
thf(fact_107_surj__pair, axiom,
    ((![P3 : produc515445032on_val]: (?[X6 : nat > option2118145160on_val, Y3 : list_char > option_val]: (P3 = (produc52622304on_val @ X6 @ Y3)))))). % surj_pair
thf(fact_108_converse__rtrancl__into__rtrancl, axiom,
    ((![A : list_char, B : list_char, R : set_Pr164112643t_char, C6 : list_char]: ((member89690956t_char @ (produc1304532571t_char @ A @ B) @ R) => ((member89690956t_char @ (produc1304532571t_char @ B @ C6) @ (transi1879726366t_char @ R)) => (member89690956t_char @ (produc1304532571t_char @ A @ C6) @ (transi1879726366t_char @ R))))))). % converse_rtrancl_into_rtrancl
thf(fact_109_converse__rtrancl__into__rtrancl, axiom,
    ((![A : produc1097884484on_val, B : produc1097884484on_val, R : set_Pr1189492743on_val, C6 : produc1097884484on_val]: ((member354538064on_val @ (produc1069526295on_val @ A @ B) @ R) => ((member354538064on_val @ (produc1069526295on_val @ B @ C6) @ (transi111096263on_val @ R)) => (member354538064on_val @ (produc1069526295on_val @ A @ C6) @ (transi111096263on_val @ R))))))). % converse_rtrancl_into_rtrancl
thf(fact_110_rtrancl_Ortrancl__into__rtrancl, axiom,
    ((![A : list_char, B : list_char, R : set_Pr164112643t_char, C6 : list_char]: ((member89690956t_char @ (produc1304532571t_char @ A @ B) @ (transi1879726366t_char @ R)) => ((member89690956t_char @ (produc1304532571t_char @ B @ C6) @ R) => (member89690956t_char @ (produc1304532571t_char @ A @ C6) @ (transi1879726366t_char @ R))))))). % rtrancl.rtrancl_into_rtrancl
thf(fact_111_rtrancl_Ortrancl__into__rtrancl, axiom,
    ((![A : produc1097884484on_val, B : produc1097884484on_val, R : set_Pr1189492743on_val, C6 : produc1097884484on_val]: ((member354538064on_val @ (produc1069526295on_val @ A @ B) @ (transi111096263on_val @ R)) => ((member354538064on_val @ (produc1069526295on_val @ B @ C6) @ R) => (member354538064on_val @ (produc1069526295on_val @ A @ C6) @ (transi111096263on_val @ R))))))). % rtrancl.rtrancl_into_rtrancl
thf(fact_112_converse__rtrancl__induct, axiom,
    ((![A : list_char, B : list_char, R : set_Pr164112643t_char, P : list_char > $o]: ((member89690956t_char @ (produc1304532571t_char @ A @ B) @ (transi1879726366t_char @ R)) => ((P @ B) => ((![Y3 : list_char, Z : list_char]: ((member89690956t_char @ (produc1304532571t_char @ Y3 @ Z) @ R) => ((member89690956t_char @ (produc1304532571t_char @ Z @ B) @ (transi1879726366t_char @ R)) => ((P @ Z) => (P @ Y3))))) => (P @ A))))))). % converse_rtrancl_induct
thf(fact_113_converse__rtrancl__induct, axiom,
    ((![A : produc1097884484on_val, B : produc1097884484on_val, R : set_Pr1189492743on_val, P : produc1097884484on_val > $o]: ((member354538064on_val @ (produc1069526295on_val @ A @ B) @ (transi111096263on_val @ R)) => ((P @ B) => ((![Y3 : produc1097884484on_val, Z : produc1097884484on_val]: ((member354538064on_val @ (produc1069526295on_val @ Y3 @ Z) @ R) => ((member354538064on_val @ (produc1069526295on_val @ Z @ B) @ (transi111096263on_val @ R)) => ((P @ Z) => (P @ Y3))))) => (P @ A))))))). % converse_rtrancl_induct
thf(fact_114_rtrancl_Ortrancl__refl, axiom,
    ((![A : list_char, R : set_Pr164112643t_char]: (member89690956t_char @ (produc1304532571t_char @ A @ A) @ (transi1879726366t_char @ R))))). % rtrancl.rtrancl_refl
thf(fact_115_rtrancl_Ortrancl__refl, axiom,
    ((![A : produc1097884484on_val, R : set_Pr1189492743on_val]: (member354538064on_val @ (produc1069526295on_val @ A @ A) @ (transi111096263on_val @ R))))). % rtrancl.rtrancl_refl
thf(fact_116_converse__rtranclE, axiom,
    ((![X4 : list_char, Z2 : list_char, R : set_Pr164112643t_char]: ((member89690956t_char @ (produc1304532571t_char @ X4 @ Z2) @ (transi1879726366t_char @ R)) => ((~ ((X4 = Z2))) => (~ ((![Y3 : list_char]: ((member89690956t_char @ (produc1304532571t_char @ X4 @ Y3) @ R) => (~ ((member89690956t_char @ (produc1304532571t_char @ Y3 @ Z2) @ (transi1879726366t_char @ R))))))))))))). % converse_rtranclE
thf(fact_117_converse__rtranclE, axiom,
    ((![X4 : produc1097884484on_val, Z2 : produc1097884484on_val, R : set_Pr1189492743on_val]: ((member354538064on_val @ (produc1069526295on_val @ X4 @ Z2) @ (transi111096263on_val @ R)) => ((~ ((X4 = Z2))) => (~ ((![Y3 : produc1097884484on_val]: ((member354538064on_val @ (produc1069526295on_val @ X4 @ Y3) @ R) => (~ ((member354538064on_val @ (produc1069526295on_val @ Y3 @ Z2) @ (transi111096263on_val @ R))))))))))))). % converse_rtranclE
thf(fact_118_rtrancl_Oinducts, axiom,
    ((![X1 : list_char, X2 : list_char, R : set_Pr164112643t_char, P : list_char > list_char > $o]: ((member89690956t_char @ (produc1304532571t_char @ X1 @ X2) @ (transi1879726366t_char @ R)) => ((![A4 : list_char]: (P @ A4 @ A4)) => ((![A4 : list_char, B3 : list_char, C5 : list_char]: ((member89690956t_char @ (produc1304532571t_char @ A4 @ B3) @ (transi1879726366t_char @ R)) => ((P @ A4 @ B3) => ((member89690956t_char @ (produc1304532571t_char @ B3 @ C5) @ R) => (P @ A4 @ C5))))) => (P @ X1 @ X2))))))). % rtrancl.inducts
thf(fact_119_rtrancl_Oinducts, axiom,
    ((![X1 : produc1097884484on_val, X2 : produc1097884484on_val, R : set_Pr1189492743on_val, P : produc1097884484on_val > produc1097884484on_val > $o]: ((member354538064on_val @ (produc1069526295on_val @ X1 @ X2) @ (transi111096263on_val @ R)) => ((![A4 : produc1097884484on_val]: (P @ A4 @ A4)) => ((![A4 : produc1097884484on_val, B3 : produc1097884484on_val, C5 : produc1097884484on_val]: ((member354538064on_val @ (produc1069526295on_val @ A4 @ B3) @ (transi111096263on_val @ R)) => ((P @ A4 @ B3) => ((member354538064on_val @ (produc1069526295on_val @ B3 @ C5) @ R) => (P @ A4 @ C5))))) => (P @ X1 @ X2))))))). % rtrancl.inducts
thf(fact_120_rtrancl__induct, axiom,
    ((![A : list_char, B : list_char, R : set_Pr164112643t_char, P : list_char > $o]: ((member89690956t_char @ (produc1304532571t_char @ A @ B) @ (transi1879726366t_char @ R)) => ((P @ A) => ((![Y3 : list_char, Z : list_char]: ((member89690956t_char @ (produc1304532571t_char @ A @ Y3) @ (transi1879726366t_char @ R)) => ((member89690956t_char @ (produc1304532571t_char @ Y3 @ Z) @ R) => ((P @ Y3) => (P @ Z))))) => (P @ B))))))). % rtrancl_induct
thf(fact_121_rtrancl__induct, axiom,
    ((![A : produc1097884484on_val, B : produc1097884484on_val, R : set_Pr1189492743on_val, P : produc1097884484on_val > $o]: ((member354538064on_val @ (produc1069526295on_val @ A @ B) @ (transi111096263on_val @ R)) => ((P @ A) => ((![Y3 : produc1097884484on_val, Z : produc1097884484on_val]: ((member354538064on_val @ (produc1069526295on_val @ A @ Y3) @ (transi111096263on_val @ R)) => ((member354538064on_val @ (produc1069526295on_val @ Y3 @ Z) @ R) => ((P @ Y3) => (P @ Z))))) => (P @ B))))))). % rtrancl_induct
thf(fact_122_rtrancl__trans, axiom,
    ((![X4 : list_char, Y : list_char, R : set_Pr164112643t_char, Z2 : list_char]: ((member89690956t_char @ (produc1304532571t_char @ X4 @ Y) @ (transi1879726366t_char @ R)) => ((member89690956t_char @ (produc1304532571t_char @ Y @ Z2) @ (transi1879726366t_char @ R)) => (member89690956t_char @ (produc1304532571t_char @ X4 @ Z2) @ (transi1879726366t_char @ R))))))). % rtrancl_trans
thf(fact_123_rtrancl__trans, axiom,
    ((![X4 : produc1097884484on_val, Y : produc1097884484on_val, R : set_Pr1189492743on_val, Z2 : produc1097884484on_val]: ((member354538064on_val @ (produc1069526295on_val @ X4 @ Y) @ (transi111096263on_val @ R)) => ((member354538064on_val @ (produc1069526295on_val @ Y @ Z2) @ (transi111096263on_val @ R)) => (member354538064on_val @ (produc1069526295on_val @ X4 @ Z2) @ (transi111096263on_val @ R))))))). % rtrancl_trans
thf(fact_124_rtrancl_Osimps, axiom,
    ((![A12 : list_char, A22 : list_char, R : set_Pr164112643t_char]: ((member89690956t_char @ (produc1304532571t_char @ A12 @ A22) @ (transi1879726366t_char @ R)) = (((?[A6 : list_char]: (((A12 = A6)) & ((A22 = A6))))) | ((?[A6 : list_char]: (?[B4 : list_char]: (?[C7 : list_char]: (((A12 = A6)) & ((((A22 = C7)) & ((((member89690956t_char @ (produc1304532571t_char @ A6 @ B4) @ (transi1879726366t_char @ R))) & ((member89690956t_char @ (produc1304532571t_char @ B4 @ C7) @ R)))))))))))))))). % rtrancl.simps
thf(fact_125_rtrancl_Osimps, axiom,
    ((![A12 : produc1097884484on_val, A22 : produc1097884484on_val, R : set_Pr1189492743on_val]: ((member354538064on_val @ (produc1069526295on_val @ A12 @ A22) @ (transi111096263on_val @ R)) = (((?[A6 : produc1097884484on_val]: (((A12 = A6)) & ((A22 = A6))))) | ((?[A6 : produc1097884484on_val]: (?[B4 : produc1097884484on_val]: (?[C7 : produc1097884484on_val]: (((A12 = A6)) & ((((A22 = C7)) & ((((member354538064on_val @ (produc1069526295on_val @ A6 @ B4) @ (transi111096263on_val @ R))) & ((member354538064on_val @ (produc1069526295on_val @ B4 @ C7) @ R)))))))))))))))). % rtrancl.simps
thf(fact_126_rtrancl_Ocases, axiom,
    ((![A12 : list_char, A22 : list_char, R : set_Pr164112643t_char]: ((member89690956t_char @ (produc1304532571t_char @ A12 @ A22) @ (transi1879726366t_char @ R)) => ((~ ((A22 = A12))) => (~ ((![B3 : list_char]: ((member89690956t_char @ (produc1304532571t_char @ A12 @ B3) @ (transi1879726366t_char @ R)) => (~ ((member89690956t_char @ (produc1304532571t_char @ B3 @ A22) @ R)))))))))))). % rtrancl.cases
thf(fact_127_rtrancl_Ocases, axiom,
    ((![A12 : produc1097884484on_val, A22 : produc1097884484on_val, R : set_Pr1189492743on_val]: ((member354538064on_val @ (produc1069526295on_val @ A12 @ A22) @ (transi111096263on_val @ R)) => ((~ ((A22 = A12))) => (~ ((![B3 : produc1097884484on_val]: ((member354538064on_val @ (produc1069526295on_val @ A12 @ B3) @ (transi111096263on_val @ R)) => (~ ((member354538064on_val @ (produc1069526295on_val @ B3 @ A22) @ R)))))))))))). % rtrancl.cases
thf(fact_128_rtranclE, axiom,
    ((![A : list_char, B : list_char, R : set_Pr164112643t_char]: ((member89690956t_char @ (produc1304532571t_char @ A @ B) @ (transi1879726366t_char @ R)) => ((~ ((A = B))) => (~ ((![Y3 : list_char]: ((member89690956t_char @ (produc1304532571t_char @ A @ Y3) @ (transi1879726366t_char @ R)) => (~ ((member89690956t_char @ (produc1304532571t_char @ Y3 @ B) @ R)))))))))))). % rtranclE
thf(fact_129_rtranclE, axiom,
    ((![A : produc1097884484on_val, B : produc1097884484on_val, R : set_Pr1189492743on_val]: ((member354538064on_val @ (produc1069526295on_val @ A @ B) @ (transi111096263on_val @ R)) => ((~ ((A = B))) => (~ ((![Y3 : produc1097884484on_val]: ((member354538064on_val @ (produc1069526295on_val @ A @ Y3) @ (transi111096263on_val @ R)) => (~ ((member354538064on_val @ (produc1069526295on_val @ Y3 @ B) @ R)))))))))))). % rtranclE
thf(fact_130_ty_Odistinct_I19_J, axiom,
    ((![X5 : list_char]: (~ ((nt = (class @ X5))))))). % ty.distinct(19)
thf(fact_131_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_132_sees__wf__mdecl, axiom,
    ((![Wf_md : list_P1234162913t_char > list_char > produc1259892823t_char > $o, P : list_P1234162913t_char, C2 : list_char, M : list_char, Ts : list_ty, T2 : ty, M2 : produc1294284815t_char, D : list_char]: ((wf_pro1229751607t_char @ Wf_md @ P) => ((method297381284t_char @ P @ C2 @ M @ Ts @ T2 @ M2 @ D) => (wf_mde297024346t_char @ Wf_md @ P @ D @ (produc1238538255t_char @ M @ (produc1730359111t_char @ Ts @ (produc248075743t_char @ T2 @ M2))))))))). % sees_wf_mdecl
thf(fact_133_method__def2, axiom,
    ((![P : list_P1234162913t_char, C2 : list_char, M : list_char, Ts : list_ty, T2 : ty, M2 : produc1294284815t_char, D : list_char]: ((method297381284t_char @ P @ C2 @ M @ Ts @ T2 @ M2 @ D) => ((method667690372t_char @ P @ C2 @ M) = (produc1238538255t_char @ D @ (produc1730359111t_char @ Ts @ (produc248075743t_char @ T2 @ M2)))))))). % method_def2
thf(fact_134_has__field__mono, axiom,
    ((![P : list_P1234162913t_char, C2 : list_char, F : list_char, T2 : ty, D : list_char, C : list_char]: ((has_fi599584195t_char @ P @ C2 @ F @ T2 @ D) => ((member89690956t_char @ (produc1304532571t_char @ C @ C2) @ (transi1879726366t_char @ (subcls880436836t_char @ P))) => (has_fi599584195t_char @ P @ C @ F @ T2 @ D)))))). % has_field_mono
thf(fact_135_singletonI, axiom,
    ((![A : produc1257910179t_char]: (member89690956t_char @ A @ (insert1354671475t_char @ A @ bot_bo346063215t_char))))). % singletonI
thf(fact_136_singletonI, axiom,
    ((![A : produc1172664615on_val]: (member354538064on_val @ A @ (insert1971494647on_val @ A @ bot_bo1575563891on_val))))). % singletonI
thf(fact_137_singletonI, axiom,
    ((![A : produc1777519579t_char]: (member958036996t_char @ A @ (insert1233103275t_char @ A @ bot_bo632162855t_char))))). % singletonI
thf(fact_138_singletonI, axiom,
    ((![A : produc1259892823t_char]: (member397625600t_char @ A @ (insert1354659367t_char @ A @ bot_bo956740899t_char))))). % singletonI
thf(fact_139_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_140_all__not__in__conv, axiom,
    ((![A5 : set_Pr164112643t_char]: ((![X3 : produc1257910179t_char]: (~ ((member89690956t_char @ X3 @ A5)))) = (A5 = bot_bo346063215t_char))))). % all_not_in_conv
thf(fact_141_all__not__in__conv, axiom,
    ((![A5 : set_Pr1189492743on_val]: ((![X3 : produc1172664615on_val]: (~ ((member354538064on_val @ X3 @ A5)))) = (A5 = bot_bo1575563891on_val))))). % all_not_in_conv
thf(fact_142_all__not__in__conv, axiom,
    ((![A5 : set_Pr2090064827t_char]: ((![X3 : produc1777519579t_char]: (~ ((member958036996t_char @ X3 @ A5)))) = (A5 = bot_bo632162855t_char))))). % all_not_in_conv
thf(fact_143_all__not__in__conv, axiom,
    ((![A5 : set_Pr1344692407t_char]: ((![X3 : produc1259892823t_char]: (~ ((member397625600t_char @ X3 @ A5)))) = (A5 = bot_bo956740899t_char))))). % all_not_in_conv
thf(fact_144_empty__iff, axiom,
    ((![C6 : produc1257910179t_char]: (~ ((member89690956t_char @ C6 @ bot_bo346063215t_char)))))). % empty_iff
thf(fact_145_empty__iff, axiom,
    ((![C6 : produc1172664615on_val]: (~ ((member354538064on_val @ C6 @ bot_bo1575563891on_val)))))). % empty_iff
thf(fact_146_empty__iff, axiom,
    ((![C6 : produc1777519579t_char]: (~ ((member958036996t_char @ C6 @ bot_bo632162855t_char)))))). % empty_iff
thf(fact_147_empty__iff, axiom,
    ((![C6 : produc1259892823t_char]: (~ ((member397625600t_char @ C6 @ bot_bo956740899t_char)))))). % empty_iff
thf(fact_148_insert__iff, axiom,
    ((![A : produc1257910179t_char, B : produc1257910179t_char, A5 : set_Pr164112643t_char]: ((member89690956t_char @ A @ (insert1354671475t_char @ B @ A5)) = (((A = B)) | ((member89690956t_char @ A @ A5))))))). % insert_iff
thf(fact_149_insert__iff, axiom,
    ((![A : produc1172664615on_val, B : produc1172664615on_val, A5 : set_Pr1189492743on_val]: ((member354538064on_val @ A @ (insert1971494647on_val @ B @ A5)) = (((A = B)) | ((member354538064on_val @ A @ A5))))))). % insert_iff
thf(fact_150_insert__iff, axiom,
    ((![A : produc1777519579t_char, B : produc1777519579t_char, A5 : set_Pr2090064827t_char]: ((member958036996t_char @ A @ (insert1233103275t_char @ B @ A5)) = (((A = B)) | ((member958036996t_char @ A @ A5))))))). % insert_iff
thf(fact_151_insert__iff, axiom,
    ((![A : produc1259892823t_char, B : produc1259892823t_char, A5 : set_Pr1344692407t_char]: ((member397625600t_char @ A @ (insert1354659367t_char @ B @ A5)) = (((A = B)) | ((member397625600t_char @ A @ A5))))))). % insert_iff
thf(fact_152_insertCI, axiom,
    ((![A : produc1257910179t_char, B5 : set_Pr164112643t_char, B : produc1257910179t_char]: (((~ ((member89690956t_char @ A @ B5))) => (A = B)) => (member89690956t_char @ A @ (insert1354671475t_char @ B @ B5)))))). % insertCI
thf(fact_153_insertCI, axiom,
    ((![A : produc1172664615on_val, B5 : set_Pr1189492743on_val, B : produc1172664615on_val]: (((~ ((member354538064on_val @ A @ B5))) => (A = B)) => (member354538064on_val @ A @ (insert1971494647on_val @ B @ B5)))))). % insertCI
thf(fact_154_insertCI, axiom,
    ((![A : produc1777519579t_char, B5 : set_Pr2090064827t_char, B : produc1777519579t_char]: (((~ ((member958036996t_char @ A @ B5))) => (A = B)) => (member958036996t_char @ A @ (insert1233103275t_char @ B @ B5)))))). % insertCI
thf(fact_155_insertCI, axiom,
    ((![A : produc1259892823t_char, B5 : set_Pr1344692407t_char, B : produc1259892823t_char]: (((~ ((member397625600t_char @ A @ B5))) => (A = B)) => (member397625600t_char @ A @ (insert1354659367t_char @ B @ B5)))))). % insertCI
thf(fact_156_ex__in__conv, axiom,
    ((![A5 : set_Pr164112643t_char]: ((?[X3 : produc1257910179t_char]: (member89690956t_char @ X3 @ A5)) = (~ ((A5 = bot_bo346063215t_char))))))). % ex_in_conv
thf(fact_157_ex__in__conv, axiom,
    ((![A5 : set_Pr1189492743on_val]: ((?[X3 : produc1172664615on_val]: (member354538064on_val @ X3 @ A5)) = (~ ((A5 = bot_bo1575563891on_val))))))). % ex_in_conv
thf(fact_158_ex__in__conv, axiom,
    ((![A5 : set_Pr2090064827t_char]: ((?[X3 : produc1777519579t_char]: (member958036996t_char @ X3 @ A5)) = (~ ((A5 = bot_bo632162855t_char))))))). % ex_in_conv
thf(fact_159_ex__in__conv, axiom,
    ((![A5 : set_Pr1344692407t_char]: ((?[X3 : produc1259892823t_char]: (member397625600t_char @ X3 @ A5)) = (~ ((A5 = bot_bo956740899t_char))))))). % ex_in_conv
thf(fact_160_equals0I, axiom,
    ((![A5 : set_Pr164112643t_char]: ((![Y3 : produc1257910179t_char]: (~ ((member89690956t_char @ Y3 @ A5)))) => (A5 = bot_bo346063215t_char))))). % equals0I
thf(fact_161_equals0I, axiom,
    ((![A5 : set_Pr1189492743on_val]: ((![Y3 : produc1172664615on_val]: (~ ((member354538064on_val @ Y3 @ A5)))) => (A5 = bot_bo1575563891on_val))))). % equals0I
thf(fact_162_equals0I, axiom,
    ((![A5 : set_Pr2090064827t_char]: ((![Y3 : produc1777519579t_char]: (~ ((member958036996t_char @ Y3 @ A5)))) => (A5 = bot_bo632162855t_char))))). % equals0I
thf(fact_163_equals0I, axiom,
    ((![A5 : set_Pr1344692407t_char]: ((![Y3 : produc1259892823t_char]: (~ ((member397625600t_char @ Y3 @ A5)))) => (A5 = bot_bo956740899t_char))))). % equals0I
thf(fact_164_equals0D, axiom,
    ((![A5 : set_Pr164112643t_char, A : produc1257910179t_char]: ((A5 = bot_bo346063215t_char) => (~ ((member89690956t_char @ A @ A5))))))). % equals0D
thf(fact_165_equals0D, axiom,
    ((![A5 : set_Pr1189492743on_val, A : produc1172664615on_val]: ((A5 = bot_bo1575563891on_val) => (~ ((member354538064on_val @ A @ A5))))))). % equals0D
thf(fact_166_equals0D, axiom,
    ((![A5 : set_Pr2090064827t_char, A : produc1777519579t_char]: ((A5 = bot_bo632162855t_char) => (~ ((member958036996t_char @ A @ A5))))))). % equals0D
thf(fact_167_equals0D, axiom,
    ((![A5 : set_Pr1344692407t_char, A : produc1259892823t_char]: ((A5 = bot_bo956740899t_char) => (~ ((member397625600t_char @ A @ A5))))))). % equals0D
thf(fact_168_emptyE, axiom,
    ((![A : produc1257910179t_char]: (~ ((member89690956t_char @ A @ bot_bo346063215t_char)))))). % emptyE
thf(fact_169_emptyE, axiom,
    ((![A : produc1172664615on_val]: (~ ((member354538064on_val @ A @ bot_bo1575563891on_val)))))). % emptyE
thf(fact_170_emptyE, axiom,
    ((![A : produc1777519579t_char]: (~ ((member958036996t_char @ A @ bot_bo632162855t_char)))))). % emptyE
thf(fact_171_emptyE, axiom,
    ((![A : produc1259892823t_char]: (~ ((member397625600t_char @ A @ bot_bo956740899t_char)))))). % emptyE
thf(fact_172_mk__disjoint__insert, axiom,
    ((![A : produc1257910179t_char, A5 : set_Pr164112643t_char]: ((member89690956t_char @ A @ A5) => (?[B6 : set_Pr164112643t_char]: ((A5 = (insert1354671475t_char @ A @ B6)) & (~ ((member89690956t_char @ A @ B6))))))))). % mk_disjoint_insert
thf(fact_173_mk__disjoint__insert, axiom,
    ((![A : produc1172664615on_val, A5 : set_Pr1189492743on_val]: ((member354538064on_val @ A @ A5) => (?[B6 : set_Pr1189492743on_val]: ((A5 = (insert1971494647on_val @ A @ B6)) & (~ ((member354538064on_val @ A @ B6))))))))). % mk_disjoint_insert
thf(fact_174_mk__disjoint__insert, axiom,
    ((![A : produc1777519579t_char, A5 : set_Pr2090064827t_char]: ((member958036996t_char @ A @ A5) => (?[B6 : set_Pr2090064827t_char]: ((A5 = (insert1233103275t_char @ A @ B6)) & (~ ((member958036996t_char @ A @ B6))))))))). % mk_disjoint_insert
thf(fact_175_mk__disjoint__insert, axiom,
    ((![A : produc1259892823t_char, A5 : set_Pr1344692407t_char]: ((member397625600t_char @ A @ A5) => (?[B6 : set_Pr1344692407t_char]: ((A5 = (insert1354659367t_char @ A @ B6)) & (~ ((member397625600t_char @ A @ B6))))))))). % mk_disjoint_insert
thf(fact_176_insert__eq__iff, axiom,
    ((![A : produc1257910179t_char, A5 : set_Pr164112643t_char, B : produc1257910179t_char, B5 : set_Pr164112643t_char]: ((~ ((member89690956t_char @ A @ A5))) => ((~ ((member89690956t_char @ B @ B5))) => (((insert1354671475t_char @ A @ A5) = (insert1354671475t_char @ B @ B5)) = (((((A = B)) => ((A5 = B5)))) & ((((~ ((A = B)))) => ((?[C4 : set_Pr164112643t_char]: (((A5 = (insert1354671475t_char @ B @ C4))) & ((((~ ((member89690956t_char @ B @ C4)))) & ((((B5 = (insert1354671475t_char @ A @ C4))) & ((~ ((member89690956t_char @ A @ C4)))))))))))))))))))). % insert_eq_iff
thf(fact_177_insert__eq__iff, axiom,
    ((![A : produc1172664615on_val, A5 : set_Pr1189492743on_val, B : produc1172664615on_val, B5 : set_Pr1189492743on_val]: ((~ ((member354538064on_val @ A @ A5))) => ((~ ((member354538064on_val @ B @ B5))) => (((insert1971494647on_val @ A @ A5) = (insert1971494647on_val @ B @ B5)) = (((((A = B)) => ((A5 = B5)))) & ((((~ ((A = B)))) => ((?[C4 : set_Pr1189492743on_val]: (((A5 = (insert1971494647on_val @ B @ C4))) & ((((~ ((member354538064on_val @ B @ C4)))) & ((((B5 = (insert1971494647on_val @ A @ C4))) & ((~ ((member354538064on_val @ A @ C4)))))))))))))))))))). % insert_eq_iff
thf(fact_178_insert__eq__iff, axiom,
    ((![A : produc1777519579t_char, A5 : set_Pr2090064827t_char, B : produc1777519579t_char, B5 : set_Pr2090064827t_char]: ((~ ((member958036996t_char @ A @ A5))) => ((~ ((member958036996t_char @ B @ B5))) => (((insert1233103275t_char @ A @ A5) = (insert1233103275t_char @ B @ B5)) = (((((A = B)) => ((A5 = B5)))) & ((((~ ((A = B)))) => ((?[C4 : set_Pr2090064827t_char]: (((A5 = (insert1233103275t_char @ B @ C4))) & ((((~ ((member958036996t_char @ B @ C4)))) & ((((B5 = (insert1233103275t_char @ A @ C4))) & ((~ ((member958036996t_char @ A @ C4)))))))))))))))))))). % insert_eq_iff
thf(fact_179_insert__eq__iff, axiom,
    ((![A : produc1259892823t_char, A5 : set_Pr1344692407t_char, B : produc1259892823t_char, B5 : set_Pr1344692407t_char]: ((~ ((member397625600t_char @ A @ A5))) => ((~ ((member397625600t_char @ B @ B5))) => (((insert1354659367t_char @ A @ A5) = (insert1354659367t_char @ B @ B5)) = (((((A = B)) => ((A5 = B5)))) & ((((~ ((A = B)))) => ((?[C4 : set_Pr1344692407t_char]: (((A5 = (insert1354659367t_char @ B @ C4))) & ((((~ ((member397625600t_char @ B @ C4)))) & ((((B5 = (insert1354659367t_char @ A @ C4))) & ((~ ((member397625600t_char @ A @ C4)))))))))))))))))))). % insert_eq_iff
thf(fact_180_insert__absorb, axiom,
    ((![A : produc1257910179t_char, A5 : set_Pr164112643t_char]: ((member89690956t_char @ A @ A5) => ((insert1354671475t_char @ A @ A5) = A5))))). % insert_absorb
thf(fact_181_insert__absorb, axiom,
    ((![A : produc1172664615on_val, A5 : set_Pr1189492743on_val]: ((member354538064on_val @ A @ A5) => ((insert1971494647on_val @ A @ A5) = A5))))). % insert_absorb
thf(fact_182_insert__absorb, axiom,
    ((![A : produc1777519579t_char, A5 : set_Pr2090064827t_char]: ((member958036996t_char @ A @ A5) => ((insert1233103275t_char @ A @ A5) = A5))))). % insert_absorb
thf(fact_183_insert__absorb, axiom,
    ((![A : produc1259892823t_char, A5 : set_Pr1344692407t_char]: ((member397625600t_char @ A @ A5) => ((insert1354659367t_char @ A @ A5) = A5))))). % insert_absorb
thf(fact_184_insert__ident, axiom,
    ((![X4 : produc1257910179t_char, A5 : set_Pr164112643t_char, B5 : set_Pr164112643t_char]: ((~ ((member89690956t_char @ X4 @ A5))) => ((~ ((member89690956t_char @ X4 @ B5))) => (((insert1354671475t_char @ X4 @ A5) = (insert1354671475t_char @ X4 @ B5)) = (A5 = B5))))))). % insert_ident
thf(fact_185_insert__ident, axiom,
    ((![X4 : produc1172664615on_val, A5 : set_Pr1189492743on_val, B5 : set_Pr1189492743on_val]: ((~ ((member354538064on_val @ X4 @ A5))) => ((~ ((member354538064on_val @ X4 @ B5))) => (((insert1971494647on_val @ X4 @ A5) = (insert1971494647on_val @ X4 @ B5)) = (A5 = B5))))))). % insert_ident
thf(fact_186_insert__ident, axiom,
    ((![X4 : produc1777519579t_char, A5 : set_Pr2090064827t_char, B5 : set_Pr2090064827t_char]: ((~ ((member958036996t_char @ X4 @ A5))) => ((~ ((member958036996t_char @ X4 @ B5))) => (((insert1233103275t_char @ X4 @ A5) = (insert1233103275t_char @ X4 @ B5)) = (A5 = B5))))))). % insert_ident
thf(fact_187_insert__ident, axiom,
    ((![X4 : produc1259892823t_char, A5 : set_Pr1344692407t_char, B5 : set_Pr1344692407t_char]: ((~ ((member397625600t_char @ X4 @ A5))) => ((~ ((member397625600t_char @ X4 @ B5))) => (((insert1354659367t_char @ X4 @ A5) = (insert1354659367t_char @ X4 @ B5)) = (A5 = B5))))))). % insert_ident
thf(fact_188_Set_Oset__insert, axiom,
    ((![X4 : produc1257910179t_char, A5 : set_Pr164112643t_char]: ((member89690956t_char @ X4 @ A5) => (~ ((![B6 : set_Pr164112643t_char]: ((A5 = (insert1354671475t_char @ X4 @ B6)) => (member89690956t_char @ X4 @ B6))))))))). % Set.set_insert
thf(fact_189_Set_Oset__insert, axiom,
    ((![X4 : produc1172664615on_val, A5 : set_Pr1189492743on_val]: ((member354538064on_val @ X4 @ A5) => (~ ((![B6 : set_Pr1189492743on_val]: ((A5 = (insert1971494647on_val @ X4 @ B6)) => (member354538064on_val @ X4 @ B6))))))))). % Set.set_insert
thf(fact_190_Set_Oset__insert, axiom,
    ((![X4 : produc1777519579t_char, A5 : set_Pr2090064827t_char]: ((member958036996t_char @ X4 @ A5) => (~ ((![B6 : set_Pr2090064827t_char]: ((A5 = (insert1233103275t_char @ X4 @ B6)) => (member958036996t_char @ X4 @ B6))))))))). % Set.set_insert
thf(fact_191_Set_Oset__insert, axiom,
    ((![X4 : produc1259892823t_char, A5 : set_Pr1344692407t_char]: ((member397625600t_char @ X4 @ A5) => (~ ((![B6 : set_Pr1344692407t_char]: ((A5 = (insert1354659367t_char @ X4 @ B6)) => (member397625600t_char @ X4 @ B6))))))))). % Set.set_insert
thf(fact_192_insertI2, axiom,
    ((![A : produc1257910179t_char, B5 : set_Pr164112643t_char, B : produc1257910179t_char]: ((member89690956t_char @ A @ B5) => (member89690956t_char @ A @ (insert1354671475t_char @ B @ B5)))))). % insertI2
thf(fact_193_insertI2, axiom,
    ((![A : produc1172664615on_val, B5 : set_Pr1189492743on_val, B : produc1172664615on_val]: ((member354538064on_val @ A @ B5) => (member354538064on_val @ A @ (insert1971494647on_val @ B @ B5)))))). % insertI2
thf(fact_194_insertI2, axiom,
    ((![A : produc1777519579t_char, B5 : set_Pr2090064827t_char, B : produc1777519579t_char]: ((member958036996t_char @ A @ B5) => (member958036996t_char @ A @ (insert1233103275t_char @ B @ B5)))))). % insertI2
thf(fact_195_insertI2, axiom,
    ((![A : produc1259892823t_char, B5 : set_Pr1344692407t_char, B : produc1259892823t_char]: ((member397625600t_char @ A @ B5) => (member397625600t_char @ A @ (insert1354659367t_char @ B @ B5)))))). % insertI2
thf(fact_196_insertI1, axiom,
    ((![A : produc1257910179t_char, B5 : set_Pr164112643t_char]: (member89690956t_char @ A @ (insert1354671475t_char @ A @ B5))))). % insertI1
thf(fact_197_insertI1, axiom,
    ((![A : produc1172664615on_val, B5 : set_Pr1189492743on_val]: (member354538064on_val @ A @ (insert1971494647on_val @ A @ B5))))). % insertI1
thf(fact_198_insertI1, axiom,
    ((![A : produc1777519579t_char, B5 : set_Pr2090064827t_char]: (member958036996t_char @ A @ (insert1233103275t_char @ A @ B5))))). % insertI1
thf(fact_199_insertI1, axiom,
    ((![A : produc1259892823t_char, B5 : set_Pr1344692407t_char]: (member397625600t_char @ A @ (insert1354659367t_char @ A @ B5))))). % insertI1
thf(fact_200_insertE, axiom,
    ((![A : produc1257910179t_char, B : produc1257910179t_char, A5 : set_Pr164112643t_char]: ((member89690956t_char @ A @ (insert1354671475t_char @ B @ A5)) => ((~ ((A = B))) => (member89690956t_char @ A @ A5)))))). % insertE
thf(fact_201_insertE, axiom,
    ((![A : produc1172664615on_val, B : produc1172664615on_val, A5 : set_Pr1189492743on_val]: ((member354538064on_val @ A @ (insert1971494647on_val @ B @ A5)) => ((~ ((A = B))) => (member354538064on_val @ A @ A5)))))). % insertE
thf(fact_202_insertE, axiom,
    ((![A : produc1777519579t_char, B : produc1777519579t_char, A5 : set_Pr2090064827t_char]: ((member958036996t_char @ A @ (insert1233103275t_char @ B @ A5)) => ((~ ((A = B))) => (member958036996t_char @ A @ A5)))))). % insertE
thf(fact_203_insertE, axiom,
    ((![A : produc1259892823t_char, B : produc1259892823t_char, A5 : set_Pr1344692407t_char]: ((member397625600t_char @ A @ (insert1354659367t_char @ B @ A5)) => ((~ ((A = B))) => (member397625600t_char @ A @ A5)))))). % insertE
thf(fact_204_insert__compr, axiom,
    ((insert1354671475t_char = (^[A6 : produc1257910179t_char]: (^[B7 : set_Pr164112643t_char]: (collec768236686t_char @ (^[X3 : produc1257910179t_char]: (((X3 = A6)) | ((member89690956t_char @ X3 @ B7)))))))))). % insert_compr
thf(fact_205_insert__compr, axiom,
    ((insert1971494647on_val = (^[A6 : produc1172664615on_val]: (^[B7 : set_Pr1189492743on_val]: (collec2055896722on_val @ (^[X3 : produc1172664615on_val]: (((X3 = A6)) | ((member354538064on_val @ X3 @ B7)))))))))). % insert_compr
thf(fact_206_insert__compr, axiom,
    ((insert1233103275t_char = (^[A6 : produc1777519579t_char]: (^[B7 : set_Pr2090064827t_char]: (collec178542150t_char @ (^[X3 : produc1777519579t_char]: (((X3 = A6)) | ((member958036996t_char @ X3 @ B7)))))))))). % insert_compr
thf(fact_207_insert__compr, axiom,
    ((insert1354659367t_char = (^[A6 : produc1259892823t_char]: (^[B7 : set_Pr1344692407t_char]: (collec1549347906t_char @ (^[X3 : produc1259892823t_char]: (((X3 = A6)) | ((member397625600t_char @ X3 @ B7)))))))))). % insert_compr
thf(fact_208_singleton__iff, axiom,
    ((![B : produc1257910179t_char, A : produc1257910179t_char]: ((member89690956t_char @ B @ (insert1354671475t_char @ A @ bot_bo346063215t_char)) = (B = A))))). % singleton_iff
thf(fact_209_singleton__iff, axiom,
    ((![B : produc1172664615on_val, A : produc1172664615on_val]: ((member354538064on_val @ B @ (insert1971494647on_val @ A @ bot_bo1575563891on_val)) = (B = A))))). % singleton_iff
thf(fact_210_singleton__iff, axiom,
    ((![B : produc1777519579t_char, A : produc1777519579t_char]: ((member958036996t_char @ B @ (insert1233103275t_char @ A @ bot_bo632162855t_char)) = (B = A))))). % singleton_iff
thf(fact_211_singleton__iff, axiom,
    ((![B : produc1259892823t_char, A : produc1259892823t_char]: ((member397625600t_char @ B @ (insert1354659367t_char @ A @ bot_bo956740899t_char)) = (B = A))))). % singleton_iff
thf(fact_212_singletonD, axiom,
    ((![B : produc1257910179t_char, A : produc1257910179t_char]: ((member89690956t_char @ B @ (insert1354671475t_char @ A @ bot_bo346063215t_char)) => (B = A))))). % singletonD
thf(fact_213_singletonD, axiom,
    ((![B : produc1172664615on_val, A : produc1172664615on_val]: ((member354538064on_val @ B @ (insert1971494647on_val @ A @ bot_bo1575563891on_val)) => (B = A))))). % singletonD
thf(fact_214_singletonD, axiom,
    ((![B : produc1777519579t_char, A : produc1777519579t_char]: ((member958036996t_char @ B @ (insert1233103275t_char @ A @ bot_bo632162855t_char)) => (B = A))))). % singletonD
thf(fact_215_singletonD, axiom,
    ((![B : produc1259892823t_char, A : produc1259892823t_char]: ((member397625600t_char @ B @ (insert1354659367t_char @ A @ bot_bo956740899t_char)) => (B = A))))). % singletonD
thf(fact_216_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, R2 : 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]: (R2 @ 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)) => ((R2 @ E_1 @ H_1 @ L_1 @ E5 @ H4 @ L4) => (R2 @ E_0 @ H_0 @ L_0 @ E5 @ H4 @ L4)))) => (R2 @ E2 @ H @ L @ E3 @ H2 @ L2))))))). % converse_rtrancl_induct_red
thf(fact_217_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_218_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_219_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_220_is__singletonI_H, axiom,
    ((![A5 : set_Pr164112643t_char]: ((~ ((A5 = bot_bo346063215t_char))) => ((![X6 : produc1257910179t_char, Y3 : produc1257910179t_char]: ((member89690956t_char @ X6 @ A5) => ((member89690956t_char @ Y3 @ A5) => (X6 = Y3)))) => (is_sin1522322583t_char @ A5)))))). % is_singletonI'
thf(fact_221_is__singletonI_H, axiom,
    ((![A5 : set_Pr1189492743on_val]: ((~ ((A5 = bot_bo1575563891on_val))) => ((![X6 : produc1172664615on_val, Y3 : produc1172664615on_val]: ((member354538064on_val @ X6 @ A5) => ((member354538064on_val @ Y3 @ A5) => (X6 = Y3)))) => (is_sin1880980507on_val @ A5)))))). % is_singletonI'
thf(fact_222_is__singletonI_H, axiom,
    ((![A5 : set_Pr2090064827t_char]: ((~ ((A5 = bot_bo632162855t_char))) => ((![X6 : produc1777519579t_char, Y3 : produc1777519579t_char]: ((member958036996t_char @ X6 @ A5) => ((member958036996t_char @ Y3 @ A5) => (X6 = Y3)))) => (is_sin1233863375t_char @ A5)))))). % is_singletonI'
thf(fact_223_is__singletonI_H, axiom,
    ((![A5 : set_Pr1344692407t_char]: ((~ ((A5 = bot_bo956740899t_char))) => ((![X6 : produc1259892823t_char, Y3 : produc1259892823t_char]: ((member397625600t_char @ X6 @ A5) => ((member397625600t_char @ Y3 @ A5) => (X6 = Y3)))) => (is_sin1700589899t_char @ A5)))))). % is_singletonI'
thf(fact_224_bot__empty__eq, axiom,
    ((bot_bo2060516910char_o = (^[X3 : produc1257910179t_char]: (member89690956t_char @ X3 @ bot_bo346063215t_char))))). % bot_empty_eq
thf(fact_225_bot__empty__eq, axiom,
    ((bot_bo824611882_val_o = (^[X3 : produc1172664615on_val]: (member354538064on_val @ X3 @ bot_bo1575563891on_val))))). % bot_empty_eq
thf(fact_226_bot__empty__eq, axiom,
    ((bot_bo659345782char_o = (^[X3 : produc1777519579t_char]: (member958036996t_char @ X3 @ bot_bo632162855t_char))))). % bot_empty_eq
thf(fact_227_bot__empty__eq, axiom,
    ((bot_bo453584762char_o = (^[X3 : produc1259892823t_char]: (member397625600t_char @ X3 @ bot_bo956740899t_char))))). % bot_empty_eq
thf(fact_228_bot__empty__eq2, axiom,
    ((bot_bo1918180954_val_o = (^[X3 : produc1097884484on_val]: (^[Y4 : produc1097884484on_val]: (member354538064on_val @ (produc1069526295on_val @ X3 @ Y4) @ bot_bo1575563891on_val)))))). % bot_empty_eq2
thf(fact_229_bot__empty__eq2, axiom,
    ((bot_bo1672137852char_o = (^[X3 : list_char]: (^[Y4 : produc1451990293t_char]: (member397625600t_char @ (produc1238538255t_char @ X3 @ Y4) @ bot_bo956740899t_char)))))). % bot_empty_eq2
thf(fact_230_bot__empty__eq2, axiom,
    ((bot_bo1825738872char_o = (^[X3 : list_char]: (^[Y4 : produc1675325977t_char]: (member958036996t_char @ (produc1548560403t_char @ X3 @ Y4) @ bot_bo632162855t_char)))))). % bot_empty_eq2
thf(fact_231_bot__empty__eq2, axiom,
    ((bot_bo1359030064char_o = (^[X3 : list_char]: (^[Y4 : list_char]: (member89690956t_char @ (produc1304532571t_char @ X3 @ Y4) @ bot_bo346063215t_char)))))). % bot_empty_eq2
thf(fact_232_bot__empty__eq2, axiom,
    ((bot_bo1821121046char_o = (^[X3 : list_list_char]: (^[Y4 : exp_list_char]: (member605104934t_char @ (produc713467969t_char @ X3 @ Y4) @ bot_bo1987439961t_char)))))). % bot_empty_eq2
thf(fact_233_bot__empty__eq2, axiom,
    ((bot_bo1487430909_val_o = (^[X3 : exp_list_char]: (^[Y4 : produc515445032on_val]: (member1888679917on_val @ (produc2023458740on_val @ X3 @ Y4) @ bot_bo1575411088on_val)))))). % bot_empty_eq2
thf(fact_234_bot__empty__eq2, axiom,
    ((bot_bo1949275371_val_o = (^[X3 : nat > option2118145160on_val]: (^[Y4 : list_char > option_val]: (member652041809on_val @ (produc52622304on_val @ X3 @ Y4) @ bot_bo923954676on_val)))))). % bot_empty_eq2
thf(fact_235_pred__equals__eq2, axiom,
    ((![R2 : set_Pr1189492743on_val, S : set_Pr1189492743on_val]: (((^[X3 : produc1097884484on_val]: (^[Y4 : produc1097884484on_val]: (member354538064on_val @ (produc1069526295on_val @ X3 @ Y4) @ R2))) = (^[X3 : produc1097884484on_val]: (^[Y4 : produc1097884484on_val]: (member354538064on_val @ (produc1069526295on_val @ X3 @ Y4) @ S)))) = (R2 = S))))). % pred_equals_eq2
thf(fact_236_pred__equals__eq2, axiom,
    ((![R2 : set_Pr1344692407t_char, S : set_Pr1344692407t_char]: (((^[X3 : list_char]: (^[Y4 : produc1451990293t_char]: (member397625600t_char @ (produc1238538255t_char @ X3 @ Y4) @ R2))) = (^[X3 : list_char]: (^[Y4 : produc1451990293t_char]: (member397625600t_char @ (produc1238538255t_char @ X3 @ Y4) @ S)))) = (R2 = S))))). % pred_equals_eq2
thf(fact_237_pred__equals__eq2, axiom,
    ((![R2 : set_Pr2090064827t_char, S : set_Pr2090064827t_char]: (((^[X3 : list_char]: (^[Y4 : produc1675325977t_char]: (member958036996t_char @ (produc1548560403t_char @ X3 @ Y4) @ R2))) = (^[X3 : list_char]: (^[Y4 : produc1675325977t_char]: (member958036996t_char @ (produc1548560403t_char @ X3 @ Y4) @ S)))) = (R2 = S))))). % pred_equals_eq2
thf(fact_238_pred__equals__eq2, axiom,
    ((![R2 : set_Pr164112643t_char, S : set_Pr164112643t_char]: (((^[X3 : list_char]: (^[Y4 : list_char]: (member89690956t_char @ (produc1304532571t_char @ X3 @ Y4) @ R2))) = (^[X3 : list_char]: (^[Y4 : list_char]: (member89690956t_char @ (produc1304532571t_char @ X3 @ Y4) @ S)))) = (R2 = S))))). % pred_equals_eq2
thf(fact_239_pred__equals__eq2, axiom,
    ((![R2 : set_Pr2063914181t_char, S : set_Pr2063914181t_char]: (((^[X3 : list_list_char]: (^[Y4 : exp_list_char]: (member605104934t_char @ (produc713467969t_char @ X3 @ Y4) @ R2))) = (^[X3 : list_list_char]: (^[Y4 : exp_list_char]: (member605104934t_char @ (produc713467969t_char @ X3 @ Y4) @ S)))) = (R2 = S))))). % pred_equals_eq2
thf(fact_240_pred__equals__eq2, axiom,
    ((![R2 : set_Pr556513572on_val, S : set_Pr556513572on_val]: (((^[X3 : exp_list_char]: (^[Y4 : produc515445032on_val]: (member1888679917on_val @ (produc2023458740on_val @ X3 @ Y4) @ R2))) = (^[X3 : exp_list_char]: (^[Y4 : produc515445032on_val]: (member1888679917on_val @ (produc2023458740on_val @ X3 @ Y4) @ S)))) = (R2 = S))))). % pred_equals_eq2
thf(fact_241_pred__equals__eq2, axiom,
    ((![R2 : set_Pr723149704on_val, S : set_Pr723149704on_val]: (((^[X3 : nat > option2118145160on_val]: (^[Y4 : list_char > option_val]: (member652041809on_val @ (produc52622304on_val @ X3 @ Y4) @ R2))) = (^[X3 : nat > option2118145160on_val]: (^[Y4 : list_char > option_val]: (member652041809on_val @ (produc52622304on_val @ X3 @ Y4) @ S)))) = (R2 = S))))). % pred_equals_eq2
thf(fact_242_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_243_Call__lemma, axiom,
    ((![P : list_P1234162913t_char, C2 : list_char, M : list_char, Ts : list_ty, T2 : ty, M2 : produc1294284815t_char, D : list_char, C : list_char, Wf_md : list_P1234162913t_char > list_char > produc1259892823t_char > $o]: ((method297381284t_char @ P @ C2 @ M @ Ts @ T2 @ M2 @ D) => ((member89690956t_char @ (produc1304532571t_char @ C @ C2) @ (transi1879726366t_char @ (subcls880436836t_char @ P))) => ((wf_pro1229751607t_char @ Wf_md @ P) => (?[D5 : list_char, Ts3 : list_ty, T : ty, M4 : produc1294284815t_char]: ((method297381284t_char @ P @ C @ M @ Ts3 @ T @ M4 @ D5) & ((list_all2_ty_ty @ (widen_917054840t_char @ P) @ Ts @ Ts3) & ((widen_917054840t_char @ P @ T @ T2) & ((member89690956t_char @ (produc1304532571t_char @ C @ D5) @ (transi1879726366t_char @ (subcls880436836t_char @ P))) & ((is_typ250416522t_char @ P @ T) & ((![X7 : ty]: ((member_ty @ X7 @ (set_ty2 @ Ts3)) => (is_typ250416522t_char @ P @ X7))) & (Wf_md @ P @ D5 @ (produc1238538255t_char @ M @ (produc1730359111t_char @ Ts3 @ (produc248075743t_char @ T @ M4))))))))))))))))). % Call_lemma
thf(fact_244_list_Orel__refl__strong, axiom,
    ((![X4 : list_P942933805on_val, Ra : produc1172664615on_val > produc1172664615on_val > $o]: ((![Z : produc1172664615on_val]: ((member354538064on_val @ Z @ (set_Pr348738748on_val @ X4)) => (Ra @ Z @ Z))) => (list_a1344266055on_val @ Ra @ X4 @ X4))))). % list.rel_refl_strong
thf(fact_245_list_Orel__refl__strong, axiom,
    ((![X4 : list_P1234162913t_char, Ra : produc1777519579t_char > produc1777519579t_char > $o]: ((![Z : produc1777519579t_char]: ((member958036996t_char @ Z @ (set_Pr1611739760t_char @ X4)) => (Ra @ Z @ Z))) => (list_a364623943t_char @ Ra @ X4 @ X4))))). % list.rel_refl_strong
thf(fact_246_list_Orel__refl__strong, axiom,
    ((![X4 : list_P1653548253t_char, Ra : produc1259892823t_char > produc1259892823t_char > $o]: ((![Z : produc1259892823t_char]: ((member397625600t_char @ Z @ (set_Pr1045701996t_char @ X4)) => (Ra @ Z @ Z))) => (list_a1436933959t_char @ Ra @ X4 @ X4))))). % list.rel_refl_strong
thf(fact_247_list_Orel__refl__strong, axiom,
    ((![X4 : list_ty, Ra : ty > ty > $o]: ((![Z : ty]: ((member_ty @ Z @ (set_ty2 @ X4)) => (Ra @ Z @ Z))) => (list_all2_ty_ty @ Ra @ X4 @ X4))))). % list.rel_refl_strong
thf(fact_248_wf__J__prog__wf__J__mdecl, axiom,
    ((![P : list_P1234162913t_char, C2 : list_char, D : list_char, Fds : list_P1126587903har_ty, Mths : list_P1653548253t_char, Jmdcl : produc1259892823t_char]: ((wf_pro1229751607t_char @ wf_J_mdecl @ P) => ((member958036996t_char @ (produc1548560403t_char @ C2 @ (produc1972337867t_char @ D @ (produc1107711029t_char @ Fds @ Mths))) @ (set_Pr1611739760t_char @ P)) => ((member397625600t_char @ Jmdcl @ (set_Pr1045701996t_char @ Mths)) => (wf_J_mdecl @ P @ C2 @ Jmdcl))))))). % wf_J_prog_wf_J_mdecl

% 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 @ t))))).
