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    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_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_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__List__Olist_It__String__Ochar_J_Mt__Type__Oty_J, type,
    member325880354har_ty : produc2086909177har_ty > set_Pr349050585har_ty > $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__List__Olist_It__String__Ochar_J_J_Mt__Type__Oty_J, type,
    member1618759584har_ty : produc954616457har_ty > set_Pr1278374975har_ty > $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__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_Mt__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, type,
    member1263191824t_char : produc1938415079t_char > set_Pr1996500167t_char > $o).
thf(sy_c_member_001t__Product____Type__Oprod_It__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_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,
    member384501940t_char : produc985840395t_char > set_Pr1449697899t_char > $o).
thf(sy_c_member_001t__Product____Type__Oprod_It__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_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, type,
    member1723509520t_char : produc89475815t_char > set_Pr236946631t_char > $o).
thf(sy_c_member_001t__Type__Oty, type,
    member_ty : ty > set_ty > $o).
thf(sy_v_C_H____, type,
    c : list_char).
thf(sy_v_C____, type,
    c2 : list_char).
thf(sy_v_D____, type,
    d : list_char).
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_pns____, type,
    pns : list_list_char).
thf(sy_v_thesis____, type,
    thesis : $o).

% Relevant facts (187)
thf(fact_0_subs, axiom,
    ((list_all2_ty_ty @ (widen_917054840t_char @ p) @ us @ ts))). % subs
thf(fact_1_local_Owf, axiom,
    ((wf_pro1229751607t_char @ wf_J_mdecl @ p))). % local.wf
thf(fact_2_method, axiom,
    ((method297381284t_char @ p @ c2 @ m @ ts @ t @ (produc713467969t_char @ pns @ body) @ d))). % method
thf(fact_3__092_060open_062_092_060exists_062D_H_ATs_H_AT_H_Am_H_O_AP_A_092_060turnstile_062_AC_H_Asees_AM_058_ATs_H_092_060rightarrow_062T_H_A_061_Am_H_Ain_AD_H_A_092_060and_062_AP_A_092_060turnstile_062_ATs_A_091_092_060le_062_093_ATs_H_A_092_060and_062_AP_A_092_060turnstile_062_AT_H_A_092_060le_062_AT_A_092_060and_062_AP_A_092_060turnstile_062_AC_H_A_092_060preceq_062_092_060_094sup_062_K_AD_H_A_092_060and_062_Ais__type_AP_AT_H_A_092_060and_062_A_I_092_060forall_062T_092_060in_062set_ATs_H_O_Ais__type_AP_AT_J_A_092_060and_062_Awf__J__mdecl_AP_AD_H_A_IM_M_ATs_H_M_AT_H_M_Am_H_J_092_060close_062, axiom,
    ((?[D : list_char, Ts : list_ty, T : ty, M : produc1294284815t_char]: ((method297381284t_char @ p @ c @ m @ Ts @ T @ M @ D) & ((list_all2_ty_ty @ (widen_917054840t_char @ p) @ ts @ Ts) & ((widen_917054840t_char @ p @ T @ t) & ((member89690956t_char @ (produc1304532571t_char @ c @ D) @ (transi1879726366t_char @ (subcls880436836t_char @ p))) & ((is_typ250416522t_char @ p @ T) & ((![X : ty]: ((member_ty @ X @ (set_ty2 @ Ts)) => (is_typ250416522t_char @ p @ X))) & (wf_J_mdecl @ p @ D @ (produc1238538255t_char @ m @ (produc1730359111t_char @ Ts @ (produc248075743t_char @ T @ M))))))))))))). % \<open>\<exists>D' Ts' T' m'. P \<turnstile> C' sees M: Ts'\<rightarrow>T' = m' in D' \<and> P \<turnstile> Ts [\<le>] Ts' \<and> P \<turnstile> T' \<le> T \<and> P \<turnstile> C' \<preceq>\<^sup>* D' \<and> is_type P T' \<and> (\<forall>T\<in>set Ts'. is_type P T) \<and> wf_J_mdecl P D' (M, Ts', T', m')\<close>
thf(fact_4_widens__refl, axiom,
    ((![P : list_P1234162913t_char, Xs : list_ty]: (list_all2_ty_ty @ (widen_917054840t_char @ P) @ Xs @ Xs)))). % widens_refl
thf(fact_5__Csubclass_C, axiom,
    ((member89690956t_char @ (produc1304532571t_char @ c @ c2) @ (transi1879726366t_char @ (subcls880436836t_char @ p))))). % "subclass"
thf(fact_6_prod_Oinject, axiom,
    ((![X1 : list_char, X2 : produc1451990293t_char, Y1 : list_char, Y2 : produc1451990293t_char]: (((produc1238538255t_char @ X1 @ X2) = (produc1238538255t_char @ Y1 @ Y2)) = (((X1 = Y1)) & ((X2 = Y2))))))). % prod.inject
thf(fact_7_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_8_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_9_prod_Oinject, axiom,
    ((![X1 : list_ty, X2 : produc1490933927t_char, Y1 : list_ty, Y2 : produc1490933927t_char]: (((produc1730359111t_char @ X1 @ X2) = (produc1730359111t_char @ Y1 @ Y2)) = (((X1 = Y1)) & ((X2 = Y2))))))). % prod.inject
thf(fact_10_prod_Oinject, axiom,
    ((![X1 : ty, X2 : produc1294284815t_char, Y1 : ty, Y2 : produc1294284815t_char]: (((produc248075743t_char @ X1 @ X2) = (produc248075743t_char @ Y1 @ Y2)) = (((X1 = Y1)) & ((X2 = Y2))))))). % prod.inject
thf(fact_11_old_Oprod_Oinject, axiom,
    ((![A : list_char, B : produc1451990293t_char, A2 : list_char, B2 : produc1451990293t_char]: (((produc1238538255t_char @ A @ B) = (produc1238538255t_char @ A2 @ B2)) = (((A = A2)) & ((B = B2))))))). % old.prod.inject
thf(fact_12_old_Oprod_Oinject, axiom,
    ((![A : list_char, B : list_char, A2 : list_char, B2 : list_char]: (((produc1304532571t_char @ A @ B) = (produc1304532571t_char @ A2 @ B2)) = (((A = A2)) & ((B = B2))))))). % old.prod.inject
thf(fact_13_old_Oprod_Oinject, axiom,
    ((![A : list_list_char, B : exp_list_char, A2 : list_list_char, B2 : exp_list_char]: (((produc713467969t_char @ A @ B) = (produc713467969t_char @ A2 @ B2)) = (((A = A2)) & ((B = B2))))))). % old.prod.inject
thf(fact_14_old_Oprod_Oinject, axiom,
    ((![A : list_ty, B : produc1490933927t_char, A2 : list_ty, B2 : produc1490933927t_char]: (((produc1730359111t_char @ A @ B) = (produc1730359111t_char @ A2 @ B2)) = (((A = A2)) & ((B = B2))))))). % old.prod.inject
thf(fact_15_old_Oprod_Oinject, axiom,
    ((![A : ty, B : produc1294284815t_char, A2 : ty, B2 : produc1294284815t_char]: (((produc248075743t_char @ A @ B) = (produc248075743t_char @ A2 @ B2)) = (((A = A2)) & ((B = B2))))))). % old.prod.inject
thf(fact_16_widens__trans, axiom,
    ((![P : list_P1234162913t_char, Ss : list_ty, Ts2 : list_ty, Us : list_ty]: ((list_all2_ty_ty @ (widen_917054840t_char @ P) @ Ss @ Ts2) => ((list_all2_ty_ty @ (widen_917054840t_char @ P) @ Ts2 @ Us) => (list_all2_ty_ty @ (widen_917054840t_char @ P) @ Ss @ Us)))))). % widens_trans
thf(fact_17_UClass, axiom,
    ((u = (class @ c)))). % UClass
thf(fact_18_sees__method__fun, axiom,
    ((![P : list_P1234162913t_char, C : list_char, M2 : list_char, TS : list_ty, T2 : ty, M3 : produc1294284815t_char, D2 : list_char, TS2 : list_ty, T3 : ty, M4 : produc1294284815t_char, D3 : list_char]: ((method297381284t_char @ P @ C @ M2 @ TS @ T2 @ M3 @ D2) => ((method297381284t_char @ P @ C @ M2 @ TS2 @ T3 @ M4 @ D3) => ((TS2 = TS) & ((T3 = T2) & ((M4 = M3) & (D3 = D2))))))))). % sees_method_fun
thf(fact_19_sees__method__idemp, axiom,
    ((![P : list_P1234162913t_char, C : list_char, M2 : list_char, Ts2 : list_ty, T2 : ty, M3 : produc1294284815t_char, D2 : list_char]: ((method297381284t_char @ P @ C @ M2 @ Ts2 @ T2 @ M3 @ D2) => (method297381284t_char @ P @ D2 @ M2 @ Ts2 @ T2 @ M3 @ D2))))). % sees_method_idemp
thf(fact_20_widen__trans, axiom,
    ((![P : list_P1234162913t_char, S : ty, U : ty, T2 : ty]: ((widen_917054840t_char @ P @ S @ U) => ((widen_917054840t_char @ P @ U @ T2) => (widen_917054840t_char @ P @ S @ T2)))))). % widen_trans
thf(fact_21_widen__refl, axiom,
    ((![P : list_P1234162913t_char, T2 : ty]: (widen_917054840t_char @ P @ T2 @ T2)))). % widen_refl
thf(fact_22_UsubC, axiom,
    ((widen_917054840t_char @ p @ u @ (class @ c2)))). % UsubC
thf(fact_23_Class__widen__Class, axiom,
    ((![P : list_P1234162913t_char, C : list_char, D2 : list_char]: ((widen_917054840t_char @ P @ (class @ C) @ (class @ D2)) = (member89690956t_char @ (produc1304532571t_char @ C @ D2) @ (transi1879726366t_char @ (subcls880436836t_char @ P))))))). % Class_widen_Class
thf(fact_24_widen__subcls, axiom,
    ((![C : list_char, D2 : list_char, P : list_P1234162913t_char]: ((member89690956t_char @ (produc1304532571t_char @ C @ D2) @ (transi1879726366t_char @ (subcls880436836t_char @ P))) => (widen_917054840t_char @ P @ (class @ C) @ (class @ D2)))))). % widen_subcls
thf(fact_25_Class__widen, axiom,
    ((![P : list_P1234162913t_char, C : list_char, T2 : ty]: ((widen_917054840t_char @ P @ (class @ C) @ T2) => (?[D4 : list_char]: (T2 = (class @ D4))))))). % Class_widen
thf(fact_26_sees__method__decl__above, axiom,
    ((![P : list_P1234162913t_char, C : list_char, M2 : list_char, Ts2 : list_ty, T2 : ty, M3 : produc1294284815t_char, D2 : list_char]: ((method297381284t_char @ P @ C @ M2 @ Ts2 @ T2 @ M3 @ D2) => (member89690956t_char @ (produc1304532571t_char @ C @ D2) @ (transi1879726366t_char @ (subcls880436836t_char @ P))))))). % sees_method_decl_above
thf(fact_27_sees__method__decl__mono, axiom,
    ((![C2 : list_char, C : list_char, P : list_P1234162913t_char, M2 : list_char, Ts2 : list_ty, T2 : ty, M3 : produc1294284815t_char, D2 : list_char, Ts3 : list_ty, T3 : ty, M4 : produc1294284815t_char, D3 : list_char]: ((member89690956t_char @ (produc1304532571t_char @ C2 @ C) @ (transi1879726366t_char @ (subcls880436836t_char @ P))) => ((method297381284t_char @ P @ C @ M2 @ Ts2 @ T2 @ M3 @ D2) => ((method297381284t_char @ P @ C2 @ M2 @ Ts3 @ T3 @ M4 @ D3) => (member89690956t_char @ (produc1304532571t_char @ D3 @ D2) @ (transi1879726366t_char @ (subcls880436836t_char @ P))))))))). % sees_method_decl_mono
thf(fact_28_old_Oprod_Oinducts, axiom,
    ((![P : produc1259892823t_char > $o, Prod : produc1259892823t_char]: ((![A3 : list_char, B3 : produc1451990293t_char]: (P @ (produc1238538255t_char @ A3 @ B3))) => (P @ Prod))))). % old.prod.inducts
thf(fact_29_old_Oprod_Oinducts, axiom,
    ((![P : produc1257910179t_char > $o, Prod : produc1257910179t_char]: ((![A3 : list_char, B3 : list_char]: (P @ (produc1304532571t_char @ A3 @ B3))) => (P @ Prod))))). % old.prod.inducts
thf(fact_30_old_Oprod_Oinducts, axiom,
    ((![P : produc1294284815t_char > $o, Prod : produc1294284815t_char]: ((![A3 : list_list_char, B3 : exp_list_char]: (P @ (produc713467969t_char @ A3 @ B3))) => (P @ Prod))))). % old.prod.inducts
thf(fact_31_old_Oprod_Oinducts, axiom,
    ((![P : produc1451990293t_char > $o, Prod : produc1451990293t_char]: ((![A3 : list_ty, B3 : produc1490933927t_char]: (P @ (produc1730359111t_char @ A3 @ B3))) => (P @ Prod))))). % old.prod.inducts
thf(fact_32_old_Oprod_Oinducts, axiom,
    ((![P : produc1490933927t_char > $o, Prod : produc1490933927t_char]: ((![A3 : ty, B3 : produc1294284815t_char]: (P @ (produc248075743t_char @ A3 @ B3))) => (P @ Prod))))). % old.prod.inducts
thf(fact_33_old_Oprod_Oexhaust, axiom,
    ((![Y : produc1259892823t_char]: (~ ((![A3 : list_char, B3 : produc1451990293t_char]: (~ ((Y = (produc1238538255t_char @ A3 @ B3)))))))))). % old.prod.exhaust
thf(fact_34_old_Oprod_Oexhaust, axiom,
    ((![Y : produc1257910179t_char]: (~ ((![A3 : list_char, B3 : list_char]: (~ ((Y = (produc1304532571t_char @ A3 @ B3)))))))))). % old.prod.exhaust
thf(fact_35_old_Oprod_Oexhaust, axiom,
    ((![Y : produc1294284815t_char]: (~ ((![A3 : list_list_char, B3 : exp_list_char]: (~ ((Y = (produc713467969t_char @ A3 @ B3)))))))))). % old.prod.exhaust
thf(fact_36_old_Oprod_Oexhaust, axiom,
    ((![Y : produc1451990293t_char]: (~ ((![A3 : list_ty, B3 : produc1490933927t_char]: (~ ((Y = (produc1730359111t_char @ A3 @ B3)))))))))). % old.prod.exhaust
thf(fact_37_old_Oprod_Oexhaust, axiom,
    ((![Y : produc1490933927t_char]: (~ ((![A3 : ty, B3 : produc1294284815t_char]: (~ ((Y = (produc248075743t_char @ A3 @ B3)))))))))). % old.prod.exhaust
thf(fact_38_prod__induct5, axiom,
    ((![P : produc1259892823t_char > $o, X3 : produc1259892823t_char]: ((![A3 : list_char, B3 : list_ty, C3 : ty, D5 : list_list_char, E : exp_list_char]: (P @ (produc1238538255t_char @ A3 @ (produc1730359111t_char @ B3 @ (produc248075743t_char @ C3 @ (produc713467969t_char @ D5 @ E)))))) => (P @ X3))))). % prod_induct5
thf(fact_39_prod__induct4, axiom,
    ((![P : produc1259892823t_char > $o, X3 : produc1259892823t_char]: ((![A3 : list_char, B3 : list_ty, C3 : ty, D5 : produc1294284815t_char]: (P @ (produc1238538255t_char @ A3 @ (produc1730359111t_char @ B3 @ (produc248075743t_char @ C3 @ D5))))) => (P @ X3))))). % prod_induct4
thf(fact_40_prod__induct4, axiom,
    ((![P : produc1451990293t_char > $o, X3 : produc1451990293t_char]: ((![A3 : list_ty, B3 : ty, C3 : list_list_char, D5 : exp_list_char]: (P @ (produc1730359111t_char @ A3 @ (produc248075743t_char @ B3 @ (produc713467969t_char @ C3 @ D5))))) => (P @ X3))))). % prod_induct4
thf(fact_41_prod__induct3, axiom,
    ((![P : produc1259892823t_char > $o, X3 : produc1259892823t_char]: ((![A3 : list_char, B3 : list_ty, C3 : produc1490933927t_char]: (P @ (produc1238538255t_char @ A3 @ (produc1730359111t_char @ B3 @ C3)))) => (P @ X3))))). % prod_induct3
thf(fact_42_prod__induct3, axiom,
    ((![P : produc1451990293t_char > $o, X3 : produc1451990293t_char]: ((![A3 : list_ty, B3 : ty, C3 : produc1294284815t_char]: (P @ (produc1730359111t_char @ A3 @ (produc248075743t_char @ B3 @ C3)))) => (P @ X3))))). % prod_induct3
thf(fact_43_prod__induct3, axiom,
    ((![P : produc1490933927t_char > $o, X3 : produc1490933927t_char]: ((![A3 : ty, B3 : list_list_char, C3 : exp_list_char]: (P @ (produc248075743t_char @ A3 @ (produc713467969t_char @ B3 @ C3)))) => (P @ X3))))). % prod_induct3
thf(fact_44_prod__cases5, axiom,
    ((![Y : produc1259892823t_char]: (~ ((![A3 : list_char, B3 : list_ty, C3 : ty, D5 : list_list_char, E : exp_list_char]: (~ ((Y = (produc1238538255t_char @ A3 @ (produc1730359111t_char @ B3 @ (produc248075743t_char @ C3 @ (produc713467969t_char @ D5 @ E))))))))))))). % prod_cases5
thf(fact_45_prod__cases4, axiom,
    ((![Y : produc1259892823t_char]: (~ ((![A3 : list_char, B3 : list_ty, C3 : ty, D5 : produc1294284815t_char]: (~ ((Y = (produc1238538255t_char @ A3 @ (produc1730359111t_char @ B3 @ (produc248075743t_char @ C3 @ D5)))))))))))). % prod_cases4
thf(fact_46_prod__cases4, axiom,
    ((![Y : produc1451990293t_char]: (~ ((![A3 : list_ty, B3 : ty, C3 : list_list_char, D5 : exp_list_char]: (~ ((Y = (produc1730359111t_char @ A3 @ (produc248075743t_char @ B3 @ (produc713467969t_char @ C3 @ D5)))))))))))). % prod_cases4
thf(fact_47_prod__cases3, axiom,
    ((![Y : produc1259892823t_char]: (~ ((![A3 : list_char, B3 : list_ty, C3 : produc1490933927t_char]: (~ ((Y = (produc1238538255t_char @ A3 @ (produc1730359111t_char @ B3 @ C3))))))))))). % prod_cases3
thf(fact_48_prod__cases3, axiom,
    ((![Y : produc1451990293t_char]: (~ ((![A3 : list_ty, B3 : ty, C3 : produc1294284815t_char]: (~ ((Y = (produc1730359111t_char @ A3 @ (produc248075743t_char @ B3 @ C3))))))))))). % prod_cases3
thf(fact_49_prod__cases3, axiom,
    ((![Y : produc1490933927t_char]: (~ ((![A3 : ty, B3 : list_list_char, C3 : exp_list_char]: (~ ((Y = (produc248075743t_char @ A3 @ (produc713467969t_char @ B3 @ C3))))))))))). % prod_cases3
thf(fact_50_Pair__inject, axiom,
    ((![A : list_char, B : produc1451990293t_char, A2 : list_char, B2 : produc1451990293t_char]: (((produc1238538255t_char @ A @ B) = (produc1238538255t_char @ A2 @ B2)) => (~ (((A = A2) => (~ ((B = B2)))))))))). % Pair_inject
thf(fact_51_Pair__inject, axiom,
    ((![A : list_char, B : list_char, A2 : list_char, B2 : list_char]: (((produc1304532571t_char @ A @ B) = (produc1304532571t_char @ A2 @ B2)) => (~ (((A = A2) => (~ ((B = B2)))))))))). % Pair_inject
thf(fact_52_Pair__inject, axiom,
    ((![A : list_list_char, B : exp_list_char, A2 : list_list_char, B2 : exp_list_char]: (((produc713467969t_char @ A @ B) = (produc713467969t_char @ A2 @ B2)) => (~ (((A = A2) => (~ ((B = B2)))))))))). % Pair_inject
thf(fact_53_Pair__inject, axiom,
    ((![A : list_ty, B : produc1490933927t_char, A2 : list_ty, B2 : produc1490933927t_char]: (((produc1730359111t_char @ A @ B) = (produc1730359111t_char @ A2 @ B2)) => (~ (((A = A2) => (~ ((B = B2)))))))))). % Pair_inject
thf(fact_54_Pair__inject, axiom,
    ((![A : ty, B : produc1294284815t_char, A2 : ty, B2 : produc1294284815t_char]: (((produc248075743t_char @ A @ B) = (produc248075743t_char @ A2 @ B2)) => (~ (((A = A2) => (~ ((B = B2)))))))))). % Pair_inject
thf(fact_55_prod__cases, axiom,
    ((![P : produc1259892823t_char > $o, P2 : produc1259892823t_char]: ((![A3 : list_char, B3 : produc1451990293t_char]: (P @ (produc1238538255t_char @ A3 @ B3))) => (P @ P2))))). % prod_cases
thf(fact_56_prod__cases, axiom,
    ((![P : produc1257910179t_char > $o, P2 : produc1257910179t_char]: ((![A3 : list_char, B3 : list_char]: (P @ (produc1304532571t_char @ A3 @ B3))) => (P @ P2))))). % prod_cases
thf(fact_57_prod__cases, axiom,
    ((![P : produc1294284815t_char > $o, P2 : produc1294284815t_char]: ((![A3 : list_list_char, B3 : exp_list_char]: (P @ (produc713467969t_char @ A3 @ B3))) => (P @ P2))))). % prod_cases
thf(fact_58_prod__cases, axiom,
    ((![P : produc1451990293t_char > $o, P2 : produc1451990293t_char]: ((![A3 : list_ty, B3 : produc1490933927t_char]: (P @ (produc1730359111t_char @ A3 @ B3))) => (P @ P2))))). % prod_cases
thf(fact_59_prod__cases, axiom,
    ((![P : produc1490933927t_char > $o, P2 : produc1490933927t_char]: ((![A3 : ty, B3 : produc1294284815t_char]: (P @ (produc248075743t_char @ A3 @ B3))) => (P @ P2))))). % prod_cases
thf(fact_60_surj__pair, axiom,
    ((![P2 : produc1259892823t_char]: (?[X4 : list_char, Y3 : produc1451990293t_char]: (P2 = (produc1238538255t_char @ X4 @ Y3)))))). % surj_pair
thf(fact_61_surj__pair, axiom,
    ((![P2 : produc1257910179t_char]: (?[X4 : list_char, Y3 : list_char]: (P2 = (produc1304532571t_char @ X4 @ Y3)))))). % surj_pair
thf(fact_62_surj__pair, axiom,
    ((![P2 : produc1294284815t_char]: (?[X4 : list_list_char, Y3 : exp_list_char]: (P2 = (produc713467969t_char @ X4 @ Y3)))))). % surj_pair
thf(fact_63_surj__pair, axiom,
    ((![P2 : produc1451990293t_char]: (?[X4 : list_ty, Y3 : produc1490933927t_char]: (P2 = (produc1730359111t_char @ X4 @ Y3)))))). % surj_pair
thf(fact_64_surj__pair, axiom,
    ((![P2 : produc1490933927t_char]: (?[X4 : ty, Y3 : produc1294284815t_char]: (P2 = (produc248075743t_char @ X4 @ Y3)))))). % surj_pair
thf(fact_65_Call__lemma, axiom,
    ((![P : list_P1234162913t_char, C : list_char, M2 : list_char, Ts2 : list_ty, T2 : ty, M3 : produc1294284815t_char, D2 : list_char, C2 : list_char, Wf_md : list_P1234162913t_char > list_char > produc1259892823t_char > $o]: ((method297381284t_char @ P @ C @ M2 @ Ts2 @ T2 @ M3 @ D2) => ((member89690956t_char @ (produc1304532571t_char @ C2 @ C) @ (transi1879726366t_char @ (subcls880436836t_char @ P))) => ((wf_pro1229751607t_char @ Wf_md @ P) => (?[D : list_char, Ts : list_ty, T : ty, M : produc1294284815t_char]: ((method297381284t_char @ P @ C2 @ M2 @ Ts @ T @ M @ D) & ((list_all2_ty_ty @ (widen_917054840t_char @ P) @ Ts2 @ Ts) & ((widen_917054840t_char @ P @ T @ T2) & ((member89690956t_char @ (produc1304532571t_char @ C2 @ D) @ (transi1879726366t_char @ (subcls880436836t_char @ P))) & ((is_typ250416522t_char @ P @ T) & ((![X : ty]: ((member_ty @ X @ (set_ty2 @ Ts)) => (is_typ250416522t_char @ P @ X))) & (Wf_md @ P @ D @ (produc1238538255t_char @ M2 @ (produc1730359111t_char @ Ts @ (produc248075743t_char @ T @ M))))))))))))))))). % Call_lemma
thf(fact_66_method__def2, axiom,
    ((![P : list_P1234162913t_char, C : list_char, M2 : list_char, Ts2 : list_ty, T2 : ty, M3 : produc1294284815t_char, D2 : list_char]: ((method297381284t_char @ P @ C @ M2 @ Ts2 @ T2 @ M3 @ D2) => ((method667690372t_char @ P @ C @ M2) = (produc1238538255t_char @ D2 @ (produc1730359111t_char @ Ts2 @ (produc248075743t_char @ T2 @ M3)))))))). % method_def2
thf(fact_67_sees__method__mono2, axiom,
    ((![C2 : list_char, C : list_char, P : list_P1234162913t_char, Wf_md : list_P1234162913t_char > list_char > produc1259892823t_char > $o, M2 : list_char, Ts2 : list_ty, T2 : ty, M3 : produc1294284815t_char, D2 : list_char, Ts3 : list_ty, T3 : ty, M4 : produc1294284815t_char, D3 : list_char]: ((member89690956t_char @ (produc1304532571t_char @ C2 @ C) @ (transi1879726366t_char @ (subcls880436836t_char @ P))) => ((wf_pro1229751607t_char @ Wf_md @ P) => ((method297381284t_char @ P @ C @ M2 @ Ts2 @ T2 @ M3 @ D2) => ((method297381284t_char @ P @ C2 @ M2 @ Ts3 @ T3 @ M4 @ D3) => ((list_all2_ty_ty @ (widen_917054840t_char @ P) @ Ts2 @ Ts3) & (widen_917054840t_char @ P @ T3 @ T2))))))))). % sees_method_mono2
thf(fact_68_sees__method__mono, axiom,
    ((![C2 : list_char, C : list_char, P : list_P1234162913t_char, Wf_md : list_P1234162913t_char > list_char > produc1259892823t_char > $o, M2 : list_char, Ts2 : list_ty, T2 : ty, M3 : produc1294284815t_char, D2 : list_char]: ((member89690956t_char @ (produc1304532571t_char @ C2 @ C) @ (transi1879726366t_char @ (subcls880436836t_char @ P))) => ((wf_pro1229751607t_char @ Wf_md @ P) => ((method297381284t_char @ P @ C @ M2 @ Ts2 @ T2 @ M3 @ D2) => (?[D : list_char, Ts : list_ty, T : ty, M : produc1294284815t_char]: ((method297381284t_char @ P @ C2 @ M2 @ Ts @ T @ M @ D) & ((list_all2_ty_ty @ (widen_917054840t_char @ P) @ Ts2 @ Ts) & (widen_917054840t_char @ P @ T @ T2)))))))))). % sees_method_mono
thf(fact_69_sees__wf__mdecl, axiom,
    ((![Wf_md : list_P1234162913t_char > list_char > produc1259892823t_char > $o, P : list_P1234162913t_char, C : list_char, M2 : list_char, Ts2 : list_ty, T2 : ty, M3 : produc1294284815t_char, D2 : list_char]: ((wf_pro1229751607t_char @ Wf_md @ P) => ((method297381284t_char @ P @ C @ M2 @ Ts2 @ T2 @ M3 @ D2) => (wf_mde297024346t_char @ Wf_md @ P @ D2 @ (produc1238538255t_char @ M2 @ (produc1730359111t_char @ Ts2 @ (produc248075743t_char @ T2 @ M3))))))))). % sees_wf_mdecl
thf(fact_70_ty_Oinject, axiom,
    ((![X5 : list_char, Y5 : list_char]: (((class @ X5) = (class @ Y5)) = (X5 = Y5))))). % ty.inject
thf(fact_71_has__method__def, axiom,
    ((has_me170134744t_char = (^[P3 : list_P1234162913t_char]: (^[C4 : list_char]: (^[M5 : list_char]: (?[Ts4 : list_ty]: (?[T4 : ty]: (?[M6 : produc1294284815t_char]: (?[X6 : list_char]: (method297381284t_char @ P3 @ C4 @ M5 @ Ts4 @ T4 @ M6 @ X6))))))))))). % has_method_def
thf(fact_72_rtrancl__idemp, axiom,
    ((![R : set_Pr164112643t_char]: ((transi1879726366t_char @ (transi1879726366t_char @ R)) = (transi1879726366t_char @ R))))). % rtrancl_idemp
thf(fact_73_r__into__rtrancl, axiom,
    ((![P2 : produc1257910179t_char, R : set_Pr164112643t_char]: ((member89690956t_char @ P2 @ R) => (member89690956t_char @ P2 @ (transi1879726366t_char @ R)))))). % r_into_rtrancl
thf(fact_74_mem__Collect__eq, axiom,
    ((![A : produc1257910179t_char, P : produc1257910179t_char > $o]: ((member89690956t_char @ A @ (collec768236686t_char @ P)) = (P @ A))))). % mem_Collect_eq
thf(fact_75_mem__Collect__eq, axiom,
    ((![A : produc1777519579t_char, P : produc1777519579t_char > $o]: ((member958036996t_char @ A @ (collec178542150t_char @ P)) = (P @ A))))). % mem_Collect_eq
thf(fact_76_mem__Collect__eq, axiom,
    ((![A : produc1259892823t_char, P : produc1259892823t_char > $o]: ((member397625600t_char @ A @ (collec1549347906t_char @ P)) = (P @ A))))). % mem_Collect_eq
thf(fact_77_Collect__mem__eq, axiom,
    ((![A4 : set_Pr164112643t_char]: ((collec768236686t_char @ (^[X7 : produc1257910179t_char]: (member89690956t_char @ X7 @ A4))) = A4)))). % Collect_mem_eq
thf(fact_78_Collect__mem__eq, axiom,
    ((![A4 : set_Pr2090064827t_char]: ((collec178542150t_char @ (^[X7 : produc1777519579t_char]: (member958036996t_char @ X7 @ A4))) = A4)))). % Collect_mem_eq
thf(fact_79_Collect__mem__eq, axiom,
    ((![A4 : set_Pr1344692407t_char]: ((collec1549347906t_char @ (^[X7 : produc1259892823t_char]: (member397625600t_char @ X7 @ A4))) = A4)))). % Collect_mem_eq
thf(fact_80_converse__rtrancl__induct2, axiom,
    ((![Ax : list_char, Ay : produc1451990293t_char, Bx : list_char, By : produc1451990293t_char, R : set_Pr1996500167t_char, P : list_char > produc1451990293t_char > $o]: ((member1263191824t_char @ (produc693115735t_char @ (produc1238538255t_char @ Ax @ Ay) @ (produc1238538255t_char @ Bx @ By)) @ (transi203893466t_char @ R)) => ((P @ Bx @ By) => ((![A3 : list_char, B3 : produc1451990293t_char, Aa : list_char, Ba : produc1451990293t_char]: ((member1263191824t_char @ (produc693115735t_char @ (produc1238538255t_char @ A3 @ B3) @ (produc1238538255t_char @ Aa @ Ba)) @ R) => ((member1263191824t_char @ (produc693115735t_char @ (produc1238538255t_char @ Aa @ Ba) @ (produc1238538255t_char @ Bx @ By)) @ (transi203893466t_char @ R)) => ((P @ Aa @ Ba) => (P @ A3 @ B3))))) => (P @ Ax @ Ay))))))). % converse_rtrancl_induct2
thf(fact_81_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) => ((![A3 : list_char, B3 : list_char, Aa : list_char, Ba : list_char]: ((member803902992t_char @ (produc395356247t_char @ (produc1304532571t_char @ A3 @ 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 @ A3 @ B3))))) => (P @ Ax @ Ay))))))). % converse_rtrancl_induct2
thf(fact_82_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) => ((![A3 : list_list_char, B3 : exp_list_char, Aa : list_list_char, Ba : exp_list_char]: ((member1392938152t_char @ (produc618657463t_char @ (produc713467969t_char @ A3 @ B3) @ (produc713467969t_char @ Aa @ Ba)) @ R) => ((member1392938152t_char @ (produc618657463t_char @ (produc713467969t_char @ Aa @ Ba) @ (produc713467969t_char @ Bx @ By)) @ (transi1892282060t_char @ R)) => ((P @ Aa @ Ba) => (P @ A3 @ B3))))) => (P @ Ax @ Ay))))))). % converse_rtrancl_induct2
thf(fact_83_converse__rtrancl__induct2, axiom,
    ((![Ax : list_ty, Ay : produc1490933927t_char, Bx : list_ty, By : produc1490933927t_char, R : set_Pr1449697899t_char, P : list_ty > produc1490933927t_char > $o]: ((member384501940t_char @ (produc993523139t_char @ (produc1730359111t_char @ Ax @ Ay) @ (produc1730359111t_char @ Bx @ By)) @ (transi1520230866t_char @ R)) => ((P @ Bx @ By) => ((![A3 : list_ty, B3 : produc1490933927t_char, Aa : list_ty, Ba : produc1490933927t_char]: ((member384501940t_char @ (produc993523139t_char @ (produc1730359111t_char @ A3 @ B3) @ (produc1730359111t_char @ Aa @ Ba)) @ R) => ((member384501940t_char @ (produc993523139t_char @ (produc1730359111t_char @ Aa @ Ba) @ (produc1730359111t_char @ Bx @ By)) @ (transi1520230866t_char @ R)) => ((P @ Aa @ Ba) => (P @ A3 @ B3))))) => (P @ Ax @ Ay))))))). % converse_rtrancl_induct2
thf(fact_84_converse__rtrancl__induct2, axiom,
    ((![Ax : ty, Ay : produc1294284815t_char, Bx : ty, By : produc1294284815t_char, R : set_Pr236946631t_char, P : ty > produc1294284815t_char > $o]: ((member1723509520t_char @ (produc1065632599t_char @ (produc248075743t_char @ Ax @ Ay) @ (produc248075743t_char @ Bx @ By)) @ (transi761127338t_char @ R)) => ((P @ Bx @ By) => ((![A3 : ty, B3 : produc1294284815t_char, Aa : ty, Ba : produc1294284815t_char]: ((member1723509520t_char @ (produc1065632599t_char @ (produc248075743t_char @ A3 @ B3) @ (produc248075743t_char @ Aa @ Ba)) @ R) => ((member1723509520t_char @ (produc1065632599t_char @ (produc248075743t_char @ Aa @ Ba) @ (produc248075743t_char @ Bx @ By)) @ (transi761127338t_char @ R)) => ((P @ Aa @ Ba) => (P @ A3 @ B3))))) => (P @ Ax @ Ay))))))). % converse_rtrancl_induct2
thf(fact_85_converse__rtranclE2, axiom,
    ((![Xa : list_char, Xb : produc1451990293t_char, Za : list_char, Zb : produc1451990293t_char, R : set_Pr1996500167t_char]: ((member1263191824t_char @ (produc693115735t_char @ (produc1238538255t_char @ Xa @ Xb) @ (produc1238538255t_char @ Za @ Zb)) @ (transi203893466t_char @ R)) => ((~ (((produc1238538255t_char @ Xa @ Xb) = (produc1238538255t_char @ Za @ Zb)))) => (~ ((![A3 : list_char, B3 : produc1451990293t_char]: ((member1263191824t_char @ (produc693115735t_char @ (produc1238538255t_char @ Xa @ Xb) @ (produc1238538255t_char @ A3 @ B3)) @ R) => (~ ((member1263191824t_char @ (produc693115735t_char @ (produc1238538255t_char @ A3 @ B3) @ (produc1238538255t_char @ Za @ Zb)) @ (transi203893466t_char @ R))))))))))))). % converse_rtranclE2
thf(fact_86_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)))) => (~ ((![A3 : list_char, B3 : list_char]: ((member803902992t_char @ (produc395356247t_char @ (produc1304532571t_char @ Xa @ Xb) @ (produc1304532571t_char @ A3 @ B3)) @ R) => (~ ((member803902992t_char @ (produc395356247t_char @ (produc1304532571t_char @ A3 @ B3) @ (produc1304532571t_char @ Za @ Zb)) @ (transi858104614t_char @ R))))))))))))). % converse_rtranclE2
thf(fact_87_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)))) => (~ ((![A3 : list_list_char, B3 : exp_list_char]: ((member1392938152t_char @ (produc618657463t_char @ (produc713467969t_char @ Xa @ Xb) @ (produc713467969t_char @ A3 @ B3)) @ R) => (~ ((member1392938152t_char @ (produc618657463t_char @ (produc713467969t_char @ A3 @ B3) @ (produc713467969t_char @ Za @ Zb)) @ (transi1892282060t_char @ R))))))))))))). % converse_rtranclE2
thf(fact_88_converse__rtranclE2, axiom,
    ((![Xa : list_ty, Xb : produc1490933927t_char, Za : list_ty, Zb : produc1490933927t_char, R : set_Pr1449697899t_char]: ((member384501940t_char @ (produc993523139t_char @ (produc1730359111t_char @ Xa @ Xb) @ (produc1730359111t_char @ Za @ Zb)) @ (transi1520230866t_char @ R)) => ((~ (((produc1730359111t_char @ Xa @ Xb) = (produc1730359111t_char @ Za @ Zb)))) => (~ ((![A3 : list_ty, B3 : produc1490933927t_char]: ((member384501940t_char @ (produc993523139t_char @ (produc1730359111t_char @ Xa @ Xb) @ (produc1730359111t_char @ A3 @ B3)) @ R) => (~ ((member384501940t_char @ (produc993523139t_char @ (produc1730359111t_char @ A3 @ B3) @ (produc1730359111t_char @ Za @ Zb)) @ (transi1520230866t_char @ R))))))))))))). % converse_rtranclE2
thf(fact_89_converse__rtranclE2, axiom,
    ((![Xa : ty, Xb : produc1294284815t_char, Za : ty, Zb : produc1294284815t_char, R : set_Pr236946631t_char]: ((member1723509520t_char @ (produc1065632599t_char @ (produc248075743t_char @ Xa @ Xb) @ (produc248075743t_char @ Za @ Zb)) @ (transi761127338t_char @ R)) => ((~ (((produc248075743t_char @ Xa @ Xb) = (produc248075743t_char @ Za @ Zb)))) => (~ ((![A3 : ty, B3 : produc1294284815t_char]: ((member1723509520t_char @ (produc1065632599t_char @ (produc248075743t_char @ Xa @ Xb) @ (produc248075743t_char @ A3 @ B3)) @ R) => (~ ((member1723509520t_char @ (produc1065632599t_char @ (produc248075743t_char @ A3 @ B3) @ (produc248075743t_char @ Za @ Zb)) @ (transi761127338t_char @ R))))))))))))). % converse_rtranclE2
thf(fact_90_rtrancl__induct2, axiom,
    ((![Ax : list_char, Ay : produc1451990293t_char, Bx : list_char, By : produc1451990293t_char, R : set_Pr1996500167t_char, P : list_char > produc1451990293t_char > $o]: ((member1263191824t_char @ (produc693115735t_char @ (produc1238538255t_char @ Ax @ Ay) @ (produc1238538255t_char @ Bx @ By)) @ (transi203893466t_char @ R)) => ((P @ Ax @ Ay) => ((![A3 : list_char, B3 : produc1451990293t_char, Aa : list_char, Ba : produc1451990293t_char]: ((member1263191824t_char @ (produc693115735t_char @ (produc1238538255t_char @ Ax @ Ay) @ (produc1238538255t_char @ A3 @ B3)) @ (transi203893466t_char @ R)) => ((member1263191824t_char @ (produc693115735t_char @ (produc1238538255t_char @ A3 @ B3) @ (produc1238538255t_char @ Aa @ Ba)) @ R) => ((P @ A3 @ B3) => (P @ Aa @ Ba))))) => (P @ Bx @ By))))))). % rtrancl_induct2
thf(fact_91_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) => ((![A3 : list_char, B3 : list_char, Aa : list_char, Ba : list_char]: ((member803902992t_char @ (produc395356247t_char @ (produc1304532571t_char @ Ax @ Ay) @ (produc1304532571t_char @ A3 @ B3)) @ (transi858104614t_char @ R)) => ((member803902992t_char @ (produc395356247t_char @ (produc1304532571t_char @ A3 @ B3) @ (produc1304532571t_char @ Aa @ Ba)) @ R) => ((P @ A3 @ B3) => (P @ Aa @ Ba))))) => (P @ Bx @ By))))))). % rtrancl_induct2
thf(fact_92_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) => ((![A3 : list_list_char, B3 : exp_list_char, Aa : list_list_char, Ba : exp_list_char]: ((member1392938152t_char @ (produc618657463t_char @ (produc713467969t_char @ Ax @ Ay) @ (produc713467969t_char @ A3 @ B3)) @ (transi1892282060t_char @ R)) => ((member1392938152t_char @ (produc618657463t_char @ (produc713467969t_char @ A3 @ B3) @ (produc713467969t_char @ Aa @ Ba)) @ R) => ((P @ A3 @ B3) => (P @ Aa @ Ba))))) => (P @ Bx @ By))))))). % rtrancl_induct2
thf(fact_93_rtrancl__induct2, axiom,
    ((![Ax : list_ty, Ay : produc1490933927t_char, Bx : list_ty, By : produc1490933927t_char, R : set_Pr1449697899t_char, P : list_ty > produc1490933927t_char > $o]: ((member384501940t_char @ (produc993523139t_char @ (produc1730359111t_char @ Ax @ Ay) @ (produc1730359111t_char @ Bx @ By)) @ (transi1520230866t_char @ R)) => ((P @ Ax @ Ay) => ((![A3 : list_ty, B3 : produc1490933927t_char, Aa : list_ty, Ba : produc1490933927t_char]: ((member384501940t_char @ (produc993523139t_char @ (produc1730359111t_char @ Ax @ Ay) @ (produc1730359111t_char @ A3 @ B3)) @ (transi1520230866t_char @ R)) => ((member384501940t_char @ (produc993523139t_char @ (produc1730359111t_char @ A3 @ B3) @ (produc1730359111t_char @ Aa @ Ba)) @ R) => ((P @ A3 @ B3) => (P @ Aa @ Ba))))) => (P @ Bx @ By))))))). % rtrancl_induct2
thf(fact_94_rtrancl__induct2, axiom,
    ((![Ax : ty, Ay : produc1294284815t_char, Bx : ty, By : produc1294284815t_char, R : set_Pr236946631t_char, P : ty > produc1294284815t_char > $o]: ((member1723509520t_char @ (produc1065632599t_char @ (produc248075743t_char @ Ax @ Ay) @ (produc248075743t_char @ Bx @ By)) @ (transi761127338t_char @ R)) => ((P @ Ax @ Ay) => ((![A3 : ty, B3 : produc1294284815t_char, Aa : ty, Ba : produc1294284815t_char]: ((member1723509520t_char @ (produc1065632599t_char @ (produc248075743t_char @ Ax @ Ay) @ (produc248075743t_char @ A3 @ B3)) @ (transi761127338t_char @ R)) => ((member1723509520t_char @ (produc1065632599t_char @ (produc248075743t_char @ A3 @ B3) @ (produc248075743t_char @ Aa @ Ba)) @ R) => ((P @ A3 @ B3) => (P @ Aa @ Ba))))) => (P @ Bx @ By))))))). % rtrancl_induct2
thf(fact_95_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_96_rtrancl_Ocases, axiom,
    ((![A1 : list_char, A22 : list_char, R : set_Pr164112643t_char]: ((member89690956t_char @ (produc1304532571t_char @ A1 @ A22) @ (transi1879726366t_char @ R)) => ((~ ((A22 = A1))) => (~ ((![B3 : list_char]: ((member89690956t_char @ (produc1304532571t_char @ A1 @ B3) @ (transi1879726366t_char @ R)) => (~ ((member89690956t_char @ (produc1304532571t_char @ B3 @ A22) @ R)))))))))))). % rtrancl.cases
thf(fact_97_rtrancl_Osimps, axiom,
    ((![A1 : list_char, A22 : list_char, R : set_Pr164112643t_char]: ((member89690956t_char @ (produc1304532571t_char @ A1 @ A22) @ (transi1879726366t_char @ R)) = (((?[A5 : list_char]: (((A1 = A5)) & ((A22 = A5))))) | ((?[A5 : list_char]: (?[B4 : list_char]: (?[C5 : list_char]: (((A1 = A5)) & ((((A22 = C5)) & ((((member89690956t_char @ (produc1304532571t_char @ A5 @ B4) @ (transi1879726366t_char @ R))) & ((member89690956t_char @ (produc1304532571t_char @ B4 @ C5) @ R)))))))))))))))). % rtrancl.simps
thf(fact_98_rtrancl__trans, axiom,
    ((![X3 : list_char, Y : list_char, R : set_Pr164112643t_char, Z : list_char]: ((member89690956t_char @ (produc1304532571t_char @ X3 @ Y) @ (transi1879726366t_char @ R)) => ((member89690956t_char @ (produc1304532571t_char @ Y @ Z) @ (transi1879726366t_char @ R)) => (member89690956t_char @ (produc1304532571t_char @ X3 @ Z) @ (transi1879726366t_char @ R))))))). % rtrancl_trans
thf(fact_99_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, Z2 : list_char]: ((member89690956t_char @ (produc1304532571t_char @ A @ Y3) @ (transi1879726366t_char @ R)) => ((member89690956t_char @ (produc1304532571t_char @ Y3 @ Z2) @ R) => ((P @ Y3) => (P @ Z2))))) => (P @ B))))))). % rtrancl_induct
thf(fact_100_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)) => ((![A3 : list_char]: (P @ A3 @ A3)) => ((![A3 : list_char, B3 : list_char, C3 : list_char]: ((member89690956t_char @ (produc1304532571t_char @ A3 @ B3) @ (transi1879726366t_char @ R)) => ((P @ A3 @ B3) => ((member89690956t_char @ (produc1304532571t_char @ B3 @ C3) @ R) => (P @ A3 @ C3))))) => (P @ X1 @ X2))))))). % rtrancl.inducts
thf(fact_101_converse__rtranclE, axiom,
    ((![X3 : list_char, Z : list_char, R : set_Pr164112643t_char]: ((member89690956t_char @ (produc1304532571t_char @ X3 @ Z) @ (transi1879726366t_char @ R)) => ((~ ((X3 = Z))) => (~ ((![Y3 : list_char]: ((member89690956t_char @ (produc1304532571t_char @ X3 @ Y3) @ R) => (~ ((member89690956t_char @ (produc1304532571t_char @ Y3 @ Z) @ (transi1879726366t_char @ R))))))))))))). % converse_rtranclE
thf(fact_102_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_103_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, Z2 : list_char]: ((member89690956t_char @ (produc1304532571t_char @ Y3 @ Z2) @ R) => ((member89690956t_char @ (produc1304532571t_char @ Z2 @ B) @ (transi1879726366t_char @ R)) => ((P @ Z2) => (P @ Y3))))) => (P @ A))))))). % converse_rtrancl_induct
thf(fact_104_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_105_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_106_widen_Oinducts, axiom,
    ((![P : list_P1234162913t_char, X1 : ty, X2 : ty, Pa : ty > ty > $o]: ((widen_917054840t_char @ P @ X1 @ X2) => ((![T5 : ty]: (Pa @ T5 @ T5)) => ((![C7 : list_char, D4 : list_char]: ((member89690956t_char @ (produc1304532571t_char @ C7 @ D4) @ (transi1879726366t_char @ (subcls880436836t_char @ P))) => (Pa @ (class @ C7) @ (class @ D4)))) => ((![C7 : list_char]: (Pa @ nt @ (class @ C7))) => (Pa @ X1 @ X2)))))))). % widen.inducts
thf(fact_107_widen__Class, axiom,
    ((![P : list_P1234162913t_char, T2 : ty, C : list_char]: ((widen_917054840t_char @ P @ T2 @ (class @ C)) = (((T2 = nt)) | ((?[D6 : list_char]: (((T2 = (class @ D6))) & ((member89690956t_char @ (produc1304532571t_char @ D6 @ C) @ (transi1879726366t_char @ (subcls880436836t_char @ P)))))))))))). % widen_Class
thf(fact_108_widen_Osimps, axiom,
    ((widen_917054840t_char = (^[P3 : list_P1234162913t_char]: (^[A12 : ty]: (^[A23 : ty]: (((?[T4 : ty]: (((A12 = T4)) & ((A23 = T4))))) | ((((?[C4 : list_char]: (?[D6 : list_char]: (((A12 = (class @ C4))) & ((((A23 = (class @ D6))) & ((member89690956t_char @ (produc1304532571t_char @ C4 @ D6) @ (transi1879726366t_char @ (subcls880436836t_char @ P3)))))))))) | ((?[C4 : list_char]: (((A12 = nt)) & ((A23 = (class @ C4))))))))))))))). % widen.simps
thf(fact_109_widen_Ocases, axiom,
    ((![P : list_P1234162913t_char, A1 : ty, A22 : ty]: ((widen_917054840t_char @ P @ A1 @ A22) => ((~ ((A22 = A1))) => ((![C7 : list_char]: ((A1 = (class @ C7)) => (![D4 : list_char]: ((A22 = (class @ D4)) => (~ ((member89690956t_char @ (produc1304532571t_char @ C7 @ D4) @ (transi1879726366t_char @ (subcls880436836t_char @ P))))))))) => (~ (((A1 = nt) => (![C7 : list_char]: (~ ((A22 = (class @ C7)))))))))))))). % widen.cases
thf(fact_110_list__all2__same, axiom,
    ((![P : produc1777519579t_char > produc1777519579t_char > $o, Xs : list_P1234162913t_char]: ((list_a364623943t_char @ P @ Xs @ Xs) = (![X7 : produc1777519579t_char]: (((member958036996t_char @ X7 @ (set_Pr1611739760t_char @ Xs))) => ((P @ X7 @ X7)))))))). % list_all2_same
thf(fact_111_list__all2__same, axiom,
    ((![P : produc1259892823t_char > produc1259892823t_char > $o, Xs : list_P1653548253t_char]: ((list_a1436933959t_char @ P @ Xs @ Xs) = (![X7 : produc1259892823t_char]: (((member397625600t_char @ X7 @ (set_Pr1045701996t_char @ Xs))) => ((P @ X7 @ X7)))))))). % list_all2_same
thf(fact_112_list__all2__same, axiom,
    ((![P : ty > ty > $o, Xs : list_ty]: ((list_all2_ty_ty @ P @ Xs @ Xs) = (![X7 : ty]: (((member_ty @ X7 @ (set_ty2 @ Xs))) => ((P @ X7 @ X7)))))))). % list_all2_same
thf(fact_113_list_Orel__cong, axiom,
    ((![X3 : list_ty, Ya : list_ty, Y : list_ty, Xa : list_ty, R2 : ty > ty > $o, Ra : ty > ty > $o]: ((X3 = Ya) => ((Y = Xa) => ((![Z2 : ty, Yb : ty]: ((member_ty @ Z2 @ (set_ty2 @ Ya)) => ((member_ty @ Yb @ (set_ty2 @ Xa)) => ((R2 @ Z2 @ Yb) = (Ra @ Z2 @ Yb))))) => ((list_all2_ty_ty @ R2 @ X3 @ Y) = (list_all2_ty_ty @ Ra @ Ya @ Xa)))))))). % list.rel_cong
thf(fact_114_list_Orel__cong, axiom,
    ((![X3 : list_P757710633t_char, Ya : list_P757710633t_char, Y : list_ty, Xa : list_ty, R2 : produc1257910179t_char > ty > $o, Ra : produc1257910179t_char > ty > $o]: ((X3 = Ya) => ((Y = Xa) => ((![Z2 : produc1257910179t_char, Yb : ty]: ((member89690956t_char @ Z2 @ (set_Pr1342796728t_char @ Ya)) => ((member_ty @ Yb @ (set_ty2 @ Xa)) => ((R2 @ Z2 @ Yb) = (Ra @ Z2 @ Yb))))) => ((list_a995664787har_ty @ R2 @ X3 @ Y) = (list_a995664787har_ty @ Ra @ Ya @ Xa)))))))). % list.rel_cong
thf(fact_115_list_Orel__cong, axiom,
    ((![X3 : list_ty, Ya : list_ty, Y : list_P757710633t_char, Xa : list_P757710633t_char, R2 : ty > produc1257910179t_char > $o, Ra : ty > produc1257910179t_char > $o]: ((X3 = Ya) => ((Y = Xa) => ((![Z2 : ty, Yb : produc1257910179t_char]: ((member_ty @ Z2 @ (set_ty2 @ Ya)) => ((member89690956t_char @ Yb @ (set_Pr1342796728t_char @ Xa)) => ((R2 @ Z2 @ Yb) = (Ra @ Z2 @ Yb))))) => ((list_a741223907t_char @ R2 @ X3 @ Y) = (list_a741223907t_char @ Ra @ Ya @ Xa)))))))). % list.rel_cong
thf(fact_116_list_Orel__cong, axiom,
    ((![X3 : list_P757710633t_char, Ya : list_P757710633t_char, Y : list_P757710633t_char, Xa : list_P757710633t_char, R2 : produc1257910179t_char > produc1257910179t_char > $o, Ra : produc1257910179t_char > produc1257910179t_char > $o]: ((X3 = Ya) => ((Y = Xa) => ((![Z2 : produc1257910179t_char, Yb : produc1257910179t_char]: ((member89690956t_char @ Z2 @ (set_Pr1342796728t_char @ Ya)) => ((member89690956t_char @ Yb @ (set_Pr1342796728t_char @ Xa)) => ((R2 @ Z2 @ Yb) = (Ra @ Z2 @ Yb))))) => ((list_a1368132679t_char @ R2 @ X3 @ Y) = (list_a1368132679t_char @ Ra @ Ya @ Xa)))))))). % list.rel_cong
thf(fact_117_list_Orel__cong, axiom,
    ((![X3 : list_ty, Ya : list_ty, Y : list_P1653548253t_char, Xa : list_P1653548253t_char, R2 : ty > produc1259892823t_char > $o, Ra : ty > produc1259892823t_char > $o]: ((X3 = Ya) => ((Y = Xa) => ((![Z2 : ty, Yb : produc1259892823t_char]: ((member_ty @ Z2 @ (set_ty2 @ Ya)) => ((member397625600t_char @ Yb @ (set_Pr1045701996t_char @ Xa)) => ((R2 @ Z2 @ Yb) = (Ra @ Z2 @ Yb))))) => ((list_a552447639t_char @ R2 @ X3 @ Y) = (list_a552447639t_char @ Ra @ Ya @ Xa)))))))). % list.rel_cong
thf(fact_118_list_Orel__cong, axiom,
    ((![X3 : list_P1653548253t_char, Ya : list_P1653548253t_char, Y : list_ty, Xa : list_ty, R2 : produc1259892823t_char > ty > $o, Ra : produc1259892823t_char > ty > $o]: ((X3 = Ya) => ((Y = Xa) => ((![Z2 : produc1259892823t_char, Yb : ty]: ((member397625600t_char @ Z2 @ (set_Pr1045701996t_char @ Ya)) => ((member_ty @ Yb @ (set_ty2 @ Xa)) => ((R2 @ Z2 @ Yb) = (Ra @ Z2 @ Yb))))) => ((list_a693914695har_ty @ R2 @ X3 @ Y) = (list_a693914695har_ty @ Ra @ Ya @ Xa)))))))). % list.rel_cong
thf(fact_119_list_Orel__cong, axiom,
    ((![X3 : list_P757710633t_char, Ya : list_P757710633t_char, Y : list_P1653548253t_char, Xa : list_P1653548253t_char, R2 : produc1257910179t_char > produc1259892823t_char > $o, Ra : produc1257910179t_char > produc1259892823t_char > $o]: ((X3 = Ya) => ((Y = Xa) => ((![Z2 : produc1257910179t_char, Yb : produc1259892823t_char]: ((member89690956t_char @ Z2 @ (set_Pr1342796728t_char @ Ya)) => ((member397625600t_char @ Yb @ (set_Pr1045701996t_char @ Xa)) => ((R2 @ Z2 @ Yb) = (Ra @ Z2 @ Yb))))) => ((list_a1221730555t_char @ R2 @ X3 @ Y) = (list_a1221730555t_char @ Ra @ Ya @ Xa)))))))). % list.rel_cong
thf(fact_120_list_Orel__cong, axiom,
    ((![X3 : list_P1653548253t_char, Ya : list_P1653548253t_char, Y : list_P757710633t_char, Xa : list_P757710633t_char, R2 : produc1259892823t_char > produc1257910179t_char > $o, Ra : produc1259892823t_char > produc1257910179t_char > $o]: ((X3 = Ya) => ((Y = Xa) => ((![Z2 : produc1259892823t_char, Yb : produc1257910179t_char]: ((member397625600t_char @ Z2 @ (set_Pr1045701996t_char @ Ya)) => ((member89690956t_char @ Yb @ (set_Pr1342796728t_char @ Xa)) => ((R2 @ Z2 @ Yb) = (Ra @ Z2 @ Yb))))) => ((list_a72576659t_char @ R2 @ X3 @ Y) = (list_a72576659t_char @ Ra @ Ya @ Xa)))))))). % list.rel_cong
thf(fact_121_list_Orel__cong, axiom,
    ((![X3 : list_ty, Ya : list_ty, Y : list_P1234162913t_char, Xa : list_P1234162913t_char, R2 : ty > produc1777519579t_char > $o, Ra : ty > produc1777519579t_char > $o]: ((X3 = Ya) => ((Y = Xa) => ((![Z2 : ty, Yb : produc1777519579t_char]: ((member_ty @ Z2 @ (set_ty2 @ Ya)) => ((member958036996t_char @ Yb @ (set_Pr1611739760t_char @ Xa)) => ((R2 @ Z2 @ Yb) = (Ra @ Z2 @ Yb))))) => ((list_a962849307t_char @ R2 @ X3 @ Y) = (list_a962849307t_char @ Ra @ Ya @ Xa)))))))). % list.rel_cong
thf(fact_122_list_Orel__cong, axiom,
    ((![X3 : list_P1234162913t_char, Ya : list_P1234162913t_char, Y : list_ty, Xa : list_ty, R2 : produc1777519579t_char > ty > $o, Ra : produc1777519579t_char > ty > $o]: ((X3 = Ya) => ((Y = Xa) => ((![Z2 : produc1777519579t_char, Yb : ty]: ((member958036996t_char @ Z2 @ (set_Pr1611739760t_char @ Ya)) => ((member_ty @ Yb @ (set_ty2 @ Xa)) => ((R2 @ Z2 @ Yb) = (Ra @ Z2 @ Yb))))) => ((list_a1455926219har_ty @ R2 @ X3 @ Y) = (list_a1455926219har_ty @ Ra @ Ya @ Xa)))))))). % list.rel_cong
thf(fact_123_ty_Odistinct_I19_J, axiom,
    ((![X5 : list_char]: (~ ((nt = (class @ X5))))))). % ty.distinct(19)
thf(fact_124_widen__null, axiom,
    ((![P : list_P1234162913t_char, C : list_char]: (widen_917054840t_char @ P @ nt @ (class @ C))))). % widen_null
thf(fact_125_mdecl__visible, axiom,
    ((![Wf_md : list_P1234162913t_char > list_char > produc1259892823t_char > $o, P : list_P1234162913t_char, C : list_char, S : list_char, Fs : list_P1126587903har_ty, Ms : list_P1653548253t_char, M2 : list_char, Ts2 : list_ty, T2 : ty, M3 : produc1294284815t_char]: ((wf_pro1229751607t_char @ Wf_md @ P) => ((member958036996t_char @ (produc1548560403t_char @ C @ (produc1972337867t_char @ S @ (produc1107711029t_char @ Fs @ Ms))) @ (set_Pr1611739760t_char @ P)) => ((member397625600t_char @ (produc1238538255t_char @ M2 @ (produc1730359111t_char @ Ts2 @ (produc248075743t_char @ T2 @ M3))) @ (set_Pr1045701996t_char @ Ms)) => (method297381284t_char @ P @ C @ M2 @ Ts2 @ T2 @ M3 @ C))))))). % mdecl_visible
thf(fact_126_list_Orel__refl, axiom,
    ((![Ra : ty > ty > $o, X3 : list_ty]: ((![X4 : ty]: (Ra @ X4 @ X4)) => (list_all2_ty_ty @ Ra @ X3 @ X3))))). % list.rel_refl
thf(fact_127_list__all2__antisym, axiom,
    ((![P : ty > ty > $o, Q : ty > ty > $o, Xs : list_ty, Ys : list_ty]: ((![X4 : ty, Y3 : ty]: ((P @ X4 @ Y3) => ((Q @ Y3 @ X4) => (X4 = Y3)))) => ((list_all2_ty_ty @ P @ Xs @ Ys) => ((list_all2_ty_ty @ Q @ Ys @ Xs) => (Xs = Ys))))))). % list_all2_antisym
thf(fact_128_list_Orel__eq, axiom,
    (((list_all2_ty_ty @ (^[Y4 : ty]: (^[Z3 : ty]: (Y4 = Z3)))) = (^[Y4 : list_ty]: (^[Z3 : list_ty]: (Y4 = Z3)))))). % list.rel_eq
thf(fact_129_list__all2__trans, axiom,
    ((![P1 : ty > ty > $o, P22 : ty > ty > $o, P32 : ty > ty > $o, As : list_ty, Bs : list_ty, Cs : list_ty]: ((![A3 : ty, B3 : ty, C3 : ty]: ((P1 @ A3 @ B3) => ((P22 @ B3 @ C3) => (P32 @ A3 @ C3)))) => ((list_all2_ty_ty @ P1 @ As @ Bs) => ((list_all2_ty_ty @ P22 @ Bs @ Cs) => (list_all2_ty_ty @ P32 @ As @ Cs))))))). % list_all2_trans
thf(fact_130_list__all2__refl, axiom,
    ((![P : ty > ty > $o, Xs : list_ty]: ((![X4 : ty]: (P @ X4 @ X4)) => (list_all2_ty_ty @ P @ Xs @ Xs))))). % list_all2_refl
thf(fact_131_list__all2__mono, axiom,
    ((![P : ty > ty > $o, Xs : list_ty, Ys : list_ty, Q : ty > ty > $o]: ((list_all2_ty_ty @ P @ Xs @ Ys) => ((![Xs2 : ty, Ys2 : ty]: ((P @ Xs2 @ Ys2) => (Q @ Xs2 @ Ys2))) => (list_all2_ty_ty @ Q @ Xs @ Ys)))))). % list_all2_mono
thf(fact_132_list__all2__eq, axiom,
    (((^[Y4 : list_ty]: (^[Z3 : list_ty]: (Y4 = Z3))) = (list_all2_ty_ty @ (^[Y4 : ty]: (^[Z3 : ty]: (Y4 = Z3))))))). % list_all2_eq
thf(fact_133_list_Orel__refl__strong, axiom,
    ((![X3 : list_P757710633t_char, Ra : produc1257910179t_char > produc1257910179t_char > $o]: ((![Z2 : produc1257910179t_char]: ((member89690956t_char @ Z2 @ (set_Pr1342796728t_char @ X3)) => (Ra @ Z2 @ Z2))) => (list_a1368132679t_char @ Ra @ X3 @ X3))))). % list.rel_refl_strong
thf(fact_134_list_Orel__refl__strong, axiom,
    ((![X3 : list_P1234162913t_char, Ra : produc1777519579t_char > produc1777519579t_char > $o]: ((![Z2 : produc1777519579t_char]: ((member958036996t_char @ Z2 @ (set_Pr1611739760t_char @ X3)) => (Ra @ Z2 @ Z2))) => (list_a364623943t_char @ Ra @ X3 @ X3))))). % list.rel_refl_strong
thf(fact_135_list_Orel__refl__strong, axiom,
    ((![X3 : list_P1653548253t_char, Ra : produc1259892823t_char > produc1259892823t_char > $o]: ((![Z2 : produc1259892823t_char]: ((member397625600t_char @ Z2 @ (set_Pr1045701996t_char @ X3)) => (Ra @ Z2 @ Z2))) => (list_a1436933959t_char @ Ra @ X3 @ X3))))). % list.rel_refl_strong
thf(fact_136_list_Orel__refl__strong, axiom,
    ((![X3 : list_ty, Ra : ty > ty > $o]: ((![Z2 : ty]: ((member_ty @ Z2 @ (set_ty2 @ X3)) => (Ra @ Z2 @ Z2))) => (list_all2_ty_ty @ Ra @ X3 @ X3))))). % list.rel_refl_strong
thf(fact_137_list_Orel__mono__strong, axiom,
    ((![R2 : ty > ty > $o, X3 : list_ty, Y : list_ty, Ra : ty > ty > $o]: ((list_all2_ty_ty @ R2 @ X3 @ Y) => ((![Z2 : ty, Yb : ty]: ((member_ty @ Z2 @ (set_ty2 @ X3)) => ((member_ty @ Yb @ (set_ty2 @ Y)) => ((R2 @ Z2 @ Yb) => (Ra @ Z2 @ Yb))))) => (list_all2_ty_ty @ Ra @ X3 @ Y)))))). % list.rel_mono_strong
thf(fact_138_list_Orel__mono__strong, axiom,
    ((![R2 : produc1257910179t_char > ty > $o, X3 : list_P757710633t_char, Y : list_ty, Ra : produc1257910179t_char > ty > $o]: ((list_a995664787har_ty @ R2 @ X3 @ Y) => ((![Z2 : produc1257910179t_char, Yb : ty]: ((member89690956t_char @ Z2 @ (set_Pr1342796728t_char @ X3)) => ((member_ty @ Yb @ (set_ty2 @ Y)) => ((R2 @ Z2 @ Yb) => (Ra @ Z2 @ Yb))))) => (list_a995664787har_ty @ Ra @ X3 @ Y)))))). % list.rel_mono_strong
thf(fact_139_list_Orel__mono__strong, axiom,
    ((![R2 : ty > produc1257910179t_char > $o, X3 : list_ty, Y : list_P757710633t_char, Ra : ty > produc1257910179t_char > $o]: ((list_a741223907t_char @ R2 @ X3 @ Y) => ((![Z2 : ty, Yb : produc1257910179t_char]: ((member_ty @ Z2 @ (set_ty2 @ X3)) => ((member89690956t_char @ Yb @ (set_Pr1342796728t_char @ Y)) => ((R2 @ Z2 @ Yb) => (Ra @ Z2 @ Yb))))) => (list_a741223907t_char @ Ra @ X3 @ Y)))))). % list.rel_mono_strong
thf(fact_140_list_Orel__mono__strong, axiom,
    ((![R2 : produc1257910179t_char > produc1257910179t_char > $o, X3 : list_P757710633t_char, Y : list_P757710633t_char, Ra : produc1257910179t_char > produc1257910179t_char > $o]: ((list_a1368132679t_char @ R2 @ X3 @ Y) => ((![Z2 : produc1257910179t_char, Yb : produc1257910179t_char]: ((member89690956t_char @ Z2 @ (set_Pr1342796728t_char @ X3)) => ((member89690956t_char @ Yb @ (set_Pr1342796728t_char @ Y)) => ((R2 @ Z2 @ Yb) => (Ra @ Z2 @ Yb))))) => (list_a1368132679t_char @ Ra @ X3 @ Y)))))). % list.rel_mono_strong
thf(fact_141_list_Orel__mono__strong, axiom,
    ((![R2 : ty > produc1259892823t_char > $o, X3 : list_ty, Y : list_P1653548253t_char, Ra : ty > produc1259892823t_char > $o]: ((list_a552447639t_char @ R2 @ X3 @ Y) => ((![Z2 : ty, Yb : produc1259892823t_char]: ((member_ty @ Z2 @ (set_ty2 @ X3)) => ((member397625600t_char @ Yb @ (set_Pr1045701996t_char @ Y)) => ((R2 @ Z2 @ Yb) => (Ra @ Z2 @ Yb))))) => (list_a552447639t_char @ Ra @ X3 @ Y)))))). % list.rel_mono_strong
thf(fact_142_list_Orel__mono__strong, axiom,
    ((![R2 : produc1259892823t_char > ty > $o, X3 : list_P1653548253t_char, Y : list_ty, Ra : produc1259892823t_char > ty > $o]: ((list_a693914695har_ty @ R2 @ X3 @ Y) => ((![Z2 : produc1259892823t_char, Yb : ty]: ((member397625600t_char @ Z2 @ (set_Pr1045701996t_char @ X3)) => ((member_ty @ Yb @ (set_ty2 @ Y)) => ((R2 @ Z2 @ Yb) => (Ra @ Z2 @ Yb))))) => (list_a693914695har_ty @ Ra @ X3 @ Y)))))). % list.rel_mono_strong
thf(fact_143_list_Orel__mono__strong, axiom,
    ((![R2 : produc1257910179t_char > produc1259892823t_char > $o, X3 : list_P757710633t_char, Y : list_P1653548253t_char, Ra : produc1257910179t_char > produc1259892823t_char > $o]: ((list_a1221730555t_char @ R2 @ X3 @ Y) => ((![Z2 : produc1257910179t_char, Yb : produc1259892823t_char]: ((member89690956t_char @ Z2 @ (set_Pr1342796728t_char @ X3)) => ((member397625600t_char @ Yb @ (set_Pr1045701996t_char @ Y)) => ((R2 @ Z2 @ Yb) => (Ra @ Z2 @ Yb))))) => (list_a1221730555t_char @ Ra @ X3 @ Y)))))). % list.rel_mono_strong
thf(fact_144_list_Orel__mono__strong, axiom,
    ((![R2 : produc1259892823t_char > produc1257910179t_char > $o, X3 : list_P1653548253t_char, Y : list_P757710633t_char, Ra : produc1259892823t_char > produc1257910179t_char > $o]: ((list_a72576659t_char @ R2 @ X3 @ Y) => ((![Z2 : produc1259892823t_char, Yb : produc1257910179t_char]: ((member397625600t_char @ Z2 @ (set_Pr1045701996t_char @ X3)) => ((member89690956t_char @ Yb @ (set_Pr1342796728t_char @ Y)) => ((R2 @ Z2 @ Yb) => (Ra @ Z2 @ Yb))))) => (list_a72576659t_char @ Ra @ X3 @ Y)))))). % list.rel_mono_strong
thf(fact_145_list_Orel__mono__strong, axiom,
    ((![R2 : ty > produc1777519579t_char > $o, X3 : list_ty, Y : list_P1234162913t_char, Ra : ty > produc1777519579t_char > $o]: ((list_a962849307t_char @ R2 @ X3 @ Y) => ((![Z2 : ty, Yb : produc1777519579t_char]: ((member_ty @ Z2 @ (set_ty2 @ X3)) => ((member958036996t_char @ Yb @ (set_Pr1611739760t_char @ Y)) => ((R2 @ Z2 @ Yb) => (Ra @ Z2 @ Yb))))) => (list_a962849307t_char @ Ra @ X3 @ Y)))))). % list.rel_mono_strong
thf(fact_146_list_Orel__mono__strong, axiom,
    ((![R2 : produc1777519579t_char > ty > $o, X3 : list_P1234162913t_char, Y : list_ty, Ra : produc1777519579t_char > ty > $o]: ((list_a1455926219har_ty @ R2 @ X3 @ Y) => ((![Z2 : produc1777519579t_char, Yb : ty]: ((member958036996t_char @ Z2 @ (set_Pr1611739760t_char @ X3)) => ((member_ty @ Yb @ (set_ty2 @ Y)) => ((R2 @ Z2 @ Yb) => (Ra @ Z2 @ Yb))))) => (list_a1455926219har_ty @ Ra @ X3 @ Y)))))). % list.rel_mono_strong
thf(fact_147_wf__J__prog__wf__J__mdecl, axiom,
    ((![P : list_P1234162913t_char, C : list_char, D2 : list_char, Fds : list_P1126587903har_ty, Mths : list_P1653548253t_char, Jmdcl : produc1259892823t_char]: ((wf_pro1229751607t_char @ wf_J_mdecl @ P) => ((member958036996t_char @ (produc1548560403t_char @ C @ (produc1972337867t_char @ D2 @ (produc1107711029t_char @ Fds @ Mths))) @ (set_Pr1611739760t_char @ P)) => ((member397625600t_char @ Jmdcl @ (set_Pr1045701996t_char @ Mths)) => (wf_J_mdecl @ P @ C @ Jmdcl))))))). % wf_J_prog_wf_J_mdecl
thf(fact_148_is__type__pTs, axiom,
    ((![Wf_md : list_P1234162913t_char > list_char > produc1259892823t_char > $o, P : list_P1234162913t_char, C : list_char, S : list_char, Fs : list_P1126587903har_ty, Ms : list_P1653548253t_char, M2 : list_char, Ts2 : list_ty, T2 : ty, M3 : produc1294284815t_char]: ((wf_pro1229751607t_char @ Wf_md @ P) => ((member958036996t_char @ (produc1548560403t_char @ C @ (produc1972337867t_char @ S @ (produc1107711029t_char @ Fs @ Ms))) @ (set_Pr1611739760t_char @ P)) => ((member397625600t_char @ (produc1238538255t_char @ M2 @ (produc1730359111t_char @ Ts2 @ (produc248075743t_char @ T2 @ M3))) @ (set_Pr1045701996t_char @ Ms)) => (ord_less_eq_set_ty @ (set_ty2 @ Ts2) @ (collect_ty @ (is_typ250416522t_char @ P))))))))). % is_type_pTs
thf(fact_149_has__field__mono, axiom,
    ((![P : list_P1234162913t_char, C : list_char, F : list_char, T2 : ty, D2 : list_char, C2 : list_char]: ((has_fi599584195t_char @ P @ C @ F @ T2 @ D2) => ((member89690956t_char @ (produc1304532571t_char @ C2 @ C) @ (transi1879726366t_char @ (subcls880436836t_char @ P))) => (has_fi599584195t_char @ P @ C2 @ F @ T2 @ D2)))))). % has_field_mono
thf(fact_150_has__fields__decl__above, axiom,
    ((![P : list_P1234162913t_char, C : list_char, FDTs : list_P1991792281har_ty, F : list_char, D2 : list_char, T2 : ty]: ((fields1441617180t_char @ P @ C @ FDTs) => ((member1618759584har_ty @ (produc112044931har_ty @ (produc1304532571t_char @ F @ D2) @ T2) @ (set_Pr1123858484har_ty @ FDTs)) => (member89690956t_char @ (produc1304532571t_char @ C @ D2) @ (transi1879726366t_char @ (subcls880436836t_char @ P)))))))). % has_fields_decl_above
thf(fact_151_subset__code_I1_J, axiom,
    ((![Xs : list_P757710633t_char, B5 : set_Pr164112643t_char]: ((ord_le167891107t_char @ (set_Pr1342796728t_char @ Xs) @ B5) = (![X7 : produc1257910179t_char]: (((member89690956t_char @ X7 @ (set_Pr1342796728t_char @ Xs))) => ((member89690956t_char @ X7 @ B5)))))))). % subset_code(1)
thf(fact_152_subset__code_I1_J, axiom,
    ((![Xs : list_ty, B5 : set_ty]: ((ord_less_eq_set_ty @ (set_ty2 @ Xs) @ B5) = (![X7 : ty]: (((member_ty @ X7 @ (set_ty2 @ Xs))) => ((member_ty @ X7 @ B5)))))))). % subset_code(1)
thf(fact_153_subset__code_I1_J, axiom,
    ((![Xs : list_P1234162913t_char, B5 : set_Pr2090064827t_char]: ((ord_le2010927963t_char @ (set_Pr1611739760t_char @ Xs) @ B5) = (![X7 : produc1777519579t_char]: (((member958036996t_char @ X7 @ (set_Pr1611739760t_char @ Xs))) => ((member958036996t_char @ X7 @ B5)))))))). % subset_code(1)
thf(fact_154_subset__code_I1_J, axiom,
    ((![Xs : list_P1653548253t_char, B5 : set_Pr1344692407t_char]: ((ord_le1781475415t_char @ (set_Pr1045701996t_char @ Xs) @ B5) = (![X7 : produc1259892823t_char]: (((member397625600t_char @ X7 @ (set_Pr1045701996t_char @ Xs))) => ((member397625600t_char @ X7 @ B5)))))))). % subset_code(1)
thf(fact_155_has__fields__types, axiom,
    ((![P : list_P1234162913t_char, C : list_char, FDTs : list_P1991792281har_ty, FD : produc1257910179t_char, T2 : ty, Wf_md : list_P1234162913t_char > list_char > produc1259892823t_char > $o]: ((fields1441617180t_char @ P @ C @ FDTs) => ((member1618759584har_ty @ (produc112044931har_ty @ FD @ T2) @ (set_Pr1123858484har_ty @ FDTs)) => ((wf_pro1229751607t_char @ Wf_md @ P) => (is_typ250416522t_char @ P @ T2))))))). % has_fields_types
thf(fact_156_subsetI, axiom,
    ((![A4 : set_Pr164112643t_char, B5 : set_Pr164112643t_char]: ((![X4 : produc1257910179t_char]: ((member89690956t_char @ X4 @ A4) => (member89690956t_char @ X4 @ B5))) => (ord_le167891107t_char @ A4 @ B5))))). % subsetI
thf(fact_157_subsetI, axiom,
    ((![A4 : set_Pr2090064827t_char, B5 : set_Pr2090064827t_char]: ((![X4 : produc1777519579t_char]: ((member958036996t_char @ X4 @ A4) => (member958036996t_char @ X4 @ B5))) => (ord_le2010927963t_char @ A4 @ B5))))). % subsetI
thf(fact_158_subsetI, axiom,
    ((![A4 : set_Pr1344692407t_char, B5 : set_Pr1344692407t_char]: ((![X4 : produc1259892823t_char]: ((member397625600t_char @ X4 @ A4) => (member397625600t_char @ X4 @ B5))) => (ord_le1781475415t_char @ A4 @ B5))))). % subsetI
thf(fact_159_list_Orel__mono, axiom,
    ((![R2 : ty > ty > $o, Ra : ty > ty > $o]: ((ord_less_eq_ty_ty_o @ R2 @ Ra) => (ord_le312888472t_ty_o @ (list_all2_ty_ty @ R2) @ (list_all2_ty_ty @ Ra)))))). % list.rel_mono
thf(fact_160_rtrancl__mono, axiom,
    ((![R : set_Pr164112643t_char, S2 : set_Pr164112643t_char]: ((ord_le167891107t_char @ R @ S2) => (ord_le167891107t_char @ (transi1879726366t_char @ R) @ (transi1879726366t_char @ S2)))))). % rtrancl_mono
thf(fact_161_rtrancl__subset, axiom,
    ((![R2 : set_Pr164112643t_char, S : set_Pr164112643t_char]: ((ord_le167891107t_char @ R2 @ S) => ((ord_le167891107t_char @ S @ (transi1879726366t_char @ R2)) => ((transi1879726366t_char @ S) = (transi1879726366t_char @ R2))))))). % rtrancl_subset
thf(fact_162_rtrancl__subset__rtrancl, axiom,
    ((![R : set_Pr164112643t_char, S2 : set_Pr164112643t_char]: ((ord_le167891107t_char @ R @ (transi1879726366t_char @ S2)) => (ord_le167891107t_char @ (transi1879726366t_char @ R) @ (transi1879726366t_char @ S2)))))). % rtrancl_subset_rtrancl
thf(fact_163_in__mono, axiom,
    ((![A4 : set_Pr164112643t_char, B5 : set_Pr164112643t_char, X3 : produc1257910179t_char]: ((ord_le167891107t_char @ A4 @ B5) => ((member89690956t_char @ X3 @ A4) => (member89690956t_char @ X3 @ B5)))))). % in_mono
thf(fact_164_in__mono, axiom,
    ((![A4 : set_Pr2090064827t_char, B5 : set_Pr2090064827t_char, X3 : produc1777519579t_char]: ((ord_le2010927963t_char @ A4 @ B5) => ((member958036996t_char @ X3 @ A4) => (member958036996t_char @ X3 @ B5)))))). % in_mono
thf(fact_165_in__mono, axiom,
    ((![A4 : set_Pr1344692407t_char, B5 : set_Pr1344692407t_char, X3 : produc1259892823t_char]: ((ord_le1781475415t_char @ A4 @ B5) => ((member397625600t_char @ X3 @ A4) => (member397625600t_char @ X3 @ B5)))))). % in_mono
thf(fact_166_subsetD, axiom,
    ((![A4 : set_Pr164112643t_char, B5 : set_Pr164112643t_char, C6 : produc1257910179t_char]: ((ord_le167891107t_char @ A4 @ B5) => ((member89690956t_char @ C6 @ A4) => (member89690956t_char @ C6 @ B5)))))). % subsetD
thf(fact_167_subsetD, axiom,
    ((![A4 : set_Pr2090064827t_char, B5 : set_Pr2090064827t_char, C6 : produc1777519579t_char]: ((ord_le2010927963t_char @ A4 @ B5) => ((member958036996t_char @ C6 @ A4) => (member958036996t_char @ C6 @ B5)))))). % subsetD
thf(fact_168_subsetD, axiom,
    ((![A4 : set_Pr1344692407t_char, B5 : set_Pr1344692407t_char, C6 : produc1259892823t_char]: ((ord_le1781475415t_char @ A4 @ B5) => ((member397625600t_char @ C6 @ A4) => (member397625600t_char @ C6 @ B5)))))). % subsetD
thf(fact_169_subset__eq, axiom,
    ((ord_le167891107t_char = (^[A6 : set_Pr164112643t_char]: (^[B6 : set_Pr164112643t_char]: (![X7 : produc1257910179t_char]: (((member89690956t_char @ X7 @ A6)) => ((member89690956t_char @ X7 @ B6))))))))). % subset_eq
thf(fact_170_subset__eq, axiom,
    ((ord_le2010927963t_char = (^[A6 : set_Pr2090064827t_char]: (^[B6 : set_Pr2090064827t_char]: (![X7 : produc1777519579t_char]: (((member958036996t_char @ X7 @ A6)) => ((member958036996t_char @ X7 @ B6))))))))). % subset_eq
thf(fact_171_subset__eq, axiom,
    ((ord_le1781475415t_char = (^[A6 : set_Pr1344692407t_char]: (^[B6 : set_Pr1344692407t_char]: (![X7 : produc1259892823t_char]: (((member397625600t_char @ X7 @ A6)) => ((member397625600t_char @ X7 @ B6))))))))). % subset_eq
thf(fact_172_subset__iff, axiom,
    ((ord_le167891107t_char = (^[A6 : set_Pr164112643t_char]: (^[B6 : set_Pr164112643t_char]: (![T6 : produc1257910179t_char]: (((member89690956t_char @ T6 @ A6)) => ((member89690956t_char @ T6 @ B6))))))))). % subset_iff
thf(fact_173_subset__iff, axiom,
    ((ord_le2010927963t_char = (^[A6 : set_Pr2090064827t_char]: (^[B6 : set_Pr2090064827t_char]: (![T6 : produc1777519579t_char]: (((member958036996t_char @ T6 @ A6)) => ((member958036996t_char @ T6 @ B6))))))))). % subset_iff
thf(fact_174_subset__iff, axiom,
    ((ord_le1781475415t_char = (^[A6 : set_Pr1344692407t_char]: (^[B6 : set_Pr1344692407t_char]: (![T6 : produc1259892823t_char]: (((member397625600t_char @ T6 @ A6)) => ((member397625600t_char @ T6 @ B6))))))))). % subset_iff
thf(fact_175_subcls__notin__has__fields, axiom,
    ((![P : list_P1234162913t_char, C : list_char, FDTs : list_P1991792281har_ty, F : list_char, D2 : list_char, T2 : ty]: ((fields1441617180t_char @ P @ C @ FDTs) => ((member1618759584har_ty @ (produc112044931har_ty @ (produc1304532571t_char @ F @ D2) @ T2) @ (set_Pr1123858484har_ty @ FDTs)) => (~ ((member89690956t_char @ (produc1304532571t_char @ D2 @ C) @ (transi648092672t_char @ (subcls880436836t_char @ P)))))))))). % subcls_notin_has_fields
thf(fact_176_all__fields__in__has__fields, axiom,
    ((![P : list_P1234162913t_char, C : list_char, FDTs : list_P1991792281har_ty, D2 : list_char, D3 : list_char, Fs : list_P1126587903har_ty, Ms : list_P1653548253t_char, F : list_char, T2 : ty]: ((fields1441617180t_char @ P @ C @ FDTs) => ((member89690956t_char @ (produc1304532571t_char @ C @ D2) @ (transi1879726366t_char @ (subcls880436836t_char @ P))) => (((class_2113391730t_char @ P @ D2) = (some_P882570996t_char @ (produc1972337867t_char @ D3 @ (produc1107711029t_char @ Fs @ Ms)))) => ((member325880354har_ty @ (produc1017542449har_ty @ F @ T2) @ (set_Pr1046707342har_ty @ Fs)) => (member1618759584har_ty @ (produc112044931har_ty @ (produc1304532571t_char @ F @ D2) @ T2) @ (set_Pr1123858484har_ty @ FDTs))))))))). % all_fields_in_has_fields
thf(fact_177_rtrancl__trancl__absorb, axiom,
    ((![R2 : set_Pr164112643t_char]: ((transi648092672t_char @ (transi1879726366t_char @ R2)) = (transi1879726366t_char @ R2))))). % rtrancl_trancl_absorb
thf(fact_178_trancl__rtrancl__absorb, axiom,
    ((![R2 : set_Pr164112643t_char]: ((transi1879726366t_char @ (transi648092672t_char @ R2)) = (transi1879726366t_char @ R2))))). % trancl_rtrancl_absorb
thf(fact_179_trancl__mono, axiom,
    ((![P2 : produc1257910179t_char, R : set_Pr164112643t_char, S2 : set_Pr164112643t_char]: ((member89690956t_char @ P2 @ (transi648092672t_char @ R)) => ((ord_le167891107t_char @ R @ S2) => (member89690956t_char @ P2 @ (transi648092672t_char @ S2))))))). % trancl_mono
thf(fact_180_r__into__trancl_H, axiom,
    ((![P2 : produc1257910179t_char, R : set_Pr164112643t_char]: ((member89690956t_char @ P2 @ R) => (member89690956t_char @ P2 @ (transi648092672t_char @ R)))))). % r_into_trancl'
thf(fact_181_trancl_Otrancl__into__trancl, axiom,
    ((![A : list_char, B : list_char, R : set_Pr164112643t_char, C6 : list_char]: ((member89690956t_char @ (produc1304532571t_char @ A @ B) @ (transi648092672t_char @ R)) => ((member89690956t_char @ (produc1304532571t_char @ B @ C6) @ R) => (member89690956t_char @ (produc1304532571t_char @ A @ C6) @ (transi648092672t_char @ R))))))). % trancl.trancl_into_trancl
thf(fact_182_converse__trancl__induct, axiom,
    ((![A : list_char, B : list_char, R : set_Pr164112643t_char, P : list_char > $o]: ((member89690956t_char @ (produc1304532571t_char @ A @ B) @ (transi648092672t_char @ R)) => ((![Y3 : list_char]: ((member89690956t_char @ (produc1304532571t_char @ Y3 @ B) @ R) => (P @ Y3))) => ((![Y3 : list_char, Z2 : list_char]: ((member89690956t_char @ (produc1304532571t_char @ Y3 @ Z2) @ R) => ((member89690956t_char @ (produc1304532571t_char @ Z2 @ B) @ (transi648092672t_char @ R)) => ((P @ Z2) => (P @ Y3))))) => (P @ A))))))). % converse_trancl_induct
thf(fact_183_trancl_Or__into__trancl, axiom,
    ((![A : list_char, B : list_char, R : set_Pr164112643t_char]: ((member89690956t_char @ (produc1304532571t_char @ A @ B) @ R) => (member89690956t_char @ (produc1304532571t_char @ A @ B) @ (transi648092672t_char @ R)))))). % trancl.r_into_trancl
thf(fact_184_trancl__trans__induct, axiom,
    ((![X3 : list_char, Y : list_char, R : set_Pr164112643t_char, P : list_char > list_char > $o]: ((member89690956t_char @ (produc1304532571t_char @ X3 @ Y) @ (transi648092672t_char @ R)) => ((![X4 : list_char, Y3 : list_char]: ((member89690956t_char @ (produc1304532571t_char @ X4 @ Y3) @ R) => (P @ X4 @ Y3))) => ((![X4 : list_char, Y3 : list_char, Z2 : list_char]: ((member89690956t_char @ (produc1304532571t_char @ X4 @ Y3) @ (transi648092672t_char @ R)) => ((P @ X4 @ Y3) => ((member89690956t_char @ (produc1304532571t_char @ Y3 @ Z2) @ (transi648092672t_char @ R)) => ((P @ Y3 @ Z2) => (P @ X4 @ Z2)))))) => (P @ X3 @ Y))))))). % trancl_trans_induct
thf(fact_185_trancl__into__trancl2, 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) @ (transi648092672t_char @ R)) => (member89690956t_char @ (produc1304532571t_char @ A @ C6) @ (transi648092672t_char @ R))))))). % trancl_into_trancl2
thf(fact_186_irrefl__trancl__rD, axiom,
    ((![R : set_Pr164112643t_char, X3 : list_char, Y : list_char]: ((![X4 : list_char]: (~ ((member89690956t_char @ (produc1304532571t_char @ X4 @ X4) @ (transi648092672t_char @ R))))) => ((member89690956t_char @ (produc1304532571t_char @ X3 @ Y) @ R) => (~ ((X3 = Y)))))))). % irrefl_trancl_rD

% Conjectures (2)
thf(conj_0, hypothesis,
    ((![Ts5 : list_ty, T7 : ty, Pns : list_list_char, Body : exp_list_char, D7 : list_char]: ((method297381284t_char @ p @ c @ m @ Ts5 @ T7 @ (produc713467969t_char @ Pns @ Body) @ D7) => ((list_all2_ty_ty @ (widen_917054840t_char @ p) @ ts @ Ts5) => ((widen_917054840t_char @ p @ T7 @ t) => thesis)))))).
thf(conj_1, conjecture,
    (thesis)).
