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thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_J, type,
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thf(ty_n_t__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J, type,
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thf(ty_n_t__List__Olist_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__Type__Oty_J_J, type,
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thf(ty_n_t__List__Olist_It__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_J, type,
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thf(ty_n_t__List__Olist_It__List__Olist_It__String__Ochar_J_J, type,
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thf(ty_n_t__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J, type,
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thf(ty_n_t__Option__Ooption_It__Value__Oval_J, type,
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thf(ty_n_t__Option__Ooption_It__Type__Oty_J, type,
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thf(ty_n_t__List__Olist_It__String__Ochar_J, type,
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thf(ty_n_t__List__Olist_It__Type__Oty_J, type,
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thf(ty_n_t__Set__Oset_It__Type__Oty_J, type,
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thf(ty_n_t__Value__Oval, type,
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thf(ty_n_t__Type__Oty, type,
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thf(ty_n_t__Nat__Onat, type,
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% Explicit typings (132)
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thf(sy_c_Expr_Oexp_Othrow_001t__List__Olist_It__String__Ochar_J, type,
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% Relevant facts (249)
thf(fact_0_UClass, axiom,
    ((u = (class @ c)))). % UClass
thf(fact_1_wte_H, axiom,
    ((wTrt @ p @ h_a @ e @ e_a @ u))). % wte'
thf(fact_2__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062U_O_A_092_060lbrakk_062P_ME_Mh_H_A_092_060turnstile_062_Ae_H_A_058_AU_059_AP_A_092_060turnstile_062_AU_A_092_060le_062_AClass_AC_092_060rbrakk_062_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062, axiom,
    ((~ ((![U : ty]: ((wTrt @ p @ h_a @ e @ e_a @ U) => (~ ((widen_917054840t_char @ p @ U @ (class @ c2)))))))))). % \<open>\<And>thesis. (\<And>U. \<lbrakk>P,E,h' \<turnstile> e' : U; P \<turnstile> U \<le> Class C\<rbrakk> \<Longrightarrow> thesis) \<Longrightarrow> thesis\<close>
thf(fact_3_ty_Oinject, axiom,
    ((![X5 : list_char, Y5 : list_char]: (((class @ X5) = (class @ Y5)) = (X5 = Y5))))). % ty.inject
thf(fact_4_local_Owf, axiom,
    ((wf_pro1229751607t_char @ wf_J_mdecl @ p))). % local.wf
thf(fact_5_wte, axiom,
    ((wTrt @ p @ ha @ e @ ea @ (class @ c2)))). % wte
thf(fact_6_UsubC, axiom,
    ((widen_917054840t_char @ p @ u @ (class @ c2)))). % UsubC
thf(fact_7_wtes, axiom,
    ((wTrts @ p @ ha @ e @ esa @ us))). % wtes
thf(fact_8__Csubclass_C, axiom,
    ((member89690956t_char @ (produc1304532571t_char @ c @ c2) @ (transi1879726366t_char @ (subcls880436836t_char @ p))))). % "subclass"
thf(fact_9_IH, axiom,
    ((![E : list_char > option_ty, T : ty]: ((typeSa1777264139_sconf @ p @ E @ (produc52622304on_val @ ha @ la)) => ((wTrt @ p @ ha @ E @ ea @ T) => (?[U : ty]: ((wTrt @ p @ h_a @ E @ e_a @ U) & (widen_917054840t_char @ p @ U @ T)))))))). % IH
thf(fact_10_conf, axiom,
    ((typeSa1777264139_sconf @ p @ e @ (produc52622304on_val @ ha @ la)))). % conf
thf(fact_11_calculation, axiom,
    (((u = nt) => (?[T2 : ty]: ((wTrt @ p @ h_a @ e @ (call_list_char @ e_a @ m @ esa) @ T2) & (widen_917054840t_char @ p @ T2 @ t)))))). % calculation
thf(fact_12_wt, axiom,
    ((wTrt @ p @ ha @ e @ (call_list_char @ ea @ m @ esa) @ t))). % wt
thf(fact_13_CallObj_Oprems_I1_J, axiom,
    ((typeSa1777264139_sconf @ p @ e @ (produc52622304on_val @ ha @ la)))). % CallObj.prems(1)
thf(fact_14_CallObj_Oprems_I2_J, axiom,
    ((wTrt @ p @ ha @ e @ (call_list_char @ ea @ m @ esa) @ t))). % CallObj.prems(2)
thf(fact_15_CallObj_Ohyps_I2_J, axiom,
    ((![E : list_char > option_ty, T : ty]: ((typeSa1777264139_sconf @ p @ E @ (produc52622304on_val @ ha @ la)) => ((wTrt @ p @ ha @ E @ ea @ T) => (?[T2 : ty]: ((wTrt @ p @ h_a @ E @ e_a @ T2) & (widen_917054840t_char @ p @ T2 @ T)))))))). % CallObj.hyps(2)
thf(fact_16__092_060open_062_092_060And_062Ts_O_A_092_060lbrakk_062P_ME_Mh_A_092_060turnstile_062_Ae_A_058_ANT_059_AP_ME_Mh_A_092_060turnstile_062_Aes_A_091_058_093_ATs_092_060rbrakk_062_A_092_060Longrightarrow_062_A_092_060exists_062T_H_O_AP_ME_Mh_H_A_092_060turnstile_062_Ae_H_092_060bullet_062M_Ies_J_A_058_AT_H_A_092_060and_062_AP_A_092_060turnstile_062_AT_H_A_092_060le_062_AT_092_060close_062, axiom,
    ((![Ts : list_ty]: ((wTrt @ p @ ha @ e @ ea @ nt) => ((wTrts @ p @ ha @ e @ esa @ Ts) => (?[T2 : ty]: ((wTrt @ p @ h_a @ e @ (call_list_char @ e_a @ m @ esa) @ T2) & (widen_917054840t_char @ p @ T2 @ 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_17_ty_Odistinct_I19_J, axiom,
    ((![X5 : list_char]: (~ ((nt = (class @ X5))))))). % ty.distinct(19)
thf(fact_18_Class__widen__Class, axiom,
    ((![P : list_P1234162913t_char, C : list_char, D : list_char]: ((widen_917054840t_char @ P @ (class @ C) @ (class @ D)) = (member89690956t_char @ (produc1304532571t_char @ C @ D) @ (transi1879726366t_char @ (subcls880436836t_char @ P))))))). % Class_widen_Class
thf(fact_19_widen_Ocases, axiom,
    ((![P : list_P1234162913t_char, A1 : ty, A2 : ty]: ((widen_917054840t_char @ P @ A1 @ A2) => ((~ ((A2 = A1))) => ((![C2 : list_char]: ((A1 = (class @ C2)) => (![D2 : list_char]: ((A2 = (class @ D2)) => (~ ((member89690956t_char @ (produc1304532571t_char @ C2 @ D2) @ (transi1879726366t_char @ (subcls880436836t_char @ P))))))))) => (~ (((A1 = nt) => (![C2 : list_char]: (~ ((A2 = (class @ C2)))))))))))))). % widen.cases
thf(fact_20_widen_Osimps, axiom,
    ((widen_917054840t_char = (^[P2 : list_P1234162913t_char]: (^[A12 : ty]: (^[A22 : ty]: (((?[T3 : ty]: (((A12 = T3)) & ((A22 = T3))))) | ((((?[C3 : list_char]: (?[D3 : list_char]: (((A12 = (class @ C3))) & ((((A22 = (class @ D3))) & ((member89690956t_char @ (produc1304532571t_char @ C3 @ D3) @ (transi1879726366t_char @ (subcls880436836t_char @ P2)))))))))) | ((?[C3 : list_char]: (((A12 = nt)) & ((A22 = (class @ C3))))))))))))))). % widen.simps
thf(fact_21_widen__Class, axiom,
    ((![P : list_P1234162913t_char, T : ty, C : list_char]: ((widen_917054840t_char @ P @ T @ (class @ C)) = (((T = nt)) | ((?[D3 : list_char]: (((T = (class @ D3))) & ((member89690956t_char @ (produc1304532571t_char @ D3 @ C) @ (transi1879726366t_char @ (subcls880436836t_char @ P)))))))))))). % widen_Class
thf(fact_22_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)) => ((![C2 : list_char, D2 : list_char]: ((member89690956t_char @ (produc1304532571t_char @ C2 @ D2) @ (transi1879726366t_char @ (subcls880436836t_char @ P))) => (Pa @ (class @ C2) @ (class @ D2)))) => ((![C2 : list_char]: (Pa @ nt @ (class @ C2))) => (Pa @ X1 @ X2)))))))). % widen.inducts
thf(fact_23_widen__subcls, axiom,
    ((![C : list_char, D : list_char, P : list_P1234162913t_char]: ((member89690956t_char @ (produc1304532571t_char @ C @ D) @ (transi1879726366t_char @ (subcls880436836t_char @ P))) => (widen_917054840t_char @ P @ (class @ C) @ (class @ D)))))). % widen_subcls
thf(fact_24_subs, axiom,
    ((list_all2_ty_ty @ (widen_917054840t_char @ p) @ us @ ts))). % subs
thf(fact_25_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, T : ty]: ((wTrt @ P @ H @ E @ E2 @ nt) => ((wTrts @ P @ H @ E @ Es @ Ts) => (wTrt @ P @ H @ E @ (call_list_char @ E2 @ M @ Es) @ T)))))). % WTrtCallNT
thf(fact_26_widen__null, axiom,
    ((![P : list_P1234162913t_char, C : list_char]: (widen_917054840t_char @ P @ nt @ (class @ C))))). % widen_null
thf(fact_27_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_28_widens__refl, axiom,
    ((![P : list_P1234162913t_char, Xs : list_ty]: (list_all2_ty_ty @ (widen_917054840t_char @ P) @ Xs @ Xs)))). % widens_refl
thf(fact_29_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_30_widen__refl, axiom,
    ((![P : list_P1234162913t_char, T : ty]: (widen_917054840t_char @ P @ T @ T)))). % widen_refl
thf(fact_31_widen__trans, axiom,
    ((![P : list_P1234162913t_char, S : ty, U2 : ty, T : ty]: ((widen_917054840t_char @ P @ S @ U2) => ((widen_917054840t_char @ P @ U2 @ T) => (widen_917054840t_char @ P @ S @ T)))))). % widen_trans
thf(fact_32_Class__widen, axiom,
    ((![P : list_P1234162913t_char, C : list_char, T : ty]: ((widen_917054840t_char @ P @ (class @ C) @ T) => (?[D2 : list_char]: (T = (class @ D2))))))). % Class_widen
thf(fact_33_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_34_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_35_r__into__rtrancl, axiom,
    ((![P3 : produc655058983on_val, R : set_Pr208351751on_val]: ((member1689761872on_val @ P3 @ R) => (member1689761872on_val @ P3 @ (transi325225921on_val @ R)))))). % r_into_rtrancl
thf(fact_36_rtrancl__idemp, axiom,
    ((![R : set_Pr164112643t_char]: ((transi1879726366t_char @ (transi1879726366t_char @ R)) = (transi1879726366t_char @ R))))). % rtrancl_idemp
thf(fact_37_rtrancl__idemp, axiom,
    ((![R : set_Pr1189492743on_val]: ((transi111096263on_val @ (transi111096263on_val @ R)) = (transi111096263on_val @ R))))). % rtrancl_idemp
thf(fact_38_rtrancl__idemp, axiom,
    ((![R : set_Pr208351751on_val]: ((transi325225921on_val @ (transi325225921on_val @ R)) = (transi325225921on_val @ R))))). % rtrancl_idemp
thf(fact_39_method, axiom,
    ((method297381284t_char @ p @ c2 @ m @ ts @ t @ (produc713467969t_char @ pns @ body) @ d))). % method
thf(fact_40_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_41_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_42_old_Oprod_Oinject, axiom,
    ((![A : list_exp_list_char, B : produc515445032on_val, A3 : list_exp_list_char, B2 : produc515445032on_val]: (((produc1725134254on_val @ A @ B) = (produc1725134254on_val @ A3 @ B2)) = (((A = A3)) & ((B = B2))))))). % old.prod.inject
thf(fact_43_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_44_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_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 : list_exp_list_char, X2 : produc515445032on_val, Y1 : list_exp_list_char, Y2 : produc515445032on_val]: (((produc1725134254on_val @ X1 @ X2) = (produc1725134254on_val @ Y1 @ Y2)) = (((X1 = Y1)) & ((X2 = Y2))))))). % prod.inject
thf(fact_48_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_49_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_50_converse__rtrancl__into__rtrancl, axiom,
    ((![A : list_char, B : list_char, R : set_Pr164112643t_char, C4 : list_char]: ((member89690956t_char @ (produc1304532571t_char @ A @ B) @ R) => ((member89690956t_char @ (produc1304532571t_char @ B @ C4) @ (transi1879726366t_char @ R)) => (member89690956t_char @ (produc1304532571t_char @ A @ C4) @ (transi1879726366t_char @ R))))))). % converse_rtrancl_into_rtrancl
thf(fact_51_converse__rtrancl__into__rtrancl, axiom,
    ((![A : produc1097884484on_val, B : produc1097884484on_val, R : set_Pr1189492743on_val, C4 : produc1097884484on_val]: ((member354538064on_val @ (produc1069526295on_val @ A @ B) @ R) => ((member354538064on_val @ (produc1069526295on_val @ B @ C4) @ (transi111096263on_val @ R)) => (member354538064on_val @ (produc1069526295on_val @ A @ C4) @ (transi111096263on_val @ R))))))). % converse_rtrancl_into_rtrancl
thf(fact_52_converse__rtrancl__into__rtrancl, axiom,
    ((![A : produc335961278on_val, B : produc335961278on_val, R : set_Pr208351751on_val, C4 : produc335961278on_val]: ((member1689761872on_val @ (produc245869591on_val @ A @ B) @ R) => ((member1689761872on_val @ (produc245869591on_val @ B @ C4) @ (transi325225921on_val @ R)) => (member1689761872on_val @ (produc245869591on_val @ A @ C4) @ (transi325225921on_val @ R))))))). % converse_rtrancl_into_rtrancl
thf(fact_53_rtrancl_Ortrancl__into__rtrancl, axiom,
    ((![A : list_char, B : list_char, R : set_Pr164112643t_char, C4 : list_char]: ((member89690956t_char @ (produc1304532571t_char @ A @ B) @ (transi1879726366t_char @ R)) => ((member89690956t_char @ (produc1304532571t_char @ B @ C4) @ R) => (member89690956t_char @ (produc1304532571t_char @ A @ C4) @ (transi1879726366t_char @ R))))))). % rtrancl.rtrancl_into_rtrancl
thf(fact_54_rtrancl_Ortrancl__into__rtrancl, axiom,
    ((![A : produc1097884484on_val, B : produc1097884484on_val, R : set_Pr1189492743on_val, C4 : produc1097884484on_val]: ((member354538064on_val @ (produc1069526295on_val @ A @ B) @ (transi111096263on_val @ R)) => ((member354538064on_val @ (produc1069526295on_val @ B @ C4) @ R) => (member354538064on_val @ (produc1069526295on_val @ A @ C4) @ (transi111096263on_val @ R))))))). % rtrancl.rtrancl_into_rtrancl
thf(fact_55_rtrancl_Ortrancl__into__rtrancl, axiom,
    ((![A : produc335961278on_val, B : produc335961278on_val, R : set_Pr208351751on_val, C4 : produc335961278on_val]: ((member1689761872on_val @ (produc245869591on_val @ A @ B) @ (transi325225921on_val @ R)) => ((member1689761872on_val @ (produc245869591on_val @ B @ C4) @ R) => (member1689761872on_val @ (produc245869591on_val @ A @ C4) @ (transi325225921on_val @ R))))))). % rtrancl.rtrancl_into_rtrancl
thf(fact_56_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) => ((![Y : list_char, Z : list_char]: ((member89690956t_char @ (produc1304532571t_char @ Y @ Z) @ R) => ((member89690956t_char @ (produc1304532571t_char @ Z @ B) @ (transi1879726366t_char @ R)) => ((P @ Z) => (P @ Y))))) => (P @ A))))))). % converse_rtrancl_induct
thf(fact_57_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) => ((![Y : produc1097884484on_val, Z : produc1097884484on_val]: ((member354538064on_val @ (produc1069526295on_val @ Y @ Z) @ R) => ((member354538064on_val @ (produc1069526295on_val @ Z @ B) @ (transi111096263on_val @ R)) => ((P @ Z) => (P @ Y))))) => (P @ A))))))). % converse_rtrancl_induct
thf(fact_58_converse__rtrancl__induct, axiom,
    ((![A : produc335961278on_val, B : produc335961278on_val, R : set_Pr208351751on_val, P : produc335961278on_val > $o]: ((member1689761872on_val @ (produc245869591on_val @ A @ B) @ (transi325225921on_val @ R)) => ((P @ B) => ((![Y : produc335961278on_val, Z : produc335961278on_val]: ((member1689761872on_val @ (produc245869591on_val @ Y @ Z) @ R) => ((member1689761872on_val @ (produc245869591on_val @ Z @ B) @ (transi325225921on_val @ R)) => ((P @ Z) => (P @ Y))))) => (P @ A))))))). % converse_rtrancl_induct
thf(fact_59_sees__method__idemp, axiom,
    ((![P : list_P1234162913t_char, C : list_char, M : list_char, Ts : list_ty, T : ty, M2 : produc1294284815t_char, D : list_char]: ((method297381284t_char @ P @ C @ M @ Ts @ T @ M2 @ D) => (method297381284t_char @ P @ D @ M @ Ts @ T @ M2 @ D))))). % sees_method_idemp
thf(fact_60_sees__method__fun, axiom,
    ((![P : list_P1234162913t_char, C : list_char, M : list_char, TS : list_ty, T : ty, M2 : produc1294284815t_char, D : list_char, TS2 : list_ty, T5 : ty, M3 : produc1294284815t_char, D4 : list_char]: ((method297381284t_char @ P @ C @ M @ TS @ T @ M2 @ D) => ((method297381284t_char @ P @ C @ M @ TS2 @ T5 @ M3 @ D4) => ((TS2 = TS) & ((T5 = T) & ((M3 = M2) & (D4 = D))))))))). % sees_method_fun
thf(fact_61_mem__Collect__eq, axiom,
    ((![A : produc1257910179t_char, P : produc1257910179t_char > $o]: ((member89690956t_char @ A @ (collec768236686t_char @ P)) = (P @ A))))). % mem_Collect_eq
thf(fact_62_mem__Collect__eq, axiom,
    ((![A : produc1172664615on_val, P : produc1172664615on_val > $o]: ((member354538064on_val @ A @ (collec2055896722on_val @ P)) = (P @ A))))). % mem_Collect_eq
thf(fact_63_mem__Collect__eq, axiom,
    ((![A : produc1777519579t_char, P : produc1777519579t_char > $o]: ((member958036996t_char @ A @ (collec178542150t_char @ P)) = (P @ A))))). % mem_Collect_eq
thf(fact_64_mem__Collect__eq, axiom,
    ((![A : produc1259892823t_char, P : produc1259892823t_char > $o]: ((member397625600t_char @ A @ (collec1549347906t_char @ P)) = (P @ A))))). % mem_Collect_eq
thf(fact_65_mem__Collect__eq, axiom,
    ((![A : produc655058983on_val, P : produc655058983on_val > $o]: ((member1689761872on_val @ A @ (collec105960082on_val @ P)) = (P @ A))))). % mem_Collect_eq
thf(fact_66_Collect__mem__eq, axiom,
    ((![A4 : set_Pr164112643t_char]: ((collec768236686t_char @ (^[X : produc1257910179t_char]: (member89690956t_char @ X @ A4))) = A4)))). % Collect_mem_eq
thf(fact_67_Collect__mem__eq, axiom,
    ((![A4 : set_Pr1189492743on_val]: ((collec2055896722on_val @ (^[X : produc1172664615on_val]: (member354538064on_val @ X @ A4))) = A4)))). % Collect_mem_eq
thf(fact_68_Collect__mem__eq, axiom,
    ((![A4 : set_Pr2090064827t_char]: ((collec178542150t_char @ (^[X : produc1777519579t_char]: (member958036996t_char @ X @ A4))) = A4)))). % Collect_mem_eq
thf(fact_69_Collect__mem__eq, axiom,
    ((![A4 : set_Pr1344692407t_char]: ((collec1549347906t_char @ (^[X : produc1259892823t_char]: (member397625600t_char @ X @ A4))) = A4)))). % Collect_mem_eq
thf(fact_70_Collect__mem__eq, axiom,
    ((![A4 : set_Pr208351751on_val]: ((collec105960082on_val @ (^[X : produc655058983on_val]: (member1689761872on_val @ X @ A4))) = A4)))). % Collect_mem_eq
thf(fact_71_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) => ((![A5 : list_char, B3 : list_char, Aa : list_char, Ba : list_char]: ((member803902992t_char @ (produc395356247t_char @ (produc1304532571t_char @ A5 @ 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 @ A5 @ B3))))) => (P @ Ax @ Ay))))))). % converse_rtrancl_induct2
thf(fact_72_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) => ((![A5 : list_list_char, B3 : exp_list_char, Aa : list_list_char, Ba : exp_list_char]: ((member1392938152t_char @ (produc618657463t_char @ (produc713467969t_char @ A5 @ 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 @ A5 @ B3))))) => (P @ Ax @ Ay))))))). % converse_rtrancl_induct2
thf(fact_73_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) => ((![A5 : nat > option2118145160on_val, B3 : list_char > option_val, Aa : nat > option2118145160on_val, Ba : list_char > option_val]: ((member2027247312on_val @ (produc2106877847on_val @ (produc52622304on_val @ A5 @ 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 @ A5 @ B3))))) => (P @ Ax @ Ay))))))). % converse_rtrancl_induct2
thf(fact_74_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) => ((![A5 : exp_list_char, B3 : produc515445032on_val, Aa : exp_list_char, Ba : produc515445032on_val]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ A5 @ 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 @ A5 @ B3))))) => (P @ Ax @ Ay))))))). % converse_rtrancl_induct2
thf(fact_75_converse__rtrancl__induct2, axiom,
    ((![Ax : list_exp_list_char, Ay : produc515445032on_val, Bx : list_exp_list_char, By : produc515445032on_val, R : set_Pr208351751on_val, P : list_exp_list_char > produc515445032on_val > $o]: ((member1689761872on_val @ (produc245869591on_val @ (produc1725134254on_val @ Ax @ Ay) @ (produc1725134254on_val @ Bx @ By)) @ (transi325225921on_val @ R)) => ((P @ Bx @ By) => ((![A5 : list_exp_list_char, B3 : produc515445032on_val, Aa : list_exp_list_char, Ba : produc515445032on_val]: ((member1689761872on_val @ (produc245869591on_val @ (produc1725134254on_val @ A5 @ B3) @ (produc1725134254on_val @ Aa @ Ba)) @ R) => ((member1689761872on_val @ (produc245869591on_val @ (produc1725134254on_val @ Aa @ Ba) @ (produc1725134254on_val @ Bx @ By)) @ (transi325225921on_val @ R)) => ((P @ Aa @ Ba) => (P @ A5 @ B3))))) => (P @ Ax @ Ay))))))). % converse_rtrancl_induct2
thf(fact_76_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)))) => (~ ((![A5 : list_char, B3 : list_char]: ((member803902992t_char @ (produc395356247t_char @ (produc1304532571t_char @ Xa @ Xb) @ (produc1304532571t_char @ A5 @ B3)) @ R) => (~ ((member803902992t_char @ (produc395356247t_char @ (produc1304532571t_char @ A5 @ B3) @ (produc1304532571t_char @ Za @ Zb)) @ (transi858104614t_char @ R))))))))))))). % converse_rtranclE2
thf(fact_77_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)))) => (~ ((![A5 : list_list_char, B3 : exp_list_char]: ((member1392938152t_char @ (produc618657463t_char @ (produc713467969t_char @ Xa @ Xb) @ (produc713467969t_char @ A5 @ B3)) @ R) => (~ ((member1392938152t_char @ (produc618657463t_char @ (produc713467969t_char @ A5 @ B3) @ (produc713467969t_char @ Za @ Zb)) @ (transi1892282060t_char @ R))))))))))))). % converse_rtranclE2
thf(fact_78_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)))) => (~ ((![A5 : nat > option2118145160on_val, B3 : list_char > option_val]: ((member2027247312on_val @ (produc2106877847on_val @ (produc52622304on_val @ Xa @ Xb) @ (produc52622304on_val @ A5 @ B3)) @ R) => (~ ((member2027247312on_val @ (produc2106877847on_val @ (produc52622304on_val @ A5 @ B3) @ (produc52622304on_val @ Za @ Zb)) @ (transi432893227on_val @ R))))))))))))). % converse_rtranclE2
thf(fact_79_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)))) => (~ ((![A5 : exp_list_char, B3 : produc515445032on_val]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ Xa @ Xb) @ (produc2023458740on_val @ A5 @ B3)) @ R) => (~ ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ A5 @ B3) @ (produc2023458740on_val @ Za @ Zb)) @ (transi111096263on_val @ R))))))))))))). % converse_rtranclE2
thf(fact_80_converse__rtranclE2, axiom,
    ((![Xa : list_exp_list_char, Xb : produc515445032on_val, Za : list_exp_list_char, Zb : produc515445032on_val, R : set_Pr208351751on_val]: ((member1689761872on_val @ (produc245869591on_val @ (produc1725134254on_val @ Xa @ Xb) @ (produc1725134254on_val @ Za @ Zb)) @ (transi325225921on_val @ R)) => ((~ (((produc1725134254on_val @ Xa @ Xb) = (produc1725134254on_val @ Za @ Zb)))) => (~ ((![A5 : list_exp_list_char, B3 : produc515445032on_val]: ((member1689761872on_val @ (produc245869591on_val @ (produc1725134254on_val @ Xa @ Xb) @ (produc1725134254on_val @ A5 @ B3)) @ R) => (~ ((member1689761872on_val @ (produc245869591on_val @ (produc1725134254on_val @ A5 @ B3) @ (produc1725134254on_val @ Za @ Zb)) @ (transi325225921on_val @ R))))))))))))). % converse_rtranclE2
thf(fact_81_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) => ((![A5 : list_char, B3 : list_char, Aa : list_char, Ba : list_char]: ((member803902992t_char @ (produc395356247t_char @ (produc1304532571t_char @ Ax @ Ay) @ (produc1304532571t_char @ A5 @ B3)) @ (transi858104614t_char @ R)) => ((member803902992t_char @ (produc395356247t_char @ (produc1304532571t_char @ A5 @ B3) @ (produc1304532571t_char @ Aa @ Ba)) @ R) => ((P @ A5 @ B3) => (P @ Aa @ Ba))))) => (P @ Bx @ By))))))). % rtrancl_induct2
thf(fact_82_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) => ((![A5 : 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 @ A5 @ B3)) @ (transi1892282060t_char @ R)) => ((member1392938152t_char @ (produc618657463t_char @ (produc713467969t_char @ A5 @ B3) @ (produc713467969t_char @ Aa @ Ba)) @ R) => ((P @ A5 @ B3) => (P @ Aa @ Ba))))) => (P @ Bx @ By))))))). % rtrancl_induct2
thf(fact_83_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) => ((![A5 : 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 @ A5 @ B3)) @ (transi432893227on_val @ R)) => ((member2027247312on_val @ (produc2106877847on_val @ (produc52622304on_val @ A5 @ B3) @ (produc52622304on_val @ Aa @ Ba)) @ R) => ((P @ A5 @ B3) => (P @ Aa @ Ba))))) => (P @ Bx @ By))))))). % rtrancl_induct2
thf(fact_84_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) => ((![A5 : exp_list_char, B3 : produc515445032on_val, Aa : exp_list_char, Ba : produc515445032on_val]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ Ax @ Ay) @ (produc2023458740on_val @ A5 @ B3)) @ (transi111096263on_val @ R)) => ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ A5 @ B3) @ (produc2023458740on_val @ Aa @ Ba)) @ R) => ((P @ A5 @ B3) => (P @ Aa @ Ba))))) => (P @ Bx @ By))))))). % rtrancl_induct2
thf(fact_85_rtrancl__induct2, axiom,
    ((![Ax : list_exp_list_char, Ay : produc515445032on_val, Bx : list_exp_list_char, By : produc515445032on_val, R : set_Pr208351751on_val, P : list_exp_list_char > produc515445032on_val > $o]: ((member1689761872on_val @ (produc245869591on_val @ (produc1725134254on_val @ Ax @ Ay) @ (produc1725134254on_val @ Bx @ By)) @ (transi325225921on_val @ R)) => ((P @ Ax @ Ay) => ((![A5 : list_exp_list_char, B3 : produc515445032on_val, Aa : list_exp_list_char, Ba : produc515445032on_val]: ((member1689761872on_val @ (produc245869591on_val @ (produc1725134254on_val @ Ax @ Ay) @ (produc1725134254on_val @ A5 @ B3)) @ (transi325225921on_val @ R)) => ((member1689761872on_val @ (produc245869591on_val @ (produc1725134254on_val @ A5 @ B3) @ (produc1725134254on_val @ Aa @ Ba)) @ R) => ((P @ A5 @ B3) => (P @ Aa @ Ba))))) => (P @ Bx @ By))))))). % rtrancl_induct2
thf(fact_86_surj__pair, axiom,
    ((![P3 : produc1257910179t_char]: (?[X3 : list_char, Y : list_char]: (P3 = (produc1304532571t_char @ X3 @ Y)))))). % surj_pair
thf(fact_87_surj__pair, axiom,
    ((![P3 : produc1294284815t_char]: (?[X3 : list_list_char, Y : exp_list_char]: (P3 = (produc713467969t_char @ X3 @ Y)))))). % surj_pair
thf(fact_88_surj__pair, axiom,
    ((![P3 : produc335961278on_val]: (?[X3 : list_exp_list_char, Y : produc515445032on_val]: (P3 = (produc1725134254on_val @ X3 @ Y)))))). % surj_pair
thf(fact_89_surj__pair, axiom,
    ((![P3 : produc1097884484on_val]: (?[X3 : exp_list_char, Y : produc515445032on_val]: (P3 = (produc2023458740on_val @ X3 @ Y)))))). % surj_pair
thf(fact_90_surj__pair, axiom,
    ((![P3 : produc515445032on_val]: (?[X3 : nat > option2118145160on_val, Y : list_char > option_val]: (P3 = (produc52622304on_val @ X3 @ Y)))))). % surj_pair
thf(fact_91_prod__cases, axiom,
    ((![P : produc1257910179t_char > $o, P3 : produc1257910179t_char]: ((![A5 : list_char, B3 : list_char]: (P @ (produc1304532571t_char @ A5 @ B3))) => (P @ P3))))). % prod_cases
thf(fact_92_prod__cases, axiom,
    ((![P : produc1294284815t_char > $o, P3 : produc1294284815t_char]: ((![A5 : list_list_char, B3 : exp_list_char]: (P @ (produc713467969t_char @ A5 @ B3))) => (P @ P3))))). % prod_cases
thf(fact_93_prod__cases, axiom,
    ((![P : produc335961278on_val > $o, P3 : produc335961278on_val]: ((![A5 : list_exp_list_char, B3 : produc515445032on_val]: (P @ (produc1725134254on_val @ A5 @ B3))) => (P @ P3))))). % prod_cases
thf(fact_94_prod__cases, axiom,
    ((![P : produc1097884484on_val > $o, P3 : produc1097884484on_val]: ((![A5 : exp_list_char, B3 : produc515445032on_val]: (P @ (produc2023458740on_val @ A5 @ B3))) => (P @ P3))))). % prod_cases
thf(fact_95_prod__cases, axiom,
    ((![P : produc515445032on_val > $o, P3 : produc515445032on_val]: ((![A5 : nat > option2118145160on_val, B3 : list_char > option_val]: (P @ (produc52622304on_val @ A5 @ B3))) => (P @ P3))))). % prod_cases
thf(fact_96_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_97_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_98_Pair__inject, axiom,
    ((![A : list_exp_list_char, B : produc515445032on_val, A3 : list_exp_list_char, B2 : produc515445032on_val]: (((produc1725134254on_val @ A @ B) = (produc1725134254on_val @ A3 @ B2)) => (~ (((A = A3) => (~ ((B = B2)))))))))). % Pair_inject
thf(fact_99_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_100_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_101_prod__cases3, axiom,
    ((![Y3 : produc335961278on_val]: (~ ((![A5 : list_exp_list_char, B3 : nat > option2118145160on_val, C5 : list_char > option_val]: (~ ((Y3 = (produc1725134254on_val @ A5 @ (produc52622304on_val @ B3 @ C5))))))))))). % prod_cases3
thf(fact_102_prod__cases3, axiom,
    ((![Y3 : produc1097884484on_val]: (~ ((![A5 : exp_list_char, B3 : nat > option2118145160on_val, C5 : list_char > option_val]: (~ ((Y3 = (produc2023458740on_val @ A5 @ (produc52622304on_val @ B3 @ C5))))))))))). % prod_cases3
thf(fact_103_prod__induct3, axiom,
    ((![P : produc335961278on_val > $o, X4 : produc335961278on_val]: ((![A5 : list_exp_list_char, B3 : nat > option2118145160on_val, C5 : list_char > option_val]: (P @ (produc1725134254on_val @ A5 @ (produc52622304on_val @ B3 @ C5)))) => (P @ X4))))). % prod_induct3
thf(fact_104_prod__induct3, axiom,
    ((![P : produc1097884484on_val > $o, X4 : produc1097884484on_val]: ((![A5 : exp_list_char, B3 : nat > option2118145160on_val, C5 : list_char > option_val]: (P @ (produc2023458740on_val @ A5 @ (produc52622304on_val @ B3 @ C5)))) => (P @ X4))))). % prod_induct3
thf(fact_105_old_Oprod_Oexhaust, axiom,
    ((![Y3 : produc1257910179t_char]: (~ ((![A5 : list_char, B3 : list_char]: (~ ((Y3 = (produc1304532571t_char @ A5 @ B3)))))))))). % old.prod.exhaust
thf(fact_106_old_Oprod_Oexhaust, axiom,
    ((![Y3 : produc1294284815t_char]: (~ ((![A5 : list_list_char, B3 : exp_list_char]: (~ ((Y3 = (produc713467969t_char @ A5 @ B3)))))))))). % old.prod.exhaust
thf(fact_107_old_Oprod_Oexhaust, axiom,
    ((![Y3 : produc335961278on_val]: (~ ((![A5 : list_exp_list_char, B3 : produc515445032on_val]: (~ ((Y3 = (produc1725134254on_val @ A5 @ B3)))))))))). % old.prod.exhaust
thf(fact_108_old_Oprod_Oexhaust, axiom,
    ((![Y3 : produc1097884484on_val]: (~ ((![A5 : exp_list_char, B3 : produc515445032on_val]: (~ ((Y3 = (produc2023458740on_val @ A5 @ B3)))))))))). % old.prod.exhaust
thf(fact_109_old_Oprod_Oexhaust, axiom,
    ((![Y3 : produc515445032on_val]: (~ ((![A5 : nat > option2118145160on_val, B3 : list_char > option_val]: (~ ((Y3 = (produc52622304on_val @ A5 @ B3)))))))))). % old.prod.exhaust
thf(fact_110_old_Oprod_Oinducts, axiom,
    ((![P : produc1257910179t_char > $o, Prod : produc1257910179t_char]: ((![A5 : list_char, B3 : list_char]: (P @ (produc1304532571t_char @ A5 @ B3))) => (P @ Prod))))). % old.prod.inducts
thf(fact_111_old_Oprod_Oinducts, axiom,
    ((![P : produc1294284815t_char > $o, Prod : produc1294284815t_char]: ((![A5 : list_list_char, B3 : exp_list_char]: (P @ (produc713467969t_char @ A5 @ B3))) => (P @ Prod))))). % old.prod.inducts
thf(fact_112_old_Oprod_Oinducts, axiom,
    ((![P : produc335961278on_val > $o, Prod : produc335961278on_val]: ((![A5 : list_exp_list_char, B3 : produc515445032on_val]: (P @ (produc1725134254on_val @ A5 @ B3))) => (P @ Prod))))). % old.prod.inducts
thf(fact_113_old_Oprod_Oinducts, axiom,
    ((![P : produc1097884484on_val > $o, Prod : produc1097884484on_val]: ((![A5 : exp_list_char, B3 : produc515445032on_val]: (P @ (produc2023458740on_val @ A5 @ B3))) => (P @ Prod))))). % old.prod.inducts
thf(fact_114_old_Oprod_Oinducts, axiom,
    ((![P : produc515445032on_val > $o, Prod : produc515445032on_val]: ((![A5 : nat > option2118145160on_val, B3 : list_char > option_val]: (P @ (produc52622304on_val @ A5 @ B3))) => (P @ Prod))))). % old.prod.inducts
thf(fact_115_WTrtCall, axiom,
    ((![P : list_P1234162913t_char, H : nat > option2118145160on_val, E : list_char > option_ty, E2 : exp_list_char, C : list_char, M : list_char, Ts : list_ty, T : 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 @ C)) => ((method297381284t_char @ P @ C @ M @ Ts @ T @ (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) @ T)))))))). % WTrtCall
thf(fact_116_sees__method__decl__mono, axiom,
    ((![C6 : list_char, C : list_char, P : list_P1234162913t_char, M : list_char, Ts : list_ty, T : ty, M2 : produc1294284815t_char, D : list_char, Ts2 : list_ty, T5 : ty, M3 : produc1294284815t_char, D4 : list_char]: ((member89690956t_char @ (produc1304532571t_char @ C6 @ C) @ (transi1879726366t_char @ (subcls880436836t_char @ P))) => ((method297381284t_char @ P @ C @ M @ Ts @ T @ M2 @ D) => ((method297381284t_char @ P @ C6 @ M @ Ts2 @ T5 @ M3 @ D4) => (member89690956t_char @ (produc1304532571t_char @ D4 @ D) @ (transi1879726366t_char @ (subcls880436836t_char @ P))))))))). % sees_method_decl_mono
thf(fact_117_sees__method__decl__above, axiom,
    ((![P : list_P1234162913t_char, C : list_char, M : list_char, Ts : list_ty, T : ty, M2 : produc1294284815t_char, D : list_char]: ((method297381284t_char @ P @ C @ M @ Ts @ T @ M2 @ D) => (member89690956t_char @ (produc1304532571t_char @ C @ D) @ (transi1879726366t_char @ (subcls880436836t_char @ P))))))). % sees_method_decl_above
thf(fact_118_rtranclE, axiom,
    ((![A : list_char, B : list_char, R : set_Pr164112643t_char]: ((member89690956t_char @ (produc1304532571t_char @ A @ B) @ (transi1879726366t_char @ R)) => ((~ ((A = B))) => (~ ((![Y : list_char]: ((member89690956t_char @ (produc1304532571t_char @ A @ Y) @ (transi1879726366t_char @ R)) => (~ ((member89690956t_char @ (produc1304532571t_char @ Y @ B) @ R)))))))))))). % rtranclE
thf(fact_119_rtranclE, axiom,
    ((![A : produc1097884484on_val, B : produc1097884484on_val, R : set_Pr1189492743on_val]: ((member354538064on_val @ (produc1069526295on_val @ A @ B) @ (transi111096263on_val @ R)) => ((~ ((A = B))) => (~ ((![Y : produc1097884484on_val]: ((member354538064on_val @ (produc1069526295on_val @ A @ Y) @ (transi111096263on_val @ R)) => (~ ((member354538064on_val @ (produc1069526295on_val @ Y @ B) @ R)))))))))))). % rtranclE
thf(fact_120_rtranclE, axiom,
    ((![A : produc335961278on_val, B : produc335961278on_val, R : set_Pr208351751on_val]: ((member1689761872on_val @ (produc245869591on_val @ A @ B) @ (transi325225921on_val @ R)) => ((~ ((A = B))) => (~ ((![Y : produc335961278on_val]: ((member1689761872on_val @ (produc245869591on_val @ A @ Y) @ (transi325225921on_val @ R)) => (~ ((member1689761872on_val @ (produc245869591on_val @ Y @ B) @ R)))))))))))). % rtranclE
thf(fact_121_rtrancl_Ocases, axiom,
    ((![A1 : list_char, A2 : list_char, R : set_Pr164112643t_char]: ((member89690956t_char @ (produc1304532571t_char @ A1 @ A2) @ (transi1879726366t_char @ R)) => ((~ ((A2 = A1))) => (~ ((![B3 : list_char]: ((member89690956t_char @ (produc1304532571t_char @ A1 @ B3) @ (transi1879726366t_char @ R)) => (~ ((member89690956t_char @ (produc1304532571t_char @ B3 @ A2) @ R)))))))))))). % rtrancl.cases
thf(fact_122_rtrancl_Ocases, axiom,
    ((![A1 : produc1097884484on_val, A2 : produc1097884484on_val, R : set_Pr1189492743on_val]: ((member354538064on_val @ (produc1069526295on_val @ A1 @ A2) @ (transi111096263on_val @ R)) => ((~ ((A2 = A1))) => (~ ((![B3 : produc1097884484on_val]: ((member354538064on_val @ (produc1069526295on_val @ A1 @ B3) @ (transi111096263on_val @ R)) => (~ ((member354538064on_val @ (produc1069526295on_val @ B3 @ A2) @ R)))))))))))). % rtrancl.cases
thf(fact_123_rtrancl_Ocases, axiom,
    ((![A1 : produc335961278on_val, A2 : produc335961278on_val, R : set_Pr208351751on_val]: ((member1689761872on_val @ (produc245869591on_val @ A1 @ A2) @ (transi325225921on_val @ R)) => ((~ ((A2 = A1))) => (~ ((![B3 : produc335961278on_val]: ((member1689761872on_val @ (produc245869591on_val @ A1 @ B3) @ (transi325225921on_val @ R)) => (~ ((member1689761872on_val @ (produc245869591on_val @ B3 @ A2) @ R)))))))))))). % rtrancl.cases
thf(fact_124_rtrancl_Osimps, axiom,
    ((![A1 : list_char, A2 : list_char, R : set_Pr164112643t_char]: ((member89690956t_char @ (produc1304532571t_char @ A1 @ A2) @ (transi1879726366t_char @ R)) = (((?[A6 : list_char]: (((A1 = A6)) & ((A2 = A6))))) | ((?[A6 : list_char]: (?[B4 : list_char]: (?[C7 : list_char]: (((A1 = A6)) & ((((A2 = 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,
    ((![A1 : produc1097884484on_val, A2 : produc1097884484on_val, R : set_Pr1189492743on_val]: ((member354538064on_val @ (produc1069526295on_val @ A1 @ A2) @ (transi111096263on_val @ R)) = (((?[A6 : produc1097884484on_val]: (((A1 = A6)) & ((A2 = A6))))) | ((?[A6 : produc1097884484on_val]: (?[B4 : produc1097884484on_val]: (?[C7 : produc1097884484on_val]: (((A1 = A6)) & ((((A2 = C7)) & ((((member354538064on_val @ (produc1069526295on_val @ A6 @ B4) @ (transi111096263on_val @ R))) & ((member354538064on_val @ (produc1069526295on_val @ B4 @ C7) @ R)))))))))))))))). % rtrancl.simps
thf(fact_126_rtrancl_Osimps, axiom,
    ((![A1 : produc335961278on_val, A2 : produc335961278on_val, R : set_Pr208351751on_val]: ((member1689761872on_val @ (produc245869591on_val @ A1 @ A2) @ (transi325225921on_val @ R)) = (((?[A6 : produc335961278on_val]: (((A1 = A6)) & ((A2 = A6))))) | ((?[A6 : produc335961278on_val]: (?[B4 : produc335961278on_val]: (?[C7 : produc335961278on_val]: (((A1 = A6)) & ((((A2 = C7)) & ((((member1689761872on_val @ (produc245869591on_val @ A6 @ B4) @ (transi325225921on_val @ R))) & ((member1689761872on_val @ (produc245869591on_val @ B4 @ C7) @ R)))))))))))))))). % rtrancl.simps
thf(fact_127_rtrancl__trans, axiom,
    ((![X4 : list_char, Y3 : list_char, R : set_Pr164112643t_char, Z2 : list_char]: ((member89690956t_char @ (produc1304532571t_char @ X4 @ Y3) @ (transi1879726366t_char @ R)) => ((member89690956t_char @ (produc1304532571t_char @ Y3 @ Z2) @ (transi1879726366t_char @ R)) => (member89690956t_char @ (produc1304532571t_char @ X4 @ Z2) @ (transi1879726366t_char @ R))))))). % rtrancl_trans
thf(fact_128_rtrancl__trans, axiom,
    ((![X4 : produc1097884484on_val, Y3 : produc1097884484on_val, R : set_Pr1189492743on_val, Z2 : produc1097884484on_val]: ((member354538064on_val @ (produc1069526295on_val @ X4 @ Y3) @ (transi111096263on_val @ R)) => ((member354538064on_val @ (produc1069526295on_val @ Y3 @ Z2) @ (transi111096263on_val @ R)) => (member354538064on_val @ (produc1069526295on_val @ X4 @ Z2) @ (transi111096263on_val @ R))))))). % rtrancl_trans
thf(fact_129_rtrancl__trans, axiom,
    ((![X4 : produc335961278on_val, Y3 : produc335961278on_val, R : set_Pr208351751on_val, Z2 : produc335961278on_val]: ((member1689761872on_val @ (produc245869591on_val @ X4 @ Y3) @ (transi325225921on_val @ R)) => ((member1689761872on_val @ (produc245869591on_val @ Y3 @ Z2) @ (transi325225921on_val @ R)) => (member1689761872on_val @ (produc245869591on_val @ X4 @ Z2) @ (transi325225921on_val @ R))))))). % rtrancl_trans
thf(fact_130_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) => ((![Y : list_char, Z : list_char]: ((member89690956t_char @ (produc1304532571t_char @ A @ Y) @ (transi1879726366t_char @ R)) => ((member89690956t_char @ (produc1304532571t_char @ Y @ Z) @ R) => ((P @ Y) => (P @ Z))))) => (P @ B))))))). % rtrancl_induct
thf(fact_131_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) => ((![Y : produc1097884484on_val, Z : produc1097884484on_val]: ((member354538064on_val @ (produc1069526295on_val @ A @ Y) @ (transi111096263on_val @ R)) => ((member354538064on_val @ (produc1069526295on_val @ Y @ Z) @ R) => ((P @ Y) => (P @ Z))))) => (P @ B))))))). % rtrancl_induct
thf(fact_132_rtrancl__induct, axiom,
    ((![A : produc335961278on_val, B : produc335961278on_val, R : set_Pr208351751on_val, P : produc335961278on_val > $o]: ((member1689761872on_val @ (produc245869591on_val @ A @ B) @ (transi325225921on_val @ R)) => ((P @ A) => ((![Y : produc335961278on_val, Z : produc335961278on_val]: ((member1689761872on_val @ (produc245869591on_val @ A @ Y) @ (transi325225921on_val @ R)) => ((member1689761872on_val @ (produc245869591on_val @ Y @ Z) @ R) => ((P @ Y) => (P @ Z))))) => (P @ B))))))). % rtrancl_induct
thf(fact_133_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)) => ((![A5 : list_char]: (P @ A5 @ A5)) => ((![A5 : list_char, B3 : list_char, C5 : list_char]: ((member89690956t_char @ (produc1304532571t_char @ A5 @ B3) @ (transi1879726366t_char @ R)) => ((P @ A5 @ B3) => ((member89690956t_char @ (produc1304532571t_char @ B3 @ C5) @ R) => (P @ A5 @ C5))))) => (P @ X1 @ X2))))))). % rtrancl.inducts
thf(fact_134_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)) => ((![A5 : produc1097884484on_val]: (P @ A5 @ A5)) => ((![A5 : produc1097884484on_val, B3 : produc1097884484on_val, C5 : produc1097884484on_val]: ((member354538064on_val @ (produc1069526295on_val @ A5 @ B3) @ (transi111096263on_val @ R)) => ((P @ A5 @ B3) => ((member354538064on_val @ (produc1069526295on_val @ B3 @ C5) @ R) => (P @ A5 @ C5))))) => (P @ X1 @ X2))))))). % rtrancl.inducts
thf(fact_135_rtrancl_Oinducts, axiom,
    ((![X1 : produc335961278on_val, X2 : produc335961278on_val, R : set_Pr208351751on_val, P : produc335961278on_val > produc335961278on_val > $o]: ((member1689761872on_val @ (produc245869591on_val @ X1 @ X2) @ (transi325225921on_val @ R)) => ((![A5 : produc335961278on_val]: (P @ A5 @ A5)) => ((![A5 : produc335961278on_val, B3 : produc335961278on_val, C5 : produc335961278on_val]: ((member1689761872on_val @ (produc245869591on_val @ A5 @ B3) @ (transi325225921on_val @ R)) => ((P @ A5 @ B3) => ((member1689761872on_val @ (produc245869591on_val @ B3 @ C5) @ R) => (P @ A5 @ C5))))) => (P @ X1 @ X2))))))). % rtrancl.inducts
thf(fact_136_converse__rtranclE, axiom,
    ((![X4 : list_char, Z2 : list_char, R : set_Pr164112643t_char]: ((member89690956t_char @ (produc1304532571t_char @ X4 @ Z2) @ (transi1879726366t_char @ R)) => ((~ ((X4 = Z2))) => (~ ((![Y : list_char]: ((member89690956t_char @ (produc1304532571t_char @ X4 @ Y) @ R) => (~ ((member89690956t_char @ (produc1304532571t_char @ Y @ Z2) @ (transi1879726366t_char @ R))))))))))))). % converse_rtranclE
thf(fact_137_converse__rtranclE, axiom,
    ((![X4 : produc1097884484on_val, Z2 : produc1097884484on_val, R : set_Pr1189492743on_val]: ((member354538064on_val @ (produc1069526295on_val @ X4 @ Z2) @ (transi111096263on_val @ R)) => ((~ ((X4 = Z2))) => (~ ((![Y : produc1097884484on_val]: ((member354538064on_val @ (produc1069526295on_val @ X4 @ Y) @ R) => (~ ((member354538064on_val @ (produc1069526295on_val @ Y @ Z2) @ (transi111096263on_val @ R))))))))))))). % converse_rtranclE
thf(fact_138_converse__rtranclE, axiom,
    ((![X4 : produc335961278on_val, Z2 : produc335961278on_val, R : set_Pr208351751on_val]: ((member1689761872on_val @ (produc245869591on_val @ X4 @ Z2) @ (transi325225921on_val @ R)) => ((~ ((X4 = Z2))) => (~ ((![Y : produc335961278on_val]: ((member1689761872on_val @ (produc245869591on_val @ X4 @ Y) @ R) => (~ ((member1689761872on_val @ (produc245869591on_val @ Y @ Z2) @ (transi325225921on_val @ R))))))))))))). % converse_rtranclE
thf(fact_139_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_140_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_141_rtrancl_Ortrancl__refl, axiom,
    ((![A : produc335961278on_val, R : set_Pr208351751on_val]: (member1689761872on_val @ (produc245869591on_val @ A @ A) @ (transi325225921on_val @ R))))). % rtrancl.rtrancl_refl
thf(fact_142_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_143_sees__method__mono, axiom,
    ((![C6 : list_char, C : list_char, P : list_P1234162913t_char, Wf_md : list_P1234162913t_char > list_char > produc1259892823t_char > $o, M : list_char, Ts : list_ty, T : ty, M2 : produc1294284815t_char, D : list_char]: ((member89690956t_char @ (produc1304532571t_char @ C6 @ C) @ (transi1879726366t_char @ (subcls880436836t_char @ P))) => ((wf_pro1229751607t_char @ Wf_md @ P) => ((method297381284t_char @ P @ C @ M @ Ts @ T @ M2 @ D) => (?[D5 : list_char, Ts3 : list_ty, T2 : ty, M4 : produc1294284815t_char]: ((method297381284t_char @ P @ C6 @ M @ Ts3 @ T2 @ M4 @ D5) & ((list_all2_ty_ty @ (widen_917054840t_char @ P) @ Ts @ Ts3) & (widen_917054840t_char @ P @ T2 @ T)))))))))). % sees_method_mono
thf(fact_144_sees__method__mono2, axiom,
    ((![C6 : list_char, C : list_char, P : list_P1234162913t_char, Wf_md : list_P1234162913t_char > list_char > produc1259892823t_char > $o, M : list_char, Ts : list_ty, T : ty, M2 : produc1294284815t_char, D : list_char, Ts2 : list_ty, T5 : ty, M3 : produc1294284815t_char, D4 : list_char]: ((member89690956t_char @ (produc1304532571t_char @ C6 @ C) @ (transi1879726366t_char @ (subcls880436836t_char @ P))) => ((wf_pro1229751607t_char @ Wf_md @ P) => ((method297381284t_char @ P @ C @ M @ Ts @ T @ M2 @ D) => ((method297381284t_char @ P @ C6 @ M @ Ts2 @ T5 @ M3 @ D4) => ((list_all2_ty_ty @ (widen_917054840t_char @ P) @ Ts @ Ts2) & (widen_917054840t_char @ P @ T5 @ T))))))))). % sees_method_mono2
thf(fact_145_has__method__def, axiom,
    ((has_me170134744t_char = (^[P2 : list_P1234162913t_char]: (^[C3 : list_char]: (^[M5 : list_char]: (?[Ts4 : list_ty]: (?[T3 : ty]: (?[M6 : produc1294284815t_char]: (?[X6 : list_char]: (method297381284t_char @ P2 @ C3 @ M5 @ Ts4 @ T3 @ M6 @ X6))))))))))). % has_method_def
thf(fact_146_method__def2, axiom,
    ((![P : list_P1234162913t_char, C : list_char, M : list_char, Ts : list_ty, T : ty, M2 : produc1294284815t_char, D : list_char]: ((method297381284t_char @ P @ C @ M @ Ts @ T @ M2 @ D) => ((method667690372t_char @ P @ C @ M) = (produc1238538255t_char @ D @ (produc1730359111t_char @ Ts @ (produc248075743t_char @ T @ M2)))))))). % method_def2
thf(fact_147_sees__wf__mdecl, axiom,
    ((![Wf_md : list_P1234162913t_char > list_char > produc1259892823t_char > $o, P : list_P1234162913t_char, C : list_char, M : list_char, Ts : list_ty, T : ty, M2 : produc1294284815t_char, D : list_char]: ((wf_pro1229751607t_char @ Wf_md @ P) => ((method297381284t_char @ P @ C @ M @ Ts @ T @ M2 @ D) => (wf_mde297024346t_char @ Wf_md @ P @ D @ (produc1238538255t_char @ M @ (produc1730359111t_char @ Ts @ (produc248075743t_char @ T @ M2))))))))). % sees_wf_mdecl
thf(fact_148_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_149_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_150_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_151_red__preserves__hconf, axiom,
    ((![E2 : exp_list_char, H : nat > option2118145160on_val, L : list_char > option_val, E3 : exp_list_char, H2 : nat > option2118145160on_val, L2 : list_char > option_val, P : list_P1234162913t_char, E : list_char > option_ty, T : ty]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E2 @ (produc52622304on_val @ H @ L)) @ (produc2023458740on_val @ E3 @ (produc52622304on_val @ H2 @ L2))) @ (red @ P)) => ((wTrt @ P @ H @ E @ E2 @ T) => ((hconf_1244167010t_char @ P @ H) => (hconf_1244167010t_char @ P @ H2))))))). % red_preserves_hconf
thf(fact_152_red__preserves__lconf, axiom,
    ((![E2 : exp_list_char, H : nat > option2118145160on_val, L : list_char > option_val, E3 : exp_list_char, H2 : nat > option2118145160on_val, L2 : list_char > option_val, P : list_P1234162913t_char, E : list_char > option_ty, T : ty]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E2 @ (produc52622304on_val @ H @ L)) @ (produc2023458740on_val @ E3 @ (produc52622304on_val @ H2 @ L2))) @ (red @ P)) => ((wTrt @ P @ H @ E @ E2 @ T) => ((lconf_485928294t_char @ P @ H @ L @ E) => (lconf_485928294t_char @ P @ H2 @ L2 @ E))))))). % red_preserves_lconf
thf(fact_153_red__preserves__sconf, axiom,
    ((![E2 : exp_list_char, S2 : produc515445032on_val, E3 : exp_list_char, S3 : produc515445032on_val, P : list_P1234162913t_char, E : list_char > option_ty, T : ty]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E2 @ S2) @ (produc2023458740on_val @ E3 @ S3)) @ (red @ P)) => ((wTrt @ P @ (hp @ S2) @ E @ E2 @ T) => ((typeSa1777264139_sconf @ P @ E @ S2) => (typeSa1777264139_sconf @ P @ E @ S3))))))). % red_preserves_sconf
thf(fact_154_Call__lemma, axiom,
    ((![P : list_P1234162913t_char, C : list_char, M : list_char, Ts : list_ty, T : ty, M2 : produc1294284815t_char, D : list_char, C6 : list_char, Wf_md : list_P1234162913t_char > list_char > produc1259892823t_char > $o]: ((method297381284t_char @ P @ C @ M @ Ts @ T @ M2 @ D) => ((member89690956t_char @ (produc1304532571t_char @ C6 @ C) @ (transi1879726366t_char @ (subcls880436836t_char @ P))) => ((wf_pro1229751607t_char @ Wf_md @ P) => (?[D5 : list_char, Ts3 : list_ty, T2 : ty, M4 : produc1294284815t_char]: ((method297381284t_char @ P @ C6 @ M @ Ts3 @ T2 @ M4 @ D5) & ((list_all2_ty_ty @ (widen_917054840t_char @ P) @ Ts @ Ts3) & ((widen_917054840t_char @ P @ T2 @ T) & ((member89690956t_char @ (produc1304532571t_char @ C6 @ D5) @ (transi1879726366t_char @ (subcls880436836t_char @ P))) & ((is_typ250416522t_char @ P @ T2) & ((![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 @ T2 @ M4))))))))))))))))). % Call_lemma
thf(fact_155_Red__lcl__add, axiom,
    ((![E2 : exp_list_char, H : nat > option2118145160on_val, L : list_char > option_val, E3 : exp_list_char, H2 : nat > option2118145160on_val, L2 : list_char > option_val, P : list_P1234162913t_char, L_02 : list_char > option_val]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E2 @ (produc52622304on_val @ H @ L)) @ (produc2023458740on_val @ E3 @ (produc52622304on_val @ H2 @ L2))) @ (transi111096263on_val @ (red @ P))) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E2 @ (produc52622304on_val @ H @ (map_ad1615113112ar_val @ L_02 @ L))) @ (produc2023458740on_val @ E3 @ (produc52622304on_val @ H2 @ (map_ad1615113112ar_val @ L_02 @ L2)))) @ (transi111096263on_val @ (red @ P))))))). % Red_lcl_add
thf(fact_156_red__hext__incr, axiom,
    ((![E2 : exp_list_char, H : nat > option2118145160on_val, L : list_char > option_val, E3 : exp_list_char, H2 : nat > option2118145160on_val, L2 : list_char > option_val, P : list_P1234162913t_char]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E2 @ (produc52622304on_val @ H @ L)) @ (produc2023458740on_val @ E3 @ (produc52622304on_val @ H2 @ L2))) @ (red @ P)) => (hext @ H @ H2))))). % red_hext_incr
thf(fact_157_WTrt__hext__mono, axiom,
    ((![P : list_P1234162913t_char, H : nat > option2118145160on_val, E : list_char > option_ty, E2 : exp_list_char, T : ty, H2 : nat > option2118145160on_val]: ((wTrt @ P @ H @ E @ E2 @ T) => ((hext @ H @ H2) => (wTrt @ P @ H2 @ E @ E2 @ T)))))). % WTrt_hext_mono
thf(fact_158_WTrts__hext__mono, axiom,
    ((![P : list_P1234162913t_char, H : nat > option2118145160on_val, E : list_char > option_ty, Es : list_exp_list_char, Ts : list_ty, H2 : nat > option2118145160on_val]: ((wTrts @ P @ H @ E @ Es @ Ts) => ((hext @ H @ H2) => (wTrts @ P @ H2 @ E @ Es @ Ts)))))). % WTrts_hext_mono
thf(fact_159_red__lcl__add, axiom,
    ((![E2 : exp_list_char, H : nat > option2118145160on_val, L : list_char > option_val, E3 : exp_list_char, H2 : nat > option2118145160on_val, L2 : list_char > option_val, P : list_P1234162913t_char, L_02 : list_char > option_val]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E2 @ (produc52622304on_val @ H @ L)) @ (produc2023458740on_val @ E3 @ (produc52622304on_val @ H2 @ L2))) @ (red @ P)) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E2 @ (produc52622304on_val @ H @ (map_ad1615113112ar_val @ L_02 @ L))) @ (produc2023458740on_val @ E3 @ (produc52622304on_val @ H2 @ (map_ad1615113112ar_val @ L_02 @ L2)))) @ (red @ P)))))). % red_lcl_add
thf(fact_160_list_Orel__refl__strong, axiom,
    ((![X4 : list_P757710633t_char, Ra : produc1257910179t_char > produc1257910179t_char > $o]: ((![Z : produc1257910179t_char]: ((member89690956t_char @ Z @ (set_Pr1342796728t_char @ X4)) => (Ra @ Z @ Z))) => (list_a1368132679t_char @ Ra @ X4 @ X4))))). % list.rel_refl_strong
thf(fact_161_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_162_list_Orel__refl__strong, axiom,
    ((![X4 : list_P1429269293on_val, Ra : produc655058983on_val > produc655058983on_val > $o]: ((![Z : produc655058983on_val]: ((member1689761872on_val @ Z @ (set_Pr406187708on_val @ X4)) => (Ra @ Z @ Z))) => (list_a196826951on_val @ Ra @ X4 @ X4))))). % list.rel_refl_strong
thf(fact_163_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_164_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_165_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_166_list_Orel__mono__strong, axiom,
    ((![R2 : ty > ty > $o, X4 : list_ty, Y3 : list_ty, Ra : ty > ty > $o]: ((list_all2_ty_ty @ R2 @ X4 @ Y3) => ((![Z : ty, Yb : ty]: ((member_ty @ Z @ (set_ty2 @ X4)) => ((member_ty @ Yb @ (set_ty2 @ Y3)) => ((R2 @ Z @ Yb) => (Ra @ Z @ Yb))))) => (list_all2_ty_ty @ Ra @ X4 @ Y3)))))). % list.rel_mono_strong
thf(fact_167_list_Orel__mono__strong, axiom,
    ((![R2 : produc1257910179t_char > produc1257910179t_char > $o, X4 : list_P757710633t_char, Y3 : list_P757710633t_char, Ra : produc1257910179t_char > produc1257910179t_char > $o]: ((list_a1368132679t_char @ R2 @ X4 @ Y3) => ((![Z : produc1257910179t_char, Yb : produc1257910179t_char]: ((member89690956t_char @ Z @ (set_Pr1342796728t_char @ X4)) => ((member89690956t_char @ Yb @ (set_Pr1342796728t_char @ Y3)) => ((R2 @ Z @ Yb) => (Ra @ Z @ Yb))))) => (list_a1368132679t_char @ Ra @ X4 @ Y3)))))). % list.rel_mono_strong
thf(fact_168_list_Orel__mono__strong, axiom,
    ((![R2 : produc1257910179t_char > produc1259892823t_char > $o, X4 : list_P757710633t_char, Y3 : list_P1653548253t_char, Ra : produc1257910179t_char > produc1259892823t_char > $o]: ((list_a1221730555t_char @ R2 @ X4 @ Y3) => ((![Z : produc1257910179t_char, Yb : produc1259892823t_char]: ((member89690956t_char @ Z @ (set_Pr1342796728t_char @ X4)) => ((member397625600t_char @ Yb @ (set_Pr1045701996t_char @ Y3)) => ((R2 @ Z @ Yb) => (Ra @ Z @ Yb))))) => (list_a1221730555t_char @ Ra @ X4 @ Y3)))))). % list.rel_mono_strong
thf(fact_169_list_Orel__mono__strong, axiom,
    ((![R2 : produc1259892823t_char > produc1257910179t_char > $o, X4 : list_P1653548253t_char, Y3 : list_P757710633t_char, Ra : produc1259892823t_char > produc1257910179t_char > $o]: ((list_a72576659t_char @ R2 @ X4 @ Y3) => ((![Z : produc1259892823t_char, Yb : produc1257910179t_char]: ((member397625600t_char @ Z @ (set_Pr1045701996t_char @ X4)) => ((member89690956t_char @ Yb @ (set_Pr1342796728t_char @ Y3)) => ((R2 @ Z @ Yb) => (Ra @ Z @ Yb))))) => (list_a72576659t_char @ Ra @ X4 @ Y3)))))). % list.rel_mono_strong
thf(fact_170_list_Orel__mono__strong, axiom,
    ((![R2 : produc1259892823t_char > produc1259892823t_char > $o, X4 : list_P1653548253t_char, Y3 : list_P1653548253t_char, Ra : produc1259892823t_char > produc1259892823t_char > $o]: ((list_a1436933959t_char @ R2 @ X4 @ Y3) => ((![Z : produc1259892823t_char, Yb : produc1259892823t_char]: ((member397625600t_char @ Z @ (set_Pr1045701996t_char @ X4)) => ((member397625600t_char @ Yb @ (set_Pr1045701996t_char @ Y3)) => ((R2 @ Z @ Yb) => (Ra @ Z @ Yb))))) => (list_a1436933959t_char @ Ra @ X4 @ Y3)))))). % list.rel_mono_strong
thf(fact_171_list_Orel__mono__strong, axiom,
    ((![R2 : produc1257910179t_char > produc1777519579t_char > $o, X4 : list_P757710633t_char, Y3 : list_P1234162913t_char, Ra : produc1257910179t_char > produc1777519579t_char > $o]: ((list_a467720831t_char @ R2 @ X4 @ Y3) => ((![Z : produc1257910179t_char, Yb : produc1777519579t_char]: ((member89690956t_char @ Z @ (set_Pr1342796728t_char @ X4)) => ((member958036996t_char @ Yb @ (set_Pr1611739760t_char @ Y3)) => ((R2 @ Z @ Yb) => (Ra @ Z @ Yb))))) => (list_a467720831t_char @ Ra @ X4 @ Y3)))))). % list.rel_mono_strong
thf(fact_172_list_Orel__mono__strong, axiom,
    ((![R2 : produc1777519579t_char > produc1257910179t_char > $o, X4 : list_P1234162913t_char, Y3 : list_P757710633t_char, Ra : produc1777519579t_char > produc1257910179t_char > $o]: ((list_a1947354639t_char @ R2 @ X4 @ Y3) => ((![Z : produc1777519579t_char, Yb : produc1257910179t_char]: ((member958036996t_char @ Z @ (set_Pr1611739760t_char @ X4)) => ((member89690956t_char @ Yb @ (set_Pr1342796728t_char @ Y3)) => ((R2 @ Z @ Yb) => (Ra @ Z @ Yb))))) => (list_a1947354639t_char @ Ra @ X4 @ Y3)))))). % list.rel_mono_strong
thf(fact_173_list_Orel__mono__strong, axiom,
    ((![R2 : produc1777519579t_char > produc1259892823t_char > $o, X4 : list_P1234162913t_char, Y3 : list_P1653548253t_char, Ra : produc1777519579t_char > produc1259892823t_char > $o]: ((list_a1931379395t_char @ R2 @ X4 @ Y3) => ((![Z : produc1777519579t_char, Yb : produc1259892823t_char]: ((member958036996t_char @ Z @ (set_Pr1611739760t_char @ X4)) => ((member397625600t_char @ Yb @ (set_Pr1045701996t_char @ Y3)) => ((R2 @ Z @ Yb) => (Ra @ Z @ Yb))))) => (list_a1931379395t_char @ Ra @ X4 @ Y3)))))). % list.rel_mono_strong
thf(fact_174_list_Orel__mono__strong, axiom,
    ((![R2 : produc1259892823t_char > produc1777519579t_char > $o, X4 : list_P1653548253t_char, Y3 : list_P1234162913t_char, Ra : produc1259892823t_char > produc1777519579t_char > $o]: ((list_a1858601675t_char @ R2 @ X4 @ Y3) => ((![Z : produc1259892823t_char, Yb : produc1777519579t_char]: ((member397625600t_char @ Z @ (set_Pr1045701996t_char @ X4)) => ((member958036996t_char @ Yb @ (set_Pr1611739760t_char @ Y3)) => ((R2 @ Z @ Yb) => (Ra @ Z @ Yb))))) => (list_a1858601675t_char @ Ra @ X4 @ Y3)))))). % list.rel_mono_strong
thf(fact_175_list_Orel__mono__strong, axiom,
    ((![R2 : produc1257910179t_char > produc1172664615on_val > $o, X4 : list_P757710633t_char, Y3 : list_P942933805on_val, Ra : produc1257910179t_char > produc1172664615on_val > $o]: ((list_a56902603on_val @ R2 @ X4 @ Y3) => ((![Z : produc1257910179t_char, Yb : produc1172664615on_val]: ((member89690956t_char @ Z @ (set_Pr1342796728t_char @ X4)) => ((member354538064on_val @ Yb @ (set_Pr348738748on_val @ Y3)) => ((R2 @ Z @ Yb) => (Ra @ Z @ Yb))))) => (list_a56902603on_val @ Ra @ X4 @ Y3)))))). % list.rel_mono_strong
thf(fact_176_list_Orel__cong, axiom,
    ((![X4 : list_ty, Ya : list_ty, Y3 : list_ty, Xa : list_ty, R2 : ty > ty > $o, Ra : ty > ty > $o]: ((X4 = Ya) => ((Y3 = Xa) => ((![Z : ty, Yb : ty]: ((member_ty @ Z @ (set_ty2 @ Ya)) => ((member_ty @ Yb @ (set_ty2 @ Xa)) => ((R2 @ Z @ Yb) = (Ra @ Z @ Yb))))) => ((list_all2_ty_ty @ R2 @ X4 @ Y3) = (list_all2_ty_ty @ Ra @ Ya @ Xa)))))))). % list.rel_cong
thf(fact_177_list_Orel__cong, axiom,
    ((![X4 : list_P757710633t_char, Ya : list_P757710633t_char, Y3 : list_P757710633t_char, Xa : list_P757710633t_char, R2 : produc1257910179t_char > produc1257910179t_char > $o, Ra : produc1257910179t_char > produc1257910179t_char > $o]: ((X4 = Ya) => ((Y3 = Xa) => ((![Z : produc1257910179t_char, Yb : produc1257910179t_char]: ((member89690956t_char @ Z @ (set_Pr1342796728t_char @ Ya)) => ((member89690956t_char @ Yb @ (set_Pr1342796728t_char @ Xa)) => ((R2 @ Z @ Yb) = (Ra @ Z @ Yb))))) => ((list_a1368132679t_char @ R2 @ X4 @ Y3) = (list_a1368132679t_char @ Ra @ Ya @ Xa)))))))). % list.rel_cong
thf(fact_178_list_Orel__cong, axiom,
    ((![X4 : list_P757710633t_char, Ya : list_P757710633t_char, Y3 : list_P1653548253t_char, Xa : list_P1653548253t_char, R2 : produc1257910179t_char > produc1259892823t_char > $o, Ra : produc1257910179t_char > produc1259892823t_char > $o]: ((X4 = Ya) => ((Y3 = Xa) => ((![Z : produc1257910179t_char, Yb : produc1259892823t_char]: ((member89690956t_char @ Z @ (set_Pr1342796728t_char @ Ya)) => ((member397625600t_char @ Yb @ (set_Pr1045701996t_char @ Xa)) => ((R2 @ Z @ Yb) = (Ra @ Z @ Yb))))) => ((list_a1221730555t_char @ R2 @ X4 @ Y3) = (list_a1221730555t_char @ Ra @ Ya @ Xa)))))))). % list.rel_cong
thf(fact_179_list_Orel__cong, axiom,
    ((![X4 : list_P1653548253t_char, Ya : list_P1653548253t_char, Y3 : list_P757710633t_char, Xa : list_P757710633t_char, R2 : produc1259892823t_char > produc1257910179t_char > $o, Ra : produc1259892823t_char > produc1257910179t_char > $o]: ((X4 = Ya) => ((Y3 = Xa) => ((![Z : produc1259892823t_char, Yb : produc1257910179t_char]: ((member397625600t_char @ Z @ (set_Pr1045701996t_char @ Ya)) => ((member89690956t_char @ Yb @ (set_Pr1342796728t_char @ Xa)) => ((R2 @ Z @ Yb) = (Ra @ Z @ Yb))))) => ((list_a72576659t_char @ R2 @ X4 @ Y3) = (list_a72576659t_char @ Ra @ Ya @ Xa)))))))). % list.rel_cong
thf(fact_180_list_Orel__cong, axiom,
    ((![X4 : list_P1653548253t_char, Ya : list_P1653548253t_char, Y3 : list_P1653548253t_char, Xa : list_P1653548253t_char, R2 : produc1259892823t_char > produc1259892823t_char > $o, Ra : produc1259892823t_char > produc1259892823t_char > $o]: ((X4 = Ya) => ((Y3 = Xa) => ((![Z : produc1259892823t_char, Yb : produc1259892823t_char]: ((member397625600t_char @ Z @ (set_Pr1045701996t_char @ Ya)) => ((member397625600t_char @ Yb @ (set_Pr1045701996t_char @ Xa)) => ((R2 @ Z @ Yb) = (Ra @ Z @ Yb))))) => ((list_a1436933959t_char @ R2 @ X4 @ Y3) = (list_a1436933959t_char @ Ra @ Ya @ Xa)))))))). % list.rel_cong
thf(fact_181_list_Orel__cong, axiom,
    ((![X4 : list_P757710633t_char, Ya : list_P757710633t_char, Y3 : list_P1234162913t_char, Xa : list_P1234162913t_char, R2 : produc1257910179t_char > produc1777519579t_char > $o, Ra : produc1257910179t_char > produc1777519579t_char > $o]: ((X4 = Ya) => ((Y3 = Xa) => ((![Z : produc1257910179t_char, Yb : produc1777519579t_char]: ((member89690956t_char @ Z @ (set_Pr1342796728t_char @ Ya)) => ((member958036996t_char @ Yb @ (set_Pr1611739760t_char @ Xa)) => ((R2 @ Z @ Yb) = (Ra @ Z @ Yb))))) => ((list_a467720831t_char @ R2 @ X4 @ Y3) = (list_a467720831t_char @ Ra @ Ya @ Xa)))))))). % list.rel_cong
thf(fact_182_list_Orel__cong, axiom,
    ((![X4 : list_P1234162913t_char, Ya : list_P1234162913t_char, Y3 : list_P757710633t_char, Xa : list_P757710633t_char, R2 : produc1777519579t_char > produc1257910179t_char > $o, Ra : produc1777519579t_char > produc1257910179t_char > $o]: ((X4 = Ya) => ((Y3 = Xa) => ((![Z : produc1777519579t_char, Yb : produc1257910179t_char]: ((member958036996t_char @ Z @ (set_Pr1611739760t_char @ Ya)) => ((member89690956t_char @ Yb @ (set_Pr1342796728t_char @ Xa)) => ((R2 @ Z @ Yb) = (Ra @ Z @ Yb))))) => ((list_a1947354639t_char @ R2 @ X4 @ Y3) = (list_a1947354639t_char @ Ra @ Ya @ Xa)))))))). % list.rel_cong
thf(fact_183_list_Orel__cong, axiom,
    ((![X4 : list_P1234162913t_char, Ya : list_P1234162913t_char, Y3 : list_P1653548253t_char, Xa : list_P1653548253t_char, R2 : produc1777519579t_char > produc1259892823t_char > $o, Ra : produc1777519579t_char > produc1259892823t_char > $o]: ((X4 = Ya) => ((Y3 = Xa) => ((![Z : produc1777519579t_char, Yb : produc1259892823t_char]: ((member958036996t_char @ Z @ (set_Pr1611739760t_char @ Ya)) => ((member397625600t_char @ Yb @ (set_Pr1045701996t_char @ Xa)) => ((R2 @ Z @ Yb) = (Ra @ Z @ Yb))))) => ((list_a1931379395t_char @ R2 @ X4 @ Y3) = (list_a1931379395t_char @ Ra @ Ya @ Xa)))))))). % list.rel_cong
thf(fact_184_list_Orel__cong, axiom,
    ((![X4 : list_P1653548253t_char, Ya : list_P1653548253t_char, Y3 : list_P1234162913t_char, Xa : list_P1234162913t_char, R2 : produc1259892823t_char > produc1777519579t_char > $o, Ra : produc1259892823t_char > produc1777519579t_char > $o]: ((X4 = Ya) => ((Y3 = Xa) => ((![Z : produc1259892823t_char, Yb : produc1777519579t_char]: ((member397625600t_char @ Z @ (set_Pr1045701996t_char @ Ya)) => ((member958036996t_char @ Yb @ (set_Pr1611739760t_char @ Xa)) => ((R2 @ Z @ Yb) = (Ra @ Z @ Yb))))) => ((list_a1858601675t_char @ R2 @ X4 @ Y3) = (list_a1858601675t_char @ Ra @ Ya @ Xa)))))))). % list.rel_cong
thf(fact_185_list_Orel__cong, axiom,
    ((![X4 : list_P757710633t_char, Ya : list_P757710633t_char, Y3 : list_P942933805on_val, Xa : list_P942933805on_val, R2 : produc1257910179t_char > produc1172664615on_val > $o, Ra : produc1257910179t_char > produc1172664615on_val > $o]: ((X4 = Ya) => ((Y3 = Xa) => ((![Z : produc1257910179t_char, Yb : produc1172664615on_val]: ((member89690956t_char @ Z @ (set_Pr1342796728t_char @ Ya)) => ((member354538064on_val @ Yb @ (set_Pr348738748on_val @ Xa)) => ((R2 @ Z @ Yb) = (Ra @ Z @ Yb))))) => ((list_a56902603on_val @ R2 @ X4 @ Y3) = (list_a56902603on_val @ Ra @ Ya @ Xa)))))))). % list.rel_cong
thf(fact_186_mdecl__visible, axiom,
    ((![Wf_md : list_P1234162913t_char > list_char > produc1259892823t_char > $o, P : list_P1234162913t_char, C : list_char, S : list_char, Fs : list_P1126587903har_ty, Ms : list_P1653548253t_char, M : list_char, Ts : list_ty, T : ty, M2 : produc1294284815t_char]: ((wf_pro1229751607t_char @ Wf_md @ P) => ((member958036996t_char @ (produc1548560403t_char @ C @ (produc1972337867t_char @ S @ (produc1107711029t_char @ Fs @ Ms))) @ (set_Pr1611739760t_char @ P)) => ((member397625600t_char @ (produc1238538255t_char @ M @ (produc1730359111t_char @ Ts @ (produc248075743t_char @ T @ M2))) @ (set_Pr1045701996t_char @ Ms)) => (method297381284t_char @ P @ C @ M @ Ts @ T @ M2 @ C))))))). % mdecl_visible
thf(fact_187_list_Orel__refl, axiom,
    ((![Ra : ty > ty > $o, X4 : list_ty]: ((![X3 : ty]: (Ra @ X3 @ X3)) => (list_all2_ty_ty @ Ra @ X4 @ X4))))). % list.rel_refl
thf(fact_188_list__all2__antisym, axiom,
    ((![P : ty > ty > $o, Q : ty > ty > $o, Xs : list_ty, Ys : list_ty]: ((![X3 : ty, Y : ty]: ((P @ X3 @ Y) => ((Q @ Y @ X3) => (X3 = Y)))) => ((list_all2_ty_ty @ P @ Xs @ Ys) => ((list_all2_ty_ty @ Q @ Ys @ Xs) => (Xs = Ys))))))). % list_all2_antisym
thf(fact_189_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_190_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]: ((![A5 : ty, B3 : ty, C5 : ty]: ((P1 @ A5 @ B3) => ((P22 @ B3 @ C5) => (P32 @ A5 @ C5)))) => ((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_191_list__all2__refl, axiom,
    ((![P : ty > ty > $o, Xs : list_ty]: ((![X3 : ty]: (P @ X3 @ X3)) => (list_all2_ty_ty @ P @ Xs @ Xs))))). % list_all2_refl
thf(fact_192_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_193_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_194_list__all2__same, axiom,
    ((![P : produc1777519579t_char > produc1777519579t_char > $o, Xs : list_P1234162913t_char]: ((list_a364623943t_char @ P @ Xs @ Xs) = (![X : produc1777519579t_char]: (((member958036996t_char @ X @ (set_Pr1611739760t_char @ Xs))) => ((P @ X @ X)))))))). % list_all2_same
thf(fact_195_list__all2__same, axiom,
    ((![P : produc1259892823t_char > produc1259892823t_char > $o, Xs : list_P1653548253t_char]: ((list_a1436933959t_char @ P @ Xs @ Xs) = (![X : produc1259892823t_char]: (((member397625600t_char @ X @ (set_Pr1045701996t_char @ Xs))) => ((P @ X @ X)))))))). % list_all2_same
thf(fact_196_list__all2__same, axiom,
    ((![P : ty > ty > $o, Xs : list_ty]: ((list_all2_ty_ty @ P @ Xs @ Xs) = (![X : ty]: (((member_ty @ X @ (set_ty2 @ Xs))) => ((P @ X @ X)))))))). % list_all2_same
thf(fact_197_wf__J__prog__wf__J__mdecl, axiom,
    ((![P : list_P1234162913t_char, C : 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 @ C @ (produc1972337867t_char @ D @ (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_198_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, M : list_char, Ts : list_ty, T : ty, M2 : produc1294284815t_char]: ((wf_pro1229751607t_char @ Wf_md @ P) => ((member958036996t_char @ (produc1548560403t_char @ C @ (produc1972337867t_char @ S @ (produc1107711029t_char @ Fs @ Ms))) @ (set_Pr1611739760t_char @ P)) => ((member397625600t_char @ (produc1238538255t_char @ M @ (produc1730359111t_char @ Ts @ (produc248075743t_char @ T @ M2))) @ (set_Pr1045701996t_char @ Ms)) => (ord_less_eq_set_ty @ (set_ty2 @ Ts) @ (collect_ty @ (is_typ250416522t_char @ P))))))))). % is_type_pTs
thf(fact_199_has__field__mono, axiom,
    ((![P : list_P1234162913t_char, C : list_char, F : list_char, T : ty, D : list_char, C6 : list_char]: ((has_fi599584195t_char @ P @ C @ F @ T @ D) => ((member89690956t_char @ (produc1304532571t_char @ C6 @ C) @ (transi1879726366t_char @ (subcls880436836t_char @ P))) => (has_fi599584195t_char @ P @ C6 @ F @ T @ D)))))). % has_field_mono
thf(fact_200_CallRedsThrowObj, axiom,
    ((![E2 : exp_list_char, S0 : produc515445032on_val, A : exp_list_char, S_1 : produc515445032on_val, P : list_P1234162913t_char, M : list_char, Es : list_exp_list_char]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E2 @ S0) @ (produc2023458740on_val @ (throw_list_char @ A) @ S_1)) @ (transi111096263on_val @ (red @ P))) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (call_list_char @ E2 @ M @ Es) @ S0) @ (produc2023458740on_val @ (throw_list_char @ A) @ S_1)) @ (transi111096263on_val @ (red @ P))))))). % CallRedsThrowObj
thf(fact_201_exp_Oinject_I14_J, axiom,
    ((![X14 : exp_list_char, Y14 : exp_list_char]: (((throw_list_char @ X14) = (throw_list_char @ Y14)) = (X14 = Y14))))). % exp.inject(14)
thf(fact_202_exp_Odistinct_I177_J, axiom,
    ((![X91 : exp_list_char, X92 : list_char, X93 : list_exp_list_char, X14 : exp_list_char]: (~ (((call_list_char @ X91 @ X92 @ X93) = (throw_list_char @ X14))))))). % exp.distinct(177)
thf(fact_203_red__reds_OThrowThrow, axiom,
    ((![E2 : exp_list_char, S2 : produc515445032on_val, P : list_P1234162913t_char]: (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (throw_list_char @ (throw_list_char @ E2)) @ S2) @ (produc2023458740on_val @ (throw_list_char @ E2) @ S2)) @ (red @ P))))). % red_reds.ThrowThrow
thf(fact_204_red__reds_OThrowRed, axiom,
    ((![E2 : exp_list_char, S2 : produc515445032on_val, E3 : exp_list_char, S3 : produc515445032on_val, P : list_P1234162913t_char]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E2 @ S2) @ (produc2023458740on_val @ E3 @ S3)) @ (red @ P)) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (throw_list_char @ E2) @ S2) @ (produc2023458740on_val @ (throw_list_char @ E3) @ S3)) @ (red @ P)))))). % red_reds.ThrowRed
thf(fact_205_ThrowRedsThrow, axiom,
    ((![E2 : exp_list_char, S2 : produc515445032on_val, A : exp_list_char, S3 : produc515445032on_val, P : list_P1234162913t_char]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E2 @ S2) @ (produc2023458740on_val @ (throw_list_char @ A) @ S3)) @ (transi111096263on_val @ (red @ P))) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (throw_list_char @ E2) @ S2) @ (produc2023458740on_val @ (throw_list_char @ A) @ S3)) @ (transi111096263on_val @ (red @ P))))))). % ThrowRedsThrow
thf(fact_206_ThrowReds, axiom,
    ((![E2 : exp_list_char, S2 : produc515445032on_val, E3 : exp_list_char, S3 : produc515445032on_val, P : list_P1234162913t_char]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E2 @ S2) @ (produc2023458740on_val @ E3 @ S3)) @ (transi111096263on_val @ (red @ P))) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (throw_list_char @ E2) @ S2) @ (produc2023458740on_val @ (throw_list_char @ E3) @ S3)) @ (transi111096263on_val @ (red @ P))))))). % ThrowReds
thf(fact_207_red__reds_OCallThrowObj, axiom,
    ((![E2 : exp_list_char, M : list_char, Es : list_exp_list_char, S2 : produc515445032on_val, P : list_P1234162913t_char]: (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (call_list_char @ (throw_list_char @ E2) @ M @ Es) @ S2) @ (produc2023458740on_val @ (throw_list_char @ E2) @ S2)) @ (red @ P))))). % red_reds.CallThrowObj
thf(fact_208_Collect__subset, axiom,
    ((![A4 : set_Pr164112643t_char, P : produc1257910179t_char > $o]: (ord_le167891107t_char @ (collec768236686t_char @ (^[X : produc1257910179t_char]: (((member89690956t_char @ X @ A4)) & ((P @ X))))) @ A4)))). % Collect_subset
thf(fact_209_Collect__subset, axiom,
    ((![A4 : set_Pr1189492743on_val, P : produc1172664615on_val > $o]: (ord_le837504935on_val @ (collec2055896722on_val @ (^[X : produc1172664615on_val]: (((member354538064on_val @ X @ A4)) & ((P @ X))))) @ A4)))). % Collect_subset
thf(fact_210_Collect__subset, axiom,
    ((![A4 : set_Pr2090064827t_char, P : produc1777519579t_char > $o]: (ord_le2010927963t_char @ (collec178542150t_char @ (^[X : produc1777519579t_char]: (((member958036996t_char @ X @ A4)) & ((P @ X))))) @ A4)))). % Collect_subset
thf(fact_211_Collect__subset, axiom,
    ((![A4 : set_Pr1344692407t_char, P : produc1259892823t_char > $o]: (ord_le1781475415t_char @ (collec1549347906t_char @ (^[X : produc1259892823t_char]: (((member397625600t_char @ X @ A4)) & ((P @ X))))) @ A4)))). % Collect_subset
thf(fact_212_Collect__subset, axiom,
    ((![A4 : set_Pr208351751on_val, P : produc655058983on_val > $o]: (ord_le1331145127on_val @ (collec105960082on_val @ (^[X : produc655058983on_val]: (((member1689761872on_val @ X @ A4)) & ((P @ X))))) @ A4)))). % Collect_subset
thf(fact_213_insert__compr, axiom,
    ((insert1354671475t_char = (^[A6 : produc1257910179t_char]: (^[B5 : set_Pr164112643t_char]: (collec768236686t_char @ (^[X : produc1257910179t_char]: (((X = A6)) | ((member89690956t_char @ X @ B5)))))))))). % insert_compr
thf(fact_214_insert__compr, axiom,
    ((insert1971494647on_val = (^[A6 : produc1172664615on_val]: (^[B5 : set_Pr1189492743on_val]: (collec2055896722on_val @ (^[X : produc1172664615on_val]: (((X = A6)) | ((member354538064on_val @ X @ B5)))))))))). % insert_compr
thf(fact_215_insert__compr, axiom,
    ((insert1233103275t_char = (^[A6 : produc1777519579t_char]: (^[B5 : set_Pr2090064827t_char]: (collec178542150t_char @ (^[X : produc1777519579t_char]: (((X = A6)) | ((member958036996t_char @ X @ B5)))))))))). % insert_compr
thf(fact_216_insert__compr, axiom,
    ((insert1354659367t_char = (^[A6 : produc1259892823t_char]: (^[B5 : set_Pr1344692407t_char]: (collec1549347906t_char @ (^[X : produc1259892823t_char]: (((X = A6)) | ((member397625600t_char @ X @ B5)))))))))). % insert_compr
thf(fact_217_insert__compr, axiom,
    ((insert363480567on_val = (^[A6 : produc655058983on_val]: (^[B5 : set_Pr208351751on_val]: (collec105960082on_val @ (^[X : produc655058983on_val]: (((X = A6)) | ((member1689761872on_val @ X @ B5)))))))))). % insert_compr
thf(fact_218_set__rec, axiom,
    ((set_Pr1611739760t_char = (rec_li2113358230t_char @ bot_bo632162855t_char @ (^[X : produc1777519579t_char]: (^[Uu : list_P1234162913t_char]: (insert1233103275t_char @ X))))))). % set_rec
thf(fact_219_set__rec, axiom,
    ((set_Pr1045701996t_char = (rec_li725092118t_char @ bot_bo956740899t_char @ (^[X : produc1259892823t_char]: (^[Uu : list_P1653548253t_char]: (insert1354659367t_char @ X))))))). % set_rec
thf(fact_220_subset__singleton__iff__Uniq, axiom,
    ((![A4 : set_Pr164112643t_char]: ((?[A6 : produc1257910179t_char]: (ord_le167891107t_char @ A4 @ (insert1354671475t_char @ A6 @ bot_bo346063215t_char))) = (uniq_P1653439656t_char @ (^[X : produc1257910179t_char]: (member89690956t_char @ X @ A4))))))). % subset_singleton_iff_Uniq
thf(fact_221_subset__singleton__iff__Uniq, axiom,
    ((![A4 : set_Pr1189492743on_val]: ((?[A6 : produc1172664615on_val]: (ord_le837504935on_val @ A4 @ (insert1971494647on_val @ A6 @ bot_bo1575563891on_val))) = (uniq_P1083360684on_val @ (^[X : produc1172664615on_val]: (member354538064on_val @ X @ A4))))))). % subset_singleton_iff_Uniq
thf(fact_222_subset__singleton__iff__Uniq, axiom,
    ((![A4 : set_Pr2090064827t_char]: ((?[A6 : produc1777519579t_char]: (ord_le2010927963t_char @ A4 @ (insert1233103275t_char @ A6 @ bot_bo632162855t_char))) = (uniq_P1353069408t_char @ (^[X : produc1777519579t_char]: (member958036996t_char @ X @ A4))))))). % subset_singleton_iff_Uniq
thf(fact_223_subset__singleton__iff__Uniq, axiom,
    ((![A4 : set_Pr1344692407t_char]: ((?[A6 : produc1259892823t_char]: (ord_le1781475415t_char @ A4 @ (insert1354659367t_char @ A6 @ bot_bo956740899t_char))) = (uniq_P688807516t_char @ (^[X : produc1259892823t_char]: (member397625600t_char @ X @ A4))))))). % subset_singleton_iff_Uniq
thf(fact_224_subset__singleton__iff__Uniq, axiom,
    ((![A4 : set_Pr208351751on_val]: ((?[A6 : produc655058983on_val]: (ord_le1331145127on_val @ A4 @ (insert363480567on_val @ A6 @ bot_bo1426907251on_val))) = (uniq_P892399532on_val @ (^[X : produc655058983on_val]: (member1689761872on_val @ X @ A4))))))). % subset_singleton_iff_Uniq
thf(fact_225_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_226_rtrancl__subset__rtrancl, axiom,
    ((![R : set_Pr1189492743on_val, S2 : set_Pr1189492743on_val]: ((ord_le837504935on_val @ R @ (transi111096263on_val @ S2)) => (ord_le837504935on_val @ (transi111096263on_val @ R) @ (transi111096263on_val @ S2)))))). % rtrancl_subset_rtrancl
thf(fact_227_rtrancl__subset__rtrancl, axiom,
    ((![R : set_Pr208351751on_val, S2 : set_Pr208351751on_val]: ((ord_le1331145127on_val @ R @ (transi325225921on_val @ S2)) => (ord_le1331145127on_val @ (transi325225921on_val @ R) @ (transi325225921on_val @ S2)))))). % rtrancl_subset_rtrancl
thf(fact_228_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_229_rtrancl__subset, axiom,
    ((![R2 : set_Pr1189492743on_val, S : set_Pr1189492743on_val]: ((ord_le837504935on_val @ R2 @ S) => ((ord_le837504935on_val @ S @ (transi111096263on_val @ R2)) => ((transi111096263on_val @ S) = (transi111096263on_val @ R2))))))). % rtrancl_subset
thf(fact_230_rtrancl__subset, axiom,
    ((![R2 : set_Pr208351751on_val, S : set_Pr208351751on_val]: ((ord_le1331145127on_val @ R2 @ S) => ((ord_le1331145127on_val @ S @ (transi325225921on_val @ R2)) => ((transi325225921on_val @ S) = (transi325225921on_val @ R2))))))). % rtrancl_subset
thf(fact_231_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_232_rtrancl__mono, axiom,
    ((![R : set_Pr1189492743on_val, S2 : set_Pr1189492743on_val]: ((ord_le837504935on_val @ R @ S2) => (ord_le837504935on_val @ (transi111096263on_val @ R) @ (transi111096263on_val @ S2)))))). % rtrancl_mono
thf(fact_233_rtrancl__mono, axiom,
    ((![R : set_Pr208351751on_val, S2 : set_Pr208351751on_val]: ((ord_le1331145127on_val @ R @ S2) => (ord_le1331145127on_val @ (transi325225921on_val @ R) @ (transi325225921on_val @ S2)))))). % rtrancl_mono
thf(fact_234_subrelI, axiom,
    ((![R : set_Pr1344692407t_char, S2 : set_Pr1344692407t_char]: ((![X3 : list_char, Y : produc1451990293t_char]: ((member397625600t_char @ (produc1238538255t_char @ X3 @ Y) @ R) => (member397625600t_char @ (produc1238538255t_char @ X3 @ Y) @ S2))) => (ord_le1781475415t_char @ R @ S2))))). % subrelI
thf(fact_235_subrelI, axiom,
    ((![R : set_Pr208351751on_val, S2 : set_Pr208351751on_val]: ((![X3 : produc335961278on_val, Y : produc335961278on_val]: ((member1689761872on_val @ (produc245869591on_val @ X3 @ Y) @ R) => (member1689761872on_val @ (produc245869591on_val @ X3 @ Y) @ S2))) => (ord_le1331145127on_val @ R @ S2))))). % subrelI
thf(fact_236_subrelI, axiom,
    ((![R : set_Pr164112643t_char, S2 : set_Pr164112643t_char]: ((![X3 : list_char, Y : list_char]: ((member89690956t_char @ (produc1304532571t_char @ X3 @ Y) @ R) => (member89690956t_char @ (produc1304532571t_char @ X3 @ Y) @ S2))) => (ord_le167891107t_char @ R @ S2))))). % subrelI
thf(fact_237_subrelI, axiom,
    ((![R : set_Pr2063914181t_char, S2 : set_Pr2063914181t_char]: ((![X3 : list_list_char, Y : exp_list_char]: ((member605104934t_char @ (produc713467969t_char @ X3 @ Y) @ R) => (member605104934t_char @ (produc713467969t_char @ X3 @ Y) @ S2))) => (ord_le722986277t_char @ R @ S2))))). % subrelI
thf(fact_238_subrelI, axiom,
    ((![R : set_Pr1511552798on_val, S2 : set_Pr1511552798on_val]: ((![X3 : list_exp_list_char, Y : produc515445032on_val]: ((member184158439on_val @ (produc1725134254on_val @ X3 @ Y) @ R) => (member184158439on_val @ (produc1725134254on_val @ X3 @ Y) @ S2))) => (ord_le1881566910on_val @ R @ S2))))). % subrelI
thf(fact_239_subrelI, axiom,
    ((![R : set_Pr556513572on_val, S2 : set_Pr556513572on_val]: ((![X3 : exp_list_char, Y : produc515445032on_val]: ((member1888679917on_val @ (produc2023458740on_val @ X3 @ Y) @ R) => (member1888679917on_val @ (produc2023458740on_val @ X3 @ Y) @ S2))) => (ord_le131203268on_val @ R @ S2))))). % subrelI
thf(fact_240_subrelI, axiom,
    ((![R : set_Pr723149704on_val, S2 : set_Pr723149704on_val]: ((![X3 : nat > option2118145160on_val, Y : list_char > option_val]: ((member652041809on_val @ (produc52622304on_val @ X3 @ Y) @ R) => (member652041809on_val @ (produc52622304on_val @ X3 @ Y) @ S2))) => (ord_le930806568on_val @ R @ S2))))). % subrelI
thf(fact_241_reds__preserves__sconf, axiom,
    ((![Es : list_exp_list_char, S2 : produc515445032on_val, Es2 : list_exp_list_char, S3 : produc515445032on_val, P : list_P1234162913t_char, E : list_char > option_ty, Ts : list_ty]: ((member1689761872on_val @ (produc245869591on_val @ (produc1725134254on_val @ Es @ S2) @ (produc1725134254on_val @ Es2 @ S3)) @ (reds @ P)) => ((wTrts @ P @ (hp @ S2) @ E @ Es @ Ts) => ((typeSa1777264139_sconf @ P @ E @ S2) => (typeSa1777264139_sconf @ P @ E @ S3))))))). % reds_preserves_sconf
thf(fact_242_reds__hext__incr, axiom,
    ((![Es : list_exp_list_char, H : nat > option2118145160on_val, L : list_char > option_val, Es2 : list_exp_list_char, H2 : nat > option2118145160on_val, L2 : list_char > option_val, P : list_P1234162913t_char]: ((member1689761872on_val @ (produc245869591on_val @ (produc1725134254on_val @ Es @ (produc52622304on_val @ H @ L)) @ (produc1725134254on_val @ Es2 @ (produc52622304on_val @ H2 @ L2))) @ (reds @ P)) => (hext @ H @ H2))))). % reds_hext_incr
thf(fact_243_reds__preserves__hconf, axiom,
    ((![Es : list_exp_list_char, H : nat > option2118145160on_val, L : list_char > option_val, Es2 : list_exp_list_char, H2 : nat > option2118145160on_val, L2 : list_char > option_val, P : list_P1234162913t_char, E : list_char > option_ty, Ts : list_ty]: ((member1689761872on_val @ (produc245869591on_val @ (produc1725134254on_val @ Es @ (produc52622304on_val @ H @ L)) @ (produc1725134254on_val @ Es2 @ (produc52622304on_val @ H2 @ L2))) @ (reds @ P)) => ((wTrts @ P @ H @ E @ Es @ Ts) => ((hconf_1244167010t_char @ P @ H) => (hconf_1244167010t_char @ P @ H2))))))). % reds_preserves_hconf
thf(fact_244_reds__preserves__lconf, axiom,
    ((![Es : list_exp_list_char, H : nat > option2118145160on_val, L : list_char > option_val, Es2 : list_exp_list_char, H2 : nat > option2118145160on_val, L2 : list_char > option_val, P : list_P1234162913t_char, E : list_char > option_ty, Ts : list_ty]: ((member1689761872on_val @ (produc245869591on_val @ (produc1725134254on_val @ Es @ (produc52622304on_val @ H @ L)) @ (produc1725134254on_val @ Es2 @ (produc52622304on_val @ H2 @ L2))) @ (reds @ P)) => ((wTrts @ P @ H @ E @ Es @ Ts) => ((lconf_485928294t_char @ P @ H @ L @ E) => (lconf_485928294t_char @ P @ H2 @ L2 @ E))))))). % reds_preserves_lconf
thf(fact_245_CallRedsParams, axiom,
    ((![Es : list_exp_list_char, S2 : produc515445032on_val, Es2 : list_exp_list_char, S3 : produc515445032on_val, P : list_P1234162913t_char, V : val, M : list_char]: ((member1689761872on_val @ (produc245869591on_val @ (produc1725134254on_val @ Es @ S2) @ (produc1725134254on_val @ Es2 @ S3)) @ (transi325225921on_val @ (reds @ P))) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (call_list_char @ (val_list_char @ V) @ M @ Es) @ S2) @ (produc2023458740on_val @ (call_list_char @ (val_list_char @ V) @ M @ Es2) @ S3)) @ (transi111096263on_val @ (red @ P))))))). % CallRedsParams
thf(fact_246_ListReds1, axiom,
    ((![E2 : exp_list_char, S2 : produc515445032on_val, E3 : exp_list_char, S3 : produc515445032on_val, P : list_P1234162913t_char, Es : list_exp_list_char]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E2 @ S2) @ (produc2023458740on_val @ E3 @ S3)) @ (transi111096263on_val @ (red @ P))) => (member1689761872on_val @ (produc245869591on_val @ (produc1725134254on_val @ (cons_exp_list_char @ E2 @ Es) @ S2) @ (produc1725134254on_val @ (cons_exp_list_char @ E3 @ Es) @ S3)) @ (transi325225921on_val @ (reds @ P))))))). % ListReds1
thf(fact_247_ListReds2, axiom,
    ((![Es : list_exp_list_char, S2 : produc515445032on_val, Es2 : list_exp_list_char, S3 : produc515445032on_val, P : list_P1234162913t_char, V : val]: ((member1689761872on_val @ (produc245869591on_val @ (produc1725134254on_val @ Es @ S2) @ (produc1725134254on_val @ Es2 @ S3)) @ (transi325225921on_val @ (reds @ P))) => (member1689761872on_val @ (produc245869591on_val @ (produc1725134254on_val @ (cons_exp_list_char @ (val_list_char @ V) @ Es) @ S2) @ (produc1725134254on_val @ (cons_exp_list_char @ (val_list_char @ V) @ Es2) @ S3)) @ (transi325225921on_val @ (reds @ P))))))). % ListReds2
thf(fact_248_red__reds_OListRed2, axiom,
    ((![Es : list_exp_list_char, S2 : produc515445032on_val, Es2 : list_exp_list_char, S3 : produc515445032on_val, P : list_P1234162913t_char, V : val]: ((member1689761872on_val @ (produc245869591on_val @ (produc1725134254on_val @ Es @ S2) @ (produc1725134254on_val @ Es2 @ S3)) @ (reds @ P)) => (member1689761872on_val @ (produc245869591on_val @ (produc1725134254on_val @ (cons_exp_list_char @ (val_list_char @ V) @ Es) @ S2) @ (produc1725134254on_val @ (cons_exp_list_char @ (val_list_char @ V) @ Es2) @ S3)) @ (reds @ P)))))). % red_reds.ListRed2

% Conjectures (1)
thf(conj_0, conjecture,
    ((wTrt @ p @ h_a @ e @ e_a @ (class @ c)))).
