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% This file was generated by Isabelle (most likely Sledgehammer)
% 2020-12-16 14:21:44.607

% Could-be-implicit typings (27)
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    is_sin412639003on_val : set_Pr208351751on_val > $o).
thf(sy_c_SmallStep_Ored, type,
    red : list_P1234162913t_char > set_Pr1189492743on_val).
thf(sy_c_SmallStep_Oreds, type,
    reds : list_P1234162913t_char > set_Pr208351751on_val).
thf(sy_c_SmallStep_Oredsp, type,
    redsp : list_P1234162913t_char > list_exp_list_char > produc515445032on_val > list_exp_list_char > produc515445032on_val > $o).
thf(sy_c_State_Ohp, type,
    hp : produc515445032on_val > nat > option2118145160on_val).
thf(sy_c_TypeRel_OMethod_001t__Product____Type__Oprod_It__List__Olist_It__List__Olist_It__String__Ochar_J_J_Mt__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_J, type,
    method297381284t_char : list_P1234162913t_char > list_char > list_char > list_ty > ty > produc1294284815t_char > list_char > $o).
thf(sy_c_TypeRel_Ohas__method_001t__Product____Type__Oprod_It__List__Olist_It__List__Olist_It__String__Ochar_J_J_Mt__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_J, type,
    has_me170134744t_char : list_P1234162913t_char > list_char > list_char > $o).
thf(sy_c_TypeRel_Omethod_001t__Product____Type__Oprod_It__List__Olist_It__List__Olist_It__String__Ochar_J_J_Mt__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_J, type,
    method667690372t_char : list_P1234162913t_char > list_char > list_char > produc1259892823t_char).
thf(sy_c_TypeRel_Owiden_001t__Product____Type__Oprod_It__List__Olist_It__List__Olist_It__String__Ochar_J_J_Mt__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_J, type,
    widen_917054840t_char : list_P1234162913t_char > ty > ty > $o).
thf(sy_c_TypeSafe__Mirabelle__osrwgqrerx_Osconf, type,
    typeSa1777264139_sconf : list_P1234162913t_char > (list_char > option_ty) > produc515445032on_val > $o).
thf(sy_c_Type_Oty_OClass, type,
    class : list_char > ty).
thf(sy_c_Type_Oty_ONT, type,
    nt : ty).
thf(sy_c_WellForm_Owf__mdecl_001t__Product____Type__Oprod_It__List__Olist_It__List__Olist_It__String__Ochar_J_J_Mt__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_J, type,
    wf_mde297024346t_char : (list_P1234162913t_char > list_char > produc1259892823t_char > $o) > list_P1234162913t_char > list_char > produc1259892823t_char > $o).
thf(sy_c_WellForm_Owf__prog_001t__Product____Type__Oprod_It__List__Olist_It__List__Olist_It__String__Ochar_J_J_Mt__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_J, type,
    wf_pro1229751607t_char : (list_P1234162913t_char > list_char > produc1259892823t_char > $o) > list_P1234162913t_char > $o).
thf(sy_c_WellTypeRT_OWTrt, type,
    wTrt2 : list_P1234162913t_char > (nat > option2118145160on_val) > (list_char > option_ty) > exp_list_char > ty > $o).
thf(sy_c_WellTypeRT_OWTrts, type,
    wTrts2 : list_P1234162913t_char > (nat > option2118145160on_val) > (list_char > option_ty) > list_exp_list_char > list_ty > $o).
thf(sy_c_WellType_OWT, type,
    wt : list_P1234162913t_char > (list_char > option_ty) > exp_list_char > ty > $o).
thf(sy_c_WellType_OWTs, type,
    wTs : list_P1234162913t_char > (list_char > option_ty) > list_exp_list_char > list_ty > $o).
thf(sy_c_member_001t__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_M_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_J, type,
    member652041809on_val : produc515445032on_val > set_Pr723149704on_val > $o).
thf(sy_c_member_001t__Product____Type__Oprod_It__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_Mt__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_M_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J, type,
    member1888679917on_val : produc1097884484on_val > set_Pr556513572on_val > $o).
thf(sy_c_member_001t__Product____Type__Oprod_It__List__Olist_It__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_J_Mt__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_M_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J, type,
    member184158439on_val : produc335961278on_val > set_Pr1511552798on_val > $o).
thf(sy_c_member_001t__Product____Type__Oprod_It__List__Olist_It__List__Olist_It__String__Ochar_J_J_Mt__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_J, type,
    member605104934t_char : produc1294284815t_char > set_Pr2063914181t_char > $o).
thf(sy_c_member_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_Mt__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_M_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_Mt__Product____Type__Oprod_It__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_Mt__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_M_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J, type,
    member354538064on_val : produc1172664615on_val > set_Pr1189492743on_val > $o).
thf(sy_c_member_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__List__Olist_It__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_J_Mt__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_M_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_Mt__Product____Type__Oprod_It__List__Olist_It__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_J_Mt__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_M_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J, type,
    member1689761872on_val : produc655058983on_val > set_Pr208351751on_val > $o).
thf(sy_v_C____, type,
    c : list_char).
thf(sy_v_D____, type,
    d : list_char).
thf(sy_v_E____, type,
    e : list_char > option_ty).
thf(sy_v_M____, type,
    m : list_char).
thf(sy_v_P, type,
    p : list_P1234162913t_char).
thf(sy_v_T____, type,
    t : ty).
thf(sy_v_Ts____, type,
    ts : list_ty).
thf(sy_v_U____, type,
    u : ty).
thf(sy_v_Us____, type,
    us : list_ty).
thf(sy_v_body____, type,
    body : exp_list_char).
thf(sy_v_e_Ha____, type,
    e_a : exp_list_char).
thf(sy_v_ea____, type,
    ea : exp_list_char).
thf(sy_v_esa____, type,
    esa : list_exp_list_char).
thf(sy_v_h_Ha____, type,
    h_a : nat > option2118145160on_val).
thf(sy_v_ha____, type,
    ha : nat > option2118145160on_val).
thf(sy_v_l_Ha____, type,
    l_a : list_char > option_val).
thf(sy_v_la____, type,
    la : list_char > option_val).
thf(sy_v_pns____, type,
    pns : list_list_char).

% Relevant facts (195)
thf(fact_0_wtes, axiom,
    ((wTrts2 @ p @ ha @ e @ esa @ us))). % wtes
thf(fact_1_local_Owf, axiom,
    ((wf_pro1229751607t_char @ wf_J_mdecl @ p))). % local.wf
thf(fact_2_wte_H, axiom,
    ((wTrt2 @ p @ h_a @ e @ e_a @ u))). % wte'
thf(fact_3_subs, axiom,
    ((list_all2_ty_ty @ (widen_917054840t_char @ p) @ us @ ts))). % subs
thf(fact_4_calculation, axiom,
    ((u = nt))). % calculation
thf(fact_5__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]: ((wTrt2 @ p @ h_a @ e @ e_a @ U) => (~ ((widen_917054840t_char @ p @ U @ (class @ c)))))))))). % \<open>\<And>thesis. (\<And>U. \<lbrakk>P,E,h' \<turnstile> e' : U; P \<turnstile> U \<le> Class C\<rbrakk> \<Longrightarrow> thesis) \<Longrightarrow> thesis\<close>
thf(fact_6_conf, axiom,
    ((typeSa1777264139_sconf @ p @ e @ (produc52622304on_val @ ha @ la)))). % conf
thf(fact_7_wt, axiom,
    ((wTrt2 @ p @ ha @ e @ (call_list_char @ ea @ m @ esa) @ t))). % wt
thf(fact_8_WTs__implies__WTrts, axiom,
    ((![P : list_P1234162913t_char, E : list_char > option_ty, Es : list_exp_list_char, Ts : list_ty, H : nat > option2118145160on_val]: ((wTs @ P @ E @ Es @ Ts) => (wTrts2 @ P @ H @ E @ Es @ Ts))))). % WTs_implies_WTrts
thf(fact_9_wts_H__wts, axiom,
    ((![P : list_P1234162913t_char, H : nat > option2118145160on_val, E : list_char > option_ty, Es : list_exp_list_char, Ts : list_ty]: ((wTrts @ P @ H @ E @ Es @ Ts) => (wTrts2 @ P @ H @ E @ Es @ Ts))))). % wts'_wts
thf(fact_10_wts__wts_H, axiom,
    ((![P : list_P1234162913t_char, H : nat > option2118145160on_val, E : list_char > option_ty, Es : list_exp_list_char, Ts : list_ty]: ((wTrts2 @ P @ H @ E @ Es @ Ts) => (wTrts @ P @ H @ E @ Es @ Ts))))). % wts_wts'
thf(fact_11_wts_H__iff__wts, axiom,
    ((wTrts = wTrts2))). % wts'_iff_wts
thf(fact_12_wte, axiom,
    ((wTrt2 @ p @ ha @ e @ ea @ (class @ c)))). % wte
thf(fact_13_UsubC, axiom,
    ((widen_917054840t_char @ p @ u @ (class @ c)))). % UsubC
thf(fact_14_IH, axiom,
    ((![E : list_char > option_ty, T : ty]: ((typeSa1777264139_sconf @ p @ E @ (produc52622304on_val @ ha @ la)) => ((wTrt2 @ p @ ha @ E @ ea @ T) => (?[U : ty]: ((wTrt2 @ p @ h_a @ E @ e_a @ U) & (widen_917054840t_char @ p @ U @ T)))))))). % IH
thf(fact_15_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]: ((wTrt2 @ P @ H @ E @ E2 @ nt) => ((wTrts2 @ P @ H @ E @ Es @ Ts) => (wTrt2 @ P @ H @ E @ (call_list_char @ E2 @ M @ Es) @ T)))))). % WTrtCallNT
thf(fact_16_widens__refl, axiom,
    ((![P : list_P1234162913t_char, Xs : list_ty]: (list_all2_ty_ty @ (widen_917054840t_char @ P) @ Xs @ Xs)))). % widens_refl
thf(fact_17_CallObj_Oprems_I2_J, axiom,
    ((wTrt2 @ p @ ha @ e @ (call_list_char @ ea @ m @ esa) @ t))). % CallObj.prems(2)
thf(fact_18__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]: ((wTrt2 @ p @ ha @ e @ ea @ nt) => ((wTrts2 @ p @ ha @ e @ esa @ Ts) => (?[T2 : ty]: ((wTrt2 @ 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_19_widen__null, axiom,
    ((![P : list_P1234162913t_char, C : list_char]: (widen_917054840t_char @ P @ nt @ (class @ C))))). % widen_null
thf(fact_20_CallObj_Ohyps_I2_J, axiom,
    ((![E : list_char > option_ty, T : ty]: ((typeSa1777264139_sconf @ p @ E @ (produc52622304on_val @ ha @ la)) => ((wTrt2 @ p @ ha @ E @ ea @ T) => (?[T2 : ty]: ((wTrt2 @ p @ h_a @ E @ e_a @ T2) & (widen_917054840t_char @ p @ T2 @ T)))))))). % CallObj.hyps(2)
thf(fact_21_CallObj_Oprems_I1_J, axiom,
    ((typeSa1777264139_sconf @ p @ e @ (produc52622304on_val @ ha @ la)))). % CallObj.prems(1)
thf(fact_22_ty_Oinject, axiom,
    ((![X5 : list_char, Y5 : list_char]: (((class @ X5) = (class @ Y5)) = (X5 = Y5))))). % ty.inject
thf(fact_23_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_24_method, axiom,
    ((method297381284t_char @ p @ c @ m @ ts @ t @ (produc713467969t_char @ pns @ body) @ d))). % method
thf(fact_25_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_26_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_27_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, T3 : ty, M3 : produc1294284815t_char, D2 : list_char]: ((method297381284t_char @ P @ C @ M @ TS @ T @ M2 @ D) => ((method297381284t_char @ P @ C @ M @ TS2 @ T3 @ M3 @ D2) => ((TS2 = TS) & ((T3 = T) & ((M3 = M2) & (D2 = D))))))))). % sees_method_fun
thf(fact_28_WTrtCall, axiom,
    ((![P : list_P1234162913t_char, H : nat > option2118145160on_val, E : list_char > option_ty, E2 : exp_list_char, C : list_char, M : list_char, Ts : list_ty, T : ty, Pns : list_list_char, Body : exp_list_char, D : list_char, Es : list_exp_list_char, Ts2 : list_ty]: ((wTrt2 @ P @ H @ E @ E2 @ (class @ C)) => ((method297381284t_char @ P @ C @ M @ Ts @ T @ (produc713467969t_char @ Pns @ Body) @ D) => ((wTrts2 @ P @ H @ E @ Es @ Ts2) => ((list_all2_ty_ty @ (widen_917054840t_char @ P) @ Ts2 @ Ts) => (wTrt2 @ P @ H @ E @ (call_list_char @ E2 @ M @ Es) @ T)))))))). % WTrtCall
thf(fact_29_widen__refl, axiom,
    ((![P : list_P1234162913t_char, T : ty]: (widen_917054840t_char @ P @ T @ T)))). % widen_refl
thf(fact_30_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_31_Class__widen, axiom,
    ((![P : list_P1234162913t_char, C : list_char, T : ty]: ((widen_917054840t_char @ P @ (class @ C) @ T) => (?[D3 : list_char]: (T = (class @ D3))))))). % Class_widen
thf(fact_32_ty_Odistinct_I19_J, axiom,
    ((![X5 : list_char]: (~ ((nt = (class @ X5))))))). % ty.distinct(19)
thf(fact_33_has__method__def, axiom,
    ((has_me170134744t_char = (^[P2 : list_P1234162913t_char]: (^[C2 : list_char]: (^[M4 : list_char]: (?[Ts3 : list_ty]: (?[T4 : ty]: (?[M5 : produc1294284815t_char]: (?[X : list_char]: (method297381284t_char @ P2 @ C2 @ M4 @ Ts3 @ T4 @ M5 @ X))))))))))). % has_method_def
thf(fact_34_WTrt_H__WTrts_H_Ointros_I12_J, 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)))))))). % WTrt'_WTrts'.intros(12)
thf(fact_35_old_Oprod_Oinject, axiom,
    ((![A : produc1097884484on_val, B : produc1097884484on_val, A2 : produc1097884484on_val, B2 : produc1097884484on_val]: (((produc1069526295on_val @ A @ B) = (produc1069526295on_val @ A2 @ B2)) = (((A = A2)) & ((B = B2))))))). % old.prod.inject
thf(fact_36_old_Oprod_Oinject, axiom,
    ((![A : list_list_char, B : exp_list_char, A2 : list_list_char, B2 : exp_list_char]: (((produc713467969t_char @ A @ B) = (produc713467969t_char @ A2 @ B2)) = (((A = A2)) & ((B = B2))))))). % old.prod.inject
thf(fact_37_old_Oprod_Oinject, axiom,
    ((![A : list_exp_list_char, B : produc515445032on_val, A2 : list_exp_list_char, B2 : produc515445032on_val]: (((produc1725134254on_val @ A @ B) = (produc1725134254on_val @ A2 @ B2)) = (((A = A2)) & ((B = B2))))))). % old.prod.inject
thf(fact_38_old_Oprod_Oinject, axiom,
    ((![A : exp_list_char, B : produc515445032on_val, A2 : exp_list_char, B2 : produc515445032on_val]: (((produc2023458740on_val @ A @ B) = (produc2023458740on_val @ A2 @ B2)) = (((A = A2)) & ((B = B2))))))). % old.prod.inject
thf(fact_39_old_Oprod_Oinject, axiom,
    ((![A : nat > option2118145160on_val, B : list_char > option_val, A2 : nat > option2118145160on_val, B2 : list_char > option_val]: (((produc52622304on_val @ A @ B) = (produc52622304on_val @ A2 @ B2)) = (((A = A2)) & ((B = B2))))))). % old.prod.inject
thf(fact_40_prod_Oinject, axiom,
    ((![X1 : produc1097884484on_val, X2 : produc1097884484on_val, Y1 : produc1097884484on_val, Y2 : produc1097884484on_val]: (((produc1069526295on_val @ X1 @ X2) = (produc1069526295on_val @ Y1 @ Y2)) = (((X1 = Y1)) & ((X2 = Y2))))))). % prod.inject
thf(fact_41_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_42_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_43_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_44_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_45_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_46_WTCall, axiom,
    ((![P : list_P1234162913t_char, 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]: ((wt @ P @ E @ E2 @ (class @ C)) => ((method297381284t_char @ P @ C @ M @ Ts @ T @ (produc713467969t_char @ Pns @ Body) @ D) => ((wTs @ P @ E @ Es @ Ts2) => ((list_all2_ty_ty @ (widen_917054840t_char @ P) @ Ts2 @ Ts) => (wt @ P @ E @ (call_list_char @ E2 @ M @ Es) @ T)))))))). % WTCall
thf(fact_47_WT__elim__cases_I11_J, axiom,
    ((![P : list_P1234162913t_char, E : list_char > option_ty, E2 : exp_list_char, M : list_char, Ps : list_exp_list_char, T : ty]: ((wt @ P @ E @ (call_list_char @ E2 @ M @ Ps) @ T) => (~ ((![C3 : list_char]: ((wt @ P @ E @ E2 @ (class @ C3)) => (![Ts4 : list_ty]: ((?[Pns2 : list_list_char, Body2 : exp_list_char, X_1 : list_char]: (method297381284t_char @ P @ C3 @ M @ Ts4 @ T @ (produc713467969t_char @ Pns2 @ Body2) @ X_1)) => (![Ts5 : list_ty]: ((wTs @ P @ E @ Ps @ Ts5) => (~ ((list_all2_ty_ty @ (widen_917054840t_char @ P) @ Ts5 @ Ts4))))))))))))))). % WT_elim_cases(11)
thf(fact_48_WT__implies__WTrt, axiom,
    ((![P : list_P1234162913t_char, E : list_char > option_ty, E2 : exp_list_char, T : ty, H : nat > option2118145160on_val]: ((wt @ P @ E @ E2 @ T) => (wTrt2 @ P @ H @ E @ E2 @ T))))). % WT_implies_WTrt
thf(fact_49_wt_H__wt, axiom,
    ((![P : list_P1234162913t_char, H : nat > option2118145160on_val, E : list_char > option_ty, E2 : exp_list_char, T : ty]: ((wTrt @ P @ H @ E @ E2 @ T) => (wTrt2 @ P @ H @ E @ E2 @ T))))). % wt'_wt
thf(fact_50_wt__wt_H, axiom,
    ((![P : list_P1234162913t_char, H : nat > option2118145160on_val, E : list_char > option_ty, E2 : exp_list_char, T : ty]: ((wTrt2 @ P @ H @ E @ E2 @ T) => (wTrt @ P @ H @ E @ E2 @ T))))). % wt_wt'
thf(fact_51_wt_H__iff__wt, axiom,
    ((wTrt = wTrt2))). % wt'_iff_wt
thf(fact_52_mem__Collect__eq, axiom,
    ((![A : produc1172664615on_val, P : produc1172664615on_val > $o]: ((member354538064on_val @ A @ (collec2055896722on_val @ P)) = (P @ A))))). % mem_Collect_eq
thf(fact_53_mem__Collect__eq, axiom,
    ((![A : produc655058983on_val, P : produc655058983on_val > $o]: ((member1689761872on_val @ A @ (collec105960082on_val @ P)) = (P @ A))))). % mem_Collect_eq
thf(fact_54_Collect__mem__eq, axiom,
    ((![A3 : set_Pr1189492743on_val]: ((collec2055896722on_val @ (^[X3 : produc1172664615on_val]: (member354538064on_val @ X3 @ A3))) = A3)))). % Collect_mem_eq
thf(fact_55_Collect__mem__eq, axiom,
    ((![A3 : set_Pr208351751on_val]: ((collec105960082on_val @ (^[X3 : produc655058983on_val]: (member1689761872on_val @ X3 @ A3))) = A3)))). % Collect_mem_eq
thf(fact_56_surj__pair, axiom,
    ((![P3 : produc1172664615on_val]: (?[X4 : produc1097884484on_val, Y : produc1097884484on_val]: (P3 = (produc1069526295on_val @ X4 @ Y)))))). % surj_pair
thf(fact_57_surj__pair, axiom,
    ((![P3 : produc1294284815t_char]: (?[X4 : list_list_char, Y : exp_list_char]: (P3 = (produc713467969t_char @ X4 @ Y)))))). % surj_pair
thf(fact_58_surj__pair, axiom,
    ((![P3 : produc335961278on_val]: (?[X4 : list_exp_list_char, Y : produc515445032on_val]: (P3 = (produc1725134254on_val @ X4 @ Y)))))). % surj_pair
thf(fact_59_surj__pair, axiom,
    ((![P3 : produc1097884484on_val]: (?[X4 : exp_list_char, Y : produc515445032on_val]: (P3 = (produc2023458740on_val @ X4 @ Y)))))). % surj_pair
thf(fact_60_surj__pair, axiom,
    ((![P3 : produc515445032on_val]: (?[X4 : nat > option2118145160on_val, Y : list_char > option_val]: (P3 = (produc52622304on_val @ X4 @ Y)))))). % surj_pair
thf(fact_61_prod__cases, axiom,
    ((![P : produc1172664615on_val > $o, P3 : produc1172664615on_val]: ((![A4 : produc1097884484on_val, B3 : produc1097884484on_val]: (P @ (produc1069526295on_val @ A4 @ B3))) => (P @ P3))))). % prod_cases
thf(fact_62_prod__cases, axiom,
    ((![P : produc1294284815t_char > $o, P3 : produc1294284815t_char]: ((![A4 : list_list_char, B3 : exp_list_char]: (P @ (produc713467969t_char @ A4 @ B3))) => (P @ P3))))). % prod_cases
thf(fact_63_prod__cases, axiom,
    ((![P : produc335961278on_val > $o, P3 : produc335961278on_val]: ((![A4 : list_exp_list_char, B3 : produc515445032on_val]: (P @ (produc1725134254on_val @ A4 @ B3))) => (P @ P3))))). % prod_cases
thf(fact_64_prod__cases, axiom,
    ((![P : produc1097884484on_val > $o, P3 : produc1097884484on_val]: ((![A4 : exp_list_char, B3 : produc515445032on_val]: (P @ (produc2023458740on_val @ A4 @ B3))) => (P @ P3))))). % prod_cases
thf(fact_65_prod__cases, axiom,
    ((![P : produc515445032on_val > $o, P3 : produc515445032on_val]: ((![A4 : nat > option2118145160on_val, B3 : list_char > option_val]: (P @ (produc52622304on_val @ A4 @ B3))) => (P @ P3))))). % prod_cases
thf(fact_66_Pair__inject, axiom,
    ((![A : produc1097884484on_val, B : produc1097884484on_val, A2 : produc1097884484on_val, B2 : produc1097884484on_val]: (((produc1069526295on_val @ A @ B) = (produc1069526295on_val @ A2 @ B2)) => (~ (((A = A2) => (~ ((B = B2)))))))))). % Pair_inject
thf(fact_67_Pair__inject, axiom,
    ((![A : list_list_char, B : exp_list_char, A2 : list_list_char, B2 : exp_list_char]: (((produc713467969t_char @ A @ B) = (produc713467969t_char @ A2 @ B2)) => (~ (((A = A2) => (~ ((B = B2)))))))))). % Pair_inject
thf(fact_68_Pair__inject, axiom,
    ((![A : list_exp_list_char, B : produc515445032on_val, A2 : list_exp_list_char, B2 : produc515445032on_val]: (((produc1725134254on_val @ A @ B) = (produc1725134254on_val @ A2 @ B2)) => (~ (((A = A2) => (~ ((B = B2)))))))))). % Pair_inject
thf(fact_69_Pair__inject, axiom,
    ((![A : exp_list_char, B : produc515445032on_val, A2 : exp_list_char, B2 : produc515445032on_val]: (((produc2023458740on_val @ A @ B) = (produc2023458740on_val @ A2 @ B2)) => (~ (((A = A2) => (~ ((B = B2)))))))))). % Pair_inject
thf(fact_70_Pair__inject, axiom,
    ((![A : nat > option2118145160on_val, B : list_char > option_val, A2 : nat > option2118145160on_val, B2 : list_char > option_val]: (((produc52622304on_val @ A @ B) = (produc52622304on_val @ A2 @ B2)) => (~ (((A = A2) => (~ ((B = B2)))))))))). % Pair_inject
thf(fact_71_prod__cases3, axiom,
    ((![Y3 : produc1172664615on_val]: (~ ((![A4 : produc1097884484on_val, B3 : exp_list_char, C4 : produc515445032on_val]: (~ ((Y3 = (produc1069526295on_val @ A4 @ (produc2023458740on_val @ B3 @ C4))))))))))). % prod_cases3
thf(fact_72_prod__cases3, axiom,
    ((![Y3 : produc335961278on_val]: (~ ((![A4 : list_exp_list_char, B3 : nat > option2118145160on_val, C4 : list_char > option_val]: (~ ((Y3 = (produc1725134254on_val @ A4 @ (produc52622304on_val @ B3 @ C4))))))))))). % prod_cases3
thf(fact_73_prod__cases3, axiom,
    ((![Y3 : produc1097884484on_val]: (~ ((![A4 : exp_list_char, B3 : nat > option2118145160on_val, C4 : list_char > option_val]: (~ ((Y3 = (produc2023458740on_val @ A4 @ (produc52622304on_val @ B3 @ C4))))))))))). % prod_cases3
thf(fact_74_prod__cases4, axiom,
    ((![Y3 : produc1172664615on_val]: (~ ((![A4 : produc1097884484on_val, B3 : exp_list_char, C4 : nat > option2118145160on_val, D4 : list_char > option_val]: (~ ((Y3 = (produc1069526295on_val @ A4 @ (produc2023458740on_val @ B3 @ (produc52622304on_val @ C4 @ D4)))))))))))). % prod_cases4
thf(fact_75_prod__induct3, axiom,
    ((![P : produc1172664615on_val > $o, X6 : produc1172664615on_val]: ((![A4 : produc1097884484on_val, B3 : exp_list_char, C4 : produc515445032on_val]: (P @ (produc1069526295on_val @ A4 @ (produc2023458740on_val @ B3 @ C4)))) => (P @ X6))))). % prod_induct3
thf(fact_76_prod__induct3, axiom,
    ((![P : produc335961278on_val > $o, X6 : produc335961278on_val]: ((![A4 : list_exp_list_char, B3 : nat > option2118145160on_val, C4 : list_char > option_val]: (P @ (produc1725134254on_val @ A4 @ (produc52622304on_val @ B3 @ C4)))) => (P @ X6))))). % prod_induct3
thf(fact_77_prod__induct3, axiom,
    ((![P : produc1097884484on_val > $o, X6 : produc1097884484on_val]: ((![A4 : exp_list_char, B3 : nat > option2118145160on_val, C4 : list_char > option_val]: (P @ (produc2023458740on_val @ A4 @ (produc52622304on_val @ B3 @ C4)))) => (P @ X6))))). % prod_induct3
thf(fact_78_prod__induct4, axiom,
    ((![P : produc1172664615on_val > $o, X6 : produc1172664615on_val]: ((![A4 : produc1097884484on_val, B3 : exp_list_char, C4 : nat > option2118145160on_val, D4 : list_char > option_val]: (P @ (produc1069526295on_val @ A4 @ (produc2023458740on_val @ B3 @ (produc52622304on_val @ C4 @ D4))))) => (P @ X6))))). % prod_induct4
thf(fact_79_old_Oprod_Oexhaust, axiom,
    ((![Y3 : produc1172664615on_val]: (~ ((![A4 : produc1097884484on_val, B3 : produc1097884484on_val]: (~ ((Y3 = (produc1069526295on_val @ A4 @ B3)))))))))). % old.prod.exhaust
thf(fact_80_old_Oprod_Oexhaust, axiom,
    ((![Y3 : produc1294284815t_char]: (~ ((![A4 : list_list_char, B3 : exp_list_char]: (~ ((Y3 = (produc713467969t_char @ A4 @ B3)))))))))). % old.prod.exhaust
thf(fact_81_old_Oprod_Oexhaust, axiom,
    ((![Y3 : produc335961278on_val]: (~ ((![A4 : list_exp_list_char, B3 : produc515445032on_val]: (~ ((Y3 = (produc1725134254on_val @ A4 @ B3)))))))))). % old.prod.exhaust
thf(fact_82_old_Oprod_Oexhaust, axiom,
    ((![Y3 : produc1097884484on_val]: (~ ((![A4 : exp_list_char, B3 : produc515445032on_val]: (~ ((Y3 = (produc2023458740on_val @ A4 @ B3)))))))))). % old.prod.exhaust
thf(fact_83_old_Oprod_Oexhaust, axiom,
    ((![Y3 : produc515445032on_val]: (~ ((![A4 : nat > option2118145160on_val, B3 : list_char > option_val]: (~ ((Y3 = (produc52622304on_val @ A4 @ B3)))))))))). % old.prod.exhaust
thf(fact_84_old_Oprod_Oinducts, axiom,
    ((![P : produc1172664615on_val > $o, Prod : produc1172664615on_val]: ((![A4 : produc1097884484on_val, B3 : produc1097884484on_val]: (P @ (produc1069526295on_val @ A4 @ B3))) => (P @ Prod))))). % old.prod.inducts
thf(fact_85_old_Oprod_Oinducts, axiom,
    ((![P : produc1294284815t_char > $o, Prod : produc1294284815t_char]: ((![A4 : list_list_char, B3 : exp_list_char]: (P @ (produc713467969t_char @ A4 @ B3))) => (P @ Prod))))). % old.prod.inducts
thf(fact_86_old_Oprod_Oinducts, axiom,
    ((![P : produc335961278on_val > $o, Prod : produc335961278on_val]: ((![A4 : list_exp_list_char, B3 : produc515445032on_val]: (P @ (produc1725134254on_val @ A4 @ B3))) => (P @ Prod))))). % old.prod.inducts
thf(fact_87_old_Oprod_Oinducts, axiom,
    ((![P : produc1097884484on_val > $o, Prod : produc1097884484on_val]: ((![A4 : exp_list_char, B3 : produc515445032on_val]: (P @ (produc2023458740on_val @ A4 @ B3))) => (P @ Prod))))). % old.prod.inducts
thf(fact_88_old_Oprod_Oinducts, axiom,
    ((![P : produc515445032on_val > $o, Prod : produc515445032on_val]: ((![A4 : nat > option2118145160on_val, B3 : list_char > option_val]: (P @ (produc52622304on_val @ A4 @ B3))) => (P @ Prod))))). % old.prod.inducts
thf(fact_89_WTrt_H__WTrts_H_Ointros_I13_J, 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)))))). % WTrt'_WTrts'.intros(13)
thf(fact_90_singletonI, axiom,
    ((![A : produc1172664615on_val]: (member354538064on_val @ A @ (insert1971494647on_val @ A @ bot_bo1575563891on_val))))). % singletonI
thf(fact_91_singletonI, axiom,
    ((![A : produc655058983on_val]: (member1689761872on_val @ A @ (insert363480567on_val @ A @ bot_bo1426907251on_val))))). % singletonI
thf(fact_92_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_93_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_94_all__not__in__conv, axiom,
    ((![A3 : set_Pr1189492743on_val]: ((![X3 : produc1172664615on_val]: (~ ((member354538064on_val @ X3 @ A3)))) = (A3 = bot_bo1575563891on_val))))). % all_not_in_conv
thf(fact_95_all__not__in__conv, axiom,
    ((![A3 : set_Pr208351751on_val]: ((![X3 : produc655058983on_val]: (~ ((member1689761872on_val @ X3 @ A3)))) = (A3 = bot_bo1426907251on_val))))). % all_not_in_conv
thf(fact_96_empty__iff, axiom,
    ((![C5 : produc1172664615on_val]: (~ ((member354538064on_val @ C5 @ bot_bo1575563891on_val)))))). % empty_iff
thf(fact_97_empty__iff, axiom,
    ((![C5 : produc655058983on_val]: (~ ((member1689761872on_val @ C5 @ bot_bo1426907251on_val)))))). % empty_iff
thf(fact_98_insert__iff, axiom,
    ((![A : produc1172664615on_val, B : produc1172664615on_val, A3 : set_Pr1189492743on_val]: ((member354538064on_val @ A @ (insert1971494647on_val @ B @ A3)) = (((A = B)) | ((member354538064on_val @ A @ A3))))))). % insert_iff
thf(fact_99_insert__iff, axiom,
    ((![A : produc655058983on_val, B : produc655058983on_val, A3 : set_Pr208351751on_val]: ((member1689761872on_val @ A @ (insert363480567on_val @ B @ A3)) = (((A = B)) | ((member1689761872on_val @ A @ A3))))))). % insert_iff
thf(fact_100_insertCI, axiom,
    ((![A : produc1172664615on_val, B4 : set_Pr1189492743on_val, B : produc1172664615on_val]: (((~ ((member354538064on_val @ A @ B4))) => (A = B)) => (member354538064on_val @ A @ (insert1971494647on_val @ B @ B4)))))). % insertCI
thf(fact_101_insertCI, axiom,
    ((![A : produc655058983on_val, B4 : set_Pr208351751on_val, B : produc655058983on_val]: (((~ ((member1689761872on_val @ A @ B4))) => (A = B)) => (member1689761872on_val @ A @ (insert363480567on_val @ B @ B4)))))). % insertCI
thf(fact_102_ex__in__conv, axiom,
    ((![A3 : set_Pr1189492743on_val]: ((?[X3 : produc1172664615on_val]: (member354538064on_val @ X3 @ A3)) = (~ ((A3 = bot_bo1575563891on_val))))))). % ex_in_conv
thf(fact_103_ex__in__conv, axiom,
    ((![A3 : set_Pr208351751on_val]: ((?[X3 : produc655058983on_val]: (member1689761872on_val @ X3 @ A3)) = (~ ((A3 = bot_bo1426907251on_val))))))). % ex_in_conv
thf(fact_104_equals0I, axiom,
    ((![A3 : set_Pr1189492743on_val]: ((![Y : produc1172664615on_val]: (~ ((member354538064on_val @ Y @ A3)))) => (A3 = bot_bo1575563891on_val))))). % equals0I
thf(fact_105_equals0I, axiom,
    ((![A3 : set_Pr208351751on_val]: ((![Y : produc655058983on_val]: (~ ((member1689761872on_val @ Y @ A3)))) => (A3 = bot_bo1426907251on_val))))). % equals0I
thf(fact_106_equals0D, axiom,
    ((![A3 : set_Pr1189492743on_val, A : produc1172664615on_val]: ((A3 = bot_bo1575563891on_val) => (~ ((member354538064on_val @ A @ A3))))))). % equals0D
thf(fact_107_equals0D, axiom,
    ((![A3 : set_Pr208351751on_val, A : produc655058983on_val]: ((A3 = bot_bo1426907251on_val) => (~ ((member1689761872on_val @ A @ A3))))))). % equals0D
thf(fact_108_emptyE, axiom,
    ((![A : produc1172664615on_val]: (~ ((member354538064on_val @ A @ bot_bo1575563891on_val)))))). % emptyE
thf(fact_109_emptyE, axiom,
    ((![A : produc655058983on_val]: (~ ((member1689761872on_val @ A @ bot_bo1426907251on_val)))))). % emptyE
thf(fact_110_mk__disjoint__insert, axiom,
    ((![A : produc1172664615on_val, A3 : set_Pr1189492743on_val]: ((member354538064on_val @ A @ A3) => (?[B5 : set_Pr1189492743on_val]: ((A3 = (insert1971494647on_val @ A @ B5)) & (~ ((member354538064on_val @ A @ B5))))))))). % mk_disjoint_insert
thf(fact_111_mk__disjoint__insert, axiom,
    ((![A : produc655058983on_val, A3 : set_Pr208351751on_val]: ((member1689761872on_val @ A @ A3) => (?[B5 : set_Pr208351751on_val]: ((A3 = (insert363480567on_val @ A @ B5)) & (~ ((member1689761872on_val @ A @ B5))))))))). % mk_disjoint_insert
thf(fact_112_insert__eq__iff, axiom,
    ((![A : produc1172664615on_val, A3 : set_Pr1189492743on_val, B : produc1172664615on_val, B4 : set_Pr1189492743on_val]: ((~ ((member354538064on_val @ A @ A3))) => ((~ ((member354538064on_val @ B @ B4))) => (((insert1971494647on_val @ A @ A3) = (insert1971494647on_val @ B @ B4)) = (((((A = B)) => ((A3 = B4)))) & ((((~ ((A = B)))) => ((?[C2 : set_Pr1189492743on_val]: (((A3 = (insert1971494647on_val @ B @ C2))) & ((((~ ((member354538064on_val @ B @ C2)))) & ((((B4 = (insert1971494647on_val @ A @ C2))) & ((~ ((member354538064on_val @ A @ C2)))))))))))))))))))). % insert_eq_iff
thf(fact_113_insert__eq__iff, axiom,
    ((![A : produc655058983on_val, A3 : set_Pr208351751on_val, B : produc655058983on_val, B4 : set_Pr208351751on_val]: ((~ ((member1689761872on_val @ A @ A3))) => ((~ ((member1689761872on_val @ B @ B4))) => (((insert363480567on_val @ A @ A3) = (insert363480567on_val @ B @ B4)) = (((((A = B)) => ((A3 = B4)))) & ((((~ ((A = B)))) => ((?[C2 : set_Pr208351751on_val]: (((A3 = (insert363480567on_val @ B @ C2))) & ((((~ ((member1689761872on_val @ B @ C2)))) & ((((B4 = (insert363480567on_val @ A @ C2))) & ((~ ((member1689761872on_val @ A @ C2)))))))))))))))))))). % insert_eq_iff
thf(fact_114_insert__absorb, axiom,
    ((![A : produc1172664615on_val, A3 : set_Pr1189492743on_val]: ((member354538064on_val @ A @ A3) => ((insert1971494647on_val @ A @ A3) = A3))))). % insert_absorb
thf(fact_115_insert__absorb, axiom,
    ((![A : produc655058983on_val, A3 : set_Pr208351751on_val]: ((member1689761872on_val @ A @ A3) => ((insert363480567on_val @ A @ A3) = A3))))). % insert_absorb
thf(fact_116_insert__ident, axiom,
    ((![X6 : produc1172664615on_val, A3 : set_Pr1189492743on_val, B4 : set_Pr1189492743on_val]: ((~ ((member354538064on_val @ X6 @ A3))) => ((~ ((member354538064on_val @ X6 @ B4))) => (((insert1971494647on_val @ X6 @ A3) = (insert1971494647on_val @ X6 @ B4)) = (A3 = B4))))))). % insert_ident
thf(fact_117_insert__ident, axiom,
    ((![X6 : produc655058983on_val, A3 : set_Pr208351751on_val, B4 : set_Pr208351751on_val]: ((~ ((member1689761872on_val @ X6 @ A3))) => ((~ ((member1689761872on_val @ X6 @ B4))) => (((insert363480567on_val @ X6 @ A3) = (insert363480567on_val @ X6 @ B4)) = (A3 = B4))))))). % insert_ident
thf(fact_118_Set_Oset__insert, axiom,
    ((![X6 : produc1172664615on_val, A3 : set_Pr1189492743on_val]: ((member354538064on_val @ X6 @ A3) => (~ ((![B5 : set_Pr1189492743on_val]: ((A3 = (insert1971494647on_val @ X6 @ B5)) => (member354538064on_val @ X6 @ B5))))))))). % Set.set_insert
thf(fact_119_Set_Oset__insert, axiom,
    ((![X6 : produc655058983on_val, A3 : set_Pr208351751on_val]: ((member1689761872on_val @ X6 @ A3) => (~ ((![B5 : set_Pr208351751on_val]: ((A3 = (insert363480567on_val @ X6 @ B5)) => (member1689761872on_val @ X6 @ B5))))))))). % Set.set_insert
thf(fact_120_insertI2, axiom,
    ((![A : produc1172664615on_val, B4 : set_Pr1189492743on_val, B : produc1172664615on_val]: ((member354538064on_val @ A @ B4) => (member354538064on_val @ A @ (insert1971494647on_val @ B @ B4)))))). % insertI2
thf(fact_121_insertI2, axiom,
    ((![A : produc655058983on_val, B4 : set_Pr208351751on_val, B : produc655058983on_val]: ((member1689761872on_val @ A @ B4) => (member1689761872on_val @ A @ (insert363480567on_val @ B @ B4)))))). % insertI2
thf(fact_122_insertI1, axiom,
    ((![A : produc1172664615on_val, B4 : set_Pr1189492743on_val]: (member354538064on_val @ A @ (insert1971494647on_val @ A @ B4))))). % insertI1
thf(fact_123_insertI1, axiom,
    ((![A : produc655058983on_val, B4 : set_Pr208351751on_val]: (member1689761872on_val @ A @ (insert363480567on_val @ A @ B4))))). % insertI1
thf(fact_124_insertE, axiom,
    ((![A : produc1172664615on_val, B : produc1172664615on_val, A3 : set_Pr1189492743on_val]: ((member354538064on_val @ A @ (insert1971494647on_val @ B @ A3)) => ((~ ((A = B))) => (member354538064on_val @ A @ A3)))))). % insertE
thf(fact_125_insertE, axiom,
    ((![A : produc655058983on_val, B : produc655058983on_val, A3 : set_Pr208351751on_val]: ((member1689761872on_val @ A @ (insert363480567on_val @ B @ A3)) => ((~ ((A = B))) => (member1689761872on_val @ A @ A3)))))). % insertE
thf(fact_126_insert__compr, axiom,
    ((insert1971494647on_val = (^[A5 : produc1172664615on_val]: (^[B6 : set_Pr1189492743on_val]: (collec2055896722on_val @ (^[X3 : produc1172664615on_val]: (((X3 = A5)) | ((member354538064on_val @ X3 @ B6)))))))))). % insert_compr
thf(fact_127_insert__compr, axiom,
    ((insert363480567on_val = (^[A5 : produc655058983on_val]: (^[B6 : set_Pr208351751on_val]: (collec105960082on_val @ (^[X3 : produc655058983on_val]: (((X3 = A5)) | ((member1689761872on_val @ X3 @ B6)))))))))). % insert_compr
thf(fact_128_singleton__iff, axiom,
    ((![B : produc1172664615on_val, A : produc1172664615on_val]: ((member354538064on_val @ B @ (insert1971494647on_val @ A @ bot_bo1575563891on_val)) = (B = A))))). % singleton_iff
thf(fact_129_singleton__iff, axiom,
    ((![B : produc655058983on_val, A : produc655058983on_val]: ((member1689761872on_val @ B @ (insert363480567on_val @ A @ bot_bo1426907251on_val)) = (B = A))))). % singleton_iff
thf(fact_130_singletonD, axiom,
    ((![B : produc1172664615on_val, A : produc1172664615on_val]: ((member354538064on_val @ B @ (insert1971494647on_val @ A @ bot_bo1575563891on_val)) => (B = A))))). % singletonD
thf(fact_131_singletonD, axiom,
    ((![B : produc655058983on_val, A : produc655058983on_val]: ((member1689761872on_val @ B @ (insert363480567on_val @ A @ bot_bo1426907251on_val)) => (B = A))))). % singletonD
thf(fact_132_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_133_red__preserves__hconf, axiom,
    ((![E2 : exp_list_char, H : nat > option2118145160on_val, L : list_char > option_val, E3 : exp_list_char, H2 : nat > option2118145160on_val, L2 : list_char > option_val, P : list_P1234162913t_char, E : list_char > option_ty, T : ty]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E2 @ (produc52622304on_val @ H @ L)) @ (produc2023458740on_val @ E3 @ (produc52622304on_val @ H2 @ L2))) @ (red @ P)) => ((wTrt2 @ P @ H @ E @ E2 @ T) => ((hconf_1244167010t_char @ P @ H) => (hconf_1244167010t_char @ P @ H2))))))). % red_preserves_hconf
thf(fact_134_red__preserves__lconf, axiom,
    ((![E2 : exp_list_char, H : nat > option2118145160on_val, L : list_char > option_val, E3 : exp_list_char, H2 : nat > option2118145160on_val, L2 : list_char > option_val, P : list_P1234162913t_char, E : list_char > option_ty, T : ty]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E2 @ (produc52622304on_val @ H @ L)) @ (produc2023458740on_val @ E3 @ (produc52622304on_val @ H2 @ L2))) @ (red @ P)) => ((wTrt2 @ P @ H @ E @ E2 @ T) => ((lconf_485928294t_char @ P @ H @ L @ E) => (lconf_485928294t_char @ P @ H2 @ L2 @ E))))))). % red_preserves_lconf
thf(fact_135_red__preserves__sconf, axiom,
    ((![E2 : exp_list_char, S2 : produc515445032on_val, E3 : exp_list_char, S3 : produc515445032on_val, P : list_P1234162913t_char, E : list_char > option_ty, T : ty]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E2 @ S2) @ (produc2023458740on_val @ E3 @ S3)) @ (red @ P)) => ((wTrt2 @ P @ (hp @ S2) @ E @ E2 @ T) => ((typeSa1777264139_sconf @ P @ E @ S2) => (typeSa1777264139_sconf @ P @ E @ S3))))))). % red_preserves_sconf
thf(fact_136_is__singletonI_H, axiom,
    ((![A3 : set_Pr1189492743on_val]: ((~ ((A3 = bot_bo1575563891on_val))) => ((![X4 : produc1172664615on_val, Y : produc1172664615on_val]: ((member354538064on_val @ X4 @ A3) => ((member354538064on_val @ Y @ A3) => (X4 = Y)))) => (is_sin1880980507on_val @ A3)))))). % is_singletonI'
thf(fact_137_is__singletonI_H, axiom,
    ((![A3 : set_Pr208351751on_val]: ((~ ((A3 = bot_bo1426907251on_val))) => ((![X4 : produc655058983on_val, Y : produc655058983on_val]: ((member1689761872on_val @ X4 @ A3) => ((member1689761872on_val @ Y @ A3) => (X4 = Y)))) => (is_sin412639003on_val @ A3)))))). % is_singletonI'
thf(fact_138_bot__empty__eq, axiom,
    ((bot_bo824611882_val_o = (^[X3 : produc1172664615on_val]: (member354538064on_val @ X3 @ bot_bo1575563891on_val))))). % bot_empty_eq
thf(fact_139_bot__empty__eq, axiom,
    ((bot_bo523622954_val_o = (^[X3 : produc655058983on_val]: (member1689761872on_val @ X3 @ bot_bo1426907251on_val))))). % bot_empty_eq
thf(fact_140_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_141_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]: ((wTrts2 @ P @ H @ E @ Es @ Ts) => ((hext @ H @ H2) => (wTrts2 @ P @ H2 @ E @ Es @ Ts)))))). % WTrts_hext_mono
thf(fact_142_WTrt__hext__mono, axiom,
    ((![P : list_P1234162913t_char, H : nat > option2118145160on_val, E : list_char > option_ty, E2 : exp_list_char, T : ty, H2 : nat > option2118145160on_val]: ((wTrt2 @ P @ H @ E @ E2 @ T) => ((hext @ H @ H2) => (wTrt2 @ P @ H2 @ E @ E2 @ T)))))). % WTrt_hext_mono
thf(fact_143_bot__empty__eq2, axiom,
    ((bot_bo2035215066_val_o = (^[X3 : produc335961278on_val]: (^[Y4 : produc335961278on_val]: (member1689761872on_val @ (produc245869591on_val @ X3 @ Y4) @ bot_bo1426907251on_val)))))). % bot_empty_eq2
thf(fact_144_bot__empty__eq2, axiom,
    ((bot_bo1918180954_val_o = (^[X3 : produc1097884484on_val]: (^[Y4 : produc1097884484on_val]: (member354538064on_val @ (produc1069526295on_val @ X3 @ Y4) @ bot_bo1575563891on_val)))))). % bot_empty_eq2
thf(fact_145_bot__empty__eq2, axiom,
    ((bot_bo1821121046char_o = (^[X3 : list_list_char]: (^[Y4 : exp_list_char]: (member605104934t_char @ (produc713467969t_char @ X3 @ Y4) @ bot_bo1987439961t_char)))))). % bot_empty_eq2
thf(fact_146_bot__empty__eq2, axiom,
    ((bot_bo1774766339_val_o = (^[X3 : list_exp_list_char]: (^[Y4 : produc515445032on_val]: (member184158439on_val @ (produc1725134254on_val @ X3 @ Y4) @ bot_bo509638026on_val)))))). % bot_empty_eq2
thf(fact_147_bot__empty__eq2, axiom,
    ((bot_bo1487430909_val_o = (^[X3 : exp_list_char]: (^[Y4 : produc515445032on_val]: (member1888679917on_val @ (produc2023458740on_val @ X3 @ Y4) @ bot_bo1575411088on_val)))))). % bot_empty_eq2
thf(fact_148_bot__empty__eq2, axiom,
    ((bot_bo1949275371_val_o = (^[X3 : nat > option2118145160on_val]: (^[Y4 : list_char > option_val]: (member652041809on_val @ (produc52622304on_val @ X3 @ Y4) @ bot_bo923954676on_val)))))). % bot_empty_eq2
thf(fact_149_pred__equals__eq2, axiom,
    ((![R : set_Pr208351751on_val, S : set_Pr208351751on_val]: (((^[X3 : produc335961278on_val]: (^[Y4 : produc335961278on_val]: (member1689761872on_val @ (produc245869591on_val @ X3 @ Y4) @ R))) = (^[X3 : produc335961278on_val]: (^[Y4 : produc335961278on_val]: (member1689761872on_val @ (produc245869591on_val @ X3 @ Y4) @ S)))) = (R = S))))). % pred_equals_eq2
thf(fact_150_pred__equals__eq2, axiom,
    ((![R : set_Pr1189492743on_val, S : set_Pr1189492743on_val]: (((^[X3 : produc1097884484on_val]: (^[Y4 : produc1097884484on_val]: (member354538064on_val @ (produc1069526295on_val @ X3 @ Y4) @ R))) = (^[X3 : produc1097884484on_val]: (^[Y4 : produc1097884484on_val]: (member354538064on_val @ (produc1069526295on_val @ X3 @ Y4) @ S)))) = (R = S))))). % pred_equals_eq2
thf(fact_151_pred__equals__eq2, axiom,
    ((![R : set_Pr2063914181t_char, S : set_Pr2063914181t_char]: (((^[X3 : list_list_char]: (^[Y4 : exp_list_char]: (member605104934t_char @ (produc713467969t_char @ X3 @ Y4) @ R))) = (^[X3 : list_list_char]: (^[Y4 : exp_list_char]: (member605104934t_char @ (produc713467969t_char @ X3 @ Y4) @ S)))) = (R = S))))). % pred_equals_eq2
thf(fact_152_pred__equals__eq2, axiom,
    ((![R : set_Pr1511552798on_val, S : set_Pr1511552798on_val]: (((^[X3 : list_exp_list_char]: (^[Y4 : produc515445032on_val]: (member184158439on_val @ (produc1725134254on_val @ X3 @ Y4) @ R))) = (^[X3 : list_exp_list_char]: (^[Y4 : produc515445032on_val]: (member184158439on_val @ (produc1725134254on_val @ X3 @ Y4) @ S)))) = (R = S))))). % pred_equals_eq2
thf(fact_153_pred__equals__eq2, axiom,
    ((![R : set_Pr556513572on_val, S : set_Pr556513572on_val]: (((^[X3 : exp_list_char]: (^[Y4 : produc515445032on_val]: (member1888679917on_val @ (produc2023458740on_val @ X3 @ Y4) @ R))) = (^[X3 : exp_list_char]: (^[Y4 : produc515445032on_val]: (member1888679917on_val @ (produc2023458740on_val @ X3 @ Y4) @ S)))) = (R = S))))). % pred_equals_eq2
thf(fact_154_pred__equals__eq2, axiom,
    ((![R : set_Pr723149704on_val, S : set_Pr723149704on_val]: (((^[X3 : nat > option2118145160on_val]: (^[Y4 : list_char > option_val]: (member652041809on_val @ (produc52622304on_val @ X3 @ Y4) @ R))) = (^[X3 : nat > option2118145160on_val]: (^[Y4 : list_char > option_val]: (member652041809on_val @ (produc52622304on_val @ X3 @ Y4) @ S)))) = (R = S))))). % pred_equals_eq2
thf(fact_155_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)) => ((wTrts2 @ P @ (hp @ S2) @ E @ Es @ Ts) => ((typeSa1777264139_sconf @ P @ E @ S2) => (typeSa1777264139_sconf @ P @ E @ S3))))))). % reds_preserves_sconf
thf(fact_156_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)) => ((wTrts2 @ P @ H @ E @ Es @ Ts) => ((lconf_485928294t_char @ P @ H @ L @ E) => (lconf_485928294t_char @ P @ H2 @ L2 @ E))))))). % reds_preserves_lconf
thf(fact_157_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_158_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)) => ((wTrts2 @ P @ H @ E @ Es @ Ts) => ((hconf_1244167010t_char @ P @ H) => (hconf_1244167010t_char @ P @ H2))))))). % reds_preserves_hconf
thf(fact_159_red__reds_OCallParams, 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)) @ (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)) @ (red @ P)))))). % red_reds.CallParams
thf(fact_160_redsp__reds__eq, axiom,
    ((redsp = (^[P2 : list_P1234162913t_char]: (^[X3 : list_exp_list_char]: (^[Y4 : produc515445032on_val]: (^[Z : list_exp_list_char]: (^[Aa : produc515445032on_val]: (member1689761872on_val @ (produc245869591on_val @ (produc1725134254on_val @ X3 @ Y4) @ (produc1725134254on_val @ Z @ Aa)) @ (reds @ P2)))))))))). % redsp_reds_eq
thf(fact_161_exp_Oinject_I3_J, axiom,
    ((![X32 : val, Y32 : val]: (((val_list_char @ X32) = (val_list_char @ Y32)) = (X32 = Y32))))). % exp.inject(3)
thf(fact_162_exp_Odistinct_I65_J, axiom,
    ((![X32 : val, X91 : exp_list_char, X92 : list_char, X93 : list_exp_list_char]: (~ (((val_list_char @ X32) = (call_list_char @ X91 @ X92 @ X93))))))). % exp.distinct(65)
thf(fact_163_reds_Ocases, axiom,
    ((![A1 : list_exp_list_char, A22 : produc515445032on_val, A32 : list_exp_list_char, A42 : produc515445032on_val, P : list_P1234162913t_char]: ((member1689761872on_val @ (produc245869591on_val @ (produc1725134254on_val @ A1 @ A22) @ (produc1725134254on_val @ A32 @ A42)) @ (reds @ P)) => ((![E4 : exp_list_char, S4 : produc515445032on_val, E5 : exp_list_char, S5 : produc515445032on_val, Es3 : list_exp_list_char]: ((A1 = (cons_exp_list_char @ E4 @ Es3)) => ((A22 = S4) => ((A32 = (cons_exp_list_char @ E5 @ Es3)) => ((A42 = S5) => (~ ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E4 @ S4) @ (produc2023458740on_val @ E5 @ S5)) @ (red @ P))))))))) => (~ ((![Es3 : list_exp_list_char, S4 : produc515445032on_val, Es4 : list_exp_list_char, S5 : produc515445032on_val, V2 : val]: ((A1 = (cons_exp_list_char @ (val_list_char @ V2) @ Es3)) => ((A22 = S4) => ((A32 = (cons_exp_list_char @ (val_list_char @ V2) @ Es4)) => ((A42 = S5) => (~ ((member1689761872on_val @ (produc245869591on_val @ (produc1725134254on_val @ Es3 @ S4) @ (produc1725134254on_val @ Es4 @ S5)) @ (reds @ P)))))))))))))))). % reds.cases
thf(fact_164_reds_Osimps, axiom,
    ((![A1 : list_exp_list_char, A22 : produc515445032on_val, A32 : list_exp_list_char, A42 : produc515445032on_val, P : list_P1234162913t_char]: ((member1689761872on_val @ (produc245869591on_val @ (produc1725134254on_val @ A1 @ A22) @ (produc1725134254on_val @ A32 @ A42)) @ (reds @ P)) = (((?[E6 : exp_list_char]: (?[S6 : produc515445032on_val]: (?[E7 : exp_list_char]: (?[S7 : produc515445032on_val]: (?[Es5 : list_exp_list_char]: (((A1 = (cons_exp_list_char @ E6 @ Es5))) & ((((A22 = S6)) & ((((A32 = (cons_exp_list_char @ E7 @ Es5))) & ((((A42 = S7)) & ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E6 @ S6) @ (produc2023458740on_val @ E7 @ S7)) @ (red @ P)))))))))))))))) | ((?[Es5 : list_exp_list_char]: (?[S6 : produc515445032on_val]: (?[Es6 : list_exp_list_char]: (?[S7 : produc515445032on_val]: (?[V3 : val]: (((A1 = (cons_exp_list_char @ (val_list_char @ V3) @ Es5))) & ((((A22 = S6)) & ((((A32 = (cons_exp_list_char @ (val_list_char @ V3) @ Es6))) & ((((A42 = S7)) & ((member1689761872on_val @ (produc245869591on_val @ (produc1725134254on_val @ Es5 @ S6) @ (produc1725134254on_val @ Es6 @ S7)) @ (reds @ P))))))))))))))))))))). % reds.simps
thf(fact_165_redp__redsp_OListRed2, axiom,
    ((![P : list_P1234162913t_char, Es : list_exp_list_char, S2 : produc515445032on_val, Es2 : list_exp_list_char, S3 : produc515445032on_val, V : val]: ((redsp @ P @ Es @ S2 @ Es2 @ S3) => (redsp @ P @ (cons_exp_list_char @ (val_list_char @ V) @ Es) @ S2 @ (cons_exp_list_char @ (val_list_char @ V) @ Es2) @ S3))))). % redp_redsp.ListRed2
thf(fact_166_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
thf(fact_167_red__reds_OListRed1, 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)) @ (red @ P)) => (member1689761872on_val @ (produc245869591on_val @ (produc1725134254on_val @ (cons_exp_list_char @ E2 @ Es) @ S2) @ (produc1725134254on_val @ (cons_exp_list_char @ E3 @ Es) @ S3)) @ (reds @ P)))))). % red_reds.ListRed1
thf(fact_168_list_Orel__inject_I2_J, axiom,
    ((![R : exp_list_char > exp_list_char > $o, X21 : exp_list_char, X22 : list_exp_list_char, Y21 : exp_list_char, Y22 : list_exp_list_char]: ((list_a1702871623t_char @ R @ (cons_exp_list_char @ X21 @ X22) @ (cons_exp_list_char @ Y21 @ Y22)) = (((R @ X21 @ Y21)) & ((list_a1702871623t_char @ R @ X22 @ Y22))))))). % list.rel_inject(2)
thf(fact_169_list_Orel__inject_I2_J, axiom,
    ((![R : exp_list_char > ty > $o, X21 : exp_list_char, X22 : list_exp_list_char, Y21 : ty, Y22 : list_ty]: ((list_a295513531har_ty @ R @ (cons_exp_list_char @ X21 @ X22) @ (cons_ty @ Y21 @ Y22)) = (((R @ X21 @ Y21)) & ((list_a295513531har_ty @ R @ X22 @ Y22))))))). % list.rel_inject(2)
thf(fact_170_list_Orel__inject_I2_J, axiom,
    ((![R : ty > exp_list_char > $o, X21 : ty, X22 : list_ty, Y21 : exp_list_char, Y22 : list_exp_list_char]: ((list_a212154379t_char @ R @ (cons_ty @ X21 @ X22) @ (cons_exp_list_char @ Y21 @ Y22)) = (((R @ X21 @ Y21)) & ((list_a212154379t_char @ R @ X22 @ Y22))))))). % list.rel_inject(2)
thf(fact_171_list_Orel__inject_I2_J, axiom,
    ((![R : ty > ty > $o, X21 : ty, X22 : list_ty, Y21 : ty, Y22 : list_ty]: ((list_all2_ty_ty @ R @ (cons_ty @ X21 @ X22) @ (cons_ty @ Y21 @ Y22)) = (((R @ X21 @ Y21)) & ((list_all2_ty_ty @ R @ X22 @ Y22))))))). % list.rel_inject(2)
thf(fact_172_list_Orel__intros_I2_J, axiom,
    ((![R : exp_list_char > exp_list_char > $o, X21 : exp_list_char, Y21 : exp_list_char, X22 : list_exp_list_char, Y22 : list_exp_list_char]: ((R @ X21 @ Y21) => ((list_a1702871623t_char @ R @ X22 @ Y22) => (list_a1702871623t_char @ R @ (cons_exp_list_char @ X21 @ X22) @ (cons_exp_list_char @ Y21 @ Y22))))))). % list.rel_intros(2)
thf(fact_173_list_Orel__intros_I2_J, axiom,
    ((![R : exp_list_char > ty > $o, X21 : exp_list_char, Y21 : ty, X22 : list_exp_list_char, Y22 : list_ty]: ((R @ X21 @ Y21) => ((list_a295513531har_ty @ R @ X22 @ Y22) => (list_a295513531har_ty @ R @ (cons_exp_list_char @ X21 @ X22) @ (cons_ty @ Y21 @ Y22))))))). % list.rel_intros(2)
thf(fact_174_list_Orel__intros_I2_J, axiom,
    ((![R : ty > exp_list_char > $o, X21 : ty, Y21 : exp_list_char, X22 : list_ty, Y22 : list_exp_list_char]: ((R @ X21 @ Y21) => ((list_a212154379t_char @ R @ X22 @ Y22) => (list_a212154379t_char @ R @ (cons_ty @ X21 @ X22) @ (cons_exp_list_char @ Y21 @ Y22))))))). % list.rel_intros(2)
thf(fact_175_list_Orel__intros_I2_J, axiom,
    ((![R : ty > ty > $o, X21 : ty, Y21 : ty, X22 : list_ty, Y22 : list_ty]: ((R @ X21 @ Y21) => ((list_all2_ty_ty @ R @ X22 @ Y22) => (list_all2_ty_ty @ R @ (cons_ty @ X21 @ X22) @ (cons_ty @ Y21 @ Y22))))))). % list.rel_intros(2)
thf(fact_176_widens__Cons, axiom,
    ((![P : list_P1234162913t_char, X6 : ty, Xs : list_ty, Ys : list_ty]: ((list_all2_ty_ty @ (widen_917054840t_char @ P) @ (cons_ty @ X6 @ Xs) @ Ys) = (?[Z : ty]: (?[Zs : list_ty]: (((Ys = (cons_ty @ Z @ Zs))) & ((((widen_917054840t_char @ P @ X6 @ Z)) & ((list_all2_ty_ty @ (widen_917054840t_char @ P) @ Xs @ Zs))))))))))). % widens_Cons
thf(fact_177_list__all2__eq, axiom,
    (((^[Y6 : list_ty]: (^[Z2 : list_ty]: (Y6 = Z2))) = (list_all2_ty_ty @ (^[Y6 : ty]: (^[Z2 : ty]: (Y6 = Z2))))))). % list_all2_eq
thf(fact_178_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_179_list__all2__refl, axiom,
    ((![P : ty > ty > $o, Xs : list_ty]: ((![X4 : ty]: (P @ X4 @ X4)) => (list_all2_ty_ty @ P @ Xs @ Xs))))). % list_all2_refl
thf(fact_180_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]: ((![A4 : ty, B3 : ty, C4 : ty]: ((P1 @ A4 @ B3) => ((P22 @ B3 @ C4) => (P32 @ A4 @ C4)))) => ((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_181_list_Orel__eq, axiom,
    (((list_all2_ty_ty @ (^[Y6 : ty]: (^[Z2 : ty]: (Y6 = Z2)))) = (^[Y6 : list_ty]: (^[Z2 : list_ty]: (Y6 = Z2)))))). % list.rel_eq
thf(fact_182_list__all2__antisym, axiom,
    ((![P : ty > ty > $o, Q : ty > ty > $o, Xs : list_ty, Ys : list_ty]: ((![X4 : ty, Y : ty]: ((P @ X4 @ Y) => ((Q @ Y @ X4) => (X4 = Y)))) => ((list_all2_ty_ty @ P @ Xs @ Ys) => ((list_all2_ty_ty @ Q @ Ys @ Xs) => (Xs = Ys))))))). % list_all2_antisym
thf(fact_183_list_Orel__refl, axiom,
    ((![Ra : ty > ty > $o, X6 : list_ty]: ((![X4 : ty]: (Ra @ X4 @ X4)) => (list_all2_ty_ty @ Ra @ X6 @ X6))))). % list.rel_refl
thf(fact_184_WTrtCons, axiom,
    ((![P : list_P1234162913t_char, H : nat > option2118145160on_val, E : list_char > option_ty, E2 : exp_list_char, T : ty, Es : list_exp_list_char, Ts : list_ty]: ((wTrt2 @ P @ H @ E @ E2 @ T) => ((wTrts2 @ P @ H @ E @ Es @ Ts) => (wTrts2 @ P @ H @ E @ (cons_exp_list_char @ E2 @ Es) @ (cons_ty @ T @ Ts))))))). % WTrtCons
thf(fact_185_WTrt_H__WTrts_H_Ointros_I15_J, axiom,
    ((![P : list_P1234162913t_char, H : nat > option2118145160on_val, E : list_char > option_ty, E2 : exp_list_char, T : ty, Es : list_exp_list_char, Ts : list_ty]: ((wTrt @ P @ H @ E @ E2 @ T) => ((wTrts @ P @ H @ E @ Es @ Ts) => (wTrts @ P @ H @ E @ (cons_exp_list_char @ E2 @ Es) @ (cons_ty @ T @ Ts))))))). % WTrt'_WTrts'.intros(15)
thf(fact_186_WTCons, axiom,
    ((![P : list_P1234162913t_char, E : list_char > option_ty, E2 : exp_list_char, T : ty, Es : list_exp_list_char, Ts : list_ty]: ((wt @ P @ E @ E2 @ T) => ((wTs @ P @ E @ Es @ Ts) => (wTs @ P @ E @ (cons_exp_list_char @ E2 @ Es) @ (cons_ty @ T @ Ts))))))). % WTCons
thf(fact_187_list__all2__Cons2, axiom,
    ((![P : exp_list_char > exp_list_char > $o, Xs : list_exp_list_char, Y3 : exp_list_char, Ys : list_exp_list_char]: ((list_a1702871623t_char @ P @ Xs @ (cons_exp_list_char @ Y3 @ Ys)) = (?[Z : exp_list_char]: (?[Zs : list_exp_list_char]: (((Xs = (cons_exp_list_char @ Z @ Zs))) & ((((P @ Z @ Y3)) & ((list_a1702871623t_char @ P @ Zs @ Ys))))))))))). % list_all2_Cons2
thf(fact_188_list__all2__Cons2, axiom,
    ((![P : ty > exp_list_char > $o, Xs : list_ty, Y3 : exp_list_char, Ys : list_exp_list_char]: ((list_a212154379t_char @ P @ Xs @ (cons_exp_list_char @ Y3 @ Ys)) = (?[Z : ty]: (?[Zs : list_ty]: (((Xs = (cons_ty @ Z @ Zs))) & ((((P @ Z @ Y3)) & ((list_a212154379t_char @ P @ Zs @ Ys))))))))))). % list_all2_Cons2
thf(fact_189_list__all2__Cons2, axiom,
    ((![P : exp_list_char > ty > $o, Xs : list_exp_list_char, Y3 : ty, Ys : list_ty]: ((list_a295513531har_ty @ P @ Xs @ (cons_ty @ Y3 @ Ys)) = (?[Z : exp_list_char]: (?[Zs : list_exp_list_char]: (((Xs = (cons_exp_list_char @ Z @ Zs))) & ((((P @ Z @ Y3)) & ((list_a295513531har_ty @ P @ Zs @ Ys))))))))))). % list_all2_Cons2
thf(fact_190_list__all2__Cons2, axiom,
    ((![P : ty > ty > $o, Xs : list_ty, Y3 : ty, Ys : list_ty]: ((list_all2_ty_ty @ P @ Xs @ (cons_ty @ Y3 @ Ys)) = (?[Z : ty]: (?[Zs : list_ty]: (((Xs = (cons_ty @ Z @ Zs))) & ((((P @ Z @ Y3)) & ((list_all2_ty_ty @ P @ Zs @ Ys))))))))))). % list_all2_Cons2
thf(fact_191_list__all2__Cons1, axiom,
    ((![P : exp_list_char > exp_list_char > $o, X6 : exp_list_char, Xs : list_exp_list_char, Ys : list_exp_list_char]: ((list_a1702871623t_char @ P @ (cons_exp_list_char @ X6 @ Xs) @ Ys) = (?[Z : exp_list_char]: (?[Zs : list_exp_list_char]: (((Ys = (cons_exp_list_char @ Z @ Zs))) & ((((P @ X6 @ Z)) & ((list_a1702871623t_char @ P @ Xs @ Zs))))))))))). % list_all2_Cons1
thf(fact_192_list__all2__Cons1, axiom,
    ((![P : exp_list_char > ty > $o, X6 : exp_list_char, Xs : list_exp_list_char, Ys : list_ty]: ((list_a295513531har_ty @ P @ (cons_exp_list_char @ X6 @ Xs) @ Ys) = (?[Z : ty]: (?[Zs : list_ty]: (((Ys = (cons_ty @ Z @ Zs))) & ((((P @ X6 @ Z)) & ((list_a295513531har_ty @ P @ Xs @ Zs))))))))))). % list_all2_Cons1
thf(fact_193_list__all2__Cons1, axiom,
    ((![P : ty > exp_list_char > $o, X6 : ty, Xs : list_ty, Ys : list_exp_list_char]: ((list_a212154379t_char @ P @ (cons_ty @ X6 @ Xs) @ Ys) = (?[Z : exp_list_char]: (?[Zs : list_exp_list_char]: (((Ys = (cons_exp_list_char @ Z @ Zs))) & ((((P @ X6 @ Z)) & ((list_a212154379t_char @ P @ Xs @ Zs))))))))))). % list_all2_Cons1
thf(fact_194_list__all2__Cons1, axiom,
    ((![P : ty > ty > $o, X6 : ty, Xs : list_ty, Ys : list_ty]: ((list_all2_ty_ty @ P @ (cons_ty @ X6 @ Xs) @ Ys) = (?[Z : ty]: (?[Zs : list_ty]: (((Ys = (cons_ty @ Z @ Zs))) & ((((P @ X6 @ Z)) & ((list_all2_ty_ty @ P @ Xs @ Zs))))))))))). % list_all2_Cons1

% Conjectures (1)
thf(conj_0, conjecture,
    ((wTrts2 @ p @ h_a @ e @ esa @ us))).
