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% This file was generated by Isabelle (most likely Sledgehammer)
% 2020-12-16 14:20:21.044

% Could-be-implicit typings (21)
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% Explicit typings (63)
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thf(sy_c_Expr_Obop_OEq, type,
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thf(sy_c_Expr_Oexp_Othrow_001t__List__Olist_It__String__Ochar_J, type,
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thf(sy_c_Groups_Ozero__class_Ozero_001t__Nat__Onat, type,
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thf(sy_c_Map_Omap__add_001t__List__Olist_It__String__Ochar_J_001t__Value__Oval, type,
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thf(sy_c_Nat_Osize__class_Osize_001t__Type__Oty, type,
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thf(sy_c_SmallStep_Ored, type,
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thf(sy_c_Transitive__Closure_Ortrancl_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,
    transi111096263on_val : set_Pr1189492743on_val > set_Pr1189492743on_val).
thf(sy_c_Transitive__Closure_Ortrancl_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,
    transi100378922on_val : set_Pr1368603847on_val > set_Pr1368603847on_val).
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_Ois__refT, type,
    is_refT : ty > $o).
thf(sy_c_Type_Oty_OBoolean, type,
    boolean : ty).
thf(sy_c_Type_Oty_OClass, type,
    class : list_char > ty).
thf(sy_c_Type_Oty_OInteger, type,
    integer : ty).
thf(sy_c_Type_Oty_ONT, type,
    nt : ty).
thf(sy_c_Type_Oty_OVoid, type,
    void : ty).
thf(sy_c_Type_Oty_Osize__ty, type,
    size_ty : ty > nat).
thf(sy_c_WellForm_Owf__prog_001t__Product____Type__Oprod_It__List__Olist_It__List__Olist_It__String__Ochar_J_J_Mt__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_J, type,
    wf_pro1229751607t_char : (list_P1234162913t_char > list_char > produc1259892823t_char > $o) > list_P1234162913t_char > $o).
thf(sy_c_WellTypeRT_OWTrt, type,
    wTrt : list_P1234162913t_char > (nat > option2118145160on_val) > (list_char > option_ty) > exp_list_char > ty > $o).
thf(sy_c_WellType_OWT, type,
    wt : list_P1234162913t_char > (list_char > option_ty) > exp_list_char > 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__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_M_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_Mt__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_M_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J, type,
    member2027247312on_val : produc744932519on_val > set_Pr148564103on_val > $o).
thf(sy_c_member_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_Mt__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_M_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_Mt__Product____Type__Oprod_It__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_Mt__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_M_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J, type,
    member354538064on_val : produc1172664615on_val > set_Pr1189492743on_val > $o).
thf(sy_c_member_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__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_Mt__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_J, type,
    member208988944on_val : produc1161703655on_val > set_Pr1368603847on_val > $o).
thf(sy_v_E____, type,
    e : list_char > option_ty).
thf(sy_v_P, type,
    p : list_P1234162913t_char).
thf(sy_v_T____, type,
    t : ty).
thf(sy_v_bop____, type,
    bop2 : bop).
thf(sy_v_e_092_060_094sub_0621_H____, type,
    e_1 : exp_list_char).
thf(sy_v_e_092_060_094sub_0621____, type,
    e_12 : exp_list_char).
thf(sy_v_e_092_060_094sub_0622____, type,
    e_2 : 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).

% Relevant facts (163)
thf(fact_0_wt, axiom,
    ((wTrt @ p @ ha @ e @ (binOp_list_char @ e_12 @ bop2 @ e_2) @ t))). % wt
thf(fact_1_BinOpRed1_Oprems_I2_J, axiom,
    ((wTrt @ p @ ha @ e @ (binOp_list_char @ e_12 @ bop2 @ e_2) @ t))). % BinOpRed1.prems(2)
thf(fact_2_ty_Odistinct_I9_J, axiom,
    ((~ ((boolean = integer))))). % ty.distinct(9)
thf(fact_3_ty_Odistinct_I15_J, axiom,
    ((~ ((integer = nt))))). % ty.distinct(15)
thf(fact_4_ty_Odistinct_I3_J, axiom,
    ((~ ((void = integer))))). % ty.distinct(3)
thf(fact_5_ty_Odistinct_I17_J, axiom,
    ((![X5 : list_char]: (~ ((integer = (class @ X5))))))). % ty.distinct(17)
thf(fact_6_ty_Osize__gen_I3_J, axiom,
    (((size_ty @ integer) = zero_zero_nat))). % ty.size_gen(3)
thf(fact_7_WTrtBinOpAdd, axiom,
    ((![P : list_P1234162913t_char, H : nat > option2118145160on_val, E : list_char > option_ty, E_1 : exp_list_char, E_2 : exp_list_char]: ((wTrt @ P @ H @ E @ E_1 @ integer) => ((wTrt @ P @ H @ E @ E_2 @ integer) => (wTrt @ P @ H @ E @ (binOp_list_char @ E_1 @ add @ E_2) @ integer)))))). % WTrtBinOpAdd
thf(fact_8_ty_Osize_I8_J, axiom,
    (((size_size_ty @ integer) = zero_zero_nat))). % ty.size(8)
thf(fact_9_local_Owf, axiom,
    ((wf_pro1229751607t_char @ wf_J_mdecl @ p))). % local.wf
thf(fact_10_ty_Oinject, axiom,
    ((![X5 : list_char, Y5 : list_char]: (((class @ X5) = (class @ Y5)) = (X5 = Y5))))). % ty.inject
thf(fact_11__092_060open_062bop_A_061_AAdd_092_060close_062, axiom,
    ((bop2 = add))). % \<open>bop = Add\<close>
thf(fact_12_ty_Osize_I10_J, axiom,
    ((![X5 : list_char]: ((size_size_ty @ (class @ X5)) = zero_zero_nat)))). % ty.size(10)
thf(fact_13_ty_Osize_I9_J, axiom,
    (((size_size_ty @ nt) = zero_zero_nat))). % ty.size(9)
thf(fact_14_ty_Osize_I7_J, axiom,
    (((size_size_ty @ boolean) = zero_zero_nat))). % ty.size(7)
thf(fact_15_ty_Osize_I6_J, axiom,
    (((size_size_ty @ void) = zero_zero_nat))). % ty.size(6)
thf(fact_16_ty_Odistinct_I19_J, axiom,
    ((![X5 : list_char]: (~ ((nt = (class @ X5))))))). % ty.distinct(19)
thf(fact_17_ty_Odistinct_I13_J, axiom,
    ((![X5 : list_char]: (~ ((boolean = (class @ X5))))))). % ty.distinct(13)
thf(fact_18_ty_Odistinct_I11_J, axiom,
    ((~ ((boolean = nt))))). % ty.distinct(11)
thf(fact_19_ty_Odistinct_I7_J, axiom,
    ((![X5 : list_char]: (~ ((void = (class @ X5))))))). % ty.distinct(7)
thf(fact_20_ty_Odistinct_I5_J, axiom,
    ((~ ((void = nt))))). % ty.distinct(5)
thf(fact_21_ty_Odistinct_I1_J, axiom,
    ((~ ((void = boolean))))). % ty.distinct(1)
thf(fact_22_ty_Osize__gen_I5_J, axiom,
    ((![X5 : list_char]: ((size_ty @ (class @ X5)) = zero_zero_nat)))). % ty.size_gen(5)
thf(fact_23_ty_Osize__gen_I4_J, axiom,
    (((size_ty @ nt) = zero_zero_nat))). % ty.size_gen(4)
thf(fact_24_ty_Osize__gen_I2_J, axiom,
    (((size_ty @ boolean) = zero_zero_nat))). % ty.size_gen(2)
thf(fact_25_ty_Osize__gen_I1_J, axiom,
    (((size_ty @ void) = zero_zero_nat))). % ty.size_gen(1)
thf(fact_26_ty_Oinduct, axiom,
    ((![P : ty > $o, Ty : ty]: ((P @ void) => ((P @ boolean) => ((P @ integer) => ((P @ nt) => ((![X : list_char]: (P @ (class @ X))) => (P @ Ty))))))))). % ty.induct
thf(fact_27_ty_Oexhaust, axiom,
    ((![Y : ty]: ((~ ((Y = void))) => ((~ ((Y = boolean))) => ((~ ((Y = integer))) => ((~ ((Y = nt))) => (~ ((![X52 : list_char]: (~ ((Y = (class @ X52)))))))))))))). % ty.exhaust
thf(fact_28_exp_Oinject_I4_J, axiom,
    ((![X41 : exp_list_char, X42 : bop, X43 : exp_list_char, Y41 : exp_list_char, Y42 : bop, Y43 : exp_list_char]: (((binOp_list_char @ X41 @ X42 @ X43) = (binOp_list_char @ Y41 @ Y42 @ Y43)) = (((X41 = Y41)) & ((((X42 = Y42)) & ((X43 = Y43))))))))). % exp.inject(4)
thf(fact_29_WTrt__elim__cases_I9_J, axiom,
    ((![P : list_P1234162913t_char, H : nat > option2118145160on_val, E : list_char > option_ty, E_1 : exp_list_char, Bop : bop, E_2 : exp_list_char, T : ty]: ((wTrt @ P @ H @ E @ (binOp_list_char @ E_1 @ Bop @ E_2) @ T) => (((Bop = c_Expr_Obop_OEq) => ((T = boolean) => ((?[X_1 : ty]: (wTrt @ P @ H @ E @ E_1 @ X_1)) => (![T_2 : ty]: (~ ((wTrt @ P @ H @ E @ E_2 @ T_2))))))) => (~ (((Bop = add) => ((T = integer) => ((wTrt @ P @ H @ E @ E_1 @ integer) => (~ ((wTrt @ P @ H @ E @ E_2 @ integer))))))))))))). % WTrt_elim_cases(9)
thf(fact_30_not__refTE, axiom,
    ((![T : ty]: ((~ ((is_refT @ T))) => ((T = void) | ((T = boolean) | (T = integer))))))). % not_refTE
thf(fact_31_BinOpRed1_Oprems_I1_J, axiom,
    ((typeSa1777264139_sconf @ p @ e @ (produc52622304on_val @ ha @ la)))). % BinOpRed1.prems(1)
thf(fact_32_WTrtBinOpEq, axiom,
    ((![P : list_P1234162913t_char, H : nat > option2118145160on_val, E : list_char > option_ty, E_1 : exp_list_char, T_1 : ty, E_2 : exp_list_char, T_22 : ty]: ((wTrt @ P @ H @ E @ E_1 @ T_1) => ((wTrt @ P @ H @ E @ E_2 @ T_22) => (wTrt @ P @ H @ E @ (binOp_list_char @ E_1 @ c_Expr_Obop_OEq @ E_2) @ boolean)))))). % WTrtBinOpEq
thf(fact_33_mem__Collect__eq, axiom,
    ((![A : produc1172664615on_val, P : produc1172664615on_val > $o]: ((member354538064on_val @ A @ (collec2055896722on_val @ P)) = (P @ A))))). % mem_Collect_eq
thf(fact_34_Collect__mem__eq, axiom,
    ((![A2 : set_Pr1189492743on_val]: ((collec2055896722on_val @ (^[X2 : produc1172664615on_val]: (member354538064on_val @ X2 @ A2))) = A2)))). % Collect_mem_eq
thf(fact_35_refTE, axiom,
    ((![T : ty]: ((is_refT @ T) => ((~ ((T = nt))) => (~ ((![C : list_char]: (~ ((T = (class @ C)))))))))))). % refTE
thf(fact_36_is__refT__def, axiom,
    ((is_refT = (^[T2 : ty]: (((T2 = nt)) | ((?[C2 : list_char]: (T2 = (class @ C2))))))))). % is_refT_def
thf(fact_37_conf, axiom,
    ((typeSa1777264139_sconf @ p @ e @ (produc52622304on_val @ ha @ la)))). % conf
thf(fact_38_bop_Oexhaust, axiom,
    ((![Y : bop]: ((~ ((Y = c_Expr_Obop_OEq))) => (Y = add))))). % bop.exhaust
thf(fact_39_bop_Oinduct, axiom,
    ((![P : bop > $o, Bop : bop]: ((P @ c_Expr_Obop_OEq) => ((P @ add) => (P @ Bop)))))). % bop.induct
thf(fact_40_bop_Odistinct_I1_J, axiom,
    ((~ ((c_Expr_Obop_OEq = add))))). % bop.distinct(1)
thf(fact_41_zero__reorient, axiom,
    ((![X3 : nat]: ((zero_zero_nat = X3) = (X3 = zero_zero_nat))))). % zero_reorient
thf(fact_42_bop_Osize__gen_I1_J, axiom,
    (((size_bop @ c_Expr_Obop_OEq) = zero_zero_nat))). % bop.size_gen(1)
thf(fact_43_bop_Osize__gen_I2_J, axiom,
    (((size_bop @ add) = zero_zero_nat))). % bop.size_gen(2)
thf(fact_44_BinOpRed1_Ohyps_I2_J, axiom,
    ((![E : list_char > option_ty, T : ty]: ((typeSa1777264139_sconf @ p @ E @ (produc52622304on_val @ ha @ la)) => ((wTrt @ p @ ha @ E @ e_12 @ T) => (?[T3 : ty]: ((wTrt @ p @ h_a @ E @ e_1 @ T3) & (widen_917054840t_char @ p @ T3 @ T)))))))). % BinOpRed1.hyps(2)
thf(fact_45_IH, axiom,
    ((![E : list_char > option_ty, T : ty]: ((typeSa1777264139_sconf @ p @ E @ (produc52622304on_val @ ha @ la)) => ((wTrt @ p @ ha @ E @ e_12 @ T) => (?[U : ty]: ((wTrt @ p @ h_a @ E @ e_1 @ U) & (widen_917054840t_char @ p @ U @ T)))))))). % IH
thf(fact_46_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_47_old_Oprod_Oinject, axiom,
    ((![A : produc1097884484on_val, B : produc1097884484on_val, A3 : produc1097884484on_val, B2 : produc1097884484on_val]: (((produc1069526295on_val @ A @ B) = (produc1069526295on_val @ A3 @ B2)) = (((A = A3)) & ((B = B2))))))). % old.prod.inject
thf(fact_48_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_49_prod_Oinject, axiom,
    ((![X1 : nat > option2118145160on_val, X22 : list_char > option_val, Y1 : nat > option2118145160on_val, Y2 : list_char > option_val]: (((produc52622304on_val @ X1 @ X22) = (produc52622304on_val @ Y1 @ Y2)) = (((X1 = Y1)) & ((X22 = Y2))))))). % prod.inject
thf(fact_50_prod_Oinject, axiom,
    ((![X1 : produc1097884484on_val, X22 : produc1097884484on_val, Y1 : produc1097884484on_val, Y2 : produc1097884484on_val]: (((produc1069526295on_val @ X1 @ X22) = (produc1069526295on_val @ Y1 @ Y2)) = (((X1 = Y1)) & ((X22 = Y2))))))). % prod.inject
thf(fact_51_prod_Oinject, axiom,
    ((![X1 : exp_list_char, X22 : produc515445032on_val, Y1 : exp_list_char, Y2 : produc515445032on_val]: (((produc2023458740on_val @ X1 @ X22) = (produc2023458740on_val @ Y1 @ Y2)) = (((X1 = Y1)) & ((X22 = Y2))))))). % prod.inject
thf(fact_52_surj__pair, axiom,
    ((![P2 : produc515445032on_val]: (?[X : nat > option2118145160on_val, Y3 : list_char > option_val]: (P2 = (produc52622304on_val @ X @ Y3)))))). % surj_pair
thf(fact_53_surj__pair, axiom,
    ((![P2 : produc1172664615on_val]: (?[X : produc1097884484on_val, Y3 : produc1097884484on_val]: (P2 = (produc1069526295on_val @ X @ Y3)))))). % surj_pair
thf(fact_54_surj__pair, axiom,
    ((![P2 : produc1097884484on_val]: (?[X : exp_list_char, Y3 : produc515445032on_val]: (P2 = (produc2023458740on_val @ X @ Y3)))))). % surj_pair
thf(fact_55_prod__cases, axiom,
    ((![P : produc515445032on_val > $o, P2 : produc515445032on_val]: ((![A4 : nat > option2118145160on_val, B3 : list_char > option_val]: (P @ (produc52622304on_val @ A4 @ B3))) => (P @ P2))))). % prod_cases
thf(fact_56_prod__cases, axiom,
    ((![P : produc1172664615on_val > $o, P2 : produc1172664615on_val]: ((![A4 : produc1097884484on_val, B3 : produc1097884484on_val]: (P @ (produc1069526295on_val @ A4 @ B3))) => (P @ P2))))). % prod_cases
thf(fact_57_prod__cases, axiom,
    ((![P : produc1097884484on_val > $o, P2 : produc1097884484on_val]: ((![A4 : exp_list_char, B3 : produc515445032on_val]: (P @ (produc2023458740on_val @ A4 @ B3))) => (P @ P2))))). % prod_cases
thf(fact_58_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_59_Pair__inject, axiom,
    ((![A : produc1097884484on_val, B : produc1097884484on_val, A3 : produc1097884484on_val, B2 : produc1097884484on_val]: (((produc1069526295on_val @ A @ B) = (produc1069526295on_val @ A3 @ B2)) => (~ (((A = A3) => (~ ((B = B2)))))))))). % Pair_inject
thf(fact_60_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_61_prod__cases3, axiom,
    ((![Y : produc1172664615on_val]: (~ ((![A4 : produc1097884484on_val, B3 : exp_list_char, C3 : produc515445032on_val]: (~ ((Y = (produc1069526295on_val @ A4 @ (produc2023458740on_val @ B3 @ C3))))))))))). % prod_cases3
thf(fact_62_prod__cases3, axiom,
    ((![Y : produc1097884484on_val]: (~ ((![A4 : exp_list_char, B3 : nat > option2118145160on_val, C3 : list_char > option_val]: (~ ((Y = (produc2023458740on_val @ A4 @ (produc52622304on_val @ B3 @ C3))))))))))). % prod_cases3
thf(fact_63_prod__cases4, axiom,
    ((![Y : produc1172664615on_val]: (~ ((![A4 : produc1097884484on_val, B3 : exp_list_char, C3 : nat > option2118145160on_val, D : list_char > option_val]: (~ ((Y = (produc1069526295on_val @ A4 @ (produc2023458740on_val @ B3 @ (produc52622304on_val @ C3 @ D)))))))))))). % prod_cases4
thf(fact_64_prod__induct3, axiom,
    ((![P : produc1172664615on_val > $o, X3 : produc1172664615on_val]: ((![A4 : produc1097884484on_val, B3 : exp_list_char, C3 : produc515445032on_val]: (P @ (produc1069526295on_val @ A4 @ (produc2023458740on_val @ B3 @ C3)))) => (P @ X3))))). % prod_induct3
thf(fact_65_prod__induct3, axiom,
    ((![P : produc1097884484on_val > $o, X3 : produc1097884484on_val]: ((![A4 : exp_list_char, B3 : nat > option2118145160on_val, C3 : list_char > option_val]: (P @ (produc2023458740on_val @ A4 @ (produc52622304on_val @ B3 @ C3)))) => (P @ X3))))). % prod_induct3
thf(fact_66_prod__induct4, axiom,
    ((![P : produc1172664615on_val > $o, X3 : produc1172664615on_val]: ((![A4 : produc1097884484on_val, B3 : exp_list_char, C3 : nat > option2118145160on_val, D : list_char > option_val]: (P @ (produc1069526295on_val @ A4 @ (produc2023458740on_val @ B3 @ (produc52622304on_val @ C3 @ D))))) => (P @ X3))))). % prod_induct4
thf(fact_67_old_Oprod_Oexhaust, axiom,
    ((![Y : produc515445032on_val]: (~ ((![A4 : nat > option2118145160on_val, B3 : list_char > option_val]: (~ ((Y = (produc52622304on_val @ A4 @ B3)))))))))). % old.prod.exhaust
thf(fact_68_old_Oprod_Oexhaust, axiom,
    ((![Y : produc1172664615on_val]: (~ ((![A4 : produc1097884484on_val, B3 : produc1097884484on_val]: (~ ((Y = (produc1069526295on_val @ A4 @ B3)))))))))). % old.prod.exhaust
thf(fact_69_old_Oprod_Oexhaust, axiom,
    ((![Y : produc1097884484on_val]: (~ ((![A4 : exp_list_char, B3 : produc515445032on_val]: (~ ((Y = (produc2023458740on_val @ A4 @ B3)))))))))). % old.prod.exhaust
thf(fact_70_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_71_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_72_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_73_red, axiom,
    ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ e_12 @ (produc52622304on_val @ ha @ la)) @ (produc2023458740on_val @ e_1 @ (produc52622304on_val @ h_a @ l_a))) @ (red @ p)))). % red
thf(fact_74_widen__null, axiom,
    ((![P : list_P1234162913t_char, C4 : list_char]: (widen_917054840t_char @ P @ nt @ (class @ C4))))). % widen_null
thf(fact_75_Class__widen, axiom,
    ((![P : list_P1234162913t_char, C4 : list_char, T : ty]: ((widen_917054840t_char @ P @ (class @ C4) @ T) => (?[D2 : list_char]: (T = (class @ D2))))))). % Class_widen
thf(fact_76_bop_Osize_I3_J, axiom,
    (((size_size_bop @ c_Expr_Obop_OEq) = zero_zero_nat))). % bop.size(3)
thf(fact_77_widen__refl, axiom,
    ((![P : list_P1234162913t_char, T : ty]: (widen_917054840t_char @ P @ T @ T)))). % widen_refl
thf(fact_78_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_79_bop_Osize_I4_J, axiom,
    (((size_size_bop @ add) = zero_zero_nat))). % bop.size(4)
thf(fact_80_red__reds_OBinOpRed1, axiom,
    ((![E2 : exp_list_char, S2 : produc515445032on_val, E3 : exp_list_char, S3 : produc515445032on_val, P : list_P1234162913t_char, Bop : bop, E_2 : exp_list_char]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E2 @ S2) @ (produc2023458740on_val @ E3 @ S3)) @ (red @ P)) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (binOp_list_char @ E2 @ Bop @ E_2) @ S2) @ (produc2023458740on_val @ (binOp_list_char @ E3 @ Bop @ E_2) @ S3)) @ (red @ P)))))). % red_reds.BinOpRed1
thf(fact_81_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_82_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_83_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_84_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_85_WT__elim__cases_I9_J, axiom,
    ((![P : list_P1234162913t_char, E : list_char > option_ty, E_1 : exp_list_char, Bop : bop, E_2 : exp_list_char, T : ty]: ((wt @ P @ E @ (binOp_list_char @ E_1 @ Bop @ E_2) @ T) => (((Bop = c_Expr_Obop_OEq) => ((T = boolean) => (![T_12 : ty]: ((wt @ P @ E @ E_1 @ T_12) => (![T_2 : ty]: ((wt @ P @ E @ E_2 @ T_2) => (~ (((widen_917054840t_char @ P @ T_12 @ T_2) | (widen_917054840t_char @ P @ T_2 @ T_12)))))))))) => (~ (((Bop = add) => ((T = integer) => ((wt @ P @ E @ E_1 @ integer) => (~ ((wt @ P @ E @ E_2 @ integer))))))))))))). % WT_elim_cases(9)
thf(fact_86_pred__equals__eq2, axiom,
    ((![R : set_Pr723149704on_val, S : set_Pr723149704on_val]: (((^[X2 : nat > option2118145160on_val]: (^[Y4 : list_char > option_val]: (member652041809on_val @ (produc52622304on_val @ X2 @ Y4) @ R))) = (^[X2 : nat > option2118145160on_val]: (^[Y4 : list_char > option_val]: (member652041809on_val @ (produc52622304on_val @ X2 @ Y4) @ S)))) = (R = S))))). % pred_equals_eq2
thf(fact_87_pred__equals__eq2, axiom,
    ((![R : set_Pr1189492743on_val, S : set_Pr1189492743on_val]: (((^[X2 : produc1097884484on_val]: (^[Y4 : produc1097884484on_val]: (member354538064on_val @ (produc1069526295on_val @ X2 @ Y4) @ R))) = (^[X2 : produc1097884484on_val]: (^[Y4 : produc1097884484on_val]: (member354538064on_val @ (produc1069526295on_val @ X2 @ Y4) @ S)))) = (R = S))))). % pred_equals_eq2
thf(fact_88_pred__equals__eq2, axiom,
    ((![R : set_Pr556513572on_val, S : set_Pr556513572on_val]: (((^[X2 : exp_list_char]: (^[Y4 : produc515445032on_val]: (member1888679917on_val @ (produc2023458740on_val @ X2 @ Y4) @ R))) = (^[X2 : exp_list_char]: (^[Y4 : produc515445032on_val]: (member1888679917on_val @ (produc2023458740on_val @ X2 @ Y4) @ S)))) = (R = S))))). % pred_equals_eq2
thf(fact_89_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_90_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) => (wTrt @ P @ H @ E @ E2 @ T))))). % WT_implies_WTrt
thf(fact_91_WTBinOpAdd, axiom,
    ((![P : list_P1234162913t_char, E : list_char > option_ty, E_1 : exp_list_char, E_2 : exp_list_char]: ((wt @ P @ E @ E_1 @ integer) => ((wt @ P @ E @ E_2 @ integer) => (wt @ P @ E @ (binOp_list_char @ E_1 @ add @ E_2) @ integer)))))). % WTBinOpAdd
thf(fact_92_WTBinOpEq, axiom,
    ((![P : list_P1234162913t_char, E : list_char > option_ty, E_1 : exp_list_char, T_1 : ty, E_2 : exp_list_char, T_22 : ty]: ((wt @ P @ E @ E_1 @ T_1) => ((wt @ P @ E @ E_2 @ T_22) => (((widen_917054840t_char @ P @ T_1 @ T_22) | (widen_917054840t_char @ P @ T_22 @ T_1)) => (wt @ P @ E @ (binOp_list_char @ E_1 @ c_Expr_Obop_OEq @ E_2) @ boolean))))))). % WTBinOpEq
thf(fact_93_lconf__hext, axiom,
    ((![P : list_P1234162913t_char, H : nat > option2118145160on_val, L : list_char > option_val, E : list_char > option_ty, H2 : nat > option2118145160on_val]: ((lconf_485928294t_char @ P @ H @ L @ E) => ((hext @ H @ H2) => (lconf_485928294t_char @ P @ H2 @ L @ E)))))). % lconf_hext
thf(fact_94_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_0 : 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_0 @ L))) @ (produc2023458740on_val @ E3 @ (produc52622304on_val @ H2 @ (map_ad1615113112ar_val @ L_0 @ L2)))) @ (red @ P)))))). % red_lcl_add
thf(fact_95_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_0 : 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_0 @ L))) @ (produc2023458740on_val @ E3 @ (produc52622304on_val @ H2 @ (map_ad1615113112ar_val @ L_0 @ L2)))) @ (transi111096263on_val @ (red @ P))))))). % Red_lcl_add
thf(fact_96_sconf__def, axiom,
    ((typeSa1777264139_sconf = (^[P3 : list_P1234162913t_char]: (^[E4 : list_char > option_ty]: (produc99536995_val_o @ (^[H3 : nat > option2118145160on_val]: (^[L3 : list_char > option_val]: (((hconf_1244167010t_char @ P3 @ H3)) & ((lconf_485928294t_char @ P3 @ H3 @ L3 @ E4))))))))))). % sconf_def
thf(fact_97_red__reds_OBinOpRed2, axiom,
    ((![E2 : exp_list_char, S2 : produc515445032on_val, E3 : exp_list_char, S3 : produc515445032on_val, P : list_P1234162913t_char, V_1 : val, Bop : bop]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E2 @ S2) @ (produc2023458740on_val @ E3 @ S3)) @ (red @ P)) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (binOp_list_char @ (val_list_char @ V_1) @ Bop @ E2) @ S2) @ (produc2023458740on_val @ (binOp_list_char @ (val_list_char @ V_1) @ Bop @ E3) @ S3)) @ (red @ P)))))). % red_reds.BinOpRed2
thf(fact_98_exp_Oinject_I3_J, axiom,
    ((![X32 : val, Y32 : val]: (((val_list_char @ X32) = (val_list_char @ Y32)) = (X32 = Y32))))). % exp.inject(3)
thf(fact_99_split__part, axiom,
    ((![P : $o, Q : (nat > option2118145160on_val) > (list_char > option_val) > $o]: ((produc99536995_val_o @ (^[A5 : nat > option2118145160on_val]: (^[B4 : list_char > option_val]: ((P) & ((Q @ A5 @ B4)))))) = (^[Ab : produc515445032on_val]: ((P) & ((produc99536995_val_o @ Q @ Ab)))))))). % split_part
thf(fact_100_case__prod__conv, axiom,
    ((![F : (nat > option2118145160on_val) > (list_char > option_val) > $o, A : nat > option2118145160on_val, B : list_char > option_val]: ((produc99536995_val_o @ F @ (produc52622304on_val @ A @ B)) = (F @ A @ B))))). % case_prod_conv
thf(fact_101_case__prodI, axiom,
    ((![F : produc1097884484on_val > produc1097884484on_val > $o, A : produc1097884484on_val, B : produc1097884484on_val]: ((F @ A @ B) => (produc50362220_val_o @ F @ (produc1069526295on_val @ A @ B)))))). % case_prodI
thf(fact_102_case__prodI, axiom,
    ((![F : exp_list_char > produc515445032on_val > $o, A : exp_list_char, B : produc515445032on_val]: ((F @ A @ B) => (produc199145871_val_o @ F @ (produc2023458740on_val @ A @ B)))))). % case_prodI
thf(fact_103_case__prodI, axiom,
    ((![F : (nat > option2118145160on_val) > (list_char > option_val) > $o, A : nat > option2118145160on_val, B : list_char > option_val]: ((F @ A @ B) => (produc99536995_val_o @ F @ (produc52622304on_val @ A @ B)))))). % case_prodI
thf(fact_104_case__prodI2, axiom,
    ((![P2 : produc1172664615on_val, C5 : produc1097884484on_val > produc1097884484on_val > $o]: ((![A4 : produc1097884484on_val, B3 : produc1097884484on_val]: ((P2 = (produc1069526295on_val @ A4 @ B3)) => (C5 @ A4 @ B3))) => (produc50362220_val_o @ C5 @ P2))))). % case_prodI2
thf(fact_105_case__prodI2, axiom,
    ((![P2 : produc1097884484on_val, C5 : exp_list_char > produc515445032on_val > $o]: ((![A4 : exp_list_char, B3 : produc515445032on_val]: ((P2 = (produc2023458740on_val @ A4 @ B3)) => (C5 @ A4 @ B3))) => (produc199145871_val_o @ C5 @ P2))))). % case_prodI2
thf(fact_106_case__prodI2, axiom,
    ((![P2 : produc515445032on_val, C5 : (nat > option2118145160on_val) > (list_char > option_val) > $o]: ((![A4 : nat > option2118145160on_val, B3 : list_char > option_val]: ((P2 = (produc52622304on_val @ A4 @ B3)) => (C5 @ A4 @ B3))) => (produc99536995_val_o @ C5 @ P2))))). % case_prodI2
thf(fact_107_prod_Odisc__eq__case, axiom,
    ((![Prod : produc515445032on_val]: (produc99536995_val_o @ (^[Uu : nat > option2118145160on_val]: (^[Uv : list_char > option_val]: $true)) @ Prod)))). % prod.disc_eq_case
thf(fact_108_prod_Ocase__distrib, axiom,
    ((![H : $o > $o, F : (nat > option2118145160on_val) > (list_char > option_val) > $o, Prod : produc515445032on_val]: ((H @ (produc99536995_val_o @ F @ Prod)) = (produc99536995_val_o @ (^[X12 : nat > option2118145160on_val]: (^[X23 : list_char > option_val]: (H @ (F @ X12 @ X23)))) @ Prod))))). % prod.case_distrib
thf(fact_109_case__prodE2, axiom,
    ((![Q : $o > $o, P : (nat > option2118145160on_val) > (list_char > option_val) > $o, Z : produc515445032on_val]: ((Q @ (produc99536995_val_o @ P @ Z)) => (~ ((![X : nat > option2118145160on_val, Y3 : list_char > option_val]: ((Z = (produc52622304on_val @ X @ Y3)) => (~ ((Q @ (P @ X @ Y3)))))))))))). % case_prodE2
thf(fact_110_case__prod__eta, axiom,
    ((![F : produc515445032on_val > $o]: ((produc99536995_val_o @ (^[X2 : nat > option2118145160on_val]: (^[Y4 : list_char > option_val]: (F @ (produc52622304on_val @ X2 @ Y4))))) = F)))). % case_prod_eta
thf(fact_111_cond__case__prod__eta, axiom,
    ((![F : (nat > option2118145160on_val) > (list_char > option_val) > $o, G : produc515445032on_val > $o]: ((![X : nat > option2118145160on_val, Y3 : list_char > option_val]: ((F @ X @ Y3) = (G @ (produc52622304on_val @ X @ Y3)))) => ((produc99536995_val_o @ F) = G))))). % cond_case_prod_eta
thf(fact_112_case__prodD, axiom,
    ((![F : produc1097884484on_val > produc1097884484on_val > $o, A : produc1097884484on_val, B : produc1097884484on_val]: ((produc50362220_val_o @ F @ (produc1069526295on_val @ A @ B)) => (F @ A @ B))))). % case_prodD
thf(fact_113_case__prodD, axiom,
    ((![F : exp_list_char > produc515445032on_val > $o, A : exp_list_char, B : produc515445032on_val]: ((produc199145871_val_o @ F @ (produc2023458740on_val @ A @ B)) => (F @ A @ B))))). % case_prodD
thf(fact_114_case__prodD, axiom,
    ((![F : (nat > option2118145160on_val) > (list_char > option_val) > $o, A : nat > option2118145160on_val, B : list_char > option_val]: ((produc99536995_val_o @ F @ (produc52622304on_val @ A @ B)) => (F @ A @ B))))). % case_prodD
thf(fact_115_case__prodE, axiom,
    ((![C5 : produc1097884484on_val > produc1097884484on_val > $o, P2 : produc1172664615on_val]: ((produc50362220_val_o @ C5 @ P2) => (~ ((![X : produc1097884484on_val, Y3 : produc1097884484on_val]: ((P2 = (produc1069526295on_val @ X @ Y3)) => (~ ((C5 @ X @ Y3))))))))))). % case_prodE
thf(fact_116_case__prodE, axiom,
    ((![C5 : exp_list_char > produc515445032on_val > $o, P2 : produc1097884484on_val]: ((produc199145871_val_o @ C5 @ P2) => (~ ((![X : exp_list_char, Y3 : produc515445032on_val]: ((P2 = (produc2023458740on_val @ X @ Y3)) => (~ ((C5 @ X @ Y3))))))))))). % case_prodE
thf(fact_117_case__prodE, axiom,
    ((![C5 : (nat > option2118145160on_val) > (list_char > option_val) > $o, P2 : produc515445032on_val]: ((produc99536995_val_o @ C5 @ P2) => (~ ((![X : nat > option2118145160on_val, Y3 : list_char > option_val]: ((P2 = (produc52622304on_val @ X @ Y3)) => (~ ((C5 @ X @ Y3))))))))))). % case_prodE
thf(fact_118_exp_Odistinct_I55_J, axiom,
    ((![X32 : val, X41 : exp_list_char, X42 : bop, X43 : exp_list_char]: (~ (((val_list_char @ X32) = (binOp_list_char @ X41 @ X42 @ X43))))))). % exp.distinct(55)
thf(fact_119_old_Oprod_Ocase, axiom,
    ((![F : (nat > option2118145160on_val) > (list_char > option_val) > $o, X1 : nat > option2118145160on_val, X22 : list_char > option_val]: ((produc99536995_val_o @ F @ (produc52622304on_val @ X1 @ X22)) = (F @ X1 @ X22))))). % old.prod.case
thf(fact_120_internal__case__prod__def, axiom,
    ((produc563955725_val_o = produc99536995_val_o))). % internal_case_prod_def
thf(fact_121_converse__rtrancl__induct__red, axiom,
    ((![E2 : exp_list_char, H : nat > option2118145160on_val, L : list_char > option_val, E3 : exp_list_char, H2 : nat > option2118145160on_val, L2 : list_char > option_val, P : list_P1234162913t_char, R : exp_list_char > (nat > option2118145160on_val) > (list_char > option_val) > exp_list_char > (nat > option2118145160on_val) > (list_char > option_val) > $o]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E2 @ (produc52622304on_val @ H @ L)) @ (produc2023458740on_val @ E3 @ (produc52622304on_val @ H2 @ L2))) @ (transi111096263on_val @ (red @ P))) => ((![E5 : exp_list_char, H4 : nat > option2118145160on_val, L4 : list_char > option_val]: (R @ E5 @ H4 @ L4 @ E5 @ H4 @ L4)) => ((![E_0 : exp_list_char, H_0 : nat > option2118145160on_val, L_02 : list_char > option_val, E_12 : exp_list_char, H_1 : nat > option2118145160on_val, L_1 : list_char > option_val, E6 : exp_list_char, H5 : nat > option2118145160on_val, L5 : list_char > option_val]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E_0 @ (produc52622304on_val @ H_0 @ L_02)) @ (produc2023458740on_val @ E_12 @ (produc52622304on_val @ H_1 @ L_1))) @ (red @ P)) => ((R @ E_12 @ H_1 @ L_1 @ E6 @ H5 @ L5) => (R @ E_0 @ H_0 @ L_02 @ E6 @ H5 @ L5)))) => (R @ E2 @ H @ L @ E3 @ H2 @ L2))))))). % converse_rtrancl_induct_red
thf(fact_122_BinOp2Reds, axiom,
    ((![E2 : exp_list_char, S2 : produc515445032on_val, E3 : exp_list_char, S3 : produc515445032on_val, P : list_P1234162913t_char, V : val, Bop : bop]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E2 @ S2) @ (produc2023458740on_val @ E3 @ S3)) @ (transi111096263on_val @ (red @ P))) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (binOp_list_char @ (val_list_char @ V) @ Bop @ E2) @ S2) @ (produc2023458740on_val @ (binOp_list_char @ (val_list_char @ V) @ Bop @ E3) @ S3)) @ (transi111096263on_val @ (red @ P))))))). % BinOp2Reds
thf(fact_123_BinOp1Reds, axiom,
    ((![E2 : exp_list_char, S2 : produc515445032on_val, E3 : exp_list_char, S3 : produc515445032on_val, P : list_P1234162913t_char, Bop : bop, E_2 : 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 @ (binOp_list_char @ E2 @ Bop @ E_2) @ S2) @ (produc2023458740on_val @ (binOp_list_char @ E3 @ Bop @ E_2) @ S3)) @ (transi111096263on_val @ (red @ P))))))). % BinOp1Reds
thf(fact_124_rtrancl__induct2, axiom,
    ((![Ax : nat > option2118145160on_val, Ay : list_char > option_val, Bx : nat > option2118145160on_val, By : list_char > option_val, R2 : set_Pr148564103on_val, P : (nat > option2118145160on_val) > (list_char > option_val) > $o]: ((member2027247312on_val @ (produc2106877847on_val @ (produc52622304on_val @ Ax @ Ay) @ (produc52622304on_val @ Bx @ By)) @ (transi432893227on_val @ R2)) => ((P @ Ax @ Ay) => ((![A4 : nat > option2118145160on_val, B3 : list_char > option_val, Aa : nat > option2118145160on_val, Ba : list_char > option_val]: ((member2027247312on_val @ (produc2106877847on_val @ (produc52622304on_val @ Ax @ Ay) @ (produc52622304on_val @ A4 @ B3)) @ (transi432893227on_val @ R2)) => ((member2027247312on_val @ (produc2106877847on_val @ (produc52622304on_val @ A4 @ B3) @ (produc52622304on_val @ Aa @ Ba)) @ R2) => ((P @ A4 @ B3) => (P @ Aa @ Ba))))) => (P @ Bx @ By))))))). % rtrancl_induct2
thf(fact_125_rtrancl__induct2, axiom,
    ((![Ax : produc1097884484on_val, Ay : produc1097884484on_val, Bx : produc1097884484on_val, By : produc1097884484on_val, R2 : set_Pr1368603847on_val, P : produc1097884484on_val > produc1097884484on_val > $o]: ((member208988944on_val @ (produc564964183on_val @ (produc1069526295on_val @ Ax @ Ay) @ (produc1069526295on_val @ Bx @ By)) @ (transi100378922on_val @ R2)) => ((P @ Ax @ Ay) => ((![A4 : produc1097884484on_val, B3 : produc1097884484on_val, Aa : produc1097884484on_val, Ba : produc1097884484on_val]: ((member208988944on_val @ (produc564964183on_val @ (produc1069526295on_val @ Ax @ Ay) @ (produc1069526295on_val @ A4 @ B3)) @ (transi100378922on_val @ R2)) => ((member208988944on_val @ (produc564964183on_val @ (produc1069526295on_val @ A4 @ B3) @ (produc1069526295on_val @ Aa @ Ba)) @ R2) => ((P @ A4 @ B3) => (P @ Aa @ Ba))))) => (P @ Bx @ By))))))). % rtrancl_induct2
thf(fact_126_rtrancl__induct2, axiom,
    ((![Ax : exp_list_char, Ay : produc515445032on_val, Bx : exp_list_char, By : produc515445032on_val, R2 : set_Pr1189492743on_val, P : exp_list_char > produc515445032on_val > $o]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ Ax @ Ay) @ (produc2023458740on_val @ Bx @ By)) @ (transi111096263on_val @ R2)) => ((P @ Ax @ Ay) => ((![A4 : exp_list_char, B3 : produc515445032on_val, Aa : exp_list_char, Ba : produc515445032on_val]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ Ax @ Ay) @ (produc2023458740on_val @ A4 @ B3)) @ (transi111096263on_val @ R2)) => ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ A4 @ B3) @ (produc2023458740on_val @ Aa @ Ba)) @ R2) => ((P @ A4 @ B3) => (P @ Aa @ Ba))))) => (P @ Bx @ By))))))). % rtrancl_induct2
thf(fact_127_mem__case__prodI, axiom,
    ((![Z : produc1172664615on_val, C5 : (nat > option2118145160on_val) > (list_char > option_val) > set_Pr1189492743on_val, A : nat > option2118145160on_val, B : list_char > option_val]: ((member354538064on_val @ Z @ (C5 @ A @ B)) => (member354538064on_val @ Z @ (produc1919805778on_val @ C5 @ (produc52622304on_val @ A @ B))))))). % mem_case_prodI
thf(fact_128_mem__case__prodI, axiom,
    ((![Z : produc1172664615on_val, C5 : produc1097884484on_val > produc1097884484on_val > set_Pr1189492743on_val, A : produc1097884484on_val, B : produc1097884484on_val]: ((member354538064on_val @ Z @ (C5 @ A @ B)) => (member354538064on_val @ Z @ (produc493625819on_val @ C5 @ (produc1069526295on_val @ A @ B))))))). % mem_case_prodI
thf(fact_129_mem__case__prodI, axiom,
    ((![Z : produc1172664615on_val, C5 : exp_list_char > produc515445032on_val > set_Pr1189492743on_val, A : exp_list_char, B : produc515445032on_val]: ((member354538064on_val @ Z @ (C5 @ A @ B)) => (member354538064on_val @ Z @ (produc848217214on_val @ C5 @ (produc2023458740on_val @ A @ B))))))). % mem_case_prodI
thf(fact_130_mem__case__prodI2, axiom,
    ((![P2 : produc515445032on_val, Z : produc1172664615on_val, C5 : (nat > option2118145160on_val) > (list_char > option_val) > set_Pr1189492743on_val]: ((![A4 : nat > option2118145160on_val, B3 : list_char > option_val]: ((P2 = (produc52622304on_val @ A4 @ B3)) => (member354538064on_val @ Z @ (C5 @ A4 @ B3)))) => (member354538064on_val @ Z @ (produc1919805778on_val @ C5 @ P2)))))). % mem_case_prodI2
thf(fact_131_mem__case__prodI2, axiom,
    ((![P2 : produc1172664615on_val, Z : produc1172664615on_val, C5 : produc1097884484on_val > produc1097884484on_val > set_Pr1189492743on_val]: ((![A4 : produc1097884484on_val, B3 : produc1097884484on_val]: ((P2 = (produc1069526295on_val @ A4 @ B3)) => (member354538064on_val @ Z @ (C5 @ A4 @ B3)))) => (member354538064on_val @ Z @ (produc493625819on_val @ C5 @ P2)))))). % mem_case_prodI2
thf(fact_132_mem__case__prodI2, axiom,
    ((![P2 : produc1097884484on_val, Z : produc1172664615on_val, C5 : exp_list_char > produc515445032on_val > set_Pr1189492743on_val]: ((![A4 : exp_list_char, B3 : produc515445032on_val]: ((P2 = (produc2023458740on_val @ A4 @ B3)) => (member354538064on_val @ Z @ (C5 @ A4 @ B3)))) => (member354538064on_val @ Z @ (produc848217214on_val @ C5 @ P2)))))). % mem_case_prodI2
thf(fact_133_case__prod__Pair__iden, axiom,
    ((![P2 : produc515445032on_val]: ((produc2088825459on_val @ produc52622304on_val @ P2) = P2)))). % case_prod_Pair_iden
thf(fact_134_case__prod__Pair__iden, axiom,
    ((![P2 : produc1172664615on_val]: ((produc64793339on_val @ produc1069526295on_val @ P2) = P2)))). % case_prod_Pair_iden
thf(fact_135_case__prod__Pair__iden, axiom,
    ((![P2 : produc1097884484on_val]: ((produc1537230907on_val @ produc2023458740on_val @ P2) = P2)))). % case_prod_Pair_iden
thf(fact_136_mem__case__prodE, axiom,
    ((![Z : produc1172664615on_val, C5 : (nat > option2118145160on_val) > (list_char > option_val) > set_Pr1189492743on_val, P2 : produc515445032on_val]: ((member354538064on_val @ Z @ (produc1919805778on_val @ C5 @ P2)) => (~ ((![X : nat > option2118145160on_val, Y3 : list_char > option_val]: ((P2 = (produc52622304on_val @ X @ Y3)) => (~ ((member354538064on_val @ Z @ (C5 @ X @ Y3)))))))))))). % mem_case_prodE
thf(fact_137_mem__case__prodE, axiom,
    ((![Z : produc1172664615on_val, C5 : produc1097884484on_val > produc1097884484on_val > set_Pr1189492743on_val, P2 : produc1172664615on_val]: ((member354538064on_val @ Z @ (produc493625819on_val @ C5 @ P2)) => (~ ((![X : produc1097884484on_val, Y3 : produc1097884484on_val]: ((P2 = (produc1069526295on_val @ X @ Y3)) => (~ ((member354538064on_val @ Z @ (C5 @ X @ Y3)))))))))))). % mem_case_prodE
thf(fact_138_mem__case__prodE, axiom,
    ((![Z : produc1172664615on_val, C5 : exp_list_char > produc515445032on_val > set_Pr1189492743on_val, P2 : produc1097884484on_val]: ((member354538064on_val @ Z @ (produc848217214on_val @ C5 @ P2)) => (~ ((![X : exp_list_char, Y3 : produc515445032on_val]: ((P2 = (produc2023458740on_val @ X @ Y3)) => (~ ((member354538064on_val @ Z @ (C5 @ X @ Y3)))))))))))). % mem_case_prodE
thf(fact_139_converse__rtrancl__into__rtrancl, axiom,
    ((![A : produc1097884484on_val, B : produc1097884484on_val, R2 : set_Pr1189492743on_val, C5 : produc1097884484on_val]: ((member354538064on_val @ (produc1069526295on_val @ A @ B) @ R2) => ((member354538064on_val @ (produc1069526295on_val @ B @ C5) @ (transi111096263on_val @ R2)) => (member354538064on_val @ (produc1069526295on_val @ A @ C5) @ (transi111096263on_val @ R2))))))). % converse_rtrancl_into_rtrancl
thf(fact_140_rtrancl_Ortrancl__into__rtrancl, axiom,
    ((![A : produc1097884484on_val, B : produc1097884484on_val, R2 : set_Pr1189492743on_val, C5 : produc1097884484on_val]: ((member354538064on_val @ (produc1069526295on_val @ A @ B) @ (transi111096263on_val @ R2)) => ((member354538064on_val @ (produc1069526295on_val @ B @ C5) @ R2) => (member354538064on_val @ (produc1069526295on_val @ A @ C5) @ (transi111096263on_val @ R2))))))). % rtrancl.rtrancl_into_rtrancl
thf(fact_141_converse__rtrancl__induct, axiom,
    ((![A : produc1097884484on_val, B : produc1097884484on_val, R2 : set_Pr1189492743on_val, P : produc1097884484on_val > $o]: ((member354538064on_val @ (produc1069526295on_val @ A @ B) @ (transi111096263on_val @ R2)) => ((P @ B) => ((![Y3 : produc1097884484on_val, Z2 : produc1097884484on_val]: ((member354538064on_val @ (produc1069526295on_val @ Y3 @ Z2) @ R2) => ((member354538064on_val @ (produc1069526295on_val @ Z2 @ B) @ (transi111096263on_val @ R2)) => ((P @ Z2) => (P @ Y3))))) => (P @ A))))))). % converse_rtrancl_induct
thf(fact_142_rtrancl_Ortrancl__refl, axiom,
    ((![A : produc1097884484on_val, R2 : set_Pr1189492743on_val]: (member354538064on_val @ (produc1069526295on_val @ A @ A) @ (transi111096263on_val @ R2))))). % rtrancl.rtrancl_refl
thf(fact_143_converse__rtranclE, axiom,
    ((![X3 : produc1097884484on_val, Z : produc1097884484on_val, R2 : set_Pr1189492743on_val]: ((member354538064on_val @ (produc1069526295on_val @ X3 @ Z) @ (transi111096263on_val @ R2)) => ((~ ((X3 = Z))) => (~ ((![Y3 : produc1097884484on_val]: ((member354538064on_val @ (produc1069526295on_val @ X3 @ Y3) @ R2) => (~ ((member354538064on_val @ (produc1069526295on_val @ Y3 @ Z) @ (transi111096263on_val @ R2))))))))))))). % converse_rtranclE
thf(fact_144_rtrancl_Oinducts, axiom,
    ((![X1 : produc1097884484on_val, X22 : produc1097884484on_val, R2 : set_Pr1189492743on_val, P : produc1097884484on_val > produc1097884484on_val > $o]: ((member354538064on_val @ (produc1069526295on_val @ X1 @ X22) @ (transi111096263on_val @ R2)) => ((![A4 : produc1097884484on_val]: (P @ A4 @ A4)) => ((![A4 : produc1097884484on_val, B3 : produc1097884484on_val, C3 : produc1097884484on_val]: ((member354538064on_val @ (produc1069526295on_val @ A4 @ B3) @ (transi111096263on_val @ R2)) => ((P @ A4 @ B3) => ((member354538064on_val @ (produc1069526295on_val @ B3 @ C3) @ R2) => (P @ A4 @ C3))))) => (P @ X1 @ X22))))))). % rtrancl.inducts
thf(fact_145_rtrancl__induct, axiom,
    ((![A : produc1097884484on_val, B : produc1097884484on_val, R2 : set_Pr1189492743on_val, P : produc1097884484on_val > $o]: ((member354538064on_val @ (produc1069526295on_val @ A @ B) @ (transi111096263on_val @ R2)) => ((P @ A) => ((![Y3 : produc1097884484on_val, Z2 : produc1097884484on_val]: ((member354538064on_val @ (produc1069526295on_val @ A @ Y3) @ (transi111096263on_val @ R2)) => ((member354538064on_val @ (produc1069526295on_val @ Y3 @ Z2) @ R2) => ((P @ Y3) => (P @ Z2))))) => (P @ B))))))). % rtrancl_induct
thf(fact_146_rtrancl__trans, axiom,
    ((![X3 : produc1097884484on_val, Y : produc1097884484on_val, R2 : set_Pr1189492743on_val, Z : produc1097884484on_val]: ((member354538064on_val @ (produc1069526295on_val @ X3 @ Y) @ (transi111096263on_val @ R2)) => ((member354538064on_val @ (produc1069526295on_val @ Y @ Z) @ (transi111096263on_val @ R2)) => (member354538064on_val @ (produc1069526295on_val @ X3 @ Z) @ (transi111096263on_val @ R2))))))). % rtrancl_trans
thf(fact_147_rtrancl_Osimps, axiom,
    ((![A1 : produc1097884484on_val, A22 : produc1097884484on_val, R2 : set_Pr1189492743on_val]: ((member354538064on_val @ (produc1069526295on_val @ A1 @ A22) @ (transi111096263on_val @ R2)) = (((?[A5 : produc1097884484on_val]: (((A1 = A5)) & ((A22 = A5))))) | ((?[A5 : produc1097884484on_val]: (?[B4 : produc1097884484on_val]: (?[C6 : produc1097884484on_val]: (((A1 = A5)) & ((((A22 = C6)) & ((((member354538064on_val @ (produc1069526295on_val @ A5 @ B4) @ (transi111096263on_val @ R2))) & ((member354538064on_val @ (produc1069526295on_val @ B4 @ C6) @ R2)))))))))))))))). % rtrancl.simps
thf(fact_148_rtrancl_Ocases, axiom,
    ((![A1 : produc1097884484on_val, A22 : produc1097884484on_val, R2 : set_Pr1189492743on_val]: ((member354538064on_val @ (produc1069526295on_val @ A1 @ A22) @ (transi111096263on_val @ R2)) => ((~ ((A22 = A1))) => (~ ((![B3 : produc1097884484on_val]: ((member354538064on_val @ (produc1069526295on_val @ A1 @ B3) @ (transi111096263on_val @ R2)) => (~ ((member354538064on_val @ (produc1069526295on_val @ B3 @ A22) @ R2)))))))))))). % rtrancl.cases
thf(fact_149_rtranclE, axiom,
    ((![A : produc1097884484on_val, B : produc1097884484on_val, R2 : set_Pr1189492743on_val]: ((member354538064on_val @ (produc1069526295on_val @ A @ B) @ (transi111096263on_val @ R2)) => ((~ ((A = B))) => (~ ((![Y3 : produc1097884484on_val]: ((member354538064on_val @ (produc1069526295on_val @ A @ Y3) @ (transi111096263on_val @ R2)) => (~ ((member354538064on_val @ (produc1069526295on_val @ Y3 @ B) @ R2)))))))))))). % rtranclE
thf(fact_150_converse__rtrancl__induct2, axiom,
    ((![Ax : nat > option2118145160on_val, Ay : list_char > option_val, Bx : nat > option2118145160on_val, By : list_char > option_val, R2 : set_Pr148564103on_val, P : (nat > option2118145160on_val) > (list_char > option_val) > $o]: ((member2027247312on_val @ (produc2106877847on_val @ (produc52622304on_val @ Ax @ Ay) @ (produc52622304on_val @ Bx @ By)) @ (transi432893227on_val @ R2)) => ((P @ Bx @ By) => ((![A4 : nat > option2118145160on_val, B3 : list_char > option_val, Aa : nat > option2118145160on_val, Ba : list_char > option_val]: ((member2027247312on_val @ (produc2106877847on_val @ (produc52622304on_val @ A4 @ B3) @ (produc52622304on_val @ Aa @ Ba)) @ R2) => ((member2027247312on_val @ (produc2106877847on_val @ (produc52622304on_val @ Aa @ Ba) @ (produc52622304on_val @ Bx @ By)) @ (transi432893227on_val @ R2)) => ((P @ Aa @ Ba) => (P @ A4 @ B3))))) => (P @ Ax @ Ay))))))). % converse_rtrancl_induct2
thf(fact_151_converse__rtrancl__induct2, axiom,
    ((![Ax : produc1097884484on_val, Ay : produc1097884484on_val, Bx : produc1097884484on_val, By : produc1097884484on_val, R2 : set_Pr1368603847on_val, P : produc1097884484on_val > produc1097884484on_val > $o]: ((member208988944on_val @ (produc564964183on_val @ (produc1069526295on_val @ Ax @ Ay) @ (produc1069526295on_val @ Bx @ By)) @ (transi100378922on_val @ R2)) => ((P @ Bx @ By) => ((![A4 : produc1097884484on_val, B3 : produc1097884484on_val, Aa : produc1097884484on_val, Ba : produc1097884484on_val]: ((member208988944on_val @ (produc564964183on_val @ (produc1069526295on_val @ A4 @ B3) @ (produc1069526295on_val @ Aa @ Ba)) @ R2) => ((member208988944on_val @ (produc564964183on_val @ (produc1069526295on_val @ Aa @ Ba) @ (produc1069526295on_val @ Bx @ By)) @ (transi100378922on_val @ R2)) => ((P @ Aa @ Ba) => (P @ A4 @ B3))))) => (P @ Ax @ Ay))))))). % converse_rtrancl_induct2
thf(fact_152_converse__rtrancl__induct2, axiom,
    ((![Ax : exp_list_char, Ay : produc515445032on_val, Bx : exp_list_char, By : produc515445032on_val, R2 : set_Pr1189492743on_val, P : exp_list_char > produc515445032on_val > $o]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ Ax @ Ay) @ (produc2023458740on_val @ Bx @ By)) @ (transi111096263on_val @ R2)) => ((P @ Bx @ By) => ((![A4 : exp_list_char, B3 : produc515445032on_val, Aa : exp_list_char, Ba : produc515445032on_val]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ A4 @ B3) @ (produc2023458740on_val @ Aa @ Ba)) @ R2) => ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ Aa @ Ba) @ (produc2023458740on_val @ Bx @ By)) @ (transi111096263on_val @ R2)) => ((P @ Aa @ Ba) => (P @ A4 @ B3))))) => (P @ Ax @ Ay))))))). % converse_rtrancl_induct2
thf(fact_153_converse__rtranclE2, axiom,
    ((![Xa : nat > option2118145160on_val, Xb : list_char > option_val, Za : nat > option2118145160on_val, Zb : list_char > option_val, R2 : set_Pr148564103on_val]: ((member2027247312on_val @ (produc2106877847on_val @ (produc52622304on_val @ Xa @ Xb) @ (produc52622304on_val @ Za @ Zb)) @ (transi432893227on_val @ R2)) => ((~ (((produc52622304on_val @ Xa @ Xb) = (produc52622304on_val @ Za @ Zb)))) => (~ ((![A4 : nat > option2118145160on_val, B3 : list_char > option_val]: ((member2027247312on_val @ (produc2106877847on_val @ (produc52622304on_val @ Xa @ Xb) @ (produc52622304on_val @ A4 @ B3)) @ R2) => (~ ((member2027247312on_val @ (produc2106877847on_val @ (produc52622304on_val @ A4 @ B3) @ (produc52622304on_val @ Za @ Zb)) @ (transi432893227on_val @ R2))))))))))))). % converse_rtranclE2
thf(fact_154_converse__rtranclE2, axiom,
    ((![Xa : produc1097884484on_val, Xb : produc1097884484on_val, Za : produc1097884484on_val, Zb : produc1097884484on_val, R2 : set_Pr1368603847on_val]: ((member208988944on_val @ (produc564964183on_val @ (produc1069526295on_val @ Xa @ Xb) @ (produc1069526295on_val @ Za @ Zb)) @ (transi100378922on_val @ R2)) => ((~ (((produc1069526295on_val @ Xa @ Xb) = (produc1069526295on_val @ Za @ Zb)))) => (~ ((![A4 : produc1097884484on_val, B3 : produc1097884484on_val]: ((member208988944on_val @ (produc564964183on_val @ (produc1069526295on_val @ Xa @ Xb) @ (produc1069526295on_val @ A4 @ B3)) @ R2) => (~ ((member208988944on_val @ (produc564964183on_val @ (produc1069526295on_val @ A4 @ B3) @ (produc1069526295on_val @ Za @ Zb)) @ (transi100378922on_val @ R2))))))))))))). % converse_rtranclE2
thf(fact_155_converse__rtranclE2, axiom,
    ((![Xa : exp_list_char, Xb : produc515445032on_val, Za : exp_list_char, Zb : produc515445032on_val, R2 : set_Pr1189492743on_val]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ Xa @ Xb) @ (produc2023458740on_val @ Za @ Zb)) @ (transi111096263on_val @ R2)) => ((~ (((produc2023458740on_val @ Xa @ Xb) = (produc2023458740on_val @ Za @ Zb)))) => (~ ((![A4 : exp_list_char, B3 : produc515445032on_val]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ Xa @ Xb) @ (produc2023458740on_val @ A4 @ B3)) @ R2) => (~ ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ A4 @ B3) @ (produc2023458740on_val @ Za @ Zb)) @ (transi111096263on_val @ R2))))))))))))). % converse_rtranclE2
thf(fact_156_split__cong, axiom,
    ((![Q2 : produc515445032on_val, F : (nat > option2118145160on_val) > (list_char > option_val) > $o, G : (nat > option2118145160on_val) > (list_char > option_val) > $o, P2 : produc515445032on_val]: ((![X : nat > option2118145160on_val, Y3 : list_char > option_val]: (((produc52622304on_val @ X @ Y3) = Q2) => ((F @ X @ Y3) = (G @ X @ Y3)))) => ((P2 = Q2) => ((produc99536995_val_o @ F @ P2) = (produc99536995_val_o @ G @ Q2))))))). % split_cong
thf(fact_157_BinOpRedsThrow2, axiom,
    ((![E_1 : exp_list_char, S_0 : produc515445032on_val, V_1 : val, S_1 : produc515445032on_val, P : list_P1234162913t_char, E_2 : exp_list_char, E2 : exp_list_char, S_2 : produc515445032on_val, Bop : bop]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E_1 @ S_0) @ (produc2023458740on_val @ (val_list_char @ V_1) @ S_1)) @ (transi111096263on_val @ (red @ P))) => ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E_2 @ S_1) @ (produc2023458740on_val @ (throw_list_char @ E2) @ S_2)) @ (transi111096263on_val @ (red @ P))) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (binOp_list_char @ E_1 @ Bop @ E_2) @ S_0) @ (produc2023458740on_val @ (throw_list_char @ E2) @ S_2)) @ (transi111096263on_val @ (red @ P)))))))). % BinOpRedsThrow2
thf(fact_158_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_159_exp_Odistinct_I75_J, axiom,
    ((![X32 : val, X14 : exp_list_char]: (~ (((val_list_char @ X32) = (throw_list_char @ X14))))))). % exp.distinct(75)
thf(fact_160_WTrt__elim__cases_I4_J, axiom,
    ((![P : list_P1234162913t_char, H : nat > option2118145160on_val, E : list_char > option_ty, E2 : exp_list_char, T : ty]: ((wTrt @ P @ H @ E @ (throw_list_char @ E2) @ T) => (~ ((![T_r : ty]: ((wTrt @ P @ H @ E @ E2 @ T_r) => (~ ((is_refT @ T_r))))))))))). % WTrt_elim_cases(4)
thf(fact_161_WTrtThrow, axiom,
    ((![P : list_P1234162913t_char, H : nat > option2118145160on_val, E : list_char > option_ty, E2 : exp_list_char, T_r2 : ty, T : ty]: ((wTrt @ P @ H @ E @ E2 @ T_r2) => ((is_refT @ T_r2) => (wTrt @ P @ H @ E @ (throw_list_char @ E2) @ T)))))). % WTrtThrow
thf(fact_162_exp_Odistinct_I97_J, axiom,
    ((![X41 : exp_list_char, X42 : bop, X43 : exp_list_char, X14 : exp_list_char]: (~ (((binOp_list_char @ X41 @ X42 @ X43) = (throw_list_char @ X14))))))). % exp.distinct(97)

% Conjectures (1)
thf(conj_0, conjecture,
    ((t = integer))).
