% TIMEFORMAT='%3R'; { time (exec 2>&1; /home/martin/bin/satallax -E /home/martin/.isabelle/contrib/e-2.5-1/x86_64-linux/eprover -p tstp -t 5 /home/martin/judgement-day/tptp-thf/tptp/TypeSafe/prob_623__5342506_1 ) ; }
% This file was generated by Isabelle (most likely Sledgehammer)
% 2020-12-16 14:22:52.923

% Could-be-implicit typings (27)
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thf(ty_n_t__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,
    produc515445032on_val : $tType).
thf(ty_n_t__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__Product____Type__Oprod_It__List__Olist_It__Type__Oty_J_Mt__Product____Type__Oprod_It__Type__Oty_Mt__Product____Type__Oprod_It__List__Olist_It__List__Olist_It__String__Ochar_J_J_Mt__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_J_J_J_J, type,
    produc1259892823t_char : $tType).
thf(ty_n_t__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, type,
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thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_I_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_M_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J, type,
    set_Pr1104486497on_val : $tType).
thf(ty_n_t__Product____Type__Oprod_I_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_M_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_J, type,
    produc1335728385on_val : $tType).
thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_Mt__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_J_J, type,
    set_Pr224372167t_char : $tType).
thf(ty_n_t__Product____Type__Oprod_It__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_Mt__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_J, type,
    produc677445863t_char : $tType).
thf(ty_n_t__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J, type,
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thf(ty_n_t__Option__Ooption_It__Value__Oval_J, type,
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thf(ty_n_t__Option__Ooption_It__Type__Oty_J, type,
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thf(ty_n_t__List__Olist_It__String__Ochar_J, type,
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thf(ty_n_t__Value__Oval, type,
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thf(ty_n_t__Expr__Obop, type,
    bop : $tType).
thf(ty_n_t__Type__Oty, type,
    ty : $tType).
thf(ty_n_t__Nat__Onat, type,
    nat : $tType).

% Explicit typings (66)
thf(sy_c_BigStep_Oeval, type,
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thf(sy_c_BigStep_Ofinal_001t__List__Olist_It__String__Ochar_J, type,
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thf(sy_c_Conform_Ohconf_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,
    hconf_1244167010t_char : list_P1234162913t_char > (nat > option2118145160on_val) > $o).
thf(sy_c_Conform_Olconf_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,
    lconf_485928294t_char : list_P1234162913t_char > (nat > option2118145160on_val) > (list_char > option_val) > (list_char > option_ty) > $o).
thf(sy_c_Expr_Oexp_OBinOp_001t__List__Olist_It__String__Ochar_J, type,
    binOp_list_char : exp_list_char > bop > exp_list_char > exp_list_char).
thf(sy_c_Expr_Oexp_OCast_001t__List__Olist_It__String__Ochar_J, type,
    cast_list_char : list_char > exp_list_char > exp_list_char).
thf(sy_c_Expr_Oexp_OCond_001t__List__Olist_It__String__Ochar_J, type,
    cond_list_char : exp_list_char > exp_list_char > exp_list_char > exp_list_char).
thf(sy_c_Expr_Oexp_OFAcc_001t__List__Olist_It__String__Ochar_J, type,
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thf(sy_c_Expr_Oexp_OLAss_001t__List__Olist_It__String__Ochar_J, type,
    lAss_list_char : list_char > exp_list_char > exp_list_char).
thf(sy_c_Expr_Oexp_OSeq_001t__List__Olist_It__String__Ochar_J, type,
    seq_list_char : exp_list_char > exp_list_char > exp_list_char).
thf(sy_c_Expr_Oexp_OVal_001t__List__Olist_It__String__Ochar_J, type,
    val_list_char : val > exp_list_char).
thf(sy_c_Expr_Oexp_OWhile_001t__List__Olist_It__String__Ochar_J, type,
    while_list_char : exp_list_char > exp_list_char > exp_list_char).
thf(sy_c_Expr_Oexp_Othrow_001t__List__Olist_It__String__Ochar_J, type,
    throw_list_char : exp_list_char > exp_list_char).
thf(sy_c_JWellForm_Owf__J__mdecl, type,
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thf(sy_c_Map_Omap__add_001t__List__Olist_It__String__Ochar_J_001t__Value__Oval, type,
    map_ad1615113112ar_val : (list_char > option_val) > (list_char > option_val) > list_char > option_val).
thf(sy_c_Objects_Ohext, type,
    hext : (nat > option2118145160on_val) > (nat > option2118145160on_val) > $o).
thf(sy_c_Product__Type_OPair_001_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_001_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J, type,
    produc746553401on_val : (list_char > option_val) > (list_char > option_val) > produc1335728385on_val).
thf(sy_c_Product__Type_OPair_001_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_001_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J, type,
    produc52622304on_val : (nat > option2118145160on_val) > (list_char > option_val) > produc515445032on_val).
thf(sy_c_Product__Type_OPair_001_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_001_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, type,
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thf(sy_c_Wfrec_Osame__fst_001t__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_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,
    same_f366220041on_val : (exp_list_char > $o) > (exp_list_char > set_Pr148564103on_val) > set_Pr1189492743on_val).
thf(sy_c_Wfrec_Osame__fst_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_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,
    same_f962657004on_val : (produc1097884484on_val > $o) > (produc1097884484on_val > set_Pr1189492743on_val) > set_Pr1368603847on_val).
thf(sy_c_member_001t__Product____Type__Oprod_I_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_M_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_J, type,
    member1177709994on_val : produc1335728385on_val > set_Pr1104486497on_val > $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_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__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_J, type,
    member78096504on_val : produc1914020559on_val > set_Pr1465729071on_val > $o).
thf(sy_c_member_001t__Product____Type__Oprod_It__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_Mt__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_J, type,
    member1699993616t_char : produc677445863t_char > set_Pr224372167t_char > $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_e, type,
    e2 : exp_list_char).
thf(sy_v_e_H, type,
    e3 : exp_list_char).
thf(sy_v_s, type,
    s : produc515445032on_val).
thf(sy_v_s_H, type,
    s2 : produc515445032on_val).

% Relevant facts (179)
thf(fact_0_prod__cases4, axiom,
    ((![Y : produc1172664615on_val]: (~ ((![A : produc1097884484on_val, B : exp_list_char, C : nat > option2118145160on_val, D : list_char > option_val]: (~ ((Y = (produc1069526295on_val @ A @ (produc2023458740on_val @ B @ (produc52622304on_val @ C @ D)))))))))))). % prod_cases4
thf(fact_1_prod__induct4, axiom,
    ((![P : produc1172664615on_val > $o, X : produc1172664615on_val]: ((![A : produc1097884484on_val, B : exp_list_char, C : nat > option2118145160on_val, D : list_char > option_val]: (P @ (produc1069526295on_val @ A @ (produc2023458740on_val @ B @ (produc52622304on_val @ C @ D))))) => (P @ X))))). % prod_induct4
thf(fact_2_local_Owf, axiom,
    ((wf_pro1229751607t_char @ wf_J_mdecl @ p))). % local.wf
thf(fact_3_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_4_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_5_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_6_old_Oprod_Oinject, axiom,
    ((![A2 : produc1097884484on_val, B2 : produc1097884484on_val, A3 : produc1097884484on_val, B3 : produc1097884484on_val]: (((produc1069526295on_val @ A2 @ B2) = (produc1069526295on_val @ A3 @ B3)) = (((A2 = A3)) & ((B2 = B3))))))). % old.prod.inject
thf(fact_7_old_Oprod_Oinject, axiom,
    ((![A2 : exp_list_char, B2 : produc515445032on_val, A3 : exp_list_char, B3 : produc515445032on_val]: (((produc2023458740on_val @ A2 @ B2) = (produc2023458740on_val @ A3 @ B3)) = (((A2 = A3)) & ((B2 = B3))))))). % old.prod.inject
thf(fact_8_old_Oprod_Oinject, axiom,
    ((![A2 : nat > option2118145160on_val, B2 : list_char > option_val, A3 : nat > option2118145160on_val, B3 : list_char > option_val]: (((produc52622304on_val @ A2 @ B2) = (produc52622304on_val @ A3 @ B3)) = (((A2 = A3)) & ((B2 = B3))))))). % old.prod.inject
thf(fact_9_prod__cases3, axiom,
    ((![Y : produc1172664615on_val]: (~ ((![A : produc1097884484on_val, B : exp_list_char, C : produc515445032on_val]: (~ ((Y = (produc1069526295on_val @ A @ (produc2023458740on_val @ B @ C))))))))))). % prod_cases3
thf(fact_10_prod__cases3, axiom,
    ((![Y : produc1097884484on_val]: (~ ((![A : exp_list_char, B : nat > option2118145160on_val, C : list_char > option_val]: (~ ((Y = (produc2023458740on_val @ A @ (produc52622304on_val @ B @ C))))))))))). % prod_cases3
thf(fact_11_old_Oprod_Oinducts, axiom,
    ((![P : produc1172664615on_val > $o, Prod : produc1172664615on_val]: ((![A : produc1097884484on_val, B : produc1097884484on_val]: (P @ (produc1069526295on_val @ A @ B))) => (P @ Prod))))). % old.prod.inducts
thf(fact_12_old_Oprod_Oinducts, axiom,
    ((![P : produc1097884484on_val > $o, Prod : produc1097884484on_val]: ((![A : exp_list_char, B : produc515445032on_val]: (P @ (produc2023458740on_val @ A @ B))) => (P @ Prod))))). % old.prod.inducts
thf(fact_13_old_Oprod_Oinducts, axiom,
    ((![P : produc515445032on_val > $o, Prod : produc515445032on_val]: ((![A : nat > option2118145160on_val, B : list_char > option_val]: (P @ (produc52622304on_val @ A @ B))) => (P @ Prod))))). % old.prod.inducts
thf(fact_14_old_Oprod_Oexhaust, axiom,
    ((![Y : produc1172664615on_val]: (~ ((![A : produc1097884484on_val, B : produc1097884484on_val]: (~ ((Y = (produc1069526295on_val @ A @ B)))))))))). % old.prod.exhaust
thf(fact_15_old_Oprod_Oexhaust, axiom,
    ((![Y : produc1097884484on_val]: (~ ((![A : exp_list_char, B : produc515445032on_val]: (~ ((Y = (produc2023458740on_val @ A @ B)))))))))). % old.prod.exhaust
thf(fact_16_old_Oprod_Oexhaust, axiom,
    ((![Y : produc515445032on_val]: (~ ((![A : nat > option2118145160on_val, B : list_char > option_val]: (~ ((Y = (produc52622304on_val @ A @ B)))))))))). % old.prod.exhaust
thf(fact_17_Pair__inject, axiom,
    ((![A2 : produc1097884484on_val, B2 : produc1097884484on_val, A3 : produc1097884484on_val, B3 : produc1097884484on_val]: (((produc1069526295on_val @ A2 @ B2) = (produc1069526295on_val @ A3 @ B3)) => (~ (((A2 = A3) => (~ ((B2 = B3)))))))))). % Pair_inject
thf(fact_18_Pair__inject, axiom,
    ((![A2 : exp_list_char, B2 : produc515445032on_val, A3 : exp_list_char, B3 : produc515445032on_val]: (((produc2023458740on_val @ A2 @ B2) = (produc2023458740on_val @ A3 @ B3)) => (~ (((A2 = A3) => (~ ((B2 = B3)))))))))). % Pair_inject
thf(fact_19_Pair__inject, axiom,
    ((![A2 : nat > option2118145160on_val, B2 : list_char > option_val, A3 : nat > option2118145160on_val, B3 : list_char > option_val]: (((produc52622304on_val @ A2 @ B2) = (produc52622304on_val @ A3 @ B3)) => (~ (((A2 = A3) => (~ ((B2 = B3)))))))))). % Pair_inject
thf(fact_20_prod__cases, axiom,
    ((![P : produc1172664615on_val > $o, P2 : produc1172664615on_val]: ((![A : produc1097884484on_val, B : produc1097884484on_val]: (P @ (produc1069526295on_val @ A @ B))) => (P @ P2))))). % prod_cases
thf(fact_21_prod__cases, axiom,
    ((![P : produc1097884484on_val > $o, P2 : produc1097884484on_val]: ((![A : exp_list_char, B : produc515445032on_val]: (P @ (produc2023458740on_val @ A @ B))) => (P @ P2))))). % prod_cases
thf(fact_22_prod__cases, axiom,
    ((![P : produc515445032on_val > $o, P2 : produc515445032on_val]: ((![A : nat > option2118145160on_val, B : list_char > option_val]: (P @ (produc52622304on_val @ A @ B))) => (P @ P2))))). % prod_cases
thf(fact_23_surj__pair, axiom,
    ((![P2 : produc1172664615on_val]: (?[X3 : produc1097884484on_val, Y3 : produc1097884484on_val]: (P2 = (produc1069526295on_val @ X3 @ Y3)))))). % surj_pair
thf(fact_24_surj__pair, axiom,
    ((![P2 : produc1097884484on_val]: (?[X3 : exp_list_char, Y3 : produc515445032on_val]: (P2 = (produc2023458740on_val @ X3 @ Y3)))))). % surj_pair
thf(fact_25_surj__pair, axiom,
    ((![P2 : produc515445032on_val]: (?[X3 : nat > option2118145160on_val, Y3 : list_char > option_val]: (P2 = (produc52622304on_val @ X3 @ Y3)))))). % surj_pair
thf(fact_26_prod__induct3, axiom,
    ((![P : produc1172664615on_val > $o, X : produc1172664615on_val]: ((![A : produc1097884484on_val, B : exp_list_char, C : produc515445032on_val]: (P @ (produc1069526295on_val @ A @ (produc2023458740on_val @ B @ C)))) => (P @ X))))). % prod_induct3
thf(fact_27_prod__induct3, axiom,
    ((![P : produc1097884484on_val > $o, X : produc1097884484on_val]: ((![A : exp_list_char, B : nat > option2118145160on_val, C : list_char > option_val]: (P @ (produc2023458740on_val @ A @ (produc52622304on_val @ B @ C)))) => (P @ X))))). % prod_induct3
thf(fact_28_same__fstI, axiom,
    ((![P : (nat > option2118145160on_val) > $o, X : nat > option2118145160on_val, Y4 : list_char > option_val, Y : list_char > option_val, R : (nat > option2118145160on_val) > set_Pr1104486497on_val]: ((P @ X) => ((member1177709994on_val @ (produc746553401on_val @ Y4 @ Y) @ (R @ X)) => (member2027247312on_val @ (produc2106877847on_val @ (produc52622304on_val @ X @ Y4) @ (produc52622304on_val @ X @ Y)) @ (same_f1752972725on_val @ P @ R))))))). % same_fstI
thf(fact_29_same__fstI, axiom,
    ((![P : exp_list_char > $o, X : exp_list_char, Y4 : produc515445032on_val, Y : produc515445032on_val, R : exp_list_char > set_Pr148564103on_val]: ((P @ X) => ((member2027247312on_val @ (produc2106877847on_val @ Y4 @ Y) @ (R @ X)) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ X @ Y4) @ (produc2023458740on_val @ X @ Y)) @ (same_f366220041on_val @ P @ R))))))). % same_fstI
thf(fact_30_same__fstI, axiom,
    ((![P : produc1097884484on_val > $o, X : produc1097884484on_val, Y4 : produc1097884484on_val, Y : produc1097884484on_val, R : produc1097884484on_val > set_Pr1189492743on_val]: ((P @ X) => ((member354538064on_val @ (produc1069526295on_val @ Y4 @ Y) @ (R @ X)) => (member208988944on_val @ (produc564964183on_val @ (produc1069526295on_val @ X @ Y4) @ (produc1069526295on_val @ X @ Y)) @ (same_f962657004on_val @ P @ R))))))). % same_fstI
thf(fact_31_widen__refl, axiom,
    ((![P : list_P1234162913t_char, T : ty]: (widen_917054840t_char @ P @ T @ T)))). % widen_refl
thf(fact_32_widen__trans, axiom,
    ((![P : list_P1234162913t_char, S : ty, U : ty, T : ty]: ((widen_917054840t_char @ P @ S @ U) => ((widen_917054840t_char @ P @ U @ T) => (widen_917054840t_char @ P @ S @ T)))))). % widen_trans
thf(fact_33_subject__reduction2, axiom,
    ((![P : list_P1234162913t_char, E : exp_list_char, H : nat > option2118145160on_val, L : list_char > option_val, E2 : exp_list_char, H2 : nat > option2118145160on_val, L2 : list_char > option_val, E3 : list_char > option_ty, T : ty]: ((wf_pro1229751607t_char @ wf_J_mdecl @ P) => ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E @ (produc52622304on_val @ H @ L)) @ (produc2023458740on_val @ E2 @ (produc52622304on_val @ H2 @ L2))) @ (red @ P)) => ((typeSa1777264139_sconf @ P @ E3 @ (produc52622304on_val @ H @ L)) => ((wTrt @ P @ H @ E3 @ E @ T) => (?[T2 : ty]: ((wTrt @ P @ H2 @ E3 @ E2 @ T2) & (widen_917054840t_char @ P @ T2 @ T)))))))))). % subject_reduction2
thf(fact_34_ssubst__Pair__rhs, axiom,
    ((![R2 : produc1097884484on_val, S2 : produc1097884484on_val, R : set_Pr1189492743on_val, S3 : produc1097884484on_val]: ((member354538064on_val @ (produc1069526295on_val @ R2 @ S2) @ R) => ((S3 = S2) => (member354538064on_val @ (produc1069526295on_val @ R2 @ S3) @ R)))))). % ssubst_Pair_rhs
thf(fact_35_ssubst__Pair__rhs, axiom,
    ((![R2 : exp_list_char, S2 : produc515445032on_val, R : set_Pr556513572on_val, S3 : produc515445032on_val]: ((member1888679917on_val @ (produc2023458740on_val @ R2 @ S2) @ R) => ((S3 = S2) => (member1888679917on_val @ (produc2023458740on_val @ R2 @ S3) @ R)))))). % ssubst_Pair_rhs
thf(fact_36_ssubst__Pair__rhs, axiom,
    ((![R2 : nat > option2118145160on_val, S2 : list_char > option_val, R : set_Pr723149704on_val, S3 : list_char > option_val]: ((member652041809on_val @ (produc52622304on_val @ R2 @ S2) @ R) => ((S3 = S2) => (member652041809on_val @ (produc52622304on_val @ R2 @ S3) @ R)))))). % ssubst_Pair_rhs
thf(fact_37_in__lex__prod, axiom,
    ((![A2 : produc1097884484on_val, B2 : produc1097884484on_val, A3 : produc1097884484on_val, B3 : produc1097884484on_val, R2 : set_Pr1189492743on_val, S2 : set_Pr1189492743on_val]: ((member208988944on_val @ (produc564964183on_val @ (produc1069526295on_val @ A2 @ B2) @ (produc1069526295on_val @ A3 @ B3)) @ (lex_pr186272047on_val @ R2 @ S2)) = (((member354538064on_val @ (produc1069526295on_val @ A2 @ A3) @ R2)) | ((((A2 = A3)) & ((member354538064on_val @ (produc1069526295on_val @ B2 @ B3) @ S2))))))))). % in_lex_prod
thf(fact_38_in__lex__prod, axiom,
    ((![A2 : nat > option2118145160on_val, B2 : list_char > option_val, A3 : nat > option2118145160on_val, B3 : list_char > option_val, R2 : set_Pr1465729071on_val, S2 : set_Pr1104486497on_val]: ((member2027247312on_val @ (produc2106877847on_val @ (produc52622304on_val @ A2 @ B2) @ (produc52622304on_val @ A3 @ B3)) @ (lex_pr683585528on_val @ R2 @ S2)) = (((member78096504on_val @ (produc1392944775on_val @ A2 @ A3) @ R2)) | ((((A2 = A3)) & ((member1177709994on_val @ (produc746553401on_val @ B2 @ B3) @ S2))))))))). % in_lex_prod
thf(fact_39_in__lex__prod, axiom,
    ((![A2 : exp_list_char, B2 : produc515445032on_val, A3 : exp_list_char, B3 : produc515445032on_val, R2 : set_Pr224372167t_char, S2 : set_Pr148564103on_val]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ A2 @ B2) @ (produc2023458740on_val @ A3 @ B3)) @ (lex_pr1764546508on_val @ R2 @ S2)) = (((member1699993616t_char @ (produc240508503t_char @ A2 @ A3) @ R2)) | ((((A2 = A3)) & ((member2027247312on_val @ (produc2106877847on_val @ B2 @ B3) @ S2))))))))). % in_lex_prod
thf(fact_40_red__hext__incr, axiom,
    ((![E : exp_list_char, H : nat > option2118145160on_val, L : list_char > option_val, E2 : exp_list_char, H2 : nat > option2118145160on_val, L2 : list_char > option_val, P : list_P1234162913t_char]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E @ (produc52622304on_val @ H @ L)) @ (produc2023458740on_val @ E2 @ (produc52622304on_val @ H2 @ L2))) @ (red @ P)) => (hext @ H @ H2))))). % red_hext_incr
thf(fact_41_curryI, axiom,
    ((![F : produc1172664615on_val > $o, A2 : produc1097884484on_val, B2 : produc1097884484on_val]: ((F @ (produc1069526295on_val @ A2 @ B2)) => (produc360843917_val_o @ F @ A2 @ B2))))). % curryI
thf(fact_42_curryI, axiom,
    ((![F : produc1097884484on_val > $o, A2 : exp_list_char, B2 : produc515445032on_val]: ((F @ (produc2023458740on_val @ A2 @ B2)) => (produc699483184_val_o @ F @ A2 @ B2))))). % curryI
thf(fact_43_curryI, axiom,
    ((![F : produc515445032on_val > $o, A2 : nat > option2118145160on_val, B2 : list_char > option_val]: ((F @ (produc52622304on_val @ A2 @ B2)) => (produc761261956_val_o @ F @ A2 @ B2))))). % curryI
thf(fact_44_curryD, axiom,
    ((![F : produc1172664615on_val > $o, A2 : produc1097884484on_val, B2 : produc1097884484on_val]: ((produc360843917_val_o @ F @ A2 @ B2) => (F @ (produc1069526295on_val @ A2 @ B2)))))). % curryD
thf(fact_45_curryD, axiom,
    ((![F : produc1097884484on_val > $o, A2 : exp_list_char, B2 : produc515445032on_val]: ((produc699483184_val_o @ F @ A2 @ B2) => (F @ (produc2023458740on_val @ A2 @ B2)))))). % curryD
thf(fact_46_curryD, axiom,
    ((![F : produc515445032on_val > $o, A2 : nat > option2118145160on_val, B2 : list_char > option_val]: ((produc761261956_val_o @ F @ A2 @ B2) => (F @ (produc52622304on_val @ A2 @ B2)))))). % curryD
thf(fact_47_curryE, axiom,
    ((![F : produc1172664615on_val > $o, A2 : produc1097884484on_val, B2 : produc1097884484on_val]: ((produc360843917_val_o @ F @ A2 @ B2) => (F @ (produc1069526295on_val @ A2 @ B2)))))). % curryE
thf(fact_48_curryE, axiom,
    ((![F : produc1097884484on_val > $o, A2 : exp_list_char, B2 : produc515445032on_val]: ((produc699483184_val_o @ F @ A2 @ B2) => (F @ (produc2023458740on_val @ A2 @ B2)))))). % curryE
thf(fact_49_curryE, axiom,
    ((![F : produc515445032on_val > $o, A2 : nat > option2118145160on_val, B2 : list_char > option_val]: ((produc761261956_val_o @ F @ A2 @ B2) => (F @ (produc52622304on_val @ A2 @ B2)))))). % curryE
thf(fact_50_hext__refl, axiom,
    ((![H : nat > option2118145160on_val]: (hext @ H @ H)))). % hext_refl
thf(fact_51_subject__reduction, axiom,
    ((![P : list_P1234162913t_char, E : exp_list_char, S2 : produc515445032on_val, E2 : exp_list_char, S3 : produc515445032on_val, E3 : list_char > option_ty, T : ty]: ((wf_pro1229751607t_char @ wf_J_mdecl @ P) => ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E @ S2) @ (produc2023458740on_val @ E2 @ S3)) @ (red @ P)) => ((typeSa1777264139_sconf @ P @ E3 @ S2) => ((wTrt @ P @ (hp @ S2) @ E3 @ E @ T) => (?[T2 : ty]: ((wTrt @ P @ (hp @ S3) @ E3 @ E2 @ T2) & (widen_917054840t_char @ P @ T2 @ T)))))))))). % subject_reduction
thf(fact_52_red__preserves__hconf, axiom,
    ((![E : exp_list_char, H : nat > option2118145160on_val, L : list_char > option_val, E2 : exp_list_char, H2 : nat > option2118145160on_val, L2 : list_char > option_val, P : list_P1234162913t_char, E3 : list_char > option_ty, T : ty]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E @ (produc52622304on_val @ H @ L)) @ (produc2023458740on_val @ E2 @ (produc52622304on_val @ H2 @ L2))) @ (red @ P)) => ((wTrt @ P @ H @ E3 @ E @ T) => ((hconf_1244167010t_char @ P @ H) => (hconf_1244167010t_char @ P @ H2))))))). % red_preserves_hconf
thf(fact_53_WTrt__hext__mono, axiom,
    ((![P : list_P1234162913t_char, H : nat > option2118145160on_val, E3 : list_char > option_ty, E : exp_list_char, T : ty, H2 : nat > option2118145160on_val]: ((wTrt @ P @ H @ E3 @ E @ T) => ((hext @ H @ H2) => (wTrt @ P @ H2 @ E3 @ E @ T)))))). % WTrt_hext_mono
thf(fact_54_red__preserves__lconf, axiom,
    ((![E : exp_list_char, H : nat > option2118145160on_val, L : list_char > option_val, E2 : exp_list_char, H2 : nat > option2118145160on_val, L2 : list_char > option_val, P : list_P1234162913t_char, E3 : list_char > option_ty, T : ty]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E @ (produc52622304on_val @ H @ L)) @ (produc2023458740on_val @ E2 @ (produc52622304on_val @ H2 @ L2))) @ (red @ P)) => ((wTrt @ P @ H @ E3 @ E @ T) => ((lconf_485928294t_char @ P @ H @ L @ E3) => (lconf_485928294t_char @ P @ H2 @ L2 @ E3))))))). % red_preserves_lconf
thf(fact_55_red__preserves__sconf, axiom,
    ((![E : exp_list_char, S2 : produc515445032on_val, E2 : exp_list_char, S3 : produc515445032on_val, P : list_P1234162913t_char, E3 : list_char > option_ty, T : ty]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E @ S2) @ (produc2023458740on_val @ E2 @ S3)) @ (red @ P)) => ((wTrt @ P @ (hp @ S2) @ E3 @ E @ T) => ((typeSa1777264139_sconf @ P @ E3 @ S2) => (typeSa1777264139_sconf @ P @ E3 @ S3))))))). % red_preserves_sconf
thf(fact_56_wf__config__def, axiom,
    ((typeSa1969945757config = (^[P3 : list_P1234162913t_char]: (^[E4 : list_char > option_ty]: (^[S4 : produc515445032on_val]: (^[E5 : exp_list_char]: (^[T3 : ty]: (((typeSa1777264139_sconf @ P3 @ E4 @ S4)) & ((wTrt @ P3 @ (hp @ S4) @ E4 @ E5 @ T3))))))))))). % wf_config_def
thf(fact_57_Red__preserves__type, axiom,
    ((![P : list_P1234162913t_char, E : exp_list_char, S2 : produc515445032on_val, E2 : exp_list_char, S3 : produc515445032on_val, E3 : list_char > option_ty, T : ty]: ((wf_pro1229751607t_char @ wf_J_mdecl @ P) => ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E @ S2) @ (produc2023458740on_val @ E2 @ S3)) @ (transi111096263on_val @ (red @ P))) => ((typeSa1777264139_sconf @ P @ E3 @ S2) => ((wTrt @ P @ (hp @ S2) @ E3 @ E @ T) => (?[T2 : ty]: ((widen_917054840t_char @ P @ T2 @ T) & (wTrt @ P @ (hp @ S3) @ E3 @ E2 @ T2)))))))))). % Red_preserves_type
thf(fact_58_converse__rtrancl__induct__red, axiom,
    ((![E : exp_list_char, H : nat > option2118145160on_val, L : list_char > option_val, E2 : 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 @ E @ (produc52622304on_val @ H @ L)) @ (produc2023458740on_val @ E2 @ (produc52622304on_val @ H2 @ L2))) @ (transi111096263on_val @ (red @ P))) => ((![E6 : exp_list_char, H3 : nat > option2118145160on_val, L3 : list_char > option_val]: (R @ E6 @ H3 @ L3 @ E6 @ H3 @ L3)) => ((![E_0 : exp_list_char, H_0 : nat > option2118145160on_val, L_0 : list_char > option_val, E_1 : exp_list_char, H_1 : nat > option2118145160on_val, L_1 : list_char > option_val, E7 : exp_list_char, H4 : nat > option2118145160on_val, L4 : list_char > option_val]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E_0 @ (produc52622304on_val @ H_0 @ L_0)) @ (produc2023458740on_val @ E_1 @ (produc52622304on_val @ H_1 @ L_1))) @ (red @ P)) => ((R @ E_1 @ H_1 @ L_1 @ E7 @ H4 @ L4) => (R @ E_0 @ H_0 @ L_0 @ E7 @ H4 @ L4)))) => (R @ E @ H @ L @ E2 @ H2 @ L2))))))). % converse_rtrancl_induct_red
thf(fact_59_Red__preserves__sconf, axiom,
    ((![P : list_P1234162913t_char, E : exp_list_char, S2 : produc515445032on_val, E2 : exp_list_char, S3 : produc515445032on_val, E3 : list_char > option_ty, T : ty]: ((wf_pro1229751607t_char @ wf_J_mdecl @ P) => ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E @ S2) @ (produc2023458740on_val @ E2 @ S3)) @ (transi111096263on_val @ (red @ P))) => ((wTrt @ P @ (hp @ S2) @ E3 @ E @ T) => ((typeSa1777264139_sconf @ P @ E3 @ S2) => (typeSa1777264139_sconf @ P @ E3 @ S3)))))))). % Red_preserves_sconf
thf(fact_60_hext__trans, axiom,
    ((![H : nat > option2118145160on_val, H2 : nat > option2118145160on_val, H5 : nat > option2118145160on_val]: ((hext @ H @ H2) => ((hext @ H2 @ H5) => (hext @ H @ H5)))))). % hext_trans
thf(fact_61_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) => ((![A : produc1097884484on_val, B : produc1097884484on_val, Aa : produc1097884484on_val, Ba : produc1097884484on_val]: ((member208988944on_val @ (produc564964183on_val @ (produc1069526295on_val @ A @ B) @ (produc1069526295on_val @ Aa @ Ba)) @ R2) => ((member208988944on_val @ (produc564964183on_val @ (produc1069526295on_val @ Aa @ Ba) @ (produc1069526295on_val @ Bx @ By)) @ (transi100378922on_val @ R2)) => ((P @ Aa @ Ba) => (P @ A @ B))))) => (P @ Ax @ Ay))))))). % converse_rtrancl_induct2
thf(fact_62_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) => ((![A : nat > option2118145160on_val, B : list_char > option_val, Aa : nat > option2118145160on_val, Ba : list_char > option_val]: ((member2027247312on_val @ (produc2106877847on_val @ (produc52622304on_val @ A @ B) @ (produc52622304on_val @ Aa @ Ba)) @ R2) => ((member2027247312on_val @ (produc2106877847on_val @ (produc52622304on_val @ Aa @ Ba) @ (produc52622304on_val @ Bx @ By)) @ (transi432893227on_val @ R2)) => ((P @ Aa @ Ba) => (P @ A @ B))))) => (P @ Ax @ Ay))))))). % converse_rtrancl_induct2
thf(fact_63_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) => ((![A : exp_list_char, B : produc515445032on_val, Aa : exp_list_char, Ba : produc515445032on_val]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ A @ B) @ (produc2023458740on_val @ Aa @ Ba)) @ R2) => ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ Aa @ Ba) @ (produc2023458740on_val @ Bx @ By)) @ (transi111096263on_val @ R2)) => ((P @ Aa @ Ba) => (P @ A @ B))))) => (P @ Ax @ Ay))))))). % converse_rtrancl_induct2
thf(fact_64_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)))) => (~ ((![A : produc1097884484on_val, B : produc1097884484on_val]: ((member208988944on_val @ (produc564964183on_val @ (produc1069526295on_val @ Xa @ Xb) @ (produc1069526295on_val @ A @ B)) @ R2) => (~ ((member208988944on_val @ (produc564964183on_val @ (produc1069526295on_val @ A @ B) @ (produc1069526295on_val @ Za @ Zb)) @ (transi100378922on_val @ R2))))))))))))). % converse_rtranclE2
thf(fact_65_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)))) => (~ ((![A : nat > option2118145160on_val, B : list_char > option_val]: ((member2027247312on_val @ (produc2106877847on_val @ (produc52622304on_val @ Xa @ Xb) @ (produc52622304on_val @ A @ B)) @ R2) => (~ ((member2027247312on_val @ (produc2106877847on_val @ (produc52622304on_val @ A @ B) @ (produc52622304on_val @ Za @ Zb)) @ (transi432893227on_val @ R2))))))))))))). % converse_rtranclE2
thf(fact_66_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)))) => (~ ((![A : exp_list_char, B : produc515445032on_val]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ Xa @ Xb) @ (produc2023458740on_val @ A @ B)) @ R2) => (~ ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ A @ B) @ (produc2023458740on_val @ Za @ Zb)) @ (transi111096263on_val @ R2))))))))))))). % converse_rtranclE2
thf(fact_67_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) => ((![A : produc1097884484on_val, B : produc1097884484on_val, Aa : produc1097884484on_val, Ba : produc1097884484on_val]: ((member208988944on_val @ (produc564964183on_val @ (produc1069526295on_val @ Ax @ Ay) @ (produc1069526295on_val @ A @ B)) @ (transi100378922on_val @ R2)) => ((member208988944on_val @ (produc564964183on_val @ (produc1069526295on_val @ A @ B) @ (produc1069526295on_val @ Aa @ Ba)) @ R2) => ((P @ A @ B) => (P @ Aa @ Ba))))) => (P @ Bx @ By))))))). % rtrancl_induct2
thf(fact_68_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) => ((![A : nat > option2118145160on_val, B : list_char > option_val, Aa : nat > option2118145160on_val, Ba : list_char > option_val]: ((member2027247312on_val @ (produc2106877847on_val @ (produc52622304on_val @ Ax @ Ay) @ (produc52622304on_val @ A @ B)) @ (transi432893227on_val @ R2)) => ((member2027247312on_val @ (produc2106877847on_val @ (produc52622304on_val @ A @ B) @ (produc52622304on_val @ Aa @ Ba)) @ R2) => ((P @ A @ B) => (P @ Aa @ Ba))))) => (P @ Bx @ By))))))). % rtrancl_induct2
thf(fact_69_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) => ((![A : exp_list_char, B : produc515445032on_val, Aa : exp_list_char, Ba : produc515445032on_val]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ Ax @ Ay) @ (produc2023458740on_val @ A @ B)) @ (transi111096263on_val @ R2)) => ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ A @ B) @ (produc2023458740on_val @ Aa @ Ba)) @ R2) => ((P @ A @ B) => (P @ Aa @ Ba))))) => (P @ Bx @ By))))))). % rtrancl_induct2
thf(fact_70_mem__Collect__eq, axiom,
    ((![A2 : produc1172664615on_val, P : produc1172664615on_val > $o]: ((member354538064on_val @ A2 @ (collec2055896722on_val @ P)) = (P @ A2))))). % mem_Collect_eq
thf(fact_71_Collect__mem__eq, axiom,
    ((![A4 : set_Pr1189492743on_val]: ((collec2055896722on_val @ (^[X4 : produc1172664615on_val]: (member354538064on_val @ X4 @ A4))) = A4)))). % Collect_mem_eq
thf(fact_72_lconf__hext, axiom,
    ((![P : list_P1234162913t_char, H : nat > option2118145160on_val, L : list_char > option_val, E3 : list_char > option_ty, H2 : nat > option2118145160on_val]: ((lconf_485928294t_char @ P @ H @ L @ E3) => ((hext @ H @ H2) => (lconf_485928294t_char @ P @ H2 @ L @ E3)))))). % lconf_hext
thf(fact_73_rtrancl__idemp, axiom,
    ((![R2 : set_Pr1189492743on_val]: ((transi111096263on_val @ (transi111096263on_val @ R2)) = (transi111096263on_val @ R2))))). % rtrancl_idemp
thf(fact_74_r__into__rtrancl, axiom,
    ((![P2 : produc1172664615on_val, R2 : set_Pr1189492743on_val]: ((member354538064on_val @ P2 @ R2) => (member354538064on_val @ P2 @ (transi111096263on_val @ R2)))))). % r_into_rtrancl
thf(fact_75_converse__rtrancl__into__rtrancl, axiom,
    ((![A2 : produc1097884484on_val, B2 : produc1097884484on_val, R2 : set_Pr1189492743on_val, C2 : produc1097884484on_val]: ((member354538064on_val @ (produc1069526295on_val @ A2 @ B2) @ R2) => ((member354538064on_val @ (produc1069526295on_val @ B2 @ C2) @ (transi111096263on_val @ R2)) => (member354538064on_val @ (produc1069526295on_val @ A2 @ C2) @ (transi111096263on_val @ R2))))))). % converse_rtrancl_into_rtrancl
thf(fact_76_rtranclE, axiom,
    ((![A2 : produc1097884484on_val, B2 : produc1097884484on_val, R2 : set_Pr1189492743on_val]: ((member354538064on_val @ (produc1069526295on_val @ A2 @ B2) @ (transi111096263on_val @ R2)) => ((~ ((A2 = B2))) => (~ ((![Y3 : produc1097884484on_val]: ((member354538064on_val @ (produc1069526295on_val @ A2 @ Y3) @ (transi111096263on_val @ R2)) => (~ ((member354538064on_val @ (produc1069526295on_val @ Y3 @ B2) @ R2)))))))))))). % rtranclE
thf(fact_77_rtrancl_Ocases, axiom,
    ((![A1 : produc1097884484on_val, A22 : produc1097884484on_val, R2 : set_Pr1189492743on_val]: ((member354538064on_val @ (produc1069526295on_val @ A1 @ A22) @ (transi111096263on_val @ R2)) => ((~ ((A22 = A1))) => (~ ((![B : produc1097884484on_val]: ((member354538064on_val @ (produc1069526295on_val @ A1 @ B) @ (transi111096263on_val @ R2)) => (~ ((member354538064on_val @ (produc1069526295on_val @ B @ A22) @ R2)))))))))))). % rtrancl.cases
thf(fact_78_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]: (?[C3 : produc1097884484on_val]: (((A1 = A5)) & ((((A22 = C3)) & ((((member354538064on_val @ (produc1069526295on_val @ A5 @ B4) @ (transi111096263on_val @ R2))) & ((member354538064on_val @ (produc1069526295on_val @ B4 @ C3) @ R2)))))))))))))))). % rtrancl.simps
thf(fact_79_rtrancl__trans, axiom,
    ((![X : produc1097884484on_val, Y : produc1097884484on_val, R2 : set_Pr1189492743on_val, Z : produc1097884484on_val]: ((member354538064on_val @ (produc1069526295on_val @ X @ Y) @ (transi111096263on_val @ R2)) => ((member354538064on_val @ (produc1069526295on_val @ Y @ Z) @ (transi111096263on_val @ R2)) => (member354538064on_val @ (produc1069526295on_val @ X @ Z) @ (transi111096263on_val @ R2))))))). % rtrancl_trans
thf(fact_80_rtrancl__induct, axiom,
    ((![A2 : produc1097884484on_val, B2 : produc1097884484on_val, R2 : set_Pr1189492743on_val, P : produc1097884484on_val > $o]: ((member354538064on_val @ (produc1069526295on_val @ A2 @ B2) @ (transi111096263on_val @ R2)) => ((P @ A2) => ((![Y3 : produc1097884484on_val, Z2 : produc1097884484on_val]: ((member354538064on_val @ (produc1069526295on_val @ A2 @ Y3) @ (transi111096263on_val @ R2)) => ((member354538064on_val @ (produc1069526295on_val @ Y3 @ Z2) @ R2) => ((P @ Y3) => (P @ Z2))))) => (P @ B2))))))). % rtrancl_induct
thf(fact_81_rtrancl_Oinducts, axiom,
    ((![X1 : produc1097884484on_val, X2 : produc1097884484on_val, R2 : set_Pr1189492743on_val, P : produc1097884484on_val > produc1097884484on_val > $o]: ((member354538064on_val @ (produc1069526295on_val @ X1 @ X2) @ (transi111096263on_val @ R2)) => ((![A : produc1097884484on_val]: (P @ A @ A)) => ((![A : produc1097884484on_val, B : produc1097884484on_val, C : produc1097884484on_val]: ((member354538064on_val @ (produc1069526295on_val @ A @ B) @ (transi111096263on_val @ R2)) => ((P @ A @ B) => ((member354538064on_val @ (produc1069526295on_val @ B @ C) @ R2) => (P @ A @ C))))) => (P @ X1 @ X2))))))). % rtrancl.inducts
thf(fact_82_converse__rtranclE, axiom,
    ((![X : produc1097884484on_val, Z : produc1097884484on_val, R2 : set_Pr1189492743on_val]: ((member354538064on_val @ (produc1069526295on_val @ X @ Z) @ (transi111096263on_val @ R2)) => ((~ ((X = Z))) => (~ ((![Y3 : produc1097884484on_val]: ((member354538064on_val @ (produc1069526295on_val @ X @ Y3) @ R2) => (~ ((member354538064on_val @ (produc1069526295on_val @ Y3 @ Z) @ (transi111096263on_val @ R2))))))))))))). % converse_rtranclE
thf(fact_83_rtrancl_Ortrancl__refl, axiom,
    ((![A2 : produc1097884484on_val, R2 : set_Pr1189492743on_val]: (member354538064on_val @ (produc1069526295on_val @ A2 @ A2) @ (transi111096263on_val @ R2))))). % rtrancl.rtrancl_refl
thf(fact_84_converse__rtrancl__induct, axiom,
    ((![A2 : produc1097884484on_val, B2 : produc1097884484on_val, R2 : set_Pr1189492743on_val, P : produc1097884484on_val > $o]: ((member354538064on_val @ (produc1069526295on_val @ A2 @ B2) @ (transi111096263on_val @ R2)) => ((P @ B2) => ((![Y3 : produc1097884484on_val, Z2 : produc1097884484on_val]: ((member354538064on_val @ (produc1069526295on_val @ Y3 @ Z2) @ R2) => ((member354538064on_val @ (produc1069526295on_val @ Z2 @ B2) @ (transi111096263on_val @ R2)) => ((P @ Z2) => (P @ Y3))))) => (P @ A2))))))). % converse_rtrancl_induct
thf(fact_85_rtrancl_Ortrancl__into__rtrancl, axiom,
    ((![A2 : produc1097884484on_val, B2 : produc1097884484on_val, R2 : set_Pr1189492743on_val, C2 : produc1097884484on_val]: ((member354538064on_val @ (produc1069526295on_val @ A2 @ B2) @ (transi111096263on_val @ R2)) => ((member354538064on_val @ (produc1069526295on_val @ B2 @ C2) @ R2) => (member354538064on_val @ (produc1069526295on_val @ A2 @ C2) @ (transi111096263on_val @ R2))))))). % rtrancl.rtrancl_into_rtrancl
thf(fact_86_Red__lcl__add, axiom,
    ((![E : exp_list_char, H : nat > option2118145160on_val, L : list_char > option_val, E2 : exp_list_char, H2 : nat > option2118145160on_val, L2 : list_char > option_val, P : list_P1234162913t_char, L_02 : list_char > option_val]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E @ (produc52622304on_val @ H @ L)) @ (produc2023458740on_val @ E2 @ (produc52622304on_val @ H2 @ L2))) @ (transi111096263on_val @ (red @ P))) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E @ (produc52622304on_val @ H @ (map_ad1615113112ar_val @ L_02 @ L))) @ (produc2023458740on_val @ E2 @ (produc52622304on_val @ H2 @ (map_ad1615113112ar_val @ L_02 @ L2)))) @ (transi111096263on_val @ (red @ P))))))). % Red_lcl_add
thf(fact_87_red__lcl__add, axiom,
    ((![E : exp_list_char, H : nat > option2118145160on_val, L : list_char > option_val, E2 : exp_list_char, H2 : nat > option2118145160on_val, L2 : list_char > option_val, P : list_P1234162913t_char, L_02 : list_char > option_val]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E @ (produc52622304on_val @ H @ L)) @ (produc2023458740on_val @ E2 @ (produc52622304on_val @ H2 @ L2))) @ (red @ P)) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E @ (produc52622304on_val @ H @ (map_ad1615113112ar_val @ L_02 @ L))) @ (produc2023458740on_val @ E2 @ (produc52622304on_val @ H2 @ (map_ad1615113112ar_val @ L_02 @ L2)))) @ (red @ P)))))). % red_lcl_add
thf(fact_88_eval__preserves__type, axiom,
    ((![P : list_P1234162913t_char, E : exp_list_char, S2 : produc515445032on_val, E2 : exp_list_char, S3 : produc515445032on_val, E3 : list_char > option_ty, T : ty]: ((wf_pro1229751607t_char @ wf_J_mdecl @ P) => ((eval @ P @ E @ S2 @ E2 @ S3) => ((typeSa1777264139_sconf @ P @ E3 @ S2) => ((wt @ P @ E3 @ E @ T) => (?[T2 : ty]: ((widen_917054840t_char @ P @ T2 @ T) & (wTrt @ P @ (hp @ S3) @ E3 @ E2 @ T2)))))))))). % eval_preserves_type
thf(fact_89_single__valued__confluent, axiom,
    ((![R2 : set_Pr1189492743on_val, X : produc1097884484on_val, Y : produc1097884484on_val, Z : produc1097884484on_val]: ((single747474179on_val @ R2) => ((member354538064on_val @ (produc1069526295on_val @ X @ Y) @ (transi111096263on_val @ R2)) => ((member354538064on_val @ (produc1069526295on_val @ X @ Z) @ (transi111096263on_val @ R2)) => ((member354538064on_val @ (produc1069526295on_val @ Y @ Z) @ (transi111096263on_val @ R2)) | (member354538064on_val @ (produc1069526295on_val @ Z @ Y) @ (transi111096263on_val @ R2))))))))). % single_valued_confluent
thf(fact_90_red__reds_OThrowRed, axiom,
    ((![E : exp_list_char, S2 : produc515445032on_val, E2 : exp_list_char, S3 : produc515445032on_val, P : list_P1234162913t_char]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E @ S2) @ (produc2023458740on_val @ E2 @ S3)) @ (red @ P)) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (throw_list_char @ E) @ S2) @ (produc2023458740on_val @ (throw_list_char @ E2) @ S3)) @ (red @ P)))))). % red_reds.ThrowRed
thf(fact_91_red__reds_OThrowThrow, axiom,
    ((![E : exp_list_char, S2 : produc515445032on_val, P : list_P1234162913t_char]: (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (throw_list_char @ (throw_list_char @ E)) @ S2) @ (produc2023458740on_val @ (throw_list_char @ E) @ S2)) @ (red @ P))))). % red_reds.ThrowThrow
thf(fact_92_WT__implies__WTrt, axiom,
    ((![P : list_P1234162913t_char, E3 : list_char > option_ty, E : exp_list_char, T : ty, H : nat > option2118145160on_val]: ((wt @ P @ E3 @ E @ T) => (wTrt @ P @ H @ E3 @ E @ T))))). % WT_implies_WTrt
thf(fact_93_eval__preserves__sconf, axiom,
    ((![P : list_P1234162913t_char, E : exp_list_char, S2 : produc515445032on_val, E2 : exp_list_char, S3 : produc515445032on_val, E3 : list_char > option_ty, T : ty]: ((wf_pro1229751607t_char @ wf_J_mdecl @ P) => ((eval @ P @ E @ S2 @ E2 @ S3) => ((wt @ P @ E3 @ E @ T) => ((typeSa1777264139_sconf @ P @ E3 @ S2) => (typeSa1777264139_sconf @ P @ E3 @ S3)))))))). % eval_preserves_sconf
thf(fact_94_ThrowRedsThrow, axiom,
    ((![E : exp_list_char, S2 : produc515445032on_val, A2 : exp_list_char, S3 : produc515445032on_val, P : list_P1234162913t_char]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E @ S2) @ (produc2023458740on_val @ (throw_list_char @ A2) @ S3)) @ (transi111096263on_val @ (red @ P))) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (throw_list_char @ E) @ S2) @ (produc2023458740on_val @ (throw_list_char @ A2) @ S3)) @ (transi111096263on_val @ (red @ P))))))). % ThrowRedsThrow
thf(fact_95_ThrowReds, axiom,
    ((![E : exp_list_char, S2 : produc515445032on_val, E2 : exp_list_char, S3 : produc515445032on_val, P : list_P1234162913t_char]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E @ S2) @ (produc2023458740on_val @ E2 @ S3)) @ (transi111096263on_val @ (red @ P))) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (throw_list_char @ E) @ S2) @ (produc2023458740on_val @ (throw_list_char @ E2) @ S3)) @ (transi111096263on_val @ (red @ P))))))). % ThrowReds
thf(fact_96_eval__hext, axiom,
    ((![P : list_P1234162913t_char, E : exp_list_char, H : nat > option2118145160on_val, L : list_char > option_val, E2 : exp_list_char, H2 : nat > option2118145160on_val, L2 : list_char > option_val]: ((eval @ P @ E @ (produc52622304on_val @ H @ L) @ E2 @ (produc52622304on_val @ H2 @ L2)) => (hext @ H @ H2))))). % eval_hext
thf(fact_97_map__add__assoc, axiom,
    ((![M1 : list_char > option_val, M2 : list_char > option_val, M3 : list_char > option_val]: ((map_ad1615113112ar_val @ M1 @ (map_ad1615113112ar_val @ M2 @ M3)) = (map_ad1615113112ar_val @ (map_ad1615113112ar_val @ M1 @ M2) @ M3))))). % map_add_assoc
thf(fact_98_eval__evals_OThrowThrow, axiom,
    ((![P : list_P1234162913t_char, E : exp_list_char, S_0 : produc515445032on_val, E2 : exp_list_char, S_1 : produc515445032on_val]: ((eval @ P @ E @ S_0 @ (throw_list_char @ E2) @ S_1) => (eval @ P @ (throw_list_char @ E) @ S_0 @ (throw_list_char @ E2) @ S_1))))). % eval_evals.ThrowThrow
thf(fact_99_extend__eval, axiom,
    ((![P : list_P1234162913t_char, E : exp_list_char, S2 : produc515445032on_val, E8 : exp_list_char, S5 : produc515445032on_val, E2 : exp_list_char, S3 : produc515445032on_val]: ((wf_pro1229751607t_char @ wwf_J_mdecl @ P) => ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E @ S2) @ (produc2023458740on_val @ E8 @ S5)) @ (transi111096263on_val @ (red @ P))) => ((eval @ P @ E8 @ S5 @ E2 @ S3) => (eval @ P @ E @ S2 @ E2 @ S3))))))). % extend_eval
thf(fact_100_big__by__small, axiom,
    ((![P : list_P1234162913t_char, E : exp_list_char, S2 : produc515445032on_val, E2 : exp_list_char, S3 : produc515445032on_val]: ((wf_pro1229751607t_char @ wwf_J_mdecl @ P) => ((eval @ P @ E @ S2 @ E2 @ S3) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E @ S2) @ (produc2023458740on_val @ E2 @ S3)) @ (transi111096263on_val @ (red @ P)))))))). % big_by_small
thf(fact_101_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_102_extend__1__eval, axiom,
    ((![P : list_P1234162913t_char, E : exp_list_char, S2 : produc515445032on_val, E8 : exp_list_char, S5 : produc515445032on_val, E2 : exp_list_char, S3 : produc515445032on_val]: ((wf_pro1229751607t_char @ wwf_J_mdecl @ P) => ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E @ S2) @ (produc2023458740on_val @ E8 @ S5)) @ (red @ P)) => ((eval @ P @ E8 @ S5 @ E2 @ S3) => (eval @ P @ E @ S2 @ E2 @ S3))))))). % extend_1_eval
thf(fact_103_wf__prog__wwf__prog, axiom,
    ((![P : list_P1234162913t_char]: ((wf_pro1229751607t_char @ wf_J_mdecl @ P) => (wf_pro1229751607t_char @ wwf_J_mdecl @ P))))). % wf_prog_wwf_prog
thf(fact_104_big__iff__small, axiom,
    ((![P : list_P1234162913t_char, E : exp_list_char, S2 : produc515445032on_val, E2 : exp_list_char, S3 : produc515445032on_val]: ((wf_pro1229751607t_char @ wwf_J_mdecl @ P) => ((eval @ P @ E @ S2 @ E2 @ S3) = (((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E @ S2) @ (produc2023458740on_val @ E2 @ S3)) @ (transi111096263on_val @ (red @ P)))) & ((final_list_char @ E2)))))))). % big_iff_small
thf(fact_105_small__by__big, axiom,
    ((![P : list_P1234162913t_char, E : exp_list_char, S2 : produc515445032on_val, E2 : exp_list_char, S3 : produc515445032on_val]: ((wf_pro1229751607t_char @ wwf_J_mdecl @ P) => ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E @ S2) @ (produc2023458740on_val @ E2 @ S3)) @ (transi111096263on_val @ (red @ P))) => ((final_list_char @ E2) => (eval @ P @ E @ S2 @ E2 @ S3))))))). % small_by_big
thf(fact_106_wf__mdecl__wwf__mdecl, axiom,
    ((![P : list_P1234162913t_char, C4 : list_char, Md : produc1259892823t_char]: ((wf_J_mdecl @ P @ C4 @ Md) => (wwf_J_mdecl @ P @ C4 @ Md))))). % wf_mdecl_wwf_mdecl
thf(fact_107_eval__final, axiom,
    ((![P : list_P1234162913t_char, E : exp_list_char, S2 : produc515445032on_val, E2 : exp_list_char, S3 : produc515445032on_val]: ((eval @ P @ E @ S2 @ E2 @ S3) => (final_list_char @ E2))))). % eval_final
thf(fact_108_eval__finalId, axiom,
    ((![E : exp_list_char, P : list_P1234162913t_char, S2 : produc515445032on_val]: ((final_list_char @ E) => (eval @ P @ E @ S2 @ E @ S2))))). % eval_finalId
thf(fact_109_single__valued__def, axiom,
    ((single747474179on_val = (^[R3 : set_Pr1189492743on_val]: (![X4 : produc1097884484on_val]: (![Y5 : produc1097884484on_val]: (((member354538064on_val @ (produc1069526295on_val @ X4 @ Y5) @ R3)) => ((![Z3 : produc1097884484on_val]: (((member354538064on_val @ (produc1069526295on_val @ X4 @ Z3) @ R3)) => ((Y5 = Z3)))))))))))). % single_valued_def
thf(fact_110_single__valued__def, axiom,
    ((single1293603232on_val = (^[R3 : set_Pr556513572on_val]: (![X4 : exp_list_char]: (![Y5 : produc515445032on_val]: (((member1888679917on_val @ (produc2023458740on_val @ X4 @ Y5) @ R3)) => ((![Z3 : produc515445032on_val]: (((member1888679917on_val @ (produc2023458740on_val @ X4 @ Z3) @ R3)) => ((Y5 = Z3)))))))))))). % single_valued_def
thf(fact_111_single__valued__def, axiom,
    ((single2124932044on_val = (^[R3 : set_Pr723149704on_val]: (![X4 : nat > option2118145160on_val]: (![Y5 : list_char > option_val]: (((member652041809on_val @ (produc52622304on_val @ X4 @ Y5) @ R3)) => ((![Z3 : list_char > option_val]: (((member652041809on_val @ (produc52622304on_val @ X4 @ Z3) @ R3)) => ((Y5 = Z3)))))))))))). % single_valued_def
thf(fact_112_single__valuedI, axiom,
    ((![R2 : set_Pr1189492743on_val]: ((![X3 : produc1097884484on_val, Y3 : produc1097884484on_val, Z2 : produc1097884484on_val]: ((member354538064on_val @ (produc1069526295on_val @ X3 @ Y3) @ R2) => ((member354538064on_val @ (produc1069526295on_val @ X3 @ Z2) @ R2) => (Y3 = Z2)))) => (single747474179on_val @ R2))))). % single_valuedI
thf(fact_113_single__valuedI, axiom,
    ((![R2 : set_Pr556513572on_val]: ((![X3 : exp_list_char, Y3 : produc515445032on_val, Z2 : produc515445032on_val]: ((member1888679917on_val @ (produc2023458740on_val @ X3 @ Y3) @ R2) => ((member1888679917on_val @ (produc2023458740on_val @ X3 @ Z2) @ R2) => (Y3 = Z2)))) => (single1293603232on_val @ R2))))). % single_valuedI
thf(fact_114_single__valuedI, axiom,
    ((![R2 : set_Pr723149704on_val]: ((![X3 : nat > option2118145160on_val, Y3 : list_char > option_val, Z2 : list_char > option_val]: ((member652041809on_val @ (produc52622304on_val @ X3 @ Y3) @ R2) => ((member652041809on_val @ (produc52622304on_val @ X3 @ Z2) @ R2) => (Y3 = Z2)))) => (single2124932044on_val @ R2))))). % single_valuedI
thf(fact_115_single__valuedD, axiom,
    ((![R2 : set_Pr1189492743on_val, X : produc1097884484on_val, Y : produc1097884484on_val, Z : produc1097884484on_val]: ((single747474179on_val @ R2) => ((member354538064on_val @ (produc1069526295on_val @ X @ Y) @ R2) => ((member354538064on_val @ (produc1069526295on_val @ X @ Z) @ R2) => (Y = Z))))))). % single_valuedD
thf(fact_116_single__valuedD, axiom,
    ((![R2 : set_Pr556513572on_val, X : exp_list_char, Y : produc515445032on_val, Z : produc515445032on_val]: ((single1293603232on_val @ R2) => ((member1888679917on_val @ (produc2023458740on_val @ X @ Y) @ R2) => ((member1888679917on_val @ (produc2023458740on_val @ X @ Z) @ R2) => (Y = Z))))))). % single_valuedD
thf(fact_117_single__valuedD, axiom,
    ((![R2 : set_Pr723149704on_val, X : nat > option2118145160on_val, Y : list_char > option_val, Z : list_char > option_val]: ((single2124932044on_val @ R2) => ((member652041809on_val @ (produc52622304on_val @ X @ Y) @ R2) => ((member652041809on_val @ (produc52622304on_val @ X @ Z) @ R2) => (Y = Z))))))). % single_valuedD
thf(fact_118_WhileRedsThrow, axiom,
    ((![B2 : exp_list_char, S2 : produc515445032on_val, E : exp_list_char, S3 : produc515445032on_val, P : list_P1234162913t_char, C2 : exp_list_char]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ B2 @ S2) @ (produc2023458740on_val @ (throw_list_char @ E) @ S3)) @ (transi111096263on_val @ (red @ P))) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (while_list_char @ B2 @ C2) @ S2) @ (produc2023458740on_val @ (throw_list_char @ E) @ S3)) @ (transi111096263on_val @ (red @ P))))))). % WhileRedsThrow
thf(fact_119_exp_Odistinct_I205_J, axiom,
    ((![X131 : exp_list_char, X132 : exp_list_char, X14 : exp_list_char]: (~ (((while_list_char @ X131 @ X132) = (throw_list_char @ X14))))))). % exp.distinct(205)
thf(fact_120_WhileCondThrow, axiom,
    ((![P : list_P1234162913t_char, E : exp_list_char, S_0 : produc515445032on_val, E2 : exp_list_char, S_1 : produc515445032on_val, C2 : exp_list_char]: ((eval @ P @ E @ S_0 @ (throw_list_char @ E2) @ S_1) => (eval @ P @ (while_list_char @ E @ C2) @ S_0 @ (throw_list_char @ E2) @ S_1))))). % WhileCondThrow
thf(fact_121_FAccRedsThrow, axiom,
    ((![E : exp_list_char, S2 : produc515445032on_val, A2 : exp_list_char, S3 : produc515445032on_val, P : list_P1234162913t_char, F2 : list_char, D2 : list_char]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E @ S2) @ (produc2023458740on_val @ (throw_list_char @ A2) @ S3)) @ (transi111096263on_val @ (red @ P))) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (fAcc_list_char @ E @ F2 @ D2) @ S2) @ (produc2023458740on_val @ (throw_list_char @ A2) @ S3)) @ (transi111096263on_val @ (red @ P))))))). % FAccRedsThrow
thf(fact_122_CastRedsThrow, axiom,
    ((![E : exp_list_char, S2 : produc515445032on_val, A2 : exp_list_char, S3 : produc515445032on_val, P : list_P1234162913t_char, C4 : list_char]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E @ S2) @ (produc2023458740on_val @ (throw_list_char @ A2) @ S3)) @ (transi111096263on_val @ (red @ P))) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (cast_list_char @ C4 @ E) @ S2) @ (produc2023458740on_val @ (throw_list_char @ A2) @ S3)) @ (transi111096263on_val @ (red @ P))))))). % CastRedsThrow
thf(fact_123_CondRedsThrow, axiom,
    ((![E : exp_list_char, S2 : produc515445032on_val, A2 : exp_list_char, S3 : produc515445032on_val, P : list_P1234162913t_char, E_12 : exp_list_char, E_2 : exp_list_char]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E @ S2) @ (produc2023458740on_val @ (throw_list_char @ A2) @ S3)) @ (transi111096263on_val @ (red @ P))) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (cond_list_char @ E @ E_12 @ E_2) @ S2) @ (produc2023458740on_val @ (throw_list_char @ A2) @ S3)) @ (transi111096263on_val @ (red @ P))))))). % CondRedsThrow
thf(fact_124_exp_Odistinct_I51_J, axiom,
    ((![X21 : list_char, X22 : exp_list_char, X14 : exp_list_char]: (~ (((cast_list_char @ X21 @ X22) = (throw_list_char @ X14))))))). % exp.distinct(51)
thf(fact_125_exp_Odistinct_I151_J, axiom,
    ((![X71 : exp_list_char, X72 : list_char, X73 : list_char, X14 : exp_list_char]: (~ (((fAcc_list_char @ X71 @ X72 @ X73) = (throw_list_char @ X14))))))). % exp.distinct(151)
thf(fact_126_exp_Odistinct_I201_J, axiom,
    ((![X121 : exp_list_char, X122 : exp_list_char, X123 : exp_list_char, X14 : exp_list_char]: (~ (((cond_list_char @ X121 @ X122 @ X123) = (throw_list_char @ X14))))))). % exp.distinct(201)
thf(fact_127_eval__evals_OCondThrow, axiom,
    ((![P : list_P1234162913t_char, E : exp_list_char, S_0 : produc515445032on_val, E2 : exp_list_char, S_1 : produc515445032on_val, E_12 : exp_list_char, E_2 : exp_list_char]: ((eval @ P @ E @ S_0 @ (throw_list_char @ E2) @ S_1) => (eval @ P @ (cond_list_char @ E @ E_12 @ E_2) @ S_0 @ (throw_list_char @ E2) @ S_1))))). % eval_evals.CondThrow
thf(fact_128_eval__evals_OCastThrow, axiom,
    ((![P : list_P1234162913t_char, E : exp_list_char, S_0 : produc515445032on_val, E2 : exp_list_char, S_1 : produc515445032on_val, C4 : list_char]: ((eval @ P @ E @ S_0 @ (throw_list_char @ E2) @ S_1) => (eval @ P @ (cast_list_char @ C4 @ E) @ S_0 @ (throw_list_char @ E2) @ S_1))))). % eval_evals.CastThrow
thf(fact_129_eval__evals_OFAccThrow, axiom,
    ((![P : list_P1234162913t_char, E : exp_list_char, S_0 : produc515445032on_val, E2 : exp_list_char, S_1 : produc515445032on_val, F2 : list_char, D2 : list_char]: ((eval @ P @ E @ S_0 @ (throw_list_char @ E2) @ S_1) => (eval @ P @ (fAcc_list_char @ E @ F2 @ D2) @ S_0 @ (throw_list_char @ E2) @ S_1))))). % eval_evals.FAccThrow
thf(fact_130_red__reds_OCondRed, axiom,
    ((![E : exp_list_char, S2 : produc515445032on_val, E2 : exp_list_char, S3 : produc515445032on_val, P : list_P1234162913t_char, E_12 : exp_list_char, E_2 : exp_list_char]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E @ S2) @ (produc2023458740on_val @ E2 @ S3)) @ (red @ P)) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (cond_list_char @ E @ E_12 @ E_2) @ S2) @ (produc2023458740on_val @ (cond_list_char @ E2 @ E_12 @ E_2) @ S3)) @ (red @ P)))))). % red_reds.CondRed
thf(fact_131_red__reds_OCastRed, axiom,
    ((![E : exp_list_char, S2 : produc515445032on_val, E2 : exp_list_char, S3 : produc515445032on_val, P : list_P1234162913t_char, C4 : list_char]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E @ S2) @ (produc2023458740on_val @ E2 @ S3)) @ (red @ P)) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (cast_list_char @ C4 @ E) @ S2) @ (produc2023458740on_val @ (cast_list_char @ C4 @ E2) @ S3)) @ (red @ P)))))). % red_reds.CastRed
thf(fact_132_red__reds_OFAccRed, axiom,
    ((![E : exp_list_char, S2 : produc515445032on_val, E2 : exp_list_char, S3 : produc515445032on_val, P : list_P1234162913t_char, F2 : list_char, D2 : list_char]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E @ S2) @ (produc2023458740on_val @ E2 @ S3)) @ (red @ P)) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (fAcc_list_char @ E @ F2 @ D2) @ S2) @ (produc2023458740on_val @ (fAcc_list_char @ E2 @ F2 @ D2) @ S3)) @ (red @ P)))))). % red_reds.FAccRed
thf(fact_133_red__reds_OCondThrow, axiom,
    ((![E : exp_list_char, E_12 : exp_list_char, E_2 : exp_list_char, S2 : produc515445032on_val, P : list_P1234162913t_char]: (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (cond_list_char @ (throw_list_char @ E) @ E_12 @ E_2) @ S2) @ (produc2023458740on_val @ (throw_list_char @ E) @ S2)) @ (red @ P))))). % red_reds.CondThrow
thf(fact_134_red__reds_OCastThrow, axiom,
    ((![C4 : list_char, E : exp_list_char, S2 : produc515445032on_val, P : list_P1234162913t_char]: (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (cast_list_char @ C4 @ (throw_list_char @ E)) @ S2) @ (produc2023458740on_val @ (throw_list_char @ E) @ S2)) @ (red @ P))))). % red_reds.CastThrow
thf(fact_135_CondReds, axiom,
    ((![E : exp_list_char, S2 : produc515445032on_val, E2 : exp_list_char, S3 : produc515445032on_val, P : list_P1234162913t_char, E_12 : exp_list_char, E_2 : exp_list_char]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E @ S2) @ (produc2023458740on_val @ E2 @ S3)) @ (transi111096263on_val @ (red @ P))) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (cond_list_char @ E @ E_12 @ E_2) @ S2) @ (produc2023458740on_val @ (cond_list_char @ E2 @ E_12 @ E_2) @ S3)) @ (transi111096263on_val @ (red @ P))))))). % CondReds
thf(fact_136_red__reds_OFAccThrow, axiom,
    ((![E : exp_list_char, F2 : list_char, D2 : list_char, S2 : produc515445032on_val, P : list_P1234162913t_char]: (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (fAcc_list_char @ (throw_list_char @ E) @ F2 @ D2) @ S2) @ (produc2023458740on_val @ (throw_list_char @ E) @ S2)) @ (red @ P))))). % red_reds.FAccThrow
thf(fact_137_CastReds, axiom,
    ((![E : exp_list_char, S2 : produc515445032on_val, E2 : exp_list_char, S3 : produc515445032on_val, P : list_P1234162913t_char, C4 : list_char]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E @ S2) @ (produc2023458740on_val @ E2 @ S3)) @ (transi111096263on_val @ (red @ P))) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (cast_list_char @ C4 @ E) @ S2) @ (produc2023458740on_val @ (cast_list_char @ C4 @ E2) @ S3)) @ (transi111096263on_val @ (red @ P))))))). % CastReds
thf(fact_138_FAccReds, axiom,
    ((![E : exp_list_char, S2 : produc515445032on_val, E2 : exp_list_char, S3 : produc515445032on_val, P : list_P1234162913t_char, F2 : list_char, D2 : list_char]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E @ S2) @ (produc2023458740on_val @ E2 @ S3)) @ (transi111096263on_val @ (red @ P))) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (fAcc_list_char @ E @ F2 @ D2) @ S2) @ (produc2023458740on_val @ (fAcc_list_char @ E2 @ F2 @ D2) @ S3)) @ (transi111096263on_val @ (red @ P))))))). % FAccReds
thf(fact_139_BinOpRedsThrow1, axiom,
    ((![E : exp_list_char, S2 : produc515445032on_val, E2 : exp_list_char, S3 : produc515445032on_val, P : list_P1234162913t_char, Bop : bop, E_2 : exp_list_char]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E @ S2) @ (produc2023458740on_val @ (throw_list_char @ E2) @ S3)) @ (transi111096263on_val @ (red @ P))) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (binOp_list_char @ E @ Bop @ E_2) @ S2) @ (produc2023458740on_val @ (throw_list_char @ E2) @ S3)) @ (transi111096263on_val @ (red @ P))))))). % BinOpRedsThrow1
thf(fact_140_LAssRedsThrow, axiom,
    ((![E : exp_list_char, S2 : produc515445032on_val, A2 : exp_list_char, S3 : produc515445032on_val, P : list_P1234162913t_char, V : list_char]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E @ S2) @ (produc2023458740on_val @ (throw_list_char @ A2) @ S3)) @ (transi111096263on_val @ (red @ P))) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (lAss_list_char @ V @ E) @ S2) @ (produc2023458740on_val @ (throw_list_char @ A2) @ S3)) @ (transi111096263on_val @ (red @ P))))))). % LAssRedsThrow
thf(fact_141_SeqRedsThrow, axiom,
    ((![E : exp_list_char, S2 : produc515445032on_val, E2 : exp_list_char, S3 : produc515445032on_val, P : list_P1234162913t_char, E_2 : exp_list_char]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E @ S2) @ (produc2023458740on_val @ (throw_list_char @ E2) @ S3)) @ (transi111096263on_val @ (red @ P))) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (seq_list_char @ E @ E_2) @ S2) @ (produc2023458740on_val @ (throw_list_char @ E2) @ S3)) @ (transi111096263on_val @ (red @ P))))))). % SeqRedsThrow
thf(fact_142_WTrtSeq, axiom,
    ((![P : list_P1234162913t_char, H : nat > option2118145160on_val, E3 : list_char > option_ty, E_12 : exp_list_char, T_1 : ty, E_2 : exp_list_char, T_2 : ty]: ((wTrt @ P @ H @ E3 @ E_12 @ T_1) => ((wTrt @ P @ H @ E3 @ E_2 @ T_2) => (wTrt @ P @ H @ E3 @ (seq_list_char @ E_12 @ E_2) @ T_2)))))). % WTrtSeq
thf(fact_143_exp_Odistinct_I195_J, axiom,
    ((![X111 : exp_list_char, X112 : exp_list_char, X14 : exp_list_char]: (~ (((seq_list_char @ X111 @ X112) = (throw_list_char @ X14))))))). % exp.distinct(195)
thf(fact_144_exp_Odistinct_I135_J, axiom,
    ((![X61 : list_char, X62 : exp_list_char, X14 : exp_list_char]: (~ (((lAss_list_char @ X61 @ X62) = (throw_list_char @ X14))))))). % exp.distinct(135)
thf(fact_145_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)
thf(fact_146_eval__evals_OSeqThrow, axiom,
    ((![P : list_P1234162913t_char, E_02 : exp_list_char, S_0 : produc515445032on_val, E : exp_list_char, S_1 : produc515445032on_val, E_12 : exp_list_char]: ((eval @ P @ E_02 @ S_0 @ (throw_list_char @ E) @ S_1) => (eval @ P @ (seq_list_char @ E_02 @ E_12) @ S_0 @ (throw_list_char @ E) @ S_1))))). % eval_evals.SeqThrow
thf(fact_147_eval__evals_OLAssThrow, axiom,
    ((![P : list_P1234162913t_char, E : exp_list_char, S_0 : produc515445032on_val, E2 : exp_list_char, S_1 : produc515445032on_val, V : list_char]: ((eval @ P @ E @ S_0 @ (throw_list_char @ E2) @ S_1) => (eval @ P @ (lAss_list_char @ V @ E) @ S_0 @ (throw_list_char @ E2) @ S_1))))). % eval_evals.LAssThrow
thf(fact_148_eval__evals_OBinOpThrow1, axiom,
    ((![P : list_P1234162913t_char, E_12 : exp_list_char, S_0 : produc515445032on_val, E : exp_list_char, S_1 : produc515445032on_val, Bop : bop, E_2 : exp_list_char]: ((eval @ P @ E_12 @ S_0 @ (throw_list_char @ E) @ S_1) => (eval @ P @ (binOp_list_char @ E_12 @ Bop @ E_2) @ S_0 @ (throw_list_char @ E) @ S_1))))). % eval_evals.BinOpThrow1
thf(fact_149_red__reds_OLAssRed, axiom,
    ((![E : exp_list_char, S2 : produc515445032on_val, E2 : exp_list_char, S3 : produc515445032on_val, P : list_P1234162913t_char, V : list_char]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E @ S2) @ (produc2023458740on_val @ E2 @ S3)) @ (red @ P)) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (lAss_list_char @ V @ E) @ S2) @ (produc2023458740on_val @ (lAss_list_char @ V @ E2) @ S3)) @ (red @ P)))))). % red_reds.LAssRed
thf(fact_150_red__reds_OSeqRed, axiom,
    ((![E : exp_list_char, S2 : produc515445032on_val, E2 : exp_list_char, S3 : produc515445032on_val, P : list_P1234162913t_char, E_2 : exp_list_char]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E @ S2) @ (produc2023458740on_val @ E2 @ S3)) @ (red @ P)) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (seq_list_char @ E @ E_2) @ S2) @ (produc2023458740on_val @ (seq_list_char @ E2 @ E_2) @ S3)) @ (red @ P)))))). % red_reds.SeqRed
thf(fact_151_red__reds_OBinOpRed1, axiom,
    ((![E : exp_list_char, S2 : produc515445032on_val, E2 : exp_list_char, S3 : produc515445032on_val, P : list_P1234162913t_char, Bop : bop, E_2 : exp_list_char]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E @ S2) @ (produc2023458740on_val @ E2 @ S3)) @ (red @ P)) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (binOp_list_char @ E @ Bop @ E_2) @ S2) @ (produc2023458740on_val @ (binOp_list_char @ E2 @ Bop @ E_2) @ S3)) @ (red @ P)))))). % red_reds.BinOpRed1
thf(fact_152_red__reds_OLAssThrow, axiom,
    ((![V : list_char, E : exp_list_char, S2 : produc515445032on_val, P : list_P1234162913t_char]: (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (lAss_list_char @ V @ (throw_list_char @ E)) @ S2) @ (produc2023458740on_val @ (throw_list_char @ E) @ S2)) @ (red @ P))))). % red_reds.LAssThrow
thf(fact_153_red__reds_OSeqThrow, axiom,
    ((![E : exp_list_char, E_2 : exp_list_char, S2 : produc515445032on_val, P : list_P1234162913t_char]: (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (seq_list_char @ (throw_list_char @ E) @ E_2) @ S2) @ (produc2023458740on_val @ (throw_list_char @ E) @ S2)) @ (red @ P))))). % red_reds.SeqThrow
thf(fact_154_red__reds_OBinOpThrow1, axiom,
    ((![E : exp_list_char, Bop : bop, E_2 : exp_list_char, S2 : produc515445032on_val, P : list_P1234162913t_char]: (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (binOp_list_char @ (throw_list_char @ E) @ Bop @ E_2) @ S2) @ (produc2023458740on_val @ (throw_list_char @ E) @ S2)) @ (red @ P))))). % red_reds.BinOpThrow1
thf(fact_155_LAssReds, axiom,
    ((![E : exp_list_char, S2 : produc515445032on_val, E2 : exp_list_char, S3 : produc515445032on_val, P : list_P1234162913t_char, V : list_char]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E @ S2) @ (produc2023458740on_val @ E2 @ S3)) @ (transi111096263on_val @ (red @ P))) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (lAss_list_char @ V @ E) @ S2) @ (produc2023458740on_val @ (lAss_list_char @ V @ E2) @ S3)) @ (transi111096263on_val @ (red @ P))))))). % LAssReds
thf(fact_156_SeqReds, axiom,
    ((![E : exp_list_char, S2 : produc515445032on_val, E2 : exp_list_char, S3 : produc515445032on_val, P : list_P1234162913t_char, E_2 : exp_list_char]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E @ S2) @ (produc2023458740on_val @ E2 @ S3)) @ (transi111096263on_val @ (red @ P))) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (seq_list_char @ E @ E_2) @ S2) @ (produc2023458740on_val @ (seq_list_char @ E2 @ E_2) @ S3)) @ (transi111096263on_val @ (red @ P))))))). % SeqReds
thf(fact_157_BinOp1Reds, axiom,
    ((![E : exp_list_char, S2 : produc515445032on_val, E2 : exp_list_char, S3 : produc515445032on_val, P : list_P1234162913t_char, Bop : bop, E_2 : exp_list_char]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E @ S2) @ (produc2023458740on_val @ E2 @ S3)) @ (transi111096263on_val @ (red @ P))) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (binOp_list_char @ E @ Bop @ E_2) @ S2) @ (produc2023458740on_val @ (binOp_list_char @ E2 @ Bop @ E_2) @ S3)) @ (transi111096263on_val @ (red @ P))))))). % BinOp1Reds
thf(fact_158_WTSeq, axiom,
    ((![P : list_P1234162913t_char, E3 : list_char > option_ty, E_12 : exp_list_char, T_1 : ty, E_2 : exp_list_char, T_2 : ty]: ((wt @ P @ E3 @ E_12 @ T_1) => ((wt @ P @ E3 @ E_2 @ T_2) => (wt @ P @ E3 @ (seq_list_char @ E_12 @ E_2) @ T_2)))))). % WTSeq
thf(fact_159_BinOpRedsThrow2, axiom,
    ((![E_12 : exp_list_char, S_0 : produc515445032on_val, V_1 : val, S_1 : produc515445032on_val, P : list_P1234162913t_char, E_2 : exp_list_char, E : exp_list_char, S_2 : produc515445032on_val, Bop : bop]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E_12 @ 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 @ E) @ S_2)) @ (transi111096263on_val @ (red @ P))) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (binOp_list_char @ E_12 @ Bop @ E_2) @ S_0) @ (produc2023458740on_val @ (throw_list_char @ E) @ S_2)) @ (transi111096263on_val @ (red @ P)))))))). % BinOpRedsThrow2
thf(fact_160_exp_Odistinct_I75_J, axiom,
    ((![X32 : val, X14 : exp_list_char]: (~ (((val_list_char @ X32) = (throw_list_char @ X14))))))). % exp.distinct(75)
thf(fact_161_Val, axiom,
    ((![P : list_P1234162913t_char, V2 : val, S2 : produc515445032on_val]: (eval @ P @ (val_list_char @ V2) @ S2 @ (val_list_char @ V2) @ S2)))). % Val
thf(fact_162_eval__cases_I2_J, axiom,
    ((![P : list_P1234162913t_char, V2 : val, S2 : produc515445032on_val, E2 : exp_list_char, S3 : produc515445032on_val]: ((eval @ P @ (val_list_char @ V2) @ S2 @ E2 @ S3) => (~ (((E2 = (val_list_char @ V2)) => (~ ((S3 = S2)))))))))). % eval_cases(2)
thf(fact_163_Seq, axiom,
    ((![P : list_P1234162913t_char, E_02 : exp_list_char, S_0 : produc515445032on_val, V2 : val, S_1 : produc515445032on_val, E_12 : exp_list_char, E_2 : exp_list_char, S_2 : produc515445032on_val]: ((eval @ P @ E_02 @ S_0 @ (val_list_char @ V2) @ S_1) => ((eval @ P @ E_12 @ S_1 @ E_2 @ S_2) => (eval @ P @ (seq_list_char @ E_02 @ E_12) @ S_0 @ E_2 @ S_2)))))). % Seq
thf(fact_164_eval__cases_I9_J, axiom,
    ((![P : list_P1234162913t_char, E_12 : exp_list_char, E_2 : exp_list_char, S2 : produc515445032on_val, E2 : exp_list_char, S3 : produc515445032on_val]: ((eval @ P @ (seq_list_char @ E_12 @ E_2) @ S2 @ E2 @ S3) => ((![V3 : val, S_12 : produc515445032on_val]: ((eval @ P @ E_12 @ S2 @ (val_list_char @ V3) @ S_12) => (~ ((eval @ P @ E_2 @ S_12 @ E2 @ S3))))) => (~ ((![E6 : exp_list_char]: ((E2 = (throw_list_char @ E6)) => (~ ((eval @ P @ E_12 @ S2 @ (throw_list_char @ E6) @ S3)))))))))))). % eval_cases(9)
thf(fact_165_eval__evals_OBinOpThrow2, axiom,
    ((![P : list_P1234162913t_char, E_12 : exp_list_char, S_0 : produc515445032on_val, V_1 : val, S_1 : produc515445032on_val, E_2 : exp_list_char, E : exp_list_char, S_2 : produc515445032on_val, Bop : bop]: ((eval @ P @ E_12 @ S_0 @ (val_list_char @ V_1) @ S_1) => ((eval @ P @ E_2 @ S_1 @ (throw_list_char @ E) @ S_2) => (eval @ P @ (binOp_list_char @ E_12 @ Bop @ E_2) @ S_0 @ (throw_list_char @ E) @ S_2)))))). % eval_evals.BinOpThrow2
thf(fact_166_red__reds_ORedSeq, axiom,
    ((![V2 : val, E_2 : exp_list_char, S2 : produc515445032on_val, P : list_P1234162913t_char]: (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (seq_list_char @ (val_list_char @ V2) @ E_2) @ S2) @ (produc2023458740on_val @ E_2 @ S2)) @ (red @ P))))). % red_reds.RedSeq
thf(fact_167_red__reds_OBinOpRed2, axiom,
    ((![E : exp_list_char, S2 : produc515445032on_val, E2 : exp_list_char, S3 : produc515445032on_val, P : list_P1234162913t_char, V_1 : val, Bop : bop]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E @ S2) @ (produc2023458740on_val @ E2 @ S3)) @ (red @ P)) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (binOp_list_char @ (val_list_char @ V_1) @ Bop @ E) @ S2) @ (produc2023458740on_val @ (binOp_list_char @ (val_list_char @ V_1) @ Bop @ E2) @ S3)) @ (red @ P)))))). % red_reds.BinOpRed2
thf(fact_168_red__reds_OBinOpThrow2, axiom,
    ((![V_1 : val, Bop : bop, E : exp_list_char, S2 : produc515445032on_val, P : list_P1234162913t_char]: (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (binOp_list_char @ (val_list_char @ V_1) @ Bop @ (throw_list_char @ E)) @ S2) @ (produc2023458740on_val @ (throw_list_char @ E) @ S2)) @ (red @ P))))). % red_reds.BinOpThrow2
thf(fact_169_SeqReds2, axiom,
    ((![E_12 : exp_list_char, S_0 : produc515445032on_val, V_1 : val, S_1 : produc515445032on_val, P : list_P1234162913t_char, E_2 : exp_list_char, E_22 : exp_list_char, S_2 : produc515445032on_val]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E_12 @ 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 @ E_22 @ S_2)) @ (transi111096263on_val @ (red @ P))) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (seq_list_char @ E_12 @ E_2) @ S_0) @ (produc2023458740on_val @ E_22 @ S_2)) @ (transi111096263on_val @ (red @ P)))))))). % SeqReds2
thf(fact_170_BinOp2Reds, axiom,
    ((![E : exp_list_char, S2 : produc515445032on_val, E2 : exp_list_char, S3 : produc515445032on_val, P : list_P1234162913t_char, V2 : val, Bop : bop]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E @ S2) @ (produc2023458740on_val @ E2 @ S3)) @ (transi111096263on_val @ (red @ P))) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (binOp_list_char @ (val_list_char @ V2) @ Bop @ E) @ S2) @ (produc2023458740on_val @ (binOp_list_char @ (val_list_char @ V2) @ Bop @ E2) @ S3)) @ (transi111096263on_val @ (red @ P))))))). % BinOp2Reds
thf(fact_171_red__reds_ORedWhile, axiom,
    ((![B2 : exp_list_char, C2 : exp_list_char, S2 : produc515445032on_val, P : list_P1234162913t_char]: (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (while_list_char @ B2 @ C2) @ S2) @ (produc2023458740on_val @ (cond_list_char @ B2 @ (seq_list_char @ C2 @ (while_list_char @ B2 @ C2)) @ (val_list_char @ unit)) @ S2)) @ (red @ P))))). % red_reds.RedWhile
thf(fact_172_WhileTRedsThrow, axiom,
    ((![B2 : exp_list_char, S_0 : produc515445032on_val, S_1 : produc515445032on_val, P : list_P1234162913t_char, C2 : exp_list_char, E : exp_list_char, S_2 : produc515445032on_val]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ B2 @ S_0) @ (produc2023458740on_val @ (val_list_char @ (bool @ $true)) @ S_1)) @ (transi111096263on_val @ (red @ P))) => ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ C2 @ S_1) @ (produc2023458740on_val @ (throw_list_char @ E) @ S_2)) @ (transi111096263on_val @ (red @ P))) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (while_list_char @ B2 @ C2) @ S_0) @ (produc2023458740on_val @ (throw_list_char @ E) @ S_2)) @ (transi111096263on_val @ (red @ P)))))))). % WhileTRedsThrow
thf(fact_173_eval__cases_I11_J, axiom,
    ((![P : list_P1234162913t_char, B2 : exp_list_char, C2 : exp_list_char, S2 : produc515445032on_val, E2 : exp_list_char, S3 : produc515445032on_val]: ((eval @ P @ (while_list_char @ B2 @ C2) @ S2 @ E2 @ S3) => (((E2 = (val_list_char @ unit)) => (~ ((eval @ P @ B2 @ S2 @ (val_list_char @ (bool @ $false)) @ S3)))) => ((![S_12 : produc515445032on_val]: ((eval @ P @ B2 @ S2 @ (val_list_char @ (bool @ $true)) @ S_12) => (![V_12 : val, S_22 : produc515445032on_val]: ((eval @ P @ C2 @ S_12 @ (val_list_char @ V_12) @ S_22) => (~ ((eval @ P @ (while_list_char @ B2 @ C2) @ S_22 @ E2 @ S3))))))) => ((![E7 : exp_list_char]: ((E2 = (throw_list_char @ E7)) => (~ ((eval @ P @ B2 @ S2 @ (throw_list_char @ E7) @ S3))))) => (~ ((![S_12 : produc515445032on_val, E7 : exp_list_char]: ((E2 = (throw_list_char @ E7)) => ((eval @ P @ B2 @ S2 @ (val_list_char @ (bool @ $true)) @ S_12) => (~ ((eval @ P @ C2 @ S_12 @ (throw_list_char @ E7) @ S3))))))))))))))). % eval_cases(11)
thf(fact_174_WhileF, axiom,
    ((![P : list_P1234162913t_char, E : exp_list_char, S_0 : produc515445032on_val, S_1 : produc515445032on_val, C2 : exp_list_char]: ((eval @ P @ E @ S_0 @ (val_list_char @ (bool @ $false)) @ S_1) => (eval @ P @ (while_list_char @ E @ C2) @ S_0 @ (val_list_char @ unit) @ S_1))))). % WhileF
thf(fact_175_WhileFReds, axiom,
    ((![B2 : exp_list_char, S2 : produc515445032on_val, S3 : produc515445032on_val, P : list_P1234162913t_char, C2 : exp_list_char]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ B2 @ S2) @ (produc2023458740on_val @ (val_list_char @ (bool @ $false)) @ S3)) @ (transi111096263on_val @ (red @ P))) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (while_list_char @ B2 @ C2) @ S2) @ (produc2023458740on_val @ (val_list_char @ unit) @ S3)) @ (transi111096263on_val @ (red @ P))))))). % WhileFReds
thf(fact_176_CondF, axiom,
    ((![P : list_P1234162913t_char, E : exp_list_char, S_0 : produc515445032on_val, S_1 : produc515445032on_val, E_2 : exp_list_char, E2 : exp_list_char, S_2 : produc515445032on_val, E_12 : exp_list_char]: ((eval @ P @ E @ S_0 @ (val_list_char @ (bool @ $false)) @ S_1) => ((eval @ P @ E_2 @ S_1 @ E2 @ S_2) => (eval @ P @ (cond_list_char @ E @ E_12 @ E_2) @ S_0 @ E2 @ S_2)))))). % CondF
thf(fact_177_CondT, axiom,
    ((![P : list_P1234162913t_char, E : exp_list_char, S_0 : produc515445032on_val, S_1 : produc515445032on_val, E_12 : exp_list_char, E2 : exp_list_char, S_2 : produc515445032on_val, E_2 : exp_list_char]: ((eval @ P @ E @ S_0 @ (val_list_char @ (bool @ $true)) @ S_1) => ((eval @ P @ E_12 @ S_1 @ E2 @ S_2) => (eval @ P @ (cond_list_char @ E @ E_12 @ E_2) @ S_0 @ E2 @ S_2)))))). % CondT
thf(fact_178_WhileT, axiom,
    ((![P : list_P1234162913t_char, E : exp_list_char, S_0 : produc515445032on_val, S_1 : produc515445032on_val, C2 : exp_list_char, V_1 : val, S_2 : produc515445032on_val, E_3 : exp_list_char, S_3 : produc515445032on_val]: ((eval @ P @ E @ S_0 @ (val_list_char @ (bool @ $true)) @ S_1) => ((eval @ P @ C2 @ S_1 @ (val_list_char @ V_1) @ S_2) => ((eval @ P @ (while_list_char @ E @ C2) @ S_2 @ E_3 @ S_3) => (eval @ P @ (while_list_char @ E @ C2) @ S_0 @ E_3 @ S_3))))))). % WhileT

% Conjectures (3)
thf(conj_0, hypothesis,
    ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ e2 @ s) @ (produc2023458740on_val @ e3 @ s2)) @ (red @ p)))).
thf(conj_1, hypothesis,
    ((typeSa1969945757config @ p @ e @ s @ e2 @ t))).
thf(conj_2, conjecture,
    ((?[T4 : ty]: ((typeSa1969945757config @ p @ e @ s2 @ e3 @ T4) & (widen_917054840t_char @ p @ T4 @ t))))).
