% 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_399__5338670_1 ) ; }
% This file was generated by Isabelle (most likely Sledgehammer)
% 2020-12-16 14:21:31.548

% Could-be-implicit typings (29)
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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__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_J_J, type,
    set_Pr729957319t_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,
    option2118145160on_val : $tType).
thf(ty_n_t__Product____Type__Oprod_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_J, type,
    produc442406631t_char : $tType).
thf(ty_n_t__Set__Oset_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,
    set_Pr2075231726on_val : $tType).
thf(ty_n_t__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, type,
    produc266837688on_val : $tType).
thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_J, type,
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thf(ty_n_t__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J, type,
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thf(ty_n_t__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,
    option_ty : $tType).
thf(ty_n_t__List__Olist_It__String__Ochar_J, type,
    list_char : $tType).
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 (68)
thf(sy_c_BigStep_Oeval, type,
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thf(sy_c_BigStep_Ofinal_001t__List__Olist_It__String__Ochar_J, type,
    final_list_char : exp_list_char > $o).
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_OBlock_001t__List__Olist_It__String__Ochar_J, type,
    block_list_char : list_char > ty > exp_list_char > exp_list_char).
thf(sy_c_Expr_Oexp_OFAcc_001t__List__Olist_It__String__Ochar_J, type,
    fAcc_list_char : exp_list_char > list_char > list_char > exp_list_char).
thf(sy_c_Expr_Oexp_OFAss_001t__List__Olist_It__String__Ochar_J, type,
    fAss_list_char : exp_list_char > list_char > list_char > exp_list_char > exp_list_char).
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_OTryCatch_001t__List__Olist_It__String__Ochar_J, type,
    tryCatch_list_char : exp_list_char > list_char > 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_Othrow_001t__List__Olist_It__String__Ochar_J, type,
    throw_list_char : exp_list_char > exp_list_char).
thf(sy_c_Fun_Ofun__upd_001t__List__Olist_It__String__Ochar_J_001t__Option__Ooption_It__Value__Oval_J, type,
    fun_up1252458416on_val : (list_char > option_val) > list_char > option_val > list_char > option_val).
thf(sy_c_Fun_Ofun__upd_001t__Nat__Onat_001t__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,
    fun_up262443479on_val : (nat > option2118145160on_val) > nat > option2118145160on_val > nat > option2118145160on_val).
thf(sy_c_Fun_Ofun__upd_001t__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_001t__Option__Ooption_It__Value__Oval_J, type,
    fun_up356838326on_val : (produc1257910179t_char > option_val) > produc1257910179t_char > option_val > produc1257910179t_char > option_val).
thf(sy_c_If_001t__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,
    if_opt451925058on_val : $o > option2118145160on_val > option2118145160on_val > option2118145160on_val).
thf(sy_c_If_001t__Option__Ooption_It__Value__Oval_J, type,
    if_option_val : $o > option_val > option_val > option_val).
thf(sy_c_JWellForm_Owf__J__mdecl, type,
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thf(sy_c_member_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_J, type,
    member803902992t_char : produc442406631t_char > set_Pr729957319t_char > $o).
thf(sy_c_member_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__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_C______, type,
    c : list_char).
thf(sy_v_D______, type,
    d : list_char).
thf(sy_v_E____, type,
    e : list_char > option_ty).
thf(sy_v_F______, type,
    f : list_char).
thf(sy_v_P, type,
    p : list_P1234162913t_char).
thf(sy_v_T____, type,
    t : ty).
thf(sy_v_a______, type,
    a : nat).
thf(sy_v_fs______, type,
    fs : produc1257910179t_char > option_val).
thf(sy_v_ha______, type,
    ha : nat > option2118145160on_val).
thf(sy_v_la______, type,
    la : list_char > option_val).
thf(sy_v_v______, type,
    v : val).

% Relevant facts (228)
thf(fact_0_RedFAss_Oprems_I1_J, axiom,
    ((typeSa1777264139_sconf @ p @ e @ (produc52622304on_val @ ha @ la)))). % RedFAss.prems(1)
thf(fact_1_RedFAss_Ohyps, axiom,
    (((ha @ a) = (some_P1299442195on_val @ (produc904988266on_val @ c @ fs))))). % RedFAss.hyps
thf(fact_2_RedFAss_Oprems_I2_J, axiom,
    ((wTrt @ p @ ha @ e @ (fAss_list_char @ (val_list_char @ (addr @ a)) @ f @ d @ (val_list_char @ v)) @ t))). % RedFAss.prems(2)
thf(fact_3_local_Owf, axiom,
    ((wf_pro1229751607t_char @ wf_J_mdecl @ p))). % local.wf
thf(fact_4_fun__upd__upd, axiom,
    ((![F : nat > option2118145160on_val, X : nat, Y : option2118145160on_val, Z : option2118145160on_val]: ((fun_up262443479on_val @ (fun_up262443479on_val @ F @ X @ Y) @ X @ Z) = (fun_up262443479on_val @ F @ X @ Z))))). % fun_upd_upd
thf(fact_5_fun__upd__upd, axiom,
    ((![F : produc1257910179t_char > option_val, X : produc1257910179t_char, Y : option_val, Z : option_val]: ((fun_up356838326on_val @ (fun_up356838326on_val @ F @ X @ Y) @ X @ Z) = (fun_up356838326on_val @ F @ X @ Z))))). % fun_upd_upd
thf(fact_6_fun__upd__upd, axiom,
    ((![F : list_char > option_val, X : list_char, Y : option_val, Z : option_val]: ((fun_up1252458416on_val @ (fun_up1252458416on_val @ F @ X @ Y) @ X @ Z) = (fun_up1252458416on_val @ F @ X @ Z))))). % fun_upd_upd
thf(fact_7_fun__upd__triv, axiom,
    ((![F : nat > option2118145160on_val, X : nat]: ((fun_up262443479on_val @ F @ X @ (F @ X)) = F)))). % fun_upd_triv
thf(fact_8_fun__upd__triv, axiom,
    ((![F : produc1257910179t_char > option_val, X : produc1257910179t_char]: ((fun_up356838326on_val @ F @ X @ (F @ X)) = F)))). % fun_upd_triv
thf(fact_9_fun__upd__triv, axiom,
    ((![F : list_char > option_val, X : list_char]: ((fun_up1252458416on_val @ F @ X @ (F @ X)) = F)))). % fun_upd_triv
thf(fact_10_fun__upd__apply, axiom,
    ((fun_up262443479on_val = (^[F2 : nat > option2118145160on_val]: (^[X2 : nat]: (^[Y2 : option2118145160on_val]: (^[Z2 : nat]: (if_opt451925058on_val @ (Z2 = X2) @ Y2 @ (F2 @ Z2))))))))). % fun_upd_apply
thf(fact_11_fun__upd__apply, axiom,
    ((fun_up356838326on_val = (^[F2 : produc1257910179t_char > option_val]: (^[X2 : produc1257910179t_char]: (^[Y2 : option_val]: (^[Z2 : produc1257910179t_char]: (if_option_val @ (Z2 = X2) @ Y2 @ (F2 @ Z2))))))))). % fun_upd_apply
thf(fact_12_fun__upd__apply, axiom,
    ((fun_up1252458416on_val = (^[F2 : list_char > option_val]: (^[X2 : list_char]: (^[Y2 : option_val]: (^[Z2 : list_char]: (if_option_val @ (Z2 = X2) @ Y2 @ (F2 @ Z2))))))))). % fun_upd_apply
thf(fact_13_exp_Oinject_I3_J, axiom,
    ((![X3 : val, Y3 : val]: (((val_list_char @ X3) = (val_list_char @ Y3)) = (X3 = Y3))))). % exp.inject(3)
thf(fact_14_option_Oinject, axiom,
    ((![X22 : produc266837688on_val, Y22 : produc266837688on_val]: (((some_P1299442195on_val @ X22) = (some_P1299442195on_val @ Y22)) = (X22 = Y22))))). % option.inject
thf(fact_15_option_Oinject, axiom,
    ((![X22 : val, Y22 : val]: (((some_val @ X22) = (some_val @ Y22)) = (X22 = Y22))))). % option.inject
thf(fact_16_prod_Oinject, axiom,
    ((![X1 : list_char, X22 : produc1257910179t_char > option_val, Y1 : list_char, Y22 : produc1257910179t_char > option_val]: (((produc904988266on_val @ X1 @ X22) = (produc904988266on_val @ Y1 @ Y22)) = (((X1 = Y1)) & ((X22 = Y22))))))). % prod.inject
thf(fact_17_prod_Oinject, axiom,
    ((![X1 : list_char, X22 : list_char, Y1 : list_char, Y22 : list_char]: (((produc1304532571t_char @ X1 @ X22) = (produc1304532571t_char @ Y1 @ Y22)) = (((X1 = Y1)) & ((X22 = Y22))))))). % prod.inject
thf(fact_18_prod_Oinject, axiom,
    ((![X1 : nat > option2118145160on_val, X22 : list_char > option_val, Y1 : nat > option2118145160on_val, Y22 : list_char > option_val]: (((produc52622304on_val @ X1 @ X22) = (produc52622304on_val @ Y1 @ Y22)) = (((X1 = Y1)) & ((X22 = Y22))))))). % prod.inject
thf(fact_19_prod_Oinject, axiom,
    ((![X1 : produc1097884484on_val, X22 : produc1097884484on_val, Y1 : produc1097884484on_val, Y22 : produc1097884484on_val]: (((produc1069526295on_val @ X1 @ X22) = (produc1069526295on_val @ Y1 @ Y22)) = (((X1 = Y1)) & ((X22 = Y22))))))). % prod.inject
thf(fact_20_prod_Oinject, axiom,
    ((![X1 : exp_list_char, X22 : produc515445032on_val, Y1 : exp_list_char, Y22 : produc515445032on_val]: (((produc2023458740on_val @ X1 @ X22) = (produc2023458740on_val @ Y1 @ Y22)) = (((X1 = Y1)) & ((X22 = Y22))))))). % prod.inject
thf(fact_21_old_Oprod_Oinject, axiom,
    ((![A : list_char, B : produc1257910179t_char > option_val, A2 : list_char, B2 : produc1257910179t_char > option_val]: (((produc904988266on_val @ A @ B) = (produc904988266on_val @ A2 @ B2)) = (((A = A2)) & ((B = B2))))))). % old.prod.inject
thf(fact_22_old_Oprod_Oinject, axiom,
    ((![A : list_char, B : list_char, A2 : list_char, B2 : list_char]: (((produc1304532571t_char @ A @ B) = (produc1304532571t_char @ A2 @ B2)) = (((A = A2)) & ((B = B2))))))). % old.prod.inject
thf(fact_23_old_Oprod_Oinject, axiom,
    ((![A : nat > option2118145160on_val, B : list_char > option_val, A2 : nat > option2118145160on_val, B2 : list_char > option_val]: (((produc52622304on_val @ A @ B) = (produc52622304on_val @ A2 @ B2)) = (((A = A2)) & ((B = B2))))))). % old.prod.inject
thf(fact_24_old_Oprod_Oinject, axiom,
    ((![A : produc1097884484on_val, B : produc1097884484on_val, A2 : produc1097884484on_val, B2 : produc1097884484on_val]: (((produc1069526295on_val @ A @ B) = (produc1069526295on_val @ A2 @ B2)) = (((A = A2)) & ((B = B2))))))). % old.prod.inject
thf(fact_25_old_Oprod_Oinject, axiom,
    ((![A : exp_list_char, B : produc515445032on_val, A2 : exp_list_char, B2 : produc515445032on_val]: (((produc2023458740on_val @ A @ B) = (produc2023458740on_val @ A2 @ B2)) = (((A = A2)) & ((B = B2))))))). % old.prod.inject
thf(fact_26_map__upd__eqD1, axiom,
    ((![M : nat > option2118145160on_val, A : nat, X : produc266837688on_val, N : nat > option2118145160on_val, Y : produc266837688on_val]: (((fun_up262443479on_val @ M @ A @ (some_P1299442195on_val @ X)) = (fun_up262443479on_val @ N @ A @ (some_P1299442195on_val @ Y))) => (X = Y))))). % map_upd_eqD1
thf(fact_27_map__upd__eqD1, axiom,
    ((![M : produc1257910179t_char > option_val, A : produc1257910179t_char, X : val, N : produc1257910179t_char > option_val, Y : val]: (((fun_up356838326on_val @ M @ A @ (some_val @ X)) = (fun_up356838326on_val @ N @ A @ (some_val @ Y))) => (X = Y))))). % map_upd_eqD1
thf(fact_28_map__upd__eqD1, axiom,
    ((![M : list_char > option_val, A : list_char, X : val, N : list_char > option_val, Y : val]: (((fun_up1252458416on_val @ M @ A @ (some_val @ X)) = (fun_up1252458416on_val @ N @ A @ (some_val @ Y))) => (X = Y))))). % map_upd_eqD1
thf(fact_29_map__upd__triv, axiom,
    ((![T : nat > option2118145160on_val, K : nat, X : produc266837688on_val]: (((T @ K) = (some_P1299442195on_val @ X)) => ((fun_up262443479on_val @ T @ K @ (some_P1299442195on_val @ X)) = T))))). % map_upd_triv
thf(fact_30_map__upd__triv, axiom,
    ((![T : produc1257910179t_char > option_val, K : produc1257910179t_char, X : val]: (((T @ K) = (some_val @ X)) => ((fun_up356838326on_val @ T @ K @ (some_val @ X)) = T))))). % map_upd_triv
thf(fact_31_map__upd__triv, axiom,
    ((![T : list_char > option_val, K : list_char, X : val]: (((T @ K) = (some_val @ X)) => ((fun_up1252458416on_val @ T @ K @ (some_val @ X)) = T))))). % map_upd_triv
thf(fact_32_map__upd__Some__unfold, axiom,
    ((![M : nat > option2118145160on_val, A : nat, B : produc266837688on_val, X : nat, Y : produc266837688on_val]: (((fun_up262443479on_val @ M @ A @ (some_P1299442195on_val @ B) @ X) = (some_P1299442195on_val @ Y)) = (((((X = A)) & ((B = Y)))) | ((((~ ((X = A)))) & (((M @ X) = (some_P1299442195on_val @ Y)))))))))). % map_upd_Some_unfold
thf(fact_33_map__upd__Some__unfold, axiom,
    ((![M : produc1257910179t_char > option_val, A : produc1257910179t_char, B : val, X : produc1257910179t_char, Y : val]: (((fun_up356838326on_val @ M @ A @ (some_val @ B) @ X) = (some_val @ Y)) = (((((X = A)) & ((B = Y)))) | ((((~ ((X = A)))) & (((M @ X) = (some_val @ Y)))))))))). % map_upd_Some_unfold
thf(fact_34_map__upd__Some__unfold, axiom,
    ((![M : list_char > option_val, A : list_char, B : val, X : list_char, Y : val]: (((fun_up1252458416on_val @ M @ A @ (some_val @ B) @ X) = (some_val @ Y)) = (((((X = A)) & ((B = Y)))) | ((((~ ((X = A)))) & (((M @ X) = (some_val @ Y)))))))))). % map_upd_Some_unfold
thf(fact_35_pred__equals__eq2, axiom,
    ((![R : set_Pr2075231726on_val, S : set_Pr2075231726on_val]: (((^[X2 : list_char]: (^[Y2 : produc1257910179t_char > option_val]: (member1296415951on_val @ (produc904988266on_val @ X2 @ Y2) @ R))) = (^[X2 : list_char]: (^[Y2 : produc1257910179t_char > option_val]: (member1296415951on_val @ (produc904988266on_val @ X2 @ Y2) @ S)))) = (R = S))))). % pred_equals_eq2
thf(fact_36_pred__equals__eq2, axiom,
    ((![R : set_Pr164112643t_char, S : set_Pr164112643t_char]: (((^[X2 : list_char]: (^[Y2 : list_char]: (member89690956t_char @ (produc1304532571t_char @ X2 @ Y2) @ R))) = (^[X2 : list_char]: (^[Y2 : list_char]: (member89690956t_char @ (produc1304532571t_char @ X2 @ Y2) @ S)))) = (R = S))))). % pred_equals_eq2
thf(fact_37_pred__equals__eq2, axiom,
    ((![R : set_Pr723149704on_val, S : set_Pr723149704on_val]: (((^[X2 : nat > option2118145160on_val]: (^[Y2 : list_char > option_val]: (member652041809on_val @ (produc52622304on_val @ X2 @ Y2) @ R))) = (^[X2 : nat > option2118145160on_val]: (^[Y2 : list_char > option_val]: (member652041809on_val @ (produc52622304on_val @ X2 @ Y2) @ S)))) = (R = S))))). % pred_equals_eq2
thf(fact_38_pred__equals__eq2, axiom,
    ((![R : set_Pr1189492743on_val, S : set_Pr1189492743on_val]: (((^[X2 : produc1097884484on_val]: (^[Y2 : produc1097884484on_val]: (member354538064on_val @ (produc1069526295on_val @ X2 @ Y2) @ R))) = (^[X2 : produc1097884484on_val]: (^[Y2 : produc1097884484on_val]: (member354538064on_val @ (produc1069526295on_val @ X2 @ Y2) @ S)))) = (R = S))))). % pred_equals_eq2
thf(fact_39_pred__equals__eq2, axiom,
    ((![R : set_Pr556513572on_val, S : set_Pr556513572on_val]: (((^[X2 : exp_list_char]: (^[Y2 : produc515445032on_val]: (member1888679917on_val @ (produc2023458740on_val @ X2 @ Y2) @ R))) = (^[X2 : exp_list_char]: (^[Y2 : produc515445032on_val]: (member1888679917on_val @ (produc2023458740on_val @ X2 @ Y2) @ S)))) = (R = S))))). % pred_equals_eq2
thf(fact_40_exp_Oinject_I8_J, axiom,
    ((![X81 : exp_list_char, X82 : list_char, X83 : list_char, X84 : exp_list_char, Y81 : exp_list_char, Y82 : list_char, Y83 : list_char, Y84 : exp_list_char]: (((fAss_list_char @ X81 @ X82 @ X83 @ X84) = (fAss_list_char @ Y81 @ Y82 @ Y83 @ Y84)) = (((X81 = Y81)) & ((((X82 = Y82)) & ((((X83 = Y83)) & ((X84 = Y84))))))))))). % exp.inject(8)
thf(fact_41_exp_Odistinct_I63_J, axiom,
    ((![X3 : val, X81 : exp_list_char, X82 : list_char, X83 : list_char, X84 : exp_list_char]: (~ (((val_list_char @ X3) = (fAss_list_char @ X81 @ X82 @ X83 @ X84))))))). % exp.distinct(63)
thf(fact_42_old_Oprod_Oinducts, axiom,
    ((![P : produc266837688on_val > $o, Prod : produc266837688on_val]: ((![A3 : list_char, B3 : produc1257910179t_char > option_val]: (P @ (produc904988266on_val @ A3 @ B3))) => (P @ Prod))))). % old.prod.inducts
thf(fact_43_old_Oprod_Oinducts, axiom,
    ((![P : produc1257910179t_char > $o, Prod : produc1257910179t_char]: ((![A3 : list_char, B3 : list_char]: (P @ (produc1304532571t_char @ A3 @ B3))) => (P @ Prod))))). % old.prod.inducts
thf(fact_44_old_Oprod_Oinducts, axiom,
    ((![P : produc515445032on_val > $o, Prod : produc515445032on_val]: ((![A3 : nat > option2118145160on_val, B3 : list_char > option_val]: (P @ (produc52622304on_val @ A3 @ B3))) => (P @ Prod))))). % old.prod.inducts
thf(fact_45_old_Oprod_Oinducts, axiom,
    ((![P : produc1172664615on_val > $o, Prod : produc1172664615on_val]: ((![A3 : produc1097884484on_val, B3 : produc1097884484on_val]: (P @ (produc1069526295on_val @ A3 @ B3))) => (P @ Prod))))). % old.prod.inducts
thf(fact_46_old_Oprod_Oinducts, axiom,
    ((![P : produc1097884484on_val > $o, Prod : produc1097884484on_val]: ((![A3 : exp_list_char, B3 : produc515445032on_val]: (P @ (produc2023458740on_val @ A3 @ B3))) => (P @ Prod))))). % old.prod.inducts
thf(fact_47_old_Oprod_Oexhaust, axiom,
    ((![Y : produc266837688on_val]: (~ ((![A3 : list_char, B3 : produc1257910179t_char > option_val]: (~ ((Y = (produc904988266on_val @ A3 @ B3)))))))))). % old.prod.exhaust
thf(fact_48_old_Oprod_Oexhaust, axiom,
    ((![Y : produc1257910179t_char]: (~ ((![A3 : list_char, B3 : list_char]: (~ ((Y = (produc1304532571t_char @ A3 @ B3)))))))))). % old.prod.exhaust
thf(fact_49_old_Oprod_Oexhaust, axiom,
    ((![Y : produc515445032on_val]: (~ ((![A3 : nat > option2118145160on_val, B3 : list_char > option_val]: (~ ((Y = (produc52622304on_val @ A3 @ B3)))))))))). % old.prod.exhaust
thf(fact_50_old_Oprod_Oexhaust, axiom,
    ((![Y : produc1172664615on_val]: (~ ((![A3 : produc1097884484on_val, B3 : produc1097884484on_val]: (~ ((Y = (produc1069526295on_val @ A3 @ B3)))))))))). % old.prod.exhaust
thf(fact_51_old_Oprod_Oexhaust, axiom,
    ((![Y : produc1097884484on_val]: (~ ((![A3 : exp_list_char, B3 : produc515445032on_val]: (~ ((Y = (produc2023458740on_val @ A3 @ B3)))))))))). % old.prod.exhaust
thf(fact_52_prod__induct4, axiom,
    ((![P : produc1172664615on_val > $o, X : produc1172664615on_val]: ((![A3 : produc1097884484on_val, B3 : exp_list_char, C : nat > option2118145160on_val, D : list_char > option_val]: (P @ (produc1069526295on_val @ A3 @ (produc2023458740on_val @ B3 @ (produc52622304on_val @ C @ D))))) => (P @ X))))). % prod_induct4
thf(fact_53_prod__induct3, axiom,
    ((![P : produc1172664615on_val > $o, X : produc1172664615on_val]: ((![A3 : produc1097884484on_val, B3 : exp_list_char, C : produc515445032on_val]: (P @ (produc1069526295on_val @ A3 @ (produc2023458740on_val @ B3 @ C)))) => (P @ X))))). % prod_induct3
thf(fact_54_prod__induct3, axiom,
    ((![P : produc1097884484on_val > $o, X : produc1097884484on_val]: ((![A3 : exp_list_char, B3 : nat > option2118145160on_val, C : list_char > option_val]: (P @ (produc2023458740on_val @ A3 @ (produc52622304on_val @ B3 @ C)))) => (P @ X))))). % prod_induct3
thf(fact_55_prod__cases4, axiom,
    ((![Y : produc1172664615on_val]: (~ ((![A3 : produc1097884484on_val, B3 : exp_list_char, C : nat > option2118145160on_val, D : list_char > option_val]: (~ ((Y = (produc1069526295on_val @ A3 @ (produc2023458740on_val @ B3 @ (produc52622304on_val @ C @ D)))))))))))). % prod_cases4
thf(fact_56_prod__cases3, axiom,
    ((![Y : produc1172664615on_val]: (~ ((![A3 : produc1097884484on_val, B3 : exp_list_char, C : produc515445032on_val]: (~ ((Y = (produc1069526295on_val @ A3 @ (produc2023458740on_val @ B3 @ C))))))))))). % prod_cases3
thf(fact_57_prod__cases3, axiom,
    ((![Y : produc1097884484on_val]: (~ ((![A3 : exp_list_char, B3 : nat > option2118145160on_val, C : list_char > option_val]: (~ ((Y = (produc2023458740on_val @ A3 @ (produc52622304on_val @ B3 @ C))))))))))). % prod_cases3
thf(fact_58_Pair__inject, axiom,
    ((![A : list_char, B : produc1257910179t_char > option_val, A2 : list_char, B2 : produc1257910179t_char > option_val]: (((produc904988266on_val @ A @ B) = (produc904988266on_val @ A2 @ B2)) => (~ (((A = A2) => (~ ((B = B2)))))))))). % Pair_inject
thf(fact_59_Pair__inject, axiom,
    ((![A : list_char, B : list_char, A2 : list_char, B2 : list_char]: (((produc1304532571t_char @ A @ B) = (produc1304532571t_char @ A2 @ B2)) => (~ (((A = A2) => (~ ((B = B2)))))))))). % Pair_inject
thf(fact_60_Pair__inject, axiom,
    ((![A : nat > option2118145160on_val, B : list_char > option_val, A2 : nat > option2118145160on_val, B2 : list_char > option_val]: (((produc52622304on_val @ A @ B) = (produc52622304on_val @ A2 @ B2)) => (~ (((A = A2) => (~ ((B = B2)))))))))). % Pair_inject
thf(fact_61_Pair__inject, axiom,
    ((![A : produc1097884484on_val, B : produc1097884484on_val, A2 : produc1097884484on_val, B2 : produc1097884484on_val]: (((produc1069526295on_val @ A @ B) = (produc1069526295on_val @ A2 @ B2)) => (~ (((A = A2) => (~ ((B = B2)))))))))). % Pair_inject
thf(fact_62_Pair__inject, axiom,
    ((![A : exp_list_char, B : produc515445032on_val, A2 : exp_list_char, B2 : produc515445032on_val]: (((produc2023458740on_val @ A @ B) = (produc2023458740on_val @ A2 @ B2)) => (~ (((A = A2) => (~ ((B = B2)))))))))). % Pair_inject
thf(fact_63_prod__cases, axiom,
    ((![P : produc266837688on_val > $o, P2 : produc266837688on_val]: ((![A3 : list_char, B3 : produc1257910179t_char > option_val]: (P @ (produc904988266on_val @ A3 @ B3))) => (P @ P2))))). % prod_cases
thf(fact_64_prod__cases, axiom,
    ((![P : produc1257910179t_char > $o, P2 : produc1257910179t_char]: ((![A3 : list_char, B3 : list_char]: (P @ (produc1304532571t_char @ A3 @ B3))) => (P @ P2))))). % prod_cases
thf(fact_65_prod__cases, axiom,
    ((![P : produc515445032on_val > $o, P2 : produc515445032on_val]: ((![A3 : nat > option2118145160on_val, B3 : list_char > option_val]: (P @ (produc52622304on_val @ A3 @ B3))) => (P @ P2))))). % prod_cases
thf(fact_66_prod__cases, axiom,
    ((![P : produc1172664615on_val > $o, P2 : produc1172664615on_val]: ((![A3 : produc1097884484on_val, B3 : produc1097884484on_val]: (P @ (produc1069526295on_val @ A3 @ B3))) => (P @ P2))))). % prod_cases
thf(fact_67_prod__cases, axiom,
    ((![P : produc1097884484on_val > $o, P2 : produc1097884484on_val]: ((![A3 : exp_list_char, B3 : produc515445032on_val]: (P @ (produc2023458740on_val @ A3 @ B3))) => (P @ P2))))). % prod_cases
thf(fact_68_surj__pair, axiom,
    ((![P2 : produc266837688on_val]: (?[X4 : list_char, Y4 : produc1257910179t_char > option_val]: (P2 = (produc904988266on_val @ X4 @ Y4)))))). % surj_pair
thf(fact_69_surj__pair, axiom,
    ((![P2 : produc1257910179t_char]: (?[X4 : list_char, Y4 : list_char]: (P2 = (produc1304532571t_char @ X4 @ Y4)))))). % surj_pair
thf(fact_70_surj__pair, axiom,
    ((![P2 : produc515445032on_val]: (?[X4 : nat > option2118145160on_val, Y4 : list_char > option_val]: (P2 = (produc52622304on_val @ X4 @ Y4)))))). % surj_pair
thf(fact_71_surj__pair, axiom,
    ((![P2 : produc1172664615on_val]: (?[X4 : produc1097884484on_val, Y4 : produc1097884484on_val]: (P2 = (produc1069526295on_val @ X4 @ Y4)))))). % surj_pair
thf(fact_72_surj__pair, axiom,
    ((![P2 : produc1097884484on_val]: (?[X4 : exp_list_char, Y4 : produc515445032on_val]: (P2 = (produc2023458740on_val @ X4 @ Y4)))))). % surj_pair
thf(fact_73_fun__upd__idem__iff, axiom,
    ((![F : nat > option2118145160on_val, X : nat, Y : option2118145160on_val]: (((fun_up262443479on_val @ F @ X @ Y) = F) = ((F @ X) = Y))))). % fun_upd_idem_iff
thf(fact_74_fun__upd__idem__iff, axiom,
    ((![F : produc1257910179t_char > option_val, X : produc1257910179t_char, Y : option_val]: (((fun_up356838326on_val @ F @ X @ Y) = F) = ((F @ X) = Y))))). % fun_upd_idem_iff
thf(fact_75_fun__upd__idem__iff, axiom,
    ((![F : list_char > option_val, X : list_char, Y : option_val]: (((fun_up1252458416on_val @ F @ X @ Y) = F) = ((F @ X) = Y))))). % fun_upd_idem_iff
thf(fact_76_fun__upd__twist, axiom,
    ((![A : nat, C2 : nat, M : nat > option2118145160on_val, B : option2118145160on_val, D2 : option2118145160on_val]: ((~ ((A = C2))) => ((fun_up262443479on_val @ (fun_up262443479on_val @ M @ A @ B) @ C2 @ D2) = (fun_up262443479on_val @ (fun_up262443479on_val @ M @ C2 @ D2) @ A @ B)))))). % fun_upd_twist
thf(fact_77_fun__upd__twist, axiom,
    ((![A : produc1257910179t_char, C2 : produc1257910179t_char, M : produc1257910179t_char > option_val, B : option_val, D2 : option_val]: ((~ ((A = C2))) => ((fun_up356838326on_val @ (fun_up356838326on_val @ M @ A @ B) @ C2 @ D2) = (fun_up356838326on_val @ (fun_up356838326on_val @ M @ C2 @ D2) @ A @ B)))))). % fun_upd_twist
thf(fact_78_fun__upd__twist, axiom,
    ((![A : list_char, C2 : list_char, M : list_char > option_val, B : option_val, D2 : option_val]: ((~ ((A = C2))) => ((fun_up1252458416on_val @ (fun_up1252458416on_val @ M @ A @ B) @ C2 @ D2) = (fun_up1252458416on_val @ (fun_up1252458416on_val @ M @ C2 @ D2) @ A @ B)))))). % fun_upd_twist
thf(fact_79_fun__upd__other, axiom,
    ((![Z : nat, X : nat, F : nat > option2118145160on_val, Y : option2118145160on_val]: ((~ ((Z = X))) => ((fun_up262443479on_val @ F @ X @ Y @ Z) = (F @ Z)))))). % fun_upd_other
thf(fact_80_fun__upd__other, axiom,
    ((![Z : produc1257910179t_char, X : produc1257910179t_char, F : produc1257910179t_char > option_val, Y : option_val]: ((~ ((Z = X))) => ((fun_up356838326on_val @ F @ X @ Y @ Z) = (F @ Z)))))). % fun_upd_other
thf(fact_81_fun__upd__other, axiom,
    ((![Z : list_char, X : list_char, F : list_char > option_val, Y : option_val]: ((~ ((Z = X))) => ((fun_up1252458416on_val @ F @ X @ Y @ Z) = (F @ Z)))))). % fun_upd_other
thf(fact_82_fun__upd__same, axiom,
    ((![F : nat > option2118145160on_val, X : nat, Y : option2118145160on_val]: ((fun_up262443479on_val @ F @ X @ Y @ X) = Y)))). % fun_upd_same
thf(fact_83_fun__upd__same, axiom,
    ((![F : produc1257910179t_char > option_val, X : produc1257910179t_char, Y : option_val]: ((fun_up356838326on_val @ F @ X @ Y @ X) = Y)))). % fun_upd_same
thf(fact_84_fun__upd__same, axiom,
    ((![F : list_char > option_val, X : list_char, Y : option_val]: ((fun_up1252458416on_val @ F @ X @ Y @ X) = Y)))). % fun_upd_same
thf(fact_85_fun__upd__idem, axiom,
    ((![F : nat > option2118145160on_val, X : nat, Y : option2118145160on_val]: (((F @ X) = Y) => ((fun_up262443479on_val @ F @ X @ Y) = F))))). % fun_upd_idem
thf(fact_86_fun__upd__idem, axiom,
    ((![F : produc1257910179t_char > option_val, X : produc1257910179t_char, Y : option_val]: (((F @ X) = Y) => ((fun_up356838326on_val @ F @ X @ Y) = F))))). % fun_upd_idem
thf(fact_87_fun__upd__idem, axiom,
    ((![F : list_char > option_val, X : list_char, Y : option_val]: (((F @ X) = Y) => ((fun_up1252458416on_val @ F @ X @ Y) = F))))). % fun_upd_idem
thf(fact_88_fun__upd__eqD, axiom,
    ((![F : nat > option2118145160on_val, X : nat, Y : option2118145160on_val, G : nat > option2118145160on_val, Z : option2118145160on_val]: (((fun_up262443479on_val @ F @ X @ Y) = (fun_up262443479on_val @ G @ X @ Z)) => (Y = Z))))). % fun_upd_eqD
thf(fact_89_fun__upd__eqD, axiom,
    ((![F : produc1257910179t_char > option_val, X : produc1257910179t_char, Y : option_val, G : produc1257910179t_char > option_val, Z : option_val]: (((fun_up356838326on_val @ F @ X @ Y) = (fun_up356838326on_val @ G @ X @ Z)) => (Y = Z))))). % fun_upd_eqD
thf(fact_90_fun__upd__eqD, axiom,
    ((![F : list_char > option_val, X : list_char, Y : option_val, G : list_char > option_val, Z : option_val]: (((fun_up1252458416on_val @ F @ X @ Y) = (fun_up1252458416on_val @ G @ X @ Z)) => (Y = Z))))). % fun_upd_eqD
thf(fact_91_fun__upd__def, axiom,
    ((fun_up262443479on_val = (^[F2 : nat > option2118145160on_val]: (^[A4 : nat]: (^[B4 : option2118145160on_val]: (^[X2 : nat]: (if_opt451925058on_val @ (X2 = A4) @ B4 @ (F2 @ X2))))))))). % fun_upd_def
thf(fact_92_fun__upd__def, axiom,
    ((fun_up356838326on_val = (^[F2 : produc1257910179t_char > option_val]: (^[A4 : produc1257910179t_char]: (^[B4 : option_val]: (^[X2 : produc1257910179t_char]: (if_option_val @ (X2 = A4) @ B4 @ (F2 @ X2))))))))). % fun_upd_def
thf(fact_93_fun__upd__def, axiom,
    ((fun_up1252458416on_val = (^[F2 : list_char > option_val]: (^[A4 : list_char]: (^[B4 : option_val]: (^[X2 : list_char]: (if_option_val @ (X2 = A4) @ B4 @ (F2 @ X2))))))))). % fun_upd_def
thf(fact_94_val_Oinject_I3_J, axiom,
    ((![X5 : nat, Y5 : nat]: (((addr @ X5) = (addr @ Y5)) = (X5 = Y5))))). % val.inject(3)
thf(fact_95_red__reds_ORedFAss, axiom,
    ((![H : nat > option2118145160on_val, A : nat, C3 : list_char, Fs : produc1257910179t_char > option_val, F3 : list_char, D3 : list_char, V : val, L : list_char > option_val, P : list_P1234162913t_char]: (((H @ A) = (some_P1299442195on_val @ (produc904988266on_val @ C3 @ Fs))) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (fAss_list_char @ (val_list_char @ (addr @ A)) @ F3 @ D3 @ (val_list_char @ V)) @ (produc52622304on_val @ H @ L)) @ (produc2023458740on_val @ (val_list_char @ unit) @ (produc52622304on_val @ (fun_up262443479on_val @ H @ A @ (some_P1299442195on_val @ (produc904988266on_val @ C3 @ (fun_up356838326on_val @ Fs @ (produc1304532571t_char @ F3 @ D3) @ (some_val @ V))))) @ L))) @ (red @ P)))))). % red_reds.RedFAss
thf(fact_96_redp__redsp_ORedFAss, axiom,
    ((![H : nat > option2118145160on_val, A : nat, C3 : list_char, Fs : produc1257910179t_char > option_val, P : list_P1234162913t_char, F3 : list_char, D3 : list_char, V : val, L : list_char > option_val]: (((H @ A) = (some_P1299442195on_val @ (produc904988266on_val @ C3 @ Fs))) => (redp @ P @ (fAss_list_char @ (val_list_char @ (addr @ A)) @ F3 @ D3 @ (val_list_char @ V)) @ (produc52622304on_val @ H @ L) @ (val_list_char @ unit) @ (produc52622304on_val @ (fun_up262443479on_val @ H @ A @ (some_P1299442195on_val @ (produc904988266on_val @ C3 @ (fun_up356838326on_val @ Fs @ (produc1304532571t_char @ F3 @ D3) @ (some_val @ V))))) @ L)))))). % redp_redsp.RedFAss
thf(fact_97_FAss, axiom,
    ((![P : list_P1234162913t_char, E_1 : exp_list_char, S_0 : produc515445032on_val, A : nat, S_1 : produc515445032on_val, E_2 : exp_list_char, V : val, H_2 : nat > option2118145160on_val, L_2 : list_char > option_val, C3 : list_char, Fs : produc1257910179t_char > option_val, Fs2 : produc1257910179t_char > option_val, F3 : list_char, D3 : list_char, H_22 : nat > option2118145160on_val]: ((eval @ P @ E_1 @ S_0 @ (val_list_char @ (addr @ A)) @ S_1) => ((eval @ P @ E_2 @ S_1 @ (val_list_char @ V) @ (produc52622304on_val @ H_2 @ L_2)) => (((H_2 @ A) = (some_P1299442195on_val @ (produc904988266on_val @ C3 @ Fs))) => ((Fs2 = (fun_up356838326on_val @ Fs @ (produc1304532571t_char @ F3 @ D3) @ (some_val @ V))) => ((H_22 = (fun_up262443479on_val @ H_2 @ A @ (some_P1299442195on_val @ (produc904988266on_val @ C3 @ Fs2)))) => (eval @ P @ (fAss_list_char @ E_1 @ F3 @ D3 @ E_2) @ S_0 @ (val_list_char @ unit) @ (produc52622304on_val @ H_22 @ L_2)))))))))). % FAss
thf(fact_98_val_Odistinct_I7_J, axiom,
    ((![X5 : nat]: (~ ((unit = (addr @ X5))))))). % val.distinct(7)
thf(fact_99_mem__Collect__eq, axiom,
    ((![A : produc1172664615on_val, P : produc1172664615on_val > $o]: ((member354538064on_val @ A @ (collec2055896722on_val @ P)) = (P @ A))))). % mem_Collect_eq
thf(fact_100_mem__Collect__eq, axiom,
    ((![A : produc1257910179t_char, P : produc1257910179t_char > $o]: ((member89690956t_char @ A @ (collec768236686t_char @ P)) = (P @ A))))). % mem_Collect_eq
thf(fact_101_Collect__mem__eq, axiom,
    ((![A5 : set_Pr1189492743on_val]: ((collec2055896722on_val @ (^[X2 : produc1172664615on_val]: (member354538064on_val @ X2 @ A5))) = A5)))). % Collect_mem_eq
thf(fact_102_Collect__mem__eq, axiom,
    ((![A5 : set_Pr164112643t_char]: ((collec768236686t_char @ (^[X2 : produc1257910179t_char]: (member89690956t_char @ X2 @ A5))) = A5)))). % Collect_mem_eq
thf(fact_103_FAssRedsVal, axiom,
    ((![E_1 : exp_list_char, S_0 : produc515445032on_val, A : nat, S_1 : produc515445032on_val, P : list_P1234162913t_char, E_2 : exp_list_char, V : val, H_2 : nat > option2118145160on_val, L_2 : list_char > option_val, C3 : list_char, Fs : produc1257910179t_char > option_val, F3 : list_char, D3 : list_char]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E_1 @ S_0) @ (produc2023458740on_val @ (val_list_char @ (addr @ A)) @ S_1)) @ (transi111096263on_val @ (red @ P))) => ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E_2 @ S_1) @ (produc2023458740on_val @ (val_list_char @ V) @ (produc52622304on_val @ H_2 @ L_2))) @ (transi111096263on_val @ (red @ P))) => (((some_P1299442195on_val @ (produc904988266on_val @ C3 @ Fs)) = (H_2 @ A)) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (fAss_list_char @ E_1 @ F3 @ D3 @ E_2) @ S_0) @ (produc2023458740on_val @ (val_list_char @ unit) @ (produc52622304on_val @ (fun_up262443479on_val @ H_2 @ A @ (some_P1299442195on_val @ (produc904988266on_val @ C3 @ (fun_up356838326on_val @ Fs @ (produc1304532571t_char @ F3 @ D3) @ (some_val @ V))))) @ L_2))) @ (transi111096263on_val @ (red @ P))))))))). % FAssRedsVal
thf(fact_104_widen__refl, axiom,
    ((![P : list_P1234162913t_char, T2 : ty]: (widen_917054840t_char @ P @ T2 @ T2)))). % widen_refl
thf(fact_105_widen__trans, axiom,
    ((![P : list_P1234162913t_char, S : ty, U : ty, T2 : ty]: ((widen_917054840t_char @ P @ S @ U) => ((widen_917054840t_char @ P @ U @ T2) => (widen_917054840t_char @ P @ S @ T2)))))). % widen_trans
thf(fact_106_FAssReds1, axiom,
    ((![E : exp_list_char, S2 : produc515445032on_val, E2 : exp_list_char, S3 : produc515445032on_val, P : list_P1234162913t_char, F3 : list_char, D3 : 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 @ (fAss_list_char @ E @ F3 @ D3 @ E_2) @ S2) @ (produc2023458740on_val @ (fAss_list_char @ E2 @ F3 @ D3 @ E_2) @ S3)) @ (transi111096263on_val @ (red @ P))))))). % FAssReds1
thf(fact_107_redp__red__eq, axiom,
    ((redp = (^[P3 : list_P1234162913t_char]: (^[X2 : exp_list_char]: (^[Y2 : produc515445032on_val]: (^[Z2 : exp_list_char]: (^[Aa : produc515445032on_val]: (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ X2 @ Y2) @ (produc2023458740on_val @ Z2 @ Aa)) @ (red @ P3)))))))))). % redp_red_eq
thf(fact_108_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))) => ((![E3 : exp_list_char, H3 : nat > option2118145160on_val, L3 : list_char > option_val]: (R @ E3 @ H3 @ L3 @ E3 @ H3 @ L3)) => ((![E_0 : exp_list_char, H_0 : nat > option2118145160on_val, L_0 : list_char > option_val, E_12 : exp_list_char, H_1 : nat > option2118145160on_val, L_1 : list_char > option_val, E4 : 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_12 @ (produc52622304on_val @ H_1 @ L_1))) @ (red @ P)) => ((R @ E_12 @ H_1 @ L_1 @ E4 @ H4 @ L4) => (R @ E_0 @ H_0 @ L_0 @ E4 @ H4 @ L4)))) => (R @ E @ H @ L @ E2 @ H2 @ L2))))))). % converse_rtrancl_induct_red
thf(fact_109_Val, axiom,
    ((![P : list_P1234162913t_char, V : val, S2 : produc515445032on_val]: (eval @ P @ (val_list_char @ V) @ S2 @ (val_list_char @ V) @ S2)))). % Val
thf(fact_110_eval__cases_I2_J, axiom,
    ((![P : list_P1234162913t_char, V : val, S2 : produc515445032on_val, E2 : exp_list_char, S3 : produc515445032on_val]: ((eval @ P @ (val_list_char @ V) @ S2 @ E2 @ S3) => (~ (((E2 = (val_list_char @ V)) => (~ ((S3 = S2)))))))))). % eval_cases(2)
thf(fact_111_redp__redsp_OFAssRed1, axiom,
    ((![P : list_P1234162913t_char, E : exp_list_char, S2 : produc515445032on_val, E2 : exp_list_char, S3 : produc515445032on_val, F3 : list_char, D3 : list_char, E_2 : exp_list_char]: ((redp @ P @ E @ S2 @ E2 @ S3) => (redp @ P @ (fAss_list_char @ E @ F3 @ D3 @ E_2) @ S2 @ (fAss_list_char @ E2 @ F3 @ D3 @ E_2) @ S3))))). % redp_redsp.FAssRed1
thf(fact_112_red__reds_OFAssRed1, axiom,
    ((![E : exp_list_char, S2 : produc515445032on_val, E2 : exp_list_char, S3 : produc515445032on_val, P : list_P1234162913t_char, F3 : list_char, D3 : 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 @ (fAss_list_char @ E @ F3 @ D3 @ E_2) @ S2) @ (produc2023458740on_val @ (fAss_list_char @ E2 @ F3 @ D3 @ E_2) @ S3)) @ (red @ P)))))). % red_reds.FAssRed1
thf(fact_113_FAssReds2, axiom,
    ((![E : exp_list_char, S2 : produc515445032on_val, E2 : exp_list_char, S3 : produc515445032on_val, P : list_P1234162913t_char, V : val, F3 : list_char, D3 : list_char]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E @ S2) @ (produc2023458740on_val @ E2 @ S3)) @ (transi111096263on_val @ (red @ P))) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (fAss_list_char @ (val_list_char @ V) @ F3 @ D3 @ E) @ S2) @ (produc2023458740on_val @ (fAss_list_char @ (val_list_char @ V) @ F3 @ D3 @ E2) @ S3)) @ (transi111096263on_val @ (red @ P))))))). % FAssReds2
thf(fact_114_redp__redsp_OFAssRed2, axiom,
    ((![P : list_P1234162913t_char, E : exp_list_char, S2 : produc515445032on_val, E2 : exp_list_char, S3 : produc515445032on_val, V : val, F3 : list_char, D3 : list_char]: ((redp @ P @ E @ S2 @ E2 @ S3) => (redp @ P @ (fAss_list_char @ (val_list_char @ V) @ F3 @ D3 @ E) @ S2 @ (fAss_list_char @ (val_list_char @ V) @ F3 @ D3 @ E2) @ S3))))). % redp_redsp.FAssRed2
thf(fact_115_red__reds_OFAssRed2, axiom,
    ((![E : exp_list_char, S2 : produc515445032on_val, E2 : exp_list_char, S3 : produc515445032on_val, P : list_P1234162913t_char, V : val, F3 : list_char, D3 : list_char]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E @ S2) @ (produc2023458740on_val @ E2 @ S3)) @ (red @ P)) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (fAss_list_char @ (val_list_char @ V) @ F3 @ D3 @ E) @ S2) @ (produc2023458740on_val @ (fAss_list_char @ (val_list_char @ V) @ F3 @ D3 @ E2) @ S3)) @ (red @ P)))))). % red_reds.FAssRed2
thf(fact_116_converse__rtrancl__induct2, axiom,
    ((![Ax : list_char, Ay : produc1257910179t_char > option_val, Bx : list_char, By : produc1257910179t_char > option_val, R2 : set_Pr2110063281on_val, P : list_char > (produc1257910179t_char > option_val) > $o]: ((member197592058on_val @ (produc881885833on_val @ (produc904988266on_val @ Ax @ Ay) @ (produc904988266on_val @ Bx @ By)) @ (transi2071064181on_val @ R2)) => ((P @ Bx @ By) => ((![A3 : list_char, B3 : produc1257910179t_char > option_val, Aa2 : list_char, Ba : produc1257910179t_char > option_val]: ((member197592058on_val @ (produc881885833on_val @ (produc904988266on_val @ A3 @ B3) @ (produc904988266on_val @ Aa2 @ Ba)) @ R2) => ((member197592058on_val @ (produc881885833on_val @ (produc904988266on_val @ Aa2 @ Ba) @ (produc904988266on_val @ Bx @ By)) @ (transi2071064181on_val @ R2)) => ((P @ Aa2 @ Ba) => (P @ A3 @ B3))))) => (P @ Ax @ Ay))))))). % converse_rtrancl_induct2
thf(fact_117_converse__rtrancl__induct2, axiom,
    ((![Ax : list_char, Ay : list_char, Bx : list_char, By : list_char, R2 : set_Pr729957319t_char, P : list_char > list_char > $o]: ((member803902992t_char @ (produc395356247t_char @ (produc1304532571t_char @ Ax @ Ay) @ (produc1304532571t_char @ Bx @ By)) @ (transi858104614t_char @ R2)) => ((P @ Bx @ By) => ((![A3 : list_char, B3 : list_char, Aa2 : list_char, Ba : list_char]: ((member803902992t_char @ (produc395356247t_char @ (produc1304532571t_char @ A3 @ B3) @ (produc1304532571t_char @ Aa2 @ Ba)) @ R2) => ((member803902992t_char @ (produc395356247t_char @ (produc1304532571t_char @ Aa2 @ Ba) @ (produc1304532571t_char @ Bx @ By)) @ (transi858104614t_char @ R2)) => ((P @ Aa2 @ Ba) => (P @ A3 @ B3))))) => (P @ Ax @ Ay))))))). % converse_rtrancl_induct2
thf(fact_118_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) => ((![A3 : nat > option2118145160on_val, B3 : list_char > option_val, Aa2 : nat > option2118145160on_val, Ba : list_char > option_val]: ((member2027247312on_val @ (produc2106877847on_val @ (produc52622304on_val @ A3 @ B3) @ (produc52622304on_val @ Aa2 @ Ba)) @ R2) => ((member2027247312on_val @ (produc2106877847on_val @ (produc52622304on_val @ Aa2 @ Ba) @ (produc52622304on_val @ Bx @ By)) @ (transi432893227on_val @ R2)) => ((P @ Aa2 @ Ba) => (P @ A3 @ B3))))) => (P @ Ax @ Ay))))))). % converse_rtrancl_induct2
thf(fact_119_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) => ((![A3 : produc1097884484on_val, B3 : produc1097884484on_val, Aa2 : produc1097884484on_val, Ba : produc1097884484on_val]: ((member208988944on_val @ (produc564964183on_val @ (produc1069526295on_val @ A3 @ B3) @ (produc1069526295on_val @ Aa2 @ Ba)) @ R2) => ((member208988944on_val @ (produc564964183on_val @ (produc1069526295on_val @ Aa2 @ Ba) @ (produc1069526295on_val @ Bx @ By)) @ (transi100378922on_val @ R2)) => ((P @ Aa2 @ Ba) => (P @ A3 @ B3))))) => (P @ Ax @ Ay))))))). % converse_rtrancl_induct2
thf(fact_120_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) => ((![A3 : exp_list_char, B3 : produc515445032on_val, Aa2 : exp_list_char, Ba : produc515445032on_val]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ A3 @ B3) @ (produc2023458740on_val @ Aa2 @ Ba)) @ R2) => ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ Aa2 @ Ba) @ (produc2023458740on_val @ Bx @ By)) @ (transi111096263on_val @ R2)) => ((P @ Aa2 @ Ba) => (P @ A3 @ B3))))) => (P @ Ax @ Ay))))))). % converse_rtrancl_induct2
thf(fact_121_converse__rtranclE2, axiom,
    ((![Xa : list_char, Xb : produc1257910179t_char > option_val, Za : list_char, Zb : produc1257910179t_char > option_val, R2 : set_Pr2110063281on_val]: ((member197592058on_val @ (produc881885833on_val @ (produc904988266on_val @ Xa @ Xb) @ (produc904988266on_val @ Za @ Zb)) @ (transi2071064181on_val @ R2)) => ((~ (((produc904988266on_val @ Xa @ Xb) = (produc904988266on_val @ Za @ Zb)))) => (~ ((![A3 : list_char, B3 : produc1257910179t_char > option_val]: ((member197592058on_val @ (produc881885833on_val @ (produc904988266on_val @ Xa @ Xb) @ (produc904988266on_val @ A3 @ B3)) @ R2) => (~ ((member197592058on_val @ (produc881885833on_val @ (produc904988266on_val @ A3 @ B3) @ (produc904988266on_val @ Za @ Zb)) @ (transi2071064181on_val @ R2))))))))))))). % converse_rtranclE2
thf(fact_122_converse__rtranclE2, axiom,
    ((![Xa : list_char, Xb : list_char, Za : list_char, Zb : list_char, R2 : set_Pr729957319t_char]: ((member803902992t_char @ (produc395356247t_char @ (produc1304532571t_char @ Xa @ Xb) @ (produc1304532571t_char @ Za @ Zb)) @ (transi858104614t_char @ R2)) => ((~ (((produc1304532571t_char @ Xa @ Xb) = (produc1304532571t_char @ Za @ Zb)))) => (~ ((![A3 : list_char, B3 : list_char]: ((member803902992t_char @ (produc395356247t_char @ (produc1304532571t_char @ Xa @ Xb) @ (produc1304532571t_char @ A3 @ B3)) @ R2) => (~ ((member803902992t_char @ (produc395356247t_char @ (produc1304532571t_char @ A3 @ B3) @ (produc1304532571t_char @ Za @ Zb)) @ (transi858104614t_char @ R2))))))))))))). % converse_rtranclE2
thf(fact_123_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)))) => (~ ((![A3 : nat > option2118145160on_val, B3 : list_char > option_val]: ((member2027247312on_val @ (produc2106877847on_val @ (produc52622304on_val @ Xa @ Xb) @ (produc52622304on_val @ A3 @ B3)) @ R2) => (~ ((member2027247312on_val @ (produc2106877847on_val @ (produc52622304on_val @ A3 @ B3) @ (produc52622304on_val @ Za @ Zb)) @ (transi432893227on_val @ R2))))))))))))). % converse_rtranclE2
thf(fact_124_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)))) => (~ ((![A3 : produc1097884484on_val, B3 : produc1097884484on_val]: ((member208988944on_val @ (produc564964183on_val @ (produc1069526295on_val @ Xa @ Xb) @ (produc1069526295on_val @ A3 @ B3)) @ R2) => (~ ((member208988944on_val @ (produc564964183on_val @ (produc1069526295on_val @ A3 @ B3) @ (produc1069526295on_val @ Za @ Zb)) @ (transi100378922on_val @ R2))))))))))))). % converse_rtranclE2
thf(fact_125_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)))) => (~ ((![A3 : exp_list_char, B3 : produc515445032on_val]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ Xa @ Xb) @ (produc2023458740on_val @ A3 @ B3)) @ R2) => (~ ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ A3 @ B3) @ (produc2023458740on_val @ Za @ Zb)) @ (transi111096263on_val @ R2))))))))))))). % converse_rtranclE2
thf(fact_126_rtrancl__induct2, axiom,
    ((![Ax : list_char, Ay : produc1257910179t_char > option_val, Bx : list_char, By : produc1257910179t_char > option_val, R2 : set_Pr2110063281on_val, P : list_char > (produc1257910179t_char > option_val) > $o]: ((member197592058on_val @ (produc881885833on_val @ (produc904988266on_val @ Ax @ Ay) @ (produc904988266on_val @ Bx @ By)) @ (transi2071064181on_val @ R2)) => ((P @ Ax @ Ay) => ((![A3 : list_char, B3 : produc1257910179t_char > option_val, Aa2 : list_char, Ba : produc1257910179t_char > option_val]: ((member197592058on_val @ (produc881885833on_val @ (produc904988266on_val @ Ax @ Ay) @ (produc904988266on_val @ A3 @ B3)) @ (transi2071064181on_val @ R2)) => ((member197592058on_val @ (produc881885833on_val @ (produc904988266on_val @ A3 @ B3) @ (produc904988266on_val @ Aa2 @ Ba)) @ R2) => ((P @ A3 @ B3) => (P @ Aa2 @ Ba))))) => (P @ Bx @ By))))))). % rtrancl_induct2
thf(fact_127_rtrancl__induct2, axiom,
    ((![Ax : list_char, Ay : list_char, Bx : list_char, By : list_char, R2 : set_Pr729957319t_char, P : list_char > list_char > $o]: ((member803902992t_char @ (produc395356247t_char @ (produc1304532571t_char @ Ax @ Ay) @ (produc1304532571t_char @ Bx @ By)) @ (transi858104614t_char @ R2)) => ((P @ Ax @ Ay) => ((![A3 : list_char, B3 : list_char, Aa2 : list_char, Ba : list_char]: ((member803902992t_char @ (produc395356247t_char @ (produc1304532571t_char @ Ax @ Ay) @ (produc1304532571t_char @ A3 @ B3)) @ (transi858104614t_char @ R2)) => ((member803902992t_char @ (produc395356247t_char @ (produc1304532571t_char @ A3 @ B3) @ (produc1304532571t_char @ Aa2 @ Ba)) @ R2) => ((P @ A3 @ B3) => (P @ Aa2 @ Ba))))) => (P @ Bx @ By))))))). % rtrancl_induct2
thf(fact_128_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) => ((![A3 : nat > option2118145160on_val, B3 : list_char > option_val, Aa2 : nat > option2118145160on_val, Ba : list_char > option_val]: ((member2027247312on_val @ (produc2106877847on_val @ (produc52622304on_val @ Ax @ Ay) @ (produc52622304on_val @ A3 @ B3)) @ (transi432893227on_val @ R2)) => ((member2027247312on_val @ (produc2106877847on_val @ (produc52622304on_val @ A3 @ B3) @ (produc52622304on_val @ Aa2 @ Ba)) @ R2) => ((P @ A3 @ B3) => (P @ Aa2 @ Ba))))) => (P @ Bx @ By))))))). % rtrancl_induct2
thf(fact_129_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) => ((![A3 : produc1097884484on_val, B3 : produc1097884484on_val, Aa2 : produc1097884484on_val, Ba : produc1097884484on_val]: ((member208988944on_val @ (produc564964183on_val @ (produc1069526295on_val @ Ax @ Ay) @ (produc1069526295on_val @ A3 @ B3)) @ (transi100378922on_val @ R2)) => ((member208988944on_val @ (produc564964183on_val @ (produc1069526295on_val @ A3 @ B3) @ (produc1069526295on_val @ Aa2 @ Ba)) @ R2) => ((P @ A3 @ B3) => (P @ Aa2 @ Ba))))) => (P @ Bx @ By))))))). % rtrancl_induct2
thf(fact_130_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) => ((![A3 : exp_list_char, B3 : produc515445032on_val, Aa2 : exp_list_char, Ba : produc515445032on_val]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ Ax @ Ay) @ (produc2023458740on_val @ A3 @ B3)) @ (transi111096263on_val @ R2)) => ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ A3 @ B3) @ (produc2023458740on_val @ Aa2 @ Ba)) @ R2) => ((P @ A3 @ B3) => (P @ Aa2 @ Ba))))) => (P @ Bx @ By))))))). % rtrancl_induct2
thf(fact_131_extend__eval, axiom,
    ((![P : list_P1234162913t_char, E : exp_list_char, S2 : produc515445032on_val, E5 : exp_list_char, S4 : 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 @ E5 @ S4)) @ (transi111096263on_val @ (red @ P))) => ((eval @ P @ E5 @ S4 @ E2 @ S3) => (eval @ P @ E @ S2 @ E2 @ S3))))))). % extend_eval
thf(fact_132_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_133_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_134_r__into__rtrancl, axiom,
    ((![P2 : produc1257910179t_char, R2 : set_Pr164112643t_char]: ((member89690956t_char @ P2 @ R2) => (member89690956t_char @ P2 @ (transi1879726366t_char @ R2)))))). % r_into_rtrancl
thf(fact_135_rtrancl__idemp, axiom,
    ((![R2 : set_Pr1189492743on_val]: ((transi111096263on_val @ (transi111096263on_val @ R2)) = (transi111096263on_val @ R2))))). % rtrancl_idemp
thf(fact_136_rtrancl__idemp, axiom,
    ((![R2 : set_Pr164112643t_char]: ((transi1879726366t_char @ (transi1879726366t_char @ R2)) = (transi1879726366t_char @ R2))))). % rtrancl_idemp
thf(fact_137_rtranclE, axiom,
    ((![A : produc1097884484on_val, B : produc1097884484on_val, R2 : set_Pr1189492743on_val]: ((member354538064on_val @ (produc1069526295on_val @ A @ B) @ (transi111096263on_val @ R2)) => ((~ ((A = B))) => (~ ((![Y4 : produc1097884484on_val]: ((member354538064on_val @ (produc1069526295on_val @ A @ Y4) @ (transi111096263on_val @ R2)) => (~ ((member354538064on_val @ (produc1069526295on_val @ Y4 @ B) @ R2)))))))))))). % rtranclE
thf(fact_138_rtranclE, axiom,
    ((![A : list_char, B : list_char, R2 : set_Pr164112643t_char]: ((member89690956t_char @ (produc1304532571t_char @ A @ B) @ (transi1879726366t_char @ R2)) => ((~ ((A = B))) => (~ ((![Y4 : list_char]: ((member89690956t_char @ (produc1304532571t_char @ A @ Y4) @ (transi1879726366t_char @ R2)) => (~ ((member89690956t_char @ (produc1304532571t_char @ Y4 @ B) @ R2)))))))))))). % rtranclE
thf(fact_139_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_140_rtrancl_Ocases, axiom,
    ((![A1 : list_char, A22 : list_char, R2 : set_Pr164112643t_char]: ((member89690956t_char @ (produc1304532571t_char @ A1 @ A22) @ (transi1879726366t_char @ R2)) => ((~ ((A22 = A1))) => (~ ((![B3 : list_char]: ((member89690956t_char @ (produc1304532571t_char @ A1 @ B3) @ (transi1879726366t_char @ R2)) => (~ ((member89690956t_char @ (produc1304532571t_char @ B3 @ A22) @ R2)))))))))))). % rtrancl.cases
thf(fact_141_rtrancl_Osimps, axiom,
    ((![A1 : produc1097884484on_val, A22 : produc1097884484on_val, R2 : set_Pr1189492743on_val]: ((member354538064on_val @ (produc1069526295on_val @ A1 @ A22) @ (transi111096263on_val @ R2)) = (((?[A4 : produc1097884484on_val]: (((A1 = A4)) & ((A22 = A4))))) | ((?[A4 : produc1097884484on_val]: (?[B4 : produc1097884484on_val]: (?[C4 : produc1097884484on_val]: (((A1 = A4)) & ((((A22 = C4)) & ((((member354538064on_val @ (produc1069526295on_val @ A4 @ B4) @ (transi111096263on_val @ R2))) & ((member354538064on_val @ (produc1069526295on_val @ B4 @ C4) @ R2)))))))))))))))). % rtrancl.simps
thf(fact_142_rtrancl_Osimps, axiom,
    ((![A1 : list_char, A22 : list_char, R2 : set_Pr164112643t_char]: ((member89690956t_char @ (produc1304532571t_char @ A1 @ A22) @ (transi1879726366t_char @ R2)) = (((?[A4 : list_char]: (((A1 = A4)) & ((A22 = A4))))) | ((?[A4 : list_char]: (?[B4 : list_char]: (?[C4 : list_char]: (((A1 = A4)) & ((((A22 = C4)) & ((((member89690956t_char @ (produc1304532571t_char @ A4 @ B4) @ (transi1879726366t_char @ R2))) & ((member89690956t_char @ (produc1304532571t_char @ B4 @ C4) @ R2)))))))))))))))). % rtrancl.simps
thf(fact_143_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_144_rtrancl__trans, axiom,
    ((![X : list_char, Y : list_char, R2 : set_Pr164112643t_char, Z : list_char]: ((member89690956t_char @ (produc1304532571t_char @ X @ Y) @ (transi1879726366t_char @ R2)) => ((member89690956t_char @ (produc1304532571t_char @ Y @ Z) @ (transi1879726366t_char @ R2)) => (member89690956t_char @ (produc1304532571t_char @ X @ Z) @ (transi1879726366t_char @ R2))))))). % rtrancl_trans
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) => ((![Y4 : produc1097884484on_val, Z3 : produc1097884484on_val]: ((member354538064on_val @ (produc1069526295on_val @ A @ Y4) @ (transi111096263on_val @ R2)) => ((member354538064on_val @ (produc1069526295on_val @ Y4 @ Z3) @ R2) => ((P @ Y4) => (P @ Z3))))) => (P @ B))))))). % rtrancl_induct
thf(fact_146_rtrancl__induct, axiom,
    ((![A : list_char, B : list_char, R2 : set_Pr164112643t_char, P : list_char > $o]: ((member89690956t_char @ (produc1304532571t_char @ A @ B) @ (transi1879726366t_char @ R2)) => ((P @ A) => ((![Y4 : list_char, Z3 : list_char]: ((member89690956t_char @ (produc1304532571t_char @ A @ Y4) @ (transi1879726366t_char @ R2)) => ((member89690956t_char @ (produc1304532571t_char @ Y4 @ Z3) @ R2) => ((P @ Y4) => (P @ Z3))))) => (P @ B))))))). % rtrancl_induct
thf(fact_147_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)) => ((![A3 : produc1097884484on_val]: (P @ A3 @ A3)) => ((![A3 : produc1097884484on_val, B3 : produc1097884484on_val, C : produc1097884484on_val]: ((member354538064on_val @ (produc1069526295on_val @ A3 @ B3) @ (transi111096263on_val @ R2)) => ((P @ A3 @ B3) => ((member354538064on_val @ (produc1069526295on_val @ B3 @ C) @ R2) => (P @ A3 @ C))))) => (P @ X1 @ X22))))))). % rtrancl.inducts
thf(fact_148_rtrancl_Oinducts, axiom,
    ((![X1 : list_char, X22 : list_char, R2 : set_Pr164112643t_char, P : list_char > list_char > $o]: ((member89690956t_char @ (produc1304532571t_char @ X1 @ X22) @ (transi1879726366t_char @ R2)) => ((![A3 : list_char]: (P @ A3 @ A3)) => ((![A3 : list_char, B3 : list_char, C : list_char]: ((member89690956t_char @ (produc1304532571t_char @ A3 @ B3) @ (transi1879726366t_char @ R2)) => ((P @ A3 @ B3) => ((member89690956t_char @ (produc1304532571t_char @ B3 @ C) @ R2) => (P @ A3 @ C))))) => (P @ X1 @ X22))))))). % rtrancl.inducts
thf(fact_149_converse__rtranclE, axiom,
    ((![X : produc1097884484on_val, Z : produc1097884484on_val, R2 : set_Pr1189492743on_val]: ((member354538064on_val @ (produc1069526295on_val @ X @ Z) @ (transi111096263on_val @ R2)) => ((~ ((X = Z))) => (~ ((![Y4 : produc1097884484on_val]: ((member354538064on_val @ (produc1069526295on_val @ X @ Y4) @ R2) => (~ ((member354538064on_val @ (produc1069526295on_val @ Y4 @ Z) @ (transi111096263on_val @ R2))))))))))))). % converse_rtranclE
thf(fact_150_converse__rtranclE, axiom,
    ((![X : list_char, Z : list_char, R2 : set_Pr164112643t_char]: ((member89690956t_char @ (produc1304532571t_char @ X @ Z) @ (transi1879726366t_char @ R2)) => ((~ ((X = Z))) => (~ ((![Y4 : list_char]: ((member89690956t_char @ (produc1304532571t_char @ X @ Y4) @ R2) => (~ ((member89690956t_char @ (produc1304532571t_char @ Y4 @ Z) @ (transi1879726366t_char @ R2))))))))))))). % converse_rtranclE
thf(fact_151_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_152_rtrancl_Ortrancl__refl, axiom,
    ((![A : list_char, R2 : set_Pr164112643t_char]: (member89690956t_char @ (produc1304532571t_char @ A @ A) @ (transi1879726366t_char @ R2))))). % rtrancl.rtrancl_refl
thf(fact_153_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) => ((![Y4 : produc1097884484on_val, Z3 : produc1097884484on_val]: ((member354538064on_val @ (produc1069526295on_val @ Y4 @ Z3) @ R2) => ((member354538064on_val @ (produc1069526295on_val @ Z3 @ B) @ (transi111096263on_val @ R2)) => ((P @ Z3) => (P @ Y4))))) => (P @ A))))))). % converse_rtrancl_induct
thf(fact_154_converse__rtrancl__induct, axiom,
    ((![A : list_char, B : list_char, R2 : set_Pr164112643t_char, P : list_char > $o]: ((member89690956t_char @ (produc1304532571t_char @ A @ B) @ (transi1879726366t_char @ R2)) => ((P @ B) => ((![Y4 : list_char, Z3 : list_char]: ((member89690956t_char @ (produc1304532571t_char @ Y4 @ Z3) @ R2) => ((member89690956t_char @ (produc1304532571t_char @ Z3 @ B) @ (transi1879726366t_char @ R2)) => ((P @ Z3) => (P @ Y4))))) => (P @ A))))))). % converse_rtrancl_induct
thf(fact_155_rtrancl_Ortrancl__into__rtrancl, axiom,
    ((![A : produc1097884484on_val, B : produc1097884484on_val, R2 : set_Pr1189492743on_val, C2 : produc1097884484on_val]: ((member354538064on_val @ (produc1069526295on_val @ A @ B) @ (transi111096263on_val @ R2)) => ((member354538064on_val @ (produc1069526295on_val @ B @ C2) @ R2) => (member354538064on_val @ (produc1069526295on_val @ A @ C2) @ (transi111096263on_val @ R2))))))). % rtrancl.rtrancl_into_rtrancl
thf(fact_156_rtrancl_Ortrancl__into__rtrancl, axiom,
    ((![A : list_char, B : list_char, R2 : set_Pr164112643t_char, C2 : list_char]: ((member89690956t_char @ (produc1304532571t_char @ A @ B) @ (transi1879726366t_char @ R2)) => ((member89690956t_char @ (produc1304532571t_char @ B @ C2) @ R2) => (member89690956t_char @ (produc1304532571t_char @ A @ C2) @ (transi1879726366t_char @ R2))))))). % rtrancl.rtrancl_into_rtrancl
thf(fact_157_converse__rtrancl__into__rtrancl, axiom,
    ((![A : produc1097884484on_val, B : produc1097884484on_val, R2 : set_Pr1189492743on_val, C2 : produc1097884484on_val]: ((member354538064on_val @ (produc1069526295on_val @ A @ B) @ R2) => ((member354538064on_val @ (produc1069526295on_val @ B @ C2) @ (transi111096263on_val @ R2)) => (member354538064on_val @ (produc1069526295on_val @ A @ C2) @ (transi111096263on_val @ R2))))))). % converse_rtrancl_into_rtrancl
thf(fact_158_converse__rtrancl__into__rtrancl, axiom,
    ((![A : list_char, B : list_char, R2 : set_Pr164112643t_char, C2 : list_char]: ((member89690956t_char @ (produc1304532571t_char @ A @ B) @ R2) => ((member89690956t_char @ (produc1304532571t_char @ B @ C2) @ (transi1879726366t_char @ R2)) => (member89690956t_char @ (produc1304532571t_char @ A @ C2) @ (transi1879726366t_char @ R2))))))). % converse_rtrancl_into_rtrancl
thf(fact_159_extend__1__eval, axiom,
    ((![P : list_P1234162913t_char, E : exp_list_char, S2 : produc515445032on_val, E5 : exp_list_char, S4 : 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 @ E5 @ S4)) @ (red @ P)) => ((eval @ P @ E5 @ S4 @ E2 @ S3) => (eval @ P @ E @ S2 @ E2 @ S3))))))). % extend_1_eval
thf(fact_160_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_161_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_162_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_163_wf__mdecl__wwf__mdecl, axiom,
    ((![P : list_P1234162913t_char, C3 : list_char, Md : produc1259892823t_char]: ((wf_J_mdecl @ P @ C3 @ Md) => (wwf_J_mdecl @ P @ C3 @ Md))))). % wf_mdecl_wwf_mdecl
thf(fact_164_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_165_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_166_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, E6 : list_char > option_ty, T2 : ty]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E @ (produc52622304on_val @ H @ L)) @ (produc2023458740on_val @ E2 @ (produc52622304on_val @ H2 @ L2))) @ (red @ P)) => ((wTrt @ P @ H @ E6 @ E @ T2) => ((hconf_1244167010t_char @ P @ H) => (hconf_1244167010t_char @ P @ H2))))))). % red_preserves_hconf
thf(fact_167_FAcc, axiom,
    ((![P : list_P1234162913t_char, E : exp_list_char, S_0 : produc515445032on_val, A : nat, H : nat > option2118145160on_val, L : list_char > option_val, C3 : list_char, Fs : produc1257910179t_char > option_val, F3 : list_char, D3 : list_char, V : val]: ((eval @ P @ E @ S_0 @ (val_list_char @ (addr @ A)) @ (produc52622304on_val @ H @ L)) => (((H @ A) = (some_P1299442195on_val @ (produc904988266on_val @ C3 @ Fs))) => (((Fs @ (produc1304532571t_char @ F3 @ D3)) = (some_val @ V)) => (eval @ P @ (fAcc_list_char @ E @ F3 @ D3) @ S_0 @ (val_list_char @ V) @ (produc52622304on_val @ H @ L)))))))). % FAcc
thf(fact_168_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, E6 : list_char > option_ty, T2 : ty]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E @ (produc52622304on_val @ H @ L)) @ (produc2023458740on_val @ E2 @ (produc52622304on_val @ H2 @ L2))) @ (red @ P)) => ((wTrt @ P @ H @ E6 @ E @ T2) => ((lconf_485928294t_char @ P @ H @ L @ E6) => (lconf_485928294t_char @ P @ H2 @ L2 @ E6))))))). % red_preserves_lconf
thf(fact_169_red__preserves__sconf, axiom,
    ((![E : exp_list_char, S2 : produc515445032on_val, E2 : exp_list_char, S3 : produc515445032on_val, P : list_P1234162913t_char, E6 : list_char > option_ty, T2 : ty]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E @ S2) @ (produc2023458740on_val @ E2 @ S3)) @ (red @ P)) => ((wTrt @ P @ (hp @ S2) @ E6 @ E @ T2) => ((typeSa1777264139_sconf @ P @ E6 @ S2) => (typeSa1777264139_sconf @ P @ E6 @ S3))))))). % red_preserves_sconf
thf(fact_170_exp_Oinject_I7_J, axiom,
    ((![X71 : exp_list_char, X72 : list_char, X73 : list_char, Y71 : exp_list_char, Y72 : list_char, Y73 : list_char]: (((fAcc_list_char @ X71 @ X72 @ X73) = (fAcc_list_char @ Y71 @ Y72 @ Y73)) = (((X71 = Y71)) & ((((X72 = Y72)) & ((X73 = Y73))))))))). % exp.inject(7)
thf(fact_171_exp_Odistinct_I139_J, axiom,
    ((![X71 : exp_list_char, X72 : list_char, X73 : list_char, X81 : exp_list_char, X82 : list_char, X83 : list_char, X84 : exp_list_char]: (~ (((fAcc_list_char @ X71 @ X72 @ X73) = (fAss_list_char @ X81 @ X82 @ X83 @ X84))))))). % exp.distinct(139)
thf(fact_172_exp_Odistinct_I61_J, axiom,
    ((![X3 : val, X71 : exp_list_char, X72 : list_char, X73 : list_char]: (~ (((val_list_char @ X3) = (fAcc_list_char @ X71 @ X72 @ X73))))))). % exp.distinct(61)
thf(fact_173_redp__redsp_OFAccRed, axiom,
    ((![P : list_P1234162913t_char, E : exp_list_char, S2 : produc515445032on_val, E2 : exp_list_char, S3 : produc515445032on_val, F3 : list_char, D3 : list_char]: ((redp @ P @ E @ S2 @ E2 @ S3) => (redp @ P @ (fAcc_list_char @ E @ F3 @ D3) @ S2 @ (fAcc_list_char @ E2 @ F3 @ D3) @ S3))))). % redp_redsp.FAccRed
thf(fact_174_red__reds_OFAccRed, axiom,
    ((![E : exp_list_char, S2 : produc515445032on_val, E2 : exp_list_char, S3 : produc515445032on_val, P : list_P1234162913t_char, F3 : list_char, D3 : 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 @ F3 @ D3) @ S2) @ (produc2023458740on_val @ (fAcc_list_char @ E2 @ F3 @ D3) @ S3)) @ (red @ P)))))). % red_reds.FAccRed
thf(fact_175_FAccReds, axiom,
    ((![E : exp_list_char, S2 : produc515445032on_val, E2 : exp_list_char, S3 : produc515445032on_val, P : list_P1234162913t_char, F3 : list_char, D3 : 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 @ F3 @ D3) @ S2) @ (produc2023458740on_val @ (fAcc_list_char @ E2 @ F3 @ D3) @ S3)) @ (transi111096263on_val @ (red @ P))))))). % FAccReds
thf(fact_176_redp__redsp_ORedFAcc, axiom,
    ((![S2 : produc515445032on_val, A : nat, C3 : list_char, Fs : produc1257910179t_char > option_val, F3 : list_char, D3 : list_char, V : val, P : list_P1234162913t_char]: (((hp @ S2 @ A) = (some_P1299442195on_val @ (produc904988266on_val @ C3 @ Fs))) => (((Fs @ (produc1304532571t_char @ F3 @ D3)) = (some_val @ V)) => (redp @ P @ (fAcc_list_char @ (val_list_char @ (addr @ A)) @ F3 @ D3) @ S2 @ (val_list_char @ V) @ S2)))))). % redp_redsp.RedFAcc
thf(fact_177_red__reds_ORedFAcc, axiom,
    ((![S2 : produc515445032on_val, A : nat, C3 : list_char, Fs : produc1257910179t_char > option_val, F3 : list_char, D3 : list_char, V : val, P : list_P1234162913t_char]: (((hp @ S2 @ A) = (some_P1299442195on_val @ (produc904988266on_val @ C3 @ Fs))) => (((Fs @ (produc1304532571t_char @ F3 @ D3)) = (some_val @ V)) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (fAcc_list_char @ (val_list_char @ (addr @ A)) @ F3 @ D3) @ S2) @ (produc2023458740on_val @ (val_list_char @ V) @ S2)) @ (red @ P))))))). % red_reds.RedFAcc
thf(fact_178_FAccRedsVal, axiom,
    ((![E : exp_list_char, S2 : produc515445032on_val, A : nat, S3 : produc515445032on_val, P : list_P1234162913t_char, C3 : list_char, Fs : produc1257910179t_char > option_val, F3 : list_char, D3 : list_char, V : val]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E @ S2) @ (produc2023458740on_val @ (val_list_char @ (addr @ A)) @ S3)) @ (transi111096263on_val @ (red @ P))) => (((hp @ S3 @ A) = (some_P1299442195on_val @ (produc904988266on_val @ C3 @ Fs))) => (((Fs @ (produc1304532571t_char @ F3 @ D3)) = (some_val @ V)) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (fAcc_list_char @ E @ F3 @ D3) @ S2) @ (produc2023458740on_val @ (val_list_char @ V) @ S3)) @ (transi111096263on_val @ (red @ P))))))))). % FAccRedsVal
thf(fact_179_LAssRedsVal, axiom,
    ((![E : exp_list_char, S2 : produc515445032on_val, V : val, H2 : nat > option2118145160on_val, L2 : list_char > option_val, P : list_P1234162913t_char, V2 : list_char]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E @ S2) @ (produc2023458740on_val @ (val_list_char @ V) @ (produc52622304on_val @ H2 @ L2))) @ (transi111096263on_val @ (red @ P))) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (lAss_list_char @ V2 @ E) @ S2) @ (produc2023458740on_val @ (val_list_char @ unit) @ (produc52622304on_val @ H2 @ (fun_up1252458416on_val @ L2 @ V2 @ (some_val @ V))))) @ (transi111096263on_val @ (red @ P))))))). % LAssRedsVal
thf(fact_180_red__reds_ORedLAss, axiom,
    ((![V2 : list_char, V : val, H : nat > option2118145160on_val, L : list_char > option_val, P : list_P1234162913t_char]: (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (lAss_list_char @ V2 @ (val_list_char @ V)) @ (produc52622304on_val @ H @ L)) @ (produc2023458740on_val @ (val_list_char @ unit) @ (produc52622304on_val @ H @ (fun_up1252458416on_val @ L @ V2 @ (some_val @ V))))) @ (red @ P))))). % red_reds.RedLAss
thf(fact_181_FAssRedsThrow2, axiom,
    ((![E_1 : exp_list_char, S_0 : produc515445032on_val, V : val, S_1 : produc515445032on_val, P : list_P1234162913t_char, E_2 : exp_list_char, E : exp_list_char, S_2 : produc515445032on_val, F3 : list_char, D3 : list_char]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E_1 @ S_0) @ (produc2023458740on_val @ (val_list_char @ V) @ 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 @ (fAss_list_char @ E_1 @ F3 @ D3 @ E_2) @ S_0) @ (produc2023458740on_val @ (throw_list_char @ E) @ S_2)) @ (transi111096263on_val @ (red @ P)))))))). % FAssRedsThrow2
thf(fact_182_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_183_exp_Oinject_I6_J, axiom,
    ((![X61 : list_char, X62 : exp_list_char, Y61 : list_char, Y62 : exp_list_char]: (((lAss_list_char @ X61 @ X62) = (lAss_list_char @ Y61 @ Y62)) = (((X61 = Y61)) & ((X62 = Y62))))))). % exp.inject(6)
thf(fact_184_exp_Odistinct_I121_J, axiom,
    ((![X61 : list_char, X62 : exp_list_char, X71 : exp_list_char, X72 : list_char, X73 : list_char]: (~ (((lAss_list_char @ X61 @ X62) = (fAcc_list_char @ X71 @ X72 @ X73))))))). % exp.distinct(121)
thf(fact_185_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_186_redp__redsp_OLAssRed, axiom,
    ((![P : list_P1234162913t_char, E : exp_list_char, S2 : produc515445032on_val, E2 : exp_list_char, S3 : produc515445032on_val, V2 : list_char]: ((redp @ P @ E @ S2 @ E2 @ S3) => (redp @ P @ (lAss_list_char @ V2 @ E) @ S2 @ (lAss_list_char @ V2 @ E2) @ S3))))). % redp_redsp.LAssRed
thf(fact_187_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_188_exp_Odistinct_I75_J, axiom,
    ((![X3 : val, X14 : exp_list_char]: (~ (((val_list_char @ X3) = (throw_list_char @ X14))))))). % exp.distinct(75)
thf(fact_189_exp_Odistinct_I59_J, axiom,
    ((![X3 : val, X61 : list_char, X62 : exp_list_char]: (~ (((val_list_char @ X3) = (lAss_list_char @ X61 @ X62))))))). % exp.distinct(59)
thf(fact_190_redp__redsp_OThrowRed, axiom,
    ((![P : list_P1234162913t_char, E : exp_list_char, S2 : produc515445032on_val, E2 : exp_list_char, S3 : produc515445032on_val]: ((redp @ P @ E @ S2 @ E2 @ S3) => (redp @ P @ (throw_list_char @ E) @ S2 @ (throw_list_char @ E2) @ S3))))). % redp_redsp.ThrowRed
thf(fact_191_redp__redsp_OThrowThrow, axiom,
    ((![P : list_P1234162913t_char, E : exp_list_char, S2 : produc515445032on_val]: (redp @ P @ (throw_list_char @ (throw_list_char @ E)) @ S2 @ (throw_list_char @ E) @ S2)))). % redp_redsp.ThrowThrow
thf(fact_192_exp_Odistinct_I165_J, axiom,
    ((![X81 : exp_list_char, X82 : list_char, X83 : list_char, X84 : exp_list_char, X14 : exp_list_char]: (~ (((fAss_list_char @ X81 @ X82 @ X83 @ X84) = (throw_list_char @ X14))))))). % exp.distinct(165)
thf(fact_193_exp_Odistinct_I123_J, axiom,
    ((![X61 : list_char, X62 : exp_list_char, X81 : exp_list_char, X82 : list_char, X83 : list_char, X84 : exp_list_char]: (~ (((lAss_list_char @ X61 @ X62) = (fAss_list_char @ X81 @ X82 @ X83 @ X84))))))). % exp.distinct(123)
thf(fact_194_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_195_eval__evals_OLAssThrow, axiom,
    ((![P : list_P1234162913t_char, E : exp_list_char, S_0 : produc515445032on_val, E2 : exp_list_char, S_1 : produc515445032on_val, V2 : list_char]: ((eval @ P @ E @ S_0 @ (throw_list_char @ E2) @ S_1) => (eval @ P @ (lAss_list_char @ V2 @ E) @ S_0 @ (throw_list_char @ E2) @ S_1))))). % eval_evals.LAssThrow
thf(fact_196_redp__redsp_OLAssThrow, axiom,
    ((![P : list_P1234162913t_char, V2 : list_char, E : exp_list_char, S2 : produc515445032on_val]: (redp @ P @ (lAss_list_char @ V2 @ (throw_list_char @ E)) @ S2 @ (throw_list_char @ E) @ S2)))). % redp_redsp.LAssThrow
thf(fact_197_red__reds_OLAssThrow, axiom,
    ((![V2 : list_char, E : exp_list_char, S2 : produc515445032on_val, P : list_P1234162913t_char]: (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (lAss_list_char @ V2 @ (throw_list_char @ E)) @ S2) @ (produc2023458740on_val @ (throw_list_char @ E) @ S2)) @ (red @ P))))). % red_reds.LAssThrow
thf(fact_198_LAssRedsThrow, axiom,
    ((![E : exp_list_char, S2 : produc515445032on_val, A : exp_list_char, S3 : produc515445032on_val, P : list_P1234162913t_char, V2 : list_char]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E @ S2) @ (produc2023458740on_val @ (throw_list_char @ A) @ S3)) @ (transi111096263on_val @ (red @ P))) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (lAss_list_char @ V2 @ E) @ S2) @ (produc2023458740on_val @ (throw_list_char @ A) @ S3)) @ (transi111096263on_val @ (red @ P))))))). % LAssRedsThrow
thf(fact_199_eval__evals_OFAssThrow1, axiom,
    ((![P : list_P1234162913t_char, E_1 : exp_list_char, S_0 : produc515445032on_val, E2 : exp_list_char, S_1 : produc515445032on_val, F3 : list_char, D3 : list_char, E_2 : exp_list_char]: ((eval @ P @ E_1 @ S_0 @ (throw_list_char @ E2) @ S_1) => (eval @ P @ (fAss_list_char @ E_1 @ F3 @ D3 @ E_2) @ S_0 @ (throw_list_char @ E2) @ S_1))))). % eval_evals.FAssThrow1
thf(fact_200_eval__evals_OFAccThrow, axiom,
    ((![P : list_P1234162913t_char, E : exp_list_char, S_0 : produc515445032on_val, E2 : exp_list_char, S_1 : produc515445032on_val, F3 : list_char, D3 : list_char]: ((eval @ P @ E @ S_0 @ (throw_list_char @ E2) @ S_1) => (eval @ P @ (fAcc_list_char @ E @ F3 @ D3) @ S_0 @ (throw_list_char @ E2) @ S_1))))). % eval_evals.FAccThrow
thf(fact_201_redp__redsp_OFAssThrow1, axiom,
    ((![P : list_P1234162913t_char, E : exp_list_char, F3 : list_char, D3 : list_char, E_2 : exp_list_char, S2 : produc515445032on_val]: (redp @ P @ (fAss_list_char @ (throw_list_char @ E) @ F3 @ D3 @ E_2) @ S2 @ (throw_list_char @ E) @ S2)))). % redp_redsp.FAssThrow1
thf(fact_202_redp__redsp_OFAccThrow, axiom,
    ((![P : list_P1234162913t_char, E : exp_list_char, F3 : list_char, D3 : list_char, S2 : produc515445032on_val]: (redp @ P @ (fAcc_list_char @ (throw_list_char @ E) @ F3 @ D3) @ S2 @ (throw_list_char @ E) @ S2)))). % redp_redsp.FAccThrow
thf(fact_203_eval__cases_I4_J, axiom,
    ((![P : list_P1234162913t_char, V2 : list_char, E : exp_list_char, S2 : produc515445032on_val, E2 : exp_list_char, S3 : produc515445032on_val]: ((eval @ P @ (lAss_list_char @ V2 @ E) @ S2 @ E2 @ S3) => (((E2 = (val_list_char @ unit)) => (![V3 : val, H3 : nat > option2118145160on_val, L3 : list_char > option_val]: ((S3 = (produc52622304on_val @ H3 @ (fun_up1252458416on_val @ L3 @ V2 @ (some_val @ V3)))) => (~ ((eval @ P @ E @ S2 @ (val_list_char @ V3) @ (produc52622304on_val @ H3 @ L3))))))) => (~ ((![E4 : exp_list_char]: ((E2 = (throw_list_char @ E4)) => (~ ((eval @ P @ E @ S2 @ (throw_list_char @ E4) @ S3)))))))))))). % eval_cases(4)
thf(fact_204_red__reds_OLAssRed, axiom,
    ((![E : exp_list_char, S2 : produc515445032on_val, E2 : exp_list_char, S3 : produc515445032on_val, P : list_P1234162913t_char, V2 : 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 @ V2 @ E) @ S2) @ (produc2023458740on_val @ (lAss_list_char @ V2 @ E2) @ S3)) @ (red @ P)))))). % red_reds.LAssRed
thf(fact_205_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_206_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_207_Throw, axiom,
    ((![P : list_P1234162913t_char, E : exp_list_char, S_0 : produc515445032on_val, A : nat, S_1 : produc515445032on_val]: ((eval @ P @ E @ S_0 @ (val_list_char @ (addr @ A)) @ S_1) => (eval @ P @ (throw_list_char @ E) @ S_0 @ (throw_list_char @ (val_list_char @ (addr @ A))) @ S_1))))). % Throw
thf(fact_208_eval__evals_OFAssThrow2, axiom,
    ((![P : list_P1234162913t_char, E_1 : exp_list_char, S_0 : produc515445032on_val, V : val, S_1 : produc515445032on_val, E_2 : exp_list_char, E2 : exp_list_char, S_2 : produc515445032on_val, F3 : list_char, D3 : list_char]: ((eval @ P @ E_1 @ S_0 @ (val_list_char @ V) @ S_1) => ((eval @ P @ E_2 @ S_1 @ (throw_list_char @ E2) @ S_2) => (eval @ P @ (fAss_list_char @ E_1 @ F3 @ D3 @ E_2) @ S_0 @ (throw_list_char @ E2) @ S_2)))))). % eval_evals.FAssThrow2
thf(fact_209_redp__redsp_OFAssThrow2, axiom,
    ((![P : list_P1234162913t_char, V : val, F3 : list_char, D3 : list_char, E : exp_list_char, S2 : produc515445032on_val]: (redp @ P @ (fAss_list_char @ (val_list_char @ V) @ F3 @ D3 @ (throw_list_char @ E)) @ S2 @ (throw_list_char @ E) @ S2)))). % redp_redsp.FAssThrow2
thf(fact_210_final__def, axiom,
    ((final_list_char = (^[E7 : exp_list_char]: (((?[V4 : val]: (E7 = (val_list_char @ V4)))) | ((?[A4 : nat]: (E7 = (throw_list_char @ (val_list_char @ (addr @ A4))))))))))). % final_def
thf(fact_211_finalE, axiom,
    ((![E : exp_list_char]: ((final_list_char @ E) => ((![V3 : val]: (~ ((E = (val_list_char @ V3))))) => (~ ((![A3 : nat]: (~ ((E = (throw_list_char @ (val_list_char @ (addr @ A3)))))))))))))). % finalE
thf(fact_212_LAssReds, axiom,
    ((![E : exp_list_char, S2 : produc515445032on_val, E2 : exp_list_char, S3 : produc515445032on_val, P : list_P1234162913t_char, V2 : 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 @ V2 @ E) @ S2) @ (produc2023458740on_val @ (lAss_list_char @ V2 @ E2) @ S3)) @ (transi111096263on_val @ (red @ P))))))). % LAssReds
thf(fact_213_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_214_ThrowRedsThrow, axiom,
    ((![E : exp_list_char, S2 : produc515445032on_val, A : exp_list_char, S3 : produc515445032on_val, P : list_P1234162913t_char]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E @ S2) @ (produc2023458740on_val @ (throw_list_char @ A) @ S3)) @ (transi111096263on_val @ (red @ P))) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (throw_list_char @ E) @ S2) @ (produc2023458740on_val @ (throw_list_char @ A) @ S3)) @ (transi111096263on_val @ (red @ P))))))). % ThrowRedsThrow
thf(fact_215_red__reds_OFAssThrow1, axiom,
    ((![E : exp_list_char, F3 : list_char, D3 : list_char, E_2 : exp_list_char, S2 : produc515445032on_val, P : list_P1234162913t_char]: (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (fAss_list_char @ (throw_list_char @ E) @ F3 @ D3 @ E_2) @ S2) @ (produc2023458740on_val @ (throw_list_char @ E) @ S2)) @ (red @ P))))). % red_reds.FAssThrow1
thf(fact_216_red__reds_OFAccThrow, axiom,
    ((![E : exp_list_char, F3 : list_char, D3 : list_char, S2 : produc515445032on_val, P : list_P1234162913t_char]: (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (fAcc_list_char @ (throw_list_char @ E) @ F3 @ D3) @ S2) @ (produc2023458740on_val @ (throw_list_char @ E) @ S2)) @ (red @ P))))). % red_reds.FAccThrow
thf(fact_217_LAss, axiom,
    ((![P : list_P1234162913t_char, E : exp_list_char, S_0 : produc515445032on_val, V : val, H : nat > option2118145160on_val, L : list_char > option_val, L2 : list_char > option_val, V2 : list_char]: ((eval @ P @ E @ S_0 @ (val_list_char @ V) @ (produc52622304on_val @ H @ L)) => ((L2 = (fun_up1252458416on_val @ L @ V2 @ (some_val @ V))) => (eval @ P @ (lAss_list_char @ V2 @ E) @ S_0 @ (val_list_char @ unit) @ (produc52622304on_val @ H @ L2))))))). % LAss
thf(fact_218_redp__redsp_ORedLAss, axiom,
    ((![P : list_P1234162913t_char, V2 : list_char, V : val, H : nat > option2118145160on_val, L : list_char > option_val]: (redp @ P @ (lAss_list_char @ V2 @ (val_list_char @ V)) @ (produc52622304on_val @ H @ L) @ (val_list_char @ unit) @ (produc52622304on_val @ H @ (fun_up1252458416on_val @ L @ V2 @ (some_val @ V))))))). % redp_redsp.RedLAss
thf(fact_219_red__reds_OFAssThrow2, axiom,
    ((![V : val, F3 : list_char, D3 : list_char, E : exp_list_char, S2 : produc515445032on_val, P : list_P1234162913t_char]: (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (fAss_list_char @ (val_list_char @ V) @ F3 @ D3 @ (throw_list_char @ E)) @ S2) @ (produc2023458740on_val @ (throw_list_char @ E) @ S2)) @ (red @ P))))). % red_reds.FAssThrow2
thf(fact_220_FAssRedsThrow1, axiom,
    ((![E : exp_list_char, S2 : produc515445032on_val, E2 : exp_list_char, S3 : produc515445032on_val, P : list_P1234162913t_char, F3 : list_char, D3 : list_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 @ (fAss_list_char @ E @ F3 @ D3 @ E_2) @ S2) @ (produc2023458740on_val @ (throw_list_char @ E2) @ S3)) @ (transi111096263on_val @ (red @ P))))))). % FAssRedsThrow1
thf(fact_221_FAccRedsThrow, axiom,
    ((![E : exp_list_char, S2 : produc515445032on_val, A : exp_list_char, S3 : produc515445032on_val, P : list_P1234162913t_char, F3 : list_char, D3 : list_char]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E @ S2) @ (produc2023458740on_val @ (throw_list_char @ A) @ S3)) @ (transi111096263on_val @ (red @ P))) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (fAcc_list_char @ E @ F3 @ D3) @ S2) @ (produc2023458740on_val @ (throw_list_char @ A) @ S3)) @ (transi111096263on_val @ (red @ P))))))). % FAccRedsThrow
thf(fact_222_TryCatchRedsFinal, axiom,
    ((![E_1 : exp_list_char, S_0 : produc515445032on_val, A : nat, H_12 : nat > option2118145160on_val, L_12 : list_char > option_val, P : list_P1234162913t_char, D3 : list_char, Fs : produc1257910179t_char > option_val, C3 : list_char, E_2 : exp_list_char, V2 : list_char, E_22 : exp_list_char, H_2 : nat > option2118145160on_val, L_2 : list_char > option_val]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E_1 @ S_0) @ (produc2023458740on_val @ (throw_list_char @ (val_list_char @ (addr @ A))) @ (produc52622304on_val @ H_12 @ L_12))) @ (transi111096263on_val @ (red @ P))) => (((H_12 @ A) = (some_P1299442195on_val @ (produc904988266on_val @ D3 @ Fs))) => ((member89690956t_char @ (produc1304532571t_char @ D3 @ C3) @ (transi1879726366t_char @ (subcls880436836t_char @ P))) => ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E_2 @ (produc52622304on_val @ H_12 @ (fun_up1252458416on_val @ L_12 @ V2 @ (some_val @ (addr @ A))))) @ (produc2023458740on_val @ E_22 @ (produc52622304on_val @ H_2 @ L_2))) @ (transi111096263on_val @ (red @ P))) => ((final_list_char @ E_22) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (tryCatch_list_char @ E_1 @ C3 @ V2 @ E_2) @ S_0) @ (produc2023458740on_val @ E_22 @ (produc52622304on_val @ H_2 @ (fun_up1252458416on_val @ L_2 @ V2 @ (L_12 @ V2))))) @ (transi111096263on_val @ (red @ P))))))))))). % TryCatchRedsFinal
thf(fact_223_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, E : 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 @ E) @ 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 @ E) @ S_2)) @ (transi111096263on_val @ (red @ P)))))))). % BinOpRedsThrow2
thf(fact_224_red__reds_OBlockThrow, axiom,
    ((![V2 : list_char, T2 : ty, A : nat, S2 : produc515445032on_val, P : list_P1234162913t_char]: (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (block_list_char @ V2 @ T2 @ (throw_list_char @ (val_list_char @ (addr @ A)))) @ S2) @ (produc2023458740on_val @ (throw_list_char @ (val_list_char @ (addr @ A))) @ S2)) @ (red @ P))))). % red_reds.BlockThrow
thf(fact_225_exp_Oinject_I10_J, axiom,
    ((![X101 : list_char, X102 : ty, X103 : exp_list_char, Y101 : list_char, Y102 : ty, Y103 : exp_list_char]: (((block_list_char @ X101 @ X102 @ X103) = (block_list_char @ Y101 @ Y102 @ Y103)) = (((X101 = Y101)) & ((((X102 = Y102)) & ((X103 = Y103))))))))). % exp.inject(10)
thf(fact_226_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_227_exp_Oinject_I15_J, axiom,
    ((![X151 : exp_list_char, X152 : list_char, X153 : list_char, X154 : exp_list_char, Y151 : exp_list_char, Y152 : list_char, Y153 : list_char, Y154 : exp_list_char]: (((tryCatch_list_char @ X151 @ X152 @ X153 @ X154) = (tryCatch_list_char @ Y151 @ Y152 @ Y153 @ Y154)) = (((X151 = Y151)) & ((((X152 = Y152)) & ((((X153 = Y153)) & ((X154 = Y154))))))))))). % exp.inject(15)

% Helper facts (5)
thf(help_If_2_1_If_001t__Option__Ooption_It__Value__Oval_J_T, axiom,
    ((![X : option_val, Y : option_val]: ((if_option_val @ $false @ X @ Y) = Y)))).
thf(help_If_1_1_If_001t__Option__Ooption_It__Value__Oval_J_T, axiom,
    ((![X : option_val, Y : option_val]: ((if_option_val @ $true @ X @ Y) = X)))).
thf(help_If_3_1_If_001t__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_T, axiom,
    ((![P : $o]: ((P = $true) | (P = $false))))).
thf(help_If_2_1_If_001t__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_T, axiom,
    ((![X : option2118145160on_val, Y : option2118145160on_val]: ((if_opt451925058on_val @ $false @ X @ Y) = Y)))).
thf(help_If_1_1_If_001t__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_T, axiom,
    ((![X : option2118145160on_val, Y : option2118145160on_val]: ((if_opt451925058on_val @ $true @ X @ Y) = X)))).

% Conjectures (1)
thf(conj_0, conjecture,
    ((?[T3 : ty]: ((wTrt @ p @ (fun_up262443479on_val @ ha @ a @ (some_P1299442195on_val @ (produc904988266on_val @ c @ (fun_up356838326on_val @ fs @ (produc1304532571t_char @ f @ d) @ (some_val @ v))))) @ e @ (val_list_char @ unit) @ T3) & (widen_917054840t_char @ p @ T3 @ t))))).
