% 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_330__5337956_1 ) ; }
% This file was generated by Isabelle (most likely Sledgehammer)
% 2020-12-16 14:20:53.021

% Could-be-implicit typings (28)
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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,
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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,
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    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,
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thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_J, type,
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thf(ty_n_t__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J, type,
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thf(ty_n_t__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J, type,
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thf(ty_n_t__Option__Ooption_It__Value__Oval_J, type,
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thf(ty_n_t__Option__Ooption_It__Type__Oty_J, type,
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thf(ty_n_t__List__Olist_It__String__Ochar_J, type,
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thf(ty_n_t__Value__Oval, type,
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thf(ty_n_t__Type__Oty, type,
    ty : $tType).
thf(ty_n_t__Nat__Onat, type,
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% Explicit typings (71)
thf(sy_c_BigStep_Oeval, type,
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thf(sy_c_BigStep_Ofinal_001t__List__Olist_It__String__Ochar_J, type,
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thf(sy_c_Conform_Oconf_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,
    conf_P93989998t_char : list_P1234162913t_char > (nat > option2118145160on_val) > val > ty > $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_OCond_001t__List__Olist_It__String__Ochar_J, type,
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thf(sy_c_Expr_Oexp_OFAcc_001t__List__Olist_It__String__Ochar_J, type,
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thf(sy_c_Expr_Oexp_OSeq_001t__List__Olist_It__String__Ochar_J, type,
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thf(sy_c_Expr_Oexp_OVal_001t__List__Olist_It__String__Ochar_J, type,
    val_list_char : val > exp_list_char).
thf(sy_c_Expr_Oexp_OWhile_001t__List__Olist_It__String__Ochar_J, type,
    while_list_char : exp_list_char > exp_list_char > exp_list_char).
thf(sy_c_Expr_Oexp_Othrow_001t__List__Olist_It__String__Ochar_J, type,
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thf(sy_c_JWellForm_Owf__J__mdecl, type,
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thf(sy_c_Map_Omap__add_001t__List__Olist_It__String__Ochar_J_001t__Type__Oty, type,
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thf(sy_c_Map_Omap__add_001t__List__Olist_It__String__Ochar_J_001t__Value__Oval, type,
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thf(sy_c_Map_Omap__le_001t__List__Olist_It__String__Ochar_J_001t__Type__Oty, type,
    map_le_list_char_ty : (list_char > option_ty) > (list_char > option_ty) > $o).
thf(sy_c_Map_Omap__le_001t__List__Olist_It__String__Ochar_J_001t__Value__Oval, type,
    map_le_list_char_val : (list_char > option_val) > (list_char > option_val) > $o).
thf(sy_c_Objects_Ohext, type,
    hext : (nat > option2118145160on_val) > (nat > option2118145160on_val) > $o).
thf(sy_c_Objects_Otypeof__h, type,
    typeof_h : (nat > option2118145160on_val) > val > option_ty).
thf(sy_c_Option_Ooption_OSome_001t__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,
    some_P1299442195on_val : produc266837688on_val > option2118145160on_val).
thf(sy_c_Option_Ooption_OSome_001t__Type__Oty, type,
    some_ty : ty > option_ty).
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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 > option2118145160on_val).
thf(sy_v_aa______, type,
    aa : nat).
thf(sy_v_b______, type,
    b : list_char > option_val).
thf(sy_v_fs______, type,
    fs : produc1257910179t_char > option_val).
thf(sy_v_v______, type,
    v : val).

% Relevant facts (198)
thf(fact_0_RedFAcc_Ohyps_I2_J, axiom,
    (((fs @ (produc1304532571t_char @ f @ d)) = (some_val @ v)))). % RedFAcc.hyps(2)
thf(fact_1_RedFAcc_Oprems_I1_J, axiom,
    ((typeSa1777264139_sconf @ p @ e @ (produc52622304on_val @ a @ b)))). % RedFAcc.prems(1)
thf(fact_2_RedFAcc_Ohyps_I1_J, axiom,
    (((hp @ (produc52622304on_val @ a @ b) @ aa) = (some_P1299442195on_val @ (produc904988266on_val @ c @ fs))))). % RedFAcc.hyps(1)
thf(fact_3_RedFAcc_Oprems_I2_J, axiom,
    ((wTrt @ p @ a @ e @ (fAcc_list_char @ (val_list_char @ (addr @ aa)) @ f @ d) @ t))). % RedFAcc.prems(2)
thf(fact_4_local_Owf, axiom,
    ((wf_pro1229751607t_char @ wf_J_mdecl @ p))). % local.wf
thf(fact_5_exp_Oinject_I3_J, axiom,
    ((![X3 : val, Y3 : val]: (((val_list_char @ X3) = (val_list_char @ Y3)) = (X3 = Y3))))). % exp.inject(3)
thf(fact_6_widen__trans, axiom,
    ((![P : list_P1234162913t_char, S : ty, U : ty, T : ty]: ((widen_917054840t_char @ P @ S @ U) => ((widen_917054840t_char @ P @ U @ T) => (widen_917054840t_char @ P @ S @ T)))))). % widen_trans
thf(fact_7_widen__refl, axiom,
    ((![P : list_P1234162913t_char, T : ty]: (widen_917054840t_char @ P @ T @ T)))). % widen_refl
thf(fact_8_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_9_WTrt__elim__cases_I2_J, axiom,
    ((![P : list_P1234162913t_char, H : nat > option2118145160on_val, E : list_char > option_ty, E2 : exp_list_char, E_1 : exp_list_char, E_2 : exp_list_char, T : ty]: ((wTrt @ P @ H @ E @ (cond_list_char @ E2 @ E_1 @ E_2) @ T) => (~ (((wTrt @ P @ H @ E @ E2 @ boolean) => (![T_1 : ty]: ((wTrt @ P @ H @ E @ E_1 @ T_1) => (![T_2 : ty]: ((wTrt @ P @ H @ E @ E_2 @ T_2) => (((widen_917054840t_char @ P @ T_1 @ T_2) | (widen_917054840t_char @ P @ T_2 @ T_1)) => (((widen_917054840t_char @ P @ T_1 @ T_2) => (T = T_2)) => (~ (((widen_917054840t_char @ P @ T_2 @ T_1) => (T = T_1))))))))))))))))). % WTrt_elim_cases(2)
thf(fact_10_WTrtCond, axiom,
    ((![P : list_P1234162913t_char, H : nat > option2118145160on_val, E : list_char > option_ty, E2 : exp_list_char, E_1 : exp_list_char, T_12 : ty, E_2 : exp_list_char, T_22 : ty, T : ty]: ((wTrt @ P @ H @ E @ E2 @ boolean) => ((wTrt @ P @ H @ E @ E_1 @ T_12) => ((wTrt @ P @ H @ E @ E_2 @ T_22) => (((widen_917054840t_char @ P @ T_12 @ T_22) | (widen_917054840t_char @ P @ T_22 @ T_12)) => (((widen_917054840t_char @ P @ T_12 @ T_22) => (T = T_22)) => (((widen_917054840t_char @ P @ T_22 @ T_12) => (T = T_12)) => (wTrt @ P @ H @ E @ (cond_list_char @ E2 @ E_1 @ E_2) @ T)))))))))). % WTrtCond
thf(fact_11_WTrt__hext__mono, axiom,
    ((![P : list_P1234162913t_char, H : nat > option2118145160on_val, E : list_char > option_ty, E2 : exp_list_char, T : ty, H2 : nat > option2118145160on_val]: ((wTrt @ P @ H @ E @ E2 @ T) => ((hext @ H @ H2) => (wTrt @ P @ H2 @ E @ E2 @ T)))))). % WTrt_hext_mono
thf(fact_12_WTrtVal, axiom,
    ((![H : nat > option2118145160on_val, V : val, T : ty, P : list_P1234162913t_char, E : list_char > option_ty]: (((typeof_h @ H @ V) = (some_ty @ T)) => (wTrt @ P @ H @ E @ (val_list_char @ V) @ T))))). % WTrtVal
thf(fact_13_WTrt__env__mono, axiom,
    ((![P : list_P1234162913t_char, H : nat > option2118145160on_val, E : list_char > option_ty, E2 : exp_list_char, T : ty, E3 : list_char > option_ty]: ((wTrt @ P @ H @ E @ E2 @ T) => ((map_le_list_char_ty @ E @ E3) => (wTrt @ P @ H @ E3 @ E2 @ T)))))). % WTrt_env_mono
thf(fact_14_conf__widen, axiom,
    ((![P : list_P1234162913t_char, H : nat > option2118145160on_val, V : val, T : ty, T2 : ty]: ((conf_P93989998t_char @ P @ H @ V @ T) => ((widen_917054840t_char @ P @ T @ T2) => (conf_P93989998t_char @ P @ H @ V @ T2)))))). % conf_widen
thf(fact_15_exp_Oinject_I12_J, axiom,
    ((![X121 : exp_list_char, X122 : exp_list_char, X123 : exp_list_char, Y121 : exp_list_char, Y122 : exp_list_char, Y123 : exp_list_char]: (((cond_list_char @ X121 @ X122 @ X123) = (cond_list_char @ Y121 @ Y122 @ Y123)) = (((X121 = Y121)) & ((((X122 = Y122)) & ((X123 = Y123))))))))). % exp.inject(12)
thf(fact_16_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_17_exp_Odistinct_I147_J, axiom,
    ((![X71 : exp_list_char, X72 : list_char, X73 : list_char, X121 : exp_list_char, X122 : exp_list_char, X123 : exp_list_char]: (~ (((fAcc_list_char @ X71 @ X72 @ X73) = (cond_list_char @ X121 @ X122 @ X123))))))). % exp.distinct(147)
thf(fact_18_conf__def, axiom,
    ((conf_P93989998t_char = (^[P2 : list_P1234162913t_char]: (^[H3 : nat > option2118145160on_val]: (^[V2 : val]: (^[T3 : ty]: (?[T4 : ty]: ((((typeof_h @ H3 @ V2) = (some_ty @ T4))) & ((widen_917054840t_char @ P2 @ T4 @ T3))))))))))). % conf_def
thf(fact_19_exp_Odistinct_I71_J, axiom,
    ((![X3 : val, X121 : exp_list_char, X122 : exp_list_char, X123 : exp_list_char]: (~ (((val_list_char @ X3) = (cond_list_char @ X121 @ X122 @ X123))))))). % exp.distinct(71)
thf(fact_20_hext__typeof__mono, axiom,
    ((![H : nat > option2118145160on_val, H2 : nat > option2118145160on_val, V : val, T : ty]: ((hext @ H @ H2) => (((typeof_h @ H @ V) = (some_ty @ T)) => ((typeof_h @ H2 @ V) = (some_ty @ T))))))). % hext_typeof_mono
thf(fact_21_hextI, axiom,
    ((![H : nat > option2118145160on_val, H2 : nat > option2118145160on_val]: ((![A : nat, C : list_char, Fs : produc1257910179t_char > option_val]: (((H @ A) = (some_P1299442195on_val @ (produc904988266on_val @ C @ Fs))) => (?[Fs2 : produc1257910179t_char > option_val]: ((H2 @ A) = (some_P1299442195on_val @ (produc904988266on_val @ C @ Fs2)))))) => (hext @ H @ H2))))). % hextI
thf(fact_22_hext__def, axiom,
    ((hext = (^[H3 : nat > option2118145160on_val]: (^[H4 : nat > option2118145160on_val]: (![A2 : nat]: (![C2 : list_char]: (![Fs3 : produc1257910179t_char > option_val]: ((((H3 @ A2) = (some_P1299442195on_val @ (produc904988266on_val @ C2 @ Fs3)))) => ((?[Fs4 : produc1257910179t_char > option_val]: ((H4 @ A2) = (some_P1299442195on_val @ (produc904988266on_val @ C2 @ Fs4)))))))))))))). % hext_def
thf(fact_23_hext__objD, axiom,
    ((![H : nat > option2118145160on_val, H2 : nat > option2118145160on_val, A3 : nat, C3 : list_char, Fs5 : produc1257910179t_char > option_val]: ((hext @ H @ H2) => (((H @ A3) = (some_P1299442195on_val @ (produc904988266on_val @ C3 @ Fs5))) => (?[Fs6 : produc1257910179t_char > option_val]: ((H2 @ A3) = (some_P1299442195on_val @ (produc904988266on_val @ C3 @ Fs6))))))))). % hext_objD
thf(fact_24_hext__refl, axiom,
    ((![H : nat > option2118145160on_val]: (hext @ H @ H)))). % hext_refl
thf(fact_25_val_Oinject_I3_J, axiom,
    ((![X5 : nat, Y5 : nat]: (((addr @ X5) = (addr @ Y5)) = (X5 = Y5))))). % val.inject(3)
thf(fact_26_option_Oinject, axiom,
    ((![X2 : val, Y2 : val]: (((some_val @ X2) = (some_val @ Y2)) = (X2 = Y2))))). % option.inject
thf(fact_27_option_Oinject, axiom,
    ((![X2 : produc266837688on_val, Y2 : produc266837688on_val]: (((some_P1299442195on_val @ X2) = (some_P1299442195on_val @ Y2)) = (X2 = Y2))))). % option.inject
thf(fact_28_option_Oinject, axiom,
    ((![X2 : ty, Y2 : ty]: (((some_ty @ X2) = (some_ty @ Y2)) = (X2 = Y2))))). % option.inject
thf(fact_29_prod_Oinject, axiom,
    ((![X1 : list_char, X2 : list_char, Y1 : list_char, Y2 : list_char]: (((produc1304532571t_char @ X1 @ X2) = (produc1304532571t_char @ Y1 @ Y2)) = (((X1 = Y1)) & ((X2 = Y2))))))). % prod.inject
thf(fact_30_prod_Oinject, axiom,
    ((![X1 : nat > option2118145160on_val, X2 : list_char > option_val, Y1 : nat > option2118145160on_val, Y2 : list_char > option_val]: (((produc52622304on_val @ X1 @ X2) = (produc52622304on_val @ Y1 @ Y2)) = (((X1 = Y1)) & ((X2 = Y2))))))). % prod.inject
thf(fact_31_prod_Oinject, axiom,
    ((![X1 : list_char, X2 : produc1257910179t_char > option_val, Y1 : list_char, Y2 : produc1257910179t_char > option_val]: (((produc904988266on_val @ X1 @ X2) = (produc904988266on_val @ Y1 @ Y2)) = (((X1 = Y1)) & ((X2 = Y2))))))). % prod.inject
thf(fact_32_prod_Oinject, axiom,
    ((![X1 : produc1097884484on_val, X2 : produc1097884484on_val, Y1 : produc1097884484on_val, Y2 : produc1097884484on_val]: (((produc1069526295on_val @ X1 @ X2) = (produc1069526295on_val @ Y1 @ Y2)) = (((X1 = Y1)) & ((X2 = Y2))))))). % prod.inject
thf(fact_33_prod_Oinject, axiom,
    ((![X1 : exp_list_char, X2 : produc515445032on_val, Y1 : exp_list_char, Y2 : produc515445032on_val]: (((produc2023458740on_val @ X1 @ X2) = (produc2023458740on_val @ Y1 @ Y2)) = (((X1 = Y1)) & ((X2 = Y2))))))). % prod.inject
thf(fact_34_old_Oprod_Oinject, axiom,
    ((![A3 : list_char, B : list_char, A4 : list_char, B2 : list_char]: (((produc1304532571t_char @ A3 @ B) = (produc1304532571t_char @ A4 @ B2)) = (((A3 = A4)) & ((B = B2))))))). % old.prod.inject
thf(fact_35_old_Oprod_Oinject, axiom,
    ((![A3 : nat > option2118145160on_val, B : list_char > option_val, A4 : nat > option2118145160on_val, B2 : list_char > option_val]: (((produc52622304on_val @ A3 @ B) = (produc52622304on_val @ A4 @ B2)) = (((A3 = A4)) & ((B = B2))))))). % old.prod.inject
thf(fact_36_old_Oprod_Oinject, axiom,
    ((![A3 : list_char, B : produc1257910179t_char > option_val, A4 : list_char, B2 : produc1257910179t_char > option_val]: (((produc904988266on_val @ A3 @ B) = (produc904988266on_val @ A4 @ B2)) = (((A3 = A4)) & ((B = B2))))))). % old.prod.inject
thf(fact_37_old_Oprod_Oinject, axiom,
    ((![A3 : produc1097884484on_val, B : produc1097884484on_val, A4 : produc1097884484on_val, B2 : produc1097884484on_val]: (((produc1069526295on_val @ A3 @ B) = (produc1069526295on_val @ A4 @ B2)) = (((A3 = A4)) & ((B = B2))))))). % old.prod.inject
thf(fact_38_old_Oprod_Oinject, axiom,
    ((![A3 : exp_list_char, B : produc515445032on_val, A4 : exp_list_char, B2 : produc515445032on_val]: (((produc2023458740on_val @ A3 @ B) = (produc2023458740on_val @ A4 @ B2)) = (((A3 = A4)) & ((B = B2))))))). % old.prod.inject
thf(fact_39_old_Oprod_Oinducts, axiom,
    ((![P : produc1257910179t_char > $o, Prod : produc1257910179t_char]: ((![A : list_char, B3 : list_char]: (P @ (produc1304532571t_char @ A @ B3))) => (P @ Prod))))). % old.prod.inducts
thf(fact_40_old_Oprod_Oinducts, axiom,
    ((![P : produc515445032on_val > $o, Prod : produc515445032on_val]: ((![A : nat > option2118145160on_val, B3 : list_char > option_val]: (P @ (produc52622304on_val @ A @ B3))) => (P @ Prod))))). % old.prod.inducts
thf(fact_41_old_Oprod_Oinducts, axiom,
    ((![P : produc266837688on_val > $o, Prod : produc266837688on_val]: ((![A : list_char, B3 : produc1257910179t_char > option_val]: (P @ (produc904988266on_val @ A @ B3))) => (P @ Prod))))). % old.prod.inducts
thf(fact_42_old_Oprod_Oinducts, axiom,
    ((![P : produc1172664615on_val > $o, Prod : produc1172664615on_val]: ((![A : produc1097884484on_val, B3 : produc1097884484on_val]: (P @ (produc1069526295on_val @ A @ B3))) => (P @ Prod))))). % old.prod.inducts
thf(fact_43_old_Oprod_Oinducts, axiom,
    ((![P : produc1097884484on_val > $o, Prod : produc1097884484on_val]: ((![A : exp_list_char, B3 : produc515445032on_val]: (P @ (produc2023458740on_val @ A @ B3))) => (P @ Prod))))). % old.prod.inducts
thf(fact_44_old_Oprod_Oexhaust, axiom,
    ((![Y : produc1257910179t_char]: (~ ((![A : list_char, B3 : list_char]: (~ ((Y = (produc1304532571t_char @ A @ B3)))))))))). % old.prod.exhaust
thf(fact_45_old_Oprod_Oexhaust, axiom,
    ((![Y : produc515445032on_val]: (~ ((![A : nat > option2118145160on_val, B3 : list_char > option_val]: (~ ((Y = (produc52622304on_val @ A @ B3)))))))))). % old.prod.exhaust
thf(fact_46_old_Oprod_Oexhaust, axiom,
    ((![Y : produc266837688on_val]: (~ ((![A : list_char, B3 : produc1257910179t_char > option_val]: (~ ((Y = (produc904988266on_val @ A @ B3)))))))))). % old.prod.exhaust
thf(fact_47_old_Oprod_Oexhaust, axiom,
    ((![Y : produc1172664615on_val]: (~ ((![A : produc1097884484on_val, B3 : produc1097884484on_val]: (~ ((Y = (produc1069526295on_val @ A @ B3)))))))))). % old.prod.exhaust
thf(fact_48_old_Oprod_Oexhaust, axiom,
    ((![Y : produc1097884484on_val]: (~ ((![A : exp_list_char, B3 : produc515445032on_val]: (~ ((Y = (produc2023458740on_val @ A @ B3)))))))))). % old.prod.exhaust
thf(fact_49_prod__induct4, axiom,
    ((![P : produc1172664615on_val > $o, X : produc1172664615on_val]: ((![A : produc1097884484on_val, B3 : exp_list_char, C4 : nat > option2118145160on_val, D : list_char > option_val]: (P @ (produc1069526295on_val @ A @ (produc2023458740on_val @ B3 @ (produc52622304on_val @ C4 @ D))))) => (P @ X))))). % prod_induct4
thf(fact_50_prod__induct3, axiom,
    ((![P : produc1172664615on_val > $o, X : produc1172664615on_val]: ((![A : produc1097884484on_val, B3 : exp_list_char, C4 : produc515445032on_val]: (P @ (produc1069526295on_val @ A @ (produc2023458740on_val @ B3 @ C4)))) => (P @ X))))). % prod_induct3
thf(fact_51_prod__induct3, axiom,
    ((![P : produc1097884484on_val > $o, X : produc1097884484on_val]: ((![A : exp_list_char, B3 : nat > option2118145160on_val, C4 : list_char > option_val]: (P @ (produc2023458740on_val @ A @ (produc52622304on_val @ B3 @ C4)))) => (P @ X))))). % prod_induct3
thf(fact_52_mem__Collect__eq, axiom,
    ((![A3 : produc1172664615on_val, P : produc1172664615on_val > $o]: ((member354538064on_val @ A3 @ (collec2055896722on_val @ P)) = (P @ A3))))). % mem_Collect_eq
thf(fact_53_Collect__mem__eq, axiom,
    ((![A5 : set_Pr1189492743on_val]: ((collec2055896722on_val @ (^[X4 : produc1172664615on_val]: (member354538064on_val @ X4 @ A5))) = A5)))). % Collect_mem_eq
thf(fact_54_prod__cases4, axiom,
    ((![Y : produc1172664615on_val]: (~ ((![A : produc1097884484on_val, B3 : exp_list_char, C4 : nat > option2118145160on_val, D : list_char > option_val]: (~ ((Y = (produc1069526295on_val @ A @ (produc2023458740on_val @ B3 @ (produc52622304on_val @ C4 @ D)))))))))))). % prod_cases4
thf(fact_55_prod__cases3, axiom,
    ((![Y : produc1172664615on_val]: (~ ((![A : produc1097884484on_val, B3 : exp_list_char, C4 : produc515445032on_val]: (~ ((Y = (produc1069526295on_val @ A @ (produc2023458740on_val @ B3 @ C4))))))))))). % prod_cases3
thf(fact_56_prod__cases3, axiom,
    ((![Y : produc1097884484on_val]: (~ ((![A : exp_list_char, B3 : nat > option2118145160on_val, C4 : list_char > option_val]: (~ ((Y = (produc2023458740on_val @ A @ (produc52622304on_val @ B3 @ C4))))))))))). % prod_cases3
thf(fact_57_Pair__inject, axiom,
    ((![A3 : list_char, B : list_char, A4 : list_char, B2 : list_char]: (((produc1304532571t_char @ A3 @ B) = (produc1304532571t_char @ A4 @ B2)) => (~ (((A3 = A4) => (~ ((B = B2)))))))))). % Pair_inject
thf(fact_58_Pair__inject, axiom,
    ((![A3 : nat > option2118145160on_val, B : list_char > option_val, A4 : nat > option2118145160on_val, B2 : list_char > option_val]: (((produc52622304on_val @ A3 @ B) = (produc52622304on_val @ A4 @ B2)) => (~ (((A3 = A4) => (~ ((B = B2)))))))))). % Pair_inject
thf(fact_59_Pair__inject, axiom,
    ((![A3 : list_char, B : produc1257910179t_char > option_val, A4 : list_char, B2 : produc1257910179t_char > option_val]: (((produc904988266on_val @ A3 @ B) = (produc904988266on_val @ A4 @ B2)) => (~ (((A3 = A4) => (~ ((B = B2)))))))))). % Pair_inject
thf(fact_60_Pair__inject, axiom,
    ((![A3 : produc1097884484on_val, B : produc1097884484on_val, A4 : produc1097884484on_val, B2 : produc1097884484on_val]: (((produc1069526295on_val @ A3 @ B) = (produc1069526295on_val @ A4 @ B2)) => (~ (((A3 = A4) => (~ ((B = B2)))))))))). % Pair_inject
thf(fact_61_Pair__inject, axiom,
    ((![A3 : exp_list_char, B : produc515445032on_val, A4 : exp_list_char, B2 : produc515445032on_val]: (((produc2023458740on_val @ A3 @ B) = (produc2023458740on_val @ A4 @ B2)) => (~ (((A3 = A4) => (~ ((B = B2)))))))))). % Pair_inject
thf(fact_62_prod__cases, axiom,
    ((![P : produc1257910179t_char > $o, P3 : produc1257910179t_char]: ((![A : list_char, B3 : list_char]: (P @ (produc1304532571t_char @ A @ B3))) => (P @ P3))))). % prod_cases
thf(fact_63_prod__cases, axiom,
    ((![P : produc515445032on_val > $o, P3 : produc515445032on_val]: ((![A : nat > option2118145160on_val, B3 : list_char > option_val]: (P @ (produc52622304on_val @ A @ B3))) => (P @ P3))))). % prod_cases
thf(fact_64_prod__cases, axiom,
    ((![P : produc266837688on_val > $o, P3 : produc266837688on_val]: ((![A : list_char, B3 : produc1257910179t_char > option_val]: (P @ (produc904988266on_val @ A @ B3))) => (P @ P3))))). % prod_cases
thf(fact_65_prod__cases, axiom,
    ((![P : produc1172664615on_val > $o, P3 : produc1172664615on_val]: ((![A : produc1097884484on_val, B3 : produc1097884484on_val]: (P @ (produc1069526295on_val @ A @ B3))) => (P @ P3))))). % prod_cases
thf(fact_66_prod__cases, axiom,
    ((![P : produc1097884484on_val > $o, P3 : produc1097884484on_val]: ((![A : exp_list_char, B3 : produc515445032on_val]: (P @ (produc2023458740on_val @ A @ B3))) => (P @ P3))))). % prod_cases
thf(fact_67_surj__pair, axiom,
    ((![P3 : produc1257910179t_char]: (?[X6 : list_char, Y4 : list_char]: (P3 = (produc1304532571t_char @ X6 @ Y4)))))). % surj_pair
thf(fact_68_surj__pair, axiom,
    ((![P3 : produc515445032on_val]: (?[X6 : nat > option2118145160on_val, Y4 : list_char > option_val]: (P3 = (produc52622304on_val @ X6 @ Y4)))))). % surj_pair
thf(fact_69_surj__pair, axiom,
    ((![P3 : produc266837688on_val]: (?[X6 : list_char, Y4 : produc1257910179t_char > option_val]: (P3 = (produc904988266on_val @ X6 @ Y4)))))). % surj_pair
thf(fact_70_surj__pair, axiom,
    ((![P3 : produc1172664615on_val]: (?[X6 : produc1097884484on_val, Y4 : produc1097884484on_val]: (P3 = (produc1069526295on_val @ X6 @ Y4)))))). % surj_pair
thf(fact_71_surj__pair, axiom,
    ((![P3 : produc1097884484on_val]: (?[X6 : exp_list_char, Y4 : produc515445032on_val]: (P3 = (produc2023458740on_val @ X6 @ Y4)))))). % surj_pair
thf(fact_72_hext__trans, axiom,
    ((![H : nat > option2118145160on_val, H2 : nat > option2118145160on_val, H5 : nat > option2118145160on_val]: ((hext @ H @ H2) => ((hext @ H2 @ H5) => (hext @ H @ H5)))))). % hext_trans
thf(fact_73_lconf__def, axiom,
    ((lconf_485928294t_char = (^[P2 : list_P1234162913t_char]: (^[H3 : nat > option2118145160on_val]: (^[L : list_char > option_val]: (^[E4 : list_char > option_ty]: (![V3 : list_char]: (![V2 : val]: ((((L @ V3) = (some_val @ V2))) => ((?[T3 : ty]: ((((E4 @ V3) = (some_ty @ T3))) & ((conf_P93989998t_char @ P2 @ H3 @ V2 @ T3))))))))))))))). % lconf_def
thf(fact_74_red__reds_ORedFAcc, axiom,
    ((![S2 : produc515445032on_val, A3 : nat, C3 : list_char, Fs5 : produc1257910179t_char > option_val, F : list_char, D2 : list_char, V : val, P : list_P1234162913t_char]: (((hp @ S2 @ A3) = (some_P1299442195on_val @ (produc904988266on_val @ C3 @ Fs5))) => (((Fs5 @ (produc1304532571t_char @ F @ D2)) = (some_val @ V)) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (fAcc_list_char @ (val_list_char @ (addr @ A3)) @ F @ D2) @ S2) @ (produc2023458740on_val @ (val_list_char @ V) @ S2)) @ (red @ P))))))). % red_reds.RedFAcc
thf(fact_75_redp__redsp_ORedFAcc, axiom,
    ((![S2 : produc515445032on_val, A3 : nat, C3 : list_char, Fs5 : produc1257910179t_char > option_val, F : list_char, D2 : list_char, V : val, P : list_P1234162913t_char]: (((hp @ S2 @ A3) = (some_P1299442195on_val @ (produc904988266on_val @ C3 @ Fs5))) => (((Fs5 @ (produc1304532571t_char @ F @ D2)) = (some_val @ V)) => (redp @ P @ (fAcc_list_char @ (val_list_char @ (addr @ A3)) @ F @ D2) @ S2 @ (val_list_char @ V) @ S2)))))). % redp_redsp.RedFAcc
thf(fact_76_FAcc, axiom,
    ((![P : list_P1234162913t_char, E2 : exp_list_char, S_0 : produc515445032on_val, A3 : nat, H : nat > option2118145160on_val, L2 : list_char > option_val, C3 : list_char, Fs5 : produc1257910179t_char > option_val, F : list_char, D2 : list_char, V : val]: ((eval @ P @ E2 @ S_0 @ (val_list_char @ (addr @ A3)) @ (produc52622304on_val @ H @ L2)) => (((H @ A3) = (some_P1299442195on_val @ (produc904988266on_val @ C3 @ Fs5))) => (((Fs5 @ (produc1304532571t_char @ F @ D2)) = (some_val @ V)) => (eval @ P @ (fAcc_list_char @ E2 @ F @ D2) @ S_0 @ (val_list_char @ V) @ (produc52622304on_val @ H @ L2)))))))). % FAcc
thf(fact_77_the__Addr_Osimps, axiom,
    ((![A3 : nat]: ((the_Addr @ (addr @ A3)) = A3)))). % the_Addr.simps
thf(fact_78_pred__equals__eq2, axiom,
    ((![R : set_Pr164112643t_char, S : set_Pr164112643t_char]: (((^[X4 : list_char]: (^[Y6 : list_char]: (member89690956t_char @ (produc1304532571t_char @ X4 @ Y6) @ R))) = (^[X4 : list_char]: (^[Y6 : list_char]: (member89690956t_char @ (produc1304532571t_char @ X4 @ Y6) @ S)))) = (R = S))))). % pred_equals_eq2
thf(fact_79_pred__equals__eq2, axiom,
    ((![R : set_Pr723149704on_val, S : set_Pr723149704on_val]: (((^[X4 : nat > option2118145160on_val]: (^[Y6 : list_char > option_val]: (member652041809on_val @ (produc52622304on_val @ X4 @ Y6) @ R))) = (^[X4 : nat > option2118145160on_val]: (^[Y6 : list_char > option_val]: (member652041809on_val @ (produc52622304on_val @ X4 @ Y6) @ S)))) = (R = S))))). % pred_equals_eq2
thf(fact_80_pred__equals__eq2, axiom,
    ((![R : set_Pr2075231726on_val, S : set_Pr2075231726on_val]: (((^[X4 : list_char]: (^[Y6 : produc1257910179t_char > option_val]: (member1296415951on_val @ (produc904988266on_val @ X4 @ Y6) @ R))) = (^[X4 : list_char]: (^[Y6 : produc1257910179t_char > option_val]: (member1296415951on_val @ (produc904988266on_val @ X4 @ Y6) @ S)))) = (R = S))))). % pred_equals_eq2
thf(fact_81_pred__equals__eq2, axiom,
    ((![R : set_Pr1189492743on_val, S : set_Pr1189492743on_val]: (((^[X4 : produc1097884484on_val]: (^[Y6 : produc1097884484on_val]: (member354538064on_val @ (produc1069526295on_val @ X4 @ Y6) @ R))) = (^[X4 : produc1097884484on_val]: (^[Y6 : produc1097884484on_val]: (member354538064on_val @ (produc1069526295on_val @ X4 @ Y6) @ S)))) = (R = S))))). % pred_equals_eq2
thf(fact_82_pred__equals__eq2, axiom,
    ((![R : set_Pr556513572on_val, S : set_Pr556513572on_val]: (((^[X4 : exp_list_char]: (^[Y6 : produc515445032on_val]: (member1888679917on_val @ (produc2023458740on_val @ X4 @ Y6) @ R))) = (^[X4 : exp_list_char]: (^[Y6 : produc515445032on_val]: (member1888679917on_val @ (produc2023458740on_val @ X4 @ Y6) @ S)))) = (R = S))))). % pred_equals_eq2
thf(fact_83_redp__red__eq, axiom,
    ((redp = (^[P2 : list_P1234162913t_char]: (^[X4 : exp_list_char]: (^[Y6 : produc515445032on_val]: (^[Z : exp_list_char]: (^[Aa : produc515445032on_val]: (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ X4 @ Y6) @ (produc2023458740on_val @ Z @ Aa)) @ (red @ P2)))))))))). % redp_red_eq
thf(fact_84_red__reds_OCondRed, axiom,
    ((![E2 : exp_list_char, S2 : produc515445032on_val, E5 : exp_list_char, S3 : produc515445032on_val, P : list_P1234162913t_char, E_1 : exp_list_char, E_2 : exp_list_char]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E2 @ S2) @ (produc2023458740on_val @ E5 @ S3)) @ (red @ P)) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (cond_list_char @ E2 @ E_1 @ E_2) @ S2) @ (produc2023458740on_val @ (cond_list_char @ E5 @ E_1 @ E_2) @ S3)) @ (red @ P)))))). % red_reds.CondRed
thf(fact_85_red__reds_OFAccRed, axiom,
    ((![E2 : exp_list_char, S2 : produc515445032on_val, E5 : exp_list_char, S3 : produc515445032on_val, P : list_P1234162913t_char, F : list_char, D2 : list_char]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E2 @ S2) @ (produc2023458740on_val @ E5 @ S3)) @ (red @ P)) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (fAcc_list_char @ E2 @ F @ D2) @ S2) @ (produc2023458740on_val @ (fAcc_list_char @ E5 @ F @ D2) @ S3)) @ (red @ P)))))). % red_reds.FAccRed
thf(fact_86_redp__redsp_OFAccRed, axiom,
    ((![P : list_P1234162913t_char, E2 : exp_list_char, S2 : produc515445032on_val, E5 : exp_list_char, S3 : produc515445032on_val, F : list_char, D2 : list_char]: ((redp @ P @ E2 @ S2 @ E5 @ S3) => (redp @ P @ (fAcc_list_char @ E2 @ F @ D2) @ S2 @ (fAcc_list_char @ E5 @ F @ D2) @ S3))))). % redp_redsp.FAccRed
thf(fact_87_redp__redsp_OCondRed, axiom,
    ((![P : list_P1234162913t_char, E2 : exp_list_char, S2 : produc515445032on_val, E5 : exp_list_char, S3 : produc515445032on_val, E_1 : exp_list_char, E_2 : exp_list_char]: ((redp @ P @ E2 @ S2 @ E5 @ S3) => (redp @ P @ (cond_list_char @ E2 @ E_1 @ E_2) @ S2 @ (cond_list_char @ E5 @ E_1 @ E_2) @ S3))))). % redp_redsp.CondRed
thf(fact_88_eval__cases_I2_J, axiom,
    ((![P : list_P1234162913t_char, V : val, S2 : produc515445032on_val, E5 : exp_list_char, S3 : produc515445032on_val]: ((eval @ P @ (val_list_char @ V) @ S2 @ E5 @ S3) => (~ (((E5 = (val_list_char @ V)) => (~ ((S3 = S2)))))))))). % eval_cases(2)
thf(fact_89_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_90_red__preserves__lconf, axiom,
    ((![E2 : exp_list_char, H : nat > option2118145160on_val, L2 : list_char > option_val, E5 : exp_list_char, H2 : nat > option2118145160on_val, L3 : list_char > option_val, P : list_P1234162913t_char, E : list_char > option_ty, T : ty]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E2 @ (produc52622304on_val @ H @ L2)) @ (produc2023458740on_val @ E5 @ (produc52622304on_val @ H2 @ L3))) @ (red @ P)) => ((wTrt @ P @ H @ E @ E2 @ T) => ((lconf_485928294t_char @ P @ H @ L2 @ E) => (lconf_485928294t_char @ P @ H2 @ L3 @ E))))))). % red_preserves_lconf
thf(fact_91_eval__hext, axiom,
    ((![P : list_P1234162913t_char, E2 : exp_list_char, H : nat > option2118145160on_val, L2 : list_char > option_val, E5 : exp_list_char, H2 : nat > option2118145160on_val, L3 : list_char > option_val]: ((eval @ P @ E2 @ (produc52622304on_val @ H @ L2) @ E5 @ (produc52622304on_val @ H2 @ L3)) => (hext @ H @ H2))))). % eval_hext
thf(fact_92_red__hext__incr, axiom,
    ((![E2 : exp_list_char, H : nat > option2118145160on_val, L2 : list_char > option_val, E5 : exp_list_char, H2 : nat > option2118145160on_val, L3 : list_char > option_val, P : list_P1234162913t_char]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E2 @ (produc52622304on_val @ H @ L2)) @ (produc2023458740on_val @ E5 @ (produc52622304on_val @ H2 @ L3))) @ (red @ P)) => (hext @ H @ H2))))). % red_hext_incr
thf(fact_93_lconf__hext, axiom,
    ((![P : list_P1234162913t_char, H : nat > option2118145160on_val, L2 : list_char > option_val, E : list_char > option_ty, H2 : nat > option2118145160on_val]: ((lconf_485928294t_char @ P @ H @ L2 @ E) => ((hext @ H @ H2) => (lconf_485928294t_char @ P @ H2 @ L2 @ E)))))). % lconf_hext
thf(fact_94_red__preserves__sconf, axiom,
    ((![E2 : exp_list_char, S2 : produc515445032on_val, E5 : exp_list_char, S3 : produc515445032on_val, P : list_P1234162913t_char, E : list_char > option_ty, T : ty]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E2 @ S2) @ (produc2023458740on_val @ E5 @ S3)) @ (red @ P)) => ((wTrt @ P @ (hp @ S2) @ E @ E2 @ T) => ((typeSa1777264139_sconf @ P @ E @ S2) => (typeSa1777264139_sconf @ P @ E @ S3))))))). % red_preserves_sconf
thf(fact_95_FAccRedsVal, axiom,
    ((![E2 : exp_list_char, S2 : produc515445032on_val, A3 : nat, S3 : produc515445032on_val, P : list_P1234162913t_char, C3 : list_char, Fs5 : produc1257910179t_char > option_val, F : list_char, D2 : list_char, V : val]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E2 @ S2) @ (produc2023458740on_val @ (val_list_char @ (addr @ A3)) @ S3)) @ (transi111096263on_val @ (red @ P))) => (((hp @ S3 @ A3) = (some_P1299442195on_val @ (produc904988266on_val @ C3 @ Fs5))) => (((Fs5 @ (produc1304532571t_char @ F @ D2)) = (some_val @ V)) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (fAcc_list_char @ E2 @ F @ D2) @ S2) @ (produc2023458740on_val @ (val_list_char @ V) @ S3)) @ (transi111096263on_val @ (red @ P))))))))). % FAccRedsVal
thf(fact_96_red__preserves__hconf, axiom,
    ((![E2 : exp_list_char, H : nat > option2118145160on_val, L2 : list_char > option_val, E5 : exp_list_char, H2 : nat > option2118145160on_val, L3 : list_char > option_val, P : list_P1234162913t_char, E : list_char > option_ty, T : ty]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E2 @ (produc52622304on_val @ H @ L2)) @ (produc2023458740on_val @ E5 @ (produc52622304on_val @ H2 @ L3))) @ (red @ P)) => ((wTrt @ P @ H @ E @ E2 @ T) => ((hconf_1244167010t_char @ P @ H) => (hconf_1244167010t_char @ P @ H2))))))). % red_preserves_hconf
thf(fact_97_red__reds_ORedCondT, axiom,
    ((![E_1 : exp_list_char, E_2 : exp_list_char, S2 : produc515445032on_val, P : list_P1234162913t_char]: (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (cond_list_char @ (val_list_char @ (bool @ $true)) @ E_1 @ E_2) @ S2) @ (produc2023458740on_val @ E_1 @ S2)) @ (red @ P))))). % red_reds.RedCondT
thf(fact_98_red__reds_ORedCondF, axiom,
    ((![E_1 : exp_list_char, E_2 : exp_list_char, S2 : produc515445032on_val, P : list_P1234162913t_char]: (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (cond_list_char @ (val_list_char @ (bool @ $false)) @ E_1 @ E_2) @ S2) @ (produc2023458740on_val @ E_2 @ S2)) @ (red @ P))))). % red_reds.RedCondF
thf(fact_99_extend__1__eval, axiom,
    ((![P : list_P1234162913t_char, E2 : exp_list_char, S2 : produc515445032on_val, E6 : exp_list_char, S4 : produc515445032on_val, E5 : exp_list_char, S3 : produc515445032on_val]: ((wf_pro1229751607t_char @ wwf_J_mdecl @ P) => ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E2 @ S2) @ (produc2023458740on_val @ E6 @ S4)) @ (red @ P)) => ((eval @ P @ E6 @ S4 @ E5 @ S3) => (eval @ P @ E2 @ S2 @ E5 @ S3))))))). % extend_1_eval
thf(fact_100_val_Oinject_I1_J, axiom,
    ((![X3 : $o, Y3 : $o]: (((bool @ X3) = (bool @ Y3)) = (X3 = Y3))))). % val.inject(1)
thf(fact_101_val_Odistinct_I17_J, axiom,
    ((![X3 : $o, X5 : nat]: (~ (((bool @ X3) = (addr @ X5))))))). % val.distinct(17)
thf(fact_102_CondReds2T, axiom,
    ((![E2 : exp_list_char, S_0 : produc515445032on_val, S_1 : produc515445032on_val, P : list_P1234162913t_char, E_1 : exp_list_char, E5 : exp_list_char, S_2 : produc515445032on_val, E_2 : exp_list_char]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E2 @ S_0) @ (produc2023458740on_val @ (val_list_char @ (bool @ $true)) @ S_1)) @ (transi111096263on_val @ (red @ P))) => ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E_1 @ S_1) @ (produc2023458740on_val @ E5 @ S_2)) @ (transi111096263on_val @ (red @ P))) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (cond_list_char @ E2 @ E_1 @ E_2) @ S_0) @ (produc2023458740on_val @ E5 @ S_2)) @ (transi111096263on_val @ (red @ P)))))))). % CondReds2T
thf(fact_103_CondReds2F, axiom,
    ((![E2 : exp_list_char, S_0 : produc515445032on_val, S_1 : produc515445032on_val, P : list_P1234162913t_char, E_2 : exp_list_char, E5 : exp_list_char, S_2 : produc515445032on_val, E_1 : exp_list_char]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E2 @ S_0) @ (produc2023458740on_val @ (val_list_char @ (bool @ $false)) @ S_1)) @ (transi111096263on_val @ (red @ P))) => ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E_2 @ S_1) @ (produc2023458740on_val @ E5 @ S_2)) @ (transi111096263on_val @ (red @ P))) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (cond_list_char @ E2 @ E_1 @ E_2) @ S_0) @ (produc2023458740on_val @ E5 @ S_2)) @ (transi111096263on_val @ (red @ P)))))))). % CondReds2F
thf(fact_104_big__by__small, axiom,
    ((![P : list_P1234162913t_char, E2 : exp_list_char, S2 : produc515445032on_val, E5 : exp_list_char, S3 : produc515445032on_val]: ((wf_pro1229751607t_char @ wwf_J_mdecl @ P) => ((eval @ P @ E2 @ S2 @ E5 @ S3) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E2 @ S2) @ (produc2023458740on_val @ E5 @ S3)) @ (transi111096263on_val @ (red @ P)))))))). % big_by_small
thf(fact_105_extend__eval, axiom,
    ((![P : list_P1234162913t_char, E2 : exp_list_char, S2 : produc515445032on_val, E6 : exp_list_char, S4 : produc515445032on_val, E5 : exp_list_char, S3 : produc515445032on_val]: ((wf_pro1229751607t_char @ wwf_J_mdecl @ P) => ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E2 @ S2) @ (produc2023458740on_val @ E6 @ S4)) @ (transi111096263on_val @ (red @ P))) => ((eval @ P @ E6 @ S4 @ E5 @ S3) => (eval @ P @ E2 @ S2 @ E5 @ S3))))))). % extend_eval
thf(fact_106_FAccReds, axiom,
    ((![E2 : exp_list_char, S2 : produc515445032on_val, E5 : exp_list_char, S3 : produc515445032on_val, P : list_P1234162913t_char, F : list_char, D2 : list_char]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E2 @ S2) @ (produc2023458740on_val @ E5 @ S3)) @ (transi111096263on_val @ (red @ P))) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (fAcc_list_char @ E2 @ F @ D2) @ S2) @ (produc2023458740on_val @ (fAcc_list_char @ E5 @ F @ D2) @ S3)) @ (transi111096263on_val @ (red @ P))))))). % FAccReds
thf(fact_107_CondReds, axiom,
    ((![E2 : exp_list_char, S2 : produc515445032on_val, E5 : exp_list_char, S3 : produc515445032on_val, P : list_P1234162913t_char, E_1 : exp_list_char, E_2 : exp_list_char]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E2 @ S2) @ (produc2023458740on_val @ E5 @ S3)) @ (transi111096263on_val @ (red @ P))) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (cond_list_char @ E2 @ E_1 @ E_2) @ S2) @ (produc2023458740on_val @ (cond_list_char @ E5 @ E_1 @ E_2) @ S3)) @ (transi111096263on_val @ (red @ P))))))). % CondReds
thf(fact_108_converse__rtrancl__induct__red, axiom,
    ((![E2 : exp_list_char, H : nat > option2118145160on_val, L2 : list_char > option_val, E5 : exp_list_char, H2 : nat > option2118145160on_val, L3 : list_char > option_val, P : list_P1234162913t_char, R : exp_list_char > (nat > option2118145160on_val) > (list_char > option_val) > exp_list_char > (nat > option2118145160on_val) > (list_char > option_val) > $o]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E2 @ (produc52622304on_val @ H @ L2)) @ (produc2023458740on_val @ E5 @ (produc52622304on_val @ H2 @ L3))) @ (transi111096263on_val @ (red @ P))) => ((![E7 : exp_list_char, H6 : nat > option2118145160on_val, L4 : list_char > option_val]: (R @ E7 @ H6 @ L4 @ E7 @ H6 @ L4)) => ((![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, E8 : exp_list_char, H7 : nat > option2118145160on_val, L5 : 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 @ E8 @ H7 @ L5) => (R @ E_0 @ H_0 @ L_0 @ E8 @ H7 @ L5)))) => (R @ E2 @ H @ L2 @ E5 @ H2 @ L3))))))). % converse_rtrancl_induct_red
thf(fact_109_CondF, axiom,
    ((![P : list_P1234162913t_char, E2 : exp_list_char, S_0 : produc515445032on_val, S_1 : produc515445032on_val, E_2 : exp_list_char, E5 : exp_list_char, S_2 : produc515445032on_val, E_1 : exp_list_char]: ((eval @ P @ E2 @ S_0 @ (val_list_char @ (bool @ $false)) @ S_1) => ((eval @ P @ E_2 @ S_1 @ E5 @ S_2) => (eval @ P @ (cond_list_char @ E2 @ E_1 @ E_2) @ S_0 @ E5 @ S_2)))))). % CondF
thf(fact_110_CondT, axiom,
    ((![P : list_P1234162913t_char, E2 : exp_list_char, S_0 : produc515445032on_val, S_1 : produc515445032on_val, E_1 : exp_list_char, E5 : exp_list_char, S_2 : produc515445032on_val, E_2 : exp_list_char]: ((eval @ P @ E2 @ S_0 @ (val_list_char @ (bool @ $true)) @ S_1) => ((eval @ P @ E_1 @ S_1 @ E5 @ S_2) => (eval @ P @ (cond_list_char @ E2 @ E_1 @ E_2) @ S_0 @ E5 @ S_2)))))). % CondT
thf(fact_111_redp__redsp_ORedCondF, axiom,
    ((![P : list_P1234162913t_char, E_1 : exp_list_char, E_2 : exp_list_char, S2 : produc515445032on_val]: (redp @ P @ (cond_list_char @ (val_list_char @ (bool @ $false)) @ E_1 @ E_2) @ S2 @ E_2 @ S2)))). % redp_redsp.RedCondF
thf(fact_112_redp__redsp_ORedCondT, axiom,
    ((![P : list_P1234162913t_char, E_1 : exp_list_char, E_2 : exp_list_char, S2 : produc515445032on_val]: (redp @ P @ (cond_list_char @ (val_list_char @ (bool @ $true)) @ E_1 @ E_2) @ S2 @ E_1 @ S2)))). % redp_redsp.RedCondT
thf(fact_113_typeof__h_Osimps_I3_J, axiom,
    ((![H : nat > option2118145160on_val, B : $o]: ((typeof_h @ H @ (bool @ B)) = (some_ty @ boolean))))). % typeof_h.simps(3)
thf(fact_114_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_115_big__iff__small, axiom,
    ((![P : list_P1234162913t_char, E2 : exp_list_char, S2 : produc515445032on_val, E5 : exp_list_char, S3 : produc515445032on_val]: ((wf_pro1229751607t_char @ wwf_J_mdecl @ P) => ((eval @ P @ E2 @ S2 @ E5 @ S3) = (((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E2 @ S2) @ (produc2023458740on_val @ E5 @ S3)) @ (transi111096263on_val @ (red @ P)))) & ((final_list_char @ E5)))))))). % big_iff_small
thf(fact_116_small__by__big, axiom,
    ((![P : list_P1234162913t_char, E2 : exp_list_char, S2 : produc515445032on_val, E5 : exp_list_char, S3 : produc515445032on_val]: ((wf_pro1229751607t_char @ wwf_J_mdecl @ P) => ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E2 @ S2) @ (produc2023458740on_val @ E5 @ S3)) @ (transi111096263on_val @ (red @ P))) => ((final_list_char @ E5) => (eval @ P @ E2 @ S2 @ E5 @ S3))))))). % small_by_big
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) => ((![A : list_char, B3 : list_char, Aa2 : list_char, Ba : list_char]: ((member803902992t_char @ (produc395356247t_char @ (produc1304532571t_char @ A @ 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 @ A @ 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) => ((![A : nat > option2118145160on_val, B3 : list_char > option_val, Aa2 : nat > option2118145160on_val, Ba : list_char > option_val]: ((member2027247312on_val @ (produc2106877847on_val @ (produc52622304on_val @ A @ 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 @ A @ B3))))) => (P @ Ax @ Ay))))))). % converse_rtrancl_induct2
thf(fact_119_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) => ((![A : list_char, B3 : produc1257910179t_char > option_val, Aa2 : list_char, Ba : produc1257910179t_char > option_val]: ((member197592058on_val @ (produc881885833on_val @ (produc904988266on_val @ A @ 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 @ A @ B3))))) => (P @ Ax @ Ay))))))). % converse_rtrancl_induct2
thf(fact_120_converse__rtrancl__induct2, axiom,
    ((![Ax : produc1097884484on_val, Ay : produc1097884484on_val, Bx : produc1097884484on_val, By : produc1097884484on_val, R2 : set_Pr1368603847on_val, P : produc1097884484on_val > produc1097884484on_val > $o]: ((member208988944on_val @ (produc564964183on_val @ (produc1069526295on_val @ Ax @ Ay) @ (produc1069526295on_val @ Bx @ By)) @ (transi100378922on_val @ R2)) => ((P @ Bx @ By) => ((![A : produc1097884484on_val, B3 : produc1097884484on_val, Aa2 : produc1097884484on_val, Ba : produc1097884484on_val]: ((member208988944on_val @ (produc564964183on_val @ (produc1069526295on_val @ A @ 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 @ A @ B3))))) => (P @ Ax @ Ay))))))). % converse_rtrancl_induct2
thf(fact_121_converse__rtrancl__induct2, axiom,
    ((![Ax : exp_list_char, Ay : produc515445032on_val, Bx : exp_list_char, By : produc515445032on_val, R2 : set_Pr1189492743on_val, P : exp_list_char > produc515445032on_val > $o]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ Ax @ Ay) @ (produc2023458740on_val @ Bx @ By)) @ (transi111096263on_val @ R2)) => ((P @ Bx @ By) => ((![A : exp_list_char, B3 : produc515445032on_val, Aa2 : exp_list_char, Ba : produc515445032on_val]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ A @ 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 @ A @ B3))))) => (P @ Ax @ Ay))))))). % converse_rtrancl_induct2
thf(fact_122_rtrancl__idemp, axiom,
    ((![R2 : set_Pr1189492743on_val]: ((transi111096263on_val @ (transi111096263on_val @ R2)) = (transi111096263on_val @ R2))))). % rtrancl_idemp
thf(fact_123_r__into__rtrancl, axiom,
    ((![P3 : produc1172664615on_val, R2 : set_Pr1189492743on_val]: ((member354538064on_val @ P3 @ R2) => (member354538064on_val @ P3 @ (transi111096263on_val @ R2)))))). % r_into_rtrancl
thf(fact_124_eval__final, axiom,
    ((![P : list_P1234162913t_char, E2 : exp_list_char, S2 : produc515445032on_val, E5 : exp_list_char, S3 : produc515445032on_val]: ((eval @ P @ E2 @ S2 @ E5 @ S3) => (final_list_char @ E5))))). % eval_final
thf(fact_125_eval__finalId, axiom,
    ((![E2 : exp_list_char, P : list_P1234162913t_char, S2 : produc515445032on_val]: ((final_list_char @ E2) => (eval @ P @ E2 @ S2 @ E2 @ S2))))). % eval_finalId
thf(fact_126_converse__rtrancl__into__rtrancl, axiom,
    ((![A3 : list_char, B : list_char, R2 : set_Pr164112643t_char, C5 : list_char]: ((member89690956t_char @ (produc1304532571t_char @ A3 @ B) @ R2) => ((member89690956t_char @ (produc1304532571t_char @ B @ C5) @ (transi1879726366t_char @ R2)) => (member89690956t_char @ (produc1304532571t_char @ A3 @ C5) @ (transi1879726366t_char @ R2))))))). % converse_rtrancl_into_rtrancl
thf(fact_127_converse__rtrancl__into__rtrancl, axiom,
    ((![A3 : produc1097884484on_val, B : produc1097884484on_val, R2 : set_Pr1189492743on_val, C5 : produc1097884484on_val]: ((member354538064on_val @ (produc1069526295on_val @ A3 @ B) @ R2) => ((member354538064on_val @ (produc1069526295on_val @ B @ C5) @ (transi111096263on_val @ R2)) => (member354538064on_val @ (produc1069526295on_val @ A3 @ C5) @ (transi111096263on_val @ R2))))))). % converse_rtrancl_into_rtrancl
thf(fact_128_rtrancl_Ortrancl__into__rtrancl, axiom,
    ((![A3 : list_char, B : list_char, R2 : set_Pr164112643t_char, C5 : list_char]: ((member89690956t_char @ (produc1304532571t_char @ A3 @ B) @ (transi1879726366t_char @ R2)) => ((member89690956t_char @ (produc1304532571t_char @ B @ C5) @ R2) => (member89690956t_char @ (produc1304532571t_char @ A3 @ C5) @ (transi1879726366t_char @ R2))))))). % rtrancl.rtrancl_into_rtrancl
thf(fact_129_rtrancl_Ortrancl__into__rtrancl, axiom,
    ((![A3 : produc1097884484on_val, B : produc1097884484on_val, R2 : set_Pr1189492743on_val, C5 : produc1097884484on_val]: ((member354538064on_val @ (produc1069526295on_val @ A3 @ B) @ (transi111096263on_val @ R2)) => ((member354538064on_val @ (produc1069526295on_val @ B @ C5) @ R2) => (member354538064on_val @ (produc1069526295on_val @ A3 @ C5) @ (transi111096263on_val @ R2))))))). % rtrancl.rtrancl_into_rtrancl
thf(fact_130_converse__rtrancl__induct, axiom,
    ((![A3 : list_char, B : list_char, R2 : set_Pr164112643t_char, P : list_char > $o]: ((member89690956t_char @ (produc1304532571t_char @ A3 @ B) @ (transi1879726366t_char @ R2)) => ((P @ B) => ((![Y4 : list_char, Z2 : list_char]: ((member89690956t_char @ (produc1304532571t_char @ Y4 @ Z2) @ R2) => ((member89690956t_char @ (produc1304532571t_char @ Z2 @ B) @ (transi1879726366t_char @ R2)) => ((P @ Z2) => (P @ Y4))))) => (P @ A3))))))). % converse_rtrancl_induct
thf(fact_131_converse__rtrancl__induct, axiom,
    ((![A3 : produc1097884484on_val, B : produc1097884484on_val, R2 : set_Pr1189492743on_val, P : produc1097884484on_val > $o]: ((member354538064on_val @ (produc1069526295on_val @ A3 @ B) @ (transi111096263on_val @ R2)) => ((P @ B) => ((![Y4 : produc1097884484on_val, Z2 : produc1097884484on_val]: ((member354538064on_val @ (produc1069526295on_val @ Y4 @ Z2) @ R2) => ((member354538064on_val @ (produc1069526295on_val @ Z2 @ B) @ (transi111096263on_val @ R2)) => ((P @ Z2) => (P @ Y4))))) => (P @ A3))))))). % converse_rtrancl_induct
thf(fact_132_rtrancl_Ortrancl__refl, axiom,
    ((![A3 : list_char, R2 : set_Pr164112643t_char]: (member89690956t_char @ (produc1304532571t_char @ A3 @ A3) @ (transi1879726366t_char @ R2))))). % rtrancl.rtrancl_refl
thf(fact_133_rtrancl_Ortrancl__refl, axiom,
    ((![A3 : produc1097884484on_val, R2 : set_Pr1189492743on_val]: (member354538064on_val @ (produc1069526295on_val @ A3 @ A3) @ (transi111096263on_val @ R2))))). % rtrancl.rtrancl_refl
thf(fact_134_converse__rtranclE, axiom,
    ((![X : list_char, Z3 : list_char, R2 : set_Pr164112643t_char]: ((member89690956t_char @ (produc1304532571t_char @ X @ Z3) @ (transi1879726366t_char @ R2)) => ((~ ((X = Z3))) => (~ ((![Y4 : list_char]: ((member89690956t_char @ (produc1304532571t_char @ X @ Y4) @ R2) => (~ ((member89690956t_char @ (produc1304532571t_char @ Y4 @ Z3) @ (transi1879726366t_char @ R2))))))))))))). % converse_rtranclE
thf(fact_135_converse__rtranclE, axiom,
    ((![X : produc1097884484on_val, Z3 : produc1097884484on_val, R2 : set_Pr1189492743on_val]: ((member354538064on_val @ (produc1069526295on_val @ X @ Z3) @ (transi111096263on_val @ R2)) => ((~ ((X = Z3))) => (~ ((![Y4 : produc1097884484on_val]: ((member354538064on_val @ (produc1069526295on_val @ X @ Y4) @ R2) => (~ ((member354538064on_val @ (produc1069526295on_val @ Y4 @ Z3) @ (transi111096263on_val @ R2))))))))))))). % converse_rtranclE
thf(fact_136_rtrancl_Oinducts, axiom,
    ((![X1 : list_char, X2 : list_char, R2 : set_Pr164112643t_char, P : list_char > list_char > $o]: ((member89690956t_char @ (produc1304532571t_char @ X1 @ X2) @ (transi1879726366t_char @ R2)) => ((![A : list_char]: (P @ A @ A)) => ((![A : list_char, B3 : list_char, C4 : list_char]: ((member89690956t_char @ (produc1304532571t_char @ A @ B3) @ (transi1879726366t_char @ R2)) => ((P @ A @ B3) => ((member89690956t_char @ (produc1304532571t_char @ B3 @ C4) @ R2) => (P @ A @ C4))))) => (P @ X1 @ X2))))))). % rtrancl.inducts
thf(fact_137_rtrancl_Oinducts, axiom,
    ((![X1 : produc1097884484on_val, X2 : produc1097884484on_val, R2 : set_Pr1189492743on_val, P : produc1097884484on_val > produc1097884484on_val > $o]: ((member354538064on_val @ (produc1069526295on_val @ X1 @ X2) @ (transi111096263on_val @ R2)) => ((![A : produc1097884484on_val]: (P @ A @ A)) => ((![A : produc1097884484on_val, B3 : produc1097884484on_val, C4 : produc1097884484on_val]: ((member354538064on_val @ (produc1069526295on_val @ A @ B3) @ (transi111096263on_val @ R2)) => ((P @ A @ B3) => ((member354538064on_val @ (produc1069526295on_val @ B3 @ C4) @ R2) => (P @ A @ C4))))) => (P @ X1 @ X2))))))). % rtrancl.inducts
thf(fact_138_rtrancl__induct, axiom,
    ((![A3 : list_char, B : list_char, R2 : set_Pr164112643t_char, P : list_char > $o]: ((member89690956t_char @ (produc1304532571t_char @ A3 @ B) @ (transi1879726366t_char @ R2)) => ((P @ A3) => ((![Y4 : list_char, Z2 : list_char]: ((member89690956t_char @ (produc1304532571t_char @ A3 @ Y4) @ (transi1879726366t_char @ R2)) => ((member89690956t_char @ (produc1304532571t_char @ Y4 @ Z2) @ R2) => ((P @ Y4) => (P @ Z2))))) => (P @ B))))))). % rtrancl_induct
thf(fact_139_rtrancl__induct, axiom,
    ((![A3 : produc1097884484on_val, B : produc1097884484on_val, R2 : set_Pr1189492743on_val, P : produc1097884484on_val > $o]: ((member354538064on_val @ (produc1069526295on_val @ A3 @ B) @ (transi111096263on_val @ R2)) => ((P @ A3) => ((![Y4 : produc1097884484on_val, Z2 : produc1097884484on_val]: ((member354538064on_val @ (produc1069526295on_val @ A3 @ Y4) @ (transi111096263on_val @ R2)) => ((member354538064on_val @ (produc1069526295on_val @ Y4 @ Z2) @ R2) => ((P @ Y4) => (P @ Z2))))) => (P @ B))))))). % rtrancl_induct
thf(fact_140_rtrancl__trans, axiom,
    ((![X : list_char, Y : list_char, R2 : set_Pr164112643t_char, Z3 : list_char]: ((member89690956t_char @ (produc1304532571t_char @ X @ Y) @ (transi1879726366t_char @ R2)) => ((member89690956t_char @ (produc1304532571t_char @ Y @ Z3) @ (transi1879726366t_char @ R2)) => (member89690956t_char @ (produc1304532571t_char @ X @ Z3) @ (transi1879726366t_char @ R2))))))). % rtrancl_trans
thf(fact_141_rtrancl__trans, axiom,
    ((![X : produc1097884484on_val, Y : produc1097884484on_val, R2 : set_Pr1189492743on_val, Z3 : produc1097884484on_val]: ((member354538064on_val @ (produc1069526295on_val @ X @ Y) @ (transi111096263on_val @ R2)) => ((member354538064on_val @ (produc1069526295on_val @ Y @ Z3) @ (transi111096263on_val @ R2)) => (member354538064on_val @ (produc1069526295on_val @ X @ Z3) @ (transi111096263on_val @ R2))))))). % rtrancl_trans
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)) = (((?[A2 : list_char]: (((A1 = A2)) & ((A22 = A2))))) | ((?[A2 : list_char]: (?[B4 : list_char]: (?[C6 : list_char]: (((A1 = A2)) & ((((A22 = C6)) & ((((member89690956t_char @ (produc1304532571t_char @ A2 @ B4) @ (transi1879726366t_char @ R2))) & ((member89690956t_char @ (produc1304532571t_char @ B4 @ C6) @ R2)))))))))))))))). % rtrancl.simps
thf(fact_143_rtrancl_Osimps, axiom,
    ((![A1 : produc1097884484on_val, A22 : produc1097884484on_val, R2 : set_Pr1189492743on_val]: ((member354538064on_val @ (produc1069526295on_val @ A1 @ A22) @ (transi111096263on_val @ R2)) = (((?[A2 : produc1097884484on_val]: (((A1 = A2)) & ((A22 = A2))))) | ((?[A2 : produc1097884484on_val]: (?[B4 : produc1097884484on_val]: (?[C6 : produc1097884484on_val]: (((A1 = A2)) & ((((A22 = C6)) & ((((member354538064on_val @ (produc1069526295on_val @ A2 @ B4) @ (transi111096263on_val @ R2))) & ((member354538064on_val @ (produc1069526295on_val @ B4 @ C6) @ R2)))))))))))))))). % rtrancl.simps
thf(fact_144_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_145_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_146_rtranclE, axiom,
    ((![A3 : list_char, B : list_char, R2 : set_Pr164112643t_char]: ((member89690956t_char @ (produc1304532571t_char @ A3 @ B) @ (transi1879726366t_char @ R2)) => ((~ ((A3 = B))) => (~ ((![Y4 : list_char]: ((member89690956t_char @ (produc1304532571t_char @ A3 @ Y4) @ (transi1879726366t_char @ R2)) => (~ ((member89690956t_char @ (produc1304532571t_char @ Y4 @ B) @ R2)))))))))))). % rtranclE
thf(fact_147_rtranclE, axiom,
    ((![A3 : produc1097884484on_val, B : produc1097884484on_val, R2 : set_Pr1189492743on_val]: ((member354538064on_val @ (produc1069526295on_val @ A3 @ B) @ (transi111096263on_val @ R2)) => ((~ ((A3 = B))) => (~ ((![Y4 : produc1097884484on_val]: ((member354538064on_val @ (produc1069526295on_val @ A3 @ Y4) @ (transi111096263on_val @ R2)) => (~ ((member354538064on_val @ (produc1069526295on_val @ Y4 @ B) @ R2)))))))))))). % rtranclE
thf(fact_148_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_149_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) => ((![A : list_char, B3 : list_char, Aa2 : list_char, Ba : list_char]: ((member803902992t_char @ (produc395356247t_char @ (produc1304532571t_char @ Ax @ Ay) @ (produc1304532571t_char @ A @ B3)) @ (transi858104614t_char @ R2)) => ((member803902992t_char @ (produc395356247t_char @ (produc1304532571t_char @ A @ B3) @ (produc1304532571t_char @ Aa2 @ Ba)) @ R2) => ((P @ A @ B3) => (P @ Aa2 @ Ba))))) => (P @ Bx @ By))))))). % rtrancl_induct2
thf(fact_150_rtrancl__induct2, axiom,
    ((![Ax : nat > option2118145160on_val, Ay : list_char > option_val, Bx : nat > option2118145160on_val, By : list_char > option_val, R2 : set_Pr148564103on_val, P : (nat > option2118145160on_val) > (list_char > option_val) > $o]: ((member2027247312on_val @ (produc2106877847on_val @ (produc52622304on_val @ Ax @ Ay) @ (produc52622304on_val @ Bx @ By)) @ (transi432893227on_val @ R2)) => ((P @ Ax @ Ay) => ((![A : nat > option2118145160on_val, B3 : list_char > option_val, Aa2 : nat > option2118145160on_val, Ba : list_char > option_val]: ((member2027247312on_val @ (produc2106877847on_val @ (produc52622304on_val @ Ax @ Ay) @ (produc52622304on_val @ A @ B3)) @ (transi432893227on_val @ R2)) => ((member2027247312on_val @ (produc2106877847on_val @ (produc52622304on_val @ A @ B3) @ (produc52622304on_val @ Aa2 @ Ba)) @ R2) => ((P @ A @ B3) => (P @ Aa2 @ Ba))))) => (P @ Bx @ By))))))). % rtrancl_induct2
thf(fact_151_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) => ((![A : 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 @ A @ B3)) @ (transi2071064181on_val @ R2)) => ((member197592058on_val @ (produc881885833on_val @ (produc904988266on_val @ A @ B3) @ (produc904988266on_val @ Aa2 @ Ba)) @ R2) => ((P @ A @ B3) => (P @ Aa2 @ Ba))))) => (P @ Bx @ By))))))). % rtrancl_induct2
thf(fact_152_rtrancl__induct2, axiom,
    ((![Ax : produc1097884484on_val, Ay : produc1097884484on_val, Bx : produc1097884484on_val, By : produc1097884484on_val, R2 : set_Pr1368603847on_val, P : produc1097884484on_val > produc1097884484on_val > $o]: ((member208988944on_val @ (produc564964183on_val @ (produc1069526295on_val @ Ax @ Ay) @ (produc1069526295on_val @ Bx @ By)) @ (transi100378922on_val @ R2)) => ((P @ Ax @ Ay) => ((![A : produc1097884484on_val, B3 : produc1097884484on_val, Aa2 : produc1097884484on_val, Ba : produc1097884484on_val]: ((member208988944on_val @ (produc564964183on_val @ (produc1069526295on_val @ Ax @ Ay) @ (produc1069526295on_val @ A @ B3)) @ (transi100378922on_val @ R2)) => ((member208988944on_val @ (produc564964183on_val @ (produc1069526295on_val @ A @ B3) @ (produc1069526295on_val @ Aa2 @ Ba)) @ R2) => ((P @ A @ B3) => (P @ Aa2 @ Ba))))) => (P @ Bx @ By))))))). % rtrancl_induct2
thf(fact_153_rtrancl__induct2, axiom,
    ((![Ax : exp_list_char, Ay : produc515445032on_val, Bx : exp_list_char, By : produc515445032on_val, R2 : set_Pr1189492743on_val, P : exp_list_char > produc515445032on_val > $o]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ Ax @ Ay) @ (produc2023458740on_val @ Bx @ By)) @ (transi111096263on_val @ R2)) => ((P @ Ax @ Ay) => ((![A : exp_list_char, B3 : produc515445032on_val, Aa2 : exp_list_char, Ba : produc515445032on_val]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ Ax @ Ay) @ (produc2023458740on_val @ A @ B3)) @ (transi111096263on_val @ R2)) => ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ A @ B3) @ (produc2023458740on_val @ Aa2 @ Ba)) @ R2) => ((P @ A @ B3) => (P @ Aa2 @ Ba))))) => (P @ Bx @ By))))))). % rtrancl_induct2
thf(fact_154_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)))) => (~ ((![A : list_char, B3 : list_char]: ((member803902992t_char @ (produc395356247t_char @ (produc1304532571t_char @ Xa @ Xb) @ (produc1304532571t_char @ A @ B3)) @ R2) => (~ ((member803902992t_char @ (produc395356247t_char @ (produc1304532571t_char @ A @ B3) @ (produc1304532571t_char @ Za @ Zb)) @ (transi858104614t_char @ R2))))))))))))). % converse_rtranclE2
thf(fact_155_converse__rtranclE2, axiom,
    ((![Xa : nat > option2118145160on_val, Xb : list_char > option_val, Za : nat > option2118145160on_val, Zb : list_char > option_val, R2 : set_Pr148564103on_val]: ((member2027247312on_val @ (produc2106877847on_val @ (produc52622304on_val @ Xa @ Xb) @ (produc52622304on_val @ Za @ Zb)) @ (transi432893227on_val @ R2)) => ((~ (((produc52622304on_val @ Xa @ Xb) = (produc52622304on_val @ Za @ Zb)))) => (~ ((![A : nat > option2118145160on_val, B3 : list_char > option_val]: ((member2027247312on_val @ (produc2106877847on_val @ (produc52622304on_val @ Xa @ Xb) @ (produc52622304on_val @ A @ B3)) @ R2) => (~ ((member2027247312on_val @ (produc2106877847on_val @ (produc52622304on_val @ A @ B3) @ (produc52622304on_val @ Za @ Zb)) @ (transi432893227on_val @ R2))))))))))))). % converse_rtranclE2
thf(fact_156_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)))) => (~ ((![A : list_char, B3 : produc1257910179t_char > option_val]: ((member197592058on_val @ (produc881885833on_val @ (produc904988266on_val @ Xa @ Xb) @ (produc904988266on_val @ A @ B3)) @ R2) => (~ ((member197592058on_val @ (produc881885833on_val @ (produc904988266on_val @ A @ B3) @ (produc904988266on_val @ Za @ Zb)) @ (transi2071064181on_val @ R2))))))))))))). % converse_rtranclE2
thf(fact_157_converse__rtranclE2, axiom,
    ((![Xa : produc1097884484on_val, Xb : produc1097884484on_val, Za : produc1097884484on_val, Zb : produc1097884484on_val, R2 : set_Pr1368603847on_val]: ((member208988944on_val @ (produc564964183on_val @ (produc1069526295on_val @ Xa @ Xb) @ (produc1069526295on_val @ Za @ Zb)) @ (transi100378922on_val @ R2)) => ((~ (((produc1069526295on_val @ Xa @ Xb) = (produc1069526295on_val @ Za @ Zb)))) => (~ ((![A : produc1097884484on_val, B3 : produc1097884484on_val]: ((member208988944on_val @ (produc564964183on_val @ (produc1069526295on_val @ Xa @ Xb) @ (produc1069526295on_val @ A @ B3)) @ R2) => (~ ((member208988944on_val @ (produc564964183on_val @ (produc1069526295on_val @ A @ B3) @ (produc1069526295on_val @ Za @ Zb)) @ (transi100378922on_val @ R2))))))))))))). % converse_rtranclE2
thf(fact_158_converse__rtranclE2, axiom,
    ((![Xa : exp_list_char, Xb : produc515445032on_val, Za : exp_list_char, Zb : produc515445032on_val, R2 : set_Pr1189492743on_val]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ Xa @ Xb) @ (produc2023458740on_val @ Za @ Zb)) @ (transi111096263on_val @ R2)) => ((~ (((produc2023458740on_val @ Xa @ Xb) = (produc2023458740on_val @ Za @ Zb)))) => (~ ((![A : exp_list_char, B3 : produc515445032on_val]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ Xa @ Xb) @ (produc2023458740on_val @ A @ B3)) @ R2) => (~ ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ A @ B3) @ (produc2023458740on_val @ Za @ Zb)) @ (transi111096263on_val @ R2))))))))))))). % converse_rtranclE2
thf(fact_159_WhileTReds, axiom,
    ((![B : exp_list_char, S_0 : produc515445032on_val, S_1 : produc515445032on_val, P : list_P1234162913t_char, C5 : exp_list_char, V_1 : val, S_2 : produc515445032on_val, E2 : exp_list_char, S_3 : produc515445032on_val]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ B @ S_0) @ (produc2023458740on_val @ (val_list_char @ (bool @ $true)) @ S_1)) @ (transi111096263on_val @ (red @ P))) => ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ C5 @ S_1) @ (produc2023458740on_val @ (val_list_char @ V_1) @ S_2)) @ (transi111096263on_val @ (red @ P))) => ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (while_list_char @ B @ C5) @ S_2) @ (produc2023458740on_val @ E2 @ S_3)) @ (transi111096263on_val @ (red @ P))) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (while_list_char @ B @ C5) @ S_0) @ (produc2023458740on_val @ E2 @ S_3)) @ (transi111096263on_val @ (red @ P))))))))). % WhileTReds
thf(fact_160_Red__lcl__add, axiom,
    ((![E2 : exp_list_char, H : nat > option2118145160on_val, L2 : list_char > option_val, E5 : exp_list_char, H2 : nat > option2118145160on_val, L3 : list_char > option_val, P : list_P1234162913t_char, L_02 : list_char > option_val]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E2 @ (produc52622304on_val @ H @ L2)) @ (produc2023458740on_val @ E5 @ (produc52622304on_val @ H2 @ L3))) @ (transi111096263on_val @ (red @ P))) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E2 @ (produc52622304on_val @ H @ (map_ad1615113112ar_val @ L_02 @ L2))) @ (produc2023458740on_val @ E5 @ (produc52622304on_val @ H2 @ (map_ad1615113112ar_val @ L_02 @ L3)))) @ (transi111096263on_val @ (red @ P))))))). % Red_lcl_add
thf(fact_161_default__val_Osimps_I2_J, axiom,
    (((default_val @ boolean) = (bool @ $false)))). % default_val.simps(2)
thf(fact_162_exp_Oinject_I13_J, axiom,
    ((![X131 : exp_list_char, X132 : exp_list_char, Y131 : exp_list_char, Y132 : exp_list_char]: (((while_list_char @ X131 @ X132) = (while_list_char @ Y131 @ Y132)) = (((X131 = Y131)) & ((X132 = Y132))))))). % exp.inject(13)
thf(fact_163_exp_Odistinct_I149_J, axiom,
    ((![X71 : exp_list_char, X72 : list_char, X73 : list_char, X131 : exp_list_char, X132 : exp_list_char]: (~ (((fAcc_list_char @ X71 @ X72 @ X73) = (while_list_char @ X131 @ X132))))))). % exp.distinct(149)
thf(fact_164_exp_Odistinct_I199_J, axiom,
    ((![X121 : exp_list_char, X122 : exp_list_char, X123 : exp_list_char, X131 : exp_list_char, X132 : exp_list_char]: (~ (((cond_list_char @ X121 @ X122 @ X123) = (while_list_char @ X131 @ X132))))))). % exp.distinct(199)
thf(fact_165_exp_Odistinct_I73_J, axiom,
    ((![X3 : val, X131 : exp_list_char, X132 : exp_list_char]: (~ (((val_list_char @ X3) = (while_list_char @ X131 @ X132))))))). % exp.distinct(73)
thf(fact_166_WhileT, axiom,
    ((![P : list_P1234162913t_char, E2 : exp_list_char, S_0 : produc515445032on_val, S_1 : produc515445032on_val, C5 : exp_list_char, V_1 : val, S_2 : produc515445032on_val, E_3 : exp_list_char, S_3 : produc515445032on_val]: ((eval @ P @ E2 @ S_0 @ (val_list_char @ (bool @ $true)) @ S_1) => ((eval @ P @ C5 @ S_1 @ (val_list_char @ V_1) @ S_2) => ((eval @ P @ (while_list_char @ E2 @ C5) @ S_2 @ E_3 @ S_3) => (eval @ P @ (while_list_char @ E2 @ C5) @ S_0 @ E_3 @ S_3))))))). % WhileT
thf(fact_167_red__lcl__add, axiom,
    ((![E2 : exp_list_char, H : nat > option2118145160on_val, L2 : list_char > option_val, E5 : exp_list_char, H2 : nat > option2118145160on_val, L3 : list_char > option_val, P : list_P1234162913t_char, L_02 : list_char > option_val]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E2 @ (produc52622304on_val @ H @ L2)) @ (produc2023458740on_val @ E5 @ (produc52622304on_val @ H2 @ L3))) @ (red @ P)) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E2 @ (produc52622304on_val @ H @ (map_ad1615113112ar_val @ L_02 @ L2))) @ (produc2023458740on_val @ E5 @ (produc52622304on_val @ H2 @ (map_ad1615113112ar_val @ L_02 @ L3)))) @ (red @ P)))))). % red_lcl_add
thf(fact_168_map__add__find__right, axiom,
    ((![N : list_char > option_val, K : list_char, Xx : val, M : list_char > option_val]: (((N @ K) = (some_val @ Xx)) => ((map_ad1615113112ar_val @ M @ N @ K) = (some_val @ Xx)))))). % map_add_find_right
thf(fact_169_WhileFReds, axiom,
    ((![B : exp_list_char, S2 : produc515445032on_val, S3 : produc515445032on_val, P : list_P1234162913t_char, C5 : exp_list_char]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ B @ S2) @ (produc2023458740on_val @ (val_list_char @ (bool @ $false)) @ S3)) @ (transi111096263on_val @ (red @ P))) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (while_list_char @ B @ C5) @ S2) @ (produc2023458740on_val @ (val_list_char @ unit) @ S3)) @ (transi111096263on_val @ (red @ P))))))). % WhileFReds
thf(fact_170_val_Odistinct_I3_J, axiom,
    ((![X3 : $o]: (~ ((unit = (bool @ X3))))))). % val.distinct(3)
thf(fact_171_val_Odistinct_I7_J, axiom,
    ((![X5 : nat]: (~ ((unit = (addr @ X5))))))). % val.distinct(7)
thf(fact_172_map__le__refl, axiom,
    ((![F2 : list_char > option_ty]: (map_le_list_char_ty @ F2 @ F2)))). % map_le_refl
thf(fact_173_map__le__trans, axiom,
    ((![M1 : list_char > option_ty, M2 : list_char > option_ty, M3 : list_char > option_ty]: ((map_le_list_char_ty @ M1 @ M2) => ((map_le_list_char_ty @ M2 @ M3) => (map_le_list_char_ty @ M1 @ M3)))))). % map_le_trans
thf(fact_174_map__le__antisym, axiom,
    ((![F2 : list_char > option_ty, G : list_char > option_ty]: ((map_le_list_char_ty @ F2 @ G) => ((map_le_list_char_ty @ G @ F2) => (F2 = G)))))). % map_le_antisym
thf(fact_175_WhileF, axiom,
    ((![P : list_P1234162913t_char, E2 : exp_list_char, S_0 : produc515445032on_val, S_1 : produc515445032on_val, C5 : exp_list_char]: ((eval @ P @ E2 @ S_0 @ (val_list_char @ (bool @ $false)) @ S_1) => (eval @ P @ (while_list_char @ E2 @ C5) @ S_0 @ (val_list_char @ unit) @ S_1))))). % WhileF
thf(fact_176_map__le__iff__map__add__commute, axiom,
    ((![F2 : list_char > option_ty, G : list_char > option_ty]: ((map_le_list_char_ty @ F2 @ (map_add_list_char_ty @ F2 @ G)) = ((map_add_list_char_ty @ F2 @ G) = (map_add_list_char_ty @ G @ F2)))))). % map_le_iff_map_add_commute
thf(fact_177_map__le__iff__map__add__commute, axiom,
    ((![F2 : list_char > option_val, G : list_char > option_val]: ((map_le_list_char_val @ F2 @ (map_ad1615113112ar_val @ F2 @ G)) = ((map_ad1615113112ar_val @ F2 @ G) = (map_ad1615113112ar_val @ G @ F2)))))). % map_le_iff_map_add_commute
thf(fact_178_map__add__subsumed2, axiom,
    ((![F2 : list_char > option_ty, G : list_char > option_ty]: ((map_le_list_char_ty @ F2 @ G) => ((map_add_list_char_ty @ G @ F2) = G))))). % map_add_subsumed2
thf(fact_179_map__add__subsumed2, axiom,
    ((![F2 : list_char > option_val, G : list_char > option_val]: ((map_le_list_char_val @ F2 @ G) => ((map_ad1615113112ar_val @ G @ F2) = G))))). % map_add_subsumed2
thf(fact_180_map__add__subsumed1, axiom,
    ((![F2 : list_char > option_ty, G : list_char > option_ty]: ((map_le_list_char_ty @ F2 @ G) => ((map_add_list_char_ty @ F2 @ G) = G))))). % map_add_subsumed1
thf(fact_181_map__add__subsumed1, axiom,
    ((![F2 : list_char > option_val, G : list_char > option_val]: ((map_le_list_char_val @ F2 @ G) => ((map_ad1615113112ar_val @ F2 @ G) = G))))). % map_add_subsumed1
thf(fact_182_map__add__le__mapI, axiom,
    ((![F2 : list_char > option_ty, H : list_char > option_ty, G : list_char > option_ty]: ((map_le_list_char_ty @ F2 @ H) => ((map_le_list_char_ty @ G @ H) => (map_le_list_char_ty @ (map_add_list_char_ty @ F2 @ G) @ H)))))). % map_add_le_mapI
thf(fact_183_map__add__le__mapI, axiom,
    ((![F2 : list_char > option_val, H : list_char > option_val, G : list_char > option_val]: ((map_le_list_char_val @ F2 @ H) => ((map_le_list_char_val @ G @ H) => (map_le_list_char_val @ (map_ad1615113112ar_val @ F2 @ G) @ H)))))). % map_add_le_mapI
thf(fact_184_map__add__le__mapE, axiom,
    ((![F2 : list_char > option_ty, G : list_char > option_ty, H : list_char > option_ty]: ((map_le_list_char_ty @ (map_add_list_char_ty @ F2 @ G) @ H) => (map_le_list_char_ty @ G @ H))))). % map_add_le_mapE
thf(fact_185_map__add__le__mapE, axiom,
    ((![F2 : list_char > option_val, G : list_char > option_val, H : list_char > option_val]: ((map_le_list_char_val @ (map_ad1615113112ar_val @ F2 @ G) @ H) => (map_le_list_char_val @ G @ H))))). % map_add_le_mapE
thf(fact_186_map__le__map__add, axiom,
    ((![F2 : list_char > option_ty, G : list_char > option_ty]: (map_le_list_char_ty @ F2 @ (map_add_list_char_ty @ G @ F2))))). % map_le_map_add
thf(fact_187_map__le__map__add, axiom,
    ((![F2 : list_char > option_val, G : list_char > option_val]: (map_le_list_char_val @ F2 @ (map_ad1615113112ar_val @ G @ F2))))). % map_le_map_add
thf(fact_188_WhileTRedsThrow, axiom,
    ((![B : exp_list_char, S_0 : produc515445032on_val, S_1 : produc515445032on_val, P : list_P1234162913t_char, C5 : exp_list_char, E2 : exp_list_char, S_2 : produc515445032on_val]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ B @ S_0) @ (produc2023458740on_val @ (val_list_char @ (bool @ $true)) @ S_1)) @ (transi111096263on_val @ (red @ P))) => ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ C5 @ S_1) @ (produc2023458740on_val @ (throw_list_char @ E2) @ S_2)) @ (transi111096263on_val @ (red @ P))) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (while_list_char @ B @ C5) @ S_0) @ (produc2023458740on_val @ (throw_list_char @ E2) @ S_2)) @ (transi111096263on_val @ (red @ P)))))))). % WhileTRedsThrow
thf(fact_189_red__reds_ORedWhile, axiom,
    ((![B : exp_list_char, C5 : exp_list_char, S2 : produc515445032on_val, P : list_P1234162913t_char]: (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (while_list_char @ B @ C5) @ S2) @ (produc2023458740on_val @ (cond_list_char @ B @ (seq_list_char @ C5 @ (while_list_char @ B @ C5)) @ (val_list_char @ unit)) @ S2)) @ (red @ P))))). % red_reds.RedWhile
thf(fact_190_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_191_exp_Oinject_I11_J, axiom,
    ((![X111 : exp_list_char, X112 : exp_list_char, Y111 : exp_list_char, Y112 : exp_list_char]: (((seq_list_char @ X111 @ X112) = (seq_list_char @ Y111 @ Y112)) = (((X111 = Y111)) & ((X112 = Y112))))))). % exp.inject(11)
thf(fact_192_WhileCondThrow, axiom,
    ((![P : list_P1234162913t_char, E2 : exp_list_char, S_0 : produc515445032on_val, E5 : exp_list_char, S_1 : produc515445032on_val, C5 : exp_list_char]: ((eval @ P @ E2 @ S_0 @ (throw_list_char @ E5) @ S_1) => (eval @ P @ (while_list_char @ E2 @ C5) @ S_0 @ (throw_list_char @ E5) @ S_1))))). % WhileCondThrow
thf(fact_193_exp_Odistinct_I205_J, axiom,
    ((![X131 : exp_list_char, X132 : exp_list_char, X14 : exp_list_char]: (~ (((while_list_char @ X131 @ X132) = (throw_list_char @ X14))))))). % exp.distinct(205)
thf(fact_194_exp_Odistinct_I193_J, axiom,
    ((![X111 : exp_list_char, X112 : exp_list_char, X131 : exp_list_char, X132 : exp_list_char]: (~ (((seq_list_char @ X111 @ X112) = (while_list_char @ X131 @ X132))))))). % exp.distinct(193)
thf(fact_195_red__reds_OSeqThrow, axiom,
    ((![E2 : exp_list_char, E_2 : exp_list_char, S2 : produc515445032on_val, P : list_P1234162913t_char]: (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (seq_list_char @ (throw_list_char @ E2) @ E_2) @ S2) @ (produc2023458740on_val @ (throw_list_char @ E2) @ S2)) @ (red @ P))))). % red_reds.SeqThrow
thf(fact_196_eval__evals_OSeqThrow, axiom,
    ((![P : list_P1234162913t_char, E_02 : exp_list_char, S_0 : produc515445032on_val, E2 : exp_list_char, S_1 : produc515445032on_val, E_1 : exp_list_char]: ((eval @ P @ E_02 @ S_0 @ (throw_list_char @ E2) @ S_1) => (eval @ P @ (seq_list_char @ E_02 @ E_1) @ S_0 @ (throw_list_char @ E2) @ S_1))))). % eval_evals.SeqThrow
thf(fact_197_redp__redsp_OSeqRed, axiom,
    ((![P : list_P1234162913t_char, E2 : exp_list_char, S2 : produc515445032on_val, E5 : exp_list_char, S3 : produc515445032on_val, E_2 : exp_list_char]: ((redp @ P @ E2 @ S2 @ E5 @ S3) => (redp @ P @ (seq_list_char @ E2 @ E_2) @ S2 @ (seq_list_char @ E5 @ E_2) @ S3))))). % redp_redsp.SeqRed

% Conjectures (1)
thf(conj_0, conjecture,
    ((?[T5 : ty]: ((wTrt @ p @ a @ e @ (val_list_char @ v) @ T5) & (widen_917054840t_char @ p @ T5 @ t))))).
