% 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_38__5332186_1 ) ; }
% This file was generated by Isabelle (most likely Sledgehammer)
% 2020-12-16 14:18:51.240

% Could-be-implicit typings (28)
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% Explicit typings (72)
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thf(sy_c_Expr_Oexp_OVal_001t__List__Olist_It__String__Ochar_J, 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_thesis____, type,
    thesis : $o).
thf(sy_v_v____, type,
    v : val).

% Relevant facts (239)
thf(fact_0_ha, axiom,
    (((ha @ a) = (some_P1299442195on_val @ (produc904988266on_val @ c @ fs))))). % ha
thf(fact_1_wt, axiom,
    ((wTrt2 @ p @ ha @ e @ (fAss_list_char @ (val_list_char @ (addr @ a)) @ f @ d @ (val_list_char @ v)) @ t))). % wt
thf(fact_2_hconf, axiom,
    ((hconf_1244167010t_char @ p @ ha))). % hconf
thf(fact_3_option_Oinject, axiom,
    ((![X2 : ty, Y2 : ty]: (((some_ty @ X2) = (some_ty @ Y2)) = (X2 = Y2))))). % option.inject
thf(fact_4_option_Oinject, axiom,
    ((![X2 : produc266837688on_val, Y2 : produc266837688on_val]: (((some_P1299442195on_val @ X2) = (some_P1299442195on_val @ Y2)) = (X2 = Y2))))). % option.inject
thf(fact_5_option_Oinject, axiom,
    ((![X2 : val, Y2 : val]: (((some_val @ X2) = (some_val @ Y2)) = (X2 = Y2))))). % option.inject
thf(fact_6_RedFAss_Oprems_I1_J, axiom,
    ((wTrt2 @ p @ ha @ e @ (fAss_list_char @ (val_list_char @ (addr @ a)) @ f @ d @ (val_list_char @ v)) @ t))). % RedFAss.prems(1)
thf(fact_7_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_8_widen__refl, axiom,
    ((![P : list_P1234162913t_char, T : ty]: (widen_917054840t_char @ P @ T @ T)))). % widen_refl
thf(fact_9_RedFAss_Oprems_I2_J, axiom,
    ((hconf_1244167010t_char @ p @ ha))). % RedFAss.prems(2)
thf(fact_10_conf__def, axiom,
    ((conf_P93989998t_char = (^[P2 : list_P1234162913t_char]: (^[H : nat > option2118145160on_val]: (^[V : val]: (^[T2 : ty]: (?[T3 : ty]: ((((typeof_h @ H @ V) = (some_ty @ T3))) & ((widen_917054840t_char @ P2 @ T3 @ T2))))))))))). % conf_def
thf(fact_11_WTrtVal, axiom,
    ((![H2 : nat > option2118145160on_val, V2 : val, T : ty, P : list_P1234162913t_char, E : list_char > option_ty]: (((typeof_h @ H2 @ V2) = (some_ty @ T)) => (wTrt2 @ P @ H2 @ E @ (val_list_char @ V2) @ T))))). % WTrtVal
thf(fact_12_hext__typeof__mono, axiom,
    ((![H2 : nat > option2118145160on_val, H3 : nat > option2118145160on_val, V2 : val, T : ty]: ((hext @ H2 @ H3) => (((typeof_h @ H2 @ V2) = (some_ty @ T)) => ((typeof_h @ H3 @ V2) = (some_ty @ T))))))). % hext_typeof_mono
thf(fact_13_typeof__conf, axiom,
    ((![H2 : nat > option2118145160on_val, V2 : val, T : ty, P : list_P1234162913t_char]: (((typeof_h @ H2 @ V2) = (some_ty @ T)) => (conf_P93989998t_char @ P @ H2 @ V2 @ T))))). % typeof_conf
thf(fact_14_WTrt_H__WTrts_H_Ointros_I3_J, axiom,
    ((![H2 : nat > option2118145160on_val, V2 : val, T : ty, P : list_P1234162913t_char, E : list_char > option_ty]: (((typeof_h @ H2 @ V2) = (some_ty @ T)) => (wTrt @ P @ H2 @ E @ (val_list_char @ V2) @ T))))). % WTrt'_WTrts'.intros(3)
thf(fact_15_typeof__h_Osimps_I4_J, axiom,
    ((![H2 : nat > option2118145160on_val, I : int]: ((typeof_h @ H2 @ (intg @ I)) = (some_ty @ integer))))). % typeof_h.simps(4)
thf(fact_16_hext__refl, axiom,
    ((![H2 : nat > option2118145160on_val]: (hext @ H2 @ H2)))). % hext_refl
thf(fact_17_hextI, axiom,
    ((![H2 : nat > option2118145160on_val, H3 : nat > option2118145160on_val]: ((![A : nat, C : list_char, Fs : produc1257910179t_char > option_val]: (((H2 @ A) = (some_P1299442195on_val @ (produc904988266on_val @ C @ Fs))) => (?[Fs2 : produc1257910179t_char > option_val]: ((H3 @ A) = (some_P1299442195on_val @ (produc904988266on_val @ C @ Fs2)))))) => (hext @ H2 @ H3))))). % hextI
thf(fact_18_wt_H__wt, axiom,
    ((![P : list_P1234162913t_char, H2 : nat > option2118145160on_val, E : list_char > option_ty, E2 : exp_list_char, T : ty]: ((wTrt @ P @ H2 @ E @ E2 @ T) => (wTrt2 @ P @ H2 @ E @ E2 @ T))))). % wt'_wt
thf(fact_19_wt__wt_H, axiom,
    ((![P : list_P1234162913t_char, H2 : nat > option2118145160on_val, E : list_char > option_ty, E2 : exp_list_char, T : ty]: ((wTrt2 @ P @ H2 @ E @ E2 @ T) => (wTrt @ P @ H2 @ E @ E2 @ T))))). % wt_wt'
thf(fact_20_hext__def, axiom,
    ((hext = (^[H : nat > option2118145160on_val]: (^[H4 : nat > option2118145160on_val]: (![A2 : nat]: (![C2 : list_char]: (![Fs3 : produc1257910179t_char > option_val]: ((((H @ 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_21_conf__hext, axiom,
    ((![H2 : nat > option2118145160on_val, H3 : nat > option2118145160on_val, P : list_P1234162913t_char, V2 : val, T : ty]: ((hext @ H2 @ H3) => ((conf_P93989998t_char @ P @ H2 @ V2 @ T) => (conf_P93989998t_char @ P @ H3 @ V2 @ T)))))). % conf_hext
thf(fact_22_hext__objD, axiom,
    ((![H2 : nat > option2118145160on_val, H3 : nat > option2118145160on_val, A3 : nat, C3 : list_char, Fs5 : produc1257910179t_char > option_val]: ((hext @ H2 @ H3) => (((H2 @ A3) = (some_P1299442195on_val @ (produc904988266on_val @ C3 @ Fs5))) => (?[Fs6 : produc1257910179t_char > option_val]: ((H3 @ A3) = (some_P1299442195on_val @ (produc904988266on_val @ C3 @ Fs6))))))))). % hext_objD
thf(fact_23_hext__trans, axiom,
    ((![H2 : nat > option2118145160on_val, H3 : nat > option2118145160on_val, H5 : nat > option2118145160on_val]: ((hext @ H2 @ H3) => ((hext @ H3 @ H5) => (hext @ H2 @ H5)))))). % hext_trans
thf(fact_24_wt_H__iff__wt, axiom,
    ((wTrt = wTrt2))). % wt'_iff_wt
thf(fact_25_WTrt__hext__mono, axiom,
    ((![P : list_P1234162913t_char, H2 : nat > option2118145160on_val, E : list_char > option_ty, E2 : exp_list_char, T : ty, H3 : nat > option2118145160on_val]: ((wTrt2 @ P @ H2 @ E @ E2 @ T) => ((hext @ H2 @ H3) => (wTrt2 @ P @ H3 @ E @ E2 @ T)))))). % WTrt_hext_mono
thf(fact_26_conf__widen, axiom,
    ((![P : list_P1234162913t_char, H2 : nat > option2118145160on_val, V2 : val, T : ty, T4 : ty]: ((conf_P93989998t_char @ P @ H2 @ V2 @ T) => ((widen_917054840t_char @ P @ T @ T4) => (conf_P93989998t_char @ P @ H2 @ V2 @ T4)))))). % conf_widen
thf(fact_27_val_Oinject_I2_J, axiom,
    ((![X4 : int, Y4 : int]: (((intg @ X4) = (intg @ Y4)) = (X4 = Y4))))). % val.inject(2)
thf(fact_28_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_29_val_Oinject_I3_J, axiom,
    ((![X5 : nat, Y5 : nat]: (((addr @ X5) = (addr @ Y5)) = (X5 = Y5))))). % val.inject(3)
thf(fact_30_exp_Oinject_I3_J, axiom,
    ((![X3 : val, Y3 : val]: (((val_list_char @ X3) = (val_list_char @ Y3)) = (X3 = Y3))))). % exp.inject(3)
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_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_35_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_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_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_40_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_41_val_Odistinct_I19_J, axiom,
    ((![X4 : int, X5 : nat]: (~ (((intg @ X4) = (addr @ X5))))))). % val.distinct(19)
thf(fact_42_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_43_lconf__def, axiom,
    ((lconf_485928294t_char = (^[P2 : list_P1234162913t_char]: (^[H : nat > option2118145160on_val]: (^[L : list_char > option_val]: (^[E3 : list_char > option_ty]: (![V3 : list_char]: (![V : val]: ((((L @ V3) = (some_val @ V))) => ((?[T2 : ty]: ((((E3 @ V3) = (some_ty @ T2))) & ((conf_P93989998t_char @ P2 @ H @ V @ T2))))))))))))))). % lconf_def
thf(fact_44_pred__equals__eq2, axiom,
    ((![R : set_Pr2075231726on_val, S : set_Pr2075231726on_val]: (((^[X : list_char]: (^[Y : produc1257910179t_char > option_val]: (member1296415951on_val @ (produc904988266on_val @ X @ Y) @ R))) = (^[X : list_char]: (^[Y : produc1257910179t_char > option_val]: (member1296415951on_val @ (produc904988266on_val @ X @ Y) @ S)))) = (R = S))))). % pred_equals_eq2
thf(fact_45_pred__equals__eq2, axiom,
    ((![R : set_Pr1189492743on_val, S : set_Pr1189492743on_val]: (((^[X : produc1097884484on_val]: (^[Y : produc1097884484on_val]: (member354538064on_val @ (produc1069526295on_val @ X @ Y) @ R))) = (^[X : produc1097884484on_val]: (^[Y : produc1097884484on_val]: (member354538064on_val @ (produc1069526295on_val @ X @ Y) @ S)))) = (R = S))))). % pred_equals_eq2
thf(fact_46_pred__equals__eq2, axiom,
    ((![R : set_Pr556513572on_val, S : set_Pr556513572on_val]: (((^[X : exp_list_char]: (^[Y : produc515445032on_val]: (member1888679917on_val @ (produc2023458740on_val @ X @ Y) @ R))) = (^[X : exp_list_char]: (^[Y : produc515445032on_val]: (member1888679917on_val @ (produc2023458740on_val @ X @ Y) @ S)))) = (R = S))))). % pred_equals_eq2
thf(fact_47_pred__equals__eq2, axiom,
    ((![R : set_Pr723149704on_val, S : set_Pr723149704on_val]: (((^[X : nat > option2118145160on_val]: (^[Y : list_char > option_val]: (member652041809on_val @ (produc52622304on_val @ X @ Y) @ R))) = (^[X : nat > option2118145160on_val]: (^[Y : list_char > option_val]: (member652041809on_val @ (produc52622304on_val @ X @ Y) @ S)))) = (R = S))))). % pred_equals_eq2
thf(fact_48_pred__equals__eq2, axiom,
    ((![R : set_Pr164112643t_char, S : set_Pr164112643t_char]: (((^[X : list_char]: (^[Y : list_char]: (member89690956t_char @ (produc1304532571t_char @ X @ Y) @ R))) = (^[X : list_char]: (^[Y : list_char]: (member89690956t_char @ (produc1304532571t_char @ X @ Y) @ S)))) = (R = S))))). % pred_equals_eq2
thf(fact_49_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_50_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_51_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_52_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_53_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_54_old_Oprod_Oexhaust, axiom,
    ((![Y6 : produc266837688on_val]: (~ ((![A : list_char, B3 : produc1257910179t_char > option_val]: (~ ((Y6 = (produc904988266on_val @ A @ B3)))))))))). % old.prod.exhaust
thf(fact_55_old_Oprod_Oexhaust, axiom,
    ((![Y6 : produc1172664615on_val]: (~ ((![A : produc1097884484on_val, B3 : produc1097884484on_val]: (~ ((Y6 = (produc1069526295on_val @ A @ B3)))))))))). % old.prod.exhaust
thf(fact_56_old_Oprod_Oexhaust, axiom,
    ((![Y6 : produc1097884484on_val]: (~ ((![A : exp_list_char, B3 : produc515445032on_val]: (~ ((Y6 = (produc2023458740on_val @ A @ B3)))))))))). % old.prod.exhaust
thf(fact_57_old_Oprod_Oexhaust, axiom,
    ((![Y6 : produc515445032on_val]: (~ ((![A : nat > option2118145160on_val, B3 : list_char > option_val]: (~ ((Y6 = (produc52622304on_val @ A @ B3)))))))))). % old.prod.exhaust
thf(fact_58_old_Oprod_Oexhaust, axiom,
    ((![Y6 : produc1257910179t_char]: (~ ((![A : list_char, B3 : list_char]: (~ ((Y6 = (produc1304532571t_char @ A @ B3)))))))))). % old.prod.exhaust
thf(fact_59_prod__induct4, axiom,
    ((![P : produc1172664615on_val > $o, X6 : 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 @ X6))))). % prod_induct4
thf(fact_60_prod__induct3, axiom,
    ((![P : produc1172664615on_val > $o, X6 : produc1172664615on_val]: ((![A : produc1097884484on_val, B3 : exp_list_char, C4 : produc515445032on_val]: (P @ (produc1069526295on_val @ A @ (produc2023458740on_val @ B3 @ C4)))) => (P @ X6))))). % prod_induct3
thf(fact_61_prod__induct3, axiom,
    ((![P : produc1097884484on_val > $o, X6 : produc1097884484on_val]: ((![A : exp_list_char, B3 : nat > option2118145160on_val, C4 : list_char > option_val]: (P @ (produc2023458740on_val @ A @ (produc52622304on_val @ B3 @ C4)))) => (P @ X6))))). % prod_induct3
thf(fact_62_mem__Collect__eq, axiom,
    ((![A3 : produc1172664615on_val, P : produc1172664615on_val > $o]: ((member354538064on_val @ A3 @ (collec2055896722on_val @ P)) = (P @ A3))))). % mem_Collect_eq
thf(fact_63_Collect__mem__eq, axiom,
    ((![A5 : set_Pr1189492743on_val]: ((collec2055896722on_val @ (^[X : produc1172664615on_val]: (member354538064on_val @ X @ A5))) = A5)))). % Collect_mem_eq
thf(fact_64_prod__cases4, axiom,
    ((![Y6 : produc1172664615on_val]: (~ ((![A : produc1097884484on_val, B3 : exp_list_char, C4 : nat > option2118145160on_val, D : list_char > option_val]: (~ ((Y6 = (produc1069526295on_val @ A @ (produc2023458740on_val @ B3 @ (produc52622304on_val @ C4 @ D)))))))))))). % prod_cases4
thf(fact_65_prod__cases3, axiom,
    ((![Y6 : produc1172664615on_val]: (~ ((![A : produc1097884484on_val, B3 : exp_list_char, C4 : produc515445032on_val]: (~ ((Y6 = (produc1069526295on_val @ A @ (produc2023458740on_val @ B3 @ C4))))))))))). % prod_cases3
thf(fact_66_prod__cases3, axiom,
    ((![Y6 : produc1097884484on_val]: (~ ((![A : exp_list_char, B3 : nat > option2118145160on_val, C4 : list_char > option_val]: (~ ((Y6 = (produc2023458740on_val @ A @ (produc52622304on_val @ B3 @ C4))))))))))). % prod_cases3
thf(fact_67_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_68_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_69_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_70_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_71_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_72_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_73_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_74_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_75_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_76_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_77_surj__pair, axiom,
    ((![P3 : produc266837688on_val]: (?[X7 : list_char, Y7 : produc1257910179t_char > option_val]: (P3 = (produc904988266on_val @ X7 @ Y7)))))). % surj_pair
thf(fact_78_surj__pair, axiom,
    ((![P3 : produc1172664615on_val]: (?[X7 : produc1097884484on_val, Y7 : produc1097884484on_val]: (P3 = (produc1069526295on_val @ X7 @ Y7)))))). % surj_pair
thf(fact_79_surj__pair, axiom,
    ((![P3 : produc1097884484on_val]: (?[X7 : exp_list_char, Y7 : produc515445032on_val]: (P3 = (produc2023458740on_val @ X7 @ Y7)))))). % surj_pair
thf(fact_80_surj__pair, axiom,
    ((![P3 : produc515445032on_val]: (?[X7 : nat > option2118145160on_val, Y7 : list_char > option_val]: (P3 = (produc52622304on_val @ X7 @ Y7)))))). % surj_pair
thf(fact_81_surj__pair, axiom,
    ((![P3 : produc1257910179t_char]: (?[X7 : list_char, Y7 : list_char]: (P3 = (produc1304532571t_char @ X7 @ Y7)))))). % surj_pair
thf(fact_82_the__Intg_Osimps, axiom,
    ((![I : int]: ((the_Intg @ (intg @ I)) = I)))). % the_Intg.simps
thf(fact_83_the__Addr_Osimps, axiom,
    ((![A3 : nat]: ((the_Addr @ (addr @ A3)) = A3)))). % the_Addr.simps
thf(fact_84_lconf__upd, axiom,
    ((![P : list_P1234162913t_char, H2 : nat > option2118145160on_val, L2 : list_char > option_val, E : list_char > option_ty, V2 : val, T : ty, V4 : list_char]: ((lconf_485928294t_char @ P @ H2 @ L2 @ E) => ((conf_P93989998t_char @ P @ H2 @ V2 @ T) => (((E @ V4) = (some_ty @ T)) => (lconf_485928294t_char @ P @ H2 @ (fun_up1252458416on_val @ L2 @ V4 @ (some_val @ V2)) @ E))))))). % lconf_upd
thf(fact_85_hconfD, axiom,
    ((![P : list_P1234162913t_char, H2 : nat > option2118145160on_val, A3 : nat, Obj : produc266837688on_val]: ((hconf_1244167010t_char @ P @ H2) => (((H2 @ A3) = (some_P1299442195on_val @ Obj)) => (oconf_454120169t_char @ P @ H2 @ Obj)))))). % hconfD
thf(fact_86_typeof__lit__conf, axiom,
    ((![V2 : val, T : ty, P : list_P1234162913t_char, H2 : nat > option2118145160on_val]: (((typeof_h @ (^[X : nat]: none_P1535574167on_val) @ V2) = (some_ty @ T)) => (conf_P93989998t_char @ P @ H2 @ V2 @ T))))). % typeof_lit_conf
thf(fact_87_not__Some__eq, axiom,
    ((![X6 : option_ty]: ((![Y : ty]: (~ ((X6 = (some_ty @ Y))))) = (X6 = none_ty))))). % not_Some_eq
thf(fact_88_not__Some__eq, axiom,
    ((![X6 : option2118145160on_val]: ((![Y : produc266837688on_val]: (~ ((X6 = (some_P1299442195on_val @ Y))))) = (X6 = none_P1535574167on_val))))). % not_Some_eq
thf(fact_89_not__Some__eq, axiom,
    ((![X6 : option_val]: ((![Y : val]: (~ ((X6 = (some_val @ Y))))) = (X6 = none_val))))). % not_Some_eq
thf(fact_90_not__None__eq, axiom,
    ((![X6 : option_ty]: ((~ ((X6 = none_ty))) = (?[Y : ty]: (X6 = (some_ty @ Y))))))). % not_None_eq
thf(fact_91_not__None__eq, axiom,
    ((![X6 : option2118145160on_val]: ((~ ((X6 = none_P1535574167on_val))) = (?[Y : produc266837688on_val]: (X6 = (some_P1299442195on_val @ Y))))))). % not_None_eq
thf(fact_92_not__None__eq, axiom,
    ((![X6 : option_val]: ((~ ((X6 = none_val))) = (?[Y : val]: (X6 = (some_val @ Y))))))). % not_None_eq
thf(fact_93_empty__upd__none, axiom,
    ((![X6 : produc1257910179t_char]: ((fun_up356838326on_val @ (^[X : produc1257910179t_char]: none_val) @ X6 @ none_val) = (^[X : produc1257910179t_char]: none_val))))). % empty_upd_none
thf(fact_94_empty__upd__none, axiom,
    ((![X6 : list_char]: ((fun_up1252458416on_val @ (^[X : list_char]: none_val) @ X6 @ none_val) = (^[X : list_char]: none_val))))). % empty_upd_none
thf(fact_95_empty__upd__none, axiom,
    ((![X6 : nat]: ((fun_up262443479on_val @ (^[X : nat]: none_P1535574167on_val) @ X6 @ none_P1535574167on_val) = (^[X : nat]: none_P1535574167on_val))))). % empty_upd_none
thf(fact_96_map__upd__nonempty, axiom,
    ((![T5 : nat > option2118145160on_val, K : nat, X6 : produc266837688on_val]: (~ (((fun_up262443479on_val @ T5 @ K @ (some_P1299442195on_val @ X6)) = (^[X : nat]: none_P1535574167on_val))))))). % map_upd_nonempty
thf(fact_97_map__upd__nonempty, axiom,
    ((![T5 : produc1257910179t_char > option_val, K : produc1257910179t_char, X6 : val]: (~ (((fun_up356838326on_val @ T5 @ K @ (some_val @ X6)) = (^[X : produc1257910179t_char]: none_val))))))). % map_upd_nonempty
thf(fact_98_map__upd__nonempty, axiom,
    ((![T5 : list_char > option_val, K : list_char, X6 : val]: (~ (((fun_up1252458416on_val @ T5 @ K @ (some_val @ X6)) = (^[X : list_char]: none_val))))))). % map_upd_nonempty
thf(fact_99_map__upd__Some__unfold, axiom,
    ((![M : nat > option2118145160on_val, A3 : nat, B : produc266837688on_val, X6 : nat, Y6 : produc266837688on_val]: (((fun_up262443479on_val @ M @ A3 @ (some_P1299442195on_val @ B) @ X6) = (some_P1299442195on_val @ Y6)) = (((((X6 = A3)) & ((B = Y6)))) | ((((~ ((X6 = A3)))) & (((M @ X6) = (some_P1299442195on_val @ Y6)))))))))). % map_upd_Some_unfold
thf(fact_100_map__upd__Some__unfold, axiom,
    ((![M : produc1257910179t_char > option_val, A3 : produc1257910179t_char, B : val, X6 : produc1257910179t_char, Y6 : val]: (((fun_up356838326on_val @ M @ A3 @ (some_val @ B) @ X6) = (some_val @ Y6)) = (((((X6 = A3)) & ((B = Y6)))) | ((((~ ((X6 = A3)))) & (((M @ X6) = (some_val @ Y6)))))))))). % map_upd_Some_unfold
thf(fact_101_map__upd__Some__unfold, axiom,
    ((![M : list_char > option_val, A3 : list_char, B : val, X6 : list_char, Y6 : val]: (((fun_up1252458416on_val @ M @ A3 @ (some_val @ B) @ X6) = (some_val @ Y6)) = (((((X6 = A3)) & ((B = Y6)))) | ((((~ ((X6 = A3)))) & (((M @ X6) = (some_val @ Y6)))))))))). % map_upd_Some_unfold
thf(fact_102_map__upd__triv, axiom,
    ((![T5 : nat > option2118145160on_val, K : nat, X6 : produc266837688on_val]: (((T5 @ K) = (some_P1299442195on_val @ X6)) => ((fun_up262443479on_val @ T5 @ K @ (some_P1299442195on_val @ X6)) = T5))))). % map_upd_triv
thf(fact_103_map__upd__triv, axiom,
    ((![T5 : produc1257910179t_char > option_val, K : produc1257910179t_char, X6 : val]: (((T5 @ K) = (some_val @ X6)) => ((fun_up356838326on_val @ T5 @ K @ (some_val @ X6)) = T5))))). % map_upd_triv
thf(fact_104_map__upd__triv, axiom,
    ((![T5 : list_char > option_val, K : list_char, X6 : val]: (((T5 @ K) = (some_val @ X6)) => ((fun_up1252458416on_val @ T5 @ K @ (some_val @ X6)) = T5))))). % map_upd_triv
thf(fact_105_map__upd__eqD1, axiom,
    ((![M : nat > option2118145160on_val, A3 : nat, X6 : produc266837688on_val, N : nat > option2118145160on_val, Y6 : produc266837688on_val]: (((fun_up262443479on_val @ M @ A3 @ (some_P1299442195on_val @ X6)) = (fun_up262443479on_val @ N @ A3 @ (some_P1299442195on_val @ Y6))) => (X6 = Y6))))). % map_upd_eqD1
thf(fact_106_map__upd__eqD1, axiom,
    ((![M : produc1257910179t_char > option_val, A3 : produc1257910179t_char, X6 : val, N : produc1257910179t_char > option_val, Y6 : val]: (((fun_up356838326on_val @ M @ A3 @ (some_val @ X6)) = (fun_up356838326on_val @ N @ A3 @ (some_val @ Y6))) => (X6 = Y6))))). % map_upd_eqD1
thf(fact_107_map__upd__eqD1, axiom,
    ((![M : list_char > option_val, A3 : list_char, X6 : val, N : list_char > option_val, Y6 : val]: (((fun_up1252458416on_val @ M @ A3 @ (some_val @ X6)) = (fun_up1252458416on_val @ N @ A3 @ (some_val @ Y6))) => (X6 = Y6))))). % map_upd_eqD1
thf(fact_108_combine__options__cases, axiom,
    ((![X6 : option_ty, P : option_ty > option_ty > $o, Y6 : option_ty]: (((X6 = none_ty) => (P @ X6 @ Y6)) => (((Y6 = none_ty) => (P @ X6 @ Y6)) => ((![A : ty, B3 : ty]: ((X6 = (some_ty @ A)) => ((Y6 = (some_ty @ B3)) => (P @ X6 @ Y6)))) => (P @ X6 @ Y6))))))). % combine_options_cases
thf(fact_109_combine__options__cases, axiom,
    ((![X6 : option_ty, P : option_ty > option2118145160on_val > $o, Y6 : option2118145160on_val]: (((X6 = none_ty) => (P @ X6 @ Y6)) => (((Y6 = none_P1535574167on_val) => (P @ X6 @ Y6)) => ((![A : ty, B3 : produc266837688on_val]: ((X6 = (some_ty @ A)) => ((Y6 = (some_P1299442195on_val @ B3)) => (P @ X6 @ Y6)))) => (P @ X6 @ Y6))))))). % combine_options_cases
thf(fact_110_combine__options__cases, axiom,
    ((![X6 : option_ty, P : option_ty > option_val > $o, Y6 : option_val]: (((X6 = none_ty) => (P @ X6 @ Y6)) => (((Y6 = none_val) => (P @ X6 @ Y6)) => ((![A : ty, B3 : val]: ((X6 = (some_ty @ A)) => ((Y6 = (some_val @ B3)) => (P @ X6 @ Y6)))) => (P @ X6 @ Y6))))))). % combine_options_cases
thf(fact_111_combine__options__cases, axiom,
    ((![X6 : option2118145160on_val, P : option2118145160on_val > option_ty > $o, Y6 : option_ty]: (((X6 = none_P1535574167on_val) => (P @ X6 @ Y6)) => (((Y6 = none_ty) => (P @ X6 @ Y6)) => ((![A : produc266837688on_val, B3 : ty]: ((X6 = (some_P1299442195on_val @ A)) => ((Y6 = (some_ty @ B3)) => (P @ X6 @ Y6)))) => (P @ X6 @ Y6))))))). % combine_options_cases
thf(fact_112_combine__options__cases, axiom,
    ((![X6 : option2118145160on_val, P : option2118145160on_val > option2118145160on_val > $o, Y6 : option2118145160on_val]: (((X6 = none_P1535574167on_val) => (P @ X6 @ Y6)) => (((Y6 = none_P1535574167on_val) => (P @ X6 @ Y6)) => ((![A : produc266837688on_val, B3 : produc266837688on_val]: ((X6 = (some_P1299442195on_val @ A)) => ((Y6 = (some_P1299442195on_val @ B3)) => (P @ X6 @ Y6)))) => (P @ X6 @ Y6))))))). % combine_options_cases
thf(fact_113_combine__options__cases, axiom,
    ((![X6 : option2118145160on_val, P : option2118145160on_val > option_val > $o, Y6 : option_val]: (((X6 = none_P1535574167on_val) => (P @ X6 @ Y6)) => (((Y6 = none_val) => (P @ X6 @ Y6)) => ((![A : produc266837688on_val, B3 : val]: ((X6 = (some_P1299442195on_val @ A)) => ((Y6 = (some_val @ B3)) => (P @ X6 @ Y6)))) => (P @ X6 @ Y6))))))). % combine_options_cases
thf(fact_114_combine__options__cases, axiom,
    ((![X6 : option_val, P : option_val > option_ty > $o, Y6 : option_ty]: (((X6 = none_val) => (P @ X6 @ Y6)) => (((Y6 = none_ty) => (P @ X6 @ Y6)) => ((![A : val, B3 : ty]: ((X6 = (some_val @ A)) => ((Y6 = (some_ty @ B3)) => (P @ X6 @ Y6)))) => (P @ X6 @ Y6))))))). % combine_options_cases
thf(fact_115_combine__options__cases, axiom,
    ((![X6 : option_val, P : option_val > option2118145160on_val > $o, Y6 : option2118145160on_val]: (((X6 = none_val) => (P @ X6 @ Y6)) => (((Y6 = none_P1535574167on_val) => (P @ X6 @ Y6)) => ((![A : val, B3 : produc266837688on_val]: ((X6 = (some_val @ A)) => ((Y6 = (some_P1299442195on_val @ B3)) => (P @ X6 @ Y6)))) => (P @ X6 @ Y6))))))). % combine_options_cases
thf(fact_116_combine__options__cases, axiom,
    ((![X6 : option_val, P : option_val > option_val > $o, Y6 : option_val]: (((X6 = none_val) => (P @ X6 @ Y6)) => (((Y6 = none_val) => (P @ X6 @ Y6)) => ((![A : val, B3 : val]: ((X6 = (some_val @ A)) => ((Y6 = (some_val @ B3)) => (P @ X6 @ Y6)))) => (P @ X6 @ Y6))))))). % combine_options_cases
thf(fact_117_split__option__all, axiom,
    (((^[P4 : option_ty > $o]: (![X8 : option_ty]: (P4 @ X8))) = (^[P2 : option_ty > $o]: (((P2 @ none_ty)) & ((![X : ty]: (P2 @ (some_ty @ X))))))))). % split_option_all
thf(fact_118_split__option__all, axiom,
    (((^[P4 : option2118145160on_val > $o]: (![X8 : option2118145160on_val]: (P4 @ X8))) = (^[P2 : option2118145160on_val > $o]: (((P2 @ none_P1535574167on_val)) & ((![X : produc266837688on_val]: (P2 @ (some_P1299442195on_val @ X))))))))). % split_option_all
thf(fact_119_split__option__all, axiom,
    (((^[P4 : option_val > $o]: (![X8 : option_val]: (P4 @ X8))) = (^[P2 : option_val > $o]: (((P2 @ none_val)) & ((![X : val]: (P2 @ (some_val @ X))))))))). % split_option_all
thf(fact_120_split__option__ex, axiom,
    (((^[P4 : option_ty > $o]: (?[X8 : option_ty]: (P4 @ X8))) = (^[P2 : option_ty > $o]: (((P2 @ none_ty)) | ((?[X : ty]: (P2 @ (some_ty @ X))))))))). % split_option_ex
thf(fact_121_split__option__ex, axiom,
    (((^[P4 : option2118145160on_val > $o]: (?[X8 : option2118145160on_val]: (P4 @ X8))) = (^[P2 : option2118145160on_val > $o]: (((P2 @ none_P1535574167on_val)) | ((?[X : produc266837688on_val]: (P2 @ (some_P1299442195on_val @ X))))))))). % split_option_ex
thf(fact_122_split__option__ex, axiom,
    (((^[P4 : option_val > $o]: (?[X8 : option_val]: (P4 @ X8))) = (^[P2 : option_val > $o]: (((P2 @ none_val)) | ((?[X : val]: (P2 @ (some_val @ X))))))))). % split_option_ex
thf(fact_123_option_Oinducts, axiom,
    ((![P : option_ty > $o, Option : option_ty]: ((P @ none_ty) => ((![X7 : ty]: (P @ (some_ty @ X7))) => (P @ Option)))))). % option.inducts
thf(fact_124_option_Oinducts, axiom,
    ((![P : option2118145160on_val > $o, Option : option2118145160on_val]: ((P @ none_P1535574167on_val) => ((![X7 : produc266837688on_val]: (P @ (some_P1299442195on_val @ X7))) => (P @ Option)))))). % option.inducts
thf(fact_125_option_Oinducts, axiom,
    ((![P : option_val > $o, Option : option_val]: ((P @ none_val) => ((![X7 : val]: (P @ (some_val @ X7))) => (P @ Option)))))). % option.inducts
thf(fact_126_option_Oexhaust, axiom,
    ((![Y6 : option_ty]: ((~ ((Y6 = none_ty))) => (~ ((![X22 : ty]: (~ ((Y6 = (some_ty @ X22))))))))))). % option.exhaust
thf(fact_127_option_Oexhaust, axiom,
    ((![Y6 : option2118145160on_val]: ((~ ((Y6 = none_P1535574167on_val))) => (~ ((![X22 : produc266837688on_val]: (~ ((Y6 = (some_P1299442195on_val @ X22))))))))))). % option.exhaust
thf(fact_128_option_Oexhaust, axiom,
    ((![Y6 : option_val]: ((~ ((Y6 = none_val))) => (~ ((![X22 : val]: (~ ((Y6 = (some_val @ X22))))))))))). % option.exhaust
thf(fact_129_option_OdiscI, axiom,
    ((![Option : option_ty, X2 : ty]: ((Option = (some_ty @ X2)) => (~ ((Option = none_ty))))))). % option.discI
thf(fact_130_option_OdiscI, axiom,
    ((![Option : option2118145160on_val, X2 : produc266837688on_val]: ((Option = (some_P1299442195on_val @ X2)) => (~ ((Option = none_P1535574167on_val))))))). % option.discI
thf(fact_131_option_OdiscI, axiom,
    ((![Option : option_val, X2 : val]: ((Option = (some_val @ X2)) => (~ ((Option = none_val))))))). % option.discI
thf(fact_132_option_Odistinct_I1_J, axiom,
    ((![X2 : ty]: (~ ((none_ty = (some_ty @ X2))))))). % option.distinct(1)
thf(fact_133_option_Odistinct_I1_J, axiom,
    ((![X2 : produc266837688on_val]: (~ ((none_P1535574167on_val = (some_P1299442195on_val @ X2))))))). % option.distinct(1)
thf(fact_134_option_Odistinct_I1_J, axiom,
    ((![X2 : val]: (~ ((none_val = (some_val @ X2))))))). % option.distinct(1)
thf(fact_135_typeof__lit__typeof, axiom,
    ((![V2 : val, T : ty, H2 : nat > option2118145160on_val]: (((typeof_h @ (^[X : nat]: none_P1535574167on_val) @ V2) = (some_ty @ T)) => ((typeof_h @ H2 @ V2) = (some_ty @ T)))))). % typeof_lit_typeof
thf(fact_136_fun__upd__upd, axiom,
    ((![F : nat > option2118145160on_val, X6 : nat, Y6 : option2118145160on_val, Z : option2118145160on_val]: ((fun_up262443479on_val @ (fun_up262443479on_val @ F @ X6 @ Y6) @ X6 @ Z) = (fun_up262443479on_val @ F @ X6 @ Z))))). % fun_upd_upd
thf(fact_137_fun__upd__upd, axiom,
    ((![F : produc1257910179t_char > option_val, X6 : produc1257910179t_char, Y6 : option_val, Z : option_val]: ((fun_up356838326on_val @ (fun_up356838326on_val @ F @ X6 @ Y6) @ X6 @ Z) = (fun_up356838326on_val @ F @ X6 @ Z))))). % fun_upd_upd
thf(fact_138_fun__upd__upd, axiom,
    ((![F : list_char > option_val, X6 : list_char, Y6 : option_val, Z : option_val]: ((fun_up1252458416on_val @ (fun_up1252458416on_val @ F @ X6 @ Y6) @ X6 @ Z) = (fun_up1252458416on_val @ F @ X6 @ Z))))). % fun_upd_upd
thf(fact_139_fun__upd__triv, axiom,
    ((![F : nat > option2118145160on_val, X6 : nat]: ((fun_up262443479on_val @ F @ X6 @ (F @ X6)) = F)))). % fun_upd_triv
thf(fact_140_fun__upd__triv, axiom,
    ((![F : produc1257910179t_char > option_val, X6 : produc1257910179t_char]: ((fun_up356838326on_val @ F @ X6 @ (F @ X6)) = F)))). % fun_upd_triv
thf(fact_141_fun__upd__triv, axiom,
    ((![F : list_char > option_val, X6 : list_char]: ((fun_up1252458416on_val @ F @ X6 @ (F @ X6)) = F)))). % fun_upd_triv
thf(fact_142_fun__upd__apply, axiom,
    ((fun_up262443479on_val = (^[F2 : nat > option2118145160on_val]: (^[X : nat]: (^[Y : option2118145160on_val]: (^[Z2 : nat]: (if_opt451925058on_val @ (Z2 = X) @ Y @ (F2 @ Z2))))))))). % fun_upd_apply
thf(fact_143_fun__upd__apply, axiom,
    ((fun_up356838326on_val = (^[F2 : produc1257910179t_char > option_val]: (^[X : produc1257910179t_char]: (^[Y : option_val]: (^[Z2 : produc1257910179t_char]: (if_option_val @ (Z2 = X) @ Y @ (F2 @ Z2))))))))). % fun_upd_apply
thf(fact_144_fun__upd__apply, axiom,
    ((fun_up1252458416on_val = (^[F2 : list_char > option_val]: (^[X : list_char]: (^[Y : option_val]: (^[Z2 : list_char]: (if_option_val @ (Z2 = X) @ Y @ (F2 @ Z2))))))))). % fun_upd_apply
thf(fact_145_hconf__def, axiom,
    ((hconf_1244167010t_char = (^[P2 : list_P1234162913t_char]: (^[H : nat > option2118145160on_val]: (((![A2 : nat]: (![Obj2 : produc266837688on_val]: ((((H @ A2) = (some_P1299442195on_val @ Obj2))) => ((oconf_454120169t_char @ P2 @ H @ Obj2)))))) & ((preallocated @ H)))))))). % hconf_def
thf(fact_146_conf__upd__obj, axiom,
    ((![H2 : nat > option2118145160on_val, A3 : nat, C3 : list_char, Fs5 : produc1257910179t_char > option_val, P : list_P1234162913t_char, Fs7 : produc1257910179t_char > option_val, X6 : val, T : ty]: (((H2 @ A3) = (some_P1299442195on_val @ (produc904988266on_val @ C3 @ Fs5))) => ((conf_P93989998t_char @ P @ (fun_up262443479on_val @ H2 @ A3 @ (some_P1299442195on_val @ (produc904988266on_val @ C3 @ Fs7))) @ X6 @ T) = (conf_P93989998t_char @ P @ H2 @ X6 @ T)))))). % conf_upd_obj
thf(fact_147_hext__upd__obj, axiom,
    ((![H2 : nat > option2118145160on_val, A3 : nat, C3 : list_char, Fs5 : produc1257910179t_char > option_val, Fs7 : produc1257910179t_char > option_val]: (((H2 @ A3) = (some_P1299442195on_val @ (produc904988266on_val @ C3 @ Fs5))) => (hext @ H2 @ (fun_up262443479on_val @ H2 @ A3 @ (some_P1299442195on_val @ (produc904988266on_val @ C3 @ Fs7)))))))). % hext_upd_obj
thf(fact_148_hext__new, axiom,
    ((![H2 : nat > option2118145160on_val, A3 : nat, X6 : produc266837688on_val]: (((H2 @ A3) = none_P1535574167on_val) => (hext @ H2 @ (fun_up262443479on_val @ H2 @ A3 @ (some_P1299442195on_val @ X6))))))). % hext_new
thf(fact_149_fun__upd__idem__iff, axiom,
    ((![F : nat > option2118145160on_val, X6 : nat, Y6 : option2118145160on_val]: (((fun_up262443479on_val @ F @ X6 @ Y6) = F) = ((F @ X6) = Y6))))). % fun_upd_idem_iff
thf(fact_150_fun__upd__idem__iff, axiom,
    ((![F : produc1257910179t_char > option_val, X6 : produc1257910179t_char, Y6 : option_val]: (((fun_up356838326on_val @ F @ X6 @ Y6) = F) = ((F @ X6) = Y6))))). % fun_upd_idem_iff
thf(fact_151_fun__upd__idem__iff, axiom,
    ((![F : list_char > option_val, X6 : list_char, Y6 : option_val]: (((fun_up1252458416on_val @ F @ X6 @ Y6) = F) = ((F @ X6) = Y6))))). % fun_upd_idem_iff
thf(fact_152_fun__upd__twist, axiom,
    ((![A3 : nat, C5 : nat, M : nat > option2118145160on_val, B : option2118145160on_val, D2 : option2118145160on_val]: ((~ ((A3 = C5))) => ((fun_up262443479on_val @ (fun_up262443479on_val @ M @ A3 @ B) @ C5 @ D2) = (fun_up262443479on_val @ (fun_up262443479on_val @ M @ C5 @ D2) @ A3 @ B)))))). % fun_upd_twist
thf(fact_153_fun__upd__twist, axiom,
    ((![A3 : produc1257910179t_char, C5 : produc1257910179t_char, M : produc1257910179t_char > option_val, B : option_val, D2 : option_val]: ((~ ((A3 = C5))) => ((fun_up356838326on_val @ (fun_up356838326on_val @ M @ A3 @ B) @ C5 @ D2) = (fun_up356838326on_val @ (fun_up356838326on_val @ M @ C5 @ D2) @ A3 @ B)))))). % fun_upd_twist
thf(fact_154_fun__upd__twist, axiom,
    ((![A3 : list_char, C5 : list_char, M : list_char > option_val, B : option_val, D2 : option_val]: ((~ ((A3 = C5))) => ((fun_up1252458416on_val @ (fun_up1252458416on_val @ M @ A3 @ B) @ C5 @ D2) = (fun_up1252458416on_val @ (fun_up1252458416on_val @ M @ C5 @ D2) @ A3 @ B)))))). % fun_upd_twist
thf(fact_155_fun__upd__other, axiom,
    ((![Z : nat, X6 : nat, F : nat > option2118145160on_val, Y6 : option2118145160on_val]: ((~ ((Z = X6))) => ((fun_up262443479on_val @ F @ X6 @ Y6 @ Z) = (F @ Z)))))). % fun_upd_other
thf(fact_156_fun__upd__other, axiom,
    ((![Z : produc1257910179t_char, X6 : produc1257910179t_char, F : produc1257910179t_char > option_val, Y6 : option_val]: ((~ ((Z = X6))) => ((fun_up356838326on_val @ F @ X6 @ Y6 @ Z) = (F @ Z)))))). % fun_upd_other
thf(fact_157_fun__upd__other, axiom,
    ((![Z : list_char, X6 : list_char, F : list_char > option_val, Y6 : option_val]: ((~ ((Z = X6))) => ((fun_up1252458416on_val @ F @ X6 @ Y6 @ Z) = (F @ Z)))))). % fun_upd_other
thf(fact_158_fun__upd__same, axiom,
    ((![F : nat > option2118145160on_val, X6 : nat, Y6 : option2118145160on_val]: ((fun_up262443479on_val @ F @ X6 @ Y6 @ X6) = Y6)))). % fun_upd_same
thf(fact_159_fun__upd__same, axiom,
    ((![F : produc1257910179t_char > option_val, X6 : produc1257910179t_char, Y6 : option_val]: ((fun_up356838326on_val @ F @ X6 @ Y6 @ X6) = Y6)))). % fun_upd_same
thf(fact_160_fun__upd__same, axiom,
    ((![F : list_char > option_val, X6 : list_char, Y6 : option_val]: ((fun_up1252458416on_val @ F @ X6 @ Y6 @ X6) = Y6)))). % fun_upd_same
thf(fact_161_fun__upd__idem, axiom,
    ((![F : nat > option2118145160on_val, X6 : nat, Y6 : option2118145160on_val]: (((F @ X6) = Y6) => ((fun_up262443479on_val @ F @ X6 @ Y6) = F))))). % fun_upd_idem
thf(fact_162_fun__upd__idem, axiom,
    ((![F : produc1257910179t_char > option_val, X6 : produc1257910179t_char, Y6 : option_val]: (((F @ X6) = Y6) => ((fun_up356838326on_val @ F @ X6 @ Y6) = F))))). % fun_upd_idem
thf(fact_163_fun__upd__idem, axiom,
    ((![F : list_char > option_val, X6 : list_char, Y6 : option_val]: (((F @ X6) = Y6) => ((fun_up1252458416on_val @ F @ X6 @ Y6) = F))))). % fun_upd_idem
thf(fact_164_fun__upd__eqD, axiom,
    ((![F : nat > option2118145160on_val, X6 : nat, Y6 : option2118145160on_val, G : nat > option2118145160on_val, Z : option2118145160on_val]: (((fun_up262443479on_val @ F @ X6 @ Y6) = (fun_up262443479on_val @ G @ X6 @ Z)) => (Y6 = Z))))). % fun_upd_eqD
thf(fact_165_fun__upd__eqD, axiom,
    ((![F : produc1257910179t_char > option_val, X6 : produc1257910179t_char, Y6 : option_val, G : produc1257910179t_char > option_val, Z : option_val]: (((fun_up356838326on_val @ F @ X6 @ Y6) = (fun_up356838326on_val @ G @ X6 @ Z)) => (Y6 = Z))))). % fun_upd_eqD
thf(fact_166_fun__upd__eqD, axiom,
    ((![F : list_char > option_val, X6 : list_char, Y6 : option_val, G : list_char > option_val, Z : option_val]: (((fun_up1252458416on_val @ F @ X6 @ Y6) = (fun_up1252458416on_val @ G @ X6 @ Z)) => (Y6 = Z))))). % fun_upd_eqD
thf(fact_167_fun__upd__def, axiom,
    ((fun_up262443479on_val = (^[F2 : nat > option2118145160on_val]: (^[A2 : nat]: (^[B4 : option2118145160on_val]: (^[X : nat]: (if_opt451925058on_val @ (X = A2) @ B4 @ (F2 @ X))))))))). % fun_upd_def
thf(fact_168_fun__upd__def, axiom,
    ((fun_up356838326on_val = (^[F2 : produc1257910179t_char > option_val]: (^[A2 : produc1257910179t_char]: (^[B4 : option_val]: (^[X : produc1257910179t_char]: (if_option_val @ (X = A2) @ B4 @ (F2 @ X))))))))). % fun_upd_def
thf(fact_169_fun__upd__def, axiom,
    ((fun_up1252458416on_val = (^[F2 : list_char > option_val]: (^[A2 : list_char]: (^[B4 : option_val]: (^[X : list_char]: (if_option_val @ (X = A2) @ B4 @ (F2 @ X))))))))). % fun_upd_def
thf(fact_170_hconf__upd__obj, axiom,
    ((![P : list_P1234162913t_char, H2 : nat > option2118145160on_val, A3 : nat, C3 : list_char, Fs5 : produc1257910179t_char > option_val, Fs7 : produc1257910179t_char > option_val]: ((hconf_1244167010t_char @ P @ H2) => (((H2 @ A3) = (some_P1299442195on_val @ (produc904988266on_val @ C3 @ Fs5))) => ((oconf_454120169t_char @ P @ H2 @ (produc904988266on_val @ C3 @ Fs7)) => (hconf_1244167010t_char @ P @ (fun_up262443479on_val @ H2 @ A3 @ (some_P1299442195on_val @ (produc904988266on_val @ C3 @ Fs7)))))))))). % hconf_upd_obj
thf(fact_171_hconf__new, axiom,
    ((![P : list_P1234162913t_char, H2 : nat > option2118145160on_val, A3 : nat, Obj : produc266837688on_val]: ((hconf_1244167010t_char @ P @ H2) => (((H2 @ A3) = none_P1535574167on_val) => ((oconf_454120169t_char @ P @ H2 @ Obj) => (hconf_1244167010t_char @ P @ (fun_up262443479on_val @ H2 @ A3 @ (some_P1299442195on_val @ Obj))))))))). % hconf_new
thf(fact_172_lconf__upd2, axiom,
    ((![P : list_P1234162913t_char, H2 : nat > option2118145160on_val, L2 : list_char > option_val, E : list_char > option_ty, V2 : val, T : ty, V4 : list_char]: ((lconf_485928294t_char @ P @ H2 @ L2 @ E) => ((conf_P93989998t_char @ P @ H2 @ V2 @ T) => (lconf_485928294t_char @ P @ H2 @ (fun_up1252458416on_val @ L2 @ V4 @ (some_val @ V2)) @ (fun_up9191ion_ty @ E @ V4 @ (some_ty @ T)))))))). % lconf_upd2
thf(fact_173_oconf__fupd, axiom,
    ((![P : list_P1234162913t_char, C3 : list_char, F3 : list_char, T : ty, D3 : list_char, H2 : nat > option2118145160on_val, V2 : val, Fs5 : produc1257910179t_char > option_val]: ((has_fi599584195t_char @ P @ C3 @ F3 @ T @ D3) => ((conf_P93989998t_char @ P @ H2 @ V2 @ T) => ((oconf_454120169t_char @ P @ H2 @ (produc904988266on_val @ C3 @ Fs5)) => (oconf_454120169t_char @ P @ H2 @ (produc904988266on_val @ C3 @ (fun_up356838326on_val @ Fs5 @ (produc1304532571t_char @ F3 @ D3) @ (some_val @ V2)))))))))). % oconf_fupd
thf(fact_174_preallocated__new, axiom,
    ((![H2 : nat > option2118145160on_val, A3 : nat, X6 : produc266837688on_val]: ((preallocated @ H2) => (((H2 @ A3) = none_P1535574167on_val) => (preallocated @ (fun_up262443479on_val @ H2 @ A3 @ (some_P1299442195on_val @ X6)))))))). % preallocated_new
thf(fact_175_preallocated__upd__obj, axiom,
    ((![H2 : nat > option2118145160on_val, A3 : nat, C3 : list_char, Fs5 : produc1257910179t_char > option_val, Fs7 : produc1257910179t_char > option_val]: ((preallocated @ H2) => (((H2 @ A3) = (some_P1299442195on_val @ (produc904988266on_val @ C3 @ Fs5))) => (preallocated @ (fun_up262443479on_val @ H2 @ A3 @ (some_P1299442195on_val @ (produc904988266on_val @ C3 @ Fs7))))))))). % preallocated_upd_obj
thf(fact_176_preallocated__hext, axiom,
    ((![H2 : nat > option2118145160on_val, H3 : nat > option2118145160on_val]: ((preallocated @ H2) => ((hext @ H2 @ H3) => (preallocated @ H3)))))). % preallocated_hext
thf(fact_177_red__reds_ORedFAss, axiom,
    ((![H2 : nat > option2118145160on_val, A3 : nat, C3 : list_char, Fs5 : produc1257910179t_char > option_val, F3 : list_char, D3 : list_char, V2 : val, L2 : list_char > option_val, P : list_P1234162913t_char]: (((H2 @ A3) = (some_P1299442195on_val @ (produc904988266on_val @ C3 @ Fs5))) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (fAss_list_char @ (val_list_char @ (addr @ A3)) @ F3 @ D3 @ (val_list_char @ V2)) @ (produc52622304on_val @ H2 @ L2)) @ (produc2023458740on_val @ (val_list_char @ unit) @ (produc52622304on_val @ (fun_up262443479on_val @ H2 @ A3 @ (some_P1299442195on_val @ (produc904988266on_val @ C3 @ (fun_up356838326on_val @ Fs5 @ (produc1304532571t_char @ F3 @ D3) @ (some_val @ V2))))) @ L2))) @ (red @ P)))))). % red_reds.RedFAss
thf(fact_178_redp__redsp_ORedFAss, axiom,
    ((![H2 : nat > option2118145160on_val, A3 : nat, C3 : list_char, Fs5 : produc1257910179t_char > option_val, P : list_P1234162913t_char, F3 : list_char, D3 : list_char, V2 : val, L2 : list_char > option_val]: (((H2 @ A3) = (some_P1299442195on_val @ (produc904988266on_val @ C3 @ Fs5))) => (redp @ P @ (fAss_list_char @ (val_list_char @ (addr @ A3)) @ F3 @ D3 @ (val_list_char @ V2)) @ (produc52622304on_val @ H2 @ L2) @ (val_list_char @ unit) @ (produc52622304on_val @ (fun_up262443479on_val @ H2 @ A3 @ (some_P1299442195on_val @ (produc904988266on_val @ C3 @ (fun_up356838326on_val @ Fs5 @ (produc1304532571t_char @ F3 @ D3) @ (some_val @ V2))))) @ L2)))))). % redp_redsp.RedFAss
thf(fact_179_red__reds_OFAssRed2, axiom,
    ((![E2 : exp_list_char, S2 : produc515445032on_val, E4 : exp_list_char, S3 : produc515445032on_val, P : list_P1234162913t_char, V2 : val, F3 : list_char, D3 : list_char]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E2 @ S2) @ (produc2023458740on_val @ E4 @ S3)) @ (red @ P)) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (fAss_list_char @ (val_list_char @ V2) @ F3 @ D3 @ E2) @ S2) @ (produc2023458740on_val @ (fAss_list_char @ (val_list_char @ V2) @ F3 @ D3 @ E4) @ S3)) @ (red @ P)))))). % red_reds.FAssRed2
thf(fact_180_red__reds_OFAssRed1, axiom,
    ((![E2 : exp_list_char, S2 : produc515445032on_val, E4 : 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 @ E2 @ S2) @ (produc2023458740on_val @ E4 @ S3)) @ (red @ P)) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (fAss_list_char @ E2 @ F3 @ D3 @ E_2) @ S2) @ (produc2023458740on_val @ (fAss_list_char @ E4 @ F3 @ D3 @ E_2) @ S3)) @ (red @ P)))))). % red_reds.FAssRed1
thf(fact_181_red__hext__incr, axiom,
    ((![E2 : exp_list_char, H2 : nat > option2118145160on_val, L2 : list_char > option_val, E4 : exp_list_char, H3 : nat > option2118145160on_val, L3 : list_char > option_val, P : list_P1234162913t_char]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E2 @ (produc52622304on_val @ H2 @ L2)) @ (produc2023458740on_val @ E4 @ (produc52622304on_val @ H3 @ L3))) @ (red @ P)) => (hext @ H2 @ H3))))). % red_hext_incr
thf(fact_182_redp__red__eq, axiom,
    ((redp = (^[P2 : list_P1234162913t_char]: (^[X : exp_list_char]: (^[Y : produc515445032on_val]: (^[Z2 : exp_list_char]: (^[Aa : produc515445032on_val]: (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ X @ Y) @ (produc2023458740on_val @ Z2 @ Aa)) @ (red @ P2)))))))))). % redp_red_eq
thf(fact_183_val_Odistinct_I5_J, axiom,
    ((![X4 : int]: (~ ((unit = (intg @ X4))))))). % val.distinct(5)
thf(fact_184_redp__redsp_OFAssRed1, axiom,
    ((![P : list_P1234162913t_char, E2 : exp_list_char, S2 : produc515445032on_val, E4 : exp_list_char, S3 : produc515445032on_val, F3 : list_char, D3 : list_char, E_2 : exp_list_char]: ((redp @ P @ E2 @ S2 @ E4 @ S3) => (redp @ P @ (fAss_list_char @ E2 @ F3 @ D3 @ E_2) @ S2 @ (fAss_list_char @ E4 @ F3 @ D3 @ E_2) @ S3))))). % redp_redsp.FAssRed1
thf(fact_185_val_Odistinct_I7_J, axiom,
    ((![X5 : nat]: (~ ((unit = (addr @ X5))))))). % val.distinct(7)
thf(fact_186_redp__redsp_OFAssRed2, axiom,
    ((![P : list_P1234162913t_char, E2 : exp_list_char, S2 : produc515445032on_val, E4 : exp_list_char, S3 : produc515445032on_val, V2 : val, F3 : list_char, D3 : list_char]: ((redp @ P @ E2 @ S2 @ E4 @ S3) => (redp @ P @ (fAss_list_char @ (val_list_char @ V2) @ F3 @ D3 @ E2) @ S2 @ (fAss_list_char @ (val_list_char @ V2) @ F3 @ D3 @ E4) @ S3))))). % redp_redsp.FAssRed2
thf(fact_187_FAssRedsVal, axiom,
    ((![E_1 : exp_list_char, S_0 : produc515445032on_val, A3 : nat, S_1 : produc515445032on_val, P : list_P1234162913t_char, E_2 : exp_list_char, V2 : val, H_2 : nat > option2118145160on_val, L_2 : list_char > option_val, C3 : list_char, Fs5 : 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 @ A3)) @ S_1)) @ (transi111096263on_val @ (red @ P))) => ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E_2 @ S_1) @ (produc2023458740on_val @ (val_list_char @ V2) @ (produc52622304on_val @ H_2 @ L_2))) @ (transi111096263on_val @ (red @ P))) => (((some_P1299442195on_val @ (produc904988266on_val @ C3 @ Fs5)) = (H_2 @ A3)) => (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 @ A3 @ (some_P1299442195on_val @ (produc904988266on_val @ C3 @ (fun_up356838326on_val @ Fs5 @ (produc1304532571t_char @ F3 @ D3) @ (some_val @ V2))))) @ L_2))) @ (transi111096263on_val @ (red @ P))))))))). % FAssRedsVal
thf(fact_188_FAss, axiom,
    ((![P : list_P1234162913t_char, E_1 : exp_list_char, S_0 : produc515445032on_val, A3 : nat, S_1 : produc515445032on_val, E_2 : exp_list_char, V2 : val, H_2 : nat > option2118145160on_val, L_2 : list_char > option_val, C3 : list_char, Fs5 : produc1257910179t_char > option_val, Fs7 : 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 @ A3)) @ S_1) => ((eval @ P @ E_2 @ S_1 @ (val_list_char @ V2) @ (produc52622304on_val @ H_2 @ L_2)) => (((H_2 @ A3) = (some_P1299442195on_val @ (produc904988266on_val @ C3 @ Fs5))) => ((Fs7 = (fun_up356838326on_val @ Fs5 @ (produc1304532571t_char @ F3 @ D3) @ (some_val @ V2))) => ((H_22 = (fun_up262443479on_val @ H_2 @ A3 @ (some_P1299442195on_val @ (produc904988266on_val @ C3 @ Fs7)))) => (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_189_eval__hext, axiom,
    ((![P : list_P1234162913t_char, E2 : exp_list_char, H2 : nat > option2118145160on_val, L2 : list_char > option_val, E4 : exp_list_char, H3 : nat > option2118145160on_val, L3 : list_char > option_val]: ((eval @ P @ E2 @ (produc52622304on_val @ H2 @ L2) @ E4 @ (produc52622304on_val @ H3 @ L3)) => (hext @ H2 @ H3))))). % eval_hext
thf(fact_190_eval__cases_I2_J, axiom,
    ((![P : list_P1234162913t_char, V2 : val, S2 : produc515445032on_val, E4 : exp_list_char, S3 : produc515445032on_val]: ((eval @ P @ (val_list_char @ V2) @ S2 @ E4 @ S3) => (~ (((E4 = (val_list_char @ V2)) => (~ ((S3 = S2)))))))))). % eval_cases(2)
thf(fact_191_Val, axiom,
    ((![P : list_P1234162913t_char, V2 : val, S2 : produc515445032on_val]: (eval @ P @ (val_list_char @ V2) @ S2 @ (val_list_char @ V2) @ S2)))). % Val
thf(fact_192_FAssReds1, axiom,
    ((![E2 : exp_list_char, S2 : produc515445032on_val, E4 : 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 @ E2 @ S2) @ (produc2023458740on_val @ E4 @ S3)) @ (transi111096263on_val @ (red @ P))) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (fAss_list_char @ E2 @ F3 @ D3 @ E_2) @ S2) @ (produc2023458740on_val @ (fAss_list_char @ E4 @ F3 @ D3 @ E_2) @ S3)) @ (transi111096263on_val @ (red @ P))))))). % FAssReds1
thf(fact_193_FAssReds2, axiom,
    ((![E2 : exp_list_char, S2 : produc515445032on_val, E4 : exp_list_char, S3 : produc515445032on_val, P : list_P1234162913t_char, V2 : val, F3 : list_char, D3 : list_char]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E2 @ S2) @ (produc2023458740on_val @ E4 @ S3)) @ (transi111096263on_val @ (red @ P))) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (fAss_list_char @ (val_list_char @ V2) @ F3 @ D3 @ E2) @ S2) @ (produc2023458740on_val @ (fAss_list_char @ (val_list_char @ V2) @ F3 @ D3 @ E4) @ S3)) @ (transi111096263on_val @ (red @ P))))))). % FAssReds2
thf(fact_194_converse__rtrancl__induct__red, axiom,
    ((![E2 : exp_list_char, H2 : nat > option2118145160on_val, L2 : list_char > option_val, E4 : exp_list_char, H3 : 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 @ H2 @ L2)) @ (produc2023458740on_val @ E4 @ (produc52622304on_val @ H3 @ L3))) @ (transi111096263on_val @ (red @ P))) => ((![E5 : exp_list_char, H6 : nat > option2118145160on_val, L4 : list_char > option_val]: (R @ E5 @ H6 @ L4 @ E5 @ 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, E6 : 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 @ E6 @ H7 @ L5) => (R @ E_0 @ H_0 @ L_0 @ E6 @ H7 @ L5)))) => (R @ E2 @ H2 @ L2 @ E4 @ H3 @ L3))))))). % converse_rtrancl_induct_red
thf(fact_195_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_196_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_197_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_198_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_199_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_200_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_201_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_202_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_203_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_204_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_205_rtranclE, axiom,
    ((![A3 : list_char, B : list_char, R2 : set_Pr164112643t_char]: ((member89690956t_char @ (produc1304532571t_char @ A3 @ B) @ (transi1879726366t_char @ R2)) => ((~ ((A3 = B))) => (~ ((![Y7 : list_char]: ((member89690956t_char @ (produc1304532571t_char @ A3 @ Y7) @ (transi1879726366t_char @ R2)) => (~ ((member89690956t_char @ (produc1304532571t_char @ Y7 @ B) @ R2)))))))))))). % rtranclE
thf(fact_206_rtranclE, axiom,
    ((![A3 : produc1097884484on_val, B : produc1097884484on_val, R2 : set_Pr1189492743on_val]: ((member354538064on_val @ (produc1069526295on_val @ A3 @ B) @ (transi111096263on_val @ R2)) => ((~ ((A3 = B))) => (~ ((![Y7 : produc1097884484on_val]: ((member354538064on_val @ (produc1069526295on_val @ A3 @ Y7) @ (transi111096263on_val @ R2)) => (~ ((member354538064on_val @ (produc1069526295on_val @ Y7 @ B) @ R2)))))))))))). % rtranclE
thf(fact_207_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_208_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_209_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_210_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_211_rtrancl__trans, axiom,
    ((![X6 : list_char, Y6 : list_char, R2 : set_Pr164112643t_char, Z : list_char]: ((member89690956t_char @ (produc1304532571t_char @ X6 @ Y6) @ (transi1879726366t_char @ R2)) => ((member89690956t_char @ (produc1304532571t_char @ Y6 @ Z) @ (transi1879726366t_char @ R2)) => (member89690956t_char @ (produc1304532571t_char @ X6 @ Z) @ (transi1879726366t_char @ R2))))))). % rtrancl_trans
thf(fact_212_rtrancl__trans, axiom,
    ((![X6 : produc1097884484on_val, Y6 : produc1097884484on_val, R2 : set_Pr1189492743on_val, Z : produc1097884484on_val]: ((member354538064on_val @ (produc1069526295on_val @ X6 @ Y6) @ (transi111096263on_val @ R2)) => ((member354538064on_val @ (produc1069526295on_val @ Y6 @ Z) @ (transi111096263on_val @ R2)) => (member354538064on_val @ (produc1069526295on_val @ X6 @ Z) @ (transi111096263on_val @ R2))))))). % rtrancl_trans
thf(fact_213_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) => ((![Y7 : list_char, Z3 : list_char]: ((member89690956t_char @ (produc1304532571t_char @ A3 @ Y7) @ (transi1879726366t_char @ R2)) => ((member89690956t_char @ (produc1304532571t_char @ Y7 @ Z3) @ R2) => ((P @ Y7) => (P @ Z3))))) => (P @ B))))))). % rtrancl_induct
thf(fact_214_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) => ((![Y7 : produc1097884484on_val, Z3 : produc1097884484on_val]: ((member354538064on_val @ (produc1069526295on_val @ A3 @ Y7) @ (transi111096263on_val @ R2)) => ((member354538064on_val @ (produc1069526295on_val @ Y7 @ Z3) @ R2) => ((P @ Y7) => (P @ Z3))))) => (P @ B))))))). % rtrancl_induct
thf(fact_215_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_216_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_217_converse__rtranclE, axiom,
    ((![X6 : list_char, Z : list_char, R2 : set_Pr164112643t_char]: ((member89690956t_char @ (produc1304532571t_char @ X6 @ Z) @ (transi1879726366t_char @ R2)) => ((~ ((X6 = Z))) => (~ ((![Y7 : list_char]: ((member89690956t_char @ (produc1304532571t_char @ X6 @ Y7) @ R2) => (~ ((member89690956t_char @ (produc1304532571t_char @ Y7 @ Z) @ (transi1879726366t_char @ R2))))))))))))). % converse_rtranclE
thf(fact_218_converse__rtranclE, axiom,
    ((![X6 : produc1097884484on_val, Z : produc1097884484on_val, R2 : set_Pr1189492743on_val]: ((member354538064on_val @ (produc1069526295on_val @ X6 @ Z) @ (transi111096263on_val @ R2)) => ((~ ((X6 = Z))) => (~ ((![Y7 : produc1097884484on_val]: ((member354538064on_val @ (produc1069526295on_val @ X6 @ Y7) @ R2) => (~ ((member354538064on_val @ (produc1069526295on_val @ Y7 @ Z) @ (transi111096263on_val @ R2))))))))))))). % converse_rtranclE
thf(fact_219_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_220_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_221_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) => ((![Y7 : list_char, Z3 : list_char]: ((member89690956t_char @ (produc1304532571t_char @ Y7 @ Z3) @ R2) => ((member89690956t_char @ (produc1304532571t_char @ Z3 @ B) @ (transi1879726366t_char @ R2)) => ((P @ Z3) => (P @ Y7))))) => (P @ A3))))))). % converse_rtrancl_induct
thf(fact_222_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) => ((![Y7 : produc1097884484on_val, Z3 : produc1097884484on_val]: ((member354538064on_val @ (produc1069526295on_val @ Y7 @ Z3) @ R2) => ((member354538064on_val @ (produc1069526295on_val @ Z3 @ B) @ (transi111096263on_val @ R2)) => ((P @ Z3) => (P @ Y7))))) => (P @ A3))))))). % converse_rtrancl_induct
thf(fact_223_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_224_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_225_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_226_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_227_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_228_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_229_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_230_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_231_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_232_LAssRedsVal, axiom,
    ((![E2 : exp_list_char, S2 : produc515445032on_val, V2 : val, H3 : nat > option2118145160on_val, L3 : list_char > option_val, P : list_P1234162913t_char, V4 : list_char]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E2 @ S2) @ (produc2023458740on_val @ (val_list_char @ V2) @ (produc52622304on_val @ H3 @ L3))) @ (transi111096263on_val @ (red @ P))) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (lAss_list_char @ V4 @ E2) @ S2) @ (produc2023458740on_val @ (val_list_char @ unit) @ (produc52622304on_val @ H3 @ (fun_up1252458416on_val @ L3 @ V4 @ (some_val @ V2))))) @ (transi111096263on_val @ (red @ P))))))). % LAssRedsVal
thf(fact_233_FAcc, axiom,
    ((![P : list_P1234162913t_char, E2 : exp_list_char, S_0 : produc515445032on_val, A3 : nat, H2 : nat > option2118145160on_val, L2 : list_char > option_val, C3 : list_char, Fs5 : produc1257910179t_char > option_val, F3 : list_char, D3 : list_char, V2 : val]: ((eval @ P @ E2 @ S_0 @ (val_list_char @ (addr @ A3)) @ (produc52622304on_val @ H2 @ L2)) => (((H2 @ A3) = (some_P1299442195on_val @ (produc904988266on_val @ C3 @ Fs5))) => (((Fs5 @ (produc1304532571t_char @ F3 @ D3)) = (some_val @ V2)) => (eval @ P @ (fAcc_list_char @ E2 @ F3 @ D3) @ S_0 @ (val_list_char @ V2) @ (produc52622304on_val @ H2 @ L2)))))))). % FAcc
thf(fact_234_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_235_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_236_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_237_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_238_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)

% Helper facts (5)
thf(help_If_2_1_If_001t__Option__Ooption_It__Value__Oval_J_T, axiom,
    ((![X6 : option_val, Y6 : option_val]: ((if_option_val @ $false @ X6 @ Y6) = Y6)))).
thf(help_If_1_1_If_001t__Option__Ooption_It__Value__Oval_J_T, axiom,
    ((![X6 : option_val, Y6 : option_val]: ((if_option_val @ $true @ X6 @ Y6) = X6)))).
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,
    ((![X6 : option2118145160on_val, Y6 : option2118145160on_val]: ((if_opt451925058on_val @ $false @ X6 @ Y6) = Y6)))).
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,
    ((![X6 : option2118145160on_val, Y6 : option2118145160on_val]: ((if_opt451925058on_val @ $true @ X6 @ Y6) = X6)))).

% Conjectures (2)
thf(conj_0, hypothesis,
    ((![Tv : ty, TF : ty]: (((typeof_h @ ha @ v) = (some_ty @ Tv)) => ((has_fi599584195t_char @ p @ c @ f @ TF @ d) => ((widen_917054840t_char @ p @ Tv @ TF) => thesis)))))).
thf(conj_1, conjecture,
    (thesis)).
