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% This file was generated by Isabelle (most likely Sledgehammer)
% 2020-12-16 14:19:13.237

% Could-be-implicit typings (24)
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% Explicit typings (61)
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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_Option_Ooption_OSome_001t__Value__Oval, type,
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thf(sy_c_Product__Type_OPair_001_062_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_001_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J, type,
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thf(sy_c_Product__Type_OPair_001t__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_001t__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_M_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_J, type,
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thf(sy_c_SmallStep_Oassigned, type,
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thf(sy_c_SmallStep_Ored, type,
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thf(sy_c_WellTypeRT_OWTrt, type,
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thf(sy_v_E____, type,
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thf(sy_v_P, type,
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thf(sy_v_T_H____, type,
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thf(sy_v_T____, type,
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thf(sy_v_V____, type,
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thf(sy_v_e_Ha____, type,
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thf(sy_v_ea____, type,
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thf(sy_v_h_Ha____, type,
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thf(sy_v_ha____, type,
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thf(sy_v_l_Ha____, type,
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thf(sy_v_la____, type,
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% Relevant facts (215)
thf(fact_0__092_060open_062P_Mh_H_A_092_060turnstile_062_Al_A_I_058_092_060le_062_J_AE_092_060close_062, axiom,
    ((lconf_485928294t_char @ p @ h_a @ la @ e))). % \<open>P,h' \<turnstile> l (:\<le>) E\<close>
thf(fact_1__092_060open_062P_Mh_H_A_092_060turnstile_062_Al_H_A_I_058_092_060le_062_J_AE_IV_A_092_060mapsto_062_AT_J_092_060close_062, axiom,
    ((lconf_485928294t_char @ p @ h_a @ l_a @ (fun_up9191ion_ty @ e @ v @ (some_ty @ t2))))). % \<open>P,h' \<turnstile> l' (:\<le>) E(V \<mapsto> T)\<close>
thf(fact_2_BlockRedNone_Ohyps_I3_J, axiom,
    (((l_a @ v) = none_val))). % BlockRedNone.hyps(3)
thf(fact_3_BlockRedNone_Ohyps_I4_J, axiom,
    ((~ ((assigned @ v @ ea))))). % BlockRedNone.hyps(4)
thf(fact_4_lconf, axiom,
    ((lconf_485928294t_char @ p @ ha @ la @ e))). % lconf
thf(fact_5_fun__upd__upd, axiom,
    ((![F : list_char > option_val, X : list_char, Y : option_val, Z : option_val]: ((fun_up1252458416on_val @ (fun_up1252458416on_val @ F @ X @ Y) @ X @ Z) = (fun_up1252458416on_val @ F @ X @ Z))))). % fun_upd_upd
thf(fact_6_fun__upd__upd, axiom,
    ((![F : list_char > option_ty, X : list_char, Y : option_ty, Z : option_ty]: ((fun_up9191ion_ty @ (fun_up9191ion_ty @ F @ X @ Y) @ X @ Z) = (fun_up9191ion_ty @ F @ X @ Z))))). % fun_upd_upd
thf(fact_7_fun__upd__upd, axiom,
    ((![F : nat > option2118145160on_val, X : nat, Y : option2118145160on_val, Z : option2118145160on_val]: ((fun_up262443479on_val @ (fun_up262443479on_val @ F @ X @ Y) @ X @ Z) = (fun_up262443479on_val @ F @ X @ Z))))). % fun_upd_upd
thf(fact_8_fun__upd__triv, axiom,
    ((![F : list_char > option_val, X : list_char]: ((fun_up1252458416on_val @ F @ X @ (F @ X)) = F)))). % fun_upd_triv
thf(fact_9_fun__upd__triv, axiom,
    ((![F : list_char > option_ty, X : list_char]: ((fun_up9191ion_ty @ F @ X @ (F @ X)) = F)))). % fun_upd_triv
thf(fact_10_fun__upd__triv, axiom,
    ((![F : nat > option2118145160on_val, X : nat]: ((fun_up262443479on_val @ F @ X @ (F @ X)) = F)))). % fun_upd_triv
thf(fact_11_fun__upd__apply, axiom,
    ((fun_up1252458416on_val = (^[F2 : list_char > option_val]: (^[X2 : list_char]: (^[Y2 : option_val]: (^[Z2 : list_char]: (if_option_val @ (Z2 = X2) @ Y2 @ (F2 @ Z2))))))))). % fun_upd_apply
thf(fact_12_fun__upd__apply, axiom,
    ((fun_up9191ion_ty = (^[F2 : list_char > option_ty]: (^[X2 : list_char]: (^[Y2 : option_ty]: (^[Z2 : list_char]: (if_option_ty @ (Z2 = X2) @ Y2 @ (F2 @ Z2))))))))). % fun_upd_apply
thf(fact_13_fun__upd__apply, axiom,
    ((fun_up262443479on_val = (^[F2 : nat > option2118145160on_val]: (^[X2 : nat]: (^[Y2 : option2118145160on_val]: (^[Z2 : nat]: (if_opt451925058on_val @ (Z2 = X2) @ Y2 @ (F2 @ Z2))))))))). % fun_upd_apply
thf(fact_14_IH, axiom,
    ((![E : list_char > option_ty, T : ty]: ((wTrt @ p @ ha @ E @ ea @ T) => ((lconf_485928294t_char @ p @ ha @ (fun_up1252458416on_val @ la @ v @ none_val) @ E) => (lconf_485928294t_char @ p @ h_a @ l_a @ E)))))). % IH
thf(fact_15_BlockRedNone_Oprems_I2_J, axiom,
    ((lconf_485928294t_char @ p @ ha @ la @ e))). % BlockRedNone.prems(2)
thf(fact_16_fun__upd__def, axiom,
    ((fun_up1252458416on_val = (^[F2 : list_char > option_val]: (^[A : list_char]: (^[B : option_val]: (^[X2 : list_char]: (if_option_val @ (X2 = A) @ B @ (F2 @ X2))))))))). % fun_upd_def
thf(fact_17_fun__upd__def, axiom,
    ((fun_up9191ion_ty = (^[F2 : list_char > option_ty]: (^[A : list_char]: (^[B : option_ty]: (^[X2 : list_char]: (if_option_ty @ (X2 = A) @ B @ (F2 @ X2))))))))). % fun_upd_def
thf(fact_18_fun__upd__def, axiom,
    ((fun_up262443479on_val = (^[F2 : nat > option2118145160on_val]: (^[A : nat]: (^[B : option2118145160on_val]: (^[X2 : nat]: (if_opt451925058on_val @ (X2 = A) @ B @ (F2 @ X2))))))))). % fun_upd_def
thf(fact_19_fun__upd__eqD, axiom,
    ((![F : list_char > option_val, X : list_char, Y : option_val, G : list_char > option_val, Z : option_val]: (((fun_up1252458416on_val @ F @ X @ Y) = (fun_up1252458416on_val @ G @ X @ Z)) => (Y = Z))))). % fun_upd_eqD
thf(fact_20_fun__upd__eqD, axiom,
    ((![F : list_char > option_ty, X : list_char, Y : option_ty, G : list_char > option_ty, Z : option_ty]: (((fun_up9191ion_ty @ F @ X @ Y) = (fun_up9191ion_ty @ G @ X @ Z)) => (Y = Z))))). % fun_upd_eqD
thf(fact_21_fun__upd__eqD, axiom,
    ((![F : nat > option2118145160on_val, X : nat, Y : option2118145160on_val, G : nat > option2118145160on_val, Z : option2118145160on_val]: (((fun_up262443479on_val @ F @ X @ Y) = (fun_up262443479on_val @ G @ X @ Z)) => (Y = Z))))). % fun_upd_eqD
thf(fact_22_fun__upd__idem, axiom,
    ((![F : list_char > option_val, X : list_char, Y : option_val]: (((F @ X) = Y) => ((fun_up1252458416on_val @ F @ X @ Y) = F))))). % fun_upd_idem
thf(fact_23_fun__upd__idem, axiom,
    ((![F : list_char > option_ty, X : list_char, Y : option_ty]: (((F @ X) = Y) => ((fun_up9191ion_ty @ F @ X @ Y) = F))))). % fun_upd_idem
thf(fact_24_fun__upd__idem, axiom,
    ((![F : nat > option2118145160on_val, X : nat, Y : option2118145160on_val]: (((F @ X) = Y) => ((fun_up262443479on_val @ F @ X @ Y) = F))))). % fun_upd_idem
thf(fact_25_fun__upd__same, axiom,
    ((![F : list_char > option_val, X : list_char, Y : option_val]: ((fun_up1252458416on_val @ F @ X @ Y @ X) = Y)))). % fun_upd_same
thf(fact_26_fun__upd__same, axiom,
    ((![F : list_char > option_ty, X : list_char, Y : option_ty]: ((fun_up9191ion_ty @ F @ X @ Y @ X) = Y)))). % fun_upd_same
thf(fact_27_fun__upd__same, axiom,
    ((![F : nat > option2118145160on_val, X : nat, Y : option2118145160on_val]: ((fun_up262443479on_val @ F @ X @ Y @ X) = Y)))). % fun_upd_same
thf(fact_28_fun__upd__other, axiom,
    ((![Z : list_char, X : list_char, F : list_char > option_val, Y : option_val]: ((~ ((Z = X))) => ((fun_up1252458416on_val @ F @ X @ Y @ Z) = (F @ Z)))))). % fun_upd_other
thf(fact_29_fun__upd__other, axiom,
    ((![Z : list_char, X : list_char, F : list_char > option_ty, Y : option_ty]: ((~ ((Z = X))) => ((fun_up9191ion_ty @ F @ X @ Y @ Z) = (F @ Z)))))). % fun_upd_other
thf(fact_30_fun__upd__other, axiom,
    ((![Z : nat, X : nat, F : nat > option2118145160on_val, Y : option2118145160on_val]: ((~ ((Z = X))) => ((fun_up262443479on_val @ F @ X @ Y @ Z) = (F @ Z)))))). % fun_upd_other
thf(fact_31_BlockRedNone_Ohyps_I2_J, axiom,
    ((![E : list_char > option_ty, T : ty]: ((wTrt @ p @ ha @ E @ ea @ T) => ((lconf_485928294t_char @ p @ ha @ (fun_up1252458416on_val @ la @ v @ none_val) @ E) => (lconf_485928294t_char @ p @ h_a @ l_a @ E)))))). % BlockRedNone.hyps(2)
thf(fact_32_fun__upd__idem__iff, axiom,
    ((![F : list_char > option_val, X : list_char, Y : option_val]: (((fun_up1252458416on_val @ F @ X @ Y) = F) = ((F @ X) = Y))))). % fun_upd_idem_iff
thf(fact_33_fun__upd__idem__iff, axiom,
    ((![F : list_char > option_ty, X : list_char, Y : option_ty]: (((fun_up9191ion_ty @ F @ X @ Y) = F) = ((F @ X) = Y))))). % fun_upd_idem_iff
thf(fact_34_fun__upd__idem__iff, axiom,
    ((![F : nat > option2118145160on_val, X : nat, Y : option2118145160on_val]: (((fun_up262443479on_val @ F @ X @ Y) = F) = ((F @ X) = Y))))). % fun_upd_idem_iff
thf(fact_35_fun__upd__twist, axiom,
    ((![A2 : list_char, C : list_char, M : list_char > option_val, B2 : option_val, D : option_val]: ((~ ((A2 = C))) => ((fun_up1252458416on_val @ (fun_up1252458416on_val @ M @ A2 @ B2) @ C @ D) = (fun_up1252458416on_val @ (fun_up1252458416on_val @ M @ C @ D) @ A2 @ B2)))))). % fun_upd_twist
thf(fact_36_fun__upd__twist, axiom,
    ((![A2 : list_char, C : list_char, M : list_char > option_ty, B2 : option_ty, D : option_ty]: ((~ ((A2 = C))) => ((fun_up9191ion_ty @ (fun_up9191ion_ty @ M @ A2 @ B2) @ C @ D) = (fun_up9191ion_ty @ (fun_up9191ion_ty @ M @ C @ D) @ A2 @ B2)))))). % fun_upd_twist
thf(fact_37_fun__upd__twist, axiom,
    ((![A2 : nat, C : nat, M : nat > option2118145160on_val, B2 : option2118145160on_val, D : option2118145160on_val]: ((~ ((A2 = C))) => ((fun_up262443479on_val @ (fun_up262443479on_val @ M @ A2 @ B2) @ C @ D) = (fun_up262443479on_val @ (fun_up262443479on_val @ M @ C @ D) @ A2 @ B2)))))). % fun_upd_twist
thf(fact_38_BlockRedNone_Oprems_I1_J, axiom,
    ((wTrt @ p @ ha @ e @ (block_list_char @ v @ t2 @ ea) @ t))). % BlockRedNone.prems(1)
thf(fact_39_lconf__empty, axiom,
    ((![P : list_P1234162913t_char, H : nat > option2118145160on_val, E : list_char > option_ty]: (lconf_485928294t_char @ P @ H @ (^[X2 : list_char]: none_val) @ E)))). % lconf_empty
thf(fact_40_empty__upd__none, axiom,
    ((![X : list_char]: ((fun_up9191ion_ty @ (^[X2 : list_char]: none_ty) @ X @ none_ty) = (^[X2 : list_char]: none_ty))))). % empty_upd_none
thf(fact_41_empty__upd__none, axiom,
    ((![X : list_char]: ((fun_up1252458416on_val @ (^[X2 : list_char]: none_val) @ X @ none_val) = (^[X2 : list_char]: none_val))))). % empty_upd_none
thf(fact_42_empty__upd__none, axiom,
    ((![X : nat]: ((fun_up262443479on_val @ (^[X2 : nat]: none_P1535574167on_val) @ X @ none_P1535574167on_val) = (^[X2 : nat]: none_P1535574167on_val))))). % empty_upd_none
thf(fact_43_not__None__eq, axiom,
    ((![X : option_ty]: ((~ ((X = none_ty))) = (?[Y2 : ty]: (X = (some_ty @ Y2))))))). % not_None_eq
thf(fact_44_not__None__eq, axiom,
    ((![X : option2118145160on_val]: ((~ ((X = none_P1535574167on_val))) = (?[Y2 : produc266837688on_val]: (X = (some_P1299442195on_val @ Y2))))))). % not_None_eq
thf(fact_45_not__None__eq, axiom,
    ((![X : option_val]: ((~ ((X = none_val))) = (?[Y2 : val]: (X = (some_val @ Y2))))))). % not_None_eq
thf(fact_46_not__Some__eq, axiom,
    ((![X : option_ty]: ((![Y2 : ty]: (~ ((X = (some_ty @ Y2))))) = (X = none_ty))))). % not_Some_eq
thf(fact_47_not__Some__eq, axiom,
    ((![X : option2118145160on_val]: ((![Y2 : produc266837688on_val]: (~ ((X = (some_P1299442195on_val @ Y2))))) = (X = none_P1535574167on_val))))). % not_Some_eq
thf(fact_48_not__Some__eq, axiom,
    ((![X : option_val]: ((![Y2 : val]: (~ ((X = (some_val @ Y2))))) = (X = none_val))))). % not_Some_eq
thf(fact_49_wt, axiom,
    ((wTrt @ p @ ha @ e @ (block_list_char @ v @ t2 @ ea) @ t))). % wt
thf(fact_50_map__upd__nonempty, axiom,
    ((![T2 : list_char > option_ty, K : list_char, X : ty]: (~ (((fun_up9191ion_ty @ T2 @ K @ (some_ty @ X)) = (^[X2 : list_char]: none_ty))))))). % map_upd_nonempty
thf(fact_51_map__upd__nonempty, axiom,
    ((![T2 : nat > option2118145160on_val, K : nat, X : produc266837688on_val]: (~ (((fun_up262443479on_val @ T2 @ K @ (some_P1299442195on_val @ X)) = (^[X2 : nat]: none_P1535574167on_val))))))). % map_upd_nonempty
thf(fact_52_map__upd__nonempty, axiom,
    ((![T2 : list_char > option_val, K : list_char, X : val]: (~ (((fun_up1252458416on_val @ T2 @ K @ (some_val @ X)) = (^[X2 : list_char]: none_val))))))). % map_upd_nonempty
thf(fact_53_option_Oinject, axiom,
    ((![X22 : ty, Y22 : ty]: (((some_ty @ X22) = (some_ty @ Y22)) = (X22 = Y22))))). % option.inject
thf(fact_54_option_Oinject, axiom,
    ((![X22 : produc266837688on_val, Y22 : produc266837688on_val]: (((some_P1299442195on_val @ X22) = (some_P1299442195on_val @ Y22)) = (X22 = Y22))))). % option.inject
thf(fact_55_option_Oinject, axiom,
    ((![X22 : val, Y22 : val]: (((some_val @ X22) = (some_val @ Y22)) = (X22 = Y22))))). % option.inject
thf(fact_56_map__upd__Some__unfold, axiom,
    ((![M : list_char > option_ty, A2 : list_char, B2 : ty, X : list_char, Y : ty]: (((fun_up9191ion_ty @ M @ A2 @ (some_ty @ B2) @ X) = (some_ty @ Y)) = (((((X = A2)) & ((B2 = Y)))) | ((((~ ((X = A2)))) & (((M @ X) = (some_ty @ Y)))))))))). % map_upd_Some_unfold
thf(fact_57_map__upd__Some__unfold, axiom,
    ((![M : nat > option2118145160on_val, A2 : nat, B2 : produc266837688on_val, X : nat, Y : produc266837688on_val]: (((fun_up262443479on_val @ M @ A2 @ (some_P1299442195on_val @ B2) @ X) = (some_P1299442195on_val @ Y)) = (((((X = A2)) & ((B2 = Y)))) | ((((~ ((X = A2)))) & (((M @ X) = (some_P1299442195on_val @ Y)))))))))). % map_upd_Some_unfold
thf(fact_58_map__upd__Some__unfold, axiom,
    ((![M : list_char > option_val, A2 : list_char, B2 : val, X : list_char, Y : val]: (((fun_up1252458416on_val @ M @ A2 @ (some_val @ B2) @ X) = (some_val @ Y)) = (((((X = A2)) & ((B2 = Y)))) | ((((~ ((X = A2)))) & (((M @ X) = (some_val @ Y)))))))))). % map_upd_Some_unfold
thf(fact_59_map__upd__triv, axiom,
    ((![T2 : list_char > option_ty, K : list_char, X : ty]: (((T2 @ K) = (some_ty @ X)) => ((fun_up9191ion_ty @ T2 @ K @ (some_ty @ X)) = T2))))). % map_upd_triv
thf(fact_60_map__upd__triv, axiom,
    ((![T2 : nat > option2118145160on_val, K : nat, X : produc266837688on_val]: (((T2 @ K) = (some_P1299442195on_val @ X)) => ((fun_up262443479on_val @ T2 @ K @ (some_P1299442195on_val @ X)) = T2))))). % map_upd_triv
thf(fact_61_map__upd__triv, axiom,
    ((![T2 : list_char > option_val, K : list_char, X : val]: (((T2 @ K) = (some_val @ X)) => ((fun_up1252458416on_val @ T2 @ K @ (some_val @ X)) = T2))))). % map_upd_triv
thf(fact_62_combine__options__cases, axiom,
    ((![X : option_ty, P : option_ty > option_ty > $o, Y : option_ty]: (((X = none_ty) => (P @ X @ Y)) => (((Y = none_ty) => (P @ X @ Y)) => ((![A3 : ty, B3 : ty]: ((X = (some_ty @ A3)) => ((Y = (some_ty @ B3)) => (P @ X @ Y)))) => (P @ X @ Y))))))). % combine_options_cases
thf(fact_63_combine__options__cases, axiom,
    ((![X : option_ty, P : option_ty > option2118145160on_val > $o, Y : option2118145160on_val]: (((X = none_ty) => (P @ X @ Y)) => (((Y = none_P1535574167on_val) => (P @ X @ Y)) => ((![A3 : ty, B3 : produc266837688on_val]: ((X = (some_ty @ A3)) => ((Y = (some_P1299442195on_val @ B3)) => (P @ X @ Y)))) => (P @ X @ Y))))))). % combine_options_cases
thf(fact_64_combine__options__cases, axiom,
    ((![X : option_ty, P : option_ty > option_val > $o, Y : option_val]: (((X = none_ty) => (P @ X @ Y)) => (((Y = none_val) => (P @ X @ Y)) => ((![A3 : ty, B3 : val]: ((X = (some_ty @ A3)) => ((Y = (some_val @ B3)) => (P @ X @ Y)))) => (P @ X @ Y))))))). % combine_options_cases
thf(fact_65_combine__options__cases, axiom,
    ((![X : option2118145160on_val, P : option2118145160on_val > option_ty > $o, Y : option_ty]: (((X = none_P1535574167on_val) => (P @ X @ Y)) => (((Y = none_ty) => (P @ X @ Y)) => ((![A3 : produc266837688on_val, B3 : ty]: ((X = (some_P1299442195on_val @ A3)) => ((Y = (some_ty @ B3)) => (P @ X @ Y)))) => (P @ X @ Y))))))). % combine_options_cases
thf(fact_66_combine__options__cases, axiom,
    ((![X : option2118145160on_val, P : option2118145160on_val > option2118145160on_val > $o, Y : option2118145160on_val]: (((X = none_P1535574167on_val) => (P @ X @ Y)) => (((Y = none_P1535574167on_val) => (P @ X @ Y)) => ((![A3 : produc266837688on_val, B3 : produc266837688on_val]: ((X = (some_P1299442195on_val @ A3)) => ((Y = (some_P1299442195on_val @ B3)) => (P @ X @ Y)))) => (P @ X @ Y))))))). % combine_options_cases
thf(fact_67_combine__options__cases, axiom,
    ((![X : option2118145160on_val, P : option2118145160on_val > option_val > $o, Y : option_val]: (((X = none_P1535574167on_val) => (P @ X @ Y)) => (((Y = none_val) => (P @ X @ Y)) => ((![A3 : produc266837688on_val, B3 : val]: ((X = (some_P1299442195on_val @ A3)) => ((Y = (some_val @ B3)) => (P @ X @ Y)))) => (P @ X @ Y))))))). % combine_options_cases
thf(fact_68_combine__options__cases, axiom,
    ((![X : option_val, P : option_val > option_ty > $o, Y : option_ty]: (((X = none_val) => (P @ X @ Y)) => (((Y = none_ty) => (P @ X @ Y)) => ((![A3 : val, B3 : ty]: ((X = (some_val @ A3)) => ((Y = (some_ty @ B3)) => (P @ X @ Y)))) => (P @ X @ Y))))))). % combine_options_cases
thf(fact_69_combine__options__cases, axiom,
    ((![X : option_val, P : option_val > option2118145160on_val > $o, Y : option2118145160on_val]: (((X = none_val) => (P @ X @ Y)) => (((Y = none_P1535574167on_val) => (P @ X @ Y)) => ((![A3 : val, B3 : produc266837688on_val]: ((X = (some_val @ A3)) => ((Y = (some_P1299442195on_val @ B3)) => (P @ X @ Y)))) => (P @ X @ Y))))))). % combine_options_cases
thf(fact_70_combine__options__cases, axiom,
    ((![X : option_val, P : option_val > option_val > $o, Y : option_val]: (((X = none_val) => (P @ X @ Y)) => (((Y = none_val) => (P @ X @ Y)) => ((![A3 : val, B3 : val]: ((X = (some_val @ A3)) => ((Y = (some_val @ B3)) => (P @ X @ Y)))) => (P @ X @ Y))))))). % combine_options_cases
thf(fact_71_split__option__all, axiom,
    (((^[P2 : option_ty > $o]: (![X3 : option_ty]: (P2 @ X3))) = (^[P3 : option_ty > $o]: (((P3 @ none_ty)) & ((![X2 : ty]: (P3 @ (some_ty @ X2))))))))). % split_option_all
thf(fact_72_split__option__all, axiom,
    (((^[P2 : option2118145160on_val > $o]: (![X3 : option2118145160on_val]: (P2 @ X3))) = (^[P3 : option2118145160on_val > $o]: (((P3 @ none_P1535574167on_val)) & ((![X2 : produc266837688on_val]: (P3 @ (some_P1299442195on_val @ X2))))))))). % split_option_all
thf(fact_73_split__option__all, axiom,
    (((^[P2 : option_val > $o]: (![X3 : option_val]: (P2 @ X3))) = (^[P3 : option_val > $o]: (((P3 @ none_val)) & ((![X2 : val]: (P3 @ (some_val @ X2))))))))). % split_option_all
thf(fact_74_split__option__ex, axiom,
    (((^[P2 : option_ty > $o]: (?[X3 : option_ty]: (P2 @ X3))) = (^[P3 : option_ty > $o]: (((P3 @ none_ty)) | ((?[X2 : ty]: (P3 @ (some_ty @ X2))))))))). % split_option_ex
thf(fact_75_split__option__ex, axiom,
    (((^[P2 : option2118145160on_val > $o]: (?[X3 : option2118145160on_val]: (P2 @ X3))) = (^[P3 : option2118145160on_val > $o]: (((P3 @ none_P1535574167on_val)) | ((?[X2 : produc266837688on_val]: (P3 @ (some_P1299442195on_val @ X2))))))))). % split_option_ex
thf(fact_76_split__option__ex, axiom,
    (((^[P2 : option_val > $o]: (?[X3 : option_val]: (P2 @ X3))) = (^[P3 : option_val > $o]: (((P3 @ none_val)) | ((?[X2 : val]: (P3 @ (some_val @ X2))))))))). % split_option_ex
thf(fact_77_option_Oinducts, axiom,
    ((![P : option_ty > $o, Option : option_ty]: ((P @ none_ty) => ((![X4 : ty]: (P @ (some_ty @ X4))) => (P @ Option)))))). % option.inducts
thf(fact_78_option_Oinducts, axiom,
    ((![P : option2118145160on_val > $o, Option : option2118145160on_val]: ((P @ none_P1535574167on_val) => ((![X4 : produc266837688on_val]: (P @ (some_P1299442195on_val @ X4))) => (P @ Option)))))). % option.inducts
thf(fact_79_option_Oinducts, axiom,
    ((![P : option_val > $o, Option : option_val]: ((P @ none_val) => ((![X4 : val]: (P @ (some_val @ X4))) => (P @ Option)))))). % option.inducts
thf(fact_80_option_Oexhaust, axiom,
    ((![Y : option_ty]: ((~ ((Y = none_ty))) => (~ ((![X23 : ty]: (~ ((Y = (some_ty @ X23))))))))))). % option.exhaust
thf(fact_81_option_Oexhaust, axiom,
    ((![Y : option2118145160on_val]: ((~ ((Y = none_P1535574167on_val))) => (~ ((![X23 : produc266837688on_val]: (~ ((Y = (some_P1299442195on_val @ X23))))))))))). % option.exhaust
thf(fact_82_option_Oexhaust, axiom,
    ((![Y : option_val]: ((~ ((Y = none_val))) => (~ ((![X23 : val]: (~ ((Y = (some_val @ X23))))))))))). % option.exhaust
thf(fact_83_option_OdiscI, axiom,
    ((![Option : option_ty, X22 : ty]: ((Option = (some_ty @ X22)) => (~ ((Option = none_ty))))))). % option.discI
thf(fact_84_option_OdiscI, axiom,
    ((![Option : option2118145160on_val, X22 : produc266837688on_val]: ((Option = (some_P1299442195on_val @ X22)) => (~ ((Option = none_P1535574167on_val))))))). % option.discI
thf(fact_85_option_OdiscI, axiom,
    ((![Option : option_val, X22 : val]: ((Option = (some_val @ X22)) => (~ ((Option = none_val))))))). % option.discI
thf(fact_86_option_Odistinct_I1_J, axiom,
    ((![X22 : ty]: (~ ((none_ty = (some_ty @ X22))))))). % option.distinct(1)
thf(fact_87_option_Odistinct_I1_J, axiom,
    ((![X22 : produc266837688on_val]: (~ ((none_P1535574167on_val = (some_P1299442195on_val @ X22))))))). % option.distinct(1)
thf(fact_88_option_Odistinct_I1_J, axiom,
    ((![X22 : val]: (~ ((none_val = (some_val @ X22))))))). % option.distinct(1)
thf(fact_89_map__upd__eqD1, axiom,
    ((![M : list_char > option_ty, A2 : list_char, X : ty, N : list_char > option_ty, Y : ty]: (((fun_up9191ion_ty @ M @ A2 @ (some_ty @ X)) = (fun_up9191ion_ty @ N @ A2 @ (some_ty @ Y))) => (X = Y))))). % map_upd_eqD1
thf(fact_90_map__upd__eqD1, axiom,
    ((![M : nat > option2118145160on_val, A2 : nat, X : produc266837688on_val, N : nat > option2118145160on_val, Y : produc266837688on_val]: (((fun_up262443479on_val @ M @ A2 @ (some_P1299442195on_val @ X)) = (fun_up262443479on_val @ N @ A2 @ (some_P1299442195on_val @ Y))) => (X = Y))))). % map_upd_eqD1
thf(fact_91_map__upd__eqD1, axiom,
    ((![M : list_char > option_val, A2 : list_char, X : val, N : list_char > option_val, Y : val]: (((fun_up1252458416on_val @ M @ A2 @ (some_val @ X)) = (fun_up1252458416on_val @ N @ A2 @ (some_val @ Y))) => (X = Y))))). % map_upd_eqD1
thf(fact_92_WTrtBlock, axiom,
    ((![P : list_P1234162913t_char, H : nat > option2118145160on_val, E : list_char > option_ty, V : list_char, T : ty, E2 : exp_list_char, T3 : ty]: ((wTrt @ P @ H @ (fun_up9191ion_ty @ E @ V @ (some_ty @ T)) @ E2 @ T3) => (wTrt @ P @ H @ E @ (block_list_char @ V @ T @ E2) @ T3))))). % WTrtBlock
thf(fact_93_exp_Oinject_I10_J, axiom,
    ((![X101 : list_char, X102 : ty, X103 : exp_list_char, Y101 : list_char, Y102 : ty, Y103 : exp_list_char]: (((block_list_char @ X101 @ X102 @ X103) = (block_list_char @ Y101 @ Y102 @ Y103)) = (((X101 = Y101)) & ((((X102 = Y102)) & ((X103 = Y103))))))))). % exp.inject(10)
thf(fact_94_lconf__upd2, axiom,
    ((![P : list_P1234162913t_char, H : nat > option2118145160on_val, L : list_char > option_val, E : list_char > option_ty, V2 : val, T : ty, V : list_char]: ((lconf_485928294t_char @ P @ H @ L @ E) => ((conf_P93989998t_char @ P @ H @ V2 @ T) => (lconf_485928294t_char @ P @ H @ (fun_up1252458416on_val @ L @ V @ (some_val @ V2)) @ (fun_up9191ion_ty @ E @ V @ (some_ty @ T)))))))). % lconf_upd2
thf(fact_95_red, axiom,
    ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ ea @ (produc52622304on_val @ ha @ (fun_up1252458416on_val @ la @ v @ none_val))) @ (produc2023458740on_val @ e_a @ (produc52622304on_val @ h_a @ l_a))) @ (red @ p)))). % red
thf(fact_96_lconf__upd, axiom,
    ((![P : list_P1234162913t_char, H : nat > option2118145160on_val, L : list_char > option_val, E : list_char > option_ty, V2 : val, T : ty, V : list_char]: ((lconf_485928294t_char @ P @ H @ L @ E) => ((conf_P93989998t_char @ P @ H @ V2 @ T) => (((E @ V) = (some_ty @ T)) => (lconf_485928294t_char @ P @ H @ (fun_up1252458416on_val @ L @ V @ (some_val @ V2)) @ E))))))). % lconf_upd
thf(fact_97_mem__Collect__eq, axiom,
    ((![A2 : produc1172664615on_val, P : produc1172664615on_val > $o]: ((member354538064on_val @ A2 @ (collec2055896722on_val @ P)) = (P @ A2))))). % mem_Collect_eq
thf(fact_98_Collect__mem__eq, axiom,
    ((![A4 : set_Pr1189492743on_val]: ((collec2055896722on_val @ (^[X2 : produc1172664615on_val]: (member354538064on_val @ X2 @ A4))) = A4)))). % Collect_mem_eq
thf(fact_99_lconf__def, axiom,
    ((lconf_485928294t_char = (^[P3 : list_P1234162913t_char]: (^[H2 : nat > option2118145160on_val]: (^[L2 : list_char > option_val]: (^[E3 : list_char > option_ty]: (![V3 : list_char]: (![V4 : val]: ((((L2 @ V3) = (some_val @ V4))) => ((?[T4 : ty]: ((((E3 @ V3) = (some_ty @ T4))) & ((conf_P93989998t_char @ P3 @ H2 @ V4 @ T4))))))))))))))). % lconf_def
thf(fact_100_red__reds_OBlockRedNone, axiom,
    ((![E2 : exp_list_char, H : nat > option2118145160on_val, L : list_char > option_val, V : list_char, E4 : exp_list_char, H3 : nat > option2118145160on_val, L3 : list_char > option_val, P : list_P1234162913t_char, T : ty]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E2 @ (produc52622304on_val @ H @ (fun_up1252458416on_val @ L @ V @ none_val))) @ (produc2023458740on_val @ E4 @ (produc52622304on_val @ H3 @ L3))) @ (red @ P)) => (((L3 @ V) = none_val) => ((~ ((assigned @ V @ E2))) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (block_list_char @ V @ T @ E2) @ (produc52622304on_val @ H @ L)) @ (produc2023458740on_val @ (block_list_char @ V @ T @ E4) @ (produc52622304on_val @ H3 @ (fun_up1252458416on_val @ L3 @ V @ (L @ V))))) @ (red @ P)))))))). % red_reds.BlockRedNone
thf(fact_101_prod__cases4, axiom,
    ((![Y : produc1172664615on_val]: (~ ((![A3 : produc1097884484on_val, B3 : exp_list_char, C2 : nat > option2118145160on_val, D2 : list_char > option_val]: (~ ((Y = (produc1069526295on_val @ A3 @ (produc2023458740on_val @ B3 @ (produc52622304on_val @ C2 @ D2)))))))))))). % prod_cases4
thf(fact_102_prod__induct4, axiom,
    ((![P : produc1172664615on_val > $o, X : produc1172664615on_val]: ((![A3 : produc1097884484on_val, B3 : exp_list_char, C2 : nat > option2118145160on_val, D2 : list_char > option_val]: (P @ (produc1069526295on_val @ A3 @ (produc2023458740on_val @ B3 @ (produc52622304on_val @ C2 @ D2))))) => (P @ X))))). % prod_induct4
thf(fact_103_old_Oprod_Oinject, axiom,
    ((![A2 : produc1097884484on_val, B2 : produc1097884484on_val, A5 : produc1097884484on_val, B4 : produc1097884484on_val]: (((produc1069526295on_val @ A2 @ B2) = (produc1069526295on_val @ A5 @ B4)) = (((A2 = A5)) & ((B2 = B4))))))). % old.prod.inject
thf(fact_104_old_Oprod_Oinject, axiom,
    ((![A2 : exp_list_char, B2 : produc515445032on_val, A5 : exp_list_char, B4 : produc515445032on_val]: (((produc2023458740on_val @ A2 @ B2) = (produc2023458740on_val @ A5 @ B4)) = (((A2 = A5)) & ((B2 = B4))))))). % old.prod.inject
thf(fact_105_old_Oprod_Oinject, axiom,
    ((![A2 : nat > option2118145160on_val, B2 : list_char > option_val, A5 : nat > option2118145160on_val, B4 : list_char > option_val]: (((produc52622304on_val @ A2 @ B2) = (produc52622304on_val @ A5 @ B4)) = (((A2 = A5)) & ((B2 = B4))))))). % old.prod.inject
thf(fact_106_old_Oprod_Oinject, axiom,
    ((![A2 : list_char, B2 : produc1257910179t_char > option_val, A5 : list_char, B4 : produc1257910179t_char > option_val]: (((produc904988266on_val @ A2 @ B2) = (produc904988266on_val @ A5 @ B4)) = (((A2 = A5)) & ((B2 = B4))))))). % old.prod.inject
thf(fact_107_prod_Oinject, axiom,
    ((![X1 : produc1097884484on_val, X22 : produc1097884484on_val, Y1 : produc1097884484on_val, Y22 : produc1097884484on_val]: (((produc1069526295on_val @ X1 @ X22) = (produc1069526295on_val @ Y1 @ Y22)) = (((X1 = Y1)) & ((X22 = Y22))))))). % prod.inject
thf(fact_108_prod_Oinject, axiom,
    ((![X1 : exp_list_char, X22 : produc515445032on_val, Y1 : exp_list_char, Y22 : produc515445032on_val]: (((produc2023458740on_val @ X1 @ X22) = (produc2023458740on_val @ Y1 @ Y22)) = (((X1 = Y1)) & ((X22 = Y22))))))). % prod.inject
thf(fact_109_prod_Oinject, axiom,
    ((![X1 : nat > option2118145160on_val, X22 : list_char > option_val, Y1 : nat > option2118145160on_val, Y22 : list_char > option_val]: (((produc52622304on_val @ X1 @ X22) = (produc52622304on_val @ Y1 @ Y22)) = (((X1 = Y1)) & ((X22 = Y22))))))). % prod.inject
thf(fact_110_prod_Oinject, axiom,
    ((![X1 : list_char, X22 : produc1257910179t_char > option_val, Y1 : list_char, Y22 : produc1257910179t_char > option_val]: (((produc904988266on_val @ X1 @ X22) = (produc904988266on_val @ Y1 @ Y22)) = (((X1 = Y1)) & ((X22 = Y22))))))). % prod.inject
thf(fact_111_old_Oprod_Oinducts, axiom,
    ((![P : produc1172664615on_val > $o, Prod : produc1172664615on_val]: ((![A3 : produc1097884484on_val, B3 : produc1097884484on_val]: (P @ (produc1069526295on_val @ A3 @ B3))) => (P @ Prod))))). % old.prod.inducts
thf(fact_112_old_Oprod_Oinducts, axiom,
    ((![P : produc1097884484on_val > $o, Prod : produc1097884484on_val]: ((![A3 : exp_list_char, B3 : produc515445032on_val]: (P @ (produc2023458740on_val @ A3 @ B3))) => (P @ Prod))))). % old.prod.inducts
thf(fact_113_old_Oprod_Oinducts, axiom,
    ((![P : produc515445032on_val > $o, Prod : produc515445032on_val]: ((![A3 : nat > option2118145160on_val, B3 : list_char > option_val]: (P @ (produc52622304on_val @ A3 @ B3))) => (P @ Prod))))). % old.prod.inducts
thf(fact_114_old_Oprod_Oinducts, axiom,
    ((![P : produc266837688on_val > $o, Prod : produc266837688on_val]: ((![A3 : list_char, B3 : produc1257910179t_char > option_val]: (P @ (produc904988266on_val @ A3 @ B3))) => (P @ Prod))))). % old.prod.inducts
thf(fact_115_old_Oprod_Oexhaust, axiom,
    ((![Y : produc1172664615on_val]: (~ ((![A3 : produc1097884484on_val, B3 : produc1097884484on_val]: (~ ((Y = (produc1069526295on_val @ A3 @ B3)))))))))). % old.prod.exhaust
thf(fact_116_old_Oprod_Oexhaust, axiom,
    ((![Y : produc1097884484on_val]: (~ ((![A3 : exp_list_char, B3 : produc515445032on_val]: (~ ((Y = (produc2023458740on_val @ A3 @ B3)))))))))). % old.prod.exhaust
thf(fact_117_old_Oprod_Oexhaust, axiom,
    ((![Y : produc515445032on_val]: (~ ((![A3 : nat > option2118145160on_val, B3 : list_char > option_val]: (~ ((Y = (produc52622304on_val @ A3 @ B3)))))))))). % old.prod.exhaust
thf(fact_118_old_Oprod_Oexhaust, axiom,
    ((![Y : produc266837688on_val]: (~ ((![A3 : list_char, B3 : produc1257910179t_char > option_val]: (~ ((Y = (produc904988266on_val @ A3 @ B3)))))))))). % old.prod.exhaust
thf(fact_119_Pair__inject, axiom,
    ((![A2 : produc1097884484on_val, B2 : produc1097884484on_val, A5 : produc1097884484on_val, B4 : produc1097884484on_val]: (((produc1069526295on_val @ A2 @ B2) = (produc1069526295on_val @ A5 @ B4)) => (~ (((A2 = A5) => (~ ((B2 = B4)))))))))). % Pair_inject
thf(fact_120_Pair__inject, axiom,
    ((![A2 : exp_list_char, B2 : produc515445032on_val, A5 : exp_list_char, B4 : produc515445032on_val]: (((produc2023458740on_val @ A2 @ B2) = (produc2023458740on_val @ A5 @ B4)) => (~ (((A2 = A5) => (~ ((B2 = B4)))))))))). % Pair_inject
thf(fact_121_Pair__inject, axiom,
    ((![A2 : nat > option2118145160on_val, B2 : list_char > option_val, A5 : nat > option2118145160on_val, B4 : list_char > option_val]: (((produc52622304on_val @ A2 @ B2) = (produc52622304on_val @ A5 @ B4)) => (~ (((A2 = A5) => (~ ((B2 = B4)))))))))). % Pair_inject
thf(fact_122_Pair__inject, axiom,
    ((![A2 : list_char, B2 : produc1257910179t_char > option_val, A5 : list_char, B4 : produc1257910179t_char > option_val]: (((produc904988266on_val @ A2 @ B2) = (produc904988266on_val @ A5 @ B4)) => (~ (((A2 = A5) => (~ ((B2 = B4)))))))))). % Pair_inject
thf(fact_123_prod__cases, axiom,
    ((![P : produc1172664615on_val > $o, P4 : produc1172664615on_val]: ((![A3 : produc1097884484on_val, B3 : produc1097884484on_val]: (P @ (produc1069526295on_val @ A3 @ B3))) => (P @ P4))))). % prod_cases
thf(fact_124_prod__cases, axiom,
    ((![P : produc1097884484on_val > $o, P4 : produc1097884484on_val]: ((![A3 : exp_list_char, B3 : produc515445032on_val]: (P @ (produc2023458740on_val @ A3 @ B3))) => (P @ P4))))). % prod_cases
thf(fact_125_prod__cases, axiom,
    ((![P : produc515445032on_val > $o, P4 : produc515445032on_val]: ((![A3 : nat > option2118145160on_val, B3 : list_char > option_val]: (P @ (produc52622304on_val @ A3 @ B3))) => (P @ P4))))). % prod_cases
thf(fact_126_prod__cases, axiom,
    ((![P : produc266837688on_val > $o, P4 : produc266837688on_val]: ((![A3 : list_char, B3 : produc1257910179t_char > option_val]: (P @ (produc904988266on_val @ A3 @ B3))) => (P @ P4))))). % prod_cases
thf(fact_127_surj__pair, axiom,
    ((![P4 : produc1172664615on_val]: (?[X4 : produc1097884484on_val, Y3 : produc1097884484on_val]: (P4 = (produc1069526295on_val @ X4 @ Y3)))))). % surj_pair
thf(fact_128_surj__pair, axiom,
    ((![P4 : produc1097884484on_val]: (?[X4 : exp_list_char, Y3 : produc515445032on_val]: (P4 = (produc2023458740on_val @ X4 @ Y3)))))). % surj_pair
thf(fact_129_surj__pair, axiom,
    ((![P4 : produc515445032on_val]: (?[X4 : nat > option2118145160on_val, Y3 : list_char > option_val]: (P4 = (produc52622304on_val @ X4 @ Y3)))))). % surj_pair
thf(fact_130_surj__pair, axiom,
    ((![P4 : produc266837688on_val]: (?[X4 : list_char, Y3 : produc1257910179t_char > option_val]: (P4 = (produc904988266on_val @ X4 @ Y3)))))). % surj_pair
thf(fact_131_prod__induct3, axiom,
    ((![P : produc1172664615on_val > $o, X : produc1172664615on_val]: ((![A3 : produc1097884484on_val, B3 : exp_list_char, C2 : produc515445032on_val]: (P @ (produc1069526295on_val @ A3 @ (produc2023458740on_val @ B3 @ C2)))) => (P @ X))))). % prod_induct3
thf(fact_132_prod__induct3, axiom,
    ((![P : produc1097884484on_val > $o, X : produc1097884484on_val]: ((![A3 : exp_list_char, B3 : nat > option2118145160on_val, C2 : list_char > option_val]: (P @ (produc2023458740on_val @ A3 @ (produc52622304on_val @ B3 @ C2)))) => (P @ X))))). % prod_induct3
thf(fact_133_prod__cases3, axiom,
    ((![Y : produc1172664615on_val]: (~ ((![A3 : produc1097884484on_val, B3 : exp_list_char, C2 : produc515445032on_val]: (~ ((Y = (produc1069526295on_val @ A3 @ (produc2023458740on_val @ B3 @ C2))))))))))). % prod_cases3
thf(fact_134_prod__cases3, axiom,
    ((![Y : produc1097884484on_val]: (~ ((![A3 : exp_list_char, B3 : nat > option2118145160on_val, C2 : list_char > option_val]: (~ ((Y = (produc2023458740on_val @ A3 @ (produc52622304on_val @ B3 @ C2))))))))))). % prod_cases3
thf(fact_135_red__preserves__hconf, axiom,
    ((![E2 : exp_list_char, H : nat > option2118145160on_val, L : list_char > option_val, E4 : exp_list_char, H3 : 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 @ L)) @ (produc2023458740on_val @ E4 @ (produc52622304on_val @ H3 @ L3))) @ (red @ P)) => ((wTrt @ P @ H @ E @ E2 @ T) => ((hconf_1244167010t_char @ P @ H) => (hconf_1244167010t_char @ P @ H3))))))). % red_preserves_hconf
thf(fact_136_redp__redsp_OBlockRedNone, axiom,
    ((![P : list_P1234162913t_char, E2 : exp_list_char, H : nat > option2118145160on_val, L : list_char > option_val, V : list_char, E4 : exp_list_char, H3 : nat > option2118145160on_val, L3 : list_char > option_val, T : ty]: ((redp @ P @ E2 @ (produc52622304on_val @ H @ (fun_up1252458416on_val @ L @ V @ none_val)) @ E4 @ (produc52622304on_val @ H3 @ L3)) => (((L3 @ V) = none_val) => ((~ ((assigned @ V @ E2))) => (redp @ P @ (block_list_char @ V @ T @ E2) @ (produc52622304on_val @ H @ L) @ (block_list_char @ V @ T @ E4) @ (produc52622304on_val @ H3 @ (fun_up1252458416on_val @ L3 @ V @ (L @ V)))))))))). % redp_redsp.BlockRedNone
thf(fact_137_red__hext__incr, axiom,
    ((![E2 : exp_list_char, H : nat > option2118145160on_val, L : 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 @ H @ L)) @ (produc2023458740on_val @ E4 @ (produc52622304on_val @ H3 @ L3))) @ (red @ P)) => (hext @ H @ H3))))). % red_hext_incr
thf(fact_138_pred__equals__eq2, axiom,
    ((![R : set_Pr1189492743on_val, S : set_Pr1189492743on_val]: (((^[X2 : produc1097884484on_val]: (^[Y2 : produc1097884484on_val]: (member354538064on_val @ (produc1069526295on_val @ X2 @ Y2) @ R))) = (^[X2 : produc1097884484on_val]: (^[Y2 : produc1097884484on_val]: (member354538064on_val @ (produc1069526295on_val @ X2 @ Y2) @ S)))) = (R = S))))). % pred_equals_eq2
thf(fact_139_pred__equals__eq2, axiom,
    ((![R : set_Pr556513572on_val, S : set_Pr556513572on_val]: (((^[X2 : exp_list_char]: (^[Y2 : produc515445032on_val]: (member1888679917on_val @ (produc2023458740on_val @ X2 @ Y2) @ R))) = (^[X2 : exp_list_char]: (^[Y2 : produc515445032on_val]: (member1888679917on_val @ (produc2023458740on_val @ X2 @ Y2) @ S)))) = (R = S))))). % pred_equals_eq2
thf(fact_140_pred__equals__eq2, axiom,
    ((![R : set_Pr723149704on_val, S : set_Pr723149704on_val]: (((^[X2 : nat > option2118145160on_val]: (^[Y2 : list_char > option_val]: (member652041809on_val @ (produc52622304on_val @ X2 @ Y2) @ R))) = (^[X2 : nat > option2118145160on_val]: (^[Y2 : list_char > option_val]: (member652041809on_val @ (produc52622304on_val @ X2 @ Y2) @ S)))) = (R = S))))). % pred_equals_eq2
thf(fact_141_pred__equals__eq2, axiom,
    ((![R : set_Pr2075231726on_val, S : set_Pr2075231726on_val]: (((^[X2 : list_char]: (^[Y2 : produc1257910179t_char > option_val]: (member1296415951on_val @ (produc904988266on_val @ X2 @ Y2) @ R))) = (^[X2 : list_char]: (^[Y2 : produc1257910179t_char > option_val]: (member1296415951on_val @ (produc904988266on_val @ X2 @ Y2) @ S)))) = (R = S))))). % pred_equals_eq2
thf(fact_142_WTrt__hext__mono, axiom,
    ((![P : list_P1234162913t_char, H : nat > option2118145160on_val, E : list_char > option_ty, E2 : exp_list_char, T : ty, H3 : nat > option2118145160on_val]: ((wTrt @ P @ H @ E @ E2 @ T) => ((hext @ H @ H3) => (wTrt @ P @ H3 @ E @ E2 @ T)))))). % WTrt_hext_mono
thf(fact_143_lconf__hext, axiom,
    ((![P : list_P1234162913t_char, H : nat > option2118145160on_val, L : list_char > option_val, E : list_char > option_ty, H3 : nat > option2118145160on_val]: ((lconf_485928294t_char @ P @ H @ L @ E) => ((hext @ H @ H3) => (lconf_485928294t_char @ P @ H3 @ L @ E)))))). % lconf_hext
thf(fact_144_redp__red__eq, axiom,
    ((redp = (^[P3 : list_P1234162913t_char]: (^[X2 : exp_list_char]: (^[Y2 : produc515445032on_val]: (^[Z2 : exp_list_char]: (^[Aa : produc515445032on_val]: (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ X2 @ Y2) @ (produc2023458740on_val @ Z2 @ Aa)) @ (red @ P3)))))))))). % redp_red_eq
thf(fact_145_hext__upd__obj, axiom,
    ((![H : nat > option2118145160on_val, A2 : nat, C3 : list_char, Fs : produc1257910179t_char > option_val, Fs2 : produc1257910179t_char > option_val]: (((H @ A2) = (some_P1299442195on_val @ (produc904988266on_val @ C3 @ Fs))) => (hext @ H @ (fun_up262443479on_val @ H @ A2 @ (some_P1299442195on_val @ (produc904988266on_val @ C3 @ Fs2)))))))). % hext_upd_obj
thf(fact_146_hext__new, axiom,
    ((![H : nat > option2118145160on_val, A2 : nat, X : produc266837688on_val]: (((H @ A2) = none_P1535574167on_val) => (hext @ H @ (fun_up262443479on_val @ H @ A2 @ (some_P1299442195on_val @ X))))))). % hext_new
thf(fact_147_hextI, axiom,
    ((![H : nat > option2118145160on_val, H3 : nat > option2118145160on_val]: ((![A3 : nat, C4 : list_char, Fs3 : produc1257910179t_char > option_val]: (((H @ A3) = (some_P1299442195on_val @ (produc904988266on_val @ C4 @ Fs3))) => (?[Fs4 : produc1257910179t_char > option_val]: ((H3 @ A3) = (some_P1299442195on_val @ (produc904988266on_val @ C4 @ Fs4)))))) => (hext @ H @ H3))))). % hextI
thf(fact_148_hext__def, axiom,
    ((hext = (^[H2 : nat > option2118145160on_val]: (^[H4 : nat > option2118145160on_val]: (![A : nat]: (![C5 : list_char]: (![Fs5 : produc1257910179t_char > option_val]: ((((H2 @ A) = (some_P1299442195on_val @ (produc904988266on_val @ C5 @ Fs5)))) => ((?[Fs6 : produc1257910179t_char > option_val]: ((H4 @ A) = (some_P1299442195on_val @ (produc904988266on_val @ C5 @ Fs6)))))))))))))). % hext_def
thf(fact_149_hext__refl, axiom,
    ((![H : nat > option2118145160on_val]: (hext @ H @ H)))). % hext_refl
thf(fact_150_hext__trans, axiom,
    ((![H : nat > option2118145160on_val, H3 : nat > option2118145160on_val, H5 : nat > option2118145160on_val]: ((hext @ H @ H3) => ((hext @ H3 @ H5) => (hext @ H @ H5)))))). % hext_trans
thf(fact_151_hext__objD, axiom,
    ((![H : nat > option2118145160on_val, H3 : nat > option2118145160on_val, A2 : nat, C3 : list_char, Fs : produc1257910179t_char > option_val]: ((hext @ H @ H3) => (((H @ A2) = (some_P1299442195on_val @ (produc904988266on_val @ C3 @ Fs))) => (?[Fs7 : produc1257910179t_char > option_val]: ((H3 @ A2) = (some_P1299442195on_val @ (produc904988266on_val @ C3 @ Fs7))))))))). % hext_objD
thf(fact_152_hconf__new, axiom,
    ((![P : list_P1234162913t_char, H : nat > option2118145160on_val, A2 : nat, Obj : produc266837688on_val]: ((hconf_1244167010t_char @ P @ H) => (((H @ A2) = none_P1535574167on_val) => ((oconf_454120169t_char @ P @ H @ Obj) => (hconf_1244167010t_char @ P @ (fun_up262443479on_val @ H @ A2 @ (some_P1299442195on_val @ Obj))))))))). % hconf_new
thf(fact_153_hconf__upd__obj, axiom,
    ((![P : list_P1234162913t_char, H : nat > option2118145160on_val, A2 : nat, C3 : list_char, Fs : produc1257910179t_char > option_val, Fs2 : produc1257910179t_char > option_val]: ((hconf_1244167010t_char @ P @ H) => (((H @ A2) = (some_P1299442195on_val @ (produc904988266on_val @ C3 @ Fs))) => ((oconf_454120169t_char @ P @ H @ (produc904988266on_val @ C3 @ Fs2)) => (hconf_1244167010t_char @ P @ (fun_up262443479on_val @ H @ A2 @ (some_P1299442195on_val @ (produc904988266on_val @ C3 @ Fs2)))))))))). % hconf_upd_obj
thf(fact_154_hconfD, axiom,
    ((![P : list_P1234162913t_char, H : nat > option2118145160on_val, A2 : nat, Obj : produc266837688on_val]: ((hconf_1244167010t_char @ P @ H) => (((H @ A2) = (some_P1299442195on_val @ Obj)) => (oconf_454120169t_char @ P @ H @ Obj)))))). % hconfD
thf(fact_155_hconf__def, axiom,
    ((hconf_1244167010t_char = (^[P3 : list_P1234162913t_char]: (^[H2 : nat > option2118145160on_val]: (((![A : nat]: (![Obj2 : produc266837688on_val]: ((((H2 @ A) = (some_P1299442195on_val @ Obj2))) => ((oconf_454120169t_char @ P3 @ H2 @ Obj2)))))) & ((preallocated @ H2)))))))). % hconf_def
thf(fact_156_hext__typeof__mono, axiom,
    ((![H : nat > option2118145160on_val, H3 : nat > option2118145160on_val, V2 : val, T : ty]: ((hext @ H @ H3) => (((typeof_h @ H @ V2) = (some_ty @ T)) => ((typeof_h @ H3 @ V2) = (some_ty @ T))))))). % hext_typeof_mono
thf(fact_157_typeof__lit__typeof, axiom,
    ((![V2 : val, T : ty, H : nat > option2118145160on_val]: (((typeof_h @ (^[X2 : nat]: none_P1535574167on_val) @ V2) = (some_ty @ T)) => ((typeof_h @ H @ V2) = (some_ty @ T)))))). % typeof_lit_typeof
thf(fact_158_preallocated__new, axiom,
    ((![H : nat > option2118145160on_val, A2 : nat, X : produc266837688on_val]: ((preallocated @ H) => (((H @ A2) = none_P1535574167on_val) => (preallocated @ (fun_up262443479on_val @ H @ A2 @ (some_P1299442195on_val @ X)))))))). % preallocated_new
thf(fact_159_preallocated__upd__obj, axiom,
    ((![H : nat > option2118145160on_val, A2 : nat, C3 : list_char, Fs : produc1257910179t_char > option_val, Fs2 : produc1257910179t_char > option_val]: ((preallocated @ H) => (((H @ A2) = (some_P1299442195on_val @ (produc904988266on_val @ C3 @ Fs))) => (preallocated @ (fun_up262443479on_val @ H @ A2 @ (some_P1299442195on_val @ (produc904988266on_val @ C3 @ Fs2))))))))). % preallocated_upd_obj
thf(fact_160_preallocated__hext, axiom,
    ((![H : nat > option2118145160on_val, H3 : nat > option2118145160on_val]: ((preallocated @ H) => ((hext @ H @ H3) => (preallocated @ H3)))))). % preallocated_hext
thf(fact_161_red__lcl__add, axiom,
    ((![E2 : exp_list_char, H : nat > option2118145160on_val, L : list_char > option_val, E4 : exp_list_char, H3 : nat > option2118145160on_val, L3 : list_char > option_val, P : list_P1234162913t_char, L_0 : list_char > option_val]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E2 @ (produc52622304on_val @ H @ L)) @ (produc2023458740on_val @ E4 @ (produc52622304on_val @ H3 @ L3))) @ (red @ P)) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E2 @ (produc52622304on_val @ H @ (map_ad1615113112ar_val @ L_0 @ L))) @ (produc2023458740on_val @ E4 @ (produc52622304on_val @ H3 @ (map_ad1615113112ar_val @ L_0 @ L3)))) @ (red @ P)))))). % red_lcl_add
thf(fact_162_map__add__assoc, axiom,
    ((![M1 : list_char > option_val, M2 : list_char > option_val, M3 : list_char > option_val]: ((map_ad1615113112ar_val @ M1 @ (map_ad1615113112ar_val @ M2 @ M3)) = (map_ad1615113112ar_val @ (map_ad1615113112ar_val @ M1 @ M2) @ M3))))). % map_add_assoc
thf(fact_163_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_164_map__add__None, axiom,
    ((![M : list_char > option_val, N : list_char > option_val, K : list_char]: (((map_ad1615113112ar_val @ M @ N @ K) = none_val) = ((((N @ K) = none_val)) & (((M @ K) = none_val))))))). % map_add_None
thf(fact_165_map__add__eq__empty__iff, axiom,
    ((![F : list_char > option_val, G : list_char > option_val]: (((map_ad1615113112ar_val @ F @ G) = (^[X2 : list_char]: none_val)) = (((F = (^[X2 : list_char]: none_val))) & ((G = (^[X2 : list_char]: none_val)))))))). % map_add_eq_empty_iff
thf(fact_166_empty__eq__map__add__iff, axiom,
    ((![F : list_char > option_val, G : list_char > option_val]: (((^[X2 : list_char]: none_val) = (map_ad1615113112ar_val @ F @ G)) = (((F = (^[X2 : list_char]: none_val))) & ((G = (^[X2 : list_char]: none_val)))))))). % empty_eq_map_add_iff
thf(fact_167_map__add__empty, axiom,
    ((![M : list_char > option_val]: ((map_ad1615113112ar_val @ M @ (^[X2 : list_char]: none_val)) = M)))). % map_add_empty
thf(fact_168_empty__map__add, axiom,
    ((![M : list_char > option_val]: ((map_ad1615113112ar_val @ (^[X2 : list_char]: none_val) @ M) = M)))). % empty_map_add
thf(fact_169_map__add__upd, axiom,
    ((![F : list_char > option_ty, G : list_char > option_ty, X : list_char, Y : ty]: ((map_add_list_char_ty @ F @ (fun_up9191ion_ty @ G @ X @ (some_ty @ Y))) = (fun_up9191ion_ty @ (map_add_list_char_ty @ F @ G) @ X @ (some_ty @ Y)))))). % map_add_upd
thf(fact_170_map__add__upd, axiom,
    ((![F : nat > option2118145160on_val, G : nat > option2118145160on_val, X : nat, Y : produc266837688on_val]: ((map_ad109059391on_val @ F @ (fun_up262443479on_val @ G @ X @ (some_P1299442195on_val @ Y))) = (fun_up262443479on_val @ (map_ad109059391on_val @ F @ G) @ X @ (some_P1299442195on_val @ Y)))))). % map_add_upd
thf(fact_171_map__add__upd, axiom,
    ((![F : list_char > option_val, G : list_char > option_val, X : list_char, Y : val]: ((map_ad1615113112ar_val @ F @ (fun_up1252458416on_val @ G @ X @ (some_val @ Y))) = (fun_up1252458416on_val @ (map_ad1615113112ar_val @ F @ G) @ X @ (some_val @ Y)))))). % map_add_upd
thf(fact_172_map__add__Some__iff, axiom,
    ((![M : list_char > option_val, N : list_char > option_val, K : list_char, X : val]: (((map_ad1615113112ar_val @ M @ N @ K) = (some_val @ X)) = ((((N @ K) = (some_val @ X))) | (((((N @ K) = none_val)) & (((M @ K) = (some_val @ X)))))))))). % map_add_Some_iff
thf(fact_173_map__add__SomeD, axiom,
    ((![M : list_char > option_val, N : list_char > option_val, K : list_char, X : val]: (((map_ad1615113112ar_val @ M @ N @ K) = (some_val @ X)) => (((N @ K) = (some_val @ X)) | (((N @ K) = none_val) & ((M @ K) = (some_val @ X)))))))). % map_add_SomeD
thf(fact_174_Red__lcl__add, axiom,
    ((![E2 : exp_list_char, H : nat > option2118145160on_val, L : list_char > option_val, E4 : exp_list_char, H3 : nat > option2118145160on_val, L3 : list_char > option_val, P : list_P1234162913t_char, L_0 : list_char > option_val]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E2 @ (produc52622304on_val @ H @ L)) @ (produc2023458740on_val @ E4 @ (produc52622304on_val @ H3 @ L3))) @ (transi111096263on_val @ (red @ P))) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E2 @ (produc52622304on_val @ H @ (map_ad1615113112ar_val @ L_0 @ L))) @ (produc2023458740on_val @ E4 @ (produc52622304on_val @ H3 @ (map_ad1615113112ar_val @ L_0 @ L3)))) @ (transi111096263on_val @ (red @ P))))))). % Red_lcl_add
thf(fact_175_red__reds_ORedBlock, axiom,
    ((![V : list_char, T : ty, U : val, S2 : produc515445032on_val, P : list_P1234162913t_char]: (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (block_list_char @ V @ T @ (val_list_char @ U)) @ S2) @ (produc2023458740on_val @ (val_list_char @ U) @ S2)) @ (red @ P))))). % red_reds.RedBlock
thf(fact_176_exp_Oinject_I3_J, axiom,
    ((![X32 : val, Y32 : val]: (((val_list_char @ X32) = (val_list_char @ Y32)) = (X32 = Y32))))). % exp.inject(3)
thf(fact_177_exp_Odistinct_I67_J, axiom,
    ((![X32 : val, X101 : list_char, X102 : ty, X103 : exp_list_char]: (~ (((val_list_char @ X32) = (block_list_char @ X101 @ X102 @ X103))))))). % exp.distinct(67)
thf(fact_178_redp__redsp_ORedBlock, axiom,
    ((![P : list_P1234162913t_char, V : list_char, T : ty, U : val, S2 : produc515445032on_val]: (redp @ P @ (block_list_char @ V @ T @ (val_list_char @ U)) @ S2 @ (val_list_char @ U) @ S2)))). % redp_redsp.RedBlock
thf(fact_179_WTrtVal, axiom,
    ((![H : nat > option2118145160on_val, V2 : val, T : ty, P : list_P1234162913t_char, E : list_char > option_ty]: (((typeof_h @ H @ V2) = (some_ty @ T)) => (wTrt @ P @ H @ E @ (val_list_char @ V2) @ T))))). % WTrtVal
thf(fact_180_converse__rtrancl__induct__red, axiom,
    ((![E2 : exp_list_char, H : nat > option2118145160on_val, L : 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 @ H @ L)) @ (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_02 : list_char > option_val, E_1 : 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_02)) @ (produc2023458740on_val @ E_1 @ (produc52622304on_val @ H_1 @ L_1))) @ (red @ P)) => ((R @ E_1 @ H_1 @ L_1 @ E6 @ H7 @ L5) => (R @ E_0 @ H_0 @ L_02 @ E6 @ H7 @ L5)))) => (R @ E2 @ H @ L @ E4 @ H3 @ L3))))))). % converse_rtrancl_induct_red
thf(fact_181_rtrancl__induct2, axiom,
    ((![Ax : produc1097884484on_val, Ay : produc1097884484on_val, Bx : produc1097884484on_val, By : produc1097884484on_val, R2 : set_Pr1368603847on_val, P : produc1097884484on_val > produc1097884484on_val > $o]: ((member208988944on_val @ (produc564964183on_val @ (produc1069526295on_val @ Ax @ Ay) @ (produc1069526295on_val @ Bx @ By)) @ (transi100378922on_val @ R2)) => ((P @ Ax @ Ay) => ((![A3 : produc1097884484on_val, B3 : produc1097884484on_val, Aa2 : produc1097884484on_val, Ba : produc1097884484on_val]: ((member208988944on_val @ (produc564964183on_val @ (produc1069526295on_val @ Ax @ Ay) @ (produc1069526295on_val @ A3 @ B3)) @ (transi100378922on_val @ R2)) => ((member208988944on_val @ (produc564964183on_val @ (produc1069526295on_val @ A3 @ B3) @ (produc1069526295on_val @ Aa2 @ Ba)) @ R2) => ((P @ A3 @ B3) => (P @ Aa2 @ Ba))))) => (P @ Bx @ By))))))). % rtrancl_induct2
thf(fact_182_rtrancl__induct2, axiom,
    ((![Ax : nat > option2118145160on_val, Ay : list_char > option_val, Bx : nat > option2118145160on_val, By : list_char > option_val, R2 : set_Pr148564103on_val, P : (nat > option2118145160on_val) > (list_char > option_val) > $o]: ((member2027247312on_val @ (produc2106877847on_val @ (produc52622304on_val @ Ax @ Ay) @ (produc52622304on_val @ Bx @ By)) @ (transi432893227on_val @ R2)) => ((P @ Ax @ Ay) => ((![A3 : nat > option2118145160on_val, B3 : list_char > option_val, Aa2 : nat > option2118145160on_val, Ba : list_char > option_val]: ((member2027247312on_val @ (produc2106877847on_val @ (produc52622304on_val @ Ax @ Ay) @ (produc52622304on_val @ A3 @ B3)) @ (transi432893227on_val @ R2)) => ((member2027247312on_val @ (produc2106877847on_val @ (produc52622304on_val @ A3 @ B3) @ (produc52622304on_val @ Aa2 @ Ba)) @ R2) => ((P @ A3 @ B3) => (P @ Aa2 @ Ba))))) => (P @ Bx @ By))))))). % rtrancl_induct2
thf(fact_183_rtrancl__induct2, axiom,
    ((![Ax : list_char, Ay : produc1257910179t_char > option_val, Bx : list_char, By : produc1257910179t_char > option_val, R2 : set_Pr2110063281on_val, P : list_char > (produc1257910179t_char > option_val) > $o]: ((member197592058on_val @ (produc881885833on_val @ (produc904988266on_val @ Ax @ Ay) @ (produc904988266on_val @ Bx @ By)) @ (transi2071064181on_val @ R2)) => ((P @ Ax @ Ay) => ((![A3 : list_char, B3 : produc1257910179t_char > option_val, Aa2 : list_char, Ba : produc1257910179t_char > option_val]: ((member197592058on_val @ (produc881885833on_val @ (produc904988266on_val @ Ax @ Ay) @ (produc904988266on_val @ A3 @ B3)) @ (transi2071064181on_val @ R2)) => ((member197592058on_val @ (produc881885833on_val @ (produc904988266on_val @ A3 @ B3) @ (produc904988266on_val @ Aa2 @ Ba)) @ R2) => ((P @ A3 @ B3) => (P @ Aa2 @ Ba))))) => (P @ Bx @ By))))))). % rtrancl_induct2
thf(fact_184_rtrancl__induct2, axiom,
    ((![Ax : exp_list_char, Ay : produc515445032on_val, Bx : exp_list_char, By : produc515445032on_val, R2 : set_Pr1189492743on_val, P : exp_list_char > produc515445032on_val > $o]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ Ax @ Ay) @ (produc2023458740on_val @ Bx @ By)) @ (transi111096263on_val @ R2)) => ((P @ Ax @ Ay) => ((![A3 : exp_list_char, B3 : produc515445032on_val, Aa2 : exp_list_char, Ba : produc515445032on_val]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ Ax @ Ay) @ (produc2023458740on_val @ A3 @ B3)) @ (transi111096263on_val @ R2)) => ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ A3 @ B3) @ (produc2023458740on_val @ Aa2 @ Ba)) @ R2) => ((P @ A3 @ B3) => (P @ Aa2 @ Ba))))) => (P @ Bx @ By))))))). % rtrancl_induct2
thf(fact_185_converse__rtranclE2, axiom,
    ((![Xa : produc1097884484on_val, Xb : produc1097884484on_val, Za : produc1097884484on_val, Zb : produc1097884484on_val, R2 : set_Pr1368603847on_val]: ((member208988944on_val @ (produc564964183on_val @ (produc1069526295on_val @ Xa @ Xb) @ (produc1069526295on_val @ Za @ Zb)) @ (transi100378922on_val @ R2)) => ((~ (((produc1069526295on_val @ Xa @ Xb) = (produc1069526295on_val @ Za @ Zb)))) => (~ ((![A3 : produc1097884484on_val, B3 : produc1097884484on_val]: ((member208988944on_val @ (produc564964183on_val @ (produc1069526295on_val @ Xa @ Xb) @ (produc1069526295on_val @ A3 @ B3)) @ R2) => (~ ((member208988944on_val @ (produc564964183on_val @ (produc1069526295on_val @ A3 @ B3) @ (produc1069526295on_val @ Za @ Zb)) @ (transi100378922on_val @ R2))))))))))))). % converse_rtranclE2
thf(fact_186_converse__rtranclE2, axiom,
    ((![Xa : nat > option2118145160on_val, Xb : list_char > option_val, Za : nat > option2118145160on_val, Zb : list_char > option_val, R2 : set_Pr148564103on_val]: ((member2027247312on_val @ (produc2106877847on_val @ (produc52622304on_val @ Xa @ Xb) @ (produc52622304on_val @ Za @ Zb)) @ (transi432893227on_val @ R2)) => ((~ (((produc52622304on_val @ Xa @ Xb) = (produc52622304on_val @ Za @ Zb)))) => (~ ((![A3 : nat > option2118145160on_val, B3 : list_char > option_val]: ((member2027247312on_val @ (produc2106877847on_val @ (produc52622304on_val @ Xa @ Xb) @ (produc52622304on_val @ A3 @ B3)) @ R2) => (~ ((member2027247312on_val @ (produc2106877847on_val @ (produc52622304on_val @ A3 @ B3) @ (produc52622304on_val @ Za @ Zb)) @ (transi432893227on_val @ R2))))))))))))). % converse_rtranclE2
thf(fact_187_converse__rtranclE2, axiom,
    ((![Xa : list_char, Xb : produc1257910179t_char > option_val, Za : list_char, Zb : produc1257910179t_char > option_val, R2 : set_Pr2110063281on_val]: ((member197592058on_val @ (produc881885833on_val @ (produc904988266on_val @ Xa @ Xb) @ (produc904988266on_val @ Za @ Zb)) @ (transi2071064181on_val @ R2)) => ((~ (((produc904988266on_val @ Xa @ Xb) = (produc904988266on_val @ Za @ Zb)))) => (~ ((![A3 : list_char, B3 : produc1257910179t_char > option_val]: ((member197592058on_val @ (produc881885833on_val @ (produc904988266on_val @ Xa @ Xb) @ (produc904988266on_val @ A3 @ B3)) @ R2) => (~ ((member197592058on_val @ (produc881885833on_val @ (produc904988266on_val @ A3 @ B3) @ (produc904988266on_val @ Za @ Zb)) @ (transi2071064181on_val @ R2))))))))))))). % converse_rtranclE2
thf(fact_188_converse__rtranclE2, axiom,
    ((![Xa : exp_list_char, Xb : produc515445032on_val, Za : exp_list_char, Zb : produc515445032on_val, R2 : set_Pr1189492743on_val]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ Xa @ Xb) @ (produc2023458740on_val @ Za @ Zb)) @ (transi111096263on_val @ R2)) => ((~ (((produc2023458740on_val @ Xa @ Xb) = (produc2023458740on_val @ Za @ Zb)))) => (~ ((![A3 : exp_list_char, B3 : produc515445032on_val]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ Xa @ Xb) @ (produc2023458740on_val @ A3 @ B3)) @ R2) => (~ ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ A3 @ B3) @ (produc2023458740on_val @ Za @ Zb)) @ (transi111096263on_val @ R2))))))))))))). % converse_rtranclE2
thf(fact_189_converse__rtrancl__into__rtrancl, axiom,
    ((![A2 : produc1097884484on_val, B2 : produc1097884484on_val, R2 : set_Pr1189492743on_val, C : produc1097884484on_val]: ((member354538064on_val @ (produc1069526295on_val @ A2 @ B2) @ R2) => ((member354538064on_val @ (produc1069526295on_val @ B2 @ C) @ (transi111096263on_val @ R2)) => (member354538064on_val @ (produc1069526295on_val @ A2 @ C) @ (transi111096263on_val @ R2))))))). % converse_rtrancl_into_rtrancl
thf(fact_190_rtrancl_Ortrancl__into__rtrancl, axiom,
    ((![A2 : produc1097884484on_val, B2 : produc1097884484on_val, R2 : set_Pr1189492743on_val, C : produc1097884484on_val]: ((member354538064on_val @ (produc1069526295on_val @ A2 @ B2) @ (transi111096263on_val @ R2)) => ((member354538064on_val @ (produc1069526295on_val @ B2 @ C) @ R2) => (member354538064on_val @ (produc1069526295on_val @ A2 @ C) @ (transi111096263on_val @ R2))))))). % rtrancl.rtrancl_into_rtrancl
thf(fact_191_converse__rtrancl__induct, axiom,
    ((![A2 : produc1097884484on_val, B2 : produc1097884484on_val, R2 : set_Pr1189492743on_val, P : produc1097884484on_val > $o]: ((member354538064on_val @ (produc1069526295on_val @ A2 @ B2) @ (transi111096263on_val @ R2)) => ((P @ B2) => ((![Y3 : produc1097884484on_val, Z3 : produc1097884484on_val]: ((member354538064on_val @ (produc1069526295on_val @ Y3 @ Z3) @ R2) => ((member354538064on_val @ (produc1069526295on_val @ Z3 @ B2) @ (transi111096263on_val @ R2)) => ((P @ Z3) => (P @ Y3))))) => (P @ A2))))))). % converse_rtrancl_induct
thf(fact_192_rtrancl_Ortrancl__refl, axiom,
    ((![A2 : produc1097884484on_val, R2 : set_Pr1189492743on_val]: (member354538064on_val @ (produc1069526295on_val @ A2 @ A2) @ (transi111096263on_val @ R2))))). % rtrancl.rtrancl_refl
thf(fact_193_converse__rtranclE, axiom,
    ((![X : produc1097884484on_val, Z : produc1097884484on_val, R2 : set_Pr1189492743on_val]: ((member354538064on_val @ (produc1069526295on_val @ X @ Z) @ (transi111096263on_val @ R2)) => ((~ ((X = Z))) => (~ ((![Y3 : produc1097884484on_val]: ((member354538064on_val @ (produc1069526295on_val @ X @ Y3) @ R2) => (~ ((member354538064on_val @ (produc1069526295on_val @ Y3 @ Z) @ (transi111096263on_val @ R2))))))))))))). % converse_rtranclE
thf(fact_194_rtrancl_Oinducts, axiom,
    ((![X1 : produc1097884484on_val, X22 : produc1097884484on_val, R2 : set_Pr1189492743on_val, P : produc1097884484on_val > produc1097884484on_val > $o]: ((member354538064on_val @ (produc1069526295on_val @ X1 @ X22) @ (transi111096263on_val @ R2)) => ((![A3 : produc1097884484on_val]: (P @ A3 @ A3)) => ((![A3 : produc1097884484on_val, B3 : produc1097884484on_val, C2 : produc1097884484on_val]: ((member354538064on_val @ (produc1069526295on_val @ A3 @ B3) @ (transi111096263on_val @ R2)) => ((P @ A3 @ B3) => ((member354538064on_val @ (produc1069526295on_val @ B3 @ C2) @ R2) => (P @ A3 @ C2))))) => (P @ X1 @ X22))))))). % rtrancl.inducts
thf(fact_195_rtrancl__induct, axiom,
    ((![A2 : produc1097884484on_val, B2 : produc1097884484on_val, R2 : set_Pr1189492743on_val, P : produc1097884484on_val > $o]: ((member354538064on_val @ (produc1069526295on_val @ A2 @ B2) @ (transi111096263on_val @ R2)) => ((P @ A2) => ((![Y3 : produc1097884484on_val, Z3 : produc1097884484on_val]: ((member354538064on_val @ (produc1069526295on_val @ A2 @ Y3) @ (transi111096263on_val @ R2)) => ((member354538064on_val @ (produc1069526295on_val @ Y3 @ Z3) @ R2) => ((P @ Y3) => (P @ Z3))))) => (P @ B2))))))). % rtrancl_induct
thf(fact_196_rtrancl__trans, axiom,
    ((![X : produc1097884484on_val, Y : produc1097884484on_val, R2 : set_Pr1189492743on_val, Z : produc1097884484on_val]: ((member354538064on_val @ (produc1069526295on_val @ X @ Y) @ (transi111096263on_val @ R2)) => ((member354538064on_val @ (produc1069526295on_val @ Y @ Z) @ (transi111096263on_val @ R2)) => (member354538064on_val @ (produc1069526295on_val @ X @ Z) @ (transi111096263on_val @ R2))))))). % rtrancl_trans
thf(fact_197_rtrancl_Osimps, axiom,
    ((![A1 : produc1097884484on_val, A22 : produc1097884484on_val, R2 : set_Pr1189492743on_val]: ((member354538064on_val @ (produc1069526295on_val @ A1 @ A22) @ (transi111096263on_val @ R2)) = (((?[A : produc1097884484on_val]: (((A1 = A)) & ((A22 = A))))) | ((?[A : produc1097884484on_val]: (?[B : produc1097884484on_val]: (?[C6 : produc1097884484on_val]: (((A1 = A)) & ((((A22 = C6)) & ((((member354538064on_val @ (produc1069526295on_val @ A @ B) @ (transi111096263on_val @ R2))) & ((member354538064on_val @ (produc1069526295on_val @ B @ C6) @ R2)))))))))))))))). % rtrancl.simps
thf(fact_198_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_199_rtranclE, axiom,
    ((![A2 : produc1097884484on_val, B2 : produc1097884484on_val, R2 : set_Pr1189492743on_val]: ((member354538064on_val @ (produc1069526295on_val @ A2 @ B2) @ (transi111096263on_val @ R2)) => ((~ ((A2 = B2))) => (~ ((![Y3 : produc1097884484on_val]: ((member354538064on_val @ (produc1069526295on_val @ A2 @ Y3) @ (transi111096263on_val @ R2)) => (~ ((member354538064on_val @ (produc1069526295on_val @ Y3 @ B2) @ R2)))))))))))). % rtranclE
thf(fact_200_converse__rtrancl__induct2, axiom,
    ((![Ax : produc1097884484on_val, Ay : produc1097884484on_val, Bx : produc1097884484on_val, By : produc1097884484on_val, R2 : set_Pr1368603847on_val, P : produc1097884484on_val > produc1097884484on_val > $o]: ((member208988944on_val @ (produc564964183on_val @ (produc1069526295on_val @ Ax @ Ay) @ (produc1069526295on_val @ Bx @ By)) @ (transi100378922on_val @ R2)) => ((P @ Bx @ By) => ((![A3 : produc1097884484on_val, B3 : produc1097884484on_val, Aa2 : produc1097884484on_val, Ba : produc1097884484on_val]: ((member208988944on_val @ (produc564964183on_val @ (produc1069526295on_val @ A3 @ B3) @ (produc1069526295on_val @ Aa2 @ Ba)) @ R2) => ((member208988944on_val @ (produc564964183on_val @ (produc1069526295on_val @ Aa2 @ Ba) @ (produc1069526295on_val @ Bx @ By)) @ (transi100378922on_val @ R2)) => ((P @ Aa2 @ Ba) => (P @ A3 @ B3))))) => (P @ Ax @ Ay))))))). % converse_rtrancl_induct2
thf(fact_201_converse__rtrancl__induct2, axiom,
    ((![Ax : nat > option2118145160on_val, Ay : list_char > option_val, Bx : nat > option2118145160on_val, By : list_char > option_val, R2 : set_Pr148564103on_val, P : (nat > option2118145160on_val) > (list_char > option_val) > $o]: ((member2027247312on_val @ (produc2106877847on_val @ (produc52622304on_val @ Ax @ Ay) @ (produc52622304on_val @ Bx @ By)) @ (transi432893227on_val @ R2)) => ((P @ Bx @ By) => ((![A3 : nat > option2118145160on_val, B3 : list_char > option_val, Aa2 : nat > option2118145160on_val, Ba : list_char > option_val]: ((member2027247312on_val @ (produc2106877847on_val @ (produc52622304on_val @ A3 @ B3) @ (produc52622304on_val @ Aa2 @ Ba)) @ R2) => ((member2027247312on_val @ (produc2106877847on_val @ (produc52622304on_val @ Aa2 @ Ba) @ (produc52622304on_val @ Bx @ By)) @ (transi432893227on_val @ R2)) => ((P @ Aa2 @ Ba) => (P @ A3 @ B3))))) => (P @ Ax @ Ay))))))). % converse_rtrancl_induct2
thf(fact_202_converse__rtrancl__induct2, axiom,
    ((![Ax : list_char, Ay : produc1257910179t_char > option_val, Bx : list_char, By : produc1257910179t_char > option_val, R2 : set_Pr2110063281on_val, P : list_char > (produc1257910179t_char > option_val) > $o]: ((member197592058on_val @ (produc881885833on_val @ (produc904988266on_val @ Ax @ Ay) @ (produc904988266on_val @ Bx @ By)) @ (transi2071064181on_val @ R2)) => ((P @ Bx @ By) => ((![A3 : list_char, B3 : produc1257910179t_char > option_val, Aa2 : list_char, Ba : produc1257910179t_char > option_val]: ((member197592058on_val @ (produc881885833on_val @ (produc904988266on_val @ A3 @ B3) @ (produc904988266on_val @ Aa2 @ Ba)) @ R2) => ((member197592058on_val @ (produc881885833on_val @ (produc904988266on_val @ Aa2 @ Ba) @ (produc904988266on_val @ Bx @ By)) @ (transi2071064181on_val @ R2)) => ((P @ Aa2 @ Ba) => (P @ A3 @ B3))))) => (P @ Ax @ Ay))))))). % converse_rtrancl_induct2
thf(fact_203_converse__rtrancl__induct2, axiom,
    ((![Ax : exp_list_char, Ay : produc515445032on_val, Bx : exp_list_char, By : produc515445032on_val, R2 : set_Pr1189492743on_val, P : exp_list_char > produc515445032on_val > $o]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ Ax @ Ay) @ (produc2023458740on_val @ Bx @ By)) @ (transi111096263on_val @ R2)) => ((P @ Bx @ By) => ((![A3 : exp_list_char, B3 : produc515445032on_val, Aa2 : exp_list_char, Ba : produc515445032on_val]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ A3 @ B3) @ (produc2023458740on_val @ Aa2 @ Ba)) @ R2) => ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ Aa2 @ Ba) @ (produc2023458740on_val @ Bx @ By)) @ (transi111096263on_val @ R2)) => ((P @ Aa2 @ Ba) => (P @ A3 @ B3))))) => (P @ Ax @ Ay))))))). % converse_rtrancl_induct2
thf(fact_204_BlockRedsFinal, axiom,
    ((![E_02 : exp_list_char, S_0 : produc515445032on_val, E_2 : exp_list_char, H_2 : nat > option2118145160on_val, L_2 : list_char > option_val, P : list_P1234162913t_char, H_02 : nat > option2118145160on_val, L_0 : list_char > option_val, V : list_char, T : ty]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E_02 @ S_0) @ (produc2023458740on_val @ E_2 @ (produc52622304on_val @ H_2 @ L_2))) @ (transi111096263on_val @ (red @ P))) => ((final_list_char @ E_2) => ((S_0 = (produc52622304on_val @ H_02 @ (fun_up1252458416on_val @ L_0 @ V @ none_val))) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (block_list_char @ V @ T @ E_02) @ (produc52622304on_val @ H_02 @ L_0)) @ (produc2023458740on_val @ E_2 @ (produc52622304on_val @ H_2 @ (fun_up1252458416on_val @ L_2 @ V @ (L_0 @ V))))) @ (transi111096263on_val @ (red @ P))))))))). % BlockRedsFinal
thf(fact_205_red__reds_OBlockRedSome, axiom,
    ((![E2 : exp_list_char, H : nat > option2118145160on_val, L : list_char > option_val, V : list_char, E4 : exp_list_char, H3 : nat > option2118145160on_val, L3 : list_char > option_val, P : list_P1234162913t_char, V2 : val, T : ty]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E2 @ (produc52622304on_val @ H @ (fun_up1252458416on_val @ L @ V @ none_val))) @ (produc2023458740on_val @ E4 @ (produc52622304on_val @ H3 @ L3))) @ (red @ P)) => (((L3 @ V) = (some_val @ V2)) => ((~ ((assigned @ V @ E2))) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (block_list_char @ V @ T @ E2) @ (produc52622304on_val @ H @ L)) @ (produc2023458740on_val @ (block_list_char @ V @ T @ (seq_list_char @ (lAss_list_char @ V @ (val_list_char @ V2)) @ E4)) @ (produc52622304on_val @ H3 @ (fun_up1252458416on_val @ L3 @ V @ (L @ V))))) @ (red @ P)))))))). % red_reds.BlockRedSome
thf(fact_206_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_207_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_208_red__reds_ORedInitBlock, axiom,
    ((![V : list_char, T : ty, V2 : val, U : val, S2 : produc515445032on_val, P : list_P1234162913t_char]: (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (block_list_char @ V @ T @ (seq_list_char @ (lAss_list_char @ V @ (val_list_char @ V2)) @ (val_list_char @ U))) @ S2) @ (produc2023458740on_val @ (val_list_char @ U) @ S2)) @ (red @ P))))). % red_reds.RedInitBlock
thf(fact_209_assigned__def, axiom,
    ((assigned = (^[V3 : list_char]: (^[E7 : exp_list_char]: (?[V4 : val]: (?[E8 : exp_list_char]: (E7 = (seq_list_char @ (lAss_list_char @ V3 @ (val_list_char @ V4)) @ E8))))))))). % assigned_def
thf(fact_210_exp_Odistinct_I59_J, axiom,
    ((![X32 : val, X61 : list_char, X62 : exp_list_char]: (~ (((val_list_char @ X32) = (lAss_list_char @ X61 @ X62))))))). % exp.distinct(59)
thf(fact_211_exp_Odistinct_I69_J, axiom,
    ((![X32 : val, X111 : exp_list_char, X112 : exp_list_char]: (~ (((val_list_char @ X32) = (seq_list_char @ X111 @ X112))))))). % exp.distinct(69)
thf(fact_212_redp__redsp_ORedSeq, axiom,
    ((![P : list_P1234162913t_char, V2 : val, E_2 : exp_list_char, S2 : produc515445032on_val]: (redp @ P @ (seq_list_char @ (val_list_char @ V2) @ E_2) @ S2 @ E_2 @ S2)))). % redp_redsp.RedSeq
thf(fact_213_redp__redsp_ORedInitBlock, axiom,
    ((![P : list_P1234162913t_char, V : list_char, T : ty, V2 : val, U : val, S2 : produc515445032on_val]: (redp @ P @ (block_list_char @ V @ T @ (seq_list_char @ (lAss_list_char @ V @ (val_list_char @ V2)) @ (val_list_char @ U))) @ S2 @ (val_list_char @ U) @ S2)))). % redp_redsp.RedInitBlock
thf(fact_214_exp_Odistinct_I129_J, axiom,
    ((![X61 : list_char, X62 : exp_list_char, X111 : exp_list_char, X112 : exp_list_char]: (~ (((lAss_list_char @ X61 @ X62) = (seq_list_char @ X111 @ X112))))))). % exp.distinct(129)

% Helper facts (7)
thf(help_If_2_1_If_001t__Option__Ooption_It__Type__Oty_J_T, axiom,
    ((![X : option_ty, Y : option_ty]: ((if_option_ty @ $false @ X @ Y) = Y)))).
thf(help_If_1_1_If_001t__Option__Ooption_It__Type__Oty_J_T, axiom,
    ((![X : option_ty, Y : option_ty]: ((if_option_ty @ $true @ X @ Y) = X)))).
thf(help_If_2_1_If_001t__Option__Ooption_It__Value__Oval_J_T, axiom,
    ((![X : option_val, Y : option_val]: ((if_option_val @ $false @ X @ Y) = Y)))).
thf(help_If_1_1_If_001t__Option__Ooption_It__Value__Oval_J_T, axiom,
    ((![X : option_val, Y : option_val]: ((if_option_val @ $true @ X @ Y) = X)))).
thf(help_If_3_1_If_001t__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_T, axiom,
    ((![P : $o]: ((P = $true) | (P = $false))))).
thf(help_If_2_1_If_001t__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_T, axiom,
    ((![X : option2118145160on_val, Y : option2118145160on_val]: ((if_opt451925058on_val @ $false @ X @ Y) = Y)))).
thf(help_If_1_1_If_001t__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_T, axiom,
    ((![X : option2118145160on_val, Y : option2118145160on_val]: ((if_opt451925058on_val @ $true @ X @ Y) = X)))).

% Conjectures (1)
thf(conj_0, conjecture,
    ((lconf_485928294t_char @ p @ h_a @ (fun_up1252458416on_val @ l_a @ v @ (la @ v)) @ e))).
