% 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_76__5333446_1 ) ; }
% This file was generated by Isabelle (most likely Sledgehammer)
% 2020-12-16 14:19:08.973

% Could-be-implicit typings (24)
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thf(ty_n_t__Option__Ooption_It__Value__Oval_J, type,
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thf(ty_n_t__Option__Ooption_It__Type__Oty_J, type,
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thf(ty_n_t__List__Olist_It__String__Ochar_J, type,
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thf(ty_n_t__Value__Oval, type,
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thf(ty_n_t__Type__Oty, type,
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thf(ty_n_t__Nat__Onat, type,
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% Explicit typings (68)
thf(sy_c_BigStep_Ofinal_001t__List__Olist_It__String__Ochar_J, type,
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thf(sy_c_Conform_Oconf_001t__Product____Type__Oprod_It__List__Olist_It__List__Olist_It__String__Ochar_J_J_Mt__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_J, type,
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thf(sy_c_Conform_Olconf_001t__Product____Type__Oprod_It__List__Olist_It__List__Olist_It__String__Ochar_J_J_Mt__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_J, type,
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thf(sy_c_Expr_Oexp_OBlock_001t__List__Olist_It__String__Ochar_J, type,
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thf(sy_c_Expr_Oexp_OFAss_001t__List__Olist_It__String__Ochar_J, type,
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thf(sy_c_Expr_Oexp_OLAss_001t__List__Olist_It__String__Ochar_J, type,
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thf(sy_c_Expr_Oexp_OSeq_001t__List__Olist_It__String__Ochar_J, type,
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thf(sy_c_Expr_Oexp_OVal_001t__List__Olist_It__String__Ochar_J, type,
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thf(sy_c_Fun_Ofun__upd_001t__List__Olist_It__String__Ochar_J_001t__Option__Ooption_It__Type__Oty_J, type,
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thf(sy_c_Fun_Ofun__upd_001t__List__Olist_It__String__Ochar_J_001t__Option__Ooption_It__Value__Oval_J, type,
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thf(sy_c_If_001t__Option__Ooption_It__Type__Oty_J, type,
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thf(sy_c_If_001t__Option__Ooption_It__Value__Oval_J, type,
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thf(sy_c_Map_Omap__add_001t__List__Olist_It__String__Ochar_J_001t__Value__Oval, type,
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thf(sy_c_Option_Ooption_ONone_001t__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J, type,
    none_P1535574167on_val : option2118145160on_val).
thf(sy_c_Option_Ooption_ONone_001t__Type__Oty, type,
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thf(sy_c_Option_Ooption_ONone_001t__Value__Oval, type,
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thf(sy_c_Option_Ooption_OSome_001t__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J, type,
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thf(sy_c_Option_Ooption_OSome_001t__Type__Oty, type,
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thf(sy_c_Option_Ooption_OSome_001t__Value__Oval, type,
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thf(sy_c_Option_Ooption_Othe_001t__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J, type,
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thf(sy_c_Option_Ooption_Othe_001t__Type__Oty, type,
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thf(sy_c_Value_Oval_OUnit, 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_l_Ha____, type,
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thf(sy_v_la____, type,
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% Relevant facts (248)
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_lconf, axiom,
    ((lconf_485928294t_char @ p @ ha @ la @ e))). % lconf
thf(fact_3_l_HV, axiom,
    (((l_a @ v) = (some_val @ v2)))). % l'V
thf(fact_4_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_5_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_6_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_7_fun__upd__upd, axiom,
    ((![F : produc1257910179t_char > option_val, X : produc1257910179t_char, Y : option_val, Z : option_val]: ((fun_up356838326on_val @ (fun_up356838326on_val @ F @ X @ Y) @ X @ Z) = (fun_up356838326on_val @ F @ X @ Z))))). % fun_upd_upd
thf(fact_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__triv, axiom,
    ((![F : produc1257910179t_char > option_val, X : produc1257910179t_char]: ((fun_up356838326on_val @ F @ X @ (F @ X)) = F)))). % fun_upd_triv
thf(fact_12_fun__upd__apply, axiom,
    ((fun_up1252458416on_val = (^[F2 : list_char > option_val]: (^[X2 : list_char]: (^[Y2 : option_val]: (^[Z2 : list_char]: (if_option_val @ (Z2 = X2) @ Y2 @ (F2 @ Z2))))))))). % fun_upd_apply
thf(fact_13_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_14_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_15_fun__upd__apply, axiom,
    ((fun_up356838326on_val = (^[F2 : produc1257910179t_char > option_val]: (^[X2 : produc1257910179t_char]: (^[Y2 : option_val]: (^[Z2 : produc1257910179t_char]: (if_option_val @ (Z2 = X2) @ Y2 @ (F2 @ Z2))))))))). % fun_upd_apply
thf(fact_16_InitBlockRed_Oprems_I2_J, axiom,
    ((lconf_485928294t_char @ p @ ha @ la @ e))). % InitBlockRed.prems(2)
thf(fact_17_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 @ (some_val @ v3)) @ E) => (lconf_485928294t_char @ p @ h_a @ l_a @ E)))))). % IH
thf(fact_18_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_19_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_20_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_21_fun__upd__def, axiom,
    ((fun_up356838326on_val = (^[F2 : produc1257910179t_char > option_val]: (^[A : produc1257910179t_char]: (^[B : option_val]: (^[X2 : produc1257910179t_char]: (if_option_val @ (X2 = A) @ B @ (F2 @ X2))))))))). % fun_upd_def
thf(fact_22_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_23_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_24_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_25_fun__upd__eqD, axiom,
    ((![F : produc1257910179t_char > option_val, X : produc1257910179t_char, Y : option_val, G : produc1257910179t_char > option_val, Z : option_val]: (((fun_up356838326on_val @ F @ X @ Y) = (fun_up356838326on_val @ G @ X @ Z)) => (Y = Z))))). % fun_upd_eqD
thf(fact_26_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_27_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_28_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_29_fun__upd__idem, axiom,
    ((![F : produc1257910179t_char > option_val, X : produc1257910179t_char, Y : option_val]: (((F @ X) = Y) => ((fun_up356838326on_val @ F @ X @ Y) = F))))). % fun_upd_idem
thf(fact_30_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_31_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_32_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_33_fun__upd__same, axiom,
    ((![F : produc1257910179t_char > option_val, X : produc1257910179t_char, Y : option_val]: ((fun_up356838326on_val @ F @ X @ Y @ X) = Y)))). % fun_upd_same
thf(fact_34_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_35_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_36_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_37_fun__upd__other, axiom,
    ((![Z : produc1257910179t_char, X : produc1257910179t_char, F : produc1257910179t_char > option_val, Y : option_val]: ((~ ((Z = X))) => ((fun_up356838326on_val @ F @ X @ Y @ Z) = (F @ Z)))))). % fun_upd_other
thf(fact_38_InitBlockRed_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 @ (some_val @ v3)) @ E) => (lconf_485928294t_char @ p @ h_a @ l_a @ E)))))). % InitBlockRed.hyps(2)
thf(fact_39_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_40_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_41_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_42_fun__upd__idem__iff, axiom,
    ((![F : produc1257910179t_char > option_val, X : produc1257910179t_char, Y : option_val]: (((fun_up356838326on_val @ F @ X @ Y) = F) = ((F @ X) = Y))))). % fun_upd_idem_iff
thf(fact_43_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_44_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_45_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_46_fun__upd__twist, axiom,
    ((![A2 : produc1257910179t_char, C : produc1257910179t_char, M : produc1257910179t_char > option_val, B2 : option_val, D : option_val]: ((~ ((A2 = C))) => ((fun_up356838326on_val @ (fun_up356838326on_val @ M @ A2 @ B2) @ C @ D) = (fun_up356838326on_val @ (fun_up356838326on_val @ M @ C @ D) @ A2 @ B2)))))). % fun_upd_twist
thf(fact_47_option_Oinject, axiom,
    ((![X22 : ty, Y22 : ty]: (((some_ty @ X22) = (some_ty @ Y22)) = (X22 = Y22))))). % option.inject
thf(fact_48_option_Oinject, axiom,
    ((![X22 : val, Y22 : val]: (((some_val @ X22) = (some_val @ Y22)) = (X22 = Y22))))). % option.inject
thf(fact_49_option_Oinject, axiom,
    ((![X22 : produc266837688on_val, Y22 : produc266837688on_val]: (((some_P1299442195on_val @ X22) = (some_P1299442195on_val @ Y22)) = (X22 = Y22))))). % option.inject
thf(fact_50_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_51_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_52_map__upd__Some__unfold, axiom,
    ((![M : produc1257910179t_char > option_val, A2 : produc1257910179t_char, B2 : val, X : produc1257910179t_char, Y : val]: (((fun_up356838326on_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_53_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_54_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_55_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_56_map__upd__triv, axiom,
    ((![T2 : produc1257910179t_char > option_val, K : produc1257910179t_char, X : val]: (((T2 @ K) = (some_val @ X)) => ((fun_up356838326on_val @ T2 @ K @ (some_val @ X)) = T2))))). % map_upd_triv
thf(fact_57_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_58_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_59_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_60_map__upd__eqD1, axiom,
    ((![M : produc1257910179t_char > option_val, A2 : produc1257910179t_char, X : val, N : produc1257910179t_char > option_val, Y : val]: (((fun_up356838326on_val @ M @ A2 @ (some_val @ X)) = (fun_up356838326on_val @ N @ A2 @ (some_val @ Y))) => (X = Y))))). % map_upd_eqD1
thf(fact_61_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_62_red, axiom,
    ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ ea @ (produc52622304on_val @ ha @ (fun_up1252458416on_val @ la @ v @ (some_val @ v3)))) @ (produc2023458740on_val @ e_a @ (produc52622304on_val @ h_a @ l_a))) @ (red @ p)))). % red
thf(fact_63_lconf__upd2, axiom,
    ((![P : list_P1234162913t_char, H : nat > option2118145160on_val, L : list_char > option_val, E : list_char > option_ty, V : val, T : ty, V2 : list_char]: ((lconf_485928294t_char @ P @ H @ L @ E) => ((conf_P93989998t_char @ P @ H @ V @ T) => (lconf_485928294t_char @ P @ H @ (fun_up1252458416on_val @ L @ V2 @ (some_val @ V)) @ (fun_up9191ion_ty @ E @ V2 @ (some_ty @ T)))))))). % lconf_upd2
thf(fact_64_InitBlockRed_Oprems_I1_J, axiom,
    ((wTrt @ p @ ha @ e @ (block_list_char @ v @ t2 @ (seq_list_char @ (lAss_list_char @ v @ (val_list_char @ v3)) @ ea)) @ t))). % InitBlockRed.prems(1)
thf(fact_65_wt, axiom,
    ((wTrt @ p @ ha @ e @ (block_list_char @ v @ t2 @ (seq_list_char @ (lAss_list_char @ v @ (val_list_char @ v3)) @ ea)) @ t))). % wt
thf(fact_66_lconf__upd, axiom,
    ((![P : list_P1234162913t_char, H : nat > option2118145160on_val, L : list_char > option_val, E : list_char > option_ty, V : val, T : ty, V2 : list_char]: ((lconf_485928294t_char @ P @ H @ L @ E) => ((conf_P93989998t_char @ P @ H @ V @ T) => (((E @ V2) = (some_ty @ T)) => (lconf_485928294t_char @ P @ H @ (fun_up1252458416on_val @ L @ V2 @ (some_val @ V)) @ E))))))). % lconf_upd
thf(fact_67_lconf__def, axiom,
    ((lconf_485928294t_char = (^[P2 : list_P1234162913t_char]: (^[H2 : nat > option2118145160on_val]: (^[L2 : list_char > option_val]: (^[E2 : list_char > option_ty]: (![V3 : list_char]: (![V4 : val]: ((((L2 @ V3) = (some_val @ V4))) => ((?[T3 : ty]: ((((E2 @ V3) = (some_ty @ T3))) & ((conf_P93989998t_char @ P2 @ H2 @ V4 @ T3))))))))))))))). % lconf_def
thf(fact_68_red__reds_OInitBlockRed, axiom,
    ((![E3 : exp_list_char, H : nat > option2118145160on_val, L : list_char > option_val, V2 : list_char, V : val, E4 : exp_list_char, H3 : nat > option2118145160on_val, L3 : list_char > option_val, P : list_P1234162913t_char, V5 : val, T : ty]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E3 @ (produc52622304on_val @ H @ (fun_up1252458416on_val @ L @ V2 @ (some_val @ V)))) @ (produc2023458740on_val @ E4 @ (produc52622304on_val @ H3 @ L3))) @ (red @ P)) => (((L3 @ V2) = (some_val @ V5)) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (block_list_char @ V2 @ T @ (seq_list_char @ (lAss_list_char @ V2 @ (val_list_char @ V)) @ E3)) @ (produc52622304on_val @ H @ L)) @ (produc2023458740on_val @ (block_list_char @ V2 @ T @ (seq_list_char @ (lAss_list_char @ V2 @ (val_list_char @ V5)) @ E4)) @ (produc52622304on_val @ H3 @ (fun_up1252458416on_val @ L3 @ V2 @ (L @ V2))))) @ (red @ P))))))). % red_reds.InitBlockRed
thf(fact_69_red__reds_ORedInitBlock, axiom,
    ((![V2 : list_char, T : ty, V : val, U : val, S : produc515445032on_val, P : list_P1234162913t_char]: (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (block_list_char @ V2 @ T @ (seq_list_char @ (lAss_list_char @ V2 @ (val_list_char @ V)) @ (val_list_char @ U))) @ S) @ (produc2023458740on_val @ (val_list_char @ U) @ S)) @ (red @ P))))). % red_reds.RedInitBlock
thf(fact_70_red__reds_ORedBlock, axiom,
    ((![V2 : list_char, T : ty, U : val, S : produc515445032on_val, P : list_P1234162913t_char]: (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (block_list_char @ V2 @ T @ (val_list_char @ U)) @ S) @ (produc2023458740on_val @ (val_list_char @ U) @ S)) @ (red @ P))))). % red_reds.RedBlock
thf(fact_71_red__reds_ORedSeq, axiom,
    ((![V : val, E_2 : exp_list_char, S : produc515445032on_val, P : list_P1234162913t_char]: (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (seq_list_char @ (val_list_char @ V) @ E_2) @ S) @ (produc2023458740on_val @ E_2 @ S)) @ (red @ P))))). % red_reds.RedSeq
thf(fact_72_WTrtBlock, axiom,
    ((![P : list_P1234162913t_char, H : nat > option2118145160on_val, E : list_char > option_ty, V2 : list_char, T : ty, E3 : exp_list_char, T4 : ty]: ((wTrt @ P @ H @ (fun_up9191ion_ty @ E @ V2 @ (some_ty @ T)) @ E3 @ T4) => (wTrt @ P @ H @ E @ (block_list_char @ V2 @ T @ E3) @ T4))))). % WTrtBlock
thf(fact_73_red__reds_OLAssRed, axiom,
    ((![E3 : exp_list_char, S : produc515445032on_val, E4 : exp_list_char, S2 : produc515445032on_val, P : list_P1234162913t_char, V2 : list_char]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E3 @ S) @ (produc2023458740on_val @ E4 @ S2)) @ (red @ P)) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (lAss_list_char @ V2 @ E3) @ S) @ (produc2023458740on_val @ (lAss_list_char @ V2 @ E4) @ S2)) @ (red @ P)))))). % red_reds.LAssRed
thf(fact_74_red__reds_OSeqRed, axiom,
    ((![E3 : exp_list_char, S : produc515445032on_val, E4 : exp_list_char, S2 : produc515445032on_val, P : list_P1234162913t_char, E_2 : exp_list_char]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E3 @ S) @ (produc2023458740on_val @ E4 @ S2)) @ (red @ P)) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (seq_list_char @ E3 @ E_2) @ S) @ (produc2023458740on_val @ (seq_list_char @ E4 @ E_2) @ S2)) @ (red @ P)))))). % red_reds.SeqRed
thf(fact_75_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_76_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_77_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_78_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_79_prod_Oinject, axiom,
    ((![X1 : list_char, X22 : list_char, Y1 : list_char, Y22 : list_char]: (((produc1304532571t_char @ X1 @ X22) = (produc1304532571t_char @ Y1 @ Y22)) = (((X1 = Y1)) & ((X22 = Y22))))))). % prod.inject
thf(fact_80_old_Oprod_Oinject, axiom,
    ((![A2 : produc1097884484on_val, B2 : produc1097884484on_val, A3 : produc1097884484on_val, B3 : produc1097884484on_val]: (((produc1069526295on_val @ A2 @ B2) = (produc1069526295on_val @ A3 @ B3)) = (((A2 = A3)) & ((B2 = B3))))))). % old.prod.inject
thf(fact_81_old_Oprod_Oinject, axiom,
    ((![A2 : exp_list_char, B2 : produc515445032on_val, A3 : exp_list_char, B3 : produc515445032on_val]: (((produc2023458740on_val @ A2 @ B2) = (produc2023458740on_val @ A3 @ B3)) = (((A2 = A3)) & ((B2 = B3))))))). % old.prod.inject
thf(fact_82_old_Oprod_Oinject, axiom,
    ((![A2 : nat > option2118145160on_val, B2 : list_char > option_val, A3 : nat > option2118145160on_val, B3 : list_char > option_val]: (((produc52622304on_val @ A2 @ B2) = (produc52622304on_val @ A3 @ B3)) = (((A2 = A3)) & ((B2 = B3))))))). % old.prod.inject
thf(fact_83_old_Oprod_Oinject, axiom,
    ((![A2 : list_char, B2 : produc1257910179t_char > option_val, A3 : list_char, B3 : produc1257910179t_char > option_val]: (((produc904988266on_val @ A2 @ B2) = (produc904988266on_val @ A3 @ B3)) = (((A2 = A3)) & ((B2 = B3))))))). % old.prod.inject
thf(fact_84_old_Oprod_Oinject, axiom,
    ((![A2 : list_char, B2 : list_char, A3 : list_char, B3 : list_char]: (((produc1304532571t_char @ A2 @ B2) = (produc1304532571t_char @ A3 @ B3)) = (((A2 = A3)) & ((B2 = B3))))))). % old.prod.inject
thf(fact_85_surj__pair, axiom,
    ((![P3 : produc1172664615on_val]: (?[X3 : produc1097884484on_val, Y3 : produc1097884484on_val]: (P3 = (produc1069526295on_val @ X3 @ Y3)))))). % surj_pair
thf(fact_86_surj__pair, axiom,
    ((![P3 : produc1097884484on_val]: (?[X3 : exp_list_char, Y3 : produc515445032on_val]: (P3 = (produc2023458740on_val @ X3 @ Y3)))))). % surj_pair
thf(fact_87_surj__pair, axiom,
    ((![P3 : produc515445032on_val]: (?[X3 : nat > option2118145160on_val, Y3 : list_char > option_val]: (P3 = (produc52622304on_val @ X3 @ Y3)))))). % surj_pair
thf(fact_88_surj__pair, axiom,
    ((![P3 : produc266837688on_val]: (?[X3 : list_char, Y3 : produc1257910179t_char > option_val]: (P3 = (produc904988266on_val @ X3 @ Y3)))))). % surj_pair
thf(fact_89_surj__pair, axiom,
    ((![P3 : produc1257910179t_char]: (?[X3 : list_char, Y3 : list_char]: (P3 = (produc1304532571t_char @ X3 @ Y3)))))). % surj_pair
thf(fact_90_prod__cases, axiom,
    ((![P : produc1172664615on_val > $o, P3 : produc1172664615on_val]: ((![A4 : produc1097884484on_val, B4 : produc1097884484on_val]: (P @ (produc1069526295on_val @ A4 @ B4))) => (P @ P3))))). % prod_cases
thf(fact_91_prod__cases, axiom,
    ((![P : produc1097884484on_val > $o, P3 : produc1097884484on_val]: ((![A4 : exp_list_char, B4 : produc515445032on_val]: (P @ (produc2023458740on_val @ A4 @ B4))) => (P @ P3))))). % prod_cases
thf(fact_92_prod__cases, axiom,
    ((![P : produc515445032on_val > $o, P3 : produc515445032on_val]: ((![A4 : nat > option2118145160on_val, B4 : list_char > option_val]: (P @ (produc52622304on_val @ A4 @ B4))) => (P @ P3))))). % prod_cases
thf(fact_93_prod__cases, axiom,
    ((![P : produc266837688on_val > $o, P3 : produc266837688on_val]: ((![A4 : list_char, B4 : produc1257910179t_char > option_val]: (P @ (produc904988266on_val @ A4 @ B4))) => (P @ P3))))). % prod_cases
thf(fact_94_prod__cases, axiom,
    ((![P : produc1257910179t_char > $o, P3 : produc1257910179t_char]: ((![A4 : list_char, B4 : list_char]: (P @ (produc1304532571t_char @ A4 @ B4))) => (P @ P3))))). % prod_cases
thf(fact_95_Pair__inject, axiom,
    ((![A2 : produc1097884484on_val, B2 : produc1097884484on_val, A3 : produc1097884484on_val, B3 : produc1097884484on_val]: (((produc1069526295on_val @ A2 @ B2) = (produc1069526295on_val @ A3 @ B3)) => (~ (((A2 = A3) => (~ ((B2 = B3)))))))))). % Pair_inject
thf(fact_96_Pair__inject, axiom,
    ((![A2 : exp_list_char, B2 : produc515445032on_val, A3 : exp_list_char, B3 : produc515445032on_val]: (((produc2023458740on_val @ A2 @ B2) = (produc2023458740on_val @ A3 @ B3)) => (~ (((A2 = A3) => (~ ((B2 = B3)))))))))). % Pair_inject
thf(fact_97_Pair__inject, axiom,
    ((![A2 : nat > option2118145160on_val, B2 : list_char > option_val, A3 : nat > option2118145160on_val, B3 : list_char > option_val]: (((produc52622304on_val @ A2 @ B2) = (produc52622304on_val @ A3 @ B3)) => (~ (((A2 = A3) => (~ ((B2 = B3)))))))))). % Pair_inject
thf(fact_98_Pair__inject, axiom,
    ((![A2 : list_char, B2 : produc1257910179t_char > option_val, A3 : list_char, B3 : produc1257910179t_char > option_val]: (((produc904988266on_val @ A2 @ B2) = (produc904988266on_val @ A3 @ B3)) => (~ (((A2 = A3) => (~ ((B2 = B3)))))))))). % Pair_inject
thf(fact_99_Pair__inject, axiom,
    ((![A2 : list_char, B2 : list_char, A3 : list_char, B3 : list_char]: (((produc1304532571t_char @ A2 @ B2) = (produc1304532571t_char @ A3 @ B3)) => (~ (((A2 = A3) => (~ ((B2 = B3)))))))))). % Pair_inject
thf(fact_100_old_Oprod_Oexhaust, axiom,
    ((![Y : produc1172664615on_val]: (~ ((![A4 : produc1097884484on_val, B4 : produc1097884484on_val]: (~ ((Y = (produc1069526295on_val @ A4 @ B4)))))))))). % old.prod.exhaust
thf(fact_101_old_Oprod_Oexhaust, axiom,
    ((![Y : produc1097884484on_val]: (~ ((![A4 : exp_list_char, B4 : produc515445032on_val]: (~ ((Y = (produc2023458740on_val @ A4 @ B4)))))))))). % old.prod.exhaust
thf(fact_102_old_Oprod_Oexhaust, axiom,
    ((![Y : produc515445032on_val]: (~ ((![A4 : nat > option2118145160on_val, B4 : list_char > option_val]: (~ ((Y = (produc52622304on_val @ A4 @ B4)))))))))). % old.prod.exhaust
thf(fact_103_old_Oprod_Oexhaust, axiom,
    ((![Y : produc266837688on_val]: (~ ((![A4 : list_char, B4 : produc1257910179t_char > option_val]: (~ ((Y = (produc904988266on_val @ A4 @ B4)))))))))). % old.prod.exhaust
thf(fact_104_old_Oprod_Oexhaust, axiom,
    ((![Y : produc1257910179t_char]: (~ ((![A4 : list_char, B4 : list_char]: (~ ((Y = (produc1304532571t_char @ A4 @ B4)))))))))). % old.prod.exhaust
thf(fact_105_old_Oprod_Oinducts, axiom,
    ((![P : produc1172664615on_val > $o, Prod : produc1172664615on_val]: ((![A4 : produc1097884484on_val, B4 : produc1097884484on_val]: (P @ (produc1069526295on_val @ A4 @ B4))) => (P @ Prod))))). % old.prod.inducts
thf(fact_106_old_Oprod_Oinducts, axiom,
    ((![P : produc1097884484on_val > $o, Prod : produc1097884484on_val]: ((![A4 : exp_list_char, B4 : produc515445032on_val]: (P @ (produc2023458740on_val @ A4 @ B4))) => (P @ Prod))))). % old.prod.inducts
thf(fact_107_old_Oprod_Oinducts, axiom,
    ((![P : produc515445032on_val > $o, Prod : produc515445032on_val]: ((![A4 : nat > option2118145160on_val, B4 : list_char > option_val]: (P @ (produc52622304on_val @ A4 @ B4))) => (P @ Prod))))). % old.prod.inducts
thf(fact_108_old_Oprod_Oinducts, axiom,
    ((![P : produc266837688on_val > $o, Prod : produc266837688on_val]: ((![A4 : list_char, B4 : produc1257910179t_char > option_val]: (P @ (produc904988266on_val @ A4 @ B4))) => (P @ Prod))))). % old.prod.inducts
thf(fact_109_old_Oprod_Oinducts, axiom,
    ((![P : produc1257910179t_char > $o, Prod : produc1257910179t_char]: ((![A4 : list_char, B4 : list_char]: (P @ (produc1304532571t_char @ A4 @ B4))) => (P @ Prod))))). % old.prod.inducts
thf(fact_110_prod__cases3, axiom,
    ((![Y : produc1172664615on_val]: (~ ((![A4 : produc1097884484on_val, B4 : exp_list_char, C2 : produc515445032on_val]: (~ ((Y = (produc1069526295on_val @ A4 @ (produc2023458740on_val @ B4 @ C2))))))))))). % prod_cases3
thf(fact_111_prod__cases3, axiom,
    ((![Y : produc1097884484on_val]: (~ ((![A4 : exp_list_char, B4 : nat > option2118145160on_val, C2 : list_char > option_val]: (~ ((Y = (produc2023458740on_val @ A4 @ (produc52622304on_val @ B4 @ C2))))))))))). % prod_cases3
thf(fact_112_prod__induct3, axiom,
    ((![P : produc1172664615on_val > $o, X : produc1172664615on_val]: ((![A4 : produc1097884484on_val, B4 : exp_list_char, C2 : produc515445032on_val]: (P @ (produc1069526295on_val @ A4 @ (produc2023458740on_val @ B4 @ C2)))) => (P @ X))))). % prod_induct3
thf(fact_113_prod__induct3, axiom,
    ((![P : produc1097884484on_val > $o, X : produc1097884484on_val]: ((![A4 : exp_list_char, B4 : nat > option2118145160on_val, C2 : list_char > option_val]: (P @ (produc2023458740on_val @ A4 @ (produc52622304on_val @ B4 @ C2)))) => (P @ X))))). % prod_induct3
thf(fact_114_mem__Collect__eq, axiom,
    ((![A2 : produc1172664615on_val, P : produc1172664615on_val > $o]: ((member354538064on_val @ A2 @ (collec2055896722on_val @ P)) = (P @ A2))))). % mem_Collect_eq
thf(fact_115_Collect__mem__eq, axiom,
    ((![A5 : set_Pr1189492743on_val]: ((collec2055896722on_val @ (^[X2 : produc1172664615on_val]: (member354538064on_val @ X2 @ A5))) = A5)))). % Collect_mem_eq
thf(fact_116_WTrtSeq, axiom,
    ((![P : list_P1234162913t_char, H : nat > option2118145160on_val, E : list_char > option_ty, E_1 : exp_list_char, T_1 : ty, E_2 : exp_list_char, T_2 : ty]: ((wTrt @ P @ H @ E @ E_1 @ T_1) => ((wTrt @ P @ H @ E @ E_2 @ T_2) => (wTrt @ P @ H @ E @ (seq_list_char @ E_1 @ E_2) @ T_2)))))). % WTrtSeq
thf(fact_117_prod__cases4, axiom,
    ((![Y : produc1172664615on_val]: (~ ((![A4 : produc1097884484on_val, B4 : exp_list_char, C2 : nat > option2118145160on_val, D2 : list_char > option_val]: (~ ((Y = (produc1069526295on_val @ A4 @ (produc2023458740on_val @ B4 @ (produc52622304on_val @ C2 @ D2)))))))))))). % prod_cases4
thf(fact_118_prod__induct4, axiom,
    ((![P : produc1172664615on_val > $o, X : produc1172664615on_val]: ((![A4 : produc1097884484on_val, B4 : exp_list_char, C2 : nat > option2118145160on_val, D2 : list_char > option_val]: (P @ (produc1069526295on_val @ A4 @ (produc2023458740on_val @ B4 @ (produc52622304on_val @ C2 @ D2))))) => (P @ X))))). % prod_induct4
thf(fact_119_red__reds_ORedLAss, axiom,
    ((![V2 : list_char, V : val, H : nat > option2118145160on_val, L : list_char > option_val, P : list_P1234162913t_char]: (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (lAss_list_char @ V2 @ (val_list_char @ V)) @ (produc52622304on_val @ H @ L)) @ (produc2023458740on_val @ (val_list_char @ unit) @ (produc52622304on_val @ H @ (fun_up1252458416on_val @ L @ V2 @ (some_val @ V))))) @ (red @ P))))). % red_reds.RedLAss
thf(fact_120_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_121_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_122_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_123_exp_Oinject_I3_J, axiom,
    ((![X32 : val, Y32 : val]: (((val_list_char @ X32) = (val_list_char @ Y32)) = (X32 = Y32))))). % exp.inject(3)
thf(fact_124_red__preserves__hconf, axiom,
    ((![E3 : 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 @ E3 @ (produc52622304on_val @ H @ L)) @ (produc2023458740on_val @ E4 @ (produc52622304on_val @ H3 @ L3))) @ (red @ P)) => ((wTrt @ P @ H @ E @ E3 @ T) => ((hconf_1244167010t_char @ P @ H) => (hconf_1244167010t_char @ P @ H3))))))). % red_preserves_hconf
thf(fact_125_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_126_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_127_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_128_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)
thf(fact_129_exp_Odistinct_I127_J, axiom,
    ((![X61 : list_char, X62 : exp_list_char, X101 : list_char, X102 : ty, X103 : exp_list_char]: (~ (((lAss_list_char @ X61 @ X62) = (block_list_char @ X101 @ X102 @ X103))))))). % exp.distinct(127)
thf(fact_130_exp_Odistinct_I181_J, axiom,
    ((![X101 : list_char, X102 : ty, X103 : exp_list_char, X111 : exp_list_char, X112 : exp_list_char]: (~ (((block_list_char @ X101 @ X102 @ X103) = (seq_list_char @ X111 @ X112))))))). % exp.distinct(181)
thf(fact_131_assigned__def, axiom,
    ((assigned = (^[V3 : list_char]: (^[E5 : exp_list_char]: (?[V4 : val]: (?[E6 : exp_list_char]: (E5 = (seq_list_char @ (lAss_list_char @ V3 @ (val_list_char @ V4)) @ E6))))))))). % assigned_def
thf(fact_132_red__reds_OBlockRedSome, axiom,
    ((![E3 : exp_list_char, H : nat > option2118145160on_val, L : list_char > option_val, V2 : list_char, E4 : exp_list_char, H3 : nat > option2118145160on_val, L3 : list_char > option_val, P : list_P1234162913t_char, V : val, T : ty]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E3 @ (produc52622304on_val @ H @ (fun_up1252458416on_val @ L @ V2 @ none_val))) @ (produc2023458740on_val @ E4 @ (produc52622304on_val @ H3 @ L3))) @ (red @ P)) => (((L3 @ V2) = (some_val @ V)) => ((~ ((assigned @ V2 @ E3))) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (block_list_char @ V2 @ T @ E3) @ (produc52622304on_val @ H @ L)) @ (produc2023458740on_val @ (block_list_char @ V2 @ T @ (seq_list_char @ (lAss_list_char @ V2 @ (val_list_char @ V)) @ E4)) @ (produc52622304on_val @ H3 @ (fun_up1252458416on_val @ L3 @ V2 @ (L @ V2))))) @ (red @ P)))))))). % red_reds.BlockRedSome
thf(fact_133_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_134_redp__redsp_OInitBlockRed, axiom,
    ((![P : list_P1234162913t_char, E3 : exp_list_char, H : nat > option2118145160on_val, L : list_char > option_val, V2 : list_char, V : val, E4 : exp_list_char, H3 : nat > option2118145160on_val, L3 : list_char > option_val, V5 : val, T : ty]: ((redp @ P @ E3 @ (produc52622304on_val @ H @ (fun_up1252458416on_val @ L @ V2 @ (some_val @ V))) @ E4 @ (produc52622304on_val @ H3 @ L3)) => (((L3 @ V2) = (some_val @ V5)) => (redp @ P @ (block_list_char @ V2 @ T @ (seq_list_char @ (lAss_list_char @ V2 @ (val_list_char @ V)) @ E3)) @ (produc52622304on_val @ H @ L) @ (block_list_char @ V2 @ T @ (seq_list_char @ (lAss_list_char @ V2 @ (val_list_char @ V5)) @ E4)) @ (produc52622304on_val @ H3 @ (fun_up1252458416on_val @ L3 @ V2 @ (L @ V2))))))))). % redp_redsp.InitBlockRed
thf(fact_135_LAssRedsVal, axiom,
    ((![E3 : exp_list_char, S : produc515445032on_val, V : val, H3 : nat > option2118145160on_val, L3 : list_char > option_val, P : list_P1234162913t_char, V2 : list_char]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E3 @ S) @ (produc2023458740on_val @ (val_list_char @ V) @ (produc52622304on_val @ H3 @ L3))) @ (transi111096263on_val @ (red @ P))) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (lAss_list_char @ V2 @ E3) @ S) @ (produc2023458740on_val @ (val_list_char @ unit) @ (produc52622304on_val @ H3 @ (fun_up1252458416on_val @ L3 @ V2 @ (some_val @ V))))) @ (transi111096263on_val @ (red @ P))))))). % LAssRedsVal
thf(fact_136_not__None__eq, axiom,
    ((![X : option_ty]: ((~ ((X = none_ty))) = (?[Y2 : ty]: (X = (some_ty @ Y2))))))). % not_None_eq
thf(fact_137_not__None__eq, axiom,
    ((![X : option_val]: ((~ ((X = none_val))) = (?[Y2 : val]: (X = (some_val @ Y2))))))). % not_None_eq
thf(fact_138_not__None__eq, axiom,
    ((![X : option2118145160on_val]: ((~ ((X = none_P1535574167on_val))) = (?[Y2 : produc266837688on_val]: (X = (some_P1299442195on_val @ Y2))))))). % not_None_eq
thf(fact_139_not__Some__eq, axiom,
    ((![X : option_ty]: ((![Y2 : ty]: (~ ((X = (some_ty @ Y2))))) = (X = none_ty))))). % not_Some_eq
thf(fact_140_not__Some__eq, axiom,
    ((![X : option_val]: ((![Y2 : val]: (~ ((X = (some_val @ Y2))))) = (X = none_val))))). % not_Some_eq
thf(fact_141_not__Some__eq, axiom,
    ((![X : option2118145160on_val]: ((![Y2 : produc266837688on_val]: (~ ((X = (some_P1299442195on_val @ Y2))))) = (X = none_P1535574167on_val))))). % not_Some_eq
thf(fact_142_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_143_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_144_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_145_empty__upd__none, axiom,
    ((![X : produc1257910179t_char]: ((fun_up356838326on_val @ (^[X2 : produc1257910179t_char]: none_val) @ X @ none_val) = (^[X2 : produc1257910179t_char]: none_val))))). % empty_upd_none
thf(fact_146_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_147_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)) => ((![A4 : ty, B4 : ty]: ((X = (some_ty @ A4)) => ((Y = (some_ty @ B4)) => (P @ X @ Y)))) => (P @ X @ Y))))))). % combine_options_cases
thf(fact_148_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)) => ((![A4 : ty, B4 : val]: ((X = (some_ty @ A4)) => ((Y = (some_val @ B4)) => (P @ X @ Y)))) => (P @ X @ Y))))))). % combine_options_cases
thf(fact_149_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)) => ((![A4 : ty, B4 : produc266837688on_val]: ((X = (some_ty @ A4)) => ((Y = (some_P1299442195on_val @ B4)) => (P @ X @ Y)))) => (P @ X @ Y))))))). % combine_options_cases
thf(fact_150_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)) => ((![A4 : val, B4 : ty]: ((X = (some_val @ A4)) => ((Y = (some_ty @ B4)) => (P @ X @ Y)))) => (P @ X @ Y))))))). % combine_options_cases
thf(fact_151_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)) => ((![A4 : val, B4 : val]: ((X = (some_val @ A4)) => ((Y = (some_val @ B4)) => (P @ X @ Y)))) => (P @ X @ Y))))))). % combine_options_cases
thf(fact_152_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)) => ((![A4 : val, B4 : produc266837688on_val]: ((X = (some_val @ A4)) => ((Y = (some_P1299442195on_val @ B4)) => (P @ X @ Y)))) => (P @ X @ Y))))))). % combine_options_cases
thf(fact_153_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)) => ((![A4 : produc266837688on_val, B4 : ty]: ((X = (some_P1299442195on_val @ A4)) => ((Y = (some_ty @ B4)) => (P @ X @ Y)))) => (P @ X @ Y))))))). % combine_options_cases
thf(fact_154_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)) => ((![A4 : produc266837688on_val, B4 : val]: ((X = (some_P1299442195on_val @ A4)) => ((Y = (some_val @ B4)) => (P @ X @ Y)))) => (P @ X @ Y))))))). % combine_options_cases
thf(fact_155_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)) => ((![A4 : produc266837688on_val, B4 : produc266837688on_val]: ((X = (some_P1299442195on_val @ A4)) => ((Y = (some_P1299442195on_val @ B4)) => (P @ X @ Y)))) => (P @ X @ Y))))))). % combine_options_cases
thf(fact_156_split__option__all, axiom,
    (((^[P4 : option_ty > $o]: (![X4 : option_ty]: (P4 @ X4))) = (^[P2 : option_ty > $o]: (((P2 @ none_ty)) & ((![X2 : ty]: (P2 @ (some_ty @ X2))))))))). % split_option_all
thf(fact_157_split__option__all, axiom,
    (((^[P4 : option_val > $o]: (![X4 : option_val]: (P4 @ X4))) = (^[P2 : option_val > $o]: (((P2 @ none_val)) & ((![X2 : val]: (P2 @ (some_val @ X2))))))))). % split_option_all
thf(fact_158_split__option__all, axiom,
    (((^[P4 : option2118145160on_val > $o]: (![X4 : option2118145160on_val]: (P4 @ X4))) = (^[P2 : option2118145160on_val > $o]: (((P2 @ none_P1535574167on_val)) & ((![X2 : produc266837688on_val]: (P2 @ (some_P1299442195on_val @ X2))))))))). % split_option_all
thf(fact_159_split__option__ex, axiom,
    (((^[P4 : option_ty > $o]: (?[X4 : option_ty]: (P4 @ X4))) = (^[P2 : option_ty > $o]: (((P2 @ none_ty)) | ((?[X2 : ty]: (P2 @ (some_ty @ X2))))))))). % split_option_ex
thf(fact_160_split__option__ex, axiom,
    (((^[P4 : option_val > $o]: (?[X4 : option_val]: (P4 @ X4))) = (^[P2 : option_val > $o]: (((P2 @ none_val)) | ((?[X2 : val]: (P2 @ (some_val @ X2))))))))). % split_option_ex
thf(fact_161_split__option__ex, axiom,
    (((^[P4 : option2118145160on_val > $o]: (?[X4 : option2118145160on_val]: (P4 @ X4))) = (^[P2 : option2118145160on_val > $o]: (((P2 @ none_P1535574167on_val)) | ((?[X2 : produc266837688on_val]: (P2 @ (some_P1299442195on_val @ X2))))))))). % split_option_ex
thf(fact_162_option_Oinducts, axiom,
    ((![P : option_ty > $o, Option : option_ty]: ((P @ none_ty) => ((![X3 : ty]: (P @ (some_ty @ X3))) => (P @ Option)))))). % option.inducts
thf(fact_163_option_Oinducts, axiom,
    ((![P : option_val > $o, Option : option_val]: ((P @ none_val) => ((![X3 : val]: (P @ (some_val @ X3))) => (P @ Option)))))). % option.inducts
thf(fact_164_option_Oinducts, axiom,
    ((![P : option2118145160on_val > $o, Option : option2118145160on_val]: ((P @ none_P1535574167on_val) => ((![X3 : produc266837688on_val]: (P @ (some_P1299442195on_val @ X3))) => (P @ Option)))))). % option.inducts
thf(fact_165_option_Oexhaust, axiom,
    ((![Y : option_ty]: ((~ ((Y = none_ty))) => (~ ((![X23 : ty]: (~ ((Y = (some_ty @ X23))))))))))). % option.exhaust
thf(fact_166_option_Oexhaust, axiom,
    ((![Y : option_val]: ((~ ((Y = none_val))) => (~ ((![X23 : val]: (~ ((Y = (some_val @ X23))))))))))). % option.exhaust
thf(fact_167_option_Oexhaust, axiom,
    ((![Y : option2118145160on_val]: ((~ ((Y = none_P1535574167on_val))) => (~ ((![X23 : produc266837688on_val]: (~ ((Y = (some_P1299442195on_val @ X23))))))))))). % option.exhaust
thf(fact_168_option_OdiscI, axiom,
    ((![Option : option_ty, X22 : ty]: ((Option = (some_ty @ X22)) => (~ ((Option = none_ty))))))). % option.discI
thf(fact_169_option_OdiscI, axiom,
    ((![Option : option_val, X22 : val]: ((Option = (some_val @ X22)) => (~ ((Option = none_val))))))). % option.discI
thf(fact_170_option_OdiscI, axiom,
    ((![Option : option2118145160on_val, X22 : produc266837688on_val]: ((Option = (some_P1299442195on_val @ X22)) => (~ ((Option = none_P1535574167on_val))))))). % option.discI
thf(fact_171_option_Odistinct_I1_J, axiom,
    ((![X22 : ty]: (~ ((none_ty = (some_ty @ X22))))))). % option.distinct(1)
thf(fact_172_option_Odistinct_I1_J, axiom,
    ((![X22 : val]: (~ ((none_val = (some_val @ X22))))))). % option.distinct(1)
thf(fact_173_option_Odistinct_I1_J, axiom,
    ((![X22 : produc266837688on_val]: (~ ((none_P1535574167on_val = (some_P1299442195on_val @ X22))))))). % option.distinct(1)
thf(fact_174_redp__redsp_OLAssRed, axiom,
    ((![P : list_P1234162913t_char, E3 : exp_list_char, S : produc515445032on_val, E4 : exp_list_char, S2 : produc515445032on_val, V2 : list_char]: ((redp @ P @ E3 @ S @ E4 @ S2) => (redp @ P @ (lAss_list_char @ V2 @ E3) @ S @ (lAss_list_char @ V2 @ E4) @ S2))))). % redp_redsp.LAssRed
thf(fact_175_redp__redsp_OSeqRed, axiom,
    ((![P : list_P1234162913t_char, E3 : exp_list_char, S : produc515445032on_val, E4 : exp_list_char, S2 : produc515445032on_val, E_2 : exp_list_char]: ((redp @ P @ E3 @ S @ E4 @ S2) => (redp @ P @ (seq_list_char @ E3 @ E_2) @ S @ (seq_list_char @ E4 @ E_2) @ S2))))). % redp_redsp.SeqRed
thf(fact_176_redp__redsp_OBlockRedNone, axiom,
    ((![P : list_P1234162913t_char, E3 : exp_list_char, H : nat > option2118145160on_val, L : list_char > option_val, V2 : list_char, E4 : exp_list_char, H3 : nat > option2118145160on_val, L3 : list_char > option_val, T : ty]: ((redp @ P @ E3 @ (produc52622304on_val @ H @ (fun_up1252458416on_val @ L @ V2 @ none_val)) @ E4 @ (produc52622304on_val @ H3 @ L3)) => (((L3 @ V2) = none_val) => ((~ ((assigned @ V2 @ E3))) => (redp @ P @ (block_list_char @ V2 @ T @ E3) @ (produc52622304on_val @ H @ L) @ (block_list_char @ V2 @ T @ E4) @ (produc52622304on_val @ H3 @ (fun_up1252458416on_val @ L3 @ V2 @ (L @ V2)))))))))). % redp_redsp.BlockRedNone
thf(fact_177_redp__redsp_ORedSeq, axiom,
    ((![P : list_P1234162913t_char, V : val, E_2 : exp_list_char, S : produc515445032on_val]: (redp @ P @ (seq_list_char @ (val_list_char @ V) @ E_2) @ S @ E_2 @ S)))). % redp_redsp.RedSeq
thf(fact_178_redp__redsp_ORedBlock, axiom,
    ((![P : list_P1234162913t_char, V2 : list_char, T : ty, U : val, S : produc515445032on_val]: (redp @ P @ (block_list_char @ V2 @ T @ (val_list_char @ U)) @ S @ (val_list_char @ U) @ S)))). % redp_redsp.RedBlock
thf(fact_179_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_180_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_181_map__upd__nonempty, axiom,
    ((![T2 : produc1257910179t_char > option_val, K : produc1257910179t_char, X : val]: (~ (((fun_up356838326on_val @ T2 @ K @ (some_val @ X)) = (^[X2 : produc1257910179t_char]: none_val))))))). % map_upd_nonempty
thf(fact_182_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_183_SeqReds, axiom,
    ((![E3 : exp_list_char, S : produc515445032on_val, E4 : exp_list_char, S2 : produc515445032on_val, P : list_P1234162913t_char, E_2 : exp_list_char]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E3 @ S) @ (produc2023458740on_val @ E4 @ S2)) @ (transi111096263on_val @ (red @ P))) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (seq_list_char @ E3 @ E_2) @ S) @ (produc2023458740on_val @ (seq_list_char @ E4 @ E_2) @ S2)) @ (transi111096263on_val @ (red @ P))))))). % SeqReds
thf(fact_184_LAssReds, axiom,
    ((![E3 : exp_list_char, S : produc515445032on_val, E4 : exp_list_char, S2 : produc515445032on_val, P : list_P1234162913t_char, V2 : list_char]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E3 @ S) @ (produc2023458740on_val @ E4 @ S2)) @ (transi111096263on_val @ (red @ P))) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (lAss_list_char @ V2 @ E3) @ S) @ (produc2023458740on_val @ (lAss_list_char @ V2 @ E4) @ S2)) @ (transi111096263on_val @ (red @ P))))))). % LAssReds
thf(fact_185_redp__redsp_OBlockRedSome, axiom,
    ((![P : list_P1234162913t_char, E3 : exp_list_char, H : nat > option2118145160on_val, L : list_char > option_val, V2 : list_char, E4 : exp_list_char, H3 : nat > option2118145160on_val, L3 : list_char > option_val, V : val, T : ty]: ((redp @ P @ E3 @ (produc52622304on_val @ H @ (fun_up1252458416on_val @ L @ V2 @ none_val)) @ E4 @ (produc52622304on_val @ H3 @ L3)) => (((L3 @ V2) = (some_val @ V)) => ((~ ((assigned @ V2 @ E3))) => (redp @ P @ (block_list_char @ V2 @ T @ E3) @ (produc52622304on_val @ H @ L) @ (block_list_char @ V2 @ T @ (seq_list_char @ (lAss_list_char @ V2 @ (val_list_char @ V)) @ E4)) @ (produc52622304on_val @ H3 @ (fun_up1252458416on_val @ L3 @ V2 @ (L @ V2)))))))))). % redp_redsp.BlockRedSome
thf(fact_186_SeqReds2, axiom,
    ((![E_1 : exp_list_char, S_0 : produc515445032on_val, V_1 : val, S_1 : produc515445032on_val, P : list_P1234162913t_char, E_2 : exp_list_char, E_22 : exp_list_char, S_2 : produc515445032on_val]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E_1 @ S_0) @ (produc2023458740on_val @ (val_list_char @ V_1) @ S_1)) @ (transi111096263on_val @ (red @ P))) => ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E_2 @ S_1) @ (produc2023458740on_val @ E_22 @ S_2)) @ (transi111096263on_val @ (red @ P))) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (seq_list_char @ E_1 @ E_2) @ S_0) @ (produc2023458740on_val @ E_22 @ S_2)) @ (transi111096263on_val @ (red @ P)))))))). % SeqReds2
thf(fact_187_redp__red__eq, axiom,
    ((redp = (^[P2 : 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 @ P2)))))))))). % redp_red_eq
thf(fact_188_converse__rtrancl__induct__red, axiom,
    ((![E3 : 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 @ E3 @ (produc52622304on_val @ H @ L)) @ (produc2023458740on_val @ E4 @ (produc52622304on_val @ H3 @ L3))) @ (transi111096263on_val @ (red @ P))) => ((![E7 : exp_list_char, H4 : nat > option2118145160on_val, L4 : list_char > option_val]: (R @ E7 @ H4 @ L4 @ E7 @ H4 @ L4)) => ((![E_0 : exp_list_char, H_0 : nat > option2118145160on_val, L_0 : list_char > option_val, E_12 : exp_list_char, H_1 : nat > option2118145160on_val, L_1 : list_char > option_val, E8 : exp_list_char, H5 : nat > option2118145160on_val, L5 : list_char > option_val]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E_0 @ (produc52622304on_val @ H_0 @ L_0)) @ (produc2023458740on_val @ E_12 @ (produc52622304on_val @ H_1 @ L_1))) @ (red @ P)) => ((R @ E_12 @ H_1 @ L_1 @ E8 @ H5 @ L5) => (R @ E_0 @ H_0 @ L_0 @ E8 @ H5 @ L5)))) => (R @ E3 @ H @ L @ E4 @ H3 @ L3))))))). % converse_rtrancl_induct_red
thf(fact_189_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_190_redp__redsp_ORedInitBlock, axiom,
    ((![P : list_P1234162913t_char, V2 : list_char, T : ty, V : val, U : val, S : produc515445032on_val]: (redp @ P @ (block_list_char @ V2 @ T @ (seq_list_char @ (lAss_list_char @ V2 @ (val_list_char @ V)) @ (val_list_char @ U))) @ S @ (val_list_char @ U) @ S)))). % redp_redsp.RedInitBlock
thf(fact_191_red__reds_OBlockRedNone, axiom,
    ((![E3 : exp_list_char, H : nat > option2118145160on_val, L : list_char > option_val, V2 : 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 @ E3 @ (produc52622304on_val @ H @ (fun_up1252458416on_val @ L @ V2 @ none_val))) @ (produc2023458740on_val @ E4 @ (produc52622304on_val @ H3 @ L3))) @ (red @ P)) => (((L3 @ V2) = none_val) => ((~ ((assigned @ V2 @ E3))) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (block_list_char @ V2 @ T @ E3) @ (produc52622304on_val @ H @ L)) @ (produc2023458740on_val @ (block_list_char @ V2 @ T @ E4) @ (produc52622304on_val @ H3 @ (fun_up1252458416on_val @ L3 @ V2 @ (L @ V2))))) @ (red @ P)))))))). % red_reds.BlockRedNone
thf(fact_192_redp__redsp_ORedLAss, axiom,
    ((![P : list_P1234162913t_char, V2 : list_char, V : val, H : nat > option2118145160on_val, L : list_char > option_val]: (redp @ P @ (lAss_list_char @ V2 @ (val_list_char @ V)) @ (produc52622304on_val @ H @ L) @ (val_list_char @ unit) @ (produc52622304on_val @ H @ (fun_up1252458416on_val @ L @ V2 @ (some_val @ V))))))). % redp_redsp.RedLAss
thf(fact_193_InitBlockRedsFinal, axiom,
    ((![E3 : exp_list_char, H : nat > option2118145160on_val, L : list_char > option_val, V2 : list_char, V : val, 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 @ E3 @ (produc52622304on_val @ H @ (fun_up1252458416on_val @ L @ V2 @ (some_val @ V)))) @ (produc2023458740on_val @ E4 @ (produc52622304on_val @ H3 @ L3))) @ (transi111096263on_val @ (red @ P))) => ((final_list_char @ E4) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (block_list_char @ V2 @ T @ (seq_list_char @ (lAss_list_char @ V2 @ (val_list_char @ V)) @ E3)) @ (produc52622304on_val @ H @ L)) @ (produc2023458740on_val @ E4 @ (produc52622304on_val @ H3 @ (fun_up1252458416on_val @ L3 @ V2 @ (L @ V2))))) @ (transi111096263on_val @ (red @ P)))))))). % InitBlockRedsFinal
thf(fact_194_InitBlockReds__aux, axiom,
    ((![E3 : exp_list_char, S : produc515445032on_val, E4 : exp_list_char, S2 : produc515445032on_val, P : list_P1234162913t_char, V2 : list_char, T : ty]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E3 @ S) @ (produc2023458740on_val @ E4 @ S2)) @ (transi111096263on_val @ (red @ P))) => (![H6 : nat > option2118145160on_val, L6 : list_char > option_val, H7 : nat > option2118145160on_val, L7 : list_char > option_val, V6 : val]: ((S = (produc52622304on_val @ H6 @ (fun_up1252458416on_val @ L6 @ V2 @ (some_val @ V6)))) => ((S2 = (produc52622304on_val @ H7 @ L7)) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (block_list_char @ V2 @ T @ (seq_list_char @ (lAss_list_char @ V2 @ (val_list_char @ V6)) @ E3)) @ (produc52622304on_val @ H6 @ L6)) @ (produc2023458740on_val @ (block_list_char @ V2 @ T @ (seq_list_char @ (lAss_list_char @ V2 @ (val_list_char @ (the_val @ (L7 @ V2)))) @ E4)) @ (produc52622304on_val @ H7 @ (fun_up1252458416on_val @ L7 @ V2 @ (L6 @ V2))))) @ (transi111096263on_val @ (red @ P)))))))))). % InitBlockReds_aux
thf(fact_195_InitBlockReds, axiom,
    ((![E3 : exp_list_char, H : nat > option2118145160on_val, L : list_char > option_val, V2 : list_char, V : val, 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 @ E3 @ (produc52622304on_val @ H @ (fun_up1252458416on_val @ L @ V2 @ (some_val @ V)))) @ (produc2023458740on_val @ E4 @ (produc52622304on_val @ H3 @ L3))) @ (transi111096263on_val @ (red @ P))) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (block_list_char @ V2 @ T @ (seq_list_char @ (lAss_list_char @ V2 @ (val_list_char @ V)) @ E3)) @ (produc52622304on_val @ H @ L)) @ (produc2023458740on_val @ (block_list_char @ V2 @ T @ (seq_list_char @ (lAss_list_char @ V2 @ (val_list_char @ (the_val @ (L3 @ V2)))) @ E4)) @ (produc52622304on_val @ H3 @ (fun_up1252458416on_val @ L3 @ V2 @ (L @ V2))))) @ (transi111096263on_val @ (red @ P))))))). % InitBlockReds
thf(fact_196_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_02 : list_char > option_val, V2 : 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_02 @ V2 @ none_val))) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (block_list_char @ V2 @ T @ E_02) @ (produc52622304on_val @ H_02 @ L_02)) @ (produc2023458740on_val @ E_2 @ (produc52622304on_val @ H_2 @ (fun_up1252458416on_val @ L_2 @ V2 @ (L_02 @ V2))))) @ (transi111096263on_val @ (red @ P))))))))). % BlockRedsFinal
thf(fact_197_option_Ocollapse, axiom,
    ((![Option : option_ty]: ((~ ((Option = none_ty))) => ((some_ty @ (the_ty @ Option)) = Option))))). % option.collapse
thf(fact_198_option_Ocollapse, axiom,
    ((![Option : option_val]: ((~ ((Option = none_val))) => ((some_val @ (the_val @ Option)) = Option))))). % option.collapse
thf(fact_199_option_Ocollapse, axiom,
    ((![Option : option2118145160on_val]: ((~ ((Option = none_P1535574167on_val))) => ((some_P1299442195on_val @ (the_Pr901949220on_val @ Option)) = Option))))). % option.collapse
thf(fact_200_option_Oexpand, axiom,
    ((![Option : option_val, Option2 : option_val]: (((Option = none_val) = (Option2 = none_val)) => (((~ ((Option = none_val))) => ((~ ((Option2 = none_val))) => ((the_val @ Option) = (the_val @ Option2)))) => (Option = Option2)))))). % option.expand
thf(fact_201_option_Osel, axiom,
    ((![X22 : ty]: ((the_ty @ (some_ty @ X22)) = X22)))). % option.sel
thf(fact_202_option_Osel, axiom,
    ((![X22 : val]: ((the_val @ (some_val @ X22)) = X22)))). % option.sel
thf(fact_203_option_Osel, axiom,
    ((![X22 : produc266837688on_val]: ((the_Pr901949220on_val @ (some_P1299442195on_val @ X22)) = X22)))). % option.sel
thf(fact_204_option_Oexhaust__sel, axiom,
    ((![Option : option_ty]: ((~ ((Option = none_ty))) => (Option = (some_ty @ (the_ty @ Option))))))). % option.exhaust_sel
thf(fact_205_option_Oexhaust__sel, axiom,
    ((![Option : option_val]: ((~ ((Option = none_val))) => (Option = (some_val @ (the_val @ Option))))))). % option.exhaust_sel
thf(fact_206_option_Oexhaust__sel, axiom,
    ((![Option : option2118145160on_val]: ((~ ((Option = none_P1535574167on_val))) => (Option = (some_P1299442195on_val @ (the_Pr901949220on_val @ Option))))))). % option.exhaust_sel
thf(fact_207_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_208_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) => ((![A4 : produc1097884484on_val, B4 : produc1097884484on_val, Aa2 : produc1097884484on_val, Ba : produc1097884484on_val]: ((member208988944on_val @ (produc564964183on_val @ (produc1069526295on_val @ A4 @ B4) @ (produc1069526295on_val @ Aa2 @ Ba)) @ R2) => ((member208988944on_val @ (produc564964183on_val @ (produc1069526295on_val @ Aa2 @ Ba) @ (produc1069526295on_val @ Bx @ By)) @ (transi100378922on_val @ R2)) => ((P @ Aa2 @ Ba) => (P @ A4 @ B4))))) => (P @ Ax @ Ay))))))). % converse_rtrancl_induct2
thf(fact_209_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) => ((![A4 : nat > option2118145160on_val, B4 : list_char > option_val, Aa2 : nat > option2118145160on_val, Ba : list_char > option_val]: ((member2027247312on_val @ (produc2106877847on_val @ (produc52622304on_val @ A4 @ B4) @ (produc52622304on_val @ Aa2 @ Ba)) @ R2) => ((member2027247312on_val @ (produc2106877847on_val @ (produc52622304on_val @ Aa2 @ Ba) @ (produc52622304on_val @ Bx @ By)) @ (transi432893227on_val @ R2)) => ((P @ Aa2 @ Ba) => (P @ A4 @ B4))))) => (P @ Ax @ Ay))))))). % converse_rtrancl_induct2
thf(fact_210_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) => ((![A4 : list_char, B4 : produc1257910179t_char > option_val, Aa2 : list_char, Ba : produc1257910179t_char > option_val]: ((member197592058on_val @ (produc881885833on_val @ (produc904988266on_val @ A4 @ B4) @ (produc904988266on_val @ Aa2 @ Ba)) @ R2) => ((member197592058on_val @ (produc881885833on_val @ (produc904988266on_val @ Aa2 @ Ba) @ (produc904988266on_val @ Bx @ By)) @ (transi2071064181on_val @ R2)) => ((P @ Aa2 @ Ba) => (P @ A4 @ B4))))) => (P @ Ax @ Ay))))))). % converse_rtrancl_induct2
thf(fact_211_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) => ((![A4 : list_char, B4 : list_char, Aa2 : list_char, Ba : list_char]: ((member803902992t_char @ (produc395356247t_char @ (produc1304532571t_char @ A4 @ B4) @ (produc1304532571t_char @ Aa2 @ Ba)) @ R2) => ((member803902992t_char @ (produc395356247t_char @ (produc1304532571t_char @ Aa2 @ Ba) @ (produc1304532571t_char @ Bx @ By)) @ (transi858104614t_char @ R2)) => ((P @ Aa2 @ Ba) => (P @ A4 @ B4))))) => (P @ Ax @ Ay))))))). % converse_rtrancl_induct2
thf(fact_212_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) => ((![A4 : exp_list_char, B4 : produc515445032on_val, Aa2 : exp_list_char, Ba : produc515445032on_val]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ A4 @ B4) @ (produc2023458740on_val @ Aa2 @ Ba)) @ R2) => ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ Aa2 @ Ba) @ (produc2023458740on_val @ Bx @ By)) @ (transi111096263on_val @ R2)) => ((P @ Aa2 @ Ba) => (P @ A4 @ B4))))) => (P @ Ax @ Ay))))))). % converse_rtrancl_induct2
thf(fact_213_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)))) => (~ ((![A4 : produc1097884484on_val, B4 : produc1097884484on_val]: ((member208988944on_val @ (produc564964183on_val @ (produc1069526295on_val @ Xa @ Xb) @ (produc1069526295on_val @ A4 @ B4)) @ R2) => (~ ((member208988944on_val @ (produc564964183on_val @ (produc1069526295on_val @ A4 @ B4) @ (produc1069526295on_val @ Za @ Zb)) @ (transi100378922on_val @ R2))))))))))))). % converse_rtranclE2
thf(fact_214_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)))) => (~ ((![A4 : nat > option2118145160on_val, B4 : list_char > option_val]: ((member2027247312on_val @ (produc2106877847on_val @ (produc52622304on_val @ Xa @ Xb) @ (produc52622304on_val @ A4 @ B4)) @ R2) => (~ ((member2027247312on_val @ (produc2106877847on_val @ (produc52622304on_val @ A4 @ B4) @ (produc52622304on_val @ Za @ Zb)) @ (transi432893227on_val @ R2))))))))))))). % converse_rtranclE2
thf(fact_215_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)))) => (~ ((![A4 : list_char, B4 : produc1257910179t_char > option_val]: ((member197592058on_val @ (produc881885833on_val @ (produc904988266on_val @ Xa @ Xb) @ (produc904988266on_val @ A4 @ B4)) @ R2) => (~ ((member197592058on_val @ (produc881885833on_val @ (produc904988266on_val @ A4 @ B4) @ (produc904988266on_val @ Za @ Zb)) @ (transi2071064181on_val @ R2))))))))))))). % converse_rtranclE2
thf(fact_216_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)))) => (~ ((![A4 : list_char, B4 : list_char]: ((member803902992t_char @ (produc395356247t_char @ (produc1304532571t_char @ Xa @ Xb) @ (produc1304532571t_char @ A4 @ B4)) @ R2) => (~ ((member803902992t_char @ (produc395356247t_char @ (produc1304532571t_char @ A4 @ B4) @ (produc1304532571t_char @ Za @ Zb)) @ (transi858104614t_char @ R2))))))))))))). % converse_rtranclE2
thf(fact_217_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)))) => (~ ((![A4 : exp_list_char, B4 : produc515445032on_val]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ Xa @ Xb) @ (produc2023458740on_val @ A4 @ B4)) @ R2) => (~ ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ A4 @ B4) @ (produc2023458740on_val @ Za @ Zb)) @ (transi111096263on_val @ R2))))))))))))). % converse_rtranclE2
thf(fact_218_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) => ((![A4 : produc1097884484on_val, B4 : produc1097884484on_val, Aa2 : produc1097884484on_val, Ba : produc1097884484on_val]: ((member208988944on_val @ (produc564964183on_val @ (produc1069526295on_val @ Ax @ Ay) @ (produc1069526295on_val @ A4 @ B4)) @ (transi100378922on_val @ R2)) => ((member208988944on_val @ (produc564964183on_val @ (produc1069526295on_val @ A4 @ B4) @ (produc1069526295on_val @ Aa2 @ Ba)) @ R2) => ((P @ A4 @ B4) => (P @ Aa2 @ Ba))))) => (P @ Bx @ By))))))). % rtrancl_induct2
thf(fact_219_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) => ((![A4 : nat > option2118145160on_val, B4 : list_char > option_val, Aa2 : nat > option2118145160on_val, Ba : list_char > option_val]: ((member2027247312on_val @ (produc2106877847on_val @ (produc52622304on_val @ Ax @ Ay) @ (produc52622304on_val @ A4 @ B4)) @ (transi432893227on_val @ R2)) => ((member2027247312on_val @ (produc2106877847on_val @ (produc52622304on_val @ A4 @ B4) @ (produc52622304on_val @ Aa2 @ Ba)) @ R2) => ((P @ A4 @ B4) => (P @ Aa2 @ Ba))))) => (P @ Bx @ By))))))). % rtrancl_induct2
thf(fact_220_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) => ((![A4 : list_char, B4 : produc1257910179t_char > option_val, Aa2 : list_char, Ba : produc1257910179t_char > option_val]: ((member197592058on_val @ (produc881885833on_val @ (produc904988266on_val @ Ax @ Ay) @ (produc904988266on_val @ A4 @ B4)) @ (transi2071064181on_val @ R2)) => ((member197592058on_val @ (produc881885833on_val @ (produc904988266on_val @ A4 @ B4) @ (produc904988266on_val @ Aa2 @ Ba)) @ R2) => ((P @ A4 @ B4) => (P @ Aa2 @ Ba))))) => (P @ Bx @ By))))))). % rtrancl_induct2
thf(fact_221_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) => ((![A4 : list_char, B4 : list_char, Aa2 : list_char, Ba : list_char]: ((member803902992t_char @ (produc395356247t_char @ (produc1304532571t_char @ Ax @ Ay) @ (produc1304532571t_char @ A4 @ B4)) @ (transi858104614t_char @ R2)) => ((member803902992t_char @ (produc395356247t_char @ (produc1304532571t_char @ A4 @ B4) @ (produc1304532571t_char @ Aa2 @ Ba)) @ R2) => ((P @ A4 @ B4) => (P @ Aa2 @ Ba))))) => (P @ Bx @ By))))))). % rtrancl_induct2
thf(fact_222_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) => ((![A4 : exp_list_char, B4 : produc515445032on_val, Aa2 : exp_list_char, Ba : produc515445032on_val]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ Ax @ Ay) @ (produc2023458740on_val @ A4 @ B4)) @ (transi111096263on_val @ R2)) => ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ A4 @ B4) @ (produc2023458740on_val @ Aa2 @ Ba)) @ R2) => ((P @ A4 @ B4) => (P @ Aa2 @ Ba))))) => (P @ Bx @ By))))))). % rtrancl_induct2
thf(fact_223_rtrancl__idemp, axiom,
    ((![R2 : set_Pr1189492743on_val]: ((transi111096263on_val @ (transi111096263on_val @ R2)) = (transi111096263on_val @ R2))))). % rtrancl_idemp
thf(fact_224_r__into__rtrancl, axiom,
    ((![P3 : produc1172664615on_val, R2 : set_Pr1189492743on_val]: ((member354538064on_val @ P3 @ R2) => (member354538064on_val @ P3 @ (transi111096263on_val @ R2)))))). % r_into_rtrancl
thf(fact_225_converse__rtrancl__into__rtrancl, axiom,
    ((![A2 : list_char, B2 : list_char, R2 : set_Pr164112643t_char, C : list_char]: ((member89690956t_char @ (produc1304532571t_char @ A2 @ B2) @ R2) => ((member89690956t_char @ (produc1304532571t_char @ B2 @ C) @ (transi1879726366t_char @ R2)) => (member89690956t_char @ (produc1304532571t_char @ A2 @ C) @ (transi1879726366t_char @ R2))))))). % converse_rtrancl_into_rtrancl
thf(fact_226_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_227_rtrancl_Ortrancl__into__rtrancl, axiom,
    ((![A2 : list_char, B2 : list_char, R2 : set_Pr164112643t_char, C : list_char]: ((member89690956t_char @ (produc1304532571t_char @ A2 @ B2) @ (transi1879726366t_char @ R2)) => ((member89690956t_char @ (produc1304532571t_char @ B2 @ C) @ R2) => (member89690956t_char @ (produc1304532571t_char @ A2 @ C) @ (transi1879726366t_char @ R2))))))). % rtrancl.rtrancl_into_rtrancl
thf(fact_228_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_229_converse__rtrancl__induct, axiom,
    ((![A2 : list_char, B2 : list_char, R2 : set_Pr164112643t_char, P : list_char > $o]: ((member89690956t_char @ (produc1304532571t_char @ A2 @ B2) @ (transi1879726366t_char @ R2)) => ((P @ B2) => ((![Y3 : list_char, Z3 : list_char]: ((member89690956t_char @ (produc1304532571t_char @ Y3 @ Z3) @ R2) => ((member89690956t_char @ (produc1304532571t_char @ Z3 @ B2) @ (transi1879726366t_char @ R2)) => ((P @ Z3) => (P @ Y3))))) => (P @ A2))))))). % converse_rtrancl_induct
thf(fact_230_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_231_rtrancl_Ortrancl__refl, axiom,
    ((![A2 : list_char, R2 : set_Pr164112643t_char]: (member89690956t_char @ (produc1304532571t_char @ A2 @ A2) @ (transi1879726366t_char @ R2))))). % rtrancl.rtrancl_refl
thf(fact_232_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_233_converse__rtranclE, axiom,
    ((![X : list_char, Z : list_char, R2 : set_Pr164112643t_char]: ((member89690956t_char @ (produc1304532571t_char @ X @ Z) @ (transi1879726366t_char @ R2)) => ((~ ((X = Z))) => (~ ((![Y3 : list_char]: ((member89690956t_char @ (produc1304532571t_char @ X @ Y3) @ R2) => (~ ((member89690956t_char @ (produc1304532571t_char @ Y3 @ Z) @ (transi1879726366t_char @ R2))))))))))))). % converse_rtranclE
thf(fact_234_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_235_rtrancl_Oinducts, axiom,
    ((![X1 : list_char, X22 : list_char, R2 : set_Pr164112643t_char, P : list_char > list_char > $o]: ((member89690956t_char @ (produc1304532571t_char @ X1 @ X22) @ (transi1879726366t_char @ R2)) => ((![A4 : list_char]: (P @ A4 @ A4)) => ((![A4 : list_char, B4 : list_char, C2 : list_char]: ((member89690956t_char @ (produc1304532571t_char @ A4 @ B4) @ (transi1879726366t_char @ R2)) => ((P @ A4 @ B4) => ((member89690956t_char @ (produc1304532571t_char @ B4 @ C2) @ R2) => (P @ A4 @ C2))))) => (P @ X1 @ X22))))))). % rtrancl.inducts
thf(fact_236_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)) => ((![A4 : produc1097884484on_val]: (P @ A4 @ A4)) => ((![A4 : produc1097884484on_val, B4 : produc1097884484on_val, C2 : produc1097884484on_val]: ((member354538064on_val @ (produc1069526295on_val @ A4 @ B4) @ (transi111096263on_val @ R2)) => ((P @ A4 @ B4) => ((member354538064on_val @ (produc1069526295on_val @ B4 @ C2) @ R2) => (P @ A4 @ C2))))) => (P @ X1 @ X22))))))). % rtrancl.inducts
thf(fact_237_rtrancl__induct, axiom,
    ((![A2 : list_char, B2 : list_char, R2 : set_Pr164112643t_char, P : list_char > $o]: ((member89690956t_char @ (produc1304532571t_char @ A2 @ B2) @ (transi1879726366t_char @ R2)) => ((P @ A2) => ((![Y3 : list_char, Z3 : list_char]: ((member89690956t_char @ (produc1304532571t_char @ A2 @ Y3) @ (transi1879726366t_char @ R2)) => ((member89690956t_char @ (produc1304532571t_char @ Y3 @ Z3) @ R2) => ((P @ Y3) => (P @ Z3))))) => (P @ B2))))))). % rtrancl_induct
thf(fact_238_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_239_rtrancl__trans, axiom,
    ((![X : list_char, Y : list_char, R2 : set_Pr164112643t_char, Z : list_char]: ((member89690956t_char @ (produc1304532571t_char @ X @ Y) @ (transi1879726366t_char @ R2)) => ((member89690956t_char @ (produc1304532571t_char @ Y @ Z) @ (transi1879726366t_char @ R2)) => (member89690956t_char @ (produc1304532571t_char @ X @ Z) @ (transi1879726366t_char @ R2))))))). % rtrancl_trans
thf(fact_240_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_241_rtrancl_Osimps, axiom,
    ((![A1 : list_char, A22 : list_char, R2 : set_Pr164112643t_char]: ((member89690956t_char @ (produc1304532571t_char @ A1 @ A22) @ (transi1879726366t_char @ R2)) = (((?[A : list_char]: (((A1 = A)) & ((A22 = A))))) | ((?[A : list_char]: (?[B : list_char]: (?[C4 : list_char]: (((A1 = A)) & ((((A22 = C4)) & ((((member89690956t_char @ (produc1304532571t_char @ A @ B) @ (transi1879726366t_char @ R2))) & ((member89690956t_char @ (produc1304532571t_char @ B @ C4) @ R2)))))))))))))))). % rtrancl.simps
thf(fact_242_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]: (?[C4 : produc1097884484on_val]: (((A1 = A)) & ((((A22 = C4)) & ((((member354538064on_val @ (produc1069526295on_val @ A @ B) @ (transi111096263on_val @ R2))) & ((member354538064on_val @ (produc1069526295on_val @ B @ C4) @ R2)))))))))))))))). % rtrancl.simps
thf(fact_243_Red__lcl__add, axiom,
    ((![E3 : 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_02 : list_char > option_val]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E3 @ (produc52622304on_val @ H @ L)) @ (produc2023458740on_val @ E4 @ (produc52622304on_val @ H3 @ L3))) @ (transi111096263on_val @ (red @ P))) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E3 @ (produc52622304on_val @ H @ (map_ad1615113112ar_val @ L_02 @ L))) @ (produc2023458740on_val @ E4 @ (produc52622304on_val @ H3 @ (map_ad1615113112ar_val @ L_02 @ L3)))) @ (transi111096263on_val @ (red @ P))))))). % Red_lcl_add
thf(fact_244_red__lcl__add, axiom,
    ((![E3 : 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_02 : list_char > option_val]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E3 @ (produc52622304on_val @ H @ L)) @ (produc2023458740on_val @ E4 @ (produc52622304on_val @ H3 @ L3))) @ (red @ P)) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E3 @ (produc52622304on_val @ H @ (map_ad1615113112ar_val @ L_02 @ L))) @ (produc2023458740on_val @ E4 @ (produc52622304on_val @ H3 @ (map_ad1615113112ar_val @ L_02 @ L3)))) @ (red @ P)))))). % red_lcl_add
thf(fact_245_FAssRedsVal, axiom,
    ((![E_1 : exp_list_char, S_0 : produc515445032on_val, A2 : nat, S_1 : produc515445032on_val, P : list_P1234162913t_char, E_2 : exp_list_char, V : val, H_2 : nat > option2118145160on_val, L_2 : list_char > option_val, C3 : list_char, Fs : produc1257910179t_char > option_val, F3 : list_char, D3 : list_char]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E_1 @ S_0) @ (produc2023458740on_val @ (val_list_char @ (addr @ A2)) @ S_1)) @ (transi111096263on_val @ (red @ P))) => ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E_2 @ S_1) @ (produc2023458740on_val @ (val_list_char @ V) @ (produc52622304on_val @ H_2 @ L_2))) @ (transi111096263on_val @ (red @ P))) => (((some_P1299442195on_val @ (produc904988266on_val @ C3 @ Fs)) = (H_2 @ A2)) => (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 @ A2 @ (some_P1299442195on_val @ (produc904988266on_val @ C3 @ (fun_up356838326on_val @ Fs @ (produc1304532571t_char @ F3 @ D3) @ (some_val @ V))))) @ L_2))) @ (transi111096263on_val @ (red @ P))))))))). % FAssRedsVal
thf(fact_246_red__reds_ORedFAss, axiom,
    ((![H : nat > option2118145160on_val, A2 : nat, C3 : list_char, Fs : produc1257910179t_char > option_val, F3 : list_char, D3 : list_char, V : val, L : list_char > option_val, P : list_P1234162913t_char]: (((H @ A2) = (some_P1299442195on_val @ (produc904988266on_val @ C3 @ Fs))) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (fAss_list_char @ (val_list_char @ (addr @ A2)) @ F3 @ D3 @ (val_list_char @ V)) @ (produc52622304on_val @ H @ L)) @ (produc2023458740on_val @ (val_list_char @ unit) @ (produc52622304on_val @ (fun_up262443479on_val @ H @ A2 @ (some_P1299442195on_val @ (produc904988266on_val @ C3 @ (fun_up356838326on_val @ Fs @ (produc1304532571t_char @ F3 @ D3) @ (some_val @ V))))) @ L))) @ (red @ P)))))). % red_reds.RedFAss
thf(fact_247_redp__redsp_OFAssRed2, axiom,
    ((![P : list_P1234162913t_char, E3 : exp_list_char, S : produc515445032on_val, E4 : exp_list_char, S2 : produc515445032on_val, V : val, F3 : list_char, D3 : list_char]: ((redp @ P @ E3 @ S @ E4 @ S2) => (redp @ P @ (fAss_list_char @ (val_list_char @ V) @ F3 @ D3 @ E3) @ S @ (fAss_list_char @ (val_list_char @ V) @ F3 @ D3 @ E4) @ S2))))). % redp_redsp.FAssRed2

% 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))).
