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% This file was generated by Isabelle (most likely Sledgehammer)
% 2020-12-16 14:22:13.192

% Could-be-implicit typings (16)
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% Explicit typings (59)
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    ea : exp_list_char).
thf(sy_v_h_Ha____, type,
    h_a : nat > option2118145160on_val).
thf(sy_v_ha____, type,
    ha : nat > option2118145160on_val).
thf(sy_v_l_Ha____, type,
    l_a : list_char > option_val).
thf(sy_v_la____, type,
    la : list_char > option_val).
thf(sy_v_v_H____, type,
    v2 : val).
thf(sy_v_v____, type,
    v3 : val).

% Relevant facts (210)
thf(fact_0_v_H, axiom,
    (((l_a @ v) = (some_val @ v2)))). % v'
thf(fact_1_T1subT, axiom,
    ((widen_917054840t_char @ p @ t_1 @ t2))). % T1subT
thf(fact_2__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_3_option_Oinject, axiom,
    ((![X2 : ty, Y2 : ty]: (((some_ty @ X2) = (some_ty @ Y2)) = (X2 = Y2))))). % option.inject
thf(fact_4_option_Oinject, axiom,
    ((![X2 : val, Y2 : val]: (((some_val @ X2) = (some_val @ Y2)) = (X2 = Y2))))). % option.inject
thf(fact_5_option_Oinject, axiom,
    ((![X2 : produc266837688on_val, Y2 : produc266837688on_val]: (((some_P1299442195on_val @ X2) = (some_P1299442195on_val @ Y2)) = (X2 = Y2))))). % option.inject
thf(fact_6_local_Owf, axiom,
    ((wf_pro1229751607t_char @ wf_J_mdecl @ p))). % local.wf
thf(fact_7_widen__trans, axiom,
    ((![P : list_P1234162913t_char, S : ty, U : ty, T : ty]: ((widen_917054840t_char @ P @ S @ U) => ((widen_917054840t_char @ P @ U @ T) => (widen_917054840t_char @ P @ S @ T)))))). % widen_trans
thf(fact_8_widen__refl, axiom,
    ((![P : list_P1234162913t_char, T : ty]: (widen_917054840t_char @ P @ T @ T)))). % widen_refl
thf(fact_9_conf__def, axiom,
    ((conf_P93989998t_char = (^[P2 : list_P1234162913t_char]: (^[H : nat > option2118145160on_val]: (^[V : val]: (^[T2 : ty]: (?[T3 : ty]: ((((typeof_h @ H @ V) = (some_ty @ T3))) & ((widen_917054840t_char @ P2 @ T3 @ T2))))))))))). % conf_def
thf(fact_10_wt_092_060_094sub_0621, axiom,
    (((typeof_h @ ha @ v3) = (some_ty @ t_1)))). % wt\<^sub>1
thf(fact_11_hext__typeof__mono, axiom,
    ((![H2 : nat > option2118145160on_val, H3 : nat > option2118145160on_val, V2 : val, T : ty]: ((hext @ H2 @ H3) => (((typeof_h @ H2 @ V2) = (some_ty @ T)) => ((typeof_h @ H3 @ V2) = (some_ty @ T))))))). % hext_typeof_mono
thf(fact_12_typeof__conf, axiom,
    ((![H2 : nat > option2118145160on_val, V2 : val, T : ty, P : list_P1234162913t_char]: (((typeof_h @ H2 @ V2) = (some_ty @ T)) => (conf_P93989998t_char @ P @ H2 @ V2 @ T))))). % typeof_conf
thf(fact_13_wt_092_060_094sub_0622, axiom,
    ((wTrt2 @ p @ ha @ (fun_up9191ion_ty @ e @ v @ (some_ty @ t2)) @ ea @ t))). % wt\<^sub>2
thf(fact_14__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062T_092_060_094sub_0621_O_A_092_060lbrakk_062typeof_092_060_094bsub_062h_092_060_094esub_062_Av_A_061_A_092_060lfloor_062T_092_060_094sub_0621_092_060rfloor_062_059_AP_A_092_060turnstile_062_AT_092_060_094sub_0621_A_092_060le_062_AT_059_AP_ME_IV_A_092_060mapsto_062_AT_J_Mh_A_092_060turnstile_062_Ae_A_058_AT_H_092_060rbrakk_062_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062, axiom,
    ((~ ((![T_1 : ty]: (((typeof_h @ ha @ v3) = (some_ty @ T_1)) => ((widen_917054840t_char @ p @ T_1 @ t2) => (~ ((wTrt2 @ p @ ha @ (fun_up9191ion_ty @ e @ v @ (some_ty @ t2)) @ ea @ t)))))))))). % \<open>\<And>thesis. (\<And>T\<^sub>1. \<lbrakk>typeof\<^bsub>h\<^esub> v = \<lfloor>T\<^sub>1\<rfloor>; P \<turnstile> T\<^sub>1 \<le> T; P,E(V \<mapsto> T),h \<turnstile> e : T'\<rbrakk> \<Longrightarrow> thesis) \<Longrightarrow> thesis\<close>
thf(fact_15_map__upd__eqD1, axiom,
    ((![M : list_char > option_ty, A : list_char, X : ty, N : list_char > option_ty, Y : ty]: (((fun_up9191ion_ty @ M @ A @ (some_ty @ X)) = (fun_up9191ion_ty @ N @ A @ (some_ty @ Y))) => (X = Y))))). % map_upd_eqD1
thf(fact_16_map__upd__eqD1, axiom,
    ((![M : list_char > option_val, A : list_char, X : val, N : list_char > option_val, Y : val]: (((fun_up1252458416on_val @ M @ A @ (some_val @ X)) = (fun_up1252458416on_val @ N @ A @ (some_val @ Y))) => (X = Y))))). % map_upd_eqD1
thf(fact_17_map__upd__eqD1, axiom,
    ((![M : nat > option2118145160on_val, A : nat, X : produc266837688on_val, N : nat > option2118145160on_val, Y : produc266837688on_val]: (((fun_up262443479on_val @ M @ A @ (some_P1299442195on_val @ X)) = (fun_up262443479on_val @ N @ A @ (some_P1299442195on_val @ Y))) => (X = Y))))). % map_upd_eqD1
thf(fact_18_map__upd__triv, axiom,
    ((![T4 : list_char > option_ty, K : list_char, X : ty]: (((T4 @ K) = (some_ty @ X)) => ((fun_up9191ion_ty @ T4 @ K @ (some_ty @ X)) = T4))))). % map_upd_triv
thf(fact_19_map__upd__triv, axiom,
    ((![T4 : list_char > option_val, K : list_char, X : val]: (((T4 @ K) = (some_val @ X)) => ((fun_up1252458416on_val @ T4 @ K @ (some_val @ X)) = T4))))). % map_upd_triv
thf(fact_20_map__upd__triv, axiom,
    ((![T4 : nat > option2118145160on_val, K : nat, X : produc266837688on_val]: (((T4 @ K) = (some_P1299442195on_val @ X)) => ((fun_up262443479on_val @ T4 @ K @ (some_P1299442195on_val @ X)) = T4))))). % map_upd_triv
thf(fact_21_hext__refl, axiom,
    ((![H2 : nat > option2118145160on_val]: (hext @ H2 @ H2)))). % hext_refl
thf(fact_22_conf__hext, axiom,
    ((![H2 : nat > option2118145160on_val, H3 : nat > option2118145160on_val, P : list_P1234162913t_char, V2 : val, T : ty]: ((hext @ H2 @ H3) => ((conf_P93989998t_char @ P @ H2 @ V2 @ T) => (conf_P93989998t_char @ P @ H3 @ V2 @ T)))))). % conf_hext
thf(fact_23_lconf__upd, axiom,
    ((![P : list_P1234162913t_char, H2 : nat > option2118145160on_val, L : list_char > option_val, E : list_char > option_ty, V2 : val, T : ty, V3 : list_char]: ((lconf_485928294t_char @ P @ H2 @ L @ E) => ((conf_P93989998t_char @ P @ H2 @ V2 @ T) => (((E @ V3) = (some_ty @ T)) => (lconf_485928294t_char @ P @ H2 @ (fun_up1252458416on_val @ L @ V3 @ (some_val @ V2)) @ E))))))). % lconf_upd
thf(fact_24_lconf__hext, axiom,
    ((![P : list_P1234162913t_char, H2 : nat > option2118145160on_val, L : list_char > option_val, E : list_char > option_ty, H3 : nat > option2118145160on_val]: ((lconf_485928294t_char @ P @ H2 @ L @ E) => ((hext @ H2 @ H3) => (lconf_485928294t_char @ P @ H3 @ L @ E)))))). % lconf_hext
thf(fact_25_lconf__upd2, axiom,
    ((![P : list_P1234162913t_char, H2 : nat > option2118145160on_val, L : list_char > option_val, E : list_char > option_ty, V2 : val, T : ty, V3 : list_char]: ((lconf_485928294t_char @ P @ H2 @ L @ E) => ((conf_P93989998t_char @ P @ H2 @ V2 @ T) => (lconf_485928294t_char @ P @ H2 @ (fun_up1252458416on_val @ L @ V3 @ (some_val @ V2)) @ (fun_up9191ion_ty @ E @ V3 @ (some_ty @ T)))))))). % lconf_upd2
thf(fact_26_hext__trans, axiom,
    ((![H2 : nat > option2118145160on_val, H3 : nat > option2118145160on_val, H4 : nat > option2118145160on_val]: ((hext @ H2 @ H3) => ((hext @ H3 @ H4) => (hext @ H2 @ H4)))))). % hext_trans
thf(fact_27_lconf__def, axiom,
    ((lconf_485928294t_char = (^[P2 : list_P1234162913t_char]: (^[H : nat > option2118145160on_val]: (^[L2 : list_char > option_val]: (^[E2 : list_char > option_ty]: (![V4 : list_char]: (![V : val]: ((((L2 @ V4) = (some_val @ V))) => ((?[T2 : ty]: ((((E2 @ V4) = (some_ty @ T2))) & ((conf_P93989998t_char @ P2 @ H @ V @ T2))))))))))))))). % lconf_def
thf(fact_28_conf__widen, axiom,
    ((![P : list_P1234162913t_char, H2 : nat > option2118145160on_val, V2 : val, T : ty, T5 : ty]: ((conf_P93989998t_char @ P @ H2 @ V2 @ T) => ((widen_917054840t_char @ P @ T @ T5) => (conf_P93989998t_char @ P @ H2 @ V2 @ T5)))))). % conf_widen
thf(fact_29_map__upd__Some__unfold, axiom,
    ((![M : list_char > option_ty, A : list_char, B : ty, X : list_char, Y : ty]: (((fun_up9191ion_ty @ M @ A @ (some_ty @ B) @ X) = (some_ty @ Y)) = (((((X = A)) & ((B = Y)))) | ((((~ ((X = A)))) & (((M @ X) = (some_ty @ Y)))))))))). % map_upd_Some_unfold
thf(fact_30_map__upd__Some__unfold, axiom,
    ((![M : list_char > option_val, A : list_char, B : val, X : list_char, Y : val]: (((fun_up1252458416on_val @ M @ A @ (some_val @ B) @ X) = (some_val @ Y)) = (((((X = A)) & ((B = Y)))) | ((((~ ((X = A)))) & (((M @ X) = (some_val @ Y)))))))))). % map_upd_Some_unfold
thf(fact_31_map__upd__Some__unfold, axiom,
    ((![M : nat > option2118145160on_val, A : nat, B : produc266837688on_val, X : nat, Y : produc266837688on_val]: (((fun_up262443479on_val @ M @ A @ (some_P1299442195on_val @ B) @ X) = (some_P1299442195on_val @ Y)) = (((((X = A)) & ((B = Y)))) | ((((~ ((X = A)))) & (((M @ X) = (some_P1299442195on_val @ Y)))))))))). % map_upd_Some_unfold
thf(fact_32_lconf_092_060_094sub_0622, axiom,
    ((lconf_485928294t_char @ p @ ha @ (fun_up1252458416on_val @ la @ v @ (some_val @ v3)) @ (fun_up9191ion_ty @ e @ v @ (some_ty @ t2))))). % lconf\<^sub>2
thf(fact_33_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_34_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_35_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_36_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_37_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_38_fun__upd__triv, axiom,
    ((![F : nat > option2118145160on_val, X : nat]: ((fun_up262443479on_val @ F @ X @ (F @ X)) = F)))). % fun_upd_triv
thf(fact_39_fun__upd__apply, axiom,
    ((fun_up9191ion_ty = (^[F2 : list_char > option_ty]: (^[X3 : list_char]: (^[Y3 : option_ty]: (^[Z2 : list_char]: (if_option_ty @ (Z2 = X3) @ Y3 @ (F2 @ Z2))))))))). % fun_upd_apply
thf(fact_40_fun__upd__apply, axiom,
    ((fun_up1252458416on_val = (^[F2 : list_char > option_val]: (^[X3 : list_char]: (^[Y3 : option_val]: (^[Z2 : list_char]: (if_option_val @ (Z2 = X3) @ Y3 @ (F2 @ Z2))))))))). % fun_upd_apply
thf(fact_41_fun__upd__apply, axiom,
    ((fun_up262443479on_val = (^[F2 : nat > option2118145160on_val]: (^[X3 : nat]: (^[Y3 : option2118145160on_val]: (^[Z2 : nat]: (if_opt451925058on_val @ (Z2 = X3) @ Y3 @ (F2 @ Z2))))))))). % fun_upd_apply
thf(fact_42_WTrt__hext__mono, axiom,
    ((![P : list_P1234162913t_char, H2 : nat > option2118145160on_val, E : list_char > option_ty, E3 : exp_list_char, T : ty, H3 : nat > option2118145160on_val]: ((wTrt2 @ P @ H2 @ E @ E3 @ T) => ((hext @ H2 @ H3) => (wTrt2 @ P @ H3 @ E @ E3 @ T)))))). % WTrt_hext_mono
thf(fact_43_IH, axiom,
    ((![E : list_char > option_ty, T : ty]: ((typeSa1777264139_sconf @ p @ E @ (produc52622304on_val @ ha @ (fun_up1252458416on_val @ la @ v @ (some_val @ v3)))) => ((wTrt2 @ p @ ha @ E @ ea @ T) => (?[U2 : ty]: ((wTrt2 @ p @ h_a @ E @ e_a @ U2) & (widen_917054840t_char @ p @ U2 @ T)))))))). % IH
thf(fact_44_wt, axiom,
    ((wTrt2 @ p @ ha @ e @ (block_list_char @ v @ t2 @ (seq_list_char @ (lAss_list_char @ v @ (val_list_char @ v3)) @ ea)) @ t))). % wt
thf(fact_45_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_46_fun__upd__def, axiom,
    ((fun_up9191ion_ty = (^[F2 : list_char > option_ty]: (^[A2 : list_char]: (^[B2 : option_ty]: (^[X3 : list_char]: (if_option_ty @ (X3 = A2) @ B2 @ (F2 @ X3))))))))). % fun_upd_def
thf(fact_47_fun__upd__def, axiom,
    ((fun_up1252458416on_val = (^[F2 : list_char > option_val]: (^[A2 : list_char]: (^[B2 : option_val]: (^[X3 : list_char]: (if_option_val @ (X3 = A2) @ B2 @ (F2 @ X3))))))))). % fun_upd_def
thf(fact_48_fun__upd__def, axiom,
    ((fun_up262443479on_val = (^[F2 : nat > option2118145160on_val]: (^[A2 : nat]: (^[B2 : option2118145160on_val]: (^[X3 : nat]: (if_opt451925058on_val @ (X3 = A2) @ B2 @ (F2 @ X3))))))))). % fun_upd_def
thf(fact_49_conf, axiom,
    ((typeSa1777264139_sconf @ p @ e @ (produc52622304on_val @ ha @ la)))). % conf
thf(fact_50_red__preserves__lconf, axiom,
    ((![E3 : exp_list_char, H2 : 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 @ H2 @ L)) @ (produc2023458740on_val @ E4 @ (produc52622304on_val @ H3 @ L3))) @ (red @ P)) => ((wTrt2 @ P @ H2 @ E @ E3 @ T) => ((lconf_485928294t_char @ P @ H2 @ L @ E) => (lconf_485928294t_char @ P @ H3 @ L3 @ E))))))). % red_preserves_lconf
thf(fact_51_WTrtSeq, axiom,
    ((![P : list_P1234162913t_char, H2 : nat > option2118145160on_val, E : list_char > option_ty, E_1 : exp_list_char, T_12 : ty, E_2 : exp_list_char, T_2 : ty]: ((wTrt2 @ P @ H2 @ E @ E_1 @ T_12) => ((wTrt2 @ P @ H2 @ E @ E_2 @ T_2) => (wTrt2 @ P @ H2 @ E @ (seq_list_char @ E_1 @ E_2) @ T_2)))))). % WTrtSeq
thf(fact_52_WTrtBlock, axiom,
    ((![P : list_P1234162913t_char, H2 : nat > option2118145160on_val, E : list_char > option_ty, V3 : list_char, T : ty, E3 : exp_list_char, T5 : ty]: ((wTrt2 @ P @ H2 @ (fun_up9191ion_ty @ E @ V3 @ (some_ty @ T)) @ E3 @ T5) => (wTrt2 @ P @ H2 @ E @ (block_list_char @ V3 @ T @ E3) @ T5))))). % WTrtBlock
thf(fact_53_WTrtVal, axiom,
    ((![H2 : nat > option2118145160on_val, V2 : val, T : ty, P : list_P1234162913t_char, E : list_char > option_ty]: (((typeof_h @ H2 @ V2) = (some_ty @ T)) => (wTrt2 @ P @ H2 @ E @ (val_list_char @ V2) @ T))))). % WTrtVal
thf(fact_54_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_55_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_56_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_57_fun__upd__twist, axiom,
    ((![A : list_char, C : list_char, M : list_char > option_ty, B : option_ty, D : option_ty]: ((~ ((A = C))) => ((fun_up9191ion_ty @ (fun_up9191ion_ty @ M @ A @ B) @ C @ D) = (fun_up9191ion_ty @ (fun_up9191ion_ty @ M @ C @ D) @ A @ B)))))). % fun_upd_twist
thf(fact_58_fun__upd__twist, axiom,
    ((![A : list_char, C : list_char, M : list_char > option_val, B : option_val, D : option_val]: ((~ ((A = C))) => ((fun_up1252458416on_val @ (fun_up1252458416on_val @ M @ A @ B) @ C @ D) = (fun_up1252458416on_val @ (fun_up1252458416on_val @ M @ C @ D) @ A @ B)))))). % fun_upd_twist
thf(fact_59_fun__upd__twist, axiom,
    ((![A : nat, C : nat, M : nat > option2118145160on_val, B : option2118145160on_val, D : option2118145160on_val]: ((~ ((A = C))) => ((fun_up262443479on_val @ (fun_up262443479on_val @ M @ A @ B) @ C @ D) = (fun_up262443479on_val @ (fun_up262443479on_val @ M @ C @ D) @ A @ B)))))). % fun_upd_twist
thf(fact_60_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_61_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_62_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_63_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_64_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_65_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_66_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_67_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_68_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_69_mem__Collect__eq, axiom,
    ((![A : produc1172664615on_val, P : produc1172664615on_val > $o]: ((member354538064on_val @ A @ (collec2055896722on_val @ P)) = (P @ A))))). % mem_Collect_eq
thf(fact_70_Collect__mem__eq, axiom,
    ((![A3 : set_Pr1189492743on_val]: ((collec2055896722on_val @ (^[X3 : produc1172664615on_val]: (member354538064on_val @ X3 @ A3))) = A3)))). % Collect_mem_eq
thf(fact_71_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_72_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_73_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_74_red__reds_OInitBlockRed, axiom,
    ((![E3 : exp_list_char, H2 : nat > option2118145160on_val, L : list_char > option_val, V3 : list_char, V2 : 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 @ H2 @ (fun_up1252458416on_val @ L @ V3 @ (some_val @ V2)))) @ (produc2023458740on_val @ E4 @ (produc52622304on_val @ H3 @ L3))) @ (red @ P)) => (((L3 @ V3) = (some_val @ V5)) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (block_list_char @ V3 @ T @ (seq_list_char @ (lAss_list_char @ V3 @ (val_list_char @ V2)) @ E3)) @ (produc52622304on_val @ H2 @ L)) @ (produc2023458740on_val @ (block_list_char @ V3 @ T @ (seq_list_char @ (lAss_list_char @ V3 @ (val_list_char @ V5)) @ E4)) @ (produc52622304on_val @ H3 @ (fun_up1252458416on_val @ L3 @ V3 @ (L @ V3))))) @ (red @ P))))))). % red_reds.InitBlockRed
thf(fact_75_red__reds_ORedInitBlock, axiom,
    ((![V3 : list_char, T : ty, V2 : val, U3 : val, S2 : produc515445032on_val, P : list_P1234162913t_char]: (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (block_list_char @ V3 @ T @ (seq_list_char @ (lAss_list_char @ V3 @ (val_list_char @ V2)) @ (val_list_char @ U3))) @ S2) @ (produc2023458740on_val @ (val_list_char @ U3) @ S2)) @ (red @ P))))). % red_reds.RedInitBlock
thf(fact_76_InitBlockRed_Oprems_I2_J, axiom,
    ((wTrt2 @ p @ ha @ e @ (block_list_char @ v @ t2 @ (seq_list_char @ (lAss_list_char @ v @ (val_list_char @ v3)) @ ea)) @ t))). % InitBlockRed.prems(2)
thf(fact_77_red__hext__incr, axiom,
    ((![E3 : exp_list_char, H2 : nat > option2118145160on_val, L : list_char > option_val, E4 : exp_list_char, H3 : nat > option2118145160on_val, L3 : list_char > option_val, P : list_P1234162913t_char]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E3 @ (produc52622304on_val @ H2 @ L)) @ (produc2023458740on_val @ E4 @ (produc52622304on_val @ H3 @ L3))) @ (red @ P)) => (hext @ H2 @ H3))))). % red_hext_incr
thf(fact_78_red__reds_ORedBlock, axiom,
    ((![V3 : list_char, T : ty, U3 : val, S2 : produc515445032on_val, P : list_P1234162913t_char]: (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (block_list_char @ V3 @ T @ (val_list_char @ U3)) @ S2) @ (produc2023458740on_val @ (val_list_char @ U3) @ S2)) @ (red @ P))))). % red_reds.RedBlock
thf(fact_79_red__reds_ORedSeq, axiom,
    ((![V2 : val, E_2 : exp_list_char, S2 : produc515445032on_val, P : list_P1234162913t_char]: (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (seq_list_char @ (val_list_char @ V2) @ E_2) @ S2) @ (produc2023458740on_val @ E_2 @ S2)) @ (red @ P))))). % red_reds.RedSeq
thf(fact_80_InitBlockRed_Ohyps_I2_J, axiom,
    ((![E : list_char > option_ty, T : ty]: ((typeSa1777264139_sconf @ p @ E @ (produc52622304on_val @ ha @ (fun_up1252458416on_val @ la @ v @ (some_val @ v3)))) => ((wTrt2 @ p @ ha @ E @ ea @ T) => (?[T6 : ty]: ((wTrt2 @ p @ h_a @ E @ e_a @ T6) & (widen_917054840t_char @ p @ T6 @ T)))))))). % InitBlockRed.hyps(2)
thf(fact_81_InitBlockRed_Oprems_I1_J, axiom,
    ((typeSa1777264139_sconf @ p @ e @ (produc52622304on_val @ ha @ la)))). % InitBlockRed.prems(1)
thf(fact_82_red__reds_OSeqRed, axiom,
    ((![E3 : exp_list_char, S2 : produc515445032on_val, E4 : exp_list_char, S3 : produc515445032on_val, P : list_P1234162913t_char, E_2 : exp_list_char]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E3 @ S2) @ (produc2023458740on_val @ E4 @ S3)) @ (red @ P)) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (seq_list_char @ E3 @ E_2) @ S2) @ (produc2023458740on_val @ (seq_list_char @ E4 @ E_2) @ S3)) @ (red @ P)))))). % red_reds.SeqRed
thf(fact_83_red__reds_OLAssRed, axiom,
    ((![E3 : exp_list_char, S2 : produc515445032on_val, E4 : exp_list_char, S3 : produc515445032on_val, P : list_P1234162913t_char, V3 : list_char]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E3 @ S2) @ (produc2023458740on_val @ E4 @ S3)) @ (red @ P)) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (lAss_list_char @ V3 @ E3) @ S2) @ (produc2023458740on_val @ (lAss_list_char @ V3 @ E4) @ S3)) @ (red @ P)))))). % red_reds.LAssRed
thf(fact_84_red__reds_ORedLAss, axiom,
    ((![V3 : list_char, V2 : val, H2 : nat > option2118145160on_val, L : list_char > option_val, P : list_P1234162913t_char]: (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (lAss_list_char @ V3 @ (val_list_char @ V2)) @ (produc52622304on_val @ H2 @ L)) @ (produc2023458740on_val @ (val_list_char @ unit) @ (produc52622304on_val @ H2 @ (fun_up1252458416on_val @ L @ V3 @ (some_val @ V2))))) @ (red @ P))))). % red_reds.RedLAss
thf(fact_85_prod__cases4, axiom,
    ((![Y : produc1172664615on_val]: (~ ((![A4 : produc1097884484on_val, B3 : exp_list_char, C2 : nat > option2118145160on_val, D2 : list_char > option_val]: (~ ((Y = (produc1069526295on_val @ A4 @ (produc2023458740on_val @ B3 @ (produc52622304on_val @ C2 @ D2)))))))))))). % prod_cases4
thf(fact_86_old_Oprod_Oinject, axiom,
    ((![A : nat > option2118145160on_val, B : list_char > option_val, A5 : nat > option2118145160on_val, B4 : list_char > option_val]: (((produc52622304on_val @ A @ B) = (produc52622304on_val @ A5 @ B4)) = (((A = A5)) & ((B = B4))))))). % old.prod.inject
thf(fact_87_old_Oprod_Oinject, axiom,
    ((![A : produc1097884484on_val, B : produc1097884484on_val, A5 : produc1097884484on_val, B4 : produc1097884484on_val]: (((produc1069526295on_val @ A @ B) = (produc1069526295on_val @ A5 @ B4)) = (((A = A5)) & ((B = B4))))))). % old.prod.inject
thf(fact_88_old_Oprod_Oinject, axiom,
    ((![A : exp_list_char, B : produc515445032on_val, A5 : exp_list_char, B4 : produc515445032on_val]: (((produc2023458740on_val @ A @ B) = (produc2023458740on_val @ A5 @ B4)) = (((A = A5)) & ((B = B4))))))). % old.prod.inject
thf(fact_89_old_Oprod_Oinject, axiom,
    ((![A : list_char, B : produc1257910179t_char > option_val, A5 : list_char, B4 : produc1257910179t_char > option_val]: (((produc904988266on_val @ A @ B) = (produc904988266on_val @ A5 @ B4)) = (((A = A5)) & ((B = B4))))))). % old.prod.inject
thf(fact_90_prod_Oinject, axiom,
    ((![X1 : nat > option2118145160on_val, X2 : list_char > option_val, Y1 : nat > option2118145160on_val, Y2 : list_char > option_val]: (((produc52622304on_val @ X1 @ X2) = (produc52622304on_val @ Y1 @ Y2)) = (((X1 = Y1)) & ((X2 = Y2))))))). % prod.inject
thf(fact_91_prod_Oinject, axiom,
    ((![X1 : produc1097884484on_val, X2 : produc1097884484on_val, Y1 : produc1097884484on_val, Y2 : produc1097884484on_val]: (((produc1069526295on_val @ X1 @ X2) = (produc1069526295on_val @ Y1 @ Y2)) = (((X1 = Y1)) & ((X2 = Y2))))))). % prod.inject
thf(fact_92_prod_Oinject, axiom,
    ((![X1 : exp_list_char, X2 : produc515445032on_val, Y1 : exp_list_char, Y2 : produc515445032on_val]: (((produc2023458740on_val @ X1 @ X2) = (produc2023458740on_val @ Y1 @ Y2)) = (((X1 = Y1)) & ((X2 = Y2))))))). % prod.inject
thf(fact_93_prod_Oinject, axiom,
    ((![X1 : list_char, X2 : produc1257910179t_char > option_val, Y1 : list_char, Y2 : produc1257910179t_char > option_val]: (((produc904988266on_val @ X1 @ X2) = (produc904988266on_val @ Y1 @ Y2)) = (((X1 = Y1)) & ((X2 = Y2))))))). % prod.inject
thf(fact_94_conf__upd__obj, axiom,
    ((![H2 : nat > option2118145160on_val, A : nat, C3 : list_char, Fs : produc1257910179t_char > option_val, P : list_P1234162913t_char, Fs2 : produc1257910179t_char > option_val, X : val, T : ty]: (((H2 @ A) = (some_P1299442195on_val @ (produc904988266on_val @ C3 @ Fs))) => ((conf_P93989998t_char @ P @ (fun_up262443479on_val @ H2 @ A @ (some_P1299442195on_val @ (produc904988266on_val @ C3 @ Fs2))) @ X @ T) = (conf_P93989998t_char @ P @ H2 @ X @ T)))))). % conf_upd_obj
thf(fact_95_hext__upd__obj, axiom,
    ((![H2 : nat > option2118145160on_val, A : nat, C3 : list_char, Fs : produc1257910179t_char > option_val, Fs2 : produc1257910179t_char > option_val]: (((H2 @ A) = (some_P1299442195on_val @ (produc904988266on_val @ C3 @ Fs))) => (hext @ H2 @ (fun_up262443479on_val @ H2 @ A @ (some_P1299442195on_val @ (produc904988266on_val @ C3 @ Fs2)))))))). % hext_upd_obj
thf(fact_96_hext__objD, axiom,
    ((![H2 : nat > option2118145160on_val, H3 : nat > option2118145160on_val, A : nat, C3 : list_char, Fs : produc1257910179t_char > option_val]: ((hext @ H2 @ H3) => (((H2 @ A) = (some_P1299442195on_val @ (produc904988266on_val @ C3 @ Fs))) => (?[Fs3 : produc1257910179t_char > option_val]: ((H3 @ A) = (some_P1299442195on_val @ (produc904988266on_val @ C3 @ Fs3))))))))). % hext_objD
thf(fact_97_hext__def, axiom,
    ((hext = (^[H : nat > option2118145160on_val]: (^[H5 : nat > option2118145160on_val]: (![A2 : nat]: (![C4 : list_char]: (![Fs4 : produc1257910179t_char > option_val]: ((((H @ A2) = (some_P1299442195on_val @ (produc904988266on_val @ C4 @ Fs4)))) => ((?[Fs5 : produc1257910179t_char > option_val]: ((H5 @ A2) = (some_P1299442195on_val @ (produc904988266on_val @ C4 @ Fs5)))))))))))))). % hext_def
thf(fact_98_hextI, axiom,
    ((![H2 : nat > option2118145160on_val, H3 : nat > option2118145160on_val]: ((![A4 : nat, C5 : list_char, Fs6 : produc1257910179t_char > option_val]: (((H2 @ A4) = (some_P1299442195on_val @ (produc904988266on_val @ C5 @ Fs6))) => (?[Fs7 : produc1257910179t_char > option_val]: ((H3 @ A4) = (some_P1299442195on_val @ (produc904988266on_val @ C5 @ Fs7)))))) => (hext @ H2 @ H3))))). % hextI
thf(fact_99_old_Oprod_Oinducts, axiom,
    ((![P : produc515445032on_val > $o, Prod : produc515445032on_val]: ((![A4 : nat > option2118145160on_val, B3 : list_char > option_val]: (P @ (produc52622304on_val @ A4 @ B3))) => (P @ Prod))))). % old.prod.inducts
thf(fact_100_old_Oprod_Oinducts, axiom,
    ((![P : produc1172664615on_val > $o, Prod : produc1172664615on_val]: ((![A4 : produc1097884484on_val, B3 : produc1097884484on_val]: (P @ (produc1069526295on_val @ A4 @ B3))) => (P @ Prod))))). % old.prod.inducts
thf(fact_101_old_Oprod_Oinducts, axiom,
    ((![P : produc1097884484on_val > $o, Prod : produc1097884484on_val]: ((![A4 : exp_list_char, B3 : produc515445032on_val]: (P @ (produc2023458740on_val @ A4 @ B3))) => (P @ Prod))))). % old.prod.inducts
thf(fact_102_old_Oprod_Oinducts, axiom,
    ((![P : produc266837688on_val > $o, Prod : produc266837688on_val]: ((![A4 : list_char, B3 : produc1257910179t_char > option_val]: (P @ (produc904988266on_val @ A4 @ B3))) => (P @ Prod))))). % old.prod.inducts
thf(fact_103_old_Oprod_Oexhaust, axiom,
    ((![Y : produc515445032on_val]: (~ ((![A4 : nat > option2118145160on_val, B3 : list_char > option_val]: (~ ((Y = (produc52622304on_val @ A4 @ B3)))))))))). % old.prod.exhaust
thf(fact_104_old_Oprod_Oexhaust, axiom,
    ((![Y : produc1172664615on_val]: (~ ((![A4 : produc1097884484on_val, B3 : produc1097884484on_val]: (~ ((Y = (produc1069526295on_val @ A4 @ B3)))))))))). % old.prod.exhaust
thf(fact_105_old_Oprod_Oexhaust, axiom,
    ((![Y : produc1097884484on_val]: (~ ((![A4 : exp_list_char, B3 : produc515445032on_val]: (~ ((Y = (produc2023458740on_val @ A4 @ B3)))))))))). % old.prod.exhaust
thf(fact_106_old_Oprod_Oexhaust, axiom,
    ((![Y : produc266837688on_val]: (~ ((![A4 : list_char, B3 : produc1257910179t_char > option_val]: (~ ((Y = (produc904988266on_val @ A4 @ B3)))))))))). % old.prod.exhaust
thf(fact_107_Pair__inject, axiom,
    ((![A : nat > option2118145160on_val, B : list_char > option_val, A5 : nat > option2118145160on_val, B4 : list_char > option_val]: (((produc52622304on_val @ A @ B) = (produc52622304on_val @ A5 @ B4)) => (~ (((A = A5) => (~ ((B = B4)))))))))). % Pair_inject
thf(fact_108_Pair__inject, axiom,
    ((![A : produc1097884484on_val, B : produc1097884484on_val, A5 : produc1097884484on_val, B4 : produc1097884484on_val]: (((produc1069526295on_val @ A @ B) = (produc1069526295on_val @ A5 @ B4)) => (~ (((A = A5) => (~ ((B = B4)))))))))). % Pair_inject
thf(fact_109_Pair__inject, axiom,
    ((![A : exp_list_char, B : produc515445032on_val, A5 : exp_list_char, B4 : produc515445032on_val]: (((produc2023458740on_val @ A @ B) = (produc2023458740on_val @ A5 @ B4)) => (~ (((A = A5) => (~ ((B = B4)))))))))). % Pair_inject
thf(fact_110_Pair__inject, axiom,
    ((![A : list_char, B : produc1257910179t_char > option_val, A5 : list_char, B4 : produc1257910179t_char > option_val]: (((produc904988266on_val @ A @ B) = (produc904988266on_val @ A5 @ B4)) => (~ (((A = A5) => (~ ((B = B4)))))))))). % Pair_inject
thf(fact_111_prod__cases, axiom,
    ((![P : produc515445032on_val > $o, P3 : produc515445032on_val]: ((![A4 : nat > option2118145160on_val, B3 : list_char > option_val]: (P @ (produc52622304on_val @ A4 @ B3))) => (P @ P3))))). % prod_cases
thf(fact_112_prod__cases, axiom,
    ((![P : produc1172664615on_val > $o, P3 : produc1172664615on_val]: ((![A4 : produc1097884484on_val, B3 : produc1097884484on_val]: (P @ (produc1069526295on_val @ A4 @ B3))) => (P @ P3))))). % prod_cases
thf(fact_113_prod__cases, axiom,
    ((![P : produc1097884484on_val > $o, P3 : produc1097884484on_val]: ((![A4 : exp_list_char, B3 : produc515445032on_val]: (P @ (produc2023458740on_val @ A4 @ B3))) => (P @ P3))))). % prod_cases
thf(fact_114_prod__cases, axiom,
    ((![P : produc266837688on_val > $o, P3 : produc266837688on_val]: ((![A4 : list_char, B3 : produc1257910179t_char > option_val]: (P @ (produc904988266on_val @ A4 @ B3))) => (P @ P3))))). % prod_cases
thf(fact_115_surj__pair, axiom,
    ((![P3 : produc515445032on_val]: (?[X4 : nat > option2118145160on_val, Y4 : list_char > option_val]: (P3 = (produc52622304on_val @ X4 @ Y4)))))). % surj_pair
thf(fact_116_surj__pair, axiom,
    ((![P3 : produc1172664615on_val]: (?[X4 : produc1097884484on_val, Y4 : produc1097884484on_val]: (P3 = (produc1069526295on_val @ X4 @ Y4)))))). % surj_pair
thf(fact_117_surj__pair, axiom,
    ((![P3 : produc1097884484on_val]: (?[X4 : exp_list_char, Y4 : produc515445032on_val]: (P3 = (produc2023458740on_val @ X4 @ Y4)))))). % surj_pair
thf(fact_118_surj__pair, axiom,
    ((![P3 : produc266837688on_val]: (?[X4 : list_char, Y4 : produc1257910179t_char > option_val]: (P3 = (produc904988266on_val @ X4 @ Y4)))))). % surj_pair
thf(fact_119_prod__induct3, axiom,
    ((![P : produc1172664615on_val > $o, X : produc1172664615on_val]: ((![A4 : produc1097884484on_val, B3 : exp_list_char, C2 : produc515445032on_val]: (P @ (produc1069526295on_val @ A4 @ (produc2023458740on_val @ B3 @ C2)))) => (P @ X))))). % prod_induct3
thf(fact_120_prod__induct3, axiom,
    ((![P : produc1097884484on_val > $o, X : produc1097884484on_val]: ((![A4 : exp_list_char, B3 : nat > option2118145160on_val, C2 : list_char > option_val]: (P @ (produc2023458740on_val @ A4 @ (produc52622304on_val @ B3 @ C2)))) => (P @ X))))). % prod_induct3
thf(fact_121_prod__cases3, axiom,
    ((![Y : produc1172664615on_val]: (~ ((![A4 : produc1097884484on_val, B3 : exp_list_char, C2 : produc515445032on_val]: (~ ((Y = (produc1069526295on_val @ A4 @ (produc2023458740on_val @ B3 @ C2))))))))))). % prod_cases3
thf(fact_122_prod__cases3, axiom,
    ((![Y : produc1097884484on_val]: (~ ((![A4 : exp_list_char, B3 : nat > option2118145160on_val, C2 : list_char > option_val]: (~ ((Y = (produc2023458740on_val @ A4 @ (produc52622304on_val @ B3 @ C2))))))))))). % prod_cases3
thf(fact_123_prod__induct4, axiom,
    ((![P : produc1172664615on_val > $o, X : produc1172664615on_val]: ((![A4 : produc1097884484on_val, B3 : exp_list_char, C2 : nat > option2118145160on_val, D2 : list_char > option_val]: (P @ (produc1069526295on_val @ A4 @ (produc2023458740on_val @ B3 @ (produc52622304on_val @ C2 @ D2))))) => (P @ X))))). % prod_induct4
thf(fact_124_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_125_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_126_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_127_exp_Oinject_I3_J, axiom,
    ((![X32 : val, Y32 : val]: (((val_list_char @ X32) = (val_list_char @ Y32)) = (X32 = Y32))))). % exp.inject(3)
thf(fact_128_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_129_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_130_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_131_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_132_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_133_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_134_red__preserves__hconf, axiom,
    ((![E3 : exp_list_char, H2 : 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 @ H2 @ L)) @ (produc2023458740on_val @ E4 @ (produc52622304on_val @ H3 @ L3))) @ (red @ P)) => ((wTrt2 @ P @ H2 @ E @ E3 @ T) => ((hconf_1244167010t_char @ P @ H2) => (hconf_1244167010t_char @ P @ H3))))))). % red_preserves_hconf
thf(fact_135_red__preserves__sconf, axiom,
    ((![E3 : exp_list_char, S2 : produc515445032on_val, E4 : exp_list_char, S3 : produc515445032on_val, P : list_P1234162913t_char, E : list_char > option_ty, T : ty]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E3 @ S2) @ (produc2023458740on_val @ E4 @ S3)) @ (red @ P)) => ((wTrt2 @ P @ (hp @ S2) @ E @ E3 @ T) => ((typeSa1777264139_sconf @ P @ E @ S2) => (typeSa1777264139_sconf @ P @ E @ S3))))))). % red_preserves_sconf
thf(fact_136_assigned__def, axiom,
    ((assigned = (^[V4 : list_char]: (^[E5 : exp_list_char]: (?[V : val]: (?[E6 : exp_list_char]: (E5 = (seq_list_char @ (lAss_list_char @ V4 @ (val_list_char @ V)) @ E6))))))))). % assigned_def
thf(fact_137_red__reds_OBlockRedSome, axiom,
    ((![E3 : exp_list_char, H2 : nat > option2118145160on_val, L : list_char > option_val, V3 : list_char, E4 : exp_list_char, H3 : nat > option2118145160on_val, L3 : list_char > option_val, P : list_P1234162913t_char, V2 : val, T : ty]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E3 @ (produc52622304on_val @ H2 @ (fun_up1252458416on_val @ L @ V3 @ none_val))) @ (produc2023458740on_val @ E4 @ (produc52622304on_val @ H3 @ L3))) @ (red @ P)) => (((L3 @ V3) = (some_val @ V2)) => ((~ ((assigned @ V3 @ E3))) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (block_list_char @ V3 @ T @ E3) @ (produc52622304on_val @ H2 @ L)) @ (produc2023458740on_val @ (block_list_char @ V3 @ T @ (seq_list_char @ (lAss_list_char @ V3 @ (val_list_char @ V2)) @ E4)) @ (produc52622304on_val @ H3 @ (fun_up1252458416on_val @ L3 @ V3 @ (L @ V3))))) @ (red @ P)))))))). % red_reds.BlockRedSome
thf(fact_138_red__reds_OBlockRedNone, axiom,
    ((![E3 : exp_list_char, H2 : nat > option2118145160on_val, L : list_char > option_val, V3 : 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 @ H2 @ (fun_up1252458416on_val @ L @ V3 @ none_val))) @ (produc2023458740on_val @ E4 @ (produc52622304on_val @ H3 @ L3))) @ (red @ P)) => (((L3 @ V3) = none_val) => ((~ ((assigned @ V3 @ E3))) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (block_list_char @ V3 @ T @ E3) @ (produc52622304on_val @ H2 @ L)) @ (produc2023458740on_val @ (block_list_char @ V3 @ T @ E4) @ (produc52622304on_val @ H3 @ (fun_up1252458416on_val @ L3 @ V3 @ (L @ V3))))) @ (red @ P)))))))). % red_reds.BlockRedNone
thf(fact_139_hconf__upd__obj, axiom,
    ((![P : list_P1234162913t_char, H2 : nat > option2118145160on_val, A : nat, C3 : list_char, Fs : produc1257910179t_char > option_val, Fs2 : produc1257910179t_char > option_val]: ((hconf_1244167010t_char @ P @ H2) => (((H2 @ A) = (some_P1299442195on_val @ (produc904988266on_val @ C3 @ Fs))) => ((oconf_454120169t_char @ P @ H2 @ (produc904988266on_val @ C3 @ Fs2)) => (hconf_1244167010t_char @ P @ (fun_up262443479on_val @ H2 @ A @ (some_P1299442195on_val @ (produc904988266on_val @ C3 @ Fs2)))))))))). % hconf_upd_obj
thf(fact_140_not__None__eq, axiom,
    ((![X : option_ty]: ((~ ((X = none_ty))) = (?[Y3 : ty]: (X = (some_ty @ Y3))))))). % not_None_eq
thf(fact_141_not__None__eq, axiom,
    ((![X : option_val]: ((~ ((X = none_val))) = (?[Y3 : val]: (X = (some_val @ Y3))))))). % not_None_eq
thf(fact_142_not__None__eq, axiom,
    ((![X : option2118145160on_val]: ((~ ((X = none_P1535574167on_val))) = (?[Y3 : produc266837688on_val]: (X = (some_P1299442195on_val @ Y3))))))). % not_None_eq
thf(fact_143_not__Some__eq, axiom,
    ((![X : option_ty]: ((![Y3 : ty]: (~ ((X = (some_ty @ Y3))))) = (X = none_ty))))). % not_Some_eq
thf(fact_144_not__Some__eq, axiom,
    ((![X : option_val]: ((![Y3 : val]: (~ ((X = (some_val @ Y3))))) = (X = none_val))))). % not_Some_eq
thf(fact_145_not__Some__eq, axiom,
    ((![X : option2118145160on_val]: ((![Y3 : produc266837688on_val]: (~ ((X = (some_P1299442195on_val @ Y3))))) = (X = none_P1535574167on_val))))). % not_Some_eq
thf(fact_146_empty__upd__none, axiom,
    ((![X : list_char]: ((fun_up9191ion_ty @ (^[X3 : list_char]: none_ty) @ X @ none_ty) = (^[X3 : list_char]: none_ty))))). % empty_upd_none
thf(fact_147_empty__upd__none, axiom,
    ((![X : list_char]: ((fun_up1252458416on_val @ (^[X3 : list_char]: none_val) @ X @ none_val) = (^[X3 : list_char]: none_val))))). % empty_upd_none
thf(fact_148_empty__upd__none, axiom,
    ((![X : nat]: ((fun_up262443479on_val @ (^[X3 : nat]: none_P1535574167on_val) @ X @ none_P1535574167on_val) = (^[X3 : nat]: none_P1535574167on_val))))). % empty_upd_none
thf(fact_149_lconf__empty, axiom,
    ((![P : list_P1234162913t_char, H2 : nat > option2118145160on_val, E : list_char > option_ty]: (lconf_485928294t_char @ P @ H2 @ (^[X3 : list_char]: none_val) @ E)))). % lconf_empty
thf(fact_150_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, B3 : ty]: ((X = (some_ty @ A4)) => ((Y = (some_ty @ B3)) => (P @ X @ Y)))) => (P @ X @ Y))))))). % combine_options_cases
thf(fact_151_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, B3 : val]: ((X = (some_ty @ A4)) => ((Y = (some_val @ B3)) => (P @ X @ Y)))) => (P @ X @ Y))))))). % combine_options_cases
thf(fact_152_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, B3 : produc266837688on_val]: ((X = (some_ty @ A4)) => ((Y = (some_P1299442195on_val @ B3)) => (P @ X @ Y)))) => (P @ X @ Y))))))). % combine_options_cases
thf(fact_153_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, B3 : ty]: ((X = (some_val @ A4)) => ((Y = (some_ty @ B3)) => (P @ X @ Y)))) => (P @ X @ Y))))))). % combine_options_cases
thf(fact_154_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, B3 : val]: ((X = (some_val @ A4)) => ((Y = (some_val @ B3)) => (P @ X @ Y)))) => (P @ X @ Y))))))). % combine_options_cases
thf(fact_155_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, B3 : produc266837688on_val]: ((X = (some_val @ A4)) => ((Y = (some_P1299442195on_val @ B3)) => (P @ X @ Y)))) => (P @ X @ Y))))))). % combine_options_cases
thf(fact_156_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, B3 : ty]: ((X = (some_P1299442195on_val @ A4)) => ((Y = (some_ty @ B3)) => (P @ X @ Y)))) => (P @ X @ Y))))))). % combine_options_cases
thf(fact_157_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, B3 : val]: ((X = (some_P1299442195on_val @ A4)) => ((Y = (some_val @ B3)) => (P @ X @ Y)))) => (P @ X @ Y))))))). % combine_options_cases
thf(fact_158_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, B3 : produc266837688on_val]: ((X = (some_P1299442195on_val @ A4)) => ((Y = (some_P1299442195on_val @ B3)) => (P @ X @ Y)))) => (P @ X @ Y))))))). % combine_options_cases
thf(fact_159_split__option__all, axiom,
    (((^[P4 : option_ty > $o]: (![X5 : option_ty]: (P4 @ X5))) = (^[P2 : option_ty > $o]: (((P2 @ none_ty)) & ((![X3 : ty]: (P2 @ (some_ty @ X3))))))))). % split_option_all
thf(fact_160_split__option__all, axiom,
    (((^[P4 : option_val > $o]: (![X5 : option_val]: (P4 @ X5))) = (^[P2 : option_val > $o]: (((P2 @ none_val)) & ((![X3 : val]: (P2 @ (some_val @ X3))))))))). % split_option_all
thf(fact_161_split__option__all, axiom,
    (((^[P4 : option2118145160on_val > $o]: (![X5 : option2118145160on_val]: (P4 @ X5))) = (^[P2 : option2118145160on_val > $o]: (((P2 @ none_P1535574167on_val)) & ((![X3 : produc266837688on_val]: (P2 @ (some_P1299442195on_val @ X3))))))))). % split_option_all
thf(fact_162_split__option__ex, axiom,
    (((^[P4 : option_ty > $o]: (?[X5 : option_ty]: (P4 @ X5))) = (^[P2 : option_ty > $o]: (((P2 @ none_ty)) | ((?[X3 : ty]: (P2 @ (some_ty @ X3))))))))). % split_option_ex
thf(fact_163_split__option__ex, axiom,
    (((^[P4 : option_val > $o]: (?[X5 : option_val]: (P4 @ X5))) = (^[P2 : option_val > $o]: (((P2 @ none_val)) | ((?[X3 : val]: (P2 @ (some_val @ X3))))))))). % split_option_ex
thf(fact_164_split__option__ex, axiom,
    (((^[P4 : option2118145160on_val > $o]: (?[X5 : option2118145160on_val]: (P4 @ X5))) = (^[P2 : option2118145160on_val > $o]: (((P2 @ none_P1535574167on_val)) | ((?[X3 : produc266837688on_val]: (P2 @ (some_P1299442195on_val @ X3))))))))). % split_option_ex
thf(fact_165_option_Oinducts, axiom,
    ((![P : option_ty > $o, Option : option_ty]: ((P @ none_ty) => ((![X4 : ty]: (P @ (some_ty @ X4))) => (P @ Option)))))). % option.inducts
thf(fact_166_option_Oinducts, axiom,
    ((![P : option_val > $o, Option : option_val]: ((P @ none_val) => ((![X4 : val]: (P @ (some_val @ X4))) => (P @ Option)))))). % option.inducts
thf(fact_167_option_Oinducts, axiom,
    ((![P : option2118145160on_val > $o, Option : option2118145160on_val]: ((P @ none_P1535574167on_val) => ((![X4 : produc266837688on_val]: (P @ (some_P1299442195on_val @ X4))) => (P @ Option)))))). % option.inducts
thf(fact_168_option_Oexhaust, axiom,
    ((![Y : option_ty]: ((~ ((Y = none_ty))) => (~ ((![X22 : ty]: (~ ((Y = (some_ty @ X22))))))))))). % option.exhaust
thf(fact_169_option_Oexhaust, axiom,
    ((![Y : option_val]: ((~ ((Y = none_val))) => (~ ((![X22 : val]: (~ ((Y = (some_val @ X22))))))))))). % option.exhaust
thf(fact_170_option_Oexhaust, axiom,
    ((![Y : option2118145160on_val]: ((~ ((Y = none_P1535574167on_val))) => (~ ((![X22 : produc266837688on_val]: (~ ((Y = (some_P1299442195on_val @ X22))))))))))). % option.exhaust
thf(fact_171_option_OdiscI, axiom,
    ((![Option : option_ty, X2 : ty]: ((Option = (some_ty @ X2)) => (~ ((Option = none_ty))))))). % option.discI
thf(fact_172_option_OdiscI, axiom,
    ((![Option : option_val, X2 : val]: ((Option = (some_val @ X2)) => (~ ((Option = none_val))))))). % option.discI
thf(fact_173_option_OdiscI, axiom,
    ((![Option : option2118145160on_val, X2 : produc266837688on_val]: ((Option = (some_P1299442195on_val @ X2)) => (~ ((Option = none_P1535574167on_val))))))). % option.discI
thf(fact_174_option_Odistinct_I1_J, axiom,
    ((![X2 : ty]: (~ ((none_ty = (some_ty @ X2))))))). % option.distinct(1)
thf(fact_175_option_Odistinct_I1_J, axiom,
    ((![X2 : val]: (~ ((none_val = (some_val @ X2))))))). % option.distinct(1)
thf(fact_176_option_Odistinct_I1_J, axiom,
    ((![X2 : produc266837688on_val]: (~ ((none_P1535574167on_val = (some_P1299442195on_val @ X2))))))). % option.distinct(1)
thf(fact_177_map__upd__nonempty, axiom,
    ((![T4 : list_char > option_ty, K : list_char, X : ty]: (~ (((fun_up9191ion_ty @ T4 @ K @ (some_ty @ X)) = (^[X3 : list_char]: none_ty))))))). % map_upd_nonempty
thf(fact_178_map__upd__nonempty, axiom,
    ((![T4 : list_char > option_val, K : list_char, X : val]: (~ (((fun_up1252458416on_val @ T4 @ K @ (some_val @ X)) = (^[X3 : list_char]: none_val))))))). % map_upd_nonempty
thf(fact_179_map__upd__nonempty, axiom,
    ((![T4 : nat > option2118145160on_val, K : nat, X : produc266837688on_val]: (~ (((fun_up262443479on_val @ T4 @ K @ (some_P1299442195on_val @ X)) = (^[X3 : nat]: none_P1535574167on_val))))))). % map_upd_nonempty
thf(fact_180_hconfD, axiom,
    ((![P : list_P1234162913t_char, H2 : nat > option2118145160on_val, A : nat, Obj : produc266837688on_val]: ((hconf_1244167010t_char @ P @ H2) => (((H2 @ A) = (some_P1299442195on_val @ Obj)) => (oconf_454120169t_char @ P @ H2 @ Obj)))))). % hconfD
thf(fact_181_redp__redsp_OBlockRedSome, axiom,
    ((![P : list_P1234162913t_char, E3 : exp_list_char, H2 : nat > option2118145160on_val, L : list_char > option_val, V3 : list_char, E4 : exp_list_char, H3 : nat > option2118145160on_val, L3 : list_char > option_val, V2 : val, T : ty]: ((redp @ P @ E3 @ (produc52622304on_val @ H2 @ (fun_up1252458416on_val @ L @ V3 @ none_val)) @ E4 @ (produc52622304on_val @ H3 @ L3)) => (((L3 @ V3) = (some_val @ V2)) => ((~ ((assigned @ V3 @ E3))) => (redp @ P @ (block_list_char @ V3 @ T @ E3) @ (produc52622304on_val @ H2 @ L) @ (block_list_char @ V3 @ T @ (seq_list_char @ (lAss_list_char @ V3 @ (val_list_char @ V2)) @ E4)) @ (produc52622304on_val @ H3 @ (fun_up1252458416on_val @ L3 @ V3 @ (L @ V3)))))))))). % redp_redsp.BlockRedSome
thf(fact_182_oconf__fupd, axiom,
    ((![P : list_P1234162913t_char, C3 : list_char, F3 : list_char, T : ty, D3 : list_char, H2 : nat > option2118145160on_val, V2 : val, Fs : produc1257910179t_char > option_val]: ((has_fi599584195t_char @ P @ C3 @ F3 @ T @ D3) => ((conf_P93989998t_char @ P @ H2 @ V2 @ T) => ((oconf_454120169t_char @ P @ H2 @ (produc904988266on_val @ C3 @ Fs)) => (oconf_454120169t_char @ P @ H2 @ (produc904988266on_val @ C3 @ (fun_up356838326on_val @ Fs @ (produc1304532571t_char @ F3 @ D3) @ (some_val @ V2)))))))))). % oconf_fupd
thf(fact_183_redp__redsp_OInitBlockRed, axiom,
    ((![P : list_P1234162913t_char, E3 : exp_list_char, H2 : nat > option2118145160on_val, L : list_char > option_val, V3 : list_char, V2 : val, E4 : exp_list_char, H3 : nat > option2118145160on_val, L3 : list_char > option_val, V5 : val, T : ty]: ((redp @ P @ E3 @ (produc52622304on_val @ H2 @ (fun_up1252458416on_val @ L @ V3 @ (some_val @ V2))) @ E4 @ (produc52622304on_val @ H3 @ L3)) => (((L3 @ V3) = (some_val @ V5)) => (redp @ P @ (block_list_char @ V3 @ T @ (seq_list_char @ (lAss_list_char @ V3 @ (val_list_char @ V2)) @ E3)) @ (produc52622304on_val @ H2 @ L) @ (block_list_char @ V3 @ T @ (seq_list_char @ (lAss_list_char @ V3 @ (val_list_char @ V5)) @ E4)) @ (produc52622304on_val @ H3 @ (fun_up1252458416on_val @ L3 @ V3 @ (L @ V3))))))))). % redp_redsp.InitBlockRed
thf(fact_184_redp__redsp_OSeqRed, axiom,
    ((![P : list_P1234162913t_char, E3 : exp_list_char, S2 : produc515445032on_val, E4 : exp_list_char, S3 : produc515445032on_val, E_2 : exp_list_char]: ((redp @ P @ E3 @ S2 @ E4 @ S3) => (redp @ P @ (seq_list_char @ E3 @ E_2) @ S2 @ (seq_list_char @ E4 @ E_2) @ S3))))). % redp_redsp.SeqRed
thf(fact_185_redp__redsp_OLAssRed, axiom,
    ((![P : list_P1234162913t_char, E3 : exp_list_char, S2 : produc515445032on_val, E4 : exp_list_char, S3 : produc515445032on_val, V3 : list_char]: ((redp @ P @ E3 @ S2 @ E4 @ S3) => (redp @ P @ (lAss_list_char @ V3 @ E3) @ S2 @ (lAss_list_char @ V3 @ E4) @ S3))))). % redp_redsp.LAssRed
thf(fact_186_redp__redsp_ORedSeq, axiom,
    ((![P : list_P1234162913t_char, V2 : val, E_2 : exp_list_char, S2 : produc515445032on_val]: (redp @ P @ (seq_list_char @ (val_list_char @ V2) @ E_2) @ S2 @ E_2 @ S2)))). % redp_redsp.RedSeq
thf(fact_187_redp__redsp_ORedBlock, axiom,
    ((![P : list_P1234162913t_char, V3 : list_char, T : ty, U3 : val, S2 : produc515445032on_val]: (redp @ P @ (block_list_char @ V3 @ T @ (val_list_char @ U3)) @ S2 @ (val_list_char @ U3) @ S2)))). % redp_redsp.RedBlock
thf(fact_188_typeof__lit__typeof, axiom,
    ((![V2 : val, T : ty, H2 : nat > option2118145160on_val]: (((typeof_h @ (^[X3 : nat]: none_P1535574167on_val) @ V2) = (some_ty @ T)) => ((typeof_h @ H2 @ V2) = (some_ty @ T)))))). % typeof_lit_typeof
thf(fact_189_hext__new, axiom,
    ((![H2 : nat > option2118145160on_val, A : nat, X : produc266837688on_val]: (((H2 @ A) = none_P1535574167on_val) => (hext @ H2 @ (fun_up262443479on_val @ H2 @ A @ (some_P1299442195on_val @ X))))))). % hext_new
thf(fact_190_redp__red__eq, axiom,
    ((redp = (^[P2 : list_P1234162913t_char]: (^[X3 : exp_list_char]: (^[Y3 : produc515445032on_val]: (^[Z2 : exp_list_char]: (^[Aa : produc515445032on_val]: (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ X3 @ Y3) @ (produc2023458740on_val @ Z2 @ Aa)) @ (red @ P2)))))))))). % redp_red_eq
thf(fact_191_typeof__lit__conf, axiom,
    ((![V2 : val, T : ty, P : list_P1234162913t_char, H2 : nat > option2118145160on_val]: (((typeof_h @ (^[X3 : nat]: none_P1535574167on_val) @ V2) = (some_ty @ T)) => (conf_P93989998t_char @ P @ H2 @ V2 @ T))))). % typeof_lit_conf
thf(fact_192_redp__redsp_ORedInitBlock, axiom,
    ((![P : list_P1234162913t_char, V3 : list_char, T : ty, V2 : val, U3 : val, S2 : produc515445032on_val]: (redp @ P @ (block_list_char @ V3 @ T @ (seq_list_char @ (lAss_list_char @ V3 @ (val_list_char @ V2)) @ (val_list_char @ U3))) @ S2 @ (val_list_char @ U3) @ S2)))). % redp_redsp.RedInitBlock
thf(fact_193_hconf__new, axiom,
    ((![P : list_P1234162913t_char, H2 : nat > option2118145160on_val, A : nat, Obj : produc266837688on_val]: ((hconf_1244167010t_char @ P @ H2) => (((H2 @ A) = none_P1535574167on_val) => ((oconf_454120169t_char @ P @ H2 @ Obj) => (hconf_1244167010t_char @ P @ (fun_up262443479on_val @ H2 @ A @ (some_P1299442195on_val @ Obj))))))))). % hconf_new
thf(fact_194_redp__redsp_OBlockRedNone, axiom,
    ((![P : list_P1234162913t_char, E3 : exp_list_char, H2 : nat > option2118145160on_val, L : list_char > option_val, V3 : list_char, E4 : exp_list_char, H3 : nat > option2118145160on_val, L3 : list_char > option_val, T : ty]: ((redp @ P @ E3 @ (produc52622304on_val @ H2 @ (fun_up1252458416on_val @ L @ V3 @ none_val)) @ E4 @ (produc52622304on_val @ H3 @ L3)) => (((L3 @ V3) = none_val) => ((~ ((assigned @ V3 @ E3))) => (redp @ P @ (block_list_char @ V3 @ T @ E3) @ (produc52622304on_val @ H2 @ L) @ (block_list_char @ V3 @ T @ E4) @ (produc52622304on_val @ H3 @ (fun_up1252458416on_val @ L3 @ V3 @ (L @ V3)))))))))). % redp_redsp.BlockRedNone
thf(fact_195_redp__redsp_ORedLAss, axiom,
    ((![P : list_P1234162913t_char, V3 : list_char, V2 : val, H2 : nat > option2118145160on_val, L : list_char > option_val]: (redp @ P @ (lAss_list_char @ V3 @ (val_list_char @ V2)) @ (produc52622304on_val @ H2 @ L) @ (val_list_char @ unit) @ (produc52622304on_val @ H2 @ (fun_up1252458416on_val @ L @ V3 @ (some_val @ V2))))))). % redp_redsp.RedLAss
thf(fact_196_WTrt_H__WTrts_H_Ointros_I16_J, axiom,
    ((![H2 : nat > option2118145160on_val, V2 : val, T_12 : ty, P : list_P1234162913t_char, T : ty, E : list_char > option_ty, V3 : list_char, E_2 : exp_list_char, T_2 : ty]: (((typeof_h @ H2 @ V2) = (some_ty @ T_12)) => ((widen_917054840t_char @ P @ T_12 @ T) => ((wTrt @ P @ H2 @ (fun_up9191ion_ty @ E @ V3 @ (some_ty @ T)) @ E_2 @ T_2) => (wTrt @ P @ H2 @ E @ (block_list_char @ V3 @ T @ (seq_list_char @ (lAss_list_char @ V3 @ (val_list_char @ V2)) @ E_2)) @ T_2))))))). % WTrt'_WTrts'.intros(16)
thf(fact_197_LAssRedsVal, axiom,
    ((![E3 : exp_list_char, S2 : produc515445032on_val, V2 : val, H3 : nat > option2118145160on_val, L3 : list_char > option_val, P : list_P1234162913t_char, V3 : list_char]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E3 @ S2) @ (produc2023458740on_val @ (val_list_char @ V2) @ (produc52622304on_val @ H3 @ L3))) @ (transi111096263on_val @ (red @ P))) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (lAss_list_char @ V3 @ E3) @ S2) @ (produc2023458740on_val @ (val_list_char @ unit) @ (produc52622304on_val @ H3 @ (fun_up1252458416on_val @ L3 @ V3 @ (some_val @ V2))))) @ (transi111096263on_val @ (red @ P))))))). % LAssRedsVal
thf(fact_198_WTrt_H__WTrts_H_Ointros_I3_J, axiom,
    ((![H2 : nat > option2118145160on_val, V2 : val, T : ty, P : list_P1234162913t_char, E : list_char > option_ty]: (((typeof_h @ H2 @ V2) = (some_ty @ T)) => (wTrt @ P @ H2 @ E @ (val_list_char @ V2) @ T))))). % WTrt'_WTrts'.intros(3)
thf(fact_199_wt_H__iff__wt, axiom,
    ((wTrt = wTrt2))). % wt'_iff_wt
thf(fact_200_wt__wt_H, axiom,
    ((![P : list_P1234162913t_char, H2 : nat > option2118145160on_val, E : list_char > option_ty, E3 : exp_list_char, T : ty]: ((wTrt2 @ P @ H2 @ E @ E3 @ T) => (wTrt @ P @ H2 @ E @ E3 @ T))))). % wt_wt'
thf(fact_201_wt_H__wt, axiom,
    ((![P : list_P1234162913t_char, H2 : nat > option2118145160on_val, E : list_char > option_ty, E3 : exp_list_char, T : ty]: ((wTrt @ P @ H2 @ E @ E3 @ T) => (wTrt2 @ P @ H2 @ E @ E3 @ T))))). % wt'_wt
thf(fact_202_WTrt_H__WTrts_H_Ointros_I18_J, axiom,
    ((![P : list_P1234162913t_char, H2 : nat > option2118145160on_val, E : list_char > option_ty, E_1 : exp_list_char, T_12 : ty, E_2 : exp_list_char, T_2 : ty]: ((wTrt @ P @ H2 @ E @ E_1 @ T_12) => ((wTrt @ P @ H2 @ E @ E_2 @ T_2) => (wTrt @ P @ H2 @ E @ (seq_list_char @ E_1 @ E_2) @ T_2)))))). % WTrt'_WTrts'.intros(18)
thf(fact_203_SeqReds, axiom,
    ((![E3 : exp_list_char, S2 : produc515445032on_val, E4 : exp_list_char, S3 : produc515445032on_val, P : list_P1234162913t_char, E_2 : exp_list_char]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E3 @ S2) @ (produc2023458740on_val @ E4 @ S3)) @ (transi111096263on_val @ (red @ P))) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (seq_list_char @ E3 @ E_2) @ S2) @ (produc2023458740on_val @ (seq_list_char @ E4 @ E_2) @ S3)) @ (transi111096263on_val @ (red @ P))))))). % SeqReds
thf(fact_204_LAssReds, axiom,
    ((![E3 : exp_list_char, S2 : produc515445032on_val, E4 : exp_list_char, S3 : produc515445032on_val, P : list_P1234162913t_char, V3 : list_char]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E3 @ S2) @ (produc2023458740on_val @ E4 @ S3)) @ (transi111096263on_val @ (red @ P))) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (lAss_list_char @ V3 @ E3) @ S2) @ (produc2023458740on_val @ (lAss_list_char @ V3 @ E4) @ S3)) @ (transi111096263on_val @ (red @ P))))))). % LAssReds
thf(fact_205_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_206_WTrt_H__WTrts_H_Ointros_I17_J, axiom,
    ((![P : list_P1234162913t_char, H2 : nat > option2118145160on_val, E : list_char > option_ty, V3 : list_char, T : ty, E3 : exp_list_char, T5 : ty]: ((wTrt @ P @ H2 @ (fun_up9191ion_ty @ E @ V3 @ (some_ty @ T)) @ E3 @ T5) => ((~ ((assigned @ V3 @ E3))) => (wTrt @ P @ H2 @ E @ (block_list_char @ V3 @ T @ E3) @ T5)))))). % WTrt'_WTrts'.intros(17)
thf(fact_207_converse__rtrancl__induct__red, axiom,
    ((![E3 : exp_list_char, H2 : 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 @ H2 @ L)) @ (produc2023458740on_val @ E4 @ (produc52622304on_val @ H3 @ L3))) @ (transi111096263on_val @ (red @ P))) => ((![E7 : exp_list_char, H6 : nat > option2118145160on_val, L4 : list_char > option_val]: (R @ E7 @ H6 @ L4 @ E7 @ H6 @ L4)) => ((![E_0 : exp_list_char, H_0 : nat > option2118145160on_val, L_0 : list_char > option_val, E_12 : exp_list_char, H_1 : nat > option2118145160on_val, L_1 : list_char > option_val, E8 : exp_list_char, H7 : nat > option2118145160on_val, L5 : list_char > option_val]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E_0 @ (produc52622304on_val @ H_0 @ L_0)) @ (produc2023458740on_val @ E_12 @ (produc52622304on_val @ H_1 @ L_1))) @ (red @ P)) => ((R @ E_12 @ H_1 @ L_1 @ E8 @ H7 @ L5) => (R @ E_0 @ H_0 @ L_0 @ E8 @ H7 @ L5)))) => (R @ E3 @ H2 @ L @ E4 @ H3 @ L3))))))). % converse_rtrancl_induct_red
thf(fact_208_InitBlockRedsFinal, axiom,
    ((![E3 : exp_list_char, H2 : nat > option2118145160on_val, L : list_char > option_val, V3 : list_char, V2 : 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 @ H2 @ (fun_up1252458416on_val @ L @ V3 @ (some_val @ V2)))) @ (produc2023458740on_val @ E4 @ (produc52622304on_val @ H3 @ L3))) @ (transi111096263on_val @ (red @ P))) => ((final_list_char @ E4) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (block_list_char @ V3 @ T @ (seq_list_char @ (lAss_list_char @ V3 @ (val_list_char @ V2)) @ E3)) @ (produc52622304on_val @ H2 @ L)) @ (produc2023458740on_val @ E4 @ (produc52622304on_val @ H3 @ (fun_up1252458416on_val @ L3 @ V3 @ (L @ V3))))) @ (transi111096263on_val @ (red @ P)))))))). % InitBlockRedsFinal
thf(fact_209_InitBlockReds__aux, axiom,
    ((![E3 : exp_list_char, S2 : produc515445032on_val, E4 : exp_list_char, S3 : produc515445032on_val, P : list_P1234162913t_char, V3 : list_char, T : ty]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E3 @ S2) @ (produc2023458740on_val @ E4 @ S3)) @ (transi111096263on_val @ (red @ P))) => (![H8 : nat > option2118145160on_val, L6 : list_char > option_val, H9 : nat > option2118145160on_val, L7 : list_char > option_val, V6 : val]: ((S2 = (produc52622304on_val @ H8 @ (fun_up1252458416on_val @ L6 @ V3 @ (some_val @ V6)))) => ((S3 = (produc52622304on_val @ H9 @ L7)) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (block_list_char @ V3 @ T @ (seq_list_char @ (lAss_list_char @ V3 @ (val_list_char @ V6)) @ E3)) @ (produc52622304on_val @ H8 @ L6)) @ (produc2023458740on_val @ (block_list_char @ V3 @ T @ (seq_list_char @ (lAss_list_char @ V3 @ (val_list_char @ (the_val @ (L7 @ V3)))) @ E4)) @ (produc52622304on_val @ H9 @ (fun_up1252458416on_val @ L7 @ V3 @ (L6 @ V3))))) @ (transi111096263on_val @ (red @ P)))))))))). % InitBlockReds_aux

% 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,
    ((?[T_13 : ty]: (((typeof_h @ h_a @ v2) = (some_ty @ T_13)) & (widen_917054840t_char @ p @ T_13 @ t2))))).
