% 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_232__5336674_1 ) ; }
% This file was generated by Isabelle (most likely Sledgehammer)
% 2020-12-16 14:20:08.331

% Could-be-implicit typings (28)
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% Explicit typings (97)
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thf(sy_c_List_Olist_OCons_001t__Value__Oval, type,
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thf(sy_c_List_Olist_Olist__all2_001t__Value__Oval_001t__Type__Oty, type,
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thf(sy_c_List_Olist_Omap_001t__List__Olist_It__String__Ochar_J_001t__Option__Ooption_It__Type__Oty_J, type,
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thf(sy_c_List_Olist_Omap_001t__List__Olist_It__String__Ochar_J_001t__Value__Oval, type,
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thf(sy_c_List_Olist_Omap_001t__Type__Oty_001t__List__Olist_It__String__Ochar_J, type,
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thf(sy_c_List_Olist_Omap_001t__Type__Oty_001t__Value__Oval, type,
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thf(sy_c_List_Olist_Omap_001t__Value__Oval_001t__Value__Oval, type,
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thf(sy_c_Map_Omap__upds_001t__List__Olist_It__String__Ochar_J_001t__Type__Oty, type,
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thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_J, type,
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thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__List__Olist_It__String__Ochar_J_J, type,
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thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Value__Oval_J, type,
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thf(sy_c_Objects_Otypeof__h, type,
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thf(sy_c_Product__Type_OPair_001t__List__Olist_It__String__Ochar_J_001t__List__Olist_It__String__Ochar_J, type,
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thf(sy_c_Product__Type_OPair_001t__List__Olist_It__String__Ochar_J_001t__Product____Type__Oprod_It__List__Olist_It__Type__Oty_J_Mt__Product____Type__Oprod_It__Type__Oty_Mt__Product____Type__Oprod_It__List__Olist_It__List__Olist_It__String__Ochar_J_J_Mt__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_J_J_J, type,
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    produc1806338192t_char : list_ty > produc1109669680t_char > produc111478616t_char).
thf(sy_c_Product__Type_OPair_001t__List__Olist_It__Type__Oty_J_001t__Product____Type__Oprod_It__Type__Oty_Mt__Product____Type__Oprod_It__List__Olist_It__List__Olist_It__String__Ochar_J_J_Mt__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_J_J, type,
    produc1730359111t_char : list_ty > produc1490933927t_char > produc1451990293t_char).
thf(sy_c_Product__Type_OPair_001t__List__Olist_It__Value__Oval_J_001t__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J, type,
    produc823987298t_char : list_val > exp_list_char > produc1109669680t_char).
thf(sy_c_Product__Type_OPair_001t__Product____Type__Oprod_It__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_Mt__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_M_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_001t__Product____Type__Oprod_It__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_Mt__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_M_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J, type,
    produc1069526295on_val : produc1097884484on_val > produc1097884484on_val > produc1172664615on_val).
thf(sy_c_Product__Type_OPair_001t__Type__Oty_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,
    produc248075743t_char : ty > produc1294284815t_char > produc1490933927t_char).
thf(sy_c_Set_OCollect_001t__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J, type,
    collec768236686t_char : (produc1257910179t_char > $o) > set_Pr164112643t_char).
thf(sy_c_Set_OCollect_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_Mt__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_M_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_Mt__Product____Type__Oprod_It__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_Mt__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_M_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J, type,
    collec2055896722on_val : (produc1172664615on_val > $o) > set_Pr1189492743on_val).
thf(sy_c_SmallStep_Oblocks, type,
    blocks : produc81045532t_char > exp_list_char).
thf(sy_c_SmallStep_Ored, type,
    red : list_P1234162913t_char > set_Pr1189492743on_val).
thf(sy_c_SmallStep_Oredp, type,
    redp : list_P1234162913t_char > exp_list_char > produc515445032on_val > exp_list_char > produc515445032on_val > $o).
thf(sy_c_State_Ohp, type,
    hp : produc515445032on_val > nat > option2118145160on_val).
thf(sy_c_Transitive__Closure_Ortrancl_001t__List__Olist_It__String__Ochar_J, type,
    transi1879726366t_char : set_Pr164112643t_char > set_Pr164112643t_char).
thf(sy_c_Transitive__Closure_Ortrancl_001t__Product____Type__Oprod_It__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_Mt__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_M_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J, type,
    transi111096263on_val : set_Pr1189492743on_val > set_Pr1189492743on_val).
thf(sy_c_TypeRel_OMethod_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,
    method297381284t_char : list_P1234162913t_char > list_char > list_char > list_ty > ty > produc1294284815t_char > list_char > $o).
thf(sy_c_TypeRel_Osubcls1_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,
    subcls880436836t_char : list_P1234162913t_char > set_Pr164112643t_char).
thf(sy_c_TypeRel_Owiden_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,
    widen_917054840t_char : list_P1234162913t_char > ty > ty > $o).
thf(sy_c_TypeSafe__Mirabelle__osrwgqrerx_Osconf, type,
    typeSa1777264139_sconf : list_P1234162913t_char > (list_char > option_ty) > produc515445032on_val > $o).
thf(sy_c_Type_Othis, type,
    this : list_char).
thf(sy_c_Type_Oty_OClass, type,
    class : list_char > ty).
thf(sy_c_Value_Oval_OAddr, type,
    addr : nat > val).
thf(sy_c_WellForm_Owf__mdecl_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,
    wf_mde297024346t_char : (list_P1234162913t_char > list_char > produc1259892823t_char > $o) > list_P1234162913t_char > list_char > produc1259892823t_char > $o).
thf(sy_c_WellForm_Owf__prog_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,
    wf_pro1229751607t_char : (list_P1234162913t_char > list_char > produc1259892823t_char > $o) > list_P1234162913t_char > $o).
thf(sy_c_WellTypeRT_OWTrt, type,
    wTrt : list_P1234162913t_char > (nat > option2118145160on_val) > (list_char > option_ty) > exp_list_char > ty > $o).
thf(sy_c_WellTypeRT_OWTrts, type,
    wTrts : list_P1234162913t_char > (nat > option2118145160on_val) > (list_char > option_ty) > list_exp_list_char > list_ty > $o).
thf(sy_c_WellType_OWT, type,
    wt : list_P1234162913t_char > (list_char > option_ty) > exp_list_char > ty > $o).
thf(sy_c_WellType_OWTs, type,
    wTs : list_P1234162913t_char > (list_char > option_ty) > list_exp_list_char > list_ty > $o).
thf(sy_c_member_001t__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J, type,
    member89690956t_char : produc1257910179t_char > set_Pr164112643t_char > $o).
thf(sy_c_member_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_Mt__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_M_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_Mt__Product____Type__Oprod_It__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_Mt__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_M_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J, type,
    member354538064on_val : produc1172664615on_val > set_Pr1189492743on_val > $o).
thf(sy_v_C____, type,
    c : list_char).
thf(sy_v_D____, type,
    d : list_char).
thf(sy_v_E____, type,
    e : list_char > option_ty).
thf(sy_v_M____, type,
    m : list_char).
thf(sy_v_P, type,
    p : list_P1234162913t_char).
thf(sy_v_T_H_H____, type,
    t : ty).
thf(sy_v_T_H____, type,
    t2 : ty).
thf(sy_v_T____, type,
    t3 : ty).
thf(sy_v_Ts_H____, type,
    ts : list_ty).
thf(sy_v_Ts____, type,
    ts2 : list_ty).
thf(sy_v_a____, type,
    a : nat).
thf(sy_v_body____, type,
    body : exp_list_char).
thf(sy_v_fs____, type,
    fs : produc1257910179t_char > option_val).
thf(sy_v_ha____, type,
    ha : nat > option2118145160on_val).
thf(sy_v_la____, type,
    la : list_char > option_val).
thf(sy_v_pns____, type,
    pns : list_list_char).
thf(sy_v_vs____, type,
    vs : list_val).

% Relevant facts (249)
thf(fact_0_length__pns, axiom,
    (((size_s2008079621t_char @ pns) = (size_size_list_ty @ ts2)))). % length_pns
thf(fact_1_length__vs, axiom,
    (((size_size_list_val @ vs) = (size_size_list_ty @ ts2)))). % length_vs
thf(fact_2_subs, axiom,
    ((list_all2_ty_ty @ (widen_917054840t_char @ p) @ ts @ ts2))). % subs
thf(fact_3__092_060open_062P_A_092_060turnstile_062_AC_A_092_060preceq_062_092_060_094sup_062_K_AD_092_060close_062, axiom,
    ((member89690956t_char @ (produc1304532571t_char @ c @ d) @ (transi1879726366t_char @ (subcls880436836t_char @ p))))). % \<open>P \<turnstile> C \<preceq>\<^sup>* D\<close>
thf(fact_4_RedCall_Ohyps_I3_J, axiom,
    (((size_size_list_val @ vs) = (size_s2008079621t_char @ pns)))). % RedCall.hyps(3)
thf(fact_5_wtes, axiom,
    ((wTrts @ p @ ha @ e @ (map_va1515327237t_char @ val_list_char @ vs) @ ts))). % wtes
thf(fact_6_hp, axiom,
    (((hp @ (produc52622304on_val @ ha @ la) @ a) = (some_P1299442195on_val @ (produc904988266on_val @ c @ fs))))). % hp
thf(fact_7__092_060open_062P_ME_Ithis_A_D_Apns_A_091_092_060mapsto_062_093_AClass_AD_A_D_ATs_J_Mh_A_092_060turnstile_062_Abody_A_058_AT_H_H_092_060close_062, axiom,
    ((wTrt @ p @ ha @ (map_up703499792har_ty @ e @ (cons_list_char @ this @ pns) @ (cons_ty @ (class @ d) @ ts2)) @ body @ t))). % \<open>P,E(this # pns [\<mapsto>] Class D # Ts),h \<turnstile> body : T''\<close>
thf(fact_8_T_H_HsubT, axiom,
    ((widen_917054840t_char @ p @ t @ t3))). % T''subT
thf(fact_9_prod__cases4, axiom,
    ((![Y : produc1451990293t_char]: (~ ((![A : list_ty, B : ty, C : list_list_char, D : exp_list_char]: (~ ((Y = (produc1730359111t_char @ A @ (produc248075743t_char @ B @ (produc713467969t_char @ C @ D)))))))))))). % prod_cases4
thf(fact_10_prod__induct4, axiom,
    ((![P : produc1451990293t_char > $o, X : produc1451990293t_char]: ((![A : list_ty, B : ty, C : list_list_char, D : exp_list_char]: (P @ (produc1730359111t_char @ A @ (produc248075743t_char @ B @ (produc713467969t_char @ C @ D))))) => (P @ X))))). % prod_induct4
thf(fact_11_ty_Oinject, axiom,
    ((![X5 : list_char, Y5 : list_char]: (((class @ X5) = (class @ Y5)) = (X5 = Y5))))). % ty.inject
thf(fact_12_val_Oinject_I3_J, axiom,
    ((![X5 : nat, Y5 : nat]: (((addr @ X5) = (addr @ Y5)) = (X5 = Y5))))). % val.inject(3)
thf(fact_13_list_Oinject, axiom,
    ((![X21 : list_char, X22 : list_list_char, Y21 : list_char, Y22 : list_list_char]: (((cons_list_char @ X21 @ X22) = (cons_list_char @ Y21 @ Y22)) = (((X21 = Y21)) & ((X22 = Y22))))))). % list.inject
thf(fact_14_list_Oinject, axiom,
    ((![X21 : ty, X22 : list_ty, Y21 : ty, Y22 : list_ty]: (((cons_ty @ X21 @ X22) = (cons_ty @ Y21 @ Y22)) = (((X21 = Y21)) & ((X22 = Y22))))))). % list.inject
thf(fact_15_list_Oinject, axiom,
    ((![X21 : val, X22 : list_val, Y21 : val, Y22 : list_val]: (((cons_val @ X21 @ X22) = (cons_val @ Y21 @ Y22)) = (((X21 = Y21)) & ((X22 = Y22))))))). % list.inject
thf(fact_16_list_Oinject, axiom,
    ((![X21 : exp_list_char, X22 : list_exp_list_char, Y21 : exp_list_char, Y22 : list_exp_list_char]: (((cons_exp_list_char @ X21 @ X22) = (cons_exp_list_char @ Y21 @ Y22)) = (((X21 = Y21)) & ((X22 = Y22))))))). % list.inject
thf(fact_17_prod_Oinject, axiom,
    ((![X1 : list_ty, X2 : produc1109669680t_char, Y1 : list_ty, Y2 : produc1109669680t_char]: (((produc1806338192t_char @ X1 @ X2) = (produc1806338192t_char @ Y1 @ Y2)) = (((X1 = Y1)) & ((X2 = Y2))))))). % prod.inject
thf(fact_18_prod_Oinject, axiom,
    ((![X1 : list_ty, X2 : produc1490933927t_char, Y1 : list_ty, Y2 : produc1490933927t_char]: (((produc1730359111t_char @ X1 @ X2) = (produc1730359111t_char @ Y1 @ Y2)) = (((X1 = Y1)) & ((X2 = Y2))))))). % prod.inject
thf(fact_19_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_20_prod_Oinject, axiom,
    ((![X1 : ty, X2 : produc1294284815t_char, Y1 : ty, Y2 : produc1294284815t_char]: (((produc248075743t_char @ X1 @ X2) = (produc248075743t_char @ Y1 @ Y2)) = (((X1 = Y1)) & ((X2 = Y2))))))). % prod.inject
thf(fact_21_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_22_prod_Oinject, axiom,
    ((![X1 : list_list_char, X2 : exp_list_char, Y1 : list_list_char, Y2 : exp_list_char]: (((produc713467969t_char @ X1 @ X2) = (produc713467969t_char @ Y1 @ Y2)) = (((X1 = Y1)) & ((X2 = Y2))))))). % prod.inject
thf(fact_23_T_HisT, axiom,
    ((t2 = t3))). % T'isT
thf(fact_24_old_Oprod_Oinject, axiom,
    ((![A2 : list_ty, B2 : produc1109669680t_char, A3 : list_ty, B3 : produc1109669680t_char]: (((produc1806338192t_char @ A2 @ B2) = (produc1806338192t_char @ A3 @ B3)) = (((A2 = A3)) & ((B2 = B3))))))). % old.prod.inject
thf(fact_25_old_Oprod_Oinject, axiom,
    ((![A2 : list_ty, B2 : produc1490933927t_char, A3 : list_ty, B3 : produc1490933927t_char]: (((produc1730359111t_char @ A2 @ B2) = (produc1730359111t_char @ A3 @ B3)) = (((A2 = A3)) & ((B2 = B3))))))). % old.prod.inject
thf(fact_26_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_27_old_Oprod_Oinject, axiom,
    ((![A2 : ty, B2 : produc1294284815t_char, A3 : ty, B3 : produc1294284815t_char]: (((produc248075743t_char @ A2 @ B2) = (produc248075743t_char @ A3 @ B3)) = (((A2 = A3)) & ((B2 = B3))))))). % old.prod.inject
thf(fact_28_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_29_old_Oprod_Oinject, axiom,
    ((![A2 : list_list_char, B2 : exp_list_char, A3 : list_list_char, B3 : exp_list_char]: (((produc713467969t_char @ A2 @ B2) = (produc713467969t_char @ A3 @ B3)) = (((A2 = A3)) & ((B2 = B3))))))). % old.prod.inject
thf(fact_30_Cons__eq__map__conv, axiom,
    ((![X : ty, Xs : list_ty, F : ty > ty, Ys : list_ty]: (((cons_ty @ X @ Xs) = (map_ty_ty @ F @ Ys)) = (?[Z : ty]: (?[Zs : list_ty]: (((Ys = (cons_ty @ Z @ Zs))) & ((((X = (F @ Z))) & ((Xs = (map_ty_ty @ F @ Zs)))))))))))). % Cons_eq_map_conv
thf(fact_31_Cons__eq__map__conv, axiom,
    ((![X : ty, Xs : list_ty, F : val > ty, Ys : list_val]: (((cons_ty @ X @ Xs) = (map_val_ty @ F @ Ys)) = (?[Z : val]: (?[Zs : list_val]: (((Ys = (cons_val @ Z @ Zs))) & ((((X = (F @ Z))) & ((Xs = (map_val_ty @ F @ Zs)))))))))))). % Cons_eq_map_conv
thf(fact_32_Cons__eq__map__conv, axiom,
    ((![X : val, Xs : list_val, F : ty > val, Ys : list_ty]: (((cons_val @ X @ Xs) = (map_ty_val @ F @ Ys)) = (?[Z : ty]: (?[Zs : list_ty]: (((Ys = (cons_ty @ Z @ Zs))) & ((((X = (F @ Z))) & ((Xs = (map_ty_val @ F @ Zs)))))))))))). % Cons_eq_map_conv
thf(fact_33_Cons__eq__map__conv, axiom,
    ((![X : val, Xs : list_val, F : val > val, Ys : list_val]: (((cons_val @ X @ Xs) = (map_val_val @ F @ Ys)) = (?[Z : val]: (?[Zs : list_val]: (((Ys = (cons_val @ Z @ Zs))) & ((((X = (F @ Z))) & ((Xs = (map_val_val @ F @ Zs)))))))))))). % Cons_eq_map_conv
thf(fact_34_Cons__eq__map__conv, axiom,
    ((![X : option_ty, Xs : list_option_ty, F : ty > option_ty, Ys : list_ty]: (((cons_option_ty @ X @ Xs) = (map_ty_option_ty @ F @ Ys)) = (?[Z : ty]: (?[Zs : list_ty]: (((Ys = (cons_ty @ Z @ Zs))) & ((((X = (F @ Z))) & ((Xs = (map_ty_option_ty @ F @ Zs)))))))))))). % Cons_eq_map_conv
thf(fact_35_Cons__eq__map__conv, axiom,
    ((![X : option_ty, Xs : list_option_ty, F : val > option_ty, Ys : list_val]: (((cons_option_ty @ X @ Xs) = (map_val_option_ty @ F @ Ys)) = (?[Z : val]: (?[Zs : list_val]: (((Ys = (cons_val @ Z @ Zs))) & ((((X = (F @ Z))) & ((Xs = (map_val_option_ty @ F @ Zs)))))))))))). % Cons_eq_map_conv
thf(fact_36_Cons__eq__map__conv, axiom,
    ((![X : list_char, Xs : list_list_char, F : ty > list_char, Ys : list_ty]: (((cons_list_char @ X @ Xs) = (map_ty_list_char @ F @ Ys)) = (?[Z : ty]: (?[Zs : list_ty]: (((Ys = (cons_ty @ Z @ Zs))) & ((((X = (F @ Z))) & ((Xs = (map_ty_list_char @ F @ Zs)))))))))))). % Cons_eq_map_conv
thf(fact_37_Cons__eq__map__conv, axiom,
    ((![X : list_char, Xs : list_list_char, F : val > list_char, Ys : list_val]: (((cons_list_char @ X @ Xs) = (map_val_list_char @ F @ Ys)) = (?[Z : val]: (?[Zs : list_val]: (((Ys = (cons_val @ Z @ Zs))) & ((((X = (F @ Z))) & ((Xs = (map_val_list_char @ F @ Zs)))))))))))). % Cons_eq_map_conv
thf(fact_38_Cons__eq__map__conv, axiom,
    ((![X : ty, Xs : list_ty, F : list_char > ty, Ys : list_list_char]: (((cons_ty @ X @ Xs) = (map_list_char_ty @ F @ Ys)) = (?[Z : list_char]: (?[Zs : list_list_char]: (((Ys = (cons_list_char @ Z @ Zs))) & ((((X = (F @ Z))) & ((Xs = (map_list_char_ty @ F @ Zs)))))))))))). % Cons_eq_map_conv
thf(fact_39_Cons__eq__map__conv, axiom,
    ((![X : val, Xs : list_val, F : list_char > val, Ys : list_list_char]: (((cons_val @ X @ Xs) = (map_list_char_val @ F @ Ys)) = (?[Z : list_char]: (?[Zs : list_list_char]: (((Ys = (cons_list_char @ Z @ Zs))) & ((((X = (F @ Z))) & ((Xs = (map_list_char_val @ F @ Zs)))))))))))). % Cons_eq_map_conv
thf(fact_40_length__map, axiom,
    ((![F : ty > ty, Xs : list_ty]: ((size_size_list_ty @ (map_ty_ty @ F @ Xs)) = (size_size_list_ty @ Xs))))). % length_map
thf(fact_41_length__map, axiom,
    ((![F : val > ty, Xs : list_val]: ((size_size_list_ty @ (map_val_ty @ F @ Xs)) = (size_size_list_val @ Xs))))). % length_map
thf(fact_42_length__map, axiom,
    ((![F : ty > val, Xs : list_ty]: ((size_size_list_val @ (map_ty_val @ F @ Xs)) = (size_size_list_ty @ Xs))))). % length_map
thf(fact_43_length__map, axiom,
    ((![F : val > val, Xs : list_val]: ((size_size_list_val @ (map_val_val @ F @ Xs)) = (size_size_list_val @ Xs))))). % length_map
thf(fact_44_length__map, axiom,
    ((![F : ty > option_ty, Xs : list_ty]: ((size_s1569909163ion_ty @ (map_ty_option_ty @ F @ Xs)) = (size_size_list_ty @ Xs))))). % length_map
thf(fact_45_length__map, axiom,
    ((![F : val > option_ty, Xs : list_val]: ((size_s1569909163ion_ty @ (map_val_option_ty @ F @ Xs)) = (size_size_list_val @ Xs))))). % length_map
thf(fact_46_length__map, axiom,
    ((![F : ty > list_char, Xs : list_ty]: ((size_s2008079621t_char @ (map_ty_list_char @ F @ Xs)) = (size_size_list_ty @ Xs))))). % length_map
thf(fact_47_length__map, axiom,
    ((![F : val > list_char, Xs : list_val]: ((size_s2008079621t_char @ (map_val_list_char @ F @ Xs)) = (size_size_list_val @ Xs))))). % length_map
thf(fact_48_length__map, axiom,
    ((![F : list_char > ty, Xs : list_list_char]: ((size_size_list_ty @ (map_list_char_ty @ F @ Xs)) = (size_s2008079621t_char @ Xs))))). % length_map
thf(fact_49_length__map, axiom,
    ((![F : list_char > val, Xs : list_list_char]: ((size_size_list_val @ (map_list_char_val @ F @ Xs)) = (size_s2008079621t_char @ Xs))))). % length_map
thf(fact_50__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062Ts_H_O_A_092_060lbrakk_062P_ME_Mh_A_092_060turnstile_062_Amap_AVal_Avs_A_091_058_093_ATs_H_059_AP_A_092_060turnstile_062_ATs_H_A_091_092_060le_062_093_ATs_059_AT_H_A_061_AT_092_060rbrakk_062_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062, axiom,
    ((~ ((![Ts : list_ty]: ((wTrts @ p @ ha @ e @ (map_va1515327237t_char @ val_list_char @ vs) @ Ts) => ((list_all2_ty_ty @ (widen_917054840t_char @ p) @ Ts @ ts2) => (~ ((t2 = t3)))))))))). % \<open>\<And>thesis. (\<And>Ts'. \<lbrakk>P,E,h \<turnstile> map Val vs [:] Ts'; P \<turnstile> Ts' [\<le>] Ts; T' = T\<rbrakk> \<Longrightarrow> thesis) \<Longrightarrow> thesis\<close>
thf(fact_51_list__all2__eq, axiom,
    (((^[Y3 : list_ty]: (^[Z2 : list_ty]: (Y3 = Z2))) = (list_all2_ty_ty @ (^[Y3 : ty]: (^[Z2 : ty]: (Y3 = Z2))))))). % list_all2_eq
thf(fact_52_list__all2__mono, axiom,
    ((![P : ty > ty > $o, Xs : list_ty, Ys : list_ty, Q : ty > ty > $o]: ((list_all2_ty_ty @ P @ Xs @ Ys) => ((![Xs2 : ty, Ys2 : ty]: ((P @ Xs2 @ Ys2) => (Q @ Xs2 @ Ys2))) => (list_all2_ty_ty @ Q @ Xs @ Ys)))))). % list_all2_mono
thf(fact_53_list__all2__refl, axiom,
    ((![P : ty > ty > $o, Xs : list_ty]: ((![X3 : ty]: (P @ X3 @ X3)) => (list_all2_ty_ty @ P @ Xs @ Xs))))). % list_all2_refl
thf(fact_54_list__all2__trans, axiom,
    ((![P1 : ty > ty > $o, P2 : ty > ty > $o, P3 : ty > ty > $o, As : list_ty, Bs : list_ty, Cs : list_ty]: ((![A : ty, B : ty, C : ty]: ((P1 @ A @ B) => ((P2 @ B @ C) => (P3 @ A @ C)))) => ((list_all2_ty_ty @ P1 @ As @ Bs) => ((list_all2_ty_ty @ P2 @ Bs @ Cs) => (list_all2_ty_ty @ P3 @ As @ Cs))))))). % list_all2_trans
thf(fact_55_list_Orel__eq, axiom,
    (((list_all2_ty_ty @ (^[Y3 : ty]: (^[Z2 : ty]: (Y3 = Z2)))) = (^[Y3 : list_ty]: (^[Z2 : list_ty]: (Y3 = Z2)))))). % list.rel_eq
thf(fact_56_Ex__list__of__length, axiom,
    ((![N : nat]: (?[Xs2 : list_list_char]: ((size_s2008079621t_char @ Xs2) = N))))). % Ex_list_of_length
thf(fact_57_Ex__list__of__length, axiom,
    ((![N : nat]: (?[Xs2 : list_ty]: ((size_size_list_ty @ Xs2) = N))))). % Ex_list_of_length
thf(fact_58_Ex__list__of__length, axiom,
    ((![N : nat]: (?[Xs2 : list_val]: ((size_size_list_val @ Xs2) = N))))). % Ex_list_of_length
thf(fact_59_Ex__list__of__length, axiom,
    ((![N : nat]: (?[Xs2 : list_exp_list_char]: ((size_s329991613t_char @ Xs2) = N))))). % Ex_list_of_length
thf(fact_60_list__all2__antisym, axiom,
    ((![P : ty > ty > $o, Q : ty > ty > $o, Xs : list_ty, Ys : list_ty]: ((![X3 : ty, Y4 : ty]: ((P @ X3 @ Y4) => ((Q @ Y4 @ X3) => (X3 = Y4)))) => ((list_all2_ty_ty @ P @ Xs @ Ys) => ((list_all2_ty_ty @ Q @ Ys @ Xs) => (Xs = Ys))))))). % list_all2_antisym
thf(fact_61_list__all2__lengthD, axiom,
    ((![P : ty > ty > $o, Xs : list_ty, Ys : list_ty]: ((list_all2_ty_ty @ P @ Xs @ Ys) => ((size_size_list_ty @ Xs) = (size_size_list_ty @ Ys)))))). % list_all2_lengthD
thf(fact_62_list__all2__lengthD, axiom,
    ((![P : ty > val > $o, Xs : list_ty, Ys : list_val]: ((list_all2_ty_val @ P @ Xs @ Ys) => ((size_size_list_ty @ Xs) = (size_size_list_val @ Ys)))))). % list_all2_lengthD
thf(fact_63_list__all2__lengthD, axiom,
    ((![P : val > ty > $o, Xs : list_val, Ys : list_ty]: ((list_all2_val_ty @ P @ Xs @ Ys) => ((size_size_list_val @ Xs) = (size_size_list_ty @ Ys)))))). % list_all2_lengthD
thf(fact_64_list__all2__lengthD, axiom,
    ((![P : val > val > $o, Xs : list_val, Ys : list_val]: ((list_all2_val_val @ P @ Xs @ Ys) => ((size_size_list_val @ Xs) = (size_size_list_val @ Ys)))))). % list_all2_lengthD
thf(fact_65_list__all2__lengthD, axiom,
    ((![P : list_char > ty > $o, Xs : list_list_char, Ys : list_ty]: ((list_a1770748705har_ty @ P @ Xs @ Ys) => ((size_s2008079621t_char @ Xs) = (size_size_list_ty @ Ys)))))). % list_all2_lengthD
thf(fact_66_list__all2__lengthD, axiom,
    ((![P : list_char > val > $o, Xs : list_list_char, Ys : list_val]: ((list_a280217834ar_val @ P @ Xs @ Ys) => ((size_s2008079621t_char @ Xs) = (size_size_list_val @ Ys)))))). % list_all2_lengthD
thf(fact_67_list__all2__lengthD, axiom,
    ((![P : ty > list_char > $o, Xs : list_ty, Ys : list_list_char]: ((list_a1504214817t_char @ P @ Xs @ Ys) => ((size_size_list_ty @ Xs) = (size_s2008079621t_char @ Ys)))))). % list_all2_lengthD
thf(fact_68_list__all2__lengthD, axiom,
    ((![P : val > list_char > $o, Xs : list_val, Ys : list_list_char]: ((list_a1248766058t_char @ P @ Xs @ Ys) => ((size_size_list_val @ Xs) = (size_s2008079621t_char @ Ys)))))). % list_all2_lengthD
thf(fact_69_list__all2__lengthD, axiom,
    ((![P : list_char > list_char > $o, Xs : list_list_char, Ys : list_list_char]: ((list_a2051666507t_char @ P @ Xs @ Ys) => ((size_s2008079621t_char @ Xs) = (size_s2008079621t_char @ Ys)))))). % list_all2_lengthD
thf(fact_70_list__all2__lengthD, axiom,
    ((![P : ty > exp_list_char > $o, Xs : list_ty, Ys : list_exp_list_char]: ((list_a212154379t_char @ P @ Xs @ Ys) => ((size_size_list_ty @ Xs) = (size_s329991613t_char @ Ys)))))). % list_all2_lengthD
thf(fact_71_neq__if__length__neq, axiom,
    ((![Xs : list_list_char, Ys : list_list_char]: ((~ (((size_s2008079621t_char @ Xs) = (size_s2008079621t_char @ Ys)))) => (~ ((Xs = Ys))))))). % neq_if_length_neq
thf(fact_72_neq__if__length__neq, axiom,
    ((![Xs : list_ty, Ys : list_ty]: ((~ (((size_size_list_ty @ Xs) = (size_size_list_ty @ Ys)))) => (~ ((Xs = Ys))))))). % neq_if_length_neq
thf(fact_73_neq__if__length__neq, axiom,
    ((![Xs : list_val, Ys : list_val]: ((~ (((size_size_list_val @ Xs) = (size_size_list_val @ Ys)))) => (~ ((Xs = Ys))))))). % neq_if_length_neq
thf(fact_74_neq__if__length__neq, axiom,
    ((![Xs : list_exp_list_char, Ys : list_exp_list_char]: ((~ (((size_s329991613t_char @ Xs) = (size_s329991613t_char @ Ys)))) => (~ ((Xs = Ys))))))). % neq_if_length_neq
thf(fact_75_list_Orel__refl, axiom,
    ((![Ra : ty > ty > $o, X : list_ty]: ((![X3 : ty]: (Ra @ X3 @ X3)) => (list_all2_ty_ty @ Ra @ X @ X))))). % list.rel_refl
thf(fact_76_map__eq__imp__length__eq, axiom,
    ((![F : ty > option_ty, Xs : list_ty, G : ty > option_ty, Ys : list_ty]: (((map_ty_option_ty @ F @ Xs) = (map_ty_option_ty @ G @ Ys)) => ((size_size_list_ty @ Xs) = (size_size_list_ty @ Ys)))))). % map_eq_imp_length_eq
thf(fact_77_map__eq__imp__length__eq, axiom,
    ((![F : ty > option_ty, Xs : list_ty, G : val > option_ty, Ys : list_val]: (((map_ty_option_ty @ F @ Xs) = (map_val_option_ty @ G @ Ys)) => ((size_size_list_ty @ Xs) = (size_size_list_val @ Ys)))))). % map_eq_imp_length_eq
thf(fact_78_map__eq__imp__length__eq, axiom,
    ((![F : val > option_ty, Xs : list_val, G : ty > option_ty, Ys : list_ty]: (((map_val_option_ty @ F @ Xs) = (map_ty_option_ty @ G @ Ys)) => ((size_size_list_val @ Xs) = (size_size_list_ty @ Ys)))))). % map_eq_imp_length_eq
thf(fact_79_map__eq__imp__length__eq, axiom,
    ((![F : val > option_ty, Xs : list_val, G : val > option_ty, Ys : list_val]: (((map_val_option_ty @ F @ Xs) = (map_val_option_ty @ G @ Ys)) => ((size_size_list_val @ Xs) = (size_size_list_val @ Ys)))))). % map_eq_imp_length_eq
thf(fact_80_map__eq__imp__length__eq, axiom,
    ((![F : list_char > option_ty, Xs : list_list_char, G : ty > option_ty, Ys : list_ty]: (((map_li427973166ion_ty @ F @ Xs) = (map_ty_option_ty @ G @ Ys)) => ((size_s2008079621t_char @ Xs) = (size_size_list_ty @ Ys)))))). % map_eq_imp_length_eq
thf(fact_81_map__eq__imp__length__eq, axiom,
    ((![F : list_char > option_ty, Xs : list_list_char, G : val > option_ty, Ys : list_val]: (((map_li427973166ion_ty @ F @ Xs) = (map_val_option_ty @ G @ Ys)) => ((size_s2008079621t_char @ Xs) = (size_size_list_val @ Ys)))))). % map_eq_imp_length_eq
thf(fact_82_map__eq__imp__length__eq, axiom,
    ((![F : ty > option_ty, Xs : list_ty, G : list_char > option_ty, Ys : list_list_char]: (((map_ty_option_ty @ F @ Xs) = (map_li427973166ion_ty @ G @ Ys)) => ((size_size_list_ty @ Xs) = (size_s2008079621t_char @ Ys)))))). % map_eq_imp_length_eq
thf(fact_83_map__eq__imp__length__eq, axiom,
    ((![F : ty > exp_list_char, Xs : list_ty, G : val > exp_list_char, Ys : list_val]: (((map_ty_exp_list_char @ F @ Xs) = (map_va1515327237t_char @ G @ Ys)) => ((size_size_list_ty @ Xs) = (size_size_list_val @ Ys)))))). % map_eq_imp_length_eq
thf(fact_84_map__eq__imp__length__eq, axiom,
    ((![F : val > option_ty, Xs : list_val, G : list_char > option_ty, Ys : list_list_char]: (((map_val_option_ty @ F @ Xs) = (map_li427973166ion_ty @ G @ Ys)) => ((size_size_list_val @ Xs) = (size_s2008079621t_char @ Ys)))))). % map_eq_imp_length_eq
thf(fact_85_map__eq__imp__length__eq, axiom,
    ((![F : val > exp_list_char, Xs : list_val, G : ty > exp_list_char, Ys : list_ty]: (((map_va1515327237t_char @ F @ Xs) = (map_ty_exp_list_char @ G @ Ys)) => ((size_size_list_val @ Xs) = (size_size_list_ty @ Ys)))))). % map_eq_imp_length_eq
thf(fact_86_list__all2__Cons2, axiom,
    ((![P : val > ty > $o, Xs : list_val, Y : ty, Ys : list_ty]: ((list_all2_val_ty @ P @ Xs @ (cons_ty @ Y @ Ys)) = (?[Z : val]: (?[Zs : list_val]: (((Xs = (cons_val @ Z @ Zs))) & ((((P @ Z @ Y)) & ((list_all2_val_ty @ P @ Zs @ Ys))))))))))). % list_all2_Cons2
thf(fact_87_list__all2__Cons2, axiom,
    ((![P : ty > val > $o, Xs : list_ty, Y : val, Ys : list_val]: ((list_all2_ty_val @ P @ Xs @ (cons_val @ Y @ Ys)) = (?[Z : ty]: (?[Zs : list_ty]: (((Xs = (cons_ty @ Z @ Zs))) & ((((P @ Z @ Y)) & ((list_all2_ty_val @ P @ Zs @ Ys))))))))))). % list_all2_Cons2
thf(fact_88_list__all2__Cons2, axiom,
    ((![P : val > val > $o, Xs : list_val, Y : val, Ys : list_val]: ((list_all2_val_val @ P @ Xs @ (cons_val @ Y @ Ys)) = (?[Z : val]: (?[Zs : list_val]: (((Xs = (cons_val @ Z @ Zs))) & ((((P @ Z @ Y)) & ((list_all2_val_val @ P @ Zs @ Ys))))))))))). % list_all2_Cons2
thf(fact_89_list__all2__Cons2, axiom,
    ((![P : ty > ty > $o, Xs : list_ty, Y : ty, Ys : list_ty]: ((list_all2_ty_ty @ P @ Xs @ (cons_ty @ Y @ Ys)) = (?[Z : ty]: (?[Zs : list_ty]: (((Xs = (cons_ty @ Z @ Zs))) & ((((P @ Z @ Y)) & ((list_all2_ty_ty @ P @ Zs @ Ys))))))))))). % list_all2_Cons2
thf(fact_90_list__all2__Cons2, axiom,
    ((![P : ty > list_char > $o, Xs : list_ty, Y : list_char, Ys : list_list_char]: ((list_a1504214817t_char @ P @ Xs @ (cons_list_char @ Y @ Ys)) = (?[Z : ty]: (?[Zs : list_ty]: (((Xs = (cons_ty @ Z @ Zs))) & ((((P @ Z @ Y)) & ((list_a1504214817t_char @ P @ Zs @ Ys))))))))))). % list_all2_Cons2
thf(fact_91_list__all2__Cons2, axiom,
    ((![P : val > list_char > $o, Xs : list_val, Y : list_char, Ys : list_list_char]: ((list_a1248766058t_char @ P @ Xs @ (cons_list_char @ Y @ Ys)) = (?[Z : val]: (?[Zs : list_val]: (((Xs = (cons_val @ Z @ Zs))) & ((((P @ Z @ Y)) & ((list_a1248766058t_char @ P @ Zs @ Ys))))))))))). % list_all2_Cons2
thf(fact_92_list__all2__Cons2, axiom,
    ((![P : list_char > ty > $o, Xs : list_list_char, Y : ty, Ys : list_ty]: ((list_a1770748705har_ty @ P @ Xs @ (cons_ty @ Y @ Ys)) = (?[Z : list_char]: (?[Zs : list_list_char]: (((Xs = (cons_list_char @ Z @ Zs))) & ((((P @ Z @ Y)) & ((list_a1770748705har_ty @ P @ Zs @ Ys))))))))))). % list_all2_Cons2
thf(fact_93_list__all2__Cons2, axiom,
    ((![P : list_char > val > $o, Xs : list_list_char, Y : val, Ys : list_val]: ((list_a280217834ar_val @ P @ Xs @ (cons_val @ Y @ Ys)) = (?[Z : list_char]: (?[Zs : list_list_char]: (((Xs = (cons_list_char @ Z @ Zs))) & ((((P @ Z @ Y)) & ((list_a280217834ar_val @ P @ Zs @ Ys))))))))))). % list_all2_Cons2
thf(fact_94_list__all2__Cons2, axiom,
    ((![P : list_char > list_char > $o, Xs : list_list_char, Y : list_char, Ys : list_list_char]: ((list_a2051666507t_char @ P @ Xs @ (cons_list_char @ Y @ Ys)) = (?[Z : list_char]: (?[Zs : list_list_char]: (((Xs = (cons_list_char @ Z @ Zs))) & ((((P @ Z @ Y)) & ((list_a2051666507t_char @ P @ Zs @ Ys))))))))))). % list_all2_Cons2
thf(fact_95_list__all2__Cons2, axiom,
    ((![P : exp_list_char > ty > $o, Xs : list_exp_list_char, Y : ty, Ys : list_ty]: ((list_a295513531har_ty @ P @ Xs @ (cons_ty @ Y @ Ys)) = (?[Z : exp_list_char]: (?[Zs : list_exp_list_char]: (((Xs = (cons_exp_list_char @ Z @ Zs))) & ((((P @ Z @ Y)) & ((list_a295513531har_ty @ P @ Zs @ Ys))))))))))). % list_all2_Cons2
thf(fact_96_list__all2__Cons1, axiom,
    ((![P : ty > val > $o, X : ty, Xs : list_ty, Ys : list_val]: ((list_all2_ty_val @ P @ (cons_ty @ X @ Xs) @ Ys) = (?[Z : val]: (?[Zs : list_val]: (((Ys = (cons_val @ Z @ Zs))) & ((((P @ X @ Z)) & ((list_all2_ty_val @ P @ Xs @ Zs))))))))))). % list_all2_Cons1
thf(fact_97_list__all2__Cons1, axiom,
    ((![P : val > ty > $o, X : val, Xs : list_val, Ys : list_ty]: ((list_all2_val_ty @ P @ (cons_val @ X @ Xs) @ Ys) = (?[Z : ty]: (?[Zs : list_ty]: (((Ys = (cons_ty @ Z @ Zs))) & ((((P @ X @ Z)) & ((list_all2_val_ty @ P @ Xs @ Zs))))))))))). % list_all2_Cons1
thf(fact_98_list__all2__Cons1, axiom,
    ((![P : val > val > $o, X : val, Xs : list_val, Ys : list_val]: ((list_all2_val_val @ P @ (cons_val @ X @ Xs) @ Ys) = (?[Z : val]: (?[Zs : list_val]: (((Ys = (cons_val @ Z @ Zs))) & ((((P @ X @ Z)) & ((list_all2_val_val @ P @ Xs @ Zs))))))))))). % list_all2_Cons1
thf(fact_99_list__all2__Cons1, axiom,
    ((![P : ty > ty > $o, X : ty, Xs : list_ty, Ys : list_ty]: ((list_all2_ty_ty @ P @ (cons_ty @ X @ Xs) @ Ys) = (?[Z : ty]: (?[Zs : list_ty]: (((Ys = (cons_ty @ Z @ Zs))) & ((((P @ X @ Z)) & ((list_all2_ty_ty @ P @ Xs @ Zs))))))))))). % list_all2_Cons1
thf(fact_100_list__all2__Cons1, axiom,
    ((![P : list_char > ty > $o, X : list_char, Xs : list_list_char, Ys : list_ty]: ((list_a1770748705har_ty @ P @ (cons_list_char @ X @ Xs) @ Ys) = (?[Z : ty]: (?[Zs : list_ty]: (((Ys = (cons_ty @ Z @ Zs))) & ((((P @ X @ Z)) & ((list_a1770748705har_ty @ P @ Xs @ Zs))))))))))). % list_all2_Cons1
thf(fact_101_list__all2__Cons1, axiom,
    ((![P : list_char > val > $o, X : list_char, Xs : list_list_char, Ys : list_val]: ((list_a280217834ar_val @ P @ (cons_list_char @ X @ Xs) @ Ys) = (?[Z : val]: (?[Zs : list_val]: (((Ys = (cons_val @ Z @ Zs))) & ((((P @ X @ Z)) & ((list_a280217834ar_val @ P @ Xs @ Zs))))))))))). % list_all2_Cons1
thf(fact_102_list__all2__Cons1, axiom,
    ((![P : ty > list_char > $o, X : ty, Xs : list_ty, Ys : list_list_char]: ((list_a1504214817t_char @ P @ (cons_ty @ X @ Xs) @ Ys) = (?[Z : list_char]: (?[Zs : list_list_char]: (((Ys = (cons_list_char @ Z @ Zs))) & ((((P @ X @ Z)) & ((list_a1504214817t_char @ P @ Xs @ Zs))))))))))). % list_all2_Cons1
thf(fact_103_list__all2__Cons1, axiom,
    ((![P : val > list_char > $o, X : val, Xs : list_val, Ys : list_list_char]: ((list_a1248766058t_char @ P @ (cons_val @ X @ Xs) @ Ys) = (?[Z : list_char]: (?[Zs : list_list_char]: (((Ys = (cons_list_char @ Z @ Zs))) & ((((P @ X @ Z)) & ((list_a1248766058t_char @ P @ Xs @ Zs))))))))))). % list_all2_Cons1
thf(fact_104_list__all2__Cons1, axiom,
    ((![P : list_char > list_char > $o, X : list_char, Xs : list_list_char, Ys : list_list_char]: ((list_a2051666507t_char @ P @ (cons_list_char @ X @ Xs) @ Ys) = (?[Z : list_char]: (?[Zs : list_list_char]: (((Ys = (cons_list_char @ Z @ Zs))) & ((((P @ X @ Z)) & ((list_a2051666507t_char @ P @ Xs @ Zs))))))))))). % list_all2_Cons1
thf(fact_105_list__all2__Cons1, axiom,
    ((![P : ty > exp_list_char > $o, X : ty, Xs : list_ty, Ys : list_exp_list_char]: ((list_a212154379t_char @ P @ (cons_ty @ X @ Xs) @ Ys) = (?[Z : exp_list_char]: (?[Zs : list_exp_list_char]: (((Ys = (cons_exp_list_char @ Z @ Zs))) & ((((P @ X @ Z)) & ((list_a212154379t_char @ P @ Xs @ Zs))))))))))). % list_all2_Cons1
thf(fact_106_list__all2__Cons, axiom,
    ((![P : ty > val > $o, X : ty, Xs : list_ty, Y : val, Ys : list_val]: ((list_all2_ty_val @ P @ (cons_ty @ X @ Xs) @ (cons_val @ Y @ Ys)) = (((P @ X @ Y)) & ((list_all2_ty_val @ P @ Xs @ Ys))))))). % list_all2_Cons
thf(fact_107_list__all2__Cons, axiom,
    ((![P : val > ty > $o, X : val, Xs : list_val, Y : ty, Ys : list_ty]: ((list_all2_val_ty @ P @ (cons_val @ X @ Xs) @ (cons_ty @ Y @ Ys)) = (((P @ X @ Y)) & ((list_all2_val_ty @ P @ Xs @ Ys))))))). % list_all2_Cons
thf(fact_108_list__all2__Cons, axiom,
    ((![P : val > val > $o, X : val, Xs : list_val, Y : val, Ys : list_val]: ((list_all2_val_val @ P @ (cons_val @ X @ Xs) @ (cons_val @ Y @ Ys)) = (((P @ X @ Y)) & ((list_all2_val_val @ P @ Xs @ Ys))))))). % list_all2_Cons
thf(fact_109_list__all2__Cons, axiom,
    ((![P : ty > ty > $o, X : ty, Xs : list_ty, Y : ty, Ys : list_ty]: ((list_all2_ty_ty @ P @ (cons_ty @ X @ Xs) @ (cons_ty @ Y @ Ys)) = (((P @ X @ Y)) & ((list_all2_ty_ty @ P @ Xs @ Ys))))))). % list_all2_Cons
thf(fact_110_list__all2__Cons, axiom,
    ((![P : list_char > ty > $o, X : list_char, Xs : list_list_char, Y : ty, Ys : list_ty]: ((list_a1770748705har_ty @ P @ (cons_list_char @ X @ Xs) @ (cons_ty @ Y @ Ys)) = (((P @ X @ Y)) & ((list_a1770748705har_ty @ P @ Xs @ Ys))))))). % list_all2_Cons
thf(fact_111_list__all2__Cons, axiom,
    ((![P : list_char > val > $o, X : list_char, Xs : list_list_char, Y : val, Ys : list_val]: ((list_a280217834ar_val @ P @ (cons_list_char @ X @ Xs) @ (cons_val @ Y @ Ys)) = (((P @ X @ Y)) & ((list_a280217834ar_val @ P @ Xs @ Ys))))))). % list_all2_Cons
thf(fact_112_list__all2__Cons, axiom,
    ((![P : ty > list_char > $o, X : ty, Xs : list_ty, Y : list_char, Ys : list_list_char]: ((list_a1504214817t_char @ P @ (cons_ty @ X @ Xs) @ (cons_list_char @ Y @ Ys)) = (((P @ X @ Y)) & ((list_a1504214817t_char @ P @ Xs @ Ys))))))). % list_all2_Cons
thf(fact_113_list__all2__Cons, axiom,
    ((![P : val > list_char > $o, X : val, Xs : list_val, Y : list_char, Ys : list_list_char]: ((list_a1248766058t_char @ P @ (cons_val @ X @ Xs) @ (cons_list_char @ Y @ Ys)) = (((P @ X @ Y)) & ((list_a1248766058t_char @ P @ Xs @ Ys))))))). % list_all2_Cons
thf(fact_114_list__all2__Cons, axiom,
    ((![P : list_char > list_char > $o, X : list_char, Xs : list_list_char, Y : list_char, Ys : list_list_char]: ((list_a2051666507t_char @ P @ (cons_list_char @ X @ Xs) @ (cons_list_char @ Y @ Ys)) = (((P @ X @ Y)) & ((list_a2051666507t_char @ P @ Xs @ Ys))))))). % list_all2_Cons
thf(fact_115_list__all2__Cons, axiom,
    ((![P : ty > exp_list_char > $o, X : ty, Xs : list_ty, Y : exp_list_char, Ys : list_exp_list_char]: ((list_a212154379t_char @ P @ (cons_ty @ X @ Xs) @ (cons_exp_list_char @ Y @ Ys)) = (((P @ X @ Y)) & ((list_a212154379t_char @ P @ Xs @ Ys))))))). % list_all2_Cons
thf(fact_116_list_Orel__intros_I2_J, axiom,
    ((![R : ty > val > $o, X21 : ty, Y21 : val, X22 : list_ty, Y22 : list_val]: ((R @ X21 @ Y21) => ((list_all2_ty_val @ R @ X22 @ Y22) => (list_all2_ty_val @ R @ (cons_ty @ X21 @ X22) @ (cons_val @ Y21 @ Y22))))))). % list.rel_intros(2)
thf(fact_117_list_Orel__intros_I2_J, axiom,
    ((![R : val > ty > $o, X21 : val, Y21 : ty, X22 : list_val, Y22 : list_ty]: ((R @ X21 @ Y21) => ((list_all2_val_ty @ R @ X22 @ Y22) => (list_all2_val_ty @ R @ (cons_val @ X21 @ X22) @ (cons_ty @ Y21 @ Y22))))))). % list.rel_intros(2)
thf(fact_118_list_Orel__intros_I2_J, axiom,
    ((![R : val > val > $o, X21 : val, Y21 : val, X22 : list_val, Y22 : list_val]: ((R @ X21 @ Y21) => ((list_all2_val_val @ R @ X22 @ Y22) => (list_all2_val_val @ R @ (cons_val @ X21 @ X22) @ (cons_val @ Y21 @ Y22))))))). % list.rel_intros(2)
thf(fact_119_list_Orel__intros_I2_J, axiom,
    ((![R : ty > ty > $o, X21 : ty, Y21 : ty, X22 : list_ty, Y22 : list_ty]: ((R @ X21 @ Y21) => ((list_all2_ty_ty @ R @ X22 @ Y22) => (list_all2_ty_ty @ R @ (cons_ty @ X21 @ X22) @ (cons_ty @ Y21 @ Y22))))))). % list.rel_intros(2)
thf(fact_120_list_Orel__intros_I2_J, axiom,
    ((![R : list_char > ty > $o, X21 : list_char, Y21 : ty, X22 : list_list_char, Y22 : list_ty]: ((R @ X21 @ Y21) => ((list_a1770748705har_ty @ R @ X22 @ Y22) => (list_a1770748705har_ty @ R @ (cons_list_char @ X21 @ X22) @ (cons_ty @ Y21 @ Y22))))))). % list.rel_intros(2)
thf(fact_121_list_Orel__intros_I2_J, axiom,
    ((![R : list_char > val > $o, X21 : list_char, Y21 : val, X22 : list_list_char, Y22 : list_val]: ((R @ X21 @ Y21) => ((list_a280217834ar_val @ R @ X22 @ Y22) => (list_a280217834ar_val @ R @ (cons_list_char @ X21 @ X22) @ (cons_val @ Y21 @ Y22))))))). % list.rel_intros(2)
thf(fact_122_list_Orel__intros_I2_J, axiom,
    ((![R : ty > list_char > $o, X21 : ty, Y21 : list_char, X22 : list_ty, Y22 : list_list_char]: ((R @ X21 @ Y21) => ((list_a1504214817t_char @ R @ X22 @ Y22) => (list_a1504214817t_char @ R @ (cons_ty @ X21 @ X22) @ (cons_list_char @ Y21 @ Y22))))))). % list.rel_intros(2)
thf(fact_123_list_Orel__intros_I2_J, axiom,
    ((![R : val > list_char > $o, X21 : val, Y21 : list_char, X22 : list_val, Y22 : list_list_char]: ((R @ X21 @ Y21) => ((list_a1248766058t_char @ R @ X22 @ Y22) => (list_a1248766058t_char @ R @ (cons_val @ X21 @ X22) @ (cons_list_char @ Y21 @ Y22))))))). % list.rel_intros(2)
thf(fact_124_list_Orel__intros_I2_J, axiom,
    ((![R : list_char > list_char > $o, X21 : list_char, Y21 : list_char, X22 : list_list_char, Y22 : list_list_char]: ((R @ X21 @ Y21) => ((list_a2051666507t_char @ R @ X22 @ Y22) => (list_a2051666507t_char @ R @ (cons_list_char @ X21 @ X22) @ (cons_list_char @ Y21 @ Y22))))))). % list.rel_intros(2)
thf(fact_125_list_Orel__intros_I2_J, axiom,
    ((![R : ty > exp_list_char > $o, X21 : ty, Y21 : exp_list_char, X22 : list_ty, Y22 : list_exp_list_char]: ((R @ X21 @ Y21) => ((list_a212154379t_char @ R @ X22 @ Y22) => (list_a212154379t_char @ R @ (cons_ty @ X21 @ X22) @ (cons_exp_list_char @ Y21 @ Y22))))))). % list.rel_intros(2)
thf(fact_126_list_Orel__inject_I2_J, axiom,
    ((![R : ty > val > $o, X21 : ty, X22 : list_ty, Y21 : val, Y22 : list_val]: ((list_all2_ty_val @ R @ (cons_ty @ X21 @ X22) @ (cons_val @ Y21 @ Y22)) = (((R @ X21 @ Y21)) & ((list_all2_ty_val @ R @ X22 @ Y22))))))). % list.rel_inject(2)
thf(fact_127_list_Orel__inject_I2_J, axiom,
    ((![R : val > ty > $o, X21 : val, X22 : list_val, Y21 : ty, Y22 : list_ty]: ((list_all2_val_ty @ R @ (cons_val @ X21 @ X22) @ (cons_ty @ Y21 @ Y22)) = (((R @ X21 @ Y21)) & ((list_all2_val_ty @ R @ X22 @ Y22))))))). % list.rel_inject(2)
thf(fact_128_list_Orel__inject_I2_J, axiom,
    ((![R : val > val > $o, X21 : val, X22 : list_val, Y21 : val, Y22 : list_val]: ((list_all2_val_val @ R @ (cons_val @ X21 @ X22) @ (cons_val @ Y21 @ Y22)) = (((R @ X21 @ Y21)) & ((list_all2_val_val @ R @ X22 @ Y22))))))). % list.rel_inject(2)
thf(fact_129_list_Orel__inject_I2_J, axiom,
    ((![R : ty > ty > $o, X21 : ty, X22 : list_ty, Y21 : ty, Y22 : list_ty]: ((list_all2_ty_ty @ R @ (cons_ty @ X21 @ X22) @ (cons_ty @ Y21 @ Y22)) = (((R @ X21 @ Y21)) & ((list_all2_ty_ty @ R @ X22 @ Y22))))))). % list.rel_inject(2)
thf(fact_130_list_Orel__inject_I2_J, axiom,
    ((![R : list_char > ty > $o, X21 : list_char, X22 : list_list_char, Y21 : ty, Y22 : list_ty]: ((list_a1770748705har_ty @ R @ (cons_list_char @ X21 @ X22) @ (cons_ty @ Y21 @ Y22)) = (((R @ X21 @ Y21)) & ((list_a1770748705har_ty @ R @ X22 @ Y22))))))). % list.rel_inject(2)
thf(fact_131_list_Orel__inject_I2_J, axiom,
    ((![R : list_char > val > $o, X21 : list_char, X22 : list_list_char, Y21 : val, Y22 : list_val]: ((list_a280217834ar_val @ R @ (cons_list_char @ X21 @ X22) @ (cons_val @ Y21 @ Y22)) = (((R @ X21 @ Y21)) & ((list_a280217834ar_val @ R @ X22 @ Y22))))))). % list.rel_inject(2)
thf(fact_132_list_Orel__inject_I2_J, axiom,
    ((![R : ty > list_char > $o, X21 : ty, X22 : list_ty, Y21 : list_char, Y22 : list_list_char]: ((list_a1504214817t_char @ R @ (cons_ty @ X21 @ X22) @ (cons_list_char @ Y21 @ Y22)) = (((R @ X21 @ Y21)) & ((list_a1504214817t_char @ R @ X22 @ Y22))))))). % list.rel_inject(2)
thf(fact_133_list_Orel__inject_I2_J, axiom,
    ((![R : val > list_char > $o, X21 : val, X22 : list_val, Y21 : list_char, Y22 : list_list_char]: ((list_a1248766058t_char @ R @ (cons_val @ X21 @ X22) @ (cons_list_char @ Y21 @ Y22)) = (((R @ X21 @ Y21)) & ((list_a1248766058t_char @ R @ X22 @ Y22))))))). % list.rel_inject(2)
thf(fact_134_list_Orel__inject_I2_J, axiom,
    ((![R : list_char > list_char > $o, X21 : list_char, X22 : list_list_char, Y21 : list_char, Y22 : list_list_char]: ((list_a2051666507t_char @ R @ (cons_list_char @ X21 @ X22) @ (cons_list_char @ Y21 @ Y22)) = (((R @ X21 @ Y21)) & ((list_a2051666507t_char @ R @ X22 @ Y22))))))). % list.rel_inject(2)
thf(fact_135_list_Orel__inject_I2_J, axiom,
    ((![R : ty > exp_list_char > $o, X21 : ty, X22 : list_ty, Y21 : exp_list_char, Y22 : list_exp_list_char]: ((list_a212154379t_char @ R @ (cons_ty @ X21 @ X22) @ (cons_exp_list_char @ Y21 @ Y22)) = (((R @ X21 @ Y21)) & ((list_a212154379t_char @ R @ X22 @ Y22))))))). % list.rel_inject(2)
thf(fact_136_map__eq__Cons__conv, axiom,
    ((![F : ty > ty, Xs : list_ty, Y : ty, Ys : list_ty]: (((map_ty_ty @ F @ Xs) = (cons_ty @ Y @ Ys)) = (?[Z : ty]: (?[Zs : list_ty]: (((Xs = (cons_ty @ Z @ Zs))) & (((((F @ Z) = Y)) & (((map_ty_ty @ F @ Zs) = Ys))))))))))). % map_eq_Cons_conv
thf(fact_137_map__eq__Cons__conv, axiom,
    ((![F : val > ty, Xs : list_val, Y : ty, Ys : list_ty]: (((map_val_ty @ F @ Xs) = (cons_ty @ Y @ Ys)) = (?[Z : val]: (?[Zs : list_val]: (((Xs = (cons_val @ Z @ Zs))) & (((((F @ Z) = Y)) & (((map_val_ty @ F @ Zs) = Ys))))))))))). % map_eq_Cons_conv
thf(fact_138_map__eq__Cons__conv, axiom,
    ((![F : ty > val, Xs : list_ty, Y : val, Ys : list_val]: (((map_ty_val @ F @ Xs) = (cons_val @ Y @ Ys)) = (?[Z : ty]: (?[Zs : list_ty]: (((Xs = (cons_ty @ Z @ Zs))) & (((((F @ Z) = Y)) & (((map_ty_val @ F @ Zs) = Ys))))))))))). % map_eq_Cons_conv
thf(fact_139_map__eq__Cons__conv, axiom,
    ((![F : val > val, Xs : list_val, Y : val, Ys : list_val]: (((map_val_val @ F @ Xs) = (cons_val @ Y @ Ys)) = (?[Z : val]: (?[Zs : list_val]: (((Xs = (cons_val @ Z @ Zs))) & (((((F @ Z) = Y)) & (((map_val_val @ F @ Zs) = Ys))))))))))). % map_eq_Cons_conv
thf(fact_140_map__eq__Cons__conv, axiom,
    ((![F : ty > option_ty, Xs : list_ty, Y : option_ty, Ys : list_option_ty]: (((map_ty_option_ty @ F @ Xs) = (cons_option_ty @ Y @ Ys)) = (?[Z : ty]: (?[Zs : list_ty]: (((Xs = (cons_ty @ Z @ Zs))) & (((((F @ Z) = Y)) & (((map_ty_option_ty @ F @ Zs) = Ys))))))))))). % map_eq_Cons_conv
thf(fact_141_map__eq__Cons__conv, axiom,
    ((![F : val > option_ty, Xs : list_val, Y : option_ty, Ys : list_option_ty]: (((map_val_option_ty @ F @ Xs) = (cons_option_ty @ Y @ Ys)) = (?[Z : val]: (?[Zs : list_val]: (((Xs = (cons_val @ Z @ Zs))) & (((((F @ Z) = Y)) & (((map_val_option_ty @ F @ Zs) = Ys))))))))))). % map_eq_Cons_conv
thf(fact_142_map__eq__Cons__conv, axiom,
    ((![F : ty > list_char, Xs : list_ty, Y : list_char, Ys : list_list_char]: (((map_ty_list_char @ F @ Xs) = (cons_list_char @ Y @ Ys)) = (?[Z : ty]: (?[Zs : list_ty]: (((Xs = (cons_ty @ Z @ Zs))) & (((((F @ Z) = Y)) & (((map_ty_list_char @ F @ Zs) = Ys))))))))))). % map_eq_Cons_conv
thf(fact_143_map__eq__Cons__conv, axiom,
    ((![F : val > list_char, Xs : list_val, Y : list_char, Ys : list_list_char]: (((map_val_list_char @ F @ Xs) = (cons_list_char @ Y @ Ys)) = (?[Z : val]: (?[Zs : list_val]: (((Xs = (cons_val @ Z @ Zs))) & (((((F @ Z) = Y)) & (((map_val_list_char @ F @ Zs) = Ys))))))))))). % map_eq_Cons_conv
thf(fact_144_map__eq__Cons__conv, axiom,
    ((![F : list_char > ty, Xs : list_list_char, Y : ty, Ys : list_ty]: (((map_list_char_ty @ F @ Xs) = (cons_ty @ Y @ Ys)) = (?[Z : list_char]: (?[Zs : list_list_char]: (((Xs = (cons_list_char @ Z @ Zs))) & (((((F @ Z) = Y)) & (((map_list_char_ty @ F @ Zs) = Ys))))))))))). % map_eq_Cons_conv
thf(fact_145_map__eq__Cons__conv, axiom,
    ((![F : list_char > val, Xs : list_list_char, Y : val, Ys : list_val]: (((map_list_char_val @ F @ Xs) = (cons_val @ Y @ Ys)) = (?[Z : list_char]: (?[Zs : list_list_char]: (((Xs = (cons_list_char @ Z @ Zs))) & (((((F @ Z) = Y)) & (((map_list_char_val @ F @ Zs) = Ys))))))))))). % map_eq_Cons_conv
thf(fact_146_map__eq__Cons__D, axiom,
    ((![F : ty > ty, Xs : list_ty, Y : ty, Ys : list_ty]: (((map_ty_ty @ F @ Xs) = (cons_ty @ Y @ Ys)) => (?[Z3 : ty, Zs2 : list_ty]: ((Xs = (cons_ty @ Z3 @ Zs2)) & (((F @ Z3) = Y) & ((map_ty_ty @ F @ Zs2) = Ys)))))))). % map_eq_Cons_D
thf(fact_147_map__eq__Cons__D, axiom,
    ((![F : val > ty, Xs : list_val, Y : ty, Ys : list_ty]: (((map_val_ty @ F @ Xs) = (cons_ty @ Y @ Ys)) => (?[Z3 : val, Zs2 : list_val]: ((Xs = (cons_val @ Z3 @ Zs2)) & (((F @ Z3) = Y) & ((map_val_ty @ F @ Zs2) = Ys)))))))). % map_eq_Cons_D
thf(fact_148_map__eq__Cons__D, axiom,
    ((![F : ty > val, Xs : list_ty, Y : val, Ys : list_val]: (((map_ty_val @ F @ Xs) = (cons_val @ Y @ Ys)) => (?[Z3 : ty, Zs2 : list_ty]: ((Xs = (cons_ty @ Z3 @ Zs2)) & (((F @ Z3) = Y) & ((map_ty_val @ F @ Zs2) = Ys)))))))). % map_eq_Cons_D
thf(fact_149_map__eq__Cons__D, axiom,
    ((![F : val > val, Xs : list_val, Y : val, Ys : list_val]: (((map_val_val @ F @ Xs) = (cons_val @ Y @ Ys)) => (?[Z3 : val, Zs2 : list_val]: ((Xs = (cons_val @ Z3 @ Zs2)) & (((F @ Z3) = Y) & ((map_val_val @ F @ Zs2) = Ys)))))))). % map_eq_Cons_D
thf(fact_150_map__eq__Cons__D, axiom,
    ((![F : ty > option_ty, Xs : list_ty, Y : option_ty, Ys : list_option_ty]: (((map_ty_option_ty @ F @ Xs) = (cons_option_ty @ Y @ Ys)) => (?[Z3 : ty, Zs2 : list_ty]: ((Xs = (cons_ty @ Z3 @ Zs2)) & (((F @ Z3) = Y) & ((map_ty_option_ty @ F @ Zs2) = Ys)))))))). % map_eq_Cons_D
thf(fact_151_map__eq__Cons__D, axiom,
    ((![F : val > option_ty, Xs : list_val, Y : option_ty, Ys : list_option_ty]: (((map_val_option_ty @ F @ Xs) = (cons_option_ty @ Y @ Ys)) => (?[Z3 : val, Zs2 : list_val]: ((Xs = (cons_val @ Z3 @ Zs2)) & (((F @ Z3) = Y) & ((map_val_option_ty @ F @ Zs2) = Ys)))))))). % map_eq_Cons_D
thf(fact_152_map__eq__Cons__D, axiom,
    ((![F : ty > list_char, Xs : list_ty, Y : list_char, Ys : list_list_char]: (((map_ty_list_char @ F @ Xs) = (cons_list_char @ Y @ Ys)) => (?[Z3 : ty, Zs2 : list_ty]: ((Xs = (cons_ty @ Z3 @ Zs2)) & (((F @ Z3) = Y) & ((map_ty_list_char @ F @ Zs2) = Ys)))))))). % map_eq_Cons_D
thf(fact_153_map__eq__Cons__D, axiom,
    ((![F : val > list_char, Xs : list_val, Y : list_char, Ys : list_list_char]: (((map_val_list_char @ F @ Xs) = (cons_list_char @ Y @ Ys)) => (?[Z3 : val, Zs2 : list_val]: ((Xs = (cons_val @ Z3 @ Zs2)) & (((F @ Z3) = Y) & ((map_val_list_char @ F @ Zs2) = Ys)))))))). % map_eq_Cons_D
thf(fact_154_map__eq__Cons__D, axiom,
    ((![F : list_char > ty, Xs : list_list_char, Y : ty, Ys : list_ty]: (((map_list_char_ty @ F @ Xs) = (cons_ty @ Y @ Ys)) => (?[Z3 : list_char, Zs2 : list_list_char]: ((Xs = (cons_list_char @ Z3 @ Zs2)) & (((F @ Z3) = Y) & ((map_list_char_ty @ F @ Zs2) = Ys)))))))). % map_eq_Cons_D
thf(fact_155_map__eq__Cons__D, axiom,
    ((![F : list_char > val, Xs : list_list_char, Y : val, Ys : list_val]: (((map_list_char_val @ F @ Xs) = (cons_val @ Y @ Ys)) => (?[Z3 : list_char, Zs2 : list_list_char]: ((Xs = (cons_list_char @ Z3 @ Zs2)) & (((F @ Z3) = Y) & ((map_list_char_val @ F @ Zs2) = Ys)))))))). % map_eq_Cons_D
thf(fact_156_Cons__eq__map__D, axiom,
    ((![X : ty, Xs : list_ty, F : ty > ty, Ys : list_ty]: (((cons_ty @ X @ Xs) = (map_ty_ty @ F @ Ys)) => (?[Z3 : ty, Zs2 : list_ty]: ((Ys = (cons_ty @ Z3 @ Zs2)) & ((X = (F @ Z3)) & (Xs = (map_ty_ty @ F @ Zs2))))))))). % Cons_eq_map_D
thf(fact_157_Cons__eq__map__D, axiom,
    ((![X : ty, Xs : list_ty, F : val > ty, Ys : list_val]: (((cons_ty @ X @ Xs) = (map_val_ty @ F @ Ys)) => (?[Z3 : val, Zs2 : list_val]: ((Ys = (cons_val @ Z3 @ Zs2)) & ((X = (F @ Z3)) & (Xs = (map_val_ty @ F @ Zs2))))))))). % Cons_eq_map_D
thf(fact_158_Cons__eq__map__D, axiom,
    ((![X : val, Xs : list_val, F : ty > val, Ys : list_ty]: (((cons_val @ X @ Xs) = (map_ty_val @ F @ Ys)) => (?[Z3 : ty, Zs2 : list_ty]: ((Ys = (cons_ty @ Z3 @ Zs2)) & ((X = (F @ Z3)) & (Xs = (map_ty_val @ F @ Zs2))))))))). % Cons_eq_map_D
thf(fact_159_Cons__eq__map__D, axiom,
    ((![X : val, Xs : list_val, F : val > val, Ys : list_val]: (((cons_val @ X @ Xs) = (map_val_val @ F @ Ys)) => (?[Z3 : val, Zs2 : list_val]: ((Ys = (cons_val @ Z3 @ Zs2)) & ((X = (F @ Z3)) & (Xs = (map_val_val @ F @ Zs2))))))))). % Cons_eq_map_D
thf(fact_160_Cons__eq__map__D, axiom,
    ((![X : option_ty, Xs : list_option_ty, F : ty > option_ty, Ys : list_ty]: (((cons_option_ty @ X @ Xs) = (map_ty_option_ty @ F @ Ys)) => (?[Z3 : ty, Zs2 : list_ty]: ((Ys = (cons_ty @ Z3 @ Zs2)) & ((X = (F @ Z3)) & (Xs = (map_ty_option_ty @ F @ Zs2))))))))). % Cons_eq_map_D
thf(fact_161_Cons__eq__map__D, axiom,
    ((![X : option_ty, Xs : list_option_ty, F : val > option_ty, Ys : list_val]: (((cons_option_ty @ X @ Xs) = (map_val_option_ty @ F @ Ys)) => (?[Z3 : val, Zs2 : list_val]: ((Ys = (cons_val @ Z3 @ Zs2)) & ((X = (F @ Z3)) & (Xs = (map_val_option_ty @ F @ Zs2))))))))). % Cons_eq_map_D
thf(fact_162_Cons__eq__map__D, axiom,
    ((![X : list_char, Xs : list_list_char, F : ty > list_char, Ys : list_ty]: (((cons_list_char @ X @ Xs) = (map_ty_list_char @ F @ Ys)) => (?[Z3 : ty, Zs2 : list_ty]: ((Ys = (cons_ty @ Z3 @ Zs2)) & ((X = (F @ Z3)) & (Xs = (map_ty_list_char @ F @ Zs2))))))))). % Cons_eq_map_D
thf(fact_163_Cons__eq__map__D, axiom,
    ((![X : list_char, Xs : list_list_char, F : val > list_char, Ys : list_val]: (((cons_list_char @ X @ Xs) = (map_val_list_char @ F @ Ys)) => (?[Z3 : val, Zs2 : list_val]: ((Ys = (cons_val @ Z3 @ Zs2)) & ((X = (F @ Z3)) & (Xs = (map_val_list_char @ F @ Zs2))))))))). % Cons_eq_map_D
thf(fact_164_Cons__eq__map__D, axiom,
    ((![X : ty, Xs : list_ty, F : list_char > ty, Ys : list_list_char]: (((cons_ty @ X @ Xs) = (map_list_char_ty @ F @ Ys)) => (?[Z3 : list_char, Zs2 : list_list_char]: ((Ys = (cons_list_char @ Z3 @ Zs2)) & ((X = (F @ Z3)) & (Xs = (map_list_char_ty @ F @ Zs2))))))))). % Cons_eq_map_D
thf(fact_165_Cons__eq__map__D, axiom,
    ((![X : val, Xs : list_val, F : list_char > val, Ys : list_list_char]: (((cons_val @ X @ Xs) = (map_list_char_val @ F @ Ys)) => (?[Z3 : list_char, Zs2 : list_list_char]: ((Ys = (cons_list_char @ Z3 @ Zs2)) & ((X = (F @ Z3)) & (Xs = (map_list_char_val @ F @ Zs2))))))))). % Cons_eq_map_D
thf(fact_166_mem__Collect__eq, axiom,
    ((![A2 : produc1257910179t_char, P : produc1257910179t_char > $o]: ((member89690956t_char @ A2 @ (collec768236686t_char @ P)) = (P @ A2))))). % mem_Collect_eq
thf(fact_167_mem__Collect__eq, axiom,
    ((![A2 : produc1172664615on_val, P : produc1172664615on_val > $o]: ((member354538064on_val @ A2 @ (collec2055896722on_val @ P)) = (P @ A2))))). % mem_Collect_eq
thf(fact_168_Collect__mem__eq, axiom,
    ((![A4 : set_Pr164112643t_char]: ((collec768236686t_char @ (^[X4 : produc1257910179t_char]: (member89690956t_char @ X4 @ A4))) = A4)))). % Collect_mem_eq
thf(fact_169_Collect__mem__eq, axiom,
    ((![A4 : set_Pr1189492743on_val]: ((collec2055896722on_val @ (^[X4 : produc1172664615on_val]: (member354538064on_val @ X4 @ A4))) = A4)))). % Collect_mem_eq
thf(fact_170_list_Osimps_I9_J, axiom,
    ((![F : ty > ty, X21 : ty, X22 : list_ty]: ((map_ty_ty @ F @ (cons_ty @ X21 @ X22)) = (cons_ty @ (F @ X21) @ (map_ty_ty @ F @ X22)))))). % list.simps(9)
thf(fact_171_list_Osimps_I9_J, axiom,
    ((![F : ty > val, X21 : ty, X22 : list_ty]: ((map_ty_val @ F @ (cons_ty @ X21 @ X22)) = (cons_val @ (F @ X21) @ (map_ty_val @ F @ X22)))))). % list.simps(9)
thf(fact_172_list_Osimps_I9_J, axiom,
    ((![F : val > ty, X21 : val, X22 : list_val]: ((map_val_ty @ F @ (cons_val @ X21 @ X22)) = (cons_ty @ (F @ X21) @ (map_val_ty @ F @ X22)))))). % list.simps(9)
thf(fact_173_list_Osimps_I9_J, axiom,
    ((![F : val > val, X21 : val, X22 : list_val]: ((map_val_val @ F @ (cons_val @ X21 @ X22)) = (cons_val @ (F @ X21) @ (map_val_val @ F @ X22)))))). % list.simps(9)
thf(fact_174_list_Osimps_I9_J, axiom,
    ((![F : list_char > ty, X21 : list_char, X22 : list_list_char]: ((map_list_char_ty @ F @ (cons_list_char @ X21 @ X22)) = (cons_ty @ (F @ X21) @ (map_list_char_ty @ F @ X22)))))). % list.simps(9)
thf(fact_175_list_Osimps_I9_J, axiom,
    ((![F : list_char > val, X21 : list_char, X22 : list_list_char]: ((map_list_char_val @ F @ (cons_list_char @ X21 @ X22)) = (cons_val @ (F @ X21) @ (map_list_char_val @ F @ X22)))))). % list.simps(9)
thf(fact_176_list_Osimps_I9_J, axiom,
    ((![F : ty > option_ty, X21 : ty, X22 : list_ty]: ((map_ty_option_ty @ F @ (cons_ty @ X21 @ X22)) = (cons_option_ty @ (F @ X21) @ (map_ty_option_ty @ F @ X22)))))). % list.simps(9)
thf(fact_177_list_Osimps_I9_J, axiom,
    ((![F : ty > list_char, X21 : ty, X22 : list_ty]: ((map_ty_list_char @ F @ (cons_ty @ X21 @ X22)) = (cons_list_char @ (F @ X21) @ (map_ty_list_char @ F @ X22)))))). % list.simps(9)
thf(fact_178_list_Osimps_I9_J, axiom,
    ((![F : val > option_ty, X21 : val, X22 : list_val]: ((map_val_option_ty @ F @ (cons_val @ X21 @ X22)) = (cons_option_ty @ (F @ X21) @ (map_val_option_ty @ F @ X22)))))). % list.simps(9)
thf(fact_179_list_Osimps_I9_J, axiom,
    ((![F : val > list_char, X21 : val, X22 : list_val]: ((map_val_list_char @ F @ (cons_val @ X21 @ X22)) = (cons_list_char @ (F @ X21) @ (map_val_list_char @ F @ X22)))))). % list.simps(9)
thf(fact_180_old_Oprod_Oinducts, axiom,
    ((![P : produc111478616t_char > $o, Prod : produc111478616t_char]: ((![A : list_ty, B : produc1109669680t_char]: (P @ (produc1806338192t_char @ A @ B))) => (P @ Prod))))). % old.prod.inducts
thf(fact_181_old_Oprod_Oinducts, axiom,
    ((![P : produc1451990293t_char > $o, Prod : produc1451990293t_char]: ((![A : list_ty, B : produc1490933927t_char]: (P @ (produc1730359111t_char @ A @ B))) => (P @ Prod))))). % old.prod.inducts
thf(fact_182_old_Oprod_Oinducts, axiom,
    ((![P : produc1097884484on_val > $o, Prod : produc1097884484on_val]: ((![A : exp_list_char, B : produc515445032on_val]: (P @ (produc2023458740on_val @ A @ B))) => (P @ Prod))))). % old.prod.inducts
thf(fact_183_old_Oprod_Oinducts, axiom,
    ((![P : produc1490933927t_char > $o, Prod : produc1490933927t_char]: ((![A : ty, B : produc1294284815t_char]: (P @ (produc248075743t_char @ A @ B))) => (P @ Prod))))). % old.prod.inducts
thf(fact_184_old_Oprod_Oinducts, axiom,
    ((![P : produc515445032on_val > $o, Prod : produc515445032on_val]: ((![A : nat > option2118145160on_val, B : list_char > option_val]: (P @ (produc52622304on_val @ A @ B))) => (P @ Prod))))). % old.prod.inducts
thf(fact_185_old_Oprod_Oinducts, axiom,
    ((![P : produc1294284815t_char > $o, Prod : produc1294284815t_char]: ((![A : list_list_char, B : exp_list_char]: (P @ (produc713467969t_char @ A @ B))) => (P @ Prod))))). % old.prod.inducts
thf(fact_186_old_Oprod_Oexhaust, axiom,
    ((![Y : produc111478616t_char]: (~ ((![A : list_ty, B : produc1109669680t_char]: (~ ((Y = (produc1806338192t_char @ A @ B)))))))))). % old.prod.exhaust
thf(fact_187_old_Oprod_Oexhaust, axiom,
    ((![Y : produc1451990293t_char]: (~ ((![A : list_ty, B : produc1490933927t_char]: (~ ((Y = (produc1730359111t_char @ A @ B)))))))))). % old.prod.exhaust
thf(fact_188_old_Oprod_Oexhaust, axiom,
    ((![Y : produc1097884484on_val]: (~ ((![A : exp_list_char, B : produc515445032on_val]: (~ ((Y = (produc2023458740on_val @ A @ B)))))))))). % old.prod.exhaust
thf(fact_189_old_Oprod_Oexhaust, axiom,
    ((![Y : produc1490933927t_char]: (~ ((![A : ty, B : produc1294284815t_char]: (~ ((Y = (produc248075743t_char @ A @ B)))))))))). % old.prod.exhaust
thf(fact_190_old_Oprod_Oexhaust, axiom,
    ((![Y : produc515445032on_val]: (~ ((![A : nat > option2118145160on_val, B : list_char > option_val]: (~ ((Y = (produc52622304on_val @ A @ B)))))))))). % old.prod.exhaust
thf(fact_191_old_Oprod_Oexhaust, axiom,
    ((![Y : produc1294284815t_char]: (~ ((![A : list_list_char, B : exp_list_char]: (~ ((Y = (produc713467969t_char @ A @ B)))))))))). % old.prod.exhaust
thf(fact_192_Pair__inject, axiom,
    ((![A2 : list_ty, B2 : produc1109669680t_char, A3 : list_ty, B3 : produc1109669680t_char]: (((produc1806338192t_char @ A2 @ B2) = (produc1806338192t_char @ A3 @ B3)) => (~ (((A2 = A3) => (~ ((B2 = B3)))))))))). % Pair_inject
thf(fact_193_Pair__inject, axiom,
    ((![A2 : list_ty, B2 : produc1490933927t_char, A3 : list_ty, B3 : produc1490933927t_char]: (((produc1730359111t_char @ A2 @ B2) = (produc1730359111t_char @ A3 @ B3)) => (~ (((A2 = A3) => (~ ((B2 = B3)))))))))). % Pair_inject
thf(fact_194_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_195_Pair__inject, axiom,
    ((![A2 : ty, B2 : produc1294284815t_char, A3 : ty, B3 : produc1294284815t_char]: (((produc248075743t_char @ A2 @ B2) = (produc248075743t_char @ A3 @ B3)) => (~ (((A2 = A3) => (~ ((B2 = B3)))))))))). % Pair_inject
thf(fact_196_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_197_Pair__inject, axiom,
    ((![A2 : list_list_char, B2 : exp_list_char, A3 : list_list_char, B3 : exp_list_char]: (((produc713467969t_char @ A2 @ B2) = (produc713467969t_char @ A3 @ B3)) => (~ (((A2 = A3) => (~ ((B2 = B3)))))))))). % Pair_inject
thf(fact_198_prod__cases, axiom,
    ((![P : produc111478616t_char > $o, P4 : produc111478616t_char]: ((![A : list_ty, B : produc1109669680t_char]: (P @ (produc1806338192t_char @ A @ B))) => (P @ P4))))). % prod_cases
thf(fact_199_prod__cases, axiom,
    ((![P : produc1451990293t_char > $o, P4 : produc1451990293t_char]: ((![A : list_ty, B : produc1490933927t_char]: (P @ (produc1730359111t_char @ A @ B))) => (P @ P4))))). % prod_cases
thf(fact_200_prod__cases, axiom,
    ((![P : produc1097884484on_val > $o, P4 : produc1097884484on_val]: ((![A : exp_list_char, B : produc515445032on_val]: (P @ (produc2023458740on_val @ A @ B))) => (P @ P4))))). % prod_cases
thf(fact_201_prod__cases, axiom,
    ((![P : produc1490933927t_char > $o, P4 : produc1490933927t_char]: ((![A : ty, B : produc1294284815t_char]: (P @ (produc248075743t_char @ A @ B))) => (P @ P4))))). % prod_cases
thf(fact_202_prod__cases, axiom,
    ((![P : produc515445032on_val > $o, P4 : produc515445032on_val]: ((![A : nat > option2118145160on_val, B : list_char > option_val]: (P @ (produc52622304on_val @ A @ B))) => (P @ P4))))). % prod_cases
thf(fact_203_prod__cases, axiom,
    ((![P : produc1294284815t_char > $o, P4 : produc1294284815t_char]: ((![A : list_list_char, B : exp_list_char]: (P @ (produc713467969t_char @ A @ B))) => (P @ P4))))). % prod_cases
thf(fact_204_surj__pair, axiom,
    ((![P4 : produc111478616t_char]: (?[X3 : list_ty, Y4 : produc1109669680t_char]: (P4 = (produc1806338192t_char @ X3 @ Y4)))))). % surj_pair
thf(fact_205_surj__pair, axiom,
    ((![P4 : produc1451990293t_char]: (?[X3 : list_ty, Y4 : produc1490933927t_char]: (P4 = (produc1730359111t_char @ X3 @ Y4)))))). % surj_pair
thf(fact_206_surj__pair, axiom,
    ((![P4 : produc1097884484on_val]: (?[X3 : exp_list_char, Y4 : produc515445032on_val]: (P4 = (produc2023458740on_val @ X3 @ Y4)))))). % surj_pair
thf(fact_207_surj__pair, axiom,
    ((![P4 : produc1490933927t_char]: (?[X3 : ty, Y4 : produc1294284815t_char]: (P4 = (produc248075743t_char @ X3 @ Y4)))))). % surj_pair
thf(fact_208_surj__pair, axiom,
    ((![P4 : produc515445032on_val]: (?[X3 : nat > option2118145160on_val, Y4 : list_char > option_val]: (P4 = (produc52622304on_val @ X3 @ Y4)))))). % surj_pair
thf(fact_209_surj__pair, axiom,
    ((![P4 : produc1294284815t_char]: (?[X3 : list_list_char, Y4 : exp_list_char]: (P4 = (produc713467969t_char @ X3 @ Y4)))))). % surj_pair
thf(fact_210_not__Cons__self2, axiom,
    ((![X : ty, Xs : list_ty]: (~ (((cons_ty @ X @ Xs) = Xs)))))). % not_Cons_self2
thf(fact_211_not__Cons__self2, axiom,
    ((![X : val, Xs : list_val]: (~ (((cons_val @ X @ Xs) = Xs)))))). % not_Cons_self2
thf(fact_212_not__Cons__self2, axiom,
    ((![X : exp_list_char, Xs : list_exp_list_char]: (~ (((cons_exp_list_char @ X @ Xs) = Xs)))))). % not_Cons_self2
thf(fact_213_method, axiom,
    ((method297381284t_char @ p @ c @ m @ ts2 @ t3 @ (produc713467969t_char @ pns @ body) @ d))). % method
thf(fact_214__092_060open_062wf__mdecl_Awf__J__mdecl_AP_AD_A_IM_M_ATs_M_AT_M_Apns_M_Abody_J_092_060close_062, axiom,
    ((wf_mde297024346t_char @ wf_J_mdecl @ p @ d @ (produc1238538255t_char @ m @ (produc1730359111t_char @ ts2 @ (produc248075743t_char @ t3 @ (produc713467969t_char @ pns @ body))))))). % \<open>wf_mdecl wf_J_mdecl P D (M, Ts, T, pns, body)\<close>
thf(fact_215_WTrtCons, axiom,
    ((![P : list_P1234162913t_char, H : nat > option2118145160on_val, E : list_char > option_ty, E2 : exp_list_char, T : ty, Es : list_exp_list_char, Ts2 : list_ty]: ((wTrt @ P @ H @ E @ E2 @ T) => ((wTrts @ P @ H @ E @ Es @ Ts2) => (wTrts @ P @ H @ E @ (cons_exp_list_char @ E2 @ Es) @ (cons_ty @ T @ Ts2))))))). % WTrtCons
thf(fact_216_wt, axiom,
    ((wTrt @ p @ ha @ e @ (call_list_char @ (val_list_char @ (addr @ a)) @ m @ (map_va1515327237t_char @ val_list_char @ vs)) @ t2))). % wt
thf(fact_217_local_Owf, axiom,
    ((wf_pro1229751607t_char @ wf_J_mdecl @ p))). % local.wf
thf(fact_218_WTrts__same__length, axiom,
    ((![P : list_P1234162913t_char, H : nat > option2118145160on_val, E : list_char > option_ty, Es : list_exp_list_char, Ts2 : list_ty]: ((wTrts @ P @ H @ E @ Es @ Ts2) => ((size_s329991613t_char @ Es) = (size_size_list_ty @ Ts2)))))). % WTrts_same_length
thf(fact_219_WTrtCall, axiom,
    ((![P : list_P1234162913t_char, H : nat > option2118145160on_val, E : list_char > option_ty, E2 : exp_list_char, C2 : list_char, M : list_char, Ts2 : list_ty, T : ty, Pns : list_list_char, Body : exp_list_char, D2 : list_char, Es : list_exp_list_char, Ts3 : list_ty]: ((wTrt @ P @ H @ E @ E2 @ (class @ C2)) => ((method297381284t_char @ P @ C2 @ M @ Ts2 @ T @ (produc713467969t_char @ Pns @ Body) @ D2) => ((wTrts @ P @ H @ E @ Es @ Ts3) => ((list_all2_ty_ty @ (widen_917054840t_char @ P) @ Ts3 @ Ts2) => (wTrt @ P @ H @ E @ (call_list_char @ E2 @ M @ Es) @ T)))))))). % WTrtCall
thf(fact_220_RedCall_Oprems_I2_J, axiom,
    ((wTrt @ p @ ha @ e @ (call_list_char @ (val_list_char @ (addr @ a)) @ m @ (map_va1515327237t_char @ val_list_char @ vs)) @ t2))). % RedCall.prems(2)
thf(fact_221_red__reds_ORedCall, axiom,
    ((![S : produc515445032on_val, A2 : nat, C2 : list_char, Fs : produc1257910179t_char > option_val, P : list_P1234162913t_char, M : list_char, Ts2 : list_ty, T : ty, Pns : list_list_char, Body : exp_list_char, D2 : list_char, Vs : list_val]: (((hp @ S @ A2) = (some_P1299442195on_val @ (produc904988266on_val @ C2 @ Fs))) => ((method297381284t_char @ P @ C2 @ M @ Ts2 @ T @ (produc713467969t_char @ Pns @ Body) @ D2) => (((size_size_list_val @ Vs) = (size_s2008079621t_char @ Pns)) => (((size_size_list_ty @ Ts2) = (size_s2008079621t_char @ Pns)) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (call_list_char @ (val_list_char @ (addr @ A2)) @ M @ (map_va1515327237t_char @ val_list_char @ Vs)) @ S) @ (produc2023458740on_val @ (blocks @ (produc1808722894t_char @ (cons_list_char @ this @ Pns) @ (produc1806338192t_char @ (cons_ty @ (class @ D2) @ Ts2) @ (produc823987298t_char @ (cons_val @ (addr @ A2) @ Vs) @ Body)))) @ S)) @ (red @ P))))))))). % red_reds.RedCall
thf(fact_222_redp__redsp_ORedCall, axiom,
    ((![S : produc515445032on_val, A2 : nat, C2 : list_char, Fs : produc1257910179t_char > option_val, P : list_P1234162913t_char, M : list_char, Ts2 : list_ty, T : ty, Pns : list_list_char, Body : exp_list_char, D2 : list_char, Vs : list_val]: (((hp @ S @ A2) = (some_P1299442195on_val @ (produc904988266on_val @ C2 @ Fs))) => ((method297381284t_char @ P @ C2 @ M @ Ts2 @ T @ (produc713467969t_char @ Pns @ Body) @ D2) => (((size_size_list_val @ Vs) = (size_s2008079621t_char @ Pns)) => (((size_size_list_ty @ Ts2) = (size_s2008079621t_char @ Pns)) => (redp @ P @ (call_list_char @ (val_list_char @ (addr @ A2)) @ M @ (map_va1515327237t_char @ val_list_char @ Vs)) @ S @ (blocks @ (produc1808722894t_char @ (cons_list_char @ this @ Pns) @ (produc1806338192t_char @ (cons_ty @ (class @ D2) @ Ts2) @ (produc823987298t_char @ (cons_val @ (addr @ A2) @ Vs) @ Body)))) @ S)))))))). % redp_redsp.RedCall
thf(fact_223_RedCall_Oprems_I1_J, axiom,
    ((typeSa1777264139_sconf @ p @ e @ (produc52622304on_val @ ha @ la)))). % RedCall.prems(1)
thf(fact_224_redp__red__eq, axiom,
    ((redp = (^[P5 : list_P1234162913t_char]: (^[X4 : exp_list_char]: (^[Y6 : produc515445032on_val]: (^[Z : exp_list_char]: (^[Aa : produc515445032on_val]: (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ X4 @ Y6) @ (produc2023458740on_val @ Z @ Aa)) @ (red @ P5)))))))))). % redp_red_eq
thf(fact_225_red__reds_OCallObj, axiom,
    ((![E2 : exp_list_char, S : produc515445032on_val, E3 : exp_list_char, S2 : produc515445032on_val, P : list_P1234162913t_char, M : list_char, Es : list_exp_list_char]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E2 @ S) @ (produc2023458740on_val @ E3 @ S2)) @ (red @ P)) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (call_list_char @ E2 @ M @ Es) @ S) @ (produc2023458740on_val @ (call_list_char @ E3 @ M @ Es) @ S2)) @ (red @ P)))))). % red_reds.CallObj
thf(fact_226_redp__redsp_OCallObj, axiom,
    ((![P : list_P1234162913t_char, E2 : exp_list_char, S : produc515445032on_val, E3 : exp_list_char, S2 : produc515445032on_val, M : list_char, Es : list_exp_list_char]: ((redp @ P @ E2 @ S @ E3 @ S2) => (redp @ P @ (call_list_char @ E2 @ M @ Es) @ S @ (call_list_char @ E3 @ M @ Es) @ S2))))). % redp_redsp.CallObj
thf(fact_227__092_060open_062P_M_091this_A_D_Apns_A_091_092_060mapsto_062_093_AClass_AD_A_D_ATs_093_Mh_A_092_060turnstile_062_Abody_A_058_AT_H_H_092_060close_062, axiom,
    ((wTrt @ p @ ha @ (map_up703499792har_ty @ (^[X4 : list_char]: none_ty) @ (cons_list_char @ this @ pns) @ (cons_ty @ (class @ d) @ ts2)) @ body @ t))). % \<open>P,[this # pns [\<mapsto>] Class D # Ts],h \<turnstile> body : T''\<close>
thf(fact_228_wtabody, axiom,
    ((wt @ p @ (map_up703499792har_ty @ (^[X4 : list_char]: none_ty) @ (cons_list_char @ this @ pns) @ (cons_ty @ (class @ d) @ ts2)) @ body @ t))). % wtabody
thf(fact_229_red__preserves__sconf, axiom,
    ((![E2 : exp_list_char, S : produc515445032on_val, E3 : exp_list_char, S2 : produc515445032on_val, P : list_P1234162913t_char, E : list_char > option_ty, T : ty]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E2 @ S) @ (produc2023458740on_val @ E3 @ S2)) @ (red @ P)) => ((wTrt @ P @ (hp @ S) @ E @ E2 @ T) => ((typeSa1777264139_sconf @ P @ E @ S) => (typeSa1777264139_sconf @ P @ E @ S2))))))). % red_preserves_sconf
thf(fact_230__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062T_H_H_O_A_092_060lbrakk_062P_M_091this_A_D_Apns_A_091_092_060mapsto_062_093_AClass_AD_A_D_ATs_093_A_092_060turnstile_062_Abody_A_058_058_AT_H_H_059_AP_A_092_060turnstile_062_AT_H_H_A_092_060le_062_AT_059_Alength_Apns_A_061_Alength_ATs_092_060rbrakk_062_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062, axiom,
    ((~ ((![T2 : ty]: ((wt @ p @ (map_up703499792har_ty @ (^[X4 : list_char]: none_ty) @ (cons_list_char @ this @ pns) @ (cons_ty @ (class @ d) @ ts2)) @ body @ T2) => ((widen_917054840t_char @ p @ T2 @ t3) => (~ (((size_s2008079621t_char @ pns) = (size_size_list_ty @ ts2))))))))))). % \<open>\<And>thesis. (\<And>T''. \<lbrakk>P,[this # pns [\<mapsto>] Class D # Ts] \<turnstile> body :: T''; P \<turnstile> T'' \<le> T; length pns = length Ts\<rbrakk> \<Longrightarrow> thesis) \<Longrightarrow> thesis\<close>
thf(fact_231_WT__implies__WTrt, axiom,
    ((![P : list_P1234162913t_char, E : list_char > option_ty, E2 : exp_list_char, T : ty, H : nat > option2118145160on_val]: ((wt @ P @ E @ E2 @ T) => (wTrt @ P @ H @ E @ E2 @ T))))). % WT_implies_WTrt
thf(fact_232_wt__blocks, axiom,
    ((![Vs2 : list_list_char, Ts2 : list_ty, Vs : list_val, P : list_P1234162913t_char, H : nat > option2118145160on_val, E : list_char > option_ty, E2 : exp_list_char, T : ty]: (((size_s2008079621t_char @ Vs2) = (size_size_list_ty @ Ts2)) => (((size_size_list_val @ Vs) = (size_size_list_ty @ Ts2)) => ((wTrt @ P @ H @ E @ (blocks @ (produc1808722894t_char @ Vs2 @ (produc1806338192t_char @ Ts2 @ (produc823987298t_char @ Vs @ E2)))) @ T) = (((wTrt @ P @ H @ (map_up703499792har_ty @ E @ Vs2 @ Ts2) @ E2 @ T)) & ((?[Ts4 : list_ty]: ((((map_val_option_ty @ (typeof_h @ H) @ Vs) = (map_ty_option_ty @ some_ty @ Ts4))) & ((list_all2_ty_ty @ (widen_917054840t_char @ P) @ Ts4 @ Ts2)))))))))))). % wt_blocks
thf(fact_233_red__reds_ORedCast, axiom,
    ((![S : produc515445032on_val, A2 : nat, D2 : list_char, Fs : produc1257910179t_char > option_val, C2 : list_char, P : list_P1234162913t_char]: (((hp @ S @ A2) = (some_P1299442195on_val @ (produc904988266on_val @ D2 @ Fs))) => ((member89690956t_char @ (produc1304532571t_char @ D2 @ C2) @ (transi1879726366t_char @ (subcls880436836t_char @ P))) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (cast_list_char @ C2 @ (val_list_char @ (addr @ A2))) @ S) @ (produc2023458740on_val @ (val_list_char @ (addr @ A2)) @ S)) @ (red @ P))))))). % red_reds.RedCast
thf(fact_234_WT__elim__cases_I11_J, axiom,
    ((![P : list_P1234162913t_char, E : list_char > option_ty, E2 : exp_list_char, M : list_char, Ps : list_exp_list_char, T : ty]: ((wt @ P @ E @ (call_list_char @ E2 @ M @ Ps) @ T) => (~ ((![C3 : list_char]: ((wt @ P @ E @ E2 @ (class @ C3)) => (![Ts5 : list_ty]: ((?[Pns2 : list_list_char, Body2 : exp_list_char, X_1 : list_char]: (method297381284t_char @ P @ C3 @ M @ Ts5 @ T @ (produc713467969t_char @ Pns2 @ Body2) @ X_1)) => (![Ts : list_ty]: ((wTs @ P @ E @ Ps @ Ts) => (~ ((list_all2_ty_ty @ (widen_917054840t_char @ P) @ Ts @ Ts5))))))))))))))). % WT_elim_cases(11)
thf(fact_235_WTrts__Val, axiom,
    ((![P : list_P1234162913t_char, H : nat > option2118145160on_val, E : list_char > option_ty, Vs : list_val, Ts2 : list_ty]: ((wTrts @ P @ H @ E @ (map_va1515327237t_char @ val_list_char @ Vs) @ Ts2) = ((map_val_option_ty @ (typeof_h @ H) @ Vs) = (map_ty_option_ty @ some_ty @ Ts2)))))). % WTrts_Val
thf(fact_236_redp__redsp_OCastRed, axiom,
    ((![P : list_P1234162913t_char, E2 : exp_list_char, S : produc515445032on_val, E3 : exp_list_char, S2 : produc515445032on_val, C2 : list_char]: ((redp @ P @ E2 @ S @ E3 @ S2) => (redp @ P @ (cast_list_char @ C2 @ E2) @ S @ (cast_list_char @ C2 @ E3) @ S2))))). % redp_redsp.CastRed
thf(fact_237_WTVal, axiom,
    ((![V : val, T : ty, P : list_P1234162913t_char, E : list_char > option_ty]: (((typeof_h @ (^[X4 : nat]: none_P1535574167on_val) @ V) = (some_ty @ T)) => (wt @ P @ E @ (val_list_char @ V) @ T))))). % WTVal
thf(fact_238_WTs__implies__WTrts, axiom,
    ((![P : list_P1234162913t_char, E : list_char > option_ty, Es : list_exp_list_char, Ts2 : list_ty, H : nat > option2118145160on_val]: ((wTs @ P @ E @ Es @ Ts2) => (wTrts @ P @ H @ E @ Es @ Ts2))))). % WTs_implies_WTrts
thf(fact_239_WTrtVal, axiom,
    ((![H : nat > option2118145160on_val, V : val, T : ty, P : list_P1234162913t_char, E : list_char > option_ty]: (((typeof_h @ H @ V) = (some_ty @ T)) => (wTrt @ P @ H @ E @ (val_list_char @ V) @ T))))). % WTrtVal
thf(fact_240_red__reds_OCastRed, axiom,
    ((![E2 : exp_list_char, S : produc515445032on_val, E3 : exp_list_char, S2 : produc515445032on_val, P : list_P1234162913t_char, C2 : list_char]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E2 @ S) @ (produc2023458740on_val @ E3 @ S2)) @ (red @ P)) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (cast_list_char @ C2 @ E2) @ S) @ (produc2023458740on_val @ (cast_list_char @ C2 @ E3) @ S2)) @ (red @ P)))))). % red_reds.CastRed
thf(fact_241_WTCons, axiom,
    ((![P : list_P1234162913t_char, E : list_char > option_ty, E2 : exp_list_char, T : ty, Es : list_exp_list_char, Ts2 : list_ty]: ((wt @ P @ E @ E2 @ T) => ((wTs @ P @ E @ Es @ Ts2) => (wTs @ P @ E @ (cons_exp_list_char @ E2 @ Es) @ (cons_ty @ T @ Ts2))))))). % WTCons
thf(fact_242_WTCall, axiom,
    ((![P : list_P1234162913t_char, E : list_char > option_ty, E2 : exp_list_char, C2 : list_char, M : list_char, Ts2 : list_ty, T : ty, Pns : list_list_char, Body : exp_list_char, D2 : list_char, Es : list_exp_list_char, Ts3 : list_ty]: ((wt @ P @ E @ E2 @ (class @ C2)) => ((method297381284t_char @ P @ C2 @ M @ Ts2 @ T @ (produc713467969t_char @ Pns @ Body) @ D2) => ((wTs @ P @ E @ Es @ Ts3) => ((list_all2_ty_ty @ (widen_917054840t_char @ P) @ Ts3 @ Ts2) => (wt @ P @ E @ (call_list_char @ E2 @ M @ Es) @ T)))))))). % WTCall
thf(fact_243_typeof__lit__typeof, axiom,
    ((![V : val, T : ty, H : nat > option2118145160on_val]: (((typeof_h @ (^[X4 : nat]: none_P1535574167on_val) @ V) = (some_ty @ T)) => ((typeof_h @ H @ V) = (some_ty @ T)))))). % typeof_lit_typeof
thf(fact_244_CastRedsAddr, axiom,
    ((![E2 : exp_list_char, S : produc515445032on_val, A2 : nat, S2 : produc515445032on_val, P : list_P1234162913t_char, D2 : list_char, Fs : produc1257910179t_char > option_val, C2 : list_char]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E2 @ S) @ (produc2023458740on_val @ (val_list_char @ (addr @ A2)) @ S2)) @ (transi111096263on_val @ (red @ P))) => (((hp @ S2 @ A2) = (some_P1299442195on_val @ (produc904988266on_val @ D2 @ Fs))) => ((member89690956t_char @ (produc1304532571t_char @ D2 @ C2) @ (transi1879726366t_char @ (subcls880436836t_char @ P))) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (cast_list_char @ C2 @ E2) @ S) @ (produc2023458740on_val @ (val_list_char @ (addr @ A2)) @ S2)) @ (transi111096263on_val @ (red @ P))))))))). % CastRedsAddr
thf(fact_245_CallRedsObj, axiom,
    ((![E2 : exp_list_char, S : produc515445032on_val, E3 : exp_list_char, S2 : produc515445032on_val, P : list_P1234162913t_char, M : list_char, Es : list_exp_list_char]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E2 @ S) @ (produc2023458740on_val @ E3 @ S2)) @ (transi111096263on_val @ (red @ P))) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (call_list_char @ E2 @ M @ Es) @ S) @ (produc2023458740on_val @ (call_list_char @ E3 @ M @ Es) @ S2)) @ (transi111096263on_val @ (red @ P))))))). % CallRedsObj
thf(fact_246_CastReds, axiom,
    ((![E2 : exp_list_char, S : produc515445032on_val, E3 : exp_list_char, S2 : produc515445032on_val, P : list_P1234162913t_char, C2 : list_char]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E2 @ S) @ (produc2023458740on_val @ E3 @ S2)) @ (transi111096263on_val @ (red @ P))) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (cast_list_char @ C2 @ E2) @ S) @ (produc2023458740on_val @ (cast_list_char @ C2 @ E3) @ S2)) @ (transi111096263on_val @ (red @ P))))))). % CastReds
thf(fact_247_converse__rtrancl__induct__red, axiom,
    ((![E2 : exp_list_char, H : nat > option2118145160on_val, L : list_char > option_val, E3 : exp_list_char, H2 : nat > option2118145160on_val, L2 : list_char > option_val, P : list_P1234162913t_char, R : exp_list_char > (nat > option2118145160on_val) > (list_char > option_val) > exp_list_char > (nat > option2118145160on_val) > (list_char > option_val) > $o]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E2 @ (produc52622304on_val @ H @ L)) @ (produc2023458740on_val @ E3 @ (produc52622304on_val @ H2 @ L2))) @ (transi111096263on_val @ (red @ P))) => ((![E4 : exp_list_char, H3 : nat > option2118145160on_val, L3 : list_char > option_val]: (R @ E4 @ H3 @ L3 @ E4 @ H3 @ L3)) => ((![E_0 : exp_list_char, H_0 : nat > option2118145160on_val, L_0 : list_char > option_val, E_1 : exp_list_char, H_1 : nat > option2118145160on_val, L_1 : list_char > option_val, E5 : exp_list_char, H4 : nat > option2118145160on_val, L4 : list_char > option_val]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E_0 @ (produc52622304on_val @ H_0 @ L_0)) @ (produc2023458740on_val @ E_1 @ (produc52622304on_val @ H_1 @ L_1))) @ (red @ P)) => ((R @ E_1 @ H_1 @ L_1 @ E5 @ H4 @ L4) => (R @ E_0 @ H_0 @ L_0 @ E5 @ H4 @ L4)))) => (R @ E2 @ H @ L @ E3 @ H2 @ L2))))))). % converse_rtrancl_induct_red
thf(fact_248_blocksFinal, axiom,
    ((![Vs2 : list_list_char, Ts2 : list_ty, Vs : list_val, E2 : exp_list_char, H : nat > option2118145160on_val, L : list_char > option_val, P : list_P1234162913t_char]: (((size_s2008079621t_char @ Vs2) = (size_size_list_ty @ Ts2)) => (((size_size_list_val @ Vs) = (size_size_list_ty @ Ts2)) => ((final_list_char @ E2) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (blocks @ (produc1808722894t_char @ Vs2 @ (produc1806338192t_char @ Ts2 @ (produc823987298t_char @ Vs @ E2)))) @ (produc52622304on_val @ H @ L)) @ (produc2023458740on_val @ E2 @ (produc52622304on_val @ H @ L))) @ (transi111096263on_val @ (red @ P))))))))). % blocksFinal

% Conjectures (1)
thf(conj_0, conjecture,
    ((wTrt @ p @ ha @ e @ (blocks @ (produc1808722894t_char @ (cons_list_char @ this @ pns) @ (produc1806338192t_char @ (cons_ty @ (class @ d) @ ts2) @ (produc823987298t_char @ (cons_val @ (addr @ a) @ vs) @ body)))) @ t))).
