% 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_481__5339594_1 ) ; }
% This file was generated by Isabelle (most likely Sledgehammer)
% 2020-12-16 14:22:10.518

% Could-be-implicit typings (21)
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thf(ty_n_t__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J, type,
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thf(ty_n_t__Option__Ooption_It__Value__Oval_J, type,
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thf(ty_n_t__Option__Ooption_It__Type__Oty_J, type,
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thf(ty_n_t__List__Olist_It__String__Ochar_J, type,
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thf(ty_n_t__Value__Oval, type,
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thf(ty_n_t__Type__Oty, type,
    ty : $tType).
thf(ty_n_t__Nat__Onat, type,
    nat : $tType).

% Explicit typings (64)
thf(sy_c_BigStep_Ofinal_001t__List__Olist_It__String__Ochar_J, type,
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thf(sy_c_Conform_Oconf_001t__Product____Type__Oprod_It__List__Olist_It__List__Olist_It__String__Ochar_J_J_Mt__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_J, type,
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thf(sy_c_Conform_Ohconf_001t__Product____Type__Oprod_It__List__Olist_It__List__Olist_It__String__Ochar_J_J_Mt__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_J, type,
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thf(sy_c_Conform_Olconf_001t__Product____Type__Oprod_It__List__Olist_It__List__Olist_It__String__Ochar_J_J_Mt__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_J, type,
    lconf_485928294t_char : list_P1234162913t_char > (nat > option2118145160on_val) > (list_char > option_val) > (list_char > option_ty) > $o).
thf(sy_c_Expr_Oexp_OBlock_001t__List__Olist_It__String__Ochar_J, type,
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thf(sy_c_Expr_Oexp_OLAss_001t__List__Olist_It__String__Ochar_J, type,
    lAss_list_char : list_char > exp_list_char > exp_list_char).
thf(sy_c_Expr_Oexp_OSeq_001t__List__Olist_It__String__Ochar_J, type,
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thf(sy_c_Expr_Oexp_OVal_001t__List__Olist_It__String__Ochar_J, type,
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thf(sy_c_Expr_Oexp_OVar_001t__List__Olist_It__String__Ochar_J, type,
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thf(sy_c_Fun_Ofun__upd_001t__List__Olist_It__String__Ochar_J_001t__Option__Ooption_It__Type__Oty_J, type,
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thf(sy_c_Fun_Ofun__upd_001t__List__Olist_It__String__Ochar_J_001t__Option__Ooption_It__Value__Oval_J, type,
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thf(sy_c_If_001t__Option__Ooption_It__Type__Oty_J, type,
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thf(sy_c_If_001t__Option__Ooption_It__Value__Oval_J, type,
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thf(sy_c_JWellForm_Owf__J__mdecl, type,
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thf(sy_c_Objects_Otypeof__h, type,
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thf(sy_c_Option_Ooption_ONone_001t__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J, type,
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thf(sy_c_Option_Ooption_ONone_001t__Type__Oty, type,
    none_ty : option_ty).
thf(sy_c_Option_Ooption_ONone_001t__Value__Oval, type,
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thf(sy_c_Option_Ooption_OSome_001t__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J, type,
    some_P1299442195on_val : produc266837688on_val > option2118145160on_val).
thf(sy_c_Option_Ooption_OSome_001t__Type__Oty, type,
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thf(sy_c_Option_Ooption_OSome_001t__Value__Oval, type,
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thf(sy_c_Option_Ooption_Othe_001t__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J, type,
    the_Pr901949220on_val : option2118145160on_val > produc266837688on_val).
thf(sy_c_Option_Ooption_Othe_001t__Type__Oty, type,
    the_ty : option_ty > ty).
thf(sy_c_Option_Ooption_Othe_001t__Value__Oval, type,
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thf(sy_c_Product__Type_OPair_001_062_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_001_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J, type,
    produc52622304on_val : (nat > option2118145160on_val) > (list_char > option_val) > produc515445032on_val).
thf(sy_c_Product__Type_OPair_001t__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_001t__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_M_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_J, type,
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thf(sy_c_Product__Type_OPair_001t__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_M_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_001t__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_M_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_J, type,
    produc2106877847on_val : produc515445032on_val > produc515445032on_val > produc744932519on_val).
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__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_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,
    produc564964183on_val : produc1172664615on_val > produc1172664615on_val > produc1161703655on_val).
thf(sy_c_Progress_OWTrt_H, type,
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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,
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thf(sy_c_SmallStep_Oassigned, type,
    assigned : list_char > exp_list_char > $o).
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_State_Olcl, type,
    lcl : produc515445032on_val > list_char > option_val).
thf(sy_c_Transitive__Closure_Ortrancl_001t__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_M_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_J, type,
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thf(sy_c_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,
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thf(sy_c_Transitive__Closure_Ortrancl_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,
    transi100378922on_val : set_Pr1368603847on_val > set_Pr1368603847on_val).
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_Oty_OVoid, type,
    void : ty).
thf(sy_c_Value_Oval_OUnit, type,
    unit : val).
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,
    wTrt2 : list_P1234162913t_char > (nat > option2118145160on_val) > (list_char > option_ty) > exp_list_char > ty > $o).
thf(sy_c_member_001t__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_M_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_J, type,
    member652041809on_val : produc515445032on_val > set_Pr723149704on_val > $o).
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    member1888679917on_val : produc1097884484on_val > set_Pr556513572on_val > $o).
thf(sy_c_member_001t__Product____Type__Oprod_It__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_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,
    member2027247312on_val : produc744932519on_val > set_Pr148564103on_val > $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_c_member_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__Product____Type__Oprod_It__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_Mt__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_M_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_Mt__Product____Type__Oprod_It__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_Mt__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_M_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_Mt__Product____Type__Oprod_It__Product____Type__Oprod_It__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_Mt__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_M_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_Mt__Product____Type__Oprod_It__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_Mt__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_M_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_J, type,
    member208988944on_val : produc1161703655on_val > set_Pr1368603847on_val > $o).
thf(sy_v_E____, type,
    e : list_char > option_ty).
thf(sy_v_P, type,
    p : list_P1234162913t_char).
thf(sy_v_T_H____, type,
    t : ty).
thf(sy_v_T____, type,
    t2 : ty).
thf(sy_v_V____, type,
    v : list_char).
thf(sy_v_e_Ha____, type,
    e_a : exp_list_char).
thf(sy_v_ea____, type,
    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_thesis____, type,
    thesis : $o).
thf(sy_v_v_H____, type,
    v2 : val).
thf(sy_v_v____, type,
    v3 : val).

% Relevant facts (205)
thf(fact_0_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_1_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_2_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_3_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_4_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_5_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_6_fun__upd__apply, axiom,
    ((fun_up9191ion_ty = (^[F2 : list_char > option_ty]: (^[X2 : list_char]: (^[Y2 : option_ty]: (^[Z2 : list_char]: (if_option_ty @ (Z2 = X2) @ Y2 @ (F2 @ Z2))))))))). % fun_upd_apply
thf(fact_7_fun__upd__apply, axiom,
    ((fun_up1252458416on_val = (^[F2 : list_char > option_val]: (^[X2 : list_char]: (^[Y2 : option_val]: (^[Z2 : list_char]: (if_option_val @ (Z2 = X2) @ Y2 @ (F2 @ Z2))))))))). % fun_upd_apply
thf(fact_8_option_Oinject, axiom,
    ((![X22 : ty, Y22 : ty]: (((some_ty @ X22) = (some_ty @ Y22)) = (X22 = Y22))))). % option.inject
thf(fact_9_option_Oinject, axiom,
    ((![X22 : val, Y22 : val]: (((some_val @ X22) = (some_val @ Y22)) = (X22 = Y22))))). % option.inject
thf(fact_10_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_11_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_12_map__upd__triv, axiom,
    ((![T : list_char > option_ty, K : list_char, X : ty]: (((T @ K) = (some_ty @ X)) => ((fun_up9191ion_ty @ T @ K @ (some_ty @ X)) = T))))). % map_upd_triv
thf(fact_13_map__upd__triv, axiom,
    ((![T : list_char > option_val, K : list_char, X : val]: (((T @ K) = (some_val @ X)) => ((fun_up1252458416on_val @ T @ K @ (some_val @ X)) = T))))). % map_upd_triv
thf(fact_14_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_15_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_16_local_Owf, axiom,
    ((wf_pro1229751607t_char @ wf_J_mdecl @ p))). % local.wf
thf(fact_17_WTrtVal, axiom,
    ((![H : nat > option2118145160on_val, V : val, T2 : ty, P : list_P1234162913t_char, E : list_char > option_ty]: (((typeof_h @ H @ V) = (some_ty @ T2)) => (wTrt2 @ P @ H @ E @ (val_list_char @ V) @ T2))))). % WTrtVal
thf(fact_18_WTrtBlock, axiom,
    ((![P : list_P1234162913t_char, H : nat > option2118145160on_val, E : list_char > option_ty, V2 : list_char, T2 : ty, E2 : exp_list_char, T3 : ty]: ((wTrt2 @ P @ H @ (fun_up9191ion_ty @ E @ V2 @ (some_ty @ T2)) @ E2 @ T3) => (wTrt2 @ P @ H @ E @ (block_list_char @ V2 @ T2 @ E2) @ T3))))). % WTrtBlock
thf(fact_19_v_H, axiom,
    (((l_a @ v) = (some_val @ v2)))). % v'
thf(fact_20_WTrtSeq, axiom,
    ((![P : list_P1234162913t_char, H : nat > option2118145160on_val, E : list_char > option_ty, E_1 : exp_list_char, T_1 : ty, E_2 : exp_list_char, T_2 : ty]: ((wTrt2 @ P @ H @ E @ E_1 @ T_1) => ((wTrt2 @ P @ H @ E @ E_2 @ T_2) => (wTrt2 @ P @ H @ E @ (seq_list_char @ E_1 @ E_2) @ T_2)))))). % WTrtSeq
thf(fact_21_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_22_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_23_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_24_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_25_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_26_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_27_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_28_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_29_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_30_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_31_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_32_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_33_fun__upd__def, axiom,
    ((fun_up9191ion_ty = (^[F2 : list_char > option_ty]: (^[A2 : list_char]: (^[B2 : option_ty]: (^[X2 : list_char]: (if_option_ty @ (X2 = A2) @ B2 @ (F2 @ X2))))))))). % fun_upd_def
thf(fact_34_fun__upd__def, axiom,
    ((fun_up1252458416on_val = (^[F2 : list_char > option_val]: (^[A2 : list_char]: (^[B2 : option_val]: (^[X2 : list_char]: (if_option_val @ (X2 = A2) @ B2 @ (F2 @ X2))))))))). % fun_upd_def
thf(fact_35_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_36_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_37_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_38_exp_Oinject_I3_J, axiom,
    ((![X3 : val, Y3 : val]: (((val_list_char @ X3) = (val_list_char @ Y3)) = (X3 = Y3))))). % exp.inject(3)
thf(fact_39_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_40_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_41_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_42_exp_Odistinct_I67_J, axiom,
    ((![X3 : val, X101 : list_char, X102 : ty, X103 : exp_list_char]: (~ (((val_list_char @ X3) = (block_list_char @ X101 @ X102 @ X103))))))). % exp.distinct(67)
thf(fact_43_exp_Odistinct_I69_J, axiom,
    ((![X3 : val, X111 : exp_list_char, X112 : exp_list_char]: (~ (((val_list_char @ X3) = (seq_list_char @ X111 @ X112))))))). % exp.distinct(69)
thf(fact_44_exp_Odistinct_I59_J, axiom,
    ((![X3 : val, X61 : list_char, X62 : exp_list_char]: (~ (((val_list_char @ X3) = (lAss_list_char @ X61 @ X62))))))). % exp.distinct(59)
thf(fact_45_WTrt_H__WTrts_H_Ointros_I16_J, axiom,
    ((![H : nat > option2118145160on_val, V : val, T_1 : ty, P : list_P1234162913t_char, T2 : ty, E : list_char > option_ty, V2 : list_char, E_2 : exp_list_char, T_2 : ty]: (((typeof_h @ H @ V) = (some_ty @ T_1)) => ((widen_917054840t_char @ P @ T_1 @ T2) => ((wTrt @ P @ H @ (fun_up9191ion_ty @ E @ V2 @ (some_ty @ T2)) @ E_2 @ T_2) => (wTrt @ P @ H @ E @ (block_list_char @ V2 @ T2 @ (seq_list_char @ (lAss_list_char @ V2 @ (val_list_char @ V)) @ E_2)) @ T_2))))))). % WTrt'_WTrts'.intros(16)
thf(fact_46_InitBlockRed_Oprems_I1_J, axiom,
    ((typeSa1777264139_sconf @ p @ e @ (produc52622304on_val @ ha @ la)))). % InitBlockRed.prems(1)
thf(fact_47_WTrt__elim__cases_I1_J, axiom,
    ((![P : list_P1234162913t_char, H : nat > option2118145160on_val, E : list_char > option_ty, V : list_char, E2 : exp_list_char, T2 : ty]: ((wTrt2 @ P @ H @ E @ (lAss_list_char @ V @ E2) @ T2) => (~ (((T2 = void) => (![T4 : ty]: (((E @ V) = (some_ty @ T4)) => (![T5 : ty]: ((wTrt2 @ P @ H @ E @ E2 @ T5) => (~ ((widen_917054840t_char @ P @ T5 @ T4)))))))))))))). % WTrt_elim_cases(1)
thf(fact_48_WTrtLAss, axiom,
    ((![E : list_char > option_ty, V2 : list_char, T2 : ty, P : list_P1234162913t_char, H : nat > option2118145160on_val, E2 : exp_list_char, T3 : ty]: (((E @ V2) = (some_ty @ T2)) => ((wTrt2 @ P @ H @ E @ E2 @ T3) => ((widen_917054840t_char @ P @ T3 @ T2) => (wTrt2 @ P @ H @ E @ (lAss_list_char @ V2 @ E2) @ void))))))). % WTrtLAss
thf(fact_49_InitBlockRed_Ohyps_I2_J, axiom,
    ((![E : list_char > option_ty, T2 : ty]: ((typeSa1777264139_sconf @ p @ E @ (produc52622304on_val @ ha @ (fun_up1252458416on_val @ la @ v @ (some_val @ v3)))) => ((wTrt2 @ p @ ha @ E @ ea @ T2) => (?[T5 : ty]: ((wTrt2 @ p @ h_a @ E @ e_a @ T5) & (widen_917054840t_char @ p @ T5 @ T2)))))))). % InitBlockRed.hyps(2)
thf(fact_50_IH, axiom,
    ((![E : list_char > option_ty, T2 : ty]: ((typeSa1777264139_sconf @ p @ E @ (produc52622304on_val @ ha @ (fun_up1252458416on_val @ la @ v @ (some_val @ v3)))) => ((wTrt2 @ p @ ha @ E @ ea @ T2) => (?[U : ty]: ((wTrt2 @ p @ h_a @ E @ e_a @ U) & (widen_917054840t_char @ p @ U @ T2)))))))). % IH
thf(fact_51_assigned__def, axiom,
    ((assigned = (^[V3 : list_char]: (^[E3 : exp_list_char]: (?[V4 : val]: (?[E4 : exp_list_char]: (E3 = (seq_list_char @ (lAss_list_char @ V3 @ (val_list_char @ V4)) @ E4))))))))). % assigned_def
thf(fact_52_conf, axiom,
    ((typeSa1777264139_sconf @ p @ e @ (produc52622304on_val @ ha @ la)))). % conf
thf(fact_53_wt_H__wt, axiom,
    ((![P : list_P1234162913t_char, H : nat > option2118145160on_val, E : list_char > option_ty, E2 : exp_list_char, T2 : ty]: ((wTrt @ P @ H @ E @ E2 @ T2) => (wTrt2 @ P @ H @ E @ E2 @ T2))))). % wt'_wt
thf(fact_54_wt__wt_H, axiom,
    ((![P : list_P1234162913t_char, H : nat > option2118145160on_val, E : list_char > option_ty, E2 : exp_list_char, T2 : ty]: ((wTrt2 @ P @ H @ E @ E2 @ T2) => (wTrt @ P @ H @ E @ E2 @ T2))))). % wt_wt'
thf(fact_55_wt_H__iff__wt, axiom,
    ((wTrt = wTrt2))). % wt'_iff_wt
thf(fact_56_WTrt_H__WTrts_H_Ointros_I18_J, axiom,
    ((![P : list_P1234162913t_char, H : nat > option2118145160on_val, E : list_char > option_ty, E_1 : exp_list_char, T_1 : ty, E_2 : exp_list_char, T_2 : ty]: ((wTrt @ P @ H @ E @ E_1 @ T_1) => ((wTrt @ P @ H @ E @ E_2 @ T_2) => (wTrt @ P @ H @ E @ (seq_list_char @ E_1 @ E_2) @ T_2)))))). % WTrt'_WTrts'.intros(18)
thf(fact_57_WTrt_H__WTrts_H_Ointros_I17_J, axiom,
    ((![P : list_P1234162913t_char, H : nat > option2118145160on_val, E : list_char > option_ty, V2 : list_char, T2 : ty, E2 : exp_list_char, T3 : ty]: ((wTrt @ P @ H @ (fun_up9191ion_ty @ E @ V2 @ (some_ty @ T2)) @ E2 @ T3) => ((~ ((assigned @ V2 @ E2))) => (wTrt @ P @ H @ E @ (block_list_char @ V2 @ T2 @ E2) @ T3)))))). % WTrt'_WTrts'.intros(17)
thf(fact_58_WTrt_H__WTrts_H_Ointros_I3_J, axiom,
    ((![H : nat > option2118145160on_val, V : val, T2 : ty, P : list_P1234162913t_char, E : list_char > option_ty]: (((typeof_h @ H @ V) = (some_ty @ T2)) => (wTrt @ P @ H @ E @ (val_list_char @ V) @ T2))))). % WTrt'_WTrts'.intros(3)
thf(fact_59_mem__Collect__eq, axiom,
    ((![A : produc1172664615on_val, P : produc1172664615on_val > $o]: ((member354538064on_val @ A @ (collec2055896722on_val @ P)) = (P @ A))))). % mem_Collect_eq
thf(fact_60_Collect__mem__eq, axiom,
    ((![A3 : set_Pr1189492743on_val]: ((collec2055896722on_val @ (^[X2 : produc1172664615on_val]: (member354538064on_val @ X2 @ A3))) = A3)))). % Collect_mem_eq
thf(fact_61_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_62_prod_Oinject, axiom,
    ((![X1 : nat > option2118145160on_val, X22 : list_char > option_val, Y1 : nat > option2118145160on_val, Y22 : list_char > option_val]: (((produc52622304on_val @ X1 @ X22) = (produc52622304on_val @ Y1 @ Y22)) = (((X1 = Y1)) & ((X22 = Y22))))))). % prod.inject
thf(fact_63_prod_Oinject, axiom,
    ((![X1 : produc1097884484on_val, X22 : produc1097884484on_val, Y1 : produc1097884484on_val, Y22 : produc1097884484on_val]: (((produc1069526295on_val @ X1 @ X22) = (produc1069526295on_val @ Y1 @ Y22)) = (((X1 = Y1)) & ((X22 = Y22))))))). % prod.inject
thf(fact_64_prod_Oinject, axiom,
    ((![X1 : exp_list_char, X22 : produc515445032on_val, Y1 : exp_list_char, Y22 : produc515445032on_val]: (((produc2023458740on_val @ X1 @ X22) = (produc2023458740on_val @ Y1 @ Y22)) = (((X1 = Y1)) & ((X22 = Y22))))))). % prod.inject
thf(fact_65_old_Oprod_Oinject, axiom,
    ((![A : nat > option2118145160on_val, B : list_char > option_val, A4 : nat > option2118145160on_val, B3 : list_char > option_val]: (((produc52622304on_val @ A @ B) = (produc52622304on_val @ A4 @ B3)) = (((A = A4)) & ((B = B3))))))). % old.prod.inject
thf(fact_66_old_Oprod_Oinject, axiom,
    ((![A : produc1097884484on_val, B : produc1097884484on_val, A4 : produc1097884484on_val, B3 : produc1097884484on_val]: (((produc1069526295on_val @ A @ B) = (produc1069526295on_val @ A4 @ B3)) = (((A = A4)) & ((B = B3))))))). % old.prod.inject
thf(fact_67_old_Oprod_Oinject, axiom,
    ((![A : exp_list_char, B : produc515445032on_val, A4 : exp_list_char, B3 : produc515445032on_val]: (((produc2023458740on_val @ A @ B) = (produc2023458740on_val @ A4 @ B3)) = (((A = A4)) & ((B = B3))))))). % old.prod.inject
thf(fact_68_redp__redsp_OInitBlockRed, axiom,
    ((![P : list_P1234162913t_char, E2 : exp_list_char, H : nat > option2118145160on_val, L : list_char > option_val, V2 : list_char, V : val, E5 : exp_list_char, H2 : nat > option2118145160on_val, L2 : list_char > option_val, V5 : val, T2 : ty]: ((redp @ P @ E2 @ (produc52622304on_val @ H @ (fun_up1252458416on_val @ L @ V2 @ (some_val @ V))) @ E5 @ (produc52622304on_val @ H2 @ L2)) => (((L2 @ V2) = (some_val @ V5)) => (redp @ P @ (block_list_char @ V2 @ T2 @ (seq_list_char @ (lAss_list_char @ V2 @ (val_list_char @ V)) @ E2)) @ (produc52622304on_val @ H @ L) @ (block_list_char @ V2 @ T2 @ (seq_list_char @ (lAss_list_char @ V2 @ (val_list_char @ V5)) @ E5)) @ (produc52622304on_val @ H2 @ (fun_up1252458416on_val @ L2 @ V2 @ (L @ V2))))))))). % redp_redsp.InitBlockRed
thf(fact_69_WTrt_H__elim__cases, axiom,
    ((![P : list_P1234162913t_char, H : nat > option2118145160on_val, E : list_char > option_ty, V2 : list_char, E2 : exp_list_char, T2 : ty]: ((wTrt @ P @ H @ E @ (lAss_list_char @ V2 @ E2) @ T2) => (~ (((T2 = void) => (![T4 : ty]: ((wTrt @ P @ H @ E @ (var_list_char @ V2) @ T4) => (![T5 : ty]: ((wTrt @ P @ H @ E @ E2 @ T5) => (~ ((widen_917054840t_char @ P @ T5 @ T4)))))))))))))). % WTrt'_elim_cases
thf(fact_70_WTrt_H__WTrts_H_Ointros_I7_J, axiom,
    ((![P : list_P1234162913t_char, H : nat > option2118145160on_val, E : list_char > option_ty, V2 : list_char, T2 : ty, E2 : exp_list_char, T3 : ty]: ((wTrt @ P @ H @ E @ (var_list_char @ V2) @ T2) => ((wTrt @ P @ H @ E @ E2 @ T3) => ((widen_917054840t_char @ P @ T3 @ T2) => (wTrt @ P @ H @ E @ (lAss_list_char @ V2 @ E2) @ void))))))). % WTrt'_WTrts'.intros(7)
thf(fact_71_pred__equals__eq2, axiom,
    ((![R : set_Pr723149704on_val, S : set_Pr723149704on_val]: (((^[X2 : nat > option2118145160on_val]: (^[Y2 : list_char > option_val]: (member652041809on_val @ (produc52622304on_val @ X2 @ Y2) @ R))) = (^[X2 : nat > option2118145160on_val]: (^[Y2 : list_char > option_val]: (member652041809on_val @ (produc52622304on_val @ X2 @ Y2) @ S)))) = (R = S))))). % pred_equals_eq2
thf(fact_72_pred__equals__eq2, axiom,
    ((![R : set_Pr1189492743on_val, S : set_Pr1189492743on_val]: (((^[X2 : produc1097884484on_val]: (^[Y2 : produc1097884484on_val]: (member354538064on_val @ (produc1069526295on_val @ X2 @ Y2) @ R))) = (^[X2 : produc1097884484on_val]: (^[Y2 : produc1097884484on_val]: (member354538064on_val @ (produc1069526295on_val @ X2 @ Y2) @ S)))) = (R = S))))). % pred_equals_eq2
thf(fact_73_pred__equals__eq2, axiom,
    ((![R : set_Pr556513572on_val, S : set_Pr556513572on_val]: (((^[X2 : exp_list_char]: (^[Y2 : produc515445032on_val]: (member1888679917on_val @ (produc2023458740on_val @ X2 @ Y2) @ R))) = (^[X2 : exp_list_char]: (^[Y2 : produc515445032on_val]: (member1888679917on_val @ (produc2023458740on_val @ X2 @ Y2) @ S)))) = (R = S))))). % pred_equals_eq2
thf(fact_74_exp_Oinject_I5_J, axiom,
    ((![X5 : list_char, Y5 : list_char]: (((var_list_char @ X5) = (var_list_char @ Y5)) = (X5 = Y5))))). % exp.inject(5)
thf(fact_75_red__reds_ORedSeq, axiom,
    ((![V : 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 @ V) @ E_2) @ S2) @ (produc2023458740on_val @ E_2 @ S2)) @ (red @ P))))). % red_reds.RedSeq
thf(fact_76_red__reds_OSeqRed, axiom,
    ((![E2 : exp_list_char, S2 : produc515445032on_val, E5 : exp_list_char, S3 : produc515445032on_val, P : list_P1234162913t_char, E_2 : exp_list_char]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E2 @ S2) @ (produc2023458740on_val @ E5 @ S3)) @ (red @ P)) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (seq_list_char @ E2 @ E_2) @ S2) @ (produc2023458740on_val @ (seq_list_char @ E5 @ E_2) @ S3)) @ (red @ P)))))). % red_reds.SeqRed
thf(fact_77_red__reds_OLAssRed, axiom,
    ((![E2 : exp_list_char, S2 : produc515445032on_val, E5 : exp_list_char, S3 : produc515445032on_val, P : list_P1234162913t_char, V2 : list_char]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E2 @ S2) @ (produc2023458740on_val @ E5 @ S3)) @ (red @ P)) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (lAss_list_char @ V2 @ E2) @ S2) @ (produc2023458740on_val @ (lAss_list_char @ V2 @ E5) @ S3)) @ (red @ P)))))). % red_reds.LAssRed
thf(fact_78_red__reds_ORedBlock, axiom,
    ((![V2 : list_char, T2 : ty, U2 : val, S2 : produc515445032on_val, P : list_P1234162913t_char]: (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (block_list_char @ V2 @ T2 @ (val_list_char @ U2)) @ S2) @ (produc2023458740on_val @ (val_list_char @ U2) @ S2)) @ (red @ P))))). % red_reds.RedBlock
thf(fact_79_redp__red__eq, axiom,
    ((redp = (^[P2 : list_P1234162913t_char]: (^[X2 : exp_list_char]: (^[Y2 : produc515445032on_val]: (^[Z2 : exp_list_char]: (^[Aa : produc515445032on_val]: (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ X2 @ Y2) @ (produc2023458740on_val @ Z2 @ Aa)) @ (red @ P2)))))))))). % redp_red_eq
thf(fact_80_exp_Odistinct_I57_J, axiom,
    ((![X3 : val, X5 : list_char]: (~ (((val_list_char @ X3) = (var_list_char @ X5))))))). % exp.distinct(57)
thf(fact_81_redp__redsp_OSeqRed, axiom,
    ((![P : list_P1234162913t_char, E2 : exp_list_char, S2 : produc515445032on_val, E5 : exp_list_char, S3 : produc515445032on_val, E_2 : exp_list_char]: ((redp @ P @ E2 @ S2 @ E5 @ S3) => (redp @ P @ (seq_list_char @ E2 @ E_2) @ S2 @ (seq_list_char @ E5 @ E_2) @ S3))))). % redp_redsp.SeqRed
thf(fact_82_redp__redsp_OLAssRed, axiom,
    ((![P : list_P1234162913t_char, E2 : exp_list_char, S2 : produc515445032on_val, E5 : exp_list_char, S3 : produc515445032on_val, V2 : list_char]: ((redp @ P @ E2 @ S2 @ E5 @ S3) => (redp @ P @ (lAss_list_char @ V2 @ E2) @ S2 @ (lAss_list_char @ V2 @ E5) @ S3))))). % redp_redsp.LAssRed
thf(fact_83_exp_Odistinct_I101_J, axiom,
    ((![X5 : list_char, X61 : list_char, X62 : exp_list_char]: (~ (((var_list_char @ X5) = (lAss_list_char @ X61 @ X62))))))). % exp.distinct(101)
thf(fact_84_exp_Odistinct_I111_J, axiom,
    ((![X5 : list_char, X111 : exp_list_char, X112 : exp_list_char]: (~ (((var_list_char @ X5) = (seq_list_char @ X111 @ X112))))))). % exp.distinct(111)
thf(fact_85_exp_Odistinct_I109_J, axiom,
    ((![X5 : list_char, X101 : list_char, X102 : ty, X103 : exp_list_char]: (~ (((var_list_char @ X5) = (block_list_char @ X101 @ X102 @ X103))))))). % exp.distinct(109)
thf(fact_86_red__reds_ORedInitBlock, axiom,
    ((![V2 : list_char, T2 : ty, V : val, U2 : val, S2 : produc515445032on_val, P : list_P1234162913t_char]: (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (block_list_char @ V2 @ T2 @ (seq_list_char @ (lAss_list_char @ V2 @ (val_list_char @ V)) @ (val_list_char @ U2))) @ S2) @ (produc2023458740on_val @ (val_list_char @ U2) @ S2)) @ (red @ P))))). % red_reds.RedInitBlock
thf(fact_87_redp__redsp_ORedSeq, axiom,
    ((![P : list_P1234162913t_char, V : val, E_2 : exp_list_char, S2 : produc515445032on_val]: (redp @ P @ (seq_list_char @ (val_list_char @ V) @ E_2) @ S2 @ E_2 @ S2)))). % redp_redsp.RedSeq
thf(fact_88_redp__redsp_ORedBlock, axiom,
    ((![P : list_P1234162913t_char, V2 : list_char, T2 : ty, U2 : val, S2 : produc515445032on_val]: (redp @ P @ (block_list_char @ V2 @ T2 @ (val_list_char @ U2)) @ S2 @ (val_list_char @ U2) @ S2)))). % redp_redsp.RedBlock
thf(fact_89_WTrtVar, axiom,
    ((![E : list_char > option_ty, V2 : list_char, T2 : ty, P : list_P1234162913t_char, H : nat > option2118145160on_val]: (((E @ V2) = (some_ty @ T2)) => (wTrt2 @ P @ H @ E @ (var_list_char @ V2) @ T2))))). % WTrtVar
thf(fact_90_WTrt_H__WTrts_H_Ointros_I4_J, axiom,
    ((![E : list_char > option_ty, V : list_char, T2 : ty, P : list_P1234162913t_char, H : nat > option2118145160on_val]: (((E @ V) = (some_ty @ T2)) => (wTrt @ P @ H @ E @ (var_list_char @ V) @ T2))))). % WTrt'_WTrts'.intros(4)
thf(fact_91_red__reds_OInitBlockRed, axiom,
    ((![E2 : exp_list_char, H : nat > option2118145160on_val, L : list_char > option_val, V2 : list_char, V : val, E5 : exp_list_char, H2 : nat > option2118145160on_val, L2 : list_char > option_val, P : list_P1234162913t_char, V5 : val, T2 : ty]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E2 @ (produc52622304on_val @ H @ (fun_up1252458416on_val @ L @ V2 @ (some_val @ V)))) @ (produc2023458740on_val @ E5 @ (produc52622304on_val @ H2 @ L2))) @ (red @ P)) => (((L2 @ V2) = (some_val @ V5)) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (block_list_char @ V2 @ T2 @ (seq_list_char @ (lAss_list_char @ V2 @ (val_list_char @ V)) @ E2)) @ (produc52622304on_val @ H @ L)) @ (produc2023458740on_val @ (block_list_char @ V2 @ T2 @ (seq_list_char @ (lAss_list_char @ V2 @ (val_list_char @ V5)) @ E5)) @ (produc52622304on_val @ H2 @ (fun_up1252458416on_val @ L2 @ V2 @ (L @ V2))))) @ (red @ P))))))). % red_reds.InitBlockRed
thf(fact_92_old_Oprod_Oinducts, axiom,
    ((![P : produc515445032on_val > $o, Prod : produc515445032on_val]: ((![A5 : nat > option2118145160on_val, B4 : list_char > option_val]: (P @ (produc52622304on_val @ A5 @ B4))) => (P @ Prod))))). % old.prod.inducts
thf(fact_93_old_Oprod_Oinducts, axiom,
    ((![P : produc1172664615on_val > $o, Prod : produc1172664615on_val]: ((![A5 : produc1097884484on_val, B4 : produc1097884484on_val]: (P @ (produc1069526295on_val @ A5 @ B4))) => (P @ Prod))))). % old.prod.inducts
thf(fact_94_old_Oprod_Oinducts, axiom,
    ((![P : produc1097884484on_val > $o, Prod : produc1097884484on_val]: ((![A5 : exp_list_char, B4 : produc515445032on_val]: (P @ (produc2023458740on_val @ A5 @ B4))) => (P @ Prod))))). % old.prod.inducts
thf(fact_95_old_Oprod_Oexhaust, axiom,
    ((![Y : produc515445032on_val]: (~ ((![A5 : nat > option2118145160on_val, B4 : list_char > option_val]: (~ ((Y = (produc52622304on_val @ A5 @ B4)))))))))). % old.prod.exhaust
thf(fact_96_old_Oprod_Oexhaust, axiom,
    ((![Y : produc1172664615on_val]: (~ ((![A5 : produc1097884484on_val, B4 : produc1097884484on_val]: (~ ((Y = (produc1069526295on_val @ A5 @ B4)))))))))). % old.prod.exhaust
thf(fact_97_old_Oprod_Oexhaust, axiom,
    ((![Y : produc1097884484on_val]: (~ ((![A5 : exp_list_char, B4 : produc515445032on_val]: (~ ((Y = (produc2023458740on_val @ A5 @ B4)))))))))). % old.prod.exhaust
thf(fact_98_prod__induct4, axiom,
    ((![P : produc1172664615on_val > $o, X : produc1172664615on_val]: ((![A5 : produc1097884484on_val, B4 : exp_list_char, C2 : nat > option2118145160on_val, D2 : list_char > option_val]: (P @ (produc1069526295on_val @ A5 @ (produc2023458740on_val @ B4 @ (produc52622304on_val @ C2 @ D2))))) => (P @ X))))). % prod_induct4
thf(fact_99_prod__induct3, axiom,
    ((![P : produc1172664615on_val > $o, X : produc1172664615on_val]: ((![A5 : produc1097884484on_val, B4 : exp_list_char, C2 : produc515445032on_val]: (P @ (produc1069526295on_val @ A5 @ (produc2023458740on_val @ B4 @ C2)))) => (P @ X))))). % prod_induct3
thf(fact_100_prod__induct3, axiom,
    ((![P : produc1097884484on_val > $o, X : produc1097884484on_val]: ((![A5 : exp_list_char, B4 : nat > option2118145160on_val, C2 : list_char > option_val]: (P @ (produc2023458740on_val @ A5 @ (produc52622304on_val @ B4 @ C2)))) => (P @ X))))). % prod_induct3
thf(fact_101_prod__cases4, axiom,
    ((![Y : produc1172664615on_val]: (~ ((![A5 : produc1097884484on_val, B4 : exp_list_char, C2 : nat > option2118145160on_val, D2 : list_char > option_val]: (~ ((Y = (produc1069526295on_val @ A5 @ (produc2023458740on_val @ B4 @ (produc52622304on_val @ C2 @ D2)))))))))))). % prod_cases4
thf(fact_102_prod__cases3, axiom,
    ((![Y : produc1172664615on_val]: (~ ((![A5 : produc1097884484on_val, B4 : exp_list_char, C2 : produc515445032on_val]: (~ ((Y = (produc1069526295on_val @ A5 @ (produc2023458740on_val @ B4 @ C2))))))))))). % prod_cases3
thf(fact_103_prod__cases3, axiom,
    ((![Y : produc1097884484on_val]: (~ ((![A5 : exp_list_char, B4 : nat > option2118145160on_val, C2 : list_char > option_val]: (~ ((Y = (produc2023458740on_val @ A5 @ (produc52622304on_val @ B4 @ C2))))))))))). % prod_cases3
thf(fact_104_Pair__inject, axiom,
    ((![A : nat > option2118145160on_val, B : list_char > option_val, A4 : nat > option2118145160on_val, B3 : list_char > option_val]: (((produc52622304on_val @ A @ B) = (produc52622304on_val @ A4 @ B3)) => (~ (((A = A4) => (~ ((B = B3)))))))))). % Pair_inject
thf(fact_105_Pair__inject, axiom,
    ((![A : produc1097884484on_val, B : produc1097884484on_val, A4 : produc1097884484on_val, B3 : produc1097884484on_val]: (((produc1069526295on_val @ A @ B) = (produc1069526295on_val @ A4 @ B3)) => (~ (((A = A4) => (~ ((B = B3)))))))))). % Pair_inject
thf(fact_106_Pair__inject, axiom,
    ((![A : exp_list_char, B : produc515445032on_val, A4 : exp_list_char, B3 : produc515445032on_val]: (((produc2023458740on_val @ A @ B) = (produc2023458740on_val @ A4 @ B3)) => (~ (((A = A4) => (~ ((B = B3)))))))))). % Pair_inject
thf(fact_107_prod__cases, axiom,
    ((![P : produc515445032on_val > $o, P3 : produc515445032on_val]: ((![A5 : nat > option2118145160on_val, B4 : list_char > option_val]: (P @ (produc52622304on_val @ A5 @ B4))) => (P @ P3))))). % prod_cases
thf(fact_108_prod__cases, axiom,
    ((![P : produc1172664615on_val > $o, P3 : produc1172664615on_val]: ((![A5 : produc1097884484on_val, B4 : produc1097884484on_val]: (P @ (produc1069526295on_val @ A5 @ B4))) => (P @ P3))))). % prod_cases
thf(fact_109_prod__cases, axiom,
    ((![P : produc1097884484on_val > $o, P3 : produc1097884484on_val]: ((![A5 : exp_list_char, B4 : produc515445032on_val]: (P @ (produc2023458740on_val @ A5 @ B4))) => (P @ P3))))). % prod_cases
thf(fact_110_surj__pair, axiom,
    ((![P3 : produc515445032on_val]: (?[X4 : nat > option2118145160on_val, Y4 : list_char > option_val]: (P3 = (produc52622304on_val @ X4 @ Y4)))))). % surj_pair
thf(fact_111_surj__pair, axiom,
    ((![P3 : produc1172664615on_val]: (?[X4 : produc1097884484on_val, Y4 : produc1097884484on_val]: (P3 = (produc1069526295on_val @ X4 @ Y4)))))). % surj_pair
thf(fact_112_surj__pair, axiom,
    ((![P3 : produc1097884484on_val]: (?[X4 : exp_list_char, Y4 : produc515445032on_val]: (P3 = (produc2023458740on_val @ X4 @ Y4)))))). % surj_pair
thf(fact_113_redp__redsp_ORedInitBlock, axiom,
    ((![P : list_P1234162913t_char, V2 : list_char, T2 : ty, V : val, U2 : val, S2 : produc515445032on_val]: (redp @ P @ (block_list_char @ V2 @ T2 @ (seq_list_char @ (lAss_list_char @ V2 @ (val_list_char @ V)) @ (val_list_char @ U2))) @ S2 @ (val_list_char @ U2) @ S2)))). % redp_redsp.RedInitBlock
thf(fact_114_red__reds_ORedVar, axiom,
    ((![S2 : produc515445032on_val, V2 : list_char, V : val, P : list_P1234162913t_char]: (((lcl @ S2 @ V2) = (some_val @ V)) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (var_list_char @ V2) @ S2) @ (produc2023458740on_val @ (val_list_char @ V) @ S2)) @ (red @ P)))))). % red_reds.RedVar
thf(fact_115_redp__redsp_ORedVar, axiom,
    ((![S2 : produc515445032on_val, V2 : list_char, V : val, P : list_P1234162913t_char]: (((lcl @ S2 @ V2) = (some_val @ V)) => (redp @ P @ (var_list_char @ V2) @ S2 @ (val_list_char @ V) @ S2))))). % redp_redsp.RedVar
thf(fact_116_red__reds_OBlockRedSome, axiom,
    ((![E2 : exp_list_char, H : nat > option2118145160on_val, L : list_char > option_val, V2 : list_char, E5 : exp_list_char, H2 : nat > option2118145160on_val, L2 : list_char > option_val, P : list_P1234162913t_char, V : val, T2 : ty]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E2 @ (produc52622304on_val @ H @ (fun_up1252458416on_val @ L @ V2 @ none_val))) @ (produc2023458740on_val @ E5 @ (produc52622304on_val @ H2 @ L2))) @ (red @ P)) => (((L2 @ V2) = (some_val @ V)) => ((~ ((assigned @ V2 @ E2))) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (block_list_char @ V2 @ T2 @ E2) @ (produc52622304on_val @ H @ L)) @ (produc2023458740on_val @ (block_list_char @ V2 @ T2 @ (seq_list_char @ (lAss_list_char @ V2 @ (val_list_char @ V)) @ E5)) @ (produc52622304on_val @ H2 @ (fun_up1252458416on_val @ L2 @ V2 @ (L @ V2))))) @ (red @ P)))))))). % red_reds.BlockRedSome
thf(fact_117_red__reds_ORedLAss, axiom,
    ((![V2 : list_char, V : val, H : nat > option2118145160on_val, L : list_char > option_val, P : list_P1234162913t_char]: (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (lAss_list_char @ V2 @ (val_list_char @ V)) @ (produc52622304on_val @ H @ L)) @ (produc2023458740on_val @ (val_list_char @ unit) @ (produc52622304on_val @ H @ (fun_up1252458416on_val @ L @ V2 @ (some_val @ V))))) @ (red @ P))))). % red_reds.RedLAss
thf(fact_118_not__Some__eq, axiom,
    ((![X : option2118145160on_val]: ((![Y2 : produc266837688on_val]: (~ ((X = (some_P1299442195on_val @ Y2))))) = (X = none_P1535574167on_val))))). % not_Some_eq
thf(fact_119_not__Some__eq, axiom,
    ((![X : option_ty]: ((![Y2 : ty]: (~ ((X = (some_ty @ Y2))))) = (X = none_ty))))). % not_Some_eq
thf(fact_120_not__Some__eq, axiom,
    ((![X : option_val]: ((![Y2 : val]: (~ ((X = (some_val @ Y2))))) = (X = none_val))))). % not_Some_eq
thf(fact_121_not__None__eq, axiom,
    ((![X : option2118145160on_val]: ((~ ((X = none_P1535574167on_val))) = (?[Y2 : produc266837688on_val]: (X = (some_P1299442195on_val @ Y2))))))). % not_None_eq
thf(fact_122_not__None__eq, axiom,
    ((![X : option_ty]: ((~ ((X = none_ty))) = (?[Y2 : ty]: (X = (some_ty @ Y2))))))). % not_None_eq
thf(fact_123_not__None__eq, axiom,
    ((![X : option_val]: ((~ ((X = none_val))) = (?[Y2 : val]: (X = (some_val @ Y2))))))). % not_None_eq
thf(fact_124_empty__upd__none, axiom,
    ((![X : list_char]: ((fun_up9191ion_ty @ (^[X2 : list_char]: none_ty) @ X @ none_ty) = (^[X2 : list_char]: none_ty))))). % empty_upd_none
thf(fact_125_empty__upd__none, axiom,
    ((![X : list_char]: ((fun_up1252458416on_val @ (^[X2 : list_char]: none_val) @ X @ none_val) = (^[X2 : list_char]: none_val))))). % empty_upd_none
thf(fact_126_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)) => ((![A5 : produc266837688on_val, B4 : produc266837688on_val]: ((X = (some_P1299442195on_val @ A5)) => ((Y = (some_P1299442195on_val @ B4)) => (P @ X @ Y)))) => (P @ X @ Y))))))). % combine_options_cases
thf(fact_127_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)) => ((![A5 : produc266837688on_val, B4 : ty]: ((X = (some_P1299442195on_val @ A5)) => ((Y = (some_ty @ B4)) => (P @ X @ Y)))) => (P @ X @ Y))))))). % combine_options_cases
thf(fact_128_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)) => ((![A5 : produc266837688on_val, B4 : val]: ((X = (some_P1299442195on_val @ A5)) => ((Y = (some_val @ B4)) => (P @ X @ Y)))) => (P @ X @ Y))))))). % combine_options_cases
thf(fact_129_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)) => ((![A5 : ty, B4 : produc266837688on_val]: ((X = (some_ty @ A5)) => ((Y = (some_P1299442195on_val @ B4)) => (P @ X @ Y)))) => (P @ X @ Y))))))). % combine_options_cases
thf(fact_130_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)) => ((![A5 : ty, B4 : ty]: ((X = (some_ty @ A5)) => ((Y = (some_ty @ B4)) => (P @ X @ Y)))) => (P @ X @ Y))))))). % combine_options_cases
thf(fact_131_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)) => ((![A5 : ty, B4 : val]: ((X = (some_ty @ A5)) => ((Y = (some_val @ B4)) => (P @ X @ Y)))) => (P @ X @ Y))))))). % combine_options_cases
thf(fact_132_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)) => ((![A5 : val, B4 : produc266837688on_val]: ((X = (some_val @ A5)) => ((Y = (some_P1299442195on_val @ B4)) => (P @ X @ Y)))) => (P @ X @ Y))))))). % combine_options_cases
thf(fact_133_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)) => ((![A5 : val, B4 : ty]: ((X = (some_val @ A5)) => ((Y = (some_ty @ B4)) => (P @ X @ Y)))) => (P @ X @ Y))))))). % combine_options_cases
thf(fact_134_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)) => ((![A5 : val, B4 : val]: ((X = (some_val @ A5)) => ((Y = (some_val @ B4)) => (P @ X @ Y)))) => (P @ X @ Y))))))). % combine_options_cases
thf(fact_135_split__option__all, axiom,
    (((^[P4 : option2118145160on_val > $o]: (![X6 : option2118145160on_val]: (P4 @ X6))) = (^[P2 : option2118145160on_val > $o]: (((P2 @ none_P1535574167on_val)) & ((![X2 : produc266837688on_val]: (P2 @ (some_P1299442195on_val @ X2))))))))). % split_option_all
thf(fact_136_split__option__all, axiom,
    (((^[P4 : option_ty > $o]: (![X6 : option_ty]: (P4 @ X6))) = (^[P2 : option_ty > $o]: (((P2 @ none_ty)) & ((![X2 : ty]: (P2 @ (some_ty @ X2))))))))). % split_option_all
thf(fact_137_split__option__all, axiom,
    (((^[P4 : option_val > $o]: (![X6 : option_val]: (P4 @ X6))) = (^[P2 : option_val > $o]: (((P2 @ none_val)) & ((![X2 : val]: (P2 @ (some_val @ X2))))))))). % split_option_all
thf(fact_138_split__option__ex, axiom,
    (((^[P4 : option2118145160on_val > $o]: (?[X6 : option2118145160on_val]: (P4 @ X6))) = (^[P2 : option2118145160on_val > $o]: (((P2 @ none_P1535574167on_val)) | ((?[X2 : produc266837688on_val]: (P2 @ (some_P1299442195on_val @ X2))))))))). % split_option_ex
thf(fact_139_split__option__ex, axiom,
    (((^[P4 : option_ty > $o]: (?[X6 : option_ty]: (P4 @ X6))) = (^[P2 : option_ty > $o]: (((P2 @ none_ty)) | ((?[X2 : ty]: (P2 @ (some_ty @ X2))))))))). % split_option_ex
thf(fact_140_split__option__ex, axiom,
    (((^[P4 : option_val > $o]: (?[X6 : option_val]: (P4 @ X6))) = (^[P2 : option_val > $o]: (((P2 @ none_val)) | ((?[X2 : val]: (P2 @ (some_val @ X2))))))))). % split_option_ex
thf(fact_141_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_142_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_143_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_144_option_Oexhaust, axiom,
    ((![Y : option2118145160on_val]: ((~ ((Y = none_P1535574167on_val))) => (~ ((![X23 : produc266837688on_val]: (~ ((Y = (some_P1299442195on_val @ X23))))))))))). % option.exhaust
thf(fact_145_option_Oexhaust, axiom,
    ((![Y : option_ty]: ((~ ((Y = none_ty))) => (~ ((![X23 : ty]: (~ ((Y = (some_ty @ X23))))))))))). % option.exhaust
thf(fact_146_option_Oexhaust, axiom,
    ((![Y : option_val]: ((~ ((Y = none_val))) => (~ ((![X23 : val]: (~ ((Y = (some_val @ X23))))))))))). % option.exhaust
thf(fact_147_option_OdiscI, axiom,
    ((![Option : option2118145160on_val, X22 : produc266837688on_val]: ((Option = (some_P1299442195on_val @ X22)) => (~ ((Option = none_P1535574167on_val))))))). % option.discI
thf(fact_148_option_OdiscI, axiom,
    ((![Option : option_ty, X22 : ty]: ((Option = (some_ty @ X22)) => (~ ((Option = none_ty))))))). % option.discI
thf(fact_149_option_OdiscI, axiom,
    ((![Option : option_val, X22 : val]: ((Option = (some_val @ X22)) => (~ ((Option = none_val))))))). % option.discI
thf(fact_150_option_Odistinct_I1_J, axiom,
    ((![X22 : produc266837688on_val]: (~ ((none_P1535574167on_val = (some_P1299442195on_val @ X22))))))). % option.distinct(1)
thf(fact_151_option_Odistinct_I1_J, axiom,
    ((![X22 : ty]: (~ ((none_ty = (some_ty @ X22))))))). % option.distinct(1)
thf(fact_152_option_Odistinct_I1_J, axiom,
    ((![X22 : val]: (~ ((none_val = (some_val @ X22))))))). % option.distinct(1)
thf(fact_153_map__upd__nonempty, axiom,
    ((![T : list_char > option_ty, K : list_char, X : ty]: (~ (((fun_up9191ion_ty @ T @ K @ (some_ty @ X)) = (^[X2 : list_char]: none_ty))))))). % map_upd_nonempty
thf(fact_154_map__upd__nonempty, axiom,
    ((![T : list_char > option_val, K : list_char, X : val]: (~ (((fun_up1252458416on_val @ T @ K @ (some_val @ X)) = (^[X2 : list_char]: none_val))))))). % map_upd_nonempty
thf(fact_155_redp__redsp_OBlockRedNone, axiom,
    ((![P : list_P1234162913t_char, E2 : exp_list_char, H : nat > option2118145160on_val, L : list_char > option_val, V2 : list_char, E5 : exp_list_char, H2 : nat > option2118145160on_val, L2 : list_char > option_val, T2 : ty]: ((redp @ P @ E2 @ (produc52622304on_val @ H @ (fun_up1252458416on_val @ L @ V2 @ none_val)) @ E5 @ (produc52622304on_val @ H2 @ L2)) => (((L2 @ V2) = none_val) => ((~ ((assigned @ V2 @ E2))) => (redp @ P @ (block_list_char @ V2 @ T2 @ E2) @ (produc52622304on_val @ H @ L) @ (block_list_char @ V2 @ T2 @ E5) @ (produc52622304on_val @ H2 @ (fun_up1252458416on_val @ L2 @ V2 @ (L @ V2)))))))))). % redp_redsp.BlockRedNone
thf(fact_156_red__reds_OBlockRedNone, axiom,
    ((![E2 : exp_list_char, H : nat > option2118145160on_val, L : list_char > option_val, V2 : list_char, E5 : exp_list_char, H2 : nat > option2118145160on_val, L2 : list_char > option_val, P : list_P1234162913t_char, T2 : ty]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E2 @ (produc52622304on_val @ H @ (fun_up1252458416on_val @ L @ V2 @ none_val))) @ (produc2023458740on_val @ E5 @ (produc52622304on_val @ H2 @ L2))) @ (red @ P)) => (((L2 @ V2) = none_val) => ((~ ((assigned @ V2 @ E2))) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (block_list_char @ V2 @ T2 @ E2) @ (produc52622304on_val @ H @ L)) @ (produc2023458740on_val @ (block_list_char @ V2 @ T2 @ E5) @ (produc52622304on_val @ H2 @ (fun_up1252458416on_val @ L2 @ V2 @ (L @ V2))))) @ (red @ P)))))))). % red_reds.BlockRedNone
thf(fact_157_redp__redsp_ORedLAss, axiom,
    ((![P : list_P1234162913t_char, V2 : list_char, V : val, H : nat > option2118145160on_val, L : list_char > option_val]: (redp @ P @ (lAss_list_char @ V2 @ (val_list_char @ V)) @ (produc52622304on_val @ H @ L) @ (val_list_char @ unit) @ (produc52622304on_val @ H @ (fun_up1252458416on_val @ L @ V2 @ (some_val @ V))))))). % redp_redsp.RedLAss
thf(fact_158_redp__redsp_OBlockRedSome, axiom,
    ((![P : list_P1234162913t_char, E2 : exp_list_char, H : nat > option2118145160on_val, L : list_char > option_val, V2 : list_char, E5 : exp_list_char, H2 : nat > option2118145160on_val, L2 : list_char > option_val, V : val, T2 : ty]: ((redp @ P @ E2 @ (produc52622304on_val @ H @ (fun_up1252458416on_val @ L @ V2 @ none_val)) @ E5 @ (produc52622304on_val @ H2 @ L2)) => (((L2 @ V2) = (some_val @ V)) => ((~ ((assigned @ V2 @ E2))) => (redp @ P @ (block_list_char @ V2 @ T2 @ E2) @ (produc52622304on_val @ H @ L) @ (block_list_char @ V2 @ T2 @ (seq_list_char @ (lAss_list_char @ V2 @ (val_list_char @ V)) @ E5)) @ (produc52622304on_val @ H2 @ (fun_up1252458416on_val @ L2 @ V2 @ (L @ V2)))))))))). % redp_redsp.BlockRedSome
thf(fact_159_typeof__h_Osimps_I1_J, axiom,
    ((![H : nat > option2118145160on_val]: ((typeof_h @ H @ unit) = (some_ty @ void))))). % typeof_h.simps(1)
thf(fact_160_red__preserves__hconf, axiom,
    ((![E2 : exp_list_char, H : nat > option2118145160on_val, L : list_char > option_val, E5 : exp_list_char, H2 : nat > option2118145160on_val, L2 : list_char > option_val, P : list_P1234162913t_char, E : list_char > option_ty, T2 : ty]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E2 @ (produc52622304on_val @ H @ L)) @ (produc2023458740on_val @ E5 @ (produc52622304on_val @ H2 @ L2))) @ (red @ P)) => ((wTrt2 @ P @ H @ E @ E2 @ T2) => ((hconf_1244167010t_char @ P @ H) => (hconf_1244167010t_char @ P @ H2))))))). % red_preserves_hconf
thf(fact_161_red__preserves__lconf, axiom,
    ((![E2 : exp_list_char, H : nat > option2118145160on_val, L : list_char > option_val, E5 : exp_list_char, H2 : nat > option2118145160on_val, L2 : list_char > option_val, P : list_P1234162913t_char, E : list_char > option_ty, T2 : ty]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E2 @ (produc52622304on_val @ H @ L)) @ (produc2023458740on_val @ E5 @ (produc52622304on_val @ H2 @ L2))) @ (red @ P)) => ((wTrt2 @ P @ H @ E @ E2 @ T2) => ((lconf_485928294t_char @ P @ H @ L @ E) => (lconf_485928294t_char @ P @ H2 @ L2 @ E))))))). % red_preserves_lconf
thf(fact_162_typeof__lit__typeof, axiom,
    ((![V : val, T2 : ty, H : nat > option2118145160on_val]: (((typeof_h @ (^[X2 : nat]: none_P1535574167on_val) @ V) = (some_ty @ T2)) => ((typeof_h @ H @ V) = (some_ty @ T2)))))). % typeof_lit_typeof
thf(fact_163_lconf__empty, axiom,
    ((![P : list_P1234162913t_char, H : nat > option2118145160on_val, E : list_char > option_ty]: (lconf_485928294t_char @ P @ H @ (^[X2 : list_char]: none_val) @ E)))). % lconf_empty
thf(fact_164_red__preserves__sconf, axiom,
    ((![E2 : exp_list_char, S2 : produc515445032on_val, E5 : exp_list_char, S3 : produc515445032on_val, P : list_P1234162913t_char, E : list_char > option_ty, T2 : ty]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E2 @ S2) @ (produc2023458740on_val @ E5 @ S3)) @ (red @ P)) => ((wTrt2 @ P @ (hp @ S2) @ E @ E2 @ T2) => ((typeSa1777264139_sconf @ P @ E @ S2) => (typeSa1777264139_sconf @ P @ E @ S3))))))). % red_preserves_sconf
thf(fact_165_lconf__upd2, axiom,
    ((![P : list_P1234162913t_char, H : nat > option2118145160on_val, L : list_char > option_val, E : list_char > option_ty, V : val, T2 : ty, V2 : list_char]: ((lconf_485928294t_char @ P @ H @ L @ E) => ((conf_P93989998t_char @ P @ H @ V @ T2) => (lconf_485928294t_char @ P @ H @ (fun_up1252458416on_val @ L @ V2 @ (some_val @ V)) @ (fun_up9191ion_ty @ E @ V2 @ (some_ty @ T2)))))))). % lconf_upd2
thf(fact_166_LAssRedsVal, axiom,
    ((![E2 : exp_list_char, S2 : produc515445032on_val, V : val, H2 : nat > option2118145160on_val, L2 : list_char > option_val, P : list_P1234162913t_char, V2 : list_char]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E2 @ S2) @ (produc2023458740on_val @ (val_list_char @ V) @ (produc52622304on_val @ H2 @ L2))) @ (transi111096263on_val @ (red @ P))) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (lAss_list_char @ V2 @ E2) @ S2) @ (produc2023458740on_val @ (val_list_char @ unit) @ (produc52622304on_val @ H2 @ (fun_up1252458416on_val @ L2 @ V2 @ (some_val @ V))))) @ (transi111096263on_val @ (red @ P))))))). % LAssRedsVal
thf(fact_167_conf__widen, axiom,
    ((![P : list_P1234162913t_char, H : nat > option2118145160on_val, V : val, T2 : ty, T3 : ty]: ((conf_P93989998t_char @ P @ H @ V @ T2) => ((widen_917054840t_char @ P @ T2 @ T3) => (conf_P93989998t_char @ P @ H @ V @ T3)))))). % conf_widen
thf(fact_168_SeqReds, axiom,
    ((![E2 : exp_list_char, S2 : produc515445032on_val, E5 : exp_list_char, S3 : produc515445032on_val, P : list_P1234162913t_char, E_2 : exp_list_char]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E2 @ S2) @ (produc2023458740on_val @ E5 @ S3)) @ (transi111096263on_val @ (red @ P))) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (seq_list_char @ E2 @ E_2) @ S2) @ (produc2023458740on_val @ (seq_list_char @ E5 @ E_2) @ S3)) @ (transi111096263on_val @ (red @ P))))))). % SeqReds
thf(fact_169_LAssReds, axiom,
    ((![E2 : exp_list_char, S2 : produc515445032on_val, E5 : exp_list_char, S3 : produc515445032on_val, P : list_P1234162913t_char, V2 : list_char]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E2 @ S2) @ (produc2023458740on_val @ E5 @ S3)) @ (transi111096263on_val @ (red @ P))) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (lAss_list_char @ V2 @ E2) @ S2) @ (produc2023458740on_val @ (lAss_list_char @ V2 @ E5) @ S3)) @ (transi111096263on_val @ (red @ P))))))). % LAssReds
thf(fact_170_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_171_converse__rtrancl__induct__red, axiom,
    ((![E2 : exp_list_char, H : nat > option2118145160on_val, L : list_char > option_val, E5 : 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 @ E5 @ (produc52622304on_val @ H2 @ L2))) @ (transi111096263on_val @ (red @ P))) => ((![E6 : exp_list_char, H3 : nat > option2118145160on_val, L3 : list_char > option_val]: (R @ E6 @ H3 @ L3 @ E6 @ H3 @ L3)) => ((![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, E7 : 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_12 @ (produc52622304on_val @ H_1 @ L_1))) @ (red @ P)) => ((R @ E_12 @ H_1 @ L_1 @ E7 @ H4 @ L4) => (R @ E_0 @ H_0 @ L_0 @ E7 @ H4 @ L4)))) => (R @ E2 @ H @ L @ E5 @ H2 @ L2))))))). % converse_rtrancl_induct_red
thf(fact_172_conf__def, axiom,
    ((conf_P93989998t_char = (^[P2 : list_P1234162913t_char]: (^[H5 : nat > option2118145160on_val]: (^[V4 : val]: (^[T6 : ty]: (?[T7 : ty]: ((((typeof_h @ H5 @ V4) = (some_ty @ T7))) & ((widen_917054840t_char @ P2 @ T7 @ T6))))))))))). % conf_def
thf(fact_173_lconf__def, axiom,
    ((lconf_485928294t_char = (^[P2 : list_P1234162913t_char]: (^[H5 : nat > option2118145160on_val]: (^[L5 : list_char > option_val]: (^[E8 : list_char > option_ty]: (![V3 : list_char]: (![V4 : val]: ((((L5 @ V3) = (some_val @ V4))) => ((?[T6 : ty]: ((((E8 @ V3) = (some_ty @ T6))) & ((conf_P93989998t_char @ P2 @ H5 @ V4 @ T6))))))))))))))). % lconf_def
thf(fact_174_lconf__upd, axiom,
    ((![P : list_P1234162913t_char, H : nat > option2118145160on_val, L : list_char > option_val, E : list_char > option_ty, V : val, T2 : ty, V2 : list_char]: ((lconf_485928294t_char @ P @ H @ L @ E) => ((conf_P93989998t_char @ P @ H @ V @ T2) => (((E @ V2) = (some_ty @ T2)) => (lconf_485928294t_char @ P @ H @ (fun_up1252458416on_val @ L @ V2 @ (some_val @ V)) @ E))))))). % lconf_upd
thf(fact_175_InitBlockRedsFinal, axiom,
    ((![E2 : exp_list_char, H : nat > option2118145160on_val, L : list_char > option_val, V2 : list_char, V : val, E5 : exp_list_char, H2 : nat > option2118145160on_val, L2 : list_char > option_val, P : list_P1234162913t_char, T2 : ty]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E2 @ (produc52622304on_val @ H @ (fun_up1252458416on_val @ L @ V2 @ (some_val @ V)))) @ (produc2023458740on_val @ E5 @ (produc52622304on_val @ H2 @ L2))) @ (transi111096263on_val @ (red @ P))) => ((final_list_char @ E5) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (block_list_char @ V2 @ T2 @ (seq_list_char @ (lAss_list_char @ V2 @ (val_list_char @ V)) @ E2)) @ (produc52622304on_val @ H @ L)) @ (produc2023458740on_val @ E5 @ (produc52622304on_val @ H2 @ (fun_up1252458416on_val @ L2 @ V2 @ (L @ V2))))) @ (transi111096263on_val @ (red @ P)))))))). % InitBlockRedsFinal
thf(fact_176_InitBlockReds, axiom,
    ((![E2 : exp_list_char, H : nat > option2118145160on_val, L : list_char > option_val, V2 : list_char, V : val, E5 : exp_list_char, H2 : nat > option2118145160on_val, L2 : list_char > option_val, P : list_P1234162913t_char, T2 : ty]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E2 @ (produc52622304on_val @ H @ (fun_up1252458416on_val @ L @ V2 @ (some_val @ V)))) @ (produc2023458740on_val @ E5 @ (produc52622304on_val @ H2 @ L2))) @ (transi111096263on_val @ (red @ P))) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (block_list_char @ V2 @ T2 @ (seq_list_char @ (lAss_list_char @ V2 @ (val_list_char @ V)) @ E2)) @ (produc52622304on_val @ H @ L)) @ (produc2023458740on_val @ (block_list_char @ V2 @ T2 @ (seq_list_char @ (lAss_list_char @ V2 @ (val_list_char @ (the_val @ (L2 @ V2)))) @ E5)) @ (produc52622304on_val @ H2 @ (fun_up1252458416on_val @ L2 @ V2 @ (L @ V2))))) @ (transi111096263on_val @ (red @ P))))))). % InitBlockReds
thf(fact_177_option_Ocollapse, axiom,
    ((![Option : option2118145160on_val]: ((~ ((Option = none_P1535574167on_val))) => ((some_P1299442195on_val @ (the_Pr901949220on_val @ Option)) = Option))))). % option.collapse
thf(fact_178_option_Ocollapse, axiom,
    ((![Option : option_ty]: ((~ ((Option = none_ty))) => ((some_ty @ (the_ty @ Option)) = Option))))). % option.collapse
thf(fact_179_option_Ocollapse, axiom,
    ((![Option : option_val]: ((~ ((Option = none_val))) => ((some_val @ (the_val @ Option)) = Option))))). % option.collapse
thf(fact_180_option_Osel, axiom,
    ((![X22 : ty]: ((the_ty @ (some_ty @ X22)) = X22)))). % option.sel
thf(fact_181_option_Osel, axiom,
    ((![X22 : val]: ((the_val @ (some_val @ X22)) = X22)))). % option.sel
thf(fact_182_option_Oexpand, axiom,
    ((![Option : option_val, Option2 : option_val]: (((Option = none_val) = (Option2 = none_val)) => (((~ ((Option = none_val))) => ((~ ((Option2 = none_val))) => ((the_val @ Option) = (the_val @ Option2)))) => (Option = Option2)))))). % option.expand
thf(fact_183_option_Oexpand, axiom,
    ((![Option : option2118145160on_val, Option2 : option2118145160on_val]: (((Option = none_P1535574167on_val) = (Option2 = none_P1535574167on_val)) => (((~ ((Option = none_P1535574167on_val))) => ((~ ((Option2 = none_P1535574167on_val))) => ((the_Pr901949220on_val @ Option) = (the_Pr901949220on_val @ Option2)))) => (Option = Option2)))))). % option.expand
thf(fact_184_option_Oexhaust__sel, axiom,
    ((![Option : option2118145160on_val]: ((~ ((Option = none_P1535574167on_val))) => (Option = (some_P1299442195on_val @ (the_Pr901949220on_val @ Option))))))). % option.exhaust_sel
thf(fact_185_option_Oexhaust__sel, axiom,
    ((![Option : option_ty]: ((~ ((Option = none_ty))) => (Option = (some_ty @ (the_ty @ Option))))))). % option.exhaust_sel
thf(fact_186_option_Oexhaust__sel, axiom,
    ((![Option : option_val]: ((~ ((Option = none_val))) => (Option = (some_val @ (the_val @ Option))))))). % option.exhaust_sel
thf(fact_187_BlockRedsFinal, axiom,
    ((![E_02 : exp_list_char, S_0 : produc515445032on_val, E_2 : exp_list_char, H_2 : nat > option2118145160on_val, L_2 : list_char > option_val, P : list_P1234162913t_char, H_02 : nat > option2118145160on_val, L_02 : list_char > option_val, V2 : list_char, T2 : ty]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E_02 @ S_0) @ (produc2023458740on_val @ E_2 @ (produc52622304on_val @ H_2 @ L_2))) @ (transi111096263on_val @ (red @ P))) => ((final_list_char @ E_2) => ((S_0 = (produc52622304on_val @ H_02 @ (fun_up1252458416on_val @ L_02 @ V2 @ none_val))) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (block_list_char @ V2 @ T2 @ E_02) @ (produc52622304on_val @ H_02 @ L_02)) @ (produc2023458740on_val @ E_2 @ (produc52622304on_val @ H_2 @ (fun_up1252458416on_val @ L_2 @ V2 @ (L_02 @ V2))))) @ (transi111096263on_val @ (red @ P))))))))). % BlockRedsFinal
thf(fact_188_InitBlockReds__aux, axiom,
    ((![E2 : exp_list_char, S2 : produc515445032on_val, E5 : exp_list_char, S3 : produc515445032on_val, P : list_P1234162913t_char, V2 : list_char, T2 : ty]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E2 @ S2) @ (produc2023458740on_val @ E5 @ S3)) @ (transi111096263on_val @ (red @ P))) => (![H6 : nat > option2118145160on_val, L6 : list_char > option_val, H7 : nat > option2118145160on_val, L7 : list_char > option_val, V6 : val]: ((S2 = (produc52622304on_val @ H6 @ (fun_up1252458416on_val @ L6 @ V2 @ (some_val @ V6)))) => ((S3 = (produc52622304on_val @ H7 @ L7)) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (block_list_char @ V2 @ T2 @ (seq_list_char @ (lAss_list_char @ V2 @ (val_list_char @ V6)) @ E2)) @ (produc52622304on_val @ H6 @ L6)) @ (produc2023458740on_val @ (block_list_char @ V2 @ T2 @ (seq_list_char @ (lAss_list_char @ V2 @ (val_list_char @ (the_val @ (L7 @ V2)))) @ E5)) @ (produc52622304on_val @ H7 @ (fun_up1252458416on_val @ L7 @ V2 @ (L6 @ V2))))) @ (transi111096263on_val @ (red @ P)))))))))). % InitBlockReds_aux
thf(fact_189_rtrancl__induct2, axiom,
    ((![Ax : nat > option2118145160on_val, Ay : list_char > option_val, Bx : nat > option2118145160on_val, By : list_char > option_val, R2 : set_Pr148564103on_val, P : (nat > option2118145160on_val) > (list_char > option_val) > $o]: ((member2027247312on_val @ (produc2106877847on_val @ (produc52622304on_val @ Ax @ Ay) @ (produc52622304on_val @ Bx @ By)) @ (transi432893227on_val @ R2)) => ((P @ Ax @ Ay) => ((![A5 : nat > option2118145160on_val, B4 : list_char > option_val, Aa2 : nat > option2118145160on_val, Ba : list_char > option_val]: ((member2027247312on_val @ (produc2106877847on_val @ (produc52622304on_val @ Ax @ Ay) @ (produc52622304on_val @ A5 @ B4)) @ (transi432893227on_val @ R2)) => ((member2027247312on_val @ (produc2106877847on_val @ (produc52622304on_val @ A5 @ B4) @ (produc52622304on_val @ Aa2 @ Ba)) @ R2) => ((P @ A5 @ B4) => (P @ Aa2 @ Ba))))) => (P @ Bx @ By))))))). % rtrancl_induct2
thf(fact_190_rtrancl__induct2, axiom,
    ((![Ax : produc1097884484on_val, Ay : produc1097884484on_val, Bx : produc1097884484on_val, By : produc1097884484on_val, R2 : set_Pr1368603847on_val, P : produc1097884484on_val > produc1097884484on_val > $o]: ((member208988944on_val @ (produc564964183on_val @ (produc1069526295on_val @ Ax @ Ay) @ (produc1069526295on_val @ Bx @ By)) @ (transi100378922on_val @ R2)) => ((P @ Ax @ Ay) => ((![A5 : produc1097884484on_val, B4 : produc1097884484on_val, Aa2 : produc1097884484on_val, Ba : produc1097884484on_val]: ((member208988944on_val @ (produc564964183on_val @ (produc1069526295on_val @ Ax @ Ay) @ (produc1069526295on_val @ A5 @ B4)) @ (transi100378922on_val @ R2)) => ((member208988944on_val @ (produc564964183on_val @ (produc1069526295on_val @ A5 @ B4) @ (produc1069526295on_val @ Aa2 @ Ba)) @ R2) => ((P @ A5 @ B4) => (P @ Aa2 @ Ba))))) => (P @ Bx @ By))))))). % rtrancl_induct2
thf(fact_191_rtrancl__induct2, axiom,
    ((![Ax : exp_list_char, Ay : produc515445032on_val, Bx : exp_list_char, By : produc515445032on_val, R2 : set_Pr1189492743on_val, P : exp_list_char > produc515445032on_val > $o]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ Ax @ Ay) @ (produc2023458740on_val @ Bx @ By)) @ (transi111096263on_val @ R2)) => ((P @ Ax @ Ay) => ((![A5 : exp_list_char, B4 : produc515445032on_val, Aa2 : exp_list_char, Ba : produc515445032on_val]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ Ax @ Ay) @ (produc2023458740on_val @ A5 @ B4)) @ (transi111096263on_val @ R2)) => ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ A5 @ B4) @ (produc2023458740on_val @ Aa2 @ Ba)) @ R2) => ((P @ A5 @ B4) => (P @ Aa2 @ Ba))))) => (P @ Bx @ By))))))). % rtrancl_induct2
thf(fact_192_converse__rtranclE2, axiom,
    ((![Xa : nat > option2118145160on_val, Xb : list_char > option_val, Za : nat > option2118145160on_val, Zb : list_char > option_val, R2 : set_Pr148564103on_val]: ((member2027247312on_val @ (produc2106877847on_val @ (produc52622304on_val @ Xa @ Xb) @ (produc52622304on_val @ Za @ Zb)) @ (transi432893227on_val @ R2)) => ((~ (((produc52622304on_val @ Xa @ Xb) = (produc52622304on_val @ Za @ Zb)))) => (~ ((![A5 : nat > option2118145160on_val, B4 : list_char > option_val]: ((member2027247312on_val @ (produc2106877847on_val @ (produc52622304on_val @ Xa @ Xb) @ (produc52622304on_val @ A5 @ B4)) @ R2) => (~ ((member2027247312on_val @ (produc2106877847on_val @ (produc52622304on_val @ A5 @ B4) @ (produc52622304on_val @ Za @ Zb)) @ (transi432893227on_val @ R2))))))))))))). % converse_rtranclE2
thf(fact_193_converse__rtranclE2, axiom,
    ((![Xa : produc1097884484on_val, Xb : produc1097884484on_val, Za : produc1097884484on_val, Zb : produc1097884484on_val, R2 : set_Pr1368603847on_val]: ((member208988944on_val @ (produc564964183on_val @ (produc1069526295on_val @ Xa @ Xb) @ (produc1069526295on_val @ Za @ Zb)) @ (transi100378922on_val @ R2)) => ((~ (((produc1069526295on_val @ Xa @ Xb) = (produc1069526295on_val @ Za @ Zb)))) => (~ ((![A5 : produc1097884484on_val, B4 : produc1097884484on_val]: ((member208988944on_val @ (produc564964183on_val @ (produc1069526295on_val @ Xa @ Xb) @ (produc1069526295on_val @ A5 @ B4)) @ R2) => (~ ((member208988944on_val @ (produc564964183on_val @ (produc1069526295on_val @ A5 @ B4) @ (produc1069526295on_val @ Za @ Zb)) @ (transi100378922on_val @ R2))))))))))))). % converse_rtranclE2
thf(fact_194_converse__rtranclE2, axiom,
    ((![Xa : exp_list_char, Xb : produc515445032on_val, Za : exp_list_char, Zb : produc515445032on_val, R2 : set_Pr1189492743on_val]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ Xa @ Xb) @ (produc2023458740on_val @ Za @ Zb)) @ (transi111096263on_val @ R2)) => ((~ (((produc2023458740on_val @ Xa @ Xb) = (produc2023458740on_val @ Za @ Zb)))) => (~ ((![A5 : exp_list_char, B4 : produc515445032on_val]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ Xa @ Xb) @ (produc2023458740on_val @ A5 @ B4)) @ R2) => (~ ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ A5 @ B4) @ (produc2023458740on_val @ Za @ Zb)) @ (transi111096263on_val @ R2))))))))))))). % converse_rtranclE2
thf(fact_195_rtranclE, axiom,
    ((![A : produc1097884484on_val, B : produc1097884484on_val, R2 : set_Pr1189492743on_val]: ((member354538064on_val @ (produc1069526295on_val @ A @ B) @ (transi111096263on_val @ R2)) => ((~ ((A = B))) => (~ ((![Y4 : produc1097884484on_val]: ((member354538064on_val @ (produc1069526295on_val @ A @ Y4) @ (transi111096263on_val @ R2)) => (~ ((member354538064on_val @ (produc1069526295on_val @ Y4 @ B) @ R2)))))))))))). % rtranclE
thf(fact_196_rtrancl_Ocases, axiom,
    ((![A1 : produc1097884484on_val, A22 : produc1097884484on_val, R2 : set_Pr1189492743on_val]: ((member354538064on_val @ (produc1069526295on_val @ A1 @ A22) @ (transi111096263on_val @ R2)) => ((~ ((A22 = A1))) => (~ ((![B4 : produc1097884484on_val]: ((member354538064on_val @ (produc1069526295on_val @ A1 @ B4) @ (transi111096263on_val @ R2)) => (~ ((member354538064on_val @ (produc1069526295on_val @ B4 @ A22) @ R2)))))))))))). % rtrancl.cases
thf(fact_197_rtrancl_Osimps, axiom,
    ((![A1 : produc1097884484on_val, A22 : produc1097884484on_val, R2 : set_Pr1189492743on_val]: ((member354538064on_val @ (produc1069526295on_val @ A1 @ A22) @ (transi111096263on_val @ R2)) = (((?[A2 : produc1097884484on_val]: (((A1 = A2)) & ((A22 = A2))))) | ((?[A2 : produc1097884484on_val]: (?[B2 : produc1097884484on_val]: (?[C3 : produc1097884484on_val]: (((A1 = A2)) & ((((A22 = C3)) & ((((member354538064on_val @ (produc1069526295on_val @ A2 @ B2) @ (transi111096263on_val @ R2))) & ((member354538064on_val @ (produc1069526295on_val @ B2 @ C3) @ R2)))))))))))))))). % rtrancl.simps
thf(fact_198_rtrancl__trans, axiom,
    ((![X : produc1097884484on_val, Y : produc1097884484on_val, R2 : set_Pr1189492743on_val, Z : produc1097884484on_val]: ((member354538064on_val @ (produc1069526295on_val @ X @ Y) @ (transi111096263on_val @ R2)) => ((member354538064on_val @ (produc1069526295on_val @ Y @ Z) @ (transi111096263on_val @ R2)) => (member354538064on_val @ (produc1069526295on_val @ X @ Z) @ (transi111096263on_val @ R2))))))). % rtrancl_trans
thf(fact_199_rtrancl__induct, axiom,
    ((![A : produc1097884484on_val, B : produc1097884484on_val, R2 : set_Pr1189492743on_val, P : produc1097884484on_val > $o]: ((member354538064on_val @ (produc1069526295on_val @ A @ B) @ (transi111096263on_val @ R2)) => ((P @ A) => ((![Y4 : produc1097884484on_val, Z3 : produc1097884484on_val]: ((member354538064on_val @ (produc1069526295on_val @ A @ Y4) @ (transi111096263on_val @ R2)) => ((member354538064on_val @ (produc1069526295on_val @ Y4 @ Z3) @ R2) => ((P @ Y4) => (P @ Z3))))) => (P @ B))))))). % rtrancl_induct
thf(fact_200_rtrancl_Oinducts, axiom,
    ((![X1 : produc1097884484on_val, X22 : produc1097884484on_val, R2 : set_Pr1189492743on_val, P : produc1097884484on_val > produc1097884484on_val > $o]: ((member354538064on_val @ (produc1069526295on_val @ X1 @ X22) @ (transi111096263on_val @ R2)) => ((![A5 : produc1097884484on_val]: (P @ A5 @ A5)) => ((![A5 : produc1097884484on_val, B4 : produc1097884484on_val, C2 : produc1097884484on_val]: ((member354538064on_val @ (produc1069526295on_val @ A5 @ B4) @ (transi111096263on_val @ R2)) => ((P @ A5 @ B4) => ((member354538064on_val @ (produc1069526295on_val @ B4 @ C2) @ R2) => (P @ A5 @ C2))))) => (P @ X1 @ X22))))))). % rtrancl.inducts
thf(fact_201_converse__rtranclE, axiom,
    ((![X : produc1097884484on_val, Z : produc1097884484on_val, R2 : set_Pr1189492743on_val]: ((member354538064on_val @ (produc1069526295on_val @ X @ Z) @ (transi111096263on_val @ R2)) => ((~ ((X = Z))) => (~ ((![Y4 : produc1097884484on_val]: ((member354538064on_val @ (produc1069526295on_val @ X @ Y4) @ R2) => (~ ((member354538064on_val @ (produc1069526295on_val @ Y4 @ Z) @ (transi111096263on_val @ R2))))))))))))). % converse_rtranclE
thf(fact_202_rtrancl_Ortrancl__refl, axiom,
    ((![A : produc1097884484on_val, R2 : set_Pr1189492743on_val]: (member354538064on_val @ (produc1069526295on_val @ A @ A) @ (transi111096263on_val @ R2))))). % rtrancl.rtrancl_refl
thf(fact_203_converse__rtrancl__induct, axiom,
    ((![A : produc1097884484on_val, B : produc1097884484on_val, R2 : set_Pr1189492743on_val, P : produc1097884484on_val > $o]: ((member354538064on_val @ (produc1069526295on_val @ A @ B) @ (transi111096263on_val @ R2)) => ((P @ B) => ((![Y4 : produc1097884484on_val, Z3 : produc1097884484on_val]: ((member354538064on_val @ (produc1069526295on_val @ Y4 @ Z3) @ R2) => ((member354538064on_val @ (produc1069526295on_val @ Z3 @ B) @ (transi111096263on_val @ R2)) => ((P @ Z3) => (P @ Y4))))) => (P @ A))))))). % converse_rtrancl_induct
thf(fact_204_rtrancl_Ortrancl__into__rtrancl, axiom,
    ((![A : produc1097884484on_val, B : produc1097884484on_val, R2 : set_Pr1189492743on_val, C : produc1097884484on_val]: ((member354538064on_val @ (produc1069526295on_val @ A @ B) @ (transi111096263on_val @ R2)) => ((member354538064on_val @ (produc1069526295on_val @ B @ C) @ R2) => (member354538064on_val @ (produc1069526295on_val @ A @ C) @ (transi111096263on_val @ R2))))))). % rtrancl.rtrancl_into_rtrancl

% Helper facts (5)
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_3_1_If_001t__Option__Ooption_It__Value__Oval_J_T, axiom,
    ((![P : $o]: ((P = $true) | (P = $false))))).
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)))).

% Conjectures (2)
thf(conj_0, hypothesis,
    ((![T_12 : ty]: (((typeof_h @ ha @ v3) = (some_ty @ T_12)) => ((widen_917054840t_char @ p @ T_12 @ t2) => ((wTrt2 @ p @ ha @ (fun_up9191ion_ty @ e @ v @ (some_ty @ t2)) @ ea @ t) => thesis)))))).
thf(conj_1, conjecture,
    (thesis)).
