% 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_294__5337324_1 ) ; }
% This file was generated by Isabelle (most likely Sledgehammer)
% 2020-12-16 14:20:34.718

% Could-be-implicit typings (32)
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thf(ty_n_t__Product____Type__Oprod_It__Value__Oval_Mt__Value__Oval_J, type,
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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__Expr__Obop, type,
    bop : $tType).
thf(ty_n_t__Type__Oty, type,
    ty : $tType).
thf(ty_n_t__Nat__Onat, type,
    nat : $tType).

% Explicit typings (65)
thf(sy_c_BigStep_Oeval, type,
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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,
    hconf_1244167010t_char : list_P1234162913t_char > (nat > option2118145160on_val) > $o).
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_Obinop, type,
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thf(sy_c_Expr_Obop_OEq, type,
    c_Expr_Obop_OEq : bop).
thf(sy_c_Expr_Oexp_OBinOp_001t__List__Olist_It__String__Ochar_J, type,
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thf(sy_c_Expr_Oexp_OCond_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_OWhile_001t__List__Olist_It__String__Ochar_J, type,
    while_list_char : exp_list_char > exp_list_char > exp_list_char).
thf(sy_c_Expr_Oexp_Othrow_001t__List__Olist_It__String__Ochar_J, type,
    throw_list_char : exp_list_char > exp_list_char).
thf(sy_c_JWellForm_Owf__J__mdecl, type,
    wf_J_mdecl : list_P1234162913t_char > list_char > produc1259892823t_char > $o).
thf(sy_c_Map_Omap__le_001t__List__Olist_It__String__Ochar_J_001t__Type__Oty, type,
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thf(sy_c_Objects_Ohext, type,
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thf(sy_c_Objects_Otypeof__h, type,
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thf(sy_c_Option_Ooption_OSome_001t__Type__Oty, type,
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thf(sy_c_Option_Ooption_OSome_001t__Value__Oval, type,
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thf(sy_c_Product__Type_OPair_001_062_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_001_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J, type,
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thf(sy_c_Product__Type_OPair_001t__Expr__Obop_001t__Product____Type__Oprod_It__Value__Oval_Mt__Value__Oval_J, type,
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thf(sy_c_Product__Type_OPair_001t__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_001t__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_M_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_J, type,
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thf(sy_c_Product__Type_OPair_001t__List__Olist_It__String__Ochar_J_001_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, type,
    produc904988266on_val : list_char > (produc1257910179t_char > option_val) > produc266837688on_val).
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__Obop_Mt__Product____Type__Oprod_It__Value__Oval_Mt__Value__Oval_J_J_001t__Product____Type__Oprod_It__Expr__Obop_Mt__Product____Type__Oprod_It__Value__Oval_Mt__Value__Oval_J_J, type,
    produc1144711447al_val : produc1373793468al_val > produc1373793468al_val > produc674182439al_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__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_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,
    produc881885833on_val : produc266837688on_val > produc266837688on_val > produc1085126737on_val).
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    produc1931530455al_val : product_prod_val_val > product_prod_val_val > produc1743387751al_val).
thf(sy_c_Product__Type_OPair_001t__Value__Oval_001t__Value__Oval, type,
    product_Pair_val_val : val > val > product_prod_val_val).
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_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__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,
    transi432893227on_val : set_Pr148564103on_val > set_Pr148564103on_val).
thf(sy_c_Transitive__Closure_Ortrancl_001t__Product____Type__Oprod_It__Expr__Obop_Mt__Product____Type__Oprod_It__Value__Oval_Mt__Value__Oval_J_J, type,
    transi531594559al_val : set_Pr711661575al_val > set_Pr711661575al_val).
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_Transitive__Closure_Ortrancl_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,
    transi2071064181on_val : set_Pr2110063281on_val > set_Pr2110063281on_val).
thf(sy_c_Transitive__Closure_Ortrancl_001t__Product____Type__Oprod_It__Value__Oval_Mt__Value__Oval_J, type,
    transi1202724708al_val : set_Pr488475975al_val > set_Pr488475975al_val).
thf(sy_c_Transitive__Closure_Ortrancl_001t__Value__Oval, type,
    transi196325053cl_val : set_Pr1870322241al_val > set_Pr1870322241al_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_OBoolean, type,
    boolean : ty).
thf(sy_c_Value_Oval_OBool, type,
    bool : $o > val).
thf(sy_c_WWellForm_Owwf__J__mdecl, type,
    wwf_J_mdecl : 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_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).
thf(sy_c_member_001t__Product____Type__Oprod_It__Expr__Obop_Mt__Product____Type__Oprod_It__Value__Oval_Mt__Value__Oval_J_J, type,
    member772310885al_val : produc1373793468al_val > set_Pr624825500al_val > $o).
thf(sy_c_member_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,
    member1888679917on_val : produc1097884484on_val > set_Pr556513572on_val > $o).
thf(sy_c_member_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,
    member1296415951on_val : produc266837688on_val > set_Pr2075231726on_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__Obop_Mt__Product____Type__Oprod_It__Value__Oval_Mt__Value__Oval_J_J_Mt__Product____Type__Oprod_It__Expr__Obop_Mt__Product____Type__Oprod_It__Value__Oval_Mt__Value__Oval_J_J_J, type,
    member1528603216al_val : produc674182439al_val > set_Pr711661575al_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__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_Mt__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, type,
    member197592058on_val : produc1085126737on_val > set_Pr2110063281on_val > $o).
thf(sy_c_member_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__Value__Oval_Mt__Value__Oval_J_Mt__Product____Type__Oprod_It__Value__Oval_Mt__Value__Oval_J_J, type,
    member635678608al_val : produc1743387751al_val > set_Pr488475975al_val > $o).
thf(sy_c_member_001t__Product____Type__Oprod_It__Value__Oval_Mt__Value__Oval_J, type,
    member1494223754al_val : product_prod_val_val > set_Pr1870322241al_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____, type,
    t : ty).
thf(sy_v_a______, type,
    a : nat > option2118145160on_val).
thf(sy_v_b______, type,
    b : list_char > option_val).
thf(sy_v_bop____, type,
    bop2 : bop).
thf(sy_v_v_092_060_094sub_0621______, type,
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thf(sy_v_v______, type,
    v : val).

% Relevant facts (190)
thf(fact_0_RedBinOp_Oprems_I1_J, axiom,
    ((typeSa1777264139_sconf @ p @ e @ (produc52622304on_val @ a @ b)))). % RedBinOp.prems(1)
thf(fact_1_RedBinOp_Ohyps, axiom,
    (((binop @ (produc1753769388al_val @ bop2 @ (product_Pair_val_val @ v_1 @ v_2))) = (some_val @ v)))). % RedBinOp.hyps
thf(fact_2_RedBinOp_Oprems_I2_J, axiom,
    ((wTrt @ p @ a @ e @ (binOp_list_char @ (val_list_char @ v_1) @ bop2 @ (val_list_char @ v_2)) @ t))). % RedBinOp.prems(2)
thf(fact_3_local_Owf, axiom,
    ((wf_pro1229751607t_char @ wf_J_mdecl @ p))). % local.wf
thf(fact_4_exp_Oinject_I3_J, axiom,
    ((![X3 : val, Y3 : val]: (((val_list_char @ X3) = (val_list_char @ Y3)) = (X3 = Y3))))). % exp.inject(3)
thf(fact_5_widen__trans, axiom,
    ((![P : list_P1234162913t_char, S : ty, U : ty, T : ty]: ((widen_917054840t_char @ P @ S @ U) => ((widen_917054840t_char @ P @ U @ T) => (widen_917054840t_char @ P @ S @ T)))))). % widen_trans
thf(fact_6_widen__refl, axiom,
    ((![P : list_P1234162913t_char, T : ty]: (widen_917054840t_char @ P @ T @ T)))). % widen_refl
thf(fact_7_exp_Odistinct_I55_J, axiom,
    ((![X3 : val, X41 : exp_list_char, X42 : bop, X43 : exp_list_char]: (~ (((val_list_char @ X3) = (binOp_list_char @ X41 @ X42 @ X43))))))). % exp.distinct(55)
thf(fact_8_WTrt__elim__cases_I2_J, axiom,
    ((![P : list_P1234162913t_char, H : nat > option2118145160on_val, E : list_char > option_ty, E2 : exp_list_char, E_1 : exp_list_char, E_2 : exp_list_char, T : ty]: ((wTrt @ P @ H @ E @ (cond_list_char @ E2 @ E_1 @ E_2) @ T) => (~ (((wTrt @ P @ H @ E @ E2 @ boolean) => (![T_1 : ty]: ((wTrt @ P @ H @ E @ E_1 @ T_1) => (![T_2 : ty]: ((wTrt @ P @ H @ E @ E_2 @ T_2) => (((widen_917054840t_char @ P @ T_1 @ T_2) | (widen_917054840t_char @ P @ T_2 @ T_1)) => (((widen_917054840t_char @ P @ T_1 @ T_2) => (T = T_2)) => (~ (((widen_917054840t_char @ P @ T_2 @ T_1) => (T = T_1))))))))))))))))). % WTrt_elim_cases(2)
thf(fact_9_WTrtCond, axiom,
    ((![P : list_P1234162913t_char, H : nat > option2118145160on_val, E : list_char > option_ty, E2 : exp_list_char, E_1 : exp_list_char, T_12 : ty, E_2 : exp_list_char, T_22 : ty, T : ty]: ((wTrt @ P @ H @ E @ E2 @ boolean) => ((wTrt @ P @ H @ E @ E_1 @ T_12) => ((wTrt @ P @ H @ E @ E_2 @ T_22) => (((widen_917054840t_char @ P @ T_12 @ T_22) | (widen_917054840t_char @ P @ T_22 @ T_12)) => (((widen_917054840t_char @ P @ T_12 @ T_22) => (T = T_22)) => (((widen_917054840t_char @ P @ T_22 @ T_12) => (T = T_12)) => (wTrt @ P @ H @ E @ (cond_list_char @ E2 @ E_1 @ E_2) @ T)))))))))). % WTrtCond
thf(fact_10_WTrt__hext__mono, axiom,
    ((![P : list_P1234162913t_char, H : nat > option2118145160on_val, E : list_char > option_ty, E2 : exp_list_char, T : ty, H2 : nat > option2118145160on_val]: ((wTrt @ P @ H @ E @ E2 @ T) => ((hext @ H @ H2) => (wTrt @ P @ H2 @ E @ E2 @ T)))))). % WTrt_hext_mono
thf(fact_11_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_12_WTrt__env__mono, axiom,
    ((![P : list_P1234162913t_char, H : nat > option2118145160on_val, E : list_char > option_ty, E2 : exp_list_char, T : ty, E3 : list_char > option_ty]: ((wTrt @ P @ H @ E @ E2 @ T) => ((map_le_list_char_ty @ E @ E3) => (wTrt @ P @ H @ E3 @ E2 @ T)))))). % WTrt_env_mono
thf(fact_13_conf__widen, axiom,
    ((![P : list_P1234162913t_char, H : nat > option2118145160on_val, V : val, T : ty, T2 : ty]: ((conf_P93989998t_char @ P @ H @ V @ T) => ((widen_917054840t_char @ P @ T @ T2) => (conf_P93989998t_char @ P @ H @ V @ T2)))))). % conf_widen
thf(fact_14_exp_Oinject_I4_J, axiom,
    ((![X41 : exp_list_char, X42 : bop, X43 : exp_list_char, Y41 : exp_list_char, Y42 : bop, Y43 : exp_list_char]: (((binOp_list_char @ X41 @ X42 @ X43) = (binOp_list_char @ Y41 @ Y42 @ Y43)) = (((X41 = Y41)) & ((((X42 = Y42)) & ((X43 = Y43))))))))). % exp.inject(4)
thf(fact_15_exp_Oinject_I12_J, axiom,
    ((![X121 : exp_list_char, X122 : exp_list_char, X123 : exp_list_char, Y121 : exp_list_char, Y122 : exp_list_char, Y123 : exp_list_char]: (((cond_list_char @ X121 @ X122 @ X123) = (cond_list_char @ Y121 @ Y122 @ Y123)) = (((X121 = Y121)) & ((((X122 = Y122)) & ((X123 = Y123))))))))). % exp.inject(12)
thf(fact_16_exp_Odistinct_I93_J, axiom,
    ((![X41 : exp_list_char, X42 : bop, X43 : exp_list_char, X121 : exp_list_char, X122 : exp_list_char, X123 : exp_list_char]: (~ (((binOp_list_char @ X41 @ X42 @ X43) = (cond_list_char @ X121 @ X122 @ X123))))))). % exp.distinct(93)
thf(fact_17_conf__def, axiom,
    ((conf_P93989998t_char = (^[P2 : list_P1234162913t_char]: (^[H3 : nat > option2118145160on_val]: (^[V2 : val]: (^[T3 : ty]: (?[T4 : ty]: ((((typeof_h @ H3 @ V2) = (some_ty @ T4))) & ((widen_917054840t_char @ P2 @ T4 @ T3))))))))))). % conf_def
thf(fact_18_exp_Odistinct_I71_J, axiom,
    ((![X3 : val, X121 : exp_list_char, X122 : exp_list_char, X123 : exp_list_char]: (~ (((val_list_char @ X3) = (cond_list_char @ X121 @ X122 @ X123))))))). % exp.distinct(71)
thf(fact_19_hext__typeof__mono, axiom,
    ((![H : nat > option2118145160on_val, H2 : nat > option2118145160on_val, V : val, T : ty]: ((hext @ H @ H2) => (((typeof_h @ H @ V) = (some_ty @ T)) => ((typeof_h @ H2 @ V) = (some_ty @ T))))))). % hext_typeof_mono
thf(fact_20_hext__refl, axiom,
    ((![H : nat > option2118145160on_val]: (hext @ H @ H)))). % hext_refl
thf(fact_21_option_Oinject, axiom,
    ((![X2 : val, Y2 : val]: (((some_val @ X2) = (some_val @ Y2)) = (X2 = Y2))))). % option.inject
thf(fact_22_option_Oinject, axiom,
    ((![X2 : ty, Y2 : ty]: (((some_ty @ X2) = (some_ty @ Y2)) = (X2 = Y2))))). % option.inject
thf(fact_23_option_Oinject, axiom,
    ((![X2 : produc266837688on_val, Y2 : produc266837688on_val]: (((some_P1299442195on_val @ X2) = (some_P1299442195on_val @ Y2)) = (X2 = Y2))))). % option.inject
thf(fact_24_prod_Oinject, axiom,
    ((![X1 : val, X2 : val, Y1 : val, Y2 : val]: (((product_Pair_val_val @ X1 @ X2) = (product_Pair_val_val @ Y1 @ Y2)) = (((X1 = Y1)) & ((X2 = Y2))))))). % prod.inject
thf(fact_25_prod_Oinject, axiom,
    ((![X1 : list_char, X2 : produc1257910179t_char > option_val, Y1 : list_char, Y2 : produc1257910179t_char > option_val]: (((produc904988266on_val @ X1 @ X2) = (produc904988266on_val @ Y1 @ Y2)) = (((X1 = Y1)) & ((X2 = Y2))))))). % prod.inject
thf(fact_26_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_27_prod_Oinject, axiom,
    ((![X1 : bop, X2 : product_prod_val_val, Y1 : bop, Y2 : product_prod_val_val]: (((produc1753769388al_val @ X1 @ X2) = (produc1753769388al_val @ Y1 @ Y2)) = (((X1 = Y1)) & ((X2 = Y2))))))). % prod.inject
thf(fact_28_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_29_old_Oprod_Oinject, axiom,
    ((![A : val, B : val, A2 : val, B2 : val]: (((product_Pair_val_val @ A @ B) = (product_Pair_val_val @ A2 @ B2)) = (((A = A2)) & ((B = B2))))))). % old.prod.inject
thf(fact_30_old_Oprod_Oinject, axiom,
    ((![A : list_char, B : produc1257910179t_char > option_val, A2 : list_char, B2 : produc1257910179t_char > option_val]: (((produc904988266on_val @ A @ B) = (produc904988266on_val @ A2 @ B2)) = (((A = A2)) & ((B = B2))))))). % old.prod.inject
thf(fact_31_old_Oprod_Oinject, axiom,
    ((![A : exp_list_char, B : produc515445032on_val, A2 : exp_list_char, B2 : produc515445032on_val]: (((produc2023458740on_val @ A @ B) = (produc2023458740on_val @ A2 @ B2)) = (((A = A2)) & ((B = B2))))))). % old.prod.inject
thf(fact_32_old_Oprod_Oinject, axiom,
    ((![A : bop, B : product_prod_val_val, A2 : bop, B2 : product_prod_val_val]: (((produc1753769388al_val @ A @ B) = (produc1753769388al_val @ A2 @ B2)) = (((A = A2)) & ((B = B2))))))). % old.prod.inject
thf(fact_33_old_Oprod_Oinject, axiom,
    ((![A : nat > option2118145160on_val, B : list_char > option_val, A2 : nat > option2118145160on_val, B2 : list_char > option_val]: (((produc52622304on_val @ A @ B) = (produc52622304on_val @ A2 @ B2)) = (((A = A2)) & ((B = B2))))))). % old.prod.inject
thf(fact_34_lconf__def, axiom,
    ((lconf_485928294t_char = (^[P2 : list_P1234162913t_char]: (^[H3 : nat > option2118145160on_val]: (^[L : list_char > option_val]: (^[E4 : list_char > option_ty]: (![V3 : list_char]: (![V2 : val]: ((((L @ V3) = (some_val @ V2))) => ((?[T3 : ty]: ((((E4 @ V3) = (some_ty @ T3))) & ((conf_P93989998t_char @ P2 @ H3 @ V2 @ T3))))))))))))))). % lconf_def
thf(fact_35_prod__cases3, axiom,
    ((![Y : produc1097884484on_val]: (~ ((![A3 : exp_list_char, B3 : nat > option2118145160on_val, C : list_char > option_val]: (~ ((Y = (produc2023458740on_val @ A3 @ (produc52622304on_val @ B3 @ C))))))))))). % prod_cases3
thf(fact_36_prod__cases3, axiom,
    ((![Y : produc1373793468al_val]: (~ ((![A3 : bop, B3 : val, C : val]: (~ ((Y = (produc1753769388al_val @ A3 @ (product_Pair_val_val @ B3 @ C))))))))))). % prod_cases3
thf(fact_37_hextI, axiom,
    ((![H : nat > option2118145160on_val, H2 : nat > option2118145160on_val]: ((![A3 : nat, C2 : list_char, Fs : produc1257910179t_char > option_val]: (((H @ A3) = (some_P1299442195on_val @ (produc904988266on_val @ C2 @ Fs))) => (?[Fs2 : produc1257910179t_char > option_val]: ((H2 @ A3) = (some_P1299442195on_val @ (produc904988266on_val @ C2 @ Fs2)))))) => (hext @ H @ H2))))). % hextI
thf(fact_38_hext__def, axiom,
    ((hext = (^[H3 : nat > option2118145160on_val]: (^[H4 : nat > option2118145160on_val]: (![A4 : nat]: (![C3 : list_char]: (![Fs3 : produc1257910179t_char > option_val]: ((((H3 @ A4) = (some_P1299442195on_val @ (produc904988266on_val @ C3 @ Fs3)))) => ((?[Fs4 : produc1257910179t_char > option_val]: ((H4 @ A4) = (some_P1299442195on_val @ (produc904988266on_val @ C3 @ Fs4)))))))))))))). % hext_def
thf(fact_39_hext__objD, axiom,
    ((![H : nat > option2118145160on_val, H2 : nat > option2118145160on_val, A : nat, C4 : list_char, Fs5 : produc1257910179t_char > option_val]: ((hext @ H @ H2) => (((H @ A) = (some_P1299442195on_val @ (produc904988266on_val @ C4 @ Fs5))) => (?[Fs6 : produc1257910179t_char > option_val]: ((H2 @ A) = (some_P1299442195on_val @ (produc904988266on_val @ C4 @ Fs6))))))))). % hext_objD
thf(fact_40_lconf__hext, axiom,
    ((![P : list_P1234162913t_char, H : nat > option2118145160on_val, L2 : list_char > option_val, E : list_char > option_ty, H2 : nat > option2118145160on_val]: ((lconf_485928294t_char @ P @ H @ L2 @ E) => ((hext @ H @ H2) => (lconf_485928294t_char @ P @ H2 @ L2 @ E)))))). % lconf_hext
thf(fact_41_old_Oprod_Oinducts, axiom,
    ((![P : product_prod_val_val > $o, Prod : product_prod_val_val]: ((![A3 : val, B3 : val]: (P @ (product_Pair_val_val @ A3 @ B3))) => (P @ Prod))))). % old.prod.inducts
thf(fact_42_old_Oprod_Oinducts, axiom,
    ((![P : produc266837688on_val > $o, Prod : produc266837688on_val]: ((![A3 : list_char, B3 : produc1257910179t_char > option_val]: (P @ (produc904988266on_val @ A3 @ B3))) => (P @ Prod))))). % old.prod.inducts
thf(fact_43_old_Oprod_Oinducts, axiom,
    ((![P : produc1097884484on_val > $o, Prod : produc1097884484on_val]: ((![A3 : exp_list_char, B3 : produc515445032on_val]: (P @ (produc2023458740on_val @ A3 @ B3))) => (P @ Prod))))). % old.prod.inducts
thf(fact_44_old_Oprod_Oinducts, axiom,
    ((![P : produc1373793468al_val > $o, Prod : produc1373793468al_val]: ((![A3 : bop, B3 : product_prod_val_val]: (P @ (produc1753769388al_val @ A3 @ B3))) => (P @ Prod))))). % old.prod.inducts
thf(fact_45_old_Oprod_Oinducts, axiom,
    ((![P : produc515445032on_val > $o, Prod : produc515445032on_val]: ((![A3 : nat > option2118145160on_val, B3 : list_char > option_val]: (P @ (produc52622304on_val @ A3 @ B3))) => (P @ Prod))))). % old.prod.inducts
thf(fact_46_old_Oprod_Oexhaust, axiom,
    ((![Y : product_prod_val_val]: (~ ((![A3 : val, B3 : val]: (~ ((Y = (product_Pair_val_val @ A3 @ B3)))))))))). % old.prod.exhaust
thf(fact_47_old_Oprod_Oexhaust, axiom,
    ((![Y : produc266837688on_val]: (~ ((![A3 : list_char, B3 : produc1257910179t_char > option_val]: (~ ((Y = (produc904988266on_val @ A3 @ B3)))))))))). % old.prod.exhaust
thf(fact_48_old_Oprod_Oexhaust, axiom,
    ((![Y : produc1097884484on_val]: (~ ((![A3 : exp_list_char, B3 : produc515445032on_val]: (~ ((Y = (produc2023458740on_val @ A3 @ B3)))))))))). % old.prod.exhaust
thf(fact_49_old_Oprod_Oexhaust, axiom,
    ((![Y : produc1373793468al_val]: (~ ((![A3 : bop, B3 : product_prod_val_val]: (~ ((Y = (produc1753769388al_val @ A3 @ B3)))))))))). % old.prod.exhaust
thf(fact_50_old_Oprod_Oexhaust, axiom,
    ((![Y : produc515445032on_val]: (~ ((![A3 : nat > option2118145160on_val, B3 : list_char > option_val]: (~ ((Y = (produc52622304on_val @ A3 @ B3)))))))))). % old.prod.exhaust
thf(fact_51_Pair__inject, axiom,
    ((![A : val, B : val, A2 : val, B2 : val]: (((product_Pair_val_val @ A @ B) = (product_Pair_val_val @ A2 @ B2)) => (~ (((A = A2) => (~ ((B = B2)))))))))). % Pair_inject
thf(fact_52_Pair__inject, axiom,
    ((![A : list_char, B : produc1257910179t_char > option_val, A2 : list_char, B2 : produc1257910179t_char > option_val]: (((produc904988266on_val @ A @ B) = (produc904988266on_val @ A2 @ B2)) => (~ (((A = A2) => (~ ((B = B2)))))))))). % Pair_inject
thf(fact_53_Pair__inject, axiom,
    ((![A : exp_list_char, B : produc515445032on_val, A2 : exp_list_char, B2 : produc515445032on_val]: (((produc2023458740on_val @ A @ B) = (produc2023458740on_val @ A2 @ B2)) => (~ (((A = A2) => (~ ((B = B2)))))))))). % Pair_inject
thf(fact_54_Pair__inject, axiom,
    ((![A : bop, B : product_prod_val_val, A2 : bop, B2 : product_prod_val_val]: (((produc1753769388al_val @ A @ B) = (produc1753769388al_val @ A2 @ B2)) => (~ (((A = A2) => (~ ((B = B2)))))))))). % Pair_inject
thf(fact_55_Pair__inject, axiom,
    ((![A : nat > option2118145160on_val, B : list_char > option_val, A2 : nat > option2118145160on_val, B2 : list_char > option_val]: (((produc52622304on_val @ A @ B) = (produc52622304on_val @ A2 @ B2)) => (~ (((A = A2) => (~ ((B = B2)))))))))). % Pair_inject
thf(fact_56_prod__cases, axiom,
    ((![P : product_prod_val_val > $o, P3 : product_prod_val_val]: ((![A3 : val, B3 : val]: (P @ (product_Pair_val_val @ A3 @ B3))) => (P @ P3))))). % prod_cases
thf(fact_57_prod__cases, axiom,
    ((![P : produc266837688on_val > $o, P3 : produc266837688on_val]: ((![A3 : list_char, B3 : produc1257910179t_char > option_val]: (P @ (produc904988266on_val @ A3 @ B3))) => (P @ P3))))). % prod_cases
thf(fact_58_prod__cases, axiom,
    ((![P : produc1097884484on_val > $o, P3 : produc1097884484on_val]: ((![A3 : exp_list_char, B3 : produc515445032on_val]: (P @ (produc2023458740on_val @ A3 @ B3))) => (P @ P3))))). % prod_cases
thf(fact_59_prod__cases, axiom,
    ((![P : produc1373793468al_val > $o, P3 : produc1373793468al_val]: ((![A3 : bop, B3 : product_prod_val_val]: (P @ (produc1753769388al_val @ A3 @ B3))) => (P @ P3))))). % prod_cases
thf(fact_60_prod__cases, axiom,
    ((![P : produc515445032on_val > $o, P3 : produc515445032on_val]: ((![A3 : nat > option2118145160on_val, B3 : list_char > option_val]: (P @ (produc52622304on_val @ A3 @ B3))) => (P @ P3))))). % prod_cases
thf(fact_61_surj__pair, axiom,
    ((![P3 : product_prod_val_val]: (?[X : val, Y4 : val]: (P3 = (product_Pair_val_val @ X @ Y4)))))). % surj_pair
thf(fact_62_surj__pair, axiom,
    ((![P3 : produc266837688on_val]: (?[X : list_char, Y4 : produc1257910179t_char > option_val]: (P3 = (produc904988266on_val @ X @ Y4)))))). % surj_pair
thf(fact_63_surj__pair, axiom,
    ((![P3 : produc1097884484on_val]: (?[X : exp_list_char, Y4 : produc515445032on_val]: (P3 = (produc2023458740on_val @ X @ Y4)))))). % surj_pair
thf(fact_64_surj__pair, axiom,
    ((![P3 : produc1373793468al_val]: (?[X : bop, Y4 : product_prod_val_val]: (P3 = (produc1753769388al_val @ X @ Y4)))))). % surj_pair
thf(fact_65_surj__pair, axiom,
    ((![P3 : produc515445032on_val]: (?[X : nat > option2118145160on_val, Y4 : list_char > option_val]: (P3 = (produc52622304on_val @ X @ Y4)))))). % surj_pair
thf(fact_66_hext__trans, axiom,
    ((![H : nat > option2118145160on_val, H2 : nat > option2118145160on_val, H5 : nat > option2118145160on_val]: ((hext @ H @ H2) => ((hext @ H2 @ H5) => (hext @ H @ H5)))))). % hext_trans
thf(fact_67_mem__Collect__eq, axiom,
    ((![A : produc1172664615on_val, P : produc1172664615on_val > $o]: ((member354538064on_val @ A @ (collec2055896722on_val @ P)) = (P @ A))))). % mem_Collect_eq
thf(fact_68_Collect__mem__eq, axiom,
    ((![A5 : set_Pr1189492743on_val]: ((collec2055896722on_val @ (^[X4 : produc1172664615on_val]: (member354538064on_val @ X4 @ A5))) = A5)))). % Collect_mem_eq
thf(fact_69_prod__induct3, axiom,
    ((![P : produc1097884484on_val > $o, X5 : produc1097884484on_val]: ((![A3 : exp_list_char, B3 : nat > option2118145160on_val, C : list_char > option_val]: (P @ (produc2023458740on_val @ A3 @ (produc52622304on_val @ B3 @ C)))) => (P @ X5))))). % prod_induct3
thf(fact_70_prod__induct3, axiom,
    ((![P : produc1373793468al_val > $o, X5 : produc1373793468al_val]: ((![A3 : bop, B3 : val, C : val]: (P @ (produc1753769388al_val @ A3 @ (product_Pair_val_val @ B3 @ C)))) => (P @ X5))))). % prod_induct3
thf(fact_71_WTrtBinOpEq, axiom,
    ((![P : list_P1234162913t_char, H : nat > option2118145160on_val, E : list_char > option_ty, E_1 : exp_list_char, T_12 : ty, E_2 : exp_list_char, T_22 : ty]: ((wTrt @ P @ H @ E @ E_1 @ T_12) => ((wTrt @ P @ H @ E @ E_2 @ T_22) => (wTrt @ P @ H @ E @ (binOp_list_char @ E_1 @ c_Expr_Obop_OEq @ E_2) @ boolean)))))). % WTrtBinOpEq
thf(fact_72_red__reds_ORedBinOp, axiom,
    ((![Bop : bop, V_1 : val, V_2 : val, V : val, S2 : produc515445032on_val, P : list_P1234162913t_char]: (((binop @ (produc1753769388al_val @ Bop @ (product_Pair_val_val @ V_1 @ V_2))) = (some_val @ V)) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (binOp_list_char @ (val_list_char @ V_1) @ Bop @ (val_list_char @ V_2)) @ S2) @ (produc2023458740on_val @ (val_list_char @ V) @ S2)) @ (red @ P)))))). % red_reds.RedBinOp
thf(fact_73_redp__redsp_ORedBinOp, axiom,
    ((![Bop : bop, V_1 : val, V_2 : val, V : val, P : list_P1234162913t_char, S2 : produc515445032on_val]: (((binop @ (produc1753769388al_val @ Bop @ (product_Pair_val_val @ V_1 @ V_2))) = (some_val @ V)) => (redp @ P @ (binOp_list_char @ (val_list_char @ V_1) @ Bop @ (val_list_char @ V_2)) @ S2 @ (val_list_char @ V) @ S2))))). % redp_redsp.RedBinOp
thf(fact_74_BinOp, axiom,
    ((![P : list_P1234162913t_char, E_1 : exp_list_char, S_0 : produc515445032on_val, V_1 : val, S_1 : produc515445032on_val, E_2 : exp_list_char, V_2 : val, S_2 : produc515445032on_val, Bop : bop, V : val]: ((eval @ P @ E_1 @ S_0 @ (val_list_char @ V_1) @ S_1) => ((eval @ P @ E_2 @ S_1 @ (val_list_char @ V_2) @ S_2) => (((binop @ (produc1753769388al_val @ Bop @ (product_Pair_val_val @ V_1 @ V_2))) = (some_val @ V)) => (eval @ P @ (binOp_list_char @ E_1 @ Bop @ E_2) @ S_0 @ (val_list_char @ V) @ S_2))))))). % BinOp
thf(fact_75_pred__equals__eq2, axiom,
    ((![R : set_Pr1189492743on_val, S : set_Pr1189492743on_val]: (((^[X4 : produc1097884484on_val]: (^[Y5 : produc1097884484on_val]: (member354538064on_val @ (produc1069526295on_val @ X4 @ Y5) @ R))) = (^[X4 : produc1097884484on_val]: (^[Y5 : produc1097884484on_val]: (member354538064on_val @ (produc1069526295on_val @ X4 @ Y5) @ S)))) = (R = S))))). % pred_equals_eq2
thf(fact_76_pred__equals__eq2, axiom,
    ((![R : set_Pr1870322241al_val, S : set_Pr1870322241al_val]: (((^[X4 : val]: (^[Y5 : val]: (member1494223754al_val @ (product_Pair_val_val @ X4 @ Y5) @ R))) = (^[X4 : val]: (^[Y5 : val]: (member1494223754al_val @ (product_Pair_val_val @ X4 @ Y5) @ S)))) = (R = S))))). % pred_equals_eq2
thf(fact_77_pred__equals__eq2, axiom,
    ((![R : set_Pr2075231726on_val, S : set_Pr2075231726on_val]: (((^[X4 : list_char]: (^[Y5 : produc1257910179t_char > option_val]: (member1296415951on_val @ (produc904988266on_val @ X4 @ Y5) @ R))) = (^[X4 : list_char]: (^[Y5 : produc1257910179t_char > option_val]: (member1296415951on_val @ (produc904988266on_val @ X4 @ Y5) @ S)))) = (R = S))))). % pred_equals_eq2
thf(fact_78_pred__equals__eq2, axiom,
    ((![R : set_Pr556513572on_val, S : set_Pr556513572on_val]: (((^[X4 : exp_list_char]: (^[Y5 : produc515445032on_val]: (member1888679917on_val @ (produc2023458740on_val @ X4 @ Y5) @ R))) = (^[X4 : exp_list_char]: (^[Y5 : produc515445032on_val]: (member1888679917on_val @ (produc2023458740on_val @ X4 @ Y5) @ S)))) = (R = S))))). % pred_equals_eq2
thf(fact_79_pred__equals__eq2, axiom,
    ((![R : set_Pr624825500al_val, S : set_Pr624825500al_val]: (((^[X4 : bop]: (^[Y5 : product_prod_val_val]: (member772310885al_val @ (produc1753769388al_val @ X4 @ Y5) @ R))) = (^[X4 : bop]: (^[Y5 : product_prod_val_val]: (member772310885al_val @ (produc1753769388al_val @ X4 @ Y5) @ S)))) = (R = S))))). % pred_equals_eq2
thf(fact_80_pred__equals__eq2, axiom,
    ((![R : set_Pr723149704on_val, S : set_Pr723149704on_val]: (((^[X4 : nat > option2118145160on_val]: (^[Y5 : list_char > option_val]: (member652041809on_val @ (produc52622304on_val @ X4 @ Y5) @ R))) = (^[X4 : nat > option2118145160on_val]: (^[Y5 : list_char > option_val]: (member652041809on_val @ (produc52622304on_val @ X4 @ Y5) @ S)))) = (R = S))))). % pred_equals_eq2
thf(fact_81_redp__red__eq, axiom,
    ((redp = (^[P2 : list_P1234162913t_char]: (^[X4 : exp_list_char]: (^[Y5 : produc515445032on_val]: (^[Z : exp_list_char]: (^[Aa : produc515445032on_val]: (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ X4 @ Y5) @ (produc2023458740on_val @ Z @ Aa)) @ (red @ P2)))))))))). % redp_red_eq
thf(fact_82_red__reds_OCondRed, axiom,
    ((![E2 : exp_list_char, S2 : produc515445032on_val, E5 : exp_list_char, S3 : produc515445032on_val, P : list_P1234162913t_char, E_1 : exp_list_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 @ (cond_list_char @ E2 @ E_1 @ E_2) @ S2) @ (produc2023458740on_val @ (cond_list_char @ E5 @ E_1 @ E_2) @ S3)) @ (red @ P)))))). % red_reds.CondRed
thf(fact_83_red__reds_OBinOpRed1, axiom,
    ((![E2 : exp_list_char, S2 : produc515445032on_val, E5 : exp_list_char, S3 : produc515445032on_val, P : list_P1234162913t_char, Bop : bop, 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 @ (binOp_list_char @ E2 @ Bop @ E_2) @ S2) @ (produc2023458740on_val @ (binOp_list_char @ E5 @ Bop @ E_2) @ S3)) @ (red @ P)))))). % red_reds.BinOpRed1
thf(fact_84_redp__redsp_OBinOpRed1, axiom,
    ((![P : list_P1234162913t_char, E2 : exp_list_char, S2 : produc515445032on_val, E5 : exp_list_char, S3 : produc515445032on_val, Bop : bop, E_2 : exp_list_char]: ((redp @ P @ E2 @ S2 @ E5 @ S3) => (redp @ P @ (binOp_list_char @ E2 @ Bop @ E_2) @ S2 @ (binOp_list_char @ E5 @ Bop @ E_2) @ S3))))). % redp_redsp.BinOpRed1
thf(fact_85_redp__redsp_OCondRed, axiom,
    ((![P : list_P1234162913t_char, E2 : exp_list_char, S2 : produc515445032on_val, E5 : exp_list_char, S3 : produc515445032on_val, E_1 : exp_list_char, E_2 : exp_list_char]: ((redp @ P @ E2 @ S2 @ E5 @ S3) => (redp @ P @ (cond_list_char @ E2 @ E_1 @ E_2) @ S2 @ (cond_list_char @ E5 @ E_1 @ E_2) @ S3))))). % redp_redsp.CondRed
thf(fact_86_eval__cases_I2_J, axiom,
    ((![P : list_P1234162913t_char, V : val, S2 : produc515445032on_val, E5 : exp_list_char, S3 : produc515445032on_val]: ((eval @ P @ (val_list_char @ V) @ S2 @ E5 @ S3) => (~ (((E5 = (val_list_char @ V)) => (~ ((S3 = S2)))))))))). % eval_cases(2)
thf(fact_87_Val, axiom,
    ((![P : list_P1234162913t_char, V : val, S2 : produc515445032on_val]: (eval @ P @ (val_list_char @ V) @ S2 @ (val_list_char @ V) @ S2)))). % Val
thf(fact_88_redp__redsp_OBinOpRed2, axiom,
    ((![P : list_P1234162913t_char, E2 : exp_list_char, S2 : produc515445032on_val, E5 : exp_list_char, S3 : produc515445032on_val, V_1 : val, Bop : bop]: ((redp @ P @ E2 @ S2 @ E5 @ S3) => (redp @ P @ (binOp_list_char @ (val_list_char @ V_1) @ Bop @ E2) @ S2 @ (binOp_list_char @ (val_list_char @ V_1) @ Bop @ E5) @ S3))))). % redp_redsp.BinOpRed2
thf(fact_89_eval__hext, axiom,
    ((![P : list_P1234162913t_char, E2 : exp_list_char, H : nat > option2118145160on_val, L2 : list_char > option_val, E5 : exp_list_char, H2 : nat > option2118145160on_val, L3 : list_char > option_val]: ((eval @ P @ E2 @ (produc52622304on_val @ H @ L2) @ E5 @ (produc52622304on_val @ H2 @ L3)) => (hext @ H @ H2))))). % eval_hext
thf(fact_90_red__reds_OBinOpRed2, axiom,
    ((![E2 : exp_list_char, S2 : produc515445032on_val, E5 : exp_list_char, S3 : produc515445032on_val, P : list_P1234162913t_char, V_1 : val, Bop : bop]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E2 @ S2) @ (produc2023458740on_val @ E5 @ S3)) @ (red @ P)) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (binOp_list_char @ (val_list_char @ V_1) @ Bop @ E2) @ S2) @ (produc2023458740on_val @ (binOp_list_char @ (val_list_char @ V_1) @ Bop @ E5) @ S3)) @ (red @ P)))))). % red_reds.BinOpRed2
thf(fact_91_red__hext__incr, axiom,
    ((![E2 : exp_list_char, H : nat > option2118145160on_val, L2 : list_char > option_val, E5 : exp_list_char, H2 : nat > option2118145160on_val, L3 : list_char > option_val, P : list_P1234162913t_char]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E2 @ (produc52622304on_val @ H @ L2)) @ (produc2023458740on_val @ E5 @ (produc52622304on_val @ H2 @ L3))) @ (red @ P)) => (hext @ H @ H2))))). % red_hext_incr
thf(fact_92_red__preserves__lconf, axiom,
    ((![E2 : exp_list_char, H : nat > option2118145160on_val, L2 : list_char > option_val, E5 : exp_list_char, H2 : nat > option2118145160on_val, L3 : list_char > option_val, P : list_P1234162913t_char, E : list_char > option_ty, T : ty]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E2 @ (produc52622304on_val @ H @ L2)) @ (produc2023458740on_val @ E5 @ (produc52622304on_val @ H2 @ L3))) @ (red @ P)) => ((wTrt @ P @ H @ E @ E2 @ T) => ((lconf_485928294t_char @ P @ H @ L2 @ E) => (lconf_485928294t_char @ P @ H2 @ L3 @ E))))))). % red_preserves_lconf
thf(fact_93_red__preserves__hconf, axiom,
    ((![E2 : exp_list_char, H : nat > option2118145160on_val, L2 : list_char > option_val, E5 : exp_list_char, H2 : nat > option2118145160on_val, L3 : list_char > option_val, P : list_P1234162913t_char, E : list_char > option_ty, T : ty]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E2 @ (produc52622304on_val @ H @ L2)) @ (produc2023458740on_val @ E5 @ (produc52622304on_val @ H2 @ L3))) @ (red @ P)) => ((wTrt @ P @ H @ E @ E2 @ T) => ((hconf_1244167010t_char @ P @ H) => (hconf_1244167010t_char @ P @ H2))))))). % red_preserves_hconf
thf(fact_94_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, T : ty]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E2 @ S2) @ (produc2023458740on_val @ E5 @ S3)) @ (red @ P)) => ((wTrt @ P @ (hp @ S2) @ E @ E2 @ T) => ((typeSa1777264139_sconf @ P @ E @ S2) => (typeSa1777264139_sconf @ P @ E @ S3))))))). % red_preserves_sconf
thf(fact_95_eval__cases_I3_J, axiom,
    ((![P : list_P1234162913t_char, E_1 : exp_list_char, Bop : bop, E_2 : exp_list_char, S2 : produc515445032on_val, E5 : exp_list_char, S3 : produc515445032on_val]: ((eval @ P @ (binOp_list_char @ E_1 @ Bop @ E_2) @ S2 @ E5 @ S3) => ((![V_12 : val, S_12 : produc515445032on_val, V_22 : val, V4 : val]: ((E5 = (val_list_char @ V4)) => ((eval @ P @ E_1 @ S2 @ (val_list_char @ V_12) @ S_12) => ((eval @ P @ E_2 @ S_12 @ (val_list_char @ V_22) @ S3) => (~ (((binop @ (produc1753769388al_val @ Bop @ (product_Pair_val_val @ V_12 @ V_22))) = (some_val @ V4)))))))) => ((![E6 : exp_list_char]: ((E5 = (throw_list_char @ E6)) => (~ ((eval @ P @ E_1 @ S2 @ (throw_list_char @ E6) @ S3))))) => (~ ((![V_12 : val, S_12 : produc515445032on_val, E6 : exp_list_char]: ((E5 = (throw_list_char @ E6)) => ((eval @ P @ E_1 @ S2 @ (val_list_char @ V_12) @ S_12) => (~ ((eval @ P @ E_2 @ S_12 @ (throw_list_char @ E6) @ S3)))))))))))))). % eval_cases(3)
thf(fact_96_BinOpRedsVal, 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, V_2 : val, S_2 : produc515445032on_val, Bop : bop, V : 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 @ (val_list_char @ V_2) @ S_2)) @ (transi111096263on_val @ (red @ P))) => (((binop @ (produc1753769388al_val @ Bop @ (product_Pair_val_val @ V_1 @ V_2))) = (some_val @ V)) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (binOp_list_char @ E_1 @ Bop @ E_2) @ S_0) @ (produc2023458740on_val @ (val_list_char @ V) @ S_2)) @ (transi111096263on_val @ (red @ P))))))))). % BinOpRedsVal
thf(fact_97_binop_Osimps_I1_J, axiom,
    ((![V_1 : val, V_2 : val]: ((binop @ (produc1753769388al_val @ c_Expr_Obop_OEq @ (product_Pair_val_val @ V_1 @ V_2))) = (some_val @ (bool @ (V_1 = V_2))))))). % binop.simps(1)
thf(fact_98_exp_Oinject_I14_J, axiom,
    ((![X14 : exp_list_char, Y14 : exp_list_char]: (((throw_list_char @ X14) = (throw_list_char @ Y14)) = (X14 = Y14))))). % exp.inject(14)
thf(fact_99_ThrowReds, axiom,
    ((![E2 : exp_list_char, S2 : produc515445032on_val, E5 : exp_list_char, S3 : produc515445032on_val, P : list_P1234162913t_char]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E2 @ S2) @ (produc2023458740on_val @ E5 @ S3)) @ (transi111096263on_val @ (red @ P))) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (throw_list_char @ E2) @ S2) @ (produc2023458740on_val @ (throw_list_char @ E5) @ S3)) @ (transi111096263on_val @ (red @ P))))))). % ThrowReds
thf(fact_100_ThrowRedsThrow, axiom,
    ((![E2 : exp_list_char, S2 : produc515445032on_val, A : exp_list_char, S3 : produc515445032on_val, P : list_P1234162913t_char]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E2 @ S2) @ (produc2023458740on_val @ (throw_list_char @ A) @ S3)) @ (transi111096263on_val @ (red @ P))) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (throw_list_char @ E2) @ S2) @ (produc2023458740on_val @ (throw_list_char @ A) @ S3)) @ (transi111096263on_val @ (red @ P))))))). % ThrowRedsThrow
thf(fact_101_eval__evals_OThrowThrow, axiom,
    ((![P : list_P1234162913t_char, E2 : exp_list_char, S_0 : produc515445032on_val, E5 : exp_list_char, S_1 : produc515445032on_val]: ((eval @ P @ E2 @ S_0 @ (throw_list_char @ E5) @ S_1) => (eval @ P @ (throw_list_char @ E2) @ S_0 @ (throw_list_char @ E5) @ S_1))))). % eval_evals.ThrowThrow
thf(fact_102_exp_Odistinct_I75_J, axiom,
    ((![X3 : val, X14 : exp_list_char]: (~ (((val_list_char @ X3) = (throw_list_char @ X14))))))). % exp.distinct(75)
thf(fact_103_redp__redsp_OThrowThrow, axiom,
    ((![P : list_P1234162913t_char, E2 : exp_list_char, S2 : produc515445032on_val]: (redp @ P @ (throw_list_char @ (throw_list_char @ E2)) @ S2 @ (throw_list_char @ E2) @ S2)))). % redp_redsp.ThrowThrow
thf(fact_104_redp__redsp_OThrowRed, axiom,
    ((![P : list_P1234162913t_char, E2 : exp_list_char, S2 : produc515445032on_val, E5 : exp_list_char, S3 : produc515445032on_val]: ((redp @ P @ E2 @ S2 @ E5 @ S3) => (redp @ P @ (throw_list_char @ E2) @ S2 @ (throw_list_char @ E5) @ S3))))). % redp_redsp.ThrowRed
thf(fact_105_exp_Odistinct_I97_J, axiom,
    ((![X41 : exp_list_char, X42 : bop, X43 : exp_list_char, X14 : exp_list_char]: (~ (((binOp_list_char @ X41 @ X42 @ X43) = (throw_list_char @ X14))))))). % exp.distinct(97)
thf(fact_106_exp_Odistinct_I201_J, axiom,
    ((![X121 : exp_list_char, X122 : exp_list_char, X123 : exp_list_char, X14 : exp_list_char]: (~ (((cond_list_char @ X121 @ X122 @ X123) = (throw_list_char @ X14))))))). % exp.distinct(201)
thf(fact_107_BinOpRedsThrow1, axiom,
    ((![E2 : exp_list_char, S2 : produc515445032on_val, E5 : exp_list_char, S3 : produc515445032on_val, P : list_P1234162913t_char, Bop : bop, E_2 : exp_list_char]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E2 @ S2) @ (produc2023458740on_val @ (throw_list_char @ E5) @ S3)) @ (transi111096263on_val @ (red @ P))) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (binOp_list_char @ E2 @ Bop @ E_2) @ S2) @ (produc2023458740on_val @ (throw_list_char @ E5) @ S3)) @ (transi111096263on_val @ (red @ P))))))). % BinOpRedsThrow1
thf(fact_108_CondRedsThrow, axiom,
    ((![E2 : exp_list_char, S2 : produc515445032on_val, A : exp_list_char, S3 : produc515445032on_val, P : list_P1234162913t_char, E_1 : exp_list_char, E_2 : exp_list_char]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E2 @ S2) @ (produc2023458740on_val @ (throw_list_char @ A) @ S3)) @ (transi111096263on_val @ (red @ P))) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (cond_list_char @ E2 @ E_1 @ E_2) @ S2) @ (produc2023458740on_val @ (throw_list_char @ A) @ S3)) @ (transi111096263on_val @ (red @ P))))))). % CondRedsThrow
thf(fact_109_eval__cases_I10_J, axiom,
    ((![P : list_P1234162913t_char, E2 : exp_list_char, E_1 : exp_list_char, E_2 : exp_list_char, S2 : produc515445032on_val, E5 : exp_list_char, S3 : produc515445032on_val]: ((eval @ P @ (cond_list_char @ E2 @ E_1 @ E_2) @ S2 @ E5 @ S3) => ((![S_12 : produc515445032on_val]: ((eval @ P @ E2 @ S2 @ (val_list_char @ (bool @ $true)) @ S_12) => (~ ((eval @ P @ E_1 @ S_12 @ E5 @ S3))))) => ((![S_12 : produc515445032on_val]: ((eval @ P @ E2 @ S2 @ (val_list_char @ (bool @ $false)) @ S_12) => (~ ((eval @ P @ E_2 @ S_12 @ E5 @ S3))))) => (~ ((![E7 : exp_list_char]: ((E5 = (throw_list_char @ E7)) => (~ ((eval @ P @ E2 @ S2 @ (throw_list_char @ E7) @ S3))))))))))))). % eval_cases(10)
thf(fact_110_BinOpRedsThrow2, 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, E2 : exp_list_char, S_2 : produc515445032on_val, Bop : bop]: ((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 @ (throw_list_char @ E2) @ S_2)) @ (transi111096263on_val @ (red @ P))) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (binOp_list_char @ E_1 @ Bop @ E_2) @ S_0) @ (produc2023458740on_val @ (throw_list_char @ E2) @ S_2)) @ (transi111096263on_val @ (red @ P)))))))). % BinOpRedsThrow2
thf(fact_111_CondReds2T, axiom,
    ((![E2 : exp_list_char, S_0 : produc515445032on_val, S_1 : produc515445032on_val, P : list_P1234162913t_char, E_1 : exp_list_char, E5 : exp_list_char, S_2 : produc515445032on_val, E_2 : exp_list_char]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E2 @ S_0) @ (produc2023458740on_val @ (val_list_char @ (bool @ $true)) @ S_1)) @ (transi111096263on_val @ (red @ P))) => ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E_1 @ S_1) @ (produc2023458740on_val @ E5 @ S_2)) @ (transi111096263on_val @ (red @ P))) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (cond_list_char @ E2 @ E_1 @ E_2) @ S_0) @ (produc2023458740on_val @ E5 @ S_2)) @ (transi111096263on_val @ (red @ P)))))))). % CondReds2T
thf(fact_112_CondReds2F, axiom,
    ((![E2 : exp_list_char, S_0 : produc515445032on_val, S_1 : produc515445032on_val, P : list_P1234162913t_char, E_2 : exp_list_char, E5 : exp_list_char, S_2 : produc515445032on_val, E_1 : exp_list_char]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E2 @ S_0) @ (produc2023458740on_val @ (val_list_char @ (bool @ $false)) @ S_1)) @ (transi111096263on_val @ (red @ P))) => ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E_2 @ S_1) @ (produc2023458740on_val @ E5 @ S_2)) @ (transi111096263on_val @ (red @ P))) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (cond_list_char @ E2 @ E_1 @ E_2) @ S_0) @ (produc2023458740on_val @ E5 @ S_2)) @ (transi111096263on_val @ (red @ P)))))))). % CondReds2F
thf(fact_113_eval__evals_OBinOpThrow1, axiom,
    ((![P : list_P1234162913t_char, E_1 : exp_list_char, S_0 : produc515445032on_val, E2 : exp_list_char, S_1 : produc515445032on_val, Bop : bop, E_2 : exp_list_char]: ((eval @ P @ E_1 @ S_0 @ (throw_list_char @ E2) @ S_1) => (eval @ P @ (binOp_list_char @ E_1 @ Bop @ E_2) @ S_0 @ (throw_list_char @ E2) @ S_1))))). % eval_evals.BinOpThrow1
thf(fact_114_eval__evals_OCondThrow, axiom,
    ((![P : list_P1234162913t_char, E2 : exp_list_char, S_0 : produc515445032on_val, E5 : exp_list_char, S_1 : produc515445032on_val, E_1 : exp_list_char, E_2 : exp_list_char]: ((eval @ P @ E2 @ S_0 @ (throw_list_char @ E5) @ S_1) => (eval @ P @ (cond_list_char @ E2 @ E_1 @ E_2) @ S_0 @ (throw_list_char @ E5) @ S_1))))). % eval_evals.CondThrow
thf(fact_115_redp__redsp_OBinOpThrow1, axiom,
    ((![P : list_P1234162913t_char, E2 : exp_list_char, Bop : bop, E_2 : exp_list_char, S2 : produc515445032on_val]: (redp @ P @ (binOp_list_char @ (throw_list_char @ E2) @ Bop @ E_2) @ S2 @ (throw_list_char @ E2) @ S2)))). % redp_redsp.BinOpThrow1
thf(fact_116_redp__redsp_OCondThrow, axiom,
    ((![P : list_P1234162913t_char, E2 : exp_list_char, E_1 : exp_list_char, E_2 : exp_list_char, S2 : produc515445032on_val]: (redp @ P @ (cond_list_char @ (throw_list_char @ E2) @ E_1 @ E_2) @ S2 @ (throw_list_char @ E2) @ S2)))). % redp_redsp.CondThrow
thf(fact_117_BinOp1Reds, axiom,
    ((![E2 : exp_list_char, S2 : produc515445032on_val, E5 : exp_list_char, S3 : produc515445032on_val, P : list_P1234162913t_char, Bop : bop, 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 @ (binOp_list_char @ E2 @ Bop @ E_2) @ S2) @ (produc2023458740on_val @ (binOp_list_char @ E5 @ Bop @ E_2) @ S3)) @ (transi111096263on_val @ (red @ P))))))). % BinOp1Reds
thf(fact_118_CondReds, axiom,
    ((![E2 : exp_list_char, S2 : produc515445032on_val, E5 : exp_list_char, S3 : produc515445032on_val, P : list_P1234162913t_char, E_1 : exp_list_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 @ (cond_list_char @ E2 @ E_1 @ E_2) @ S2) @ (produc2023458740on_val @ (cond_list_char @ E5 @ E_1 @ E_2) @ S3)) @ (transi111096263on_val @ (red @ P))))))). % CondReds
thf(fact_119_red__reds_OThrowThrow, axiom,
    ((![E2 : exp_list_char, S2 : produc515445032on_val, P : list_P1234162913t_char]: (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (throw_list_char @ (throw_list_char @ E2)) @ S2) @ (produc2023458740on_val @ (throw_list_char @ E2) @ S2)) @ (red @ P))))). % red_reds.ThrowThrow
thf(fact_120_red__reds_OThrowRed, axiom,
    ((![E2 : exp_list_char, S2 : produc515445032on_val, E5 : exp_list_char, S3 : produc515445032on_val, P : list_P1234162913t_char]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E2 @ S2) @ (produc2023458740on_val @ E5 @ S3)) @ (red @ P)) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (throw_list_char @ E2) @ S2) @ (produc2023458740on_val @ (throw_list_char @ E5) @ S3)) @ (red @ P)))))). % red_reds.ThrowRed
thf(fact_121_eval__evals_OBinOpThrow2, axiom,
    ((![P : list_P1234162913t_char, E_1 : exp_list_char, S_0 : produc515445032on_val, V_1 : val, S_1 : produc515445032on_val, E_2 : exp_list_char, E2 : exp_list_char, S_2 : produc515445032on_val, Bop : bop]: ((eval @ P @ E_1 @ S_0 @ (val_list_char @ V_1) @ S_1) => ((eval @ P @ E_2 @ S_1 @ (throw_list_char @ E2) @ S_2) => (eval @ P @ (binOp_list_char @ E_1 @ Bop @ E_2) @ S_0 @ (throw_list_char @ E2) @ S_2)))))). % eval_evals.BinOpThrow2
thf(fact_122_redp__redsp_OBinOpThrow2, axiom,
    ((![P : list_P1234162913t_char, V_1 : val, Bop : bop, E2 : exp_list_char, S2 : produc515445032on_val]: (redp @ P @ (binOp_list_char @ (val_list_char @ V_1) @ Bop @ (throw_list_char @ E2)) @ S2 @ (throw_list_char @ E2) @ S2)))). % redp_redsp.BinOpThrow2
thf(fact_123_BinOp2Reds, axiom,
    ((![E2 : exp_list_char, S2 : produc515445032on_val, E5 : exp_list_char, S3 : produc515445032on_val, P : list_P1234162913t_char, V : val, Bop : bop]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E2 @ S2) @ (produc2023458740on_val @ E5 @ S3)) @ (transi111096263on_val @ (red @ P))) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (binOp_list_char @ (val_list_char @ V) @ Bop @ E2) @ S2) @ (produc2023458740on_val @ (binOp_list_char @ (val_list_char @ V) @ Bop @ E5) @ S3)) @ (transi111096263on_val @ (red @ P))))))). % BinOp2Reds
thf(fact_124_converse__rtrancl__induct__red, axiom,
    ((![E2 : exp_list_char, H : nat > option2118145160on_val, L2 : list_char > option_val, E5 : exp_list_char, H2 : nat > option2118145160on_val, L3 : list_char > option_val, P : list_P1234162913t_char, R : exp_list_char > (nat > option2118145160on_val) > (list_char > option_val) > exp_list_char > (nat > option2118145160on_val) > (list_char > option_val) > $o]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E2 @ (produc52622304on_val @ H @ L2)) @ (produc2023458740on_val @ E5 @ (produc52622304on_val @ H2 @ L3))) @ (transi111096263on_val @ (red @ P))) => ((![E6 : exp_list_char, H6 : nat > option2118145160on_val, L4 : list_char > option_val]: (R @ E6 @ H6 @ L4 @ E6 @ H6 @ L4)) => ((![E_0 : exp_list_char, H_0 : nat > option2118145160on_val, L_0 : list_char > option_val, E_12 : exp_list_char, H_1 : nat > option2118145160on_val, L_1 : list_char > option_val, E7 : exp_list_char, H7 : nat > option2118145160on_val, L5 : list_char > option_val]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E_0 @ (produc52622304on_val @ H_0 @ L_0)) @ (produc2023458740on_val @ E_12 @ (produc52622304on_val @ H_1 @ L_1))) @ (red @ P)) => ((R @ E_12 @ H_1 @ L_1 @ E7 @ H7 @ L5) => (R @ E_0 @ H_0 @ L_0 @ E7 @ H7 @ L5)))) => (R @ E2 @ H @ L2 @ E5 @ H2 @ L3))))))). % converse_rtrancl_induct_red
thf(fact_125_CondF, axiom,
    ((![P : list_P1234162913t_char, E2 : exp_list_char, S_0 : produc515445032on_val, S_1 : produc515445032on_val, E_2 : exp_list_char, E5 : exp_list_char, S_2 : produc515445032on_val, E_1 : exp_list_char]: ((eval @ P @ E2 @ S_0 @ (val_list_char @ (bool @ $false)) @ S_1) => ((eval @ P @ E_2 @ S_1 @ E5 @ S_2) => (eval @ P @ (cond_list_char @ E2 @ E_1 @ E_2) @ S_0 @ E5 @ S_2)))))). % CondF
thf(fact_126_CondT, axiom,
    ((![P : list_P1234162913t_char, E2 : exp_list_char, S_0 : produc515445032on_val, S_1 : produc515445032on_val, E_1 : exp_list_char, E5 : exp_list_char, S_2 : produc515445032on_val, E_2 : exp_list_char]: ((eval @ P @ E2 @ S_0 @ (val_list_char @ (bool @ $true)) @ S_1) => ((eval @ P @ E_1 @ S_1 @ E5 @ S_2) => (eval @ P @ (cond_list_char @ E2 @ E_1 @ E_2) @ S_0 @ E5 @ S_2)))))). % CondT
thf(fact_127_redp__redsp_ORedCondF, axiom,
    ((![P : list_P1234162913t_char, E_1 : exp_list_char, E_2 : exp_list_char, S2 : produc515445032on_val]: (redp @ P @ (cond_list_char @ (val_list_char @ (bool @ $false)) @ E_1 @ E_2) @ S2 @ E_2 @ S2)))). % redp_redsp.RedCondF
thf(fact_128_redp__redsp_ORedCondT, axiom,
    ((![P : list_P1234162913t_char, E_1 : exp_list_char, E_2 : exp_list_char, S2 : produc515445032on_val]: (redp @ P @ (cond_list_char @ (val_list_char @ (bool @ $true)) @ E_1 @ E_2) @ S2 @ E_1 @ S2)))). % redp_redsp.RedCondT
thf(fact_129_red__reds_OBinOpThrow1, axiom,
    ((![E2 : exp_list_char, Bop : bop, E_2 : exp_list_char, S2 : produc515445032on_val, P : list_P1234162913t_char]: (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (binOp_list_char @ (throw_list_char @ E2) @ Bop @ E_2) @ S2) @ (produc2023458740on_val @ (throw_list_char @ E2) @ S2)) @ (red @ P))))). % red_reds.BinOpThrow1
thf(fact_130_typeof__h_Osimps_I3_J, axiom,
    ((![H : nat > option2118145160on_val, B : $o]: ((typeof_h @ H @ (bool @ B)) = (some_ty @ boolean))))). % typeof_h.simps(3)
thf(fact_131_red__reds_OCondThrow, axiom,
    ((![E2 : exp_list_char, E_1 : exp_list_char, E_2 : exp_list_char, S2 : produc515445032on_val, P : list_P1234162913t_char]: (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (cond_list_char @ (throw_list_char @ E2) @ E_1 @ E_2) @ S2) @ (produc2023458740on_val @ (throw_list_char @ E2) @ S2)) @ (red @ P))))). % red_reds.CondThrow
thf(fact_132_red__reds_OBinOpThrow2, axiom,
    ((![V_1 : val, Bop : bop, E2 : exp_list_char, S2 : produc515445032on_val, P : list_P1234162913t_char]: (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (binOp_list_char @ (val_list_char @ V_1) @ Bop @ (throw_list_char @ E2)) @ S2) @ (produc2023458740on_val @ (throw_list_char @ E2) @ S2)) @ (red @ P))))). % red_reds.BinOpThrow2
thf(fact_133_red__reds_ORedCondF, axiom,
    ((![E_1 : exp_list_char, E_2 : exp_list_char, S2 : produc515445032on_val, P : list_P1234162913t_char]: (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (cond_list_char @ (val_list_char @ (bool @ $false)) @ E_1 @ E_2) @ S2) @ (produc2023458740on_val @ E_2 @ S2)) @ (red @ P))))). % red_reds.RedCondF
thf(fact_134_red__reds_ORedCondT, axiom,
    ((![E_1 : exp_list_char, E_2 : exp_list_char, S2 : produc515445032on_val, P : list_P1234162913t_char]: (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (cond_list_char @ (val_list_char @ (bool @ $true)) @ E_1 @ E_2) @ S2) @ (produc2023458740on_val @ E_1 @ S2)) @ (red @ P))))). % red_reds.RedCondT
thf(fact_135_converse__rtrancl__induct2, axiom,
    ((![Ax : val, Ay : val, Bx : val, By : val, R2 : set_Pr488475975al_val, P : val > val > $o]: ((member635678608al_val @ (produc1931530455al_val @ (product_Pair_val_val @ Ax @ Ay) @ (product_Pair_val_val @ Bx @ By)) @ (transi1202724708al_val @ R2)) => ((P @ Bx @ By) => ((![A3 : val, B3 : val, Aa2 : val, Ba : val]: ((member635678608al_val @ (produc1931530455al_val @ (product_Pair_val_val @ A3 @ B3) @ (product_Pair_val_val @ Aa2 @ Ba)) @ R2) => ((member635678608al_val @ (produc1931530455al_val @ (product_Pair_val_val @ Aa2 @ Ba) @ (product_Pair_val_val @ Bx @ By)) @ (transi1202724708al_val @ R2)) => ((P @ Aa2 @ Ba) => (P @ A3 @ B3))))) => (P @ Ax @ Ay))))))). % converse_rtrancl_induct2
thf(fact_136_converse__rtrancl__induct2, axiom,
    ((![Ax : list_char, Ay : produc1257910179t_char > option_val, Bx : list_char, By : produc1257910179t_char > option_val, R2 : set_Pr2110063281on_val, P : list_char > (produc1257910179t_char > option_val) > $o]: ((member197592058on_val @ (produc881885833on_val @ (produc904988266on_val @ Ax @ Ay) @ (produc904988266on_val @ Bx @ By)) @ (transi2071064181on_val @ R2)) => ((P @ Bx @ By) => ((![A3 : list_char, B3 : produc1257910179t_char > option_val, Aa2 : list_char, Ba : produc1257910179t_char > option_val]: ((member197592058on_val @ (produc881885833on_val @ (produc904988266on_val @ A3 @ B3) @ (produc904988266on_val @ Aa2 @ Ba)) @ R2) => ((member197592058on_val @ (produc881885833on_val @ (produc904988266on_val @ Aa2 @ Ba) @ (produc904988266on_val @ Bx @ By)) @ (transi2071064181on_val @ R2)) => ((P @ Aa2 @ Ba) => (P @ A3 @ B3))))) => (P @ Ax @ Ay))))))). % converse_rtrancl_induct2
thf(fact_137_converse__rtrancl__induct2, axiom,
    ((![Ax : bop, Ay : product_prod_val_val, Bx : bop, By : product_prod_val_val, R2 : set_Pr711661575al_val, P : bop > product_prod_val_val > $o]: ((member1528603216al_val @ (produc1144711447al_val @ (produc1753769388al_val @ Ax @ Ay) @ (produc1753769388al_val @ Bx @ By)) @ (transi531594559al_val @ R2)) => ((P @ Bx @ By) => ((![A3 : bop, B3 : product_prod_val_val, Aa2 : bop, Ba : product_prod_val_val]: ((member1528603216al_val @ (produc1144711447al_val @ (produc1753769388al_val @ A3 @ B3) @ (produc1753769388al_val @ Aa2 @ Ba)) @ R2) => ((member1528603216al_val @ (produc1144711447al_val @ (produc1753769388al_val @ Aa2 @ Ba) @ (produc1753769388al_val @ Bx @ By)) @ (transi531594559al_val @ R2)) => ((P @ Aa2 @ Ba) => (P @ A3 @ B3))))) => (P @ Ax @ Ay))))))). % converse_rtrancl_induct2
thf(fact_138_converse__rtrancl__induct2, axiom,
    ((![Ax : nat > option2118145160on_val, Ay : list_char > option_val, Bx : nat > option2118145160on_val, By : list_char > option_val, R2 : set_Pr148564103on_val, P : (nat > option2118145160on_val) > (list_char > option_val) > $o]: ((member2027247312on_val @ (produc2106877847on_val @ (produc52622304on_val @ Ax @ Ay) @ (produc52622304on_val @ Bx @ By)) @ (transi432893227on_val @ R2)) => ((P @ Bx @ By) => ((![A3 : nat > option2118145160on_val, B3 : list_char > option_val, Aa2 : nat > option2118145160on_val, Ba : list_char > option_val]: ((member2027247312on_val @ (produc2106877847on_val @ (produc52622304on_val @ A3 @ B3) @ (produc52622304on_val @ Aa2 @ Ba)) @ R2) => ((member2027247312on_val @ (produc2106877847on_val @ (produc52622304on_val @ Aa2 @ Ba) @ (produc52622304on_val @ Bx @ By)) @ (transi432893227on_val @ R2)) => ((P @ Aa2 @ Ba) => (P @ A3 @ B3))))) => (P @ Ax @ Ay))))))). % converse_rtrancl_induct2
thf(fact_139_converse__rtrancl__induct2, axiom,
    ((![Ax : exp_list_char, Ay : produc515445032on_val, Bx : exp_list_char, By : produc515445032on_val, R2 : set_Pr1189492743on_val, P : exp_list_char > produc515445032on_val > $o]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ Ax @ Ay) @ (produc2023458740on_val @ Bx @ By)) @ (transi111096263on_val @ R2)) => ((P @ Bx @ By) => ((![A3 : exp_list_char, B3 : produc515445032on_val, Aa2 : exp_list_char, Ba : produc515445032on_val]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ A3 @ B3) @ (produc2023458740on_val @ Aa2 @ Ba)) @ R2) => ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ Aa2 @ Ba) @ (produc2023458740on_val @ Bx @ By)) @ (transi111096263on_val @ R2)) => ((P @ Aa2 @ Ba) => (P @ A3 @ B3))))) => (P @ Ax @ Ay))))))). % converse_rtrancl_induct2
thf(fact_140_converse__rtranclE2, axiom,
    ((![Xa : val, Xb : val, Za : val, Zb : val, R2 : set_Pr488475975al_val]: ((member635678608al_val @ (produc1931530455al_val @ (product_Pair_val_val @ Xa @ Xb) @ (product_Pair_val_val @ Za @ Zb)) @ (transi1202724708al_val @ R2)) => ((~ (((product_Pair_val_val @ Xa @ Xb) = (product_Pair_val_val @ Za @ Zb)))) => (~ ((![A3 : val, B3 : val]: ((member635678608al_val @ (produc1931530455al_val @ (product_Pair_val_val @ Xa @ Xb) @ (product_Pair_val_val @ A3 @ B3)) @ R2) => (~ ((member635678608al_val @ (produc1931530455al_val @ (product_Pair_val_val @ A3 @ B3) @ (product_Pair_val_val @ Za @ Zb)) @ (transi1202724708al_val @ R2))))))))))))). % converse_rtranclE2
thf(fact_141_converse__rtranclE2, axiom,
    ((![Xa : list_char, Xb : produc1257910179t_char > option_val, Za : list_char, Zb : produc1257910179t_char > option_val, R2 : set_Pr2110063281on_val]: ((member197592058on_val @ (produc881885833on_val @ (produc904988266on_val @ Xa @ Xb) @ (produc904988266on_val @ Za @ Zb)) @ (transi2071064181on_val @ R2)) => ((~ (((produc904988266on_val @ Xa @ Xb) = (produc904988266on_val @ Za @ Zb)))) => (~ ((![A3 : list_char, B3 : produc1257910179t_char > option_val]: ((member197592058on_val @ (produc881885833on_val @ (produc904988266on_val @ Xa @ Xb) @ (produc904988266on_val @ A3 @ B3)) @ R2) => (~ ((member197592058on_val @ (produc881885833on_val @ (produc904988266on_val @ A3 @ B3) @ (produc904988266on_val @ Za @ Zb)) @ (transi2071064181on_val @ R2))))))))))))). % converse_rtranclE2
thf(fact_142_converse__rtranclE2, axiom,
    ((![Xa : bop, Xb : product_prod_val_val, Za : bop, Zb : product_prod_val_val, R2 : set_Pr711661575al_val]: ((member1528603216al_val @ (produc1144711447al_val @ (produc1753769388al_val @ Xa @ Xb) @ (produc1753769388al_val @ Za @ Zb)) @ (transi531594559al_val @ R2)) => ((~ (((produc1753769388al_val @ Xa @ Xb) = (produc1753769388al_val @ Za @ Zb)))) => (~ ((![A3 : bop, B3 : product_prod_val_val]: ((member1528603216al_val @ (produc1144711447al_val @ (produc1753769388al_val @ Xa @ Xb) @ (produc1753769388al_val @ A3 @ B3)) @ R2) => (~ ((member1528603216al_val @ (produc1144711447al_val @ (produc1753769388al_val @ A3 @ B3) @ (produc1753769388al_val @ Za @ Zb)) @ (transi531594559al_val @ R2))))))))))))). % converse_rtranclE2
thf(fact_143_converse__rtranclE2, axiom,
    ((![Xa : nat > option2118145160on_val, Xb : list_char > option_val, Za : nat > option2118145160on_val, Zb : list_char > option_val, R2 : set_Pr148564103on_val]: ((member2027247312on_val @ (produc2106877847on_val @ (produc52622304on_val @ Xa @ Xb) @ (produc52622304on_val @ Za @ Zb)) @ (transi432893227on_val @ R2)) => ((~ (((produc52622304on_val @ Xa @ Xb) = (produc52622304on_val @ Za @ Zb)))) => (~ ((![A3 : nat > option2118145160on_val, B3 : list_char > option_val]: ((member2027247312on_val @ (produc2106877847on_val @ (produc52622304on_val @ Xa @ Xb) @ (produc52622304on_val @ A3 @ B3)) @ R2) => (~ ((member2027247312on_val @ (produc2106877847on_val @ (produc52622304on_val @ A3 @ B3) @ (produc52622304on_val @ Za @ Zb)) @ (transi432893227on_val @ R2))))))))))))). % converse_rtranclE2
thf(fact_144_converse__rtranclE2, axiom,
    ((![Xa : exp_list_char, Xb : produc515445032on_val, Za : exp_list_char, Zb : produc515445032on_val, R2 : set_Pr1189492743on_val]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ Xa @ Xb) @ (produc2023458740on_val @ Za @ Zb)) @ (transi111096263on_val @ R2)) => ((~ (((produc2023458740on_val @ Xa @ Xb) = (produc2023458740on_val @ Za @ Zb)))) => (~ ((![A3 : exp_list_char, B3 : produc515445032on_val]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ Xa @ Xb) @ (produc2023458740on_val @ A3 @ B3)) @ R2) => (~ ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ A3 @ B3) @ (produc2023458740on_val @ Za @ Zb)) @ (transi111096263on_val @ R2))))))))))))). % converse_rtranclE2
thf(fact_145_rtrancl__induct2, axiom,
    ((![Ax : val, Ay : val, Bx : val, By : val, R2 : set_Pr488475975al_val, P : val > val > $o]: ((member635678608al_val @ (produc1931530455al_val @ (product_Pair_val_val @ Ax @ Ay) @ (product_Pair_val_val @ Bx @ By)) @ (transi1202724708al_val @ R2)) => ((P @ Ax @ Ay) => ((![A3 : val, B3 : val, Aa2 : val, Ba : val]: ((member635678608al_val @ (produc1931530455al_val @ (product_Pair_val_val @ Ax @ Ay) @ (product_Pair_val_val @ A3 @ B3)) @ (transi1202724708al_val @ R2)) => ((member635678608al_val @ (produc1931530455al_val @ (product_Pair_val_val @ A3 @ B3) @ (product_Pair_val_val @ Aa2 @ Ba)) @ R2) => ((P @ A3 @ B3) => (P @ Aa2 @ Ba))))) => (P @ Bx @ By))))))). % rtrancl_induct2
thf(fact_146_rtrancl__induct2, axiom,
    ((![Ax : list_char, Ay : produc1257910179t_char > option_val, Bx : list_char, By : produc1257910179t_char > option_val, R2 : set_Pr2110063281on_val, P : list_char > (produc1257910179t_char > option_val) > $o]: ((member197592058on_val @ (produc881885833on_val @ (produc904988266on_val @ Ax @ Ay) @ (produc904988266on_val @ Bx @ By)) @ (transi2071064181on_val @ R2)) => ((P @ Ax @ Ay) => ((![A3 : list_char, B3 : produc1257910179t_char > option_val, Aa2 : list_char, Ba : produc1257910179t_char > option_val]: ((member197592058on_val @ (produc881885833on_val @ (produc904988266on_val @ Ax @ Ay) @ (produc904988266on_val @ A3 @ B3)) @ (transi2071064181on_val @ R2)) => ((member197592058on_val @ (produc881885833on_val @ (produc904988266on_val @ A3 @ B3) @ (produc904988266on_val @ Aa2 @ Ba)) @ R2) => ((P @ A3 @ B3) => (P @ Aa2 @ Ba))))) => (P @ Bx @ By))))))). % rtrancl_induct2
thf(fact_147_rtrancl__induct2, axiom,
    ((![Ax : bop, Ay : product_prod_val_val, Bx : bop, By : product_prod_val_val, R2 : set_Pr711661575al_val, P : bop > product_prod_val_val > $o]: ((member1528603216al_val @ (produc1144711447al_val @ (produc1753769388al_val @ Ax @ Ay) @ (produc1753769388al_val @ Bx @ By)) @ (transi531594559al_val @ R2)) => ((P @ Ax @ Ay) => ((![A3 : bop, B3 : product_prod_val_val, Aa2 : bop, Ba : product_prod_val_val]: ((member1528603216al_val @ (produc1144711447al_val @ (produc1753769388al_val @ Ax @ Ay) @ (produc1753769388al_val @ A3 @ B3)) @ (transi531594559al_val @ R2)) => ((member1528603216al_val @ (produc1144711447al_val @ (produc1753769388al_val @ A3 @ B3) @ (produc1753769388al_val @ Aa2 @ Ba)) @ R2) => ((P @ A3 @ B3) => (P @ Aa2 @ Ba))))) => (P @ Bx @ By))))))). % rtrancl_induct2
thf(fact_148_rtrancl__induct2, axiom,
    ((![Ax : nat > option2118145160on_val, Ay : list_char > option_val, Bx : nat > option2118145160on_val, By : list_char > option_val, R2 : set_Pr148564103on_val, P : (nat > option2118145160on_val) > (list_char > option_val) > $o]: ((member2027247312on_val @ (produc2106877847on_val @ (produc52622304on_val @ Ax @ Ay) @ (produc52622304on_val @ Bx @ By)) @ (transi432893227on_val @ R2)) => ((P @ Ax @ Ay) => ((![A3 : nat > option2118145160on_val, B3 : list_char > option_val, Aa2 : nat > option2118145160on_val, Ba : list_char > option_val]: ((member2027247312on_val @ (produc2106877847on_val @ (produc52622304on_val @ Ax @ Ay) @ (produc52622304on_val @ A3 @ B3)) @ (transi432893227on_val @ R2)) => ((member2027247312on_val @ (produc2106877847on_val @ (produc52622304on_val @ A3 @ B3) @ (produc52622304on_val @ Aa2 @ Ba)) @ R2) => ((P @ A3 @ B3) => (P @ Aa2 @ Ba))))) => (P @ Bx @ By))))))). % rtrancl_induct2
thf(fact_149_rtrancl__induct2, axiom,
    ((![Ax : exp_list_char, Ay : produc515445032on_val, Bx : exp_list_char, By : produc515445032on_val, R2 : set_Pr1189492743on_val, P : exp_list_char > produc515445032on_val > $o]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ Ax @ Ay) @ (produc2023458740on_val @ Bx @ By)) @ (transi111096263on_val @ R2)) => ((P @ Ax @ Ay) => ((![A3 : exp_list_char, B3 : produc515445032on_val, Aa2 : exp_list_char, Ba : produc515445032on_val]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ Ax @ Ay) @ (produc2023458740on_val @ A3 @ B3)) @ (transi111096263on_val @ R2)) => ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ A3 @ B3) @ (produc2023458740on_val @ Aa2 @ Ba)) @ R2) => ((P @ A3 @ B3) => (P @ Aa2 @ Ba))))) => (P @ Bx @ By))))))). % rtrancl_induct2
thf(fact_150_val_Oinject_I1_J, axiom,
    ((![X3 : $o, Y3 : $o]: (((bool @ X3) = (bool @ Y3)) = (X3 = Y3))))). % val.inject(1)
thf(fact_151_rtrancl__idemp, axiom,
    ((![R2 : set_Pr1189492743on_val]: ((transi111096263on_val @ (transi111096263on_val @ R2)) = (transi111096263on_val @ R2))))). % rtrancl_idemp
thf(fact_152_r__into__rtrancl, axiom,
    ((![P3 : produc1172664615on_val, R2 : set_Pr1189492743on_val]: ((member354538064on_val @ P3 @ R2) => (member354538064on_val @ P3 @ (transi111096263on_val @ R2)))))). % r_into_rtrancl
thf(fact_153_converse__rtrancl__into__rtrancl, axiom,
    ((![A : val, B : val, R2 : set_Pr1870322241al_val, C5 : val]: ((member1494223754al_val @ (product_Pair_val_val @ A @ B) @ R2) => ((member1494223754al_val @ (product_Pair_val_val @ B @ C5) @ (transi196325053cl_val @ R2)) => (member1494223754al_val @ (product_Pair_val_val @ A @ C5) @ (transi196325053cl_val @ R2))))))). % converse_rtrancl_into_rtrancl
thf(fact_154_converse__rtrancl__into__rtrancl, axiom,
    ((![A : produc1097884484on_val, B : produc1097884484on_val, R2 : set_Pr1189492743on_val, C5 : produc1097884484on_val]: ((member354538064on_val @ (produc1069526295on_val @ A @ B) @ R2) => ((member354538064on_val @ (produc1069526295on_val @ B @ C5) @ (transi111096263on_val @ R2)) => (member354538064on_val @ (produc1069526295on_val @ A @ C5) @ (transi111096263on_val @ R2))))))). % converse_rtrancl_into_rtrancl
thf(fact_155_rtrancl_Ortrancl__into__rtrancl, axiom,
    ((![A : val, B : val, R2 : set_Pr1870322241al_val, C5 : val]: ((member1494223754al_val @ (product_Pair_val_val @ A @ B) @ (transi196325053cl_val @ R2)) => ((member1494223754al_val @ (product_Pair_val_val @ B @ C5) @ R2) => (member1494223754al_val @ (product_Pair_val_val @ A @ C5) @ (transi196325053cl_val @ R2))))))). % rtrancl.rtrancl_into_rtrancl
thf(fact_156_rtrancl_Ortrancl__into__rtrancl, axiom,
    ((![A : produc1097884484on_val, B : produc1097884484on_val, R2 : set_Pr1189492743on_val, C5 : produc1097884484on_val]: ((member354538064on_val @ (produc1069526295on_val @ A @ B) @ (transi111096263on_val @ R2)) => ((member354538064on_val @ (produc1069526295on_val @ B @ C5) @ R2) => (member354538064on_val @ (produc1069526295on_val @ A @ C5) @ (transi111096263on_val @ R2))))))). % rtrancl.rtrancl_into_rtrancl
thf(fact_157_converse__rtrancl__induct, axiom,
    ((![A : val, B : val, R2 : set_Pr1870322241al_val, P : val > $o]: ((member1494223754al_val @ (product_Pair_val_val @ A @ B) @ (transi196325053cl_val @ R2)) => ((P @ B) => ((![Y4 : val, Z2 : val]: ((member1494223754al_val @ (product_Pair_val_val @ Y4 @ Z2) @ R2) => ((member1494223754al_val @ (product_Pair_val_val @ Z2 @ B) @ (transi196325053cl_val @ R2)) => ((P @ Z2) => (P @ Y4))))) => (P @ A))))))). % converse_rtrancl_induct
thf(fact_158_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, Z2 : produc1097884484on_val]: ((member354538064on_val @ (produc1069526295on_val @ Y4 @ Z2) @ R2) => ((member354538064on_val @ (produc1069526295on_val @ Z2 @ B) @ (transi111096263on_val @ R2)) => ((P @ Z2) => (P @ Y4))))) => (P @ A))))))). % converse_rtrancl_induct
thf(fact_159_rtrancl_Ortrancl__refl, axiom,
    ((![A : val, R2 : set_Pr1870322241al_val]: (member1494223754al_val @ (product_Pair_val_val @ A @ A) @ (transi196325053cl_val @ R2))))). % rtrancl.rtrancl_refl
thf(fact_160_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_161_converse__rtranclE, axiom,
    ((![X5 : val, Z3 : val, R2 : set_Pr1870322241al_val]: ((member1494223754al_val @ (product_Pair_val_val @ X5 @ Z3) @ (transi196325053cl_val @ R2)) => ((~ ((X5 = Z3))) => (~ ((![Y4 : val]: ((member1494223754al_val @ (product_Pair_val_val @ X5 @ Y4) @ R2) => (~ ((member1494223754al_val @ (product_Pair_val_val @ Y4 @ Z3) @ (transi196325053cl_val @ R2))))))))))))). % converse_rtranclE
thf(fact_162_converse__rtranclE, axiom,
    ((![X5 : produc1097884484on_val, Z3 : produc1097884484on_val, R2 : set_Pr1189492743on_val]: ((member354538064on_val @ (produc1069526295on_val @ X5 @ Z3) @ (transi111096263on_val @ R2)) => ((~ ((X5 = Z3))) => (~ ((![Y4 : produc1097884484on_val]: ((member354538064on_val @ (produc1069526295on_val @ X5 @ Y4) @ R2) => (~ ((member354538064on_val @ (produc1069526295on_val @ Y4 @ Z3) @ (transi111096263on_val @ R2))))))))))))). % converse_rtranclE
thf(fact_163_rtrancl_Oinducts, axiom,
    ((![X1 : val, X2 : val, R2 : set_Pr1870322241al_val, P : val > val > $o]: ((member1494223754al_val @ (product_Pair_val_val @ X1 @ X2) @ (transi196325053cl_val @ R2)) => ((![A3 : val]: (P @ A3 @ A3)) => ((![A3 : val, B3 : val, C : val]: ((member1494223754al_val @ (product_Pair_val_val @ A3 @ B3) @ (transi196325053cl_val @ R2)) => ((P @ A3 @ B3) => ((member1494223754al_val @ (product_Pair_val_val @ B3 @ C) @ R2) => (P @ A3 @ C))))) => (P @ X1 @ X2))))))). % rtrancl.inducts
thf(fact_164_rtrancl_Oinducts, axiom,
    ((![X1 : produc1097884484on_val, X2 : produc1097884484on_val, R2 : set_Pr1189492743on_val, P : produc1097884484on_val > produc1097884484on_val > $o]: ((member354538064on_val @ (produc1069526295on_val @ X1 @ X2) @ (transi111096263on_val @ R2)) => ((![A3 : produc1097884484on_val]: (P @ A3 @ A3)) => ((![A3 : produc1097884484on_val, B3 : produc1097884484on_val, C : produc1097884484on_val]: ((member354538064on_val @ (produc1069526295on_val @ A3 @ B3) @ (transi111096263on_val @ R2)) => ((P @ A3 @ B3) => ((member354538064on_val @ (produc1069526295on_val @ B3 @ C) @ R2) => (P @ A3 @ C))))) => (P @ X1 @ X2))))))). % rtrancl.inducts
thf(fact_165_rtrancl__induct, axiom,
    ((![A : val, B : val, R2 : set_Pr1870322241al_val, P : val > $o]: ((member1494223754al_val @ (product_Pair_val_val @ A @ B) @ (transi196325053cl_val @ R2)) => ((P @ A) => ((![Y4 : val, Z2 : val]: ((member1494223754al_val @ (product_Pair_val_val @ A @ Y4) @ (transi196325053cl_val @ R2)) => ((member1494223754al_val @ (product_Pair_val_val @ Y4 @ Z2) @ R2) => ((P @ Y4) => (P @ Z2))))) => (P @ B))))))). % rtrancl_induct
thf(fact_166_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, Z2 : produc1097884484on_val]: ((member354538064on_val @ (produc1069526295on_val @ A @ Y4) @ (transi111096263on_val @ R2)) => ((member354538064on_val @ (produc1069526295on_val @ Y4 @ Z2) @ R2) => ((P @ Y4) => (P @ Z2))))) => (P @ B))))))). % rtrancl_induct
thf(fact_167_rtrancl__trans, axiom,
    ((![X5 : val, Y : val, R2 : set_Pr1870322241al_val, Z3 : val]: ((member1494223754al_val @ (product_Pair_val_val @ X5 @ Y) @ (transi196325053cl_val @ R2)) => ((member1494223754al_val @ (product_Pair_val_val @ Y @ Z3) @ (transi196325053cl_val @ R2)) => (member1494223754al_val @ (product_Pair_val_val @ X5 @ Z3) @ (transi196325053cl_val @ R2))))))). % rtrancl_trans
thf(fact_168_rtrancl__trans, axiom,
    ((![X5 : produc1097884484on_val, Y : produc1097884484on_val, R2 : set_Pr1189492743on_val, Z3 : produc1097884484on_val]: ((member354538064on_val @ (produc1069526295on_val @ X5 @ Y) @ (transi111096263on_val @ R2)) => ((member354538064on_val @ (produc1069526295on_val @ Y @ Z3) @ (transi111096263on_val @ R2)) => (member354538064on_val @ (produc1069526295on_val @ X5 @ Z3) @ (transi111096263on_val @ R2))))))). % rtrancl_trans
thf(fact_169_rtrancl_Osimps, axiom,
    ((![A1 : val, A22 : val, R2 : set_Pr1870322241al_val]: ((member1494223754al_val @ (product_Pair_val_val @ A1 @ A22) @ (transi196325053cl_val @ R2)) = (((?[A4 : val]: (((A1 = A4)) & ((A22 = A4))))) | ((?[A4 : val]: (?[B4 : val]: (?[C6 : val]: (((A1 = A4)) & ((((A22 = C6)) & ((((member1494223754al_val @ (product_Pair_val_val @ A4 @ B4) @ (transi196325053cl_val @ R2))) & ((member1494223754al_val @ (product_Pair_val_val @ B4 @ C6) @ R2)))))))))))))))). % rtrancl.simps
thf(fact_170_rtrancl_Osimps, axiom,
    ((![A1 : produc1097884484on_val, A22 : produc1097884484on_val, R2 : set_Pr1189492743on_val]: ((member354538064on_val @ (produc1069526295on_val @ A1 @ A22) @ (transi111096263on_val @ R2)) = (((?[A4 : produc1097884484on_val]: (((A1 = A4)) & ((A22 = A4))))) | ((?[A4 : produc1097884484on_val]: (?[B4 : produc1097884484on_val]: (?[C6 : produc1097884484on_val]: (((A1 = A4)) & ((((A22 = C6)) & ((((member354538064on_val @ (produc1069526295on_val @ A4 @ B4) @ (transi111096263on_val @ R2))) & ((member354538064on_val @ (produc1069526295on_val @ B4 @ C6) @ R2)))))))))))))))). % rtrancl.simps
thf(fact_171_rtrancl_Ocases, axiom,
    ((![A1 : val, A22 : val, R2 : set_Pr1870322241al_val]: ((member1494223754al_val @ (product_Pair_val_val @ A1 @ A22) @ (transi196325053cl_val @ R2)) => ((~ ((A22 = A1))) => (~ ((![B3 : val]: ((member1494223754al_val @ (product_Pair_val_val @ A1 @ B3) @ (transi196325053cl_val @ R2)) => (~ ((member1494223754al_val @ (product_Pair_val_val @ B3 @ A22) @ R2)))))))))))). % rtrancl.cases
thf(fact_172_rtrancl_Ocases, axiom,
    ((![A1 : produc1097884484on_val, A22 : produc1097884484on_val, R2 : set_Pr1189492743on_val]: ((member354538064on_val @ (produc1069526295on_val @ A1 @ A22) @ (transi111096263on_val @ R2)) => ((~ ((A22 = A1))) => (~ ((![B3 : produc1097884484on_val]: ((member354538064on_val @ (produc1069526295on_val @ A1 @ B3) @ (transi111096263on_val @ R2)) => (~ ((member354538064on_val @ (produc1069526295on_val @ B3 @ A22) @ R2)))))))))))). % rtrancl.cases
thf(fact_173_rtranclE, axiom,
    ((![A : val, B : val, R2 : set_Pr1870322241al_val]: ((member1494223754al_val @ (product_Pair_val_val @ A @ B) @ (transi196325053cl_val @ R2)) => ((~ ((A = B))) => (~ ((![Y4 : val]: ((member1494223754al_val @ (product_Pair_val_val @ A @ Y4) @ (transi196325053cl_val @ R2)) => (~ ((member1494223754al_val @ (product_Pair_val_val @ Y4 @ B) @ R2)))))))))))). % rtranclE
thf(fact_174_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_175_extend__eval, axiom,
    ((![P : list_P1234162913t_char, E2 : exp_list_char, S2 : produc515445032on_val, E8 : exp_list_char, S4 : produc515445032on_val, E5 : exp_list_char, S3 : produc515445032on_val]: ((wf_pro1229751607t_char @ wwf_J_mdecl @ P) => ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E2 @ S2) @ (produc2023458740on_val @ E8 @ S4)) @ (transi111096263on_val @ (red @ P))) => ((eval @ P @ E8 @ S4 @ E5 @ S3) => (eval @ P @ E2 @ S2 @ E5 @ S3))))))). % extend_eval
thf(fact_176_big__by__small, axiom,
    ((![P : list_P1234162913t_char, E2 : exp_list_char, S2 : produc515445032on_val, E5 : exp_list_char, S3 : produc515445032on_val]: ((wf_pro1229751607t_char @ wwf_J_mdecl @ P) => ((eval @ P @ E2 @ S2 @ E5 @ S3) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E2 @ S2) @ (produc2023458740on_val @ E5 @ S3)) @ (transi111096263on_val @ (red @ P)))))))). % big_by_small
thf(fact_177_extend__1__eval, axiom,
    ((![P : list_P1234162913t_char, E2 : exp_list_char, S2 : produc515445032on_val, E8 : exp_list_char, S4 : produc515445032on_val, E5 : exp_list_char, S3 : produc515445032on_val]: ((wf_pro1229751607t_char @ wwf_J_mdecl @ P) => ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E2 @ S2) @ (produc2023458740on_val @ E8 @ S4)) @ (red @ P)) => ((eval @ P @ E8 @ S4 @ E5 @ S3) => (eval @ P @ E2 @ S2 @ E5 @ S3))))))). % extend_1_eval
thf(fact_178_wf__prog__wwf__prog, axiom,
    ((![P : list_P1234162913t_char]: ((wf_pro1229751607t_char @ wf_J_mdecl @ P) => (wf_pro1229751607t_char @ wwf_J_mdecl @ P))))). % wf_prog_wwf_prog
thf(fact_179_big__iff__small, axiom,
    ((![P : list_P1234162913t_char, E2 : exp_list_char, S2 : produc515445032on_val, E5 : exp_list_char, S3 : produc515445032on_val]: ((wf_pro1229751607t_char @ wwf_J_mdecl @ P) => ((eval @ P @ E2 @ S2 @ E5 @ S3) = (((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E2 @ S2) @ (produc2023458740on_val @ E5 @ S3)) @ (transi111096263on_val @ (red @ P)))) & ((final_list_char @ E5)))))))). % big_iff_small
thf(fact_180_eval__finalId, axiom,
    ((![E2 : exp_list_char, P : list_P1234162913t_char, S2 : produc515445032on_val]: ((final_list_char @ E2) => (eval @ P @ E2 @ S2 @ E2 @ S2))))). % eval_finalId
thf(fact_181_eval__final, axiom,
    ((![P : list_P1234162913t_char, E2 : exp_list_char, S2 : produc515445032on_val, E5 : exp_list_char, S3 : produc515445032on_val]: ((eval @ P @ E2 @ S2 @ E5 @ S3) => (final_list_char @ E5))))). % eval_final
thf(fact_182_wf__mdecl__wwf__mdecl, axiom,
    ((![P : list_P1234162913t_char, C4 : list_char, Md : produc1259892823t_char]: ((wf_J_mdecl @ P @ C4 @ Md) => (wwf_J_mdecl @ P @ C4 @ Md))))). % wf_mdecl_wwf_mdecl
thf(fact_183_small__by__big, axiom,
    ((![P : list_P1234162913t_char, E2 : exp_list_char, S2 : produc515445032on_val, E5 : exp_list_char, S3 : produc515445032on_val]: ((wf_pro1229751607t_char @ wwf_J_mdecl @ P) => ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E2 @ S2) @ (produc2023458740on_val @ E5 @ S3)) @ (transi111096263on_val @ (red @ P))) => ((final_list_char @ E5) => (eval @ P @ E2 @ S2 @ E5 @ S3))))))). % small_by_big
thf(fact_184_WhileTRedsThrow, axiom,
    ((![B : exp_list_char, S_0 : produc515445032on_val, S_1 : produc515445032on_val, P : list_P1234162913t_char, C5 : exp_list_char, E2 : exp_list_char, S_2 : produc515445032on_val]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ B @ S_0) @ (produc2023458740on_val @ (val_list_char @ (bool @ $true)) @ S_1)) @ (transi111096263on_val @ (red @ P))) => ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ C5 @ S_1) @ (produc2023458740on_val @ (throw_list_char @ E2) @ S_2)) @ (transi111096263on_val @ (red @ P))) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (while_list_char @ B @ C5) @ S_0) @ (produc2023458740on_val @ (throw_list_char @ E2) @ S_2)) @ (transi111096263on_val @ (red @ P)))))))). % WhileTRedsThrow
thf(fact_185_WhileTReds, axiom,
    ((![B : exp_list_char, S_0 : produc515445032on_val, S_1 : produc515445032on_val, P : list_P1234162913t_char, C5 : exp_list_char, V_1 : val, S_2 : produc515445032on_val, E2 : exp_list_char, S_3 : produc515445032on_val]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ B @ S_0) @ (produc2023458740on_val @ (val_list_char @ (bool @ $true)) @ S_1)) @ (transi111096263on_val @ (red @ P))) => ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ C5 @ S_1) @ (produc2023458740on_val @ (val_list_char @ V_1) @ S_2)) @ (transi111096263on_val @ (red @ P))) => ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (while_list_char @ B @ C5) @ S_2) @ (produc2023458740on_val @ E2 @ S_3)) @ (transi111096263on_val @ (red @ P))) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (while_list_char @ B @ C5) @ S_0) @ (produc2023458740on_val @ E2 @ S_3)) @ (transi111096263on_val @ (red @ P))))))))). % WhileTReds
thf(fact_186_exp_Oinject_I13_J, axiom,
    ((![X131 : exp_list_char, X132 : exp_list_char, Y131 : exp_list_char, Y132 : exp_list_char]: (((while_list_char @ X131 @ X132) = (while_list_char @ Y131 @ Y132)) = (((X131 = Y131)) & ((X132 = Y132))))))). % exp.inject(13)
thf(fact_187_exp_Odistinct_I205_J, axiom,
    ((![X131 : exp_list_char, X132 : exp_list_char, X14 : exp_list_char]: (~ (((while_list_char @ X131 @ X132) = (throw_list_char @ X14))))))). % exp.distinct(205)
thf(fact_188_WhileCondThrow, axiom,
    ((![P : list_P1234162913t_char, E2 : exp_list_char, S_0 : produc515445032on_val, E5 : exp_list_char, S_1 : produc515445032on_val, C5 : exp_list_char]: ((eval @ P @ E2 @ S_0 @ (throw_list_char @ E5) @ S_1) => (eval @ P @ (while_list_char @ E2 @ C5) @ S_0 @ (throw_list_char @ E5) @ S_1))))). % WhileCondThrow
thf(fact_189_exp_Odistinct_I199_J, axiom,
    ((![X121 : exp_list_char, X122 : exp_list_char, X123 : exp_list_char, X131 : exp_list_char, X132 : exp_list_char]: (~ (((cond_list_char @ X121 @ X122 @ X123) = (while_list_char @ X131 @ X132))))))). % exp.distinct(199)

% Conjectures (1)
thf(conj_0, conjecture,
    ((?[T5 : ty]: ((wTrt @ p @ a @ e @ (val_list_char @ v) @ T5) & (widen_917054840t_char @ p @ T5 @ t))))).
