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thf(sy_c_Expr_Oexp_OBinOp_001t__List__Olist_It__String__Ochar_J, type,
    binOp_list_char : exp_list_char > bop > exp_list_char > exp_list_char).
thf(sy_c_Expr_Oexp_OCall_001t__List__Olist_It__String__Ochar_J, type,
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thf(sy_c_Expr_Oexp_OSeq_001t__List__Olist_It__String__Ochar_J, type,
    seq_list_char : exp_list_char > exp_list_char > exp_list_char).
thf(sy_c_Expr_Oexp_OVal_001t__List__Olist_It__String__Ochar_J, type,
    val_list_char : val > exp_list_char).
thf(sy_c_Expr_Oexp_Othrow_001t__List__Olist_It__String__Ochar_J, type,
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thf(sy_c_JWellForm_Owf__J__mdecl, type,
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thf(sy_c_List_Oappend_001t__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J, type,
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thf(sy_c_List_Olist_OCons_001t__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J, type,
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thf(sy_c_List_Olist_OCons_001t__Type__Oty, type,
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thf(sy_c_List_Olist_Olist__all2_001t__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_001t__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J, type,
    list_a1702871623t_char : (exp_list_char > exp_list_char > $o) > list_exp_list_char > list_exp_list_char > $o).
thf(sy_c_List_Olist_Olist__all2_001t__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_001t__Type__Oty, type,
    list_a295513531har_ty : (exp_list_char > ty > $o) > list_exp_list_char > list_ty > $o).
thf(sy_c_List_Olist_Olist__all2_001t__Type__Oty_001t__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J, type,
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thf(sy_c_List_Olist_Olist__all2_001t__Type__Oty_001t__Type__Oty, type,
    list_all2_ty_ty : (ty > ty > $o) > list_ty > list_ty > $o).
thf(sy_c_List_Olist_Omap_001t__Value__Oval_001t__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J, type,
    map_va1515327237t_char : (val > exp_list_char) > list_val > list_exp_list_char).
thf(sy_c_Map_Omap__add_001t__List__Olist_It__String__Ochar_J_001t__Type__Oty, type,
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thf(sy_c_Map_Omap__add_001t__List__Olist_It__String__Ochar_J_001t__Value__Oval, type,
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thf(sy_c_Map_Omap__le_001t__List__Olist_It__String__Ochar_J_001t__Type__Oty, type,
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thf(sy_c_Map_Omap__le_001t__List__Olist_It__String__Ochar_J_001t__Value__Oval, type,
    map_le_list_char_val : (list_char > option_val) > (list_char > option_val) > $o).
thf(sy_c_Objects_Ohext, 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__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__Expr__Oexp_It__List__Olist_It__String__Ochar_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,
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thf(sy_c_Product__Type_OPair_001t__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_M_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_001t__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_M_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_J, type,
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thf(sy_c_Product__Type_Oprod_Ofst_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_Oprod_Ofst_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,
    produc1141111712on_val : produc1097884484on_val > exp_list_char).
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    collec2055896722on_val : (produc1172664615on_val > $o) > set_Pr1189492743on_val).
thf(sy_c_Set_OCollect_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__List__Olist_It__Expr__Oexp_It__List__Olist_It__String__Ochar_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_Mt__Product____Type__Oprod_It__List__Olist_It__Expr__Oexp_It__List__Olist_It__String__Ochar_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_J, type,
    collec105960082on_val : (produc655058983on_val > $o) > set_Pr208351751on_val).
thf(sy_c_SmallStep_Ored, type,
    red : list_P1234162913t_char > set_Pr1189492743on_val).
thf(sy_c_SmallStep_Oreds, type,
    reds : list_P1234162913t_char > set_Pr208351751on_val).
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__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__Expr__Oexp_It__List__Olist_It__String__Ochar_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,
    transi325225921on_val : set_Pr208351751on_val > set_Pr208351751on_val).
thf(sy_c_Transitive__Closure_Ortrancl_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_Mt__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_M_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_Mt__Product____Type__Oprod_It__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_Mt__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_M_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J, type,
    transi100378922on_val : set_Pr1368603847on_val > set_Pr1368603847on_val).
thf(sy_c_Transitive__Closure_Ortrancl_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__List__Olist_It__Expr__Oexp_It__List__Olist_It__String__Ochar_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_Mt__Product____Type__Oprod_It__List__Olist_It__Expr__Oexp_It__List__Olist_It__String__Ochar_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_J, type,
    transi159622442on_val : set_Pr1301890247on_val > set_Pr1301890247on_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_WellForm_Owf__prog_001t__Product____Type__Oprod_It__List__Olist_It__List__Olist_It__String__Ochar_J_J_Mt__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_J, type,
    wf_pro1229751607t_char : (list_P1234162913t_char > list_char > produc1259892823t_char > $o) > list_P1234162913t_char > $o).
thf(sy_c_WellTypeRT_OWTrt, type,
    wTrt2 : list_P1234162913t_char > (nat > option2118145160on_val) > (list_char > option_ty) > exp_list_char > ty > $o).
thf(sy_c_WellTypeRT_OWTrts, type,
    wTrts2 : list_P1234162913t_char > (nat > option2118145160on_val) > (list_char > option_ty) > list_exp_list_char > list_ty > $o).
thf(sy_c_WellType_OWT, type,
    wt : list_P1234162913t_char > (list_char > option_ty) > exp_list_char > ty > $o).
thf(sy_c_WellType_OWTs, type,
    wTs : list_P1234162913t_char > (list_char > option_ty) > list_exp_list_char > list_ty > $o).
thf(sy_c_member_001t__Product____Type__Oprod_It__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_M_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_Mt__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_M_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J, type,
    member2027247312on_val : produc744932519on_val > set_Pr148564103on_val > $o).
thf(sy_c_member_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_Mt__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_M_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_Mt__Product____Type__Oprod_It__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_Mt__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_M_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J, type,
    member354538064on_val : produc1172664615on_val > set_Pr1189492743on_val > $o).
thf(sy_c_member_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__List__Olist_It__Expr__Oexp_It__List__Olist_It__String__Ochar_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_Mt__Product____Type__Oprod_It__List__Olist_It__Expr__Oexp_It__List__Olist_It__String__Ochar_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_J, type,
    member1689761872on_val : produc655058983on_val > set_Pr208351751on_val > $o).
thf(sy_c_member_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__Product____Type__Oprod_It__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_Mt__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_M_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_Mt__Product____Type__Oprod_It__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_Mt__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_M_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_Mt__Product____Type__Oprod_It__Product____Type__Oprod_It__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_Mt__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_M_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_Mt__Product____Type__Oprod_It__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_Mt__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_M_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_J, type,
    member208988944on_val : produc1161703655on_val > set_Pr1368603847on_val > $o).
thf(sy_c_member_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__Product____Type__Oprod_It__List__Olist_It__Expr__Oexp_It__List__Olist_It__String__Ochar_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_Mt__Product____Type__Oprod_It__List__Olist_It__Expr__Oexp_It__List__Olist_It__String__Ochar_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_J_Mt__Product____Type__Oprod_It__Product____Type__Oprod_It__List__Olist_It__Expr__Oexp_It__List__Olist_It__String__Ochar_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_Mt__Product____Type__Oprod_It__List__Olist_It__Expr__Oexp_It__List__Olist_It__String__Ochar_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_J_J, type,
    member1743964944on_val : produc1428501223on_val > set_Pr1301890247on_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_e, type,
    e2 : exp_list_char).
thf(sy_v_e_H, type,
    e3 : exp_list_char).
thf(sy_v_s, type,
    s : produc515445032on_val).
thf(sy_v_s_H, type,
    s2 : produc515445032on_val).

% Relevant facts (243)
thf(fact_0_Red, axiom,
    ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ e2 @ s) @ (produc2023458740on_val @ e3 @ s2)) @ (transi111096263on_val @ (red @ p))))). % Red
thf(fact_1_local_Owf, axiom,
    ((wf_pro1229751607t_char @ wf_J_mdecl @ p))). % local.wf
thf(fact_2_red__preserves__sconf, axiom,
    ((![E : exp_list_char, S : produc515445032on_val, E2 : exp_list_char, S2 : produc515445032on_val, P : list_P1234162913t_char, E3 : list_char > option_ty, T : ty]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E @ S) @ (produc2023458740on_val @ E2 @ S2)) @ (red @ P)) => ((wTrt2 @ P @ (hp @ S) @ E3 @ E @ T) => ((typeSa1777264139_sconf @ P @ E3 @ S) => (typeSa1777264139_sconf @ P @ E3 @ S2))))))). % red_preserves_sconf
thf(fact_3_subject__reduction, axiom,
    ((![P : list_P1234162913t_char, E : exp_list_char, S : produc515445032on_val, E2 : exp_list_char, S2 : produc515445032on_val, E3 : list_char > option_ty, T : ty]: ((wf_pro1229751607t_char @ wf_J_mdecl @ P) => ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E @ S) @ (produc2023458740on_val @ E2 @ S2)) @ (red @ P)) => ((typeSa1777264139_sconf @ P @ E3 @ S) => ((wTrt2 @ P @ (hp @ S) @ E3 @ E @ T) => (?[T2 : ty]: ((wTrt2 @ P @ (hp @ S2) @ E3 @ E2 @ T2) & (widen_917054840t_char @ P @ T2 @ T)))))))))). % subject_reduction
thf(fact_4_WTrt__hext__mono, axiom,
    ((![P : list_P1234162913t_char, H : nat > option2118145160on_val, E3 : list_char > option_ty, E : exp_list_char, T : ty, H2 : nat > option2118145160on_val]: ((wTrt2 @ P @ H @ E3 @ E @ T) => ((hext @ H @ H2) => (wTrt2 @ P @ H2 @ E3 @ E @ T)))))). % WTrt_hext_mono
thf(fact_5_WTrt__env__mono, axiom,
    ((![P : list_P1234162913t_char, H : nat > option2118145160on_val, E3 : list_char > option_ty, E : exp_list_char, T : ty, E4 : list_char > option_ty]: ((wTrt2 @ P @ H @ E3 @ E @ T) => ((map_le_list_char_ty @ E3 @ E4) => (wTrt2 @ P @ H @ E4 @ E @ T)))))). % WTrt_env_mono
thf(fact_6_hp__def, axiom,
    ((hp = produc1246629324on_val))). % hp_def
thf(fact_7_wt_H__wt, axiom,
    ((![P : list_P1234162913t_char, H : nat > option2118145160on_val, E3 : list_char > option_ty, E : exp_list_char, T : ty]: ((wTrt @ P @ H @ E3 @ E @ T) => (wTrt2 @ P @ H @ E3 @ E @ T))))). % wt'_wt
thf(fact_8_wt__wt_H, axiom,
    ((![P : list_P1234162913t_char, H : nat > option2118145160on_val, E3 : list_char > option_ty, E : exp_list_char, T : ty]: ((wTrt2 @ P @ H @ E3 @ E @ T) => (wTrt @ P @ H @ E3 @ E @ T))))). % wt_wt'
thf(fact_9_wt_H__iff__wt, axiom,
    ((wTrt = wTrt2))). % wt'_iff_wt
thf(fact_10_reds__preserves__sconf, axiom,
    ((![Es : list_exp_list_char, S : produc515445032on_val, Es2 : list_exp_list_char, S2 : produc515445032on_val, P : list_P1234162913t_char, E3 : list_char > option_ty, Ts : list_ty]: ((member1689761872on_val @ (produc245869591on_val @ (produc1725134254on_val @ Es @ S) @ (produc1725134254on_val @ Es2 @ S2)) @ (reds @ P)) => ((wTrts2 @ P @ (hp @ S) @ E3 @ Es @ Ts) => ((typeSa1777264139_sconf @ P @ E3 @ S) => (typeSa1777264139_sconf @ P @ E3 @ S2))))))). % reds_preserves_sconf
thf(fact_11_WT__implies__WTrt, axiom,
    ((![P : list_P1234162913t_char, E3 : list_char > option_ty, E : exp_list_char, T : ty, H : nat > option2118145160on_val]: ((wt @ P @ E3 @ E @ T) => (wTrt2 @ P @ H @ E3 @ E @ T))))). % WT_implies_WTrt
thf(fact_12_WTrtSeq, axiom,
    ((![P : list_P1234162913t_char, H : nat > option2118145160on_val, E3 : list_char > option_ty, E_1 : exp_list_char, T_1 : ty, E_2 : exp_list_char, T_2 : ty]: ((wTrt2 @ P @ H @ E3 @ E_1 @ T_1) => ((wTrt2 @ P @ H @ E3 @ E_2 @ T_2) => (wTrt2 @ P @ H @ E3 @ (seq_list_char @ E_1 @ E_2) @ T_2)))))). % WTrtSeq
thf(fact_13_WTrt_H__WTrts_H_Ointros_I18_J, axiom,
    ((![P : list_P1234162913t_char, H : nat > option2118145160on_val, E3 : list_char > option_ty, E_1 : exp_list_char, T_1 : ty, E_2 : exp_list_char, T_2 : ty]: ((wTrt @ P @ H @ E3 @ E_1 @ T_1) => ((wTrt @ P @ H @ E3 @ E_2 @ T_2) => (wTrt @ P @ H @ E3 @ (seq_list_char @ E_1 @ E_2) @ T_2)))))). % WTrt'_WTrts'.intros(18)
thf(fact_14_WTrts__hext__mono, axiom,
    ((![P : list_P1234162913t_char, H : nat > option2118145160on_val, E3 : list_char > option_ty, Es : list_exp_list_char, Ts : list_ty, H2 : nat > option2118145160on_val]: ((wTrts2 @ P @ H @ E3 @ Es @ Ts) => ((hext @ H @ H2) => (wTrts2 @ P @ H2 @ E3 @ Es @ Ts)))))). % WTrts_hext_mono
thf(fact_15_SeqReds, axiom,
    ((![E : exp_list_char, S : produc515445032on_val, E2 : exp_list_char, S2 : produc515445032on_val, P : list_P1234162913t_char, E_2 : exp_list_char]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E @ S) @ (produc2023458740on_val @ E2 @ S2)) @ (transi111096263on_val @ (red @ P))) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (seq_list_char @ E @ E_2) @ S) @ (produc2023458740on_val @ (seq_list_char @ E2 @ E_2) @ S2)) @ (transi111096263on_val @ (red @ P))))))). % SeqReds
thf(fact_16_red__reds_OSeqRed, axiom,
    ((![E : exp_list_char, S : produc515445032on_val, E2 : exp_list_char, S2 : produc515445032on_val, P : list_P1234162913t_char, E_2 : exp_list_char]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E @ S) @ (produc2023458740on_val @ E2 @ S2)) @ (red @ P)) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (seq_list_char @ E @ E_2) @ S) @ (produc2023458740on_val @ (seq_list_char @ E2 @ E_2) @ S2)) @ (red @ P)))))). % red_reds.SeqRed
thf(fact_17_wt__env__mono, axiom,
    ((![P : list_P1234162913t_char, E3 : list_char > option_ty, E : exp_list_char, T : ty, E4 : list_char > option_ty]: ((wt @ P @ E3 @ E @ T) => ((map_le_list_char_ty @ E3 @ E4) => (wt @ P @ E4 @ E @ T)))))). % wt_env_mono
thf(fact_18_hext__refl, axiom,
    ((![H : nat > option2118145160on_val]: (hext @ H @ H)))). % hext_refl
thf(fact_19_rtrancl__induct2, axiom,
    ((![Ax : produc1097884484on_val, Ay : produc1097884484on_val, Bx : produc1097884484on_val, By : produc1097884484on_val, R : set_Pr1368603847on_val, P : produc1097884484on_val > produc1097884484on_val > $o]: ((member208988944on_val @ (produc564964183on_val @ (produc1069526295on_val @ Ax @ Ay) @ (produc1069526295on_val @ Bx @ By)) @ (transi100378922on_val @ R)) => ((P @ Ax @ Ay) => ((![A : produc1097884484on_val, B : produc1097884484on_val, Aa : produc1097884484on_val, Ba : produc1097884484on_val]: ((member208988944on_val @ (produc564964183on_val @ (produc1069526295on_val @ Ax @ Ay) @ (produc1069526295on_val @ A @ B)) @ (transi100378922on_val @ R)) => ((member208988944on_val @ (produc564964183on_val @ (produc1069526295on_val @ A @ B) @ (produc1069526295on_val @ Aa @ Ba)) @ R) => ((P @ A @ B) => (P @ Aa @ Ba))))) => (P @ Bx @ By))))))). % rtrancl_induct2
thf(fact_20_rtrancl__induct2, axiom,
    ((![Ax : produc335961278on_val, Ay : produc335961278on_val, Bx : produc335961278on_val, By : produc335961278on_val, R : set_Pr1301890247on_val, P : produc335961278on_val > produc335961278on_val > $o]: ((member1743964944on_val @ (produc1802175319on_val @ (produc245869591on_val @ Ax @ Ay) @ (produc245869591on_val @ Bx @ By)) @ (transi159622442on_val @ R)) => ((P @ Ax @ Ay) => ((![A : produc335961278on_val, B : produc335961278on_val, Aa : produc335961278on_val, Ba : produc335961278on_val]: ((member1743964944on_val @ (produc1802175319on_val @ (produc245869591on_val @ Ax @ Ay) @ (produc245869591on_val @ A @ B)) @ (transi159622442on_val @ R)) => ((member1743964944on_val @ (produc1802175319on_val @ (produc245869591on_val @ A @ B) @ (produc245869591on_val @ Aa @ Ba)) @ R) => ((P @ A @ B) => (P @ Aa @ Ba))))) => (P @ Bx @ By))))))). % rtrancl_induct2
thf(fact_21_rtrancl__induct2, axiom,
    ((![Ax : nat > option2118145160on_val, Ay : list_char > option_val, Bx : nat > option2118145160on_val, By : list_char > option_val, R : 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 @ R)) => ((P @ Ax @ Ay) => ((![A : nat > option2118145160on_val, B : list_char > option_val, Aa : nat > option2118145160on_val, Ba : list_char > option_val]: ((member2027247312on_val @ (produc2106877847on_val @ (produc52622304on_val @ Ax @ Ay) @ (produc52622304on_val @ A @ B)) @ (transi432893227on_val @ R)) => ((member2027247312on_val @ (produc2106877847on_val @ (produc52622304on_val @ A @ B) @ (produc52622304on_val @ Aa @ Ba)) @ R) => ((P @ A @ B) => (P @ Aa @ Ba))))) => (P @ Bx @ By))))))). % rtrancl_induct2
thf(fact_22_rtrancl__induct2, axiom,
    ((![Ax : exp_list_char, Ay : produc515445032on_val, Bx : exp_list_char, By : produc515445032on_val, R : set_Pr1189492743on_val, P : exp_list_char > produc515445032on_val > $o]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ Ax @ Ay) @ (produc2023458740on_val @ Bx @ By)) @ (transi111096263on_val @ R)) => ((P @ Ax @ Ay) => ((![A : exp_list_char, B : produc515445032on_val, Aa : exp_list_char, Ba : produc515445032on_val]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ Ax @ Ay) @ (produc2023458740on_val @ A @ B)) @ (transi111096263on_val @ R)) => ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ A @ B) @ (produc2023458740on_val @ Aa @ Ba)) @ R) => ((P @ A @ B) => (P @ Aa @ Ba))))) => (P @ Bx @ By))))))). % rtrancl_induct2
thf(fact_23_rtrancl__induct2, axiom,
    ((![Ax : list_exp_list_char, Ay : produc515445032on_val, Bx : list_exp_list_char, By : produc515445032on_val, R : set_Pr208351751on_val, P : list_exp_list_char > produc515445032on_val > $o]: ((member1689761872on_val @ (produc245869591on_val @ (produc1725134254on_val @ Ax @ Ay) @ (produc1725134254on_val @ Bx @ By)) @ (transi325225921on_val @ R)) => ((P @ Ax @ Ay) => ((![A : list_exp_list_char, B : produc515445032on_val, Aa : list_exp_list_char, Ba : produc515445032on_val]: ((member1689761872on_val @ (produc245869591on_val @ (produc1725134254on_val @ Ax @ Ay) @ (produc1725134254on_val @ A @ B)) @ (transi325225921on_val @ R)) => ((member1689761872on_val @ (produc245869591on_val @ (produc1725134254on_val @ A @ B) @ (produc1725134254on_val @ Aa @ Ba)) @ R) => ((P @ A @ B) => (P @ Aa @ Ba))))) => (P @ Bx @ By))))))). % rtrancl_induct2
thf(fact_24_converse__rtranclE2, axiom,
    ((![Xa : produc1097884484on_val, Xb : produc1097884484on_val, Za : produc1097884484on_val, Zb : produc1097884484on_val, R : set_Pr1368603847on_val]: ((member208988944on_val @ (produc564964183on_val @ (produc1069526295on_val @ Xa @ Xb) @ (produc1069526295on_val @ Za @ Zb)) @ (transi100378922on_val @ R)) => ((~ (((produc1069526295on_val @ Xa @ Xb) = (produc1069526295on_val @ Za @ Zb)))) => (~ ((![A : produc1097884484on_val, B : produc1097884484on_val]: ((member208988944on_val @ (produc564964183on_val @ (produc1069526295on_val @ Xa @ Xb) @ (produc1069526295on_val @ A @ B)) @ R) => (~ ((member208988944on_val @ (produc564964183on_val @ (produc1069526295on_val @ A @ B) @ (produc1069526295on_val @ Za @ Zb)) @ (transi100378922on_val @ R))))))))))))). % converse_rtranclE2
thf(fact_25_converse__rtranclE2, axiom,
    ((![Xa : produc335961278on_val, Xb : produc335961278on_val, Za : produc335961278on_val, Zb : produc335961278on_val, R : set_Pr1301890247on_val]: ((member1743964944on_val @ (produc1802175319on_val @ (produc245869591on_val @ Xa @ Xb) @ (produc245869591on_val @ Za @ Zb)) @ (transi159622442on_val @ R)) => ((~ (((produc245869591on_val @ Xa @ Xb) = (produc245869591on_val @ Za @ Zb)))) => (~ ((![A : produc335961278on_val, B : produc335961278on_val]: ((member1743964944on_val @ (produc1802175319on_val @ (produc245869591on_val @ Xa @ Xb) @ (produc245869591on_val @ A @ B)) @ R) => (~ ((member1743964944on_val @ (produc1802175319on_val @ (produc245869591on_val @ A @ B) @ (produc245869591on_val @ Za @ Zb)) @ (transi159622442on_val @ R))))))))))))). % converse_rtranclE2
thf(fact_26_converse__rtranclE2, axiom,
    ((![Xa : nat > option2118145160on_val, Xb : list_char > option_val, Za : nat > option2118145160on_val, Zb : list_char > option_val, R : set_Pr148564103on_val]: ((member2027247312on_val @ (produc2106877847on_val @ (produc52622304on_val @ Xa @ Xb) @ (produc52622304on_val @ Za @ Zb)) @ (transi432893227on_val @ R)) => ((~ (((produc52622304on_val @ Xa @ Xb) = (produc52622304on_val @ Za @ Zb)))) => (~ ((![A : nat > option2118145160on_val, B : list_char > option_val]: ((member2027247312on_val @ (produc2106877847on_val @ (produc52622304on_val @ Xa @ Xb) @ (produc52622304on_val @ A @ B)) @ R) => (~ ((member2027247312on_val @ (produc2106877847on_val @ (produc52622304on_val @ A @ B) @ (produc52622304on_val @ Za @ Zb)) @ (transi432893227on_val @ R))))))))))))). % converse_rtranclE2
thf(fact_27_converse__rtranclE2, axiom,
    ((![Xa : exp_list_char, Xb : produc515445032on_val, Za : exp_list_char, Zb : produc515445032on_val, R : set_Pr1189492743on_val]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ Xa @ Xb) @ (produc2023458740on_val @ Za @ Zb)) @ (transi111096263on_val @ R)) => ((~ (((produc2023458740on_val @ Xa @ Xb) = (produc2023458740on_val @ Za @ Zb)))) => (~ ((![A : exp_list_char, B : produc515445032on_val]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ Xa @ Xb) @ (produc2023458740on_val @ A @ B)) @ R) => (~ ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ A @ B) @ (produc2023458740on_val @ Za @ Zb)) @ (transi111096263on_val @ R))))))))))))). % converse_rtranclE2
thf(fact_28_converse__rtranclE2, axiom,
    ((![Xa : list_exp_list_char, Xb : produc515445032on_val, Za : list_exp_list_char, Zb : produc515445032on_val, R : set_Pr208351751on_val]: ((member1689761872on_val @ (produc245869591on_val @ (produc1725134254on_val @ Xa @ Xb) @ (produc1725134254on_val @ Za @ Zb)) @ (transi325225921on_val @ R)) => ((~ (((produc1725134254on_val @ Xa @ Xb) = (produc1725134254on_val @ Za @ Zb)))) => (~ ((![A : list_exp_list_char, B : produc515445032on_val]: ((member1689761872on_val @ (produc245869591on_val @ (produc1725134254on_val @ Xa @ Xb) @ (produc1725134254on_val @ A @ B)) @ R) => (~ ((member1689761872on_val @ (produc245869591on_val @ (produc1725134254on_val @ A @ B) @ (produc1725134254on_val @ Za @ Zb)) @ (transi325225921on_val @ R))))))))))))). % converse_rtranclE2
thf(fact_29_converse__rtrancl__induct2, axiom,
    ((![Ax : produc1097884484on_val, Ay : produc1097884484on_val, Bx : produc1097884484on_val, By : produc1097884484on_val, R : set_Pr1368603847on_val, P : produc1097884484on_val > produc1097884484on_val > $o]: ((member208988944on_val @ (produc564964183on_val @ (produc1069526295on_val @ Ax @ Ay) @ (produc1069526295on_val @ Bx @ By)) @ (transi100378922on_val @ R)) => ((P @ Bx @ By) => ((![A : produc1097884484on_val, B : produc1097884484on_val, Aa : produc1097884484on_val, Ba : produc1097884484on_val]: ((member208988944on_val @ (produc564964183on_val @ (produc1069526295on_val @ A @ B) @ (produc1069526295on_val @ Aa @ Ba)) @ R) => ((member208988944on_val @ (produc564964183on_val @ (produc1069526295on_val @ Aa @ Ba) @ (produc1069526295on_val @ Bx @ By)) @ (transi100378922on_val @ R)) => ((P @ Aa @ Ba) => (P @ A @ B))))) => (P @ Ax @ Ay))))))). % converse_rtrancl_induct2
thf(fact_30_converse__rtrancl__induct2, axiom,
    ((![Ax : produc335961278on_val, Ay : produc335961278on_val, Bx : produc335961278on_val, By : produc335961278on_val, R : set_Pr1301890247on_val, P : produc335961278on_val > produc335961278on_val > $o]: ((member1743964944on_val @ (produc1802175319on_val @ (produc245869591on_val @ Ax @ Ay) @ (produc245869591on_val @ Bx @ By)) @ (transi159622442on_val @ R)) => ((P @ Bx @ By) => ((![A : produc335961278on_val, B : produc335961278on_val, Aa : produc335961278on_val, Ba : produc335961278on_val]: ((member1743964944on_val @ (produc1802175319on_val @ (produc245869591on_val @ A @ B) @ (produc245869591on_val @ Aa @ Ba)) @ R) => ((member1743964944on_val @ (produc1802175319on_val @ (produc245869591on_val @ Aa @ Ba) @ (produc245869591on_val @ Bx @ By)) @ (transi159622442on_val @ R)) => ((P @ Aa @ Ba) => (P @ A @ B))))) => (P @ Ax @ Ay))))))). % converse_rtrancl_induct2
thf(fact_31_converse__rtrancl__induct2, axiom,
    ((![Ax : nat > option2118145160on_val, Ay : list_char > option_val, Bx : nat > option2118145160on_val, By : list_char > option_val, R : 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 @ R)) => ((P @ Bx @ By) => ((![A : nat > option2118145160on_val, B : list_char > option_val, Aa : nat > option2118145160on_val, Ba : list_char > option_val]: ((member2027247312on_val @ (produc2106877847on_val @ (produc52622304on_val @ A @ B) @ (produc52622304on_val @ Aa @ Ba)) @ R) => ((member2027247312on_val @ (produc2106877847on_val @ (produc52622304on_val @ Aa @ Ba) @ (produc52622304on_val @ Bx @ By)) @ (transi432893227on_val @ R)) => ((P @ Aa @ Ba) => (P @ A @ B))))) => (P @ Ax @ Ay))))))). % converse_rtrancl_induct2
thf(fact_32_converse__rtrancl__induct2, axiom,
    ((![Ax : exp_list_char, Ay : produc515445032on_val, Bx : exp_list_char, By : produc515445032on_val, R : set_Pr1189492743on_val, P : exp_list_char > produc515445032on_val > $o]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ Ax @ Ay) @ (produc2023458740on_val @ Bx @ By)) @ (transi111096263on_val @ R)) => ((P @ Bx @ By) => ((![A : exp_list_char, B : produc515445032on_val, Aa : exp_list_char, Ba : produc515445032on_val]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ A @ B) @ (produc2023458740on_val @ Aa @ Ba)) @ R) => ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ Aa @ Ba) @ (produc2023458740on_val @ Bx @ By)) @ (transi111096263on_val @ R)) => ((P @ Aa @ Ba) => (P @ A @ B))))) => (P @ Ax @ Ay))))))). % converse_rtrancl_induct2
thf(fact_33_converse__rtrancl__induct2, axiom,
    ((![Ax : list_exp_list_char, Ay : produc515445032on_val, Bx : list_exp_list_char, By : produc515445032on_val, R : set_Pr208351751on_val, P : list_exp_list_char > produc515445032on_val > $o]: ((member1689761872on_val @ (produc245869591on_val @ (produc1725134254on_val @ Ax @ Ay) @ (produc1725134254on_val @ Bx @ By)) @ (transi325225921on_val @ R)) => ((P @ Bx @ By) => ((![A : list_exp_list_char, B : produc515445032on_val, Aa : list_exp_list_char, Ba : produc515445032on_val]: ((member1689761872on_val @ (produc245869591on_val @ (produc1725134254on_val @ A @ B) @ (produc1725134254on_val @ Aa @ Ba)) @ R) => ((member1689761872on_val @ (produc245869591on_val @ (produc1725134254on_val @ Aa @ Ba) @ (produc1725134254on_val @ Bx @ By)) @ (transi325225921on_val @ R)) => ((P @ Aa @ Ba) => (P @ A @ B))))) => (P @ Ax @ Ay))))))). % converse_rtrancl_induct2
thf(fact_34_prod__cases4, axiom,
    ((![Y : produc1172664615on_val]: (~ ((![A : produc1097884484on_val, B : exp_list_char, C : nat > option2118145160on_val, D : list_char > option_val]: (~ ((Y = (produc1069526295on_val @ A @ (produc2023458740on_val @ B @ (produc52622304on_val @ C @ D)))))))))))). % prod_cases4
thf(fact_35_prod__cases4, axiom,
    ((![Y : produc655058983on_val]: (~ ((![A : produc335961278on_val, B : list_exp_list_char, C : nat > option2118145160on_val, D : list_char > option_val]: (~ ((Y = (produc245869591on_val @ A @ (produc1725134254on_val @ B @ (produc52622304on_val @ C @ D)))))))))))). % prod_cases4
thf(fact_36_old_Oprod_Oinject, axiom,
    ((![A2 : produc1097884484on_val, B2 : produc1097884484on_val, A3 : produc1097884484on_val, B3 : produc1097884484on_val]: (((produc1069526295on_val @ A2 @ B2) = (produc1069526295on_val @ A3 @ B3)) = (((A2 = A3)) & ((B2 = B3))))))). % old.prod.inject
thf(fact_37_old_Oprod_Oinject, axiom,
    ((![A2 : exp_list_char, B2 : produc515445032on_val, A3 : exp_list_char, B3 : produc515445032on_val]: (((produc2023458740on_val @ A2 @ B2) = (produc2023458740on_val @ A3 @ B3)) = (((A2 = A3)) & ((B2 = B3))))))). % old.prod.inject
thf(fact_38_old_Oprod_Oinject, axiom,
    ((![A2 : produc335961278on_val, B2 : produc335961278on_val, A3 : produc335961278on_val, B3 : produc335961278on_val]: (((produc245869591on_val @ A2 @ B2) = (produc245869591on_val @ A3 @ B3)) = (((A2 = A3)) & ((B2 = B3))))))). % old.prod.inject
thf(fact_39_old_Oprod_Oinject, axiom,
    ((![A2 : list_exp_list_char, B2 : produc515445032on_val, A3 : list_exp_list_char, B3 : produc515445032on_val]: (((produc1725134254on_val @ A2 @ B2) = (produc1725134254on_val @ A3 @ B3)) = (((A2 = A3)) & ((B2 = B3))))))). % old.prod.inject
thf(fact_40_old_Oprod_Oinject, axiom,
    ((![A2 : nat > option2118145160on_val, B2 : list_char > option_val, A3 : nat > option2118145160on_val, B3 : list_char > option_val]: (((produc52622304on_val @ A2 @ B2) = (produc52622304on_val @ A3 @ B3)) = (((A2 = A3)) & ((B2 = B3))))))). % old.prod.inject
thf(fact_41_prod_Oinject, axiom,
    ((![X1 : produc1097884484on_val, X2 : produc1097884484on_val, Y1 : produc1097884484on_val, Y2 : produc1097884484on_val]: (((produc1069526295on_val @ X1 @ X2) = (produc1069526295on_val @ Y1 @ Y2)) = (((X1 = Y1)) & ((X2 = Y2))))))). % prod.inject
thf(fact_42_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_43_prod_Oinject, axiom,
    ((![X1 : produc335961278on_val, X2 : produc335961278on_val, Y1 : produc335961278on_val, Y2 : produc335961278on_val]: (((produc245869591on_val @ X1 @ X2) = (produc245869591on_val @ Y1 @ Y2)) = (((X1 = Y1)) & ((X2 = Y2))))))). % prod.inject
thf(fact_44_prod_Oinject, axiom,
    ((![X1 : list_exp_list_char, X2 : produc515445032on_val, Y1 : list_exp_list_char, Y2 : produc515445032on_val]: (((produc1725134254on_val @ X1 @ X2) = (produc1725134254on_val @ Y1 @ Y2)) = (((X1 = Y1)) & ((X2 = Y2))))))). % prod.inject
thf(fact_45_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_46_r__into__rtrancl, axiom,
    ((![P2 : produc1172664615on_val, R : set_Pr1189492743on_val]: ((member354538064on_val @ P2 @ R) => (member354538064on_val @ P2 @ (transi111096263on_val @ R)))))). % r_into_rtrancl
thf(fact_47_r__into__rtrancl, axiom,
    ((![P2 : produc655058983on_val, R : set_Pr208351751on_val]: ((member1689761872on_val @ P2 @ R) => (member1689761872on_val @ P2 @ (transi325225921on_val @ R)))))). % r_into_rtrancl
thf(fact_48_rtrancl__idemp, axiom,
    ((![R : set_Pr1189492743on_val]: ((transi111096263on_val @ (transi111096263on_val @ R)) = (transi111096263on_val @ R))))). % rtrancl_idemp
thf(fact_49_rtrancl__idemp, axiom,
    ((![R : set_Pr208351751on_val]: ((transi325225921on_val @ (transi325225921on_val @ R)) = (transi325225921on_val @ R))))). % rtrancl_idemp
thf(fact_50_converse__rtrancl__induct__red, axiom,
    ((![E : exp_list_char, H : nat > option2118145160on_val, L : list_char > option_val, E2 : exp_list_char, H2 : nat > option2118145160on_val, L2 : list_char > option_val, P : list_P1234162913t_char, R2 : 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 @ E @ (produc52622304on_val @ H @ L)) @ (produc2023458740on_val @ E2 @ (produc52622304on_val @ H2 @ L2))) @ (transi111096263on_val @ (red @ P))) => ((![E5 : exp_list_char, H3 : nat > option2118145160on_val, L3 : list_char > option_val]: (R2 @ E5 @ H3 @ L3 @ E5 @ H3 @ L3)) => ((![E_0 : exp_list_char, H_0 : nat > option2118145160on_val, L_0 : list_char > option_val, E_12 : exp_list_char, H_1 : nat > option2118145160on_val, L_1 : list_char > option_val, E6 : exp_list_char, H4 : nat > option2118145160on_val, L4 : list_char > option_val]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E_0 @ (produc52622304on_val @ H_0 @ L_0)) @ (produc2023458740on_val @ E_12 @ (produc52622304on_val @ H_1 @ L_1))) @ (red @ P)) => ((R2 @ E_12 @ H_1 @ L_1 @ E6 @ H4 @ L4) => (R2 @ E_0 @ H_0 @ L_0 @ E6 @ H4 @ L4)))) => (R2 @ E @ H @ L @ E2 @ H2 @ L2))))))). % converse_rtrancl_induct_red
thf(fact_51_red__hext__incr, axiom,
    ((![E : exp_list_char, H : nat > option2118145160on_val, L : list_char > option_val, E2 : exp_list_char, H2 : nat > option2118145160on_val, L2 : list_char > option_val, P : list_P1234162913t_char]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E @ (produc52622304on_val @ H @ L)) @ (produc2023458740on_val @ E2 @ (produc52622304on_val @ H2 @ L2))) @ (red @ P)) => (hext @ H @ H2))))). % red_hext_incr
thf(fact_52_old_Oprod_Oinducts, axiom,
    ((![P : produc1172664615on_val > $o, Prod : produc1172664615on_val]: ((![A : produc1097884484on_val, B : produc1097884484on_val]: (P @ (produc1069526295on_val @ A @ B))) => (P @ Prod))))). % old.prod.inducts
thf(fact_53_old_Oprod_Oinducts, axiom,
    ((![P : produc1097884484on_val > $o, Prod : produc1097884484on_val]: ((![A : exp_list_char, B : produc515445032on_val]: (P @ (produc2023458740on_val @ A @ B))) => (P @ Prod))))). % old.prod.inducts
thf(fact_54_old_Oprod_Oinducts, axiom,
    ((![P : produc655058983on_val > $o, Prod : produc655058983on_val]: ((![A : produc335961278on_val, B : produc335961278on_val]: (P @ (produc245869591on_val @ A @ B))) => (P @ Prod))))). % old.prod.inducts
thf(fact_55_old_Oprod_Oinducts, axiom,
    ((![P : produc335961278on_val > $o, Prod : produc335961278on_val]: ((![A : list_exp_list_char, B : produc515445032on_val]: (P @ (produc1725134254on_val @ A @ B))) => (P @ Prod))))). % old.prod.inducts
thf(fact_56_old_Oprod_Oinducts, axiom,
    ((![P : produc515445032on_val > $o, Prod : produc515445032on_val]: ((![A : nat > option2118145160on_val, B : list_char > option_val]: (P @ (produc52622304on_val @ A @ B))) => (P @ Prod))))). % old.prod.inducts
thf(fact_57_old_Oprod_Oexhaust, axiom,
    ((![Y : produc1172664615on_val]: (~ ((![A : produc1097884484on_val, B : produc1097884484on_val]: (~ ((Y = (produc1069526295on_val @ A @ B)))))))))). % old.prod.exhaust
thf(fact_58_old_Oprod_Oexhaust, axiom,
    ((![Y : produc1097884484on_val]: (~ ((![A : exp_list_char, B : produc515445032on_val]: (~ ((Y = (produc2023458740on_val @ A @ B)))))))))). % old.prod.exhaust
thf(fact_59_old_Oprod_Oexhaust, axiom,
    ((![Y : produc655058983on_val]: (~ ((![A : produc335961278on_val, B : produc335961278on_val]: (~ ((Y = (produc245869591on_val @ A @ B)))))))))). % old.prod.exhaust
thf(fact_60_old_Oprod_Oexhaust, axiom,
    ((![Y : produc335961278on_val]: (~ ((![A : list_exp_list_char, B : produc515445032on_val]: (~ ((Y = (produc1725134254on_val @ A @ B)))))))))). % old.prod.exhaust
thf(fact_61_old_Oprod_Oexhaust, axiom,
    ((![Y : produc515445032on_val]: (~ ((![A : nat > option2118145160on_val, B : list_char > option_val]: (~ ((Y = (produc52622304on_val @ A @ B)))))))))). % old.prod.exhaust
thf(fact_62_Pair__inject, axiom,
    ((![A2 : produc1097884484on_val, B2 : produc1097884484on_val, A3 : produc1097884484on_val, B3 : produc1097884484on_val]: (((produc1069526295on_val @ A2 @ B2) = (produc1069526295on_val @ A3 @ B3)) => (~ (((A2 = A3) => (~ ((B2 = B3)))))))))). % Pair_inject
thf(fact_63_Pair__inject, axiom,
    ((![A2 : exp_list_char, B2 : produc515445032on_val, A3 : exp_list_char, B3 : produc515445032on_val]: (((produc2023458740on_val @ A2 @ B2) = (produc2023458740on_val @ A3 @ B3)) => (~ (((A2 = A3) => (~ ((B2 = B3)))))))))). % Pair_inject
thf(fact_64_Pair__inject, axiom,
    ((![A2 : produc335961278on_val, B2 : produc335961278on_val, A3 : produc335961278on_val, B3 : produc335961278on_val]: (((produc245869591on_val @ A2 @ B2) = (produc245869591on_val @ A3 @ B3)) => (~ (((A2 = A3) => (~ ((B2 = B3)))))))))). % Pair_inject
thf(fact_65_Pair__inject, axiom,
    ((![A2 : list_exp_list_char, B2 : produc515445032on_val, A3 : list_exp_list_char, B3 : produc515445032on_val]: (((produc1725134254on_val @ A2 @ B2) = (produc1725134254on_val @ A3 @ B3)) => (~ (((A2 = A3) => (~ ((B2 = B3)))))))))). % Pair_inject
thf(fact_66_Pair__inject, axiom,
    ((![A2 : nat > option2118145160on_val, B2 : list_char > option_val, A3 : nat > option2118145160on_val, B3 : list_char > option_val]: (((produc52622304on_val @ A2 @ B2) = (produc52622304on_val @ A3 @ B3)) => (~ (((A2 = A3) => (~ ((B2 = B3)))))))))). % Pair_inject
thf(fact_67_prod__cases, axiom,
    ((![P : produc1172664615on_val > $o, P2 : produc1172664615on_val]: ((![A : produc1097884484on_val, B : produc1097884484on_val]: (P @ (produc1069526295on_val @ A @ B))) => (P @ P2))))). % prod_cases
thf(fact_68_prod__cases, axiom,
    ((![P : produc1097884484on_val > $o, P2 : produc1097884484on_val]: ((![A : exp_list_char, B : produc515445032on_val]: (P @ (produc2023458740on_val @ A @ B))) => (P @ P2))))). % prod_cases
thf(fact_69_prod__cases, axiom,
    ((![P : produc655058983on_val > $o, P2 : produc655058983on_val]: ((![A : produc335961278on_val, B : produc335961278on_val]: (P @ (produc245869591on_val @ A @ B))) => (P @ P2))))). % prod_cases
thf(fact_70_prod__cases, axiom,
    ((![P : produc335961278on_val > $o, P2 : produc335961278on_val]: ((![A : list_exp_list_char, B : produc515445032on_val]: (P @ (produc1725134254on_val @ A @ B))) => (P @ P2))))). % prod_cases
thf(fact_71_prod__cases, axiom,
    ((![P : produc515445032on_val > $o, P2 : produc515445032on_val]: ((![A : nat > option2118145160on_val, B : list_char > option_val]: (P @ (produc52622304on_val @ A @ B))) => (P @ P2))))). % prod_cases
thf(fact_72_surj__pair, axiom,
    ((![P2 : produc1172664615on_val]: (?[X : produc1097884484on_val, Y3 : produc1097884484on_val]: (P2 = (produc1069526295on_val @ X @ Y3)))))). % surj_pair
thf(fact_73_surj__pair, axiom,
    ((![P2 : produc1097884484on_val]: (?[X : exp_list_char, Y3 : produc515445032on_val]: (P2 = (produc2023458740on_val @ X @ Y3)))))). % surj_pair
thf(fact_74_surj__pair, axiom,
    ((![P2 : produc655058983on_val]: (?[X : produc335961278on_val, Y3 : produc335961278on_val]: (P2 = (produc245869591on_val @ X @ Y3)))))). % surj_pair
thf(fact_75_surj__pair, axiom,
    ((![P2 : produc335961278on_val]: (?[X : list_exp_list_char, Y3 : produc515445032on_val]: (P2 = (produc1725134254on_val @ X @ Y3)))))). % surj_pair
thf(fact_76_surj__pair, axiom,
    ((![P2 : produc515445032on_val]: (?[X : nat > option2118145160on_val, Y3 : list_char > option_val]: (P2 = (produc52622304on_val @ X @ Y3)))))). % surj_pair
thf(fact_77_reds__hext__incr, axiom,
    ((![Es : list_exp_list_char, H : nat > option2118145160on_val, L : list_char > option_val, Es2 : list_exp_list_char, H2 : nat > option2118145160on_val, L2 : list_char > option_val, P : list_P1234162913t_char]: ((member1689761872on_val @ (produc245869591on_val @ (produc1725134254on_val @ Es @ (produc52622304on_val @ H @ L)) @ (produc1725134254on_val @ Es2 @ (produc52622304on_val @ H2 @ L2))) @ (reds @ P)) => (hext @ H @ H2))))). % reds_hext_incr
thf(fact_78_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_79_prod__induct3, axiom,
    ((![P : produc1172664615on_val > $o, X3 : produc1172664615on_val]: ((![A : produc1097884484on_val, B : exp_list_char, C : produc515445032on_val]: (P @ (produc1069526295on_val @ A @ (produc2023458740on_val @ B @ C)))) => (P @ X3))))). % prod_induct3
thf(fact_80_prod__induct3, axiom,
    ((![P : produc1097884484on_val > $o, X3 : produc1097884484on_val]: ((![A : exp_list_char, B : nat > option2118145160on_val, C : list_char > option_val]: (P @ (produc2023458740on_val @ A @ (produc52622304on_val @ B @ C)))) => (P @ X3))))). % prod_induct3
thf(fact_81_prod__induct3, axiom,
    ((![P : produc655058983on_val > $o, X3 : produc655058983on_val]: ((![A : produc335961278on_val, B : list_exp_list_char, C : produc515445032on_val]: (P @ (produc245869591on_val @ A @ (produc1725134254on_val @ B @ C)))) => (P @ X3))))). % prod_induct3
thf(fact_82_prod__induct3, axiom,
    ((![P : produc335961278on_val > $o, X3 : produc335961278on_val]: ((![A : list_exp_list_char, B : nat > option2118145160on_val, C : list_char > option_val]: (P @ (produc1725134254on_val @ A @ (produc52622304on_val @ B @ C)))) => (P @ X3))))). % prod_induct3
thf(fact_83_prod__cases3, axiom,
    ((![Y : produc1172664615on_val]: (~ ((![A : produc1097884484on_val, B : exp_list_char, C : produc515445032on_val]: (~ ((Y = (produc1069526295on_val @ A @ (produc2023458740on_val @ B @ C))))))))))). % prod_cases3
thf(fact_84_prod__cases3, axiom,
    ((![Y : produc1097884484on_val]: (~ ((![A : exp_list_char, B : nat > option2118145160on_val, C : list_char > option_val]: (~ ((Y = (produc2023458740on_val @ A @ (produc52622304on_val @ B @ C))))))))))). % prod_cases3
thf(fact_85_prod__cases3, axiom,
    ((![Y : produc655058983on_val]: (~ ((![A : produc335961278on_val, B : list_exp_list_char, C : produc515445032on_val]: (~ ((Y = (produc245869591on_val @ A @ (produc1725134254on_val @ B @ C))))))))))). % prod_cases3
thf(fact_86_prod__cases3, axiom,
    ((![Y : produc335961278on_val]: (~ ((![A : list_exp_list_char, B : nat > option2118145160on_val, C : list_char > option_val]: (~ ((Y = (produc1725134254on_val @ A @ (produc52622304on_val @ B @ C))))))))))). % prod_cases3
thf(fact_87_converse__rtrancl__into__rtrancl, axiom,
    ((![A2 : produc1097884484on_val, B2 : produc1097884484on_val, R : set_Pr1189492743on_val, C2 : produc1097884484on_val]: ((member354538064on_val @ (produc1069526295on_val @ A2 @ B2) @ R) => ((member354538064on_val @ (produc1069526295on_val @ B2 @ C2) @ (transi111096263on_val @ R)) => (member354538064on_val @ (produc1069526295on_val @ A2 @ C2) @ (transi111096263on_val @ R))))))). % converse_rtrancl_into_rtrancl
thf(fact_88_converse__rtrancl__into__rtrancl, axiom,
    ((![A2 : produc335961278on_val, B2 : produc335961278on_val, R : set_Pr208351751on_val, C2 : produc335961278on_val]: ((member1689761872on_val @ (produc245869591on_val @ A2 @ B2) @ R) => ((member1689761872on_val @ (produc245869591on_val @ B2 @ C2) @ (transi325225921on_val @ R)) => (member1689761872on_val @ (produc245869591on_val @ A2 @ C2) @ (transi325225921on_val @ R))))))). % converse_rtrancl_into_rtrancl
thf(fact_89_rtrancl_Ortrancl__into__rtrancl, axiom,
    ((![A2 : produc1097884484on_val, B2 : produc1097884484on_val, R : set_Pr1189492743on_val, C2 : produc1097884484on_val]: ((member354538064on_val @ (produc1069526295on_val @ A2 @ B2) @ (transi111096263on_val @ R)) => ((member354538064on_val @ (produc1069526295on_val @ B2 @ C2) @ R) => (member354538064on_val @ (produc1069526295on_val @ A2 @ C2) @ (transi111096263on_val @ R))))))). % rtrancl.rtrancl_into_rtrancl
thf(fact_90_rtrancl_Ortrancl__into__rtrancl, axiom,
    ((![A2 : produc335961278on_val, B2 : produc335961278on_val, R : set_Pr208351751on_val, C2 : produc335961278on_val]: ((member1689761872on_val @ (produc245869591on_val @ A2 @ B2) @ (transi325225921on_val @ R)) => ((member1689761872on_val @ (produc245869591on_val @ B2 @ C2) @ R) => (member1689761872on_val @ (produc245869591on_val @ A2 @ C2) @ (transi325225921on_val @ R))))))). % rtrancl.rtrancl_into_rtrancl
thf(fact_91_converse__rtrancl__induct, axiom,
    ((![A2 : produc1097884484on_val, B2 : produc1097884484on_val, R : set_Pr1189492743on_val, P : produc1097884484on_val > $o]: ((member354538064on_val @ (produc1069526295on_val @ A2 @ B2) @ (transi111096263on_val @ R)) => ((P @ B2) => ((![Y3 : produc1097884484on_val, Z : produc1097884484on_val]: ((member354538064on_val @ (produc1069526295on_val @ Y3 @ Z) @ R) => ((member354538064on_val @ (produc1069526295on_val @ Z @ B2) @ (transi111096263on_val @ R)) => ((P @ Z) => (P @ Y3))))) => (P @ A2))))))). % converse_rtrancl_induct
thf(fact_92_converse__rtrancl__induct, axiom,
    ((![A2 : produc335961278on_val, B2 : produc335961278on_val, R : set_Pr208351751on_val, P : produc335961278on_val > $o]: ((member1689761872on_val @ (produc245869591on_val @ A2 @ B2) @ (transi325225921on_val @ R)) => ((P @ B2) => ((![Y3 : produc335961278on_val, Z : produc335961278on_val]: ((member1689761872on_val @ (produc245869591on_val @ Y3 @ Z) @ R) => ((member1689761872on_val @ (produc245869591on_val @ Z @ B2) @ (transi325225921on_val @ R)) => ((P @ Z) => (P @ Y3))))) => (P @ A2))))))). % converse_rtrancl_induct
thf(fact_93_rtrancl_Ortrancl__refl, axiom,
    ((![A2 : produc1097884484on_val, R : set_Pr1189492743on_val]: (member354538064on_val @ (produc1069526295on_val @ A2 @ A2) @ (transi111096263on_val @ R))))). % rtrancl.rtrancl_refl
thf(fact_94_rtrancl_Ortrancl__refl, axiom,
    ((![A2 : produc335961278on_val, R : set_Pr208351751on_val]: (member1689761872on_val @ (produc245869591on_val @ A2 @ A2) @ (transi325225921on_val @ R))))). % rtrancl.rtrancl_refl
thf(fact_95_converse__rtranclE, axiom,
    ((![X3 : produc1097884484on_val, Z2 : produc1097884484on_val, R : set_Pr1189492743on_val]: ((member354538064on_val @ (produc1069526295on_val @ X3 @ Z2) @ (transi111096263on_val @ R)) => ((~ ((X3 = Z2))) => (~ ((![Y3 : produc1097884484on_val]: ((member354538064on_val @ (produc1069526295on_val @ X3 @ Y3) @ R) => (~ ((member354538064on_val @ (produc1069526295on_val @ Y3 @ Z2) @ (transi111096263on_val @ R))))))))))))). % converse_rtranclE
thf(fact_96_converse__rtranclE, axiom,
    ((![X3 : produc335961278on_val, Z2 : produc335961278on_val, R : set_Pr208351751on_val]: ((member1689761872on_val @ (produc245869591on_val @ X3 @ Z2) @ (transi325225921on_val @ R)) => ((~ ((X3 = Z2))) => (~ ((![Y3 : produc335961278on_val]: ((member1689761872on_val @ (produc245869591on_val @ X3 @ Y3) @ R) => (~ ((member1689761872on_val @ (produc245869591on_val @ Y3 @ Z2) @ (transi325225921on_val @ R))))))))))))). % converse_rtranclE
thf(fact_97_mem__Collect__eq, axiom,
    ((![A2 : produc1172664615on_val, P : produc1172664615on_val > $o]: ((member354538064on_val @ A2 @ (collec2055896722on_val @ P)) = (P @ A2))))). % mem_Collect_eq
thf(fact_98_mem__Collect__eq, axiom,
    ((![A2 : produc655058983on_val, P : produc655058983on_val > $o]: ((member1689761872on_val @ A2 @ (collec105960082on_val @ P)) = (P @ A2))))). % mem_Collect_eq
thf(fact_99_Collect__mem__eq, axiom,
    ((![A4 : set_Pr1189492743on_val]: ((collec2055896722on_val @ (^[X4 : produc1172664615on_val]: (member354538064on_val @ X4 @ A4))) = A4)))). % Collect_mem_eq
thf(fact_100_Collect__mem__eq, axiom,
    ((![A4 : set_Pr208351751on_val]: ((collec105960082on_val @ (^[X4 : produc655058983on_val]: (member1689761872on_val @ X4 @ A4))) = A4)))). % Collect_mem_eq
thf(fact_101_rtrancl_Oinducts, axiom,
    ((![X1 : produc1097884484on_val, X2 : produc1097884484on_val, R : set_Pr1189492743on_val, P : produc1097884484on_val > produc1097884484on_val > $o]: ((member354538064on_val @ (produc1069526295on_val @ X1 @ X2) @ (transi111096263on_val @ R)) => ((![A : produc1097884484on_val]: (P @ A @ A)) => ((![A : produc1097884484on_val, B : produc1097884484on_val, C : produc1097884484on_val]: ((member354538064on_val @ (produc1069526295on_val @ A @ B) @ (transi111096263on_val @ R)) => ((P @ A @ B) => ((member354538064on_val @ (produc1069526295on_val @ B @ C) @ R) => (P @ A @ C))))) => (P @ X1 @ X2))))))). % rtrancl.inducts
thf(fact_102_rtrancl_Oinducts, axiom,
    ((![X1 : produc335961278on_val, X2 : produc335961278on_val, R : set_Pr208351751on_val, P : produc335961278on_val > produc335961278on_val > $o]: ((member1689761872on_val @ (produc245869591on_val @ X1 @ X2) @ (transi325225921on_val @ R)) => ((![A : produc335961278on_val]: (P @ A @ A)) => ((![A : produc335961278on_val, B : produc335961278on_val, C : produc335961278on_val]: ((member1689761872on_val @ (produc245869591on_val @ A @ B) @ (transi325225921on_val @ R)) => ((P @ A @ B) => ((member1689761872on_val @ (produc245869591on_val @ B @ C) @ R) => (P @ A @ C))))) => (P @ X1 @ X2))))))). % rtrancl.inducts
thf(fact_103_rtrancl__induct, axiom,
    ((![A2 : produc1097884484on_val, B2 : produc1097884484on_val, R : set_Pr1189492743on_val, P : produc1097884484on_val > $o]: ((member354538064on_val @ (produc1069526295on_val @ A2 @ B2) @ (transi111096263on_val @ R)) => ((P @ A2) => ((![Y3 : produc1097884484on_val, Z : produc1097884484on_val]: ((member354538064on_val @ (produc1069526295on_val @ A2 @ Y3) @ (transi111096263on_val @ R)) => ((member354538064on_val @ (produc1069526295on_val @ Y3 @ Z) @ R) => ((P @ Y3) => (P @ Z))))) => (P @ B2))))))). % rtrancl_induct
thf(fact_104_rtrancl__induct, axiom,
    ((![A2 : produc335961278on_val, B2 : produc335961278on_val, R : set_Pr208351751on_val, P : produc335961278on_val > $o]: ((member1689761872on_val @ (produc245869591on_val @ A2 @ B2) @ (transi325225921on_val @ R)) => ((P @ A2) => ((![Y3 : produc335961278on_val, Z : produc335961278on_val]: ((member1689761872on_val @ (produc245869591on_val @ A2 @ Y3) @ (transi325225921on_val @ R)) => ((member1689761872on_val @ (produc245869591on_val @ Y3 @ Z) @ R) => ((P @ Y3) => (P @ Z))))) => (P @ B2))))))). % rtrancl_induct
thf(fact_105_rtrancl__trans, axiom,
    ((![X3 : produc1097884484on_val, Y : produc1097884484on_val, R : set_Pr1189492743on_val, Z2 : produc1097884484on_val]: ((member354538064on_val @ (produc1069526295on_val @ X3 @ Y) @ (transi111096263on_val @ R)) => ((member354538064on_val @ (produc1069526295on_val @ Y @ Z2) @ (transi111096263on_val @ R)) => (member354538064on_val @ (produc1069526295on_val @ X3 @ Z2) @ (transi111096263on_val @ R))))))). % rtrancl_trans
thf(fact_106_rtrancl__trans, axiom,
    ((![X3 : produc335961278on_val, Y : produc335961278on_val, R : set_Pr208351751on_val, Z2 : produc335961278on_val]: ((member1689761872on_val @ (produc245869591on_val @ X3 @ Y) @ (transi325225921on_val @ R)) => ((member1689761872on_val @ (produc245869591on_val @ Y @ Z2) @ (transi325225921on_val @ R)) => (member1689761872on_val @ (produc245869591on_val @ X3 @ Z2) @ (transi325225921on_val @ R))))))). % rtrancl_trans
thf(fact_107_rtrancl_Osimps, axiom,
    ((![A1 : produc1097884484on_val, A22 : produc1097884484on_val, R : set_Pr1189492743on_val]: ((member354538064on_val @ (produc1069526295on_val @ A1 @ A22) @ (transi111096263on_val @ R)) = (((?[A5 : produc1097884484on_val]: (((A1 = A5)) & ((A22 = A5))))) | ((?[A5 : produc1097884484on_val]: (?[B4 : produc1097884484on_val]: (?[C3 : produc1097884484on_val]: (((A1 = A5)) & ((((A22 = C3)) & ((((member354538064on_val @ (produc1069526295on_val @ A5 @ B4) @ (transi111096263on_val @ R))) & ((member354538064on_val @ (produc1069526295on_val @ B4 @ C3) @ R)))))))))))))))). % rtrancl.simps
thf(fact_108_rtrancl_Osimps, axiom,
    ((![A1 : produc335961278on_val, A22 : produc335961278on_val, R : set_Pr208351751on_val]: ((member1689761872on_val @ (produc245869591on_val @ A1 @ A22) @ (transi325225921on_val @ R)) = (((?[A5 : produc335961278on_val]: (((A1 = A5)) & ((A22 = A5))))) | ((?[A5 : produc335961278on_val]: (?[B4 : produc335961278on_val]: (?[C3 : produc335961278on_val]: (((A1 = A5)) & ((((A22 = C3)) & ((((member1689761872on_val @ (produc245869591on_val @ A5 @ B4) @ (transi325225921on_val @ R))) & ((member1689761872on_val @ (produc245869591on_val @ B4 @ C3) @ R)))))))))))))))). % rtrancl.simps
thf(fact_109_rtrancl_Ocases, axiom,
    ((![A1 : produc1097884484on_val, A22 : produc1097884484on_val, R : set_Pr1189492743on_val]: ((member354538064on_val @ (produc1069526295on_val @ A1 @ A22) @ (transi111096263on_val @ R)) => ((~ ((A22 = A1))) => (~ ((![B : produc1097884484on_val]: ((member354538064on_val @ (produc1069526295on_val @ A1 @ B) @ (transi111096263on_val @ R)) => (~ ((member354538064on_val @ (produc1069526295on_val @ B @ A22) @ R)))))))))))). % rtrancl.cases
thf(fact_110_rtrancl_Ocases, axiom,
    ((![A1 : produc335961278on_val, A22 : produc335961278on_val, R : set_Pr208351751on_val]: ((member1689761872on_val @ (produc245869591on_val @ A1 @ A22) @ (transi325225921on_val @ R)) => ((~ ((A22 = A1))) => (~ ((![B : produc335961278on_val]: ((member1689761872on_val @ (produc245869591on_val @ A1 @ B) @ (transi325225921on_val @ R)) => (~ ((member1689761872on_val @ (produc245869591on_val @ B @ A22) @ R)))))))))))). % rtrancl.cases
thf(fact_111_rtranclE, axiom,
    ((![A2 : produc1097884484on_val, B2 : produc1097884484on_val, R : set_Pr1189492743on_val]: ((member354538064on_val @ (produc1069526295on_val @ A2 @ B2) @ (transi111096263on_val @ R)) => ((~ ((A2 = B2))) => (~ ((![Y3 : produc1097884484on_val]: ((member354538064on_val @ (produc1069526295on_val @ A2 @ Y3) @ (transi111096263on_val @ R)) => (~ ((member354538064on_val @ (produc1069526295on_val @ Y3 @ B2) @ R)))))))))))). % rtranclE
thf(fact_112_rtranclE, axiom,
    ((![A2 : produc335961278on_val, B2 : produc335961278on_val, R : set_Pr208351751on_val]: ((member1689761872on_val @ (produc245869591on_val @ A2 @ B2) @ (transi325225921on_val @ R)) => ((~ ((A2 = B2))) => (~ ((![Y3 : produc335961278on_val]: ((member1689761872on_val @ (produc245869591on_val @ A2 @ Y3) @ (transi325225921on_val @ R)) => (~ ((member1689761872on_val @ (produc245869591on_val @ Y3 @ B2) @ R)))))))))))). % rtranclE
thf(fact_113_fst__conv, axiom,
    ((![X1 : produc1097884484on_val, X2 : produc1097884484on_val]: ((produc708556547on_val @ (produc1069526295on_val @ X1 @ X2)) = X1)))). % fst_conv
thf(fact_114_fst__conv, axiom,
    ((![X1 : exp_list_char, X2 : produc515445032on_val]: ((produc1141111712on_val @ (produc2023458740on_val @ X1 @ X2)) = X1)))). % fst_conv
thf(fact_115_fst__conv, axiom,
    ((![X1 : produc335961278on_val, X2 : produc335961278on_val]: ((produc1166469635on_val @ (produc245869591on_val @ X1 @ X2)) = X1)))). % fst_conv
thf(fact_116_fst__conv, axiom,
    ((![X1 : list_exp_list_char, X2 : produc515445032on_val]: ((produc2132476826on_val @ (produc1725134254on_val @ X1 @ X2)) = X1)))). % fst_conv
thf(fact_117_fst__conv, axiom,
    ((![X1 : nat > option2118145160on_val, X2 : list_char > option_val]: ((produc1246629324on_val @ (produc52622304on_val @ X1 @ X2)) = X1)))). % fst_conv
thf(fact_118_fst__eqD, axiom,
    ((![X3 : produc1097884484on_val, Y : produc1097884484on_val, A2 : produc1097884484on_val]: (((produc708556547on_val @ (produc1069526295on_val @ X3 @ Y)) = A2) => (X3 = A2))))). % fst_eqD
thf(fact_119_fst__eqD, axiom,
    ((![X3 : exp_list_char, Y : produc515445032on_val, A2 : exp_list_char]: (((produc1141111712on_val @ (produc2023458740on_val @ X3 @ Y)) = A2) => (X3 = A2))))). % fst_eqD
thf(fact_120_fst__eqD, axiom,
    ((![X3 : produc335961278on_val, Y : produc335961278on_val, A2 : produc335961278on_val]: (((produc1166469635on_val @ (produc245869591on_val @ X3 @ Y)) = A2) => (X3 = A2))))). % fst_eqD
thf(fact_121_fst__eqD, axiom,
    ((![X3 : list_exp_list_char, Y : produc515445032on_val, A2 : list_exp_list_char]: (((produc2132476826on_val @ (produc1725134254on_val @ X3 @ Y)) = A2) => (X3 = A2))))). % fst_eqD
thf(fact_122_fst__eqD, axiom,
    ((![X3 : nat > option2118145160on_val, Y : list_char > option_val, A2 : nat > option2118145160on_val]: (((produc1246629324on_val @ (produc52622304on_val @ X3 @ Y)) = A2) => (X3 = A2))))). % fst_eqD
thf(fact_123_WTSeq, axiom,
    ((![P : list_P1234162913t_char, E3 : list_char > option_ty, E_1 : exp_list_char, T_1 : ty, E_2 : exp_list_char, T_2 : ty]: ((wt @ P @ E3 @ E_1 @ T_1) => ((wt @ P @ E3 @ E_2 @ T_2) => (wt @ P @ E3 @ (seq_list_char @ E_1 @ E_2) @ T_2)))))). % WTSeq
thf(fact_124_subject__reduction2, axiom,
    ((![P : list_P1234162913t_char, E : exp_list_char, H : nat > option2118145160on_val, L : list_char > option_val, E2 : exp_list_char, H2 : nat > option2118145160on_val, L2 : list_char > option_val, E3 : list_char > option_ty, T : ty]: ((wf_pro1229751607t_char @ wf_J_mdecl @ P) => ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E @ (produc52622304on_val @ H @ L)) @ (produc2023458740on_val @ E2 @ (produc52622304on_val @ H2 @ L2))) @ (red @ P)) => ((typeSa1777264139_sconf @ P @ E3 @ (produc52622304on_val @ H @ L)) => ((wTrt2 @ P @ H @ E3 @ E @ T) => (?[T2 : ty]: ((wTrt2 @ P @ H2 @ E3 @ E2 @ T2) & (widen_917054840t_char @ P @ T2 @ T)))))))))). % subject_reduction2
thf(fact_125_prod__induct4, axiom,
    ((![P : produc1172664615on_val > $o, X3 : produc1172664615on_val]: ((![A : produc1097884484on_val, B : exp_list_char, C : nat > option2118145160on_val, D : list_char > option_val]: (P @ (produc1069526295on_val @ A @ (produc2023458740on_val @ B @ (produc52622304on_val @ C @ D))))) => (P @ X3))))). % prod_induct4
thf(fact_126_prod__induct4, axiom,
    ((![P : produc655058983on_val > $o, X3 : produc655058983on_val]: ((![A : produc335961278on_val, B : list_exp_list_char, C : nat > option2118145160on_val, D : list_char > option_val]: (P @ (produc245869591on_val @ A @ (produc1725134254on_val @ B @ (produc52622304on_val @ C @ D))))) => (P @ X3))))). % prod_induct4
thf(fact_127_subjects__reduction, axiom,
    ((![P : list_P1234162913t_char, Es : list_exp_list_char, S : produc515445032on_val, Es2 : list_exp_list_char, S2 : produc515445032on_val, E3 : list_char > option_ty, Ts : list_ty]: ((wf_pro1229751607t_char @ wf_J_mdecl @ P) => ((member1689761872on_val @ (produc245869591on_val @ (produc1725134254on_val @ Es @ S) @ (produc1725134254on_val @ Es2 @ S2)) @ (reds @ P)) => ((typeSa1777264139_sconf @ P @ E3 @ S) => ((wTrts2 @ P @ (hp @ S) @ E3 @ Es @ Ts) => (?[Ts2 : list_ty]: ((wTrts2 @ P @ (hp @ S2) @ E3 @ Es2 @ Ts2) & (list_all2_ty_ty @ (widen_917054840t_char @ P) @ Ts2 @ Ts)))))))))). % subjects_reduction
thf(fact_128_exp_Oinject_I11_J, axiom,
    ((![X111 : exp_list_char, X112 : exp_list_char, Y111 : exp_list_char, Y112 : exp_list_char]: (((seq_list_char @ X111 @ X112) = (seq_list_char @ Y111 @ Y112)) = (((X111 = Y111)) & ((X112 = Y112))))))). % exp.inject(11)
thf(fact_129_subjects__reduction2, axiom,
    ((![P : list_P1234162913t_char, Es : list_exp_list_char, H : nat > option2118145160on_val, L : list_char > option_val, Es2 : list_exp_list_char, H2 : nat > option2118145160on_val, L2 : list_char > option_val, E3 : list_char > option_ty, Ts : list_ty]: ((wf_pro1229751607t_char @ wf_J_mdecl @ P) => ((member1689761872on_val @ (produc245869591on_val @ (produc1725134254on_val @ Es @ (produc52622304on_val @ H @ L)) @ (produc1725134254on_val @ Es2 @ (produc52622304on_val @ H2 @ L2))) @ (reds @ P)) => ((typeSa1777264139_sconf @ P @ E3 @ (produc52622304on_val @ H @ L)) => ((wTrts2 @ P @ H @ E3 @ Es @ Ts) => (?[Ts2 : list_ty]: ((wTrts2 @ P @ H2 @ E3 @ Es2 @ Ts2) & (list_all2_ty_ty @ (widen_917054840t_char @ P) @ Ts2 @ Ts)))))))))). % subjects_reduction2
thf(fact_130_ListReds1, axiom,
    ((![E : exp_list_char, S : produc515445032on_val, E2 : exp_list_char, S2 : produc515445032on_val, P : list_P1234162913t_char, Es : list_exp_list_char]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E @ S) @ (produc2023458740on_val @ E2 @ S2)) @ (transi111096263on_val @ (red @ P))) => (member1689761872on_val @ (produc245869591on_val @ (produc1725134254on_val @ (cons_exp_list_char @ E @ Es) @ S) @ (produc1725134254on_val @ (cons_exp_list_char @ E2 @ Es) @ S2)) @ (transi325225921on_val @ (reds @ P))))))). % ListReds1
thf(fact_131_reds__preserves__hconf, axiom,
    ((![Es : list_exp_list_char, H : nat > option2118145160on_val, L : list_char > option_val, Es2 : list_exp_list_char, H2 : nat > option2118145160on_val, L2 : list_char > option_val, P : list_P1234162913t_char, E3 : list_char > option_ty, Ts : list_ty]: ((member1689761872on_val @ (produc245869591on_val @ (produc1725134254on_val @ Es @ (produc52622304on_val @ H @ L)) @ (produc1725134254on_val @ Es2 @ (produc52622304on_val @ H2 @ L2))) @ (reds @ P)) => ((wTrts2 @ P @ H @ E3 @ Es @ Ts) => ((hconf_1244167010t_char @ P @ H) => (hconf_1244167010t_char @ P @ H2))))))). % reds_preserves_hconf
thf(fact_132_reds__preserves__lconf, axiom,
    ((![Es : list_exp_list_char, H : nat > option2118145160on_val, L : list_char > option_val, Es2 : list_exp_list_char, H2 : nat > option2118145160on_val, L2 : list_char > option_val, P : list_P1234162913t_char, E3 : list_char > option_ty, Ts : list_ty]: ((member1689761872on_val @ (produc245869591on_val @ (produc1725134254on_val @ Es @ (produc52622304on_val @ H @ L)) @ (produc1725134254on_val @ Es2 @ (produc52622304on_val @ H2 @ L2))) @ (reds @ P)) => ((wTrts2 @ P @ H @ E3 @ Es @ Ts) => ((lconf_485928294t_char @ P @ H @ L @ E3) => (lconf_485928294t_char @ P @ H2 @ L2 @ E3))))))). % reds_preserves_lconf
thf(fact_133_eq__fst__iff, axiom,
    ((![A2 : produc1097884484on_val, P2 : produc1172664615on_val]: ((A2 = (produc708556547on_val @ P2)) = (?[B4 : produc1097884484on_val]: (P2 = (produc1069526295on_val @ A2 @ B4))))))). % eq_fst_iff
thf(fact_134_eq__fst__iff, axiom,
    ((![A2 : exp_list_char, P2 : produc1097884484on_val]: ((A2 = (produc1141111712on_val @ P2)) = (?[B4 : produc515445032on_val]: (P2 = (produc2023458740on_val @ A2 @ B4))))))). % eq_fst_iff
thf(fact_135_eq__fst__iff, axiom,
    ((![A2 : produc335961278on_val, P2 : produc655058983on_val]: ((A2 = (produc1166469635on_val @ P2)) = (?[B4 : produc335961278on_val]: (P2 = (produc245869591on_val @ A2 @ B4))))))). % eq_fst_iff
thf(fact_136_eq__fst__iff, axiom,
    ((![A2 : list_exp_list_char, P2 : produc335961278on_val]: ((A2 = (produc2132476826on_val @ P2)) = (?[B4 : produc515445032on_val]: (P2 = (produc1725134254on_val @ A2 @ B4))))))). % eq_fst_iff
thf(fact_137_eq__fst__iff, axiom,
    ((![A2 : nat > option2118145160on_val, P2 : produc515445032on_val]: ((A2 = (produc1246629324on_val @ P2)) = (?[B4 : list_char > option_val]: (P2 = (produc52622304on_val @ A2 @ B4))))))). % eq_fst_iff
thf(fact_138_red__preserves__lconf, axiom,
    ((![E : exp_list_char, H : nat > option2118145160on_val, L : list_char > option_val, E2 : exp_list_char, H2 : nat > option2118145160on_val, L2 : list_char > option_val, P : list_P1234162913t_char, E3 : list_char > option_ty, T : ty]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E @ (produc52622304on_val @ H @ L)) @ (produc2023458740on_val @ E2 @ (produc52622304on_val @ H2 @ L2))) @ (red @ P)) => ((wTrt2 @ P @ H @ E3 @ E @ T) => ((lconf_485928294t_char @ P @ H @ L @ E3) => (lconf_485928294t_char @ P @ H2 @ L2 @ E3))))))). % red_preserves_lconf
thf(fact_139_red__reds_OListRed1, axiom,
    ((![E : exp_list_char, S : produc515445032on_val, E2 : exp_list_char, S2 : produc515445032on_val, P : list_P1234162913t_char, Es : list_exp_list_char]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E @ S) @ (produc2023458740on_val @ E2 @ S2)) @ (red @ P)) => (member1689761872on_val @ (produc245869591on_val @ (produc1725134254on_val @ (cons_exp_list_char @ E @ Es) @ S) @ (produc1725134254on_val @ (cons_exp_list_char @ E2 @ Es) @ S2)) @ (reds @ P)))))). % red_reds.ListRed1
thf(fact_140_red__preserves__hconf, axiom,
    ((![E : exp_list_char, H : nat > option2118145160on_val, L : list_char > option_val, E2 : exp_list_char, H2 : nat > option2118145160on_val, L2 : list_char > option_val, P : list_P1234162913t_char, E3 : list_char > option_ty, T : ty]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E @ (produc52622304on_val @ H @ L)) @ (produc2023458740on_val @ E2 @ (produc52622304on_val @ H2 @ L2))) @ (red @ P)) => ((wTrt2 @ P @ H @ E3 @ E @ T) => ((hconf_1244167010t_char @ P @ H) => (hconf_1244167010t_char @ P @ H2))))))). % red_preserves_hconf
thf(fact_141_widens__refl, axiom,
    ((![P : list_P1234162913t_char, Xs : list_ty]: (list_all2_ty_ty @ (widen_917054840t_char @ P) @ Xs @ Xs)))). % widens_refl
thf(fact_142_ListRedsVal, axiom,
    ((![E : exp_list_char, S_0 : produc515445032on_val, V : val, S_1 : produc515445032on_val, P : list_P1234162913t_char, Es : list_exp_list_char, Es2 : list_exp_list_char, S_2 : produc515445032on_val]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E @ S_0) @ (produc2023458740on_val @ (val_list_char @ V) @ S_1)) @ (transi111096263on_val @ (red @ P))) => ((member1689761872on_val @ (produc245869591on_val @ (produc1725134254on_val @ Es @ S_1) @ (produc1725134254on_val @ Es2 @ S_2)) @ (transi325225921on_val @ (reds @ P))) => (member1689761872on_val @ (produc245869591on_val @ (produc1725134254on_val @ (cons_exp_list_char @ E @ Es) @ S_0) @ (produc1725134254on_val @ (cons_exp_list_char @ (val_list_char @ V) @ Es2) @ S_2)) @ (transi325225921on_val @ (reds @ P)))))))). % ListRedsVal
thf(fact_143_lconf__hext, axiom,
    ((![P : list_P1234162913t_char, H : nat > option2118145160on_val, L : list_char > option_val, E3 : list_char > option_ty, H2 : nat > option2118145160on_val]: ((lconf_485928294t_char @ P @ H @ L @ E3) => ((hext @ H @ H2) => (lconf_485928294t_char @ P @ H2 @ L @ E3)))))). % lconf_hext
thf(fact_144_list_Oinject, axiom,
    ((![X21 : exp_list_char, X22 : list_exp_list_char, Y21 : exp_list_char, Y22 : list_exp_list_char]: (((cons_exp_list_char @ X21 @ X22) = (cons_exp_list_char @ Y21 @ Y22)) = (((X21 = Y21)) & ((X22 = Y22))))))). % list.inject
thf(fact_145_list_Oinject, axiom,
    ((![X21 : ty, X22 : list_ty, Y21 : ty, Y22 : list_ty]: (((cons_ty @ X21 @ X22) = (cons_ty @ Y21 @ Y22)) = (((X21 = Y21)) & ((X22 = Y22))))))). % list.inject
thf(fact_146_exp_Oinject_I3_J, axiom,
    ((![X32 : val, Y32 : val]: (((val_list_char @ X32) = (val_list_char @ Y32)) = (X32 = Y32))))). % exp.inject(3)
thf(fact_147_widens__Cons, axiom,
    ((![P : list_P1234162913t_char, X3 : ty, Xs : list_ty, Ys : list_ty]: ((list_all2_ty_ty @ (widen_917054840t_char @ P) @ (cons_ty @ X3 @ Xs) @ Ys) = (?[Z3 : ty]: (?[Zs : list_ty]: (((Ys = (cons_ty @ Z3 @ Zs))) & ((((widen_917054840t_char @ P @ X3 @ Z3)) & ((list_all2_ty_ty @ (widen_917054840t_char @ P) @ Xs @ Zs))))))))))). % widens_Cons
thf(fact_148_exp_Odistinct_I69_J, axiom,
    ((![X32 : val, X111 : exp_list_char, X112 : exp_list_char]: (~ (((val_list_char @ X32) = (seq_list_char @ X111 @ X112))))))). % exp.distinct(69)
thf(fact_149_not__Cons__self2, axiom,
    ((![X3 : exp_list_char, Xs : list_exp_list_char]: (~ (((cons_exp_list_char @ X3 @ Xs) = Xs)))))). % not_Cons_self2
thf(fact_150_not__Cons__self2, axiom,
    ((![X3 : ty, Xs : list_ty]: (~ (((cons_ty @ X3 @ Xs) = Xs)))))). % not_Cons_self2
thf(fact_151_list_Orel__refl, axiom,
    ((![Ra : ty > ty > $o, X3 : list_ty]: ((![X : ty]: (Ra @ X @ X)) => (list_all2_ty_ty @ Ra @ X3 @ X3))))). % list.rel_refl
thf(fact_152_list__all2__antisym, axiom,
    ((![P : ty > ty > $o, Q : ty > ty > $o, Xs : list_ty, Ys : list_ty]: ((![X : ty, Y3 : ty]: ((P @ X @ Y3) => ((Q @ Y3 @ X) => (X = Y3)))) => ((list_all2_ty_ty @ P @ Xs @ Ys) => ((list_all2_ty_ty @ Q @ Ys @ Xs) => (Xs = Ys))))))). % list_all2_antisym
thf(fact_153_list_Orel__eq, axiom,
    (((list_all2_ty_ty @ (^[Y4 : ty]: (^[Z4 : ty]: (Y4 = Z4)))) = (^[Y4 : list_ty]: (^[Z4 : list_ty]: (Y4 = Z4)))))). % list.rel_eq
thf(fact_154_list__all2__trans, axiom,
    ((![P1 : ty > ty > $o, P22 : ty > ty > $o, P3 : ty > ty > $o, As : list_ty, Bs : list_ty, Cs : list_ty]: ((![A : ty, B : ty, C : ty]: ((P1 @ A @ B) => ((P22 @ B @ C) => (P3 @ A @ C)))) => ((list_all2_ty_ty @ P1 @ As @ Bs) => ((list_all2_ty_ty @ P22 @ Bs @ Cs) => (list_all2_ty_ty @ P3 @ As @ Cs))))))). % list_all2_trans
thf(fact_155_list__all2__refl, axiom,
    ((![P : ty > ty > $o, Xs : list_ty]: ((![X : ty]: (P @ X @ X)) => (list_all2_ty_ty @ P @ Xs @ Xs))))). % list_all2_refl
thf(fact_156_list__all2__mono, axiom,
    ((![P : ty > ty > $o, Xs : list_ty, Ys : list_ty, Q : ty > ty > $o]: ((list_all2_ty_ty @ P @ Xs @ Ys) => ((![Xs2 : ty, Ys2 : ty]: ((P @ Xs2 @ Ys2) => (Q @ Xs2 @ Ys2))) => (list_all2_ty_ty @ Q @ Xs @ Ys)))))). % list_all2_mono
thf(fact_157_list__all2__eq, axiom,
    (((^[Y4 : list_ty]: (^[Z4 : list_ty]: (Y4 = Z4))) = (list_all2_ty_ty @ (^[Y4 : ty]: (^[Z4 : ty]: (Y4 = Z4))))))). % list_all2_eq
thf(fact_158_WTrtCons, axiom,
    ((![P : list_P1234162913t_char, H : nat > option2118145160on_val, E3 : list_char > option_ty, E : exp_list_char, T : ty, Es : list_exp_list_char, Ts : list_ty]: ((wTrt2 @ P @ H @ E3 @ E @ T) => ((wTrts2 @ P @ H @ E3 @ Es @ Ts) => (wTrts2 @ P @ H @ E3 @ (cons_exp_list_char @ E @ Es) @ (cons_ty @ T @ Ts))))))). % WTrtCons
thf(fact_159_widen__refl, axiom,
    ((![P : list_P1234162913t_char, T : ty]: (widen_917054840t_char @ P @ T @ T)))). % widen_refl
thf(fact_160_widen__trans, axiom,
    ((![P : list_P1234162913t_char, S3 : ty, U : ty, T : ty]: ((widen_917054840t_char @ P @ S3 @ U) => ((widen_917054840t_char @ P @ U @ T) => (widen_917054840t_char @ P @ S3 @ T)))))). % widen_trans
thf(fact_161_red__reds_ORedSeq, axiom,
    ((![V : val, E_2 : exp_list_char, S : produc515445032on_val, P : list_P1234162913t_char]: (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (seq_list_char @ (val_list_char @ V) @ E_2) @ S) @ (produc2023458740on_val @ E_2 @ S)) @ (red @ P))))). % red_reds.RedSeq
thf(fact_162_red__reds_OListRed2, axiom,
    ((![Es : list_exp_list_char, S : produc515445032on_val, Es2 : list_exp_list_char, S2 : produc515445032on_val, P : list_P1234162913t_char, V : val]: ((member1689761872on_val @ (produc245869591on_val @ (produc1725134254on_val @ Es @ S) @ (produc1725134254on_val @ Es2 @ S2)) @ (reds @ P)) => (member1689761872on_val @ (produc245869591on_val @ (produc1725134254on_val @ (cons_exp_list_char @ (val_list_char @ V) @ Es) @ S) @ (produc1725134254on_val @ (cons_exp_list_char @ (val_list_char @ V) @ Es2) @ S2)) @ (reds @ P)))))). % red_reds.ListRed2
thf(fact_163_SeqReds2, axiom,
    ((![E_1 : exp_list_char, S_0 : produc515445032on_val, V_1 : val, S_1 : produc515445032on_val, P : list_P1234162913t_char, E_2 : exp_list_char, E_22 : exp_list_char, S_2 : produc515445032on_val]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E_1 @ S_0) @ (produc2023458740on_val @ (val_list_char @ V_1) @ S_1)) @ (transi111096263on_val @ (red @ P))) => ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E_2 @ S_1) @ (produc2023458740on_val @ E_22 @ S_2)) @ (transi111096263on_val @ (red @ P))) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (seq_list_char @ E_1 @ E_2) @ S_0) @ (produc2023458740on_val @ E_22 @ S_2)) @ (transi111096263on_val @ (red @ P)))))))). % SeqReds2
thf(fact_164_ListReds2, axiom,
    ((![Es : list_exp_list_char, S : produc515445032on_val, Es2 : list_exp_list_char, S2 : produc515445032on_val, P : list_P1234162913t_char, V : val]: ((member1689761872on_val @ (produc245869591on_val @ (produc1725134254on_val @ Es @ S) @ (produc1725134254on_val @ Es2 @ S2)) @ (transi325225921on_val @ (reds @ P))) => (member1689761872on_val @ (produc245869591on_val @ (produc1725134254on_val @ (cons_exp_list_char @ (val_list_char @ V) @ Es) @ S) @ (produc1725134254on_val @ (cons_exp_list_char @ (val_list_char @ V) @ Es2) @ S2)) @ (transi325225921on_val @ (reds @ P))))))). % ListReds2
thf(fact_165_list__all2__Cons2, axiom,
    ((![P : exp_list_char > exp_list_char > $o, Xs : list_exp_list_char, Y : exp_list_char, Ys : list_exp_list_char]: ((list_a1702871623t_char @ P @ Xs @ (cons_exp_list_char @ Y @ Ys)) = (?[Z3 : exp_list_char]: (?[Zs : list_exp_list_char]: (((Xs = (cons_exp_list_char @ Z3 @ Zs))) & ((((P @ Z3 @ Y)) & ((list_a1702871623t_char @ P @ Zs @ Ys))))))))))). % list_all2_Cons2
thf(fact_166_list__all2__Cons2, axiom,
    ((![P : ty > exp_list_char > $o, Xs : list_ty, Y : exp_list_char, Ys : list_exp_list_char]: ((list_a212154379t_char @ P @ Xs @ (cons_exp_list_char @ Y @ Ys)) = (?[Z3 : ty]: (?[Zs : list_ty]: (((Xs = (cons_ty @ Z3 @ Zs))) & ((((P @ Z3 @ Y)) & ((list_a212154379t_char @ P @ Zs @ Ys))))))))))). % list_all2_Cons2
thf(fact_167_list__all2__Cons2, axiom,
    ((![P : exp_list_char > ty > $o, Xs : list_exp_list_char, Y : ty, Ys : list_ty]: ((list_a295513531har_ty @ P @ Xs @ (cons_ty @ Y @ Ys)) = (?[Z3 : exp_list_char]: (?[Zs : list_exp_list_char]: (((Xs = (cons_exp_list_char @ Z3 @ Zs))) & ((((P @ Z3 @ Y)) & ((list_a295513531har_ty @ P @ Zs @ Ys))))))))))). % list_all2_Cons2
thf(fact_168_list__all2__Cons2, axiom,
    ((![P : ty > ty > $o, Xs : list_ty, Y : ty, Ys : list_ty]: ((list_all2_ty_ty @ P @ Xs @ (cons_ty @ Y @ Ys)) = (?[Z3 : ty]: (?[Zs : list_ty]: (((Xs = (cons_ty @ Z3 @ Zs))) & ((((P @ Z3 @ Y)) & ((list_all2_ty_ty @ P @ Zs @ Ys))))))))))). % list_all2_Cons2
thf(fact_169_list__all2__Cons1, axiom,
    ((![P : exp_list_char > exp_list_char > $o, X3 : exp_list_char, Xs : list_exp_list_char, Ys : list_exp_list_char]: ((list_a1702871623t_char @ P @ (cons_exp_list_char @ X3 @ Xs) @ Ys) = (?[Z3 : exp_list_char]: (?[Zs : list_exp_list_char]: (((Ys = (cons_exp_list_char @ Z3 @ Zs))) & ((((P @ X3 @ Z3)) & ((list_a1702871623t_char @ P @ Xs @ Zs))))))))))). % list_all2_Cons1
thf(fact_170_list__all2__Cons1, axiom,
    ((![P : exp_list_char > ty > $o, X3 : exp_list_char, Xs : list_exp_list_char, Ys : list_ty]: ((list_a295513531har_ty @ P @ (cons_exp_list_char @ X3 @ Xs) @ Ys) = (?[Z3 : ty]: (?[Zs : list_ty]: (((Ys = (cons_ty @ Z3 @ Zs))) & ((((P @ X3 @ Z3)) & ((list_a295513531har_ty @ P @ Xs @ Zs))))))))))). % list_all2_Cons1
thf(fact_171_list__all2__Cons1, axiom,
    ((![P : ty > exp_list_char > $o, X3 : ty, Xs : list_ty, Ys : list_exp_list_char]: ((list_a212154379t_char @ P @ (cons_ty @ X3 @ Xs) @ Ys) = (?[Z3 : exp_list_char]: (?[Zs : list_exp_list_char]: (((Ys = (cons_exp_list_char @ Z3 @ Zs))) & ((((P @ X3 @ Z3)) & ((list_a212154379t_char @ P @ Xs @ Zs))))))))))). % list_all2_Cons1
thf(fact_172_list__all2__Cons1, axiom,
    ((![P : ty > ty > $o, X3 : ty, Xs : list_ty, Ys : list_ty]: ((list_all2_ty_ty @ P @ (cons_ty @ X3 @ Xs) @ Ys) = (?[Z3 : ty]: (?[Zs : list_ty]: (((Ys = (cons_ty @ Z3 @ Zs))) & ((((P @ X3 @ Z3)) & ((list_all2_ty_ty @ P @ Xs @ Zs))))))))))). % list_all2_Cons1
thf(fact_173_list__all2__Cons, axiom,
    ((![P : exp_list_char > exp_list_char > $o, X3 : exp_list_char, Xs : list_exp_list_char, Y : exp_list_char, Ys : list_exp_list_char]: ((list_a1702871623t_char @ P @ (cons_exp_list_char @ X3 @ Xs) @ (cons_exp_list_char @ Y @ Ys)) = (((P @ X3 @ Y)) & ((list_a1702871623t_char @ P @ Xs @ Ys))))))). % list_all2_Cons
thf(fact_174_list__all2__Cons, axiom,
    ((![P : exp_list_char > ty > $o, X3 : exp_list_char, Xs : list_exp_list_char, Y : ty, Ys : list_ty]: ((list_a295513531har_ty @ P @ (cons_exp_list_char @ X3 @ Xs) @ (cons_ty @ Y @ Ys)) = (((P @ X3 @ Y)) & ((list_a295513531har_ty @ P @ Xs @ Ys))))))). % list_all2_Cons
thf(fact_175_list__all2__Cons, axiom,
    ((![P : ty > exp_list_char > $o, X3 : ty, Xs : list_ty, Y : exp_list_char, Ys : list_exp_list_char]: ((list_a212154379t_char @ P @ (cons_ty @ X3 @ Xs) @ (cons_exp_list_char @ Y @ Ys)) = (((P @ X3 @ Y)) & ((list_a212154379t_char @ P @ Xs @ Ys))))))). % list_all2_Cons
thf(fact_176_list__all2__Cons, axiom,
    ((![P : ty > ty > $o, X3 : ty, Xs : list_ty, Y : ty, Ys : list_ty]: ((list_all2_ty_ty @ P @ (cons_ty @ X3 @ Xs) @ (cons_ty @ Y @ Ys)) = (((P @ X3 @ Y)) & ((list_all2_ty_ty @ P @ Xs @ Ys))))))). % list_all2_Cons
thf(fact_177_list_Orel__intros_I2_J, axiom,
    ((![R2 : exp_list_char > exp_list_char > $o, X21 : exp_list_char, Y21 : exp_list_char, X22 : list_exp_list_char, Y22 : list_exp_list_char]: ((R2 @ X21 @ Y21) => ((list_a1702871623t_char @ R2 @ X22 @ Y22) => (list_a1702871623t_char @ R2 @ (cons_exp_list_char @ X21 @ X22) @ (cons_exp_list_char @ Y21 @ Y22))))))). % list.rel_intros(2)
thf(fact_178_list_Orel__intros_I2_J, axiom,
    ((![R2 : exp_list_char > ty > $o, X21 : exp_list_char, Y21 : ty, X22 : list_exp_list_char, Y22 : list_ty]: ((R2 @ X21 @ Y21) => ((list_a295513531har_ty @ R2 @ X22 @ Y22) => (list_a295513531har_ty @ R2 @ (cons_exp_list_char @ X21 @ X22) @ (cons_ty @ Y21 @ Y22))))))). % list.rel_intros(2)
thf(fact_179_list_Orel__intros_I2_J, axiom,
    ((![R2 : ty > exp_list_char > $o, X21 : ty, Y21 : exp_list_char, X22 : list_ty, Y22 : list_exp_list_char]: ((R2 @ X21 @ Y21) => ((list_a212154379t_char @ R2 @ X22 @ Y22) => (list_a212154379t_char @ R2 @ (cons_ty @ X21 @ X22) @ (cons_exp_list_char @ Y21 @ Y22))))))). % list.rel_intros(2)
thf(fact_180_list_Orel__intros_I2_J, axiom,
    ((![R2 : ty > ty > $o, X21 : ty, Y21 : ty, X22 : list_ty, Y22 : list_ty]: ((R2 @ X21 @ Y21) => ((list_all2_ty_ty @ R2 @ X22 @ Y22) => (list_all2_ty_ty @ R2 @ (cons_ty @ X21 @ X22) @ (cons_ty @ Y21 @ Y22))))))). % list.rel_intros(2)
thf(fact_181_list_Orel__inject_I2_J, axiom,
    ((![R2 : exp_list_char > exp_list_char > $o, X21 : exp_list_char, X22 : list_exp_list_char, Y21 : exp_list_char, Y22 : list_exp_list_char]: ((list_a1702871623t_char @ R2 @ (cons_exp_list_char @ X21 @ X22) @ (cons_exp_list_char @ Y21 @ Y22)) = (((R2 @ X21 @ Y21)) & ((list_a1702871623t_char @ R2 @ X22 @ Y22))))))). % list.rel_inject(2)
thf(fact_182_list_Orel__inject_I2_J, axiom,
    ((![R2 : exp_list_char > ty > $o, X21 : exp_list_char, X22 : list_exp_list_char, Y21 : ty, Y22 : list_ty]: ((list_a295513531har_ty @ R2 @ (cons_exp_list_char @ X21 @ X22) @ (cons_ty @ Y21 @ Y22)) = (((R2 @ X21 @ Y21)) & ((list_a295513531har_ty @ R2 @ X22 @ Y22))))))). % list.rel_inject(2)
thf(fact_183_list_Orel__inject_I2_J, axiom,
    ((![R2 : ty > exp_list_char > $o, X21 : ty, X22 : list_ty, Y21 : exp_list_char, Y22 : list_exp_list_char]: ((list_a212154379t_char @ R2 @ (cons_ty @ X21 @ X22) @ (cons_exp_list_char @ Y21 @ Y22)) = (((R2 @ X21 @ Y21)) & ((list_a212154379t_char @ R2 @ X22 @ Y22))))))). % list.rel_inject(2)
thf(fact_184_list_Orel__inject_I2_J, axiom,
    ((![R2 : ty > ty > $o, X21 : ty, X22 : list_ty, Y21 : ty, Y22 : list_ty]: ((list_all2_ty_ty @ R2 @ (cons_ty @ X21 @ X22) @ (cons_ty @ Y21 @ Y22)) = (((R2 @ X21 @ Y21)) & ((list_all2_ty_ty @ R2 @ X22 @ Y22))))))). % list.rel_inject(2)
thf(fact_185_reds_Osimps, axiom,
    ((![A1 : list_exp_list_char, A22 : produc515445032on_val, A32 : list_exp_list_char, A42 : produc515445032on_val, P : list_P1234162913t_char]: ((member1689761872on_val @ (produc245869591on_val @ (produc1725134254on_val @ A1 @ A22) @ (produc1725134254on_val @ A32 @ A42)) @ (reds @ P)) = (((?[E7 : exp_list_char]: (?[S4 : produc515445032on_val]: (?[E8 : exp_list_char]: (?[S5 : produc515445032on_val]: (?[Es3 : list_exp_list_char]: (((A1 = (cons_exp_list_char @ E7 @ Es3))) & ((((A22 = S4)) & ((((A32 = (cons_exp_list_char @ E8 @ Es3))) & ((((A42 = S5)) & ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E7 @ S4) @ (produc2023458740on_val @ E8 @ S5)) @ (red @ P)))))))))))))))) | ((?[Es3 : list_exp_list_char]: (?[S4 : produc515445032on_val]: (?[Es4 : list_exp_list_char]: (?[S5 : produc515445032on_val]: (?[V2 : val]: (((A1 = (cons_exp_list_char @ (val_list_char @ V2) @ Es3))) & ((((A22 = S4)) & ((((A32 = (cons_exp_list_char @ (val_list_char @ V2) @ Es4))) & ((((A42 = S5)) & ((member1689761872on_val @ (produc245869591on_val @ (produc1725134254on_val @ Es3 @ S4) @ (produc1725134254on_val @ Es4 @ S5)) @ (reds @ P))))))))))))))))))))). % reds.simps
thf(fact_186_reds_Ocases, axiom,
    ((![A1 : list_exp_list_char, A22 : produc515445032on_val, A32 : list_exp_list_char, A42 : produc515445032on_val, P : list_P1234162913t_char]: ((member1689761872on_val @ (produc245869591on_val @ (produc1725134254on_val @ A1 @ A22) @ (produc1725134254on_val @ A32 @ A42)) @ (reds @ P)) => ((![E5 : exp_list_char, S6 : produc515445032on_val, E6 : exp_list_char, S7 : produc515445032on_val, Es5 : list_exp_list_char]: ((A1 = (cons_exp_list_char @ E5 @ Es5)) => ((A22 = S6) => ((A32 = (cons_exp_list_char @ E6 @ Es5)) => ((A42 = S7) => (~ ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E5 @ S6) @ (produc2023458740on_val @ E6 @ S7)) @ (red @ P))))))))) => (~ ((![Es5 : list_exp_list_char, S6 : produc515445032on_val, Es6 : list_exp_list_char, S7 : produc515445032on_val, V3 : val]: ((A1 = (cons_exp_list_char @ (val_list_char @ V3) @ Es5)) => ((A22 = S6) => ((A32 = (cons_exp_list_char @ (val_list_char @ V3) @ Es6)) => ((A42 = S7) => (~ ((member1689761872on_val @ (produc245869591on_val @ (produc1725134254on_val @ Es5 @ S6) @ (produc1725134254on_val @ Es6 @ S7)) @ (reds @ P)))))))))))))))). % reds.cases
thf(fact_187_widens__trans, axiom,
    ((![P : list_P1234162913t_char, Ss : list_ty, Ts : list_ty, Us : list_ty]: ((list_all2_ty_ty @ (widen_917054840t_char @ P) @ Ss @ Ts) => ((list_all2_ty_ty @ (widen_917054840t_char @ P) @ Ts @ Us) => (list_all2_ty_ty @ (widen_917054840t_char @ P) @ Ss @ Us)))))). % widens_trans
thf(fact_188_CallRedsParams, axiom,
    ((![Es : list_exp_list_char, S : produc515445032on_val, Es2 : list_exp_list_char, S2 : produc515445032on_val, P : list_P1234162913t_char, V : val, M : list_char]: ((member1689761872on_val @ (produc245869591on_val @ (produc1725134254on_val @ Es @ S) @ (produc1725134254on_val @ Es2 @ S2)) @ (transi325225921on_val @ (reds @ P))) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (call_list_char @ (val_list_char @ V) @ M @ Es) @ S) @ (produc2023458740on_val @ (call_list_char @ (val_list_char @ V) @ M @ Es2) @ S2)) @ (transi111096263on_val @ (red @ P))))))). % CallRedsParams
thf(fact_189_red__reds_OCallParams, axiom,
    ((![Es : list_exp_list_char, S : produc515445032on_val, Es2 : list_exp_list_char, S2 : produc515445032on_val, P : list_P1234162913t_char, V : val, M : list_char]: ((member1689761872on_val @ (produc245869591on_val @ (produc1725134254on_val @ Es @ S) @ (produc1725134254on_val @ Es2 @ S2)) @ (reds @ P)) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (call_list_char @ (val_list_char @ V) @ M @ Es) @ S) @ (produc2023458740on_val @ (call_list_char @ (val_list_char @ V) @ M @ Es2) @ S2)) @ (red @ P)))))). % red_reds.CallParams
thf(fact_190_fstI, axiom,
    ((![X3 : produc1172664615on_val, Y : produc1097884484on_val, Z2 : produc1097884484on_val]: ((X3 = (produc1069526295on_val @ Y @ Z2)) => ((produc708556547on_val @ X3) = Y))))). % fstI
thf(fact_191_fstI, axiom,
    ((![X3 : produc1097884484on_val, Y : exp_list_char, Z2 : produc515445032on_val]: ((X3 = (produc2023458740on_val @ Y @ Z2)) => ((produc1141111712on_val @ X3) = Y))))). % fstI
thf(fact_192_fstI, axiom,
    ((![X3 : produc655058983on_val, Y : produc335961278on_val, Z2 : produc335961278on_val]: ((X3 = (produc245869591on_val @ Y @ Z2)) => ((produc1166469635on_val @ X3) = Y))))). % fstI
thf(fact_193_fstI, axiom,
    ((![X3 : produc335961278on_val, Y : list_exp_list_char, Z2 : produc515445032on_val]: ((X3 = (produc1725134254on_val @ Y @ Z2)) => ((produc2132476826on_val @ X3) = Y))))). % fstI
thf(fact_194_fstI, axiom,
    ((![X3 : produc515445032on_val, Y : nat > option2118145160on_val, Z2 : list_char > option_val]: ((X3 = (produc52622304on_val @ Y @ Z2)) => ((produc1246629324on_val @ X3) = Y))))). % fstI
thf(fact_195_Red__lcl__add, axiom,
    ((![E : exp_list_char, H : nat > option2118145160on_val, L : list_char > option_val, E2 : exp_list_char, H2 : nat > option2118145160on_val, L2 : list_char > option_val, P : list_P1234162913t_char, L_02 : list_char > option_val]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E @ (produc52622304on_val @ H @ L)) @ (produc2023458740on_val @ E2 @ (produc52622304on_val @ H2 @ L2))) @ (transi111096263on_val @ (red @ P))) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E @ (produc52622304on_val @ H @ (map_ad1615113112ar_val @ L_02 @ L))) @ (produc2023458740on_val @ E2 @ (produc52622304on_val @ H2 @ (map_ad1615113112ar_val @ L_02 @ L2)))) @ (transi111096263on_val @ (red @ P))))))). % Red_lcl_add
thf(fact_196_exp_Oinject_I9_J, axiom,
    ((![X91 : exp_list_char, X92 : list_char, X93 : list_exp_list_char, Y91 : exp_list_char, Y92 : list_char, Y93 : list_exp_list_char]: (((call_list_char @ X91 @ X92 @ X93) = (call_list_char @ Y91 @ Y92 @ Y93)) = (((X91 = Y91)) & ((((X92 = Y92)) & ((X93 = Y93))))))))). % exp.inject(9)
thf(fact_197_exp_Odistinct_I65_J, axiom,
    ((![X32 : val, X91 : exp_list_char, X92 : list_char, X93 : list_exp_list_char]: (~ (((val_list_char @ X32) = (call_list_char @ X91 @ X92 @ X93))))))). % exp.distinct(65)
thf(fact_198_exp_Odistinct_I171_J, axiom,
    ((![X91 : exp_list_char, X92 : list_char, X93 : list_exp_list_char, X111 : exp_list_char, X112 : exp_list_char]: (~ (((call_list_char @ X91 @ X92 @ X93) = (seq_list_char @ X111 @ X112))))))). % exp.distinct(171)
thf(fact_199_red__reds_OCallObj, axiom,
    ((![E : exp_list_char, S : produc515445032on_val, E2 : exp_list_char, S2 : produc515445032on_val, P : list_P1234162913t_char, M : list_char, Es : list_exp_list_char]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E @ S) @ (produc2023458740on_val @ E2 @ S2)) @ (red @ P)) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (call_list_char @ E @ M @ Es) @ S) @ (produc2023458740on_val @ (call_list_char @ E2 @ M @ Es) @ S2)) @ (red @ P)))))). % red_reds.CallObj
thf(fact_200_CallRedsObj, axiom,
    ((![E : exp_list_char, S : produc515445032on_val, E2 : exp_list_char, S2 : produc515445032on_val, P : list_P1234162913t_char, M : list_char, Es : list_exp_list_char]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E @ S) @ (produc2023458740on_val @ E2 @ S2)) @ (transi111096263on_val @ (red @ P))) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (call_list_char @ E @ M @ Es) @ S) @ (produc2023458740on_val @ (call_list_char @ E2 @ M @ Es) @ S2)) @ (transi111096263on_val @ (red @ P))))))). % CallRedsObj
thf(fact_201_red__lcl__add, axiom,
    ((![E : exp_list_char, H : nat > option2118145160on_val, L : list_char > option_val, E2 : exp_list_char, H2 : nat > option2118145160on_val, L2 : list_char > option_val, P : list_P1234162913t_char, L_02 : list_char > option_val]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E @ (produc52622304on_val @ H @ L)) @ (produc2023458740on_val @ E2 @ (produc52622304on_val @ H2 @ L2))) @ (red @ P)) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E @ (produc52622304on_val @ H @ (map_ad1615113112ar_val @ L_02 @ L))) @ (produc2023458740on_val @ E2 @ (produc52622304on_val @ H2 @ (map_ad1615113112ar_val @ L_02 @ L2)))) @ (red @ P)))))). % red_lcl_add
thf(fact_202_map__add__assoc, axiom,
    ((![M1 : list_char > option_val, M2 : list_char > option_val, M3 : list_char > option_val]: ((map_ad1615113112ar_val @ M1 @ (map_ad1615113112ar_val @ M2 @ M3)) = (map_ad1615113112ar_val @ (map_ad1615113112ar_val @ M1 @ M2) @ M3))))). % map_add_assoc
thf(fact_203_map__le__iff__map__add__commute, axiom,
    ((![F : list_char > option_ty, G : list_char > option_ty]: ((map_le_list_char_ty @ F @ (map_add_list_char_ty @ F @ G)) = ((map_add_list_char_ty @ F @ G) = (map_add_list_char_ty @ G @ F)))))). % map_le_iff_map_add_commute
thf(fact_204_map__le__iff__map__add__commute, axiom,
    ((![F : list_char > option_val, G : list_char > option_val]: ((map_le_list_char_val @ F @ (map_ad1615113112ar_val @ F @ G)) = ((map_ad1615113112ar_val @ F @ G) = (map_ad1615113112ar_val @ G @ F)))))). % map_le_iff_map_add_commute
thf(fact_205_map__add__subsumed2, axiom,
    ((![F : list_char > option_ty, G : list_char > option_ty]: ((map_le_list_char_ty @ F @ G) => ((map_add_list_char_ty @ G @ F) = G))))). % map_add_subsumed2
thf(fact_206_map__add__subsumed2, axiom,
    ((![F : list_char > option_val, G : list_char > option_val]: ((map_le_list_char_val @ F @ G) => ((map_ad1615113112ar_val @ G @ F) = G))))). % map_add_subsumed2
thf(fact_207_map__le__antisym, axiom,
    ((![F : list_char > option_ty, G : list_char > option_ty]: ((map_le_list_char_ty @ F @ G) => ((map_le_list_char_ty @ G @ F) => (F = G)))))). % map_le_antisym
thf(fact_208_map__le__trans, axiom,
    ((![M1 : list_char > option_ty, M2 : list_char > option_ty, M3 : list_char > option_ty]: ((map_le_list_char_ty @ M1 @ M2) => ((map_le_list_char_ty @ M2 @ M3) => (map_le_list_char_ty @ M1 @ M3)))))). % map_le_trans
thf(fact_209_map__le__refl, axiom,
    ((![F : list_char > option_ty]: (map_le_list_char_ty @ F @ F)))). % map_le_refl
thf(fact_210_map__le__map__add, axiom,
    ((![F : list_char > option_ty, G : list_char > option_ty]: (map_le_list_char_ty @ F @ (map_add_list_char_ty @ G @ F))))). % map_le_map_add
thf(fact_211_map__le__map__add, axiom,
    ((![F : list_char > option_val, G : list_char > option_val]: (map_le_list_char_val @ F @ (map_ad1615113112ar_val @ G @ F))))). % map_le_map_add
thf(fact_212_map__add__le__mapE, axiom,
    ((![F : list_char > option_ty, G : list_char > option_ty, H : list_char > option_ty]: ((map_le_list_char_ty @ (map_add_list_char_ty @ F @ G) @ H) => (map_le_list_char_ty @ G @ H))))). % map_add_le_mapE
thf(fact_213_map__add__le__mapE, axiom,
    ((![F : list_char > option_val, G : list_char > option_val, H : list_char > option_val]: ((map_le_list_char_val @ (map_ad1615113112ar_val @ F @ G) @ H) => (map_le_list_char_val @ G @ H))))). % map_add_le_mapE
thf(fact_214_map__add__le__mapI, axiom,
    ((![F : list_char > option_ty, H : list_char > option_ty, G : list_char > option_ty]: ((map_le_list_char_ty @ F @ H) => ((map_le_list_char_ty @ G @ H) => (map_le_list_char_ty @ (map_add_list_char_ty @ F @ G) @ H)))))). % map_add_le_mapI
thf(fact_215_map__add__le__mapI, axiom,
    ((![F : list_char > option_val, H : list_char > option_val, G : list_char > option_val]: ((map_le_list_char_val @ F @ H) => ((map_le_list_char_val @ G @ H) => (map_le_list_char_val @ (map_ad1615113112ar_val @ F @ G) @ H)))))). % map_add_le_mapI
thf(fact_216_map__add__subsumed1, axiom,
    ((![F : list_char > option_ty, G : list_char > option_ty]: ((map_le_list_char_ty @ F @ G) => ((map_add_list_char_ty @ F @ G) = G))))). % map_add_subsumed1
thf(fact_217_map__add__subsumed1, axiom,
    ((![F : list_char > option_val, G : list_char > option_val]: ((map_le_list_char_val @ F @ G) => ((map_ad1615113112ar_val @ F @ G) = G))))). % map_add_subsumed1
thf(fact_218_WTCons, axiom,
    ((![P : list_P1234162913t_char, E3 : list_char > option_ty, E : exp_list_char, T : ty, Es : list_exp_list_char, Ts : list_ty]: ((wt @ P @ E3 @ E @ T) => ((wTs @ P @ E3 @ Es @ Ts) => (wTs @ P @ E3 @ (cons_exp_list_char @ E @ Es) @ (cons_ty @ T @ Ts))))))). % WTCons
thf(fact_219_WTrt_H__WTrts_H_Ointros_I15_J, axiom,
    ((![P : list_P1234162913t_char, H : nat > option2118145160on_val, E3 : list_char > option_ty, E : exp_list_char, T : ty, Es : list_exp_list_char, Ts : list_ty]: ((wTrt @ P @ H @ E3 @ E @ T) => ((wTrts @ P @ H @ E3 @ Es @ Ts) => (wTrts @ P @ H @ E3 @ (cons_exp_list_char @ E @ Es) @ (cons_ty @ T @ Ts))))))). % WTrt'_WTrts'.intros(15)
thf(fact_220_wts_H__iff__wts, axiom,
    ((wTrts = wTrts2))). % wts'_iff_wts
thf(fact_221_wts__wts_H, axiom,
    ((![P : list_P1234162913t_char, H : nat > option2118145160on_val, E3 : list_char > option_ty, Es : list_exp_list_char, Ts : list_ty]: ((wTrts2 @ P @ H @ E3 @ Es @ Ts) => (wTrts @ P @ H @ E3 @ Es @ Ts))))). % wts_wts'
thf(fact_222_wts_H__wts, axiom,
    ((![P : list_P1234162913t_char, H : nat > option2118145160on_val, E3 : list_char > option_ty, Es : list_exp_list_char, Ts : list_ty]: ((wTrts @ P @ H @ E3 @ Es @ Ts) => (wTrts2 @ P @ H @ E3 @ Es @ Ts))))). % wts'_wts
thf(fact_223_WTs__implies__WTrts, axiom,
    ((![P : list_P1234162913t_char, E3 : list_char > option_ty, Es : list_exp_list_char, Ts : list_ty, H : nat > option2118145160on_val]: ((wTs @ P @ E3 @ Es @ Ts) => (wTrts2 @ P @ H @ E3 @ Es @ Ts))))). % WTs_implies_WTrts
thf(fact_224_CallRedsThrowObj, axiom,
    ((![E : exp_list_char, S0 : produc515445032on_val, A2 : exp_list_char, S_1 : produc515445032on_val, P : list_P1234162913t_char, M : list_char, Es : list_exp_list_char]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E @ S0) @ (produc2023458740on_val @ (throw_list_char @ A2) @ S_1)) @ (transi111096263on_val @ (red @ P))) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (call_list_char @ E @ M @ Es) @ S0) @ (produc2023458740on_val @ (throw_list_char @ A2) @ S_1)) @ (transi111096263on_val @ (red @ P))))))). % CallRedsThrowObj
thf(fact_225_SeqRedsThrow, axiom,
    ((![E : exp_list_char, S : produc515445032on_val, E2 : exp_list_char, S2 : produc515445032on_val, P : list_P1234162913t_char, E_2 : exp_list_char]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E @ S) @ (produc2023458740on_val @ (throw_list_char @ E2) @ S2)) @ (transi111096263on_val @ (red @ P))) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (seq_list_char @ E @ E_2) @ S) @ (produc2023458740on_val @ (throw_list_char @ E2) @ S2)) @ (transi111096263on_val @ (red @ P))))))). % SeqRedsThrow
thf(fact_226_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_227_exp_Odistinct_I75_J, axiom,
    ((![X32 : val, X14 : exp_list_char]: (~ (((val_list_char @ X32) = (throw_list_char @ X14))))))). % exp.distinct(75)
thf(fact_228_exp_Odistinct_I195_J, axiom,
    ((![X111 : exp_list_char, X112 : exp_list_char, X14 : exp_list_char]: (~ (((seq_list_char @ X111 @ X112) = (throw_list_char @ X14))))))). % exp.distinct(195)
thf(fact_229_exp_Odistinct_I177_J, axiom,
    ((![X91 : exp_list_char, X92 : list_char, X93 : list_exp_list_char, X14 : exp_list_char]: (~ (((call_list_char @ X91 @ X92 @ X93) = (throw_list_char @ X14))))))). % exp.distinct(177)
thf(fact_230_red__reds_OThrowThrow, axiom,
    ((![E : exp_list_char, S : produc515445032on_val, P : list_P1234162913t_char]: (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (throw_list_char @ (throw_list_char @ E)) @ S) @ (produc2023458740on_val @ (throw_list_char @ E) @ S)) @ (red @ P))))). % red_reds.ThrowThrow
thf(fact_231_red__reds_OThrowRed, axiom,
    ((![E : exp_list_char, S : produc515445032on_val, E2 : exp_list_char, S2 : produc515445032on_val, P : list_P1234162913t_char]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E @ S) @ (produc2023458740on_val @ E2 @ S2)) @ (red @ P)) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (throw_list_char @ E) @ S) @ (produc2023458740on_val @ (throw_list_char @ E2) @ S2)) @ (red @ P)))))). % red_reds.ThrowRed
thf(fact_232_ThrowRedsThrow, axiom,
    ((![E : exp_list_char, S : produc515445032on_val, A2 : exp_list_char, S2 : produc515445032on_val, P : list_P1234162913t_char]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E @ S) @ (produc2023458740on_val @ (throw_list_char @ A2) @ S2)) @ (transi111096263on_val @ (red @ P))) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (throw_list_char @ E) @ S) @ (produc2023458740on_val @ (throw_list_char @ A2) @ S2)) @ (transi111096263on_val @ (red @ P))))))). % ThrowRedsThrow
thf(fact_233_ThrowReds, axiom,
    ((![E : exp_list_char, S : produc515445032on_val, E2 : exp_list_char, S2 : produc515445032on_val, P : list_P1234162913t_char]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E @ S) @ (produc2023458740on_val @ E2 @ S2)) @ (transi111096263on_val @ (red @ P))) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (throw_list_char @ E) @ S) @ (produc2023458740on_val @ (throw_list_char @ E2) @ S2)) @ (transi111096263on_val @ (red @ P))))))). % ThrowReds
thf(fact_234_red__reds_OSeqThrow, axiom,
    ((![E : exp_list_char, E_2 : exp_list_char, S : produc515445032on_val, P : list_P1234162913t_char]: (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (seq_list_char @ (throw_list_char @ E) @ E_2) @ S) @ (produc2023458740on_val @ (throw_list_char @ E) @ S)) @ (red @ P))))). % red_reds.SeqThrow
thf(fact_235_red__reds_OCallThrowObj, axiom,
    ((![E : exp_list_char, M : list_char, Es : list_exp_list_char, S : produc515445032on_val, P : list_P1234162913t_char]: (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (call_list_char @ (throw_list_char @ E) @ M @ Es) @ S) @ (produc2023458740on_val @ (throw_list_char @ E) @ S)) @ (red @ P))))). % red_reds.CallThrowObj
thf(fact_236_CallRedsThrowParams, axiom,
    ((![E : exp_list_char, S0 : produc515445032on_val, V : val, S_1 : produc515445032on_val, P : list_P1234162913t_char, Es : list_exp_list_char, Vs_1 : list_val, A2 : exp_list_char, Es_2 : list_exp_list_char, S_2 : produc515445032on_val, M : list_char]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E @ S0) @ (produc2023458740on_val @ (val_list_char @ V) @ S_1)) @ (transi111096263on_val @ (red @ P))) => ((member1689761872on_val @ (produc245869591on_val @ (produc1725134254on_val @ Es @ S_1) @ (produc1725134254on_val @ (append_exp_list_char @ (map_va1515327237t_char @ val_list_char @ Vs_1) @ (cons_exp_list_char @ (throw_list_char @ A2) @ Es_2)) @ S_2)) @ (transi325225921on_val @ (reds @ P))) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (call_list_char @ E @ M @ Es) @ S0) @ (produc2023458740on_val @ (throw_list_char @ A2) @ S_2)) @ (transi111096263on_val @ (red @ P)))))))). % CallRedsThrowParams
thf(fact_237_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, E : 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 @ E) @ 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 @ E) @ S_2)) @ (transi111096263on_val @ (red @ P)))))))). % BinOpRedsThrow2
thf(fact_238_same__append__eq, axiom,
    ((![Xs : list_exp_list_char, Ys : list_exp_list_char, Zs2 : list_exp_list_char]: (((append_exp_list_char @ Xs @ Ys) = (append_exp_list_char @ Xs @ Zs2)) = (Ys = Zs2))))). % same_append_eq
thf(fact_239_append__same__eq, axiom,
    ((![Ys : list_exp_list_char, Xs : list_exp_list_char, Zs2 : list_exp_list_char]: (((append_exp_list_char @ Ys @ Xs) = (append_exp_list_char @ Zs2 @ Xs)) = (Ys = Zs2))))). % append_same_eq
thf(fact_240_append__assoc, axiom,
    ((![Xs : list_exp_list_char, Ys : list_exp_list_char, Zs2 : list_exp_list_char]: ((append_exp_list_char @ (append_exp_list_char @ Xs @ Ys) @ Zs2) = (append_exp_list_char @ Xs @ (append_exp_list_char @ Ys @ Zs2)))))). % append_assoc
thf(fact_241_append_Oassoc, axiom,
    ((![A2 : list_exp_list_char, B2 : list_exp_list_char, C2 : list_exp_list_char]: ((append_exp_list_char @ (append_exp_list_char @ A2 @ B2) @ C2) = (append_exp_list_char @ A2 @ (append_exp_list_char @ B2 @ C2)))))). % append.assoc
thf(fact_242_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)

% Conjectures (3)
thf(conj_0, hypothesis,
    ((wTrt2 @ p @ (hp @ s) @ e @ e2 @ t))).
thf(conj_1, hypothesis,
    ((typeSa1777264139_sconf @ p @ e @ s))).
thf(conj_2, conjecture,
    ((typeSa1777264139_sconf @ p @ e @ s2))).
