% TIMEFORMAT='%3R'; { time (exec 2>&1; /home/martin/bin/satallax -E /home/martin/.isabelle/contrib/e-2.5-1/x86_64-linux/eprover -p tstp -t 5 /home/martin/judgement-day/tptp-thf/tptp/TypeSafe/prob_198__5336104_1 ) ; }
% This file was generated by Isabelle (most likely Sledgehammer)
% 2020-12-16 14:19:55.044

% Could-be-implicit typings (73)
thf(ty_n_t__List__Olist_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__Product____Type__Oprod_It__List__Olist_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__Type__Oty_J_J_Mt__List__Olist_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__Product____Type__Oprod_It__List__Olist_It__Type__Oty_J_Mt__Product____Type__Oprod_It__Type__Oty_Mt__Product____Type__Oprod_It__List__Olist_It__List__Olist_It__String__Ochar_J_J_Mt__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_J_J_J_J_J_J_J_J_J, type,
    list_P1234162913t_char : $tType).
thf(ty_n_t__Set__Oset_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__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_J_J, type,
    set_Pr1465729071on_val : $tType).
thf(ty_n_t__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__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_J, type,
    produc1914020559on_val : $tType).
thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_It__List__Olist_It__Type__Oty_J_Mt__Product____Type__Oprod_It__List__Olist_It__Value__Oval_J_Mt__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_J_J_Mt__Product____Type__Oprod_It__List__Olist_It__Type__Oty_J_Mt__Product____Type__Oprod_It__List__Olist_It__Value__Oval_J_Mt__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_J_J_J_J, type,
    set_Pr1314019591t_char : $tType).
thf(ty_n_t__Set__Oset_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_J, type,
    set_Pr723149704on_val : $tType).
thf(ty_n_t__Product____Type__Oprod_It__Product____Type__Oprod_It__List__Olist_It__Type__Oty_J_Mt__Product____Type__Oprod_It__List__Olist_It__Value__Oval_J_Mt__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_J_J_Mt__Product____Type__Oprod_It__List__Olist_It__Type__Oty_J_Mt__Product____Type__Oprod_It__List__Olist_It__Value__Oval_J_Mt__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_J_J_J, type,
    produc885582375t_char : $tType).
thf(ty_n_t__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,
    produc515445032on_val : $tType).
thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_It__List__Olist_It__Value__Oval_J_Mt__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_J_Mt__Product____Type__Oprod_It__List__Olist_It__Value__Oval_J_Mt__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_J_J_J, type,
    set_Pr290014113t_char : $tType).
thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__List__Olist_It__List__Olist_It__String__Ochar_J_J_Mt__Product____Type__Oprod_It__List__Olist_It__Type__Oty_J_Mt__Product____Type__Oprod_It__List__Olist_It__Value__Oval_J_Mt__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_J_J_J_J, type,
    set_Pr685054290t_char : $tType).
thf(ty_n_t__List__Olist_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_J, type,
    list_n1514066695on_val : $tType).
thf(ty_n_t__Product____Type__Oprod_It__Product____Type__Oprod_It__List__Olist_It__Value__Oval_J_Mt__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_J_Mt__Product____Type__Oprod_It__List__Olist_It__Value__Oval_J_Mt__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_J_J, type,
    produc1439662401t_char : $tType).
thf(ty_n_t__Product____Type__Oprod_It__List__Olist_It__List__Olist_It__String__Ochar_J_J_Mt__Product____Type__Oprod_It__List__Olist_It__Type__Oty_J_Mt__Product____Type__Oprod_It__List__Olist_It__Value__Oval_J_Mt__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_J_J_J, type,
    produc81045532t_char : $tType).
thf(ty_n_t__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, type,
    option2118145160on_val : $tType).
thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_I_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_M_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J, type,
    set_Pr1104486497on_val : $tType).
thf(ty_n_t__List__Olist_It__Product____Type__Oprod_It__List__Olist_It__Type__Oty_J_Mt__Product____Type__Oprod_It__List__Olist_It__Value__Oval_J_Mt__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_J_J_J, type,
    list_P364227422t_char : $tType).
thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__List__Olist_It__Type__Oty_J_Mt__Product____Type__Oprod_It__List__Olist_It__Value__Oval_J_Mt__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_J_J_J, type,
    set_Pr925902648t_char : $tType).
thf(ty_n_t__Product____Type__Oprod_I_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_M_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_J, type,
    produc1335728385on_val : $tType).
thf(ty_n_t__Product____Type__Oprod_It__List__Olist_It__Type__Oty_J_Mt__Product____Type__Oprod_It__List__Olist_It__Value__Oval_J_Mt__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_J_J, type,
    produc111478616t_char : $tType).
thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__List__Olist_It__Option__Ooption_It__Type__Oty_J_J_Mt__List__Olist_It__Option__Ooption_It__Type__Oty_J_J_J_J, type,
    set_Pr962897519ion_ty : $tType).
thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__List__Olist_It__List__Olist_It__String__Ochar_J_J_Mt__List__Olist_It__List__Olist_It__String__Ochar_J_J_J_J, type,
    set_Pr2117892643t_char : $tType).
thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_Mt__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_J_J, type,
    set_Pr224372167t_char : $tType).
thf(ty_n_t__Product____Type__Oprod_It__List__Olist_It__Option__Ooption_It__Type__Oty_J_J_Mt__List__Olist_It__Option__Ooption_It__Type__Oty_J_J_J, type,
    produc922361871ion_ty : $tType).
thf(ty_n_t__Product____Type__Oprod_It__List__Olist_It__List__Olist_It__String__Ochar_J_J_Mt__List__Olist_It__List__Olist_It__String__Ochar_J_J_J, type,
    produc1410698691t_char : $tType).
thf(ty_n_t__Product____Type__Oprod_It__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_Mt__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_J, type,
    produc677445863t_char : $tType).
thf(ty_n_t__List__Olist_It__Product____Type__Oprod_It__List__Olist_It__Value__Oval_J_Mt__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_J_J, type,
    list_P1602847424t_char : $tType).
thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__List__Olist_It__Value__Oval_J_Mt__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_J_J, type,
    set_Pr82799206t_char : $tType).
thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Option__Ooption_It__Type__Oty_J_Mt__Option__Ooption_It__Type__Oty_J_J_J, type,
    set_Pr616941135ion_ty : $tType).
thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_J, type,
    set_Pr164112643t_char : $tType).
thf(ty_n_t__Product____Type__Oprod_It__List__Olist_It__Value__Oval_J_Mt__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_J, type,
    produc1109669680t_char : $tType).
thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__List__Olist_It__Value__Oval_J_Mt__List__Olist_It__Value__Oval_J_J_J, type,
    set_Pr723931873st_val : $tType).
thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__List__Olist_It__Type__Oty_J_Mt__List__Olist_It__Type__Oty_J_J_J, type,
    set_Pr1785354703ist_ty : $tType).
thf(ty_n_t__Product____Type__Oprod_It__Option__Ooption_It__Type__Oty_J_Mt__Option__Ooption_It__Type__Oty_J_J, type,
    produc1872540399ion_ty : $tType).
thf(ty_n_t__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J, type,
    produc1257910179t_char : $tType).
thf(ty_n_t__List__Olist_I_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_J, type,
    list_l566969696on_val : $tType).
thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Value__Oval_Mt__Option__Ooption_It__Type__Oty_J_J_J, type,
    set_Pr741504840ion_ty : $tType).
thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Value__Oval_Mt__List__Olist_It__String__Ochar_J_J_J, type,
    set_Pr1557683618t_char : $tType).
thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__Value__Oval_J_J, type,
    set_Pr174107298ar_val : $tType).
thf(ty_n_t__Product____Type__Oprod_It__List__Olist_It__Value__Oval_J_Mt__List__Olist_It__Value__Oval_J_J, type,
    produc1608520577st_val : $tType).
thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Type__Oty_Mt__Option__Ooption_It__Type__Oty_J_J_J, type,
    set_Pr504292735ion_ty : $tType).
thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Type__Oty_Mt__List__Olist_It__String__Ochar_J_J_J, type,
    set_Pr1320471513t_char : $tType).
thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__Type__Oty_J_J, type,
    set_Pr349050585har_ty : $tType).
thf(ty_n_t__Product____Type__Oprod_It__List__Olist_It__Type__Oty_J_Mt__List__Olist_It__Type__Oty_J_J, type,
    produc1714969711ist_ty : $tType).
thf(ty_n_t__Product____Type__Oprod_It__Value__Oval_Mt__Option__Ooption_It__Type__Oty_J_J, type,
    produc821192552ion_ty : $tType).
thf(ty_n_t__Product____Type__Oprod_It__Value__Oval_Mt__List__Olist_It__String__Ochar_J_J, type,
    produc1259363010t_char : $tType).
thf(ty_n_t__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__Value__Oval_J, type,
    produc892282818ar_val : $tType).
thf(ty_n_t__Product____Type__Oprod_It__Type__Oty_Mt__Option__Ooption_It__Type__Oty_J_J, type,
    produc192345759ion_ty : $tType).
thf(ty_n_t__Product____Type__Oprod_It__Type__Oty_Mt__List__Olist_It__String__Ochar_J_J, type,
    produc630516217t_char : $tType).
thf(ty_n_t__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__Type__Oty_J, type,
    produc2086909177har_ty : $tType).
thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Value__Oval_Mt__Value__Oval_J_J, type,
    set_Pr1870322241al_val : $tType).
thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Value__Oval_Mt__Type__Oty_J_J, type,
    set_Pr312206840val_ty : $tType).
thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Type__Oty_Mt__Value__Oval_J_J, type,
    set_Pr1036794744ty_val : $tType).
thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Type__Oty_Mt__Type__Oty_J_J, type,
    set_Pr1194734255_ty_ty : $tType).
thf(ty_n_t__List__Olist_It__List__Olist_It__List__Olist_It__String__Ochar_J_J_J, type,
    list_list_list_char : $tType).
thf(ty_n_t__List__Olist_It__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_J, type,
    list_exp_list_char : $tType).
thf(ty_n_t__Product____Type__Oprod_It__Value__Oval_Mt__Value__Oval_J, type,
    product_prod_val_val : $tType).
thf(ty_n_t__Product____Type__Oprod_It__Value__Oval_Mt__Type__Oty_J, type,
    product_prod_val_ty : $tType).
thf(ty_n_t__Product____Type__Oprod_It__Type__Oty_Mt__Value__Oval_J, type,
    product_prod_ty_val : $tType).
thf(ty_n_t__Option__Ooption_It__Option__Ooption_It__Type__Oty_J_J, type,
    option_option_ty : $tType).
thf(ty_n_t__Option__Ooption_It__List__Olist_It__String__Ochar_J_J, type,
    option_list_char : $tType).
thf(ty_n_t__Product____Type__Oprod_It__Type__Oty_Mt__Type__Oty_J, type,
    product_prod_ty_ty : $tType).
thf(ty_n_t__List__Olist_It__Option__Ooption_It__Type__Oty_J_J, type,
    list_option_ty : $tType).
thf(ty_n_t__List__Olist_It__List__Olist_It__String__Ochar_J_J, type,
    list_list_char : $tType).
thf(ty_n_t__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J, type,
    exp_list_char : $tType).
thf(ty_n_t__List__Olist_It__List__Olist_It__Value__Oval_J_J, type,
    list_list_val : $tType).
thf(ty_n_t__List__Olist_It__List__Olist_It__Type__Oty_J_J, type,
    list_list_ty : $tType).
thf(ty_n_t__Option__Ooption_It__Value__Oval_J, type,
    option_val : $tType).
thf(ty_n_t__Option__Ooption_It__Type__Oty_J, type,
    option_ty : $tType).
thf(ty_n_t__List__Olist_It__String__Ochar_J, type,
    list_char : $tType).
thf(ty_n_t__List__Olist_It__Value__Oval_J, type,
    list_val : $tType).
thf(ty_n_t__List__Olist_It__Type__Oty_J, type,
    list_ty : $tType).
thf(ty_n_t__Value__Oval, type,
    val : $tType).
thf(ty_n_t__Type__Oty, type,
    ty : $tType).
thf(ty_n_t__Nat__Onat, type,
    nat : $tType).

% Explicit typings (155)
thf(sy_c_Auxiliary_Ofun__of_001_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_001_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J, type,
    fun_of461468542on_val : set_Pr1104486497on_val > (list_char > option_val) > (list_char > option_val) > $o).
thf(sy_c_Auxiliary_Ofun__of_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,
    fun_of1502879141on_val : set_Pr723149704on_val > (nat > option2118145160on_val) > (list_char > option_val) > $o).
thf(sy_c_Auxiliary_Ofun__of_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__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, type,
    fun_of1000097484on_val : set_Pr1465729071on_val > (nat > option2118145160on_val) > (nat > option2118145160on_val) > $o).
thf(sy_c_Auxiliary_Ofun__of_001t__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_001t__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J, type,
    fun_of64219676t_char : set_Pr224372167t_char > exp_list_char > exp_list_char > $o).
thf(sy_c_Auxiliary_Ofun__of_001t__List__Olist_It__List__Olist_It__String__Ochar_J_J_001t__List__Olist_It__List__Olist_It__String__Ochar_J_J, type,
    fun_of681401536t_char : set_Pr2117892643t_char > list_list_char > list_list_char > $o).
thf(sy_c_Auxiliary_Ofun__of_001t__List__Olist_It__List__Olist_It__String__Ochar_J_J_001t__Product____Type__Oprod_It__List__Olist_It__Type__Oty_J_Mt__Product____Type__Oprod_It__List__Olist_It__Value__Oval_J_Mt__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_J_J, type,
    fun_of1003211849t_char : set_Pr685054290t_char > list_list_char > produc111478616t_char > $o).
thf(sy_c_Auxiliary_Ofun__of_001t__List__Olist_It__String__Ochar_J_001t__Type__Oty, type,
    fun_of_list_char_ty : set_Pr349050585har_ty > list_char > ty > $o).
thf(sy_c_Auxiliary_Ofun__of_001t__List__Olist_It__String__Ochar_J_001t__Value__Oval, type,
    fun_of_list_char_val : set_Pr174107298ar_val > list_char > val > $o).
thf(sy_c_Auxiliary_Ofun__of_001t__List__Olist_It__Type__Oty_J_001t__List__Olist_It__Type__Oty_J, type,
    fun_of397150316ist_ty : set_Pr1785354703ist_ty > list_ty > list_ty > $o).
thf(sy_c_Auxiliary_Ofun__of_001t__List__Olist_It__Type__Oty_J_001t__Product____Type__Oprod_It__List__Olist_It__Value__Oval_J_Mt__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_J, type,
    fun_of1649676245t_char : set_Pr925902648t_char > list_ty > produc1109669680t_char > $o).
thf(sy_c_Auxiliary_Ofun__of_001t__List__Olist_It__Value__Oval_J_001t__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J, type,
    fun_of161265885t_char : set_Pr82799206t_char > list_val > exp_list_char > $o).
thf(sy_c_Auxiliary_Ofun__of_001t__List__Olist_It__Value__Oval_J_001t__List__Olist_It__Value__Oval_J, type,
    fun_of1684577790st_val : set_Pr723931873st_val > list_val > list_val > $o).
thf(sy_c_Auxiliary_Ofun__of_001t__Product____Type__Oprod_It__List__Olist_It__Type__Oty_J_Mt__Product____Type__Oprod_It__List__Olist_It__Value__Oval_J_Mt__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_J_J_001t__Product____Type__Oprod_It__List__Olist_It__Type__Oty_J_Mt__Product____Type__Oprod_It__List__Olist_It__Value__Oval_J_Mt__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_J_J, type,
    fun_of756510172t_char : set_Pr1314019591t_char > produc111478616t_char > produc111478616t_char > $o).
thf(sy_c_Auxiliary_Ofun__of_001t__Product____Type__Oprod_It__List__Olist_It__Value__Oval_J_Mt__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_J_001t__Product____Type__Oprod_It__List__Olist_It__Value__Oval_J_Mt__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_J, type,
    fun_of446723518t_char : set_Pr290014113t_char > produc1109669680t_char > produc1109669680t_char > $o).
thf(sy_c_Auxiliary_Ofun__of_001t__Type__Oty_001t__List__Olist_It__String__Ochar_J, type,
    fun_of_ty_list_char : set_Pr1320471513t_char > ty > list_char > $o).
thf(sy_c_Auxiliary_Ofun__of_001t__Type__Oty_001t__Option__Ooption_It__Type__Oty_J, type,
    fun_of_ty_option_ty : set_Pr504292735ion_ty > ty > option_ty > $o).
thf(sy_c_Auxiliary_Ofun__of_001t__Type__Oty_001t__Type__Oty, type,
    fun_of_ty_ty : set_Pr1194734255_ty_ty > ty > ty > $o).
thf(sy_c_Auxiliary_Ofun__of_001t__Type__Oty_001t__Value__Oval, type,
    fun_of_ty_val : set_Pr1036794744ty_val > ty > val > $o).
thf(sy_c_Auxiliary_Ofun__of_001t__Value__Oval_001t__List__Olist_It__String__Ochar_J, type,
    fun_of_val_list_char : set_Pr1557683618t_char > val > list_char > $o).
thf(sy_c_Auxiliary_Ofun__of_001t__Value__Oval_001t__Option__Ooption_It__Type__Oty_J, type,
    fun_of_val_option_ty : set_Pr741504840ion_ty > val > option_ty > $o).
thf(sy_c_Auxiliary_Ofun__of_001t__Value__Oval_001t__Type__Oty, type,
    fun_of_val_ty : set_Pr312206840val_ty > val > ty > $o).
thf(sy_c_Auxiliary_Ofun__of_001t__Value__Oval_001t__Value__Oval, type,
    fun_of_val_val : set_Pr1870322241al_val > val > val > $o).
thf(sy_c_BigStep_Oeval, type,
    eval : list_P1234162913t_char > exp_list_char > produc515445032on_val > exp_list_char > produc515445032on_val > $o).
thf(sy_c_Conform_Oconf_001t__Product____Type__Oprod_It__List__Olist_It__List__Olist_It__String__Ochar_J_J_Mt__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_J, type,
    conf_P93989998t_char : list_P1234162913t_char > (nat > option2118145160on_val) > val > ty > $o).
thf(sy_c_List_Ofind_001t__List__Olist_It__String__Ochar_J, type,
    find_list_char : (list_char > $o) > list_list_char > option_list_char).
thf(sy_c_List_Ofind_001t__Option__Ooption_It__Type__Oty_J, type,
    find_option_ty : (option_ty > $o) > list_option_ty > option_option_ty).
thf(sy_c_List_Ofind_001t__Type__Oty, type,
    find_ty : (ty > $o) > list_ty > option_ty).
thf(sy_c_List_Ofind_001t__Value__Oval, type,
    find_val : (val > $o) > list_val > option_val).
thf(sy_c_List_Olex_001t__List__Olist_It__String__Ochar_J, type,
    lex_list_char : set_Pr164112643t_char > set_Pr2117892643t_char).
thf(sy_c_List_Olex_001t__Option__Ooption_It__Type__Oty_J, type,
    lex_option_ty : set_Pr616941135ion_ty > set_Pr962897519ion_ty).
thf(sy_c_List_Olex_001t__Type__Oty, type,
    lex_ty : set_Pr1194734255_ty_ty > set_Pr1785354703ist_ty).
thf(sy_c_List_Olex_001t__Value__Oval, type,
    lex_val : set_Pr1870322241al_val > set_Pr723931873st_val).
thf(sy_c_List_Olist_OCons_001t__List__Olist_It__String__Ochar_J, type,
    cons_list_char : list_char > list_list_char > list_list_char).
thf(sy_c_List_Olist_OCons_001t__Option__Ooption_It__Type__Oty_J, type,
    cons_option_ty : option_ty > list_option_ty > list_option_ty).
thf(sy_c_List_Olist_OCons_001t__Type__Oty, type,
    cons_ty : ty > list_ty > list_ty).
thf(sy_c_List_Olist_OCons_001t__Value__Oval, type,
    cons_val : val > list_val > list_val).
thf(sy_c_List_Olist_Olist__all2_001_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_001_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J, type,
    list_a1722502185on_val : ((list_char > option_val) > (list_char > option_val) > $o) > list_l566969696on_val > list_l566969696on_val > $o).
thf(sy_c_List_Olist_Olist__all2_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,
    list_a729577424on_val : ((nat > option2118145160on_val) > (list_char > option_val) > $o) > list_n1514066695on_val > list_l566969696on_val > $o).
thf(sy_c_List_Olist_Olist__all2_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__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, type,
    list_a592044663on_val : ((nat > option2118145160on_val) > (nat > option2118145160on_val) > $o) > list_n1514066695on_val > list_n1514066695on_val > $o).
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__List__Olist_It__List__Olist_It__String__Ochar_J_J_001t__List__Olist_It__List__Olist_It__String__Ochar_J_J, type,
    list_a1460260715t_char : (list_list_char > list_list_char > $o) > list_list_list_char > list_list_list_char > $o).
thf(sy_c_List_Olist_Olist__all2_001t__List__Olist_It__List__Olist_It__String__Ochar_J_J_001t__Product____Type__Oprod_It__List__Olist_It__Type__Oty_J_Mt__Product____Type__Oprod_It__List__Olist_It__Value__Oval_J_Mt__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_J_J, type,
    list_a1227756510t_char : (list_list_char > produc111478616t_char > $o) > list_list_list_char > list_P364227422t_char > $o).
thf(sy_c_List_Olist_Olist__all2_001t__List__Olist_It__String__Ochar_J_001t__Type__Oty, type,
    list_a1770748705har_ty : (list_char > ty > $o) > list_list_char > list_ty > $o).
thf(sy_c_List_Olist_Olist__all2_001t__List__Olist_It__String__Ochar_J_001t__Value__Oval, type,
    list_a280217834ar_val : (list_char > val > $o) > list_list_char > list_val > $o).
thf(sy_c_List_Olist_Olist__all2_001t__List__Olist_It__Type__Oty_J_001t__List__Olist_It__Type__Oty_J, type,
    list_a1317958679ist_ty : (list_ty > list_ty > $o) > list_list_ty > list_list_ty > $o).
thf(sy_c_List_Olist_Olist__all2_001t__List__Olist_It__Type__Oty_J_001t__Product____Type__Oprod_It__List__Olist_It__Value__Oval_J_Mt__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_J, type,
    list_a226366592t_char : (list_ty > produc1109669680t_char > $o) > list_list_ty > list_P1602847424t_char > $o).
thf(sy_c_List_Olist_Olist__all2_001t__List__Olist_It__Value__Oval_J_001t__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J, type,
    list_a1105622130t_char : (list_val > exp_list_char > $o) > list_list_val > list_exp_list_char > $o).
thf(sy_c_List_Olist_Olist__all2_001t__List__Olist_It__Value__Oval_J_001t__List__Olist_It__Value__Oval_J, type,
    list_a602111657st_val : (list_val > list_val > $o) > list_list_val > list_list_val > $o).
thf(sy_c_List_Olist_Olist__all2_001t__Option__Ooption_It__Type__Oty_J_001t__Type__Oty, type,
    list_a1442669255_ty_ty : (option_ty > ty > $o) > list_option_ty > list_ty > $o).
thf(sy_c_List_Olist_Olist__all2_001t__Option__Ooption_It__Type__Oty_J_001t__Value__Oval, type,
    list_a1717583248ty_val : (option_ty > val > $o) > list_option_ty > list_val > $o).
thf(sy_c_List_Olist_Olist__all2_001t__Product____Type__Oprod_It__List__Olist_It__Type__Oty_J_Mt__Product____Type__Oprod_It__List__Olist_It__Value__Oval_J_Mt__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_J_J_001t__Product____Type__Oprod_It__List__Olist_It__Type__Oty_J_Mt__Product____Type__Oprod_It__List__Olist_It__Value__Oval_J_Mt__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_J_J, type,
    list_a787061767t_char : (produc111478616t_char > produc111478616t_char > $o) > list_P364227422t_char > list_P364227422t_char > $o).
thf(sy_c_List_Olist_Olist__all2_001t__Product____Type__Oprod_It__List__Olist_It__Value__Oval_J_Mt__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_J_001t__Product____Type__Oprod_It__List__Olist_It__Value__Oval_J_Mt__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_J, type,
    list_a761598825t_char : (produc1109669680t_char > produc1109669680t_char > $o) > list_P1602847424t_char > list_P1602847424t_char > $o).
thf(sy_c_List_Olist_Olist__all2_001t__Type__Oty_001t__List__Olist_It__String__Ochar_J, type,
    list_a1504214817t_char : (ty > list_char > $o) > list_ty > list_list_char > $o).
thf(sy_c_List_Olist_Olist__all2_001t__Type__Oty_001t__Option__Ooption_It__Type__Oty_J, type,
    list_a765198023ion_ty : (ty > option_ty > $o) > list_ty > list_option_ty > $o).
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_Olist__all2_001t__Type__Oty_001t__Value__Oval, type,
    list_all2_ty_val : (ty > val > $o) > list_ty > list_val > $o).
thf(sy_c_List_Olist_Olist__all2_001t__Value__Oval_001t__List__Olist_It__String__Ochar_J, type,
    list_a1248766058t_char : (val > list_char > $o) > list_val > list_list_char > $o).
thf(sy_c_List_Olist_Olist__all2_001t__Value__Oval_001t__Option__Ooption_It__Type__Oty_J, type,
    list_a509749264ion_ty : (val > option_ty > $o) > list_val > list_option_ty > $o).
thf(sy_c_List_Olist_Olist__all2_001t__Value__Oval_001t__Type__Oty, type,
    list_all2_val_ty : (val > ty > $o) > list_val > list_ty > $o).
thf(sy_c_List_Olist_Olist__all2_001t__Value__Oval_001t__Value__Oval, type,
    list_all2_val_val : (val > val > $o) > list_val > list_val > $o).
thf(sy_c_List_Olist_Omap_001t__List__Olist_It__String__Ochar_J_001t__List__Olist_It__String__Ochar_J, type,
    map_li1166989960t_char : (list_char > list_char) > list_list_char > list_list_char).
thf(sy_c_List_Olist_Omap_001t__List__Olist_It__String__Ochar_J_001t__Type__Oty, type,
    map_list_char_ty : (list_char > ty) > list_list_char > list_ty).
thf(sy_c_List_Olist_Omap_001t__List__Olist_It__String__Ochar_J_001t__Value__Oval, type,
    map_list_char_val : (list_char > val) > list_list_char > list_val).
thf(sy_c_List_Olist_Omap_001t__Option__Ooption_It__Type__Oty_J_001t__Type__Oty, type,
    map_option_ty_ty : (option_ty > ty) > list_option_ty > list_ty).
thf(sy_c_List_Olist_Omap_001t__Option__Ooption_It__Type__Oty_J_001t__Value__Oval, type,
    map_option_ty_val : (option_ty > val) > list_option_ty > list_val).
thf(sy_c_List_Olist_Omap_001t__Type__Oty_001t__List__Olist_It__String__Ochar_J, type,
    map_ty_list_char : (ty > list_char) > list_ty > list_list_char).
thf(sy_c_List_Olist_Omap_001t__Type__Oty_001t__Option__Ooption_It__Type__Oty_J, type,
    map_ty_option_ty : (ty > option_ty) > list_ty > list_option_ty).
thf(sy_c_List_Olist_Omap_001t__Type__Oty_001t__Type__Oty, type,
    map_ty_ty : (ty > ty) > list_ty > list_ty).
thf(sy_c_List_Olist_Omap_001t__Type__Oty_001t__Value__Oval, type,
    map_ty_val : (ty > val) > list_ty > list_val).
thf(sy_c_List_Olist_Omap_001t__Value__Oval_001t__List__Olist_It__String__Ochar_J, type,
    map_val_list_char : (val > list_char) > list_val > list_list_char).
thf(sy_c_List_Olist_Omap_001t__Value__Oval_001t__Option__Ooption_It__Type__Oty_J, type,
    map_val_option_ty : (val > option_ty) > list_val > list_option_ty).
thf(sy_c_List_Olist_Omap_001t__Value__Oval_001t__Type__Oty, type,
    map_val_ty : (val > ty) > list_val > list_ty).
thf(sy_c_List_Olist_Omap_001t__Value__Oval_001t__Value__Oval, type,
    map_val_val : (val > val) > list_val > list_val).
thf(sy_c_List_Omap__tailrec_001t__List__Olist_It__String__Ochar_J_001t__List__Olist_It__String__Ochar_J, type,
    map_ta1456818130t_char : (list_char > list_char) > list_list_char > list_list_char).
thf(sy_c_List_Omap__tailrec_001t__List__Olist_It__String__Ochar_J_001t__Type__Oty, type,
    map_ta1062070056har_ty : (list_char > ty) > list_list_char > list_ty).
thf(sy_c_List_Omap__tailrec_001t__Type__Oty_001t__List__Olist_It__String__Ochar_J, type,
    map_ta795536168t_char : (ty > list_char) > list_ty > list_list_char).
thf(sy_c_List_Omap__tailrec_001t__Type__Oty_001t__Option__Ooption_It__Type__Oty_J, type,
    map_ta56519374ion_ty : (ty > option_ty) > list_ty > list_option_ty).
thf(sy_c_List_Omap__tailrec_001t__Type__Oty_001t__Type__Oty, type,
    map_tailrec_ty_ty : (ty > ty) > list_ty > list_ty).
thf(sy_c_List_Omap__tailrec_001t__Type__Oty_001t__Value__Oval, type,
    map_tailrec_ty_val : (ty > val) > list_ty > list_val).
thf(sy_c_List_Omap__tailrec_001t__Value__Oval_001t__Option__Ooption_It__Type__Oty_J, type,
    map_ta1696661655ion_ty : (val > option_ty) > list_val > list_option_ty).
thf(sy_c_Map_Omap__upds_001t__List__Olist_It__String__Ochar_J_001t__Type__Oty, type,
    map_up703499792har_ty : (list_char > option_ty) > list_list_char > list_ty > list_char > option_ty).
thf(sy_c_Map_Omap__upds_001t__List__Olist_It__String__Ochar_J_001t__Value__Oval, type,
    map_up576607321ar_val : (list_char > option_val) > list_list_char > list_val > list_char > option_val).
thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__List__Olist_It__String__Ochar_J_J, type,
    size_s2008079621t_char : list_list_char > nat).
thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Option__Ooption_It__Type__Oty_J_J, type,
    size_s1569909163ion_ty : list_option_ty > nat).
thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Type__Oty_J, type,
    size_size_list_ty : list_ty > nat).
thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Value__Oval_J, type,
    size_size_list_val : list_val > nat).
thf(sy_c_Objects_Otypeof__h, type,
    typeof_h : (nat > option2118145160on_val) > val > option_ty).
thf(sy_c_Option_Ooption_OSome_001t__List__Olist_It__String__Ochar_J, type,
    some_list_char : list_char > option_list_char).
thf(sy_c_Option_Ooption_OSome_001t__Option__Ooption_It__Type__Oty_J, type,
    some_option_ty : option_ty > option_option_ty).
thf(sy_c_Option_Ooption_OSome_001t__Type__Oty, type,
    some_ty : ty > option_ty).
thf(sy_c_Option_Ooption_OSome_001t__Value__Oval, type,
    some_val : val > option_val).
thf(sy_c_Product__Type_OPair_001_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_001_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J, type,
    produc746553401on_val : (list_char > option_val) > (list_char > option_val) > produc1335728385on_val).
thf(sy_c_Product__Type_OPair_001_062_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_001_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J, type,
    produc52622304on_val : (nat > option2118145160on_val) > (list_char > option_val) > produc515445032on_val).
thf(sy_c_Product__Type_OPair_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__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, type,
    produc1392944775on_val : (nat > option2118145160on_val) > (nat > option2118145160on_val) > produc1914020559on_val).
thf(sy_c_Product__Type_OPair_001t__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_001t__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J, type,
    produc240508503t_char : exp_list_char > exp_list_char > produc677445863t_char).
thf(sy_c_Product__Type_OPair_001t__List__Olist_It__List__Olist_It__String__Ochar_J_J_001t__List__Olist_It__List__Olist_It__String__Ochar_J_J, type,
    produc1181934459t_char : list_list_char > list_list_char > produc1410698691t_char).
thf(sy_c_Product__Type_OPair_001t__List__Olist_It__List__Olist_It__String__Ochar_J_J_001t__Product____Type__Oprod_It__List__Olist_It__Type__Oty_J_Mt__Product____Type__Oprod_It__List__Olist_It__Value__Oval_J_Mt__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_J_J, type,
    produc1808722894t_char : list_list_char > produc111478616t_char > produc81045532t_char).
thf(sy_c_Product__Type_OPair_001t__List__Olist_It__Option__Ooption_It__Type__Oty_J_J_001t__List__Olist_It__Option__Ooption_It__Type__Oty_J_J, type,
    produc1071605959ion_ty : list_option_ty > list_option_ty > produc922361871ion_ty).
thf(sy_c_Product__Type_OPair_001t__List__Olist_It__String__Ochar_J_001t__List__Olist_It__String__Ochar_J, type,
    produc1304532571t_char : list_char > list_char > produc1257910179t_char).
thf(sy_c_Product__Type_OPair_001t__List__Olist_It__String__Ochar_J_001t__Type__Oty, type,
    produc1017542449har_ty : list_char > ty > produc2086909177har_ty).
thf(sy_c_Product__Type_OPair_001t__List__Olist_It__String__Ochar_J_001t__Value__Oval, type,
    produc368164090ar_val : list_char > val > produc892282818ar_val).
thf(sy_c_Product__Type_OPair_001t__List__Olist_It__Type__Oty_J_001t__List__Olist_It__Type__Oty_J, type,
    produc1089615911ist_ty : list_ty > list_ty > produc1714969711ist_ty).
thf(sy_c_Product__Type_OPair_001t__List__Olist_It__Type__Oty_J_001t__Product____Type__Oprod_It__List__Olist_It__Value__Oval_J_Mt__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_J, type,
    produc1806338192t_char : list_ty > produc1109669680t_char > produc111478616t_char).
thf(sy_c_Product__Type_OPair_001t__List__Olist_It__Value__Oval_J_001t__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J, type,
    produc823987298t_char : list_val > exp_list_char > produc1109669680t_char).
thf(sy_c_Product__Type_OPair_001t__List__Olist_It__Value__Oval_J_001t__List__Olist_It__Value__Oval_J, type,
    produc180957881st_val : list_val > list_val > produc1608520577st_val).
thf(sy_c_Product__Type_OPair_001t__Option__Ooption_It__Type__Oty_J_001t__Option__Ooption_It__Type__Oty_J, type,
    produc1618316455ion_ty : option_ty > option_ty > produc1872540399ion_ty).
thf(sy_c_Product__Type_OPair_001t__Product____Type__Oprod_It__List__Olist_It__Type__Oty_J_Mt__Product____Type__Oprod_It__List__Olist_It__Value__Oval_J_Mt__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_J_J_001t__Product____Type__Oprod_It__List__Olist_It__Type__Oty_J_Mt__Product____Type__Oprod_It__List__Olist_It__Value__Oval_J_Mt__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_J_J, type,
    produc1108858903t_char : produc111478616t_char > produc111478616t_char > produc885582375t_char).
thf(sy_c_Product__Type_OPair_001t__Product____Type__Oprod_It__List__Olist_It__Value__Oval_J_Mt__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_J_001t__Product____Type__Oprod_It__List__Olist_It__Value__Oval_J_Mt__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_J, type,
    produc183121785t_char : produc1109669680t_char > produc1109669680t_char > produc1439662401t_char).
thf(sy_c_Product__Type_OPair_001t__Type__Oty_001t__List__Olist_It__String__Ochar_J, type,
    produc751008561t_char : ty > list_char > produc630516217t_char).
thf(sy_c_Product__Type_OPair_001t__Type__Oty_001t__Option__Ooption_It__Type__Oty_J, type,
    produc11991767ion_ty : ty > option_ty > produc192345759ion_ty).
thf(sy_c_Product__Type_OPair_001t__Type__Oty_001t__Type__Oty, type,
    product_Pair_ty_ty : ty > ty > product_prod_ty_ty).
thf(sy_c_Product__Type_OPair_001t__Type__Oty_001t__Value__Oval, type,
    product_Pair_ty_val : ty > val > product_prod_ty_val).
thf(sy_c_Product__Type_OPair_001t__Value__Oval_001t__List__Olist_It__String__Ochar_J, type,
    produc1336712314t_char : val > list_char > produc1259363010t_char).
thf(sy_c_Product__Type_OPair_001t__Value__Oval_001t__Option__Ooption_It__Type__Oty_J, type,
    produc597695520ion_ty : val > option_ty > produc821192552ion_ty).
thf(sy_c_Product__Type_OPair_001t__Value__Oval_001t__Type__Oty, type,
    product_Pair_val_ty : val > ty > product_prod_val_ty).
thf(sy_c_Product__Type_OPair_001t__Value__Oval_001t__Value__Oval, type,
    product_Pair_val_val : val > val > product_prod_val_val).
thf(sy_c_SmallStep_Oblocks, type,
    blocks : produc81045532t_char > exp_list_char).
thf(sy_c_TypeRel_Owiden_001t__Product____Type__Oprod_It__List__Olist_It__List__Olist_It__String__Ochar_J_J_Mt__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_J, type,
    widen_917054840t_char : list_P1234162913t_char > ty > ty > $o).
thf(sy_c_WellTypeRT_OWTrt, type,
    wTrt : list_P1234162913t_char > (nat > option2118145160on_val) > (list_char > option_ty) > exp_list_char > ty > $o).
thf(sy_c_member_001t__Product____Type__Oprod_I_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_M_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_J, type,
    member1177709994on_val : produc1335728385on_val > set_Pr1104486497on_val > $o).
thf(sy_c_member_001t__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_M_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_J, type,
    member652041809on_val : produc515445032on_val > set_Pr723149704on_val > $o).
thf(sy_c_member_001t__Product____Type__Oprod_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__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_J, type,
    member78096504on_val : produc1914020559on_val > set_Pr1465729071on_val > $o).
thf(sy_c_member_001t__Product____Type__Oprod_It__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_Mt__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_J, type,
    member1699993616t_char : produc677445863t_char > set_Pr224372167t_char > $o).
thf(sy_c_member_001t__Product____Type__Oprod_It__List__Olist_It__List__Olist_It__String__Ochar_J_J_Mt__List__Olist_It__List__Olist_It__String__Ochar_J_J_J, type,
    member725442668t_char : produc1410698691t_char > set_Pr2117892643t_char > $o).
thf(sy_c_member_001t__Product____Type__Oprod_It__List__Olist_It__List__Olist_It__String__Ochar_J_J_Mt__Product____Type__Oprod_It__List__Olist_It__Type__Oty_J_Mt__Product____Type__Oprod_It__List__Olist_It__Value__Oval_J_Mt__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_J_J_J, type,
    member772747827t_char : produc81045532t_char > set_Pr685054290t_char > $o).
thf(sy_c_member_001t__Product____Type__Oprod_It__List__Olist_It__Option__Ooption_It__Type__Oty_J_J_Mt__List__Olist_It__Option__Ooption_It__Type__Oty_J_J_J, type,
    member237105848ion_ty : produc922361871ion_ty > set_Pr962897519ion_ty > $o).
thf(sy_c_member_001t__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J, type,
    member89690956t_char : produc1257910179t_char > set_Pr164112643t_char > $o).
thf(sy_c_member_001t__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__Type__Oty_J, type,
    member325880354har_ty : produc2086909177har_ty > set_Pr349050585har_ty > $o).
thf(sy_c_member_001t__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__Value__Oval_J, type,
    member1062074475ar_val : produc892282818ar_val > set_Pr174107298ar_val > $o).
thf(sy_c_member_001t__Product____Type__Oprod_It__List__Olist_It__Type__Oty_J_Mt__List__Olist_It__Type__Oty_J_J, type,
    member1942114840ist_ty : produc1714969711ist_ty > set_Pr1785354703ist_ty > $o).
thf(sy_c_member_001t__Product____Type__Oprod_It__List__Olist_It__Type__Oty_J_Mt__Product____Type__Oprod_It__List__Olist_It__Value__Oval_J_Mt__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_J_J, type,
    member1031340033t_char : produc111478616t_char > set_Pr925902648t_char > $o).
thf(sy_c_member_001t__Product____Type__Oprod_It__List__Olist_It__Value__Oval_J_Mt__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_J, type,
    member580484423t_char : produc1109669680t_char > set_Pr82799206t_char > $o).
thf(sy_c_member_001t__Product____Type__Oprod_It__List__Olist_It__Value__Oval_J_Mt__List__Olist_It__Value__Oval_J_J, type,
    member1382006826st_val : produc1608520577st_val > set_Pr723931873st_val > $o).
thf(sy_c_member_001t__Product____Type__Oprod_It__Option__Ooption_It__Type__Oty_J_Mt__Option__Ooption_It__Type__Oty_J_J, type,
    member704321176ion_ty : produc1872540399ion_ty > set_Pr616941135ion_ty > $o).
thf(sy_c_member_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__List__Olist_It__Type__Oty_J_Mt__Product____Type__Oprod_It__List__Olist_It__Value__Oval_J_Mt__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_J_J_Mt__Product____Type__Oprod_It__List__Olist_It__Type__Oty_J_Mt__Product____Type__Oprod_It__List__Olist_It__Value__Oval_J_Mt__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_J_J_J, type,
    member219943760t_char : produc885582375t_char > set_Pr1314019591t_char > $o).
thf(sy_c_member_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__List__Olist_It__Value__Oval_J_Mt__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_J_Mt__Product____Type__Oprod_It__List__Olist_It__Value__Oval_J_Mt__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_J_J, type,
    member89029866t_char : produc1439662401t_char > set_Pr290014113t_char > $o).
thf(sy_c_member_001t__Product____Type__Oprod_It__Type__Oty_Mt__List__Olist_It__String__Ochar_J_J, type,
    member1016971042t_char : produc630516217t_char > set_Pr1320471513t_char > $o).
thf(sy_c_member_001t__Product____Type__Oprod_It__Type__Oty_Mt__Option__Ooption_It__Type__Oty_J_J, type,
    member578800584ion_ty : produc192345759ion_ty > set_Pr504292735ion_ty > $o).
thf(sy_c_member_001t__Product____Type__Oprod_It__Type__Oty_Mt__Type__Oty_J, type,
    member2070851320_ty_ty : product_prod_ty_ty > set_Pr1194734255_ty_ty > $o).
thf(sy_c_member_001t__Product____Type__Oprod_It__Type__Oty_Mt__Value__Oval_J, type,
    member1776226881ty_val : product_prod_ty_val > set_Pr1036794744ty_val > $o).
thf(sy_c_member_001t__Product____Type__Oprod_It__Value__Oval_Mt__List__Olist_It__String__Ochar_J_J, type,
    member1429154667t_char : produc1259363010t_char > set_Pr1557683618t_char > $o).
thf(sy_c_member_001t__Product____Type__Oprod_It__Value__Oval_Mt__Option__Ooption_It__Type__Oty_J_J, type,
    member990984209ion_ty : produc821192552ion_ty > set_Pr741504840ion_ty > $o).
thf(sy_c_member_001t__Product____Type__Oprod_It__Value__Oval_Mt__Type__Oty_J, type,
    member1400634561val_ty : product_prod_val_ty > set_Pr312206840val_ty > $o).
thf(sy_c_member_001t__Product____Type__Oprod_It__Value__Oval_Mt__Value__Oval_J, type,
    member1494223754al_val : product_prod_val_val > set_Pr1870322241al_val > $o).
thf(sy_v_E, type,
    e : list_char > option_ty).
thf(sy_v_P, type,
    p : list_P1234162913t_char).
thf(sy_v_T, type,
    t : ty).
thf(sy_v_Ta, type,
    ta : ty).
thf(sy_v_Tsa, type,
    tsa : list_ty).
thf(sy_v_V, type,
    v : list_char).
thf(sy_v_Vsa, type,
    vsa : list_list_char).
thf(sy_v_ea, type,
    ea : exp_list_char).
thf(sy_v_h, type,
    h : nat > option2118145160on_val).
thf(sy_v_v, type,
    v2 : val).
thf(sy_v_vsa, type,
    vsa2 : list_val).

% Relevant facts (248)
thf(fact_0_widens__Cons, axiom,
    ((![P : list_P1234162913t_char, X : ty, Xs : list_ty, Ys : list_ty]: ((list_all2_ty_ty @ (widen_917054840t_char @ P) @ (cons_ty @ X @ Xs) @ Ys) = (?[Z : ty]: (?[Zs : list_ty]: (((Ys = (cons_ty @ Z @ Zs))) & ((((widen_917054840t_char @ P @ X @ Z)) & ((list_all2_ty_ty @ (widen_917054840t_char @ P) @ Xs @ Zs))))))))))). % widens_Cons
thf(fact_1_widens__refl, axiom,
    ((![P : list_P1234162913t_char, Xs : list_ty]: (list_all2_ty_ty @ (widen_917054840t_char @ P) @ Xs @ Xs)))). % widens_refl
thf(fact_2_length__map, axiom,
    ((![F : ty > ty, Xs : list_ty]: ((size_size_list_ty @ (map_ty_ty @ F @ Xs)) = (size_size_list_ty @ Xs))))). % length_map
thf(fact_3_length__map, axiom,
    ((![F : val > ty, Xs : list_val]: ((size_size_list_ty @ (map_val_ty @ F @ Xs)) = (size_size_list_val @ Xs))))). % length_map
thf(fact_4_length__map, axiom,
    ((![F : ty > val, Xs : list_ty]: ((size_size_list_val @ (map_ty_val @ F @ Xs)) = (size_size_list_ty @ Xs))))). % length_map
thf(fact_5_length__map, axiom,
    ((![F : val > val, Xs : list_val]: ((size_size_list_val @ (map_val_val @ F @ Xs)) = (size_size_list_val @ Xs))))). % length_map
thf(fact_6_length__map, axiom,
    ((![F : ty > option_ty, Xs : list_ty]: ((size_s1569909163ion_ty @ (map_ty_option_ty @ F @ Xs)) = (size_size_list_ty @ Xs))))). % length_map
thf(fact_7_length__map, axiom,
    ((![F : val > option_ty, Xs : list_val]: ((size_s1569909163ion_ty @ (map_val_option_ty @ F @ Xs)) = (size_size_list_val @ Xs))))). % length_map
thf(fact_8_length__map, axiom,
    ((![F : ty > list_char, Xs : list_ty]: ((size_s2008079621t_char @ (map_ty_list_char @ F @ Xs)) = (size_size_list_ty @ Xs))))). % length_map
thf(fact_9_length__map, axiom,
    ((![F : val > list_char, Xs : list_val]: ((size_s2008079621t_char @ (map_val_list_char @ F @ Xs)) = (size_size_list_val @ Xs))))). % length_map
thf(fact_10_length__map, axiom,
    ((![F : list_char > ty, Xs : list_list_char]: ((size_size_list_ty @ (map_list_char_ty @ F @ Xs)) = (size_s2008079621t_char @ Xs))))). % length_map
thf(fact_11_length__map, axiom,
    ((![F : list_char > val, Xs : list_list_char]: ((size_size_list_val @ (map_list_char_val @ F @ Xs)) = (size_s2008079621t_char @ Xs))))). % length_map
thf(fact_12_Cons__eq__map__conv, axiom,
    ((![X : ty, Xs : list_ty, F : ty > ty, Ys : list_ty]: (((cons_ty @ X @ Xs) = (map_ty_ty @ F @ Ys)) = (?[Z : ty]: (?[Zs : list_ty]: (((Ys = (cons_ty @ Z @ Zs))) & ((((X = (F @ Z))) & ((Xs = (map_ty_ty @ F @ Zs)))))))))))). % Cons_eq_map_conv
thf(fact_13_Cons__eq__map__conv, axiom,
    ((![X : ty, Xs : list_ty, F : val > ty, Ys : list_val]: (((cons_ty @ X @ Xs) = (map_val_ty @ F @ Ys)) = (?[Z : val]: (?[Zs : list_val]: (((Ys = (cons_val @ Z @ Zs))) & ((((X = (F @ Z))) & ((Xs = (map_val_ty @ F @ Zs)))))))))))). % Cons_eq_map_conv
thf(fact_14_Cons__eq__map__conv, axiom,
    ((![X : val, Xs : list_val, F : ty > val, Ys : list_ty]: (((cons_val @ X @ Xs) = (map_ty_val @ F @ Ys)) = (?[Z : ty]: (?[Zs : list_ty]: (((Ys = (cons_ty @ Z @ Zs))) & ((((X = (F @ Z))) & ((Xs = (map_ty_val @ F @ Zs)))))))))))). % Cons_eq_map_conv
thf(fact_15_Cons__eq__map__conv, axiom,
    ((![X : val, Xs : list_val, F : val > val, Ys : list_val]: (((cons_val @ X @ Xs) = (map_val_val @ F @ Ys)) = (?[Z : val]: (?[Zs : list_val]: (((Ys = (cons_val @ Z @ Zs))) & ((((X = (F @ Z))) & ((Xs = (map_val_val @ F @ Zs)))))))))))). % Cons_eq_map_conv
thf(fact_16_Cons__eq__map__conv, axiom,
    ((![X : option_ty, Xs : list_option_ty, F : ty > option_ty, Ys : list_ty]: (((cons_option_ty @ X @ Xs) = (map_ty_option_ty @ F @ Ys)) = (?[Z : ty]: (?[Zs : list_ty]: (((Ys = (cons_ty @ Z @ Zs))) & ((((X = (F @ Z))) & ((Xs = (map_ty_option_ty @ F @ Zs)))))))))))). % Cons_eq_map_conv
thf(fact_17_Cons__eq__map__conv, axiom,
    ((![X : option_ty, Xs : list_option_ty, F : val > option_ty, Ys : list_val]: (((cons_option_ty @ X @ Xs) = (map_val_option_ty @ F @ Ys)) = (?[Z : val]: (?[Zs : list_val]: (((Ys = (cons_val @ Z @ Zs))) & ((((X = (F @ Z))) & ((Xs = (map_val_option_ty @ F @ Zs)))))))))))). % Cons_eq_map_conv
thf(fact_18_Cons__eq__map__conv, axiom,
    ((![X : list_char, Xs : list_list_char, F : ty > list_char, Ys : list_ty]: (((cons_list_char @ X @ Xs) = (map_ty_list_char @ F @ Ys)) = (?[Z : ty]: (?[Zs : list_ty]: (((Ys = (cons_ty @ Z @ Zs))) & ((((X = (F @ Z))) & ((Xs = (map_ty_list_char @ F @ Zs)))))))))))). % Cons_eq_map_conv
thf(fact_19_Cons__eq__map__conv, axiom,
    ((![X : list_char, Xs : list_list_char, F : val > list_char, Ys : list_val]: (((cons_list_char @ X @ Xs) = (map_val_list_char @ F @ Ys)) = (?[Z : val]: (?[Zs : list_val]: (((Ys = (cons_val @ Z @ Zs))) & ((((X = (F @ Z))) & ((Xs = (map_val_list_char @ F @ Zs)))))))))))). % Cons_eq_map_conv
thf(fact_20_Cons__eq__map__conv, axiom,
    ((![X : ty, Xs : list_ty, F : list_char > ty, Ys : list_list_char]: (((cons_ty @ X @ Xs) = (map_list_char_ty @ F @ Ys)) = (?[Z : list_char]: (?[Zs : list_list_char]: (((Ys = (cons_list_char @ Z @ Zs))) & ((((X = (F @ Z))) & ((Xs = (map_list_char_ty @ F @ Zs)))))))))))). % Cons_eq_map_conv
thf(fact_21_Cons__eq__map__conv, axiom,
    ((![X : val, Xs : list_val, F : list_char > val, Ys : list_list_char]: (((cons_val @ X @ Xs) = (map_list_char_val @ F @ Ys)) = (?[Z : list_char]: (?[Zs : list_list_char]: (((Ys = (cons_list_char @ Z @ Zs))) & ((((X = (F @ Z))) & ((Xs = (map_list_char_val @ F @ Zs)))))))))))). % Cons_eq_map_conv
thf(fact_22_prod__cases4, axiom,
    ((![Y : produc81045532t_char]: (~ ((![A : list_list_char, B : list_ty, C : list_val, D : exp_list_char]: (~ ((Y = (produc1808722894t_char @ A @ (produc1806338192t_char @ B @ (produc823987298t_char @ C @ D)))))))))))). % prod_cases4
thf(fact_23_prod__induct4, axiom,
    ((![P : produc81045532t_char > $o, X : produc81045532t_char]: ((![A : list_list_char, B : list_ty, C : list_val, D : exp_list_char]: (P @ (produc1808722894t_char @ A @ (produc1806338192t_char @ B @ (produc823987298t_char @ C @ D))))) => (P @ X))))). % prod_induct4
thf(fact_24_old_Oprod_Oinject, axiom,
    ((![A2 : list_list_char, B2 : produc111478616t_char, A3 : list_list_char, B3 : produc111478616t_char]: (((produc1808722894t_char @ A2 @ B2) = (produc1808722894t_char @ A3 @ B3)) = (((A2 = A3)) & ((B2 = B3))))))). % old.prod.inject
thf(fact_25_old_Oprod_Oinject, axiom,
    ((![A2 : list_ty, B2 : produc1109669680t_char, A3 : list_ty, B3 : produc1109669680t_char]: (((produc1806338192t_char @ A2 @ B2) = (produc1806338192t_char @ A3 @ B3)) = (((A2 = A3)) & ((B2 = B3))))))). % old.prod.inject
thf(fact_26_old_Oprod_Oinject, axiom,
    ((![A2 : list_val, B2 : exp_list_char, A3 : list_val, B3 : exp_list_char]: (((produc823987298t_char @ A2 @ B2) = (produc823987298t_char @ A3 @ B3)) = (((A2 = A3)) & ((B2 = B3))))))). % old.prod.inject
thf(fact_27_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_28_prod_Oinject, axiom,
    ((![X1 : list_list_char, X2 : produc111478616t_char, Y1 : list_list_char, Y2 : produc111478616t_char]: (((produc1808722894t_char @ X1 @ X2) = (produc1808722894t_char @ Y1 @ Y2)) = (((X1 = Y1)) & ((X2 = Y2))))))). % prod.inject
thf(fact_29_prod_Oinject, axiom,
    ((![X1 : list_ty, X2 : produc1109669680t_char, Y1 : list_ty, Y2 : produc1109669680t_char]: (((produc1806338192t_char @ X1 @ X2) = (produc1806338192t_char @ Y1 @ Y2)) = (((X1 = Y1)) & ((X2 = Y2))))))). % prod.inject
thf(fact_30_prod_Oinject, axiom,
    ((![X1 : list_val, X2 : exp_list_char, Y1 : list_val, Y2 : exp_list_char]: (((produc823987298t_char @ X1 @ X2) = (produc823987298t_char @ Y1 @ Y2)) = (((X1 = Y1)) & ((X2 = Y2))))))). % prod.inject
thf(fact_31_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_32_list_Oinject, axiom,
    ((![X21 : list_char, X22 : list_list_char, Y21 : list_char, Y22 : list_list_char]: (((cons_list_char @ X21 @ X22) = (cons_list_char @ Y21 @ Y22)) = (((X21 = Y21)) & ((X22 = Y22))))))). % list.inject
thf(fact_33_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_34_list_Oinject, axiom,
    ((![X21 : val, X22 : list_val, Y21 : val, Y22 : list_val]: (((cons_val @ X21 @ X22) = (cons_val @ Y21 @ Y22)) = (((X21 = Y21)) & ((X22 = Y22))))))). % list.inject
thf(fact_35_list_Oinject, axiom,
    ((![X21 : option_ty, X22 : list_option_ty, Y21 : option_ty, Y22 : list_option_ty]: (((cons_option_ty @ X21 @ X22) = (cons_option_ty @ Y21 @ Y22)) = (((X21 = Y21)) & ((X22 = Y22))))))). % list.inject
thf(fact_36_old_Oprod_Oinducts, axiom,
    ((![P : produc81045532t_char > $o, Prod : produc81045532t_char]: ((![A : list_list_char, B : produc111478616t_char]: (P @ (produc1808722894t_char @ A @ B))) => (P @ Prod))))). % old.prod.inducts
thf(fact_37_old_Oprod_Oinducts, axiom,
    ((![P : produc111478616t_char > $o, Prod : produc111478616t_char]: ((![A : list_ty, B : produc1109669680t_char]: (P @ (produc1806338192t_char @ A @ B))) => (P @ Prod))))). % old.prod.inducts
thf(fact_38_old_Oprod_Oinducts, axiom,
    ((![P : produc1109669680t_char > $o, Prod : produc1109669680t_char]: ((![A : list_val, B : exp_list_char]: (P @ (produc823987298t_char @ A @ B))) => (P @ Prod))))). % old.prod.inducts
thf(fact_39_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_40_old_Oprod_Oexhaust, axiom,
    ((![Y : produc81045532t_char]: (~ ((![A : list_list_char, B : produc111478616t_char]: (~ ((Y = (produc1808722894t_char @ A @ B)))))))))). % old.prod.exhaust
thf(fact_41_old_Oprod_Oexhaust, axiom,
    ((![Y : produc111478616t_char]: (~ ((![A : list_ty, B : produc1109669680t_char]: (~ ((Y = (produc1806338192t_char @ A @ B)))))))))). % old.prod.exhaust
thf(fact_42_old_Oprod_Oexhaust, axiom,
    ((![Y : produc1109669680t_char]: (~ ((![A : list_val, B : exp_list_char]: (~ ((Y = (produc823987298t_char @ A @ B)))))))))). % old.prod.exhaust
thf(fact_43_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_44_Pair__inject, axiom,
    ((![A2 : list_list_char, B2 : produc111478616t_char, A3 : list_list_char, B3 : produc111478616t_char]: (((produc1808722894t_char @ A2 @ B2) = (produc1808722894t_char @ A3 @ B3)) => (~ (((A2 = A3) => (~ ((B2 = B3)))))))))). % Pair_inject
thf(fact_45_Pair__inject, axiom,
    ((![A2 : list_ty, B2 : produc1109669680t_char, A3 : list_ty, B3 : produc1109669680t_char]: (((produc1806338192t_char @ A2 @ B2) = (produc1806338192t_char @ A3 @ B3)) => (~ (((A2 = A3) => (~ ((B2 = B3)))))))))). % Pair_inject
thf(fact_46_Pair__inject, axiom,
    ((![A2 : list_val, B2 : exp_list_char, A3 : list_val, B3 : exp_list_char]: (((produc823987298t_char @ A2 @ B2) = (produc823987298t_char @ A3 @ B3)) => (~ (((A2 = A3) => (~ ((B2 = B3)))))))))). % Pair_inject
thf(fact_47_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_48_prod__cases, axiom,
    ((![P : produc81045532t_char > $o, P2 : produc81045532t_char]: ((![A : list_list_char, B : produc111478616t_char]: (P @ (produc1808722894t_char @ A @ B))) => (P @ P2))))). % prod_cases
thf(fact_49_prod__cases, axiom,
    ((![P : produc111478616t_char > $o, P2 : produc111478616t_char]: ((![A : list_ty, B : produc1109669680t_char]: (P @ (produc1806338192t_char @ A @ B))) => (P @ P2))))). % prod_cases
thf(fact_50_prod__cases, axiom,
    ((![P : produc1109669680t_char > $o, P2 : produc1109669680t_char]: ((![A : list_val, B : exp_list_char]: (P @ (produc823987298t_char @ A @ B))) => (P @ P2))))). % prod_cases
thf(fact_51_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_52_surj__pair, axiom,
    ((![P2 : produc81045532t_char]: (?[X3 : list_list_char, Y3 : produc111478616t_char]: (P2 = (produc1808722894t_char @ X3 @ Y3)))))). % surj_pair
thf(fact_53_surj__pair, axiom,
    ((![P2 : produc111478616t_char]: (?[X3 : list_ty, Y3 : produc1109669680t_char]: (P2 = (produc1806338192t_char @ X3 @ Y3)))))). % surj_pair
thf(fact_54_surj__pair, axiom,
    ((![P2 : produc1109669680t_char]: (?[X3 : list_val, Y3 : exp_list_char]: (P2 = (produc823987298t_char @ X3 @ Y3)))))). % surj_pair
thf(fact_55_surj__pair, axiom,
    ((![P2 : produc515445032on_val]: (?[X3 : nat > option2118145160on_val, Y3 : list_char > option_val]: (P2 = (produc52622304on_val @ X3 @ Y3)))))). % surj_pair
thf(fact_56_not__Cons__self2, axiom,
    ((![X : list_char, Xs : list_list_char]: (~ (((cons_list_char @ X @ Xs) = Xs)))))). % not_Cons_self2
thf(fact_57_not__Cons__self2, axiom,
    ((![X : ty, Xs : list_ty]: (~ (((cons_ty @ X @ Xs) = Xs)))))). % not_Cons_self2
thf(fact_58_not__Cons__self2, axiom,
    ((![X : val, Xs : list_val]: (~ (((cons_val @ X @ Xs) = Xs)))))). % not_Cons_self2
thf(fact_59_not__Cons__self2, axiom,
    ((![X : option_ty, Xs : list_option_ty]: (~ (((cons_option_ty @ X @ Xs) = Xs)))))). % not_Cons_self2
thf(fact_60_neq__if__length__neq, axiom,
    ((![Xs : list_list_char, Ys : list_list_char]: ((~ (((size_s2008079621t_char @ Xs) = (size_s2008079621t_char @ Ys)))) => (~ ((Xs = Ys))))))). % neq_if_length_neq
thf(fact_61_neq__if__length__neq, axiom,
    ((![Xs : list_ty, Ys : list_ty]: ((~ (((size_size_list_ty @ Xs) = (size_size_list_ty @ Ys)))) => (~ ((Xs = Ys))))))). % neq_if_length_neq
thf(fact_62_neq__if__length__neq, axiom,
    ((![Xs : list_val, Ys : list_val]: ((~ (((size_size_list_val @ Xs) = (size_size_list_val @ Ys)))) => (~ ((Xs = Ys))))))). % neq_if_length_neq
thf(fact_63_neq__if__length__neq, axiom,
    ((![Xs : list_option_ty, Ys : list_option_ty]: ((~ (((size_s1569909163ion_ty @ Xs) = (size_s1569909163ion_ty @ Ys)))) => (~ ((Xs = Ys))))))). % neq_if_length_neq
thf(fact_64_Ex__list__of__length, axiom,
    ((![N : nat]: (?[Xs2 : list_list_char]: ((size_s2008079621t_char @ Xs2) = N))))). % Ex_list_of_length
thf(fact_65_Ex__list__of__length, axiom,
    ((![N : nat]: (?[Xs2 : list_ty]: ((size_size_list_ty @ Xs2) = N))))). % Ex_list_of_length
thf(fact_66_Ex__list__of__length, axiom,
    ((![N : nat]: (?[Xs2 : list_val]: ((size_size_list_val @ Xs2) = N))))). % Ex_list_of_length
thf(fact_67_Ex__list__of__length, axiom,
    ((![N : nat]: (?[Xs2 : list_option_ty]: ((size_s1569909163ion_ty @ Xs2) = N))))). % Ex_list_of_length
thf(fact_68_list_Orel__refl, axiom,
    ((![Ra : ty > ty > $o, X : list_ty]: ((![X3 : ty]: (Ra @ X3 @ X3)) => (list_all2_ty_ty @ Ra @ X @ X))))). % list.rel_refl
thf(fact_69_list__all2__antisym, axiom,
    ((![P : ty > ty > $o, Q : ty > ty > $o, Xs : list_ty, Ys : list_ty]: ((![X3 : ty, Y3 : ty]: ((P @ X3 @ Y3) => ((Q @ Y3 @ X3) => (X3 = Y3)))) => ((list_all2_ty_ty @ P @ Xs @ Ys) => ((list_all2_ty_ty @ Q @ Ys @ Xs) => (Xs = Ys))))))). % list_all2_antisym
thf(fact_70_list_Orel__eq, axiom,
    (((list_all2_ty_ty @ (^[Y4 : ty]: (^[Z2 : ty]: (Y4 = Z2)))) = (^[Y4 : list_ty]: (^[Z2 : list_ty]: (Y4 = Z2)))))). % list.rel_eq
thf(fact_71_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_72_list__all2__refl, axiom,
    ((![P : ty > ty > $o, Xs : list_ty]: ((![X3 : ty]: (P @ X3 @ X3)) => (list_all2_ty_ty @ P @ Xs @ Xs))))). % list_all2_refl
thf(fact_73_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_74_list__all2__eq, axiom,
    (((^[Y4 : list_ty]: (^[Z2 : list_ty]: (Y4 = Z2))) = (list_all2_ty_ty @ (^[Y4 : ty]: (^[Z2 : ty]: (Y4 = Z2))))))). % list_all2_eq
thf(fact_75_widen__refl, axiom,
    ((![P : list_P1234162913t_char, T : ty]: (widen_917054840t_char @ P @ T @ T)))). % widen_refl
thf(fact_76_widen__trans, axiom,
    ((![P : list_P1234162913t_char, S : ty, U : ty, T : ty]: ((widen_917054840t_char @ P @ S @ U) => ((widen_917054840t_char @ P @ U @ T) => (widen_917054840t_char @ P @ S @ T)))))). % widen_trans
thf(fact_77_prod__induct3, axiom,
    ((![P : produc81045532t_char > $o, X : produc81045532t_char]: ((![A : list_list_char, B : list_ty, C : produc1109669680t_char]: (P @ (produc1808722894t_char @ A @ (produc1806338192t_char @ B @ C)))) => (P @ X))))). % prod_induct3
thf(fact_78_prod__induct3, axiom,
    ((![P : produc111478616t_char > $o, X : produc111478616t_char]: ((![A : list_ty, B : list_val, C : exp_list_char]: (P @ (produc1806338192t_char @ A @ (produc823987298t_char @ B @ C)))) => (P @ X))))). % prod_induct3
thf(fact_79_prod__cases3, axiom,
    ((![Y : produc81045532t_char]: (~ ((![A : list_list_char, B : list_ty, C : produc1109669680t_char]: (~ ((Y = (produc1808722894t_char @ A @ (produc1806338192t_char @ B @ C))))))))))). % prod_cases3
thf(fact_80_prod__cases3, axiom,
    ((![Y : produc111478616t_char]: (~ ((![A : list_ty, B : list_val, C : exp_list_char]: (~ ((Y = (produc1806338192t_char @ A @ (produc823987298t_char @ B @ C))))))))))). % prod_cases3
thf(fact_81_map__eq__Cons__conv, axiom,
    ((![F : ty > ty, Xs : list_ty, Y : ty, Ys : list_ty]: (((map_ty_ty @ F @ Xs) = (cons_ty @ Y @ Ys)) = (?[Z : ty]: (?[Zs : list_ty]: (((Xs = (cons_ty @ Z @ Zs))) & (((((F @ Z) = Y)) & (((map_ty_ty @ F @ Zs) = Ys))))))))))). % map_eq_Cons_conv
thf(fact_82_map__eq__Cons__conv, axiom,
    ((![F : val > ty, Xs : list_val, Y : ty, Ys : list_ty]: (((map_val_ty @ F @ Xs) = (cons_ty @ Y @ Ys)) = (?[Z : val]: (?[Zs : list_val]: (((Xs = (cons_val @ Z @ Zs))) & (((((F @ Z) = Y)) & (((map_val_ty @ F @ Zs) = Ys))))))))))). % map_eq_Cons_conv
thf(fact_83_map__eq__Cons__conv, axiom,
    ((![F : ty > val, Xs : list_ty, Y : val, Ys : list_val]: (((map_ty_val @ F @ Xs) = (cons_val @ Y @ Ys)) = (?[Z : ty]: (?[Zs : list_ty]: (((Xs = (cons_ty @ Z @ Zs))) & (((((F @ Z) = Y)) & (((map_ty_val @ F @ Zs) = Ys))))))))))). % map_eq_Cons_conv
thf(fact_84_map__eq__Cons__conv, axiom,
    ((![F : val > val, Xs : list_val, Y : val, Ys : list_val]: (((map_val_val @ F @ Xs) = (cons_val @ Y @ Ys)) = (?[Z : val]: (?[Zs : list_val]: (((Xs = (cons_val @ Z @ Zs))) & (((((F @ Z) = Y)) & (((map_val_val @ F @ Zs) = Ys))))))))))). % map_eq_Cons_conv
thf(fact_85_map__eq__Cons__conv, axiom,
    ((![F : ty > list_char, Xs : list_ty, Y : list_char, Ys : list_list_char]: (((map_ty_list_char @ F @ Xs) = (cons_list_char @ Y @ Ys)) = (?[Z : ty]: (?[Zs : list_ty]: (((Xs = (cons_ty @ Z @ Zs))) & (((((F @ Z) = Y)) & (((map_ty_list_char @ F @ Zs) = Ys))))))))))). % map_eq_Cons_conv
thf(fact_86_map__eq__Cons__conv, axiom,
    ((![F : val > list_char, Xs : list_val, Y : list_char, Ys : list_list_char]: (((map_val_list_char @ F @ Xs) = (cons_list_char @ Y @ Ys)) = (?[Z : val]: (?[Zs : list_val]: (((Xs = (cons_val @ Z @ Zs))) & (((((F @ Z) = Y)) & (((map_val_list_char @ F @ Zs) = Ys))))))))))). % map_eq_Cons_conv
thf(fact_87_map__eq__Cons__conv, axiom,
    ((![F : list_char > ty, Xs : list_list_char, Y : ty, Ys : list_ty]: (((map_list_char_ty @ F @ Xs) = (cons_ty @ Y @ Ys)) = (?[Z : list_char]: (?[Zs : list_list_char]: (((Xs = (cons_list_char @ Z @ Zs))) & (((((F @ Z) = Y)) & (((map_list_char_ty @ F @ Zs) = Ys))))))))))). % map_eq_Cons_conv
thf(fact_88_map__eq__Cons__conv, axiom,
    ((![F : option_ty > ty, Xs : list_option_ty, Y : ty, Ys : list_ty]: (((map_option_ty_ty @ F @ Xs) = (cons_ty @ Y @ Ys)) = (?[Z : option_ty]: (?[Zs : list_option_ty]: (((Xs = (cons_option_ty @ Z @ Zs))) & (((((F @ Z) = Y)) & (((map_option_ty_ty @ F @ Zs) = Ys))))))))))). % map_eq_Cons_conv
thf(fact_89_map__eq__Cons__conv, axiom,
    ((![F : list_char > val, Xs : list_list_char, Y : val, Ys : list_val]: (((map_list_char_val @ F @ Xs) = (cons_val @ Y @ Ys)) = (?[Z : list_char]: (?[Zs : list_list_char]: (((Xs = (cons_list_char @ Z @ Zs))) & (((((F @ Z) = Y)) & (((map_list_char_val @ F @ Zs) = Ys))))))))))). % map_eq_Cons_conv
thf(fact_90_map__eq__Cons__conv, axiom,
    ((![F : option_ty > val, Xs : list_option_ty, Y : val, Ys : list_val]: (((map_option_ty_val @ F @ Xs) = (cons_val @ Y @ Ys)) = (?[Z : option_ty]: (?[Zs : list_option_ty]: (((Xs = (cons_option_ty @ Z @ Zs))) & (((((F @ Z) = Y)) & (((map_option_ty_val @ F @ Zs) = Ys))))))))))). % map_eq_Cons_conv
thf(fact_91_map__eq__Cons__D, axiom,
    ((![F : ty > ty, Xs : list_ty, Y : ty, Ys : list_ty]: (((map_ty_ty @ F @ Xs) = (cons_ty @ Y @ Ys)) => (?[Z3 : ty, Zs2 : list_ty]: ((Xs = (cons_ty @ Z3 @ Zs2)) & (((F @ Z3) = Y) & ((map_ty_ty @ F @ Zs2) = Ys)))))))). % map_eq_Cons_D
thf(fact_92_map__eq__Cons__D, axiom,
    ((![F : val > ty, Xs : list_val, Y : ty, Ys : list_ty]: (((map_val_ty @ F @ Xs) = (cons_ty @ Y @ Ys)) => (?[Z3 : val, Zs2 : list_val]: ((Xs = (cons_val @ Z3 @ Zs2)) & (((F @ Z3) = Y) & ((map_val_ty @ F @ Zs2) = Ys)))))))). % map_eq_Cons_D
thf(fact_93_map__eq__Cons__D, axiom,
    ((![F : ty > val, Xs : list_ty, Y : val, Ys : list_val]: (((map_ty_val @ F @ Xs) = (cons_val @ Y @ Ys)) => (?[Z3 : ty, Zs2 : list_ty]: ((Xs = (cons_ty @ Z3 @ Zs2)) & (((F @ Z3) = Y) & ((map_ty_val @ F @ Zs2) = Ys)))))))). % map_eq_Cons_D
thf(fact_94_map__eq__Cons__D, axiom,
    ((![F : val > val, Xs : list_val, Y : val, Ys : list_val]: (((map_val_val @ F @ Xs) = (cons_val @ Y @ Ys)) => (?[Z3 : val, Zs2 : list_val]: ((Xs = (cons_val @ Z3 @ Zs2)) & (((F @ Z3) = Y) & ((map_val_val @ F @ Zs2) = Ys)))))))). % map_eq_Cons_D
thf(fact_95_map__eq__Cons__D, axiom,
    ((![F : ty > list_char, Xs : list_ty, Y : list_char, Ys : list_list_char]: (((map_ty_list_char @ F @ Xs) = (cons_list_char @ Y @ Ys)) => (?[Z3 : ty, Zs2 : list_ty]: ((Xs = (cons_ty @ Z3 @ Zs2)) & (((F @ Z3) = Y) & ((map_ty_list_char @ F @ Zs2) = Ys)))))))). % map_eq_Cons_D
thf(fact_96_map__eq__Cons__D, axiom,
    ((![F : val > list_char, Xs : list_val, Y : list_char, Ys : list_list_char]: (((map_val_list_char @ F @ Xs) = (cons_list_char @ Y @ Ys)) => (?[Z3 : val, Zs2 : list_val]: ((Xs = (cons_val @ Z3 @ Zs2)) & (((F @ Z3) = Y) & ((map_val_list_char @ F @ Zs2) = Ys)))))))). % map_eq_Cons_D
thf(fact_97_map__eq__Cons__D, axiom,
    ((![F : list_char > ty, Xs : list_list_char, Y : ty, Ys : list_ty]: (((map_list_char_ty @ F @ Xs) = (cons_ty @ Y @ Ys)) => (?[Z3 : list_char, Zs2 : list_list_char]: ((Xs = (cons_list_char @ Z3 @ Zs2)) & (((F @ Z3) = Y) & ((map_list_char_ty @ F @ Zs2) = Ys)))))))). % map_eq_Cons_D
thf(fact_98_map__eq__Cons__D, axiom,
    ((![F : option_ty > ty, Xs : list_option_ty, Y : ty, Ys : list_ty]: (((map_option_ty_ty @ F @ Xs) = (cons_ty @ Y @ Ys)) => (?[Z3 : option_ty, Zs2 : list_option_ty]: ((Xs = (cons_option_ty @ Z3 @ Zs2)) & (((F @ Z3) = Y) & ((map_option_ty_ty @ F @ Zs2) = Ys)))))))). % map_eq_Cons_D
thf(fact_99_map__eq__Cons__D, axiom,
    ((![F : list_char > val, Xs : list_list_char, Y : val, Ys : list_val]: (((map_list_char_val @ F @ Xs) = (cons_val @ Y @ Ys)) => (?[Z3 : list_char, Zs2 : list_list_char]: ((Xs = (cons_list_char @ Z3 @ Zs2)) & (((F @ Z3) = Y) & ((map_list_char_val @ F @ Zs2) = Ys)))))))). % map_eq_Cons_D
thf(fact_100_map__eq__Cons__D, axiom,
    ((![F : option_ty > val, Xs : list_option_ty, Y : val, Ys : list_val]: (((map_option_ty_val @ F @ Xs) = (cons_val @ Y @ Ys)) => (?[Z3 : option_ty, Zs2 : list_option_ty]: ((Xs = (cons_option_ty @ Z3 @ Zs2)) & (((F @ Z3) = Y) & ((map_option_ty_val @ F @ Zs2) = Ys)))))))). % map_eq_Cons_D
thf(fact_101_Cons__eq__map__D, axiom,
    ((![X : ty, Xs : list_ty, F : ty > ty, Ys : list_ty]: (((cons_ty @ X @ Xs) = (map_ty_ty @ F @ Ys)) => (?[Z3 : ty, Zs2 : list_ty]: ((Ys = (cons_ty @ Z3 @ Zs2)) & ((X = (F @ Z3)) & (Xs = (map_ty_ty @ F @ Zs2))))))))). % Cons_eq_map_D
thf(fact_102_Cons__eq__map__D, axiom,
    ((![X : ty, Xs : list_ty, F : val > ty, Ys : list_val]: (((cons_ty @ X @ Xs) = (map_val_ty @ F @ Ys)) => (?[Z3 : val, Zs2 : list_val]: ((Ys = (cons_val @ Z3 @ Zs2)) & ((X = (F @ Z3)) & (Xs = (map_val_ty @ F @ Zs2))))))))). % Cons_eq_map_D
thf(fact_103_Cons__eq__map__D, axiom,
    ((![X : val, Xs : list_val, F : ty > val, Ys : list_ty]: (((cons_val @ X @ Xs) = (map_ty_val @ F @ Ys)) => (?[Z3 : ty, Zs2 : list_ty]: ((Ys = (cons_ty @ Z3 @ Zs2)) & ((X = (F @ Z3)) & (Xs = (map_ty_val @ F @ Zs2))))))))). % Cons_eq_map_D
thf(fact_104_Cons__eq__map__D, axiom,
    ((![X : val, Xs : list_val, F : val > val, Ys : list_val]: (((cons_val @ X @ Xs) = (map_val_val @ F @ Ys)) => (?[Z3 : val, Zs2 : list_val]: ((Ys = (cons_val @ Z3 @ Zs2)) & ((X = (F @ Z3)) & (Xs = (map_val_val @ F @ Zs2))))))))). % Cons_eq_map_D
thf(fact_105_Cons__eq__map__D, axiom,
    ((![X : list_char, Xs : list_list_char, F : ty > list_char, Ys : list_ty]: (((cons_list_char @ X @ Xs) = (map_ty_list_char @ F @ Ys)) => (?[Z3 : ty, Zs2 : list_ty]: ((Ys = (cons_ty @ Z3 @ Zs2)) & ((X = (F @ Z3)) & (Xs = (map_ty_list_char @ F @ Zs2))))))))). % Cons_eq_map_D
thf(fact_106_Cons__eq__map__D, axiom,
    ((![X : list_char, Xs : list_list_char, F : val > list_char, Ys : list_val]: (((cons_list_char @ X @ Xs) = (map_val_list_char @ F @ Ys)) => (?[Z3 : val, Zs2 : list_val]: ((Ys = (cons_val @ Z3 @ Zs2)) & ((X = (F @ Z3)) & (Xs = (map_val_list_char @ F @ Zs2))))))))). % Cons_eq_map_D
thf(fact_107_Cons__eq__map__D, axiom,
    ((![X : ty, Xs : list_ty, F : list_char > ty, Ys : list_list_char]: (((cons_ty @ X @ Xs) = (map_list_char_ty @ F @ Ys)) => (?[Z3 : list_char, Zs2 : list_list_char]: ((Ys = (cons_list_char @ Z3 @ Zs2)) & ((X = (F @ Z3)) & (Xs = (map_list_char_ty @ F @ Zs2))))))))). % Cons_eq_map_D
thf(fact_108_Cons__eq__map__D, axiom,
    ((![X : ty, Xs : list_ty, F : option_ty > ty, Ys : list_option_ty]: (((cons_ty @ X @ Xs) = (map_option_ty_ty @ F @ Ys)) => (?[Z3 : option_ty, Zs2 : list_option_ty]: ((Ys = (cons_option_ty @ Z3 @ Zs2)) & ((X = (F @ Z3)) & (Xs = (map_option_ty_ty @ F @ Zs2))))))))). % Cons_eq_map_D
thf(fact_109_Cons__eq__map__D, axiom,
    ((![X : val, Xs : list_val, F : list_char > val, Ys : list_list_char]: (((cons_val @ X @ Xs) = (map_list_char_val @ F @ Ys)) => (?[Z3 : list_char, Zs2 : list_list_char]: ((Ys = (cons_list_char @ Z3 @ Zs2)) & ((X = (F @ Z3)) & (Xs = (map_list_char_val @ F @ Zs2))))))))). % Cons_eq_map_D
thf(fact_110_Cons__eq__map__D, axiom,
    ((![X : val, Xs : list_val, F : option_ty > val, Ys : list_option_ty]: (((cons_val @ X @ Xs) = (map_option_ty_val @ F @ Ys)) => (?[Z3 : option_ty, Zs2 : list_option_ty]: ((Ys = (cons_option_ty @ Z3 @ Zs2)) & ((X = (F @ Z3)) & (Xs = (map_option_ty_val @ F @ Zs2))))))))). % Cons_eq_map_D
thf(fact_111_list_Osimps_I9_J, axiom,
    ((![F : ty > ty, X21 : ty, X22 : list_ty]: ((map_ty_ty @ F @ (cons_ty @ X21 @ X22)) = (cons_ty @ (F @ X21) @ (map_ty_ty @ F @ X22)))))). % list.simps(9)
thf(fact_112_list_Osimps_I9_J, axiom,
    ((![F : ty > val, X21 : ty, X22 : list_ty]: ((map_ty_val @ F @ (cons_ty @ X21 @ X22)) = (cons_val @ (F @ X21) @ (map_ty_val @ F @ X22)))))). % list.simps(9)
thf(fact_113_list_Osimps_I9_J, axiom,
    ((![F : val > ty, X21 : val, X22 : list_val]: ((map_val_ty @ F @ (cons_val @ X21 @ X22)) = (cons_ty @ (F @ X21) @ (map_val_ty @ F @ X22)))))). % list.simps(9)
thf(fact_114_list_Osimps_I9_J, axiom,
    ((![F : val > val, X21 : val, X22 : list_val]: ((map_val_val @ F @ (cons_val @ X21 @ X22)) = (cons_val @ (F @ X21) @ (map_val_val @ F @ X22)))))). % list.simps(9)
thf(fact_115_list_Osimps_I9_J, axiom,
    ((![F : list_char > ty, X21 : list_char, X22 : list_list_char]: ((map_list_char_ty @ F @ (cons_list_char @ X21 @ X22)) = (cons_ty @ (F @ X21) @ (map_list_char_ty @ F @ X22)))))). % list.simps(9)
thf(fact_116_list_Osimps_I9_J, axiom,
    ((![F : list_char > val, X21 : list_char, X22 : list_list_char]: ((map_list_char_val @ F @ (cons_list_char @ X21 @ X22)) = (cons_val @ (F @ X21) @ (map_list_char_val @ F @ X22)))))). % list.simps(9)
thf(fact_117_list_Osimps_I9_J, axiom,
    ((![F : ty > list_char, X21 : ty, X22 : list_ty]: ((map_ty_list_char @ F @ (cons_ty @ X21 @ X22)) = (cons_list_char @ (F @ X21) @ (map_ty_list_char @ F @ X22)))))). % list.simps(9)
thf(fact_118_list_Osimps_I9_J, axiom,
    ((![F : ty > option_ty, X21 : ty, X22 : list_ty]: ((map_ty_option_ty @ F @ (cons_ty @ X21 @ X22)) = (cons_option_ty @ (F @ X21) @ (map_ty_option_ty @ F @ X22)))))). % list.simps(9)
thf(fact_119_list_Osimps_I9_J, axiom,
    ((![F : val > list_char, X21 : val, X22 : list_val]: ((map_val_list_char @ F @ (cons_val @ X21 @ X22)) = (cons_list_char @ (F @ X21) @ (map_val_list_char @ F @ X22)))))). % list.simps(9)
thf(fact_120_list_Osimps_I9_J, axiom,
    ((![F : val > option_ty, X21 : val, X22 : list_val]: ((map_val_option_ty @ F @ (cons_val @ X21 @ X22)) = (cons_option_ty @ (F @ X21) @ (map_val_option_ty @ F @ X22)))))). % list.simps(9)
thf(fact_121_list__all2__Cons2, axiom,
    ((![P : val > ty > $o, Xs : list_val, Y : ty, Ys : list_ty]: ((list_all2_val_ty @ P @ Xs @ (cons_ty @ Y @ Ys)) = (?[Z : val]: (?[Zs : list_val]: (((Xs = (cons_val @ Z @ Zs))) & ((((P @ Z @ Y)) & ((list_all2_val_ty @ P @ Zs @ Ys))))))))))). % list_all2_Cons2
thf(fact_122_list__all2__Cons2, axiom,
    ((![P : ty > val > $o, Xs : list_ty, Y : val, Ys : list_val]: ((list_all2_ty_val @ P @ Xs @ (cons_val @ Y @ Ys)) = (?[Z : ty]: (?[Zs : list_ty]: (((Xs = (cons_ty @ Z @ Zs))) & ((((P @ Z @ Y)) & ((list_all2_ty_val @ P @ Zs @ Ys))))))))))). % list_all2_Cons2
thf(fact_123_list__all2__Cons2, axiom,
    ((![P : val > val > $o, Xs : list_val, Y : val, Ys : list_val]: ((list_all2_val_val @ P @ Xs @ (cons_val @ Y @ Ys)) = (?[Z : val]: (?[Zs : list_val]: (((Xs = (cons_val @ Z @ Zs))) & ((((P @ Z @ Y)) & ((list_all2_val_val @ P @ Zs @ Ys))))))))))). % list_all2_Cons2
thf(fact_124_list__all2__Cons2, axiom,
    ((![P : ty > ty > $o, Xs : list_ty, Y : ty, Ys : list_ty]: ((list_all2_ty_ty @ P @ Xs @ (cons_ty @ Y @ Ys)) = (?[Z : ty]: (?[Zs : list_ty]: (((Xs = (cons_ty @ Z @ Zs))) & ((((P @ Z @ Y)) & ((list_all2_ty_ty @ P @ Zs @ Ys))))))))))). % list_all2_Cons2
thf(fact_125_list__all2__Cons2, axiom,
    ((![P : ty > list_char > $o, Xs : list_ty, Y : list_char, Ys : list_list_char]: ((list_a1504214817t_char @ P @ Xs @ (cons_list_char @ Y @ Ys)) = (?[Z : ty]: (?[Zs : list_ty]: (((Xs = (cons_ty @ Z @ Zs))) & ((((P @ Z @ Y)) & ((list_a1504214817t_char @ P @ Zs @ Ys))))))))))). % list_all2_Cons2
thf(fact_126_list__all2__Cons2, axiom,
    ((![P : val > list_char > $o, Xs : list_val, Y : list_char, Ys : list_list_char]: ((list_a1248766058t_char @ P @ Xs @ (cons_list_char @ Y @ Ys)) = (?[Z : val]: (?[Zs : list_val]: (((Xs = (cons_val @ Z @ Zs))) & ((((P @ Z @ Y)) & ((list_a1248766058t_char @ P @ Zs @ Ys))))))))))). % list_all2_Cons2
thf(fact_127_list__all2__Cons2, axiom,
    ((![P : list_char > ty > $o, Xs : list_list_char, Y : ty, Ys : list_ty]: ((list_a1770748705har_ty @ P @ Xs @ (cons_ty @ Y @ Ys)) = (?[Z : list_char]: (?[Zs : list_list_char]: (((Xs = (cons_list_char @ Z @ Zs))) & ((((P @ Z @ Y)) & ((list_a1770748705har_ty @ P @ Zs @ Ys))))))))))). % list_all2_Cons2
thf(fact_128_list__all2__Cons2, axiom,
    ((![P : option_ty > ty > $o, Xs : list_option_ty, Y : ty, Ys : list_ty]: ((list_a1442669255_ty_ty @ P @ Xs @ (cons_ty @ Y @ Ys)) = (?[Z : option_ty]: (?[Zs : list_option_ty]: (((Xs = (cons_option_ty @ Z @ Zs))) & ((((P @ Z @ Y)) & ((list_a1442669255_ty_ty @ P @ Zs @ Ys))))))))))). % list_all2_Cons2
thf(fact_129_list__all2__Cons2, axiom,
    ((![P : list_char > val > $o, Xs : list_list_char, Y : val, Ys : list_val]: ((list_a280217834ar_val @ P @ Xs @ (cons_val @ Y @ Ys)) = (?[Z : list_char]: (?[Zs : list_list_char]: (((Xs = (cons_list_char @ Z @ Zs))) & ((((P @ Z @ Y)) & ((list_a280217834ar_val @ P @ Zs @ Ys))))))))))). % list_all2_Cons2
thf(fact_130_list__all2__Cons2, axiom,
    ((![P : option_ty > val > $o, Xs : list_option_ty, Y : val, Ys : list_val]: ((list_a1717583248ty_val @ P @ Xs @ (cons_val @ Y @ Ys)) = (?[Z : option_ty]: (?[Zs : list_option_ty]: (((Xs = (cons_option_ty @ Z @ Zs))) & ((((P @ Z @ Y)) & ((list_a1717583248ty_val @ P @ Zs @ Ys))))))))))). % list_all2_Cons2
thf(fact_131_list__all2__Cons1, axiom,
    ((![P : ty > val > $o, X : ty, Xs : list_ty, Ys : list_val]: ((list_all2_ty_val @ P @ (cons_ty @ X @ Xs) @ Ys) = (?[Z : val]: (?[Zs : list_val]: (((Ys = (cons_val @ Z @ Zs))) & ((((P @ X @ Z)) & ((list_all2_ty_val @ P @ Xs @ Zs))))))))))). % list_all2_Cons1
thf(fact_132_list__all2__Cons1, axiom,
    ((![P : val > ty > $o, X : val, Xs : list_val, Ys : list_ty]: ((list_all2_val_ty @ P @ (cons_val @ X @ Xs) @ Ys) = (?[Z : ty]: (?[Zs : list_ty]: (((Ys = (cons_ty @ Z @ Zs))) & ((((P @ X @ Z)) & ((list_all2_val_ty @ P @ Xs @ Zs))))))))))). % list_all2_Cons1
thf(fact_133_list__all2__Cons1, axiom,
    ((![P : val > val > $o, X : val, Xs : list_val, Ys : list_val]: ((list_all2_val_val @ P @ (cons_val @ X @ Xs) @ Ys) = (?[Z : val]: (?[Zs : list_val]: (((Ys = (cons_val @ Z @ Zs))) & ((((P @ X @ Z)) & ((list_all2_val_val @ P @ Xs @ Zs))))))))))). % list_all2_Cons1
thf(fact_134_list__all2__Cons1, axiom,
    ((![P : ty > ty > $o, X : ty, Xs : list_ty, Ys : list_ty]: ((list_all2_ty_ty @ P @ (cons_ty @ X @ Xs) @ Ys) = (?[Z : ty]: (?[Zs : list_ty]: (((Ys = (cons_ty @ Z @ Zs))) & ((((P @ X @ Z)) & ((list_all2_ty_ty @ P @ Xs @ Zs))))))))))). % list_all2_Cons1
thf(fact_135_list__all2__Cons1, axiom,
    ((![P : list_char > ty > $o, X : list_char, Xs : list_list_char, Ys : list_ty]: ((list_a1770748705har_ty @ P @ (cons_list_char @ X @ Xs) @ Ys) = (?[Z : ty]: (?[Zs : list_ty]: (((Ys = (cons_ty @ Z @ Zs))) & ((((P @ X @ Z)) & ((list_a1770748705har_ty @ P @ Xs @ Zs))))))))))). % list_all2_Cons1
thf(fact_136_list__all2__Cons1, axiom,
    ((![P : list_char > val > $o, X : list_char, Xs : list_list_char, Ys : list_val]: ((list_a280217834ar_val @ P @ (cons_list_char @ X @ Xs) @ Ys) = (?[Z : val]: (?[Zs : list_val]: (((Ys = (cons_val @ Z @ Zs))) & ((((P @ X @ Z)) & ((list_a280217834ar_val @ P @ Xs @ Zs))))))))))). % list_all2_Cons1
thf(fact_137_list__all2__Cons1, axiom,
    ((![P : ty > list_char > $o, X : ty, Xs : list_ty, Ys : list_list_char]: ((list_a1504214817t_char @ P @ (cons_ty @ X @ Xs) @ Ys) = (?[Z : list_char]: (?[Zs : list_list_char]: (((Ys = (cons_list_char @ Z @ Zs))) & ((((P @ X @ Z)) & ((list_a1504214817t_char @ P @ Xs @ Zs))))))))))). % list_all2_Cons1
thf(fact_138_list__all2__Cons1, axiom,
    ((![P : ty > option_ty > $o, X : ty, Xs : list_ty, Ys : list_option_ty]: ((list_a765198023ion_ty @ P @ (cons_ty @ X @ Xs) @ Ys) = (?[Z : option_ty]: (?[Zs : list_option_ty]: (((Ys = (cons_option_ty @ Z @ Zs))) & ((((P @ X @ Z)) & ((list_a765198023ion_ty @ P @ Xs @ Zs))))))))))). % list_all2_Cons1
thf(fact_139_list__all2__Cons1, axiom,
    ((![P : val > list_char > $o, X : val, Xs : list_val, Ys : list_list_char]: ((list_a1248766058t_char @ P @ (cons_val @ X @ Xs) @ Ys) = (?[Z : list_char]: (?[Zs : list_list_char]: (((Ys = (cons_list_char @ Z @ Zs))) & ((((P @ X @ Z)) & ((list_a1248766058t_char @ P @ Xs @ Zs))))))))))). % list_all2_Cons1
thf(fact_140_list__all2__Cons1, axiom,
    ((![P : val > option_ty > $o, X : val, Xs : list_val, Ys : list_option_ty]: ((list_a509749264ion_ty @ P @ (cons_val @ X @ Xs) @ Ys) = (?[Z : option_ty]: (?[Zs : list_option_ty]: (((Ys = (cons_option_ty @ Z @ Zs))) & ((((P @ X @ Z)) & ((list_a509749264ion_ty @ P @ Xs @ Zs))))))))))). % list_all2_Cons1
thf(fact_141_list__all2__Cons, axiom,
    ((![P : ty > val > $o, X : ty, Xs : list_ty, Y : val, Ys : list_val]: ((list_all2_ty_val @ P @ (cons_ty @ X @ Xs) @ (cons_val @ Y @ Ys)) = (((P @ X @ Y)) & ((list_all2_ty_val @ P @ Xs @ Ys))))))). % list_all2_Cons
thf(fact_142_list__all2__Cons, axiom,
    ((![P : val > ty > $o, X : val, Xs : list_val, Y : ty, Ys : list_ty]: ((list_all2_val_ty @ P @ (cons_val @ X @ Xs) @ (cons_ty @ Y @ Ys)) = (((P @ X @ Y)) & ((list_all2_val_ty @ P @ Xs @ Ys))))))). % list_all2_Cons
thf(fact_143_list__all2__Cons, axiom,
    ((![P : val > val > $o, X : val, Xs : list_val, Y : val, Ys : list_val]: ((list_all2_val_val @ P @ (cons_val @ X @ Xs) @ (cons_val @ Y @ Ys)) = (((P @ X @ Y)) & ((list_all2_val_val @ P @ Xs @ Ys))))))). % list_all2_Cons
thf(fact_144_list__all2__Cons, axiom,
    ((![P : ty > ty > $o, X : ty, Xs : list_ty, Y : ty, Ys : list_ty]: ((list_all2_ty_ty @ P @ (cons_ty @ X @ Xs) @ (cons_ty @ Y @ Ys)) = (((P @ X @ Y)) & ((list_all2_ty_ty @ P @ Xs @ Ys))))))). % list_all2_Cons
thf(fact_145_list__all2__Cons, axiom,
    ((![P : list_char > ty > $o, X : list_char, Xs : list_list_char, Y : ty, Ys : list_ty]: ((list_a1770748705har_ty @ P @ (cons_list_char @ X @ Xs) @ (cons_ty @ Y @ Ys)) = (((P @ X @ Y)) & ((list_a1770748705har_ty @ P @ Xs @ Ys))))))). % list_all2_Cons
thf(fact_146_list__all2__Cons, axiom,
    ((![P : list_char > val > $o, X : list_char, Xs : list_list_char, Y : val, Ys : list_val]: ((list_a280217834ar_val @ P @ (cons_list_char @ X @ Xs) @ (cons_val @ Y @ Ys)) = (((P @ X @ Y)) & ((list_a280217834ar_val @ P @ Xs @ Ys))))))). % list_all2_Cons
thf(fact_147_list__all2__Cons, axiom,
    ((![P : ty > list_char > $o, X : ty, Xs : list_ty, Y : list_char, Ys : list_list_char]: ((list_a1504214817t_char @ P @ (cons_ty @ X @ Xs) @ (cons_list_char @ Y @ Ys)) = (((P @ X @ Y)) & ((list_a1504214817t_char @ P @ Xs @ Ys))))))). % list_all2_Cons
thf(fact_148_list__all2__Cons, axiom,
    ((![P : ty > option_ty > $o, X : ty, Xs : list_ty, Y : option_ty, Ys : list_option_ty]: ((list_a765198023ion_ty @ P @ (cons_ty @ X @ Xs) @ (cons_option_ty @ Y @ Ys)) = (((P @ X @ Y)) & ((list_a765198023ion_ty @ P @ Xs @ Ys))))))). % list_all2_Cons
thf(fact_149_list__all2__Cons, axiom,
    ((![P : val > list_char > $o, X : val, Xs : list_val, Y : list_char, Ys : list_list_char]: ((list_a1248766058t_char @ P @ (cons_val @ X @ Xs) @ (cons_list_char @ Y @ Ys)) = (((P @ X @ Y)) & ((list_a1248766058t_char @ P @ Xs @ Ys))))))). % list_all2_Cons
thf(fact_150_list__all2__Cons, axiom,
    ((![P : val > option_ty > $o, X : val, Xs : list_val, Y : option_ty, Ys : list_option_ty]: ((list_a509749264ion_ty @ P @ (cons_val @ X @ Xs) @ (cons_option_ty @ Y @ Ys)) = (((P @ X @ Y)) & ((list_a509749264ion_ty @ P @ Xs @ Ys))))))). % list_all2_Cons
thf(fact_151_list_Orel__intros_I2_J, axiom,
    ((![R : ty > val > $o, X21 : ty, Y21 : val, X22 : list_ty, Y22 : list_val]: ((R @ X21 @ Y21) => ((list_all2_ty_val @ R @ X22 @ Y22) => (list_all2_ty_val @ R @ (cons_ty @ X21 @ X22) @ (cons_val @ Y21 @ Y22))))))). % list.rel_intros(2)
thf(fact_152_list_Orel__intros_I2_J, axiom,
    ((![R : val > ty > $o, X21 : val, Y21 : ty, X22 : list_val, Y22 : list_ty]: ((R @ X21 @ Y21) => ((list_all2_val_ty @ R @ X22 @ Y22) => (list_all2_val_ty @ R @ (cons_val @ X21 @ X22) @ (cons_ty @ Y21 @ Y22))))))). % list.rel_intros(2)
thf(fact_153_list_Orel__intros_I2_J, axiom,
    ((![R : val > val > $o, X21 : val, Y21 : val, X22 : list_val, Y22 : list_val]: ((R @ X21 @ Y21) => ((list_all2_val_val @ R @ X22 @ Y22) => (list_all2_val_val @ R @ (cons_val @ X21 @ X22) @ (cons_val @ Y21 @ Y22))))))). % list.rel_intros(2)
thf(fact_154_list_Orel__intros_I2_J, axiom,
    ((![R : ty > ty > $o, X21 : ty, Y21 : ty, X22 : list_ty, Y22 : list_ty]: ((R @ X21 @ Y21) => ((list_all2_ty_ty @ R @ X22 @ Y22) => (list_all2_ty_ty @ R @ (cons_ty @ X21 @ X22) @ (cons_ty @ Y21 @ Y22))))))). % list.rel_intros(2)
thf(fact_155_list_Orel__intros_I2_J, axiom,
    ((![R : list_char > ty > $o, X21 : list_char, Y21 : ty, X22 : list_list_char, Y22 : list_ty]: ((R @ X21 @ Y21) => ((list_a1770748705har_ty @ R @ X22 @ Y22) => (list_a1770748705har_ty @ R @ (cons_list_char @ X21 @ X22) @ (cons_ty @ Y21 @ Y22))))))). % list.rel_intros(2)
thf(fact_156_list_Orel__intros_I2_J, axiom,
    ((![R : list_char > val > $o, X21 : list_char, Y21 : val, X22 : list_list_char, Y22 : list_val]: ((R @ X21 @ Y21) => ((list_a280217834ar_val @ R @ X22 @ Y22) => (list_a280217834ar_val @ R @ (cons_list_char @ X21 @ X22) @ (cons_val @ Y21 @ Y22))))))). % list.rel_intros(2)
thf(fact_157_list_Orel__intros_I2_J, axiom,
    ((![R : ty > list_char > $o, X21 : ty, Y21 : list_char, X22 : list_ty, Y22 : list_list_char]: ((R @ X21 @ Y21) => ((list_a1504214817t_char @ R @ X22 @ Y22) => (list_a1504214817t_char @ R @ (cons_ty @ X21 @ X22) @ (cons_list_char @ Y21 @ Y22))))))). % list.rel_intros(2)
thf(fact_158_list_Orel__intros_I2_J, axiom,
    ((![R : ty > option_ty > $o, X21 : ty, Y21 : option_ty, X22 : list_ty, Y22 : list_option_ty]: ((R @ X21 @ Y21) => ((list_a765198023ion_ty @ R @ X22 @ Y22) => (list_a765198023ion_ty @ R @ (cons_ty @ X21 @ X22) @ (cons_option_ty @ Y21 @ Y22))))))). % list.rel_intros(2)
thf(fact_159_list_Orel__intros_I2_J, axiom,
    ((![R : val > list_char > $o, X21 : val, Y21 : list_char, X22 : list_val, Y22 : list_list_char]: ((R @ X21 @ Y21) => ((list_a1248766058t_char @ R @ X22 @ Y22) => (list_a1248766058t_char @ R @ (cons_val @ X21 @ X22) @ (cons_list_char @ Y21 @ Y22))))))). % list.rel_intros(2)
thf(fact_160_list_Orel__intros_I2_J, axiom,
    ((![R : val > option_ty > $o, X21 : val, Y21 : option_ty, X22 : list_val, Y22 : list_option_ty]: ((R @ X21 @ Y21) => ((list_a509749264ion_ty @ R @ X22 @ Y22) => (list_a509749264ion_ty @ R @ (cons_val @ X21 @ X22) @ (cons_option_ty @ Y21 @ Y22))))))). % list.rel_intros(2)
thf(fact_161_list_Orel__inject_I2_J, axiom,
    ((![R : ty > val > $o, X21 : ty, X22 : list_ty, Y21 : val, Y22 : list_val]: ((list_all2_ty_val @ R @ (cons_ty @ X21 @ X22) @ (cons_val @ Y21 @ Y22)) = (((R @ X21 @ Y21)) & ((list_all2_ty_val @ R @ X22 @ Y22))))))). % list.rel_inject(2)
thf(fact_162_list_Orel__inject_I2_J, axiom,
    ((![R : val > ty > $o, X21 : val, X22 : list_val, Y21 : ty, Y22 : list_ty]: ((list_all2_val_ty @ R @ (cons_val @ X21 @ X22) @ (cons_ty @ Y21 @ Y22)) = (((R @ X21 @ Y21)) & ((list_all2_val_ty @ R @ X22 @ Y22))))))). % list.rel_inject(2)
thf(fact_163_list_Orel__inject_I2_J, axiom,
    ((![R : val > val > $o, X21 : val, X22 : list_val, Y21 : val, Y22 : list_val]: ((list_all2_val_val @ R @ (cons_val @ X21 @ X22) @ (cons_val @ Y21 @ Y22)) = (((R @ X21 @ Y21)) & ((list_all2_val_val @ R @ X22 @ Y22))))))). % list.rel_inject(2)
thf(fact_164_list_Orel__inject_I2_J, axiom,
    ((![R : ty > ty > $o, X21 : ty, X22 : list_ty, Y21 : ty, Y22 : list_ty]: ((list_all2_ty_ty @ R @ (cons_ty @ X21 @ X22) @ (cons_ty @ Y21 @ Y22)) = (((R @ X21 @ Y21)) & ((list_all2_ty_ty @ R @ X22 @ Y22))))))). % list.rel_inject(2)
thf(fact_165_list_Orel__inject_I2_J, axiom,
    ((![R : list_char > ty > $o, X21 : list_char, X22 : list_list_char, Y21 : ty, Y22 : list_ty]: ((list_a1770748705har_ty @ R @ (cons_list_char @ X21 @ X22) @ (cons_ty @ Y21 @ Y22)) = (((R @ X21 @ Y21)) & ((list_a1770748705har_ty @ R @ X22 @ Y22))))))). % list.rel_inject(2)
thf(fact_166_list_Orel__inject_I2_J, axiom,
    ((![R : list_char > val > $o, X21 : list_char, X22 : list_list_char, Y21 : val, Y22 : list_val]: ((list_a280217834ar_val @ R @ (cons_list_char @ X21 @ X22) @ (cons_val @ Y21 @ Y22)) = (((R @ X21 @ Y21)) & ((list_a280217834ar_val @ R @ X22 @ Y22))))))). % list.rel_inject(2)
thf(fact_167_list_Orel__inject_I2_J, axiom,
    ((![R : ty > list_char > $o, X21 : ty, X22 : list_ty, Y21 : list_char, Y22 : list_list_char]: ((list_a1504214817t_char @ R @ (cons_ty @ X21 @ X22) @ (cons_list_char @ Y21 @ Y22)) = (((R @ X21 @ Y21)) & ((list_a1504214817t_char @ R @ X22 @ Y22))))))). % list.rel_inject(2)
thf(fact_168_list_Orel__inject_I2_J, axiom,
    ((![R : ty > option_ty > $o, X21 : ty, X22 : list_ty, Y21 : option_ty, Y22 : list_option_ty]: ((list_a765198023ion_ty @ R @ (cons_ty @ X21 @ X22) @ (cons_option_ty @ Y21 @ Y22)) = (((R @ X21 @ Y21)) & ((list_a765198023ion_ty @ R @ X22 @ Y22))))))). % list.rel_inject(2)
thf(fact_169_list_Orel__inject_I2_J, axiom,
    ((![R : val > list_char > $o, X21 : val, X22 : list_val, Y21 : list_char, Y22 : list_list_char]: ((list_a1248766058t_char @ R @ (cons_val @ X21 @ X22) @ (cons_list_char @ Y21 @ Y22)) = (((R @ X21 @ Y21)) & ((list_a1248766058t_char @ R @ X22 @ Y22))))))). % list.rel_inject(2)
thf(fact_170_list_Orel__inject_I2_J, axiom,
    ((![R : val > option_ty > $o, X21 : val, X22 : list_val, Y21 : option_ty, Y22 : list_option_ty]: ((list_a509749264ion_ty @ R @ (cons_val @ X21 @ X22) @ (cons_option_ty @ Y21 @ Y22)) = (((R @ X21 @ Y21)) & ((list_a509749264ion_ty @ R @ X22 @ Y22))))))). % list.rel_inject(2)
thf(fact_171_map__eq__imp__length__eq, axiom,
    ((![F : ty > val, Xs : list_ty, G : ty > val, Ys : list_ty]: (((map_ty_val @ F @ Xs) = (map_ty_val @ G @ Ys)) => ((size_size_list_ty @ Xs) = (size_size_list_ty @ Ys)))))). % map_eq_imp_length_eq
thf(fact_172_map__eq__imp__length__eq, axiom,
    ((![F : ty > ty, Xs : list_ty, G : ty > ty, Ys : list_ty]: (((map_ty_ty @ F @ Xs) = (map_ty_ty @ G @ Ys)) => ((size_size_list_ty @ Xs) = (size_size_list_ty @ Ys)))))). % map_eq_imp_length_eq
thf(fact_173_map__eq__imp__length__eq, axiom,
    ((![F : ty > val, Xs : list_ty, G : val > val, Ys : list_val]: (((map_ty_val @ F @ Xs) = (map_val_val @ G @ Ys)) => ((size_size_list_ty @ Xs) = (size_size_list_val @ Ys)))))). % map_eq_imp_length_eq
thf(fact_174_map__eq__imp__length__eq, axiom,
    ((![F : ty > ty, Xs : list_ty, G : val > ty, Ys : list_val]: (((map_ty_ty @ F @ Xs) = (map_val_ty @ G @ Ys)) => ((size_size_list_ty @ Xs) = (size_size_list_val @ Ys)))))). % map_eq_imp_length_eq
thf(fact_175_map__eq__imp__length__eq, axiom,
    ((![F : val > val, Xs : list_val, G : ty > val, Ys : list_ty]: (((map_val_val @ F @ Xs) = (map_ty_val @ G @ Ys)) => ((size_size_list_val @ Xs) = (size_size_list_ty @ Ys)))))). % map_eq_imp_length_eq
thf(fact_176_map__eq__imp__length__eq, axiom,
    ((![F : val > ty, Xs : list_val, G : ty > ty, Ys : list_ty]: (((map_val_ty @ F @ Xs) = (map_ty_ty @ G @ Ys)) => ((size_size_list_val @ Xs) = (size_size_list_ty @ Ys)))))). % map_eq_imp_length_eq
thf(fact_177_map__eq__imp__length__eq, axiom,
    ((![F : list_char > val, Xs : list_list_char, G : ty > val, Ys : list_ty]: (((map_list_char_val @ F @ Xs) = (map_ty_val @ G @ Ys)) => ((size_s2008079621t_char @ Xs) = (size_size_list_ty @ Ys)))))). % map_eq_imp_length_eq
thf(fact_178_map__eq__imp__length__eq, axiom,
    ((![F : list_char > ty, Xs : list_list_char, G : ty > ty, Ys : list_ty]: (((map_list_char_ty @ F @ Xs) = (map_ty_ty @ G @ Ys)) => ((size_s2008079621t_char @ Xs) = (size_size_list_ty @ Ys)))))). % map_eq_imp_length_eq
thf(fact_179_map__eq__imp__length__eq, axiom,
    ((![F : list_char > ty, Xs : list_list_char, G : val > ty, Ys : list_val]: (((map_list_char_ty @ F @ Xs) = (map_val_ty @ G @ Ys)) => ((size_s2008079621t_char @ Xs) = (size_size_list_val @ Ys)))))). % map_eq_imp_length_eq
thf(fact_180_map__eq__imp__length__eq, axiom,
    ((![F : ty > val, Xs : list_ty, G : list_char > val, Ys : list_list_char]: (((map_ty_val @ F @ Xs) = (map_list_char_val @ G @ Ys)) => ((size_size_list_ty @ Xs) = (size_s2008079621t_char @ Ys)))))). % map_eq_imp_length_eq
thf(fact_181_list__all2__lengthD, axiom,
    ((![P : ty > ty > $o, Xs : list_ty, Ys : list_ty]: ((list_all2_ty_ty @ P @ Xs @ Ys) => ((size_size_list_ty @ Xs) = (size_size_list_ty @ Ys)))))). % list_all2_lengthD
thf(fact_182_list__all2__lengthD, axiom,
    ((![P : ty > val > $o, Xs : list_ty, Ys : list_val]: ((list_all2_ty_val @ P @ Xs @ Ys) => ((size_size_list_ty @ Xs) = (size_size_list_val @ Ys)))))). % list_all2_lengthD
thf(fact_183_list__all2__lengthD, axiom,
    ((![P : val > ty > $o, Xs : list_val, Ys : list_ty]: ((list_all2_val_ty @ P @ Xs @ Ys) => ((size_size_list_val @ Xs) = (size_size_list_ty @ Ys)))))). % list_all2_lengthD
thf(fact_184_list__all2__lengthD, axiom,
    ((![P : val > val > $o, Xs : list_val, Ys : list_val]: ((list_all2_val_val @ P @ Xs @ Ys) => ((size_size_list_val @ Xs) = (size_size_list_val @ Ys)))))). % list_all2_lengthD
thf(fact_185_list__all2__lengthD, axiom,
    ((![P : list_char > ty > $o, Xs : list_list_char, Ys : list_ty]: ((list_a1770748705har_ty @ P @ Xs @ Ys) => ((size_s2008079621t_char @ Xs) = (size_size_list_ty @ Ys)))))). % list_all2_lengthD
thf(fact_186_list__all2__lengthD, axiom,
    ((![P : list_char > val > $o, Xs : list_list_char, Ys : list_val]: ((list_a280217834ar_val @ P @ Xs @ Ys) => ((size_s2008079621t_char @ Xs) = (size_size_list_val @ Ys)))))). % list_all2_lengthD
thf(fact_187_list__all2__lengthD, axiom,
    ((![P : ty > list_char > $o, Xs : list_ty, Ys : list_list_char]: ((list_a1504214817t_char @ P @ Xs @ Ys) => ((size_size_list_ty @ Xs) = (size_s2008079621t_char @ Ys)))))). % list_all2_lengthD
thf(fact_188_list__all2__lengthD, axiom,
    ((![P : ty > option_ty > $o, Xs : list_ty, Ys : list_option_ty]: ((list_a765198023ion_ty @ P @ Xs @ Ys) => ((size_size_list_ty @ Xs) = (size_s1569909163ion_ty @ Ys)))))). % list_all2_lengthD
thf(fact_189_list__all2__lengthD, axiom,
    ((![P : val > list_char > $o, Xs : list_val, Ys : list_list_char]: ((list_a1248766058t_char @ P @ Xs @ Ys) => ((size_size_list_val @ Xs) = (size_s2008079621t_char @ Ys)))))). % list_all2_lengthD
thf(fact_190_list__all2__lengthD, axiom,
    ((![P : val > option_ty > $o, Xs : list_val, Ys : list_option_ty]: ((list_a509749264ion_ty @ P @ Xs @ Ys) => ((size_size_list_val @ Xs) = (size_s1569909163ion_ty @ Ys)))))). % list_all2_lengthD
thf(fact_191_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_192_option_Oinject, axiom,
    ((![X2 : ty, Y2 : ty]: (((some_ty @ X2) = (some_ty @ Y2)) = (X2 = Y2))))). % option.inject
thf(fact_193_Cons__in__lex, axiom,
    ((![X : list_char, Xs : list_list_char, Y : list_char, Ys : list_list_char, R2 : set_Pr164112643t_char]: ((member725442668t_char @ (produc1181934459t_char @ (cons_list_char @ X @ Xs) @ (cons_list_char @ Y @ Ys)) @ (lex_list_char @ R2)) = (((((member89690956t_char @ (produc1304532571t_char @ X @ Y) @ R2)) & (((size_s2008079621t_char @ Xs) = (size_s2008079621t_char @ Ys))))) | ((((X = Y)) & ((member725442668t_char @ (produc1181934459t_char @ Xs @ Ys) @ (lex_list_char @ R2)))))))))). % Cons_in_lex
thf(fact_194_Cons__in__lex, axiom,
    ((![X : ty, Xs : list_ty, Y : ty, Ys : list_ty, R2 : set_Pr1194734255_ty_ty]: ((member1942114840ist_ty @ (produc1089615911ist_ty @ (cons_ty @ X @ Xs) @ (cons_ty @ Y @ Ys)) @ (lex_ty @ R2)) = (((((member2070851320_ty_ty @ (product_Pair_ty_ty @ X @ Y) @ R2)) & (((size_size_list_ty @ Xs) = (size_size_list_ty @ Ys))))) | ((((X = Y)) & ((member1942114840ist_ty @ (produc1089615911ist_ty @ Xs @ Ys) @ (lex_ty @ R2)))))))))). % Cons_in_lex
thf(fact_195_Cons__in__lex, axiom,
    ((![X : val, Xs : list_val, Y : val, Ys : list_val, R2 : set_Pr1870322241al_val]: ((member1382006826st_val @ (produc180957881st_val @ (cons_val @ X @ Xs) @ (cons_val @ Y @ Ys)) @ (lex_val @ R2)) = (((((member1494223754al_val @ (product_Pair_val_val @ X @ Y) @ R2)) & (((size_size_list_val @ Xs) = (size_size_list_val @ Ys))))) | ((((X = Y)) & ((member1382006826st_val @ (produc180957881st_val @ Xs @ Ys) @ (lex_val @ R2)))))))))). % Cons_in_lex
thf(fact_196_Cons__in__lex, axiom,
    ((![X : option_ty, Xs : list_option_ty, Y : option_ty, Ys : list_option_ty, R2 : set_Pr616941135ion_ty]: ((member237105848ion_ty @ (produc1071605959ion_ty @ (cons_option_ty @ X @ Xs) @ (cons_option_ty @ Y @ Ys)) @ (lex_option_ty @ R2)) = (((((member704321176ion_ty @ (produc1618316455ion_ty @ X @ Y) @ R2)) & (((size_s1569909163ion_ty @ Xs) = (size_s1569909163ion_ty @ Ys))))) | ((((X = Y)) & ((member237105848ion_ty @ (produc1071605959ion_ty @ Xs @ Ys) @ (lex_option_ty @ R2)))))))))). % Cons_in_lex
thf(fact_197_map__eq__map__tailrec, axiom,
    ((map_val_option_ty = map_ta1696661655ion_ty))). % map_eq_map_tailrec
thf(fact_198_map__eq__map__tailrec, axiom,
    ((map_ty_option_ty = map_ta56519374ion_ty))). % map_eq_map_tailrec
thf(fact_199_map__eq__map__tailrec, axiom,
    ((map_li1166989960t_char = map_ta1456818130t_char))). % map_eq_map_tailrec
thf(fact_200_map__eq__map__tailrec, axiom,
    ((map_list_char_ty = map_ta1062070056har_ty))). % map_eq_map_tailrec
thf(fact_201_map__eq__map__tailrec, axiom,
    ((map_ty_val = map_tailrec_ty_val))). % map_eq_map_tailrec
thf(fact_202_map__eq__map__tailrec, axiom,
    ((map_ty_list_char = map_ta795536168t_char))). % map_eq_map_tailrec
thf(fact_203_map__eq__map__tailrec, axiom,
    ((map_ty_ty = map_tailrec_ty_ty))). % map_eq_map_tailrec
thf(fact_204_confs__conv__map, axiom,
    ((![P : list_P1234162913t_char, H : nat > option2118145160on_val, Vs : list_val, Ts2 : list_ty]: ((list_all2_val_ty @ (conf_P93989998t_char @ P @ H) @ Vs @ Ts2) = (?[Ts3 : list_ty]: ((((map_val_option_ty @ (typeof_h @ H) @ Vs) = (map_ty_option_ty @ some_ty @ Ts3))) & ((list_all2_ty_ty @ (widen_917054840t_char @ P) @ Ts3 @ Ts2)))))))). % confs_conv_map
thf(fact_205_blocksEval, axiom,
    ((![Ps : list_list_char, Ts : list_ty, Vs : list_val, 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]: (((size_s2008079621t_char @ Ps) = (size_size_list_ty @ Ts)) => (((size_s2008079621t_char @ Ps) = (size_size_list_val @ Vs)) => ((eval @ P @ (blocks @ (produc1808722894t_char @ Ps @ (produc1806338192t_char @ Ts @ (produc823987298t_char @ Vs @ E)))) @ (produc52622304on_val @ H @ L) @ E2 @ (produc52622304on_val @ H2 @ L2)) => (?[L3 : list_char > option_val]: (eval @ P @ E @ (produc52622304on_val @ H @ (map_up576607321ar_val @ L @ Ps @ Vs)) @ E2 @ (produc52622304on_val @ H2 @ L3))))))))). % blocksEval
thf(fact_206_find_Osimps_I2_J, axiom,
    ((![P : list_char > $o, X : list_char, Xs : list_list_char]: (((P @ X) => ((find_list_char @ P @ (cons_list_char @ X @ Xs)) = (some_list_char @ X))) & ((~ ((P @ X))) => ((find_list_char @ P @ (cons_list_char @ X @ Xs)) = (find_list_char @ P @ Xs))))))). % find.simps(2)
thf(fact_207_find_Osimps_I2_J, axiom,
    ((![P : val > $o, X : val, Xs : list_val]: (((P @ X) => ((find_val @ P @ (cons_val @ X @ Xs)) = (some_val @ X))) & ((~ ((P @ X))) => ((find_val @ P @ (cons_val @ X @ Xs)) = (find_val @ P @ Xs))))))). % find.simps(2)
thf(fact_208_find_Osimps_I2_J, axiom,
    ((![P : option_ty > $o, X : option_ty, Xs : list_option_ty]: (((P @ X) => ((find_option_ty @ P @ (cons_option_ty @ X @ Xs)) = (some_option_ty @ X))) & ((~ ((P @ X))) => ((find_option_ty @ P @ (cons_option_ty @ X @ Xs)) = (find_option_ty @ P @ Xs))))))). % find.simps(2)
thf(fact_209_find_Osimps_I2_J, axiom,
    ((![P : ty > $o, X : ty, Xs : list_ty]: (((P @ X) => ((find_ty @ P @ (cons_ty @ X @ Xs)) = (some_ty @ X))) & ((~ ((P @ X))) => ((find_ty @ P @ (cons_ty @ X @ Xs)) = (find_ty @ P @ Xs))))))). % find.simps(2)
thf(fact_210_rel__list__all2__Cons, axiom,
    ((![S : set_Pr1036794744ty_val, X : ty, Xs : list_ty, Y : val, Ys : list_val]: ((list_all2_ty_val @ (fun_of_ty_val @ S) @ (cons_ty @ X @ Xs) @ (cons_val @ Y @ Ys)) = (((member1776226881ty_val @ (product_Pair_ty_val @ X @ Y) @ S)) & ((list_all2_ty_val @ (fun_of_ty_val @ S) @ Xs @ Ys))))))). % rel_list_all2_Cons
thf(fact_211_rel__list__all2__Cons, axiom,
    ((![S : set_Pr312206840val_ty, X : val, Xs : list_val, Y : ty, Ys : list_ty]: ((list_all2_val_ty @ (fun_of_val_ty @ S) @ (cons_val @ X @ Xs) @ (cons_ty @ Y @ Ys)) = (((member1400634561val_ty @ (product_Pair_val_ty @ X @ Y) @ S)) & ((list_all2_val_ty @ (fun_of_val_ty @ S) @ Xs @ Ys))))))). % rel_list_all2_Cons
thf(fact_212_rel__list__all2__Cons, axiom,
    ((![S : set_Pr1870322241al_val, X : val, Xs : list_val, Y : val, Ys : list_val]: ((list_all2_val_val @ (fun_of_val_val @ S) @ (cons_val @ X @ Xs) @ (cons_val @ Y @ Ys)) = (((member1494223754al_val @ (product_Pair_val_val @ X @ Y) @ S)) & ((list_all2_val_val @ (fun_of_val_val @ S) @ Xs @ Ys))))))). % rel_list_all2_Cons
thf(fact_213_rel__list__all2__Cons, axiom,
    ((![S : set_Pr1194734255_ty_ty, X : ty, Xs : list_ty, Y : ty, Ys : list_ty]: ((list_all2_ty_ty @ (fun_of_ty_ty @ S) @ (cons_ty @ X @ Xs) @ (cons_ty @ Y @ Ys)) = (((member2070851320_ty_ty @ (product_Pair_ty_ty @ X @ Y) @ S)) & ((list_all2_ty_ty @ (fun_of_ty_ty @ S) @ Xs @ Ys))))))). % rel_list_all2_Cons
thf(fact_214_rel__list__all2__Cons, axiom,
    ((![S : set_Pr349050585har_ty, X : list_char, Xs : list_list_char, Y : ty, Ys : list_ty]: ((list_a1770748705har_ty @ (fun_of_list_char_ty @ S) @ (cons_list_char @ X @ Xs) @ (cons_ty @ Y @ Ys)) = (((member325880354har_ty @ (produc1017542449har_ty @ X @ Y) @ S)) & ((list_a1770748705har_ty @ (fun_of_list_char_ty @ S) @ Xs @ Ys))))))). % rel_list_all2_Cons
thf(fact_215_rel__list__all2__Cons, axiom,
    ((![S : set_Pr174107298ar_val, X : list_char, Xs : list_list_char, Y : val, Ys : list_val]: ((list_a280217834ar_val @ (fun_of_list_char_val @ S) @ (cons_list_char @ X @ Xs) @ (cons_val @ Y @ Ys)) = (((member1062074475ar_val @ (produc368164090ar_val @ X @ Y) @ S)) & ((list_a280217834ar_val @ (fun_of_list_char_val @ S) @ Xs @ Ys))))))). % rel_list_all2_Cons
thf(fact_216_rel__list__all2__Cons, axiom,
    ((![S : set_Pr1320471513t_char, X : ty, Xs : list_ty, Y : list_char, Ys : list_list_char]: ((list_a1504214817t_char @ (fun_of_ty_list_char @ S) @ (cons_ty @ X @ Xs) @ (cons_list_char @ Y @ Ys)) = (((member1016971042t_char @ (produc751008561t_char @ X @ Y) @ S)) & ((list_a1504214817t_char @ (fun_of_ty_list_char @ S) @ Xs @ Ys))))))). % rel_list_all2_Cons
thf(fact_217_rel__list__all2__Cons, axiom,
    ((![S : set_Pr504292735ion_ty, X : ty, Xs : list_ty, Y : option_ty, Ys : list_option_ty]: ((list_a765198023ion_ty @ (fun_of_ty_option_ty @ S) @ (cons_ty @ X @ Xs) @ (cons_option_ty @ Y @ Ys)) = (((member578800584ion_ty @ (produc11991767ion_ty @ X @ Y) @ S)) & ((list_a765198023ion_ty @ (fun_of_ty_option_ty @ S) @ Xs @ Ys))))))). % rel_list_all2_Cons
thf(fact_218_rel__list__all2__Cons, axiom,
    ((![S : set_Pr1557683618t_char, X : val, Xs : list_val, Y : list_char, Ys : list_list_char]: ((list_a1248766058t_char @ (fun_of_val_list_char @ S) @ (cons_val @ X @ Xs) @ (cons_list_char @ Y @ Ys)) = (((member1429154667t_char @ (produc1336712314t_char @ X @ Y) @ S)) & ((list_a1248766058t_char @ (fun_of_val_list_char @ S) @ Xs @ Ys))))))). % rel_list_all2_Cons
thf(fact_219_rel__list__all2__Cons, axiom,
    ((![S : set_Pr741504840ion_ty, X : val, Xs : list_val, Y : option_ty, Ys : list_option_ty]: ((list_a509749264ion_ty @ (fun_of_val_option_ty @ S) @ (cons_val @ X @ Xs) @ (cons_option_ty @ Y @ Ys)) = (((member990984209ion_ty @ (produc597695520ion_ty @ X @ Y) @ S)) & ((list_a509749264ion_ty @ (fun_of_val_option_ty @ S) @ Xs @ Ys))))))). % rel_list_all2_Cons
thf(fact_220_size__neq__size__imp__neq, axiom,
    ((![X : list_list_char, Y : list_list_char]: ((~ (((size_s2008079621t_char @ X) = (size_s2008079621t_char @ Y)))) => (~ ((X = Y))))))). % size_neq_size_imp_neq
thf(fact_221_size__neq__size__imp__neq, axiom,
    ((![X : list_ty, Y : list_ty]: ((~ (((size_size_list_ty @ X) = (size_size_list_ty @ Y)))) => (~ ((X = Y))))))). % size_neq_size_imp_neq
thf(fact_222_size__neq__size__imp__neq, axiom,
    ((![X : list_val, Y : list_val]: ((~ (((size_size_list_val @ X) = (size_size_list_val @ Y)))) => (~ ((X = Y))))))). % size_neq_size_imp_neq
thf(fact_223_size__neq__size__imp__neq, axiom,
    ((![X : list_option_ty, Y : list_option_ty]: ((~ (((size_s1569909163ion_ty @ X) = (size_s1569909163ion_ty @ Y)))) => (~ ((X = Y))))))). % size_neq_size_imp_neq
thf(fact_224_conf__widen, axiom,
    ((![P : list_P1234162913t_char, H : nat > option2118145160on_val, V : val, T : ty, T2 : ty]: ((conf_P93989998t_char @ P @ H @ V @ T) => ((widen_917054840t_char @ P @ T @ T2) => (conf_P93989998t_char @ P @ H @ V @ T2)))))). % conf_widen
thf(fact_225_confs__widens, axiom,
    ((![P : list_P1234162913t_char, H : nat > option2118145160on_val, Vs : list_val, Ts : list_ty, Ts2 : list_ty]: ((list_all2_val_ty @ (conf_P93989998t_char @ P @ H) @ Vs @ Ts) => ((list_all2_ty_ty @ (widen_917054840t_char @ P) @ Ts @ Ts2) => (list_all2_val_ty @ (conf_P93989998t_char @ P @ H) @ Vs @ Ts2)))))). % confs_widens
thf(fact_226_rel__list__all2__refl, axiom,
    ((![S : set_Pr1194734255_ty_ty, Xs : list_ty]: ((![X3 : ty]: (member2070851320_ty_ty @ (product_Pair_ty_ty @ X3 @ X3) @ S)) => (list_all2_ty_ty @ (fun_of_ty_ty @ S) @ Xs @ Xs))))). % rel_list_all2_refl
thf(fact_227_rel__list__all2__trans, axiom,
    ((![R : set_Pr2117892643t_char, S : set_Pr685054290t_char, T : set_Pr685054290t_char, As : list_list_list_char, Bs : list_list_list_char, Cs : list_P364227422t_char]: ((![A : list_list_char, B : list_list_char, C : produc111478616t_char]: ((member725442668t_char @ (produc1181934459t_char @ A @ B) @ R) => ((member772747827t_char @ (produc1808722894t_char @ B @ C) @ S) => (member772747827t_char @ (produc1808722894t_char @ A @ C) @ T)))) => ((list_a1460260715t_char @ (fun_of681401536t_char @ R) @ As @ Bs) => ((list_a1227756510t_char @ (fun_of1003211849t_char @ S) @ Bs @ Cs) => (list_a1227756510t_char @ (fun_of1003211849t_char @ T) @ As @ Cs))))))). % rel_list_all2_trans
thf(fact_228_rel__list__all2__trans, axiom,
    ((![R : set_Pr1785354703ist_ty, S : set_Pr925902648t_char, T : set_Pr925902648t_char, As : list_list_ty, Bs : list_list_ty, Cs : list_P1602847424t_char]: ((![A : list_ty, B : list_ty, C : produc1109669680t_char]: ((member1942114840ist_ty @ (produc1089615911ist_ty @ A @ B) @ R) => ((member1031340033t_char @ (produc1806338192t_char @ B @ C) @ S) => (member1031340033t_char @ (produc1806338192t_char @ A @ C) @ T)))) => ((list_a1317958679ist_ty @ (fun_of397150316ist_ty @ R) @ As @ Bs) => ((list_a226366592t_char @ (fun_of1649676245t_char @ S) @ Bs @ Cs) => (list_a226366592t_char @ (fun_of1649676245t_char @ T) @ As @ Cs))))))). % rel_list_all2_trans
thf(fact_229_rel__list__all2__trans, axiom,
    ((![R : set_Pr723931873st_val, S : set_Pr82799206t_char, T : set_Pr82799206t_char, As : list_list_val, Bs : list_list_val, Cs : list_exp_list_char]: ((![A : list_val, B : list_val, C : exp_list_char]: ((member1382006826st_val @ (produc180957881st_val @ A @ B) @ R) => ((member580484423t_char @ (produc823987298t_char @ B @ C) @ S) => (member580484423t_char @ (produc823987298t_char @ A @ C) @ T)))) => ((list_a602111657st_val @ (fun_of1684577790st_val @ R) @ As @ Bs) => ((list_a1105622130t_char @ (fun_of161265885t_char @ S) @ Bs @ Cs) => (list_a1105622130t_char @ (fun_of161265885t_char @ T) @ As @ Cs))))))). % rel_list_all2_trans
thf(fact_230_rel__list__all2__trans, axiom,
    ((![R : set_Pr1465729071on_val, S : set_Pr723149704on_val, T : set_Pr723149704on_val, As : list_n1514066695on_val, Bs : list_n1514066695on_val, Cs : list_l566969696on_val]: ((![A : nat > option2118145160on_val, B : nat > option2118145160on_val, C : list_char > option_val]: ((member78096504on_val @ (produc1392944775on_val @ A @ B) @ R) => ((member652041809on_val @ (produc52622304on_val @ B @ C) @ S) => (member652041809on_val @ (produc52622304on_val @ A @ C) @ T)))) => ((list_a592044663on_val @ (fun_of1000097484on_val @ R) @ As @ Bs) => ((list_a729577424on_val @ (fun_of1502879141on_val @ S) @ Bs @ Cs) => (list_a729577424on_val @ (fun_of1502879141on_val @ T) @ As @ Cs))))))). % rel_list_all2_trans
thf(fact_231_rel__list__all2__trans, axiom,
    ((![R : set_Pr685054290t_char, S : set_Pr1314019591t_char, T : set_Pr685054290t_char, As : list_list_list_char, Bs : list_P364227422t_char, Cs : list_P364227422t_char]: ((![A : list_list_char, B : produc111478616t_char, C : produc111478616t_char]: ((member772747827t_char @ (produc1808722894t_char @ A @ B) @ R) => ((member219943760t_char @ (produc1108858903t_char @ B @ C) @ S) => (member772747827t_char @ (produc1808722894t_char @ A @ C) @ T)))) => ((list_a1227756510t_char @ (fun_of1003211849t_char @ R) @ As @ Bs) => ((list_a787061767t_char @ (fun_of756510172t_char @ S) @ Bs @ Cs) => (list_a1227756510t_char @ (fun_of1003211849t_char @ T) @ As @ Cs))))))). % rel_list_all2_trans
thf(fact_232_rel__list__all2__trans, axiom,
    ((![R : set_Pr925902648t_char, S : set_Pr290014113t_char, T : set_Pr925902648t_char, As : list_list_ty, Bs : list_P1602847424t_char, Cs : list_P1602847424t_char]: ((![A : list_ty, B : produc1109669680t_char, C : produc1109669680t_char]: ((member1031340033t_char @ (produc1806338192t_char @ A @ B) @ R) => ((member89029866t_char @ (produc183121785t_char @ B @ C) @ S) => (member1031340033t_char @ (produc1806338192t_char @ A @ C) @ T)))) => ((list_a226366592t_char @ (fun_of1649676245t_char @ R) @ As @ Bs) => ((list_a761598825t_char @ (fun_of446723518t_char @ S) @ Bs @ Cs) => (list_a226366592t_char @ (fun_of1649676245t_char @ T) @ As @ Cs))))))). % rel_list_all2_trans
thf(fact_233_rel__list__all2__trans, axiom,
    ((![R : set_Pr82799206t_char, S : set_Pr224372167t_char, T : set_Pr82799206t_char, As : list_list_val, Bs : list_exp_list_char, Cs : list_exp_list_char]: ((![A : list_val, B : exp_list_char, C : exp_list_char]: ((member580484423t_char @ (produc823987298t_char @ A @ B) @ R) => ((member1699993616t_char @ (produc240508503t_char @ B @ C) @ S) => (member580484423t_char @ (produc823987298t_char @ A @ C) @ T)))) => ((list_a1105622130t_char @ (fun_of161265885t_char @ R) @ As @ Bs) => ((list_a1702871623t_char @ (fun_of64219676t_char @ S) @ Bs @ Cs) => (list_a1105622130t_char @ (fun_of161265885t_char @ T) @ As @ Cs))))))). % rel_list_all2_trans
thf(fact_234_rel__list__all2__trans, axiom,
    ((![R : set_Pr723149704on_val, S : set_Pr1104486497on_val, T : set_Pr723149704on_val, As : list_n1514066695on_val, Bs : list_l566969696on_val, Cs : list_l566969696on_val]: ((![A : nat > option2118145160on_val, B : list_char > option_val, C : list_char > option_val]: ((member652041809on_val @ (produc52622304on_val @ A @ B) @ R) => ((member1177709994on_val @ (produc746553401on_val @ B @ C) @ S) => (member652041809on_val @ (produc52622304on_val @ A @ C) @ T)))) => ((list_a729577424on_val @ (fun_of1502879141on_val @ R) @ As @ Bs) => ((list_a1722502185on_val @ (fun_of461468542on_val @ S) @ Bs @ Cs) => (list_a729577424on_val @ (fun_of1502879141on_val @ T) @ As @ Cs))))))). % rel_list_all2_trans
thf(fact_235_rel__list__all2__trans, axiom,
    ((![R : set_Pr1194734255_ty_ty, S : set_Pr1194734255_ty_ty, T : set_Pr1194734255_ty_ty, As : list_ty, Bs : list_ty, Cs : list_ty]: ((![A : ty, B : ty, C : ty]: ((member2070851320_ty_ty @ (product_Pair_ty_ty @ A @ B) @ R) => ((member2070851320_ty_ty @ (product_Pair_ty_ty @ B @ C) @ S) => (member2070851320_ty_ty @ (product_Pair_ty_ty @ A @ C) @ T)))) => ((list_all2_ty_ty @ (fun_of_ty_ty @ R) @ As @ Bs) => ((list_all2_ty_ty @ (fun_of_ty_ty @ S) @ Bs @ Cs) => (list_all2_ty_ty @ (fun_of_ty_ty @ T) @ As @ Cs))))))). % rel_list_all2_trans
thf(fact_236_rel__list__all2__antisym, axiom,
    ((![S : set_Pr1194734255_ty_ty, T : set_Pr1194734255_ty_ty, Xs : list_ty, Ys : list_ty]: ((![X3 : ty, Y3 : ty]: ((member2070851320_ty_ty @ (product_Pair_ty_ty @ X3 @ Y3) @ S) => ((member2070851320_ty_ty @ (product_Pair_ty_ty @ Y3 @ X3) @ T) => (X3 = Y3)))) => ((list_all2_ty_ty @ (fun_of_ty_ty @ S) @ Xs @ Ys) => ((list_all2_ty_ty @ (fun_of_ty_ty @ T) @ Ys @ Xs) => (Xs = Ys))))))). % rel_list_all2_antisym
thf(fact_237_rel__list__all2__Cons1, axiom,
    ((![S : set_Pr1036794744ty_val, X : ty, Xs : list_ty, Ys : list_val]: ((list_all2_ty_val @ (fun_of_ty_val @ S) @ (cons_ty @ X @ Xs) @ Ys) = (?[Z : val]: (?[Zs : list_val]: (((Ys = (cons_val @ Z @ Zs))) & ((((member1776226881ty_val @ (product_Pair_ty_val @ X @ Z) @ S)) & ((list_all2_ty_val @ (fun_of_ty_val @ S) @ Xs @ Zs))))))))))). % rel_list_all2_Cons1
thf(fact_238_rel__list__all2__Cons1, axiom,
    ((![S : set_Pr312206840val_ty, X : val, Xs : list_val, Ys : list_ty]: ((list_all2_val_ty @ (fun_of_val_ty @ S) @ (cons_val @ X @ Xs) @ Ys) = (?[Z : ty]: (?[Zs : list_ty]: (((Ys = (cons_ty @ Z @ Zs))) & ((((member1400634561val_ty @ (product_Pair_val_ty @ X @ Z) @ S)) & ((list_all2_val_ty @ (fun_of_val_ty @ S) @ Xs @ Zs))))))))))). % rel_list_all2_Cons1
thf(fact_239_rel__list__all2__Cons1, axiom,
    ((![S : set_Pr1870322241al_val, X : val, Xs : list_val, Ys : list_val]: ((list_all2_val_val @ (fun_of_val_val @ S) @ (cons_val @ X @ Xs) @ Ys) = (?[Z : val]: (?[Zs : list_val]: (((Ys = (cons_val @ Z @ Zs))) & ((((member1494223754al_val @ (product_Pair_val_val @ X @ Z) @ S)) & ((list_all2_val_val @ (fun_of_val_val @ S) @ Xs @ Zs))))))))))). % rel_list_all2_Cons1
thf(fact_240_rel__list__all2__Cons1, axiom,
    ((![S : set_Pr1194734255_ty_ty, X : ty, Xs : list_ty, Ys : list_ty]: ((list_all2_ty_ty @ (fun_of_ty_ty @ S) @ (cons_ty @ X @ Xs) @ Ys) = (?[Z : ty]: (?[Zs : list_ty]: (((Ys = (cons_ty @ Z @ Zs))) & ((((member2070851320_ty_ty @ (product_Pair_ty_ty @ X @ Z) @ S)) & ((list_all2_ty_ty @ (fun_of_ty_ty @ S) @ Xs @ Zs))))))))))). % rel_list_all2_Cons1
thf(fact_241_rel__list__all2__Cons1, axiom,
    ((![S : set_Pr349050585har_ty, X : list_char, Xs : list_list_char, Ys : list_ty]: ((list_a1770748705har_ty @ (fun_of_list_char_ty @ S) @ (cons_list_char @ X @ Xs) @ Ys) = (?[Z : ty]: (?[Zs : list_ty]: (((Ys = (cons_ty @ Z @ Zs))) & ((((member325880354har_ty @ (produc1017542449har_ty @ X @ Z) @ S)) & ((list_a1770748705har_ty @ (fun_of_list_char_ty @ S) @ Xs @ Zs))))))))))). % rel_list_all2_Cons1
thf(fact_242_rel__list__all2__Cons1, axiom,
    ((![S : set_Pr174107298ar_val, X : list_char, Xs : list_list_char, Ys : list_val]: ((list_a280217834ar_val @ (fun_of_list_char_val @ S) @ (cons_list_char @ X @ Xs) @ Ys) = (?[Z : val]: (?[Zs : list_val]: (((Ys = (cons_val @ Z @ Zs))) & ((((member1062074475ar_val @ (produc368164090ar_val @ X @ Z) @ S)) & ((list_a280217834ar_val @ (fun_of_list_char_val @ S) @ Xs @ Zs))))))))))). % rel_list_all2_Cons1
thf(fact_243_rel__list__all2__Cons1, axiom,
    ((![S : set_Pr1320471513t_char, X : ty, Xs : list_ty, Ys : list_list_char]: ((list_a1504214817t_char @ (fun_of_ty_list_char @ S) @ (cons_ty @ X @ Xs) @ Ys) = (?[Z : list_char]: (?[Zs : list_list_char]: (((Ys = (cons_list_char @ Z @ Zs))) & ((((member1016971042t_char @ (produc751008561t_char @ X @ Z) @ S)) & ((list_a1504214817t_char @ (fun_of_ty_list_char @ S) @ Xs @ Zs))))))))))). % rel_list_all2_Cons1
thf(fact_244_rel__list__all2__Cons1, axiom,
    ((![S : set_Pr504292735ion_ty, X : ty, Xs : list_ty, Ys : list_option_ty]: ((list_a765198023ion_ty @ (fun_of_ty_option_ty @ S) @ (cons_ty @ X @ Xs) @ Ys) = (?[Z : option_ty]: (?[Zs : list_option_ty]: (((Ys = (cons_option_ty @ Z @ Zs))) & ((((member578800584ion_ty @ (produc11991767ion_ty @ X @ Z) @ S)) & ((list_a765198023ion_ty @ (fun_of_ty_option_ty @ S) @ Xs @ Zs))))))))))). % rel_list_all2_Cons1
thf(fact_245_rel__list__all2__Cons1, axiom,
    ((![S : set_Pr1557683618t_char, X : val, Xs : list_val, Ys : list_list_char]: ((list_a1248766058t_char @ (fun_of_val_list_char @ S) @ (cons_val @ X @ Xs) @ Ys) = (?[Z : list_char]: (?[Zs : list_list_char]: (((Ys = (cons_list_char @ Z @ Zs))) & ((((member1429154667t_char @ (produc1336712314t_char @ X @ Z) @ S)) & ((list_a1248766058t_char @ (fun_of_val_list_char @ S) @ Xs @ Zs))))))))))). % rel_list_all2_Cons1
thf(fact_246_rel__list__all2__Cons1, axiom,
    ((![S : set_Pr741504840ion_ty, X : val, Xs : list_val, Ys : list_option_ty]: ((list_a509749264ion_ty @ (fun_of_val_option_ty @ S) @ (cons_val @ X @ Xs) @ Ys) = (?[Z : option_ty]: (?[Zs : list_option_ty]: (((Ys = (cons_option_ty @ Z @ Zs))) & ((((member990984209ion_ty @ (produc597695520ion_ty @ X @ Z) @ S)) & ((list_a509749264ion_ty @ (fun_of_val_option_ty @ S) @ Xs @ Zs))))))))))). % rel_list_all2_Cons1
thf(fact_247_rel__list__all2__Cons2, axiom,
    ((![S : set_Pr1194734255_ty_ty, Xs : list_ty, Y : ty, Ys : list_ty]: ((list_all2_ty_ty @ (fun_of_ty_ty @ S) @ Xs @ (cons_ty @ Y @ Ys)) = (?[Z : ty]: (?[Zs : list_ty]: (((Xs = (cons_ty @ Z @ Zs))) & ((((member2070851320_ty_ty @ (product_Pair_ty_ty @ Z @ Y) @ S)) & ((list_all2_ty_ty @ (fun_of_ty_ty @ S) @ Zs @ Ys))))))))))). % rel_list_all2_Cons2

% Conjectures (4)
thf(conj_0, hypothesis,
    ((![E3 : list_char > option_ty]: (((size_s2008079621t_char @ vsa) = (size_size_list_ty @ tsa)) => (((size_size_list_val @ vsa2) = (size_size_list_ty @ tsa)) => ((wTrt @ p @ h @ E3 @ (blocks @ (produc1808722894t_char @ vsa @ (produc1806338192t_char @ tsa @ (produc823987298t_char @ vsa2 @ ea)))) @ t) = (((wTrt @ p @ h @ (map_up703499792har_ty @ E3 @ vsa @ tsa) @ ea @ t)) & ((?[Ts4 : list_ty]: ((((map_val_option_ty @ (typeof_h @ h) @ vsa2) = (map_ty_option_ty @ some_ty @ Ts4))) & ((list_all2_ty_ty @ (widen_917054840t_char @ p) @ Ts4 @ tsa)))))))))))).
thf(conj_1, hypothesis,
    (((size_s2008079621t_char @ (cons_list_char @ v @ vsa)) = (size_size_list_ty @ (cons_ty @ ta @ tsa))))).
thf(conj_2, hypothesis,
    (((size_size_list_val @ (cons_val @ v2 @ vsa2)) = (size_size_list_ty @ (cons_ty @ ta @ tsa))))).
thf(conj_3, conjecture,
    (((wTrt @ p @ h @ e @ (blocks @ (produc1808722894t_char @ (cons_list_char @ v @ vsa) @ (produc1806338192t_char @ (cons_ty @ ta @ tsa) @ (produc823987298t_char @ (cons_val @ v2 @ vsa2) @ ea)))) @ t) = (((wTrt @ p @ h @ (map_up703499792har_ty @ e @ (cons_list_char @ v @ vsa) @ (cons_ty @ ta @ tsa)) @ ea @ t)) & ((?[Ts4 : list_ty]: ((((map_val_option_ty @ (typeof_h @ h) @ (cons_val @ v2 @ vsa2)) = (map_ty_option_ty @ some_ty @ Ts4))) & ((list_all2_ty_ty @ (widen_917054840t_char @ p) @ Ts4 @ (cons_ty @ ta @ tsa)))))))))).
