% 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_123__5334894_1 ) ; }
% This file was generated by Isabelle (most likely Sledgehammer)
% 2020-12-16 14:19:30.347

% Could-be-implicit typings (59)
thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_It__Product____Type__Oprod_It__List__Olist_It__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_J_Mt__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_M_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_Mt__Product____Type__Oprod_It__List__Olist_It__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_J_Mt__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_M_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_Mt__Product____Type__Oprod_It__Product____Type__Oprod_It__List__Olist_It__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_J_Mt__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_M_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_Mt__Product____Type__Oprod_It__List__Olist_It__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_J_Mt__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_M_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_J_J, type,
    set_Pr1301890247on_val : $tType).
thf(ty_n_t__Product____Type__Oprod_It__Product____Type__Oprod_It__Product____Type__Oprod_It__List__Olist_It__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_J_Mt__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_M_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_Mt__Product____Type__Oprod_It__List__Olist_It__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_J_Mt__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_M_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_Mt__Product____Type__Oprod_It__Product____Type__Oprod_It__List__Olist_It__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_J_Mt__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_M_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_Mt__Product____Type__Oprod_It__List__Olist_It__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_J_Mt__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_M_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_J, type,
    produc1428501223on_val : $tType).
thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_It__Product____Type__Oprod_It__List__Olist_It__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_J_Mt__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_M_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_Mt__Product____Type__Oprod_It__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_Mt__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_M_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_Mt__Product____Type__Oprod_It__Product____Type__Oprod_It__List__Olist_It__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_J_Mt__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_M_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_Mt__Product____Type__Oprod_It__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_Mt__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_M_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_J_J, type,
    set_Pr655264327on_val : $tType).
thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_It__Product____Type__Oprod_It__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_Mt__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_M_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_Mt__Product____Type__Oprod_It__List__Olist_It__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_J_Mt__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_M_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_Mt__Product____Type__Oprod_It__Product____Type__Oprod_It__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_Mt__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_M_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_Mt__Product____Type__Oprod_It__List__Olist_It__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_J_Mt__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_M_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_J_J, type,
    set_Pr1582577479on_val : $tType).
thf(ty_n_t__Product____Type__Oprod_It__Product____Type__Oprod_It__Product____Type__Oprod_It__List__Olist_It__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_J_Mt__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_M_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_Mt__Product____Type__Oprod_It__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_Mt__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_M_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_Mt__Product____Type__Oprod_It__Product____Type__Oprod_It__List__Olist_It__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_J_Mt__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_M_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_Mt__Product____Type__Oprod_It__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_Mt__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_M_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_J, type,
    produc1931033447on_val : $tType).
thf(ty_n_t__Product____Type__Oprod_It__Product____Type__Oprod_It__Product____Type__Oprod_It__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_Mt__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_M_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_Mt__Product____Type__Oprod_It__List__Olist_It__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_J_Mt__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_M_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_Mt__Product____Type__Oprod_It__Product____Type__Oprod_It__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_Mt__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_M_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_Mt__Product____Type__Oprod_It__List__Olist_It__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_J_Mt__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_M_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_J, type,
    produc128280679on_val : $tType).
thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_It__Product____Type__Oprod_It__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_Mt__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_M_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_Mt__Product____Type__Oprod_It__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_Mt__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_M_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_Mt__Product____Type__Oprod_It__Product____Type__Oprod_It__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_Mt__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_M_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_Mt__Product____Type__Oprod_It__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_Mt__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_M_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_J_J, type,
    set_Pr1368603847on_val : $tType).
thf(ty_n_t__Product____Type__Oprod_It__Product____Type__Oprod_It__Product____Type__Oprod_It__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_Mt__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_M_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_Mt__Product____Type__Oprod_It__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_Mt__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_M_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_Mt__Product____Type__Oprod_It__Product____Type__Oprod_It__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_Mt__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_M_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_Mt__Product____Type__Oprod_It__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_Mt__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_M_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_J, type,
    produc1161703655on_val : $tType).
thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_It__List__Olist_It__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_J_Mt__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_M_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_Mt__Product____Type__Oprod_It__List__Olist_It__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_J_Mt__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_M_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_J, type,
    set_Pr208351751on_val : $tType).
thf(ty_n_t__Product____Type__Oprod_It__Product____Type__Oprod_It__List__Olist_It__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_J_Mt__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_M_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_Mt__Product____Type__Oprod_It__List__Olist_It__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_J_Mt__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_M_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J, type,
    produc655058983on_val : $tType).
thf(ty_n_t__Product____Type__Oprod_It__Product____Type__Oprod_It__List__Olist_It__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_J_Mt__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_M_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_Mt__Product____Type__Oprod_It__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_Mt__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_M_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J, type,
    produc819823277on_val : $tType).
thf(ty_n_t__Product____Type__Oprod_It__Product____Type__Oprod_It__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_Mt__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_M_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_Mt__Product____Type__Oprod_It__List__Olist_It__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_J_Mt__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_M_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J, type,
    produc1438437793on_val : $tType).
thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_It__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_Mt__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_M_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_Mt__Product____Type__Oprod_It__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_Mt__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_M_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_J, type,
    set_Pr1189492743on_val : $tType).
thf(ty_n_t__Product____Type__Oprod_It__Product____Type__Oprod_It__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_Mt__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_M_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_Mt__Product____Type__Oprod_It__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_Mt__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_M_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J, type,
    produc1172664615on_val : $tType).
thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_M_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_Mt__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_M_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J, type,
    set_Pr148564103on_val : $tType).
thf(ty_n_t__Product____Type__Oprod_It__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_M_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_Mt__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_M_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J, type,
    produc744932519on_val : $tType).
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__List__Olist_It__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_J_Mt__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_M_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J, type,
    set_Pr1511552798on_val : $tType).
thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_Mt__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J, type,
    set_Pr2110063281on_val : $tType).
thf(ty_n_t__Product____Type__Oprod_It__List__Olist_It__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_J_Mt__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_M_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J, type,
    produc335961278on_val : $tType).
thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_Mt__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_M_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J, type,
    set_Pr556513572on_val : $tType).
thf(ty_n_t__Product____Type__Oprod_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_Mt__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J, type,
    produc1085126737on_val : $tType).
thf(ty_n_t__Product____Type__Oprod_It__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_Mt__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_M_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J, type,
    produc1097884484on_val : $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_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_I_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_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,
    set_Pr227219079on_val : $tType).
thf(ty_n_t__Product____Type__Oprod_I_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_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J, type,
    produc1731226791on_val : $tType).
thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_It__Expr__Obop_Mt__Product____Type__Oprod_It__Value__Oval_Mt__Value__Oval_J_J_Mt__Product____Type__Oprod_It__Expr__Obop_Mt__Product____Type__Oprod_It__Value__Oval_Mt__Value__Oval_J_J_J_J, type,
    set_Pr711661575al_val : $tType).
thf(ty_n_t__Product____Type__Oprod_It__Product____Type__Oprod_It__Expr__Obop_Mt__Product____Type__Oprod_It__Value__Oval_Mt__Value__Oval_J_J_Mt__Product____Type__Oprod_It__Expr__Obop_Mt__Product____Type__Oprod_It__Value__Oval_Mt__Value__Oval_J_J_J, type,
    produc674182439al_val : $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_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,
    set_Pr2075231726on_val : $tType).
thf(ty_n_t__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J, type,
    produc266837688on_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__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__Set__Oset_It__Product____Type__Oprod_It__List__Olist_It__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_J_Mt__List__Olist_It__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_J_J_J, type,
    set_Pr1932514887t_char : $tType).
thf(ty_n_t__Product____Type__Oprod_It__List__Olist_It__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_J_Mt__List__Olist_It__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_J_J, type,
    produc1813212775t_char : $tType).
thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_It__Value__Oval_Mt__Value__Oval_J_Mt__Product____Type__Oprod_It__Value__Oval_Mt__Value__Oval_J_J_J, type,
    set_Pr488475975al_val : $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__Product____Type__Oprod_It__Value__Oval_Mt__Value__Oval_J_Mt__Product____Type__Oprod_It__Value__Oval_Mt__Value__Oval_J_J, type,
    produc1743387751al_val : $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__Set__Oset_It__Product____Type__Oprod_It__Expr__Obop_Mt__Product____Type__Oprod_It__Value__Oval_Mt__Value__Oval_J_J_J, type,
    set_Pr624825500al_val : $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__Expr__Obop_Mt__Product____Type__Oprod_It__Value__Oval_Mt__Value__Oval_J_J, type,
    produc1373793468al_val : $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__Set__Oset_It__Product____Type__Oprod_It__Expr__Obop_Mt__Expr__Obop_J_J, type,
    set_Pr445896583op_bop : $tType).
thf(ty_n_t__Option__Ooption_It__Set__Oset_It__List__Olist_It__String__Ochar_J_J_J, type,
    option_set_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__Expr__Obop_Mt__Expr__Obop_J, type,
    product_prod_bop_bop : $tType).
thf(ty_n_t__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J, type,
    exp_list_char : $tType).
thf(ty_n_t__Set__Oset_It__List__Olist_It__String__Ochar_J_J, type,
    set_list_char : $tType).
thf(ty_n_t__Option__Ooption_It__Value__Oval_J, type,
    option_val : $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__Value__Oval, type,
    val : $tType).
thf(ty_n_t__Expr__Obop, type,
    bop : $tType).
thf(ty_n_t__Nat__Onat, type,
    nat : $tType).

% Explicit typings (115)
thf(sy_c_DefAss_O_092_060A_062_001t__List__Olist_It__String__Ochar_J, type,
    a_list_char : exp_list_char > option_set_list_char).
thf(sy_c_Expr_Obinop, type,
    binop : produc1373793468al_val > option_val).
thf(sy_c_Expr_Oexp_OBinOp_001t__List__Olist_It__String__Ochar_J, type,
    binOp_list_char : exp_list_char > bop > exp_list_char > exp_list_char).
thf(sy_c_Expr_Oexp_OCall_001t__List__Olist_It__String__Ochar_J, type,
    call_list_char : exp_list_char > list_char > list_exp_list_char > exp_list_char).
thf(sy_c_Expr_Oexp_OVal_001t__List__Olist_It__String__Ochar_J, type,
    val_list_char : val > exp_list_char).
thf(sy_c_Expr_Oexp_Othrow_001t__List__Olist_It__String__Ochar_J, type,
    throw_list_char : exp_list_char > exp_list_char).
thf(sy_c_Fun_Ofun__upd_001t__List__Olist_It__String__Ochar_J_001t__Option__Ooption_It__Value__Oval_J, type,
    fun_up1252458416on_val : (list_char > option_val) > list_char > option_val > list_char > option_val).
thf(sy_c_Fun_Ofun__upd_001t__Nat__Onat_001t__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,
    fun_up262443479on_val : (nat > option2118145160on_val) > nat > option2118145160on_val > nat > option2118145160on_val).
thf(sy_c_If_001t__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,
    if_opt451925058on_val : $o > option2118145160on_val > option2118145160on_val > option2118145160on_val).
thf(sy_c_List_Oappend_001t__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J, type,
    append_exp_list_char : list_exp_list_char > list_exp_list_char > list_exp_list_char).
thf(sy_c_List_Olist_OCons_001t__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J, type,
    cons_exp_list_char : exp_list_char > list_exp_list_char > list_exp_list_char).
thf(sy_c_List_Olist_Omap_001t__Value__Oval_001t__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J, type,
    map_va1515327237t_char : (val > exp_list_char) > list_val > list_exp_list_char).
thf(sy_c_Map_Omap__add_001t__List__Olist_It__String__Ochar_J_001t__Value__Oval, type,
    map_ad1615113112ar_val : (list_char > option_val) > (list_char > option_val) > list_char > option_val).
thf(sy_c_Map_Omap__add_001t__Nat__Onat_001t__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J, type,
    map_ad109059391on_val : (nat > option2118145160on_val) > (nat > option2118145160on_val) > nat > option2118145160on_val).
thf(sy_c_Objects_Ohext, type,
    hext : (nat > option2118145160on_val) > (nat > option2118145160on_val) > $o).
thf(sy_c_Option_Ooption_ONone_001t__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J, type,
    none_P1535574167on_val : option2118145160on_val).
thf(sy_c_Option_Ooption_ONone_001t__Set__Oset_It__List__Olist_It__String__Ochar_J_J, type,
    none_set_list_char : option_set_list_char).
thf(sy_c_Option_Ooption_ONone_001t__Value__Oval, type,
    none_val : option_val).
thf(sy_c_Option_Ooption_OSome_001t__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J, type,
    some_P1299442195on_val : produc266837688on_val > option2118145160on_val).
thf(sy_c_Option_Ooption_OSome_001t__Set__Oset_It__List__Olist_It__String__Ochar_J_J, type,
    some_set_list_char : set_list_char > option_set_list_char).
thf(sy_c_Option_Ooption_OSome_001t__Value__Oval, type,
    some_val : val > option_val).
thf(sy_c_Option_Ooption_Othe_001t__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J, type,
    the_Pr901949220on_val : option2118145160on_val > produc266837688on_val).
thf(sy_c_Option_Ooption_Othe_001t__Set__Oset_It__List__Olist_It__String__Ochar_J_J, type,
    the_set_list_char : option_set_list_char > set_list_char).
thf(sy_c_Option_Ooption_Othe_001t__Value__Oval, type,
    the_val : option_val > 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_001_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_001_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J, type,
    produc797901719on_val : (produc1257910179t_char > option_val) > (produc1257910179t_char > option_val) > produc1731226791on_val).
thf(sy_c_Product__Type_OPair_001t__Expr__Obop_001t__Expr__Obop, type,
    product_Pair_bop_bop : bop > bop > product_prod_bop_bop).
thf(sy_c_Product__Type_OPair_001t__Expr__Obop_001t__Product____Type__Oprod_It__Value__Oval_Mt__Value__Oval_J, type,
    produc1753769388al_val : bop > product_prod_val_val > produc1373793468al_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__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_001t__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_M_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_J, type,
    produc2023458740on_val : exp_list_char > produc515445032on_val > produc1097884484on_val).
thf(sy_c_Product__Type_OPair_001t__List__Olist_It__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_J_001t__List__Olist_It__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_J, type,
    produc1721801175t_char : list_exp_list_char > list_exp_list_char > produc1813212775t_char).
thf(sy_c_Product__Type_OPair_001t__List__Olist_It__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_J_001t__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_M_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_J, type,
    produc1725134254on_val : list_exp_list_char > produc515445032on_val > produc335961278on_val).
thf(sy_c_Product__Type_OPair_001t__List__Olist_It__String__Ochar_J_001_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J, type,
    produc904988266on_val : list_char > (produc1257910179t_char > option_val) > produc266837688on_val).
thf(sy_c_Product__Type_OPair_001t__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__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_M_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_001t__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_M_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_J, type,
    produc2106877847on_val : produc515445032on_val > produc515445032on_val > produc744932519on_val).
thf(sy_c_Product__Type_OPair_001t__Product____Type__Oprod_It__Expr__Obop_Mt__Product____Type__Oprod_It__Value__Oval_Mt__Value__Oval_J_J_001t__Product____Type__Oprod_It__Expr__Obop_Mt__Product____Type__Oprod_It__Value__Oval_Mt__Value__Oval_J_J, type,
    produc1144711447al_val : produc1373793468al_val > produc1373793468al_val > produc674182439al_val).
thf(sy_c_Product__Type_OPair_001t__Product____Type__Oprod_It__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_Mt__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_M_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_001t__Product____Type__Oprod_It__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_Mt__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_M_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J, type,
    produc1069526295on_val : produc1097884484on_val > produc1097884484on_val > produc1172664615on_val).
thf(sy_c_Product__Type_OPair_001t__Product____Type__Oprod_It__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_Mt__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_M_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_001t__Product____Type__Oprod_It__List__Olist_It__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_J_Mt__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_M_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J, type,
    produc367337745on_val : produc1097884484on_val > produc335961278on_val > produc1438437793on_val).
thf(sy_c_Product__Type_OPair_001t__Product____Type__Oprod_It__List__Olist_It__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_J_Mt__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_M_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_001t__Product____Type__Oprod_It__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_Mt__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_M_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J, type,
    produc974123805on_val : produc335961278on_val > produc1097884484on_val > produc819823277on_val).
thf(sy_c_Product__Type_OPair_001t__Product____Type__Oprod_It__List__Olist_It__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_J_Mt__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_M_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_001t__Product____Type__Oprod_It__List__Olist_It__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_J_Mt__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_M_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J, type,
    produc245869591on_val : produc335961278on_val > produc335961278on_val > produc655058983on_val).
thf(sy_c_Product__Type_OPair_001t__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_001t__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J, type,
    produc881885833on_val : produc266837688on_val > produc266837688on_val > produc1085126737on_val).
thf(sy_c_Product__Type_OPair_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_Mt__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_M_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_Mt__Product____Type__Oprod_It__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_Mt__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_M_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_Mt__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_M_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_Mt__Product____Type__Oprod_It__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_Mt__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_M_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J, type,
    produc564964183on_val : produc1172664615on_val > produc1172664615on_val > produc1161703655on_val).
thf(sy_c_Product__Type_OPair_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_Mt__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_M_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_Mt__Product____Type__Oprod_It__List__Olist_It__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_J_Mt__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_M_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_Mt__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_M_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_Mt__Product____Type__Oprod_It__List__Olist_It__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_J_Mt__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_M_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J, type,
    produc625175255on_val : produc1438437793on_val > produc1438437793on_val > produc128280679on_val).
thf(sy_c_Product__Type_OPair_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__List__Olist_It__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_J_Mt__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_M_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_Mt__Product____Type__Oprod_It__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_Mt__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_M_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__List__Olist_It__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_J_Mt__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_M_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_Mt__Product____Type__Oprod_It__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_Mt__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_M_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J, type,
    produc1914110935on_val : produc819823277on_val > produc819823277on_val > produc1931033447on_val).
thf(sy_c_Product__Type_OPair_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__List__Olist_It__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_J_Mt__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_M_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_Mt__Product____Type__Oprod_It__List__Olist_It__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_J_Mt__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_M_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__List__Olist_It__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_J_Mt__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_M_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_Mt__Product____Type__Oprod_It__List__Olist_It__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_J_Mt__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_M_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J, type,
    produc1802175319on_val : produc655058983on_val > produc655058983on_val > produc1428501223on_val).
thf(sy_c_Product__Type_OPair_001t__Product____Type__Oprod_It__Value__Oval_Mt__Value__Oval_J_001t__Product____Type__Oprod_It__Value__Oval_Mt__Value__Oval_J, type,
    produc1931530455al_val : product_prod_val_val > product_prod_val_val > produc1743387751al_val).
thf(sy_c_Product__Type_OPair_001t__Value__Oval_001t__Value__Oval, type,
    product_Pair_val_val : val > val > product_prod_val_val).
thf(sy_c_Product__Type_Ocurry_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_001_Eo, type,
    produc761261956_val_o : (produc515445032on_val > $o) > (nat > option2118145160on_val) > (list_char > option_val) > $o).
thf(sy_c_Product__Type_Ocurry_001t__Expr__Obop_001t__Product____Type__Oprod_It__Value__Oval_Mt__Value__Oval_J_001_Eo, type,
    produc1461204536_val_o : (produc1373793468al_val > $o) > bop > product_prod_val_val > $o).
thf(sy_c_Product__Type_Ocurry_001t__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_001t__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_M_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_001_Eo, type,
    produc699483184_val_o : (produc1097884484on_val > $o) > exp_list_char > produc515445032on_val > $o).
thf(sy_c_Product__Type_Ocurry_001t__List__Olist_It__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_J_001t__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_M_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_001_Eo, type,
    produc1199911222_val_o : (produc335961278on_val > $o) > list_exp_list_char > produc515445032on_val > $o).
thf(sy_c_Product__Type_Ocurry_001t__List__Olist_It__String__Ochar_J_001_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_001_Eo, type,
    produc988598624_val_o : (produc266837688on_val > $o) > list_char > (produc1257910179t_char > option_val) > $o).
thf(sy_c_Relation_Osingle__valued_001t__Product____Type__Oprod_It__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_Mt__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_M_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_001t__Product____Type__Oprod_It__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_Mt__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_M_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J, type,
    single747474179on_val : set_Pr1189492743on_val > $o).
thf(sy_c_Relation_Osingle__valued_001t__Product____Type__Oprod_It__List__Olist_It__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_J_Mt__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_M_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_001t__Product____Type__Oprod_It__List__Olist_It__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_J_Mt__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_M_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J, type,
    single965918723on_val : set_Pr208351751on_val > $o).
thf(sy_c_Set_OCollect_001t__List__Olist_It__String__Ochar_J, type,
    collect_list_char : (list_char > $o) > set_list_char).
thf(sy_c_Set_OCollect_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_Mt__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_M_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_Mt__Product____Type__Oprod_It__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_Mt__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_M_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J, type,
    collec2055896722on_val : (produc1172664615on_val > $o) > set_Pr1189492743on_val).
thf(sy_c_Set_OCollect_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__List__Olist_It__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_J_Mt__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_M_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_Mt__Product____Type__Oprod_It__List__Olist_It__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_J_Mt__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_M_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J, type,
    collec105960082on_val : (produc655058983on_val > $o) > set_Pr208351751on_val).
thf(sy_c_SmallStep_Ored, type,
    red : list_P1234162913t_char > set_Pr1189492743on_val).
thf(sy_c_SmallStep_Oredp, type,
    redp : list_P1234162913t_char > exp_list_char > produc515445032on_val > exp_list_char > produc515445032on_val > $o).
thf(sy_c_SmallStep_Oreds, type,
    reds : list_P1234162913t_char > set_Pr208351751on_val).
thf(sy_c_Transitive__Closure_Ortrancl_001t__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_M_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_J, type,
    transi432893227on_val : set_Pr148564103on_val > set_Pr148564103on_val).
thf(sy_c_Transitive__Closure_Ortrancl_001t__Product____Type__Oprod_It__Expr__Obop_Mt__Product____Type__Oprod_It__Value__Oval_Mt__Value__Oval_J_J, type,
    transi531594559al_val : set_Pr711661575al_val > set_Pr711661575al_val).
thf(sy_c_Transitive__Closure_Ortrancl_001t__Product____Type__Oprod_It__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_Mt__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_M_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J, type,
    transi111096263on_val : set_Pr1189492743on_val > set_Pr1189492743on_val).
thf(sy_c_Transitive__Closure_Ortrancl_001t__Product____Type__Oprod_It__List__Olist_It__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_J_Mt__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_M_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J, type,
    transi325225921on_val : set_Pr208351751on_val > set_Pr208351751on_val).
thf(sy_c_Transitive__Closure_Ortrancl_001t__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J, type,
    transi2071064181on_val : set_Pr2110063281on_val > set_Pr2110063281on_val).
thf(sy_c_Wellfounded_Olex__prod_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,
    lex_pr683585528on_val : set_Pr1465729071on_val > set_Pr1104486497on_val > set_Pr148564103on_val).
thf(sy_c_Wellfounded_Olex__prod_001t__Expr__Obop_001t__Product____Type__Oprod_It__Value__Oval_Mt__Value__Oval_J, type,
    lex_pr2029241796al_val : set_Pr445896583op_bop > set_Pr488475975al_val > set_Pr711661575al_val).
thf(sy_c_Wellfounded_Olex__prod_001t__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_001t__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_M_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_J, type,
    lex_pr1764546508on_val : set_Pr224372167t_char > set_Pr148564103on_val > set_Pr1189492743on_val).
thf(sy_c_Wellfounded_Olex__prod_001t__List__Olist_It__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_J_001t__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_M_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_J, type,
    lex_pr263313862on_val : set_Pr1932514887t_char > set_Pr148564103on_val > set_Pr208351751on_val).
thf(sy_c_Wellfounded_Olex__prod_001t__List__Olist_It__String__Ochar_J_001_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J, type,
    lex_pr1753065554on_val : set_Pr164112643t_char > set_Pr227219079on_val > set_Pr2110063281on_val).
thf(sy_c_Wellfounded_Olex__prod_001t__Product____Type__Oprod_It__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_Mt__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_M_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_001t__Product____Type__Oprod_It__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_Mt__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_M_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J, type,
    lex_pr186272047on_val : set_Pr1189492743on_val > set_Pr1189492743on_val > set_Pr1368603847on_val).
thf(sy_c_Wellfounded_Olex__prod_001t__Product____Type__Oprod_It__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_Mt__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_M_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_001t__Product____Type__Oprod_It__List__Olist_It__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_J_Mt__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_M_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J, type,
    lex_pr511103273on_val : set_Pr1189492743on_val > set_Pr208351751on_val > set_Pr1582577479on_val).
thf(sy_c_Wellfounded_Olex__prod_001t__Product____Type__Oprod_It__List__Olist_It__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_J_Mt__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_M_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_001t__Product____Type__Oprod_It__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_Mt__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_M_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J, type,
    lex_pr1117889333on_val : set_Pr208351751on_val > set_Pr1189492743on_val > set_Pr655264327on_val).
thf(sy_c_Wellfounded_Olex__prod_001t__Product____Type__Oprod_It__List__Olist_It__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_J_Mt__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_M_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_001t__Product____Type__Oprod_It__List__Olist_It__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_J_Mt__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_M_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J, type,
    lex_pr601255983on_val : set_Pr208351751on_val > set_Pr208351751on_val > set_Pr1301890247on_val).
thf(sy_c_Wfrec_Osame__fst_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,
    same_f1752972725on_val : ((nat > option2118145160on_val) > $o) > ((nat > option2118145160on_val) > set_Pr1104486497on_val) > set_Pr148564103on_val).
thf(sy_c_Wfrec_Osame__fst_001t__Expr__Obop_001t__Product____Type__Oprod_It__Value__Oval_Mt__Value__Oval_J, type,
    same_f915619585al_val : (bop > $o) > (bop > set_Pr488475975al_val) > set_Pr711661575al_val).
thf(sy_c_Wfrec_Osame__fst_001t__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_001t__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_M_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_J, type,
    same_f366220041on_val : (exp_list_char > $o) > (exp_list_char > set_Pr148564103on_val) > set_Pr1189492743on_val).
thf(sy_c_Wfrec_Osame__fst_001t__List__Olist_It__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_J_001t__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_M_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_J, type,
    same_f1555812995on_val : (list_exp_list_char > $o) > (list_exp_list_char > set_Pr148564103on_val) > set_Pr208351751on_val).
thf(sy_c_Wfrec_Osame__fst_001t__List__Olist_It__String__Ochar_J_001_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J, type,
    same_f2003279573on_val : (list_char > $o) > (list_char > set_Pr227219079on_val) > set_Pr2110063281on_val).
thf(sy_c_member_001t__List__Olist_It__String__Ochar_J, type,
    member_list_char : list_char > set_list_char > $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_I_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_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J, type,
    member548035792on_val : produc1731226791on_val > set_Pr227219079on_val > $o).
thf(sy_c_member_001t__Product____Type__Oprod_It__Expr__Obop_Mt__Expr__Obop_J, type,
    member843417040op_bop : product_prod_bop_bop > set_Pr445896583op_bop > $o).
thf(sy_c_member_001t__Product____Type__Oprod_It__Expr__Obop_Mt__Product____Type__Oprod_It__Value__Oval_Mt__Value__Oval_J_J, type,
    member772310885al_val : produc1373793468al_val > set_Pr624825500al_val > $o).
thf(sy_c_member_001t__Product____Type__Oprod_It__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_Mt__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__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_Mt__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_M_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J, type,
    member1888679917on_val : produc1097884484on_val > set_Pr556513572on_val > $o).
thf(sy_c_member_001t__Product____Type__Oprod_It__List__Olist_It__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_J_Mt__List__Olist_It__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_J_J, type,
    member462435472t_char : produc1813212775t_char > set_Pr1932514887t_char > $o).
thf(sy_c_member_001t__Product____Type__Oprod_It__List__Olist_It__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_J_Mt__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_M_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J, type,
    member184158439on_val : produc335961278on_val > set_Pr1511552798on_val > $o).
thf(sy_c_member_001t__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J, type,
    member1296415951on_val : produc266837688on_val > set_Pr2075231726on_val > $o).
thf(sy_c_member_001t__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J, type,
    member89690956t_char : produc1257910179t_char > set_Pr164112643t_char > $o).
thf(sy_c_member_001t__Product____Type__Oprod_It__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_M_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_Mt__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_M_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J, type,
    member2027247312on_val : produc744932519on_val > set_Pr148564103on_val > $o).
thf(sy_c_member_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__Expr__Obop_Mt__Product____Type__Oprod_It__Value__Oval_Mt__Value__Oval_J_J_Mt__Product____Type__Oprod_It__Expr__Obop_Mt__Product____Type__Oprod_It__Value__Oval_Mt__Value__Oval_J_J_J, type,
    member1528603216al_val : produc674182439al_val > set_Pr711661575al_val > $o).
thf(sy_c_member_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_Mt__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_M_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_Mt__Product____Type__Oprod_It__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_Mt__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_M_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J, type,
    member354538064on_val : produc1172664615on_val > set_Pr1189492743on_val > $o).
thf(sy_c_member_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__List__Olist_It__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_J_Mt__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_M_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_Mt__Product____Type__Oprod_It__List__Olist_It__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_J_Mt__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_M_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J, type,
    member1689761872on_val : produc655058983on_val > set_Pr208351751on_val > $o).
thf(sy_c_member_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_Mt__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J, type,
    member197592058on_val : produc1085126737on_val > set_Pr2110063281on_val > $o).
thf(sy_c_member_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__Product____Type__Oprod_It__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_Mt__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_M_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_Mt__Product____Type__Oprod_It__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_Mt__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_M_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_Mt__Product____Type__Oprod_It__Product____Type__Oprod_It__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_Mt__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_M_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_Mt__Product____Type__Oprod_It__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_Mt__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_M_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_J, type,
    member208988944on_val : produc1161703655on_val > set_Pr1368603847on_val > $o).
thf(sy_c_member_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__Product____Type__Oprod_It__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_Mt__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_M_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_Mt__Product____Type__Oprod_It__List__Olist_It__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_J_Mt__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_M_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_Mt__Product____Type__Oprod_It__Product____Type__Oprod_It__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_Mt__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_M_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_Mt__Product____Type__Oprod_It__List__Olist_It__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_J_Mt__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_M_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_J, type,
    member1284182416on_val : produc128280679on_val > set_Pr1582577479on_val > $o).
thf(sy_c_member_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__Product____Type__Oprod_It__List__Olist_It__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_J_Mt__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_M_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_Mt__Product____Type__Oprod_It__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_Mt__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_M_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_Mt__Product____Type__Oprod_It__Product____Type__Oprod_It__List__Olist_It__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_J_Mt__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_M_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_Mt__Product____Type__Oprod_It__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_Mt__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_M_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_J, type,
    member939451536on_val : produc1931033447on_val > set_Pr655264327on_val > $o).
thf(sy_c_member_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__Product____Type__Oprod_It__List__Olist_It__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_J_Mt__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_M_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_Mt__Product____Type__Oprod_It__List__Olist_It__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_J_Mt__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_M_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_Mt__Product____Type__Oprod_It__Product____Type__Oprod_It__List__Olist_It__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_J_Mt__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_M_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_Mt__Product____Type__Oprod_It__List__Olist_It__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_J_Mt__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_M_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_J, type,
    member1743964944on_val : produc1428501223on_val > set_Pr1301890247on_val > $o).
thf(sy_c_member_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__Value__Oval_Mt__Value__Oval_J_Mt__Product____Type__Oprod_It__Value__Oval_Mt__Value__Oval_J_J, type,
    member635678608al_val : produc1743387751al_val > set_Pr488475975al_val > $o).
thf(sy_v_P, type,
    p : list_P1234162913t_char).
thf(sy_v_a, type,
    a : nat > option2118145160on_val).
thf(sy_v_aa, type,
    aa : nat > option2118145160on_val).
thf(sy_v_b, type,
    b : list_char > option_val).
thf(sy_v_ba, type,
    ba : list_char > option_val).
thf(sy_v_e_092_060_094sub_0622, type,
    e_2 : exp_list_char).
thf(sy_v_e_Ha, type,
    e_a : exp_list_char).
thf(sy_v_ea, type,
    ea : exp_list_char).
thf(sy_v_x, type,
    x : list_char).
thf(sy_v_x2, type,
    x2 : set_list_char).
thf(sy_v_y, type,
    y : val).

% Relevant facts (246)
thf(fact_0_not__None__eq, axiom,
    ((![X : option_set_list_char]: ((~ ((X = none_set_list_char))) = (?[Y : set_list_char]: (X = (some_set_list_char @ Y))))))). % not_None_eq
thf(fact_1_not__None__eq, axiom,
    ((![X : option_val]: ((~ ((X = none_val))) = (?[Y : val]: (X = (some_val @ Y))))))). % not_None_eq
thf(fact_2_not__None__eq, axiom,
    ((![X : option2118145160on_val]: ((~ ((X = none_P1535574167on_val))) = (?[Y : produc266837688on_val]: (X = (some_P1299442195on_val @ Y))))))). % not_None_eq
thf(fact_3_not__Some__eq, axiom,
    ((![X : option_set_list_char]: ((![Y : set_list_char]: (~ ((X = (some_set_list_char @ Y))))) = (X = none_set_list_char))))). % not_Some_eq
thf(fact_4_not__Some__eq, axiom,
    ((![X : option_val]: ((![Y : val]: (~ ((X = (some_val @ Y))))) = (X = none_val))))). % not_Some_eq
thf(fact_5_not__Some__eq, axiom,
    ((![X : option2118145160on_val]: ((![Y : produc266837688on_val]: (~ ((X = (some_P1299442195on_val @ Y))))) = (X = none_P1535574167on_val))))). % not_Some_eq
thf(fact_6_option_Oinject, axiom,
    ((![X2 : set_list_char, Y2 : set_list_char]: (((some_set_list_char @ X2) = (some_set_list_char @ Y2)) = (X2 = Y2))))). % option.inject
thf(fact_7_option_Oinject, axiom,
    ((![X2 : val, Y2 : val]: (((some_val @ X2) = (some_val @ Y2)) = (X2 = Y2))))). % option.inject
thf(fact_8_option_Oinject, axiom,
    ((![X2 : produc266837688on_val, Y2 : produc266837688on_val]: (((some_P1299442195on_val @ X2) = (some_P1299442195on_val @ Y2)) = (X2 = Y2))))). % option.inject
thf(fact_9_prod_Oinject, axiom,
    ((![X1 : list_char, X2 : produc1257910179t_char > option_val, Y1 : list_char, Y2 : produc1257910179t_char > option_val]: (((produc904988266on_val @ X1 @ X2) = (produc904988266on_val @ Y1 @ Y2)) = (((X1 = Y1)) & ((X2 = Y2))))))). % prod.inject
thf(fact_10_prod_Oinject, axiom,
    ((![X1 : list_exp_list_char, X2 : produc515445032on_val, Y1 : list_exp_list_char, Y2 : produc515445032on_val]: (((produc1725134254on_val @ X1 @ X2) = (produc1725134254on_val @ Y1 @ Y2)) = (((X1 = Y1)) & ((X2 = Y2))))))). % prod.inject
thf(fact_11_prod_Oinject, axiom,
    ((![X1 : exp_list_char, X2 : produc515445032on_val, Y1 : exp_list_char, Y2 : produc515445032on_val]: (((produc2023458740on_val @ X1 @ X2) = (produc2023458740on_val @ Y1 @ Y2)) = (((X1 = Y1)) & ((X2 = Y2))))))). % prod.inject
thf(fact_12_prod_Oinject, axiom,
    ((![X1 : bop, X2 : product_prod_val_val, Y1 : bop, Y2 : product_prod_val_val]: (((produc1753769388al_val @ X1 @ X2) = (produc1753769388al_val @ Y1 @ Y2)) = (((X1 = Y1)) & ((X2 = Y2))))))). % prod.inject
thf(fact_13_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_14_old_Oprod_Oinject, axiom,
    ((![A : list_char, B : produc1257910179t_char > option_val, A2 : list_char, B2 : produc1257910179t_char > option_val]: (((produc904988266on_val @ A @ B) = (produc904988266on_val @ A2 @ B2)) = (((A = A2)) & ((B = B2))))))). % old.prod.inject
thf(fact_15_old_Oprod_Oinject, axiom,
    ((![A : list_exp_list_char, B : produc515445032on_val, A2 : list_exp_list_char, B2 : produc515445032on_val]: (((produc1725134254on_val @ A @ B) = (produc1725134254on_val @ A2 @ B2)) = (((A = A2)) & ((B = B2))))))). % old.prod.inject
thf(fact_16_old_Oprod_Oinject, axiom,
    ((![A : exp_list_char, B : produc515445032on_val, A2 : exp_list_char, B2 : produc515445032on_val]: (((produc2023458740on_val @ A @ B) = (produc2023458740on_val @ A2 @ B2)) = (((A = A2)) & ((B = B2))))))). % old.prod.inject
thf(fact_17_old_Oprod_Oinject, axiom,
    ((![A : bop, B : product_prod_val_val, A2 : bop, B2 : product_prod_val_val]: (((produc1753769388al_val @ A @ B) = (produc1753769388al_val @ A2 @ B2)) = (((A = A2)) & ((B = B2))))))). % old.prod.inject
thf(fact_18_old_Oprod_Oinject, axiom,
    ((![A : nat > option2118145160on_val, B : list_char > option_val, A2 : nat > option2118145160on_val, B2 : list_char > option_val]: (((produc52622304on_val @ A @ B) = (produc52622304on_val @ A2 @ B2)) = (((A = A2)) & ((B = B2))))))). % old.prod.inject
thf(fact_19_old_Oprod_Oinducts, axiom,
    ((![P : produc266837688on_val > $o, Prod : produc266837688on_val]: ((![A3 : list_char, B3 : produc1257910179t_char > option_val]: (P @ (produc904988266on_val @ A3 @ B3))) => (P @ Prod))))). % old.prod.inducts
thf(fact_20_old_Oprod_Oinducts, axiom,
    ((![P : produc335961278on_val > $o, Prod : produc335961278on_val]: ((![A3 : list_exp_list_char, B3 : produc515445032on_val]: (P @ (produc1725134254on_val @ A3 @ B3))) => (P @ Prod))))). % old.prod.inducts
thf(fact_21_old_Oprod_Oinducts, axiom,
    ((![P : produc1097884484on_val > $o, Prod : produc1097884484on_val]: ((![A3 : exp_list_char, B3 : produc515445032on_val]: (P @ (produc2023458740on_val @ A3 @ B3))) => (P @ Prod))))). % old.prod.inducts
thf(fact_22_old_Oprod_Oinducts, axiom,
    ((![P : produc1373793468al_val > $o, Prod : produc1373793468al_val]: ((![A3 : bop, B3 : product_prod_val_val]: (P @ (produc1753769388al_val @ A3 @ B3))) => (P @ Prod))))). % old.prod.inducts
thf(fact_23_old_Oprod_Oinducts, axiom,
    ((![P : produc515445032on_val > $o, Prod : produc515445032on_val]: ((![A3 : nat > option2118145160on_val, B3 : list_char > option_val]: (P @ (produc52622304on_val @ A3 @ B3))) => (P @ Prod))))). % old.prod.inducts
thf(fact_24_old_Oprod_Oexhaust, axiom,
    ((![Y3 : produc266837688on_val]: (~ ((![A3 : list_char, B3 : produc1257910179t_char > option_val]: (~ ((Y3 = (produc904988266on_val @ A3 @ B3)))))))))). % old.prod.exhaust
thf(fact_25_old_Oprod_Oexhaust, axiom,
    ((![Y3 : produc335961278on_val]: (~ ((![A3 : list_exp_list_char, B3 : produc515445032on_val]: (~ ((Y3 = (produc1725134254on_val @ A3 @ B3)))))))))). % old.prod.exhaust
thf(fact_26_old_Oprod_Oexhaust, axiom,
    ((![Y3 : produc1097884484on_val]: (~ ((![A3 : exp_list_char, B3 : produc515445032on_val]: (~ ((Y3 = (produc2023458740on_val @ A3 @ B3)))))))))). % old.prod.exhaust
thf(fact_27_old_Oprod_Oexhaust, axiom,
    ((![Y3 : produc1373793468al_val]: (~ ((![A3 : bop, B3 : product_prod_val_val]: (~ ((Y3 = (produc1753769388al_val @ A3 @ B3)))))))))). % old.prod.exhaust
thf(fact_28_old_Oprod_Oexhaust, axiom,
    ((![Y3 : produc515445032on_val]: (~ ((![A3 : nat > option2118145160on_val, B3 : list_char > option_val]: (~ ((Y3 = (produc52622304on_val @ A3 @ B3)))))))))). % old.prod.exhaust
thf(fact_29_Pair__inject, axiom,
    ((![A : list_char, B : produc1257910179t_char > option_val, A2 : list_char, B2 : produc1257910179t_char > option_val]: (((produc904988266on_val @ A @ B) = (produc904988266on_val @ A2 @ B2)) => (~ (((A = A2) => (~ ((B = B2)))))))))). % Pair_inject
thf(fact_30_Pair__inject, axiom,
    ((![A : list_exp_list_char, B : produc515445032on_val, A2 : list_exp_list_char, B2 : produc515445032on_val]: (((produc1725134254on_val @ A @ B) = (produc1725134254on_val @ A2 @ B2)) => (~ (((A = A2) => (~ ((B = B2)))))))))). % Pair_inject
thf(fact_31_Pair__inject, axiom,
    ((![A : exp_list_char, B : produc515445032on_val, A2 : exp_list_char, B2 : produc515445032on_val]: (((produc2023458740on_val @ A @ B) = (produc2023458740on_val @ A2 @ B2)) => (~ (((A = A2) => (~ ((B = B2)))))))))). % Pair_inject
thf(fact_32_Pair__inject, axiom,
    ((![A : bop, B : product_prod_val_val, A2 : bop, B2 : product_prod_val_val]: (((produc1753769388al_val @ A @ B) = (produc1753769388al_val @ A2 @ B2)) => (~ (((A = A2) => (~ ((B = B2)))))))))). % Pair_inject
thf(fact_33_Pair__inject, axiom,
    ((![A : nat > option2118145160on_val, B : list_char > option_val, A2 : nat > option2118145160on_val, B2 : list_char > option_val]: (((produc52622304on_val @ A @ B) = (produc52622304on_val @ A2 @ B2)) => (~ (((A = A2) => (~ ((B = B2)))))))))). % Pair_inject
thf(fact_34_prod__cases, axiom,
    ((![P : produc266837688on_val > $o, P2 : produc266837688on_val]: ((![A3 : list_char, B3 : produc1257910179t_char > option_val]: (P @ (produc904988266on_val @ A3 @ B3))) => (P @ P2))))). % prod_cases
thf(fact_35_prod__cases, axiom,
    ((![P : produc335961278on_val > $o, P2 : produc335961278on_val]: ((![A3 : list_exp_list_char, B3 : produc515445032on_val]: (P @ (produc1725134254on_val @ A3 @ B3))) => (P @ P2))))). % prod_cases
thf(fact_36_prod__cases, axiom,
    ((![P : produc1097884484on_val > $o, P2 : produc1097884484on_val]: ((![A3 : exp_list_char, B3 : produc515445032on_val]: (P @ (produc2023458740on_val @ A3 @ B3))) => (P @ P2))))). % prod_cases
thf(fact_37_prod__cases, axiom,
    ((![P : produc1373793468al_val > $o, P2 : produc1373793468al_val]: ((![A3 : bop, B3 : product_prod_val_val]: (P @ (produc1753769388al_val @ A3 @ B3))) => (P @ P2))))). % prod_cases
thf(fact_38_prod__cases, axiom,
    ((![P : produc515445032on_val > $o, P2 : produc515445032on_val]: ((![A3 : nat > option2118145160on_val, B3 : list_char > option_val]: (P @ (produc52622304on_val @ A3 @ B3))) => (P @ P2))))). % prod_cases
thf(fact_39_surj__pair, axiom,
    ((![P2 : produc266837688on_val]: (?[X3 : list_char, Y4 : produc1257910179t_char > option_val]: (P2 = (produc904988266on_val @ X3 @ Y4)))))). % surj_pair
thf(fact_40_surj__pair, axiom,
    ((![P2 : produc335961278on_val]: (?[X3 : list_exp_list_char, Y4 : produc515445032on_val]: (P2 = (produc1725134254on_val @ X3 @ Y4)))))). % surj_pair
thf(fact_41_surj__pair, axiom,
    ((![P2 : produc1097884484on_val]: (?[X3 : exp_list_char, Y4 : produc515445032on_val]: (P2 = (produc2023458740on_val @ X3 @ Y4)))))). % surj_pair
thf(fact_42_surj__pair, axiom,
    ((![P2 : produc1373793468al_val]: (?[X3 : bop, Y4 : product_prod_val_val]: (P2 = (produc1753769388al_val @ X3 @ Y4)))))). % surj_pair
thf(fact_43_surj__pair, axiom,
    ((![P2 : produc515445032on_val]: (?[X3 : nat > option2118145160on_val, Y4 : list_char > option_val]: (P2 = (produc52622304on_val @ X3 @ Y4)))))). % surj_pair
thf(fact_44_prod__induct3, axiom,
    ((![P : produc335961278on_val > $o, X : produc335961278on_val]: ((![A3 : list_exp_list_char, B3 : nat > option2118145160on_val, C : list_char > option_val]: (P @ (produc1725134254on_val @ A3 @ (produc52622304on_val @ B3 @ C)))) => (P @ X))))). % prod_induct3
thf(fact_45_prod__induct3, axiom,
    ((![P : produc1097884484on_val > $o, X : produc1097884484on_val]: ((![A3 : exp_list_char, B3 : nat > option2118145160on_val, C : list_char > option_val]: (P @ (produc2023458740on_val @ A3 @ (produc52622304on_val @ B3 @ C)))) => (P @ X))))). % prod_induct3
thf(fact_46_prod__induct3, axiom,
    ((![P : produc1373793468al_val > $o, X : produc1373793468al_val]: ((![A3 : bop, B3 : val, C : val]: (P @ (produc1753769388al_val @ A3 @ (product_Pair_val_val @ B3 @ C)))) => (P @ X))))). % prod_induct3
thf(fact_47_prod__cases3, axiom,
    ((![Y3 : produc335961278on_val]: (~ ((![A3 : list_exp_list_char, B3 : nat > option2118145160on_val, C : list_char > option_val]: (~ ((Y3 = (produc1725134254on_val @ A3 @ (produc52622304on_val @ B3 @ C))))))))))). % prod_cases3
thf(fact_48_prod__cases3, axiom,
    ((![Y3 : produc1097884484on_val]: (~ ((![A3 : exp_list_char, B3 : nat > option2118145160on_val, C : list_char > option_val]: (~ ((Y3 = (produc2023458740on_val @ A3 @ (produc52622304on_val @ B3 @ C))))))))))). % prod_cases3
thf(fact_49_prod__cases3, axiom,
    ((![Y3 : produc1373793468al_val]: (~ ((![A3 : bop, B3 : val, C : val]: (~ ((Y3 = (produc1753769388al_val @ A3 @ (product_Pair_val_val @ B3 @ C))))))))))). % prod_cases3
thf(fact_50_combine__options__cases, axiom,
    ((![X : option_set_list_char, P : option_set_list_char > option_set_list_char > $o, Y3 : option_set_list_char]: (((X = none_set_list_char) => (P @ X @ Y3)) => (((Y3 = none_set_list_char) => (P @ X @ Y3)) => ((![A3 : set_list_char, B3 : set_list_char]: ((X = (some_set_list_char @ A3)) => ((Y3 = (some_set_list_char @ B3)) => (P @ X @ Y3)))) => (P @ X @ Y3))))))). % combine_options_cases
thf(fact_51_combine__options__cases, axiom,
    ((![X : option_set_list_char, P : option_set_list_char > option_val > $o, Y3 : option_val]: (((X = none_set_list_char) => (P @ X @ Y3)) => (((Y3 = none_val) => (P @ X @ Y3)) => ((![A3 : set_list_char, B3 : val]: ((X = (some_set_list_char @ A3)) => ((Y3 = (some_val @ B3)) => (P @ X @ Y3)))) => (P @ X @ Y3))))))). % combine_options_cases
thf(fact_52_combine__options__cases, axiom,
    ((![X : option_set_list_char, P : option_set_list_char > option2118145160on_val > $o, Y3 : option2118145160on_val]: (((X = none_set_list_char) => (P @ X @ Y3)) => (((Y3 = none_P1535574167on_val) => (P @ X @ Y3)) => ((![A3 : set_list_char, B3 : produc266837688on_val]: ((X = (some_set_list_char @ A3)) => ((Y3 = (some_P1299442195on_val @ B3)) => (P @ X @ Y3)))) => (P @ X @ Y3))))))). % combine_options_cases
thf(fact_53_combine__options__cases, axiom,
    ((![X : option_val, P : option_val > option_set_list_char > $o, Y3 : option_set_list_char]: (((X = none_val) => (P @ X @ Y3)) => (((Y3 = none_set_list_char) => (P @ X @ Y3)) => ((![A3 : val, B3 : set_list_char]: ((X = (some_val @ A3)) => ((Y3 = (some_set_list_char @ B3)) => (P @ X @ Y3)))) => (P @ X @ Y3))))))). % combine_options_cases
thf(fact_54_combine__options__cases, axiom,
    ((![X : option_val, P : option_val > option_val > $o, Y3 : option_val]: (((X = none_val) => (P @ X @ Y3)) => (((Y3 = none_val) => (P @ X @ Y3)) => ((![A3 : val, B3 : val]: ((X = (some_val @ A3)) => ((Y3 = (some_val @ B3)) => (P @ X @ Y3)))) => (P @ X @ Y3))))))). % combine_options_cases
thf(fact_55_combine__options__cases, axiom,
    ((![X : option_val, P : option_val > option2118145160on_val > $o, Y3 : option2118145160on_val]: (((X = none_val) => (P @ X @ Y3)) => (((Y3 = none_P1535574167on_val) => (P @ X @ Y3)) => ((![A3 : val, B3 : produc266837688on_val]: ((X = (some_val @ A3)) => ((Y3 = (some_P1299442195on_val @ B3)) => (P @ X @ Y3)))) => (P @ X @ Y3))))))). % combine_options_cases
thf(fact_56_combine__options__cases, axiom,
    ((![X : option2118145160on_val, P : option2118145160on_val > option_set_list_char > $o, Y3 : option_set_list_char]: (((X = none_P1535574167on_val) => (P @ X @ Y3)) => (((Y3 = none_set_list_char) => (P @ X @ Y3)) => ((![A3 : produc266837688on_val, B3 : set_list_char]: ((X = (some_P1299442195on_val @ A3)) => ((Y3 = (some_set_list_char @ B3)) => (P @ X @ Y3)))) => (P @ X @ Y3))))))). % combine_options_cases
thf(fact_57_combine__options__cases, axiom,
    ((![X : option2118145160on_val, P : option2118145160on_val > option_val > $o, Y3 : option_val]: (((X = none_P1535574167on_val) => (P @ X @ Y3)) => (((Y3 = none_val) => (P @ X @ Y3)) => ((![A3 : produc266837688on_val, B3 : val]: ((X = (some_P1299442195on_val @ A3)) => ((Y3 = (some_val @ B3)) => (P @ X @ Y3)))) => (P @ X @ Y3))))))). % combine_options_cases
thf(fact_58_combine__options__cases, axiom,
    ((![X : option2118145160on_val, P : option2118145160on_val > option2118145160on_val > $o, Y3 : option2118145160on_val]: (((X = none_P1535574167on_val) => (P @ X @ Y3)) => (((Y3 = none_P1535574167on_val) => (P @ X @ Y3)) => ((![A3 : produc266837688on_val, B3 : produc266837688on_val]: ((X = (some_P1299442195on_val @ A3)) => ((Y3 = (some_P1299442195on_val @ B3)) => (P @ X @ Y3)))) => (P @ X @ Y3))))))). % combine_options_cases
thf(fact_59_split__option__all, axiom,
    (((^[P3 : option_set_list_char > $o]: (![X4 : option_set_list_char]: (P3 @ X4))) = (^[P4 : option_set_list_char > $o]: (((P4 @ none_set_list_char)) & ((![X5 : set_list_char]: (P4 @ (some_set_list_char @ X5))))))))). % split_option_all
thf(fact_60_split__option__all, axiom,
    (((^[P3 : option_val > $o]: (![X4 : option_val]: (P3 @ X4))) = (^[P4 : option_val > $o]: (((P4 @ none_val)) & ((![X5 : val]: (P4 @ (some_val @ X5))))))))). % split_option_all
thf(fact_61_split__option__all, axiom,
    (((^[P3 : option2118145160on_val > $o]: (![X4 : option2118145160on_val]: (P3 @ X4))) = (^[P4 : option2118145160on_val > $o]: (((P4 @ none_P1535574167on_val)) & ((![X5 : produc266837688on_val]: (P4 @ (some_P1299442195on_val @ X5))))))))). % split_option_all
thf(fact_62_split__option__ex, axiom,
    (((^[P3 : option_set_list_char > $o]: (?[X4 : option_set_list_char]: (P3 @ X4))) = (^[P4 : option_set_list_char > $o]: (((P4 @ none_set_list_char)) | ((?[X5 : set_list_char]: (P4 @ (some_set_list_char @ X5))))))))). % split_option_ex
thf(fact_63_split__option__ex, axiom,
    (((^[P3 : option_val > $o]: (?[X4 : option_val]: (P3 @ X4))) = (^[P4 : option_val > $o]: (((P4 @ none_val)) | ((?[X5 : val]: (P4 @ (some_val @ X5))))))))). % split_option_ex
thf(fact_64_split__option__ex, axiom,
    (((^[P3 : option2118145160on_val > $o]: (?[X4 : option2118145160on_val]: (P3 @ X4))) = (^[P4 : option2118145160on_val > $o]: (((P4 @ none_P1535574167on_val)) | ((?[X5 : produc266837688on_val]: (P4 @ (some_P1299442195on_val @ X5))))))))). % split_option_ex
thf(fact_65_option_Oinducts, axiom,
    ((![P : option_set_list_char > $o, Option : option_set_list_char]: ((P @ none_set_list_char) => ((![X3 : set_list_char]: (P @ (some_set_list_char @ X3))) => (P @ Option)))))). % option.inducts
thf(fact_66_option_Oinducts, axiom,
    ((![P : option_val > $o, Option : option_val]: ((P @ none_val) => ((![X3 : val]: (P @ (some_val @ X3))) => (P @ Option)))))). % option.inducts
thf(fact_67_option_Oinducts, axiom,
    ((![P : option2118145160on_val > $o, Option : option2118145160on_val]: ((P @ none_P1535574167on_val) => ((![X3 : produc266837688on_val]: (P @ (some_P1299442195on_val @ X3))) => (P @ Option)))))). % option.inducts
thf(fact_68_option_Oexhaust, axiom,
    ((![Y3 : option_set_list_char]: ((~ ((Y3 = none_set_list_char))) => (~ ((![X22 : set_list_char]: (~ ((Y3 = (some_set_list_char @ X22))))))))))). % option.exhaust
thf(fact_69_option_Oexhaust, axiom,
    ((![Y3 : option_val]: ((~ ((Y3 = none_val))) => (~ ((![X22 : val]: (~ ((Y3 = (some_val @ X22))))))))))). % option.exhaust
thf(fact_70_option_Oexhaust, axiom,
    ((![Y3 : option2118145160on_val]: ((~ ((Y3 = none_P1535574167on_val))) => (~ ((![X22 : produc266837688on_val]: (~ ((Y3 = (some_P1299442195on_val @ X22))))))))))). % option.exhaust
thf(fact_71_option_OdiscI, axiom,
    ((![Option : option_set_list_char, X2 : set_list_char]: ((Option = (some_set_list_char @ X2)) => (~ ((Option = none_set_list_char))))))). % option.discI
thf(fact_72_option_OdiscI, axiom,
    ((![Option : option_val, X2 : val]: ((Option = (some_val @ X2)) => (~ ((Option = none_val))))))). % option.discI
thf(fact_73_option_OdiscI, axiom,
    ((![Option : option2118145160on_val, X2 : produc266837688on_val]: ((Option = (some_P1299442195on_val @ X2)) => (~ ((Option = none_P1535574167on_val))))))). % option.discI
thf(fact_74_option_Odistinct_I1_J, axiom,
    ((![X2 : set_list_char]: (~ ((none_set_list_char = (some_set_list_char @ X2))))))). % option.distinct(1)
thf(fact_75_option_Odistinct_I1_J, axiom,
    ((![X2 : val]: (~ ((none_val = (some_val @ X2))))))). % option.distinct(1)
thf(fact_76_option_Odistinct_I1_J, axiom,
    ((![X2 : produc266837688on_val]: (~ ((none_P1535574167on_val = (some_P1299442195on_val @ X2))))))). % option.distinct(1)
thf(fact_77_same__fstI, axiom,
    ((![P : list_char > $o, X : list_char, Y5 : produc1257910179t_char > option_val, Y3 : produc1257910179t_char > option_val, R : list_char > set_Pr227219079on_val]: ((P @ X) => ((member548035792on_val @ (produc797901719on_val @ Y5 @ Y3) @ (R @ X)) => (member197592058on_val @ (produc881885833on_val @ (produc904988266on_val @ X @ Y5) @ (produc904988266on_val @ X @ Y3)) @ (same_f2003279573on_val @ P @ R))))))). % same_fstI
thf(fact_78_same__fstI, axiom,
    ((![P : list_exp_list_char > $o, X : list_exp_list_char, Y5 : produc515445032on_val, Y3 : produc515445032on_val, R : list_exp_list_char > set_Pr148564103on_val]: ((P @ X) => ((member2027247312on_val @ (produc2106877847on_val @ Y5 @ Y3) @ (R @ X)) => (member1689761872on_val @ (produc245869591on_val @ (produc1725134254on_val @ X @ Y5) @ (produc1725134254on_val @ X @ Y3)) @ (same_f1555812995on_val @ P @ R))))))). % same_fstI
thf(fact_79_same__fstI, axiom,
    ((![P : exp_list_char > $o, X : exp_list_char, Y5 : produc515445032on_val, Y3 : produc515445032on_val, R : exp_list_char > set_Pr148564103on_val]: ((P @ X) => ((member2027247312on_val @ (produc2106877847on_val @ Y5 @ Y3) @ (R @ X)) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ X @ Y5) @ (produc2023458740on_val @ X @ Y3)) @ (same_f366220041on_val @ P @ R))))))). % same_fstI
thf(fact_80_same__fstI, axiom,
    ((![P : bop > $o, X : bop, Y5 : product_prod_val_val, Y3 : product_prod_val_val, R : bop > set_Pr488475975al_val]: ((P @ X) => ((member635678608al_val @ (produc1931530455al_val @ Y5 @ Y3) @ (R @ X)) => (member1528603216al_val @ (produc1144711447al_val @ (produc1753769388al_val @ X @ Y5) @ (produc1753769388al_val @ X @ Y3)) @ (same_f915619585al_val @ P @ R))))))). % same_fstI
thf(fact_81_same__fstI, axiom,
    ((![P : (nat > option2118145160on_val) > $o, X : nat > option2118145160on_val, Y5 : list_char > option_val, Y3 : list_char > option_val, R : (nat > option2118145160on_val) > set_Pr1104486497on_val]: ((P @ X) => ((member1177709994on_val @ (produc746553401on_val @ Y5 @ Y3) @ (R @ X)) => (member2027247312on_val @ (produc2106877847on_val @ (produc52622304on_val @ X @ Y5) @ (produc52622304on_val @ X @ Y3)) @ (same_f1752972725on_val @ P @ R))))))). % same_fstI
thf(fact_82_red__hext__incr, axiom,
    ((![E : exp_list_char, H : nat > option2118145160on_val, L : list_char > option_val, E2 : exp_list_char, H2 : nat > option2118145160on_val, L2 : list_char > option_val, P : list_P1234162913t_char]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E @ (produc52622304on_val @ H @ L)) @ (produc2023458740on_val @ E2 @ (produc52622304on_val @ H2 @ L2))) @ (red @ P)) => (hext @ H @ H2))))). % red_hext_incr
thf(fact_83_ssubst__Pair__rhs, axiom,
    ((![R2 : produc1097884484on_val, S : produc1097884484on_val, R : set_Pr1189492743on_val, S2 : produc1097884484on_val]: ((member354538064on_val @ (produc1069526295on_val @ R2 @ S) @ R) => ((S2 = S) => (member354538064on_val @ (produc1069526295on_val @ R2 @ S2) @ R)))))). % ssubst_Pair_rhs
thf(fact_84_ssubst__Pair__rhs, axiom,
    ((![R2 : produc335961278on_val, S : produc335961278on_val, R : set_Pr208351751on_val, S2 : produc335961278on_val]: ((member1689761872on_val @ (produc245869591on_val @ R2 @ S) @ R) => ((S2 = S) => (member1689761872on_val @ (produc245869591on_val @ R2 @ S2) @ R)))))). % ssubst_Pair_rhs
thf(fact_85_ssubst__Pair__rhs, axiom,
    ((![R2 : list_char, S : produc1257910179t_char > option_val, R : set_Pr2075231726on_val, S2 : produc1257910179t_char > option_val]: ((member1296415951on_val @ (produc904988266on_val @ R2 @ S) @ R) => ((S2 = S) => (member1296415951on_val @ (produc904988266on_val @ R2 @ S2) @ R)))))). % ssubst_Pair_rhs
thf(fact_86_ssubst__Pair__rhs, axiom,
    ((![R2 : list_exp_list_char, S : produc515445032on_val, R : set_Pr1511552798on_val, S2 : produc515445032on_val]: ((member184158439on_val @ (produc1725134254on_val @ R2 @ S) @ R) => ((S2 = S) => (member184158439on_val @ (produc1725134254on_val @ R2 @ S2) @ R)))))). % ssubst_Pair_rhs
thf(fact_87_ssubst__Pair__rhs, axiom,
    ((![R2 : exp_list_char, S : produc515445032on_val, R : set_Pr556513572on_val, S2 : produc515445032on_val]: ((member1888679917on_val @ (produc2023458740on_val @ R2 @ S) @ R) => ((S2 = S) => (member1888679917on_val @ (produc2023458740on_val @ R2 @ S2) @ R)))))). % ssubst_Pair_rhs
thf(fact_88_ssubst__Pair__rhs, axiom,
    ((![R2 : bop, S : product_prod_val_val, R : set_Pr624825500al_val, S2 : product_prod_val_val]: ((member772310885al_val @ (produc1753769388al_val @ R2 @ S) @ R) => ((S2 = S) => (member772310885al_val @ (produc1753769388al_val @ R2 @ S2) @ R)))))). % ssubst_Pair_rhs
thf(fact_89_ssubst__Pair__rhs, axiom,
    ((![R2 : nat > option2118145160on_val, S : list_char > option_val, R : set_Pr723149704on_val, S2 : list_char > option_val]: ((member652041809on_val @ (produc52622304on_val @ R2 @ S) @ R) => ((S2 = S) => (member652041809on_val @ (produc52622304on_val @ R2 @ S2) @ R)))))). % ssubst_Pair_rhs
thf(fact_90_option_Ocollapse, axiom,
    ((![Option : option_set_list_char]: ((~ ((Option = none_set_list_char))) => ((some_set_list_char @ (the_set_list_char @ Option)) = Option))))). % option.collapse
thf(fact_91_option_Ocollapse, axiom,
    ((![Option : option_val]: ((~ ((Option = none_val))) => ((some_val @ (the_val @ Option)) = Option))))). % option.collapse
thf(fact_92_option_Ocollapse, axiom,
    ((![Option : option2118145160on_val]: ((~ ((Option = none_P1535574167on_val))) => ((some_P1299442195on_val @ (the_Pr901949220on_val @ Option)) = Option))))). % option.collapse
thf(fact_93_red__lcl__add, axiom,
    ((![E : exp_list_char, H : nat > option2118145160on_val, L : list_char > option_val, E2 : exp_list_char, H2 : nat > option2118145160on_val, L2 : list_char > option_val, P : list_P1234162913t_char, L_0 : list_char > option_val]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E @ (produc52622304on_val @ H @ L)) @ (produc2023458740on_val @ E2 @ (produc52622304on_val @ H2 @ L2))) @ (red @ P)) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E @ (produc52622304on_val @ H @ (map_ad1615113112ar_val @ L_0 @ L))) @ (produc2023458740on_val @ E2 @ (produc52622304on_val @ H2 @ (map_ad1615113112ar_val @ L_0 @ L2)))) @ (red @ P)))))). % red_lcl_add
thf(fact_94_in__lex__prod, axiom,
    ((![A : produc1097884484on_val, B : produc1097884484on_val, A2 : produc1097884484on_val, B2 : produc1097884484on_val, R2 : set_Pr1189492743on_val, S : set_Pr1189492743on_val]: ((member208988944on_val @ (produc564964183on_val @ (produc1069526295on_val @ A @ B) @ (produc1069526295on_val @ A2 @ B2)) @ (lex_pr186272047on_val @ R2 @ S)) = (((member354538064on_val @ (produc1069526295on_val @ A @ A2) @ R2)) | ((((A = A2)) & ((member354538064on_val @ (produc1069526295on_val @ B @ B2) @ S))))))))). % in_lex_prod
thf(fact_95_in__lex__prod, axiom,
    ((![A : produc1097884484on_val, B : produc335961278on_val, A2 : produc1097884484on_val, B2 : produc335961278on_val, R2 : set_Pr1189492743on_val, S : set_Pr208351751on_val]: ((member1284182416on_val @ (produc625175255on_val @ (produc367337745on_val @ A @ B) @ (produc367337745on_val @ A2 @ B2)) @ (lex_pr511103273on_val @ R2 @ S)) = (((member354538064on_val @ (produc1069526295on_val @ A @ A2) @ R2)) | ((((A = A2)) & ((member1689761872on_val @ (produc245869591on_val @ B @ B2) @ S))))))))). % in_lex_prod
thf(fact_96_in__lex__prod, axiom,
    ((![A : produc335961278on_val, B : produc1097884484on_val, A2 : produc335961278on_val, B2 : produc1097884484on_val, R2 : set_Pr208351751on_val, S : set_Pr1189492743on_val]: ((member939451536on_val @ (produc1914110935on_val @ (produc974123805on_val @ A @ B) @ (produc974123805on_val @ A2 @ B2)) @ (lex_pr1117889333on_val @ R2 @ S)) = (((member1689761872on_val @ (produc245869591on_val @ A @ A2) @ R2)) | ((((A = A2)) & ((member354538064on_val @ (produc1069526295on_val @ B @ B2) @ S))))))))). % in_lex_prod
thf(fact_97_in__lex__prod, axiom,
    ((![A : produc335961278on_val, B : produc335961278on_val, A2 : produc335961278on_val, B2 : produc335961278on_val, R2 : set_Pr208351751on_val, S : set_Pr208351751on_val]: ((member1743964944on_val @ (produc1802175319on_val @ (produc245869591on_val @ A @ B) @ (produc245869591on_val @ A2 @ B2)) @ (lex_pr601255983on_val @ R2 @ S)) = (((member1689761872on_val @ (produc245869591on_val @ A @ A2) @ R2)) | ((((A = A2)) & ((member1689761872on_val @ (produc245869591on_val @ B @ B2) @ S))))))))). % in_lex_prod
thf(fact_98_in__lex__prod, axiom,
    ((![A : list_char, B : produc1257910179t_char > option_val, A2 : list_char, B2 : produc1257910179t_char > option_val, R2 : set_Pr164112643t_char, S : set_Pr227219079on_val]: ((member197592058on_val @ (produc881885833on_val @ (produc904988266on_val @ A @ B) @ (produc904988266on_val @ A2 @ B2)) @ (lex_pr1753065554on_val @ R2 @ S)) = (((member89690956t_char @ (produc1304532571t_char @ A @ A2) @ R2)) | ((((A = A2)) & ((member548035792on_val @ (produc797901719on_val @ B @ B2) @ S))))))))). % in_lex_prod
thf(fact_99_in__lex__prod, axiom,
    ((![A : list_exp_list_char, B : produc515445032on_val, A2 : list_exp_list_char, B2 : produc515445032on_val, R2 : set_Pr1932514887t_char, S : set_Pr148564103on_val]: ((member1689761872on_val @ (produc245869591on_val @ (produc1725134254on_val @ A @ B) @ (produc1725134254on_val @ A2 @ B2)) @ (lex_pr263313862on_val @ R2 @ S)) = (((member462435472t_char @ (produc1721801175t_char @ A @ A2) @ R2)) | ((((A = A2)) & ((member2027247312on_val @ (produc2106877847on_val @ B @ B2) @ S))))))))). % in_lex_prod
thf(fact_100_in__lex__prod, axiom,
    ((![A : exp_list_char, B : produc515445032on_val, A2 : exp_list_char, B2 : produc515445032on_val, R2 : set_Pr224372167t_char, S : set_Pr148564103on_val]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ A @ B) @ (produc2023458740on_val @ A2 @ B2)) @ (lex_pr1764546508on_val @ R2 @ S)) = (((member1699993616t_char @ (produc240508503t_char @ A @ A2) @ R2)) | ((((A = A2)) & ((member2027247312on_val @ (produc2106877847on_val @ B @ B2) @ S))))))))). % in_lex_prod
thf(fact_101_in__lex__prod, axiom,
    ((![A : bop, B : product_prod_val_val, A2 : bop, B2 : product_prod_val_val, R2 : set_Pr445896583op_bop, S : set_Pr488475975al_val]: ((member1528603216al_val @ (produc1144711447al_val @ (produc1753769388al_val @ A @ B) @ (produc1753769388al_val @ A2 @ B2)) @ (lex_pr2029241796al_val @ R2 @ S)) = (((member843417040op_bop @ (product_Pair_bop_bop @ A @ A2) @ R2)) | ((((A = A2)) & ((member635678608al_val @ (produc1931530455al_val @ B @ B2) @ S))))))))). % in_lex_prod
thf(fact_102_in__lex__prod, axiom,
    ((![A : nat > option2118145160on_val, B : list_char > option_val, A2 : nat > option2118145160on_val, B2 : list_char > option_val, R2 : set_Pr1465729071on_val, S : set_Pr1104486497on_val]: ((member2027247312on_val @ (produc2106877847on_val @ (produc52622304on_val @ A @ B) @ (produc52622304on_val @ A2 @ B2)) @ (lex_pr683585528on_val @ R2 @ S)) = (((member78096504on_val @ (produc1392944775on_val @ A @ A2) @ R2)) | ((((A = A2)) & ((member1177709994on_val @ (produc746553401on_val @ B @ B2) @ S))))))))). % in_lex_prod
thf(fact_103_converse__rtrancl__induct__red, axiom,
    ((![E : exp_list_char, H : nat > option2118145160on_val, L : list_char > option_val, E2 : exp_list_char, H2 : nat > option2118145160on_val, L2 : list_char > option_val, P : list_P1234162913t_char, R : exp_list_char > (nat > option2118145160on_val) > (list_char > option_val) > exp_list_char > (nat > option2118145160on_val) > (list_char > option_val) > $o]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E @ (produc52622304on_val @ H @ L)) @ (produc2023458740on_val @ E2 @ (produc52622304on_val @ H2 @ L2))) @ (transi111096263on_val @ (red @ P))) => ((![E3 : exp_list_char, H3 : nat > option2118145160on_val, L3 : list_char > option_val]: (R @ E3 @ H3 @ L3 @ E3 @ H3 @ L3)) => ((![E_0 : exp_list_char, H_0 : nat > option2118145160on_val, L_02 : list_char > option_val, E_1 : exp_list_char, H_1 : nat > option2118145160on_val, L_1 : list_char > option_val, E4 : exp_list_char, H4 : nat > option2118145160on_val, L4 : list_char > option_val]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E_0 @ (produc52622304on_val @ H_0 @ L_02)) @ (produc2023458740on_val @ E_1 @ (produc52622304on_val @ H_1 @ L_1))) @ (red @ P)) => ((R @ E_1 @ H_1 @ L_1 @ E4 @ H4 @ L4) => (R @ E_0 @ H_0 @ L_02 @ E4 @ H4 @ L4)))) => (R @ E @ H @ L @ E2 @ H2 @ L2))))))). % converse_rtrancl_induct_red
thf(fact_104_curryI, axiom,
    ((![F : produc266837688on_val > $o, A : list_char, B : produc1257910179t_char > option_val]: ((F @ (produc904988266on_val @ A @ B)) => (produc988598624_val_o @ F @ A @ B))))). % curryI
thf(fact_105_curryI, axiom,
    ((![F : produc335961278on_val > $o, A : list_exp_list_char, B : produc515445032on_val]: ((F @ (produc1725134254on_val @ A @ B)) => (produc1199911222_val_o @ F @ A @ B))))). % curryI
thf(fact_106_curryI, axiom,
    ((![F : produc1097884484on_val > $o, A : exp_list_char, B : produc515445032on_val]: ((F @ (produc2023458740on_val @ A @ B)) => (produc699483184_val_o @ F @ A @ B))))). % curryI
thf(fact_107_curryI, axiom,
    ((![F : produc1373793468al_val > $o, A : bop, B : product_prod_val_val]: ((F @ (produc1753769388al_val @ A @ B)) => (produc1461204536_val_o @ F @ A @ B))))). % curryI
thf(fact_108_curryI, axiom,
    ((![F : produc515445032on_val > $o, A : nat > option2118145160on_val, B : list_char > option_val]: ((F @ (produc52622304on_val @ A @ B)) => (produc761261956_val_o @ F @ A @ B))))). % curryI
thf(fact_109_option_Osel, axiom,
    ((![X2 : set_list_char]: ((the_set_list_char @ (some_set_list_char @ X2)) = X2)))). % option.sel
thf(fact_110_option_Osel, axiom,
    ((![X2 : val]: ((the_val @ (some_val @ X2)) = X2)))). % option.sel
thf(fact_111_option_Osel, axiom,
    ((![X2 : produc266837688on_val]: ((the_Pr901949220on_val @ (some_P1299442195on_val @ X2)) = X2)))). % option.sel
thf(fact_112_option_Oexpand, axiom,
    ((![Option : option_set_list_char, Option2 : option_set_list_char]: (((Option = none_set_list_char) = (Option2 = none_set_list_char)) => (((~ ((Option = none_set_list_char))) => ((~ ((Option2 = none_set_list_char))) => ((the_set_list_char @ Option) = (the_set_list_char @ Option2)))) => (Option = Option2)))))). % option.expand
thf(fact_113_option_Oexpand, axiom,
    ((![Option : option_val, Option2 : option_val]: (((Option = none_val) = (Option2 = none_val)) => (((~ ((Option = none_val))) => ((~ ((Option2 = none_val))) => ((the_val @ Option) = (the_val @ Option2)))) => (Option = Option2)))))). % option.expand
thf(fact_114_option_Oexpand, axiom,
    ((![Option : option2118145160on_val, Option2 : option2118145160on_val]: (((Option = none_P1535574167on_val) = (Option2 = none_P1535574167on_val)) => (((~ ((Option = none_P1535574167on_val))) => ((~ ((Option2 = none_P1535574167on_val))) => ((the_Pr901949220on_val @ Option) = (the_Pr901949220on_val @ Option2)))) => (Option = Option2)))))). % option.expand
thf(fact_115_Red__lcl__add, axiom,
    ((![E : exp_list_char, H : nat > option2118145160on_val, L : list_char > option_val, E2 : exp_list_char, H2 : nat > option2118145160on_val, L2 : list_char > option_val, P : list_P1234162913t_char, L_0 : list_char > option_val]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E @ (produc52622304on_val @ H @ L)) @ (produc2023458740on_val @ E2 @ (produc52622304on_val @ H2 @ L2))) @ (transi111096263on_val @ (red @ P))) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E @ (produc52622304on_val @ H @ (map_ad1615113112ar_val @ L_0 @ L))) @ (produc2023458740on_val @ E2 @ (produc52622304on_val @ H2 @ (map_ad1615113112ar_val @ L_0 @ L2)))) @ (transi111096263on_val @ (red @ P))))))). % Red_lcl_add
thf(fact_116_curryD, axiom,
    ((![F : produc266837688on_val > $o, A : list_char, B : produc1257910179t_char > option_val]: ((produc988598624_val_o @ F @ A @ B) => (F @ (produc904988266on_val @ A @ B)))))). % curryD
thf(fact_117_curryD, axiom,
    ((![F : produc335961278on_val > $o, A : list_exp_list_char, B : produc515445032on_val]: ((produc1199911222_val_o @ F @ A @ B) => (F @ (produc1725134254on_val @ A @ B)))))). % curryD
thf(fact_118_curryD, axiom,
    ((![F : produc1097884484on_val > $o, A : exp_list_char, B : produc515445032on_val]: ((produc699483184_val_o @ F @ A @ B) => (F @ (produc2023458740on_val @ A @ B)))))). % curryD
thf(fact_119_curryD, axiom,
    ((![F : produc1373793468al_val > $o, A : bop, B : product_prod_val_val]: ((produc1461204536_val_o @ F @ A @ B) => (F @ (produc1753769388al_val @ A @ B)))))). % curryD
thf(fact_120_curryD, axiom,
    ((![F : produc515445032on_val > $o, A : nat > option2118145160on_val, B : list_char > option_val]: ((produc761261956_val_o @ F @ A @ B) => (F @ (produc52622304on_val @ A @ B)))))). % curryD
thf(fact_121_curryE, axiom,
    ((![F : produc266837688on_val > $o, A : list_char, B : produc1257910179t_char > option_val]: ((produc988598624_val_o @ F @ A @ B) => (F @ (produc904988266on_val @ A @ B)))))). % curryE
thf(fact_122_curryE, axiom,
    ((![F : produc335961278on_val > $o, A : list_exp_list_char, B : produc515445032on_val]: ((produc1199911222_val_o @ F @ A @ B) => (F @ (produc1725134254on_val @ A @ B)))))). % curryE
thf(fact_123_curryE, axiom,
    ((![F : produc1097884484on_val > $o, A : exp_list_char, B : produc515445032on_val]: ((produc699483184_val_o @ F @ A @ B) => (F @ (produc2023458740on_val @ A @ B)))))). % curryE
thf(fact_124_curryE, axiom,
    ((![F : produc1373793468al_val > $o, A : bop, B : product_prod_val_val]: ((produc1461204536_val_o @ F @ A @ B) => (F @ (produc1753769388al_val @ A @ B)))))). % curryE
thf(fact_125_curryE, axiom,
    ((![F : produc515445032on_val > $o, A : nat > option2118145160on_val, B : list_char > option_val]: ((produc761261956_val_o @ F @ A @ B) => (F @ (produc52622304on_val @ A @ B)))))). % curryE
thf(fact_126_option_Oexhaust__sel, axiom,
    ((![Option : option_set_list_char]: ((~ ((Option = none_set_list_char))) => (Option = (some_set_list_char @ (the_set_list_char @ Option))))))). % option.exhaust_sel
thf(fact_127_option_Oexhaust__sel, axiom,
    ((![Option : option_val]: ((~ ((Option = none_val))) => (Option = (some_val @ (the_val @ Option))))))). % option.exhaust_sel
thf(fact_128_option_Oexhaust__sel, axiom,
    ((![Option : option2118145160on_val]: ((~ ((Option = none_P1535574167on_val))) => (Option = (some_P1299442195on_val @ (the_Pr901949220on_val @ Option))))))). % option.exhaust_sel
thf(fact_129_mem__Collect__eq, axiom,
    ((![A : produc1172664615on_val, P : produc1172664615on_val > $o]: ((member354538064on_val @ A @ (collec2055896722on_val @ P)) = (P @ A))))). % mem_Collect_eq
thf(fact_130_mem__Collect__eq, axiom,
    ((![A : list_char, P : list_char > $o]: ((member_list_char @ A @ (collect_list_char @ P)) = (P @ A))))). % mem_Collect_eq
thf(fact_131_mem__Collect__eq, axiom,
    ((![A : produc655058983on_val, P : produc655058983on_val > $o]: ((member1689761872on_val @ A @ (collec105960082on_val @ P)) = (P @ A))))). % mem_Collect_eq
thf(fact_132_Collect__mem__eq, axiom,
    ((![A4 : set_Pr1189492743on_val]: ((collec2055896722on_val @ (^[X5 : produc1172664615on_val]: (member354538064on_val @ X5 @ A4))) = A4)))). % Collect_mem_eq
thf(fact_133_Collect__mem__eq, axiom,
    ((![A4 : set_list_char]: ((collect_list_char @ (^[X5 : list_char]: (member_list_char @ X5 @ A4))) = A4)))). % Collect_mem_eq
thf(fact_134_Collect__mem__eq, axiom,
    ((![A4 : set_Pr208351751on_val]: ((collec105960082on_val @ (^[X5 : produc655058983on_val]: (member1689761872on_val @ X5 @ A4))) = A4)))). % Collect_mem_eq
thf(fact_135_map__add__None, axiom,
    ((![M : list_char > option_val, N : list_char > option_val, K : list_char]: (((map_ad1615113112ar_val @ M @ N @ K) = none_val) = ((((N @ K) = none_val)) & (((M @ K) = none_val))))))). % map_add_None
thf(fact_136_map__add__eq__empty__iff, axiom,
    ((![F : list_char > option_val, G : list_char > option_val]: (((map_ad1615113112ar_val @ F @ G) = (^[X5 : list_char]: none_val)) = (((F = (^[X5 : list_char]: none_val))) & ((G = (^[X5 : list_char]: none_val)))))))). % map_add_eq_empty_iff
thf(fact_137_map__add__find__right, axiom,
    ((![N : list_char > option_val, K : list_char, Xx : val, M : list_char > option_val]: (((N @ K) = (some_val @ Xx)) => ((map_ad1615113112ar_val @ M @ N @ K) = (some_val @ Xx)))))). % map_add_find_right
thf(fact_138_map__add__SomeD, axiom,
    ((![M : list_char > option_val, N : list_char > option_val, K : list_char, X : val]: (((map_ad1615113112ar_val @ M @ N @ K) = (some_val @ X)) => (((N @ K) = (some_val @ X)) | (((N @ K) = none_val) & ((M @ K) = (some_val @ X)))))))). % map_add_SomeD
thf(fact_139_map__add__Some__iff, axiom,
    ((![M : list_char > option_val, N : list_char > option_val, K : list_char, X : val]: (((map_ad1615113112ar_val @ M @ N @ K) = (some_val @ X)) = ((((N @ K) = (some_val @ X))) | (((((N @ K) = none_val)) & (((M @ K) = (some_val @ X)))))))))). % map_add_Some_iff
thf(fact_140_hext__refl, axiom,
    ((![H : nat > option2118145160on_val]: (hext @ H @ H)))). % hext_refl
thf(fact_141_rtrancl__induct2, axiom,
    ((![Ax : list_char, Ay : produc1257910179t_char > option_val, Bx : list_char, By : produc1257910179t_char > option_val, R2 : set_Pr2110063281on_val, P : list_char > (produc1257910179t_char > option_val) > $o]: ((member197592058on_val @ (produc881885833on_val @ (produc904988266on_val @ Ax @ Ay) @ (produc904988266on_val @ Bx @ By)) @ (transi2071064181on_val @ R2)) => ((P @ Ax @ Ay) => ((![A3 : list_char, B3 : produc1257910179t_char > option_val, Aa : list_char, Ba : produc1257910179t_char > option_val]: ((member197592058on_val @ (produc881885833on_val @ (produc904988266on_val @ Ax @ Ay) @ (produc904988266on_val @ A3 @ B3)) @ (transi2071064181on_val @ R2)) => ((member197592058on_val @ (produc881885833on_val @ (produc904988266on_val @ A3 @ B3) @ (produc904988266on_val @ Aa @ Ba)) @ R2) => ((P @ A3 @ B3) => (P @ Aa @ Ba))))) => (P @ Bx @ By))))))). % rtrancl_induct2
thf(fact_142_rtrancl__induct2, axiom,
    ((![Ax : bop, Ay : product_prod_val_val, Bx : bop, By : product_prod_val_val, R2 : set_Pr711661575al_val, P : bop > product_prod_val_val > $o]: ((member1528603216al_val @ (produc1144711447al_val @ (produc1753769388al_val @ Ax @ Ay) @ (produc1753769388al_val @ Bx @ By)) @ (transi531594559al_val @ R2)) => ((P @ Ax @ Ay) => ((![A3 : bop, B3 : product_prod_val_val, Aa : bop, Ba : product_prod_val_val]: ((member1528603216al_val @ (produc1144711447al_val @ (produc1753769388al_val @ Ax @ Ay) @ (produc1753769388al_val @ A3 @ B3)) @ (transi531594559al_val @ R2)) => ((member1528603216al_val @ (produc1144711447al_val @ (produc1753769388al_val @ A3 @ B3) @ (produc1753769388al_val @ Aa @ Ba)) @ R2) => ((P @ A3 @ B3) => (P @ Aa @ Ba))))) => (P @ Bx @ By))))))). % rtrancl_induct2
thf(fact_143_rtrancl__induct2, axiom,
    ((![Ax : nat > option2118145160on_val, Ay : list_char > option_val, Bx : nat > option2118145160on_val, By : list_char > option_val, R2 : set_Pr148564103on_val, P : (nat > option2118145160on_val) > (list_char > option_val) > $o]: ((member2027247312on_val @ (produc2106877847on_val @ (produc52622304on_val @ Ax @ Ay) @ (produc52622304on_val @ Bx @ By)) @ (transi432893227on_val @ R2)) => ((P @ Ax @ Ay) => ((![A3 : nat > option2118145160on_val, B3 : list_char > option_val, Aa : nat > option2118145160on_val, Ba : list_char > option_val]: ((member2027247312on_val @ (produc2106877847on_val @ (produc52622304on_val @ Ax @ Ay) @ (produc52622304on_val @ A3 @ B3)) @ (transi432893227on_val @ R2)) => ((member2027247312on_val @ (produc2106877847on_val @ (produc52622304on_val @ A3 @ B3) @ (produc52622304on_val @ Aa @ Ba)) @ R2) => ((P @ A3 @ B3) => (P @ Aa @ Ba))))) => (P @ Bx @ By))))))). % rtrancl_induct2
thf(fact_144_rtrancl__induct2, axiom,
    ((![Ax : exp_list_char, Ay : produc515445032on_val, Bx : exp_list_char, By : produc515445032on_val, R2 : set_Pr1189492743on_val, P : exp_list_char > produc515445032on_val > $o]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ Ax @ Ay) @ (produc2023458740on_val @ Bx @ By)) @ (transi111096263on_val @ R2)) => ((P @ Ax @ Ay) => ((![A3 : exp_list_char, B3 : produc515445032on_val, Aa : exp_list_char, Ba : produc515445032on_val]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ Ax @ Ay) @ (produc2023458740on_val @ A3 @ B3)) @ (transi111096263on_val @ R2)) => ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ A3 @ B3) @ (produc2023458740on_val @ Aa @ Ba)) @ R2) => ((P @ A3 @ B3) => (P @ Aa @ Ba))))) => (P @ Bx @ By))))))). % rtrancl_induct2
thf(fact_145_rtrancl__induct2, axiom,
    ((![Ax : list_exp_list_char, Ay : produc515445032on_val, Bx : list_exp_list_char, By : produc515445032on_val, R2 : set_Pr208351751on_val, P : list_exp_list_char > produc515445032on_val > $o]: ((member1689761872on_val @ (produc245869591on_val @ (produc1725134254on_val @ Ax @ Ay) @ (produc1725134254on_val @ Bx @ By)) @ (transi325225921on_val @ R2)) => ((P @ Ax @ Ay) => ((![A3 : list_exp_list_char, B3 : produc515445032on_val, Aa : list_exp_list_char, Ba : produc515445032on_val]: ((member1689761872on_val @ (produc245869591on_val @ (produc1725134254on_val @ Ax @ Ay) @ (produc1725134254on_val @ A3 @ B3)) @ (transi325225921on_val @ R2)) => ((member1689761872on_val @ (produc245869591on_val @ (produc1725134254on_val @ A3 @ B3) @ (produc1725134254on_val @ Aa @ Ba)) @ R2) => ((P @ A3 @ B3) => (P @ Aa @ Ba))))) => (P @ Bx @ By))))))). % rtrancl_induct2
thf(fact_146_rtrancl__idemp, axiom,
    ((![R2 : set_Pr1189492743on_val]: ((transi111096263on_val @ (transi111096263on_val @ R2)) = (transi111096263on_val @ R2))))). % rtrancl_idemp
thf(fact_147_rtrancl__idemp, axiom,
    ((![R2 : set_Pr208351751on_val]: ((transi325225921on_val @ (transi325225921on_val @ R2)) = (transi325225921on_val @ R2))))). % rtrancl_idemp
thf(fact_148_r__into__rtrancl, axiom,
    ((![P2 : produc1172664615on_val, R2 : set_Pr1189492743on_val]: ((member354538064on_val @ P2 @ R2) => (member354538064on_val @ P2 @ (transi111096263on_val @ R2)))))). % r_into_rtrancl
thf(fact_149_r__into__rtrancl, axiom,
    ((![P2 : produc655058983on_val, R2 : set_Pr208351751on_val]: ((member1689761872on_val @ P2 @ R2) => (member1689761872on_val @ P2 @ (transi325225921on_val @ R2)))))). % r_into_rtrancl
thf(fact_150_map__add__assoc, axiom,
    ((![M1 : list_char > option_val, M2 : list_char > option_val, M3 : list_char > option_val]: ((map_ad1615113112ar_val @ M1 @ (map_ad1615113112ar_val @ M2 @ M3)) = (map_ad1615113112ar_val @ (map_ad1615113112ar_val @ M1 @ M2) @ M3))))). % map_add_assoc
thf(fact_151_hext__trans, axiom,
    ((![H : nat > option2118145160on_val, H2 : nat > option2118145160on_val, H5 : nat > option2118145160on_val]: ((hext @ H @ H2) => ((hext @ H2 @ H5) => (hext @ H @ H5)))))). % hext_trans
thf(fact_152_hext__objD, axiom,
    ((![H : nat > option2118145160on_val, H2 : nat > option2118145160on_val, A : nat, C2 : list_char, Fs : produc1257910179t_char > option_val]: ((hext @ H @ H2) => (((H @ A) = (some_P1299442195on_val @ (produc904988266on_val @ C2 @ Fs))) => (?[Fs2 : produc1257910179t_char > option_val]: ((H2 @ A) = (some_P1299442195on_val @ (produc904988266on_val @ C2 @ Fs2))))))))). % hext_objD
thf(fact_153_hext__def, axiom,
    ((hext = (^[H6 : nat > option2118145160on_val]: (^[H7 : nat > option2118145160on_val]: (![A5 : nat]: (![C3 : list_char]: (![Fs3 : produc1257910179t_char > option_val]: ((((H6 @ A5) = (some_P1299442195on_val @ (produc904988266on_val @ C3 @ Fs3)))) => ((?[Fs4 : produc1257910179t_char > option_val]: ((H7 @ A5) = (some_P1299442195on_val @ (produc904988266on_val @ C3 @ Fs4)))))))))))))). % hext_def
thf(fact_154_hextI, axiom,
    ((![H : nat > option2118145160on_val, H2 : nat > option2118145160on_val]: ((![A3 : nat, C4 : list_char, Fs5 : produc1257910179t_char > option_val]: (((H @ A3) = (some_P1299442195on_val @ (produc904988266on_val @ C4 @ Fs5))) => (?[Fs6 : produc1257910179t_char > option_val]: ((H2 @ A3) = (some_P1299442195on_val @ (produc904988266on_val @ C4 @ Fs6)))))) => (hext @ H @ H2))))). % hextI
thf(fact_155_rtranclE, axiom,
    ((![A : produc1097884484on_val, B : produc1097884484on_val, R2 : set_Pr1189492743on_val]: ((member354538064on_val @ (produc1069526295on_val @ A @ B) @ (transi111096263on_val @ R2)) => ((~ ((A = B))) => (~ ((![Y4 : produc1097884484on_val]: ((member354538064on_val @ (produc1069526295on_val @ A @ Y4) @ (transi111096263on_val @ R2)) => (~ ((member354538064on_val @ (produc1069526295on_val @ Y4 @ B) @ R2)))))))))))). % rtranclE
thf(fact_156_rtranclE, axiom,
    ((![A : produc335961278on_val, B : produc335961278on_val, R2 : set_Pr208351751on_val]: ((member1689761872on_val @ (produc245869591on_val @ A @ B) @ (transi325225921on_val @ R2)) => ((~ ((A = B))) => (~ ((![Y4 : produc335961278on_val]: ((member1689761872on_val @ (produc245869591on_val @ A @ Y4) @ (transi325225921on_val @ R2)) => (~ ((member1689761872on_val @ (produc245869591on_val @ Y4 @ B) @ R2)))))))))))). % rtranclE
thf(fact_157_rtrancl_Ocases, axiom,
    ((![A1 : produc1097884484on_val, A22 : produc1097884484on_val, R2 : set_Pr1189492743on_val]: ((member354538064on_val @ (produc1069526295on_val @ A1 @ A22) @ (transi111096263on_val @ R2)) => ((~ ((A22 = A1))) => (~ ((![B3 : produc1097884484on_val]: ((member354538064on_val @ (produc1069526295on_val @ A1 @ B3) @ (transi111096263on_val @ R2)) => (~ ((member354538064on_val @ (produc1069526295on_val @ B3 @ A22) @ R2)))))))))))). % rtrancl.cases
thf(fact_158_rtrancl_Ocases, axiom,
    ((![A1 : produc335961278on_val, A22 : produc335961278on_val, R2 : set_Pr208351751on_val]: ((member1689761872on_val @ (produc245869591on_val @ A1 @ A22) @ (transi325225921on_val @ R2)) => ((~ ((A22 = A1))) => (~ ((![B3 : produc335961278on_val]: ((member1689761872on_val @ (produc245869591on_val @ A1 @ B3) @ (transi325225921on_val @ R2)) => (~ ((member1689761872on_val @ (produc245869591on_val @ B3 @ A22) @ R2)))))))))))). % rtrancl.cases
thf(fact_159_rtrancl_Osimps, axiom,
    ((![A1 : produc1097884484on_val, A22 : produc1097884484on_val, R2 : set_Pr1189492743on_val]: ((member354538064on_val @ (produc1069526295on_val @ A1 @ A22) @ (transi111096263on_val @ R2)) = (((?[A5 : produc1097884484on_val]: (((A1 = A5)) & ((A22 = A5))))) | ((?[A5 : produc1097884484on_val]: (?[B4 : produc1097884484on_val]: (?[C5 : produc1097884484on_val]: (((A1 = A5)) & ((((A22 = C5)) & ((((member354538064on_val @ (produc1069526295on_val @ A5 @ B4) @ (transi111096263on_val @ R2))) & ((member354538064on_val @ (produc1069526295on_val @ B4 @ C5) @ R2)))))))))))))))). % rtrancl.simps
thf(fact_160_rtrancl_Osimps, axiom,
    ((![A1 : produc335961278on_val, A22 : produc335961278on_val, R2 : set_Pr208351751on_val]: ((member1689761872on_val @ (produc245869591on_val @ A1 @ A22) @ (transi325225921on_val @ R2)) = (((?[A5 : produc335961278on_val]: (((A1 = A5)) & ((A22 = A5))))) | ((?[A5 : produc335961278on_val]: (?[B4 : produc335961278on_val]: (?[C5 : produc335961278on_val]: (((A1 = A5)) & ((((A22 = C5)) & ((((member1689761872on_val @ (produc245869591on_val @ A5 @ B4) @ (transi325225921on_val @ R2))) & ((member1689761872on_val @ (produc245869591on_val @ B4 @ C5) @ R2)))))))))))))))). % rtrancl.simps
thf(fact_161_rtrancl__trans, axiom,
    ((![X : produc1097884484on_val, Y3 : produc1097884484on_val, R2 : set_Pr1189492743on_val, Z : produc1097884484on_val]: ((member354538064on_val @ (produc1069526295on_val @ X @ Y3) @ (transi111096263on_val @ R2)) => ((member354538064on_val @ (produc1069526295on_val @ Y3 @ Z) @ (transi111096263on_val @ R2)) => (member354538064on_val @ (produc1069526295on_val @ X @ Z) @ (transi111096263on_val @ R2))))))). % rtrancl_trans
thf(fact_162_rtrancl__trans, axiom,
    ((![X : produc335961278on_val, Y3 : produc335961278on_val, R2 : set_Pr208351751on_val, Z : produc335961278on_val]: ((member1689761872on_val @ (produc245869591on_val @ X @ Y3) @ (transi325225921on_val @ R2)) => ((member1689761872on_val @ (produc245869591on_val @ Y3 @ Z) @ (transi325225921on_val @ R2)) => (member1689761872on_val @ (produc245869591on_val @ X @ Z) @ (transi325225921on_val @ R2))))))). % rtrancl_trans
thf(fact_163_rtrancl__induct, axiom,
    ((![A : produc1097884484on_val, B : produc1097884484on_val, R2 : set_Pr1189492743on_val, P : produc1097884484on_val > $o]: ((member354538064on_val @ (produc1069526295on_val @ A @ B) @ (transi111096263on_val @ R2)) => ((P @ A) => ((![Y4 : produc1097884484on_val, Z2 : produc1097884484on_val]: ((member354538064on_val @ (produc1069526295on_val @ A @ Y4) @ (transi111096263on_val @ R2)) => ((member354538064on_val @ (produc1069526295on_val @ Y4 @ Z2) @ R2) => ((P @ Y4) => (P @ Z2))))) => (P @ B))))))). % rtrancl_induct
thf(fact_164_rtrancl__induct, axiom,
    ((![A : produc335961278on_val, B : produc335961278on_val, R2 : set_Pr208351751on_val, P : produc335961278on_val > $o]: ((member1689761872on_val @ (produc245869591on_val @ A @ B) @ (transi325225921on_val @ R2)) => ((P @ A) => ((![Y4 : produc335961278on_val, Z2 : produc335961278on_val]: ((member1689761872on_val @ (produc245869591on_val @ A @ Y4) @ (transi325225921on_val @ R2)) => ((member1689761872on_val @ (produc245869591on_val @ Y4 @ Z2) @ R2) => ((P @ Y4) => (P @ Z2))))) => (P @ B))))))). % rtrancl_induct
thf(fact_165_rtrancl_Oinducts, axiom,
    ((![X1 : produc1097884484on_val, X2 : produc1097884484on_val, R2 : set_Pr1189492743on_val, P : produc1097884484on_val > produc1097884484on_val > $o]: ((member354538064on_val @ (produc1069526295on_val @ X1 @ X2) @ (transi111096263on_val @ R2)) => ((![A3 : produc1097884484on_val]: (P @ A3 @ A3)) => ((![A3 : produc1097884484on_val, B3 : produc1097884484on_val, C : produc1097884484on_val]: ((member354538064on_val @ (produc1069526295on_val @ A3 @ B3) @ (transi111096263on_val @ R2)) => ((P @ A3 @ B3) => ((member354538064on_val @ (produc1069526295on_val @ B3 @ C) @ R2) => (P @ A3 @ C))))) => (P @ X1 @ X2))))))). % rtrancl.inducts
thf(fact_166_rtrancl_Oinducts, axiom,
    ((![X1 : produc335961278on_val, X2 : produc335961278on_val, R2 : set_Pr208351751on_val, P : produc335961278on_val > produc335961278on_val > $o]: ((member1689761872on_val @ (produc245869591on_val @ X1 @ X2) @ (transi325225921on_val @ R2)) => ((![A3 : produc335961278on_val]: (P @ A3 @ A3)) => ((![A3 : produc335961278on_val, B3 : produc335961278on_val, C : produc335961278on_val]: ((member1689761872on_val @ (produc245869591on_val @ A3 @ B3) @ (transi325225921on_val @ R2)) => ((P @ A3 @ B3) => ((member1689761872on_val @ (produc245869591on_val @ B3 @ C) @ R2) => (P @ A3 @ C))))) => (P @ X1 @ X2))))))). % rtrancl.inducts
thf(fact_167_converse__rtranclE, axiom,
    ((![X : produc1097884484on_val, Z : produc1097884484on_val, R2 : set_Pr1189492743on_val]: ((member354538064on_val @ (produc1069526295on_val @ X @ Z) @ (transi111096263on_val @ R2)) => ((~ ((X = Z))) => (~ ((![Y4 : produc1097884484on_val]: ((member354538064on_val @ (produc1069526295on_val @ X @ Y4) @ R2) => (~ ((member354538064on_val @ (produc1069526295on_val @ Y4 @ Z) @ (transi111096263on_val @ R2))))))))))))). % converse_rtranclE
thf(fact_168_converse__rtranclE, axiom,
    ((![X : produc335961278on_val, Z : produc335961278on_val, R2 : set_Pr208351751on_val]: ((member1689761872on_val @ (produc245869591on_val @ X @ Z) @ (transi325225921on_val @ R2)) => ((~ ((X = Z))) => (~ ((![Y4 : produc335961278on_val]: ((member1689761872on_val @ (produc245869591on_val @ X @ Y4) @ R2) => (~ ((member1689761872on_val @ (produc245869591on_val @ Y4 @ Z) @ (transi325225921on_val @ R2))))))))))))). % converse_rtranclE
thf(fact_169_rtrancl_Ortrancl__refl, axiom,
    ((![A : produc1097884484on_val, R2 : set_Pr1189492743on_val]: (member354538064on_val @ (produc1069526295on_val @ A @ A) @ (transi111096263on_val @ R2))))). % rtrancl.rtrancl_refl
thf(fact_170_rtrancl_Ortrancl__refl, axiom,
    ((![A : produc335961278on_val, R2 : set_Pr208351751on_val]: (member1689761872on_val @ (produc245869591on_val @ A @ A) @ (transi325225921on_val @ R2))))). % rtrancl.rtrancl_refl
thf(fact_171_converse__rtrancl__induct, axiom,
    ((![A : produc1097884484on_val, B : produc1097884484on_val, R2 : set_Pr1189492743on_val, P : produc1097884484on_val > $o]: ((member354538064on_val @ (produc1069526295on_val @ A @ B) @ (transi111096263on_val @ R2)) => ((P @ B) => ((![Y4 : produc1097884484on_val, Z2 : produc1097884484on_val]: ((member354538064on_val @ (produc1069526295on_val @ Y4 @ Z2) @ R2) => ((member354538064on_val @ (produc1069526295on_val @ Z2 @ B) @ (transi111096263on_val @ R2)) => ((P @ Z2) => (P @ Y4))))) => (P @ A))))))). % converse_rtrancl_induct
thf(fact_172_converse__rtrancl__induct, axiom,
    ((![A : produc335961278on_val, B : produc335961278on_val, R2 : set_Pr208351751on_val, P : produc335961278on_val > $o]: ((member1689761872on_val @ (produc245869591on_val @ A @ B) @ (transi325225921on_val @ R2)) => ((P @ B) => ((![Y4 : produc335961278on_val, Z2 : produc335961278on_val]: ((member1689761872on_val @ (produc245869591on_val @ Y4 @ Z2) @ R2) => ((member1689761872on_val @ (produc245869591on_val @ Z2 @ B) @ (transi325225921on_val @ R2)) => ((P @ Z2) => (P @ Y4))))) => (P @ A))))))). % converse_rtrancl_induct
thf(fact_173_rtrancl_Ortrancl__into__rtrancl, axiom,
    ((![A : produc1097884484on_val, B : produc1097884484on_val, R2 : set_Pr1189492743on_val, C6 : produc1097884484on_val]: ((member354538064on_val @ (produc1069526295on_val @ A @ B) @ (transi111096263on_val @ R2)) => ((member354538064on_val @ (produc1069526295on_val @ B @ C6) @ R2) => (member354538064on_val @ (produc1069526295on_val @ A @ C6) @ (transi111096263on_val @ R2))))))). % rtrancl.rtrancl_into_rtrancl
thf(fact_174_rtrancl_Ortrancl__into__rtrancl, axiom,
    ((![A : produc335961278on_val, B : produc335961278on_val, R2 : set_Pr208351751on_val, C6 : produc335961278on_val]: ((member1689761872on_val @ (produc245869591on_val @ A @ B) @ (transi325225921on_val @ R2)) => ((member1689761872on_val @ (produc245869591on_val @ B @ C6) @ R2) => (member1689761872on_val @ (produc245869591on_val @ A @ C6) @ (transi325225921on_val @ R2))))))). % rtrancl.rtrancl_into_rtrancl
thf(fact_175_converse__rtrancl__into__rtrancl, axiom,
    ((![A : produc1097884484on_val, B : produc1097884484on_val, R2 : set_Pr1189492743on_val, C6 : produc1097884484on_val]: ((member354538064on_val @ (produc1069526295on_val @ A @ B) @ R2) => ((member354538064on_val @ (produc1069526295on_val @ B @ C6) @ (transi111096263on_val @ R2)) => (member354538064on_val @ (produc1069526295on_val @ A @ C6) @ (transi111096263on_val @ R2))))))). % converse_rtrancl_into_rtrancl
thf(fact_176_converse__rtrancl__into__rtrancl, axiom,
    ((![A : produc335961278on_val, B : produc335961278on_val, R2 : set_Pr208351751on_val, C6 : produc335961278on_val]: ((member1689761872on_val @ (produc245869591on_val @ A @ B) @ R2) => ((member1689761872on_val @ (produc245869591on_val @ B @ C6) @ (transi325225921on_val @ R2)) => (member1689761872on_val @ (produc245869591on_val @ A @ C6) @ (transi325225921on_val @ R2))))))). % converse_rtrancl_into_rtrancl
thf(fact_177_converse__rtrancl__induct2, axiom,
    ((![Ax : list_char, Ay : produc1257910179t_char > option_val, Bx : list_char, By : produc1257910179t_char > option_val, R2 : set_Pr2110063281on_val, P : list_char > (produc1257910179t_char > option_val) > $o]: ((member197592058on_val @ (produc881885833on_val @ (produc904988266on_val @ Ax @ Ay) @ (produc904988266on_val @ Bx @ By)) @ (transi2071064181on_val @ R2)) => ((P @ Bx @ By) => ((![A3 : list_char, B3 : produc1257910179t_char > option_val, Aa : list_char, Ba : produc1257910179t_char > option_val]: ((member197592058on_val @ (produc881885833on_val @ (produc904988266on_val @ A3 @ B3) @ (produc904988266on_val @ Aa @ Ba)) @ R2) => ((member197592058on_val @ (produc881885833on_val @ (produc904988266on_val @ Aa @ Ba) @ (produc904988266on_val @ Bx @ By)) @ (transi2071064181on_val @ R2)) => ((P @ Aa @ Ba) => (P @ A3 @ B3))))) => (P @ Ax @ Ay))))))). % converse_rtrancl_induct2
thf(fact_178_converse__rtrancl__induct2, axiom,
    ((![Ax : bop, Ay : product_prod_val_val, Bx : bop, By : product_prod_val_val, R2 : set_Pr711661575al_val, P : bop > product_prod_val_val > $o]: ((member1528603216al_val @ (produc1144711447al_val @ (produc1753769388al_val @ Ax @ Ay) @ (produc1753769388al_val @ Bx @ By)) @ (transi531594559al_val @ R2)) => ((P @ Bx @ By) => ((![A3 : bop, B3 : product_prod_val_val, Aa : bop, Ba : product_prod_val_val]: ((member1528603216al_val @ (produc1144711447al_val @ (produc1753769388al_val @ A3 @ B3) @ (produc1753769388al_val @ Aa @ Ba)) @ R2) => ((member1528603216al_val @ (produc1144711447al_val @ (produc1753769388al_val @ Aa @ Ba) @ (produc1753769388al_val @ Bx @ By)) @ (transi531594559al_val @ R2)) => ((P @ Aa @ Ba) => (P @ A3 @ B3))))) => (P @ Ax @ Ay))))))). % converse_rtrancl_induct2
thf(fact_179_converse__rtrancl__induct2, axiom,
    ((![Ax : nat > option2118145160on_val, Ay : list_char > option_val, Bx : nat > option2118145160on_val, By : list_char > option_val, R2 : set_Pr148564103on_val, P : (nat > option2118145160on_val) > (list_char > option_val) > $o]: ((member2027247312on_val @ (produc2106877847on_val @ (produc52622304on_val @ Ax @ Ay) @ (produc52622304on_val @ Bx @ By)) @ (transi432893227on_val @ R2)) => ((P @ Bx @ By) => ((![A3 : nat > option2118145160on_val, B3 : list_char > option_val, Aa : nat > option2118145160on_val, Ba : list_char > option_val]: ((member2027247312on_val @ (produc2106877847on_val @ (produc52622304on_val @ A3 @ B3) @ (produc52622304on_val @ Aa @ Ba)) @ R2) => ((member2027247312on_val @ (produc2106877847on_val @ (produc52622304on_val @ Aa @ Ba) @ (produc52622304on_val @ Bx @ By)) @ (transi432893227on_val @ R2)) => ((P @ Aa @ Ba) => (P @ A3 @ B3))))) => (P @ Ax @ Ay))))))). % converse_rtrancl_induct2
thf(fact_180_converse__rtrancl__induct2, axiom,
    ((![Ax : exp_list_char, Ay : produc515445032on_val, Bx : exp_list_char, By : produc515445032on_val, R2 : set_Pr1189492743on_val, P : exp_list_char > produc515445032on_val > $o]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ Ax @ Ay) @ (produc2023458740on_val @ Bx @ By)) @ (transi111096263on_val @ R2)) => ((P @ Bx @ By) => ((![A3 : exp_list_char, B3 : produc515445032on_val, Aa : exp_list_char, Ba : produc515445032on_val]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ A3 @ B3) @ (produc2023458740on_val @ Aa @ Ba)) @ R2) => ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ Aa @ Ba) @ (produc2023458740on_val @ Bx @ By)) @ (transi111096263on_val @ R2)) => ((P @ Aa @ Ba) => (P @ A3 @ B3))))) => (P @ Ax @ Ay))))))). % converse_rtrancl_induct2
thf(fact_181_converse__rtrancl__induct2, axiom,
    ((![Ax : list_exp_list_char, Ay : produc515445032on_val, Bx : list_exp_list_char, By : produc515445032on_val, R2 : set_Pr208351751on_val, P : list_exp_list_char > produc515445032on_val > $o]: ((member1689761872on_val @ (produc245869591on_val @ (produc1725134254on_val @ Ax @ Ay) @ (produc1725134254on_val @ Bx @ By)) @ (transi325225921on_val @ R2)) => ((P @ Bx @ By) => ((![A3 : list_exp_list_char, B3 : produc515445032on_val, Aa : list_exp_list_char, Ba : produc515445032on_val]: ((member1689761872on_val @ (produc245869591on_val @ (produc1725134254on_val @ A3 @ B3) @ (produc1725134254on_val @ Aa @ Ba)) @ R2) => ((member1689761872on_val @ (produc245869591on_val @ (produc1725134254on_val @ Aa @ Ba) @ (produc1725134254on_val @ Bx @ By)) @ (transi325225921on_val @ R2)) => ((P @ Aa @ Ba) => (P @ A3 @ B3))))) => (P @ Ax @ Ay))))))). % converse_rtrancl_induct2
thf(fact_182_converse__rtranclE2, axiom,
    ((![Xa : list_char, Xb : produc1257910179t_char > option_val, Za : list_char, Zb : produc1257910179t_char > option_val, R2 : set_Pr2110063281on_val]: ((member197592058on_val @ (produc881885833on_val @ (produc904988266on_val @ Xa @ Xb) @ (produc904988266on_val @ Za @ Zb)) @ (transi2071064181on_val @ R2)) => ((~ (((produc904988266on_val @ Xa @ Xb) = (produc904988266on_val @ Za @ Zb)))) => (~ ((![A3 : list_char, B3 : produc1257910179t_char > option_val]: ((member197592058on_val @ (produc881885833on_val @ (produc904988266on_val @ Xa @ Xb) @ (produc904988266on_val @ A3 @ B3)) @ R2) => (~ ((member197592058on_val @ (produc881885833on_val @ (produc904988266on_val @ A3 @ B3) @ (produc904988266on_val @ Za @ Zb)) @ (transi2071064181on_val @ R2))))))))))))). % converse_rtranclE2
thf(fact_183_converse__rtranclE2, axiom,
    ((![Xa : bop, Xb : product_prod_val_val, Za : bop, Zb : product_prod_val_val, R2 : set_Pr711661575al_val]: ((member1528603216al_val @ (produc1144711447al_val @ (produc1753769388al_val @ Xa @ Xb) @ (produc1753769388al_val @ Za @ Zb)) @ (transi531594559al_val @ R2)) => ((~ (((produc1753769388al_val @ Xa @ Xb) = (produc1753769388al_val @ Za @ Zb)))) => (~ ((![A3 : bop, B3 : product_prod_val_val]: ((member1528603216al_val @ (produc1144711447al_val @ (produc1753769388al_val @ Xa @ Xb) @ (produc1753769388al_val @ A3 @ B3)) @ R2) => (~ ((member1528603216al_val @ (produc1144711447al_val @ (produc1753769388al_val @ A3 @ B3) @ (produc1753769388al_val @ Za @ Zb)) @ (transi531594559al_val @ R2))))))))))))). % converse_rtranclE2
thf(fact_184_converse__rtranclE2, axiom,
    ((![Xa : nat > option2118145160on_val, Xb : list_char > option_val, Za : nat > option2118145160on_val, Zb : list_char > option_val, R2 : set_Pr148564103on_val]: ((member2027247312on_val @ (produc2106877847on_val @ (produc52622304on_val @ Xa @ Xb) @ (produc52622304on_val @ Za @ Zb)) @ (transi432893227on_val @ R2)) => ((~ (((produc52622304on_val @ Xa @ Xb) = (produc52622304on_val @ Za @ Zb)))) => (~ ((![A3 : nat > option2118145160on_val, B3 : list_char > option_val]: ((member2027247312on_val @ (produc2106877847on_val @ (produc52622304on_val @ Xa @ Xb) @ (produc52622304on_val @ A3 @ B3)) @ R2) => (~ ((member2027247312on_val @ (produc2106877847on_val @ (produc52622304on_val @ A3 @ B3) @ (produc52622304on_val @ Za @ Zb)) @ (transi432893227on_val @ R2))))))))))))). % converse_rtranclE2
thf(fact_185_converse__rtranclE2, axiom,
    ((![Xa : exp_list_char, Xb : produc515445032on_val, Za : exp_list_char, Zb : produc515445032on_val, R2 : set_Pr1189492743on_val]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ Xa @ Xb) @ (produc2023458740on_val @ Za @ Zb)) @ (transi111096263on_val @ R2)) => ((~ (((produc2023458740on_val @ Xa @ Xb) = (produc2023458740on_val @ Za @ Zb)))) => (~ ((![A3 : exp_list_char, B3 : produc515445032on_val]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ Xa @ Xb) @ (produc2023458740on_val @ A3 @ B3)) @ R2) => (~ ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ A3 @ B3) @ (produc2023458740on_val @ Za @ Zb)) @ (transi111096263on_val @ R2))))))))))))). % converse_rtranclE2
thf(fact_186_converse__rtranclE2, axiom,
    ((![Xa : list_exp_list_char, Xb : produc515445032on_val, Za : list_exp_list_char, Zb : produc515445032on_val, R2 : set_Pr208351751on_val]: ((member1689761872on_val @ (produc245869591on_val @ (produc1725134254on_val @ Xa @ Xb) @ (produc1725134254on_val @ Za @ Zb)) @ (transi325225921on_val @ R2)) => ((~ (((produc1725134254on_val @ Xa @ Xb) = (produc1725134254on_val @ Za @ Zb)))) => (~ ((![A3 : list_exp_list_char, B3 : produc515445032on_val]: ((member1689761872on_val @ (produc245869591on_val @ (produc1725134254on_val @ Xa @ Xb) @ (produc1725134254on_val @ A3 @ B3)) @ R2) => (~ ((member1689761872on_val @ (produc245869591on_val @ (produc1725134254on_val @ A3 @ B3) @ (produc1725134254on_val @ Za @ Zb)) @ (transi325225921on_val @ R2))))))))))))). % converse_rtranclE2
thf(fact_187_reds__hext__incr, axiom,
    ((![Es : list_exp_list_char, H : nat > option2118145160on_val, L : list_char > option_val, Es2 : list_exp_list_char, H2 : nat > option2118145160on_val, L2 : list_char > option_val, P : list_P1234162913t_char]: ((member1689761872on_val @ (produc245869591on_val @ (produc1725134254on_val @ Es @ (produc52622304on_val @ H @ L)) @ (produc1725134254on_val @ Es2 @ (produc52622304on_val @ H2 @ L2))) @ (reds @ P)) => (hext @ H @ H2))))). % reds_hext_incr
thf(fact_188_hext__upd__obj, axiom,
    ((![H : nat > option2118145160on_val, A : nat, C2 : list_char, Fs : produc1257910179t_char > option_val, Fs7 : produc1257910179t_char > option_val]: (((H @ A) = (some_P1299442195on_val @ (produc904988266on_val @ C2 @ Fs))) => (hext @ H @ (fun_up262443479on_val @ H @ A @ (some_P1299442195on_val @ (produc904988266on_val @ C2 @ Fs7)))))))). % hext_upd_obj
thf(fact_189_single__valued__confluent, axiom,
    ((![R2 : set_Pr1189492743on_val, X : produc1097884484on_val, Y3 : produc1097884484on_val, Z : produc1097884484on_val]: ((single747474179on_val @ R2) => ((member354538064on_val @ (produc1069526295on_val @ X @ Y3) @ (transi111096263on_val @ R2)) => ((member354538064on_val @ (produc1069526295on_val @ X @ Z) @ (transi111096263on_val @ R2)) => ((member354538064on_val @ (produc1069526295on_val @ Y3 @ Z) @ (transi111096263on_val @ R2)) | (member354538064on_val @ (produc1069526295on_val @ Z @ Y3) @ (transi111096263on_val @ R2))))))))). % single_valued_confluent
thf(fact_190_single__valued__confluent, axiom,
    ((![R2 : set_Pr208351751on_val, X : produc335961278on_val, Y3 : produc335961278on_val, Z : produc335961278on_val]: ((single965918723on_val @ R2) => ((member1689761872on_val @ (produc245869591on_val @ X @ Y3) @ (transi325225921on_val @ R2)) => ((member1689761872on_val @ (produc245869591on_val @ X @ Z) @ (transi325225921on_val @ R2)) => ((member1689761872on_val @ (produc245869591on_val @ Y3 @ Z) @ (transi325225921on_val @ R2)) | (member1689761872on_val @ (produc245869591on_val @ Z @ Y3) @ (transi325225921on_val @ R2))))))))). % single_valued_confluent
thf(fact_191_red__reds_OThrowRed, axiom,
    ((![E : exp_list_char, S : produc515445032on_val, E2 : exp_list_char, S2 : produc515445032on_val, P : list_P1234162913t_char]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E @ S) @ (produc2023458740on_val @ E2 @ S2)) @ (red @ P)) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (throw_list_char @ E) @ S) @ (produc2023458740on_val @ (throw_list_char @ E2) @ S2)) @ (red @ P)))))). % red_reds.ThrowRed
thf(fact_192_map__add__upd, axiom,
    ((![F : list_char > option_val, G : list_char > option_val, X : list_char, Y3 : val]: ((map_ad1615113112ar_val @ F @ (fun_up1252458416on_val @ G @ X @ (some_val @ Y3))) = (fun_up1252458416on_val @ (map_ad1615113112ar_val @ F @ G) @ X @ (some_val @ Y3)))))). % map_add_upd
thf(fact_193_map__add__upd, axiom,
    ((![F : nat > option2118145160on_val, G : nat > option2118145160on_val, X : nat, Y3 : produc266837688on_val]: ((map_ad109059391on_val @ F @ (fun_up262443479on_val @ G @ X @ (some_P1299442195on_val @ Y3))) = (fun_up262443479on_val @ (map_ad109059391on_val @ F @ G) @ X @ (some_P1299442195on_val @ Y3)))))). % map_add_upd
thf(fact_194_map__upd__Some__unfold, axiom,
    ((![M : nat > option2118145160on_val, A : nat, B : produc266837688on_val, X : nat, Y3 : produc266837688on_val]: (((fun_up262443479on_val @ M @ A @ (some_P1299442195on_val @ B) @ X) = (some_P1299442195on_val @ Y3)) = (((((X = A)) & ((B = Y3)))) | ((((~ ((X = A)))) & (((M @ X) = (some_P1299442195on_val @ Y3)))))))))). % map_upd_Some_unfold
thf(fact_195_map__upd__triv, axiom,
    ((![T : nat > option2118145160on_val, K : nat, X : produc266837688on_val]: (((T @ K) = (some_P1299442195on_val @ X)) => ((fun_up262443479on_val @ T @ K @ (some_P1299442195on_val @ X)) = T))))). % map_upd_triv
thf(fact_196_map__upd__eqD1, axiom,
    ((![M : nat > option2118145160on_val, A : nat, X : produc266837688on_val, N : nat > option2118145160on_val, Y3 : produc266837688on_val]: (((fun_up262443479on_val @ M @ A @ (some_P1299442195on_val @ X)) = (fun_up262443479on_val @ N @ A @ (some_P1299442195on_val @ Y3))) => (X = Y3))))). % map_upd_eqD1
thf(fact_197_map__upd__nonempty, axiom,
    ((![T : nat > option2118145160on_val, K : nat, X : produc266837688on_val]: (~ (((fun_up262443479on_val @ T @ K @ (some_P1299442195on_val @ X)) = (^[X5 : nat]: none_P1535574167on_val))))))). % map_upd_nonempty
thf(fact_198_hext__new, axiom,
    ((![H : nat > option2118145160on_val, A : nat, X : produc266837688on_val]: (((H @ A) = none_P1535574167on_val) => (hext @ H @ (fun_up262443479on_val @ H @ A @ (some_P1299442195on_val @ X))))))). % hext_new
thf(fact_199_red__reds_OThrowThrow, axiom,
    ((![E : exp_list_char, S : produc515445032on_val, P : list_P1234162913t_char]: (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (throw_list_char @ (throw_list_char @ E)) @ S) @ (produc2023458740on_val @ (throw_list_char @ E) @ S)) @ (red @ P))))). % red_reds.ThrowThrow
thf(fact_200_ThrowRedsThrow, axiom,
    ((![E : exp_list_char, S : produc515445032on_val, A : exp_list_char, S2 : produc515445032on_val, P : list_P1234162913t_char]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E @ S) @ (produc2023458740on_val @ (throw_list_char @ A) @ S2)) @ (transi111096263on_val @ (red @ P))) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (throw_list_char @ E) @ S) @ (produc2023458740on_val @ (throw_list_char @ A) @ S2)) @ (transi111096263on_val @ (red @ P))))))). % ThrowRedsThrow
thf(fact_201_ThrowReds, axiom,
    ((![E : exp_list_char, S : produc515445032on_val, E2 : exp_list_char, S2 : produc515445032on_val, P : list_P1234162913t_char]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E @ S) @ (produc2023458740on_val @ E2 @ S2)) @ (transi111096263on_val @ (red @ P))) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (throw_list_char @ E) @ S) @ (produc2023458740on_val @ (throw_list_char @ E2) @ S2)) @ (transi111096263on_val @ (red @ P))))))). % ThrowReds
thf(fact_202__092_060A_062_Osimps_I14_J, axiom,
    ((![E : exp_list_char]: ((a_list_char @ (throw_list_char @ E)) = none_set_list_char)))). % \<A>.simps(14)
thf(fact_203_fun__upd__apply, axiom,
    ((fun_up262443479on_val = (^[F2 : nat > option2118145160on_val]: (^[X5 : nat]: (^[Y : option2118145160on_val]: (^[Z3 : nat]: (if_opt451925058on_val @ (Z3 = X5) @ Y @ (F2 @ Z3))))))))). % fun_upd_apply
thf(fact_204_fun__upd__triv, axiom,
    ((![F : nat > option2118145160on_val, X : nat]: ((fun_up262443479on_val @ F @ X @ (F @ X)) = F)))). % fun_upd_triv
thf(fact_205_fun__upd__upd, axiom,
    ((![F : nat > option2118145160on_val, X : nat, Y3 : option2118145160on_val, Z : option2118145160on_val]: ((fun_up262443479on_val @ (fun_up262443479on_val @ F @ X @ Y3) @ X @ Z) = (fun_up262443479on_val @ F @ X @ Z))))). % fun_upd_upd
thf(fact_206_fun__upd__def, axiom,
    ((fun_up262443479on_val = (^[F2 : nat > option2118145160on_val]: (^[A5 : nat]: (^[B4 : option2118145160on_val]: (^[X5 : nat]: (if_opt451925058on_val @ (X5 = A5) @ B4 @ (F2 @ X5))))))))). % fun_upd_def
thf(fact_207_fun__upd__eqD, axiom,
    ((![F : nat > option2118145160on_val, X : nat, Y3 : option2118145160on_val, G : nat > option2118145160on_val, Z : option2118145160on_val]: (((fun_up262443479on_val @ F @ X @ Y3) = (fun_up262443479on_val @ G @ X @ Z)) => (Y3 = Z))))). % fun_upd_eqD
thf(fact_208_fun__upd__idem, axiom,
    ((![F : nat > option2118145160on_val, X : nat, Y3 : option2118145160on_val]: (((F @ X) = Y3) => ((fun_up262443479on_val @ F @ X @ Y3) = F))))). % fun_upd_idem
thf(fact_209_fun__upd__same, axiom,
    ((![F : nat > option2118145160on_val, X : nat, Y3 : option2118145160on_val]: ((fun_up262443479on_val @ F @ X @ Y3 @ X) = Y3)))). % fun_upd_same
thf(fact_210_fun__upd__other, axiom,
    ((![Z : nat, X : nat, F : nat > option2118145160on_val, Y3 : option2118145160on_val]: ((~ ((Z = X))) => ((fun_up262443479on_val @ F @ X @ Y3 @ Z) = (F @ Z)))))). % fun_upd_other
thf(fact_211_fun__upd__twist, axiom,
    ((![A : nat, C6 : nat, M : nat > option2118145160on_val, B : option2118145160on_val, D : option2118145160on_val]: ((~ ((A = C6))) => ((fun_up262443479on_val @ (fun_up262443479on_val @ M @ A @ B) @ C6 @ D) = (fun_up262443479on_val @ (fun_up262443479on_val @ M @ C6 @ D) @ A @ B)))))). % fun_upd_twist
thf(fact_212_ListReds1, axiom,
    ((![E : exp_list_char, S : produc515445032on_val, E2 : exp_list_char, S2 : produc515445032on_val, P : list_P1234162913t_char, Es : list_exp_list_char]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E @ S) @ (produc2023458740on_val @ E2 @ S2)) @ (transi111096263on_val @ (red @ P))) => (member1689761872on_val @ (produc245869591on_val @ (produc1725134254on_val @ (cons_exp_list_char @ E @ Es) @ S) @ (produc1725134254on_val @ (cons_exp_list_char @ E2 @ Es) @ S2)) @ (transi325225921on_val @ (reds @ P))))))). % ListReds1
thf(fact_213_red__reds_OListRed1, axiom,
    ((![E : exp_list_char, S : produc515445032on_val, E2 : exp_list_char, S2 : produc515445032on_val, P : list_P1234162913t_char, Es : list_exp_list_char]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E @ S) @ (produc2023458740on_val @ E2 @ S2)) @ (red @ P)) => (member1689761872on_val @ (produc245869591on_val @ (produc1725134254on_val @ (cons_exp_list_char @ E @ Es) @ S) @ (produc1725134254on_val @ (cons_exp_list_char @ E2 @ Es) @ S2)) @ (reds @ P)))))). % red_reds.ListRed1
thf(fact_214_ListRedsVal, axiom,
    ((![E : exp_list_char, S_0 : produc515445032on_val, V : val, S_1 : produc515445032on_val, P : list_P1234162913t_char, Es : list_exp_list_char, Es2 : list_exp_list_char, S_2 : produc515445032on_val]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E @ S_0) @ (produc2023458740on_val @ (val_list_char @ V) @ S_1)) @ (transi111096263on_val @ (red @ P))) => ((member1689761872on_val @ (produc245869591on_val @ (produc1725134254on_val @ Es @ S_1) @ (produc1725134254on_val @ Es2 @ S_2)) @ (transi325225921on_val @ (reds @ P))) => (member1689761872on_val @ (produc245869591on_val @ (produc1725134254on_val @ (cons_exp_list_char @ E @ Es) @ S_0) @ (produc1725134254on_val @ (cons_exp_list_char @ (val_list_char @ V) @ Es2) @ S_2)) @ (transi325225921on_val @ (reds @ P)))))))). % ListRedsVal
thf(fact_215_reds_Ocases, axiom,
    ((![A1 : list_exp_list_char, A22 : produc515445032on_val, A32 : list_exp_list_char, A42 : produc515445032on_val, P : list_P1234162913t_char]: ((member1689761872on_val @ (produc245869591on_val @ (produc1725134254on_val @ A1 @ A22) @ (produc1725134254on_val @ A32 @ A42)) @ (reds @ P)) => ((![E3 : exp_list_char, S3 : produc515445032on_val, E4 : exp_list_char, S4 : produc515445032on_val, Es3 : list_exp_list_char]: ((A1 = (cons_exp_list_char @ E3 @ Es3)) => ((A22 = S3) => ((A32 = (cons_exp_list_char @ E4 @ Es3)) => ((A42 = S4) => (~ ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E3 @ S3) @ (produc2023458740on_val @ E4 @ S4)) @ (red @ P))))))))) => (~ ((![Es3 : list_exp_list_char, S3 : produc515445032on_val, Es4 : list_exp_list_char, S4 : produc515445032on_val, V2 : val]: ((A1 = (cons_exp_list_char @ (val_list_char @ V2) @ Es3)) => ((A22 = S3) => ((A32 = (cons_exp_list_char @ (val_list_char @ V2) @ Es4)) => ((A42 = S4) => (~ ((member1689761872on_val @ (produc245869591on_val @ (produc1725134254on_val @ Es3 @ S3) @ (produc1725134254on_val @ Es4 @ S4)) @ (reds @ P)))))))))))))))). % reds.cases
thf(fact_216_red__reds_OListRed2, axiom,
    ((![Es : list_exp_list_char, S : produc515445032on_val, Es2 : list_exp_list_char, S2 : produc515445032on_val, P : list_P1234162913t_char, V : val]: ((member1689761872on_val @ (produc245869591on_val @ (produc1725134254on_val @ Es @ S) @ (produc1725134254on_val @ Es2 @ S2)) @ (reds @ P)) => (member1689761872on_val @ (produc245869591on_val @ (produc1725134254on_val @ (cons_exp_list_char @ (val_list_char @ V) @ Es) @ S) @ (produc1725134254on_val @ (cons_exp_list_char @ (val_list_char @ V) @ Es2) @ S2)) @ (reds @ P)))))). % red_reds.ListRed2
thf(fact_217_ListReds2, axiom,
    ((![Es : list_exp_list_char, S : produc515445032on_val, Es2 : list_exp_list_char, S2 : produc515445032on_val, P : list_P1234162913t_char, V : val]: ((member1689761872on_val @ (produc245869591on_val @ (produc1725134254on_val @ Es @ S) @ (produc1725134254on_val @ Es2 @ S2)) @ (transi325225921on_val @ (reds @ P))) => (member1689761872on_val @ (produc245869591on_val @ (produc1725134254on_val @ (cons_exp_list_char @ (val_list_char @ V) @ Es) @ S) @ (produc1725134254on_val @ (cons_exp_list_char @ (val_list_char @ V) @ Es2) @ S2)) @ (transi325225921on_val @ (reds @ P))))))). % ListReds2
thf(fact_218_reds_Osimps, axiom,
    ((![A1 : list_exp_list_char, A22 : produc515445032on_val, A32 : list_exp_list_char, A42 : produc515445032on_val, P : list_P1234162913t_char]: ((member1689761872on_val @ (produc245869591on_val @ (produc1725134254on_val @ A1 @ A22) @ (produc1725134254on_val @ A32 @ A42)) @ (reds @ P)) = (((?[E5 : exp_list_char]: (?[S5 : produc515445032on_val]: (?[E6 : exp_list_char]: (?[S6 : produc515445032on_val]: (?[Es5 : list_exp_list_char]: (((A1 = (cons_exp_list_char @ E5 @ Es5))) & ((((A22 = S5)) & ((((A32 = (cons_exp_list_char @ E6 @ Es5))) & ((((A42 = S6)) & ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E5 @ S5) @ (produc2023458740on_val @ E6 @ S6)) @ (red @ P)))))))))))))))) | ((?[Es5 : list_exp_list_char]: (?[S5 : produc515445032on_val]: (?[Es6 : list_exp_list_char]: (?[S6 : produc515445032on_val]: (?[V3 : val]: (((A1 = (cons_exp_list_char @ (val_list_char @ V3) @ Es5))) & ((((A22 = S5)) & ((((A32 = (cons_exp_list_char @ (val_list_char @ V3) @ Es6))) & ((((A42 = S6)) & ((member1689761872on_val @ (produc245869591on_val @ (produc1725134254on_val @ Es5 @ S5) @ (produc1725134254on_val @ Es6 @ S6)) @ (reds @ P))))))))))))))))))))). % reds.simps
thf(fact_219_CallRedsParams, axiom,
    ((![Es : list_exp_list_char, S : produc515445032on_val, Es2 : list_exp_list_char, S2 : produc515445032on_val, P : list_P1234162913t_char, V : val, M4 : list_char]: ((member1689761872on_val @ (produc245869591on_val @ (produc1725134254on_val @ Es @ S) @ (produc1725134254on_val @ Es2 @ S2)) @ (transi325225921on_val @ (reds @ P))) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (call_list_char @ (val_list_char @ V) @ M4 @ Es) @ S) @ (produc2023458740on_val @ (call_list_char @ (val_list_char @ V) @ M4 @ Es2) @ S2)) @ (transi111096263on_val @ (red @ P))))))). % CallRedsParams
thf(fact_220_red__reds_OCallParams, axiom,
    ((![Es : list_exp_list_char, S : produc515445032on_val, Es2 : list_exp_list_char, S2 : produc515445032on_val, P : list_P1234162913t_char, V : val, M4 : list_char]: ((member1689761872on_val @ (produc245869591on_val @ (produc1725134254on_val @ Es @ S) @ (produc1725134254on_val @ Es2 @ S2)) @ (reds @ P)) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (call_list_char @ (val_list_char @ V) @ M4 @ Es) @ S) @ (produc2023458740on_val @ (call_list_char @ (val_list_char @ V) @ M4 @ Es2) @ S2)) @ (red @ P)))))). % red_reds.CallParams
thf(fact_221_red__reds_OCallObj, axiom,
    ((![E : exp_list_char, S : produc515445032on_val, E2 : exp_list_char, S2 : produc515445032on_val, P : list_P1234162913t_char, M4 : list_char, Es : list_exp_list_char]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E @ S) @ (produc2023458740on_val @ E2 @ S2)) @ (red @ P)) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (call_list_char @ E @ M4 @ Es) @ S) @ (produc2023458740on_val @ (call_list_char @ E2 @ M4 @ Es) @ S2)) @ (red @ P)))))). % red_reds.CallObj
thf(fact_222_red__reds_OCallThrowObj, axiom,
    ((![E : exp_list_char, M4 : list_char, Es : list_exp_list_char, S : produc515445032on_val, P : list_P1234162913t_char]: (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (call_list_char @ (throw_list_char @ E) @ M4 @ Es) @ S) @ (produc2023458740on_val @ (throw_list_char @ E) @ S)) @ (red @ P))))). % red_reds.CallThrowObj
thf(fact_223_CallRedsObj, axiom,
    ((![E : exp_list_char, S : produc515445032on_val, E2 : exp_list_char, S2 : produc515445032on_val, P : list_P1234162913t_char, M4 : list_char, Es : list_exp_list_char]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E @ S) @ (produc2023458740on_val @ E2 @ S2)) @ (transi111096263on_val @ (red @ P))) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (call_list_char @ E @ M4 @ Es) @ S) @ (produc2023458740on_val @ (call_list_char @ E2 @ M4 @ Es) @ S2)) @ (transi111096263on_val @ (red @ P))))))). % CallRedsObj
thf(fact_224_CallRedsThrowObj, axiom,
    ((![E : exp_list_char, S0 : produc515445032on_val, A : exp_list_char, S_1 : produc515445032on_val, P : list_P1234162913t_char, M4 : list_char, Es : list_exp_list_char]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E @ S0) @ (produc2023458740on_val @ (throw_list_char @ A) @ S_1)) @ (transi111096263on_val @ (red @ P))) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (call_list_char @ E @ M4 @ Es) @ S0) @ (produc2023458740on_val @ (throw_list_char @ A) @ S_1)) @ (transi111096263on_val @ (red @ P))))))). % CallRedsThrowObj
thf(fact_225_CallRedsThrowParams, axiom,
    ((![E : exp_list_char, S0 : produc515445032on_val, V : val, S_1 : produc515445032on_val, P : list_P1234162913t_char, Es : list_exp_list_char, Vs_1 : list_val, A : exp_list_char, Es_2 : list_exp_list_char, S_2 : produc515445032on_val, M4 : list_char]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E @ S0) @ (produc2023458740on_val @ (val_list_char @ V) @ S_1)) @ (transi111096263on_val @ (red @ P))) => ((member1689761872on_val @ (produc245869591on_val @ (produc1725134254on_val @ Es @ S_1) @ (produc1725134254on_val @ (append_exp_list_char @ (map_va1515327237t_char @ val_list_char @ Vs_1) @ (cons_exp_list_char @ (throw_list_char @ A) @ Es_2)) @ S_2)) @ (transi325225921on_val @ (reds @ P))) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (call_list_char @ E @ M4 @ Es) @ S0) @ (produc2023458740on_val @ (throw_list_char @ A) @ S_2)) @ (transi111096263on_val @ (red @ P)))))))). % CallRedsThrowParams
thf(fact_226_BinOpRedsThrow2, axiom,
    ((![E_12 : exp_list_char, S_0 : produc515445032on_val, V_1 : val, S_1 : produc515445032on_val, P : list_P1234162913t_char, E_2 : exp_list_char, E : exp_list_char, S_2 : produc515445032on_val, Bop : bop]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E_12 @ S_0) @ (produc2023458740on_val @ (val_list_char @ V_1) @ S_1)) @ (transi111096263on_val @ (red @ P))) => ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E_2 @ S_1) @ (produc2023458740on_val @ (throw_list_char @ E) @ S_2)) @ (transi111096263on_val @ (red @ P))) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (binOp_list_char @ E_12 @ Bop @ E_2) @ S_0) @ (produc2023458740on_val @ (throw_list_char @ E) @ S_2)) @ (transi111096263on_val @ (red @ P)))))))). % BinOpRedsThrow2
thf(fact_227_red__reds_OBinOpRed1, axiom,
    ((![E : exp_list_char, S : produc515445032on_val, E2 : exp_list_char, S2 : produc515445032on_val, P : list_P1234162913t_char, Bop : bop, E_2 : exp_list_char]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E @ S) @ (produc2023458740on_val @ E2 @ S2)) @ (red @ P)) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (binOp_list_char @ E @ Bop @ E_2) @ S) @ (produc2023458740on_val @ (binOp_list_char @ E2 @ Bop @ E_2) @ S2)) @ (red @ P)))))). % red_reds.BinOpRed1
thf(fact_228_red__reds_OCallThrowParams, axiom,
    ((![Es : list_exp_list_char, Vs : list_val, E : exp_list_char, Es2 : list_exp_list_char, V : val, M4 : list_char, S : produc515445032on_val, P : list_P1234162913t_char]: ((Es = (append_exp_list_char @ (map_va1515327237t_char @ val_list_char @ Vs) @ (cons_exp_list_char @ (throw_list_char @ E) @ Es2))) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (call_list_char @ (val_list_char @ V) @ M4 @ Es) @ S) @ (produc2023458740on_val @ (throw_list_char @ E) @ S)) @ (red @ P)))))). % red_reds.CallThrowParams
thf(fact_229_red__reds_OBinOpRed2, axiom,
    ((![E : exp_list_char, S : produc515445032on_val, E2 : exp_list_char, S2 : produc515445032on_val, P : list_P1234162913t_char, V_1 : val, Bop : bop]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E @ S) @ (produc2023458740on_val @ E2 @ S2)) @ (red @ P)) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (binOp_list_char @ (val_list_char @ V_1) @ Bop @ E) @ S) @ (produc2023458740on_val @ (binOp_list_char @ (val_list_char @ V_1) @ Bop @ E2) @ S2)) @ (red @ P)))))). % red_reds.BinOpRed2
thf(fact_230_red__reds_OBinOpThrow1, axiom,
    ((![E : exp_list_char, Bop : bop, E_2 : exp_list_char, S : produc515445032on_val, P : list_P1234162913t_char]: (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (binOp_list_char @ (throw_list_char @ E) @ Bop @ E_2) @ S) @ (produc2023458740on_val @ (throw_list_char @ E) @ S)) @ (red @ P))))). % red_reds.BinOpThrow1
thf(fact_231_BinOp1Reds, axiom,
    ((![E : exp_list_char, S : produc515445032on_val, E2 : exp_list_char, S2 : produc515445032on_val, P : list_P1234162913t_char, Bop : bop, E_2 : exp_list_char]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E @ S) @ (produc2023458740on_val @ E2 @ S2)) @ (transi111096263on_val @ (red @ P))) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (binOp_list_char @ E @ Bop @ E_2) @ S) @ (produc2023458740on_val @ (binOp_list_char @ E2 @ Bop @ E_2) @ S2)) @ (transi111096263on_val @ (red @ P))))))). % BinOp1Reds
thf(fact_232_red__reds_OBinOpThrow2, axiom,
    ((![V_1 : val, Bop : bop, E : exp_list_char, S : produc515445032on_val, P : list_P1234162913t_char]: (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (binOp_list_char @ (val_list_char @ V_1) @ Bop @ (throw_list_char @ E)) @ S) @ (produc2023458740on_val @ (throw_list_char @ E) @ S)) @ (red @ P))))). % red_reds.BinOpThrow2
thf(fact_233_BinOp2Reds, axiom,
    ((![E : exp_list_char, S : produc515445032on_val, E2 : exp_list_char, S2 : produc515445032on_val, P : list_P1234162913t_char, V : val, Bop : bop]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E @ S) @ (produc2023458740on_val @ E2 @ S2)) @ (transi111096263on_val @ (red @ P))) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (binOp_list_char @ (val_list_char @ V) @ Bop @ E) @ S) @ (produc2023458740on_val @ (binOp_list_char @ (val_list_char @ V) @ Bop @ E2) @ S2)) @ (transi111096263on_val @ (red @ P))))))). % BinOp2Reds
thf(fact_234_BinOpRedsThrow1, axiom,
    ((![E : exp_list_char, S : produc515445032on_val, E2 : exp_list_char, S2 : produc515445032on_val, P : list_P1234162913t_char, Bop : bop, E_2 : exp_list_char]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E @ S) @ (produc2023458740on_val @ (throw_list_char @ E2) @ S2)) @ (transi111096263on_val @ (red @ P))) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (binOp_list_char @ E @ Bop @ E_2) @ S) @ (produc2023458740on_val @ (throw_list_char @ E2) @ S2)) @ (transi111096263on_val @ (red @ P))))))). % BinOpRedsThrow1
thf(fact_235_BinOpRedsVal, axiom,
    ((![E_12 : exp_list_char, S_0 : produc515445032on_val, V_1 : val, S_1 : produc515445032on_val, P : list_P1234162913t_char, E_2 : exp_list_char, V_2 : val, S_2 : produc515445032on_val, Bop : bop, V : val]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E_12 @ S_0) @ (produc2023458740on_val @ (val_list_char @ V_1) @ S_1)) @ (transi111096263on_val @ (red @ P))) => ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E_2 @ S_1) @ (produc2023458740on_val @ (val_list_char @ V_2) @ S_2)) @ (transi111096263on_val @ (red @ P))) => (((binop @ (produc1753769388al_val @ Bop @ (product_Pair_val_val @ V_1 @ V_2))) = (some_val @ V)) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (binOp_list_char @ E_12 @ Bop @ E_2) @ S_0) @ (produc2023458740on_val @ (val_list_char @ V) @ S_2)) @ (transi111096263on_val @ (red @ P))))))))). % BinOpRedsVal
thf(fact_236_red__reds_ORedBinOp, axiom,
    ((![Bop : bop, V_1 : val, V_2 : val, V : val, S : produc515445032on_val, P : list_P1234162913t_char]: (((binop @ (produc1753769388al_val @ Bop @ (product_Pair_val_val @ V_1 @ V_2))) = (some_val @ V)) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (binOp_list_char @ (val_list_char @ V_1) @ Bop @ (val_list_char @ V_2)) @ S) @ (produc2023458740on_val @ (val_list_char @ V) @ S)) @ (red @ P)))))). % red_reds.RedBinOp
thf(fact_237_redp__redsp_OCallThrowParams, axiom,
    ((![Es : list_exp_list_char, Vs : list_val, E : exp_list_char, Es2 : list_exp_list_char, P : list_P1234162913t_char, V : val, M4 : list_char, S : produc515445032on_val]: ((Es = (append_exp_list_char @ (map_va1515327237t_char @ val_list_char @ Vs) @ (cons_exp_list_char @ (throw_list_char @ E) @ Es2))) => (redp @ P @ (call_list_char @ (val_list_char @ V) @ M4 @ Es) @ S @ (throw_list_char @ E) @ S))))). % redp_redsp.CallThrowParams
thf(fact_238_redp__redsp_ORedBinOp, axiom,
    ((![Bop : bop, V_1 : val, V_2 : val, V : val, P : list_P1234162913t_char, S : produc515445032on_val]: (((binop @ (produc1753769388al_val @ Bop @ (product_Pair_val_val @ V_1 @ V_2))) = (some_val @ V)) => (redp @ P @ (binOp_list_char @ (val_list_char @ V_1) @ Bop @ (val_list_char @ V_2)) @ S @ (val_list_char @ V) @ S))))). % redp_redsp.RedBinOp
thf(fact_239_redp__redsp_OBinOpRed2, axiom,
    ((![P : list_P1234162913t_char, E : exp_list_char, S : produc515445032on_val, E2 : exp_list_char, S2 : produc515445032on_val, V_1 : val, Bop : bop]: ((redp @ P @ E @ S @ E2 @ S2) => (redp @ P @ (binOp_list_char @ (val_list_char @ V_1) @ Bop @ E) @ S @ (binOp_list_char @ (val_list_char @ V_1) @ Bop @ E2) @ S2))))). % redp_redsp.BinOpRed2
thf(fact_240_redp__redsp_OBinOpThrow1, axiom,
    ((![P : list_P1234162913t_char, E : exp_list_char, Bop : bop, E_2 : exp_list_char, S : produc515445032on_val]: (redp @ P @ (binOp_list_char @ (throw_list_char @ E) @ Bop @ E_2) @ S @ (throw_list_char @ E) @ S)))). % redp_redsp.BinOpThrow1
thf(fact_241_redp__redsp_OBinOpRed1, axiom,
    ((![P : list_P1234162913t_char, E : exp_list_char, S : produc515445032on_val, E2 : exp_list_char, S2 : produc515445032on_val, Bop : bop, E_2 : exp_list_char]: ((redp @ P @ E @ S @ E2 @ S2) => (redp @ P @ (binOp_list_char @ E @ Bop @ E_2) @ S @ (binOp_list_char @ E2 @ Bop @ E_2) @ S2))))). % redp_redsp.BinOpRed1
thf(fact_242_redp__redsp_OBinOpThrow2, axiom,
    ((![P : list_P1234162913t_char, V_1 : val, Bop : bop, E : exp_list_char, S : produc515445032on_val]: (redp @ P @ (binOp_list_char @ (val_list_char @ V_1) @ Bop @ (throw_list_char @ E)) @ S @ (throw_list_char @ E) @ S)))). % redp_redsp.BinOpThrow2
thf(fact_243_redp__redsp_OThrowThrow, axiom,
    ((![P : list_P1234162913t_char, E : exp_list_char, S : produc515445032on_val]: (redp @ P @ (throw_list_char @ (throw_list_char @ E)) @ S @ (throw_list_char @ E) @ S)))). % redp_redsp.ThrowThrow
thf(fact_244_redp__redsp_OThrowRed, axiom,
    ((![P : list_P1234162913t_char, E : exp_list_char, S : produc515445032on_val, E2 : exp_list_char, S2 : produc515445032on_val]: ((redp @ P @ E @ S @ E2 @ S2) => (redp @ P @ (throw_list_char @ E) @ S @ (throw_list_char @ E2) @ S2))))). % redp_redsp.ThrowRed
thf(fact_245_redp__redsp_OCallThrowObj, axiom,
    ((![P : list_P1234162913t_char, E : exp_list_char, M4 : list_char, Es : list_exp_list_char, S : produc515445032on_val]: (redp @ P @ (call_list_char @ (throw_list_char @ E) @ M4 @ Es) @ S @ (throw_list_char @ E) @ S)))). % redp_redsp.CallThrowObj

% Helper facts (3)
thf(help_If_3_1_If_001t__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_T, axiom,
    ((![P : $o]: ((P = $true) | (P = $false))))).
thf(help_If_2_1_If_001t__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_T, axiom,
    ((![X : option2118145160on_val, Y3 : option2118145160on_val]: ((if_opt451925058on_val @ $false @ X @ Y3) = Y3)))).
thf(help_If_1_1_If_001t__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_T, axiom,
    ((![X : option2118145160on_val, Y3 : option2118145160on_val]: ((if_opt451925058on_val @ $true @ X @ Y3) = X)))).

% Conjectures (7)
thf(conj_0, hypothesis,
    ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ ea @ (produc52622304on_val @ a @ b)) @ (produc2023458740on_val @ e_a @ (produc52622304on_val @ aa @ ba))) @ (red @ p)))).
thf(conj_1, hypothesis,
    (((a_list_char @ e_a) = none_set_list_char))).
thf(conj_2, hypothesis,
    (((a_list_char @ ea) = none_set_list_char))).
thf(conj_3, hypothesis,
    (((a_list_char @ e_2) = (some_set_list_char @ x2)))).
thf(conj_4, hypothesis,
    (((b @ x) = (some_val @ y)))).
thf(conj_5, hypothesis,
    (((ba @ x) = none_val))).
thf(conj_6, conjecture,
    ((member_list_char @ x @ x2))).
