(* Title: HOL/OrderedGroup.ML
ID: $Id$
Author: Steven Obua, Tobias Nipkow, Technische Universität München
*)
structure ab_group_add_cancel_data :> ABEL_CANCEL =
struct
(*** Term order for abelian groups ***)
fun agrp_ord a = find_index_eq a ["0", "op +", "uminus", "op -"];
fun termless_agrp (a, b) = (Term.term_lpo agrp_ord (a, b) = LESS);
val cancel_ss = HOL_basic_ss settermless termless_agrp addsimps
[thm "add_assoc", thm "add_commute", thm "add_left_commute",
thm "add_0", thm "add_0_right",
thm "diff_def", thm "minus_add_distrib",
thm "minus_minus", thm "minus_zero",
thm "right_minus", thm "left_minus",
thm "add_minus_cancel", thm "minus_add_cancel"];
val eq_reflection = thm "eq_reflection"
val thy_ref = Theory.self_ref (theory "OrderedGroup")
val T = TFree("'a", ["OrderedGroup.ab_group_add"])
val eqI_rules = [thm "less_eqI", thm "le_eqI", thm "eq_eqI"]
fun dest_eqI th =
#1 (HOLogic.dest_bin "op =" HOLogic.boolT
(HOLogic.dest_Trueprop (concl_of th)))
end;
structure ab_group_add_cancel = Abel_Cancel (ab_group_add_cancel_data);
Addsimprocs [ab_group_add_cancel.sum_conv, ab_group_add_cancel.rel_conv];