# File OrderedGroup.ML

    (*  Title:      HOL/OrderedGroup.ML
        ID:         $Id: OrderedGroup.ML,v 1.3 2005/06/25 14:06:17 nipkow Exp $
        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];