Theory Product_ord

(*  Title:      HOL/Library/Product_ord.thy
    ID:         $Id: Product_ord.thy,v 1.2 2005/08/31 13:46:37 wenzelm Exp $
    Author:     Norbert Voelker
*)

header {* Order on product types *}

theory Product_ord
imports Main
begin

instance "*" :: (ord,ord) ord ..

defs (overloaded)
  prod_le_def: "(x ≤ y) ≡ (fst x < fst y) | (fst x = fst y & snd x ≤ snd y)" 
  prod_less_def: "(x < y) ≡ (fst x < fst y) | (fst x = fst y & snd x < snd y)"


lemmas prod_ord_defs = prod_less_def prod_le_def

instance "*" :: (order,order) order 
  apply (intro_classes, unfold prod_ord_defs)
  by (auto intro: order_less_trans)

instance "*":: (linorder,linorder)linorder
  by (intro_classes, unfold prod_le_def, auto)

end