(* Title: HOL/Library/Product_ord.thy
ID: $Id$
Author: Norbert Voelker
*)
header {* Order on product types *}
theory Product_ord
imports Main
begin
instance "*" :: (ord, ord) ord ..
defs (overloaded)
prod_le_def: "(x \<le> y) \<equiv> (fst x < fst y) | (fst x = fst y & snd x \<le> snd y)"
prod_less_def: "(x < y) \<equiv> (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
by default (auto simp: prod_ord_defs intro: order_less_trans)
instance * :: (linorder, linorder) linorder
by default (auto simp: prod_le_def)
end