(* 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
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