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(* Title: HOL/Library/Product_ord.thy
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ID: $Id$
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Author: Norbert Voelker
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*)
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17200
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header {* Order on product types *}
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15737
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theory Product_ord
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imports Main
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begin
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instance "*" :: (ord,ord) ord ..
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defs (overloaded)
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prod_le_def: "(x \<le> y) \<equiv> (fst x < fst y) | (fst x = fst y & snd x \<le> snd y)"
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prod_less_def: "(x < y) \<equiv> (fst x < fst y) | (fst x = fst y & snd x < snd y)"
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lemmas prod_ord_defs = prod_less_def prod_le_def
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instance "*" :: (order,order) order
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apply (intro_classes, unfold prod_ord_defs)
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by (auto intro: order_less_trans)
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instance "*":: (linorder,linorder)linorder
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by (intro_classes, unfold prod_le_def, auto)
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end |