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(* Author: Tobias Nipkow *)
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section {* Three-Way Comparison *}
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theory Cmp
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imports Main
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begin
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datatype cmp = LT | EQ | GT
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class cmp = linorder +
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fixes cmp :: "'a \<Rightarrow> 'a \<Rightarrow> cmp"
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assumes LT[simp]: "cmp x y = LT \<longleftrightarrow> x < y"
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assumes EQ[simp]: "cmp x y = EQ \<longleftrightarrow> x = y"
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assumes GT[simp]: "cmp x y = GT \<longleftrightarrow> x > y"
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lemma case_cmp_if[simp]: "(case c of EQ \<Rightarrow> e | LT \<Rightarrow> l | GT \<Rightarrow> g) =
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(if c = LT then l else if c = GT then g else e)"
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by(simp split: cmp.split)
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end
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