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43141
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theory Star imports Main
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begin
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inductive
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star :: "('a \<Rightarrow> 'a \<Rightarrow> bool) \<Rightarrow> 'a \<Rightarrow> 'a \<Rightarrow> bool"
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for r where
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refl: "star r x x" |
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step: "r x y \<Longrightarrow> star r y z \<Longrightarrow> star r x z"
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lemma star_trans:
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"star r x y \<Longrightarrow> star r y z \<Longrightarrow> star r x z"
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proof(induct rule: star.induct)
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case refl thus ?case .
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next
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case step thus ?case by (metis star.step)
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qed
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lemmas star_induct = star.induct[of "r:: 'a*'b \<Rightarrow> 'a*'b \<Rightarrow> bool", split_format(complete)]
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declare star.refl[simp,intro]
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lemma step1[simp, intro]: "r x y \<Longrightarrow> star r x y"
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by(metis refl step)
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code_pred star .
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end
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