src/LCF/ex/Ex3.thy
author blanchet
Mon, 15 Sep 2014 10:49:07 +0200
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header {* Addition with fixpoint of successor *}
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theory Ex3
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imports LCF
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begin
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axiomatization
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  s     :: "'a => 'a" and
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  p     :: "'a => 'a => 'a"
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where
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  p_strict:     "p(UU) = UU" and
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  p_s:          "p(s(x),y) = s(p(x,y))"
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declare p_strict [simp] p_s [simp]
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lemma example: "p(FIX(s),y) = FIX(s)"
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  apply (tactic {* induct_tac @{context} "s" 1 *})
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  apply simp
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  apply simp
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  done
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end