src/HOLCF/One.thy
author huffman
Sat, 04 Jun 2005 00:22:08 +0200
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child 16747 934b6b36d794
permissions -rw-r--r--
New theory with lemmas for the fixrec package
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(*  Title:      HOLCF/One.thy
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    ID:         $Id$
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    Author:     Oscar Slotosch
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The unit domain.
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*)
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header {* The unit domain *}
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theory One
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imports Lift
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begin
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types one = "unit lift"
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constdefs
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  ONE :: "one"
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  "ONE == Def ()"
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translations
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  "one" <= (type) "unit lift" 
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(* ------------------------------------------------------------------------ *)
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(* Exhaustion and Elimination for type one                                  *)
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(* ------------------------------------------------------------------------ *)
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lemma Exh_one: "t=UU | t = ONE"
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apply (unfold ONE_def)
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apply (induct t)
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apply simp
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apply simp
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done
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lemma oneE: "[| p=UU ==> Q; p = ONE ==>Q|] ==>Q"
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apply (rule Exh_one [THEN disjE])
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apply fast
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apply fast
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done
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lemma dist_less_one [simp]: "~ONE << UU"
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apply (unfold ONE_def)
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apply (simp add: inst_lift_po)
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done
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lemma dist_eq_one [simp]: "ONE~=UU" "UU~=ONE"
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apply (unfold ONE_def)
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apply (simp_all add: inst_lift_po)
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done
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end