(* Title: HOLCF/One.thy
ID: $Id$
Author: Oscar Slotosch
License: GPL (GNU GENERAL PUBLIC LICENSE)
*)
header {* The unit domain *}
theory One
imports Lift
begin
types one = "unit lift"
constdefs
ONE :: "one"
"ONE == Def ()"
translations
"one" <= (type) "unit lift"
(* Title: HOLCF/One.ML
ID: $Id$
Author: Oscar Slotosch
License: GPL (GNU GENERAL PUBLIC LICENSE)
The unit domain.
*)
(* ------------------------------------------------------------------------ *)
(* Exhaustion and Elimination for type one *)
(* ------------------------------------------------------------------------ *)
lemma Exh_one: "t=UU | t = ONE"
apply (unfold ONE_def)
apply (induct t)
apply simp
apply simp
done
lemma oneE: "[| p=UU ==> Q; p = ONE ==>Q|] ==>Q"
apply (rule Exh_one [THEN disjE])
apply fast
apply fast
done
lemma dist_less_one [simp]: "~ONE << UU"
apply (unfold ONE_def)
apply (simp add: inst_lift_po)
done
lemma dist_eq_one [simp]: "ONE~=UU" "UU~=ONE"
apply (unfold ONE_def)
apply (simp_all add: inst_lift_po)
done
end