# HG changeset patch # User skalberg # Date 1062000839 -7200 # Node ID 0590de71a016eb8f04254f59f6aa6626efdc6939 # Parent ed81cd283816e2f46cdc002a2266b35a1e7aa568 Converted to new style theories. diff -r ed81cd283816 -r 0590de71a016 src/HOL/Gfp.ML --- a/src/HOL/Gfp.ML Wed Aug 27 18:13:39 2003 +0200 +++ b/src/HOL/Gfp.ML Wed Aug 27 18:13:59 2003 +0200 @@ -8,6 +8,8 @@ (*** Proof of Knaster-Tarski Theorem using gfp ***) +val gfp_def = thm "gfp_def"; + (* gfp(f) is the least upper bound of {u. u <= f(u)} *) Goalw [gfp_def] "[| X <= f(X) |] ==> X <= gfp(f)"; diff -r ed81cd283816 -r 0590de71a016 src/HOL/Gfp.thy --- a/src/HOL/Gfp.thy Wed Aug 27 18:13:39 2003 +0200 +++ b/src/HOL/Gfp.thy Wed Aug 27 18:13:59 2003 +0200 @@ -6,10 +6,10 @@ Greatest fixed points (requires Lfp too!) *) -Gfp = Lfp + +theory Gfp = Lfp: constdefs - gfp :: ['a set=>'a set] => 'a set + gfp :: "['a set=>'a set] => 'a set" "gfp(f) == Union({u. u <= f(u)})" (*greatest fixed point*) end diff -r ed81cd283816 -r 0590de71a016 src/HOL/Lfp.ML --- a/src/HOL/Lfp.ML Wed Aug 27 18:13:39 2003 +0200 +++ b/src/HOL/Lfp.ML Wed Aug 27 18:13:59 2003 +0200 @@ -8,6 +8,8 @@ (*** Proof of Knaster-Tarski Theorem ***) +val lfp_def = thm "lfp_def"; + (* lfp(f) is the greatest lower bound of {u. f(u) <= u} *) Goalw [lfp_def] "f(A) <= A ==> lfp(f) <= A"; diff -r ed81cd283816 -r 0590de71a016 src/HOL/Lfp.thy --- a/src/HOL/Lfp.thy Wed Aug 27 18:13:39 2003 +0200 +++ b/src/HOL/Lfp.thy Wed Aug 27 18:13:59 2003 +0200 @@ -6,10 +6,10 @@ The Knaster-Tarski Theorem *) -Lfp = Product_Type + +theory Lfp = Product_Type: constdefs - lfp :: ['a set=>'a set] => 'a set + lfp :: "['a set \ 'a set] \ 'a set" "lfp(f) == Inter({u. f(u) <= u})" (*least fixed point*) end