# HG changeset patch # User paulson # Date 1430476576 -3600 # Node ID 29c826137153659a8dc86796eb16ca090fb9c4a3 # Parent 670cddd9756327c8418566e24ada0c6100ce16dc# Parent 59ebc3f2f8960033ebecc8e7fecc9d1ad56e42cc Merge diff -r 670cddd97563 -r 29c826137153 src/HOL/Set.thy --- a/src/HOL/Set.thy Thu Apr 30 17:00:43 2015 +0100 +++ b/src/HOL/Set.thy Fri May 01 11:36:16 2015 +0100 @@ -1623,6 +1623,9 @@ lemma Pow_empty [simp]: "Pow {} = {{}}" by (auto simp add: Pow_def) +lemma Pow_singleton_iff [simp]: "Pow X = {Y} \ X = {} \ Y = {}" +by blast + lemma Pow_insert: "Pow (insert a A) = Pow A \ (insert a ` Pow A)" by (blast intro: image_eqI [where ?x = "u - {a}" for u])