author | paulson <lp15@cam.ac.uk> |
Fri, 01 May 2015 11:36:16 +0100 | |
changeset 60165 | 29c826137153 |
parent 60164 | 670cddd97563 (current diff) |
parent 60161 | 59ebc3f2f896 (diff) |
child 60166 | ff6c4ff5e7ab |
child 60167 | 9a97407488cd |
--- 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} \<longleftrightarrow> X = {} \<and> Y = {}" +by blast + lemma Pow_insert: "Pow (insert a A) = Pow A \<union> (insert a ` Pow A)" by (blast intro: image_eqI [where ?x = "u - {a}" for u])