src/HOL/Set_Interval.thy
changeset 50999 3de230ed0547
parent 50417 f18b92f91818
child 51152 b52cc015429a
--- a/src/HOL/Set_Interval.thy	Thu Jan 31 11:31:22 2013 +0100
+++ b/src/HOL/Set_Interval.thy	Thu Jan 31 11:31:27 2013 +0100
@@ -117,6 +117,11 @@
 lemma atMost_Int_atLeast: "!!n:: 'a::order. atMost n Int atLeast n = {n}"
 by (blast intro: order_antisym)
 
+lemma (in linorder) lessThan_Int_lessThan: "{ a <..} \<inter> { b <..} = { max a b <..}"
+  by auto
+
+lemma (in linorder) greaterThan_Int_greaterThan: "{..< a} \<inter> {..< b} = {..< min a b}"
+  by auto
 
 subsection {* Logical Equivalences for Set Inclusion and Equality *}
 
@@ -190,6 +195,9 @@
 breaks many proofs. Since it only helps blast, it is better to leave well
 alone *}
 
+lemma greaterThanLessThan_eq: "{ a <..< b} = { a <..} \<inter> {..< b }"
+  by auto
+
 end
 
 subsubsection{* Emptyness, singletons, subset *}