author huffman Tue, 21 Aug 2007 20:53:37 +0200 changeset 24393 b9718519f3d2 parent 24392 000327cea3eb child 24394 de9997397317
declare conj_absorb [simp]
```--- a/src/HOL/Library/Boolean_Algebra.thy	Tue Aug 21 20:52:18 2007 +0200
+++ b/src/HOL/Library/Boolean_Algebra.thy	Tue Aug 21 20:53:37 2007 +0200
@@ -81,7 +81,7 @@

subsection {* Conjunction *}

-lemma conj_absorb: "x \<sqinter> x = x"
+lemma conj_absorb [simp]: "x \<sqinter> x = x"
proof -
have "x \<sqinter> x = (x \<sqinter> x) \<squnion> \<zero>" using disj_zero_right by simp
also have "... = (x \<sqinter> x) \<squnion> (x \<sqinter> \<sim> x)" using conj_cancel_right by simp
@@ -94,7 +94,7 @@
lemma conj_zero_right [simp]: "x \<sqinter> \<zero> = \<zero>"
proof -
have "x \<sqinter> \<zero> = x \<sqinter> (x \<sqinter> \<sim> x)" using conj_cancel_right by simp
-  also have "... = (x \<sqinter> x) \<sqinter> \<sim> x" using conj_assoc by simp
+  also have "... = (x \<sqinter> x) \<sqinter> \<sim> x" using conj_assoc by (simp only:)
also have "... = x \<sqinter> \<sim> x" using conj_absorb by simp
also have "... = \<zero>" using conj_cancel_right by simp
finally show ?thesis .```