src/HOL/Fun.thy
changeset 60303 00c06f1315d0
parent 59512 9bf568cc71a4
child 60758 d8d85a8172b5
--- a/src/HOL/Fun.thy	Mon May 25 22:52:17 2015 +0200
+++ b/src/HOL/Fun.thy	Tue May 26 21:58:04 2015 +0100
@@ -478,16 +478,14 @@
 
 lemma inj_on_image_Int:
    "[| inj_on f C;  A<=C;  B<=C |] ==> f`(A Int B) = f`A Int f`B"
-apply (simp add: inj_on_def, blast)
-done
+  by (simp add: inj_on_def, blast)
 
 lemma inj_on_image_set_diff:
-   "[| inj_on f C;  A<=C;  B<=C |] ==> f`(A-B) = f`A - f`B"
-apply (simp add: inj_on_def, blast)
-done
+   "[| inj_on f C;  A-B \<subseteq> C;  B \<subseteq> C |] ==> f`(A-B) = f`A - f`B"
+  by (simp add: inj_on_def, blast)
 
 lemma image_Int: "inj f ==> f`(A Int B) = f`A Int f`B"
-by (simp add: inj_on_def, blast)
+  by (simp add: inj_on_def, blast)
 
 lemma image_set_diff: "inj f ==> f`(A-B) = f`A - f`B"
 by (simp add: inj_on_def, blast)