1.1 --- a/src/HOL/Set.thy Mon Aug 23 09:04:37 2010 +0200
1.2 +++ b/src/HOL/Set.thy Mon Aug 23 11:56:30 2010 +0200
1.3 @@ -852,7 +852,7 @@
1.4 lemma image_iff: "(z : f`A) = (EX x:A. z = f x)"
1.5 by blast
1.6
1.7 -lemma image_subset_iff: "(f`A \<subseteq> B) = (\<forall>x\<in>A. f x \<in> B)"
1.8 +lemma image_subset_iff [no_atp]: "(f`A \<subseteq> B) = (\<forall>x\<in>A. f x \<in> B)"
1.9 -- {* This rewrite rule would confuse users if made default. *}
1.10 by blast
1.11
1.12 @@ -1203,7 +1203,7 @@
1.13 lemma Int_UNIV [simp,no_atp]: "(A \<inter> B = UNIV) = (A = UNIV & B = UNIV)"
1.14 by (fact inf_eq_top_iff)
1.15
1.16 -lemma Int_subset_iff [simp]: "(C \<subseteq> A \<inter> B) = (C \<subseteq> A & C \<subseteq> B)"
1.17 +lemma Int_subset_iff [no_atp, simp]: "(C \<subseteq> A \<inter> B) = (C \<subseteq> A & C \<subseteq> B)"
1.18 by (fact le_inf_iff)
1.19
1.20 lemma Int_Collect: "(x \<in> A \<inter> {x. P x}) = (x \<in> A & P x)"
1.21 @@ -1294,7 +1294,7 @@
1.22 lemma Un_empty [iff]: "(A \<union> B = {}) = (A = {} & B = {})"
1.23 by (fact sup_eq_bot_iff)
1.24
1.25 -lemma Un_subset_iff [simp]: "(A \<union> B \<subseteq> C) = (A \<subseteq> C & B \<subseteq> C)"
1.26 +lemma Un_subset_iff [no_atp, simp]: "(A \<union> B \<subseteq> C) = (A \<subseteq> C & B \<subseteq> C)"
1.27 by (fact le_sup_iff)
1.28
1.29 lemma Un_Diff_Int: "(A - B) \<union> (A \<inter> B) = A"
1.30 @@ -1490,7 +1490,7 @@
1.31 lemma set_eq_subset: "(A = B) = (A \<subseteq> B & B \<subseteq> A)"
1.32 by blast
1.33
1.34 -lemma subset_iff: "(A \<subseteq> B) = (\<forall>t. t \<in> A --> t \<in> B)"
1.35 +lemma subset_iff [no_atp]: "(A \<subseteq> B) = (\<forall>t. t \<in> A --> t \<in> B)"
1.36 by blast
1.37
1.38 lemma subset_iff_psubset_eq: "(A \<subseteq> B) = ((A \<subset> B) | (A = B))"