equal
deleted
inserted
replaced
1137 lemma subset_empty [simp]: "A \<subseteq> {} \<longleftrightarrow> A = {}" |
1137 lemma subset_empty [simp]: "A \<subseteq> {} \<longleftrightarrow> A = {}" |
1138 by (fact bot_unique) |
1138 by (fact bot_unique) |
1139 |
1139 |
1140 lemma not_psubset_empty [iff]: "\<not> (A < {})" |
1140 lemma not_psubset_empty [iff]: "\<not> (A < {})" |
1141 by (fact not_less_bot) (* FIXME: already simp *) |
1141 by (fact not_less_bot) (* FIXME: already simp *) |
|
1142 |
|
1143 lemma Collect_subset [simp]: "{x\<in>A. P x} \<subseteq> A" by auto |
1142 |
1144 |
1143 lemma Collect_empty_eq [simp]: "Collect P = {} \<longleftrightarrow> (\<forall>x. \<not> P x)" |
1145 lemma Collect_empty_eq [simp]: "Collect P = {} \<longleftrightarrow> (\<forall>x. \<not> P x)" |
1144 by blast |
1146 by blast |
1145 |
1147 |
1146 lemma empty_Collect_eq [simp]: "{} = Collect P \<longleftrightarrow> (\<forall>x. \<not> P x)" |
1148 lemma empty_Collect_eq [simp]: "{} = Collect P \<longleftrightarrow> (\<forall>x. \<not> P x)" |