[STATEMENT]
lemma inter_imp_subset: "A \<inter> B = A \<Longrightarrow> A \<subseteq> B"
[PROOF STATE]
proof (prove)
goal (1 subgoal):
 1. A \<inter> B = A \<Longrightarrow> A \<subseteq> B
[PROOF STEP]
by blast