[STATEMENT]
lemma hyper_insert_comm: "A \<squnion> \<lfloor>{a}\<rfloor> = \<lfloor>{a}\<rfloor> \<squnion> A \<and> A \<squnion> (\<lfloor>{a}\<rfloor> \<squnion> B) = \<lfloor>{a}\<rfloor> \<squnion> (A \<squnion> B)"
[PROOF STATE]
proof (prove)
goal (1 subgoal):
 1. A \<squnion> \<lfloor>{a}\<rfloor> = \<lfloor>{a}\<rfloor> \<squnion> A \<and> A \<squnion> (\<lfloor>{a}\<rfloor> \<squnion> B) = \<lfloor>{a}\<rfloor> \<squnion> (A \<squnion> B)
[PROOF STEP]
by(simp add:hyperset_defs)