[STATEMENT]
lemma subcs_news: \<open>news c z \<Longrightarrow> subcs c s z = z\<close>
[PROOF STATE]
proof (prove)
goal (1 subgoal):
 1. news c z \<Longrightarrow> subcs c s z = z
[PROOF STEP]
by (induct z) simp_all