[STATEMENT]
lemma factor_double_map: "double (map f xs) ys \<Longrightarrow> \<exists>zs. Dlist.dlist_eq xs zs \<and> ys = map f zs \<and> set zs \<subseteq> set xs"
[PROOF STATE]
proof (prove)
goal (1 subgoal):
 1. double (map f xs) ys \<Longrightarrow> \<exists>zs. Dlist.dlist_eq xs zs \<and> ys = map f zs \<and> set zs \<subseteq> set xs
[PROOF STEP]
by(auto simp add: double.simps Dlist.dlist_eq_def vimage2p_def map_eq_append_conv)
    (metis (no_types, opaque_lifting) list.simps(9) map_append remdups.simps(2) remdups_append2 set_append set_eq_subset set_remdups)