proposition: Fact list_injective_inv x ll : list_injective (x::ll) -> ~ In x ll /\ list_injective ll.
proof: Proof. split. intros H1; apply in_split in H1; destruct H1 as (l & r & ?); subst. apply (H nil x l x r); auto. intros l a m b r ?; apply (H (x::l) a m b r); subst; solve list eq. Qed.
imports: List Arith Lia Permutation Undecidability.Shared.Libs.DLW.Utils(list_focus utils_tac)