proposition: Lemma Forall_fresh_alt X xs : Forall_fresh X xs ↔ NoDup xs ∧ ∀ x, x ∈ xs → x ∉ X.
proof: Proof. split; eauto using Forall_fresh_NoDup, Forall_fresh_elem_of. rewrite <-Forall_forall. intros [Hxs Hxs']. induction Hxs; decompose_Forall_hyps; constructor; auto. Qed.
imports: stdpp(relations) stdpp(options)