proposition: Lemma maxvar_le_arg : forall f ts m t, maxvar (Fun f ts) <= m -> Vin t ts -> maxvar t <= m.
proof: Proof. intros. assert (Vforall (maxvar_le m) ts). apply maxvar_le_fun. hyp. change (maxvar_le m t). eapply Vforall_in with (n := arity f). apply H1. hyp. Qed.
imports: CoLoR(ListUtil LogicUtil EqUtil BoolUtil NatUtil VecUtil VecMax ListMax)