proposition: Lemma subAlphaSameFV: forall (suba subb : SSubstitution vc), AlphaEqSubst suba subb -> rangeFreeVars suba = rangeFreeVars subb.
proof: Proof. induction suba as [| (va,ta) suba Hind]; introv Hal; destruct subb as [| (vb,tb) subb]; repnud Hal; simpl in Hal; cpx. repnd. rw rangeFreeVars_cons. rw rangeFreeVars_cons. f_equal; cpx. apply (ALtcase alpha_preserves_free_vars). trivial. Qed.
imports: Term AssociationList Swap AlphaEqProps SubstAux