proposition: Lemma finite_incl : forall E F, E \c F -> finite F -> finite E.
proof: Proof. Proof using. introv HI HF. apply finite_of_ex_list_covers. lets (L&EQ): finite_inv_list_covers HF. unfold list_covers. set_unf. exists* L. introv Ex. applys EQ. applys~ HI. Qed.
imports: Coq.Classes.Morphisms TLC(LibTactics LibLogic LibReflect LibList LibOperation LibMonoid LibInt LibNat LibEpsilon LibRelation LibMin)