proposition: Lemma clos_rst1n_trans : forall x y z, clos_refl_sym_trans_1n R x y -> clos_refl_sym_trans_1n R y z -> clos_refl_sym_trans_1n R x z.
proof: Proof. induction 1 as [|x y z0]. - auto. - intros; right with y; eauto. Qed.
imports: Relation_Definitions Relation_Operators