proposition: Lemma clos_rstn1_trans : forall x y z, clos_refl_sym_trans_n1 R x y -> clos_refl_sym_trans_n1 R y z -> clos_refl_sym_trans_n1 R x z.
proof: Proof. intros x y z H1 H2. induction H2 as [|y0 z]. - auto. - right with y0; eauto. Qed.
imports: Relation_Definitions Relation_Operators