proposition: Lemma ct_from_ctr X (T : X -> X -> Prop): forall x y z, clos_trans X T x y -> clos_refl_trans X T y z -> clos_trans_1n X T x z.
proof: Proof. intros x y z Txy CTR. induction CTR. apply clos_trans_t1n. apply clos_tn1_trans. econstructor 2. apply H. apply clos_trans_tn1. apply Txy. apply clos_trans_t1n. apply Txy. apply IHCTR2. apply clos_t1n_trans. apply IHCTR1. apply Txy. Defined.
imports: Coq(Arith Relations Lia) AlmostFull.PropBounded(AlmostFull) AlmostFull.PropBounded(AFConstructions)