proposition: Theorem itree_le_trans : forall t t', itree_le t t' -> forall t'', itree_le t' t'' -> itree_le t t''.
proof: Proof. induction t. - constructor 1. - intros t'; case t'. + inversion 1. + intros z0 i0 H0; intro t'';case t''. * inversion 1. * intros z1 i1 H1; inversion_clear H1. constructor 2. inversion_clear H0;eauto with zarith. inversion_clear H0. intro i2; case (H4 i2). intros x H5; generalize (H i2 _ H5); intro H6. case (H3 x);intros x0 Hx0. exists x0;auto. Qed.
imports: Arith Vector List Extraction ZArith Compare_dec ZArith