proposition: Lemma islabsorb_Dcuts_mult_zero : ∏ x : Dcuts, Dcuts_mult Dcuts_zero x = Dcuts_zero.
proof: Proof. intros x. apply Dcuts_eq_is_eq ; intro r ; split. - apply hinhuniv ; intros ix. apply fromempty. now apply (Dcuts_zero_empty _ (pr1 (pr2 (pr2 ix)))). - intro Hr. now apply Dcuts_zero_empty in Hr. Qed.
imports: UniMath.MoreFoundations.Orders UniMath.MoreFoundations.Tactics UniMath.MoreFoundations.Notations UniMath.RealNumbers.Sets UniMath.Algebra.ConstructiveStructures UniMath.OrderTheory.Lattice.Lattice UniMath.RealNumbers.Prelim UniMath.RealNumbers.NonnegativeRationals