proposition: Lemma Dcuts_half_correct : ∏ x, Dcuts_half x = Dcuts_mult x (Dcuts_inv Dcuts_two Dcuts_two_ap_zero).
proof: Proof. intros x. pattern x at 2 ; rewrite (Dcuts_half_double x). rewrite Dcuts_plus_double, iscomm_Dcuts_mult, <- isassoc_Dcuts_mult, islinv_Dcuts_inv, islunit_Dcuts_mult_one. reflexivity. 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