proposition: Lemma isassoc_minusNonnegativeReals : ∏ x y z : NonnegativeReals, (x - y) - z = x - (y + z).
proof: Proof. intros x y z. apply plusNonnegativeReals_eqcompat_l with (y + z). rewrite <- maxNonnegativeReals_minus_plus. rewrite (iscomm_plusNonnegativeReals y). rewrite <- isassoc_plusNonnegativeReals. rewrite <- maxNonnegativeReals_minus_plus. rewrite isrdistr_max_plusNonnegativeReals. rewrite <- maxNonnegativeReals_minus_plus. rewrite isassoc_maxNonnegativeReals. apply maponpaths. apply maxNonnegativeReals_carac_r. now apply plusNonnegativeReals_le_r. 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