proposition: Lemma NQmax_case_strong : ∏ (P : NonnegativeRationals -> UU), ∏ x y : NonnegativeRationals, (y <= x -> P x) -> (x <= y -> P y) -> P (NQmax x y).
proof: Proof. intros P x y Hx Hy. unfold NQmax. generalize ( isdecrel_leNonnegativeRationals x y). apply coprod_rect ; [intros Hle | intros Hlt]. - now apply Hy. - apply Hx. now apply lt_leNonnegativeRationals, notge_ltNonnegativeRationals. Qed.
imports: UniMath.MoreFoundations.Tactics UniMath.MoreFoundations.PartA UniMath.MoreFoundations.Sets UniMath.MoreFoundations.Orders UniMath.RealNumbers.Sets UniMath.RealNumbers.Fields UniMath.Algebra.DivisionRig UniMath.OrderTheory.Lattice.Lattice UniMath.RealNumbers.Prelim