Proposition nat_directed_set_help_monotone {X : hSet} (PX : PartialOrder X) (D : ℕ → X) (HD : ∏ (i : ℕ), PX (D i) (D (S i))) (i k : ℕ) : PX (D i) (D (i + k)). Proof. induction k as [ | k IHk ]. - rewrite natplusr0. apply refl_PartialOrder. - rewrite <- plus_n_Sm. refine (trans_PartialOrder PX IHk _). apply HD. Qed.
Require Import UniMath.Foundations.All. Require Import UniMath.MoreFoundations.All. Require Import UniMath.OrderTheory.Posets.Basics. Require Import UniMath.OrderTheory.Posets.MonotoneFunctions.