Proposition dirprod_pr1_is_monotone {X₁ X₂ : hSet} (R₁ : PartialOrder X₁) (R₂ : PartialOrder X₂) : is_monotone (prod_PartialOrder R₁ R₂) R₁ pr1. Proof. exact (λ x₁ x₂ p, pr1 p). Qed.
Require Import UniMath.Foundations.All. Require Import UniMath.MoreFoundations.All. Require Import UniMath.OrderTheory.Posets.Basics.