Proposition prodtofun_is_monotone {W X₁ X₂ : hSet} {RW : PartialOrder W} {R₁ : PartialOrder X₁} {R₂ : PartialOrder X₂} {f : W → X₁} {g : W → X₂} (Hf : is_monotone RW R₁ f) (Hg : is_monotone RW R₂ g) : is_monotone RW (prod_PartialOrder R₁ R₂) (prodtofuntoprod (f,, g)). Proof. exact (λ x y p, Hf _ _ p ,, Hg _ _ p). Qed.
Require Import UniMath.Foundations.All. Require Import UniMath.MoreFoundations.All. Require Import UniMath.OrderTheory.Posets.Basics.