Proposition prodtofun_is_strict_and_monotone {W X₁ X₂ : hSet} {RW : pointed_PartialOrder W} {R₁ : pointed_PartialOrder X₁} {R₂ : pointed_PartialOrder X₂} {f : W → X₁} {g : W → X₂} (Hf : is_strict_and_monotone RW R₁ f) (Hg : is_strict_and_monotone RW R₂ g) : is_strict_and_monotone RW (prod_pointed_PartialOrder R₁ R₂) (prodtofuntoprod (f,, g)). Proof. split. - exact (prodtofun_is_monotone Hf Hg). - use pathsdirprod ; cbn. + exact (strict_function_on_point Hf). + exact (strict_function_on_point Hg). Qed.
Require Import UniMath.Foundations.All. Require Import UniMath.MoreFoundations.All. Require Import UniMath.OrderTheory.Posets.Basics. Require Import UniMath.OrderTheory.Posets.MonotoneFunctions.