Proposition comp_is_strict_and_monotone {X₁ X₂ X₃ : hSet} {R₁ : pointed_PartialOrder X₁} {R₂ : pointed_PartialOrder X₂} {R₃ : pointed_PartialOrder X₃} {f : X₁ → X₂} {g : X₂ → X₃} (Hf : is_strict_and_monotone R₁ R₂ f) (Hg : is_strict_and_monotone R₂ R₃ g) : is_strict_and_monotone R₁ R₃ (λ z, g(f z)). Proof. split. - exact (comp_is_monotone (pr1 Hf) (pr1 Hg)). - rewrite (strict_function_on_point Hf). rewrite (strict_function_on_point Hg). apply idpath. Qed.
Require Import UniMath.Foundations.All. Require Import UniMath.MoreFoundations.All. Require Import UniMath.OrderTheory.Posets.Basics. Require Import UniMath.OrderTheory.Posets.MonotoneFunctions.