Proposition comp_is_monotone {X₁ X₂ X₃ : hSet} {R₁ : PartialOrder X₁} {R₂ : PartialOrder X₂} {R₃ : PartialOrder X₃} {f : X₁ → X₂} {g : X₂ → X₃} (Hf : is_monotone R₁ R₂ f) (Hg : is_monotone R₂ R₃ g) : is_monotone R₁ R₃ (λ z, g(f z)). Proof. exact (λ x₁ x₂ p, Hg _ _ (Hf _ _ p)). Qed.
Require Import UniMath.Foundations.All. Require Import UniMath.MoreFoundations.All. Require Import UniMath.OrderTheory.Posets.Basics.