proposition: Proposition profunctor_comp {C₁ C₂ : category} (P : C₁ ↛ C₂) {y₁ y₂ y₃: C₂} (g₂ : y₃ --> y₂) (g₁ : y₂ --> y₁) {x₁ x₂ x₃ : C₁} (f₁ : x₁ --> x₂) (f₂ : x₂ --> x₃) (h : P y₁ x₁) : P #[ g₂ · g₁ , f₁ · f₂ ] h = P #[ g₂ , f₂ ] (P #[ g₁ , f₁ ] h).
proof: Proof. exact (eqtohomot (@functor_comp _ _ P (_ ,, _) (_ ,, _) (_ ,, _) (_ ,, _) (_ ,, _)) h). Qed.
imports: UniMath.Foundations.Preamble UniMath.Foundations.Propositions UniMath.Foundations.Sets UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Core.Univalence UniMath.CategoryTheory.Core.Functors UniMath.CategoryTheory.Core.NaturalTransformations UniMath.CategoryTheory.PrecategoryBinProduct UniMath.CategoryTheory.opp_precat UniMath.CategoryTheory.Categories.HSET.All