proposition: Lemma ψ_naturality (A B: C)(h: B --> A)(f: L A --> X): ψ B (#L h· f) = #L (#F h)· ψ A f.
proof: Proof. assert (ψ_is_nat := nat_trans_ax ψ); assert (ψ_is_nat_inst1 := ψ_is_nat _ _ h). assert (ψ_is_nat_inst2 := eqtohomot ψ_is_nat_inst1 f). apply ψ_is_nat_inst2. Qed.
imports: UniMath.Tactics.EnsureStructuredProofs UniMath.Foundations.PartD UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Core.Functors UniMath.CategoryTheory.Core.NaturalTransformations UniMath.CategoryTheory.Limits.Initial UniMath.CategoryTheory.FunctorAlgebras UniMath.CategoryTheory.Categories.HSET.Core UniMath.CategoryTheory.opp_precat UniMath.CategoryTheory.yoneda UniMath.CategoryTheory.Adjunctions.Core