proposition: Lemma preIt_ok : # L inF· preIt = ψ μF preIt.
proof: Proof. apply cancel_φ. rewrite φ_ψ_μF_eq. rewrite (φ_adj_natural_precomp (pr2 is_left_adj_L)). unfold preIt. rewrite (φ_adj_after_φ_adj_inv (pr2 is_left_adj_L)). rewrite (φ_adj_after_φ_adj_inv (pr2 is_left_adj_L)). assert (iter_eq := algebra_mor_commutes _ _ _ (InitialArrow μF_Initial ⟨_,φ (ψ (R X) (ε X))⟩)). exact iter_eq. 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