Definition lan_nat_trans_data_cocone_forms_cocone {x : C₂} {w₁ w₂ : C₁} {h₁ : P w₁ --> x} {h₂ : P w₂ --> x} {e : w₁ --> w₂} (p : h₁ · identity _ = #P e · h₂) : # F e · lan_nat_trans_data_cocone_ob x w₂ h₂ = lan_nat_trans_data_cocone_ob x w₁ h₁.
Require Import UniMath.Foundations.All. Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Core.Functors. Require Import UniMath.CategoryTheory.Core.Isos. Require Import UniMath.CategoryTheory.Core.NaturalTransformations. Require Import UniMath.CategoryTheory.Core.Univalence. Require Import UniMath.CategoryTheory.Adjunctions.Core. Require Import UniMath.CategoryTheory.Limits.Graphs.Colimits. Require Import UniMath.CategoryTheory.Categories.StandardCategories. Require Import UniMath.CategoryTheory.CommaCategories. Require Import UniMath.CategoryTheory.FunctorCategory. Require Import UniMath.CategoryTheory.whiskering.