functor_limit (diagram_equiv_inv m) HQ2 HQ1 o functor_limit m HQ1 HQ2 == idmap. Proof. apply ap10. srapply (equiv_inj (cone_precompose HQ1) _). 1: apply HQ1. etransitivity. 2:symmetry; apply cone_precompose_identity. etransitivity. 1: apply cone_precompose_comp. rewrite eisretr, cone_postcompose_precompose, eisretr. rewrite cone_postcompose_comp, diagram_inv_is_retraction. apply cone_postcompose_identity. Defined.
Require Import Basics. Require Import Diagrams.Diagram. Require Import Diagrams.Graph. Require Import Diagrams.Cone. Require Import Diagrams.ConstantDiagram.