(a : A) : equiv_O_coeq^-1 (to O (Coeq (O_functor f) (O_functor g)) (coeq (to O A a))) = to O (Coeq f g) (coeq a). Proof. apply moveR_equiv_V; symmetry; apply equiv_O_coeq_to_O. Defined.
Require Import HoTT.Basics HoTT.Types. Require Import Equiv.BiInv Extensions HProp HFiber NullHomotopy Limits.Pullback. Require Import Homotopy.IdentitySystems. Require Import Colimits.Pushout.