(b : B) : equiv_O_pushout^-1 (to O (Pushout (O_functor f) (O_functor g)) (pushl (to O B b))) = to O (Pushout f g) (pushl b). Proof. apply moveR_equiv_V; symmetry; apply equiv_O_pushout_to_O_pushl. Qed.
Require Import HoTT.Basics HoTT.Types. Require Import Equiv.BiInv Extensions HProp HFiber NullHomotopy Limits.Pullback. Require Import Homotopy.IdentitySystems. Require Import Colimits.Pushout.