{B' A' : Type} {f' g' : B' -> A'} (h : B -> B') (k : A -> A') (p : k o f == f' o h) (q : k o g == g' o h) `{O_inverts k} `{O_inverts h} : O_inverts (functor_coeq h k p q). Proof. apply O_inverts_from_extendable. intros Z Z_inO. apply extendable_functor_coeq'. all:nrapply ooextendable_O_inverts; assumption. 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.