{P Q : Type} `{In O Q} (f g : P -> Q) (pi : f == g) : O_rec (O := O) f == O_rec g. Proof. apply O_indpaths; intro x. etransitivity. { apply O_rec_beta. } { etransitivity. { exact (pi _). } { symmetry; apply O_rec_beta. } } 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.