(inh : forall b, Q b) `{IsConnMap O _ _ (functor_sigma f g)} : IsConnMap O f. Proof. intros b. refine (contr_equiv _ (equiv_O_hfiber_functor_sigma b (inh b))). 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.