(O : Modality) {A : Type} (B : A -> Type) `{A_inO : In (Sep O) A} `{B_inO : forall a, In (Sep O) (B a)} : In (Sep O) (sig B). Proof. intros [x u] [y v]. specialize (A_inO x y). pose proof (fun p:x=y => B_inO y (p # u) v). pose @inO_sigma. refine (inO_equiv_inO' _ (equiv_path_sigma B _ _)). Defined.
Require Import HoTT.Basics HoTT.Types HoTT.Cubical.DPath. Require Import HFiber Extensions Factorization Limits.Pullback. Require Import Modality Accessible Descent. Require Import Truncations.Core. Require Import Homotopy.Suspension.