fact: Definition inO_unsigma {A : Type} (B : A -> Type) `{In O A} {B_inO : In O {x:A & B x}} (x : A) : In O (B x) := inO_equiv_inO _ (hfiber_fibration x B)^-1.
imports: HoTT.Basics HoTT.Types Equiv.BiInv Extensions HProp HFiber NullHomotopy Limits.Pullback PathAny Colimits.Pushout