fact: Definition iff_inO_equiv (O : Subuniverse) {T : Type} {U : Type} (f : T <~> U) : In O T <-> In O U := (fun H => inO_equiv_inO' _ f, fun H => inO_equiv_inO' _ f^-1).
imports: HoTT.Basics HoTT.Types Equiv.BiInv Extensions HProp HFiber NullHomotopy Limits.Pullback PathAny Colimits.Pushout