fact: Definition equiv_inO_equiv `{Funext} (O : Subuniverse) {T : Type} {U : Type} (f : T <~> U) : In O T <~> In O U := equiv_iff_hprop_uncurried (iff_inO_equiv _ f).
imports: HoTT.Basics HoTT.Types Equiv.BiInv Extensions HProp HFiber NullHomotopy Limits.Pullback PathAny Colimits.Pushout