proposition: Lemma equiv_forall_inO_mapinO_pr1 `{Funext} {A : Type} (B : A -> Type) : (forall a, In O (B a)) <~> MapIn O (@pr1 A B).
proof: Proof. exact (equiv_iff_hprop_uncurried (iff_forall_inO_mapinO_pr1 B)). Defined.
imports: HoTT.Basics HoTT.Types Equiv.BiInv Extensions HProp HFiber NullHomotopy Limits.Pullback PathAny Colimits.Pushout