fact: Definition equiv_o_conn_map `{Funext} {A B : Type} (f : A -> B) `{IsConnMap O _ _ f} (P : B -> Type) `{forall b:B, In O (P b)} : (forall b, P b) <~> (forall a, P (f a)) := Build_Equiv _ _ _ (isequiv_o_conn_map f P).
imports: HoTT.Basics HoTT.Types Equiv.BiInv Extensions HProp HFiber NullHomotopy Limits.Pullback PathAny Colimits.Pushout