fact: Definition O_functor_hfiber_natural {A B} (f : A -> B) (b : B) : (O_functor_hfiber f b) o to O (hfiber f b) == functor_hfiber (fun u => (to_O_natural f u)^) b.
imports: HoTT.Basics HoTT.Types Equiv.BiInv Extensions HProp HFiber NullHomotopy Limits.Pullback PathAny Colimits.Pushout