fact: Definition O_functor_hfiber {A B} (f : A -> B) (b : B) : O (hfiber f b) -> hfiber (O_functor f) (to O B b).
imports: HoTT.Basics HoTT.Types Equiv.BiInv Extensions HProp HFiber NullHomotopy Limits.Pullback PathAny Colimits.Pushout