fact: Definition O_functor_homotopy_beta {A B : Type} (f g : A -> B) (pi : f == g) (x : A) : O_functor_homotopy f g pi (to O A x) = to_O_natural f x @ ap (to O B) (pi x) @ (to_O_natural g x)^.
imports: HoTT.Basics HoTT.Types Equiv.BiInv Extensions HProp HFiber NullHomotopy Limits.Pullback PathAny Colimits.Pushout