fact: Definition to_O_inv_natural {A B : Type} `{In O A} `{In O B} (f : A -> B) : (to O B)^-1 o (O_functor f) == f o (to O A)^-1.
imports: HoTT.Basics HoTT.Types Equiv.BiInv Extensions HProp HFiber NullHomotopy Limits.Pullback PathAny Colimits.Pushout