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