fact: Definition to_O_equiv_natural {A B} (f : A <~> B) : (equiv_O_functor f) o (to O A) == (to O B) o f := to_O_natural f.
imports: HoTT.Basics HoTT.Types Equiv.BiInv Extensions HProp HFiber NullHomotopy Limits.Pullback PathAny Colimits.Pushout