`{O : ReflectiveSubuniverse} {X Y : Type} (f : X -> Y) `{IsEquiv _ _ f} (x : O X) : O_cover X x <~> O_cover Y (O_functor O f x) := Build_Equiv _ _ (functor_O_cover f x) _.
Require Import Basics Types HFiber Truncations.Core Truncations.SeparatedTrunc Pointed