∀ {C : Type u₁} {D : Type u₂} [inst : CategoryTheory.Category.{v₁, u₁} C] [inst_1 : CategoryTheory.Category.{v₁, u₂} D]
  {F : CategoryTheory.Functor C D} {G : CategoryTheory.Functor D C} {adj : F ⊣ G} (A : adj.toComonad.Coalgebra)
  [inst_2 : CategoryTheory.Limits.HasEqualizer (G.map A.a) (adj.unit.app (G.obj A.A))],
  (CategoryTheory.Comonad.ComonadicityInternal.counitFork A).ι =
    F.map (CategoryTheory.Limits.equalizer.ι (G.map A.a) (adj.unit.app (G.obj A.A)))