∀ {C : Type u_2} [inst : CategoryTheory.Category.{u_1, u_2} C]
  {F G : CategoryTheory.Functor (CategoryTheory.Discrete CategoryTheory.Limits.WalkingPair) C}
  (f : F.obj { as := CategoryTheory.Limits.WalkingPair.left } ⟶ G.obj { as := CategoryTheory.Limits.WalkingPair.left })
  (g :
    F.obj { as := CategoryTheory.Limits.WalkingPair.right } ⟶ G.obj { as := CategoryTheory.Limits.WalkingPair.right })
  (x x : CategoryTheory.Discrete CategoryTheory.Limits.WalkingPair) (X Y : CategoryTheory.Limits.WalkingPair)
  (x : { as := X } ⟶ { as := Y }) (u : { as := X }.as = { as := Y }.as),
  CategoryTheory.CategoryStruct.comp (F.map { down := { down := u } })
      (match { as := Y } with
      | { as := CategoryTheory.Limits.WalkingPair.left } => f
      | { as := CategoryTheory.Limits.WalkingPair.right } => g) =
    CategoryTheory.CategoryStruct.comp
      (match { as := X } with
      | { as := CategoryTheory.Limits.WalkingPair.left } => f
      | { as := CategoryTheory.Limits.WalkingPair.right } => g)
      (G.map { down := { down := u } })