∀ (C : Type u_1) [inst : CategoryTheory.Category.{v_1, u_1} C] (X : CategoryTheory.WithTerminal C),
  (CategoryTheory.WithTerminal.mapId C).hom.app X =
    (match X with
      | CategoryTheory.WithTerminal.of a => CategoryTheory.Iso.refl (CategoryTheory.WithTerminal.of a)
      | CategoryTheory.WithTerminal.star => CategoryTheory.Iso.refl CategoryTheory.WithTerminal.star).hom