∀ {J : Type u_1} (x y : CategoryTheory.Limits.WidePullbackShape J)
  (f :
    CategoryTheory.WithTerminal.widePullbackShapeEquivObj✝ x ⟶
      CategoryTheory.WithTerminal.widePullbackShapeEquivObj✝¹ y),
  (match y, x,
      match x, y, f with
      | some x, some y, f => cast ⋯ (CategoryTheory.Limits.WidePullbackShape.Hom.id (some y))
      | none, some y, f => PEmpty.casesOn (fun t => f = t → (none ⟶ some y)) f ⋯
      | some x, none, f => CategoryTheory.Limits.WidePullbackShape.Hom.term x
      | none, none, f => CategoryTheory.Limits.WidePullbackShape.Hom.id none with
    | .(none), .(some j), CategoryTheory.Limits.WidePullbackShape.Hom.term j => PUnit.unit
    | y, .(y), CategoryTheory.Limits.WidePullbackShape.Hom.id .(y) =>
      CategoryTheory.CategoryStruct.id (CategoryTheory.WithTerminal.widePullbackShapeEquivObj✝² y)) =
    f