∀ {J : Type u_2} [inst : LinearOrder J] [inst_1 : SuccOrder J] {F : CategoryTheory.Functor Jᵒᵖ (Type u_1)}
  {d : F.WellOrderInductionData} [inst_2 : OrderBot J] {val₀ : F.obj (Opposite.op ⊥)} [inst_3 : WellFoundedLT J] (j : J)
  (hj : Order.IsSuccLimit j) (e : (i : J) → i < j → d.Extension val₀ i),
  F.map (CategoryTheory.homOfLE ⋯).op
      (d.lift j hj
        ⟨fun x =>
          match x with
          | Opposite.op ⟨i, hi⟩ => (e i hi).val,
          ⋯⟩) =
    val₀