∀ {R : Type u_1} {A : Type u_2} {B : Type u_3} [inst : CommSemiring R] [inst_1 : Semiring A] [inst_2 : Algebra R A]
  [inst_3 : Semiring B] [inst_4 : Algebra R B] {ι : Type u_4} [inst_5 : Nonempty ι] (K : ι → Subalgebra R A)
  (dir : Directed (fun x1 x2 => x1 ≤ x2) K) (f f_1 : (i : ι) → ↥(K i) →ₐ[R] B) (e_f : f = f_1)
  (hf : ∀ (i j : ι) (h : K i ≤ K j), f i = (f j).comp (Subalgebra.inclusion h)) (T : Subalgebra R A) (hT : T ≤ iSup K),
  Subalgebra.iSupLift K dir f hf T hT = Subalgebra.iSupLift K dir f_1 ⋯ T hT