{α : Type u_1} →
  {m0 : MeasurableSpace α} →
    {μ : MeasureTheory.Measure α} →
      {C : Set (Set α)} →
        {motive : μ.FiniteSpanningSetsIn C → Sort u} →
          ((set : ℕ → Set α) →
              (set_mem : ∀ (i : ℕ), set i ∈ C) →
                (finite : ∀ (i : ℕ), μ (set i) < ⊤) →
                  (spanning : ⋃ i, set i = Set.univ) →
                    motive { set := set, set_mem := set_mem, finite := finite, spanning := spanning }) →
            (t : μ.FiniteSpanningSetsIn C) → motive t