{α : Type u_1} →
  {C : Set (Set α)} →
    {motive : MeasureTheory.IsSetSemiring C → Sort u} →
      (t : MeasureTheory.IsSetSemiring C) →
        ((empty_mem : ∅ ∈ C) →
            (inter_mem : ∀ s ∈ C, ∀ t ∈ C, s ∩ t ∈ C) →
              (diff_eq_sUnion' : ∀ s ∈ C, ∀ t ∈ C, ∃ I, ↑I ⊆ C ∧ (↑I).PairwiseDisjoint id ∧ s \ t = ⋃₀ ↑I) → motive ⋯) →
          motive t