∀ {α : Type u_2} {𝒜 : Set (Set α)} {motive : (a : Set α) → MeasureTheory.generateSetAlgebra 𝒜 a → Prop} {a : Set α}
  (t : MeasureTheory.generateSetAlgebra 𝒜 a),
  (∀ (s : Set α) (s_mem : s ∈ 𝒜), motive s ⋯) →
    motive ∅ ⋯ →
      (∀ (s : Set α) (hs : MeasureTheory.generateSetAlgebra 𝒜 s), motive s hs → motive sᶜ ⋯) →
        (∀ (s t : Set α) (hs : MeasureTheory.generateSetAlgebra 𝒜 s) (ht : MeasureTheory.generateSetAlgebra 𝒜 t),
            motive s hs → motive t ht → motive (s ∪ t) ⋯) →
          motive a t