{α : Type u} →
  {β : Type v} →
    [inst : Group α] →
      [inst_1 : Monoid β] →
        [inst_2 : MulAction β α] →
          {H : Subgroup α} →
            {motive : MulAction.QuotientAction β H → Sort u_1} →
              (t : MulAction.QuotientAction β H) →
                ((inv_mul_mem : ∀ (b : β) {a a' : α}, a⁻¹ * a' ∈ H → (b • a)⁻¹ * b • a' ∈ H) → motive ⋯) → motive t