∀ {Ω : Type u_1} {m0 : MeasurableSpace Ω} {μ : MeasureTheory.Measure Ω} {f : ℕ → Ω → ℝ}
  {ℱ : MeasureTheory.Filtration ℕ m0} [MeasureTheory.IsFiniteMeasure μ],
  MeasureTheory.Submartingale f ℱ μ →
    ∀ (a b : ℝ) (N : ℕ),
      MeasureTheory.Submartingale
        (fun n => ∑ k ∈ Finset.range n, (1 - MeasureTheory.upcrossingStrat a b f N k) * (f (k + 1) - f k)) ℱ μ