∀ {M : Type u_1} [inst : MeasurableSpace M] {α : Type u_2} {m : MeasurableSpace α} {μ : MeasureTheory.Measure α}
  {f : α → M} [inst_1 : Max M] [MeasurableSup M], AEMeasurable f μ → ∀ (c : M), AEMeasurable (fun x => f x ⊔ c) μ