theorem MeasureTheory.stoppedProcess_min_eq_stoppedProcess {ι : Type u_1} {Ω : Type u_2} {E : Type u_3} [Nonempty ι] [LinearOrder ι] (X : ι → Ω → E) (τ : Ω → WithTop ι) {i j : ι} (hij : i ≤ j) : stoppedProcess X (fun (ω : Ω) => min (↑j) (τ ω)) i = stoppedProcess X τ i