  We derive a discrete version of the stochastic Gronwall Lemma found in
[Scheutzow, IDAQP, 2013]. The proof is based on a corresponding deterministic
version of the discrete Gronwall Lemma and an inequality bounding the supremum
in terms of the infimum for time discrete martingales. As an application the
proof of an a priori estimate for the backward Euler-Maruyama method is
included.
