Let X be a random variable with quantile function F−1. Assume the following three conditions: (i) F−1(p) = c for all p in the interval (p0, p1), (ii) either p0 = 0 or F−1(p0) < c, and (iii) either p1 = 1 or F−1(p) > c for p > p1. Prove that Pr(X = c) = p1 − p0.