Exercise 8, § 4

Let s \in S and w \in W. Show that, if l(ws) > l(w), the element w(e_s) is a linear combination with coefficients \geq 0 of the e_t for t \in S; show that, if l(ws) < l(w), w(e_s) is a linear combination with coefficients \leq 0 of the e_t. (Apply property (P_n) of no. 4 to w^{-1}, and argue by polarity.)