Assume asset price Sk,k=0,1,,N follows an N-period binomial model, the hedging process Xk+1 for the American put option is Xk+1=kSk+1+(1+r)(XkckkSk), where k is the hedging ratio and ck is the amount consumed at time k (Please refer to the lecture notes for the details of explanation of hedging process). Show that the discounted value of Xk+1 is a supermartingale under the risk-neutral probability measure