My question is prove equation 4.2 using equation 4.1.thanks

4 Question 4 A butterfly spread consists of three options on the same stock All three options have the same expiration time T The options have strike prices KiK2 and K3, which are are equally spaced. . Hence K2 is located at the midpoint of K1 and K3, so K2 = (Ki + Ks)/2. A butterfly spread can be created using three call options or three put options The spread consists of long one option at Ki, short two options at K2, long one option at Ks .1 European option butterfly spreads Suppose the market price of a stock is S at the current time t. The stock does not pay dividends. The interest rate is r >0 (a constant) For a European call and put e and p with the same strike K and expiration T, the put-call parity relation in this case is -p-s-Ke-T- Let q and p,, i = 1, 2, 3, be the values of European calls and puts with strikes Ki, K2 and K3, where K (Ki+K3)/2 Use eq.(41) to prove the following relation: (4.2) The values of a European call butterfly spread and a European put butterfly spread are equal The corresponding relation is not necessarily true for American options