# Put-Call Parity with dividends

In which book will I find the exact proof of put-call parity in the case when asset pays continuous dividend? I need a book to cite this result

$$C(S,K) - P(S,K) = F - K*DF$$
In the RHS, dividends will impact the forward $$F$$ (higher dividends imply lower forward). So the LHS should be lower as well: the Call costs less and the Put costs more.
The proof is straightforward, you just notice that at maturity $$T$$ you have:
$$S_T - K = (S_T - K)\mathbb{I}_{S_T>K} + (S_T - K)\mathbb{I}_{S_TK} - (K - S_T)\mathbb{I}_{S_T
By non-arbitrage arguments, if this equality holds at $$T$$ it must hold at any time $$t (i.e. the RHS and LHS portfolios must have same value at any time $$t). Otherwise you can construct an arbitrage by buying the cheap one and selling the expensive one.