I have following relation of random variables $$Y_1=aX_1+bX_2+N_1,\\Y_2=X_1+X_2+N_2,$$ where $X_1,X_2$ are discrete random variables which can take a value uniformly from a set and $N_1,N_2$ are Gaussian random variables with zero mean and unit variance. $a,b$ are some constants. The variables $X_1,X_2,N_1,N_2$ are all independent from each other. In this situation, how to prove that the following inequality is true $$I(X_1;Y_2)\leq I(X_1;X_1+X_2).$$ Any help in this regard will be much appreciated. Thanks in advance.
Does it depend on the Markov chain property where Markov chain is as follows $$X_1\to X_1+X_2\to Y_2?$$