m-step transition probability conditioned on previous states in a discrete time Markov chain

Question

Given a discrete time Markov chain $\{X_n\}\ (n\geq0)$ with the property $\Pr\{X_n=j|X_{n-1}=i_{n-1},X_{n-2}=i_{n-2},...,X_{0}=i_{0}\}=\Pr\{X_n=j|X_{n-1}=i_{n-1}\}$, how could I derive the result that $\Pr\{X_{n+m}=j|X_{n-1}=i_{n-1},X_{n-2}=i_{n-2},...,X_{0}=i_{0}\}=\Pr\{X_{n+m}=j|X_{n-1}=i_{n-1}\}$? Furthermore, how could I obtain $\Pr\{X_{n+m}=j|X_{n-k_1}=i_{n-k_1},X_{n-k_2}=i_{n-k_2},...,X_{n-k_r}=i_{n-k_r}\}=\Pr\{X_{n+m}=j|X_{n-k_1}=i_{n-k_1}\}$ $(0\leq k_1\leq k_2 \leq ... \leq k_r \leq n,\ 1\leq r \leq n)$ from this result?