Ramsey's infinite theorem : for all $c,d>0$ and for all function $f: [\mathbb{N}]^d \to c$ there is an infinite subset $A \subset \mathbb{N}$ such that $f|[A]^d$ is constant function.
Ramsey's finite theorem : for all $c,d>0$ for all $k>0$ there is $N>0$ such that for every function $f: [N]^d \to c$ there is subset $A \subset N$ such that $f|[A]^d$ is constant and $|A| \geq k$.
Prove Ramsey's finite theorem using Ramsey's infinite theorem and compactness theorem ?
I don't have a clue on how to start solving this, please help