Prove that if for each x,y from P exists sup(x,y) and inf(x,y)

26 Views Asked by At

Let (P,$\le$) be an ordered set. Prove that if for each x,y from P exists sup(x,y) and inf(x,y) then exists sup(A) and inf(A) for any finite A $\subseteq$ P.

I don`t know how to make a proof of it, maybe someone could help me?