I have to proof the every finite lattice is also a complete lattice but I'dont known where to start.
From definition, a lattice is a poset in which every pair of elements has a least upper bound and a greatest lower bound. If the previous conditions are valid for any subset that the lattice is also complete.
How can I prove that every finite lattice is also complete? I need some hint.
sup{ $a_1, a_2,.. a_n$ } = $a_1$ sup $a_2$ sup ... sup $a_n$