I have come across two different definitions of a lattice. The first one is that a lattice is a partially ordered set with every pair of elements having an infimum and a supremum. The other definition is that a lattice is a set with two binary operations meet and join defined on it such that L is closed under these two operations and these operations satisfy the laws of commutation, association and absorption.
Now, I want to see if both these definitions are equivalent to each other. Can anyone help?