Let f: D-R satisfy the Lipschitz condition: there exists an L such that for all x,y D |f(x)-f(y)|<=L|x-y|

Prove that f is uniformly continuous on D

Here is what I have, is this correct?

Let >0. Choose = /L. Then by the definition of uniform continuity, if |x-y|< = /L, then |f(x)-f(y)|<L /L= .