Lipschitz function and uniform continuity

[atm06001]

A function f:D\rightarrowR is called a Lipschitz function if there is some
nonnegative number C such that

absolute value(f(u)-f(v)) is less than or equal to C*absolute value(u-v) for all points u and v in D.

Prove that if f:D\rightarrowR is a Lipschitz function, then it is uniformly continuous.

I am having trouble proving this, I am not sure if I should suppose not or go about it by some other method?

 

[mathwonk]

try a direct proof.