transformation proof help

[eckiller]

I have the transformation:

z' = g(z) = f*z / (f-n) - f*n / (f-n)

f >= 0 , n>= 0 constants that define an interval [n, f].

I want to prove, z' <= z.

[amcavoy]

I have the transformation:

z' = g(z) = f*z / (f-n) - f*n / (f-n)

f >= 0 , n>= 0 constants that define an interval [n, f].

I want to prove, z' <= z.
One way I suppose you could do it is by saying the opposite, and then try to prove yourself wrong:

\frac{fz-fn}{f-n}\geq z