Is This System Time Invariant?

[ttttrigg3r]

Homework Statement

y(n)=x(4n+1). Is this system T.I or NOT T.I

The professor marked this question wrong for my homework. He says it's NOT time invariant. I proved it is time invariant.

Homework Equations

System is time invariant if a shift in time in input results in the same shift in time when the output is shifted.

The Attempt at a Solution

shift in the x:
y1=x(4(n-n0)+1)
y2=shift in y=y(n-n0)=x(4(n-n0)+1)

They are the same, therefore they system is time invariant.
The professor marked this problem wrong for me, and he gave me the run-around when I asked for him to prove it. Did I do this right?

 

[UltrafastPED]

For the definition of time invariance see http://en.wikipedia.org/wiki/LTI_system_theory

Then test y(t-T) = x(4(t-T) +1) = x(4t+1 -4T)

So it is NOT time invariant; we are shifted not by -T but by -4T.