| An example of  an arbitrary event with
| "any system of values of x,y,z,t" is:
| x = 5 m, y = 0, z = 0, t = -10 s.
| v = 10^6 m/s.
| vt !=  x
|
| The Lorentz transform:
|   tau = gamma(t - vx/c^2)
|   xi = gamma(x - vt)
|   etha = y
|   zeta = z
|
| tells us that the coordinates of this event in k are:
| xi = 10000060.6 m, etha = 0, zeta = 0, tau = -10.0006 s
|
| No problem, even if x != vt
| Thus it is plain stupidity to claim that x and t
| in the equation: tau = gamma(t - vx/c^2)
| must fulfil the equation x = vt.
|
| Happy to see that you now agree.

Agree with what, nTaul?
Obviously the tail end of the rigid rod of the k-frame will arrive at some
x, moving as it does in the direction of increasing x with the velocity v.
It should arrive at time t.

So x = vt.
Or was there some other values for v, x and t you wanted to arbitrarily
insert into Einstein's equation to make a point?

The front end of the rod, called x', is at x-vt or so Einstein claims.
That's a mighty short rod. When the light leaves the tail of the rod and
travels to x', it sure ain't got far to go. No distance at all, really.
Androcles