Apologies, I am aware of that, but don't often use terminology that makes that clear.
That would be another thing that I don't understand, namely how, or why, the time co-ordinate would include a spatial term.
Thanks for going through the above; the part I don't understand is the initial equations; I read [itex]t'=t-vx[/itex] as meaning [itex]t'[/itex] equals t minus the velocity along the X-axis, but I don't understand why the velocity comes into it.
and [itex]x'=x-vt[/itex] I read as [itex]x'[/itex] equals x minus the velocity multiplied by the time - which makes a bit more sense to me.
My interpretation of it would be that, if the clocks which give the time co-ordinates all ran at the same rate, then absolute simultaneity should prevail; and in order for RoS to prevail clocks would have to give different times (co-ordinates).
I suppose, essentially, where I have trouble is how we can go from the scenario where an event (or all events) are absolutely simultaneous across all reference frames, to a scenario where there is RoS. Presumably the initial scenario of absolute simultaneity would involve a transform (to affirm absolute simultaneity); I don't understand where a different transform could result in [the conclusion of] RoS if the initial transform leads to the conclusion of absolute simultaneity.
Hopefully that makes some bit of sense.