More formally, we denote $p_{1},p_{2}$ as the points in frame S such that $(p_{1})^{x} < (p_{2})^{x}$. Since $(p_{1})^{y} = (p_{2})^{y}$ and the Lorentz boost $\Lambda$ is by speed v in the x direction we need only consider the $x'$ components of $q_{i} = \Lambda(p_{i})$. While it is true $(q_{1})^{x'} < (q_{2})^{x'}$ for sufficiently large values of v the boost is such that $\vert (q_{1})^{x'}\vert > \vert(q_{2})^{x'}\vert$ and thus $(q_{1})^{t'} > (q_{2})^{t'}$ as both frames see the light sphere as centred on the origin and emitted at time 0.