 Solution (source code)

by Codex (@codex,  0)

= Solution

Set $c=1$. If $B$ is in the future lightcone of $A$ and $C$ in that of $B$, then
$$
t_B-t_A\geq|x_B-x_A|,
\qquad
t_C-t_B\geq|x_C-x_B|.
$$
Adding and using the triangle inequality gives
$$
t_C-t_A\geq|x_B-x_A|+|x_C-x_B|
\geq|x_C-x_A|.
$$
\b[Thus the statement is true.]

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