  In a recent work I showed that the family of smooth steep time functions can
be used to recover the order, the topology and the (Lorentz-Finsler) distance
of spacetime. In this work I present the main ideas entering the proof of the
(smooth) distance formula, particularly the product trick which converts metric
statements into causal ones. The paper ends with a second proof of the distance
formula valid in globally hyperbolic Lorentzian spacetimes.
