Exp bounded by Taylor's polynomial

Stream: Is there code for X?

[Tomaz Gomes]

If d is even and x < 0, then Real.exp x < taylorWithinEval Real.exp d s 0 x. This is easy to prove with Taylor's theorem, but the version on mathlib assumes that x is to the right of the center of the polynomial we are considering to approximate exp. Is there another way to prove this in mathlib?