Equivalence of diagonal contractions to generalized IW-contractions with integer exponents

We present a simple and rigorous proof of the claim by Weimar-Woods [E. Weimar-Woods, Contractions, generalized Inönü–Wigner contractions and deformations of finite-dimensional Lie algebras, Rev. Math. Phys. 12 (2000) 1505–1529.] that any diagonal contraction (e.g., a generalized Inönü–Wigner contraction) is equivalent to a generalized Inönü–Wigner contraction with integer parameter powers.