2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/138210This note is devoted to the theory of projective limits of finite-dimensional Lie groups, as developed in the recent monograph ``The Lie Theory of Connected Pro-Lie Groups'' by K.H. Hofmann and S.A. Morris. We replace the original, highly non-trivial proof of the One-Parameter Subgroup Lifting Lemma given in the monograph by a shorter and more elementary argument. Furthermore, we shorten (and correct) the proof of the so-called Pro-Lie Group Theorem, which asserts that pro-Lie groups and projective limits of Lie groups coincide.4 pages, LaTeX (v3: slightly expanded)Group Theory22A05 (Primary); 22E15, 22E65 (Secondary)text