  This 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.
