In the 1960s Serge Lang proved a result using this non-explicit form of auxiliary functions. The theorem implies both the Hermite–Lindemann and Gelfond–Schneider theorems. The theorem deals with a number field "K" and meromorphic functions "f"1...,"f""N" of order at most "ρ", at least two of which are algebraically independent, and such that if we differentiate any of these functions then the result is a polynomial in all of the functions. Under these hypotheses the theorem states that if there are "m" distinct complex numbers ω1...,ω"m" such that "f""i" (ω"j" ) is in "K" for all combinations of "i" and "j", then "m" is bounded by