  We show that a modification of the proof of a result of Gulliksen gives an
elementary proof of the following important theorem by Avramov: if $(A,k) \to
(B,l)$ is a homomorphism of noetherian local rings and $B$ is of finite flat
dimension over $A$, then the homomorphism induced in Andr\'e-Quillen homology
modules $H_2(A,l,l)\to H_2(B,l,l)$ is injective.
