Lemma 1

If $\mathrm{dp}_A(M) < n < +\infty$, then $\mathrm{Ext}_A^n(M, N) = 0$ for every $A$-module $N$ and $\mathrm{Tor}_n^A(P, M) = 0$ for every righthand $A$-module $P$. This follows immediately from the fact that $M$ has a projective resolution of length $< n$ and from X, p. 100, Theorem 1.