We have recently learned that the "entropy-of-a-mixture" lemma (Theorem 2.1 of our paper) was stated and proven independently by R. T. Baumel, On spontaneously broken symmetry in the P(q)2 model quantum field theory, Ph.D. thesis (physics), Princeton University, June 1979 (un- published), Proposition 5.1 and Corollary 5.2 (pp. 432-435). He applied this lemma to an approximate variational calculation. We are pleased to acknowledge Baumel's priority.