In the proof of a lemma in a paper, the authors say "Observe the distribution of $\vec{d}$ is well-defined." What does it mean mathematically?
Here is the picture of the notation, lemma, and its proof.
Reference: [Shuichi Katsumata, Shota Yamada. "Partitioning via Non-Linear Polynomial Functions: More Compact IBEs from Ideal Lattices and Bilinear Map", in Asiacrypt 2017, IACR 2017/843]
