  Huang's Lemma is an important tool in CR geometry to study rigidity problems.
This paper introduces a generalization of Huang's Lemma based on the rigidity
properties of holomorphic mappings preserving certain orthogonality on
projective spaces, which is optimal for the case of partial linearity. By
exploring the intricate relationship between rigidity and Huang's Lemma, we
establish that the rigidity properties of Segre maps or proper holomorphic
mappings between generalized balls with Levi-degenerate boundaries can be
inferred from those between generalized balls with Levi-non-degenerate
boundaries by in a coordinate-free and more geometric manner.
