Diestel has given a nice third proof of Hall's theorem in graph theory in his seminal book.
I came across the following inequality and can not make sense as to why is it correct?
$\left|N_{H}\left(A_{1} \cap A_{2} \backslash\{a\}\right)\right| \leqslant\left|B_{1} \cap B_{2}\right|$
This appears on Page 39 of Section 2.1 in his fifth edition.
