Lemma 55.3.10. Let n, m_ i, a_{ij}, w_ i, g_ i be a numerical type. Let e be the number of pairs (i, j) with i < j and a_{ij} > 0. Then the expression g_{top} = 1 - n + e is \geq 0.
Proof. If not, then e < n - 1 which means there exists an i such that a_{ij} = 0 for all j \not= i. This contradicts assumption (3) of Definition 55.3.1. \square
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