The notes also call complete induction al-qiyās al-muqassam—a syllogism by exhaustive division. The class is divided into all its relevant kinds, and the property is established for each kind.
Suppose a collection contains only categories A, B, and C, and a feature D is established for each category. Because the division is exhaustive, the whole collection has D.
Completeness of the division is part of the proof. If a relevant fourth category was missed, the conclusion no longer follows in that manner.