text: Another generalization , called complete induction ( or strong induction or course of values induction ) , says that in the second step we may assume not only that the statement holds for n = m but also that it is true for all n less than or equal to m. In complete induction it is not necessary to list the base case as a separate assumption .
simplified: State that the proof will be by induction , and state which variable will be used in the induction step .