<P> Choosing m = j − 4 (\ displaystyle m = j - 4), and observing that 15 <j ⟹ 12 ≤ j − 4 <j (\ displaystyle 15 <j \ implies 12 \ leq j - 4 <j) shows that S (j − 4) (\ displaystyle S (j - 4)) holds, by inductive hypothesis . That is, the sum j − 4 (\ displaystyle j - 4) can be formed by some combination of 4 (\ displaystyle 4) and 5 (\ displaystyle 5) dollar coins . Then, simply adding a 4 (\ displaystyle 4) dollar coin to that combination yields the sum j (\ displaystyle j). That is, S (j) (\ displaystyle S (j)) holds . Q.E.D. </P> <P> The last two steps can be reformulated as one step: </P> <Ol> <Li> Showing that if the statement holds for all n <m then the same statement also holds for n = m . </Li> </Ol> <Li> Showing that if the statement holds for all n <m then the same statement also holds for n = m . </Li>

The first step in the rule making process involves