MATH.4:9 - Consequences

The result is a reusable way to obtain witnesses, with a reason for the property each witness satisfies. Construction and justification expose the same case boundaries, making a changed premise easier to locate.

Strengthening the result can add parameters or auxiliary values. Those additions cost representation and calculation but can supply the information that makes the inductive step work.

An efficient implementation remains a further opportunity when the simple construction is too costly.