Full Idea
Defining a set by induction enables us to use the method of proof by induction to establish that all the elements of the set have a certain property.
Gist of Idea
If a set is defined by induction, then proof by induction can be applied to it
Source
José L. Zalabardo (Introduction to the Theory of Logic [2000], §2.3)
Book Reference
Zalabardo,José L.: 'Introduction to the Theory of Logic' [Westview 2000], p.48