__A statement that has an integer parameter n can often be proved by induction on a. We prove the statement is true for the basis, a finite number of cases for particular values of n and then prove the induction step : that if the statement is true for values unto n, then it is true for n+1.__

**Inductive proofs :**__We may prove a theorem about the construction objects by induction on the number of steps used in its construction. this type of induction is referred to as structural.__

**Structural Inductions :**