Here is a question about inductively defined functions and structural induction proofs. Please provide you answer with detailed explanations, and I really appreciate your help! Thumps up if help.

We defined the base-b interpretation of a string of digits d dido using the formula (di dido) SC, dib An inductive definition of this formula (inductive on the structure of the digits as a string) is also useful. (a) Define a function n 10, b 11" N inductively with the property that n(du dido) (di dido)b. Prove inductively that your function is correct. Note: homework 7 covered this problem in the case b 2: you can interpret Z as the empty string, D as the digit 0, and SD as the digit 1. (b) Use structural induction to prove that the base-b representation is unique if there are no leading 0's. We defined the base-b interpretation of a string of digits d dido using the formula (di dido) SC, dib An inductive definition of this formula (inductive on the structure of the digits as a string) is also useful. (a) Define a function n 10, b 11" N inductively with the property that n(du dido) (di dido)b. Prove inductively that your function is correct. Note: homework 7 covered this problem in the case b 2: you can interpret Z as the empty string, D as the digit 0, and SD as the digit 1. (b) Use structural induction to prove that the base-b representation is unique if there are no leading 0's