Let be an alphabet. In lectures, we have defined the inductive construction of , the string-concatenation operator , the string-reversal operator r , and the string-length function | | inductively.

Give a detailed proof in steps with annotated reasons of the following string-property using mathematical induction based on the inductive definitions of , ^r , and | |:

For all strings x and symbols c , (cx)^r = x^r c.