(a) (10 points) Prove by the Principle of Recursion, that every positive integer has a Fibonacci representation of the type discussed in class. If you can't complete the proof, you can earn at least 8 points by detailing the steps and setting up the proof correctly. (b) (5 points) Prove that in the Fibonacci representation of an integer the string '11' can be a subsequence of the representation only at the very end of the representation. (a) (10 points) Prove by the Principle of Recursion, that every positive integer has a Fibonacci representation of the type discussed in class. If you can't complete the proof, you can earn at least 8 points by detailing the steps and setting up the proof correctly. (b) (5 points) Prove that in the Fibonacci representation of an integer the string '11' can be a subsequence of the representation only at the very end of the representation