5. [4 marks] Recall the following context-free grammar from Assignment 9. S#bSSaaSb Let L5={x#y:x,y{a,b} and the number of as in x is the same as the number of bs in y} Give a detailed proof that every string generated by the grammar is in L5. (This is the converse of what you had to prove on Assignment 9.) If you use induction, state the claim you are proving by induction, the value you are doing induction on, and make sure to explicitly state your induction hypothesis