19. (40 points) 2 a,b, Lsi br, re a', and Ir 2n, n 2 1). As examples: baa e Li ba6 E L; baaa e L; a16 E L Use the RL pumping theorem to prove that L RLS the lexicographic ordering of L in your proof, and follow these guidelines carefully: . Start by expressing w in terms of k, the pumping length, and the symbols in 2, such that we L, and Iwl k. . For all possible values of y, generate w' from w by pum how many times. Convince me that w L. ping in or out. If you pump in, state . Never propose literal let w baaaa", or to assume that k 2, for some value of n. values for y or lyl: w or lwl: or make any assumptions about k beyond or example, it's against the rules to assume that lyl 1, or to include steps like . End your proof with a conclusion stating why L e RLs, in terms of the pumping theorem guarantees