Prove the following stronger form of the pumping lemma, wherein both pieces v and y must be nonempty when the string s is broken up. If A is a context-free language, then there is a number k where, if s is any string in A of length at least k, then s may be divided into five pieces, s = uvxyz, satisfying the conditions:

a. for each i ≥ 0, uvⁱxyⁱz ∈ A,

b. v ≠ ε and y ≠ ε, and

c. |vxy| ≤ k.