Fill in the basis step in the proof by mathematical induction of the following statement: Vn EN EL ( sum(I) = 2n A length(1) = n) For reference, we include the recursive step in the proof below. Proof We proceed by mathematical induction on n. Basis Step This is what you need to provide. Recursive Step: Consider an arbitrary natural number n. We will prove that 31 L sum(1) = 2n A length(1) = n) + 31 EL sum(1) = 2(n+1) Alength(1) = n+1) Assume as the induction hypothesis that there is a witness linked list of natural numbers, call it w, such that sum() = 2n and length() = n. We need to produce a witness list to prove that the property holds for n +1 as well. Consider 1 = (2,). Then l E L because 2 N and I, EL (by IH), so l is in the domain of quantification. We now evaluate the predicate, which is a conjunction so we evaluate each conjunct: sum(I) = sum( (2,1w)) def of sum 2 + sum(lv) ** 2 + 2n = 2(n +1), as required; and length(1) = length( (2,0w) ) et offength 1 + length(1) 1+n=n+1, as required. Thus, both required conjuncts have been proved and (2,1w) is a witness. Since the basis step and the recursive step have both been proved, the mathematical induction is complete