  The sequential form of a statement $\forall\xi(B(\xi) \rightarrow
\exists\zeta A(\xi,\zeta))$ is the statement $\forall\xi(\forall n B(\xi_n)
\rightarrow \exists\zeta \forall n A(\xi_n,\zeta_n))$. There are many
classically true statements of the first form whose proofs lack uniformity and
therefore the corresponding sequential form is not provable in weak classical
systems. The main culprit for this lack of uniformity is of course the law of
excluded middle. Continuing along the lines of previous work by Hirst and
Mummert, we show that if a statement of the first form satisfying certain
syntactic requirements is provable in some weak intuitionistic system, then the
proof is necessarily sufficiently uniform that the corresponding sequential
form is provable in a corresponding weak classical system. Our results depend
on Kleene's realizability with functions and the Lifschitz variant thereof.
