  Continuing earlier work of the first author with U. Berger, K. Miyamoto and
H. Tsuiki, it is shown how a division algorithm for real numbers given as a
stream of signed digits can be extracted from an appropriate formal proof. The
property of being a real number represented as a stream is formulated by means
of coinductively defined predicates, and formal proofs involve coinduction. The
proof assistant Minlog is used to generate the formal proofs and extract their
computational content as terms of the underlying theory, a form of type theory
for finite or infinite data. Some experiments with running the extracted term
are described, after its translation to Haskell.
