  We consider an extension of the modal logic of transitive closure K+ with
some inifinitary derivations and present a sequent calculus for this extension,
which allows non-well-founded proofs. For the given calculus, we obtain the
cut-elimination theorem following the lines of so called continuous cut
elimination. Our consideration also covers ordinary proofs of K+ since they
correspond to cyclic cut-free proofs of the presented sequent calculus.
