Corrigendum to "Strong normalization proof with CPS-translation for second order classical natural deduction"

Our paper [1] contains a serious error. Proposition 4.6 of [1] is actually false and hence our strong normalization proof does not work for the Curry-style λμ-calculus. However, our method still can show that (1) the correction of Proposition 5.4 of [2], and (2) the correction of the proof of strong normalization of Church-style λμ-calculus by CPS-translation. Firstly, our method is still effective for the correction of Proposition 5.4 of [2]. The proposition claims that for any Curry-style λμ-term u, which is not necessarily typable, if u is strongly normalizable, then u is strongly normalizable too. But its proof does not work, since Proposition 5.1 (i) of [2] is false because of erasing-continuation. Our method proves the similar result for the Curry-style λμ-calculus by Propositions 4.3 and 4.12 of [1].