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This research was partially supported by Grant-in-Aid for co-operative Research (No. 61302010), The Ministry of Education, Science and Culture
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Yukami, T. A theorem on generalizations of proofs. Arch Math Logic 30, 139–153 (1990). https://doi.org/10.1007/BF01621467
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DOI: https://doi.org/10.1007/BF01621467