Cut-elimination for a logic with definitions and induction. McDowell, R. & Miller, D. Theoretical Computer Science, 232:91–119, 2000.
doi  bibtex   
@article{mcdowell00tcs,
  author = {Raymond McDowell and Dale Miller},
  title = {Cut-elimination for a logic with definitions and
                 induction},
  journal = {Theoretical Computer Science},
  volume = {232},
  pages = {91--119},
  year = {2000},
  doi = {10.1016/S0304-3975(99)00171-1}
}

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