We define a generic notion of cut that applies to many first-order theories. We prove a generic cut elimination theorem showing that the cut elimination property holds for all theories having a so-called pre-model. As a corollary, we retrieve cut elimination for several axiomatic theories, including Church’s simple type theory.
Gilles Dowek. Benjamin Werner. "Proof normalization modulo." J. Symbolic Logic 68 (4) 1289 - 1316, December 2003. https://doi.org/10.2178/jsl/1067620188