This paper defines reduction on derivations (cut-elimination) in the Strict Intersection Type Assignment System of an earlier paper and shows a strong normalization result for this reduction. Using this result, new proofs are given for the approximation theorem and the characterization of normalizability of terms using intersection types.
"Cut-Elimination in the Strict Intersection Type Assignment System is Strongly Normalizing." Notre Dame J. Formal Logic 45 (1) 35 - 63, 2004. https://doi.org/10.1305/ndjfl/1094155278