Roel de Vrijer

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Barendregt’s Lemma in its original form is a statement on Combinatory Logic that holds also for the lambda calculus and gives important insight into the syntactic interplay between substitution and reduction. Its origin lies in undefinablity proofs, but there are other applications as well. It is connected to the so-called Square Brackets Lemma, introduced(More)
Proof terms in term rewriting are a representation means for reduction sequences, and more in general for contraction activity, allowing to distinguish e.g. simultaneous from sequential reduction. Proof terms for finitary, first-order, left-linear term rewriting are described in [15], ch. 8. In a previous work [12] we defined an extension of the finitary(More)
Proof. This is an easy consequence of some properties of ordinals. Namely, β < Σ i<ω αi implies that the set {k < ω / β < α0 + . . . + αk} is nonempty; we take n as the minimum of this set. Then α0 + . . . + αn−1 ≤ β < (α0 + . . . + αn−1) + αn. Basic properties of ordinals entail the existence and uniqueness of an ordinal γ verifying (α0 + . . .+αn−1) + γ =(More)
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