A formalised first-order confluence proof for the λ-calculus using one-sorted variable names

We present the titular proof development that has been verified in Isabelle/HOL. As a first, the proof is conducted exclusively by the primitive proof principles of the standard syntax and of the considered reduction relations: the naive way, so to speak. Curiously, the Barendregt Variable Convention takes on a central technical role in the proof. We also show: (i) that our presentation of the λ-calculus coincides with Curry’s and Hindley’s when terms are considered equal up to α-equivalence and (ii) that the confluence properties of all considered systems are equivalent.