Development Separation in Lambda-Calculus

We present a proof technique in λ-calculus that can facilitate inductive reasoning on λ-terms by separating certain β-developments from other β-reductions. We give proofs based on this technique for several fundamental theorems in λ-calculus such as the Church-Rosser theorem, the standardization theorem, the conservation theorem and the normalization theorem. The appealing features of these proofs lie in their inductive styles and perspicuities.