Statman\u27s 1-Section Theorem [17] is an important but little-known result in the model theory of the simply-typed λ-calculus. The λ-Section Theorem states a necessary and sufficient condition on models of the simply-typed λ-calculus for determining whether βη-equational reasoning is complete for proving equations that hold in a model. We review the statement of the theorem, give a detailed proof, and discuss its significance
