2-or-more approximation for intuitionistic logic

The correspondence between natural-deduction proofs of propositional intuitionistic logic, usually written as (logic) derivations for judgments of the form Γ ` A, and well-typed terms in the simply-typed lambda-calculus, with (typing) derivations for the judgment Γ ` t : A, is not one-to-one. In typing judgments Γ ` t : A, the context Γ is a mapping from free variables to their type. In logic derivations, the context Γ is a set of hypotheses; there is no notion of variable, and at most one hypothesis of each type in the set. This means, for example, that the following logic derivation