Abstract
This paper contains new proofs of the following two theorems of the untyped extensional ?-calculus: the Curry theorem stating that any ?-term has a β?-normal form if and only if it has a β-normal form and the normalization theorem for β?-reduction. The proposed approach is based on the following well-known results: the postponement theorem of ?-reduction and the strong normalization property of ?-reduction that allow one to naturally extend some propositions from the usual ?-calculus to the extensional case.
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