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We show that there is a purely proof-theoretic proof of the Rasiowa–Harrop disjunction property for the full intuitionistic propositional calculus ( $$\mathbf {IPC}$$ IPC ), via natural deduction, in which commuting conversions are not needed. Such proof is based on a sound and faithful embedding of $$\mathbf {IPC}$$ IPC into an atomic polymorphic system. This result strengthens a...
It is known that there is a sound and faithful translation of the full intuitionistic propositional calculus into the atomic polymorphic system Fat, a predicative calculus with only two connectives: the conditional and the second-order universal quantifier. The faithfulness of the embedding was established quite recently via a model-theoretic argument based in Kripke structures. In this paper we...
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