 The negative translation of classical into intuitionistic number theory is even simpler, since prime formulas of intuitionistic arithmetic are stable. Thus \(g(s=t)\) can be taken to be \(s=t,\) and the other clauses are unchanged. The negative translation of each instance of the schema of mathematical induction is an instance of the same schema, and the other nonlogical axioms of arithmetic are their own negative translations, so: