User blog comment:Upquark11111/Ordinals in the Calculus of Constructions/@comment-11227630-20171221035436

Another addition of naturals: $$\lambda a:\text{nat}.\lambda b:\text{nat}.\lambda A:*.\lambda f:A\rightarrow A.\lambda x:A.a\ A\ f\ (b\ A\ f\ x)$$ (seems still very complex)

Another multiplication of naturals: $$\lambda a:\text{nat}.\lambda b:\text{nat}.\lambda A:*.\lambda f:A\rightarrow A.a\ A\ (b\ A\ f)$$ (this is simpler)

An exponentiation of naturals: $$\lambda a:\text{nat}.\lambda b:\text{nat}.\lambda A:*.b\ (A\rightarrow A)\ (a\ A)$$ (also simpler)