But type theory does not require a prior definition of the naturals.

First, the question requires a definition of failure.

They require a precise definition of harm to national security before material can be withheld.

Driving a single strategy requires a single definition; a common language.

Such an approach requires a structural definition of finiteness that does not depend on natural numbers.

In pre-standard C++, all static data members required a definition outside of their class.

Nevertheless, the wording of the 1998 C++ standard still required a definition if the member was used in the program.

Turning the schools around will require fundamental changes and a new definition of what the public schools are supposed to be.

In any case, we shall require a fuller definition.

Most of all, it requires a definition of its current goals.