Axioms for the theory of proveit.numbers.exponentiation

import proveit
# Prepare this notebook for defining the axioms of a theory:
%axioms_notebook # Keep this at the top following 'import proveit'.

from proveit import ExprRange
from proveit import i, n, x
from proveit.logic import Forall, Equals
from proveit.numbers import one, Natural, Complex
from proveit.numbers import Mult, Exp

%begin axioms

Defining axioms for theory 'proveit.numbers.exponentiation'
Subsequent end-of-cell assignments will define axioms
%end_axioms will finalize the definitions

nat_exp_def = Forall((x, n), Equals(Exp(x, n), Mult(ExprRange(i, x, one, n))),
                     domains=(Complex, Natural))

nat_exp_def:

%end axioms

These axioms may now be imported from the theory package: proveit.numbers.exponentiation