Proof of proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero theorem

import proveit
theory = proveit.Theory() # the theorem's theory

%proving rational_nonzero_within_real_nonzero

With these allowed/disallowed theorem/theory presumptions (e.g., to avoid circular dependencies), we begin our proof of
rational_nonzero_within_real_nonzero:
(see dependencies)