Proof of proveit.numbers.number_sets.rational_numbers.rational_pos_within_rational_nonneg theorem

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

%proving rational_pos_within_rational_nonneg

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