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

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

%proving bounds_for_real_not_in_interval_oo

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