Proof of proveit.numbers.summation.weak_summation_from_summands_bound theorem

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

%proving weak_summation_from_summands_bound

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