Proof of proveit.statistics.prob_of_disjoint_events_is_prob_sum theorem

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

%proving prob_of_disjoint_events_is_prob_sum

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