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

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

%proving not_int_if_between_successive_int

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