import proveit
theory = proveit.Theory() # the theorem's theory
from proveit import defaults, a, x, y
from proveit.logic import Equals, InSet
from proveit.numbers import Add, Neg, subtract, Real, zero
from proveit.numbers.rounding import Floor
from proveit.numbers.rounding import floor_of_x_less_eq_x
%proving real_minus_floor_lower_bound
%qed