Show the Proof

import proveit
# Automation is not needed when only showing a stored proof:
proveit.defaults.automation = False # This will speed things up.
proveit.defaults.inline_pngs = False # Makes files smaller.
%show_proof

	step type	requirements	statement
0	instantiation	1, 2, 3, 4, 5	⊢
	: , : , :
1	theorem		⊢
	proveit.numbers.number_sets.real_numbers.in_IntervalCO
2	theorem		⊢
	proveit.numbers.number_sets.real_numbers.zero_is_real
3	instantiation	21, 19, 6	⊢
	: , : , :
4	instantiation	7, 25, 8	⊢
	: , :
5	instantiation	9, 10, 11	⊢
	: , :
6	instantiation	21, 22, 12	⊢
	: , : , :
7	theorem		⊢
	proveit.numbers.addition.add_real_closure_bin
8	instantiation	13, 14	⊢
	:
9	theorem		⊢
	proveit.logic.booleans.conjunction.and_if_both
10	instantiation	15, 25	⊢
	:
11	instantiation	16, 25	⊢
	:
12	instantiation	21, 17, 18	⊢
	: , : , :
13	theorem		⊢
	proveit.numbers.negation.real_closure
14	instantiation	21, 19, 20	⊢
	: , : , :
15	theorem		⊢
	proveit.numbers.rounding.real_minus_floor_lower_bound
16	theorem		⊢
	proveit.numbers.rounding.real_minus_floor_upper_bound
17	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
18	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
19	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
20	instantiation	21, 22, 23	⊢
	: , : , :
21	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
22	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
23	instantiation	24, 25	⊢
	:
24	axiom		⊢
	proveit.numbers.rounding.floor_is_an_int
25	assumption		⊢