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	,  ⊢
	: , : , :
1	axiom		⊢
	proveit.logic.equality.substitution
2	instantiation	3, 4, 5	,  ⊢
	: , :
3	theorem		⊢
	proveit.numbers.ordering.less_complement_is_greater_eq
4	instantiation	45, 24, 6	⊢
	: , : , :
5	instantiation	7, 8, 9, 10	⊢
	: , :
6	instantiation	45, 30, 11	⊢
	: , : , :
7	theorem		⊢
	proveit.numbers.modular.mod_abs_real_closure
8	instantiation	12, 13, 14	⊢
	: , :
9	instantiation	45, 24, 15	⊢
	: , : , :
10	instantiation	16, 42	⊢
	:
11	instantiation	45, 17, 18	⊢
	: , : , :
12	theorem		⊢
	proveit.numbers.addition.add_real_closure_bin
13	instantiation	45, 24, 19	⊢
	: , : , :
14	instantiation	20, 21	⊢
	:
15	instantiation	45, 30, 39	⊢
	: , : , :
16	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos
17	instantiation	34, 44, 22	⊢
	: , :
18	assumption		⊢
19	instantiation	45, 30, 23	⊢
	: , : , :
20	theorem		⊢
	proveit.numbers.negation.real_closure
21	instantiation	45, 24, 25	⊢
	: , : , :
22	instantiation	38, 26, 27	⊢
	: , :
23	instantiation	45, 28, 29	⊢
	: , : , :
24	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
25	instantiation	45, 30, 31	⊢
	: , : , :
26	instantiation	45, 41, 32	⊢
	: , : , :
27	instantiation	43, 33	⊢
	:
28	instantiation	34, 35, 36	⊢
	: , :
29	assumption		⊢
30	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
31	theorem		⊢
	proveit.physics.quantum.QPE._best_floor_is_int
32	theorem		⊢
	proveit.physics.quantum.QPE._two_pow_t_minus_one_is_nat_pos
33	instantiation	45, 46, 37	⊢
	: , : , :
34	theorem		⊢
	proveit.numbers.number_sets.integers.int_interval_within_int
35	theorem		⊢
	proveit.numbers.number_sets.integers.zero_is_int
36	instantiation	38, 39, 40	⊢
	: , :
37	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
38	theorem		⊢
	proveit.numbers.addition.add_int_closure_bin
39	instantiation	45, 41, 42	⊢
	: , : , :
40	instantiation	43, 44	⊢
	:
41	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_int
42	theorem		⊢
	proveit.physics.quantum.QPE._two_pow_t_is_nat_pos
43	theorem		⊢
	proveit.numbers.negation.int_closure
44	instantiation	45, 46, 47	⊢
	: , : , :
45	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
46	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
47	theorem		⊢
	proveit.numbers.numerals.decimals.nat1