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	⊢
	: , : , :
1	theorem		⊢
	proveit.logic.equality.sub_left_side_into
2	instantiation	4, 26, 5, 6, 7	⊢
	: , : , :
3	axiom		⊢
	proveit.physics.quantum.QPE._best_floor_def
4	theorem		⊢
	proveit.numbers.number_sets.integers.in_interval
5	instantiation	8, 52, 9	⊢
	: , :
6	instantiation	10, 19	⊢
	:
7	instantiation	11, 12, 13	⊢
	: , :
8	theorem		⊢
	proveit.numbers.addition.add_int_closure_bin
9	instantiation	14, 46	⊢
	:
10	axiom		⊢
	proveit.numbers.rounding.floor_is_an_int
11	theorem		⊢
	proveit.logic.booleans.conjunction.and_if_both
12	instantiation	15, 37, 19, 16, 17*	⊢
	: , :
13	instantiation	18, 19, 52, 20	⊢
	: , :
14	theorem		⊢
	proveit.numbers.negation.int_closure
15	theorem		⊢
	proveit.numbers.rounding.floor_increasing_less_eq
16	instantiation	21, 45, 37, 29, 22, 23, 24*	⊢
	: , : , :
17	instantiation	25, 26	⊢
	:
18	theorem		⊢
	proveit.numbers.rounding.floor_of_real_below_int
19	instantiation	27, 45, 29	⊢
	: , :
20	instantiation	28, 45, 29, 38, 30, 34, 31*	⊢
	: , : , :
21	theorem		⊢
	proveit.numbers.multiplication.weak_bound_via_right_factor_bound
22	instantiation	32, 37, 38, 39	⊢
	: , : , :
23	instantiation	33, 34	⊢
	: , :
24	instantiation	35, 41	⊢
	:
25	theorem		⊢
	proveit.numbers.rounding.floor_of_integer
26	theorem		⊢
	proveit.numbers.number_sets.integers.zero_is_int
27	theorem		⊢
	proveit.numbers.multiplication.mult_real_closure_bin
28	theorem		⊢
	proveit.numbers.multiplication.strong_bound_via_right_factor_bound
29	theorem		⊢
	proveit.physics.quantum.QPE._phase_is_real
30	instantiation	36, 37, 38, 39	⊢
	: , : , :
31	instantiation	40, 41	⊢
	:
32	theorem		⊢
	proveit.numbers.number_sets.real_numbers.interval_co_lower_bound
33	theorem		⊢
	proveit.numbers.ordering.relax_less
34	instantiation	42, 55	⊢
	:
35	theorem		⊢
	proveit.numbers.multiplication.mult_zero_right
36	theorem		⊢
	proveit.numbers.number_sets.real_numbers.interval_co_upper_bound
37	theorem		⊢
	proveit.numbers.number_sets.real_numbers.zero_is_real
38	instantiation	53, 47, 43	⊢
	: , : , :
39	axiom		⊢
	proveit.physics.quantum.QPE._phase_in_interval
40	theorem		⊢
	proveit.numbers.multiplication.elim_one_right
41	instantiation	53, 44, 45	⊢
	: , : , :
42	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.natural_pos_is_pos
43	instantiation	53, 51, 46	⊢
	: , : , :
44	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
45	instantiation	53, 47, 48	⊢
	: , : , :
46	instantiation	53, 49, 50	⊢
	: , : , :
47	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
48	instantiation	53, 51, 52	⊢
	: , : , :
49	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
50	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
51	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
52	instantiation	53, 54, 55	⊢
	: , : , :
53	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
54	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_int
55	theorem		⊢
	proveit.physics.quantum.QPE._two_pow_t_is_nat_pos
*equality replacement requirements