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.physics.quantum.QPE._alpha_sqrd_upper_bound
2	instantiation	4, 5, 81, 11, 6	,  ⊢
	: , : , :
3	instantiation	101, 7	,  ⊢
	:
4	theorem		⊢
	proveit.numbers.number_sets.integers.in_interval
5	instantiation	80, 52, 120	⊢
	: , :
6	instantiation	8, 9, 10	,  ⊢
	: , :
7	instantiation	49, 11, 18	,  ⊢
	:
8	theorem		⊢
	proveit.logic.booleans.conjunction.and_if_both
9	instantiation	12, 13	,  ⊢
	: , :
10	instantiation	14, 32, 81, 33	,  ⊢
	: , : , :
11	instantiation	124, 15, 33	,  ⊢
	: , : , :
12	theorem		⊢
	proveit.numbers.ordering.relax_less
13	instantiation	16, 17, 18	,  ⊢
	: , : , :
14	theorem		⊢
	proveit.numbers.number_sets.integers.interval_upper_bound
15	instantiation	70, 32, 81	⊢
	: , :
16	theorem		⊢
	proveit.numbers.ordering.transitivity_less_eq_less
17	instantiation	19, 34, 108, 20, 21, 22*, 23*	⊢
	: , : , :
18	instantiation	59, 24, 25	,  ⊢
	: , : , :
19	theorem		⊢
	proveit.numbers.addition.weak_bound_via_left_term_bound
20	instantiation	104, 105, 94	⊢
	: , : , :
21	instantiation	26, 94	⊢
	:
22	instantiation	83, 98, 27	⊢
	: , :
23	instantiation	35, 28, 29	⊢
	: , : , :
24	instantiation	30, 31	⊢
	:
25	instantiation	71, 32, 81, 33	,  ⊢
	: , : , :
26	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.natural_pos_lower_bound
27	instantiation	124, 107, 34	⊢
	: , : , :
28	instantiation	35, 36, 37	⊢
	: , : , :
29	instantiation	38, 39, 40	⊢
	: , :
30	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.natural_pos_is_pos
31	instantiation	41, 42, 92	⊢
	: , :
32	instantiation	80, 50, 120	⊢
	: , :
33	assumption		⊢
34	instantiation	124, 114, 43	⊢
	: , : , :
35	axiom		⊢
	proveit.logic.equality.equals_transitivity
36	instantiation	77, 53	⊢
	: , : , :
37	instantiation	77, 44	⊢
	: , : , :
38	theorem		⊢
	proveit.numbers.addition.subtraction.add_cancel_basic
39	instantiation	45, 46, 47	⊢
	: , :
40	instantiation	48	⊢
	:
41	theorem		⊢
	proveit.numbers.addition.add_nat_pos_closure_bin
42	instantiation	49, 50, 51	⊢
	:
43	instantiation	124, 119, 52	⊢
	: , : , :
44	instantiation	77, 53	⊢
	: , : , :
45	theorem		⊢
	proveit.numbers.multiplication.mult_complex_closure_bin
46	instantiation	54, 98, 55, 56	⊢
	: , :
47	instantiation	124, 107, 57	⊢
	: , : , :
48	axiom		⊢
	proveit.logic.equality.equals_reflexivity
49	theorem		⊢
	proveit.numbers.number_sets.integers.pos_int_is_natural_pos
50	instantiation	124, 58, 73	⊢
	: , : , :
51	instantiation	59, 60, 61	⊢
	: , : , :
52	instantiation	95, 81	⊢
	:
53	instantiation	62, 63, 64, 65	⊢
	: , : , : , :
54	theorem		⊢
	proveit.numbers.division.div_complex_closure
55	instantiation	66, 87, 98	⊢
	: , :
56	instantiation	67, 89, 68	⊢
	: , : , :
57	instantiation	104, 105, 69	⊢
	: , : , :
58	instantiation	70, 120, 72	⊢
	: , :
59	theorem		⊢
	proveit.numbers.ordering.transitivity_less_less_eq
60	theorem		⊢
	proveit.numbers.numerals.decimals.less_0_1
61	instantiation	71, 120, 72, 73	⊢
	: , : , :
62	theorem		⊢
	proveit.logic.equality.four_chain_transitivity
63	instantiation	77, 74	⊢
	: , : , :
64	instantiation	75, 76	⊢
	: , :
65	instantiation	77, 78	⊢
	: , : , :
66	theorem		⊢
	proveit.numbers.exponentiation.exp_complex_closure
67	theorem		⊢
	proveit.logic.equality.sub_left_side_into
68	instantiation	79, 87	⊢
	:
69	theorem		⊢
	proveit.physics.quantum.QPE._two_pow_t_is_nat_pos
70	theorem		⊢
	proveit.numbers.number_sets.integers.int_interval_within_int
71	theorem		⊢
	proveit.numbers.number_sets.integers.interval_lower_bound
72	instantiation	80, 81, 82	⊢
	: , :
73	assumption		⊢
74	instantiation	83, 84, 85	⊢
	: , :
75	theorem		⊢
	proveit.logic.equality.equals_reversal
76	instantiation	86, 87, 88, 96, 89	⊢
	: , : , :
77	axiom		⊢
	proveit.logic.equality.substitution
78	instantiation	90, 91, 92	⊢
	: , :
79	theorem		⊢
	proveit.numbers.exponentiation.complex_x_to_first_power_is_x
80	theorem		⊢
	proveit.numbers.addition.add_int_closure_bin
81	instantiation	124, 93, 94	⊢
	: , : , :
82	instantiation	95, 116	⊢
	:
83	theorem		⊢
	proveit.numbers.addition.commutation
84	instantiation	124, 107, 96	⊢
	: , : , :
85	instantiation	97, 98	⊢
	:
86	theorem		⊢
	proveit.numbers.exponentiation.product_of_real_powers
87	instantiation	124, 107, 99	⊢
	: , : , :
88	instantiation	100, 108	⊢
	:
89	instantiation	101, 123	⊢
	:
90	theorem		⊢
	proveit.numbers.exponentiation.neg_power_as_div
91	instantiation	124, 102, 103	⊢
	: , : , :
92	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
93	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_int
94	theorem		⊢
	proveit.physics.quantum.QPE._two_pow_t_minus_one_is_nat_pos
95	theorem		⊢
	proveit.numbers.negation.int_closure
96	instantiation	104, 105, 106	⊢
	: , : , :
97	theorem		⊢
	proveit.numbers.negation.complex_closure
98	instantiation	124, 107, 108	⊢
	: , : , :
99	instantiation	124, 114, 109	⊢
	: , : , :
100	theorem		⊢
	proveit.numbers.negation.real_closure
101	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos
102	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero
103	instantiation	124, 110, 111	⊢
	: , : , :
104	theorem		⊢
	proveit.logic.sets.inclusion.unfold_subset_eq
105	instantiation	112, 113	⊢
	: , :
106	axiom		⊢
	proveit.physics.quantum.QPE._t_in_natural_pos
107	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
108	instantiation	124, 114, 115	⊢
	: , : , :
109	instantiation	124, 119, 116	⊢
	: , : , :
110	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero
111	instantiation	124, 117, 118	⊢
	: , : , :
112	theorem		⊢
	proveit.logic.sets.inclusion.relax_proper_subset
113	theorem		⊢
	proveit.numbers.number_sets.real_numbers.nat_pos_within_real
114	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
115	instantiation	124, 119, 120	⊢
	: , : , :
116	instantiation	124, 125, 121	⊢
	: , : , :
117	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
118	instantiation	124, 122, 123	⊢
	: , : , :
119	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
120	instantiation	124, 125, 126	⊢
	: , : , :
121	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
122	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
123	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
124	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
125	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
126	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
*equality replacement requirements