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	generalization	1	⊢
1	instantiation	2, 3, 4	,  ⊢
	:
2	theorem		⊢
	proveit.physics.quantum.QPE._alpha_sqrd_upper_bound
3	instantiation	5, 6, 82, 12, 7	,  ⊢
	: , : , :
4	instantiation	102, 8	,  ⊢
	:
5	theorem		⊢
	proveit.numbers.number_sets.integers.in_interval
6	instantiation	81, 53, 121	⊢
	: , :
7	instantiation	9, 10, 11	,  ⊢
	: , :
8	instantiation	50, 12, 19	,  ⊢
	:
9	theorem		⊢
	proveit.logic.booleans.conjunction.and_if_both
10	instantiation	13, 14	,  ⊢
	: , :
11	instantiation	15, 33, 82, 34	,  ⊢
	: , : , :
12	instantiation	125, 16, 34	,  ⊢
	: , : , :
13	theorem		⊢
	proveit.numbers.ordering.relax_less
14	instantiation	17, 18, 19	,  ⊢
	: , : , :
15	theorem		⊢
	proveit.numbers.number_sets.integers.interval_upper_bound
16	instantiation	71, 33, 82	⊢
	: , :
17	theorem		⊢
	proveit.numbers.ordering.transitivity_less_eq_less
18	instantiation	20, 35, 109, 21, 22, 23*, 24*	⊢
	: , : , :
19	instantiation	60, 25, 26	,  ⊢
	: , : , :
20	theorem		⊢
	proveit.numbers.addition.weak_bound_via_left_term_bound
21	instantiation	105, 106, 95	⊢
	: , : , :
22	instantiation	27, 95	⊢
	:
23	instantiation	84, 99, 28	⊢
	: , :
24	instantiation	36, 29, 30	⊢
	: , : , :
25	instantiation	31, 32	⊢
	:
26	instantiation	72, 33, 82, 34	,  ⊢
	: , : , :
27	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.natural_pos_lower_bound
28	instantiation	125, 108, 35	⊢
	: , : , :
29	instantiation	36, 37, 38	⊢
	: , : , :
30	instantiation	39, 40, 41	⊢
	: , :
31	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.natural_pos_is_pos
32	instantiation	42, 43, 93	⊢
	: , :
33	instantiation	81, 51, 121	⊢
	: , :
34	assumption		⊢
35	instantiation	125, 115, 44	⊢
	: , : , :
36	axiom		⊢
	proveit.logic.equality.equals_transitivity
37	instantiation	78, 54	⊢
	: , : , :
38	instantiation	78, 45	⊢
	: , : , :
39	theorem		⊢
	proveit.numbers.addition.subtraction.add_cancel_basic
40	instantiation	46, 47, 48	⊢
	: , :
41	instantiation	49	⊢
	:
42	theorem		⊢
	proveit.numbers.addition.add_nat_pos_closure_bin
43	instantiation	50, 51, 52	⊢
	:
44	instantiation	125, 120, 53	⊢
	: , : , :
45	instantiation	78, 54	⊢
	: , : , :
46	theorem		⊢
	proveit.numbers.multiplication.mult_complex_closure_bin
47	instantiation	55, 99, 56, 57	⊢
	: , :
48	instantiation	125, 108, 58	⊢
	: , : , :
49	axiom		⊢
	proveit.logic.equality.equals_reflexivity
50	theorem		⊢
	proveit.numbers.number_sets.integers.pos_int_is_natural_pos
51	instantiation	125, 59, 74	⊢
	: , : , :
52	instantiation	60, 61, 62	⊢
	: , : , :
53	instantiation	96, 82	⊢
	:
54	instantiation	63, 64, 65, 66	⊢
	: , : , : , :
55	theorem		⊢
	proveit.numbers.division.div_complex_closure
56	instantiation	67, 88, 99	⊢
	: , :
57	instantiation	68, 90, 69	⊢
	: , : , :
58	instantiation	105, 106, 70	⊢
	: , : , :
59	instantiation	71, 121, 73	⊢
	: , :
60	theorem		⊢
	proveit.numbers.ordering.transitivity_less_less_eq
61	theorem		⊢
	proveit.numbers.numerals.decimals.less_0_1
62	instantiation	72, 121, 73, 74	⊢
	: , : , :
63	theorem		⊢
	proveit.logic.equality.four_chain_transitivity
64	instantiation	78, 75	⊢
	: , : , :
65	instantiation	76, 77	⊢
	: , :
66	instantiation	78, 79	⊢
	: , : , :
67	theorem		⊢
	proveit.numbers.exponentiation.exp_complex_closure
68	theorem		⊢
	proveit.logic.equality.sub_left_side_into
69	instantiation	80, 88	⊢
	:
70	theorem		⊢
	proveit.physics.quantum.QPE._two_pow_t_is_nat_pos
71	theorem		⊢
	proveit.numbers.number_sets.integers.int_interval_within_int
72	theorem		⊢
	proveit.numbers.number_sets.integers.interval_lower_bound
73	instantiation	81, 82, 83	⊢
	: , :
74	assumption		⊢
75	instantiation	84, 85, 86	⊢
	: , :
76	theorem		⊢
	proveit.logic.equality.equals_reversal
77	instantiation	87, 88, 89, 97, 90	⊢
	: , : , :
78	axiom		⊢
	proveit.logic.equality.substitution
79	instantiation	91, 92, 93	⊢
	: , :
80	theorem		⊢
	proveit.numbers.exponentiation.complex_x_to_first_power_is_x
81	theorem		⊢
	proveit.numbers.addition.add_int_closure_bin
82	instantiation	125, 94, 95	⊢
	: , : , :
83	instantiation	96, 117	⊢
	:
84	theorem		⊢
	proveit.numbers.addition.commutation
85	instantiation	125, 108, 97	⊢
	: , : , :
86	instantiation	98, 99	⊢
	:
87	theorem		⊢
	proveit.numbers.exponentiation.product_of_real_powers
88	instantiation	125, 108, 100	⊢
	: , : , :
89	instantiation	101, 109	⊢
	:
90	instantiation	102, 124	⊢
	:
91	theorem		⊢
	proveit.numbers.exponentiation.neg_power_as_div
92	instantiation	125, 103, 104	⊢
	: , : , :
93	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
94	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_int
95	theorem		⊢
	proveit.physics.quantum.QPE._two_pow_t_minus_one_is_nat_pos
96	theorem		⊢
	proveit.numbers.negation.int_closure
97	instantiation	105, 106, 107	⊢
	: , : , :
98	theorem		⊢
	proveit.numbers.negation.complex_closure
99	instantiation	125, 108, 109	⊢
	: , : , :
100	instantiation	125, 115, 110	⊢
	: , : , :
101	theorem		⊢
	proveit.numbers.negation.real_closure
102	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos
103	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero
104	instantiation	125, 111, 112	⊢
	: , : , :
105	theorem		⊢
	proveit.logic.sets.inclusion.unfold_subset_eq
106	instantiation	113, 114	⊢
	: , :
107	axiom		⊢
	proveit.physics.quantum.QPE._t_in_natural_pos
108	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
109	instantiation	125, 115, 116	⊢
	: , : , :
110	instantiation	125, 120, 117	⊢
	: , : , :
111	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero
112	instantiation	125, 118, 119	⊢
	: , : , :
113	theorem		⊢
	proveit.logic.sets.inclusion.relax_proper_subset
114	theorem		⊢
	proveit.numbers.number_sets.real_numbers.nat_pos_within_real
115	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
116	instantiation	125, 120, 121	⊢
	: , : , :
117	instantiation	125, 126, 122	⊢
	: , : , :
118	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
119	instantiation	125, 123, 124	⊢
	: , : , :
120	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
121	instantiation	125, 126, 127	⊢
	: , : , :
122	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
123	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
124	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
125	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
126	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
127	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
*equality replacement requirements