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._modabs_in_full_domain_simp
2	instantiation	4, 5, 85, 6, 7	,  ⊢
	: , : , :
3	instantiation	8, 9	,  ⊢
	:
4	theorem		⊢
	proveit.numbers.number_sets.integers.in_interval
5	instantiation	84, 53, 125	⊢
	: , :
6	instantiation	129, 10, 34	,  ⊢
	: , : , :
7	instantiation	11, 12, 13	,  ⊢
	: , :
8	theorem		⊢
	proveit.numbers.absolute_value.abs_non_neg_elim
9	instantiation	14, 19	,  ⊢
	: , :
10	instantiation	72, 33, 85	⊢
	: , :
11	theorem		⊢
	proveit.logic.booleans.conjunction.and_if_both
12	instantiation	14, 15	,  ⊢
	: , :
13	instantiation	16, 33, 85, 34	,  ⊢
	: , : , :
14	theorem		⊢
	proveit.numbers.ordering.relax_less
15	instantiation	17, 18, 19	,  ⊢
	: , : , :
16	theorem		⊢
	proveit.numbers.number_sets.integers.interval_upper_bound
17	theorem		⊢
	proveit.numbers.ordering.transitivity_less_eq_less
18	instantiation	20, 35, 81, 21, 22, 23*, 24*	⊢
	: , : , :
19	instantiation	60, 25, 26	,  ⊢
	: , : , :
20	theorem		⊢
	proveit.numbers.addition.weak_bound_via_left_term_bound
21	instantiation	109, 110, 100	⊢
	: , : , :
22	instantiation	27, 100	⊢
	:
23	instantiation	87, 68, 28	⊢
	: , :
24	instantiation	36, 29, 30	⊢
	: , : , :
25	instantiation	31, 32	⊢
	:
26	instantiation	73, 33, 85, 34	,  ⊢
	: , : , :
27	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.natural_pos_lower_bound
28	instantiation	129, 103, 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, 95	⊢
	: , :
33	instantiation	84, 51, 125	⊢
	: , :
34	assumption		⊢
35	instantiation	129, 113, 44	⊢
	: , : , :
36	axiom		⊢
	proveit.logic.equality.equals_transitivity
37	instantiation	79, 54	⊢
	: , : , :
38	instantiation	79, 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	129, 120, 53	⊢
	: , : , :
45	instantiation	79, 54	⊢
	: , : , :
46	theorem		⊢
	proveit.numbers.multiplication.mult_complex_closure_bin
47	instantiation	55, 68, 56, 57	⊢
	: , :
48	instantiation	129, 103, 58	⊢
	: , : , :
49	axiom		⊢
	proveit.logic.equality.equals_reflexivity
50	theorem		⊢
	proveit.numbers.number_sets.integers.pos_int_is_natural_pos
51	instantiation	129, 59, 75	⊢
	: , : , :
52	instantiation	60, 61, 62	⊢
	: , : , :
53	instantiation	124, 85	⊢
	:
54	instantiation	63, 64, 65, 66	⊢
	: , : , : , :
55	theorem		⊢
	proveit.numbers.division.div_complex_closure
56	instantiation	67, 91, 68	⊢
	: , :
57	instantiation	69, 92, 70	⊢
	: , : , :
58	instantiation	129, 113, 71	⊢
	: , : , :
59	instantiation	72, 125, 74	⊢
	: , :
60	theorem		⊢
	proveit.numbers.ordering.transitivity_less_less_eq
61	theorem		⊢
	proveit.numbers.numerals.decimals.less_0_1
62	instantiation	73, 125, 74, 75	⊢
	: , : , :
63	theorem		⊢
	proveit.logic.equality.four_chain_transitivity
64	instantiation	79, 76	⊢
	: , : , :
65	instantiation	77, 78	⊢
	: , :
66	instantiation	79, 80	⊢
	: , : , :
67	theorem		⊢
	proveit.numbers.exponentiation.exp_complex_closure
68	instantiation	129, 103, 81	⊢
	: , : , :
69	theorem		⊢
	proveit.logic.equality.sub_left_side_into
70	instantiation	82, 91	⊢
	:
71	instantiation	129, 120, 83	⊢
	: , : , :
72	theorem		⊢
	proveit.numbers.number_sets.integers.int_interval_within_int
73	theorem		⊢
	proveit.numbers.number_sets.integers.interval_lower_bound
74	instantiation	84, 85, 86	⊢
	: , :
75	assumption		⊢
76	instantiation	87, 88, 89	⊢
	: , :
77	theorem		⊢
	proveit.logic.equality.equals_reversal
78	instantiation	90, 91, 102, 101, 92	⊢
	: , : , :
79	axiom		⊢
	proveit.logic.equality.substitution
80	instantiation	93, 94, 95	⊢
	: , :
81	instantiation	129, 113, 96	⊢
	: , : , :
82	theorem		⊢
	proveit.numbers.exponentiation.complex_x_to_first_power_is_x
83	instantiation	97, 121, 98	⊢
	: , :
84	theorem		⊢
	proveit.numbers.addition.add_int_closure_bin
85	instantiation	129, 99, 100	⊢
	: , : , :
86	instantiation	124, 121	⊢
	:
87	theorem		⊢
	proveit.numbers.addition.commutation
88	instantiation	129, 103, 101	⊢
	: , : , :
89	instantiation	129, 103, 102	⊢
	: , : , :
90	theorem		⊢
	proveit.numbers.exponentiation.product_of_real_powers
91	instantiation	129, 103, 104	⊢
	: , : , :
92	instantiation	105, 128	⊢
	:
93	theorem		⊢
	proveit.numbers.exponentiation.neg_power_as_div
94	instantiation	129, 106, 107	⊢
	: , : , :
95	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
96	instantiation	129, 120, 125	⊢
	: , : , :
97	theorem		⊢
	proveit.numbers.exponentiation.exp_int_closure
98	instantiation	129, 108, 111	⊢
	: , : , :
99	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_int
100	theorem		⊢
	proveit.physics.quantum.QPE._two_pow_t_minus_one_is_nat_pos
101	instantiation	109, 110, 111	⊢
	: , : , :
102	instantiation	129, 113, 112	⊢
	: , : , :
103	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
104	instantiation	129, 113, 114	⊢
	: , : , :
105	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos
106	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero
107	instantiation	129, 115, 116	⊢
	: , : , :
108	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nat_pos_within_nat
109	theorem		⊢
	proveit.logic.sets.inclusion.unfold_subset_eq
110	instantiation	117, 118	⊢
	: , :
111	axiom		⊢
	proveit.physics.quantum.QPE._t_in_natural_pos
112	instantiation	129, 120, 119	⊢
	: , : , :
113	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
114	instantiation	129, 120, 121	⊢
	: , : , :
115	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero
116	instantiation	129, 122, 123	⊢
	: , : , :
117	theorem		⊢
	proveit.logic.sets.inclusion.relax_proper_subset
118	theorem		⊢
	proveit.numbers.number_sets.real_numbers.nat_pos_within_real
119	instantiation	124, 125	⊢
	:
120	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
121	instantiation	129, 130, 126	⊢
	: , : , :
122	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
123	instantiation	129, 127, 128	⊢
	: , : , :
124	theorem		⊢
	proveit.numbers.negation.int_closure
125	instantiation	129, 130, 131	⊢
	: , : , :
126	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
127	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
128	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
129	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
130	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
131	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
*equality replacement requirements