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	theorem		⊢
	proveit.numbers.absolute_value.abs_complex_closure
2	instantiation	33, 94, 3	⊢
	: , : , :
3	instantiation	33, 4, 5	⊢
	: , : , :
4	instantiation	77, 6, 34	⊢
	: , : , :
5	instantiation	7, 143, 8	⊢
	: , :
6	modus ponens	9, 10	⊢
7	theorem		⊢
	proveit.numbers.modular.int_mod_elimination
8	instantiation	12, 13, 14, 135, 11	⊢
	: , : , :
9	theorem		⊢
	proveit.physics.quantum.QPE._alpha_ideal_case
10	instantiation	12, 13, 14, 27, 15	⊢
	: , : , :
11	instantiation	19, 16, 17	⊢
	: , :
12	theorem		⊢
	proveit.numbers.number_sets.integers.in_interval
13	theorem		⊢
	proveit.numbers.number_sets.integers.zero_is_int
14	instantiation	18, 137, 53	⊢
	: , :
15	instantiation	19, 20, 21	⊢
	: , :
16	instantiation	77, 20, 34	⊢
	: , : , :
17	instantiation	77, 21, 34	⊢
	: , : , :
18	theorem		⊢
	proveit.numbers.addition.add_int_closure_bin
19	theorem		⊢
	proveit.logic.booleans.conjunction.and_if_both
20	instantiation	22, 132, 45, 100, 23, 24, 25*	⊢
	: , : , :
21	instantiation	26, 27, 137, 53, 28, 29	⊢
	: , : , :
22	theorem		⊢
	proveit.numbers.multiplication.weak_bound_via_right_factor_bound
23	instantiation	30, 45, 109, 46	⊢
	: , : , :
24	instantiation	31, 37	⊢
	: , :
25	instantiation	32, 125	⊢
	:
26	theorem		⊢
	proveit.numbers.ordering.less_add_right_weak_int
27	instantiation	33, 135, 34	⊢
	: , : , :
28	instantiation	35, 132, 100, 109, 36, 37, 108*	⊢
	: , : , :
29	instantiation	38, 39, 40	⊢
	: , :
30	theorem		⊢
	proveit.numbers.number_sets.real_numbers.interval_co_lower_bound
31	theorem		⊢
	proveit.numbers.ordering.relax_less
32	theorem		⊢
	proveit.numbers.multiplication.mult_zero_right
33	theorem		⊢
	proveit.logic.equality.sub_left_side_into
34	instantiation	41, 132, 100, 111, 42, 43*	⊢
	: , : , :
35	theorem		⊢
	proveit.numbers.multiplication.strong_bound_via_right_factor_bound
36	instantiation	44, 45, 109, 46	⊢
	: , : , :
37	instantiation	47, 143	⊢
	:
38	theorem		⊢
	proveit.numbers.ordering.relax_equal_to_less_eq
39	instantiation	141, 120, 48	⊢
	: , : , :
40	instantiation	101	⊢
	:
41	theorem		⊢
	proveit.numbers.multiplication.left_mult_eq_real
42	instantiation	49, 50	⊢
	: , :
43	instantiation	77, 51, 52	⊢
	: , : , :
44	theorem		⊢
	proveit.numbers.number_sets.real_numbers.interval_co_upper_bound
45	theorem		⊢
	proveit.numbers.number_sets.real_numbers.zero_is_real
46	axiom		⊢
	proveit.physics.quantum.QPE._phase_in_interval
47	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.natural_pos_is_pos
48	instantiation	141, 136, 53	⊢
	: , : , :
49	theorem		⊢
	proveit.logic.equality.equals_reversal
50	instantiation	54, 121, 65, 55, 66, 56*, 57*	⊢
	: , : , :
51	instantiation	77, 58, 59	⊢
	: , : , :
52	instantiation	60, 61, 62, 63	⊢
	: , : , : , :
53	instantiation	64, 126	⊢
	:
54	theorem		⊢
	proveit.numbers.addition.right_add_eq_rational
55	instantiation	77, 65, 66	⊢
	: , : , :
56	instantiation	67, 99	⊢
	:
57	instantiation	105, 68, 69	⊢
	: , : , :
58	instantiation	70, 94, 95, 71, 72	⊢
	: , : , : , : , :
59	instantiation	105, 73, 74	⊢
	: , : , :
60	theorem		⊢
	proveit.logic.equality.four_chain_transitivity
61	instantiation	115, 75	⊢
	: , : , :
62	instantiation	115, 76	⊢
	: , : , :
63	instantiation	124, 95	⊢
	:
64	theorem		⊢
	proveit.numbers.negation.int_closure
65	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.zero_is_rational
66	instantiation	77, 78, 79	⊢
	: , : , :
67	theorem		⊢
	proveit.numbers.addition.elim_zero_left
68	instantiation	80, 81, 82, 134, 83, 84, 87, 85, 99	⊢
	: , : , : , : , : , :
69	instantiation	86, 99, 87, 88	⊢
	: , : , :
70	theorem		⊢
	proveit.numbers.division.mult_frac_cancel_numer_left
71	instantiation	141, 90, 89	⊢
	: , : , :
72	instantiation	141, 90, 91	⊢
	: , : , :
73	instantiation	115, 92	⊢
	: , : , :
74	instantiation	115, 93	⊢
	: , : , :
75	instantiation	117, 94	⊢
	:
76	instantiation	117, 95	⊢
	:
77	theorem		⊢
	proveit.logic.equality.sub_right_side_into
78	instantiation	96, 135	⊢
	:
79	assumption		⊢
80	theorem		⊢
	proveit.numbers.addition.disassociation
81	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
82	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
83	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
84	instantiation	97	⊢
	: , :
85	instantiation	98, 99	⊢
	:
86	theorem		⊢
	proveit.numbers.addition.subtraction.add_cancel_triple_32
87	instantiation	141, 131, 100	⊢
	: , : , :
88	instantiation	101	⊢
	:
89	instantiation	141, 103, 102	⊢
	: , : , :
90	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero
91	instantiation	141, 103, 104	⊢
	: , : , :
92	instantiation	105, 106, 107	⊢
	: , : , :
93	instantiation	115, 108	⊢
	: , : , :
94	instantiation	141, 131, 109	⊢
	: , : , :
95	instantiation	141, 131, 110	⊢
	: , : , :
96	axiom		⊢
	proveit.physics.quantum.QPE._delta_b_def
97	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
98	theorem		⊢
	proveit.numbers.negation.complex_closure
99	instantiation	141, 131, 111	⊢
	: , : , :
100	theorem		⊢
	proveit.physics.quantum.QPE._phase_is_real
101	axiom		⊢
	proveit.logic.equality.equals_reflexivity
102	instantiation	141, 113, 112	⊢
	: , : , :
103	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero
104	instantiation	141, 113, 114	⊢
	: , : , :
105	axiom		⊢
	proveit.logic.equality.equals_transitivity
106	instantiation	115, 116	⊢
	: , : , :
107	instantiation	117, 125	⊢
	:
108	instantiation	118, 125	⊢
	:
109	instantiation	141, 120, 119	⊢
	: , : , :
110	instantiation	141, 120, 128	⊢
	: , : , :
111	instantiation	141, 120, 121	⊢
	: , : , :
112	instantiation	141, 122, 143	⊢
	: , : , :
113	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
114	instantiation	141, 122, 123	⊢
	: , : , :
115	axiom		⊢
	proveit.logic.equality.substitution
116	instantiation	124, 125	⊢
	:
117	theorem		⊢
	proveit.numbers.division.frac_one_denom
118	theorem		⊢
	proveit.numbers.multiplication.elim_one_right
119	instantiation	141, 136, 126	⊢
	: , : , :
120	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
121	instantiation	127, 128, 129, 130	⊢
	: , :
122	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
123	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
124	theorem		⊢
	proveit.numbers.multiplication.elim_one_left
125	instantiation	141, 131, 132	⊢
	: , : , :
126	instantiation	141, 133, 134	⊢
	: , : , :
127	theorem		⊢
	proveit.numbers.division.div_rational_closure
128	instantiation	141, 136, 135	⊢
	: , : , :
129	instantiation	141, 136, 137	⊢
	: , : , :
130	instantiation	138, 143	⊢
	:
131	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
132	instantiation	139, 140, 143	⊢
	: , : , :
133	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
134	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
135	theorem		⊢
	proveit.physics.quantum.QPE._best_round_is_int
136	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
137	instantiation	141, 142, 143	⊢
	: , : , :
138	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos
139	theorem		⊢
	proveit.logic.sets.inclusion.unfold_subset_eq
140	instantiation	144, 145	⊢
	: , :
141	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
142	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_int
143	theorem		⊢
	proveit.physics.quantum.QPE._two_pow_t_is_nat_pos
144	theorem		⊢
	proveit.logic.sets.inclusion.relax_proper_subset
145	theorem		⊢
	proveit.numbers.number_sets.real_numbers.nat_pos_within_real
*equality replacement requirements