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, 4, 5*	,  ⊢
	: , :
1	reference	73	⊢
2	reference	101	⊢
3	instantiation	46, 6, 7	⊢
	: , : , :
4	instantiation	8, 30, 25, 39, 9, 37	,  ⊢
	: , :
5	instantiation	17, 10, 11	,  ⊢
	: , : , :
6	instantiation	12, 13, 44	⊢
	: , :
7	instantiation	28, 110, 146, 156, 111, 14, 86, 75, 44	⊢
	: , : , : , : , : , :
8	theorem		⊢
	proveit.numbers.multiplication.mult_not_eq_zero
9	instantiation	157, 52, 15	⊢
	: , : , :
10	instantiation	65, 16	,  ⊢
	: , : , :
11	instantiation	17, 18, 19	⊢
	: , : , :
12	theorem		⊢
	proveit.numbers.multiplication.mult_complex_closure_bin
13	instantiation	157, 121, 20	⊢
	: , : , :
14	instantiation	21	⊢
	: , :
15	instantiation	157, 55, 22	⊢
	: , : , :
16	instantiation	23, 24, 25, 86, 75, 44, 87, 120, 76, 26, 27*, 77*	,  ⊢
	: , : , :
17	axiom		⊢
	proveit.logic.equality.equals_transitivity
18	instantiation	28, 156, 30, 110, 31, 111, 101, 32, 33, 34	⊢
	: , : , : , : , : , :
19	instantiation	29, 110, 30, 111, 31, 32, 33, 34	⊢
	: , : , : , :
20	instantiation	103, 119, 84	⊢
	: , :
21	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
22	instantiation	157, 143, 35	⊢
	: , : , :
23	theorem		⊢
	proveit.numbers.exponentiation.real_power_of_products
24	theorem		⊢
	proveit.numbers.numerals.decimals.posnat3
25	instantiation	42	⊢
	: , : , :
26	instantiation	36, 37	,  ⊢
	:
27	instantiation	38, 39, 40, 41*	⊢
	: , :
28	theorem		⊢
	proveit.numbers.multiplication.disassociation
29	theorem		⊢
	proveit.numbers.multiplication.elim_one_any
30	theorem		⊢
	proveit.numbers.numerals.decimals.nat3
31	instantiation	42	⊢
	: , : , :
32	instantiation	157, 121, 107	⊢
	: , : , :
33	instantiation	157, 121, 105	⊢
	: , : , :
34	instantiation	43, 44, 45	⊢
	: , :
35	instantiation	157, 150, 98	⊢
	: , : , :
36	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.nonzero_if_in_complex_nonzero
37	instantiation	46, 47, 48	,  ⊢
	: , : , :
38	theorem		⊢
	proveit.numbers.exponentiation.neg_power_as_div
39	instantiation	157, 52, 49	⊢
	: , : , :
40	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
41	instantiation	50, 86	⊢
	:
42	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_3_typical_eq
43	theorem		⊢
	proveit.numbers.exponentiation.exp_complex_closure
44	instantiation	157, 121, 51	⊢
	: , : , :
45	instantiation	157, 121, 87	⊢
	: , : , :
46	theorem		⊢
	proveit.logic.equality.sub_right_side_into
47	instantiation	157, 52, 53	,  ⊢
	: , : , :
48	instantiation	65, 54	⊢
	: , : , :
49	instantiation	157, 55, 135	⊢
	: , : , :
50	theorem		⊢
	proveit.numbers.exponentiation.complex_x_to_first_power_is_x
51	instantiation	157, 56, 57	⊢
	: , : , :
52	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero
53	instantiation	157, 58, 59	,  ⊢
	: , : , :
54	instantiation	65, 60	⊢
	: , : , :
55	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero
56	theorem		⊢
	proveit.numbers.number_sets.real_numbers.real_nonneg_within_real
57	instantiation	61, 62	⊢
	:
58	theorem		⊢
	proveit.numbers.number_sets.real_numbers.real_pos_within_real_nonzero
59	instantiation	63, 64	,  ⊢
	:
60	instantiation	65, 66	⊢
	: , : , :
61	theorem		⊢
	proveit.numbers.absolute_value.abs_complex_closure
62	instantiation	67, 68, 69	⊢
	: , :
63	theorem		⊢
	proveit.numbers.absolute_value.abs_nonzero_closure
64	instantiation	70, 71, 72	,  ⊢
	:
65	axiom		⊢
	proveit.logic.equality.substitution
66	instantiation	73, 74, 75, 76, 77*	⊢
	: , :
67	theorem		⊢
	proveit.numbers.addition.add_complex_closure_bin
68	instantiation	157, 121, 78	⊢
	: , : , :
69	instantiation	79, 80	⊢
	:
70	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.nonzero_complex_is_complex_nonzero
71	instantiation	157, 121, 81	⊢
	: , : , :
72	instantiation	82, 83	,  ⊢
	: , :
73	theorem		⊢
	proveit.numbers.division.div_as_mult
74	instantiation	157, 121, 104	⊢
	: , : , :
75	instantiation	157, 121, 84	⊢
	: , : , :
76	instantiation	129, 98	⊢
	:
77	instantiation	85, 86, 122, 87, 120, 88*	⊢
	: , : , :
78	instantiation	89, 90	⊢
	:
79	theorem		⊢
	proveit.numbers.negation.complex_closure
80	instantiation	157, 121, 91	⊢
	: , : , :
81	instantiation	92, 93, 107, 94	⊢
	: , : , :
82	theorem		⊢
	proveit.numbers.addition.subtraction.nonzero_difference_if_different
83	instantiation	95, 96, 123, 97	,  ⊢
	: , :
84	instantiation	130, 131, 98	⊢
	: , : , :
85	theorem		⊢
	proveit.numbers.exponentiation.real_power_of_real_power
86	instantiation	157, 121, 119	⊢
	: , : , :
87	instantiation	157, 127, 99	⊢
	: , : , :
88	instantiation	100, 114, 101, 102*	⊢
	: , :
89	theorem		⊢
	proveit.physics.quantum.QPE._delta_b_is_real
90	theorem		⊢
	proveit.physics.quantum.QPE._best_floor_is_int
91	instantiation	103, 104, 105	⊢
	: , :
92	theorem		⊢
	proveit.numbers.number_sets.real_numbers.all_in_interval_co__is__real
93	instantiation	106, 107	⊢
	:
94	instantiation	108, 133	⊢
	:
95	theorem		⊢
	proveit.physics.quantum.QPE._delta_b_not_eq_scaledNonzeroInt
96	instantiation	109, 110, 156, 111	⊢
	: , : , : , : , :
97	assumption		⊢
98	theorem		⊢
	proveit.physics.quantum.QPE._two_pow_t_is_nat_pos
99	instantiation	157, 137, 112	⊢
	: , : , :
100	theorem		⊢
	proveit.numbers.multiplication.mult_neg_right
101	instantiation	157, 121, 118	⊢
	: , : , :
102	instantiation	113, 114	⊢
	:
103	theorem		⊢
	proveit.numbers.multiplication.mult_real_closure_bin
104	instantiation	157, 127, 115	⊢
	: , : , :
105	instantiation	157, 127, 116	⊢
	: , : , :
106	theorem		⊢
	proveit.numbers.negation.real_closure
107	instantiation	117, 118, 119, 120	⊢
	: , :
108	theorem		⊢
	proveit.physics.quantum.QPE._delta_b_floor_diff_in_interval
109	theorem		⊢
	proveit.logic.sets.enumeration.in_enumerated_set
110	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
111	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
112	instantiation	153, 149	⊢
	:
113	theorem		⊢
	proveit.numbers.multiplication.elim_one_right
114	instantiation	157, 121, 122	⊢
	: , : , :
115	instantiation	157, 137, 123	⊢
	: , : , :
116	instantiation	157, 124, 125	⊢
	: , : , :
117	theorem		⊢
	proveit.numbers.division.div_real_closure
118	instantiation	157, 127, 126	⊢
	: , : , :
119	instantiation	157, 127, 128	⊢
	: , : , :
120	instantiation	129, 151	⊢
	:
121	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
122	instantiation	130, 131, 152	⊢
	: , : , :
123	instantiation	157, 132, 133	⊢
	: , : , :
124	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.rational_nonzero_within_rational
125	instantiation	134, 135, 136	⊢
	: , :
126	instantiation	157, 137, 149	⊢
	: , : , :
127	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
128	instantiation	157, 137, 138	⊢
	: , : , :
129	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos
130	theorem		⊢
	proveit.logic.sets.inclusion.unfold_subset_eq
131	instantiation	139, 140	⊢
	: , :
132	instantiation	141, 142, 154	⊢
	: , :
133	assumption		⊢
134	theorem		⊢
	proveit.numbers.exponentiation.exp_rational_nonzero_closure
135	instantiation	157, 143, 144	⊢
	: , : , :
136	instantiation	153, 145	⊢
	:
137	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
138	instantiation	157, 155, 146	⊢
	: , : , :
139	theorem		⊢
	proveit.logic.sets.inclusion.relax_proper_subset
140	theorem		⊢
	proveit.numbers.number_sets.real_numbers.nat_pos_within_real
141	theorem		⊢
	proveit.numbers.number_sets.integers.int_interval_within_int
142	instantiation	147, 148, 149	⊢
	: , :
143	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
144	instantiation	157, 150, 151	⊢
	: , : , :
145	instantiation	157, 158, 152	⊢
	: , : , :
146	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
147	theorem		⊢
	proveit.numbers.addition.add_int_closure_bin
148	instantiation	153, 154	⊢
	:
149	instantiation	157, 155, 156	⊢
	: , : , :
150	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
151	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
152	axiom		⊢
	proveit.physics.quantum.QPE._t_in_natural_pos
153	theorem		⊢
	proveit.numbers.negation.int_closure
154	instantiation	157, 158, 159	⊢
	: , : , :
155	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
156	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
157	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
158	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_int
159	theorem		⊢
	proveit.physics.quantum.QPE._two_pow_t_minus_one_is_nat_pos
*equality replacement requirements