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	reference	62	⊢
2	instantiation	93, 4	⊢
	: , : , :
3	instantiation	105, 119, 5, 6, 7*	,  ⊢
	: , :
4	instantiation	93, 56	⊢
	: , : , :
5	instantiation	54, 8, 9	⊢
	: , : , :
6	instantiation	10, 29, 25, 51, 11, 40	,  ⊢
	: , :
7	instantiation	62, 12, 13	,  ⊢
	: , : , :
8	instantiation	14, 15, 47	⊢
	: , :
9	instantiation	28, 145, 181, 191, 146, 16, 88, 107, 47	⊢
	: , : , : , : , : , :
10	theorem		⊢
	proveit.numbers.multiplication.mult_not_eq_zero
11	instantiation	192, 89, 17	⊢
	: , : , :
12	instantiation	93, 18	,  ⊢
	: , : , :
13	instantiation	62, 19, 20	⊢
	: , : , :
14	theorem		⊢
	proveit.numbers.multiplication.mult_complex_closure_bin
15	instantiation	192, 156, 21	⊢
	: , : , :
16	instantiation	86	⊢
	: , :
17	instantiation	192, 101, 22	⊢
	: , : , :
18	instantiation	23, 24, 25, 88, 107, 47, 120, 45, 108, 26, 27*, 109*	,  ⊢
	: , : , :
19	instantiation	28, 191, 29, 145, 30, 146, 119, 34, 35, 36	⊢
	: , : , : , : , : , :
20	instantiation	31, 145, 181, 146, 32, 33, 119, 34, 35, 36, 37*	⊢
	: , : , : , : , : , :
21	instantiation	137, 100, 117	⊢
	: , :
22	instantiation	192, 178, 38	⊢
	: , : , :
23	theorem		⊢
	proveit.numbers.exponentiation.real_power_of_products
24	theorem		⊢
	proveit.numbers.numerals.decimals.posnat3
25	instantiation	43	⊢
	: , : , :
26	instantiation	39, 40	,  ⊢
	:
27	instantiation	41, 51, 98, 42*	⊢
	: , :
28	theorem		⊢
	proveit.numbers.multiplication.disassociation
29	theorem		⊢
	proveit.numbers.numerals.decimals.nat3
30	instantiation	43	⊢
	: , : , :
31	theorem		⊢
	proveit.numbers.multiplication.association
32	instantiation	86	⊢
	: , :
33	instantiation	86	⊢
	: , :
34	instantiation	44, 135, 88, 45	⊢
	: , :
35	instantiation	192, 156, 139	⊢
	: , : , :
36	instantiation	46, 47, 48	⊢
	: , :
37	instantiation	49, 119, 135, 50, 51, 52*, 53*	⊢
	: , : , : , :
38	instantiation	192, 185, 132	⊢
	: , : , :
39	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.nonzero_if_in_complex_nonzero
40	instantiation	54, 55, 56	,  ⊢
	: , : , :
41	theorem		⊢
	proveit.numbers.exponentiation.neg_power_as_div
42	instantiation	57, 88	⊢
	:
43	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_3_typical_eq
44	theorem		⊢
	proveit.numbers.division.div_complex_closure
45	instantiation	164, 99	⊢
	:
46	theorem		⊢
	proveit.numbers.exponentiation.exp_complex_closure
47	instantiation	192, 156, 58	⊢
	: , : , :
48	instantiation	192, 156, 120	⊢
	: , : , :
49	theorem		⊢
	proveit.numbers.division.prod_of_fracs
50	instantiation	192, 89, 59	⊢
	: , : , :
51	instantiation	192, 89, 60	⊢
	: , : , :
52	instantiation	61, 119	⊢
	:
53	instantiation	62, 63, 64	⊢
	: , : , :
54	theorem		⊢
	proveit.logic.equality.sub_right_side_into
55	instantiation	192, 89, 65	,  ⊢
	: , : , :
56	instantiation	93, 66	⊢
	: , : , :
57	theorem		⊢
	proveit.numbers.exponentiation.complex_x_to_first_power_is_x
58	instantiation	192, 67, 68	⊢
	: , : , :
59	instantiation	192, 101, 69	⊢
	: , : , :
60	instantiation	192, 101, 70	⊢
	: , : , :
61	theorem		⊢
	proveit.numbers.division.frac_one_denom
62	axiom		⊢
	proveit.logic.equality.equals_transitivity
63	instantiation	71, 181, 72, 73, 77, 74	⊢
	: , : , : , :
64	instantiation	75, 76, 135, 77*, 78*	⊢
	: , : , :
65	instantiation	192, 79, 80	,  ⊢
	: , : , :
66	instantiation	93, 81	⊢
	: , : , :
67	theorem		⊢
	proveit.numbers.number_sets.real_numbers.real_nonneg_within_real
68	instantiation	82, 83	⊢
	:
69	instantiation	192, 178, 84	⊢
	: , : , :
70	instantiation	192, 178, 85	⊢
	: , : , :
71	axiom		⊢
	proveit.core_expr_types.operations.operands_substitution
72	instantiation	86	⊢
	: , :
73	instantiation	86	⊢
	: , :
74	instantiation	87, 88	⊢
	:
75	theorem		⊢
	proveit.numbers.division.frac_cancel_left
76	instantiation	192, 89, 90	⊢
	: , : , :
77	instantiation	148, 119	⊢
	:
78	theorem		⊢
	proveit.numbers.numerals.decimals.mult_2_2
79	theorem		⊢
	proveit.numbers.number_sets.real_numbers.real_pos_within_real_nonzero
80	instantiation	91, 92	,  ⊢
	:
81	instantiation	93, 94	⊢
	: , : , :
82	theorem		⊢
	proveit.numbers.absolute_value.abs_complex_closure
83	instantiation	95, 96, 97	⊢
	: , :
84	instantiation	192, 185, 98	⊢
	: , : , :
85	instantiation	192, 185, 99	⊢
	: , : , :
86	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
87	theorem		⊢
	proveit.numbers.multiplication.elim_one_left
88	instantiation	192, 156, 100	⊢
	: , : , :
89	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero
90	instantiation	192, 101, 170	⊢
	: , : , :
91	theorem		⊢
	proveit.numbers.absolute_value.abs_nonzero_closure
92	instantiation	102, 103, 104	,  ⊢
	:
93	axiom		⊢
	proveit.logic.equality.substitution
94	instantiation	105, 106, 107, 108, 109*	⊢
	: , :
95	theorem		⊢
	proveit.numbers.addition.add_complex_closure_bin
96	instantiation	192, 156, 110	⊢
	: , : , :
97	instantiation	111, 112	⊢
	:
98	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
99	theorem		⊢
	proveit.numbers.numerals.decimals.posnat4
100	instantiation	192, 162, 113	⊢
	: , : , :
101	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero
102	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.nonzero_complex_is_complex_nonzero
103	instantiation	192, 156, 114	⊢
	: , : , :
104	instantiation	115, 116	,  ⊢
	: , :
105	theorem		⊢
	proveit.numbers.division.div_as_mult
106	instantiation	192, 156, 138	⊢
	: , : , :
107	instantiation	192, 156, 117	⊢
	: , : , :
108	instantiation	164, 132	⊢
	:
109	instantiation	118, 119, 157, 120, 155, 121*	⊢
	: , : , :
110	instantiation	122, 123	⊢
	:
111	theorem		⊢
	proveit.numbers.negation.complex_closure
112	instantiation	192, 156, 124	⊢
	: , : , :
113	instantiation	192, 172, 125	⊢
	: , : , :
114	instantiation	126, 127, 142, 128	⊢
	: , : , :
115	theorem		⊢
	proveit.numbers.addition.subtraction.nonzero_difference_if_different
116	instantiation	129, 130, 158, 131	,  ⊢
	: , :
117	instantiation	165, 166, 132	⊢
	: , : , :
118	theorem		⊢
	proveit.numbers.exponentiation.real_power_of_real_power
119	instantiation	192, 156, 154	⊢
	: , : , :
120	instantiation	192, 162, 133	⊢
	: , : , :
121	instantiation	134, 149, 135, 136*	⊢
	: , :
122	theorem		⊢
	proveit.physics.quantum.QPE._delta_b_is_real
123	theorem		⊢
	proveit.physics.quantum.QPE._best_floor_is_int
124	instantiation	137, 138, 139	⊢
	: , :
125	instantiation	192, 190, 140	⊢
	: , : , :
126	theorem		⊢
	proveit.numbers.number_sets.real_numbers.all_in_interval_co__is__real
127	instantiation	141, 142	⊢
	:
128	instantiation	143, 168	⊢
	:
129	theorem		⊢
	proveit.physics.quantum.QPE._delta_b_not_eq_scaledNonzeroInt
130	instantiation	144, 145, 191, 146	⊢
	: , : , : , : , :
131	assumption		⊢
132	theorem		⊢
	proveit.physics.quantum.QPE._two_pow_t_is_nat_pos
133	instantiation	192, 172, 147	⊢
	: , : , :
134	theorem		⊢
	proveit.numbers.multiplication.mult_neg_right
135	instantiation	192, 156, 153	⊢
	: , : , :
136	instantiation	148, 149	⊢
	:
137	theorem		⊢
	proveit.numbers.multiplication.mult_real_closure_bin
138	instantiation	192, 162, 150	⊢
	: , : , :
139	instantiation	192, 162, 151	⊢
	: , : , :
140	theorem		⊢
	proveit.numbers.numerals.decimals.nat4
141	theorem		⊢
	proveit.numbers.negation.real_closure
142	instantiation	152, 153, 154, 155	⊢
	: , :
143	theorem		⊢
	proveit.physics.quantum.QPE._delta_b_floor_diff_in_interval
144	theorem		⊢
	proveit.logic.sets.enumeration.in_enumerated_set
145	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
146	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
147	instantiation	188, 184	⊢
	:
148	theorem		⊢
	proveit.numbers.multiplication.elim_one_right
149	instantiation	192, 156, 157	⊢
	: , : , :
150	instantiation	192, 172, 158	⊢
	: , : , :
151	instantiation	192, 159, 160	⊢
	: , : , :
152	theorem		⊢
	proveit.numbers.division.div_real_closure
153	instantiation	192, 162, 161	⊢
	: , : , :
154	instantiation	192, 162, 163	⊢
	: , : , :
155	instantiation	164, 186	⊢
	:
156	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
157	instantiation	165, 166, 187	⊢
	: , : , :
158	instantiation	192, 167, 168	⊢
	: , : , :
159	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.rational_nonzero_within_rational
160	instantiation	169, 170, 171	⊢
	: , :
161	instantiation	192, 172, 184	⊢
	: , : , :
162	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
163	instantiation	192, 172, 173	⊢
	: , : , :
164	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos
165	theorem		⊢
	proveit.logic.sets.inclusion.unfold_subset_eq
166	instantiation	174, 175	⊢
	: , :
167	instantiation	176, 177, 189	⊢
	: , :
168	assumption		⊢
169	theorem		⊢
	proveit.numbers.exponentiation.exp_rational_nonzero_closure
170	instantiation	192, 178, 179	⊢
	: , : , :
171	instantiation	188, 180	⊢
	:
172	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
173	instantiation	192, 190, 181	⊢
	: , : , :
174	theorem		⊢
	proveit.logic.sets.inclusion.relax_proper_subset
175	theorem		⊢
	proveit.numbers.number_sets.real_numbers.nat_pos_within_real
176	theorem		⊢
	proveit.numbers.number_sets.integers.int_interval_within_int
177	instantiation	182, 183, 184	⊢
	: , :
178	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
179	instantiation	192, 185, 186	⊢
	: , : , :
180	instantiation	192, 193, 187	⊢
	: , : , :
181	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
182	theorem		⊢
	proveit.numbers.addition.add_int_closure_bin
183	instantiation	188, 189	⊢
	:
184	instantiation	192, 190, 191	⊢
	: , : , :
185	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
186	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
187	axiom		⊢
	proveit.physics.quantum.QPE._t_in_natural_pos
188	theorem		⊢
	proveit.numbers.negation.int_closure
189	instantiation	192, 193, 194	⊢
	: , : , :
190	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
191	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
192	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
193	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_int
194	theorem		⊢
	proveit.physics.quantum.QPE._two_pow_t_minus_one_is_nat_pos
*equality replacement requirements