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	9	⊢
2	instantiation	4, 5, 6, 7*	,  ⊢
	:
3	instantiation	188, 8	⊢
	: , : , :
4	theorem		⊢
	proveit.numbers.exponentiation.unit_complex_polar_num_neq_one
5	instantiation	125, 43, 34	⊢
	: , : , :
6	instantiation	9, 10, 11	,  ⊢
	: , : , :
7	instantiation	27, 12	⊢
	: , :
8	instantiation	188, 13	⊢
	: , : , :
9	theorem		⊢
	proveit.logic.equality.sub_left_side_into
10	instantiation	14, 15, 199, 16	,  ⊢
	: , :
11	instantiation	128, 17, 18, 19	⊢
	: , : , : , :
12	instantiation	188, 20	⊢
	: , : , :
13	instantiation	188, 21	⊢
	: , : , :
14	theorem		⊢
	proveit.physics.quantum.QPE._non_int_delta_b_diff
15	instantiation	22, 118, 222, 119	⊢
	: , : , : , : , :
16	assumption		⊢
17	instantiation	57, 23, 24, 25, 26*	⊢
	: , :
18	instantiation	183	⊢
	:
19	instantiation	27, 28	⊢
	: , :
20	instantiation	177, 29, 30	⊢
	: , : , :
21	instantiation	177, 31, 32	⊢
	: , : , :
22	theorem		⊢
	proveit.logic.sets.enumeration.in_enumerated_set
23	instantiation	125, 33, 34	⊢
	: , : , :
24	instantiation	225, 203, 50	⊢
	: , : , :
25	instantiation	35, 224, 44, 146, 36	⊢
	: , :
26	instantiation	177, 37, 38	⊢
	: , : , :
27	theorem		⊢
	proveit.logic.equality.equals_reversal
28	instantiation	188, 39	⊢
	: , : , :
29	instantiation	94, 118, 89, 119, 76, 197, 158, 98, 40	⊢
	: , : , : , : , : , : , :
30	instantiation	95, 222, 89, 118, 76, 119, 40, 197, 158, 98	⊢
	: , : , : , : , : , :
31	instantiation	188, 41	⊢
	: , : , :
32	instantiation	42, 118, 224, 119, 120, 171, 121, 122, 102*	⊢
	: , : , : , : , :
33	instantiation	225, 203, 43	⊢
	: , : , :
34	instantiation	116, 118, 224, 222, 119, 44, 197, 158, 98	⊢
	: , : , : , : , : , :
35	theorem		⊢
	proveit.numbers.multiplication.mult_not_eq_zero
36	instantiation	225, 162, 137	⊢
	: , : , :
37	instantiation	188, 45	⊢
	: , : , :
38	instantiation	177, 46, 47	⊢
	: , : , :
39	instantiation	188, 48	⊢
	: , : , :
40	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.i_is_complex
41	instantiation	188, 49	⊢
	: , : , :
42	theorem		⊢
	proveit.numbers.multiplication.mult_neg_any
43	instantiation	167, 50, 111	⊢
	: , :
44	instantiation	141	⊢
	: , :
45	instantiation	51, 197, 158, 132, 106, 113, 52*	⊢
	: , : , :
46	instantiation	177, 53, 54	⊢
	: , : , :
47	instantiation	177, 55, 56	⊢
	: , : , :
48	instantiation	57, 121, 58, 59, 60*	⊢
	: , :
49	instantiation	61, 171, 103, 62*	⊢
	: , :
50	instantiation	167, 204, 173	⊢
	: , :
51	theorem		⊢
	proveit.numbers.exponentiation.real_power_of_product
52	instantiation	63, 146, 195, 64*	⊢
	: , :
53	instantiation	177, 65, 66	⊢
	: , : , :
54	instantiation	177, 67, 68	⊢
	: , : , :
55	instantiation	117, 118, 89, 119, 91, 158, 98, 97	⊢
	: , : , : , :
56	instantiation	177, 69, 70	⊢
	: , : , :
57	theorem		⊢
	proveit.numbers.division.div_as_mult
58	instantiation	225, 203, 71	⊢
	: , : , :
59	instantiation	124, 85	⊢
	:
60	instantiation	72, 197, 123, 132, 106, 73*	⊢
	: , : , :
61	theorem		⊢
	proveit.numbers.multiplication.mult_neg_left
62	instantiation	187, 103	⊢
	:
63	theorem		⊢
	proveit.numbers.exponentiation.neg_power_as_div
64	instantiation	138, 197	⊢
	:
65	instantiation	116, 118, 89, 222, 119, 76, 197, 158, 98, 74	⊢
	: , : , : , : , : , :
66	instantiation	116, 89, 224, 118, 76, 75, 119, 197, 158, 98, 92, 97	⊢
	: , : , : , : , : , :
67	instantiation	94, 118, 89, 222, 119, 76, 197, 158, 98, 92, 97	⊢
	: , : , : , : , : , : , :
68	instantiation	177, 77, 78	⊢
	: , : , :
69	instantiation	177, 79, 80	⊢
	: , : , :
70	instantiation	81, 222, 118, 119, 171, 100, 82, 83*, 84*	⊢
	: , : , : , : , : , :
71	instantiation	142, 143, 85	⊢
	: , : , :
72	theorem		⊢
	proveit.numbers.exponentiation.real_power_of_real_power
73	instantiation	86, 103, 171, 87*	⊢
	: , :
74	instantiation	88, 92, 97	⊢
	: , :
75	instantiation	141	⊢
	: , :
76	instantiation	104	⊢
	: , : , :
77	instantiation	95, 118, 224, 89, 119, 90, 91, 92, 197, 158, 98, 97	⊢
	: , : , : , : , : , :
78	instantiation	188, 93	⊢
	: , : , :
79	instantiation	94, 222, 118, 119, 158, 98, 97	⊢
	: , : , : , : , : , : , :
80	instantiation	95, 118, 224, 222, 119, 96, 158, 97, 98, 99*	⊢
	: , : , : , : , : , :
81	theorem		⊢
	proveit.numbers.multiplication.distribute_through_subtract
82	instantiation	225, 203, 154	⊢
	: , : , :
83	instantiation	187, 100	⊢
	:
84	instantiation	177, 101, 102	⊢
	: , : , :
85	theorem		⊢
	proveit.physics.quantum.QPE._two_pow_t_is_nat_pos
86	theorem		⊢
	proveit.numbers.multiplication.mult_neg_right
87	instantiation	196, 103	⊢
	:
88	theorem		⊢
	proveit.numbers.multiplication.mult_complex_closure_bin
89	theorem		⊢
	proveit.numbers.numerals.decimals.nat3
90	instantiation	141	⊢
	: , :
91	instantiation	104	⊢
	: , : , :
92	instantiation	105, 171, 197, 106	⊢
	: , :
93	instantiation	125, 107, 108	⊢
	: , : , :
94	theorem		⊢
	proveit.numbers.multiplication.leftward_commutation
95	theorem		⊢
	proveit.numbers.multiplication.association
96	instantiation	141	⊢
	: , :
97	instantiation	109, 158, 110	⊢
	: , :
98	instantiation	225, 203, 111	⊢
	: , : , :
99	instantiation	112, 158, 182, 132, 113, 114*, 115*	⊢
	: , : , :
100	instantiation	225, 203, 134	⊢
	: , : , :
101	instantiation	116, 222, 224, 118, 120, 119, 171, 121, 122	⊢
	: , : , : , : , : , :
102	instantiation	117, 118, 224, 119, 120, 121, 122	⊢
	: , : , : , :
103	instantiation	225, 203, 123	⊢
	: , : , :
104	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_3_typical_eq
105	theorem		⊢
	proveit.numbers.division.div_complex_closure
106	instantiation	124, 216	⊢
	:
107	instantiation	125, 126, 127	⊢
	: , : , :
108	instantiation	128, 129, 130, 131	⊢
	: , : , : , :
109	theorem		⊢
	proveit.numbers.exponentiation.exp_complex_closure
110	instantiation	225, 203, 132	⊢
	: , : , :
111	instantiation	133, 134, 135	⊢
	: , :
112	theorem		⊢
	proveit.numbers.exponentiation.product_of_real_powers
113	instantiation	136, 137	⊢
	:
114	instantiation	138, 158	⊢
	:
115	instantiation	177, 139, 140	⊢
	: , : , :
116	theorem		⊢
	proveit.numbers.multiplication.disassociation
117	theorem		⊢
	proveit.numbers.multiplication.elim_one_any
118	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
119	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
120	instantiation	141	⊢
	: , :
121	instantiation	225, 203, 168	⊢
	: , : , :
122	instantiation	225, 203, 169	⊢
	: , : , :
123	instantiation	142, 143, 217	⊢
	: , : , :
124	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos
125	theorem		⊢
	proveit.logic.equality.sub_right_side_into
126	instantiation	144, 171, 145, 146	⊢
	: , : , : , : , :
127	instantiation	177, 147, 148	⊢
	: , : , :
128	theorem		⊢
	proveit.logic.equality.four_chain_transitivity
129	instantiation	188, 149	⊢
	: , : , :
130	instantiation	188, 149	⊢
	: , : , :
131	instantiation	196, 171	⊢
	:
132	instantiation	225, 210, 150	⊢
	: , : , :
133	theorem		⊢
	proveit.numbers.addition.add_real_closure_bin
134	instantiation	151, 152	⊢
	:
135	instantiation	153, 154	⊢
	:
136	theorem		⊢
	proveit.numbers.number_sets.real_numbers.nonzero_if_in_real_nonzero
137	instantiation	225, 155, 185	⊢
	: , : , :
138	theorem		⊢
	proveit.numbers.exponentiation.complex_x_to_first_power_is_x
139	instantiation	188, 156	⊢
	: , : , :
140	instantiation	157, 158	⊢
	:
141	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
142	theorem		⊢
	proveit.logic.sets.inclusion.unfold_subset_eq
143	instantiation	159, 160	⊢
	: , :
144	theorem		⊢
	proveit.numbers.division.mult_frac_cancel_denom_left
145	instantiation	225, 162, 161	⊢
	: , : , :
146	instantiation	225, 162, 163	⊢
	: , : , :
147	instantiation	188, 164	⊢
	: , : , :
148	instantiation	188, 165	⊢
	: , : , :
149	instantiation	190, 171	⊢
	:
150	instantiation	225, 218, 166	⊢
	: , : , :
151	theorem		⊢
	proveit.physics.quantum.QPE._delta_b_is_real
152	theorem		⊢
	proveit.physics.quantum.QPE._best_floor_is_int
153	theorem		⊢
	proveit.numbers.negation.real_closure
154	instantiation	167, 168, 169	⊢
	: , :
155	theorem		⊢
	proveit.numbers.number_sets.real_numbers.real_pos_within_real_nonzero
156	instantiation	170, 171, 172	⊢
	: , :
157	theorem		⊢
	proveit.numbers.exponentiation.exp_zero_eq_one
158	instantiation	225, 203, 173	⊢
	: , : , :
159	theorem		⊢
	proveit.logic.sets.inclusion.relax_proper_subset
160	theorem		⊢
	proveit.numbers.number_sets.real_numbers.nat_pos_within_real
161	instantiation	225, 175, 174	⊢
	: , : , :
162	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero
163	instantiation	225, 175, 201	⊢
	: , : , :
164	instantiation	188, 176	⊢
	: , : , :
165	instantiation	177, 178, 179	⊢
	: , : , :
166	instantiation	220, 214	⊢
	:
167	theorem		⊢
	proveit.numbers.multiplication.mult_real_closure_bin
168	instantiation	225, 210, 180	⊢
	: , : , :
169	instantiation	225, 210, 181	⊢
	: , : , :
170	theorem		⊢
	proveit.numbers.addition.subtraction.add_cancel_basic
171	instantiation	225, 203, 182	⊢
	: , : , :
172	instantiation	183	⊢
	:
173	instantiation	225, 184, 185	⊢
	: , : , :
174	instantiation	225, 207, 186	⊢
	: , : , :
175	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero
176	instantiation	187, 197	⊢
	:
177	axiom		⊢
	proveit.logic.equality.equals_transitivity
178	instantiation	188, 189	⊢
	: , : , :
179	instantiation	190, 197	⊢
	:
180	instantiation	225, 218, 191	⊢
	: , : , :
181	instantiation	225, 192, 193	⊢
	: , : , :
182	instantiation	225, 210, 194	⊢
	: , : , :
183	axiom		⊢
	proveit.logic.equality.equals_reflexivity
184	theorem		⊢
	proveit.numbers.number_sets.real_numbers.real_pos_within_real
185	theorem		⊢
	proveit.numbers.number_sets.real_numbers.pi_is_real_pos
186	instantiation	225, 215, 195	⊢
	: , : , :
187	theorem		⊢
	proveit.numbers.multiplication.elim_one_left
188	axiom		⊢
	proveit.logic.equality.substitution
189	instantiation	196, 197	⊢
	:
190	theorem		⊢
	proveit.numbers.division.frac_one_denom
191	instantiation	225, 198, 199	⊢
	: , : , :
192	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.rational_nonzero_within_rational
193	instantiation	200, 201, 202	⊢
	: , :
194	instantiation	225, 218, 214	⊢
	: , : , :
195	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
196	theorem		⊢
	proveit.numbers.multiplication.elim_one_right
197	instantiation	225, 203, 204	⊢
	: , : , :
198	instantiation	205, 206, 221	⊢
	: , :
199	assumption		⊢
200	theorem		⊢
	proveit.numbers.exponentiation.exp_rational_nonzero_closure
201	instantiation	225, 207, 208	⊢
	: , : , :
202	instantiation	220, 209	⊢
	:
203	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
204	instantiation	225, 210, 211	⊢
	: , : , :
205	theorem		⊢
	proveit.numbers.number_sets.integers.int_interval_within_int
206	instantiation	212, 213, 214	⊢
	: , :
207	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
208	instantiation	225, 215, 216	⊢
	: , : , :
209	instantiation	225, 226, 217	⊢
	: , : , :
210	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
211	instantiation	225, 218, 219	⊢
	: , : , :
212	theorem		⊢
	proveit.numbers.addition.add_int_closure_bin
213	instantiation	220, 221	⊢
	:
214	instantiation	225, 223, 222	⊢
	: , : , :
215	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
216	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
217	axiom		⊢
	proveit.physics.quantum.QPE._t_in_natural_pos
218	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
219	instantiation	225, 223, 224	⊢
	: , : , :
220	theorem		⊢
	proveit.numbers.negation.int_closure
221	instantiation	225, 226, 227	⊢
	: , : , :
222	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
223	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
224	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
225	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
226	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_int
227	theorem		⊢
	proveit.physics.quantum.QPE._two_pow_t_minus_one_is_nat_pos
*equality replacement requirements