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	14	⊢
2	instantiation	14, 4, 5	,  ⊢
	: , : , :
3	instantiation	200, 6	⊢
	: , : , :
4	instantiation	7, 8, 9, 10*	,  ⊢
	:
5	instantiation	200, 11	⊢
	: , : , :
6	instantiation	189, 12, 13	⊢
	: , : , :
7	theorem		⊢
	proveit.numbers.exponentiation.unit_complex_polar_num_neq_one
8	instantiation	137, 51, 43	⊢
	: , : , :
9	instantiation	14, 15, 16	,  ⊢
	: , : , :
10	instantiation	40, 17	⊢
	: , :
11	instantiation	200, 41	⊢
	: , : , :
12	instantiation	106, 236, 234, 130, 52, 131, 209, 170, 49, 18	⊢
	: , : , : , : , : , : , :
13	instantiation	200, 19	⊢
	: , : , :
14	theorem		⊢
	proveit.logic.equality.sub_left_side_into
15	instantiation	20, 21, 211, 22	,  ⊢
	: , :
16	instantiation	140, 23, 28, 24	⊢
	: , : , : , :
17	instantiation	200, 25	⊢
	: , : , :
18	instantiation	26, 112, 27	⊢
	: , :
19	instantiation	140, 35, 28, 29	⊢
	: , : , : , :
20	theorem		⊢
	proveit.physics.quantum.QPE._non_int_delta_b_diff
21	instantiation	30, 130, 234, 131	⊢
	: , : , : , : , :
22	assumption		⊢
23	instantiation	66, 31, 32, 33, 34*	⊢
	: , :
24	instantiation	40, 35	⊢
	: , :
25	instantiation	189, 36, 37	⊢
	: , : , :
26	theorem		⊢
	proveit.numbers.addition.add_complex_closure_bin
27	instantiation	38, 39	⊢
	:
28	instantiation	195	⊢
	:
29	instantiation	40, 41	⊢
	: , :
30	theorem		⊢
	proveit.logic.sets.enumeration.in_enumerated_set
31	instantiation	137, 42, 43	⊢
	: , : , :
32	instantiation	237, 215, 59	⊢
	: , : , :
33	instantiation	44, 236, 52, 158, 45	⊢
	: , :
34	instantiation	189, 46, 47	⊢
	: , : , :
35	instantiation	200, 48	⊢
	: , : , :
36	instantiation	106, 130, 101, 131, 86, 209, 170, 110, 49	⊢
	: , : , : , : , : , : , :
37	instantiation	107, 234, 101, 130, 86, 131, 49, 209, 170, 110	⊢
	: , : , : , : , : , :
38	theorem		⊢
	proveit.numbers.negation.complex_closure
39	instantiation	117, 133, 67, 68	⊢
	: , :
40	theorem		⊢
	proveit.logic.equality.equals_reversal
41	instantiation	200, 50	⊢
	: , : , :
42	instantiation	237, 215, 51	⊢
	: , : , :
43	instantiation	128, 130, 236, 234, 131, 52, 209, 170, 110	⊢
	: , : , : , : , : , :
44	theorem		⊢
	proveit.numbers.multiplication.mult_not_eq_zero
45	instantiation	237, 174, 149	⊢
	: , : , :
46	instantiation	200, 53	⊢
	: , : , :
47	instantiation	189, 54, 55	⊢
	: , : , :
48	instantiation	200, 56	⊢
	: , : , :
49	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.i_is_complex
50	instantiation	189, 57, 58	⊢
	: , : , :
51	instantiation	179, 59, 123	⊢
	: , :
52	instantiation	153	⊢
	: , :
53	instantiation	60, 209, 170, 144, 118, 125, 61*	⊢
	: , : , :
54	instantiation	189, 62, 63	⊢
	: , : , :
55	instantiation	189, 64, 65	⊢
	: , : , :
56	instantiation	66, 133, 67, 68, 69*	⊢
	: , :
57	instantiation	200, 70	⊢
	: , : , :
58	instantiation	71, 130, 236, 131, 132, 183, 133, 134, 114*	⊢
	: , : , : , : , :
59	instantiation	179, 216, 185	⊢
	: , :
60	theorem		⊢
	proveit.numbers.exponentiation.real_power_of_product
61	instantiation	72, 158, 207, 73*	⊢
	: , :
62	instantiation	189, 74, 75	⊢
	: , : , :
63	instantiation	189, 76, 77	⊢
	: , : , :
64	instantiation	129, 130, 101, 131, 103, 170, 110, 109	⊢
	: , : , : , :
65	instantiation	189, 78, 79	⊢
	: , : , :
66	theorem		⊢
	proveit.numbers.division.div_as_mult
67	instantiation	237, 215, 80	⊢
	: , : , :
68	instantiation	136, 95	⊢
	:
69	instantiation	81, 209, 135, 144, 118, 82*	⊢
	: , : , :
70	instantiation	200, 83	⊢
	: , : , :
71	theorem		⊢
	proveit.numbers.multiplication.mult_neg_any
72	theorem		⊢
	proveit.numbers.exponentiation.neg_power_as_div
73	instantiation	150, 209	⊢
	:
74	instantiation	128, 130, 101, 234, 131, 86, 209, 170, 110, 84	⊢
	: , : , : , : , : , :
75	instantiation	128, 101, 236, 130, 86, 85, 131, 209, 170, 110, 104, 109	⊢
	: , : , : , : , : , :
76	instantiation	106, 130, 101, 234, 131, 86, 209, 170, 110, 104, 109	⊢
	: , : , : , : , : , : , :
77	instantiation	189, 87, 88	⊢
	: , : , :
78	instantiation	189, 89, 90	⊢
	: , : , :
79	instantiation	91, 234, 130, 131, 183, 112, 92, 93*, 94*	⊢
	: , : , : , : , : , :
80	instantiation	154, 155, 95	⊢
	: , : , :
81	theorem		⊢
	proveit.numbers.exponentiation.real_power_of_real_power
82	instantiation	96, 115, 183, 97*	⊢
	: , :
83	instantiation	98, 183, 115, 99*	⊢
	: , :
84	instantiation	100, 104, 109	⊢
	: , :
85	instantiation	153	⊢
	: , :
86	instantiation	116	⊢
	: , : , :
87	instantiation	107, 130, 236, 101, 131, 102, 103, 104, 209, 170, 110, 109	⊢
	: , : , : , : , : , :
88	instantiation	200, 105	⊢
	: , : , :
89	instantiation	106, 234, 130, 131, 170, 110, 109	⊢
	: , : , : , : , : , : , :
90	instantiation	107, 130, 236, 234, 131, 108, 170, 109, 110, 111*	⊢
	: , : , : , : , : , :
91	theorem		⊢
	proveit.numbers.multiplication.distribute_through_subtract
92	instantiation	237, 215, 166	⊢
	: , : , :
93	instantiation	199, 112	⊢
	:
94	instantiation	189, 113, 114	⊢
	: , : , :
95	theorem		⊢
	proveit.physics.quantum.QPE._two_pow_t_is_nat_pos
96	theorem		⊢
	proveit.numbers.multiplication.mult_neg_right
97	instantiation	208, 115	⊢
	:
98	theorem		⊢
	proveit.numbers.multiplication.mult_neg_left
99	instantiation	199, 115	⊢
	:
100	theorem		⊢
	proveit.numbers.multiplication.mult_complex_closure_bin
101	theorem		⊢
	proveit.numbers.numerals.decimals.nat3
102	instantiation	153	⊢
	: , :
103	instantiation	116	⊢
	: , : , :
104	instantiation	117, 183, 209, 118	⊢
	: , :
105	instantiation	137, 119, 120	⊢
	: , : , :
106	theorem		⊢
	proveit.numbers.multiplication.leftward_commutation
107	theorem		⊢
	proveit.numbers.multiplication.association
108	instantiation	153	⊢
	: , :
109	instantiation	121, 170, 122	⊢
	: , :
110	instantiation	237, 215, 123	⊢
	: , : , :
111	instantiation	124, 170, 194, 144, 125, 126*, 127*	⊢
	: , : , :
112	instantiation	237, 215, 146	⊢
	: , : , :
113	instantiation	128, 234, 236, 130, 132, 131, 183, 133, 134	⊢
	: , : , : , : , : , :
114	instantiation	129, 130, 236, 131, 132, 133, 134	⊢
	: , : , : , :
115	instantiation	237, 215, 135	⊢
	: , : , :
116	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_3_typical_eq
117	theorem		⊢
	proveit.numbers.division.div_complex_closure
118	instantiation	136, 228	⊢
	:
119	instantiation	137, 138, 139	⊢
	: , : , :
120	instantiation	140, 141, 142, 143	⊢
	: , : , : , :
121	theorem		⊢
	proveit.numbers.exponentiation.exp_complex_closure
122	instantiation	237, 215, 144	⊢
	: , : , :
123	instantiation	145, 146, 147	⊢
	: , :
124	theorem		⊢
	proveit.numbers.exponentiation.product_of_real_powers
125	instantiation	148, 149	⊢
	:
126	instantiation	150, 170	⊢
	:
127	instantiation	189, 151, 152	⊢
	: , : , :
128	theorem		⊢
	proveit.numbers.multiplication.disassociation
129	theorem		⊢
	proveit.numbers.multiplication.elim_one_any
130	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
131	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
132	instantiation	153	⊢
	: , :
133	instantiation	237, 215, 180	⊢
	: , : , :
134	instantiation	237, 215, 181	⊢
	: , : , :
135	instantiation	154, 155, 229	⊢
	: , : , :
136	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos
137	theorem		⊢
	proveit.logic.equality.sub_right_side_into
138	instantiation	156, 183, 157, 158	⊢
	: , : , : , : , :
139	instantiation	189, 159, 160	⊢
	: , : , :
140	theorem		⊢
	proveit.logic.equality.four_chain_transitivity
141	instantiation	200, 161	⊢
	: , : , :
142	instantiation	200, 161	⊢
	: , : , :
143	instantiation	208, 183	⊢
	:
144	instantiation	237, 222, 162	⊢
	: , : , :
145	theorem		⊢
	proveit.numbers.addition.add_real_closure_bin
146	instantiation	163, 164	⊢
	:
147	instantiation	165, 166	⊢
	:
148	theorem		⊢
	proveit.numbers.number_sets.real_numbers.nonzero_if_in_real_nonzero
149	instantiation	237, 167, 197	⊢
	: , : , :
150	theorem		⊢
	proveit.numbers.exponentiation.complex_x_to_first_power_is_x
151	instantiation	200, 168	⊢
	: , : , :
152	instantiation	169, 170	⊢
	:
153	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
154	theorem		⊢
	proveit.logic.sets.inclusion.unfold_subset_eq
155	instantiation	171, 172	⊢
	: , :
156	theorem		⊢
	proveit.numbers.division.mult_frac_cancel_denom_left
157	instantiation	237, 174, 173	⊢
	: , : , :
158	instantiation	237, 174, 175	⊢
	: , : , :
159	instantiation	200, 176	⊢
	: , : , :
160	instantiation	200, 177	⊢
	: , : , :
161	instantiation	202, 183	⊢
	:
162	instantiation	237, 230, 178	⊢
	: , : , :
163	theorem		⊢
	proveit.physics.quantum.QPE._delta_b_is_real
164	theorem		⊢
	proveit.physics.quantum.QPE._best_floor_is_int
165	theorem		⊢
	proveit.numbers.negation.real_closure
166	instantiation	179, 180, 181	⊢
	: , :
167	theorem		⊢
	proveit.numbers.number_sets.real_numbers.real_pos_within_real_nonzero
168	instantiation	182, 183, 184	⊢
	: , :
169	theorem		⊢
	proveit.numbers.exponentiation.exp_zero_eq_one
170	instantiation	237, 215, 185	⊢
	: , : , :
171	theorem		⊢
	proveit.logic.sets.inclusion.relax_proper_subset
172	theorem		⊢
	proveit.numbers.number_sets.real_numbers.nat_pos_within_real
173	instantiation	237, 187, 186	⊢
	: , : , :
174	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero
175	instantiation	237, 187, 213	⊢
	: , : , :
176	instantiation	200, 188	⊢
	: , : , :
177	instantiation	189, 190, 191	⊢
	: , : , :
178	instantiation	232, 226	⊢
	:
179	theorem		⊢
	proveit.numbers.multiplication.mult_real_closure_bin
180	instantiation	237, 222, 192	⊢
	: , : , :
181	instantiation	237, 222, 193	⊢
	: , : , :
182	theorem		⊢
	proveit.numbers.addition.subtraction.add_cancel_basic
183	instantiation	237, 215, 194	⊢
	: , : , :
184	instantiation	195	⊢
	:
185	instantiation	237, 196, 197	⊢
	: , : , :
186	instantiation	237, 219, 198	⊢
	: , : , :
187	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero
188	instantiation	199, 209	⊢
	:
189	axiom		⊢
	proveit.logic.equality.equals_transitivity
190	instantiation	200, 201	⊢
	: , : , :
191	instantiation	202, 209	⊢
	:
192	instantiation	237, 230, 203	⊢
	: , : , :
193	instantiation	237, 204, 205	⊢
	: , : , :
194	instantiation	237, 222, 206	⊢
	: , : , :
195	axiom		⊢
	proveit.logic.equality.equals_reflexivity
196	theorem		⊢
	proveit.numbers.number_sets.real_numbers.real_pos_within_real
197	theorem		⊢
	proveit.numbers.number_sets.real_numbers.pi_is_real_pos
198	instantiation	237, 227, 207	⊢
	: , : , :
199	theorem		⊢
	proveit.numbers.multiplication.elim_one_left
200	axiom		⊢
	proveit.logic.equality.substitution
201	instantiation	208, 209	⊢
	:
202	theorem		⊢
	proveit.numbers.division.frac_one_denom
203	instantiation	237, 210, 211	⊢
	: , : , :
204	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.rational_nonzero_within_rational
205	instantiation	212, 213, 214	⊢
	: , :
206	instantiation	237, 230, 226	⊢
	: , : , :
207	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
208	theorem		⊢
	proveit.numbers.multiplication.elim_one_right
209	instantiation	237, 215, 216	⊢
	: , : , :
210	instantiation	217, 218, 233	⊢
	: , :
211	assumption		⊢
212	theorem		⊢
	proveit.numbers.exponentiation.exp_rational_nonzero_closure
213	instantiation	237, 219, 220	⊢
	: , : , :
214	instantiation	232, 221	⊢
	:
215	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
216	instantiation	237, 222, 223	⊢
	: , : , :
217	theorem		⊢
	proveit.numbers.number_sets.integers.int_interval_within_int
218	instantiation	224, 225, 226	⊢
	: , :
219	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
220	instantiation	237, 227, 228	⊢
	: , : , :
221	instantiation	237, 238, 229	⊢
	: , : , :
222	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
223	instantiation	237, 230, 231	⊢
	: , : , :
224	theorem		⊢
	proveit.numbers.addition.add_int_closure_bin
225	instantiation	232, 233	⊢
	:
226	instantiation	237, 235, 234	⊢
	: , : , :
227	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
228	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
229	axiom		⊢
	proveit.physics.quantum.QPE._t_in_natural_pos
230	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
231	instantiation	237, 235, 236	⊢
	: , : , :
232	theorem		⊢
	proveit.numbers.negation.int_closure
233	instantiation	237, 238, 239	⊢
	: , : , :
234	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
235	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
236	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
237	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
238	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_int
239	theorem		⊢
	proveit.physics.quantum.QPE._two_pow_t_minus_one_is_nat_pos
*equality replacement requirements