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