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