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	175	⊢
2	instantiation	175, 4, 5, 6*	⊢
	: , : , :
3	instantiation	7, 24, 8, 9, 10, 11, 12*, 13*	⊢
	: , : , : , :
4	instantiation	14, 173	⊢
	:
5	instantiation	15, 173	⊢
	:
6	instantiation	212, 16, 17	⊢
	: , : , :
7	theorem		⊢
	proveit.numbers.summation.gen_finite_geom_sum
8	instantiation	45, 18, 19	⊢
	: , : , :
9	theorem		⊢
	proveit.numbers.number_sets.integers.zero_is_int
10	instantiation	20, 21, 197	⊢
	: , :
11	instantiation	22, 23	⊢
	: , :
12	instantiation	184, 24	⊢
	:
13	instantiation	212, 25, 26	⊢
	: , : , :
14	theorem		⊢
	proveit.physics.quantum.QPE._alpha_m_mod_as_geometric_sum
15	theorem		⊢
	proveit.physics.quantum.QPE._phase_from_best_with_delta_b
16	instantiation	68, 144, 239, 232, 146, 27, 44, 150, 28	⊢
	: , : , : , : , : , :
17	instantiation	29, 44, 150, 30	⊢
	: , : , :
18	instantiation	31, 32, 33, 34*	⊢
	:
19	instantiation	220, 35	⊢
	: , : , :
20	theorem		⊢
	proveit.numbers.addition.add_int_closure_bin
21	instantiation	237, 36, 103	⊢
	: , : , :
22	theorem		⊢
	proveit.numbers.addition.subtraction.nonneg_difference
23	instantiation	37, 103	⊢
	:
24	instantiation	161, 38, 41	⊢
	: , :
25	instantiation	220, 39	⊢
	: , : , :
26	instantiation	40, 67, 41, 71, 42*	⊢
	: , : , :
27	instantiation	157	⊢
	: , :
28	instantiation	43, 44	⊢
	:
29	theorem		⊢
	proveit.numbers.addition.subtraction.add_cancel_triple_13
30	instantiation	204	⊢
	:
31	theorem		⊢
	proveit.numbers.exponentiation.unit_complex_polar_num_neq_one
32	instantiation	175, 108, 95	⊢
	: , : , :
33	instantiation	45, 46, 47	⊢
	: , : , :
34	instantiation	48, 49	⊢
	: , :
35	instantiation	139, 239, 232, 144, 109, 146, 228, 185, 100, 150	⊢
	: , : , : , : , : , : , :
36	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_int
37	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.natural_pos_lower_bound
38	instantiation	237, 230, 50	⊢
	: , : , :
39	instantiation	212, 51, 52	⊢
	: , : , :
40	theorem		⊢
	proveit.numbers.exponentiation.complex_power_of_complex_power
41	instantiation	175, 53, 54	⊢
	: , : , :
42	instantiation	134, 144, 55, 232, 146, 56, 228, 185, 100, 150, 71	⊢
	: , : , : , : , : , :
43	theorem		⊢
	proveit.numbers.negation.complex_closure
44	instantiation	57, 58, 71, 59	⊢
	: , :
45	theorem		⊢
	proveit.logic.equality.sub_left_side_into
46	instantiation	60, 61, 62, 93, 91	⊢
	: , :
47	instantiation	178, 63, 64, 65	⊢
	: , : , : , :
48	theorem		⊢
	proveit.logic.equality.equals_reversal
49	instantiation	220, 66	⊢
	: , : , :
50	instantiation	237, 205, 67	⊢
	: , : , :
51	instantiation	68, 144, 239, 232, 146, 69, 71, 162, 203	⊢
	: , : , : , : , : , :
52	instantiation	70, 203, 71, 195	⊢
	: , : , :
53	instantiation	142, 88, 72	⊢
	: , :
54	instantiation	212, 73, 74	⊢
	: , : , :
55	theorem		⊢
	proveit.numbers.numerals.decimals.nat4
56	instantiation	75	⊢
	: , : , : , :
57	theorem		⊢
	proveit.numbers.division.div_complex_closure
58	instantiation	237, 230, 76	⊢
	: , : , :
59	instantiation	186, 103	⊢
	:
60	theorem		⊢
	proveit.logic.booleans.disjunction.right_if_not_left
61	instantiation	77, 78	⊢
	:
62	instantiation	79, 80	⊢
	: , :
63	instantiation	81, 82, 88, 83, 84*	⊢
	: , :
64	instantiation	219, 150	⊢
	:
65	instantiation	204	⊢
	:
66	instantiation	212, 85, 86	⊢
	: , : , :
67	theorem		⊢
	proveit.numbers.number_sets.real_numbers.e_is_real_pos
68	theorem		⊢
	proveit.numbers.addition.disassociation
69	instantiation	157	⊢
	: , :
70	theorem		⊢
	proveit.numbers.addition.subtraction.add_cancel_triple_32
71	instantiation	237, 230, 87	⊢
	: , : , :
72	instantiation	142, 100, 150	⊢
	: , :
73	instantiation	134, 232, 239, 144, 89, 146, 88, 100, 150	⊢
	: , : , : , : , : , :
74	instantiation	134, 144, 239, 146, 109, 89, 228, 185, 100, 150	⊢
	: , : , : , : , : , :
75	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_4_typical_eq
76	instantiation	237, 233, 90	⊢
	: , : , :
77	axiom		⊢
	proveit.logic.booleans.negation.operand_is_bool
78	instantiation	92, 91	⊢
	:
79	axiom		⊢
	proveit.logic.booleans.disjunction.right_in_bool
80	instantiation	92, 93	⊢
	:
81	theorem		⊢
	proveit.numbers.division.div_as_mult
82	instantiation	175, 94, 95	⊢
	: , : , :
83	instantiation	96, 239, 109, 190, 97	⊢
	: , :
84	instantiation	212, 98, 99	⊢
	: , : , :
85	instantiation	139, 144, 145, 146, 136, 228, 185, 150, 100	⊢
	: , : , : , : , : , : , :
86	instantiation	143, 232, 145, 144, 136, 146, 100, 228, 185, 150	⊢
	: , : , : , : , : , :
87	instantiation	101, 102, 103	⊢
	: , : , :
88	instantiation	237, 230, 116	⊢
	: , : , :
89	instantiation	157	⊢
	: , :
90	instantiation	237, 235, 173	⊢
	: , : , :
91	instantiation	104, 105	⊢
	: , :
92	theorem		⊢
	proveit.logic.booleans.in_bool_if_true
93	instantiation	106, 107	⊢
	:
94	instantiation	237, 230, 108	⊢
	: , : , :
95	instantiation	134, 144, 239, 232, 146, 109, 228, 185, 150	⊢
	: , : , : , : , : , :
96	theorem		⊢
	proveit.numbers.multiplication.mult_not_eq_zero
97	instantiation	237, 199, 166	⊢
	: , : , :
98	instantiation	220, 110	⊢
	: , : , :
99	instantiation	212, 111, 112	⊢
	: , : , :
100	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.i_is_complex
101	theorem		⊢
	proveit.logic.sets.inclusion.unfold_subset_eq
102	instantiation	113, 114	⊢
	: , :
103	theorem		⊢
	proveit.physics.quantum.QPE._two_pow_t_is_nat_pos
104	theorem		⊢
	proveit.logic.equality.unfold_not_equals
105	assumption		⊢
106	theorem		⊢
	proveit.physics.quantum.QPE._delta_b_is_zero_or_non_int
107	instantiation	115, 232, 144, 146	⊢
	: , : , : , : , :
108	instantiation	123, 116, 160	⊢
	: , :
109	instantiation	157	⊢
	: , :
110	instantiation	117, 228, 185, 174, 171, 154, 118*	⊢
	: , : , :
111	instantiation	212, 119, 120	⊢
	: , : , :
112	instantiation	212, 121, 122	⊢
	: , : , :
113	theorem		⊢
	proveit.logic.sets.inclusion.relax_proper_subset
114	theorem		⊢
	proveit.numbers.number_sets.real_numbers.nat_pos_within_real
115	theorem		⊢
	proveit.logic.sets.enumeration.in_enumerated_set
116	instantiation	123, 231, 196	⊢
	: , :
117	theorem		⊢
	proveit.numbers.exponentiation.real_power_of_product
118	instantiation	124, 190, 224, 125*	⊢
	: , :
119	instantiation	212, 126, 127	⊢
	: , : , :
120	instantiation	212, 128, 129	⊢
	: , : , :
121	instantiation	130, 144, 145, 146, 148, 185, 150, 151	⊢
	: , : , : , :
122	instantiation	212, 131, 132	⊢
	: , : , :
123	theorem		⊢
	proveit.numbers.multiplication.mult_real_closure_bin
124	theorem		⊢
	proveit.numbers.exponentiation.neg_power_as_div
125	instantiation	167, 228	⊢
	:
126	instantiation	134, 144, 145, 232, 146, 136, 228, 185, 150, 133	⊢
	: , : , : , : , : , :
127	instantiation	134, 145, 239, 144, 136, 135, 146, 228, 185, 150, 149, 151	⊢
	: , : , : , : , : , :
128	instantiation	139, 144, 145, 232, 146, 136, 228, 185, 150, 149, 151	⊢
	: , : , : , : , : , : , :
129	instantiation	212, 137, 138	⊢
	: , : , :
130	theorem		⊢
	proveit.numbers.multiplication.elim_one_any
131	instantiation	139, 232, 144, 146, 185, 150, 151	⊢
	: , : , : , : , : , : , :
132	instantiation	143, 144, 239, 232, 146, 140, 185, 151, 150, 141*	⊢
	: , : , : , : , : , :
133	instantiation	142, 149, 151	⊢
	: , :
134	theorem		⊢
	proveit.numbers.multiplication.disassociation
135	instantiation	157	⊢
	: , :
136	instantiation	158	⊢
	: , : , :
137	instantiation	143, 144, 239, 145, 146, 147, 148, 149, 228, 185, 150, 151	⊢
	: , : , : , : , : , :
138	instantiation	220, 152	⊢
	: , : , :
139	theorem		⊢
	proveit.numbers.multiplication.leftward_commutation
140	instantiation	157	⊢
	: , :
141	instantiation	153, 185, 215, 174, 154, 155*, 156*	⊢
	: , : , :
142	theorem		⊢
	proveit.numbers.multiplication.mult_complex_closure_bin
143	theorem		⊢
	proveit.numbers.multiplication.association
144	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
145	theorem		⊢
	proveit.numbers.numerals.decimals.nat3
146	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
147	instantiation	157	⊢
	: , :
148	instantiation	158	⊢
	: , : , :
149	instantiation	237, 230, 159	⊢
	: , : , :
150	instantiation	237, 230, 160	⊢
	: , : , :
151	instantiation	161, 185, 162	⊢
	: , :
152	instantiation	175, 163, 164	⊢
	: , : , :
153	theorem		⊢
	proveit.numbers.exponentiation.product_of_real_powers
154	instantiation	165, 166	⊢
	:
155	instantiation	167, 185	⊢
	:
156	instantiation	212, 168, 169	⊢
	: , : , :
157	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
158	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_3_typical_eq
159	instantiation	170, 215, 231, 171	⊢
	: , :
160	instantiation	172, 173	⊢
	:
161	theorem		⊢
	proveit.numbers.exponentiation.exp_complex_closure
162	instantiation	237, 230, 174	⊢
	: , : , :
163	instantiation	175, 176, 177	⊢
	: , : , :
164	instantiation	178, 179, 180, 181	⊢
	: , : , : , :
165	theorem		⊢
	proveit.numbers.number_sets.real_numbers.nonzero_if_in_real_nonzero
166	instantiation	237, 182, 206	⊢
	: , : , :
167	theorem		⊢
	proveit.numbers.exponentiation.complex_x_to_first_power_is_x
168	instantiation	220, 183	⊢
	: , : , :
169	instantiation	184, 185	⊢
	:
170	theorem		⊢
	proveit.numbers.division.div_real_closure
171	instantiation	186, 226	⊢
	:
172	theorem		⊢
	proveit.physics.quantum.QPE._delta_b_is_real
173	theorem		⊢
	proveit.physics.quantum.QPE._best_round_is_int
174	instantiation	237, 233, 187	⊢
	: , : , :
175	theorem		⊢
	proveit.logic.equality.sub_right_side_into
176	instantiation	188, 203, 189, 190	⊢
	: , : , : , : , :
177	instantiation	212, 191, 192	⊢
	: , : , :
178	theorem		⊢
	proveit.logic.equality.four_chain_transitivity
179	instantiation	220, 193	⊢
	: , : , :
180	instantiation	220, 193	⊢
	: , : , :
181	instantiation	227, 203	⊢
	:
182	theorem		⊢
	proveit.numbers.number_sets.real_numbers.real_pos_within_real_nonzero
183	instantiation	194, 203, 195	⊢
	: , :
184	theorem		⊢
	proveit.numbers.exponentiation.exp_zero_eq_one
185	instantiation	237, 230, 196	⊢
	: , : , :
186	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos
187	instantiation	237, 235, 197	⊢
	: , : , :
188	theorem		⊢
	proveit.numbers.division.mult_frac_cancel_denom_left
189	instantiation	237, 199, 198	⊢
	: , : , :
190	instantiation	237, 199, 200	⊢
	: , : , :
191	instantiation	220, 201	⊢
	: , : , :
192	instantiation	220, 202	⊢
	: , : , :
193	instantiation	222, 203	⊢
	:
194	theorem		⊢
	proveit.numbers.addition.subtraction.add_cancel_basic
195	instantiation	204	⊢
	:
196	instantiation	237, 205, 206	⊢
	: , : , :
197	instantiation	207, 229	⊢
	:
198	instantiation	237, 209, 208	⊢
	: , : , :
199	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero
200	instantiation	237, 209, 210	⊢
	: , : , :
201	instantiation	220, 211	⊢
	: , : , :
202	instantiation	212, 213, 214	⊢
	: , : , :
203	instantiation	237, 230, 215	⊢
	: , : , :
204	axiom		⊢
	proveit.logic.equality.equals_reflexivity
205	theorem		⊢
	proveit.numbers.number_sets.real_numbers.real_pos_within_real
206	theorem		⊢
	proveit.numbers.number_sets.real_numbers.pi_is_real_pos
207	theorem		⊢
	proveit.numbers.negation.int_closure
208	instantiation	237, 217, 216	⊢
	: , : , :
209	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero
210	instantiation	237, 217, 218	⊢
	: , : , :
211	instantiation	219, 228	⊢
	:
212	axiom		⊢
	proveit.logic.equality.equals_transitivity
213	instantiation	220, 221	⊢
	: , : , :
214	instantiation	222, 228	⊢
	:
215	instantiation	237, 233, 223	⊢
	: , : , :
216	instantiation	237, 225, 224	⊢
	: , : , :
217	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
218	instantiation	237, 225, 226	⊢
	: , : , :
219	theorem		⊢
	proveit.numbers.multiplication.elim_one_left
220	axiom		⊢
	proveit.logic.equality.substitution
221	instantiation	227, 228	⊢
	:
222	theorem		⊢
	proveit.numbers.division.frac_one_denom
223	instantiation	237, 235, 229	⊢
	: , : , :
224	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
225	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
226	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
227	theorem		⊢
	proveit.numbers.multiplication.elim_one_right
228	instantiation	237, 230, 231	⊢
	: , : , :
229	instantiation	237, 238, 232	⊢
	: , : , :
230	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
231	instantiation	237, 233, 234	⊢
	: , : , :
232	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
233	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
234	instantiation	237, 235, 236	⊢
	: , : , :
235	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
236	instantiation	237, 238, 239	⊢
	: , : , :
237	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
238	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
239	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
*equality replacement requirements