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	107, 42, 32	⊢
	: , : , :
3	instantiation	5, 6, 7	⊢
	: , : , :
4	instantiation	8, 9	⊢
	: , :
5	theorem		⊢
	proveit.logic.equality.sub_left_side_into
6	instantiation	10, 11, 12, 30, 28	⊢
	: , :
7	instantiation	110, 13, 14, 15	⊢
	: , : , : , :
8	theorem		⊢
	proveit.logic.equality.equals_reversal
9	instantiation	152, 16	⊢
	: , : , :
10	theorem		⊢
	proveit.logic.booleans.disjunction.right_if_not_left
11	instantiation	17, 18	⊢
	:
12	instantiation	19, 20	⊢
	: , :
13	instantiation	21, 22, 23, 24, 25*	⊢
	: , :
14	instantiation	151, 82	⊢
	:
15	instantiation	136	⊢
	:
16	instantiation	144, 26, 27	⊢
	: , : , :
17	axiom		⊢
	proveit.logic.booleans.negation.operand_is_bool
18	instantiation	29, 28	⊢
	:
19	axiom		⊢
	proveit.logic.booleans.disjunction.right_in_bool
20	instantiation	29, 30	⊢
	:
21	theorem		⊢
	proveit.numbers.division.div_as_mult
22	instantiation	107, 31, 32	⊢
	: , : , :
23	instantiation	169, 162, 48	⊢
	: , : , :
24	instantiation	33, 171, 43, 122, 34	⊢
	: , :
25	instantiation	144, 35, 36	⊢
	: , : , :
26	instantiation	71, 76, 77, 78, 68, 160, 117, 82, 37	⊢
	: , : , : , : , : , : , :
27	instantiation	75, 164, 77, 76, 68, 78, 37, 160, 117, 82	⊢
	: , : , : , : , : , :
28	instantiation	38, 39	⊢
	: , :
29	theorem		⊢
	proveit.logic.booleans.in_bool_if_true
30	instantiation	40, 41	⊢
	:
31	instantiation	169, 162, 42	⊢
	: , : , :
32	instantiation	66, 76, 171, 164, 78, 43, 160, 117, 82	⊢
	: , : , : , : , : , :
33	theorem		⊢
	proveit.numbers.multiplication.mult_not_eq_zero
34	instantiation	169, 131, 98	⊢
	: , : , :
35	instantiation	152, 44	⊢
	: , : , :
36	instantiation	144, 45, 46	⊢
	: , : , :
37	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.i_is_complex
38	theorem		⊢
	proveit.logic.equality.unfold_not_equals
39	assumption		⊢
40	theorem		⊢
	proveit.physics.quantum.QPE._delta_b_is_zero_or_non_int
41	instantiation	47, 164, 76, 78	⊢
	: , : , : , : , :
42	instantiation	55, 48, 92	⊢
	: , :
43	instantiation	89	⊢
	: , :
44	instantiation	49, 160, 117, 106, 103, 86, 50*	⊢
	: , : , :
45	instantiation	144, 51, 52	⊢
	: , : , :
46	instantiation	144, 53, 54	⊢
	: , : , :
47	theorem		⊢
	proveit.logic.sets.enumeration.in_enumerated_set
48	instantiation	55, 163, 128	⊢
	: , :
49	theorem		⊢
	proveit.numbers.exponentiation.real_power_of_product
50	instantiation	56, 122, 156, 57*	⊢
	: , :
51	instantiation	144, 58, 59	⊢
	: , : , :
52	instantiation	144, 60, 61	⊢
	: , : , :
53	instantiation	62, 76, 77, 78, 80, 117, 82, 83	⊢
	: , : , : , :
54	instantiation	144, 63, 64	⊢
	: , : , :
55	theorem		⊢
	proveit.numbers.multiplication.mult_real_closure_bin
56	theorem		⊢
	proveit.numbers.exponentiation.neg_power_as_div
57	instantiation	99, 160	⊢
	:
58	instantiation	66, 76, 77, 164, 78, 68, 160, 117, 82, 65	⊢
	: , : , : , : , : , :
59	instantiation	66, 77, 171, 76, 68, 67, 78, 160, 117, 82, 81, 83	⊢
	: , : , : , : , : , :
60	instantiation	71, 76, 77, 164, 78, 68, 160, 117, 82, 81, 83	⊢
	: , : , : , : , : , : , :
61	instantiation	144, 69, 70	⊢
	: , : , :
62	theorem		⊢
	proveit.numbers.multiplication.elim_one_any
63	instantiation	71, 164, 76, 78, 117, 82, 83	⊢
	: , : , : , : , : , : , :
64	instantiation	75, 76, 171, 164, 78, 72, 117, 83, 82, 73*	⊢
	: , : , : , : , : , :
65	instantiation	74, 81, 83	⊢
	: , :
66	theorem		⊢
	proveit.numbers.multiplication.disassociation
67	instantiation	89	⊢
	: , :
68	instantiation	90	⊢
	: , : , :
69	instantiation	75, 76, 171, 77, 78, 79, 80, 81, 160, 117, 82, 83	⊢
	: , : , : , : , : , :
70	instantiation	152, 84	⊢
	: , : , :
71	theorem		⊢
	proveit.numbers.multiplication.leftward_commutation
72	instantiation	89	⊢
	: , :
73	instantiation	85, 117, 147, 106, 86, 87*, 88*	⊢
	: , : , :
74	theorem		⊢
	proveit.numbers.multiplication.mult_complex_closure_bin
75	theorem		⊢
	proveit.numbers.multiplication.association
76	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
77	theorem		⊢
	proveit.numbers.numerals.decimals.nat3
78	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
79	instantiation	89	⊢
	: , :
80	instantiation	90	⊢
	: , : , :
81	instantiation	169, 162, 91	⊢
	: , : , :
82	instantiation	169, 162, 92	⊢
	: , : , :
83	instantiation	93, 117, 94	⊢
	: , :
84	instantiation	107, 95, 96	⊢
	: , : , :
85	theorem		⊢
	proveit.numbers.exponentiation.product_of_real_powers
86	instantiation	97, 98	⊢
	:
87	instantiation	99, 117	⊢
	:
88	instantiation	144, 100, 101	⊢
	: , : , :
89	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
90	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_3_typical_eq
91	instantiation	102, 147, 163, 103	⊢
	: , :
92	instantiation	104, 105	⊢
	:
93	theorem		⊢
	proveit.numbers.exponentiation.exp_complex_closure
94	instantiation	169, 162, 106	⊢
	: , : , :
95	instantiation	107, 108, 109	⊢
	: , : , :
96	instantiation	110, 111, 112, 113	⊢
	: , : , : , :
97	theorem		⊢
	proveit.numbers.number_sets.real_numbers.nonzero_if_in_real_nonzero
98	instantiation	169, 114, 138	⊢
	: , : , :
99	theorem		⊢
	proveit.numbers.exponentiation.complex_x_to_first_power_is_x
100	instantiation	152, 115	⊢
	: , : , :
101	instantiation	116, 117	⊢
	:
102	theorem		⊢
	proveit.numbers.division.div_real_closure
103	instantiation	118, 158	⊢
	:
104	theorem		⊢
	proveit.physics.quantum.QPE._delta_b_is_real
105	theorem		⊢
	proveit.physics.quantum.QPE._best_round_is_int
106	instantiation	169, 165, 119	⊢
	: , : , :
107	theorem		⊢
	proveit.logic.equality.sub_right_side_into
108	instantiation	120, 135, 121, 122	⊢
	: , : , : , : , :
109	instantiation	144, 123, 124	⊢
	: , : , :
110	theorem		⊢
	proveit.logic.equality.four_chain_transitivity
111	instantiation	152, 125	⊢
	: , : , :
112	instantiation	152, 125	⊢
	: , : , :
113	instantiation	159, 135	⊢
	:
114	theorem		⊢
	proveit.numbers.number_sets.real_numbers.real_pos_within_real_nonzero
115	instantiation	126, 135, 127	⊢
	: , :
116	theorem		⊢
	proveit.numbers.exponentiation.exp_zero_eq_one
117	instantiation	169, 162, 128	⊢
	: , : , :
118	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos
119	instantiation	169, 167, 129	⊢
	: , : , :
120	theorem		⊢
	proveit.numbers.division.mult_frac_cancel_denom_left
121	instantiation	169, 131, 130	⊢
	: , : , :
122	instantiation	169, 131, 132	⊢
	: , : , :
123	instantiation	152, 133	⊢
	: , : , :
124	instantiation	152, 134	⊢
	: , : , :
125	instantiation	154, 135	⊢
	:
126	theorem		⊢
	proveit.numbers.addition.subtraction.add_cancel_basic
127	instantiation	136	⊢
	:
128	instantiation	169, 137, 138	⊢
	: , : , :
129	instantiation	139, 161	⊢
	:
130	instantiation	169, 141, 140	⊢
	: , : , :
131	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero
132	instantiation	169, 141, 142	⊢
	: , : , :
133	instantiation	152, 143	⊢
	: , : , :
134	instantiation	144, 145, 146	⊢
	: , : , :
135	instantiation	169, 162, 147	⊢
	: , : , :
136	axiom		⊢
	proveit.logic.equality.equals_reflexivity
137	theorem		⊢
	proveit.numbers.number_sets.real_numbers.real_pos_within_real
138	theorem		⊢
	proveit.numbers.number_sets.real_numbers.pi_is_real_pos
139	theorem		⊢
	proveit.numbers.negation.int_closure
140	instantiation	169, 149, 148	⊢
	: , : , :
141	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero
142	instantiation	169, 149, 150	⊢
	: , : , :
143	instantiation	151, 160	⊢
	:
144	axiom		⊢
	proveit.logic.equality.equals_transitivity
145	instantiation	152, 153	⊢
	: , : , :
146	instantiation	154, 160	⊢
	:
147	instantiation	169, 165, 155	⊢
	: , : , :
148	instantiation	169, 157, 156	⊢
	: , : , :
149	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
150	instantiation	169, 157, 158	⊢
	: , : , :
151	theorem		⊢
	proveit.numbers.multiplication.elim_one_left
152	axiom		⊢
	proveit.logic.equality.substitution
153	instantiation	159, 160	⊢
	:
154	theorem		⊢
	proveit.numbers.division.frac_one_denom
155	instantiation	169, 167, 161	⊢
	: , : , :
156	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
157	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
158	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
159	theorem		⊢
	proveit.numbers.multiplication.elim_one_right
160	instantiation	169, 162, 163	⊢
	: , : , :
161	instantiation	169, 170, 164	⊢
	: , : , :
162	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
163	instantiation	169, 165, 166	⊢
	: , : , :
164	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
165	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
166	instantiation	169, 167, 168	⊢
	: , : , :
167	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
168	instantiation	169, 170, 171	⊢
	: , : , :
169	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
170	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
171	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
*equality replacement requirements