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	9	⊢
2	instantiation	4, 5, 6, 7*	⊢
	:
3	instantiation	156, 8	⊢
	: , : , :
4	theorem		⊢
	proveit.numbers.exponentiation.unit_complex_polar_num_neq_one
5	instantiation	111, 46, 36	⊢
	: , : , :
6	instantiation	9, 10, 11	⊢
	: , : , :
7	instantiation	12, 13	⊢
	: , :
8	instantiation	75, 175, 168, 80, 47, 82, 164, 121, 41, 86	⊢
	: , : , : , : , : , : , :
9	theorem		⊢
	proveit.logic.equality.sub_left_side_into
10	instantiation	14, 15, 16, 34, 32	⊢
	: , :
11	instantiation	114, 17, 18, 19	⊢
	: , : , : , :
12	theorem		⊢
	proveit.logic.equality.equals_reversal
13	instantiation	156, 20	⊢
	: , : , :
14	theorem		⊢
	proveit.logic.booleans.disjunction.right_if_not_left
15	instantiation	21, 22	⊢
	:
16	instantiation	23, 24	⊢
	: , :
17	instantiation	25, 26, 27, 28, 29*	⊢
	: , :
18	instantiation	155, 86	⊢
	:
19	instantiation	140	⊢
	:
20	instantiation	148, 30, 31	⊢
	: , : , :
21	axiom		⊢
	proveit.logic.booleans.negation.operand_is_bool
22	instantiation	33, 32	⊢
	:
23	axiom		⊢
	proveit.logic.booleans.disjunction.right_in_bool
24	instantiation	33, 34	⊢
	:
25	theorem		⊢
	proveit.numbers.division.div_as_mult
26	instantiation	111, 35, 36	⊢
	: , : , :
27	instantiation	173, 166, 52	⊢
	: , : , :
28	instantiation	37, 175, 47, 126, 38	⊢
	: , :
29	instantiation	148, 39, 40	⊢
	: , : , :
30	instantiation	75, 80, 81, 82, 72, 164, 121, 86, 41	⊢
	: , : , : , : , : , : , :
31	instantiation	79, 168, 81, 80, 72, 82, 41, 164, 121, 86	⊢
	: , : , : , : , : , :
32	instantiation	42, 43	⊢
	: , :
33	theorem		⊢
	proveit.logic.booleans.in_bool_if_true
34	instantiation	44, 45	⊢
	:
35	instantiation	173, 166, 46	⊢
	: , : , :
36	instantiation	70, 80, 175, 168, 82, 47, 164, 121, 86	⊢
	: , : , : , : , : , :
37	theorem		⊢
	proveit.numbers.multiplication.mult_not_eq_zero
38	instantiation	173, 135, 102	⊢
	: , : , :
39	instantiation	156, 48	⊢
	: , : , :
40	instantiation	148, 49, 50	⊢
	: , : , :
41	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.i_is_complex
42	theorem		⊢
	proveit.logic.equality.unfold_not_equals
43	assumption		⊢
44	theorem		⊢
	proveit.physics.quantum.QPE._delta_b_is_zero_or_non_int
45	instantiation	51, 168, 80, 82	⊢
	: , : , : , : , :
46	instantiation	59, 52, 96	⊢
	: , :
47	instantiation	93	⊢
	: , :
48	instantiation	53, 164, 121, 110, 107, 90, 54*	⊢
	: , : , :
49	instantiation	148, 55, 56	⊢
	: , : , :
50	instantiation	148, 57, 58	⊢
	: , : , :
51	theorem		⊢
	proveit.logic.sets.enumeration.in_enumerated_set
52	instantiation	59, 167, 132	⊢
	: , :
53	theorem		⊢
	proveit.numbers.exponentiation.real_power_of_product
54	instantiation	60, 126, 160, 61*	⊢
	: , :
55	instantiation	148, 62, 63	⊢
	: , : , :
56	instantiation	148, 64, 65	⊢
	: , : , :
57	instantiation	66, 80, 81, 82, 84, 121, 86, 87	⊢
	: , : , : , :
58	instantiation	148, 67, 68	⊢
	: , : , :
59	theorem		⊢
	proveit.numbers.multiplication.mult_real_closure_bin
60	theorem		⊢
	proveit.numbers.exponentiation.neg_power_as_div
61	instantiation	103, 164	⊢
	:
62	instantiation	70, 80, 81, 168, 82, 72, 164, 121, 86, 69	⊢
	: , : , : , : , : , :
63	instantiation	70, 81, 175, 80, 72, 71, 82, 164, 121, 86, 85, 87	⊢
	: , : , : , : , : , :
64	instantiation	75, 80, 81, 168, 82, 72, 164, 121, 86, 85, 87	⊢
	: , : , : , : , : , : , :
65	instantiation	148, 73, 74	⊢
	: , : , :
66	theorem		⊢
	proveit.numbers.multiplication.elim_one_any
67	instantiation	75, 168, 80, 82, 121, 86, 87	⊢
	: , : , : , : , : , : , :
68	instantiation	79, 80, 175, 168, 82, 76, 121, 87, 86, 77*	⊢
	: , : , : , : , : , :
69	instantiation	78, 85, 87	⊢
	: , :
70	theorem		⊢
	proveit.numbers.multiplication.disassociation
71	instantiation	93	⊢
	: , :
72	instantiation	94	⊢
	: , : , :
73	instantiation	79, 80, 175, 81, 82, 83, 84, 85, 164, 121, 86, 87	⊢
	: , : , : , : , : , :
74	instantiation	156, 88	⊢
	: , : , :
75	theorem		⊢
	proveit.numbers.multiplication.leftward_commutation
76	instantiation	93	⊢
	: , :
77	instantiation	89, 121, 151, 110, 90, 91*, 92*	⊢
	: , : , :
78	theorem		⊢
	proveit.numbers.multiplication.mult_complex_closure_bin
79	theorem		⊢
	proveit.numbers.multiplication.association
80	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
81	theorem		⊢
	proveit.numbers.numerals.decimals.nat3
82	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
83	instantiation	93	⊢
	: , :
84	instantiation	94	⊢
	: , : , :
85	instantiation	173, 166, 95	⊢
	: , : , :
86	instantiation	173, 166, 96	⊢
	: , : , :
87	instantiation	97, 121, 98	⊢
	: , :
88	instantiation	111, 99, 100	⊢
	: , : , :
89	theorem		⊢
	proveit.numbers.exponentiation.product_of_real_powers
90	instantiation	101, 102	⊢
	:
91	instantiation	103, 121	⊢
	:
92	instantiation	148, 104, 105	⊢
	: , : , :
93	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
94	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_3_typical_eq
95	instantiation	106, 151, 167, 107	⊢
	: , :
96	instantiation	108, 109	⊢
	:
97	theorem		⊢
	proveit.numbers.exponentiation.exp_complex_closure
98	instantiation	173, 166, 110	⊢
	: , : , :
99	instantiation	111, 112, 113	⊢
	: , : , :
100	instantiation	114, 115, 116, 117	⊢
	: , : , : , :
101	theorem		⊢
	proveit.numbers.number_sets.real_numbers.nonzero_if_in_real_nonzero
102	instantiation	173, 118, 142	⊢
	: , : , :
103	theorem		⊢
	proveit.numbers.exponentiation.complex_x_to_first_power_is_x
104	instantiation	156, 119	⊢
	: , : , :
105	instantiation	120, 121	⊢
	:
106	theorem		⊢
	proveit.numbers.division.div_real_closure
107	instantiation	122, 162	⊢
	:
108	theorem		⊢
	proveit.physics.quantum.QPE._delta_b_is_real
109	theorem		⊢
	proveit.physics.quantum.QPE._best_round_is_int
110	instantiation	173, 169, 123	⊢
	: , : , :
111	theorem		⊢
	proveit.logic.equality.sub_right_side_into
112	instantiation	124, 139, 125, 126	⊢
	: , : , : , : , :
113	instantiation	148, 127, 128	⊢
	: , : , :
114	theorem		⊢
	proveit.logic.equality.four_chain_transitivity
115	instantiation	156, 129	⊢
	: , : , :
116	instantiation	156, 129	⊢
	: , : , :
117	instantiation	163, 139	⊢
	:
118	theorem		⊢
	proveit.numbers.number_sets.real_numbers.real_pos_within_real_nonzero
119	instantiation	130, 139, 131	⊢
	: , :
120	theorem		⊢
	proveit.numbers.exponentiation.exp_zero_eq_one
121	instantiation	173, 166, 132	⊢
	: , : , :
122	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos
123	instantiation	173, 171, 133	⊢
	: , : , :
124	theorem		⊢
	proveit.numbers.division.mult_frac_cancel_denom_left
125	instantiation	173, 135, 134	⊢
	: , : , :
126	instantiation	173, 135, 136	⊢
	: , : , :
127	instantiation	156, 137	⊢
	: , : , :
128	instantiation	156, 138	⊢
	: , : , :
129	instantiation	158, 139	⊢
	:
130	theorem		⊢
	proveit.numbers.addition.subtraction.add_cancel_basic
131	instantiation	140	⊢
	:
132	instantiation	173, 141, 142	⊢
	: , : , :
133	instantiation	143, 165	⊢
	:
134	instantiation	173, 145, 144	⊢
	: , : , :
135	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero
136	instantiation	173, 145, 146	⊢
	: , : , :
137	instantiation	156, 147	⊢
	: , : , :
138	instantiation	148, 149, 150	⊢
	: , : , :
139	instantiation	173, 166, 151	⊢
	: , : , :
140	axiom		⊢
	proveit.logic.equality.equals_reflexivity
141	theorem		⊢
	proveit.numbers.number_sets.real_numbers.real_pos_within_real
142	theorem		⊢
	proveit.numbers.number_sets.real_numbers.pi_is_real_pos
143	theorem		⊢
	proveit.numbers.negation.int_closure
144	instantiation	173, 153, 152	⊢
	: , : , :
145	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero
146	instantiation	173, 153, 154	⊢
	: , : , :
147	instantiation	155, 164	⊢
	:
148	axiom		⊢
	proveit.logic.equality.equals_transitivity
149	instantiation	156, 157	⊢
	: , : , :
150	instantiation	158, 164	⊢
	:
151	instantiation	173, 169, 159	⊢
	: , : , :
152	instantiation	173, 161, 160	⊢
	: , : , :
153	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
154	instantiation	173, 161, 162	⊢
	: , : , :
155	theorem		⊢
	proveit.numbers.multiplication.elim_one_left
156	axiom		⊢
	proveit.logic.equality.substitution
157	instantiation	163, 164	⊢
	:
158	theorem		⊢
	proveit.numbers.division.frac_one_denom
159	instantiation	173, 171, 165	⊢
	: , : , :
160	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
161	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
162	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
163	theorem		⊢
	proveit.numbers.multiplication.elim_one_right
164	instantiation	173, 166, 167	⊢
	: , : , :
165	instantiation	173, 174, 168	⊢
	: , : , :
166	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
167	instantiation	173, 169, 170	⊢
	: , : , :
168	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
169	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
170	instantiation	173, 171, 172	⊢
	: , : , :
171	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
172	instantiation	173, 174, 175	⊢
	: , : , :
173	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
174	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
175	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
*equality replacement requirements