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	10, 3, 4	⊢
	: , : , :
3	instantiation	5, 6, 7, 8*	⊢
	:
4	instantiation	157, 9	⊢
	: , : , :
5	theorem		⊢
	proveit.numbers.exponentiation.unit_complex_polar_num_neq_one
6	instantiation	112, 47, 37	⊢
	: , : , :
7	instantiation	10, 11, 12	⊢
	: , : , :
8	instantiation	13, 14	⊢
	: , :
9	instantiation	76, 176, 169, 81, 48, 83, 165, 122, 42, 87	⊢
	: , : , : , : , : , : , :
10	theorem		⊢
	proveit.logic.equality.sub_left_side_into
11	instantiation	15, 16, 17, 35, 33	⊢
	: , :
12	instantiation	115, 18, 19, 20	⊢
	: , : , : , :
13	theorem		⊢
	proveit.logic.equality.equals_reversal
14	instantiation	157, 21	⊢
	: , : , :
15	theorem		⊢
	proveit.logic.booleans.disjunction.right_if_not_left
16	instantiation	22, 23	⊢
	:
17	instantiation	24, 25	⊢
	: , :
18	instantiation	26, 27, 28, 29, 30*	⊢
	: , :
19	instantiation	156, 87	⊢
	:
20	instantiation	141	⊢
	:
21	instantiation	149, 31, 32	⊢
	: , : , :
22	axiom		⊢
	proveit.logic.booleans.negation.operand_is_bool
23	instantiation	34, 33	⊢
	:
24	axiom		⊢
	proveit.logic.booleans.disjunction.right_in_bool
25	instantiation	34, 35	⊢
	:
26	theorem		⊢
	proveit.numbers.division.div_as_mult
27	instantiation	112, 36, 37	⊢
	: , : , :
28	instantiation	174, 167, 53	⊢
	: , : , :
29	instantiation	38, 176, 48, 127, 39	⊢
	: , :
30	instantiation	149, 40, 41	⊢
	: , : , :
31	instantiation	76, 81, 82, 83, 73, 165, 122, 87, 42	⊢
	: , : , : , : , : , : , :
32	instantiation	80, 169, 82, 81, 73, 83, 42, 165, 122, 87	⊢
	: , : , : , : , : , :
33	instantiation	43, 44	⊢
	: , :
34	theorem		⊢
	proveit.logic.booleans.in_bool_if_true
35	instantiation	45, 46	⊢
	:
36	instantiation	174, 167, 47	⊢
	: , : , :
37	instantiation	71, 81, 176, 169, 83, 48, 165, 122, 87	⊢
	: , : , : , : , : , :
38	theorem		⊢
	proveit.numbers.multiplication.mult_not_eq_zero
39	instantiation	174, 136, 103	⊢
	: , : , :
40	instantiation	157, 49	⊢
	: , : , :
41	instantiation	149, 50, 51	⊢
	: , : , :
42	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.i_is_complex
43	theorem		⊢
	proveit.logic.equality.unfold_not_equals
44	assumption		⊢
45	theorem		⊢
	proveit.physics.quantum.QPE._delta_b_is_zero_or_non_int
46	instantiation	52, 169, 81, 83	⊢
	: , : , : , : , :
47	instantiation	60, 53, 97	⊢
	: , :
48	instantiation	94	⊢
	: , :
49	instantiation	54, 165, 122, 111, 108, 91, 55*	⊢
	: , : , :
50	instantiation	149, 56, 57	⊢
	: , : , :
51	instantiation	149, 58, 59	⊢
	: , : , :
52	theorem		⊢
	proveit.logic.sets.enumeration.in_enumerated_set
53	instantiation	60, 168, 133	⊢
	: , :
54	theorem		⊢
	proveit.numbers.exponentiation.real_power_of_product
55	instantiation	61, 127, 161, 62*	⊢
	: , :
56	instantiation	149, 63, 64	⊢
	: , : , :
57	instantiation	149, 65, 66	⊢
	: , : , :
58	instantiation	67, 81, 82, 83, 85, 122, 87, 88	⊢
	: , : , : , :
59	instantiation	149, 68, 69	⊢
	: , : , :
60	theorem		⊢
	proveit.numbers.multiplication.mult_real_closure_bin
61	theorem		⊢
	proveit.numbers.exponentiation.neg_power_as_div
62	instantiation	104, 165	⊢
	:
63	instantiation	71, 81, 82, 169, 83, 73, 165, 122, 87, 70	⊢
	: , : , : , : , : , :
64	instantiation	71, 82, 176, 81, 73, 72, 83, 165, 122, 87, 86, 88	⊢
	: , : , : , : , : , :
65	instantiation	76, 81, 82, 169, 83, 73, 165, 122, 87, 86, 88	⊢
	: , : , : , : , : , : , :
66	instantiation	149, 74, 75	⊢
	: , : , :
67	theorem		⊢
	proveit.numbers.multiplication.elim_one_any
68	instantiation	76, 169, 81, 83, 122, 87, 88	⊢
	: , : , : , : , : , : , :
69	instantiation	80, 81, 176, 169, 83, 77, 122, 88, 87, 78*	⊢
	: , : , : , : , : , :
70	instantiation	79, 86, 88	⊢
	: , :
71	theorem		⊢
	proveit.numbers.multiplication.disassociation
72	instantiation	94	⊢
	: , :
73	instantiation	95	⊢
	: , : , :
74	instantiation	80, 81, 176, 82, 83, 84, 85, 86, 165, 122, 87, 88	⊢
	: , : , : , : , : , :
75	instantiation	157, 89	⊢
	: , : , :
76	theorem		⊢
	proveit.numbers.multiplication.leftward_commutation
77	instantiation	94	⊢
	: , :
78	instantiation	90, 122, 152, 111, 91, 92*, 93*	⊢
	: , : , :
79	theorem		⊢
	proveit.numbers.multiplication.mult_complex_closure_bin
80	theorem		⊢
	proveit.numbers.multiplication.association
81	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
82	theorem		⊢
	proveit.numbers.numerals.decimals.nat3
83	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
84	instantiation	94	⊢
	: , :
85	instantiation	95	⊢
	: , : , :
86	instantiation	174, 167, 96	⊢
	: , : , :
87	instantiation	174, 167, 97	⊢
	: , : , :
88	instantiation	98, 122, 99	⊢
	: , :
89	instantiation	112, 100, 101	⊢
	: , : , :
90	theorem		⊢
	proveit.numbers.exponentiation.product_of_real_powers
91	instantiation	102, 103	⊢
	:
92	instantiation	104, 122	⊢
	:
93	instantiation	149, 105, 106	⊢
	: , : , :
94	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
95	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_3_typical_eq
96	instantiation	107, 152, 168, 108	⊢
	: , :
97	instantiation	109, 110	⊢
	:
98	theorem		⊢
	proveit.numbers.exponentiation.exp_complex_closure
99	instantiation	174, 167, 111	⊢
	: , : , :
100	instantiation	112, 113, 114	⊢
	: , : , :
101	instantiation	115, 116, 117, 118	⊢
	: , : , : , :
102	theorem		⊢
	proveit.numbers.number_sets.real_numbers.nonzero_if_in_real_nonzero
103	instantiation	174, 119, 143	⊢
	: , : , :
104	theorem		⊢
	proveit.numbers.exponentiation.complex_x_to_first_power_is_x
105	instantiation	157, 120	⊢
	: , : , :
106	instantiation	121, 122	⊢
	:
107	theorem		⊢
	proveit.numbers.division.div_real_closure
108	instantiation	123, 163	⊢
	:
109	theorem		⊢
	proveit.physics.quantum.QPE._delta_b_is_real
110	theorem		⊢
	proveit.physics.quantum.QPE._best_round_is_int
111	instantiation	174, 170, 124	⊢
	: , : , :
112	theorem		⊢
	proveit.logic.equality.sub_right_side_into
113	instantiation	125, 140, 126, 127	⊢
	: , : , : , : , :
114	instantiation	149, 128, 129	⊢
	: , : , :
115	theorem		⊢
	proveit.logic.equality.four_chain_transitivity
116	instantiation	157, 130	⊢
	: , : , :
117	instantiation	157, 130	⊢
	: , : , :
118	instantiation	164, 140	⊢
	:
119	theorem		⊢
	proveit.numbers.number_sets.real_numbers.real_pos_within_real_nonzero
120	instantiation	131, 140, 132	⊢
	: , :
121	theorem		⊢
	proveit.numbers.exponentiation.exp_zero_eq_one
122	instantiation	174, 167, 133	⊢
	: , : , :
123	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos
124	instantiation	174, 172, 134	⊢
	: , : , :
125	theorem		⊢
	proveit.numbers.division.mult_frac_cancel_denom_left
126	instantiation	174, 136, 135	⊢
	: , : , :
127	instantiation	174, 136, 137	⊢
	: , : , :
128	instantiation	157, 138	⊢
	: , : , :
129	instantiation	157, 139	⊢
	: , : , :
130	instantiation	159, 140	⊢
	:
131	theorem		⊢
	proveit.numbers.addition.subtraction.add_cancel_basic
132	instantiation	141	⊢
	:
133	instantiation	174, 142, 143	⊢
	: , : , :
134	instantiation	144, 166	⊢
	:
135	instantiation	174, 146, 145	⊢
	: , : , :
136	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero
137	instantiation	174, 146, 147	⊢
	: , : , :
138	instantiation	157, 148	⊢
	: , : , :
139	instantiation	149, 150, 151	⊢
	: , : , :
140	instantiation	174, 167, 152	⊢
	: , : , :
141	axiom		⊢
	proveit.logic.equality.equals_reflexivity
142	theorem		⊢
	proveit.numbers.number_sets.real_numbers.real_pos_within_real
143	theorem		⊢
	proveit.numbers.number_sets.real_numbers.pi_is_real_pos
144	theorem		⊢
	proveit.numbers.negation.int_closure
145	instantiation	174, 154, 153	⊢
	: , : , :
146	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero
147	instantiation	174, 154, 155	⊢
	: , : , :
148	instantiation	156, 165	⊢
	:
149	axiom		⊢
	proveit.logic.equality.equals_transitivity
150	instantiation	157, 158	⊢
	: , : , :
151	instantiation	159, 165	⊢
	:
152	instantiation	174, 170, 160	⊢
	: , : , :
153	instantiation	174, 162, 161	⊢
	: , : , :
154	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
155	instantiation	174, 162, 163	⊢
	: , : , :
156	theorem		⊢
	proveit.numbers.multiplication.elim_one_left
157	axiom		⊢
	proveit.logic.equality.substitution
158	instantiation	164, 165	⊢
	:
159	theorem		⊢
	proveit.numbers.division.frac_one_denom
160	instantiation	174, 172, 166	⊢
	: , : , :
161	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
162	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
163	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
164	theorem		⊢
	proveit.numbers.multiplication.elim_one_right
165	instantiation	174, 167, 168	⊢
	: , : , :
166	instantiation	174, 175, 169	⊢
	: , : , :
167	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
168	instantiation	174, 170, 171	⊢
	: , : , :
169	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
170	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
171	instantiation	174, 172, 173	⊢
	: , : , :
172	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
173	instantiation	174, 175, 176	⊢
	: , : , :
174	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
175	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
176	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
*equality replacement requirements