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	82	⊢
2	instantiation	4, 5, 6, 7	,  ⊢
	: , : , : , :
3	instantiation	8, 75, 26, 35	⊢
	: , : , :
4	theorem		⊢
	proveit.logic.equality.four_chain_transitivity
5	instantiation	43, 9	,  ⊢
	: , : , :
6	instantiation	43, 10	⊢
	: , : , :
7	instantiation	45, 11	,  ⊢
	: , :
8	theorem		⊢
	proveit.numbers.exponentiation.product_of_complex_powers
9	instantiation	100, 12, 13	,  ⊢
	: , : , :
10	instantiation	100, 14, 15	⊢
	: , : , :
11	instantiation	16, 17, 18, 106, 19, 20	,  ⊢
	: , : , :
12	instantiation	43, 21	,  ⊢
	: , : , :
13	instantiation	45, 22	,  ⊢
	: , :
14	instantiation	43, 23	⊢
	: , : , :
15	instantiation	45, 24	⊢
	: , :
16	theorem		⊢
	proveit.numbers.exponentiation.real_power_of_product
17	instantiation	25, 39, 26	⊢
	: , :
18	instantiation	25, 39, 35	⊢
	: , :
19	instantiation	38, 39, 26, 41	⊢
	: , :
20	instantiation	27, 28, 29	⊢
	: , : , :
21	instantiation	100, 30, 31	,  ⊢
	: , : , :
22	instantiation	32, 39, 37, 41	,  ⊢
	: , :
23	instantiation	79, 111, 80, 156, 112, 33, 123, 124, 115, 96, 89	⊢
	: , : , : , : , : , :
24	instantiation	34, 39, 35, 41	⊢
	: , :
25	theorem		⊢
	proveit.numbers.exponentiation.exp_complex_closure
26	instantiation	36, 37	⊢
	:
27	theorem		⊢
	proveit.logic.equality.sub_left_side_into
28	instantiation	38, 39, 40, 41	⊢
	: , :
29	instantiation	43, 42	⊢
	: , : , :
30	instantiation	43, 44	,  ⊢
	: , : , :
31	instantiation	45, 46	,  ⊢
	: , :
32	instantiation	47, 129	⊢
	:
33	instantiation	98	⊢
	: , : , : , :
34	instantiation	48, 129	⊢
	:
35	instantiation	82, 49, 50	⊢
	: , : , :
36	theorem		⊢
	proveit.numbers.negation.complex_closure
37	instantiation	51, 62, 91, 52	⊢
	: , :
38	theorem		⊢
	proveit.numbers.exponentiation.exp_not_eq_zero
39	instantiation	154, 131, 53	⊢
	: , : , :
40	instantiation	82, 54, 55	⊢
	: , : , :
41	instantiation	56, 57	⊢
	:
42	instantiation	58, 156, 123, 124, 115, 96	⊢
	: , : , : , : , : , : , :
43	axiom		⊢
	proveit.logic.equality.substitution
44	instantiation	100, 59, 60	,  ⊢
	: , : , :
45	theorem		⊢
	proveit.logic.equality.equals_reversal
46	instantiation	61, 62, 89, 63, 64, 65*, 66*	,  ⊢
	: , : , : , :
47	theorem		⊢
	proveit.numbers.exponentiation.int_exp_of_neg_exp
48	theorem		⊢
	proveit.numbers.exponentiation.int_exp_of_exp
49	instantiation	122, 109, 67	⊢
	: , :
50	instantiation	100, 68, 69	⊢
	: , : , :
51	theorem		⊢
	proveit.numbers.division.div_complex_closure
52	instantiation	70, 151	⊢
	:
53	instantiation	154, 138, 75	⊢
	: , : , :
54	instantiation	122, 93, 71	⊢
	: , :
55	instantiation	100, 72, 73	⊢
	: , : , :
56	theorem		⊢
	proveit.numbers.number_sets.real_numbers.nonzero_if_in_real_nonzero
57	instantiation	154, 74, 75	⊢
	: , : , :
58	theorem		⊢
	proveit.numbers.multiplication.leftward_commutation
59	instantiation	76, 77, 156, 111, 78, 112, 123, 124, 115, 89, 116	,  ⊢
	: , : , : , : , : , : , :
60	instantiation	79, 111, 80, 156, 112, 81, 123, 124, 115, 116, 89	,  ⊢
	: , : , : , : , : , :
61	theorem		⊢
	proveit.numbers.division.prod_of_fracs
62	instantiation	82, 83, 84	⊢
	: , : , :
63	instantiation	154, 86, 85	⊢
	: , : , :
64	instantiation	154, 86, 87	⊢
	: , : , :
65	instantiation	88, 89	⊢
	:
66	instantiation	90, 91	⊢
	:
67	instantiation	122, 115, 96	⊢
	: , :
68	instantiation	110, 156, 149, 111, 92, 112, 109, 115, 96	⊢
	: , : , : , : , : , :
69	instantiation	110, 111, 149, 112, 113, 92, 123, 124, 115, 96	⊢
	: , : , : , : , : , :
70	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos
71	instantiation	122, 124, 96	⊢
	: , :
72	instantiation	110, 156, 149, 111, 95, 112, 93, 124, 96	⊢
	: , : , : , : , : , :
73	instantiation	110, 111, 149, 112, 94, 95, 123, 115, 124, 96	⊢
	: , : , : , : , : , :
74	theorem		⊢
	proveit.numbers.number_sets.real_numbers.real_pos_within_real_nonzero
75	theorem		⊢
	proveit.numbers.number_sets.real_numbers.e_is_real_pos
76	theorem		⊢
	proveit.numbers.multiplication.rightward_commutation
77	theorem		⊢
	proveit.numbers.numerals.decimals.nat3
78	instantiation	97	⊢
	: , : , :
79	theorem		⊢
	proveit.numbers.multiplication.association
80	theorem		⊢
	proveit.numbers.numerals.decimals.nat4
81	instantiation	98	⊢
	: , : , : , :
82	theorem		⊢
	proveit.logic.equality.sub_right_side_into
83	instantiation	122, 109, 99	⊢
	: , :
84	instantiation	100, 101, 102	⊢
	: , : , :
85	instantiation	154, 104, 103	⊢
	: , : , :
86	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero
87	instantiation	154, 104, 105	⊢
	: , : , :
88	theorem		⊢
	proveit.numbers.division.frac_one_denom
89	instantiation	154, 131, 106	⊢
	: , : , :
90	theorem		⊢
	proveit.numbers.multiplication.elim_one_right
91	instantiation	154, 131, 107	⊢
	: , : , :
92	instantiation	125	⊢
	: , :
93	instantiation	122, 123, 115	⊢
	: , :
94	instantiation	125	⊢
	: , :
95	instantiation	125	⊢
	: , :
96	instantiation	154, 131, 108	⊢
	: , : , :
97	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_3_typical_eq
98	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_4_typical_eq
99	instantiation	122, 115, 116	⊢
	: , :
100	axiom		⊢
	proveit.logic.equality.equals_transitivity
101	instantiation	110, 156, 149, 111, 114, 112, 109, 115, 116	⊢
	: , : , : , : , : , :
102	instantiation	110, 111, 149, 112, 113, 114, 123, 124, 115, 116	⊢
	: , : , : , : , : , :
103	instantiation	154, 118, 117	⊢
	: , : , :
104	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero
105	instantiation	154, 118, 119	⊢
	: , : , :
106	instantiation	154, 136, 120	⊢
	: , : , :
107	instantiation	154, 136, 121	⊢
	: , : , :
108	theorem		⊢
	proveit.physics.quantum.QPE._phase_is_real
109	instantiation	122, 123, 124	⊢
	: , :
110	theorem		⊢
	proveit.numbers.multiplication.disassociation
111	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
112	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
113	instantiation	125	⊢
	: , :
114	instantiation	125	⊢
	: , :
115	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.i_is_complex
116	instantiation	154, 131, 126	⊢
	: , : , :
117	instantiation	154, 127, 151	⊢
	: , : , :
118	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
119	instantiation	154, 127, 128	⊢
	: , : , :
120	instantiation	154, 144, 129	⊢
	: , : , :
121	instantiation	154, 144, 147	⊢
	: , : , :
122	theorem		⊢
	proveit.numbers.multiplication.mult_complex_closure_bin
123	instantiation	154, 131, 130	⊢
	: , : , :
124	instantiation	154, 131, 132	⊢
	: , : , :
125	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
126	instantiation	154, 136, 133	⊢
	: , : , :
127	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
128	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
129	instantiation	154, 134, 135	⊢
	: , : , :
130	instantiation	154, 136, 137	⊢
	: , : , :
131	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
132	instantiation	154, 138, 139	⊢
	: , : , :
133	instantiation	154, 144, 140	⊢
	: , : , :
134	instantiation	141, 142, 143	⊢
	: , :
135	assumption		⊢
136	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
137	instantiation	154, 144, 145	⊢
	: , : , :
138	theorem		⊢
	proveit.numbers.number_sets.real_numbers.real_pos_within_real
139	theorem		⊢
	proveit.numbers.number_sets.real_numbers.pi_is_real_pos
140	assumption		⊢
141	theorem		⊢
	proveit.numbers.number_sets.integers.int_interval_within_int
142	theorem		⊢
	proveit.numbers.number_sets.integers.zero_is_int
143	instantiation	146, 147, 148	⊢
	: , :
144	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
145	instantiation	154, 155, 149	⊢
	: , : , :
146	theorem		⊢
	proveit.numbers.addition.add_int_closure_bin
147	instantiation	154, 150, 151	⊢
	: , : , :
148	instantiation	152, 153	⊢
	:
149	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
150	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_int
151	theorem		⊢
	proveit.physics.quantum.QPE._two_pow_t_is_nat_pos
152	theorem		⊢
	proveit.numbers.negation.int_closure
153	instantiation	154, 155, 156	⊢
	: , : , :
154	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
155	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
156	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
*equality replacement requirements