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	85	⊢
2	instantiation	85, 4, 5	,  ⊢
	: , : , :
3	instantiation	6, 29, 38	⊢
	: , :
4	instantiation	7, 8, 9, 10	,  ⊢
	: , : , : , :
5	instantiation	11, 78, 29, 38	⊢
	: , : , :
6	theorem		⊢
	proveit.numbers.addition.commutation
7	theorem		⊢
	proveit.logic.equality.four_chain_transitivity
8	instantiation	46, 12	,  ⊢
	: , : , :
9	instantiation	46, 13	⊢
	: , : , :
10	instantiation	48, 14	,  ⊢
	: , :
11	theorem		⊢
	proveit.numbers.exponentiation.product_of_complex_powers
12	instantiation	103, 15, 16	,  ⊢
	: , : , :
13	instantiation	103, 17, 18	⊢
	: , : , :
14	instantiation	19, 20, 21, 109, 22, 23	,  ⊢
	: , : , :
15	instantiation	46, 24	,  ⊢
	: , : , :
16	instantiation	48, 25	,  ⊢
	: , :
17	instantiation	46, 26	⊢
	: , : , :
18	instantiation	48, 27	⊢
	: , :
19	theorem		⊢
	proveit.numbers.exponentiation.real_power_of_product
20	instantiation	28, 42, 29	⊢
	: , :
21	instantiation	28, 42, 38	⊢
	: , :
22	instantiation	41, 42, 29, 44	⊢
	: , :
23	instantiation	30, 31, 32	⊢
	: , : , :
24	instantiation	103, 33, 34	,  ⊢
	: , : , :
25	instantiation	35, 42, 40, 44	,  ⊢
	: , :
26	instantiation	82, 114, 83, 159, 115, 36, 126, 127, 118, 99, 92	⊢
	: , : , : , : , : , :
27	instantiation	37, 42, 38, 44	⊢
	: , :
28	theorem		⊢
	proveit.numbers.exponentiation.exp_complex_closure
29	instantiation	39, 40	⊢
	:
30	theorem		⊢
	proveit.logic.equality.sub_left_side_into
31	instantiation	41, 42, 43, 44	⊢
	: , :
32	instantiation	46, 45	⊢
	: , : , :
33	instantiation	46, 47	,  ⊢
	: , : , :
34	instantiation	48, 49	,  ⊢
	: , :
35	instantiation	50, 132	⊢
	:
36	instantiation	101	⊢
	: , : , : , :
37	instantiation	51, 132	⊢
	:
38	instantiation	85, 52, 53	⊢
	: , : , :
39	theorem		⊢
	proveit.numbers.negation.complex_closure
40	instantiation	54, 65, 94, 55	⊢
	: , :
41	theorem		⊢
	proveit.numbers.exponentiation.exp_not_eq_zero
42	instantiation	157, 134, 56	⊢
	: , : , :
43	instantiation	85, 57, 58	⊢
	: , : , :
44	instantiation	59, 60	⊢
	:
45	instantiation	61, 159, 126, 127, 118, 99	⊢
	: , : , : , : , : , : , :
46	axiom		⊢
	proveit.logic.equality.substitution
47	instantiation	103, 62, 63	,  ⊢
	: , : , :
48	theorem		⊢
	proveit.logic.equality.equals_reversal
49	instantiation	64, 65, 92, 66, 67, 68*, 69*	,  ⊢
	: , : , : , :
50	theorem		⊢
	proveit.numbers.exponentiation.int_exp_of_neg_exp
51	theorem		⊢
	proveit.numbers.exponentiation.int_exp_of_exp
52	instantiation	125, 112, 70	⊢
	: , :
53	instantiation	103, 71, 72	⊢
	: , : , :
54	theorem		⊢
	proveit.numbers.division.div_complex_closure
55	instantiation	73, 154	⊢
	:
56	instantiation	157, 141, 78	⊢
	: , : , :
57	instantiation	125, 96, 74	⊢
	: , :
58	instantiation	103, 75, 76	⊢
	: , : , :
59	theorem		⊢
	proveit.numbers.number_sets.real_numbers.nonzero_if_in_real_nonzero
60	instantiation	157, 77, 78	⊢
	: , : , :
61	theorem		⊢
	proveit.numbers.multiplication.leftward_commutation
62	instantiation	79, 80, 159, 114, 81, 115, 126, 127, 118, 92, 119	,  ⊢
	: , : , : , : , : , : , :
63	instantiation	82, 114, 83, 159, 115, 84, 126, 127, 118, 119, 92	,  ⊢
	: , : , : , : , : , :
64	theorem		⊢
	proveit.numbers.division.prod_of_fracs
65	instantiation	85, 86, 87	⊢
	: , : , :
66	instantiation	157, 89, 88	⊢
	: , : , :
67	instantiation	157, 89, 90	⊢
	: , : , :
68	instantiation	91, 92	⊢
	:
69	instantiation	93, 94	⊢
	:
70	instantiation	125, 118, 99	⊢
	: , :
71	instantiation	113, 159, 152, 114, 95, 115, 112, 118, 99	⊢
	: , : , : , : , : , :
72	instantiation	113, 114, 152, 115, 116, 95, 126, 127, 118, 99	⊢
	: , : , : , : , : , :
73	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos
74	instantiation	125, 127, 99	⊢
	: , :
75	instantiation	113, 159, 152, 114, 98, 115, 96, 127, 99	⊢
	: , : , : , : , : , :
76	instantiation	113, 114, 152, 115, 97, 98, 126, 118, 127, 99	⊢
	: , : , : , : , : , :
77	theorem		⊢
	proveit.numbers.number_sets.real_numbers.real_pos_within_real_nonzero
78	theorem		⊢
	proveit.numbers.number_sets.real_numbers.e_is_real_pos
79	theorem		⊢
	proveit.numbers.multiplication.rightward_commutation
80	theorem		⊢
	proveit.numbers.numerals.decimals.nat3
81	instantiation	100	⊢
	: , : , :
82	theorem		⊢
	proveit.numbers.multiplication.association
83	theorem		⊢
	proveit.numbers.numerals.decimals.nat4
84	instantiation	101	⊢
	: , : , : , :
85	theorem		⊢
	proveit.logic.equality.sub_right_side_into
86	instantiation	125, 112, 102	⊢
	: , :
87	instantiation	103, 104, 105	⊢
	: , : , :
88	instantiation	157, 107, 106	⊢
	: , : , :
89	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero
90	instantiation	157, 107, 108	⊢
	: , : , :
91	theorem		⊢
	proveit.numbers.division.frac_one_denom
92	instantiation	157, 134, 109	⊢
	: , : , :
93	theorem		⊢
	proveit.numbers.multiplication.elim_one_right
94	instantiation	157, 134, 110	⊢
	: , : , :
95	instantiation	128	⊢
	: , :
96	instantiation	125, 126, 118	⊢
	: , :
97	instantiation	128	⊢
	: , :
98	instantiation	128	⊢
	: , :
99	instantiation	157, 134, 111	⊢
	: , : , :
100	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_3_typical_eq
101	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_4_typical_eq
102	instantiation	125, 118, 119	⊢
	: , :
103	axiom		⊢
	proveit.logic.equality.equals_transitivity
104	instantiation	113, 159, 152, 114, 117, 115, 112, 118, 119	⊢
	: , : , : , : , : , :
105	instantiation	113, 114, 152, 115, 116, 117, 126, 127, 118, 119	⊢
	: , : , : , : , : , :
106	instantiation	157, 121, 120	⊢
	: , : , :
107	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero
108	instantiation	157, 121, 122	⊢
	: , : , :
109	instantiation	157, 139, 123	⊢
	: , : , :
110	instantiation	157, 139, 124	⊢
	: , : , :
111	theorem		⊢
	proveit.physics.quantum.QPE._phase_is_real
112	instantiation	125, 126, 127	⊢
	: , :
113	theorem		⊢
	proveit.numbers.multiplication.disassociation
114	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
115	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
116	instantiation	128	⊢
	: , :
117	instantiation	128	⊢
	: , :
118	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.i_is_complex
119	instantiation	157, 134, 129	⊢
	: , : , :
120	instantiation	157, 130, 154	⊢
	: , : , :
121	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
122	instantiation	157, 130, 131	⊢
	: , : , :
123	instantiation	157, 147, 132	⊢
	: , : , :
124	instantiation	157, 147, 150	⊢
	: , : , :
125	theorem		⊢
	proveit.numbers.multiplication.mult_complex_closure_bin
126	instantiation	157, 134, 133	⊢
	: , : , :
127	instantiation	157, 134, 135	⊢
	: , : , :
128	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
129	instantiation	157, 139, 136	⊢
	: , : , :
130	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
131	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
132	instantiation	157, 137, 138	⊢
	: , : , :
133	instantiation	157, 139, 140	⊢
	: , : , :
134	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
135	instantiation	157, 141, 142	⊢
	: , : , :
136	instantiation	157, 147, 143	⊢
	: , : , :
137	instantiation	144, 145, 146	⊢
	: , :
138	assumption		⊢
139	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
140	instantiation	157, 147, 148	⊢
	: , : , :
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	assumption		⊢
144	theorem		⊢
	proveit.numbers.number_sets.integers.int_interval_within_int
145	theorem		⊢
	proveit.numbers.number_sets.integers.zero_is_int
146	instantiation	149, 150, 151	⊢
	: , :
147	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
148	instantiation	157, 158, 152	⊢
	: , : , :
149	theorem		⊢
	proveit.numbers.addition.add_int_closure_bin
150	instantiation	157, 153, 154	⊢
	: , : , :
151	instantiation	155, 156	⊢
	:
152	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
153	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_int
154	theorem		⊢
	proveit.physics.quantum.QPE._two_pow_t_is_nat_pos
155	theorem		⊢
	proveit.numbers.negation.int_closure
156	instantiation	157, 158, 159	⊢
	: , : , :
157	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
158	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
159	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
*equality replacement requirements