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