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, 5, 6	⊢
	: , : , : , :
1	axiom		⊢
	proveit.core_expr_types.operations.operands_substitution
2	reference	164	⊢
3	instantiation	78	⊢
	: , :
4	instantiation	78	⊢
	: , :
5	instantiation	24, 7	⊢
	: , :
6	instantiation	24, 8	⊢
	: , :
7	instantiation	12, 9, 10, 11	⊢
	: , : , : , :
8	instantiation	12, 13, 14, 15	⊢
	: , : , : , :
9	instantiation	47, 112, 16, 17, 18*	⊢
	: , :
10	instantiation	23	⊢
	:
11	instantiation	24, 19	⊢
	: , :
12	theorem		⊢
	proveit.logic.equality.four_chain_transitivity
13	instantiation	47, 112, 20, 21, 22*	⊢
	: , :
14	instantiation	23	⊢
	:
15	instantiation	24, 25	⊢
	: , :
16	instantiation	31, 128, 99	⊢
	: , :
17	instantiation	32, 164, 26, 68, 27	⊢
	: , :
18	instantiation	65, 28, 29	⊢
	: , : , :
19	instantiation	80, 30	⊢
	: , : , :
20	instantiation	31, 92, 55	⊢
	: , :
21	instantiation	32, 164, 33, 76, 34	⊢
	: , :
22	instantiation	65, 35, 36	⊢
	: , : , :
23	axiom		⊢
	proveit.logic.equality.equals_reflexivity
24	theorem		⊢
	proveit.logic.equality.equals_reversal
25	instantiation	80, 37	⊢
	: , : , :
26	instantiation	78	⊢
	: , :
27	instantiation	162, 89, 38	⊢
	: , : , :
28	instantiation	80, 39	⊢
	: , : , :
29	instantiation	65, 40, 41	⊢
	: , : , :
30	instantiation	47, 112, 99, 96, 42*	⊢
	: , :
31	theorem		⊢
	proveit.numbers.multiplication.mult_complex_closure_bin
32	theorem		⊢
	proveit.numbers.multiplication.mult_not_eq_zero
33	instantiation	78	⊢
	: , :
34	instantiation	43, 55, 57	⊢
	:
35	instantiation	80, 44	⊢
	: , : , :
36	instantiation	65, 45, 46	⊢
	: , : , :
37	instantiation	47, 112, 55, 57, 48*	⊢
	: , :
38	instantiation	162, 103, 74	⊢
	: , : , :
39	instantiation	54, 128, 99, 95, 49, 96, 50*	⊢
	: , : , :
40	instantiation	59, 154, 164, 61, 51, 62, 112, 52, 53	⊢
	: , : , : , : , : , :
41	instantiation	60, 61, 164, 62, 51, 52, 53	⊢
	: , : , : , :
42	instantiation	82, 53	⊢
	:
43	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.nonzero_complex_is_complex_nonzero
44	instantiation	54, 92, 55, 95, 56, 57, 58*, 81*	⊢
	: , : , :
45	instantiation	59, 154, 164, 61, 63, 62, 112, 64, 83	⊢
	: , : , : , : , : , :
46	instantiation	60, 61, 164, 62, 63, 64, 83	⊢
	: , : , : , :
47	theorem		⊢
	proveit.numbers.division.div_as_mult
48	instantiation	65, 66, 67	⊢
	: , : , :
49	instantiation	109, 131	⊢
	:
50	instantiation	75, 68, 134, 69*	⊢
	: , :
51	instantiation	78	⊢
	: , :
52	instantiation	162, 141, 70	⊢
	: , : , :
53	instantiation	98, 99, 71	⊢
	: , :
54	theorem		⊢
	proveit.numbers.exponentiation.real_power_of_product
55	instantiation	162, 141, 72	⊢
	: , : , :
56	instantiation	109, 136	⊢
	:
57	instantiation	73, 74, 101	⊢
	: , :
58	instantiation	75, 76, 134, 77*	⊢
	: , :
59	theorem		⊢
	proveit.numbers.multiplication.disassociation
60	theorem		⊢
	proveit.numbers.multiplication.elim_one_any
61	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
62	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
63	instantiation	78	⊢
	: , :
64	instantiation	162, 141, 79	⊢
	: , : , :
65	axiom		⊢
	proveit.logic.equality.equals_transitivity
66	instantiation	80, 81	⊢
	: , : , :
67	instantiation	82, 83	⊢
	:
68	instantiation	162, 89, 84	⊢
	: , : , :
69	instantiation	91, 128	⊢
	:
70	instantiation	162, 146, 85	⊢
	: , : , :
71	instantiation	86, 112	⊢
	:
72	instantiation	87, 114, 164	⊢
	: , :
73	theorem		⊢
	proveit.numbers.exponentiation.exp_rational_non_zero__not_zero
74	instantiation	162, 118, 88	⊢
	: , : , :
75	theorem		⊢
	proveit.numbers.exponentiation.neg_power_as_div
76	instantiation	162, 89, 90	⊢
	: , : , :
77	instantiation	91, 92	⊢
	:
78	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
79	instantiation	162, 146, 93	⊢
	: , : , :
80	axiom		⊢
	proveit.logic.equality.substitution
81	instantiation	94, 99, 142, 95, 96, 97*	⊢
	: , : , :
82	theorem		⊢
	proveit.numbers.multiplication.elim_one_left
83	instantiation	98, 99, 100	⊢
	: , :
84	instantiation	162, 103, 101	⊢
	: , : , :
85	instantiation	162, 106, 102	⊢
	: , : , :
86	theorem		⊢
	proveit.numbers.negation.complex_closure
87	theorem		⊢
	proveit.numbers.exponentiation.exp_real_closure_nat_power
88	instantiation	162, 132, 110	⊢
	: , : , :
89	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero
90	instantiation	162, 103, 104	⊢
	: , : , :
91	theorem		⊢
	proveit.numbers.exponentiation.complex_x_to_first_power_is_x
92	instantiation	162, 141, 105	⊢
	: , : , :
93	instantiation	162, 106, 107	⊢
	: , : , :
94	theorem		⊢
	proveit.numbers.exponentiation.real_power_of_real_power
95	instantiation	108, 126	⊢
	:
96	instantiation	109, 110	⊢
	:
97	instantiation	111, 128, 112, 113*	⊢
	: , :
98	theorem		⊢
	proveit.numbers.exponentiation.exp_complex_closure
99	instantiation	162, 141, 114	⊢
	: , : , :
100	instantiation	162, 141, 115	⊢
	: , : , :
101	instantiation	162, 118, 116	⊢
	: , : , :
102	instantiation	121, 122, 117	⊢
	: , :
103	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero
104	instantiation	162, 118, 119	⊢
	: , : , :
105	instantiation	162, 146, 120	⊢
	: , : , :
106	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.rational_pos_within_rational
107	instantiation	121, 122, 123	⊢
	: , :
108	theorem		⊢
	proveit.numbers.negation.real_closure
109	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos
110	instantiation	124, 143, 125	⊢
	:
111	theorem		⊢
	proveit.numbers.multiplication.mult_neg_right
112	instantiation	162, 141, 126	⊢
	: , : , :
113	instantiation	127, 128	⊢
	:
114	instantiation	162, 146, 129	⊢
	: , : , :
115	instantiation	162, 146, 130	⊢
	: , : , :
116	instantiation	162, 132, 131	⊢
	: , : , :
117	instantiation	162, 135, 131	⊢
	: , : , :
118	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
119	instantiation	162, 132, 136	⊢
	: , : , :
120	instantiation	162, 150, 133	⊢
	: , : , :
121	theorem		⊢
	proveit.numbers.division.div_rational_pos_closure
122	instantiation	162, 135, 134	⊢
	: , : , :
123	instantiation	162, 135, 136	⊢
	: , : , :
124	theorem		⊢
	proveit.numbers.number_sets.integers.pos_int_is_natural_pos
125	instantiation	137, 138, 139	⊢
	: , : , :
126	instantiation	162, 146, 140	⊢
	: , : , :
127	theorem		⊢
	proveit.numbers.multiplication.elim_one_right
128	instantiation	162, 141, 142	⊢
	: , : , :
129	instantiation	162, 150, 143	⊢
	: , : , :
130	instantiation	162, 150, 157	⊢
	: , : , :
131	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
132	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
133	instantiation	162, 163, 144	⊢
	: , : , :
134	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
135	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nat_pos_within_rational_pos
136	theorem		⊢
	proveit.numbers.numerals.decimals.posnat4
137	theorem		⊢
	proveit.numbers.ordering.transitivity_less_less_eq
138	theorem		⊢
	proveit.numbers.numerals.decimals.less_0_1
139	instantiation	145, 152, 153, 149	⊢
	: , : , :
140	instantiation	162, 150, 152	⊢
	: , : , :
141	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
142	instantiation	162, 146, 147	⊢
	: , : , :
143	instantiation	162, 148, 149	⊢
	: , : , :
144	theorem		⊢
	proveit.numbers.numerals.decimals.nat4
145	theorem		⊢
	proveit.numbers.number_sets.integers.interval_lower_bound
146	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
147	instantiation	162, 150, 161	⊢
	: , : , :
148	instantiation	151, 152, 153	⊢
	: , :
149	assumption		⊢
150	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
151	theorem		⊢
	proveit.numbers.number_sets.integers.int_interval_within_int
152	instantiation	162, 163, 154	⊢
	: , : , :
153	instantiation	155, 156, 157	⊢
	: , :
154	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
155	theorem		⊢
	proveit.numbers.addition.add_int_closure_bin
156	instantiation	162, 158, 159	⊢
	: , : , :
157	instantiation	160, 161	⊢
	:
158	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_int
159	theorem		⊢
	proveit.physics.quantum.QPE._two_pow_t_minus_one_is_nat_pos
160	theorem		⊢
	proveit.numbers.negation.int_closure
161	instantiation	162, 163, 164	⊢
	: , : , :
162	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
163	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
164	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
*equality replacement requirements