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	generalization	1	⊢
1	instantiation	2, 3, 4	⊢
	: , :
2	theorem		⊢
	proveit.logic.equality.rhs_via_equality
3	instantiation	5, 144	⊢
	:
4	instantiation	57, 6, 7*, 8*	⊢
	: , : , :
5	theorem		⊢
	proveit.physics.quantum.QPE._alpha_m_evaluation
6	modus ponens	9, 10	⊢
7	instantiation	11, 135	⊢
	: , :
8	instantiation	11, 135	⊢
	: , :
9	instantiation	12, 127	⊢
	: , : , : , : , : , : , :
10	generalization	13	⊢
11	theorem		⊢
	proveit.core_expr_types.conditionals.satisfied_condition_reduction
12	theorem		⊢
	proveit.core_expr_types.lambda_maps.general_lambda_substitution
13	instantiation	16, 14, 15	,  ⊢
	: , : , :
14	instantiation	16, 17, 18	,  ⊢
	: , : , :
15	instantiation	82, 19, 20	,  ⊢
	: , : , :
16	theorem		⊢
	proveit.logic.equality.sub_left_side_into
17	instantiation	21, 89, 22, 23, 24, 25*, 26*	,  ⊢
	: , : , :
18	instantiation	82, 27, 28	,  ⊢
	: , : , :
19	instantiation	57, 29	,  ⊢
	: , : , :
20	instantiation	41, 89, 49	,  ⊢
	: , :
21	theorem		⊢
	proveit.numbers.exponentiation.exp_eq
22	instantiation	30, 31, 35	⊢
	: , :
23	instantiation	30, 31, 38	⊢
	: , :
24	instantiation	32, 121, 105, 33*, 34*	⊢
	: , :
25	instantiation	37, 54, 35, 89, 36*	,  ⊢
	: , : , :
26	instantiation	37, 54, 38, 89, 39*	,  ⊢
	: , : , :
27	instantiation	57, 40	,  ⊢
	: , : , :
28	instantiation	41, 89, 46	,  ⊢
	: , :
29	instantiation	98, 42, 43	,  ⊢
	: , : , :
30	theorem		⊢
	proveit.numbers.exponentiation.exp_complex_closure
31	instantiation	158, 132, 44	⊢
	: , : , :
32	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.exp_neg2pi_i_x
33	instantiation	45, 68, 91, 56	⊢
	: , :
34	instantiation	45, 63, 91, 56	⊢
	: , :
35	instantiation	47, 46	⊢
	:
36	instantiation	48, 46, 89	,  ⊢
	: , :
37	theorem		⊢
	proveit.numbers.exponentiation.complex_power_of_complex_power
38	instantiation	47, 49	⊢
	:
39	instantiation	48, 49, 89	,  ⊢
	: , :
40	instantiation	98, 50, 51	,  ⊢
	: , : , :
41	theorem		⊢
	proveit.numbers.multiplication.commutation
42	instantiation	57, 52	,  ⊢
	: , : , :
43	instantiation	59, 53	,  ⊢
	: , :
44	instantiation	158, 138, 54	⊢
	: , : , :
45	theorem		⊢
	proveit.numbers.division.neg_frac_neg_numerator
46	instantiation	55, 68, 91, 56	⊢
	: , :
47	theorem		⊢
	proveit.numbers.negation.complex_closure
48	theorem		⊢
	proveit.numbers.multiplication.mult_neg_left
49	instantiation	55, 63, 91, 56	⊢
	: , :
50	instantiation	57, 58	,  ⊢
	: , : , :
51	instantiation	59, 60	,  ⊢
	: , :
52	instantiation	98, 61, 62	,  ⊢
	: , : , :
53	instantiation	67, 89, 63, 69, 70, 71*, 72*	,  ⊢
	: , : , : , :
54	theorem		⊢
	proveit.numbers.number_sets.real_numbers.e_is_real_pos
55	theorem		⊢
	proveit.numbers.division.div_complex_closure
56	instantiation	64, 155	⊢
	:
57	axiom		⊢
	proveit.logic.equality.substitution
58	instantiation	98, 65, 66	,  ⊢
	: , : , :
59	theorem		⊢
	proveit.logic.equality.equals_reversal
60	instantiation	67, 89, 68, 69, 70, 71*, 72*	,  ⊢
	: , : , : , :
61	instantiation	76, 110, 77, 160, 111, 78, 123, 124, 114, 89, 107	,  ⊢
	: , : , : , : , : , : , :
62	instantiation	79, 160, 80, 110, 73, 111, 89, 123, 124, 114, 107	,  ⊢
	: , : , : , : , : , :
63	instantiation	82, 74, 75	⊢
	: , : , :
64	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos
65	instantiation	76, 110, 77, 160, 111, 78, 123, 124, 114, 89, 115	,  ⊢
	: , : , : , : , : , : , :
66	instantiation	79, 160, 80, 110, 81, 111, 89, 123, 124, 114, 115	,  ⊢
	: , : , : , : , : , :
67	theorem		⊢
	proveit.numbers.division.prod_of_fracs
68	instantiation	82, 83, 84	⊢
	: , : , :
69	instantiation	158, 86, 85	⊢
	: , : , :
70	instantiation	158, 86, 87	⊢
	: , : , :
71	instantiation	88, 89	⊢
	:
72	instantiation	90, 91	⊢
	:
73	instantiation	96	⊢
	: , : , : , :
74	instantiation	122, 108, 92	⊢
	: , :
75	instantiation	98, 93, 94	⊢
	: , : , :
76	theorem		⊢
	proveit.numbers.multiplication.leftward_commutation
77	theorem		⊢
	proveit.numbers.numerals.decimals.nat3
78	instantiation	95	⊢
	: , : , :
79	theorem		⊢
	proveit.numbers.multiplication.association
80	theorem		⊢
	proveit.numbers.numerals.decimals.nat4
81	instantiation	96	⊢
	: , : , : , :
82	theorem		⊢
	proveit.logic.equality.sub_right_side_into
83	instantiation	122, 108, 97	⊢
	: , :
84	instantiation	98, 99, 100	⊢
	: , : , :
85	instantiation	158, 102, 101	⊢
	: , : , :
86	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero
87	instantiation	158, 102, 103	⊢
	: , : , :
88	theorem		⊢
	proveit.numbers.division.frac_one_denom
89	instantiation	158, 132, 104	⊢
	: , : , :
90	theorem		⊢
	proveit.numbers.multiplication.elim_one_left
91	instantiation	158, 132, 105	⊢
	: , : , :
92	instantiation	122, 114, 107	⊢
	: , :
93	instantiation	109, 160, 145, 110, 106, 111, 108, 114, 107	⊢
	: , : , : , : , : , :
94	instantiation	109, 110, 145, 111, 112, 106, 123, 124, 114, 107	⊢
	: , : , : , : , : , :
95	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_3_typical_eq
96	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_4_typical_eq
97	instantiation	122, 114, 115	⊢
	: , :
98	axiom		⊢
	proveit.logic.equality.equals_transitivity
99	instantiation	109, 160, 145, 110, 113, 111, 108, 114, 115	⊢
	: , : , : , : , : , :
100	instantiation	109, 110, 145, 111, 112, 113, 123, 124, 114, 115	⊢
	: , : , : , : , : , :
101	instantiation	158, 117, 116	⊢
	: , : , :
102	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero
103	instantiation	158, 117, 118	⊢
	: , : , :
104	instantiation	158, 136, 119	⊢
	: , : , :
105	instantiation	158, 136, 120	⊢
	: , : , :
106	instantiation	125	⊢
	: , :
107	instantiation	158, 132, 121	⊢
	: , : , :
108	instantiation	122, 123, 124	⊢
	: , :
109	theorem		⊢
	proveit.numbers.multiplication.disassociation
110	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
111	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
112	instantiation	125	⊢
	: , :
113	instantiation	125	⊢
	: , :
114	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.i_is_complex
115	instantiation	158, 132, 126	⊢
	: , : , :
116	instantiation	158, 128, 127	⊢
	: , : , :
117	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
118	instantiation	158, 128, 155	⊢
	: , : , :
119	instantiation	158, 141, 129	⊢
	: , : , :
120	instantiation	158, 141, 152	⊢
	: , : , :
121	instantiation	158, 136, 130	⊢
	: , : , :
122	theorem		⊢
	proveit.numbers.multiplication.mult_complex_closure_bin
123	instantiation	158, 132, 131	⊢
	: , : , :
124	instantiation	158, 132, 133	⊢
	: , : , :
125	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
126	instantiation	158, 136, 134	⊢
	: , : , :
127	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
128	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
129	instantiation	158, 143, 135	⊢
	: , : , :
130	instantiation	158, 141, 150	⊢
	: , : , :
131	instantiation	158, 136, 137	⊢
	: , : , :
132	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
133	instantiation	158, 138, 139	⊢
	: , : , :
134	instantiation	158, 141, 140	⊢
	: , : , :
135	assumption		⊢
136	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
137	instantiation	158, 141, 142	⊢
	: , : , :
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	instantiation	158, 143, 144	⊢
	: , : , :
141	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
142	instantiation	158, 159, 145	⊢
	: , : , :
143	instantiation	146, 147, 148	⊢
	: , :
144	instantiation	149, 150, 155	⊢
	: , :
145	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
146	theorem		⊢
	proveit.numbers.number_sets.integers.int_interval_within_int
147	theorem		⊢
	proveit.numbers.number_sets.integers.zero_is_int
148	instantiation	151, 152, 153	⊢
	: , :
149	theorem		⊢
	proveit.numbers.modular.mod_natpos_in_interval
150	assumption		⊢
151	theorem		⊢
	proveit.numbers.addition.add_int_closure_bin
152	instantiation	158, 154, 155	⊢
	: , : , :
153	instantiation	156, 157	⊢
	:
154	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_int
155	theorem		⊢
	proveit.physics.quantum.QPE._two_pow_t_is_nat_pos
156	theorem		⊢
	proveit.numbers.negation.int_closure
157	instantiation	158, 159, 160	⊢
	: , : , :
158	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
159	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
160	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
*equality replacement requirements