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