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	⊢
	: , :
1	reference	79	⊢
2	instantiation	45, 3, 4*	⊢
	: , : , :
3	instantiation	5, 191	⊢
	:
4	instantiation	6, 141, 31, 188, 142, 24, 7, 8, 9, 10, 11, 12	⊢
	: , : , : , : , : , : , : , : , : , :
5	axiom		⊢
	proveit.physics.quantum.QPE._psi_t_def
6	theorem		⊢
	proveit.linear_algebra.tensors.tensor_prod_disassociation
7	instantiation	56, 13, 117, 17	⊢
	: , : , : , :
8	instantiation	14, 180, 181, 85, 27	⊢
	: , : , :
9	instantiation	98, 15	⊢
	:
10	instantiation	56, 16, 117, 17	⊢
	: , : , : , :
11	modus ponens	18, 19	⊢
12	axiom		⊢
	proveit.physics.quantum.QPE._u_ket_register
13	instantiation	129, 20, 24	⊢
	: , : , :
14	theorem		⊢
	proveit.logic.booleans.conjunction.redundant_conjunction_general
15	instantiation	21, 174, 22	⊢
	: , :
16	instantiation	129, 23, 24	⊢
	: , : , :
17	instantiation	79, 25	⊢
	: , :
18	instantiation	26, 180, 181, 27	⊢
	: , : , : , :
19	generalization	28	⊢
20	instantiation	30, 31	⊢
	: , : , :
21	theorem		⊢
	proveit.numbers.exponentiation.exp_natpos_closure
22	instantiation	189, 50, 29	⊢
	: , : , :
23	instantiation	30, 31	⊢
	: , : , :
24	instantiation	123, 32, 33	⊢
	: , : , :
25	instantiation	34, 35	⊢
	: , :
26	theorem		⊢
	proveit.logic.booleans.conjunction.conjunction_from_quantification
27	instantiation	101, 36, 159, 127, 37, 38*, 39*	⊢
	: , : , :
28	instantiation	84, 85, 40, 41	,  ⊢
	: , : , : , :
29	axiom		⊢
	proveit.physics.quantum.QPE._s_in_nat_pos
30	theorem		⊢
	proveit.core_expr_types.tuples.range_len
31	instantiation	42, 133, 43, 141, 44, 188	⊢
	: , :
32	instantiation	45, 46	⊢
	: , : , :
33	instantiation	56, 47, 48, 49	⊢
	: , : , : , :
34	theorem		⊢
	proveit.core_expr_types.tuples.range_from1_len
35	instantiation	189, 50, 191	⊢
	: , : , :
36	instantiation	189, 172, 51	⊢
	: , : , :
37	instantiation	52, 53	⊢
	: , :
38	instantiation	123, 54, 55	⊢
	: , : , :
39	instantiation	56, 57, 73, 58	⊢
	: , : , : , :
40	instantiation	59, 113, 60, 61	⊢
	: , :
41	instantiation	62, 85, 63, 64	,  ⊢
	: , : , : , :
42	theorem		⊢
	proveit.numbers.addition.add_nat_closure
43	instantiation	146	⊢
	: , : , :
44	instantiation	65, 66	⊢
	:
45	axiom		⊢
	proveit.logic.equality.substitution
46	instantiation	67, 114, 113, 68*	⊢
	: , :
47	instantiation	91, 188, 174, 69, 75, 116, 71, 113	⊢
	: , : , : , : , : , :
48	instantiation	76, 141, 133, 142, 70, 116, 71, 113	⊢
	: , : , : , :
49	instantiation	72, 113, 116, 73	⊢
	: , : , :
50	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nat_pos_within_nat
51	instantiation	189, 175, 180	⊢
	: , : , :
52	theorem		⊢
	proveit.numbers.ordering.relax_less
53	instantiation	74, 191	⊢
	:
54	instantiation	91, 188, 174, 141, 92, 142, 75, 114, 113	⊢
	: , : , : , : , : , :
55	instantiation	76, 141, 174, 142, 92, 114, 113	⊢
	: , : , : , :
56	theorem		⊢
	proveit.logic.equality.four_chain_transitivity
57	instantiation	123, 77, 78	⊢
	: , : , :
58	instantiation	79, 80	⊢
	: , :
59	theorem		⊢
	proveit.numbers.division.div_complex_closure
60	instantiation	81, 156	⊢
	:
61	instantiation	82, 97, 83	⊢
	: , :
62	theorem		⊢
	proveit.linear_algebra.addition.binary_closure
63	theorem		⊢
	proveit.physics.quantum.algebra.ket_zero_in_qubit_space
64	instantiation	84, 85, 86, 87	,  ⊢
	: , : , : , :
65	theorem		⊢
	proveit.numbers.negation.nat_closure
66	instantiation	88, 180, 89	⊢
	:
67	theorem		⊢
	proveit.numbers.negation.distribute_neg_through_binary_sum
68	instantiation	90, 116	⊢
	:
69	instantiation	152	⊢
	: , :
70	instantiation	146	⊢
	: , : , :
71	instantiation	165, 113	⊢
	:
72	theorem		⊢
	proveit.numbers.addition.subtraction.add_cancel_triple_32
73	instantiation	128	⊢
	:
74	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.natural_pos_is_pos
75	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.zero_is_complex
76	theorem		⊢
	proveit.numbers.addition.elim_zero_any
77	instantiation	91, 188, 174, 141, 92, 142, 116, 114, 113	⊢
	: , : , : , : , : , :
78	instantiation	93, 116, 113, 117	⊢
	: , : , :
79	theorem		⊢
	proveit.logic.equality.equals_reversal
80	instantiation	94, 113	⊢
	:
81	theorem		⊢
	proveit.numbers.exponentiation.sqrt_complex_closure
82	theorem		⊢
	proveit.numbers.exponentiation.exp_rational_non_zero__not_zero
83	instantiation	95, 96, 97	⊢
	: , :
84	theorem		⊢
	proveit.linear_algebra.scalar_multiplication.scalar_mult_closure
85	instantiation	98, 120	⊢
	:
86	instantiation	155, 99, 100	,  ⊢
	: , :
87	theorem		⊢
	proveit.physics.quantum.algebra.ket_one_in_qubit_space
88	theorem		⊢
	proveit.numbers.number_sets.integers.nonpos_int_is_int_nonpos
89	instantiation	101, 126, 160, 127, 102, 103*, 104*	⊢
	: , : , :
90	theorem		⊢
	proveit.numbers.negation.double_negation
91	theorem		⊢
	proveit.numbers.addition.disassociation
92	instantiation	152	⊢
	: , :
93	theorem		⊢
	proveit.numbers.addition.subtraction.add_cancel_triple_12
94	theorem		⊢
	proveit.numbers.addition.elim_zero_left
95	theorem		⊢
	proveit.numbers.division.div_rational_nonzero_closure
96	instantiation	189, 106, 105	⊢
	: , : , :
97	instantiation	189, 106, 107	⊢
	: , : , :
98	theorem		⊢
	proveit.linear_algebra.complex_vec_set_is_vec_space
99	instantiation	189, 169, 108	⊢
	: , : , :
100	instantiation	129, 109, 110	,  ⊢
	: , : , :
101	theorem		⊢
	proveit.numbers.addition.weak_bound_via_left_term_bound
102	instantiation	111, 191	⊢
	:
103	instantiation	112, 113, 114	⊢
	: , :
104	instantiation	115, 116, 117	⊢
	: , :
105	instantiation	189, 119, 118	⊢
	: , : , :
106	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
107	instantiation	189, 119, 120	⊢
	: , : , :
108	instantiation	189, 162, 121	⊢
	: , : , :
109	instantiation	149, 132, 122	,  ⊢
	: , :
110	instantiation	123, 124, 125	,  ⊢
	: , : , :
111	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.natural_pos_lower_bound
112	theorem		⊢
	proveit.numbers.addition.commutation
113	instantiation	189, 169, 160	⊢
	: , : , :
114	instantiation	189, 169, 126	⊢
	: , : , :
115	theorem		⊢
	proveit.numbers.addition.subtraction.add_cancel_basic
116	instantiation	189, 169, 127	⊢
	: , : , :
117	instantiation	128	⊢
	:
118	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
119	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
120	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
121	theorem		⊢
	proveit.numbers.number_sets.real_numbers.e_is_real_pos
122	instantiation	129, 130, 131	,  ⊢
	: , : , :
123	axiom		⊢
	proveit.logic.equality.equals_transitivity
124	instantiation	140, 188, 133, 141, 135, 142, 132, 150, 151, 144	,  ⊢
	: , : , : , : , : , :
125	instantiation	140, 141, 174, 133, 142, 134, 135, 156, 145, 150, 151, 144	,  ⊢
	: , : , : , : , : , :
126	instantiation	189, 172, 136	⊢
	: , : , :
127	instantiation	137, 138, 191	⊢
	: , : , :
128	axiom		⊢
	proveit.logic.equality.equals_reflexivity
129	theorem		⊢
	proveit.logic.equality.sub_right_side_into
130	instantiation	149, 139, 144	,  ⊢
	: , :
131	instantiation	140, 141, 174, 188, 142, 143, 150, 151, 144	,  ⊢
	: , : , : , : , : , :
132	instantiation	149, 156, 145	⊢
	: , :
133	theorem		⊢
	proveit.numbers.numerals.decimals.nat3
134	instantiation	152	⊢
	: , :
135	instantiation	146	⊢
	: , : , :
136	instantiation	189, 175, 183	⊢
	: , : , :
137	theorem		⊢
	proveit.logic.sets.inclusion.unfold_subset_eq
138	instantiation	147, 148	⊢
	: , :
139	instantiation	149, 150, 151	,  ⊢
	: , :
140	theorem		⊢
	proveit.numbers.multiplication.disassociation
141	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
142	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
143	instantiation	152	⊢
	: , :
144	instantiation	189, 169, 153	⊢
	: , : , :
145	instantiation	189, 169, 154	⊢
	: , : , :
146	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_3_typical_eq
147	theorem		⊢
	proveit.logic.sets.inclusion.relax_proper_subset
148	theorem		⊢
	proveit.numbers.number_sets.real_numbers.nat_pos_within_real
149	theorem		⊢
	proveit.numbers.multiplication.mult_complex_closure_bin
150	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.i_is_complex
151	instantiation	155, 156, 157	,  ⊢
	: , :
152	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
153	instantiation	158, 159, 160, 161	⊢
	: , : , :
154	instantiation	189, 162, 163	⊢
	: , : , :
155	theorem		⊢
	proveit.numbers.exponentiation.exp_complex_closure
156	instantiation	189, 169, 164	⊢
	: , : , :
157	instantiation	165, 166	,  ⊢
	:
158	theorem		⊢
	proveit.numbers.number_sets.real_numbers.all_in_interval_co__is__real
159	theorem		⊢
	proveit.numbers.number_sets.real_numbers.zero_is_real
160	instantiation	189, 172, 167	⊢
	: , : , :
161	axiom		⊢
	proveit.physics.quantum.QPE._phase_in_interval
162	theorem		⊢
	proveit.numbers.number_sets.real_numbers.real_pos_within_real
163	theorem		⊢
	proveit.numbers.number_sets.real_numbers.pi_is_real_pos
164	instantiation	189, 172, 168	⊢
	: , : , :
165	theorem		⊢
	proveit.numbers.negation.complex_closure
166	instantiation	189, 169, 170	,  ⊢
	: , : , :
167	instantiation	189, 175, 184	⊢
	: , : , :
168	instantiation	189, 175, 171	⊢
	: , : , :
169	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
170	instantiation	189, 172, 173	,  ⊢
	: , : , :
171	instantiation	189, 187, 174	⊢
	: , : , :
172	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
173	instantiation	189, 175, 176	,  ⊢
	: , : , :
174	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
175	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
176	instantiation	189, 177, 178	,  ⊢
	: , : , :
177	instantiation	179, 180, 181	⊢
	: , :
178	assumption		⊢
179	theorem		⊢
	proveit.numbers.number_sets.integers.int_interval_within_int
180	instantiation	182, 183, 184	⊢
	: , :
181	theorem		⊢
	proveit.numbers.number_sets.integers.zero_is_int
182	theorem		⊢
	proveit.numbers.addition.add_int_closure_bin
183	instantiation	185, 186	⊢
	:
184	instantiation	189, 187, 188	⊢
	: , : , :
185	theorem		⊢
	proveit.numbers.negation.int_closure
186	instantiation	189, 190, 191	⊢
	: , : , :
187	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
188	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
189	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
190	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_int
191	assumption		⊢
*equality replacement requirements