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