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	126	⊢
2	instantiation	3, 49, 4, 5, 6, 7, 8*	⊢
	: , : , : , :
3	theorem		⊢
	proveit.logic.equality.sub_in_right_operands_via_tuple
4	instantiation	97, 9, 10, 13	⊢
	: , : , : , :
5	instantiation	97, 11, 12, 13	⊢
	: , : , : , :
6	instantiation	14, 65, 15	⊢
	:
7	instantiation	16, 17, 111*	⊢
	: , : , :
8	instantiation	18, 79, 204, 68, 205, 55, 19, 132, 20, 21, 22, 23	⊢
	: , : , : , : , : , : , : , : , : , :
9	instantiation	190, 24, 25	⊢
	: , : , :
10	instantiation	188	⊢
	:
11	instantiation	26, 179, 27, 28, 29, 30, 68, 48*, 55*	⊢
	: , : , : , :
12	instantiation	126, 31	⊢
	: , :
13	instantiation	126, 32	⊢
	: , :
14	axiom		⊢
	proveit.physics.quantum.QPE._psi_t_def
15	instantiation	182, 33, 34	⊢
	: , : , :
16	theorem		⊢
	proveit.core_expr_types.tuples.partition_front
17	instantiation	35, 204, 63	⊢
	: , :
18	theorem		⊢
	proveit.linear_algebra.tensors.factor_scalar_from_tensor_prod
19	instantiation	97, 36, 173, 39	⊢
	: , : , : , :
20	instantiation	37, 242, 243, 132, 60	⊢
	: , : , :
21	instantiation	97, 38, 173, 39	⊢
	: , : , : , :
22	instantiation	190, 40, 41	⊢
	: , : , :
23	modus ponens	42, 43	⊢
24	instantiation	67, 44	⊢
	: , : , :
25	instantiation	182, 45, 46	⊢
	: , : , :
26	theorem		⊢
	proveit.core_expr_types.tuples.general_len
27	instantiation	216	⊢
	: , :
28	instantiation	216	⊢
	: , :
29	instantiation	216	⊢
	: , :
30	instantiation	47, 250, 48	⊢
	: , : , :
31	instantiation	168, 172, 169	⊢
	: , :
32	instantiation	71, 49	⊢
	: , :
33	instantiation	119, 50	⊢
	: , : , :
34	instantiation	182, 51, 52	⊢
	: , : , :
35	theorem		⊢
	proveit.numbers.addition.add_nat_closure_bin
36	instantiation	190, 53, 55	⊢
	: , : , :
37	theorem		⊢
	proveit.logic.booleans.conjunction.redundant_conjunction_general
38	instantiation	190, 54, 55	⊢
	: , : , :
39	instantiation	126, 56	⊢
	: , :
40	instantiation	103, 132, 104, 57	⊢
	: , : , : , :
41	instantiation	119, 58	⊢
	: , : , :
42	instantiation	59, 242, 243, 60	⊢
	: , : , : , :
43	generalization	61	⊢
44	instantiation	83, 194, 62, 204, 63, 250	⊢
	: , :
45	instantiation	119, 111	⊢
	: , : , :
46	instantiation	123, 204, 236, 205, 64, 172, 169	⊢
	: , : , : , :
47	theorem		⊢
	proveit.logic.equality.sub_left_side_into
48	instantiation	146, 169, 116	⊢
	: , : , :
49	instantiation	251, 226, 65	⊢
	: , : , :
50	instantiation	110, 172, 169	⊢
	: , :
51	instantiation	144, 204, 236, 250, 205, 66, 170, 114, 169	⊢
	: , : , : , : , : , :
52	instantiation	115, 169, 170, 116	⊢
	: , : , :
53	instantiation	67, 68	⊢
	: , : , :
54	instantiation	67, 68	⊢
	: , : , :
55	instantiation	182, 69, 70	⊢
	: , : , :
56	instantiation	71, 220	⊢
	: , :
57	instantiation	131, 132, 72, 134	⊢
	: , : , : , :
58	instantiation	126, 73	⊢
	: , :
59	theorem		⊢
	proveit.logic.booleans.conjunction.conjunction_from_quantification
60	instantiation	154, 74, 75, 187, 76, 77*, 78*	⊢
	: , : , :
61	instantiation	131, 132, 79, 80	,  ⊢
	: , : , : , :
62	instantiation	209	⊢
	: , : , :
63	instantiation	251, 226, 81	⊢
	: , : , :
64	instantiation	216	⊢
	: , :
65	instantiation	82, 253, 177	⊢
	: , :
66	instantiation	216	⊢
	: , :
67	theorem		⊢
	proveit.core_expr_types.tuples.range_len
68	instantiation	83, 194, 84, 204, 85, 250	⊢
	: , :
69	instantiation	119, 86	⊢
	: , : , :
70	instantiation	97, 87, 88, 89	⊢
	: , : , : , :
71	theorem		⊢
	proveit.core_expr_types.tuples.range_from1_len
72	instantiation	221, 152, 90	⊢
	: , :
73	instantiation	119, 91	⊢
	: , : , :
74	instantiation	251, 234, 92	⊢
	: , : , :
75	theorem		⊢
	proveit.numbers.number_sets.real_numbers.zero_is_real
76	instantiation	93, 94	⊢
	: , :
77	instantiation	182, 95, 96	⊢
	: , : , :
78	instantiation	97, 98, 116, 99	⊢
	: , : , : , :
79	instantiation	100, 169, 101, 102	⊢
	: , :
80	instantiation	103, 132, 104, 105	,  ⊢
	: , : , : , :
81	instantiation	106, 107	⊢
	:
82	theorem		⊢
	proveit.numbers.addition.add_nat_pos_closure_bin
83	theorem		⊢
	proveit.numbers.addition.add_nat_closure
84	instantiation	209	⊢
	: , : , :
85	instantiation	108, 109	⊢
	:
86	instantiation	110, 170, 169, 111*	⊢
	: , :
87	instantiation	144, 250, 236, 112, 122, 172, 114, 169	⊢
	: , : , : , : , : , :
88	instantiation	123, 204, 194, 205, 113, 172, 114, 169	⊢
	: , : , : , :
89	instantiation	115, 169, 172, 116	⊢
	: , : , :
90	instantiation	190, 117, 118	⊢
	: , : , :
91	instantiation	119, 120	⊢
	: , : , :
92	instantiation	251, 237, 242	⊢
	: , : , :
93	theorem		⊢
	proveit.numbers.ordering.relax_less
94	instantiation	121, 253	⊢
	:
95	instantiation	144, 250, 236, 204, 145, 205, 122, 170, 169	⊢
	: , : , : , : , : , :
96	instantiation	123, 204, 236, 205, 145, 170, 169	⊢
	: , : , : , :
97	theorem		⊢
	proveit.logic.equality.four_chain_transitivity
98	instantiation	182, 124, 125	⊢
	: , : , :
99	instantiation	126, 127	⊢
	: , :
100	theorem		⊢
	proveit.numbers.division.div_complex_closure
101	instantiation	128, 222	⊢
	:
102	instantiation	129, 150, 130	⊢
	: , :
103	theorem		⊢
	proveit.linear_algebra.addition.binary_closure
104	theorem		⊢
	proveit.physics.quantum.algebra.ket_zero_in_qubit_space
105	instantiation	131, 132, 133, 134	,  ⊢
	: , : , : , :
106	theorem		⊢
	proveit.numbers.negation.nat_pos_closure
107	instantiation	135, 253	⊢
	:
108	theorem		⊢
	proveit.numbers.negation.nat_closure
109	instantiation	136, 242, 137	⊢
	:
110	theorem		⊢
	proveit.numbers.negation.distribute_neg_through_binary_sum
111	instantiation	138, 172	⊢
	:
112	instantiation	216	⊢
	: , :
113	instantiation	209	⊢
	: , : , :
114	instantiation	228, 169	⊢
	:
115	theorem		⊢
	proveit.numbers.addition.subtraction.add_cancel_triple_32
116	instantiation	188	⊢
	:
117	instantiation	213, 193, 139	⊢
	: , :
118	instantiation	182, 140, 141	⊢
	: , : , :
119	axiom		⊢
	proveit.logic.equality.substitution
120	instantiation	142, 194, 250, 204, 143, 205, 222, 208, 214, 176, 207	⊢
	: , : , : , : , : , : , :
121	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.natural_pos_is_pos
122	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.zero_is_complex
123	theorem		⊢
	proveit.numbers.addition.elim_zero_any
124	instantiation	144, 250, 236, 204, 145, 205, 172, 170, 169	⊢
	: , : , : , : , : , :
125	instantiation	146, 172, 169, 173	⊢
	: , : , :
126	theorem		⊢
	proveit.logic.equality.equals_reversal
127	instantiation	147, 169	⊢
	:
128	theorem		⊢
	proveit.numbers.exponentiation.sqrt_complex_closure
129	theorem		⊢
	proveit.numbers.exponentiation.exp_rational_non_zero__not_zero
130	instantiation	148, 149, 150	⊢
	: , :
131	theorem		⊢
	proveit.linear_algebra.scalar_multiplication.scalar_mult_closure
132	instantiation	151, 179	⊢
	:
133	instantiation	221, 152, 153	,  ⊢
	: , :
134	theorem		⊢
	proveit.physics.quantum.algebra.ket_one_in_qubit_space
135	theorem		⊢
	proveit.numbers.negation.int_neg_closure
136	theorem		⊢
	proveit.numbers.number_sets.integers.nonpos_int_is_int_nonpos
137	instantiation	154, 186, 185, 187, 155, 156*, 157*	⊢
	: , : , :
138	theorem		⊢
	proveit.numbers.negation.double_negation
139	instantiation	190, 158, 159	⊢
	: , : , :
140	instantiation	203, 250, 194, 204, 160, 205, 193, 214, 207, 176	⊢
	: , : , : , : , : , :
141	instantiation	203, 204, 236, 194, 205, 195, 160, 222, 208, 214, 207, 176	⊢
	: , : , : , : , : , :
142	theorem		⊢
	proveit.numbers.multiplication.leftward_commutation
143	instantiation	209	⊢
	: , : , :
144	theorem		⊢
	proveit.numbers.addition.disassociation
145	instantiation	216	⊢
	: , :
146	theorem		⊢
	proveit.numbers.addition.subtraction.add_cancel_triple_12
147	theorem		⊢
	proveit.numbers.addition.elim_zero_left
148	theorem		⊢
	proveit.numbers.division.div_rational_nonzero_closure
149	instantiation	251, 162, 161	⊢
	: , : , :
150	instantiation	251, 162, 163	⊢
	: , : , :
151	theorem		⊢
	proveit.linear_algebra.complex_vec_set_is_vec_space
152	instantiation	251, 231, 164	⊢
	: , : , :
153	instantiation	190, 165, 166	,  ⊢
	: , : , :
154	theorem		⊢
	proveit.numbers.addition.weak_bound_via_left_term_bound
155	instantiation	167, 253	⊢
	:
156	instantiation	168, 169, 170	⊢
	: , :
157	instantiation	171, 172, 173	⊢
	: , :
158	instantiation	213, 174, 176	⊢
	: , :
159	instantiation	203, 204, 236, 250, 205, 175, 214, 207, 176	⊢
	: , : , : , : , : , :
160	instantiation	209	⊢
	: , : , :
161	instantiation	251, 178, 177	⊢
	: , : , :
162	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
163	instantiation	251, 178, 179	⊢
	: , : , :
164	instantiation	251, 224, 180	⊢
	: , : , :
165	instantiation	213, 193, 181	,  ⊢
	: , :
166	instantiation	182, 183, 184	,  ⊢
	: , : , :
167	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.natural_pos_lower_bound
168	theorem		⊢
	proveit.numbers.addition.commutation
169	instantiation	251, 231, 185	⊢
	: , : , :
170	instantiation	251, 231, 186	⊢
	: , : , :
171	theorem		⊢
	proveit.numbers.addition.subtraction.add_cancel_basic
172	instantiation	251, 231, 187	⊢
	: , : , :
173	instantiation	188	⊢
	:
174	instantiation	213, 214, 207	⊢
	: , :
175	instantiation	216	⊢
	: , :
176	instantiation	251, 231, 189	⊢
	: , : , :
177	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
178	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
179	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
180	theorem		⊢
	proveit.numbers.number_sets.real_numbers.e_is_real_pos
181	instantiation	190, 191, 192	,  ⊢
	: , : , :
182	axiom		⊢
	proveit.logic.equality.equals_transitivity
183	instantiation	203, 250, 194, 204, 196, 205, 193, 214, 215, 207	,  ⊢
	: , : , : , : , : , :
184	instantiation	203, 204, 236, 194, 205, 195, 196, 222, 208, 214, 215, 207	,  ⊢
	: , : , : , : , : , :
185	instantiation	251, 234, 197	⊢
	: , : , :
186	instantiation	251, 234, 198	⊢
	: , : , :
187	instantiation	199, 200, 253	⊢
	: , : , :
188	axiom		⊢
	proveit.logic.equality.equals_reflexivity
189	instantiation	251, 234, 201	⊢
	: , : , :
190	theorem		⊢
	proveit.logic.equality.sub_right_side_into
191	instantiation	213, 202, 207	,  ⊢
	: , :
192	instantiation	203, 204, 236, 250, 205, 206, 214, 215, 207	,  ⊢
	: , : , : , : , : , :
193	instantiation	213, 222, 208	⊢
	: , :
194	theorem		⊢
	proveit.numbers.numerals.decimals.nat3
195	instantiation	216	⊢
	: , :
196	instantiation	209	⊢
	: , : , :
197	instantiation	251, 237, 246	⊢
	: , : , :
198	instantiation	251, 237, 245	⊢
	: , : , :
199	theorem		⊢
	proveit.logic.sets.inclusion.unfold_subset_eq
200	instantiation	210, 211	⊢
	: , :
201	instantiation	251, 237, 212	⊢
	: , : , :
202	instantiation	213, 214, 215	,  ⊢
	: , :
203	theorem		⊢
	proveit.numbers.multiplication.disassociation
204	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
205	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
206	instantiation	216	⊢
	: , :
207	instantiation	251, 231, 217	⊢
	: , : , :
208	instantiation	251, 231, 218	⊢
	: , : , :
209	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_3_typical_eq
210	theorem		⊢
	proveit.logic.sets.inclusion.relax_proper_subset
211	theorem		⊢
	proveit.numbers.number_sets.real_numbers.nat_pos_within_real
212	instantiation	219, 233, 220	⊢
	: , :
213	theorem		⊢
	proveit.numbers.multiplication.mult_complex_closure_bin
214	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.i_is_complex
215	instantiation	221, 222, 223	,  ⊢
	: , :
216	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
217	theorem		⊢
	proveit.physics.quantum.QPE._phase_is_real
218	instantiation	251, 224, 225	⊢
	: , : , :
219	theorem		⊢
	proveit.numbers.exponentiation.exp_int_closure
220	instantiation	251, 226, 253	⊢
	: , : , :
221	theorem		⊢
	proveit.numbers.exponentiation.exp_complex_closure
222	instantiation	251, 231, 227	⊢
	: , : , :
223	instantiation	228, 229	,  ⊢
	:
224	theorem		⊢
	proveit.numbers.number_sets.real_numbers.real_pos_within_real
225	theorem		⊢
	proveit.numbers.number_sets.real_numbers.pi_is_real_pos
226	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nat_pos_within_nat
227	instantiation	251, 234, 230	⊢
	: , : , :
228	theorem		⊢
	proveit.numbers.negation.complex_closure
229	instantiation	251, 231, 232	,  ⊢
	: , : , :
230	instantiation	251, 237, 233	⊢
	: , : , :
231	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
232	instantiation	251, 234, 235	,  ⊢
	: , : , :
233	instantiation	251, 249, 236	⊢
	: , : , :
234	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
235	instantiation	251, 237, 238	,  ⊢
	: , : , :
236	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
237	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
238	instantiation	251, 239, 240	,  ⊢
	: , : , :
239	instantiation	241, 242, 243	⊢
	: , :
240	assumption		⊢
241	theorem		⊢
	proveit.numbers.number_sets.integers.int_interval_within_int
242	instantiation	244, 245, 246	⊢
	: , :
243	theorem		⊢
	proveit.numbers.number_sets.integers.zero_is_int
244	theorem		⊢
	proveit.numbers.addition.add_int_closure_bin
245	instantiation	247, 248	⊢
	:
246	instantiation	251, 249, 250	⊢
	: , : , :
247	theorem		⊢
	proveit.numbers.negation.int_closure
248	instantiation	251, 252, 253	⊢
	: , : , :
249	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
250	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
251	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
252	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_int
253	assumption		⊢
*equality replacement requirements