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