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	170	⊢
2	instantiation	120, 4	⊢
	: , : , :
3	instantiation	111, 5	⊢
	: , :
4	instantiation	6, 69, 7, 20, 8	⊢
	: , : , : , :
5	instantiation	120, 9, 10*	⊢
	: , : , :
6	theorem		⊢
	proveit.core_expr_types.operations.operands_substitution_via_tuple
7	instantiation	122, 11, 164, 36	⊢
	: , : , : , :
8	instantiation	12, 13, 14	⊢
	: , : , : , :
9	instantiation	15, 243	⊢
	:
10	instantiation	16, 193, 65, 240, 194, 49, 17, 18, 19, 20, 21, 22	⊢
	: , : , : , : , : , : , : , : , : , :
11	instantiation	23, 167, 24, 25, 26, 27, 28, 29*	⊢
	: , : , : , :
12	theorem		⊢
	proveit.core_expr_types.tuples.merge_front
13	instantiation	30, 193, 80	⊢
	: , :
14	instantiation	111, 31	⊢
	: , :
15	axiom		⊢
	proveit.physics.quantum.QPE._psi_t_def
16	theorem		⊢
	proveit.linear_algebra.tensors.tensor_prod_disassociation
17	instantiation	122, 32, 164, 36	⊢
	: , : , : , :
18	instantiation	33, 232, 233, 117, 52	⊢
	: , : , :
19	instantiation	134, 34	⊢
	:
20	instantiation	122, 35, 164, 36	⊢
	: , : , : , :
21	modus ponens	37, 38	⊢
22	axiom		⊢
	proveit.physics.quantum.QPE._u_ket_register
23	theorem		⊢
	proveit.core_expr_types.tuples.general_len
24	instantiation	204	⊢
	: , :
25	instantiation	204	⊢
	: , :
26	instantiation	204	⊢
	: , :
27	instantiation	39, 240, 59	⊢
	: , : , :
28	instantiation	181, 80, 40	⊢
	: , : , :
29	instantiation	170, 41, 42	⊢
	: , : , :
30	theorem		⊢
	proveit.numbers.addition.add_nat_closure_bin
31	instantiation	170, 43, 44	⊢
	: , : , :
32	instantiation	181, 45, 49	⊢
	: , : , :
33	theorem		⊢
	proveit.logic.booleans.conjunction.redundant_conjunction_general
34	instantiation	46, 226, 47	⊢
	: , :
35	instantiation	181, 48, 49	⊢
	: , : , :
36	instantiation	111, 50	⊢
	: , :
37	instantiation	51, 232, 233, 52	⊢
	: , : , : , :
38	generalization	53	⊢
39	theorem		⊢
	proveit.logic.equality.sub_left_side_into
40	instantiation	122, 81, 54, 55	⊢
	: , : , : , :
41	instantiation	56, 226, 57, 58, 59, 76	⊢
	: , : , : , :
42	instantiation	170, 60, 61	⊢
	: , : , :
43	instantiation	139, 193, 226, 240, 194, 128, 161, 176	⊢
	: , : , : , : , : , :
44	instantiation	144, 240, 226, 193, 62, 194, 161, 176, 174*	⊢
	: , : , : , : , : , :
45	instantiation	64, 65	⊢
	: , : , :
46	theorem		⊢
	proveit.numbers.exponentiation.exp_natpos_closure
47	instantiation	241, 85, 63	⊢
	: , : , :
48	instantiation	64, 65	⊢
	: , : , :
49	instantiation	170, 66, 67	⊢
	: , : , :
50	instantiation	68, 69	⊢
	: , :
51	theorem		⊢
	proveit.logic.booleans.conjunction.conjunction_from_quantification
52	instantiation	147, 70, 211, 179, 71, 72*, 73*	⊢
	: , : , :
53	instantiation	116, 117, 74, 75	,  ⊢
	: , : , : , :
54	instantiation	180	⊢
	:
55	instantiation	111, 76	⊢
	: , :
56	axiom		⊢
	proveit.core_expr_types.operations.operands_substitution
57	instantiation	204	⊢
	: , :
58	instantiation	204	⊢
	: , :
59	instantiation	129, 176, 107	⊢
	: , : , :
60	instantiation	139, 240, 226, 193, 103, 194, 176, 163, 105	⊢
	: , : , : , : , : , :
61	instantiation	77, 176, 163, 107	⊢
	: , : , :
62	instantiation	204	⊢
	: , :
63	axiom		⊢
	proveit.physics.quantum.QPE._s_in_nat_pos
64	theorem		⊢
	proveit.core_expr_types.tuples.range_len
65	instantiation	78, 185, 79, 193, 80, 240	⊢
	: , :
66	instantiation	120, 81	⊢
	: , : , :
67	instantiation	122, 82, 83, 84	⊢
	: , : , : , :
68	theorem		⊢
	proveit.core_expr_types.tuples.range_from1_len
69	instantiation	241, 85, 243	⊢
	: , : , :
70	instantiation	241, 224, 86	⊢
	: , : , :
71	instantiation	87, 88	⊢
	: , :
72	instantiation	170, 89, 90	⊢
	: , : , :
73	instantiation	122, 91, 107, 92	⊢
	: , : , : , :
74	instantiation	93, 176, 94, 95	⊢
	: , :
75	instantiation	96, 117, 97, 98	,  ⊢
	: , : , : , :
76	instantiation	170, 99, 100	⊢
	: , : , :
77	theorem		⊢
	proveit.numbers.addition.subtraction.add_cancel_triple_13
78	theorem		⊢
	proveit.numbers.addition.add_nat_closure
79	instantiation	198	⊢
	: , : , :
80	instantiation	101, 102	⊢
	:
81	instantiation	137, 161, 176, 138*	⊢
	: , :
82	instantiation	139, 240, 226, 103, 141, 163, 105, 176	⊢
	: , : , : , : , : , :
83	instantiation	142, 193, 185, 194, 104, 163, 105, 176	⊢
	: , : , : , :
84	instantiation	106, 176, 163, 107	⊢
	: , : , :
85	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nat_pos_within_nat
86	instantiation	241, 227, 232	⊢
	: , : , :
87	theorem		⊢
	proveit.numbers.ordering.relax_less
88	instantiation	108, 243	⊢
	:
89	instantiation	139, 240, 226, 193, 128, 194, 141, 161, 176	⊢
	: , : , : , : , : , :
90	instantiation	142, 193, 226, 194, 128, 161, 176	⊢
	: , : , : , :
91	instantiation	170, 109, 110	⊢
	: , : , :
92	instantiation	111, 112	⊢
	: , :
93	theorem		⊢
	proveit.numbers.division.div_complex_closure
94	instantiation	113, 208	⊢
	:
95	instantiation	114, 133, 115	⊢
	: , :
96	theorem		⊢
	proveit.linear_algebra.addition.binary_closure
97	theorem		⊢
	proveit.physics.quantum.algebra.ket_zero_in_qubit_space
98	instantiation	116, 117, 118, 119	,  ⊢
	: , : , : , :
99	instantiation	120, 121	⊢
	: , : , :
100	instantiation	122, 123, 124, 125	⊢
	: , : , : , :
101	theorem		⊢
	proveit.numbers.negation.nat_closure
102	instantiation	126, 232, 127	⊢
	:
103	instantiation	204	⊢
	: , :
104	instantiation	198	⊢
	: , : , :
105	instantiation	217, 176	⊢
	:
106	theorem		⊢
	proveit.numbers.addition.subtraction.add_cancel_triple_32
107	instantiation	180	⊢
	:
108	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.natural_pos_is_pos
109	instantiation	139, 240, 226, 193, 128, 194, 163, 161, 176	⊢
	: , : , : , : , : , :
110	instantiation	129, 163, 176, 164	⊢
	: , : , :
111	theorem		⊢
	proveit.logic.equality.equals_reversal
112	instantiation	130, 176	⊢
	:
113	theorem		⊢
	proveit.numbers.exponentiation.sqrt_complex_closure
114	theorem		⊢
	proveit.numbers.exponentiation.exp_rational_non_zero__not_zero
115	instantiation	131, 132, 133	⊢
	: , :
116	theorem		⊢
	proveit.linear_algebra.scalar_multiplication.scalar_mult_closure
117	instantiation	134, 167	⊢
	:
118	instantiation	207, 135, 136	,  ⊢
	: , :
119	theorem		⊢
	proveit.physics.quantum.algebra.ket_one_in_qubit_space
120	axiom		⊢
	proveit.logic.equality.substitution
121	instantiation	137, 161, 208, 138*	⊢
	: , :
122	theorem		⊢
	proveit.logic.equality.four_chain_transitivity
123	instantiation	139, 240, 226, 140, 141, 163, 177, 176	⊢
	: , : , : , : , : , :
124	instantiation	142, 193, 185, 194, 143, 163, 177, 176	⊢
	: , : , : , :
125	instantiation	144, 240, 226, 193, 145, 194, 163, 177, 176, 146*	⊢
	: , : , : , : , : , :
126	theorem		⊢
	proveit.numbers.number_sets.integers.nonpos_int_is_int_nonpos
127	instantiation	147, 178, 212, 179, 148, 149*, 150*	⊢
	: , : , :
128	instantiation	204	⊢
	: , :
129	theorem		⊢
	proveit.numbers.addition.subtraction.add_cancel_triple_12
130	theorem		⊢
	proveit.numbers.addition.elim_zero_left
131	theorem		⊢
	proveit.numbers.division.div_rational_nonzero_closure
132	instantiation	241, 152, 151	⊢
	: , : , :
133	instantiation	241, 152, 153	⊢
	: , : , :
134	theorem		⊢
	proveit.linear_algebra.complex_vec_set_is_vec_space
135	instantiation	241, 221, 154	⊢
	: , : , :
136	instantiation	181, 155, 156	,  ⊢
	: , : , :
137	theorem		⊢
	proveit.numbers.negation.distribute_neg_through_binary_sum
138	instantiation	157, 163	⊢
	:
139	theorem		⊢
	proveit.numbers.addition.disassociation
140	instantiation	204	⊢
	: , :
141	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.zero_is_complex
142	theorem		⊢
	proveit.numbers.addition.elim_zero_any
143	instantiation	198	⊢
	: , : , :
144	theorem		⊢
	proveit.numbers.addition.association
145	instantiation	204	⊢
	: , :
146	instantiation	181, 158, 159	⊢
	: , : , :
147	theorem		⊢
	proveit.numbers.addition.weak_bound_via_left_term_bound
148	instantiation	160, 243	⊢
	:
149	instantiation	175, 176, 161	⊢
	: , :
150	instantiation	162, 163, 164	⊢
	: , :
151	instantiation	241, 166, 165	⊢
	: , : , :
152	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
153	instantiation	241, 166, 167	⊢
	: , : , :
154	instantiation	241, 214, 168	⊢
	: , : , :
155	instantiation	201, 184, 169	,  ⊢
	: , :
156	instantiation	170, 171, 172	,  ⊢
	: , : , :
157	theorem		⊢
	proveit.numbers.negation.double_negation
158	instantiation	173, 176, 208, 174	⊢
	: , : , :
159	instantiation	175, 176, 177	⊢
	: , :
160	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.natural_pos_lower_bound
161	instantiation	241, 221, 178	⊢
	: , : , :
162	theorem		⊢
	proveit.numbers.addition.subtraction.add_cancel_basic
163	instantiation	241, 221, 179	⊢
	: , : , :
164	instantiation	180	⊢
	:
165	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
166	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
167	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
168	theorem		⊢
	proveit.numbers.number_sets.real_numbers.e_is_real_pos
169	instantiation	181, 182, 183	,  ⊢
	: , : , :
170	axiom		⊢
	proveit.logic.equality.equals_transitivity
171	instantiation	192, 240, 185, 193, 187, 194, 184, 202, 203, 196	,  ⊢
	: , : , : , : , : , :
172	instantiation	192, 193, 226, 185, 194, 186, 187, 208, 197, 202, 203, 196	,  ⊢
	: , : , : , : , : , :
173	theorem		⊢
	proveit.numbers.addition.subtraction.subtract_from_add_reversed
174	theorem		⊢
	proveit.numbers.numerals.decimals.add_1_1
175	theorem		⊢
	proveit.numbers.addition.commutation
176	instantiation	241, 221, 212	⊢
	: , : , :
177	instantiation	217, 208	⊢
	:
178	instantiation	241, 224, 188	⊢
	: , : , :
179	instantiation	189, 190, 243	⊢
	: , : , :
180	axiom		⊢
	proveit.logic.equality.equals_reflexivity
181	theorem		⊢
	proveit.logic.equality.sub_right_side_into
182	instantiation	201, 191, 196	,  ⊢
	: , :
183	instantiation	192, 193, 226, 240, 194, 195, 202, 203, 196	,  ⊢
	: , : , : , : , : , :
184	instantiation	201, 208, 197	⊢
	: , :
185	theorem		⊢
	proveit.numbers.numerals.decimals.nat3
186	instantiation	204	⊢
	: , :
187	instantiation	198	⊢
	: , : , :
188	instantiation	241, 227, 235	⊢
	: , : , :
189	theorem		⊢
	proveit.logic.sets.inclusion.unfold_subset_eq
190	instantiation	199, 200	⊢
	: , :
191	instantiation	201, 202, 203	,  ⊢
	: , :
192	theorem		⊢
	proveit.numbers.multiplication.disassociation
193	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
194	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
195	instantiation	204	⊢
	: , :
196	instantiation	241, 221, 205	⊢
	: , : , :
197	instantiation	241, 221, 206	⊢
	: , : , :
198	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_3_typical_eq
199	theorem		⊢
	proveit.logic.sets.inclusion.relax_proper_subset
200	theorem		⊢
	proveit.numbers.number_sets.real_numbers.nat_pos_within_real
201	theorem		⊢
	proveit.numbers.multiplication.mult_complex_closure_bin
202	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.i_is_complex
203	instantiation	207, 208, 209	,  ⊢
	: , :
204	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
205	instantiation	210, 211, 212, 213	⊢
	: , : , :
206	instantiation	241, 214, 215	⊢
	: , : , :
207	theorem		⊢
	proveit.numbers.exponentiation.exp_complex_closure
208	instantiation	241, 221, 216	⊢
	: , : , :
209	instantiation	217, 218	,  ⊢
	:
210	theorem		⊢
	proveit.numbers.number_sets.real_numbers.all_in_interval_co__is__real
211	theorem		⊢
	proveit.numbers.number_sets.real_numbers.zero_is_real
212	instantiation	241, 224, 219	⊢
	: , : , :
213	axiom		⊢
	proveit.physics.quantum.QPE._phase_in_interval
214	theorem		⊢
	proveit.numbers.number_sets.real_numbers.real_pos_within_real
215	theorem		⊢
	proveit.numbers.number_sets.real_numbers.pi_is_real_pos
216	instantiation	241, 224, 220	⊢
	: , : , :
217	theorem		⊢
	proveit.numbers.negation.complex_closure
218	instantiation	241, 221, 222	,  ⊢
	: , : , :
219	instantiation	241, 227, 236	⊢
	: , : , :
220	instantiation	241, 227, 223	⊢
	: , : , :
221	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
222	instantiation	241, 224, 225	,  ⊢
	: , : , :
223	instantiation	241, 239, 226	⊢
	: , : , :
224	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
225	instantiation	241, 227, 228	,  ⊢
	: , : , :
226	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
227	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
228	instantiation	241, 229, 230	,  ⊢
	: , : , :
229	instantiation	231, 232, 233	⊢
	: , :
230	assumption		⊢
231	theorem		⊢
	proveit.numbers.number_sets.integers.int_interval_within_int
232	instantiation	234, 235, 236	⊢
	: , :
233	theorem		⊢
	proveit.numbers.number_sets.integers.zero_is_int
234	theorem		⊢
	proveit.numbers.addition.add_int_closure_bin
235	instantiation	237, 238	⊢
	:
236	instantiation	241, 239, 240	⊢
	: , : , :
237	theorem		⊢
	proveit.numbers.negation.int_closure
238	instantiation	241, 242, 243	⊢
	: , : , :
239	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
240	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
241	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
242	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_int
243	assumption		⊢
*equality replacement requirements