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	theorem		⊢
	proveit.logic.equality.sub_left_side_into
2	instantiation	163, 4, 5	⊢
	: , : , :
3	instantiation	6, 217	⊢
	:
4	instantiation	7, 217, 8, 9, 10*	⊢
	: , : , :
5	instantiation	11, 217, 12, 13, 14, 15	⊢
	: , : , : , :
6	axiom		⊢
	proveit.physics.quantum.QPE._psi_t_def
7	theorem		⊢
	proveit.linear_algebra.tensors.tensor_prod_of_cart_exps_within_cart_exp
8	instantiation	69, 16, 138, 23	⊢
	: , : , : , :
9	instantiation	21, 206, 207, 178, 34	⊢
	: , : , :
10	instantiation	17, 18, 187, 31, 19*, 31*	⊢
	: , :
11	theorem		⊢
	proveit.linear_algebra.tensors.tensor_prod_is_in_tensor_prod_space
12	instantiation	69, 20, 138, 23	⊢
	: , : , : , :
13	instantiation	21, 206, 207, 99, 34	⊢
	: , : , :
14	instantiation	69, 22, 138, 23	⊢
	: , : , : , :
15	modus ponens	24, 25	⊢
16	instantiation	153, 26, 31	⊢
	: , : , :
17	theorem		⊢
	proveit.numbers.exponentiation.exp_nat_pos_rev
18	instantiation	102, 200, 169, 27, 170, 59, 214, 103	⊢
	: , : , : , : , :
19	instantiation	95, 28	⊢
	: , :
20	instantiation	153, 29, 31	⊢
	: , : , :
21	theorem		⊢
	proveit.logic.booleans.conjunction.redundant_conjunction_general
22	instantiation	153, 30, 31	⊢
	: , : , :
23	instantiation	95, 32	⊢
	: , :
24	instantiation	33, 206, 207, 34	⊢
	: , : , : , :
25	generalization	35	⊢
26	instantiation	40, 41	⊢
	: , : , :
27	instantiation	182	⊢
	: , :
28	instantiation	36, 209, 37, 38, 39	⊢
	: , : , : , : , : , :
29	instantiation	40, 41	⊢
	: , : , :
30	instantiation	40, 41	⊢
	: , : , :
31	instantiation	144, 42, 43	⊢
	: , : , :
32	instantiation	44, 45	⊢
	: , :
33	theorem		⊢
	proveit.logic.booleans.conjunction.conjunction_from_quantification
34	instantiation	122, 46, 47, 149, 48, 49*, 50*	⊢
	: , : , :
35	instantiation	98, 99, 51, 52	,  ⊢
	: , : , : , :
36	theorem		⊢
	proveit.core_expr_types.tuples.shift_equivalence
37	instantiation	53, 54, 59	⊢
	: , :
38	instantiation	95, 55	⊢
	: , :
39	instantiation	95, 56	⊢
	: , :
40	theorem		⊢
	proveit.core_expr_types.tuples.range_len
41	instantiation	57, 157, 58, 169, 59, 214	⊢
	: , :
42	instantiation	106, 60	⊢
	: , : , :
43	instantiation	69, 61, 62, 63	⊢
	: , : , : , :
44	theorem		⊢
	proveit.core_expr_types.tuples.range_from1_len
45	instantiation	215, 76, 217	⊢
	: , : , :
46	instantiation	215, 198, 64	⊢
	: , : , :
47	theorem		⊢
	proveit.numbers.number_sets.real_numbers.zero_is_real
48	instantiation	65, 66	⊢
	: , :
49	instantiation	144, 67, 68	⊢
	: , : , :
50	instantiation	69, 70, 89, 71	⊢
	: , : , : , :
51	instantiation	215, 195, 72	⊢
	: , : , :
52	instantiation	73, 99, 74, 75	,  ⊢
	: , : , : , :
53	theorem		⊢
	proveit.numbers.addition.add_nat_closure_bin
54	instantiation	215, 76, 77	⊢
	: , : , :
55	instantiation	144, 78, 79	⊢
	: , : , :
56	instantiation	144, 80, 81	⊢
	: , : , :
57	theorem		⊢
	proveit.numbers.addition.add_nat_closure
58	instantiation	174	⊢
	: , : , :
59	instantiation	82, 83	⊢
	:
60	instantiation	84, 135, 134, 107*	⊢
	: , :
61	instantiation	118, 214, 200, 85, 91, 137, 87, 134	⊢
	: , : , : , : , : , :
62	instantiation	92, 169, 157, 170, 86, 137, 87, 134	⊢
	: , : , : , :
63	instantiation	88, 134, 137, 89	⊢
	: , : , :
64	instantiation	215, 201, 206	⊢
	: , : , :
65	theorem		⊢
	proveit.numbers.ordering.relax_less
66	instantiation	90, 217	⊢
	:
67	instantiation	118, 214, 200, 169, 119, 170, 91, 135, 134	⊢
	: , : , : , : , : , :
68	instantiation	92, 169, 200, 170, 119, 135, 134	⊢
	: , : , : , :
69	theorem		⊢
	proveit.logic.equality.four_chain_transitivity
70	instantiation	144, 93, 94	⊢
	: , : , :
71	instantiation	95, 96	⊢
	: , :
72	instantiation	215, 189, 97	⊢
	: , : , :
73	theorem		⊢
	proveit.linear_algebra.addition.binary_closure
74	theorem		⊢
	proveit.physics.quantum.algebra.ket_zero_in_qubit_space
75	instantiation	98, 99, 100, 101	,  ⊢
	: , : , : , :
76	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nat_pos_within_nat
77	instantiation	102, 214, 169, 170, 103	⊢
	: , : , : , : , :
78	instantiation	106, 107	⊢
	: , : , :
79	instantiation	144, 104, 105	⊢
	: , : , :
80	instantiation	106, 107	⊢
	: , : , :
81	instantiation	111, 137	⊢
	:
82	theorem		⊢
	proveit.numbers.negation.nat_closure
83	instantiation	108, 206, 109	⊢
	:
84	theorem		⊢
	proveit.numbers.negation.distribute_neg_through_binary_sum
85	instantiation	182	⊢
	: , :
86	instantiation	174	⊢
	: , : , :
87	instantiation	192, 134	⊢
	:
88	theorem		⊢
	proveit.numbers.addition.subtraction.add_cancel_triple_32
89	instantiation	150	⊢
	:
90	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.natural_pos_is_pos
91	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.zero_is_complex
92	theorem		⊢
	proveit.numbers.addition.elim_zero_any
93	instantiation	118, 214, 200, 169, 119, 170, 137, 135, 134	⊢
	: , : , : , : , : , :
94	instantiation	110, 137, 134, 138	⊢
	: , : , :
95	theorem		⊢
	proveit.logic.equality.equals_reversal
96	instantiation	111, 134	⊢
	:
97	instantiation	112, 113, 141, 114	⊢
	: , :
98	theorem		⊢
	proveit.linear_algebra.scalar_multiplication.scalar_mult_closure
99	instantiation	115, 178	⊢
	:
100	instantiation	186, 116, 117	,  ⊢
	: , :
101	theorem		⊢
	proveit.physics.quantum.algebra.ket_one_in_qubit_space
102	theorem		⊢
	proveit.numbers.addition.add_nat_pos_from_nonneg
103	theorem		⊢
	proveit.numbers.numerals.decimals.less_0_1
104	instantiation	118, 169, 200, 214, 170, 119, 135, 134, 137	⊢
	: , : , : , : , : , :
105	instantiation	120, 137, 134, 138	⊢
	: , : , :
106	axiom		⊢
	proveit.logic.equality.substitution
107	instantiation	121, 137	⊢
	:
108	theorem		⊢
	proveit.numbers.number_sets.integers.nonpos_int_is_int_nonpos
109	instantiation	122, 148, 147, 149, 123, 124*, 125*	⊢
	: , : , :
110	theorem		⊢
	proveit.numbers.addition.subtraction.add_cancel_triple_12
111	theorem		⊢
	proveit.numbers.addition.elim_zero_left
112	theorem		⊢
	proveit.numbers.division.div_real_pos_closure
113	instantiation	215, 165, 126	⊢
	: , : , :
114	instantiation	127, 128	⊢
	:
115	theorem		⊢
	proveit.linear_algebra.complex_vec_set_is_vec_space
116	instantiation	215, 195, 129	⊢
	: , : , :
117	instantiation	153, 130, 131	,  ⊢
	: , : , :
118	theorem		⊢
	proveit.numbers.addition.disassociation
119	instantiation	182	⊢
	: , :
120	theorem		⊢
	proveit.numbers.addition.subtraction.add_cancel_triple_31
121	theorem		⊢
	proveit.numbers.negation.double_negation
122	theorem		⊢
	proveit.numbers.addition.weak_bound_via_left_term_bound
123	instantiation	132, 217	⊢
	:
124	instantiation	133, 134, 135	⊢
	: , :
125	instantiation	136, 137, 138	⊢
	: , :
126	instantiation	215, 177, 139	⊢
	: , : , :
127	theorem		⊢
	proveit.numbers.number_sets.real_numbers.nonzero_if_in_real_nonzero
128	instantiation	215, 140, 141	⊢
	: , : , :
129	instantiation	215, 189, 142	⊢
	: , : , :
130	instantiation	179, 156, 143	,  ⊢
	: , :
131	instantiation	144, 145, 146	,  ⊢
	: , : , :
132	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.natural_pos_lower_bound
133	theorem		⊢
	proveit.numbers.addition.commutation
134	instantiation	215, 195, 147	⊢
	: , : , :
135	instantiation	215, 195, 148	⊢
	: , : , :
136	theorem		⊢
	proveit.numbers.addition.subtraction.add_cancel_basic
137	instantiation	215, 195, 149	⊢
	: , : , :
138	instantiation	150	⊢
	:
139	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
140	theorem		⊢
	proveit.numbers.number_sets.real_numbers.real_pos_within_real_nonzero
141	instantiation	151, 152	⊢
	:
142	theorem		⊢
	proveit.numbers.number_sets.real_numbers.e_is_real_pos
143	instantiation	153, 154, 155	,  ⊢
	: , : , :
144	axiom		⊢
	proveit.logic.equality.equals_transitivity
145	instantiation	168, 214, 157, 169, 159, 170, 156, 180, 181, 172	,  ⊢
	: , : , : , : , : , :
146	instantiation	168, 169, 200, 157, 170, 158, 159, 187, 160, 180, 181, 172	,  ⊢
	: , : , : , : , : , :
147	instantiation	215, 198, 161	⊢
	: , : , :
148	instantiation	215, 198, 162	⊢
	: , : , :
149	instantiation	163, 164, 217	⊢
	: , : , :
150	axiom		⊢
	proveit.logic.equality.equals_reflexivity
151	theorem		⊢
	proveit.numbers.exponentiation.sqrt_real_pos_closure
152	instantiation	215, 165, 166	⊢
	: , : , :
153	theorem		⊢
	proveit.logic.equality.sub_right_side_into
154	instantiation	179, 167, 172	,  ⊢
	: , :
155	instantiation	168, 169, 200, 214, 170, 171, 180, 181, 172	,  ⊢
	: , : , : , : , : , :
156	instantiation	215, 195, 173	⊢
	: , : , :
157	theorem		⊢
	proveit.numbers.numerals.decimals.nat3
158	instantiation	182	⊢
	: , :
159	instantiation	174	⊢
	: , : , :
160	instantiation	215, 195, 185	⊢
	: , : , :
161	instantiation	215, 201, 210	⊢
	: , : , :
162	instantiation	215, 201, 209	⊢
	: , : , :
163	theorem		⊢
	proveit.logic.sets.inclusion.unfold_subset_eq
164	instantiation	175, 176	⊢
	: , :
165	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_pos_within_real_pos
166	instantiation	215, 177, 178	⊢
	: , : , :
167	instantiation	179, 180, 181	,  ⊢
	: , :
168	theorem		⊢
	proveit.numbers.multiplication.disassociation
169	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
170	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
171	instantiation	182	⊢
	: , :
172	instantiation	215, 195, 183	⊢
	: , : , :
173	instantiation	184, 191, 185	⊢
	: , :
174	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_3_typical_eq
175	theorem		⊢
	proveit.logic.sets.inclusion.relax_proper_subset
176	theorem		⊢
	proveit.numbers.number_sets.real_numbers.nat_pos_within_real
177	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nat_pos_within_rational_pos
178	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
179	theorem		⊢
	proveit.numbers.multiplication.mult_complex_closure_bin
180	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.i_is_complex
181	instantiation	186, 187, 188	,  ⊢
	: , :
182	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
183	theorem		⊢
	proveit.physics.quantum.QPE._phase_is_real
184	theorem		⊢
	proveit.numbers.multiplication.mult_real_closure_bin
185	instantiation	215, 189, 190	⊢
	: , : , :
186	theorem		⊢
	proveit.numbers.exponentiation.exp_complex_closure
187	instantiation	215, 195, 191	⊢
	: , : , :
188	instantiation	192, 193	,  ⊢
	:
189	theorem		⊢
	proveit.numbers.number_sets.real_numbers.real_pos_within_real
190	theorem		⊢
	proveit.numbers.number_sets.real_numbers.pi_is_real_pos
191	instantiation	215, 198, 194	⊢
	: , : , :
192	theorem		⊢
	proveit.numbers.negation.complex_closure
193	instantiation	215, 195, 196	,  ⊢
	: , : , :
194	instantiation	215, 201, 197	⊢
	: , : , :
195	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
196	instantiation	215, 198, 199	,  ⊢
	: , : , :
197	instantiation	215, 213, 200	⊢
	: , : , :
198	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
199	instantiation	215, 201, 202	,  ⊢
	: , : , :
200	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
201	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
202	instantiation	215, 203, 204	,  ⊢
	: , : , :
203	instantiation	205, 206, 207	⊢
	: , :
204	assumption		⊢
205	theorem		⊢
	proveit.numbers.number_sets.integers.int_interval_within_int
206	instantiation	208, 209, 210	⊢
	: , :
207	theorem		⊢
	proveit.numbers.number_sets.integers.zero_is_int
208	theorem		⊢
	proveit.numbers.addition.add_int_closure_bin
209	instantiation	211, 212	⊢
	:
210	instantiation	215, 213, 214	⊢
	: , : , :
211	theorem		⊢
	proveit.numbers.negation.int_closure
212	instantiation	215, 216, 217	⊢
	: , : , :
213	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
214	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
215	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
216	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_int
217	assumption		⊢
*equality replacement requirements