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, 8, 9	⊢
	: , : , : , : , : , : , : , : , : , :
1	theorem		⊢
	proveit.linear_algebra.tensors.factor_scalar_from_tensor_prod
2	instantiation	50, 135, 10, 11	⊢
	: , :
3	reference	120	⊢
4	reference	198	⊢
5	reference	122	⊢
6	reference	20	⊢
7	reference	47	⊢
8	instantiation	12, 20, 13, 14	⊢
	: , : , : , :
9	instantiation	46, 47, 15, 16	⊢
	: , : , : , :
10	instantiation	62, 154, 17	⊢
	: , :
11	instantiation	32, 18, 19	⊢
	: , : , :
12	theorem		⊢
	proveit.linear_algebra.addition.binary_closure
13	theorem		⊢
	proveit.physics.quantum.algebra.ket_zero_in_qubit_space
14	instantiation	46, 20, 21, 22	⊢
	: , : , : , :
15	instantiation	50, 135, 23, 24	⊢
	: , :
16	modus ponens	25, 26	⊢
17	instantiation	133, 27, 28	⊢
	: , :
18	instantiation	44, 161, 29	⊢
	: , :
19	instantiation	124, 30	⊢
	: , : , :
20	instantiation	60, 187	⊢
	:
21	instantiation	62, 63, 31	⊢
	: , :
22	theorem		⊢
	proveit.physics.quantum.algebra.ket_one_in_qubit_space
23	instantiation	62, 154, 37	⊢
	: , :
24	instantiation	32, 33, 34	⊢
	: , : , :
25	instantiation	35, 185, 47	⊢
	: , : , : , : , : , :
26	generalization	36	⊢
27	instantiation	50, 118, 154, 93	⊢
	: , :
28	instantiation	82, 37	⊢
	:
29	instantiation	38, 39, 161	⊢
	: , :
30	instantiation	107, 40, 41	⊢
	: , : , :
31	instantiation	97, 42, 43	⊢
	: , : , :
32	theorem		⊢
	proveit.logic.equality.sub_left_side_into
33	instantiation	44, 161, 45	⊢
	: , :
34	instantiation	124, 81	⊢
	: , : , :
35	theorem		⊢
	proveit.linear_algebra.addition.summation_closure
36	instantiation	46, 47, 48, 49	,  ⊢
	: , : , : , :
37	instantiation	50, 134, 154, 93	⊢
	: , :
38	theorem		⊢
	proveit.numbers.division.div_rational_nonzero_closure
39	instantiation	196, 170, 51	⊢
	: , : , :
40	instantiation	107, 52, 53	⊢
	: , : , :
41	instantiation	107, 54, 55	⊢
	: , : , :
42	instantiation	128, 100, 56	⊢
	: , :
43	instantiation	107, 57, 58	⊢
	: , : , :
44	theorem		⊢
	proveit.numbers.exponentiation.exp_rational_non_zero__not_zero
45	instantiation	196, 59, 127	⊢
	: , : , :
46	theorem		⊢
	proveit.linear_algebra.scalar_multiplication.scalar_mult_closure
47	instantiation	60, 61	⊢
	:
48	instantiation	62, 63, 64	,  ⊢
	: , :
49	instantiation	65, 195, 165	,  ⊢
	: , :
50	theorem		⊢
	proveit.numbers.division.div_complex_closure
51	instantiation	196, 180, 185	⊢
	: , : , :
52	instantiation	124, 66	⊢
	: , : , :
53	instantiation	124, 67	⊢
	: , : , :
54	instantiation	68, 120, 193, 198, 122, 69, 83, 138, 70	⊢
	: , : , : , : , : , :
55	instantiation	71, 83, 138, 72	⊢
	: , : , :
56	instantiation	97, 73, 74	⊢
	: , : , :
57	instantiation	113, 198, 101, 120, 75, 122, 100, 129, 130, 85	⊢
	: , : , : , : , : , :
58	instantiation	113, 120, 193, 101, 122, 102, 75, 154, 116, 129, 130, 85	⊢
	: , : , : , : , : , :
59	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.rational_pos_within_rational_nonzero
60	theorem		⊢
	proveit.linear_algebra.complex_vec_set_is_vec_space
61	instantiation	76, 193, 190	⊢
	: , :
62	theorem		⊢
	proveit.numbers.exponentiation.exp_complex_closure
63	instantiation	196, 162, 77	⊢
	: , : , :
64	instantiation	97, 78, 79	,  ⊢
	: , : , :
65	theorem		⊢
	proveit.physics.quantum.algebra.num_ket_in_register_space
66	instantiation	92, 118, 154, 93, 80*	⊢
	: , :
67	instantiation	124, 81	⊢
	: , : , :
68	theorem		⊢
	proveit.numbers.addition.disassociation
69	instantiation	136	⊢
	: , :
70	instantiation	82, 83	⊢
	:
71	theorem		⊢
	proveit.numbers.addition.subtraction.add_cancel_triple_13
72	instantiation	84	⊢
	:
73	instantiation	128, 112, 85	⊢
	: , :
74	instantiation	113, 120, 193, 198, 122, 114, 129, 130, 85	⊢
	: , : , : , : , : , :
75	instantiation	117	⊢
	: , : , :
76	theorem		⊢
	proveit.numbers.exponentiation.exp_natpos_closure
77	instantiation	196, 146, 86	⊢
	: , : , :
78	instantiation	128, 100, 87	,  ⊢
	: , :
79	instantiation	107, 88, 89	,  ⊢
	: , : , :
80	instantiation	107, 90, 91	⊢
	: , : , :
81	instantiation	92, 134, 154, 93, 94*	⊢
	: , :
82	theorem		⊢
	proveit.numbers.negation.complex_closure
83	instantiation	196, 162, 95	⊢
	: , : , :
84	axiom		⊢
	proveit.logic.equality.equals_reflexivity
85	instantiation	196, 162, 96	⊢
	: , : , :
86	theorem		⊢
	proveit.numbers.number_sets.real_numbers.e_is_real_pos
87	instantiation	97, 98, 99	,  ⊢
	: , : , :
88	instantiation	113, 198, 101, 120, 103, 122, 100, 129, 130, 115	,  ⊢
	: , : , : , : , : , :
89	instantiation	113, 120, 193, 101, 122, 102, 103, 154, 116, 129, 130, 115	,  ⊢
	: , : , : , : , : , :
90	instantiation	124, 125	⊢
	: , : , :
91	instantiation	107, 104, 105	⊢
	: , : , :
92	theorem		⊢
	proveit.numbers.division.div_as_mult
93	instantiation	106, 187	⊢
	:
94	instantiation	107, 108, 109	⊢
	: , : , :
95	instantiation	196, 172, 110	⊢
	: , : , :
96	instantiation	196, 172, 111	⊢
	: , : , :
97	theorem		⊢
	proveit.logic.equality.sub_right_side_into
98	instantiation	128, 112, 115	,  ⊢
	: , :
99	instantiation	113, 120, 193, 198, 122, 114, 129, 130, 115	,  ⊢
	: , : , : , : , : , :
100	instantiation	128, 154, 116	⊢
	: , :
101	theorem		⊢
	proveit.numbers.numerals.decimals.nat3
102	instantiation	136	⊢
	: , :
103	instantiation	117	⊢
	: , : , :
104	instantiation	126, 118, 138	⊢
	: , :
105	instantiation	119, 198, 193, 120, 121, 122, 138, 134, 135, 123*	⊢
	: , : , : , : , : , :
106	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos
107	axiom		⊢
	proveit.logic.equality.equals_transitivity
108	instantiation	124, 125	⊢
	: , : , :
109	instantiation	126, 134, 138	⊢
	: , :
110	instantiation	196, 168, 127	⊢
	: , : , :
111	instantiation	196, 181, 183	⊢
	: , : , :
112	instantiation	128, 129, 130	⊢
	: , :
113	theorem		⊢
	proveit.numbers.multiplication.disassociation
114	instantiation	136	⊢
	: , :
115	instantiation	196, 162, 131	,  ⊢
	: , : , :
116	instantiation	196, 162, 132	⊢
	: , : , :
117	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_3_typical_eq
118	instantiation	133, 134, 135	⊢
	: , :
119	theorem		⊢
	proveit.numbers.multiplication.distribute_through_sum
120	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
121	instantiation	136	⊢
	: , :
122	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
123	instantiation	137, 138	⊢
	:
124	axiom		⊢
	proveit.logic.equality.substitution
125	instantiation	139, 140, 185, 141*	⊢
	: , :
126	theorem		⊢
	proveit.numbers.multiplication.commutation
127	instantiation	142, 169, 143	⊢
	: , :
128	theorem		⊢
	proveit.numbers.multiplication.mult_complex_closure_bin
129	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.i_is_complex
130	instantiation	196, 162, 144	⊢
	: , : , :
131	instantiation	196, 172, 145	,  ⊢
	: , : , :
132	instantiation	196, 146, 147	⊢
	: , : , :
133	theorem		⊢
	proveit.numbers.addition.add_complex_closure_bin
134	instantiation	196, 162, 148	⊢
	: , : , :
135	instantiation	196, 162, 149	⊢
	: , : , :
136	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
137	theorem		⊢
	proveit.numbers.multiplication.elim_one_right
138	instantiation	196, 162, 150	⊢
	: , : , :
139	theorem		⊢
	proveit.numbers.exponentiation.neg_power_as_div
140	instantiation	196, 151, 152	⊢
	: , : , :
141	instantiation	153, 154	⊢
	:
142	theorem		⊢
	proveit.numbers.multiplication.mult_rational_pos_closure_bin
143	instantiation	196, 186, 195	⊢
	: , : , :
144	theorem		⊢
	proveit.physics.quantum.QPE._phase_is_real
145	instantiation	196, 181, 155	,  ⊢
	: , : , :
146	theorem		⊢
	proveit.numbers.number_sets.real_numbers.real_pos_within_real
147	theorem		⊢
	proveit.numbers.number_sets.real_numbers.pi_is_real_pos
148	instantiation	156, 157, 195	⊢
	: , : , :
149	instantiation	196, 172, 158	⊢
	: , : , :
150	instantiation	196, 172, 159	⊢
	: , : , :
151	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero
152	instantiation	196, 160, 161	⊢
	: , : , :
153	theorem		⊢
	proveit.numbers.exponentiation.complex_x_to_first_power_is_x
154	instantiation	196, 162, 163	⊢
	: , : , :
155	instantiation	196, 164, 165	,  ⊢
	: , : , :
156	theorem		⊢
	proveit.logic.sets.inclusion.unfold_subset_eq
157	instantiation	166, 167	⊢
	: , :
158	instantiation	196, 181, 192	⊢
	: , : , :
159	instantiation	196, 168, 169	⊢
	: , : , :
160	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero
161	instantiation	196, 170, 171	⊢
	: , : , :
162	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
163	instantiation	196, 172, 173	⊢
	: , : , :
164	instantiation	174, 175, 176	⊢
	: , :
165	assumption		⊢
166	theorem		⊢
	proveit.logic.sets.inclusion.relax_proper_subset
167	theorem		⊢
	proveit.numbers.number_sets.real_numbers.nat_pos_within_real
168	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.rational_pos_within_rational
169	instantiation	177, 178, 179	⊢
	: , :
170	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
171	instantiation	196, 180, 187	⊢
	: , : , :
172	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
173	instantiation	196, 181, 189	⊢
	: , : , :
174	theorem		⊢
	proveit.numbers.number_sets.integers.int_interval_within_int
175	theorem		⊢
	proveit.numbers.number_sets.integers.zero_is_int
176	instantiation	182, 183, 184	⊢
	: , :
177	theorem		⊢
	proveit.numbers.division.div_rational_pos_closure
178	instantiation	196, 186, 185	⊢
	: , : , :
179	instantiation	196, 186, 187	⊢
	: , : , :
180	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
181	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
182	theorem		⊢
	proveit.numbers.addition.add_int_closure_bin
183	instantiation	188, 189, 190	⊢
	: , :
184	instantiation	191, 192	⊢
	:
185	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
186	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nat_pos_within_rational_pos
187	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
188	theorem		⊢
	proveit.numbers.exponentiation.exp_int_closure
189	instantiation	196, 197, 193	⊢
	: , : , :
190	instantiation	196, 194, 195	⊢
	: , : , :
191	theorem		⊢
	proveit.numbers.negation.int_closure
192	instantiation	196, 197, 198	⊢
	: , : , :
193	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
194	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nat_pos_within_nat
195	assumption		⊢
196	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
197	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
198	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
*equality replacement requirements