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*	⊢
	: , : , :
1	reference	128	⊢
2	instantiation	11, 19, 138, 201, 140, 30, 43, 16, 5	⊢
	: , : , : , : , : , : , : , : , : , :
3	instantiation	142, 6	⊢
	: , : , :
4	instantiation	7, 8, 9, 19, 20, 10*	⊢
	: , : , : , : , :
5	instantiation	42, 43, 20, 17	⊢
	: , : , : , :
6	instantiation	11, 20, 201, 138, 140, 30, 43, 16, 17	⊢
	: , : , : , : , : , : , : , : , : , :
7	theorem		⊢
	proveit.linear_algebra.scalar_multiplication.doubly_scaled_as_singly_scaled
8	instantiation	12, 204, 14, 30, 43	⊢
	: , : , :
9	instantiation	13, 204, 14, 30, 43, 15, 16, 17	⊢
	: , : , : , :
10	instantiation	18, 19, 20	⊢
	: , :
11	theorem		⊢
	proveit.linear_algebra.tensors.factor_scalar_from_tensor_prod
12	theorem		⊢
	proveit.linear_algebra.tensors.tensor_prod_of_vec_spaces_is_vec_space
13	theorem		⊢
	proveit.linear_algebra.tensors.tensor_prod_is_in_tensor_prod_space
14	instantiation	150	⊢
	: , :
15	instantiation	150	⊢
	: , :
16	instantiation	21, 30, 22, 23	⊢
	: , : , : , :
17	modus ponens	24, 25	⊢
18	axiom		⊢
	proveit.linear_algebra.scalar_multiplication.scalar_mult_extends_number_mult
19	instantiation	73, 149, 26, 27	⊢
	: , :
20	instantiation	73, 149, 28, 29	⊢
	: , :
21	theorem		⊢
	proveit.linear_algebra.addition.binary_closure
22	theorem		⊢
	proveit.physics.quantum.algebra.ket_zero_in_qubit_space
23	instantiation	42, 30, 31, 32	⊢
	: , : , : , :
24	instantiation	33, 202, 43	⊢
	: , : , : , : , : , :
25	generalization	34	⊢
26	instantiation	56, 166, 35	⊢
	: , :
27	instantiation	38, 36, 37	⊢
	: , : , :
28	instantiation	56, 166, 60	⊢
	: , :
29	instantiation	38, 39, 40	⊢
	: , : , :
30	instantiation	54, 204	⊢
	:
31	instantiation	56, 57, 41	⊢
	: , :
32	theorem		⊢
	proveit.physics.quantum.algebra.ket_one_in_qubit_space
33	theorem		⊢
	proveit.linear_algebra.addition.summation_closure
34	instantiation	42, 43, 44, 45	,  ⊢
	: , : , : , :
35	instantiation	147, 46, 47	⊢
	: , :
36	instantiation	50, 175, 48	⊢
	: , :
37	instantiation	142, 49	⊢
	: , : , :
38	theorem		⊢
	proveit.logic.equality.sub_left_side_into
39	instantiation	50, 175, 51	⊢
	: , :
40	instantiation	142, 102	⊢
	: , : , :
41	instantiation	94, 52, 53	⊢
	: , : , :
42	theorem		⊢
	proveit.linear_algebra.scalar_multiplication.scalar_mult_closure
43	instantiation	54, 55	⊢
	:
44	instantiation	56, 57, 58	,  ⊢
	: , :
45	instantiation	59, 200, 159	,  ⊢
	: , :
46	instantiation	73, 136, 166, 116	⊢
	: , :
47	instantiation	103, 60	⊢
	:
48	instantiation	61, 62, 175	⊢
	: , :
49	instantiation	128, 63, 64	⊢
	: , : , :
50	theorem		⊢
	proveit.numbers.exponentiation.exp_rational_non_zero__not_zero
51	instantiation	205, 65, 145	⊢
	: , : , :
52	instantiation	120, 97, 66	⊢
	: , :
53	instantiation	128, 67, 68	⊢
	: , : , :
54	theorem		⊢
	proveit.linear_algebra.complex_vec_set_is_vec_space
55	instantiation	69, 207, 190	⊢
	: , :
56	theorem		⊢
	proveit.numbers.exponentiation.exp_complex_closure
57	instantiation	205, 176, 70	⊢
	: , : , :
58	instantiation	94, 71, 72	,  ⊢
	: , : , :
59	theorem		⊢
	proveit.physics.quantum.algebra.num_ket_in_register_space
60	instantiation	73, 148, 166, 116	⊢
	: , :
61	theorem		⊢
	proveit.numbers.division.div_rational_nonzero_closure
62	instantiation	205, 185, 74	⊢
	: , : , :
63	instantiation	128, 75, 76	⊢
	: , : , :
64	instantiation	128, 77, 78	⊢
	: , : , :
65	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.rational_pos_within_rational_nonzero
66	instantiation	94, 79, 80	⊢
	: , : , :
67	instantiation	108, 201, 98, 138, 81, 140, 97, 121, 122, 93	⊢
	: , : , : , : , : , :
68	instantiation	108, 138, 207, 98, 140, 99, 81, 166, 111, 121, 122, 93	⊢
	: , : , : , : , : , :
69	theorem		⊢
	proveit.numbers.exponentiation.exp_natpos_closure
70	instantiation	205, 134, 82	⊢
	: , : , :
71	instantiation	120, 97, 83	,  ⊢
	: , :
72	instantiation	128, 84, 85	,  ⊢
	: , : , :
73	theorem		⊢
	proveit.numbers.division.div_complex_closure
74	instantiation	205, 196, 202	⊢
	: , : , :
75	instantiation	142, 86	⊢
	: , : , :
76	instantiation	142, 87	⊢
	: , : , :
77	instantiation	88, 138, 207, 201, 140, 89, 104, 152, 90	⊢
	: , : , : , : , : , :
78	instantiation	91, 104, 152, 92	⊢
	: , : , :
79	instantiation	120, 107, 93	⊢
	: , :
80	instantiation	108, 138, 207, 201, 140, 109, 121, 122, 93	⊢
	: , : , : , : , : , :
81	instantiation	112	⊢
	: , : , :
82	theorem		⊢
	proveit.numbers.number_sets.real_numbers.e_is_real_pos
83	instantiation	94, 95, 96	,  ⊢
	: , : , :
84	instantiation	108, 201, 98, 138, 100, 140, 97, 121, 122, 110	,  ⊢
	: , : , : , : , : , :
85	instantiation	108, 138, 207, 98, 140, 99, 100, 166, 111, 121, 122, 110	,  ⊢
	: , : , : , : , : , :
86	instantiation	115, 136, 166, 116, 101*	⊢
	: , :
87	instantiation	142, 102	⊢
	: , : , :
88	theorem		⊢
	proveit.numbers.addition.disassociation
89	instantiation	150	⊢
	: , :
90	instantiation	103, 104	⊢
	:
91	theorem		⊢
	proveit.numbers.addition.subtraction.add_cancel_triple_13
92	instantiation	105	⊢
	:
93	instantiation	205, 176, 106	⊢
	: , : , :
94	theorem		⊢
	proveit.logic.equality.sub_right_side_into
95	instantiation	120, 107, 110	,  ⊢
	: , :
96	instantiation	108, 138, 207, 201, 140, 109, 121, 122, 110	,  ⊢
	: , : , : , : , : , :
97	instantiation	120, 166, 111	⊢
	: , :
98	theorem		⊢
	proveit.numbers.numerals.decimals.nat3
99	instantiation	150	⊢
	: , :
100	instantiation	112	⊢
	: , : , :
101	instantiation	128, 113, 114	⊢
	: , : , :
102	instantiation	115, 148, 166, 116, 117*	⊢
	: , :
103	theorem		⊢
	proveit.numbers.negation.complex_closure
104	instantiation	205, 176, 118	⊢
	: , : , :
105	axiom		⊢
	proveit.logic.equality.equals_reflexivity
106	instantiation	205, 187, 119	⊢
	: , : , :
107	instantiation	120, 121, 122	⊢
	: , :
108	theorem		⊢
	proveit.numbers.multiplication.disassociation
109	instantiation	150	⊢
	: , :
110	instantiation	205, 176, 123	,  ⊢
	: , : , :
111	instantiation	205, 176, 124	⊢
	: , : , :
112	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_3_typical_eq
113	instantiation	142, 143	⊢
	: , : , :
114	instantiation	128, 125, 126	⊢
	: , : , :
115	theorem		⊢
	proveit.numbers.division.div_as_mult
116	instantiation	127, 204	⊢
	:
117	instantiation	128, 129, 130	⊢
	: , : , :
118	instantiation	205, 187, 131	⊢
	: , : , :
119	instantiation	205, 197, 179	⊢
	: , : , :
120	theorem		⊢
	proveit.numbers.multiplication.mult_complex_closure_bin
121	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.i_is_complex
122	instantiation	205, 176, 132	⊢
	: , : , :
123	instantiation	205, 187, 133	,  ⊢
	: , : , :
124	instantiation	205, 134, 135	⊢
	: , : , :
125	instantiation	144, 136, 152	⊢
	: , :
126	instantiation	137, 201, 207, 138, 139, 140, 152, 148, 149, 141*	⊢
	: , : , : , : , : , :
127	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos
128	axiom		⊢
	proveit.logic.equality.equals_transitivity
129	instantiation	142, 143	⊢
	: , : , :
130	instantiation	144, 148, 152	⊢
	: , :
131	instantiation	205, 183, 145	⊢
	: , : , :
132	theorem		⊢
	proveit.physics.quantum.QPE._phase_is_real
133	instantiation	205, 197, 146	,  ⊢
	: , : , :
134	theorem		⊢
	proveit.numbers.number_sets.real_numbers.real_pos_within_real
135	theorem		⊢
	proveit.numbers.number_sets.real_numbers.pi_is_real_pos
136	instantiation	147, 148, 149	⊢
	: , :
137	theorem		⊢
	proveit.numbers.multiplication.distribute_through_sum
138	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
139	instantiation	150	⊢
	: , :
140	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
141	instantiation	151, 152	⊢
	:
142	axiom		⊢
	proveit.logic.equality.substitution
143	instantiation	153, 154, 202, 155*	⊢
	: , :
144	theorem		⊢
	proveit.numbers.multiplication.commutation
145	instantiation	156, 184, 157	⊢
	: , :
146	instantiation	205, 158, 159	,  ⊢
	: , : , :
147	theorem		⊢
	proveit.numbers.addition.add_complex_closure_bin
148	instantiation	205, 176, 160	⊢
	: , : , :
149	instantiation	205, 176, 161	⊢
	: , : , :
150	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
151	theorem		⊢
	proveit.numbers.multiplication.elim_one_right
152	instantiation	205, 176, 162	⊢
	: , : , :
153	theorem		⊢
	proveit.numbers.exponentiation.neg_power_as_div
154	instantiation	205, 163, 164	⊢
	: , : , :
155	instantiation	165, 166	⊢
	:
156	theorem		⊢
	proveit.numbers.multiplication.mult_rational_pos_closure_bin
157	instantiation	205, 203, 200	⊢
	: , : , :
158	instantiation	167, 168, 169	⊢
	: , :
159	assumption		⊢
160	instantiation	170, 171, 200	⊢
	: , : , :
161	instantiation	205, 187, 172	⊢
	: , : , :
162	instantiation	205, 187, 173	⊢
	: , : , :
163	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero
164	instantiation	205, 174, 175	⊢
	: , : , :
165	theorem		⊢
	proveit.numbers.exponentiation.complex_x_to_first_power_is_x
166	instantiation	205, 176, 177	⊢
	: , : , :
167	theorem		⊢
	proveit.numbers.number_sets.integers.int_interval_within_int
168	theorem		⊢
	proveit.numbers.number_sets.integers.zero_is_int
169	instantiation	178, 179, 180	⊢
	: , :
170	theorem		⊢
	proveit.logic.sets.inclusion.unfold_subset_eq
171	instantiation	181, 182	⊢
	: , :
172	instantiation	205, 197, 192	⊢
	: , : , :
173	instantiation	205, 183, 184	⊢
	: , : , :
174	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero
175	instantiation	205, 185, 186	⊢
	: , : , :
176	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
177	instantiation	205, 187, 188	⊢
	: , : , :
178	theorem		⊢
	proveit.numbers.addition.add_int_closure_bin
179	instantiation	189, 198, 190	⊢
	: , :
180	instantiation	191, 192	⊢
	:
181	theorem		⊢
	proveit.logic.sets.inclusion.relax_proper_subset
182	theorem		⊢
	proveit.numbers.number_sets.real_numbers.nat_pos_within_real
183	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.rational_pos_within_rational
184	instantiation	193, 194, 195	⊢
	: , :
185	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
186	instantiation	205, 196, 204	⊢
	: , : , :
187	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
188	instantiation	205, 197, 198	⊢
	: , : , :
189	theorem		⊢
	proveit.numbers.exponentiation.exp_int_closure
190	instantiation	205, 199, 200	⊢
	: , : , :
191	theorem		⊢
	proveit.numbers.negation.int_closure
192	instantiation	205, 206, 201	⊢
	: , : , :
193	theorem		⊢
	proveit.numbers.division.div_rational_pos_closure
194	instantiation	205, 203, 202	⊢
	: , : , :
195	instantiation	205, 203, 204	⊢
	: , : , :
196	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
197	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
198	instantiation	205, 206, 207	⊢
	: , : , :
199	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nat_pos_within_nat
200	assumption		⊢
201	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
202	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
203	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nat_pos_within_rational_pos
204	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
205	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
206	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
207	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
*equality replacement requirements