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	130	⊢
2	instantiation	27, 40, 4, 5, 6*, 7*	,  ⊢
	: , : , : , :
3	instantiation	130, 8, 9	⊢
	: , : , :
4	instantiation	201, 181, 10	⊢
	: , : , :
5	instantiation	11, 24, 41, 15	,  ⊢
	: , : , : , :
6	instantiation	12, 13	⊢
	:
7	instantiation	14, 24, 41, 15, 16, 17*	,  ⊢
	: , : , : , :
8	instantiation	116, 18	⊢
	: , : , :
9	instantiation	136, 19, 20	⊢
	: , : , :
10	instantiation	201, 174, 37	⊢
	: , : , :
11	theorem		⊢
	proveit.linear_algebra.addition.binary_closure
12	theorem		⊢
	proveit.numbers.absolute_value.abs_non_neg_elim
13	instantiation	21, 22	⊢
	:
14	theorem		⊢
	proveit.linear_algebra.addition.norm_of_sum_of_orthogonal_pair
15	instantiation	23, 24, 75, 42	,  ⊢
	: , : , : , :
16	instantiation	136, 25, 26	,  ⊢
	: , : , :
17	instantiation	27, 40, 75, 42, 28*	,  ⊢
	: , : , : , :
18	instantiation	116, 29	⊢
	: , : , :
19	instantiation	136, 30, 31	⊢
	: , : , :
20	instantiation	32, 33, 34, 35	⊢
	: , : , : , :
21	theorem		⊢
	proveit.numbers.number_sets.real_numbers.nonneg_if_in_real_nonneg
22	instantiation	201, 36, 37	⊢
	: , : , :
23	theorem		⊢
	proveit.linear_algebra.scalar_multiplication.scalar_mult_closure
24	instantiation	38, 135	⊢
	:
25	instantiation	39, 40, 75, 41, 42	,  ⊢
	: , : , : , : , :
26	instantiation	130, 43, 44	,  ⊢
	: , : , :
27	theorem		⊢
	proveit.linear_algebra.inner_products.scaled_norm
28	instantiation	130, 45, 46	,  ⊢
	: , : , :
29	instantiation	130, 47, 48	⊢
	: , : , :
30	instantiation	49, 80, 50, 51	⊢
	: , : , : , : , :
31	instantiation	130, 52, 53	⊢
	: , : , :
32	theorem		⊢
	proveit.logic.equality.four_chain_transitivity
33	instantiation	116, 54	⊢
	: , : , :
34	instantiation	116, 54	⊢
	: , : , :
35	instantiation	121, 80	⊢
	:
36	theorem		⊢
	proveit.numbers.number_sets.real_numbers.real_pos_within_real_nonneg
37	instantiation	55, 56, 89, 57	⊢
	: , :
38	theorem		⊢
	proveit.linear_algebra.complex_vec_set_is_vec_space
39	theorem		⊢
	proveit.linear_algebra.inner_products.inner_prod_scalar_mult_right
40	instantiation	58, 135	⊢
	:
41	theorem		⊢
	proveit.physics.quantum.algebra.ket_zero_in_qubit_space
42	theorem		⊢
	proveit.physics.quantum.algebra.ket_one_in_qubit_space
43	instantiation	116, 59	⊢
	: , : , :
44	instantiation	60, 75, 61, 62*	,  ⊢
	: , :
45	instantiation	116, 63	,  ⊢
	: , : , :
46	instantiation	102, 64	⊢
	:
47	instantiation	130, 65, 66	⊢
	: , : , :
48	theorem		⊢
	proveit.numbers.numerals.decimals.add_1_1
49	theorem		⊢
	proveit.numbers.division.mult_frac_cancel_denom_left
50	instantiation	201, 68, 67	⊢
	: , : , :
51	instantiation	201, 68, 73	⊢
	: , : , :
52	instantiation	116, 69	⊢
	: , : , :
53	instantiation	116, 70	⊢
	: , : , :
54	instantiation	104, 80	⊢
	:
55	theorem		⊢
	proveit.numbers.division.div_real_pos_closure
56	instantiation	201, 123, 71	⊢
	: , : , :
57	instantiation	72, 73	⊢
	:
58	theorem		⊢
	proveit.linear_algebra.inner_products.complex_vec_set_is_inner_prod_space
59	theorem		⊢
	proveit.physics.quantum.algebra.ket_zero_and_one_have_zero_inner_prod
60	axiom		⊢
	proveit.linear_algebra.scalar_multiplication.scalar_mult_extends_number_mult
61	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.zero_is_complex
62	instantiation	74, 75	,  ⊢
	:
63	instantiation	76, 77, 78*	,  ⊢
	:
64	instantiation	79, 80, 117	⊢
	: , : , :
65	instantiation	116, 81	⊢
	: , : , :
66	instantiation	116, 82	⊢
	: , : , :
67	instantiation	201, 83, 84	⊢
	: , : , :
68	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero
69	instantiation	116, 85	⊢
	: , : , :
70	instantiation	130, 86, 87	⊢
	: , : , :
71	instantiation	201, 134, 120	⊢
	: , : , :
72	theorem		⊢
	proveit.numbers.number_sets.real_numbers.nonzero_if_in_real_nonzero
73	instantiation	201, 88, 89	⊢
	: , : , :
74	theorem		⊢
	proveit.numbers.multiplication.mult_zero_right
75	instantiation	171, 90, 91	,  ⊢
	: , :
76	theorem		⊢
	proveit.numbers.absolute_value.complex_unit_length
77	instantiation	136, 92, 93	,  ⊢
	: , : , :
78	instantiation	94, 95	,  ⊢
	: , :
79	theorem		⊢
	proveit.logic.equality.sub_left_side_into
80	instantiation	201, 181, 96	⊢
	: , : , :
81	instantiation	130, 97, 99	⊢
	: , : , :
82	instantiation	130, 98, 99	⊢
	: , : , :
83	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero
84	instantiation	201, 100, 101	⊢
	: , : , :
85	instantiation	102, 122	⊢
	:
86	instantiation	116, 103	⊢
	: , : , :
87	instantiation	104, 122	⊢
	:
88	theorem		⊢
	proveit.numbers.number_sets.real_numbers.real_pos_within_real_nonzero
89	instantiation	105, 106	⊢
	:
90	instantiation	201, 181, 107	⊢
	: , : , :
91	instantiation	136, 108, 109	,  ⊢
	: , : , :
92	instantiation	167, 157, 110	,  ⊢
	: , :
93	instantiation	130, 111, 112	,  ⊢
	: , : , :
94	theorem		⊢
	proveit.logic.equality.equals_reversal
95	instantiation	116, 113	,  ⊢
	: , : , :
96	instantiation	201, 184, 114	⊢
	: , : , :
97	instantiation	116, 115	⊢
	: , : , :
98	instantiation	116, 117	⊢
	: , : , :
99	instantiation	118, 172	⊢
	:
100	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
101	instantiation	201, 119, 120	⊢
	: , : , :
102	theorem		⊢
	proveit.numbers.multiplication.elim_one_left
103	instantiation	121, 122	⊢
	:
104	theorem		⊢
	proveit.numbers.division.frac_one_denom
105	theorem		⊢
	proveit.numbers.exponentiation.sqrt_real_pos_closure
106	instantiation	201, 123, 124	⊢
	: , : , :
107	instantiation	201, 174, 125	⊢
	: , : , :
108	instantiation	162, 139, 126	,  ⊢
	: , :
109	instantiation	130, 127, 128	,  ⊢
	: , : , :
110	instantiation	167, 129, 166	,  ⊢
	: , :
111	instantiation	152, 200, 186, 153, 146, 154, 139, 164, 156	,  ⊢
	: , : , : , : , : , :
112	instantiation	152, 153, 186, 154, 145, 146, 172, 150, 164, 156	,  ⊢
	: , : , : , : , : , :
113	instantiation	130, 131, 132	,  ⊢
	: , : , :
114	instantiation	201, 187, 196	⊢
	: , : , :
115	theorem		⊢
	proveit.physics.quantum.algebra.ket_zero_norm
116	axiom		⊢
	proveit.logic.equality.substitution
117	theorem		⊢
	proveit.physics.quantum.algebra.ket_one_norm
118	theorem		⊢
	proveit.numbers.exponentiation.exponentiated_one
119	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
120	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
121	theorem		⊢
	proveit.numbers.multiplication.elim_one_right
122	instantiation	133, 172	⊢
	:
123	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_pos_within_real_pos
124	instantiation	201, 134, 135	⊢
	: , : , :
125	theorem		⊢
	proveit.numbers.number_sets.real_numbers.e_is_real_pos
126	instantiation	136, 137, 138	,  ⊢
	: , : , :
127	instantiation	152, 200, 140, 153, 141, 154, 139, 163, 164, 156	,  ⊢
	: , : , : , : , : , :
128	instantiation	152, 153, 186, 140, 154, 145, 141, 172, 150, 163, 164, 156	,  ⊢
	: , : , : , : , : , :
129	instantiation	142, 177, 143	,  ⊢
	: , :
130	axiom		⊢
	proveit.logic.equality.equals_transitivity
131	instantiation	144, 153, 186, 154, 145, 146, 172, 150, 163, 164, 156	,  ⊢
	: , : , : , : , : , : , :
132	instantiation	147, 200, 148, 153, 149, 154, 163, 172, 150, 164, 156	,  ⊢
	: , : , : , : , : , :
133	theorem		⊢
	proveit.numbers.exponentiation.sqrt_complex_closure
134	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nat_pos_within_rational_pos
135	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
136	theorem		⊢
	proveit.logic.equality.sub_right_side_into
137	instantiation	162, 151, 156	,  ⊢
	: , :
138	instantiation	152, 153, 186, 200, 154, 155, 163, 164, 156	,  ⊢
	: , : , : , : , : , :
139	instantiation	201, 181, 157	⊢
	: , : , :
140	theorem		⊢
	proveit.numbers.numerals.decimals.nat3
141	instantiation	158	⊢
	: , : , :
142	theorem		⊢
	proveit.numbers.exponentiation.exp_real_closure_nat_power
143	instantiation	159, 160	,  ⊢
	:
144	theorem		⊢
	proveit.numbers.multiplication.leftward_commutation
145	instantiation	165	⊢
	: , :
146	instantiation	165	⊢
	: , :
147	theorem		⊢
	proveit.numbers.multiplication.association
148	theorem		⊢
	proveit.numbers.numerals.decimals.nat4
149	instantiation	161	⊢
	: , : , : , :
150	instantiation	201, 181, 168	⊢
	: , : , :
151	instantiation	162, 163, 164	,  ⊢
	: , :
152	theorem		⊢
	proveit.numbers.multiplication.disassociation
153	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
154	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
155	instantiation	165	⊢
	: , :
156	instantiation	201, 181, 166	⊢
	: , : , :
157	instantiation	167, 177, 168	⊢
	: , :
158	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_3_typical_eq
159	theorem		⊢
	proveit.numbers.negation.nat_closure
160	instantiation	169, 188, 170	,  ⊢
	:
161	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_4_typical_eq
162	theorem		⊢
	proveit.numbers.multiplication.mult_complex_closure_bin
163	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.i_is_complex
164	instantiation	171, 172, 173	,  ⊢
	: , :
165	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
166	theorem		⊢
	proveit.physics.quantum.QPE._phase_is_real
167	theorem		⊢
	proveit.numbers.multiplication.mult_real_closure_bin
168	instantiation	201, 174, 175	⊢
	: , : , :
169	theorem		⊢
	proveit.numbers.number_sets.integers.nonpos_int_is_int_nonpos
170	instantiation	176, 192, 193, 190	,  ⊢
	: , : , :
171	theorem		⊢
	proveit.numbers.exponentiation.exp_complex_closure
172	instantiation	201, 181, 177	⊢
	: , : , :
173	instantiation	178, 179	,  ⊢
	:
174	theorem		⊢
	proveit.numbers.number_sets.real_numbers.real_pos_within_real
175	theorem		⊢
	proveit.numbers.number_sets.real_numbers.pi_is_real_pos
176	theorem		⊢
	proveit.numbers.number_sets.integers.interval_upper_bound
177	instantiation	201, 184, 180	⊢
	: , : , :
178	theorem		⊢
	proveit.numbers.negation.complex_closure
179	instantiation	201, 181, 182	,  ⊢
	: , : , :
180	instantiation	201, 187, 183	⊢
	: , : , :
181	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
182	instantiation	201, 184, 185	,  ⊢
	: , : , :
183	instantiation	201, 199, 186	⊢
	: , : , :
184	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
185	instantiation	201, 187, 188	,  ⊢
	: , : , :
186	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
187	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
188	instantiation	201, 189, 190	,  ⊢
	: , : , :
189	instantiation	191, 192, 193	⊢
	: , :
190	assumption		⊢
191	theorem		⊢
	proveit.numbers.number_sets.integers.int_interval_within_int
192	instantiation	194, 195, 196	⊢
	: , :
193	theorem		⊢
	proveit.numbers.number_sets.integers.zero_is_int
194	theorem		⊢
	proveit.numbers.addition.add_int_closure_bin
195	instantiation	197, 198	⊢
	:
196	instantiation	201, 199, 200	⊢
	: , : , :
197	theorem		⊢
	proveit.numbers.negation.int_closure
198	instantiation	201, 202, 203	⊢
	: , : , :
199	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
200	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
201	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
202	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_int
203	assumption		⊢
*equality replacement requirements