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	126	⊢
2	instantiation	135, 4	⊢
	: , : , :
3	instantiation	126, 5, 6	⊢
	: , : , :
4	instantiation	7, 8, 9, 10	⊢
	: , : , : , :
5	instantiation	126, 11, 12	⊢
	: , : , :
6	instantiation	15, 34, 63, 13, 32, 14*	⊢
	: , : , :
7	theorem		⊢
	proveit.logic.equality.four_chain_transitivity
8	instantiation	22, 63, 195, 117, 118, 16	⊢
	: , : , : , : , : , :
9	instantiation	19, 195, 63, 16	⊢
	: , : , : , : , :
10	instantiation	15, 184, 63, 31, 16	⊢
	: , : , :
11	instantiation	126, 17, 18	⊢
	: , : , :
12	instantiation	19, 195, 190, 63, 31, 32	⊢
	: , : , : , : , :
13	instantiation	122	⊢
	: , : , :
14	instantiation	20, 63, 21	⊢
	: , :
15	theorem		⊢
	proveit.physics.quantum.algebra.scalar_mult_factorization
16	instantiation	39, 75, 52, 41	⊢
	: , : , : , :
17	instantiation	22, 63, 195, 117, 118, 23	⊢
	: , : , : , : , : , :
18	instantiation	30, 190, 184, 117, 50, 31, 118, 24	⊢
	: , : , : , : , : , :
19	theorem		⊢
	proveit.physics.quantum.algebra.qmult_pulling_scalar_out_front
20	axiom		⊢
	proveit.linear_algebra.scalar_multiplication.scalar_mult_extends_number_mult
21	instantiation	86, 25, 37	⊢
	: , : , :
22	theorem		⊢
	proveit.physics.quantum.algebra.scalar_mult_absorption
23	instantiation	86, 32, 26	⊢
	: , : , :
24	instantiation	86, 27, 28	⊢
	: , : , :
25	instantiation	29, 75, 76, 40, 41	⊢
	: , : , : , :
26	instantiation	30, 195, 184, 117, 31, 118, 32	⊢
	: , : , : , : , : , :
27	instantiation	39, 75, 76, 33, 41	⊢
	: , : , : , :
28	instantiation	49, 34, 35	⊢
	: , : , :
29	theorem		⊢
	proveit.physics.quantum.algebra.qmult_op_ket_is_ket
30	theorem		⊢
	proveit.physics.quantum.algebra.qmult_disassociation
31	instantiation	132	⊢
	: , :
32	instantiation	86, 36, 37	⊢
	: , : , :
33	instantiation	74, 75, 76, 38	⊢
	: , : , :
34	theorem		⊢
	proveit.numbers.numerals.decimals.posnat3
35	instantiation	122	⊢
	: , : , :
36	instantiation	39, 75, 76, 40, 41	⊢
	: , : , : , :
37	instantiation	49, 184, 42	⊢
	: , : , :
38	instantiation	86, 43, 44	⊢
	: , : , :
39	theorem		⊢
	proveit.physics.quantum.algebra.qmult_op_ket_in_QmultCodomain
40	instantiation	74, 75, 76, 45	⊢
	: , : , :
41	modus ponens	46, 47	⊢
42	instantiation	132	⊢
	: , :
43	instantiation	51, 75, 76, 48, 52	⊢
	: , : , : , : , :
44	instantiation	49, 184, 50	⊢
	: , : , :
45	instantiation	51, 75, 76, 64, 52	⊢
	: , : , : , : , :
46	instantiation	53, 182, 59	⊢
	: , : , : , : , : , :
47	generalization	54	⊢
48	instantiation	74, 75, 76, 55	⊢
	: , : , :
49	axiom		⊢
	proveit.physics.quantum.algebra.multi_qmult_def
50	instantiation	132	⊢
	: , :
51	theorem		⊢
	proveit.physics.quantum.algebra.qmult_op_op_is_op
52	instantiation	56, 90, 57	⊢
	: , : , :
53	theorem		⊢
	proveit.linear_algebra.addition.summation_closure
54	instantiation	58, 59, 60, 61	⊢
	: , : , : , :
55	instantiation	62, 63, 75, 76, 64	⊢
	: , : , : , :
56	theorem		⊢
	proveit.physics.quantum.algebra.qmult_matrix_is_linmap
57	instantiation	154, 65, 66	⊢
	: , : , :
58	theorem		⊢
	proveit.linear_algebra.scalar_multiplication.scalar_mult_closure
59	instantiation	67, 90	⊢
	:
60	instantiation	84, 68, 69	⊢
	: , :
61	instantiation	70, 192, 158	⊢
	: , :
62	theorem		⊢
	proveit.physics.quantum.algebra.qmult_op_complex_closure
63	instantiation	98, 71, 72, 73	⊢
	: , :
64	instantiation	74, 75, 76, 77	⊢
	: , : , :
65	instantiation	78, 90	⊢
	:
66	instantiation	79, 192	⊢
	:
67	theorem		⊢
	proveit.linear_algebra.complex_vec_set_is_vec_space
68	instantiation	193, 161, 80	⊢
	: , : , :
69	instantiation	103, 81, 82	⊢
	: , : , :
70	theorem		⊢
	proveit.physics.quantum.algebra.num_ket_in_register_space
71	instantiation	193, 161, 83	⊢
	: , : , :
72	instantiation	84, 153, 85	⊢
	: , :
73	instantiation	86, 87, 88	⊢
	: , : , :
74	theorem		⊢
	proveit.physics.quantum.algebra.qmult_op_is_linmap
75	instantiation	89, 90	⊢
	:
76	theorem		⊢
	proveit.linear_algebra.inner_products.complex_set_is_hilbert_space
77	instantiation	91, 192, 92	⊢
	: , :
78	theorem		⊢
	proveit.linear_algebra.matrices.unitaries_are_matrices
79	theorem		⊢
	proveit.physics.quantum.QFT.invFT_is_unitary
80	instantiation	193, 142, 93	⊢
	: , : , :
81	instantiation	129, 106, 94	⊢
	: , :
82	instantiation	126, 95, 96	⊢
	: , : , :
83	instantiation	193, 172, 97	⊢
	: , : , :
84	theorem		⊢
	proveit.numbers.exponentiation.exp_complex_closure
85	instantiation	98, 138, 153, 113	⊢
	: , :
86	theorem		⊢
	proveit.logic.equality.sub_left_side_into
87	instantiation	99, 160, 100	⊢
	: , :
88	instantiation	135, 101	⊢
	: , : , :
89	theorem		⊢
	proveit.linear_algebra.inner_products.complex_vec_set_is_hilbert_space
90	instantiation	102, 190, 187	⊢
	: , :
91	theorem		⊢
	proveit.physics.quantum.algebra.num_bra_is_lin_map
92	assumption		⊢
93	theorem		⊢
	proveit.numbers.number_sets.real_numbers.e_is_real_pos
94	instantiation	103, 104, 105	⊢
	: , : , :
95	instantiation	116, 195, 107, 117, 109, 118, 106, 130, 131, 120	⊢
	: , : , : , : , : , :
96	instantiation	116, 117, 190, 107, 118, 108, 109, 153, 121, 130, 131, 120	⊢
	: , : , : , : , : , :
97	instantiation	193, 181, 189	⊢
	: , : , :
98	theorem		⊢
	proveit.numbers.division.div_complex_closure
99	theorem		⊢
	proveit.numbers.exponentiation.exp_rational_non_zero__not_zero
100	instantiation	193, 110, 111	⊢
	: , : , :
101	instantiation	112, 138, 153, 113, 114*	⊢
	: , :
102	theorem		⊢
	proveit.numbers.exponentiation.exp_natpos_closure
103	theorem		⊢
	proveit.logic.equality.sub_right_side_into
104	instantiation	129, 115, 120	⊢
	: , :
105	instantiation	116, 117, 190, 195, 118, 119, 130, 131, 120	⊢
	: , : , : , : , : , :
106	instantiation	129, 153, 121	⊢
	: , :
107	theorem		⊢
	proveit.numbers.numerals.decimals.nat3
108	instantiation	132	⊢
	: , :
109	instantiation	122	⊢
	: , : , :
110	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.rational_pos_within_rational_nonzero
111	instantiation	123, 166, 124	⊢
	: , :
112	theorem		⊢
	proveit.numbers.division.div_as_mult
113	instantiation	125, 184	⊢
	:
114	instantiation	126, 127, 128	⊢
	: , : , :
115	instantiation	129, 130, 131	⊢
	: , :
116	theorem		⊢
	proveit.numbers.multiplication.disassociation
117	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
118	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
119	instantiation	132	⊢
	: , :
120	instantiation	193, 161, 133	⊢
	: , : , :
121	instantiation	193, 161, 134	⊢
	: , : , :
122	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_3_typical_eq
123	theorem		⊢
	proveit.numbers.multiplication.mult_rational_pos_closure_bin
124	instantiation	193, 183, 192	⊢
	: , : , :
125	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos
126	axiom		⊢
	proveit.logic.equality.equals_transitivity
127	instantiation	135, 136	⊢
	: , : , :
128	instantiation	137, 138, 139	⊢
	: , :
129	theorem		⊢
	proveit.numbers.multiplication.mult_complex_closure_bin
130	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.i_is_complex
131	instantiation	193, 161, 140	⊢
	: , : , :
132	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
133	instantiation	193, 172, 141	⊢
	: , : , :
134	instantiation	193, 142, 143	⊢
	: , : , :
135	axiom		⊢
	proveit.logic.equality.substitution
136	instantiation	144, 145, 182, 146*	⊢
	: , :
137	theorem		⊢
	proveit.numbers.multiplication.commutation
138	instantiation	193, 161, 147	⊢
	: , : , :
139	instantiation	193, 161, 148	⊢
	: , : , :
140	theorem		⊢
	proveit.physics.quantum.QPE._phase_is_real
141	instantiation	193, 181, 149	⊢
	: , : , :
142	theorem		⊢
	proveit.numbers.number_sets.real_numbers.real_pos_within_real
143	theorem		⊢
	proveit.numbers.number_sets.real_numbers.pi_is_real_pos
144	theorem		⊢
	proveit.numbers.exponentiation.neg_power_as_div
145	instantiation	193, 150, 151	⊢
	: , : , :
146	instantiation	152, 153	⊢
	:
147	instantiation	154, 155, 192	⊢
	: , : , :
148	instantiation	193, 172, 156	⊢
	: , : , :
149	instantiation	193, 157, 158	⊢
	: , : , :
150	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero
151	instantiation	193, 159, 160	⊢
	: , : , :
152	theorem		⊢
	proveit.numbers.exponentiation.complex_x_to_first_power_is_x
153	instantiation	193, 161, 162	⊢
	: , : , :
154	theorem		⊢
	proveit.logic.sets.inclusion.unfold_subset_eq
155	instantiation	163, 164	⊢
	: , :
156	instantiation	193, 165, 166	⊢
	: , : , :
157	instantiation	167, 168, 169	⊢
	: , :
158	assumption		⊢
159	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero
160	instantiation	193, 170, 171	⊢
	: , : , :
161	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
162	instantiation	193, 172, 173	⊢
	: , : , :
163	theorem		⊢
	proveit.logic.sets.inclusion.relax_proper_subset
164	theorem		⊢
	proveit.numbers.number_sets.real_numbers.nat_pos_within_real
165	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.rational_pos_within_rational
166	instantiation	174, 175, 176	⊢
	: , :
167	theorem		⊢
	proveit.numbers.number_sets.integers.int_interval_within_int
168	theorem		⊢
	proveit.numbers.number_sets.integers.zero_is_int
169	instantiation	177, 178, 179	⊢
	: , :
170	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
171	instantiation	193, 180, 184	⊢
	: , : , :
172	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
173	instantiation	193, 181, 186	⊢
	: , : , :
174	theorem		⊢
	proveit.numbers.division.div_rational_pos_closure
175	instantiation	193, 183, 182	⊢
	: , : , :
176	instantiation	193, 183, 184	⊢
	: , : , :
177	theorem		⊢
	proveit.numbers.addition.add_int_closure_bin
178	instantiation	185, 186, 187	⊢
	: , :
179	instantiation	188, 189	⊢
	:
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.numerals.decimals.posnat1
183	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nat_pos_within_rational_pos
184	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
185	theorem		⊢
	proveit.numbers.exponentiation.exp_int_closure
186	instantiation	193, 194, 190	⊢
	: , : , :
187	instantiation	193, 191, 192	⊢
	: , : , :
188	theorem		⊢
	proveit.numbers.negation.int_closure
189	instantiation	193, 194, 195	⊢
	: , : , :
190	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
191	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nat_pos_within_nat
192	axiom		⊢
	proveit.physics.quantum.QPE._t_in_natural_pos
193	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
194	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
195	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
*equality replacement requirements