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