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