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