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