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