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