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	109	⊢
2	instantiation	109, 4, 5	⊢
	: , : , :
3	instantiation	6, 178, 173, 46, 14, 15	⊢
	: , : , : , : , :
4	instantiation	7, 46, 178, 100, 101, 8	⊢
	: , : , : , : , : , :
5	instantiation	13, 173, 167, 100, 33, 14, 101, 9	⊢
	: , : , : , : , : , :
6	theorem		⊢
	proveit.physics.quantum.algebra.qmult_pulling_scalar_out_front
7	theorem		⊢
	proveit.physics.quantum.algebra.scalar_mult_absorption
8	instantiation	69, 15, 10	⊢
	: , : , :
9	instantiation	69, 11, 12	⊢
	: , : , :
10	instantiation	13, 178, 167, 100, 14, 101, 15	⊢
	: , : , : , : , : , :
11	instantiation	22, 58, 59, 16, 24	⊢
	: , : , : , :
12	instantiation	32, 17, 18	⊢
	: , : , :
13	theorem		⊢
	proveit.physics.quantum.algebra.qmult_disassociation
14	instantiation	115	⊢
	: , :
15	instantiation	69, 19, 20	⊢
	: , : , :
16	instantiation	57, 58, 59, 21	⊢
	: , : , :
17	theorem		⊢
	proveit.numbers.numerals.decimals.posnat3
18	instantiation	105	⊢
	: , : , :
19	instantiation	22, 58, 59, 23, 24	⊢
	: , : , : , :
20	instantiation	32, 167, 25	⊢
	: , : , :
21	instantiation	69, 26, 27	⊢
	: , : , :
22	theorem		⊢
	proveit.physics.quantum.algebra.qmult_op_ket_in_QmultCodomain
23	instantiation	57, 58, 59, 28	⊢
	: , : , :
24	modus ponens	29, 30	⊢
25	instantiation	115	⊢
	: , :
26	instantiation	34, 58, 59, 31, 35	⊢
	: , : , : , : , :
27	instantiation	32, 167, 33	⊢
	: , : , :
28	instantiation	34, 58, 59, 47, 35	⊢
	: , : , : , : , :
29	instantiation	36, 165, 42	⊢
	: , : , : , : , : , :
30	generalization	37	⊢
31	instantiation	57, 58, 59, 38	⊢
	: , : , :
32	axiom		⊢
	proveit.physics.quantum.algebra.multi_qmult_def
33	instantiation	115	⊢
	: , :
34	theorem		⊢
	proveit.physics.quantum.algebra.qmult_op_op_is_op
35	instantiation	39, 73, 40	⊢
	: , : , :
36	theorem		⊢
	proveit.linear_algebra.addition.summation_closure
37	instantiation	41, 42, 43, 44	⊢
	: , : , : , :
38	instantiation	45, 46, 58, 59, 47	⊢
	: , : , : , :
39	theorem		⊢
	proveit.physics.quantum.algebra.qmult_matrix_is_linmap
40	instantiation	137, 48, 49	⊢
	: , : , :
41	theorem		⊢
	proveit.linear_algebra.scalar_multiplication.scalar_mult_closure
42	instantiation	50, 73	⊢
	:
43	instantiation	67, 51, 52	⊢
	: , :
44	instantiation	53, 175, 141	⊢
	: , :
45	theorem		⊢
	proveit.physics.quantum.algebra.qmult_op_complex_closure
46	instantiation	81, 54, 55, 56	⊢
	: , :
47	instantiation	57, 58, 59, 60	⊢
	: , : , :
48	instantiation	61, 73	⊢
	:
49	instantiation	62, 175	⊢
	:
50	theorem		⊢
	proveit.linear_algebra.complex_vec_set_is_vec_space
51	instantiation	176, 144, 63	⊢
	: , : , :
52	instantiation	86, 64, 65	⊢
	: , : , :
53	theorem		⊢
	proveit.physics.quantum.algebra.num_ket_in_register_space
54	instantiation	176, 144, 66	⊢
	: , : , :
55	instantiation	67, 136, 68	⊢
	: , :
56	instantiation	69, 70, 71	⊢
	: , : , :
57	theorem		⊢
	proveit.physics.quantum.algebra.qmult_op_is_linmap
58	instantiation	72, 73	⊢
	:
59	theorem		⊢
	proveit.linear_algebra.inner_products.complex_set_is_hilbert_space
60	instantiation	74, 175, 75	⊢
	: , :
61	theorem		⊢
	proveit.linear_algebra.matrices.unitaries_are_matrices
62	theorem		⊢
	proveit.physics.quantum.QFT.invFT_is_unitary
63	instantiation	176, 125, 76	⊢
	: , : , :
64	instantiation	112, 89, 77	⊢
	: , :
65	instantiation	109, 78, 79	⊢
	: , : , :
66	instantiation	176, 155, 80	⊢
	: , : , :
67	theorem		⊢
	proveit.numbers.exponentiation.exp_complex_closure
68	instantiation	81, 121, 136, 96	⊢
	: , :
69	theorem		⊢
	proveit.logic.equality.sub_left_side_into
70	instantiation	82, 143, 83	⊢
	: , :
71	instantiation	118, 84	⊢
	: , : , :
72	theorem		⊢
	proveit.linear_algebra.inner_products.complex_vec_set_is_hilbert_space
73	instantiation	85, 173, 170	⊢
	: , :
74	theorem		⊢
	proveit.physics.quantum.algebra.num_bra_is_lin_map
75	assumption		⊢
76	theorem		⊢
	proveit.numbers.number_sets.real_numbers.e_is_real_pos
77	instantiation	86, 87, 88	⊢
	: , : , :
78	instantiation	99, 178, 90, 100, 92, 101, 89, 113, 114, 103	⊢
	: , : , : , : , : , :
79	instantiation	99, 100, 173, 90, 101, 91, 92, 136, 104, 113, 114, 103	⊢
	: , : , : , : , : , :
80	instantiation	176, 164, 172	⊢
	: , : , :
81	theorem		⊢
	proveit.numbers.division.div_complex_closure
82	theorem		⊢
	proveit.numbers.exponentiation.exp_rational_non_zero__not_zero
83	instantiation	176, 93, 94	⊢
	: , : , :
84	instantiation	95, 121, 136, 96, 97*	⊢
	: , :
85	theorem		⊢
	proveit.numbers.exponentiation.exp_natpos_closure
86	theorem		⊢
	proveit.logic.equality.sub_right_side_into
87	instantiation	112, 98, 103	⊢
	: , :
88	instantiation	99, 100, 173, 178, 101, 102, 113, 114, 103	⊢
	: , : , : , : , : , :
89	instantiation	112, 136, 104	⊢
	: , :
90	theorem		⊢
	proveit.numbers.numerals.decimals.nat3
91	instantiation	115	⊢
	: , :
92	instantiation	105	⊢
	: , : , :
93	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.rational_pos_within_rational_nonzero
94	instantiation	106, 149, 107	⊢
	: , :
95	theorem		⊢
	proveit.numbers.division.div_as_mult
96	instantiation	108, 167	⊢
	:
97	instantiation	109, 110, 111	⊢
	: , : , :
98	instantiation	112, 113, 114	⊢
	: , :
99	theorem		⊢
	proveit.numbers.multiplication.disassociation
100	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
101	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
102	instantiation	115	⊢
	: , :
103	instantiation	176, 144, 116	⊢
	: , : , :
104	instantiation	176, 144, 117	⊢
	: , : , :
105	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_3_typical_eq
106	theorem		⊢
	proveit.numbers.multiplication.mult_rational_pos_closure_bin
107	instantiation	176, 166, 175	⊢
	: , : , :
108	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos
109	axiom		⊢
	proveit.logic.equality.equals_transitivity
110	instantiation	118, 119	⊢
	: , : , :
111	instantiation	120, 121, 122	⊢
	: , :
112	theorem		⊢
	proveit.numbers.multiplication.mult_complex_closure_bin
113	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.i_is_complex
114	instantiation	176, 144, 123	⊢
	: , : , :
115	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
116	instantiation	176, 155, 124	⊢
	: , : , :
117	instantiation	176, 125, 126	⊢
	: , : , :
118	axiom		⊢
	proveit.logic.equality.substitution
119	instantiation	127, 128, 165, 129*	⊢
	: , :
120	theorem		⊢
	proveit.numbers.multiplication.commutation
121	instantiation	176, 144, 130	⊢
	: , : , :
122	instantiation	176, 144, 131	⊢
	: , : , :
123	theorem		⊢
	proveit.physics.quantum.QPE._phase_is_real
124	instantiation	176, 164, 132	⊢
	: , : , :
125	theorem		⊢
	proveit.numbers.number_sets.real_numbers.real_pos_within_real
126	theorem		⊢
	proveit.numbers.number_sets.real_numbers.pi_is_real_pos
127	theorem		⊢
	proveit.numbers.exponentiation.neg_power_as_div
128	instantiation	176, 133, 134	⊢
	: , : , :
129	instantiation	135, 136	⊢
	:
130	instantiation	137, 138, 175	⊢
	: , : , :
131	instantiation	176, 155, 139	⊢
	: , : , :
132	instantiation	176, 140, 141	⊢
	: , : , :
133	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero
134	instantiation	176, 142, 143	⊢
	: , : , :
135	theorem		⊢
	proveit.numbers.exponentiation.complex_x_to_first_power_is_x
136	instantiation	176, 144, 145	⊢
	: , : , :
137	theorem		⊢
	proveit.logic.sets.inclusion.unfold_subset_eq
138	instantiation	146, 147	⊢
	: , :
139	instantiation	176, 148, 149	⊢
	: , : , :
140	instantiation	150, 151, 152	⊢
	: , :
141	assumption		⊢
142	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero
143	instantiation	176, 153, 154	⊢
	: , : , :
144	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
145	instantiation	176, 155, 156	⊢
	: , : , :
146	theorem		⊢
	proveit.logic.sets.inclusion.relax_proper_subset
147	theorem		⊢
	proveit.numbers.number_sets.real_numbers.nat_pos_within_real
148	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.rational_pos_within_rational
149	instantiation	157, 158, 159	⊢
	: , :
150	theorem		⊢
	proveit.numbers.number_sets.integers.int_interval_within_int
151	theorem		⊢
	proveit.numbers.number_sets.integers.zero_is_int
152	instantiation	160, 161, 162	⊢
	: , :
153	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
154	instantiation	176, 163, 167	⊢
	: , : , :
155	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
156	instantiation	176, 164, 169	⊢
	: , : , :
157	theorem		⊢
	proveit.numbers.division.div_rational_pos_closure
158	instantiation	176, 166, 165	⊢
	: , : , :
159	instantiation	176, 166, 167	⊢
	: , : , :
160	theorem		⊢
	proveit.numbers.addition.add_int_closure_bin
161	instantiation	168, 169, 170	⊢
	: , :
162	instantiation	171, 172	⊢
	:
163	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
164	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
165	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
166	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nat_pos_within_rational_pos
167	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
168	theorem		⊢
	proveit.numbers.exponentiation.exp_int_closure
169	instantiation	176, 177, 173	⊢
	: , : , :
170	instantiation	176, 174, 175	⊢
	: , : , :
171	theorem		⊢
	proveit.numbers.negation.int_closure
172	instantiation	176, 177, 178	⊢
	: , : , :
173	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
174	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nat_pos_within_nat
175	axiom		⊢
	proveit.physics.quantum.QPE._t_in_natural_pos
176	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
177	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
178	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
*equality replacement requirements