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