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, 7	⊢
	: , : , : , : , : , :
1	theorem		⊢
	proveit.physics.quantum.algebra.qmult_disassociation
2	reference	109	⊢
3	reference	15	⊢
4	reference	68	⊢
5	instantiation	78	⊢
	: , :
6	reference	69	⊢
7	instantiation	8, 9, 10	⊢
	: , : , :
8	theorem		⊢
	proveit.logic.equality.sub_left_side_into
9	instantiation	11, 27, 28, 12, 13	⊢
	: , : , : , :
10	instantiation	14, 15, 16	⊢
	: , : , :
11	theorem		⊢
	proveit.physics.quantum.algebra.qmult_op_ket_in_QmultCodomain
12	instantiation	26, 27, 28, 17	⊢
	: , : , :
13	modus ponens	18, 19	⊢
14	axiom		⊢
	proveit.physics.quantum.algebra.multi_qmult_def
15	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
16	instantiation	78	⊢
	: , :
17	instantiation	20, 27, 28, 21, 22	⊢
	: , : , : , : , :
18	instantiation	23, 24, 33	⊢
	: , : , : , : , : , :
19	generalization	25	⊢
20	theorem		⊢
	proveit.physics.quantum.algebra.qmult_op_op_is_op
21	instantiation	26, 27, 28, 29	⊢
	: , : , :
22	instantiation	30, 48, 31	⊢
	: , : , :
23	theorem		⊢
	proveit.linear_algebra.addition.summation_closure
24	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
25	instantiation	32, 33, 34, 35	⊢
	: , : , : , :
26	theorem		⊢
	proveit.physics.quantum.algebra.qmult_op_is_linmap
27	instantiation	36, 48	⊢
	:
28	theorem		⊢
	proveit.linear_algebra.inner_products.complex_set_is_hilbert_space
29	instantiation	37, 106, 38	⊢
	: , :
30	theorem		⊢
	proveit.physics.quantum.algebra.qmult_matrix_is_linmap
31	instantiation	39, 40, 41	⊢
	: , : , :
32	theorem		⊢
	proveit.linear_algebra.scalar_multiplication.scalar_mult_closure
33	instantiation	42, 48	⊢
	:
34	instantiation	43, 44, 45	⊢
	: , :
35	instantiation	46, 106, 92	⊢
	: , :
36	theorem		⊢
	proveit.linear_algebra.inner_products.complex_vec_set_is_hilbert_space
37	theorem		⊢
	proveit.physics.quantum.algebra.num_bra_is_lin_map
38	assumption		⊢
39	theorem		⊢
	proveit.logic.sets.inclusion.unfold_subset_eq
40	instantiation	47, 48	⊢
	:
41	instantiation	49, 106	⊢
	:
42	theorem		⊢
	proveit.linear_algebra.complex_vec_set_is_vec_space
43	theorem		⊢
	proveit.numbers.exponentiation.exp_complex_closure
44	instantiation	107, 82, 50	⊢
	: , : , :
45	instantiation	59, 51, 52	⊢
	: , : , :
46	theorem		⊢
	proveit.physics.quantum.algebra.num_ket_in_register_space
47	theorem		⊢
	proveit.linear_algebra.matrices.unitaries_are_matrices
48	instantiation	53, 104, 101	⊢
	: , :
49	theorem		⊢
	proveit.physics.quantum.QFT.invFT_is_unitary
50	instantiation	107, 87, 54	⊢
	: , : , :
51	instantiation	75, 62, 55	⊢
	: , :
52	instantiation	56, 57, 58	⊢
	: , : , :
53	theorem		⊢
	proveit.numbers.exponentiation.exp_natpos_closure
54	theorem		⊢
	proveit.numbers.number_sets.real_numbers.e_is_real_pos
55	instantiation	59, 60, 61	⊢
	: , : , :
56	axiom		⊢
	proveit.logic.equality.equals_transitivity
57	instantiation	67, 109, 63, 68, 65, 69, 62, 76, 77, 71	⊢
	: , : , : , : , : , :
58	instantiation	67, 68, 104, 63, 69, 64, 65, 72, 73, 76, 77, 71	⊢
	: , : , : , : , : , :
59	theorem		⊢
	proveit.logic.equality.sub_right_side_into
60	instantiation	75, 66, 71	⊢
	: , :
61	instantiation	67, 68, 104, 109, 69, 70, 76, 77, 71	⊢
	: , : , : , : , : , :
62	instantiation	75, 72, 73	⊢
	: , :
63	theorem		⊢
	proveit.numbers.numerals.decimals.nat3
64	instantiation	78	⊢
	: , :
65	instantiation	74	⊢
	: , : , :
66	instantiation	75, 76, 77	⊢
	: , :
67	theorem		⊢
	proveit.numbers.multiplication.disassociation
68	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
69	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
70	instantiation	78	⊢
	: , :
71	instantiation	107, 82, 79	⊢
	: , : , :
72	instantiation	107, 82, 80	⊢
	: , : , :
73	instantiation	107, 82, 81	⊢
	: , : , :
74	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_3_typical_eq
75	theorem		⊢
	proveit.numbers.multiplication.mult_complex_closure_bin
76	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.i_is_complex
77	instantiation	107, 82, 83	⊢
	: , : , :
78	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
79	instantiation	107, 85, 84	⊢
	: , : , :
80	instantiation	107, 85, 86	⊢
	: , : , :
81	instantiation	107, 87, 88	⊢
	: , : , :
82	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
83	theorem		⊢
	proveit.physics.quantum.QPE._phase_is_real
84	instantiation	107, 90, 89	⊢
	: , : , :
85	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
86	instantiation	107, 90, 100	⊢
	: , : , :
87	theorem		⊢
	proveit.numbers.number_sets.real_numbers.real_pos_within_real
88	theorem		⊢
	proveit.numbers.number_sets.real_numbers.pi_is_real_pos
89	instantiation	107, 91, 92	⊢
	: , : , :
90	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
91	instantiation	93, 94, 95	⊢
	: , :
92	assumption		⊢
93	theorem		⊢
	proveit.numbers.number_sets.integers.int_interval_within_int
94	theorem		⊢
	proveit.numbers.number_sets.integers.zero_is_int
95	instantiation	96, 97, 98	⊢
	: , :
96	theorem		⊢
	proveit.numbers.addition.add_int_closure_bin
97	instantiation	99, 100, 101	⊢
	: , :
98	instantiation	102, 103	⊢
	:
99	theorem		⊢
	proveit.numbers.exponentiation.exp_int_closure
100	instantiation	107, 108, 104	⊢
	: , : , :
101	instantiation	107, 105, 106	⊢
	: , : , :
102	theorem		⊢
	proveit.numbers.negation.int_closure
103	instantiation	107, 108, 109	⊢
	: , : , :
104	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
105	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nat_pos_within_nat
106	axiom		⊢
	proveit.physics.quantum.QPE._t_in_natural_pos
107	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
108	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
109	theorem		⊢
	proveit.numbers.numerals.decimals.nat1