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