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