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