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