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.linear_algebra.scalar_multiplication.scalar_mult_closure
2	instantiation	5, 6	⊢
	:
3	instantiation	38, 7, 8	⊢
	: , :
4	theorem		⊢
	proveit.physics.quantum.algebra.ket_one_in_qubit_space
5	theorem		⊢
	proveit.linear_algebra.complex_vec_set_is_vec_space
6	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
7	instantiation	65, 48, 9	⊢
	: , : , :
8	instantiation	17, 10, 11	⊢
	: , : , :
9	instantiation	65, 45, 12	⊢
	: , : , :
10	instantiation	32, 20, 13	⊢
	: , :
11	instantiation	14, 15, 16	⊢
	: , : , :
12	theorem		⊢
	proveit.numbers.number_sets.real_numbers.e_is_real_pos
13	instantiation	17, 18, 19	⊢
	: , : , :
14	axiom		⊢
	proveit.logic.equality.equals_transitivity
15	instantiation	25, 67, 21, 26, 23, 27, 20, 33, 34, 29	⊢
	: , : , : , : , : , :
16	instantiation	25, 26, 57, 21, 27, 22, 23, 39, 30, 33, 34, 29	⊢
	: , : , : , : , : , :
17	theorem		⊢
	proveit.logic.equality.sub_right_side_into
18	instantiation	32, 24, 29	⊢
	: , :
19	instantiation	25, 26, 57, 67, 27, 28, 33, 34, 29	⊢
	: , : , : , : , : , :
20	instantiation	32, 39, 30	⊢
	: , :
21	theorem		⊢
	proveit.numbers.numerals.decimals.nat3
22	instantiation	35	⊢
	: , :
23	instantiation	31	⊢
	: , : , :
24	instantiation	32, 33, 34	⊢
	: , :
25	theorem		⊢
	proveit.numbers.multiplication.disassociation
26	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
27	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
28	instantiation	35	⊢
	: , :
29	instantiation	65, 48, 36	⊢
	: , : , :
30	instantiation	65, 48, 37	⊢
	: , : , :
31	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_3_typical_eq
32	theorem		⊢
	proveit.numbers.multiplication.mult_complex_closure_bin
33	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.i_is_complex
34	instantiation	38, 39, 40	⊢
	: , :
35	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
36	instantiation	41, 42, 43, 44	⊢
	: , : , :
37	instantiation	65, 45, 46	⊢
	: , : , :
38	theorem		⊢
	proveit.numbers.exponentiation.exp_complex_closure
39	instantiation	65, 48, 47	⊢
	: , : , :
40	instantiation	65, 48, 49	⊢
	: , : , :
41	theorem		⊢
	proveit.numbers.number_sets.real_numbers.all_in_interval_co__is__real
42	theorem		⊢
	proveit.numbers.number_sets.real_numbers.zero_is_real
43	instantiation	65, 52, 50	⊢
	: , : , :
44	axiom		⊢
	proveit.physics.quantum.QPE._phase_in_interval
45	theorem		⊢
	proveit.numbers.number_sets.real_numbers.real_pos_within_real
46	theorem		⊢
	proveit.numbers.number_sets.real_numbers.pi_is_real_pos
47	instantiation	65, 52, 51	⊢
	: , : , :
48	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
49	instantiation	65, 52, 53	⊢
	: , : , :
50	instantiation	65, 55, 64	⊢
	: , : , :
51	instantiation	65, 55, 54	⊢
	: , : , :
52	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
53	instantiation	65, 55, 56	⊢
	: , : , :
54	instantiation	65, 66, 57	⊢
	: , : , :
55	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
56	instantiation	58, 59, 60	⊢
	: , :
57	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
58	theorem		⊢
	proveit.numbers.addition.add_int_closure_bin
59	instantiation	65, 61, 62	⊢
	: , : , :
60	instantiation	63, 64	⊢
	:
61	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_int
62	assumption		⊢
63	theorem		⊢
	proveit.numbers.negation.int_closure
64	instantiation	65, 66, 67	⊢
	: , : , :
65	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
66	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
67	theorem		⊢
	proveit.numbers.numerals.decimals.nat1