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	29	⊢
2	instantiation	4, 5, 18, 6, 7	,  ⊢
	: , : , : , : , :
3	instantiation	26, 8, 9	,  ⊢
	: , : , :
4	theorem		⊢
	proveit.linear_algebra.inner_products.inner_prod_scalar_mult_right
5	instantiation	10, 11	⊢
	:
6	theorem		⊢
	proveit.physics.quantum.algebra.ket_zero_in_qubit_space
7	theorem		⊢
	proveit.physics.quantum.algebra.ket_one_in_qubit_space
8	instantiation	12, 13	⊢
	: , : , :
9	instantiation	14, 18, 15, 16*	,  ⊢
	: , :
10	theorem		⊢
	proveit.linear_algebra.inner_products.complex_vec_set_is_inner_prod_space
11	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
12	axiom		⊢
	proveit.logic.equality.substitution
13	theorem		⊢
	proveit.physics.quantum.algebra.ket_zero_and_one_have_zero_inner_prod
14	axiom		⊢
	proveit.linear_algebra.scalar_multiplication.scalar_mult_extends_number_mult
15	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.zero_is_complex
16	instantiation	17, 18	,  ⊢
	:
17	theorem		⊢
	proveit.numbers.multiplication.mult_zero_right
18	instantiation	52, 19, 20	,  ⊢
	: , :
19	instantiation	81, 61, 21	⊢
	: , : , :
20	instantiation	29, 22, 23	,  ⊢
	: , : , :
21	instantiation	81, 55, 24	⊢
	: , : , :
22	instantiation	45, 32, 25	,  ⊢
	: , :
23	instantiation	26, 27, 28	,  ⊢
	: , : , :
24	theorem		⊢
	proveit.numbers.number_sets.real_numbers.e_is_real_pos
25	instantiation	29, 30, 31	,  ⊢
	: , : , :
26	axiom		⊢
	proveit.logic.equality.equals_transitivity
27	instantiation	38, 80, 33, 39, 35, 40, 32, 46, 47, 42	,  ⊢
	: , : , : , : , : , :
28	instantiation	38, 39, 66, 33, 40, 34, 35, 53, 36, 46, 47, 42	,  ⊢
	: , : , : , : , : , :
29	theorem		⊢
	proveit.logic.equality.sub_right_side_into
30	instantiation	45, 37, 42	,  ⊢
	: , :
31	instantiation	38, 39, 66, 80, 40, 41, 46, 47, 42	,  ⊢
	: , : , : , : , : , :
32	instantiation	81, 61, 43	⊢
	: , : , :
33	theorem		⊢
	proveit.numbers.numerals.decimals.nat3
34	instantiation	48	⊢
	: , :
35	instantiation	44	⊢
	: , : , :
36	instantiation	81, 61, 51	⊢
	: , : , :
37	instantiation	45, 46, 47	,  ⊢
	: , :
38	theorem		⊢
	proveit.numbers.multiplication.disassociation
39	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
40	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
41	instantiation	48	⊢
	: , :
42	instantiation	81, 61, 49	⊢
	: , : , :
43	instantiation	50, 57, 51	⊢
	: , :
44	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_3_typical_eq
45	theorem		⊢
	proveit.numbers.multiplication.mult_complex_closure_bin
46	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.i_is_complex
47	instantiation	52, 53, 54	,  ⊢
	: , :
48	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
49	theorem		⊢
	proveit.physics.quantum.QPE._phase_is_real
50	theorem		⊢
	proveit.numbers.multiplication.mult_real_closure_bin
51	instantiation	81, 55, 56	⊢
	: , : , :
52	theorem		⊢
	proveit.numbers.exponentiation.exp_complex_closure
53	instantiation	81, 61, 57	⊢
	: , : , :
54	instantiation	58, 59	,  ⊢
	:
55	theorem		⊢
	proveit.numbers.number_sets.real_numbers.real_pos_within_real
56	theorem		⊢
	proveit.numbers.number_sets.real_numbers.pi_is_real_pos
57	instantiation	81, 64, 60	⊢
	: , : , :
58	theorem		⊢
	proveit.numbers.negation.complex_closure
59	instantiation	81, 61, 62	,  ⊢
	: , : , :
60	instantiation	81, 67, 63	⊢
	: , : , :
61	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
62	instantiation	81, 64, 65	,  ⊢
	: , : , :
63	instantiation	81, 79, 66	⊢
	: , : , :
64	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
65	instantiation	81, 67, 68	,  ⊢
	: , : , :
66	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
67	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
68	instantiation	81, 69, 70	,  ⊢
	: , : , :
69	instantiation	71, 72, 73	⊢
	: , :
70	assumption		⊢
71	theorem		⊢
	proveit.numbers.number_sets.integers.int_interval_within_int
72	instantiation	74, 75, 76	⊢
	: , :
73	theorem		⊢
	proveit.numbers.number_sets.integers.zero_is_int
74	theorem		⊢
	proveit.numbers.addition.add_int_closure_bin
75	instantiation	77, 78	⊢
	:
76	instantiation	81, 79, 80	⊢
	: , : , :
77	theorem		⊢
	proveit.numbers.negation.int_closure
78	instantiation	81, 82, 83	⊢
	: , : , :
79	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
80	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
81	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
82	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_int
83	assumption		⊢
*equality replacement requirements