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