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.scaled_norm
2	instantiation	6, 7	⊢
	:
3	instantiation	75, 8, 9	,  ⊢
	: , :
4	theorem		⊢
	proveit.physics.quantum.algebra.ket_one_in_qubit_space
5	instantiation	51, 10, 11	,  ⊢
	: , : , :
6	theorem		⊢
	proveit.linear_algebra.inner_products.complex_vec_set_is_inner_prod_space
7	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
8	instantiation	108, 88, 12	⊢
	: , : , :
9	instantiation	32, 13, 14	,  ⊢
	: , : , :
10	instantiation	44, 15	,  ⊢
	: , : , :
11	instantiation	16, 17	⊢
	:
12	instantiation	108, 81, 18	⊢
	: , : , :
13	instantiation	47, 49, 19	,  ⊢
	: , :
14	instantiation	51, 20, 21	,  ⊢
	: , : , :
15	instantiation	22, 23, 24*	,  ⊢
	:
16	theorem		⊢
	proveit.numbers.multiplication.elim_one_left
17	instantiation	25, 26, 27	⊢
	: , : , :
18	theorem		⊢
	proveit.numbers.number_sets.real_numbers.e_is_real_pos
19	instantiation	32, 28, 29	,  ⊢
	: , : , :
20	instantiation	50, 107, 30, 62, 31, 64, 49, 65, 67, 68	,  ⊢
	: , : , : , : , : , :
21	instantiation	50, 62, 93, 30, 64, 58, 31, 76, 66, 65, 67, 68	,  ⊢
	: , : , : , : , : , :
22	theorem		⊢
	proveit.numbers.absolute_value.complex_unit_length
23	instantiation	32, 33, 34	,  ⊢
	: , : , :
24	instantiation	35, 36	,  ⊢
	: , :
25	theorem		⊢
	proveit.logic.equality.sub_left_side_into
26	instantiation	108, 88, 37	⊢
	: , : , :
27	theorem		⊢
	proveit.physics.quantum.algebra.ket_one_norm
28	instantiation	47, 38, 68	,  ⊢
	: , :
29	instantiation	50, 62, 93, 107, 64, 39, 65, 67, 68	,  ⊢
	: , : , : , : , : , :
30	theorem		⊢
	proveit.numbers.numerals.decimals.nat3
31	instantiation	40	⊢
	: , : , :
32	theorem		⊢
	proveit.logic.equality.sub_right_side_into
33	instantiation	71, 56, 41	,  ⊢
	: , :
34	instantiation	51, 42, 43	,  ⊢
	: , : , :
35	theorem		⊢
	proveit.logic.equality.equals_reversal
36	instantiation	44, 45	,  ⊢
	: , : , :
37	instantiation	108, 91, 46	⊢
	: , : , :
38	instantiation	47, 65, 67	,  ⊢
	: , :
39	instantiation	72	⊢
	: , :
40	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_3_typical_eq
41	instantiation	71, 48, 78	,  ⊢
	: , :
42	instantiation	50, 107, 93, 62, 59, 64, 49, 67, 68	,  ⊢
	: , : , : , : , : , :
43	instantiation	50, 62, 93, 64, 58, 59, 76, 66, 67, 68	,  ⊢
	: , : , : , : , : , :
44	axiom		⊢
	proveit.logic.equality.substitution
45	instantiation	51, 52, 53	,  ⊢
	: , : , :
46	instantiation	108, 94, 103	⊢
	: , : , :
47	theorem		⊢
	proveit.numbers.multiplication.mult_complex_closure_bin
48	instantiation	54, 83, 55	,  ⊢
	: , :
49	instantiation	108, 88, 56	⊢
	: , : , :
50	theorem		⊢
	proveit.numbers.multiplication.disassociation
51	axiom		⊢
	proveit.logic.equality.equals_transitivity
52	instantiation	57, 62, 93, 64, 58, 59, 76, 66, 65, 67, 68	,  ⊢
	: , : , : , : , : , : , :
53	instantiation	60, 107, 61, 62, 63, 64, 65, 76, 66, 67, 68	,  ⊢
	: , : , : , : , : , :
54	theorem		⊢
	proveit.numbers.exponentiation.exp_real_closure_nat_power
55	instantiation	69, 70	,  ⊢
	:
56	instantiation	71, 83, 74	⊢
	: , :
57	theorem		⊢
	proveit.numbers.multiplication.leftward_commutation
58	instantiation	72	⊢
	: , :
59	instantiation	72	⊢
	: , :
60	theorem		⊢
	proveit.numbers.multiplication.association
61	theorem		⊢
	proveit.numbers.numerals.decimals.nat4
62	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
63	instantiation	73	⊢
	: , : , : , :
64	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
65	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.i_is_complex
66	instantiation	108, 88, 74	⊢
	: , : , :
67	instantiation	75, 76, 77	,  ⊢
	: , :
68	instantiation	108, 88, 78	⊢
	: , : , :
69	theorem		⊢
	proveit.numbers.negation.nat_closure
70	instantiation	79, 95, 80	,  ⊢
	:
71	theorem		⊢
	proveit.numbers.multiplication.mult_real_closure_bin
72	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
73	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_4_typical_eq
74	instantiation	108, 81, 82	⊢
	: , : , :
75	theorem		⊢
	proveit.numbers.exponentiation.exp_complex_closure
76	instantiation	108, 88, 83	⊢
	: , : , :
77	instantiation	84, 85	,  ⊢
	:
78	theorem		⊢
	proveit.physics.quantum.QPE._phase_is_real
79	theorem		⊢
	proveit.numbers.number_sets.integers.nonpos_int_is_int_nonpos
80	instantiation	86, 99, 100, 97	,  ⊢
	: , : , :
81	theorem		⊢
	proveit.numbers.number_sets.real_numbers.real_pos_within_real
82	theorem		⊢
	proveit.numbers.number_sets.real_numbers.pi_is_real_pos
83	instantiation	108, 91, 87	⊢
	: , : , :
84	theorem		⊢
	proveit.numbers.negation.complex_closure
85	instantiation	108, 88, 89	,  ⊢
	: , : , :
86	theorem		⊢
	proveit.numbers.number_sets.integers.interval_upper_bound
87	instantiation	108, 94, 90	⊢
	: , : , :
88	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
89	instantiation	108, 91, 92	,  ⊢
	: , : , :
90	instantiation	108, 106, 93	⊢
	: , : , :
91	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
92	instantiation	108, 94, 95	,  ⊢
	: , : , :
93	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
94	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
95	instantiation	108, 96, 97	,  ⊢
	: , : , :
96	instantiation	98, 99, 100	⊢
	: , :
97	assumption		⊢
98	theorem		⊢
	proveit.numbers.number_sets.integers.int_interval_within_int
99	instantiation	101, 102, 103	⊢
	: , :
100	theorem		⊢
	proveit.numbers.number_sets.integers.zero_is_int
101	theorem		⊢
	proveit.numbers.addition.add_int_closure_bin
102	instantiation	104, 105	⊢
	:
103	instantiation	108, 106, 107	⊢
	: , : , :
104	theorem		⊢
	proveit.numbers.negation.int_closure
105	instantiation	108, 109, 110	⊢
	: , : , :
106	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
107	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
108	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
109	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_int
110	assumption		⊢
*equality replacement requirements