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