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	33	⊢
2	instantiation	4, 5	⊢
	: , : , :
3	instantiation	6, 15, 7*	⊢
	:
4	axiom		⊢
	proveit.logic.equality.substitution
5	instantiation	8, 9	⊢
	:
6	theorem		⊢
	proveit.numbers.absolute_value.abs_even
7	instantiation	10, 11, 12, 50, 51, 72, 52, 13*	⊢
	: , :
8	theorem		⊢
	proveit.numbers.addition.elim_zero_left
9	instantiation	14, 15	⊢
	:
10	theorem		⊢
	proveit.numbers.absolute_value.abs_prod
11	theorem		⊢
	proveit.numbers.numerals.decimals.posnat4
12	instantiation	16	⊢
	: , : , : , :
13	instantiation	33, 17, 18	⊢
	: , : , :
14	theorem		⊢
	proveit.numbers.negation.complex_closure
15	instantiation	19, 20, 21	⊢
	: , : , :
16	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_4_typical_eq
17	instantiation	22, 29, 23, 24, 25, 26, 27	⊢
	: , : , : , :
18	instantiation	28, 46, 29, 47, 30, 50, 51, 31, 52	⊢
	: , : , : , : , : , : , :
19	theorem		⊢
	proveit.logic.equality.sub_right_side_into
20	instantiation	86, 80, 32	⊢
	: , : , :
21	instantiation	33, 34, 35	⊢
	: , : , :
22	axiom		⊢
	proveit.core_expr_types.operations.operands_substitution
23	instantiation	40	⊢
	: , : , :
24	instantiation	40	⊢
	: , : , :
25	instantiation	38, 36	⊢
	:
26	instantiation	38, 37	⊢
	:
27	instantiation	38, 39	⊢
	:
28	theorem		⊢
	proveit.numbers.multiplication.leftward_commutation
29	theorem		⊢
	proveit.numbers.numerals.decimals.nat3
30	instantiation	40	⊢
	: , : , :
31	instantiation	86, 80, 41	⊢
	: , : , :
32	instantiation	65, 58, 42	⊢
	: , :
33	axiom		⊢
	proveit.logic.equality.equals_transitivity
34	instantiation	45, 43, 88, 46, 49, 47, 44, 72, 52	⊢
	: , : , : , : , : , :
35	instantiation	45, 46, 88, 47, 48, 49, 50, 51, 72, 52	⊢
	: , : , : , : , : , :
36	instantiation	53, 88	⊢
	:
37	instantiation	55, 54	⊢
	: , :
38	theorem		⊢
	proveit.numbers.absolute_value.abs_non_neg_elim
39	instantiation	55, 56	⊢
	: , :
40	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_3_typical_eq
41	instantiation	86, 76, 57	⊢
	: , : , :
42	instantiation	65, 81, 60	⊢
	: , :
43	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
44	instantiation	86, 80, 58	⊢
	: , : , :
45	theorem		⊢
	proveit.numbers.multiplication.disassociation
46	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
47	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
48	instantiation	59	⊢
	: , :
49	instantiation	59	⊢
	: , :
50	instantiation	86, 80, 66	⊢
	: , : , :
51	instantiation	86, 80, 67	⊢
	: , : , :
52	instantiation	86, 80, 60	⊢
	: , : , :
53	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.natural_lower_bound
54	instantiation	61, 77	⊢
	:
55	theorem		⊢
	proveit.numbers.ordering.relax_less
56	instantiation	62, 70	⊢
	:
57	instantiation	63, 64	⊢
	:
58	instantiation	65, 66, 67	⊢
	: , :
59	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
60	instantiation	68, 69, 70	⊢
	: , : , :
61	theorem		⊢
	proveit.numbers.number_sets.real_numbers.positive_if_in_real_pos
62	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.natural_pos_is_pos
63	theorem		⊢
	proveit.numbers.absolute_value.abs_nonzero_closure
64	instantiation	71, 72, 73	⊢
	:
65	theorem		⊢
	proveit.numbers.multiplication.mult_real_closure_bin
66	instantiation	86, 74, 75	⊢
	: , : , :
67	instantiation	86, 76, 77	⊢
	: , : , :
68	theorem		⊢
	proveit.logic.sets.inclusion.unfold_subset_eq
69	instantiation	78, 79	⊢
	: , :
70	theorem		⊢
	proveit.physics.quantum.QPE._two_pow_t_is_nat_pos
71	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.nonzero_complex_is_complex_nonzero
72	instantiation	86, 80, 81	⊢
	: , : , :
73	assumption		⊢
74	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
75	instantiation	86, 82, 83	⊢
	: , : , :
76	theorem		⊢
	proveit.numbers.number_sets.real_numbers.real_pos_within_real
77	theorem		⊢
	proveit.numbers.number_sets.real_numbers.pi_is_real_pos
78	theorem		⊢
	proveit.logic.sets.inclusion.relax_proper_subset
79	theorem		⊢
	proveit.numbers.number_sets.real_numbers.nat_pos_within_real
80	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
81	instantiation	84, 85	⊢
	:
82	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
83	instantiation	86, 87, 88	⊢
	: , : , :
84	theorem		⊢
	proveit.physics.quantum.QPE._delta_b_is_real
85	theorem		⊢
	proveit.physics.quantum.QPE._best_round_is_int
86	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
87	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
88	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
*equality replacement requirements