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	theorem		⊢
	proveit.logic.equality.sub_left_side_into
2	instantiation	86, 4, 5	⊢
	: , : , :
3	instantiation	6, 93	⊢
	:
4	theorem		⊢
	proveit.physics.quantum.QPE._precision_guarantee_lemma_01
5	instantiation	7, 38, 8, 9, 10, 11*	⊢
	: , : , :
6	theorem		⊢
	proveit.physics.quantum.QPE._success_complements_failure
7	theorem		⊢
	proveit.numbers.addition.weak_bound_via_right_term_bound
8	instantiation	25, 30, 31	⊢
	: , :
9	instantiation	33, 13	⊢
	:
10	instantiation	12, 13, 14, 15, 16*	⊢
	: , :
11	instantiation	17, 94, 105, 18, 19, 20, 21, 22, 23	⊢
	: , : , : , : , : , :
12	theorem		⊢
	proveit.numbers.negation.negated_weak_bound
13	instantiation	24, 93	⊢
	:
14	instantiation	25, 32, 34	⊢
	: , :
15	instantiation	26, 93	⊢
	:
16	instantiation	27, 28, 29	⊢
	: , :
17	theorem		⊢
	proveit.numbers.addition.disassociation
18	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
19	instantiation	55	⊢
	: , :
20	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
21	instantiation	112, 66, 38	⊢
	: , : , :
22	instantiation	112, 66, 30	⊢
	: , : , :
23	instantiation	112, 66, 31	⊢
	: , : , :
24	theorem		⊢
	proveit.physics.quantum.QPE._pfail_in_real
25	theorem		⊢
	proveit.numbers.addition.add_real_closure_bin
26	theorem		⊢
	proveit.physics.quantum.QPE._failure_upper_bound
27	theorem		⊢
	proveit.numbers.negation.distribute_neg_through_binary_sum
28	instantiation	112, 66, 32	⊢
	: , : , :
29	instantiation	112, 66, 34	⊢
	: , : , :
30	instantiation	33, 32	⊢
	:
31	instantiation	33, 34	⊢
	:
32	instantiation	37, 38, 35, 36	⊢
	: , :
33	theorem		⊢
	proveit.numbers.negation.real_closure
34	instantiation	37, 38, 39, 40	⊢
	: , :
35	instantiation	44, 67, 54	⊢
	: , :
36	instantiation	47, 105, 41, 42, 58	⊢
	: , :
37	theorem		⊢
	proveit.numbers.division.div_real_closure
38	instantiation	112, 73, 43	⊢
	: , : , :
39	instantiation	44, 45, 46	⊢
	: , :
40	instantiation	47, 105, 48, 49, 50	⊢
	: , :
41	instantiation	55	⊢
	: , :
42	instantiation	112, 64, 51	⊢
	: , : , :
43	instantiation	112, 79, 91	⊢
	: , : , :
44	theorem		⊢
	proveit.numbers.multiplication.mult_real_closure_bin
45	instantiation	112, 73, 52	⊢
	: , : , :
46	instantiation	53, 54, 105	⊢
	: , :
47	theorem		⊢
	proveit.numbers.multiplication.mult_not_eq_zero
48	instantiation	55	⊢
	: , :
49	instantiation	112, 64, 56	⊢
	: , : , :
50	instantiation	57, 58, 59	⊢
	: , :
51	instantiation	112, 71, 60	⊢
	: , : , :
52	instantiation	112, 79, 61	⊢
	: , : , :
53	theorem		⊢
	proveit.numbers.exponentiation.exp_real_closure_nat_power
54	instantiation	112, 73, 62	⊢
	: , : , :
55	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
56	instantiation	112, 71, 63	⊢
	: , : , :
57	theorem		⊢
	proveit.numbers.exponentiation.exp_complex_nonzero_closure
58	instantiation	112, 64, 65	⊢
	: , : , :
59	instantiation	112, 66, 67	⊢
	: , : , :
60	instantiation	112, 77, 68	⊢
	: , : , :
61	instantiation	112, 104, 69	⊢
	: , : , :
62	instantiation	112, 79, 83	⊢
	: , : , :
63	instantiation	112, 77, 70	⊢
	: , : , :
64	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero
65	instantiation	112, 71, 72	⊢
	: , : , :
66	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
67	instantiation	112, 73, 74	⊢
	: , : , :
68	instantiation	112, 80, 75	⊢
	: , : , :
69	theorem		⊢
	proveit.numbers.numerals.decimals.nat4
70	instantiation	112, 80, 76	⊢
	: , : , :
71	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero
72	instantiation	112, 77, 78	⊢
	: , : , :
73	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
74	instantiation	112, 79, 100	⊢
	: , : , :
75	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
76	theorem		⊢
	proveit.numbers.numerals.decimals.posnat4
77	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
78	instantiation	112, 80, 81	⊢
	: , : , :
79	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
80	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
81	instantiation	82, 83, 84	⊢
	:
82	theorem		⊢
	proveit.numbers.number_sets.integers.pos_int_is_natural_pos
83	instantiation	112, 85, 93	⊢
	: , : , :
84	instantiation	86, 87, 88	⊢
	: , : , :
85	instantiation	89, 91, 92	⊢
	: , :
86	theorem		⊢
	proveit.numbers.ordering.transitivity_less_less_eq
87	theorem		⊢
	proveit.numbers.numerals.decimals.less_0_1
88	instantiation	90, 91, 92, 93	⊢
	: , : , :
89	theorem		⊢
	proveit.numbers.number_sets.integers.int_interval_within_int
90	theorem		⊢
	proveit.numbers.number_sets.integers.interval_lower_bound
91	instantiation	112, 104, 94	⊢
	: , : , :
92	instantiation	106, 95, 96	⊢
	: , :
93	theorem		⊢
	proveit.physics.quantum.QPE._e_value_in_e_domain
94	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
95	instantiation	97, 100, 98	⊢
	: , :
96	instantiation	99, 100	⊢
	:
97	theorem		⊢
	proveit.numbers.exponentiation.exp_int_closure
98	instantiation	101, 102, 103	⊢
	:
99	theorem		⊢
	proveit.numbers.negation.int_closure
100	instantiation	112, 104, 105	⊢
	: , : , :
101	theorem		⊢
	proveit.numbers.number_sets.integers.nonneg_int_is_natural
102	instantiation	106, 107, 108	⊢
	: , :
103	instantiation	109, 110	⊢
	: , :
104	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
105	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
106	theorem		⊢
	proveit.numbers.addition.add_int_closure_bin
107	instantiation	112, 111, 116	⊢
	: , : , :
108	instantiation	112, 113, 114	⊢
	: , : , :
109	theorem		⊢
	proveit.numbers.addition.subtraction.nonneg_difference
110	instantiation	115, 116	⊢
	:
111	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_int
112	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
113	theorem		⊢
	proveit.numbers.number_sets.integers.neg_int_within_int
114	instantiation	117, 118	⊢
	:
115	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.natural_pos_lower_bound
116	axiom		⊢
	proveit.physics.quantum.QPE._t_in_natural_pos
117	theorem		⊢
	proveit.numbers.negation.int_neg_closure
118	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
*equality replacement requirements