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