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_right_side_into
2	instantiation	4, 5, 6	⊢
	: , : , :
3	instantiation	7, 97	⊢
	:
4	theorem		⊢
	proveit.logic.equality.sub_left_side_into
5	instantiation	90, 8, 9	⊢
	: , : , :
6	instantiation	10, 97	⊢
	:
7	axiom		⊢
	proveit.physics.quantum.QPE._success_def
8	theorem		⊢
	proveit.physics.quantum.QPE._precision_guarantee_lemma_01
9	instantiation	11, 42, 12, 13, 14, 15*	⊢
	: , : , :
10	theorem		⊢
	proveit.physics.quantum.QPE._success_complements_failure
11	theorem		⊢
	proveit.numbers.addition.weak_bound_via_right_term_bound
12	instantiation	29, 34, 35	⊢
	: , :
13	instantiation	37, 17	⊢
	:
14	instantiation	16, 17, 18, 19, 20*	⊢
	: , :
15	instantiation	21, 98, 109, 22, 23, 24, 25, 26, 27	⊢
	: , : , : , : , : , :
16	theorem		⊢
	proveit.numbers.negation.negated_weak_bound
17	instantiation	28, 97	⊢
	:
18	instantiation	29, 36, 38	⊢
	: , :
19	instantiation	30, 97	⊢
	:
20	instantiation	31, 32, 33	⊢
	: , :
21	theorem		⊢
	proveit.numbers.addition.disassociation
22	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
23	instantiation	59	⊢
	: , :
24	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
25	instantiation	116, 70, 42	⊢
	: , : , :
26	instantiation	116, 70, 34	⊢
	: , : , :
27	instantiation	116, 70, 35	⊢
	: , : , :
28	theorem		⊢
	proveit.physics.quantum.QPE._pfail_in_real
29	theorem		⊢
	proveit.numbers.addition.add_real_closure_bin
30	theorem		⊢
	proveit.physics.quantum.QPE._failure_upper_bound
31	theorem		⊢
	proveit.numbers.negation.distribute_neg_through_binary_sum
32	instantiation	116, 70, 36	⊢
	: , : , :
33	instantiation	116, 70, 38	⊢
	: , : , :
34	instantiation	37, 36	⊢
	:
35	instantiation	37, 38	⊢
	:
36	instantiation	41, 42, 39, 40	⊢
	: , :
37	theorem		⊢
	proveit.numbers.negation.real_closure
38	instantiation	41, 42, 43, 44	⊢
	: , :
39	instantiation	48, 71, 58	⊢
	: , :
40	instantiation	51, 109, 45, 46, 62	⊢
	: , :
41	theorem		⊢
	proveit.numbers.division.div_real_closure
42	instantiation	116, 77, 47	⊢
	: , : , :
43	instantiation	48, 49, 50	⊢
	: , :
44	instantiation	51, 109, 52, 53, 54	⊢
	: , :
45	instantiation	59	⊢
	: , :
46	instantiation	116, 68, 55	⊢
	: , : , :
47	instantiation	116, 83, 95	⊢
	: , : , :
48	theorem		⊢
	proveit.numbers.multiplication.mult_real_closure_bin
49	instantiation	116, 77, 56	⊢
	: , : , :
50	instantiation	57, 58, 109	⊢
	: , :
51	theorem		⊢
	proveit.numbers.multiplication.mult_not_eq_zero
52	instantiation	59	⊢
	: , :
53	instantiation	116, 68, 60	⊢
	: , : , :
54	instantiation	61, 62, 63	⊢
	: , :
55	instantiation	116, 75, 64	⊢
	: , : , :
56	instantiation	116, 83, 65	⊢
	: , : , :
57	theorem		⊢
	proveit.numbers.exponentiation.exp_real_closure_nat_power
58	instantiation	116, 77, 66	⊢
	: , : , :
59	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
60	instantiation	116, 75, 67	⊢
	: , : , :
61	theorem		⊢
	proveit.numbers.exponentiation.exp_complex_nonzero_closure
62	instantiation	116, 68, 69	⊢
	: , : , :
63	instantiation	116, 70, 71	⊢
	: , : , :
64	instantiation	116, 81, 72	⊢
	: , : , :
65	instantiation	116, 108, 73	⊢
	: , : , :
66	instantiation	116, 83, 87	⊢
	: , : , :
67	instantiation	116, 81, 74	⊢
	: , : , :
68	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero
69	instantiation	116, 75, 76	⊢
	: , : , :
70	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
71	instantiation	116, 77, 78	⊢
	: , : , :
72	instantiation	116, 84, 79	⊢
	: , : , :
73	theorem		⊢
	proveit.numbers.numerals.decimals.nat4
74	instantiation	116, 84, 80	⊢
	: , : , :
75	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero
76	instantiation	116, 81, 82	⊢
	: , : , :
77	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
78	instantiation	116, 83, 104	⊢
	: , : , :
79	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
80	theorem		⊢
	proveit.numbers.numerals.decimals.posnat4
81	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
82	instantiation	116, 84, 85	⊢
	: , : , :
83	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
84	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
85	instantiation	86, 87, 88	⊢
	:
86	theorem		⊢
	proveit.numbers.number_sets.integers.pos_int_is_natural_pos
87	instantiation	116, 89, 97	⊢
	: , : , :
88	instantiation	90, 91, 92	⊢
	: , : , :
89	instantiation	93, 95, 96	⊢
	: , :
90	theorem		⊢
	proveit.numbers.ordering.transitivity_less_less_eq
91	theorem		⊢
	proveit.numbers.numerals.decimals.less_0_1
92	instantiation	94, 95, 96, 97	⊢
	: , : , :
93	theorem		⊢
	proveit.numbers.number_sets.integers.int_interval_within_int
94	theorem		⊢
	proveit.numbers.number_sets.integers.interval_lower_bound
95	instantiation	116, 108, 98	⊢
	: , : , :
96	instantiation	110, 99, 100	⊢
	: , :
97	theorem		⊢
	proveit.physics.quantum.QPE._e_value_in_e_domain
98	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
99	instantiation	101, 104, 102	⊢
	: , :
100	instantiation	103, 104	⊢
	:
101	theorem		⊢
	proveit.numbers.exponentiation.exp_int_closure
102	instantiation	105, 106, 107	⊢
	:
103	theorem		⊢
	proveit.numbers.negation.int_closure
104	instantiation	116, 108, 109	⊢
	: , : , :
105	theorem		⊢
	proveit.numbers.number_sets.integers.nonneg_int_is_natural
106	instantiation	110, 111, 112	⊢
	: , :
107	instantiation	113, 114	⊢
	: , :
108	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
109	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
110	theorem		⊢
	proveit.numbers.addition.add_int_closure_bin
111	instantiation	116, 115, 120	⊢
	: , : , :
112	instantiation	116, 117, 118	⊢
	: , : , :
113	theorem		⊢
	proveit.numbers.addition.subtraction.nonneg_difference
114	instantiation	119, 120	⊢
	:
115	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_int
116	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
117	theorem		⊢
	proveit.numbers.number_sets.integers.neg_int_within_int
118	instantiation	121, 122	⊢
	:
119	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.natural_pos_lower_bound
120	axiom		⊢
	proveit.physics.quantum.QPE._t_in_natural_pos
121	theorem		⊢
	proveit.numbers.negation.int_neg_closure
122	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
*equality replacement requirements