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	105	⊢
2	instantiation	4, 5, 6	⊢
	: , : , :
3	modus ponens	7, 8	⊢
4	theorem		⊢
	proveit.logic.equality.sub_right_side_into
5	instantiation	9, 10, 11	⊢
	: , : , :
6	instantiation	12, 112	⊢
	:
7	instantiation	13, 14, 15	⊢
	: , : , : , : , : , :
8	theorem		⊢
	proveit.physics.quantum.QPE._precision_guarantee_lemma_02
9	theorem		⊢
	proveit.logic.equality.sub_left_side_into
10	instantiation	105, 16, 17	⊢
	: , : , :
11	instantiation	18, 112	⊢
	:
12	axiom		⊢
	proveit.physics.quantum.QPE._success_def
13	theorem		⊢
	proveit.statistics.constrained_event_prob_bound
14	theorem		⊢
	proveit.physics.quantum.QPE._Omega_is_sample_space
15	instantiation	39, 19	⊢
	: , :
16	theorem		⊢
	proveit.physics.quantum.QPE._precision_guarantee_lemma_01
17	instantiation	20, 57, 21, 22, 23, 24*	⊢
	: , : , :
18	theorem		⊢
	proveit.physics.quantum.QPE._success_complements_failure
19	instantiation	25, 26	⊢
	: , : , :
20	theorem		⊢
	proveit.numbers.addition.weak_bound_via_right_term_bound
21	instantiation	42, 47, 48	⊢
	: , :
22	instantiation	52, 28	⊢
	:
23	instantiation	27, 28, 29, 30, 31*	⊢
	: , :
24	instantiation	32, 113, 124, 33, 34, 35, 36, 37, 38	⊢
	: , : , : , : , : , :
25	theorem		⊢
	proveit.logic.sets.functions.injections.membership_unfolding
26	instantiation	39, 40	⊢
	: , :
27	theorem		⊢
	proveit.numbers.negation.negated_weak_bound
28	instantiation	41, 112	⊢
	:
29	instantiation	42, 51, 53	⊢
	: , :
30	instantiation	43, 112	⊢
	:
31	instantiation	44, 45, 46	⊢
	: , :
32	theorem		⊢
	proveit.numbers.addition.disassociation
33	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
34	instantiation	74	⊢
	: , :
35	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
36	instantiation	131, 85, 57	⊢
	: , : , :
37	instantiation	131, 85, 47	⊢
	: , : , :
38	instantiation	131, 85, 48	⊢
	: , : , :
39	theorem		⊢
	proveit.logic.booleans.conjunction.left_from_and
40	instantiation	49, 50	⊢
	: , : , :
41	theorem		⊢
	proveit.physics.quantum.QPE._pfail_in_real
42	theorem		⊢
	proveit.numbers.addition.add_real_closure_bin
43	theorem		⊢
	proveit.physics.quantum.QPE._failure_upper_bound
44	theorem		⊢
	proveit.numbers.negation.distribute_neg_through_binary_sum
45	instantiation	131, 85, 51	⊢
	: , : , :
46	instantiation	131, 85, 53	⊢
	: , : , :
47	instantiation	52, 51	⊢
	:
48	instantiation	52, 53	⊢
	:
49	theorem		⊢
	proveit.logic.sets.functions.bijections.membership_unfolding
50	theorem		⊢
	proveit.physics.quantum.QPE._sample_space_bijection
51	instantiation	56, 57, 54, 55	⊢
	: , :
52	theorem		⊢
	proveit.numbers.negation.real_closure
53	instantiation	56, 57, 58, 59	⊢
	: , :
54	instantiation	63, 86, 73	⊢
	: , :
55	instantiation	66, 124, 60, 61, 77	⊢
	: , :
56	theorem		⊢
	proveit.numbers.division.div_real_closure
57	instantiation	131, 92, 62	⊢
	: , : , :
58	instantiation	63, 64, 65	⊢
	: , :
59	instantiation	66, 124, 67, 68, 69	⊢
	: , :
60	instantiation	74	⊢
	: , :
61	instantiation	131, 83, 70	⊢
	: , : , :
62	instantiation	131, 98, 110	⊢
	: , : , :
63	theorem		⊢
	proveit.numbers.multiplication.mult_real_closure_bin
64	instantiation	131, 92, 71	⊢
	: , : , :
65	instantiation	72, 73, 124	⊢
	: , :
66	theorem		⊢
	proveit.numbers.multiplication.mult_not_eq_zero
67	instantiation	74	⊢
	: , :
68	instantiation	131, 83, 75	⊢
	: , : , :
69	instantiation	76, 77, 78	⊢
	: , :
70	instantiation	131, 90, 79	⊢
	: , : , :
71	instantiation	131, 98, 80	⊢
	: , : , :
72	theorem		⊢
	proveit.numbers.exponentiation.exp_real_closure_nat_power
73	instantiation	131, 92, 81	⊢
	: , : , :
74	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
75	instantiation	131, 90, 82	⊢
	: , : , :
76	theorem		⊢
	proveit.numbers.exponentiation.exp_complex_nonzero_closure
77	instantiation	131, 83, 84	⊢
	: , : , :
78	instantiation	131, 85, 86	⊢
	: , : , :
79	instantiation	131, 96, 87	⊢
	: , : , :
80	instantiation	131, 123, 88	⊢
	: , : , :
81	instantiation	131, 98, 102	⊢
	: , : , :
82	instantiation	131, 96, 89	⊢
	: , : , :
83	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero
84	instantiation	131, 90, 91	⊢
	: , : , :
85	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
86	instantiation	131, 92, 93	⊢
	: , : , :
87	instantiation	131, 99, 94	⊢
	: , : , :
88	theorem		⊢
	proveit.numbers.numerals.decimals.nat4
89	instantiation	131, 99, 95	⊢
	: , : , :
90	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero
91	instantiation	131, 96, 97	⊢
	: , : , :
92	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
93	instantiation	131, 98, 119	⊢
	: , : , :
94	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
95	theorem		⊢
	proveit.numbers.numerals.decimals.posnat4
96	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
97	instantiation	131, 99, 100	⊢
	: , : , :
98	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
99	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
100	instantiation	101, 102, 103	⊢
	:
101	theorem		⊢
	proveit.numbers.number_sets.integers.pos_int_is_natural_pos
102	instantiation	131, 104, 112	⊢
	: , : , :
103	instantiation	105, 106, 107	⊢
	: , : , :
104	instantiation	108, 110, 111	⊢
	: , :
105	theorem		⊢
	proveit.numbers.ordering.transitivity_less_less_eq
106	theorem		⊢
	proveit.numbers.numerals.decimals.less_0_1
107	instantiation	109, 110, 111, 112	⊢
	: , : , :
108	theorem		⊢
	proveit.numbers.number_sets.integers.int_interval_within_int
109	theorem		⊢
	proveit.numbers.number_sets.integers.interval_lower_bound
110	instantiation	131, 123, 113	⊢
	: , : , :
111	instantiation	125, 114, 115	⊢
	: , :
112	theorem		⊢
	proveit.physics.quantum.QPE._e_value_in_e_domain
113	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
114	instantiation	116, 119, 117	⊢
	: , :
115	instantiation	118, 119	⊢
	:
116	theorem		⊢
	proveit.numbers.exponentiation.exp_int_closure
117	instantiation	120, 121, 122	⊢
	:
118	theorem		⊢
	proveit.numbers.negation.int_closure
119	instantiation	131, 123, 124	⊢
	: , : , :
120	theorem		⊢
	proveit.numbers.number_sets.integers.nonneg_int_is_natural
121	instantiation	125, 126, 127	⊢
	: , :
122	instantiation	128, 129	⊢
	: , :
123	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
124	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
125	theorem		⊢
	proveit.numbers.addition.add_int_closure_bin
126	instantiation	131, 130, 135	⊢
	: , : , :
127	instantiation	131, 132, 133	⊢
	: , : , :
128	theorem		⊢
	proveit.numbers.addition.subtraction.nonneg_difference
129	instantiation	134, 135	⊢
	:
130	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_int
131	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
132	theorem		⊢
	proveit.numbers.number_sets.integers.neg_int_within_int
133	instantiation	136, 137	⊢
	:
134	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.natural_pos_lower_bound
135	axiom		⊢
	proveit.physics.quantum.QPE._t_in_natural_pos
136	theorem		⊢
	proveit.numbers.negation.int_neg_closure
137	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
*equality replacement requirements