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	25	⊢
2	axiom		⊢
	proveit.physics.quantum.QPE._n_ge_two
3	instantiation	40, 44, 146, 4, 5, 6*, 7*	⊢
	: , : , :
4	instantiation	59, 9, 146	⊢
	: , :
5	instantiation	8, 146, 9, 10, 116	⊢
	: , : , :
6	instantiation	127, 11, 12	⊢
	: , : , :
7	instantiation	127, 13, 14	⊢
	: , : , :
8	theorem		⊢
	proveit.numbers.ordering.less_eq_add_right
9	instantiation	59, 61, 99	⊢
	: , :
10	instantiation	25, 15, 16	⊢
	: , : , :
11	instantiation	73, 201, 172, 74, 31, 75, 133, 79, 32	⊢
	: , : , : , : , : , :
12	instantiation	78, 133, 79, 49	⊢
	: , : , :
13	instantiation	106, 17	⊢
	: , : , :
14	instantiation	18, 19, 20, 21	⊢
	: , : , : , :
15	instantiation	22, 198, 38, 23, 24*	⊢
	: , :
16	instantiation	25, 26, 27	⊢
	: , : , :
17	instantiation	73, 74, 172, 201, 75, 48, 51, 77, 133	⊢
	: , : , : , : , : , :
18	theorem		⊢
	proveit.logic.equality.four_chain_transitivity
19	instantiation	73, 74, 29, 201, 75, 30, 51, 77, 133, 28	⊢
	: , : , : , : , : , :
20	instantiation	73, 29, 172, 74, 30, 31, 75, 51, 77, 133, 79, 32	⊢
	: , : , : , : , : , :
21	instantiation	127, 33, 34	⊢
	: , : , :
22	theorem		⊢
	proveit.numbers.rounding.ceil_of_real_above_int
23	instantiation	35, 181, 55, 36	⊢
	: , :
24	theorem		⊢
	proveit.numbers.numerals.decimals.add_1_1
25	theorem		⊢
	proveit.numbers.ordering.transitivity_less_eq_less_eq
26	instantiation	37, 38, 150, 39	⊢
	: , :
27	instantiation	40, 99, 41, 61, 42, 43*	⊢
	: , : , :
28	instantiation	199, 161, 44	⊢
	: , : , :
29	theorem		⊢
	proveit.numbers.numerals.decimals.nat3
30	instantiation	45	⊢
	: , : , :
31	instantiation	152	⊢
	: , :
32	instantiation	46, 133	⊢
	:
33	instantiation	47, 172, 201, 74, 48, 75, 51, 77, 133, 79, 49	⊢
	: , : , : , : , : , : , : , :
34	instantiation	50, 79, 51, 81	⊢
	: , : , :
35	theorem		⊢
	proveit.numbers.logarithms.log_base_large_a_greater_one
36	instantiation	52, 173, 53	⊢
	: , :
37	theorem		⊢
	proveit.numbers.rounding.ceil_increasing_less_eq
38	instantiation	156, 181, 55, 158	⊢
	: , :
39	instantiation	54, 181, 55, 157, 56, 173	⊢
	: , : , :
40	theorem		⊢
	proveit.numbers.addition.weak_bound_via_left_term_bound
41	instantiation	59, 122, 100	⊢
	: , :
42	axiom		⊢
	proveit.physics.quantum.QPE._t_req
43	instantiation	127, 57, 58	⊢
	: , : , :
44	instantiation	59, 122, 60	⊢
	: , :
45	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_3_typical_eq
46	theorem		⊢
	proveit.numbers.negation.complex_closure
47	theorem		⊢
	proveit.numbers.addition.subtraction.add_cancel_general
48	instantiation	152	⊢
	: , :
49	instantiation	101	⊢
	:
50	theorem		⊢
	proveit.numbers.addition.subtraction.add_cancel_triple_32
51	instantiation	199, 161, 61	⊢
	: , : , :
52	theorem		⊢
	proveit.logic.booleans.conjunction.and_if_both
53	instantiation	62, 146, 63, 64, 65, 66*, 67*	⊢
	: , : , :
54	theorem		⊢
	proveit.numbers.logarithms.log_increasing_less_eq
55	instantiation	199, 183, 68	⊢
	: , : , :
56	instantiation	69, 146, 140, 70, 71, 72*	⊢
	: , : , :
57	instantiation	73, 74, 172, 201, 75, 76, 79, 80, 77	⊢
	: , : , : , : , : , :
58	instantiation	78, 79, 80, 81	⊢
	: , : , :
59	theorem		⊢
	proveit.numbers.addition.add_real_closure_bin
60	instantiation	121, 146	⊢
	:
61	instantiation	136, 137, 82	⊢
	: , : , :
62	theorem		⊢
	proveit.numbers.addition.strong_bound_via_left_term_bound
63	instantiation	83, 140, 192	⊢
	: , :
64	instantiation	199, 195, 84	⊢
	: , : , :
65	instantiation	85, 140, 192, 193, 86, 87	⊢
	: , : , :
66	instantiation	127, 88, 89	⊢
	: , : , :
67	instantiation	127, 90, 91	⊢
	: , : , :
68	instantiation	167, 92, 184	⊢
	: , :
69	theorem		⊢
	proveit.numbers.addition.weak_bound_via_right_term_bound
70	instantiation	199, 93, 164	⊢
	: , : , :
71	instantiation	94, 95, 179, 181, 96	⊢
	: , : , :
72	instantiation	108, 162, 198, 109*, 97*, 98*	⊢
	: , : , : , :
73	theorem		⊢
	proveit.numbers.addition.disassociation
74	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
75	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
76	instantiation	152	⊢
	: , :
77	instantiation	199, 161, 99	⊢
	: , : , :
78	theorem		⊢
	proveit.numbers.addition.subtraction.add_cancel_triple_13
79	instantiation	199, 161, 122	⊢
	: , : , :
80	instantiation	199, 161, 100	⊢
	: , : , :
81	instantiation	101	⊢
	:
82	axiom		⊢
	proveit.physics.quantum.QPE._t_in_natural_pos
83	theorem		⊢
	proveit.numbers.multiplication.mult_real_closure_bin
84	instantiation	102, 151, 196	⊢
	: , :
85	theorem		⊢
	proveit.numbers.multiplication.strong_bound_via_right_factor_bound
86	theorem		⊢
	proveit.numbers.numerals.decimals.less_0_1
87	instantiation	103, 160	⊢
	:
88	instantiation	106, 104	⊢
	: , : , :
89	instantiation	105, 133	⊢
	:
90	instantiation	106, 107	⊢
	: , : , :
91	instantiation	108, 198, 162, 109*, 110*, 117*	⊢
	: , : , : , :
92	instantiation	199, 188, 111	⊢
	: , : , :
93	theorem		⊢
	proveit.numbers.number_sets.real_numbers.real_pos_within_real
94	theorem		⊢
	proveit.numbers.division.weak_div_from_denom_bound__all_pos
95	instantiation	199, 112, 113	⊢
	: , : , :
96	instantiation	114, 146, 186, 193, 115, 116, 117*	⊢
	: , : , :
97	instantiation	127, 118, 119	⊢
	: , : , :
98	instantiation	120, 133	⊢
	:
99	instantiation	121, 122	⊢
	:
100	instantiation	199, 195, 123	⊢
	: , : , :
101	axiom		⊢
	proveit.logic.equality.equals_reflexivity
102	theorem		⊢
	proveit.numbers.multiplication.mult_rational_closure_bin
103	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.positive_if_in_rational_pos
104	instantiation	124, 125	⊢
	:
105	theorem		⊢
	proveit.numbers.addition.elim_zero_left
106	axiom		⊢
	proveit.logic.equality.substitution
107	instantiation	153, 125	⊢
	:
108	theorem		⊢
	proveit.numbers.addition.rational_pair_addition
109	instantiation	126, 133	⊢
	:
110	instantiation	127, 128, 129	⊢
	: , : , :
111	theorem		⊢
	proveit.numbers.numerals.decimals.posnat5
112	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_nonneg_within_real_nonneg
113	instantiation	199, 130, 201	⊢
	: , : , :
114	theorem		⊢
	proveit.numbers.multiplication.weak_bound_via_right_factor_bound
115	instantiation	131, 192, 193, 194	⊢
	: , : , :
116	instantiation	132, 172	⊢
	:
117	instantiation	153, 133	⊢
	:
118	instantiation	141, 172, 134, 135, 145, 144	⊢
	: , : , : , :
119	theorem		⊢
	proveit.numbers.numerals.decimals.add_4_1
120	theorem		⊢
	proveit.numbers.multiplication.elim_one_left
121	theorem		⊢
	proveit.numbers.negation.real_closure
122	instantiation	136, 137, 138	⊢
	: , : , :
123	instantiation	199, 197, 139	⊢
	: , : , :
124	theorem		⊢
	proveit.numbers.multiplication.mult_zero_right
125	instantiation	199, 161, 140	⊢
	: , : , :
126	theorem		⊢
	proveit.numbers.division.frac_one_denom
127	axiom		⊢
	proveit.logic.equality.equals_transitivity
128	instantiation	141, 172, 142, 143, 144, 145	⊢
	: , : , : , :
129	theorem		⊢
	proveit.numbers.numerals.decimals.add_1_4
130	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nat_within_rational_nonneg
131	theorem		⊢
	proveit.numbers.number_sets.real_numbers.interval_oc_upper_bound
132	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.natural_lower_bound
133	instantiation	199, 161, 146	⊢
	: , : , :
134	instantiation	152	⊢
	: , :
135	instantiation	152	⊢
	: , :
136	theorem		⊢
	proveit.logic.sets.inclusion.unfold_subset_eq
137	instantiation	147, 148	⊢
	: , :
138	axiom		⊢
	proveit.physics.quantum.QPE._n_in_natural_pos
139	instantiation	149, 150	⊢
	:
140	instantiation	199, 195, 151	⊢
	: , : , :
141	axiom		⊢
	proveit.core_expr_types.operations.operands_substitution
142	instantiation	152	⊢
	: , :
143	instantiation	152	⊢
	: , :
144	instantiation	153, 154	⊢
	:
145	theorem		⊢
	proveit.numbers.numerals.decimals.mult_2_2
146	instantiation	199, 195, 155	⊢
	: , : , :
147	theorem		⊢
	proveit.logic.sets.inclusion.relax_proper_subset
148	theorem		⊢
	proveit.numbers.number_sets.real_numbers.nat_pos_within_real
149	axiom		⊢
	proveit.numbers.rounding.ceil_is_an_int
150	instantiation	156, 181, 157, 158	⊢
	: , :
151	instantiation	199, 159, 160	⊢
	: , : , :
152	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
153	theorem		⊢
	proveit.numbers.multiplication.elim_one_right
154	instantiation	199, 161, 193	⊢
	: , : , :
155	instantiation	199, 197, 162	⊢
	: , : , :
156	theorem		⊢
	proveit.numbers.logarithms.log_real_pos_real_closure
157	instantiation	163, 181, 164	⊢
	: , :
158	instantiation	165, 166	⊢
	: , :
159	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.rational_pos_within_rational
160	instantiation	167, 174, 184	⊢
	: , :
161	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
162	instantiation	199, 200, 172	⊢
	: , : , :
163	theorem		⊢
	proveit.numbers.addition.add_real_pos_closure_bin
164	instantiation	168, 169, 179, 170	⊢
	: , :
165	theorem		⊢
	proveit.logic.equality.not_equals_symmetry
166	instantiation	171, 201, 172, 173	⊢
	: , :
167	theorem		⊢
	proveit.numbers.division.div_rational_pos_closure
168	theorem		⊢
	proveit.numbers.division.div_real_pos_closure
169	instantiation	199, 183, 174	⊢
	: , : , :
170	instantiation	175, 176	⊢
	:
171	theorem		⊢
	proveit.numbers.ordering.less_is_not_eq_nat
172	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
173	theorem		⊢
	proveit.numbers.numerals.decimals.less_1_2
174	instantiation	199, 188, 177	⊢
	: , : , :
175	theorem		⊢
	proveit.numbers.number_sets.real_numbers.nonzero_if_in_real_nonzero
176	instantiation	199, 178, 179	⊢
	: , : , :
177	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
178	theorem		⊢
	proveit.numbers.number_sets.real_numbers.real_pos_within_real_nonzero
179	instantiation	180, 181, 182	⊢
	: , :
180	theorem		⊢
	proveit.numbers.multiplication.mult_real_pos_closure_bin
181	instantiation	199, 183, 184	⊢
	: , : , :
182	instantiation	185, 186, 187	⊢
	:
183	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_pos_within_real_pos
184	instantiation	199, 188, 189	⊢
	: , : , :
185	theorem		⊢
	proveit.numbers.number_sets.real_numbers.pos_real_is_real_pos
186	instantiation	190, 192, 193, 194	⊢
	: , : , :
187	instantiation	191, 192, 193, 194	⊢
	: , : , :
188	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nat_pos_within_rational_pos
189	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
190	theorem		⊢
	proveit.numbers.number_sets.real_numbers.all_in_interval_oc__is__real
191	theorem		⊢
	proveit.numbers.number_sets.real_numbers.interval_oc_lower_bound
192	theorem		⊢
	proveit.numbers.number_sets.real_numbers.zero_is_real
193	instantiation	199, 195, 196	⊢
	: , : , :
194	axiom		⊢
	proveit.physics.quantum.QPE._eps_in_interval
195	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
196	instantiation	199, 197, 198	⊢
	: , : , :
197	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
198	instantiation	199, 200, 201	⊢
	: , : , :
199	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
200	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
201	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
*equality replacement requirements