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	⊢
	: , :
1	theorem		⊢
	proveit.numbers.addition.subtraction.nonneg_difference
2	instantiation	26, 3, 4	⊢
	: , : , :
3	axiom		⊢
	proveit.physics.quantum.QPE._n_ge_two
4	instantiation	41, 45, 147, 5, 6, 7*, 8*	⊢
	: , : , :
5	instantiation	60, 10, 147	⊢
	: , :
6	instantiation	9, 147, 10, 11, 117	⊢
	: , : , :
7	instantiation	128, 12, 13	⊢
	: , : , :
8	instantiation	128, 14, 15	⊢
	: , : , :
9	theorem		⊢
	proveit.numbers.ordering.less_eq_add_right
10	instantiation	60, 62, 100	⊢
	: , :
11	instantiation	26, 16, 17	⊢
	: , : , :
12	instantiation	74, 202, 173, 75, 32, 76, 134, 80, 33	⊢
	: , : , : , : , : , :
13	instantiation	79, 134, 80, 50	⊢
	: , : , :
14	instantiation	107, 18	⊢
	: , : , :
15	instantiation	19, 20, 21, 22	⊢
	: , : , : , :
16	instantiation	23, 199, 39, 24, 25*	⊢
	: , :
17	instantiation	26, 27, 28	⊢
	: , : , :
18	instantiation	74, 75, 173, 202, 76, 49, 52, 78, 134	⊢
	: , : , : , : , : , :
19	theorem		⊢
	proveit.logic.equality.four_chain_transitivity
20	instantiation	74, 75, 30, 202, 76, 31, 52, 78, 134, 29	⊢
	: , : , : , : , : , :
21	instantiation	74, 30, 173, 75, 31, 32, 76, 52, 78, 134, 80, 33	⊢
	: , : , : , : , : , :
22	instantiation	128, 34, 35	⊢
	: , : , :
23	theorem		⊢
	proveit.numbers.rounding.ceil_of_real_above_int
24	instantiation	36, 182, 56, 37	⊢
	: , :
25	theorem		⊢
	proveit.numbers.numerals.decimals.add_1_1
26	theorem		⊢
	proveit.numbers.ordering.transitivity_less_eq_less_eq
27	instantiation	38, 39, 151, 40	⊢
	: , :
28	instantiation	41, 100, 42, 62, 43, 44*	⊢
	: , : , :
29	instantiation	200, 162, 45	⊢
	: , : , :
30	theorem		⊢
	proveit.numbers.numerals.decimals.nat3
31	instantiation	46	⊢
	: , : , :
32	instantiation	153	⊢
	: , :
33	instantiation	47, 134	⊢
	:
34	instantiation	48, 173, 202, 75, 49, 76, 52, 78, 134, 80, 50	⊢
	: , : , : , : , : , : , : , :
35	instantiation	51, 80, 52, 82	⊢
	: , : , :
36	theorem		⊢
	proveit.numbers.logarithms.log_base_large_a_greater_one
37	instantiation	53, 174, 54	⊢
	: , :
38	theorem		⊢
	proveit.numbers.rounding.ceil_increasing_less_eq
39	instantiation	157, 182, 56, 159	⊢
	: , :
40	instantiation	55, 182, 56, 158, 57, 174	⊢
	: , : , :
41	theorem		⊢
	proveit.numbers.addition.weak_bound_via_left_term_bound
42	instantiation	60, 123, 101	⊢
	: , :
43	axiom		⊢
	proveit.physics.quantum.QPE._t_req
44	instantiation	128, 58, 59	⊢
	: , : , :
45	instantiation	60, 123, 61	⊢
	: , :
46	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_3_typical_eq
47	theorem		⊢
	proveit.numbers.negation.complex_closure
48	theorem		⊢
	proveit.numbers.addition.subtraction.add_cancel_general
49	instantiation	153	⊢
	: , :
50	instantiation	102	⊢
	:
51	theorem		⊢
	proveit.numbers.addition.subtraction.add_cancel_triple_32
52	instantiation	200, 162, 62	⊢
	: , : , :
53	theorem		⊢
	proveit.logic.booleans.conjunction.and_if_both
54	instantiation	63, 147, 64, 65, 66, 67*, 68*	⊢
	: , : , :
55	theorem		⊢
	proveit.numbers.logarithms.log_increasing_less_eq
56	instantiation	200, 184, 69	⊢
	: , : , :
57	instantiation	70, 147, 141, 71, 72, 73*	⊢
	: , : , :
58	instantiation	74, 75, 173, 202, 76, 77, 80, 81, 78	⊢
	: , : , : , : , : , :
59	instantiation	79, 80, 81, 82	⊢
	: , : , :
60	theorem		⊢
	proveit.numbers.addition.add_real_closure_bin
61	instantiation	122, 147	⊢
	:
62	instantiation	137, 138, 83	⊢
	: , : , :
63	theorem		⊢
	proveit.numbers.addition.strong_bound_via_left_term_bound
64	instantiation	84, 141, 193	⊢
	: , :
65	instantiation	200, 196, 85	⊢
	: , : , :
66	instantiation	86, 141, 193, 194, 87, 88	⊢
	: , : , :
67	instantiation	128, 89, 90	⊢
	: , : , :
68	instantiation	128, 91, 92	⊢
	: , : , :
69	instantiation	168, 93, 185	⊢
	: , :
70	theorem		⊢
	proveit.numbers.addition.weak_bound_via_right_term_bound
71	instantiation	200, 94, 165	⊢
	: , : , :
72	instantiation	95, 96, 180, 182, 97	⊢
	: , : , :
73	instantiation	109, 163, 199, 110*, 98*, 99*	⊢
	: , : , : , :
74	theorem		⊢
	proveit.numbers.addition.disassociation
75	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
76	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
77	instantiation	153	⊢
	: , :
78	instantiation	200, 162, 100	⊢
	: , : , :
79	theorem		⊢
	proveit.numbers.addition.subtraction.add_cancel_triple_13
80	instantiation	200, 162, 123	⊢
	: , : , :
81	instantiation	200, 162, 101	⊢
	: , : , :
82	instantiation	102	⊢
	:
83	axiom		⊢
	proveit.physics.quantum.QPE._t_in_natural_pos
84	theorem		⊢
	proveit.numbers.multiplication.mult_real_closure_bin
85	instantiation	103, 152, 197	⊢
	: , :
86	theorem		⊢
	proveit.numbers.multiplication.strong_bound_via_right_factor_bound
87	theorem		⊢
	proveit.numbers.numerals.decimals.less_0_1
88	instantiation	104, 161	⊢
	:
89	instantiation	107, 105	⊢
	: , : , :
90	instantiation	106, 134	⊢
	:
91	instantiation	107, 108	⊢
	: , : , :
92	instantiation	109, 199, 163, 110*, 111*, 118*	⊢
	: , : , : , :
93	instantiation	200, 189, 112	⊢
	: , : , :
94	theorem		⊢
	proveit.numbers.number_sets.real_numbers.real_pos_within_real
95	theorem		⊢
	proveit.numbers.division.weak_div_from_denom_bound__all_pos
96	instantiation	200, 113, 114	⊢
	: , : , :
97	instantiation	115, 147, 187, 194, 116, 117, 118*	⊢
	: , : , :
98	instantiation	128, 119, 120	⊢
	: , : , :
99	instantiation	121, 134	⊢
	:
100	instantiation	122, 123	⊢
	:
101	instantiation	200, 196, 124	⊢
	: , : , :
102	axiom		⊢
	proveit.logic.equality.equals_reflexivity
103	theorem		⊢
	proveit.numbers.multiplication.mult_rational_closure_bin
104	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.positive_if_in_rational_pos
105	instantiation	125, 126	⊢
	:
106	theorem		⊢
	proveit.numbers.addition.elim_zero_left
107	axiom		⊢
	proveit.logic.equality.substitution
108	instantiation	154, 126	⊢
	:
109	theorem		⊢
	proveit.numbers.addition.rational_pair_addition
110	instantiation	127, 134	⊢
	:
111	instantiation	128, 129, 130	⊢
	: , : , :
112	theorem		⊢
	proveit.numbers.numerals.decimals.posnat5
113	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_nonneg_within_real_nonneg
114	instantiation	200, 131, 202	⊢
	: , : , :
115	theorem		⊢
	proveit.numbers.multiplication.weak_bound_via_right_factor_bound
116	instantiation	132, 193, 194, 195	⊢
	: , : , :
117	instantiation	133, 173	⊢
	:
118	instantiation	154, 134	⊢
	:
119	instantiation	142, 173, 135, 136, 146, 145	⊢
	: , : , : , :
120	theorem		⊢
	proveit.numbers.numerals.decimals.add_4_1
121	theorem		⊢
	proveit.numbers.multiplication.elim_one_left
122	theorem		⊢
	proveit.numbers.negation.real_closure
123	instantiation	137, 138, 139	⊢
	: , : , :
124	instantiation	200, 198, 140	⊢
	: , : , :
125	theorem		⊢
	proveit.numbers.multiplication.mult_zero_right
126	instantiation	200, 162, 141	⊢
	: , : , :
127	theorem		⊢
	proveit.numbers.division.frac_one_denom
128	axiom		⊢
	proveit.logic.equality.equals_transitivity
129	instantiation	142, 173, 143, 144, 145, 146	⊢
	: , : , : , :
130	theorem		⊢
	proveit.numbers.numerals.decimals.add_1_4
131	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nat_within_rational_nonneg
132	theorem		⊢
	proveit.numbers.number_sets.real_numbers.interval_oc_upper_bound
133	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.natural_lower_bound
134	instantiation	200, 162, 147	⊢
	: , : , :
135	instantiation	153	⊢
	: , :
136	instantiation	153	⊢
	: , :
137	theorem		⊢
	proveit.logic.sets.inclusion.unfold_subset_eq
138	instantiation	148, 149	⊢
	: , :
139	axiom		⊢
	proveit.physics.quantum.QPE._n_in_natural_pos
140	instantiation	150, 151	⊢
	:
141	instantiation	200, 196, 152	⊢
	: , : , :
142	axiom		⊢
	proveit.core_expr_types.operations.operands_substitution
143	instantiation	153	⊢
	: , :
144	instantiation	153	⊢
	: , :
145	instantiation	154, 155	⊢
	:
146	theorem		⊢
	proveit.numbers.numerals.decimals.mult_2_2
147	instantiation	200, 196, 156	⊢
	: , : , :
148	theorem		⊢
	proveit.logic.sets.inclusion.relax_proper_subset
149	theorem		⊢
	proveit.numbers.number_sets.real_numbers.nat_pos_within_real
150	axiom		⊢
	proveit.numbers.rounding.ceil_is_an_int
151	instantiation	157, 182, 158, 159	⊢
	: , :
152	instantiation	200, 160, 161	⊢
	: , : , :
153	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
154	theorem		⊢
	proveit.numbers.multiplication.elim_one_right
155	instantiation	200, 162, 194	⊢
	: , : , :
156	instantiation	200, 198, 163	⊢
	: , : , :
157	theorem		⊢
	proveit.numbers.logarithms.log_real_pos_real_closure
158	instantiation	164, 182, 165	⊢
	: , :
159	instantiation	166, 167	⊢
	: , :
160	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.rational_pos_within_rational
161	instantiation	168, 175, 185	⊢
	: , :
162	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
163	instantiation	200, 201, 173	⊢
	: , : , :
164	theorem		⊢
	proveit.numbers.addition.add_real_pos_closure_bin
165	instantiation	169, 170, 180, 171	⊢
	: , :
166	theorem		⊢
	proveit.logic.equality.not_equals_symmetry
167	instantiation	172, 202, 173, 174	⊢
	: , :
168	theorem		⊢
	proveit.numbers.division.div_rational_pos_closure
169	theorem		⊢
	proveit.numbers.division.div_real_pos_closure
170	instantiation	200, 184, 175	⊢
	: , : , :
171	instantiation	176, 177	⊢
	:
172	theorem		⊢
	proveit.numbers.ordering.less_is_not_eq_nat
173	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
174	theorem		⊢
	proveit.numbers.numerals.decimals.less_1_2
175	instantiation	200, 189, 178	⊢
	: , : , :
176	theorem		⊢
	proveit.numbers.number_sets.real_numbers.nonzero_if_in_real_nonzero
177	instantiation	200, 179, 180	⊢
	: , : , :
178	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
179	theorem		⊢
	proveit.numbers.number_sets.real_numbers.real_pos_within_real_nonzero
180	instantiation	181, 182, 183	⊢
	: , :
181	theorem		⊢
	proveit.numbers.multiplication.mult_real_pos_closure_bin
182	instantiation	200, 184, 185	⊢
	: , : , :
183	instantiation	186, 187, 188	⊢
	:
184	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_pos_within_real_pos
185	instantiation	200, 189, 190	⊢
	: , : , :
186	theorem		⊢
	proveit.numbers.number_sets.real_numbers.pos_real_is_real_pos
187	instantiation	191, 193, 194, 195	⊢
	: , : , :
188	instantiation	192, 193, 194, 195	⊢
	: , : , :
189	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nat_pos_within_rational_pos
190	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
191	theorem		⊢
	proveit.numbers.number_sets.real_numbers.all_in_interval_oc__is__real
192	theorem		⊢
	proveit.numbers.number_sets.real_numbers.interval_oc_lower_bound
193	theorem		⊢
	proveit.numbers.number_sets.real_numbers.zero_is_real
194	instantiation	200, 196, 197	⊢
	: , : , :
195	axiom		⊢
	proveit.physics.quantum.QPE._eps_in_interval
196	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
197	instantiation	200, 198, 199	⊢
	: , : , :
198	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
199	instantiation	200, 201, 202	⊢
	: , : , :
200	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
201	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
202	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
*equality replacement requirements