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, 4, 5, 6	⊢
	: , : , :
1	reference	27	⊢
2	reference	165	⊢
3	instantiation	78, 7, 8	⊢
	: , :
4	reference	212	⊢
5	theorem		⊢
	proveit.physics.quantum.QPE._e_value_ge_two
6	instantiation	151, 220	⊢
	:
7	instantiation	9, 165, 10	⊢
	: , :
8	instantiation	140, 212	⊢
	:
9	theorem		⊢
	proveit.numbers.exponentiation.exp_real_closure_nat_power
10	instantiation	11, 12, 13	⊢
	:
11	theorem		⊢
	proveit.numbers.number_sets.integers.nonneg_int_is_natural
12	instantiation	14, 15, 16	⊢
	: , :
13	instantiation	17, 18	⊢
	: , :
14	theorem		⊢
	proveit.numbers.addition.add_int_closure_bin
15	instantiation	218, 19, 101	⊢
	: , : , :
16	instantiation	218, 20, 21	⊢
	: , : , :
17	theorem		⊢
	proveit.numbers.addition.subtraction.nonneg_difference
18	instantiation	59, 63, 165, 22, 23, 24*, 25*	⊢
	: , : , :
19	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_int
20	theorem		⊢
	proveit.numbers.number_sets.integers.neg_int_within_int
21	instantiation	26, 157	⊢
	:
22	instantiation	78, 28, 165	⊢
	: , :
23	instantiation	27, 165, 28, 29, 135	⊢
	: , : , :
24	instantiation	146, 30, 31	⊢
	: , : , :
25	instantiation	146, 32, 33	⊢
	: , : , :
26	theorem		⊢
	proveit.numbers.negation.int_neg_closure
27	theorem		⊢
	proveit.numbers.ordering.less_eq_add_right
28	instantiation	78, 80, 118	⊢
	: , :
29	instantiation	44, 34, 35	⊢
	: , : , :
30	instantiation	92, 220, 191, 93, 50, 94, 152, 98, 51	⊢
	: , : , : , : , : , :
31	instantiation	97, 152, 98, 68	⊢
	: , : , :
32	instantiation	125, 36	⊢
	: , : , :
33	instantiation	37, 38, 39, 40	⊢
	: , : , : , :
34	instantiation	41, 217, 57, 42, 43*	⊢
	: , :
35	instantiation	44, 45, 46	⊢
	: , : , :
36	instantiation	92, 93, 191, 220, 94, 67, 70, 96, 152	⊢
	: , : , : , : , : , :
37	theorem		⊢
	proveit.logic.equality.four_chain_transitivity
38	instantiation	92, 93, 48, 220, 94, 49, 70, 96, 152, 47	⊢
	: , : , : , : , : , :
39	instantiation	92, 48, 191, 93, 49, 50, 94, 70, 96, 152, 98, 51	⊢
	: , : , : , : , : , :
40	instantiation	146, 52, 53	⊢
	: , : , :
41	theorem		⊢
	proveit.numbers.rounding.ceil_of_real_above_int
42	instantiation	54, 200, 74, 55	⊢
	: , :
43	theorem		⊢
	proveit.numbers.numerals.decimals.add_1_1
44	theorem		⊢
	proveit.numbers.ordering.transitivity_less_eq_less_eq
45	instantiation	56, 57, 169, 58	⊢
	: , :
46	instantiation	59, 118, 60, 80, 61, 62*	⊢
	: , : , :
47	instantiation	218, 180, 63	⊢
	: , : , :
48	theorem		⊢
	proveit.numbers.numerals.decimals.nat3
49	instantiation	64	⊢
	: , : , :
50	instantiation	171	⊢
	: , :
51	instantiation	65, 152	⊢
	:
52	instantiation	66, 191, 220, 93, 67, 94, 70, 96, 152, 98, 68	⊢
	: , : , : , : , : , : , : , :
53	instantiation	69, 98, 70, 100	⊢
	: , : , :
54	theorem		⊢
	proveit.numbers.logarithms.log_base_large_a_greater_one
55	instantiation	71, 192, 72	⊢
	: , :
56	theorem		⊢
	proveit.numbers.rounding.ceil_increasing_less_eq
57	instantiation	175, 200, 74, 177	⊢
	: , :
58	instantiation	73, 200, 74, 176, 75, 192	⊢
	: , : , :
59	theorem		⊢
	proveit.numbers.addition.weak_bound_via_left_term_bound
60	instantiation	78, 141, 119	⊢
	: , :
61	axiom		⊢
	proveit.physics.quantum.QPE._t_req
62	instantiation	146, 76, 77	⊢
	: , : , :
63	instantiation	78, 141, 79	⊢
	: , :
64	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_3_typical_eq
65	theorem		⊢
	proveit.numbers.negation.complex_closure
66	theorem		⊢
	proveit.numbers.addition.subtraction.add_cancel_general
67	instantiation	171	⊢
	: , :
68	instantiation	120	⊢
	:
69	theorem		⊢
	proveit.numbers.addition.subtraction.add_cancel_triple_32
70	instantiation	218, 180, 80	⊢
	: , : , :
71	theorem		⊢
	proveit.logic.booleans.conjunction.and_if_both
72	instantiation	81, 165, 82, 83, 84, 85*, 86*	⊢
	: , : , :
73	theorem		⊢
	proveit.numbers.logarithms.log_increasing_less_eq
74	instantiation	218, 202, 87	⊢
	: , : , :
75	instantiation	88, 165, 159, 89, 90, 91*	⊢
	: , : , :
76	instantiation	92, 93, 191, 220, 94, 95, 98, 99, 96	⊢
	: , : , : , : , : , :
77	instantiation	97, 98, 99, 100	⊢
	: , : , :
78	theorem		⊢
	proveit.numbers.addition.add_real_closure_bin
79	instantiation	140, 165	⊢
	:
80	instantiation	155, 156, 101	⊢
	: , : , :
81	theorem		⊢
	proveit.numbers.addition.strong_bound_via_left_term_bound
82	instantiation	102, 159, 211	⊢
	: , :
83	instantiation	218, 214, 103	⊢
	: , : , :
84	instantiation	104, 159, 211, 212, 105, 106	⊢
	: , : , :
85	instantiation	146, 107, 108	⊢
	: , : , :
86	instantiation	146, 109, 110	⊢
	: , : , :
87	instantiation	186, 111, 203	⊢
	: , :
88	theorem		⊢
	proveit.numbers.addition.weak_bound_via_right_term_bound
89	instantiation	218, 112, 183	⊢
	: , : , :
90	instantiation	113, 114, 198, 200, 115	⊢
	: , : , :
91	instantiation	127, 181, 217, 128*, 116*, 117*	⊢
	: , : , : , :
92	theorem		⊢
	proveit.numbers.addition.disassociation
93	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
94	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
95	instantiation	171	⊢
	: , :
96	instantiation	218, 180, 118	⊢
	: , : , :
97	theorem		⊢
	proveit.numbers.addition.subtraction.add_cancel_triple_13
98	instantiation	218, 180, 141	⊢
	: , : , :
99	instantiation	218, 180, 119	⊢
	: , : , :
100	instantiation	120	⊢
	:
101	axiom		⊢
	proveit.physics.quantum.QPE._t_in_natural_pos
102	theorem		⊢
	proveit.numbers.multiplication.mult_real_closure_bin
103	instantiation	121, 170, 215	⊢
	: , :
104	theorem		⊢
	proveit.numbers.multiplication.strong_bound_via_right_factor_bound
105	theorem		⊢
	proveit.numbers.numerals.decimals.less_0_1
106	instantiation	122, 179	⊢
	:
107	instantiation	125, 123	⊢
	: , : , :
108	instantiation	124, 152	⊢
	:
109	instantiation	125, 126	⊢
	: , : , :
110	instantiation	127, 217, 181, 128*, 129*, 136*	⊢
	: , : , : , :
111	instantiation	218, 207, 130	⊢
	: , : , :
112	theorem		⊢
	proveit.numbers.number_sets.real_numbers.real_pos_within_real
113	theorem		⊢
	proveit.numbers.division.weak_div_from_denom_bound__all_pos
114	instantiation	218, 131, 132	⊢
	: , : , :
115	instantiation	133, 165, 205, 212, 134, 135, 136*	⊢
	: , : , :
116	instantiation	146, 137, 138	⊢
	: , : , :
117	instantiation	139, 152	⊢
	:
118	instantiation	140, 141	⊢
	:
119	instantiation	218, 214, 142	⊢
	: , : , :
120	axiom		⊢
	proveit.logic.equality.equals_reflexivity
121	theorem		⊢
	proveit.numbers.multiplication.mult_rational_closure_bin
122	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.positive_if_in_rational_pos
123	instantiation	143, 144	⊢
	:
124	theorem		⊢
	proveit.numbers.addition.elim_zero_left
125	axiom		⊢
	proveit.logic.equality.substitution
126	instantiation	172, 144	⊢
	:
127	theorem		⊢
	proveit.numbers.addition.rational_pair_addition
128	instantiation	145, 152	⊢
	:
129	instantiation	146, 147, 148	⊢
	: , : , :
130	theorem		⊢
	proveit.numbers.numerals.decimals.posnat5
131	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_nonneg_within_real_nonneg
132	instantiation	218, 149, 220	⊢
	: , : , :
133	theorem		⊢
	proveit.numbers.multiplication.weak_bound_via_right_factor_bound
134	instantiation	150, 211, 212, 213	⊢
	: , : , :
135	instantiation	151, 191	⊢
	:
136	instantiation	172, 152	⊢
	:
137	instantiation	160, 191, 153, 154, 164, 163	⊢
	: , : , : , :
138	theorem		⊢
	proveit.numbers.numerals.decimals.add_4_1
139	theorem		⊢
	proveit.numbers.multiplication.elim_one_left
140	theorem		⊢
	proveit.numbers.negation.real_closure
141	instantiation	155, 156, 157	⊢
	: , : , :
142	instantiation	218, 216, 158	⊢
	: , : , :
143	theorem		⊢
	proveit.numbers.multiplication.mult_zero_right
144	instantiation	218, 180, 159	⊢
	: , : , :
145	theorem		⊢
	proveit.numbers.division.frac_one_denom
146	axiom		⊢
	proveit.logic.equality.equals_transitivity
147	instantiation	160, 191, 161, 162, 163, 164	⊢
	: , : , : , :
148	theorem		⊢
	proveit.numbers.numerals.decimals.add_1_4
149	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nat_within_rational_nonneg
150	theorem		⊢
	proveit.numbers.number_sets.real_numbers.interval_oc_upper_bound
151	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.natural_lower_bound
152	instantiation	218, 180, 165	⊢
	: , : , :
153	instantiation	171	⊢
	: , :
154	instantiation	171	⊢
	: , :
155	theorem		⊢
	proveit.logic.sets.inclusion.unfold_subset_eq
156	instantiation	166, 167	⊢
	: , :
157	axiom		⊢
	proveit.physics.quantum.QPE._n_in_natural_pos
158	instantiation	168, 169	⊢
	:
159	instantiation	218, 214, 170	⊢
	: , : , :
160	axiom		⊢
	proveit.core_expr_types.operations.operands_substitution
161	instantiation	171	⊢
	: , :
162	instantiation	171	⊢
	: , :
163	instantiation	172, 173	⊢
	:
164	theorem		⊢
	proveit.numbers.numerals.decimals.mult_2_2
165	instantiation	218, 214, 174	⊢
	: , : , :
166	theorem		⊢
	proveit.logic.sets.inclusion.relax_proper_subset
167	theorem		⊢
	proveit.numbers.number_sets.real_numbers.nat_pos_within_real
168	axiom		⊢
	proveit.numbers.rounding.ceil_is_an_int
169	instantiation	175, 200, 176, 177	⊢
	: , :
170	instantiation	218, 178, 179	⊢
	: , : , :
171	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
172	theorem		⊢
	proveit.numbers.multiplication.elim_one_right
173	instantiation	218, 180, 212	⊢
	: , : , :
174	instantiation	218, 216, 181	⊢
	: , : , :
175	theorem		⊢
	proveit.numbers.logarithms.log_real_pos_real_closure
176	instantiation	182, 200, 183	⊢
	: , :
177	instantiation	184, 185	⊢
	: , :
178	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.rational_pos_within_rational
179	instantiation	186, 193, 203	⊢
	: , :
180	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
181	instantiation	218, 219, 191	⊢
	: , : , :
182	theorem		⊢
	proveit.numbers.addition.add_real_pos_closure_bin
183	instantiation	187, 188, 198, 189	⊢
	: , :
184	theorem		⊢
	proveit.logic.equality.not_equals_symmetry
185	instantiation	190, 220, 191, 192	⊢
	: , :
186	theorem		⊢
	proveit.numbers.division.div_rational_pos_closure
187	theorem		⊢
	proveit.numbers.division.div_real_pos_closure
188	instantiation	218, 202, 193	⊢
	: , : , :
189	instantiation	194, 195	⊢
	:
190	theorem		⊢
	proveit.numbers.ordering.less_is_not_eq_nat
191	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
192	theorem		⊢
	proveit.numbers.numerals.decimals.less_1_2
193	instantiation	218, 207, 196	⊢
	: , : , :
194	theorem		⊢
	proveit.numbers.number_sets.real_numbers.nonzero_if_in_real_nonzero
195	instantiation	218, 197, 198	⊢
	: , : , :
196	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
197	theorem		⊢
	proveit.numbers.number_sets.real_numbers.real_pos_within_real_nonzero
198	instantiation	199, 200, 201	⊢
	: , :
199	theorem		⊢
	proveit.numbers.multiplication.mult_real_pos_closure_bin
200	instantiation	218, 202, 203	⊢
	: , : , :
201	instantiation	204, 205, 206	⊢
	:
202	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_pos_within_real_pos
203	instantiation	218, 207, 208	⊢
	: , : , :
204	theorem		⊢
	proveit.numbers.number_sets.real_numbers.pos_real_is_real_pos
205	instantiation	209, 211, 212, 213	⊢
	: , : , :
206	instantiation	210, 211, 212, 213	⊢
	: , : , :
207	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nat_pos_within_rational_pos
208	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
209	theorem		⊢
	proveit.numbers.number_sets.real_numbers.all_in_interval_oc__is__real
210	theorem		⊢
	proveit.numbers.number_sets.real_numbers.interval_oc_lower_bound
211	theorem		⊢
	proveit.numbers.number_sets.real_numbers.zero_is_real
212	instantiation	218, 214, 215	⊢
	: , : , :
213	axiom		⊢
	proveit.physics.quantum.QPE._eps_in_interval
214	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
215	instantiation	218, 216, 217	⊢
	: , : , :
216	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
217	instantiation	218, 219, 220	⊢
	: , : , :
218	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
219	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
220	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
*equality replacement requirements