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	⊢
	: , :
1	theorem		⊢
	proveit.numbers.negation.negated_weak_bound
2	instantiation	7, 227, 5, 6	⊢
	: , :
3	instantiation	7, 227, 8, 9	⊢
	: , :
4	instantiation	10, 11, 26, 12, 13	⊢
	: , : , :
5	instantiation	14, 218, 75	⊢
	: , :
6	instantiation	15, 16	⊢
	:
7	theorem		⊢
	proveit.numbers.division.div_real_closure
8	instantiation	246, 209, 26	⊢
	: , : , :
9	instantiation	152, 17	⊢
	:
10	theorem		⊢
	proveit.numbers.division.weak_div_from_denom_bound__all_pos
11	instantiation	246, 18, 19	⊢
	: , : , :
12	instantiation	246, 233, 25	⊢
	: , : , :
13	instantiation	20, 218, 21, 75, 22, 23	⊢
	: , : , :
14	theorem		⊢
	proveit.numbers.multiplication.mult_real_closure_bin
15	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nonzero_if_in_rational_nonzero
16	instantiation	246, 24, 25	⊢
	: , : , :
17	instantiation	246, 162, 26	⊢
	: , : , :
18	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_nonneg_within_real_nonneg
19	instantiation	246, 27, 248	⊢
	: , : , :
20	theorem		⊢
	proveit.numbers.multiplication.weak_bound_via_right_factor_bound
21	instantiation	66, 227, 72	⊢
	: , :
22	instantiation	53, 211, 28, 122, 29, 30*	⊢
	: , : , :
23	instantiation	31, 245	⊢
	:
24	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.rational_pos_within_rational_nonzero
25	instantiation	32, 234, 33	⊢
	: , :
26	instantiation	186, 221, 34	⊢
	: , :
27	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nat_within_rational_nonneg
28	instantiation	246, 209, 114	⊢
	: , : , :
29	instantiation	35, 218, 100, 36, 189, 37, 38*	⊢
	: , : , :
30	instantiation	166, 39, 40	⊢
	: , : , :
31	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.natural_lower_bound
32	theorem		⊢
	proveit.numbers.multiplication.mult_rational_pos_closure_bin
33	instantiation	41, 84, 42	⊢
	:
34	instantiation	169, 220, 126	⊢
	: , :
35	theorem		⊢
	proveit.numbers.exponentiation.exp_monotonicity_large_base_less_eq
36	instantiation	66, 56, 54	⊢
	: , :
37	instantiation	43, 44, 45	⊢
	: , : , :
38	instantiation	46, 221, 114, 158	⊢
	: , :
39	instantiation	108, 181, 245, 248, 182, 47, 208, 61, 201	⊢
	: , : , : , : , : , :
40	instantiation	166, 48, 49	⊢
	: , : , :
41	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.pos_rational_is_rational_pos
42	instantiation	50, 51	⊢
	: , :
43	theorem		⊢
	proveit.numbers.ordering.transitivity_less_eq_less_eq
44	instantiation	52, 100	⊢
	:
45	instantiation	53, 54, 55, 56, 57, 58*	⊢
	: , : , :
46	theorem		⊢
	proveit.numbers.exponentiation.exponent_log_with_same_base
47	instantiation	197	⊢
	: , :
48	instantiation	59, 248, 181, 182, 208, 61, 201	⊢
	: , : , : , : , : , : , :
49	instantiation	110, 181, 245, 248, 182, 60, 208, 201, 61, 124*	⊢
	: , : , : , : , : , :
50	theorem		⊢
	proveit.numbers.addition.subtraction.pos_difference
51	instantiation	62, 211, 218, 63, 64, 124*, 65*	⊢
	: , : , :
52	theorem		⊢
	proveit.numbers.rounding.ceil_x_ge_x
53	theorem		⊢
	proveit.numbers.addition.weak_bound_via_left_term_bound
54	instantiation	223, 128	⊢
	:
55	instantiation	66, 128, 67	⊢
	: , :
56	instantiation	136, 137, 172	⊢
	: , : , :
57	axiom		⊢
	proveit.physics.quantum.QPE._t_req
58	instantiation	68, 69, 70, 71	⊢
	: , : , : , :
59	theorem		⊢
	proveit.numbers.addition.leftward_commutation
60	instantiation	197	⊢
	: , :
61	instantiation	246, 217, 72	⊢
	: , : , :
62	theorem		⊢
	proveit.numbers.addition.strong_bound_via_left_term_bound
63	instantiation	246, 236, 73	⊢
	: , : , :
64	instantiation	74, 218, 75, 76, 77	⊢
	: , : , :
65	instantiation	166, 78, 79	⊢
	: , : , :
66	theorem		⊢
	proveit.numbers.addition.add_real_closure_bin
67	instantiation	246, 236, 80	⊢
	: , : , :
68	theorem		⊢
	proveit.logic.equality.four_chain_transitivity
69	instantiation	166, 81, 82	⊢
	: , : , :
70	instantiation	119	⊢
	:
71	instantiation	83, 101	⊢
	: , :
72	instantiation	246, 209, 126	⊢
	: , : , :
73	instantiation	93, 84, 231	⊢
	: , :
74	theorem		⊢
	proveit.numbers.ordering.less_eq_add_right_strong
75	instantiation	246, 236, 84	⊢
	: , : , :
76	theorem		⊢
	proveit.physics.quantum.QPE._e_value_ge_two
77	instantiation	85, 242	⊢
	:
78	instantiation	164, 86	⊢
	: , : , :
79	instantiation	166, 87, 88	⊢
	: , : , :
80	instantiation	246, 243, 89	⊢
	: , : , :
81	instantiation	164, 90	⊢
	: , : , :
82	instantiation	166, 91, 92	⊢
	: , : , :
83	theorem		⊢
	proveit.logic.equality.equals_reversal
84	instantiation	93, 131, 94	⊢
	: , :
85	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.natural_pos_is_pos
86	instantiation	166, 95, 96	⊢
	: , : , :
87	instantiation	108, 181, 245, 248, 182, 97, 112, 179, 201	⊢
	: , : , : , : , : , :
88	instantiation	98, 179, 112, 99	⊢
	: , : , :
89	instantiation	147, 100	⊢
	:
90	instantiation	164, 101	⊢
	: , : , :
91	instantiation	108, 181, 245, 248, 182, 102, 117, 105, 103	⊢
	: , : , : , : , : , :
92	instantiation	104, 117, 105, 106	⊢
	: , : , :
93	theorem		⊢
	proveit.numbers.addition.add_rational_closure_bin
94	instantiation	246, 243, 107	⊢
	: , : , :
95	instantiation	108, 181, 245, 248, 182, 109, 112, 201, 208	⊢
	: , : , : , : , : , :
96	instantiation	110, 248, 245, 181, 111, 182, 112, 201, 208, 113*	⊢
	: , : , : , : , : , :
97	instantiation	197	⊢
	: , :
98	theorem		⊢
	proveit.numbers.addition.subtraction.add_cancel_triple_23
99	instantiation	119	⊢
	:
100	instantiation	156, 221, 114, 158	⊢
	: , :
101	instantiation	164, 115	⊢
	: , : , :
102	instantiation	197	⊢
	: , :
103	instantiation	116, 117	⊢
	:
104	theorem		⊢
	proveit.numbers.addition.subtraction.add_cancel_triple_13
105	instantiation	246, 217, 118	⊢
	: , : , :
106	instantiation	119	⊢
	:
107	instantiation	246, 120, 121	⊢
	: , : , :
108	theorem		⊢
	proveit.numbers.addition.disassociation
109	instantiation	197	⊢
	: , :
110	theorem		⊢
	proveit.numbers.addition.association
111	instantiation	197	⊢
	: , :
112	instantiation	246, 217, 122	⊢
	: , : , :
113	instantiation	123, 124, 125	⊢
	: , : , :
114	instantiation	169, 221, 126	⊢
	: , :
115	instantiation	164, 127	⊢
	: , : , :
116	theorem		⊢
	proveit.numbers.negation.complex_closure
117	instantiation	246, 217, 128	⊢
	: , : , :
118	instantiation	246, 236, 129	⊢
	: , : , :
119	axiom		⊢
	proveit.logic.equality.equals_reflexivity
120	theorem		⊢
	proveit.numbers.number_sets.integers.neg_int_within_int
121	instantiation	130, 240	⊢
	:
122	instantiation	246, 236, 131	⊢
	: , : , :
123	theorem		⊢
	proveit.logic.equality.sub_right_side_into
124	instantiation	132, 179, 208, 133	⊢
	: , : , :
125	instantiation	134, 208, 201	⊢
	: , :
126	instantiation	219, 220, 163, 143	⊢
	: , :
127	instantiation	164, 135	⊢
	: , : , :
128	instantiation	136, 137, 191	⊢
	: , : , :
129	instantiation	246, 243, 138	⊢
	: , : , :
130	theorem		⊢
	proveit.numbers.negation.int_neg_closure
131	instantiation	246, 139, 140	⊢
	: , : , :
132	theorem		⊢
	proveit.numbers.addition.subtraction.subtract_from_add
133	theorem		⊢
	proveit.numbers.numerals.decimals.add_1_1
134	theorem		⊢
	proveit.numbers.addition.commutation
135	instantiation	141, 179, 142, 143, 144*	⊢
	: , :
136	theorem		⊢
	proveit.logic.sets.inclusion.unfold_subset_eq
137	instantiation	145, 146	⊢
	: , :
138	instantiation	147, 148	⊢
	:
139	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.rational_nonzero_within_rational
140	instantiation	149, 216, 150	⊢
	: , :
141	theorem		⊢
	proveit.numbers.division.div_as_mult
142	instantiation	246, 217, 151	⊢
	: , : , :
143	instantiation	152, 153	⊢
	:
144	instantiation	166, 154, 155	⊢
	: , : , :
145	theorem		⊢
	proveit.logic.sets.inclusion.relax_proper_subset
146	theorem		⊢
	proveit.numbers.number_sets.real_numbers.nat_pos_within_real
147	axiom		⊢
	proveit.numbers.rounding.ceil_is_an_int
148	instantiation	156, 221, 157, 158	⊢
	: , :
149	theorem		⊢
	proveit.numbers.exponentiation.exp_rational_nonzero_closure
150	instantiation	159, 160, 161	⊢
	: , :
151	instantiation	246, 209, 163	⊢
	: , : , :
152	theorem		⊢
	proveit.numbers.number_sets.real_numbers.nonzero_if_in_real_nonzero
153	instantiation	246, 162, 163	⊢
	: , : , :
154	instantiation	164, 165	⊢
	: , : , :
155	instantiation	166, 167, 168	⊢
	: , : , :
156	theorem		⊢
	proveit.numbers.logarithms.log_real_pos_real_closure
157	instantiation	169, 221, 170	⊢
	: , :
158	instantiation	192, 171	⊢
	: , :
159	theorem		⊢
	proveit.numbers.addition.add_int_closure_bin
160	instantiation	246, 190, 172	⊢
	: , : , :
161	instantiation	173, 174	⊢
	:
162	theorem		⊢
	proveit.numbers.number_sets.real_numbers.real_pos_within_real_nonzero
163	instantiation	186, 221, 203	⊢
	: , :
164	axiom		⊢
	proveit.logic.equality.substitution
165	instantiation	175, 208, 200, 211, 222, 176, 177*	⊢
	: , : , :
166	axiom		⊢
	proveit.logic.equality.equals_transitivity
167	instantiation	178, 248, 245, 181, 183, 182, 179, 184, 185	⊢
	: , : , : , : , : , :
168	instantiation	180, 181, 245, 182, 183, 184, 185	⊢
	: , : , : , :
169	theorem		⊢
	proveit.numbers.addition.add_real_pos_closure_bin
170	instantiation	186, 210, 187	⊢
	: , :
171	instantiation	188, 248, 245, 189	⊢
	: , :
172	axiom		⊢
	proveit.physics.quantum.QPE._t_in_natural_pos
173	theorem		⊢
	proveit.numbers.negation.int_closure
174	instantiation	246, 190, 191	⊢
	: , : , :
175	theorem		⊢
	proveit.numbers.exponentiation.real_power_of_product
176	instantiation	192, 193	⊢
	: , :
177	instantiation	194, 195, 240, 196*	⊢
	: , :
178	theorem		⊢
	proveit.numbers.multiplication.disassociation
179	instantiation	246, 217, 227	⊢
	: , : , :
180	theorem		⊢
	proveit.numbers.multiplication.elim_one_any
181	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
182	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
183	instantiation	197	⊢
	: , :
184	instantiation	246, 217, 198	⊢
	: , : , :
185	instantiation	199, 200, 201	⊢
	: , :
186	theorem		⊢
	proveit.numbers.multiplication.mult_real_pos_closure_bin
187	instantiation	202, 203, 211	⊢
	: , :
188	theorem		⊢
	proveit.numbers.ordering.less_is_not_eq_nat
189	theorem		⊢
	proveit.numbers.numerals.decimals.less_1_2
190	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_int
191	axiom		⊢
	proveit.physics.quantum.QPE._n_in_natural_pos
192	theorem		⊢
	proveit.logic.equality.not_equals_symmetry
193	instantiation	204, 226, 213, 214	⊢
	: , :
194	theorem		⊢
	proveit.numbers.exponentiation.neg_power_as_div
195	instantiation	246, 205, 206	⊢
	: , : , :
196	instantiation	207, 208	⊢
	:
197	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
198	instantiation	246, 209, 210	⊢
	: , : , :
199	theorem		⊢
	proveit.numbers.exponentiation.exp_complex_closure
200	instantiation	246, 217, 213	⊢
	: , : , :
201	instantiation	246, 217, 211	⊢
	: , : , :
202	theorem		⊢
	proveit.numbers.exponentiation.exp_real_pos_closure
203	instantiation	212, 213, 214	⊢
	:
204	theorem		⊢
	proveit.numbers.ordering.less_is_not_eq
205	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero
206	instantiation	246, 215, 216	⊢
	: , : , :
207	theorem		⊢
	proveit.numbers.exponentiation.complex_x_to_first_power_is_x
208	instantiation	246, 217, 218	⊢
	: , : , :
209	theorem		⊢
	proveit.numbers.number_sets.real_numbers.real_pos_within_real
210	instantiation	219, 220, 221, 222	⊢
	: , :
211	instantiation	223, 227	⊢
	:
212	theorem		⊢
	proveit.numbers.number_sets.real_numbers.pos_real_is_real_pos
213	instantiation	224, 226, 227, 228	⊢
	: , : , :
214	instantiation	225, 226, 227, 228	⊢
	: , : , :
215	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero
216	instantiation	246, 229, 230	⊢
	: , : , :
217	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
218	instantiation	246, 236, 231	⊢
	: , : , :
219	theorem		⊢
	proveit.numbers.division.div_real_pos_closure
220	instantiation	246, 233, 232	⊢
	: , : , :
221	instantiation	246, 233, 234	⊢
	: , : , :
222	instantiation	235, 242	⊢
	:
223	theorem		⊢
	proveit.numbers.negation.real_closure
224	theorem		⊢
	proveit.numbers.number_sets.real_numbers.all_in_interval_oc__is__real
225	theorem		⊢
	proveit.numbers.number_sets.real_numbers.interval_oc_lower_bound
226	theorem		⊢
	proveit.numbers.number_sets.real_numbers.zero_is_real
227	instantiation	246, 236, 237	⊢
	: , : , :
228	axiom		⊢
	proveit.physics.quantum.QPE._eps_in_interval
229	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
230	instantiation	246, 238, 242	⊢
	: , : , :
231	instantiation	246, 243, 239	⊢
	: , : , :
232	instantiation	246, 241, 240	⊢
	: , : , :
233	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_pos_within_real_pos
234	instantiation	246, 241, 242	⊢
	: , : , :
235	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos
236	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
237	instantiation	246, 243, 244	⊢
	: , : , :
238	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
239	instantiation	246, 247, 245	⊢
	: , : , :
240	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
241	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nat_pos_within_rational_pos
242	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
243	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
244	instantiation	246, 247, 248	⊢
	: , : , :
245	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
246	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
247	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
248	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
*equality replacement requirements