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	theorem		⊢
	proveit.logic.booleans.conjunction.and_if_both
2	instantiation	14, 4, 5	⊢
	: , : , :
3	instantiation	131, 6	⊢
	: , :
4	instantiation	7, 8, 76, 9, 57, 10*, 11*	⊢
	: , : , :
5	instantiation	12, 27, 39, 13	⊢
	: , : , :
6	instantiation	14, 15, 16	⊢
	: , : , :
7	theorem		⊢
	proveit.numbers.addition.strong_bound_via_left_term_bound
8	instantiation	17, 84, 18	⊢
	: , :
9	instantiation	292, 279, 19	⊢
	: , : , :
10	instantiation	233, 20, 21	⊢
	: , : , :
11	instantiation	149, 22, 23, 24	⊢
	: , : , : , :
12	theorem		⊢
	proveit.numbers.number_sets.real_numbers.interval_cc_lower_bound
13	instantiation	25, 27, 39, 28	⊢
	: , : , :
14	theorem		⊢
	proveit.numbers.ordering.transitivity_less_less_eq
15	instantiation	26, 27, 39, 28	⊢
	: , : , :
16	instantiation	146, 29, 58	⊢
	: , : , :
17	theorem		⊢
	proveit.numbers.addition.add_real_closure_bin
18	instantiation	258, 76	⊢
	:
19	instantiation	30, 31, 100	⊢
	: , :
20	instantiation	233, 32, 33	⊢
	: , : , :
21	instantiation	233, 34, 35	⊢
	: , : , :
22	instantiation	233, 36, 37	⊢
	: , : , :
23	instantiation	86	⊢
	:
24	instantiation	110, 38	⊢
	: , :
25	theorem		⊢
	proveit.numbers.number_sets.real_numbers.relax_IntervalCO
26	theorem		⊢
	proveit.numbers.number_sets.real_numbers.interval_co_upper_bound
27	instantiation	258, 39	⊢
	:
28	instantiation	40, 84, 209, 121, 41, 42*, 43*, 56*	⊢
	: , : , : , :
29	instantiation	146, 44, 74	⊢
	: , : , :
30	theorem		⊢
	proveit.numbers.addition.add_rational_closure_bin
31	instantiation	122, 124	⊢
	: , :
32	instantiation	252, 109	⊢
	: , : , :
33	instantiation	252, 59	⊢
	: , : , :
34	instantiation	60, 294, 291, 181, 61, 182, 85, 62, 64	⊢
	: , : , : , : , : , :
35	instantiation	45, 85, 62, 46	⊢
	: , : , :
36	instantiation	233, 47, 48	⊢
	: , : , :
37	instantiation	233, 49, 50	⊢
	: , : , :
38	instantiation	252, 51	⊢
	: , : , :
39	instantiation	292, 279, 52	⊢
	: , : , :
40	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rescale_interval_co_membership
41	theorem		⊢
	proveit.physics.quantum.QPE._scaled_delta_b_round_in_interval
42	instantiation	149, 53, 54, 55	⊢
	: , : , : , :
43	instantiation	260, 97, 184, 56*	⊢
	: , :
44	instantiation	131, 57	⊢
	: , :
45	theorem		⊢
	proveit.numbers.addition.subtraction.add_cancel_triple_13
46	instantiation	86	⊢
	:
47	instantiation	252, 58	⊢
	: , : , :
48	instantiation	252, 59	⊢
	: , : , :
49	instantiation	60, 294, 291, 181, 61, 182, 184, 62, 64	⊢
	: , : , : , : , : , :
50	instantiation	63, 184, 64, 65	⊢
	: , : , :
51	instantiation	233, 66, 67	⊢
	: , : , :
52	instantiation	155, 280, 68, 69	⊢
	: , :
53	instantiation	179, 294, 291, 181, 70, 182, 97, 268, 94	⊢
	: , : , : , : , : , :
54	instantiation	233, 71, 72	⊢
	: , : , :
55	instantiation	251, 94	⊢
	:
56	instantiation	233, 73, 74	⊢
	: , : , :
57	instantiation	75, 76, 77, 78, 79, 80	⊢
	: , : , :
58	instantiation	233, 81, 82	⊢
	: , : , :
59	instantiation	252, 83	⊢
	: , : , :
60	theorem		⊢
	proveit.numbers.addition.disassociation
61	instantiation	236	⊢
	: , :
62	instantiation	292, 281, 84	⊢
	: , : , :
63	theorem		⊢
	proveit.numbers.addition.subtraction.add_cancel_triple_12
64	instantiation	264, 85	⊢
	:
65	instantiation	86	⊢
	:
66	instantiation	252, 87	⊢
	: , : , :
67	instantiation	174, 261, 88, 89, 90*	⊢
	: , :
68	instantiation	292, 286, 91	⊢
	: , : , :
69	instantiation	259, 117	⊢
	:
70	instantiation	236	⊢
	: , :
71	instantiation	92, 181, 291, 294, 182, 93, 97, 268, 94	⊢
	: , : , : , : , : , :
72	instantiation	252, 95	⊢
	: , : , :
73	instantiation	96, 97, 184	⊢
	: , :
74	instantiation	133, 261, 207, 189, 152*, 111*	⊢
	: , : , : , :
75	theorem		⊢
	proveit.numbers.ordering.less_eq_add_right_strong
76	instantiation	292, 279, 98	⊢
	: , : , :
77	instantiation	99, 102	⊢
	: , :
78	instantiation	292, 279, 100	⊢
	: , : , :
79	instantiation	101, 102, 103, 104, 105	⊢
	: , : , :
80	instantiation	164, 123	⊢
	:
81	instantiation	252, 106	⊢
	: , : , :
82	instantiation	107, 287, 278, 108*	⊢
	: , : , : , :
83	instantiation	252, 109	⊢
	: , : , :
84	instantiation	258, 209	⊢
	:
85	instantiation	112, 184, 225	⊢
	: , :
86	axiom		⊢
	proveit.logic.equality.equals_reflexivity
87	instantiation	110, 111	⊢
	: , :
88	instantiation	112, 245, 268	⊢
	: , :
89	instantiation	113, 291, 114, 207, 189	⊢
	: , :
90	instantiation	233, 115, 116	⊢
	: , : , :
91	instantiation	292, 215, 117	⊢
	: , : , :
92	theorem		⊢
	proveit.numbers.multiplication.association
93	instantiation	236	⊢
	: , :
94	instantiation	292, 281, 118	⊢
	: , : , :
95	instantiation	146, 119, 120	⊢
	: , : , :
96	theorem		⊢
	proveit.numbers.multiplication.commutation
97	instantiation	292, 281, 121	⊢
	: , : , :
98	instantiation	122, 124, 125	⊢
	: , :
99	theorem		⊢
	proveit.numbers.multiplication.mult_real_closure_bin
100	instantiation	292, 154, 123	⊢
	: , : , :
101	theorem		⊢
	proveit.numbers.multiplication.weak_bound_via_right_factor_bound
102	instantiation	292, 279, 124	⊢
	: , : , :
103	instantiation	292, 279, 125	⊢
	: , : , :
104	instantiation	126, 127, 128, 129, 130	⊢
	: , : , :
105	instantiation	131, 132	⊢
	: , :
106	instantiation	133, 261, 207, 152*, 134*	⊢
	: , : , : , :
107	theorem		⊢
	proveit.numbers.addition.rational_pair_addition
108	instantiation	233, 135, 136	⊢
	: , : , :
109	instantiation	252, 137	⊢
	: , : , :
110	theorem		⊢
	proveit.logic.equality.equals_reversal
111	instantiation	138, 245, 267, 290, 208*	⊢
	: , : , :
112	theorem		⊢
	proveit.numbers.multiplication.mult_complex_closure_bin
113	theorem		⊢
	proveit.numbers.multiplication.mult_not_eq_zero
114	instantiation	236	⊢
	: , :
115	instantiation	252, 139	⊢
	: , : , :
116	instantiation	233, 140, 141	⊢
	: , : , :
117	instantiation	142, 291, 143	⊢
	: , :
118	instantiation	144, 145	⊢
	:
119	instantiation	146, 147, 148	⊢
	: , : , :
120	instantiation	149, 150, 151, 152	⊢
	: , : , : , :
121	instantiation	229, 271, 277, 177	⊢
	: , :
122	theorem		⊢
	proveit.numbers.multiplication.mult_rational_closure_bin
123	instantiation	197, 198, 153	⊢
	: , :
124	instantiation	292, 154, 165	⊢
	: , : , :
125	instantiation	155, 280, 156, 177	⊢
	: , :
126	theorem		⊢
	proveit.numbers.division.weak_div_from_denom_bound__all_pos
127	instantiation	292, 157, 158	⊢
	: , : , :
128	instantiation	292, 159, 199	⊢
	: , : , :
129	instantiation	292, 159, 160	⊢
	: , : , :
130	instantiation	161, 263, 271, 282, 162, 163, 208*	⊢
	: , : , :
131	theorem		⊢
	proveit.numbers.ordering.relax_less
132	instantiation	164, 165	⊢
	:
133	theorem		⊢
	proveit.numbers.division.prod_of_fracs
134	theorem		⊢
	proveit.numbers.numerals.decimals.mult_2_2
135	instantiation	217, 291, 166, 167, 168, 169	⊢
	: , : , : , :
136	instantiation	170, 171, 207, 261, 172*, 173*	⊢
	: , : , :
137	instantiation	174, 261, 268, 177, 175*	⊢
	: , :
138	theorem		⊢
	proveit.numbers.exponentiation.product_of_posnat_powers
139	instantiation	176, 245, 268, 241, 242, 177, 178*, 224*	⊢
	: , : , :
140	instantiation	179, 294, 291, 181, 183, 182, 261, 184, 225	⊢
	: , : , : , : , : , :
141	instantiation	180, 181, 291, 182, 183, 184, 225	⊢
	: , : , : , :
142	theorem		⊢
	proveit.numbers.exponentiation.exp_natpos_closure
143	instantiation	185, 294, 186	⊢
	: , :
144	theorem		⊢
	proveit.physics.quantum.QPE._delta_b_is_real
145	theorem		⊢
	proveit.physics.quantum.QPE._best_round_is_int
146	theorem		⊢
	proveit.logic.equality.sub_right_side_into
147	instantiation	187, 261, 188, 189	⊢
	: , : , : , : , :
148	instantiation	233, 190, 191	⊢
	: , : , :
149	theorem		⊢
	proveit.logic.equality.four_chain_transitivity
150	instantiation	252, 192	⊢
	: , : , :
151	instantiation	252, 192	⊢
	: , : , :
152	instantiation	272, 261	⊢
	:
153	instantiation	292, 216, 193	⊢
	: , : , :
154	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.rational_pos_within_rational
155	theorem		⊢
	proveit.numbers.division.div_rational_closure
156	instantiation	292, 286, 194	⊢
	: , : , :
157	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_nonneg_within_real_nonneg
158	instantiation	292, 195, 294	⊢
	: , : , :
159	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_pos_within_real_pos
160	instantiation	292, 216, 284	⊢
	: , : , :
161	theorem		⊢
	proveit.numbers.exponentiation.exp_monotonicity_large_base_less_eq
162	theorem		⊢
	proveit.numbers.numerals.decimals.less_1_2
163	instantiation	196, 290	⊢
	:
164	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.positive_if_in_rational_pos
165	instantiation	197, 198, 199	⊢
	: , :
166	instantiation	236	⊢
	: , :
167	instantiation	236	⊢
	: , :
168	instantiation	233, 200, 201	⊢
	: , : , :
169	theorem		⊢
	proveit.numbers.numerals.decimals.mult_4_4
170	theorem		⊢
	proveit.numbers.division.frac_cancel_left
171	instantiation	292, 226, 202	⊢
	: , : , :
172	instantiation	272, 203	⊢
	:
173	theorem		⊢
	proveit.numbers.numerals.decimals.mult_8_2
174	theorem		⊢
	proveit.numbers.division.div_as_mult
175	instantiation	233, 204, 205	⊢
	: , : , :
176	theorem		⊢
	proveit.numbers.exponentiation.real_power_of_product
177	instantiation	259, 284	⊢
	:
178	instantiation	206, 207, 267, 208*	⊢
	: , :
179	theorem		⊢
	proveit.numbers.multiplication.disassociation
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	236	⊢
	: , :
184	instantiation	292, 281, 209	⊢
	: , : , :
185	theorem		⊢
	proveit.numbers.addition.add_nat_closure_bin
186	instantiation	292, 210, 290	⊢
	: , : , :
187	theorem		⊢
	proveit.numbers.division.mult_frac_cancel_denom_left
188	instantiation	292, 226, 211	⊢
	: , : , :
189	instantiation	292, 226, 212	⊢
	: , : , :
190	instantiation	252, 213	⊢
	: , : , :
191	instantiation	252, 214	⊢
	: , : , :
192	instantiation	254, 261	⊢
	:
193	theorem		⊢
	proveit.numbers.numerals.decimals.posnat4
194	instantiation	292, 215, 284	⊢
	: , : , :
195	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nat_within_rational_nonneg
196	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.natural_pos_lower_bound
197	theorem		⊢
	proveit.numbers.division.div_rational_pos_closure
198	instantiation	292, 216, 267	⊢
	: , : , :
199	instantiation	292, 216, 276	⊢
	: , : , :
200	instantiation	217, 291, 218, 219, 220, 221	⊢
	: , : , : , :
201	theorem		⊢
	proveit.numbers.numerals.decimals.add_4_4
202	instantiation	292, 247, 222	⊢
	: , : , :
203	instantiation	292, 281, 223	⊢
	: , : , :
204	instantiation	252, 224	⊢
	: , : , :
205	instantiation	251, 225	⊢
	:
206	theorem		⊢
	proveit.numbers.exponentiation.neg_power_as_div
207	instantiation	292, 226, 227	⊢
	: , : , :
208	instantiation	228, 245	⊢
	:
209	instantiation	229, 271, 263, 242	⊢
	: , :
210	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nat_pos_within_nat
211	instantiation	292, 247, 230	⊢
	: , : , :
212	instantiation	292, 247, 231	⊢
	: , : , :
213	instantiation	252, 232	⊢
	: , : , :
214	instantiation	233, 234, 235	⊢
	: , : , :
215	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_int
216	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nat_pos_within_rational_pos
217	axiom		⊢
	proveit.core_expr_types.operations.operands_substitution
218	instantiation	236	⊢
	: , :
219	instantiation	236	⊢
	: , :
220	instantiation	251, 237	⊢
	:
221	instantiation	272, 237	⊢
	:
222	instantiation	292, 265, 238	⊢
	: , : , :
223	instantiation	292, 279, 239	⊢
	: , : , :
224	instantiation	240, 245, 282, 241, 242, 243*	⊢
	: , : , :
225	instantiation	244, 245, 246	⊢
	: , :
226	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero
227	instantiation	292, 247, 248	⊢
	: , : , :
228	theorem		⊢
	proveit.numbers.exponentiation.complex_x_to_first_power_is_x
229	theorem		⊢
	proveit.numbers.division.div_real_closure
230	instantiation	292, 265, 249	⊢
	: , : , :
231	instantiation	292, 265, 250	⊢
	: , : , :
232	instantiation	251, 268	⊢
	:
233	axiom		⊢
	proveit.logic.equality.equals_transitivity
234	instantiation	252, 253	⊢
	: , : , :
235	instantiation	254, 268	⊢
	:
236	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
237	instantiation	292, 281, 255	⊢
	: , : , :
238	instantiation	292, 275, 256	⊢
	: , : , :
239	instantiation	292, 286, 257	⊢
	: , : , :
240	theorem		⊢
	proveit.numbers.exponentiation.real_power_of_real_power
241	instantiation	258, 271	⊢
	:
242	instantiation	259, 276	⊢
	:
243	instantiation	260, 273, 261, 262*	⊢
	: , :
244	theorem		⊢
	proveit.numbers.exponentiation.exp_complex_closure
245	instantiation	292, 281, 263	⊢
	: , : , :
246	instantiation	264, 273	⊢
	:
247	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero
248	instantiation	292, 265, 266	⊢
	: , : , :
249	instantiation	292, 275, 267	⊢
	: , : , :
250	instantiation	292, 275, 284	⊢
	: , : , :
251	theorem		⊢
	proveit.numbers.multiplication.elim_one_left
252	axiom		⊢
	proveit.logic.equality.substitution
253	instantiation	272, 268	⊢
	:
254	theorem		⊢
	proveit.numbers.division.frac_one_denom
255	instantiation	292, 279, 269	⊢
	: , : , :
256	theorem		⊢
	proveit.numbers.numerals.decimals.posnat8
257	instantiation	292, 293, 270	⊢
	: , : , :
258	theorem		⊢
	proveit.numbers.negation.real_closure
259	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos
260	theorem		⊢
	proveit.numbers.multiplication.mult_neg_right
261	instantiation	292, 281, 271	⊢
	: , : , :
262	instantiation	272, 273	⊢
	:
263	instantiation	292, 279, 274	⊢
	: , : , :
264	theorem		⊢
	proveit.numbers.negation.complex_closure
265	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
266	instantiation	292, 275, 276	⊢
	: , : , :
267	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
268	instantiation	292, 281, 277	⊢
	: , : , :
269	instantiation	292, 286, 278	⊢
	: , : , :
270	theorem		⊢
	proveit.numbers.numerals.decimals.nat8
271	instantiation	292, 279, 280	⊢
	: , : , :
272	theorem		⊢
	proveit.numbers.multiplication.elim_one_right
273	instantiation	292, 281, 282	⊢
	: , : , :
274	instantiation	292, 286, 283	⊢
	: , : , :
275	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
276	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
277	instantiation	288, 289, 284	⊢
	: , : , :
278	instantiation	292, 293, 285	⊢
	: , : , :
279	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
280	instantiation	292, 286, 287	⊢
	: , : , :
281	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
282	instantiation	288, 289, 290	⊢
	: , : , :
283	instantiation	292, 293, 291	⊢
	: , : , :
284	theorem		⊢
	proveit.physics.quantum.QPE._two_pow_t_is_nat_pos
285	theorem		⊢
	proveit.numbers.numerals.decimals.nat4
286	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
287	instantiation	292, 293, 294	⊢
	: , : , :
288	theorem		⊢
	proveit.logic.sets.inclusion.unfold_subset_eq
289	instantiation	295, 296	⊢
	: , :
290	axiom		⊢
	proveit.physics.quantum.QPE._t_in_natural_pos
291	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
292	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
293	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
294	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
295	theorem		⊢
	proveit.logic.sets.inclusion.relax_proper_subset
296	theorem		⊢
	proveit.numbers.number_sets.real_numbers.nat_pos_within_real
*equality replacement requirements