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	90	⊢
2	instantiation	7, 292, 228, 4, 229, 274, 5, 6	⊢
	: , : , : , : , : , :
3	instantiation	7, 295, 274, 8, 9	⊢
	: , : , : , : , : , :
4	instantiation	244	⊢
	: , :
5	instantiation	270, 15	⊢
	:
6	instantiation	13, 12, 10, 11	⊢
	: , :
7	theorem		⊢
	proveit.numbers.addition.weak_bound_via_term_bound
8	instantiation	270, 12	⊢
	:
9	instantiation	13, 14, 15, 16	⊢
	: , :
10	instantiation	25, 274, 17, 18	⊢
	: , :
11	instantiation	28, 29, 47, 19, 20	⊢
	: , : , :
12	instantiation	25, 274, 21, 22	⊢
	: , :
13	theorem		⊢
	proveit.numbers.negation.negated_weak_bound
14	instantiation	25, 274, 23, 24	⊢
	: , :
15	instantiation	25, 274, 26, 27	⊢
	: , :
16	instantiation	28, 29, 55, 30, 31	⊢
	: , : , :
17	instantiation	39, 36, 33	⊢
	: , :
18	instantiation	199, 32	⊢
	:
19	instantiation	293, 280, 52	⊢
	: , : , :
20	instantiation	45, 36, 33, 37, 34, 35	⊢
	: , : , :
21	instantiation	39, 36, 37	⊢
	: , :
22	instantiation	40, 38	⊢
	:
23	instantiation	39, 265, 122	⊢
	: , :
24	instantiation	40, 41	⊢
	:
25	theorem		⊢
	proveit.numbers.division.div_real_closure
26	instantiation	293, 256, 55	⊢
	: , : , :
27	instantiation	199, 42	⊢
	:
28	theorem		⊢
	proveit.numbers.division.weak_div_from_denom_bound__all_pos
29	instantiation	293, 43, 44	⊢
	: , : , :
30	instantiation	293, 280, 54	⊢
	: , : , :
31	instantiation	45, 265, 68, 122, 62, 46	⊢
	: , : , :
32	instantiation	293, 209, 47	⊢
	: , : , :
33	instantiation	51, 68, 292	⊢
	: , :
34	instantiation	48, 265, 68, 122, 49, 124	⊢
	: , : , :
35	instantiation	57, 75	⊢
	:
36	instantiation	293, 283, 50	⊢
	: , : , :
37	instantiation	51, 122, 292	⊢
	: , :
38	instantiation	293, 53, 52	⊢
	: , : , :
39	theorem		⊢
	proveit.numbers.multiplication.mult_real_closure_bin
40	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nonzero_if_in_rational_nonzero
41	instantiation	293, 53, 54	⊢
	: , : , :
42	instantiation	293, 209, 55	⊢
	: , : , :
43	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_nonneg_within_real_nonneg
44	instantiation	293, 56, 295	⊢
	: , : , :
45	theorem		⊢
	proveit.numbers.multiplication.weak_bound_via_right_factor_bound
46	instantiation	57, 292	⊢
	:
47	instantiation	233, 58, 59	⊢
	: , :
48	theorem		⊢
	proveit.numbers.exponentiation.exp_pos_lesseq
49	instantiation	60, 61, 62	⊢
	: , :
50	instantiation	293, 290, 63	⊢
	: , : , :
51	theorem		⊢
	proveit.numbers.exponentiation.exp_real_closure_nat_power
52	instantiation	65, 66, 64	⊢
	: , :
53	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.rational_pos_within_rational_nonzero
54	instantiation	65, 281, 77	⊢
	: , :
55	instantiation	233, 268, 89	⊢
	: , :
56	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nat_within_rational_nonneg
57	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.natural_lower_bound
58	instantiation	293, 280, 66	⊢
	: , : , :
59	instantiation	67, 68, 69	⊢
	:
60	theorem		⊢
	proveit.logic.booleans.conjunction.and_if_both
61	instantiation	70, 71	⊢
	:
62	instantiation	100, 258, 72, 169, 73, 74*	⊢
	: , : , :
63	instantiation	293, 294, 75	⊢
	: , : , :
64	instantiation	76, 77, 286	⊢
	: , :
65	theorem		⊢
	proveit.numbers.multiplication.mult_rational_pos_closure_bin
66	instantiation	293, 288, 78	⊢
	: , : , :
67	theorem		⊢
	proveit.numbers.exponentiation.sqrd_pos_closure
68	instantiation	113, 274, 119	⊢
	: , :
69	instantiation	199, 79	⊢
	:
70	theorem		⊢
	proveit.numbers.number_sets.real_numbers.nonneg_if_in_real_nonneg
71	instantiation	293, 80, 89	⊢
	: , : , :
72	instantiation	293, 256, 161	⊢
	: , : , :
73	instantiation	81, 265, 147, 82, 236, 83, 84*	⊢
	: , : , :
74	instantiation	213, 85, 86	⊢
	: , : , :
75	theorem		⊢
	proveit.numbers.numerals.decimals.nat4
76	theorem		⊢
	proveit.numbers.exponentiation.exp_rational_pos_closure
77	instantiation	87, 131, 88	⊢
	:
78	theorem		⊢
	proveit.numbers.numerals.decimals.posnat4
79	instantiation	293, 209, 89	⊢
	: , : , :
80	theorem		⊢
	proveit.numbers.number_sets.real_numbers.real_pos_within_real_nonneg
81	theorem		⊢
	proveit.numbers.exponentiation.exp_monotonicity_large_base_less_eq
82	instantiation	113, 103, 101	⊢
	: , :
83	instantiation	90, 91, 92	⊢
	: , : , :
84	instantiation	93, 268, 161, 205	⊢
	: , :
85	instantiation	155, 228, 292, 295, 229, 94, 255, 108, 248	⊢
	: , : , : , : , : , :
86	instantiation	213, 95, 96	⊢
	: , : , :
87	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.pos_rational_is_rational_pos
88	instantiation	97, 98	⊢
	: , :
89	instantiation	216, 267, 173	⊢
	: , :
90	theorem		⊢
	proveit.numbers.ordering.transitivity_less_eq_less_eq
91	instantiation	99, 147	⊢
	:
92	instantiation	100, 101, 102, 103, 104, 105*	⊢
	: , : , :
93	theorem		⊢
	proveit.numbers.exponentiation.exponent_log_with_same_base
94	instantiation	244	⊢
	: , :
95	instantiation	106, 295, 228, 229, 255, 108, 248	⊢
	: , : , : , : , : , : , :
96	instantiation	157, 228, 292, 295, 229, 107, 255, 248, 108, 171*	⊢
	: , : , : , : , : , :
97	theorem		⊢
	proveit.numbers.addition.subtraction.pos_difference
98	instantiation	109, 258, 265, 110, 111, 171*, 112*	⊢
	: , : , :
99	theorem		⊢
	proveit.numbers.rounding.ceil_x_ge_x
100	theorem		⊢
	proveit.numbers.addition.weak_bound_via_left_term_bound
101	instantiation	270, 175	⊢
	:
102	instantiation	113, 175, 114	⊢
	: , :
103	instantiation	183, 184, 219	⊢
	: , : , :
104	axiom		⊢
	proveit.physics.quantum.QPE._t_req
105	instantiation	115, 116, 117, 118	⊢
	: , : , : , :
106	theorem		⊢
	proveit.numbers.addition.leftward_commutation
107	instantiation	244	⊢
	: , :
108	instantiation	293, 264, 119	⊢
	: , : , :
109	theorem		⊢
	proveit.numbers.addition.strong_bound_via_left_term_bound
110	instantiation	293, 283, 120	⊢
	: , : , :
111	instantiation	121, 265, 122, 123, 124	⊢
	: , : , :
112	instantiation	213, 125, 126	⊢
	: , : , :
113	theorem		⊢
	proveit.numbers.addition.add_real_closure_bin
114	instantiation	293, 283, 127	⊢
	: , : , :
115	theorem		⊢
	proveit.logic.equality.four_chain_transitivity
116	instantiation	213, 128, 129	⊢
	: , : , :
117	instantiation	166	⊢
	:
118	instantiation	130, 148	⊢
	: , :
119	instantiation	293, 256, 173	⊢
	: , : , :
120	instantiation	140, 131, 278	⊢
	: , :
121	theorem		⊢
	proveit.numbers.ordering.less_eq_add_right_strong
122	instantiation	293, 283, 131	⊢
	: , : , :
123	theorem		⊢
	proveit.physics.quantum.QPE._e_value_ge_two
124	instantiation	132, 289	⊢
	:
125	instantiation	211, 133	⊢
	: , : , :
126	instantiation	213, 134, 135	⊢
	: , : , :
127	instantiation	293, 290, 136	⊢
	: , : , :
128	instantiation	211, 137	⊢
	: , : , :
129	instantiation	213, 138, 139	⊢
	: , : , :
130	theorem		⊢
	proveit.logic.equality.equals_reversal
131	instantiation	140, 178, 141	⊢
	: , :
132	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.natural_pos_is_pos
133	instantiation	213, 142, 143	⊢
	: , : , :
134	instantiation	155, 228, 292, 295, 229, 144, 159, 226, 248	⊢
	: , : , : , : , : , :
135	instantiation	145, 226, 159, 146	⊢
	: , : , :
136	instantiation	194, 147	⊢
	:
137	instantiation	211, 148	⊢
	: , : , :
138	instantiation	155, 228, 292, 295, 229, 149, 164, 152, 150	⊢
	: , : , : , : , : , :
139	instantiation	151, 164, 152, 153	⊢
	: , : , :
140	theorem		⊢
	proveit.numbers.addition.add_rational_closure_bin
141	instantiation	293, 290, 154	⊢
	: , : , :
142	instantiation	155, 228, 292, 295, 229, 156, 159, 248, 255	⊢
	: , : , : , : , : , :
143	instantiation	157, 295, 292, 228, 158, 229, 159, 248, 255, 160*	⊢
	: , : , : , : , : , :
144	instantiation	244	⊢
	: , :
145	theorem		⊢
	proveit.numbers.addition.subtraction.add_cancel_triple_23
146	instantiation	166	⊢
	:
147	instantiation	203, 268, 161, 205	⊢
	: , :
148	instantiation	211, 162	⊢
	: , : , :
149	instantiation	244	⊢
	: , :
150	instantiation	163, 164	⊢
	:
151	theorem		⊢
	proveit.numbers.addition.subtraction.add_cancel_triple_13
152	instantiation	293, 264, 165	⊢
	: , : , :
153	instantiation	166	⊢
	:
154	instantiation	293, 167, 168	⊢
	: , : , :
155	theorem		⊢
	proveit.numbers.addition.disassociation
156	instantiation	244	⊢
	: , :
157	theorem		⊢
	proveit.numbers.addition.association
158	instantiation	244	⊢
	: , :
159	instantiation	293, 264, 169	⊢
	: , : , :
160	instantiation	170, 171, 172	⊢
	: , : , :
161	instantiation	216, 268, 173	⊢
	: , :
162	instantiation	211, 174	⊢
	: , : , :
163	theorem		⊢
	proveit.numbers.negation.complex_closure
164	instantiation	293, 264, 175	⊢
	: , : , :
165	instantiation	293, 283, 176	⊢
	: , : , :
166	axiom		⊢
	proveit.logic.equality.equals_reflexivity
167	theorem		⊢
	proveit.numbers.number_sets.integers.neg_int_within_int
168	instantiation	177, 287	⊢
	:
169	instantiation	293, 283, 178	⊢
	: , : , :
170	theorem		⊢
	proveit.logic.equality.sub_right_side_into
171	instantiation	179, 226, 255, 180	⊢
	: , : , :
172	instantiation	181, 255, 248	⊢
	: , :
173	instantiation	266, 267, 210, 190	⊢
	: , :
174	instantiation	211, 182	⊢
	: , : , :
175	instantiation	183, 184, 238	⊢
	: , : , :
176	instantiation	293, 290, 185	⊢
	: , : , :
177	theorem		⊢
	proveit.numbers.negation.int_neg_closure
178	instantiation	293, 186, 187	⊢
	: , : , :
179	theorem		⊢
	proveit.numbers.addition.subtraction.subtract_from_add
180	theorem		⊢
	proveit.numbers.numerals.decimals.add_1_1
181	theorem		⊢
	proveit.numbers.addition.commutation
182	instantiation	188, 226, 189, 190, 191*	⊢
	: , :
183	theorem		⊢
	proveit.logic.sets.inclusion.unfold_subset_eq
184	instantiation	192, 193	⊢
	: , :
185	instantiation	194, 195	⊢
	:
186	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.rational_nonzero_within_rational
187	instantiation	196, 263, 197	⊢
	: , :
188	theorem		⊢
	proveit.numbers.division.div_as_mult
189	instantiation	293, 264, 198	⊢
	: , : , :
190	instantiation	199, 200	⊢
	:
191	instantiation	213, 201, 202	⊢
	: , : , :
192	theorem		⊢
	proveit.logic.sets.inclusion.relax_proper_subset
193	theorem		⊢
	proveit.numbers.number_sets.real_numbers.nat_pos_within_real
194	axiom		⊢
	proveit.numbers.rounding.ceil_is_an_int
195	instantiation	203, 268, 204, 205	⊢
	: , :
196	theorem		⊢
	proveit.numbers.exponentiation.exp_rational_nonzero_closure
197	instantiation	206, 207, 208	⊢
	: , :
198	instantiation	293, 256, 210	⊢
	: , : , :
199	theorem		⊢
	proveit.numbers.number_sets.real_numbers.nonzero_if_in_real_nonzero
200	instantiation	293, 209, 210	⊢
	: , : , :
201	instantiation	211, 212	⊢
	: , : , :
202	instantiation	213, 214, 215	⊢
	: , : , :
203	theorem		⊢
	proveit.numbers.logarithms.log_real_pos_real_closure
204	instantiation	216, 268, 217	⊢
	: , :
205	instantiation	239, 218	⊢
	: , :
206	theorem		⊢
	proveit.numbers.addition.add_int_closure_bin
207	instantiation	293, 237, 219	⊢
	: , : , :
208	instantiation	220, 221	⊢
	:
209	theorem		⊢
	proveit.numbers.number_sets.real_numbers.real_pos_within_real_nonzero
210	instantiation	233, 268, 250	⊢
	: , :
211	axiom		⊢
	proveit.logic.equality.substitution
212	instantiation	222, 255, 247, 258, 269, 223, 224*	⊢
	: , : , :
213	axiom		⊢
	proveit.logic.equality.equals_transitivity
214	instantiation	225, 295, 292, 228, 230, 229, 226, 231, 232	⊢
	: , : , : , : , : , :
215	instantiation	227, 228, 292, 229, 230, 231, 232	⊢
	: , : , : , :
216	theorem		⊢
	proveit.numbers.addition.add_real_pos_closure_bin
217	instantiation	233, 257, 234	⊢
	: , :
218	instantiation	235, 295, 292, 236	⊢
	: , :
219	axiom		⊢
	proveit.physics.quantum.QPE._t_in_natural_pos
220	theorem		⊢
	proveit.numbers.negation.int_closure
221	instantiation	293, 237, 238	⊢
	: , : , :
222	theorem		⊢
	proveit.numbers.exponentiation.real_power_of_product
223	instantiation	239, 240	⊢
	: , :
224	instantiation	241, 242, 287, 243*	⊢
	: , :
225	theorem		⊢
	proveit.numbers.multiplication.disassociation
226	instantiation	293, 264, 274	⊢
	: , : , :
227	theorem		⊢
	proveit.numbers.multiplication.elim_one_any
228	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
229	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
230	instantiation	244	⊢
	: , :
231	instantiation	293, 264, 245	⊢
	: , : , :
232	instantiation	246, 247, 248	⊢
	: , :
233	theorem		⊢
	proveit.numbers.multiplication.mult_real_pos_closure_bin
234	instantiation	249, 250, 258	⊢
	: , :
235	theorem		⊢
	proveit.numbers.ordering.less_is_not_eq_nat
236	theorem		⊢
	proveit.numbers.numerals.decimals.less_1_2
237	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_int
238	axiom		⊢
	proveit.physics.quantum.QPE._n_in_natural_pos
239	theorem		⊢
	proveit.logic.equality.not_equals_symmetry
240	instantiation	251, 273, 260, 261	⊢
	: , :
241	theorem		⊢
	proveit.numbers.exponentiation.neg_power_as_div
242	instantiation	293, 252, 253	⊢
	: , : , :
243	instantiation	254, 255	⊢
	:
244	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
245	instantiation	293, 256, 257	⊢
	: , : , :
246	theorem		⊢
	proveit.numbers.exponentiation.exp_complex_closure
247	instantiation	293, 264, 260	⊢
	: , : , :
248	instantiation	293, 264, 258	⊢
	: , : , :
249	theorem		⊢
	proveit.numbers.exponentiation.exp_real_pos_closure
250	instantiation	259, 260, 261	⊢
	:
251	theorem		⊢
	proveit.numbers.ordering.less_is_not_eq
252	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero
253	instantiation	293, 262, 263	⊢
	: , : , :
254	theorem		⊢
	proveit.numbers.exponentiation.complex_x_to_first_power_is_x
255	instantiation	293, 264, 265	⊢
	: , : , :
256	theorem		⊢
	proveit.numbers.number_sets.real_numbers.real_pos_within_real
257	instantiation	266, 267, 268, 269	⊢
	: , :
258	instantiation	270, 274	⊢
	:
259	theorem		⊢
	proveit.numbers.number_sets.real_numbers.pos_real_is_real_pos
260	instantiation	271, 273, 274, 275	⊢
	: , : , :
261	instantiation	272, 273, 274, 275	⊢
	: , : , :
262	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero
263	instantiation	293, 276, 277	⊢
	: , : , :
264	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
265	instantiation	293, 283, 278	⊢
	: , : , :
266	theorem		⊢
	proveit.numbers.division.div_real_pos_closure
267	instantiation	293, 280, 279	⊢
	: , : , :
268	instantiation	293, 280, 281	⊢
	: , : , :
269	instantiation	282, 289	⊢
	:
270	theorem		⊢
	proveit.numbers.negation.real_closure
271	theorem		⊢
	proveit.numbers.number_sets.real_numbers.all_in_interval_oc__is__real
272	theorem		⊢
	proveit.numbers.number_sets.real_numbers.interval_oc_lower_bound
273	theorem		⊢
	proveit.numbers.number_sets.real_numbers.zero_is_real
274	instantiation	293, 283, 284	⊢
	: , : , :
275	axiom		⊢
	proveit.physics.quantum.QPE._eps_in_interval
276	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
277	instantiation	293, 285, 289	⊢
	: , : , :
278	instantiation	293, 290, 286	⊢
	: , : , :
279	instantiation	293, 288, 287	⊢
	: , : , :
280	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_pos_within_real_pos
281	instantiation	293, 288, 289	⊢
	: , : , :
282	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos
283	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
284	instantiation	293, 290, 291	⊢
	: , : , :
285	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
286	instantiation	293, 294, 292	⊢
	: , : , :
287	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
288	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nat_pos_within_rational_pos
289	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
290	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
291	instantiation	293, 294, 295	⊢
	: , : , :
292	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
293	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
294	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
295	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
*equality replacement requirements