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	93	⊢
2	instantiation	144, 7, 58	⊢
	: , :
3	reference	30	⊢
4	instantiation	125, 58, 7, 59, 8	⊢
	: , : , :
5	instantiation	125, 58, 278, 59, 9, 10*	⊢
	: , : , :
6	instantiation	103, 11, 12, 13	⊢
	: , : , : , :
7	instantiation	65, 231, 14	⊢
	: , :
8	instantiation	15, 231, 94, 54, 258, 16	⊢
	: , : , :
9	instantiation	17, 18	⊢
	:
10	instantiation	19, 239, 20	⊢
	: , :
11	instantiation	158, 159, 257, 286, 160, 22, 52, 35, 21	⊢
	: , : , : , : , : , :
12	instantiation	158, 257, 159, 22, 160, 52, 35	⊢
	: , : , : , : , : , :
13	instantiation	103, 23, 24, 25	⊢
	: , : , : , :
14	instantiation	70, 26, 27	⊢
	:
15	theorem		⊢
	proveit.numbers.exponentiation.exp_monotonicity_large_base_less_eq
16	instantiation	154, 146, 184, 145, 28	⊢
	: , : , :
17	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.natural_pos_lower_bound
18	instantiation	29, 257, 66	⊢
	: , :
19	theorem		⊢
	proveit.numbers.addition.subtraction.add_cancel_basic
20	instantiation	186	⊢
	:
21	instantiation	284, 246, 30	⊢
	: , : , :
22	instantiation	237	⊢
	: , :
23	instantiation	73, 286, 52, 35	⊢
	: , : , : , : , : , : , :
24	instantiation	74, 159, 257, 160, 31, 33, 52, 35, 32*	⊢
	: , : , : , : , : , :
25	instantiation	74, 286, 257, 159, 33, 160, 34, 35, 36*	⊢
	: , : , : , : , : , :
26	instantiation	77, 78, 37	⊢
	: , :
27	instantiation	80, 87	⊢
	: , :
28	instantiation	38, 231, 207, 86	⊢
	: , :
29	theorem		⊢
	proveit.numbers.exponentiation.exp_natpos_closure
30	instantiation	144, 59, 58	⊢
	: , :
31	instantiation	237	⊢
	: , :
32	instantiation	39, 40, 41*	⊢
	: , :
33	instantiation	237	⊢
	: , :
34	instantiation	42, 218, 43	⊢
	: , :
35	instantiation	131, 239	⊢
	:
36	instantiation	44, 239, 218, 109	⊢
	: , : , :
37	instantiation	284, 84, 45	⊢
	: , : , :
38	theorem		⊢
	proveit.numbers.negation.negated_weak_bound
39	theorem		⊢
	proveit.logic.equality.equals_reversal
40	instantiation	46, 159, 257, 286, 160, 47, 239, 52, 48*	⊢
	: , : , : , : , : , :
41	instantiation	212, 49, 50	⊢
	: , : , :
42	theorem		⊢
	proveit.numbers.exponentiation.exp_complex_closure
43	instantiation	284, 246, 51	⊢
	: , : , :
44	theorem		⊢
	proveit.numbers.addition.subtraction.negated_add
45	instantiation	88, 223	⊢
	:
46	theorem		⊢
	proveit.numbers.multiplication.distribute_through_sum
47	instantiation	237	⊢
	: , :
48	instantiation	205, 52	⊢
	:
49	instantiation	191, 109	⊢
	: , : , :
50	instantiation	53, 218, 278, 54, 55, 56*, 57*	⊢
	: , : , :
51	instantiation	144, 58, 146	⊢
	: , :
52	instantiation	284, 246, 59	⊢
	: , : , :
53	theorem		⊢
	proveit.numbers.exponentiation.product_of_real_powers
54	instantiation	284, 280, 60	⊢
	: , : , :
55	instantiation	61, 274	⊢
	:
56	instantiation	62, 218	⊢
	:
57	instantiation	212, 63, 64	⊢
	: , : , :
58	instantiation	206, 278	⊢
	:
59	instantiation	65, 231, 66	⊢
	: , :
60	instantiation	284, 282, 71	⊢
	: , : , :
61	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos
62	theorem		⊢
	proveit.numbers.exponentiation.complex_x_to_first_power_is_x
63	instantiation	158, 286, 257, 159, 67, 160, 239, 136, 117	⊢
	: , : , : , : , : , :
64	instantiation	212, 68, 69	⊢
	: , : , :
65	theorem		⊢
	proveit.numbers.exponentiation.exp_real_closure_nat_power
66	instantiation	70, 71, 72	⊢
	:
67	instantiation	237	⊢
	: , :
68	instantiation	73, 286, 159, 160, 239, 136, 117	⊢
	: , : , : , : , : , : , :
69	instantiation	74, 159, 257, 286, 160, 75, 239, 117, 136, 76*	⊢
	: , : , : , : , : , :
70	theorem		⊢
	proveit.numbers.number_sets.integers.nonneg_int_is_natural
71	instantiation	77, 78, 79	⊢
	: , :
72	instantiation	80, 81	⊢
	: , :
73	theorem		⊢
	proveit.numbers.addition.leftward_commutation
74	theorem		⊢
	proveit.numbers.addition.association
75	instantiation	237	⊢
	: , :
76	instantiation	82, 239, 218, 109	⊢
	: , : , :
77	theorem		⊢
	proveit.numbers.addition.add_int_closure_bin
78	instantiation	284, 83, 167	⊢
	: , : , :
79	instantiation	284, 84, 85	⊢
	: , : , :
80	theorem		⊢
	proveit.numbers.addition.subtraction.nonneg_difference
81	instantiation	110, 86, 87	⊢
	: , : , :
82	theorem		⊢
	proveit.numbers.addition.subtraction.subtract_from_add_reversed
83	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_int
84	theorem		⊢
	proveit.numbers.number_sets.integers.neg_int_within_int
85	instantiation	88, 274	⊢
	:
86	axiom		⊢
	proveit.physics.quantum.QPE._n_ge_two
87	instantiation	125, 129, 231, 89, 90, 91*, 92*	⊢
	: , : , :
88	theorem		⊢
	proveit.numbers.negation.int_neg_closure
89	instantiation	144, 94, 231	⊢
	: , :
90	instantiation	93, 231, 94, 95, 201	⊢
	: , : , :
91	instantiation	212, 96, 97	⊢
	: , : , :
92	instantiation	212, 98, 99	⊢
	: , : , :
93	theorem		⊢
	proveit.numbers.ordering.less_eq_add_right
94	instantiation	144, 146, 184	⊢
	: , :
95	instantiation	110, 100, 101	⊢
	: , : , :
96	instantiation	158, 286, 257, 159, 116, 160, 218, 164, 117	⊢
	: , : , : , : , : , :
97	instantiation	163, 218, 164, 134	⊢
	: , : , :
98	instantiation	191, 102	⊢
	: , : , :
99	instantiation	103, 104, 105, 106	⊢
	: , : , : , :
100	instantiation	107, 283, 123, 108, 109*	⊢
	: , :
101	instantiation	110, 111, 112	⊢
	: , : , :
102	instantiation	158, 159, 257, 286, 160, 133, 136, 162, 218	⊢
	: , : , : , : , : , :
103	theorem		⊢
	proveit.logic.equality.four_chain_transitivity
104	instantiation	158, 159, 114, 286, 160, 115, 136, 162, 218, 113	⊢
	: , : , : , : , : , :
105	instantiation	158, 114, 257, 159, 115, 116, 160, 136, 162, 218, 164, 117	⊢
	: , : , : , : , : , :
106	instantiation	212, 118, 119	⊢
	: , : , :
107	theorem		⊢
	proveit.numbers.rounding.ceil_of_real_above_int
108	instantiation	120, 266, 140, 121	⊢
	: , :
109	theorem		⊢
	proveit.numbers.numerals.decimals.add_1_1
110	theorem		⊢
	proveit.numbers.ordering.transitivity_less_eq_less_eq
111	instantiation	122, 123, 235, 124	⊢
	: , :
112	instantiation	125, 184, 126, 146, 127, 128*	⊢
	: , : , :
113	instantiation	284, 246, 129	⊢
	: , : , :
114	theorem		⊢
	proveit.numbers.numerals.decimals.nat3
115	instantiation	130	⊢
	: , : , :
116	instantiation	237	⊢
	: , :
117	instantiation	131, 218	⊢
	:
118	instantiation	132, 257, 286, 159, 133, 160, 136, 162, 218, 164, 134	⊢
	: , : , : , : , : , : , : , :
119	instantiation	135, 164, 136, 166	⊢
	: , : , :
120	theorem		⊢
	proveit.numbers.logarithms.log_base_large_a_greater_one
121	instantiation	137, 258, 138	⊢
	: , :
122	theorem		⊢
	proveit.numbers.rounding.ceil_increasing_less_eq
123	instantiation	241, 266, 140, 243	⊢
	: , :
124	instantiation	139, 266, 140, 242, 141, 258	⊢
	: , : , :
125	theorem		⊢
	proveit.numbers.addition.weak_bound_via_left_term_bound
126	instantiation	144, 207, 185	⊢
	: , :
127	axiom		⊢
	proveit.physics.quantum.QPE._t_req
128	instantiation	212, 142, 143	⊢
	: , : , :
129	instantiation	144, 207, 145	⊢
	: , :
130	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_3_typical_eq
131	theorem		⊢
	proveit.numbers.negation.complex_closure
132	theorem		⊢
	proveit.numbers.addition.subtraction.add_cancel_general
133	instantiation	237	⊢
	: , :
134	instantiation	186	⊢
	:
135	theorem		⊢
	proveit.numbers.addition.subtraction.add_cancel_triple_32
136	instantiation	284, 246, 146	⊢
	: , : , :
137	theorem		⊢
	proveit.logic.booleans.conjunction.and_if_both
138	instantiation	147, 231, 148, 149, 150, 151*, 152*	⊢
	: , : , :
139	theorem		⊢
	proveit.numbers.logarithms.log_increasing_less_eq
140	instantiation	284, 268, 153	⊢
	: , : , :
141	instantiation	154, 231, 225, 155, 156, 157*	⊢
	: , : , :
142	instantiation	158, 159, 257, 286, 160, 161, 164, 165, 162	⊢
	: , : , : , : , : , :
143	instantiation	163, 164, 165, 166	⊢
	: , : , :
144	theorem		⊢
	proveit.numbers.addition.add_real_closure_bin
145	instantiation	206, 231	⊢
	:
146	instantiation	221, 222, 167	⊢
	: , : , :
147	theorem		⊢
	proveit.numbers.addition.strong_bound_via_left_term_bound
148	instantiation	168, 225, 277	⊢
	: , :
149	instantiation	284, 280, 169	⊢
	: , : , :
150	instantiation	170, 225, 277, 278, 171, 172	⊢
	: , : , :
151	instantiation	212, 173, 174	⊢
	: , : , :
152	instantiation	212, 175, 176	⊢
	: , : , :
153	instantiation	252, 177, 269	⊢
	: , :
154	theorem		⊢
	proveit.numbers.addition.weak_bound_via_right_term_bound
155	instantiation	284, 178, 249	⊢
	: , : , :
156	instantiation	179, 180, 264, 266, 181	⊢
	: , : , :
157	instantiation	193, 247, 283, 194*, 182*, 183*	⊢
	: , : , : , :
158	theorem		⊢
	proveit.numbers.addition.disassociation
159	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
160	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
161	instantiation	237	⊢
	: , :
162	instantiation	284, 246, 184	⊢
	: , : , :
163	theorem		⊢
	proveit.numbers.addition.subtraction.add_cancel_triple_13
164	instantiation	284, 246, 207	⊢
	: , : , :
165	instantiation	284, 246, 185	⊢
	: , : , :
166	instantiation	186	⊢
	:
167	axiom		⊢
	proveit.physics.quantum.QPE._t_in_natural_pos
168	theorem		⊢
	proveit.numbers.multiplication.mult_real_closure_bin
169	instantiation	187, 236, 281	⊢
	: , :
170	theorem		⊢
	proveit.numbers.multiplication.strong_bound_via_right_factor_bound
171	theorem		⊢
	proveit.numbers.numerals.decimals.less_0_1
172	instantiation	188, 245	⊢
	:
173	instantiation	191, 189	⊢
	: , : , :
174	instantiation	190, 218	⊢
	:
175	instantiation	191, 192	⊢
	: , : , :
176	instantiation	193, 283, 247, 194*, 195*, 202*	⊢
	: , : , : , :
177	instantiation	284, 273, 196	⊢
	: , : , :
178	theorem		⊢
	proveit.numbers.number_sets.real_numbers.real_pos_within_real
179	theorem		⊢
	proveit.numbers.division.weak_div_from_denom_bound__all_pos
180	instantiation	284, 197, 198	⊢
	: , : , :
181	instantiation	199, 231, 271, 278, 200, 201, 202*	⊢
	: , : , :
182	instantiation	212, 203, 204	⊢
	: , : , :
183	instantiation	205, 218	⊢
	:
184	instantiation	206, 207	⊢
	:
185	instantiation	284, 280, 208	⊢
	: , : , :
186	axiom		⊢
	proveit.logic.equality.equals_reflexivity
187	theorem		⊢
	proveit.numbers.multiplication.mult_rational_closure_bin
188	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.positive_if_in_rational_pos
189	instantiation	209, 210	⊢
	:
190	theorem		⊢
	proveit.numbers.addition.elim_zero_left
191	axiom		⊢
	proveit.logic.equality.substitution
192	instantiation	238, 210	⊢
	:
193	theorem		⊢
	proveit.numbers.addition.rational_pair_addition
194	instantiation	211, 218	⊢
	:
195	instantiation	212, 213, 214	⊢
	: , : , :
196	theorem		⊢
	proveit.numbers.numerals.decimals.posnat5
197	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_nonneg_within_real_nonneg
198	instantiation	284, 215, 286	⊢
	: , : , :
199	theorem		⊢
	proveit.numbers.multiplication.weak_bound_via_right_factor_bound
200	instantiation	216, 277, 278, 279	⊢
	: , : , :
201	instantiation	217, 257	⊢
	:
202	instantiation	238, 218	⊢
	:
203	instantiation	226, 257, 219, 220, 230, 229	⊢
	: , : , : , :
204	theorem		⊢
	proveit.numbers.numerals.decimals.add_4_1
205	theorem		⊢
	proveit.numbers.multiplication.elim_one_left
206	theorem		⊢
	proveit.numbers.negation.real_closure
207	instantiation	221, 222, 223	⊢
	: , : , :
208	instantiation	284, 282, 224	⊢
	: , : , :
209	theorem		⊢
	proveit.numbers.multiplication.mult_zero_right
210	instantiation	284, 246, 225	⊢
	: , : , :
211	theorem		⊢
	proveit.numbers.division.frac_one_denom
212	axiom		⊢
	proveit.logic.equality.equals_transitivity
213	instantiation	226, 257, 227, 228, 229, 230	⊢
	: , : , : , :
214	theorem		⊢
	proveit.numbers.numerals.decimals.add_1_4
215	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nat_within_rational_nonneg
216	theorem		⊢
	proveit.numbers.number_sets.real_numbers.interval_oc_upper_bound
217	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.natural_lower_bound
218	instantiation	284, 246, 231	⊢
	: , : , :
219	instantiation	237	⊢
	: , :
220	instantiation	237	⊢
	: , :
221	theorem		⊢
	proveit.logic.sets.inclusion.unfold_subset_eq
222	instantiation	232, 233	⊢
	: , :
223	axiom		⊢
	proveit.physics.quantum.QPE._n_in_natural_pos
224	instantiation	234, 235	⊢
	:
225	instantiation	284, 280, 236	⊢
	: , : , :
226	axiom		⊢
	proveit.core_expr_types.operations.operands_substitution
227	instantiation	237	⊢
	: , :
228	instantiation	237	⊢
	: , :
229	instantiation	238, 239	⊢
	:
230	theorem		⊢
	proveit.numbers.numerals.decimals.mult_2_2
231	instantiation	284, 280, 240	⊢
	: , : , :
232	theorem		⊢
	proveit.logic.sets.inclusion.relax_proper_subset
233	theorem		⊢
	proveit.numbers.number_sets.real_numbers.nat_pos_within_real
234	axiom		⊢
	proveit.numbers.rounding.ceil_is_an_int
235	instantiation	241, 266, 242, 243	⊢
	: , :
236	instantiation	284, 244, 245	⊢
	: , : , :
237	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
238	theorem		⊢
	proveit.numbers.multiplication.elim_one_right
239	instantiation	284, 246, 278	⊢
	: , : , :
240	instantiation	284, 282, 247	⊢
	: , : , :
241	theorem		⊢
	proveit.numbers.logarithms.log_real_pos_real_closure
242	instantiation	248, 266, 249	⊢
	: , :
243	instantiation	250, 251	⊢
	: , :
244	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.rational_pos_within_rational
245	instantiation	252, 259, 269	⊢
	: , :
246	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
247	instantiation	284, 285, 257	⊢
	: , : , :
248	theorem		⊢
	proveit.numbers.addition.add_real_pos_closure_bin
249	instantiation	253, 254, 264, 255	⊢
	: , :
250	theorem		⊢
	proveit.logic.equality.not_equals_symmetry
251	instantiation	256, 286, 257, 258	⊢
	: , :
252	theorem		⊢
	proveit.numbers.division.div_rational_pos_closure
253	theorem		⊢
	proveit.numbers.division.div_real_pos_closure
254	instantiation	284, 268, 259	⊢
	: , : , :
255	instantiation	260, 261	⊢
	:
256	theorem		⊢
	proveit.numbers.ordering.less_is_not_eq_nat
257	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
258	theorem		⊢
	proveit.numbers.numerals.decimals.less_1_2
259	instantiation	284, 273, 262	⊢
	: , : , :
260	theorem		⊢
	proveit.numbers.number_sets.real_numbers.nonzero_if_in_real_nonzero
261	instantiation	284, 263, 264	⊢
	: , : , :
262	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
263	theorem		⊢
	proveit.numbers.number_sets.real_numbers.real_pos_within_real_nonzero
264	instantiation	265, 266, 267	⊢
	: , :
265	theorem		⊢
	proveit.numbers.multiplication.mult_real_pos_closure_bin
266	instantiation	284, 268, 269	⊢
	: , : , :
267	instantiation	270, 271, 272	⊢
	:
268	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_pos_within_real_pos
269	instantiation	284, 273, 274	⊢
	: , : , :
270	theorem		⊢
	proveit.numbers.number_sets.real_numbers.pos_real_is_real_pos
271	instantiation	275, 277, 278, 279	⊢
	: , : , :
272	instantiation	276, 277, 278, 279	⊢
	: , : , :
273	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nat_pos_within_rational_pos
274	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
275	theorem		⊢
	proveit.numbers.number_sets.real_numbers.all_in_interval_oc__is__real
276	theorem		⊢
	proveit.numbers.number_sets.real_numbers.interval_oc_lower_bound
277	theorem		⊢
	proveit.numbers.number_sets.real_numbers.zero_is_real
278	instantiation	284, 280, 281	⊢
	: , : , :
279	axiom		⊢
	proveit.physics.quantum.QPE._eps_in_interval
280	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
281	instantiation	284, 282, 283	⊢
	: , : , :
282	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
283	instantiation	284, 285, 286	⊢
	: , : , :
284	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
285	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
286	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
*equality replacement requirements