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