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