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	,  ⊢
	: , : , :
1	theorem		⊢
	proveit.numbers.number_sets.real_numbers.in_IntervalOO
2	instantiation	139, 6, 197	⊢
	: , :
3	instantiation	210, 211, 47	⊢
	: , : , :
4	instantiation	139, 54, 57	,  ⊢
	: , :
5	instantiation	7, 8, 9	,  ⊢
	: , :
6	theorem		⊢
	proveit.numbers.number_sets.real_numbers.zero_is_real
7	theorem		⊢
	proveit.logic.booleans.conjunction.and_if_both
8	instantiation	12, 10, 11	,  ⊢
	: , : , :
9	instantiation	12, 13, 14	,  ⊢
	: , : , :
10	instantiation	17, 15, 16	,  ⊢
	: , : , :
11	instantiation	20, 186	⊢
	:
12	theorem		⊢
	proveit.logic.equality.sub_left_side_into
13	instantiation	17, 18, 19	,  ⊢
	: , : , :
14	instantiation	20, 151	⊢
	:
15	instantiation	56, 102, 21, 57, 22, 23*	⊢
	: , : , :
16	instantiation	24, 57, 102, 54, 25	,  ⊢
	: , : , :
17	theorem		⊢
	proveit.numbers.ordering.transitivity_less_eq_less
18	instantiation	26, 27, 28, 29*	,  ⊢
	: , : , :
19	instantiation	30, 180, 222, 31, 181, 32, 206	⊢
	: , : , : , : , :
20	theorem		⊢
	proveit.numbers.addition.elim_zero_left
21	instantiation	205, 51	⊢
	:
22	instantiation	75, 77, 51, 33	⊢
	: , :
23	instantiation	34, 104, 35, 151, 36	⊢
	: , : , :
24	theorem		⊢
	proveit.numbers.addition.strong_bound_via_left_term_bound
25	instantiation	37, 102, 117, 74	⊢
	: , : , :
26	theorem		⊢
	proveit.logic.equality.sub_right_side_into
27	instantiation	38, 39, 40	,  ⊢
	: , : , :
28	instantiation	41, 208, 42, 43, 151, 93, 128, 44*	⊢
	: , : , :
29	instantiation	167, 45, 46	⊢
	: , : , :
30	theorem		⊢
	proveit.numbers.addition.term_as_strong_upper_bound
31	instantiation	116, 47	⊢
	:
32	instantiation	48, 49	⊢
	:
33	instantiation	97, 127, 99, 110, 50, 101	⊢
	: , : , :
34	theorem		⊢
	proveit.numbers.addition.subtraction.negated_add
35	instantiation	220, 196, 51	⊢
	: , : , :
36	instantiation	167, 52, 87	⊢
	: , : , :
37	theorem		⊢
	proveit.numbers.number_sets.real_numbers.interval_oc_lower_bound
38	theorem		⊢
	proveit.numbers.ordering.transitivity_less_eq_less_eq
39	instantiation	53, 57, 54, 117, 55	,  ⊢
	: , : , :
40	instantiation	56, 117, 57, 58, 59	⊢
	: , : , :
41	theorem		⊢
	proveit.numbers.division.distribute_frac_through_sum
42	instantiation	194	⊢
	: , :
43	instantiation	220, 196, 60	⊢
	: , : , :
44	instantiation	61, 92, 93, 128, 71*	⊢
	: , :
45	instantiation	153, 62	⊢
	: , : , :
46	instantiation	167, 63, 64	⊢
	: , : , :
47	instantiation	65, 222, 180, 181, 66	⊢
	: , : , : , : , :
48	theorem		⊢
	proveit.numbers.negation.real_neg_closure
49	instantiation	67, 68, 69, 128	⊢
	: , :
50	instantiation	70, 160, 191, 143	⊢
	: , : , :
51	instantiation	126, 110, 127, 128	⊢
	: , :
52	instantiation	153, 71	⊢
	: , : , :
53	theorem		⊢
	proveit.numbers.addition.weak_bound_via_left_term_bound
54	instantiation	72, 102, 117, 74	⊢
	: , : , :
55	instantiation	73, 102, 117, 74	⊢
	: , : , :
56	theorem		⊢
	proveit.numbers.addition.weak_bound_via_right_term_bound
57	instantiation	205, 77	⊢
	:
58	instantiation	205, 76	⊢
	:
59	instantiation	75, 76, 77, 78	⊢
	: , :
60	instantiation	220, 213, 79	⊢
	: , : , :
61	theorem		⊢
	proveit.numbers.division.neg_frac_neg_numerator
62	instantiation	80, 81, 106, 82*	⊢
	: , :
63	instantiation	179, 222, 215, 180, 83, 181, 104, 86	⊢
	: , : , : , : , : , :
64	instantiation	84, 180, 215, 222, 181, 85, 104, 86, 87*	⊢
	: , : , : , : , : , :
65	theorem		⊢
	proveit.numbers.addition.add_nat_pos_from_nonneg
66	theorem		⊢
	proveit.numbers.numerals.decimals.less_0_1
67	theorem		⊢
	proveit.numbers.division.div_real_pos_closure
68	instantiation	220, 89, 88	⊢
	: , : , :
69	instantiation	220, 89, 90	⊢
	: , : , :
70	theorem		⊢
	proveit.numbers.number_sets.integers.interval_upper_bound
71	instantiation	91, 92, 93, 128, 94*	⊢
	: , :
72	theorem		⊢
	proveit.numbers.number_sets.real_numbers.all_in_interval_oc__is__real
73	theorem		⊢
	proveit.numbers.number_sets.real_numbers.interval_oc_upper_bound
74	instantiation	95, 96	⊢
	:
75	theorem		⊢
	proveit.numbers.negation.negated_weak_bound
76	instantiation	126, 98, 127, 128	⊢
	: , :
77	instantiation	126, 99, 127, 128	⊢
	: , :
78	instantiation	97, 127, 98, 99, 100, 101	⊢
	: , : , :
79	instantiation	220, 218, 174	⊢
	: , : , :
80	theorem		⊢
	proveit.numbers.negation.distribute_neg_through_binary_sum
81	instantiation	220, 196, 102	⊢
	: , : , :
82	instantiation	103, 104	⊢
	:
83	instantiation	194	⊢
	: , :
84	theorem		⊢
	proveit.numbers.addition.association
85	instantiation	194	⊢
	: , :
86	instantiation	105, 106	⊢
	:
87	instantiation	107, 219, 209, 108*	⊢
	: , : , : , :
88	instantiation	220, 109, 157	⊢
	: , : , :
89	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_pos_within_real_pos
90	instantiation	220, 109, 144	⊢
	: , : , :
91	theorem		⊢
	proveit.numbers.division.div_as_mult
92	instantiation	220, 196, 110	⊢
	: , : , :
93	instantiation	220, 196, 127	⊢
	: , : , :
94	instantiation	167, 111, 112	⊢
	: , : , :
95	theorem		⊢
	proveit.physics.quantum.QPE._delta_b_in_interval
96	assumption		⊢
97	theorem		⊢
	proveit.numbers.division.weak_div_from_numer_bound__pos_denom
98	instantiation	220, 213, 113	⊢
	: , : , :
99	instantiation	220, 213, 114	⊢
	: , : , :
100	instantiation	115, 160, 191, 143	⊢
	: , : , :
101	instantiation	116, 144	⊢
	:
102	instantiation	205, 117	⊢
	:
103	theorem		⊢
	proveit.numbers.negation.double_negation
104	instantiation	220, 196, 117	⊢
	: , : , :
105	theorem		⊢
	proveit.numbers.negation.complex_closure
106	instantiation	220, 196, 118	⊢
	: , : , :
107	theorem		⊢
	proveit.numbers.addition.rational_pair_addition
108	instantiation	167, 119, 120	⊢
	: , : , :
109	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nat_pos_within_rational_pos
110	instantiation	210, 211, 202	⊢
	: , : , :
111	instantiation	153, 121	⊢
	: , : , :
112	instantiation	122, 177, 123, 195, 137, 124*	⊢
	: , : , :
113	instantiation	220, 218, 160	⊢
	: , : , :
114	instantiation	220, 218, 125	⊢
	: , : , :
115	theorem		⊢
	proveit.numbers.number_sets.integers.interval_lower_bound
116	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.natural_pos_is_pos
117	instantiation	126, 206, 192, 137	⊢
	: , :
118	instantiation	126, 206, 127, 128	⊢
	: , :
119	instantiation	161, 215, 129, 130, 131, 132	⊢
	: , : , : , :
120	instantiation	133, 134, 135	⊢
	:
121	instantiation	136, 177, 204, 197, 137, 138*	⊢
	: , : , :
122	theorem		⊢
	proveit.numbers.exponentiation.product_of_real_powers
123	instantiation	139, 204, 197	⊢
	: , :
124	instantiation	167, 140, 141	⊢
	: , : , :
125	instantiation	220, 142, 143	⊢
	: , : , :
126	theorem		⊢
	proveit.numbers.division.div_real_closure
127	instantiation	210, 211, 144	⊢
	: , : , :
128	instantiation	149, 144	⊢
	:
129	instantiation	194	⊢
	: , :
130	instantiation	194	⊢
	: , :
131	instantiation	167, 145, 146	⊢
	: , : , :
132	theorem		⊢
	proveit.numbers.numerals.decimals.mult_2_2
133	theorem		⊢
	proveit.numbers.division.frac_cancel_complete
134	instantiation	220, 196, 147	⊢
	: , : , :
135	instantiation	149, 148	⊢
	:
136	theorem		⊢
	proveit.numbers.exponentiation.real_power_of_real_power
137	instantiation	149, 208	⊢
	:
138	instantiation	150, 185, 151, 152*	⊢
	: , :
139	theorem		⊢
	proveit.numbers.addition.add_real_closure_bin
140	instantiation	153, 154	⊢
	: , : , :
141	instantiation	155, 156, 157, 158*	⊢
	: , :
142	instantiation	159, 160, 191	⊢
	: , :
143	assumption		⊢
144	theorem		⊢
	proveit.physics.quantum.QPE._two_pow_t_is_nat_pos
145	instantiation	161, 215, 162, 163, 164, 165	⊢
	: , : , : , :
146	theorem		⊢
	proveit.numbers.numerals.decimals.add_2_2
147	instantiation	220, 213, 166	⊢
	: , : , :
148	theorem		⊢
	proveit.numbers.numerals.decimals.posnat4
149	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos
150	theorem		⊢
	proveit.numbers.multiplication.mult_neg_right
151	instantiation	220, 196, 206	⊢
	: , : , :
152	instantiation	176, 185	⊢
	:
153	axiom		⊢
	proveit.logic.equality.substitution
154	instantiation	167, 168, 169	⊢
	: , : , :
155	theorem		⊢
	proveit.numbers.exponentiation.neg_power_as_div
156	instantiation	220, 170, 171	⊢
	: , : , :
157	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
158	instantiation	172, 177	⊢
	:
159	theorem		⊢
	proveit.numbers.number_sets.integers.int_interval_within_int
160	instantiation	173, 174, 219	⊢
	: , :
161	axiom		⊢
	proveit.core_expr_types.operations.operands_substitution
162	instantiation	194	⊢
	: , :
163	instantiation	194	⊢
	: , :
164	instantiation	175, 177	⊢
	:
165	instantiation	176, 177	⊢
	:
166	instantiation	220, 218, 178	⊢
	: , : , :
167	axiom		⊢
	proveit.logic.equality.equals_transitivity
168	instantiation	179, 180, 215, 222, 181, 182, 185, 186, 183	⊢
	: , : , : , : , : , :
169	instantiation	184, 185, 186, 187	⊢
	: , : , :
170	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero
171	instantiation	220, 188, 189	⊢
	: , : , :
172	theorem		⊢
	proveit.numbers.exponentiation.complex_x_to_first_power_is_x
173	theorem		⊢
	proveit.numbers.addition.add_int_closure_bin
174	instantiation	190, 191	⊢
	:
175	theorem		⊢
	proveit.numbers.multiplication.elim_one_left
176	theorem		⊢
	proveit.numbers.multiplication.elim_one_right
177	instantiation	220, 196, 192	⊢
	: , : , :
178	instantiation	220, 221, 193	⊢
	: , : , :
179	theorem		⊢
	proveit.numbers.addition.disassociation
180	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
181	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
182	instantiation	194	⊢
	: , :
183	instantiation	220, 196, 195	⊢
	: , : , :
184	theorem		⊢
	proveit.numbers.addition.subtraction.add_cancel_triple_13
185	instantiation	220, 196, 204	⊢
	: , : , :
186	instantiation	220, 196, 197	⊢
	: , : , :
187	instantiation	198	⊢
	:
188	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero
189	instantiation	220, 199, 200	⊢
	: , : , :
190	theorem		⊢
	proveit.numbers.negation.int_closure
191	instantiation	220, 201, 202	⊢
	: , : , :
192	instantiation	220, 213, 203	⊢
	: , : , :
193	theorem		⊢
	proveit.numbers.numerals.decimals.nat4
194	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
195	instantiation	205, 204	⊢
	:
196	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
197	instantiation	205, 206	⊢
	:
198	axiom		⊢
	proveit.logic.equality.equals_reflexivity
199	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
200	instantiation	220, 207, 208	⊢
	: , : , :
201	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_int
202	theorem		⊢
	proveit.physics.quantum.QPE._two_pow_t_minus_one_is_nat_pos
203	instantiation	220, 218, 209	⊢
	: , : , :
204	instantiation	210, 211, 212	⊢
	: , : , :
205	theorem		⊢
	proveit.numbers.negation.real_closure
206	instantiation	220, 213, 214	⊢
	: , : , :
207	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
208	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
209	instantiation	220, 221, 215	⊢
	: , : , :
210	theorem		⊢
	proveit.logic.sets.inclusion.unfold_subset_eq
211	instantiation	216, 217	⊢
	: , :
212	axiom		⊢
	proveit.physics.quantum.QPE._t_in_natural_pos
213	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
214	instantiation	220, 218, 219	⊢
	: , : , :
215	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
216	theorem		⊢
	proveit.logic.sets.inclusion.relax_proper_subset
217	theorem		⊢
	proveit.numbers.number_sets.real_numbers.nat_pos_within_real
218	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
219	instantiation	220, 221, 222	⊢
	: , : , :
220	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
221	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
222	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
*equality replacement requirements