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	generalization	1	⊢
1	instantiation	2, 3, 4, 5	, ,  ⊢
	: , :
2	theorem		⊢
	proveit.numbers.number_sets.real_numbers.not_int_if_not_int_in_interval
3	theorem		⊢
	proveit.numbers.number_sets.integers.zero_is_int
4	instantiation	6, 7, 8, 9, 10	,  ⊢
	: , : , :
5	instantiation	11, 12	, ,  ⊢
	: , :
6	theorem		⊢
	proveit.numbers.number_sets.real_numbers.in_IntervalOO
7	instantiation	148, 13, 206	⊢
	: , :
8	instantiation	219, 220, 56	⊢
	: , : , :
9	instantiation	148, 63, 66	,  ⊢
	: , :
10	instantiation	14, 15, 16	,  ⊢
	: , :
11	theorem		⊢
	proveit.numbers.addition.subtraction.nonzero_difference_if_different
12	instantiation	17, 105, 134, 18	, ,  ⊢
	: , :
13	theorem		⊢
	proveit.numbers.number_sets.real_numbers.zero_is_real
14	theorem		⊢
	proveit.logic.booleans.conjunction.and_if_both
15	instantiation	21, 19, 20	,  ⊢
	: , : , :
16	instantiation	21, 22, 23	,  ⊢
	: , : , :
17	theorem		⊢
	proveit.physics.quantum.QPE._delta_b_not_eq_scaledNonzeroInt
18	assumption		⊢
19	instantiation	26, 24, 25	,  ⊢
	: , : , :
20	instantiation	29, 195	⊢
	:
21	theorem		⊢
	proveit.logic.equality.sub_left_side_into
22	instantiation	26, 27, 28	,  ⊢
	: , : , :
23	instantiation	29, 160	⊢
	:
24	instantiation	65, 111, 30, 66, 31, 32*	⊢
	: , : , :
25	instantiation	33, 66, 111, 63, 34	,  ⊢
	: , : , :
26	theorem		⊢
	proveit.numbers.ordering.transitivity_less_eq_less
27	instantiation	35, 36, 37, 38*	,  ⊢
	: , : , :
28	instantiation	39, 189, 231, 40, 190, 41, 215	⊢
	: , : , : , : , :
29	theorem		⊢
	proveit.numbers.addition.elim_zero_left
30	instantiation	214, 60	⊢
	:
31	instantiation	84, 86, 60, 42	⊢
	: , :
32	instantiation	43, 113, 44, 160, 45	⊢
	: , : , :
33	theorem		⊢
	proveit.numbers.addition.strong_bound_via_left_term_bound
34	instantiation	46, 111, 126, 83	⊢
	: , : , :
35	theorem		⊢
	proveit.logic.equality.sub_right_side_into
36	instantiation	47, 48, 49	,  ⊢
	: , : , :
37	instantiation	50, 217, 51, 52, 160, 102, 137, 53*	⊢
	: , : , :
38	instantiation	176, 54, 55	⊢
	: , : , :
39	theorem		⊢
	proveit.numbers.addition.term_as_strong_upper_bound
40	instantiation	125, 56	⊢
	:
41	instantiation	57, 58	⊢
	:
42	instantiation	106, 136, 108, 119, 59, 110	⊢
	: , : , :
43	theorem		⊢
	proveit.numbers.addition.subtraction.negated_add
44	instantiation	229, 205, 60	⊢
	: , : , :
45	instantiation	176, 61, 96	⊢
	: , : , :
46	theorem		⊢
	proveit.numbers.number_sets.real_numbers.interval_oc_lower_bound
47	theorem		⊢
	proveit.numbers.ordering.transitivity_less_eq_less_eq
48	instantiation	62, 66, 63, 126, 64	,  ⊢
	: , : , :
49	instantiation	65, 126, 66, 67, 68	⊢
	: , : , :
50	theorem		⊢
	proveit.numbers.division.distribute_frac_through_sum
51	instantiation	203	⊢
	: , :
52	instantiation	229, 205, 69	⊢
	: , : , :
53	instantiation	70, 101, 102, 137, 80*	⊢
	: , :
54	instantiation	162, 71	⊢
	: , : , :
55	instantiation	176, 72, 73	⊢
	: , : , :
56	instantiation	74, 231, 189, 190, 75	⊢
	: , : , : , : , :
57	theorem		⊢
	proveit.numbers.negation.real_neg_closure
58	instantiation	76, 77, 78, 137	⊢
	: , :
59	instantiation	79, 169, 200, 152	⊢
	: , : , :
60	instantiation	135, 119, 136, 137	⊢
	: , :
61	instantiation	162, 80	⊢
	: , : , :
62	theorem		⊢
	proveit.numbers.addition.weak_bound_via_left_term_bound
63	instantiation	81, 111, 126, 83	⊢
	: , : , :
64	instantiation	82, 111, 126, 83	⊢
	: , : , :
65	theorem		⊢
	proveit.numbers.addition.weak_bound_via_right_term_bound
66	instantiation	214, 86	⊢
	:
67	instantiation	214, 85	⊢
	:
68	instantiation	84, 85, 86, 87	⊢
	: , :
69	instantiation	229, 222, 88	⊢
	: , : , :
70	theorem		⊢
	proveit.numbers.division.neg_frac_neg_numerator
71	instantiation	89, 90, 115, 91*	⊢
	: , :
72	instantiation	188, 231, 224, 189, 92, 190, 113, 95	⊢
	: , : , : , : , : , :
73	instantiation	93, 189, 224, 231, 190, 94, 113, 95, 96*	⊢
	: , : , : , : , : , :
74	theorem		⊢
	proveit.numbers.addition.add_nat_pos_from_nonneg
75	theorem		⊢
	proveit.numbers.numerals.decimals.less_0_1
76	theorem		⊢
	proveit.numbers.division.div_real_pos_closure
77	instantiation	229, 98, 97	⊢
	: , : , :
78	instantiation	229, 98, 99	⊢
	: , : , :
79	theorem		⊢
	proveit.numbers.number_sets.integers.interval_upper_bound
80	instantiation	100, 101, 102, 137, 103*	⊢
	: , :
81	theorem		⊢
	proveit.numbers.number_sets.real_numbers.all_in_interval_oc__is__real
82	theorem		⊢
	proveit.numbers.number_sets.real_numbers.interval_oc_upper_bound
83	instantiation	104, 105	⊢
	:
84	theorem		⊢
	proveit.numbers.negation.negated_weak_bound
85	instantiation	135, 107, 136, 137	⊢
	: , :
86	instantiation	135, 108, 136, 137	⊢
	: , :
87	instantiation	106, 136, 107, 108, 109, 110	⊢
	: , : , :
88	instantiation	229, 227, 183	⊢
	: , : , :
89	theorem		⊢
	proveit.numbers.negation.distribute_neg_through_binary_sum
90	instantiation	229, 205, 111	⊢
	: , : , :
91	instantiation	112, 113	⊢
	:
92	instantiation	203	⊢
	: , :
93	theorem		⊢
	proveit.numbers.addition.association
94	instantiation	203	⊢
	: , :
95	instantiation	114, 115	⊢
	:
96	instantiation	116, 228, 218, 117*	⊢
	: , : , : , :
97	instantiation	229, 118, 166	⊢
	: , : , :
98	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_pos_within_real_pos
99	instantiation	229, 118, 153	⊢
	: , : , :
100	theorem		⊢
	proveit.numbers.division.div_as_mult
101	instantiation	229, 205, 119	⊢
	: , : , :
102	instantiation	229, 205, 136	⊢
	: , : , :
103	instantiation	176, 120, 121	⊢
	: , : , :
104	theorem		⊢
	proveit.physics.quantum.QPE._delta_b_in_interval
105	assumption		⊢
106	theorem		⊢
	proveit.numbers.division.weak_div_from_numer_bound__pos_denom
107	instantiation	229, 222, 122	⊢
	: , : , :
108	instantiation	229, 222, 123	⊢
	: , : , :
109	instantiation	124, 169, 200, 152	⊢
	: , : , :
110	instantiation	125, 153	⊢
	:
111	instantiation	214, 126	⊢
	:
112	theorem		⊢
	proveit.numbers.negation.double_negation
113	instantiation	229, 205, 126	⊢
	: , : , :
114	theorem		⊢
	proveit.numbers.negation.complex_closure
115	instantiation	229, 205, 127	⊢
	: , : , :
116	theorem		⊢
	proveit.numbers.addition.rational_pair_addition
117	instantiation	176, 128, 129	⊢
	: , : , :
118	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nat_pos_within_rational_pos
119	instantiation	219, 220, 211	⊢
	: , : , :
120	instantiation	162, 130	⊢
	: , : , :
121	instantiation	131, 186, 132, 204, 146, 133*	⊢
	: , : , :
122	instantiation	229, 227, 169	⊢
	: , : , :
123	instantiation	229, 227, 134	⊢
	: , : , :
124	theorem		⊢
	proveit.numbers.number_sets.integers.interval_lower_bound
125	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.natural_pos_is_pos
126	instantiation	135, 215, 201, 146	⊢
	: , :
127	instantiation	135, 215, 136, 137	⊢
	: , :
128	instantiation	170, 224, 138, 139, 140, 141	⊢
	: , : , : , :
129	instantiation	142, 143, 144	⊢
	:
130	instantiation	145, 186, 213, 206, 146, 147*	⊢
	: , : , :
131	theorem		⊢
	proveit.numbers.exponentiation.product_of_real_powers
132	instantiation	148, 213, 206	⊢
	: , :
133	instantiation	176, 149, 150	⊢
	: , : , :
134	instantiation	229, 151, 152	⊢
	: , : , :
135	theorem		⊢
	proveit.numbers.division.div_real_closure
136	instantiation	219, 220, 153	⊢
	: , : , :
137	instantiation	158, 153	⊢
	:
138	instantiation	203	⊢
	: , :
139	instantiation	203	⊢
	: , :
140	instantiation	176, 154, 155	⊢
	: , : , :
141	theorem		⊢
	proveit.numbers.numerals.decimals.mult_2_2
142	theorem		⊢
	proveit.numbers.division.frac_cancel_complete
143	instantiation	229, 205, 156	⊢
	: , : , :
144	instantiation	158, 157	⊢
	:
145	theorem		⊢
	proveit.numbers.exponentiation.real_power_of_real_power
146	instantiation	158, 217	⊢
	:
147	instantiation	159, 194, 160, 161*	⊢
	: , :
148	theorem		⊢
	proveit.numbers.addition.add_real_closure_bin
149	instantiation	162, 163	⊢
	: , : , :
150	instantiation	164, 165, 166, 167*	⊢
	: , :
151	instantiation	168, 169, 200	⊢
	: , :
152	assumption		⊢
153	theorem		⊢
	proveit.physics.quantum.QPE._two_pow_t_is_nat_pos
154	instantiation	170, 224, 171, 172, 173, 174	⊢
	: , : , : , :
155	theorem		⊢
	proveit.numbers.numerals.decimals.add_2_2
156	instantiation	229, 222, 175	⊢
	: , : , :
157	theorem		⊢
	proveit.numbers.numerals.decimals.posnat4
158	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos
159	theorem		⊢
	proveit.numbers.multiplication.mult_neg_right
160	instantiation	229, 205, 215	⊢
	: , : , :
161	instantiation	185, 194	⊢
	:
162	axiom		⊢
	proveit.logic.equality.substitution
163	instantiation	176, 177, 178	⊢
	: , : , :
164	theorem		⊢
	proveit.numbers.exponentiation.neg_power_as_div
165	instantiation	229, 179, 180	⊢
	: , : , :
166	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
167	instantiation	181, 186	⊢
	:
168	theorem		⊢
	proveit.numbers.number_sets.integers.int_interval_within_int
169	instantiation	182, 183, 228	⊢
	: , :
170	axiom		⊢
	proveit.core_expr_types.operations.operands_substitution
171	instantiation	203	⊢
	: , :
172	instantiation	203	⊢
	: , :
173	instantiation	184, 186	⊢
	:
174	instantiation	185, 186	⊢
	:
175	instantiation	229, 227, 187	⊢
	: , : , :
176	axiom		⊢
	proveit.logic.equality.equals_transitivity
177	instantiation	188, 189, 224, 231, 190, 191, 194, 195, 192	⊢
	: , : , : , : , : , :
178	instantiation	193, 194, 195, 196	⊢
	: , : , :
179	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero
180	instantiation	229, 197, 198	⊢
	: , : , :
181	theorem		⊢
	proveit.numbers.exponentiation.complex_x_to_first_power_is_x
182	theorem		⊢
	proveit.numbers.addition.add_int_closure_bin
183	instantiation	199, 200	⊢
	:
184	theorem		⊢
	proveit.numbers.multiplication.elim_one_left
185	theorem		⊢
	proveit.numbers.multiplication.elim_one_right
186	instantiation	229, 205, 201	⊢
	: , : , :
187	instantiation	229, 230, 202	⊢
	: , : , :
188	theorem		⊢
	proveit.numbers.addition.disassociation
189	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
190	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
191	instantiation	203	⊢
	: , :
192	instantiation	229, 205, 204	⊢
	: , : , :
193	theorem		⊢
	proveit.numbers.addition.subtraction.add_cancel_triple_13
194	instantiation	229, 205, 213	⊢
	: , : , :
195	instantiation	229, 205, 206	⊢
	: , : , :
196	instantiation	207	⊢
	:
197	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero
198	instantiation	229, 208, 209	⊢
	: , : , :
199	theorem		⊢
	proveit.numbers.negation.int_closure
200	instantiation	229, 210, 211	⊢
	: , : , :
201	instantiation	229, 222, 212	⊢
	: , : , :
202	theorem		⊢
	proveit.numbers.numerals.decimals.nat4
203	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
204	instantiation	214, 213	⊢
	:
205	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
206	instantiation	214, 215	⊢
	:
207	axiom		⊢
	proveit.logic.equality.equals_reflexivity
208	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
209	instantiation	229, 216, 217	⊢
	: , : , :
210	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_int
211	theorem		⊢
	proveit.physics.quantum.QPE._two_pow_t_minus_one_is_nat_pos
212	instantiation	229, 227, 218	⊢
	: , : , :
213	instantiation	219, 220, 221	⊢
	: , : , :
214	theorem		⊢
	proveit.numbers.negation.real_closure
215	instantiation	229, 222, 223	⊢
	: , : , :
216	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
217	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
218	instantiation	229, 230, 224	⊢
	: , : , :
219	theorem		⊢
	proveit.logic.sets.inclusion.unfold_subset_eq
220	instantiation	225, 226	⊢
	: , :
221	axiom		⊢
	proveit.physics.quantum.QPE._t_in_natural_pos
222	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
223	instantiation	229, 227, 228	⊢
	: , : , :
224	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
225	theorem		⊢
	proveit.logic.sets.inclusion.relax_proper_subset
226	theorem		⊢
	proveit.numbers.number_sets.real_numbers.nat_pos_within_real
227	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
228	instantiation	229, 230, 231	⊢
	: , : , :
229	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
230	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
231	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
*equality replacement requirements