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