| step type | requirements | statement |
0 | instantiation | 1, 2, 3, 4, 5 | ⊢ |
| : , : , : |
1 | reference | 50 | ⊢ |
2 | instantiation | 8, 6, 7 | ⊢ |
| : , : |
3 | instantiation | 8, 10, 11 | ⊢ |
| : , : |
4 | instantiation | 8, 10, 12 | ⊢ |
| : , : |
5 | instantiation | 9, 10, 11, 12, 13, 14 | ⊢ |
| : , : , : |
6 | instantiation | 189, 170, 15 | ⊢ |
| : , : , : |
7 | instantiation | 46, 161, 16, 17 | ⊢ |
| : , : |
8 | theorem | | ⊢ |
| proveit.numbers.multiplication.mult_real_closure_bin |
9 | theorem | | ⊢ |
| proveit.numbers.multiplication.weak_bound_via_right_factor_bound |
10 | instantiation | 189, 170, 18 | ⊢ |
| : , : , : |
11 | modus ponens | 19, 20 | ⊢ |
12 | instantiation | 46, 161, 123, 21 | ⊢ |
| : , : |
13 | instantiation | 22, 23, 24 | ⊢ |
| : , : , : |
14 | instantiation | 58, 25 | ⊢ |
| : , : |
15 | instantiation | 189, 28, 26 | ⊢ |
| : , : , : |
16 | instantiation | 63, 123, 191 | ⊢ |
| : , : |
17 | instantiation | 65, 27, 67 | ⊢ |
| : , : |
18 | instantiation | 189, 28, 43 | ⊢ |
| : , : , : |
19 | instantiation | 29 | ⊢ |
| : , : , : |
20 | generalization | 30 | ⊢ |
21 | instantiation | 31, 147 | ⊢ |
| : |
22 | theorem | | ⊢ |
| proveit.numbers.ordering.transitivity_less_eq_less_eq |
23 | instantiation | 32, 33, 34, 152, 139, 35, 36, 37* | ⊢ |
| : , : , : , : |
24 | instantiation | 38, 39, 40, 41 | ⊢ |
| : , : |
25 | instantiation | 42, 43 | ⊢ |
| : |
26 | instantiation | 59, 60, 44 | ⊢ |
| : , : |
27 | instantiation | 189, 79, 45 | ⊢ |
| : , : , : |
28 | theorem | | ⊢ |
| proveit.numbers.number_sets.rational_numbers.rational_pos_within_rational |
29 | theorem | | ⊢ |
| proveit.numbers.summation.summation_real_closure |
30 | instantiation | 46, 161, 47, 48 | , ⊢ |
| : , : |
31 | theorem | | ⊢ |
| proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos |
32 | theorem | | ⊢ |
| proveit.numbers.summation.integral_upper_bound_of_sum |
33 | theorem | | ⊢ |
| proveit.numbers.functions.one_over_x_sqrd_in_mon_dec_fxns |
34 | instantiation | 154, 49 | ⊢ |
| : , : |
35 | instantiation | 50, 161, 123, 95, 96, 87* | ⊢ |
| : , : , : |
36 | instantiation | 51, 52 | ⊢ |
| : , : , : |
37 | instantiation | 97, 53, 54 | ⊢ |
| : , : , : |
38 | theorem | | ⊢ |
| proveit.numbers.integration.boundedInvSqrdIntegral |
39 | instantiation | 189, 55, 56 | ⊢ |
| : , : , : |
40 | instantiation | 81, 106, 57 | ⊢ |
| : |
41 | instantiation | 58, 75 | ⊢ |
| : , : |
42 | theorem | | ⊢ |
| proveit.numbers.number_sets.rational_numbers.positive_if_in_rational_pos |
43 | instantiation | 59, 60, 61 | ⊢ |
| : , : |
44 | instantiation | 189, 76, 62 | ⊢ |
| : , : , : |
45 | instantiation | 189, 89, 147 | ⊢ |
| : , : , : |
46 | theorem | | ⊢ |
| proveit.numbers.division.div_real_closure |
47 | instantiation | 63, 64, 191 | , ⊢ |
| : , : |
48 | instantiation | 65, 66, 67 | , ⊢ |
| : , : |
49 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.real_pos_within_real |
50 | theorem | | ⊢ |
| proveit.numbers.addition.weak_bound_via_left_term_bound |
51 | theorem | | ⊢ |
| proveit.logic.sets.inclusion.fold_subset_eq |
52 | generalization | 68 | ⊢ |
53 | instantiation | 110, 113, 191, 181, 115, 69, 72, 150, 70 | ⊢ |
| : , : , : , : , : , : |
54 | instantiation | 71, 150, 72, 73 | ⊢ |
| : , : , : |
55 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.rational_pos_within_real_pos |
56 | instantiation | 189, 76, 147 | ⊢ |
| : , : , : |
57 | instantiation | 74, 159, 75 | ⊢ |
| : , : , : |
58 | theorem | | ⊢ |
| proveit.numbers.ordering.relax_less |
59 | theorem | | ⊢ |
| proveit.numbers.division.div_rational_pos_closure |
60 | instantiation | 189, 76, 174 | ⊢ |
| : , : , : |
61 | instantiation | 189, 76, 90 | ⊢ |
| : , : , : |
62 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.posnat4 |
63 | theorem | | ⊢ |
| proveit.numbers.exponentiation.exp_real_closure_nat_power |
64 | instantiation | 189, 170, 77 | , ⊢ |
| : , : , : |
65 | theorem | | ⊢ |
| proveit.numbers.exponentiation.exp_rational_non_zero__not_zero |
66 | instantiation | 189, 79, 78 | , ⊢ |
| : , : , : |
67 | instantiation | 189, 79, 80 | ⊢ |
| : , : , : |
68 | instantiation | 81, 82, 83 | , ⊢ |
| : |
69 | instantiation | 127 | ⊢ |
| : , : |
70 | instantiation | 84, 150 | ⊢ |
| : |
71 | theorem | | ⊢ |
| proveit.numbers.addition.subtraction.add_cancel_triple_23 |
72 | instantiation | 189, 160, 123 | ⊢ |
| : , : , : |
73 | instantiation | 85 | ⊢ |
| : |
74 | axiom | | ⊢ |
| proveit.numbers.ordering.transitivity_less_less |
75 | instantiation | 135, 86, 87 | ⊢ |
| : , : , : |
76 | theorem | | ⊢ |
| proveit.numbers.number_sets.rational_numbers.nat_pos_within_rational_pos |
77 | instantiation | 189, 177, 100 | , ⊢ |
| : , : , : |
78 | instantiation | 189, 89, 88 | , ⊢ |
| : , : , : |
79 | theorem | | ⊢ |
| proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero |
80 | instantiation | 189, 89, 90 | ⊢ |
| : , : , : |
81 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.pos_real_is_real_pos |
82 | instantiation | 91, 105, 106, 107 | , ⊢ |
| : , : , : |
83 | instantiation | 167, 92, 93 | , ⊢ |
| : , : , : |
84 | theorem | | ⊢ |
| proveit.numbers.negation.complex_closure |
85 | axiom | | ⊢ |
| proveit.logic.equality.equals_reflexivity |
86 | instantiation | 94, 123, 95, 161, 96, 168 | ⊢ |
| : , : , : |
87 | instantiation | 97, 98, 99 | ⊢ |
| : , : , : |
88 | instantiation | 158, 100, 101 | , ⊢ |
| : |
89 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int |
90 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.posnat2 |
91 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.all_in_interval_cc__is__real |
92 | instantiation | 102, 103 | ⊢ |
| : , : |
93 | instantiation | 104, 105, 106, 107 | , ⊢ |
| : , : , : |
94 | theorem | | ⊢ |
| proveit.numbers.ordering.less_eq_add_right_strong |
95 | instantiation | 189, 170, 108 | ⊢ |
| : , : , : |
96 | instantiation | 109, 179, 180, 176 | ⊢ |
| : , : , : |
97 | axiom | | ⊢ |
| proveit.logic.equality.equals_transitivity |
98 | instantiation | 110, 113, 191, 181, 115, 111, 116, 145, 150 | ⊢ |
| : , : , : , : , : , : |
99 | instantiation | 112, 181, 191, 113, 114, 115, 116, 145, 150, 117* | ⊢ |
| : , : , : , : , : , : |
100 | instantiation | 189, 118, 133 | , ⊢ |
| : , : , : |
101 | instantiation | 167, 119, 120 | , ⊢ |
| : , : , : |
102 | theorem | | ⊢ |
| proveit.numbers.addition.subtraction.pos_difference |
103 | instantiation | 121, 161, 122, 123, 159, 124* | ⊢ |
| : , : , : |
104 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.interval_cc_lower_bound |
105 | instantiation | 189, 170, 125 | ⊢ |
| : , : , : |
106 | instantiation | 189, 170, 126 | ⊢ |
| : , : , : |
107 | assumption | | ⊢ |
108 | instantiation | 189, 177, 180 | ⊢ |
| : , : , : |
109 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.interval_upper_bound |
110 | theorem | | ⊢ |
| proveit.numbers.addition.disassociation |
111 | instantiation | 127 | ⊢ |
| : , : |
112 | theorem | | ⊢ |
| proveit.numbers.addition.association |
113 | axiom | | ⊢ |
| proveit.numbers.number_sets.natural_numbers.zero_in_nats |
114 | instantiation | 127 | ⊢ |
| : , : |
115 | theorem | | ⊢ |
| proveit.core_expr_types.tuples.tuple_len_0_typical_eq |
116 | instantiation | 189, 160, 128 | ⊢ |
| : , : , : |
117 | instantiation | 135, 129, 130 | ⊢ |
| : , : , : |
118 | instantiation | 178, 152, 139 | ⊢ |
| : , : |
119 | instantiation | 131, 132 | ⊢ |
| : |
120 | instantiation | 175, 152, 139, 133 | , ⊢ |
| : , : , : |
121 | theorem | | ⊢ |
| proveit.numbers.addition.strong_bound_via_left_term_bound |
122 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.zero_is_real |
123 | instantiation | 189, 170, 134 | ⊢ |
| : , : , : |
124 | instantiation | 135, 136, 137 | ⊢ |
| : , : , : |
125 | instantiation | 189, 177, 138 | ⊢ |
| : , : , : |
126 | instantiation | 189, 177, 139 | ⊢ |
| : , : , : |
127 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.tuple_len_2_typical_eq |
128 | instantiation | 140, 141, 186 | ⊢ |
| : , : , : |
129 | instantiation | 142, 150, 143, 144 | ⊢ |
| : , : , : |
130 | instantiation | 149, 150, 145 | ⊢ |
| : , : |
131 | theorem | | ⊢ |
| proveit.numbers.number_sets.natural_numbers.natural_pos_is_pos |
132 | instantiation | 146, 147, 174 | ⊢ |
| : , : |
133 | assumption | | ⊢ |
134 | instantiation | 189, 177, 162 | ⊢ |
| : , : , : |
135 | theorem | | ⊢ |
| proveit.logic.equality.sub_right_side_into |
136 | instantiation | 148, 150 | ⊢ |
| : |
137 | instantiation | 149, 150, 151 | ⊢ |
| : , : |
138 | instantiation | 182, 152, 153 | ⊢ |
| : , : |
139 | instantiation | 182, 183, 153 | ⊢ |
| : , : |
140 | theorem | | ⊢ |
| proveit.logic.sets.inclusion.unfold_subset_eq |
141 | instantiation | 154, 155 | ⊢ |
| : , : |
142 | theorem | | ⊢ |
| proveit.numbers.addition.subtraction.subtract_from_add_reversed |
143 | instantiation | 189, 160, 156 | ⊢ |
| : , : , : |
144 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.add_1_1 |
145 | instantiation | 189, 160, 157 | ⊢ |
| : , : , : |
146 | theorem | | ⊢ |
| proveit.numbers.addition.add_nat_pos_closure_bin |
147 | instantiation | 158, 162, 159 | ⊢ |
| : |
148 | theorem | | ⊢ |
| proveit.numbers.addition.elim_zero_right |
149 | theorem | | ⊢ |
| proveit.numbers.addition.commutation |
150 | instantiation | 189, 160, 161 | ⊢ |
| : , : , : |
151 | theorem | | ⊢ |
| proveit.numbers.number_sets.complex_numbers.zero_is_complex |
152 | instantiation | 182, 162, 179 | ⊢ |
| : , : |
153 | instantiation | 189, 163, 164 | ⊢ |
| : , : , : |
154 | theorem | | ⊢ |
| proveit.logic.sets.inclusion.relax_proper_subset |
155 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.nat_pos_within_real |
156 | instantiation | 189, 170, 165 | ⊢ |
| : , : , : |
157 | instantiation | 189, 170, 166 | ⊢ |
| : , : , : |
158 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.pos_int_is_natural_pos |
159 | instantiation | 167, 168, 169 | ⊢ |
| : , : , : |
160 | theorem | | ⊢ |
| proveit.numbers.number_sets.complex_numbers.real_within_complex |
161 | instantiation | 189, 170, 171 | ⊢ |
| : , : , : |
162 | instantiation | 189, 172, 176 | ⊢ |
| : , : , : |
163 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.neg_int_within_int |
164 | instantiation | 173, 174 | ⊢ |
| : |
165 | instantiation | 189, 177, 188 | ⊢ |
| : , : , : |
166 | instantiation | 189, 177, 184 | ⊢ |
| : , : , : |
167 | theorem | | ⊢ |
| proveit.numbers.ordering.transitivity_less_less_eq |
168 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.less_0_1 |
169 | instantiation | 175, 179, 180, 176 | ⊢ |
| : , : , : |
170 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.rational_within_real |
171 | instantiation | 189, 177, 179 | ⊢ |
| : , : , : |
172 | instantiation | 178, 179, 180 | ⊢ |
| : , : |
173 | theorem | | ⊢ |
| proveit.numbers.negation.int_neg_closure |
174 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.posnat1 |
175 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.interval_lower_bound |
176 | assumption | | ⊢ |
177 | theorem | | ⊢ |
| proveit.numbers.number_sets.rational_numbers.int_within_rational |
178 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.int_interval_within_int |
179 | instantiation | 189, 190, 181 | ⊢ |
| : , : , : |
180 | instantiation | 182, 183, 184 | ⊢ |
| : , : |
181 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat1 |
182 | theorem | | ⊢ |
| proveit.numbers.addition.add_int_closure_bin |
183 | instantiation | 189, 185, 186 | ⊢ |
| : , : , : |
184 | instantiation | 187, 188 | ⊢ |
| : |
185 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.nat_pos_within_int |
186 | theorem | | ⊢ |
| proveit.physics.quantum.QPE._two_pow_t_minus_one_is_nat_pos |
187 | theorem | | ⊢ |
| proveit.numbers.negation.int_closure |
188 | instantiation | 189, 190, 191 | ⊢ |
| : , : , : |
189 | theorem | | ⊢ |
| proveit.logic.sets.inclusion.superset_membership_from_proper_subset |
190 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.nat_within_int |
191 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat2 |
*equality replacement requirements |