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