| step type | requirements | statement |
0 | generalization | 1 | ⊢ |
1 | instantiation | 2, 9, 3, 4, 5, 6 | ⊢ |
| : , : , : |
2 | theorem | | ⊢ |
| proveit.logic.booleans.disjunction.singular_constructive_dilemma |
3 | instantiation | 7, 9 | ⊢ |
| : |
4 | instantiation | 8, 9 | ⊢ |
| : |
5 | deduction | 10 | ⊢ |
6 | instantiation | 11, 12, 13 | ⊢ |
| : , : |
7 | theorem | | ⊢ |
| proveit.logic.booleans.negation.closure |
8 | theorem | | ⊢ |
| proveit.logic.booleans.unfold_is_bool |
9 | instantiation | 14 | ⊢ |
| : , : |
10 | instantiation | 15, 32, 16 | ⊢ |
| : , : |
11 | theorem | | ⊢ |
| proveit.logic.equality.rhs_via_equality |
12 | deduction | 17 | ⊢ |
13 | instantiation | 18, 19 | ⊢ |
| : , : , : |
14 | axiom | | ⊢ |
| proveit.logic.equality.equality_in_bool |
15 | theorem | | ⊢ |
| proveit.logic.booleans.disjunction.or_if_only_left |
16 | instantiation | 20, 21 | ⊢ |
| : , : |
17 | instantiation | 22, 23, 24 | , ⊢ |
| : , : |
18 | axiom | | ⊢ |
| proveit.logic.equality.substitution |
19 | instantiation | 25 | ⊢ |
| : , : |
20 | theorem | | ⊢ |
| proveit.logic.sets.membership.double_negated_membership |
21 | instantiation | 171, 172, 26 | ⊢ |
| : , : , : |
22 | theorem | | ⊢ |
| proveit.logic.booleans.disjunction.or_if_only_right |
23 | instantiation | 27, 31 | ⊢ |
| : , : |
24 | instantiation | 28, 29, 30, 31 | , ⊢ |
| : , : |
25 | axiom | | ⊢ |
| proveit.logic.equality.not_equals_def |
26 | instantiation | 42, 102, 32 | ⊢ |
| : , : , : |
27 | theorem | | ⊢ |
| proveit.logic.equality.unfold_not_equals |
28 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.not_int_if_not_int_in_interval |
29 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.zero_is_int |
30 | instantiation | 56, 33, 34, 35, 36 | ⊢ |
| : , : , : |
31 | assumption | | ⊢ |
32 | assumption | | ⊢ |
33 | instantiation | 80, 120, 113 | ⊢ |
| : , : |
34 | instantiation | 80, 120, 121 | ⊢ |
| : , : |
35 | instantiation | 37, 113, 121, 47 | ⊢ |
| : , : , : |
36 | instantiation | 60, 38, 39 | ⊢ |
| : , : |
37 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.all_in_interval_oo__is__real |
38 | instantiation | 42, 40, 41 | ⊢ |
| : , : , : |
39 | instantiation | 42, 43, 44 | ⊢ |
| : , : , : |
40 | instantiation | 45, 113, 121, 47 | ⊢ |
| : , : , : |
41 | instantiation | 48, 94 | ⊢ |
| : |
42 | theorem | | ⊢ |
| proveit.logic.equality.sub_left_side_into |
43 | instantiation | 46, 113, 121, 47 | ⊢ |
| : , : , : |
44 | instantiation | 48, 95 | ⊢ |
| : |
45 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.interval_oo_lower_bound |
46 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.interval_oo_upper_bound |
47 | instantiation | 49, 50 | ⊢ |
| : |
48 | theorem | | ⊢ |
| proveit.numbers.addition.elim_zero_left |
49 | instantiation | 51, 173, 52, 53, 54 | ⊢ |
| : , : , : , : |
50 | assumption | | ⊢ |
51 | theorem | | ⊢ |
| proveit.logic.sets.enumeration.true_for_each_then_true_for_all |
52 | instantiation | 151 | ⊢ |
| : , : |
53 | instantiation | 56, 113, 121, 114, 55 | ⊢ |
| : , : , : |
54 | instantiation | 56, 113, 121, 117, 57 | ⊢ |
| : , : , : |
55 | instantiation | 60, 58, 59 | ⊢ |
| : , : |
56 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.in_IntervalOO |
57 | instantiation | 60, 61, 62 | ⊢ |
| : , : |
58 | instantiation | 67, 113, 120, 63, 64, 65*, 66* | ⊢ |
| : , : , : |
59 | instantiation | 110, 120, 121, 122 | ⊢ |
| : , : , : |
60 | theorem | | ⊢ |
| proveit.logic.booleans.conjunction.and_if_both |
61 | instantiation | 67, 131, 68, 69, 70*, 71* | ⊢ |
| : , : , : |
62 | instantiation | 75, 72, 84 | ⊢ |
| : , : , : |
63 | instantiation | 80, 114, 121 | ⊢ |
| : , : |
64 | instantiation | 81, 120, 114, 121, 73, 74 | ⊢ |
| : , : , : |
65 | instantiation | 75, 76, 77 | ⊢ |
| : , : , : |
66 | instantiation | 134, 78, 79 | ⊢ |
| : , : , : |
67 | theorem | | ⊢ |
| proveit.numbers.addition.strong_bound_via_left_term_bound |
68 | instantiation | 80, 117, 141 | ⊢ |
| : , : |
69 | instantiation | 81, 131, 117, 141, 82, 112 | ⊢ |
| : , : , : |
70 | instantiation | 83, 107, 95, 84 | ⊢ |
| : , : , : |
71 | instantiation | 134, 85, 86 | ⊢ |
| : , : , : |
72 | instantiation | 87, 117, 141, 88, 89 | ⊢ |
| : , : , : |
73 | instantiation | 98, 120, 121, 122 | ⊢ |
| : , : , : |
74 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.less_0_1 |
75 | theorem | | ⊢ |
| proveit.logic.equality.sub_right_side_into |
76 | instantiation | 90, 94 | ⊢ |
| : |
77 | instantiation | 91, 94, 92 | ⊢ |
| : , : |
78 | instantiation | 101, 102, 173, 150, 103, 93, 96, 95, 94 | ⊢ |
| : , : , : , : , : , : |
79 | instantiation | 106, 95, 96, 97 | ⊢ |
| : , : , : |
80 | theorem | | ⊢ |
| proveit.numbers.addition.add_real_closure_bin |
81 | theorem | | ⊢ |
| proveit.numbers.ordering.less_eq_add_right_strong |
82 | instantiation | 98, 131, 141, 132 | ⊢ |
| : , : , : |
83 | theorem | | ⊢ |
| proveit.numbers.addition.subtraction.negated_add |
84 | instantiation | 99, 142, 170, 100* | ⊢ |
| : , : , : , : |
85 | instantiation | 101, 102, 173, 150, 103, 104, 108, 107, 105 | ⊢ |
| : , : , : , : , : , : |
86 | instantiation | 106, 107, 108, 109 | ⊢ |
| : , : , : |
87 | theorem | | ⊢ |
| proveit.numbers.ordering.less_add_right |
88 | instantiation | 110, 131, 141, 132 | ⊢ |
| : , : , : |
89 | instantiation | 111, 112 | ⊢ |
| : , : |
90 | theorem | | ⊢ |
| proveit.numbers.addition.elim_zero_right |
91 | theorem | | ⊢ |
| proveit.numbers.addition.commutation |
92 | theorem | | ⊢ |
| proveit.numbers.number_sets.complex_numbers.zero_is_complex |
93 | instantiation | 151 | ⊢ |
| : , : |
94 | instantiation | 171, 158, 113 | ⊢ |
| : , : , : |
95 | instantiation | 171, 158, 121 | ⊢ |
| : , : , : |
96 | instantiation | 171, 158, 114 | ⊢ |
| : , : , : |
97 | instantiation | 118 | ⊢ |
| : |
98 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.interval_co_lower_bound |
99 | theorem | | ⊢ |
| proveit.numbers.addition.rational_pair_addition |
100 | instantiation | 134, 115, 116 | ⊢ |
| : , : , : |
101 | theorem | | ⊢ |
| proveit.numbers.addition.disassociation |
102 | axiom | | ⊢ |
| proveit.numbers.number_sets.natural_numbers.zero_in_nats |
103 | theorem | | ⊢ |
| proveit.core_expr_types.tuples.tuple_len_0_typical_eq |
104 | instantiation | 151 | ⊢ |
| : , : |
105 | instantiation | 171, 158, 131 | ⊢ |
| : , : , : |
106 | theorem | | ⊢ |
| proveit.numbers.addition.subtraction.add_cancel_triple_23 |
107 | instantiation | 171, 158, 141 | ⊢ |
| : , : , : |
108 | instantiation | 171, 158, 117 | ⊢ |
| : , : , : |
109 | instantiation | 118 | ⊢ |
| : |
110 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.interval_co_upper_bound |
111 | theorem | | ⊢ |
| proveit.numbers.ordering.relax_less |
112 | instantiation | 119, 157 | ⊢ |
| : |
113 | instantiation | 140, 121 | ⊢ |
| : |
114 | instantiation | 130, 120, 121, 122 | ⊢ |
| : , : , : |
115 | instantiation | 143, 173, 123, 124, 125, 126 | ⊢ |
| : , : , : , : |
116 | instantiation | 127, 128, 129 | ⊢ |
| : |
117 | instantiation | 130, 131, 141, 132 | ⊢ |
| : , : , : |
118 | axiom | | ⊢ |
| proveit.logic.equality.equals_reflexivity |
119 | theorem | | ⊢ |
| proveit.numbers.number_sets.rational_numbers.positive_if_in_rational_pos |
120 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.zero_is_real |
121 | instantiation | 171, 164, 133 | ⊢ |
| : , : , : |
122 | theorem | | ⊢ |
| proveit.physics.quantum.QPE._scaled_delta_b_floor_in_interval |
123 | instantiation | 151 | ⊢ |
| : , : |
124 | instantiation | 151 | ⊢ |
| : , : |
125 | instantiation | 134, 135, 136 | ⊢ |
| : , : , : |
126 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.mult_2_2 |
127 | theorem | | ⊢ |
| proveit.numbers.division.frac_cancel_complete |
128 | instantiation | 171, 158, 137 | ⊢ |
| : , : , : |
129 | instantiation | 138, 139 | ⊢ |
| : |
130 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.all_in_interval_co__is__real |
131 | instantiation | 140, 141 | ⊢ |
| : |
132 | theorem | | ⊢ |
| proveit.physics.quantum.QPE._scaled_delta_b_round_in_interval |
133 | instantiation | 171, 169, 142 | ⊢ |
| : , : , : |
134 | axiom | | ⊢ |
| proveit.logic.equality.equals_transitivity |
135 | instantiation | 143, 173, 144, 145, 146, 147 | ⊢ |
| : , : , : , : |
136 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.add_2_2 |
137 | instantiation | 171, 164, 148 | ⊢ |
| : , : , : |
138 | theorem | | ⊢ |
| proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos |
139 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.posnat4 |
140 | theorem | | ⊢ |
| proveit.numbers.negation.real_closure |
141 | instantiation | 171, 164, 149 | ⊢ |
| : , : , : |
142 | instantiation | 171, 172, 150 | ⊢ |
| : , : , : |
143 | axiom | | ⊢ |
| proveit.core_expr_types.operations.operands_substitution |
144 | instantiation | 151 | ⊢ |
| : , : |
145 | instantiation | 151 | ⊢ |
| : , : |
146 | instantiation | 152, 154 | ⊢ |
| : |
147 | instantiation | 153, 154 | ⊢ |
| : |
148 | instantiation | 171, 169, 155 | ⊢ |
| : , : , : |
149 | instantiation | 171, 156, 157 | ⊢ |
| : , : , : |
150 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat1 |
151 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.tuple_len_2_typical_eq |
152 | theorem | | ⊢ |
| proveit.numbers.multiplication.elim_one_left |
153 | theorem | | ⊢ |
| proveit.numbers.multiplication.elim_one_right |
154 | instantiation | 171, 158, 159 | ⊢ |
| : , : , : |
155 | instantiation | 171, 172, 160 | ⊢ |
| : , : , : |
156 | theorem | | ⊢ |
| proveit.numbers.number_sets.rational_numbers.rational_pos_within_rational |
157 | instantiation | 161, 162, 163 | ⊢ |
| : , : |
158 | theorem | | ⊢ |
| proveit.numbers.number_sets.complex_numbers.real_within_complex |
159 | instantiation | 171, 164, 165 | ⊢ |
| : , : , : |
160 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat4 |
161 | theorem | | ⊢ |
| proveit.numbers.division.div_rational_pos_closure |
162 | instantiation | 171, 167, 166 | ⊢ |
| : , : , : |
163 | instantiation | 171, 167, 168 | ⊢ |
| : , : , : |
164 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.rational_within_real |
165 | instantiation | 171, 169, 170 | ⊢ |
| : , : , : |
166 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.posnat1 |
167 | theorem | | ⊢ |
| proveit.numbers.number_sets.rational_numbers.nat_pos_within_rational_pos |
168 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.posnat2 |
169 | theorem | | ⊢ |
| proveit.numbers.number_sets.rational_numbers.int_within_rational |
170 | instantiation | 171, 172, 173 | ⊢ |
| : , : , : |
171 | theorem | | ⊢ |
| proveit.logic.sets.inclusion.superset_membership_from_proper_subset |
172 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.nat_within_int |
173 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat2 |
*equality replacement requirements |