| step type | requirements | statement |
0 | instantiation | 1, 2, 3 | , , ⊢ |
| : , : |
1 | reference | 20 | ⊢ |
2 | instantiation | 4, 122, 5, 115, 6 | , , ⊢ |
| : , : , : |
3 | instantiation | 7, 8 | , , ⊢ |
| : , : |
4 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.in_interval |
5 | instantiation | 133, 13 | ⊢ |
| : |
6 | instantiation | 9, 10, 11 | , , ⊢ |
| : , : |
7 | theorem | | ⊢ |
| proveit.logic.sets.membership.unfold_not_in_set |
8 | instantiation | 12, 13, 131, 115, 14 | , , ⊢ |
| : , : , : |
9 | theorem | | ⊢ |
| proveit.logic.booleans.conjunction.and_if_both |
10 | instantiation | 93, 122, 131, 119 | ⊢ |
| : , : , : |
11 | instantiation | 15, 96, 110, 16, 17, 18*, 19* | , , ⊢ |
| : , : , : |
12 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.int_not_in_interval |
13 | instantiation | 129, 116, 128 | ⊢ |
| : , : |
14 | instantiation | 20, 21, 22 | , , ⊢ |
| : , : |
15 | theorem | | ⊢ |
| proveit.numbers.addition.weak_bound_via_left_term_bound |
16 | instantiation | 42, 43, 24 | , , ⊢ |
| : , : , : |
17 | instantiation | 23, 24 | , , ⊢ |
| : |
18 | instantiation | 58, 25, 26 | ⊢ |
| : , : , : |
19 | instantiation | 48, 27 | , ⊢ |
| : , : |
20 | theorem | | ⊢ |
| proveit.logic.booleans.disjunction.or_if_only_left |
21 | instantiation | 28, 103, 29 | , ⊢ |
| : , : , : |
22 | instantiation | 30, 106, 31, 32 | ⊢ |
| : , : |
23 | theorem | | ⊢ |
| proveit.numbers.number_sets.natural_numbers.natural_pos_lower_bound |
24 | instantiation | 33, 34 | , , ⊢ |
| : |
25 | instantiation | 83, 132, 139, 88, 85, 89, 101, 91, 92 | ⊢ |
| : , : , : , : , : , : |
26 | instantiation | 35, 101, 91, 36 | ⊢ |
| : , : , : |
27 | instantiation | 70, 37, 38, 39 | , ⊢ |
| : , : , : , : |
28 | axiom | | ⊢ |
| proveit.numbers.ordering.transitivity_less_less |
29 | instantiation | 40, 41 | ⊢ |
| : |
30 | theorem | | ⊢ |
| proveit.numbers.ordering.not_less_from_less_eq |
31 | instantiation | 42, 43, 136 | ⊢ |
| : , : , : |
32 | instantiation | 44, 122, 131, 119 | ⊢ |
| : , : , : |
33 | theorem | | ⊢ |
| proveit.numbers.negation.nat_pos_closure |
34 | instantiation | 45, 46, 47 | , , ⊢ |
| : |
35 | theorem | | ⊢ |
| proveit.numbers.addition.subtraction.add_cancel_triple_13 |
36 | instantiation | 80 | ⊢ |
| : |
37 | instantiation | 81, 99, 101 | ⊢ |
| : , : |
38 | instantiation | 80 | ⊢ |
| : |
39 | instantiation | 48, 49 | , ⊢ |
| : , : |
40 | theorem | | ⊢ |
| proveit.numbers.number_sets.natural_numbers.natural_pos_is_pos |
41 | instantiation | 50, 51, 52 | ⊢ |
| : , : |
42 | theorem | | ⊢ |
| proveit.logic.sets.inclusion.unfold_subset_eq |
43 | instantiation | 53, 54 | ⊢ |
| : , : |
44 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.interval_upper_bound |
45 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.neg_int_is_int_neg |
46 | instantiation | 129, 116, 115 | , ⊢ |
| : , : |
47 | instantiation | 55, 106, 107, 98, 56, 57* | , , ⊢ |
| : , : , : |
48 | theorem | | ⊢ |
| proveit.logic.equality.equals_reversal |
49 | instantiation | 58, 59, 60 | , ⊢ |
| : , : , : |
50 | theorem | | ⊢ |
| proveit.numbers.addition.add_nat_pos_closure_bin |
51 | instantiation | 61, 116, 62 | ⊢ |
| : |
52 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.posnat1 |
53 | theorem | | ⊢ |
| proveit.logic.sets.inclusion.relax_proper_subset |
54 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.nat_pos_within_real |
55 | theorem | | ⊢ |
| proveit.numbers.addition.strong_bound_via_left_term_bound |
56 | instantiation | 63, 64, 65 | , ⊢ |
| : , : , : |
57 | instantiation | 66, 91, 67 | ⊢ |
| : , : |
58 | axiom | | ⊢ |
| proveit.logic.equality.equals_transitivity |
59 | instantiation | 68, 69 | , ⊢ |
| : , : , : |
60 | instantiation | 70, 71, 72, 73 | , ⊢ |
| : , : , : , : |
61 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.pos_int_is_natural_pos |
62 | instantiation | 74, 75, 76 | ⊢ |
| : , : , : |
63 | theorem | | ⊢ |
| proveit.logic.equality.sub_right_side_into |
64 | instantiation | 77, 124 | ⊢ |
| : , : |
65 | instantiation | 78, 119, 79* | , ⊢ |
| : |
66 | theorem | | ⊢ |
| proveit.numbers.addition.subtraction.add_cancel_reverse |
67 | instantiation | 80 | ⊢ |
| : |
68 | axiom | | ⊢ |
| proveit.logic.equality.substitution |
69 | instantiation | 81, 99, 91 | , ⊢ |
| : , : |
70 | theorem | | ⊢ |
| proveit.logic.equality.four_chain_transitivity |
71 | instantiation | 83, 88, 139, 132, 89, 84, 90, 86, 82 | , ⊢ |
| : , : , : , : , : , : |
72 | instantiation | 83, 139, 88, 84, 85, 89, 90, 86, 91, 92 | , ⊢ |
| : , : , : , : , : , : |
73 | instantiation | 87, 132, 88, 89, 90, 91, 92 | , ⊢ |
| : , : , : , : , : , : , : , : |
74 | theorem | | ⊢ |
| proveit.numbers.ordering.transitivity_less_less_eq |
75 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.less_0_1 |
76 | instantiation | 93, 128, 126, 121 | ⊢ |
| : , : , : |
77 | theorem | | ⊢ |
| proveit.logic.booleans.conjunction.right_from_and |
78 | theorem | | ⊢ |
| proveit.physics.quantum.QPE._modabs_in_full_domain_simp |
79 | instantiation | 94, 95 | ⊢ |
| : |
80 | axiom | | ⊢ |
| proveit.logic.equality.equals_reflexivity |
81 | theorem | | ⊢ |
| proveit.numbers.negation.distribute_neg_through_binary_sum |
82 | instantiation | 137, 108, 96 | ⊢ |
| : , : , : |
83 | theorem | | ⊢ |
| proveit.numbers.addition.disassociation |
84 | instantiation | 97 | ⊢ |
| : , : |
85 | instantiation | 97 | ⊢ |
| : , : |
86 | instantiation | 137, 108, 98 | ⊢ |
| : , : , : |
87 | theorem | | ⊢ |
| proveit.numbers.addition.subtraction.add_cancel_general_rev |
88 | axiom | | ⊢ |
| proveit.numbers.number_sets.natural_numbers.zero_in_nats |
89 | theorem | | ⊢ |
| proveit.core_expr_types.tuples.tuple_len_0_typical_eq |
90 | instantiation | 100, 99 | ⊢ |
| : |
91 | instantiation | 137, 108, 106 | ⊢ |
| : , : , : |
92 | instantiation | 100, 101 | ⊢ |
| : |
93 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.interval_lower_bound |
94 | theorem | | ⊢ |
| proveit.numbers.absolute_value.abs_neg_elim |
95 | instantiation | 102, 103 | ⊢ |
| : , : |
96 | instantiation | 104, 106, 105 | ⊢ |
| : , : |
97 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.tuple_len_2_typical_eq |
98 | instantiation | 109, 106 | ⊢ |
| : |
99 | instantiation | 137, 108, 107 | ⊢ |
| : , : , : |
100 | theorem | | ⊢ |
| proveit.numbers.negation.complex_closure |
101 | instantiation | 137, 108, 110 | ⊢ |
| : , : , : |
102 | theorem | | ⊢ |
| proveit.numbers.ordering.relax_less |
103 | assumption | | ⊢ |
104 | theorem | | ⊢ |
| proveit.numbers.addition.add_real_closure_bin |
105 | instantiation | 109, 110 | ⊢ |
| : |
106 | instantiation | 137, 113, 111 | ⊢ |
| : , : , : |
107 | instantiation | 137, 113, 112 | ⊢ |
| : , : , : |
108 | theorem | | ⊢ |
| proveit.numbers.number_sets.complex_numbers.real_within_complex |
109 | theorem | | ⊢ |
| proveit.numbers.negation.real_closure |
110 | instantiation | 137, 113, 114 | ⊢ |
| : , : , : |
111 | instantiation | 137, 117, 115 | ⊢ |
| : , : , : |
112 | instantiation | 137, 117, 116 | ⊢ |
| : , : , : |
113 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.rational_within_real |
114 | instantiation | 137, 117, 128 | ⊢ |
| : , : , : |
115 | instantiation | 137, 118, 119 | ⊢ |
| : , : , : |
116 | instantiation | 137, 120, 121 | ⊢ |
| : , : , : |
117 | theorem | | ⊢ |
| proveit.numbers.number_sets.rational_numbers.int_within_rational |
118 | instantiation | 125, 122, 131 | ⊢ |
| : , : |
119 | instantiation | 123, 124 | ⊢ |
| : , : |
120 | instantiation | 125, 128, 126 | ⊢ |
| : , : |
121 | assumption | | ⊢ |
122 | instantiation | 129, 127, 128 | ⊢ |
| : , : |
123 | theorem | | ⊢ |
| proveit.logic.booleans.conjunction.left_from_and |
124 | assumption | | ⊢ |
125 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.int_interval_within_int |
126 | instantiation | 129, 131, 130 | ⊢ |
| : , : |
127 | instantiation | 133, 131 | ⊢ |
| : |
128 | instantiation | 137, 138, 132 | ⊢ |
| : , : , : |
129 | theorem | | ⊢ |
| proveit.numbers.addition.add_int_closure_bin |
130 | instantiation | 133, 134 | ⊢ |
| : |
131 | instantiation | 137, 135, 136 | ⊢ |
| : , : , : |
132 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat1 |
133 | theorem | | ⊢ |
| proveit.numbers.negation.int_closure |
134 | instantiation | 137, 138, 139 | ⊢ |
| : , : , : |
135 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.nat_pos_within_int |
136 | theorem | | ⊢ |
| proveit.physics.quantum.QPE._two_pow_t_minus_one_is_nat_pos |
137 | theorem | | ⊢ |
| proveit.logic.sets.inclusion.superset_membership_from_proper_subset |
138 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.nat_within_int |
139 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat2 |
*equality replacement requirements |