| step type | requirements | statement |
0 | instantiation | 1, 2, 3 | ⊢ |
| : , : , : |
1 | theorem | | ⊢ |
| proveit.logic.equality.sub_left_side_into |
2 | instantiation | 4, 71, 79, 5 | ⊢ |
| : , : , : |
3 | instantiation | 6, 53 | ⊢ |
| : |
4 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.interval_oo_upper_bound |
5 | instantiation | 7, 8 | ⊢ |
| : |
6 | theorem | | ⊢ |
| proveit.numbers.addition.elim_zero_left |
7 | instantiation | 9, 131, 10, 11, 12 | ⊢ |
| : , : , : , : |
8 | assumption | | ⊢ |
9 | theorem | | ⊢ |
| proveit.logic.sets.enumeration.true_for_each_then_true_for_all |
10 | instantiation | 109 | ⊢ |
| : , : |
11 | instantiation | 14, 71, 79, 72, 13 | ⊢ |
| : , : , : |
12 | instantiation | 14, 71, 79, 75, 15 | ⊢ |
| : , : , : |
13 | instantiation | 18, 16, 17 | ⊢ |
| : , : |
14 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.in_IntervalOO |
15 | instantiation | 18, 19, 20 | ⊢ |
| : , : |
16 | instantiation | 25, 71, 78, 21, 22, 23*, 24* | ⊢ |
| : , : , : |
17 | instantiation | 68, 78, 79, 80 | ⊢ |
| : , : , : |
18 | theorem | | ⊢ |
| proveit.logic.booleans.conjunction.and_if_both |
19 | instantiation | 25, 89, 26, 27, 28*, 29* | ⊢ |
| : , : , : |
20 | instantiation | 33, 30, 42 | ⊢ |
| : , : , : |
21 | instantiation | 38, 72, 79 | ⊢ |
| : , : |
22 | instantiation | 39, 78, 72, 79, 31, 32 | ⊢ |
| : , : , : |
23 | instantiation | 33, 34, 35 | ⊢ |
| : , : , : |
24 | instantiation | 92, 36, 37 | ⊢ |
| : , : , : |
25 | theorem | | ⊢ |
| proveit.numbers.addition.strong_bound_via_left_term_bound |
26 | instantiation | 38, 75, 99 | ⊢ |
| : , : |
27 | instantiation | 39, 89, 75, 99, 40, 70 | ⊢ |
| : , : , : |
28 | instantiation | 41, 65, 53, 42 | ⊢ |
| : , : , : |
29 | instantiation | 92, 43, 44 | ⊢ |
| : , : , : |
30 | instantiation | 45, 75, 99, 46, 47 | ⊢ |
| : , : , : |
31 | instantiation | 56, 78, 79, 80 | ⊢ |
| : , : , : |
32 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.less_0_1 |
33 | theorem | | ⊢ |
| proveit.logic.equality.sub_right_side_into |
34 | instantiation | 48, 52 | ⊢ |
| : |
35 | instantiation | 49, 52, 50 | ⊢ |
| : , : |
36 | instantiation | 59, 60, 131, 108, 61, 51, 54, 53, 52 | ⊢ |
| : , : , : , : , : , : |
37 | instantiation | 64, 53, 54, 55 | ⊢ |
| : , : , : |
38 | theorem | | ⊢ |
| proveit.numbers.addition.add_real_closure_bin |
39 | theorem | | ⊢ |
| proveit.numbers.ordering.less_eq_add_right_strong |
40 | instantiation | 56, 89, 99, 90 | ⊢ |
| : , : , : |
41 | theorem | | ⊢ |
| proveit.numbers.addition.subtraction.negated_add |
42 | instantiation | 57, 100, 128, 58* | ⊢ |
| : , : , : , : |
43 | instantiation | 59, 60, 131, 108, 61, 62, 66, 65, 63 | ⊢ |
| : , : , : , : , : , : |
44 | instantiation | 64, 65, 66, 67 | ⊢ |
| : , : , : |
45 | theorem | | ⊢ |
| proveit.numbers.ordering.less_add_right |
46 | instantiation | 68, 89, 99, 90 | ⊢ |
| : , : , : |
47 | instantiation | 69, 70 | ⊢ |
| : , : |
48 | theorem | | ⊢ |
| proveit.numbers.addition.elim_zero_right |
49 | theorem | | ⊢ |
| proveit.numbers.addition.commutation |
50 | theorem | | ⊢ |
| proveit.numbers.number_sets.complex_numbers.zero_is_complex |
51 | instantiation | 109 | ⊢ |
| : , : |
52 | instantiation | 129, 116, 71 | ⊢ |
| : , : , : |
53 | instantiation | 129, 116, 79 | ⊢ |
| : , : , : |
54 | instantiation | 129, 116, 72 | ⊢ |
| : , : , : |
55 | instantiation | 76 | ⊢ |
| : |
56 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.interval_co_lower_bound |
57 | theorem | | ⊢ |
| proveit.numbers.addition.rational_pair_addition |
58 | instantiation | 92, 73, 74 | ⊢ |
| : , : , : |
59 | theorem | | ⊢ |
| proveit.numbers.addition.disassociation |
60 | axiom | | ⊢ |
| proveit.numbers.number_sets.natural_numbers.zero_in_nats |
61 | theorem | | ⊢ |
| proveit.core_expr_types.tuples.tuple_len_0_typical_eq |
62 | instantiation | 109 | ⊢ |
| : , : |
63 | instantiation | 129, 116, 89 | ⊢ |
| : , : , : |
64 | theorem | | ⊢ |
| proveit.numbers.addition.subtraction.add_cancel_triple_23 |
65 | instantiation | 129, 116, 99 | ⊢ |
| : , : , : |
66 | instantiation | 129, 116, 75 | ⊢ |
| : , : , : |
67 | instantiation | 76 | ⊢ |
| : |
68 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.interval_co_upper_bound |
69 | theorem | | ⊢ |
| proveit.numbers.ordering.relax_less |
70 | instantiation | 77, 115 | ⊢ |
| : |
71 | instantiation | 98, 79 | ⊢ |
| : |
72 | instantiation | 88, 78, 79, 80 | ⊢ |
| : , : , : |
73 | instantiation | 101, 131, 81, 82, 83, 84 | ⊢ |
| : , : , : , : |
74 | instantiation | 85, 86, 87 | ⊢ |
| : |
75 | instantiation | 88, 89, 99, 90 | ⊢ |
| : , : , : |
76 | axiom | | ⊢ |
| proveit.logic.equality.equals_reflexivity |
77 | theorem | | ⊢ |
| proveit.numbers.number_sets.rational_numbers.positive_if_in_rational_pos |
78 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.zero_is_real |
79 | instantiation | 129, 122, 91 | ⊢ |
| : , : , : |
80 | theorem | | ⊢ |
| proveit.physics.quantum.QPE._scaled_delta_b_floor_in_interval |
81 | instantiation | 109 | ⊢ |
| : , : |
82 | instantiation | 109 | ⊢ |
| : , : |
83 | instantiation | 92, 93, 94 | ⊢ |
| : , : , : |
84 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.mult_2_2 |
85 | theorem | | ⊢ |
| proveit.numbers.division.frac_cancel_complete |
86 | instantiation | 129, 116, 95 | ⊢ |
| : , : , : |
87 | instantiation | 96, 97 | ⊢ |
| : |
88 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.all_in_interval_co__is__real |
89 | instantiation | 98, 99 | ⊢ |
| : |
90 | theorem | | ⊢ |
| proveit.physics.quantum.QPE._scaled_delta_b_round_in_interval |
91 | instantiation | 129, 127, 100 | ⊢ |
| : , : , : |
92 | axiom | | ⊢ |
| proveit.logic.equality.equals_transitivity |
93 | instantiation | 101, 131, 102, 103, 104, 105 | ⊢ |
| : , : , : , : |
94 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.add_2_2 |
95 | instantiation | 129, 122, 106 | ⊢ |
| : , : , : |
96 | theorem | | ⊢ |
| proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos |
97 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.posnat4 |
98 | theorem | | ⊢ |
| proveit.numbers.negation.real_closure |
99 | instantiation | 129, 122, 107 | ⊢ |
| : , : , : |
100 | instantiation | 129, 130, 108 | ⊢ |
| : , : , : |
101 | axiom | | ⊢ |
| proveit.core_expr_types.operations.operands_substitution |
102 | instantiation | 109 | ⊢ |
| : , : |
103 | instantiation | 109 | ⊢ |
| : , : |
104 | instantiation | 110, 112 | ⊢ |
| : |
105 | instantiation | 111, 112 | ⊢ |
| : |
106 | instantiation | 129, 127, 113 | ⊢ |
| : , : , : |
107 | instantiation | 129, 114, 115 | ⊢ |
| : , : , : |
108 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat1 |
109 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.tuple_len_2_typical_eq |
110 | theorem | | ⊢ |
| proveit.numbers.multiplication.elim_one_left |
111 | theorem | | ⊢ |
| proveit.numbers.multiplication.elim_one_right |
112 | instantiation | 129, 116, 117 | ⊢ |
| : , : , : |
113 | instantiation | 129, 130, 118 | ⊢ |
| : , : , : |
114 | theorem | | ⊢ |
| proveit.numbers.number_sets.rational_numbers.rational_pos_within_rational |
115 | instantiation | 119, 120, 121 | ⊢ |
| : , : |
116 | theorem | | ⊢ |
| proveit.numbers.number_sets.complex_numbers.real_within_complex |
117 | instantiation | 129, 122, 123 | ⊢ |
| : , : , : |
118 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat4 |
119 | theorem | | ⊢ |
| proveit.numbers.division.div_rational_pos_closure |
120 | instantiation | 129, 125, 124 | ⊢ |
| : , : , : |
121 | instantiation | 129, 125, 126 | ⊢ |
| : , : , : |
122 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.rational_within_real |
123 | instantiation | 129, 127, 128 | ⊢ |
| : , : , : |
124 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.posnat1 |
125 | theorem | | ⊢ |
| proveit.numbers.number_sets.rational_numbers.nat_pos_within_rational_pos |
126 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.posnat2 |
127 | theorem | | ⊢ |
| proveit.numbers.number_sets.rational_numbers.int_within_rational |
128 | instantiation | 129, 130, 131 | ⊢ |
| : , : , : |
129 | theorem | | ⊢ |
| proveit.logic.sets.inclusion.superset_membership_from_proper_subset |
130 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.nat_within_int |
131 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat2 |
*equality replacement requirements |