| step type | requirements | statement |
0 | modus ponens | 1, 2 | ⊢ |
1 | instantiation | 3 | ⊢ |
| : , : , : |
2 | generalization | 4 | ⊢ |
3 | theorem | | ⊢ |
| proveit.numbers.summation.weak_summation_from_summands_bound |
4 | instantiation | 5, 6, 7, 8, 9 | , ⊢ |
| : , : , : |
5 | theorem | | ⊢ |
| proveit.numbers.division.weak_div_from_denom_bound__all_pos |
6 | instantiation | 128, 10, 11 | ⊢ |
| : , : , : |
7 | instantiation | 13, 58, 12 | , ⊢ |
| : |
8 | instantiation | 13, 22, 14 | , ⊢ |
| : |
9 | instantiation | 15, 93, 22, 58, 16, 17 | , ⊢ |
| : , : , : |
10 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.rational_nonneg_within_real_nonneg |
11 | instantiation | 128, 18, 120 | ⊢ |
| : , : , : |
12 | instantiation | 19, 78, 20, 34 | , ⊢ |
| : , : |
13 | theorem | | ⊢ |
| proveit.numbers.exponentiation.sqrd_pos_closure |
14 | instantiation | 21, 22, 50, 23 | , ⊢ |
| : , : |
15 | theorem | | ⊢ |
| proveit.numbers.exponentiation.exp_even_neg_base_lesseq |
16 | instantiation | 24, 25, 34 | , ⊢ |
| : , : |
17 | instantiation | 26 | ⊢ |
| : |
18 | theorem | | ⊢ |
| proveit.numbers.number_sets.rational_numbers.nat_within_rational_nonneg |
19 | theorem | | ⊢ |
| proveit.numbers.ordering.less_is_not_eq_int |
20 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.zero_is_int |
21 | theorem | | ⊢ |
| proveit.numbers.ordering.less_is_not_eq |
22 | instantiation | 27, 58, 31 | , ⊢ |
| : , : |
23 | instantiation | 28, 29 | , ⊢ |
| : , : |
24 | theorem | | ⊢ |
| proveit.logic.booleans.conjunction.and_if_both |
25 | instantiation | 30, 58, 31, 50, 32, 33* | , ⊢ |
| : , : , : |
26 | axiom | | ⊢ |
| proveit.logic.equality.equals_reflexivity |
27 | theorem | | ⊢ |
| proveit.numbers.addition.add_real_closure_bin |
28 | theorem | | ⊢ |
| proveit.numbers.addition.subtraction.neg_difference |
29 | instantiation | 100, 34, 38 | , ⊢ |
| : , : , : |
30 | theorem | | ⊢ |
| proveit.numbers.addition.weak_bound_via_right_term_bound |
31 | instantiation | 47, 37 | ⊢ |
| : |
32 | instantiation | 35, 36, 50, 37, 38, 39, 40*, 41* | ⊢ |
| : , : , : |
33 | instantiation | 42, 43 | , ⊢ |
| : |
34 | instantiation | 44, 45, 46 | , ⊢ |
| : , : , : |
35 | theorem | | ⊢ |
| proveit.numbers.multiplication.reversed_weak_bound_via_right_factor_bound |
36 | instantiation | 47, 82 | ⊢ |
| : |
37 | instantiation | 48, 50, 82, 51 | ⊢ |
| : , : , : |
38 | instantiation | 49, 50, 82, 51 | ⊢ |
| : , : , : |
39 | instantiation | 52, 53 | ⊢ |
| : , : |
40 | instantiation | 54, 55, 56 | ⊢ |
| : , : , : |
41 | instantiation | 57, 64 | ⊢ |
| : |
42 | theorem | | ⊢ |
| proveit.numbers.addition.elim_zero_right |
43 | instantiation | 128, 94, 58 | , ⊢ |
| : , : , : |
44 | theorem | | ⊢ |
| proveit.numbers.ordering.transitivity_less_eq_less |
45 | instantiation | 59, 98, 99, 89 | , ⊢ |
| : , : , : |
46 | instantiation | 61, 60 | ⊢ |
| : |
47 | theorem | | ⊢ |
| proveit.numbers.negation.real_closure |
48 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.all_in_interval_co__is__real |
49 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.interval_co_lower_bound |
50 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.zero_is_real |
51 | theorem | | ⊢ |
| proveit.physics.quantum.QPE._scaled_delta_b_floor_in_interval |
52 | theorem | | ⊢ |
| proveit.numbers.ordering.relax_less |
53 | instantiation | 61, 62 | ⊢ |
| : |
54 | axiom | | ⊢ |
| proveit.logic.equality.equals_transitivity |
55 | instantiation | 63, 120, 130, 73, 75, 74, 64, 76, 77 | ⊢ |
| : , : , : , : , : , : |
56 | instantiation | 65, 73, 130, 74, 75, 71, 76, 77, 66* | ⊢ |
| : , : , : , : , : |
57 | theorem | | ⊢ |
| proveit.numbers.multiplication.mult_zero_right |
58 | instantiation | 128, 103, 67 | , ⊢ |
| : , : , : |
59 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.interval_upper_bound |
60 | instantiation | 69, 68 | ⊢ |
| : |
61 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.negative_if_in_neg_int |
62 | instantiation | 69, 81 | ⊢ |
| : |
63 | theorem | | ⊢ |
| proveit.numbers.multiplication.disassociation |
64 | instantiation | 70, 71 | ⊢ |
| : |
65 | theorem | | ⊢ |
| proveit.numbers.multiplication.mult_neg_any |
66 | instantiation | 72, 73, 130, 74, 75, 76, 77 | ⊢ |
| : , : , : , : |
67 | instantiation | 128, 111, 78 | , ⊢ |
| : , : , : |
68 | instantiation | 79, 80, 81 | ⊢ |
| : , : |
69 | theorem | | ⊢ |
| proveit.numbers.negation.int_neg_closure |
70 | theorem | | ⊢ |
| proveit.numbers.negation.complex_closure |
71 | instantiation | 128, 94, 82 | ⊢ |
| : , : , : |
72 | theorem | | ⊢ |
| proveit.numbers.multiplication.elim_one_any |
73 | axiom | | ⊢ |
| proveit.numbers.number_sets.natural_numbers.zero_in_nats |
74 | theorem | | ⊢ |
| proveit.core_expr_types.tuples.tuple_len_0_typical_eq |
75 | instantiation | 83 | ⊢ |
| : , : |
76 | instantiation | 84, 85, 86 | ⊢ |
| : , : |
77 | instantiation | 128, 94, 87 | ⊢ |
| : , : , : |
78 | instantiation | 128, 88, 89 | , ⊢ |
| : , : , : |
79 | theorem | | ⊢ |
| proveit.numbers.addition.add_nat_pos_closure_bin |
80 | instantiation | 90, 114, 91 | ⊢ |
| : |
81 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.posnat1 |
82 | instantiation | 128, 103, 92 | ⊢ |
| : , : , : |
83 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.tuple_len_2_typical_eq |
84 | theorem | | ⊢ |
| proveit.numbers.exponentiation.exp_complex_closure |
85 | instantiation | 128, 94, 93 | ⊢ |
| : , : , : |
86 | instantiation | 128, 94, 95 | ⊢ |
| : , : , : |
87 | instantiation | 96, 97 | ⊢ |
| : |
88 | instantiation | 117, 98, 99 | ⊢ |
| : , : |
89 | assumption | | ⊢ |
90 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.pos_int_is_natural_pos |
91 | instantiation | 100, 101, 102 | ⊢ |
| : , : , : |
92 | instantiation | 128, 111, 118 | ⊢ |
| : , : , : |
93 | instantiation | 128, 103, 104 | ⊢ |
| : , : , : |
94 | theorem | | ⊢ |
| proveit.numbers.number_sets.complex_numbers.real_within_complex |
95 | instantiation | 105, 106, 107 | ⊢ |
| : , : , : |
96 | theorem | | ⊢ |
| proveit.physics.quantum.QPE._delta_b_is_real |
97 | theorem | | ⊢ |
| proveit.physics.quantum.QPE._best_floor_is_int |
98 | instantiation | 121, 108, 118 | ⊢ |
| : , : |
99 | instantiation | 126, 109 | ⊢ |
| : |
100 | theorem | | ⊢ |
| proveit.numbers.ordering.transitivity_less_less_eq |
101 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.less_0_1 |
102 | instantiation | 110, 118, 119, 116 | ⊢ |
| : , : , : |
103 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.rational_within_real |
104 | instantiation | 128, 111, 127 | ⊢ |
| : , : , : |
105 | theorem | | ⊢ |
| proveit.logic.sets.inclusion.unfold_subset_eq |
106 | instantiation | 112, 113 | ⊢ |
| : , : |
107 | axiom | | ⊢ |
| proveit.physics.quantum.QPE._t_in_natural_pos |
108 | instantiation | 126, 122 | ⊢ |
| : |
109 | instantiation | 121, 114, 118 | ⊢ |
| : , : |
110 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.interval_lower_bound |
111 | theorem | | ⊢ |
| proveit.numbers.number_sets.rational_numbers.int_within_rational |
112 | theorem | | ⊢ |
| proveit.logic.sets.inclusion.relax_proper_subset |
113 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.nat_pos_within_real |
114 | instantiation | 128, 115, 116 | ⊢ |
| : , : , : |
115 | instantiation | 117, 118, 119 | ⊢ |
| : , : |
116 | assumption | | ⊢ |
117 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.int_interval_within_int |
118 | instantiation | 128, 129, 120 | ⊢ |
| : , : , : |
119 | instantiation | 121, 122, 123 | ⊢ |
| : , : |
120 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat1 |
121 | theorem | | ⊢ |
| proveit.numbers.addition.add_int_closure_bin |
122 | instantiation | 128, 124, 125 | ⊢ |
| : , : , : |
123 | instantiation | 126, 127 | ⊢ |
| : |
124 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.nat_pos_within_int |
125 | theorem | | ⊢ |
| proveit.physics.quantum.QPE._two_pow_t_minus_one_is_nat_pos |
126 | theorem | | ⊢ |
| proveit.numbers.negation.int_closure |
127 | instantiation | 128, 129, 130 | ⊢ |
| : , : , : |
128 | theorem | | ⊢ |
| proveit.logic.sets.inclusion.superset_membership_from_proper_subset |
129 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.nat_within_int |
130 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat2 |
*equality replacement requirements |