| step type | requirements | statement |
0 | generalization | 1 | ⊢ |
1 | instantiation | 2, 3, 4, 5, 6 | , ⊢ |
| : , : , : |
2 | theorem | | ⊢ |
| proveit.numbers.division.strong_div_from_denom_bound__all_pos |
3 | instantiation | 135, 8, 7 | ⊢ |
| : , : , : |
4 | instantiation | 135, 8, 9 | , ⊢ |
| : , : , : |
5 | instantiation | 10, 27, 11 | , ⊢ |
| : |
6 | instantiation | 12, 101, 13, 27, 14, 15 | , ⊢ |
| : , : , : |
7 | instantiation | 135, 16, 71 | ⊢ |
| : , : , : |
8 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.rational_pos_within_real_pos |
9 | instantiation | 135, 16, 17 | , ⊢ |
| : , : , : |
10 | theorem | | ⊢ |
| proveit.numbers.exponentiation.sqrd_pos_closure |
11 | instantiation | 18, 19 | , ⊢ |
| : , : |
12 | theorem | | ⊢ |
| proveit.numbers.exponentiation.exp_pos_less |
13 | instantiation | 34, 35, 39 | , ⊢ |
| : , : |
14 | instantiation | 20, 33, 21 | , ⊢ |
| : , : |
15 | instantiation | 22, 23 | ⊢ |
| : |
16 | theorem | | ⊢ |
| proveit.numbers.number_sets.rational_numbers.nat_pos_within_rational_pos |
17 | instantiation | 24, 25, 137 | , ⊢ |
| : , : |
18 | theorem | | ⊢ |
| proveit.logic.equality.not_equals_symmetry |
19 | instantiation | 26, 83, 27, 28 | , ⊢ |
| : , : |
20 | theorem | | ⊢ |
| proveit.logic.booleans.conjunction.and_if_both |
21 | instantiation | 29, 35, 39, 36, 30 | , ⊢ |
| : , : , : |
22 | theorem | | ⊢ |
| proveit.numbers.number_sets.natural_numbers.natural_pos_is_pos |
23 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.posnat2 |
24 | theorem | | ⊢ |
| proveit.numbers.exponentiation.exp_natpos_closure |
25 | instantiation | 31, 32, 33 | , ⊢ |
| : |
26 | theorem | | ⊢ |
| proveit.numbers.ordering.less_is_not_eq |
27 | instantiation | 34, 35, 36 | , ⊢ |
| : , : |
28 | instantiation | 59, 37 | , ⊢ |
| : , : |
29 | theorem | | ⊢ |
| proveit.numbers.addition.strong_bound_via_right_term_bound |
30 | instantiation | 38, 39, 47, 118, 49, 40, 41*, 42* | ⊢ |
| : , : , : |
31 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.nonneg_int_is_natural |
32 | instantiation | 125, 61, 43 | , ⊢ |
| : , : |
33 | instantiation | 44, 45 | , ⊢ |
| : , : |
34 | theorem | | ⊢ |
| proveit.numbers.addition.add_real_closure_bin |
35 | instantiation | 135, 123, 46 | , ⊢ |
| : , : , : |
36 | instantiation | 50, 47 | ⊢ |
| : |
37 | instantiation | 48, 49, 60 | , ⊢ |
| : , : , : |
38 | theorem | | ⊢ |
| proveit.numbers.multiplication.reversed_strong_bound_via_right_factor_bound |
39 | instantiation | 50, 118 | ⊢ |
| : |
40 | instantiation | 51, 58 | ⊢ |
| : |
41 | instantiation | 52, 109, 53* | ⊢ |
| : , : |
42 | instantiation | 54, 55, 56 | ⊢ |
| : , : , : |
43 | instantiation | 135, 57, 58 | ⊢ |
| : , : , : |
44 | theorem | | ⊢ |
| proveit.numbers.ordering.relax_less |
45 | instantiation | 59, 60 | , ⊢ |
| : , : |
46 | instantiation | 135, 128, 61 | , ⊢ |
| : , : , : |
47 | instantiation | 62, 83, 118, 64 | ⊢ |
| : , : , : |
48 | axiom | | ⊢ |
| proveit.numbers.ordering.transitivity_less_less |
49 | instantiation | 63, 83, 118, 64 | ⊢ |
| : , : , : |
50 | theorem | | ⊢ |
| proveit.numbers.negation.real_closure |
51 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.negative_if_in_neg_int |
52 | theorem | | ⊢ |
| proveit.numbers.multiplication.mult_neg_left |
53 | instantiation | 65, 109 | ⊢ |
| : |
54 | axiom | | ⊢ |
| proveit.logic.equality.equals_transitivity |
55 | instantiation | 66, 134, 137, 77, 79, 78, 67, 80, 81 | ⊢ |
| : , : , : , : , : , : |
56 | instantiation | 68, 77, 137, 78, 79, 109, 80, 81, 69* | ⊢ |
| : , : , : , : , : |
57 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.neg_int_within_int |
58 | instantiation | 70, 71 | ⊢ |
| : |
59 | theorem | | ⊢ |
| proveit.numbers.addition.subtraction.pos_difference |
60 | instantiation | 95, 72, 73 | , ⊢ |
| : , : , : |
61 | instantiation | 135, 74, 87 | , ⊢ |
| : , : , : |
62 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.all_in_interval_co__is__real |
63 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.interval_co_upper_bound |
64 | theorem | | ⊢ |
| proveit.physics.quantum.QPE._scaled_delta_b_floor_in_interval |
65 | theorem | | ⊢ |
| proveit.numbers.multiplication.elim_one_right |
66 | theorem | | ⊢ |
| proveit.numbers.multiplication.disassociation |
67 | instantiation | 75, 109 | ⊢ |
| : |
68 | theorem | | ⊢ |
| proveit.numbers.multiplication.mult_neg_any |
69 | instantiation | 76, 77, 137, 78, 79, 80, 81 | ⊢ |
| : , : , : , : |
70 | theorem | | ⊢ |
| proveit.numbers.negation.int_neg_closure |
71 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.posnat1 |
72 | instantiation | 82, 118, 83, 84, 85, 86* | ⊢ |
| : , : , : |
73 | instantiation | 106, 88, 126, 87 | , ⊢ |
| : , : , : |
74 | instantiation | 121, 88, 126 | ⊢ |
| : , : |
75 | theorem | | ⊢ |
| proveit.numbers.negation.complex_closure |
76 | theorem | | ⊢ |
| proveit.numbers.multiplication.elim_one_any |
77 | axiom | | ⊢ |
| proveit.numbers.number_sets.natural_numbers.zero_in_nats |
78 | theorem | | ⊢ |
| proveit.core_expr_types.tuples.tuple_len_0_typical_eq |
79 | instantiation | 89 | ⊢ |
| : , : |
80 | instantiation | 90, 91, 92 | ⊢ |
| : , : |
81 | instantiation | 135, 117, 93 | ⊢ |
| : , : , : |
82 | theorem | | ⊢ |
| proveit.numbers.addition.strong_bound_via_left_term_bound |
83 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.zero_is_real |
84 | instantiation | 135, 123, 94 | ⊢ |
| : , : , : |
85 | instantiation | 95, 96, 97 | ⊢ |
| : , : , : |
86 | instantiation | 98, 99, 100 | ⊢ |
| : , : , : |
87 | assumption | | ⊢ |
88 | instantiation | 125, 105, 129 | ⊢ |
| : , : |
89 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.tuple_len_2_typical_eq |
90 | theorem | | ⊢ |
| proveit.numbers.exponentiation.exp_complex_closure |
91 | instantiation | 135, 117, 101 | ⊢ |
| : , : , : |
92 | instantiation | 135, 117, 102 | ⊢ |
| : , : , : |
93 | instantiation | 103, 104 | ⊢ |
| : |
94 | instantiation | 135, 128, 105 | ⊢ |
| : , : , : |
95 | theorem | | ⊢ |
| proveit.numbers.ordering.transitivity_less_less_eq |
96 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.less_0_1 |
97 | instantiation | 106, 129, 122, 116 | ⊢ |
| : , : , : |
98 | theorem | | ⊢ |
| proveit.logic.equality.sub_right_side_into |
99 | instantiation | 107, 109 | ⊢ |
| : |
100 | instantiation | 108, 109, 110 | ⊢ |
| : , : |
101 | instantiation | 135, 123, 111 | ⊢ |
| : , : , : |
102 | instantiation | 112, 113, 114 | ⊢ |
| : , : , : |
103 | theorem | | ⊢ |
| proveit.physics.quantum.QPE._delta_b_is_real |
104 | theorem | | ⊢ |
| proveit.physics.quantum.QPE._best_floor_is_int |
105 | instantiation | 135, 115, 116 | ⊢ |
| : , : , : |
106 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.interval_lower_bound |
107 | theorem | | ⊢ |
| proveit.numbers.addition.elim_zero_right |
108 | theorem | | ⊢ |
| proveit.numbers.addition.commutation |
109 | instantiation | 135, 117, 118 | ⊢ |
| : , : , : |
110 | theorem | | ⊢ |
| proveit.numbers.number_sets.complex_numbers.zero_is_complex |
111 | instantiation | 135, 128, 133 | ⊢ |
| : , : , : |
112 | theorem | | ⊢ |
| proveit.logic.sets.inclusion.unfold_subset_eq |
113 | instantiation | 119, 120 | ⊢ |
| : , : |
114 | axiom | | ⊢ |
| proveit.physics.quantum.QPE._t_in_natural_pos |
115 | instantiation | 121, 129, 122 | ⊢ |
| : , : |
116 | assumption | | ⊢ |
117 | theorem | | ⊢ |
| proveit.numbers.number_sets.complex_numbers.real_within_complex |
118 | instantiation | 135, 123, 124 | ⊢ |
| : , : , : |
119 | theorem | | ⊢ |
| proveit.logic.sets.inclusion.relax_proper_subset |
120 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.nat_pos_within_real |
121 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.int_interval_within_int |
122 | instantiation | 125, 126, 127 | ⊢ |
| : , : |
123 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.rational_within_real |
124 | instantiation | 135, 128, 129 | ⊢ |
| : , : , : |
125 | theorem | | ⊢ |
| proveit.numbers.addition.add_int_closure_bin |
126 | instantiation | 135, 130, 131 | ⊢ |
| : , : , : |
127 | instantiation | 132, 133 | ⊢ |
| : |
128 | theorem | | ⊢ |
| proveit.numbers.number_sets.rational_numbers.int_within_rational |
129 | instantiation | 135, 136, 134 | ⊢ |
| : , : , : |
130 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.nat_pos_within_int |
131 | theorem | | ⊢ |
| proveit.physics.quantum.QPE._two_pow_t_minus_one_is_nat_pos |
132 | theorem | | ⊢ |
| proveit.numbers.negation.int_closure |
133 | instantiation | 135, 136, 137 | ⊢ |
| : , : , : |
134 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat1 |
135 | theorem | | ⊢ |
| proveit.logic.sets.inclusion.superset_membership_from_proper_subset |
136 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.nat_within_int |
137 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat2 |
*equality replacement requirements |