| step type | requirements | statement |
0 | generalization | 1 | ⊢ |
1 | instantiation | 45, 2 | , ⊢ |
| : , : |
2 | instantiation | 3, 4, 5, 6, 7 | , ⊢ |
| : , : , : |
3 | theorem | | ⊢ |
| proveit.numbers.division.strong_div_from_denom_bound__all_pos |
4 | instantiation | 136, 9, 8 | ⊢ |
| : , : , : |
5 | instantiation | 136, 9, 10 | , ⊢ |
| : , : , : |
6 | instantiation | 11, 28, 12 | , ⊢ |
| : |
7 | instantiation | 13, 102, 14, 28, 15, 16 | , ⊢ |
| : , : , : |
8 | instantiation | 136, 17, 72 | ⊢ |
| : , : , : |
9 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.rational_pos_within_real_pos |
10 | instantiation | 136, 17, 18 | , ⊢ |
| : , : , : |
11 | theorem | | ⊢ |
| proveit.numbers.exponentiation.sqrd_pos_closure |
12 | instantiation | 19, 20 | , ⊢ |
| : , : |
13 | theorem | | ⊢ |
| proveit.numbers.exponentiation.exp_pos_less |
14 | instantiation | 35, 36, 40 | , ⊢ |
| : , : |
15 | instantiation | 21, 34, 22 | , ⊢ |
| : , : |
16 | instantiation | 23, 24 | ⊢ |
| : |
17 | theorem | | ⊢ |
| proveit.numbers.number_sets.rational_numbers.nat_pos_within_rational_pos |
18 | instantiation | 25, 26, 138 | , ⊢ |
| : , : |
19 | theorem | | ⊢ |
| proveit.logic.equality.not_equals_symmetry |
20 | instantiation | 27, 84, 28, 29 | , ⊢ |
| : , : |
21 | theorem | | ⊢ |
| proveit.logic.booleans.conjunction.and_if_both |
22 | instantiation | 30, 36, 40, 37, 31 | , ⊢ |
| : , : , : |
23 | theorem | | ⊢ |
| proveit.numbers.number_sets.natural_numbers.natural_pos_is_pos |
24 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.posnat2 |
25 | theorem | | ⊢ |
| proveit.numbers.exponentiation.exp_natpos_closure |
26 | instantiation | 32, 33, 34 | , ⊢ |
| : |
27 | theorem | | ⊢ |
| proveit.numbers.ordering.less_is_not_eq |
28 | instantiation | 35, 36, 37 | , ⊢ |
| : , : |
29 | instantiation | 60, 38 | , ⊢ |
| : , : |
30 | theorem | | ⊢ |
| proveit.numbers.addition.strong_bound_via_right_term_bound |
31 | instantiation | 39, 40, 48, 119, 50, 41, 42*, 43* | ⊢ |
| : , : , : |
32 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.nonneg_int_is_natural |
33 | instantiation | 126, 62, 44 | , ⊢ |
| : , : |
34 | instantiation | 45, 46 | , ⊢ |
| : , : |
35 | theorem | | ⊢ |
| proveit.numbers.addition.add_real_closure_bin |
36 | instantiation | 136, 124, 47 | , ⊢ |
| : , : , : |
37 | instantiation | 51, 48 | ⊢ |
| : |
38 | instantiation | 49, 50, 61 | , ⊢ |
| : , : , : |
39 | theorem | | ⊢ |
| proveit.numbers.multiplication.reversed_strong_bound_via_right_factor_bound |
40 | instantiation | 51, 119 | ⊢ |
| : |
41 | instantiation | 52, 59 | ⊢ |
| : |
42 | instantiation | 53, 110, 54* | ⊢ |
| : , : |
43 | instantiation | 55, 56, 57 | ⊢ |
| : , : , : |
44 | instantiation | 136, 58, 59 | ⊢ |
| : , : , : |
45 | theorem | | ⊢ |
| proveit.numbers.ordering.relax_less |
46 | instantiation | 60, 61 | , ⊢ |
| : , : |
47 | instantiation | 136, 129, 62 | , ⊢ |
| : , : , : |
48 | instantiation | 63, 84, 119, 65 | ⊢ |
| : , : , : |
49 | axiom | | ⊢ |
| proveit.numbers.ordering.transitivity_less_less |
50 | instantiation | 64, 84, 119, 65 | ⊢ |
| : , : , : |
51 | theorem | | ⊢ |
| proveit.numbers.negation.real_closure |
52 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.negative_if_in_neg_int |
53 | theorem | | ⊢ |
| proveit.numbers.multiplication.mult_neg_left |
54 | instantiation | 66, 110 | ⊢ |
| : |
55 | axiom | | ⊢ |
| proveit.logic.equality.equals_transitivity |
56 | instantiation | 67, 135, 138, 78, 80, 79, 68, 81, 82 | ⊢ |
| : , : , : , : , : , : |
57 | instantiation | 69, 78, 138, 79, 80, 110, 81, 82, 70* | ⊢ |
| : , : , : , : , : |
58 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.neg_int_within_int |
59 | instantiation | 71, 72 | ⊢ |
| : |
60 | theorem | | ⊢ |
| proveit.numbers.addition.subtraction.pos_difference |
61 | instantiation | 96, 73, 74 | , ⊢ |
| : , : , : |
62 | instantiation | 136, 75, 88 | , ⊢ |
| : , : , : |
63 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.all_in_interval_co__is__real |
64 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.interval_co_upper_bound |
65 | theorem | | ⊢ |
| proveit.physics.quantum.QPE._scaled_delta_b_floor_in_interval |
66 | theorem | | ⊢ |
| proveit.numbers.multiplication.elim_one_right |
67 | theorem | | ⊢ |
| proveit.numbers.multiplication.disassociation |
68 | instantiation | 76, 110 | ⊢ |
| : |
69 | theorem | | ⊢ |
| proveit.numbers.multiplication.mult_neg_any |
70 | instantiation | 77, 78, 138, 79, 80, 81, 82 | ⊢ |
| : , : , : , : |
71 | theorem | | ⊢ |
| proveit.numbers.negation.int_neg_closure |
72 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.posnat1 |
73 | instantiation | 83, 119, 84, 85, 86, 87* | ⊢ |
| : , : , : |
74 | instantiation | 107, 89, 127, 88 | , ⊢ |
| : , : , : |
75 | instantiation | 122, 89, 127 | ⊢ |
| : , : |
76 | theorem | | ⊢ |
| proveit.numbers.negation.complex_closure |
77 | theorem | | ⊢ |
| proveit.numbers.multiplication.elim_one_any |
78 | axiom | | ⊢ |
| proveit.numbers.number_sets.natural_numbers.zero_in_nats |
79 | theorem | | ⊢ |
| proveit.core_expr_types.tuples.tuple_len_0_typical_eq |
80 | instantiation | 90 | ⊢ |
| : , : |
81 | instantiation | 91, 92, 93 | ⊢ |
| : , : |
82 | instantiation | 136, 118, 94 | ⊢ |
| : , : , : |
83 | theorem | | ⊢ |
| proveit.numbers.addition.strong_bound_via_left_term_bound |
84 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.zero_is_real |
85 | instantiation | 136, 124, 95 | ⊢ |
| : , : , : |
86 | instantiation | 96, 97, 98 | ⊢ |
| : , : , : |
87 | instantiation | 99, 100, 101 | ⊢ |
| : , : , : |
88 | assumption | | ⊢ |
89 | instantiation | 126, 106, 130 | ⊢ |
| : , : |
90 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.tuple_len_2_typical_eq |
91 | theorem | | ⊢ |
| proveit.numbers.exponentiation.exp_complex_closure |
92 | instantiation | 136, 118, 102 | ⊢ |
| : , : , : |
93 | instantiation | 136, 118, 103 | ⊢ |
| : , : , : |
94 | instantiation | 104, 105 | ⊢ |
| : |
95 | instantiation | 136, 129, 106 | ⊢ |
| : , : , : |
96 | theorem | | ⊢ |
| proveit.numbers.ordering.transitivity_less_less_eq |
97 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.less_0_1 |
98 | instantiation | 107, 130, 123, 117 | ⊢ |
| : , : , : |
99 | theorem | | ⊢ |
| proveit.logic.equality.sub_right_side_into |
100 | instantiation | 108, 110 | ⊢ |
| : |
101 | instantiation | 109, 110, 111 | ⊢ |
| : , : |
102 | instantiation | 136, 124, 112 | ⊢ |
| : , : , : |
103 | instantiation | 113, 114, 115 | ⊢ |
| : , : , : |
104 | theorem | | ⊢ |
| proveit.physics.quantum.QPE._delta_b_is_real |
105 | theorem | | ⊢ |
| proveit.physics.quantum.QPE._best_floor_is_int |
106 | instantiation | 136, 116, 117 | ⊢ |
| : , : , : |
107 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.interval_lower_bound |
108 | theorem | | ⊢ |
| proveit.numbers.addition.elim_zero_right |
109 | theorem | | ⊢ |
| proveit.numbers.addition.commutation |
110 | instantiation | 136, 118, 119 | ⊢ |
| : , : , : |
111 | theorem | | ⊢ |
| proveit.numbers.number_sets.complex_numbers.zero_is_complex |
112 | instantiation | 136, 129, 134 | ⊢ |
| : , : , : |
113 | theorem | | ⊢ |
| proveit.logic.sets.inclusion.unfold_subset_eq |
114 | instantiation | 120, 121 | ⊢ |
| : , : |
115 | axiom | | ⊢ |
| proveit.physics.quantum.QPE._t_in_natural_pos |
116 | instantiation | 122, 130, 123 | ⊢ |
| : , : |
117 | assumption | | ⊢ |
118 | theorem | | ⊢ |
| proveit.numbers.number_sets.complex_numbers.real_within_complex |
119 | instantiation | 136, 124, 125 | ⊢ |
| : , : , : |
120 | theorem | | ⊢ |
| proveit.logic.sets.inclusion.relax_proper_subset |
121 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.nat_pos_within_real |
122 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.int_interval_within_int |
123 | instantiation | 126, 127, 128 | ⊢ |
| : , : |
124 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.rational_within_real |
125 | instantiation | 136, 129, 130 | ⊢ |
| : , : , : |
126 | theorem | | ⊢ |
| proveit.numbers.addition.add_int_closure_bin |
127 | instantiation | 136, 131, 132 | ⊢ |
| : , : , : |
128 | instantiation | 133, 134 | ⊢ |
| : |
129 | theorem | | ⊢ |
| proveit.numbers.number_sets.rational_numbers.int_within_rational |
130 | instantiation | 136, 137, 135 | ⊢ |
| : , : , : |
131 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.nat_pos_within_int |
132 | theorem | | ⊢ |
| proveit.physics.quantum.QPE._two_pow_t_minus_one_is_nat_pos |
133 | theorem | | ⊢ |
| proveit.numbers.negation.int_closure |
134 | instantiation | 136, 137, 138 | ⊢ |
| : , : , : |
135 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat1 |
136 | theorem | | ⊢ |
| proveit.logic.sets.inclusion.superset_membership_from_proper_subset |
137 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.nat_within_int |
138 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat2 |
*equality replacement requirements |