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