| step type | requirements | statement |
0 | instantiation | 1, 2, 3 | ⊢ |
| : , : |
1 | theorem | | ⊢ |
| proveit.numbers.multiplication.mult_rational_pos_closure_bin |
2 | instantiation | 92, 4, 5 | ⊢ |
| : , : , : |
3 | instantiation | 6, 7, 79 | ⊢ |
| : , : |
4 | theorem | | ⊢ |
| proveit.numbers.number_sets.rational_numbers.nat_pos_within_rational_pos |
5 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.posnat4 |
6 | theorem | | ⊢ |
| proveit.numbers.exponentiation.exp_rational_pos_closure |
7 | instantiation | 8, 23, 9 | ⊢ |
| : |
8 | theorem | | ⊢ |
| proveit.numbers.number_sets.rational_numbers.pos_rational_is_rational_pos |
9 | instantiation | 10, 11 | ⊢ |
| : , : |
10 | theorem | | ⊢ |
| proveit.numbers.addition.subtraction.pos_difference |
11 | instantiation | 12, 67, 65, 13, 14, 52*, 15* | ⊢ |
| : , : , : |
12 | theorem | | ⊢ |
| proveit.numbers.addition.strong_bound_via_left_term_bound |
13 | instantiation | 92, 80, 16 | ⊢ |
| : , : , : |
14 | instantiation | 17, 65, 18, 19, 20 | ⊢ |
| : , : , : |
15 | instantiation | 31, 21, 22 | ⊢ |
| : , : , : |
16 | instantiation | 29, 23, 71 | ⊢ |
| : , : |
17 | theorem | | ⊢ |
| proveit.numbers.ordering.less_eq_add_right_strong |
18 | instantiation | 92, 80, 23 | ⊢ |
| : , : , : |
19 | theorem | | ⊢ |
| proveit.physics.quantum.QPE._e_value_ge_two |
20 | instantiation | 24, 83 | ⊢ |
| : |
21 | instantiation | 25, 26 | ⊢ |
| : , : , : |
22 | instantiation | 31, 27, 28 | ⊢ |
| : , : , : |
23 | instantiation | 29, 56, 30 | ⊢ |
| : , : |
24 | theorem | | ⊢ |
| proveit.numbers.number_sets.natural_numbers.natural_pos_is_pos |
25 | axiom | | ⊢ |
| proveit.logic.equality.substitution |
26 | instantiation | 31, 32, 33 | ⊢ |
| : , : , : |
27 | instantiation | 38, 41, 87, 94, 43, 34, 44, 58, 62 | ⊢ |
| : , : , : , : , : , : |
28 | instantiation | 35, 58, 44, 36 | ⊢ |
| : , : , : |
29 | theorem | | ⊢ |
| proveit.numbers.addition.add_rational_closure_bin |
30 | instantiation | 92, 88, 37 | ⊢ |
| : , : , : |
31 | axiom | | ⊢ |
| proveit.logic.equality.equals_transitivity |
32 | instantiation | 38, 41, 87, 94, 43, 39, 44, 62, 61 | ⊢ |
| : , : , : , : , : , : |
33 | instantiation | 40, 94, 87, 41, 42, 43, 44, 62, 61, 45* | ⊢ |
| : , : , : , : , : , : |
34 | instantiation | 49 | ⊢ |
| : , : |
35 | theorem | | ⊢ |
| proveit.numbers.addition.subtraction.add_cancel_triple_23 |
36 | instantiation | 46 | ⊢ |
| : |
37 | instantiation | 92, 47, 48 | ⊢ |
| : , : , : |
38 | theorem | | ⊢ |
| proveit.numbers.addition.disassociation |
39 | instantiation | 49 | ⊢ |
| : , : |
40 | theorem | | ⊢ |
| proveit.numbers.addition.association |
41 | axiom | | ⊢ |
| proveit.numbers.number_sets.natural_numbers.zero_in_nats |
42 | instantiation | 49 | ⊢ |
| : , : |
43 | theorem | | ⊢ |
| proveit.core_expr_types.tuples.tuple_len_0_typical_eq |
44 | instantiation | 92, 66, 50 | ⊢ |
| : , : , : |
45 | instantiation | 51, 52, 53 | ⊢ |
| : , : , : |
46 | axiom | | ⊢ |
| proveit.logic.equality.equals_reflexivity |
47 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.neg_int_within_int |
48 | instantiation | 54, 55 | ⊢ |
| : |
49 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.tuple_len_2_typical_eq |
50 | instantiation | 92, 80, 56 | ⊢ |
| : , : , : |
51 | theorem | | ⊢ |
| proveit.logic.equality.sub_right_side_into |
52 | instantiation | 57, 58, 61, 59 | ⊢ |
| : , : , : |
53 | instantiation | 60, 61, 62 | ⊢ |
| : , : |
54 | theorem | | ⊢ |
| proveit.numbers.negation.int_neg_closure |
55 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.posnat1 |
56 | instantiation | 92, 63, 64 | ⊢ |
| : , : , : |
57 | theorem | | ⊢ |
| proveit.numbers.addition.subtraction.subtract_from_add |
58 | instantiation | 92, 66, 73 | ⊢ |
| : , : , : |
59 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.add_1_1 |
60 | theorem | | ⊢ |
| proveit.numbers.addition.commutation |
61 | instantiation | 92, 66, 65 | ⊢ |
| : , : , : |
62 | instantiation | 92, 66, 67 | ⊢ |
| : , : , : |
63 | theorem | | ⊢ |
| proveit.numbers.number_sets.rational_numbers.rational_nonzero_within_rational |
64 | instantiation | 68, 69, 70 | ⊢ |
| : , : |
65 | instantiation | 92, 80, 71 | ⊢ |
| : , : , : |
66 | theorem | | ⊢ |
| proveit.numbers.number_sets.complex_numbers.real_within_complex |
67 | instantiation | 72, 73 | ⊢ |
| : |
68 | theorem | | ⊢ |
| proveit.numbers.exponentiation.exp_rational_nonzero_closure |
69 | instantiation | 92, 74, 75 | ⊢ |
| : , : , : |
70 | instantiation | 76, 77, 78 | ⊢ |
| : , : |
71 | instantiation | 92, 88, 79 | ⊢ |
| : , : , : |
72 | theorem | | ⊢ |
| proveit.numbers.negation.real_closure |
73 | instantiation | 92, 80, 81 | ⊢ |
| : , : , : |
74 | theorem | | ⊢ |
| proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero |
75 | instantiation | 92, 82, 83 | ⊢ |
| : , : , : |
76 | theorem | | ⊢ |
| proveit.numbers.addition.add_int_closure_bin |
77 | instantiation | 92, 90, 84 | ⊢ |
| : , : , : |
78 | instantiation | 85, 86 | ⊢ |
| : |
79 | instantiation | 92, 93, 87 | ⊢ |
| : , : , : |
80 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.rational_within_real |
81 | instantiation | 92, 88, 89 | ⊢ |
| : , : , : |
82 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int |
83 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.posnat2 |
84 | axiom | | ⊢ |
| proveit.physics.quantum.QPE._t_in_natural_pos |
85 | theorem | | ⊢ |
| proveit.numbers.negation.int_closure |
86 | instantiation | 92, 90, 91 | ⊢ |
| : , : , : |
87 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat2 |
88 | theorem | | ⊢ |
| proveit.numbers.number_sets.rational_numbers.int_within_rational |
89 | instantiation | 92, 93, 94 | ⊢ |
| : , : , : |
90 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.nat_pos_within_int |
91 | axiom | | ⊢ |
| proveit.physics.quantum.QPE._n_in_natural_pos |
92 | theorem | | ⊢ |
| proveit.logic.sets.inclusion.superset_membership_from_proper_subset |
93 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.nat_within_int |
94 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat1 |
*equality replacement requirements |