| step type | requirements | statement |
0 | instantiation | 1, 2, 3, 4 | ⊢ |
| : , : , : , : |
1 | reference | 27 | ⊢ |
2 | instantiation | 5, 6, 7, 8, 9, 10, 11, 15*, 18* | ⊢ |
| : , : , : , : |
3 | instantiation | 62 | ⊢ |
| : |
4 | instantiation | 12, 13 | ⊢ |
| : , : |
5 | theorem | | ⊢ |
| proveit.core_expr_types.tuples.general_len |
6 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.posnat2 |
7 | instantiation | 56 | ⊢ |
| : , : |
8 | instantiation | 56 | ⊢ |
| : , : |
9 | instantiation | 56 | ⊢ |
| : , : |
10 | instantiation | 16, 14, 15 | ⊢ |
| : , : , : |
11 | instantiation | 16, 17, 18 | ⊢ |
| : , : , : |
12 | theorem | | ⊢ |
| proveit.logic.equality.equals_reversal |
13 | instantiation | 19, 20 | ⊢ |
| : , : |
14 | instantiation | 83, 23, 82 | ⊢ |
| : , : , : |
15 | instantiation | 51, 52, 48, 54 | ⊢ |
| : , : , : |
16 | theorem | | ⊢ |
| proveit.logic.equality.sub_left_side_into |
17 | instantiation | 83, 23, 70 | ⊢ |
| : , : , : |
18 | instantiation | 38, 21, 22 | ⊢ |
| : , : , : |
19 | theorem | | ⊢ |
| proveit.core_expr_types.tuples.range_from1_len |
20 | instantiation | 83, 23, 24 | ⊢ |
| : , : , : |
21 | instantiation | 25, 26 | ⊢ |
| : , : , : |
22 | instantiation | 27, 28, 29, 30 | ⊢ |
| : , : , : , : |
23 | theorem | | ⊢ |
| proveit.numbers.number_sets.natural_numbers.nat_pos_within_nat |
24 | instantiation | 31, 82, 70 | ⊢ |
| : , : |
25 | axiom | | ⊢ |
| proveit.logic.equality.substitution |
26 | instantiation | 32, 48, 52 | ⊢ |
| : , : |
27 | theorem | | ⊢ |
| proveit.logic.equality.four_chain_transitivity |
28 | instantiation | 35, 44, 45, 46, 36, 33, 48, 53, 34, 52 | ⊢ |
| : , : , : , : , : , : |
29 | instantiation | 35, 45, 85, 36, 37, 48, 53, 42, 49, 52 | ⊢ |
| : , : , : , : , : , : |
30 | instantiation | 38, 39, 40 | ⊢ |
| : , : , : |
31 | theorem | | ⊢ |
| proveit.numbers.addition.add_nat_pos_closure_bin |
32 | theorem | | ⊢ |
| proveit.numbers.negation.distribute_neg_through_binary_sum |
33 | instantiation | 56 | ⊢ |
| : , : |
34 | instantiation | 41, 42, 49 | ⊢ |
| : , : |
35 | theorem | | ⊢ |
| proveit.numbers.addition.disassociation |
36 | instantiation | 56 | ⊢ |
| : , : |
37 | instantiation | 56 | ⊢ |
| : , : |
38 | axiom | | ⊢ |
| proveit.logic.equality.equals_transitivity |
39 | instantiation | 43, 44, 85, 45, 46, 47, 48, 53, 49, 52, 50 | ⊢ |
| : , : , : , : , : , : , : , : |
40 | instantiation | 51, 52, 53, 54 | ⊢ |
| : , : , : |
41 | theorem | | ⊢ |
| proveit.numbers.addition.add_complex_closure_bin |
42 | instantiation | 83, 60, 55 | ⊢ |
| : , : , : |
43 | theorem | | ⊢ |
| proveit.numbers.addition.subtraction.add_cancel_general |
44 | axiom | | ⊢ |
| proveit.numbers.number_sets.natural_numbers.zero_in_nats |
45 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat2 |
46 | theorem | | ⊢ |
| proveit.core_expr_types.tuples.tuple_len_0_typical_eq |
47 | instantiation | 56 | ⊢ |
| : , : |
48 | instantiation | 83, 60, 57 | ⊢ |
| : , : , : |
49 | instantiation | 83, 60, 58 | ⊢ |
| : , : , : |
50 | instantiation | 62 | ⊢ |
| : |
51 | theorem | | ⊢ |
| proveit.numbers.addition.subtraction.add_cancel_triple_32 |
52 | instantiation | 83, 60, 59 | ⊢ |
| : , : , : |
53 | instantiation | 83, 60, 61 | ⊢ |
| : , : , : |
54 | instantiation | 62 | ⊢ |
| : |
55 | instantiation | 83, 63, 64 | ⊢ |
| : , : , : |
56 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.tuple_len_2_typical_eq |
57 | instantiation | 68, 69, 82 | ⊢ |
| : , : , : |
58 | instantiation | 83, 66, 65 | ⊢ |
| : , : , : |
59 | instantiation | 83, 66, 67 | ⊢ |
| : , : , : |
60 | theorem | | ⊢ |
| proveit.numbers.number_sets.complex_numbers.real_within_complex |
61 | instantiation | 68, 69, 70 | ⊢ |
| : , : , : |
62 | axiom | | ⊢ |
| proveit.logic.equality.equals_reflexivity |
63 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.real_neg_within_real |
64 | instantiation | 83, 71, 72 | ⊢ |
| : , : , : |
65 | instantiation | 83, 74, 73 | ⊢ |
| : , : , : |
66 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.rational_within_real |
67 | instantiation | 83, 74, 80 | ⊢ |
| : , : , : |
68 | theorem | | ⊢ |
| proveit.logic.sets.inclusion.unfold_subset_eq |
69 | instantiation | 75, 76 | ⊢ |
| : , : |
70 | axiom | | ⊢ |
| proveit.physics.quantum.QPE._s_in_nat_pos |
71 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.rational_neg_within_real_neg |
72 | instantiation | 83, 77, 78 | ⊢ |
| : , : , : |
73 | instantiation | 79, 80 | ⊢ |
| : |
74 | theorem | | ⊢ |
| proveit.numbers.number_sets.rational_numbers.int_within_rational |
75 | theorem | | ⊢ |
| proveit.logic.sets.inclusion.relax_proper_subset |
76 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.nat_pos_within_real |
77 | theorem | | ⊢ |
| proveit.numbers.number_sets.rational_numbers.neg_int_within_rational_neg |
78 | instantiation | 81, 82 | ⊢ |
| : |
79 | theorem | | ⊢ |
| proveit.numbers.negation.int_closure |
80 | instantiation | 83, 84, 85 | ⊢ |
| : , : , : |
81 | theorem | | ⊢ |
| proveit.numbers.negation.int_neg_closure |
82 | axiom | | ⊢ |
| proveit.physics.quantum.QPE._t_in_natural_pos |
83 | theorem | | ⊢ |
| proveit.logic.sets.inclusion.superset_membership_from_proper_subset |
84 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.nat_within_int |
85 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat1 |
*equality replacement requirements |