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