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