| step type | requirements | statement |
0 | instantiation | 1, 2, 3 | , , ⊢ |
| : , : , : |
1 | reference | 39 | ⊢ |
2 | instantiation | 39, 4, 5 | , , ⊢ |
| : , : , : |
3 | instantiation | 24, 67, 6, 7, 8, 17, 9, 49, 18, 10* | , , ⊢ |
| : , : , : , : , : , : |
4 | instantiation | 24, 44, 68, 11, 45, 12, 13, 26, 27, 28, 60, 49, 18, 14* | , , ⊢ |
| : , : , : , : , : , : |
5 | instantiation | 24, 74, 67, 69, 15, 16, 17, 60, 49, 18, 19* | , , ⊢ |
| : , : , : , : , : , : |
6 | instantiation | 56 | ⊢ |
| : , : |
7 | instantiation | 56 | ⊢ |
| : , : |
8 | instantiation | 56 | ⊢ |
| : , : |
9 | instantiation | 20, 26, 60 | ⊢ |
| : , : |
10 | instantiation | 32, 21, 34* | ⊢ |
| : , : |
11 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat6 |
12 | instantiation | 22 | ⊢ |
| : , : , : |
13 | instantiation | 23 | ⊢ |
| : , : , : , : , : , : |
14 | instantiation | 24, 44, 67, 74, 45, 25, 26, 27, 28, 29* | ⊢ |
| : , : , : , : , : , : |
15 | instantiation | 56 | ⊢ |
| : , : |
16 | instantiation | 30 | ⊢ |
| : , : , : , : |
17 | instantiation | 72, 57, 31 | ⊢ |
| : , : , : |
18 | assumption | | ⊢ |
19 | instantiation | 32, 33, 34* | ⊢ |
| : , : |
20 | theorem | | ⊢ |
| proveit.numbers.multiplication.mult_complex_closure_bin |
21 | instantiation | 43, 44, 67, 74, 45, 46, 47, 49, 35* | ⊢ |
| : , : , : , : , : , : |
22 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.tuple_len_3_typical_eq |
23 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.tuple_len_6_typical_eq |
24 | theorem | | ⊢ |
| proveit.numbers.addition.association |
25 | instantiation | 56 | ⊢ |
| : , : |
26 | instantiation | 72, 57, 36 | ⊢ |
| : , : , : |
27 | instantiation | 72, 57, 37 | ⊢ |
| : , : , : |
28 | instantiation | 72, 57, 38 | ⊢ |
| : , : , : |
29 | instantiation | 39, 40, 41 | ⊢ |
| : , : , : |
30 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.tuple_len_4_typical_eq |
31 | instantiation | 72, 65, 42 | ⊢ |
| : , : , : |
32 | theorem | | ⊢ |
| proveit.logic.equality.equals_reversal |
33 | instantiation | 43, 44, 67, 74, 45, 46, 47, 60, 48* | ⊢ |
| : , : , : , : , : , : |
34 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.add_1_1 |
35 | instantiation | 59, 49 | ⊢ |
| : |
36 | instantiation | 72, 65, 50 | ⊢ |
| : , : , : |
37 | instantiation | 72, 65, 51 | ⊢ |
| : , : , : |
38 | instantiation | 72, 65, 52 | ⊢ |
| : , : , : |
39 | axiom | | ⊢ |
| proveit.logic.equality.equals_transitivity |
40 | instantiation | 53, 54 | ⊢ |
| : , : , : |
41 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.add_5_4 |
42 | instantiation | 72, 70, 55 | ⊢ |
| : , : , : |
43 | theorem | | ⊢ |
| proveit.numbers.multiplication.distribute_through_sum |
44 | axiom | | ⊢ |
| proveit.numbers.number_sets.natural_numbers.zero_in_nats |
45 | theorem | | ⊢ |
| proveit.core_expr_types.tuples.tuple_len_0_typical_eq |
46 | instantiation | 56 | ⊢ |
| : , : |
47 | instantiation | 72, 57, 58 | ⊢ |
| : , : , : |
48 | instantiation | 59, 60 | ⊢ |
| : |
49 | assumption | | ⊢ |
50 | instantiation | 72, 70, 61 | ⊢ |
| : , : , : |
51 | instantiation | 72, 70, 62 | ⊢ |
| : , : , : |
52 | instantiation | 72, 70, 63 | ⊢ |
| : , : , : |
53 | axiom | | ⊢ |
| proveit.logic.equality.substitution |
54 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.add_2_3 |
55 | instantiation | 72, 73, 64 | ⊢ |
| : , : , : |
56 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.tuple_len_2_typical_eq |
57 | theorem | | ⊢ |
| proveit.numbers.number_sets.complex_numbers.real_within_complex |
58 | instantiation | 72, 65, 66 | ⊢ |
| : , : , : |
59 | theorem | | ⊢ |
| proveit.numbers.multiplication.elim_one_left |
60 | assumption | | ⊢ |
61 | instantiation | 72, 73, 67 | ⊢ |
| : , : , : |
62 | instantiation | 72, 73, 68 | ⊢ |
| : , : , : |
63 | instantiation | 72, 73, 69 | ⊢ |
| : , : , : |
64 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat9 |
65 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.rational_within_real |
66 | instantiation | 72, 70, 71 | ⊢ |
| : , : , : |
67 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat2 |
68 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat3 |
69 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat4 |
70 | theorem | | ⊢ |
| proveit.numbers.number_sets.rational_numbers.int_within_rational |
71 | instantiation | 72, 73, 74 | ⊢ |
| : , : , : |
72 | theorem | | ⊢ |
| proveit.logic.sets.inclusion.superset_membership_from_proper_subset |
73 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.nat_within_int |
74 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat1 |
*equality replacement requirements |