| step type | requirements | statement |
0 | instantiation | 1, 2, 3 | , , ⊢ |
| : , : , : |
1 | reference | 31 | ⊢ |
2 | instantiation | 31, 4, 5 | , , ⊢ |
| : , : , : |
3 | instantiation | 18, 75, 79, 47, 6, 7, 8, 52, 53, 56, 54, 55, 9* | , , ⊢ |
| : , : , : , : , : , : |
4 | instantiation | 31, 10, 11 | , , ⊢ |
| : , : , : |
5 | instantiation | 18, 48, 76, 12, 51, 13, 14, 60, 52, 53, 56, 54, 55, 15* | , , ⊢ |
| : , : , : , : , : , : |
6 | instantiation | 16 | ⊢ |
| : , : , : |
7 | instantiation | 62 | ⊢ |
| : , : , : , : , : |
8 | instantiation | 17, 53, 60 | ⊢ |
| : , : |
9 | instantiation | 18, 48, 76, 75, 51, 19, 52, 53, 56, 20* | ⊢ |
| : , : , : , : , : , : |
10 | instantiation | 31, 21, 22 | , , ⊢ |
| : , : , : |
11 | instantiation | 45, 23, 76, 48, 24, 36, 51, 60, 52, 53, 56, 54, 55 | , , ⊢ |
| : , : , : , : , : , : , : |
12 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat8 |
13 | instantiation | 58 | ⊢ |
| : , : |
14 | instantiation | 25 | ⊢ |
| : , : , : , : , : , : , : , : |
15 | instantiation | 26, 27, 28* | ⊢ |
| : , : |
16 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.tuple_len_3_typical_eq |
17 | theorem | | ⊢ |
| proveit.numbers.multiplication.mult_complex_closure_bin |
18 | theorem | | ⊢ |
| proveit.numbers.addition.association |
19 | instantiation | 58 | ⊢ |
| : , : |
20 | instantiation | 31, 29, 30 | ⊢ |
| : , : , : |
21 | instantiation | 31, 32, 33 | , , ⊢ |
| : , : , : |
22 | instantiation | 45, 34, 76, 75, 35, 36, 60, 52, 53, 56, 54, 55 | , , ⊢ |
| : , : , : , : , : , : , : |
23 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat7 |
24 | instantiation | 37 | ⊢ |
| : , : , : , : , : , : , : |
25 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.tuple_len_8_typical_eq |
26 | theorem | | ⊢ |
| proveit.logic.equality.equals_reversal |
27 | instantiation | 38, 48, 76, 75, 51, 39, 52, 60, 40* | ⊢ |
| : , : , : , : , : , : |
28 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.add_1_1 |
29 | instantiation | 41, 42 | ⊢ |
| : , : , : |
30 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.add_3_3 |
31 | axiom | | ⊢ |
| proveit.logic.equality.equals_transitivity |
32 | instantiation | 45, 75, 46, 43, 44, 60, 52, 53, 54, 55, 56 | , , ⊢ |
| : , : , : , : , : , : , : |
33 | instantiation | 45, 46, 47, 48, 49, 50, 51, 60, 52, 53, 54, 55, 56 | , , ⊢ |
| : , : , : , : , : , : , : |
34 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat6 |
35 | instantiation | 57 | ⊢ |
| : , : , : , : , : , : |
36 | instantiation | 58 | ⊢ |
| : , : |
37 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.tuple_len_7_typical_eq |
38 | theorem | | ⊢ |
| proveit.numbers.multiplication.distribute_through_sum |
39 | instantiation | 58 | ⊢ |
| : , : |
40 | instantiation | 59, 60 | ⊢ |
| : |
41 | axiom | | ⊢ |
| proveit.logic.equality.substitution |
42 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.add_1_2 |
43 | instantiation | 61 | ⊢ |
| : , : , : , : |
44 | instantiation | 61 | ⊢ |
| : , : , : , : |
45 | theorem | | ⊢ |
| proveit.numbers.addition.leftward_commutation |
46 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat4 |
47 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat5 |
48 | axiom | | ⊢ |
| proveit.numbers.number_sets.natural_numbers.zero_in_nats |
49 | instantiation | 61 | ⊢ |
| : , : , : , : |
50 | instantiation | 62 | ⊢ |
| : , : , : , : , : |
51 | theorem | | ⊢ |
| proveit.core_expr_types.tuples.tuple_len_0_typical_eq |
52 | instantiation | 77, 65, 63 | ⊢ |
| : , : , : |
53 | instantiation | 77, 65, 64 | ⊢ |
| : , : , : |
54 | assumption | | ⊢ |
55 | assumption | | ⊢ |
56 | instantiation | 77, 65, 66 | ⊢ |
| : , : , : |
57 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.tuple_len_6_typical_eq |
58 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.tuple_len_2_typical_eq |
59 | theorem | | ⊢ |
| proveit.numbers.multiplication.elim_one_left |
60 | assumption | | ⊢ |
61 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.tuple_len_4_typical_eq |
62 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.tuple_len_5_typical_eq |
63 | instantiation | 77, 69, 67 | ⊢ |
| : , : , : |
64 | instantiation | 77, 69, 68 | ⊢ |
| : , : , : |
65 | theorem | | ⊢ |
| proveit.numbers.number_sets.complex_numbers.real_within_complex |
66 | instantiation | 77, 69, 70 | ⊢ |
| : , : , : |
67 | instantiation | 77, 73, 71 | ⊢ |
| : , : , : |
68 | instantiation | 77, 73, 72 | ⊢ |
| : , : , : |
69 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.rational_within_real |
70 | instantiation | 77, 73, 74 | ⊢ |
| : , : , : |
71 | instantiation | 77, 78, 75 | ⊢ |
| : , : , : |
72 | instantiation | 77, 78, 76 | ⊢ |
| : , : , : |
73 | theorem | | ⊢ |
| proveit.numbers.number_sets.rational_numbers.int_within_rational |
74 | instantiation | 77, 78, 79 | ⊢ |
| : , : , : |
75 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat1 |
76 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat2 |
77 | theorem | | ⊢ |
| proveit.logic.sets.inclusion.superset_membership_from_proper_subset |
78 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.nat_within_int |
79 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat3 |
*equality replacement requirements |