| step type | requirements | statement |
0 | instantiation | 1, 2, 3 | , , ⊢  |
| : , : , :  |
1 | reference | 20 | ⊢  |
2 | instantiation | 20, 4, 5 | , , ⊢  |
| : , : , :  |
3 | instantiation | 32, 29, 33, 28, 6, 7, 39, 40, 41 | , , ⊢  |
| : , : , : , : , : , : , :  |
4 | instantiation | 20, 8, 9 | , , ⊢  |
| : , : , :  |
5 | instantiation | 32, 15, 28, 34, 10, 11, 39, 40, 41 | , , ⊢  |
| : , : , : , : , : , : , :  |
6 | instantiation | 42 | ⊢  |
| : , : , : , : , : , : , :  |
7 | instantiation | 43 | ⊢  |
| : , :  |
8 | instantiation | 20, 12, 13 | , , ⊢  |
| : , : , :  |
9 | instantiation | 32, 14, 15, 16, 17, 18, 19, 39, 40, 41 | , , ⊢  |
| : , : , : , : , : , : , :  |
10 | instantiation | 27 | ⊢  |
| : , : , : , : , : , :  |
11 | instantiation | 44 | ⊢  |
| : , : , :  |
12 | instantiation | 20, 21, 22 | , , ⊢  |
| : , : , :  |
13 | instantiation | 32, 34, 35, 33, 23, 24, 25, 39, 40, 41 | , , ⊢  |
| : , : , : , : , : , : , :  |
14 | theorem | | ⊢  |
| proveit.numbers.numerals.decimals.nat4 |
15 | theorem | | ⊢  |
| proveit.numbers.numerals.decimals.nat6 |
16 | axiom | | ⊢  |
| proveit.numbers.number_sets.natural_numbers.zero_in_nats |
17 | instantiation | 26 | ⊢  |
| : , : , : , :  |
18 | instantiation | 27 | ⊢  |
| : , : , : , : , : , :  |
19 | theorem | | ⊢  |
| proveit.core_expr_types.tuples.tuple_len_0_typical_eq |
20 | axiom | | ⊢  |
| proveit.logic.equality.equals_transitivity |
21 | instantiation | 32, 28, 33, 29, 30, 31, 39, 40, 41 | , , ⊢  |
| : , : , : , : , : , : , :  |
22 | instantiation | 32, 33, 34, 35, 36, 37, 38, 39, 40, 41 | , , ⊢  |
| : , : , : , : , : , : , :  |
23 | instantiation | 44 | ⊢  |
| : , : , :  |
24 | instantiation | 45 | ⊢  |
| : , : , : , : , :  |
25 | instantiation | 43 | ⊢  |
| : , :  |
26 | theorem | | ⊢  |
| proveit.numbers.numerals.decimals.tuple_len_4_typical_eq |
27 | theorem | | ⊢  |
| proveit.numbers.numerals.decimals.tuple_len_6_typical_eq |
28 | theorem | | ⊢  |
| proveit.numbers.numerals.decimals.nat1 |
29 | theorem | | ⊢  |
| proveit.numbers.numerals.decimals.nat7 |
30 | instantiation | 43 | ⊢  |
| : , :  |
31 | instantiation | 42 | ⊢  |
| : , : , : , : , : , : , :  |
32 | theorem | | ⊢  |
| proveit.numbers.addition.leftward_commutation |
33 | theorem | | ⊢  |
| proveit.numbers.numerals.decimals.nat2 |
34 | theorem | | ⊢  |
| proveit.numbers.numerals.decimals.nat3 |
35 | theorem | | ⊢  |
| proveit.numbers.numerals.decimals.nat5 |
36 | instantiation | 43 | ⊢  |
| : , :  |
37 | instantiation | 44 | ⊢  |
| : , : , :  |
38 | instantiation | 45 | ⊢  |
| : , : , : , : , :  |
39 | assumption | | ⊢  |
40 | assumption | | ⊢  |
41 | assumption | | ⊢  |
42 | theorem | | ⊢  |
| proveit.numbers.numerals.decimals.tuple_len_7_typical_eq |
43 | theorem | | ⊢  |
| proveit.numbers.numerals.decimals.tuple_len_2_typical_eq |
44 | theorem | | ⊢  |
| proveit.numbers.numerals.decimals.tuple_len_3_typical_eq |
45 | theorem | | ⊢  |
| proveit.numbers.numerals.decimals.tuple_len_5_typical_eq |