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