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