| step type | requirements | statement |
0 | instantiation | 1, 2, 3 | , , ⊢  |
| : , : , :  |
1 | reference | 8 | ⊢  |
2 | instantiation | 8, 4, 5 | , , ⊢  |
| : , : , :  |
3 | instantiation | 17, 6, 50, 20, 7, 13, 23, 24, 25, 26, 29, 27, 28 | , , ⊢  |
| : , : , : , : , : , : , :  |
4 | instantiation | 8, 9, 10 | , , ⊢  |
| : , : , :  |
5 | instantiation | 17, 11, 50, 49, 12, 13, 24, 25, 26, 29, 27, 28 | , , ⊢  |
| : , : , : , : , : , : , :  |
6 | theorem | | ⊢  |
| proveit.numbers.numerals.decimals.nat7 |
7 | instantiation | 14 | ⊢  |
| : , : , : , : , : , : , :  |
8 | axiom | | ⊢  |
| proveit.logic.equality.equals_transitivity |
9 | instantiation | 17, 49, 18, 15, 16, 24, 25, 26, 27, 28, 29 | , , ⊢  |
| : , : , : , : , : , : , :  |
10 | instantiation | 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29 | , , ⊢  |
| : , : , : , : , : , : , :  |
11 | theorem | | ⊢  |
| proveit.numbers.numerals.decimals.nat6 |
12 | instantiation | 30 | ⊢  |
| : , : , : , : , : , :  |
13 | instantiation | 31 | ⊢  |
| : , :  |
14 | theorem | | ⊢  |
| proveit.numbers.numerals.decimals.tuple_len_7_typical_eq |
15 | instantiation | 32 | ⊢  |
| : , : , : , :  |
16 | instantiation | 32 | ⊢  |
| : , : , : , :  |
17 | theorem | | ⊢  |
| proveit.numbers.addition.leftward_commutation |
18 | theorem | | ⊢  |
| proveit.numbers.numerals.decimals.nat4 |
19 | theorem | | ⊢  |
| proveit.numbers.numerals.decimals.nat5 |
20 | axiom | | ⊢  |
| proveit.numbers.number_sets.natural_numbers.zero_in_nats |
21 | instantiation | 32 | ⊢  |
| : , : , : , :  |
22 | instantiation | 33 | ⊢  |
| : , : , : , : , :  |
23 | theorem | | ⊢  |
| proveit.core_expr_types.tuples.tuple_len_0_typical_eq |
24 | instantiation | 51, 39, 34 | ⊢  |
| : , : , :  |
25 | instantiation | 51, 39, 35 | ⊢  |
| : , : , :  |
26 | instantiation | 51, 39, 36 | ⊢  |
| : , : , :  |
27 | instantiation | 51, 39, 37 | ⊢  |
| : , : , :  |
28 | instantiation | 51, 39, 38 | ⊢  |
| : , : , :  |
29 | instantiation | 51, 39, 40 | ⊢  |
| : , : , :  |
30 | theorem | | ⊢  |
| proveit.numbers.numerals.decimals.tuple_len_6_typical_eq |
31 | theorem | | ⊢  |
| proveit.numbers.numerals.decimals.tuple_len_2_typical_eq |
32 | theorem | | ⊢  |
| proveit.numbers.numerals.decimals.tuple_len_4_typical_eq |
33 | theorem | | ⊢  |
| proveit.numbers.numerals.decimals.tuple_len_5_typical_eq |
34 | assumption | | ⊢  |
35 | instantiation | 51, 43, 41 | ⊢  |
| : , : , :  |
36 | instantiation | 51, 43, 42 | ⊢  |
| : , : , :  |
37 | assumption | | ⊢  |
38 | assumption | | ⊢  |
39 | theorem | | ⊢  |
| proveit.numbers.number_sets.complex_numbers.real_within_complex |
40 | instantiation | 51, 43, 44 | ⊢  |
| : , : , :  |
41 | instantiation | 51, 47, 45 | ⊢  |
| : , : , :  |
42 | instantiation | 51, 47, 46 | ⊢  |
| : , : , :  |
43 | theorem | | ⊢  |
| proveit.numbers.number_sets.real_numbers.rational_within_real |
44 | instantiation | 51, 47, 48 | ⊢  |
| : , : , :  |
45 | instantiation | 51, 52, 49 | ⊢  |
| : , : , :  |
46 | instantiation | 51, 52, 50 | ⊢  |
| : , : , :  |
47 | theorem | | ⊢  |
| proveit.numbers.number_sets.rational_numbers.int_within_rational |
48 | instantiation | 51, 52, 53 | ⊢  |
| : , : , :  |
49 | theorem | | ⊢  |
| proveit.numbers.numerals.decimals.nat1 |
50 | theorem | | ⊢  |
| proveit.numbers.numerals.decimals.nat2 |
51 | theorem | | ⊢  |
| proveit.logic.sets.inclusion.superset_membership_from_proper_subset |
52 | theorem | | ⊢  |
| proveit.numbers.number_sets.integers.nat_within_int |
53 | theorem | | ⊢  |
| proveit.numbers.numerals.decimals.nat3 |