| step type | requirements | statement |
0 | instantiation | 1, 2, 3 | , , , , , ⊢ |
| : , : , : |
1 | reference | 4 | ⊢ |
2 | instantiation | 4, 5, 6 | , , , , , ⊢ |
| : , : , : |
3 | instantiation | 7, 21, 8, 12, 9, 14, 17, 24, 18, 25, 26, 10* | , , , , , ⊢ |
| : , : , : , : , : , : |
4 | axiom | | ⊢ |
| proveit.logic.equality.equals_transitivity |
5 | instantiation | 15, 21, 11, 12, 13, 14, 17, 25, 18, 26, 24 | , , , , , ⊢ |
| : , : , : , : , : , : , : |
6 | instantiation | 15, 22, 21, 16, 17, 24, 25, 18, 26 | , , , , , ⊢ |
| : , : , : , : , : , : , : |
7 | theorem | | ⊢ |
| proveit.numbers.multiplication.association |
8 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat4 |
9 | instantiation | 19 | ⊢ |
| : , : , : , : |
10 | instantiation | 20, 21, 22, 23, 24, 30, 37, 25, 26 | , , , , ⊢ |
| : , : , : , : , : , : |
11 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat3 |
12 | axiom | | ⊢ |
| proveit.numbers.number_sets.natural_numbers.zero_in_nats |
13 | instantiation | 27 | ⊢ |
| : , : , : |
14 | theorem | | ⊢ |
| proveit.core_expr_types.tuples.tuple_len_0_typical_eq |
15 | theorem | | ⊢ |
| proveit.numbers.multiplication.leftward_commutation |
16 | instantiation | 32 | ⊢ |
| : , : |
17 | instantiation | 41, 33, 28 | ⊢ |
| : , : , : |
18 | instantiation | 29, 30, 31 | , ⊢ |
| : , : |
19 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.tuple_len_4_typical_eq |
20 | theorem | | ⊢ |
| proveit.numbers.multiplication.distribute_through_subtract |
21 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat1 |
22 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat2 |
23 | instantiation | 32 | ⊢ |
| : , : |
24 | assumption | | ⊢ |
25 | instantiation | 41, 33, 34 | ⊢ |
| : , : , : |
26 | assumption | | ⊢ |
27 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.tuple_len_3_typical_eq |
28 | instantiation | 41, 38, 35 | ⊢ |
| : , : , : |
29 | theorem | | ⊢ |
| proveit.numbers.addition.add_complex_closure_bin |
30 | assumption | | ⊢ |
31 | instantiation | 36, 37 | ⊢ |
| : |
32 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.tuple_len_2_typical_eq |
33 | theorem | | ⊢ |
| proveit.numbers.number_sets.complex_numbers.real_within_complex |
34 | instantiation | 41, 38, 39 | ⊢ |
| : , : , : |
35 | instantiation | 41, 42, 40 | ⊢ |
| : , : , : |
36 | theorem | | ⊢ |
| proveit.numbers.negation.complex_closure |
37 | assumption | | ⊢ |
38 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.rational_within_real |
39 | instantiation | 41, 42, 43 | ⊢ |
| : , : , : |
40 | assumption | | ⊢ |
41 | theorem | | ⊢ |
| proveit.logic.sets.inclusion.superset_membership_from_proper_subset |
42 | theorem | | ⊢ |
| proveit.numbers.number_sets.rational_numbers.int_within_rational |
43 | assumption | | ⊢ |
*equality replacement requirements |