| step type | requirements | statement |
0 | instantiation | 1, 2, 3, 4, 5, 6, 7, 8, 9, 10* | , , , ⊢  |
| : , : , : , : , : , :  |
1 | theorem | | ⊢  |
| proveit.numbers.multiplication.association |
2 | reference | 47 | ⊢  |
3 | reference | 48 | ⊢  |
4 | reference | 65 | ⊢  |
5 | reference | 49 | ⊢  |
6 | instantiation | 53 | ⊢  |
| : , :  |
7 | instantiation | 11, 14, 56 | , ⊢  |
| : , :  |
8 | instantiation | 11, 14, 12 | , , , ⊢  |
| : , :  |
9 | reference | 56 | ⊢  |
10 | instantiation | 13, 14, 60, 17, 15, 16* | , , , ⊢  |
| : , : , :  |
11 | theorem | | ⊢  |
| proveit.numbers.exponentiation.exp_complex_closure |
12 | instantiation | 63, 59, 17 | , , ⊢  |
| : , : , :  |
13 | theorem | | ⊢  |
| proveit.numbers.exponentiation.product_of_real_powers |
14 | instantiation | 63, 59, 18 | ⊢  |
| : , : , :  |
15 | instantiation | 19, 20 | ⊢  |
| :  |
16 | instantiation | 30, 21, 22 | , , ⊢  |
| : , : , :  |
17 | instantiation | 23, 28, 29, 41, 60, 42 | , , ⊢  |
| : , :  |
18 | instantiation | 63, 24, 26 | ⊢  |
| : , : , :  |
19 | theorem | | ⊢  |
| proveit.numbers.number_sets.real_numbers.nonzero_if_in_real_nonzero |
20 | instantiation | 63, 25, 26 | ⊢  |
| : , : , :  |
21 | instantiation | 27, 65, 28, 47, 29, 49, 56, 38, 39 | , , ⊢  |
| : , : , : , : , : , :  |
22 | instantiation | 30, 31, 32 | , , ⊢  |
| : , : , :  |
23 | theorem | | ⊢  |
| proveit.numbers.addition.add_real_closure |
24 | theorem | | ⊢  |
| proveit.numbers.number_sets.real_numbers.real_pos_within_real |
25 | theorem | | ⊢  |
| proveit.numbers.number_sets.real_numbers.real_pos_within_real_nonzero |
26 | assumption | | ⊢  |
27 | theorem | | ⊢  |
| proveit.numbers.addition.disassociation |
28 | theorem | | ⊢  |
| proveit.numbers.numerals.decimals.nat3 |
29 | instantiation | 33 | ⊢  |
| : , : , :  |
30 | axiom | | ⊢  |
| proveit.logic.equality.equals_transitivity |
31 | instantiation | 34, 65, 56, 38, 39 | , , ⊢  |
| : , : , : , : , : , : , :  |
32 | instantiation | 35, 47, 48, 49, 36, 37, 56, 38, 39, 40* | , , ⊢  |
| : , : , : , : , : , :  |
33 | theorem | | ⊢  |
| proveit.numbers.numerals.decimals.tuple_len_3_typical_eq |
34 | theorem | | ⊢  |
| proveit.numbers.addition.leftward_commutation |
35 | theorem | | ⊢  |
| proveit.numbers.addition.association |
36 | instantiation | 53 | ⊢  |
| : , :  |
37 | instantiation | 53 | ⊢  |
| : , :  |
38 | instantiation | 63, 59, 41 | ⊢  |
| : , : , :  |
39 | instantiation | 63, 59, 42 | ⊢  |
| : , : , :  |
40 | instantiation | 43, 44, 45* | ⊢  |
| : , :  |
41 | assumption | | ⊢  |
42 | assumption | | ⊢  |
43 | theorem | | ⊢  |
| proveit.logic.equality.equals_reversal |
44 | instantiation | 46, 47, 48, 65, 49, 50, 51, 56, 52* | ⊢  |
| : , : , : , : , : , :  |
45 | theorem | | ⊢  |
| proveit.numbers.numerals.decimals.add_1_1 |
46 | theorem | | ⊢  |
| proveit.numbers.multiplication.distribute_through_sum |
47 | axiom | | ⊢  |
| proveit.numbers.number_sets.natural_numbers.zero_in_nats |
48 | theorem | | ⊢  |
| proveit.numbers.numerals.decimals.nat2 |
49 | theorem | | ⊢  |
| proveit.core_expr_types.tuples.tuple_len_0_typical_eq |
50 | instantiation | 53 | ⊢  |
| : , :  |
51 | instantiation | 63, 59, 54 | ⊢  |
| : , : , :  |
52 | instantiation | 55, 56 | ⊢  |
| :  |
53 | theorem | | ⊢  |
| proveit.numbers.numerals.decimals.tuple_len_2_typical_eq |
54 | instantiation | 63, 57, 58 | ⊢  |
| : , : , :  |
55 | theorem | | ⊢  |
| proveit.numbers.multiplication.elim_one_left |
56 | instantiation | 63, 59, 60 | ⊢  |
| : , : , :  |
57 | theorem | | ⊢  |
| proveit.numbers.number_sets.real_numbers.rational_within_real |
58 | instantiation | 63, 61, 62 | ⊢  |
| : , : , :  |
59 | theorem | | ⊢  |
| proveit.numbers.number_sets.complex_numbers.real_within_complex |
60 | assumption | | ⊢  |
61 | theorem | | ⊢  |
| proveit.numbers.number_sets.rational_numbers.int_within_rational |
62 | instantiation | 63, 64, 65 | ⊢  |
| : , : , :  |
63 | theorem | | ⊢  |
| proveit.logic.sets.inclusion.superset_membership_from_proper_subset |
64 | theorem | | ⊢  |
| proveit.numbers.number_sets.integers.nat_within_int |
65 | theorem | | ⊢  |
| proveit.numbers.numerals.decimals.nat1 |
*equality replacement requirements |