| step type | requirements | statement |
0 | instantiation | 1, 2, 3 | , , ⊢  |
| : , : , :  |
1 | reference | 35 | ⊢  |
2 | instantiation | 35, 4, 5 | , , ⊢  |
| : , : , :  |
3 | instantiation | 6, 42, 43, 69, 44, 7, 12, 13, 31 | , , ⊢  |
| : , : , : , : , : , :  |
4 | instantiation | 35, 8, 9 | , , ⊢  |
| : , : , :  |
5 | instantiation | 10, 69, 43, 42, 11, 44, 12, 13, 31 | , , ⊢  |
| : , : , : , : , : , :  |
6 | theorem | | ⊢  |
| proveit.numbers.multiplication.association |
7 | instantiation | 53 | ⊢  |
| : , :  |
8 | instantiation | 35, 14, 15 | , , ⊢  |
| : , : , :  |
9 | instantiation | 19, 16 | , ⊢  |
| : , : , :  |
10 | theorem | | ⊢  |
| proveit.numbers.multiplication.disassociation |
11 | instantiation | 53 | ⊢  |
| : , :  |
12 | instantiation | 17, 27, 48 | , ⊢  |
| : , :  |
13 | instantiation | 17, 31, 18 | , ⊢  |
| : , :  |
14 | instantiation | 19, 20 | , ⊢  |
| : , : , :  |
15 | instantiation | 21, 27, 31, 62 | , , ⊢  |
| : , : , :  |
16 | instantiation | 22, 50, 56, 25, 60, 23, 24* | , ⊢  |
| : , : , : , :  |
17 | theorem | | ⊢  |
| proveit.numbers.exponentiation.exp_complex_closure |
18 | instantiation | 67, 59, 25 | ⊢  |
| : , : , :  |
19 | axiom | | ⊢  |
| proveit.logic.equality.substitution |
20 | instantiation | 26, 31, 27 | , ⊢  |
| : , :  |
21 | theorem | | ⊢  |
| proveit.numbers.exponentiation.pos_power_of_product |
22 | theorem | | ⊢  |
| proveit.numbers.exponentiation.exp_factored_real |
23 | instantiation | 28, 29 | ⊢  |
| : , :  |
24 | instantiation | 30, 31 | ⊢  |
| :  |
25 | instantiation | 32, 56, 33 | ⊢  |
| : , :  |
26 | theorem | | ⊢  |
| proveit.numbers.multiplication.commutation |
27 | instantiation | 67, 59, 34 | ⊢  |
| : , : , :  |
28 | theorem | | ⊢  |
| proveit.logic.equality.equals_reversal |
29 | instantiation | 35, 36, 37 | ⊢  |
| : , : , :  |
30 | theorem | | ⊢  |
| proveit.numbers.exponentiation.complex_x_to_first_power_is_x |
31 | instantiation | 67, 59, 38 | ⊢  |
| : , : , :  |
32 | theorem | | ⊢  |
| proveit.numbers.addition.add_real_closure_bin |
33 | instantiation | 67, 63, 39 | ⊢  |
| : , : , :  |
34 | instantiation | 67, 63, 40 | ⊢  |
| : , : , :  |
35 | axiom | | ⊢  |
| proveit.logic.equality.equals_transitivity |
36 | instantiation | 41, 42, 43, 69, 44, 45, 48, 46, 55 | ⊢  |
| : , : , : , : , : , :  |
37 | instantiation | 47, 55, 48, 49 | ⊢  |
| : , : , :  |
38 | instantiation | 67, 61, 50 | ⊢  |
| : , : , :  |
39 | instantiation | 67, 65, 51 | ⊢  |
| : , : , :  |
40 | instantiation | 67, 65, 52 | ⊢  |
| : , : , :  |
41 | theorem | | ⊢  |
| proveit.numbers.addition.disassociation |
42 | axiom | | ⊢  |
| proveit.numbers.number_sets.natural_numbers.zero_in_nats |
43 | theorem | | ⊢  |
| proveit.numbers.numerals.decimals.nat2 |
44 | theorem | | ⊢  |
| proveit.core_expr_types.tuples.tuple_len_0_typical_eq |
45 | instantiation | 53 | ⊢  |
| : , :  |
46 | instantiation | 54, 55 | ⊢  |
| :  |
47 | theorem | | ⊢  |
| proveit.numbers.addition.subtraction.add_cancel_triple_32 |
48 | instantiation | 67, 59, 56 | ⊢  |
| : , : , :  |
49 | instantiation | 57 | ⊢  |
| :  |
50 | assumption | | ⊢  |
51 | instantiation | 58, 66 | ⊢  |
| :  |
52 | assumption | | ⊢  |
53 | theorem | | ⊢  |
| proveit.numbers.numerals.decimals.tuple_len_2_typical_eq |
54 | theorem | | ⊢  |
| proveit.numbers.negation.complex_closure |
55 | instantiation | 67, 59, 60 | ⊢  |
| : , : , :  |
56 | instantiation | 67, 61, 62 | ⊢  |
| : , : , :  |
57 | axiom | | ⊢  |
| proveit.logic.equality.equals_reflexivity |
58 | theorem | | ⊢  |
| proveit.numbers.negation.int_closure |
59 | theorem | | ⊢  |
| proveit.numbers.number_sets.complex_numbers.real_within_complex |
60 | instantiation | 67, 63, 64 | ⊢  |
| : , : , :  |
61 | theorem | | ⊢  |
| proveit.numbers.number_sets.real_numbers.real_pos_within_real |
62 | assumption | | ⊢  |
63 | theorem | | ⊢  |
| proveit.numbers.number_sets.real_numbers.rational_within_real |
64 | instantiation | 67, 65, 66 | ⊢  |
| : , : , :  |
65 | theorem | | ⊢  |
| proveit.numbers.number_sets.rational_numbers.int_within_rational |
66 | instantiation | 67, 68, 69 | ⊢  |
| : , : , :  |
67 | theorem | | ⊢  |
| proveit.logic.sets.inclusion.superset_membership_from_proper_subset |
68 | theorem | | ⊢  |
| proveit.numbers.number_sets.integers.nat_within_int |
69 | theorem | | ⊢  |
| proveit.numbers.numerals.decimals.nat1 |
*equality replacement requirements |