| step type | requirements | statement |
0 | instantiation | 1, 2, 3, 4, 5, 6, 7, 8, 9, 10* | , , , , ⊢ |
| : , : , : , : , : , : |
1 | theorem | | ⊢ |
| proveit.numbers.multiplication.association |
2 | reference | 51 | ⊢ |
3 | reference | 80 | ⊢ |
4 | reference | 54 | ⊢ |
5 | instantiation | 64 | ⊢ |
| : , : |
6 | reference | 55 | ⊢ |
7 | instantiation | 78, 68, 11 | , ⊢ |
| : , : , : |
8 | instantiation | 12, 13, 15 | , , ⊢ |
| : , : |
9 | instantiation | 12, 13, 16 | ⊢ |
| : , : |
10 | instantiation | 14, 24, 15, 16 | , , , ⊢ |
| : , : , : |
11 | instantiation | 17, 18, 48 | , ⊢ |
| : , : |
12 | theorem | | ⊢ |
| proveit.numbers.exponentiation.exp_complex_closure |
13 | instantiation | 78, 68, 19 | ⊢ |
| : , : , : |
14 | theorem | | ⊢ |
| proveit.numbers.exponentiation.product_of_complex_powers |
15 | instantiation | 61, 20, 21 | , , ⊢ |
| : , : |
16 | instantiation | 34, 22, 23 | ⊢ |
| : , : , : |
17 | theorem | | ⊢ |
| proveit.numbers.addition.add_real_closure_bin |
18 | assumption | | ⊢ |
19 | instantiation | 78, 74, 24 | ⊢ |
| : , : , : |
20 | instantiation | 25, 26, 27 | , ⊢ |
| : , : |
21 | instantiation | 78, 68, 28 | ⊢ |
| : , : , : |
22 | instantiation | 61, 52, 29 | ⊢ |
| : , : |
23 | instantiation | 44, 30, 31 | ⊢ |
| : , : , : |
24 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.e_is_real_pos |
25 | theorem | | ⊢ |
| proveit.numbers.addition.add_complex_closure_bin |
26 | instantiation | 34, 32, 33 | ⊢ |
| : , : , : |
27 | instantiation | 34, 35, 36 | ⊢ |
| : , : , : |
28 | instantiation | 78, 72, 37 | ⊢ |
| : , : , : |
29 | instantiation | 61, 58, 39 | ⊢ |
| : , : |
30 | instantiation | 53, 51, 80, 54, 38, 55, 52, 58, 39 | ⊢ |
| : , : , : , : , : , : |
31 | instantiation | 53, 54, 80, 55, 56, 38, 62, 63, 58, 39 | ⊢ |
| : , : , : , : , : , : |
32 | instantiation | 61, 52, 40 | ⊢ |
| : , : |
33 | instantiation | 44, 41, 42 | ⊢ |
| : , : , : |
34 | theorem | | ⊢ |
| proveit.logic.equality.sub_right_side_into |
35 | instantiation | 61, 52, 43 | ⊢ |
| : , : |
36 | instantiation | 44, 45, 46 | ⊢ |
| : , : , : |
37 | instantiation | 78, 76, 47 | ⊢ |
| : , : , : |
38 | instantiation | 64 | ⊢ |
| : , : |
39 | instantiation | 78, 68, 48 | ⊢ |
| : , : , : |
40 | instantiation | 61, 58, 50 | ⊢ |
| : , : |
41 | instantiation | 53, 51, 80, 54, 49, 55, 52, 58, 50 | ⊢ |
| : , : , : , : , : , : |
42 | instantiation | 53, 54, 80, 55, 56, 49, 62, 63, 58, 50 | ⊢ |
| : , : , : , : , : , : |
43 | instantiation | 61, 58, 59 | ⊢ |
| : , : |
44 | axiom | | ⊢ |
| proveit.logic.equality.equals_transitivity |
45 | instantiation | 53, 51, 80, 54, 57, 55, 52, 58, 59 | ⊢ |
| : , : , : , : , : , : |
46 | instantiation | 53, 54, 80, 55, 56, 57, 62, 63, 58, 59 | ⊢ |
| : , : , : , : , : , : |
47 | assumption | | ⊢ |
48 | assumption | | ⊢ |
49 | instantiation | 64 | ⊢ |
| : , : |
50 | instantiation | 78, 68, 60 | ⊢ |
| : , : , : |
51 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat1 |
52 | instantiation | 61, 62, 63 | ⊢ |
| : , : |
53 | theorem | | ⊢ |
| proveit.numbers.multiplication.disassociation |
54 | axiom | | ⊢ |
| proveit.numbers.number_sets.natural_numbers.zero_in_nats |
55 | theorem | | ⊢ |
| proveit.core_expr_types.tuples.tuple_len_0_typical_eq |
56 | instantiation | 64 | ⊢ |
| : , : |
57 | instantiation | 64 | ⊢ |
| : , : |
58 | theorem | | ⊢ |
| proveit.numbers.number_sets.complex_numbers.i_is_complex |
59 | instantiation | 78, 68, 65 | ⊢ |
| : , : , : |
60 | instantiation | 78, 72, 66 | ⊢ |
| : , : , : |
61 | theorem | | ⊢ |
| proveit.numbers.multiplication.mult_complex_closure_bin |
62 | instantiation | 78, 68, 67 | ⊢ |
| : , : , : |
63 | instantiation | 78, 68, 69 | ⊢ |
| : , : , : |
64 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.tuple_len_2_typical_eq |
65 | instantiation | 78, 74, 70 | ⊢ |
| : , : , : |
66 | instantiation | 78, 76, 71 | ⊢ |
| : , : , : |
67 | instantiation | 78, 72, 73 | ⊢ |
| : , : , : |
68 | theorem | | ⊢ |
| proveit.numbers.number_sets.complex_numbers.real_within_complex |
69 | instantiation | 78, 74, 75 | ⊢ |
| : , : , : |
70 | assumption | | ⊢ |
71 | assumption | | ⊢ |
72 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.rational_within_real |
73 | instantiation | 78, 76, 77 | ⊢ |
| : , : , : |
74 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.real_pos_within_real |
75 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.pi_is_real_pos |
76 | theorem | | ⊢ |
| proveit.numbers.number_sets.rational_numbers.int_within_rational |
77 | instantiation | 78, 79, 80 | ⊢ |
| : , : , : |
78 | theorem | | ⊢ |
| proveit.logic.sets.inclusion.superset_membership_from_proper_subset |
79 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.nat_within_int |
80 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat2 |
*equality replacement requirements |