| step type | requirements | statement |
0 | instantiation | 1, 2, 3 | , , , ⊢ |
| : , : , : |
1 | reference | 18 | ⊢ |
2 | instantiation | 27, 4 | ⊢ |
| : , : , : |
3 | instantiation | 18, 5, 6 | , , , ⊢ |
| : , : , : |
4 | instantiation | 7, 30, 54, 46, 8* | ⊢ |
| : , : |
5 | instantiation | 9, 77, 74, 10, 14, 50, 15, 16 | , , , ⊢ |
| : , : , : , : , : , : , : |
6 | instantiation | 11, 74, 77, 12, 13, 14, 50, 15, 16, 17* | , , , ⊢ |
| : , : , : , : , : , : |
7 | theorem | | ⊢ |
| proveit.numbers.division.div_as_mult |
8 | instantiation | 18, 19, 20 | ⊢ |
| : , : , : |
9 | theorem | | ⊢ |
| proveit.numbers.addition.leftward_commutation |
10 | instantiation | 48 | ⊢ |
| : , : |
11 | theorem | | ⊢ |
| proveit.numbers.addition.association |
12 | instantiation | 48 | ⊢ |
| : , : |
13 | instantiation | 48 | ⊢ |
| : , : |
14 | instantiation | 75, 62, 21 | ⊢ |
| : , : , : |
15 | instantiation | 23, 54, 22 | ⊢ |
| : , : |
16 | instantiation | 23, 31, 30 | ⊢ |
| : , : |
17 | instantiation | 24, 25, 26* | ⊢ |
| : , : |
18 | axiom | | ⊢ |
| proveit.logic.equality.equals_transitivity |
19 | instantiation | 27, 28 | ⊢ |
| : , : , : |
20 | instantiation | 29, 30, 31 | ⊢ |
| : , : |
21 | instantiation | 75, 55, 32 | ⊢ |
| : , : , : |
22 | instantiation | 75, 62, 33 | ⊢ |
| : , : , : |
23 | theorem | | ⊢ |
| proveit.numbers.multiplication.mult_complex_closure_bin |
24 | theorem | | ⊢ |
| proveit.logic.equality.equals_reversal |
25 | instantiation | 34, 35, 77, 74, 36, 37, 45, 50, 38* | ⊢ |
| : , : , : , : , : , : |
26 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.add_1_1 |
27 | axiom | | ⊢ |
| proveit.logic.equality.substitution |
28 | instantiation | 39, 40, 41, 42* | ⊢ |
| : , : |
29 | theorem | | ⊢ |
| proveit.numbers.multiplication.commutation |
30 | instantiation | 75, 62, 43 | ⊢ |
| : , : , : |
31 | instantiation | 44, 45, 54, 46 | ⊢ |
| : , : |
32 | assumption | | ⊢ |
33 | instantiation | 75, 55, 47 | ⊢ |
| : , : , : |
34 | theorem | | ⊢ |
| proveit.numbers.multiplication.distribute_through_sum |
35 | axiom | | ⊢ |
| proveit.numbers.number_sets.natural_numbers.zero_in_nats |
36 | theorem | | ⊢ |
| proveit.core_expr_types.tuples.tuple_len_0_typical_eq |
37 | instantiation | 48 | ⊢ |
| : , : |
38 | instantiation | 49, 50 | ⊢ |
| : |
39 | theorem | | ⊢ |
| proveit.numbers.exponentiation.neg_power_as_div |
40 | instantiation | 75, 51, 52 | ⊢ |
| : , : , : |
41 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.posnat1 |
42 | instantiation | 53, 54 | ⊢ |
| : |
43 | instantiation | 75, 55, 56 | ⊢ |
| : , : , : |
44 | theorem | | ⊢ |
| proveit.numbers.division.div_complex_closure |
45 | instantiation | 75, 62, 57 | ⊢ |
| : , : , : |
46 | instantiation | 58, 71 | ⊢ |
| : |
47 | assumption | | ⊢ |
48 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.tuple_len_2_typical_eq |
49 | theorem | | ⊢ |
| proveit.numbers.multiplication.elim_one_left |
50 | instantiation | 75, 62, 59 | ⊢ |
| : , : , : |
51 | theorem | | ⊢ |
| proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero |
52 | instantiation | 75, 60, 61 | ⊢ |
| : , : , : |
53 | theorem | | ⊢ |
| proveit.numbers.exponentiation.complex_x_to_first_power_is_x |
54 | instantiation | 75, 62, 63 | ⊢ |
| : , : , : |
55 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.real_neg_within_real |
56 | assumption | | ⊢ |
57 | instantiation | 75, 67, 64 | ⊢ |
| : , : , : |
58 | theorem | | ⊢ |
| proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos |
59 | assumption | | ⊢ |
60 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero |
61 | instantiation | 75, 65, 66 | ⊢ |
| : , : , : |
62 | theorem | | ⊢ |
| proveit.numbers.number_sets.complex_numbers.real_within_complex |
63 | instantiation | 75, 67, 68 | ⊢ |
| : , : , : |
64 | instantiation | 75, 72, 69 | ⊢ |
| : , : , : |
65 | theorem | | ⊢ |
| proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero |
66 | instantiation | 75, 70, 71 | ⊢ |
| : , : , : |
67 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.rational_within_real |
68 | instantiation | 75, 72, 73 | ⊢ |
| : , : , : |
69 | instantiation | 75, 76, 74 | ⊢ |
| : , : , : |
70 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int |
71 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.posnat2 |
72 | theorem | | ⊢ |
| proveit.numbers.number_sets.rational_numbers.int_within_rational |
73 | instantiation | 75, 76, 77 | ⊢ |
| : , : , : |
74 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat1 |
75 | theorem | | ⊢ |
| proveit.logic.sets.inclusion.superset_membership_from_proper_subset |
76 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.nat_within_int |
77 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat2 |
*equality replacement requirements |