| step type | requirements | statement |
0 | instantiation | 1, 2, 3 | , , , ⊢ |
| : , : , : |
1 | reference | 4 | ⊢ |
2 | instantiation | 4, 5, 6 | , , , ⊢ |
| : , : , : |
3 | instantiation | 10, 7, 76, 8, 14, 16, 17, 18, 9, 20, 21 | , , , ⊢ |
| : , : , : , : , : , : , : |
4 | axiom | | ⊢ |
| proveit.logic.equality.equals_transitivity |
5 | instantiation | 10, 79, 11, 12, 17, 18, 49, 20, 19, 21 | , , , ⊢ |
| : , : , : , : , : , : , : |
6 | instantiation | 13, 76, 14, 15, 16, 17, 18, 49, 19, 20, 21, 22* | , , , ⊢ |
| : , : , : , : , : , : |
7 | axiom | | ⊢ |
| proveit.numbers.number_sets.natural_numbers.zero_in_nats |
8 | theorem | | ⊢ |
| proveit.core_expr_types.tuples.tuple_len_0_typical_eq |
9 | instantiation | 29, 23, 51, 30 | ⊢ |
| : , : |
10 | theorem | | ⊢ |
| proveit.numbers.multiplication.leftward_commutation |
11 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat1 |
12 | instantiation | 24 | ⊢ |
| : , : , : |
13 | theorem | | ⊢ |
| proveit.numbers.multiplication.association |
14 | instantiation | 25 | ⊢ |
| : , : |
15 | instantiation | 25 | ⊢ |
| : , : |
16 | instantiation | 25 | ⊢ |
| : , : |
17 | instantiation | 77, 60, 26 | ⊢ |
| : , : , : |
18 | instantiation | 27, 28 | ⊢ |
| : |
19 | instantiation | 29, 49, 51, 30 | ⊢ |
| : , : |
20 | instantiation | 31, 32, 49 | ⊢ |
| : , : |
21 | instantiation | 77, 60, 33 | ⊢ |
| : , : , : |
22 | instantiation | 34, 49, 35, 36, 37*, 38*, 39* | ⊢ |
| : , : , : , : |
23 | instantiation | 77, 60, 40 | ⊢ |
| : , : , : |
24 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.tuple_len_3_typical_eq |
25 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.tuple_len_2_typical_eq |
26 | instantiation | 77, 54, 41 | ⊢ |
| : , : , : |
27 | theorem | | ⊢ |
| proveit.numbers.exponentiation.sqrt_complex_closure |
28 | instantiation | 77, 60, 42 | ⊢ |
| : , : , : |
29 | theorem | | ⊢ |
| proveit.numbers.division.div_complex_closure |
30 | instantiation | 43, 72 | ⊢ |
| : |
31 | theorem | | ⊢ |
| proveit.numbers.exponentiation.exp_complex_closure |
32 | instantiation | 77, 60, 44 | ⊢ |
| : , : , : |
33 | assumption | | ⊢ |
34 | theorem | | ⊢ |
| proveit.numbers.division.prod_of_fracs |
35 | instantiation | 77, 46, 45 | ⊢ |
| : , : , : |
36 | instantiation | 77, 46, 47 | ⊢ |
| : , : , : |
37 | instantiation | 48, 49 | ⊢ |
| : |
38 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.mult_2_2 |
39 | instantiation | 50, 51 | ⊢ |
| : |
40 | instantiation | 77, 67, 52 | ⊢ |
| : , : , : |
41 | assumption | | ⊢ |
42 | instantiation | 77, 54, 53 | ⊢ |
| : , : , : |
43 | theorem | | ⊢ |
| proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos |
44 | instantiation | 77, 54, 55 | ⊢ |
| : , : , : |
45 | instantiation | 77, 57, 56 | ⊢ |
| : , : , : |
46 | theorem | | ⊢ |
| proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero |
47 | instantiation | 77, 57, 58 | ⊢ |
| : , : , : |
48 | theorem | | ⊢ |
| proveit.numbers.division.frac_one_denom |
49 | instantiation | 77, 60, 59 | ⊢ |
| : , : , : |
50 | theorem | | ⊢ |
| proveit.numbers.multiplication.elim_one_left |
51 | instantiation | 77, 60, 61 | ⊢ |
| : , : , : |
52 | instantiation | 77, 74, 62 | ⊢ |
| : , : , : |
53 | assumption | | ⊢ |
54 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.real_neg_within_real |
55 | assumption | | ⊢ |
56 | instantiation | 77, 64, 63 | ⊢ |
| : , : , : |
57 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero |
58 | instantiation | 77, 64, 65 | ⊢ |
| : , : , : |
59 | instantiation | 77, 67, 66 | ⊢ |
| : , : , : |
60 | theorem | | ⊢ |
| proveit.numbers.number_sets.complex_numbers.real_within_complex |
61 | instantiation | 77, 67, 68 | ⊢ |
| : , : , : |
62 | instantiation | 77, 78, 69 | ⊢ |
| : , : , : |
63 | instantiation | 77, 71, 70 | ⊢ |
| : , : , : |
64 | theorem | | ⊢ |
| proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero |
65 | instantiation | 77, 71, 72 | ⊢ |
| : , : , : |
66 | instantiation | 77, 74, 73 | ⊢ |
| : , : , : |
67 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.rational_within_real |
68 | instantiation | 77, 74, 75 | ⊢ |
| : , : , : |
69 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat4 |
70 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.posnat1 |
71 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int |
72 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.posnat3 |
73 | instantiation | 77, 78, 76 | ⊢ |
| : , : , : |
74 | theorem | | ⊢ |
| proveit.numbers.number_sets.rational_numbers.int_within_rational |
75 | instantiation | 77, 78, 79 | ⊢ |
| : , : , : |
76 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat2 |
77 | theorem | | ⊢ |
| proveit.logic.sets.inclusion.superset_membership_from_proper_subset |
78 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.nat_within_int |
79 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat3 |
*equality replacement requirements |