| step type | requirements | statement |
0 | instantiation | 1, 2, 3, 4, 5* | , , ⊢ |
| : , : , : , : |
1 | reference | 10 | ⊢ |
2 | instantiation | 7, 6 | , , ⊢ |
| : , : , : |
3 | instantiation | 7, 8 | , , ⊢ |
| : , : , : |
4 | instantiation | 15, 9 | , , ⊢ |
| : , : |
5 | instantiation | 10, 11, 12, 13 | , ⊢ |
| : , : , : , : |
6 | instantiation | 15, 14 | , , ⊢ |
| : , : |
7 | axiom | | ⊢ |
| proveit.logic.equality.substitution |
8 | instantiation | 15, 16 | , , ⊢ |
| : , : |
9 | instantiation | 17, 74, 77, 24, 18, 25, 19, 33, 35 | , , ⊢ |
| : , : , : , : , : , : |
10 | theorem | | ⊢ |
| proveit.logic.equality.four_chain_transitivity |
11 | instantiation | 20, 24, 77, 74, 25, 21, 39, 40, 35 | , ⊢ |
| : , : , : , : , : , : |
12 | instantiation | 20, 77, 24, 21, 22, 25, 39, 40, 45, 41 | , ⊢ |
| : , : , : , : , : , : |
13 | instantiation | 23, 74, 24, 25, 39, 45, 41 | , ⊢ |
| : , : , : , : , : , : , : , : |
14 | instantiation | 27, 39, 33, 30, 31, 26* | , , ⊢ |
| : , : , : |
15 | theorem | | ⊢ |
| proveit.logic.equality.equals_reversal |
16 | instantiation | 27, 39, 35, 30, 31, 28* | , , ⊢ |
| : , : , : |
17 | theorem | | ⊢ |
| proveit.numbers.multiplication.distribute_through_sum |
18 | instantiation | 32 | ⊢ |
| : , : |
19 | instantiation | 29, 39, 30, 31 | , ⊢ |
| : , : |
20 | theorem | | ⊢ |
| proveit.numbers.addition.disassociation |
21 | instantiation | 32 | ⊢ |
| : , : |
22 | instantiation | 32 | ⊢ |
| : , : |
23 | theorem | | ⊢ |
| proveit.numbers.addition.subtraction.add_cancel_general_rev |
24 | axiom | | ⊢ |
| proveit.numbers.number_sets.natural_numbers.zero_in_nats |
25 | theorem | | ⊢ |
| proveit.core_expr_types.tuples.tuple_len_0_typical_eq |
26 | instantiation | 34, 33 | , ⊢ |
| : |
27 | theorem | | ⊢ |
| proveit.numbers.division.mult_frac_left |
28 | instantiation | 34, 35 | , ⊢ |
| : |
29 | theorem | | ⊢ |
| proveit.numbers.division.div_complex_closure |
30 | instantiation | 54, 39, 36 | ⊢ |
| : , : |
31 | instantiation | 37, 38 | ⊢ |
| : , : |
32 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.tuple_len_2_typical_eq |
33 | instantiation | 54, 39, 40 | , ⊢ |
| : , : |
34 | theorem | | ⊢ |
| proveit.numbers.multiplication.elim_one_left |
35 | instantiation | 54, 45, 41 | , ⊢ |
| : , : |
36 | instantiation | 46, 51 | ⊢ |
| : |
37 | theorem | | ⊢ |
| proveit.numbers.addition.subtraction.nonzero_difference_if_different |
38 | instantiation | 42, 43 | ⊢ |
| : , : |
39 | instantiation | 75, 59, 44 | ⊢ |
| : , : , : |
40 | instantiation | 46, 45 | , ⊢ |
| : |
41 | instantiation | 46, 47 | , ⊢ |
| : |
42 | theorem | | ⊢ |
| proveit.logic.equality.not_equals_symmetry |
43 | assumption | | ⊢ |
44 | instantiation | 75, 62, 48 | ⊢ |
| : , : , : |
45 | instantiation | 50, 51, 49 | , ⊢ |
| : , : |
46 | theorem | | ⊢ |
| proveit.numbers.negation.complex_closure |
47 | instantiation | 50, 51, 52 | , ⊢ |
| : , : |
48 | instantiation | 75, 69, 68 | ⊢ |
| : , : , : |
49 | instantiation | 75, 59, 53 | ⊢ |
| : , : , : |
50 | theorem | | ⊢ |
| proveit.numbers.exponentiation.exp_complex_closure |
51 | assumption | | ⊢ |
52 | instantiation | 54, 55, 56 | ⊢ |
| : , : |
53 | instantiation | 75, 62, 57 | ⊢ |
| : , : , : |
54 | theorem | | ⊢ |
| proveit.numbers.addition.add_complex_closure_bin |
55 | instantiation | 75, 59, 58 | ⊢ |
| : , : , : |
56 | instantiation | 75, 59, 60 | ⊢ |
| : , : , : |
57 | instantiation | 75, 69, 61 | ⊢ |
| : , : , : |
58 | instantiation | 75, 62, 63 | ⊢ |
| : , : , : |
59 | theorem | | ⊢ |
| proveit.numbers.number_sets.complex_numbers.real_within_complex |
60 | instantiation | 64, 65, 73 | ⊢ |
| : , : , : |
61 | instantiation | 66, 67, 68 | ⊢ |
| : , : |
62 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.rational_within_real |
63 | instantiation | 75, 69, 70 | ⊢ |
| : , : , : |
64 | theorem | | ⊢ |
| proveit.logic.sets.inclusion.unfold_subset_eq |
65 | instantiation | 71, 72 | ⊢ |
| : , : |
66 | theorem | | ⊢ |
| proveit.numbers.addition.add_int_closure_bin |
67 | instantiation | 75, 76, 73 | ⊢ |
| : , : , : |
68 | instantiation | 75, 76, 74 | ⊢ |
| : , : , : |
69 | theorem | | ⊢ |
| proveit.numbers.number_sets.rational_numbers.int_within_rational |
70 | instantiation | 75, 76, 77 | ⊢ |
| : , : , : |
71 | theorem | | ⊢ |
| proveit.logic.sets.inclusion.relax_proper_subset |
72 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.nat_within_real |
73 | assumption | | ⊢ |
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 |