| step type | requirements | statement |
0 | instantiation | 1, 2, 3 | ⊢ |
| : , : , : |
1 | reference | 23 | ⊢ |
2 | instantiation | 4, 31, 64, 62, 32, 5, 11, 34, 12 | ⊢ |
| : , : , : , : , : , : |
3 | instantiation | 23, 6, 7 | ⊢ |
| : , : , : |
4 | theorem | | ⊢ |
| proveit.numbers.addition.disassociation |
5 | instantiation | 42 | ⊢ |
| : , : |
6 | instantiation | 8, 62, 31, 32, 11, 34, 12 | ⊢ |
| : , : , : , : , : , : , : |
7 | instantiation | 9, 31, 64, 62, 32, 10, 11, 12, 34, 13* | ⊢ |
| : , : , : , : , : , : |
8 | theorem | | ⊢ |
| proveit.numbers.addition.leftward_commutation |
9 | theorem | | ⊢ |
| proveit.numbers.addition.association |
10 | instantiation | 42 | ⊢ |
| : , : |
11 | instantiation | 65, 50, 14 | ⊢ |
| : , : , : |
12 | instantiation | 65, 50, 15 | ⊢ |
| : , : , : |
13 | instantiation | 23, 16, 17, 18* | ⊢ |
| : , : , : |
14 | instantiation | 65, 54, 19 | ⊢ |
| : , : , : |
15 | instantiation | 65, 54, 20 | ⊢ |
| : , : , : |
16 | instantiation | 35, 21 | ⊢ |
| : , : , : |
17 | instantiation | 28, 22 | ⊢ |
| : , : |
18 | instantiation | 23, 24, 25 | ⊢ |
| : , : , : |
19 | instantiation | 65, 58, 26 | ⊢ |
| : , : , : |
20 | instantiation | 65, 58, 27 | ⊢ |
| : , : , : |
21 | instantiation | 28, 29 | ⊢ |
| : , : |
22 | instantiation | 30, 31, 64, 62, 32, 33, 46, 34, 41 | ⊢ |
| : , : , : , : , : , : |
23 | axiom | | ⊢ |
| proveit.logic.equality.equals_transitivity |
24 | instantiation | 35, 36 | ⊢ |
| : , : , : |
25 | instantiation | 37, 41 | ⊢ |
| : |
26 | instantiation | 38, 60, 56 | ⊢ |
| : , : |
27 | instantiation | 39, 56 | ⊢ |
| : |
28 | theorem | | ⊢ |
| proveit.logic.equality.equals_reversal |
29 | instantiation | 40, 41 | ⊢ |
| : |
30 | theorem | | ⊢ |
| proveit.numbers.multiplication.distribute_through_sum |
31 | axiom | | ⊢ |
| proveit.numbers.number_sets.natural_numbers.zero_in_nats |
32 | theorem | | ⊢ |
| proveit.core_expr_types.tuples.tuple_len_0_typical_eq |
33 | instantiation | 42 | ⊢ |
| : , : |
34 | instantiation | 43, 45 | ⊢ |
| : |
35 | axiom | | ⊢ |
| proveit.logic.equality.substitution |
36 | instantiation | 44, 45, 46, 47 | ⊢ |
| : , : , : |
37 | theorem | | ⊢ |
| proveit.numbers.multiplication.elim_one_left |
38 | theorem | | ⊢ |
| proveit.numbers.multiplication.mult_int_closure_bin |
39 | theorem | | ⊢ |
| proveit.numbers.negation.int_closure |
40 | theorem | | ⊢ |
| proveit.numbers.negation.mult_neg_one_left |
41 | instantiation | 65, 50, 48 | ⊢ |
| : , : , : |
42 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.tuple_len_2_typical_eq |
43 | theorem | | ⊢ |
| proveit.numbers.negation.complex_closure |
44 | theorem | | ⊢ |
| proveit.numbers.addition.subtraction.subtract_from_add |
45 | instantiation | 65, 50, 49 | ⊢ |
| : , : , : |
46 | instantiation | 65, 50, 51 | ⊢ |
| : , : , : |
47 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.add_1_1 |
48 | instantiation | 65, 54, 52 | ⊢ |
| : , : , : |
49 | instantiation | 65, 54, 53 | ⊢ |
| : , : , : |
50 | theorem | | ⊢ |
| proveit.numbers.number_sets.complex_numbers.real_within_complex |
51 | instantiation | 65, 54, 55 | ⊢ |
| : , : , : |
52 | instantiation | 65, 58, 56 | ⊢ |
| : , : , : |
53 | instantiation | 65, 58, 57 | ⊢ |
| : , : , : |
54 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.rational_within_real |
55 | instantiation | 65, 58, 60 | ⊢ |
| : , : , : |
56 | instantiation | 59, 60, 61 | ⊢ |
| : , : |
57 | instantiation | 65, 63, 62 | ⊢ |
| : , : , : |
58 | theorem | | ⊢ |
| proveit.numbers.number_sets.rational_numbers.int_within_rational |
59 | theorem | | ⊢ |
| proveit.numbers.exponentiation.exp_int_closure |
60 | instantiation | 65, 63, 64 | ⊢ |
| : , : , : |
61 | instantiation | 65, 66, 67 | ⊢ |
| : , : , : |
62 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat1 |
63 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.nat_within_int |
64 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat2 |
65 | theorem | | ⊢ |
| proveit.logic.sets.inclusion.superset_membership_from_proper_subset |
66 | theorem | | ⊢ |
| proveit.numbers.number_sets.natural_numbers.nat_pos_within_nat |
67 | assumption | | ⊢ |
*equality replacement requirements |