| step type | requirements | statement |
0 | instantiation | 1, 2, 3 | , , ⊢  |
| : , : , :  |
1 | reference | 62 | ⊢  |
2 | instantiation | 62, 4, 5 | , , ⊢  |
| : , : , :  |
3 | instantiation | 47, 66, 48, 6, 12, 49, 13, 7, 42, 8* | , , ⊢  |
| : , : , : , : , : , :  |
4 | instantiation | 62, 9, 10 | , , ⊢  |
| : , : , :  |
5 | instantiation | 47, 76, 66, 11, 12, 13, 54, 42, 14* | , , ⊢  |
| : , : , : , : , : , :  |
6 | instantiation | 59 | ⊢  |
| : , :  |
7 | instantiation | 24, 15, 54 | ⊢  |
| : , :  |
8 | instantiation | 36, 16, 70* | ⊢  |
| : , :  |
9 | instantiation | 17, 18, 19, 20 | , , ⊢  |
| : , : , : , :  |
10 | instantiation | 47, 48, 71, 34, 49, 21, 22, 58, 54, 42, 23* | , , ⊢  |
| : , : , : , : , : , :  |
11 | instantiation | 59 | ⊢  |
| : , :  |
12 | instantiation | 59 | ⊢  |
| : , :  |
13 | instantiation | 24, 25, 58 | ⊢  |
| : , :  |
14 | instantiation | 36, 26, 70* | ⊢  |
| : , :  |
15 | instantiation | 74, 60, 27 | ⊢  |
| : , : , :  |
16 | instantiation | 44, 48, 66, 76, 49, 50, 51, 42, 28* | ⊢  |
| : , : , : , : , : , :  |
17 | theorem | | ⊢  |
| proveit.logic.equality.four_chain_transitivity |
18 | instantiation | 33, 76, 66, 71, 29, 30, 58, 54, 42 | , , ⊢  |
| : , : , : , : , : , : , :  |
19 | instantiation | 33, 66, 71, 76, 31, 32, 58, 54, 42 | , , ⊢  |
| : , : , : , : , : , : , :  |
20 | instantiation | 33, 34, 76, 35, 58, 54, 42 | , , ⊢  |
| : , : , : , : , : , : , :  |
21 | instantiation | 56 | ⊢  |
| : , : , :  |
22 | instantiation | 43 | ⊢  |
| : , : , : , :  |
23 | instantiation | 36, 37, 38* | ⊢  |
| : , :  |
24 | theorem | | ⊢  |
| proveit.numbers.multiplication.mult_complex_closure_bin |
25 | instantiation | 74, 60, 39 | ⊢  |
| : , : , :  |
26 | instantiation | 44, 48, 66, 76, 49, 50, 51, 54, 40* | ⊢  |
| : , : , : , : , : , :  |
27 | instantiation | 74, 67, 41 | ⊢  |
| : , : , :  |
28 | instantiation | 57, 42 | ⊢  |
| :  |
29 | instantiation | 59 | ⊢  |
| : , :  |
30 | instantiation | 56 | ⊢  |
| : , : , :  |
31 | instantiation | 59 | ⊢  |
| : , :  |
32 | instantiation | 56 | ⊢  |
| : , : , :  |
33 | theorem | | ⊢  |
| proveit.numbers.addition.leftward_commutation |
34 | theorem | | ⊢  |
| proveit.numbers.numerals.decimals.nat4 |
35 | instantiation | 43 | ⊢  |
| : , : , : , :  |
36 | theorem | | ⊢  |
| proveit.logic.equality.equals_reversal |
37 | instantiation | 44, 48, 71, 76, 49, 45, 51, 58, 46* | ⊢  |
| : , : , : , : , : , :  |
38 | instantiation | 47, 48, 66, 76, 49, 50, 51, 52* | ⊢  |
| : , : , : , : , : , :  |
39 | instantiation | 74, 67, 53 | ⊢  |
| : , : , :  |
40 | instantiation | 57, 54 | ⊢  |
| :  |
41 | instantiation | 74, 72, 55 | ⊢  |
| : , : , :  |
42 | assumption | | ⊢  |
43 | theorem | | ⊢  |
| proveit.numbers.numerals.decimals.tuple_len_4_typical_eq |
44 | theorem | | ⊢  |
| proveit.numbers.multiplication.distribute_through_sum |
45 | instantiation | 56 | ⊢  |
| : , : , :  |
46 | instantiation | 57, 58 | ⊢  |
| :  |
47 | theorem | | ⊢  |
| proveit.numbers.addition.association |
48 | axiom | | ⊢  |
| proveit.numbers.number_sets.natural_numbers.zero_in_nats |
49 | theorem | | ⊢  |
| proveit.core_expr_types.tuples.tuple_len_0_typical_eq |
50 | instantiation | 59 | ⊢  |
| : , :  |
51 | instantiation | 74, 60, 61 | ⊢  |
| : , : , :  |
52 | instantiation | 62, 63, 64 | ⊢  |
| : , : , :  |
53 | instantiation | 74, 72, 65 | ⊢  |
| : , : , :  |
54 | assumption | | ⊢  |
55 | instantiation | 74, 75, 66 | ⊢  |
| : , : , :  |
56 | theorem | | ⊢  |
| proveit.numbers.numerals.decimals.tuple_len_3_typical_eq |
57 | theorem | | ⊢  |
| proveit.numbers.multiplication.elim_one_left |
58 | assumption | | ⊢  |
59 | theorem | | ⊢  |
| proveit.numbers.numerals.decimals.tuple_len_2_typical_eq |
60 | theorem | | ⊢  |
| proveit.numbers.number_sets.complex_numbers.real_within_complex |
61 | instantiation | 74, 67, 68 | ⊢  |
| : , : , :  |
62 | axiom | | ⊢  |
| proveit.logic.equality.equals_transitivity |
63 | instantiation | 69, 70 | ⊢  |
| : , : , :  |
64 | theorem | | ⊢  |
| proveit.numbers.numerals.decimals.add_2_1 |
65 | instantiation | 74, 75, 71 | ⊢  |
| : , : , :  |
66 | theorem | | ⊢  |
| proveit.numbers.numerals.decimals.nat2 |
67 | theorem | | ⊢  |
| proveit.numbers.number_sets.real_numbers.rational_within_real |
68 | instantiation | 74, 72, 73 | ⊢  |
| : , : , :  |
69 | axiom | | ⊢  |
| proveit.logic.equality.substitution |
70 | theorem | | ⊢  |
| proveit.numbers.numerals.decimals.add_1_1 |
71 | theorem | | ⊢  |
| proveit.numbers.numerals.decimals.nat3 |
72 | theorem | | ⊢  |
| proveit.numbers.number_sets.rational_numbers.int_within_rational |
73 | instantiation | 74, 75, 76 | ⊢  |
| : , : , :  |
74 | theorem | | ⊢  |
| proveit.logic.sets.inclusion.superset_membership_from_proper_subset |
75 | theorem | | ⊢  |
| proveit.numbers.number_sets.integers.nat_within_int |
76 | theorem | | ⊢  |
| proveit.numbers.numerals.decimals.nat1 |
*equality replacement requirements |