| step type | requirements | statement |
0 | instantiation | 1, 2, 3 | , ⊢  |
| : , : , :  |
1 | reference | 6 | ⊢  |
2 | instantiation | 6, 4, 5 | ⊢  |
| : , : , :  |
3 | instantiation | 6, 7, 8 | , ⊢  |
| : , : , :  |
4 | instantiation | 10, 9 | ⊢  |
| : , : , :  |
5 | instantiation | 10, 39 | ⊢  |
| : , : , :  |
6 | axiom | | ⊢  |
| proveit.logic.equality.equals_transitivity |
7 | instantiation | 11, 62, 63, 12, 45, 46, 49, 28, 29, 13 | , ⊢  |
| : , : , : , : , : , : , : , :  |
8 | instantiation | 14, 15, 16, 17 | , ⊢  |
| : , : , : , :  |
9 | instantiation | 48, 45 | ⊢  |
| :  |
10 | axiom | | ⊢  |
| proveit.logic.equality.substitution |
11 | theorem | | ⊢  |
| proveit.numbers.addition.subtraction.add_cancel_general |
12 | instantiation | 18 | ⊢  |
| : , : , :  |
13 | instantiation | 19 | ⊢  |
| :  |
14 | theorem | | ⊢  |
| proveit.logic.equality.four_chain_transitivity |
15 | instantiation | 20, 66, 41, 21, 26, 42, 45, 49, 28, 29 | , ⊢  |
| : , : , : , : , : , : , :  |
16 | instantiation | 24, 62, 66, 22, 26, 45, 49, 28, 29, 23* | , ⊢  |
| : , : , : , : , : , :  |
17 | instantiation | 24, 66, 41, 25, 26, 42, 45, 27, 28, 29, 30* | , ⊢  |
| : , : , : , : , : , :  |
18 | theorem | | ⊢  |
| proveit.numbers.numerals.decimals.tuple_len_3_typical_eq |
19 | axiom | | ⊢  |
| proveit.logic.equality.equals_reflexivity |
20 | theorem | | ⊢  |
| proveit.numbers.addition.leftward_commutation |
21 | instantiation | 50 | ⊢  |
| : , :  |
22 | instantiation | 50 | ⊢  |
| : , :  |
23 | instantiation | 34, 31, 32* | ⊢  |
| : , :  |
24 | theorem | | ⊢  |
| proveit.numbers.addition.association |
25 | instantiation | 50 | ⊢  |
| : , :  |
26 | instantiation | 50 | ⊢  |
| : , :  |
27 | instantiation | 33, 45, 49 | ⊢  |
| : , :  |
28 | instantiation | 33, 44, 46 | ⊢  |
| : , :  |
29 | instantiation | 33, 45, 46 | ⊢  |
| : , :  |
30 | instantiation | 34, 35, 36* | ⊢  |
| : , :  |
31 | instantiation | 40, 41, 66, 62, 42, 37, 38, 49, 39* | ⊢  |
| : , : , : , : , : , :  |
32 | theorem | | ⊢  |
| proveit.numbers.numerals.decimals.add_1_1 |
33 | theorem | | ⊢  |
| proveit.numbers.multiplication.mult_complex_closure_bin |
34 | theorem | | ⊢  |
| proveit.logic.equality.equals_reversal |
35 | instantiation | 40, 41, 66, 62, 42, 43, 44, 45, 46 | ⊢  |
| : , : , : , : , : , :  |
36 | theorem | | ⊢  |
| proveit.numbers.numerals.decimals.add_3_2 |
37 | instantiation | 50 | ⊢  |
| : , :  |
38 | instantiation | 64, 52, 47 | ⊢  |
| : , : , :  |
39 | instantiation | 48, 49 | ⊢  |
| :  |
40 | theorem | | ⊢  |
| proveit.numbers.multiplication.distribute_through_sum |
41 | axiom | | ⊢  |
| proveit.numbers.number_sets.natural_numbers.zero_in_nats |
42 | theorem | | ⊢  |
| proveit.core_expr_types.tuples.tuple_len_0_typical_eq |
43 | instantiation | 50 | ⊢  |
| : , :  |
44 | instantiation | 64, 52, 51 | ⊢  |
| : , : , :  |
45 | instantiation | 64, 52, 53 | ⊢  |
| : , : , :  |
46 | assumption | | ⊢  |
47 | instantiation | 64, 56, 54 | ⊢  |
| : , : , :  |
48 | theorem | | ⊢  |
| proveit.numbers.multiplication.elim_one_left |
49 | assumption | | ⊢  |
50 | theorem | | ⊢  |
| proveit.numbers.numerals.decimals.tuple_len_2_typical_eq |
51 | instantiation | 64, 56, 55 | ⊢  |
| : , : , :  |
52 | theorem | | ⊢  |
| proveit.numbers.number_sets.complex_numbers.real_within_complex |
53 | instantiation | 64, 56, 57 | ⊢  |
| : , : , :  |
54 | instantiation | 64, 60, 58 | ⊢  |
| : , : , :  |
55 | instantiation | 64, 60, 59 | ⊢  |
| : , : , :  |
56 | theorem | | ⊢  |
| proveit.numbers.number_sets.real_numbers.rational_within_real |
57 | instantiation | 64, 60, 61 | ⊢  |
| : , : , :  |
58 | instantiation | 64, 65, 62 | ⊢  |
| : , : , :  |
59 | instantiation | 64, 65, 63 | ⊢  |
| : , : , :  |
60 | theorem | | ⊢  |
| proveit.numbers.number_sets.rational_numbers.int_within_rational |
61 | instantiation | 64, 65, 66 | ⊢  |
| : , : , :  |
62 | theorem | | ⊢  |
| proveit.numbers.numerals.decimals.nat1 |
63 | theorem | | ⊢  |
| proveit.numbers.numerals.decimals.nat3 |
64 | theorem | | ⊢  |
| proveit.logic.sets.inclusion.superset_membership_from_proper_subset |
65 | theorem | | ⊢  |
| proveit.numbers.number_sets.integers.nat_within_int |
66 | theorem | | ⊢  |
| proveit.numbers.numerals.decimals.nat2 |
*equality replacement requirements |