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