| step type | requirements | statement |
0 | instantiation | 1, 2 | , , , ⊢  |
| : , :  |
1 | theorem | | ⊢  |
| proveit.logic.equality.equals_reversal |
2 | instantiation | 5, 3, 4 | , , , ⊢  |
| : , : , :  |
3 | instantiation | 5, 6, 7 | , , , ⊢  |
| : , : , :  |
4 | instantiation | 11, 8, 77, 9, 15, 17, 18, 19, 10, 21, 22 | , , , ⊢  |
| : , : , : , : , : , : , :  |
5 | axiom | | ⊢  |
| proveit.logic.equality.equals_transitivity |
6 | instantiation | 11, 80, 12, 13, 18, 19, 50, 21, 20, 22 | , , , ⊢  |
| : , : , : , : , : , : , :  |
7 | instantiation | 14, 77, 15, 16, 17, 18, 19, 50, 20, 21, 22, 23* | , , , ⊢  |
| : , : , : , : , : , :  |
8 | axiom | | ⊢  |
| proveit.numbers.number_sets.natural_numbers.zero_in_nats |
9 | theorem | | ⊢  |
| proveit.core_expr_types.tuples.tuple_len_0_typical_eq |
10 | instantiation | 30, 24, 52, 31 | ⊢  |
| : , :  |
11 | theorem | | ⊢  |
| proveit.numbers.multiplication.leftward_commutation |
12 | theorem | | ⊢  |
| proveit.numbers.numerals.decimals.nat1 |
13 | instantiation | 25 | ⊢  |
| : , : , :  |
14 | theorem | | ⊢  |
| proveit.numbers.multiplication.association |
15 | instantiation | 26 | ⊢  |
| : , :  |
16 | instantiation | 26 | ⊢  |
| : , :  |
17 | instantiation | 26 | ⊢  |
| : , :  |
18 | instantiation | 78, 61, 27 | ⊢  |
| : , : , :  |
19 | instantiation | 28, 29 | ⊢  |
| :  |
20 | instantiation | 30, 50, 52, 31 | ⊢  |
| : , :  |
21 | instantiation | 32, 33, 50 | ⊢  |
| : , :  |
22 | instantiation | 78, 61, 34 | ⊢  |
| : , : , :  |
23 | instantiation | 35, 50, 36, 37, 38*, 39*, 40* | ⊢  |
| : , : , : , :  |
24 | instantiation | 78, 61, 41 | ⊢  |
| : , : , :  |
25 | theorem | | ⊢  |
| proveit.numbers.numerals.decimals.tuple_len_3_typical_eq |
26 | theorem | | ⊢  |
| proveit.numbers.numerals.decimals.tuple_len_2_typical_eq |
27 | instantiation | 78, 55, 42 | ⊢  |
| : , : , :  |
28 | theorem | | ⊢  |
| proveit.numbers.exponentiation.sqrt_complex_closure |
29 | instantiation | 78, 61, 43 | ⊢  |
| : , : , :  |
30 | theorem | | ⊢  |
| proveit.numbers.division.div_complex_closure |
31 | instantiation | 44, 73 | ⊢  |
| :  |
32 | theorem | | ⊢  |
| proveit.numbers.exponentiation.exp_complex_closure |
33 | instantiation | 78, 61, 45 | ⊢  |
| : , : , :  |
34 | assumption | | ⊢  |
35 | theorem | | ⊢  |
| proveit.numbers.division.prod_of_fracs |
36 | instantiation | 78, 47, 46 | ⊢  |
| : , : , :  |
37 | instantiation | 78, 47, 48 | ⊢  |
| : , : , :  |
38 | instantiation | 49, 50 | ⊢  |
| :  |
39 | theorem | | ⊢  |
| proveit.numbers.numerals.decimals.mult_2_2 |
40 | instantiation | 51, 52 | ⊢  |
| :  |
41 | instantiation | 78, 68, 53 | ⊢  |
| : , : , :  |
42 | assumption | | ⊢  |
43 | instantiation | 78, 55, 54 | ⊢  |
| : , : , :  |
44 | theorem | | ⊢  |
| proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos |
45 | instantiation | 78, 55, 56 | ⊢  |
| : , : , :  |
46 | instantiation | 78, 58, 57 | ⊢  |
| : , : , :  |
47 | theorem | | ⊢  |
| proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero |
48 | instantiation | 78, 58, 59 | ⊢  |
| : , : , :  |
49 | theorem | | ⊢  |
| proveit.numbers.division.frac_one_denom |
50 | instantiation | 78, 61, 60 | ⊢  |
| : , : , :  |
51 | theorem | | ⊢  |
| proveit.numbers.multiplication.elim_one_left |
52 | instantiation | 78, 61, 62 | ⊢  |
| : , : , :  |
53 | instantiation | 78, 75, 63 | ⊢  |
| : , : , :  |
54 | assumption | | ⊢  |
55 | theorem | | ⊢  |
| proveit.numbers.number_sets.real_numbers.real_neg_within_real |
56 | assumption | | ⊢  |
57 | instantiation | 78, 65, 64 | ⊢  |
| : , : , :  |
58 | theorem | | ⊢  |
| proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero |
59 | instantiation | 78, 65, 66 | ⊢  |
| : , : , :  |
60 | instantiation | 78, 68, 67 | ⊢  |
| : , : , :  |
61 | theorem | | ⊢  |
| proveit.numbers.number_sets.complex_numbers.real_within_complex |
62 | instantiation | 78, 68, 69 | ⊢  |
| : , : , :  |
63 | instantiation | 78, 79, 70 | ⊢  |
| : , : , :  |
64 | instantiation | 78, 72, 71 | ⊢  |
| : , : , :  |
65 | theorem | | ⊢  |
| proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero |
66 | instantiation | 78, 72, 73 | ⊢  |
| : , : , :  |
67 | instantiation | 78, 75, 74 | ⊢  |
| : , : , :  |
68 | theorem | | ⊢  |
| proveit.numbers.number_sets.real_numbers.rational_within_real |
69 | instantiation | 78, 75, 76 | ⊢  |
| : , : , :  |
70 | theorem | | ⊢  |
| proveit.numbers.numerals.decimals.nat4 |
71 | theorem | | ⊢  |
| proveit.numbers.numerals.decimals.posnat1 |
72 | theorem | | ⊢  |
| proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int |
73 | theorem | | ⊢  |
| proveit.numbers.numerals.decimals.posnat3 |
74 | instantiation | 78, 79, 77 | ⊢  |
| : , : , :  |
75 | theorem | | ⊢  |
| proveit.numbers.number_sets.rational_numbers.int_within_rational |
76 | instantiation | 78, 79, 80 | ⊢  |
| : , : , :  |
77 | theorem | | ⊢  |
| proveit.numbers.numerals.decimals.nat2 |
78 | theorem | | ⊢  |
| proveit.logic.sets.inclusion.superset_membership_from_proper_subset |
79 | theorem | | ⊢  |
| proveit.numbers.number_sets.integers.nat_within_int |
80 | theorem | | ⊢  |
| proveit.numbers.numerals.decimals.nat3 |
*equality replacement requirements |