| step type | requirements | statement |
0 | instantiation | 1, 2, 3 | , , ⊢ |
| : , : , : |
1 | reference | 29 | ⊢ |
2 | instantiation | 4, 62, 78, 5, 47, 13, 14, 12, 15 | , , ⊢ |
| : , : , : , : , : , : , : |
3 | instantiation | 6, 7, 78, 8, 9, 10, 11, 47, 12, 13, 14, 15, 16* | , , ⊢ |
| : , : , : , : , : , : |
4 | theorem | | ⊢ |
| proveit.numbers.multiplication.leftward_commutation |
5 | instantiation | 46 | ⊢ |
| : , : |
6 | theorem | | ⊢ |
| proveit.numbers.multiplication.association |
7 | axiom | | ⊢ |
| proveit.numbers.number_sets.natural_numbers.zero_in_nats |
8 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat3 |
9 | theorem | | ⊢ |
| proveit.core_expr_types.tuples.tuple_len_0_typical_eq |
10 | instantiation | 46 | ⊢ |
| : , : |
11 | instantiation | 17 | ⊢ |
| : , : , : |
12 | instantiation | 18, 24, 54, 19 | ⊢ |
| : , : |
13 | assumption | | ⊢ |
14 | assumption | | ⊢ |
15 | instantiation | 20, 21, 22 | ⊢ |
| : , : |
16 | instantiation | 23, 47, 24, 41, 40, 25*, 26* | ⊢ |
| : , : , : , : |
17 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.tuple_len_3_typical_eq |
18 | theorem | | ⊢ |
| proveit.numbers.division.div_complex_closure |
19 | instantiation | 27, 70 | ⊢ |
| : |
20 | theorem | | ⊢ |
| proveit.numbers.exponentiation.exp_complex_closure |
21 | assumption | | ⊢ |
22 | instantiation | 76, 60, 28 | ⊢ |
| : , : , : |
23 | theorem | | ⊢ |
| proveit.numbers.division.prod_of_fracs |
24 | instantiation | 76, 60, 33 | ⊢ |
| : , : , : |
25 | instantiation | 53, 47 | ⊢ |
| : |
26 | instantiation | 29, 30, 31 | ⊢ |
| : , : , : |
27 | theorem | | ⊢ |
| proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos |
28 | instantiation | 32, 33 | ⊢ |
| : |
29 | axiom | | ⊢ |
| proveit.logic.equality.equals_transitivity |
30 | instantiation | 34, 78, 35, 36, 37, 38 | ⊢ |
| : , : , : , : |
31 | instantiation | 39, 40, 41, 54, 42*, 43*, 44* | ⊢ |
| : , : , : |
32 | theorem | | ⊢ |
| proveit.numbers.negation.real_closure |
33 | instantiation | 76, 67, 45 | ⊢ |
| : , : , : |
34 | axiom | | ⊢ |
| proveit.core_expr_types.operations.operands_substitution |
35 | instantiation | 46 | ⊢ |
| : , : |
36 | instantiation | 46 | ⊢ |
| : , : |
37 | instantiation | 52, 47 | ⊢ |
| : |
38 | instantiation | 48, 54 | ⊢ |
| : |
39 | theorem | | ⊢ |
| proveit.numbers.division.frac_cancel_left |
40 | instantiation | 76, 50, 49 | ⊢ |
| : , : , : |
41 | instantiation | 76, 50, 51 | ⊢ |
| : , : , : |
42 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.mult_2_2 |
43 | instantiation | 52, 54 | ⊢ |
| : |
44 | instantiation | 53, 54 | ⊢ |
| : |
45 | instantiation | 76, 73, 55 | ⊢ |
| : , : , : |
46 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.tuple_len_2_typical_eq |
47 | instantiation | 76, 60, 56 | ⊢ |
| : , : , : |
48 | theorem | | ⊢ |
| proveit.numbers.multiplication.elim_one_left |
49 | instantiation | 76, 58, 57 | ⊢ |
| : , : , : |
50 | theorem | | ⊢ |
| proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero |
51 | instantiation | 76, 58, 59 | ⊢ |
| : , : , : |
52 | theorem | | ⊢ |
| proveit.numbers.multiplication.elim_one_right |
53 | theorem | | ⊢ |
| proveit.numbers.division.frac_one_denom |
54 | instantiation | 76, 60, 61 | ⊢ |
| : , : , : |
55 | instantiation | 76, 77, 62 | ⊢ |
| : , : , : |
56 | instantiation | 76, 67, 63 | ⊢ |
| : , : , : |
57 | instantiation | 76, 65, 64 | ⊢ |
| : , : , : |
58 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero |
59 | instantiation | 76, 65, 66 | ⊢ |
| : , : , : |
60 | theorem | | ⊢ |
| proveit.numbers.number_sets.complex_numbers.real_within_complex |
61 | instantiation | 76, 67, 68 | ⊢ |
| : , : , : |
62 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat1 |
63 | instantiation | 76, 73, 69 | ⊢ |
| : , : , : |
64 | instantiation | 76, 71, 70 | ⊢ |
| : , : , : |
65 | theorem | | ⊢ |
| proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero |
66 | instantiation | 76, 71, 72 | ⊢ |
| : , : , : |
67 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.rational_within_real |
68 | instantiation | 76, 73, 74 | ⊢ |
| : , : , : |
69 | instantiation | 76, 77, 75 | ⊢ |
| : , : , : |
70 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.posnat2 |
71 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int |
72 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.posnat1 |
73 | theorem | | ⊢ |
| proveit.numbers.number_sets.rational_numbers.int_within_rational |
74 | instantiation | 76, 77, 78 | ⊢ |
| : , : , : |
75 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat4 |
76 | theorem | | ⊢ |
| proveit.logic.sets.inclusion.superset_membership_from_proper_subset |
77 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.nat_within_int |
78 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat2 |
*equality replacement requirements |