| step type | requirements | statement |
0 | instantiation | 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13* | , , , ⊢ |
| : , : , : , : , : , : |
1 | theorem | | ⊢ |
| proveit.numbers.addition.association |
2 | reference | 37 | ⊢ |
3 | reference | 82 | ⊢ |
4 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat4 |
5 | reference | 38 | ⊢ |
6 | instantiation | 64 | ⊢ |
| : , : |
7 | instantiation | 14 | ⊢ |
| : , : , : , : |
8 | reference | 52 | ⊢ |
9 | instantiation | 50, 15 | ⊢ |
| : |
10 | instantiation | 85, 77, 16 | ⊢ |
| : , : , : |
11 | instantiation | 85, 77, 17 | ⊢ |
| : , : , : |
12 | instantiation | 22, 66, 18 | ⊢ |
| : , : |
13 | instantiation | 46, 19, 20, 21* | ⊢ |
| : , : , : |
14 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.tuple_len_4_typical_eq |
15 | instantiation | 22, 51, 52 | ⊢ |
| : , : |
16 | instantiation | 85, 71, 23 | ⊢ |
| : , : , : |
17 | instantiation | 85, 71, 24 | ⊢ |
| : , : , : |
18 | instantiation | 85, 77, 25 | ⊢ |
| : , : , : |
19 | instantiation | 26, 27 | ⊢ |
| : , : , : |
20 | instantiation | 34, 28 | ⊢ |
| : , : |
21 | instantiation | 29, 84, 30, 79, 31*, 32*, 33* | ⊢ |
| : , : , : , : |
22 | theorem | | ⊢ |
| proveit.numbers.multiplication.mult_complex_closure_bin |
23 | assumption | | ⊢ |
24 | assumption | | ⊢ |
25 | assumption | | ⊢ |
26 | axiom | | ⊢ |
| proveit.logic.equality.substitution |
27 | instantiation | 34, 35 | ⊢ |
| : , : |
28 | instantiation | 36, 37, 82, 87, 38, 39, 75, 40, 52, 41* | ⊢ |
| : , : , : , : , : , : |
29 | theorem | | ⊢ |
| proveit.numbers.addition.rational_pair_addition |
30 | instantiation | 42, 84 | ⊢ |
| : |
31 | instantiation | 43, 75, 44 | ⊢ |
| : |
32 | instantiation | 45, 75, 66, 62 | ⊢ |
| : , : |
33 | instantiation | 46, 47, 48 | ⊢ |
| : , : , : |
34 | theorem | | ⊢ |
| proveit.logic.equality.equals_reversal |
35 | instantiation | 49, 51, 52 | ⊢ |
| : , : |
36 | theorem | | ⊢ |
| proveit.numbers.multiplication.distribute_through_sum |
37 | axiom | | ⊢ |
| proveit.numbers.number_sets.natural_numbers.zero_in_nats |
38 | theorem | | ⊢ |
| proveit.core_expr_types.tuples.tuple_len_0_typical_eq |
39 | instantiation | 64 | ⊢ |
| : , : |
40 | instantiation | 50, 51 | ⊢ |
| : |
41 | instantiation | 65, 52 | ⊢ |
| : |
42 | theorem | | ⊢ |
| proveit.numbers.negation.int_closure |
43 | theorem | | ⊢ |
| proveit.numbers.division.frac_cancel_complete |
44 | instantiation | 69, 53 | ⊢ |
| : |
45 | theorem | | ⊢ |
| proveit.numbers.division.neg_frac_neg_numerator |
46 | axiom | | ⊢ |
| proveit.logic.equality.equals_transitivity |
47 | instantiation | 54, 82, 55, 56, 57, 58 | ⊢ |
| : , : , : , : |
48 | instantiation | 59, 75, 66, 60 | ⊢ |
| : , : , : |
49 | theorem | | ⊢ |
| proveit.numbers.negation.neg_times_pos |
50 | theorem | | ⊢ |
| proveit.numbers.negation.complex_closure |
51 | instantiation | 61, 75, 66, 62 | ⊢ |
| : , : |
52 | instantiation | 85, 77, 63 | ⊢ |
| : , : , : |
53 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.posnat1 |
54 | axiom | | ⊢ |
| proveit.core_expr_types.operations.operands_substitution |
55 | instantiation | 64 | ⊢ |
| : , : |
56 | instantiation | 64 | ⊢ |
| : , : |
57 | instantiation | 65, 66 | ⊢ |
| : |
58 | instantiation | 67, 75, 68* | ⊢ |
| : , : |
59 | theorem | | ⊢ |
| proveit.numbers.addition.subtraction.subtract_from_add |
60 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.add_1_1 |
61 | theorem | | ⊢ |
| proveit.numbers.division.div_complex_closure |
62 | instantiation | 69, 70 | ⊢ |
| : |
63 | instantiation | 85, 71, 72 | ⊢ |
| : , : , : |
64 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.tuple_len_2_typical_eq |
65 | theorem | | ⊢ |
| proveit.numbers.multiplication.elim_one_left |
66 | instantiation | 85, 77, 73 | ⊢ |
| : , : , : |
67 | theorem | | ⊢ |
| proveit.numbers.negation.pos_times_neg |
68 | instantiation | 74, 75 | ⊢ |
| : |
69 | theorem | | ⊢ |
| proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos |
70 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.posnat2 |
71 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.real_neg_within_real |
72 | assumption | | ⊢ |
73 | instantiation | 85, 80, 76 | ⊢ |
| : , : , : |
74 | theorem | | ⊢ |
| proveit.numbers.multiplication.elim_one_right |
75 | instantiation | 85, 77, 78 | ⊢ |
| : , : , : |
76 | instantiation | 85, 83, 79 | ⊢ |
| : , : , : |
77 | theorem | | ⊢ |
| proveit.numbers.number_sets.complex_numbers.real_within_complex |
78 | instantiation | 85, 80, 81 | ⊢ |
| : , : , : |
79 | instantiation | 85, 86, 82 | ⊢ |
| : , : , : |
80 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.rational_within_real |
81 | instantiation | 85, 83, 84 | ⊢ |
| : , : , : |
82 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat2 |
83 | theorem | | ⊢ |
| proveit.numbers.number_sets.rational_numbers.int_within_rational |
84 | instantiation | 85, 86, 87 | ⊢ |
| : , : , : |
85 | theorem | | ⊢ |
| proveit.logic.sets.inclusion.superset_membership_from_proper_subset |
86 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.nat_within_int |
87 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat1 |
*equality replacement requirements |