| step type | requirements | statement |
0 | instantiation | 1, 2 | ⊢ |
| : , : |
1 | theorem | | ⊢ |
| proveit.logic.equality.equals_reversal |
2 | instantiation | 42, 3 | ⊢ |
| : , : , : |
3 | instantiation | 42, 4 | ⊢ |
| : , : , : |
4 | instantiation | 32, 5, 6 | ⊢ |
| : , : , : |
5 | instantiation | 32, 7, 8 | ⊢ |
| : , : , : |
6 | instantiation | 32, 9, 10 | ⊢ |
| : , : , : |
7 | instantiation | 42, 11 | ⊢ |
| : , : , : |
8 | instantiation | 42, 12 | ⊢ |
| : , : , : |
9 | instantiation | 13, 38, 94, 82, 40, 14, 21, 51, 15 | ⊢ |
| : , : , : , : , : , : |
10 | instantiation | 16, 21, 51, 17 | ⊢ |
| : , : , : |
11 | instantiation | 25, 36, 63, 26, 18* | ⊢ |
| : , : |
12 | instantiation | 42, 19 | ⊢ |
| : , : , : |
13 | theorem | | ⊢ |
| proveit.numbers.addition.disassociation |
14 | instantiation | 49 | ⊢ |
| : , : |
15 | instantiation | 20, 21 | ⊢ |
| : |
16 | theorem | | ⊢ |
| proveit.numbers.addition.subtraction.add_cancel_triple_13 |
17 | instantiation | 22 | ⊢ |
| : |
18 | instantiation | 32, 23, 24 | ⊢ |
| : , : , : |
19 | instantiation | 25, 47, 63, 26, 27* | ⊢ |
| : , : |
20 | theorem | | ⊢ |
| proveit.numbers.negation.complex_closure |
21 | instantiation | 92, 71, 28 | ⊢ |
| : , : , : |
22 | axiom | | ⊢ |
| proveit.logic.equality.equals_reflexivity |
23 | instantiation | 42, 43 | ⊢ |
| : , : , : |
24 | instantiation | 32, 29, 30 | ⊢ |
| : , : , : |
25 | theorem | | ⊢ |
| proveit.numbers.division.div_as_mult |
26 | instantiation | 31, 91 | ⊢ |
| : |
27 | instantiation | 32, 33, 34 | ⊢ |
| : , : , : |
28 | instantiation | 92, 80, 35 | ⊢ |
| : , : , : |
29 | instantiation | 44, 36, 51 | ⊢ |
| : , : |
30 | instantiation | 37, 82, 94, 38, 39, 40, 51, 47, 48, 41* | ⊢ |
| : , : , : , : , : , : |
31 | theorem | | ⊢ |
| proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos |
32 | axiom | | ⊢ |
| proveit.logic.equality.equals_transitivity |
33 | instantiation | 42, 43 | ⊢ |
| : , : , : |
34 | instantiation | 44, 47, 51 | ⊢ |
| : , : |
35 | instantiation | 92, 76, 45 | ⊢ |
| : , : , : |
36 | instantiation | 46, 47, 48 | ⊢ |
| : , : |
37 | theorem | | ⊢ |
| proveit.numbers.multiplication.distribute_through_sum |
38 | axiom | | ⊢ |
| proveit.numbers.number_sets.natural_numbers.zero_in_nats |
39 | instantiation | 49 | ⊢ |
| : , : |
40 | theorem | | ⊢ |
| proveit.core_expr_types.tuples.tuple_len_0_typical_eq |
41 | instantiation | 50, 51 | ⊢ |
| : |
42 | axiom | | ⊢ |
| proveit.logic.equality.substitution |
43 | instantiation | 52, 53, 89, 54* | ⊢ |
| : , : |
44 | theorem | | ⊢ |
| proveit.numbers.multiplication.commutation |
45 | instantiation | 55, 77, 56 | ⊢ |
| : , : |
46 | theorem | | ⊢ |
| proveit.numbers.addition.add_complex_closure_bin |
47 | instantiation | 92, 71, 57 | ⊢ |
| : , : , : |
48 | instantiation | 92, 71, 58 | ⊢ |
| : , : , : |
49 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.tuple_len_2_typical_eq |
50 | theorem | | ⊢ |
| proveit.numbers.multiplication.elim_one_right |
51 | instantiation | 92, 71, 59 | ⊢ |
| : , : , : |
52 | theorem | | ⊢ |
| proveit.numbers.exponentiation.neg_power_as_div |
53 | instantiation | 92, 60, 61 | ⊢ |
| : , : , : |
54 | instantiation | 62, 63 | ⊢ |
| : |
55 | theorem | | ⊢ |
| proveit.numbers.multiplication.mult_rational_pos_closure_bin |
56 | instantiation | 92, 90, 66 | ⊢ |
| : , : , : |
57 | instantiation | 64, 65, 66 | ⊢ |
| : , : , : |
58 | instantiation | 92, 80, 67 | ⊢ |
| : , : , : |
59 | instantiation | 92, 80, 68 | ⊢ |
| : , : , : |
60 | theorem | | ⊢ |
| proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero |
61 | instantiation | 92, 69, 70 | ⊢ |
| : , : , : |
62 | theorem | | ⊢ |
| proveit.numbers.exponentiation.complex_x_to_first_power_is_x |
63 | instantiation | 92, 71, 72 | ⊢ |
| : , : , : |
64 | theorem | | ⊢ |
| proveit.logic.sets.inclusion.unfold_subset_eq |
65 | instantiation | 73, 74 | ⊢ |
| : , : |
66 | assumption | | ⊢ |
67 | instantiation | 92, 87, 75 | ⊢ |
| : , : , : |
68 | instantiation | 92, 76, 77 | ⊢ |
| : , : , : |
69 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero |
70 | instantiation | 92, 78, 79 | ⊢ |
| : , : , : |
71 | theorem | | ⊢ |
| proveit.numbers.number_sets.complex_numbers.real_within_complex |
72 | instantiation | 92, 80, 81 | ⊢ |
| : , : , : |
73 | theorem | | ⊢ |
| proveit.logic.sets.inclusion.relax_proper_subset |
74 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.nat_pos_within_real |
75 | instantiation | 92, 93, 82 | ⊢ |
| : , : , : |
76 | theorem | | ⊢ |
| proveit.numbers.number_sets.rational_numbers.rational_pos_within_rational |
77 | instantiation | 83, 84, 85 | ⊢ |
| : , : |
78 | theorem | | ⊢ |
| proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero |
79 | instantiation | 92, 86, 91 | ⊢ |
| : , : , : |
80 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.rational_within_real |
81 | instantiation | 92, 87, 88 | ⊢ |
| : , : , : |
82 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat1 |
83 | theorem | | ⊢ |
| proveit.numbers.division.div_rational_pos_closure |
84 | instantiation | 92, 90, 89 | ⊢ |
| : , : , : |
85 | instantiation | 92, 90, 91 | ⊢ |
| : , : , : |
86 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int |
87 | theorem | | ⊢ |
| proveit.numbers.number_sets.rational_numbers.int_within_rational |
88 | instantiation | 92, 93, 94 | ⊢ |
| : , : , : |
89 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.posnat1 |
90 | theorem | | ⊢ |
| proveit.numbers.number_sets.rational_numbers.nat_pos_within_rational_pos |
91 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.posnat2 |
92 | theorem | | ⊢ |
| proveit.logic.sets.inclusion.superset_membership_from_proper_subset |
93 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.nat_within_int |
94 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat2 |
*equality replacement requirements |