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