| step type | requirements | statement |
0 | instantiation | 1, 2, 3 | , , , ⊢ |
| : , : , : |
1 | reference | 10 | ⊢ |
2 | instantiation | 4, 5, 6 | , , , ⊢ |
| : , : , : |
3 | instantiation | 7, 67, 97, 69, 74, 63, 33, 8*, 9* | , ⊢ |
| : , : , : , : , : , : |
4 | theorem | | ⊢ |
| proveit.logic.equality.sub_left_side_into |
5 | instantiation | 10, 11, 12 | , ⊢ |
| : , : , : |
6 | instantiation | 13, 14, 15, 33, 16*, 17* | , , ⊢ |
| : , : , : |
7 | theorem | | ⊢ |
| proveit.numbers.multiplication.distribute_through_subtract |
8 | instantiation | 18, 33 | , ⊢ |
| : |
9 | instantiation | 19, 63, 77, 38, 20*, 21* | , ⊢ |
| : , : , : |
10 | theorem | | ⊢ |
| proveit.logic.equality.sub_right_side_into |
11 | instantiation | 22, 23, 83, 24, 25* | ⊢ |
| : , : , : , : |
12 | assumption | | ⊢ |
13 | theorem | | ⊢ |
| proveit.numbers.division.frac_cancel_left |
14 | instantiation | 26, 31, 27 | , ⊢ |
| : |
15 | instantiation | 95, 28, 29 | ⊢ |
| : , : , : |
16 | instantiation | 30, 31 | ⊢ |
| : |
17 | instantiation | 32, 33 | , ⊢ |
| : |
18 | theorem | | ⊢ |
| proveit.numbers.multiplication.elim_one_left |
19 | theorem | | ⊢ |
| proveit.numbers.exponentiation.product_of_posnat_powers |
20 | instantiation | 34, 63 | ⊢ |
| : |
21 | instantiation | 49, 35, 36 | ⊢ |
| : , : , : |
22 | axiom | | ⊢ |
| proveit.numbers.summation.sum_split_last |
23 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.zero_is_int |
24 | instantiation | 37, 38 | ⊢ |
| : |
25 | instantiation | 49, 39, 40 | ⊢ |
| : , : , : |
26 | theorem | | ⊢ |
| proveit.numbers.number_sets.complex_numbers.nonzero_complex_is_complex_nonzero |
27 | instantiation | 41, 42 | ⊢ |
| : , : |
28 | theorem | | ⊢ |
| proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero |
29 | instantiation | 95, 43, 44 | ⊢ |
| : , : , : |
30 | theorem | | ⊢ |
| proveit.numbers.multiplication.elim_one_right |
31 | instantiation | 45, 74, 46 | ⊢ |
| : , : |
32 | theorem | | ⊢ |
| proveit.numbers.division.frac_one_denom |
33 | instantiation | 47, 63, 48 | , ⊢ |
| : , : |
34 | theorem | | ⊢ |
| proveit.numbers.exponentiation.complex_x_to_first_power_is_x |
35 | instantiation | 54, 97, 68, 67, 55, 69, 74, 71 | ⊢ |
| : , : , : , : , : , : |
36 | instantiation | 49, 50, 51 | ⊢ |
| : , : , : |
37 | theorem | | ⊢ |
| proveit.numbers.number_sets.natural_numbers.natural_pos_is_pos |
38 | instantiation | 52, 97, 67, 69, 94, 53 | ⊢ |
| : , : , : , : , : |
39 | instantiation | 54, 67, 68, 97, 69, 55, 71, 74, 56 | ⊢ |
| : , : , : , : , : , : |
40 | instantiation | 57, 74, 71, 58 | ⊢ |
| : , : , : |
41 | theorem | | ⊢ |
| proveit.numbers.addition.subtraction.nonzero_difference_if_different |
42 | instantiation | 59, 60 | ⊢ |
| : , : |
43 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero |
44 | instantiation | 95, 61, 62 | ⊢ |
| : , : , : |
45 | theorem | | ⊢ |
| proveit.numbers.addition.add_complex_closure_bin |
46 | instantiation | 73, 63 | ⊢ |
| : |
47 | theorem | | ⊢ |
| proveit.numbers.exponentiation.exp_complex_closure |
48 | instantiation | 95, 81, 64 | ⊢ |
| : , : , : |
49 | axiom | | ⊢ |
| proveit.logic.equality.equals_transitivity |
50 | instantiation | 65, 97, 67, 69, 74, 71 | ⊢ |
| : , : , : , : , : , : , : |
51 | instantiation | 66, 67, 68, 97, 69, 70, 74, 71, 72* | ⊢ |
| : , : , : , : , : , : |
52 | theorem | | ⊢ |
| proveit.numbers.addition.add_nat_pos_from_nonneg |
53 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.less_0_1 |
54 | theorem | | ⊢ |
| proveit.numbers.addition.disassociation |
55 | instantiation | 79 | ⊢ |
| : , : |
56 | instantiation | 73, 74 | ⊢ |
| : |
57 | theorem | | ⊢ |
| proveit.numbers.addition.subtraction.add_cancel_triple_23 |
58 | instantiation | 75 | ⊢ |
| : |
59 | theorem | | ⊢ |
| proveit.logic.equality.not_equals_symmetry |
60 | assumption | | ⊢ |
61 | theorem | | ⊢ |
| proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero |
62 | instantiation | 95, 76, 77 | ⊢ |
| : , : , : |
63 | assumption | | ⊢ |
64 | instantiation | 95, 86, 78 | ⊢ |
| : , : , : |
65 | theorem | | ⊢ |
| proveit.numbers.addition.leftward_commutation |
66 | theorem | | ⊢ |
| proveit.numbers.addition.association |
67 | axiom | | ⊢ |
| proveit.numbers.number_sets.natural_numbers.zero_in_nats |
68 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat2 |
69 | theorem | | ⊢ |
| proveit.core_expr_types.tuples.tuple_len_0_typical_eq |
70 | instantiation | 79 | ⊢ |
| : , : |
71 | instantiation | 95, 81, 80 | ⊢ |
| : , : , : |
72 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.add_1_1 |
73 | theorem | | ⊢ |
| proveit.numbers.negation.complex_closure |
74 | instantiation | 95, 81, 82 | ⊢ |
| : , : , : |
75 | axiom | | ⊢ |
| proveit.logic.equality.equals_reflexivity |
76 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int |
77 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.posnat1 |
78 | instantiation | 95, 92, 83 | ⊢ |
| : , : , : |
79 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.tuple_len_2_typical_eq |
80 | instantiation | 84, 85, 94 | ⊢ |
| : , : , : |
81 | theorem | | ⊢ |
| proveit.numbers.number_sets.complex_numbers.real_within_complex |
82 | instantiation | 95, 86, 87 | ⊢ |
| : , : , : |
83 | instantiation | 88, 89, 93 | ⊢ |
| : , : |
84 | theorem | | ⊢ |
| proveit.logic.sets.inclusion.unfold_subset_eq |
85 | instantiation | 90, 91 | ⊢ |
| : , : |
86 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.rational_within_real |
87 | instantiation | 95, 92, 93 | ⊢ |
| : , : , : |
88 | theorem | | ⊢ |
| proveit.numbers.addition.add_int_closure_bin |
89 | instantiation | 95, 96, 94 | ⊢ |
| : , : , : |
90 | theorem | | ⊢ |
| proveit.logic.sets.inclusion.relax_proper_subset |
91 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.nat_within_real |
92 | theorem | | ⊢ |
| proveit.numbers.number_sets.rational_numbers.int_within_rational |
93 | instantiation | 95, 96, 97 | ⊢ |
| : , : , : |
94 | assumption | | ⊢ |
95 | theorem | | ⊢ |
| proveit.logic.sets.inclusion.superset_membership_from_proper_subset |
96 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.nat_within_int |
97 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat1 |
*equality replacement requirements |