| step type | requirements | statement |
0 | instantiation | 1, 2, 3 | ⊢ |
| : , : , : |
1 | reference | 12 | ⊢ |
2 | instantiation | 4, 33, 5, 6, 7, 8 | ⊢ |
| : , : , : , : |
3 | instantiation | 12, 9, 10 | ⊢ |
| : , : , : |
4 | axiom | | ⊢ |
| proveit.core_expr_types.operations.operands_substitution |
5 | instantiation | 43 | ⊢ |
| : , : , : |
6 | instantiation | 43 | ⊢ |
| : , : , : |
7 | instantiation | 11, 53, 18 | ⊢ |
| : , : , : |
8 | instantiation | 12, 13, 14 | ⊢ |
| : , : , : |
9 | instantiation | 29, 73, 78, 15, 53, 42, 16 | ⊢ |
| : , : , : , : , : , : |
10 | instantiation | 17, 36, 73, 38, 53, 42, 18 | ⊢ |
| : , : , : , : , : , : , : , : |
11 | theorem | | ⊢ |
| proveit.numbers.addition.subtraction.add_cancel_triple_12 |
12 | axiom | | ⊢ |
| proveit.logic.equality.equals_transitivity |
13 | instantiation | 19, 20 | ⊢ |
| : , : , : |
14 | instantiation | 21, 22, 23, 24 | ⊢ |
| : , : , : , : |
15 | instantiation | 44 | ⊢ |
| : , : |
16 | instantiation | 59, 53 | ⊢ |
| : |
17 | theorem | | ⊢ |
| proveit.numbers.addition.subtraction.add_cancel_general |
18 | instantiation | 25 | ⊢ |
| : |
19 | axiom | | ⊢ |
| proveit.logic.equality.substitution |
20 | instantiation | 26, 27, 60, 28* | ⊢ |
| : , : |
21 | theorem | | ⊢ |
| proveit.logic.equality.four_chain_transitivity |
22 | instantiation | 29, 73, 78, 30, 31, 42, 54, 53 | ⊢ |
| : , : , : , : , : , : |
23 | instantiation | 32, 36, 33, 38, 34, 42, 54, 53 | ⊢ |
| : , : , : , : |
24 | instantiation | 35, 73, 78, 36, 37, 38, 42, 54, 53, 39* | ⊢ |
| : , : , : , : , : , : |
25 | axiom | | ⊢ |
| proveit.logic.equality.equals_reflexivity |
26 | theorem | | ⊢ |
| proveit.numbers.negation.distribute_neg_through_binary_sum |
27 | instantiation | 76, 66, 40 | ⊢ |
| : , : , : |
28 | instantiation | 41, 42 | ⊢ |
| : |
29 | theorem | | ⊢ |
| proveit.numbers.addition.disassociation |
30 | instantiation | 44 | ⊢ |
| : , : |
31 | theorem | | ⊢ |
| proveit.numbers.number_sets.complex_numbers.zero_is_complex |
32 | theorem | | ⊢ |
| proveit.numbers.addition.elim_zero_any |
33 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat3 |
34 | instantiation | 43 | ⊢ |
| : , : , : |
35 | theorem | | ⊢ |
| proveit.numbers.addition.association |
36 | axiom | | ⊢ |
| proveit.numbers.number_sets.natural_numbers.zero_in_nats |
37 | instantiation | 44 | ⊢ |
| : , : |
38 | theorem | | ⊢ |
| proveit.core_expr_types.tuples.tuple_len_0_typical_eq |
39 | instantiation | 45, 46, 47 | ⊢ |
| : , : , : |
40 | instantiation | 76, 71, 48 | ⊢ |
| : , : , : |
41 | theorem | | ⊢ |
| proveit.numbers.negation.double_negation |
42 | instantiation | 76, 66, 49 | ⊢ |
| : , : , : |
43 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.tuple_len_3_typical_eq |
44 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.tuple_len_2_typical_eq |
45 | theorem | | ⊢ |
| proveit.logic.equality.sub_right_side_into |
46 | instantiation | 50, 53, 60, 51 | ⊢ |
| : , : , : |
47 | instantiation | 52, 53, 54 | ⊢ |
| : , : |
48 | instantiation | 76, 74, 55 | ⊢ |
| : , : , : |
49 | instantiation | 56, 57, 69 | ⊢ |
| : , : , : |
50 | theorem | | ⊢ |
| proveit.numbers.addition.subtraction.subtract_from_add_reversed |
51 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.add_1_1 |
52 | theorem | | ⊢ |
| proveit.numbers.addition.commutation |
53 | instantiation | 76, 66, 58 | ⊢ |
| : , : , : |
54 | instantiation | 59, 60 | ⊢ |
| : |
55 | instantiation | 61, 62 | ⊢ |
| : |
56 | theorem | | ⊢ |
| proveit.logic.sets.inclusion.unfold_subset_eq |
57 | instantiation | 63, 64 | ⊢ |
| : , : |
58 | instantiation | 76, 71, 65 | ⊢ |
| : , : , : |
59 | theorem | | ⊢ |
| proveit.numbers.negation.complex_closure |
60 | instantiation | 76, 66, 67 | ⊢ |
| : , : , : |
61 | theorem | | ⊢ |
| proveit.numbers.negation.int_closure |
62 | instantiation | 76, 68, 69 | ⊢ |
| : , : , : |
63 | theorem | | ⊢ |
| proveit.logic.sets.inclusion.relax_proper_subset |
64 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.nat_pos_within_real |
65 | instantiation | 76, 74, 70 | ⊢ |
| : , : , : |
66 | theorem | | ⊢ |
| proveit.numbers.number_sets.complex_numbers.real_within_complex |
67 | instantiation | 76, 71, 72 | ⊢ |
| : , : , : |
68 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.nat_pos_within_int |
69 | assumption | | ⊢ |
70 | instantiation | 76, 77, 73 | ⊢ |
| : , : , : |
71 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.rational_within_real |
72 | instantiation | 76, 74, 75 | ⊢ |
| : , : , : |
73 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat1 |
74 | theorem | | ⊢ |
| proveit.numbers.number_sets.rational_numbers.int_within_rational |
75 | instantiation | 76, 77, 78 | ⊢ |
| : , : , : |
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 |