| step type | requirements | statement |
0 | instantiation | 1, 2, 3 | , ⊢ |
| : , : , : |
1 | reference | 19 | ⊢ |
2 | instantiation | 19, 4, 5 | ⊢ |
| : , : , : |
3 | assumption | | ⊢ |
4 | instantiation | 6, 82, 7, 8, 9* | ⊢ |
| : , : , : , : |
5 | instantiation | 10, 85, 60, 59, 62, 61, 23, 65, 69 | ⊢ |
| : , : , : , : , : , : |
6 | axiom | | ⊢ |
| proveit.numbers.summation.sum_split_last |
7 | instantiation | 11, 53, 82 | ⊢ |
| : , : |
8 | instantiation | 12, 73, 13, 70, 14, 15* | ⊢ |
| : , : , : |
9 | instantiation | 54, 16, 17 | ⊢ |
| : , : , : |
10 | theorem | | ⊢ |
| proveit.numbers.addition.association |
11 | theorem | | ⊢ |
| proveit.numbers.addition.add_int_closure_bin |
12 | theorem | | ⊢ |
| proveit.numbers.addition.strong_bound_via_left_term_bound |
13 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.zero_is_real |
14 | instantiation | 18, 76 | ⊢ |
| : |
15 | instantiation | 19, 20, 21 | ⊢ |
| : , : , : |
16 | instantiation | 50, 22 | ⊢ |
| : , : , : |
17 | instantiation | 58, 85, 60, 59, 62, 61, 23, 65, 69 | ⊢ |
| : , : , : , : , : , : |
18 | theorem | | ⊢ |
| proveit.numbers.number_sets.natural_numbers.natural_pos_is_pos |
19 | theorem | | ⊢ |
| proveit.logic.equality.sub_right_side_into |
20 | instantiation | 24, 69 | ⊢ |
| : |
21 | instantiation | 25, 69, 26 | ⊢ |
| : , : |
22 | instantiation | 27, 28, 29, 30, 31, 32 | ⊢ |
| : , : , : |
23 | modus ponens | 33, 34 | ⊢ |
24 | theorem | | ⊢ |
| proveit.numbers.addition.elim_zero_right |
25 | theorem | | ⊢ |
| proveit.numbers.addition.commutation |
26 | theorem | | ⊢ |
| proveit.numbers.number_sets.complex_numbers.zero_is_complex |
27 | theorem | | ⊢ |
| proveit.core_expr_types.tuples.tuple_eq_via_elem_eq |
28 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.posnat2 |
29 | instantiation | 67 | ⊢ |
| : , : |
30 | instantiation | 67 | ⊢ |
| : , : |
31 | instantiation | 50, 35 | ⊢ |
| : , : , : |
32 | instantiation | 71 | ⊢ |
| : |
33 | instantiation | 36 | ⊢ |
| : , : , : |
34 | generalization | 37 | ⊢ |
35 | modus ponens | 38, 39 | ⊢ |
36 | theorem | | ⊢ |
| proveit.numbers.summation.summation_complex_closure |
37 | instantiation | 83, 72, 40 | , ⊢ |
| : , : , : |
38 | instantiation | 41, 42 | ⊢ |
| : , : , : , : , : , : |
39 | generalization | 43 | ⊢ |
40 | instantiation | 83, 77, 44 | , ⊢ |
| : , : , : |
41 | axiom | | ⊢ |
| proveit.core_expr_types.lambda_maps.lambda_substitution |
42 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.posnat1 |
43 | instantiation | 50, 45 | ⊢ |
| : , : , : |
44 | instantiation | 83, 81, 46 | , ⊢ |
| : , : , : |
45 | instantiation | 50, 47 | ⊢ |
| : , : , : |
46 | instantiation | 83, 48, 49 | , ⊢ |
| : , : , : |
47 | instantiation | 50, 51 | ⊢ |
| : , : , : |
48 | instantiation | 52, 82, 53 | ⊢ |
| : , : |
49 | assumption | | ⊢ |
50 | axiom | | ⊢ |
| proveit.logic.equality.substitution |
51 | instantiation | 54, 55, 56 | ⊢ |
| : , : , : |
52 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.int_interval_within_int |
53 | instantiation | 83, 57, 76 | ⊢ |
| : , : , : |
54 | axiom | | ⊢ |
| proveit.logic.equality.equals_transitivity |
55 | instantiation | 58, 59, 60, 85, 61, 62, 65, 69, 63 | ⊢ |
| : , : , : , : , : , : |
56 | instantiation | 64, 69, 65, 66 | ⊢ |
| : , : , : |
57 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.nat_pos_within_int |
58 | theorem | | ⊢ |
| proveit.numbers.addition.disassociation |
59 | axiom | | ⊢ |
| proveit.numbers.number_sets.natural_numbers.zero_in_nats |
60 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat2 |
61 | theorem | | ⊢ |
| proveit.core_expr_types.tuples.tuple_len_0_typical_eq |
62 | instantiation | 67 | ⊢ |
| : , : |
63 | instantiation | 68, 69 | ⊢ |
| : |
64 | theorem | | ⊢ |
| proveit.numbers.addition.subtraction.add_cancel_triple_23 |
65 | instantiation | 83, 72, 70 | ⊢ |
| : , : , : |
66 | instantiation | 71 | ⊢ |
| : |
67 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.tuple_len_2_typical_eq |
68 | theorem | | ⊢ |
| proveit.numbers.negation.complex_closure |
69 | instantiation | 83, 72, 73 | ⊢ |
| : , : , : |
70 | instantiation | 74, 75, 76 | ⊢ |
| : , : , : |
71 | axiom | | ⊢ |
| proveit.logic.equality.equals_reflexivity |
72 | theorem | | ⊢ |
| proveit.numbers.number_sets.complex_numbers.real_within_complex |
73 | instantiation | 83, 77, 78 | ⊢ |
| : , : , : |
74 | theorem | | ⊢ |
| proveit.logic.sets.inclusion.unfold_subset_eq |
75 | instantiation | 79, 80 | ⊢ |
| : , : |
76 | assumption | | ⊢ |
77 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.rational_within_real |
78 | instantiation | 83, 81, 82 | ⊢ |
| : , : , : |
79 | theorem | | ⊢ |
| proveit.logic.sets.inclusion.relax_proper_subset |
80 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.nat_pos_within_real |
81 | theorem | | ⊢ |
| proveit.numbers.number_sets.rational_numbers.int_within_rational |
82 | instantiation | 83, 84, 85 | ⊢ |
| : , : , : |
83 | theorem | | ⊢ |
| proveit.logic.sets.inclusion.superset_membership_from_proper_subset |
84 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.nat_within_int |
85 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat1 |
*equality replacement requirements |