| step type | requirements | statement |
0 | instantiation | 1, 2, 3, 4 | ⊢ |
| : , : , : , : |
1 | reference | 22 | ⊢ |
2 | instantiation | 5, 6, 7 | ⊢ |
| : , : , : |
3 | reference | 61 | ⊢ |
4 | instantiation | 8, 9 | ⊢ |
| : , : |
5 | theorem | | ⊢ |
| proveit.logic.equality.sub_right_side_into |
6 | instantiation | 10, 11 | ⊢ |
| : , : , : |
7 | instantiation | 12, 13, 14 | ⊢ |
| : , : , : |
8 | theorem | | ⊢ |
| proveit.logic.equality.equals_reversal |
9 | instantiation | 15, 16 | ⊢ |
| : , : |
10 | theorem | | ⊢ |
| proveit.core_expr_types.tuples.range_len |
11 | instantiation | 17, 37, 18, 36, 19, 78 | ⊢ |
| : , : |
12 | axiom | | ⊢ |
| proveit.logic.equality.equals_transitivity |
13 | instantiation | 20, 21 | ⊢ |
| : , : , : |
14 | instantiation | 22, 23, 24, 25 | ⊢ |
| : , : , : , : |
15 | theorem | | ⊢ |
| proveit.core_expr_types.tuples.range_from1_len |
16 | instantiation | 81, 26, 83 | ⊢ |
| : , : , : |
17 | theorem | | ⊢ |
| proveit.numbers.addition.add_nat_closure |
18 | instantiation | 48 | ⊢ |
| : , : , : |
19 | instantiation | 27, 28 | ⊢ |
| : |
20 | axiom | | ⊢ |
| proveit.logic.equality.substitution |
21 | instantiation | 29, 58, 57, 30* | ⊢ |
| : , : |
22 | theorem | | ⊢ |
| proveit.logic.equality.four_chain_transitivity |
23 | instantiation | 31, 78, 32, 33, 34, 60, 40, 57 | ⊢ |
| : , : , : , : , : , : |
24 | instantiation | 35, 36, 37, 38, 39, 60, 40, 57 | ⊢ |
| : , : , : , : |
25 | instantiation | 41, 57, 60, 42 | ⊢ |
| : , : , : |
26 | theorem | | ⊢ |
| proveit.numbers.number_sets.natural_numbers.nat_pos_within_nat |
27 | theorem | | ⊢ |
| proveit.numbers.negation.nat_closure |
28 | instantiation | 43, 44, 45 | ⊢ |
| : |
29 | theorem | | ⊢ |
| proveit.numbers.negation.distribute_neg_through_binary_sum |
30 | instantiation | 46, 60 | ⊢ |
| : |
31 | theorem | | ⊢ |
| proveit.numbers.addition.disassociation |
32 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat2 |
33 | instantiation | 47 | ⊢ |
| : , : |
34 | theorem | | ⊢ |
| proveit.numbers.number_sets.complex_numbers.zero_is_complex |
35 | theorem | | ⊢ |
| proveit.numbers.addition.elim_zero_any |
36 | axiom | | ⊢ |
| proveit.numbers.number_sets.natural_numbers.zero_in_nats |
37 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat3 |
38 | theorem | | ⊢ |
| proveit.core_expr_types.tuples.tuple_len_0_typical_eq |
39 | instantiation | 48 | ⊢ |
| : , : , : |
40 | instantiation | 49, 57 | ⊢ |
| : |
41 | theorem | | ⊢ |
| proveit.numbers.addition.subtraction.add_cancel_triple_32 |
42 | instantiation | 66 | ⊢ |
| : |
43 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.nonpos_int_is_int_nonpos |
44 | instantiation | 50, 74, 72 | ⊢ |
| : , : |
45 | instantiation | 51, 63, 62, 65, 52, 53*, 54* | ⊢ |
| : , : , : |
46 | theorem | | ⊢ |
| proveit.numbers.negation.double_negation |
47 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.tuple_len_2_typical_eq |
48 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.tuple_len_3_typical_eq |
49 | theorem | | ⊢ |
| proveit.numbers.negation.complex_closure |
50 | theorem | | ⊢ |
| proveit.numbers.addition.add_int_closure_bin |
51 | theorem | | ⊢ |
| proveit.numbers.addition.weak_bound_via_left_term_bound |
52 | instantiation | 55, 83 | ⊢ |
| : |
53 | instantiation | 56, 57, 58 | ⊢ |
| : , : |
54 | instantiation | 59, 60, 61 | ⊢ |
| : , : |
55 | theorem | | ⊢ |
| proveit.numbers.number_sets.natural_numbers.natural_pos_lower_bound |
56 | theorem | | ⊢ |
| proveit.numbers.addition.commutation |
57 | instantiation | 81, 64, 62 | ⊢ |
| : , : , : |
58 | instantiation | 81, 64, 63 | ⊢ |
| : , : , : |
59 | theorem | | ⊢ |
| proveit.numbers.addition.subtraction.add_cancel_basic |
60 | instantiation | 81, 64, 65 | ⊢ |
| : , : , : |
61 | instantiation | 66 | ⊢ |
| : |
62 | instantiation | 81, 68, 67 | ⊢ |
| : , : , : |
63 | instantiation | 81, 68, 69 | ⊢ |
| : , : , : |
64 | theorem | | ⊢ |
| proveit.numbers.number_sets.complex_numbers.real_within_complex |
65 | instantiation | 70, 71, 83 | ⊢ |
| : , : , : |
66 | axiom | | ⊢ |
| proveit.logic.equality.equals_reflexivity |
67 | instantiation | 81, 73, 72 | ⊢ |
| : , : , : |
68 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.rational_within_real |
69 | instantiation | 81, 73, 74 | ⊢ |
| : , : , : |
70 | theorem | | ⊢ |
| proveit.logic.sets.inclusion.unfold_subset_eq |
71 | instantiation | 75, 76 | ⊢ |
| : , : |
72 | instantiation | 81, 77, 78 | ⊢ |
| : , : , : |
73 | theorem | | ⊢ |
| proveit.numbers.number_sets.rational_numbers.int_within_rational |
74 | instantiation | 79, 80 | ⊢ |
| : |
75 | theorem | | ⊢ |
| proveit.logic.sets.inclusion.relax_proper_subset |
76 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.nat_pos_within_real |
77 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.nat_within_int |
78 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat1 |
79 | theorem | | ⊢ |
| proveit.numbers.negation.int_closure |
80 | instantiation | 81, 82, 83 | ⊢ |
| : , : , : |
81 | theorem | | ⊢ |
| proveit.logic.sets.inclusion.superset_membership_from_proper_subset |
82 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.nat_pos_within_int |
83 | assumption | | ⊢ |
*equality replacement requirements |