| step type | requirements | statement |
0 | instantiation | 1, 2, 3, 4, 5, 6, 7, 8*, 9* | ⊢ |
| : , : , : , : |
1 | theorem | | ⊢ |
| proveit.core_expr_types.tuples.general_len |
2 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.posnat2 |
3 | instantiation | 50 | ⊢ |
| : , : |
4 | instantiation | 50 | ⊢ |
| : , : |
5 | instantiation | 50 | ⊢ |
| : , : |
6 | instantiation | 10, 76, 11 | ⊢ |
| : , : , : |
7 | instantiation | 12, 38, 13, 37, 14, 76 | ⊢ |
| : , : |
8 | reference | 11 | ⊢ |
9 | instantiation | 15, 16, 17 | ⊢ |
| : , : , : |
10 | theorem | | ⊢ |
| proveit.logic.equality.sub_left_side_into |
11 | instantiation | 18, 55, 43 | ⊢ |
| : , : , : |
12 | theorem | | ⊢ |
| proveit.numbers.addition.add_nat_closure |
13 | instantiation | 51 | ⊢ |
| : , : , : |
14 | instantiation | 19, 20 | ⊢ |
| : |
15 | axiom | | ⊢ |
| proveit.logic.equality.equals_transitivity |
16 | instantiation | 21, 22 | ⊢ |
| : , : , : |
17 | instantiation | 23, 24, 25, 26 | ⊢ |
| : , : , : , : |
18 | theorem | | ⊢ |
| proveit.numbers.addition.subtraction.add_cancel_triple_12 |
19 | theorem | | ⊢ |
| proveit.numbers.negation.nat_closure |
20 | instantiation | 27, 28, 29 | ⊢ |
| : |
21 | axiom | | ⊢ |
| proveit.logic.equality.substitution |
22 | instantiation | 30, 56, 55, 31* | ⊢ |
| : , : |
23 | theorem | | ⊢ |
| proveit.logic.equality.four_chain_transitivity |
24 | instantiation | 32, 76, 33, 34, 35, 58, 41, 55 | ⊢ |
| : , : , : , : , : , : |
25 | instantiation | 36, 37, 38, 39, 40, 58, 41, 55 | ⊢ |
| : , : , : , : |
26 | instantiation | 42, 55, 58, 43 | ⊢ |
| : , : , : |
27 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.nonpos_int_is_int_nonpos |
28 | instantiation | 44, 72, 70 | ⊢ |
| : , : |
29 | instantiation | 45, 61, 60, 63, 46, 47*, 48* | ⊢ |
| : , : , : |
30 | theorem | | ⊢ |
| proveit.numbers.negation.distribute_neg_through_binary_sum |
31 | instantiation | 49, 58 | ⊢ |
| : |
32 | theorem | | ⊢ |
| proveit.numbers.addition.disassociation |
33 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat2 |
34 | instantiation | 50 | ⊢ |
| : , : |
35 | theorem | | ⊢ |
| proveit.numbers.number_sets.complex_numbers.zero_is_complex |
36 | theorem | | ⊢ |
| proveit.numbers.addition.elim_zero_any |
37 | axiom | | ⊢ |
| proveit.numbers.number_sets.natural_numbers.zero_in_nats |
38 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat3 |
39 | theorem | | ⊢ |
| proveit.core_expr_types.tuples.tuple_len_0_typical_eq |
40 | instantiation | 51 | ⊢ |
| : , : , : |
41 | instantiation | 52, 55 | ⊢ |
| : |
42 | theorem | | ⊢ |
| proveit.numbers.addition.subtraction.add_cancel_triple_32 |
43 | instantiation | 64 | ⊢ |
| : |
44 | theorem | | ⊢ |
| proveit.numbers.addition.add_int_closure_bin |
45 | theorem | | ⊢ |
| proveit.numbers.addition.weak_bound_via_left_term_bound |
46 | instantiation | 53, 81 | ⊢ |
| : |
47 | instantiation | 54, 55, 56 | ⊢ |
| : , : |
48 | instantiation | 57, 58, 59 | ⊢ |
| : , : |
49 | theorem | | ⊢ |
| proveit.numbers.negation.double_negation |
50 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.tuple_len_2_typical_eq |
51 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.tuple_len_3_typical_eq |
52 | theorem | | ⊢ |
| proveit.numbers.negation.complex_closure |
53 | theorem | | ⊢ |
| proveit.numbers.number_sets.natural_numbers.natural_pos_lower_bound |
54 | theorem | | ⊢ |
| proveit.numbers.addition.commutation |
55 | instantiation | 79, 62, 60 | ⊢ |
| : , : , : |
56 | instantiation | 79, 62, 61 | ⊢ |
| : , : , : |
57 | theorem | | ⊢ |
| proveit.numbers.addition.subtraction.add_cancel_basic |
58 | instantiation | 79, 62, 63 | ⊢ |
| : , : , : |
59 | instantiation | 64 | ⊢ |
| : |
60 | instantiation | 79, 66, 65 | ⊢ |
| : , : , : |
61 | instantiation | 79, 66, 67 | ⊢ |
| : , : , : |
62 | theorem | | ⊢ |
| proveit.numbers.number_sets.complex_numbers.real_within_complex |
63 | instantiation | 68, 69, 81 | ⊢ |
| : , : , : |
64 | axiom | | ⊢ |
| proveit.logic.equality.equals_reflexivity |
65 | instantiation | 79, 71, 70 | ⊢ |
| : , : , : |
66 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.rational_within_real |
67 | instantiation | 79, 71, 72 | ⊢ |
| : , : , : |
68 | theorem | | ⊢ |
| proveit.logic.sets.inclusion.unfold_subset_eq |
69 | instantiation | 73, 74 | ⊢ |
| : , : |
70 | instantiation | 79, 75, 76 | ⊢ |
| : , : , : |
71 | theorem | | ⊢ |
| proveit.numbers.number_sets.rational_numbers.int_within_rational |
72 | instantiation | 77, 78 | ⊢ |
| : |
73 | theorem | | ⊢ |
| proveit.logic.sets.inclusion.relax_proper_subset |
74 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.nat_pos_within_real |
75 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.nat_within_int |
76 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat1 |
77 | theorem | | ⊢ |
| proveit.numbers.negation.int_closure |
78 | instantiation | 79, 80, 81 | ⊢ |
| : , : , : |
79 | theorem | | ⊢ |
| proveit.logic.sets.inclusion.superset_membership_from_proper_subset |
80 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.nat_pos_within_int |
81 | assumption | | ⊢ |
*equality replacement requirements |