| step type | requirements | statement |
0 | instantiation | 1, 2, 3, 4 | ⊢ |
| : , : , : , : |
1 | theorem | | ⊢ |
| proveit.logic.booleans.conjunction.conjunction_from_quantification |
2 | reference | 70 | ⊢ |
3 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.zero_is_int |
4 | instantiation | 5, 6, 45, 59, 7, 8*, 9* | ⊢ |
| : , : , : |
5 | theorem | | ⊢ |
| proveit.numbers.addition.weak_bound_via_left_term_bound |
6 | instantiation | 82, 68, 10 | ⊢ |
| : , : , : |
7 | instantiation | 11, 84 | ⊢ |
| : |
8 | instantiation | 15, 12, 13, 14 | ⊢ |
| : , : , : , : |
9 | instantiation | 15, 16, 17, 18 | ⊢ |
| : , : , : , : |
10 | instantiation | 82, 74, 19 | ⊢ |
| : , : , : |
11 | theorem | | ⊢ |
| proveit.numbers.number_sets.natural_numbers.natural_pos_lower_bound |
12 | instantiation | 40, 20, 21 | ⊢ |
| : , : , : |
13 | instantiation | 22, 44, 52, 53, 23 | ⊢ |
| : , : , : |
14 | instantiation | 62 | ⊢ |
| : |
15 | theorem | | ⊢ |
| proveit.logic.equality.four_chain_transitivity |
16 | instantiation | 40, 24, 25 | ⊢ |
| : , : , : |
17 | instantiation | 62 | ⊢ |
| : |
18 | instantiation | 26, 27 | ⊢ |
| : , : |
19 | instantiation | 75, 76, 64 | ⊢ |
| : , : |
20 | instantiation | 46, 71, 81, 47, 33, 49, 38, 50 | ⊢ |
| : , : , : , : , : , : |
21 | instantiation | 40, 28, 29 | ⊢ |
| : , : , : |
22 | theorem | | ⊢ |
| proveit.numbers.addition.subtraction.subtract_from_add |
23 | instantiation | 30, 31, 32 | ⊢ |
| : , : , : |
24 | instantiation | 46, 71, 81, 47, 33, 49, 52, 50, 38 | ⊢ |
| : , : , : , : , : , : |
25 | instantiation | 51, 52, 38, 54 | ⊢ |
| : , : , : |
26 | theorem | | ⊢ |
| proveit.logic.equality.equals_reversal |
27 | instantiation | 34, 38 | ⊢ |
| : |
28 | instantiation | 35, 71, 47, 49, 38, 50 | ⊢ |
| : , : , : , : , : , : , : |
29 | instantiation | 36, 47, 81, 71, 49, 37, 38, 50, 39* | ⊢ |
| : , : , : , : , : , : |
30 | theorem | | ⊢ |
| proveit.logic.equality.sub_right_side_into |
31 | instantiation | 40, 41, 42 | ⊢ |
| : , : , : |
32 | instantiation | 43, 52, 44 | ⊢ |
| : , : |
33 | instantiation | 57 | ⊢ |
| : , : |
34 | theorem | | ⊢ |
| proveit.numbers.addition.elim_zero_left |
35 | theorem | | ⊢ |
| proveit.numbers.addition.leftward_commutation |
36 | theorem | | ⊢ |
| proveit.numbers.addition.association |
37 | instantiation | 57 | ⊢ |
| : , : |
38 | instantiation | 82, 60, 45 | ⊢ |
| : , : , : |
39 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.add_1_1 |
40 | axiom | | ⊢ |
| proveit.logic.equality.equals_transitivity |
41 | instantiation | 46, 71, 81, 47, 48, 49, 52, 50, 53 | ⊢ |
| : , : , : , : , : , : |
42 | instantiation | 51, 52, 53, 54 | ⊢ |
| : , : , : |
43 | theorem | | ⊢ |
| proveit.numbers.addition.commutation |
44 | instantiation | 82, 60, 55 | ⊢ |
| : , : , : |
45 | instantiation | 82, 68, 56 | ⊢ |
| : , : , : |
46 | theorem | | ⊢ |
| proveit.numbers.addition.disassociation |
47 | axiom | | ⊢ |
| proveit.numbers.number_sets.natural_numbers.zero_in_nats |
48 | instantiation | 57 | ⊢ |
| : , : |
49 | theorem | | ⊢ |
| proveit.core_expr_types.tuples.tuple_len_0_typical_eq |
50 | instantiation | 82, 60, 58 | ⊢ |
| : , : , : |
51 | theorem | | ⊢ |
| proveit.numbers.addition.subtraction.add_cancel_triple_12 |
52 | instantiation | 82, 60, 59 | ⊢ |
| : , : , : |
53 | instantiation | 82, 60, 61 | ⊢ |
| : , : , : |
54 | instantiation | 62 | ⊢ |
| : |
55 | instantiation | 82, 68, 63 | ⊢ |
| : , : , : |
56 | instantiation | 82, 74, 64 | ⊢ |
| : , : , : |
57 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.tuple_len_2_typical_eq |
58 | instantiation | 82, 68, 65 | ⊢ |
| : , : , : |
59 | instantiation | 66, 67, 84 | ⊢ |
| : , : , : |
60 | theorem | | ⊢ |
| proveit.numbers.number_sets.complex_numbers.real_within_complex |
61 | instantiation | 82, 68, 69 | ⊢ |
| : , : , : |
62 | axiom | | ⊢ |
| proveit.logic.equality.equals_reflexivity |
63 | instantiation | 82, 74, 70 | ⊢ |
| : , : , : |
64 | instantiation | 82, 80, 71 | ⊢ |
| : , : , : |
65 | instantiation | 82, 74, 76 | ⊢ |
| : , : , : |
66 | theorem | | ⊢ |
| proveit.logic.sets.inclusion.unfold_subset_eq |
67 | instantiation | 72, 73 | ⊢ |
| : , : |
68 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.rational_within_real |
69 | instantiation | 82, 74, 77 | ⊢ |
| : , : , : |
70 | instantiation | 75, 76, 77 | ⊢ |
| : , : |
71 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat1 |
72 | theorem | | ⊢ |
| proveit.logic.sets.inclusion.relax_proper_subset |
73 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.nat_pos_within_real |
74 | theorem | | ⊢ |
| proveit.numbers.number_sets.rational_numbers.int_within_rational |
75 | theorem | | ⊢ |
| proveit.numbers.addition.add_int_closure_bin |
76 | instantiation | 78, 79 | ⊢ |
| : |
77 | instantiation | 82, 80, 81 | ⊢ |
| : , : , : |
78 | theorem | | ⊢ |
| proveit.numbers.negation.int_closure |
79 | instantiation | 82, 83, 84 | ⊢ |
| : , : , : |
80 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.nat_within_int |
81 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat2 |
82 | theorem | | ⊢ |
| proveit.logic.sets.inclusion.superset_membership_from_proper_subset |
83 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.nat_pos_within_int |
84 | assumption | | ⊢ |
*equality replacement requirements |