| step type | requirements | statement |
0 | instantiation | 1, 2, 3, 4 | ⊢ |
| : , : , : , : |
1 | reference | 56 | ⊢ |
2 | instantiation | 5, 6, 7, 8, 9, 10, 11, 12* | ⊢ |
| : , : , : , : |
3 | reference | 53 | ⊢ |
4 | instantiation | 36, 13 | ⊢ |
| : , : |
5 | theorem | | ⊢ |
| proveit.core_expr_types.tuples.general_len |
6 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.posnat2 |
7 | instantiation | 79 | ⊢ |
| : , : |
8 | instantiation | 79 | ⊢ |
| : , : |
9 | instantiation | 79 | ⊢ |
| : , : |
10 | instantiation | 14, 108, 29 | ⊢ |
| : , : , : |
11 | instantiation | 80, 15, 16 | ⊢ |
| : , : , : |
12 | instantiation | 48, 17, 18 | ⊢ |
| : , : , : |
13 | instantiation | 19, 20 | ⊢ |
| : , : |
14 | theorem | | ⊢ |
| proveit.logic.equality.sub_left_side_into |
15 | instantiation | 21, 22 | ⊢ |
| : |
16 | instantiation | 56, 23, 24, 25 | ⊢ |
| : , : , : , : |
17 | instantiation | 26, 113, 27, 28, 29, 37 | ⊢ |
| : , : , : , : |
18 | instantiation | 48, 30, 31 | ⊢ |
| : , : , : |
19 | theorem | | ⊢ |
| proveit.core_expr_types.tuples.range_from1_len |
20 | instantiation | 111, 32, 104 | ⊢ |
| : , : , : |
21 | theorem | | ⊢ |
| proveit.numbers.negation.nat_closure |
22 | instantiation | 33, 34, 35 | ⊢ |
| : |
23 | instantiation | 61, 62, 88, 63* | ⊢ |
| : , : |
24 | instantiation | 60 | ⊢ |
| : |
25 | instantiation | 36, 37 | ⊢ |
| : , : |
26 | axiom | | ⊢ |
| proveit.core_expr_types.operations.operands_substitution |
27 | instantiation | 79 | ⊢ |
| : , : |
28 | instantiation | 79 | ⊢ |
| : , : |
29 | instantiation | 38, 88, 42 | ⊢ |
| : , : , : |
30 | instantiation | 64, 108, 113, 71, 39, 73, 88, 77, 40 | ⊢ |
| : , : , : , : , : , : |
31 | instantiation | 41, 88, 77, 42 | ⊢ |
| : , : , : |
32 | theorem | | ⊢ |
| proveit.numbers.number_sets.natural_numbers.nat_pos_within_nat |
33 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.nonpos_int_is_int_nonpos |
34 | instantiation | 43, 90, 105 | ⊢ |
| : , : |
35 | instantiation | 44, 75, 93, 84, 45, 46*, 47* | ⊢ |
| : , : , : |
36 | theorem | | ⊢ |
| proveit.logic.equality.equals_reversal |
37 | instantiation | 48, 49, 50 | ⊢ |
| : , : , : |
38 | theorem | | ⊢ |
| proveit.numbers.addition.subtraction.add_cancel_triple_12 |
39 | instantiation | 79 | ⊢ |
| : , : |
40 | instantiation | 94, 88 | ⊢ |
| : |
41 | theorem | | ⊢ |
| proveit.numbers.addition.subtraction.add_cancel_triple_13 |
42 | instantiation | 60 | ⊢ |
| : |
43 | theorem | | ⊢ |
| proveit.numbers.addition.add_int_closure_bin |
44 | theorem | | ⊢ |
| proveit.numbers.addition.weak_bound_via_left_term_bound |
45 | instantiation | 51, 104 | ⊢ |
| : |
46 | instantiation | 87, 88, 62 | ⊢ |
| : , : |
47 | instantiation | 52, 77, 53 | ⊢ |
| : , : |
48 | axiom | | ⊢ |
| proveit.logic.equality.equals_transitivity |
49 | instantiation | 54, 55 | ⊢ |
| : , : , : |
50 | instantiation | 56, 57, 58, 59 | ⊢ |
| : , : , : , : |
51 | theorem | | ⊢ |
| proveit.numbers.number_sets.natural_numbers.natural_pos_lower_bound |
52 | theorem | | ⊢ |
| proveit.numbers.addition.subtraction.add_cancel_basic |
53 | instantiation | 60 | ⊢ |
| : |
54 | axiom | | ⊢ |
| proveit.logic.equality.substitution |
55 | instantiation | 61, 62, 95, 63* | ⊢ |
| : , : |
56 | theorem | | ⊢ |
| proveit.logic.equality.four_chain_transitivity |
57 | instantiation | 64, 108, 113, 65, 66, 77, 89, 88 | ⊢ |
| : , : , : , : , : , : |
58 | instantiation | 67, 71, 68, 73, 69, 77, 89, 88 | ⊢ |
| : , : , : , : |
59 | instantiation | 70, 108, 113, 71, 72, 73, 77, 89, 88, 74* | ⊢ |
| : , : , : , : , : , : |
60 | axiom | | ⊢ |
| proveit.logic.equality.equals_reflexivity |
61 | theorem | | ⊢ |
| proveit.numbers.negation.distribute_neg_through_binary_sum |
62 | instantiation | 111, 101, 75 | ⊢ |
| : , : , : |
63 | instantiation | 76, 77 | ⊢ |
| : |
64 | theorem | | ⊢ |
| proveit.numbers.addition.disassociation |
65 | instantiation | 79 | ⊢ |
| : , : |
66 | theorem | | ⊢ |
| proveit.numbers.number_sets.complex_numbers.zero_is_complex |
67 | theorem | | ⊢ |
| proveit.numbers.addition.elim_zero_any |
68 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat3 |
69 | instantiation | 78 | ⊢ |
| : , : , : |
70 | theorem | | ⊢ |
| proveit.numbers.addition.association |
71 | axiom | | ⊢ |
| proveit.numbers.number_sets.natural_numbers.zero_in_nats |
72 | instantiation | 79 | ⊢ |
| : , : |
73 | theorem | | ⊢ |
| proveit.core_expr_types.tuples.tuple_len_0_typical_eq |
74 | instantiation | 80, 81, 82 | ⊢ |
| : , : , : |
75 | instantiation | 111, 106, 83 | ⊢ |
| : , : , : |
76 | theorem | | ⊢ |
| proveit.numbers.negation.double_negation |
77 | instantiation | 111, 101, 84 | ⊢ |
| : , : , : |
78 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.tuple_len_3_typical_eq |
79 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.tuple_len_2_typical_eq |
80 | theorem | | ⊢ |
| proveit.logic.equality.sub_right_side_into |
81 | instantiation | 85, 88, 95, 86 | ⊢ |
| : , : , : |
82 | instantiation | 87, 88, 89 | ⊢ |
| : , : |
83 | instantiation | 111, 109, 90 | ⊢ |
| : , : , : |
84 | instantiation | 91, 92, 104 | ⊢ |
| : , : , : |
85 | theorem | | ⊢ |
| proveit.numbers.addition.subtraction.subtract_from_add_reversed |
86 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.add_1_1 |
87 | theorem | | ⊢ |
| proveit.numbers.addition.commutation |
88 | instantiation | 111, 101, 93 | ⊢ |
| : , : , : |
89 | instantiation | 94, 95 | ⊢ |
| : |
90 | instantiation | 96, 97 | ⊢ |
| : |
91 | theorem | | ⊢ |
| proveit.logic.sets.inclusion.unfold_subset_eq |
92 | instantiation | 98, 99 | ⊢ |
| : , : |
93 | instantiation | 111, 106, 100 | ⊢ |
| : , : , : |
94 | theorem | | ⊢ |
| proveit.numbers.negation.complex_closure |
95 | instantiation | 111, 101, 102 | ⊢ |
| : , : , : |
96 | theorem | | ⊢ |
| proveit.numbers.negation.int_closure |
97 | instantiation | 111, 103, 104 | ⊢ |
| : , : , : |
98 | theorem | | ⊢ |
| proveit.logic.sets.inclusion.relax_proper_subset |
99 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.nat_pos_within_real |
100 | instantiation | 111, 109, 105 | ⊢ |
| : , : , : |
101 | theorem | | ⊢ |
| proveit.numbers.number_sets.complex_numbers.real_within_complex |
102 | instantiation | 111, 106, 107 | ⊢ |
| : , : , : |
103 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.nat_pos_within_int |
104 | assumption | | ⊢ |
105 | instantiation | 111, 112, 108 | ⊢ |
| : , : , : |
106 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.rational_within_real |
107 | instantiation | 111, 109, 110 | ⊢ |
| : , : , : |
108 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat1 |
109 | theorem | | ⊢ |
| proveit.numbers.number_sets.rational_numbers.int_within_rational |
110 | instantiation | 111, 112, 113 | ⊢ |
| : , : , : |
111 | theorem | | ⊢ |
| proveit.logic.sets.inclusion.superset_membership_from_proper_subset |
112 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.nat_within_int |
113 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat2 |
*equality replacement requirements |