| step type | requirements | statement |
0 | instantiation | 1, 2, 3, 4 | ⊢ |
| : , : , : , : |
1 | reference | 59 | ⊢ |
2 | instantiation | 5, 6, 7, 8, 9, 10, 11, 12* | ⊢ |
| : , : , : , : |
3 | instantiation | 63 | ⊢ |
| : |
4 | instantiation | 37, 13 | ⊢ |
| : , : |
5 | theorem | | ⊢ |
| proveit.core_expr_types.tuples.general_len |
6 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.posnat3 |
7 | instantiation | 81 | ⊢ |
| : , : , : |
8 | instantiation | 81 | ⊢ |
| : , : , : |
9 | instantiation | 81 | ⊢ |
| : , : , : |
10 | instantiation | 14, 111, 29 | ⊢ |
| : , : , : |
11 | instantiation | 83, 15, 16 | ⊢ |
| : , : , : |
12 | instantiation | 51, 17, 18 | ⊢ |
| : , : , : |
13 | instantiation | 19, 20 | ⊢ |
| : , : |
14 | theorem | | ⊢ |
| proveit.logic.equality.sub_left_side_into |
15 | instantiation | 21, 22 | ⊢ |
| : |
16 | instantiation | 59, 23, 24, 25 | ⊢ |
| : , : , : , : |
17 | instantiation | 26, 71, 27, 28, 29, 38 | ⊢ |
| : , : , : , : |
18 | instantiation | 51, 30, 31 | ⊢ |
| : , : , : |
19 | theorem | | ⊢ |
| proveit.core_expr_types.tuples.range_from1_len |
20 | instantiation | 114, 32, 33 | ⊢ |
| : , : , : |
21 | theorem | | ⊢ |
| proveit.numbers.negation.nat_closure |
22 | instantiation | 34, 35, 36 | ⊢ |
| : |
23 | instantiation | 64, 65, 91, 66* | ⊢ |
| : , : |
24 | instantiation | 63 | ⊢ |
| : |
25 | instantiation | 37, 38 | ⊢ |
| : , : |
26 | axiom | | ⊢ |
| proveit.core_expr_types.operations.operands_substitution |
27 | instantiation | 81 | ⊢ |
| : , : , : |
28 | instantiation | 81 | ⊢ |
| : , : , : |
29 | instantiation | 39, 91, 43 | ⊢ |
| : , : , : |
30 | instantiation | 67, 111, 116, 40, 91, 80, 41 | ⊢ |
| : , : , : , : , : , : |
31 | instantiation | 42, 74, 111, 76, 91, 80, 43 | ⊢ |
| : , : , : , : , : , : , : , : |
32 | theorem | | ⊢ |
| proveit.numbers.number_sets.natural_numbers.nat_pos_within_nat |
33 | instantiation | 44, 107, 45 | ⊢ |
| : , : |
34 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.nonpos_int_is_int_nonpos |
35 | instantiation | 46, 93, 108 | ⊢ |
| : , : |
36 | instantiation | 47, 78, 96, 87, 48, 49*, 50* | ⊢ |
| : , : , : |
37 | theorem | | ⊢ |
| proveit.logic.equality.equals_reversal |
38 | instantiation | 51, 52, 53 | ⊢ |
| : , : , : |
39 | theorem | | ⊢ |
| proveit.numbers.addition.subtraction.add_cancel_triple_12 |
40 | instantiation | 82 | ⊢ |
| : , : |
41 | instantiation | 97, 91 | ⊢ |
| : |
42 | theorem | | ⊢ |
| proveit.numbers.addition.subtraction.add_cancel_general |
43 | instantiation | 63 | ⊢ |
| : |
44 | theorem | | ⊢ |
| proveit.numbers.addition.add_nat_pos_closure_bin |
45 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.posnat1 |
46 | theorem | | ⊢ |
| proveit.numbers.addition.add_int_closure_bin |
47 | theorem | | ⊢ |
| proveit.numbers.addition.weak_bound_via_left_term_bound |
48 | instantiation | 54, 107 | ⊢ |
| : |
49 | instantiation | 90, 91, 65 | ⊢ |
| : , : |
50 | instantiation | 55, 80, 56 | ⊢ |
| : , : |
51 | axiom | | ⊢ |
| proveit.logic.equality.equals_transitivity |
52 | instantiation | 57, 58 | ⊢ |
| : , : , : |
53 | instantiation | 59, 60, 61, 62 | ⊢ |
| : , : , : , : |
54 | theorem | | ⊢ |
| proveit.numbers.number_sets.natural_numbers.natural_pos_lower_bound |
55 | theorem | | ⊢ |
| proveit.numbers.addition.subtraction.add_cancel_basic |
56 | instantiation | 63 | ⊢ |
| : |
57 | axiom | | ⊢ |
| proveit.logic.equality.substitution |
58 | instantiation | 64, 65, 98, 66* | ⊢ |
| : , : |
59 | theorem | | ⊢ |
| proveit.logic.equality.four_chain_transitivity |
60 | instantiation | 67, 111, 116, 68, 69, 80, 92, 91 | ⊢ |
| : , : , : , : , : , : |
61 | instantiation | 70, 74, 71, 76, 72, 80, 92, 91 | ⊢ |
| : , : , : , : |
62 | instantiation | 73, 111, 116, 74, 75, 76, 80, 92, 91, 77* | ⊢ |
| : , : , : , : , : , : |
63 | axiom | | ⊢ |
| proveit.logic.equality.equals_reflexivity |
64 | theorem | | ⊢ |
| proveit.numbers.negation.distribute_neg_through_binary_sum |
65 | instantiation | 114, 104, 78 | ⊢ |
| : , : , : |
66 | instantiation | 79, 80 | ⊢ |
| : |
67 | theorem | | ⊢ |
| proveit.numbers.addition.disassociation |
68 | instantiation | 82 | ⊢ |
| : , : |
69 | theorem | | ⊢ |
| proveit.numbers.number_sets.complex_numbers.zero_is_complex |
70 | theorem | | ⊢ |
| proveit.numbers.addition.elim_zero_any |
71 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat3 |
72 | instantiation | 81 | ⊢ |
| : , : , : |
73 | theorem | | ⊢ |
| proveit.numbers.addition.association |
74 | axiom | | ⊢ |
| proveit.numbers.number_sets.natural_numbers.zero_in_nats |
75 | instantiation | 82 | ⊢ |
| : , : |
76 | theorem | | ⊢ |
| proveit.core_expr_types.tuples.tuple_len_0_typical_eq |
77 | instantiation | 83, 84, 85 | ⊢ |
| : , : , : |
78 | instantiation | 114, 109, 86 | ⊢ |
| : , : , : |
79 | theorem | | ⊢ |
| proveit.numbers.negation.double_negation |
80 | instantiation | 114, 104, 87 | ⊢ |
| : , : , : |
81 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.tuple_len_3_typical_eq |
82 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.tuple_len_2_typical_eq |
83 | theorem | | ⊢ |
| proveit.logic.equality.sub_right_side_into |
84 | instantiation | 88, 91, 98, 89 | ⊢ |
| : , : , : |
85 | instantiation | 90, 91, 92 | ⊢ |
| : , : |
86 | instantiation | 114, 112, 93 | ⊢ |
| : , : , : |
87 | instantiation | 94, 95, 107 | ⊢ |
| : , : , : |
88 | theorem | | ⊢ |
| proveit.numbers.addition.subtraction.subtract_from_add_reversed |
89 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.add_1_1 |
90 | theorem | | ⊢ |
| proveit.numbers.addition.commutation |
91 | instantiation | 114, 104, 96 | ⊢ |
| : , : , : |
92 | instantiation | 97, 98 | ⊢ |
| : |
93 | instantiation | 99, 100 | ⊢ |
| : |
94 | theorem | | ⊢ |
| proveit.logic.sets.inclusion.unfold_subset_eq |
95 | instantiation | 101, 102 | ⊢ |
| : , : |
96 | instantiation | 114, 109, 103 | ⊢ |
| : , : , : |
97 | theorem | | ⊢ |
| proveit.numbers.negation.complex_closure |
98 | instantiation | 114, 104, 105 | ⊢ |
| : , : , : |
99 | theorem | | ⊢ |
| proveit.numbers.negation.int_closure |
100 | instantiation | 114, 106, 107 | ⊢ |
| : , : , : |
101 | theorem | | ⊢ |
| proveit.logic.sets.inclusion.relax_proper_subset |
102 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.nat_pos_within_real |
103 | instantiation | 114, 112, 108 | ⊢ |
| : , : , : |
104 | theorem | | ⊢ |
| proveit.numbers.number_sets.complex_numbers.real_within_complex |
105 | instantiation | 114, 109, 110 | ⊢ |
| : , : , : |
106 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.nat_pos_within_int |
107 | assumption | | ⊢ |
108 | instantiation | 114, 115, 111 | ⊢ |
| : , : , : |
109 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.rational_within_real |
110 | instantiation | 114, 112, 113 | ⊢ |
| : , : , : |
111 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat1 |
112 | theorem | | ⊢ |
| proveit.numbers.number_sets.rational_numbers.int_within_rational |
113 | instantiation | 114, 115, 116 | ⊢ |
| : , : , : |
114 | theorem | | ⊢ |
| proveit.logic.sets.inclusion.superset_membership_from_proper_subset |
115 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.nat_within_int |
116 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat2 |
*equality replacement requirements |