| step type | requirements | statement |
0 | instantiation | 1, 2 | ⊢ |
| : , : , : |
1 | reference | 73 | ⊢ |
2 | instantiation | 3, 35, 4, 5, 6 | ⊢ |
| : , : , : , : |
3 | theorem | | ⊢ |
| proveit.core_expr_types.operations.operands_substitution_via_tuple |
4 | instantiation | 75, 7, 100, 9 | ⊢ |
| : , : , : , : |
5 | instantiation | 75, 8, 100, 9 | ⊢ |
| : , : , : , : |
6 | instantiation | 10, 11, 12 | ⊢ |
| : , : , : , : |
7 | instantiation | 13, 14, 15, 16, 17, 18, 19, 20* | ⊢ |
| : , : , : , : |
8 | instantiation | 105, 21, 22 | ⊢ |
| : , : , : |
9 | instantiation | 56, 23 | ⊢ |
| : , : |
10 | theorem | | ⊢ |
| proveit.core_expr_types.tuples.merge_front |
11 | instantiation | 24, 93, 48 | ⊢ |
| : , : |
12 | instantiation | 56, 25 | ⊢ |
| : , : |
13 | theorem | | ⊢ |
| proveit.core_expr_types.tuples.general_len |
14 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.posnat2 |
15 | instantiation | 104 | ⊢ |
| : , : |
16 | instantiation | 104 | ⊢ |
| : , : |
17 | instantiation | 104 | ⊢ |
| : , : |
18 | instantiation | 26, 135, 43 | ⊢ |
| : , : , : |
19 | instantiation | 105, 48, 27 | ⊢ |
| : , : , : |
20 | instantiation | 67, 28, 29 | ⊢ |
| : , : , : |
21 | instantiation | 30, 31 | ⊢ |
| : , : , : |
22 | instantiation | 67, 32, 33 | ⊢ |
| : , : , : |
23 | instantiation | 34, 35 | ⊢ |
| : , : |
24 | theorem | | ⊢ |
| proveit.numbers.addition.add_nat_closure_bin |
25 | instantiation | 67, 36, 37 | ⊢ |
| : , : , : |
26 | theorem | | ⊢ |
| proveit.logic.equality.sub_left_side_into |
27 | instantiation | 75, 49, 38, 39 | ⊢ |
| : , : , : , : |
28 | instantiation | 40, 140, 41, 42, 43, 57 | ⊢ |
| : , : , : , : |
29 | instantiation | 67, 44, 45 | ⊢ |
| : , : , : |
30 | theorem | | ⊢ |
| proveit.core_expr_types.tuples.range_len |
31 | instantiation | 46, 90, 47, 93, 48, 135 | ⊢ |
| : , : |
32 | instantiation | 73, 49 | ⊢ |
| : , : , : |
33 | instantiation | 75, 50, 51, 52 | ⊢ |
| : , : , : , : |
34 | theorem | | ⊢ |
| proveit.core_expr_types.tuples.range_from1_len |
35 | instantiation | 138, 53, 134 | ⊢ |
| : , : , : |
36 | instantiation | 86, 93, 140, 135, 95, 54, 98, 114 | ⊢ |
| : , : , : , : , : , : |
37 | instantiation | 92, 135, 140, 93, 55, 95, 98, 114, 112* | ⊢ |
| : , : , : , : , : , : |
38 | instantiation | 109 | ⊢ |
| : |
39 | instantiation | 56, 57 | ⊢ |
| : , : |
40 | axiom | | ⊢ |
| proveit.core_expr_types.operations.operands_substitution |
41 | instantiation | 104 | ⊢ |
| : , : |
42 | instantiation | 104 | ⊢ |
| : , : |
43 | instantiation | 58, 114, 66 | ⊢ |
| : , : , : |
44 | instantiation | 86, 135, 140, 93, 62, 95, 114, 102, 64 | ⊢ |
| : , : , : , : , : , : |
45 | instantiation | 59, 114, 102, 66 | ⊢ |
| : , : , : |
46 | theorem | | ⊢ |
| proveit.numbers.addition.add_nat_closure |
47 | instantiation | 103 | ⊢ |
| : , : , : |
48 | instantiation | 60, 61 | ⊢ |
| : |
49 | instantiation | 84, 98, 114, 85* | ⊢ |
| : , : |
50 | instantiation | 86, 135, 140, 62, 88, 102, 64, 114 | ⊢ |
| : , : , : , : , : , : |
51 | instantiation | 89, 93, 90, 95, 63, 102, 64, 114 | ⊢ |
| : , : , : , : |
52 | instantiation | 65, 114, 102, 66 | ⊢ |
| : , : , : |
53 | theorem | | ⊢ |
| proveit.numbers.number_sets.natural_numbers.nat_pos_within_nat |
54 | instantiation | 104 | ⊢ |
| : , : |
55 | instantiation | 104 | ⊢ |
| : , : |
56 | theorem | | ⊢ |
| proveit.logic.equality.equals_reversal |
57 | instantiation | 67, 68, 69 | ⊢ |
| : , : , : |
58 | theorem | | ⊢ |
| proveit.numbers.addition.subtraction.add_cancel_triple_12 |
59 | theorem | | ⊢ |
| proveit.numbers.addition.subtraction.add_cancel_triple_13 |
60 | theorem | | ⊢ |
| proveit.numbers.negation.nat_closure |
61 | instantiation | 70, 71, 72 | ⊢ |
| : |
62 | instantiation | 104 | ⊢ |
| : , : |
63 | instantiation | 103 | ⊢ |
| : , : , : |
64 | instantiation | 120, 114 | ⊢ |
| : |
65 | theorem | | ⊢ |
| proveit.numbers.addition.subtraction.add_cancel_triple_32 |
66 | instantiation | 109 | ⊢ |
| : |
67 | axiom | | ⊢ |
| proveit.logic.equality.equals_transitivity |
68 | instantiation | 73, 74 | ⊢ |
| : , : , : |
69 | instantiation | 75, 76, 77, 78 | ⊢ |
| : , : , : , : |
70 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.nonpos_int_is_int_nonpos |
71 | instantiation | 79, 122, 130 | ⊢ |
| : , : |
72 | instantiation | 80, 108, 119, 110, 81, 82*, 83* | ⊢ |
| : , : , : |
73 | axiom | | ⊢ |
| proveit.logic.equality.substitution |
74 | instantiation | 84, 98, 121, 85* | ⊢ |
| : , : |
75 | theorem | | ⊢ |
| proveit.logic.equality.four_chain_transitivity |
76 | instantiation | 86, 135, 140, 87, 88, 102, 115, 114 | ⊢ |
| : , : , : , : , : , : |
77 | instantiation | 89, 93, 90, 95, 91, 102, 115, 114 | ⊢ |
| : , : , : , : |
78 | instantiation | 92, 135, 140, 93, 94, 95, 102, 115, 114, 96* | ⊢ |
| : , : , : , : , : , : |
79 | theorem | | ⊢ |
| proveit.numbers.addition.add_int_closure_bin |
80 | theorem | | ⊢ |
| proveit.numbers.addition.weak_bound_via_left_term_bound |
81 | instantiation | 97, 134 | ⊢ |
| : |
82 | instantiation | 113, 114, 98 | ⊢ |
| : , : |
83 | instantiation | 99, 102, 100 | ⊢ |
| : , : |
84 | theorem | | ⊢ |
| proveit.numbers.negation.distribute_neg_through_binary_sum |
85 | instantiation | 101, 102 | ⊢ |
| : |
86 | theorem | | ⊢ |
| proveit.numbers.addition.disassociation |
87 | instantiation | 104 | ⊢ |
| : , : |
88 | theorem | | ⊢ |
| proveit.numbers.number_sets.complex_numbers.zero_is_complex |
89 | theorem | | ⊢ |
| proveit.numbers.addition.elim_zero_any |
90 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat3 |
91 | instantiation | 103 | ⊢ |
| : , : , : |
92 | theorem | | ⊢ |
| proveit.numbers.addition.association |
93 | axiom | | ⊢ |
| proveit.numbers.number_sets.natural_numbers.zero_in_nats |
94 | instantiation | 104 | ⊢ |
| : , : |
95 | theorem | | ⊢ |
| proveit.core_expr_types.tuples.tuple_len_0_typical_eq |
96 | instantiation | 105, 106, 107 | ⊢ |
| : , : , : |
97 | theorem | | ⊢ |
| proveit.numbers.number_sets.natural_numbers.natural_pos_lower_bound |
98 | instantiation | 138, 126, 108 | ⊢ |
| : , : , : |
99 | theorem | | ⊢ |
| proveit.numbers.addition.subtraction.add_cancel_basic |
100 | instantiation | 109 | ⊢ |
| : |
101 | theorem | | ⊢ |
| proveit.numbers.negation.double_negation |
102 | instantiation | 138, 126, 110 | ⊢ |
| : , : , : |
103 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.tuple_len_3_typical_eq |
104 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.tuple_len_2_typical_eq |
105 | theorem | | ⊢ |
| proveit.logic.equality.sub_right_side_into |
106 | instantiation | 111, 114, 121, 112 | ⊢ |
| : , : , : |
107 | instantiation | 113, 114, 115 | ⊢ |
| : , : |
108 | instantiation | 138, 131, 116 | ⊢ |
| : , : , : |
109 | axiom | | ⊢ |
| proveit.logic.equality.equals_reflexivity |
110 | instantiation | 117, 118, 134 | ⊢ |
| : , : , : |
111 | theorem | | ⊢ |
| proveit.numbers.addition.subtraction.subtract_from_add_reversed |
112 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.add_1_1 |
113 | theorem | | ⊢ |
| proveit.numbers.addition.commutation |
114 | instantiation | 138, 126, 119 | ⊢ |
| : , : , : |
115 | instantiation | 120, 121 | ⊢ |
| : |
116 | instantiation | 138, 136, 122 | ⊢ |
| : , : , : |
117 | theorem | | ⊢ |
| proveit.logic.sets.inclusion.unfold_subset_eq |
118 | instantiation | 123, 124 | ⊢ |
| : , : |
119 | instantiation | 138, 131, 125 | ⊢ |
| : , : , : |
120 | theorem | | ⊢ |
| proveit.numbers.negation.complex_closure |
121 | instantiation | 138, 126, 127 | ⊢ |
| : , : , : |
122 | instantiation | 128, 129 | ⊢ |
| : |
123 | theorem | | ⊢ |
| proveit.logic.sets.inclusion.relax_proper_subset |
124 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.nat_pos_within_real |
125 | instantiation | 138, 136, 130 | ⊢ |
| : , : , : |
126 | theorem | | ⊢ |
| proveit.numbers.number_sets.complex_numbers.real_within_complex |
127 | instantiation | 138, 131, 132 | ⊢ |
| : , : , : |
128 | theorem | | ⊢ |
| proveit.numbers.negation.int_closure |
129 | instantiation | 138, 133, 134 | ⊢ |
| : , : , : |
130 | instantiation | 138, 139, 135 | ⊢ |
| : , : , : |
131 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.rational_within_real |
132 | instantiation | 138, 136, 137 | ⊢ |
| : , : , : |
133 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.nat_pos_within_int |
134 | assumption | | ⊢ |
135 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat1 |
136 | theorem | | ⊢ |
| proveit.numbers.number_sets.rational_numbers.int_within_rational |
137 | instantiation | 138, 139, 140 | ⊢ |
| : , : , : |
138 | theorem | | ⊢ |
| proveit.logic.sets.inclusion.superset_membership_from_proper_subset |
139 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.nat_within_int |
140 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat2 |
*equality replacement requirements |