| step type | requirements | statement |
0 | instantiation | 1, 2, 3, 4, 5, 6, 7, 8, 9, 10* | ⊢ |
| : , : , : , : |
1 | theorem | | ⊢ |
| proveit.core_expr_types.tuples.general_len |
2 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.posnat5 |
3 | instantiation | 29 | ⊢ |
| : , : , : , : , : |
4 | instantiation | 29 | ⊢ |
| : , : , : , : , : |
5 | instantiation | 29 | ⊢ |
| : , : , : , : , : |
6 | instantiation | 13, 11, 23 | ⊢ |
| : , : , : |
7 | instantiation | 13, 12, 60 | ⊢ |
| : , : , : |
8 | instantiation | 13, 12, 24 | ⊢ |
| : , : , : |
9 | instantiation | 13, 14, 25 | ⊢ |
| : , : , : |
10 | instantiation | 100, 15, 16 | ⊢ |
| : , : , : |
11 | instantiation | 128, 17, 127 | ⊢ |
| : , : , : |
12 | instantiation | 128, 17, 119 | ⊢ |
| : , : , : |
13 | theorem | | ⊢ |
| proveit.logic.equality.sub_left_side_into |
14 | instantiation | 128, 17, 18 | ⊢ |
| : , : , : |
15 | instantiation | 19, 20, 21, 22, 23, 60, 24, 25 | ⊢ |
| : , : , : , : |
16 | instantiation | 100, 26, 27 | ⊢ |
| : , : , : |
17 | theorem | | ⊢ |
| proveit.numbers.number_sets.natural_numbers.nat_pos_within_nat |
18 | instantiation | 28, 127, 119 | ⊢ |
| : , : |
19 | axiom | | ⊢ |
| proveit.core_expr_types.operations.operands_substitution |
20 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat5 |
21 | instantiation | 29 | ⊢ |
| : , : , : , : , : |
22 | instantiation | 29 | ⊢ |
| : , : , : , : , : |
23 | instantiation | 77, 92, 94, 78 | ⊢ |
| : , : , : |
24 | instantiation | 100, 30, 31 | ⊢ |
| : , : , : |
25 | instantiation | 100, 32, 33 | ⊢ |
| : , : , : |
26 | instantiation | 56, 34, 86, 85, 35, 57, 87, 94, 98 | ⊢ |
| : , : , : , : , : , : |
27 | instantiation | 40, 36, 37, 38 | ⊢ |
| : , : , : , : |
28 | theorem | | ⊢ |
| proveit.numbers.addition.add_nat_pos_closure_bin |
29 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.tuple_len_5_typical_eq |
30 | instantiation | 110, 39 | ⊢ |
| : , : , : |
31 | instantiation | 40, 41, 42, 43 | ⊢ |
| : , : , : , : |
32 | instantiation | 56, 85, 86, 87, 57, 74, 94, 98, 75, 92 | ⊢ |
| : , : , : , : , : , : |
33 | instantiation | 44, 86, 85, 57, 87, 94, 98, 92 | ⊢ |
| : , : , : , : , : , : , : , : |
34 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat4 |
35 | instantiation | 45 | ⊢ |
| : , : , : , : |
36 | instantiation | 100, 46, 47 | ⊢ |
| : , : , : |
37 | instantiation | 84, 85, 116, 87, 48, 50, 94, 98, 49* | ⊢ |
| : , : , : , : , : , : |
38 | instantiation | 84, 130, 116, 85, 50, 87, 51, 98, 52* | ⊢ |
| : , : , : , : , : , : |
39 | instantiation | 53, 94, 92 | ⊢ |
| : , : |
40 | theorem | | ⊢ |
| proveit.logic.equality.four_chain_transitivity |
41 | instantiation | 56, 85, 86, 87, 57, 54, 94, 98, 55, 92 | ⊢ |
| : , : , : , : , : , : |
42 | instantiation | 56, 86, 130, 57, 58, 94, 98, 72, 75, 92 | ⊢ |
| : , : , : , : , : , : |
43 | instantiation | 100, 59, 60 | ⊢ |
| : , : , : |
44 | theorem | | ⊢ |
| proveit.numbers.addition.subtraction.add_cancel_general_rev |
45 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.tuple_len_4_typical_eq |
46 | instantiation | 62, 130, 116, 61, 94, 98 | ⊢ |
| : , : , : , : , : , : , : |
47 | instantiation | 62, 86, 130, 63, 64, 94, 98 | ⊢ |
| : , : , : , : , : , : , : |
48 | instantiation | 96 | ⊢ |
| : , : , : |
49 | instantiation | 68, 65, 70* | ⊢ |
| : , : |
50 | instantiation | 96 | ⊢ |
| : , : , : |
51 | instantiation | 66, 67, 94 | ⊢ |
| : , : |
52 | instantiation | 68, 69, 70* | ⊢ |
| : , : |
53 | theorem | | ⊢ |
| proveit.numbers.negation.distribute_neg_through_binary_sum |
54 | instantiation | 99 | ⊢ |
| : , : |
55 | instantiation | 71, 72, 75 | ⊢ |
| : , : |
56 | theorem | | ⊢ |
| proveit.numbers.addition.disassociation |
57 | instantiation | 99 | ⊢ |
| : , : |
58 | instantiation | 99 | ⊢ |
| : , : |
59 | instantiation | 73, 85, 130, 86, 87, 74, 94, 98, 75, 92, 76 | ⊢ |
| : , : , : , : , : , : , : , : |
60 | instantiation | 77, 92, 98, 78 | ⊢ |
| : , : , : |
61 | instantiation | 96 | ⊢ |
| : , : , : |
62 | theorem | | ⊢ |
| proveit.numbers.addition.leftward_commutation |
63 | instantiation | 99 | ⊢ |
| : , : |
64 | instantiation | 99 | ⊢ |
| : , : |
65 | instantiation | 81, 85, 116, 130, 87, 82, 92, 94, 79* | ⊢ |
| : , : , : , : , : , : |
66 | theorem | | ⊢ |
| proveit.numbers.multiplication.mult_complex_closure_bin |
67 | instantiation | 128, 108, 80 | ⊢ |
| : , : , : |
68 | theorem | | ⊢ |
| proveit.logic.equality.equals_reversal |
69 | instantiation | 81, 85, 116, 130, 87, 82, 92, 98, 83* | ⊢ |
| : , : , : , : , : , : |
70 | instantiation | 84, 85, 86, 130, 87, 88, 92, 89* | ⊢ |
| : , : , : , : , : , : |
71 | theorem | | ⊢ |
| proveit.numbers.addition.add_complex_closure_bin |
72 | instantiation | 128, 108, 90 | ⊢ |
| : , : , : |
73 | theorem | | ⊢ |
| proveit.numbers.addition.subtraction.add_cancel_general |
74 | instantiation | 99 | ⊢ |
| : , : |
75 | instantiation | 91, 92 | ⊢ |
| : |
76 | instantiation | 93 | ⊢ |
| : |
77 | theorem | | ⊢ |
| proveit.numbers.addition.subtraction.add_cancel_triple_32 |
78 | instantiation | 93 | ⊢ |
| : |
79 | instantiation | 97, 94 | ⊢ |
| : |
80 | instantiation | 128, 114, 95 | ⊢ |
| : , : , : |
81 | theorem | | ⊢ |
| proveit.numbers.multiplication.distribute_through_sum |
82 | instantiation | 96 | ⊢ |
| : , : , : |
83 | instantiation | 97, 98 | ⊢ |
| : |
84 | theorem | | ⊢ |
| proveit.numbers.addition.association |
85 | axiom | | ⊢ |
| proveit.numbers.number_sets.natural_numbers.zero_in_nats |
86 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat2 |
87 | theorem | | ⊢ |
| proveit.core_expr_types.tuples.tuple_len_0_typical_eq |
88 | instantiation | 99 | ⊢ |
| : , : |
89 | instantiation | 100, 101, 102 | ⊢ |
| : , : , : |
90 | instantiation | 128, 103, 104 | ⊢ |
| : , : , : |
91 | theorem | | ⊢ |
| proveit.numbers.negation.complex_closure |
92 | instantiation | 128, 108, 105 | ⊢ |
| : , : , : |
93 | axiom | | ⊢ |
| proveit.logic.equality.equals_reflexivity |
94 | instantiation | 128, 108, 106 | ⊢ |
| : , : , : |
95 | instantiation | 128, 122, 107 | ⊢ |
| : , : , : |
96 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.tuple_len_3_typical_eq |
97 | theorem | | ⊢ |
| proveit.numbers.multiplication.elim_one_left |
98 | instantiation | 128, 108, 109 | ⊢ |
| : , : , : |
99 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.tuple_len_2_typical_eq |
100 | axiom | | ⊢ |
| proveit.logic.equality.equals_transitivity |
101 | instantiation | 110, 111 | ⊢ |
| : , : , : |
102 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.add_2_1 |
103 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.real_neg_within_real |
104 | instantiation | 128, 112, 113 | ⊢ |
| : , : , : |
105 | instantiation | 128, 114, 115 | ⊢ |
| : , : , : |
106 | instantiation | 117, 118, 127 | ⊢ |
| : , : , : |
107 | instantiation | 128, 129, 116 | ⊢ |
| : , : , : |
108 | theorem | | ⊢ |
| proveit.numbers.number_sets.complex_numbers.real_within_complex |
109 | instantiation | 117, 118, 119 | ⊢ |
| : , : , : |
110 | axiom | | ⊢ |
| proveit.logic.equality.substitution |
111 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.add_1_1 |
112 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.rational_neg_within_real_neg |
113 | instantiation | 128, 120, 121 | ⊢ |
| : , : , : |
114 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.rational_within_real |
115 | instantiation | 128, 122, 123 | ⊢ |
| : , : , : |
116 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat3 |
117 | theorem | | ⊢ |
| proveit.logic.sets.inclusion.unfold_subset_eq |
118 | instantiation | 124, 125 | ⊢ |
| : , : |
119 | axiom | | ⊢ |
| proveit.physics.quantum.QPE._s_in_nat_pos |
120 | theorem | | ⊢ |
| proveit.numbers.number_sets.rational_numbers.neg_int_within_rational_neg |
121 | instantiation | 126, 127 | ⊢ |
| : |
122 | theorem | | ⊢ |
| proveit.numbers.number_sets.rational_numbers.int_within_rational |
123 | instantiation | 128, 129, 130 | ⊢ |
| : , : , : |
124 | theorem | | ⊢ |
| proveit.logic.sets.inclusion.relax_proper_subset |
125 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.nat_pos_within_real |
126 | theorem | | ⊢ |
| proveit.numbers.negation.int_neg_closure |
127 | axiom | | ⊢ |
| proveit.physics.quantum.QPE._t_in_natural_pos |
128 | theorem | | ⊢ |
| proveit.logic.sets.inclusion.superset_membership_from_proper_subset |
129 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.nat_within_int |
130 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat1 |
*equality replacement requirements |