| step type | requirements | statement |
0 | instantiation | 1, 2, 3, 4, 5, 6, 7, 8, 9* | ⊢ |
| : , : , : , : |
1 | theorem | | ⊢ |
| proveit.core_expr_types.tuples.general_len |
2 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.posnat6 |
3 | instantiation | 25 | ⊢ |
| : , : , : , : , : , : |
4 | instantiation | 25 | ⊢ |
| : , : , : , : , : , : |
5 | instantiation | 25 | ⊢ |
| : , : , : , : , : , : |
6 | instantiation | 11, 10, 20 | ⊢ |
| : , : , : |
7 | instantiation | 11, 12, 57 | ⊢ |
| : , : , : |
8 | instantiation | 11, 12, 21 | ⊢ |
| : , : , : |
9 | instantiation | 83, 13, 14 | ⊢ |
| : , : , : |
10 | instantiation | 118, 15, 117 | ⊢ |
| : , : , : |
11 | theorem | | ⊢ |
| proveit.logic.equality.sub_left_side_into |
12 | instantiation | 118, 15, 105 | ⊢ |
| : , : , : |
13 | instantiation | 16, 17, 18, 19, 20, 57, 21 | ⊢ |
| : , : , : , : |
14 | instantiation | 36, 22, 23, 24 | ⊢ |
| : , : , : , : |
15 | theorem | | ⊢ |
| proveit.numbers.number_sets.natural_numbers.nat_pos_within_nat |
16 | axiom | | ⊢ |
| proveit.core_expr_types.operations.operands_substitution |
17 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat6 |
18 | instantiation | 25 | ⊢ |
| : , : , : , : , : , : |
19 | instantiation | 25 | ⊢ |
| : , : , : , : , : , : |
20 | instantiation | 75, 76, 78, 77 | ⊢ |
| : , : , : |
21 | instantiation | 83, 26, 27 | ⊢ |
| : , : , : |
22 | instantiation | 83, 28, 29 | ⊢ |
| : , : , : |
23 | instantiation | 63, 69, 102, 71, 30, 32, 78, 82, 31* | ⊢ |
| : , : , : , : , : , : |
24 | instantiation | 63, 120, 102, 69, 32, 71, 33, 82, 34* | ⊢ |
| : , : , : , : , : , : |
25 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.tuple_len_6_typical_eq |
26 | instantiation | 95, 35 | ⊢ |
| : , : , : |
27 | instantiation | 36, 37, 38, 39 | ⊢ |
| : , : , : , : |
28 | instantiation | 41, 120, 102, 40, 78, 82 | ⊢ |
| : , : , : , : , : , : , : |
29 | instantiation | 41, 70, 120, 42, 43, 78, 82 | ⊢ |
| : , : , : , : , : , : , : |
30 | instantiation | 80 | ⊢ |
| : , : , : |
31 | instantiation | 47, 44, 49* | ⊢ |
| : , : |
32 | instantiation | 80 | ⊢ |
| : , : , : |
33 | instantiation | 45, 46, 78 | ⊢ |
| : , : |
34 | instantiation | 47, 48, 49* | ⊢ |
| : , : |
35 | instantiation | 50, 78, 76 | ⊢ |
| : , : |
36 | theorem | | ⊢ |
| proveit.logic.equality.four_chain_transitivity |
37 | instantiation | 53, 69, 70, 71, 54, 51, 78, 82, 52, 76 | ⊢ |
| : , : , : , : , : , : |
38 | instantiation | 53, 70, 120, 54, 55, 78, 82, 67, 73, 76 | ⊢ |
| : , : , : , : , : , : |
39 | instantiation | 83, 56, 57 | ⊢ |
| : , : , : |
40 | instantiation | 80 | ⊢ |
| : , : , : |
41 | theorem | | ⊢ |
| proveit.numbers.addition.leftward_commutation |
42 | instantiation | 87 | ⊢ |
| : , : |
43 | instantiation | 87 | ⊢ |
| : , : |
44 | instantiation | 60, 69, 102, 120, 71, 61, 76, 78, 58* | ⊢ |
| : , : , : , : , : , : |
45 | theorem | | ⊢ |
| proveit.numbers.multiplication.mult_complex_closure_bin |
46 | instantiation | 118, 93, 59 | ⊢ |
| : , : , : |
47 | theorem | | ⊢ |
| proveit.logic.equality.equals_reversal |
48 | instantiation | 60, 69, 102, 120, 71, 61, 76, 82, 62* | ⊢ |
| : , : , : , : , : , : |
49 | instantiation | 63, 69, 70, 120, 71, 64, 76, 65* | ⊢ |
| : , : , : , : , : , : |
50 | theorem | | ⊢ |
| proveit.numbers.negation.distribute_neg_through_binary_sum |
51 | instantiation | 87 | ⊢ |
| : , : |
52 | instantiation | 66, 67, 73 | ⊢ |
| : , : |
53 | theorem | | ⊢ |
| proveit.numbers.addition.disassociation |
54 | instantiation | 87 | ⊢ |
| : , : |
55 | instantiation | 87 | ⊢ |
| : , : |
56 | instantiation | 68, 69, 120, 70, 71, 72, 78, 82, 73, 76, 74 | ⊢ |
| : , : , : , : , : , : , : , : |
57 | instantiation | 75, 76, 82, 77 | ⊢ |
| : , : , : |
58 | instantiation | 81, 78 | ⊢ |
| : |
59 | instantiation | 118, 100, 79 | ⊢ |
| : , : , : |
60 | theorem | | ⊢ |
| proveit.numbers.multiplication.distribute_through_sum |
61 | instantiation | 80 | ⊢ |
| : , : , : |
62 | instantiation | 81, 82 | ⊢ |
| : |
63 | theorem | | ⊢ |
| proveit.numbers.addition.association |
64 | instantiation | 87 | ⊢ |
| : , : |
65 | instantiation | 83, 84, 85 | ⊢ |
| : , : , : |
66 | theorem | | ⊢ |
| proveit.numbers.addition.add_complex_closure_bin |
67 | instantiation | 118, 93, 86 | ⊢ |
| : , : , : |
68 | theorem | | ⊢ |
| proveit.numbers.addition.subtraction.add_cancel_general |
69 | axiom | | ⊢ |
| proveit.numbers.number_sets.natural_numbers.zero_in_nats |
70 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat2 |
71 | theorem | | ⊢ |
| proveit.core_expr_types.tuples.tuple_len_0_typical_eq |
72 | instantiation | 87 | ⊢ |
| : , : |
73 | instantiation | 118, 93, 88 | ⊢ |
| : , : , : |
74 | instantiation | 90 | ⊢ |
| : |
75 | theorem | | ⊢ |
| proveit.numbers.addition.subtraction.add_cancel_triple_32 |
76 | instantiation | 118, 93, 89 | ⊢ |
| : , : , : |
77 | instantiation | 90 | ⊢ |
| : |
78 | instantiation | 118, 93, 91 | ⊢ |
| : , : , : |
79 | instantiation | 118, 109, 92 | ⊢ |
| : , : , : |
80 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.tuple_len_3_typical_eq |
81 | theorem | | ⊢ |
| proveit.numbers.multiplication.elim_one_left |
82 | instantiation | 118, 93, 94 | ⊢ |
| : , : , : |
83 | axiom | | ⊢ |
| proveit.logic.equality.equals_transitivity |
84 | instantiation | 95, 96 | ⊢ |
| : , : , : |
85 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.add_2_1 |
86 | instantiation | 118, 97, 98 | ⊢ |
| : , : , : |
87 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.tuple_len_2_typical_eq |
88 | instantiation | 118, 100, 99 | ⊢ |
| : , : , : |
89 | instantiation | 118, 100, 101 | ⊢ |
| : , : , : |
90 | axiom | | ⊢ |
| proveit.logic.equality.equals_reflexivity |
91 | instantiation | 103, 104, 117 | ⊢ |
| : , : , : |
92 | instantiation | 118, 119, 102 | ⊢ |
| : , : , : |
93 | theorem | | ⊢ |
| proveit.numbers.number_sets.complex_numbers.real_within_complex |
94 | instantiation | 103, 104, 105 | ⊢ |
| : , : , : |
95 | axiom | | ⊢ |
| proveit.logic.equality.substitution |
96 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.add_1_1 |
97 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.real_neg_within_real |
98 | instantiation | 118, 106, 107 | ⊢ |
| : , : , : |
99 | instantiation | 118, 109, 108 | ⊢ |
| : , : , : |
100 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.rational_within_real |
101 | instantiation | 118, 109, 115 | ⊢ |
| : , : , : |
102 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat3 |
103 | theorem | | ⊢ |
| proveit.logic.sets.inclusion.unfold_subset_eq |
104 | instantiation | 110, 111 | ⊢ |
| : , : |
105 | axiom | | ⊢ |
| proveit.physics.quantum.QPE._s_in_nat_pos |
106 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.rational_neg_within_real_neg |
107 | instantiation | 118, 112, 113 | ⊢ |
| : , : , : |
108 | instantiation | 114, 115 | ⊢ |
| : |
109 | theorem | | ⊢ |
| proveit.numbers.number_sets.rational_numbers.int_within_rational |
110 | theorem | | ⊢ |
| proveit.logic.sets.inclusion.relax_proper_subset |
111 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.nat_pos_within_real |
112 | theorem | | ⊢ |
| proveit.numbers.number_sets.rational_numbers.neg_int_within_rational_neg |
113 | instantiation | 116, 117 | ⊢ |
| : |
114 | theorem | | ⊢ |
| proveit.numbers.negation.int_closure |
115 | instantiation | 118, 119, 120 | ⊢ |
| : , : , : |
116 | theorem | | ⊢ |
| proveit.numbers.negation.int_neg_closure |
117 | axiom | | ⊢ |
| proveit.physics.quantum.QPE._t_in_natural_pos |
118 | theorem | | ⊢ |
| proveit.logic.sets.inclusion.superset_membership_from_proper_subset |
119 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.nat_within_int |
120 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat1 |
*equality replacement requirements |