| step type | requirements | statement |
0 | instantiation | 1, 2, 3, 4 | ⊢ |
| : , : , : , : |
1 | reference | 50 | ⊢ |
2 | instantiation | 5, 6, 7, 8, 9, 10, 11, 12, 13* | ⊢ |
| : , : , : , : |
3 | instantiation | 66, 14 | ⊢ |
| : , : |
4 | instantiation | 66, 15 | ⊢ |
| : , : |
5 | theorem | | ⊢ |
| proveit.core_expr_types.tuples.general_len |
6 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.posnat8 |
7 | instantiation | 37 | ⊢ |
| : , : , : , : , : , : , : , : |
8 | instantiation | 37 | ⊢ |
| : , : , : , : , : , : , : , : |
9 | instantiation | 37 | ⊢ |
| : , : , : , : , : , : , : , : |
10 | instantiation | 17, 16, 29 | ⊢ |
| : , : , : |
11 | instantiation | 17, 18, 76 | ⊢ |
| : , : , : |
12 | instantiation | 17, 18, 30 | ⊢ |
| : , : , : |
13 | instantiation | 122, 19, 20 | ⊢ |
| : , : , : |
14 | instantiation | 81, 143, 140, 108, 73, 109, 65, 101, 97 | ⊢ |
| : , : , : , : , : , : |
15 | instantiation | 21, 22, 23, 24 | ⊢ |
| : , : , : |
16 | instantiation | 141, 35, 127 | ⊢ |
| : , : , : |
17 | theorem | | ⊢ |
| proveit.logic.equality.sub_left_side_into |
18 | instantiation | 141, 35, 117 | ⊢ |
| : , : , : |
19 | instantiation | 25, 26, 27, 28, 29, 76, 30 | ⊢ |
| : , : , : , : |
20 | instantiation | 50, 31, 32, 33 | ⊢ |
| : , : , : , : |
21 | theorem | | ⊢ |
| proveit.core_expr_types.tuples.len_of_ranges_with_repeated_indices_from_1 |
22 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.posnat4 |
23 | instantiation | 34, 116 | ⊢ |
| : , : |
24 | instantiation | 141, 35, 36 | ⊢ |
| : , : , : |
25 | axiom | | ⊢ |
| proveit.core_expr_types.operations.operands_substitution |
26 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat8 |
27 | instantiation | 37 | ⊢ |
| : , : , : , : , : , : , : , : |
28 | instantiation | 37 | ⊢ |
| : , : , : , : , : , : , : , : |
29 | instantiation | 92, 112, 101, 93 | ⊢ |
| : , : , : |
30 | instantiation | 122, 38, 39 | ⊢ |
| : , : , : |
31 | instantiation | 50, 40, 41, 42 | ⊢ |
| : , : , : , : |
32 | instantiation | 107, 108, 116, 109, 43, 45, 101, 97, 44* | ⊢ |
| : , : , : , : , : , : |
33 | instantiation | 107, 143, 116, 108, 45, 109, 46, 97, 47* | ⊢ |
| : , : , : , : , : , : |
34 | theorem | | ⊢ |
| proveit.core_expr_types.tuples.range_from1_len_typical_eq |
35 | theorem | | ⊢ |
| proveit.numbers.number_sets.natural_numbers.nat_pos_within_nat |
36 | instantiation | 48, 127, 117 | ⊢ |
| : , : |
37 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.tuple_len_8_typical_eq |
38 | instantiation | 132, 49 | ⊢ |
| : , : , : |
39 | instantiation | 50, 51, 52, 53 | ⊢ |
| : , : , : , : |
40 | instantiation | 59, 143, 54, 55, 101, 97 | ⊢ |
| : , : , : , : , : , : , : |
41 | instantiation | 59, 140, 60, 56, 57, 58, 101, 97 | ⊢ |
| : , : , : , : , : , : , : |
42 | instantiation | 59, 60, 143, 61, 62, 101, 97 | ⊢ |
| : , : , : , : , : , : , : |
43 | instantiation | 95 | ⊢ |
| : , : , : , : |
44 | instantiation | 66, 63, 68* | ⊢ |
| : , : |
45 | instantiation | 95 | ⊢ |
| : , : , : , : |
46 | instantiation | 64, 65, 101 | ⊢ |
| : , : |
47 | instantiation | 66, 67, 68* | ⊢ |
| : , : |
48 | theorem | | ⊢ |
| proveit.numbers.addition.add_nat_pos_closure_bin |
49 | instantiation | 69, 101, 112 | ⊢ |
| : , : |
50 | theorem | | ⊢ |
| proveit.logic.equality.four_chain_transitivity |
51 | instantiation | 72, 108, 140, 109, 73, 70, 101, 97, 71, 112 | ⊢ |
| : , : , : , : , : , : |
52 | instantiation | 72, 140, 143, 73, 74, 101, 97, 87, 90, 112 | ⊢ |
| : , : , : , : , : , : |
53 | instantiation | 122, 75, 76 | ⊢ |
| : , : , : |
54 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat5 |
55 | instantiation | 77 | ⊢ |
| : , : , : , : , : |
56 | instantiation | 118 | ⊢ |
| : , : |
57 | instantiation | 118 | ⊢ |
| : , : |
58 | instantiation | 78 | ⊢ |
| : , : , : |
59 | theorem | | ⊢ |
| proveit.numbers.addition.leftward_commutation |
60 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat3 |
61 | instantiation | 78 | ⊢ |
| : , : , : |
62 | instantiation | 78 | ⊢ |
| : , : , : |
63 | instantiation | 81, 108, 116, 143, 109, 82, 112, 101, 79* | ⊢ |
| : , : , : , : , : , : |
64 | theorem | | ⊢ |
| proveit.numbers.multiplication.mult_complex_closure_bin |
65 | instantiation | 141, 120, 80 | ⊢ |
| : , : , : |
66 | theorem | | ⊢ |
| proveit.logic.equality.equals_reversal |
67 | instantiation | 81, 108, 116, 143, 109, 82, 112, 97, 83* | ⊢ |
| : , : , : , : , : , : |
68 | instantiation | 107, 108, 140, 109, 84, 112, 85* | ⊢ |
| : , : , : , : , : , : |
69 | theorem | | ⊢ |
| proveit.numbers.negation.distribute_neg_through_binary_sum |
70 | instantiation | 118 | ⊢ |
| : , : |
71 | instantiation | 86, 87, 90 | ⊢ |
| : , : |
72 | theorem | | ⊢ |
| proveit.numbers.addition.disassociation |
73 | instantiation | 118 | ⊢ |
| : , : |
74 | instantiation | 118 | ⊢ |
| : , : |
75 | instantiation | 88, 108, 143, 140, 109, 89, 101, 97, 90, 112, 91 | ⊢ |
| : , : , : , : , : , : , : , : |
76 | instantiation | 92, 112, 97, 93 | ⊢ |
| : , : , : |
77 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.tuple_len_5_typical_eq |
78 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.tuple_len_3_typical_eq |
79 | instantiation | 96, 101 | ⊢ |
| : |
80 | instantiation | 141, 130, 94 | ⊢ |
| : , : , : |
81 | theorem | | ⊢ |
| proveit.numbers.multiplication.distribute_through_sum |
82 | instantiation | 95 | ⊢ |
| : , : , : , : |
83 | instantiation | 96, 97 | ⊢ |
| : |
84 | instantiation | 118 | ⊢ |
| : , : |
85 | instantiation | 122, 98, 99 | ⊢ |
| : , : , : |
86 | theorem | | ⊢ |
| proveit.numbers.addition.add_complex_closure_bin |
87 | instantiation | 100, 101 | ⊢ |
| : |
88 | theorem | | ⊢ |
| proveit.numbers.addition.subtraction.add_cancel_general |
89 | instantiation | 118 | ⊢ |
| : , : |
90 | instantiation | 141, 120, 102 | ⊢ |
| : , : , : |
91 | instantiation | 103 | ⊢ |
| : |
92 | theorem | | ⊢ |
| proveit.numbers.addition.subtraction.add_cancel_triple_32 |
93 | instantiation | 103 | ⊢ |
| : |
94 | instantiation | 141, 138, 104 | ⊢ |
| : , : , : |
95 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.tuple_len_4_typical_eq |
96 | theorem | | ⊢ |
| proveit.numbers.multiplication.elim_one_left |
97 | instantiation | 141, 120, 105 | ⊢ |
| : , : , : |
98 | instantiation | 132, 106 | ⊢ |
| : , : , : |
99 | instantiation | 107, 108, 140, 143, 109, 110, 111, 112, 113* | ⊢ |
| : , : , : , : , : , : |
100 | theorem | | ⊢ |
| proveit.numbers.negation.complex_closure |
101 | instantiation | 141, 120, 114 | ⊢ |
| : , : , : |
102 | instantiation | 141, 130, 115 | ⊢ |
| : , : , : |
103 | axiom | | ⊢ |
| proveit.logic.equality.equals_reflexivity |
104 | instantiation | 141, 142, 116 | ⊢ |
| : , : , : |
105 | instantiation | 125, 126, 117 | ⊢ |
| : , : , : |
106 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.add_1_1 |
107 | theorem | | ⊢ |
| proveit.numbers.addition.association |
108 | axiom | | ⊢ |
| proveit.numbers.number_sets.natural_numbers.zero_in_nats |
109 | theorem | | ⊢ |
| proveit.core_expr_types.tuples.tuple_len_0_typical_eq |
110 | instantiation | 118 | ⊢ |
| : , : |
111 | instantiation | 141, 120, 119 | ⊢ |
| : , : , : |
112 | instantiation | 141, 120, 121 | ⊢ |
| : , : , : |
113 | instantiation | 122, 123, 124 | ⊢ |
| : , : , : |
114 | instantiation | 125, 126, 127 | ⊢ |
| : , : , : |
115 | instantiation | 141, 138, 128 | ⊢ |
| : , : , : |
116 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat4 |
117 | axiom | | ⊢ |
| proveit.physics.quantum.QPE._s_in_nat_pos |
118 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.tuple_len_2_typical_eq |
119 | instantiation | 141, 130, 129 | ⊢ |
| : , : , : |
120 | theorem | | ⊢ |
| proveit.numbers.number_sets.complex_numbers.real_within_complex |
121 | instantiation | 141, 130, 131 | ⊢ |
| : , : , : |
122 | axiom | | ⊢ |
| proveit.logic.equality.equals_transitivity |
123 | instantiation | 132, 133 | ⊢ |
| : , : , : |
124 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.add_3_1 |
125 | theorem | | ⊢ |
| proveit.logic.sets.inclusion.unfold_subset_eq |
126 | instantiation | 134, 135 | ⊢ |
| : , : |
127 | axiom | | ⊢ |
| proveit.physics.quantum.QPE._t_in_natural_pos |
128 | instantiation | 136, 139 | ⊢ |
| : |
129 | instantiation | 141, 138, 137 | ⊢ |
| : , : , : |
130 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.rational_within_real |
131 | instantiation | 141, 138, 139 | ⊢ |
| : , : , : |
132 | axiom | | ⊢ |
| proveit.logic.equality.substitution |
133 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.add_2_1 |
134 | theorem | | ⊢ |
| proveit.logic.sets.inclusion.relax_proper_subset |
135 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.nat_pos_within_real |
136 | theorem | | ⊢ |
| proveit.numbers.negation.int_closure |
137 | instantiation | 141, 142, 140 | ⊢ |
| : , : , : |
138 | theorem | | ⊢ |
| proveit.numbers.number_sets.rational_numbers.int_within_rational |
139 | instantiation | 141, 142, 143 | ⊢ |
| : , : , : |
140 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat2 |
141 | theorem | | ⊢ |
| proveit.logic.sets.inclusion.superset_membership_from_proper_subset |
142 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.nat_within_int |
143 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat1 |
*equality replacement requirements |