| step type | requirements | statement |
0 | instantiation | 1, 2, 3 | ⊢ |
| : , : , : |
1 | reference | 68 | ⊢ |
2 | instantiation | 4, 5, 6, 7, 8, 9, 10 | ⊢ |
| : , : , : , : |
3 | instantiation | 68, 11, 12 | ⊢ |
| : , : , : |
4 | axiom | | ⊢ |
| proveit.core_expr_types.operations.operands_substitution |
5 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat5 |
6 | instantiation | 13 | ⊢ |
| : , : , : , : , : |
7 | instantiation | 13 | ⊢ |
| : , : , : , : , : |
8 | instantiation | 68, 14, 15 | ⊢ |
| : , : , : |
9 | instantiation | 16, 59, 61, 17 | ⊢ |
| : , : , : |
10 | instantiation | 16, 59, 65, 17 | ⊢ |
| : , : , : |
11 | instantiation | 24, 55, 56, 18, 57, 28, 19, 61, 65 | ⊢ |
| : , : , : , : , : , : |
12 | instantiation | 20, 21, 22, 23 | ⊢ |
| : , : , : , : |
13 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.tuple_len_5_typical_eq |
14 | instantiation | 24, 55, 56, 57, 28, 25, 61, 65, 26, 59 | ⊢ |
| : , : , : , : , : , : |
15 | instantiation | 27, 56, 55, 28, 57, 61, 65, 59 | ⊢ |
| : , : , : , : , : , : , : , : |
16 | theorem | | ⊢ |
| proveit.numbers.addition.subtraction.add_cancel_triple_32 |
17 | instantiation | 29 | ⊢ |
| : |
18 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat4 |
19 | instantiation | 30 | ⊢ |
| : , : , : , : |
20 | theorem | | ⊢ |
| proveit.logic.equality.four_chain_transitivity |
21 | instantiation | 68, 31, 32 | ⊢ |
| : , : , : |
22 | instantiation | 54, 55, 80, 57, 33, 35, 61, 65, 34* | ⊢ |
| : , : , : , : , : , : |
23 | instantiation | 54, 90, 80, 55, 35, 57, 36, 65, 37* | ⊢ |
| : , : , : , : , : , : |
24 | theorem | | ⊢ |
| proveit.numbers.addition.disassociation |
25 | instantiation | 66 | ⊢ |
| : , : |
26 | instantiation | 38, 59 | ⊢ |
| : |
27 | theorem | | ⊢ |
| proveit.numbers.addition.subtraction.add_cancel_general_rev |
28 | instantiation | 66 | ⊢ |
| : , : |
29 | axiom | | ⊢ |
| proveit.logic.equality.equals_reflexivity |
30 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.tuple_len_4_typical_eq |
31 | instantiation | 40, 90, 80, 39, 61, 65 | ⊢ |
| : , : , : , : , : , : , : |
32 | instantiation | 40, 56, 90, 41, 42, 61, 65 | ⊢ |
| : , : , : , : , : , : , : |
33 | instantiation | 63 | ⊢ |
| : , : , : |
34 | instantiation | 46, 43, 48* | ⊢ |
| : , : |
35 | instantiation | 63 | ⊢ |
| : , : , : |
36 | instantiation | 44, 45, 61 | ⊢ |
| : , : |
37 | instantiation | 46, 47, 48* | ⊢ |
| : , : |
38 | theorem | | ⊢ |
| proveit.numbers.negation.complex_closure |
39 | instantiation | 63 | ⊢ |
| : , : , : |
40 | theorem | | ⊢ |
| proveit.numbers.addition.leftward_commutation |
41 | instantiation | 66 | ⊢ |
| : , : |
42 | instantiation | 66 | ⊢ |
| : , : |
43 | instantiation | 51, 55, 80, 90, 57, 52, 59, 61, 49* | ⊢ |
| : , : , : , : , : , : |
44 | theorem | | ⊢ |
| proveit.numbers.multiplication.mult_complex_closure_bin |
45 | instantiation | 88, 73, 50 | ⊢ |
| : , : , : |
46 | theorem | | ⊢ |
| proveit.logic.equality.equals_reversal |
47 | instantiation | 51, 55, 80, 90, 57, 52, 59, 65, 53* | ⊢ |
| : , : , : , : , : , : |
48 | instantiation | 54, 55, 56, 90, 57, 58, 59, 60* | ⊢ |
| : , : , : , : , : , : |
49 | instantiation | 64, 61 | ⊢ |
| : |
50 | instantiation | 88, 75, 62 | ⊢ |
| : , : , : |
51 | theorem | | ⊢ |
| proveit.numbers.multiplication.distribute_through_sum |
52 | instantiation | 63 | ⊢ |
| : , : , : |
53 | instantiation | 64, 65 | ⊢ |
| : |
54 | theorem | | ⊢ |
| proveit.numbers.addition.association |
55 | axiom | | ⊢ |
| proveit.numbers.number_sets.natural_numbers.zero_in_nats |
56 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat2 |
57 | theorem | | ⊢ |
| proveit.core_expr_types.tuples.tuple_len_0_typical_eq |
58 | instantiation | 66 | ⊢ |
| : , : |
59 | instantiation | 88, 73, 67 | ⊢ |
| : , : , : |
60 | instantiation | 68, 69, 70 | ⊢ |
| : , : , : |
61 | instantiation | 88, 73, 71 | ⊢ |
| : , : , : |
62 | instantiation | 88, 84, 72 | ⊢ |
| : , : , : |
63 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.tuple_len_3_typical_eq |
64 | theorem | | ⊢ |
| proveit.numbers.multiplication.elim_one_left |
65 | instantiation | 88, 73, 74 | ⊢ |
| : , : , : |
66 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.tuple_len_2_typical_eq |
67 | instantiation | 88, 75, 76 | ⊢ |
| : , : , : |
68 | axiom | | ⊢ |
| proveit.logic.equality.equals_transitivity |
69 | instantiation | 77, 78 | ⊢ |
| : , : , : |
70 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.add_2_1 |
71 | instantiation | 81, 82, 79 | ⊢ |
| : , : , : |
72 | instantiation | 88, 89, 80 | ⊢ |
| : , : , : |
73 | theorem | | ⊢ |
| proveit.numbers.number_sets.complex_numbers.real_within_complex |
74 | instantiation | 81, 82, 83 | ⊢ |
| : , : , : |
75 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.rational_within_real |
76 | instantiation | 88, 84, 85 | ⊢ |
| : , : , : |
77 | axiom | | ⊢ |
| proveit.logic.equality.substitution |
78 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.add_1_1 |
79 | axiom | | ⊢ |
| proveit.physics.quantum.QPE._t_in_natural_pos |
80 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat3 |
81 | theorem | | ⊢ |
| proveit.logic.sets.inclusion.unfold_subset_eq |
82 | instantiation | 86, 87 | ⊢ |
| : , : |
83 | axiom | | ⊢ |
| proveit.physics.quantum.QPE._s_in_nat_pos |
84 | theorem | | ⊢ |
| proveit.numbers.number_sets.rational_numbers.int_within_rational |
85 | instantiation | 88, 89, 90 | ⊢ |
| : , : , : |
86 | theorem | | ⊢ |
| proveit.logic.sets.inclusion.relax_proper_subset |
87 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.nat_pos_within_real |
88 | theorem | | ⊢ |
| proveit.logic.sets.inclusion.superset_membership_from_proper_subset |
89 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.nat_within_int |
90 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat1 |
*equality replacement requirements |