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