| step type | requirements | statement |
0 | instantiation | 1, 2, 3 | ⊢ |
| : , : , : |
1 | reference | 16 | ⊢ |
2 | instantiation | 4, 5 | ⊢ |
| : , : , : |
3 | instantiation | 6, 7, 8, 9 | ⊢ |
| : , : , : , : |
4 | axiom | | ⊢ |
| proveit.logic.equality.substitution |
5 | instantiation | 11, 24, 56, 23, 26, 25, 32, 27, 28 | ⊢ |
| : , : , : , : , : , : |
6 | theorem | | ⊢ |
| proveit.logic.equality.four_chain_transitivity |
7 | instantiation | 11, 24, 12, 23, 26, 13, 32, 27, 28, 10 | ⊢ |
| : , : , : , : , : , : |
8 | instantiation | 11, 12, 56, 24, 13, 14, 26, 32, 27, 28, 31, 15 | ⊢ |
| : , : , : , : , : , : |
9 | instantiation | 16, 17, 18 | ⊢ |
| : , : , : |
10 | instantiation | 54, 38, 19 | ⊢ |
| : , : , : |
11 | theorem | | ⊢ |
| proveit.numbers.addition.disassociation |
12 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat3 |
13 | instantiation | 20 | ⊢ |
| : , : , : |
14 | instantiation | 36 | ⊢ |
| : , : |
15 | instantiation | 21, 28 | ⊢ |
| : |
16 | axiom | | ⊢ |
| proveit.logic.equality.equals_transitivity |
17 | instantiation | 22, 56, 23, 24, 25, 26, 32, 27, 28, 31, 29 | ⊢ |
| : , : , : , : , : , : , : , : |
18 | instantiation | 30, 31, 32, 33 | ⊢ |
| : , : , : |
19 | instantiation | 34, 43, 35 | ⊢ |
| : , : |
20 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.tuple_len_3_typical_eq |
21 | theorem | | ⊢ |
| proveit.numbers.negation.complex_closure |
22 | theorem | | ⊢ |
| proveit.numbers.addition.subtraction.add_cancel_general |
23 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat1 |
24 | axiom | | ⊢ |
| proveit.numbers.number_sets.natural_numbers.zero_in_nats |
25 | instantiation | 36 | ⊢ |
| : , : |
26 | theorem | | ⊢ |
| proveit.core_expr_types.tuples.tuple_len_0_typical_eq |
27 | instantiation | 54, 38, 37 | ⊢ |
| : , : , : |
28 | instantiation | 54, 38, 41 | ⊢ |
| : , : , : |
29 | instantiation | 40 | ⊢ |
| : |
30 | theorem | | ⊢ |
| proveit.numbers.addition.subtraction.add_cancel_triple_32 |
31 | instantiation | 54, 38, 43 | ⊢ |
| : , : , : |
32 | instantiation | 54, 38, 39 | ⊢ |
| : , : , : |
33 | instantiation | 40 | ⊢ |
| : |
34 | theorem | | ⊢ |
| proveit.numbers.addition.add_real_closure_bin |
35 | instantiation | 42, 41 | ⊢ |
| : |
36 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.tuple_len_2_typical_eq |
37 | instantiation | 42, 43 | ⊢ |
| : |
38 | theorem | | ⊢ |
| proveit.numbers.number_sets.complex_numbers.real_within_complex |
39 | instantiation | 47, 48, 44 | ⊢ |
| : , : , : |
40 | axiom | | ⊢ |
| proveit.logic.equality.equals_reflexivity |
41 | instantiation | 54, 45, 46 | ⊢ |
| : , : , : |
42 | theorem | | ⊢ |
| proveit.numbers.negation.real_closure |
43 | instantiation | 47, 48, 49 | ⊢ |
| : , : , : |
44 | axiom | | ⊢ |
| proveit.physics.quantum.QPE._t_in_natural_pos |
45 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.rational_within_real |
46 | instantiation | 54, 50, 51 | ⊢ |
| : , : , : |
47 | theorem | | ⊢ |
| proveit.logic.sets.inclusion.unfold_subset_eq |
48 | instantiation | 52, 53 | ⊢ |
| : , : |
49 | axiom | | ⊢ |
| proveit.physics.quantum.QPE._n_in_natural_pos |
50 | theorem | | ⊢ |
| proveit.numbers.number_sets.rational_numbers.int_within_rational |
51 | instantiation | 54, 55, 56 | ⊢ |
| : , : , : |
52 | theorem | | ⊢ |
| proveit.logic.sets.inclusion.relax_proper_subset |
53 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.nat_pos_within_real |
54 | theorem | | ⊢ |
| proveit.logic.sets.inclusion.superset_membership_from_proper_subset |
55 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.nat_within_int |
56 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat2 |