| step type | requirements | statement |
0 | instantiation | 1, 2, 3, 4, 5* | ⊢ |
| : , : , : |
1 | theorem | | ⊢ |
| proveit.numbers.division.frac_cancel_left |
2 | instantiation | 76, 7, 6 | ⊢ |
| : , : , : |
3 | instantiation | 76, 7, 8 | ⊢ |
| : , : , : |
4 | instantiation | 24, 9, 10 | ⊢ |
| : , : , : |
5 | instantiation | 11, 12 | ⊢ |
| : |
6 | instantiation | 76, 14, 13 | ⊢ |
| : , : , : |
7 | theorem | | ⊢ |
| proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero |
8 | instantiation | 76, 14, 15 | ⊢ |
| : , : , : |
9 | instantiation | 46, 27, 16 | ⊢ |
| : , : |
10 | instantiation | 17, 18, 19 | ⊢ |
| : , : , : |
11 | theorem | | ⊢ |
| proveit.numbers.multiplication.elim_one_right |
12 | instantiation | 76, 53, 20 | ⊢ |
| : , : , : |
13 | instantiation | 76, 22, 21 | ⊢ |
| : , : , : |
14 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero |
15 | instantiation | 76, 22, 23 | ⊢ |
| : , : , : |
16 | instantiation | 24, 25, 26 | ⊢ |
| : , : , : |
17 | axiom | | ⊢ |
| proveit.logic.equality.equals_transitivity |
18 | instantiation | 36, 78, 28, 37, 30, 38, 27, 47, 48, 40 | ⊢ |
| : , : , : , : , : , : |
19 | instantiation | 36, 37, 63, 28, 38, 29, 30, 41, 42, 47, 48, 40 | ⊢ |
| : , : , : , : , : , : |
20 | instantiation | 31, 32, 73 | ⊢ |
| : , : , : |
21 | instantiation | 76, 33, 73 | ⊢ |
| : , : , : |
22 | theorem | | ⊢ |
| proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero |
23 | instantiation | 76, 33, 34 | ⊢ |
| : , : , : |
24 | theorem | | ⊢ |
| proveit.logic.equality.sub_right_side_into |
25 | instantiation | 46, 35, 40 | ⊢ |
| : , : |
26 | instantiation | 36, 37, 63, 78, 38, 39, 47, 48, 40 | ⊢ |
| : , : , : , : , : , : |
27 | instantiation | 46, 41, 42 | ⊢ |
| : , : |
28 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat3 |
29 | instantiation | 49 | ⊢ |
| : , : |
30 | instantiation | 43 | ⊢ |
| : , : , : |
31 | theorem | | ⊢ |
| proveit.logic.sets.inclusion.unfold_subset_eq |
32 | instantiation | 44, 45 | ⊢ |
| : , : |
33 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int |
34 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.posnat1 |
35 | instantiation | 46, 47, 48 | ⊢ |
| : , : |
36 | theorem | | ⊢ |
| proveit.numbers.multiplication.disassociation |
37 | axiom | | ⊢ |
| proveit.numbers.number_sets.natural_numbers.zero_in_nats |
38 | theorem | | ⊢ |
| proveit.core_expr_types.tuples.tuple_len_0_typical_eq |
39 | instantiation | 49 | ⊢ |
| : , : |
40 | instantiation | 76, 53, 50 | ⊢ |
| : , : , : |
41 | instantiation | 76, 53, 51 | ⊢ |
| : , : , : |
42 | instantiation | 76, 53, 52 | ⊢ |
| : , : , : |
43 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.tuple_len_3_typical_eq |
44 | theorem | | ⊢ |
| proveit.logic.sets.inclusion.relax_proper_subset |
45 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.nat_pos_within_real |
46 | theorem | | ⊢ |
| proveit.numbers.multiplication.mult_complex_closure_bin |
47 | theorem | | ⊢ |
| proveit.numbers.number_sets.complex_numbers.i_is_complex |
48 | instantiation | 76, 53, 54 | ⊢ |
| : , : , : |
49 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.tuple_len_2_typical_eq |
50 | theorem | | ⊢ |
| proveit.physics.quantum.QPE._phase_is_real |
51 | instantiation | 76, 58, 55 | ⊢ |
| : , : , : |
52 | instantiation | 76, 56, 57 | ⊢ |
| : , : , : |
53 | theorem | | ⊢ |
| proveit.numbers.number_sets.complex_numbers.real_within_complex |
54 | instantiation | 76, 58, 59 | ⊢ |
| : , : , : |
55 | instantiation | 76, 61, 60 | ⊢ |
| : , : , : |
56 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.real_pos_within_real |
57 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.pi_is_real_pos |
58 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.rational_within_real |
59 | instantiation | 76, 61, 62 | ⊢ |
| : , : , : |
60 | instantiation | 76, 77, 63 | ⊢ |
| : , : , : |
61 | theorem | | ⊢ |
| proveit.numbers.number_sets.rational_numbers.int_within_rational |
62 | instantiation | 76, 64, 65 | ⊢ |
| : , : , : |
63 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat2 |
64 | instantiation | 66, 67, 68 | ⊢ |
| : , : |
65 | assumption | | ⊢ |
66 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.int_interval_within_int |
67 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.zero_is_int |
68 | instantiation | 69, 70, 71 | ⊢ |
| : , : |
69 | theorem | | ⊢ |
| proveit.numbers.addition.add_int_closure_bin |
70 | instantiation | 76, 72, 73 | ⊢ |
| : , : , : |
71 | instantiation | 74, 75 | ⊢ |
| : |
72 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.nat_pos_within_int |
73 | theorem | | ⊢ |
| proveit.physics.quantum.QPE._two_pow_t_is_nat_pos |
74 | theorem | | ⊢ |
| proveit.numbers.negation.int_closure |
75 | instantiation | 76, 77, 78 | ⊢ |
| : , : , : |
76 | theorem | | ⊢ |
| proveit.logic.sets.inclusion.superset_membership_from_proper_subset |
77 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.nat_within_int |
78 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat1 |
*equality replacement requirements |