| step type | requirements | statement |
0 | instantiation | 1, 2, 3 | ⊢ |
| : , : , : |
1 | reference | 19 | ⊢ |
2 | instantiation | 12, 4 | ⊢ |
| : , : , : |
3 | instantiation | 19, 5, 6 | ⊢ |
| : , : , : |
4 | instantiation | 7, 73, 76, 29, 8, 31, 33, 32, 34 | ⊢ |
| : , : , : , : , : , : |
5 | instantiation | 19, 9, 10 | ⊢ |
| : , : , : |
6 | instantiation | 11, 17 | ⊢ |
| : |
7 | theorem | | ⊢ |
| proveit.numbers.multiplication.disassociation |
8 | instantiation | 39 | ⊢ |
| : , : |
9 | instantiation | 12, 13 | ⊢ |
| : , : , : |
10 | instantiation | 14, 15, 16, 17, 18* | ⊢ |
| : , : , : |
11 | theorem | | ⊢ |
| proveit.numbers.division.frac_one_denom |
12 | axiom | | ⊢ |
| proveit.logic.equality.substitution |
13 | instantiation | 19, 20, 21 | ⊢ |
| : , : , : |
14 | theorem | | ⊢ |
| proveit.numbers.division.frac_cancel_left |
15 | instantiation | 74, 23, 22 | ⊢ |
| : , : , : |
16 | instantiation | 74, 23, 24 | ⊢ |
| : , : , : |
17 | instantiation | 74, 52, 25 | ⊢ |
| : , : , : |
18 | instantiation | 26, 32 | ⊢ |
| : |
19 | axiom | | ⊢ |
| proveit.logic.equality.equals_transitivity |
20 | instantiation | 27, 29, 73, 31, 33, 32, 34 | ⊢ |
| : , : , : , : , : , : , : |
21 | instantiation | 28, 73, 76, 29, 30, 31, 32, 33, 34 | ⊢ |
| : , : , : , : , : , : |
22 | instantiation | 74, 35, 45 | ⊢ |
| : , : , : |
23 | theorem | | ⊢ |
| proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero |
24 | instantiation | 74, 36, 37 | ⊢ |
| : , : , : |
25 | instantiation | 38, 63, 41 | ⊢ |
| : , : |
26 | theorem | | ⊢ |
| proveit.numbers.multiplication.elim_one_right |
27 | theorem | | ⊢ |
| proveit.numbers.multiplication.leftward_commutation |
28 | theorem | | ⊢ |
| proveit.numbers.multiplication.association |
29 | axiom | | ⊢ |
| proveit.numbers.number_sets.natural_numbers.zero_in_nats |
30 | instantiation | 39 | ⊢ |
| : , : |
31 | theorem | | ⊢ |
| proveit.core_expr_types.tuples.tuple_len_0_typical_eq |
32 | instantiation | 74, 52, 40 | ⊢ |
| : , : , : |
33 | instantiation | 74, 52, 63 | ⊢ |
| : , : , : |
34 | instantiation | 74, 52, 41 | ⊢ |
| : , : , : |
35 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.real_pos_within_real_nonzero |
36 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero |
37 | instantiation | 74, 42, 43 | ⊢ |
| : , : , : |
38 | theorem | | ⊢ |
| proveit.numbers.multiplication.mult_real_closure_bin |
39 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.tuple_len_2_typical_eq |
40 | instantiation | 74, 44, 45 | ⊢ |
| : , : , : |
41 | instantiation | 74, 46, 47 | ⊢ |
| : , : , : |
42 | theorem | | ⊢ |
| proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero |
43 | instantiation | 74, 48, 49 | ⊢ |
| : , : , : |
44 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.real_pos_within_real |
45 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.pi_is_real_pos |
46 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.real_nonneg_within_real |
47 | instantiation | 50, 51 | ⊢ |
| : |
48 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int |
49 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.posnat1 |
50 | theorem | | ⊢ |
| proveit.numbers.absolute_value.abs_complex_closure |
51 | instantiation | 74, 52, 53 | ⊢ |
| : , : , : |
52 | theorem | | ⊢ |
| proveit.numbers.number_sets.complex_numbers.real_within_complex |
53 | instantiation | 54, 55, 58, 56 | ⊢ |
| : , : , : |
54 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.all_in_interval_co__is__real |
55 | instantiation | 57, 58 | ⊢ |
| : |
56 | instantiation | 59, 60 | ⊢ |
| : |
57 | theorem | | ⊢ |
| proveit.numbers.negation.real_closure |
58 | instantiation | 61, 62, 63, 64 | ⊢ |
| : , : |
59 | theorem | | ⊢ |
| proveit.physics.quantum.QPE._delta_b_floor_diff_in_interval |
60 | assumption | | ⊢ |
61 | theorem | | ⊢ |
| proveit.numbers.division.div_real_closure |
62 | instantiation | 74, 66, 65 | ⊢ |
| : , : , : |
63 | instantiation | 74, 66, 67 | ⊢ |
| : , : , : |
64 | instantiation | 68, 69 | ⊢ |
| : |
65 | instantiation | 74, 71, 70 | ⊢ |
| : , : , : |
66 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.rational_within_real |
67 | instantiation | 74, 71, 72 | ⊢ |
| : , : , : |
68 | theorem | | ⊢ |
| proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos |
69 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.posnat2 |
70 | instantiation | 74, 75, 73 | ⊢ |
| : , : , : |
71 | theorem | | ⊢ |
| proveit.numbers.number_sets.rational_numbers.int_within_rational |
72 | instantiation | 74, 75, 76 | ⊢ |
| : , : , : |
73 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat1 |
74 | theorem | | ⊢ |
| proveit.logic.sets.inclusion.superset_membership_from_proper_subset |
75 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.nat_within_int |
76 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat2 |
*equality replacement requirements |