| step type | requirements | statement |
0 | instantiation | 1, 2, 3 | ⊢ |
| : , : , : |
1 | reference | 14 | ⊢ |
2 | instantiation | 14, 4, 5 | ⊢ |
| : , : , : |
3 | instantiation | 6, 12 | ⊢ |
| : |
4 | instantiation | 7, 8 | ⊢ |
| : , : , : |
5 | instantiation | 9, 10, 11, 12, 13* | ⊢ |
| : , : , : |
6 | theorem | | ⊢ |
| proveit.numbers.division.frac_one_denom |
7 | axiom | | ⊢ |
| proveit.logic.equality.substitution |
8 | instantiation | 14, 15, 16 | ⊢ |
| : , : , : |
9 | theorem | | ⊢ |
| proveit.numbers.division.frac_cancel_left |
10 | instantiation | 75, 18, 17 | ⊢ |
| : , : , : |
11 | instantiation | 75, 18, 19 | ⊢ |
| : , : , : |
12 | instantiation | 20, 21, 22 | ⊢ |
| : , : , : |
13 | instantiation | 23, 29 | ⊢ |
| : |
14 | axiom | | ⊢ |
| proveit.logic.equality.equals_transitivity |
15 | instantiation | 24, 35, 36, 69, 37, 25, 39, 29, 40, 41 | ⊢ |
| : , : , : , : , : , : , : |
16 | instantiation | 26, 36, 27, 35, 28, 37, 29, 39, 40, 41 | ⊢ |
| : , : , : , : , : , : |
17 | instantiation | 75, 31, 30 | ⊢ |
| : , : , : |
18 | theorem | | ⊢ |
| proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero |
19 | instantiation | 75, 31, 32 | ⊢ |
| : , : , : |
20 | theorem | | ⊢ |
| proveit.logic.equality.sub_right_side_into |
21 | instantiation | 75, 76, 33 | ⊢ |
| : , : , : |
22 | instantiation | 34, 35, 69, 36, 37, 38, 39, 40, 41 | ⊢ |
| : , : , : , : , : , : |
23 | theorem | | ⊢ |
| proveit.numbers.multiplication.elim_one_right |
24 | theorem | | ⊢ |
| proveit.numbers.multiplication.leftward_commutation |
25 | instantiation | 48 | ⊢ |
| : , : |
26 | theorem | | ⊢ |
| proveit.numbers.multiplication.association |
27 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat3 |
28 | instantiation | 42 | ⊢ |
| : , : , : |
29 | instantiation | 75, 76, 43 | ⊢ |
| : , : , : |
30 | instantiation | 75, 45, 44 | ⊢ |
| : , : , : |
31 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero |
32 | instantiation | 75, 45, 46 | ⊢ |
| : , : , : |
33 | instantiation | 55, 47, 49 | ⊢ |
| : , : |
34 | theorem | | ⊢ |
| proveit.numbers.multiplication.disassociation |
35 | axiom | | ⊢ |
| proveit.numbers.number_sets.natural_numbers.zero_in_nats |
36 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat1 |
37 | theorem | | ⊢ |
| proveit.core_expr_types.tuples.tuple_len_0_typical_eq |
38 | instantiation | 48 | ⊢ |
| : , : |
39 | instantiation | 75, 76, 56 | ⊢ |
| : , : , : |
40 | instantiation | 75, 76, 57 | ⊢ |
| : , : , : |
41 | instantiation | 75, 76, 49 | ⊢ |
| : , : , : |
42 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.tuple_len_3_typical_eq |
43 | instantiation | 75, 50, 51 | ⊢ |
| : , : , : |
44 | instantiation | 75, 53, 52 | ⊢ |
| : , : , : |
45 | theorem | | ⊢ |
| proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero |
46 | instantiation | 75, 53, 54 | ⊢ |
| : , : , : |
47 | instantiation | 55, 56, 57 | ⊢ |
| : , : |
48 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.tuple_len_2_typical_eq |
49 | instantiation | 75, 64, 58 | ⊢ |
| : , : , : |
50 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.rational_within_real |
51 | instantiation | 75, 59, 60 | ⊢ |
| : , : , : |
52 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.posnat2 |
53 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int |
54 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.posnat1 |
55 | theorem | | ⊢ |
| proveit.numbers.multiplication.mult_real_closure_bin |
56 | instantiation | 61, 62, 63 | ⊢ |
| : , : , : |
57 | instantiation | 75, 64, 65 | ⊢ |
| : , : , : |
58 | instantiation | 66, 67 | ⊢ |
| : |
59 | theorem | | ⊢ |
| proveit.numbers.number_sets.rational_numbers.int_within_rational |
60 | instantiation | 75, 68, 69 | ⊢ |
| : , : , : |
61 | theorem | | ⊢ |
| proveit.logic.sets.inclusion.unfold_subset_eq |
62 | instantiation | 70, 71 | ⊢ |
| : , : |
63 | theorem | | ⊢ |
| proveit.physics.quantum.QPE._two_pow_t_is_nat_pos |
64 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.real_pos_within_real |
65 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.pi_is_real_pos |
66 | theorem | | ⊢ |
| proveit.numbers.absolute_value.abs_nonzero_closure |
67 | instantiation | 72, 73, 74 | ⊢ |
| : |
68 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.nat_within_int |
69 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat2 |
70 | theorem | | ⊢ |
| proveit.logic.sets.inclusion.relax_proper_subset |
71 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.nat_pos_within_real |
72 | theorem | | ⊢ |
| proveit.numbers.number_sets.complex_numbers.nonzero_complex_is_complex_nonzero |
73 | instantiation | 75, 76, 77 | ⊢ |
| : , : , : |
74 | assumption | | ⊢ |
75 | theorem | | ⊢ |
| proveit.logic.sets.inclusion.superset_membership_from_proper_subset |
76 | theorem | | ⊢ |
| proveit.numbers.number_sets.complex_numbers.real_within_complex |
77 | instantiation | 78, 79 | ⊢ |
| : |
78 | theorem | | ⊢ |
| proveit.physics.quantum.QPE._delta_b_is_real |
79 | theorem | | ⊢ |
| proveit.physics.quantum.QPE._best_round_is_int |
*equality replacement requirements |