| step type | requirements | statement |
0 | instantiation | 1, 2, 3, 4 | ⊢ |
| : , : , : |
1 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.interval_co_upper_bound |
2 | reference | 7 | ⊢ |
3 | instantiation | 86, 76, 5 | ⊢ |
| : , : , : |
4 | instantiation | 6, 7, 68, 33, 8, 9*, 10*, 11* | ⊢ |
| : , : , : , : |
5 | instantiation | 12, 77, 13, 38 | ⊢ |
| : , : |
6 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.rescale_interval_co_membership |
7 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.zero_is_real |
8 | theorem | | ⊢ |
| proveit.physics.quantum.QPE._scaled_delta_b_floor_in_interval |
9 | instantiation | 44, 14, 15, 16 | ⊢ |
| : , : , : , : |
10 | instantiation | 17, 29 | ⊢ |
| : |
11 | instantiation | 80, 29 | ⊢ |
| : |
12 | theorem | | ⊢ |
| proveit.numbers.division.div_rational_closure |
13 | instantiation | 86, 82, 18 | ⊢ |
| : , : , : |
14 | instantiation | 19, 88, 26, 25, 20, 27, 29, 81, 30 | ⊢ |
| : , : , : , : , : , : |
15 | instantiation | 65, 21, 22 | ⊢ |
| : , : , : |
16 | instantiation | 72, 30 | ⊢ |
| : |
17 | theorem | | ⊢ |
| proveit.numbers.multiplication.mult_zero_right |
18 | instantiation | 86, 23, 91 | ⊢ |
| : , : , : |
19 | theorem | | ⊢ |
| proveit.numbers.multiplication.disassociation |
20 | instantiation | 32 | ⊢ |
| : , : |
21 | instantiation | 24, 25, 26, 88, 27, 28, 29, 81, 30 | ⊢ |
| : , : , : , : , : , : |
22 | instantiation | 73, 31 | ⊢ |
| : , : , : |
23 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.nat_pos_within_int |
24 | theorem | | ⊢ |
| proveit.numbers.multiplication.association |
25 | axiom | | ⊢ |
| proveit.numbers.number_sets.natural_numbers.zero_in_nats |
26 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat2 |
27 | theorem | | ⊢ |
| proveit.core_expr_types.tuples.tuple_len_0_typical_eq |
28 | instantiation | 32 | ⊢ |
| : , : |
29 | instantiation | 86, 84, 33 | ⊢ |
| : , : , : |
30 | instantiation | 86, 84, 34 | ⊢ |
| : , : , : |
31 | instantiation | 41, 35, 36 | ⊢ |
| : , : , : |
32 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.tuple_len_2_typical_eq |
33 | instantiation | 37, 68, 85, 38 | ⊢ |
| : , : |
34 | instantiation | 39, 40 | ⊢ |
| : |
35 | instantiation | 41, 42, 43 | ⊢ |
| : , : , : |
36 | instantiation | 44, 45, 46, 47 | ⊢ |
| : , : , : , : |
37 | theorem | | ⊢ |
| proveit.numbers.division.div_real_closure |
38 | instantiation | 48, 91 | ⊢ |
| : |
39 | theorem | | ⊢ |
| proveit.physics.quantum.QPE._delta_b_is_real |
40 | theorem | | ⊢ |
| proveit.physics.quantum.QPE._best_floor_is_int |
41 | theorem | | ⊢ |
| proveit.logic.equality.sub_right_side_into |
42 | instantiation | 49, 60, 50, 51 | ⊢ |
| : , : , : , : , : |
43 | instantiation | 65, 52, 53 | ⊢ |
| : , : , : |
44 | theorem | | ⊢ |
| proveit.logic.equality.four_chain_transitivity |
45 | instantiation | 73, 54 | ⊢ |
| : , : , : |
46 | instantiation | 73, 54 | ⊢ |
| : , : , : |
47 | instantiation | 80, 60 | ⊢ |
| : |
48 | theorem | | ⊢ |
| proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos |
49 | theorem | | ⊢ |
| proveit.numbers.division.mult_frac_cancel_denom_left |
50 | instantiation | 86, 56, 55 | ⊢ |
| : , : , : |
51 | instantiation | 86, 56, 57 | ⊢ |
| : , : , : |
52 | instantiation | 73, 58 | ⊢ |
| : , : , : |
53 | instantiation | 73, 59 | ⊢ |
| : , : , : |
54 | instantiation | 75, 60 | ⊢ |
| : |
55 | instantiation | 86, 62, 61 | ⊢ |
| : , : , : |
56 | theorem | | ⊢ |
| proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero |
57 | instantiation | 86, 62, 63 | ⊢ |
| : , : , : |
58 | instantiation | 73, 64 | ⊢ |
| : , : , : |
59 | instantiation | 65, 66, 67 | ⊢ |
| : , : , : |
60 | instantiation | 86, 84, 68 | ⊢ |
| : , : , : |
61 | instantiation | 86, 70, 69 | ⊢ |
| : , : , : |
62 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero |
63 | instantiation | 86, 70, 71 | ⊢ |
| : , : , : |
64 | instantiation | 72, 81 | ⊢ |
| : |
65 | axiom | | ⊢ |
| proveit.logic.equality.equals_transitivity |
66 | instantiation | 73, 74 | ⊢ |
| : , : , : |
67 | instantiation | 75, 81 | ⊢ |
| : |
68 | instantiation | 86, 76, 77 | ⊢ |
| : , : , : |
69 | instantiation | 86, 79, 78 | ⊢ |
| : , : , : |
70 | theorem | | ⊢ |
| proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero |
71 | instantiation | 86, 79, 91 | ⊢ |
| : , : , : |
72 | theorem | | ⊢ |
| proveit.numbers.multiplication.elim_one_left |
73 | axiom | | ⊢ |
| proveit.logic.equality.substitution |
74 | instantiation | 80, 81 | ⊢ |
| : |
75 | theorem | | ⊢ |
| proveit.numbers.division.frac_one_denom |
76 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.rational_within_real |
77 | instantiation | 86, 82, 83 | ⊢ |
| : , : , : |
78 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.posnat1 |
79 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int |
80 | theorem | | ⊢ |
| proveit.numbers.multiplication.elim_one_right |
81 | instantiation | 86, 84, 85 | ⊢ |
| : , : , : |
82 | theorem | | ⊢ |
| proveit.numbers.number_sets.rational_numbers.int_within_rational |
83 | instantiation | 86, 87, 88 | ⊢ |
| : , : , : |
84 | theorem | | ⊢ |
| proveit.numbers.number_sets.complex_numbers.real_within_complex |
85 | instantiation | 89, 90, 91 | ⊢ |
| : , : , : |
86 | theorem | | ⊢ |
| proveit.logic.sets.inclusion.superset_membership_from_proper_subset |
87 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.nat_within_int |
88 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat1 |
89 | theorem | | ⊢ |
| proveit.logic.sets.inclusion.unfold_subset_eq |
90 | instantiation | 92, 93 | ⊢ |
| : , : |
91 | theorem | | ⊢ |
| proveit.physics.quantum.QPE._two_pow_t_is_nat_pos |
92 | theorem | | ⊢ |
| proveit.logic.sets.inclusion.relax_proper_subset |
93 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.nat_pos_within_real |
*equality replacement requirements |