| step type | requirements | statement |
0 | instantiation | 1, 2, 3 | ⊢ |
| : , : , : |
1 | reference | 4 | ⊢ |
2 | instantiation | 4, 5, 6 | ⊢ |
| : , : , : |
3 | instantiation | 7, 31, 57, 85, 8* | ⊢ |
| : , : |
4 | theorem | | ⊢ |
| proveit.logic.equality.sub_left_side_into |
5 | instantiation | 9, 46, 10, 72, 11, 12, 13*, 17* | ⊢ |
| : , : , : |
6 | instantiation | 14, 24, 99, 26, 38, 31, 27 | ⊢ |
| : , : , : , : , : , : , : |
7 | theorem | | ⊢ |
| proveit.numbers.division.div_as_mult |
8 | instantiation | 15, 16, 17 | ⊢ |
| : , : , : |
9 | theorem | | ⊢ |
| proveit.numbers.multiplication.weak_bound_via_right_factor_bound |
10 | instantiation | 18, 50, 41 | ⊢ |
| : , : |
11 | instantiation | 19, 20, 21 | ⊢ |
| : , : , : |
12 | instantiation | 65, 22 | ⊢ |
| : , : |
13 | instantiation | 23, 99, 102, 24, 25, 26, 31, 38, 27 | ⊢ |
| : , : , : , : , : , : |
14 | theorem | | ⊢ |
| proveit.numbers.multiplication.leftward_commutation |
15 | axiom | | ⊢ |
| proveit.logic.equality.equals_transitivity |
16 | instantiation | 28, 29 | ⊢ |
| : , : , : |
17 | instantiation | 30, 31, 32 | ⊢ |
| : , : |
18 | theorem | | ⊢ |
| proveit.numbers.multiplication.mult_real_closure_bin |
19 | theorem | | ⊢ |
| proveit.logic.equality.sub_right_side_into |
20 | instantiation | 33, 34, 35 | ⊢ |
| : , : |
21 | instantiation | 36, 93, 37, 38, 78, 39* | ⊢ |
| : , : |
22 | instantiation | 40, 59 | ⊢ |
| : |
23 | theorem | | ⊢ |
| proveit.numbers.multiplication.disassociation |
24 | axiom | | ⊢ |
| proveit.numbers.number_sets.natural_numbers.zero_in_nats |
25 | instantiation | 49 | ⊢ |
| : , : |
26 | theorem | | ⊢ |
| proveit.core_expr_types.tuples.tuple_len_0_typical_eq |
27 | instantiation | 100, 86, 41 | ⊢ |
| : , : , : |
28 | axiom | | ⊢ |
| proveit.logic.equality.substitution |
29 | instantiation | 42, 43, 44, 45* | ⊢ |
| : , : |
30 | theorem | | ⊢ |
| proveit.numbers.multiplication.commutation |
31 | instantiation | 100, 86, 46 | ⊢ |
| : , : , : |
32 | instantiation | 100, 86, 72 | ⊢ |
| : , : , : |
33 | theorem | | ⊢ |
| proveit.numbers.absolute_value.weak_upper_bound |
34 | instantiation | 47, 61, 72, 62 | ⊢ |
| : , : , : |
35 | instantiation | 65, 48 | ⊢ |
| : , : |
36 | theorem | | ⊢ |
| proveit.numbers.absolute_value.abs_prod |
37 | instantiation | 49 | ⊢ |
| : , : |
38 | instantiation | 100, 86, 50 | ⊢ |
| : , : , : |
39 | instantiation | 51, 52 | ⊢ |
| : |
40 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.positive_if_in_real_pos |
41 | instantiation | 100, 58, 53 | ⊢ |
| : , : , : |
42 | theorem | | ⊢ |
| proveit.numbers.exponentiation.neg_power_as_div |
43 | instantiation | 100, 54, 55 | ⊢ |
| : , : , : |
44 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.posnat1 |
45 | instantiation | 56, 57 | ⊢ |
| : |
46 | instantiation | 100, 58, 59 | ⊢ |
| : , : , : |
47 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.interval_co_lower_bound |
48 | instantiation | 60, 61, 72, 62 | ⊢ |
| : , : , : |
49 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.tuple_len_2_typical_eq |
50 | instantiation | 63, 64, 76 | ⊢ |
| : , : , : |
51 | theorem | | ⊢ |
| proveit.numbers.absolute_value.abs_non_neg_elim |
52 | instantiation | 65, 66 | ⊢ |
| : , : |
53 | instantiation | 67, 68 | ⊢ |
| : |
54 | theorem | | ⊢ |
| proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero |
55 | instantiation | 100, 69, 70 | ⊢ |
| : , : , : |
56 | theorem | | ⊢ |
| proveit.numbers.exponentiation.complex_x_to_first_power_is_x |
57 | instantiation | 100, 86, 84 | ⊢ |
| : , : , : |
58 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.real_pos_within_real |
59 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.pi_is_real_pos |
60 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.interval_co_upper_bound |
61 | instantiation | 71, 72 | ⊢ |
| : |
62 | theorem | | ⊢ |
| proveit.physics.quantum.QPE._scaled_delta_b_round_in_interval |
63 | theorem | | ⊢ |
| proveit.logic.sets.inclusion.unfold_subset_eq |
64 | instantiation | 73, 74 | ⊢ |
| : , : |
65 | theorem | | ⊢ |
| proveit.numbers.ordering.relax_less |
66 | instantiation | 75, 76 | ⊢ |
| : |
67 | theorem | | ⊢ |
| proveit.numbers.absolute_value.abs_nonzero_closure |
68 | instantiation | 77, 78, 79 | ⊢ |
| : |
69 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero |
70 | instantiation | 100, 80, 81 | ⊢ |
| : , : , : |
71 | theorem | | ⊢ |
| proveit.numbers.negation.real_closure |
72 | instantiation | 82, 83, 84, 85 | ⊢ |
| : , : |
73 | theorem | | ⊢ |
| proveit.logic.sets.inclusion.relax_proper_subset |
74 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.nat_pos_within_real |
75 | theorem | | ⊢ |
| proveit.numbers.number_sets.natural_numbers.natural_pos_is_pos |
76 | theorem | | ⊢ |
| proveit.physics.quantum.QPE._two_pow_t_is_nat_pos |
77 | theorem | | ⊢ |
| proveit.numbers.number_sets.complex_numbers.nonzero_complex_is_complex_nonzero |
78 | instantiation | 100, 86, 87 | ⊢ |
| : , : , : |
79 | assumption | | ⊢ |
80 | theorem | | ⊢ |
| proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero |
81 | instantiation | 100, 88, 93 | ⊢ |
| : , : , : |
82 | theorem | | ⊢ |
| proveit.numbers.division.div_real_closure |
83 | instantiation | 100, 90, 89 | ⊢ |
| : , : , : |
84 | instantiation | 100, 90, 91 | ⊢ |
| : , : , : |
85 | instantiation | 92, 93 | ⊢ |
| : |
86 | theorem | | ⊢ |
| proveit.numbers.number_sets.complex_numbers.real_within_complex |
87 | instantiation | 94, 95 | ⊢ |
| : |
88 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int |
89 | instantiation | 100, 97, 96 | ⊢ |
| : , : , : |
90 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.rational_within_real |
91 | instantiation | 100, 97, 98 | ⊢ |
| : , : , : |
92 | theorem | | ⊢ |
| proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos |
93 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.posnat2 |
94 | theorem | | ⊢ |
| proveit.physics.quantum.QPE._delta_b_is_real |
95 | theorem | | ⊢ |
| proveit.physics.quantum.QPE._best_round_is_int |
96 | instantiation | 100, 101, 99 | ⊢ |
| : , : , : |
97 | theorem | | ⊢ |
| proveit.numbers.number_sets.rational_numbers.int_within_rational |
98 | instantiation | 100, 101, 102 | ⊢ |
| : , : , : |
99 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat1 |
100 | theorem | | ⊢ |
| proveit.logic.sets.inclusion.superset_membership_from_proper_subset |
101 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.nat_within_int |
102 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat2 |
*equality replacement requirements |