| step type | requirements | statement |
0 | instantiation | 1, 2, 3 | ⊢ |
| : , : , : |
1 | reference | 33 | ⊢ |
2 | instantiation | 4, 114, 5, 8, 6, 9, 62, 12, 13, 14 | ⊢ |
| : , : , : , : , : , : |
3 | instantiation | 7, 8, 87, 9, 10, 11, 62, 12, 13, 14, 15* | ⊢ |
| : , : , : , : , : , : |
4 | theorem | | ⊢ |
| proveit.numbers.multiplication.disassociation |
5 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat3 |
6 | instantiation | 16 | ⊢ |
| : , : , : |
7 | theorem | | ⊢ |
| proveit.numbers.multiplication.association |
8 | axiom | | ⊢ |
| proveit.numbers.number_sets.natural_numbers.zero_in_nats |
9 | theorem | | ⊢ |
| proveit.core_expr_types.tuples.tuple_len_0_typical_eq |
10 | instantiation | 55 | ⊢ |
| : , : |
11 | instantiation | 55 | ⊢ |
| : , : |
12 | instantiation | 17, 47, 57, 18 | ⊢ |
| : , : |
13 | instantiation | 115, 79, 85 | ⊢ |
| : , : , : |
14 | instantiation | 19, 20, 21 | ⊢ |
| : , : |
15 | instantiation | 22, 62, 47, 23, 24, 25*, 26* | ⊢ |
| : , : , : , : |
16 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.tuple_len_3_typical_eq |
17 | theorem | | ⊢ |
| proveit.numbers.division.div_complex_closure |
18 | instantiation | 27, 67 | ⊢ |
| : |
19 | theorem | | ⊢ |
| proveit.numbers.exponentiation.exp_complex_closure |
20 | instantiation | 115, 79, 28 | ⊢ |
| : , : , : |
21 | instantiation | 115, 79, 29 | ⊢ |
| : , : , : |
22 | theorem | | ⊢ |
| proveit.numbers.division.prod_of_fracs |
23 | instantiation | 115, 58, 30 | ⊢ |
| : , : , : |
24 | instantiation | 115, 58, 31 | ⊢ |
| : , : , : |
25 | instantiation | 32, 62 | ⊢ |
| : |
26 | instantiation | 33, 34, 35 | ⊢ |
| : , : , : |
27 | theorem | | ⊢ |
| proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos |
28 | instantiation | 115, 36, 37 | ⊢ |
| : , : , : |
29 | instantiation | 115, 89, 38 | ⊢ |
| : , : , : |
30 | instantiation | 115, 69, 39 | ⊢ |
| : , : , : |
31 | instantiation | 115, 69, 40 | ⊢ |
| : , : , : |
32 | theorem | | ⊢ |
| proveit.numbers.division.frac_one_denom |
33 | axiom | | ⊢ |
| proveit.logic.equality.equals_transitivity |
34 | instantiation | 41, 87, 42, 43, 48, 44 | ⊢ |
| : , : , : , : |
35 | instantiation | 45, 46, 47, 48*, 49* | ⊢ |
| : , : , : |
36 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.real_nonneg_within_real |
37 | instantiation | 50, 51 | ⊢ |
| : |
38 | instantiation | 115, 91, 52 | ⊢ |
| : , : , : |
39 | instantiation | 115, 102, 53 | ⊢ |
| : , : , : |
40 | instantiation | 115, 102, 54 | ⊢ |
| : , : , : |
41 | axiom | | ⊢ |
| proveit.core_expr_types.operations.operands_substitution |
42 | instantiation | 55 | ⊢ |
| : , : |
43 | instantiation | 55 | ⊢ |
| : , : |
44 | instantiation | 56, 57 | ⊢ |
| : |
45 | theorem | | ⊢ |
| proveit.numbers.division.frac_cancel_left |
46 | instantiation | 115, 58, 59 | ⊢ |
| : , : , : |
47 | instantiation | 115, 79, 60 | ⊢ |
| : , : , : |
48 | instantiation | 61, 62 | ⊢ |
| : |
49 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.mult_2_2 |
50 | theorem | | ⊢ |
| proveit.numbers.absolute_value.abs_complex_closure |
51 | instantiation | 63, 64, 65 | ⊢ |
| : , : |
52 | instantiation | 111, 107 | ⊢ |
| : |
53 | instantiation | 115, 108, 66 | ⊢ |
| : , : , : |
54 | instantiation | 115, 108, 67 | ⊢ |
| : , : , : |
55 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.tuple_len_2_typical_eq |
56 | theorem | | ⊢ |
| proveit.numbers.multiplication.elim_one_left |
57 | instantiation | 115, 79, 68 | ⊢ |
| : , : , : |
58 | theorem | | ⊢ |
| proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero |
59 | instantiation | 115, 69, 98 | ⊢ |
| : , : , : |
60 | instantiation | 115, 89, 70 | ⊢ |
| : , : , : |
61 | theorem | | ⊢ |
| proveit.numbers.multiplication.elim_one_right |
62 | instantiation | 115, 79, 71 | ⊢ |
| : , : , : |
63 | theorem | | ⊢ |
| proveit.numbers.addition.add_complex_closure_bin |
64 | instantiation | 115, 79, 72 | ⊢ |
| : , : , : |
65 | instantiation | 73, 74 | ⊢ |
| : |
66 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.posnat1 |
67 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.posnat4 |
68 | instantiation | 115, 89, 75 | ⊢ |
| : , : , : |
69 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero |
70 | instantiation | 115, 91, 107 | ⊢ |
| : , : , : |
71 | instantiation | 115, 89, 76 | ⊢ |
| : , : , : |
72 | instantiation | 77, 78 | ⊢ |
| : |
73 | theorem | | ⊢ |
| proveit.numbers.negation.complex_closure |
74 | instantiation | 115, 79, 80 | ⊢ |
| : , : , : |
75 | instantiation | 115, 91, 81 | ⊢ |
| : , : , : |
76 | instantiation | 115, 91, 82 | ⊢ |
| : , : , : |
77 | theorem | | ⊢ |
| proveit.physics.quantum.QPE._delta_b_is_real |
78 | theorem | | ⊢ |
| proveit.physics.quantum.QPE._best_floor_is_int |
79 | theorem | | ⊢ |
| proveit.numbers.number_sets.complex_numbers.real_within_complex |
80 | instantiation | 83, 84, 85 | ⊢ |
| : , : |
81 | instantiation | 115, 113, 86 | ⊢ |
| : , : , : |
82 | instantiation | 115, 113, 87 | ⊢ |
| : , : , : |
83 | theorem | | ⊢ |
| proveit.numbers.multiplication.mult_real_closure_bin |
84 | instantiation | 115, 89, 88 | ⊢ |
| : , : , : |
85 | instantiation | 115, 89, 90 | ⊢ |
| : , : , : |
86 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat4 |
87 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat2 |
88 | instantiation | 115, 91, 92 | ⊢ |
| : , : , : |
89 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.rational_within_real |
90 | instantiation | 115, 93, 94 | ⊢ |
| : , : , : |
91 | theorem | | ⊢ |
| proveit.numbers.number_sets.rational_numbers.int_within_rational |
92 | instantiation | 115, 95, 96 | ⊢ |
| : , : , : |
93 | theorem | | ⊢ |
| proveit.numbers.number_sets.rational_numbers.rational_nonzero_within_rational |
94 | instantiation | 97, 98, 99 | ⊢ |
| : , : |
95 | instantiation | 100, 101, 112 | ⊢ |
| : , : |
96 | assumption | | ⊢ |
97 | theorem | | ⊢ |
| proveit.numbers.exponentiation.exp_rational_nonzero_closure |
98 | instantiation | 115, 102, 103 | ⊢ |
| : , : , : |
99 | instantiation | 111, 104 | ⊢ |
| : |
100 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.int_interval_within_int |
101 | instantiation | 105, 106, 107 | ⊢ |
| : , : |
102 | theorem | | ⊢ |
| proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero |
103 | instantiation | 115, 108, 109 | ⊢ |
| : , : , : |
104 | instantiation | 115, 116, 110 | ⊢ |
| : , : , : |
105 | theorem | | ⊢ |
| proveit.numbers.addition.add_int_closure_bin |
106 | instantiation | 111, 112 | ⊢ |
| : |
107 | instantiation | 115, 113, 114 | ⊢ |
| : , : , : |
108 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int |
109 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.posnat2 |
110 | axiom | | ⊢ |
| proveit.physics.quantum.QPE._t_in_natural_pos |
111 | theorem | | ⊢ |
| proveit.numbers.negation.int_closure |
112 | instantiation | 115, 116, 117 | ⊢ |
| : , : , : |
113 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.nat_within_int |
114 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat1 |
115 | theorem | | ⊢ |
| proveit.logic.sets.inclusion.superset_membership_from_proper_subset |
116 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.nat_pos_within_int |
117 | theorem | | ⊢ |
| proveit.physics.quantum.QPE._two_pow_t_minus_one_is_nat_pos |
*equality replacement requirements |