| step type | requirements | statement |
0 | instantiation | 1, 2 | ⊢ |
| : , : , : |
1 | reference | 46 | ⊢ |
2 | instantiation | 46, 3 | ⊢ |
| : , : , : |
3 | instantiation | 4, 5, 6, 7 | ⊢ |
| : , : , : , : |
4 | theorem | | ⊢ |
| proveit.logic.equality.four_chain_transitivity |
5 | instantiation | 46, 8 | ⊢ |
| : , : , : |
6 | instantiation | 10, 9 | ⊢ |
| : , : |
7 | instantiation | 10, 11 | ⊢ |
| : , : |
8 | instantiation | 46, 12 | ⊢ |
| : , : , : |
9 | instantiation | 13, 14, 15 | ⊢ |
| : , : |
10 | theorem | | ⊢ |
| proveit.logic.equality.equals_reversal |
11 | instantiation | 46, 16 | ⊢ |
| : , : , : |
12 | instantiation | 17, 52, 18, 19, 20* | ⊢ |
| : , : |
13 | theorem | | ⊢ |
| proveit.numbers.addition.commutation |
14 | instantiation | 21, 22 | ⊢ |
| : |
15 | instantiation | 102, 72, 23 | ⊢ |
| : , : , : |
16 | instantiation | 24, 25, 26 | ⊢ |
| : , : , : |
17 | theorem | | ⊢ |
| proveit.numbers.division.div_as_mult |
18 | instantiation | 102, 72, 27 | ⊢ |
| : , : , : |
19 | instantiation | 42, 39 | ⊢ |
| : |
20 | instantiation | 28, 29, 73, 30, 31, 32* | ⊢ |
| : , : , : |
21 | theorem | | ⊢ |
| proveit.numbers.negation.complex_closure |
22 | instantiation | 102, 72, 33 | ⊢ |
| : , : , : |
23 | instantiation | 34, 35 | ⊢ |
| : |
24 | axiom | | ⊢ |
| proveit.logic.equality.equals_transitivity |
25 | instantiation | 46, 36 | ⊢ |
| : , : , : |
26 | instantiation | 37, 49, 69, 50, 51, 58, 52, 53, 38* | ⊢ |
| : , : , : , : , : |
27 | instantiation | 78, 79, 39 | ⊢ |
| : , : , : |
28 | theorem | | ⊢ |
| proveit.numbers.exponentiation.real_power_of_real_power |
29 | instantiation | 102, 72, 40 | ⊢ |
| : , : , : |
30 | instantiation | 102, 70, 41 | ⊢ |
| : , : , : |
31 | instantiation | 42, 96 | ⊢ |
| : |
32 | instantiation | 43, 66, 58, 44* | ⊢ |
| : , : |
33 | instantiation | 45, 61, 62 | ⊢ |
| : , : |
34 | theorem | | ⊢ |
| proveit.physics.quantum.QPE._delta_b_is_real |
35 | theorem | | ⊢ |
| proveit.physics.quantum.QPE._best_floor_is_int |
36 | instantiation | 46, 47 | ⊢ |
| : , : , : |
37 | theorem | | ⊢ |
| proveit.numbers.multiplication.mult_neg_any |
38 | instantiation | 48, 49, 69, 50, 51, 52, 53 | ⊢ |
| : , : , : , : |
39 | theorem | | ⊢ |
| proveit.physics.quantum.QPE._two_pow_t_is_nat_pos |
40 | instantiation | 102, 70, 54 | ⊢ |
| : , : , : |
41 | instantiation | 102, 77, 55 | ⊢ |
| : , : , : |
42 | theorem | | ⊢ |
| proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos |
43 | theorem | | ⊢ |
| proveit.numbers.multiplication.mult_neg_right |
44 | instantiation | 56, 66 | ⊢ |
| : |
45 | theorem | | ⊢ |
| proveit.numbers.multiplication.mult_real_closure_bin |
46 | axiom | | ⊢ |
| proveit.logic.equality.substitution |
47 | instantiation | 57, 58, 66, 59* | ⊢ |
| : , : |
48 | theorem | | ⊢ |
| proveit.numbers.multiplication.elim_one_any |
49 | axiom | | ⊢ |
| proveit.numbers.number_sets.natural_numbers.zero_in_nats |
50 | theorem | | ⊢ |
| proveit.core_expr_types.tuples.tuple_len_0_typical_eq |
51 | instantiation | 60 | ⊢ |
| : , : |
52 | instantiation | 102, 72, 61 | ⊢ |
| : , : , : |
53 | instantiation | 102, 72, 62 | ⊢ |
| : , : , : |
54 | instantiation | 102, 77, 63 | ⊢ |
| : , : , : |
55 | instantiation | 98, 94 | ⊢ |
| : |
56 | theorem | | ⊢ |
| proveit.numbers.multiplication.elim_one_right |
57 | theorem | | ⊢ |
| proveit.numbers.multiplication.mult_neg_left |
58 | instantiation | 102, 72, 64 | ⊢ |
| : , : , : |
59 | instantiation | 65, 66 | ⊢ |
| : |
60 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.tuple_len_2_typical_eq |
61 | instantiation | 102, 70, 67 | ⊢ |
| : , : , : |
62 | instantiation | 102, 70, 68 | ⊢ |
| : , : , : |
63 | instantiation | 102, 100, 69 | ⊢ |
| : , : , : |
64 | instantiation | 102, 70, 71 | ⊢ |
| : , : , : |
65 | theorem | | ⊢ |
| proveit.numbers.multiplication.elim_one_left |
66 | instantiation | 102, 72, 73 | ⊢ |
| : , : , : |
67 | instantiation | 102, 77, 74 | ⊢ |
| : , : , : |
68 | instantiation | 102, 75, 76 | ⊢ |
| : , : , : |
69 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat2 |
70 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.rational_within_real |
71 | instantiation | 102, 77, 94 | ⊢ |
| : , : , : |
72 | theorem | | ⊢ |
| proveit.numbers.number_sets.complex_numbers.real_within_complex |
73 | instantiation | 78, 79, 97 | ⊢ |
| : , : , : |
74 | instantiation | 102, 80, 81 | ⊢ |
| : , : , : |
75 | theorem | | ⊢ |
| proveit.numbers.number_sets.rational_numbers.rational_nonzero_within_rational |
76 | instantiation | 82, 83, 84 | ⊢ |
| : , : |
77 | theorem | | ⊢ |
| proveit.numbers.number_sets.rational_numbers.int_within_rational |
78 | theorem | | ⊢ |
| proveit.logic.sets.inclusion.unfold_subset_eq |
79 | instantiation | 85, 86 | ⊢ |
| : , : |
80 | instantiation | 87, 88, 99 | ⊢ |
| : , : |
81 | assumption | | ⊢ |
82 | theorem | | ⊢ |
| proveit.numbers.exponentiation.exp_rational_nonzero_closure |
83 | instantiation | 102, 89, 90 | ⊢ |
| : , : , : |
84 | instantiation | 98, 91 | ⊢ |
| : |
85 | theorem | | ⊢ |
| proveit.logic.sets.inclusion.relax_proper_subset |
86 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.nat_pos_within_real |
87 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.int_interval_within_int |
88 | instantiation | 92, 93, 94 | ⊢ |
| : , : |
89 | theorem | | ⊢ |
| proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero |
90 | instantiation | 102, 95, 96 | ⊢ |
| : , : , : |
91 | instantiation | 102, 103, 97 | ⊢ |
| : , : , : |
92 | theorem | | ⊢ |
| proveit.numbers.addition.add_int_closure_bin |
93 | instantiation | 98, 99 | ⊢ |
| : |
94 | instantiation | 102, 100, 101 | ⊢ |
| : , : , : |
95 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int |
96 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.posnat2 |
97 | axiom | | ⊢ |
| proveit.physics.quantum.QPE._t_in_natural_pos |
98 | theorem | | ⊢ |
| proveit.numbers.negation.int_closure |
99 | instantiation | 102, 103, 104 | ⊢ |
| : , : , : |
100 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.nat_within_int |
101 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat1 |
102 | theorem | | ⊢ |
| proveit.logic.sets.inclusion.superset_membership_from_proper_subset |
103 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.nat_pos_within_int |
104 | theorem | | ⊢ |
| proveit.physics.quantum.QPE._two_pow_t_minus_one_is_nat_pos |
*equality replacement requirements |