| step type | requirements | statement |
0 | instantiation | 1, 2, 3 | ⊢ |
| : , : , : |
1 | reference | 9 | ⊢ |
2 | instantiation | 9, 4, 5 | ⊢ |
| : , : , : |
3 | instantiation | 6, 20, 87, 79, 22, 7, 27, 50, 32, 8* | ⊢ |
| : , : , : , : , : , : |
4 | instantiation | 9, 10, 11 | ⊢ |
| : , : , : |
5 | instantiation | 12, 20, 79, 87, 22, 13, 36, 27, 50, 32, 14 | ⊢ |
| : , : , : , : , : , : , : , : |
6 | theorem | | ⊢ |
| proveit.numbers.addition.association |
7 | instantiation | 33 | ⊢ |
| : , : |
8 | instantiation | 15, 16, 17 | ⊢ |
| : , : , : |
9 | axiom | | ⊢ |
| proveit.logic.equality.equals_transitivity |
10 | instantiation | 19, 20, 87, 79, 22, 21, 36, 27, 18 | ⊢ |
| : , : , : , : , : , : |
11 | instantiation | 19, 87, 29, 20, 21, 30, 22, 36, 27, 31, 50, 32 | ⊢ |
| : , : , : , : , : , : |
12 | theorem | | ⊢ |
| proveit.numbers.addition.subtraction.add_cancel_general |
13 | instantiation | 33 | ⊢ |
| : , : |
14 | instantiation | 23 | ⊢ |
| : |
15 | theorem | | ⊢ |
| proveit.logic.equality.sub_right_side_into |
16 | instantiation | 24, 50, 60, 25 | ⊢ |
| : , : , : |
17 | instantiation | 26, 50, 27 | ⊢ |
| : , : |
18 | instantiation | 28, 29, 30, 31, 50, 32 | ⊢ |
| : , : |
19 | theorem | | ⊢ |
| proveit.numbers.addition.disassociation |
20 | axiom | | ⊢ |
| proveit.numbers.number_sets.natural_numbers.zero_in_nats |
21 | instantiation | 33 | ⊢ |
| : , : |
22 | theorem | | ⊢ |
| proveit.core_expr_types.tuples.tuple_len_0_typical_eq |
23 | axiom | | ⊢ |
| proveit.logic.equality.equals_reflexivity |
24 | theorem | | ⊢ |
| proveit.numbers.addition.subtraction.subtract_from_add_reversed |
25 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.add_1_1 |
26 | theorem | | ⊢ |
| proveit.numbers.addition.commutation |
27 | instantiation | 85, 65, 34 | ⊢ |
| : , : , : |
28 | theorem | | ⊢ |
| proveit.numbers.addition.add_complex_closure |
29 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat3 |
30 | instantiation | 35 | ⊢ |
| : , : , : |
31 | instantiation | 37, 36 | ⊢ |
| : |
32 | instantiation | 37, 38 | ⊢ |
| : |
33 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.tuple_len_2_typical_eq |
34 | instantiation | 85, 72, 39 | ⊢ |
| : , : , : |
35 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.tuple_len_3_typical_eq |
36 | instantiation | 40, 41, 42 | ⊢ |
| : , : |
37 | theorem | | ⊢ |
| proveit.numbers.negation.complex_closure |
38 | instantiation | 85, 65, 43 | ⊢ |
| : , : , : |
39 | instantiation | 85, 80, 78 | ⊢ |
| : , : , : |
40 | theorem | | ⊢ |
| proveit.numbers.multiplication.mult_complex_closure_bin |
41 | instantiation | 44, 50, 45, 46 | ⊢ |
| : , : |
42 | instantiation | 85, 65, 47 | ⊢ |
| : , : , : |
43 | instantiation | 85, 72, 48 | ⊢ |
| : , : , : |
44 | theorem | | ⊢ |
| proveit.numbers.division.div_complex_closure |
45 | instantiation | 49, 60, 50 | ⊢ |
| : , : |
46 | instantiation | 51, 52, 53 | ⊢ |
| : , : , : |
47 | instantiation | 85, 72, 54 | ⊢ |
| : , : , : |
48 | instantiation | 85, 80, 55 | ⊢ |
| : , : , : |
49 | theorem | | ⊢ |
| proveit.numbers.exponentiation.exp_complex_closure |
50 | instantiation | 85, 65, 56 | ⊢ |
| : , : , : |
51 | theorem | | ⊢ |
| proveit.logic.equality.sub_left_side_into |
52 | instantiation | 57, 58 | ⊢ |
| : |
53 | instantiation | 59, 60 | ⊢ |
| : |
54 | instantiation | 85, 80, 61 | ⊢ |
| : , : , : |
55 | instantiation | 85, 62, 63 | ⊢ |
| : , : , : |
56 | instantiation | 85, 72, 64 | ⊢ |
| : , : , : |
57 | theorem | | ⊢ |
| proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos |
58 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.posnat2 |
59 | theorem | | ⊢ |
| proveit.numbers.exponentiation.complex_x_to_first_power_is_x |
60 | instantiation | 85, 65, 66 | ⊢ |
| : , : , : |
61 | instantiation | 67, 84, 68 | ⊢ |
| : , : |
62 | instantiation | 69, 71, 70 | ⊢ |
| : , : |
63 | assumption | | ⊢ |
64 | instantiation | 85, 80, 71 | ⊢ |
| : , : , : |
65 | theorem | | ⊢ |
| proveit.numbers.number_sets.complex_numbers.real_within_complex |
66 | instantiation | 85, 72, 73 | ⊢ |
| : , : , : |
67 | theorem | | ⊢ |
| proveit.numbers.exponentiation.exp_int_closure |
68 | instantiation | 85, 74, 75 | ⊢ |
| : , : , : |
69 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.int_interval_within_int |
70 | instantiation | 76, 77, 78 | ⊢ |
| : , : |
71 | instantiation | 85, 86, 79 | ⊢ |
| : , : , : |
72 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.rational_within_real |
73 | instantiation | 85, 80, 84 | ⊢ |
| : , : , : |
74 | theorem | | ⊢ |
| proveit.numbers.number_sets.natural_numbers.nat_pos_within_nat |
75 | axiom | | ⊢ |
| proveit.physics.quantum.QPE._t_in_natural_pos |
76 | theorem | | ⊢ |
| proveit.numbers.addition.add_int_closure_bin |
77 | instantiation | 85, 81, 82 | ⊢ |
| : , : , : |
78 | instantiation | 83, 84 | ⊢ |
| : |
79 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat1 |
80 | theorem | | ⊢ |
| proveit.numbers.number_sets.rational_numbers.int_within_rational |
81 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.nat_pos_within_int |
82 | theorem | | ⊢ |
| proveit.physics.quantum.QPE._two_pow_t_minus_one_is_nat_pos |
83 | theorem | | ⊢ |
| proveit.numbers.negation.int_closure |
84 | instantiation | 85, 86, 87 | ⊢ |
| : , : , : |
85 | theorem | | ⊢ |
| proveit.logic.sets.inclusion.superset_membership_from_proper_subset |
86 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.nat_within_int |
87 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat2 |
*equality replacement requirements |