| step type | requirements | statement |
0 | modus ponens | 1, 2 | ⊢ |
1 | instantiation | 3, 4 | ⊢ |
| : , : , : , : , : , : , : |
2 | generalization | 5 | ⊢ |
3 | theorem | | ⊢ |
| proveit.core_expr_types.lambda_maps.general_lambda_substitution |
4 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.posnat1 |
5 | instantiation | 6, 73, 59, 57, 7* | , ⊢ |
| : , : , : |
6 | theorem | | ⊢ |
| proveit.physics.quantum.QFT.invFT_on_matrix_elem |
7 | instantiation | 8, 9, 10, 11 | , ⊢ |
| : , : |
8 | theorem | | ⊢ |
| proveit.numbers.division.neg_frac_neg_numerator |
9 | instantiation | 23, 12, 13 | , ⊢ |
| : , : , : |
10 | instantiation | 74, 46, 14 | ⊢ |
| : , : , : |
11 | instantiation | 15, 16 | ⊢ |
| : |
12 | instantiation | 39, 26, 17 | , ⊢ |
| : , : |
13 | instantiation | 18, 19, 20 | , ⊢ |
| : , : , : |
14 | instantiation | 74, 52, 21 | ⊢ |
| : , : , : |
15 | theorem | | ⊢ |
| proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos |
16 | instantiation | 22, 71, 68 | ⊢ |
| : , : |
17 | instantiation | 23, 24, 25 | , ⊢ |
| : , : , : |
18 | axiom | | ⊢ |
| proveit.logic.equality.equals_transitivity |
19 | instantiation | 31, 76, 27, 32, 29, 33, 26, 40, 41, 35 | , ⊢ |
| : , : , : , : , : , : |
20 | instantiation | 31, 32, 71, 27, 33, 28, 29, 36, 37, 40, 41, 35 | , ⊢ |
| : , : , : , : , : , : |
21 | instantiation | 74, 55, 64 | ⊢ |
| : , : , : |
22 | theorem | | ⊢ |
| proveit.numbers.exponentiation.exp_natpos_closure |
23 | theorem | | ⊢ |
| proveit.logic.equality.sub_right_side_into |
24 | instantiation | 39, 30, 35 | , ⊢ |
| : , : |
25 | instantiation | 31, 32, 71, 76, 33, 34, 40, 41, 35 | , ⊢ |
| : , : , : , : , : , : |
26 | instantiation | 39, 36, 37 | ⊢ |
| : , : |
27 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat3 |
28 | instantiation | 42 | ⊢ |
| : , : |
29 | instantiation | 38 | ⊢ |
| : , : , : |
30 | instantiation | 39, 40, 41 | ⊢ |
| : , : |
31 | theorem | | ⊢ |
| proveit.numbers.multiplication.disassociation |
32 | axiom | | ⊢ |
| proveit.numbers.number_sets.natural_numbers.zero_in_nats |
33 | theorem | | ⊢ |
| proveit.core_expr_types.tuples.tuple_len_0_typical_eq |
34 | instantiation | 42 | ⊢ |
| : , : |
35 | instantiation | 74, 46, 43 | ⊢ |
| : , : , : |
36 | instantiation | 74, 46, 44 | ⊢ |
| : , : , : |
37 | instantiation | 74, 46, 45 | ⊢ |
| : , : , : |
38 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.tuple_len_3_typical_eq |
39 | theorem | | ⊢ |
| proveit.numbers.multiplication.mult_complex_closure_bin |
40 | theorem | | ⊢ |
| proveit.numbers.number_sets.complex_numbers.i_is_complex |
41 | instantiation | 74, 46, 47 | ⊢ |
| : , : , : |
42 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.tuple_len_2_typical_eq |
43 | instantiation | 74, 52, 48 | ⊢ |
| : , : , : |
44 | instantiation | 74, 52, 49 | ⊢ |
| : , : , : |
45 | instantiation | 74, 50, 51 | ⊢ |
| : , : , : |
46 | theorem | | ⊢ |
| proveit.numbers.number_sets.complex_numbers.real_within_complex |
47 | instantiation | 74, 52, 53 | ⊢ |
| : , : , : |
48 | instantiation | 74, 55, 54 | ⊢ |
| : , : , : |
49 | instantiation | 74, 55, 67 | ⊢ |
| : , : , : |
50 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.real_pos_within_real |
51 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.pi_is_real_pos |
52 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.rational_within_real |
53 | instantiation | 74, 55, 56 | ⊢ |
| : , : , : |
54 | instantiation | 74, 58, 57 | ⊢ |
| : , : , : |
55 | theorem | | ⊢ |
| proveit.numbers.number_sets.rational_numbers.int_within_rational |
56 | instantiation | 74, 58, 59 | ⊢ |
| : , : , : |
57 | assumption | | ⊢ |
58 | instantiation | 60, 61, 62 | ⊢ |
| : , : |
59 | assumption | | ⊢ |
60 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.int_interval_within_int |
61 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.zero_is_int |
62 | instantiation | 63, 64, 65 | ⊢ |
| : , : |
63 | theorem | | ⊢ |
| proveit.numbers.addition.add_int_closure_bin |
64 | instantiation | 66, 67, 68 | ⊢ |
| : , : |
65 | instantiation | 69, 70 | ⊢ |
| : |
66 | theorem | | ⊢ |
| proveit.numbers.exponentiation.exp_int_closure |
67 | instantiation | 74, 75, 71 | ⊢ |
| : , : , : |
68 | instantiation | 74, 72, 73 | ⊢ |
| : , : , : |
69 | theorem | | ⊢ |
| proveit.numbers.negation.int_closure |
70 | instantiation | 74, 75, 76 | ⊢ |
| : , : , : |
71 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat2 |
72 | theorem | | ⊢ |
| proveit.numbers.number_sets.natural_numbers.nat_pos_within_nat |
73 | axiom | | ⊢ |
| proveit.physics.quantum.QPE._t_in_natural_pos |
74 | theorem | | ⊢ |
| proveit.logic.sets.inclusion.superset_membership_from_proper_subset |
75 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.nat_within_int |
76 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat1 |
*equality replacement requirements |