| step type | requirements | statement |
0 | instantiation | 1, 2, 3 | ⊢ |
| : , : , : |
1 | reference | 6 | ⊢ |
2 | instantiation | 11, 4 | ⊢ |
| : , : , : |
3 | instantiation | 13, 5 | ⊢ |
| : , : |
4 | instantiation | 6, 7, 8 | ⊢ |
| : , : , : |
5 | instantiation | 9, 33, 10 | ⊢ |
| : , : |
6 | axiom | | ⊢ |
| proveit.logic.equality.equals_transitivity |
7 | instantiation | 11, 12 | ⊢ |
| : , : , : |
8 | instantiation | 13, 14 | ⊢ |
| : , : |
9 | theorem | | ⊢ |
| proveit.numbers.multiplication.mult_neg_right |
10 | instantiation | 15, 21, 35, 16 | ⊢ |
| : , : |
11 | axiom | | ⊢ |
| proveit.logic.equality.substitution |
12 | instantiation | 17, 50, 18, 51, 52, 19, 59, 60, 54, 21 | ⊢ |
| : , : , : , : , : , : |
13 | theorem | | ⊢ |
| proveit.logic.equality.equals_reversal |
14 | instantiation | 20, 33, 21, 22, 23, 24*, 25* | ⊢ |
| : , : , : , : |
15 | theorem | | ⊢ |
| proveit.numbers.division.div_complex_closure |
16 | instantiation | 26, 67 | ⊢ |
| : |
17 | theorem | | ⊢ |
| proveit.numbers.multiplication.association |
18 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat3 |
19 | instantiation | 27 | ⊢ |
| : , : , : |
20 | theorem | | ⊢ |
| proveit.numbers.division.prod_of_fracs |
21 | instantiation | 74, 64, 28 | ⊢ |
| : , : , : |
22 | instantiation | 74, 30, 29 | ⊢ |
| : , : , : |
23 | instantiation | 74, 30, 31 | ⊢ |
| : , : , : |
24 | instantiation | 32, 33 | ⊢ |
| : |
25 | instantiation | 34, 35 | ⊢ |
| : |
26 | theorem | | ⊢ |
| proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos |
27 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.tuple_len_3_typical_eq |
28 | instantiation | 74, 68, 36 | ⊢ |
| : , : , : |
29 | instantiation | 74, 38, 37 | ⊢ |
| : , : , : |
30 | theorem | | ⊢ |
| proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero |
31 | instantiation | 74, 38, 39 | ⊢ |
| : , : , : |
32 | theorem | | ⊢ |
| proveit.numbers.division.frac_one_denom |
33 | instantiation | 40, 41, 42 | ⊢ |
| : , : , : |
34 | theorem | | ⊢ |
| proveit.numbers.multiplication.elim_one_left |
35 | instantiation | 74, 64, 43 | ⊢ |
| : , : , : |
36 | instantiation | 74, 72, 44 | ⊢ |
| : , : , : |
37 | instantiation | 74, 46, 45 | ⊢ |
| : , : , : |
38 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero |
39 | instantiation | 74, 46, 47 | ⊢ |
| : , : , : |
40 | theorem | | ⊢ |
| proveit.logic.equality.sub_right_side_into |
41 | instantiation | 58, 48, 54 | ⊢ |
| : , : |
42 | instantiation | 49, 50, 76, 51, 52, 53, 59, 60, 54 | ⊢ |
| : , : , : , : , : , : |
43 | instantiation | 74, 68, 55 | ⊢ |
| : , : , : |
44 | assumption | | ⊢ |
45 | instantiation | 74, 57, 56 | ⊢ |
| : , : , : |
46 | theorem | | ⊢ |
| proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero |
47 | instantiation | 74, 57, 67 | ⊢ |
| : , : , : |
48 | instantiation | 58, 59, 60 | ⊢ |
| : , : |
49 | theorem | | ⊢ |
| proveit.numbers.multiplication.disassociation |
50 | axiom | | ⊢ |
| proveit.numbers.number_sets.natural_numbers.zero_in_nats |
51 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat1 |
52 | theorem | | ⊢ |
| proveit.core_expr_types.tuples.tuple_len_0_typical_eq |
53 | instantiation | 61 | ⊢ |
| : , : |
54 | theorem | | ⊢ |
| proveit.numbers.number_sets.complex_numbers.i_is_complex |
55 | instantiation | 74, 72, 62 | ⊢ |
| : , : , : |
56 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.posnat1 |
57 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int |
58 | theorem | | ⊢ |
| proveit.numbers.multiplication.mult_complex_closure_bin |
59 | instantiation | 74, 64, 63 | ⊢ |
| : , : , : |
60 | instantiation | 74, 64, 65 | ⊢ |
| : , : , : |
61 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.tuple_len_2_typical_eq |
62 | instantiation | 74, 66, 67 | ⊢ |
| : , : , : |
63 | instantiation | 74, 68, 69 | ⊢ |
| : , : , : |
64 | theorem | | ⊢ |
| proveit.numbers.number_sets.complex_numbers.real_within_complex |
65 | instantiation | 74, 70, 71 | ⊢ |
| : , : , : |
66 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.nat_pos_within_int |
67 | theorem | | ⊢ |
| proveit.physics.quantum.QPE._two_pow_t_is_nat_pos |
68 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.rational_within_real |
69 | instantiation | 74, 72, 73 | ⊢ |
| : , : , : |
70 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.real_pos_within_real |
71 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.pi_is_real_pos |
72 | theorem | | ⊢ |
| proveit.numbers.number_sets.rational_numbers.int_within_rational |
73 | instantiation | 74, 75, 76 | ⊢ |
| : , : , : |
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.nat2 |
*equality replacement requirements |