| step type | requirements | statement |
0 | instantiation | 1, 2 | ⊢ |
| : , : , : |
1 | reference | 12 | ⊢ |
2 | instantiation | 7, 3, 4 | ⊢ |
| : , : , : |
3 | instantiation | 12, 5 | ⊢ |
| : , : , : |
4 | instantiation | 14, 6 | ⊢ |
| : , : |
5 | instantiation | 7, 8, 9 | ⊢ |
| : , : , : |
6 | instantiation | 10, 34, 11 | ⊢ |
| : , : |
7 | axiom | | ⊢ |
| proveit.logic.equality.equals_transitivity |
8 | instantiation | 12, 13 | ⊢ |
| : , : , : |
9 | instantiation | 14, 15 | ⊢ |
| : , : |
10 | theorem | | ⊢ |
| proveit.numbers.multiplication.mult_neg_right |
11 | instantiation | 16, 22, 36, 17 | ⊢ |
| : , : |
12 | axiom | | ⊢ |
| proveit.logic.equality.substitution |
13 | instantiation | 18, 51, 19, 52, 53, 20, 60, 61, 55, 22 | ⊢ |
| : , : , : , : , : , : |
14 | theorem | | ⊢ |
| proveit.logic.equality.equals_reversal |
15 | instantiation | 21, 34, 22, 23, 24, 25*, 26* | ⊢ |
| : , : , : , : |
16 | theorem | | ⊢ |
| proveit.numbers.division.div_complex_closure |
17 | instantiation | 27, 68 | ⊢ |
| : |
18 | theorem | | ⊢ |
| proveit.numbers.multiplication.association |
19 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat3 |
20 | instantiation | 28 | ⊢ |
| : , : , : |
21 | theorem | | ⊢ |
| proveit.numbers.division.prod_of_fracs |
22 | instantiation | 75, 65, 29 | ⊢ |
| : , : , : |
23 | instantiation | 75, 31, 30 | ⊢ |
| : , : , : |
24 | instantiation | 75, 31, 32 | ⊢ |
| : , : , : |
25 | instantiation | 33, 34 | ⊢ |
| : |
26 | instantiation | 35, 36 | ⊢ |
| : |
27 | theorem | | ⊢ |
| proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos |
28 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.tuple_len_3_typical_eq |
29 | instantiation | 75, 69, 37 | ⊢ |
| : , : , : |
30 | instantiation | 75, 39, 38 | ⊢ |
| : , : , : |
31 | theorem | | ⊢ |
| proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero |
32 | instantiation | 75, 39, 40 | ⊢ |
| : , : , : |
33 | theorem | | ⊢ |
| proveit.numbers.division.frac_one_denom |
34 | instantiation | 41, 42, 43 | ⊢ |
| : , : , : |
35 | theorem | | ⊢ |
| proveit.numbers.multiplication.elim_one_left |
36 | instantiation | 75, 65, 44 | ⊢ |
| : , : , : |
37 | instantiation | 75, 73, 45 | ⊢ |
| : , : , : |
38 | instantiation | 75, 47, 46 | ⊢ |
| : , : , : |
39 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero |
40 | instantiation | 75, 47, 48 | ⊢ |
| : , : , : |
41 | theorem | | ⊢ |
| proveit.logic.equality.sub_right_side_into |
42 | instantiation | 59, 49, 55 | ⊢ |
| : , : |
43 | instantiation | 50, 51, 77, 52, 53, 54, 60, 61, 55 | ⊢ |
| : , : , : , : , : , : |
44 | instantiation | 75, 69, 56 | ⊢ |
| : , : , : |
45 | assumption | | ⊢ |
46 | instantiation | 75, 58, 57 | ⊢ |
| : , : , : |
47 | theorem | | ⊢ |
| proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero |
48 | instantiation | 75, 58, 68 | ⊢ |
| : , : , : |
49 | instantiation | 59, 60, 61 | ⊢ |
| : , : |
50 | theorem | | ⊢ |
| proveit.numbers.multiplication.disassociation |
51 | axiom | | ⊢ |
| proveit.numbers.number_sets.natural_numbers.zero_in_nats |
52 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat1 |
53 | theorem | | ⊢ |
| proveit.core_expr_types.tuples.tuple_len_0_typical_eq |
54 | instantiation | 62 | ⊢ |
| : , : |
55 | theorem | | ⊢ |
| proveit.numbers.number_sets.complex_numbers.i_is_complex |
56 | instantiation | 75, 73, 63 | ⊢ |
| : , : , : |
57 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.posnat1 |
58 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int |
59 | theorem | | ⊢ |
| proveit.numbers.multiplication.mult_complex_closure_bin |
60 | instantiation | 75, 65, 64 | ⊢ |
| : , : , : |
61 | instantiation | 75, 65, 66 | ⊢ |
| : , : , : |
62 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.tuple_len_2_typical_eq |
63 | instantiation | 75, 67, 68 | ⊢ |
| : , : , : |
64 | instantiation | 75, 69, 70 | ⊢ |
| : , : , : |
65 | theorem | | ⊢ |
| proveit.numbers.number_sets.complex_numbers.real_within_complex |
66 | instantiation | 75, 71, 72 | ⊢ |
| : , : , : |
67 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.nat_pos_within_int |
68 | theorem | | ⊢ |
| proveit.physics.quantum.QPE._two_pow_t_is_nat_pos |
69 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.rational_within_real |
70 | instantiation | 75, 73, 74 | ⊢ |
| : , : , : |
71 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.real_pos_within_real |
72 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.pi_is_real_pos |
73 | theorem | | ⊢ |
| proveit.numbers.number_sets.rational_numbers.int_within_rational |
74 | instantiation | 75, 76, 77 | ⊢ |
| : , : , : |
75 | theorem | | ⊢ |
| proveit.logic.sets.inclusion.superset_membership_from_proper_subset |
76 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.nat_within_int |
77 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat2 |
*equality replacement requirements |