| step type | requirements | statement |
0 | instantiation | 1, 2 | ⊢ |
| : , : , : |
1 | reference | 32 | ⊢ |
2 | instantiation | 6, 3, 4 | ⊢ |
| : , : , : |
3 | instantiation | 32, 5 | ⊢ |
| : , : , : |
4 | instantiation | 6, 7, 8 | ⊢ |
| : , : , : |
5 | instantiation | 32, 9 | ⊢ |
| : , : , : |
6 | axiom | | ⊢ |
| proveit.logic.equality.equals_transitivity |
7 | instantiation | 10, 13, 88, 85, 15, 11, 16, 39, 55 | ⊢ |
| : , : , : , : , : , : |
8 | instantiation | 12, 85, 88, 13, 14, 15, 16, 39, 55, 17* | ⊢ |
| : , : , : , : , : , : |
9 | instantiation | 18, 19, 20, 21 | ⊢ |
| : , : , : , : |
10 | theorem | | ⊢ |
| proveit.numbers.addition.disassociation |
11 | instantiation | 22 | ⊢ |
| : , : |
12 | theorem | | ⊢ |
| proveit.numbers.addition.association |
13 | axiom | | ⊢ |
| proveit.numbers.number_sets.natural_numbers.zero_in_nats |
14 | instantiation | 22 | ⊢ |
| : , : |
15 | theorem | | ⊢ |
| proveit.core_expr_types.tuples.tuple_len_0_typical_eq |
16 | instantiation | 23, 24, 25 | ⊢ |
| : , : |
17 | instantiation | 26, 27, 28 | ⊢ |
| : , : , : |
18 | theorem | | ⊢ |
| proveit.logic.equality.four_chain_transitivity |
19 | instantiation | 32, 29 | ⊢ |
| : , : , : |
20 | instantiation | 30, 31 | ⊢ |
| : , : |
21 | instantiation | 32, 33 | ⊢ |
| : , : , : |
22 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.tuple_len_2_typical_eq |
23 | theorem | | ⊢ |
| proveit.numbers.multiplication.mult_complex_closure_bin |
24 | instantiation | 34, 55, 35, 36 | ⊢ |
| : , : |
25 | instantiation | 48, 61, 41 | ⊢ |
| : , : |
26 | theorem | | ⊢ |
| proveit.logic.equality.sub_right_side_into |
27 | instantiation | 37, 55, 61, 38 | ⊢ |
| : , : , : |
28 | instantiation | 40, 55, 39 | ⊢ |
| : , : |
29 | instantiation | 40, 41, 42 | ⊢ |
| : , : |
30 | theorem | | ⊢ |
| proveit.logic.equality.equals_reversal |
31 | instantiation | 43, 61, 44, 53, 50 | ⊢ |
| : , : , : |
32 | axiom | | ⊢ |
| proveit.logic.equality.substitution |
33 | instantiation | 45, 46, 47 | ⊢ |
| : , : |
34 | theorem | | ⊢ |
| proveit.numbers.division.div_complex_closure |
35 | instantiation | 48, 61, 55 | ⊢ |
| : , : |
36 | instantiation | 49, 50, 51 | ⊢ |
| : , : , : |
37 | theorem | | ⊢ |
| proveit.numbers.addition.subtraction.subtract_from_add_reversed |
38 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.add_1_1 |
39 | instantiation | 86, 69, 52 | ⊢ |
| : , : , : |
40 | theorem | | ⊢ |
| proveit.numbers.addition.commutation |
41 | instantiation | 86, 69, 53 | ⊢ |
| : , : , : |
42 | instantiation | 54, 55 | ⊢ |
| : |
43 | theorem | | ⊢ |
| proveit.numbers.exponentiation.product_of_real_powers |
44 | instantiation | 56, 66 | ⊢ |
| : |
45 | theorem | | ⊢ |
| proveit.numbers.exponentiation.neg_power_as_div |
46 | instantiation | 86, 57, 58 | ⊢ |
| : , : , : |
47 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.posnat1 |
48 | theorem | | ⊢ |
| proveit.numbers.exponentiation.exp_complex_closure |
49 | theorem | | ⊢ |
| proveit.logic.equality.sub_left_side_into |
50 | instantiation | 59, 82 | ⊢ |
| : |
51 | instantiation | 60, 61 | ⊢ |
| : |
52 | instantiation | 86, 77, 62 | ⊢ |
| : , : , : |
53 | instantiation | 63, 64, 65 | ⊢ |
| : , : , : |
54 | theorem | | ⊢ |
| proveit.numbers.negation.complex_closure |
55 | instantiation | 86, 69, 66 | ⊢ |
| : , : , : |
56 | theorem | | ⊢ |
| proveit.numbers.negation.real_closure |
57 | theorem | | ⊢ |
| proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero |
58 | instantiation | 86, 67, 68 | ⊢ |
| : , : , : |
59 | theorem | | ⊢ |
| proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos |
60 | theorem | | ⊢ |
| proveit.numbers.exponentiation.complex_x_to_first_power_is_x |
61 | instantiation | 86, 69, 70 | ⊢ |
| : , : , : |
62 | instantiation | 86, 83, 71 | ⊢ |
| : , : , : |
63 | theorem | | ⊢ |
| proveit.logic.sets.inclusion.unfold_subset_eq |
64 | instantiation | 72, 73 | ⊢ |
| : , : |
65 | axiom | | ⊢ |
| proveit.physics.quantum.QPE._t_in_natural_pos |
66 | instantiation | 86, 77, 74 | ⊢ |
| : , : , : |
67 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero |
68 | instantiation | 86, 75, 76 | ⊢ |
| : , : , : |
69 | theorem | | ⊢ |
| proveit.numbers.number_sets.complex_numbers.real_within_complex |
70 | instantiation | 86, 77, 78 | ⊢ |
| : , : , : |
71 | instantiation | 79, 84 | ⊢ |
| : |
72 | theorem | | ⊢ |
| proveit.logic.sets.inclusion.relax_proper_subset |
73 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.nat_pos_within_real |
74 | instantiation | 86, 83, 80 | ⊢ |
| : , : , : |
75 | theorem | | ⊢ |
| proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero |
76 | instantiation | 86, 81, 82 | ⊢ |
| : , : , : |
77 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.rational_within_real |
78 | instantiation | 86, 83, 84 | ⊢ |
| : , : , : |
79 | theorem | | ⊢ |
| proveit.numbers.negation.int_closure |
80 | instantiation | 86, 87, 85 | ⊢ |
| : , : , : |
81 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int |
82 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.posnat2 |
83 | theorem | | ⊢ |
| proveit.numbers.number_sets.rational_numbers.int_within_rational |
84 | instantiation | 86, 87, 88 | ⊢ |
| : , : , : |
85 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat1 |
86 | theorem | | ⊢ |
| proveit.logic.sets.inclusion.superset_membership_from_proper_subset |
87 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.nat_within_int |
88 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat2 |
*equality replacement requirements |