| step type | requirements | statement |
0 | instantiation | 1, 2 | ⊢ |
| : , : |
1 | reference | 11 | ⊢ |
2 | instantiation | 3, 4, 5, 6 | ⊢ |
| : , : , : , : |
3 | theorem | | ⊢ |
| proveit.logic.equality.four_chain_transitivity |
4 | instantiation | 26, 61, 7, 8, 9* | ⊢ |
| : , : |
5 | instantiation | 10 | ⊢ |
| : |
6 | instantiation | 11, 12 | ⊢ |
| : , : |
7 | instantiation | 13, 57, 51 | ⊢ |
| : , : |
8 | instantiation | 14, 105, 15, 46, 16 | ⊢ |
| : , : |
9 | instantiation | 23, 17, 18 | ⊢ |
| : , : , : |
10 | axiom | | ⊢ |
| proveit.logic.equality.equals_reflexivity |
11 | theorem | | ⊢ |
| proveit.logic.equality.equals_reversal |
12 | instantiation | 21, 19 | ⊢ |
| : , : , : |
13 | theorem | | ⊢ |
| proveit.numbers.multiplication.mult_complex_closure_bin |
14 | theorem | | ⊢ |
| proveit.numbers.multiplication.mult_not_eq_zero |
15 | instantiation | 48 | ⊢ |
| : , : |
16 | instantiation | 103, 54, 20 | ⊢ |
| : , : , : |
17 | instantiation | 21, 22 | ⊢ |
| : , : , : |
18 | instantiation | 23, 24, 25 | ⊢ |
| : , : , : |
19 | instantiation | 26, 61, 51, 32, 27* | ⊢ |
| : , : |
20 | instantiation | 103, 64, 28 | ⊢ |
| : , : , : |
21 | axiom | | ⊢ |
| proveit.logic.equality.substitution |
22 | instantiation | 29, 57, 51, 30, 31, 32, 33* | ⊢ |
| : , : , : |
23 | axiom | | ⊢ |
| proveit.logic.equality.equals_transitivity |
24 | instantiation | 34, 95, 105, 36, 38, 37, 61, 39, 41 | ⊢ |
| : , : , : , : , : , : |
25 | instantiation | 35, 36, 105, 37, 38, 39, 41 | ⊢ |
| : , : , : , : |
26 | theorem | | ⊢ |
| proveit.numbers.division.div_as_mult |
27 | instantiation | 40, 41 | ⊢ |
| : |
28 | instantiation | 103, 75, 42 | ⊢ |
| : , : , : |
29 | theorem | | ⊢ |
| proveit.numbers.exponentiation.real_power_of_product |
30 | instantiation | 43, 71 | ⊢ |
| : |
31 | instantiation | 44, 88 | ⊢ |
| : |
32 | instantiation | 44, 53 | ⊢ |
| : |
33 | instantiation | 45, 46, 86, 47* | ⊢ |
| : , : |
34 | theorem | | ⊢ |
| proveit.numbers.multiplication.disassociation |
35 | theorem | | ⊢ |
| proveit.numbers.multiplication.elim_one_any |
36 | axiom | | ⊢ |
| proveit.numbers.number_sets.natural_numbers.zero_in_nats |
37 | theorem | | ⊢ |
| proveit.core_expr_types.tuples.tuple_len_0_typical_eq |
38 | instantiation | 48 | ⊢ |
| : , : |
39 | instantiation | 103, 70, 49 | ⊢ |
| : , : , : |
40 | theorem | | ⊢ |
| proveit.numbers.multiplication.elim_one_left |
41 | instantiation | 50, 51, 52 | ⊢ |
| : , : |
42 | instantiation | 103, 85, 53 | ⊢ |
| : , : , : |
43 | theorem | | ⊢ |
| proveit.numbers.negation.real_closure |
44 | theorem | | ⊢ |
| proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos |
45 | theorem | | ⊢ |
| proveit.numbers.exponentiation.neg_power_as_div |
46 | instantiation | 103, 54, 55 | ⊢ |
| : , : , : |
47 | instantiation | 56, 57 | ⊢ |
| : |
48 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.tuple_len_2_typical_eq |
49 | instantiation | 103, 82, 58 | ⊢ |
| : , : , : |
50 | theorem | | ⊢ |
| proveit.numbers.exponentiation.exp_complex_closure |
51 | instantiation | 103, 70, 59 | ⊢ |
| : , : , : |
52 | instantiation | 60, 61 | ⊢ |
| : |
53 | instantiation | 62, 81, 63 | ⊢ |
| : |
54 | theorem | | ⊢ |
| proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero |
55 | instantiation | 103, 64, 65 | ⊢ |
| : , : , : |
56 | theorem | | ⊢ |
| proveit.numbers.exponentiation.complex_x_to_first_power_is_x |
57 | instantiation | 103, 70, 66 | ⊢ |
| : , : , : |
58 | instantiation | 103, 67, 68 | ⊢ |
| : , : , : |
59 | instantiation | 103, 82, 69 | ⊢ |
| : , : , : |
60 | theorem | | ⊢ |
| proveit.numbers.negation.complex_closure |
61 | instantiation | 103, 70, 71 | ⊢ |
| : , : , : |
62 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.pos_int_is_natural_pos |
63 | instantiation | 72, 73, 74 | ⊢ |
| : , : , : |
64 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero |
65 | instantiation | 103, 75, 76 | ⊢ |
| : , : , : |
66 | instantiation | 103, 82, 77 | ⊢ |
| : , : , : |
67 | theorem | | ⊢ |
| proveit.numbers.number_sets.rational_numbers.rational_pos_within_rational |
68 | instantiation | 78, 79, 80 | ⊢ |
| : , : |
69 | instantiation | 103, 91, 81 | ⊢ |
| : , : , : |
70 | theorem | | ⊢ |
| proveit.numbers.number_sets.complex_numbers.real_within_complex |
71 | instantiation | 103, 82, 83 | ⊢ |
| : , : , : |
72 | theorem | | ⊢ |
| proveit.numbers.ordering.transitivity_less_less_eq |
73 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.less_0_1 |
74 | instantiation | 84, 93, 94, 90 | ⊢ |
| : , : , : |
75 | theorem | | ⊢ |
| proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero |
76 | instantiation | 103, 85, 88 | ⊢ |
| : , : , : |
77 | instantiation | 103, 91, 102 | ⊢ |
| : , : , : |
78 | theorem | | ⊢ |
| proveit.numbers.division.div_rational_pos_closure |
79 | instantiation | 103, 87, 86 | ⊢ |
| : , : , : |
80 | instantiation | 103, 87, 88 | ⊢ |
| : , : , : |
81 | instantiation | 103, 89, 90 | ⊢ |
| : , : , : |
82 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.rational_within_real |
83 | instantiation | 103, 91, 93 | ⊢ |
| : , : , : |
84 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.interval_lower_bound |
85 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int |
86 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.posnat1 |
87 | theorem | | ⊢ |
| proveit.numbers.number_sets.rational_numbers.nat_pos_within_rational_pos |
88 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.posnat2 |
89 | instantiation | 92, 93, 94 | ⊢ |
| : , : |
90 | assumption | | ⊢ |
91 | theorem | | ⊢ |
| proveit.numbers.number_sets.rational_numbers.int_within_rational |
92 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.int_interval_within_int |
93 | instantiation | 103, 104, 95 | ⊢ |
| : , : , : |
94 | instantiation | 96, 97, 98 | ⊢ |
| : , : |
95 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat1 |
96 | theorem | | ⊢ |
| proveit.numbers.addition.add_int_closure_bin |
97 | instantiation | 103, 99, 100 | ⊢ |
| : , : , : |
98 | instantiation | 101, 102 | ⊢ |
| : |
99 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.nat_pos_within_int |
100 | theorem | | ⊢ |
| proveit.physics.quantum.QPE._two_pow_t_minus_one_is_nat_pos |
101 | theorem | | ⊢ |
| proveit.numbers.negation.int_closure |
102 | instantiation | 103, 104, 105 | ⊢ |
| : , : , : |
103 | theorem | | ⊢ |
| proveit.logic.sets.inclusion.superset_membership_from_proper_subset |
104 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.nat_within_int |
105 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat2 |
*equality replacement requirements |