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