| step type | requirements | statement |
0 | instantiation | 1, 2, 3 | ⊢ |
| : , : |
1 | axiom | | ⊢ |
| proveit.linear_algebra.scalar_multiplication.scalar_mult_extends_number_mult |
2 | instantiation | 27, 70, 4, 5 | ⊢ |
| : , : |
3 | instantiation | 27, 70, 6, 7 | ⊢ |
| : , : |
4 | instantiation | 11, 85, 8 | ⊢ |
| : , : |
5 | instantiation | 12, 9, 10 | ⊢ |
| : , : , : |
6 | instantiation | 11, 85, 21 | ⊢ |
| : , : |
7 | instantiation | 12, 13, 14 | ⊢ |
| : , : , : |
8 | instantiation | 68, 15, 16 | ⊢ |
| : , : |
9 | instantiation | 19, 92, 17 | ⊢ |
| : , : |
10 | instantiation | 64, 18 | ⊢ |
| : , : , : |
11 | theorem | | ⊢ |
| proveit.numbers.exponentiation.exp_complex_closure |
12 | theorem | | ⊢ |
| proveit.logic.equality.sub_left_side_into |
13 | instantiation | 19, 92, 20 | ⊢ |
| : , : |
14 | instantiation | 64, 41 | ⊢ |
| : , : , : |
15 | instantiation | 27, 58, 85, 48 | ⊢ |
| : , : |
16 | instantiation | 42, 21 | ⊢ |
| : |
17 | instantiation | 22, 23, 92 | ⊢ |
| : , : |
18 | instantiation | 54, 24, 25 | ⊢ |
| : , : , : |
19 | theorem | | ⊢ |
| proveit.numbers.exponentiation.exp_rational_non_zero__not_zero |
20 | instantiation | 114, 26, 67 | ⊢ |
| : , : , : |
21 | instantiation | 27, 69, 85, 48 | ⊢ |
| : , : |
22 | theorem | | ⊢ |
| proveit.numbers.division.div_rational_nonzero_closure |
23 | instantiation | 114, 100, 28 | ⊢ |
| : , : , : |
24 | instantiation | 54, 29, 30 | ⊢ |
| : , : , : |
25 | instantiation | 54, 31, 32 | ⊢ |
| : , : , : |
26 | theorem | | ⊢ |
| proveit.numbers.number_sets.rational_numbers.rational_pos_within_rational_nonzero |
27 | theorem | | ⊢ |
| proveit.numbers.division.div_complex_closure |
28 | instantiation | 114, 108, 111 | ⊢ |
| : , : , : |
29 | instantiation | 64, 33 | ⊢ |
| : , : , : |
30 | instantiation | 64, 34 | ⊢ |
| : , : , : |
31 | instantiation | 35, 60, 116, 104, 62, 36, 43, 73, 37 | ⊢ |
| : , : , : , : , : , : |
32 | instantiation | 38, 43, 73, 39 | ⊢ |
| : , : , : |
33 | instantiation | 47, 58, 85, 48, 40* | ⊢ |
| : , : |
34 | instantiation | 64, 41 | ⊢ |
| : , : , : |
35 | theorem | | ⊢ |
| proveit.numbers.addition.disassociation |
36 | instantiation | 71 | ⊢ |
| : , : |
37 | instantiation | 42, 43 | ⊢ |
| : |
38 | theorem | | ⊢ |
| proveit.numbers.addition.subtraction.add_cancel_triple_13 |
39 | instantiation | 44 | ⊢ |
| : |
40 | instantiation | 54, 45, 46 | ⊢ |
| : , : , : |
41 | instantiation | 47, 69, 85, 48, 49* | ⊢ |
| : , : |
42 | theorem | | ⊢ |
| proveit.numbers.negation.complex_closure |
43 | instantiation | 114, 93, 50 | ⊢ |
| : , : , : |
44 | axiom | | ⊢ |
| proveit.logic.equality.equals_reflexivity |
45 | instantiation | 64, 65 | ⊢ |
| : , : , : |
46 | instantiation | 54, 51, 52 | ⊢ |
| : , : , : |
47 | theorem | | ⊢ |
| proveit.numbers.division.div_as_mult |
48 | instantiation | 53, 113 | ⊢ |
| : |
49 | instantiation | 54, 55, 56 | ⊢ |
| : , : , : |
50 | instantiation | 114, 102, 57 | ⊢ |
| : , : , : |
51 | instantiation | 66, 58, 73 | ⊢ |
| : , : |
52 | instantiation | 59, 104, 116, 60, 61, 62, 73, 69, 70, 63* | ⊢ |
| : , : , : , : , : , : |
53 | theorem | | ⊢ |
| proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos |
54 | axiom | | ⊢ |
| proveit.logic.equality.equals_transitivity |
55 | instantiation | 64, 65 | ⊢ |
| : , : , : |
56 | instantiation | 66, 69, 73 | ⊢ |
| : , : |
57 | instantiation | 114, 98, 67 | ⊢ |
| : , : , : |
58 | instantiation | 68, 69, 70 | ⊢ |
| : , : |
59 | theorem | | ⊢ |
| proveit.numbers.multiplication.distribute_through_sum |
60 | axiom | | ⊢ |
| proveit.numbers.number_sets.natural_numbers.zero_in_nats |
61 | instantiation | 71 | ⊢ |
| : , : |
62 | theorem | | ⊢ |
| proveit.core_expr_types.tuples.tuple_len_0_typical_eq |
63 | instantiation | 72, 73 | ⊢ |
| : |
64 | axiom | | ⊢ |
| proveit.logic.equality.substitution |
65 | instantiation | 74, 75, 111, 76* | ⊢ |
| : , : |
66 | theorem | | ⊢ |
| proveit.numbers.multiplication.commutation |
67 | instantiation | 77, 99, 78 | ⊢ |
| : , : |
68 | theorem | | ⊢ |
| proveit.numbers.addition.add_complex_closure_bin |
69 | instantiation | 114, 93, 79 | ⊢ |
| : , : , : |
70 | instantiation | 114, 93, 80 | ⊢ |
| : , : , : |
71 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.tuple_len_2_typical_eq |
72 | theorem | | ⊢ |
| proveit.numbers.multiplication.elim_one_right |
73 | instantiation | 114, 93, 81 | ⊢ |
| : , : , : |
74 | theorem | | ⊢ |
| proveit.numbers.exponentiation.neg_power_as_div |
75 | instantiation | 114, 82, 83 | ⊢ |
| : , : , : |
76 | instantiation | 84, 85 | ⊢ |
| : |
77 | theorem | | ⊢ |
| proveit.numbers.multiplication.mult_rational_pos_closure_bin |
78 | instantiation | 114, 112, 88 | ⊢ |
| : , : , : |
79 | instantiation | 86, 87, 88 | ⊢ |
| : , : , : |
80 | instantiation | 114, 102, 89 | ⊢ |
| : , : , : |
81 | instantiation | 114, 102, 90 | ⊢ |
| : , : , : |
82 | theorem | | ⊢ |
| proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero |
83 | instantiation | 114, 91, 92 | ⊢ |
| : , : , : |
84 | theorem | | ⊢ |
| proveit.numbers.exponentiation.complex_x_to_first_power_is_x |
85 | instantiation | 114, 93, 94 | ⊢ |
| : , : , : |
86 | theorem | | ⊢ |
| proveit.logic.sets.inclusion.unfold_subset_eq |
87 | instantiation | 95, 96 | ⊢ |
| : , : |
88 | assumption | | ⊢ |
89 | instantiation | 114, 109, 97 | ⊢ |
| : , : , : |
90 | instantiation | 114, 98, 99 | ⊢ |
| : , : , : |
91 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero |
92 | instantiation | 114, 100, 101 | ⊢ |
| : , : , : |
93 | theorem | | ⊢ |
| proveit.numbers.number_sets.complex_numbers.real_within_complex |
94 | instantiation | 114, 102, 103 | ⊢ |
| : , : , : |
95 | theorem | | ⊢ |
| proveit.logic.sets.inclusion.relax_proper_subset |
96 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.nat_pos_within_real |
97 | instantiation | 114, 115, 104 | ⊢ |
| : , : , : |
98 | theorem | | ⊢ |
| proveit.numbers.number_sets.rational_numbers.rational_pos_within_rational |
99 | instantiation | 105, 106, 107 | ⊢ |
| : , : |
100 | theorem | | ⊢ |
| proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero |
101 | instantiation | 114, 108, 113 | ⊢ |
| : , : , : |
102 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.rational_within_real |
103 | instantiation | 114, 109, 110 | ⊢ |
| : , : , : |
104 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat1 |
105 | theorem | | ⊢ |
| proveit.numbers.division.div_rational_pos_closure |
106 | instantiation | 114, 112, 111 | ⊢ |
| : , : , : |
107 | instantiation | 114, 112, 113 | ⊢ |
| : , : , : |
108 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int |
109 | theorem | | ⊢ |
| proveit.numbers.number_sets.rational_numbers.int_within_rational |
110 | instantiation | 114, 115, 116 | ⊢ |
| : , : , : |
111 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.posnat1 |
112 | theorem | | ⊢ |
| proveit.numbers.number_sets.rational_numbers.nat_pos_within_rational_pos |
113 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.posnat2 |
114 | theorem | | ⊢ |
| proveit.logic.sets.inclusion.superset_membership_from_proper_subset |
115 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.nat_within_int |
116 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat2 |
*equality replacement requirements |