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