| step type | requirements | statement |
0 | instantiation | 1, 2, 3 | , ⊢ |
| : , : , : |
1 | reference | 32 | ⊢ |
2 | instantiation | 4, 5 | , ⊢ |
| : , : , : |
3 | instantiation | 6, 7 | , ⊢ |
| : , : |
4 | axiom | | ⊢ |
| proveit.logic.equality.substitution |
5 | instantiation | 32, 8, 9 | , ⊢ |
| : , : , : |
6 | theorem | | ⊢ |
| proveit.logic.equality.equals_reversal |
7 | instantiation | 10, 11, 12, 13 | , ⊢ |
| : , : |
8 | instantiation | 14, 15, 38, 41, 16, 42, 49, 50, 45, 20, 46 | , ⊢ |
| : , : , : , : , : , : , : |
9 | instantiation | 17, 41, 18, 38, 42, 19, 49, 50, 45, 46, 20 | , ⊢ |
| : , : , : , : , : , : |
10 | instantiation | 21, 47 | ⊢ |
| : |
11 | instantiation | 64, 54, 22 | ⊢ |
| : , : , : |
12 | instantiation | 23, 24, 25 | ⊢ |
| : , : , : |
13 | instantiation | 26, 27 | ⊢ |
| : |
14 | theorem | | ⊢ |
| proveit.numbers.multiplication.rightward_commutation |
15 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat3 |
16 | instantiation | 28 | ⊢ |
| : , : , : |
17 | theorem | | ⊢ |
| proveit.numbers.multiplication.association |
18 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat4 |
19 | instantiation | 29 | ⊢ |
| : , : , : , : |
20 | instantiation | 64, 54, 30 | ⊢ |
| : , : , : |
21 | theorem | | ⊢ |
| proveit.numbers.exponentiation.int_exp_of_exp |
22 | instantiation | 64, 59, 36 | ⊢ |
| : , : , : |
23 | theorem | | ⊢ |
| proveit.logic.equality.sub_right_side_into |
24 | instantiation | 48, 39, 31 | ⊢ |
| : , : |
25 | instantiation | 32, 33, 34 | ⊢ |
| : , : , : |
26 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.nonzero_if_in_real_nonzero |
27 | instantiation | 64, 35, 36 | ⊢ |
| : , : , : |
28 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.tuple_len_3_typical_eq |
29 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.tuple_len_4_typical_eq |
30 | instantiation | 64, 57, 37 | ⊢ |
| : , : , : |
31 | instantiation | 48, 45, 46 | ⊢ |
| : , : |
32 | axiom | | ⊢ |
| proveit.logic.equality.equals_transitivity |
33 | instantiation | 40, 38, 66, 41, 44, 42, 39, 45, 46 | ⊢ |
| : , : , : , : , : , : |
34 | instantiation | 40, 41, 66, 42, 43, 44, 49, 50, 45, 46 | ⊢ |
| : , : , : , : , : , : |
35 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.real_pos_within_real_nonzero |
36 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.e_is_real_pos |
37 | instantiation | 64, 62, 47 | ⊢ |
| : , : , : |
38 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat1 |
39 | instantiation | 48, 49, 50 | ⊢ |
| : , : |
40 | theorem | | ⊢ |
| proveit.numbers.multiplication.disassociation |
41 | axiom | | ⊢ |
| proveit.numbers.number_sets.natural_numbers.zero_in_nats |
42 | theorem | | ⊢ |
| proveit.core_expr_types.tuples.tuple_len_0_typical_eq |
43 | instantiation | 51 | ⊢ |
| : , : |
44 | instantiation | 51 | ⊢ |
| : , : |
45 | theorem | | ⊢ |
| proveit.numbers.number_sets.complex_numbers.i_is_complex |
46 | instantiation | 64, 54, 52 | ⊢ |
| : , : , : |
47 | assumption | | ⊢ |
48 | theorem | | ⊢ |
| proveit.numbers.multiplication.mult_complex_closure_bin |
49 | instantiation | 64, 54, 53 | ⊢ |
| : , : , : |
50 | instantiation | 64, 54, 55 | ⊢ |
| : , : , : |
51 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.tuple_len_2_typical_eq |
52 | instantiation | 64, 57, 56 | ⊢ |
| : , : , : |
53 | instantiation | 64, 57, 58 | ⊢ |
| : , : , : |
54 | theorem | | ⊢ |
| proveit.numbers.number_sets.complex_numbers.real_within_complex |
55 | instantiation | 64, 59, 60 | ⊢ |
| : , : , : |
56 | instantiation | 64, 62, 61 | ⊢ |
| : , : , : |
57 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.rational_within_real |
58 | instantiation | 64, 62, 63 | ⊢ |
| : , : , : |
59 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.real_pos_within_real |
60 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.pi_is_real_pos |
61 | assumption | | ⊢ |
62 | theorem | | ⊢ |
| proveit.numbers.number_sets.rational_numbers.int_within_rational |
63 | instantiation | 64, 65, 66 | ⊢ |
| : , : , : |
64 | theorem | | ⊢ |
| proveit.logic.sets.inclusion.superset_membership_from_proper_subset |
65 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.nat_within_int |
66 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat2 |