| step type | requirements | statement |
0 | instantiation | 1, 2 | , ⊢  |
| : , : , :  |
1 | reference | 5 | ⊢  |
2 | instantiation | 33, 3, 4 | , ⊢  |
| : , : , :  |
3 | instantiation | 5, 6 | , ⊢  |
| : , : , :  |
4 | instantiation | 7, 8 | , ⊢  |
| : , :  |
5 | axiom | | ⊢  |
| proveit.logic.equality.substitution |
6 | instantiation | 33, 9, 10 | , ⊢  |
| : , : , :  |
7 | theorem | | ⊢  |
| proveit.logic.equality.equals_reversal |
8 | instantiation | 11, 12, 13, 14 | , ⊢  |
| : , :  |
9 | instantiation | 15, 16, 39, 42, 17, 43, 50, 51, 46, 21, 47 | , ⊢  |
| : , : , : , : , : , : , :  |
10 | instantiation | 18, 42, 19, 39, 43, 20, 50, 51, 46, 47, 21 | , ⊢  |
| : , : , : , : , : , :  |
11 | instantiation | 22, 48 | ⊢  |
| :  |
12 | instantiation | 65, 55, 23 | ⊢  |
| : , : , :  |
13 | instantiation | 24, 25, 26 | ⊢  |
| : , : , :  |
14 | instantiation | 27, 28 | ⊢  |
| :  |
15 | theorem | | ⊢  |
| proveit.numbers.multiplication.rightward_commutation |
16 | theorem | | ⊢  |
| proveit.numbers.numerals.decimals.nat3 |
17 | instantiation | 29 | ⊢  |
| : , : , :  |
18 | theorem | | ⊢  |
| proveit.numbers.multiplication.association |
19 | theorem | | ⊢  |
| proveit.numbers.numerals.decimals.nat4 |
20 | instantiation | 30 | ⊢  |
| : , : , : , :  |
21 | instantiation | 65, 55, 31 | ⊢  |
| : , : , :  |
22 | theorem | | ⊢  |
| proveit.numbers.exponentiation.int_exp_of_exp |
23 | instantiation | 65, 60, 37 | ⊢  |
| : , : , :  |
24 | theorem | | ⊢  |
| proveit.logic.equality.sub_right_side_into |
25 | instantiation | 49, 40, 32 | ⊢  |
| : , :  |
26 | instantiation | 33, 34, 35 | ⊢  |
| : , : , :  |
27 | theorem | | ⊢  |
| proveit.numbers.number_sets.real_numbers.nonzero_if_in_real_nonzero |
28 | instantiation | 65, 36, 37 | ⊢  |
| : , : , :  |
29 | theorem | | ⊢  |
| proveit.numbers.numerals.decimals.tuple_len_3_typical_eq |
30 | theorem | | ⊢  |
| proveit.numbers.numerals.decimals.tuple_len_4_typical_eq |
31 | instantiation | 65, 58, 38 | ⊢  |
| : , : , :  |
32 | instantiation | 49, 46, 47 | ⊢  |
| : , :  |
33 | axiom | | ⊢  |
| proveit.logic.equality.equals_transitivity |
34 | instantiation | 41, 39, 67, 42, 45, 43, 40, 46, 47 | ⊢  |
| : , : , : , : , : , :  |
35 | instantiation | 41, 42, 67, 43, 44, 45, 50, 51, 46, 47 | ⊢  |
| : , : , : , : , : , :  |
36 | theorem | | ⊢  |
| proveit.numbers.number_sets.real_numbers.real_pos_within_real_nonzero |
37 | theorem | | ⊢  |
| proveit.numbers.number_sets.real_numbers.e_is_real_pos |
38 | instantiation | 65, 63, 48 | ⊢  |
| : , : , :  |
39 | theorem | | ⊢  |
| proveit.numbers.numerals.decimals.nat1 |
40 | instantiation | 49, 50, 51 | ⊢  |
| : , :  |
41 | theorem | | ⊢  |
| proveit.numbers.multiplication.disassociation |
42 | axiom | | ⊢  |
| proveit.numbers.number_sets.natural_numbers.zero_in_nats |
43 | theorem | | ⊢  |
| proveit.core_expr_types.tuples.tuple_len_0_typical_eq |
44 | instantiation | 52 | ⊢  |
| : , :  |
45 | instantiation | 52 | ⊢  |
| : , :  |
46 | theorem | | ⊢  |
| proveit.numbers.number_sets.complex_numbers.i_is_complex |
47 | instantiation | 65, 55, 53 | ⊢  |
| : , : , :  |
48 | assumption | | ⊢  |
49 | theorem | | ⊢  |
| proveit.numbers.multiplication.mult_complex_closure_bin |
50 | instantiation | 65, 55, 54 | ⊢  |
| : , : , :  |
51 | instantiation | 65, 55, 56 | ⊢  |
| : , : , :  |
52 | theorem | | ⊢  |
| proveit.numbers.numerals.decimals.tuple_len_2_typical_eq |
53 | instantiation | 65, 58, 57 | ⊢  |
| : , : , :  |
54 | instantiation | 65, 58, 59 | ⊢  |
| : , : , :  |
55 | theorem | | ⊢  |
| proveit.numbers.number_sets.complex_numbers.real_within_complex |
56 | instantiation | 65, 60, 61 | ⊢  |
| : , : , :  |
57 | instantiation | 65, 63, 62 | ⊢  |
| : , : , :  |
58 | theorem | | ⊢  |
| proveit.numbers.number_sets.real_numbers.rational_within_real |
59 | instantiation | 65, 63, 64 | ⊢  |
| : , : , :  |
60 | theorem | | ⊢  |
| proveit.numbers.number_sets.real_numbers.real_pos_within_real |
61 | theorem | | ⊢  |
| proveit.numbers.number_sets.real_numbers.pi_is_real_pos |
62 | assumption | | ⊢  |
63 | theorem | | ⊢  |
| proveit.numbers.number_sets.rational_numbers.int_within_rational |
64 | instantiation | 65, 66, 67 | ⊢  |
| : , : , :  |
65 | theorem | | ⊢  |
| proveit.logic.sets.inclusion.superset_membership_from_proper_subset |
66 | theorem | | ⊢  |
| proveit.numbers.number_sets.integers.nat_within_int |
67 | theorem | | ⊢  |
| proveit.numbers.numerals.decimals.nat2 |