| step type | requirements | statement |
0 | instantiation | 1, 2, 3, 4 | , , ⊢  |
| : , : , : , :  |
1 | theorem | | ⊢  |
| proveit.logic.equality.four_chain_transitivity |
2 | instantiation | 36, 5 | , ⊢  |
| : , : , :  |
3 | instantiation | 36, 6 | , ⊢  |
| : , : , :  |
4 | instantiation | 20, 7 | , , ⊢  |
| : , :  |
5 | instantiation | 67, 8, 9 | , ⊢  |
| : , : , :  |
6 | instantiation | 67, 10, 11 | , ⊢  |
| : , : , :  |
7 | instantiation | 12, 13, 14, 59, 15, 16 | , , ⊢  |
| : , : , :  |
8 | instantiation | 36, 17 | , ⊢  |
| : , : , :  |
9 | instantiation | 20, 18 | , ⊢  |
| : , :  |
10 | instantiation | 36, 19 | , ⊢  |
| : , : , :  |
11 | instantiation | 20, 21 | , ⊢  |
| : , :  |
12 | theorem | | ⊢  |
| proveit.numbers.exponentiation.real_power_of_product |
13 | instantiation | 22, 33, 28 | ⊢  |
| : , :  |
14 | instantiation | 22, 33, 31 | ⊢  |
| : , :  |
15 | instantiation | 23, 24, 25 | ⊢  |
| : , : , :  |
16 | instantiation | 32, 33, 31, 35 | ⊢  |
| : , :  |
17 | instantiation | 67, 26, 27 | , ⊢  |
| : , : , :  |
18 | instantiation | 30, 33, 28, 35 | , ⊢  |
| : , :  |
19 | instantiation | 41, 79, 42, 76, 80, 29, 88, 89, 84, 75, 44 | , ⊢  |
| : , : , : , : , : , :  |
20 | theorem | | ⊢  |
| proveit.logic.equality.equals_reversal |
21 | instantiation | 30, 33, 31, 35 | , ⊢  |
| : , :  |
22 | theorem | | ⊢  |
| proveit.numbers.exponentiation.exp_complex_closure |
23 | theorem | | ⊢  |
| proveit.logic.equality.sub_left_side_into |
24 | instantiation | 32, 33, 34, 35 | ⊢  |
| : , :  |
25 | instantiation | 36, 37 | ⊢  |
| : , : , :  |
26 | instantiation | 38, 39, 76, 79, 40, 80, 88, 89, 84, 44, 83 | , ⊢  |
| : , : , : , : , : , : , :  |
27 | instantiation | 41, 79, 42, 76, 80, 43, 88, 89, 84, 83, 44 | , ⊢  |
| : , : , : , : , : , :  |
28 | instantiation | 51, 45, 46 | ⊢  |
| : , : , :  |
29 | instantiation | 58 | ⊢  |
| : , : , : , :  |
30 | instantiation | 47, 85 | ⊢  |
| :  |
31 | instantiation | 51, 48, 49 | ⊢  |
| : , : , :  |
32 | theorem | | ⊢  |
| proveit.numbers.exponentiation.exp_not_eq_zero |
33 | instantiation | 104, 94, 50 | ⊢  |
| : , : , :  |
34 | instantiation | 51, 52, 53 | ⊢  |
| : , : , :  |
35 | instantiation | 54, 55 | ⊢  |
| :  |
36 | axiom | | ⊢  |
| proveit.logic.equality.substitution |
37 | instantiation | 56, 106, 76, 79, 81, 80, 88, 89, 84, 83 | ⊢  |
| : , : , : , : , : , : , :  |
38 | theorem | | ⊢  |
| proveit.numbers.multiplication.rightward_commutation |
39 | theorem | | ⊢  |
| proveit.numbers.numerals.decimals.nat3 |
40 | instantiation | 57 | ⊢  |
| : , : , :  |
41 | theorem | | ⊢  |
| proveit.numbers.multiplication.association |
42 | theorem | | ⊢  |
| proveit.numbers.numerals.decimals.nat4 |
43 | instantiation | 58 | ⊢  |
| : , : , : , :  |
44 | instantiation | 104, 94, 59 | ⊢  |
| : , : , :  |
45 | instantiation | 87, 77, 60 | ⊢  |
| : , :  |
46 | instantiation | 67, 61, 62 | ⊢  |
| : , : , :  |
47 | theorem | | ⊢  |
| proveit.numbers.exponentiation.int_exp_of_exp |
48 | instantiation | 87, 77, 63 | ⊢  |
| : , :  |
49 | instantiation | 67, 64, 65 | ⊢  |
| : , : , :  |
50 | instantiation | 104, 99, 71 | ⊢  |
| : , : , :  |
51 | theorem | | ⊢  |
| proveit.logic.equality.sub_right_side_into |
52 | instantiation | 87, 77, 66 | ⊢  |
| : , :  |
53 | instantiation | 67, 68, 69 | ⊢  |
| : , : , :  |
54 | theorem | | ⊢  |
| proveit.numbers.number_sets.real_numbers.nonzero_if_in_real_nonzero |
55 | instantiation | 104, 70, 71 | ⊢  |
| : , : , :  |
56 | theorem | | ⊢  |
| proveit.numbers.multiplication.leftward_commutation |
57 | theorem | | ⊢  |
| proveit.numbers.numerals.decimals.tuple_len_3_typical_eq |
58 | theorem | | ⊢  |
| proveit.numbers.numerals.decimals.tuple_len_4_typical_eq |
59 | instantiation | 104, 97, 72 | ⊢  |
| : , : , :  |
60 | instantiation | 87, 84, 83 | ⊢  |
| : , :  |
61 | instantiation | 78, 76, 106, 79, 73, 80, 77, 84, 83 | ⊢  |
| : , : , : , : , : , :  |
62 | instantiation | 78, 79, 106, 80, 81, 73, 88, 89, 84, 83 | ⊢  |
| : , : , : , : , : , :  |
63 | instantiation | 87, 84, 75 | ⊢  |
| : , :  |
64 | instantiation | 78, 76, 106, 79, 74, 80, 77, 84, 75 | ⊢  |
| : , : , : , : , : , :  |
65 | instantiation | 78, 79, 106, 80, 81, 74, 88, 89, 84, 75 | ⊢  |
| : , : , : , : , : , :  |
66 | instantiation | 87, 83, 84 | ⊢  |
| : , :  |
67 | axiom | | ⊢  |
| proveit.logic.equality.equals_transitivity |
68 | instantiation | 78, 76, 106, 79, 82, 80, 77, 83, 84 | ⊢  |
| : , : , : , : , : , :  |
69 | instantiation | 78, 79, 106, 80, 81, 82, 88, 89, 83, 84 | ⊢  |
| : , : , : , : , : , :  |
70 | theorem | | ⊢  |
| proveit.numbers.number_sets.real_numbers.real_pos_within_real_nonzero |
71 | theorem | | ⊢  |
| proveit.numbers.number_sets.real_numbers.e_is_real_pos |
72 | instantiation | 104, 102, 85 | ⊢  |
| : , : , :  |
73 | instantiation | 90 | ⊢  |
| : , :  |
74 | instantiation | 90 | ⊢  |
| : , :  |
75 | instantiation | 104, 94, 86 | ⊢  |
| : , : , :  |
76 | theorem | | ⊢  |
| proveit.numbers.numerals.decimals.nat1 |
77 | instantiation | 87, 88, 89 | ⊢  |
| : , :  |
78 | theorem | | ⊢  |
| proveit.numbers.multiplication.disassociation |
79 | axiom | | ⊢  |
| proveit.numbers.number_sets.natural_numbers.zero_in_nats |
80 | theorem | | ⊢  |
| proveit.core_expr_types.tuples.tuple_len_0_typical_eq |
81 | instantiation | 90 | ⊢  |
| : , :  |
82 | instantiation | 90 | ⊢  |
| : , :  |
83 | instantiation | 104, 94, 91 | ⊢  |
| : , : , :  |
84 | theorem | | ⊢  |
| proveit.numbers.number_sets.complex_numbers.i_is_complex |
85 | assumption | | ⊢  |
86 | instantiation | 104, 99, 92 | ⊢  |
| : , : , :  |
87 | theorem | | ⊢  |
| proveit.numbers.multiplication.mult_complex_closure_bin |
88 | instantiation | 104, 94, 93 | ⊢  |
| : , : , :  |
89 | instantiation | 104, 94, 95 | ⊢  |
| : , : , :  |
90 | theorem | | ⊢  |
| proveit.numbers.numerals.decimals.tuple_len_2_typical_eq |
91 | instantiation | 104, 97, 96 | ⊢  |
| : , : , :  |
92 | assumption | | ⊢  |
93 | instantiation | 104, 97, 98 | ⊢  |
| : , : , :  |
94 | theorem | | ⊢  |
| proveit.numbers.number_sets.complex_numbers.real_within_complex |
95 | instantiation | 104, 99, 100 | ⊢  |
| : , : , :  |
96 | instantiation | 104, 102, 101 | ⊢  |
| : , : , :  |
97 | theorem | | ⊢  |
| proveit.numbers.number_sets.real_numbers.rational_within_real |
98 | instantiation | 104, 102, 103 | ⊢  |
| : , : , :  |
99 | theorem | | ⊢  |
| proveit.numbers.number_sets.real_numbers.real_pos_within_real |
100 | theorem | | ⊢  |
| proveit.numbers.number_sets.real_numbers.pi_is_real_pos |
101 | assumption | | ⊢  |
102 | theorem | | ⊢  |
| proveit.numbers.number_sets.rational_numbers.int_within_rational |
103 | instantiation | 104, 105, 106 | ⊢  |
| : , : , :  |
104 | theorem | | ⊢  |
| proveit.logic.sets.inclusion.superset_membership_from_proper_subset |
105 | theorem | | ⊢  |
| proveit.numbers.number_sets.integers.nat_within_int |
106 | theorem | | ⊢  |
| proveit.numbers.numerals.decimals.nat2 |