| step type | requirements | statement |
0 | instantiation | 1, 2, 3, 4 | , , , ⊢ |
| : , : |
1 | theorem | | ⊢ |
| proveit.numbers.divisibility.even__if__power_is_even |
2 | instantiation | 108, 13, 90 | ⊢ |
| : , : , : |
3 | reference | 34 | ⊢ |
4 | instantiation | 45, 5, 6 | , , , ⊢ |
| : , : , : |
5 | instantiation | 7, 8, 9, 10 | ⊢ |
| : , : |
6 | instantiation | 45, 11, 12 | , , , ⊢ |
| : , : , : |
7 | theorem | | ⊢ |
| proveit.numbers.divisibility.left_factor_divisibility |
8 | instantiation | 108, 103, 16 | ⊢ |
| : , : , : |
9 | instantiation | 108, 13, 14 | ⊢ |
| : , : , : |
10 | instantiation | 44, 110 | ⊢ |
| : |
11 | instantiation | 15, 16, 17, 81, 18 | , , , ⊢ |
| : , : , : |
12 | instantiation | 19, 20, 97, 110, 21* | , ⊢ |
| : , : , : |
13 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.nat_pos_within_int |
14 | instantiation | 22, 23, 55 | ⊢ |
| : , : |
15 | theorem | | ⊢ |
| proveit.numbers.exponentiation.exp_eq_real |
16 | instantiation | 108, 91, 24 | ⊢ |
| : , : , : |
17 | instantiation | 25, 30, 104 | , ⊢ |
| : , : |
18 | instantiation | 26, 104, 30, 27, 28, 29* | , , , ⊢ |
| : , : , : |
19 | theorem | | ⊢ |
| proveit.numbers.exponentiation.posnat_power_of_product |
20 | instantiation | 108, 103, 30 | ⊢ |
| : , : , : |
21 | instantiation | 31, 73, 32* | ⊢ |
| : |
22 | theorem | | ⊢ |
| proveit.numbers.exponentiation.exp_natpos_closure |
23 | instantiation | 108, 33, 113 | ⊢ |
| : , : , : |
24 | instantiation | 108, 98, 34 | ⊢ |
| : , : , : |
25 | theorem | | ⊢ |
| proveit.numbers.multiplication.mult_real_closure_bin |
26 | theorem | | ⊢ |
| proveit.numbers.multiplication.right_mult_eq_real |
27 | instantiation | 35, 81, 104, 36 | , ⊢ |
| : , : |
28 | instantiation | 37, 38 | ⊢ |
| : , : |
29 | instantiation | 45, 39, 40 | , ⊢ |
| : , : , : |
30 | instantiation | 108, 91, 41 | ⊢ |
| : , : , : |
31 | theorem | | ⊢ |
| proveit.numbers.exponentiation.square_abs_rational_simp |
32 | instantiation | 42, 110, 43 | ⊢ |
| : , : |
33 | theorem | | ⊢ |
| proveit.numbers.number_sets.natural_numbers.nat_pos_within_nat |
34 | instantiation | 108, 105, 55 | ⊢ |
| : , : , : |
35 | theorem | | ⊢ |
| proveit.numbers.division.div_real_closure |
36 | instantiation | 44, 113 | ⊢ |
| : |
37 | theorem | | ⊢ |
| proveit.logic.booleans.conjunction.left_from_and |
38 | assumption | | ⊢ |
39 | instantiation | 45, 46, 47 | , ⊢ |
| : , : , : |
40 | instantiation | 48, 49, 50, 51 | ⊢ |
| : , : , : , : |
41 | instantiation | 108, 52, 53 | ⊢ |
| : , : , : |
42 | theorem | | ⊢ |
| proveit.numbers.exponentiation.nth_power_of_nth_root |
43 | instantiation | 54, 55 | ⊢ |
| : |
44 | theorem | | ⊢ |
| proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos |
45 | theorem | | ⊢ |
| proveit.logic.equality.sub_right_side_into |
46 | instantiation | 56, 70, 71, 57, 58 | , ⊢ |
| : , : , : , : , : |
47 | instantiation | 78, 59, 60 | ⊢ |
| : , : , : |
48 | theorem | | ⊢ |
| proveit.logic.equality.four_chain_transitivity |
49 | instantiation | 87, 61 | ⊢ |
| : , : , : |
50 | instantiation | 87, 62 | ⊢ |
| : , : , : |
51 | instantiation | 96, 70 | ⊢ |
| : |
52 | theorem | | ⊢ |
| proveit.numbers.number_sets.rational_numbers.rational_pos_within_rational |
53 | instantiation | 63, 64 | ⊢ |
| : |
54 | theorem | | ⊢ |
| proveit.numbers.number_sets.natural_numbers.natural_lower_bound |
55 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat2 |
56 | theorem | | ⊢ |
| proveit.numbers.division.mult_frac_cancel_denom_left |
57 | instantiation | 108, 66, 65 | ⊢ |
| : , : , : |
58 | instantiation | 108, 66, 67 | ⊢ |
| : , : , : |
59 | instantiation | 87, 68 | ⊢ |
| : , : , : |
60 | instantiation | 87, 69 | ⊢ |
| : , : , : |
61 | instantiation | 89, 70 | ⊢ |
| : |
62 | instantiation | 89, 71 | ⊢ |
| : |
63 | theorem | | ⊢ |
| proveit.numbers.absolute_value.abs_rational_nonzero_closure |
64 | instantiation | 72, 73, 74 | ⊢ |
| : |
65 | instantiation | 108, 75, 94 | ⊢ |
| : , : , : |
66 | theorem | | ⊢ |
| proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero |
67 | instantiation | 108, 75, 76 | ⊢ |
| : , : , : |
68 | instantiation | 87, 77 | ⊢ |
| : , : , : |
69 | instantiation | 78, 79, 80 | ⊢ |
| : , : , : |
70 | instantiation | 108, 103, 81 | ⊢ |
| : , : , : |
71 | instantiation | 108, 103, 82 | ⊢ |
| : , : , : |
72 | theorem | | ⊢ |
| proveit.numbers.number_sets.rational_numbers.nonzero_rational_is_rational_nonzero |
73 | assumption | | ⊢ |
74 | instantiation | 83, 95, 84 | ⊢ |
| : , : |
75 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero |
76 | instantiation | 108, 101, 85 | ⊢ |
| : , : , : |
77 | instantiation | 86, 97 | ⊢ |
| : |
78 | axiom | | ⊢ |
| proveit.logic.equality.equals_transitivity |
79 | instantiation | 87, 88 | ⊢ |
| : , : , : |
80 | instantiation | 89, 97 | ⊢ |
| : |
81 | instantiation | 111, 112, 90 | ⊢ |
| : , : , : |
82 | instantiation | 108, 91, 92 | ⊢ |
| : , : , : |
83 | theorem | | ⊢ |
| proveit.numbers.exponentiation.exp_rational_non_zero__not_zero |
84 | instantiation | 93, 94, 95 | ⊢ |
| : , : |
85 | instantiation | 108, 109, 113 | ⊢ |
| : , : , : |
86 | theorem | | ⊢ |
| proveit.numbers.multiplication.elim_one_left |
87 | axiom | | ⊢ |
| proveit.logic.equality.substitution |
88 | instantiation | 96, 97 | ⊢ |
| : |
89 | theorem | | ⊢ |
| proveit.numbers.division.frac_one_denom |
90 | assumption | | ⊢ |
91 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.rational_within_real |
92 | instantiation | 108, 98, 99 | ⊢ |
| : , : , : |
93 | theorem | | ⊢ |
| proveit.numbers.division.div_rational_nonzero_closure |
94 | instantiation | 108, 101, 100 | ⊢ |
| : , : , : |
95 | instantiation | 108, 101, 102 | ⊢ |
| : , : , : |
96 | theorem | | ⊢ |
| proveit.numbers.multiplication.elim_one_right |
97 | instantiation | 108, 103, 104 | ⊢ |
| : , : , : |
98 | theorem | | ⊢ |
| proveit.numbers.number_sets.rational_numbers.int_within_rational |
99 | instantiation | 108, 105, 106 | ⊢ |
| : , : , : |
100 | instantiation | 108, 109, 107 | ⊢ |
| : , : , : |
101 | theorem | | ⊢ |
| proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero |
102 | instantiation | 108, 109, 110 | ⊢ |
| : , : , : |
103 | theorem | | ⊢ |
| proveit.numbers.number_sets.complex_numbers.real_within_complex |
104 | instantiation | 111, 112, 113 | ⊢ |
| : , : , : |
105 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.nat_within_int |
106 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat1 |
107 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.posnat1 |
108 | theorem | | ⊢ |
| proveit.logic.sets.inclusion.superset_membership_from_proper_subset |
109 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int |
110 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.posnat2 |
111 | theorem | | ⊢ |
| proveit.logic.sets.inclusion.unfold_subset_eq |
112 | instantiation | 114, 115 | ⊢ |
| : , : |
113 | assumption | | ⊢ |
114 | theorem | | ⊢ |
| proveit.logic.sets.inclusion.relax_proper_subset |
115 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.nat_pos_within_real |
*equality replacement requirements |