| step type | requirements | statement |
0 | instantiation | 1, 2, 3 | , , , ⊢ |
| : , : , : |
1 | theorem | | ⊢ |
| proveit.logic.equality.sub_left_side_into |
2 | instantiation | 4, 38, 7, 114, 5 | , , , ⊢ |
| : , : , : |
3 | reference | 10 | , , , ⊢ |
4 | theorem | | ⊢ |
| proveit.numbers.divisibility.common_exponent_introduction |
5 | instantiation | 6, 7, 38, 8 | , , , ⊢ |
| : , : |
6 | theorem | | ⊢ |
| proveit.numbers.divisibility.even__if__power_is_even |
7 | instantiation | 112, 17, 94 | ⊢ |
| : , : , : |
8 | instantiation | 49, 9, 10 | , , , ⊢ |
| : , : , : |
9 | instantiation | 11, 12, 13, 14 | ⊢ |
| : , : |
10 | instantiation | 49, 15, 16 | , , , ⊢ |
| : , : , : |
11 | theorem | | ⊢ |
| proveit.numbers.divisibility.left_factor_divisibility |
12 | instantiation | 112, 107, 20 | ⊢ |
| : , : , : |
13 | instantiation | 112, 17, 18 | ⊢ |
| : , : , : |
14 | instantiation | 48, 114 | ⊢ |
| : |
15 | instantiation | 19, 20, 21, 85, 22 | , , , ⊢ |
| : , : , : |
16 | instantiation | 23, 24, 101, 114, 25* | , ⊢ |
| : , : , : |
17 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.nat_pos_within_int |
18 | instantiation | 26, 27, 59 | ⊢ |
| : , : |
19 | theorem | | ⊢ |
| proveit.numbers.exponentiation.exp_eq_real |
20 | instantiation | 112, 95, 28 | ⊢ |
| : , : , : |
21 | instantiation | 29, 34, 108 | , ⊢ |
| : , : |
22 | instantiation | 30, 108, 34, 31, 32, 33* | , , , ⊢ |
| : , : , : |
23 | theorem | | ⊢ |
| proveit.numbers.exponentiation.posnat_power_of_product |
24 | instantiation | 112, 107, 34 | ⊢ |
| : , : , : |
25 | instantiation | 35, 77, 36* | ⊢ |
| : |
26 | theorem | | ⊢ |
| proveit.numbers.exponentiation.exp_natpos_closure |
27 | instantiation | 112, 37, 117 | ⊢ |
| : , : , : |
28 | instantiation | 112, 102, 38 | ⊢ |
| : , : , : |
29 | theorem | | ⊢ |
| proveit.numbers.multiplication.mult_real_closure_bin |
30 | theorem | | ⊢ |
| proveit.numbers.multiplication.right_mult_eq_real |
31 | instantiation | 39, 85, 108, 40 | , ⊢ |
| : , : |
32 | instantiation | 41, 42 | ⊢ |
| : , : |
33 | instantiation | 49, 43, 44 | , ⊢ |
| : , : , : |
34 | instantiation | 112, 95, 45 | ⊢ |
| : , : , : |
35 | theorem | | ⊢ |
| proveit.numbers.exponentiation.square_abs_rational_simp |
36 | instantiation | 46, 114, 47 | ⊢ |
| : , : |
37 | theorem | | ⊢ |
| proveit.numbers.number_sets.natural_numbers.nat_pos_within_nat |
38 | instantiation | 112, 109, 59 | ⊢ |
| : , : , : |
39 | theorem | | ⊢ |
| proveit.numbers.division.div_real_closure |
40 | instantiation | 48, 117 | ⊢ |
| : |
41 | theorem | | ⊢ |
| proveit.logic.booleans.conjunction.left_from_and |
42 | assumption | | ⊢ |
43 | instantiation | 49, 50, 51 | , ⊢ |
| : , : , : |
44 | instantiation | 52, 53, 54, 55 | ⊢ |
| : , : , : , : |
45 | instantiation | 112, 56, 57 | ⊢ |
| : , : , : |
46 | theorem | | ⊢ |
| proveit.numbers.exponentiation.nth_power_of_nth_root |
47 | instantiation | 58, 59 | ⊢ |
| : |
48 | theorem | | ⊢ |
| proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos |
49 | theorem | | ⊢ |
| proveit.logic.equality.sub_right_side_into |
50 | instantiation | 60, 74, 75, 61, 62 | , ⊢ |
| : , : , : , : , : |
51 | instantiation | 82, 63, 64 | ⊢ |
| : , : , : |
52 | theorem | | ⊢ |
| proveit.logic.equality.four_chain_transitivity |
53 | instantiation | 91, 65 | ⊢ |
| : , : , : |
54 | instantiation | 91, 66 | ⊢ |
| : , : , : |
55 | instantiation | 100, 74 | ⊢ |
| : |
56 | theorem | | ⊢ |
| proveit.numbers.number_sets.rational_numbers.rational_pos_within_rational |
57 | instantiation | 67, 68 | ⊢ |
| : |
58 | theorem | | ⊢ |
| proveit.numbers.number_sets.natural_numbers.natural_lower_bound |
59 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat2 |
60 | theorem | | ⊢ |
| proveit.numbers.division.mult_frac_cancel_denom_left |
61 | instantiation | 112, 70, 69 | ⊢ |
| : , : , : |
62 | instantiation | 112, 70, 71 | ⊢ |
| : , : , : |
63 | instantiation | 91, 72 | ⊢ |
| : , : , : |
64 | instantiation | 91, 73 | ⊢ |
| : , : , : |
65 | instantiation | 93, 74 | ⊢ |
| : |
66 | instantiation | 93, 75 | ⊢ |
| : |
67 | theorem | | ⊢ |
| proveit.numbers.absolute_value.abs_rational_nonzero_closure |
68 | instantiation | 76, 77, 78 | ⊢ |
| : |
69 | instantiation | 112, 79, 98 | ⊢ |
| : , : , : |
70 | theorem | | ⊢ |
| proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero |
71 | instantiation | 112, 79, 80 | ⊢ |
| : , : , : |
72 | instantiation | 91, 81 | ⊢ |
| : , : , : |
73 | instantiation | 82, 83, 84 | ⊢ |
| : , : , : |
74 | instantiation | 112, 107, 85 | ⊢ |
| : , : , : |
75 | instantiation | 112, 107, 86 | ⊢ |
| : , : , : |
76 | theorem | | ⊢ |
| proveit.numbers.number_sets.rational_numbers.nonzero_rational_is_rational_nonzero |
77 | assumption | | ⊢ |
78 | instantiation | 87, 99, 88 | ⊢ |
| : , : |
79 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero |
80 | instantiation | 112, 105, 89 | ⊢ |
| : , : , : |
81 | instantiation | 90, 101 | ⊢ |
| : |
82 | axiom | | ⊢ |
| proveit.logic.equality.equals_transitivity |
83 | instantiation | 91, 92 | ⊢ |
| : , : , : |
84 | instantiation | 93, 101 | ⊢ |
| : |
85 | instantiation | 115, 116, 94 | ⊢ |
| : , : , : |
86 | instantiation | 112, 95, 96 | ⊢ |
| : , : , : |
87 | theorem | | ⊢ |
| proveit.numbers.exponentiation.exp_rational_non_zero__not_zero |
88 | instantiation | 97, 98, 99 | ⊢ |
| : , : |
89 | instantiation | 112, 113, 117 | ⊢ |
| : , : , : |
90 | theorem | | ⊢ |
| proveit.numbers.multiplication.elim_one_left |
91 | axiom | | ⊢ |
| proveit.logic.equality.substitution |
92 | instantiation | 100, 101 | ⊢ |
| : |
93 | theorem | | ⊢ |
| proveit.numbers.division.frac_one_denom |
94 | assumption | | ⊢ |
95 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.rational_within_real |
96 | instantiation | 112, 102, 103 | ⊢ |
| : , : , : |
97 | theorem | | ⊢ |
| proveit.numbers.division.div_rational_nonzero_closure |
98 | instantiation | 112, 105, 104 | ⊢ |
| : , : , : |
99 | instantiation | 112, 105, 106 | ⊢ |
| : , : , : |
100 | theorem | | ⊢ |
| proveit.numbers.multiplication.elim_one_right |
101 | instantiation | 112, 107, 108 | ⊢ |
| : , : , : |
102 | theorem | | ⊢ |
| proveit.numbers.number_sets.rational_numbers.int_within_rational |
103 | instantiation | 112, 109, 110 | ⊢ |
| : , : , : |
104 | instantiation | 112, 113, 111 | ⊢ |
| : , : , : |
105 | theorem | | ⊢ |
| proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero |
106 | instantiation | 112, 113, 114 | ⊢ |
| : , : , : |
107 | theorem | | ⊢ |
| proveit.numbers.number_sets.complex_numbers.real_within_complex |
108 | instantiation | 115, 116, 117 | ⊢ |
| : , : , : |
109 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.nat_within_int |
110 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat1 |
111 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.posnat1 |
112 | theorem | | ⊢ |
| proveit.logic.sets.inclusion.superset_membership_from_proper_subset |
113 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int |
114 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.posnat2 |
115 | theorem | | ⊢ |
| proveit.logic.sets.inclusion.unfold_subset_eq |
116 | instantiation | 118, 119 | ⊢ |
| : , : |
117 | assumption | | ⊢ |
118 | theorem | | ⊢ |
| proveit.logic.sets.inclusion.relax_proper_subset |
119 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.nat_pos_within_real |
*equality replacement requirements |