| step type | requirements | statement |
0 | instantiation | 1, 2, 3, 4 | , , , ⊢ |
| : , : |
1 | reference | 16 | ⊢ |
2 | instantiation | 122, 27, 127 | ⊢ |
| : , : , : |
3 | reference | 48 | ⊢ |
4 | instantiation | 5, 22, 6, 7, 24 | , , , ⊢ |
| : , : , : |
5 | theorem | | ⊢ |
| proveit.numbers.divisibility.common_factor_elimination |
6 | instantiation | 122, 117, 8 | ⊢ |
| : , : , : |
7 | instantiation | 59, 9, 10 | , , , ⊢ |
| : , : , : |
8 | instantiation | 125, 126, 28 | ⊢ |
| : , : , : |
9 | instantiation | 11, 12, 20 | , , , ⊢ |
| : , : , : |
10 | instantiation | 13, 22 | ⊢ |
| : |
11 | theorem | | ⊢ |
| proveit.logic.equality.sub_left_side_into |
12 | instantiation | 14, 48, 17, 124, 15 | , , , ⊢ |
| : , : , : |
13 | theorem | | ⊢ |
| proveit.numbers.exponentiation.square_expansion |
14 | theorem | | ⊢ |
| proveit.numbers.divisibility.common_exponent_introduction |
15 | instantiation | 16, 17, 48, 18 | , , , ⊢ |
| : , : |
16 | theorem | | ⊢ |
| proveit.numbers.divisibility.even__if__power_is_even |
17 | instantiation | 122, 27, 104 | ⊢ |
| : , : , : |
18 | instantiation | 59, 19, 20 | , , , ⊢ |
| : , : , : |
19 | instantiation | 21, 22, 23, 24 | ⊢ |
| : , : |
20 | instantiation | 59, 25, 26 | , , , ⊢ |
| : , : , : |
21 | theorem | | ⊢ |
| proveit.numbers.divisibility.left_factor_divisibility |
22 | instantiation | 122, 117, 30 | ⊢ |
| : , : , : |
23 | instantiation | 122, 27, 28 | ⊢ |
| : , : , : |
24 | instantiation | 58, 124 | ⊢ |
| : |
25 | instantiation | 29, 30, 31, 95, 32 | , , , ⊢ |
| : , : , : |
26 | instantiation | 33, 34, 111, 124, 35* | , ⊢ |
| : , : , : |
27 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.nat_pos_within_int |
28 | instantiation | 36, 37, 69 | ⊢ |
| : , : |
29 | theorem | | ⊢ |
| proveit.numbers.exponentiation.exp_eq_real |
30 | instantiation | 122, 105, 38 | ⊢ |
| : , : , : |
31 | instantiation | 39, 44, 118 | , ⊢ |
| : , : |
32 | instantiation | 40, 118, 44, 41, 42, 43* | , , , ⊢ |
| : , : , : |
33 | theorem | | ⊢ |
| proveit.numbers.exponentiation.posnat_power_of_product |
34 | instantiation | 122, 117, 44 | ⊢ |
| : , : , : |
35 | instantiation | 45, 87, 46* | ⊢ |
| : |
36 | theorem | | ⊢ |
| proveit.numbers.exponentiation.exp_natpos_closure |
37 | instantiation | 122, 47, 127 | ⊢ |
| : , : , : |
38 | instantiation | 122, 112, 48 | ⊢ |
| : , : , : |
39 | theorem | | ⊢ |
| proveit.numbers.multiplication.mult_real_closure_bin |
40 | theorem | | ⊢ |
| proveit.numbers.multiplication.right_mult_eq_real |
41 | instantiation | 49, 95, 118, 50 | , ⊢ |
| : , : |
42 | instantiation | 51, 52 | ⊢ |
| : , : |
43 | instantiation | 59, 53, 54 | , ⊢ |
| : , : , : |
44 | instantiation | 122, 105, 55 | ⊢ |
| : , : , : |
45 | theorem | | ⊢ |
| proveit.numbers.exponentiation.square_abs_rational_simp |
46 | instantiation | 56, 124, 57 | ⊢ |
| : , : |
47 | theorem | | ⊢ |
| proveit.numbers.number_sets.natural_numbers.nat_pos_within_nat |
48 | instantiation | 122, 119, 69 | ⊢ |
| : , : , : |
49 | theorem | | ⊢ |
| proveit.numbers.division.div_real_closure |
50 | instantiation | 58, 127 | ⊢ |
| : |
51 | theorem | | ⊢ |
| proveit.logic.booleans.conjunction.left_from_and |
52 | assumption | | ⊢ |
53 | instantiation | 59, 60, 61 | , ⊢ |
| : , : , : |
54 | instantiation | 62, 63, 64, 65 | ⊢ |
| : , : , : , : |
55 | instantiation | 122, 66, 67 | ⊢ |
| : , : , : |
56 | theorem | | ⊢ |
| proveit.numbers.exponentiation.nth_power_of_nth_root |
57 | instantiation | 68, 69 | ⊢ |
| : |
58 | theorem | | ⊢ |
| proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos |
59 | theorem | | ⊢ |
| proveit.logic.equality.sub_right_side_into |
60 | instantiation | 70, 84, 85, 71, 72 | , ⊢ |
| : , : , : , : , : |
61 | instantiation | 92, 73, 74 | ⊢ |
| : , : , : |
62 | theorem | | ⊢ |
| proveit.logic.equality.four_chain_transitivity |
63 | instantiation | 101, 75 | ⊢ |
| : , : , : |
64 | instantiation | 101, 76 | ⊢ |
| : , : , : |
65 | instantiation | 110, 84 | ⊢ |
| : |
66 | theorem | | ⊢ |
| proveit.numbers.number_sets.rational_numbers.rational_pos_within_rational |
67 | instantiation | 77, 78 | ⊢ |
| : |
68 | theorem | | ⊢ |
| proveit.numbers.number_sets.natural_numbers.natural_lower_bound |
69 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat2 |
70 | theorem | | ⊢ |
| proveit.numbers.division.mult_frac_cancel_denom_left |
71 | instantiation | 122, 80, 79 | ⊢ |
| : , : , : |
72 | instantiation | 122, 80, 81 | ⊢ |
| : , : , : |
73 | instantiation | 101, 82 | ⊢ |
| : , : , : |
74 | instantiation | 101, 83 | ⊢ |
| : , : , : |
75 | instantiation | 103, 84 | ⊢ |
| : |
76 | instantiation | 103, 85 | ⊢ |
| : |
77 | theorem | | ⊢ |
| proveit.numbers.absolute_value.abs_rational_nonzero_closure |
78 | instantiation | 86, 87, 88 | ⊢ |
| : |
79 | instantiation | 122, 89, 108 | ⊢ |
| : , : , : |
80 | theorem | | ⊢ |
| proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero |
81 | instantiation | 122, 89, 90 | ⊢ |
| : , : , : |
82 | instantiation | 101, 91 | ⊢ |
| : , : , : |
83 | instantiation | 92, 93, 94 | ⊢ |
| : , : , : |
84 | instantiation | 122, 117, 95 | ⊢ |
| : , : , : |
85 | instantiation | 122, 117, 96 | ⊢ |
| : , : , : |
86 | theorem | | ⊢ |
| proveit.numbers.number_sets.rational_numbers.nonzero_rational_is_rational_nonzero |
87 | assumption | | ⊢ |
88 | instantiation | 97, 109, 98 | ⊢ |
| : , : |
89 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero |
90 | instantiation | 122, 115, 99 | ⊢ |
| : , : , : |
91 | instantiation | 100, 111 | ⊢ |
| : |
92 | axiom | | ⊢ |
| proveit.logic.equality.equals_transitivity |
93 | instantiation | 101, 102 | ⊢ |
| : , : , : |
94 | instantiation | 103, 111 | ⊢ |
| : |
95 | instantiation | 125, 126, 104 | ⊢ |
| : , : , : |
96 | instantiation | 122, 105, 106 | ⊢ |
| : , : , : |
97 | theorem | | ⊢ |
| proveit.numbers.exponentiation.exp_rational_non_zero__not_zero |
98 | instantiation | 107, 108, 109 | ⊢ |
| : , : |
99 | instantiation | 122, 123, 127 | ⊢ |
| : , : , : |
100 | theorem | | ⊢ |
| proveit.numbers.multiplication.elim_one_left |
101 | axiom | | ⊢ |
| proveit.logic.equality.substitution |
102 | instantiation | 110, 111 | ⊢ |
| : |
103 | theorem | | ⊢ |
| proveit.numbers.division.frac_one_denom |
104 | assumption | | ⊢ |
105 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.rational_within_real |
106 | instantiation | 122, 112, 113 | ⊢ |
| : , : , : |
107 | theorem | | ⊢ |
| proveit.numbers.division.div_rational_nonzero_closure |
108 | instantiation | 122, 115, 114 | ⊢ |
| : , : , : |
109 | instantiation | 122, 115, 116 | ⊢ |
| : , : , : |
110 | theorem | | ⊢ |
| proveit.numbers.multiplication.elim_one_right |
111 | instantiation | 122, 117, 118 | ⊢ |
| : , : , : |
112 | theorem | | ⊢ |
| proveit.numbers.number_sets.rational_numbers.int_within_rational |
113 | instantiation | 122, 119, 120 | ⊢ |
| : , : , : |
114 | instantiation | 122, 123, 121 | ⊢ |
| : , : , : |
115 | theorem | | ⊢ |
| proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero |
116 | instantiation | 122, 123, 124 | ⊢ |
| : , : , : |
117 | theorem | | ⊢ |
| proveit.numbers.number_sets.complex_numbers.real_within_complex |
118 | instantiation | 125, 126, 127 | ⊢ |
| : , : , : |
119 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.nat_within_int |
120 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat1 |
121 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.posnat1 |
122 | theorem | | ⊢ |
| proveit.logic.sets.inclusion.superset_membership_from_proper_subset |
123 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int |
124 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.posnat2 |
125 | theorem | | ⊢ |
| proveit.logic.sets.inclusion.unfold_subset_eq |
126 | instantiation | 128, 129 | ⊢ |
| : , : |
127 | assumption | | ⊢ |
128 | theorem | | ⊢ |
| proveit.logic.sets.inclusion.relax_proper_subset |
129 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.nat_pos_within_real |
*equality replacement requirements |