| step type | requirements | statement |
0 | instantiation | 1, 2, 3, 4 | ⊢ |
| : , : , : , : |
1 | reference | 5 | ⊢ |
2 | instantiation | 5, 6, 7, 8 | ⊢ |
| : , : , : , : |
3 | instantiation | 21, 97, 16, 10, 23, 17, 24, 11, 50, 38, 9* | ⊢ |
| : , : , : , : , : , : |
4 | instantiation | 34, 16, 97, 17, 10, 24, 11, 12 | ⊢ |
| : , : , : , : , : , : , : |
5 | theorem | | ⊢ |
| proveit.logic.equality.four_chain_transitivity |
6 | instantiation | 13, 14, 15 | ⊢ |
| : , : , : |
7 | instantiation | 21, 16, 97, 99, 17, 18, 19, 57, 36, 37, 62, 50, 38, 20* | ⊢ |
| : , : , : , : , : , : |
8 | instantiation | 21, 100, 97, 22, 23, 24, 37, 62, 50, 38, 25* | ⊢ |
| : , : , : , : , : , : |
9 | instantiation | 26, 50, 59, 27, 28, 29*, 30*, 31* | ⊢ |
| : , : , : , : |
10 | instantiation | 41 | ⊢ |
| : , : |
11 | instantiation | 53, 62, 32 | ⊢ |
| : , : |
12 | instantiation | 54, 50, 55, 56 | ⊢ |
| : , : |
13 | axiom | | ⊢ |
| proveit.logic.equality.equals_transitivity |
14 | instantiation | 34, 100, 103, 33, 57, 37, 36, 50, 62, 38 | ⊢ |
| : , : , : , : , : , : , : |
15 | instantiation | 34, 103, 100, 35, 57, 36, 37, 50, 62, 38 | ⊢ |
| : , : , : , : , : , : , : |
16 | axiom | | ⊢ |
| proveit.numbers.number_sets.natural_numbers.zero_in_nats |
17 | theorem | | ⊢ |
| proveit.core_expr_types.tuples.tuple_len_0_typical_eq |
18 | instantiation | 41 | ⊢ |
| : , : |
19 | instantiation | 39 | ⊢ |
| : , : , : , : |
20 | instantiation | 43, 57, 86, 83, 40* | ⊢ |
| : , : , : |
21 | theorem | | ⊢ |
| proveit.numbers.multiplication.association |
22 | instantiation | 41 | ⊢ |
| : , : |
23 | instantiation | 41 | ⊢ |
| : , : |
24 | instantiation | 53, 57, 42 | ⊢ |
| : , : |
25 | instantiation | 43, 62, 83, 86, 44* | ⊢ |
| : , : , : |
26 | theorem | | ⊢ |
| proveit.numbers.division.prod_of_fracs |
27 | instantiation | 101, 46, 45 | ⊢ |
| : , : , : |
28 | instantiation | 101, 46, 47 | ⊢ |
| : , : , : |
29 | instantiation | 48, 50 | ⊢ |
| : |
30 | instantiation | 49, 50 | ⊢ |
| : |
31 | instantiation | 51, 55 | ⊢ |
| : |
32 | instantiation | 58, 60, 59 | ⊢ |
| : , : |
33 | instantiation | 52 | ⊢ |
| : , : , : |
34 | theorem | | ⊢ |
| proveit.numbers.multiplication.leftward_commutation |
35 | instantiation | 52 | ⊢ |
| : , : , : |
36 | instantiation | 53, 57, 60 | ⊢ |
| : , : |
37 | instantiation | 53, 62, 60 | ⊢ |
| : , : |
38 | instantiation | 54, 59, 55, 56 | ⊢ |
| : , : |
39 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.tuple_len_4_typical_eq |
40 | instantiation | 61, 57 | ⊢ |
| : |
41 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.tuple_len_2_typical_eq |
42 | instantiation | 58, 59, 60 | ⊢ |
| : , : |
43 | theorem | | ⊢ |
| proveit.numbers.exponentiation.product_of_posnat_powers |
44 | instantiation | 61, 62 | ⊢ |
| : |
45 | instantiation | 101, 64, 63 | ⊢ |
| : , : , : |
46 | theorem | | ⊢ |
| proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero |
47 | instantiation | 101, 64, 65 | ⊢ |
| : , : , : |
48 | theorem | | ⊢ |
| proveit.numbers.division.frac_one_denom |
49 | theorem | | ⊢ |
| proveit.numbers.multiplication.elim_one_right |
50 | instantiation | 101, 72, 66 | ⊢ |
| : , : , : |
51 | theorem | | ⊢ |
| proveit.numbers.multiplication.elim_one_left |
52 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.tuple_len_3_typical_eq |
53 | theorem | | ⊢ |
| proveit.numbers.exponentiation.exp_complex_closure |
54 | theorem | | ⊢ |
| proveit.numbers.division.div_complex_closure |
55 | instantiation | 101, 72, 67 | ⊢ |
| : , : , : |
56 | instantiation | 68, 88 | ⊢ |
| : |
57 | instantiation | 101, 72, 69 | ⊢ |
| : , : , : |
58 | theorem | | ⊢ |
| proveit.numbers.addition.add_complex_closure_bin |
59 | instantiation | 101, 72, 70 | ⊢ |
| : , : , : |
60 | instantiation | 101, 72, 71 | ⊢ |
| : , : , : |
61 | theorem | | ⊢ |
| proveit.numbers.exponentiation.complex_x_to_first_power_is_x |
62 | instantiation | 101, 72, 73 | ⊢ |
| : , : , : |
63 | instantiation | 101, 75, 74 | ⊢ |
| : , : , : |
64 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero |
65 | instantiation | 101, 75, 76 | ⊢ |
| : , : , : |
66 | instantiation | 101, 84, 77 | ⊢ |
| : , : , : |
67 | instantiation | 101, 84, 78 | ⊢ |
| : , : , : |
68 | theorem | | ⊢ |
| proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos |
69 | instantiation | 101, 84, 79 | ⊢ |
| : , : , : |
70 | instantiation | 101, 84, 80 | ⊢ |
| : , : , : |
71 | instantiation | 81, 82, 83 | ⊢ |
| : , : , : |
72 | theorem | | ⊢ |
| proveit.numbers.number_sets.complex_numbers.real_within_complex |
73 | instantiation | 101, 84, 85 | ⊢ |
| : , : , : |
74 | instantiation | 101, 87, 86 | ⊢ |
| : , : , : |
75 | theorem | | ⊢ |
| proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero |
76 | instantiation | 101, 87, 88 | ⊢ |
| : , : , : |
77 | instantiation | 101, 95, 89 | ⊢ |
| : , : , : |
78 | instantiation | 101, 95, 90 | ⊢ |
| : , : , : |
79 | instantiation | 101, 95, 91 | ⊢ |
| : , : , : |
80 | instantiation | 101, 95, 92 | ⊢ |
| : , : , : |
81 | theorem | | ⊢ |
| proveit.logic.sets.inclusion.unfold_subset_eq |
82 | instantiation | 93, 94 | ⊢ |
| : , : |
83 | assumption | | ⊢ |
84 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.rational_within_real |
85 | instantiation | 101, 95, 96 | ⊢ |
| : , : , : |
86 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.posnat1 |
87 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int |
88 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.posnat5 |
89 | instantiation | 101, 102, 97 | ⊢ |
| : , : , : |
90 | instantiation | 101, 102, 98 | ⊢ |
| : , : , : |
91 | instantiation | 101, 102, 99 | ⊢ |
| : , : , : |
92 | instantiation | 101, 102, 100 | ⊢ |
| : , : , : |
93 | theorem | | ⊢ |
| proveit.logic.sets.inclusion.relax_proper_subset |
94 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.nat_pos_within_real |
95 | theorem | | ⊢ |
| proveit.numbers.number_sets.rational_numbers.int_within_rational |
96 | instantiation | 101, 102, 103 | ⊢ |
| : , : , : |
97 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat2 |
98 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat5 |
99 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat4 |
100 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat1 |
101 | theorem | | ⊢ |
| proveit.logic.sets.inclusion.superset_membership_from_proper_subset |
102 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.nat_within_int |
103 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat3 |
*equality replacement requirements |