| step type | requirements | statement |
0 | instantiation | 1, 2 | ⊢  |
| : , :  |
1 | theorem | | ⊢  |
| proveit.logic.sets.inclusion.relax_proper_subset |
2 | instantiation | 3, 4, 5 | ⊢  |
| : , : , :  |
3 | theorem | | ⊢  |
| proveit.logic.equality.sub_left_side_into |
4 | instantiation | 6, 101, 98, 12, 7 | ⊢  |
| : , : , : , : , :  |
5 | instantiation | 8, 101, 98, 9, 12, 10 | ⊢  |
| : , : , : , : , : , : , :  |
6 | theorem | | ⊢  |
| proveit.logic.sets.enumeration.proper_subset_of_superset |
7 | instantiation | 11, 101, 12, 13, 14, 15, 16, 17 | ⊢  |
| : , : , :  |
8 | theorem | | ⊢  |
| proveit.logic.sets.enumeration.leftward_permutation |
9 | axiom | | ⊢  |
| proveit.numbers.number_sets.natural_numbers.zero_in_nats |
10 | theorem | | ⊢  |
| proveit.core_expr_types.tuples.tuple_len_0_typical_eq |
11 | theorem | | ⊢  |
| proveit.logic.sets.enumeration.nonmembership_fold |
12 | instantiation | 18 | ⊢  |
| : , : , : , : , :  |
13 | instantiation | 23, 19 | ⊢  |
| : , :  |
14 | instantiation | 23, 20 | ⊢  |
| : , :  |
15 | instantiation | 23, 21 | ⊢  |
| : , :  |
16 | instantiation | 23, 22 | ⊢  |
| : , :  |
17 | instantiation | 23, 24 | ⊢  |
| : , :  |
18 | theorem | | ⊢  |
| proveit.numbers.numerals.decimals.tuple_len_5_typical_eq |
19 | instantiation | 29, 98, 30, 25 | ⊢  |
| : , :  |
20 | instantiation | 29, 104, 30, 26 | ⊢  |
| : , :  |
21 | instantiation | 29, 100, 30, 27 | ⊢  |
| : , :  |
22 | instantiation | 29, 99, 30, 28 | ⊢  |
| : , :  |
23 | theorem | | ⊢  |
| proveit.logic.equality.not_equals_symmetry |
24 | instantiation | 29, 101, 30, 31 | ⊢  |
| : , :  |
25 | instantiation | 43, 80, 44, 32, 33, 34*, 35* | ⊢  |
| : , : , :  |
26 | instantiation | 43, 85, 44, 83, 36, 37*, 68* | ⊢  |
| : , : , :  |
27 | instantiation | 43, 82, 44, 81, 38, 39*, 61* | ⊢  |
| : , : , :  |
28 | instantiation | 43, 81, 44, 82, 40, 41*, 42* | ⊢  |
| : , : , :  |
29 | theorem | | ⊢  |
| proveit.numbers.ordering.less_is_not_eq_nat |
30 | theorem | | ⊢  |
| proveit.numbers.numerals.decimals.nat7 |
31 | instantiation | 43, 83, 44, 85, 45, 46*, 47* | ⊢  |
| : , : , :  |
32 | instantiation | 102, 90, 48 | ⊢  |
| : , : , :  |
33 | instantiation | 63, 49 | ⊢  |
| :  |
34 | instantiation | 67, 50, 51 | ⊢  |
| : , : , :  |
35 | theorem | | ⊢  |
| proveit.numbers.numerals.decimals.add_6_1 |
36 | instantiation | 63, 52 | ⊢  |
| :  |
37 | instantiation | 67, 53, 54 | ⊢  |
| : , : , :  |
38 | instantiation | 63, 55 | ⊢  |
| :  |
39 | instantiation | 67, 56, 57 | ⊢  |
| : , : , :  |
40 | instantiation | 63, 58 | ⊢  |
| :  |
41 | instantiation | 67, 59, 60 | ⊢  |
| : , : , :  |
42 | instantiation | 67, 61, 62 | ⊢  |
| : , : , :  |
43 | theorem | | ⊢  |
| proveit.numbers.addition.strong_bound_via_left_term_bound |
44 | theorem | | ⊢  |
| proveit.numbers.number_sets.real_numbers.zero_is_real |
45 | instantiation | 63, 64 | ⊢  |
| :  |
46 | instantiation | 67, 65, 66 | ⊢  |
| : , : , :  |
47 | instantiation | 67, 68, 69 | ⊢  |
| : , : , :  |
48 | instantiation | 102, 96, 70 | ⊢  |
| : , : , :  |
49 | theorem | | ⊢  |
| proveit.numbers.numerals.decimals.posnat6 |
50 | instantiation | 74, 71 | ⊢  |
| :  |
51 | instantiation | 76, 71, 75 | ⊢  |
| : , :  |
52 | theorem | | ⊢  |
| proveit.numbers.numerals.decimals.posnat5 |
53 | instantiation | 74, 78 | ⊢  |
| :  |
54 | instantiation | 76, 78, 75 | ⊢  |
| : , :  |
55 | theorem | | ⊢  |
| proveit.numbers.numerals.decimals.posnat4 |
56 | instantiation | 74, 73 | ⊢  |
| :  |
57 | instantiation | 76, 73, 75 | ⊢  |
| : , :  |
58 | theorem | | ⊢  |
| proveit.numbers.numerals.decimals.posnat3 |
59 | instantiation | 74, 72 | ⊢  |
| :  |
60 | instantiation | 76, 72, 75 | ⊢  |
| : , :  |
61 | theorem | | ⊢  |
| proveit.numbers.numerals.decimals.add_4_3 |
62 | instantiation | 76, 72, 73 | ⊢  |
| : , :  |
63 | theorem | | ⊢  |
| proveit.numbers.number_sets.natural_numbers.natural_pos_is_pos |
64 | theorem | | ⊢  |
| proveit.numbers.numerals.decimals.posnat2 |
65 | instantiation | 74, 77 | ⊢  |
| :  |
66 | instantiation | 76, 77, 75 | ⊢  |
| : , :  |
67 | theorem | | ⊢  |
| proveit.logic.equality.sub_right_side_into |
68 | theorem | | ⊢  |
| proveit.numbers.numerals.decimals.add_5_2 |
69 | instantiation | 76, 77, 78 | ⊢  |
| : , :  |
70 | instantiation | 102, 103, 79 | ⊢  |
| : , : , :  |
71 | instantiation | 102, 84, 80 | ⊢  |
| : , : , :  |
72 | instantiation | 102, 84, 81 | ⊢  |
| : , : , :  |
73 | instantiation | 102, 84, 82 | ⊢  |
| : , : , :  |
74 | theorem | | ⊢  |
| proveit.numbers.addition.elim_zero_right |
75 | theorem | | ⊢  |
| proveit.numbers.number_sets.complex_numbers.zero_is_complex |
76 | theorem | | ⊢  |
| proveit.numbers.addition.commutation |
77 | instantiation | 102, 84, 83 | ⊢  |
| : , : , :  |
78 | instantiation | 102, 84, 85 | ⊢  |
| : , : , :  |
79 | theorem | | ⊢  |
| proveit.numbers.numerals.decimals.nat6 |
80 | instantiation | 102, 90, 86 | ⊢  |
| : , : , :  |
81 | instantiation | 102, 90, 87 | ⊢  |
| : , : , :  |
82 | instantiation | 102, 90, 88 | ⊢  |
| : , : , :  |
83 | instantiation | 102, 90, 89 | ⊢  |
| : , : , :  |
84 | theorem | | ⊢  |
| proveit.numbers.number_sets.complex_numbers.real_within_complex |
85 | instantiation | 102, 90, 91 | ⊢  |
| : , : , :  |
86 | instantiation | 102, 96, 92 | ⊢  |
| : , : , :  |
87 | instantiation | 102, 96, 93 | ⊢  |
| : , : , :  |
88 | instantiation | 102, 96, 94 | ⊢  |
| : , : , :  |
89 | instantiation | 102, 96, 95 | ⊢  |
| : , : , :  |
90 | theorem | | ⊢  |
| proveit.numbers.number_sets.real_numbers.rational_within_real |
91 | instantiation | 102, 96, 97 | ⊢  |
| : , : , :  |
92 | instantiation | 102, 103, 98 | ⊢  |
| : , : , :  |
93 | instantiation | 102, 103, 99 | ⊢  |
| : , : , :  |
94 | instantiation | 102, 103, 100 | ⊢  |
| : , : , :  |
95 | instantiation | 102, 103, 101 | ⊢  |
| : , : , :  |
96 | theorem | | ⊢  |
| proveit.numbers.number_sets.rational_numbers.int_within_rational |
97 | instantiation | 102, 103, 104 | ⊢  |
| : , : , :  |
98 | theorem | | ⊢  |
| proveit.numbers.numerals.decimals.nat1 |
99 | theorem | | ⊢  |
| proveit.numbers.numerals.decimals.nat4 |
100 | theorem | | ⊢  |
| proveit.numbers.numerals.decimals.nat3 |
101 | theorem | | ⊢  |
| proveit.numbers.numerals.decimals.nat5 |
102 | theorem | | ⊢  |
| proveit.logic.sets.inclusion.superset_membership_from_proper_subset |
103 | theorem | | ⊢  |
| proveit.numbers.number_sets.integers.nat_within_int |
104 | theorem | | ⊢  |
| proveit.numbers.numerals.decimals.nat2 |
*equality replacement requirements |