| step type | requirements | statement |
0 | instantiation | 1, 2, 3, 4 | , , , , , ⊢ |
| : , : , : , : |
1 | reference | 5 | ⊢ |
2 | instantiation | 5, 6, 7, 8 | , , , , , ⊢ |
| : , : , : , : |
3 | instantiation | 31, 46, 65, 9, 48, 10, 11, 50, 32, 24, 60, 25, 26, 27, 28, 12* | , , , , , ⊢ |
| : , : , : , : , : , : |
4 | instantiation | 31, 47, 21, 13, 14, 23, 15, 24, 60, 25, 26, 27, 28, 16* | , , , , , ⊢ |
| : , : , : , : , : , : |
5 | theorem | | ⊢ |
| proveit.logic.equality.four_chain_transitivity |
6 | instantiation | 20, 70, 18, 47, 19, 17, 50, 24, 60, 25, 26, 27, 28, 32 | , , , , , ⊢ |
| : , : , : , : , : , : , : |
7 | instantiation | 20, 47, 18, 70, 49, 19, 50, 24, 60, 25, 26, 27, 28, 32 | , , , , , ⊢ |
| : , : , : , : , : , : , : |
8 | instantiation | 20, 62, 21, 46, 22, 23, 48, 50, 32, 24, 60, 25, 26, 27, 28 | , , , , , ⊢ |
| : , : , : , : , : , : , : |
9 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat7 |
10 | instantiation | 29 | ⊢ |
| : , : , : |
11 | instantiation | 30 | ⊢ |
| : , : , : , : , : , : , : |
12 | instantiation | 31, 46, 47, 70, 48, 49, 50, 32, 33* | ⊢ |
| : , : , : , : , : , : |
13 | instantiation | 56 | ⊢ |
| : , : |
14 | instantiation | 56 | ⊢ |
| : , : |
15 | instantiation | 68, 57, 34 | ⊢ |
| : , : , : |
16 | instantiation | 35, 36, 54* | ⊢ |
| : , : |
17 | instantiation | 56 | ⊢ |
| : , : |
18 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat6 |
19 | instantiation | 37 | ⊢ |
| : , : , : , : , : , : |
20 | theorem | | ⊢ |
| proveit.numbers.addition.leftward_commutation |
21 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat4 |
22 | instantiation | 38 | ⊢ |
| : , : , : , : , : |
23 | instantiation | 39 | ⊢ |
| : , : , : , : |
24 | assumption | | ⊢ |
25 | assumption | | ⊢ |
26 | assumption | | ⊢ |
27 | assumption | | ⊢ |
28 | assumption | | ⊢ |
29 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.tuple_len_3_typical_eq |
30 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.tuple_len_7_typical_eq |
31 | theorem | | ⊢ |
| proveit.numbers.addition.association |
32 | instantiation | 68, 57, 40 | ⊢ |
| : , : , : |
33 | instantiation | 41, 42, 43 | ⊢ |
| : , : , : |
34 | instantiation | 68, 63, 44 | ⊢ |
| : , : , : |
35 | theorem | | ⊢ |
| proveit.logic.equality.equals_reversal |
36 | instantiation | 45, 46, 47, 70, 48, 49, 50, 60, 51* | ⊢ |
| : , : , : , : , : , : |
37 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.tuple_len_6_typical_eq |
38 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.tuple_len_5_typical_eq |
39 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.tuple_len_4_typical_eq |
40 | instantiation | 68, 63, 52 | ⊢ |
| : , : , : |
41 | axiom | | ⊢ |
| proveit.logic.equality.equals_transitivity |
42 | instantiation | 53, 54 | ⊢ |
| : , : , : |
43 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.add_2_3 |
44 | instantiation | 68, 66, 55 | ⊢ |
| : , : , : |
45 | theorem | | ⊢ |
| proveit.numbers.multiplication.distribute_through_sum |
46 | axiom | | ⊢ |
| proveit.numbers.number_sets.natural_numbers.zero_in_nats |
47 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat2 |
48 | theorem | | ⊢ |
| proveit.core_expr_types.tuples.tuple_len_0_typical_eq |
49 | instantiation | 56 | ⊢ |
| : , : |
50 | instantiation | 68, 57, 58 | ⊢ |
| : , : , : |
51 | instantiation | 59, 60 | ⊢ |
| : |
52 | instantiation | 68, 66, 61 | ⊢ |
| : , : , : |
53 | axiom | | ⊢ |
| proveit.logic.equality.substitution |
54 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.add_1_1 |
55 | instantiation | 68, 69, 62 | ⊢ |
| : , : , : |
56 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.tuple_len_2_typical_eq |
57 | theorem | | ⊢ |
| proveit.numbers.number_sets.complex_numbers.real_within_complex |
58 | instantiation | 68, 63, 64 | ⊢ |
| : , : , : |
59 | theorem | | ⊢ |
| proveit.numbers.multiplication.elim_one_left |
60 | assumption | | ⊢ |
61 | instantiation | 68, 69, 65 | ⊢ |
| : , : , : |
62 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat5 |
63 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.rational_within_real |
64 | instantiation | 68, 66, 67 | ⊢ |
| : , : , : |
65 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat3 |
66 | theorem | | ⊢ |
| proveit.numbers.number_sets.rational_numbers.int_within_rational |
67 | instantiation | 68, 69, 70 | ⊢ |
| : , : , : |
68 | theorem | | ⊢ |
| proveit.logic.sets.inclusion.superset_membership_from_proper_subset |
69 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.nat_within_int |
70 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat1 |
*equality replacement requirements |