| step type | requirements | statement |
0 | instantiation | 1, 2, 3 | , , , , , ⊢ |
| : , : , : |
1 | reference | 46 | ⊢ |
2 | instantiation | 4, 70, 14, 5, 6, 55, 29, 65, 30, 31, 32, 33, 37 | , , , , , ⊢ |
| : , : , : , : |
3 | instantiation | 10, 7, 8, 9 | , , , , , ⊢ |
| : , : , : , : |
4 | theorem | | ⊢ |
| proveit.numbers.addition.elim_zero_any |
5 | instantiation | 34 | ⊢ |
| : , : , : |
6 | instantiation | 35 | ⊢ |
| : , : , : , : , : , : , : |
7 | instantiation | 10, 11, 12, 13 | , , , , , ⊢ |
| : , : , : , : |
8 | instantiation | 36, 51, 70, 14, 53, 15, 16, 55, 37, 29, 65, 30, 31, 32, 33, 17* | , , , , , ⊢ |
| : , : , : , : , : , : |
9 | instantiation | 36, 52, 26, 18, 19, 28, 20, 29, 65, 30, 31, 32, 33, 21* | , , , , , ⊢ |
| : , : , : , : , : , : |
10 | theorem | | ⊢ |
| proveit.logic.equality.four_chain_transitivity |
11 | instantiation | 25, 75, 23, 52, 24, 22, 55, 29, 65, 30, 31, 32, 33, 37 | , , , , , ⊢ |
| : , : , : , : , : , : , : |
12 | instantiation | 25, 52, 23, 75, 54, 24, 55, 29, 65, 30, 31, 32, 33, 37 | , , , , , ⊢ |
| : , : , : , : , : , : , : |
13 | instantiation | 25, 67, 26, 51, 27, 28, 53, 55, 37, 29, 65, 30, 31, 32, 33 | , , , , , ⊢ |
| : , : , : , : , : , : , : |
14 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat7 |
15 | instantiation | 34 | ⊢ |
| : , : , : |
16 | instantiation | 35 | ⊢ |
| : , : , : , : , : , : , : |
17 | instantiation | 36, 51, 52, 75, 53, 54, 55, 37, 38* | ⊢ |
| : , : , : , : , : , : |
18 | instantiation | 61 | ⊢ |
| : , : |
19 | instantiation | 61 | ⊢ |
| : , : |
20 | instantiation | 73, 62, 39 | ⊢ |
| : , : , : |
21 | instantiation | 40, 41, 59* | ⊢ |
| : , : |
22 | instantiation | 61 | ⊢ |
| : , : |
23 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat6 |
24 | instantiation | 42 | ⊢ |
| : , : , : , : , : , : |
25 | theorem | | ⊢ |
| proveit.numbers.addition.leftward_commutation |
26 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat4 |
27 | instantiation | 43 | ⊢ |
| : , : , : , : , : |
28 | instantiation | 44 | ⊢ |
| : , : , : , : |
29 | assumption | | ⊢ |
30 | assumption | | ⊢ |
31 | assumption | | ⊢ |
32 | assumption | | ⊢ |
33 | assumption | | ⊢ |
34 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.tuple_len_3_typical_eq |
35 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.tuple_len_7_typical_eq |
36 | theorem | | ⊢ |
| proveit.numbers.addition.association |
37 | instantiation | 73, 62, 45 | ⊢ |
| : , : , : |
38 | instantiation | 46, 47, 48 | ⊢ |
| : , : , : |
39 | instantiation | 73, 68, 49 | ⊢ |
| : , : , : |
40 | theorem | | ⊢ |
| proveit.logic.equality.equals_reversal |
41 | instantiation | 50, 51, 52, 75, 53, 54, 55, 65, 56* | ⊢ |
| : , : , : , : , : , : |
42 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.tuple_len_6_typical_eq |
43 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.tuple_len_5_typical_eq |
44 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.tuple_len_4_typical_eq |
45 | instantiation | 73, 68, 57 | ⊢ |
| : , : , : |
46 | axiom | | ⊢ |
| proveit.logic.equality.equals_transitivity |
47 | instantiation | 58, 59 | ⊢ |
| : , : , : |
48 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.add_2_3 |
49 | instantiation | 73, 71, 60 | ⊢ |
| : , : , : |
50 | theorem | | ⊢ |
| proveit.numbers.multiplication.distribute_through_sum |
51 | axiom | | ⊢ |
| proveit.numbers.number_sets.natural_numbers.zero_in_nats |
52 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat2 |
53 | theorem | | ⊢ |
| proveit.core_expr_types.tuples.tuple_len_0_typical_eq |
54 | instantiation | 61 | ⊢ |
| : , : |
55 | instantiation | 73, 62, 63 | ⊢ |
| : , : , : |
56 | instantiation | 64, 65 | ⊢ |
| : |
57 | instantiation | 73, 71, 66 | ⊢ |
| : , : , : |
58 | axiom | | ⊢ |
| proveit.logic.equality.substitution |
59 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.add_1_1 |
60 | instantiation | 73, 74, 67 | ⊢ |
| : , : , : |
61 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.tuple_len_2_typical_eq |
62 | theorem | | ⊢ |
| proveit.numbers.number_sets.complex_numbers.real_within_complex |
63 | instantiation | 73, 68, 69 | ⊢ |
| : , : , : |
64 | theorem | | ⊢ |
| proveit.numbers.multiplication.elim_one_left |
65 | assumption | | ⊢ |
66 | instantiation | 73, 74, 70 | ⊢ |
| : , : , : |
67 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat5 |
68 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.rational_within_real |
69 | instantiation | 73, 71, 72 | ⊢ |
| : , : , : |
70 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat3 |
71 | theorem | | ⊢ |
| proveit.numbers.number_sets.rational_numbers.int_within_rational |
72 | instantiation | 73, 74, 75 | ⊢ |
| : , : , : |
73 | theorem | | ⊢ |
| proveit.logic.sets.inclusion.superset_membership_from_proper_subset |
74 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.nat_within_int |
75 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat1 |
*equality replacement requirements |