| step type | requirements | statement |
0 | instantiation | 1, 2, 3, 4, 5, 6*, 7* | ⊢ |
| : , : , : |
1 | theorem | | ⊢ |
| proveit.numbers.addition.strong_bound_via_left_term_bound |
2 | instantiation | 57, 47, 8 | ⊢ |
| : , : , : |
3 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.zero_is_real |
4 | reference | 45 | ⊢ |
5 | instantiation | 9, 10 | ⊢ |
| : |
6 | instantiation | 13, 11, 12 | ⊢ |
| : , : , : |
7 | instantiation | 13, 14, 15 | ⊢ |
| : , : , : |
8 | instantiation | 57, 50, 16 | ⊢ |
| : , : , : |
9 | theorem | | ⊢ |
| proveit.numbers.number_sets.natural_numbers.natural_pos_is_pos |
10 | instantiation | 17, 56, 54 | ⊢ |
| : , : |
11 | instantiation | 20, 49, 56, 34, 21, 35, 18, 42, 24 | ⊢ |
| : , : , : , : , : , : |
12 | instantiation | 19, 34, 56, 35, 21, 42, 24 | ⊢ |
| : , : , : , : |
13 | axiom | | ⊢ |
| proveit.logic.equality.equals_transitivity |
14 | instantiation | 20, 49, 56, 34, 21, 35, 42, 24 | ⊢ |
| : , : , : , : , : , : |
15 | instantiation | 22, 34, 56, 49, 35, 23, 42, 24, 25* | ⊢ |
| : , : , : , : , : , : |
16 | instantiation | 26, 51, 27 | ⊢ |
| : , : |
17 | theorem | | ⊢ |
| proveit.numbers.exponentiation.exp_natpos_closure |
18 | theorem | | ⊢ |
| proveit.numbers.number_sets.complex_numbers.zero_is_complex |
19 | theorem | | ⊢ |
| proveit.numbers.addition.elim_zero_any |
20 | theorem | | ⊢ |
| proveit.numbers.addition.disassociation |
21 | instantiation | 39 | ⊢ |
| : , : |
22 | theorem | | ⊢ |
| proveit.numbers.addition.association |
23 | instantiation | 39 | ⊢ |
| : , : |
24 | instantiation | 28, 37 | ⊢ |
| : |
25 | instantiation | 29, 30, 31* | ⊢ |
| : , : |
26 | theorem | | ⊢ |
| proveit.numbers.addition.add_int_closure_bin |
27 | instantiation | 32, 46 | ⊢ |
| : |
28 | theorem | | ⊢ |
| proveit.numbers.negation.complex_closure |
29 | theorem | | ⊢ |
| proveit.logic.equality.equals_reversal |
30 | instantiation | 33, 34, 56, 49, 35, 36, 37, 42, 38* | ⊢ |
| : , : , : , : , : , : |
31 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.add_1_1 |
32 | theorem | | ⊢ |
| proveit.numbers.negation.int_closure |
33 | theorem | | ⊢ |
| proveit.numbers.multiplication.distribute_through_sum |
34 | axiom | | ⊢ |
| proveit.numbers.number_sets.natural_numbers.zero_in_nats |
35 | theorem | | ⊢ |
| proveit.core_expr_types.tuples.tuple_len_0_typical_eq |
36 | instantiation | 39 | ⊢ |
| : , : |
37 | instantiation | 57, 44, 40 | ⊢ |
| : , : , : |
38 | instantiation | 41, 42 | ⊢ |
| : |
39 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.tuple_len_2_typical_eq |
40 | instantiation | 57, 47, 43 | ⊢ |
| : , : , : |
41 | theorem | | ⊢ |
| proveit.numbers.multiplication.elim_one_left |
42 | instantiation | 57, 44, 45 | ⊢ |
| : , : , : |
43 | instantiation | 57, 50, 46 | ⊢ |
| : , : , : |
44 | theorem | | ⊢ |
| proveit.numbers.number_sets.complex_numbers.real_within_complex |
45 | instantiation | 57, 47, 48 | ⊢ |
| : , : , : |
46 | instantiation | 57, 55, 49 | ⊢ |
| : , : , : |
47 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.rational_within_real |
48 | instantiation | 57, 50, 51 | ⊢ |
| : , : , : |
49 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat1 |
50 | theorem | | ⊢ |
| proveit.numbers.number_sets.rational_numbers.int_within_rational |
51 | instantiation | 52, 53, 54 | ⊢ |
| : , : |
52 | theorem | | ⊢ |
| proveit.numbers.exponentiation.exp_int_closure |
53 | instantiation | 57, 55, 56 | ⊢ |
| : , : , : |
54 | instantiation | 57, 58, 59 | ⊢ |
| : , : , : |
55 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.nat_within_int |
56 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat2 |
57 | theorem | | ⊢ |
| proveit.logic.sets.inclusion.superset_membership_from_proper_subset |
58 | theorem | | ⊢ |
| proveit.numbers.number_sets.natural_numbers.nat_pos_within_nat |
59 | assumption | | ⊢ |
*equality replacement requirements |