| step type | requirements | statement |
0 | instantiation | 1, 2, 3, 4, 5*, 6* | ⊢ |
| : , : |
1 | theorem | | ⊢ |
| proveit.numbers.exponentiation.exp_nat_pos_rev |
2 | instantiation | 48, 66, 65, 7, 67, 25, 95, 49 | ⊢ |
| : , : , : , : , : |
3 | instantiation | 98, 81, 8 | ⊢ |
| : , : , : |
4 | reference | 6 | ⊢ |
5 | instantiation | 27, 9 | ⊢ |
| : , : |
6 | instantiation | 53, 10, 11 | ⊢ |
| : , : , : |
7 | instantiation | 78 | ⊢ |
| : , : |
8 | instantiation | 98, 85, 12 | ⊢ |
| : , : , : |
9 | instantiation | 13, 91, 14, 15, 16 | ⊢ |
| : , : , : , : , : , : |
10 | instantiation | 56, 17 | ⊢ |
| : , : , : |
11 | instantiation | 18, 19, 20, 21 | ⊢ |
| : , : , : , : |
12 | instantiation | 98, 90, 22 | ⊢ |
| : , : , : |
13 | theorem | | ⊢ |
| proveit.core_expr_types.tuples.shift_equivalence |
14 | instantiation | 23, 24, 25 | ⊢ |
| : , : |
15 | instantiation | 27, 26 | ⊢ |
| : , : |
16 | instantiation | 27, 28 | ⊢ |
| : , : |
17 | instantiation | 29, 74, 73, 57* | ⊢ |
| : , : |
18 | theorem | | ⊢ |
| proveit.logic.equality.four_chain_transitivity |
19 | instantiation | 64, 95, 66, 30, 31, 76, 35, 73 | ⊢ |
| : , : , : , : , : , : |
20 | instantiation | 32, 65, 33, 67, 34, 76, 35, 73 | ⊢ |
| : , : , : , : |
21 | instantiation | 36, 73, 76, 37 | ⊢ |
| : , : , : |
22 | instantiation | 98, 94, 66 | ⊢ |
| : , : , : |
23 | theorem | | ⊢ |
| proveit.numbers.addition.add_nat_closure_bin |
24 | instantiation | 98, 38, 39 | ⊢ |
| : , : , : |
25 | instantiation | 40, 41 | ⊢ |
| : |
26 | instantiation | 53, 42, 43 | ⊢ |
| : , : , : |
27 | theorem | | ⊢ |
| proveit.logic.equality.equals_reversal |
28 | instantiation | 53, 44, 45 | ⊢ |
| : , : , : |
29 | theorem | | ⊢ |
| proveit.numbers.negation.distribute_neg_through_binary_sum |
30 | instantiation | 78 | ⊢ |
| : , : |
31 | theorem | | ⊢ |
| proveit.numbers.number_sets.complex_numbers.zero_is_complex |
32 | theorem | | ⊢ |
| proveit.numbers.addition.elim_zero_any |
33 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat3 |
34 | instantiation | 46 | ⊢ |
| : , : , : |
35 | instantiation | 47, 73 | ⊢ |
| : |
36 | theorem | | ⊢ |
| proveit.numbers.addition.subtraction.add_cancel_triple_32 |
37 | instantiation | 83 | ⊢ |
| : |
38 | theorem | | ⊢ |
| proveit.numbers.number_sets.natural_numbers.nat_pos_within_nat |
39 | instantiation | 48, 95, 65, 67, 49 | ⊢ |
| : , : , : , : , : |
40 | theorem | | ⊢ |
| proveit.numbers.negation.nat_closure |
41 | instantiation | 50, 51, 52 | ⊢ |
| : |
42 | instantiation | 56, 57 | ⊢ |
| : , : , : |
43 | instantiation | 53, 54, 55 | ⊢ |
| : , : , : |
44 | instantiation | 56, 57 | ⊢ |
| : , : , : |
45 | instantiation | 58, 76 | ⊢ |
| : |
46 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.tuple_len_3_typical_eq |
47 | theorem | | ⊢ |
| proveit.numbers.negation.complex_closure |
48 | theorem | | ⊢ |
| proveit.numbers.addition.add_nat_pos_from_nonneg |
49 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.less_0_1 |
50 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.nonpos_int_is_int_nonpos |
51 | instantiation | 59, 91, 89 | ⊢ |
| : , : |
52 | instantiation | 60, 80, 79, 82, 61, 62*, 63* | ⊢ |
| : , : , : |
53 | axiom | | ⊢ |
| proveit.logic.equality.equals_transitivity |
54 | instantiation | 64, 65, 66, 95, 67, 68, 74, 73, 76 | ⊢ |
| : , : , : , : , : , : |
55 | instantiation | 69, 76, 73, 77 | ⊢ |
| : , : , : |
56 | axiom | | ⊢ |
| proveit.logic.equality.substitution |
57 | instantiation | 70, 76 | ⊢ |
| : |
58 | theorem | | ⊢ |
| proveit.numbers.addition.elim_zero_left |
59 | theorem | | ⊢ |
| proveit.numbers.addition.add_int_closure_bin |
60 | theorem | | ⊢ |
| proveit.numbers.addition.weak_bound_via_left_term_bound |
61 | instantiation | 71, 100 | ⊢ |
| : |
62 | instantiation | 72, 73, 74 | ⊢ |
| : , : |
63 | instantiation | 75, 76, 77 | ⊢ |
| : , : |
64 | theorem | | ⊢ |
| proveit.numbers.addition.disassociation |
65 | axiom | | ⊢ |
| proveit.numbers.number_sets.natural_numbers.zero_in_nats |
66 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat2 |
67 | theorem | | ⊢ |
| proveit.core_expr_types.tuples.tuple_len_0_typical_eq |
68 | instantiation | 78 | ⊢ |
| : , : |
69 | theorem | | ⊢ |
| proveit.numbers.addition.subtraction.add_cancel_triple_31 |
70 | theorem | | ⊢ |
| proveit.numbers.negation.double_negation |
71 | theorem | | ⊢ |
| proveit.numbers.number_sets.natural_numbers.natural_pos_lower_bound |
72 | theorem | | ⊢ |
| proveit.numbers.addition.commutation |
73 | instantiation | 98, 81, 79 | ⊢ |
| : , : , : |
74 | instantiation | 98, 81, 80 | ⊢ |
| : , : , : |
75 | theorem | | ⊢ |
| proveit.numbers.addition.subtraction.add_cancel_basic |
76 | instantiation | 98, 81, 82 | ⊢ |
| : , : , : |
77 | instantiation | 83 | ⊢ |
| : |
78 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.tuple_len_2_typical_eq |
79 | instantiation | 98, 85, 84 | ⊢ |
| : , : , : |
80 | instantiation | 98, 85, 86 | ⊢ |
| : , : , : |
81 | theorem | | ⊢ |
| proveit.numbers.number_sets.complex_numbers.real_within_complex |
82 | instantiation | 87, 88, 100 | ⊢ |
| : , : , : |
83 | axiom | | ⊢ |
| proveit.logic.equality.equals_reflexivity |
84 | instantiation | 98, 90, 89 | ⊢ |
| : , : , : |
85 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.rational_within_real |
86 | instantiation | 98, 90, 91 | ⊢ |
| : , : , : |
87 | theorem | | ⊢ |
| proveit.logic.sets.inclusion.unfold_subset_eq |
88 | instantiation | 92, 93 | ⊢ |
| : , : |
89 | instantiation | 98, 94, 95 | ⊢ |
| : , : , : |
90 | theorem | | ⊢ |
| proveit.numbers.number_sets.rational_numbers.int_within_rational |
91 | instantiation | 96, 97 | ⊢ |
| : |
92 | theorem | | ⊢ |
| proveit.logic.sets.inclusion.relax_proper_subset |
93 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.nat_pos_within_real |
94 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.nat_within_int |
95 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat1 |
96 | theorem | | ⊢ |
| proveit.numbers.negation.int_closure |
97 | instantiation | 98, 99, 100 | ⊢ |
| : , : , : |
98 | theorem | | ⊢ |
| proveit.logic.sets.inclusion.superset_membership_from_proper_subset |
99 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.nat_pos_within_int |
100 | assumption | | ⊢ |
*equality replacement requirements |