| step type | requirements | statement |
0 | instantiation | 1, 2 | ⊢ |
| : , : , : |
1 | reference | 35 | ⊢ |
2 | instantiation | 3, 4, 5, 6 | ⊢ |
| : , : , : , : |
3 | theorem | | ⊢ |
| proveit.logic.equality.four_chain_transitivity |
4 | instantiation | 35, 7 | ⊢ |
| : , : , : |
5 | instantiation | 8 | ⊢ |
| : |
6 | instantiation | 9, 10 | ⊢ |
| : , : |
7 | instantiation | 35, 11 | ⊢ |
| : , : , : |
8 | axiom | | ⊢ |
| proveit.logic.equality.equals_reflexivity |
9 | theorem | | ⊢ |
| proveit.logic.equality.equals_reversal |
10 | instantiation | 35, 12 | ⊢ |
| : , : , : |
11 | instantiation | 13, 41, 14, 15, 16* | ⊢ |
| : , : |
12 | instantiation | 17, 18, 19 | ⊢ |
| : , : , : |
13 | theorem | | ⊢ |
| proveit.numbers.division.div_as_mult |
14 | instantiation | 91, 61, 20 | ⊢ |
| : , : , : |
15 | instantiation | 32, 29 | ⊢ |
| : |
16 | instantiation | 21, 22, 62, 23, 24, 25* | ⊢ |
| : , : , : |
17 | axiom | | ⊢ |
| proveit.logic.equality.equals_transitivity |
18 | instantiation | 35, 26 | ⊢ |
| : , : , : |
19 | instantiation | 27, 38, 58, 39, 40, 47, 41, 42, 28* | ⊢ |
| : , : , : , : , : |
20 | instantiation | 67, 68, 29 | ⊢ |
| : , : , : |
21 | theorem | | ⊢ |
| proveit.numbers.exponentiation.real_power_of_real_power |
22 | instantiation | 91, 61, 30 | ⊢ |
| : , : , : |
23 | instantiation | 91, 59, 31 | ⊢ |
| : , : , : |
24 | instantiation | 32, 85 | ⊢ |
| : |
25 | instantiation | 33, 55, 47, 34* | ⊢ |
| : , : |
26 | instantiation | 35, 36 | ⊢ |
| : , : , : |
27 | theorem | | ⊢ |
| proveit.numbers.multiplication.mult_neg_any |
28 | instantiation | 37, 38, 58, 39, 40, 41, 42 | ⊢ |
| : , : , : , : |
29 | theorem | | ⊢ |
| proveit.physics.quantum.QPE._two_pow_t_is_nat_pos |
30 | instantiation | 91, 59, 43 | ⊢ |
| : , : , : |
31 | instantiation | 91, 66, 44 | ⊢ |
| : , : , : |
32 | theorem | | ⊢ |
| proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos |
33 | theorem | | ⊢ |
| proveit.numbers.multiplication.mult_neg_right |
34 | instantiation | 45, 55 | ⊢ |
| : |
35 | axiom | | ⊢ |
| proveit.logic.equality.substitution |
36 | instantiation | 46, 47, 55, 48* | ⊢ |
| : , : |
37 | theorem | | ⊢ |
| proveit.numbers.multiplication.elim_one_any |
38 | axiom | | ⊢ |
| proveit.numbers.number_sets.natural_numbers.zero_in_nats |
39 | theorem | | ⊢ |
| proveit.core_expr_types.tuples.tuple_len_0_typical_eq |
40 | instantiation | 49 | ⊢ |
| : , : |
41 | instantiation | 91, 61, 50 | ⊢ |
| : , : , : |
42 | instantiation | 91, 61, 51 | ⊢ |
| : , : , : |
43 | instantiation | 91, 66, 52 | ⊢ |
| : , : , : |
44 | instantiation | 87, 83 | ⊢ |
| : |
45 | theorem | | ⊢ |
| proveit.numbers.multiplication.elim_one_right |
46 | theorem | | ⊢ |
| proveit.numbers.multiplication.mult_neg_left |
47 | instantiation | 91, 61, 53 | ⊢ |
| : , : , : |
48 | instantiation | 54, 55 | ⊢ |
| : |
49 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.tuple_len_2_typical_eq |
50 | instantiation | 91, 59, 56 | ⊢ |
| : , : , : |
51 | instantiation | 91, 59, 57 | ⊢ |
| : , : , : |
52 | instantiation | 91, 89, 58 | ⊢ |
| : , : , : |
53 | instantiation | 91, 59, 60 | ⊢ |
| : , : , : |
54 | theorem | | ⊢ |
| proveit.numbers.multiplication.elim_one_left |
55 | instantiation | 91, 61, 62 | ⊢ |
| : , : , : |
56 | instantiation | 91, 66, 63 | ⊢ |
| : , : , : |
57 | instantiation | 91, 64, 65 | ⊢ |
| : , : , : |
58 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat2 |
59 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.rational_within_real |
60 | instantiation | 91, 66, 83 | ⊢ |
| : , : , : |
61 | theorem | | ⊢ |
| proveit.numbers.number_sets.complex_numbers.real_within_complex |
62 | instantiation | 67, 68, 86 | ⊢ |
| : , : , : |
63 | instantiation | 91, 69, 70 | ⊢ |
| : , : , : |
64 | theorem | | ⊢ |
| proveit.numbers.number_sets.rational_numbers.rational_nonzero_within_rational |
65 | instantiation | 71, 72, 73 | ⊢ |
| : , : |
66 | theorem | | ⊢ |
| proveit.numbers.number_sets.rational_numbers.int_within_rational |
67 | theorem | | ⊢ |
| proveit.logic.sets.inclusion.unfold_subset_eq |
68 | instantiation | 74, 75 | ⊢ |
| : , : |
69 | instantiation | 76, 77, 88 | ⊢ |
| : , : |
70 | assumption | | ⊢ |
71 | theorem | | ⊢ |
| proveit.numbers.exponentiation.exp_rational_nonzero_closure |
72 | instantiation | 91, 78, 79 | ⊢ |
| : , : , : |
73 | instantiation | 87, 80 | ⊢ |
| : |
74 | theorem | | ⊢ |
| proveit.logic.sets.inclusion.relax_proper_subset |
75 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.nat_pos_within_real |
76 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.int_interval_within_int |
77 | instantiation | 81, 82, 83 | ⊢ |
| : , : |
78 | theorem | | ⊢ |
| proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero |
79 | instantiation | 91, 84, 85 | ⊢ |
| : , : , : |
80 | instantiation | 91, 92, 86 | ⊢ |
| : , : , : |
81 | theorem | | ⊢ |
| proveit.numbers.addition.add_int_closure_bin |
82 | instantiation | 87, 88 | ⊢ |
| : |
83 | instantiation | 91, 89, 90 | ⊢ |
| : , : , : |
84 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int |
85 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.posnat2 |
86 | axiom | | ⊢ |
| proveit.physics.quantum.QPE._t_in_natural_pos |
87 | theorem | | ⊢ |
| proveit.numbers.negation.int_closure |
88 | instantiation | 91, 92, 93 | ⊢ |
| : , : , : |
89 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.nat_within_int |
90 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat1 |
91 | theorem | | ⊢ |
| proveit.logic.sets.inclusion.superset_membership_from_proper_subset |
92 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.nat_pos_within_int |
93 | theorem | | ⊢ |
| proveit.physics.quantum.QPE._two_pow_t_minus_one_is_nat_pos |
*equality replacement requirements |