| step type | requirements | statement |
0 | instantiation | 1, 2, 3 | ⊢ |
| : , : , : |
1 | reference | 5 | ⊢ |
2 | instantiation | 36, 4 | ⊢ |
| : , : , : |
3 | instantiation | 5, 6, 7 | ⊢ |
| : , : , : |
4 | instantiation | 36, 8 | ⊢ |
| : , : , : |
5 | axiom | | ⊢ |
| proveit.logic.equality.equals_transitivity |
6 | instantiation | 9, 94, 10, 14, 11, 15, 21, 17, 57, 12 | ⊢ |
| : , : , : , : , : , : |
7 | instantiation | 13, 14, 97, 15, 16, 21, 17, 57, 18 | ⊢ |
| : , : , : , : , : , : , : , : |
8 | instantiation | 36, 19 | ⊢ |
| : , : , : |
9 | theorem | | ⊢ |
| proveit.numbers.addition.disassociation |
10 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat3 |
11 | instantiation | 20 | ⊢ |
| : , : , : |
12 | instantiation | 56, 21 | ⊢ |
| : |
13 | theorem | | ⊢ |
| proveit.numbers.addition.subtraction.add_cancel_general |
14 | axiom | | ⊢ |
| proveit.numbers.number_sets.natural_numbers.zero_in_nats |
15 | theorem | | ⊢ |
| proveit.core_expr_types.tuples.tuple_len_0_typical_eq |
16 | instantiation | 22 | ⊢ |
| : , : |
17 | instantiation | 56, 23 | ⊢ |
| : |
18 | instantiation | 24 | ⊢ |
| : |
19 | instantiation | 25, 26, 27, 28 | ⊢ |
| : , : , : , : |
20 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.tuple_len_3_typical_eq |
21 | instantiation | 95, 74, 29 | ⊢ |
| : , : , : |
22 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.tuple_len_2_typical_eq |
23 | instantiation | 30, 31, 32 | ⊢ |
| : , : |
24 | axiom | | ⊢ |
| proveit.logic.equality.equals_reflexivity |
25 | theorem | | ⊢ |
| proveit.logic.equality.four_chain_transitivity |
26 | instantiation | 36, 33 | ⊢ |
| : , : , : |
27 | instantiation | 34, 35 | ⊢ |
| : , : |
28 | instantiation | 36, 37 | ⊢ |
| : , : , : |
29 | instantiation | 95, 84, 38 | ⊢ |
| : , : , : |
30 | theorem | | ⊢ |
| proveit.numbers.multiplication.mult_complex_closure_bin |
31 | instantiation | 39, 57, 40, 41 | ⊢ |
| : , : |
32 | instantiation | 51, 65, 43 | ⊢ |
| : , : |
33 | instantiation | 42, 43, 44 | ⊢ |
| : , : |
34 | theorem | | ⊢ |
| proveit.logic.equality.equals_reversal |
35 | instantiation | 45, 65, 46, 55, 53 | ⊢ |
| : , : , : |
36 | axiom | | ⊢ |
| proveit.logic.equality.substitution |
37 | instantiation | 47, 48, 49 | ⊢ |
| : , : |
38 | instantiation | 95, 92, 50 | ⊢ |
| : , : , : |
39 | theorem | | ⊢ |
| proveit.numbers.division.div_complex_closure |
40 | instantiation | 51, 65, 57 | ⊢ |
| : , : |
41 | instantiation | 52, 53, 54 | ⊢ |
| : , : , : |
42 | theorem | | ⊢ |
| proveit.numbers.addition.commutation |
43 | instantiation | 95, 74, 55 | ⊢ |
| : , : , : |
44 | instantiation | 56, 57 | ⊢ |
| : |
45 | theorem | | ⊢ |
| proveit.numbers.exponentiation.product_of_real_powers |
46 | instantiation | 58, 69 | ⊢ |
| : |
47 | theorem | | ⊢ |
| proveit.numbers.exponentiation.neg_power_as_div |
48 | instantiation | 95, 59, 60 | ⊢ |
| : , : , : |
49 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.posnat1 |
50 | instantiation | 95, 61, 62 | ⊢ |
| : , : , : |
51 | theorem | | ⊢ |
| proveit.numbers.exponentiation.exp_complex_closure |
52 | theorem | | ⊢ |
| proveit.logic.equality.sub_left_side_into |
53 | instantiation | 63, 88 | ⊢ |
| : |
54 | instantiation | 64, 65 | ⊢ |
| : |
55 | instantiation | 66, 67, 68 | ⊢ |
| : , : , : |
56 | theorem | | ⊢ |
| proveit.numbers.negation.complex_closure |
57 | instantiation | 95, 74, 69 | ⊢ |
| : , : , : |
58 | theorem | | ⊢ |
| proveit.numbers.negation.real_closure |
59 | theorem | | ⊢ |
| proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero |
60 | instantiation | 95, 70, 71 | ⊢ |
| : , : , : |
61 | instantiation | 72, 86, 73 | ⊢ |
| : , : |
62 | assumption | | ⊢ |
63 | theorem | | ⊢ |
| proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos |
64 | theorem | | ⊢ |
| proveit.numbers.exponentiation.complex_x_to_first_power_is_x |
65 | instantiation | 95, 74, 75 | ⊢ |
| : , : , : |
66 | theorem | | ⊢ |
| proveit.logic.sets.inclusion.unfold_subset_eq |
67 | instantiation | 76, 77 | ⊢ |
| : , : |
68 | axiom | | ⊢ |
| proveit.physics.quantum.QPE._t_in_natural_pos |
69 | instantiation | 95, 84, 78 | ⊢ |
| : , : , : |
70 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero |
71 | instantiation | 95, 79, 80 | ⊢ |
| : , : , : |
72 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.int_interval_within_int |
73 | instantiation | 81, 82, 83 | ⊢ |
| : , : |
74 | theorem | | ⊢ |
| proveit.numbers.number_sets.complex_numbers.real_within_complex |
75 | instantiation | 95, 84, 85 | ⊢ |
| : , : , : |
76 | theorem | | ⊢ |
| proveit.logic.sets.inclusion.relax_proper_subset |
77 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.nat_pos_within_real |
78 | instantiation | 95, 92, 86 | ⊢ |
| : , : , : |
79 | theorem | | ⊢ |
| proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero |
80 | instantiation | 95, 87, 88 | ⊢ |
| : , : , : |
81 | theorem | | ⊢ |
| proveit.numbers.addition.add_int_closure_bin |
82 | instantiation | 95, 89, 90 | ⊢ |
| : , : , : |
83 | instantiation | 91, 93 | ⊢ |
| : |
84 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.rational_within_real |
85 | instantiation | 95, 92, 93 | ⊢ |
| : , : , : |
86 | instantiation | 95, 96, 94 | ⊢ |
| : , : , : |
87 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int |
88 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.posnat2 |
89 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.nat_pos_within_int |
90 | theorem | | ⊢ |
| proveit.physics.quantum.QPE._two_pow_t_minus_one_is_nat_pos |
91 | theorem | | ⊢ |
| proveit.numbers.negation.int_closure |
92 | theorem | | ⊢ |
| proveit.numbers.number_sets.rational_numbers.int_within_rational |
93 | instantiation | 95, 96, 97 | ⊢ |
| : , : , : |
94 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat1 |
95 | theorem | | ⊢ |
| proveit.logic.sets.inclusion.superset_membership_from_proper_subset |
96 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.nat_within_int |
97 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat2 |