| step type | requirements | statement |
0 | instantiation | 1, 2, 3 | ⊢ |
| : , : , : |
1 | reference | 39 | ⊢ |
2 | instantiation | 39, 4, 5 | ⊢ |
| : , : , : |
3 | instantiation | 6, 101, 45, 44, 7, 46, 66, 8, 22, 9*, 10* | ⊢ |
| : , : , : , : , : , : |
4 | instantiation | 11, 101, 44, 46, 59, 15, 14 | ⊢ |
| : , : , : , : , : , : , : |
5 | instantiation | 12, 44, 45, 101, 46, 13, 59, 14, 15, 16* | ⊢ |
| : , : , : , : , : , : |
6 | theorem | | ⊢ |
| proveit.numbers.multiplication.distribute_through_sum |
7 | instantiation | 60 | ⊢ |
| : , : |
8 | instantiation | 17, 19 | ⊢ |
| : |
9 | instantiation | 18, 66, 19, 20* | ⊢ |
| : , : |
10 | instantiation | 21, 22 | ⊢ |
| : |
11 | theorem | | ⊢ |
| proveit.numbers.multiplication.leftward_commutation |
12 | theorem | | ⊢ |
| proveit.numbers.multiplication.association |
13 | instantiation | 60 | ⊢ |
| : , : |
14 | instantiation | 23, 59, 24 | ⊢ |
| : , : |
15 | instantiation | 102, 71, 25 | ⊢ |
| : , : , : |
16 | instantiation | 26, 59, 72, 32, 27, 28*, 29* | ⊢ |
| : , : , : |
17 | theorem | | ⊢ |
| proveit.numbers.negation.complex_closure |
18 | theorem | | ⊢ |
| proveit.numbers.multiplication.mult_neg_right |
19 | instantiation | 102, 71, 52 | ⊢ |
| : , : , : |
20 | instantiation | 39, 30, 31 | ⊢ |
| : , : , : |
21 | theorem | | ⊢ |
| proveit.numbers.multiplication.elim_one_left |
22 | instantiation | 102, 71, 35 | ⊢ |
| : , : , : |
23 | theorem | | ⊢ |
| proveit.numbers.exponentiation.exp_complex_closure |
24 | instantiation | 102, 71, 32 | ⊢ |
| : , : , : |
25 | instantiation | 33, 34, 35 | ⊢ |
| : , : |
26 | theorem | | ⊢ |
| proveit.numbers.exponentiation.product_of_real_powers |
27 | instantiation | 36, 37 | ⊢ |
| : |
28 | instantiation | 38, 59 | ⊢ |
| : |
29 | instantiation | 39, 40, 41 | ⊢ |
| : , : , : |
30 | instantiation | 42, 101, 45, 44, 47, 46, 66, 48, 49 | ⊢ |
| : , : , : , : , : , : |
31 | instantiation | 43, 44, 45, 46, 47, 48, 49 | ⊢ |
| : , : , : , : |
32 | instantiation | 102, 79, 50 | ⊢ |
| : , : , : |
33 | theorem | | ⊢ |
| proveit.numbers.addition.add_real_closure_bin |
34 | instantiation | 51, 52 | ⊢ |
| : |
35 | instantiation | 53, 54 | ⊢ |
| : |
36 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.nonzero_if_in_real_nonzero |
37 | instantiation | 102, 55, 75 | ⊢ |
| : , : , : |
38 | theorem | | ⊢ |
| proveit.numbers.exponentiation.complex_x_to_first_power_is_x |
39 | axiom | | ⊢ |
| proveit.logic.equality.equals_transitivity |
40 | instantiation | 56, 57 | ⊢ |
| : , : , : |
41 | instantiation | 58, 59 | ⊢ |
| : |
42 | theorem | | ⊢ |
| proveit.numbers.multiplication.disassociation |
43 | theorem | | ⊢ |
| proveit.numbers.multiplication.elim_one_any |
44 | axiom | | ⊢ |
| proveit.numbers.number_sets.natural_numbers.zero_in_nats |
45 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat2 |
46 | theorem | | ⊢ |
| proveit.core_expr_types.tuples.tuple_len_0_typical_eq |
47 | instantiation | 60 | ⊢ |
| : , : |
48 | instantiation | 102, 71, 63 | ⊢ |
| : , : , : |
49 | instantiation | 102, 71, 64 | ⊢ |
| : , : , : |
50 | instantiation | 102, 86, 61 | ⊢ |
| : , : , : |
51 | theorem | | ⊢ |
| proveit.numbers.negation.real_closure |
52 | instantiation | 62, 63, 64 | ⊢ |
| : , : |
53 | theorem | | ⊢ |
| proveit.physics.quantum.QPE._delta_b_is_real |
54 | theorem | | ⊢ |
| proveit.physics.quantum.QPE._best_floor_is_int |
55 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.real_pos_within_real_nonzero |
56 | axiom | | ⊢ |
| proveit.logic.equality.substitution |
57 | instantiation | 65, 66, 67 | ⊢ |
| : , : |
58 | theorem | | ⊢ |
| proveit.numbers.exponentiation.exp_zero_eq_one |
59 | instantiation | 102, 71, 68 | ⊢ |
| : , : , : |
60 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.tuple_len_2_typical_eq |
61 | instantiation | 98, 94 | ⊢ |
| : |
62 | theorem | | ⊢ |
| proveit.numbers.multiplication.mult_real_closure_bin |
63 | instantiation | 102, 79, 69 | ⊢ |
| : , : , : |
64 | instantiation | 102, 79, 70 | ⊢ |
| : , : , : |
65 | theorem | | ⊢ |
| proveit.numbers.addition.subtraction.add_cancel_basic |
66 | instantiation | 102, 71, 72 | ⊢ |
| : , : , : |
67 | instantiation | 73 | ⊢ |
| : |
68 | instantiation | 102, 74, 75 | ⊢ |
| : , : , : |
69 | instantiation | 102, 86, 76 | ⊢ |
| : , : , : |
70 | instantiation | 102, 77, 78 | ⊢ |
| : , : , : |
71 | theorem | | ⊢ |
| proveit.numbers.number_sets.complex_numbers.real_within_complex |
72 | instantiation | 102, 79, 80 | ⊢ |
| : , : , : |
73 | axiom | | ⊢ |
| proveit.logic.equality.equals_reflexivity |
74 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.real_pos_within_real |
75 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.pi_is_real_pos |
76 | instantiation | 102, 81, 82 | ⊢ |
| : , : , : |
77 | theorem | | ⊢ |
| proveit.numbers.number_sets.rational_numbers.rational_nonzero_within_rational |
78 | instantiation | 83, 84, 85 | ⊢ |
| : , : |
79 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.rational_within_real |
80 | instantiation | 102, 86, 94 | ⊢ |
| : , : , : |
81 | instantiation | 87, 88, 99 | ⊢ |
| : , : |
82 | assumption | | ⊢ |
83 | theorem | | ⊢ |
| proveit.numbers.exponentiation.exp_rational_nonzero_closure |
84 | instantiation | 102, 89, 90 | ⊢ |
| : , : , : |
85 | instantiation | 98, 91 | ⊢ |
| : |
86 | theorem | | ⊢ |
| proveit.numbers.number_sets.rational_numbers.int_within_rational |
87 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.int_interval_within_int |
88 | instantiation | 92, 93, 94 | ⊢ |
| : , : |
89 | theorem | | ⊢ |
| proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero |
90 | instantiation | 102, 95, 96 | ⊢ |
| : , : , : |
91 | instantiation | 102, 103, 97 | ⊢ |
| : , : , : |
92 | theorem | | ⊢ |
| proveit.numbers.addition.add_int_closure_bin |
93 | instantiation | 98, 99 | ⊢ |
| : |
94 | instantiation | 102, 100, 101 | ⊢ |
| : , : , : |
95 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int |
96 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.posnat2 |
97 | axiom | | ⊢ |
| proveit.physics.quantum.QPE._t_in_natural_pos |
98 | theorem | | ⊢ |
| proveit.numbers.negation.int_closure |
99 | instantiation | 102, 103, 104 | ⊢ |
| : , : , : |
100 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.nat_within_int |
101 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat1 |
102 | theorem | | ⊢ |
| proveit.logic.sets.inclusion.superset_membership_from_proper_subset |
103 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.nat_pos_within_int |
104 | theorem | | ⊢ |
| proveit.physics.quantum.QPE._two_pow_t_minus_one_is_nat_pos |
*equality replacement requirements |