| step type | requirements | statement |
0 | instantiation | 1, 2, 3 | ⊢ |
| : , : , : |
1 | reference | 36 | ⊢ |
2 | instantiation | 4, 77, 109, 57, 5, 58, 41, 6, 7, 8 | ⊢ |
| : , : , : , : , : , : , : |
3 | instantiation | 54, 9 | ⊢ |
| : , : , : |
4 | theorem | | ⊢ |
| proveit.numbers.multiplication.leftward_commutation |
5 | instantiation | 68 | ⊢ |
| : , : |
6 | instantiation | 110, 80, 10 | ⊢ |
| : , : , : |
7 | theorem | | ⊢ |
| proveit.numbers.number_sets.complex_numbers.i_is_complex |
8 | instantiation | 11, 12, 13 | ⊢ |
| : , : |
9 | instantiation | 14, 15, 16, 17 | ⊢ |
| : , : , : , : |
10 | instantiation | 110, 18, 19 | ⊢ |
| : , : , : |
11 | theorem | | ⊢ |
| proveit.numbers.addition.add_complex_closure_bin |
12 | instantiation | 110, 80, 20 | ⊢ |
| : , : , : |
13 | instantiation | 21, 22 | ⊢ |
| : |
14 | theorem | | ⊢ |
| proveit.logic.equality.four_chain_transitivity |
15 | instantiation | 54, 23 | ⊢ |
| : , : , : |
16 | instantiation | 24 | ⊢ |
| : |
17 | instantiation | 25, 26 | ⊢ |
| : , : |
18 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.real_pos_within_real |
19 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.pi_is_real_pos |
20 | instantiation | 27, 28 | ⊢ |
| : |
21 | theorem | | ⊢ |
| proveit.numbers.negation.complex_closure |
22 | instantiation | 29, 60, 33, 34 | ⊢ |
| : , : |
23 | instantiation | 54, 30 | ⊢ |
| : , : , : |
24 | axiom | | ⊢ |
| proveit.logic.equality.equals_reflexivity |
25 | theorem | | ⊢ |
| proveit.logic.equality.equals_reversal |
26 | instantiation | 54, 31 | ⊢ |
| : , : , : |
27 | theorem | | ⊢ |
| proveit.physics.quantum.QPE._delta_b_is_real |
28 | theorem | | ⊢ |
| proveit.physics.quantum.QPE._best_floor_is_int |
29 | theorem | | ⊢ |
| proveit.numbers.division.div_complex_closure |
30 | instantiation | 32, 60, 33, 34, 35* | ⊢ |
| : , : |
31 | instantiation | 36, 37, 38 | ⊢ |
| : , : , : |
32 | theorem | | ⊢ |
| proveit.numbers.division.div_as_mult |
33 | instantiation | 110, 80, 39 | ⊢ |
| : , : , : |
34 | instantiation | 51, 48 | ⊢ |
| : |
35 | instantiation | 40, 41, 81, 42, 43, 44* | ⊢ |
| : , : , : |
36 | axiom | | ⊢ |
| proveit.logic.equality.equals_transitivity |
37 | instantiation | 54, 45 | ⊢ |
| : , : , : |
38 | instantiation | 46, 57, 77, 58, 59, 66, 60, 61, 47* | ⊢ |
| : , : , : , : , : |
39 | instantiation | 86, 87, 48 | ⊢ |
| : , : , : |
40 | theorem | | ⊢ |
| proveit.numbers.exponentiation.real_power_of_real_power |
41 | instantiation | 110, 80, 49 | ⊢ |
| : , : , : |
42 | instantiation | 110, 78, 50 | ⊢ |
| : , : , : |
43 | instantiation | 51, 104 | ⊢ |
| : |
44 | instantiation | 52, 74, 66, 53* | ⊢ |
| : , : |
45 | instantiation | 54, 55 | ⊢ |
| : , : , : |
46 | theorem | | ⊢ |
| proveit.numbers.multiplication.mult_neg_any |
47 | instantiation | 56, 57, 77, 58, 59, 60, 61 | ⊢ |
| : , : , : , : |
48 | theorem | | ⊢ |
| proveit.physics.quantum.QPE._two_pow_t_is_nat_pos |
49 | instantiation | 110, 78, 62 | ⊢ |
| : , : , : |
50 | instantiation | 110, 85, 63 | ⊢ |
| : , : , : |
51 | theorem | | ⊢ |
| proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos |
52 | theorem | | ⊢ |
| proveit.numbers.multiplication.mult_neg_right |
53 | instantiation | 64, 74 | ⊢ |
| : |
54 | axiom | | ⊢ |
| proveit.logic.equality.substitution |
55 | instantiation | 65, 66, 74, 67* | ⊢ |
| : , : |
56 | theorem | | ⊢ |
| proveit.numbers.multiplication.elim_one_any |
57 | axiom | | ⊢ |
| proveit.numbers.number_sets.natural_numbers.zero_in_nats |
58 | theorem | | ⊢ |
| proveit.core_expr_types.tuples.tuple_len_0_typical_eq |
59 | instantiation | 68 | ⊢ |
| : , : |
60 | instantiation | 110, 80, 69 | ⊢ |
| : , : , : |
61 | instantiation | 110, 80, 70 | ⊢ |
| : , : , : |
62 | instantiation | 110, 85, 71 | ⊢ |
| : , : , : |
63 | instantiation | 106, 102 | ⊢ |
| : |
64 | theorem | | ⊢ |
| proveit.numbers.multiplication.elim_one_right |
65 | theorem | | ⊢ |
| proveit.numbers.multiplication.mult_neg_left |
66 | instantiation | 110, 80, 72 | ⊢ |
| : , : , : |
67 | instantiation | 73, 74 | ⊢ |
| : |
68 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.tuple_len_2_typical_eq |
69 | instantiation | 110, 78, 75 | ⊢ |
| : , : , : |
70 | instantiation | 110, 78, 76 | ⊢ |
| : , : , : |
71 | instantiation | 110, 108, 77 | ⊢ |
| : , : , : |
72 | instantiation | 110, 78, 79 | ⊢ |
| : , : , : |
73 | theorem | | ⊢ |
| proveit.numbers.multiplication.elim_one_left |
74 | instantiation | 110, 80, 81 | ⊢ |
| : , : , : |
75 | instantiation | 110, 85, 82 | ⊢ |
| : , : , : |
76 | instantiation | 110, 83, 84 | ⊢ |
| : , : , : |
77 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat2 |
78 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.rational_within_real |
79 | instantiation | 110, 85, 102 | ⊢ |
| : , : , : |
80 | theorem | | ⊢ |
| proveit.numbers.number_sets.complex_numbers.real_within_complex |
81 | instantiation | 86, 87, 105 | ⊢ |
| : , : , : |
82 | instantiation | 110, 88, 89 | ⊢ |
| : , : , : |
83 | theorem | | ⊢ |
| proveit.numbers.number_sets.rational_numbers.rational_nonzero_within_rational |
84 | instantiation | 90, 91, 92 | ⊢ |
| : , : |
85 | theorem | | ⊢ |
| proveit.numbers.number_sets.rational_numbers.int_within_rational |
86 | theorem | | ⊢ |
| proveit.logic.sets.inclusion.unfold_subset_eq |
87 | instantiation | 93, 94 | ⊢ |
| : , : |
88 | instantiation | 95, 96, 107 | ⊢ |
| : , : |
89 | assumption | | ⊢ |
90 | theorem | | ⊢ |
| proveit.numbers.exponentiation.exp_rational_nonzero_closure |
91 | instantiation | 110, 97, 98 | ⊢ |
| : , : , : |
92 | instantiation | 106, 99 | ⊢ |
| : |
93 | theorem | | ⊢ |
| proveit.logic.sets.inclusion.relax_proper_subset |
94 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.nat_pos_within_real |
95 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.int_interval_within_int |
96 | instantiation | 100, 101, 102 | ⊢ |
| : , : |
97 | theorem | | ⊢ |
| proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero |
98 | instantiation | 110, 103, 104 | ⊢ |
| : , : , : |
99 | instantiation | 110, 111, 105 | ⊢ |
| : , : , : |
100 | theorem | | ⊢ |
| proveit.numbers.addition.add_int_closure_bin |
101 | instantiation | 106, 107 | ⊢ |
| : |
102 | instantiation | 110, 108, 109 | ⊢ |
| : , : , : |
103 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int |
104 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.posnat2 |
105 | axiom | | ⊢ |
| proveit.physics.quantum.QPE._t_in_natural_pos |
106 | theorem | | ⊢ |
| proveit.numbers.negation.int_closure |
107 | instantiation | 110, 111, 112 | ⊢ |
| : , : , : |
108 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.nat_within_int |
109 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat1 |
110 | theorem | | ⊢ |
| proveit.logic.sets.inclusion.superset_membership_from_proper_subset |
111 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.nat_pos_within_int |
112 | theorem | | ⊢ |
| proveit.physics.quantum.QPE._two_pow_t_minus_one_is_nat_pos |
*equality replacement requirements |