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