| step type | requirements | statement |
0 | instantiation | 1, 2, 3 | ⊢ |
| : , : , : |
1 | theorem | | ⊢ |
| proveit.logic.equality.sub_left_side_into |
2 | reference | 91 | ⊢ |
3 | instantiation | 4, 88, 56, 67, 5, 6* | ⊢ |
| : , : , : |
4 | theorem | | ⊢ |
| proveit.numbers.multiplication.left_mult_eq_real |
5 | instantiation | 7, 8 | ⊢ |
| : , : |
6 | instantiation | 33, 9, 10 | ⊢ |
| : , : , : |
7 | theorem | | ⊢ |
| proveit.logic.equality.equals_reversal |
8 | instantiation | 11, 77, 21, 12, 22, 13*, 14* | ⊢ |
| : , : , : |
9 | instantiation | 33, 15, 16 | ⊢ |
| : , : , : |
10 | instantiation | 17, 18, 19, 20 | ⊢ |
| : , : , : , : |
11 | theorem | | ⊢ |
| proveit.numbers.addition.right_add_eq_rational |
12 | instantiation | 33, 21, 22 | ⊢ |
| : , : , : |
13 | instantiation | 23, 55 | ⊢ |
| : |
14 | instantiation | 61, 24, 25 | ⊢ |
| : , : , : |
15 | instantiation | 26, 50, 51, 27, 28 | ⊢ |
| : , : , : , : , : |
16 | instantiation | 61, 29, 30 | ⊢ |
| : , : , : |
17 | theorem | | ⊢ |
| proveit.logic.equality.four_chain_transitivity |
18 | instantiation | 71, 31 | ⊢ |
| : , : , : |
19 | instantiation | 71, 32 | ⊢ |
| : , : , : |
20 | instantiation | 80, 51 | ⊢ |
| : |
21 | theorem | | ⊢ |
| proveit.numbers.number_sets.rational_numbers.zero_is_rational |
22 | instantiation | 33, 34, 35 | ⊢ |
| : , : , : |
23 | theorem | | ⊢ |
| proveit.numbers.addition.elim_zero_left |
24 | instantiation | 36, 37, 38, 90, 39, 40, 43, 41, 55 | ⊢ |
| : , : , : , : , : , : |
25 | instantiation | 42, 55, 43, 44 | ⊢ |
| : , : , : |
26 | theorem | | ⊢ |
| proveit.numbers.division.mult_frac_cancel_numer_left |
27 | instantiation | 97, 46, 45 | ⊢ |
| : , : , : |
28 | instantiation | 97, 46, 47 | ⊢ |
| : , : , : |
29 | instantiation | 71, 48 | ⊢ |
| : , : , : |
30 | instantiation | 71, 49 | ⊢ |
| : , : , : |
31 | instantiation | 73, 50 | ⊢ |
| : |
32 | instantiation | 73, 51 | ⊢ |
| : |
33 | theorem | | ⊢ |
| proveit.logic.equality.sub_right_side_into |
34 | instantiation | 52, 91 | ⊢ |
| : |
35 | assumption | | ⊢ |
36 | theorem | | ⊢ |
| proveit.numbers.addition.disassociation |
37 | axiom | | ⊢ |
| proveit.numbers.number_sets.natural_numbers.zero_in_nats |
38 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat2 |
39 | theorem | | ⊢ |
| proveit.core_expr_types.tuples.tuple_len_0_typical_eq |
40 | instantiation | 53 | ⊢ |
| : , : |
41 | instantiation | 54, 55 | ⊢ |
| : |
42 | theorem | | ⊢ |
| proveit.numbers.addition.subtraction.add_cancel_triple_32 |
43 | instantiation | 97, 87, 56 | ⊢ |
| : , : , : |
44 | instantiation | 57 | ⊢ |
| : |
45 | instantiation | 97, 59, 58 | ⊢ |
| : , : , : |
46 | theorem | | ⊢ |
| proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero |
47 | instantiation | 97, 59, 60 | ⊢ |
| : , : , : |
48 | instantiation | 61, 62, 63 | ⊢ |
| : , : , : |
49 | instantiation | 71, 64 | ⊢ |
| : , : , : |
50 | instantiation | 97, 87, 65 | ⊢ |
| : , : , : |
51 | instantiation | 97, 87, 66 | ⊢ |
| : , : , : |
52 | axiom | | ⊢ |
| proveit.physics.quantum.QPE._delta_b_def |
53 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.tuple_len_2_typical_eq |
54 | theorem | | ⊢ |
| proveit.numbers.negation.complex_closure |
55 | instantiation | 97, 87, 67 | ⊢ |
| : , : , : |
56 | theorem | | ⊢ |
| proveit.physics.quantum.QPE._phase_is_real |
57 | axiom | | ⊢ |
| proveit.logic.equality.equals_reflexivity |
58 | instantiation | 97, 69, 68 | ⊢ |
| : , : , : |
59 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero |
60 | instantiation | 97, 69, 70 | ⊢ |
| : , : , : |
61 | axiom | | ⊢ |
| proveit.logic.equality.equals_transitivity |
62 | instantiation | 71, 72 | ⊢ |
| : , : , : |
63 | instantiation | 73, 81 | ⊢ |
| : |
64 | instantiation | 74, 81 | ⊢ |
| : |
65 | instantiation | 97, 76, 75 | ⊢ |
| : , : , : |
66 | instantiation | 97, 76, 84 | ⊢ |
| : , : , : |
67 | instantiation | 97, 76, 77 | ⊢ |
| : , : , : |
68 | instantiation | 97, 78, 99 | ⊢ |
| : , : , : |
69 | theorem | | ⊢ |
| proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero |
70 | instantiation | 97, 78, 79 | ⊢ |
| : , : , : |
71 | axiom | | ⊢ |
| proveit.logic.equality.substitution |
72 | instantiation | 80, 81 | ⊢ |
| : |
73 | theorem | | ⊢ |
| proveit.numbers.division.frac_one_denom |
74 | theorem | | ⊢ |
| proveit.numbers.multiplication.elim_one_right |
75 | instantiation | 97, 92, 82 | ⊢ |
| : , : , : |
76 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.rational_within_real |
77 | instantiation | 83, 84, 85, 86 | ⊢ |
| : , : |
78 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int |
79 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.posnat1 |
80 | theorem | | ⊢ |
| proveit.numbers.multiplication.elim_one_left |
81 | instantiation | 97, 87, 88 | ⊢ |
| : , : , : |
82 | instantiation | 97, 89, 90 | ⊢ |
| : , : , : |
83 | theorem | | ⊢ |
| proveit.numbers.division.div_rational_closure |
84 | instantiation | 97, 92, 91 | ⊢ |
| : , : , : |
85 | instantiation | 97, 92, 93 | ⊢ |
| : , : , : |
86 | instantiation | 94, 99 | ⊢ |
| : |
87 | theorem | | ⊢ |
| proveit.numbers.number_sets.complex_numbers.real_within_complex |
88 | instantiation | 95, 96, 99 | ⊢ |
| : , : , : |
89 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.nat_within_int |
90 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat1 |
91 | theorem | | ⊢ |
| proveit.physics.quantum.QPE._best_round_is_int |
92 | theorem | | ⊢ |
| proveit.numbers.number_sets.rational_numbers.int_within_rational |
93 | instantiation | 97, 98, 99 | ⊢ |
| : , : , : |
94 | theorem | | ⊢ |
| proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos |
95 | theorem | | ⊢ |
| proveit.logic.sets.inclusion.unfold_subset_eq |
96 | instantiation | 100, 101 | ⊢ |
| : , : |
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_is_nat_pos |
100 | theorem | | ⊢ |
| proveit.logic.sets.inclusion.relax_proper_subset |
101 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.nat_pos_within_real |
*equality replacement requirements |