| step type | requirements | statement |
0 | instantiation | 1, 2, 3 | ⊢ |
| : , : , : |
1 | reference | 44 | ⊢ |
2 | instantiation | 4, 99, 12, 67, 5, 6, 7* | ⊢ |
| : , : , : |
3 | instantiation | 8, 99, 67, 78, 9, 10* | ⊢ |
| : , : , : |
4 | theorem | | ⊢ |
| proveit.numbers.multiplication.weak_bound_via_right_factor_bound |
5 | instantiation | 11, 12, 76, 13 | ⊢ |
| : , : , : |
6 | instantiation | 14, 15 | ⊢ |
| : , : |
7 | instantiation | 16, 92 | ⊢ |
| : |
8 | theorem | | ⊢ |
| proveit.numbers.multiplication.left_mult_eq_real |
9 | instantiation | 17, 18 | ⊢ |
| : , : |
10 | instantiation | 44, 19, 20 | ⊢ |
| : , : , : |
11 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.interval_co_lower_bound |
12 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.zero_is_real |
13 | axiom | | ⊢ |
| proveit.physics.quantum.QPE._phase_in_interval |
14 | theorem | | ⊢ |
| proveit.numbers.ordering.relax_less |
15 | instantiation | 21, 110 | ⊢ |
| : |
16 | theorem | | ⊢ |
| proveit.numbers.multiplication.mult_zero_right |
17 | theorem | | ⊢ |
| proveit.logic.equality.equals_reversal |
18 | instantiation | 22, 88, 32, 23, 33, 24*, 25* | ⊢ |
| : , : , : |
19 | instantiation | 44, 26, 27 | ⊢ |
| : , : , : |
20 | instantiation | 28, 29, 30, 31 | ⊢ |
| : , : , : , : |
21 | theorem | | ⊢ |
| proveit.numbers.number_sets.natural_numbers.natural_pos_is_pos |
22 | theorem | | ⊢ |
| proveit.numbers.addition.right_add_eq_rational |
23 | instantiation | 44, 32, 33 | ⊢ |
| : , : , : |
24 | instantiation | 34, 66 | ⊢ |
| : |
25 | instantiation | 72, 35, 36 | ⊢ |
| : , : , : |
26 | instantiation | 37, 61, 62, 38, 39 | ⊢ |
| : , : , : , : , : |
27 | instantiation | 72, 40, 41 | ⊢ |
| : , : , : |
28 | theorem | | ⊢ |
| proveit.logic.equality.four_chain_transitivity |
29 | instantiation | 82, 42 | ⊢ |
| : , : , : |
30 | instantiation | 82, 43 | ⊢ |
| : , : , : |
31 | instantiation | 91, 62 | ⊢ |
| : |
32 | theorem | | ⊢ |
| proveit.numbers.number_sets.rational_numbers.zero_is_rational |
33 | instantiation | 44, 45, 46 | ⊢ |
| : , : , : |
34 | theorem | | ⊢ |
| proveit.numbers.addition.elim_zero_left |
35 | instantiation | 47, 48, 49, 101, 50, 51, 54, 52, 66 | ⊢ |
| : , : , : , : , : , : |
36 | instantiation | 53, 66, 54, 55 | ⊢ |
| : , : , : |
37 | theorem | | ⊢ |
| proveit.numbers.division.mult_frac_cancel_numer_left |
38 | instantiation | 108, 57, 56 | ⊢ |
| : , : , : |
39 | instantiation | 108, 57, 58 | ⊢ |
| : , : , : |
40 | instantiation | 82, 59 | ⊢ |
| : , : , : |
41 | instantiation | 82, 60 | ⊢ |
| : , : , : |
42 | instantiation | 84, 61 | ⊢ |
| : |
43 | instantiation | 84, 62 | ⊢ |
| : |
44 | theorem | | ⊢ |
| proveit.logic.equality.sub_right_side_into |
45 | instantiation | 63, 102 | ⊢ |
| : |
46 | assumption | | ⊢ |
47 | theorem | | ⊢ |
| proveit.numbers.addition.disassociation |
48 | axiom | | ⊢ |
| proveit.numbers.number_sets.natural_numbers.zero_in_nats |
49 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat2 |
50 | theorem | | ⊢ |
| proveit.core_expr_types.tuples.tuple_len_0_typical_eq |
51 | instantiation | 64 | ⊢ |
| : , : |
52 | instantiation | 65, 66 | ⊢ |
| : |
53 | theorem | | ⊢ |
| proveit.numbers.addition.subtraction.add_cancel_triple_32 |
54 | instantiation | 108, 98, 67 | ⊢ |
| : , : , : |
55 | instantiation | 68 | ⊢ |
| : |
56 | instantiation | 108, 70, 69 | ⊢ |
| : , : , : |
57 | theorem | | ⊢ |
| proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero |
58 | instantiation | 108, 70, 71 | ⊢ |
| : , : , : |
59 | instantiation | 72, 73, 74 | ⊢ |
| : , : , : |
60 | instantiation | 82, 75 | ⊢ |
| : , : , : |
61 | instantiation | 108, 98, 76 | ⊢ |
| : , : , : |
62 | instantiation | 108, 98, 77 | ⊢ |
| : , : , : |
63 | axiom | | ⊢ |
| proveit.physics.quantum.QPE._delta_b_def |
64 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.tuple_len_2_typical_eq |
65 | theorem | | ⊢ |
| proveit.numbers.negation.complex_closure |
66 | instantiation | 108, 98, 78 | ⊢ |
| : , : , : |
67 | theorem | | ⊢ |
| proveit.physics.quantum.QPE._phase_is_real |
68 | axiom | | ⊢ |
| proveit.logic.equality.equals_reflexivity |
69 | instantiation | 108, 80, 79 | ⊢ |
| : , : , : |
70 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero |
71 | instantiation | 108, 80, 81 | ⊢ |
| : , : , : |
72 | axiom | | ⊢ |
| proveit.logic.equality.equals_transitivity |
73 | instantiation | 82, 83 | ⊢ |
| : , : , : |
74 | instantiation | 84, 92 | ⊢ |
| : |
75 | instantiation | 85, 92 | ⊢ |
| : |
76 | instantiation | 108, 87, 86 | ⊢ |
| : , : , : |
77 | instantiation | 108, 87, 95 | ⊢ |
| : , : , : |
78 | instantiation | 108, 87, 88 | ⊢ |
| : , : , : |
79 | instantiation | 108, 89, 110 | ⊢ |
| : , : , : |
80 | theorem | | ⊢ |
| proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero |
81 | instantiation | 108, 89, 90 | ⊢ |
| : , : , : |
82 | axiom | | ⊢ |
| proveit.logic.equality.substitution |
83 | instantiation | 91, 92 | ⊢ |
| : |
84 | theorem | | ⊢ |
| proveit.numbers.division.frac_one_denom |
85 | theorem | | ⊢ |
| proveit.numbers.multiplication.elim_one_right |
86 | instantiation | 108, 103, 93 | ⊢ |
| : , : , : |
87 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.rational_within_real |
88 | instantiation | 94, 95, 96, 97 | ⊢ |
| : , : |
89 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int |
90 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.posnat1 |
91 | theorem | | ⊢ |
| proveit.numbers.multiplication.elim_one_left |
92 | instantiation | 108, 98, 99 | ⊢ |
| : , : , : |
93 | instantiation | 108, 100, 101 | ⊢ |
| : , : , : |
94 | theorem | | ⊢ |
| proveit.numbers.division.div_rational_closure |
95 | instantiation | 108, 103, 102 | ⊢ |
| : , : , : |
96 | instantiation | 108, 103, 104 | ⊢ |
| : , : , : |
97 | instantiation | 105, 110 | ⊢ |
| : |
98 | theorem | | ⊢ |
| proveit.numbers.number_sets.complex_numbers.real_within_complex |
99 | instantiation | 106, 107, 110 | ⊢ |
| : , : , : |
100 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.nat_within_int |
101 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat1 |
102 | theorem | | ⊢ |
| proveit.physics.quantum.QPE._best_round_is_int |
103 | theorem | | ⊢ |
| proveit.numbers.number_sets.rational_numbers.int_within_rational |
104 | instantiation | 108, 109, 110 | ⊢ |
| : , : , : |
105 | theorem | | ⊢ |
| proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos |
106 | theorem | | ⊢ |
| proveit.logic.sets.inclusion.unfold_subset_eq |
107 | instantiation | 111, 112 | ⊢ |
| : , : |
108 | theorem | | ⊢ |
| proveit.logic.sets.inclusion.superset_membership_from_proper_subset |
109 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.nat_pos_within_int |
110 | theorem | | ⊢ |
| proveit.physics.quantum.QPE._two_pow_t_is_nat_pos |
111 | theorem | | ⊢ |
| proveit.logic.sets.inclusion.relax_proper_subset |
112 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.nat_pos_within_real |
*equality replacement requirements |