| step type | requirements | statement |
0 | instantiation | 1, 2, 3 | ⊢ |
| : , : |
1 | theorem | | ⊢ |
| proveit.logic.booleans.conjunction.and_if_both |
2 | instantiation | 4, 114, 27, 82, 5, 6, 7* | ⊢ |
| : , : , : |
3 | instantiation | 8, 9, 119, 35, 10, 11 | ⊢ |
| : , : , : |
4 | theorem | | ⊢ |
| proveit.numbers.multiplication.weak_bound_via_right_factor_bound |
5 | instantiation | 12, 27, 91, 28 | ⊢ |
| : , : , : |
6 | instantiation | 13, 19 | ⊢ |
| : , : |
7 | instantiation | 14, 107 | ⊢ |
| : |
8 | theorem | | ⊢ |
| proveit.numbers.ordering.less_add_right_weak_int |
9 | instantiation | 15, 117, 16 | ⊢ |
| : , : , : |
10 | instantiation | 17, 114, 82, 91, 18, 19, 90* | ⊢ |
| : , : , : |
11 | instantiation | 20, 21, 22 | ⊢ |
| : , : |
12 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.interval_co_lower_bound |
13 | theorem | | ⊢ |
| proveit.numbers.ordering.relax_less |
14 | theorem | | ⊢ |
| proveit.numbers.multiplication.mult_zero_right |
15 | theorem | | ⊢ |
| proveit.logic.equality.sub_left_side_into |
16 | instantiation | 23, 114, 82, 93, 24, 25* | ⊢ |
| : , : , : |
17 | theorem | | ⊢ |
| proveit.numbers.multiplication.strong_bound_via_right_factor_bound |
18 | instantiation | 26, 27, 91, 28 | ⊢ |
| : , : , : |
19 | instantiation | 29, 125 | ⊢ |
| : |
20 | theorem | | ⊢ |
| proveit.numbers.ordering.relax_equal_to_less_eq |
21 | instantiation | 123, 102, 30 | ⊢ |
| : , : , : |
22 | instantiation | 83 | ⊢ |
| : |
23 | theorem | | ⊢ |
| proveit.numbers.multiplication.left_mult_eq_real |
24 | instantiation | 31, 32 | ⊢ |
| : , : |
25 | instantiation | 59, 33, 34 | ⊢ |
| : , : , : |
26 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.interval_co_upper_bound |
27 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.zero_is_real |
28 | axiom | | ⊢ |
| proveit.physics.quantum.QPE._phase_in_interval |
29 | theorem | | ⊢ |
| proveit.numbers.number_sets.natural_numbers.natural_pos_is_pos |
30 | instantiation | 123, 118, 35 | ⊢ |
| : , : , : |
31 | theorem | | ⊢ |
| proveit.logic.equality.equals_reversal |
32 | instantiation | 36, 103, 47, 37, 48, 38*, 39* | ⊢ |
| : , : , : |
33 | instantiation | 59, 40, 41 | ⊢ |
| : , : , : |
34 | instantiation | 42, 43, 44, 45 | ⊢ |
| : , : , : , : |
35 | instantiation | 46, 108 | ⊢ |
| : |
36 | theorem | | ⊢ |
| proveit.numbers.addition.right_add_eq_rational |
37 | instantiation | 59, 47, 48 | ⊢ |
| : , : , : |
38 | instantiation | 49, 81 | ⊢ |
| : |
39 | instantiation | 87, 50, 51 | ⊢ |
| : , : , : |
40 | instantiation | 52, 76, 77, 53, 54 | ⊢ |
| : , : , : , : , : |
41 | instantiation | 87, 55, 56 | ⊢ |
| : , : , : |
42 | theorem | | ⊢ |
| proveit.logic.equality.four_chain_transitivity |
43 | instantiation | 97, 57 | ⊢ |
| : , : , : |
44 | instantiation | 97, 58 | ⊢ |
| : , : , : |
45 | instantiation | 106, 77 | ⊢ |
| : |
46 | theorem | | ⊢ |
| proveit.numbers.negation.int_closure |
47 | theorem | | ⊢ |
| proveit.numbers.number_sets.rational_numbers.zero_is_rational |
48 | instantiation | 59, 60, 61 | ⊢ |
| : , : , : |
49 | theorem | | ⊢ |
| proveit.numbers.addition.elim_zero_left |
50 | instantiation | 62, 63, 64, 116, 65, 66, 69, 67, 81 | ⊢ |
| : , : , : , : , : , : |
51 | instantiation | 68, 81, 69, 70 | ⊢ |
| : , : , : |
52 | theorem | | ⊢ |
| proveit.numbers.division.mult_frac_cancel_numer_left |
53 | instantiation | 123, 72, 71 | ⊢ |
| : , : , : |
54 | instantiation | 123, 72, 73 | ⊢ |
| : , : , : |
55 | instantiation | 97, 74 | ⊢ |
| : , : , : |
56 | instantiation | 97, 75 | ⊢ |
| : , : , : |
57 | instantiation | 99, 76 | ⊢ |
| : |
58 | instantiation | 99, 77 | ⊢ |
| : |
59 | theorem | | ⊢ |
| proveit.logic.equality.sub_right_side_into |
60 | instantiation | 78, 117 | ⊢ |
| : |
61 | assumption | | ⊢ |
62 | theorem | | ⊢ |
| proveit.numbers.addition.disassociation |
63 | axiom | | ⊢ |
| proveit.numbers.number_sets.natural_numbers.zero_in_nats |
64 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat2 |
65 | theorem | | ⊢ |
| proveit.core_expr_types.tuples.tuple_len_0_typical_eq |
66 | instantiation | 79 | ⊢ |
| : , : |
67 | instantiation | 80, 81 | ⊢ |
| : |
68 | theorem | | ⊢ |
| proveit.numbers.addition.subtraction.add_cancel_triple_32 |
69 | instantiation | 123, 113, 82 | ⊢ |
| : , : , : |
70 | instantiation | 83 | ⊢ |
| : |
71 | instantiation | 123, 85, 84 | ⊢ |
| : , : , : |
72 | theorem | | ⊢ |
| proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero |
73 | instantiation | 123, 85, 86 | ⊢ |
| : , : , : |
74 | instantiation | 87, 88, 89 | ⊢ |
| : , : , : |
75 | instantiation | 97, 90 | ⊢ |
| : , : , : |
76 | instantiation | 123, 113, 91 | ⊢ |
| : , : , : |
77 | instantiation | 123, 113, 92 | ⊢ |
| : , : , : |
78 | axiom | | ⊢ |
| proveit.physics.quantum.QPE._delta_b_def |
79 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.tuple_len_2_typical_eq |
80 | theorem | | ⊢ |
| proveit.numbers.negation.complex_closure |
81 | instantiation | 123, 113, 93 | ⊢ |
| : , : , : |
82 | theorem | | ⊢ |
| proveit.physics.quantum.QPE._phase_is_real |
83 | axiom | | ⊢ |
| proveit.logic.equality.equals_reflexivity |
84 | instantiation | 123, 95, 94 | ⊢ |
| : , : , : |
85 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero |
86 | instantiation | 123, 95, 96 | ⊢ |
| : , : , : |
87 | axiom | | ⊢ |
| proveit.logic.equality.equals_transitivity |
88 | instantiation | 97, 98 | ⊢ |
| : , : , : |
89 | instantiation | 99, 107 | ⊢ |
| : |
90 | instantiation | 100, 107 | ⊢ |
| : |
91 | instantiation | 123, 102, 101 | ⊢ |
| : , : , : |
92 | instantiation | 123, 102, 110 | ⊢ |
| : , : , : |
93 | instantiation | 123, 102, 103 | ⊢ |
| : , : , : |
94 | instantiation | 123, 104, 125 | ⊢ |
| : , : , : |
95 | theorem | | ⊢ |
| proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero |
96 | instantiation | 123, 104, 105 | ⊢ |
| : , : , : |
97 | axiom | | ⊢ |
| proveit.logic.equality.substitution |
98 | instantiation | 106, 107 | ⊢ |
| : |
99 | theorem | | ⊢ |
| proveit.numbers.division.frac_one_denom |
100 | theorem | | ⊢ |
| proveit.numbers.multiplication.elim_one_right |
101 | instantiation | 123, 118, 108 | ⊢ |
| : , : , : |
102 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.rational_within_real |
103 | instantiation | 109, 110, 111, 112 | ⊢ |
| : , : |
104 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int |
105 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.posnat1 |
106 | theorem | | ⊢ |
| proveit.numbers.multiplication.elim_one_left |
107 | instantiation | 123, 113, 114 | ⊢ |
| : , : , : |
108 | instantiation | 123, 115, 116 | ⊢ |
| : , : , : |
109 | theorem | | ⊢ |
| proveit.numbers.division.div_rational_closure |
110 | instantiation | 123, 118, 117 | ⊢ |
| : , : , : |
111 | instantiation | 123, 118, 119 | ⊢ |
| : , : , : |
112 | instantiation | 120, 125 | ⊢ |
| : |
113 | theorem | | ⊢ |
| proveit.numbers.number_sets.complex_numbers.real_within_complex |
114 | instantiation | 121, 122, 125 | ⊢ |
| : , : , : |
115 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.nat_within_int |
116 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat1 |
117 | theorem | | ⊢ |
| proveit.physics.quantum.QPE._best_round_is_int |
118 | theorem | | ⊢ |
| proveit.numbers.number_sets.rational_numbers.int_within_rational |
119 | instantiation | 123, 124, 125 | ⊢ |
| : , : , : |
120 | theorem | | ⊢ |
| proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos |
121 | theorem | | ⊢ |
| proveit.logic.sets.inclusion.unfold_subset_eq |
122 | instantiation | 126, 127 | ⊢ |
| : , : |
123 | theorem | | ⊢ |
| proveit.logic.sets.inclusion.superset_membership_from_proper_subset |
124 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.nat_pos_within_int |
125 | theorem | | ⊢ |
| proveit.physics.quantum.QPE._two_pow_t_is_nat_pos |
126 | theorem | | ⊢ |
| proveit.logic.sets.inclusion.relax_proper_subset |
127 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.nat_pos_within_real |
*equality replacement requirements |