| step type | requirements | statement |
0 | deduction | 1 | ⊢ |
1 | instantiation | 2, 3, 4 | , ⊢ |
| : , : |
2 | theorem | | ⊢ |
| proveit.logic.booleans.disjunction.or_if_only_right |
3 | instantiation | 5, 9 | ⊢ |
| : , : |
4 | instantiation | 6, 7, 8, 9 | , ⊢ |
| : , : |
5 | theorem | | ⊢ |
| proveit.logic.equality.unfold_not_equals |
6 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.not_int_if_not_int_in_interval |
7 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.zero_is_int |
8 | instantiation | 10, 11, 12, 66, 13 | ⊢ |
| : , : , : |
9 | assumption | | ⊢ |
10 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.in_IntervalOO |
11 | instantiation | 29, 15, 14 | ⊢ |
| : , : |
12 | instantiation | 29, 15, 83 | ⊢ |
| : , : |
13 | instantiation | 16, 17, 18 | ⊢ |
| : , : |
14 | instantiation | 124, 120, 19 | ⊢ |
| : , : , : |
15 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.zero_is_real |
16 | theorem | | ⊢ |
| proveit.logic.booleans.conjunction.and_if_both |
17 | instantiation | 20, 74, 21, 22, 23*, 24* | ⊢ |
| : , : , : |
18 | instantiation | 25, 26, 27 | ⊢ |
| : , : , : |
19 | instantiation | 124, 122, 28 | ⊢ |
| : , : , : |
20 | theorem | | ⊢ |
| proveit.numbers.addition.strong_bound_via_left_term_bound |
21 | instantiation | 29, 66, 85 | ⊢ |
| : , : |
22 | instantiation | 30, 74, 66, 85, 31, 32 | ⊢ |
| : , : , : |
23 | instantiation | 40, 33, 34, 35 | ⊢ |
| : , : , : , : |
24 | instantiation | 88, 36, 37 | ⊢ |
| : , : , : |
25 | theorem | | ⊢ |
| proveit.logic.equality.sub_right_side_into |
26 | instantiation | 38, 66, 85, 39, 46 | ⊢ |
| : , : , : |
27 | instantiation | 40, 48, 41, 42 | ⊢ |
| : , : , : , : |
28 | instantiation | 43, 102 | ⊢ |
| : |
29 | theorem | | ⊢ |
| proveit.numbers.addition.add_real_closure_bin |
30 | theorem | | ⊢ |
| proveit.numbers.ordering.less_add_right |
31 | instantiation | 44, 74, 85, 75 | ⊢ |
| : , : , : |
32 | instantiation | 45, 46 | ⊢ |
| : , : |
33 | instantiation | 47, 56, 72, 48 | ⊢ |
| : , : , : |
34 | instantiation | 67 | ⊢ |
| : |
35 | instantiation | 60, 49 | ⊢ |
| : , : |
36 | instantiation | 50, 51, 126, 110, 52, 53, 57, 56, 54 | ⊢ |
| : , : , : , : , : , : |
37 | instantiation | 55, 56, 57, 58 | ⊢ |
| : , : , : |
38 | theorem | | ⊢ |
| proveit.numbers.ordering.less_eq_add_right_strong |
39 | instantiation | 59, 74, 85, 75 | ⊢ |
| : , : , : |
40 | theorem | | ⊢ |
| proveit.logic.equality.four_chain_transitivity |
41 | instantiation | 67 | ⊢ |
| : |
42 | instantiation | 60, 61 | ⊢ |
| : , : |
43 | theorem | | ⊢ |
| proveit.numbers.negation.int_closure |
44 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.interval_oc_lower_bound |
45 | theorem | | ⊢ |
| proveit.numbers.ordering.relax_less |
46 | instantiation | 62, 104 | ⊢ |
| : |
47 | theorem | | ⊢ |
| proveit.numbers.addition.subtraction.negated_add |
48 | instantiation | 63, 102, 123, 64* | ⊢ |
| : , : , : , : |
49 | instantiation | 68, 65 | ⊢ |
| : |
50 | theorem | | ⊢ |
| proveit.numbers.addition.disassociation |
51 | axiom | | ⊢ |
| proveit.numbers.number_sets.natural_numbers.zero_in_nats |
52 | theorem | | ⊢ |
| proveit.core_expr_types.tuples.tuple_len_0_typical_eq |
53 | instantiation | 105 | ⊢ |
| : , : |
54 | instantiation | 124, 114, 74 | ⊢ |
| : , : , : |
55 | theorem | | ⊢ |
| proveit.numbers.addition.subtraction.add_cancel_triple_23 |
56 | instantiation | 124, 114, 85 | ⊢ |
| : , : , : |
57 | instantiation | 124, 114, 66 | ⊢ |
| : , : , : |
58 | instantiation | 67 | ⊢ |
| : |
59 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.interval_oc_upper_bound |
60 | theorem | | ⊢ |
| proveit.logic.equality.equals_reversal |
61 | instantiation | 68, 72 | ⊢ |
| : |
62 | theorem | | ⊢ |
| proveit.numbers.number_sets.rational_numbers.positive_if_in_rational_pos |
63 | theorem | | ⊢ |
| proveit.numbers.addition.rational_pair_addition |
64 | instantiation | 88, 69, 70 | ⊢ |
| : , : , : |
65 | instantiation | 71, 72 | ⊢ |
| : |
66 | instantiation | 73, 74, 85, 75 | ⊢ |
| : , : , : |
67 | axiom | | ⊢ |
| proveit.logic.equality.equals_reflexivity |
68 | theorem | | ⊢ |
| proveit.numbers.addition.elim_zero_left |
69 | instantiation | 96, 126, 76, 77, 78, 79 | ⊢ |
| : , : , : , : |
70 | instantiation | 80, 81, 82 | ⊢ |
| : |
71 | theorem | | ⊢ |
| proveit.numbers.negation.complex_closure |
72 | instantiation | 124, 114, 83 | ⊢ |
| : , : , : |
73 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.all_in_interval_oc__is__real |
74 | instantiation | 84, 85 | ⊢ |
| : |
75 | instantiation | 86, 87 | ⊢ |
| : |
76 | instantiation | 105 | ⊢ |
| : , : |
77 | instantiation | 105 | ⊢ |
| : , : |
78 | instantiation | 88, 89, 90 | ⊢ |
| : , : , : |
79 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.mult_2_2 |
80 | theorem | | ⊢ |
| proveit.numbers.division.frac_cancel_complete |
81 | instantiation | 124, 114, 91 | ⊢ |
| : , : , : |
82 | instantiation | 92, 93 | ⊢ |
| : |
83 | instantiation | 124, 120, 94 | ⊢ |
| : , : , : |
84 | theorem | | ⊢ |
| proveit.numbers.negation.real_closure |
85 | instantiation | 124, 120, 95 | ⊢ |
| : , : , : |
86 | theorem | | ⊢ |
| proveit.physics.quantum.QPE._delta_b_in_interval |
87 | assumption | | ⊢ |
88 | axiom | | ⊢ |
| proveit.logic.equality.equals_transitivity |
89 | instantiation | 96, 126, 97, 98, 99, 100 | ⊢ |
| : , : , : , : |
90 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.add_2_2 |
91 | instantiation | 124, 120, 101 | ⊢ |
| : , : , : |
92 | theorem | | ⊢ |
| proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos |
93 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.posnat4 |
94 | instantiation | 124, 122, 102 | ⊢ |
| : , : , : |
95 | instantiation | 124, 103, 104 | ⊢ |
| : , : , : |
96 | axiom | | ⊢ |
| proveit.core_expr_types.operations.operands_substitution |
97 | instantiation | 105 | ⊢ |
| : , : |
98 | instantiation | 105 | ⊢ |
| : , : |
99 | instantiation | 106, 108 | ⊢ |
| : |
100 | instantiation | 107, 108 | ⊢ |
| : |
101 | instantiation | 124, 122, 109 | ⊢ |
| : , : , : |
102 | instantiation | 124, 125, 110 | ⊢ |
| : , : , : |
103 | theorem | | ⊢ |
| proveit.numbers.number_sets.rational_numbers.rational_pos_within_rational |
104 | instantiation | 111, 112, 113 | ⊢ |
| : , : |
105 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.tuple_len_2_typical_eq |
106 | theorem | | ⊢ |
| proveit.numbers.multiplication.elim_one_left |
107 | theorem | | ⊢ |
| proveit.numbers.multiplication.elim_one_right |
108 | instantiation | 124, 114, 115 | ⊢ |
| : , : , : |
109 | instantiation | 124, 125, 116 | ⊢ |
| : , : , : |
110 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat1 |
111 | theorem | | ⊢ |
| proveit.numbers.division.div_rational_pos_closure |
112 | instantiation | 124, 118, 117 | ⊢ |
| : , : , : |
113 | instantiation | 124, 118, 119 | ⊢ |
| : , : , : |
114 | theorem | | ⊢ |
| proveit.numbers.number_sets.complex_numbers.real_within_complex |
115 | instantiation | 124, 120, 121 | ⊢ |
| : , : , : |
116 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat4 |
117 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.posnat1 |
118 | theorem | | ⊢ |
| proveit.numbers.number_sets.rational_numbers.nat_pos_within_rational_pos |
119 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.posnat2 |
120 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.rational_within_real |
121 | instantiation | 124, 122, 123 | ⊢ |
| : , : , : |
122 | theorem | | ⊢ |
| proveit.numbers.number_sets.rational_numbers.int_within_rational |
123 | instantiation | 124, 125, 126 | ⊢ |
| : , : , : |
124 | theorem | | ⊢ |
| proveit.logic.sets.inclusion.superset_membership_from_proper_subset |
125 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.nat_within_int |
126 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat2 |
*equality replacement requirements |