| step type | requirements | statement |
0 | instantiation | 1, 2, 3, 4, 5, 6*, 7* | ⊢ |
| : , : , : |
1 | theorem | | ⊢ |
| proveit.numbers.addition.strong_bound_via_left_term_bound |
2 | reference | 38 | ⊢ |
3 | reference | 9 | ⊢ |
4 | instantiation | 47, 49, 92 | ⊢ |
| : , : |
5 | instantiation | 8, 9, 49, 92, 10, 11 | ⊢ |
| : , : , : |
6 | instantiation | 69, 12 | ⊢ |
| : , : |
7 | instantiation | 26, 13, 14, 15 | ⊢ |
| : , : , : , : |
8 | theorem | | ⊢ |
| proveit.numbers.ordering.less_add_right |
9 | instantiation | 57, 92, 17 | ⊢ |
| : , : |
10 | instantiation | 16, 92, 17, 88, 18, 19 | ⊢ |
| : , : , : |
11 | instantiation | 20, 115 | ⊢ |
| : |
12 | instantiation | 26, 21, 22, 23 | ⊢ |
| : , : , : , : |
13 | instantiation | 64, 72, 115, 105, 73, 25, 41, 86, 24 | ⊢ |
| : , : , : , : , : , : |
14 | instantiation | 64, 115, 72, 25, 67, 73, 41, 86, 68, 75 | ⊢ |
| : , : , : , : , : , : |
15 | instantiation | 26, 27, 28, 29 | ⊢ |
| : , : , : , : |
16 | theorem | | ⊢ |
| proveit.numbers.multiplication.strong_bound_via_right_factor_bound |
17 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.zero_is_real |
18 | instantiation | 30, 31, 32 | ⊢ |
| : , : , : |
19 | instantiation | 33, 34 | ⊢ |
| : |
20 | theorem | | ⊢ |
| proveit.numbers.number_sets.natural_numbers.natural_lower_bound |
21 | instantiation | 35, 81, 85 | ⊢ |
| : , : |
22 | instantiation | 36 | ⊢ |
| : |
23 | instantiation | 69, 37 | ⊢ |
| : , : |
24 | instantiation | 113, 91, 38 | ⊢ |
| : , : , : |
25 | instantiation | 82 | ⊢ |
| : , : |
26 | theorem | | ⊢ |
| proveit.logic.equality.four_chain_transitivity |
27 | instantiation | 39, 105, 41, 86, 68, 75 | ⊢ |
| : , : , : , : , : , : , : |
28 | instantiation | 43, 72, 115, 73, 40, 74, 41, 68, 86, 75, 42* | ⊢ |
| : , : , : , : , : , : |
29 | instantiation | 43, 105, 115, 72, 74, 73, 81, 86, 75, 77* | ⊢ |
| : , : , : , : , : , : |
30 | theorem | | ⊢ |
| proveit.numbers.ordering.transitivity_less_less_eq |
31 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.less_0_1 |
32 | instantiation | 44, 103, 104, 101 | ⊢ |
| : , : , : |
33 | theorem | | ⊢ |
| proveit.numbers.number_sets.natural_numbers.natural_pos_is_pos |
34 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.posnat2 |
35 | theorem | | ⊢ |
| proveit.numbers.negation.distribute_neg_through_binary_sum |
36 | axiom | | ⊢ |
| proveit.logic.equality.equals_reflexivity |
37 | instantiation | 60, 45, 46 | ⊢ |
| : , : , : |
38 | instantiation | 47, 48, 83 | ⊢ |
| : , : |
39 | theorem | | ⊢ |
| proveit.numbers.addition.leftward_commutation |
40 | instantiation | 82 | ⊢ |
| : , : |
41 | instantiation | 113, 91, 49 | ⊢ |
| : , : , : |
42 | instantiation | 60, 50, 51, 52* | ⊢ |
| : , : , : |
43 | theorem | | ⊢ |
| proveit.numbers.addition.association |
44 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.interval_lower_bound |
45 | instantiation | 76, 53 | ⊢ |
| : , : , : |
46 | instantiation | 60, 54, 55 | ⊢ |
| : , : , : |
47 | theorem | | ⊢ |
| proveit.numbers.addition.add_real_closure_bin |
48 | instantiation | 56, 88 | ⊢ |
| : |
49 | instantiation | 57, 92, 88 | ⊢ |
| : , : |
50 | instantiation | 76, 58 | ⊢ |
| : , : , : |
51 | instantiation | 69, 59 | ⊢ |
| : , : |
52 | instantiation | 60, 61, 62 | ⊢ |
| : , : , : |
53 | instantiation | 63, 86 | ⊢ |
| : |
54 | instantiation | 64, 105, 115, 72, 67, 73, 65, 68, 75 | ⊢ |
| : , : , : , : , : , : |
55 | instantiation | 66, 72, 115, 73, 67, 68, 75 | ⊢ |
| : , : , : , : |
56 | theorem | | ⊢ |
| proveit.numbers.negation.real_closure |
57 | theorem | | ⊢ |
| proveit.numbers.multiplication.mult_real_closure_bin |
58 | instantiation | 69, 70 | ⊢ |
| : , : |
59 | instantiation | 71, 72, 115, 105, 73, 74, 86, 75, 81 | ⊢ |
| : , : , : , : , : , : |
60 | axiom | | ⊢ |
| proveit.logic.equality.equals_transitivity |
61 | instantiation | 76, 77 | ⊢ |
| : , : , : |
62 | instantiation | 78, 81 | ⊢ |
| : |
63 | theorem | | ⊢ |
| proveit.numbers.multiplication.mult_zero_right |
64 | theorem | | ⊢ |
| proveit.numbers.addition.disassociation |
65 | theorem | | ⊢ |
| proveit.numbers.number_sets.complex_numbers.zero_is_complex |
66 | theorem | | ⊢ |
| proveit.numbers.addition.elim_zero_any |
67 | instantiation | 82 | ⊢ |
| : , : |
68 | instantiation | 79, 81 | ⊢ |
| : |
69 | theorem | | ⊢ |
| proveit.logic.equality.equals_reversal |
70 | instantiation | 80, 81 | ⊢ |
| : |
71 | theorem | | ⊢ |
| proveit.numbers.multiplication.distribute_through_sum |
72 | axiom | | ⊢ |
| proveit.numbers.number_sets.natural_numbers.zero_in_nats |
73 | theorem | | ⊢ |
| proveit.core_expr_types.tuples.tuple_len_0_typical_eq |
74 | instantiation | 82 | ⊢ |
| : , : |
75 | instantiation | 113, 91, 83 | ⊢ |
| : , : , : |
76 | axiom | | ⊢ |
| proveit.logic.equality.substitution |
77 | instantiation | 84, 85, 86, 87 | ⊢ |
| : , : , : |
78 | theorem | | ⊢ |
| proveit.numbers.multiplication.elim_one_left |
79 | theorem | | ⊢ |
| proveit.numbers.negation.complex_closure |
80 | theorem | | ⊢ |
| proveit.numbers.negation.mult_neg_one_left |
81 | instantiation | 113, 91, 88 | ⊢ |
| : , : , : |
82 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.tuple_len_2_typical_eq |
83 | instantiation | 113, 96, 89 | ⊢ |
| : , : , : |
84 | theorem | | ⊢ |
| proveit.numbers.addition.subtraction.subtract_from_add |
85 | instantiation | 113, 91, 90 | ⊢ |
| : , : , : |
86 | instantiation | 113, 91, 92 | ⊢ |
| : , : , : |
87 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.add_1_1 |
88 | instantiation | 113, 96, 93 | ⊢ |
| : , : , : |
89 | instantiation | 113, 99, 94 | ⊢ |
| : , : , : |
90 | instantiation | 113, 96, 95 | ⊢ |
| : , : , : |
91 | theorem | | ⊢ |
| proveit.numbers.number_sets.complex_numbers.real_within_complex |
92 | instantiation | 113, 96, 97 | ⊢ |
| : , : , : |
93 | instantiation | 113, 99, 98 | ⊢ |
| : , : , : |
94 | instantiation | 111, 103 | ⊢ |
| : |
95 | instantiation | 113, 99, 103 | ⊢ |
| : , : , : |
96 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.rational_within_real |
97 | instantiation | 113, 99, 112 | ⊢ |
| : , : , : |
98 | instantiation | 113, 100, 101 | ⊢ |
| : , : , : |
99 | theorem | | ⊢ |
| proveit.numbers.number_sets.rational_numbers.int_within_rational |
100 | instantiation | 102, 103, 104 | ⊢ |
| : , : |
101 | assumption | | ⊢ |
102 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.int_interval_within_int |
103 | instantiation | 113, 114, 105 | ⊢ |
| : , : , : |
104 | instantiation | 106, 107, 108 | ⊢ |
| : , : |
105 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat1 |
106 | theorem | | ⊢ |
| proveit.numbers.addition.add_int_closure_bin |
107 | instantiation | 113, 109, 110 | ⊢ |
| : , : , : |
108 | instantiation | 111, 112 | ⊢ |
| : |
109 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.nat_pos_within_int |
110 | theorem | | ⊢ |
| proveit.physics.quantum.QPE._two_pow_t_minus_one_is_nat_pos |
111 | theorem | | ⊢ |
| proveit.numbers.negation.int_closure |
112 | instantiation | 113, 114, 115 | ⊢ |
| : , : , : |
113 | theorem | | ⊢ |
| proveit.logic.sets.inclusion.superset_membership_from_proper_subset |
114 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.nat_within_int |
115 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat2 |
*equality replacement requirements |