| step type | requirements | statement |
0 | instantiation | 1, 2, 3, 4, 5, 6, 7, 8* | ⊢ |
| : , : , : , : |
1 | theorem | | ⊢ |
| proveit.numbers.summation.integral_upper_bound_of_sum |
2 | theorem | | ⊢ |
| proveit.numbers.functions.one_over_x_sqrd_in_mon_dec_fxns |
3 | instantiation | 61, 9 | ⊢ |
| : , : |
4 | reference | 88 | ⊢ |
5 | reference | 82 | ⊢ |
6 | instantiation | 10, 91, 67, 11, 12, 13* | ⊢ |
| : , : , : |
7 | instantiation | 14, 15 | ⊢ |
| : , : , : |
8 | instantiation | 20, 16, 17 | ⊢ |
| : , : , : |
9 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.real_pos_within_real |
10 | theorem | | ⊢ |
| proveit.numbers.addition.weak_bound_via_left_term_bound |
11 | instantiation | 113, 95, 18 | ⊢ |
| : , : , : |
12 | instantiation | 19, 103, 104, 98 | ⊢ |
| : , : , : |
13 | instantiation | 20, 21, 22 | ⊢ |
| : , : , : |
14 | theorem | | ⊢ |
| proveit.logic.sets.inclusion.fold_subset_eq |
15 | generalization | 23 | ⊢ |
16 | instantiation | 29, 32, 115, 105, 34, 24, 27, 86, 25 | ⊢ |
| : , : , : , : , : , : |
17 | instantiation | 26, 86, 27, 28 | ⊢ |
| : , : , : |
18 | instantiation | 113, 101, 104 | ⊢ |
| : , : , : |
19 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.interval_upper_bound |
20 | axiom | | ⊢ |
| proveit.logic.equality.equals_transitivity |
21 | instantiation | 29, 32, 115, 105, 34, 30, 35, 54, 86 | ⊢ |
| : , : , : , : , : , : |
22 | instantiation | 31, 105, 115, 32, 33, 34, 35, 54, 86, 36* | ⊢ |
| : , : , : , : , : , : |
23 | instantiation | 37, 38, 39 | , ⊢ |
| : |
24 | instantiation | 42 | ⊢ |
| : , : |
25 | instantiation | 40, 86 | ⊢ |
| : |
26 | theorem | | ⊢ |
| proveit.numbers.addition.subtraction.add_cancel_triple_23 |
27 | instantiation | 113, 90, 67 | ⊢ |
| : , : , : |
28 | instantiation | 41 | ⊢ |
| : |
29 | theorem | | ⊢ |
| proveit.numbers.addition.disassociation |
30 | instantiation | 42 | ⊢ |
| : , : |
31 | theorem | | ⊢ |
| proveit.numbers.addition.association |
32 | axiom | | ⊢ |
| proveit.numbers.number_sets.natural_numbers.zero_in_nats |
33 | instantiation | 42 | ⊢ |
| : , : |
34 | theorem | | ⊢ |
| proveit.core_expr_types.tuples.tuple_len_0_typical_eq |
35 | instantiation | 113, 90, 43 | ⊢ |
| : , : , : |
36 | instantiation | 78, 44, 45 | ⊢ |
| : , : , : |
37 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.pos_real_is_real_pos |
38 | instantiation | 46, 58, 59, 60 | , ⊢ |
| : , : , : |
39 | instantiation | 75, 47, 48 | , ⊢ |
| : , : , : |
40 | theorem | | ⊢ |
| proveit.numbers.negation.complex_closure |
41 | axiom | | ⊢ |
| proveit.logic.equality.equals_reflexivity |
42 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.tuple_len_2_typical_eq |
43 | instantiation | 49, 50, 110 | ⊢ |
| : , : , : |
44 | instantiation | 51, 86, 52, 53 | ⊢ |
| : , : , : |
45 | instantiation | 85, 86, 54 | ⊢ |
| : , : |
46 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.all_in_interval_cc__is__real |
47 | instantiation | 55, 56 | ⊢ |
| : , : |
48 | instantiation | 57, 58, 59, 60 | , ⊢ |
| : , : , : |
49 | theorem | | ⊢ |
| proveit.logic.sets.inclusion.unfold_subset_eq |
50 | instantiation | 61, 62 | ⊢ |
| : , : |
51 | theorem | | ⊢ |
| proveit.numbers.addition.subtraction.subtract_from_add_reversed |
52 | instantiation | 113, 90, 63 | ⊢ |
| : , : , : |
53 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.add_1_1 |
54 | instantiation | 113, 90, 64 | ⊢ |
| : , : , : |
55 | theorem | | ⊢ |
| proveit.numbers.addition.subtraction.pos_difference |
56 | instantiation | 65, 91, 66, 67, 68, 69* | ⊢ |
| : , : , : |
57 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.interval_cc_lower_bound |
58 | instantiation | 113, 95, 70 | ⊢ |
| : , : , : |
59 | instantiation | 113, 95, 71 | ⊢ |
| : , : , : |
60 | assumption | | ⊢ |
61 | theorem | | ⊢ |
| proveit.logic.sets.inclusion.relax_proper_subset |
62 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.nat_pos_within_real |
63 | instantiation | 113, 95, 72 | ⊢ |
| : , : , : |
64 | instantiation | 113, 95, 73 | ⊢ |
| : , : , : |
65 | theorem | | ⊢ |
| proveit.numbers.addition.strong_bound_via_left_term_bound |
66 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.zero_is_real |
67 | instantiation | 113, 95, 74 | ⊢ |
| : , : , : |
68 | instantiation | 75, 76, 77 | ⊢ |
| : , : , : |
69 | instantiation | 78, 79, 80 | ⊢ |
| : , : , : |
70 | instantiation | 113, 101, 81 | ⊢ |
| : , : , : |
71 | instantiation | 113, 101, 82 | ⊢ |
| : , : , : |
72 | instantiation | 113, 101, 112 | ⊢ |
| : , : , : |
73 | instantiation | 113, 101, 108 | ⊢ |
| : , : , : |
74 | instantiation | 113, 101, 92 | ⊢ |
| : , : , : |
75 | theorem | | ⊢ |
| proveit.numbers.ordering.transitivity_less_less_eq |
76 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.less_0_1 |
77 | instantiation | 83, 103, 104, 98 | ⊢ |
| : , : , : |
78 | theorem | | ⊢ |
| proveit.logic.equality.sub_right_side_into |
79 | instantiation | 84, 86 | ⊢ |
| : |
80 | instantiation | 85, 86, 87 | ⊢ |
| : , : |
81 | instantiation | 106, 88, 89 | ⊢ |
| : , : |
82 | instantiation | 106, 107, 89 | ⊢ |
| : , : |
83 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.interval_lower_bound |
84 | theorem | | ⊢ |
| proveit.numbers.addition.elim_zero_right |
85 | theorem | | ⊢ |
| proveit.numbers.addition.commutation |
86 | instantiation | 113, 90, 91 | ⊢ |
| : , : , : |
87 | theorem | | ⊢ |
| proveit.numbers.number_sets.complex_numbers.zero_is_complex |
88 | instantiation | 106, 92, 103 | ⊢ |
| : , : |
89 | instantiation | 113, 93, 94 | ⊢ |
| : , : , : |
90 | theorem | | ⊢ |
| proveit.numbers.number_sets.complex_numbers.real_within_complex |
91 | instantiation | 113, 95, 96 | ⊢ |
| : , : , : |
92 | instantiation | 113, 97, 98 | ⊢ |
| : , : , : |
93 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.neg_int_within_int |
94 | instantiation | 99, 100 | ⊢ |
| : |
95 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.rational_within_real |
96 | instantiation | 113, 101, 103 | ⊢ |
| : , : , : |
97 | instantiation | 102, 103, 104 | ⊢ |
| : , : |
98 | assumption | | ⊢ |
99 | theorem | | ⊢ |
| proveit.numbers.negation.int_neg_closure |
100 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.posnat1 |
101 | theorem | | ⊢ |
| proveit.numbers.number_sets.rational_numbers.int_within_rational |
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 |