| step type | requirements | statement |
0 | instantiation | 1, 2, 3, 4, 5, 6* | ⊢ |
| : , : , : |
1 | theorem | | ⊢ |
| proveit.numbers.addition.weak_bound_via_right_term_bound |
2 | reference | 33 | ⊢ |
3 | instantiation | 20, 25, 26 | ⊢ |
| : , : |
4 | instantiation | 28, 8 | ⊢ |
| : |
5 | instantiation | 7, 8, 9, 10, 11* | ⊢ |
| : , : |
6 | instantiation | 12, 89, 100, 13, 14, 15, 16, 17, 18 | ⊢ |
| : , : , : , : , : , : |
7 | theorem | | ⊢ |
| proveit.numbers.negation.negated_weak_bound |
8 | instantiation | 19, 88 | ⊢ |
| : |
9 | instantiation | 20, 27, 29 | ⊢ |
| : , : |
10 | instantiation | 21, 88 | ⊢ |
| : |
11 | instantiation | 22, 23, 24 | ⊢ |
| : , : |
12 | theorem | | ⊢ |
| proveit.numbers.addition.disassociation |
13 | axiom | | ⊢ |
| proveit.numbers.number_sets.natural_numbers.zero_in_nats |
14 | instantiation | 50 | ⊢ |
| : , : |
15 | theorem | | ⊢ |
| proveit.core_expr_types.tuples.tuple_len_0_typical_eq |
16 | instantiation | 107, 61, 33 | ⊢ |
| : , : , : |
17 | instantiation | 107, 61, 25 | ⊢ |
| : , : , : |
18 | instantiation | 107, 61, 26 | ⊢ |
| : , : , : |
19 | theorem | | ⊢ |
| proveit.physics.quantum.QPE._pfail_in_real |
20 | theorem | | ⊢ |
| proveit.numbers.addition.add_real_closure_bin |
21 | theorem | | ⊢ |
| proveit.physics.quantum.QPE._failure_upper_bound |
22 | theorem | | ⊢ |
| proveit.numbers.negation.distribute_neg_through_binary_sum |
23 | instantiation | 107, 61, 27 | ⊢ |
| : , : , : |
24 | instantiation | 107, 61, 29 | ⊢ |
| : , : , : |
25 | instantiation | 28, 27 | ⊢ |
| : |
26 | instantiation | 28, 29 | ⊢ |
| : |
27 | instantiation | 32, 33, 30, 31 | ⊢ |
| : , : |
28 | theorem | | ⊢ |
| proveit.numbers.negation.real_closure |
29 | instantiation | 32, 33, 34, 35 | ⊢ |
| : , : |
30 | instantiation | 39, 62, 49 | ⊢ |
| : , : |
31 | instantiation | 42, 100, 36, 37, 53 | ⊢ |
| : , : |
32 | theorem | | ⊢ |
| proveit.numbers.division.div_real_closure |
33 | instantiation | 107, 68, 38 | ⊢ |
| : , : , : |
34 | instantiation | 39, 40, 41 | ⊢ |
| : , : |
35 | instantiation | 42, 100, 43, 44, 45 | ⊢ |
| : , : |
36 | instantiation | 50 | ⊢ |
| : , : |
37 | instantiation | 107, 59, 46 | ⊢ |
| : , : , : |
38 | instantiation | 107, 74, 86 | ⊢ |
| : , : , : |
39 | theorem | | ⊢ |
| proveit.numbers.multiplication.mult_real_closure_bin |
40 | instantiation | 107, 68, 47 | ⊢ |
| : , : , : |
41 | instantiation | 48, 49, 100 | ⊢ |
| : , : |
42 | theorem | | ⊢ |
| proveit.numbers.multiplication.mult_not_eq_zero |
43 | instantiation | 50 | ⊢ |
| : , : |
44 | instantiation | 107, 59, 51 | ⊢ |
| : , : , : |
45 | instantiation | 52, 53, 54 | ⊢ |
| : , : |
46 | instantiation | 107, 66, 55 | ⊢ |
| : , : , : |
47 | instantiation | 107, 74, 56 | ⊢ |
| : , : , : |
48 | theorem | | ⊢ |
| proveit.numbers.exponentiation.exp_real_closure_nat_power |
49 | instantiation | 107, 68, 57 | ⊢ |
| : , : , : |
50 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.tuple_len_2_typical_eq |
51 | instantiation | 107, 66, 58 | ⊢ |
| : , : , : |
52 | theorem | | ⊢ |
| proveit.numbers.exponentiation.exp_complex_nonzero_closure |
53 | instantiation | 107, 59, 60 | ⊢ |
| : , : , : |
54 | instantiation | 107, 61, 62 | ⊢ |
| : , : , : |
55 | instantiation | 107, 72, 63 | ⊢ |
| : , : , : |
56 | instantiation | 107, 99, 64 | ⊢ |
| : , : , : |
57 | instantiation | 107, 74, 78 | ⊢ |
| : , : , : |
58 | instantiation | 107, 72, 65 | ⊢ |
| : , : , : |
59 | theorem | | ⊢ |
| proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero |
60 | instantiation | 107, 66, 67 | ⊢ |
| : , : , : |
61 | theorem | | ⊢ |
| proveit.numbers.number_sets.complex_numbers.real_within_complex |
62 | instantiation | 107, 68, 69 | ⊢ |
| : , : , : |
63 | instantiation | 107, 75, 70 | ⊢ |
| : , : , : |
64 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat4 |
65 | instantiation | 107, 75, 71 | ⊢ |
| : , : , : |
66 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero |
67 | instantiation | 107, 72, 73 | ⊢ |
| : , : , : |
68 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.rational_within_real |
69 | instantiation | 107, 74, 95 | ⊢ |
| : , : , : |
70 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.posnat2 |
71 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.posnat4 |
72 | theorem | | ⊢ |
| proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero |
73 | instantiation | 107, 75, 76 | ⊢ |
| : , : , : |
74 | theorem | | ⊢ |
| proveit.numbers.number_sets.rational_numbers.int_within_rational |
75 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int |
76 | instantiation | 77, 78, 79 | ⊢ |
| : |
77 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.pos_int_is_natural_pos |
78 | instantiation | 107, 80, 88 | ⊢ |
| : , : , : |
79 | instantiation | 81, 82, 83 | ⊢ |
| : , : , : |
80 | instantiation | 84, 86, 87 | ⊢ |
| : , : |
81 | theorem | | ⊢ |
| proveit.numbers.ordering.transitivity_less_less_eq |
82 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.less_0_1 |
83 | instantiation | 85, 86, 87, 88 | ⊢ |
| : , : , : |
84 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.int_interval_within_int |
85 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.interval_lower_bound |
86 | instantiation | 107, 99, 89 | ⊢ |
| : , : , : |
87 | instantiation | 101, 90, 91 | ⊢ |
| : , : |
88 | theorem | | ⊢ |
| proveit.physics.quantum.QPE._e_value_in_e_domain |
89 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat1 |
90 | instantiation | 92, 95, 93 | ⊢ |
| : , : |
91 | instantiation | 94, 95 | ⊢ |
| : |
92 | theorem | | ⊢ |
| proveit.numbers.exponentiation.exp_int_closure |
93 | instantiation | 96, 97, 98 | ⊢ |
| : |
94 | theorem | | ⊢ |
| proveit.numbers.negation.int_closure |
95 | instantiation | 107, 99, 100 | ⊢ |
| : , : , : |
96 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.nonneg_int_is_natural |
97 | instantiation | 101, 102, 103 | ⊢ |
| : , : |
98 | instantiation | 104, 105 | ⊢ |
| : , : |
99 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.nat_within_int |
100 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat2 |
101 | theorem | | ⊢ |
| proveit.numbers.addition.add_int_closure_bin |
102 | instantiation | 107, 106, 111 | ⊢ |
| : , : , : |
103 | instantiation | 107, 108, 109 | ⊢ |
| : , : , : |
104 | theorem | | ⊢ |
| proveit.numbers.addition.subtraction.nonneg_difference |
105 | instantiation | 110, 111 | ⊢ |
| : |
106 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.nat_pos_within_int |
107 | theorem | | ⊢ |
| proveit.logic.sets.inclusion.superset_membership_from_proper_subset |
108 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.neg_int_within_int |
109 | instantiation | 112, 113 | ⊢ |
| : |
110 | theorem | | ⊢ |
| proveit.numbers.number_sets.natural_numbers.natural_pos_lower_bound |
111 | axiom | | ⊢ |
| proveit.physics.quantum.QPE._t_in_natural_pos |
112 | theorem | | ⊢ |
| proveit.numbers.negation.int_neg_closure |
113 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.posnat1 |
*equality replacement requirements |