| step type | requirements | statement |
0 | instantiation | 1, 2, 3, 4, 5 | , ⊢ |
| : , : , : |
1 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.in_interval |
2 | instantiation | 77, 49, 117 | ⊢ |
| : , : |
3 | reference | 78 | ⊢ |
4 | instantiation | 121, 6, 30 | , ⊢ |
| : , : , : |
5 | instantiation | 7, 8, 9 | , ⊢ |
| : , : |
6 | instantiation | 67, 29, 78 | ⊢ |
| : , : |
7 | theorem | | ⊢ |
| proveit.logic.booleans.conjunction.and_if_both |
8 | instantiation | 10, 11 | , ⊢ |
| : , : |
9 | instantiation | 12, 29, 78, 30 | , ⊢ |
| : , : , : |
10 | theorem | | ⊢ |
| proveit.numbers.ordering.relax_less |
11 | instantiation | 13, 14, 15 | , ⊢ |
| : , : , : |
12 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.interval_upper_bound |
13 | theorem | | ⊢ |
| proveit.numbers.ordering.transitivity_less_eq_less |
14 | instantiation | 16, 31, 105, 17, 18, 19*, 20* | ⊢ |
| : , : , : |
15 | instantiation | 56, 21, 22 | , ⊢ |
| : , : , : |
16 | theorem | | ⊢ |
| proveit.numbers.addition.weak_bound_via_left_term_bound |
17 | instantiation | 101, 102, 91 | ⊢ |
| : , : , : |
18 | instantiation | 23, 91 | ⊢ |
| : |
19 | instantiation | 80, 95, 24 | ⊢ |
| : , : |
20 | instantiation | 32, 25, 26 | ⊢ |
| : , : , : |
21 | instantiation | 27, 28 | ⊢ |
| : |
22 | instantiation | 68, 29, 78, 30 | , ⊢ |
| : , : , : |
23 | theorem | | ⊢ |
| proveit.numbers.number_sets.natural_numbers.natural_pos_lower_bound |
24 | instantiation | 121, 104, 31 | ⊢ |
| : , : , : |
25 | instantiation | 32, 33, 34 | ⊢ |
| : , : , : |
26 | instantiation | 35, 36, 37 | ⊢ |
| : , : |
27 | theorem | | ⊢ |
| proveit.numbers.number_sets.natural_numbers.natural_pos_is_pos |
28 | instantiation | 38, 39, 89 | ⊢ |
| : , : |
29 | instantiation | 77, 47, 117 | ⊢ |
| : , : |
30 | assumption | | ⊢ |
31 | instantiation | 121, 111, 40 | ⊢ |
| : , : , : |
32 | axiom | | ⊢ |
| proveit.logic.equality.equals_transitivity |
33 | instantiation | 74, 50 | ⊢ |
| : , : , : |
34 | instantiation | 74, 41 | ⊢ |
| : , : , : |
35 | theorem | | ⊢ |
| proveit.numbers.addition.subtraction.add_cancel_basic |
36 | instantiation | 42, 43, 44 | ⊢ |
| : , : |
37 | instantiation | 45 | ⊢ |
| : |
38 | theorem | | ⊢ |
| proveit.numbers.addition.add_nat_pos_closure_bin |
39 | instantiation | 46, 47, 48 | ⊢ |
| : |
40 | instantiation | 121, 116, 49 | ⊢ |
| : , : , : |
41 | instantiation | 74, 50 | ⊢ |
| : , : , : |
42 | theorem | | ⊢ |
| proveit.numbers.multiplication.mult_complex_closure_bin |
43 | instantiation | 51, 95, 52, 53 | ⊢ |
| : , : |
44 | instantiation | 121, 104, 54 | ⊢ |
| : , : , : |
45 | axiom | | ⊢ |
| proveit.logic.equality.equals_reflexivity |
46 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.pos_int_is_natural_pos |
47 | instantiation | 121, 55, 70 | ⊢ |
| : , : , : |
48 | instantiation | 56, 57, 58 | ⊢ |
| : , : , : |
49 | instantiation | 92, 78 | ⊢ |
| : |
50 | instantiation | 59, 60, 61, 62 | ⊢ |
| : , : , : , : |
51 | theorem | | ⊢ |
| proveit.numbers.division.div_complex_closure |
52 | instantiation | 63, 84, 95 | ⊢ |
| : , : |
53 | instantiation | 64, 86, 65 | ⊢ |
| : , : , : |
54 | instantiation | 101, 102, 66 | ⊢ |
| : , : , : |
55 | instantiation | 67, 117, 69 | ⊢ |
| : , : |
56 | theorem | | ⊢ |
| proveit.numbers.ordering.transitivity_less_less_eq |
57 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.less_0_1 |
58 | instantiation | 68, 117, 69, 70 | ⊢ |
| : , : , : |
59 | theorem | | ⊢ |
| proveit.logic.equality.four_chain_transitivity |
60 | instantiation | 74, 71 | ⊢ |
| : , : , : |
61 | instantiation | 72, 73 | ⊢ |
| : , : |
62 | instantiation | 74, 75 | ⊢ |
| : , : , : |
63 | theorem | | ⊢ |
| proveit.numbers.exponentiation.exp_complex_closure |
64 | theorem | | ⊢ |
| proveit.logic.equality.sub_left_side_into |
65 | instantiation | 76, 84 | ⊢ |
| : |
66 | theorem | | ⊢ |
| proveit.physics.quantum.QPE._two_pow_t_is_nat_pos |
67 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.int_interval_within_int |
68 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.interval_lower_bound |
69 | instantiation | 77, 78, 79 | ⊢ |
| : , : |
70 | assumption | | ⊢ |
71 | instantiation | 80, 81, 82 | ⊢ |
| : , : |
72 | theorem | | ⊢ |
| proveit.logic.equality.equals_reversal |
73 | instantiation | 83, 84, 85, 93, 86 | ⊢ |
| : , : , : |
74 | axiom | | ⊢ |
| proveit.logic.equality.substitution |
75 | instantiation | 87, 88, 89 | ⊢ |
| : , : |
76 | theorem | | ⊢ |
| proveit.numbers.exponentiation.complex_x_to_first_power_is_x |
77 | theorem | | ⊢ |
| proveit.numbers.addition.add_int_closure_bin |
78 | instantiation | 121, 90, 91 | ⊢ |
| : , : , : |
79 | instantiation | 92, 113 | ⊢ |
| : |
80 | theorem | | ⊢ |
| proveit.numbers.addition.commutation |
81 | instantiation | 121, 104, 93 | ⊢ |
| : , : , : |
82 | instantiation | 94, 95 | ⊢ |
| : |
83 | theorem | | ⊢ |
| proveit.numbers.exponentiation.product_of_real_powers |
84 | instantiation | 121, 104, 96 | ⊢ |
| : , : , : |
85 | instantiation | 97, 105 | ⊢ |
| : |
86 | instantiation | 98, 120 | ⊢ |
| : |
87 | theorem | | ⊢ |
| proveit.numbers.exponentiation.neg_power_as_div |
88 | instantiation | 121, 99, 100 | ⊢ |
| : , : , : |
89 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.posnat1 |
90 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.nat_pos_within_int |
91 | theorem | | ⊢ |
| proveit.physics.quantum.QPE._two_pow_t_minus_one_is_nat_pos |
92 | theorem | | ⊢ |
| proveit.numbers.negation.int_closure |
93 | instantiation | 101, 102, 103 | ⊢ |
| : , : , : |
94 | theorem | | ⊢ |
| proveit.numbers.negation.complex_closure |
95 | instantiation | 121, 104, 105 | ⊢ |
| : , : , : |
96 | instantiation | 121, 111, 106 | ⊢ |
| : , : , : |
97 | theorem | | ⊢ |
| proveit.numbers.negation.real_closure |
98 | theorem | | ⊢ |
| proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos |
99 | theorem | | ⊢ |
| proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero |
100 | instantiation | 121, 107, 108 | ⊢ |
| : , : , : |
101 | theorem | | ⊢ |
| proveit.logic.sets.inclusion.unfold_subset_eq |
102 | instantiation | 109, 110 | ⊢ |
| : , : |
103 | axiom | | ⊢ |
| proveit.physics.quantum.QPE._t_in_natural_pos |
104 | theorem | | ⊢ |
| proveit.numbers.number_sets.complex_numbers.real_within_complex |
105 | instantiation | 121, 111, 112 | ⊢ |
| : , : , : |
106 | instantiation | 121, 116, 113 | ⊢ |
| : , : , : |
107 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero |
108 | instantiation | 121, 114, 115 | ⊢ |
| : , : , : |
109 | theorem | | ⊢ |
| proveit.logic.sets.inclusion.relax_proper_subset |
110 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.nat_pos_within_real |
111 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.rational_within_real |
112 | instantiation | 121, 116, 117 | ⊢ |
| : , : , : |
113 | instantiation | 121, 122, 118 | ⊢ |
| : , : , : |
114 | theorem | | ⊢ |
| proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero |
115 | instantiation | 121, 119, 120 | ⊢ |
| : , : , : |
116 | theorem | | ⊢ |
| proveit.numbers.number_sets.rational_numbers.int_within_rational |
117 | instantiation | 121, 122, 123 | ⊢ |
| : , : , : |
118 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat2 |
119 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int |
120 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.posnat2 |
121 | theorem | | ⊢ |
| proveit.logic.sets.inclusion.superset_membership_from_proper_subset |
122 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.nat_within_int |
123 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat1 |
*equality replacement requirements |