| step type | requirements | statement |
0 | instantiation | 1, 2 | , ⊢ |
| : |
1 | theorem | | ⊢ |
| proveit.trigonometry.sine_pos_interval |
2 | instantiation | 3, 26, 86, 4, 5 | , ⊢ |
| : , : , : |
3 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.in_IntervalOO |
4 | instantiation | 6, 26, 17, 15 | , ⊢ |
| : , : , : |
5 | instantiation | 7, 8, 9 | , ⊢ |
| : , : |
6 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.all_in_interval_oc__is__real |
7 | theorem | | ⊢ |
| proveit.logic.booleans.conjunction.and_if_both |
8 | instantiation | 10, 26, 17, 15 | , ⊢ |
| : , : , : |
9 | instantiation | 11, 12, 13 | , ⊢ |
| : , : , : |
10 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.interval_oc_lower_bound |
11 | theorem | | ⊢ |
| proveit.numbers.ordering.transitivity_less_eq_less |
12 | instantiation | 14, 26, 17, 15 | , ⊢ |
| : , : , : |
13 | instantiation | 16, 17, 18, 55, 19, 20*, 21* | ⊢ |
| : , : , : |
14 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.interval_oc_upper_bound |
15 | instantiation | 22, 23, 24 | , ⊢ |
| : |
16 | theorem | | ⊢ |
| proveit.numbers.addition.strong_bound_via_left_term_bound |
17 | instantiation | 101, 86, 125, 103 | ⊢ |
| : , : |
18 | instantiation | 60, 61, 26 | ⊢ |
| : , : |
19 | instantiation | 25, 61, 26, 86, 27, 28 | ⊢ |
| : , : , : |
20 | instantiation | 29, 30, 31, 32 | ⊢ |
| : , : , : , : |
21 | instantiation | 91, 33, 34 | ⊢ |
| : , : , : |
22 | theorem | | ⊢ |
| proveit.physics.quantum.QPE._scaled_abs_delta_b_floor_diff_interval |
23 | assumption | | ⊢ |
24 | assumption | | ⊢ |
25 | theorem | | ⊢ |
| proveit.numbers.multiplication.strong_bound_via_right_factor_bound |
26 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.zero_is_real |
27 | instantiation | 35, 100 | ⊢ |
| : |
28 | instantiation | 36, 75 | ⊢ |
| : |
29 | theorem | | ⊢ |
| proveit.logic.equality.four_chain_transitivity |
30 | instantiation | 91, 37, 38 | ⊢ |
| : , : , : |
31 | instantiation | 39 | ⊢ |
| : |
32 | instantiation | 40, 54 | ⊢ |
| : , : |
33 | instantiation | 69, 54 | ⊢ |
| : , : , : |
34 | instantiation | 40, 41, 42* | ⊢ |
| : , : |
35 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.positive_if_in_real_pos |
36 | theorem | | ⊢ |
| proveit.numbers.number_sets.rational_numbers.positive_if_in_rational_pos |
37 | instantiation | 91, 43, 44 | ⊢ |
| : , : , : |
38 | instantiation | 45, 46 | ⊢ |
| : |
39 | axiom | | ⊢ |
| proveit.logic.equality.equals_reflexivity |
40 | theorem | | ⊢ |
| proveit.logic.equality.equals_reversal |
41 | instantiation | 47, 48, 136, 129, 49, 50, 73, 72 | ⊢ |
| : , : , : , : , : , : |
42 | instantiation | 91, 51, 52 | ⊢ |
| : , : , : |
43 | instantiation | 69, 53 | ⊢ |
| : , : , : |
44 | instantiation | 69, 54 | ⊢ |
| : , : , : |
45 | theorem | | ⊢ |
| proveit.numbers.addition.elim_zero_left |
46 | instantiation | 134, 124, 55 | ⊢ |
| : , : , : |
47 | theorem | | ⊢ |
| proveit.numbers.multiplication.distribute_through_sum |
48 | axiom | | ⊢ |
| proveit.numbers.number_sets.natural_numbers.zero_in_nats |
49 | theorem | | ⊢ |
| proveit.core_expr_types.tuples.tuple_len_0_typical_eq |
50 | instantiation | 116 | ⊢ |
| : , : |
51 | instantiation | 69, 56 | ⊢ |
| : , : , : |
52 | instantiation | 117, 72 | ⊢ |
| : |
53 | instantiation | 57, 73 | ⊢ |
| : |
54 | instantiation | 58, 72, 119, 103, 59* | ⊢ |
| : , : |
55 | instantiation | 60, 61, 86 | ⊢ |
| : , : |
56 | instantiation | 62, 123, 133, 63* | ⊢ |
| : , : , : , : |
57 | theorem | | ⊢ |
| proveit.numbers.multiplication.mult_zero_right |
58 | theorem | | ⊢ |
| proveit.numbers.division.div_as_mult |
59 | instantiation | 91, 64, 65 | ⊢ |
| : , : , : |
60 | theorem | | ⊢ |
| proveit.numbers.multiplication.mult_real_closure_bin |
61 | instantiation | 134, 130, 66 | ⊢ |
| : , : , : |
62 | theorem | | ⊢ |
| proveit.numbers.addition.rational_pair_addition |
63 | instantiation | 91, 67, 68 | ⊢ |
| : , : , : |
64 | instantiation | 69, 70 | ⊢ |
| : , : , : |
65 | instantiation | 71, 72, 73 | ⊢ |
| : , : |
66 | instantiation | 134, 74, 75 | ⊢ |
| : , : , : |
67 | instantiation | 106, 136, 76, 77, 78, 79 | ⊢ |
| : , : , : , : |
68 | instantiation | 80, 81, 82 | ⊢ |
| : |
69 | axiom | | ⊢ |
| proveit.logic.equality.substitution |
70 | instantiation | 83, 84, 104, 85* | ⊢ |
| : , : |
71 | theorem | | ⊢ |
| proveit.numbers.multiplication.commutation |
72 | instantiation | 134, 124, 86 | ⊢ |
| : , : , : |
73 | instantiation | 134, 124, 87 | ⊢ |
| : , : , : |
74 | theorem | | ⊢ |
| proveit.numbers.number_sets.rational_numbers.rational_pos_within_rational |
75 | instantiation | 88, 89, 90 | ⊢ |
| : , : |
76 | instantiation | 116 | ⊢ |
| : , : |
77 | instantiation | 116 | ⊢ |
| : , : |
78 | instantiation | 91, 92, 93 | ⊢ |
| : , : , : |
79 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.mult_2_2 |
80 | theorem | | ⊢ |
| proveit.numbers.division.frac_cancel_complete |
81 | instantiation | 134, 124, 94 | ⊢ |
| : , : , : |
82 | instantiation | 115, 95 | ⊢ |
| : |
83 | theorem | | ⊢ |
| proveit.numbers.exponentiation.neg_power_as_div |
84 | instantiation | 134, 96, 97 | ⊢ |
| : , : , : |
85 | instantiation | 98, 119 | ⊢ |
| : |
86 | instantiation | 134, 99, 100 | ⊢ |
| : , : , : |
87 | instantiation | 101, 102, 125, 103 | ⊢ |
| : , : |
88 | theorem | | ⊢ |
| proveit.numbers.division.div_rational_pos_closure |
89 | instantiation | 134, 105, 104 | ⊢ |
| : , : , : |
90 | instantiation | 134, 105, 128 | ⊢ |
| : , : , : |
91 | axiom | | ⊢ |
| proveit.logic.equality.equals_transitivity |
92 | instantiation | 106, 136, 107, 108, 109, 110 | ⊢ |
| : , : , : , : |
93 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.add_2_2 |
94 | instantiation | 134, 130, 111 | ⊢ |
| : , : , : |
95 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.posnat4 |
96 | theorem | | ⊢ |
| proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero |
97 | instantiation | 134, 112, 113 | ⊢ |
| : , : , : |
98 | theorem | | ⊢ |
| proveit.numbers.exponentiation.complex_x_to_first_power_is_x |
99 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.real_pos_within_real |
100 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.pi_is_real_pos |
101 | theorem | | ⊢ |
| proveit.numbers.division.div_real_closure |
102 | instantiation | 134, 130, 114 | ⊢ |
| : , : , : |
103 | instantiation | 115, 128 | ⊢ |
| : |
104 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.posnat1 |
105 | theorem | | ⊢ |
| proveit.numbers.number_sets.rational_numbers.nat_pos_within_rational_pos |
106 | axiom | | ⊢ |
| proveit.core_expr_types.operations.operands_substitution |
107 | instantiation | 116 | ⊢ |
| : , : |
108 | instantiation | 116 | ⊢ |
| : , : |
109 | instantiation | 117, 119 | ⊢ |
| : |
110 | instantiation | 118, 119 | ⊢ |
| : |
111 | instantiation | 134, 132, 120 | ⊢ |
| : , : , : |
112 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero |
113 | instantiation | 134, 121, 122 | ⊢ |
| : , : , : |
114 | instantiation | 134, 132, 123 | ⊢ |
| : , : , : |
115 | theorem | | ⊢ |
| proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos |
116 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.tuple_len_2_typical_eq |
117 | theorem | | ⊢ |
| proveit.numbers.multiplication.elim_one_left |
118 | theorem | | ⊢ |
| proveit.numbers.multiplication.elim_one_right |
119 | instantiation | 134, 124, 125 | ⊢ |
| : , : , : |
120 | instantiation | 134, 135, 126 | ⊢ |
| : , : , : |
121 | theorem | | ⊢ |
| proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero |
122 | instantiation | 134, 127, 128 | ⊢ |
| : , : , : |
123 | instantiation | 134, 135, 129 | ⊢ |
| : , : , : |
124 | theorem | | ⊢ |
| proveit.numbers.number_sets.complex_numbers.real_within_complex |
125 | instantiation | 134, 130, 131 | ⊢ |
| : , : , : |
126 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat4 |
127 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int |
128 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.posnat2 |
129 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat1 |
130 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.rational_within_real |
131 | instantiation | 134, 132, 133 | ⊢ |
| : , : , : |
132 | theorem | | ⊢ |
| proveit.numbers.number_sets.rational_numbers.int_within_rational |
133 | instantiation | 134, 135, 136 | ⊢ |
| : , : , : |
134 | theorem | | ⊢ |
| proveit.logic.sets.inclusion.superset_membership_from_proper_subset |
135 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.nat_within_int |
136 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat2 |
*equality replacement requirements |