| step type | requirements | statement |
0 | instantiation | 1, 2, 3 | , ⊢ |
| : , : |
1 | theorem | | ⊢ |
| proveit.numbers.multiplication.mult_complex_nonzero_closure_bin |
2 | reference | 96 | ⊢ |
3 | instantiation | 4, 5, 6 | , ⊢ |
| : |
4 | theorem | | ⊢ |
| proveit.numbers.number_sets.complex_numbers.nonzero_complex_is_complex_nonzero |
5 | instantiation | 146, 136, 10 | , ⊢ |
| : , : , : |
6 | instantiation | 7, 8 | , ⊢ |
| : , : |
7 | theorem | | ⊢ |
| proveit.logic.equality.not_equals_symmetry |
8 | instantiation | 9, 38, 10, 11 | , ⊢ |
| : , : |
9 | theorem | | ⊢ |
| proveit.numbers.ordering.less_is_not_eq |
10 | instantiation | 18, 38, 114, 12 | , ⊢ |
| : , : , : |
11 | instantiation | 22, 38, 114, 12 | , ⊢ |
| : , : , : |
12 | instantiation | 13, 14 | , ⊢ |
| : |
13 | theorem | | ⊢ |
| proveit.trigonometry.sine_pos_interval |
14 | instantiation | 15, 38, 98, 16, 17 | , ⊢ |
| : , : , : |
15 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.in_IntervalOO |
16 | instantiation | 18, 38, 29, 27 | , ⊢ |
| : , : , : |
17 | instantiation | 19, 20, 21 | , ⊢ |
| : , : |
18 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.all_in_interval_oc__is__real |
19 | theorem | | ⊢ |
| proveit.logic.booleans.conjunction.and_if_both |
20 | instantiation | 22, 38, 29, 27 | , ⊢ |
| : , : , : |
21 | instantiation | 23, 24, 25 | , ⊢ |
| : , : , : |
22 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.interval_oc_lower_bound |
23 | theorem | | ⊢ |
| proveit.numbers.ordering.transitivity_less_eq_less |
24 | instantiation | 26, 38, 29, 27 | , ⊢ |
| : , : , : |
25 | instantiation | 28, 29, 30, 67, 31, 32*, 33* | ⊢ |
| : , : , : |
26 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.interval_oc_upper_bound |
27 | instantiation | 34, 35, 36 | , ⊢ |
| : |
28 | theorem | | ⊢ |
| proveit.numbers.addition.strong_bound_via_left_term_bound |
29 | instantiation | 113, 98, 137, 115 | ⊢ |
| : , : |
30 | instantiation | 72, 73, 38 | ⊢ |
| : , : |
31 | instantiation | 37, 73, 38, 98, 39, 40 | ⊢ |
| : , : , : |
32 | instantiation | 41, 42, 43, 44 | ⊢ |
| : , : , : , : |
33 | instantiation | 103, 45, 46 | ⊢ |
| : , : , : |
34 | theorem | | ⊢ |
| proveit.physics.quantum.QPE._scaled_abs_delta_b_floor_diff_interval |
35 | assumption | | ⊢ |
36 | assumption | | ⊢ |
37 | theorem | | ⊢ |
| proveit.numbers.multiplication.strong_bound_via_right_factor_bound |
38 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.zero_is_real |
39 | instantiation | 47, 112 | ⊢ |
| : |
40 | instantiation | 48, 87 | ⊢ |
| : |
41 | theorem | | ⊢ |
| proveit.logic.equality.four_chain_transitivity |
42 | instantiation | 103, 49, 50 | ⊢ |
| : , : , : |
43 | instantiation | 51 | ⊢ |
| : |
44 | instantiation | 52, 66 | ⊢ |
| : , : |
45 | instantiation | 81, 66 | ⊢ |
| : , : , : |
46 | instantiation | 52, 53, 54* | ⊢ |
| : , : |
47 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.positive_if_in_real_pos |
48 | theorem | | ⊢ |
| proveit.numbers.number_sets.rational_numbers.positive_if_in_rational_pos |
49 | instantiation | 103, 55, 56 | ⊢ |
| : , : , : |
50 | instantiation | 57, 58 | ⊢ |
| : |
51 | axiom | | ⊢ |
| proveit.logic.equality.equals_reflexivity |
52 | theorem | | ⊢ |
| proveit.logic.equality.equals_reversal |
53 | instantiation | 59, 60, 148, 141, 61, 62, 85, 84 | ⊢ |
| : , : , : , : , : , : |
54 | instantiation | 103, 63, 64 | ⊢ |
| : , : , : |
55 | instantiation | 81, 65 | ⊢ |
| : , : , : |
56 | instantiation | 81, 66 | ⊢ |
| : , : , : |
57 | theorem | | ⊢ |
| proveit.numbers.addition.elim_zero_left |
58 | instantiation | 146, 136, 67 | ⊢ |
| : , : , : |
59 | theorem | | ⊢ |
| proveit.numbers.multiplication.distribute_through_sum |
60 | axiom | | ⊢ |
| proveit.numbers.number_sets.natural_numbers.zero_in_nats |
61 | theorem | | ⊢ |
| proveit.core_expr_types.tuples.tuple_len_0_typical_eq |
62 | instantiation | 128 | ⊢ |
| : , : |
63 | instantiation | 81, 68 | ⊢ |
| : , : , : |
64 | instantiation | 129, 84 | ⊢ |
| : |
65 | instantiation | 69, 85 | ⊢ |
| : |
66 | instantiation | 70, 84, 131, 115, 71* | ⊢ |
| : , : |
67 | instantiation | 72, 73, 98 | ⊢ |
| : , : |
68 | instantiation | 74, 135, 145, 75* | ⊢ |
| : , : , : , : |
69 | theorem | | ⊢ |
| proveit.numbers.multiplication.mult_zero_right |
70 | theorem | | ⊢ |
| proveit.numbers.division.div_as_mult |
71 | instantiation | 103, 76, 77 | ⊢ |
| : , : , : |
72 | theorem | | ⊢ |
| proveit.numbers.multiplication.mult_real_closure_bin |
73 | instantiation | 146, 142, 78 | ⊢ |
| : , : , : |
74 | theorem | | ⊢ |
| proveit.numbers.addition.rational_pair_addition |
75 | instantiation | 103, 79, 80 | ⊢ |
| : , : , : |
76 | instantiation | 81, 82 | ⊢ |
| : , : , : |
77 | instantiation | 83, 84, 85 | ⊢ |
| : , : |
78 | instantiation | 146, 86, 87 | ⊢ |
| : , : , : |
79 | instantiation | 118, 148, 88, 89, 90, 91 | ⊢ |
| : , : , : , : |
80 | instantiation | 92, 93, 94 | ⊢ |
| : |
81 | axiom | | ⊢ |
| proveit.logic.equality.substitution |
82 | instantiation | 95, 96, 116, 97* | ⊢ |
| : , : |
83 | theorem | | ⊢ |
| proveit.numbers.multiplication.commutation |
84 | instantiation | 146, 136, 98 | ⊢ |
| : , : , : |
85 | instantiation | 146, 136, 99 | ⊢ |
| : , : , : |
86 | theorem | | ⊢ |
| proveit.numbers.number_sets.rational_numbers.rational_pos_within_rational |
87 | instantiation | 100, 101, 102 | ⊢ |
| : , : |
88 | instantiation | 128 | ⊢ |
| : , : |
89 | instantiation | 128 | ⊢ |
| : , : |
90 | instantiation | 103, 104, 105 | ⊢ |
| : , : , : |
91 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.mult_2_2 |
92 | theorem | | ⊢ |
| proveit.numbers.division.frac_cancel_complete |
93 | instantiation | 146, 136, 106 | ⊢ |
| : , : , : |
94 | instantiation | 127, 107 | ⊢ |
| : |
95 | theorem | | ⊢ |
| proveit.numbers.exponentiation.neg_power_as_div |
96 | instantiation | 146, 108, 109 | ⊢ |
| : , : , : |
97 | instantiation | 110, 131 | ⊢ |
| : |
98 | instantiation | 146, 111, 112 | ⊢ |
| : , : , : |
99 | instantiation | 113, 114, 137, 115 | ⊢ |
| : , : |
100 | theorem | | ⊢ |
| proveit.numbers.division.div_rational_pos_closure |
101 | instantiation | 146, 117, 116 | ⊢ |
| : , : , : |
102 | instantiation | 146, 117, 140 | ⊢ |
| : , : , : |
103 | axiom | | ⊢ |
| proveit.logic.equality.equals_transitivity |
104 | instantiation | 118, 148, 119, 120, 121, 122 | ⊢ |
| : , : , : , : |
105 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.add_2_2 |
106 | instantiation | 146, 142, 123 | ⊢ |
| : , : , : |
107 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.posnat4 |
108 | theorem | | ⊢ |
| proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero |
109 | instantiation | 146, 124, 125 | ⊢ |
| : , : , : |
110 | theorem | | ⊢ |
| proveit.numbers.exponentiation.complex_x_to_first_power_is_x |
111 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.real_pos_within_real |
112 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.pi_is_real_pos |
113 | theorem | | ⊢ |
| proveit.numbers.division.div_real_closure |
114 | instantiation | 146, 142, 126 | ⊢ |
| : , : , : |
115 | instantiation | 127, 140 | ⊢ |
| : |
116 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.posnat1 |
117 | theorem | | ⊢ |
| proveit.numbers.number_sets.rational_numbers.nat_pos_within_rational_pos |
118 | axiom | | ⊢ |
| proveit.core_expr_types.operations.operands_substitution |
119 | instantiation | 128 | ⊢ |
| : , : |
120 | instantiation | 128 | ⊢ |
| : , : |
121 | instantiation | 129, 131 | ⊢ |
| : |
122 | instantiation | 130, 131 | ⊢ |
| : |
123 | instantiation | 146, 144, 132 | ⊢ |
| : , : , : |
124 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero |
125 | instantiation | 146, 133, 134 | ⊢ |
| : , : , : |
126 | instantiation | 146, 144, 135 | ⊢ |
| : , : , : |
127 | theorem | | ⊢ |
| proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos |
128 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.tuple_len_2_typical_eq |
129 | theorem | | ⊢ |
| proveit.numbers.multiplication.elim_one_left |
130 | theorem | | ⊢ |
| proveit.numbers.multiplication.elim_one_right |
131 | instantiation | 146, 136, 137 | ⊢ |
| : , : , : |
132 | instantiation | 146, 147, 138 | ⊢ |
| : , : , : |
133 | theorem | | ⊢ |
| proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero |
134 | instantiation | 146, 139, 140 | ⊢ |
| : , : , : |
135 | instantiation | 146, 147, 141 | ⊢ |
| : , : , : |
136 | theorem | | ⊢ |
| proveit.numbers.number_sets.complex_numbers.real_within_complex |
137 | instantiation | 146, 142, 143 | ⊢ |
| : , : , : |
138 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat4 |
139 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int |
140 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.posnat2 |
141 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat1 |
142 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.rational_within_real |
143 | instantiation | 146, 144, 145 | ⊢ |
| : , : , : |
144 | theorem | | ⊢ |
| proveit.numbers.number_sets.rational_numbers.int_within_rational |
145 | instantiation | 146, 147, 148 | ⊢ |
| : , : , : |
146 | theorem | | ⊢ |
| proveit.logic.sets.inclusion.superset_membership_from_proper_subset |
147 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.nat_within_int |
148 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat2 |
*equality replacement requirements |