| step type | requirements | statement |
0 | instantiation | 1, 2, 3, 4, 5, 6*, 7* | ⊢ |
| : , : , : |
1 | theorem | | ⊢ |
| proveit.numbers.addition.weak_bound_via_left_term_bound |
2 | instantiation | 8, 70, 9, 10, 116, 11 | ⊢ |
| : , : |
3 | reference | 95 | ⊢ |
4 | instantiation | 146, 135, 12 | ⊢ |
| : , : , : |
5 | instantiation | 13, 134, 133, 124 | ⊢ |
| : , : , : |
6 | instantiation | 65, 14, 15, 16 | ⊢ |
| : , : , : , : |
7 | instantiation | 77, 17 | ⊢ |
| : , : |
8 | theorem | | ⊢ |
| proveit.numbers.addition.add_real_closure |
9 | instantiation | 81 | ⊢ |
| : , : , : |
10 | instantiation | 146, 135, 18 | ⊢ |
| : , : , : |
11 | instantiation | 97, 95 | ⊢ |
| : |
12 | instantiation | 146, 141, 133 | ⊢ |
| : , : , : |
13 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.interval_upper_bound |
14 | instantiation | 46, 19, 20 | ⊢ |
| : , : , : |
15 | instantiation | 61 | ⊢ |
| : |
16 | instantiation | 77, 21 | ⊢ |
| : , : |
17 | instantiation | 65, 22, 23, 24 | ⊢ |
| : , : , : , : |
18 | instantiation | 146, 141, 25 | ⊢ |
| : , : , : |
19 | instantiation | 79, 39 | ⊢ |
| : , : , : |
20 | instantiation | 46, 26, 27 | ⊢ |
| : , : , : |
21 | instantiation | 79, 45 | ⊢ |
| : , : , : |
22 | instantiation | 28, 83, 108 | ⊢ |
| : , : |
23 | instantiation | 85, 73, 86 | ⊢ |
| : , : |
24 | instantiation | 77, 29 | ⊢ |
| : , : |
25 | instantiation | 144, 138 | ⊢ |
| : |
26 | instantiation | 57, 140, 70, 58, 71, 60, 83, 72, 108, 73 | ⊢ |
| : , : , : , : , : , : |
27 | instantiation | 49, 58, 148, 60, 30, 83, 72, 108, 31 | ⊢ |
| : , : , : , : , : , : , : , : |
28 | theorem | | ⊢ |
| proveit.numbers.negation.distribute_neg_through_binary_sum |
29 | instantiation | 46, 32, 33 | ⊢ |
| : , : , : |
30 | instantiation | 74 | ⊢ |
| : , : |
31 | instantiation | 61 | ⊢ |
| : |
32 | instantiation | 46, 34, 35 | ⊢ |
| : , : , : |
33 | instantiation | 46, 36, 37 | ⊢ |
| : , : , : |
34 | instantiation | 79, 38 | ⊢ |
| : , : , : |
35 | instantiation | 79, 39 | ⊢ |
| : , : , : |
36 | instantiation | 46, 40, 41 | ⊢ |
| : , : , : |
37 | instantiation | 42, 58, 148, 140, 60, 43, 64, 108, 73, 44* | ⊢ |
| : , : , : , : , : , : |
38 | instantiation | 79, 55 | ⊢ |
| : , : , : |
39 | instantiation | 79, 45 | ⊢ |
| : , : , : |
40 | instantiation | 46, 47, 48 | ⊢ |
| : , : , : |
41 | instantiation | 49, 58, 140, 148, 60, 50, 82, 64, 108, 73, 51 | ⊢ |
| : , : , : , : , : , : , : , : |
42 | theorem | | ⊢ |
| proveit.numbers.addition.association |
43 | instantiation | 74 | ⊢ |
| : , : |
44 | instantiation | 52, 53, 54 | ⊢ |
| : , : , : |
45 | instantiation | 79, 55 | ⊢ |
| : , : , : |
46 | axiom | | ⊢ |
| proveit.logic.equality.equals_transitivity |
47 | instantiation | 57, 58, 148, 140, 60, 59, 82, 64, 56 | ⊢ |
| : , : , : , : , : , : |
48 | instantiation | 57, 148, 70, 58, 59, 71, 60, 82, 64, 72, 108, 73 | ⊢ |
| : , : , : , : , : , : |
49 | theorem | | ⊢ |
| proveit.numbers.addition.subtraction.add_cancel_general |
50 | instantiation | 74 | ⊢ |
| : , : |
51 | instantiation | 61 | ⊢ |
| : |
52 | theorem | | ⊢ |
| proveit.logic.equality.sub_right_side_into |
53 | instantiation | 62, 108, 119, 63 | ⊢ |
| : , : , : |
54 | instantiation | 85, 108, 64 | ⊢ |
| : , : |
55 | instantiation | 65, 66, 67, 68 | ⊢ |
| : , : , : , : |
56 | instantiation | 69, 70, 71, 72, 108, 73 | ⊢ |
| : , : |
57 | theorem | | ⊢ |
| proveit.numbers.addition.disassociation |
58 | axiom | | ⊢ |
| proveit.numbers.number_sets.natural_numbers.zero_in_nats |
59 | instantiation | 74 | ⊢ |
| : , : |
60 | theorem | | ⊢ |
| proveit.core_expr_types.tuples.tuple_len_0_typical_eq |
61 | axiom | | ⊢ |
| proveit.logic.equality.equals_reflexivity |
62 | theorem | | ⊢ |
| proveit.numbers.addition.subtraction.subtract_from_add_reversed |
63 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.add_1_1 |
64 | instantiation | 146, 128, 75 | ⊢ |
| : , : , : |
65 | theorem | | ⊢ |
| proveit.logic.equality.four_chain_transitivity |
66 | instantiation | 79, 76 | ⊢ |
| : , : , : |
67 | instantiation | 77, 78 | ⊢ |
| : , : |
68 | instantiation | 79, 80 | ⊢ |
| : , : , : |
69 | theorem | | ⊢ |
| proveit.numbers.addition.add_complex_closure |
70 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat3 |
71 | instantiation | 81 | ⊢ |
| : , : , : |
72 | instantiation | 96, 82 | ⊢ |
| : |
73 | instantiation | 96, 83 | ⊢ |
| : |
74 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.tuple_len_2_typical_eq |
75 | instantiation | 146, 135, 84 | ⊢ |
| : , : , : |
76 | instantiation | 85, 103, 86 | ⊢ |
| : , : |
77 | theorem | | ⊢ |
| proveit.logic.equality.equals_reversal |
78 | instantiation | 87, 119, 88, 112, 110 | ⊢ |
| : , : , : |
79 | axiom | | ⊢ |
| proveit.logic.equality.substitution |
80 | instantiation | 89, 90, 91 | ⊢ |
| : , : |
81 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.tuple_len_3_typical_eq |
82 | instantiation | 92, 93, 94 | ⊢ |
| : , : |
83 | instantiation | 146, 128, 95 | ⊢ |
| : , : , : |
84 | instantiation | 146, 141, 139 | ⊢ |
| : , : , : |
85 | theorem | | ⊢ |
| proveit.numbers.addition.commutation |
86 | instantiation | 96, 108 | ⊢ |
| : |
87 | theorem | | ⊢ |
| proveit.numbers.exponentiation.product_of_real_powers |
88 | instantiation | 97, 116 | ⊢ |
| : |
89 | theorem | | ⊢ |
| proveit.numbers.exponentiation.neg_power_as_div |
90 | instantiation | 146, 98, 99 | ⊢ |
| : , : , : |
91 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.posnat1 |
92 | theorem | | ⊢ |
| proveit.numbers.multiplication.mult_complex_closure_bin |
93 | instantiation | 100, 108, 101, 102 | ⊢ |
| : , : |
94 | instantiation | 107, 119, 103 | ⊢ |
| : , : |
95 | instantiation | 146, 135, 104 | ⊢ |
| : , : , : |
96 | theorem | | ⊢ |
| proveit.numbers.negation.complex_closure |
97 | theorem | | ⊢ |
| proveit.numbers.negation.real_closure |
98 | theorem | | ⊢ |
| proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero |
99 | instantiation | 146, 105, 106 | ⊢ |
| : , : , : |
100 | theorem | | ⊢ |
| proveit.numbers.division.div_complex_closure |
101 | instantiation | 107, 119, 108 | ⊢ |
| : , : |
102 | instantiation | 109, 110, 111 | ⊢ |
| : , : , : |
103 | instantiation | 146, 128, 112 | ⊢ |
| : , : , : |
104 | instantiation | 146, 141, 113 | ⊢ |
| : , : , : |
105 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero |
106 | instantiation | 146, 114, 115 | ⊢ |
| : , : , : |
107 | theorem | | ⊢ |
| proveit.numbers.exponentiation.exp_complex_closure |
108 | instantiation | 146, 128, 116 | ⊢ |
| : , : , : |
109 | theorem | | ⊢ |
| proveit.logic.equality.sub_left_side_into |
110 | instantiation | 117, 126 | ⊢ |
| : |
111 | instantiation | 118, 119 | ⊢ |
| : |
112 | instantiation | 120, 121, 122 | ⊢ |
| : , : , : |
113 | instantiation | 146, 123, 124 | ⊢ |
| : , : , : |
114 | theorem | | ⊢ |
| proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero |
115 | instantiation | 146, 125, 126 | ⊢ |
| : , : , : |
116 | instantiation | 146, 135, 127 | ⊢ |
| : , : , : |
117 | theorem | | ⊢ |
| proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos |
118 | theorem | | ⊢ |
| proveit.numbers.exponentiation.complex_x_to_first_power_is_x |
119 | instantiation | 146, 128, 129 | ⊢ |
| : , : , : |
120 | theorem | | ⊢ |
| proveit.logic.sets.inclusion.unfold_subset_eq |
121 | instantiation | 130, 131 | ⊢ |
| : , : |
122 | axiom | | ⊢ |
| proveit.physics.quantum.QPE._t_in_natural_pos |
123 | instantiation | 132, 134, 133 | ⊢ |
| : , : |
124 | assumption | | ⊢ |
125 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int |
126 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.posnat2 |
127 | instantiation | 146, 141, 134 | ⊢ |
| : , : , : |
128 | theorem | | ⊢ |
| proveit.numbers.number_sets.complex_numbers.real_within_complex |
129 | instantiation | 146, 135, 136 | ⊢ |
| : , : , : |
130 | theorem | | ⊢ |
| proveit.logic.sets.inclusion.relax_proper_subset |
131 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.nat_pos_within_real |
132 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.int_interval_within_int |
133 | instantiation | 137, 138, 139 | ⊢ |
| : , : |
134 | instantiation | 146, 147, 140 | ⊢ |
| : , : , : |
135 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.rational_within_real |
136 | instantiation | 146, 141, 145 | ⊢ |
| : , : , : |
137 | theorem | | ⊢ |
| proveit.numbers.addition.add_int_closure_bin |
138 | instantiation | 146, 142, 143 | ⊢ |
| : , : , : |
139 | instantiation | 144, 145 | ⊢ |
| : |
140 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat1 |
141 | theorem | | ⊢ |
| proveit.numbers.number_sets.rational_numbers.int_within_rational |
142 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.nat_pos_within_int |
143 | theorem | | ⊢ |
| proveit.physics.quantum.QPE._two_pow_t_minus_one_is_nat_pos |
144 | theorem | | ⊢ |
| proveit.numbers.negation.int_closure |
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 |