| step type | requirements | statement |
0 | instantiation | 1, 2 | ⊢ |
| : , : |
1 | reference | 15 | ⊢ |
2 | instantiation | 75, 3, 4, 5 | ⊢ |
| : , : , : , : |
3 | instantiation | 58, 102, 6, 7, 8* | ⊢ |
| : , : |
4 | instantiation | 128, 9 | ⊢ |
| : , : , : |
5 | instantiation | 15, 10 | ⊢ |
| : , : |
6 | instantiation | 164, 151, 11 | ⊢ |
| : , : , : |
7 | instantiation | 81, 12 | ⊢ |
| : |
8 | instantiation | 115, 13, 14 | ⊢ |
| : , : , : |
9 | instantiation | 15, 16 | ⊢ |
| : , : |
10 | instantiation | 115, 17, 18 | ⊢ |
| : , : , : |
11 | instantiation | 164, 157, 19 | ⊢ |
| : , : , : |
12 | instantiation | 20, 166, 36 | ⊢ |
| : , : |
13 | instantiation | 128, 21 | ⊢ |
| : , : , : |
14 | instantiation | 141, 22 | ⊢ |
| : |
15 | theorem | | ⊢ |
| proveit.logic.equality.equals_reversal |
16 | instantiation | 23, 85, 142, 24* | ⊢ |
| : , : |
17 | instantiation | 128, 25 | ⊢ |
| : , : , : |
18 | instantiation | 67, 142, 26, 152, 68 | ⊢ |
| : , : , : |
19 | instantiation | 164, 162, 27 | ⊢ |
| : , : , : |
20 | theorem | | ⊢ |
| proveit.numbers.exponentiation.exp_natpos_closure |
21 | instantiation | 67, 142, 125, 106, 68, 28* | ⊢ |
| : , : , : |
22 | instantiation | 70, 142, 29 | ⊢ |
| : , : |
23 | theorem | | ⊢ |
| proveit.numbers.multiplication.mult_neg_left |
24 | instantiation | 75, 30, 31, 38 | ⊢ |
| : , : , : , : |
25 | instantiation | 115, 32, 33 | ⊢ |
| : , : , : |
26 | instantiation | 34, 98 | ⊢ |
| : |
27 | instantiation | 35, 163, 36 | ⊢ |
| : , : |
28 | instantiation | 37, 112, 102, 38* | ⊢ |
| : , : |
29 | instantiation | 84, 112 | ⊢ |
| : |
30 | instantiation | 94, 108, 166, 153, 110, 109, 111, 112, 142 | ⊢ |
| : , : , : , : , : , : |
31 | instantiation | 115, 39, 40 | ⊢ |
| : , : , : |
32 | instantiation | 128, 41 | ⊢ |
| : , : , : |
33 | instantiation | 58, 102, 42, 43, 44* | ⊢ |
| : , : |
34 | theorem | | ⊢ |
| proveit.numbers.negation.real_closure |
35 | theorem | | ⊢ |
| proveit.numbers.exponentiation.exp_int_closure |
36 | instantiation | 164, 45, 150 | ⊢ |
| : , : , : |
37 | theorem | | ⊢ |
| proveit.numbers.multiplication.mult_neg_right |
38 | instantiation | 131, 112 | ⊢ |
| : |
39 | instantiation | 46, 108, 166, 110, 47, 111, 112, 142 | ⊢ |
| : , : , : , : , : , : , : |
40 | instantiation | 115, 48, 49 | ⊢ |
| : , : , : |
41 | instantiation | 128, 50 | ⊢ |
| : , : , : |
42 | instantiation | 70, 142, 85 | ⊢ |
| : , : |
43 | instantiation | 51, 121, 52 | ⊢ |
| : , : |
44 | instantiation | 115, 53, 54 | ⊢ |
| : , : , : |
45 | theorem | | ⊢ |
| proveit.numbers.number_sets.natural_numbers.nat_pos_within_nat |
46 | theorem | | ⊢ |
| proveit.numbers.multiplication.rightward_commutation |
47 | instantiation | 123 | ⊢ |
| : , : |
48 | instantiation | 55, 153, 166, 108, 56, 110, 112, 142, 111 | ⊢ |
| : , : , : , : , : , : |
49 | instantiation | 128, 57 | ⊢ |
| : , : , : |
50 | instantiation | 58, 112, 142, 68, 59* | ⊢ |
| : , : |
51 | theorem | | ⊢ |
| proveit.numbers.exponentiation.exp_rational_non_zero__not_zero |
52 | instantiation | 164, 60, 126 | ⊢ |
| : , : , : |
53 | instantiation | 128, 61 | ⊢ |
| : , : , : |
54 | instantiation | 141, 62 | ⊢ |
| : |
55 | theorem | | ⊢ |
| proveit.numbers.multiplication.association |
56 | instantiation | 123 | ⊢ |
| : , : |
57 | instantiation | 72, 63, 64 | ⊢ |
| : , : , : |
58 | theorem | | ⊢ |
| proveit.numbers.division.div_as_mult |
59 | instantiation | 115, 65, 66 | ⊢ |
| : , : , : |
60 | theorem | | ⊢ |
| proveit.numbers.number_sets.rational_numbers.rational_pos_within_rational_nonzero |
61 | instantiation | 67, 142, 98, 106, 68, 69* | ⊢ |
| : , : , : |
62 | instantiation | 70, 142, 71 | ⊢ |
| : , : |
63 | instantiation | 72, 73, 74 | ⊢ |
| : , : , : |
64 | instantiation | 75, 76, 77, 78 | ⊢ |
| : , : , : , : |
65 | instantiation | 128, 79 | ⊢ |
| : , : , : |
66 | instantiation | 80, 112, 111 | ⊢ |
| : , : |
67 | theorem | | ⊢ |
| proveit.numbers.exponentiation.real_power_of_real_power |
68 | instantiation | 81, 161 | ⊢ |
| : |
69 | instantiation | 115, 82, 83 | ⊢ |
| : , : , : |
70 | theorem | | ⊢ |
| proveit.numbers.exponentiation.exp_complex_closure |
71 | instantiation | 84, 85 | ⊢ |
| : |
72 | theorem | | ⊢ |
| proveit.logic.equality.sub_right_side_into |
73 | instantiation | 86, 102, 92, 87 | ⊢ |
| : , : , : , : , : |
74 | instantiation | 115, 88, 89 | ⊢ |
| : , : , : |
75 | theorem | | ⊢ |
| proveit.logic.equality.four_chain_transitivity |
76 | instantiation | 128, 90 | ⊢ |
| : , : , : |
77 | instantiation | 128, 90 | ⊢ |
| : , : , : |
78 | instantiation | 131, 102 | ⊢ |
| : |
79 | instantiation | 91, 92, 159, 93* | ⊢ |
| : , : |
80 | theorem | | ⊢ |
| proveit.numbers.multiplication.commutation |
81 | theorem | | ⊢ |
| proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos |
82 | instantiation | 94, 108, 166, 153, 110, 109, 111, 112, 95 | ⊢ |
| : , : , : , : , : , : |
83 | instantiation | 96, 166, 108, 109, 110, 111, 112, 102, 97* | ⊢ |
| : , : , : , : , : |
84 | theorem | | ⊢ |
| proveit.numbers.negation.complex_closure |
85 | instantiation | 164, 151, 98 | ⊢ |
| : , : , : |
86 | theorem | | ⊢ |
| proveit.numbers.division.mult_frac_cancel_numer_left |
87 | instantiation | 164, 103, 99 | ⊢ |
| : , : , : |
88 | instantiation | 128, 100 | ⊢ |
| : , : , : |
89 | instantiation | 128, 101 | ⊢ |
| : , : , : |
90 | instantiation | 130, 102 | ⊢ |
| : |
91 | theorem | | ⊢ |
| proveit.numbers.exponentiation.neg_power_as_div |
92 | instantiation | 164, 103, 104 | ⊢ |
| : , : , : |
93 | instantiation | 105, 142 | ⊢ |
| : |
94 | theorem | | ⊢ |
| proveit.numbers.multiplication.disassociation |
95 | instantiation | 164, 151, 106 | ⊢ |
| : , : , : |
96 | theorem | | ⊢ |
| proveit.numbers.multiplication.mult_neg_any |
97 | instantiation | 107, 166, 108, 109, 110, 111, 112 | ⊢ |
| : , : , : , : |
98 | instantiation | 164, 157, 113 | ⊢ |
| : , : , : |
99 | instantiation | 164, 120, 114 | ⊢ |
| : , : , : |
100 | instantiation | 115, 116, 117 | ⊢ |
| : , : , : |
101 | instantiation | 128, 118 | ⊢ |
| : , : , : |
102 | instantiation | 164, 151, 119 | ⊢ |
| : , : , : |
103 | theorem | | ⊢ |
| proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero |
104 | instantiation | 164, 120, 121 | ⊢ |
| : , : , : |
105 | theorem | | ⊢ |
| proveit.numbers.exponentiation.complex_x_to_first_power_is_x |
106 | instantiation | 164, 157, 122 | ⊢ |
| : , : , : |
107 | theorem | | ⊢ |
| proveit.numbers.multiplication.elim_one_any |
108 | axiom | | ⊢ |
| proveit.numbers.number_sets.natural_numbers.zero_in_nats |
109 | instantiation | 123 | ⊢ |
| : , : |
110 | theorem | | ⊢ |
| proveit.core_expr_types.tuples.tuple_len_0_typical_eq |
111 | instantiation | 164, 151, 124 | ⊢ |
| : , : , : |
112 | instantiation | 164, 151, 125 | ⊢ |
| : , : , : |
113 | instantiation | 164, 146, 126 | ⊢ |
| : , : , : |
114 | instantiation | 164, 133, 127 | ⊢ |
| : , : , : |
115 | axiom | | ⊢ |
| proveit.logic.equality.equals_transitivity |
116 | instantiation | 128, 129 | ⊢ |
| : , : , : |
117 | instantiation | 130, 142 | ⊢ |
| : |
118 | instantiation | 131, 142 | ⊢ |
| : |
119 | instantiation | 164, 157, 132 | ⊢ |
| : , : , : |
120 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero |
121 | instantiation | 164, 133, 134 | ⊢ |
| : , : , : |
122 | instantiation | 164, 162, 135 | ⊢ |
| : , : , : |
123 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.tuple_len_2_typical_eq |
124 | instantiation | 164, 157, 136 | ⊢ |
| : , : , : |
125 | instantiation | 137, 138, 150 | ⊢ |
| : , : , : |
126 | instantiation | 139, 147, 140 | ⊢ |
| : , : |
127 | instantiation | 164, 143, 159 | ⊢ |
| : , : , : |
128 | axiom | | ⊢ |
| proveit.logic.equality.substitution |
129 | instantiation | 141, 142 | ⊢ |
| : |
130 | theorem | | ⊢ |
| proveit.numbers.division.frac_one_denom |
131 | theorem | | ⊢ |
| proveit.numbers.multiplication.elim_one_right |
132 | instantiation | 164, 162, 145 | ⊢ |
| : , : , : |
133 | theorem | | ⊢ |
| proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero |
134 | instantiation | 164, 143, 161 | ⊢ |
| : , : , : |
135 | instantiation | 144, 145 | ⊢ |
| : |
136 | instantiation | 164, 146, 147 | ⊢ |
| : , : , : |
137 | theorem | | ⊢ |
| proveit.logic.sets.inclusion.unfold_subset_eq |
138 | instantiation | 148, 149 | ⊢ |
| : , : |
139 | theorem | | ⊢ |
| proveit.numbers.multiplication.mult_rational_pos_closure_bin |
140 | instantiation | 164, 160, 150 | ⊢ |
| : , : , : |
141 | theorem | | ⊢ |
| proveit.numbers.multiplication.elim_one_left |
142 | instantiation | 164, 151, 152 | ⊢ |
| : , : , : |
143 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int |
144 | theorem | | ⊢ |
| proveit.numbers.negation.int_closure |
145 | instantiation | 164, 165, 153 | ⊢ |
| : , : , : |
146 | theorem | | ⊢ |
| proveit.numbers.number_sets.rational_numbers.rational_pos_within_rational |
147 | instantiation | 154, 155, 156 | ⊢ |
| : , : |
148 | theorem | | ⊢ |
| proveit.logic.sets.inclusion.relax_proper_subset |
149 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.nat_pos_within_real |
150 | axiom | | ⊢ |
| proveit.physics.quantum.QPE._t_in_natural_pos |
151 | theorem | | ⊢ |
| proveit.numbers.number_sets.complex_numbers.real_within_complex |
152 | instantiation | 164, 157, 158 | ⊢ |
| : , : , : |
153 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat1 |
154 | theorem | | ⊢ |
| proveit.numbers.division.div_rational_pos_closure |
155 | instantiation | 164, 160, 159 | ⊢ |
| : , : , : |
156 | instantiation | 164, 160, 161 | ⊢ |
| : , : , : |
157 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.rational_within_real |
158 | instantiation | 164, 162, 163 | ⊢ |
| : , : , : |
159 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.posnat1 |
160 | theorem | | ⊢ |
| proveit.numbers.number_sets.rational_numbers.nat_pos_within_rational_pos |
161 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.posnat2 |
162 | theorem | | ⊢ |
| proveit.numbers.number_sets.rational_numbers.int_within_rational |
163 | instantiation | 164, 165, 166 | ⊢ |
| : , : , : |
164 | theorem | | ⊢ |
| proveit.logic.sets.inclusion.superset_membership_from_proper_subset |
165 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.nat_within_int |
166 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat2 |
*equality replacement requirements |