| step type | requirements | statement |
0 | instantiation | 1, 2, 3, 4, 5, 6, 7, 8, 9 | , ⊢ |
| : , : , : , : , : , : |
1 | theorem | | ⊢ |
| proveit.numbers.multiplication.association |
2 | reference | 150 | ⊢ |
3 | reference | 145 | ⊢ |
4 | reference | 85 | ⊢ |
5 | instantiation | 101 | ⊢ |
| : , : |
6 | reference | 86 | ⊢ |
7 | instantiation | 35, 10, 11, 12 | ⊢ |
| : , : |
8 | instantiation | 17, 14, 13 | ⊢ |
| : , : |
9 | instantiation | 17, 14, 15 | , ⊢ |
| : , : |
10 | instantiation | 148, 111, 16 | ⊢ |
| : , : , : |
11 | instantiation | 17, 94, 18 | ⊢ |
| : , : |
12 | instantiation | 19, 20, 21 | ⊢ |
| : , : , : |
13 | instantiation | 70, 22, 23 | ⊢ |
| : , : , : |
14 | instantiation | 148, 111, 24 | ⊢ |
| : , : , : |
15 | instantiation | 25, 26 | , ⊢ |
| : |
16 | instantiation | 148, 122, 27 | ⊢ |
| : , : , : |
17 | theorem | | ⊢ |
| proveit.numbers.exponentiation.exp_complex_closure |
18 | instantiation | 35, 67, 94, 42 | ⊢ |
| : , : |
19 | theorem | | ⊢ |
| proveit.logic.equality.sub_left_side_into |
20 | instantiation | 28, 105, 29 | ⊢ |
| : , : |
21 | instantiation | 64, 30 | ⊢ |
| : , : , : |
22 | instantiation | 98, 73, 31 | ⊢ |
| : , : |
23 | instantiation | 59, 32, 33 | ⊢ |
| : , : , : |
24 | instantiation | 148, 114, 34 | ⊢ |
| : , : , : |
25 | theorem | | ⊢ |
| proveit.numbers.negation.complex_closure |
26 | instantiation | 35, 36, 37, 38 | , ⊢ |
| : , : |
27 | instantiation | 148, 129, 144 | ⊢ |
| : , : , : |
28 | theorem | | ⊢ |
| proveit.numbers.exponentiation.exp_rational_non_zero__not_zero |
29 | instantiation | 148, 39, 40 | ⊢ |
| : , : , : |
30 | instantiation | 41, 67, 94, 42, 43* | ⊢ |
| : , : |
31 | instantiation | 70, 44, 45 | ⊢ |
| : , : , : |
32 | instantiation | 84, 150, 74, 85, 46, 86, 73, 99, 69, 100 | ⊢ |
| : , : , : , : , : , : |
33 | instantiation | 84, 85, 145, 74, 86, 75, 46, 94, 89, 99, 69, 100 | ⊢ |
| : , : , : , : , : , : |
34 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.e_is_real_pos |
35 | theorem | | ⊢ |
| proveit.numbers.division.div_complex_closure |
36 | instantiation | 70, 47, 48 | , ⊢ |
| : , : , : |
37 | instantiation | 148, 111, 49 | ⊢ |
| : , : , : |
38 | instantiation | 53, 50 | ⊢ |
| : |
39 | theorem | | ⊢ |
| proveit.numbers.number_sets.rational_numbers.rational_pos_within_rational_nonzero |
40 | instantiation | 51, 110, 52 | ⊢ |
| : , : |
41 | theorem | | ⊢ |
| proveit.numbers.division.div_as_mult |
42 | instantiation | 53, 128 | ⊢ |
| : |
43 | instantiation | 59, 54, 55 | ⊢ |
| : , : , : |
44 | instantiation | 98, 56, 100 | ⊢ |
| : , : |
45 | instantiation | 84, 85, 145, 150, 86, 57, 99, 69, 100 | ⊢ |
| : , : , : , : , : , : |
46 | instantiation | 90 | ⊢ |
| : , : , : |
47 | instantiation | 98, 73, 58 | , ⊢ |
| : , : |
48 | instantiation | 59, 60, 61 | , ⊢ |
| : , : , : |
49 | instantiation | 148, 122, 62 | ⊢ |
| : , : , : |
50 | instantiation | 63, 145, 142 | ⊢ |
| : , : |
51 | theorem | | ⊢ |
| proveit.numbers.multiplication.mult_rational_pos_closure_bin |
52 | instantiation | 148, 127, 147 | ⊢ |
| : , : , : |
53 | theorem | | ⊢ |
| proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos |
54 | instantiation | 64, 65 | ⊢ |
| : , : , : |
55 | instantiation | 66, 67, 68 | ⊢ |
| : , : |
56 | instantiation | 98, 99, 69 | ⊢ |
| : , : |
57 | instantiation | 101 | ⊢ |
| : , : |
58 | instantiation | 70, 71, 72 | , ⊢ |
| : , : , : |
59 | axiom | | ⊢ |
| proveit.logic.equality.equals_transitivity |
60 | instantiation | 84, 150, 74, 85, 76, 86, 73, 99, 100, 88 | , ⊢ |
| : , : , : , : , : , : |
61 | instantiation | 84, 85, 145, 74, 86, 75, 76, 94, 89, 99, 100, 88 | , ⊢ |
| : , : , : , : , : , : |
62 | instantiation | 148, 129, 138 | ⊢ |
| : , : , : |
63 | theorem | | ⊢ |
| proveit.numbers.exponentiation.exp_natpos_closure |
64 | axiom | | ⊢ |
| proveit.logic.equality.substitution |
65 | instantiation | 77, 78, 126, 79* | ⊢ |
| : , : |
66 | theorem | | ⊢ |
| proveit.numbers.multiplication.commutation |
67 | instantiation | 148, 111, 80 | ⊢ |
| : , : , : |
68 | instantiation | 148, 111, 81 | ⊢ |
| : , : , : |
69 | instantiation | 148, 111, 82 | ⊢ |
| : , : , : |
70 | theorem | | ⊢ |
| proveit.logic.equality.sub_right_side_into |
71 | instantiation | 98, 83, 88 | , ⊢ |
| : , : |
72 | instantiation | 84, 85, 145, 150, 86, 87, 99, 100, 88 | , ⊢ |
| : , : , : , : , : , : |
73 | instantiation | 98, 94, 89 | ⊢ |
| : , : |
74 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat3 |
75 | instantiation | 101 | ⊢ |
| : , : |
76 | instantiation | 90 | ⊢ |
| : , : , : |
77 | theorem | | ⊢ |
| proveit.numbers.exponentiation.neg_power_as_div |
78 | instantiation | 148, 91, 92 | ⊢ |
| : , : , : |
79 | instantiation | 93, 94 | ⊢ |
| : |
80 | instantiation | 95, 96, 147 | ⊢ |
| : , : , : |
81 | instantiation | 148, 122, 97 | ⊢ |
| : , : , : |
82 | theorem | | ⊢ |
| proveit.physics.quantum.QPE._phase_is_real |
83 | instantiation | 98, 99, 100 | ⊢ |
| : , : |
84 | theorem | | ⊢ |
| proveit.numbers.multiplication.disassociation |
85 | axiom | | ⊢ |
| proveit.numbers.number_sets.natural_numbers.zero_in_nats |
86 | theorem | | ⊢ |
| proveit.core_expr_types.tuples.tuple_len_0_typical_eq |
87 | instantiation | 101 | ⊢ |
| : , : |
88 | instantiation | 148, 111, 102 | ⊢ |
| : , : , : |
89 | instantiation | 148, 111, 103 | ⊢ |
| : , : , : |
90 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.tuple_len_3_typical_eq |
91 | theorem | | ⊢ |
| proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero |
92 | instantiation | 148, 104, 105 | ⊢ |
| : , : , : |
93 | theorem | | ⊢ |
| proveit.numbers.exponentiation.complex_x_to_first_power_is_x |
94 | instantiation | 148, 111, 106 | ⊢ |
| : , : , : |
95 | theorem | | ⊢ |
| proveit.logic.sets.inclusion.unfold_subset_eq |
96 | instantiation | 107, 108 | ⊢ |
| : , : |
97 | instantiation | 148, 109, 110 | ⊢ |
| : , : , : |
98 | theorem | | ⊢ |
| proveit.numbers.multiplication.mult_complex_closure_bin |
99 | theorem | | ⊢ |
| proveit.numbers.number_sets.complex_numbers.i_is_complex |
100 | instantiation | 148, 111, 112 | ⊢ |
| : , : , : |
101 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.tuple_len_2_typical_eq |
102 | instantiation | 148, 122, 113 | ⊢ |
| : , : , : |
103 | instantiation | 148, 114, 115 | ⊢ |
| : , : , : |
104 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero |
105 | instantiation | 148, 116, 117 | ⊢ |
| : , : , : |
106 | instantiation | 148, 122, 118 | ⊢ |
| : , : , : |
107 | theorem | | ⊢ |
| proveit.logic.sets.inclusion.relax_proper_subset |
108 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.nat_pos_within_real |
109 | theorem | | ⊢ |
| proveit.numbers.number_sets.rational_numbers.rational_pos_within_rational |
110 | instantiation | 119, 120, 121 | ⊢ |
| : , : |
111 | theorem | | ⊢ |
| proveit.numbers.number_sets.complex_numbers.real_within_complex |
112 | instantiation | 148, 122, 123 | ⊢ |
| : , : , : |
113 | instantiation | 148, 129, 124 | ⊢ |
| : , : , : |
114 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.real_pos_within_real |
115 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.pi_is_real_pos |
116 | theorem | | ⊢ |
| proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero |
117 | instantiation | 148, 125, 128 | ⊢ |
| : , : , : |
118 | instantiation | 148, 129, 141 | ⊢ |
| : , : , : |
119 | theorem | | ⊢ |
| proveit.numbers.division.div_rational_pos_closure |
120 | instantiation | 148, 127, 126 | ⊢ |
| : , : , : |
121 | instantiation | 148, 127, 128 | ⊢ |
| : , : , : |
122 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.rational_within_real |
123 | instantiation | 148, 129, 130 | ⊢ |
| : , : , : |
124 | instantiation | 148, 132, 131 | ⊢ |
| : , : , : |
125 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int |
126 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.posnat1 |
127 | theorem | | ⊢ |
| proveit.numbers.number_sets.rational_numbers.nat_pos_within_rational_pos |
128 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.posnat2 |
129 | theorem | | ⊢ |
| proveit.numbers.number_sets.rational_numbers.int_within_rational |
130 | instantiation | 148, 132, 133 | ⊢ |
| : , : , : |
131 | assumption | | ⊢ |
132 | instantiation | 134, 135, 136 | ⊢ |
| : , : |
133 | assumption | | ⊢ |
134 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.int_interval_within_int |
135 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.zero_is_int |
136 | instantiation | 137, 138, 139 | ⊢ |
| : , : |
137 | theorem | | ⊢ |
| proveit.numbers.addition.add_int_closure_bin |
138 | instantiation | 140, 141, 142 | ⊢ |
| : , : |
139 | instantiation | 143, 144 | ⊢ |
| : |
140 | theorem | | ⊢ |
| proveit.numbers.exponentiation.exp_int_closure |
141 | instantiation | 148, 149, 145 | ⊢ |
| : , : , : |
142 | instantiation | 148, 146, 147 | ⊢ |
| : , : , : |
143 | theorem | | ⊢ |
| proveit.numbers.negation.int_closure |
144 | instantiation | 148, 149, 150 | ⊢ |
| : , : , : |
145 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat2 |
146 | theorem | | ⊢ |
| proveit.numbers.number_sets.natural_numbers.nat_pos_within_nat |
147 | axiom | | ⊢ |
| proveit.physics.quantum.QPE._t_in_natural_pos |
148 | theorem | | ⊢ |
| proveit.logic.sets.inclusion.superset_membership_from_proper_subset |
149 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.nat_within_int |
150 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat1 |
*equality replacement requirements |