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