| step type | requirements | statement |
0 | modus ponens | 1, 2 | ⊢ |
1 | instantiation | 3, 99 | ⊢ |
| : , : , : , : , : , : |
2 | generalization | 4 | ⊢ |
3 | axiom | | ⊢ |
| proveit.core_expr_types.lambda_maps.lambda_substitution |
4 | instantiation | 5, 6 | ⊢ |
| : , : , : |
5 | axiom | | ⊢ |
| proveit.core_expr_types.conditionals.conditional_substitution |
6 | deduction | 7 | ⊢ |
7 | instantiation | 80, 8, 9 | ⊢ |
| : , : , : |
8 | instantiation | 52, 10 | ⊢ |
| : , : , : |
9 | instantiation | 11, 38, 12, 30, 13* | ⊢ |
| : , : , : |
10 | instantiation | 14, 15, 16, 17, 18, 19 | ⊢ |
| : , : , : |
11 | theorem | | ⊢ |
| proveit.numbers.exponentiation.product_of_complex_powers |
12 | instantiation | 20, 57 | ⊢ |
| : |
13 | instantiation | 80, 21, 22 | ⊢ |
| : , : , : |
14 | theorem | | ⊢ |
| proveit.core_expr_types.tuples.tuple_eq_via_elem_eq |
15 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.posnat2 |
16 | instantiation | 114 | ⊢ |
| : , : |
17 | instantiation | 114 | ⊢ |
| : , : |
18 | instantiation | 52, 23 | ⊢ |
| : , : , : |
19 | instantiation | 24 | ⊢ |
| : |
20 | theorem | | ⊢ |
| proveit.numbers.negation.complex_closure |
21 | instantiation | 52, 25 | ⊢ |
| : , : , : |
22 | instantiation | 26, 27 | ⊢ |
| : |
23 | instantiation | 52, 28 | ⊢ |
| : , : , : |
24 | axiom | | ⊢ |
| proveit.logic.equality.equals_reflexivity |
25 | instantiation | 29, 57, 30, 31 | ⊢ |
| : , : |
26 | theorem | | ⊢ |
| proveit.numbers.exponentiation.exp_zero_eq_one |
27 | instantiation | 141, 118, 32 | ⊢ |
| : , : , : |
28 | instantiation | 80, 33, 34 | ⊢ |
| : , : , : |
29 | theorem | | ⊢ |
| proveit.numbers.addition.subtraction.add_cancel_reverse |
30 | instantiation | 89, 35, 36 | ⊢ |
| : , : , : |
31 | instantiation | 69, 93, 143, 102, 37, 103, 106, 107, 112, 113, 105 | ⊢ |
| : , : , : , : , : , : , : |
32 | instantiation | 141, 121, 38 | ⊢ |
| : , : , : |
33 | instantiation | 52, 39 | ⊢ |
| : , : , : |
34 | instantiation | 80, 40, 41 | ⊢ |
| : , : , : |
35 | instantiation | 111, 92, 42 | ⊢ |
| : , : |
36 | instantiation | 80, 43, 44 | ⊢ |
| : , : , : |
37 | instantiation | 108 | ⊢ |
| : , : , : |
38 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.e_is_real_pos |
39 | instantiation | 101, 70, 128, 102, 71, 45, 103, 106, 107, 112, 113, 75, 105 | ⊢ |
| : , : , : , : , : , : |
40 | instantiation | 80, 46, 47 | ⊢ |
| : , : , : |
41 | instantiation | 48, 57 | ⊢ |
| : |
42 | instantiation | 89, 49, 50 | ⊢ |
| : , : , : |
43 | instantiation | 101, 143, 93, 102, 51, 103, 92, 112, 105, 113 | ⊢ |
| : , : , : , : , : , : |
44 | instantiation | 101, 102, 128, 93, 103, 94, 51, 106, 107, 112, 105, 113 | ⊢ |
| : , : , : , : , : , : |
45 | instantiation | 114 | ⊢ |
| : , : |
46 | instantiation | 52, 53 | ⊢ |
| : , : , : |
47 | instantiation | 54, 55, 56, 57, 58* | ⊢ |
| : , : , : |
48 | theorem | | ⊢ |
| proveit.numbers.division.frac_one_denom |
49 | instantiation | 111, 59, 113 | ⊢ |
| : , : |
50 | instantiation | 101, 102, 128, 143, 103, 60, 112, 105, 113 | ⊢ |
| : , : , : , : , : , : |
51 | instantiation | 108 | ⊢ |
| : , : , : |
52 | axiom | | ⊢ |
| proveit.logic.equality.substitution |
53 | instantiation | 80, 61, 62 | ⊢ |
| : , : , : |
54 | theorem | | ⊢ |
| proveit.numbers.division.frac_cancel_left |
55 | instantiation | 141, 64, 63 | ⊢ |
| : , : , : |
56 | instantiation | 141, 64, 65 | ⊢ |
| : , : , : |
57 | instantiation | 89, 66, 67 | ⊢ |
| : , : , : |
58 | instantiation | 68, 75 | ⊢ |
| : |
59 | instantiation | 111, 112, 105 | ⊢ |
| : , : |
60 | instantiation | 114 | ⊢ |
| : , : |
61 | instantiation | 69, 102, 70, 143, 103, 71, 106, 107, 112, 113, 75, 105 | ⊢ |
| : , : , : , : , : , : , : |
62 | instantiation | 72, 143, 73, 102, 74, 103, 75, 106, 107, 112, 113, 105 | ⊢ |
| : , : , : , : , : , : |
63 | instantiation | 141, 77, 76 | ⊢ |
| : , : , : |
64 | theorem | | ⊢ |
| proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero |
65 | instantiation | 141, 77, 78 | ⊢ |
| : , : , : |
66 | instantiation | 111, 92, 79 | ⊢ |
| : , : |
67 | instantiation | 80, 81, 82 | ⊢ |
| : , : , : |
68 | theorem | | ⊢ |
| proveit.numbers.multiplication.elim_one_right |
69 | theorem | | ⊢ |
| proveit.numbers.multiplication.leftward_commutation |
70 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat4 |
71 | instantiation | 83 | ⊢ |
| : , : , : , : |
72 | theorem | | ⊢ |
| proveit.numbers.multiplication.association |
73 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat5 |
74 | instantiation | 84 | ⊢ |
| : , : , : , : , : |
75 | instantiation | 141, 118, 85 | ⊢ |
| : , : , : |
76 | instantiation | 141, 87, 86 | ⊢ |
| : , : , : |
77 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero |
78 | instantiation | 141, 87, 88 | ⊢ |
| : , : , : |
79 | instantiation | 89, 90, 91 | ⊢ |
| : , : , : |
80 | axiom | | ⊢ |
| proveit.logic.equality.equals_transitivity |
81 | instantiation | 101, 143, 93, 102, 95, 103, 92, 112, 113, 105 | ⊢ |
| : , : , : , : , : , : |
82 | instantiation | 101, 102, 128, 93, 103, 94, 95, 106, 107, 112, 113, 105 | ⊢ |
| : , : , : , : , : , : |
83 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.tuple_len_4_typical_eq |
84 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.tuple_len_5_typical_eq |
85 | instantiation | 96, 97, 138 | ⊢ |
| : , : , : |
86 | instantiation | 141, 98, 138 | ⊢ |
| : , : , : |
87 | theorem | | ⊢ |
| proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero |
88 | instantiation | 141, 98, 99 | ⊢ |
| : , : , : |
89 | theorem | | ⊢ |
| proveit.logic.equality.sub_right_side_into |
90 | instantiation | 111, 100, 105 | ⊢ |
| : , : |
91 | instantiation | 101, 102, 128, 143, 103, 104, 112, 113, 105 | ⊢ |
| : , : , : , : , : , : |
92 | instantiation | 111, 106, 107 | ⊢ |
| : , : |
93 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat3 |
94 | instantiation | 114 | ⊢ |
| : , : |
95 | instantiation | 108 | ⊢ |
| : , : , : |
96 | theorem | | ⊢ |
| proveit.logic.sets.inclusion.unfold_subset_eq |
97 | instantiation | 109, 110 | ⊢ |
| : , : |
98 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int |
99 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.posnat1 |
100 | instantiation | 111, 112, 113 | ⊢ |
| : , : |
101 | theorem | | ⊢ |
| proveit.numbers.multiplication.disassociation |
102 | axiom | | ⊢ |
| proveit.numbers.number_sets.natural_numbers.zero_in_nats |
103 | theorem | | ⊢ |
| proveit.core_expr_types.tuples.tuple_len_0_typical_eq |
104 | instantiation | 114 | ⊢ |
| : , : |
105 | instantiation | 141, 118, 115 | ⊢ |
| : , : , : |
106 | instantiation | 141, 118, 116 | ⊢ |
| : , : , : |
107 | instantiation | 141, 118, 117 | ⊢ |
| : , : , : |
108 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.tuple_len_3_typical_eq |
109 | theorem | | ⊢ |
| proveit.logic.sets.inclusion.relax_proper_subset |
110 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.nat_pos_within_real |
111 | theorem | | ⊢ |
| proveit.numbers.multiplication.mult_complex_closure_bin |
112 | theorem | | ⊢ |
| proveit.numbers.number_sets.complex_numbers.i_is_complex |
113 | instantiation | 141, 118, 119 | ⊢ |
| : , : , : |
114 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.tuple_len_2_typical_eq |
115 | theorem | | ⊢ |
| proveit.physics.quantum.QPE._phase_is_real |
116 | instantiation | 141, 123, 120 | ⊢ |
| : , : , : |
117 | instantiation | 141, 121, 122 | ⊢ |
| : , : , : |
118 | theorem | | ⊢ |
| proveit.numbers.number_sets.complex_numbers.real_within_complex |
119 | instantiation | 141, 123, 124 | ⊢ |
| : , : , : |
120 | instantiation | 141, 126, 125 | ⊢ |
| : , : , : |
121 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.real_pos_within_real |
122 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.pi_is_real_pos |
123 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.rational_within_real |
124 | instantiation | 141, 126, 127 | ⊢ |
| : , : , : |
125 | instantiation | 141, 142, 128 | ⊢ |
| : , : , : |
126 | theorem | | ⊢ |
| proveit.numbers.number_sets.rational_numbers.int_within_rational |
127 | instantiation | 141, 129, 130 | ⊢ |
| : , : , : |
128 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat2 |
129 | instantiation | 131, 132, 133 | ⊢ |
| : , : |
130 | assumption | | ⊢ |
131 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.int_interval_within_int |
132 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.zero_is_int |
133 | instantiation | 134, 135, 136 | ⊢ |
| : , : |
134 | theorem | | ⊢ |
| proveit.numbers.addition.add_int_closure_bin |
135 | instantiation | 141, 137, 138 | ⊢ |
| : , : , : |
136 | instantiation | 139, 140 | ⊢ |
| : |
137 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.nat_pos_within_int |
138 | theorem | | ⊢ |
| proveit.physics.quantum.QPE._two_pow_t_is_nat_pos |
139 | theorem | | ⊢ |
| proveit.numbers.negation.int_closure |
140 | instantiation | 141, 142, 143 | ⊢ |
| : , : , : |
141 | theorem | | ⊢ |
| proveit.logic.sets.inclusion.superset_membership_from_proper_subset |
142 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.nat_within_int |
143 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat1 |
*equality replacement requirements |