| step type | requirements | statement |
0 | instantiation | 1, 2, 3, 4, 5, 6 | ⊢ |
| : , : |
1 | theorem | | ⊢ |
| proveit.logic.booleans.conjunction.and_if_all |
2 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat3 |
3 | instantiation | 7 | ⊢ |
| : , : , : |
4 | instantiation | 8, 9, 10 | ⊢ |
| : , : , : |
5 | instantiation | 16, 131, 25, 11, 12, 13* | ⊢ |
| : , : , : |
6 | instantiation | 14, 17, 15 | ⊢ |
| : , : |
7 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.tuple_len_3_typical_eq |
8 | theorem | | ⊢ |
| proveit.numbers.ordering.transitivity_less_eq_less_eq |
9 | instantiation | 16, 43, 131, 17, 18, 19*, 20* | ⊢ |
| : , : , : |
10 | instantiation | 21, 22 | ⊢ |
| : , : |
11 | instantiation | 23, 26, 131 | ⊢ |
| : , : |
12 | instantiation | 24, 25, 26, 131, 27, 28 | ⊢ |
| : , : , : |
13 | instantiation | 88, 29, 47, 30 | ⊢ |
| : , : , : , : |
14 | theorem | | ⊢ |
| proveit.numbers.ordering.relax_equal_to_less_eq |
15 | instantiation | 72 | ⊢ |
| : |
16 | theorem | | ⊢ |
| proveit.numbers.addition.weak_bound_via_left_term_bound |
17 | instantiation | 137, 138, 100 | ⊢ |
| : , : , : |
18 | instantiation | 31, 100 | ⊢ |
| : |
19 | instantiation | 113, 121, 32 | ⊢ |
| : , : |
20 | instantiation | 69, 33, 34 | ⊢ |
| : , : , : |
21 | theorem | | ⊢ |
| proveit.numbers.ordering.relax_less |
22 | instantiation | 35, 36 | ⊢ |
| : |
23 | theorem | | ⊢ |
| proveit.numbers.addition.add_real_closure_bin |
24 | theorem | | ⊢ |
| proveit.numbers.ordering.less_eq_add_right |
25 | instantiation | 164, 153, 37 | ⊢ |
| : , : , : |
26 | instantiation | 164, 153, 38 | ⊢ |
| : , : , : |
27 | instantiation | 39, 158, 75, 76 | ⊢ |
| : , : , : |
28 | instantiation | 40, 163 | ⊢ |
| : |
29 | instantiation | 69, 41, 42 | ⊢ |
| : , : , : |
30 | instantiation | 102, 77 | ⊢ |
| : , : |
31 | theorem | | ⊢ |
| proveit.numbers.number_sets.natural_numbers.natural_pos_lower_bound |
32 | instantiation | 164, 143, 43 | ⊢ |
| : , : , : |
33 | instantiation | 69, 44, 45 | ⊢ |
| : , : , : |
34 | instantiation | 46, 84, 47 | ⊢ |
| : , : |
35 | theorem | | ⊢ |
| proveit.numbers.number_sets.natural_numbers.natural_pos_is_pos |
36 | instantiation | 48, 49, 119 | ⊢ |
| : , : |
37 | instantiation | 164, 161, 56 | ⊢ |
| : , : , : |
38 | instantiation | 164, 161, 75 | ⊢ |
| : , : , : |
39 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.interval_upper_bound |
40 | theorem | | ⊢ |
| proveit.numbers.number_sets.natural_numbers.natural_lower_bound |
41 | instantiation | 104, 50 | ⊢ |
| : , : , : |
42 | instantiation | 69, 51, 52 | ⊢ |
| : , : , : |
43 | instantiation | 164, 153, 53 | ⊢ |
| : , : , : |
44 | instantiation | 104, 77 | ⊢ |
| : , : , : |
45 | instantiation | 104, 54 | ⊢ |
| : , : , : |
46 | theorem | | ⊢ |
| proveit.numbers.addition.subtraction.add_cancel_basic |
47 | instantiation | 72 | ⊢ |
| : |
48 | theorem | | ⊢ |
| proveit.numbers.addition.add_nat_pos_closure_bin |
49 | instantiation | 55, 56, 57 | ⊢ |
| : |
50 | instantiation | 69, 58, 59 | ⊢ |
| : , : , : |
51 | instantiation | 78, 81, 166, 163, 83, 60, 84, 115, 121 | ⊢ |
| : , : , : , : , : , : |
52 | instantiation | 61, 121, 84, 62 | ⊢ |
| : , : , : |
53 | instantiation | 164, 161, 63 | ⊢ |
| : , : , : |
54 | instantiation | 104, 77 | ⊢ |
| : , : , : |
55 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.pos_int_is_natural_pos |
56 | instantiation | 164, 64, 76 | ⊢ |
| : , : , : |
57 | instantiation | 65, 66, 67 | ⊢ |
| : , : , : |
58 | instantiation | 104, 68 | ⊢ |
| : , : , : |
59 | instantiation | 69, 70, 71 | ⊢ |
| : , : , : |
60 | instantiation | 92 | ⊢ |
| : , : |
61 | theorem | | ⊢ |
| proveit.numbers.addition.subtraction.add_cancel_triple_32 |
62 | instantiation | 72 | ⊢ |
| : |
63 | instantiation | 157, 87 | ⊢ |
| : |
64 | instantiation | 73, 158, 75 | ⊢ |
| : , : |
65 | theorem | | ⊢ |
| proveit.numbers.ordering.transitivity_less_less_eq |
66 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.less_0_1 |
67 | instantiation | 74, 158, 75, 76 | ⊢ |
| : , : , : |
68 | instantiation | 104, 77 | ⊢ |
| : , : , : |
69 | axiom | | ⊢ |
| proveit.logic.equality.equals_transitivity |
70 | instantiation | 78, 81, 166, 163, 83, 79, 84, 112, 121 | ⊢ |
| : , : , : , : , : , : |
71 | instantiation | 80, 163, 166, 81, 82, 83, 84, 112, 121, 85* | ⊢ |
| : , : , : , : , : , : |
72 | axiom | | ⊢ |
| proveit.logic.equality.equals_reflexivity |
73 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.int_interval_within_int |
74 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.interval_lower_bound |
75 | instantiation | 86, 87, 147 | ⊢ |
| : , : |
76 | assumption | | ⊢ |
77 | instantiation | 88, 89, 90, 91 | ⊢ |
| : , : , : , : |
78 | theorem | | ⊢ |
| proveit.numbers.addition.disassociation |
79 | instantiation | 92 | ⊢ |
| : , : |
80 | theorem | | ⊢ |
| proveit.numbers.addition.association |
81 | axiom | | ⊢ |
| proveit.numbers.number_sets.natural_numbers.zero_in_nats |
82 | instantiation | 92 | ⊢ |
| : , : |
83 | theorem | | ⊢ |
| proveit.core_expr_types.tuples.tuple_len_0_typical_eq |
84 | instantiation | 93, 94, 95 | ⊢ |
| : , : |
85 | instantiation | 96, 97, 98 | ⊢ |
| : , : , : |
86 | theorem | | ⊢ |
| proveit.numbers.addition.add_int_closure_bin |
87 | instantiation | 164, 99, 100 | ⊢ |
| : , : , : |
88 | theorem | | ⊢ |
| proveit.logic.equality.four_chain_transitivity |
89 | instantiation | 104, 101 | ⊢ |
| : , : , : |
90 | instantiation | 102, 103 | ⊢ |
| : , : |
91 | instantiation | 104, 105 | ⊢ |
| : , : , : |
92 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.tuple_len_2_typical_eq |
93 | theorem | | ⊢ |
| proveit.numbers.multiplication.mult_complex_closure_bin |
94 | instantiation | 106, 121, 107, 108 | ⊢ |
| : , : |
95 | instantiation | 164, 143, 109 | ⊢ |
| : , : , : |
96 | theorem | | ⊢ |
| proveit.logic.equality.sub_right_side_into |
97 | instantiation | 110, 121, 134, 111 | ⊢ |
| : , : , : |
98 | instantiation | 113, 121, 112 | ⊢ |
| : , : |
99 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.nat_pos_within_int |
100 | theorem | | ⊢ |
| proveit.physics.quantum.QPE._two_pow_t_minus_one_is_nat_pos |
101 | instantiation | 113, 114, 115 | ⊢ |
| : , : |
102 | theorem | | ⊢ |
| proveit.logic.equality.equals_reversal |
103 | instantiation | 116, 134, 128, 127, 123 | ⊢ |
| : , : , : |
104 | axiom | | ⊢ |
| proveit.logic.equality.substitution |
105 | instantiation | 117, 118, 119 | ⊢ |
| : , : |
106 | theorem | | ⊢ |
| proveit.numbers.division.div_complex_closure |
107 | instantiation | 120, 134, 121 | ⊢ |
| : , : |
108 | instantiation | 122, 123, 124 | ⊢ |
| : , : , : |
109 | instantiation | 164, 153, 125 | ⊢ |
| : , : , : |
110 | theorem | | ⊢ |
| proveit.numbers.addition.subtraction.subtract_from_add_reversed |
111 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.add_1_1 |
112 | instantiation | 164, 143, 126 | ⊢ |
| : , : , : |
113 | theorem | | ⊢ |
| proveit.numbers.addition.commutation |
114 | instantiation | 164, 143, 127 | ⊢ |
| : , : , : |
115 | instantiation | 164, 143, 128 | ⊢ |
| : , : , : |
116 | theorem | | ⊢ |
| proveit.numbers.exponentiation.product_of_real_powers |
117 | theorem | | ⊢ |
| proveit.numbers.exponentiation.neg_power_as_div |
118 | instantiation | 164, 129, 130 | ⊢ |
| : , : , : |
119 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.posnat1 |
120 | theorem | | ⊢ |
| proveit.numbers.exponentiation.exp_complex_closure |
121 | instantiation | 164, 143, 131 | ⊢ |
| : , : , : |
122 | theorem | | ⊢ |
| proveit.logic.equality.sub_left_side_into |
123 | instantiation | 132, 160 | ⊢ |
| : |
124 | instantiation | 133, 134 | ⊢ |
| : |
125 | instantiation | 164, 161, 135 | ⊢ |
| : , : , : |
126 | instantiation | 164, 153, 136 | ⊢ |
| : , : , : |
127 | instantiation | 137, 138, 156 | ⊢ |
| : , : , : |
128 | instantiation | 164, 153, 139 | ⊢ |
| : , : , : |
129 | theorem | | ⊢ |
| proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero |
130 | instantiation | 164, 140, 141 | ⊢ |
| : , : , : |
131 | instantiation | 164, 153, 142 | ⊢ |
| : , : , : |
132 | theorem | | ⊢ |
| proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos |
133 | theorem | | ⊢ |
| proveit.numbers.exponentiation.complex_x_to_first_power_is_x |
134 | instantiation | 164, 143, 144 | ⊢ |
| : , : , : |
135 | instantiation | 145, 162, 146 | ⊢ |
| : , : |
136 | instantiation | 164, 161, 147 | ⊢ |
| : , : , : |
137 | theorem | | ⊢ |
| proveit.logic.sets.inclusion.unfold_subset_eq |
138 | instantiation | 148, 149 | ⊢ |
| : , : |
139 | instantiation | 164, 161, 150 | ⊢ |
| : , : , : |
140 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero |
141 | instantiation | 164, 151, 152 | ⊢ |
| : , : , : |
142 | instantiation | 164, 161, 158 | ⊢ |
| : , : , : |
143 | theorem | | ⊢ |
| proveit.numbers.number_sets.complex_numbers.real_within_complex |
144 | instantiation | 164, 153, 154 | ⊢ |
| : , : , : |
145 | theorem | | ⊢ |
| proveit.numbers.exponentiation.exp_int_closure |
146 | instantiation | 164, 155, 156 | ⊢ |
| : , : , : |
147 | instantiation | 157, 162 | ⊢ |
| : |
148 | theorem | | ⊢ |
| proveit.logic.sets.inclusion.relax_proper_subset |
149 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.nat_pos_within_real |
150 | instantiation | 157, 158 | ⊢ |
| : |
151 | theorem | | ⊢ |
| proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero |
152 | instantiation | 164, 159, 160 | ⊢ |
| : , : , : |
153 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.rational_within_real |
154 | instantiation | 164, 161, 162 | ⊢ |
| : , : , : |
155 | theorem | | ⊢ |
| proveit.numbers.number_sets.natural_numbers.nat_pos_within_nat |
156 | axiom | | ⊢ |
| proveit.physics.quantum.QPE._t_in_natural_pos |
157 | theorem | | ⊢ |
| proveit.numbers.negation.int_closure |
158 | instantiation | 164, 165, 163 | ⊢ |
| : , : , : |
159 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int |
160 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.posnat2 |
161 | theorem | | ⊢ |
| proveit.numbers.number_sets.rational_numbers.int_within_rational |
162 | instantiation | 164, 165, 166 | ⊢ |
| : , : , : |
163 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat1 |
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 |