| step type | requirements | statement |
0 | instantiation | 1, 2 | ⊢ |
| : , : |
1 | theorem | | ⊢ |
| proveit.numbers.addition.subtraction.pos_difference |
2 | instantiation | 3, 123, 10, 4, 5, 6*, 7* | ⊢ |
| : , : , : |
3 | theorem | | ⊢ |
| proveit.numbers.addition.strong_bound_via_left_term_bound |
4 | instantiation | 165, 161, 8 | ⊢ |
| : , : , : |
5 | instantiation | 9, 10, 11, 133, 12, 13 | ⊢ |
| : , : , : |
6 | instantiation | 129, 14, 15 | ⊢ |
| : , : , : |
7 | instantiation | 91, 16, 17, 18 | ⊢ |
| : , : , : , : |
8 | instantiation | 165, 163, 19 | ⊢ |
| : , : , : |
9 | theorem | | ⊢ |
| proveit.numbers.ordering.less_eq_add_right_strong |
10 | instantiation | 165, 161, 20 | ⊢ |
| : , : , : |
11 | instantiation | 165, 21, 22 | ⊢ |
| : , : , : |
12 | instantiation | 23, 159, 133, 24, 25, 26 | ⊢ |
| : , : , : |
13 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.less_0_1 |
14 | instantiation | 141, 132 | ⊢ |
| : , : , : |
15 | instantiation | 27, 121, 153, 28 | ⊢ |
| : , : , : |
16 | instantiation | 129, 29, 30 | ⊢ |
| : , : , : |
17 | instantiation | 129, 31, 32 | ⊢ |
| : , : , : |
18 | instantiation | 64 | ⊢ |
| : |
19 | instantiation | 165, 166, 33 | ⊢ |
| : , : , : |
20 | instantiation | 165, 163, 34 | ⊢ |
| : , : , : |
21 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.real_pos_within_real |
22 | instantiation | 165, 35, 36 | ⊢ |
| : , : , : |
23 | theorem | | ⊢ |
| proveit.numbers.multiplication.weak_bound_via_right_factor_bound |
24 | instantiation | 134, 135, 70 | ⊢ |
| : , : , : |
25 | instantiation | 37, 70 | ⊢ |
| : |
26 | instantiation | 38, 167 | ⊢ |
| : |
27 | theorem | | ⊢ |
| proveit.numbers.addition.subtraction.subtract_from_add |
28 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.add_1_1 |
29 | instantiation | 141, 39 | ⊢ |
| : , : , : |
30 | instantiation | 129, 40, 41 | ⊢ |
| : , : , : |
31 | instantiation | 141, 42 | ⊢ |
| : , : , : |
32 | instantiation | 129, 43, 44 | ⊢ |
| : , : , : |
33 | instantiation | 45, 46, 160 | ⊢ |
| : , : |
34 | instantiation | 165, 166, 47 | ⊢ |
| : , : , : |
35 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.rational_pos_within_real_pos |
36 | instantiation | 165, 48, 58 | ⊢ |
| : , : , : |
37 | theorem | | ⊢ |
| proveit.numbers.number_sets.natural_numbers.natural_pos_lower_bound |
38 | theorem | | ⊢ |
| proveit.numbers.number_sets.natural_numbers.natural_lower_bound |
39 | instantiation | 141, 49 | ⊢ |
| : , : , : |
40 | instantiation | 50, 75, 167, 160, 76, 51, 53, 121, 110 | ⊢ |
| : , : , : , : , : , : |
41 | instantiation | 52, 121, 53, 54 | ⊢ |
| : , : , : |
42 | instantiation | 141, 117 | ⊢ |
| : , : , : |
43 | instantiation | 129, 55, 56 | ⊢ |
| : , : , : |
44 | instantiation | 152, 78 | ⊢ |
| : |
45 | theorem | | ⊢ |
| proveit.numbers.addition.add_nat_closure_bin |
46 | instantiation | 165, 57, 58 | ⊢ |
| : , : , : |
47 | instantiation | 59, 167, 160 | ⊢ |
| : , : |
48 | theorem | | ⊢ |
| proveit.numbers.number_sets.rational_numbers.nat_pos_within_rational_pos |
49 | instantiation | 129, 60, 61 | ⊢ |
| : , : , : |
50 | theorem | | ⊢ |
| proveit.numbers.addition.disassociation |
51 | instantiation | 86 | ⊢ |
| : , : |
52 | theorem | | ⊢ |
| proveit.numbers.addition.subtraction.add_cancel_triple_23 |
53 | instantiation | 88, 62, 63 | ⊢ |
| : , : , : |
54 | instantiation | 64 | ⊢ |
| : |
55 | instantiation | 65, 75, 167, 160, 76, 66, 153, 67, 78 | ⊢ |
| : , : , : , : , : , : |
56 | instantiation | 141, 68 | ⊢ |
| : , : , : |
57 | theorem | | ⊢ |
| proveit.numbers.number_sets.natural_numbers.nat_pos_within_nat |
58 | instantiation | 69, 157, 70 | ⊢ |
| : , : |
59 | theorem | | ⊢ |
| proveit.numbers.multiplication.mult_nat_closure_bin |
60 | instantiation | 141, 71 | ⊢ |
| : , : , : |
61 | instantiation | 74, 160, 167, 75, 72, 76, 153, 85, 78 | ⊢ |
| : , : , : , : , : , : |
62 | instantiation | 84, 73, 78 | ⊢ |
| : , : |
63 | instantiation | 74, 75, 167, 160, 76, 77, 153, 85, 78 | ⊢ |
| : , : , : , : , : , : |
64 | axiom | | ⊢ |
| proveit.logic.equality.equals_reflexivity |
65 | theorem | | ⊢ |
| proveit.numbers.multiplication.association |
66 | instantiation | 86 | ⊢ |
| : , : |
67 | instantiation | 99, 121, 153, 116 | ⊢ |
| : , : |
68 | instantiation | 88, 79, 80 | ⊢ |
| : , : , : |
69 | theorem | | ⊢ |
| proveit.numbers.multiplication.mult_nat_pos_closure_bin |
70 | theorem | | ⊢ |
| proveit.physics.quantum.QPE._two_pow_t_minus_one_is_nat_pos |
71 | instantiation | 91, 81, 82, 83 | ⊢ |
| : , : , : , : |
72 | instantiation | 86 | ⊢ |
| : , : |
73 | instantiation | 84, 153, 85 | ⊢ |
| : , : |
74 | theorem | | ⊢ |
| proveit.numbers.multiplication.disassociation |
75 | axiom | | ⊢ |
| proveit.numbers.number_sets.natural_numbers.zero_in_nats |
76 | theorem | | ⊢ |
| proveit.core_expr_types.tuples.tuple_len_0_typical_eq |
77 | instantiation | 86 | ⊢ |
| : , : |
78 | instantiation | 165, 158, 87 | ⊢ |
| : , : , : |
79 | instantiation | 88, 89, 90 | ⊢ |
| : , : , : |
80 | instantiation | 91, 92, 93, 94 | ⊢ |
| : , : , : , : |
81 | instantiation | 141, 95 | ⊢ |
| : , : , : |
82 | instantiation | 96, 97 | ⊢ |
| : , : |
83 | instantiation | 141, 98 | ⊢ |
| : , : , : |
84 | theorem | | ⊢ |
| proveit.numbers.multiplication.mult_complex_closure_bin |
85 | instantiation | 99, 121, 100, 101 | ⊢ |
| : , : |
86 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.tuple_len_2_typical_eq |
87 | instantiation | 134, 135, 102 | ⊢ |
| : , : , : |
88 | theorem | | ⊢ |
| proveit.logic.equality.sub_right_side_into |
89 | instantiation | 103, 121, 113, 104 | ⊢ |
| : , : , : , : , : |
90 | instantiation | 129, 105, 106 | ⊢ |
| : , : , : |
91 | theorem | | ⊢ |
| proveit.logic.equality.four_chain_transitivity |
92 | instantiation | 141, 107 | ⊢ |
| : , : , : |
93 | instantiation | 141, 107 | ⊢ |
| : , : , : |
94 | instantiation | 144, 121 | ⊢ |
| : |
95 | instantiation | 108, 109, 110 | ⊢ |
| : , : |
96 | theorem | | ⊢ |
| proveit.logic.equality.equals_reversal |
97 | instantiation | 111, 153, 123, 122, 116 | ⊢ |
| : , : , : |
98 | instantiation | 112, 113, 151 | ⊢ |
| : , : |
99 | theorem | | ⊢ |
| proveit.numbers.division.div_complex_closure |
100 | instantiation | 114, 153, 121 | ⊢ |
| : , : |
101 | instantiation | 115, 116, 117 | ⊢ |
| : , : , : |
102 | theorem | | ⊢ |
| proveit.physics.quantum.QPE._two_pow_t_is_nat_pos |
103 | theorem | | ⊢ |
| proveit.numbers.division.mult_frac_cancel_numer_left |
104 | instantiation | 165, 124, 118 | ⊢ |
| : , : , : |
105 | instantiation | 141, 119 | ⊢ |
| : , : , : |
106 | instantiation | 141, 120 | ⊢ |
| : , : , : |
107 | instantiation | 143, 121 | ⊢ |
| : |
108 | theorem | | ⊢ |
| proveit.numbers.addition.commutation |
109 | instantiation | 165, 158, 122 | ⊢ |
| : , : , : |
110 | instantiation | 165, 158, 123 | ⊢ |
| : , : , : |
111 | theorem | | ⊢ |
| proveit.numbers.exponentiation.product_of_real_powers |
112 | theorem | | ⊢ |
| proveit.numbers.exponentiation.neg_power_as_div |
113 | instantiation | 165, 124, 125 | ⊢ |
| : , : , : |
114 | theorem | | ⊢ |
| proveit.numbers.exponentiation.exp_complex_closure |
115 | theorem | | ⊢ |
| proveit.logic.equality.sub_left_side_into |
116 | instantiation | 126, 157 | ⊢ |
| : |
117 | instantiation | 127, 153 | ⊢ |
| : |
118 | instantiation | 165, 138, 128 | ⊢ |
| : , : , : |
119 | instantiation | 129, 130, 131 | ⊢ |
| : , : , : |
120 | instantiation | 141, 132 | ⊢ |
| : , : , : |
121 | instantiation | 165, 158, 133 | ⊢ |
| : , : , : |
122 | instantiation | 134, 135, 136 | ⊢ |
| : , : , : |
123 | instantiation | 165, 161, 137 | ⊢ |
| : , : , : |
124 | theorem | | ⊢ |
| proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero |
125 | instantiation | 165, 138, 139 | ⊢ |
| : , : , : |
126 | theorem | | ⊢ |
| proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos |
127 | theorem | | ⊢ |
| proveit.numbers.exponentiation.complex_x_to_first_power_is_x |
128 | instantiation | 165, 149, 140 | ⊢ |
| : , : , : |
129 | axiom | | ⊢ |
| proveit.logic.equality.equals_transitivity |
130 | instantiation | 141, 142 | ⊢ |
| : , : , : |
131 | instantiation | 143, 153 | ⊢ |
| : |
132 | instantiation | 144, 153 | ⊢ |
| : |
133 | instantiation | 165, 161, 145 | ⊢ |
| : , : , : |
134 | theorem | | ⊢ |
| proveit.logic.sets.inclusion.unfold_subset_eq |
135 | instantiation | 146, 147 | ⊢ |
| : , : |
136 | axiom | | ⊢ |
| proveit.physics.quantum.QPE._t_in_natural_pos |
137 | instantiation | 165, 163, 148 | ⊢ |
| : , : , : |
138 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero |
139 | instantiation | 165, 149, 150 | ⊢ |
| : , : , : |
140 | instantiation | 165, 156, 151 | ⊢ |
| : , : , : |
141 | axiom | | ⊢ |
| proveit.logic.equality.substitution |
142 | instantiation | 152, 153 | ⊢ |
| : |
143 | theorem | | ⊢ |
| proveit.numbers.division.frac_one_denom |
144 | theorem | | ⊢ |
| proveit.numbers.multiplication.elim_one_right |
145 | instantiation | 165, 163, 155 | ⊢ |
| : , : , : |
146 | theorem | | ⊢ |
| proveit.logic.sets.inclusion.relax_proper_subset |
147 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.nat_pos_within_real |
148 | instantiation | 154, 155 | ⊢ |
| : |
149 | theorem | | ⊢ |
| proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero |
150 | instantiation | 165, 156, 157 | ⊢ |
| : , : , : |
151 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.posnat1 |
152 | theorem | | ⊢ |
| proveit.numbers.multiplication.elim_one_left |
153 | instantiation | 165, 158, 159 | ⊢ |
| : , : , : |
154 | theorem | | ⊢ |
| proveit.numbers.negation.int_closure |
155 | instantiation | 165, 166, 160 | ⊢ |
| : , : , : |
156 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int |
157 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.posnat2 |
158 | theorem | | ⊢ |
| proveit.numbers.number_sets.complex_numbers.real_within_complex |
159 | instantiation | 165, 161, 162 | ⊢ |
| : , : , : |
160 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat1 |
161 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.rational_within_real |
162 | instantiation | 165, 163, 164 | ⊢ |
| : , : , : |
163 | theorem | | ⊢ |
| proveit.numbers.number_sets.rational_numbers.int_within_rational |
164 | instantiation | 165, 166, 167 | ⊢ |
| : , : , : |
165 | theorem | | ⊢ |
| proveit.logic.sets.inclusion.superset_membership_from_proper_subset |
166 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.nat_within_int |
167 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat2 |
*equality replacement requirements |