| step type | requirements | statement |
0 | instantiation | 1, 2, 3, 4, 5, 6, 7, 8, 9, 10* | ⊢ |
| : , : , : , : , : , : |
1 | theorem | | ⊢ |
| proveit.numbers.multiplication.association |
2 | axiom | | ⊢ |
| proveit.numbers.number_sets.natural_numbers.zero_in_nats |
3 | reference | 123 | ⊢ |
4 | reference | 113 | ⊢ |
5 | theorem | | ⊢ |
| proveit.core_expr_types.tuples.tuple_len_0_typical_eq |
6 | instantiation | 51 | ⊢ |
| : , : |
7 | instantiation | 121, 69, 11 | ⊢ |
| : , : , : |
8 | reference | 58 | ⊢ |
9 | instantiation | 121, 69, 12 | ⊢ |
| : , : , : |
10 | instantiation | 13, 40, 58, 14, 15, 16*, 17* | ⊢ |
| : , : , : , : |
11 | instantiation | 121, 76, 18 | ⊢ |
| : , : , : |
12 | modus ponens | 19, 20 | ⊢ |
13 | theorem | | ⊢ |
| proveit.numbers.division.prod_of_fracs |
14 | instantiation | 121, 54, 21 | ⊢ |
| : , : , : |
15 | instantiation | 121, 54, 22 | ⊢ |
| : , : , : |
16 | instantiation | 23, 58 | ⊢ |
| : |
17 | instantiation | 24, 25, 26 | ⊢ |
| : , : , : |
18 | instantiation | 121, 27, 28 | ⊢ |
| : , : , : |
19 | instantiation | 29 | ⊢ |
| : , : , : |
20 | generalization | 30 | ⊢ |
21 | instantiation | 121, 66, 31 | ⊢ |
| : , : , : |
22 | instantiation | 121, 66, 32 | ⊢ |
| : , : , : |
23 | theorem | | ⊢ |
| proveit.numbers.division.frac_one_denom |
24 | axiom | | ⊢ |
| proveit.logic.equality.equals_transitivity |
25 | instantiation | 33, 123, 34, 35, 36, 37 | ⊢ |
| : , : , : , : |
26 | instantiation | 38, 39, 40, 41*, 42* | ⊢ |
| : , : , : |
27 | theorem | | ⊢ |
| proveit.numbers.number_sets.rational_numbers.rational_pos_within_rational |
28 | instantiation | 43, 44, 45 | ⊢ |
| : , : |
29 | theorem | | ⊢ |
| proveit.numbers.summation.summation_real_closure |
30 | instantiation | 46, 56, 47, 48 | , ⊢ |
| : , : |
31 | instantiation | 121, 74, 49 | ⊢ |
| : , : , : |
32 | instantiation | 121, 74, 50 | ⊢ |
| : , : , : |
33 | axiom | | ⊢ |
| proveit.core_expr_types.operations.operands_substitution |
34 | instantiation | 51 | ⊢ |
| : , : |
35 | instantiation | 51 | ⊢ |
| : , : |
36 | instantiation | 52, 58 | ⊢ |
| : |
37 | instantiation | 57, 53 | ⊢ |
| : |
38 | theorem | | ⊢ |
| proveit.numbers.division.frac_cancel_left |
39 | instantiation | 121, 54, 55 | ⊢ |
| : , : , : |
40 | instantiation | 121, 69, 56 | ⊢ |
| : , : , : |
41 | instantiation | 57, 58 | ⊢ |
| : |
42 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.mult_2_2 |
43 | theorem | | ⊢ |
| proveit.numbers.division.div_rational_pos_closure |
44 | instantiation | 121, 59, 107 | ⊢ |
| : , : , : |
45 | instantiation | 121, 59, 64 | ⊢ |
| : , : , : |
46 | theorem | | ⊢ |
| proveit.numbers.division.div_real_closure |
47 | instantiation | 60, 61, 123 | , ⊢ |
| : , : |
48 | instantiation | 62, 63, 67 | , ⊢ |
| : , : |
49 | instantiation | 121, 80, 64 | ⊢ |
| : , : , : |
50 | instantiation | 121, 80, 107 | ⊢ |
| : , : , : |
51 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.tuple_len_2_typical_eq |
52 | theorem | | ⊢ |
| proveit.numbers.multiplication.elim_one_left |
53 | instantiation | 121, 69, 65 | ⊢ |
| : , : , : |
54 | theorem | | ⊢ |
| proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero |
55 | instantiation | 121, 66, 67 | ⊢ |
| : , : , : |
56 | instantiation | 121, 76, 68 | ⊢ |
| : , : , : |
57 | theorem | | ⊢ |
| proveit.numbers.multiplication.elim_one_right |
58 | instantiation | 121, 69, 70 | ⊢ |
| : , : , : |
59 | theorem | | ⊢ |
| proveit.numbers.number_sets.rational_numbers.nat_pos_within_rational_pos |
60 | theorem | | ⊢ |
| proveit.numbers.exponentiation.exp_real_closure_nat_power |
61 | instantiation | 121, 76, 71 | , ⊢ |
| : , : , : |
62 | theorem | | ⊢ |
| proveit.numbers.exponentiation.exp_rational_non_zero__not_zero |
63 | instantiation | 121, 74, 72 | , ⊢ |
| : , : , : |
64 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.posnat4 |
65 | instantiation | 121, 76, 73 | ⊢ |
| : , : , : |
66 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero |
67 | instantiation | 121, 74, 75 | ⊢ |
| : , : , : |
68 | instantiation | 121, 82, 110 | ⊢ |
| : , : , : |
69 | theorem | | ⊢ |
| proveit.numbers.number_sets.complex_numbers.real_within_complex |
70 | instantiation | 121, 76, 77 | ⊢ |
| : , : , : |
71 | instantiation | 121, 82, 83 | , ⊢ |
| : , : , : |
72 | instantiation | 121, 80, 78 | , ⊢ |
| : , : , : |
73 | instantiation | 121, 82, 79 | ⊢ |
| : , : , : |
74 | theorem | | ⊢ |
| proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero |
75 | instantiation | 121, 80, 81 | ⊢ |
| : , : , : |
76 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.rational_within_real |
77 | instantiation | 121, 82, 120 | ⊢ |
| : , : , : |
78 | instantiation | 97, 83, 84 | , ⊢ |
| : |
79 | instantiation | 121, 122, 85 | ⊢ |
| : , : , : |
80 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int |
81 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.posnat2 |
82 | theorem | | ⊢ |
| proveit.numbers.number_sets.rational_numbers.int_within_rational |
83 | instantiation | 121, 86, 93 | , ⊢ |
| : , : , : |
84 | instantiation | 103, 87, 88 | , ⊢ |
| : , : , : |
85 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat4 |
86 | instantiation | 108, 91, 92 | ⊢ |
| : , : |
87 | instantiation | 89, 90 | ⊢ |
| : |
88 | instantiation | 109, 91, 92, 93 | , ⊢ |
| : , : , : |
89 | theorem | | ⊢ |
| proveit.numbers.number_sets.natural_numbers.natural_pos_is_pos |
90 | instantiation | 94, 95, 107 | ⊢ |
| : , : |
91 | instantiation | 114, 98, 110 | ⊢ |
| : , : |
92 | instantiation | 114, 115, 96 | ⊢ |
| : , : |
93 | assumption | | ⊢ |
94 | theorem | | ⊢ |
| proveit.numbers.addition.add_nat_pos_closure_bin |
95 | instantiation | 97, 98, 99 | ⊢ |
| : |
96 | instantiation | 121, 100, 101 | ⊢ |
| : , : , : |
97 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.pos_int_is_natural_pos |
98 | instantiation | 121, 102, 112 | ⊢ |
| : , : , : |
99 | instantiation | 103, 104, 105 | ⊢ |
| : , : , : |
100 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.neg_int_within_int |
101 | instantiation | 106, 107 | ⊢ |
| : |
102 | instantiation | 108, 110, 111 | ⊢ |
| : , : |
103 | theorem | | ⊢ |
| proveit.numbers.ordering.transitivity_less_less_eq |
104 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.less_0_1 |
105 | instantiation | 109, 110, 111, 112 | ⊢ |
| : , : , : |
106 | theorem | | ⊢ |
| proveit.numbers.negation.int_neg_closure |
107 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.posnat1 |
108 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.int_interval_within_int |
109 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.interval_lower_bound |
110 | instantiation | 121, 122, 113 | ⊢ |
| : , : , : |
111 | instantiation | 114, 115, 116 | ⊢ |
| : , : |
112 | assumption | | ⊢ |
113 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat1 |
114 | theorem | | ⊢ |
| proveit.numbers.addition.add_int_closure_bin |
115 | instantiation | 121, 117, 118 | ⊢ |
| : , : , : |
116 | instantiation | 119, 120 | ⊢ |
| : |
117 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.nat_pos_within_int |
118 | theorem | | ⊢ |
| proveit.physics.quantum.QPE._two_pow_t_minus_one_is_nat_pos |
119 | theorem | | ⊢ |
| proveit.numbers.negation.int_closure |
120 | instantiation | 121, 122, 123 | ⊢ |
| : , : , : |
121 | theorem | | ⊢ |
| proveit.logic.sets.inclusion.superset_membership_from_proper_subset |
122 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.nat_within_int |
123 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat2 |
*equality replacement requirements |