| step type | requirements | statement |
0 | instantiation | 1, 2 | ⊢ |
| : , : |
1 | reference | 48 | ⊢ |
2 | instantiation | 17, 3, 4 | ⊢ |
| : , : , : |
3 | instantiation | 17, 5, 6 | ⊢ |
| : , : , : |
4 | instantiation | 17, 7, 8 | ⊢ |
| : , : , : |
5 | instantiation | 50, 9 | ⊢ |
| : , : , : |
6 | instantiation | 50, 10 | ⊢ |
| : , : , : |
7 | instantiation | 17, 11, 12 | ⊢ |
| : , : , : |
8 | instantiation | 13, 29, 119, 111, 31, 14, 35, 79, 44, 15* | ⊢ |
| : , : , : , : , : , : |
9 | instantiation | 50, 26 | ⊢ |
| : , : , : |
10 | instantiation | 50, 16 | ⊢ |
| : , : , : |
11 | instantiation | 17, 18, 19 | ⊢ |
| : , : , : |
12 | instantiation | 20, 29, 111, 119, 31, 21, 53, 35, 79, 44, 22 | ⊢ |
| : , : , : , : , : , : , : , : |
13 | theorem | | ⊢ |
| proveit.numbers.addition.association |
14 | instantiation | 45 | ⊢ |
| : , : |
15 | instantiation | 23, 24, 25 | ⊢ |
| : , : , : |
16 | instantiation | 50, 26 | ⊢ |
| : , : , : |
17 | axiom | | ⊢ |
| proveit.logic.equality.equals_transitivity |
18 | instantiation | 28, 29, 119, 111, 31, 30, 53, 35, 27 | ⊢ |
| : , : , : , : , : , : |
19 | instantiation | 28, 119, 41, 29, 30, 42, 31, 53, 35, 43, 79, 44 | ⊢ |
| : , : , : , : , : , : |
20 | theorem | | ⊢ |
| proveit.numbers.addition.subtraction.add_cancel_general |
21 | instantiation | 45 | ⊢ |
| : , : |
22 | instantiation | 32 | ⊢ |
| : |
23 | theorem | | ⊢ |
| proveit.logic.equality.sub_right_side_into |
24 | instantiation | 33, 79, 90, 34 | ⊢ |
| : , : , : |
25 | instantiation | 56, 79, 35 | ⊢ |
| : , : |
26 | instantiation | 36, 37, 38, 39 | ⊢ |
| : , : , : , : |
27 | instantiation | 40, 41, 42, 43, 79, 44 | ⊢ |
| : , : |
28 | theorem | | ⊢ |
| proveit.numbers.addition.disassociation |
29 | axiom | | ⊢ |
| proveit.numbers.number_sets.natural_numbers.zero_in_nats |
30 | instantiation | 45 | ⊢ |
| : , : |
31 | theorem | | ⊢ |
| proveit.core_expr_types.tuples.tuple_len_0_typical_eq |
32 | axiom | | ⊢ |
| proveit.logic.equality.equals_reflexivity |
33 | theorem | | ⊢ |
| proveit.numbers.addition.subtraction.subtract_from_add_reversed |
34 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.add_1_1 |
35 | instantiation | 117, 99, 46 | ⊢ |
| : , : , : |
36 | theorem | | ⊢ |
| proveit.logic.equality.four_chain_transitivity |
37 | instantiation | 50, 47 | ⊢ |
| : , : , : |
38 | instantiation | 48, 49 | ⊢ |
| : , : |
39 | instantiation | 50, 51 | ⊢ |
| : , : , : |
40 | theorem | | ⊢ |
| proveit.numbers.addition.add_complex_closure |
41 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat3 |
42 | instantiation | 52 | ⊢ |
| : , : , : |
43 | instantiation | 67, 53 | ⊢ |
| : |
44 | instantiation | 67, 54 | ⊢ |
| : |
45 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.tuple_len_2_typical_eq |
46 | instantiation | 117, 106, 55 | ⊢ |
| : , : , : |
47 | instantiation | 56, 74, 57 | ⊢ |
| : , : |
48 | theorem | | ⊢ |
| proveit.logic.equality.equals_reversal |
49 | instantiation | 58, 90, 59, 83, 81 | ⊢ |
| : , : , : |
50 | axiom | | ⊢ |
| proveit.logic.equality.substitution |
51 | instantiation | 60, 61, 62 | ⊢ |
| : , : |
52 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.tuple_len_3_typical_eq |
53 | instantiation | 63, 64, 65 | ⊢ |
| : , : |
54 | instantiation | 117, 99, 66 | ⊢ |
| : , : , : |
55 | instantiation | 117, 112, 110 | ⊢ |
| : , : , : |
56 | theorem | | ⊢ |
| proveit.numbers.addition.commutation |
57 | instantiation | 67, 79 | ⊢ |
| : |
58 | theorem | | ⊢ |
| proveit.numbers.exponentiation.product_of_real_powers |
59 | instantiation | 68, 87 | ⊢ |
| : |
60 | theorem | | ⊢ |
| proveit.numbers.exponentiation.neg_power_as_div |
61 | instantiation | 117, 69, 70 | ⊢ |
| : , : , : |
62 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.posnat1 |
63 | theorem | | ⊢ |
| proveit.numbers.multiplication.mult_complex_closure_bin |
64 | instantiation | 71, 79, 72, 73 | ⊢ |
| : , : |
65 | instantiation | 78, 90, 74 | ⊢ |
| : , : |
66 | instantiation | 117, 106, 75 | ⊢ |
| : , : , : |
67 | theorem | | ⊢ |
| proveit.numbers.negation.complex_closure |
68 | theorem | | ⊢ |
| proveit.numbers.negation.real_closure |
69 | theorem | | ⊢ |
| proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero |
70 | instantiation | 117, 76, 77 | ⊢ |
| : , : , : |
71 | theorem | | ⊢ |
| proveit.numbers.division.div_complex_closure |
72 | instantiation | 78, 90, 79 | ⊢ |
| : , : |
73 | instantiation | 80, 81, 82 | ⊢ |
| : , : , : |
74 | instantiation | 117, 99, 83 | ⊢ |
| : , : , : |
75 | instantiation | 117, 112, 84 | ⊢ |
| : , : , : |
76 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero |
77 | instantiation | 117, 85, 86 | ⊢ |
| : , : , : |
78 | theorem | | ⊢ |
| proveit.numbers.exponentiation.exp_complex_closure |
79 | instantiation | 117, 99, 87 | ⊢ |
| : , : , : |
80 | theorem | | ⊢ |
| proveit.logic.equality.sub_left_side_into |
81 | instantiation | 88, 97 | ⊢ |
| : |
82 | instantiation | 89, 90 | ⊢ |
| : |
83 | instantiation | 91, 92, 93 | ⊢ |
| : , : , : |
84 | instantiation | 117, 94, 95 | ⊢ |
| : , : , : |
85 | theorem | | ⊢ |
| proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero |
86 | instantiation | 117, 96, 97 | ⊢ |
| : , : , : |
87 | instantiation | 117, 106, 98 | ⊢ |
| : , : , : |
88 | theorem | | ⊢ |
| proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos |
89 | theorem | | ⊢ |
| proveit.numbers.exponentiation.complex_x_to_first_power_is_x |
90 | instantiation | 117, 99, 100 | ⊢ |
| : , : , : |
91 | theorem | | ⊢ |
| proveit.logic.sets.inclusion.unfold_subset_eq |
92 | instantiation | 101, 102 | ⊢ |
| : , : |
93 | axiom | | ⊢ |
| proveit.physics.quantum.QPE._t_in_natural_pos |
94 | instantiation | 103, 105, 104 | ⊢ |
| : , : |
95 | assumption | | ⊢ |
96 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int |
97 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.posnat2 |
98 | instantiation | 117, 112, 105 | ⊢ |
| : , : , : |
99 | theorem | | ⊢ |
| proveit.numbers.number_sets.complex_numbers.real_within_complex |
100 | instantiation | 117, 106, 107 | ⊢ |
| : , : , : |
101 | theorem | | ⊢ |
| proveit.logic.sets.inclusion.relax_proper_subset |
102 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.nat_pos_within_real |
103 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.int_interval_within_int |
104 | instantiation | 108, 109, 110 | ⊢ |
| : , : |
105 | instantiation | 117, 118, 111 | ⊢ |
| : , : , : |
106 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.rational_within_real |
107 | instantiation | 117, 112, 116 | ⊢ |
| : , : , : |
108 | theorem | | ⊢ |
| proveit.numbers.addition.add_int_closure_bin |
109 | instantiation | 117, 113, 114 | ⊢ |
| : , : , : |
110 | instantiation | 115, 116 | ⊢ |
| : |
111 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat1 |
112 | theorem | | ⊢ |
| proveit.numbers.number_sets.rational_numbers.int_within_rational |
113 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.nat_pos_within_int |
114 | theorem | | ⊢ |
| proveit.physics.quantum.QPE._two_pow_t_minus_one_is_nat_pos |
115 | theorem | | ⊢ |
| proveit.numbers.negation.int_closure |
116 | instantiation | 117, 118, 119 | ⊢ |
| : , : , : |
117 | theorem | | ⊢ |
| proveit.logic.sets.inclusion.superset_membership_from_proper_subset |
118 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.nat_within_int |
119 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat2 |
*equality replacement requirements |