| step type | requirements | statement |
0 | instantiation | 1, 2 | ⊢ |
| : , : |
1 | reference | 53 | ⊢ |
2 | instantiation | 41, 3, 4, 5 | ⊢ |
| : , : , : , : |
3 | instantiation | 6, 59, 84 | ⊢ |
| : , : |
4 | instantiation | 61, 49, 62 | ⊢ |
| : , : |
5 | instantiation | 53, 7 | ⊢ |
| : , : |
6 | theorem | | ⊢ |
| proveit.numbers.negation.distribute_neg_through_binary_sum |
7 | instantiation | 22, 8, 9 | ⊢ |
| : , : , : |
8 | instantiation | 22, 10, 11 | ⊢ |
| : , : , : |
9 | instantiation | 22, 12, 13 | ⊢ |
| : , : , : |
10 | instantiation | 55, 14 | ⊢ |
| : , : , : |
11 | instantiation | 55, 15 | ⊢ |
| : , : , : |
12 | instantiation | 22, 16, 17 | ⊢ |
| : , : , : |
13 | instantiation | 18, 34, 124, 116, 36, 19, 40, 84, 49, 20* | ⊢ |
| : , : , : , : , : , : |
14 | instantiation | 55, 31 | ⊢ |
| : , : , : |
15 | instantiation | 55, 21 | ⊢ |
| : , : , : |
16 | instantiation | 22, 23, 24 | ⊢ |
| : , : , : |
17 | instantiation | 25, 34, 116, 124, 36, 26, 58, 40, 84, 49, 27 | ⊢ |
| : , : , : , : , : , : , : , : |
18 | theorem | | ⊢ |
| proveit.numbers.addition.association |
19 | instantiation | 50 | ⊢ |
| : , : |
20 | instantiation | 28, 29, 30 | ⊢ |
| : , : , : |
21 | instantiation | 55, 31 | ⊢ |
| : , : , : |
22 | axiom | | ⊢ |
| proveit.logic.equality.equals_transitivity |
23 | instantiation | 33, 34, 124, 116, 36, 35, 58, 40, 32 | ⊢ |
| : , : , : , : , : , : |
24 | instantiation | 33, 124, 46, 34, 35, 47, 36, 58, 40, 48, 84, 49 | ⊢ |
| : , : , : , : , : , : |
25 | theorem | | ⊢ |
| proveit.numbers.addition.subtraction.add_cancel_general |
26 | instantiation | 50 | ⊢ |
| : , : |
27 | instantiation | 37 | ⊢ |
| : |
28 | theorem | | ⊢ |
| proveit.logic.equality.sub_right_side_into |
29 | instantiation | 38, 84, 95, 39 | ⊢ |
| : , : , : |
30 | instantiation | 61, 84, 40 | ⊢ |
| : , : |
31 | instantiation | 41, 42, 43, 44 | ⊢ |
| : , : , : , : |
32 | instantiation | 45, 46, 47, 48, 84, 49 | ⊢ |
| : , : |
33 | theorem | | ⊢ |
| proveit.numbers.addition.disassociation |
34 | axiom | | ⊢ |
| proveit.numbers.number_sets.natural_numbers.zero_in_nats |
35 | instantiation | 50 | ⊢ |
| : , : |
36 | theorem | | ⊢ |
| proveit.core_expr_types.tuples.tuple_len_0_typical_eq |
37 | axiom | | ⊢ |
| proveit.logic.equality.equals_reflexivity |
38 | theorem | | ⊢ |
| proveit.numbers.addition.subtraction.subtract_from_add_reversed |
39 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.add_1_1 |
40 | instantiation | 122, 104, 51 | ⊢ |
| : , : , : |
41 | theorem | | ⊢ |
| proveit.logic.equality.four_chain_transitivity |
42 | instantiation | 55, 52 | ⊢ |
| : , : , : |
43 | instantiation | 53, 54 | ⊢ |
| : , : |
44 | instantiation | 55, 56 | ⊢ |
| : , : , : |
45 | theorem | | ⊢ |
| proveit.numbers.addition.add_complex_closure |
46 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat3 |
47 | instantiation | 57 | ⊢ |
| : , : , : |
48 | instantiation | 72, 58 | ⊢ |
| : |
49 | instantiation | 72, 59 | ⊢ |
| : |
50 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.tuple_len_2_typical_eq |
51 | instantiation | 122, 111, 60 | ⊢ |
| : , : , : |
52 | instantiation | 61, 79, 62 | ⊢ |
| : , : |
53 | theorem | | ⊢ |
| proveit.logic.equality.equals_reversal |
54 | instantiation | 63, 95, 64, 88, 86 | ⊢ |
| : , : , : |
55 | axiom | | ⊢ |
| proveit.logic.equality.substitution |
56 | instantiation | 65, 66, 67 | ⊢ |
| : , : |
57 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.tuple_len_3_typical_eq |
58 | instantiation | 68, 69, 70 | ⊢ |
| : , : |
59 | instantiation | 122, 104, 71 | ⊢ |
| : , : , : |
60 | instantiation | 122, 117, 115 | ⊢ |
| : , : , : |
61 | theorem | | ⊢ |
| proveit.numbers.addition.commutation |
62 | instantiation | 72, 84 | ⊢ |
| : |
63 | theorem | | ⊢ |
| proveit.numbers.exponentiation.product_of_real_powers |
64 | instantiation | 73, 92 | ⊢ |
| : |
65 | theorem | | ⊢ |
| proveit.numbers.exponentiation.neg_power_as_div |
66 | instantiation | 122, 74, 75 | ⊢ |
| : , : , : |
67 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.posnat1 |
68 | theorem | | ⊢ |
| proveit.numbers.multiplication.mult_complex_closure_bin |
69 | instantiation | 76, 84, 77, 78 | ⊢ |
| : , : |
70 | instantiation | 83, 95, 79 | ⊢ |
| : , : |
71 | instantiation | 122, 111, 80 | ⊢ |
| : , : , : |
72 | theorem | | ⊢ |
| proveit.numbers.negation.complex_closure |
73 | theorem | | ⊢ |
| proveit.numbers.negation.real_closure |
74 | theorem | | ⊢ |
| proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero |
75 | instantiation | 122, 81, 82 | ⊢ |
| : , : , : |
76 | theorem | | ⊢ |
| proveit.numbers.division.div_complex_closure |
77 | instantiation | 83, 95, 84 | ⊢ |
| : , : |
78 | instantiation | 85, 86, 87 | ⊢ |
| : , : , : |
79 | instantiation | 122, 104, 88 | ⊢ |
| : , : , : |
80 | instantiation | 122, 117, 89 | ⊢ |
| : , : , : |
81 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero |
82 | instantiation | 122, 90, 91 | ⊢ |
| : , : , : |
83 | theorem | | ⊢ |
| proveit.numbers.exponentiation.exp_complex_closure |
84 | instantiation | 122, 104, 92 | ⊢ |
| : , : , : |
85 | theorem | | ⊢ |
| proveit.logic.equality.sub_left_side_into |
86 | instantiation | 93, 102 | ⊢ |
| : |
87 | instantiation | 94, 95 | ⊢ |
| : |
88 | instantiation | 96, 97, 98 | ⊢ |
| : , : , : |
89 | instantiation | 122, 99, 100 | ⊢ |
| : , : , : |
90 | theorem | | ⊢ |
| proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero |
91 | instantiation | 122, 101, 102 | ⊢ |
| : , : , : |
92 | instantiation | 122, 111, 103 | ⊢ |
| : , : , : |
93 | theorem | | ⊢ |
| proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos |
94 | theorem | | ⊢ |
| proveit.numbers.exponentiation.complex_x_to_first_power_is_x |
95 | instantiation | 122, 104, 105 | ⊢ |
| : , : , : |
96 | theorem | | ⊢ |
| proveit.logic.sets.inclusion.unfold_subset_eq |
97 | instantiation | 106, 107 | ⊢ |
| : , : |
98 | axiom | | ⊢ |
| proveit.physics.quantum.QPE._t_in_natural_pos |
99 | instantiation | 108, 110, 109 | ⊢ |
| : , : |
100 | assumption | | ⊢ |
101 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int |
102 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.posnat2 |
103 | instantiation | 122, 117, 110 | ⊢ |
| : , : , : |
104 | theorem | | ⊢ |
| proveit.numbers.number_sets.complex_numbers.real_within_complex |
105 | instantiation | 122, 111, 112 | ⊢ |
| : , : , : |
106 | theorem | | ⊢ |
| proveit.logic.sets.inclusion.relax_proper_subset |
107 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.nat_pos_within_real |
108 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.int_interval_within_int |
109 | instantiation | 113, 114, 115 | ⊢ |
| : , : |
110 | instantiation | 122, 123, 116 | ⊢ |
| : , : , : |
111 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.rational_within_real |
112 | instantiation | 122, 117, 121 | ⊢ |
| : , : , : |
113 | theorem | | ⊢ |
| proveit.numbers.addition.add_int_closure_bin |
114 | instantiation | 122, 118, 119 | ⊢ |
| : , : , : |
115 | instantiation | 120, 121 | ⊢ |
| : |
116 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat1 |
117 | theorem | | ⊢ |
| proveit.numbers.number_sets.rational_numbers.int_within_rational |
118 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.nat_pos_within_int |
119 | theorem | | ⊢ |
| proveit.physics.quantum.QPE._two_pow_t_minus_one_is_nat_pos |
120 | theorem | | ⊢ |
| proveit.numbers.negation.int_closure |
121 | instantiation | 122, 123, 124 | ⊢ |
| : , : , : |
122 | theorem | | ⊢ |
| proveit.logic.sets.inclusion.superset_membership_from_proper_subset |
123 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.nat_within_int |
124 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat2 |
*equality replacement requirements |