| step type | requirements | statement |
0 | instantiation | 1, 2, 3 | ⊢ |
| : , : , : |
1 | reference | 101 | ⊢ |
2 | instantiation | 109, 4 | ⊢ |
| : , : , : |
3 | instantiation | 101, 5, 6 | ⊢ |
| : , : , : |
4 | instantiation | 7, 117, 74, 63, 60, 43, 8* | ⊢ |
| : , : , : |
5 | instantiation | 101, 9, 10 | ⊢ |
| : , : , : |
6 | instantiation | 101, 11, 12 | ⊢ |
| : , : , : |
7 | theorem | | ⊢ |
| proveit.numbers.exponentiation.real_power_of_product |
8 | instantiation | 13, 79, 113, 14* | ⊢ |
| : , : |
9 | instantiation | 101, 15, 16 | ⊢ |
| : , : , : |
10 | instantiation | 101, 17, 18 | ⊢ |
| : , : , : |
11 | instantiation | 19, 33, 34, 35, 37, 74, 39, 40 | ⊢ |
| : , : , : , : |
12 | instantiation | 101, 20, 21 | ⊢ |
| : , : , : |
13 | theorem | | ⊢ |
| proveit.numbers.exponentiation.neg_power_as_div |
14 | instantiation | 56, 117 | ⊢ |
| : |
15 | instantiation | 23, 33, 34, 121, 35, 25, 117, 74, 39, 22 | ⊢ |
| : , : , : , : , : , : |
16 | instantiation | 23, 34, 128, 33, 25, 24, 35, 117, 74, 39, 38, 40 | ⊢ |
| : , : , : , : , : , : |
17 | instantiation | 28, 33, 34, 121, 35, 25, 117, 74, 39, 38, 40 | ⊢ |
| : , : , : , : , : , : , : |
18 | instantiation | 101, 26, 27 | ⊢ |
| : , : , : |
19 | theorem | | ⊢ |
| proveit.numbers.multiplication.elim_one_any |
20 | instantiation | 28, 121, 33, 35, 74, 39, 40 | ⊢ |
| : , : , : , : , : , : , : |
21 | instantiation | 32, 33, 128, 121, 35, 29, 74, 40, 39, 30* | ⊢ |
| : , : , : , : , : , : |
22 | instantiation | 31, 38, 40 | ⊢ |
| : , : |
23 | theorem | | ⊢ |
| proveit.numbers.multiplication.disassociation |
24 | instantiation | 46 | ⊢ |
| : , : |
25 | instantiation | 47 | ⊢ |
| : , : , : |
26 | instantiation | 32, 33, 128, 34, 35, 36, 37, 38, 117, 74, 39, 40 | ⊢ |
| : , : , : , : , : , : |
27 | instantiation | 109, 41 | ⊢ |
| : , : , : |
28 | theorem | | ⊢ |
| proveit.numbers.multiplication.leftward_commutation |
29 | instantiation | 46 | ⊢ |
| : , : |
30 | instantiation | 42, 74, 104, 63, 43, 44*, 45* | ⊢ |
| : , : , : |
31 | theorem | | ⊢ |
| proveit.numbers.multiplication.mult_complex_closure_bin |
32 | theorem | | ⊢ |
| proveit.numbers.multiplication.association |
33 | axiom | | ⊢ |
| proveit.numbers.number_sets.natural_numbers.zero_in_nats |
34 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat3 |
35 | theorem | | ⊢ |
| proveit.core_expr_types.tuples.tuple_len_0_typical_eq |
36 | instantiation | 46 | ⊢ |
| : , : |
37 | instantiation | 47 | ⊢ |
| : , : , : |
38 | instantiation | 126, 119, 48 | ⊢ |
| : , : , : |
39 | instantiation | 126, 119, 49 | ⊢ |
| : , : , : |
40 | instantiation | 50, 74, 51 | ⊢ |
| : , : |
41 | instantiation | 64, 52, 53 | ⊢ |
| : , : , : |
42 | theorem | | ⊢ |
| proveit.numbers.exponentiation.product_of_real_powers |
43 | instantiation | 54, 55 | ⊢ |
| : |
44 | instantiation | 56, 74 | ⊢ |
| : |
45 | instantiation | 101, 57, 58 | ⊢ |
| : , : , : |
46 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.tuple_len_2_typical_eq |
47 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.tuple_len_3_typical_eq |
48 | instantiation | 59, 104, 120, 60 | ⊢ |
| : , : |
49 | instantiation | 61, 62 | ⊢ |
| : |
50 | theorem | | ⊢ |
| proveit.numbers.exponentiation.exp_complex_closure |
51 | instantiation | 126, 119, 63 | ⊢ |
| : , : , : |
52 | instantiation | 64, 65, 66 | ⊢ |
| : , : , : |
53 | instantiation | 67, 68, 69, 70 | ⊢ |
| : , : , : , : |
54 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.nonzero_if_in_real_nonzero |
55 | instantiation | 126, 71, 95 | ⊢ |
| : , : , : |
56 | theorem | | ⊢ |
| proveit.numbers.exponentiation.complex_x_to_first_power_is_x |
57 | instantiation | 109, 72 | ⊢ |
| : , : , : |
58 | instantiation | 73, 74 | ⊢ |
| : |
59 | theorem | | ⊢ |
| proveit.numbers.division.div_real_closure |
60 | instantiation | 75, 115 | ⊢ |
| : |
61 | theorem | | ⊢ |
| proveit.physics.quantum.QPE._delta_b_is_real |
62 | theorem | | ⊢ |
| proveit.physics.quantum.QPE._best_round_is_int |
63 | instantiation | 126, 122, 76 | ⊢ |
| : , : , : |
64 | theorem | | ⊢ |
| proveit.logic.equality.sub_right_side_into |
65 | instantiation | 77, 92, 78, 79 | ⊢ |
| : , : , : , : , : |
66 | instantiation | 101, 80, 81 | ⊢ |
| : , : , : |
67 | theorem | | ⊢ |
| proveit.logic.equality.four_chain_transitivity |
68 | instantiation | 109, 82 | ⊢ |
| : , : , : |
69 | instantiation | 109, 82 | ⊢ |
| : , : , : |
70 | instantiation | 116, 92 | ⊢ |
| : |
71 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.real_pos_within_real_nonzero |
72 | instantiation | 83, 92, 84 | ⊢ |
| : , : |
73 | theorem | | ⊢ |
| proveit.numbers.exponentiation.exp_zero_eq_one |
74 | instantiation | 126, 119, 85 | ⊢ |
| : , : , : |
75 | theorem | | ⊢ |
| proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos |
76 | instantiation | 126, 124, 86 | ⊢ |
| : , : , : |
77 | theorem | | ⊢ |
| proveit.numbers.division.mult_frac_cancel_denom_left |
78 | instantiation | 126, 88, 87 | ⊢ |
| : , : , : |
79 | instantiation | 126, 88, 89 | ⊢ |
| : , : , : |
80 | instantiation | 109, 90 | ⊢ |
| : , : , : |
81 | instantiation | 109, 91 | ⊢ |
| : , : , : |
82 | instantiation | 111, 92 | ⊢ |
| : |
83 | theorem | | ⊢ |
| proveit.numbers.addition.subtraction.add_cancel_basic |
84 | instantiation | 93 | ⊢ |
| : |
85 | instantiation | 126, 94, 95 | ⊢ |
| : , : , : |
86 | instantiation | 96, 118 | ⊢ |
| : |
87 | instantiation | 126, 98, 97 | ⊢ |
| : , : , : |
88 | theorem | | ⊢ |
| proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero |
89 | instantiation | 126, 98, 99 | ⊢ |
| : , : , : |
90 | instantiation | 109, 100 | ⊢ |
| : , : , : |
91 | instantiation | 101, 102, 103 | ⊢ |
| : , : , : |
92 | instantiation | 126, 119, 104 | ⊢ |
| : , : , : |
93 | axiom | | ⊢ |
| proveit.logic.equality.equals_reflexivity |
94 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.real_pos_within_real |
95 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.pi_is_real_pos |
96 | theorem | | ⊢ |
| proveit.numbers.negation.int_closure |
97 | instantiation | 126, 106, 105 | ⊢ |
| : , : , : |
98 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero |
99 | instantiation | 126, 106, 107 | ⊢ |
| : , : , : |
100 | instantiation | 108, 117 | ⊢ |
| : |
101 | axiom | | ⊢ |
| proveit.logic.equality.equals_transitivity |
102 | instantiation | 109, 110 | ⊢ |
| : , : , : |
103 | instantiation | 111, 117 | ⊢ |
| : |
104 | instantiation | 126, 122, 112 | ⊢ |
| : , : , : |
105 | instantiation | 126, 114, 113 | ⊢ |
| : , : , : |
106 | theorem | | ⊢ |
| proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero |
107 | instantiation | 126, 114, 115 | ⊢ |
| : , : , : |
108 | theorem | | ⊢ |
| proveit.numbers.multiplication.elim_one_left |
109 | axiom | | ⊢ |
| proveit.logic.equality.substitution |
110 | instantiation | 116, 117 | ⊢ |
| : |
111 | theorem | | ⊢ |
| proveit.numbers.division.frac_one_denom |
112 | instantiation | 126, 124, 118 | ⊢ |
| : , : , : |
113 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.posnat1 |
114 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int |
115 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.posnat2 |
116 | theorem | | ⊢ |
| proveit.numbers.multiplication.elim_one_right |
117 | instantiation | 126, 119, 120 | ⊢ |
| : , : , : |
118 | instantiation | 126, 127, 121 | ⊢ |
| : , : , : |
119 | theorem | | ⊢ |
| proveit.numbers.number_sets.complex_numbers.real_within_complex |
120 | instantiation | 126, 122, 123 | ⊢ |
| : , : , : |
121 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat1 |
122 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.rational_within_real |
123 | instantiation | 126, 124, 125 | ⊢ |
| : , : , : |
124 | theorem | | ⊢ |
| proveit.numbers.number_sets.rational_numbers.int_within_rational |
125 | instantiation | 126, 127, 128 | ⊢ |
| : , : , : |
126 | theorem | | ⊢ |
| proveit.logic.sets.inclusion.superset_membership_from_proper_subset |
127 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.nat_within_int |
128 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat2 |
*equality replacement requirements |