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