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