| step type | requirements | statement |
0 | instantiation | 1, 2, 3, 4*, 5*, 6* | ⊢ |
| : , : |
1 | theorem | | ⊢ |
| proveit.trigonometry.complex_unit_circle_chord_length |
2 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.zero_is_real |
3 | instantiation | 70, 81, 72 | ⊢ |
| : , : , : |
4 | instantiation | 26, 7, 8 | ⊢ |
| : , : , : |
5 | instantiation | 9, 10 | ⊢ |
| : , : |
6 | instantiation | 26, 11, 12 | ⊢ |
| : , : , : |
7 | instantiation | 37, 13 | ⊢ |
| : , : , : |
8 | instantiation | 14, 15 | ⊢ |
| : |
9 | theorem | | ⊢ |
| proveit.logic.equality.equals_reversal |
10 | instantiation | 37, 16 | ⊢ |
| : , : , : |
11 | instantiation | 37, 17 | ⊢ |
| : , : , : |
12 | instantiation | 26, 18, 19 | ⊢ |
| : , : , : |
13 | instantiation | 20, 33 | ⊢ |
| : |
14 | theorem | | ⊢ |
| proveit.numbers.exponentiation.exp_zero_eq_one |
15 | instantiation | 113, 103, 21 | ⊢ |
| : , : , : |
16 | instantiation | 26, 22, 23 | ⊢ |
| : , : , : |
17 | instantiation | 26, 24, 25 | ⊢ |
| : , : , : |
18 | instantiation | 26, 27, 28 | ⊢ |
| : , : , : |
19 | instantiation | 29, 42 | ⊢ |
| : |
20 | theorem | | ⊢ |
| proveit.numbers.multiplication.mult_zero_right |
21 | instantiation | 113, 107, 30 | ⊢ |
| : , : , : |
22 | instantiation | 31, 83, 115, 84, 85, 86, 87, 88, 33, 98 | ⊢ |
| : , : , : , : , : , : , : |
23 | instantiation | 51, 84, 32, 83, 48, 85, 33, 87, 88, 98 | ⊢ |
| : , : , : , : , : , : |
24 | instantiation | 37, 34 | ⊢ |
| : , : , : |
25 | instantiation | 35, 60, 36* | ⊢ |
| : |
26 | axiom | | ⊢ |
| proveit.logic.equality.equals_transitivity |
27 | instantiation | 37, 38 | ⊢ |
| : , : , : |
28 | instantiation | 39, 40, 41, 42, 43* | ⊢ |
| : , : , : |
29 | theorem | | ⊢ |
| proveit.numbers.division.frac_one_denom |
30 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.e_is_real_pos |
31 | theorem | | ⊢ |
| proveit.numbers.multiplication.leftward_commutation |
32 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat3 |
33 | theorem | | ⊢ |
| proveit.numbers.number_sets.complex_numbers.i_is_complex |
34 | instantiation | 44, 45 | ⊢ |
| : |
35 | theorem | | ⊢ |
| proveit.numbers.absolute_value.abs_even |
36 | instantiation | 46, 47, 48, 87, 88, 98, 49*, 50* | ⊢ |
| : , : |
37 | axiom | | ⊢ |
| proveit.logic.equality.substitution |
38 | instantiation | 51, 84, 115, 83, 52, 85, 87, 88, 53 | ⊢ |
| : , : , : , : , : , : |
39 | theorem | | ⊢ |
| proveit.numbers.division.frac_cancel_left |
40 | instantiation | 113, 55, 54 | ⊢ |
| : , : , : |
41 | instantiation | 113, 55, 56 | ⊢ |
| : , : , : |
42 | instantiation | 113, 103, 57 | ⊢ |
| : , : , : |
43 | instantiation | 58, 87 | ⊢ |
| : |
44 | theorem | | ⊢ |
| proveit.numbers.addition.elim_zero_left |
45 | instantiation | 59, 60 | ⊢ |
| : |
46 | theorem | | ⊢ |
| proveit.numbers.absolute_value.abs_prod |
47 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.posnat3 |
48 | instantiation | 61 | ⊢ |
| : , : , : |
49 | instantiation | 63, 62 | ⊢ |
| : |
50 | instantiation | 63, 64 | ⊢ |
| : |
51 | theorem | | ⊢ |
| proveit.numbers.multiplication.association |
52 | instantiation | 96 | ⊢ |
| : , : |
53 | instantiation | 113, 103, 65 | ⊢ |
| : , : , : |
54 | instantiation | 113, 67, 66 | ⊢ |
| : , : , : |
55 | theorem | | ⊢ |
| proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero |
56 | instantiation | 113, 67, 68 | ⊢ |
| : , : , : |
57 | instantiation | 113, 107, 69 | ⊢ |
| : , : , : |
58 | theorem | | ⊢ |
| proveit.numbers.multiplication.elim_one_right |
59 | theorem | | ⊢ |
| proveit.numbers.negation.complex_closure |
60 | instantiation | 70, 71, 72 | ⊢ |
| : , : , : |
61 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.tuple_len_3_typical_eq |
62 | instantiation | 73, 115 | ⊢ |
| : |
63 | theorem | | ⊢ |
| proveit.numbers.absolute_value.abs_non_neg_elim |
64 | instantiation | 74, 75 | ⊢ |
| : , : |
65 | instantiation | 113, 107, 80 | ⊢ |
| : , : , : |
66 | instantiation | 113, 77, 76 | ⊢ |
| : , : , : |
67 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero |
68 | instantiation | 113, 77, 78 | ⊢ |
| : , : , : |
69 | instantiation | 79, 108, 80 | ⊢ |
| : , : |
70 | theorem | | ⊢ |
| proveit.logic.equality.sub_right_side_into |
71 | instantiation | 113, 103, 81 | ⊢ |
| : , : , : |
72 | instantiation | 82, 83, 115, 84, 85, 86, 87, 88, 98 | ⊢ |
| : , : , : , : , : , : |
73 | theorem | | ⊢ |
| proveit.numbers.number_sets.natural_numbers.natural_lower_bound |
74 | theorem | | ⊢ |
| proveit.numbers.ordering.relax_less |
75 | instantiation | 89, 108 | ⊢ |
| : |
76 | instantiation | 113, 91, 90 | ⊢ |
| : , : , : |
77 | theorem | | ⊢ |
| proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero |
78 | instantiation | 113, 91, 92 | ⊢ |
| : , : , : |
79 | theorem | | ⊢ |
| proveit.numbers.multiplication.mult_real_pos_closure_bin |
80 | instantiation | 93, 94 | ⊢ |
| : |
81 | instantiation | 100, 95, 104 | ⊢ |
| : , : |
82 | theorem | | ⊢ |
| proveit.numbers.multiplication.disassociation |
83 | axiom | | ⊢ |
| proveit.numbers.number_sets.natural_numbers.zero_in_nats |
84 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat1 |
85 | theorem | | ⊢ |
| proveit.core_expr_types.tuples.tuple_len_0_typical_eq |
86 | instantiation | 96 | ⊢ |
| : , : |
87 | instantiation | 113, 103, 101 | ⊢ |
| : , : , : |
88 | instantiation | 113, 103, 102 | ⊢ |
| : , : , : |
89 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.positive_if_in_real_pos |
90 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.posnat2 |
91 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int |
92 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.posnat1 |
93 | theorem | | ⊢ |
| proveit.numbers.absolute_value.abs_nonzero_closure |
94 | instantiation | 97, 98, 99 | ⊢ |
| : |
95 | instantiation | 100, 101, 102 | ⊢ |
| : , : |
96 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.tuple_len_2_typical_eq |
97 | theorem | | ⊢ |
| proveit.numbers.number_sets.complex_numbers.nonzero_complex_is_complex_nonzero |
98 | instantiation | 113, 103, 104 | ⊢ |
| : , : , : |
99 | assumption | | ⊢ |
100 | theorem | | ⊢ |
| proveit.numbers.multiplication.mult_real_closure_bin |
101 | instantiation | 113, 105, 106 | ⊢ |
| : , : , : |
102 | instantiation | 113, 107, 108 | ⊢ |
| : , : , : |
103 | theorem | | ⊢ |
| proveit.numbers.number_sets.complex_numbers.real_within_complex |
104 | instantiation | 109, 110 | ⊢ |
| : |
105 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.rational_within_real |
106 | instantiation | 113, 111, 112 | ⊢ |
| : , : , : |
107 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.real_pos_within_real |
108 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.pi_is_real_pos |
109 | theorem | | ⊢ |
| proveit.physics.quantum.QPE._delta_b_is_real |
110 | theorem | | ⊢ |
| proveit.physics.quantum.QPE._best_round_is_int |
111 | theorem | | ⊢ |
| proveit.numbers.number_sets.rational_numbers.int_within_rational |
112 | instantiation | 113, 114, 115 | ⊢ |
| : , : , : |
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 |
*equality replacement requirements |