| step type | requirements | statement |
0 | instantiation | 1, 2, 3, 4, 5, 6*, 7* | ⊢ |
| : , : , : |
1 | theorem | | ⊢ |
| proveit.numbers.addition.strong_bound_via_left_term_bound |
2 | instantiation | 8, 66 | ⊢ |
| : |
3 | instantiation | 9, 11, 71, 12 | ⊢ |
| : , : , : |
4 | reference | 71 | ⊢ |
5 | instantiation | 10, 11, 71, 12 | ⊢ |
| : , : , : |
6 | instantiation | 30, 13, 14 | ⊢ |
| : , : , : |
7 | instantiation | 15, 84, 16, 86, 17*, 18*, 19* | ⊢ |
| : , : , : , : |
8 | theorem | | ⊢ |
| proveit.numbers.negation.real_closure |
9 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.all_in_interval_co__is__real |
10 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.interval_co_upper_bound |
11 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.zero_is_real |
12 | instantiation | 20, 62, 21* | ⊢ |
| : |
13 | instantiation | 33, 34, 22, 87, 35, 23, 37, 40, 38, 24 | ⊢ |
| : , : , : , : , : , : |
14 | instantiation | 25, 87, 34, 35, 37, 40, 38, 26 | ⊢ |
| : , : , : , : , : , : , : , : |
15 | theorem | | ⊢ |
| proveit.numbers.addition.rational_pair_addition |
16 | instantiation | 27, 84 | ⊢ |
| : |
17 | instantiation | 28, 59 | ⊢ |
| : |
18 | instantiation | 29, 59, 53, 73 | ⊢ |
| : , : |
19 | instantiation | 30, 31, 32 | ⊢ |
| : , : , : |
20 | theorem | | ⊢ |
| proveit.numbers.rounding.real_minus_floor_interval |
21 | instantiation | 33, 34, 90, 87, 35, 36, 37, 40, 38 | ⊢ |
| : , : , : , : , : , : |
22 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat3 |
23 | instantiation | 39 | ⊢ |
| : , : , : |
24 | instantiation | 49, 40 | ⊢ |
| : |
25 | theorem | | ⊢ |
| proveit.numbers.addition.subtraction.add_cancel_general |
26 | instantiation | 41 | ⊢ |
| : |
27 | theorem | | ⊢ |
| proveit.numbers.negation.int_closure |
28 | theorem | | ⊢ |
| proveit.numbers.division.frac_one_denom |
29 | theorem | | ⊢ |
| proveit.numbers.division.neg_frac_neg_numerator |
30 | axiom | | ⊢ |
| proveit.logic.equality.equals_transitivity |
31 | instantiation | 42, 90, 43, 44, 45, 46 | ⊢ |
| : , : , : , : |
32 | instantiation | 47, 59, 53, 48 | ⊢ |
| : , : , : |
33 | theorem | | ⊢ |
| proveit.numbers.addition.disassociation |
34 | axiom | | ⊢ |
| proveit.numbers.number_sets.natural_numbers.zero_in_nats |
35 | theorem | | ⊢ |
| proveit.core_expr_types.tuples.tuple_len_0_typical_eq |
36 | instantiation | 51 | ⊢ |
| : , : |
37 | instantiation | 88, 63, 65 | ⊢ |
| : , : , : |
38 | instantiation | 49, 50 | ⊢ |
| : |
39 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.tuple_len_3_typical_eq |
40 | instantiation | 88, 63, 66 | ⊢ |
| : , : , : |
41 | axiom | | ⊢ |
| proveit.logic.equality.equals_reflexivity |
42 | axiom | | ⊢ |
| proveit.core_expr_types.operations.operands_substitution |
43 | instantiation | 51 | ⊢ |
| : , : |
44 | instantiation | 51 | ⊢ |
| : , : |
45 | instantiation | 52, 53 | ⊢ |
| : |
46 | instantiation | 54, 59, 55* | ⊢ |
| : , : |
47 | theorem | | ⊢ |
| proveit.numbers.addition.subtraction.subtract_from_add |
48 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.add_1_1 |
49 | theorem | | ⊢ |
| proveit.numbers.negation.complex_closure |
50 | instantiation | 74, 56, 57 | ⊢ |
| : , : , : |
51 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.tuple_len_2_typical_eq |
52 | theorem | | ⊢ |
| proveit.numbers.multiplication.elim_one_left |
53 | instantiation | 88, 63, 72 | ⊢ |
| : , : , : |
54 | theorem | | ⊢ |
| proveit.numbers.multiplication.mult_neg_right |
55 | instantiation | 58, 59 | ⊢ |
| : |
56 | instantiation | 82, 60 | ⊢ |
| : , : |
57 | instantiation | 61, 62 | ⊢ |
| : |
58 | theorem | | ⊢ |
| proveit.numbers.multiplication.elim_one_right |
59 | instantiation | 88, 63, 71 | ⊢ |
| : , : , : |
60 | theorem | | ⊢ |
| proveit.numbers.number_sets.complex_numbers.int_within_complex |
61 | axiom | | ⊢ |
| proveit.numbers.rounding.floor_is_an_int |
62 | instantiation | 64, 65, 66 | ⊢ |
| : , : |
63 | theorem | | ⊢ |
| proveit.numbers.number_sets.complex_numbers.real_within_complex |
64 | theorem | | ⊢ |
| proveit.numbers.addition.add_real_closure_bin |
65 | instantiation | 67, 68, 69 | ⊢ |
| : , : |
66 | instantiation | 70, 71, 72, 73 | ⊢ |
| : , : |
67 | theorem | | ⊢ |
| proveit.numbers.multiplication.mult_real_closure_bin |
68 | instantiation | 74, 75, 76 | ⊢ |
| : , : , : |
69 | theorem | | ⊢ |
| proveit.physics.quantum.QPE._phase_is_real |
70 | theorem | | ⊢ |
| proveit.numbers.division.div_real_closure |
71 | instantiation | 88, 78, 77 | ⊢ |
| : , : , : |
72 | instantiation | 88, 78, 79 | ⊢ |
| : , : , : |
73 | instantiation | 80, 81 | ⊢ |
| : |
74 | theorem | | ⊢ |
| proveit.logic.sets.inclusion.unfold_subset_eq |
75 | instantiation | 82, 83 | ⊢ |
| : , : |
76 | theorem | | ⊢ |
| proveit.physics.quantum.QPE._two_pow_t_is_nat_pos |
77 | instantiation | 88, 85, 84 | ⊢ |
| : , : , : |
78 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.rational_within_real |
79 | instantiation | 88, 85, 86 | ⊢ |
| : , : , : |
80 | theorem | | ⊢ |
| proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos |
81 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.posnat2 |
82 | theorem | | ⊢ |
| proveit.logic.sets.inclusion.relax_proper_subset |
83 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.nat_pos_within_real |
84 | instantiation | 88, 89, 87 | ⊢ |
| : , : , : |
85 | theorem | | ⊢ |
| proveit.numbers.number_sets.rational_numbers.int_within_rational |
86 | instantiation | 88, 89, 90 | ⊢ |
| : , : , : |
87 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat1 |
88 | theorem | | ⊢ |
| proveit.logic.sets.inclusion.superset_membership_from_proper_subset |
89 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.nat_within_int |
90 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat2 |
*equality replacement requirements |