| step type | requirements | statement |
0 | instantiation | 1, 2 | ⊢ |
| : , : |
1 | theorem | | ⊢ |
| proveit.numbers.ordering.relax_less |
2 | instantiation | 3, 4, 5, 86, 6, 7*, 8* | ⊢ |
| : , : , : |
3 | theorem | | ⊢ |
| proveit.numbers.addition.strong_bound_via_left_term_bound |
4 | instantiation | 118, 107, 9 | ⊢ |
| : , : , : |
5 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.zero_is_real |
6 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.less_0_1 |
7 | instantiation | 41, 10, 11, 12 | ⊢ |
| : , : , : , : |
8 | instantiation | 41, 13, 14, 15 | ⊢ |
| : , : , : , : |
9 | instantiation | 118, 114, 16 | ⊢ |
| : , : , : |
10 | instantiation | 25, 17, 18 | ⊢ |
| : , : , : |
11 | instantiation | 49 | ⊢ |
| : |
12 | instantiation | 54, 24 | ⊢ |
| : , : |
13 | instantiation | 25, 19, 20 | ⊢ |
| : , : , : |
14 | instantiation | 49 | ⊢ |
| : |
15 | instantiation | 54, 31 | ⊢ |
| : , : |
16 | instantiation | 62, 21, 64 | ⊢ |
| : , : |
17 | instantiation | 56, 24 | ⊢ |
| : , : , : |
18 | instantiation | 25, 22, 23 | ⊢ |
| : , : , : |
19 | instantiation | 56, 24 | ⊢ |
| : , : , : |
20 | instantiation | 25, 26, 27 | ⊢ |
| : , : , : |
21 | instantiation | 118, 79, 28 | ⊢ |
| : , : , : |
22 | instantiation | 32, 113, 120, 33, 34, 35, 29, 37, 69 | ⊢ |
| : , : , : , : , : , : |
23 | instantiation | 30, 33, 120, 35, 34, 37, 69 | ⊢ |
| : , : , : , : |
24 | instantiation | 56, 31 | ⊢ |
| : , : , : |
25 | axiom | | ⊢ |
| proveit.logic.equality.equals_transitivity |
26 | instantiation | 32, 113, 120, 33, 34, 35, 74, 37, 69 | ⊢ |
| : , : , : , : , : , : |
27 | instantiation | 36, 74, 37, 38 | ⊢ |
| : , : , : |
28 | instantiation | 39, 120, 40 | ⊢ |
| : , : |
29 | theorem | | ⊢ |
| proveit.numbers.number_sets.complex_numbers.zero_is_complex |
30 | theorem | | ⊢ |
| proveit.numbers.addition.elim_zero_any |
31 | instantiation | 41, 42, 43, 44 | ⊢ |
| : , : , : , : |
32 | theorem | | ⊢ |
| proveit.numbers.addition.disassociation |
33 | axiom | | ⊢ |
| proveit.numbers.number_sets.natural_numbers.zero_in_nats |
34 | instantiation | 45 | ⊢ |
| : , : |
35 | theorem | | ⊢ |
| proveit.core_expr_types.tuples.tuple_len_0_typical_eq |
36 | theorem | | ⊢ |
| proveit.numbers.addition.subtraction.add_cancel_triple_13 |
37 | instantiation | 46, 47, 48 | ⊢ |
| : , : |
38 | instantiation | 49 | ⊢ |
| : |
39 | theorem | | ⊢ |
| proveit.numbers.exponentiation.exp_natpos_closure |
40 | instantiation | 50, 51, 52 | ⊢ |
| : |
41 | theorem | | ⊢ |
| proveit.logic.equality.four_chain_transitivity |
42 | instantiation | 56, 53 | ⊢ |
| : , : , : |
43 | instantiation | 54, 55 | ⊢ |
| : , : |
44 | instantiation | 56, 57 | ⊢ |
| : , : , : |
45 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.tuple_len_2_typical_eq |
46 | theorem | | ⊢ |
| proveit.numbers.multiplication.mult_complex_closure_bin |
47 | instantiation | 58, 74, 59, 60 | ⊢ |
| : , : |
48 | instantiation | 118, 98, 61 | ⊢ |
| : , : , : |
49 | axiom | | ⊢ |
| proveit.logic.equality.equals_reflexivity |
50 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.nonneg_int_is_natural |
51 | instantiation | 62, 63, 64 | ⊢ |
| : , : |
52 | instantiation | 65, 66 | ⊢ |
| : , : |
53 | instantiation | 67, 68, 69 | ⊢ |
| : , : |
54 | theorem | | ⊢ |
| proveit.logic.equality.equals_reversal |
55 | instantiation | 70, 89, 83, 82, 76 | ⊢ |
| : , : , : |
56 | axiom | | ⊢ |
| proveit.logic.equality.substitution |
57 | instantiation | 71, 72, 117 | ⊢ |
| : , : |
58 | theorem | | ⊢ |
| proveit.numbers.division.div_complex_closure |
59 | instantiation | 73, 89, 74 | ⊢ |
| : , : |
60 | instantiation | 75, 76, 77 | ⊢ |
| : , : , : |
61 | instantiation | 90, 91, 78 | ⊢ |
| : , : , : |
62 | theorem | | ⊢ |
| proveit.numbers.addition.add_int_closure_bin |
63 | instantiation | 118, 79, 92 | ⊢ |
| : , : , : |
64 | instantiation | 118, 80, 110 | ⊢ |
| : , : , : |
65 | theorem | | ⊢ |
| proveit.numbers.addition.subtraction.nonneg_difference |
66 | instantiation | 81, 92 | ⊢ |
| : |
67 | theorem | | ⊢ |
| proveit.numbers.addition.commutation |
68 | instantiation | 118, 98, 82 | ⊢ |
| : , : , : |
69 | instantiation | 118, 98, 83 | ⊢ |
| : , : , : |
70 | theorem | | ⊢ |
| proveit.numbers.exponentiation.product_of_real_powers |
71 | theorem | | ⊢ |
| proveit.numbers.exponentiation.neg_power_as_div |
72 | instantiation | 118, 84, 85 | ⊢ |
| : , : , : |
73 | theorem | | ⊢ |
| proveit.numbers.exponentiation.exp_complex_closure |
74 | instantiation | 118, 98, 86 | ⊢ |
| : , : , : |
75 | theorem | | ⊢ |
| proveit.logic.equality.sub_left_side_into |
76 | instantiation | 87, 112 | ⊢ |
| : |
77 | instantiation | 88, 89 | ⊢ |
| : |
78 | theorem | | ⊢ |
| proveit.physics.quantum.QPE._two_pow_t_is_nat_pos |
79 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.nat_pos_within_int |
80 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.neg_int_within_int |
81 | theorem | | ⊢ |
| proveit.numbers.number_sets.natural_numbers.natural_pos_lower_bound |
82 | instantiation | 90, 91, 92 | ⊢ |
| : , : , : |
83 | instantiation | 118, 93, 94 | ⊢ |
| : , : , : |
84 | theorem | | ⊢ |
| proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero |
85 | instantiation | 118, 95, 96 | ⊢ |
| : , : , : |
86 | instantiation | 118, 107, 97 | ⊢ |
| : , : , : |
87 | theorem | | ⊢ |
| proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos |
88 | theorem | | ⊢ |
| proveit.numbers.exponentiation.complex_x_to_first_power_is_x |
89 | instantiation | 118, 98, 99 | ⊢ |
| : , : , : |
90 | theorem | | ⊢ |
| proveit.logic.sets.inclusion.unfold_subset_eq |
91 | instantiation | 100, 101 | ⊢ |
| : , : |
92 | axiom | | ⊢ |
| proveit.physics.quantum.QPE._t_in_natural_pos |
93 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.real_neg_within_real |
94 | instantiation | 118, 102, 103 | ⊢ |
| : , : , : |
95 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero |
96 | instantiation | 118, 104, 105 | ⊢ |
| : , : , : |
97 | instantiation | 118, 114, 106 | ⊢ |
| : , : , : |
98 | theorem | | ⊢ |
| proveit.numbers.number_sets.complex_numbers.real_within_complex |
99 | instantiation | 118, 107, 108 | ⊢ |
| : , : , : |
100 | theorem | | ⊢ |
| proveit.logic.sets.inclusion.relax_proper_subset |
101 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.nat_pos_within_real |
102 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.rational_neg_within_real_neg |
103 | instantiation | 118, 109, 110 | ⊢ |
| : , : , : |
104 | theorem | | ⊢ |
| proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero |
105 | instantiation | 118, 111, 112 | ⊢ |
| : , : , : |
106 | instantiation | 118, 119, 113 | ⊢ |
| : , : , : |
107 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.rational_within_real |
108 | instantiation | 118, 114, 115 | ⊢ |
| : , : , : |
109 | theorem | | ⊢ |
| proveit.numbers.number_sets.rational_numbers.neg_int_within_rational_neg |
110 | instantiation | 116, 117 | ⊢ |
| : |
111 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int |
112 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.posnat2 |
113 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat1 |
114 | theorem | | ⊢ |
| proveit.numbers.number_sets.rational_numbers.int_within_rational |
115 | instantiation | 118, 119, 120 | ⊢ |
| : , : , : |
116 | theorem | | ⊢ |
| proveit.numbers.negation.int_neg_closure |
117 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.posnat1 |
118 | theorem | | ⊢ |
| proveit.logic.sets.inclusion.superset_membership_from_proper_subset |
119 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.nat_within_int |
120 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat2 |
*equality replacement requirements |