| step type | requirements | statement |
0 | instantiation | 1, 2, 3 | ⊢ |
| : , : , : |
1 | reference | 46 | ⊢ |
2 | instantiation | 4, 25, 19 | ⊢ |
| : , : |
3 | instantiation | 5, 19, 25, 6* | ⊢ |
| : , : |
4 | theorem | | ⊢ |
| proveit.numbers.ordering.max_bin_args_commute |
5 | axiom | | ⊢ |
| proveit.numbers.ordering.max_def_bin |
6 | instantiation | 46, 7, 8 | ⊢ |
| : , : , : |
7 | instantiation | 9, 141, 10, 11, 12, 13 | ⊢ |
| : , : , : , : |
8 | instantiation | 14, 54, 134, 56 | ⊢ |
| : , : , : , : , : |
9 | axiom | | ⊢ |
| proveit.core_expr_types.operations.operands_substitution |
10 | instantiation | 66 | ⊢ |
| : , : |
11 | instantiation | 66 | ⊢ |
| : , : |
12 | instantiation | 15, 20 | ⊢ |
| : , : |
13 | instantiation | 16, 17 | ⊢ |
| : , : |
14 | axiom | | ⊢ |
| proveit.core_expr_types.conditionals.true_case_reduction |
15 | theorem | | ⊢ |
| proveit.core_expr_types.conditionals.satisfied_condition_reduction |
16 | theorem | | ⊢ |
| proveit.core_expr_types.conditionals.dissatisfied_condition_reduction |
17 | instantiation | 18, 25, 19, 20 | ⊢ |
| : , : |
18 | theorem | | ⊢ |
| proveit.numbers.ordering.not_less_from_less_eq |
19 | instantiation | 139, 128, 21 | ⊢ |
| : , : , : |
20 | instantiation | 22, 23 | ⊢ |
| : , : |
21 | instantiation | 139, 135, 42 | ⊢ |
| : , : , : |
22 | theorem | | ⊢ |
| proveit.numbers.ordering.relax_less |
23 | instantiation | 24, 25, 26, 107, 27, 28*, 29* | ⊢ |
| : , : , : |
24 | theorem | | ⊢ |
| proveit.numbers.addition.strong_bound_via_left_term_bound |
25 | instantiation | 139, 128, 30 | ⊢ |
| : , : , : |
26 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.zero_is_real |
27 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.less_0_1 |
28 | instantiation | 62, 31, 32, 33 | ⊢ |
| : , : , : , : |
29 | instantiation | 62, 34, 35, 36 | ⊢ |
| : , : , : , : |
30 | instantiation | 139, 135, 37 | ⊢ |
| : , : , : |
31 | instantiation | 46, 38, 39 | ⊢ |
| : , : , : |
32 | instantiation | 70 | ⊢ |
| : |
33 | instantiation | 75, 45 | ⊢ |
| : , : |
34 | instantiation | 46, 40, 41 | ⊢ |
| : , : , : |
35 | instantiation | 70 | ⊢ |
| : |
36 | instantiation | 75, 52 | ⊢ |
| : , : |
37 | instantiation | 83, 42, 85 | ⊢ |
| : , : |
38 | instantiation | 77, 45 | ⊢ |
| : , : , : |
39 | instantiation | 46, 43, 44 | ⊢ |
| : , : , : |
40 | instantiation | 77, 45 | ⊢ |
| : , : , : |
41 | instantiation | 46, 47, 48 | ⊢ |
| : , : , : |
42 | instantiation | 139, 100, 49 | ⊢ |
| : , : , : |
43 | instantiation | 53, 134, 141, 54, 55, 56, 50, 58, 90 | ⊢ |
| : , : , : , : , : , : |
44 | instantiation | 51, 54, 141, 56, 55, 58, 90 | ⊢ |
| : , : , : , : |
45 | instantiation | 77, 52 | ⊢ |
| : , : , : |
46 | axiom | | ⊢ |
| proveit.logic.equality.equals_transitivity |
47 | instantiation | 53, 134, 141, 54, 55, 56, 95, 58, 90 | ⊢ |
| : , : , : , : , : , : |
48 | instantiation | 57, 95, 58, 59 | ⊢ |
| : , : , : |
49 | instantiation | 60, 141, 61 | ⊢ |
| : , : |
50 | theorem | | ⊢ |
| proveit.numbers.number_sets.complex_numbers.zero_is_complex |
51 | theorem | | ⊢ |
| proveit.numbers.addition.elim_zero_any |
52 | instantiation | 62, 63, 64, 65 | ⊢ |
| : , : , : , : |
53 | theorem | | ⊢ |
| proveit.numbers.addition.disassociation |
54 | axiom | | ⊢ |
| proveit.numbers.number_sets.natural_numbers.zero_in_nats |
55 | instantiation | 66 | ⊢ |
| : , : |
56 | theorem | | ⊢ |
| proveit.core_expr_types.tuples.tuple_len_0_typical_eq |
57 | theorem | | ⊢ |
| proveit.numbers.addition.subtraction.add_cancel_triple_13 |
58 | instantiation | 67, 68, 69 | ⊢ |
| : , : |
59 | instantiation | 70 | ⊢ |
| : |
60 | theorem | | ⊢ |
| proveit.numbers.exponentiation.exp_natpos_closure |
61 | instantiation | 71, 72, 73 | ⊢ |
| : |
62 | theorem | | ⊢ |
| proveit.logic.equality.four_chain_transitivity |
63 | instantiation | 77, 74 | ⊢ |
| : , : , : |
64 | instantiation | 75, 76 | ⊢ |
| : , : |
65 | instantiation | 77, 78 | ⊢ |
| : , : , : |
66 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.tuple_len_2_typical_eq |
67 | theorem | | ⊢ |
| proveit.numbers.multiplication.mult_complex_closure_bin |
68 | instantiation | 79, 95, 80, 81 | ⊢ |
| : , : |
69 | instantiation | 139, 119, 82 | ⊢ |
| : , : , : |
70 | axiom | | ⊢ |
| proveit.logic.equality.equals_reflexivity |
71 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.nonneg_int_is_natural |
72 | instantiation | 83, 84, 85 | ⊢ |
| : , : |
73 | instantiation | 86, 87 | ⊢ |
| : , : |
74 | instantiation | 88, 89, 90 | ⊢ |
| : , : |
75 | theorem | | ⊢ |
| proveit.logic.equality.equals_reversal |
76 | instantiation | 91, 110, 104, 103, 97 | ⊢ |
| : , : , : |
77 | axiom | | ⊢ |
| proveit.logic.equality.substitution |
78 | instantiation | 92, 93, 138 | ⊢ |
| : , : |
79 | theorem | | ⊢ |
| proveit.numbers.division.div_complex_closure |
80 | instantiation | 94, 110, 95 | ⊢ |
| : , : |
81 | instantiation | 96, 97, 98 | ⊢ |
| : , : , : |
82 | instantiation | 111, 112, 99 | ⊢ |
| : , : , : |
83 | theorem | | ⊢ |
| proveit.numbers.addition.add_int_closure_bin |
84 | instantiation | 139, 100, 113 | ⊢ |
| : , : , : |
85 | instantiation | 139, 101, 131 | ⊢ |
| : , : , : |
86 | theorem | | ⊢ |
| proveit.numbers.addition.subtraction.nonneg_difference |
87 | instantiation | 102, 113 | ⊢ |
| : |
88 | theorem | | ⊢ |
| proveit.numbers.addition.commutation |
89 | instantiation | 139, 119, 103 | ⊢ |
| : , : , : |
90 | instantiation | 139, 119, 104 | ⊢ |
| : , : , : |
91 | theorem | | ⊢ |
| proveit.numbers.exponentiation.product_of_real_powers |
92 | theorem | | ⊢ |
| proveit.numbers.exponentiation.neg_power_as_div |
93 | instantiation | 139, 105, 106 | ⊢ |
| : , : , : |
94 | theorem | | ⊢ |
| proveit.numbers.exponentiation.exp_complex_closure |
95 | instantiation | 139, 119, 107 | ⊢ |
| : , : , : |
96 | theorem | | ⊢ |
| proveit.logic.equality.sub_left_side_into |
97 | instantiation | 108, 133 | ⊢ |
| : |
98 | instantiation | 109, 110 | ⊢ |
| : |
99 | theorem | | ⊢ |
| proveit.physics.quantum.QPE._two_pow_t_is_nat_pos |
100 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.nat_pos_within_int |
101 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.neg_int_within_int |
102 | theorem | | ⊢ |
| proveit.numbers.number_sets.natural_numbers.natural_pos_lower_bound |
103 | instantiation | 111, 112, 113 | ⊢ |
| : , : , : |
104 | instantiation | 139, 114, 115 | ⊢ |
| : , : , : |
105 | theorem | | ⊢ |
| proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero |
106 | instantiation | 139, 116, 117 | ⊢ |
| : , : , : |
107 | instantiation | 139, 128, 118 | ⊢ |
| : , : , : |
108 | theorem | | ⊢ |
| proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos |
109 | theorem | | ⊢ |
| proveit.numbers.exponentiation.complex_x_to_first_power_is_x |
110 | instantiation | 139, 119, 120 | ⊢ |
| : , : , : |
111 | theorem | | ⊢ |
| proveit.logic.sets.inclusion.unfold_subset_eq |
112 | instantiation | 121, 122 | ⊢ |
| : , : |
113 | axiom | | ⊢ |
| proveit.physics.quantum.QPE._t_in_natural_pos |
114 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.real_neg_within_real |
115 | instantiation | 139, 123, 124 | ⊢ |
| : , : , : |
116 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero |
117 | instantiation | 139, 125, 126 | ⊢ |
| : , : , : |
118 | instantiation | 139, 135, 127 | ⊢ |
| : , : , : |
119 | theorem | | ⊢ |
| proveit.numbers.number_sets.complex_numbers.real_within_complex |
120 | instantiation | 139, 128, 129 | ⊢ |
| : , : , : |
121 | theorem | | ⊢ |
| proveit.logic.sets.inclusion.relax_proper_subset |
122 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.nat_pos_within_real |
123 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.rational_neg_within_real_neg |
124 | instantiation | 139, 130, 131 | ⊢ |
| : , : , : |
125 | theorem | | ⊢ |
| proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero |
126 | instantiation | 139, 132, 133 | ⊢ |
| : , : , : |
127 | instantiation | 139, 140, 134 | ⊢ |
| : , : , : |
128 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.rational_within_real |
129 | instantiation | 139, 135, 136 | ⊢ |
| : , : , : |
130 | theorem | | ⊢ |
| proveit.numbers.number_sets.rational_numbers.neg_int_within_rational_neg |
131 | instantiation | 137, 138 | ⊢ |
| : |
132 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int |
133 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.posnat2 |
134 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat1 |
135 | theorem | | ⊢ |
| proveit.numbers.number_sets.rational_numbers.int_within_rational |
136 | instantiation | 139, 140, 141 | ⊢ |
| : , : , : |
137 | theorem | | ⊢ |
| proveit.numbers.negation.int_neg_closure |
138 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.posnat1 |
139 | theorem | | ⊢ |
| proveit.logic.sets.inclusion.superset_membership_from_proper_subset |
140 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.nat_within_int |
141 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat2 |
*equality replacement requirements |