| step type | requirements | statement |
0 | instantiation | 1, 2, 3*, 4* | ⊢ |
| : , : , : |
1 | axiom | | ⊢ |
| proveit.logic.equality.substitution |
2 | modus ponens | 5, 6 | ⊢ |
3 | instantiation | 7, 141 | ⊢ |
| : , : |
4 | instantiation | 7, 141 | ⊢ |
| : , : |
5 | instantiation | 8, 9 | ⊢ |
| : , : , : , : , : , : , : |
6 | generalization | 10 | ⊢ |
7 | theorem | | ⊢ |
| proveit.core_expr_types.conditionals.satisfied_condition_reduction |
8 | theorem | | ⊢ |
| proveit.core_expr_types.lambda_maps.general_lambda_substitution |
9 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.posnat5 |
10 | instantiation | 11, 12 | ⊢ |
| : , : , : |
11 | axiom | | ⊢ |
| proveit.core_expr_types.conditionals.condition_replacement |
12 | instantiation | 13, 14, 15 | ⊢ |
| : , : |
13 | theorem | | ⊢ |
| proveit.logic.booleans.implication.iff_intro |
14 | deduction | 16 | ⊢ |
15 | deduction | 17 | ⊢ |
16 | instantiation | 22, 27, 18, 19, 20, 21 | ⊢ |
| : , : |
17 | instantiation | 22, 23, 24, 99, 93, 25, 26 | , ⊢ |
| : , : |
18 | instantiation | 35 | ⊢ |
| : , : , : |
19 | instantiation | 111, 112, 27, 113, 28, 30 | ⊢ |
| : , : , : , : , : |
20 | instantiation | 111, 132, 138, 29, 30 | ⊢ |
| : , : , : , : , : |
21 | instantiation | 111, 138, 132, 32, 30 | ⊢ |
| : , : , : , : , : |
22 | theorem | | ⊢ |
| proveit.logic.booleans.conjunction.and_if_all |
23 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat4 |
24 | instantiation | 31 | ⊢ |
| : , : , : , : |
25 | instantiation | 111, 138, 112, 32, 113, 115 | ⊢ |
| : , : , : , : , : |
26 | instantiation | 33, 63, 80, 99, 34 | , ⊢ |
| : , : , : |
27 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat3 |
28 | instantiation | 35 | ⊢ |
| : , : , : |
29 | instantiation | 124 | ⊢ |
| : , : |
30 | assumption | | ⊢ |
31 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.tuple_len_4_typical_eq |
32 | instantiation | 124 | ⊢ |
| : , : |
33 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.in_IntervalCO |
34 | instantiation | 36, 37, 38 | , ⊢ |
| : , : |
35 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.tuple_len_3_typical_eq |
36 | theorem | | ⊢ |
| proveit.logic.booleans.conjunction.and_if_both |
37 | instantiation | 53, 110, 63, 54, 39, 57, 40*, 58* | , ⊢ |
| : , : , : |
38 | instantiation | 41, 42, 43 | , ⊢ |
| : , : , : |
39 | instantiation | 44, 104, 105, 93 | , ⊢ |
| : , : , : |
40 | instantiation | 45, 98, 77 | ⊢ |
| : |
41 | theorem | | ⊢ |
| proveit.numbers.ordering.transitivity_less_eq_less |
42 | instantiation | 46, 47, 48 | , ⊢ |
| : , : , : |
43 | instantiation | 49, 80, 50, 63, 51, 52* | ⊢ |
| : , : , : |
44 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.interval_lower_bound |
45 | theorem | | ⊢ |
| proveit.numbers.division.frac_zero_numer |
46 | theorem | | ⊢ |
| proveit.logic.equality.sub_right_side_into |
47 | instantiation | 53, 110, 54, 55, 56, 57, 58* | , ⊢ |
| : , : , : |
48 | instantiation | 59, 98, 68, 77, 60* | ⊢ |
| : , : , : |
49 | theorem | | ⊢ |
| proveit.numbers.addition.strong_bound_via_right_term_bound |
50 | instantiation | 61, 64 | ⊢ |
| : |
51 | instantiation | 62, 63, 64, 65, 66* | ⊢ |
| : , : |
52 | instantiation | 67, 68 | ⊢ |
| : |
53 | theorem | | ⊢ |
| proveit.numbers.division.weak_div_from_numer_bound__pos_denom |
54 | instantiation | 139, 122, 69 | , ⊢ |
| : , : , : |
55 | instantiation | 139, 122, 70 | ⊢ |
| : , : , : |
56 | instantiation | 71, 104, 105, 93 | , ⊢ |
| : , : , : |
57 | instantiation | 72, 127 | ⊢ |
| : |
58 | instantiation | 73, 74, 75 | , ⊢ |
| : , : , : |
59 | theorem | | ⊢ |
| proveit.numbers.division.distribute_frac_through_subtract |
60 | instantiation | 76, 98, 77 | ⊢ |
| : |
61 | theorem | | ⊢ |
| proveit.numbers.negation.real_closure |
62 | theorem | | ⊢ |
| proveit.numbers.negation.negated_strong_bound |
63 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.zero_is_real |
64 | instantiation | 139, 122, 78 | ⊢ |
| : , : , : |
65 | instantiation | 79, 90 | ⊢ |
| : |
66 | theorem | | ⊢ |
| proveit.numbers.negation.negated_zero |
67 | theorem | | ⊢ |
| proveit.numbers.addition.elim_zero_right |
68 | instantiation | 139, 109, 80 | ⊢ |
| : , : , : |
69 | instantiation | 139, 130, 81 | , ⊢ |
| : , : , : |
70 | instantiation | 139, 130, 105 | ⊢ |
| : , : , : |
71 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.interval_upper_bound |
72 | theorem | | ⊢ |
| proveit.numbers.number_sets.natural_numbers.natural_pos_is_pos |
73 | axiom | | ⊢ |
| proveit.logic.equality.equals_transitivity |
74 | instantiation | 82, 83, 84, 87, 85* | , ⊢ |
| : , : , : |
75 | instantiation | 86, 87 | ⊢ |
| : |
76 | theorem | | ⊢ |
| proveit.numbers.division.frac_cancel_complete |
77 | instantiation | 88, 127 | ⊢ |
| : |
78 | instantiation | 139, 89, 90 | ⊢ |
| : , : , : |
79 | theorem | | ⊢ |
| proveit.numbers.number_sets.rational_numbers.positive_if_in_rational_pos |
80 | instantiation | 139, 122, 91 | ⊢ |
| : , : , : |
81 | instantiation | 139, 92, 93 | , ⊢ |
| : , : , : |
82 | theorem | | ⊢ |
| proveit.numbers.division.frac_cancel_left |
83 | instantiation | 139, 95, 94 | ⊢ |
| : , : , : |
84 | instantiation | 139, 95, 96 | ⊢ |
| : , : , : |
85 | instantiation | 97, 98 | ⊢ |
| : |
86 | theorem | | ⊢ |
| proveit.numbers.division.frac_one_denom |
87 | instantiation | 139, 109, 99 | ⊢ |
| : , : , : |
88 | theorem | | ⊢ |
| proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos |
89 | theorem | | ⊢ |
| proveit.numbers.number_sets.rational_numbers.rational_pos_within_rational |
90 | instantiation | 100, 101, 102 | ⊢ |
| : , : |
91 | instantiation | 139, 130, 126 | ⊢ |
| : , : , : |
92 | instantiation | 103, 104, 105 | ⊢ |
| : , : |
93 | instantiation | 111, 132, 115 | ⊢ |
| : , : , : , : , : |
94 | instantiation | 139, 107, 106 | ⊢ |
| : , : , : |
95 | theorem | | ⊢ |
| proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero |
96 | instantiation | 139, 107, 108 | ⊢ |
| : , : , : |
97 | theorem | | ⊢ |
| proveit.numbers.multiplication.elim_one_right |
98 | instantiation | 139, 109, 110 | ⊢ |
| : , : , : |
99 | instantiation | 111, 112, 138, 113, 114, 115 | ⊢ |
| : , : , : , : , : |
100 | theorem | | ⊢ |
| proveit.numbers.division.div_rational_pos_closure |
101 | instantiation | 139, 116, 129 | ⊢ |
| : , : , : |
102 | instantiation | 139, 116, 127 | ⊢ |
| : , : , : |
103 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.int_interval_within_int |
104 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.zero_is_int |
105 | instantiation | 117, 131, 118 | ⊢ |
| : , : |
106 | instantiation | 139, 120, 119 | ⊢ |
| : , : , : |
107 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero |
108 | instantiation | 139, 120, 121 | ⊢ |
| : , : , : |
109 | theorem | | ⊢ |
| proveit.numbers.number_sets.complex_numbers.real_within_complex |
110 | instantiation | 139, 122, 123 | ⊢ |
| : , : , : |
111 | theorem | | ⊢ |
| proveit.logic.booleans.conjunction.any_from_and |
112 | axiom | | ⊢ |
| proveit.numbers.number_sets.natural_numbers.zero_in_nats |
113 | theorem | | ⊢ |
| proveit.core_expr_types.tuples.tuple_len_0_typical_eq |
114 | instantiation | 124 | ⊢ |
| : , : |
115 | assumption | | ⊢ |
116 | theorem | | ⊢ |
| proveit.numbers.number_sets.rational_numbers.nat_pos_within_rational_pos |
117 | theorem | | ⊢ |
| proveit.numbers.addition.add_int_closure_bin |
118 | instantiation | 125, 126 | ⊢ |
| : |
119 | instantiation | 139, 128, 127 | ⊢ |
| : , : , : |
120 | theorem | | ⊢ |
| proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero |
121 | instantiation | 139, 128, 129 | ⊢ |
| : , : , : |
122 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.rational_within_real |
123 | instantiation | 139, 130, 131 | ⊢ |
| : , : , : |
124 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.tuple_len_2_typical_eq |
125 | theorem | | ⊢ |
| proveit.numbers.negation.int_closure |
126 | instantiation | 139, 137, 132 | ⊢ |
| : , : , : |
127 | instantiation | 133, 138, 136 | ⊢ |
| : , : |
128 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int |
129 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.posnat1 |
130 | theorem | | ⊢ |
| proveit.numbers.number_sets.rational_numbers.int_within_rational |
131 | instantiation | 134, 135, 136 | ⊢ |
| : , : |
132 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat1 |
133 | theorem | | ⊢ |
| proveit.numbers.exponentiation.exp_natpos_closure |
134 | theorem | | ⊢ |
| proveit.numbers.exponentiation.exp_int_closure |
135 | instantiation | 139, 137, 138 | ⊢ |
| : , : , : |
136 | instantiation | 139, 140, 141 | ⊢ |
| : , : , : |
137 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.nat_within_int |
138 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat2 |
139 | theorem | | ⊢ |
| proveit.logic.sets.inclusion.superset_membership_from_proper_subset |
140 | theorem | | ⊢ |
| proveit.numbers.number_sets.natural_numbers.nat_pos_within_nat |
141 | assumption | | ⊢ |
*equality replacement requirements |