| 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 | 120, 115, 8 | ⊢ |
| : , : , : |
3 | reference | 11 | ⊢ |
4 | instantiation | 9, 12, 13 | ⊢ |
| : , : |
5 | instantiation | 10, 11, 12, 13, 14, 15 | , ⊢ |
| : , : , : |
6 | instantiation | 16, 17 | ⊢ |
| : , : |
7 | instantiation | 75, 18, 19 | ⊢ |
| : , : , : |
8 | instantiation | 120, 118, 45 | ⊢ |
| : , : , : |
9 | theorem | | ⊢ |
| proveit.numbers.addition.add_real_closure_bin |
10 | theorem | | ⊢ |
| proveit.numbers.ordering.less_add_right |
11 | instantiation | 20, 61, 60 | ⊢ |
| : , : |
12 | instantiation | 20, 61, 23 | ⊢ |
| : , : |
13 | instantiation | 120, 115, 21 | ⊢ |
| : , : , : |
14 | instantiation | 22, 61, 60, 23, 24, 25 | , ⊢ |
| : , : , : |
15 | instantiation | 26, 27 | ⊢ |
| : , : |
16 | theorem | | ⊢ |
| proveit.logic.equality.equals_reversal |
17 | instantiation | 48, 28 | ⊢ |
| : , : , : |
18 | instantiation | 48, 29 | ⊢ |
| : , : , : |
19 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.add_2_3 |
20 | theorem | | ⊢ |
| proveit.numbers.multiplication.mult_real_closure_bin |
21 | instantiation | 120, 85, 32 | ⊢ |
| : , : , : |
22 | theorem | | ⊢ |
| proveit.numbers.multiplication.strong_bound_via_right_factor_bound |
23 | instantiation | 120, 115, 30 | ⊢ |
| : , : , : |
24 | assumption | | ⊢ |
25 | instantiation | 31, 86 | ⊢ |
| : |
26 | theorem | | ⊢ |
| proveit.numbers.ordering.relax_less |
27 | instantiation | 31, 32 | ⊢ |
| : |
28 | instantiation | 33, 51, 102, 34, 35* | ⊢ |
| : , : |
29 | instantiation | 75, 36, 37 | ⊢ |
| : , : , : |
30 | instantiation | 120, 118, 44 | ⊢ |
| : , : , : |
31 | theorem | | ⊢ |
| proveit.numbers.number_sets.rational_numbers.positive_if_in_rational_pos |
32 | instantiation | 97, 38, 99 | ⊢ |
| : , : |
33 | theorem | | ⊢ |
| proveit.numbers.division.div_as_mult |
34 | instantiation | 39, 108 | ⊢ |
| : |
35 | instantiation | 75, 40, 41 | ⊢ |
| : , : , : |
36 | instantiation | 48, 42 | ⊢ |
| : , : , : |
37 | instantiation | 43, 44, 119, 45, 46* | ⊢ |
| : , : , : , : |
38 | instantiation | 120, 107, 47 | ⊢ |
| : , : , : |
39 | theorem | | ⊢ |
| proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos |
40 | instantiation | 48, 49 | ⊢ |
| : , : , : |
41 | instantiation | 50, 51, 52 | ⊢ |
| : , : |
42 | instantiation | 81, 52 | ⊢ |
| : |
43 | theorem | | ⊢ |
| proveit.numbers.addition.rational_pair_addition |
44 | instantiation | 120, 121, 53 | ⊢ |
| : , : , : |
45 | instantiation | 120, 121, 54 | ⊢ |
| : , : , : |
46 | instantiation | 75, 55, 56 | ⊢ |
| : , : , : |
47 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.posnat3 |
48 | axiom | | ⊢ |
| proveit.logic.equality.substitution |
49 | instantiation | 57, 58, 113, 59* | ⊢ |
| : , : |
50 | theorem | | ⊢ |
| proveit.numbers.multiplication.commutation |
51 | instantiation | 120, 109, 60 | ⊢ |
| : , : , : |
52 | instantiation | 120, 109, 61 | ⊢ |
| : , : , : |
53 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat1 |
54 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat3 |
55 | instantiation | 87, 122, 62, 63, 64, 65 | ⊢ |
| : , : , : , : |
56 | instantiation | 66, 67, 68, 102, 69*, 70*, 71* | ⊢ |
| : , : , : |
57 | theorem | | ⊢ |
| proveit.numbers.exponentiation.neg_power_as_div |
58 | instantiation | 120, 79, 72 | ⊢ |
| : , : , : |
59 | instantiation | 73, 102 | ⊢ |
| : |
60 | assumption | | ⊢ |
61 | instantiation | 120, 115, 74 | ⊢ |
| : , : , : |
62 | instantiation | 100 | ⊢ |
| : , : |
63 | instantiation | 100 | ⊢ |
| : , : |
64 | instantiation | 75, 76, 77 | ⊢ |
| : , : , : |
65 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.mult_2_2 |
66 | theorem | | ⊢ |
| proveit.numbers.division.frac_cancel_left |
67 | instantiation | 120, 79, 78 | ⊢ |
| : , : , : |
68 | instantiation | 120, 79, 80 | ⊢ |
| : , : , : |
69 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.mult_4_2 |
70 | instantiation | 81, 82 | ⊢ |
| : |
71 | instantiation | 83, 102 | ⊢ |
| : |
72 | instantiation | 120, 93, 84 | ⊢ |
| : , : , : |
73 | theorem | | ⊢ |
| proveit.numbers.exponentiation.complex_x_to_first_power_is_x |
74 | instantiation | 120, 85, 86 | ⊢ |
| : , : , : |
75 | axiom | | ⊢ |
| proveit.logic.equality.equals_transitivity |
76 | instantiation | 87, 122, 88, 89, 90, 91 | ⊢ |
| : , : , : , : |
77 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.add_2_6 |
78 | instantiation | 120, 93, 92 | ⊢ |
| : , : , : |
79 | theorem | | ⊢ |
| proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero |
80 | instantiation | 120, 93, 94 | ⊢ |
| : , : , : |
81 | theorem | | ⊢ |
| proveit.numbers.multiplication.elim_one_right |
82 | instantiation | 120, 109, 95 | ⊢ |
| : , : , : |
83 | theorem | | ⊢ |
| proveit.numbers.division.frac_one_denom |
84 | instantiation | 120, 104, 96 | ⊢ |
| : , : , : |
85 | theorem | | ⊢ |
| proveit.numbers.number_sets.rational_numbers.rational_pos_within_rational |
86 | instantiation | 97, 98, 99 | ⊢ |
| : , : |
87 | axiom | | ⊢ |
| proveit.core_expr_types.operations.operands_substitution |
88 | instantiation | 100 | ⊢ |
| : , : |
89 | instantiation | 100 | ⊢ |
| : , : |
90 | instantiation | 101, 102 | ⊢ |
| : |
91 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.mult_2_3 |
92 | instantiation | 120, 104, 103 | ⊢ |
| : , : , : |
93 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero |
94 | instantiation | 120, 104, 105 | ⊢ |
| : , : , : |
95 | instantiation | 120, 115, 106 | ⊢ |
| : , : , : |
96 | instantiation | 120, 112, 108 | ⊢ |
| : , : , : |
97 | theorem | | ⊢ |
| proveit.numbers.division.div_rational_pos_closure |
98 | instantiation | 120, 107, 113 | ⊢ |
| : , : , : |
99 | instantiation | 120, 107, 108 | ⊢ |
| : , : , : |
100 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.tuple_len_2_typical_eq |
101 | theorem | | ⊢ |
| proveit.numbers.multiplication.elim_one_left |
102 | instantiation | 120, 109, 110 | ⊢ |
| : , : , : |
103 | instantiation | 120, 112, 111 | ⊢ |
| : , : , : |
104 | theorem | | ⊢ |
| proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero |
105 | instantiation | 120, 112, 113 | ⊢ |
| : , : , : |
106 | instantiation | 120, 118, 114 | ⊢ |
| : , : , : |
107 | theorem | | ⊢ |
| proveit.numbers.number_sets.rational_numbers.nat_pos_within_rational_pos |
108 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.posnat2 |
109 | theorem | | ⊢ |
| proveit.numbers.number_sets.complex_numbers.real_within_complex |
110 | instantiation | 120, 115, 116 | ⊢ |
| : , : , : |
111 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.posnat4 |
112 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int |
113 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.posnat1 |
114 | instantiation | 120, 121, 117 | ⊢ |
| : , : , : |
115 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.rational_within_real |
116 | instantiation | 120, 118, 119 | ⊢ |
| : , : , : |
117 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat4 |
118 | theorem | | ⊢ |
| proveit.numbers.number_sets.rational_numbers.int_within_rational |
119 | instantiation | 120, 121, 122 | ⊢ |
| : , : , : |
120 | theorem | | ⊢ |
| proveit.logic.sets.inclusion.superset_membership_from_proper_subset |
121 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.nat_within_int |
122 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat2 |
*equality replacement requirements |