| step type | requirements | statement |
0 | instantiation | 1, 2 | , , , ⊢ |
| : , : |
1 | reference | 53 | ⊢ |
2 | instantiation | 65, 3, 4 | , , , ⊢ |
| : , : , : |
3 | instantiation | 50, 5 | ⊢ |
| : , : , : |
4 | instantiation | 6, 7, 8, 9 | , , , ⊢ |
| : , : , : , : |
5 | instantiation | 50, 10 | ⊢ |
| : , : , : |
6 | theorem | | ⊢ |
| proveit.logic.equality.four_chain_transitivity |
7 | instantiation | 11, 12, 120, 13, 75, 17, 68, 22, 23 | , , , ⊢ |
| : , : , : , : , : , : , : |
8 | instantiation | 19, 56, 115, 14, 57, 15, 16, 75, 17, 68, 22, 23, 18* | , , , ⊢ |
| : , : , : , : , : , : |
9 | instantiation | 19, 120, 115, 20, 21, 29, 68, 22, 23, 24* | , , , ⊢ |
| : , : , : , : , : , : |
10 | instantiation | 25, 75, 93, 89, 26* | ⊢ |
| : , : |
11 | theorem | | ⊢ |
| proveit.numbers.addition.leftward_commutation |
12 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat3 |
13 | instantiation | 27 | ⊢ |
| : , : , : |
14 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat4 |
15 | instantiation | 91 | ⊢ |
| : , : |
16 | instantiation | 28 | ⊢ |
| : , : , : , : |
17 | instantiation | 73, 29 | ⊢ |
| : |
18 | instantiation | 65, 30, 31, 32* | ⊢ |
| : , : , : |
19 | theorem | | ⊢ |
| proveit.numbers.addition.association |
20 | instantiation | 91 | ⊢ |
| : , : |
21 | instantiation | 91 | ⊢ |
| : , : |
22 | instantiation | 118, 108, 33 | ⊢ |
| : , : , : |
23 | instantiation | 38, 93, 34 | ⊢ |
| : , : |
24 | instantiation | 53, 35, 83* | ⊢ |
| : , : |
25 | theorem | | ⊢ |
| proveit.numbers.division.div_as_mult |
26 | instantiation | 65, 36, 37 | ⊢ |
| : , : , : |
27 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.tuple_len_3_typical_eq |
28 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.tuple_len_4_typical_eq |
29 | instantiation | 38, 74, 75 | ⊢ |
| : , : |
30 | instantiation | 50, 39 | ⊢ |
| : , : , : |
31 | instantiation | 53, 40 | ⊢ |
| : , : |
32 | instantiation | 41, 117, 42, 112, 43*, 44*, 45* | ⊢ |
| : , : , : , : |
33 | instantiation | 118, 100, 46 | ⊢ |
| : , : , : |
34 | instantiation | 118, 108, 47 | ⊢ |
| : , : , : |
35 | instantiation | 55, 56, 115, 120, 57, 48, 104, 68, 49* | ⊢ |
| : , : , : , : , : , : |
36 | instantiation | 50, 51 | ⊢ |
| : , : , : |
37 | instantiation | 52, 75, 74 | ⊢ |
| : , : |
38 | theorem | | ⊢ |
| proveit.numbers.multiplication.mult_complex_closure_bin |
39 | instantiation | 53, 54 | ⊢ |
| : , : |
40 | instantiation | 55, 56, 115, 120, 57, 58, 104, 59, 75, 60* | ⊢ |
| : , : , : , : , : , : |
41 | theorem | | ⊢ |
| proveit.numbers.addition.rational_pair_addition |
42 | instantiation | 61, 117 | ⊢ |
| : |
43 | instantiation | 62, 104, 63 | ⊢ |
| : |
44 | instantiation | 64, 104, 93, 89 | ⊢ |
| : , : |
45 | instantiation | 65, 66, 67 | ⊢ |
| : , : , : |
46 | assumption | | ⊢ |
47 | assumption | | ⊢ |
48 | instantiation | 91 | ⊢ |
| : , : |
49 | instantiation | 92, 68 | ⊢ |
| : |
50 | axiom | | ⊢ |
| proveit.logic.equality.substitution |
51 | instantiation | 69, 70, 76, 71* | ⊢ |
| : , : |
52 | theorem | | ⊢ |
| proveit.numbers.multiplication.commutation |
53 | theorem | | ⊢ |
| proveit.logic.equality.equals_reversal |
54 | instantiation | 72, 74, 75 | ⊢ |
| : , : |
55 | theorem | | ⊢ |
| proveit.numbers.multiplication.distribute_through_sum |
56 | axiom | | ⊢ |
| proveit.numbers.number_sets.natural_numbers.zero_in_nats |
57 | theorem | | ⊢ |
| proveit.core_expr_types.tuples.tuple_len_0_typical_eq |
58 | instantiation | 91 | ⊢ |
| : , : |
59 | instantiation | 73, 74 | ⊢ |
| : |
60 | instantiation | 92, 75 | ⊢ |
| : |
61 | theorem | | ⊢ |
| proveit.numbers.negation.int_closure |
62 | theorem | | ⊢ |
| proveit.numbers.division.frac_cancel_complete |
63 | instantiation | 99, 76 | ⊢ |
| : |
64 | theorem | | ⊢ |
| proveit.numbers.division.neg_frac_neg_numerator |
65 | axiom | | ⊢ |
| proveit.logic.equality.equals_transitivity |
66 | instantiation | 77, 115, 78, 79, 80, 81 | ⊢ |
| : , : , : , : |
67 | instantiation | 82, 104, 93, 83 | ⊢ |
| : , : , : |
68 | instantiation | 118, 108, 84 | ⊢ |
| : , : , : |
69 | theorem | | ⊢ |
| proveit.numbers.exponentiation.neg_power_as_div |
70 | instantiation | 118, 85, 86 | ⊢ |
| : , : , : |
71 | instantiation | 87, 93 | ⊢ |
| : |
72 | theorem | | ⊢ |
| proveit.numbers.negation.neg_times_pos |
73 | theorem | | ⊢ |
| proveit.numbers.negation.complex_closure |
74 | instantiation | 88, 104, 93, 89 | ⊢ |
| : , : |
75 | instantiation | 118, 108, 90 | ⊢ |
| : , : , : |
76 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.posnat1 |
77 | axiom | | ⊢ |
| proveit.core_expr_types.operations.operands_substitution |
78 | instantiation | 91 | ⊢ |
| : , : |
79 | instantiation | 91 | ⊢ |
| : , : |
80 | instantiation | 92, 93 | ⊢ |
| : |
81 | instantiation | 94, 104, 95* | ⊢ |
| : , : |
82 | theorem | | ⊢ |
| proveit.numbers.addition.subtraction.subtract_from_add |
83 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.add_1_1 |
84 | instantiation | 118, 100, 96 | ⊢ |
| : , : , : |
85 | theorem | | ⊢ |
| proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero |
86 | instantiation | 118, 97, 98 | ⊢ |
| : , : , : |
87 | theorem | | ⊢ |
| proveit.numbers.exponentiation.complex_x_to_first_power_is_x |
88 | theorem | | ⊢ |
| proveit.numbers.division.div_complex_closure |
89 | instantiation | 99, 111 | ⊢ |
| : |
90 | instantiation | 118, 100, 101 | ⊢ |
| : , : , : |
91 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.tuple_len_2_typical_eq |
92 | theorem | | ⊢ |
| proveit.numbers.multiplication.elim_one_left |
93 | instantiation | 118, 108, 102 | ⊢ |
| : , : , : |
94 | theorem | | ⊢ |
| proveit.numbers.negation.pos_times_neg |
95 | instantiation | 103, 104 | ⊢ |
| : |
96 | assumption | | ⊢ |
97 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero |
98 | instantiation | 118, 105, 106 | ⊢ |
| : , : , : |
99 | theorem | | ⊢ |
| proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos |
100 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.real_neg_within_real |
101 | assumption | | ⊢ |
102 | instantiation | 118, 113, 107 | ⊢ |
| : , : , : |
103 | theorem | | ⊢ |
| proveit.numbers.multiplication.elim_one_right |
104 | instantiation | 118, 108, 109 | ⊢ |
| : , : , : |
105 | theorem | | ⊢ |
| proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero |
106 | instantiation | 118, 110, 111 | ⊢ |
| : , : , : |
107 | instantiation | 118, 116, 112 | ⊢ |
| : , : , : |
108 | theorem | | ⊢ |
| proveit.numbers.number_sets.complex_numbers.real_within_complex |
109 | instantiation | 118, 113, 114 | ⊢ |
| : , : , : |
110 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int |
111 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.posnat2 |
112 | instantiation | 118, 119, 115 | ⊢ |
| : , : , : |
113 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.rational_within_real |
114 | instantiation | 118, 116, 117 | ⊢ |
| : , : , : |
115 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat2 |
116 | theorem | | ⊢ |
| proveit.numbers.number_sets.rational_numbers.int_within_rational |
117 | instantiation | 118, 119, 120 | ⊢ |
| : , : , : |
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.nat1 |
*equality replacement requirements |