| step type | requirements | statement |
0 | instantiation | 1, 2, 3 | ⊢  |
| : , : , :  |
1 | reference | 33 | ⊢  |
2 | instantiation | 4, 5, 6, 7 | ⊢  |
| : , : , : , :  |
3 | instantiation | 33, 8, 9 | ⊢  |
| : , : , :  |
4 | theorem | | ⊢  |
| proveit.logic.equality.four_chain_transitivity |
5 | instantiation | 40, 10 | ⊢  |
| : , : , :  |
6 | instantiation | 40, 11 | ⊢  |
| : , : , :  |
7 | instantiation | 40, 12 | ⊢  |
| : , : , :  |
8 | instantiation | 33, 13, 14 | ⊢  |
| : , : , :  |
9 | instantiation | 28, 15 | ⊢  |
| :  |
10 | instantiation | 40, 31 | ⊢  |
| : , : , :  |
11 | instantiation | 33, 16, 17 | ⊢  |
| : , : , :  |
12 | instantiation | 40, 31 | ⊢  |
| : , : , :  |
13 | instantiation | 40, 18 | ⊢  |
| : , : , :  |
14 | instantiation | 40, 19 | ⊢  |
| : , : , :  |
15 | instantiation | 20, 94, 21, 22 | ⊢  |
| : , :  |
16 | instantiation | 33, 23, 24 | ⊢  |
| : , : , :  |
17 | instantiation | 25, 26* | ⊢  |
| : , :  |
18 | instantiation | 28, 27 | ⊢  |
| :  |
19 | instantiation | 28, 29 | ⊢  |
| :  |
20 | theorem | | ⊢  |
| proveit.logic.booleans.conjunction.and_if_all |
21 | instantiation | 30 | ⊢  |
| : , : , :  |
22 | axiom | | ⊢  |
| proveit.logic.booleans.true_axiom |
23 | instantiation | 40, 31 | ⊢  |
| : , : , :  |
24 | instantiation | 40, 32 | ⊢  |
| : , : , :  |
25 | axiom | | ⊢  |
| proveit.logic.equality.not_equals_def |
26 | instantiation | 33, 34, 35 | ⊢  |
| : , : , :  |
27 | instantiation | 68, 36 | ⊢  |
| : , :  |
28 | axiom | | ⊢  |
| proveit.logic.booleans.eq_true_intro |
29 | instantiation | 68, 37 | ⊢  |
| : , :  |
30 | theorem | | ⊢  |
| proveit.numbers.numerals.decimals.tuple_len_3_typical_eq |
31 | assumption | | ⊢  |
32 | instantiation | 65, 38, 39 | ⊢  |
| : , : , :  |
33 | axiom | | ⊢  |
| proveit.logic.equality.equals_transitivity |
34 | instantiation | 40, 41 | ⊢  |
| : , : , :  |
35 | axiom | | ⊢  |
| proveit.logic.booleans.negation.not_f |
36 | instantiation | 77, 93, 78, 42 | ⊢  |
| : , :  |
37 | instantiation | 77, 94, 78, 43 | ⊢  |
| : , :  |
38 | theorem | | ⊢  |
| proveit.numbers.numerals.decimals.add_3_1 |
39 | instantiation | 74, 75, 71 | ⊢  |
| : , :  |
40 | axiom | | ⊢  |
| proveit.logic.equality.substitution |
41 | instantiation | 44, 45 | ⊢  |
| :  |
42 | instantiation | 50, 81, 51, 46, 47, 48*, 49* | ⊢  |
| : , : , :  |
43 | instantiation | 50, 82, 51, 84, 52, 53*, 54* | ⊢  |
| : , : , :  |
44 | axiom | | ⊢  |
| proveit.logic.booleans.negation.negation_elim |
45 | instantiation | 55, 56 | ⊢  |
| : , :  |
46 | instantiation | 95, 87, 57 | ⊢  |
| : , : , :  |
47 | instantiation | 61, 58 | ⊢  |
| :  |
48 | instantiation | 65, 59, 60 | ⊢  |
| : , : , :  |
49 | theorem | | ⊢  |
| proveit.numbers.numerals.decimals.add_4_1 |
50 | theorem | | ⊢  |
| proveit.numbers.addition.strong_bound_via_left_term_bound |
51 | theorem | | ⊢  |
| proveit.numbers.number_sets.real_numbers.zero_is_real |
52 | instantiation | 61, 62 | ⊢  |
| :  |
53 | instantiation | 65, 63, 64 | ⊢  |
| : , : , :  |
54 | instantiation | 65, 66, 67 | ⊢  |
| : , : , :  |
55 | theorem | | ⊢  |
| proveit.logic.equality.unfold_not_equals |
56 | instantiation | 68, 69 | ⊢  |
| : , :  |
57 | instantiation | 95, 91, 70 | ⊢  |
| : , : , :  |
58 | theorem | | ⊢  |
| proveit.numbers.numerals.decimals.posnat4 |
59 | instantiation | 72, 71 | ⊢  |
| :  |
60 | instantiation | 74, 71, 73 | ⊢  |
| : , :  |
61 | theorem | | ⊢  |
| proveit.numbers.number_sets.natural_numbers.natural_pos_is_pos |
62 | theorem | | ⊢  |
| proveit.numbers.numerals.decimals.posnat2 |
63 | instantiation | 72, 75 | ⊢  |
| :  |
64 | instantiation | 74, 75, 73 | ⊢  |
| : , :  |
65 | theorem | | ⊢  |
| proveit.logic.equality.sub_right_side_into |
66 | theorem | | ⊢  |
| proveit.numbers.numerals.decimals.add_3_2 |
67 | instantiation | 74, 75, 76 | ⊢  |
| : , :  |
68 | theorem | | ⊢  |
| proveit.logic.equality.not_equals_symmetry |
69 | instantiation | 77, 80, 78, 79 | ⊢  |
| : , :  |
70 | instantiation | 95, 96, 80 | ⊢  |
| : , : , :  |
71 | instantiation | 95, 83, 81 | ⊢  |
| : , : , :  |
72 | theorem | | ⊢  |
| proveit.numbers.addition.elim_zero_right |
73 | theorem | | ⊢  |
| proveit.numbers.number_sets.complex_numbers.zero_is_complex |
74 | theorem | | ⊢  |
| proveit.numbers.addition.commutation |
75 | instantiation | 95, 83, 82 | ⊢  |
| : , : , :  |
76 | instantiation | 95, 83, 84 | ⊢  |
| : , : , :  |
77 | theorem | | ⊢  |
| proveit.numbers.ordering.less_is_not_eq_nat |
78 | theorem | | ⊢  |
| proveit.numbers.numerals.decimals.nat5 |
79 | theorem | | ⊢  |
| proveit.numbers.numerals.decimals.less_4_5 |
80 | theorem | | ⊢  |
| proveit.numbers.numerals.decimals.nat4 |
81 | instantiation | 95, 87, 85 | ⊢  |
| : , : , :  |
82 | instantiation | 95, 87, 86 | ⊢  |
| : , : , :  |
83 | theorem | | ⊢  |
| proveit.numbers.number_sets.complex_numbers.real_within_complex |
84 | instantiation | 95, 87, 88 | ⊢  |
| : , : , :  |
85 | instantiation | 95, 91, 89 | ⊢  |
| : , : , :  |
86 | instantiation | 95, 91, 90 | ⊢  |
| : , : , :  |
87 | theorem | | ⊢  |
| proveit.numbers.number_sets.real_numbers.rational_within_real |
88 | instantiation | 95, 91, 92 | ⊢  |
| : , : , :  |
89 | instantiation | 95, 96, 93 | ⊢  |
| : , : , :  |
90 | instantiation | 95, 96, 94 | ⊢  |
| : , : , :  |
91 | theorem | | ⊢  |
| proveit.numbers.number_sets.rational_numbers.int_within_rational |
92 | instantiation | 95, 96, 97 | ⊢  |
| : , : , :  |
93 | theorem | | ⊢  |
| proveit.numbers.numerals.decimals.nat1 |
94 | theorem | | ⊢  |
| proveit.numbers.numerals.decimals.nat3 |
95 | theorem | | ⊢  |
| proveit.logic.sets.inclusion.superset_membership_from_proper_subset |
96 | theorem | | ⊢  |
| proveit.numbers.number_sets.integers.nat_within_int |
97 | theorem | | ⊢  |
| proveit.numbers.numerals.decimals.nat2 |
*equality replacement requirements |