| step type | requirements | statement |
0 | instantiation | 1, 2, 3 | ⊢  |
| : , : , :  |
1 | reference | 80 | ⊢  |
2 | instantiation | 92, 4 | ⊢  |
| : , : , :  |
3 | instantiation | 49, 112, 95, 45, 114, 5, 6, 7, 123, 27, 8* | ⊢  |
| : , : , : , : , : , :  |
4 | theorem | | ⊢  |
| proveit.numbers.numerals.decimals.add_2_1 |
5 | instantiation | 105 | ⊢  |
| : , :  |
6 | instantiation | 9 | ⊢  |
| : , : , : , : , :  |
7 | instantiation | 131, 125, 10 | ⊢  |
| : , : , :  |
8 | instantiation | 80, 11, 12 | ⊢  |
| : , : , :  |
9 | theorem | | ⊢  |
| proveit.numbers.numerals.decimals.tuple_len_5_typical_eq |
10 | instantiation | 131, 127, 13 | ⊢  |
| : , : , :  |
11 | instantiation | 92, 14 | ⊢  |
| : , : , :  |
12 | instantiation | 49, 112, 95, 46, 114, 15, 16, 27, 123, 17* | ⊢  |
| : , : , : , : , : , :  |
13 | instantiation | 131, 129, 18 | ⊢  |
| : , : , :  |
14 | theorem | | ⊢  |
| proveit.numbers.numerals.decimals.add_3_1 |
15 | instantiation | 105 | ⊢  |
| : , :  |
16 | instantiation | 19 | ⊢  |
| : , : , : , :  |
17 | instantiation | 80, 20, 21 | ⊢  |
| : , : , :  |
18 | instantiation | 131, 132, 23 | ⊢  |
| : , : , :  |
19 | theorem | | ⊢  |
| proveit.numbers.numerals.decimals.tuple_len_4_typical_eq |
20 | instantiation | 92, 22 | ⊢  |
| : , : , :  |
21 | instantiation | 49, 112, 95, 23, 114, 24, 25, 26, 27, 123, 28* | ⊢  |
| : , : , : , : , : , :  |
22 | theorem | | ⊢  |
| proveit.numbers.numerals.decimals.add_4_1 |
23 | theorem | | ⊢  |
| proveit.numbers.numerals.decimals.nat3 |
24 | instantiation | 105 | ⊢  |
| : , :  |
25 | instantiation | 29 | ⊢  |
| : , : , :  |
26 | instantiation | 131, 125, 30 | ⊢  |
| : , : , :  |
27 | instantiation | 131, 125, 31 | ⊢  |
| : , : , :  |
28 | instantiation | 80, 32, 33 | ⊢  |
| : , : , :  |
29 | theorem | | ⊢  |
| proveit.numbers.numerals.decimals.tuple_len_3_typical_eq |
30 | instantiation | 131, 127, 34 | ⊢  |
| : , : , :  |
31 | instantiation | 131, 127, 35 | ⊢  |
| : , : , :  |
32 | instantiation | 92, 36 | ⊢  |
| : , : , :  |
33 | instantiation | 49, 112, 95, 114, 37, 96, 38, 123, 39* | ⊢  |
| : , : , : , : , : , :  |
34 | instantiation | 131, 129, 40 | ⊢  |
| : , : , :  |
35 | instantiation | 131, 129, 41 | ⊢  |
| : , : , :  |
36 | theorem | | ⊢  |
| proveit.numbers.numerals.decimals.add_5_4 |
37 | instantiation | 105 | ⊢  |
| : , :  |
38 | instantiation | 131, 125, 42 | ⊢  |
| : , : , :  |
39 | instantiation | 80, 43, 44 | ⊢  |
| : , : , :  |
40 | instantiation | 131, 132, 45 | ⊢  |
| : , : , :  |
41 | instantiation | 131, 132, 46 | ⊢  |
| : , : , :  |
42 | instantiation | 131, 127, 47 | ⊢  |
| : , : , :  |
43 | instantiation | 92, 48 | ⊢  |
| : , : , :  |
44 | instantiation | 49, 112, 95, 133, 114, 50, 51, 123, 52* | ⊢  |
| : , : , : , : , : , :  |
45 | theorem | | ⊢  |
| proveit.numbers.numerals.decimals.nat5 |
46 | theorem | | ⊢  |
| proveit.numbers.numerals.decimals.nat4 |
47 | instantiation | 131, 129, 53 | ⊢  |
| : , : , :  |
48 | theorem | | ⊢  |
| proveit.numbers.numerals.decimals.add_9_1 |
49 | theorem | | ⊢  |
| proveit.numbers.addition.association |
50 | instantiation | 105 | ⊢  |
| : , :  |
51 | instantiation | 131, 125, 54 | ⊢  |
| : , : , :  |
52 | instantiation | 80, 55, 56 | ⊢  |
| : , : , :  |
53 | instantiation | 131, 132, 113 | ⊢  |
| : , : , :  |
54 | instantiation | 131, 127, 57 | ⊢  |
| : , : , :  |
55 | instantiation | 92, 58 | ⊢  |
| : , : , :  |
56 | instantiation | 63, 133, 112, 89, 59, 60*, 61* | ⊢  |
| : , : , : , :  |
57 | instantiation | 131, 129, 62 | ⊢  |
| : , : , :  |
58 | instantiation | 63, 133, 112, 89, 90, 64, 65*, 66* | ⊢  |
| : , : , : , :  |
59 | instantiation | 67, 126, 68, 69, 70, 108*, 71* | ⊢  |
| : , : , :  |
60 | instantiation | 94, 95, 112, 96, 78, 114, 79 | ⊢  |
| : , : , : , : , : , : , :  |
61 | instantiation | 80, 72, 73 | ⊢  |
| : , : , :  |
62 | instantiation | 131, 74, 75 | ⊢  |
| : , : , :  |
63 | theorem | | ⊢  |
| proveit.numbers.numerals.decimals.md_nine_add_one |
64 | instantiation | 84, 76 | ⊢  |
| :  |
65 | instantiation | 94, 95, 112, 77, 78, 114, 79 | ⊢  |
| : , : , : , : , : , : , :  |
66 | instantiation | 80, 81, 82 | ⊢  |
| : , : , :  |
67 | theorem | | ⊢  |
| proveit.numbers.addition.strong_bound_via_left_term_bound |
68 | theorem | | ⊢  |
| proveit.numbers.number_sets.real_numbers.zero_is_real |
69 | instantiation | 131, 127, 83 | ⊢  |
| : , : , :  |
70 | instantiation | 84, 85 | ⊢  |
| :  |
71 | theorem | | ⊢  |
| proveit.numbers.numerals.decimals.add_8_1 |
72 | instantiation | 92, 86 | ⊢  |
| : , : , :  |
73 | instantiation | 94, 95, 112, 87, 97, 114, 98 | ⊢  |
| : , : , : , : , : , : , :  |
74 | theorem | | ⊢  |
| proveit.numbers.number_sets.integers.nat_pos_within_int |
75 | instantiation | 88, 133, 89, 90, 91 | ⊢  |
| : , : , :  |
76 | theorem | | ⊢  |
| proveit.numbers.numerals.decimals.posnat9 |
77 | instantiation | 105 | ⊢  |
| : , :  |
78 | instantiation | 106, 112 | ⊢  |
| : , :  |
79 | instantiation | 107, 108 | ⊢  |
| : , : , :  |
80 | axiom | | ⊢  |
| proveit.logic.equality.equals_transitivity |
81 | instantiation | 92, 93 | ⊢  |
| : , : , :  |
82 | instantiation | 94, 95, 112, 96, 97, 114, 98 | ⊢  |
| : , : , : , : , : , : , :  |
83 | instantiation | 131, 129, 99 | ⊢  |
| : , : , :  |
84 | theorem | | ⊢  |
| proveit.numbers.number_sets.natural_numbers.natural_pos_is_pos |
85 | theorem | | ⊢  |
| proveit.numbers.numerals.decimals.posnat8 |
86 | theorem | | ⊢  |
| proveit.numbers.numerals.decimals.add_1_1 |
87 | instantiation | 105 | ⊢  |
| : , :  |
88 | theorem | | ⊢  |
| proveit.numbers.numerals.decimals.deci_sequence_is_nat_pos |
89 | instantiation | 101, 100, 103 | ⊢  |
| : , : , :  |
90 | instantiation | 101, 102, 103 | ⊢  |
| : , : , :  |
91 | theorem | | ⊢  |
| proveit.numbers.numerals.decimals.less_0_1 |
92 | axiom | | ⊢  |
| proveit.logic.equality.substitution |
93 | instantiation | 104, 123 | ⊢  |
| :  |
94 | theorem | | ⊢  |
| proveit.core_expr_types.tuples.tuple_portion_substitution |
95 | theorem | | ⊢  |
| proveit.numbers.numerals.decimals.nat2 |
96 | instantiation | 105 | ⊢  |
| : , :  |
97 | instantiation | 106, 112 | ⊢  |
| : , :  |
98 | instantiation | 107, 108 | ⊢  |
| : , : , :  |
99 | instantiation | 131, 132, 109 | ⊢  |
| : , : , :  |
100 | instantiation | 111, 133, 109, 110 | ⊢  |
| : , : , : , : , :  |
101 | theorem | | ⊢  |
| proveit.logic.equality.sub_left_side_into |
102 | instantiation | 111, 112, 113, 114, 115 | ⊢  |
| : , : , : , : , :  |
103 | theorem | | ⊢  |
| proveit.numbers.numerals.decimals.N_leq_9_enumSet |
104 | theorem | | ⊢  |
| proveit.numbers.addition.elim_zero_left |
105 | theorem | | ⊢  |
| proveit.numbers.numerals.decimals.tuple_len_2_typical_eq |
106 | theorem | | ⊢  |
| proveit.core_expr_types.tuples.range_from1_len_typical_eq |
107 | axiom | | ⊢  |
| proveit.core_expr_types.tuples.empty_range_def |
108 | instantiation | 116, 117, 118 | ⊢  |
| : , : , :  |
109 | theorem | | ⊢  |
| proveit.numbers.numerals.decimals.nat8 |
110 | instantiation | 119 | ⊢  |
| : , : , : , : , : , : , : , :  |
111 | theorem | | ⊢  |
| proveit.logic.sets.enumeration.in_enumerated_set |
112 | axiom | | ⊢  |
| proveit.numbers.number_sets.natural_numbers.zero_in_nats |
113 | theorem | | ⊢  |
| proveit.numbers.numerals.decimals.nat9 |
114 | theorem | | ⊢  |
| proveit.core_expr_types.tuples.tuple_len_0_typical_eq |
115 | instantiation | 120 | ⊢  |
| : , : , : , : , : , : , : , : , :  |
116 | theorem | | ⊢  |
| proveit.logic.equality.sub_right_side_into |
117 | instantiation | 121, 123 | ⊢  |
| :  |
118 | instantiation | 122, 123, 124 | ⊢  |
| : , :  |
119 | theorem | | ⊢  |
| proveit.numbers.numerals.decimals.tuple_len_8_typical_eq |
120 | theorem | | ⊢  |
| proveit.numbers.numerals.decimals.tuple_len_9_typical_eq |
121 | theorem | | ⊢  |
| proveit.numbers.addition.elim_zero_right |
122 | theorem | | ⊢  |
| proveit.numbers.addition.commutation |
123 | instantiation | 131, 125, 126 | ⊢  |
| : , : , :  |
124 | theorem | | ⊢  |
| proveit.numbers.number_sets.complex_numbers.zero_is_complex |
125 | theorem | | ⊢  |
| proveit.numbers.number_sets.complex_numbers.real_within_complex |
126 | instantiation | 131, 127, 128 | ⊢  |
| : , : , :  |
127 | theorem | | ⊢  |
| proveit.numbers.number_sets.real_numbers.rational_within_real |
128 | instantiation | 131, 129, 130 | ⊢  |
| : , : , :  |
129 | theorem | | ⊢  |
| proveit.numbers.number_sets.rational_numbers.int_within_rational |
130 | instantiation | 131, 132, 133 | ⊢  |
| : , : , :  |
131 | theorem | | ⊢  |
| proveit.logic.sets.inclusion.superset_membership_from_proper_subset |
132 | theorem | | ⊢  |
| proveit.numbers.number_sets.integers.nat_within_int |
133 | theorem | | ⊢  |
| proveit.numbers.numerals.decimals.nat1 |
*equality replacement requirements |