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Mirrors > Home > MPE Home > Th. List > df-frmd | Structured version Visualization version Unicode version |
Description: Define a free monoid over a set of generators, defined as the set of finite strings on with the operation of concatenation. (Contributed by Mario Carneiro, 27-Sep-2015.) |
Ref | Expression |
---|---|
df-frmd | freeMnd Word ++ Word Word |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | cfrmd 17384 | . 2 freeMnd | |
2 | vi | . . 3 | |
3 | cvv 3200 | . . 3 | |
4 | cnx 15854 | . . . . . 6 | |
5 | cbs 15857 | . . . . . 6 | |
6 | 4, 5 | cfv 5888 | . . . . 5 |
7 | 2 | cv 1482 | . . . . . 6 |
8 | 7 | cword 13291 | . . . . 5 Word |
9 | 6, 8 | cop 4183 | . . . 4 Word |
10 | cplusg 15941 | . . . . . 6 | |
11 | 4, 10 | cfv 5888 | . . . . 5 |
12 | cconcat 13293 | . . . . . 6 ++ | |
13 | 8, 8 | cxp 5112 | . . . . . 6 Word Word |
14 | 12, 13 | cres 5116 | . . . . 5 ++ Word Word |
15 | 11, 14 | cop 4183 | . . . 4 ++ Word Word |
16 | 9, 15 | cpr 4179 | . . 3 Word ++ Word Word |
17 | 2, 3, 16 | cmpt 4729 | . 2 Word ++ Word Word |
18 | 1, 17 | wceq 1483 | 1 freeMnd Word ++ Word Word |
Colors of variables: wff setvar class |
This definition is referenced by: frmdval 17388 |
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