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Mirrors > Home > MPE Home > Th. List > df-wwlksn | Structured version Visualization version Unicode version |
Description: Define the set of all walks (in an undirected graph) of a fixed length n as words over the set of vertices. Such a word corresponds to the sequence p(0) p(1) ... p(n) of the vertices in a walk p(0) e(f(1)) p(1) e(f(2)) ... p(n-1) e(f(n)) p(n) as defined in df-wlks 26495. (Contributed by Alexander van der Vekens, 15-Jul-2018.) (Revised by AV, 8-Apr-2021.) |
Ref | Expression |
---|---|
df-wwlksn | WWalksN WWalks |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | cwwlksn 26718 | . 2 WWalksN | |
2 | vn | . . 3 | |
3 | vg | . . 3 | |
4 | cn0 11292 | . . 3 | |
5 | cvv 3200 | . . 3 | |
6 | vw | . . . . . . 7 | |
7 | 6 | cv 1482 | . . . . . 6 |
8 | chash 13117 | . . . . . 6 | |
9 | 7, 8 | cfv 5888 | . . . . 5 |
10 | 2 | cv 1482 | . . . . . 6 |
11 | c1 9937 | . . . . . 6 | |
12 | caddc 9939 | . . . . . 6 | |
13 | 10, 11, 12 | co 6650 | . . . . 5 |
14 | 9, 13 | wceq 1483 | . . . 4 |
15 | 3 | cv 1482 | . . . . 5 |
16 | cwwlks 26717 | . . . . 5 WWalks | |
17 | 15, 16 | cfv 5888 | . . . 4 WWalks |
18 | 14, 6, 17 | crab 2916 | . . 3 WWalks |
19 | 2, 3, 4, 5, 18 | cmpt2 6652 | . 2 WWalks |
20 | 1, 19 | wceq 1483 | 1 WWalksN WWalks |
Colors of variables: wff setvar class |
This definition is referenced by: wwlksn 26729 wwlknbp 26733 wspthsn 26735 iswwlksnon 26740 |
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