Mathbox for Alexander van der Vekens < Previous   Next > Nearby theorems Mirrors  >  Home  >  MPE Home  >  Th. List  >   Mathboxes  >  df-clwwlkn Structured version   Unicode version

Definition df-clwwlkn 30557
 Description: Define the set of all Closed 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-1) of the vertices in a closed walk p(0) e(f(1)) p(1) e(f(2)) ... p(n-1) e(f(n)) p(n)=p(0) as defined in df-clwlk 30555. (Contributed by Alexander van der Vekens, 20-Mar-2018.)
Assertion
Ref Expression
df-clwwlkn ClWWalksN ClWWalks
Distinct variable group:   ,,,

Detailed syntax breakdown of Definition df-clwwlkn
StepHypRef Expression
1 cclwwlkn 30554 . 2 ClWWalksN
2 vv . . 3
3 ve . . 3
4 cvv 3070 . . 3
5 vn . . . 4
6 cn0 10682 . . . 4
7 vw . . . . . . . 8
87cv 1369 . . . . . . 7
9 chash 12206 . . . . . . 7
108, 9cfv 5518 . . . . . 6
115cv 1369 . . . . . 6
1210, 11wceq 1370 . . . . 5
132cv 1369 . . . . . 6
143cv 1369 . . . . . 6
15 cclwwlk 30553 . . . . . 6 ClWWalks
1613, 14, 15co 6192 . . . . 5 ClWWalks
1712, 7, 16crab 2799 . . . 4 ClWWalks
185, 6, 17cmpt 4450 . . 3 ClWWalks
192, 3, 4, 4, 18cmpt2 6194 . 2 ClWWalks
201, 19wceq 1370 1 ClWWalksN ClWWalks
 Colors of variables: wff setvar class This definition is referenced by:  clwwlkn  30570  clwwlknprop  30575
 Copyright terms: Public domain W3C validator