Metamath Proof Explorer


Theorem clwwlksclwwlkn

Description: The closed walks of a fixed length as words are closed walks (in an undirected graph) as words. (Contributed by Alexander van der Vekens, 15-Mar-2018) (Revised by AV, 12-Apr-2021)

Ref Expression
Assertion clwwlksclwwlkn
|- ( N ClWWalksN G ) C_ ( ClWWalks ` G )

Proof

Step Hyp Ref Expression
1 clwwlkclwwlkn
 |-  ( w e. ( N ClWWalksN G ) -> w e. ( ClWWalks ` G ) )
2 1 ssriv
 |-  ( N ClWWalksN G ) C_ ( ClWWalks ` G )