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	$$⊢N\mathrm{ClWWalksN}G\subseteq \mathrm{ClWWalks}\left(G\right)$$

Proof

Step	Hyp	Ref	Expression
1		clwwlkclwwlkn	$$⊢w\in \left(N\mathrm{ClWWalksN}G\right)\to w\in \mathrm{ClWWalks}\left(G\right)$$
2	1	ssriv	$$⊢N\mathrm{ClWWalksN}G\subseteq \mathrm{ClWWalks}\left(G\right)$$