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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	$⊢ N ClWWalksN G \subseteq ClWWalks (G)$

Proof

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