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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 ) ⊆ ( ClWWalks ‘ 𝐺 )

Proof

Step	Hyp	Ref	Expression
1		clwwlkclwwlkn	⊢ ( 𝑤 ∈ ( 𝑁 ClWWalksN 𝐺 ) → 𝑤 ∈ ( ClWWalks ‘ 𝐺 ) )
2	1	ssriv	⊢ ( 𝑁 ClWWalksN 𝐺 ) ⊆ ( ClWWalks ‘ 𝐺 )