Theorem wwlkssswwlksn

Description: The walks of a fixed length as words are walks (in an undirected graph) as words. (Contributed by Alexander van der Vekens, 17-Jul-2018) (Revised by AV, 12-Apr-2021)

	Ref	Expression
Assertion	wwlkssswwlksn	⊢ ( 𝑁 WWalksN 𝐺 ) ⊆ ( WWalks ‘ 𝐺 )

Proof

Step	Hyp	Ref	Expression
1		wwlkswwlksn	⊢ ( 𝑤 ∈ ( 𝑁 WWalksN 𝐺 ) → 𝑤 ∈ ( WWalks ‘ 𝐺 ) )
2	1	ssriv	⊢ ( 𝑁 WWalksN 𝐺 ) ⊆ ( WWalks ‘ 𝐺 )