Theorem clwlkiswlk

Description: A closed walk is a walk (in an undirected graph). (Contributed by Alexander van der Vekens, 15-Mar-2018) (Revised by AV, 16-Feb-2021) (Proof shortened by AV, 30-Oct-2021)

	Ref	Expression
Assertion	clwlkiswlk	$$⊢F\mathrm{ClWalks}\left(G\right)P\to F\mathrm{Walks}\left(G\right)P$$

Proof

Step	Hyp	Ref	Expression
1		isclwlk	$$⊢F\mathrm{ClWalks}\left(G\right)P\leftrightarrow \left(F\mathrm{Walks}\left(G\right)P\wedge P\left(0\right)=P\left(\left|F\right|\right)\right)$$
2	1	simplbi	$$⊢F\mathrm{ClWalks}\left(G\right)P\to F\mathrm{Walks}\left(G\right)P$$