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Metamath Proof Explorer

Theorem wlkcl

Description: A walk has length # ( F ) , which is an integer. Formerly proven for an Eulerian path, see eupthcl . (Contributed by Mario Carneiro, 12-Mar-2015) (Revised by AV, 18-Feb-2021)

		Ref	Expression
	Assertion	wlkcl	\|- ( F ( Walks ` G ) P -> ( # ` F ) e. NN0 )

Proof

Step	Hyp	Ref	Expression
1		eqid	\|- ( iEdg ` G ) = ( iEdg ` G )
2	1	wlkf	\|- ( F ( Walks ` G ) P -> F e. Word dom ( iEdg ` G ) )
3		lencl	\|- ( F e. Word dom ( iEdg ` G ) -> ( # ` F ) e. NN0 )
4	2 3	syl	\|- ( F ( Walks ` G ) P -> ( # ` F ) e. NN0 )