This is an inofficial mirror of http://metamath.tirix.org for personal testing of a visualizer extension only.

Metamath Proof Explorer

Theorem wlklnwwlklnupgr2

Description: A walk of length N as word corresponds to the sequence of vertices in a walk of length N in a pseudograph. This variant of wlklnwwlkln2 does not require G to be a simple pseudograph, but it requires (indirectly) the Axiom of Choice. (Contributed by Alexander van der Vekens, 21-Jul-2018) (Revised by AV, 12-Apr-2021)

		Ref	Expression
	Assertion	wlklnwwlklnupgr2	$⊢ G \in UPGraph \to (P \in (N WWalksN G) \to \exists f (f Walks (G) P \land \|f\| = N))$

Proof

Step	Hyp	Ref	Expression
1		wlkiswwlksupgr2	$⊢ G \in UPGraph \to (P \in WWalks (G) \to \exists f f Walks (G) P)$
2	1	wlklnwwlkln2lem	$⊢ G \in UPGraph \to (P \in (N WWalksN G) \to \exists f (f Walks (G) P \land \|f\| = N))$