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 e. UPGraph -> ( P e. ( N WWalksN G ) -> E. f ( f ( Walks ` G ) P /\ ( # ` f ) = N ) ) )

Proof

Step	Hyp	Ref	Expression
1		wlkiswwlksupgr2	|- ( G e. UPGraph -> ( P e. ( WWalks ` G ) -> E. f f ( Walks ` G ) P ) )
2	1	wlklnwwlkln2lem	|- ( G e. UPGraph -> ( P e. ( N WWalksN G ) -> E. f ( f ( Walks ` G ) P /\ ( # ` f ) = N ) ) )