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 ( ClWalks ` G ) P -> F ( Walks ` G ) P ) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | isclwlk | |- ( F ( ClWalks ` G ) P <-> ( F ( Walks ` G ) P /\ ( P ` 0 ) = ( P ` ( # ` F ) ) ) ) |
|
| 2 | 1 | simplbi | |- ( F ( ClWalks ` G ) P -> F ( Walks ` G ) P ) |