Description: A path is a trail (in an undirected graph). (Contributed by Alexander van der Vekens, 21-Oct-2017) (Revised by AV, 9-Jan-2021) (Proof shortened by AV, 30-Oct-2021)
| Ref | Expression | ||
|---|---|---|---|
| Assertion | pthistrl | |- ( F ( Paths ` G ) P -> F ( Trails ` G ) P ) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | ispth | |- ( F ( Paths ` G ) P <-> ( F ( Trails ` G ) P /\ Fun `' ( P |` ( 1 ..^ ( # ` F ) ) ) /\ ( ( P " { 0 , ( # ` F ) } ) i^i ( P " ( 1 ..^ ( # ` F ) ) ) ) = (/) ) ) |
|
| 2 | 1 | simp1bi | |- ( F ( Paths ` G ) P -> F ( Trails ` G ) P ) |