Description: The set of trails (in an undirected graph). (Contributed by Alexander van der Vekens, 20-Oct-2017) (Revised by AV, 28-Dec-2020) (Revised by AV, 29-Oct-2021)
Ref | Expression | ||
---|---|---|---|
Assertion | trlsfval | |- ( Trails ` G ) = { <. f , p >. | ( f ( Walks ` G ) p /\ Fun `' f ) } |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | biidd | |- ( g = G -> ( Fun `' f <-> Fun `' f ) ) |
|
2 | df-trls | |- Trails = ( g e. _V |-> { <. f , p >. | ( f ( Walks ` g ) p /\ Fun `' f ) } ) |
|
3 | 1 2 | fvmptopab | |- ( Trails ` G ) = { <. f , p >. | ( f ( Walks ` G ) p /\ Fun `' f ) } |