Description: The F function in an Eulerian path is a bijection from a half-open range of nonnegative integers to the set of edges. (Contributed by Mario Carneiro, 12-Mar-2015) (Revised by AV, 18-Feb-2021)
| Ref | Expression | ||
|---|---|---|---|
| Hypothesis | eupths.i | |- I = ( iEdg ` G ) |
|
| Assertion | eupthf1o | |- ( F ( EulerPaths ` G ) P -> F : ( 0 ..^ ( # ` F ) ) -1-1-onto-> dom I ) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | eupths.i | |- I = ( iEdg ` G ) |
|
| 2 | 1 | eupthi | |- ( F ( EulerPaths ` G ) P -> ( F ( Walks ` G ) P /\ F : ( 0 ..^ ( # ` F ) ) -1-1-onto-> dom I ) ) |
| 3 | 2 | simprd | |- ( F ( EulerPaths ` G ) P -> F : ( 0 ..^ ( # ` F ) ) -1-1-onto-> dom I ) |