Description: Value of the subword extractor as function with domain. (Contributed by Alexander van der Vekens, 28-Mar-2018) (Proof shortened by AV, 2-May-2020)
| Ref | Expression | ||
|---|---|---|---|
| Assertion | swrdvalfn | |- ( ( S e. Word V /\ F e. ( 0 ... L ) /\ L e. ( 0 ... ( # ` S ) ) ) -> ( S substr <. F , L >. ) Fn ( 0 ..^ ( L - F ) ) ) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | swrdf | |- ( ( S e. Word V /\ F e. ( 0 ... L ) /\ L e. ( 0 ... ( # ` S ) ) ) -> ( S substr <. F , L >. ) : ( 0 ..^ ( L - F ) ) --> V ) |
|
| 2 | 1 | ffnd | |- ( ( S e. Word V /\ F e. ( 0 ... L ) /\ L e. ( 0 ... ( # ` S ) ) ) -> ( S substr <. F , L >. ) Fn ( 0 ..^ ( L - F ) ) ) |