Metamath Proof Explorer


Theorem swrdvalfn

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 ) ) )

Proof

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 ) ) )