Metamath Proof Explorer


Theorem cshwfn

Description: A cyclically shifted word is a function with a half-open range of integers of the same length as the word as domain. (Contributed by AV, 12-Nov-2018)

Ref Expression
Assertion cshwfn
|- ( ( W e. Word V /\ N e. ZZ ) -> ( W cyclShift N ) Fn ( 0 ..^ ( # ` W ) ) )

Proof

Step Hyp Ref Expression
1 cshwf
 |-  ( ( W e. Word V /\ N e. ZZ ) -> ( W cyclShift N ) : ( 0 ..^ ( # ` W ) ) --> V )
2 1 ffnd
 |-  ( ( W e. Word V /\ N e. ZZ ) -> ( W cyclShift N ) Fn ( 0 ..^ ( # ` W ) ) )