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 ∈ Word 𝑉 ∧ 𝑁 ∈ ℤ ) → ( 𝑊 cyclShift 𝑁 ) Fn ( 0 ..^ ( ♯ ‘ 𝑊 ) ) )

Proof

Step	Hyp	Ref	Expression
1		cshwf	⊢ ( ( 𝑊 ∈ Word 𝑉 ∧ 𝑁 ∈ ℤ ) → ( 𝑊 cyclShift 𝑁 ) : ( 0 ..^ ( ♯ ‘ 𝑊 ) ) ⟶ 𝑉 )
2	1	ffnd	⊢ ( ( 𝑊 ∈ Word 𝑉 ∧ 𝑁 ∈ ℤ ) → ( 𝑊 cyclShift 𝑁 ) Fn ( 0 ..^ ( ♯ ‘ 𝑊 ) ) )