Theorem wrdfn

Description: A word is a function with a zero-based sequence of integers as domain. (Contributed by Alexander van der Vekens, 13-Apr-2018)

	Ref	Expression
Assertion	wrdfn	⊢ ( 𝑊 ∈ Word 𝑆 → 𝑊 Fn ( 0 ..^ ( ♯ ‘ 𝑊 ) ) )

Proof

Step	Hyp	Ref	Expression
1		wrdf	⊢ ( 𝑊 ∈ Word 𝑆 → 𝑊 : ( 0 ..^ ( ♯ ‘ 𝑊 ) ) ⟶ 𝑆 )
2	1	ffnd	⊢ ( 𝑊 ∈ Word 𝑆 → 𝑊 Fn ( 0 ..^ ( ♯ ‘ 𝑊 ) ) )