Theorem repsw

Description: A function mapping a half-open range of nonnegative integers to a constant is a word consisting of one symbol repeated several times ("repeated symbol word"). (Contributed by AV, 4-Nov-2018)

	Ref	Expression
Assertion	repsw	⊢ ( ( 𝑆 ∈ 𝑉 ∧ 𝑁 ∈ ℕ0 ) → ( 𝑆 repeatS 𝑁 ) ∈ Word 𝑉 )

Proof

Step	Hyp	Ref	Expression
1		repsf	⊢ ( ( 𝑆 ∈ 𝑉 ∧ 𝑁 ∈ ℕ0 ) → ( 𝑆 repeatS 𝑁 ) : ( 0 ..^ 𝑁 ) ⟶ 𝑉 )
2		iswrdi	⊢ ( ( 𝑆 repeatS 𝑁 ) : ( 0 ..^ 𝑁 ) ⟶ 𝑉 → ( 𝑆 repeatS 𝑁 ) ∈ Word 𝑉 )
3	1 2	syl	⊢ ( ( 𝑆 ∈ 𝑉 ∧ 𝑁 ∈ ℕ0 ) → ( 𝑆 repeatS 𝑁 ) ∈ Word 𝑉 )