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 e. V /\ N e. NN0 ) -> ( S repeatS N ) e. Word V )

Proof

Step	Hyp	Ref	Expression
1		repsf	|- ( ( S e. V /\ N e. NN0 ) -> ( S repeatS N ) : ( 0 ..^ N ) --> V )
2		iswrdi	|- ( ( S repeatS N ) : ( 0 ..^ N ) --> V -> ( S repeatS N ) e. Word V )
3	1 2	syl	|- ( ( S e. V /\ N e. NN0 ) -> ( S repeatS N ) e. Word V )