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Metamath Proof Explorer

Theorem iswrdb

Description: A word over an alphabet is a function from an open range of nonnegative integers (of length equal to the length of the word) into the alphabet. (Contributed by Alexander van der Vekens, 30-Jul-2018)

		Ref	Expression
	Assertion	iswrdb	$⊢ W \in Word S \leftrightarrow W : (0 ..^\|W\|) ⟶ S$

Proof

Step	Hyp	Ref	Expression
1		wrdf	$⊢ W \in Word S \to W : (0 ..^\|W\|) ⟶ S$
2		iswrdi	$⊢ W : (0 ..^\|W\|) ⟶ S \to W \in Word S$
3	1 2	impbii	$⊢ W \in Word S \leftrightarrow W : (0 ..^\|W\|) ⟶ S$