Metamath Proof Explorer

Theorem swrdvalfn

Description: Value of the subword extractor as function with domain. (Contributed by Alexander van der Vekens, 28-Mar-2018) (Proof shortened by AV, 2-May-2020)

		Ref	Expression
	Assertion	swrdvalfn	$⊢ (S \in Word V \land F \in (0 \dots L) \land L \in (0 \dots \|S\|)) \to (S substr ⟨F, L⟩) Fn (0 ..^L - F)$

Proof

Step	Hyp	Ref	Expression
1		swrdf	$⊢ (S \in Word V \land F \in (0 \dots L) \land L \in (0 \dots \|S\|)) \to (S substr ⟨F, L⟩) : (0 ..^L - F) ⟶ V$
2	1	ffnd	$⊢ (S \in Word V \land F \in (0 \dots L) \land L \in (0 \dots \|S\|)) \to (S substr ⟨F, L⟩) Fn (0 ..^L - F)$