This is an inofficial mirror of http://metamath.tirix.org for personal testing of a visualizer extension only.

Metamath Proof Explorer

Theorem pfxfn

Description: Value of the prefix extractor as function with domain. (Contributed by AV, 2-May-2020)

		Ref	Expression
	Assertion	pfxfn	$⊢ (S \in Word V \land L \in (0 \dots \|S\|)) \to (S prefix L) Fn (0 ..^L)$

Step	Hyp	Ref	Expression
1		pfxf	$⊢ (S \in Word V \land L \in (0 \dots \|S\|)) \to (S prefix L) : (0 ..^L) ⟶ V$
2	1	ffnd	$⊢ (S \in Word V \land L \in (0 \dots \|S\|)) \to (S prefix L) Fn (0 ..^L)$