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Metamath Proof Explorer

Theorem cshwrn

Description: The range of a cyclically shifted word is a subset of the set of symbols for the word. (Contributed by AV, 12-Nov-2018)

		Ref	Expression
	Assertion	cshwrn	$⊢ (W \in Word V \land N \in ℤ) \to ran (W cyclShift N) \subseteq V$

Step	Hyp	Ref	Expression
1		cshwf	$⊢ (W \in Word V \land N \in ℤ) \to (W cyclShift N) : (0 ..^\|W\|) ⟶ V$
2	1	frnd	$⊢ (W \in Word V \land N \in ℤ) \to ran (W cyclShift N) \subseteq V$