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Metamath Proof Explorer

Theorem disjwrdpfx

Description: Sets of words are disjoint if each set contains exactly the extensions of distinct words of a fixed length. Remark: A word W is called an "extension" of a word P if P is a prefix of W . (Contributed by AV, 29-Jul-2018) (Revised by AV, 6-May-2020)

		Ref	Expression
	Assertion	disjwrdpfx	⊢ Disj 𝑦 ∈ 𝑊 { 𝑥 ∈ Word 𝑉 ∣ ( 𝑥 prefix 𝑁 ) = 𝑦 }

Proof

Step	Hyp	Ref	Expression
1		invdisjrab	⊢ Disj 𝑦 ∈ 𝑊 { 𝑥 ∈ Word 𝑉 ∣ ( 𝑥 prefix 𝑁 ) = 𝑦 }