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	$$⊢\underset{y\in W}{Disj}\left\{x\in \mathrm{Word}V|x\mathrm{prefix}N=y\right\}$$

Proof

Step	Hyp	Ref	Expression
1		invdisjrab	$$⊢\underset{y\in W}{Disj}\left\{x\in \mathrm{Word}V|x\mathrm{prefix}N=y\right\}$$