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 e. W { x e. Word V | ( x prefix N ) = y }

Proof

Step Hyp Ref Expression
1 invdisjrab
 |-  Disj_ y e. W { x e. Word V | ( x prefix N ) = y }