Theorem disjwrdpfx 11232

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.)

Assertion

Ref	Expression
disjwrdpfx	|- Disj y e. W { x e. Word V | ( x prefix N ) = y }

Distinct variable groups:   y, N   x, V   x, y

Allowed substitution hints:   N( x)   V( y)   W( x, y)

Proof of Theorem disjwrdpfx

Step	Hyp	Ref	Expression
1		invdisjrab 4077	1 |- Disj y e. W { x e. Word V | ( x prefix N ) = y }

Syntax hints:   = wceq 1395   {crab 2512  Disj wdisj 4059  (class class class)co 6001  Word cword 11071   prefix cpfx 11204

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-io 714  ax-5 1493  ax-7 1494  ax-gen 1495  ax-ie1 1539  ax-ie2 1540  ax-8 1550  ax-10 1551  ax-11 1552  ax-i12 1553  ax-bndl 1555  ax-4 1556  ax-17 1572  ax-i9 1576  ax-ial 1580  ax-i5r 1581  ax-ext 2211

This theorem depends on definitions:  df-bi 117  df-tru 1398  df-nf 1507  df-sb 1809  df-eu 2080  df-mo 2081  df-clab 2216  df-cleq 2222  df-clel 2225  df-nfc 2361  df-ral 2513  df-rmo 2516  df-rab 2517  df-v 2801  df-sbc 3029  df-csb 3125  df-disj 4060

This theorem is referenced by: (None)