Theorem disjwrdpfx 11388

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 4102	1 |- Disj y e. W { x e. Word V | ( x prefix N ) = y }

Syntax hints:   = wceq 1398   {crab 2524  Disj wdisj 4084  (class class class)co 6049  Word cword 11220   prefix cpfx 11360

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 717  ax-5 1496  ax-7 1497  ax-gen 1498  ax-ie1 1542  ax-ie2 1543  ax-8 1553  ax-10 1554  ax-11 1555  ax-i12 1556  ax-bndl 1558  ax-4 1559  ax-17 1575  ax-i9 1579  ax-ial 1583  ax-i5r 1584  ax-ext 2214

This theorem depends on definitions:  df-bi 117  df-tru 1401  df-nf 1510  df-sb 1812  df-eu 2083  df-mo 2084  df-clab 2219  df-cleq 2225  df-clel 2228  df-nfc 2373  df-ral 2525  df-rmo 2528  df-rab 2529  df-v 2814  df-sbc 3042  df-csb 3138  df-disj 4085

This theorem is referenced by: (None)