Theorem disjxwrd 13455

Description: Sets of words are disjoint if each set contains extensions of distinct words of a fixed length. (Contributed by AV, 29-Jul-2018.) (Proof shortened by AV, 7-May-2020.)

Assertion

Ref	Expression
disjxwrd	|- Disj y e. W { x e. Word V | ( x substr <. 0 , N >. ) = y }

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

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

Proof of Theorem disjxwrd

Step	Hyp	Ref	Expression
1		invdisjrab 4639	1 |- Disj y e. W { x e. Word V | ( x substr <. 0 , N >. ) = y }

Syntax hints:   = wceq 1483   {crab 2916   <.cop 4183  Disj wdisj 4620  (class class class)co 6650   0cc0 9936  Word cword 13291   substr csubstr 13295

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1722  ax-4 1737  ax-5 1839  ax-6 1888  ax-7 1935  ax-9 1999  ax-10 2019  ax-11 2034  ax-12 2047  ax-13 2246  ax-ext 2602

This theorem depends on definitions:  df-bi 197  df-or 385  df-an 386  df-tru 1486  df-ex 1705  df-nf 1710  df-sb 1881  df-eu 2474  df-mo 2475  df-clab 2609  df-cleq 2615  df-clel 2618  df-nfc 2753  df-ral 2917  df-rmo 2920  df-rab 2921  df-v 3202  df-sbc 3436  df-csb 3534  df-disj 4621

This theorem is referenced by:  disjxwwlksn  26799  disjxwwlkn  26808