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Definition df-word 11425
Description: Define the class of words over a set. A word is a finite sequence of symbols from a set. The domain is forced so that two words with the same symbols in the same order will be the same. This is sometimes denoted with the Kleene star, although properly speaking that is an operator on languages. (Contributed by FL, 14-Jan-2014.) (Revised by Stefan O'Rear, 14-Aug-2015.) (Revised by Mario Carneiro, 26-Feb-2016.)
Assertion
Ref Expression
df-word  |- Word  S  =  { w  |  E. l  e.  NN0  w : ( 0..^ l ) --> S }
Distinct variable group:    w, l, S

Detailed syntax breakdown of Definition df-word
StepHypRef Expression
1 cS . . 3  class  S
21cword 11419 . 2  class Word  S
3 cc0 8753 . . . . . 6  class  0
4 vl . . . . . . 7  set  l
54cv 1631 . . . . . 6  class  l
6 cfzo 10886 . . . . . 6  class ..^
73, 5, 6co 5874 . . . . 5  class  ( 0..^ l )
8 vw . . . . . 6  set  w
98cv 1631 . . . . 5  class  w
107, 1, 9wf 5267 . . . 4  wff  w : ( 0..^ l ) --> S
11 cn0 9981 . . . 4  class  NN0
1210, 4, 11wrex 2557 . . 3  wff  E. l  e.  NN0  w : ( 0..^ l ) --> S
1312, 8cab 2282 . 2  class  { w  |  E. l  e.  NN0  w : ( 0..^ l ) --> S }
142, 13wceq 1632 1  wff Word  S  =  { w  |  E. l  e.  NN0  w : ( 0..^ l ) --> S }
Colors of variables: wff set class
This definition is referenced by:  iswrd  11431  wrdval  11432  nfwrd  11442
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