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Definition df-word 12221
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 12213 . 2  class Word  S
3 cc0 9274 . . . . . 6  class  0
4 vl . . . . . . 7  setvar  l
54cv 1368 . . . . . 6  class  l
6 cfzo 11540 . . . . . 6  class ..^
73, 5, 6co 6086 . . . . 5  class  ( 0..^ l )
8 vw . . . . . 6  setvar  w
98cv 1368 . . . . 5  class  w
107, 1, 9wf 5409 . . . 4  wff  w : ( 0..^ l ) --> S
11 cn0 10571 . . . 4  class  NN0
1210, 4, 11wrex 2711 . . 3  wff  E. l  e.  NN0  w : ( 0..^ l ) --> S
1312, 8cab 2424 . 2  class  { w  |  E. l  e.  NN0  w : ( 0..^ l ) --> S }
142, 13wceq 1369 1  wff Word  S  =  { w  |  E. l  e.  NN0  w : ( 0..^ l ) --> S }
Colors of variables: wff setvar class
This definition is referenced by:  iswrd  12229  wrdval  12230  nfwrd  12248  csbwrdg  12249
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