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Definition df-word 12350
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 12342 . 2  class Word  S
3 cc0 9396 . . . . . 6  class  0
4 vl . . . . . . 7  setvar  l
54cv 1369 . . . . . 6  class  l
6 cfzo 11668 . . . . . 6  class ..^
73, 5, 6co 6203 . . . . 5  class  ( 0..^ l )
8 vw . . . . . 6  setvar  w
98cv 1369 . . . . 5  class  w
107, 1, 9wf 5525 . . . 4  wff  w : ( 0..^ l ) --> S
11 cn0 10693 . . . 4  class  NN0
1210, 4, 11wrex 2800 . . 3  wff  E. l  e.  NN0  w : ( 0..^ l ) --> S
1312, 8cab 2439 . 2  class  { w  |  E. l  e.  NN0  w : ( 0..^ l ) --> S }
142, 13wceq 1370 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  12358  wrdval  12359  nfwrd  12377  csbwrdg  12378
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