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Definition df-word 12215
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 12207 . 2  class Word  S
3 cc0 9272 . . . . . 6  class  0
4 vl . . . . . . 7  setvar  l
54cv 1363 . . . . . 6  class  l
6 cfzo 11534 . . . . . 6  class ..^
73, 5, 6co 6082 . . . . 5  class  ( 0..^ l )
8 vw . . . . . 6  setvar  w
98cv 1363 . . . . 5  class  w
107, 1, 9wf 5404 . . . 4  wff  w : ( 0..^ l ) --> S
11 cn0 10569 . . . 4  class  NN0
1210, 4, 11wrex 2708 . . 3  wff  E. l  e.  NN0  w : ( 0..^ l ) --> S
1312, 8cab 2421 . 2  class  { w  |  E. l  e.  NN0  w : ( 0..^ l ) --> S }
142, 13wceq 1364 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  12223  wrdval  12224  nfwrd  12242  csbwrdg  12243
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