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Definition df-word 12523
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 12515 . 2  class Word  S
3 cc0 9495 . . . . . 6  class  0
4 vl . . . . . . 7  setvar  l
54cv 1382 . . . . . 6  class  l
6 cfzo 11805 . . . . . 6  class ..^
73, 5, 6co 6281 . . . . 5  class  ( 0..^ l )
8 vw . . . . . 6  setvar  w
98cv 1382 . . . . 5  class  w
107, 1, 9wf 5574 . . . 4  wff  w : ( 0..^ l ) --> S
11 cn0 10802 . . . 4  class  NN0
1210, 4, 11wrex 2794 . . 3  wff  E. l  e.  NN0  w : ( 0..^ l ) --> S
1312, 8cab 2428 . 2  class  { w  |  E. l  e.  NN0  w : ( 0..^ l ) --> S }
142, 13wceq 1383 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  12531  wrdval  12532  nfwrd  12550  csbwrdg  12551
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