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Definition df-word 12507
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 12499 . 2  class Word  S
3 cc0 9491 . . . . . 6  class  0
4 vl . . . . . . 7  setvar  l
54cv 1378 . . . . . 6  class  l
6 cfzo 11791 . . . . . 6  class ..^
73, 5, 6co 6283 . . . . 5  class  ( 0..^ l )
8 vw . . . . . 6  setvar  w
98cv 1378 . . . . 5  class  w
107, 1, 9wf 5583 . . . 4  wff  w : ( 0..^ l ) --> S
11 cn0 10794 . . . 4  class  NN0
1210, 4, 11wrex 2815 . . 3  wff  E. l  e.  NN0  w : ( 0..^ l ) --> S
1312, 8cab 2452 . 2  class  { w  |  E. l  e.  NN0  w : ( 0..^ l ) --> S }
142, 13wceq 1379 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  12515  wrdval  12516  nfwrd  12534  csbwrdg  12535
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