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Definition df-word 12591
Description: Define the class of words over a set. A word (or sometimes also called a string) is a finite sequence of symbols from a set (alphabet)  S. Definition in section 9.1 of [AhoHopUll] p. 318. 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 12583 . 2  class Word  S
3 cc0 9522 . . . . . 6  class  0
4 vl . . . . . . 7  setvar  l
54cv 1404 . . . . . 6  class  l
6 cfzo 11854 . . . . . 6  class ..^
73, 5, 6co 6278 . . . . 5  class  ( 0..^ l )
8 vw . . . . . 6  setvar  w
98cv 1404 . . . . 5  class  w
107, 1, 9wf 5565 . . . 4  wff  w : ( 0..^ l ) --> S
11 cn0 10836 . . . 4  class  NN0
1210, 4, 11wrex 2755 . . 3  wff  E. l  e.  NN0  w : ( 0..^ l ) --> S
1312, 8cab 2387 . 2  class  { w  |  E. l  e.  NN0  w : ( 0..^ l ) --> S }
142, 13wceq 1405 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  12599  iswrdOLD  12600  wrdval  12601  nfwrd  12622  csbwrdg  12623
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