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Definition df-word 12662
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 12654 . 2  class Word  S
3 cc0 9541 . . . . . 6  class  0
4 vl . . . . . . 7  setvar  l
54cv 1437 . . . . . 6  class  l
6 cfzo 11917 . . . . . 6  class ..^
73, 5, 6co 6303 . . . . 5  class  ( 0..^ l )
8 vw . . . . . 6  setvar  w
98cv 1437 . . . . 5  class  w
107, 1, 9wf 5595 . . . 4  wff  w : ( 0..^ l ) --> S
11 cn0 10871 . . . 4  class  NN0
1210, 4, 11wrex 2777 . . 3  wff  E. l  e.  NN0  w : ( 0..^ l ) --> S
1312, 8cab 2408 . 2  class  { w  |  E. l  e.  NN0  w : ( 0..^ l ) --> S }
142, 13wceq 1438 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  12670  iswrdOLD  12671  wrdval  12672  nfwrd  12693  csbwrdg  12694
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