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Definition df-word 11678
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 11672 . 2  class Word  S
3 cc0 8946 . . . . . 6  class  0
4 vl . . . . . . 7  set  l
54cv 1648 . . . . . 6  class  l
6 cfzo 11090 . . . . . 6  class ..^
73, 5, 6co 6040 . . . . 5  class  ( 0..^ l )
8 vw . . . . . 6  set  w
98cv 1648 . . . . 5  class  w
107, 1, 9wf 5409 . . . 4  wff  w : ( 0..^ l ) --> S
11 cn0 10177 . . . 4  class  NN0
1210, 4, 11wrex 2667 . . 3  wff  E. l  e.  NN0  w : ( 0..^ l ) --> S
1312, 8cab 2390 . 2  class  { w  |  E. l  e.  NN0  w : ( 0..^ l ) --> S }
142, 13wceq 1649 1  wff Word  S  =  { w  |  E. l  e.  NN0  w : ( 0..^ l ) --> S }
Colors of variables: wff set class
This definition is referenced by:  iswrd  11684  wrdval  11685  nfwrd  11695
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