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Definition df-words 25394
Description: The words of size  y over an alphabet  x are the finite sequences over  x of size  y. Their domains are fiercely set to  ( 1 ... y ) so that I can concatenate them easily. The case  y  =  0 is a bit tricky and corresponds to the unique empty word (often denoted by an epsilon or by  1 in textbooks.) Experimental. (Contributed by FL, 14-Jan-2014.)
Assertion
Ref Expression
df-words  |-  Words  =  ( x  e.  _V , 
y  e.  NN0  |->  ( x  ^m  ( 1 ... y ) ) )
Distinct variable group:    x, y

Detailed syntax breakdown of Definition df-words
StepHypRef Expression
1 cwrd 25393 . 2  class  Words
2 vx . . 3  set  x
3 vy . . 3  set  y
4 cvv 2788 . . 3  class  _V
5 cn0 9965 . . 3  class  NN0
62cv 1622 . . . 4  class  x
7 c1 8738 . . . . 5  class  1
83cv 1622 . . . . 5  class  y
9 cfz 10782 . . . . 5  class  ...
107, 8, 9co 5858 . . . 4  class  ( 1 ... y )
11 cmap 6772 . . . 4  class  ^m
126, 10, 11co 5858 . . 3  class  ( x  ^m  ( 1 ... y ) )
132, 3, 4, 5, 12cmpt2 5860 . 2  class  ( x  e.  _V ,  y  e.  NN0  |->  ( x  ^m  ( 1 ... y ) ) )
141, 13wceq 1623 1  wff  Words  =  ( x  e.  _V , 
y  e.  NN0  |->  ( x  ^m  ( 1 ... y ) ) )
Colors of variables: wff set class
This definition is referenced by:  isword  25395
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