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

Step	Hyp	Ref	Expression
1		cS	. . 3 class S
2	1	cword 12583	. 2 class Word S
3		cc0 9522	. . . . . 6 class 0
4		vl	. . . . . . 7 setvar l
5	4	cv 1404	. . . . . 6 class l
6		cfzo 11854	. . . . . 6 class ..^
7	3, 5, 6	co 6278	. . . . 5 class ( 0..^ l )
8		vw	. . . . . 6 setvar w
9	8	cv 1404	. . . . 5 class w
10	7, 1, 9	wf 5565	. . . 4 wff w : ( 0..^ l ) --> S
11		cn0 10836	. . . 4 class NN0
12	10, 4, 11	wrex 2755	. . 3 wff E. l e. NN0 w : ( 0..^ l ) --> S
13	12, 8	cab 2387	. 2 class { w | E. l e. NN0 w : ( 0..^ l ) --> S }
14	2, 13	wceq 1405	1 wff Word S = { w | E. l e. NN0 w : ( 0..^ l ) --> S }

This definition is referenced by:  iswrd  12599  iswrdOLD  12600  wrdval  12601  nfwrd  12622  csbwrdg  12623