Definition df-word 12711

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 12703	. 2 class Word S
3		cc0 9557	. . . . . 6 class 0
4		vl	. . . . . . 7 setvar l
5	4	cv 1451	. . . . . 6 class l
6		cfzo 11942	. . . . . 6 class ..^
7	3, 5, 6	co 6308	. . . . 5 class ( 0..^ l )
8		vw	. . . . . 6 setvar w
9	8	cv 1451	. . . . 5 class w
10	7, 1, 9	wf 5585	. . . 4 wff w : ( 0..^ l ) --> S
11		cn0 10893	. . . 4 class NN0
12	10, 4, 11	wrex 2757	. . 3 wff E. l e. NN0 w : ( 0..^ l ) --> S
13	12, 8	cab 2457	. 2 class { w | E. l e. NN0 w : ( 0..^ l ) --> S }
14	2, 13	wceq 1452	1 wff Word S = { w | E. l e. NN0 w : ( 0..^ l ) --> S }

This definition is referenced by:  iswrd  12719  iswrdOLD  12720  wrdval  12721  nfwrd  12746  csbwrdg  12747