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

Step	Hyp	Ref	Expression
1		cS	. . 3 class S
2	1	cword 12654	. 2 class Word S
3		cc0 9541	. . . . . 6 class 0
4		vl	. . . . . . 7 setvar l
5	4	cv 1437	. . . . . 6 class l
6		cfzo 11917	. . . . . 6 class ..^
7	3, 5, 6	co 6303	. . . . 5 class ( 0..^ l )
8		vw	. . . . . 6 setvar w
9	8	cv 1437	. . . . 5 class w
10	7, 1, 9	wf 5595	. . . 4 wff w : ( 0..^ l ) --> S
11		cn0 10871	. . . 4 class NN0
12	10, 4, 11	wrex 2777	. . 3 wff E. l e. NN0 w : ( 0..^ l ) --> S
13	12, 8	cab 2408	. 2 class { w | E. l e. NN0 w : ( 0..^ l ) --> S }
14	2, 13	wceq 1438	1 wff Word S = { w | E. l e. NN0 w : ( 0..^ l ) --> S }

This definition is referenced by:  iswrd  12670  iswrdOLD  12671  wrdval  12672  nfwrd  12693  csbwrdg  12694