Definition df-word 12507

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

Step	Hyp	Ref	Expression
1		cS	. . 3 class S
2	1	cword 12499	. 2 class Word S
3		cc0 9491	. . . . . 6 class 0
4		vl	. . . . . . 7 setvar l
5	4	cv 1378	. . . . . 6 class l
6		cfzo 11791	. . . . . 6 class ..^
7	3, 5, 6	co 6283	. . . . 5 class ( 0..^ l )
8		vw	. . . . . 6 setvar w
9	8	cv 1378	. . . . 5 class w
10	7, 1, 9	wf 5583	. . . 4 wff w : ( 0..^ l ) --> S
11		cn0 10794	. . . 4 class NN0
12	10, 4, 11	wrex 2815	. . 3 wff E. l e. NN0 w : ( 0..^ l ) --> S
13	12, 8	cab 2452	. 2 class { w | E. l e. NN0 w : ( 0..^ l ) --> S }
14	2, 13	wceq 1379	1 wff Word S = { w | E. l e. NN0 w : ( 0..^ l ) --> S }

This definition is referenced by:  iswrd  12515  wrdval  12516  nfwrd  12534  csbwrdg  12535