Definition df-word 12523

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 12515	. 2 class Word S
3		cc0 9495	. . . . . 6 class 0
4		vl	. . . . . . 7 setvar l
5	4	cv 1382	. . . . . 6 class l
6		cfzo 11805	. . . . . 6 class ..^
7	3, 5, 6	co 6281	. . . . 5 class ( 0..^ l )
8		vw	. . . . . 6 setvar w
9	8	cv 1382	. . . . 5 class w
10	7, 1, 9	wf 5574	. . . 4 wff w : ( 0..^ l ) --> S
11		cn0 10802	. . . 4 class NN0
12	10, 4, 11	wrex 2794	. . 3 wff E. l e. NN0 w : ( 0..^ l ) --> S
13	12, 8	cab 2428	. 2 class { w | E. l e. NN0 w : ( 0..^ l ) --> S }
14	2, 13	wceq 1383	1 wff Word S = { w | E. l e. NN0 w : ( 0..^ l ) --> S }

This definition is referenced by:  iswrd  12531  wrdval  12532  nfwrd  12550  csbwrdg  12551