Definition df-word 12215

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 12207	. 2 class Word S
3		cc0 9272	. . . . . 6 class 0
4		vl	. . . . . . 7 setvar l
5	4	cv 1363	. . . . . 6 class l
6		cfzo 11534	. . . . . 6 class ..^
7	3, 5, 6	co 6082	. . . . 5 class ( 0..^ l )
8		vw	. . . . . 6 setvar w
9	8	cv 1363	. . . . 5 class w
10	7, 1, 9	wf 5404	. . . 4 wff w : ( 0..^ l ) --> S
11		cn0 10569	. . . 4 class NN0
12	10, 4, 11	wrex 2708	. . 3 wff E. l e. NN0 w : ( 0..^ l ) --> S
13	12, 8	cab 2421	. 2 class { w | E. l e. NN0 w : ( 0..^ l ) --> S }
14	2, 13	wceq 1364	1 wff Word S = { w | E. l e. NN0 w : ( 0..^ l ) --> S }

This definition is referenced by:  iswrd  12223  wrdval  12224  nfwrd  12242  csbwrdg  12243