Definition df-word 12221

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 12213	. 2 class Word S
3		cc0 9274	. . . . . 6 class 0
4		vl	. . . . . . 7 setvar l
5	4	cv 1368	. . . . . 6 class l
6		cfzo 11540	. . . . . 6 class ..^
7	3, 5, 6	co 6086	. . . . 5 class ( 0..^ l )
8		vw	. . . . . 6 setvar w
9	8	cv 1368	. . . . 5 class w
10	7, 1, 9	wf 5409	. . . 4 wff w : ( 0..^ l ) --> S
11		cn0 10571	. . . 4 class NN0
12	10, 4, 11	wrex 2711	. . 3 wff E. l e. NN0 w : ( 0..^ l ) --> S
13	12, 8	cab 2424	. 2 class { w | E. l e. NN0 w : ( 0..^ l ) --> S }
14	2, 13	wceq 1369	1 wff Word S = { w | E. l e. NN0 w : ( 0..^ l ) --> S }

This definition is referenced by:  iswrd  12229  wrdval  12230  nfwrd  12248  csbwrdg  12249