Definition df-word 12350

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 12342	. 2 class Word S
3		cc0 9396	. . . . . 6 class 0
4		vl	. . . . . . 7 setvar l
5	4	cv 1369	. . . . . 6 class l
6		cfzo 11668	. . . . . 6 class ..^
7	3, 5, 6	co 6203	. . . . 5 class ( 0..^ l )
8		vw	. . . . . 6 setvar w
9	8	cv 1369	. . . . 5 class w
10	7, 1, 9	wf 5525	. . . 4 wff w : ( 0..^ l ) --> S
11		cn0 10693	. . . 4 class NN0
12	10, 4, 11	wrex 2800	. . 3 wff E. l e. NN0 w : ( 0..^ l ) --> S
13	12, 8	cab 2439	. 2 class { w | E. l e. NN0 w : ( 0..^ l ) --> S }
14	2, 13	wceq 1370	1 wff Word S = { w | E. l e. NN0 w : ( 0..^ l ) --> S }

This definition is referenced by:  iswrd  12358  wrdval  12359  nfwrd  12377  csbwrdg  12378