Definition df-tail 17231

Description: Define the tail function for directed sets. (Contributed by Jeff Hankins, 25-Nov-2009.)

Assertion

Ref	Expression
df-tail	|- tail = ( r e. DirRel |-> ( x e. U. U. r |-> ( r " { x } ) ) )

Distinct variable group:   x, r

Detailed syntax breakdown of Definition df-tail

Step	Hyp	Ref	Expression
1		ctail 17229	. 2 class tail
2		vr	. . 3 setvar r
3		cdir 17228	. . 3 class DirRel
4		vx	. . . 4 setvar x
5	2	cv 1482	. . . . . 6 class r
6	5	cuni 4436	. . . . 5 class U. r
7	6	cuni 4436	. . . 4 class U. U. r
8	4	cv 1482	. . . . . 6 class x
9	8	csn 4177	. . . . 5 class { x }
10	5, 9	cima 5117	. . . 4 class ( r " { x } )
11	4, 7, 10	cmpt 4729	. . 3 class ( x e. U. U. r |-> ( r " { x } ) )
12	2, 3, 11	cmpt 4729	. 2 class ( r e. DirRel |-> ( x e. U. U. r |-> ( r " { x } ) ) )
13	1, 12	wceq 1483	1 wff tail = ( r e. DirRel |-> ( x e. U. U. r |-> ( r " { x } ) ) )

This definition is referenced by:  tailfval  32367