Definition df-pmap 34790

Description: Define projective map for k at a. Definition in Theorem 15.5 of [MaedaMaeda] p. 62. (Contributed by NM, 2-Oct-2011.)

Assertion

Ref	Expression
df-pmap	|- pmap = ( k e. _V |-> ( a e. ( Base ` k ) |-> { p e. ( Atoms ` k ) | p ( le ` k ) a } ) )

Distinct variable group:   k, a, p

Detailed syntax breakdown of Definition df-pmap

Step	Hyp	Ref	Expression
1		cpmap 34783	. 2 class pmap
2		vk	. . 3 setvar k
3		cvv 3200	. . 3 class _V
4		va	. . . 4 setvar a
5	2	cv 1482	. . . . 5 class k
6		cbs 15857	. . . . 5 class Base
7	5, 6	cfv 5888	. . . 4 class ( Base ` k )
8		vp	. . . . . . 7 setvar p
9	8	cv 1482	. . . . . 6 class p
10	4	cv 1482	. . . . . 6 class a
11		cple 15948	. . . . . . 7 class le
12	5, 11	cfv 5888	. . . . . 6 class ( le ` k )
13	9, 10, 12	wbr 4653	. . . . 5 wff p ( le ` k ) a
14		catm 34550	. . . . . 6 class Atoms
15	5, 14	cfv 5888	. . . . 5 class ( Atoms ` k )
16	13, 8, 15	crab 2916	. . . 4 class { p e. ( Atoms ` k ) | p ( le ` k ) a }
17	4, 7, 16	cmpt 4729	. . 3 class ( a e. ( Base ` k ) |-> { p e. ( Atoms ` k ) | p ( le ` k ) a } )
18	2, 3, 17	cmpt 4729	. 2 class ( k e. _V |-> ( a e. ( Base ` k ) |-> { p e. ( Atoms ` k ) | p ( le ` k ) a } ) )
19	1, 18	wceq 1483	1 wff pmap = ( k e. _V |-> ( a e. ( Base ` k ) |-> { p e. ( Atoms ` k ) | p ( le ` k ) a } ) )

This definition is referenced by:  pmapfval  35042