Definition df-chsup 28170

Description: Define the supremum of a set of Hilbert lattice elements. See chsupval2 28269 for its value. We actually define the supremum for an arbitrary collection of Hilbert space subsets, not just elements of the Hilbert lattice CH, to allow more general theorems. Even for general subsets the supremum still a Hilbert lattice element; see hsupcl 28198. (Contributed by NM, 9-Dec-2003.) (New usage is discouraged.)

Assertion

Ref	Expression
df-chsup	|- \/H = ( x e. ~P ~P ~H |-> ( _|_ ` ( _|_ ` U. x ) ) )

Detailed syntax breakdown of Definition df-chsup

Step	Hyp	Ref	Expression
1		chsup 27791	. 2 class \/H
2		vx	. . 3 setvar x
3		chil 27776	. . . . 5 class ~H
4	3	cpw 4158	. . . 4 class ~P ~H
5	4	cpw 4158	. . 3 class ~P ~P ~H
6	2	cv 1482	. . . . . 6 class x
7	6	cuni 4436	. . . . 5 class U. x
8		cort 27787	. . . . 5 class _|_
9	7, 8	cfv 5888	. . . 4 class ( _|_ ` U. x )
10	9, 8	cfv 5888	. . 3 class ( _|_ ` ( _|_ ` U. x ) )
11	2, 5, 10	cmpt 4729	. 2 class ( x e. ~P ~P ~H |-> ( _|_ ` ( _|_ ` U. x ) ) )
12	1, 11	wceq 1483	1 wff \/H = ( x e. ~P ~P ~H |-> ( _|_ ` ( _|_ ` U. x ) ) )

This definition is referenced by:  hsupval  28193