Definition df-chsup 31240

Description: Define the supremum of a set of Hilbert lattice elements. See chsupval2 31339 for its value. We actually define the supremum for an arbitrary collection of Hilbert space subsets, not just elements of the Hilbert lattice C_ℋ, to allow more general theorems. Even for general subsets the supremum still a Hilbert lattice element; see hsupcl 31268. (Contributed by NM, 9-Dec-2003.) (New usage is discouraged.)

Assertion

Ref	Expression
df-chsup	⊢ ∨ℋ = (𝑥 ∈ 𝒫 𝒫 ℋ ↦ (⊥‘(⊥‘∪ 𝑥)))

Detailed syntax breakdown of Definition df-chsup

Step	Hyp	Ref	Expression
1		chsup 30863	. 2 class ∨ℋ
2		vx	. . 3 setvar 𝑥
3		chba 30848	. . . . 5 class ℋ
4	3	cpw 4563	. . . 4 class 𝒫 ℋ
5	4	cpw 4563	. . 3 class 𝒫 𝒫 ℋ
6	2	cv 1539	. . . . . 6 class 𝑥
7	6	cuni 4871	. . . . 5 class ∪ 𝑥
8		cort 30859	. . . . 5 class ⊥
9	7, 8	cfv 6511	. . . 4 class (⊥‘∪ 𝑥)
10	9, 8	cfv 6511	. . 3 class (⊥‘(⊥‘∪ 𝑥))
11	2, 5, 10	cmpt 5188	. 2 class (𝑥 ∈ 𝒫 𝒫 ℋ ↦ (⊥‘(⊥‘∪ 𝑥)))
12	1, 11	wceq 1540	1 wff ∨ℋ = (𝑥 ∈ 𝒫 𝒫 ℋ ↦ (⊥‘(⊥‘∪ 𝑥)))

This definition is referenced by:  hsupval  31263