Definition df-chsup 31120

Description: Define the supremum of a set of Hilbert lattice elements. See chsupval2 31219 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 31148. (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 30743	. 2 class ∨ℋ
2		vx	. . 3 setvar 𝑥
3		chba 30728	. . . . 5 class ℋ
4	3	cpw 4603	. . . 4 class 𝒫 ℋ
5	4	cpw 4603	. . 3 class 𝒫 𝒫 ℋ
6	2	cv 1533	. . . . . 6 class 𝑥
7	6	cuni 4908	. . . . 5 class ∪ 𝑥
8		cort 30739	. . . . 5 class ⊥
9	7, 8	cfv 6548	. . . 4 class (⊥‘∪ 𝑥)
10	9, 8	cfv 6548	. . 3 class (⊥‘(⊥‘∪ 𝑥))
11	2, 5, 10	cmpt 5231	. 2 class (𝑥 ∈ 𝒫 𝒫 ℋ ↦ (⊥‘(⊥‘∪ 𝑥)))
12	1, 11	wceq 1534	1 wff ∨ℋ = (𝑥 ∈ 𝒫 𝒫 ℋ ↦ (⊥‘(⊥‘∪ 𝑥)))

This definition is referenced by:  hsupval  31143