Definition df-chsup 29246

Description: Define the supremum of a set of Hilbert lattice elements. See chsupval2 29345 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 29274. (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 28869	. 2 class ∨ℋ
2		vx	. . 3 setvar 𝑥
3		chba 28854	. . . . 5 class ℋ
4	3	cpw 4488	. . . 4 class 𝒫 ℋ
5	4	cpw 4488	. . 3 class 𝒫 𝒫 ℋ
6	2	cv 1541	. . . . . 6 class 𝑥
7	6	cuni 4796	. . . . 5 class ∪ 𝑥
8		cort 28865	. . . . 5 class ⊥
9	7, 8	cfv 6339	. . . 4 class (⊥‘∪ 𝑥)
10	9, 8	cfv 6339	. . 3 class (⊥‘(⊥‘∪ 𝑥))
11	2, 5, 10	cmpt 5110	. 2 class (𝑥 ∈ 𝒫 𝒫 ℋ ↦ (⊥‘(⊥‘∪ 𝑥)))
12	1, 11	wceq 1542	1 wff ∨ℋ = (𝑥 ∈ 𝒫 𝒫 ℋ ↦ (⊥‘(⊥‘∪ 𝑥)))

This definition is referenced by:  hsupval  29269