Definition df-chsup 31258

Description: Define the supremum of a set of Hilbert lattice elements. See chsupval2 31357 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 31286. (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 30881	. 2 class ∨ℋ
2		vx	. . 3 setvar 𝑥
3		chba 30866	. . . . 5 class ℋ
4	3	cpw 4580	. . . 4 class 𝒫 ℋ
5	4	cpw 4580	. . 3 class 𝒫 𝒫 ℋ
6	2	cv 1538	. . . . . 6 class 𝑥
7	6	cuni 4887	. . . . 5 class ∪ 𝑥
8		cort 30877	. . . . 5 class ⊥
9	7, 8	cfv 6541	. . . 4 class (⊥‘∪ 𝑥)
10	9, 8	cfv 6541	. . 3 class (⊥‘(⊥‘∪ 𝑥))
11	2, 5, 10	cmpt 5205	. 2 class (𝑥 ∈ 𝒫 𝒫 ℋ ↦ (⊥‘(⊥‘∪ 𝑥)))
12	1, 11	wceq 1539	1 wff ∨ℋ = (𝑥 ∈ 𝒫 𝒫 ℋ ↦ (⊥‘(⊥‘∪ 𝑥)))

This definition is referenced by:  hsupval  31281