Definition df-chsup 31343

Description: Define the supremum of a set of Hilbert lattice elements. See chsupval2 31442 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 31371. (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 30966	. 2 class ∨ℋ
2		vx	. . 3 setvar 𝑥
3		chba 30951	. . . . 5 class ℋ
4	3	cpw 4622	. . . 4 class 𝒫 ℋ
5	4	cpw 4622	. . 3 class 𝒫 𝒫 ℋ
6	2	cv 1536	. . . . . 6 class 𝑥
7	6	cuni 4931	. . . . 5 class ∪ 𝑥
8		cort 30962	. . . . 5 class ⊥
9	7, 8	cfv 6573	. . . 4 class (⊥‘∪ 𝑥)
10	9, 8	cfv 6573	. . 3 class (⊥‘(⊥‘∪ 𝑥))
11	2, 5, 10	cmpt 5249	. 2 class (𝑥 ∈ 𝒫 𝒫 ℋ ↦ (⊥‘(⊥‘∪ 𝑥)))
12	1, 11	wceq 1537	1 wff ∨ℋ = (𝑥 ∈ 𝒫 𝒫 ℋ ↦ (⊥‘(⊥‘∪ 𝑥)))

This definition is referenced by:  hsupval  31366