Definition df-chsup 31943

Description: Define the supremum of a set of Hilbert lattice elements. See chsupval2 32042 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 31971. (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 31566	. 2 class ∨ℋ
2		vx	. . 3 setvar 𝑥
3		chba 31551	. . . . 5 class ℋ
4	3	cpw 4560	. . . 4 class 𝒫 ℋ
5	4	cpw 4560	. . 3 class 𝒫 𝒫 ℋ
6	2	cv 1569	. . . . . 6 class 𝑥
7	6	cuni 4870	. . . . 5 class ∪ 𝑥
8		cort 31562	. . . . 5 class ⊥
9	7, 8	cfv 6558	. . . 4 class (⊥‘∪ 𝑥)
10	9, 8	cfv 6558	. . 3 class (⊥‘(⊥‘∪ 𝑥))
11	2, 5, 10	cmpt 5189	. 2 class (𝑥 ∈ 𝒫 𝒫 ℋ ↦ (⊥‘(⊥‘∪ 𝑥)))
12	1, 11	wceq 1570	1 wff ∨ℋ = (𝑥 ∈ 𝒫 𝒫 ℋ ↦ (⊥‘(⊥‘∪ 𝑥)))

This definition is used by:  hsupval  31966