Definition df-chsup 31895

Description: Define the supremum of a set of Hilbert lattice elements. See chsupval2 31994 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 31923. (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 31518	. 2 class ∨ℋ
2		vx	. . 3 setvar 𝑥
3		chba 31503	. . . . 5 class ℋ
4	3	cpw 4557	. . . 4 class 𝒫 ℋ
5	4	cpw 4557	. . 3 class 𝒫 𝒫 ℋ
6	2	cv 1569	. . . . . 6 class 𝑥
7	6	cuni 4867	. . . . 5 class ∪ 𝑥
8		cort 31514	. . . . 5 class ⊥
9	7, 8	cfv 6531	. . . 4 class (⊥‘∪ 𝑥)
10	9, 8	cfv 6531	. . 3 class (⊥‘(⊥‘∪ 𝑥))
11	2, 5, 10	cmpt 5186	. 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  31918