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Definition df-chsup 31120
Description: Define the supremum of a set of Hilbert lattice elements. See chsupval2 31219 for its value. We actually define the supremum for an arbitrary collection of Hilbert space subsets, not just elements of the Hilbert lattice C, to allow more general theorems. Even for general subsets the supremum still a Hilbert lattice element; see hsupcl 31148. (Contributed by NM, 9-Dec-2003.) (New usage is discouraged.)
Assertion
Ref Expression
df-chsup = (𝑥 ∈ 𝒫 𝒫 ℋ ↦ (⊥‘(⊥‘ 𝑥)))

Detailed syntax breakdown of Definition df-chsup
StepHypRef Expression
1 chsup 30743 . 2 class
2 vx . . 3 setvar 𝑥
3 chba 30728 . . . . 5 class
43cpw 4603 . . . 4 class 𝒫 ℋ
54cpw 4603 . . 3 class 𝒫 𝒫 ℋ
62cv 1533 . . . . . 6 class 𝑥
76cuni 4908 . . . . 5 class 𝑥
8 cort 30739 . . . . 5 class
97, 8cfv 6548 . . . 4 class (⊥‘ 𝑥)
109, 8cfv 6548 . . 3 class (⊥‘(⊥‘ 𝑥))
112, 5, 10cmpt 5231 . 2 class (𝑥 ∈ 𝒫 𝒫 ℋ ↦ (⊥‘(⊥‘ 𝑥)))
121, 11wceq 1534 1 wff = (𝑥 ∈ 𝒫 𝒫 ℋ ↦ (⊥‘(⊥‘ 𝑥)))
Colors of variables: wff setvar class
This definition is referenced by:  hsupval  31143
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