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Definition df-chsup 28471
Description: Define the supremum of a set of Hilbert lattice elements. See chsupval2 28570 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 28499. (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 28092 . 2 class
2 vx . . 3 setvar 𝑥
3 chil 28077 . . . . 5 class
43cpw 4294 . . . 4 class 𝒫 ℋ
54cpw 4294 . . 3 class 𝒫 𝒫 ℋ
62cv 1623 . . . . . 6 class 𝑥
76cuni 4580 . . . . 5 class 𝑥
8 cort 28088 . . . . 5 class
97, 8cfv 6041 . . . 4 class (⊥‘ 𝑥)
109, 8cfv 6041 . . 3 class (⊥‘(⊥‘ 𝑥))
112, 5, 10cmpt 4873 . 2 class (𝑥 ∈ 𝒫 𝒫 ℋ ↦ (⊥‘(⊥‘ 𝑥)))
121, 11wceq 1624 1 wff = (𝑥 ∈ 𝒫 𝒫 ℋ ↦ (⊥‘(⊥‘ 𝑥)))
Colors of variables: wff setvar class
This definition is referenced by:  hsupval  28494
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