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Definition df-chsup 27336
Description: Define the supremum of a set of Hilbert lattice elements. See chsupval2 27435 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 27364. (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 26957 . 2 class
2 vx . . 3 setvar 𝑥
3 chil 26942 . . . . 5 class
43cpw 4011 . . . 4 class 𝒫 ℋ
54cpw 4011 . . 3 class 𝒫 𝒫 ℋ
62cv 1473 . . . . . 6 class 𝑥
76cuni 4270 . . . . 5 class 𝑥
8 cort 26953 . . . . 5 class
97, 8cfv 5694 . . . 4 class (⊥‘ 𝑥)
109, 8cfv 5694 . . 3 class (⊥‘(⊥‘ 𝑥))
112, 5, 10cmpt 4541 . 2 class (𝑥 ∈ 𝒫 𝒫 ℋ ↦ (⊥‘(⊥‘ 𝑥)))
121, 11wceq 1474 1 wff = (𝑥 ∈ 𝒫 𝒫 ℋ ↦ (⊥‘(⊥‘ 𝑥)))
Colors of variables: wff setvar class
This definition is referenced by:  hsupval  27359
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