Hilbert Space Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  HSE Home  >  Th. List  >  df-chsup Structured version   Visualization version   GIF version

Definition df-chsup 28154
 Description: Define the supremum of a set of Hilbert lattice elements. See chsupval2 28253 for its value. We actually define the supremum for an arbitrary collection of Hilbert space subsets, not just elements of the Hilbert lattice Cℋ, to allow more general theorems. Even for general subsets the supremum still a Hilbert lattice element; see hsupcl 28182. (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 27775 . 2 class
2 vx . . 3 setvar 𝑥
3 chil 27760 . . . . 5 class
43cpw 4156 . . . 4 class 𝒫 ℋ
54cpw 4156 . . 3 class 𝒫 𝒫 ℋ
62cv 1481 . . . . . 6 class 𝑥
76cuni 4434 . . . . 5 class 𝑥
8 cort 27771 . . . . 5 class
97, 8cfv 5886 . . . 4 class (⊥‘ 𝑥)
109, 8cfv 5886 . . 3 class (⊥‘(⊥‘ 𝑥))
112, 5, 10cmpt 4727 . 2 class (𝑥 ∈ 𝒫 𝒫 ℋ ↦ (⊥‘(⊥‘ 𝑥)))
121, 11wceq 1482 1 wff = (𝑥 ∈ 𝒫 𝒫 ℋ ↦ (⊥‘(⊥‘ 𝑥)))
 Colors of variables: wff setvar class This definition is referenced by:  hsupval  28177
 Copyright terms: Public domain W3C validator