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

Definition df-chj 29071
 Description: Define Hilbert lattice join. See chjval 29113 for its value and chjcl 29118 for its closure law. Note that we define it over all Hilbert space subsets to allow proving more general theorems. Even for general subsets the join belongs to Cℋ; see sshjcl 29116. (Contributed by NM, 1-Nov-2000.) (New usage is discouraged.)
Assertion
Ref Expression
df-chj = (𝑥 ∈ 𝒫 ℋ, 𝑦 ∈ 𝒫 ℋ ↦ (⊥‘(⊥‘(𝑥𝑦))))
Distinct variable group:   𝑥,𝑦

Detailed syntax breakdown of Definition df-chj
StepHypRef Expression
1 chj 28694 . 2 class
2 vx . . 3 setvar 𝑥
3 vy . . 3 setvar 𝑦
4 chba 28680 . . . 4 class
54cpw 4512 . . 3 class 𝒫 ℋ
62cv 1537 . . . . . 6 class 𝑥
73cv 1537 . . . . . 6 class 𝑦
86, 7cun 3908 . . . . 5 class (𝑥𝑦)
9 cort 28691 . . . . 5 class
108, 9cfv 6328 . . . 4 class (⊥‘(𝑥𝑦))
1110, 9cfv 6328 . . 3 class (⊥‘(⊥‘(𝑥𝑦)))
122, 3, 5, 5, 11cmpo 7132 . 2 class (𝑥 ∈ 𝒫 ℋ, 𝑦 ∈ 𝒫 ℋ ↦ (⊥‘(⊥‘(𝑥𝑦))))
131, 12wceq 1538 1 wff = (𝑥 ∈ 𝒫 ℋ, 𝑦 ∈ 𝒫 ℋ ↦ (⊥‘(⊥‘(𝑥𝑦))))
 Colors of variables: wff setvar class This definition is referenced by:  sshjval  29111
 Copyright terms: Public domain W3C validator