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Mirrors > Home > HSE Home > Th. List > df-chj | Structured version Visualization version GIF version |
Description: Define Hilbert lattice join. See chjval 29460 for its value and chjcl 29465 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 29463. (Contributed by NM, 1-Nov-2000.) (New usage is discouraged.) |
Ref | Expression |
---|---|
df-chj | ⊢ ∨ℋ = (𝑥 ∈ 𝒫 ℋ, 𝑦 ∈ 𝒫 ℋ ↦ (⊥‘(⊥‘(𝑥 ∪ 𝑦)))) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | chj 29041 | . 2 class ∨ℋ | |
2 | vx | . . 3 setvar 𝑥 | |
3 | vy | . . 3 setvar 𝑦 | |
4 | chba 29027 | . . . 4 class ℋ | |
5 | 4 | cpw 4528 | . . 3 class 𝒫 ℋ |
6 | 2 | cv 1542 | . . . . . 6 class 𝑥 |
7 | 3 | cv 1542 | . . . . . 6 class 𝑦 |
8 | 6, 7 | cun 3879 | . . . . 5 class (𝑥 ∪ 𝑦) |
9 | cort 29038 | . . . . 5 class ⊥ | |
10 | 8, 9 | cfv 6398 | . . . 4 class (⊥‘(𝑥 ∪ 𝑦)) |
11 | 10, 9 | cfv 6398 | . . 3 class (⊥‘(⊥‘(𝑥 ∪ 𝑦))) |
12 | 2, 3, 5, 5, 11 | cmpo 7234 | . 2 class (𝑥 ∈ 𝒫 ℋ, 𝑦 ∈ 𝒫 ℋ ↦ (⊥‘(⊥‘(𝑥 ∪ 𝑦)))) |
13 | 1, 12 | wceq 1543 | 1 wff ∨ℋ = (𝑥 ∈ 𝒫 ℋ, 𝑦 ∈ 𝒫 ℋ ↦ (⊥‘(⊥‘(𝑥 ∪ 𝑦)))) |
Colors of variables: wff setvar class |
This definition is referenced by: sshjval 29458 |
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