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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 28211 for its value and chjcl 28216 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 28214. (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 27790 | . 2 class ∨ℋ | |
2 | vx | . . 3 setvar 𝑥 | |
3 | vy | . . 3 setvar 𝑦 | |
4 | chil 27776 | . . . 4 class ℋ | |
5 | 4 | cpw 4158 | . . 3 class 𝒫 ℋ |
6 | 2 | cv 1482 | . . . . . 6 class 𝑥 |
7 | 3 | cv 1482 | . . . . . 6 class 𝑦 |
8 | 6, 7 | cun 3572 | . . . . 5 class (𝑥 ∪ 𝑦) |
9 | cort 27787 | . . . . 5 class ⊥ | |
10 | 8, 9 | cfv 5888 | . . . 4 class (⊥‘(𝑥 ∪ 𝑦)) |
11 | 10, 9 | cfv 5888 | . . 3 class (⊥‘(⊥‘(𝑥 ∪ 𝑦))) |
12 | 2, 3, 5, 5, 11 | cmpt2 6652 | . 2 class (𝑥 ∈ 𝒫 ℋ, 𝑦 ∈ 𝒫 ℋ ↦ (⊥‘(⊥‘(𝑥 ∪ 𝑦)))) |
13 | 1, 12 | wceq 1483 | 1 wff ∨ℋ = (𝑥 ∈ 𝒫 ℋ, 𝑦 ∈ 𝒫 ℋ ↦ (⊥‘(⊥‘(𝑥 ∪ 𝑦)))) |
Colors of variables: wff setvar class |
This definition is referenced by: sshjval 28209 |
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