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Mirrors > Home > HSE Home > Th. List > df-at | Structured version Visualization version GIF version |
Description: Define the set of atoms in a Hilbert lattice. An atom is a nonzero element of a lattice such that anything less than it is zero, i.e. it is the smallest nonzero element of the lattice. Definition of atom in [Kalmbach] p. 15. See ela 30695 and elat2 30696 for membership relations. (Contributed by NM, 14-Aug-2002.) (New usage is discouraged.) |
Ref | Expression |
---|---|
df-at | ⊢ HAtoms = {𝑥 ∈ Cℋ ∣ 0ℋ ⋖ℋ 𝑥} |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | cat 29321 | . 2 class HAtoms | |
2 | c0h 29291 | . . . 4 class 0ℋ | |
3 | vx | . . . . 5 setvar 𝑥 | |
4 | 3 | cv 1541 | . . . 4 class 𝑥 |
5 | ccv 29320 | . . . 4 class ⋖ℋ | |
6 | 2, 4, 5 | wbr 5079 | . . 3 wff 0ℋ ⋖ℋ 𝑥 |
7 | cch 29285 | . . 3 class Cℋ | |
8 | 6, 3, 7 | crab 3070 | . 2 class {𝑥 ∈ Cℋ ∣ 0ℋ ⋖ℋ 𝑥} |
9 | 1, 8 | wceq 1542 | 1 wff HAtoms = {𝑥 ∈ Cℋ ∣ 0ℋ ⋖ℋ 𝑥} |
Colors of variables: wff setvar class |
This definition is referenced by: ela 30695 atssch 30699 |
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