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

Definition df-at 29537
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 29538 and elat2 29539 for membership relations. (Contributed by NM, 14-Aug-2002.) (New usage is discouraged.)
Assertion
Ref Expression
df-at HAtoms = {𝑥C ∣ 0 𝑥}

Detailed syntax breakdown of Definition df-at
StepHypRef Expression
1 cat 28162 . 2 class HAtoms
2 c0h 28132 . . . 4 class 0
3 vx . . . . 5 setvar 𝑥
43cv 1630 . . . 4 class 𝑥
5 ccv 28161 . . . 4 class
62, 4, 5wbr 4786 . . 3 wff 0 𝑥
7 cch 28126 . . 3 class C
86, 3, 7crab 3065 . 2 class {𝑥C ∣ 0 𝑥}
91, 8wceq 1631 1 wff HAtoms = {𝑥C ∣ 0 𝑥}
Colors of variables: wff setvar class
This definition is referenced by:  ela  29538  atssch  29542
  Copyright terms: Public domain W3C validator