Theorems · Theorem · order theory
isAtom_iff_eq_top
∀ {α : Type u_2} [inst : PartialOrder α] [inst_1 : BoundedOrder α] [IsSimpleOrder α] {a : α}, IsAtom a ↔ a = ⊤- Defined in
- Mathlib.Order.Atoms
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 11 from the axioms · uses no axioms
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Top.topstatement and proof · cited by 9,680
- PartialOrderstatement and proof · cited by 6,410
- BoundedOrderstatement and proof · cited by 270
- IsAtomstatement and proof · cited by 130
- IsSimpleOrderstatement and proof · cited by 54
- IsSimpleOrder.eq_bot_or_eq_topproof · cited by 32
- isAtom_topproof · cited by 5
Cited by3
Results whose statement or proof uses this declaration.
- LieAlgebra.IsSimple.isAtom_iff_eq_topproof · cited by 0
- IsIsotypicOfType.of_isSimpleModuleproof · cited by 0
- LieAlgebra.IsSimple.eq_top_of_isAtomproof · cited by 0