Theorems · Theorem · order theory
isSimpleOrder_iff
∀ (α : Type u_4) [inst : LE α] [inst_1 : BoundedOrder α], IsSimpleOrder α ↔ Nontrivial α ∧ ∀ (a : α), a = ⊥ ∨ a = ⊤
- Defined in
- Mathlib.Order.Atoms
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 6 from the axioms · uses no axioms
- Assumes
- LEBoundedOrder
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
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
- Bot.botstatement and proof · cited by 4,720
- Nontrivialstatement and proof · cited by 2,416
- BoundedOrderstatement and proof · cited by 270
- IsSimpleOrderstatement and proof · cited by 54
- IsSimpleOrder.casesOnproof · cited by 1
Cited by1
Results whose statement or proof uses this declaration.
- Order.krullDim_eq_one_iff_of_boundedOrderproof · cited by 2