Theorems · Inductive type · order theory
IsSimpleOrder
(α : Type u_4) → [inst : LE α] → [BoundedOrder α] → Prop
An order is simple iff it has exactly two elements, ⊥ and ⊤.
- Defined in
- Mathlib.Order.Atoms
- Cited by
- 54 results in Mathlib
- Foundations
- Depth 2 from the axioms · uses no axioms
- Assumes
- LEBoundedOrder
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites1
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- BoundedOrderstatement · cited by 270
Cited by71
Results whose statement or proof uses this declaration.
- IsSimpleOrder.eq_bot_or_eq_topstatement and proof · cited by 32
- IsSimpleModule.congrproof · cited by 15
- isSimpleModule_iffstatement and proof · cited by 12
- OrderIso.isSimpleOrder_iffstatement and proof · cited by 12
- Representation.IsIrreducibleproof · cited by 10
- isSimpleModule_iff_isAtomproof · cited by 7
- isSimpleModule_iff_isCoatomproof · cited by 6
- isAtom_topstatement and proof · cited by 5
- LieModule.IsIrreducibleproof · cited by 5
- Module.length_eq_one_iffproof · cited by 4
- MulAction.isCoatom_stabilizer_iff_preprimitiveproof · cited by 4
- IsSimpleOrder.equivBoolstatement and proof · cited by 4