Theorems · Definition · order theory
IsComplemented
{α : Type u_1} → [inst : Lattice α] → [BoundedOrder α] → α → PropAn element is complemented if it has a complement.
- Defined in
- Mathlib.Order.Disjoint
- Cited by
- 22 results in Mathlib
- Foundations
- Depth 4 from the axioms · uses no axioms
- Assumes
- LatticeBoundedOrder
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites3
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Latticestatement and proof · cited by 916
- IsComplproof · cited by 351
- BoundedOrderstatement and proof · cited by 270
Cited by23
Results whose statement or proof uses this declaration.
- Complementedsproof · cited by 12
- Complementeds.coe_injstatement · cited by 2
- IsComplemented.infstatement and proof · cited by 1
- IsComplemented.supstatement and proof · cited by 1
- Complementeds.coe_botstatement · cited by 1
- Complementeds.coe_infstatement · cited by 1
- Complementeds.coe_supstatement · cited by 1
- Complementeds.coe_topstatement · cited by 1
- isComplemented_botstatement · cited by 1
- isComplemented_topstatement · cited by 1
- LinearMap.surjective_comp_subtype_of_isComplementedstatement and proof · cited by 1
- Complementeds.codisjoint_coestatement · cited by 0