Theorems · Theorem · order theory
isCompl_iff
∀ {α : Type u_1} [inst : PartialOrder α] [inst_1 : BoundedOrder α] {a b : α},
IsCompl a b ↔ Disjoint a b ∧ Codisjoint a b- Defined in
- Mathlib.Order.Disjoint
- Cited by
- 8 results in Mathlib
- Foundations
- Depth 5 from the axioms · uses no axioms
- Assumes
- PartialOrderBoundedOrder
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.
- PartialOrderstatement and proof · cited by 6,410
- Disjointstatement and proof · cited by 2,201
- IsComplstatement and proof · cited by 351
- BoundedOrderstatement and proof · cited by 270
- Codisjointstatement and proof · cited by 197
- IsCompl.disjointproof · cited by 42
- IsCompl.codisjointproof · cited by 32
Cited by8
Results whose statement or proof uses this declaration.
- CompleteSublattice.isCompl_iffproof · cited by 1
- symmDiff_eq_topproof · cited by 0
- Subspace.isCompl_dualAnnihilatorproof · cited by 0
- Set.Icc.isCompl_iffproof · cited by 0
- bihimp_eq_botproof · cited by 0
- Set.Ici.isCompl_iffproof · cited by 0
- Set.Iic.isCompl_iffproof · cited by 0
- Prop.isCompl_iffproof · cited by 0