Theorems · Theorem · order theory
ComplementedLattice.exists_isCompl
∀ {α : Type u_2} {inst : Lattice α} {inst_1 : BoundedOrder α} [self : ComplementedLattice α] (a : α), ∃ b, IsCompl a bIn a ComplementedLattice, every element admits a complement.
- Defined in
- Mathlib.Order.Disjoint
- Cited by
- 15 results in Mathlib
- Foundations
- Depth 5 from the axioms · uses no axioms
- Assumes
- ComplementedLattice
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Latticestatement and proof · cited by 916
- IsComplstatement · cited by 351
- BoundedOrderstatement and proof · cited by 270
- ComplementedLatticestatement and proof · cited by 30
Cited by15
Results whose statement or proof uses this declaration.
- OrderIso.complementedLatticeproof · cited by 4
- ComplementedLattice.isStronglyAtomicproof · cited by 2
- IsModularLattice.exists_inf_eq_and_sup_eqproof · cited by 2
- IsSemisimpleModule.extension_propertyproof · cited by 2
- isCoatomic_of_isAtomic_of_complementedLattice_of_isModularproof · cited by 2
- Submodule.le_linearEquiv_of_sSup_eq_topproof · cited by 2
- Disjoint.exists_isComplproof · cited by 1
- jacobson_densityproof · cited by 1
- IsSemisimpleModule.exists_submodule_linearEquiv_quotientproof · cited by 1
- IsSemisimpleModule.lifting_propertyproof · cited by 1
- Module.End.isSemisimple_zeroproof · cited by 0
- Codisjoint.exists_isComplproof · cited by 0