Theorems · Theorem · order theory
codisjoint_iff
∀ {α : Type u_1} [inst : SemilatticeSup α] [inst_1 : OrderTop α] {a b : α}, Codisjoint a b ↔ a ⊔ b = ⊤- Defined in
- Mathlib.Order.Disjoint
- Cited by
- 53 results in Mathlib
- Foundations
- Depth 9 from the axioms · uses no axioms
- Assumes
- SemilatticeSupOrderTop
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 · cited by 9,680
- SemilatticeSupstatement and proof · cited by 785
- OrderTopstatement and proof · cited by 493
- Codisjointstatement · cited by 197
- top_le_iffproof · cited by 175
- codisjoint_iff_le_supproof · cited by 15
Cited by53
Results whose statement or proof uses this declaration.
- Ideal.isCoprime_iff_sup_eqproof · cited by 10
- IsCompl.of_eqproof · cited by 7
- Ideal.isCoprime_iff_codisjointproof · cited by 6
- Ideal.isCoprime_iff_addproof · cited by 3
- iSupIndep.le_iff_eq_of_iSup_eq_topproof · cited by 3
- LinearMap.isCompl_span_singleton_orthogonalproof · cited by 2
- LinearMap.BilinForm.isCompl_orthogonal_iff_disjointproof · cited by 2
- Module.Dual.isCompl_ker_of_disjoint_of_ne_botproof · cited by 2
- Finsupp.codisjoint_supported_supportedproof · cited by 2
- Submodule.codisjoint_iff_exists_add_eqproof · cited by 2
- iInf_codisjoint_iffproof · cited by 2
- Ideal.isCoprime_iff_gcdproof · cited by 2