Theorems · Theorem · order theory
Codisjoint.eq_top
∀ {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
- 22 results in Mathlib
- Foundations
- Depth 8 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_uniqueproof · cited by 102
- Codisjoint.top_leproof · cited by 9
Cited by22
Results whose statement or proof uses this declaration.
- IsCompl.sup_eq_topproof · cited by 20
- Codisjoint.himp_eq_rightproof · cited by 4
- Disjoint.le_of_codisjointproof · cited by 3
- Codisjoint.codisjoint_inf_right_of_codisjoint_inf_leftproof · cited by 2
- NumberField.Ideal.primesOverSpanEquivMonicFactorsMod_symm_apply_eq_spanproof · cited by 2
- hnot_sup_selfproof · cited by 2
- Codisjoint.le_of_disjointproof · cited by 2
- sup_hnot_selfproof · cited by 2
- Submodule.finrank_add_eq_of_isComplproof · cited by 2
- IsModularLattice.exists_inf_eq_and_sup_eqproof · cited by 2
- Submodule.FG.cofg_of_codisjointproof · cited by 1