Theorems · Theorem · order theory
codisjoint_iff_le_sup
∀ {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
- 15 results in Mathlib
- Foundations
- Depth 6 from the axioms · uses no axioms
- Assumes
- SemilatticeSupOrderTop
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Top.topstatement and proof · cited by 9,680
- SemilatticeSupstatement and proof · cited by 785
- OrderTopstatement and proof · cited by 493
- le_sup_leftproof · cited by 265
- le_sup_rightproof · cited by 242
- Codisjointstatement and proof · cited by 197
- sup_leproof · cited by 159
- LE.le.trans'proof · cited by 140
Cited by15
Results whose statement or proof uses this declaration.
- codisjoint_iffproof · cited by 53
- Codisjoint.top_leproof · cited by 9
- hnot_le_iff_codisjoint_leftproof · cited by 8
- codisjoint_hnot_leftproof · cited by 7
- HasProd.of_nat_of_neg_add_oneproof · cited by 5
- LinearMap.isCompl_of_projproof · cited by 5
- HasSum.of_nat_of_neg_add_oneproof · cited by 5
- Codisjoint.codisjoint_inf_right_of_codisjoint_inf_leftproof · cited by 2
- Subgroup.IsComplement'.isComplproof · cited by 2
- Codisjoint.map_orderIsoproof · cited by 2
- LinearMap.isCompl_range_inl_inrproof · cited by 1
- Concept.codisjoint_extent_intentproof · cited by 1