Theorems · Theorem · order theory
covBy_top_iff
∀ {α : Type u_2} [inst : PartialOrder α] [inst_1 : OrderTop α] {a : α}, a ⋖ ⊤ ↔ IsCoatom a- Defined in
- Mathlib.Order.Atoms
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 15 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- PartialOrderOrderTop
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.
- Top.topstatement · cited by 9,680
- PartialOrderstatement and proof · cited by 6,410
- OrderTopstatement and proof · cited by 493
- CovBystatement · cited by 290
- IsCoatomstatement · cited by 114
- bot_covBy_iffproof · cited by 4
- toDual_covBy_toDual_iffproof · cited by 4
Cited by4
Results whose statement or proof uses this declaration.
- Submodule.isCompl_span_singleton_of_isCoatom_of_notMemproof · cited by 1
- CovBy.isCoatomproof · cited by 0
- IsCoatom.covBy_topproof · cited by 0
- Set.Iic.isCoatom_iffproof · cited by 0