Theorems · Theorem · order theory
IsCoatom.lt_iff
∀ {α : Type u_2} [inst : PartialOrder α] [inst_1 : OrderTop α] {a x : α}, IsCoatom a → (a < x ↔ x = ⊤)- Defined in
- Mathlib.Order.Atoms
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 16 from the axioms · uses Quot.sound
- Assumes
- PartialOrderOrderTop
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
- PartialOrderstatement and proof · cited by 6,410
- OrderTopstatement and proof · cited by 493
- IsCoatomstatement and proof · cited by 114
- IsCoatom.dualproof · cited by 6
- IsAtom.lt_iffproof · cited by 5
Cited by1
Results whose statement or proof uses this declaration.
- IsCoatom.lt_topproof · cited by 1