Theorems · Theorem · order theory
IsCoatom.le_iff_eq
∀ {α : Type u_2} [inst : PartialOrder α] [inst_1 : OrderTop α] {a b : α}, IsCoatom a → b ≠ ⊤ → (a ≤ b ↔ b = a)- Defined in
- Mathlib.Order.Atoms
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 16 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.
Cites6
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
- PartialOrderstatement and proof · cited by 6,410
- OrderTopstatement and proof · cited by 493
- IsCoatomstatement and proof · cited by 114
- IsAtom.le_iff_eqproof · cited by 8
- IsCoatom.dualproof · cited by 6
Cited by4
Results whose statement or proof uses this declaration.
- Ideal.comap_map_eq_self_of_isMaximalproof · cited by 2
- Ideal.mem_primesOver_iff_mem_normalizedFactorsproof · cited by 2
- Ideal.under_map_eq_map_underproof · cited by 1
- Ideal.liesOver_iff_dvd_mapproof · cited by 1