Theorems · Theorem · order theory
Order.Ideal.isProper_iff_top_notMem
∀ {P : Type u_1} [inst : LE P] [inst_1 : OrderTop P] {I : Order.Ideal P}, I.IsProper ↔ ⊤ ∉ I- Defined in
- Mathlib.Order.Ideal
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 27 from the axioms · uses propext, Quot.sound
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
- OrderTopstatement and proof · cited by 493
- Order.Idealstatement and proof · cited by 102
- Order.Ideal.IsProperstatement · cited by 23
- Order.Ideal.top_mem_iff_eq_topproof · cited by 3
- Order.Ideal.isProper_iff_ne_topproof · cited by 1
Cited by2
Results whose statement or proof uses this declaration.
- Order.Ideal.isProper_principal_iffproof · cited by 1
- Order.Ideal.IsProper.top_notMemproof · cited by 1