Theorems · Theorem · order theory
Order.Ideal.IsProper.exists_le_maximal
∀ {P : Type u_1} [inst : LE P] [OrderTop P] {I : Order.Ideal P}, I.IsProper → ∃ J, I ≤ J ∧ J.IsMaximalEvery proper ideal is contained in some maximal ideal.
- Defined in
- Mathlib.Order.Ideal
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 72 from the axioms · uses propext, Classical.choice, Quot.sound
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.topproof · cited by 9,680
- OrderTopstatement and proof · cited by 493
- IsCoatomproof · cited by 114
- Order.Idealstatement and proof · cited by 102
- Order.Ideal.IsProperstatement and proof · cited by 23
- IsCoatomic.eq_top_or_exists_le_coatomproof · cited by 9
- Order.Ideal.IsMaximalstatement · cited by 8
- Order.Ideal.isMaximal_iff_isCoatomproof · cited by 1
Cited by1
Results whose statement or proof uses this declaration.
- Order.Ideal.exists_maximalproof · cited by 0