Theorems · Theorem · order theory
Order.Ideal.isMaximal_iff
∀ {P : Type u_1} [inst : LE P] (I : Order.Ideal P),
I.IsMaximal ↔ I.IsProper ∧ ∀ ⦃J : Order.Ideal P⦄, I < J → ↑J = Set.univ- Defined in
- Mathlib.Order.Ideal
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 27 from the axioms · uses propext, Quot.sound
- Assumes
- LE
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.
- Setstatement · cited by 53,352
- SetLike.coestatement and proof · cited by 8,199
- Set.univstatement and proof · cited by 3,945
- Order.Idealstatement and proof · cited by 102
- Order.Ideal.IsProperstatement and proof · cited by 23
- Order.Ideal.IsMaximalstatement and proof · cited by 8
- Order.Ideal.IsMaximal.casesOnproof · cited by 1
Cited by0
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