Theorems · Theorem · order theory
Order.Ideal.IsMaximal.maximal_proper
∀ {P : Type u_1} {inst : LE P} {I : Order.Ideal P} [self : I.IsMaximal] ⦃J : Order.Ideal P⦄, I < J → ↑J = Set.univThis ideal is maximal in the collection of proper ideals.
- Defined in
- Mathlib.Order.Ideal
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 24 from the axioms · uses propext, Quot.sound
- Assumes
- Order.Ideal.IsMaximal
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
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 · cited by 8,199
- Set.univstatement · cited by 3,945
- Order.Idealstatement and proof · cited by 102
- Order.Ideal.IsMaximalstatement and proof · cited by 8
Cited by1
Results whose statement or proof uses this declaration.
- Order.Ideal.IsMaximal.isCoatomproof · cited by 2