Theorems · Inductive type · order theory
Order.Ideal.IsMaximal
{P : Type u_1} → [inst : LE P] → Order.Ideal P → PropAn ideal is maximal if it is maximal in the collection of proper ideals.
Note that IsCoatom is less general because ideals only have a top element when P is directed
and nonempty.
- Defined in
- Mathlib.Order.Ideal
- Cited by
- 8 results in Mathlib
- Foundations
- Depth 2 from the axioms · uses no axioms
- Assumes
- LE
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites1
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Order.Idealstatement · cited by 102
Cited by10
Results whose statement or proof uses this declaration.
- Order.Ideal.IsMaximal.isCoatomstatement and proof · cited by 2
- Order.Ideal.IsMaximal.casesOnstatement and proof · cited by 1
- IsCoatom.isMaximalstatement · cited by 1
- Order.Ideal.IsMaximal.maximal_properstatement and proof · cited by 1
- Order.Ideal.IsProper.exists_le_maximalstatement · cited by 1
- Order.Ideal.isMaximal_iff_isCoatomstatement and proof · cited by 1
- Order.Ideal.exists_maximalstatement and proof · cited by 0
- Order.Ideal.IsMaximal.isCoatom'statement and proof · cited by 0
- Order.Ideal.IsMaximal.recOnstatement and proof · cited by 0
- Order.Ideal.isMaximal_iffstatement and proof · cited by 0