Theorems · Inductive type · order theory
Order.Ideal.IsProper
{P : Type u_1} → [inst : LE P] → Order.Ideal P → PropA proper ideal is one that is not the whole set. Note that the whole set might not be an ideal.
- Defined in
- Mathlib.Order.Ideal
- Cited by
- 23 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 by29
Results whose statement or proof uses this declaration.
- Order.Ideal.IsProper.ne_topstatement and proof · cited by 2
- Order.Ideal.isProper_iff_top_notMemstatement · cited by 2
- Order.Ideal.isProper_of_ne_topstatement · cited by 2
- Order.Ideal.isProper_of_notMemstatement · cited by 2
- Order.Ideal.IsMaximal.casesOnstatement and proof · cited by 1
- Order.Ideal.IsPrime.casesOnstatement and proof · cited by 1
- Order.Ideal.IsPrime.of_mem_or_memstatement and proof · cited by 1
- Order.Ideal.IsProper.casesOnstatement and proof · cited by 1
- Order.Ideal.IsProper.exists_le_maximalstatement and proof · cited by 1
- Order.Ideal.IsProper.ne_univstatement and proof · cited by 1
- Order.Ideal.IsProper.notMem_of_compl_memstatement and proof · cited by 1
- Order.Ideal.IsProper.top_notMemstatement · cited by 1