Theorems · Inductive type · order theory
Order.Ideal.IsPrime
{P : Type u_1} → [inst : Preorder P] → Order.Ideal P → PropAn ideal I is prime if its complement is a filter.
- Defined in
- Mathlib.Order.PrimeIdeal
- Cited by
- 11 results in Mathlib
- Foundations
- Depth 2 from the axioms · uses no axioms
- Assumes
- Preorder
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites2
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Preorderstatement · cited by 7,952
- Order.Idealstatement · cited by 102
Cited by14
Results whose statement or proof uses this declaration.
- Order.Ideal.IsPrime.mem_or_compl_memstatement and proof · cited by 2
- Order.Ideal.IsPrime.mem_or_memstatement and proof · cited by 2
- Order.Ideal.isPrime_iff_mem_or_memstatement · cited by 1
- Order.Ideal.isPrime_of_mem_or_compl_memstatement · cited by 1
- Order.Ideal.IsPrime.casesOnstatement and proof · cited by 1
- Order.Ideal.IsPrime.compl_filterstatement and proof · cited by 1
- Order.Ideal.IsPrime.of_mem_or_memstatement · cited by 1
- Order.Ideal.isPrime_iffstatement and proof · cited by 1
- Order.Ideal.isPrime_iff_mem_or_compl_memstatement and proof · cited by 0
- Order.Ideal.IsPrime.compl_mem_of_notMemstatement and proof · cited by 0
- Order.Ideal.IsPrime.recOnstatement and proof · cited by 0
- Order.Ideal.IsPrime.toPrimePairstatement and proof · cited by 0