Theorems · Inductive type · order theory
Order.PFilter.IsPrime
{P : Type u_1} → [inst : Preorder P] → Order.PFilter P → PropA filter F is prime if its complement is an ideal.
- Defined in
- Mathlib.Order.PrimeIdeal
- Cited by
- 3 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.PFilterstatement · cited by 32
Cited by6
Results whose statement or proof uses this declaration.
- Order.PFilter.IsPrime.casesOnstatement and proof · cited by 1
- Order.PFilter.isPrime_iffstatement and proof · cited by 0
- Order.PFilter.IsPrime.recOnstatement and proof · cited by 0
- Order.PFilter.IsPrime.toPrimePairstatement and proof · cited by 0
- Order.Ideal.PrimePair.F_isPrimestatement · cited by 0
- Order.PFilter.IsPrime.compl_idealstatement and proof · cited by 0