Theorems · Theorem · order theory
Order.Ideal.isPrime_iff_mem_or_mem
∀ {P : Type u_1} [inst : SemilatticeInf P] {I : Order.Ideal P} [I.IsProper],
I.IsPrime ↔ ∀ {x y : P}, x ⊓ y ∈ I → x ∈ I ∨ y ∈ I- Defined in
- Mathlib.Order.PrimeIdeal
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 26 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- SemilatticeInfstatement and proof · cited by 634
- Order.Idealstatement and proof · cited by 102
- Order.Ideal.IsProperstatement and proof · cited by 23
- Order.Ideal.IsPrimestatement · cited by 11
- Order.Ideal.IsPrime.mem_or_memproof · cited by 2
- Order.Ideal.IsPrime.of_mem_or_memproof · cited by 1
Cited by1
Results whose statement or proof uses this declaration.
- DistribLattice.prime_ideal_of_disjoint_filter_idealproof · cited by 0