Theorems · Theorem · order theory
Order.Ideal.IsPrime.mem_or_mem
∀ {P : Type u_1} [inst : SemilatticeInf P] {I : Order.Ideal P}, I.IsPrime → ∀ {x y : P}, x ⊓ y ∈ I → x ∈ I ∨ y ∈ I- Defined in
- Mathlib.Order.PrimeIdeal
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 18 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- SemilatticeInf
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
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.PFilterproof · cited by 32
- Order.Ideal.IsPrimestatement and proof · cited by 11
- Order.PFilter.inf_memproof · cited by 4
- Order.IsPFilter.toPFilterproof · cited by 1
- Order.Ideal.IsPrime.compl_filterproof · cited by 1
Cited by2
Results whose statement or proof uses this declaration.
- Order.Ideal.IsPrime.mem_or_compl_memproof · cited by 2
- Order.Ideal.isPrime_iff_mem_or_memproof · cited by 1