Theorems · Theorem · commutative algebra
Ideal.IsPrime.inf_le
∀ {R : Type u} [inst : CommSemiring R] {I J P : Ideal R}, P.IsPrime → (I ⊓ J ≤ P ↔ I ≤ P ∨ J ≤ P)- Defined in
- Mathlib.RingTheory.Ideal.Operations
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 72 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommSemiring
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CommSemiringstatement and proof · cited by 10,911
- Idealstatement and proof · cited by 4,748
- LE.le.transproof · cited by 3,151
- Ideal.IsPrimestatement and proof · cited by 827
- inf_le_leftproof · cited by 286
- inf_le_rightproof · cited by 238
- Ideal.mul_le_infproof · cited by 10
- Ideal.IsPrime.mul_leproof · cited by 8
Cited by3
Results whose statement or proof uses this declaration.
- PrimeSpectrum.zeroLocus_infproof · cited by 2
- Ideal.subset_union_prime'proof · cited by 1
- ProjectiveSpectrum.zeroLocus_infproof · cited by 1