Theorems · Theorem · commutative algebra
Ideal.isCoprime_biInf
∀ {R : Type u} {ι : Type u_1} [inst : CommSemiring R] {I : Ideal R} {J : ι → Ideal R} {s : Finset ι},
(∀ j ∈ s, IsCoprime I (J j)) → IsCoprime I (⨅ j ∈ s, J j)- Defined in
- Mathlib.RingTheory.Ideal.Operations
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 81 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.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Finsetstatement and proof · cited by 13,712
- CommSemiringstatement and proof · cited by 10,911
- Idealstatement and proof · cited by 4,748
- iInfstatement and proof · cited by 1,690
- IsCoprimestatement and proof · cited by 321
- Ideal.one_eq_topproof · cited by 83
- Ideal.sup_iInf_eq_topproof · cited by 5
Cited by2
Results whose statement or proof uses this declaration.
- Ideal.prod_eq_iInf_of_pairwise_isCoprimeproof · cited by 4
- Ideal.quotientInfToPiQuotient_surjproof · cited by 2