Theorems · Theorem · commutative algebra
Ideal.sup_prod_eq_top
∀ {R : Type u} {ι : Type u_1} [inst : CommSemiring R] {I : Ideal R} {s : Finset ι} {J : ι → Ideal R},
(∀ i ∈ s, I ⊔ J i = ⊤) → I ⊔ ∏ i ∈ s, J i = ⊤- Defined in
- Mathlib.RingTheory.Ideal.Operations
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 78 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.
Cites9
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
- Top.topstatement and proof · cited by 9,680
- Idealstatement and proof · cited by 4,748
- Finset.prodstatement · cited by 2,356
- Ideal.one_eq_topproof · cited by 83
- Finset.prod_inductionproof · cited by 18
- sup_top_eqproof · cited by 6
- Ideal.sup_mul_eq_of_coprime_leftproof · cited by 4
Cited by1
Results whose statement or proof uses this declaration.
- Ideal.prod_sup_eq_topproof · cited by 0