Theorems · Theorem · commutative algebra
Ideal.multiset_prod_le_inf
∀ {R : Type u} [inst : CommSemiring R] {s : Multiset (Ideal R)}, s.prod ≤ s.inf- 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.
Cites15
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
- Multisetstatement and proof · cited by 2,627
- le_rflproof · cited by 1,558
- le_transproof · cited by 985
- Multiset.prodstatement and proof · cited by 528
- le_topproof · cited by 411
- Multiset.consproof · cited by 313
- Multiset.induction_onproof · cited by 109
- Multiset.prod_consproof · cited by 68
- inf_le_infproof · cited by 54
- Multiset.infstatement and proof · cited by 19
Cited by1
Results whose statement or proof uses this declaration.
- Ideal.prod_le_infproof · cited by 3