Theorems · Theorem · commutative algebra
Ideal.le_colon
∀ {R : Type u_1} [inst : Semiring R] {I : Ideal R} {S : Set R} [I.IsTwoSided], I ≤ Submodule.colon I S- Defined in
- Mathlib.RingTheory.Ideal.Colon
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 66 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- SemiringIdeal.IsTwoSided
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- Semiringstatement and proof · cited by 13,802
- Idealstatement and proof · cited by 4,748
- le_rflproof · cited by 1,558
- Set.subset_univproof · cited by 228
- Ideal.IsTwoSidedstatement and proof · cited by 179
- Eq.trans_leproof · cited by 155
- Submodule.colonstatement · cited by 80
- Submodule.colon_univproof · cited by 7
- Submodule.colon_monoproof · cited by 4
Cited by1
Results whose statement or proof uses this declaration.
- Ideal.IsOka.isPrime_of_maximal_notproof · cited by 1