Theorems · Theorem · ring theory
TwoSidedIdeal.mul_mem_left
∀ {R : Type u_1} [inst : NonUnitalNonAssocRing R] (I : TwoSidedIdeal R) (x y : R), y ∈ I → x * y ∈ I- Defined in
- Mathlib.RingTheory.TwoSidedIdeal.Basic
- Cited by
- 8 results in Mathlib
- Foundations
- Depth 41 from the axioms · uses propext, Quot.sound
- Assumes
- NonUnitalNonAssocRing
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.
- DFunLike.coeproof · cited by 62,936
- MulZeroClass.mul_zeroproof · cited by 2,091
- NonUnitalNonAssocRingstatement and proof · cited by 354
- TwoSidedIdealstatement and proof · cited by 151
- TwoSidedIdeal.ringConproof · cited by 40
- RingCon.reflproof · cited by 10
- RingCon.mulproof · cited by 8
Cited by8
Results whose statement or proof uses this declaration.
- IsLinearTopology.hasBasis_twoSidedIdealproof · cited by 3
- TwoSidedIdeal.set_mul_subsetproof · cited by 2
- TwoSidedIdeal.one_mem_iffproof · cited by 2
- TwoSidedIdeal.listProd_memproof · cited by 1
- TwoSidedIdeal.mem_supproof · cited by 0
- TwoSidedIdeal.span_inductionstatement and proof · cited by 0
- isLinearTopology_iff_hasBasis_open_twoSidedIdealproof · cited by 0
- isLinearTopology_iff_hasBasis_twoSidedIdealproof · cited by 0