Theorems · Theorem · ring theory
TwoSidedIdeal.add_mem
∀ {R : Type u_1} [inst : NonUnitalNonAssocRing R] (I : TwoSidedIdeal R) {x y : R}, x ∈ I → y ∈ I → x + y ∈ I- Defined in
- Mathlib.RingTheory.TwoSidedIdeal.Basic
- Cited by
- 3 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.
Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- add_zeroproof · cited by 2,707
- NonUnitalNonAssocRingstatement and proof · cited by 354
- TwoSidedIdealstatement and proof · cited by 151
- TwoSidedIdeal.ringConproof · cited by 40
- RingCon.addproof · cited by 5
Cited by3
Results whose statement or proof uses this declaration.
- TwoSidedIdeal.mem_span_iff_mem_addSubgroup_closure_absorbingproof · cited by 2
- TwoSidedIdeal.mem_supproof · cited by 0
- TwoSidedIdeal.span_inductionstatement and proof · cited by 0