Theorems · Theorem · ring theory
TwoSidedIdeal.mem_iff
∀ {R : Type u_1} [inst : NonUnitalNonAssocRing R] (I : TwoSidedIdeal R) (x : R), x ∈ I ↔ I.ringCon x 0- Defined in
- Mathlib.RingTheory.TwoSidedIdeal.Basic
- Cited by
- 9 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.
Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- NonUnitalNonAssocRingstatement and proof · cited by 354
- RingConstatement · cited by 219
- TwoSidedIdealstatement and proof · cited by 151
- TwoSidedIdeal.ringConstatement · cited by 40
Cited by9
Results whose statement or proof uses this declaration.
- TwoSidedIdeal.rel_iffproof · cited by 4
- TwoSidedIdeal.subset_spanproof · cited by 4
- TwoSidedIdeal.mem_mk'proof · cited by 3
- TwoSidedIdeal.finsetSum_memproof · cited by 2
- IsSimpleRing.iff_injective_ringHom_or_subsingleton_codomainproof · cited by 1
- TwoSidedIdeal.mem_kerproof · cited by 1
- TwoSidedIdeal.listSum_memproof · cited by 0
- TwoSidedIdeal.coe_equivMatrix_symm_applyproof · cited by 0
- TwoSidedIdeal.multisetSum_memproof · cited by 0