Theorems · Theorem · ring theory
TwoSidedIdeal.ext
∀ {R : Type u_1} [inst : NonUnitalNonAssocRing R] {I J : TwoSidedIdeal R}, (∀ (x : R), x ∈ I ↔ x ∈ J) → I = J- Defined in
- Mathlib.RingTheory.TwoSidedIdeal.Basic
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 44 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.
- Set.extproof · cited by 2,266
- NonUnitalNonAssocRingstatement and proof · cited by 354
- TwoSidedIdealstatement and proof · cited by 151
- RelEmbedding.injectiveproof · cited by 41
- TwoSidedIdeal.coeOrderEmbeddingproof · cited by 2
Cited by3
Results whose statement or proof uses this declaration.
- Ideal.toTwoSided_asIdealproof · cited by 0
- TwoSidedIdeal.comap_comapproof · cited by 0
- TwoSidedIdeal.ext_iffproof · cited by 0