Theorems · Theorem · ring theory
NonUnitalSubring.ext
∀ {R : Type u} [inst : NonUnitalNonAssocRing R] {S T : NonUnitalSubring R}, (∀ (x : R), x ∈ S ↔ x ∈ T) → S = TTwo non-unital subrings are equal if they have the same elements.
- Defined in
- Mathlib.RingTheory.NonUnitalSubring.Defs
- Cited by
- 7 results in Mathlib
- Foundations
- Depth 17 from the axioms · uses propext, Quot.sound
- Assumes
- NonUnitalNonAssocRing
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites3
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- NonUnitalNonAssocRingstatement and proof · cited by 354
- NonUnitalSubringstatement and proof · cited by 185
- SetLike.extproof · cited by 92
Cited by7
Results whose statement or proof uses this declaration.
- NonUnitalRingHom.range_eq_mapproof · cited by 1
- NonUnitalSubring.top_prodproof · cited by 1
- NonUnitalSubring.toAddSubgroup_injectiveproof · cited by 0
- NonUnitalSubring.prod_topproof · cited by 0
- NonUnitalSubring.toNonUnitalSubsemiring_injectiveproof · cited by 0
- NonUnitalSubring.ext_iffproof · cited by 0
- NonUnitalSubring.toSubsemigroup_injectiveproof · cited by 0