Theorems · Theorem · ring theory
NonUnitalStarSubalgebra.ext
∀ {R : Type u} {A : Type v} [inst : CommSemiring R] [inst_1 : NonUnitalNonAssocSemiring A] [inst_2 : Module R A]
[inst_3 : Star A] {S T : NonUnitalStarSubalgebra R A}, (∀ (x : A), x ∈ S ↔ x ∈ T) → S = T- Defined in
- Mathlib.Algebra.Star.NonUnitalSubalgebra
- Cited by
- 7 results in Mathlib
- Foundations
- Depth 17 from the axioms · uses propext, Quot.sound
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.
- Modulestatement and proof · cited by 20,661
- CommSemiringstatement and proof · cited by 10,911
- NonUnitalNonAssocSemiringstatement and proof · cited by 1,081
- Starstatement and proof · cited by 496
- NonUnitalStarSubalgebrastatement and proof · cited by 196
- SetLike.extproof · cited by 92
Cited by7
Results whose statement or proof uses this declaration.
- NonUnitalStarSubalgebra.toNonUnitalSubalgebra_injectiveproof · cited by 3
- NonUnitalStarAlgebra.eq_top_iffproof · cited by 2
- NonUnitalStarSubalgebra.toNonUnitalSubring_injectiveproof · cited by 1
- NonUnitalStarSubalgebra.map_injectiveproof · cited by 0
- NonUnitalStarSubalgebra.ext_iffproof · cited by 0
- NonUnitalStarSubalgebra.prod_topproof · cited by 0
- NonUnitalStarSubalgebra.range_valproof · cited by 0