Theorems · Theorem · ring theory
StarSubalgebra.mem_toSubalgebra
∀ {R : Type u_2} {A : Type u_3} [inst : CommSemiring R] [inst_1 : StarRing R] [inst_2 : Semiring A]
[inst_3 : StarRing A] [inst_4 : Algebra R A] [inst_5 : StarModule R A] {S : StarSubalgebra R A} {x : A},
x ∈ S.toSubalgebra ↔ x ∈ S- Defined in
- Mathlib.Algebra.Star.Subalgebra
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 21 from the axioms · uses no axioms
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Semiringstatement and proof · cited by 13,802
- Algebrastatement and proof · cited by 11,388
- CommSemiringstatement and proof · cited by 10,911
- StarRingstatement and proof · cited by 1,686
- Subalgebrastatement · cited by 1,353
- StarModulestatement and proof · cited by 570
- StarSubalgebrastatement and proof · cited by 194
- StarSubalgebra.toSubalgebrastatement · cited by 58
Cited by5
Results whose statement or proof uses this declaration.
- StarSubalgebra.toSubalgebra_injectiveproof · cited by 3
- ContinuousMap.adjoin_id_eq_span_one_addproof · cited by 1
- StarAlgebra.elemental.induction_onproof · cited by 0
- ContinuousMap.adjoin_id_eq_span_one_unionproof · cited by 0