Theorems · Theorem · ring theory
NonUnitalStarAlgebra.eq_top_iff
∀ {R : Type u} {A : Type v} [inst : CommSemiring R] [inst_1 : StarRing R] [inst_2 : NonUnitalSemiring A]
[inst_3 : StarRing A] [inst_4 : Module R A] [inst_5 : IsScalarTower R A A] [inst_6 : SMulCommClass R A A]
[inst_7 : StarModule R A] {S : NonUnitalStarSubalgebra R A}, S = ⊤ ↔ ∀ (x : A), x ∈ S- Defined in
- Mathlib.Algebra.Star.NonUnitalSubalgebra
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 80 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
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
- Top.topstatement and proof · cited by 9,680
- IsScalarTowerstatement and proof · cited by 3,896
- SMulCommClassstatement and proof · cited by 1,927
- StarRingstatement and proof · cited by 1,686
- StarModulestatement and proof · cited by 570
- NonUnitalSemiringstatement and proof · cited by 339
- NonUnitalStarSubalgebrastatement and proof · cited by 196
- NonUnitalStarSubalgebra.extproof · cited by 7
- NonUnitalStarAlgebra.mem_topproof · cited by 2
Cited by2
Results whose statement or proof uses this declaration.
- NonUnitalStarAlgebra.range_eq_topproof · cited by 0
- NonUnitalStarAlgebra.comap_topproof · cited by 0