Theorems · Theorem · ring theory
NonUnitalStarSubalgebra.coe_iSup_of_directed
∀ {R : Type u} {A : Type v} [inst : CommSemiring R] [inst_1 : NonUnitalSemiring A] [inst_2 : StarRing A]
[inst_3 : Module R A] {ι : Type u_1} [inst_4 : StarRing R] [inst_5 : IsScalarTower R A A]
[inst_6 : SMulCommClass R A A] [inst_7 : StarModule R A] [Nonempty ι] {S : ι → NonUnitalStarSubalgebra R A},
Directed (fun x1 x2 => x1 ≤ x2) S → ↑(iSup S) = ⋃ i, ↑(S i)- Defined in
- Mathlib.Algebra.Star.NonUnitalSubalgebra
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 79 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites28
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- Modulestatement and proof · cited by 20,661
- CommSemiringstatement and proof · cited by 10,911
- SetLike.coestatement and proof · cited by 8,199
- IsScalarTowerstatement and proof · cited by 3,896
- Set.iUnionstatement and proof · cited by 2,483
- iSupstatement and proof · cited by 2,415
- le_antisymmproof · cited by 2,068
- SMulCommClassstatement and proof · cited by 1,927
- StarRingstatement and proof · cited by 1,686
- Star.starproof · cited by 1,082
- StarModulestatement and proof · cited by 570
Cited by2
Results whose statement or proof uses this declaration.
- StarSubalgebra.coe_iSup_of_directedproof · cited by 1
- NonUnitalStarSubalgebra.isMulCommutative_iSupproof · cited by 0