Theorems · Theorem · ring theory
StarSubalgebra.coe_iSup_of_directed
∀ {R : Type u_1} {A : Type u_2} [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] {ι : Type u_3} [Nonempty ι]
{S : ι → StarSubalgebra R A}, Directed (fun x1 x2 => x1 ≤ x2) S → ↑(iSup S) = ⋃ i, ↑(S i)- Defined in
- Mathlib.Algebra.Star.Subalgebra
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 81 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites33
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Setstatement · cited by 53,352
- Semiringstatement and proof · cited by 13,802
- Algebrastatement and proof · cited by 11,388
- CommSemiringstatement and proof · cited by 10,911
- SetLike.coestatement and proof · cited by 8,199
- Algebra.algebraMapproof · cited by 4,706
- Set.iUnionstatement and proof · cited by 2,483
- iSupstatement and proof · cited by 2,415
- le_antisymmproof · cited by 2,068
- StarRingstatement and proof · cited by 1,686
- StarModulestatement and proof · cited by 570
Cited by1
Results whose statement or proof uses this declaration.
- StarSubalgebra.isMulCommutative_iSupproof · cited by 0