Theorems · Theorem · functional analysis
StarAlgebra.elemental.le_of_mem
∀ {R : Type u_1} {A : Type u_2} [inst : CommSemiring R] [inst_1 : StarRing R] [inst_2 : TopologicalSpace A]
[inst_3 : Semiring A] [inst_4 : StarRing A] [inst_5 : IsSemitopologicalSemiring A] [inst_6 : ContinuousStar A]
[inst_7 : Algebra R A] [inst_8 : StarModule R A] {S : StarSubalgebra R A},
IsClosed ↑S → ∀ {x : A}, x ∈ S → StarAlgebra.elemental R x ≤ S- Defined in
- Mathlib.Topology.Algebra.StarSubalgebra
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 88 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites15
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- TopologicalSpacestatement and proof · cited by 24,529
- 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
- StarRingstatement and proof · cited by 1,686
- IsClosedstatement and proof · cited by 1,639
- StarModulestatement and proof · cited by 570
- ContinuousStarstatement and proof · cited by 543
- Set.singleton_subset_iffproof · cited by 206
- StarSubalgebrastatement and proof · cited by 194
- IsSemitopologicalSemiringstatement and proof · cited by 88
Cited by1
Results whose statement or proof uses this declaration.
- StarAlgebra.elemental.le_iff_memproof · cited by 0