Theorems · Theorem · functional analysis
NonUnitalStarAlgebra.elemental.le_of_mem
∀ {R : Type u_1} {A : Type u_2} [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] [inst_8 : TopologicalSpace A] [inst_9 : IsSemitopologicalSemiring A]
[inst_10 : ContinuousConstSMul R A] [inst_11 : ContinuousStar A] {x : A} {s : NonUnitalStarSubalgebra R A},
IsClosed ↑s → x ∈ s → NonUnitalStarAlgebra.elemental R x ≤ s- 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.
Cites18
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
- 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
- SMulCommClassstatement and proof · cited by 1,927
- StarRingstatement and proof · cited by 1,686
- IsClosedstatement and proof · cited by 1,639
- ContinuousConstSMulstatement and proof · cited by 832
- StarModulestatement and proof · cited by 570
- ContinuousStarstatement and proof · cited by 543
- NonUnitalSemiringstatement and proof · cited by 339
Cited by1
Results whose statement or proof uses this declaration.
- NonUnitalStarAlgebra.elemental.le_iff_memproof · cited by 0