Theorems · Theorem · functional analysis
NonUnitalAlgebra.elemental.le_iff_mem
∀ {R : Type u_1} {A : Type u_2} [inst : CommSemiring R] [inst_1 : NonUnitalSemiring A] [inst_2 : Module R A]
[inst_3 : IsScalarTower R A A] [inst_4 : SMulCommClass R A A] [inst_5 : TopologicalSpace A]
[inst_6 : IsSemitopologicalSemiring A] [inst_7 : ContinuousConstSMul R A] {x : A} {s : NonUnitalSubalgebra R A},
IsClosed ↑s → (NonUnitalAlgebra.elemental R x ≤ s ↔ x ∈ s)- Cited by
- 0 results in Mathlib
- Foundations
- Depth 87 from the axioms · uses propext, Classical.choice, Quot.sound
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Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites14
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
- IsClosedstatement and proof · cited by 1,639
- ContinuousConstSMulstatement and proof · cited by 832
- NonUnitalSemiringstatement and proof · cited by 339
- NonUnitalSubalgebrastatement and proof · cited by 215
- IsSemitopologicalSemiringstatement and proof · cited by 88
- NonUnitalAlgebra.elementalstatement and proof · cited by 6
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