Theorems · Theorem · functional analysis
Algebra.elemental.le_iff_mem
∀ {R : Type u_1} [inst : CommSemiring R] {A : Type u} [inst_1 : TopologicalSpace A] [inst_2 : Semiring A]
[inst_3 : Algebra R A] [inst_4 : IsSemitopologicalSemiring A] {x : A} {s : Subalgebra R A},
IsClosed ↑s → (Algebra.elemental R x ≤ s ↔ x ∈ s)- Defined in
- Mathlib.Topology.Algebra.Algebra
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 87 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites11
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
- IsClosedstatement and proof · cited by 1,639
- Subalgebrastatement and proof · cited by 1,353
- IsSemitopologicalSemiringstatement and proof · cited by 88
- Algebra.elementalstatement and proof · cited by 6
- Algebra.elemental.le_of_memproof · cited by 1
- Algebra.elemental.self_memproof · cited by 1
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