Theorems · Theorem · functional analysis
Algebra.elemental.le_of_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 → x ∈ s → Algebra.elemental R x ≤ s- Defined in
- Mathlib.Topology.Algebra.Algebra
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 86 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
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.adjoin_leproof · cited by 36
- Algebra.elementalstatement · cited by 6
- Subalgebra.topologicalClosure_minimalproof · cited by 4
Cited by1
Results whose statement or proof uses this declaration.
- Algebra.elemental.le_iff_memproof · cited by 0