Theorems · Theorem · linear algebra
Submodule.finset_span_isCompactElement
∀ {R : Type u_1} {M : Type u_4} [inst : Semiring R] [inst_1 : AddCommMonoid M] [inst_2 : Module R M] (S : Finset M),
IsCompactElement (Submodule.span R ↑S)The span of a finite subset is compact in the lattice of submodules.
- Defined in
- Mathlib.LinearAlgebra.Span.Basic
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 80 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- SemiringAddCommMonoidModule
Around this declaration
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.
- Modulestatement and proof · cited by 20,661
- Semiringstatement and proof · cited by 13,802
- Finsetstatement and proof · cited by 13,712
- AddCommMonoidstatement and proof · cited by 12,281
- SetLike.coestatement and proof · cited by 8,199
- Submodulestatement and proof · cited by 7,192
- iSupproof · cited by 2,415
- Submodule.spanstatement and proof · cited by 1,504
- iSup_congr_Propproof · cited by 247
- IsCompactElementstatement and proof · cited by 34
- Finset.sup_eq_iSupproof · cited by 30
- Submodule.singleton_span_isCompactElementproof · cited by 4
Cited by1
Results whose statement or proof uses this declaration.
- Submodule.finite_span_isCompactElementproof · cited by 0