Theorems · Theorem · linear algebra
LinearIndependent.iSupIndep_span_singleton
∀ {ι : Type u'} {R : Type u_2} {M : Type u_4} {v : ι → M} [inst : Semiring R] [inst_1 : AddCommMonoid M]
[inst_2 : Module R M], LinearIndependent R v → iSupIndep fun i => R ∙ v iSee also iSupIndep_iff_linearIndependent_of_ne_zero.
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 79 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.
Cites19
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Setstatement · cited by 53,352
- Modulestatement and proof · cited by 20,661
- Semiringstatement and proof · cited by 13,802
- AddCommMonoidstatement and proof · cited by 12,281
- Submodulestatement and proof · cited by 7,192
- Finsuppproof · cited by 5,255
- Submodule.spanstatement and proof · cited by 1,504
- CompleteLatticeproof · cited by 1,048
- LinearMap.rangeproof · cited by 893
- Submodule.mapproof · cited by 614
- LinearIndependentstatement and proof · cited by 560
Cited by3
Results whose statement or proof uses this declaration.
- LinearIndependent.finite_of_isNoetherianproof · cited by 2
- iSupIndep_iff_linearIndependent_of_ne_zeroproof · cited by 1
- IsArtinian.finite_of_linearIndependentproof · cited by 0