Theorems · Theorem · linear algebra
LinearIndependent.finite
∀ {R : Type u} {M : Type v} [inst : Semiring R] [inst_1 : AddCommMonoid M] [inst_2 : Module R M] [StrongRankCondition R]
[Module.Finite R M] {ι : Type u_1} {f : ι → M}, LinearIndependent R f → Finite ι- Defined in
- Mathlib.LinearAlgebra.Dimension.Finite
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 102 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
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
- AddCommMonoidstatement and proof · cited by 12,281
- Finitestatement · cited by 3,029
- Module.Finitestatement and proof · cited by 1,032
- LinearIndependentstatement and proof · cited by 560
- StrongRankConditionstatement and proof · cited by 286
- Cardinal.lt_aleph0_iff_finiteproof · cited by 8
- LinearIndependent.lt_aleph0_of_finiteproof · cited by 3
Cited by3
Results whose statement or proof uses this declaration.
- IsSl2Triple.HasPrimitiveVectorWith.exists_natproof · cited by 2
- Module.Finite.not_linearIndependent_of_infiniteproof · cited by 0
- IsSl2Triple.exists_hasPrimitiveVectorWithproof · cited by 0