Theorems · Theorem · linear algebra
Module.Finite.not_linearIndependent_of_infinite
∀ {R : Type u} {M : Type v} [inst : Semiring R] [inst_1 : AddCommMonoid M] [inst_2 : Module R M] [Module.Finite R M]
[StrongRankCondition R] {ι : Type u_1} [Infinite ι] (v : ι → M), ¬LinearIndependent R v- Defined in
- Mathlib.LinearAlgebra.Dimension.Finite
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 103 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
- Module.Finitestatement and proof · cited by 1,032
- LinearIndependentstatement · cited by 560
- Infinitestatement and proof · cited by 352
- StrongRankConditionstatement and proof · cited by 286
- not_finiteproof · cited by 10
- LinearIndependent.finiteproof · cited by 3
Cited by0
Results whose statement or proof uses this declaration.
Nothing cites this yet.