Theorems · Theorem · linear algebra
LinearIndependent.lt_aleph0_of_finite
∀ {R : Type u} {M : Type v} [inst : Semiring R] [inst_1 : AddCommMonoid M] [inst_2 : Module R M] [StrongRankCondition R]
{ι : Type w} [Module.Finite R M] {v : ι → M}, LinearIndependent R v → Cardinal.mk ι < Cardinal.aleph0- Defined in
- Mathlib.LinearAlgebra.Dimension.Finite
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 101 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites18
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
- Cardinalstatement and proof · cited by 2,598
- Module.finrankproof · cited by 1,770
- Module.Finitestatement and proof · cited by 1,032
- Cardinal.mkstatement · cited by 942
- Cardinal.liftproof · cited by 583
- LinearIndependentstatement and proof · cited by 560
- Cardinal.aleph0statement and proof · cited by 521
- lt_of_le_of_ltproof · cited by 432
- StrongRankConditionstatement and proof · cited by 286
Cited by3
Results whose statement or proof uses this declaration.
- LinearIndependent.finiteproof · cited by 3
- LinearIndependent.setFiniteproof · cited by 2
- LinearIndependent.lt_aleph0_of_finiteDimensionalproof · cited by 0