Theorems · Theorem · linear algebra
LinearIndependent.aleph0_le_rank
∀ {R : Type u} {M : Type v} [inst : Semiring R] [inst_1 : AddCommMonoid M] [inst_2 : Module R M] [Nontrivial R]
{ι : Type w} [Infinite ι] {v : ι → M}, LinearIndependent R v → Cardinal.aleph0 ≤ Module.rank R M- Defined in
- Mathlib.LinearAlgebra.Dimension.Basic
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 86 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
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
- LE.le.transproof · cited by 3,151
- Cardinalstatement · cited by 2,598
- Nontrivialstatement and proof · cited by 2,416
- LinearIndependentstatement and proof · cited by 560
- Cardinal.aleph0statement · cited by 521
- Module.rankstatement · cited by 496
- Infinitestatement and proof · cited by 352
- Cardinal.aleph0_le_mkproof · cited by 32
- LinearIndependent.cardinal_lift_le_rankproof · cited by 16
Cited by1
Results whose statement or proof uses this declaration.
- LinearIndependent.finrank_eq_zero_of_infiniteproof · cited by 2