Theorems · Theorem · linear algebra
LinearIndependent.cardinalMk_le_finrank
∀ {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 w} {b : ι → M}, LinearIndependent R b → Cardinal.mk ι ≤ ↑(Module.finrank R M)- Defined in
- Mathlib.LinearAlgebra.Dimension.Finite
- Cited by
- 2 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.
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
- Cardinalstatement · cited by 2,598
- Module.finrankstatement and proof · cited by 1,770
- Module.Finitestatement and proof · cited by 1,032
- Cardinal.mkstatement and proof · cited by 942
- Cardinal.liftproof · cited by 583
- LinearIndependentstatement and proof · cited by 560
- StrongRankConditionstatement and proof · cited by 286
- Cardinal.lift_leproof · cited by 78
- Cardinal.lift_natCastproof · cited by 39
Cited by2
Results whose statement or proof uses this declaration.
- LinearIndependent.fintype_card_le_finrankproof · cited by 4
- cardinalMk_algHomproof · cited by 0