Theorems · Theorem · linear algebra
LinearIndependent.finset_card_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] {b : Finset M}, (LinearIndependent R fun x => ↑x) → b.card ≤ Module.finrank R M- Defined in
- Mathlib.LinearAlgebra.Dimension.Finite
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 104 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
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
- Finsetstatement and proof · cited by 13,712
- AddCommMonoidstatement and proof · cited by 12,281
- Finset.cardstatement · cited by 2,327
- Module.finrankstatement and proof · cited by 1,770
- Module.Finitestatement and proof · cited by 1,032
- LinearIndependentstatement and proof · cited by 560
- StrongRankConditionstatement and proof · cited by 286
- Fintype.card_coeproof · cited by 72
- LinearIndependent.fintype_card_le_finrankproof · cited by 4
Cited by1
Results whose statement or proof uses this declaration.
- Module.exists_nontrivial_relation_of_finrank_lt_cardproof · cited by 1